LMFDB - Embedded newform 189.2.w.a.184.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			184.18
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.337831 + 1.91594i) q^{2} +(-1.21495 - 1.23446i) q^{3} +(-1.67729 + 0.610485i) q^{4} +(0.582582 - 3.30399i) q^{5} +(1.95469 - 2.74481i) q^{6} +(0.666452 - 2.56044i) q^{7} +(0.209199 + 0.362343i) q^{8} +(-0.0477764 + 2.99962i) q^{9} +O(q^{10})$	\(q+(0.337831 + 1.91594i) q^{2} +(-1.21495 - 1.23446i) q^{3} +(-1.67729 + 0.610485i) q^{4} +(0.582582 - 3.30399i) q^{5} +(1.95469 - 2.74481i) q^{6} +(0.666452 - 2.56044i) q^{7} +(0.209199 + 0.362343i) q^{8} +(-0.0477764 + 2.99962i) q^{9} +6.52704 q^{10} +(-0.778751 - 4.41652i) q^{11} +(2.79145 + 1.32884i) q^{12} +(2.58000 + 2.16488i) q^{13} +(5.13078 + 0.411883i) q^{14} +(-4.78645 + 3.29502i) q^{15} +(-3.35824 + 2.81790i) q^{16} -3.96521 q^{17} +(-5.76322 + 0.921828i) q^{18} +4.97740 q^{19} +(1.03987 + 5.89742i) q^{20} +(-3.97046 + 2.28811i) q^{21} +(8.19868 - 2.98408i) q^{22} +(1.70156 + 1.42778i) q^{23} +(0.193131 - 0.698477i) q^{24} +(-5.87847 - 2.13959i) q^{25} +(-3.27617 + 5.67449i) q^{26} +(3.76095 - 3.58542i) q^{27} +(0.445273 + 4.70147i) q^{28} +(-3.26643 + 2.74086i) q^{29} +(-7.93005 - 8.05737i) q^{30} +(2.19236 - 0.797953i) q^{31} +(-5.89240 - 4.94431i) q^{32} +(-4.50586 + 6.32720i) q^{33} +(-1.33957 - 7.59708i) q^{34} +(-8.07139 - 3.69362i) q^{35} +(-1.75109 - 5.06041i) q^{36} +(1.49965 + 2.59748i) q^{37} +(1.68152 + 9.53637i) q^{38} +(-0.462129 - 5.81514i) q^{39} +(1.31905 - 0.480096i) q^{40} +(0.219856 + 0.184481i) q^{41} +(-5.72521 - 6.83416i) q^{42} +(9.46658 + 3.44555i) q^{43} +(4.00242 + 6.93239i) q^{44} +(9.88287 + 1.90538i) q^{45} +(-2.16069 + 3.74243i) q^{46} +(-5.08474 - 1.85069i) q^{47} +(7.55868 + 0.721993i) q^{48} +(-6.11168 - 3.41282i) q^{49} +(2.11338 - 11.9856i) q^{50} +(4.81754 + 4.89489i) q^{51} +(-5.64906 - 2.05609i) q^{52} +(5.11933 + 8.86693i) q^{53} +(8.14000 + 5.99448i) q^{54} -15.0458 q^{55} +(1.06718 - 0.294156i) q^{56} +(-6.04730 - 6.14439i) q^{57} +(-6.35481 - 5.33232i) q^{58} +(2.56062 + 2.14861i) q^{59} +(6.01672 - 8.44877i) q^{60} +(-9.73706 - 3.54400i) q^{61} +(2.26947 + 3.93084i) q^{62} +(7.64850 + 2.12143i) q^{63} +(3.09848 - 5.36673i) q^{64} +(8.65580 - 7.26308i) q^{65} +(-13.6447 - 6.49542i) q^{66} +(-2.20525 + 12.5066i) q^{67} +(6.65082 - 2.42070i) q^{68} +(-0.304783 - 3.83519i) q^{69} +(4.34996 - 16.7121i) q^{70} +(2.77738 - 4.81056i) q^{71} +(-1.09689 + 0.610205i) q^{72} +(-2.30040 + 3.98440i) q^{73} +(-4.46997 + 3.75075i) q^{74} +(4.50084 + 9.85623i) q^{75} +(-8.34856 + 3.03863i) q^{76} +(-11.8272 - 0.949453i) q^{77} +(10.9853 - 2.84994i) q^{78} +(0.215339 + 1.22125i) q^{79} +(7.35385 + 12.7372i) q^{80} +(-8.99543 - 0.286622i) q^{81} +(-0.279180 + 0.483554i) q^{82} +(-8.72055 + 7.31741i) q^{83} +(5.26278 - 6.26174i) q^{84} +(-2.31006 + 13.1010i) q^{85} +(-3.40335 + 19.3014i) q^{86} +(7.35204 + 0.702255i) q^{87} +(1.43738 - 1.20611i) q^{88} +12.2622 q^{89} +(-0.311839 + 19.5786i) q^{90} +(7.26249 - 5.16315i) q^{91} +(-3.72566 - 1.35603i) q^{92} +(-3.64865 - 1.73690i) q^{93} +(1.82803 - 10.3673i) q^{94} +(2.89974 - 16.4453i) q^{95} +(1.05545 + 13.2810i) q^{96} +(10.3763 + 3.77665i) q^{97} +(4.47402 - 12.8625i) q^{98} +(13.2851 - 2.12495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.337831	+	1.91594i	0.238883	+	1.35477i	0.834281	+	0.551340i	$0.185883\pi$
$2$	0.337831	+	1.91594i	0.238883	+	1.35477i	−0.595398	+	0.803431i	$0.703006\pi$
$3$	−1.21495	−	1.23446i	−0.701454	−	0.712715i
$3$	−1.21495	−	1.23446i	−0.701454	−	0.712715i
$4$	−1.67729	+	0.610485i	−0.838647	+	0.305243i
$5$	0.582582	−	3.30399i	0.260539	−	1.47759i	−0.520906	−	0.853614i	$-0.674406\pi$
$5$	0.582582	−	3.30399i	0.260539	−	1.47759i	0.781445	−	0.623974i	$-0.214483\pi$
$6$	1.95469	−	2.74481i	0.798001	−	1.12056i
$7$	0.666452	−	2.56044i	0.251895	−	0.967755i
$7$	0.666452	−	2.56044i	0.251895	−	0.967755i
$8$	0.209199	+	0.362343i	0.0739629	+	0.128108i
$9$	−0.0477764	+	2.99962i	−0.0159255	+	0.999873i
$10$	6.52704			2.06403
$11$	−0.778751	−	4.41652i	−0.234802	−	1.33163i	−0.843029	−	0.537867i	$-0.819230\pi$
$11$	−0.778751	−	4.41652i	−0.234802	−	1.33163i	0.608227	−	0.793763i	$-0.291881\pi$
$12$	2.79145	+	1.32884i	0.805823	+	0.383603i
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	0.926154	−	0.377145i	$-0.123094\pi$
$13$	2.58000	+	2.16488i	0.715564	+	0.600430i	−0.210590	+	0.977574i	$0.567538\pi$
$14$	5.13078	+	0.411883i	1.37126	+	0.110080i
$15$	−4.78645	+	3.29502i	−1.23586	+	0.850770i
$16$	−3.35824	+	2.81790i	−0.839560	+	0.704474i
$17$	−3.96521			−0.961704			−0.480852	−	0.876802i	$-0.659673\pi$
$17$	−3.96521			−0.961704			−0.480852	+	0.876802i	$0.659673\pi$
$18$	−5.76322	+	0.921828i	−1.35840	+	0.217277i
$19$	4.97740			1.14189			0.570946	−	0.820987i	$-0.306576\pi$
$19$	4.97740			1.14189			0.570946	+	0.820987i	$0.306576\pi$
$20$	1.03987	+	5.89742i	0.232523	+	1.31870i
$21$	−3.97046	+	2.28811i	−0.866426	+	0.499306i
$22$	8.19868	−	2.98408i	1.74796	−	0.636207i
$23$	1.70156	+	1.42778i	0.354800	+	0.297713i	0.802714	−	0.596364i	$-0.203389\pi$
$23$	1.70156	+	1.42778i	0.354800	+	0.297713i	−0.447914	+	0.894077i	$0.647833\pi$
$24$	0.193131	−	0.698477i	0.0394226	−	0.142576i
$25$	−5.87847	−	2.13959i	−1.17569	−	0.427918i
$26$	−3.27617	+	5.67449i	−0.642509	+	1.11286i
$27$	3.76095	−	3.58542i	0.723796	−	0.690014i
$28$	0.445273	+	4.70147i	0.0841488	+	0.888494i
$29$	−3.26643	+	2.74086i	−0.606561	+	0.508965i	−0.893547	−	0.448970i	$-0.851791\pi$
$29$	−3.26643	+	2.74086i	−0.606561	+	0.508965i	0.286986	+	0.957935i	$0.407347\pi$
$30$	−7.93005	−	8.05737i	−1.44782	−	1.47107i
$31$	2.19236	−	0.797953i	0.393759	−	0.143317i	−0.137550	−	0.990495i	$-0.543923\pi$
$31$	2.19236	−	0.797953i	0.393759	−	0.143317i	0.531309	+	0.847178i	$0.321700\pi$
$32$	−5.89240	−	4.94431i	−1.04164	−	0.874040i
$33$	−4.50586	+	6.32720i	−0.784370	+	1.10142i
$34$	−1.33957	−	7.59708i	−0.229734	−	1.30289i
$35$	−8.07139	−	3.69362i	−1.36431	−	0.624335i
$36$	−1.75109	−	5.06041i	−0.291848	−	0.843402i
$37$	1.49965	+	2.59748i	0.246541	+	0.427022i	0.962564	−	0.271055i	$-0.0873725\pi$
$37$	1.49965	+	2.59748i	0.246541	+	0.427022i	−0.716022	+	0.698077i	$0.754039\pi$
$38$	1.68152	+	9.53637i	0.272778	+	1.54700i
$39$	−0.462129	−	5.81514i	−0.0739999	−	0.931167i
$40$	1.31905	−	0.480096i	0.208560	−	0.0759098i
$41$	0.219856	+	0.184481i	0.0343358	+	0.0288112i	0.659794	−	0.751446i	$-0.270644\pi$
$41$	0.219856	+	0.184481i	0.0343358	+	0.0288112i	−0.625458	+	0.780258i	$0.715088\pi$
$42$	−5.72521	−	6.83416i	−0.883419	−	1.05453i
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.940807	−	0.338942i	$-0.110069\pi$
$43$	9.46658	+	3.44555i	1.44364	+	0.525442i	0.502833	+	0.864384i	$0.332291\pi$
$44$	4.00242	+	6.93239i	0.603387	+	1.04510i
$45$	9.88287	+	1.90538i	1.47325	+	0.284037i
$46$	−2.16069	+	3.74243i	−0.318577	+	0.551791i
$47$	−5.08474	−	1.85069i	−0.741686	−	0.269952i	−0.0565829	−	0.998398i	$-0.518021\pi$
$47$	−5.08474	−	1.85069i	−0.741686	−	0.269952i	−0.685103	+	0.728446i	$0.740243\pi$
$48$	7.55868	+	0.721993i	1.09100	+	0.104211i
$49$	−6.11168	−	3.41282i	−0.873098	−	0.487545i
$50$	2.11338	−	11.9856i	0.298878	−	1.69502i
$51$	4.81754	+	4.89489i	0.674591	+	0.685421i
$52$	−5.64906	−	2.05609i	−0.783383	−	0.285128i
$53$	5.11933	+	8.86693i	0.703194	+	1.21797i	0.967340	+	0.253484i	$0.0815766\pi$
$53$	5.11933	+	8.86693i	0.703194	+	1.21797i	−0.264146	+	0.964483i	$0.585090\pi$
$54$	8.14000	+	5.99448i	1.10771	+	0.815745i
$55$	−15.0458			−2.02878
$56$	1.06718	−	0.294156i	0.142608	−	0.0393083i
$57$	−6.04730	−	6.14439i	−0.800985	−	0.813844i
$58$	−6.35481	−	5.33232i	−0.834428	−	0.700168i
$59$	2.56062	+	2.14861i	0.333364	+	0.279726i	0.794069	−	0.607828i	$-0.207959\pi$
$59$	2.56062	+	2.14861i	0.333364	+	0.279726i	−0.460705	+	0.887553i	$0.652403\pi$
$60$	6.01672	−	8.44877i	0.776756	−	1.09073i
$61$	−9.73706	−	3.54400i	−1.24670	−	0.453763i	−0.367417	−	0.930057i	$-0.619758\pi$
$61$	−9.73706	−	3.54400i	−1.24670	−	0.453763i	−0.879286	+	0.476294i	$0.841980\pi$
$62$	2.26947	+	3.93084i	0.288223	+	0.499218i
$63$	7.64850	+	2.12143i	0.963620	+	0.267275i
$64$	3.09848	−	5.36673i	0.387310	−	0.670841i
$65$	8.65580	−	7.26308i	1.07362	−	0.900875i
$66$	−13.6447	−	6.49542i	−1.67955	−	0.799531i
$67$	−2.20525	+	12.5066i	−0.269414	+	1.52792i	0.486749	+	0.873542i	$0.338183\pi$
$67$	−2.20525	+	12.5066i	−0.269414	+	1.52792i	−0.756163	+	0.654383i	$0.772928\pi$
$68$	6.65082	−	2.42070i	0.806531	−	0.293553i
$69$	−0.304783	−	3.83519i	−0.0366916	−	0.461703i
$70$	4.34996	−	16.7121i	0.519920	−	1.99748i
$71$	2.77738	−	4.81056i	0.329614	−	0.570908i	−0.652821	−	0.757512i	$-0.726415\pi$
$71$	2.77738	−	4.81056i	0.329614	−	0.570908i	0.982435	+	0.186604i	$0.0597480\pi$
$72$	−1.09689	+	0.610205i	−0.129269	+	0.0719134i
