LMFDB - Embedded newform 189.2.v.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(22,189)]

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([14, 0]))

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

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

chi := DirichletCharacter("189.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	189.43
Dual form			189.2.v.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0808704 + 0.0678583i) q^{2} +(1.71585 + 0.236354i) q^{3} +(-0.345361 - 1.95864i) q^{4} +(0.0449304 + 0.0163533i) q^{5} +(0.122723 + 0.135549i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.210549 - 0.364682i) q^{8} +(2.88827 + 0.811094i) q^{9} +O(q^{10})$	\(q+(0.0808704 + 0.0678583i) q^{2} +(1.71585 + 0.236354i) q^{3} +(-0.345361 - 1.95864i) q^{4} +(0.0449304 + 0.0163533i) q^{5} +(0.122723 + 0.135549i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.210549 - 0.364682i) q^{8} +(2.88827 + 0.811094i) q^{9} +(0.00252383 + 0.00437140i) q^{10} +(-2.08078 + 0.757342i) q^{11} +(-0.129656 - 3.44236i) q^{12} +(1.63110 - 1.36865i) q^{13} +(0.0808704 - 0.0678583i) q^{14} +(0.0732287 + 0.0386793i) q^{15} +(-3.69605 + 1.34525i) q^{16} +(1.30215 + 2.25539i) q^{17} +(0.178536 + 0.261587i) q^{18} +(-1.12700 + 1.95202i) q^{19} +(0.0165131 - 0.0936504i) q^{20} +(0.530717 - 1.64874i) q^{21} +(-0.219665 - 0.0799517i) q^{22} +(1.36751 + 7.75556i) q^{23} +(0.447465 - 0.575975i) q^{24} +(-3.82847 - 3.21247i) q^{25} +0.224782 q^{26} +(4.76414 + 2.07437i) q^{27} -1.98886 q^{28} +(0.516050 + 0.433017i) q^{29} +(0.00329732 + 0.00809719i) q^{30} +(-0.714158 - 4.05019i) q^{31} +(-1.18159 - 0.430065i) q^{32} +(-3.74930 + 0.807684i) q^{33} +(-0.0477416 + 0.270756i) q^{34} +(0.0239070 - 0.0414081i) q^{35} +(0.591144 - 5.93721i) q^{36} +(1.50163 + 2.60090i) q^{37} +(-0.223602 + 0.0813846i) q^{38} +(3.12220 - 1.96288i) q^{39} +(0.0154238 - 0.0129421i) q^{40} +(-4.51243 + 3.78637i) q^{41} +(0.154800 - 0.0973206i) q^{42} +(-7.25196 + 2.63950i) q^{43} +(2.20198 + 3.81394i) q^{44} +(0.116507 + 0.0836758i) q^{45} +(-0.415688 + 0.719992i) q^{46} +(0.831280 - 4.71442i) q^{47} +(-6.65982 + 1.43467i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.0916172 - 0.519587i) q^{50} +(1.70122 + 4.17768i) q^{51} +(-3.24401 - 2.72205i) q^{52} -2.27812 q^{53} +(0.244514 + 0.491041i) q^{54} -0.105875 q^{55} +(-0.322580 - 0.270677i) q^{56} +(-2.39513 + 3.08301i) q^{57} +(0.0123493 + 0.0700365i) q^{58} +(-11.3193 - 4.11987i) q^{59} +(0.0504686 - 0.156787i) q^{60} +(0.115915 - 0.657385i) q^{61} +(0.217085 - 0.376002i) q^{62} +(1.30032 - 2.70355i) q^{63} +(3.86688 + 6.69764i) q^{64} +(0.0956679 - 0.0348203i) q^{65} +(-0.358016 - 0.189104i) q^{66} +(7.86315 - 6.59797i) q^{67} +(3.96779 - 3.32937i) q^{68} +(0.513393 + 13.6306i) q^{69} +(0.00474325 - 0.00172640i) q^{70} +(7.10068 + 12.2987i) q^{71} +(0.903916 - 0.882527i) q^{72} +(1.97659 - 3.42355i) q^{73} +(-0.0550553 + 0.312234i) q^{74} +(-5.80980 - 6.41698i) q^{75} +(4.21254 + 1.53324i) q^{76} +(0.384513 + 2.18068i) q^{77} +(0.385691 + 0.0531280i) q^{78} +(2.63514 + 2.21115i) q^{79} -0.188065 q^{80} +(7.68425 + 4.68533i) q^{81} -0.621859 q^{82} +(-9.22727 - 7.74259i) q^{83} +(-3.41257 - 0.470073i) q^{84} +(0.0216230 + 0.122630i) q^{85} +(-0.765580 - 0.278649i) q^{86} +(0.783118 + 0.864962i) q^{87} +(-0.161918 + 0.918281i) q^{88} +(5.98967 - 10.3744i) q^{89} +(0.00374390 + 0.0146729i) q^{90} +(-1.06462 - 1.84398i) q^{91} +(14.7181 - 5.35694i) q^{92} +(-0.268110 - 7.11831i) q^{93} +(0.387139 - 0.324848i) q^{94} +(-0.0825588 + 0.0692751i) q^{95} +(-1.92579 - 1.01720i) q^{96} +(17.1653 - 6.24766i) q^{97} +(-0.0527844 - 0.0914253i) q^{98} +(-6.62414 + 0.499702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.0808704	+	0.0678583i	0.0571840	+	0.0479831i	0.670932	−	0.741519i	$-0.265894\pi$
$2$	0.0808704	+	0.0678583i	0.0571840	+	0.0479831i	−0.613748	+	0.789502i	$0.710339\pi$
$3$	1.71585	+	0.236354i	0.990646	+	0.136459i
$3$	1.71585	+	0.236354i	0.990646	+	0.136459i
$4$	−0.345361	−	1.95864i	−0.172681	−	0.979320i
$5$	0.0449304	+	0.0163533i	0.0200935	+	0.00731344i	0.352047	−	0.935982i	$-0.385486\pi$
$5$	0.0449304	+	0.0163533i	0.0200935	+	0.00731344i	−0.331954	+	0.943296i	$0.607708\pi$
$6$	0.122723	+	0.135549i	0.0501014	+	0.0553375i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	0.210549	−	0.364682i	0.0744404	−	0.128935i
$9$	2.88827	+	0.811094i	0.962758	+	0.270365i
$10$	0.00252383	+	0.00437140i	0.000798106	+	0.00138236i
$11$	−2.08078	+	0.757342i	−0.627379	+	0.228347i	−0.636090	−	0.771615i	$-0.719449\pi$
$11$	−2.08078	+	0.757342i	−0.627379	+	0.228347i	0.00871123	+	0.999962i	$0.497227\pi$
$12$	−0.129656	−	3.44236i	−0.0374284	−	0.993723i
$13$	1.63110	−	1.36865i	0.452385	−	0.379596i	−0.387935	−	0.921687i	$-0.626812\pi$
$13$	1.63110	−	1.36865i	0.452385	−	0.379596i	0.840320	+	0.542091i	$0.182367\pi$
$14$	0.0808704	−	0.0678583i	0.0216135	−	0.0181359i
$15$	0.0732287	+	0.0386793i	0.0189076	+	0.00998696i
$16$	−3.69605	+	1.34525i	−0.924013	+	0.336313i
$17$	1.30215	+	2.25539i	0.315818	+	0.547013i	0.979611	−	0.200903i	$-0.0643878\pi$
$17$	1.30215	+	2.25539i	0.315818	+	0.547013i	−0.663793	+	0.747916i	$0.731054\pi$
$18$	0.178536	+	0.261587i	0.0420814	+	0.0616566i
$19$	−1.12700	+	1.95202i	−0.258552	+	0.447825i	−0.965854	−	0.259086i	$-0.916579\pi$
$19$	−1.12700	+	1.95202i	−0.258552	+	0.447825i	0.707302	+	0.706911i	$0.249912\pi$
$20$	0.0165131	−	0.0936504i	0.00369244	−	0.0209409i
$21$	0.530717	−	1.64874i	0.115812	−	0.359784i
$22$	−0.219665	−	0.0799517i	−0.0468328	−	0.0170458i
$23$	1.36751	+	7.75556i	0.285146	+	1.61715i	0.704762	+	0.709444i	$0.251054\pi$
$23$	1.36751	+	7.75556i	0.285146	+	1.61715i	−0.419615	+	0.907702i	$0.637835\pi$
$24$	0.447465	−	0.575975i	0.0913384	−	0.117570i
$25$	−3.82847	−	3.21247i	−0.765694	−	0.642494i
$26$	0.224782			0.0440833
$27$	4.76414	+	2.07437i	0.916858	+	0.399213i
$28$	−1.98886			−0.375858
$29$	0.516050	+	0.433017i	0.0958280	+	0.0804093i	0.689443	−	0.724340i	$-0.257855\pi$
$29$	0.516050	+	0.433017i	0.0958280	+	0.0804093i	−0.593615	+	0.804749i	$0.702300\pi$
$30$	0.00329732	+	0.00809719i	0.000602005	+	0.00147834i
$31$	−0.714158	−	4.05019i	−0.128267	−	0.727436i	−0.979314	−	0.202347i	$-0.935143\pi$
$31$	−0.714158	−	4.05019i	−0.128267	−	0.727436i	0.851047	−	0.525089i	$-0.175968\pi$
$32$	−1.18159	−	0.430065i	−0.208878	−	0.0760255i
$33$	−3.74930	+	0.807684i	−0.652670	+	0.140600i
$34$	−0.0477416	+	0.270756i	−0.00818762	+	0.0464343i
$35$	0.0239070	−	0.0414081i	0.00404102	−	0.00699925i
$36$	0.591144	−	5.93721i	0.0985241	−	0.989535i
$37$	1.50163	+	2.60090i	0.246867	+	0.427586i	0.962655	−	0.270732i	$-0.0872657\pi$
$37$	1.50163	+	2.60090i	0.246867	+	0.427586i	−0.715788	+	0.698318i	$0.753932\pi$
$38$	−0.223602	+	0.0813846i	−0.0362731	+	0.0132023i
$39$	3.12220	−	1.96288i	0.499952	−	0.314313i
$40$	0.0154238	−	0.0129421i	0.00243872	−	0.00204633i
$41$	−4.51243	+	3.78637i	−0.704723	+	0.591332i	−0.923113	−	0.384529i	$-0.874364\pi$
$41$	−4.51243	+	3.78637i	−0.704723	+	0.591332i	0.218390	+	0.975861i	$0.429919\pi$
$42$	0.154800	−	0.0973206i	0.0238861	−	0.0150169i
$43$	−7.25196	+	2.63950i	−1.10591	+	0.402519i	−0.829493	−	0.558517i	$-0.811370\pi$
$43$	−7.25196	+	2.63950i	−1.10591	+	0.402519i	−0.276420	+	0.961037i	$0.589148\pi$
$44$	2.20198	+	3.81394i	0.331961	+	0.574973i
$45$	0.116507	+	0.0836758i	0.0173679	+	0.0124736i
$46$	−0.415688	+	0.719992i	−0.0612898	+	0.106157i
$47$	0.831280	−	4.71442i	0.121255	−	0.687669i	−0.862208	−	0.506555i	$-0.830919\pi$
$47$	0.831280	−	4.71442i	0.121255	−	0.687669i	0.983462	−	0.181114i	$-0.0579703\pi$
$48$	−6.65982	+	1.43467i	−0.961262	+	0.207077i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	−0.0916172	−	0.519587i	−0.0129566	−	0.0734807i
$51$	1.70122	+	4.17768i	0.238219	+	0.584992i
$52$	−3.24401	−	2.72205i	−0.449864	−	0.377480i
$53$	−2.27812			−0.312924			−0.156462	−	0.987684i	$-0.550009\pi$
$53$	−2.27812			−0.312924			−0.156462	+	0.987684i	$0.550009\pi$
$54$	0.244514	+	0.491041i	0.0332742	+	0.0668223i
$55$	−0.105875			−0.0142762
$56$	−0.322580	−	0.270677i	−0.0431066	−	0.0361707i
$57$	−2.39513	+	3.08301i	−0.317243	+	0.408354i
$58$	0.0123493	+	0.0700365i	0.00162155	+	0.00919625i
$59$	−11.3193	−	4.11987i	−1.47364	−	0.536361i	−0.524554	−	0.851377i	$-0.675768\pi$
$59$	−11.3193	−	4.11987i	−1.47364	−	0.536361i	−0.949087	+	0.315015i	$0.897990\pi$
$60$	0.0504686	−	0.156787i	0.00651546	−	0.0202411i
$61$	0.115915	−	0.657385i	0.0148414	−	0.0841695i	−0.976487	−	0.215574i	$-0.930838\pi$
$61$	0.115915	−	0.657385i	0.0148414	−	0.0841695i	0.991329	+	0.131405i	$0.0419488\pi$
$62$	0.217085	−	0.376002i	0.0275698	−	0.0477523i
$63$	1.30032	−	2.70355i	0.163824	−	0.340615i
$64$	3.86688	+	6.69764i	0.483360	+	0.837205i
$65$	0.0956679	−	0.0348203i	0.0118661	−	0.00431892i
$66$	−0.358016	−	0.189104i	−0.0440687	−	0.0232771i
$67$	7.86315	−	6.59797i	0.960637	−	0.806070i	−0.0204194	−	0.999792i	$-0.506500\pi$
$67$	7.86315	−	6.59797i	0.960637	−	0.806070i	0.981057	+	0.193721i	$0.0620557\pi$
$68$	3.96779	−	3.32937i	0.481165	−	0.403745i
$69$	0.513393	+	13.6306i	0.0618052	+	1.64093i
$70$	0.00474325	−	0.00172640i	0.000566927	−	0.000206345i
$71$	7.10068	+	12.2987i	0.842695	+	1.45959i	0.887608	+	0.460600i	$0.152366\pi$
$71$	7.10068	+	12.2987i	0.842695	+	1.45959i	−0.0449125	+	0.998991i	$0.514301\pi$
$72$	0.903916	−	0.882527i	0.106527	−	0.104007i
$73$	1.97659	−	3.42355i	0.231342	−	0.400697i	−0.726861	−	0.686784i	$-0.759022\pi$
$73$	1.97659	−	3.42355i	0.231342	−	0.400697i	0.958203	+	0.286088i	$0.0923549\pi$