$73$	−2.30040	+	3.98440i	−0.269241	+	0.466339i	−0.968666	−	0.248367i	$-0.920106\pi$
$73$	−2.30040	+	3.98440i	−0.269241	+	0.466339i	0.699425	+	0.714706i	$0.253440\pi$
$74$	−4.46997	+	3.75075i	−0.519623	+	0.436016i
$75$	4.50084	+	9.85623i	0.519712	+	1.13810i
$76$	−8.34856	+	3.03863i	−0.957646	+	0.348554i
$77$	−11.8272	−	0.949453i	−1.34784	−	0.108200i
$78$	10.9853	−	2.84994i	1.24384	−	0.322693i
$79$	0.215339	+	1.22125i	0.0242276	+	0.137401i	0.994522	−	0.104524i	$-0.0333320\pi$
$79$	0.215339	+	1.22125i	0.0242276	+	0.137401i	−0.970295	+	0.241926i	$0.922221\pi$
$80$	7.35385	+	12.7372i	0.822185	+	1.42407i
$81$	−8.99543	−	0.286622i	−0.999493	−	0.0318469i
$82$	−0.279180	+	0.483554i	−0.0308303	+	0.0533996i
$83$	−8.72055	+	7.31741i	−0.957205	+	0.803190i	−0.980496	−	0.196539i	$-0.937030\pi$
$83$	−8.72055	+	7.31741i	−0.957205	+	0.803190i	0.0232914	+	0.999729i	$0.492585\pi$
$84$	5.26278	−	6.26174i	0.574217	−	0.683212i
$85$	−2.31006	+	13.1010i	−0.250561	+	1.42100i
$86$	−3.40335	+	19.3014i	−0.366993	+	2.08132i
$87$	7.35204	+	0.702255i	0.788221	+	0.0752896i
$88$	1.43738	−	1.20611i	0.153225	−	0.128571i
$89$	12.2622			1.29979			0.649896	−	0.760023i	$-0.274812\pi$
$89$	12.2622			1.29979			0.649896	+	0.760023i	$0.274812\pi$
$90$	−0.311839	+	19.5786i	−0.0328707	+	2.06377i
$91$	7.26249	−	5.16315i	0.761316	−	0.541245i
$92$	−3.72566	−	1.35603i	−0.388427	−	0.141376i
$93$	−3.64865	−	1.73690i	−0.378348	−	0.180108i
$94$	1.82803	−	10.3673i	0.188547	−	1.06930i
$95$	2.89974	−	16.4453i	0.297507	−	1.68725i
$96$	1.05545	+	13.2810i	0.107721	+	1.35549i
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.810001	−	0.586428i	$-0.199466\pi$
$97$	10.3763	+	3.77665i	1.05355	+	0.383461i	0.243548	+	0.969889i	$0.421689\pi$
$98$	4.47402	−	12.8625i	0.451944	−	1.29931i
$99$	13.2851	−	2.12495i	1.33520	−	0.213566i
$100$	11.1661			1.11661
$101$	0.654384	−	0.549094i	0.0651137	−	0.0546369i	−0.609650	−	0.792671i	$-0.708690\pi$
$101$	0.654384	−	0.549094i	0.0651137	−	0.0546369i	0.674764	+	0.738034i	$0.264246\pi$
$102$	−7.75077	+	10.8837i	−0.767441	+	1.07765i
$103$	−0.125872	+	0.713854i	−0.0124025	+	0.0703381i	−0.990381	−	0.138368i	$-0.955814\pi$
$103$	−0.125872	+	0.713854i	−0.0124025	+	0.0703381i	0.977978	+	0.208706i	$0.0669253\pi$
$104$	−0.244695	+	1.38774i	−0.0239944	+	0.136079i
$105$	5.24675	+	14.4514i	0.512031	+	1.41031i
$106$	−15.2590	+	12.8038i	−1.48209	+	1.24362i
$107$	6.26413	−	10.8498i	0.605577	−	1.04889i	−0.386384	−	0.922338i	$-0.626276\pi$
$107$	6.26413	−	10.8498i	0.605577	−	1.04889i	0.991960	−	0.126551i	$-0.0403908\pi$
$108$	−4.11938	+	8.30981i	−0.396388	+	0.799612i
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	0.959243	−	0.282581i	$-0.0911906\pi$
$109$	2.45242	+	4.24772i	0.234899	+	0.406857i	−0.724344	+	0.689439i	$0.757857\pi$
$110$	−5.08295	−	28.8268i	−0.484640	−	2.74853i
$111$	1.38447	−	5.00707i	0.131408	−	0.475250i
$112$	4.97694	+	10.4766i	0.470277	+	0.989941i
$113$	−4.66204	+	1.69685i	−0.438568	+	0.159626i	−0.551861	−	0.833936i	$-0.686082\pi$
$113$	−4.66204	+	1.69685i	−0.438568	+	0.159626i	0.113293	+	0.993562i	$0.463860\pi$
$114$	9.72929	−	13.6620i	0.911231	−	1.27956i
$115$	5.70867	−	4.79014i	0.532336	−	0.446683i
$116$	3.80551	−	6.59134i	0.353333	−	0.611990i
$117$	−6.61708	+	7.63560i	−0.611749	+	0.705912i
$118$	−3.25155	+	5.63185i	−0.299329	+	0.518454i
$119$	−2.64262	+	10.1527i	−0.242249	+	0.930694i
$120$	−2.19525	−	1.04502i	−0.200398	−	0.0953970i
$121$	−8.56257	+	3.11652i	−0.778415	+	0.283320i
$122$	3.50059	−	19.8529i	0.316929	−	1.79739i
$123$	−0.0393806	−	0.495540i	−0.00355083	−	0.0446813i
$124$	−3.19009	+	2.67681i	−0.286479	+	0.240384i
$125$	−2.10648	+	3.64853i	−0.188409	+	0.326334i
$126$	−1.48062	+	15.3707i	−0.131904	+	1.36933i
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	0.823392	−	0.567473i	$-0.192079\pi$
$127$	−0.898740	−	1.55666i	−0.0797503	−	0.138132i	−0.903142	+	0.429342i	$0.858746\pi$
$128$	−3.12714	−	1.13818i	−0.276402	−	0.100602i
$129$	−7.24806	−	15.8723i	−0.638156	−	1.39748i
$130$	16.8398	+	14.1303i	1.47695	+	1.23931i
$131$	−6.83829	−	5.73801i	−0.597464	−	0.501332i	0.293165	−	0.956062i	$-0.405291\pi$
$131$	−6.83829	−	5.73801i	−0.597464	−	0.501332i	−0.890629	+	0.454730i	$0.849736\pi$
$132$	3.69500	−	13.3633i	0.321608	−	1.16313i
$133$	3.31719	−	12.7443i	0.287637	−	1.10507i
$134$	−24.7069			−2.13435
$135$	−9.65512	−	14.5149i	−0.830981	−	1.24925i
$136$	−0.829517	−	1.43676i	−0.0711305	−	0.123202i
$137$	17.6751	+	6.43321i	1.51009	+	0.549627i	0.958649	−	0.284590i	$-0.0918574\pi$
$137$	17.6751	+	6.43321i	1.51009	+	0.549627i	0.551437	+	0.834216i	$0.314080\pi$
$138$	7.24502	−	1.87959i	0.616737	−	0.160002i
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	−0.575899	−	0.817521i	$-0.695348\pi$
$139$	2.88707	−	16.3734i	0.244878	−	1.38877i	0.820777	−	0.571249i	$-0.193541\pi$
$140$	15.7930	+	1.26781i	1.33475	+	0.107150i
$141$	3.89312	+	8.52541i	0.327860	+	0.717969i
$142$	10.1550	+	3.69612i	0.852189	+	0.310172i
$143$	7.55205	−	13.0805i	0.631535	−	1.09385i
$144$	−8.29217	−	10.2081i	−0.691014	−	0.850672i
$145$	7.15280	+	12.3890i	0.594008	+	1.02885i
$146$	−8.41101	−	3.06136i	−0.696100	−	0.253360i
$147$	3.21243	+	11.6910i	0.264957	+	0.964260i
$148$	−4.10108	−	3.44122i	−0.337107	−	0.282866i
$149$	−0.861789	+	0.313665i	−0.0706005	+	0.0256965i	−0.377079	−	0.926181i	$-0.623071\pi$
$149$	−0.861789	+	0.313665i	−0.0706005	+	0.0256965i	0.306478	+	0.951878i	$0.400849\pi$
$150$	−17.3634	+	11.9531i	−1.41771	+	0.975963i
$151$	−1.77206	−	10.0499i	−0.144208	−	0.817847i	−0.967999	−	0.250953i	$-0.919256\pi$
$151$	−1.77206	−	10.0499i	−0.144208	−	0.817847i	0.823791	−	0.566894i	$-0.191855\pi$
$152$	1.04127	+	1.80352i	0.0844578	+	0.146285i
$153$	0.189443	−	11.8941i	0.0153156	−	0.961582i
$154$	−2.17651	−	22.9810i	−0.175388	−	1.85186i
$155$	−1.35920	−	7.70840i	−0.109173	−	0.619153i
$156$	4.32518	+	9.47158i	0.346292	+	0.758333i
$157$	−3.20692	−	2.69093i	−0.255940	−	0.214759i	0.505785	−	0.862660i	$-0.331203\pi$
$157$	−3.20692	−	2.69093i	−0.255940	−	0.214759i	−0.761725	+	0.647900i	$0.775647\pi$
$158$	−2.26709	+	0.825153i	−0.180360	+	0.0656456i
$159$	4.72612	−	17.0925i	0.374806	−	1.35552i
$160$	−19.7688	+	16.5880i	−1.56286	+	1.31139i
$161$	4.78975	−	3.40520i	0.377485	−	0.268367i
$162$	−2.48979	−	17.3315i	−0.195616	−	1.36169i
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	−0.600175	−	0.799868i	$-0.704903\pi$
$163$	5.01262	−	8.68211i	0.392619	−	0.680036i	0.992794	+	0.119833i	$0.0382359\pi$
$164$	−0.481387	−	0.175211i	−0.0375900	−	0.0136816i
$165$	18.2800	+	18.5734i	1.42309	+	1.44594i
$166$	−16.9658	−	14.2360i	−1.31680	−	1.10493i
$167$	−14.3390	+	5.21896i	−1.10958	+	0.403855i	−0.830841	−	0.556510i	$-0.812140\pi$
$167$	−14.3390	+	5.21896i	−1.10958	+	0.403855i	−0.278743	+	0.960366i	$0.589918\pi$
$168$	−1.65969	−	0.960000i	−0.128048	−	0.0740656i
$169$	−0.287712	−	1.63170i	−0.0221317	−	0.125515i
$170$	−25.8811			−1.98499
$171$	−0.237802	+	14.9303i	−0.0181852	+	1.14175i
$172$	−17.9817			−1.37109
$173$	−7.20431	+	6.04513i	−0.547733	+	0.459603i	−0.874173	−	0.485615i	$-0.838596\pi$
$173$	−7.20431	+	6.04513i	−0.547733	+	0.459603i	0.326439	+	0.945218i	$0.394151\pi$
$174$	1.13827	+	14.3233i	0.0862921	+	1.08584i
$175$	−9.39600	+	13.6255i	−0.710271	+	1.02999i
$176$	15.0605	+	12.6373i	1.13523	+	0.952571i
$177$	−0.458657	−	5.77144i	−0.0344748	−	0.433808i
$178$	4.14256	+	23.4936i	0.310498	+	1.76092i
$179$	2.87366			0.214787			0.107394	−	0.994217i	$-0.465750\pi$
$179$	2.87366			0.214787			0.107394	+	0.994217i	$0.465750\pi$
$180$	−17.7397	+	2.83747i	−1.32224	+	0.211493i
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	0.769009	−	0.639238i	$-0.220750\pi$
$181$	−2.27490	−	3.94025i	−0.169092	−	0.292876i	−0.938101	+	0.346362i	$0.887417\pi$
$182$	12.3458	+	12.1702i	0.915129	+	0.902115i
$183$	7.45515	+	16.3258i	0.551101	+	1.20684i
$184$	−0.161381	+	0.915238i	−0.0118972	+	0.0674723i
$185$	9.45570	−	3.44159i	0.695197	−	0.253031i
$186$	2.09516	−	7.57736i	0.153625	−	0.555599i
$187$	3.08791	+	17.5124i	0.225810	+	1.28063i
$188$	9.65843			0.704414
$189$	−6.67375	−	12.0192i	−0.485444	−	0.874268i
$190$	32.4877			2.35690
$191$	−3.07816	−	17.4571i	−0.222728	−	1.26315i	−0.866982	−	0.498340i	$-0.833943\pi$
$191$	−3.07816	−	17.4571i	−0.222728	−	1.26315i	0.644254	−	0.764812i	$-0.277168\pi$
$192$	−10.3895	+	2.69538i	−0.749799	+	0.194522i
$193$	−18.5038	+	6.73485i	−1.33194	+	0.484785i	−0.907264	−	0.420563i	$-0.861833\pi$
$193$	−18.5038	+	6.73485i	−1.33194	+	0.484785i	−0.424672	+	0.905347i	$0.639611\pi$
$194$	−3.73040	+	21.1561i	−0.267827	+	1.51892i
$195$	−19.4824	−	1.86093i	−1.39516	−	0.133264i
$196$	12.3346	+	1.99321i	0.881041	+	0.142372i
$197$	9.63644	+	16.6908i	0.686568	+	1.18917i	0.972941	+	0.231052i	$0.0742169\pi$
$197$	9.63644	+	16.6908i	0.686568	+	1.18917i	−0.286373	+	0.958118i	$0.592450\pi$
$198$	8.55939	+	24.7355i	0.608289	+	1.75787i
$199$	−11.5653			−0.819841			−0.409921	−	0.912121i	$-0.634444\pi$
$199$	−11.5653			−0.819841			−0.409921	+	0.912121i	$0.634444\pi$
$200$	−0.454504	−	2.57762i	−0.0321383	−	0.182265i
$201$	18.1182	−	12.4726i	1.27796	−	0.879753i
$202$	1.27310	+	1.06826i	0.0895750	+	0.0751623i
$203$	4.84088	+	10.1901i	0.339763	+	0.715207i
$204$	−11.0687	−	5.26913i	−0.774964	−	0.368913i
$205$	0.737609	−	0.618927i	0.0515168	−	0.0432277i
$206$	−1.41022			−0.0982548
$207$	−4.36409	+	5.03582i	−0.303325	+	0.350014i
$208$	−14.7647			−1.02375
$209$	−3.87615	−	21.9828i	−0.268119	−	1.52058i
$210$	−25.9154	+	14.9346i	−1.78833	+	1.03058i
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.938079	−	0.346422i	$-0.887397\pi$
$211$	−20.8302	+	7.58159i	−1.43401	+	0.521938i	−0.495934	+	0.868360i	$0.665174\pi$
$212$	−13.9998	−	11.7472i	−0.961507	−	0.806800i
$213$	−9.31282	+	2.41605i	−0.638104	+	0.165545i
$214$	22.9037	+	8.33628i	1.56567	+	0.569856i
$215$	16.8991	−	29.2701i	1.15251	−	1.99621i
$216$	2.08594	+	0.612689i	0.141930	+	0.0416882i
$217$	−0.582008	−	6.14519i	−0.0395093	−	0.417163i
$218$	−7.30985	+	6.13369i	−0.495085	+	0.415426i
$219$	7.71346	−	2.00112i	0.521227	−	0.135223i
$220$	25.2363	−	9.18525i	1.70143	−	0.619269i
$221$	−10.2303	−	8.58420i	−0.688161	−	0.577436i
$222$	10.0609	+	0.961006i	0.675246	+	0.0644985i
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	−0.894104	−	0.447860i	$-0.852186\pi$
$223$	−3.09264	−	17.5392i	−0.207098	−	1.17451i	0.687005	−	0.726652i	$-0.258925\pi$
$224$	−16.5866	+	11.7920i	−1.10824	+	0.787885i
$225$	6.69881	−	17.5310i	0.446587	−	1.16873i
$226$	−4.82603	−	8.35893i	−0.321023	−	0.556028i
$227$	0.557083	+	3.15938i	0.0369749	+	0.209695i	0.997698	−	0.0678137i	$-0.0216023\pi$
$227$	0.557083	+	3.15938i	0.0369749	+	0.209695i	−0.960723	+	0.277509i	$0.910491\pi$
$228$	13.8942	+	6.61416i	0.920164	+	0.438034i
$229$	3.80028	−	1.38319i	0.251129	−	0.0914036i	−0.213388	−	0.976967i	$-0.568450\pi$
$229$	3.80028	−	1.38319i	0.251129	−	0.0914036i	0.464518	+	0.885564i	$0.346228\pi$
$230$	11.1062	+	9.31918i	0.732319	+	0.614489i
$231$	13.1975	+	15.7538i	0.868329	+	1.03652i
$232$	−1.67646	−	0.610183i	−0.110065	−	0.0400605i
$233$	7.67364	+	13.2911i	0.502717	+	0.870732i	0.999995	+	0.00314038i	$0.000999615\pi$
$233$	7.67364	+	13.2911i	0.502717	+	0.870732i	−0.497278	+	0.867591i	$0.665667\pi$
$234$	−16.8648	−	10.0984i	−1.10249	−	0.660150i
$235$	−9.07695	+	15.7217i	−0.592115	+	1.02557i
$236$	−5.60661	−	2.04064i	−0.364959	−	0.132834i
$237$	1.24596	−	1.74959i	0.0809335	−	0.113648i
$238$	−20.3446	−	1.63320i	−1.31875	−	0.105865i
$239$	−0.262379	+	1.48803i	−0.0169719	+	0.0962524i	−0.992117	−	0.125315i	$-0.960006\pi$
$239$	−0.262379	+	1.48803i	−0.0169719	+	0.0962524i	0.975145	+	0.221567i	$0.0711171\pi$
$240$	6.78901	−	24.5532i	0.438229	−	1.58490i
$241$	−18.0343	−	6.56396i	−1.16169	−	0.422822i	−0.311991	−	0.950085i	$-0.600996\pi$
$241$	−18.0343	−	6.56396i	−1.16169	−	0.422822i	−0.849702	+	0.527263i	$0.823218\pi$
$242$	−8.86376	−	15.3525i	−0.569784	−	0.986894i
$243$	10.5752	+	11.4527i	0.678400	+	0.734693i
$244$	18.4955			1.18405
$245$	−14.8365	+	18.2047i	−0.947867	+	1.16305i
$246$	0.936119	−	0.242859i	0.0596847	−	0.0154842i
$247$	12.8417	+	10.7755i	0.817098	+	0.685627i
$248$	0.747771	+	0.627455i	0.0474835	+	0.0398434i
$249$	19.6281	+	1.87485i	1.24388	+	0.118814i
$250$	−7.70198	−	2.80329i	−0.487116	−	0.177296i
$251$	4.44988	+	7.70741i	0.280874	+	0.486488i	0.971600	−	0.236629i	$-0.0760424\pi$
$251$	4.44988	+	7.70741i	0.280874	+	0.486488i	−0.690726	+	0.723116i	$0.742709\pi$
$252$	−14.1239	+	1.11103i	−0.889721	+	0.0699884i
$253$	4.98072	−	8.62686i	0.313135	−	0.542366i
$254$	2.67884	−	2.24782i	0.168086	−	0.141041i
$255$	18.9793	−	13.0654i	1.18853	−	0.818189i
$256$	3.27643	−	18.5815i	0.204777	−	1.16135i
$257$	−9.22466	+	3.35750i	−0.575418	+	0.209435i	−0.613304	−	0.789847i	$-0.710160\pi$
$257$	−9.22466	+	3.35750i	−0.575418	+	0.209435i	0.0378856	+	0.999282i	$0.487938\pi$
$258$	27.9617	−	19.2490i	1.74082	−	1.19839i
$259$	7.65012	−	2.10868i	0.475355	−	0.131027i
$260$	−10.0843	+	17.4666i	−0.625404	+	1.08323i
$261$	−8.06548	−	9.92899i	−0.499240	−	0.614589i
$262$	8.68346	−	15.0402i	0.536466	−	0.929187i
$263$	5.70996	−	4.79123i	0.352091	−	0.295440i	−0.449538	−	0.893261i	$-0.648411\pi$
$263$	5.70996	−	4.79123i	0.352091	−	0.295440i	0.801629	+	0.597822i	$0.203967\pi$
$264$	−3.23524	−	0.309025i	−0.199115	−	0.0190192i
$265$	32.2787	−	11.7485i	1.98286	−	0.721703i
$266$	25.5379	+	2.05011i	1.56583	+	0.125700i
$267$	−14.8980	−	15.1372i	−0.911744	−	0.926381i
$268$	−3.93624	−	22.3235i	−0.240444	−	1.36363i
$269$	8.61215	+	14.9167i	0.525092	+	0.909486i	0.999573	+	0.0292204i	$0.00930245\pi$
$269$	8.61215	+	14.9167i	0.525092	+	0.909486i	−0.474481	+	0.880266i	$0.657364\pi$
$270$	24.5479	−	23.4022i	1.49394	−	1.42421i
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	−0.853223	−	0.521546i	$-0.825355\pi$
$271$	0.412552	−	0.714562i	0.0250608	−	0.0434065i	0.878284	+	0.478140i	$0.158689\pi$
$272$	13.3161	−	11.1735i	0.807408	−	0.677496i
$273$	−15.1973	−	2.69226i	−0.919782	−	0.162943i
$274$	−6.35442	+	36.0377i	−0.383885	+	2.17712i
$275$	−4.87167	+	27.6286i	−0.293773	+	1.66607i
$276$	2.85254	+	6.24668i	0.171703	+	0.376006i
$277$	8.81649	−	7.39791i	0.529731	−	0.444497i	−0.338277	−	0.941046i	$-0.609844\pi$
$277$	8.81649	−	7.39791i	0.529731	−	0.444497i	0.868009	+	0.496549i	$0.165400\pi$
$278$	32.3456			1.93996
$279$	2.28881	+	6.61436i	0.137028	+	0.395992i
$280$	−0.350170	−	3.69731i	−0.0209267	−	0.220957i
$281$	−22.9354	−	8.34780i	−1.36821	−	0.497988i	−0.449628	−	0.893216i	$-0.648443\pi$
$281$	−22.9354	−	8.34780i	−1.36821	−	0.497988i	−0.918583	+	0.395228i	$0.870666\pi$
$282$	−15.0189	+	10.3391i	−0.894364	+	0.615685i
$283$	0.104052	−	0.590109i	0.00618526	−	0.0350784i	−0.981559	−	0.191160i	$-0.938775\pi$
$283$	0.104052	−	0.590109i	0.00618526	−	0.0350784i	0.987744	+	0.156081i	$0.0498862\pi$
$284$	−1.72171	+	9.76428i	−0.102164	+	0.579403i
$285$	−23.8240	+	16.4006i	−1.41121	+	0.971488i
$286$	27.6128	+	10.0502i	1.63278	+	0.594283i
$287$	0.618877	−	0.439981i	0.0365311	−	0.0259712i
$288$	15.1126	−	17.4388i	0.890517	−	1.02759i
$289$	−1.27713			−0.0751252
$290$	−21.3201	+	17.8897i	−1.25196	+	1.05052i
$291$	−7.94456	−	17.3975i	−0.465718	−	1.01986i
$292$	1.42602	−	8.08738i	0.0834517	−	0.473278i
$293$	1.42904	−	8.10449i	0.0834854	−	0.473469i	−0.914188	−	0.405291i	$-0.867170\pi$
$293$	1.42904	−	8.10449i	0.0834854	−	0.473469i	0.997673	−	0.0681782i	$-0.0217187\pi$
$294$	−21.3140	+	10.1044i	−1.24306	+	0.589301i
$295$	8.59076	−	7.20851i	0.500174	−	0.419695i
$296$	−0.627451	+	1.08678i	−0.0364699	+	0.0631677i
$297$	−18.7639	−	13.8182i	−1.08879	−	0.801811i
$298$	−0.892102	−	1.54517i	−0.0516781	−	0.0895091i
$299$	1.29906	+	7.36735i	0.0751268	+	0.426065i
$300$	−13.5663	−	13.7841i	−0.783252	−	0.795826i
$301$	15.1311	−	21.9423i	0.872145	−	1.26473i
$302$	18.6562	−	6.79032i	1.07355	−	0.390739i
$303$	−1.47288	−	0.140687i	−0.0846147	−	0.00808227i
$304$	−16.7153	+	14.0258i	−0.958687	+	0.804434i
$305$	−17.3820	+	30.1065i	−0.995289	+	1.72389i
$306$	22.8524	−	3.65524i	1.30638	−	0.208956i
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	0.312349	+	0.949967i	$0.398884\pi$
$307$	−11.6784	+	20.2276i	−0.666521	+	1.15445i	−0.978870	+	0.204482i	$0.934449\pi$
$308$	20.4174	−	5.62783i	1.16339	−	0.320676i
$309$	1.03415	−	0.711916i	0.0588308	−	0.0404995i
$310$	14.3096	−	5.20827i	0.812732	−	0.295810i
$311$	−4.32728	+	24.5412i	−0.245378	+	1.39161i	0.574236	+	0.818690i	$0.305299\pi$
$311$	−4.32728	+	24.5412i	−0.245378	+	1.39161i	−0.819614	+	0.572917i	$0.805812\pi$
$312$	2.01040	−	1.38397i	0.113816	−	0.0783518i
$313$	−18.0599	+	15.1540i	−1.02080	+	0.856557i	−0.989728	−	0.142960i	$-0.954338\pi$
$313$	−18.0599	+	15.1540i	−1.02080	+	0.856557i	−0.0310764	+	0.999517i	$0.509894\pi$
$314$	4.07224	−	7.05333i	0.229810	−	0.398042i
$315$	11.4651	−	24.0346i	0.645983	−	1.35420i
$316$	−1.10674	−	1.91694i	−0.0622592	−	0.107836i
$317$	14.2494	+	5.18635i	0.800326	+	0.291295i	0.709621	−	0.704583i	$-0.248866\pi$
$317$	14.2494	+	5.18635i	0.800326	+	0.291295i	0.0907041	+	0.995878i	$0.471088\pi$
$318$	34.3448	+	3.28056i	1.92596	+	0.183965i
$319$	14.6488	+	12.2918i	0.820175	+	0.688208i
$320$	−15.9265	−	13.3639i	−0.890318	−	0.747065i
$321$	−21.0043	+	5.44918i	−1.17234	+	0.304144i
$322$	8.14226	+	8.02647i	0.453751	+	0.447298i
$323$	−19.7364			−1.09816
$324$	15.2630	−	5.01083i	0.847943	−	0.278380i
$325$	−10.5345	−	18.2463i	−0.584351	−	1.01212i
$326$	18.3278	+	6.67077i	1.01508	+	0.369460i
$327$	2.26405	−	8.18819i	0.125202	−	0.452808i
$328$	−0.0208518	+	0.118257i	−0.00115135	+	0.00652963i
$329$	−8.12732	+	11.7858i	−0.448074	+	0.649770i