$74$	−0.0550553	+	0.312234i	−0.00640005	+	0.0362965i
$75$	−5.80980	−	6.41698i	−0.670858	−	0.740969i
$76$	4.21254	+	1.53324i	0.483211	+	0.175874i
$77$	0.384513	+	2.18068i	0.0438193	+	0.248511i
$78$	0.385691	+	0.0531280i	0.0436710	+	0.00601556i
$79$	2.63514	+	2.21115i	0.296477	+	0.248774i	0.778876	−	0.627178i	$-0.215790\pi$
$79$	2.63514	+	2.21115i	0.296477	+	0.248774i	−0.482399	+	0.875951i	$0.660235\pi$
$80$	−0.188065			−0.0210263
$81$	7.68425	+	4.68533i	0.853806	+	0.520592i
$82$	−0.621859			−0.0686728
$83$	−9.22727	−	7.74259i	−1.01282	−	0.849860i	−0.0241150	−	0.999709i	$-0.507677\pi$
$83$	−9.22727	−	7.74259i	−1.01282	−	0.849860i	−0.988709	+	0.149849i	$0.952121\pi$
$84$	−3.41257	−	0.470073i	−0.372342	−	0.0512892i
$85$	0.0216230	+	0.122630i	0.00234535	+	0.0133011i
$86$	−0.765580	−	0.278649i	−0.0825547	−	0.0300474i
$87$	0.783118	+	0.864962i	0.0839591	+	0.0927337i
$88$	−0.161918	+	0.918281i	−0.0172605	+	0.0978891i
$89$	5.98967	−	10.3744i	0.634903	−	1.09968i	−0.351632	−	0.936138i	$-0.614373\pi$
$89$	5.98967	−	10.3744i	0.634903	−	1.09968i	0.986536	−	0.163547i	$-0.0522935\pi$
$90$	0.00374390	+	0.0146729i	0.000394641	+	0.00154666i
$91$	−1.06462	−	1.84398i	−0.111603	−	0.193302i
$92$	14.7181	−	5.35694i	1.53446	−	0.558499i
$93$	−0.268110	−	7.11831i	−0.0278017	−	0.738134i
$94$	0.387139	−	0.324848i	0.0399303	−	0.0335055i
$95$	−0.0825588	+	0.0692751i	−0.00847036	+	0.00710747i
$96$	−1.92579	−	1.01720i	−0.196550	−	0.103818i
$97$	17.1653	−	6.24766i	1.74287	−	0.634354i	0.743465	−	0.668775i	$-0.233181\pi$
$97$	17.1653	−	6.24766i	1.74287	−	0.634354i	0.999407	+	0.0344215i	$0.0109589\pi$
$98$	−0.0527844	−	0.0914253i	−0.00533203	−	0.00923535i
$99$	−6.62414	+	0.499702i	−0.665751	+	0.0502220i
$100$	−4.96986	+	8.60806i	−0.496986	+	0.860806i
$101$	3.05705	−	17.3374i	0.304187	−	1.72513i	−0.323118	−	0.946359i	$-0.604731\pi$
$101$	3.05705	−	17.3374i	0.304187	−	1.72513i	0.627305	−	0.778774i	$-0.284158\pi$
$102$	−0.145912	+	0.453293i	−0.0144474	+	0.0448827i
$103$	2.61069	+	0.950212i	0.257238	+	0.0936271i	0.467420	−	0.884035i	$-0.345183\pi$
$103$	2.61069	+	0.950212i	0.257238	+	0.0936271i	−0.210182	+	0.977662i	$0.567406\pi$
$104$	−0.155697	−	0.883000i	−0.0152673	−	0.0865853i
$105$	0.0508077	−	0.0653996i	0.00495833	−	0.00638234i
$106$	−0.184232	−	0.154589i	−0.0178942	−	0.0150150i
$107$	9.20339			0.889725			0.444863	−	0.895599i	$-0.353253\pi$
$107$	9.20339			0.889725			0.444863	+	0.895599i	$0.353253\pi$
$108$	2.41760	−	10.0476i	0.232633	−	0.966834i
$109$	13.7809			1.31997			0.659984	−	0.751279i	$-0.270563\pi$
$109$	13.7809			1.31997			0.659984	+	0.751279i	$0.270563\pi$
$110$	−0.00856219	−	0.00718453i	−0.000816373	−	0.000685018i
$111$	1.96184	+	4.81767i	0.186210	+	0.457273i
$112$	0.683003	+	3.87350i	0.0645377	+	0.366011i
$113$	−13.0043	−	4.73319i	−1.22334	−	0.445261i	−0.352031	−	0.935988i	$-0.614509\pi$
$113$	−13.0043	−	4.73319i	−1.22334	−	0.445261i	−0.871313	+	0.490728i	$0.836731\pi$
$114$	−0.402903	+	0.0867944i	−0.0377353	+	0.00812904i
$115$	−0.0653863	+	0.370824i	−0.00609730	+	0.0345795i
$116$	0.669901	−	1.16030i	0.0621988	−	0.107731i
$117$	5.82116	−	2.63007i	0.538166	−	0.243150i
$118$	−0.635825	−	1.10128i	−0.0585324	−	0.101381i
$119$	2.44724	−	0.890724i	0.224338	−	0.0816525i
$120$	0.0295239	−	0.0185613i	0.00269515	−	0.00169441i
$121$	−4.67041	+	3.91894i	−0.424583	+	0.356267i
$122$	0.0539831	−	0.0452972i	0.00488740	−	0.00410102i
$123$	−8.63756	+	5.43032i	−0.778823	+	0.489635i
$124$	−7.68622	+	2.79756i	−0.690243	+	0.251228i
$125$	−0.239015	−	0.413986i	−0.0213782	−	0.0370281i
$126$	0.288615	−	0.130400i	0.0257119	−	0.0116169i
$127$	−2.94106	+	5.09406i	−0.260977	+	0.452025i	−0.966502	−	0.256660i	$-0.917378\pi$
$127$	−2.94106	+	5.09406i	−0.260977	+	0.452025i	0.705525	+	0.708685i	$0.250711\pi$
$128$	−0.578474	+	3.28069i	−0.0511303	+	0.289975i
$129$	−13.0671	+	2.81495i	−1.15050	+	0.247843i
$130$	0.0100995	+	0.00367593i	0.000885788	+	0.000322401i
$131$	3.05420	+	17.3212i	0.266847	+	1.51336i	0.763724	+	0.645543i	$0.223369\pi$
$131$	3.05420	+	17.3212i	0.266847	+	1.51336i	−0.496877	+	0.867821i	$0.665520\pi$
$132$	2.87683	+	7.06460i	0.250396	+	0.614894i
$133$	1.72667	+	1.44885i	0.149721	+	0.125631i
$134$	1.08362			0.0936108
$135$	0.180132	+	0.171112i	0.0155033	+	0.0147270i
$136$	1.09667			0.0940385
$137$	−7.00858	−	5.88089i	−0.598783	−	0.502439i	0.292271	−	0.956335i	$-0.405589\pi$
$137$	−7.00858	−	5.88089i	−0.598783	−	0.502439i	−0.891054	+	0.453897i	$0.850033\pi$
$138$	−0.883430	+	1.13715i	−0.0752026	+	0.0968005i
$139$	0.922429	+	5.23136i	0.0782394	+	0.443718i	0.998612	+	0.0526746i	$0.0167746\pi$
$139$	0.922429	+	5.23136i	0.0782394	+	0.443718i	−0.920372	+	0.391043i	$0.872114\pi$
$140$	−0.0893601	−	0.0325244i	−0.00755231	−	0.00274882i
$141$	2.54062	−	7.89276i	0.213959	−	0.664690i
$142$	−0.260337	+	1.47644i	−0.0218470	+	0.123900i
$143$	−2.35741	+	4.08316i	−0.197137	+	0.341451i
$144$	−11.7663	+	0.887612i	−0.980528	+	0.0739677i
$145$	0.0161051	+	0.0278948i	0.00133745	+	0.00231654i
$146$	0.392164	−	0.142736i	0.0324557	−	0.0118129i
$147$	−1.53153	−	0.808955i	−0.126319	−	0.0667215i
$148$	4.57563	−	3.83941i	0.376114	−	0.315597i
$149$	12.3904	−	10.3968i	1.01506	−	0.851735i	0.0260597	−	0.999660i	$-0.491704\pi$
$149$	12.3904	−	10.3968i	1.01506	−	0.851735i	0.988999	+	0.147925i	$0.0472595\pi$
$150$	−0.0343950	−	0.913187i	−0.00280834	−	0.0745614i
$151$	−11.6602	+	4.24395i	−0.948891	+	0.345368i	−0.769671	−	0.638441i	$-0.779580\pi$
$151$	−11.6602	+	4.24395i	−0.948891	+	0.345368i	−0.179220	+	0.983809i	$0.557357\pi$
$152$	0.474579	+	0.821995i	0.0384934	+	0.0666726i
$153$	1.93163	+	7.57036i	0.156163	+	0.612027i
$154$	−0.116882	+	0.202445i	−0.00941858	+	0.0163135i
$155$	0.0341467	−	0.193656i	0.00274273	−	0.0155548i
$156$	−4.92287	−	5.43736i	−0.394145	−	0.435337i
$157$	7.03913	+	2.56204i	0.561784	+	0.204473i	0.607275	−	0.794492i	$-0.292263\pi$
$157$	7.03913	+	2.56204i	0.561784	+	0.204473i	−0.0454904	+	0.998965i	$0.514485\pi$
$158$	0.0630603	+	0.357633i	0.00501681	+	0.0284517i
$159$	−3.90891	−	0.538442i	−0.309997	−	0.0427012i
$160$	−0.0460565	−	0.0386460i	−0.00364109	−	0.00305524i
$161$	7.87520			0.620653
$162$	0.303490	+	0.900344i	0.0238444	+	0.0707377i
$163$	−6.90048			−0.540488			−0.270244	−	0.962792i	$-0.587104\pi$
$163$	−6.90048			−0.540488			−0.270244	+	0.962792i	$0.587104\pi$
$164$	8.97456	+	7.53055i	0.700796	+	0.588037i
$165$	−0.181666	−	0.0250240i	−0.0141427	−	0.00194812i
$166$	−0.220813	−	1.25229i	−0.0171384	−	0.0971968i
$167$	−16.9249	−	6.16016i	−1.30969	−	0.476687i	−0.409548	−	0.912289i	$-0.634314\pi$
$167$	−16.9249	−	6.16016i	−1.30969	−	0.476687i	−0.900140	+	0.435601i	$0.856536\pi$
$168$	−0.489523	−	0.540684i	−0.0377676	−	0.0417147i
$169$	−1.47016	+	8.33770i	−0.113089	+	0.641361i
$170$	−0.00657282	+	0.0113845i	−0.000504112	+	0.000873148i
$171$	−4.83837	+	4.72388i	−0.369999	+	0.361244i
$172$	7.67437	+	13.2924i	0.585165	+	1.01354i
$173$	−14.6159	+	5.31976i	−1.11123	+	0.404454i	−0.831443	−	0.555610i	$-0.812485\pi$
$173$	−14.6159	+	5.31976i	−1.11123	+	0.404454i	−0.279784	+	0.960063i	$0.590263\pi$
$174$	0.00463619	+	0.123091i	0.000351469	+	0.00933150i
$175$	−3.82847	+	3.21247i	−0.289405	+	0.242840i
$176$	6.67185	−	5.59835i	0.502910	−	0.421991i
$177$	−18.4484	−	9.74442i	−1.38666	−	0.732436i
$178$	1.18838	−	0.432534i	0.0890726	−	0.0324198i
$179$	−9.72046	−	16.8363i	−0.726541	−	1.25841i	−0.958336	−	0.285642i	$-0.907793\pi$
$179$	−9.72046	−	16.8363i	−0.726541	−	1.25841i	0.231795	−	0.972765i	$-0.425540\pi$
$180$	0.123654	−	0.257094i	0.00921659	−	0.0191627i
$181$	8.62738	−	14.9431i	0.641268	−	1.11071i	−0.343882	−	0.939013i	$-0.611742\pi$
$181$	8.62738	−	14.9431i	0.641268	−	1.11071i	0.985150	−	0.171696i	$-0.0549248\pi$
$182$	0.0390329	−	0.221367i	0.00289331	−	0.0164088i
$183$	0.354268	−	1.10058i	0.0261882	−	0.0813570i
$184$	3.11624	+	1.13422i	0.229733	+	0.0836158i
$185$	0.0249355	+	0.141416i	0.00183330	+	0.0103971i
$186$	0.461354	−	0.593854i	0.0338281	−	0.0435435i
$187$	−4.41759	−	3.70680i	−0.323046	−	0.271068i
$188$	−9.52095			−0.694386
$189$	2.87014	−	4.33155i	0.208772	−	0.315074i
$190$	−0.0113775			−0.000825407
$191$	4.75336	+	3.98855i	0.343941	+	0.288601i	0.798352	−	0.602191i	$-0.205706\pi$
$191$	4.75336	+	3.98855i	0.343941	+	0.288601i	−0.454410	+	0.890792i	$0.650150\pi$
$192$	5.05198	+	12.4061i	0.364595	+	0.895332i
$193$	−2.63729	−	14.9568i	−0.189836	−	1.07661i	−0.919583	−	0.392896i	$-0.871473\pi$
$193$	−2.63729	−	14.9568i	−0.189836	−	1.07661i	0.729747	−	0.683718i	$-0.239638\pi$
$194$	1.81212	+	0.659558i	0.130103	+	0.0473535i
$195$	0.172381	−	0.0371348i	0.0123445	−	0.00265928i
$196$	−0.345361	+	1.95864i	−0.0246686	+	0.139903i
$197$	−4.97901	+	8.62390i	−0.354740	+	0.614427i	−0.987073	−	0.160269i	$-0.948764\pi$
$197$	−4.97901	+	8.62390i	−0.354740	+	0.614427i	0.632334	+	0.774696i	$0.282097\pi$
$198$	−0.569606	−	0.409092i	−0.0404801	−	0.0290729i
$199$	2.16427	+	3.74863i	0.153421	+	0.265733i	0.932483	−	0.361214i	$-0.117638\pi$
$199$	2.16427	+	3.74863i	0.153421	+	0.265733i	−0.779062	+	0.626947i	$0.784304\pi$
$200$	−1.97761	+	0.719792i	−0.139838	+	0.0508970i
$201$	15.0514	−	9.46263i	1.06165	−	0.667443i
$202$	1.42371	−	1.19463i	0.100172	−	0.0840541i
$203$	0.516050	−	0.433017i	0.0362196	−	0.0303919i
$204$	7.59503	−	4.77489i	0.531759	−	0.334309i
$205$	−0.264665	+	0.0963302i	−0.0184850	+	0.00672800i
$206$	0.146647	+	0.254001i	0.0102174	+	0.0176971i
$207$	−2.34073	+	23.5094i	−0.162692	+	1.63401i
$208$	−4.18743	+	7.25284i	−0.290346	+	0.502894i
$209$	0.866693	−	4.91526i	0.0599504	−	0.339996i
$210$	0.00854675	−	0.00184116i	0.000589781	−	0.000127052i