$330$	−29.4100	+	41.2979i	−1.61897	+	2.27338i
$331$	15.3332	+	5.58083i	0.842789	+	0.306750i	0.727097	−	0.686535i	$-0.240869\pi$
$331$	15.3332	+	5.58083i	0.842789	+	0.306750i	0.115692	+	0.993285i	$0.463091\pi$
$332$	10.1598	−	17.5972i	0.557589	−	0.965773i
$333$	−7.86309	+	4.37429i	−0.430894	+	0.239710i
$334$	−14.8434	−	25.7094i	−0.812192	−	1.40676i
$335$	40.0369	+	14.5723i	2.18745	+	0.796167i
$336$	6.88612	−	18.8724i	0.375668	−	1.02957i
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	0.644961	−	0.764215i	$-0.276874\pi$
$337$	0.0798940	+	0.0670390i	0.00435210	+	0.00365185i	−0.640609	+	0.767867i	$0.721318\pi$
$338$	3.02903	−	1.10248i	0.164758	−	0.0599669i
$339$	7.75885	+	3.69351i	0.421403	+	0.200604i
$340$	−4.12332	−	23.3845i	−0.223618	−	1.26820i
$341$	−5.23148	−	9.06118i	−0.283300	−	0.490691i
$342$	−28.6858	+	4.58830i	−1.55115	+	0.248107i
$343$	−12.8115	+	13.3741i	−0.691753	+	0.722134i
$344$	0.731925	+	4.15095i	0.0394628	+	0.223804i
$345$	−12.8490	−	1.22732i	−0.691767	−	0.0660765i
$346$	−14.0159	−	11.7608i	−0.753501	−	0.632262i
$347$	−23.4434	+	8.53269i	−1.25851	+	0.458059i	−0.883268	−	0.468869i	$-0.844661\pi$
$347$	−23.4434	+	8.53269i	−1.25851	+	0.458059i	−0.375239	+	0.926928i	$0.622439\pi$
$348$	−12.7602	+	3.31042i	−0.684021	+	0.177457i
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.191675	−	0.981458i	$-0.438608\pi$
$349$	22.2592	−	18.6777i	1.19151	−	0.999793i	0.999832	−	0.0183346i	$-0.00583640\pi$
$350$	−29.2799	−	13.3990i	−1.56508	−	0.716207i
$351$	17.4653	−	1.10839i	0.932228	−	0.0591613i
$352$	−17.2479	+	29.8743i	−0.919318	+	1.59231i
$353$	4.12531	+	1.50149i	0.219568	+	0.0799162i	0.449462	−	0.893299i	$-0.351616\pi$
$353$	4.12531	+	1.50149i	0.219568	+	0.0799162i	−0.229894	+	0.973216i	$0.573838\pi$
$354$	10.9028	−	2.82853i	0.579475	−	0.150335i
$355$	−14.2760	−	11.9790i	−0.757690	−	0.635778i
$356$	−20.5673	+	7.48590i	−1.09007	+	0.396752i
$357$	15.7437	−	9.07281i	0.833245	−	0.480184i
$358$	0.970810	+	5.50574i	0.0513089	+	0.290987i
$359$	6.73487			0.355453			0.177727	−	0.984080i	$-0.443126\pi$
$359$	6.73487			0.355453			0.177727	+	0.984080i	$0.443126\pi$
$360$	1.37709	+	3.97959i	0.0725788	+	0.209743i
$361$	5.77447			0.303919
$362$	6.78073	−	5.68971i	0.356387	−	0.299044i
$363$	14.2503	+	6.78371i	0.747949	+	0.356052i
$364$	−9.02931	+	13.0938i	−0.473264	+	0.686300i
$365$	11.8243	+	9.92173i	0.618910	+	0.519327i
$366$	−28.7606	+	19.7990i	−1.50334	+	1.03491i
$367$	1.44020	+	8.16779i	0.0751779	+	0.426355i	0.999047	+	0.0436465i	$0.0138975\pi$
$367$	1.44020	+	8.16779i	0.0751779	+	0.426355i	−0.923869	+	0.382709i	$0.874991\pi$
$368$	−9.73758			−0.507607
$369$	−0.563878	+	0.650672i	−0.0293543	+	0.0338726i
$370$	9.78830	+	16.9538i	0.508870	+	0.881388i
$371$	26.1150	−	7.19833i	1.35582	−	0.373719i
$372$	7.18022	+	0.685843i	0.372277	+	0.0355593i
$373$	2.03256	−	11.5272i	0.105242	−	0.596858i	−0.885881	−	0.463912i	$-0.846445\pi$
$373$	2.03256	−	11.5272i	0.105242	−	0.596858i	0.991123	−	0.132946i	$-0.0424436\pi$
$374$	−32.5095	+	11.8325i	−1.68102	+	0.611843i
$375$	7.06323	−	1.83243i	0.364743	−	0.0946263i
$376$	−0.393136	−	2.22958i	−0.0202744	−	0.114982i
$377$	−14.3610			−0.739631
$378$	20.7734	−	16.8469i	1.06847	−	0.866513i
$379$	−26.9202			−1.38280			−0.691398	−	0.722474i	$-0.743005\pi$
$379$	−26.9202			−1.38280			−0.691398	+	0.722474i	$0.743005\pi$
$380$	5.17587	+	29.3538i	0.265516	+	1.50582i
$381$	−0.829709	+	3.00073i	−0.0425073	+	0.153732i
$382$	32.4068	−	11.7951i	1.65808	−	0.603490i
$383$	2.90547	−	16.4777i	0.148463	−	0.841973i	−0.816059	−	0.577969i	$-0.803846\pi$
$383$	2.90547	−	16.4777i	0.148463	−	0.841973i	0.964522	−	0.264004i	$-0.0850433\pi$
$384$	2.39428	+	5.24316i	0.122183	+	0.267564i
$385$	−10.0273	+	38.5239i	−0.511039	+	1.96336i
$386$	−19.1547	−	33.1769i	−0.974949	−	1.68866i
$387$	−10.7876	+	28.2315i	−0.548366	+	1.43509i
$388$	−19.7096			−1.00061
$389$	0.278066	+	1.57699i	0.0140985	+	0.0799567i	0.991045	−	0.133527i	$-0.0426302\pi$
$389$	0.278066	+	1.57699i	0.0140985	+	0.0799567i	−0.976947	+	0.213483i	$0.931519\pi$
$390$	−3.01634	−	37.9557i	−0.152738	−	1.92196i
$391$	−6.74704	−	5.66144i	−0.341213	−	0.286311i
$392$	−0.0419465	−	2.92848i	−0.00211862	−	0.147911i
$393$	1.22487	+	15.4130i	0.0617866	+	0.777483i
$394$	−28.7230	+	24.1015i	−1.44704	+	1.21421i
$395$	4.16045			0.209335
$396$	−20.9858	+	11.6745i	−1.05457	+	0.586667i
$397$	11.8414			0.594301			0.297150	−	0.954831i	$-0.403964\pi$
$397$	11.8414			0.594301			0.297150	+	0.954831i	$0.403964\pi$
$398$	−3.90711	−	22.1583i	−0.195846	−	1.11070i
$399$	−19.7626	+	11.3888i	−0.989366	+	0.570153i
$400$	25.7705	−	9.37968i	1.28852	−	0.468984i
$401$	0.120005	+	0.100696i	0.00599275	+	0.00502852i	0.645779	−	0.763524i	$-0.276533\pi$
$401$	0.120005	+	0.100696i	0.00599275	+	0.00502852i	−0.639786	+	0.768553i	$0.720977\pi$
$402$	30.0177	+	30.4996i	1.49715	+	1.52118i
$403$	7.38377	+	2.68747i	0.367812	+	0.133872i
$404$	−0.762382	+	1.32048i	−0.0379299	+	0.0656965i
$405$	−6.18758	+	29.5538i	−0.307463	+	1.46854i
$406$	−17.8882	+	12.7174i	−0.887779	+	0.631152i
$407$	10.3039	−	8.64603i	0.510748	−	0.428568i
$408$	−0.765803	+	2.76961i	−0.0379129	+	0.137116i
$409$	25.2545	−	9.19188i	1.24875	−	0.454509i	0.368774	−	0.929519i	$-0.379778\pi$
$409$	25.2545	−	9.19188i	1.24875	−	0.454509i	0.879981	+	0.475010i	$0.157555\pi$
$410$	1.43501	+	1.20412i	0.0708702	+	0.0594672i
$411$	−13.5329	−	29.6352i	−0.667529	−	1.46180i
$412$	−0.224673	−	1.27419i	−0.0110689	−	0.0627747i
$413$	7.20792	−	5.12435i	0.354678	−	0.252153i
$414$	−11.1226	−	6.66006i	−0.546648	−	0.327324i
$415$	19.0962	+	33.0756i	0.937396	+	1.62362i
$416$	−4.49858	−	25.5127i	−0.220561	−	1.25086i
$417$	−23.7199	+	16.3289i	−1.16157	+	0.799630i
$418$	40.8081	−	14.8529i	1.99599	−	0.726480i
$419$	−18.4551	−	15.4857i	−0.901593	−	0.756526i	0.0689084	−	0.997623i	$-0.478048\pi$
$419$	−18.4551	−	15.4857i	−0.901593	−	0.756526i	−0.970501	+	0.241097i	$0.922493\pi$
$420$	−17.6227	−	21.0361i	−0.859900	−	1.02646i
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	0.255980	−	0.966682i	$-0.417602\pi$
$421$	−3.47375	−	1.26434i	−0.169300	−	0.0616202i	−0.425280	+	0.905062i	$0.639824\pi$
$422$	−21.5629	−	37.3481i	−1.04967	−	1.81808i
$423$	5.79431	−	15.1639i	0.281729	−	0.737293i
$424$	−2.14191	+	3.70990i	−0.104021	+	0.180169i
$425$	23.3094	+	8.48392i	1.13067	+	0.411530i
$426$	−7.77515	−	17.0266i	−0.376707	−	0.824939i
$427$	−15.5635	+	22.5692i	−0.753169	+	1.09220i
$428$	−3.88316	+	22.0225i	−0.187699	+	1.06450i
$429$	−25.3228	+	6.56955i	−1.22260	+	0.317181i
$430$	61.7888	+	22.4893i	2.97972	+	1.08453i
$431$	1.18001	+	2.04383i	0.0568390	+	0.0984480i	0.893045	−	0.449968i	$-0.148564\pi$
$431$	1.18001	+	2.04383i	0.0568390	+	0.0984480i	−0.836206	+	0.548416i	$0.815231\pi$
$432$	−2.52683	+	22.6387i	−0.121572	+	1.08920i
$433$	15.5635			0.747935			0.373968	−	0.927442i	$-0.377997\pi$
$433$	15.5635			0.747935			0.373968	+	0.927442i	$0.377997\pi$
$434$	11.5772	−	3.19113i	0.555722	−	0.153179i
$435$	6.60341	−	23.8819i	0.316609	−	1.14505i
$436$	−6.70660	−	5.62751i	−0.321188	−	0.269509i
$437$	8.46934	+	7.10662i	0.405144	+	0.339956i
$438$	6.43987	+	14.1024i	0.307709	+	0.673841i
$439$	−37.0202	−	13.4742i	−1.76688	−	0.643090i	−0.999999	−	0.00129654i	$-0.999587\pi$
$439$	−37.0202	−	13.4742i	−1.76688	−	0.643090i	−0.766877	−	0.641794i	$-0.778190\pi$
$440$	−3.14757	−	5.45174i	−0.150054	−	0.259902i
$441$	10.5291	−	18.1697i	0.501388	−	0.865223i
$442$	12.9907	−	22.5005i	0.617904	−	1.07024i
$443$	−2.38457	+	2.00089i	−0.113295	+	0.0950654i	−0.697675	−	0.716414i	$-0.745782\pi$
$443$	−2.38457	+	2.00089i	−0.113295	+	0.0950654i	0.584380	+	0.811480i	$0.301338\pi$
$444$	0.734584	+	9.24353i	0.0348618	+	0.438679i
$445$	7.14375	−	40.5142i	0.338646	−	1.92056i
$446$	32.5592	−	11.8506i	1.54172	−	0.561142i
$447$	1.43424	+	0.682754i	0.0678372	+	0.0322931i
$448$	−11.6762	−	11.5101i	−0.551648	−	0.543803i
$449$	−7.45557	+	12.9134i	−0.351850	+	0.609422i	−0.986574	−	0.163317i	$-0.947781\pi$
$449$	−7.45557	+	12.9134i	−0.351850	+	0.609422i	0.634724	+	0.772739i	$0.281114\pi$
$450$	35.8513	+	6.91198i	1.69004	+	0.325834i
$451$	0.643552	−	1.11466i	0.0303037	−	0.0524875i
$452$	6.78372	−	5.69222i	0.319080	−	0.267740i
$453$	−10.2532	+	14.3977i	−0.481736	+	0.676461i
$454$	−5.86496	+	2.13467i	−0.275256	+	0.100185i
$455$	−12.8280	−	27.0031i	−0.601386	−	1.26593i
$456$	0.961287	−	3.47660i	0.0450164	−	0.162807i
$457$	−4.80493	−	27.2501i	−0.224765	−	1.27471i	−0.863133	−	0.504976i	$-0.831501\pi$
$457$	−4.80493	−	27.2501i	−0.224765	−	1.27471i	0.638368	−	0.769731i	$-0.279610\pi$
$458$	3.93395	+	6.81380i	0.183821	+	0.318388i
$459$	−14.9130	+	14.2169i	−0.696077	+	0.663590i
$460$	−6.65081	+	11.5195i	−0.310095	+	0.537101i
$461$	−26.9668	+	22.6278i	−1.25597	+	1.05388i	−0.259868	+	0.965644i	$0.583679\pi$
$461$	−26.9668	+	22.6278i	−1.25597	+	1.05388i	−0.996099	+	0.0882379i	$0.971876\pi$
$462$	−25.7247	+	30.6076i	−1.19682	+	1.42399i
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	0.774874	+	0.632115i	$0.217813\pi$
$463$	−3.64646	+	20.6801i	−0.169465	+	0.961086i	−0.944340	+	0.328971i	$0.893298\pi$
$464$	3.24599	−	18.4089i	0.150691	−	0.854612i
$465$	−7.86434	+	11.0432i	−0.364700	+	0.512117i
$466$	−22.8726	+	19.1924i	−1.05955	+	0.889070i
$467$	−36.2367			−1.67684			−0.838418	−	0.545028i	$-0.816519\pi$
$467$	−36.2367			−1.67684			−0.838418	+	0.545028i	$0.816519\pi$
$468$	6.43737	−	16.8468i	0.297568	−	0.778743i
$469$	30.5527	+	13.9815i	1.41079	+	0.645604i
$470$	−33.1883	−	12.0796i	−1.53086	−	0.557189i
$471$	0.574422	+	7.22816i	0.0264680	+	0.333056i
$472$	−0.242857	+	1.37731i	−0.0111784	+	0.0633958i
$473$	7.84524	−	44.4926i	0.360724	−	2.04577i
$474$	3.77302	+	1.79611i	0.173301	+	0.0824978i
$475$	−29.2595	−	10.6496i	−1.34252	−	0.488636i
$476$	−1.76560	−	18.6423i	−0.0809262	−	0.854468i
$477$	−26.8420	+	14.9324i	−1.22901	+	0.683708i
$478$	−2.93960			−0.134454
$479$	−24.9795	+	20.9603i	−1.14134	+	0.957701i	−0.999482	−	0.0321859i	$-0.989753\pi$
$479$	−24.9795	+	20.9603i	−1.14134	+	0.957701i	−0.141861	+	0.989887i	$0.545309\pi$
$480$	44.4953	+	4.25012i	2.03092	+	0.193991i
$481$	−1.75411	+	9.94807i	−0.0799807	+	0.453593i
$482$	6.48356	−	36.7701i	0.295318	−	1.67483i
$483$	−10.0229	−	1.77559i	−0.456058	−	0.0807923i
$484$	12.4594	−	10.4546i	0.566335	−	0.475211i
$485$	18.5230	−	32.0828i	0.841088	−	1.45681i
$486$	−18.3700	+	24.1305i	−0.833282	+	1.09458i
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	−0.967624	−	0.252394i	$-0.918782\pi$
$487$	−15.5004	−	26.8476i	−0.702392	−	1.21658i	0.265232	−	0.964185i	$-0.414551\pi$
$488$	−0.752838	−	4.26956i	−0.0340794	−	0.193274i
$489$	−16.8078	+	4.36049i	−0.760076	+	0.197188i
$490$	−39.8912	−	22.2756i	−1.80210	−	1.00631i
$491$	39.1653	−	14.2550i	1.76751	−	0.643320i	0.767509	−	0.641038i	$-0.221496\pi$
$491$	39.1653	−	14.2550i	1.76751	−	0.643320i	0.999997	−	0.00228119i	$-0.000726125\pi$
$492$	0.368573	+	0.807125i	0.0166165	+	0.0363880i
$493$	12.9521	−	10.8681i	0.583332	−	0.489473i
$494$	−16.3068	+	28.2442i	−0.733677	+	1.27077i
$495$	0.718835	−	45.1317i	0.0323092	−	2.02852i
$496$	−5.11391	+	8.85756i	−0.229621	+	0.397716i
$497$	−10.4662	−	10.3173i	−0.469471	−	0.462795i
$498$	3.03890	+	38.2396i	0.136176	+	1.71356i
$499$	−16.7437	+	6.09421i	−0.749552	+	0.272814i	−0.688417	−	0.725315i	$-0.741694\pi$
$499$	−16.7437	+	6.09421i	−0.749552	+	0.272814i	−0.0611345	+	0.998130i	$0.519472\pi$
$500$	1.30581	−	7.40563i	0.0583977	−	0.331190i
$501$	23.8638	+	11.3601i	1.06616	+	0.507531i
$502$	−13.2636	+	11.1295i	−0.591984	+	0.496733i
$503$	13.0372	−	22.5811i	0.581300	−	1.00684i	−0.414025	−	0.910265i	$-0.635878\pi$
$503$	13.0372	−	22.5811i	0.581300	−	1.00684i	0.995326	−	0.0965762i	$-0.0307891\pi$
$504$	0.831371	+	3.21518i	0.0370322	+	0.143216i
$505$	−1.43297	−	2.48197i	−0.0637662	−	0.110446i
$506$	18.2112	+	6.62832i	0.809585	+	0.294665i
$507$	−1.66471	+	2.33761i	−0.0739322	+	0.103817i
$508$	2.45777	+	2.06232i	0.109046	+	0.0915005i
$509$	4.02263	+	3.37539i	0.178300	+	0.149611i	0.727570	−	0.686034i	$-0.240650\pi$
$509$	4.02263	+	3.37539i	0.178300	+	0.149611i	−0.549270	+	0.835645i	$0.685094\pi$
$510$	31.4443	+	31.9491i	1.39238	+	1.41473i
$511$	8.66871	+	8.54544i	0.383481	+	0.378028i
$512$	30.0523			1.32814
$513$	18.7197	−	17.8461i	0.826497	−	0.787923i
$514$	−9.54914	−	16.5396i	−0.421194	−	0.729530i
$515$	2.28523	+	0.831757i	0.100699	+	0.0366516i
$516$	21.8469	+	22.1977i	0.961758	+	0.977198i
$517$	−4.21388	+	23.8981i	−0.185326	+	1.05104i
$518$	6.62454	+	13.9448i	0.291065	+	0.612698i
$519$	16.2154	+	1.54887i	0.711775	+	0.0679877i
$520$	4.44251	+	1.61694i	0.194817	+	0.0709076i
$521$	13.7210	−	23.7655i	0.601130	−	1.04119i	−0.391520	−	0.920169i	$-0.628051\pi$
$521$	13.7210	−	23.7655i	0.601130	−	1.04119i	0.992650	−	0.121018i	$-0.0386159\pi$
$522$	16.2985	−	18.8073i	0.713368	−	0.823171i
$523$	7.93861	+	13.7501i	0.347131	+	0.601249i	0.985739	−	0.168284i	$-0.0538225\pi$
$523$	7.93861	+	13.7501i	0.347131	+	0.601249i	−0.638607	+	0.769533i	$0.720489\pi$
$524$	14.9728	+	5.44965i	0.654090	+	0.238069i
$525$	28.2359	−	4.95541i	1.23231	−	0.216272i
$526$	11.1087	+	9.32129i	0.484362	+	0.406428i
$527$	−8.69316	+	3.16405i	−0.378680	+	0.137828i
$528$	−2.69764	−	33.9453i	−0.117400	−	1.47728i
$529$	−3.13715	−	17.7917i	−0.136398	−	0.773551i
$530$	33.4141	+	57.8749i	1.45141	+	2.51392i
$531$	−6.56736	+	7.57822i	−0.284999	+	0.328867i
$532$	2.21630	+	23.4011i	0.0960889	+	1.01456i
$533$	0.167850	+	0.951925i	0.00727040	+	0.0412325i
$534$	23.9689	−	33.6575i	1.03723	−	1.45650i
$535$	−32.1982	−	27.0175i	−1.39205	−	1.16807i
$536$	−4.99302	+	1.81731i	−0.215665	+	0.0784958i
$537$	−3.49136	−	3.54741i	−0.150663	−	0.153082i
$538$	−25.6700	+	21.5396i	−1.10671	+	0.928640i
$539$	−10.3133	+	29.6501i	−0.444225	+	1.27712i
$540$	25.0556	+	18.4515i	1.07822	+	0.794028i
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	−0.664133	−	0.747615i	$-0.731199\pi$
$541$	7.33572	−	12.7058i	0.315387	−	0.546267i	0.979520	+	0.201348i	$0.0645323\pi$
$542$	1.50843	+	0.549023i	0.0647925	+	0.0235825i
$543$	−2.10017	+	7.59549i	−0.0901270	+	0.325954i
$544$	23.3646	+	19.6052i	1.00175	+	0.840568i
$545$	15.4631	−	5.62812i	0.662368	−	0.241082i
$546$	0.0240738	−	30.0266i	0.00103026	−	1.28502i
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	0.976389	−	0.216021i	$-0.0693078\pi$
$547$	−0.350819	−	1.98960i	−0.0150000	−	0.0850690i	−0.991389	+	0.130952i	$0.958197\pi$
$548$	−33.5738			−1.43420
$549$	11.0959	−	29.0382i	0.473559	−	1.23932i
$550$	−54.5804			−2.32732
$551$	−16.2583	+	13.6423i	−0.692627	+	0.581183i
$552$	1.32589	−	0.912754i	0.0564338	−	0.0388494i
$553$	3.27045	+	0.262542i	0.139074	+	0.0111644i
$554$	17.1524	+	14.3926i	0.728736	+	0.611482i
$555$	−15.7367	−	7.49130i	−0.667987	−	0.317988i
$556$	5.15324	+	29.2255i	0.218546	+	1.23944i
$557$	−12.8589			−0.544848			−0.272424	−	0.962177i	$-0.587825\pi$
$557$	−12.8589			−0.544848			−0.272424	+	0.962177i	$0.587825\pi$
$558$	−11.8995	+	6.61976i	−0.503744	+	0.280237i
$559$	16.9646	+	29.3836i	0.717526	+	1.24279i
$560$	37.5139	−	10.3403i	1.58525	−	0.436958i
$561$	17.8667	−	25.0887i	0.754332	−	1.05924i
$562$	8.24556	−	46.7629i	0.347818	−	1.97257i
$563$	−2.36642	+	0.861307i	−0.0997327	+	0.0362998i	−0.391405	−	0.920219i	$-0.628011\pi$
$563$	−2.36642	+	0.861307i	−0.0997327	+	0.0362998i	0.291672	+	0.956518i	$0.405788\pi$
$564$	−11.7345	−	11.9229i	−0.494113	−	0.502046i
$565$	2.89033	+	16.3919i	0.121597	+	0.689612i
$566$	1.16576			0.0490007
$567$	−6.72890	+	22.8412i	−0.282587	+	0.959242i
$568$	2.32410			0.0975169
$569$	6.15504	+	34.9070i	0.258033	+	1.46338i	0.788166	+	0.615463i	$0.211031\pi$
$569$	6.15504	+	34.9070i	0.258033	+	1.46338i	−0.530133	+	0.847914i	$0.677858\pi$
$570$	−39.4710	−	40.1047i	−1.65326	−	1.67980i
$571$	1.23492	−	0.449474i	0.0516797	−	0.0188099i	−0.316051	−	0.948742i	$-0.602357\pi$
$571$	1.23492	−	0.449474i	0.0516797	−	0.0188099i	0.367731	+	0.929932i	$0.380135\pi$
$572$	−4.68154	+	26.5503i	−0.195745	+	1.11013i
$573$	−17.8103	+	25.0094i	−0.744034	+	1.04478i
$574$	1.05205	+	1.03709i	0.0439117	+	0.0432873i
$575$	−6.94772	−	12.0338i	−0.289740	−	0.501844i
$576$	15.9501	+	9.55067i	0.664588	+	0.397945i
$577$	−6.32197			−0.263187			−0.131594	−	0.991304i	$-0.542009\pi$
$577$	−6.32197			−0.263187			−0.131594	+	0.991304i	$0.542009\pi$
$578$	−0.431454	−	2.44689i	−0.0179461	−	0.101777i
$579$	30.7952	+	14.6597i	1.27980	+	0.609236i
$580$	−19.5607	−	16.4134i	−0.812213	−	0.681527i
$581$	12.9239	+	27.2051i	0.536176	+	1.12866i
$582$	30.6486	−	21.0987i	1.27043	−	0.874569i
$583$	35.1743	−	29.5147i	1.45677	−	1.22238i
$584$	−1.92496			−0.0796554
$585$	21.3729	+	26.3111i	0.883662	+	1.08783i
$586$	16.0104			0.661386
$587$	1.97608	+	11.2069i	0.0815614	+	0.462558i	0.998046	+	0.0624873i	$0.0199033\pi$
$587$	1.97608	+	11.2069i	0.0815614	+	0.462558i	−0.916484	+	0.400071i	$0.868986\pi$
$588$	−12.5254	−	17.6482i	−0.516539	−	0.727798i
$589$	10.9122	−	3.97173i	0.449631	−	0.163652i
$590$	16.7133	+	14.0241i	0.688074	+	0.577363i
$591$	8.89628	−	32.1743i	0.365944	−	1.32348i
$592$	−12.3556	−	4.49707i	−0.507812	−	0.184829i
$593$	−22.5967	+	39.1386i	−0.927935	+	1.60723i	−0.141162	+	0.989986i	$0.545084\pi$
$593$	−22.5967	+	39.1386i	−0.927935	+	1.60723i	−0.786772	+	0.617243i	$0.788249\pi$
$594$	20.1357	−	40.6187i	0.826177	−	1.66660i
$595$	32.0048	+	14.6460i	1.31207	+	0.600425i
$596$	1.25399	−	1.05222i	0.0513653	−	0.0431006i
$597$	14.0513	+	14.2769i	0.575081	+	0.584313i
$598$	−13.6765	+	4.97784i	−0.559274	+	0.203559i
$599$	11.4990	+	9.64879i	0.469836	+	0.394239i	0.846735	−	0.532016i	$-0.178565\pi$
$599$	11.4990	+	9.64879i	0.469836	+	0.394239i	−0.376899	+	0.926254i	$0.623010\pi$