$211$	−17.4247	−	6.34206i	−1.19956	−	0.436605i	−0.336491	−	0.941687i	$-0.609240\pi$
$211$	−17.4247	−	6.34206i	−1.19956	−	0.436605i	−0.863072	+	0.505082i	$0.831462\pi$
$212$	0.786774	+	4.46201i	0.0540358	+	0.306452i
$213$	9.27684	+	22.7810i	0.635638	+	1.56093i
$214$	0.744282	+	0.624526i	0.0508780	+	0.0426918i
$215$	−0.368998			−0.0251655
$216$	1.75957	−	1.30064i	0.119724	−	0.0884972i
$217$	−4.11267			−0.279186
$218$	1.11446	+	0.935147i	0.0754811	+	0.0633361i
$219$	4.20070	−	5.40712i	0.283857	−	0.365380i
$220$	0.0365653	+	0.207372i	0.00246523	+	0.0139810i
$221$	5.21078	+	1.89657i	0.350515	+	0.127577i
$222$	−0.168264	+	0.522734i	−0.0112932	+	0.0350836i
$223$	3.98630	−	22.6075i	0.266943	−	1.51391i	−0.496503	−	0.868035i	$-0.665383\pi$
$223$	3.98630	−	22.6075i	0.266943	−	1.51391i	0.763446	−	0.645872i	$-0.223506\pi$
$224$	−0.628713	+	1.08896i	−0.0420077	+	0.0727594i
$225$	−8.45206	−	12.3837i	−0.563471	−	0.825583i
$226$	−0.730479	−	1.26523i	−0.0485907	−	0.0841616i
$227$	−9.42513	+	3.43047i	−0.625568	+	0.227688i	−0.635301	−	0.772265i	$-0.719124\pi$
$227$	−9.42513	+	3.43047i	−0.625568	+	0.227688i	0.00973318	+	0.999953i	$0.496902\pi$
$228$	6.86569	+	3.62645i	0.454691	+	0.240168i
$229$	−1.73941	+	1.45954i	−0.114943	+	0.0964490i	−0.698448	−	0.715661i	$-0.746126\pi$
$229$	−1.73941	+	1.45954i	−0.114943	+	0.0964490i	0.583504	+	0.812110i	$0.301681\pi$
$230$	−0.0304513	+	0.0255517i	−0.00200790	+	0.00168483i
$231$	0.144354	+	3.83260i	0.00949779	+	0.252166i
$232$	0.266568	−	0.0970227i	0.0175010	−	0.00636985i
$233$	−10.8572	−	18.8052i	−0.711278	−	1.23197i	−0.964378	−	0.264529i	$-0.914784\pi$
$233$	−10.8572	−	18.8052i	−0.711278	−	1.23197i	0.253100	−	0.967440i	$-0.418550\pi$
$234$	0.649231	+	0.182319i	0.0424416	+	0.0119186i
$235$	0.114446	−	0.198227i	0.00746565	−	0.0129309i
$236$	−4.16011	+	23.5932i	−0.270800	+	1.53579i
$237$	3.99889	+	4.41682i	0.259756	+	0.286903i
$238$	0.258353	+	0.0940326i	0.0167465	+	0.00609523i
$239$	2.57538	+	14.6057i	0.166588	+	0.944766i	0.947412	+	0.320016i	$0.103688\pi$
$239$	2.57538	+	14.6057i	0.166588	+	0.944766i	−0.780824	+	0.624750i	$0.785201\pi$
$240$	−0.322690	−	0.0444498i	−0.0208296	−	0.00286922i
$241$	15.2735	+	12.8160i	0.983850	+	0.825548i	0.984666	−	0.174451i	$-0.0558152\pi$
$241$	15.2735	+	12.8160i	0.983850	+	0.825548i	−0.000815769		1.00000i	$0.500260\pi$
$242$	−0.643631			−0.0413741
$243$	12.0776	+	9.85551i	0.774780	+	0.632231i
$244$	−1.32761			−0.0849917
$245$	−0.0366276	−	0.0307342i	−0.00234005	−	0.00196354i
$246$	−1.06702	−	0.146979i	−0.0680304	−	0.00937101i
$247$	0.833394	+	4.72641i	0.0530276	+	0.300734i
$248$	−1.62740	−	0.592324i	−0.103340	−	0.0376126i
$249$	−14.0026	−	15.4660i	−0.887379	−	0.980119i
$250$	0.00876317	−	0.0496984i	0.000554232	−	0.00314320i
$251$	−2.71457	+	4.70177i	−0.171342	+	0.296773i	−0.938889	−	0.344219i	$-0.888144\pi$
$251$	−2.71457	+	4.70177i	−0.171342	+	0.296773i	0.767547	+	0.640992i	$0.221477\pi$
$252$	−5.74436	−	1.61315i	−0.361861	−	0.101619i
$253$	−8.71911	−	15.1019i	−0.548166	−	0.949451i
$254$	−0.583519	+	0.212384i	−0.0366132	+	0.0133261i
$255$	0.00811773	+	0.215526i	0.000508352	+	0.0134967i
$256$	11.5794	−	9.71628i	0.723713	−	0.607268i
$257$	9.87540	−	8.28644i	0.616011	−	0.516894i	−0.280536	−	0.959843i	$-0.590512\pi$
$257$	9.87540	−	8.28644i	0.616011	−	0.516894i	0.896547	+	0.442949i	$0.146068\pi$
$258$	−1.24776	−	0.659066i	−0.0776822	−	0.0410317i
$259$	2.82214	−	1.02718i	0.175359	−	0.0638256i
$260$	−0.101240	−	0.175353i	−0.00627866	−	0.0108750i
$261$	1.13928	+	1.66924i	0.0705194	+	0.103323i
$262$	−0.928396	+	1.60803i	−0.0573565	+	0.0993444i
$263$	−5.20032	+	29.4925i	−0.320666	+	1.81858i	0.217865	+	0.975979i	$0.430091\pi$
$263$	−5.20032	+	29.4925i	−0.320666	+	1.81858i	−0.538531	+	0.842606i	$0.681020\pi$
$264$	−0.494865	+	1.53736i	−0.0304569	+	0.0946181i
$265$	−0.102357	−	0.0372549i	−0.00628773	−	0.00228855i
$266$	0.0413200	+	0.234337i	0.00253349	+	0.0143682i
$267$	12.7294	−	16.3852i	0.779026	−	1.00276i
$268$	−15.6387	−	13.1224i	−0.955284	−	0.801579i
$269$	8.35546			0.509441			0.254721	−	0.967015i	$-0.418016\pi$
$269$	8.35546			0.509441			0.254721	+	0.967015i	$0.418016\pi$
$270$	0.00295597	+	0.0260613i	0.000179895	+	0.00158604i
$271$	2.44853			0.148737			0.0743687	−	0.997231i	$-0.476306\pi$
$271$	2.44853			0.148737			0.0743687	+	0.997231i	$0.476306\pi$
$272$	−7.84689	−	6.58432i	−0.475788	−	0.399233i
$273$	−1.39090	−	3.41562i	−0.0841810	−	0.206723i
$274$	−0.167719	−	0.951180i	−0.0101323	−	0.0574629i
$275$	10.3991	+	3.78498i	0.627092	+	0.228243i
$276$	26.5201	−	5.71303i	1.59632	−	0.343884i
$277$	−1.13897	+	6.45940i	−0.0684338	+	0.388107i	0.931283	+	0.364297i	$0.118691\pi$
$277$	−1.13897	+	6.45940i	−0.0684338	+	0.388107i	−0.999716	+	0.0238101i	$0.992420\pi$
$278$	−0.280394	+	0.485656i	−0.0168169	+	0.0291277i
$279$	1.22240	−	12.2773i	0.0731834	−	0.735023i
$280$	−0.0100672	−	0.0174369i	−0.000601630	−	0.00104205i
$281$	12.1311	−	4.41537i	0.723683	−	0.263399i	0.0461944	−	0.998932i	$-0.485291\pi$
$281$	12.1311	−	4.41537i	0.723683	−	0.263399i	0.677488	+	0.735533i	$0.263068\pi$
$282$	0.741050	−	0.465888i	0.0441289	−	0.0277432i
$283$	−12.2500	+	10.2789i	−0.728185	+	0.611019i	−0.929636	−	0.368479i	$-0.879879\pi$
$283$	−12.2500	+	10.2789i	−0.728185	+	0.611019i	0.201451	+	0.979499i	$0.435434\pi$
$284$	21.6365	−	18.1552i	1.28389	−	1.07731i
$285$	−0.158032	+	0.0993525i	−0.00936100	+	0.00588513i
$286$	−0.467721	+	0.170237i	−0.0276569	+	0.0100663i
$287$	2.94528	+	5.10137i	0.173854	+	0.301124i
$288$	−3.06394	−	2.20053i	−0.180545	−	0.129667i
$289$	5.10881	−	8.84871i	0.300518	−	0.520512i
$290$	−0.000590471		0.00334873i	−3.46736e−5		0.000196644i
$291$	30.9297	−	6.66295i	1.81313	−	0.390589i
$292$	−7.38814	−	2.68906i	−0.432358	−	0.157366i
$293$	0.173966	+	0.986612i	0.0101632	+	0.0576385i	0.989468	−	0.144755i	$-0.0462393\pi$
$293$	0.173966	+	0.986612i	0.0101632	+	0.0576385i	−0.979304	+	0.202393i	$0.935128\pi$
$294$	−0.0689614	−	0.169348i	−0.00402191	−	0.00987656i
$295$	−0.441205	−	0.370215i	−0.0256880	−	0.0215548i
$296$	1.26467			0.0735074
$297$	−11.4841	−	0.708226i	−0.666377	−	0.0410954i
$298$	1.70752			0.0989140
$299$	12.8452	+	10.7784i	0.742858	+	0.623331i
$300$	−10.5621	+	13.5955i	−0.609802	+	0.784935i
$301$	1.34011	+	7.60013i	0.0772425	+	0.438064i
$302$	−1.23095	−	0.448029i	−0.0708332	−	0.0257812i
$303$	9.34318	−	29.0258i	0.536752	−	1.66749i
$304$	1.53949	−	8.73089i	0.0882959	−	0.500751i
$305$	0.0159585	−	0.0276410i	0.000913784	−	0.00158272i
$306$	−0.357500	+	0.743295i	−0.0204369	+	0.0424914i
$307$	−17.3639	−	30.0752i	−0.991010	−	1.71648i	−0.611369	−	0.791346i	$-0.709381\pi$
$307$	−17.3639	−	30.0752i	−0.991010	−	1.71648i	−0.379641	−	0.925134i	$-0.623953\pi$
$308$	4.13837	−	1.50624i	0.235806	−	0.0858262i
$309$	4.25496	+	2.24746i	0.242056	+	0.127854i
$310$	0.0159026	−	0.0133439i	0.000903208	−	0.000757881i
$311$	−1.69583	+	1.42297i	−0.0961615	+	0.0806891i	−0.689601	−	0.724190i	$-0.742214\pi$
$311$	−1.69583	+	1.42297i	−0.0961615	+	0.0806891i	0.593440	+	0.804879i	$0.297770\pi$
$312$	−0.0584517	−	1.55189i	−0.00330918	−	0.0878587i
$313$	2.22955	−	0.811489i	0.126021	−	0.0458681i	−0.278240	−	0.960512i	$-0.589751\pi$
$313$	2.22955	−	0.811489i	0.126021	−	0.0458681i	0.404261	+	0.914644i	$0.367529\pi$
$314$	0.395402	+	0.684857i	0.0223138	+	0.0386487i
$315$	0.102636	−	0.100207i	0.00578287	−	0.00564603i
$316$	3.42077	−	5.92494i	0.192433	−	0.333304i
$317$	1.42162	−	8.06239i	0.0798460	−	0.452829i	−0.918504	−	0.395411i	$-0.870602\pi$
$317$	1.42162	−	8.06239i	0.0798460	−	0.452829i	0.998350	−	0.0574179i	$-0.0182867\pi$
$318$	−0.279577	−	0.308796i	−0.0156779	−	0.0173164i
$319$	−1.40173	−	0.510187i	−0.0784817	−	0.0285650i
$320$	0.0642120	+	0.364164i	0.00358956	+	0.0203574i
$321$	15.7916	+	2.17525i	0.881402	+	0.121411i
$322$	0.636871	+	0.534398i	0.0354914	+	0.0297808i
$323$	−5.87011			−0.326622
$324$	6.52302	−	16.6688i	0.362390	−	0.926045i
$325$	−10.6414			−0.590276
$326$	−0.558045	−	0.468255i	−0.0309072	−	0.0259343i
$327$	23.6459	+	3.25716i	1.30762	+	0.180121i
$328$	0.430735	+	2.44282i	0.0237834	+	0.134882i
$329$	−4.49845	−	1.63730i	−0.248008	−	0.0902674i
$330$	−0.0129933	−	0.0143513i	−0.000715259	−	0.000790011i
$331$	−1.10168	+	6.24791i	−0.0605536	+	0.343416i	0.939446	+	0.342697i	$0.111340\pi$
$331$	−1.10168	+	6.24791i	−0.0605536	+	0.343416i	−1.00000		0.000719872i	$0.999771\pi$
$332$	−11.9782	+	20.7469i	−0.657390	+	1.13863i
$333$	2.22755	+	8.73008i	0.122069	+	0.478406i
$334$	−0.950705	−	1.64667i	−0.0520203	−	0.0901017i
$335$	0.461194	−	0.167861i	0.0251977	−	0.00917122i
$336$	0.256413	+	6.80777i	0.0139885	+	0.371394i
$337$	−19.3497	+	16.2363i	−1.05404	+	0.884448i	−0.993513	−	0.113718i	$-0.963724\pi$
$337$	−19.3497	+	16.2363i	−1.05404	+	0.884448i	−0.0605315	+	0.998166i	$0.519280\pi$
$338$	−0.684675	+	0.574510i	−0.0372414	+	0.0312492i
$339$	−21.1948	−	11.1951i	−1.15114	−	0.608032i
$340$	0.232721	−	0.0847034i	0.0126211	−	0.00459369i
$341$	4.55339	+	7.88670i	0.246580	+	0.427089i
$342$	−0.711835	+	0.0536984i	−0.0384916	+	0.00290368i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−0.564318	+	3.20040i	−0.0304260	+	0.172554i
$345$	−0.199839	+	0.620824i	−0.0107590	+	0.0334240i
$346$	−1.54298	−	0.561600i	−0.0829513	−	0.0301918i
$347$	4.76192	+	27.0062i	0.255633	+	1.44977i	0.794442	+	0.607340i	$0.207763\pi$
$347$	4.76192	+	27.0062i	0.255633	+	1.44977i	−0.538809	+	0.842428i	$0.681126\pi$
$348$	1.42369	−	1.83257i	0.0763179	−	0.0982361i
$349$	23.1748	+	19.4460i	1.24052	+	1.04092i	0.997483	+	0.0709015i	$0.0225876\pi$