$600$	−2.62977	+	3.69276i	−0.107360	+	0.150756i
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	0.493276	+	0.869873i	$0.335799\pi$
$601$	8.02293	+	45.5003i	0.327262	+	1.85600i	−0.166014	+	0.986123i	$0.553090\pi$
$602$	47.1518	+	21.5775i	1.92176	+	0.879434i
$603$	−37.4097	−	7.21244i	−1.52344	−	0.293713i
$604$	9.10757	+	15.7748i	0.370582	+	0.641866i
$605$	5.30855	+	30.1063i	0.215823	+	1.22399i
$606$	−0.228037	−	2.86947i	−0.00926337	−	0.116564i
$607$	34.1836	−	12.4418i	1.38747	−	0.504998i	0.463037	−	0.886339i	$-0.346760\pi$
$607$	34.1836	−	12.4418i	1.38747	−	0.504998i	0.924434	+	0.381341i	$0.124538\pi$
$608$	−29.3288	−	24.6098i	−1.18944	−	0.998060i
$609$	6.69786	−	18.3564i	0.271411	−	0.743839i
$610$	−63.5542	−	23.1318i	−2.57323	−	0.936581i
$611$	−9.11212	−	15.7827i	−0.368637	−	0.638498i
$612$	6.94343	+	20.0656i	0.280672	+	0.811103i
$613$	8.08643	−	14.0061i	0.326608	−	0.565701i	−0.655229	−	0.755431i	$-0.727428\pi$
$613$	8.08643	−	14.0061i	0.326608	−	0.565701i	0.981836	+	0.189729i	$0.0607611\pi$
$614$	−42.7001	−	15.5416i	−1.72323	−	0.627206i
$615$	−1.66020	−	0.158580i	−0.0669457	−	0.00639455i
$616$	−2.13021	−	4.48414i	−0.0858287	−	0.180671i
$617$	8.46705	−	48.0190i	0.340871	−	1.93317i	−0.0181293	−	0.999836i	$-0.505771\pi$
$617$	8.46705	−	48.0190i	0.340871	−	1.93317i	0.359000	−	0.933338i	$-0.383118\pi$
$618$	1.71335	+	1.74086i	0.0689212	+	0.0700277i
$619$	−7.95236	−	2.89442i	−0.319633	−	0.116337i	0.177221	−	0.984171i	$-0.443289\pi$
$619$	−7.95236	−	2.89442i	−0.319633	−	0.116337i	−0.496854	+	0.867834i	$0.665511\pi$
$620$	6.98564	+	12.0995i	0.280550	+	0.485927i
$621$	11.5187	−	0.731001i	0.462229	−	0.0293341i
$622$	−48.4813			−1.94392
$623$	8.17218	−	31.3966i	0.327411	−	1.25788i
$624$	17.9384	+	18.2264i	0.718111	+	0.729639i
$625$	−13.1334	−	11.0202i	−0.525335	−	0.440809i
$626$	−35.1354	−	29.4821i	−1.40429	−	1.17834i
$627$	−22.4275	+	31.4930i	−0.895667	+	1.25771i
$628$	7.02172	+	2.55570i	0.280197	+	0.101983i
$629$	−5.94644	−	10.2995i	−0.237100	−	0.410669i
$630$	49.9221	+	13.8467i	1.98894	+	0.551665i
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	−0.266433	−	0.963853i	$-0.585845\pi$
$631$	17.6216	−	30.5215i	0.701505	−	1.21504i	0.967938	−	0.251189i	$-0.0808216\pi$
$632$	−0.397463	+	0.333511i	−0.0158102	+	0.0132663i
$633$	34.6669	+	16.5028i	1.37789	+	0.655927i
$634$	−5.12283	+	29.0530i	−0.203454	+	1.15384i
$635$	−5.66679	+	2.06254i	−0.224880	+	0.0818495i
$636$	2.50763	+	31.5544i	0.0994340	+	1.25121i
$637$	−8.37983	−	22.0361i	−0.332021	−	0.873104i
$638$	−18.6015	+	32.2187i	−0.736439	+	1.27555i
$639$	14.2972	+	8.56091i	0.565587	+	0.338664i
$640$	−5.58236	+	9.66894i	−0.220662	+	0.382198i
$641$	4.44072	−	3.72621i	0.175398	−	0.147176i	−0.550863	−	0.834596i	$-0.685701\pi$
$641$	4.44072	−	3.72621i	0.175398	−	0.147176i	0.726260	+	0.687420i	$0.241257\pi$
$642$	−17.5362	−	38.4019i	−0.692098	−	1.51560i
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	−0.242781	−	0.970081i	$-0.578060\pi$
$643$	4.93946	−	1.79782i	0.194793	−	0.0708990i	0.437575	+	0.899182i	$0.355838\pi$
$644$	−5.95500	+	8.63559i	−0.234660	+	0.340290i
$645$	−56.6644	+	14.7006i	−2.23116	+	0.578835i
$646$	−6.66757	−	37.8137i	−0.262332	−	1.48776i
$647$	−9.29941	−	16.1071i	−0.365598	−	0.633234i	0.623274	−	0.782003i	$-0.285802\pi$
$647$	−9.29941	−	16.1071i	−0.365598	−	0.633234i	−0.988872	+	0.148770i	$0.952469\pi$
$648$	−1.77798	−	3.31939i	−0.0698456	−	0.130398i
$649$	7.49531	−	12.9823i	0.294217	−	0.509598i
$650$	31.3999	−	26.3477i	1.23161	−	1.03344i
$651$	−6.87888	+	8.18459i	−0.269604	+	0.320779i
$652$	−3.10734	+	17.6226i	−0.121693	+	0.690154i
$653$	3.41885	−	19.3892i	0.133790	−	0.758760i	−0.841905	−	0.539626i	$-0.818566\pi$
$653$	3.41885	−	19.3892i	0.133790	−	0.758760i	0.975695	−	0.219134i	$-0.0703232\pi$
$654$	16.4529	+	1.57156i	0.643360	+	0.0614527i
$655$	−22.9422	+	19.2508i	−0.896425	+	0.752190i
$656$	−1.25818			−0.0491237
$657$	−11.8418	−	7.09068i	−0.461992	−	0.276634i
$658$	−25.3264	−	11.5898i	−0.987327	−	0.451819i
$659$	39.3495	+	14.3220i	1.53284	+	0.557907i	0.964314	−	0.264760i	$-0.0852929\pi$
$659$	39.3495	+	14.3220i	1.53284	+	0.557907i	0.568523	+	0.822667i	$0.307515\pi$
$660$	−41.9997	−	19.9935i	−1.63484	−	0.778245i
$661$	−6.38080	+	36.1873i	−0.248184	+	1.40752i	0.564795	+	0.825231i	$0.308955\pi$
$661$	−6.38080	+	36.1873i	−0.248184	+	1.40752i	−0.812980	+	0.582292i	$0.802156\pi$
$662$	−5.51247	+	31.2628i	−0.214248	+	1.21506i
$663$	1.83244	+	23.0582i	0.0711660	+	0.895507i
$664$	−4.47574	−	1.62904i	−0.173692	−	0.0632189i
$665$	−40.1745	−	18.3846i	−1.55790	−	0.712924i
$666$	−11.0373	−	13.5874i	−0.427685	−	0.526501i
$667$	−9.47137			−0.366733
$668$	20.8646	−	17.5075i	0.807276	−	0.677385i
$669$	−17.8940	+	25.1271i	−0.691823	+	0.971468i
$670$	−14.3938	+	81.6311i	−0.556080	+	3.15369i
$671$	−8.06939	+	45.7638i	−0.311515	+	1.76669i
$672$	34.7087	+	6.14877i	1.33892	+	0.237194i
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	−0.910613	−	0.413261i	$-0.864390\pi$
$673$	−17.1674	+	14.4052i	−0.661756	+	0.555280i	0.248856	+	0.968540i	$0.419945\pi$
$674$	−0.101452	+	0.175720i	−0.00390778	+	0.00676847i
$675$	−29.7800	+	13.0299i	−1.14623	+	0.501521i
$676$	1.47871	+	2.56120i	0.0568733	+	0.0985075i
$677$	−2.90202	−	16.4582i	−0.111534	−	0.632540i	−0.988408	−	0.151820i	$-0.951487\pi$
$677$	−2.90202	−	16.4582i	−0.111534	−	0.632540i	0.876874	−	0.480720i	$-0.159625\pi$
$678$	−4.45535	+	16.1132i	−0.171107	+	0.618826i
$679$	16.5852	−	24.0508i	0.636480	−	0.922986i
$680$	−5.23032	+	1.90368i	−0.200573	+	0.0730028i
$681$	3.22329	−	4.52619i	0.123517	−	0.173444i
$682$	15.5933	−	13.0843i	0.597098	−	0.501025i
$683$	11.7796	−	20.4029i	0.450734	−	0.780693i	−0.547698	−	0.836676i	$-0.684496\pi$
$683$	11.7796	−	20.4029i	0.450734	−	0.780693i	0.998432	+	0.0559825i	$0.0178291\pi$
$684$	−8.71586	−	25.1877i	−0.333259	−	0.963075i
$685$	31.5525	−	54.6505i	1.20556	−	2.08809i
$686$	−29.9520	−	20.0277i	−1.14357	−	0.764662i
$687$	−6.32464	−	3.01077i	−0.241300	−	0.114868i
$688$	−41.5002	+	15.1049i	−1.58218	+	0.575867i
$689$	−5.98797	+	33.9595i	−0.228123	+	1.29375i
$690$	−1.98933	−	25.0325i	−0.0757326	−	0.952970i
$691$	−0.829616	+	0.696131i	−0.0315601	+	0.0264821i	−0.658431	−	0.752641i	$-0.728780\pi$
$691$	−0.829616	+	0.696131i	−0.0315601	+	0.0264821i	0.626871	+	0.779123i	$0.284335\pi$
$692$	8.39328	−	14.5376i	0.319065	−	0.552636i
$693$	3.41306	−	35.4318i	0.129651	−	1.34594i
$694$	−24.2680	−	42.0334i	−0.921200	−	1.59557i
$695$	−52.4154	−	19.0777i	−1.98823	−	0.723657i
$696$	1.28358	+	2.81087i	0.0486540	+	0.106546i
$697$	−0.871776	−	0.731507i	−0.0330209	−	0.0277078i
$698$	43.3051	+	36.3373i	1.63912	+	1.37539i
$699$	7.08425	−	25.6209i	0.267951	−	0.969072i
$700$	7.44168	−	28.5902i	0.281269	−	1.08061i
$701$	39.4989			1.49185			0.745927	−	0.666028i	$-0.232007\pi$
$701$	39.4989			1.49185			0.745927	+	0.666028i	$0.232007\pi$
$702$	8.02391	+	33.0879i	0.302843	+	1.24882i
$703$	7.46437	+	12.9287i	0.281524	+	0.487614i
$704$	−26.1152	−	9.50516i	−0.984254	−	0.358239i
$705$	30.4359	−	7.89606i	1.14628	−	0.297383i
$706$	−1.48310	+	8.41107i	−0.0558172	+	0.316555i
$707$	−0.969804	−	2.04145i	−0.0364732	−	0.0767768i
$708$	4.29268	+	9.40041i	0.161329	+	0.353289i
$709$	44.8746	+	16.3330i	1.68530	+	0.613400i	0.994021	−	0.109187i	$-0.0348247\pi$
$709$	44.8746	+	16.3330i	1.68530	+	0.613400i	0.691280	+	0.722587i	$0.257047\pi$
$710$	18.1281	−	31.3987i	0.680334	−	1.17837i
$711$	−3.67357	+	0.587589i	−0.137770	+	0.0220363i
$712$	2.56524	+	4.44313i	0.0961364	+	0.166513i
$713$	4.86973	+	1.77244i	0.182373	+	0.0663783i
$714$	22.7016	+	27.0989i	0.849588	+	1.01415i
$715$	−38.8183	−	32.5724i	−1.45172	−	1.21814i
$716$	−4.81997	+	1.75432i	−0.180131	+	0.0655622i
$717$	2.15568	−	1.48399i	0.0805055	−	0.0554205i
$718$	2.27525	+	12.9036i	0.0849116	+	0.481558i
$719$	−0.374888	−	0.649326i	−0.0139810	−	0.0242158i	0.858950	−	0.512059i	$-0.171117\pi$
$719$	−0.374888	−	0.649326i	−0.0139810	−	0.0242158i	−0.872931	+	0.487843i	$0.837784\pi$
$720$	−38.5582	+	21.4502i	−1.43698	+	0.799402i
$721$	1.74389	+	0.798036i	0.0649459	+	0.0297204i
$722$	1.95079	+	11.0635i	0.0726011	+	0.411741i
$723$	13.8079	+	30.2375i	0.513522	+	1.12455i
$724$	6.22115	+	5.22016i	0.231207	+	0.194006i
$725$	25.0659	−	9.12325i	0.930925	−	0.338829i
$726$	−8.18295	+	29.5945i	−0.303698	+	1.09835i
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.241798	−	0.970327i	$-0.422263\pi$
$727$	33.4171	−	28.0403i	1.23937	−	1.03996i	0.997573	−	0.0696290i	$-0.0221815\pi$
$728$	3.39014	+	1.55139i	0.125647	+	0.0574982i
$729$	1.28953	−	26.9692i	0.0477602	−	0.998859i
$730$	−15.0148	+	26.0064i	−0.555722	+	0.962539i
$731$	−37.5370	−	13.6623i	−1.38835	−	0.505320i
$732$	−22.4711	−	22.8319i	−0.830558	−	0.843892i