$349$	23.1748	+	19.4460i	1.24052	+	1.04092i	0.243036	+	0.970017i	$0.421857\pi$
$350$	−0.527603			−0.0282015
$351$	10.6099	−	3.13695i	0.566312	−	0.167438i
$352$	2.78434			0.148406
$353$	14.6203	+	12.2679i	0.778159	+	0.652953i	0.942784	−	0.333403i	$-0.108197\pi$
$353$	14.6203	+	12.2679i	0.778159	+	0.652953i	−0.164625	+	0.986356i	$0.552641\pi$
$354$	−0.830687	−	2.03991i	−0.0441505	−	0.108420i
$355$	0.117911	+	0.668707i	0.00625807	+	0.0354913i
$356$	−22.3883	−	8.14868i	−1.18658	−	0.431879i
$357$	4.40963	−	0.949932i	0.233382	−	0.0502757i
$358$	0.356388	−	2.02117i	0.0188357	−	0.106822i
$359$	0.0467450	−	0.0809648i	0.00246711	−	0.00427316i	−0.864789	−	0.502135i	$-0.832548\pi$
$359$	0.0467450	−	0.0809648i	0.00246711	−	0.00427316i	0.867256	+	0.497862i	$0.165881\pi$
$360$	0.0550456	−	0.0248703i	0.00290116	−	0.00131078i
$361$	6.95973	+	12.0546i	0.366302	+	0.634453i
$362$	1.71171	−	0.623012i	0.0899655	−	0.0327448i
$363$	−8.93997	+	5.62044i	−0.469227	+	0.294997i
$364$	−3.24401	+	2.72205i	−0.170032	+	0.142674i
$365$	0.144796	−	0.121498i	0.00757895	−	0.00635949i
$366$	0.103333	−	0.0649641i	0.00540130	−	0.00339573i
$367$	18.1715	−	6.61390i	0.948547	−	0.345243i	0.179011	−	0.983847i	$-0.442710\pi$
$367$	18.1715	−	6.61390i	0.948547	−	0.345243i	0.769535	+	0.638604i	$0.220488\pi$
$368$	−15.4876	−	26.8253i	−0.807347	−	1.39837i
$369$	−16.1042	+	7.27608i	−0.838353	+	0.378778i
$370$	−0.00757973	+	0.0131285i	−0.000394051	+	0.000682517i
$371$	−0.395591	+	2.24351i	−0.0205381	+	0.116477i
$372$	−13.8496	+	2.98352i	−0.718069	+	0.154688i
$373$	−17.8957	−	6.51350i	−0.926604	−	0.337256i	−0.165741	−	0.986169i	$-0.553002\pi$
$373$	−17.8957	−	6.51350i	−0.926604	−	0.337256i	−0.760863	+	0.648913i	$0.775224\pi$
$374$	−0.105715	−	0.599541i	−0.00546640	−	0.0310015i
$375$	−0.312267	−	0.766830i	−0.0161254	−	0.0395989i
$376$	−1.54424	−	1.29577i	−0.0796381	−	0.0668243i
$377$	1.43438			0.0738741
$378$	0.526041	−	0.155531i	0.0270566	−	0.00799966i
$379$	−17.4412			−0.895894			−0.447947	−	0.894060i	$-0.647845\pi$
$379$	−17.4412			−0.895894			−0.447947	+	0.894060i	$0.647845\pi$
$380$	0.164198	+	0.137778i	0.00842316	+	0.00706787i
$381$	−6.25041	+	8.04551i	−0.320218	+	0.412184i
$382$	0.113750	+	0.645111i	0.00581998	+	0.0330067i
$383$	12.9295	+	4.70596i	0.660667	+	0.240463i	0.650524	−	0.759485i	$-0.274549\pi$
$383$	12.9295	+	4.70596i	0.660667	+	0.240463i	0.0101426	+	0.999949i	$0.496771\pi$
$384$	−1.76798	+	5.49244i	−0.0902216	+	0.280285i
$385$	−0.0183851	+	0.104267i	−0.000936990	+	0.00531394i
$386$	0.801665	−	1.38852i	0.0408037	−	0.0706740i
$387$	−23.0865	+	1.74157i	−1.17355	+	0.0885289i
$388$	−18.1651	−	31.4629i	−0.922195	−	1.59729i
$389$	−16.0006	+	5.82376i	−0.811265	+	0.295276i	−0.714146	−	0.699997i	$-0.753185\pi$
$389$	−16.0006	+	5.82376i	−0.811265	+	0.295276i	−0.0971185	+	0.995273i	$0.530963\pi$
$390$	0.0164605	+	0.00869441i	0.000833508	+	0.000440258i
$391$	−15.7111	+	13.1832i	−0.794545	+	0.666703i
$392$	−0.322580	+	0.270677i	−0.0162928	+	0.0136713i
$393$	1.14661	+	30.4425i	0.0578388	+	1.53562i
$394$	−0.987858	+	0.359551i	−0.0497676	+	0.0181139i
$395$	0.0822385	+	0.142441i	0.00413787	+	0.00716700i
$396$	3.26646	+	12.8017i	0.164146	+	0.643311i
$397$	4.94769	−	8.56965i	0.248317	−	0.430099i	−0.714742	−	0.699389i	$-0.753456\pi$
$397$	4.94769	−	8.56965i	0.248317	−	0.430099i	0.963059	+	0.269290i	$0.0867890\pi$
$398$	−0.0793502	+	0.450017i	−0.00397747	+	0.0225573i
$399$	2.62026	+	2.89410i	0.131177	+	0.144886i
$400$	18.4718	+	6.72319i	0.923590	+	0.336159i
$401$	−0.707807	−	4.01417i	−0.0353462	−	0.200458i	0.962021	−	0.272976i	$-0.0880078\pi$
$401$	−0.707807	−	4.01417i	−0.0353462	−	0.200458i	−0.997367	+	0.0725173i	$0.976897\pi$
$402$	1.85933	+	0.256118i	0.0927352	+	0.0127740i
$403$	−6.70816	−	5.62882i	−0.334157	−	0.280391i
$404$	−35.0134			−1.74198
$405$	0.268636	+	0.336177i	0.0133486	+	0.0167048i
$406$	0.0711170			0.00352948
$407$	−5.09434	−	4.27466i	−0.252517	−	0.211887i
$408$	1.88172	+	0.259202i	0.0931589	+	0.0128324i
$409$	5.00771	+	28.4001i	0.247615	+	1.40430i	0.814340	+	0.580389i	$0.197099\pi$
$409$	5.00771	+	28.4001i	0.247615	+	1.40430i	−0.566724	+	0.823907i	$0.691790\pi$
$410$	−0.0279404	−	0.0101695i	−0.00137988	−	0.000502234i
$411$	−10.6357	−	11.7472i	−0.524620	−	0.579448i
$412$	0.959494	−	5.44156i	0.0472709	−	0.268086i
$413$	−6.02285	+	10.4319i	−0.296365	+	0.513319i
$414$	−1.78460	+	1.74237i	−0.0877084	+	0.0856330i
$415$	−0.287968	−	0.498775i	−0.0141358	−	0.0244839i
$416$	−2.51590	+	0.915714i	−0.123352	+	0.0448966i
$417$	0.346299	+	9.19424i	0.0169583	+	0.450244i
$418$	0.403631	−	0.338687i	0.0197422	−	0.0165657i
$419$	11.2026	−	9.40013i	0.547285	−	0.459226i	−0.326736	−	0.945116i	$-0.605949\pi$
$419$	11.2026	−	9.40013i	0.547285	−	0.459226i	0.874020	+	0.485889i	$0.161504\pi$
$420$	−0.145641	−	0.0769276i	−0.00710656	−	0.00375368i
$421$	30.1366	−	10.9688i	1.46877	−	0.534588i	0.521002	−	0.853555i	$-0.325558\pi$
$421$	30.1366	−	10.9688i	1.46877	−	0.534588i	0.947766	+	0.318968i	$0.103336\pi$
$422$	−0.978777	−	1.69529i	−0.0476461	−	0.0825255i
$423$	6.22480	−	12.9423i	0.302660	−	0.629276i
$424$	−0.479656	+	0.830789i	−0.0232942	+	0.0403467i
$425$	2.26013	−	12.8178i	0.109632	−	0.621756i
$426$	−0.795661	+	2.47182i	−0.0385499	+	0.119760i
$427$	−0.627270	−	0.228307i	−0.0303557	−	0.0110486i
$428$	−3.17849	−	18.0261i	−0.153638	−	0.871326i
$429$	−5.01004	+	6.44890i	−0.241887	+	0.311356i
$430$	−0.0298410	−	0.0250396i	−0.00143906	−	0.00120752i
$431$	2.09915			0.101113			0.0505563	−	0.998721i	$-0.483901\pi$
$431$	2.09915			0.101113			0.0505563	+	0.998721i	$0.483901\pi$
$432$	−20.3990	−	1.25801i	−0.981449	−	0.0605260i
$433$	−4.97773			−0.239214			−0.119607	−	0.992821i	$-0.538164\pi$
$433$	−4.97773			−0.239214			−0.119607	+	0.992821i	$0.538164\pi$
$434$	−0.332593	−	0.279079i	−0.0159650	−	0.0133962i
$435$	0.0210408	+	0.0516697i	0.00100883	+	0.00247737i
$436$	−4.75938	−	26.9918i	−0.227933	−	1.29267i
$437$	−16.6802	−	6.07111i	−0.797924	−	0.290421i
$438$	0.706630	−	0.152224i	0.0337641	−	0.00727355i
$439$	−4.93634	+	27.9954i	−0.235599	+	1.33615i	0.605751	+	0.795654i	$0.292873\pi$
$439$	−4.93634	+	27.9954i	−0.235599	+	1.33615i	−0.841349	+	0.540492i	$0.818238\pi$
$440$	−0.0222920	+	0.0386109i	−0.00106273	+	0.00184070i
$441$	−2.43668	−	1.75003i	−0.116032	−	0.0833346i
$442$	0.292700	+	0.506971i	0.0139223	+	0.0241141i
$443$	−27.8701	+	10.1439i	−1.32415	+	0.481951i	−0.904785	−	0.425868i	$-0.859969\pi$
$443$	−27.8701	+	10.1439i	−1.32415	+	0.481951i	−0.419363	+	0.907818i	$0.637747\pi$
$444$	8.75854	−	5.50637i	0.415662	−	0.261321i
$445$	0.438775	−	0.368176i	0.0207999	−	0.0174532i
$446$	1.85648	−	1.55777i	0.0879068	−	0.0737625i
$447$	23.7173	−	14.9107i	1.12179	−	0.705254i
$448$	7.26736	−	2.64510i	0.343351	−	0.124969i
$449$	3.34561	+	5.79477i	0.157889	+	0.273472i	0.934107	−	0.356992i	$-0.116198\pi$
$449$	3.34561	+	5.79477i	0.157889	+	0.273472i	−0.776218	+	0.630464i	$0.782864\pi$
$450$	0.156819	−	1.57502i	0.00739250	−	0.0742472i
$451$	6.52179	−	11.2961i	0.307099	−	0.531911i
$452$	−4.77942	+	27.1055i	−0.224805	+	1.27493i
$453$	−21.0102	+	4.52606i	−0.987143	+	0.212653i
$454$	−0.995000	−	0.362150i	−0.0466977	−	0.0169966i
$455$	−0.0176787	−	0.100261i	−0.000828791	−	0.00470030i
$456$	0.620024	+	1.52259i	0.0290353	+	0.0713017i
$457$	13.3387	+	11.1925i	0.623958	+	0.523563i	0.899045	−	0.437857i	$-0.144262\pi$
$457$	13.3387	+	11.1925i	0.623958	+	0.523563i	−0.275087	+	0.961419i	$0.588707\pi$
$458$	−0.239709			−0.0112008
$459$	1.52511	+	13.4461i	0.0711860	+	0.627612i
$460$	0.748893			0.0349173
$461$	8.95670	+	7.51556i	0.417155	+	0.350035i	0.827080	−	0.562085i	$-0.190001\pi$
$461$	8.95670	+	7.51556i	0.417155	+	0.350035i	−0.409925	+	0.912119i	$0.634445\pi$
$462$	−0.248400	+	0.319739i	−0.0115566	+	0.0148756i
$463$	5.04729	+	28.6246i	0.234567	+	1.33030i	0.843523	+	0.537093i	$0.180478\pi$
$463$	5.04729	+	28.6246i	0.234567	+	1.33030i	−0.608956	+	0.793204i	$0.708411\pi$
$464$	−2.48986	−	0.906236i	−0.115589	−	0.0420710i
$465$	0.104362	−	0.324213i	0.00483967	−	0.0150350i
$466$	0.398064	−	2.25753i	0.0184400	−	0.104578i
$467$	19.9136	−	34.4914i	0.921492	−	1.59607i	0.124384	−	0.992234i	$-0.460305\pi$
$467$	19.9136	−	34.4914i	0.921492	−	1.59607i	0.797108	−	0.603837i	$-0.206362\pi$
$468$	−7.16176	−	10.4932i	−0.331052	−	0.485050i
$469$	−5.13231	−	8.88942i	−0.236988	−	0.410475i
$470$	0.0227067	−	0.00826455i	0.00104738	−	0.000381215i
$471$	11.4725	+	6.05979i	0.528627	+	0.279220i
$472$	−3.88570	+	3.26049i	−0.178854	+	0.150076i
$473$	13.0907	−	10.9844i	0.601912	−	0.505064i
$474$	0.0236741	+	0.628548i	0.00108739	+	0.0288702i
$475$	10.5855	−	3.85281i	0.485697	−	0.176779i
$476$	−2.58979	−	4.48565i	−0.118703	−	0.205599i
$477$	−6.57983	−	1.84777i	−0.301270	−	0.0846035i
$478$	−0.782848	+	1.35593i	−0.0358066	+	0.0620189i
$479$	7.23541	−	41.0341i	0.330595	−	1.87489i	−0.136429	−	0.990650i	$-0.543563\pi$
$479$	7.23541	−	41.0341i	0.330595	−	1.87489i	0.467024	−	0.884245i	$-0.345326\pi$
$480$	−0.0698919	−	0.0771964i	−0.00319012	−	0.00352352i
$481$	6.00903	+	2.18711i	0.273988	+	0.0997236i
$482$	0.365502	+	2.07286i	0.0166481	+	0.0944163i
$483$	13.5127	+	1.86133i	0.614847	+	0.0846936i
$484$	9.28877	+	7.79420i	0.422217	+	0.354282i
$485$	0.873415			0.0396597
$486$	0.307944	+	1.61659i	0.0139686	+	0.0733298i
$487$	−1.17610			−0.0532942			−0.0266471	−	0.999645i	$-0.508483\pi$
$487$	−1.17610			−0.0532942			−0.0266471	+	0.999645i	$0.508483\pi$
$488$	−0.215331	−	0.180684i	−0.00974757	−	0.00817918i
$489$	−11.8402	−	1.63095i	−0.535432	−	0.0737543i
$490$	−0.000876518	−	0.00497098i	−3.95970e−5	−	0.000224566i
$491$	8.49669	+	3.09254i	0.383450	+	0.139564i	0.526551	−	0.850144i	$-0.323485\pi$
$491$	8.49669	+	3.09254i	0.383450	+	0.139564i	−0.143101	+	0.989708i	$0.545707\pi$
$492$	13.6191	+	15.0425i	0.613997	+	0.678166i
$493$	−0.304649	+	1.72775i	−0.0137207	+	0.0778139i
$494$	−0.253329	+	0.438780i	−0.0113978	+	0.0197416i
$495$	−0.305797	−	0.0858750i	−0.0137446	−	0.00385979i
$496$	8.08810	+	14.0090i	0.363166	+	0.629022i
$497$	13.3449	−	4.85715i	0.598601	−	0.217873i
$498$	−0.0828978	−	2.20094i	−0.00371474	−	0.0986263i
$499$	5.72426	−	4.80323i	0.256253	−	0.215022i	−0.505606	−	0.862764i	$-0.668731\pi$
$499$	5.72426	−	4.80323i	0.256253	−	0.215022i	0.761859	+	0.647742i	$0.224287\pi$
$500$	−0.728304	+	0.611120i	−0.0325707	+	0.0273301i
$501$	−27.5846	−	14.5702i	−1.23239	−	0.650947i
$502$	−0.538582	+	0.196028i	−0.0240381	+	0.00874916i
$503$	13.4363	+	23.2723i	0.599094	+	1.03766i	0.992955	+	0.118492i	$0.0378059\pi$
$503$	13.4363	+	23.2723i	0.599094	+	1.03766i	−0.393861	+	0.919170i	$0.628861\pi$
$504$	−0.712156	−	1.04343i	−0.0317219	−	0.0464782i
$505$	0.420878	−	0.728983i	0.0187288	−	0.0324393i
$506$	0.319674	−	1.81296i	0.0142113	−	0.0805961i
$507$	−4.49322	+	13.9587i	−0.199551	+	0.619930i
$508$	10.9932	+	4.00118i	0.487743	+	0.177524i
$509$	−3.76876	−	21.3737i	−0.167047	−	0.947373i	−0.946928	−	0.321445i	$-0.895832\pi$
$509$	−3.76876	−	21.3737i	−0.167047	−	0.947373i	0.779881	−	0.625928i	$-0.215280\pi$
$510$	−0.0139687	+	0.0179805i	−0.000618546	+	0.000796190i
$511$	−3.02831	−	2.54105i	−0.133965	−	0.112410i
$512$	8.25836			0.364971
$513$	−9.41841	+	6.96189i	−0.415833	+	0.307375i
$514$	1.36093			0.0600281
$515$	0.101760	+	0.0853869i	0.00448409	+	0.00376259i
$516$	10.0263	+	24.6216i	0.441385	+	1.08391i
$517$	1.84072	+	10.4392i	0.0809547	+	0.459117i
$518$	0.297930	+	0.108438i	0.0130903	+	0.00476448i
$519$	−26.3360	+	5.67337i	−1.15602	+	0.249033i
$520$	0.00744448	−	0.0422197i	0.000326462	−	0.00185146i
$521$	2.71989	−	4.71098i	0.119160	−	0.206392i	−0.800275	−	0.599633i	$-0.795313\pi$
$521$	2.71989	−	4.71098i	0.119160	−	0.206392i	0.919435	+	0.393242i	$0.128646\pi$
$522$	−0.0211380	+	0.212301i	−0.000925185	+	0.00929217i
$523$	19.5453	+	33.8534i	0.854655	+	1.48031i	0.876965	+	0.480555i	$0.159565\pi$
$523$	19.5453	+	33.8534i	0.854655	+	1.48031i	−0.0223099	+	0.999751i	$0.507102\pi$
$524$	32.8713	−	11.9642i	1.43599	−	0.522657i
$525$	−7.32836	+	4.60724i	−0.319836	+	0.201076i
$526$	−2.42186	+	2.03218i	−0.105598	+	0.0886074i
$527$	8.20483	−	6.88467i	0.357408	−	0.299901i
$528$	12.7711	−	8.02900i	0.555790	−	0.349418i
$529$	−36.6657	+	13.3452i	−1.59416	+	0.580227i
$530$	−0.00574959	−	0.00995858i	−0.000249746	−	0.000432573i
$531$	−29.3515	−	21.0803i	−1.27375	−	0.914807i
$532$	2.24144	−	3.88230i	0.0971789	−	0.168319i
$533$	−2.17797	+	12.3519i	−0.0943383	+	0.535019i
$534$	2.14131	−	0.461285i	0.0926633	−	0.0199618i
$535$	0.413512	+	0.150506i	0.0178777	+	0.00650695i
$536$	−0.750580	−	4.25675i	−0.0324201	−	0.183864i
$537$	−12.6995	−	31.1861i	−0.548024	−	1.34578i
$538$	0.675709	+	0.566988i	0.0291319	+	0.0244446i
$539$	2.21432			0.0953775
$540$	0.272936	−	0.411909i	0.0117453	−	0.0177257i
$541$	12.6914			0.545648			0.272824	−	0.962064i	$-0.412042\pi$
$541$	12.6914			0.545648			0.272824	+	0.962064i	$0.412042\pi$
$542$	0.198013	+	0.166153i	0.00850540	+	0.00713688i
$543$	18.3351	−	23.6009i	0.786836	−	1.01281i
$544$	−0.568649	−	3.22497i	−0.0243806	−	0.138269i
$545$	0.619181	+	0.225363i	0.0265228	+	0.00965351i
$546$	0.119295	−	0.370606i	0.00510538	−	0.0158605i
$547$	3.32842	−	18.8764i	0.142313	−	0.807097i	−0.827173	−	0.561948i	$-0.810052\pi$
$547$	3.32842	−	18.8764i	0.142313	−	0.807097i	0.969485	−	0.245149i	$-0.0788368\pi$
$548$	−9.09807	+	15.7583i	−0.388650	+	0.673162i
$549$	0.867995	−	1.80469i	0.0370451	−	0.0770223i
$550$	0.584141	+	1.01176i	0.0249078	+	0.0431416i
$551$	−1.42685	+	0.519331i	−0.0607858	+	0.0221242i
$552$	5.07893	+	2.68269i	0.216173	+	0.114183i
$553$	2.63514	−	2.21115i	0.112058	−	0.0940276i
$554$	−0.530432	+	0.445086i	−0.0225359	+	0.0189099i
$555$	0.00936130	+	0.248543i	0.000397365	+	0.0105500i
$556$	9.92777	−	3.61341i	0.421031	−	0.153243i
$557$	−15.4423	−	26.7469i	−0.654312	−	1.13330i	−0.982066	−	0.188539i	$-0.939625\pi$
$557$	−15.4423	−	26.7469i	−0.654312	−	1.13330i	0.327753	−	0.944763i	$-0.393709\pi$
$558$	0.931974	−	0.909921i	0.0394536	−	0.0385200i
$559$	−8.21608	+	14.2307i	−0.347503	+	0.601893i
$560$	−0.0326571	+	0.185207i	−0.00138001	+	0.00782644i
$561$	−6.70381	−	7.40442i	−0.283035	−	0.312615i
$562$	1.28067	+	0.466126i	0.0540218	+	0.0196623i
$563$	0.220230	+	1.24899i	0.00928160	+	0.0526386i	0.989097	−	0.147267i	$-0.0470476\pi$
$563$	0.220230	+	1.24899i	0.00928160	+	0.0526386i	−0.979815	+	0.199905i	$0.935936\pi$
$564$	−16.3365	−	2.25031i	−0.687891	−	0.0947552i
$565$	−0.506887	−	0.425328i	−0.0213249	−	0.0178937i
$566$	−1.68817			−0.0709591
$567$	5.94850	−	6.75391i	0.249814	−	0.283638i
$568$	5.98017			0.250922
$569$	22.0655	+	18.5151i	0.925033	+	0.776195i	0.974919	−	0.222560i	$-0.0714414\pi$
$569$	22.0655	+	18.5151i	0.925033	+	0.776195i	−0.0498862	+	0.998755i	$0.515886\pi$
$570$	−0.0195220	−	0.00268910i	−0.000817686	−	0.000112634i
$571$	−5.88358	−	33.3674i	−0.246220	−	1.39638i	−0.817642	−	0.575727i	$-0.804719\pi$
$571$	−5.88358	−	33.3674i	−0.246220	−	1.39638i	0.571422	−	0.820656i	$-0.306392\pi$
$572$	8.81160	+	3.20716i	0.368432	+	0.134098i
$573$	7.21335	+	7.96722i	0.301342	+	0.332835i
$574$	−0.107985	+	0.612411i	−0.00450719	+	0.0255616i
$575$	19.6790	−	34.0850i	0.820671	−	1.42144i
$576$	5.73620	+	22.4810i	0.239008	+	0.936709i
$577$	−1.16820	−	2.02338i	−0.0486329	−	0.0842346i	0.840684	−	0.541526i	$-0.182153\pi$
$577$	−1.16820	−	2.02338i	−0.0486329	−	0.0842346i	−0.889317	+	0.457291i	$0.848820\pi$
$578$	1.01361	−	0.368924i	0.0421606	−	0.0153452i
$579$	−0.990092	−	26.2869i	−0.0411468	−	1.09245i
$580$	0.0490738	−	0.0411778i	0.00203768	−	0.00170982i
$581$	−9.22727	+	7.74259i	−0.382811	+	0.321217i
$582$	2.95344	+	1.56000i	0.122424	+	0.0646642i
$583$	4.74026	−	1.72532i	0.196322	−	0.0714552i
$584$	−0.832339	−	1.44165i	−0.0344424	−	0.0596560i
$585$	0.304558	−	0.0229748i	0.0125919	−	0.000949890i
$586$	−0.0528811	+	0.0915928i	−0.00218450	+	0.00378366i
$587$	2.13337	−	12.0990i	0.0880538	−	0.499378i	−0.908602	−	0.417663i	$-0.862849\pi$
$587$	2.13337	−	12.0990i	0.0880538	−	0.499378i	0.996656	−	0.0817148i	$-0.0260397\pi$
$588$	−1.05552	+	3.27910i	−0.0435289	+	0.135228i
$589$	8.71093	+	3.17052i	0.358928	+	0.130639i
$590$	−0.0105583	−	0.0598789i	−0.000434677	−	0.00246518i
$591$	−10.5815	+	13.6205i	−0.435266	+	0.560272i
$592$	−9.04898	−	7.59299i	−0.371911	−	0.312070i
$593$	−30.6098			−1.25699			−0.628497	−	0.777812i	$-0.716330\pi$
$593$	−30.6098			−1.25699			−0.628497	+	0.777812i	$0.716330\pi$
$594$	−0.880667	−	0.836568i	−0.0361342	−	0.0343248i
$595$	0.124522			0.00510491
$596$	−24.6426	−	20.6776i	−1.00940	−	0.846989i
$597$	2.82756	+	6.94362i	0.115724	+	0.284183i
$598$	0.307392	+	1.74331i	0.0125702	+	0.0712892i
$599$	43.0953	+	15.6854i	1.76083	+	0.640888i	0.999968	−	0.00803083i	$-0.00255632\pi$
$599$	43.0953	+	15.6854i	1.76083	+	0.640888i	0.760858	+	0.648919i	$0.224779\pi$
$600$	−3.56341	+	0.767638i	−0.145476	+	0.0313387i
$601$	−6.32071	+	35.8465i	−0.257827	+	1.46221i	0.530883	+	0.847445i	$0.321861\pi$
$601$	−6.32071	+	35.8465i	−0.257827	+	1.46221i	−0.788710	+	0.614766i	$0.789251\pi$
$602$	−0.407357	+	0.705563i	−0.0166026	+	0.0287566i
$603$	28.0625	−	12.6790i	1.14279	−	0.516328i
$604$	12.3393	+	21.3724i	0.502081	+	0.869630i
$605$	−0.273931	+	0.0997028i	−0.0111369	+	0.00405350i
$606$	2.72523	−	1.71331i	0.110705	−	0.0695985i
$607$	30.1352	−	25.2865i	1.22315	−	1.02635i	0.224497	−	0.974475i	$-0.427926\pi$
$607$	30.1352	−	25.2865i	1.22315	−	1.02635i	0.998654	−	0.0518707i	$-0.0165184\pi$
$608$	2.17116	−	1.82182i	0.0880521	−	0.0738844i
$609$	0.987809	−	0.621022i	0.0400280	−	0.0251651i
$610$	0.00316625	−	0.00115242i	0.000128198	−	4.66601e-5i
$611$	−5.09650	−	8.82740i	−0.206183	−	0.357119i
$612$	14.1605	−	6.39788i	0.572404	−	0.258619i
$613$	−3.14950	+	5.45509i	−0.127207	+	0.220329i	−0.922594	−	0.385774i	$-0.873935\pi$
$613$	−3.14950	+	5.45509i	−0.127207	+	0.220329i	0.795386	+	0.606103i	$0.207268\pi$
$614$	0.636624	−	3.61047i	0.0256921	−	0.145707i
$615$	−0.476893	+	0.102734i	−0.0192302	+	0.00414262i
$616$	0.876214	+	0.318916i	0.0353037	+	0.0128495i
$617$	0.786407	+	4.45994i	0.0316596	+	0.179550i	0.996537	−	0.0831500i	$-0.0264981\pi$
$617$	0.786407	+	4.45994i	0.0316596	+	0.179550i	−0.964877	+	0.262700i	$0.915387\pi$
$618$	0.191591	+	0.470487i	0.00770691	+	0.0189258i
$619$	−1.43509	−	1.20418i	−0.0576812	−	0.0484003i	0.613491	−	0.789701i	$-0.289765\pi$
$619$	−1.43509	−	1.20418i	−0.0576812	−	0.0484003i	−0.671172	+	0.741301i	$0.734209\pi$
$620$	−0.391095			−0.0157067
$621$	−9.57287	+	39.7853i	−0.384146	+	1.59653i
$622$	−0.233702			−0.00937061
$623$	−9.17670	−	7.70017i	−0.367657	−	0.308501i
$624$	−8.89923	+	11.4551i	−0.356254	+	0.458570i
$625$	4.33525	+	24.5864i	0.173410	+	0.983457i
$626$	0.235371	+	0.0856679i	0.00940730	+	0.00342398i
$627$	2.64885	−	8.22900i	0.105785	−	0.328635i
$628$	2.58706	−	14.6720i	0.103235	−	0.585475i
$629$	−3.91070	+	6.77353i	−0.155930	+	0.270079i
$630$	0.0151001	−	0.00113910i	0.000601602	−	4.53828e-5i
$631$	−15.2094	−	26.3435i	−0.605478	−	1.04872i	−0.991976	−	0.126428i	$-0.959649\pi$
$631$	−15.2094	−	26.3435i	−0.605478	−	1.04872i	0.386498	−	0.922290i	$-0.373685\pi$
$632$	1.36119	−	0.495434i	0.0541454	−	0.0197073i
$633$	−28.3991	−	15.0004i	−1.12876	−	0.596212i
$634$	0.662067	−	0.555540i	0.0262940	−	0.0220633i