$733$	−16.8320	−	14.1238i	−0.621705	−	0.521673i	0.276634	−	0.960975i	$-0.410781\pi$
$733$	−16.8320	−	14.1238i	−0.621705	−	0.521673i	−0.898339	+	0.439303i	$0.855226\pi$
$734$	−15.1624	+	5.51867i	−0.559655	+	0.203698i
$735$	40.4985	−	3.80284i	1.49381	−	0.140270i
$736$	−2.96690	−	16.8261i	−0.109361	−	0.620219i
$737$	56.9530			2.09789
$738$	−1.43714	−	0.860537i	−0.0529019	−	0.0316768i
$739$	40.1114			1.47552			0.737761	−	0.675062i	$-0.235883\pi$
$739$	40.1114			1.47552			0.737761	+	0.675062i	$0.235883\pi$
$740$	−13.7590	+	11.5451i	−0.505789	+	0.424408i
$741$	−2.30020	−	28.9442i	−0.0845000	−	1.06329i
$742$	22.6140	+	47.6029i	0.830186	+	1.74756i
$743$	−6.31887	−	5.30216i	−0.231817	−	0.194518i	0.519479	−	0.854484i	$-0.326126\pi$
$743$	−6.31887	−	5.30216i	−0.231817	−	0.194518i	−0.751295	+	0.659966i	$0.770571\pi$
$744$	−0.133940	−	1.68542i	−0.00491050	−	0.0617905i
$745$	0.534284	+	3.03008i	0.0195747	+	0.111013i
$746$	22.7721			0.833747
$747$	−21.5328	−	26.5079i	−0.787844	−	0.969874i
$748$	−15.8704	−	27.4884i	−0.580280	−	1.00507i
$749$	−23.6055	−	23.2698i	−0.862526	−	0.850260i
$750$	5.89700	+	12.9136i	0.215328	+	0.471539i
$751$	−4.27142	+	24.2244i	−0.155866	+	0.883962i	0.802123	+	0.597159i	$0.203704\pi$
$751$	−4.27142	+	24.2244i	−0.155866	+	0.883962i	−0.957989	+	0.286803i	$0.907407\pi$
$752$	22.2908	−	8.11320i	0.812863	−	0.295858i
$753$	4.10809	−	14.8573i	0.149707	−	0.541431i
$754$	−4.85160	−	27.5148i	−0.176685	−	1.00203i
$755$	−34.2370			−1.24601
$756$	18.5314	+	16.0855i	0.673980	+	0.585024i
$757$	−20.6308			−0.749839			−0.374920	−	0.927057i	$-0.622330\pi$
$757$	−20.6308			−0.749839			−0.374920	+	0.927057i	$0.622330\pi$
$758$	−9.09447	−	51.5773i	−0.330326	−	1.87337i
$759$	−16.7009	+	4.33274i	−0.606203	+	0.157269i
$760$	6.56544	−	2.38963i	0.238154	−	0.0866809i
$761$	−2.38678	+	13.5361i	−0.0865206	+	0.490682i	0.910498	+	0.413514i	$0.135699\pi$
$761$	−2.38678	+	13.5361i	−0.0865206	+	0.490682i	−0.997018	+	0.0771680i	$0.975412\pi$
$762$	−6.02951	−	0.575929i	−0.218426	−	0.0208637i
$763$	12.5104	−	3.44837i	0.452908	−	0.124839i
$764$	15.8203	+	27.4015i	0.572358	+	0.991353i
$765$	−39.1876	−	7.55522i	−1.41683	−	0.273160i
$766$	32.5518			1.17615
$767$	1.95491	+	11.0869i	0.0705878	+	0.400323i
$768$	−26.9189	+	18.5311i	−0.971351	+	0.668683i
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	0.828099	−	0.560582i	$-0.189423\pi$
$769$	11.6423	+	9.76902i	0.419831	+	0.352280i	−0.408268	+	0.912862i	$0.633867\pi$
$770$	−77.1968	−	6.19712i	−2.78198	−	0.223329i
$771$	15.3522	+	7.30825i	0.552897	+	0.263200i
$772$	26.9249	−	22.5926i	0.969047	−	0.813127i
$773$	38.0394			1.36818			0.684091	−	0.729397i	$-0.260199\pi$
$773$	38.0394			1.36818			0.684091	+	0.729397i	$0.260199\pi$
$774$	−57.7342	−	11.1309i	−2.07521	−	0.400092i
$775$	−14.5950			−0.524268
$776$	0.802259	+	4.54984i	0.0287994	+	0.163330i
$777$	−11.8976	−	6.88182i	−0.426825	−	0.246884i
$778$	−2.92748	+	1.06551i	−0.104955	+	0.0382005i
$779$	1.09431	+	0.918237i	0.0392078	+	0.0328992i
$780$	33.8138	−	8.77238i	1.21073	−	0.314102i
$781$	−23.4088	−	8.52011i	−0.837633	−	0.304874i
$782$	8.56760	−	14.8395i	0.306377	−	0.530660i
$783$	−2.45775	+	22.0198i	−0.0878329	+	0.786922i
$784$	30.1415	−	5.76104i	1.07648	−	0.205751i
$785$	−10.7591	+	9.02794i	−0.384008	+	0.322221i
$786$	−29.1165	+	7.55377i	−1.03855	+	0.269434i
$787$	−14.2005	+	5.16858i	−0.506195	+	0.184240i	−0.582478	−	0.812846i	$-0.697917\pi$
$787$	−14.2005	+	5.16858i	−0.506195	+	0.184240i	0.0762834	+	0.997086i	$0.475695\pi$
$788$	−26.3526	−	22.1125i	−0.938774	−	0.787725i
$789$	−12.8519	−	1.22759i	−0.457540	−	0.0437035i
$790$	1.40553	+	7.97115i	0.0500065	+	0.283601i
$791$	1.23764	+	13.0677i	0.0440054	+	0.464635i
$792$	3.54918	+	4.36922i	0.126115	+	0.155253i
$793$	−17.4493	−	30.2231i	−0.619643	−	1.07325i
$794$	4.00038	+	22.6873i	0.141968	+	0.805141i
$795$	−53.7201	−	25.5728i	−1.90526	−	0.906975i
$796$	19.3984	−	7.06044i	0.687558	−	0.250251i
$797$	−0.774338	−	0.649747i	−0.0274285	−	0.0230152i	0.628970	−	0.777429i	$-0.283477\pi$
$797$	−0.774338	−	0.649747i	−0.0274285	−	0.0230152i	−0.656399	+	0.754414i	$0.727921\pi$
$798$	−28.4966	−	34.0163i	−1.00877	−	1.20416i
$799$	20.1621	+	7.33839i	0.713282	+	0.259613i
$800$	24.0595	+	41.6723i	0.850633	+	1.47334i
$801$	−0.585844	+	36.7820i	−0.0206998	+	1.29963i
$802$	−0.152386	+	0.263940i	−0.00538093	+	0.00932004i
$803$	19.3886	+	7.05689i	0.684210	+	0.249032i
$804$	−22.7751	+	31.9812i	−0.803217	+	1.12789i
$805$	−8.46030	−	17.8091i	−0.298187	−	0.627688i
$806$	−2.65456	+	15.0547i	−0.0935027	+	0.530280i
$807$	7.95067	−	28.7544i	0.279877	−	1.01220i
$808$	0.335857	+	0.122242i	0.0118154	+	0.00430045i
$809$	1.37661	+	2.38435i	0.0483989	+	0.0838293i	0.889210	−	0.457499i	$-0.151255\pi$
$809$	1.37661	+	2.38435i	0.0483989	+	0.0838293i	−0.840811	+	0.541329i	$0.817921\pi$
$810$	−58.7136	−	1.87079i	−2.06299	−	0.0657330i
$811$	33.2392			1.16718			0.583592	−	0.812047i	$-0.301647\pi$
$811$	33.2392			1.16718			0.583592	+	0.812047i	$0.301647\pi$
$812$	−14.3405	−	14.1366i	−0.503253	−	0.496097i
$813$	−1.38333	+	0.358880i	−0.0485155	+	0.0125865i
$814$	20.0462	+	16.8208i	0.702620	+	0.589569i
$815$	−25.7653	−	21.6197i	−0.902520	−	0.757305i
$816$	−29.9717	−	2.86285i	−1.04922	−	0.100220i
$817$	47.1189	+	17.1499i	1.64848	+	0.599998i
$818$	26.1428	+	45.2807i	0.914062	+	1.58320i
$819$	15.1405	+	22.0314i	0.529052	+	0.769839i
$820$	−0.859341	+	1.48842i	−0.0300095	+	0.0519780i
$821$	14.3062	−	12.0043i	0.499289	−	0.418953i	−0.358053	−	0.933701i	$-0.616559\pi$
$821$	14.3062	−	12.0043i	0.499289	−	0.418953i	0.857341	+	0.514749i	$0.172115\pi$
$822$	52.2074	−	35.9399i	1.82094	−	1.25355i
$823$	3.20620	−	18.1833i	0.111761	−	0.633829i	−0.876542	−	0.481326i	$-0.840155\pi$
$823$	3.20620	−	18.1833i	0.111761	−	0.633829i	0.988303	−	0.152503i	$-0.0487334\pi$
$824$	−0.284992	+	0.103729i	−0.00992817	+	0.00361356i
$825$	40.0252	−	27.5536i	1.39350	−	0.959293i
$826$	12.2530	+	12.0787i	0.426336	+	0.420273i
$827$	−9.06140	+	15.6948i	−0.315096	+	0.545762i	−0.979458	−	0.201649i	$-0.935370\pi$
$827$	−9.06140	+	15.6948i	−0.315096	+	0.545762i	0.664362	+	0.747411i	$0.268703\pi$
$828$	4.24557	−	11.1108i	0.147544	−	0.386126i
$829$	−4.26434	+	7.38606i	−0.148107	+	0.256529i	−0.930528	−	0.366221i	$-0.880651\pi$
$829$	−4.26434	+	7.38606i	−0.148107	+	0.256529i	0.782421	+	0.622750i	$0.213985\pi$
$830$	−56.9194	+	47.7611i	−1.97570	+	1.65781i
$831$	−19.8440	−	1.89547i	−0.688382	−	0.0657532i
$832$	19.6124	−	7.13834i	0.679939	−	0.247477i
$833$	24.2341	+	13.5325i	0.839662	+	0.468874i
$834$	−39.2985	−	39.9294i	−1.36079	−	1.38264i
$835$	8.88975	+	50.4163i	0.307643	+	1.74473i
$836$	19.9216	+	34.5052i	0.689003	+	1.19339i
$837$	5.38436	−	10.8616i	0.186111	−	0.375431i
$838$	23.4349	−	40.5904i	0.809545	−	1.40217i
$839$	−24.2173	+	20.3207i	−0.836073	+	0.701548i	−0.956677	−	0.291153i	$-0.905961\pi$
$839$	−24.2173	+	20.3207i	−0.836073	+	0.701548i	0.120604	+	0.992701i	$0.461517\pi$
$840$	−4.13874	+	4.92433i	−0.142800	+	0.169906i
$841$	−1.87855	+	10.6538i	−0.0647776	+	0.367372i
$842$	1.24886	−	7.08261i	0.0430384	−	0.244083i
$843$	17.5604	+	38.4550i	0.604813	+	1.32446i
$844$	30.3100	−	25.4331i	1.04331	−	0.875444i
$845$	−5.55873			−0.191226
$846$	31.0105	+	5.97870i	1.06616	+	0.205552i
$847$	2.27312	+	24.0009i	0.0781052	+	0.824682i
$848$	−42.1780	−	15.3515i	−1.44840	−	0.527174i
$849$	−0.854884	+	0.588507i	−0.0293395	+	0.0201975i
$850$	−8.38001	+	47.5254i	−0.287432	+	1.63011i
$851$	−1.15687	+	6.56094i	−0.0396570	+	0.224906i
$852$	14.1454	−	9.73777i	0.484613	−	0.333610i
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	0.00599331	−	0.999982i	$-0.498092\pi$
$853$	−18.4639	−	6.72031i	−0.632192	−	0.230099i	−0.638185	+	0.769883i	$0.720314\pi$
$854$	−48.4990	−	22.1940i	−1.65960	−	0.759464i
$855$	49.1910	+	9.48382i	1.68230	+	0.324340i
$856$	5.24180			0.179161
$857$	1.19408	−	1.00195i	0.0407889	−	0.0342260i	−0.622165	−	0.782886i	$-0.713747\pi$
$857$	1.19408	−	1.00195i	0.0407889	−	0.0342260i	0.662954	+	0.748660i	$0.269302\pi$
$858$	−21.1417	−	46.2974i	−0.721764	−	1.58057i
$859$	−8.53280	+	48.3919i	−0.291135	+	1.65111i	0.391372	+	0.920233i	$0.372001\pi$
$859$	−8.53280	+	48.3919i	−0.291135	+	1.65111i	−0.682507	+	0.730879i	$0.739110\pi$
$860$	−10.4758	+	59.4113i	−0.357223	+	2.02591i
$861$	−1.29504	−	0.229422i	−0.0441350	−	0.00781868i
$862$	−3.51721	+	2.95129i	−0.119797	+	0.100521i
$863$	4.07047	−	7.05026i	0.138560	−	0.239994i	−0.788391	−	0.615174i	$-0.789086\pi$
$863$	4.07047	−	7.05026i	0.138560	−	0.239994i	0.926952	+	0.375180i	$0.122419\pi$
$864$	−39.8885	+	2.53141i	−1.35703	+	0.0861204i
$865$	15.7759	+	27.3247i	0.536398	+	0.929069i
$866$	5.25784	+	29.8187i	0.178669	+	1.01328i
$867$	1.55165	+	1.57656i	0.0526968	+	0.0535428i
$868$	4.72775	+	9.95200i	0.160470	+	0.337793i
$869$	5.22598	−	1.90210i	0.177279	−	0.0645243i