$635$	−0.215448	+	0.180782i	−0.00854979	+	0.00717413i
$636$	0.295371	+	7.84210i	0.0117122	+	0.310959i
$637$	−2.00083	+	0.728244i	−0.0792760	+	0.0288541i
$638$	−0.0787379	−	0.136378i	−0.00311726	−	0.00539926i
$639$	10.5333	+	41.2814i	0.416690	+	1.63307i
$640$	−0.0796413	+	0.137943i	−0.00314810	+	0.00545267i
$641$	−1.14041	+	6.46760i	−0.0450436	+	0.255455i	−0.999011	−	0.0444540i	$-0.985845\pi$
$641$	−1.14041	+	6.46760i	−0.0450436	+	0.255455i	0.953968	+	0.299909i	$0.0969563\pi$
$642$	1.12947	+	1.24751i	0.0445765	+	0.0492352i
$643$	−4.18213	−	1.52217i	−0.164927	−	0.0600285i	0.258237	−	0.966082i	$-0.416858\pi$
$643$	−4.18213	−	1.52217i	−0.164927	−	0.0600285i	−0.423164	+	0.906053i	$0.639081\pi$
$644$	−2.71979	−	15.4247i	−0.107175	−	0.607818i
$645$	−0.633145	−	0.0872141i	−0.0249301	−	0.00343405i
$646$	−0.474718	−	0.398336i	−0.0186775	−	0.0156723i
$647$	34.1036			1.34075			0.670375	−	0.742023i	$-0.266133\pi$
$647$	34.1036			1.34075			0.670375	+	0.742023i	$0.266133\pi$
$648$	3.32657	−	1.81582i	0.130680	−	0.0713320i
$649$	26.6730			1.04701
$650$	−0.860570	−	0.722104i	−0.0337543	−	0.0283233i
$651$	−7.05672	−	0.972045i	−0.276575	−	0.0380975i
$652$	2.38316	+	13.5156i	0.0933317	+	0.529310i
$653$	0.0454216	+	0.0165321i	0.00177749	+	0.000646952i	0.342909	−	0.939369i	$-0.388588\pi$
$653$	0.0454216	+	0.0165321i	0.00177749	+	0.000646952i	−0.341131	+	0.940016i	$0.610810\pi$
$654$	1.69123	+	1.86798i	0.0661322	+	0.0730437i
$655$	−0.146034	+	0.828198i	−0.00570600	+	0.0323604i
$656$	11.5845	−	20.0650i	0.452300	−	0.783406i
$657$	8.48576	−	8.28496i	0.331061	−	0.323227i
$658$	−0.252687	−	0.437666i	−0.00985076	−	0.0170620i
$659$	−19.8969	+	7.24187i	−0.775072	+	0.282103i	−0.699116	−	0.715008i	$-0.746423\pi$
$659$	−19.8969	+	7.24187i	−0.775072	+	0.282103i	−0.0759557	+	0.997111i	$0.524201\pi$
$660$	0.0137273	+	0.364461i	0.000534336	+	0.0141866i
$661$	−2.18952	+	1.83723i	−0.0851627	+	0.0714599i	−0.684375	−	0.729130i	$-0.739925\pi$
$661$	−2.18952	+	1.83723i	−0.0851627	+	0.0714599i	0.599212	+	0.800590i	$0.295480\pi$
$662$	−0.513066	+	0.430513i	−0.0199409	+	0.0167324i
$663$	8.49265	+	4.48581i	0.329827	+	0.174214i
$664$	−4.76638	+	1.73482i	−0.184971	+	0.0673241i
$665$	0.0538864	+	0.0933341i	0.00208963	+	0.00361934i
$666$	−0.412266	+	0.857163i	−0.0159750	+	0.0332144i
$667$	−2.65259	+	4.59441i	−0.102709	+	0.177896i
$668$	−6.22033	+	35.2773i	−0.240672	+	1.36492i
$669$	12.1832	−	37.8488i	0.471032	−	1.46332i
$670$	0.0486877	+	0.0177209i	0.00188097	+	0.000684617i
$671$	0.256672	+	1.45566i	0.00990872	+	0.0561952i
$672$	−1.33616	+	1.71990i	−0.0515434	+	0.0663465i
$673$	7.80007	+	6.54504i	0.300671	+	0.252293i	0.780623	−	0.625002i	$-0.214902\pi$
$673$	7.80007	+	6.54504i	0.300671	+	0.252293i	−0.479953	+	0.877294i	$0.659346\pi$
$674$	−2.66659			−0.102713
$675$	−11.5755	−	23.2463i	−0.445542	−	0.894750i
$676$	16.8383			0.647626
$677$	−14.1407	−	11.8655i	−0.543473	−	0.456028i	0.329251	−	0.944243i	$-0.393204\pi$
$677$	−14.1407	−	11.8655i	−0.543473	−	0.456028i	−0.872724	+	0.488215i	$0.837648\pi$
$678$	−0.954350	−	2.34359i	−0.0366516	−	0.0900050i
$679$	−3.17202	−	17.9894i	−0.121731	−	0.690370i
$680$	0.0492738	+	0.0179342i	0.00188956	+	0.000687745i
$681$	−16.9829	+	3.65850i	−0.650786	+	0.140194i
$682$	−0.166944	+	0.946785i	−0.00639261	+	0.0362543i
$683$	5.58052	−	9.66575i	0.213533	−	0.369850i	−0.739285	−	0.673393i	$-0.764836\pi$
$683$	5.58052	−	9.66575i	0.213533	−	0.369850i	0.952818	+	0.303543i	$0.0981696\pi$
$684$	10.9234	+	7.84518i	0.417665	+	0.299968i
$685$	−0.218726	−	0.378845i	−0.00835710	−	0.0144749i
$686$	−0.0992022	+	0.0361067i	−0.00378756	+	0.00137856i
$687$	−3.32953	+	2.09323i	−0.127030	+	0.0798617i
$688$	23.2528	−	19.5114i	0.886505	−	0.743866i
$689$	−3.71583	+	3.11795i	−0.141562	+	0.118784i
$690$	−0.0582891	+	0.0366456i	−0.00221903	+	0.00139507i
$691$	−36.6561	+	13.3417i	−1.39446	+	0.507543i	−0.926530	−	0.376220i	$-0.877224\pi$
$691$	−36.6561	+	13.3417i	−1.39446	+	0.507543i	−0.467934	+	0.883764i	$0.655001\pi$
$692$	15.4673	+	26.7901i	0.587977	+	1.01841i
$693$	−0.658159	+	6.61028i	−0.0250014	+	0.251104i
$694$	−1.44750	+	2.50714i	−0.0549462	+	0.0951696i
$695$	−0.0441050	+	0.250132i	−0.00167300	+	0.00948804i
$696$	0.480321	−	0.103472i	0.0182065	−	0.00392210i
$697$	−14.4156	−	5.24686i	−0.546030	−	0.198739i
$698$	0.554585	+	3.14521i	0.0209913	+	0.119048i
$699$	−14.1846	−	34.8330i	−0.536511	−	1.31750i
$700$	7.61427	+	6.38913i	0.287793	+	0.241487i
$701$	−29.4093			−1.11077			−0.555387	−	0.831592i	$-0.687430\pi$
$701$	−29.4093			−1.11077			−0.555387	+	0.831592i	$0.687430\pi$
$702$	1.07089	+	0.466280i	0.0404182	+	0.0175986i
$703$	−6.76937			−0.255312
$704$	−13.1185	−	11.0078i	−0.494423	−	0.414871i
$705$	0.243224	−	0.313077i	0.00916035	−	0.0117912i
$706$	0.349871	+	1.98422i	0.0131676	+	0.0746770i
$707$	−16.5431	−	6.02120i	−0.622168	−	0.226451i
$708$	−12.7145	+	39.4991i	−0.477839	+	1.48447i
$709$	0.526940	−	2.98842i	0.0197896	−	0.112233i	−0.973313	−	0.229482i	$-0.926297\pi$
$709$	0.526940	−	2.98842i	0.0197896	−	0.112233i	0.993102	+	0.117250i	$0.0374078\pi$
$710$	−0.0358418	+	0.0620799i	−0.00134512	+	0.00232982i
$711$	5.81757	+	8.52375i	0.218176	+	0.319666i
$712$	−2.52224	−	4.36865i	−0.0945250	−	0.163722i
$713$	30.4349	−	11.0774i	1.13980	−	0.414852i
$714$	0.421069	+	0.222408i	0.0157581	+	0.00832342i
$715$	−0.172693	+	0.144907i	−0.00645835	+	0.00541920i
$716$	−29.6192	+	24.8535i	−1.10692	+	0.928819i
$717$	0.966852	+	25.6699i	0.0361077	+	0.958661i
$718$	0.00927442	−	0.00337561i	0.000346118	−	0.000125977i
$719$	16.4133	+	28.4287i	0.612114	+	1.06021i	0.990884	+	0.134721i	$0.0430138\pi$
$719$	16.4133	+	28.4287i	0.612114	+	1.06021i	−0.378770	+	0.925491i	$0.623653\pi$
$720$	−0.543182	−	0.152538i	−0.0202432	−	0.00568476i
$721$	1.38912	−	2.40602i	0.0517334	−	0.0896049i
$722$	−0.255169	+	1.44714i	−0.00949642	+	0.0538569i
$723$	23.1778	+	25.6002i	0.861993	+	0.952081i
$724$	−32.2477	−	11.7372i	−1.19847	−	0.436209i
$725$	−0.584628	−	3.31559i	−0.0217125	−	0.123138i
$726$	−1.10437	−	0.152124i	−0.0409871	−	0.00564587i
$727$	−28.6154	−	24.0112i	−1.06129	−	0.890526i	−0.0670522	−	0.997749i	$-0.521359\pi$
$727$	−28.6154	−	24.0112i	−1.06129	−	0.890526i	−0.994235	+	0.107224i	$0.965804\pi$
$728$	−0.896622			−0.0332310
$729$	18.3940	+	19.7652i	0.681259	+	0.732043i
$730$	0.0199543			0.000738542
$731$	−15.3962	−	12.9190i	−0.569451	−	0.477826i
$732$	−2.27798	−	0.313786i	−0.0841967	−	0.0115979i
$733$	−9.33587	−	52.9464i	−0.344828	−	1.95562i	−0.289613	−	0.957144i	$-0.593527\pi$
$733$	−9.33587	−	52.9464i	−0.344828	−	1.95562i	−0.0552151	−	0.998474i	$-0.517584\pi$
$734$	1.91835	+	0.698222i	0.0708075	+	0.0257718i
$735$	−0.0555833	−	0.0613924i	−0.00205022	−	0.00226449i
$736$	1.71955	−	9.75205i	0.0633834	−	0.359465i
$737$	−11.3646	+	19.6840i	−0.418619	+	0.725070i
$738$	−1.79610	−	0.504386i	−0.0661153	−	0.0185667i
$739$	18.8178	+	32.5934i	0.692224	+	1.19897i	0.971107	+	0.238643i	$0.0767025\pi$
$739$	18.8178	+	32.5934i	0.692224	+	1.19897i	−0.278883	+	0.960325i	$0.589964\pi$
$740$	0.268372	−	0.0976794i	0.00986555	−	0.00359077i
$741$	0.312873	+	8.30678i	0.0114937	+	0.305157i
$742$	−0.184232	+	0.154589i	−0.00676338	+	0.00567515i
$743$	−24.0622	+	20.1906i	−0.882757	+	0.740721i	−0.966744	−	0.255746i	$-0.917679\pi$
$743$	−24.0622	+	20.1906i	−0.882757	+	0.740721i	0.0839870	+	0.996467i	$0.473235\pi$
$744$	−2.65237	−	1.40098i	−0.0972406	−	0.0513624i
$745$	0.726726	−	0.264507i	0.0266252	−	0.00969077i
$746$	−1.00524	−	1.74112i	−0.0368043	−	0.0637470i
$747$	−20.3709	−	29.8469i	−0.745332	−	1.09204i
$748$	−5.73462	+	9.93266i	−0.209679	+	0.363174i
$749$	1.59815	−	9.06357i	0.0583952	−	0.331176i
$750$	0.0267827	−	0.0832038i	0.000977965	−	0.00303817i
$751$	25.2279	+	9.18220i	0.920579	+	0.335063i	0.758469	−	0.651709i	$-0.225948\pi$
$751$	25.2279	+	9.18220i	0.920579	+	0.335063i	0.162110	+	0.986773i	$0.448170\pi$
$752$	3.26964	+	18.5430i	0.119231	+	0.676195i
$753$	−5.76907	+	7.42593i	−0.210237	+	0.270616i
$754$	0.115999	+	0.0973344i	0.00422442	+	0.00354471i
$755$	−0.593299			−0.0215924
$756$	−9.47518	−	4.12562i	−0.344609	−	0.150047i
$757$	−11.5926			−0.421339			−0.210670	−	0.977557i	$-0.567564\pi$
$757$	−11.5926			−0.421339			−0.210670	+	0.977557i	$0.567564\pi$
$758$	−1.41048	−	1.18353i	−0.0512308	−	0.0429878i
$759$	−11.3913	−	27.9734i	−0.413477	−	1.01537i
$760$	0.00788068	+	0.0446936i	0.000285862	+	0.00162121i
$761$	−28.2342	−	10.2764i	−1.02349	−	0.372520i	−0.224891	−	0.974384i	$-0.572203\pi$
$761$	−28.2342	−	10.2764i	−1.02349	−	0.372520i	−0.798599	+	0.601864i	$0.794425\pi$
$762$	−1.05143	+	0.226501i	−0.0380892	+	0.00820527i
$763$	2.39302	−	13.5715i	0.0866333	−	0.491322i
$764$	6.17050	−	10.6876i	0.223241	−	0.386664i
$765$	−0.0370115	+	0.371728i	−0.00133815	+	0.0134399i
$766$	0.726276	+	1.25795i	0.0262414	+	0.0454515i
$767$	−24.1014	+	8.77221i	−0.870253	+	0.316746i
$768$	22.1650	−	13.9348i	0.799811	−	0.502830i
$769$	−35.2211	+	29.5540i	−1.27011	+	1.06574i	−0.275576	+	0.961279i	$0.588869\pi$
$769$	−35.2211	+	29.5540i	−1.27011	+	1.06574i	−0.994529	+	0.104465i	$0.966687\pi$
$770$	−0.00856219	+	0.00718453i	−0.000308560	+	0.000258912i
$771$	18.9032	−	11.8842i	0.680783	−	0.427999i
$772$	−28.3842	+	10.3310i	−1.02157	+	0.371821i
$773$	4.44232	+	7.69433i	0.159779	+	0.276746i	0.934789	−	0.355204i	$-0.115588\pi$
$773$	4.44232	+	7.69433i	0.159779	+	0.276746i	−0.775010	+	0.631949i	$0.782255\pi$
$774$	−1.98520	−	1.42577i	−0.0713564	−	0.0512483i
$775$	−10.2770	+	17.8003i	−0.369160	+	0.639404i
$776$	1.33573	−	7.57532i	0.0479500	−	0.271938i
$777$	5.08515	−	1.09546i	0.182429	−	0.0392992i
$778$	−1.68917	−	0.614807i	−0.0605596	−	0.0220419i
$779$	−2.30558	−	13.0756i	−0.0826061	−	0.468483i
$780$	−0.132268	−	0.324808i	−0.00473594	−	0.0116300i
$781$	−24.0893	−	20.2133i	−0.861983	−	0.723289i
$782$	−2.16515			−0.0774257
$783$	1.56029	+	3.13343i	0.0557604	+	0.111980i
$784$	3.93326			0.140473
$785$	0.274374	+	0.230227i	0.00979281	+	0.00821714i
$786$	−1.97305	+	2.53970i	−0.0703764	+	0.0905883i
$787$	2.50608	+	14.2127i	0.0893319	+	0.506627i	0.996337	+	0.0855080i	$0.0272513\pi$
$787$	2.50608	+	14.2127i	0.0893319	+	0.506627i	−0.907006	+	0.421119i	$0.861638\pi$
$788$	18.6107	+	6.77373i	0.662978	+	0.241304i
$789$	−15.8936	+	49.3755i	−0.565828	+	1.75782i
$790$	−0.00301516	+	0.0170998i	−0.000107275	+	0.000608385i
$791$	−6.91946	+	11.9849i	−0.246028	+	0.426132i
$792$	−1.21248	+	2.52092i	−0.0430834	+	0.0895769i
$793$	−0.710663	−	1.23090i	−0.0252364	−	0.0437107i
$794$	0.981644	−	0.357289i	0.0348372	−	0.0126797i
$795$	−0.166824	−	0.0881161i	−0.00591662	−	0.00312516i
$796$	6.59476	−	5.53366i	0.233745	−	0.196136i
$797$	−36.0070	+	30.2134i	−1.27543	+	1.07021i	−0.281576	+	0.959539i	$0.590857\pi$
$797$	−36.0070	+	30.2134i	−1.27543	+	1.07021i	−0.993857	+	0.110676i	$0.964698\pi$
$798$	0.0155124	+	0.411854i	0.000549132	+	0.0145795i
$799$	11.7153	−	4.26403i	0.414458	−	0.150850i
$800$	3.14213	+	5.44233i	0.111091	+	0.192415i
$801$	25.7144	−	25.1059i	0.908574	−	0.887075i
$802$	0.215154	−	0.372659i	0.00759737	−	0.0131590i
$803$	−1.52005	+	8.62061i	−0.0536413	+	0.304215i
$804$	−23.7321	−	26.2123i	−0.836966	−	0.924437i
$805$	0.353836	+	0.128786i	0.0124711	+	0.00453911i
$806$	−0.160530	−	0.910409i	−0.00565442	−	0.0320678i
$807$	14.3367	+	1.97484i	0.504676	+	0.0695178i
$808$	−5.67897	−	4.76522i	−0.199785	−	0.167640i
$809$	42.1543			1.48207			0.741034	−	0.671468i	$-0.234336\pi$
$809$	42.1543			1.48207			0.741034	+	0.671468i	$0.234336\pi$
$810$	−0.00108769	+	0.0454160i	−3.82176e−5	+	0.00159575i
$811$	−31.3380			−1.10043			−0.550214	−	0.835024i	$-0.685454\pi$
$811$	−31.3380			−1.10043			−0.550214	+	0.835024i	$0.685454\pi$
$812$	−1.02635	−	0.861209i	−0.0360178	−	0.0302225i
$813$	4.20130	+	0.578718i	0.147346	+	0.0202965i
$814$	−0.121910	−	0.691386i	−0.00427295	−	0.0242331i
$815$	−0.310042	−	0.112846i	−0.0108603	−	0.00395282i
$816$	−11.9078	−	13.1523i	−0.416858	−	0.460424i
$817$	3.02061	−	17.1307i	0.105678	−	0.599328i
$818$	−1.52221	+	2.63654i	−0.0532228	+	0.0921846i
$819$	−1.57928	−	6.18943i	−0.0551845	−	0.216276i
$820$	0.280081	+	0.485115i	0.00978086	+	0.0169410i
$821$	−1.00932	+	0.367363i	−0.0352256	+	0.0128211i	−0.359573	−	0.933117i	$-0.617078\pi$
$821$	−1.00932	+	0.367363i	−0.0352256	+	0.0128211i	0.324347	+	0.945938i	$0.394855\pi$
$822$	−0.0629651	−	1.67172i	−0.00219616	−	0.0583080i
$823$	21.3176	−	17.8876i	0.743086	−	0.623523i	−0.190578	−	0.981672i	$-0.561036\pi$
$823$	21.3176	−	17.8876i	0.743086	−	0.623523i	0.933665	+	0.358149i	$0.116592\pi$
$824$	0.896203	−	0.752004i	0.0312207	−	0.0261973i
$825$	16.9488	+	8.95233i	0.590080	+	0.311680i
$826$	−1.19496	+	0.434930i	−0.0415780	+	0.0151331i
$827$	18.8878	+	32.7146i	0.656792	+	1.13760i	0.981441	+	0.191763i	$0.0614205\pi$
$827$	18.8878	+	32.7146i	0.656792	+	1.13760i	−0.324649	+	0.945835i	$0.605246\pi$
$828$	46.8548	−	3.53456i	1.62832	−	0.122835i
$829$	−8.12770	+	14.0776i	−0.282287	+	0.488935i	−0.971948	−	0.235197i	$-0.924426\pi$
$829$	−8.12770	+	14.0776i	−0.282287	+	0.488935i	0.689661	+	0.724133i	$0.257760\pi$
$830$	0.0105580	−	0.0598771i	0.000366472	−	0.00207837i
$831$	−3.48100	+	10.8141i	−0.120754	+	0.375139i
$832$	15.4740	+	5.63207i	0.536464	+	0.195257i
$833$	−0.452232	−	2.56474i	−0.0156689	−	0.0888629i
$834$	−0.595900	+	0.767041i	−0.0206343	+	0.0265604i
$835$	−0.659704	−	0.553557i	−0.0228300	−	0.0191566i
$836$	−9.92655			−0.343317
$837$	4.99925	−	20.7771i	0.172799	−	0.718161i
$838$	1.54384			0.0533310
$839$	37.3943	+	31.3775i	1.29099	+	1.08327i	0.991627	+	0.129135i	$0.0412199\pi$
$839$	37.3943	+	31.3775i	1.29099	+	1.08327i	0.299367	+	0.954138i	$0.403225\pi$
$840$	−0.0131525	−	0.0322985i	−0.000453805	−	0.00111440i
$841$	−4.95699	−	28.1125i	−0.170931	−	0.969397i
$842$	3.18148	+	1.15797i	0.109641	+	0.0399061i
$843$	21.8588	−	4.70887i	0.752856	−	0.162182i
$844$	−6.40401	+	36.3189i	−0.220435	+	1.25015i
$845$	−0.202404	+	0.350574i	−0.00696292	+	0.0120601i
$846$	1.38164	−	0.624244i	0.0475019	−	0.0214619i
$847$	3.04839	+	5.27997i	0.104744	+	0.181422i
$848$	8.42004	−	3.06465i	0.289145	−	0.105240i
$849$	−23.4485	+	14.7418i	−0.804752	+	0.505937i
$850$	1.05257	−	0.883214i	0.0361030	−	0.0302940i
$851$	−18.1179	+	15.2028i	−0.621075	+	0.521144i
$852$	41.4160	−	26.0377i	1.41889	−	0.892036i
$853$	−8.71154	+	3.17074i	−0.298278	+	0.108564i	−0.486824	−	0.873500i	$-0.661845\pi$
$853$	−8.71154	+	3.17074i	−0.298278	+	0.108564i	0.188546	+	0.982064i	$0.439622\pi$
$854$	−0.0352350	−	0.0610288i	−0.00120572	−	0.00208836i
$855$	−0.294641	+	0.133122i	−0.0100765	+	0.00455269i
$856$	1.93777	−	3.35631i	0.0662315	−	0.114716i
$857$	8.30525	−	47.1014i	0.283702	−	1.60895i	−0.426184	−	0.904637i	$-0.640142\pi$
$857$	8.30525	−	47.1014i	0.283702	−	1.60895i	0.709886	−	0.704317i	$-0.248747\pi$
$858$	−0.842775	+	0.181553i	−0.0287719	+	0.00619811i
$859$	−18.2144	−	6.62951i	−0.621468	−	0.226196i	0.0120455	−	0.999927i	$-0.496166\pi$
$859$	−18.2144	−	6.62951i	−0.621468	−	0.226196i	−0.633514	+	0.773732i	$0.718388\pi$
$860$	0.127438	+	0.722735i	0.00434559	+	0.0246450i
$861$	3.84792	+	9.44930i	0.131137	+	0.322031i
$862$	0.169759	+	0.142445i	0.00578202	+	0.00485169i
$863$	−3.11961			−0.106193			−0.0530963	−	0.998589i	$-0.516909\pi$
$863$	−3.11961			−0.106193			−0.0530963	+	0.998589i	$0.516909\pi$
$864$	−4.73716	−	4.49995i	−0.161162	−	0.153091i
$865$	−0.743695			−0.0252864
$866$	−0.402551	−	0.337780i	−0.0136792	−	0.0114782i
$867$	10.8574	−	13.9756i	0.368735	−	0.474635i
$868$	1.42036	+	8.05524i	0.0482101	+	0.273413i
$869$	−7.15775	−	2.60521i	−0.242810	−	0.0883756i
$870$	−0.00180464	+	0.00560635i	−6.11831e−5	+	0.000190073i
$871$	3.79523	−	21.5238i	0.128597	−	0.729307i
$872$	2.90155	−	5.02564i	0.0982590	−	0.170190i
$873$	54.6455	−	4.12227i	1.84947	−	0.139518i
$874$	−0.936962	−	1.62287i	−0.0316932	−	0.0548943i
$875$	−0.449202	+	0.163496i	−0.0151858	+	0.00552717i
$876$	−12.0414	−	6.36024i	−0.406840	−	0.214893i
$877$	8.42052	−	7.06565i	0.284341	−	0.238590i	−0.489450	−	0.872031i	$-0.662803\pi$
$877$	8.42052	−	7.06565i	0.284341	−	0.238590i	0.773791	+	0.633441i	$0.218358\pi$
$878$	−2.29892	+	1.92902i	−0.0775849	+	0.0651014i
$879$	0.0653105	+	1.73400i	0.00220287	+	0.0584862i
$880$	0.391321	−	0.142429i	0.0131914	−	0.00480129i
$881$	24.3642	+	42.2000i	0.820850	+	1.42175i	0.905050	+	0.425305i	$0.139833\pi$
$881$	24.3642	+	42.2000i	0.820850	+	1.42175i	−0.0842002	+	0.996449i	$0.526834\pi$
$882$	−0.0783013	−	0.306874i	−0.00263654	−	0.0103330i
$883$	18.4060	−	31.8802i	0.619413	−	1.07285i	−0.370180	−	0.928960i	$-0.620704\pi$
$883$	18.4060	−	31.8802i	0.619413	−	1.07285i	0.989593	−	0.143894i	$-0.0459625\pi$
$884$	1.91509	−	10.8610i	0.0644116	−	0.365296i
$885$	−0.669540	−	0.739514i	−0.0225063	−	0.0248585i
$886$	−2.94221	−	1.07088i	−0.0988456	−	0.0359769i
$887$	0.694851	+	3.94070i	0.0233308	+	0.132316i	0.994248	−	0.107098i	$-0.0341559\pi$
$887$	0.694851	+	3.94070i	0.0233308	+	0.132316i	−0.970918	+	0.239414i	$0.923045\pi$
$888$	2.16998	+	0.298909i	0.0728198	+	0.0100307i
$889$	4.50596	+	3.78095i	0.151125	+	0.126809i
$890$	0.0604676			0.00202688
$891$	−19.5376	−	3.92952i	−0.654535	−	0.131644i
$892$	−45.6566			−1.52870
$893$	8.26581	+	6.93584i	0.276605	+	0.232099i
$894$	2.92985	+	0.403579i	0.0979887	+	0.0134977i
$895$	−0.161414	−	0.915426i	−0.00539548	−	0.0305993i
$896$	3.13040	+	1.13937i	0.104579	+	0.0380637i
$897$	19.4929	+	21.5301i	0.650850	+	0.718870i
$898$	−0.122662	+	0.695653i	−0.00409329	+	0.0232142i
$899$	1.38526	−	2.39934i	0.0462011	−	0.0800226i
$900$	−21.3363	+	20.8314i	−0.711209	+	0.694380i
$901$	−2.96645	−	5.13805i	−0.0988269	−	0.171173i
$902$	1.29395	−	0.470960i	0.0430839	−	0.0156812i
$903$	0.503104	+	13.3574i	0.0167422	+	0.444507i
$904$	−4.46416	+	3.74588i	−0.148476	+	0.124586i
$905$	0.632001	−	0.530312i	0.0210084	−	0.0176282i
$906$	−2.00623	−	1.05969i	−0.0666525	−	0.0352058i
$907$	−14.0718	+	5.12171i	−0.467246	+	0.170064i	−0.564904	−	0.825156i	$-0.691087\pi$
$907$	−14.0718	+	5.12171i	−0.467246	+	0.170064i	0.0976583	+	0.995220i	$0.468865\pi$
$908$	9.97412	+	17.2757i	0.331003	+	0.573314i
$909$	22.8918	−	47.5955i	0.759274	−	1.57864i
$910$	0.00537385	−	0.00930779i	0.000178142	−	0.000308550i
$911$	4.27470	−	24.2430i	0.141627	−	0.803207i	−0.828387	−	0.560157i	$-0.810741\pi$
$911$	4.27470	−	24.2430i	0.141627	−	0.803207i	0.970014	−	0.243050i	$-0.0781479\pi$
$912$	4.70511	−	14.6170i	0.155802	−	0.484018i
$913$	25.0637	+	9.12244i	0.829487	+	0.301909i
$914$	0.319202	+	1.81028i	0.0105582	+	0.0598788i
$915$	0.0339155	−	0.0436559i	0.00112121	−	0.00144322i
$916$	3.45943	+	2.90281i	0.114303	+	0.0959116i
$917$	17.5885			0.580822
$918$	−0.789096	+	1.19089i	−0.0260440	+	0.0393051i
$919$	31.8826			1.05171			0.525854	−	0.850575i	$-0.323746\pi$
$919$	31.8826			1.05171			0.525854	+	0.850575i	$0.323746\pi$
$920$	0.121466	+	0.101922i	0.00400461	+	0.00336027i
$921$	−22.6854	−	55.7084i	−0.747511	−	1.83566i
$922$	0.214338	+	1.21557i	0.00705886	+	0.0400328i
$923$	28.4146	+	10.3421i	0.935277	+	0.340413i
$924$	7.45682	−	1.60637i	0.245311	−	0.0528456i
$925$	2.60636	−	14.7814i	0.0856967	−	0.486010i
$926$	−1.53424	+	2.65738i	−0.0504182	+	0.0873270i
$927$	6.76966	+	4.86198i	0.222345	+	0.159689i
$928$	−0.423536	−	0.733586i	−0.0139032	−	0.0240811i
$929$	−17.2543	+	6.28006i	−0.566096	+	0.206042i	−0.609184	−	0.793029i	$-0.708503\pi$
$929$	−17.2543	+	6.28006i	−0.566096	+	0.206042i	0.0430875	+	0.999071i	$0.486281\pi$
$930$	0.0304404	−	0.0191374i	0.000998178	−	0.000627541i
$931$	1.72667	−	1.44885i	0.0565892	−	0.0474840i
$932$	−33.0829	+	27.7599i	−1.08367	+	0.909305i
$933$	−3.24610	+	2.04078i	−0.106273	+	0.0668122i
$934$	3.95095	−	1.43803i	0.129279	−	0.0470537i
$935$	−0.137866	−	0.238791i	−0.00450869	−	0.00780929i
$936$	0.266502	−	2.67663i	0.00871087	−	0.0874884i
$937$	1.76262	−	3.05294i	0.0575822	−	0.0997352i	−0.835797	−	0.549038i	$-0.814994\pi$
$937$	1.76262	−	3.05294i	0.0575822	−	0.0997352i	0.893380	+	0.449303i	$0.148328\pi$
$938$	0.188169	−	1.06716i	0.00614394	−	0.0348440i
$939$	4.01736	−	0.865430i	0.131102	−	0.0282423i
$940$	−0.427780	−	0.155699i	−0.0139527	−	0.00507835i
$941$	−6.55503	−	37.1754i	−0.213688	−	1.21188i	−0.883169	−	0.469055i	$-0.844594\pi$
$941$	−6.55503	−	37.1754i	−0.213688	−	1.21188i	0.669481	−	0.742829i	$-0.266517\pi$
$942$	0.516582	+	1.26857i	0.0168311	+	0.0413321i
$943$	−35.5363	−	29.8185i	−1.15722	−	0.971023i
$944$	47.3788			1.54205
$945$	0.199792	−	0.147682i	0.00649923	−	0.00480409i
$946$	1.80404			0.0586543
$947$	−14.5422	−	12.2024i	−0.472558	−	0.396524i	0.375168	−	0.926957i	$-0.377585\pi$
$947$	−14.5422	−	12.2024i	−0.472558	−	0.396524i	−0.847727	+	0.530433i	$0.822029\pi$
$948$	7.26990	−	9.35779i	0.236115	−	0.303927i
$949$	−1.46165	−	8.28940i	−0.0474470	−	0.269085i
$950$	1.11750	+	0.406737i	0.0362565	+	0.0131963i
$951$	4.34486	−	13.4978i	0.140892	−	0.437697i
$952$	0.190434	−	1.08001i	0.00617201	−	0.0350032i
$953$	−9.58499	+	16.6017i	−0.310488	+	0.537781i	−0.978468	−	0.206398i	$-0.933826\pi$
$953$	−9.58499	+	16.6017i	−0.310488	+	0.537781i	0.667980	+	0.744179i	$0.267159\pi$
$954$	−0.406727	−	0.595926i	−0.0131683	−	0.0192938i
$955$	0.148345	+	0.256940i	0.00480032	+	0.00831440i
$956$	27.7179	−	10.0885i	0.896462	−	0.326285i
$957$	−2.28457	−	1.20671i	−0.0738496	−	0.0390073i
$958$	3.36963	−	2.82746i	0.108868	−	0.0913510i
$959$	−7.00858	+	5.88089i	−0.226319	+	0.189904i
$960$	0.0241065	+	0.640028i	0.000778034	+	0.0206568i
$961$	13.2364	−	4.81767i	0.426982	−	0.155409i
$962$	0.337539	+	0.584635i	0.0108827	+	0.0188494i
$963$	26.5819	+	7.46482i	0.856590	+	0.240550i
$964$	19.8270	−	34.3413i	0.638584	−	1.10606i
$965$	0.126099	−	0.715144i	0.00405928	−	0.0230213i
$966$	0.966467	+	1.06747i	0.0310956	+	0.0343454i
$967$	16.3315	+	5.94419i	0.525187	+	0.191152i	0.590988	−	0.806680i	$-0.298738\pi$
$967$	16.3315	+	5.94419i	0.525187	+	0.191152i	−0.0658012	+	0.997833i	$0.520960\pi$
$968$	0.445815	+	2.52835i	0.0143291	+	0.0812641i
$969$	−10.0722	−	1.38742i	−0.323566	−	0.0445704i
$970$	0.0706334	+	0.0592684i	0.00226790	+	0.00190299i
$971$	−50.0419			−1.60592			−0.802961	−	0.596032i	$-0.796743\pi$
$971$	−50.0419			−1.60592			−0.802961	+	0.596032i	$0.796743\pi$
$972$	15.1323	−	27.0594i	0.485367	−	0.867931i
$973$	5.31206			0.170297
$974$	−0.0951117	−	0.0798082i	−0.00304758	−	0.00255722i
$975$	−18.2590	−	2.51512i	−0.584754	−	0.0805484i
$976$	0.455922	+	2.58566i	0.0145937	+	0.0827651i
$977$	18.9119	+	6.88338i	0.605046	+	0.220219i	0.626334	−	0.779555i	$-0.284555\pi$
$977$	18.9119	+	6.88338i	0.605046	+	0.220219i	−0.0212882	+	0.999773i	$0.506777\pi$
$978$	−0.846847	−	0.935351i	−0.0270792	−	0.0299092i
$979$	−4.60620	+	26.1231i	−0.147215	+	0.834897i
$980$	−0.0475475	+	0.0823547i	−0.00151885	+	0.00263073i
$981$	39.8029	+	11.1776i	1.27081	+	0.356873i
$982$	0.477276	+	0.826666i	0.0152305	+	0.0263800i
$983$	19.6809	−	7.16328i	0.627725	−	0.228473i	−0.00851605	−	0.999964i	$-0.502711\pi$
$983$	19.6809	−	7.16328i	0.627725	−	0.228473i	0.636241	+	0.771491i	$0.280489\pi$
$984$	0.161707	+	4.29332i	0.00515502	+	0.136866i
$985$	−0.364739	+	0.306052i	−0.0116215	+	0.00975163i
$986$	−0.141879	+	0.119051i	−0.00451835	+	0.00379135i
$987$	−7.33168	−	3.87259i	−0.233370	−	0.123266i
$988$	8.96952	−	3.26464i	0.285358	−	0.103862i
$989$	−30.3879	−	52.6334i	−0.966280	−	1.67365i
$990$	−0.0189026	−	0.0276956i	−0.000600764	−	0.000880225i
$991$	−27.0635	+	46.8753i	−0.859700	+	1.48904i	0.0125160	+	0.999922i	$0.496016\pi$
$991$	−27.0635	+	46.8753i	−0.859700	+	1.48904i	−0.872216	+	0.489122i	$0.837317\pi$
$992$	−0.898001	+	5.09282i	−0.0285116	+	0.161697i
$993$	−3.36703	+	10.4601i	−0.106849	+	0.331941i
$994$	1.40881	+	0.512763i	0.0446846	+	0.0162639i
$995$	0.0359391	+	0.203821i	0.00113935	+	0.00646155i
$996$	−25.4564	+	32.7674i	−0.806617	+	1.03828i
$997$	9.72628	+	8.16132i	0.308034	+	0.258471i	0.783679	−	0.621166i	$-0.213341\pi$
$997$	9.72628	+	8.16132i	0.308034	+	0.258471i	−0.475645	+	0.879638i	$0.657785\pi$
$998$	0.788863			0.0249710
$999$	1.75875	+	15.5060i	0.0556442	+	0.490588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.4	yes	54
3.2	odd	2		567.2.v.b.127.6		54
27.5	odd	18		567.2.v.b.442.6		54
27.7	even	9		5103.2.a.i.1.13		27
27.20	odd	18		5103.2.a.f.1.15		27
27.22	even	9	inner	189.2.v.a.22.4	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.4	✓	54	27.22	even	9	inner
189.2.v.a.43.4	yes	54	1.1	even	1	trivial
567.2.v.b.127.6		54	3.2	odd	2
567.2.v.b.442.6		54	27.5	odd	18
5103.2.a.f.1.15		27	27.20	odd	18
5103.2.a.i.1.13		27	27.7	even	9

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.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0808704 + 0.0678583i) q^{2} +(1.71585 + 0.236354i) q^{3} +(-0.345361 - 1.95864i) q^{4} +(0.0449304 + 0.0163533i) q^{5} +(0.122723 + 0.135549i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.210549 - 0.364682i) q^{8} +(2.88827 + 0.811094i) q^{9} +O(q^{10})\)	\(q+(0.0808704 + 0.0678583i) q^{2} +(1.71585 + 0.236354i) q^{3} +(-0.345361 - 1.95864i) q^{4} +(0.0449304 + 0.0163533i) q^{5} +(0.122723 + 0.135549i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.210549 - 0.364682i) q^{8} +(2.88827 + 0.811094i) q^{9} +(0.00252383 + 0.00437140i) q^{10} +(-2.08078 + 0.757342i) q^{11} +(-0.129656 - 3.44236i) q^{12} +(1.63110 - 1.36865i) q^{13} +(0.0808704 - 0.0678583i) q^{14} +(0.0732287 + 0.0386793i) q^{15} +(-3.69605 + 1.34525i) q^{16} +(1.30215 + 2.25539i) q^{17} +(0.178536 + 0.261587i) q^{18} +(-1.12700 + 1.95202i) q^{19} +(0.0165131 - 0.0936504i) q^{20} +(0.530717 - 1.64874i) q^{21} +(-0.219665 - 0.0799517i) q^{22} +(1.36751 + 7.75556i) q^{23} +(0.447465 - 0.575975i) q^{24} +(-3.82847 - 3.21247i) q^{25} +0.224782 q^{26} +(4.76414 + 2.07437i) q^{27} -1.98886 q^{28} +(0.516050 + 0.433017i) q^{29} +(0.00329732 + 0.00809719i) q^{30} +(-0.714158 - 4.05019i) q^{31} +(-1.18159 - 0.430065i) q^{32} +(-3.74930 + 0.807684i) q^{33} +(-0.0477416 + 0.270756i) q^{34} +(0.0239070 - 0.0414081i) q^{35} +(0.591144 - 5.93721i) q^{36} +(1.50163 + 2.60090i) q^{37} +(-0.223602 + 0.0813846i) q^{38} +(3.12220 - 1.96288i) q^{39} +(0.0154238 - 0.0129421i) q^{40} +(-4.51243 + 3.78637i) q^{41} +(0.154800 - 0.0973206i) q^{42} +(-7.25196 + 2.63950i) q^{43} +(2.20198 + 3.81394i) q^{44} +(0.116507 + 0.0836758i) q^{45} +(-0.415688 + 0.719992i) q^{46} +(0.831280 - 4.71442i) q^{47} +(-6.65982 + 1.43467i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(-0.0916172 - 0.519587i) q^{50} +(1.70122 + 4.17768i) q^{51} +(-3.24401 - 2.72205i) q^{52} -2.27812 q^{53} +(0.244514 + 0.491041i) q^{54} -0.105875 q^{55} +(-0.322580 - 0.270677i) q^{56} +(-2.39513 + 3.08301i) q^{57} +(0.0123493 + 0.0700365i) q^{58} +(-11.3193 - 4.11987i) q^{59} +(0.0504686 - 0.156787i) q^{60} +(0.115915 - 0.657385i) q^{61} +(0.217085 - 0.376002i) q^{62} +(1.30032 - 2.70355i) q^{63} +(3.86688 + 6.69764i) q^{64} +(0.0956679 - 0.0348203i) q^{65} +(-0.358016 - 0.189104i) q^{66} +(7.86315 - 6.59797i) q^{67} +(3.96779 - 3.32937i) q^{68} +(0.513393 + 13.6306i) q^{69} +(0.00474325 - 0.00172640i) q^{70} +(7.10068 + 12.2987i) q^{71} +(0.903916 - 0.882527i) q^{72} +(1.97659 - 3.42355i) q^{73} +(-0.0550553 + 0.312234i) q^{74} +(-5.80980 - 6.41698i) q^{75} +(4.21254 + 1.53324i) q^{76} +(0.384513 + 2.18068i) q^{77} +(0.385691 + 0.0531280i) q^{78} +(2.63514 + 2.21115i) q^{79} -0.188065 q^{80} +(7.68425 + 4.68533i) q^{81} -0.621859 q^{82} +(-9.22727 - 7.74259i) q^{83} +(-3.41257 - 0.470073i) q^{84} +(0.0216230 + 0.122630i) q^{85} +(-0.765580 - 0.278649i) q^{86} +(0.783118 + 0.864962i) q^{87} +(-0.161918 + 0.918281i) q^{88} +(5.98967 - 10.3744i) q^{89} +(0.00374390 + 0.0146729i) q^{90} +(-1.06462 - 1.84398i) q^{91} +(14.7181 - 5.35694i) q^{92} +(-0.268110 - 7.11831i) q^{93} +(0.387139 - 0.324848i) q^{94} +(-0.0825588 + 0.0692751i) q^{95} +(-1.92579 - 1.01720i) q^{96} +(17.1653 - 6.24766i) q^{97} +(-0.0527844 - 0.0914253i) q^{98} +(-6.62414 + 0.499702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27} + 54 q^{28} + 6 q^{29} - 72 q^{30} - 9 q^{31} - 9 q^{32} - 36 q^{33} - 9 q^{34} - 12 q^{35} + 54 q^{38} + 12 q^{39} - 45 q^{40} - 15 q^{41} - 18 q^{42} - 9 q^{43} - 42 q^{44} - 9 q^{45} - 45 q^{47} - 93 q^{48} + 18 q^{50} + 72 q^{51} - 63 q^{52} + 132 q^{53} + 54 q^{54} - 9 q^{56} + 3 q^{57} - 27 q^{58} - 9 q^{60} - 36 q^{62} - 9 q^{63} - 27 q^{64} + 66 q^{65} + 153 q^{66} + 45 q^{67} + 87 q^{68} - 72 q^{71} - 45 q^{72} - 72 q^{74} - 39 q^{75} + 54 q^{76} + 3 q^{77} - 54 q^{78} - 36 q^{79} + 42 q^{80} + 27 q^{81} + 24 q^{83} - 12 q^{84} + 18 q^{85} - 90 q^{86} - 99 q^{87} + 54 q^{88} - 42 q^{89} - 9 q^{90} + 87 q^{92} + 93 q^{93} - 90 q^{94} + 12 q^{95} + 108 q^{96} - 18 q^{97} - 9 q^{98} - 117 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Introduction

L-functions

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