$870$	47.9871	+	4.58365i	1.62691	+	0.155400i
$871$	−32.7649	+	27.4930i	−1.11019	+	0.931564i
$872$	−1.02609	+	1.77723i	−0.0347477	+	0.0601847i
$873$	−11.8243	+	30.9444i	−0.400190	+	1.04731i
$874$	−10.7546	+	18.6276i	−0.363781	+	0.630087i
$875$	7.93796	+	7.82507i	0.268352	+	0.264536i
$876$	−11.7161	+	8.06542i	−0.395850	+	0.272505i
$877$	−42.5608	+	15.4908i	−1.43717	+	0.523089i	−0.938979	−	0.343976i	$-0.888226\pi$
$877$	−42.5608	+	15.4908i	−1.43717	+	0.523089i	−0.498196	+	0.867064i	$0.666004\pi$
$878$	13.3092	−	75.4803i	0.449164	−	2.54734i
$879$	−11.7409	+	8.08248i	−0.396010	+	0.272615i
$880$	50.5274	−	42.3976i	1.70328	−	1.42922i
$881$	0.111855	−	0.193739i	0.00376850	−	0.00652724i	−0.864135	−	0.503260i	$-0.832134\pi$
$881$	0.111855	−	0.193739i	0.00376850	−	0.00652724i	0.867904	+	0.496733i	$0.165467\pi$
$882$	38.3690	+	14.0349i	1.29195	+	0.472579i
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.741443	+	0.671016i	$0.234142\pi$
$883$	28.2842	+	48.9896i	0.951838	+	1.64863i	0.210396	+	0.977616i	$0.432525\pi$
$884$	22.3997	+	8.15282i	0.753383	+	0.274209i
$885$	−19.3360	−	1.84694i	−0.649972	−	0.0620843i
$886$	−4.63917	−	3.89273i	−0.155856	−	0.130779i
$887$	−0.835656	−	0.701199i	−0.0280586	−	0.0235440i	0.628651	−	0.777688i	$-0.283608\pi$
$887$	−0.835656	−	0.701199i	−0.0280586	−	0.0235440i	−0.656709	+	0.754144i	$0.728052\pi$
$888$	2.10391	−	0.545821i	0.0706025	−	0.0183166i
$889$	−4.58471	+	1.26373i	−0.153766	+	0.0423840i
$890$	80.0360			2.68281
$891$	5.73934	+	39.9517i	0.192275	+	1.33843i
$892$	15.8947	+	27.5304i	0.532194	+	0.921787i
$893$	−25.3088	−	9.21164i	−0.846926	−	0.308256i
$894$	−0.823581	+	2.97857i	−0.0275447	+	0.0996182i
$895$	1.67414	−	9.49452i	0.0559603	−	0.317367i
$896$	−4.99834	+	7.24829i	−0.166983	+	0.242148i
$897$	7.51639	−	10.5546i	0.250965	−	0.352409i
$898$	−27.2600	−	9.92183i	−0.909678	−	0.331096i
$899$	−4.97410	+	8.61540i	−0.165896	+	0.287340i
$900$	−0.533477	+	33.4941i	−0.0177826	+	1.11647i
$901$	−20.2992	−	35.1592i	−0.676264	−	1.17132i
$902$	2.35304	+	0.856436i	0.0783476	+	0.0285162i
$903$	−45.4705	+	7.98009i	−1.51316	+	0.265561i
$904$	−1.59013	−	1.33428i	−0.0528871	−	0.0443775i
$905$	−14.3439	+	5.22074i	−0.476806	+	0.173543i
$906$	−31.0488	−	14.7804i	−1.03153	−	0.491047i
$907$	7.18272	+	40.7352i	0.238498	+	1.35259i	0.835120	+	0.550068i	$0.185398\pi$
$907$	7.18272	+	40.7352i	0.238498	+	1.35259i	−0.596621	+	0.802523i	$0.703490\pi$
$908$	−2.86315	−	4.95911i	−0.0950168	−	0.164574i
$909$	1.61581	+	1.98914i	0.0535930	+	0.0659755i
$910$	47.4026	−	33.7001i	1.57138	−	1.11715i
$911$	−6.65639	−	37.7502i	−0.220536	−	1.25072i	−0.871037	−	0.491217i	$-0.836552\pi$
$911$	−6.65639	−	37.7502i	−0.220536	−	1.25072i	0.650502	−	0.759505i	$-0.274559\pi$
$912$	37.6225	+	3.59365i	1.24581	+	0.118998i
$913$	39.1086	+	32.8160i	1.29431	+	1.08605i
$914$	50.5863	−	18.4119i	1.67324	−	0.609011i
$915$	58.2835	−	15.1206i	1.92679	−	0.499872i
$916$	−5.52977	+	4.64003i	−0.182709	+	0.153311i
$917$	−19.2492	+	13.6849i	−0.635665	+	0.451916i
$918$	−32.2768	−	23.7693i	−1.06529	−	0.784505i
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	−0.904003	−	0.427526i	$-0.859385\pi$
$919$	−2.47835	+	4.29263i	−0.0817533	+	0.141601i	0.822250	+	0.569127i	$0.192719\pi$
$920$	2.92992	+	1.06640i	0.0965966	+	0.0351583i
$921$	39.1588	−	10.1591i	1.29033	−	0.334753i
$922$	−52.4636	−	44.0222i	−1.72780	−	1.44979i
$923$	17.5799	−	6.39857i	0.578651	−	0.210612i
$924$	−31.7535	−	18.3668i	−1.04461	−	0.604225i
$925$	−3.25814	−	18.4778i	−0.107127	−	0.607547i
$926$	−40.8537			−1.34253
$927$	−2.13528	−	0.411673i	−0.0701317	−	0.0135211i
$928$	32.7988			1.07667
$929$	18.8911	−	15.8515i	0.619796	−	0.520071i	−0.277943	−	0.960597i	$-0.589653\pi$
$929$	18.8911	−	15.8515i	0.619796	−	0.520071i	0.897739	+	0.440527i	$0.145208\pi$
$930$	−23.8149	−	11.3368i	−0.780922	−	0.371749i
$931$	−30.4203	−	16.9869i	−0.996984	−	0.556725i
$932$	−20.9850	−	17.6085i	−0.687387	−	0.576786i
$933$	35.5526	−	24.4746i	1.16394	−	0.801263i
$934$	−12.2419	−	69.4273i	−0.400567	−	2.27173i
$935$	59.6598			1.95108
$936$	−4.15099	−	0.800294i	−0.135679	−	0.0261584i
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	−0.980173	−	0.198144i	$-0.936509\pi$
$937$	−20.2545	−	35.0818i	−0.661684	−	1.14607i	0.318488	−	0.947927i	$-0.396825\pi$
$938$	−16.4659	+	63.2604i	−0.537632	+	2.06552i
$939$	40.6490	+	3.88272i	1.32653	+	0.126708i
$940$	5.62683	−	31.9113i	0.183527	−	1.04083i
$941$	22.1138	−	8.04877i	0.720890	−	0.262382i	0.0445863	−	0.999006i	$-0.485803\pi$
$941$	22.1138	−	8.04877i	0.720890	−	0.262382i	0.676303	+	0.736623i	$0.263581\pi$
$942$	−13.6546	+	3.54245i	−0.444892	+	0.115419i
$943$	0.110700	+	0.627813i	0.00360490	+	0.0204444i
$944$	−14.6537			−0.476938
$945$	−43.5993	+	15.0478i	−1.41828	+	0.489506i
$946$	87.8953			2.85772
$947$	4.82267	+	27.3507i	0.156716	+	0.888779i	0.957200	+	0.289426i	$0.0934644\pi$
$947$	4.82267	+	27.3507i	0.156716	+	0.888779i	−0.800485	+	0.599353i	$0.795425\pi$
$948$	−1.02174	+	3.69522i	−0.0331844	+	0.120015i
$949$	−14.5608	+	5.29970i	−0.472663	+	0.172035i
$950$	10.5191	−	59.6571i	0.341286	−	1.93553i
$951$	−10.9100	−	23.8915i	−0.353781	−	0.774734i
$952$	−4.23158	+	1.16639i	−0.137146	+	0.0378029i
$953$	−21.0460	−	36.4528i	−0.681748	−	1.18082i	−0.974447	−	0.224617i	$-0.927887\pi$
$953$	−21.0460	−	36.4528i	−0.681748	−	1.18082i	0.292699	−	0.956204i	$-0.405446\pi$
$954$	−37.6776	−	46.3829i	−1.21986	−	1.50170i
$955$	−59.4713			−1.92445
$956$	−0.468331	−	2.65604i	−0.0151469	−	0.0859024i
$957$	−2.62389	−	33.0173i	−0.0848182	−	1.06730i
$958$	−48.5975	−	40.7781i	−1.57011	−	1.31748i
$959$	28.2515	−	40.9686i	0.912287	−	1.32294i
$960$	2.85275	+	35.8971i	0.0920720	+	1.15857i
$961$	−19.5777	+	16.4276i	−0.631538	+	0.529923i
$962$	−19.6525			−0.633621
$963$	32.2460	+	19.3084i	1.03911	+	0.622204i
$964$	34.2561			1.10331
$965$	11.4718	+	65.0601i	0.369292	+	2.09436i
$966$	0.0158771	−	19.8031i	0.000510838	−	0.637154i
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.524417	−	0.851461i	$-0.324283\pi$
$967$	45.8194	−	16.6769i	1.47345	−	0.536293i	0.949036	+	0.315168i	$0.102061\pi$
$968$	−2.92053	−	2.45061i	−0.0938693	−	0.0787657i
$969$	23.9788	+	24.3638i	0.770311	+	0.782677i
$970$	67.7263	+	24.6504i	2.17456	+	0.791475i
$971$	−1.76073	+	3.04968i	−0.0565045	+	0.0978687i	−0.892894	−	0.450267i	$-0.851329\pi$
$971$	−1.76073	+	3.04968i	−0.0565045	+	0.0978687i	0.836390	+	0.548136i	$0.184662\pi$
$972$	−24.7295	−	12.7536i	−0.793198	−	0.409071i
$973$	−39.9989	−	18.3042i	−1.28231	−	0.586806i
$974$	46.2017	−	38.7678i	1.48040	−	1.24220i
$975$	−9.72539	+	35.1729i	−0.311462	+	1.12643i
$976$	42.6860	−	15.5364i	1.36635	−	0.497309i
$977$	2.69837	+	2.26420i	0.0863286	+	0.0724383i	0.684931	−	0.728608i	$-0.259832\pi$
$977$	2.69837	+	2.26420i	0.0863286	+	0.0724383i	−0.598602	+	0.801047i	$0.704277\pi$
$978$	−14.0326	−	30.7296i	−0.448714	−	0.982624i
$979$	−9.54922	−	54.1563i	−0.305194	−	1.73084i
$980$	13.7714	−	39.5921i	0.439912	−	1.26472i
$981$	−12.8587	+	7.15339i	−0.410547	+	0.228390i
$982$	40.5430	+	70.2225i	1.29378	+	2.24089i
$983$	−4.48086	−	25.4122i	−0.142917	−	0.810524i	−0.969016	−	0.246999i	$-0.920556\pi$
$983$	−4.48086	−	25.4122i	−0.142917	−	0.810524i	0.826098	−	0.563526i	$-0.190555\pi$
$984$	0.171317	−	0.117936i	0.00546139	−	0.00375965i
$985$	60.7602	−	22.1149i	1.93598	−	0.704640i
$986$	25.1981	+	21.1438i	0.802472	+	0.673354i
$987$	24.4234	−	4.28631i	0.777404	−	0.136435i
$988$	−28.1176	−	10.2340i	−0.894540	−	0.325586i
$989$	11.1885	+	19.3790i	0.355773	+	0.616217i
$990$	86.7123	−	13.8697i	2.75590	−	0.440807i
$991$	23.5548	−	40.7982i	0.748244	−	1.29600i	−0.200420	−	0.979710i	$-0.564231\pi$
$991$	23.5548	−	40.7982i	0.748244	−	1.29600i	0.948664	−	0.316287i	$-0.102436\pi$
$992$	−16.8636	−	6.13785i	−0.535420	−	0.194877i
$993$	−11.7398	−	25.7086i	−0.372552	−	0.815839i
$994$	16.2315	−	23.5380i	0.514832	−	0.746579i
$995$	−6.73773	+	38.2116i	−0.213600	+	1.21139i
$996$	−34.0667	+	8.83800i	−1.07944	+	0.280043i
$997$	0.455226	+	0.165689i	0.0144172	+	0.00524742i	0.349219	−	0.937041i	$-0.386447\pi$
$997$	0.455226	+	0.165689i	0.0144172	+	0.00524742i	−0.334801	+	0.942289i	$0.608669\pi$
$998$	−17.3327	−	30.0211i	−0.548656	−	0.950300i
$999$	14.9532	+	4.39210i	0.473097	+	0.138960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.18	yes	132
3.2	odd	2		567.2.w.a.37.5		132
7.4	even	3		189.2.u.a.130.5	yes	132
21.11	odd	6		567.2.u.a.361.18		132
27.11	odd	18		567.2.u.a.289.18		132
27.16	even	9		189.2.u.a.16.5	✓	132
189.11	odd	18		567.2.w.a.46.5		132
189.151	even	9	inner	189.2.w.a.151.18	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.5	✓	132	27.16	even	9
189.2.u.a.130.5	yes	132	7.4	even	3
189.2.w.a.151.18	yes	132	189.151	even	9	inner
189.2.w.a.184.18	yes	132	1.1	even	1	trivial
567.2.u.a.289.18		132	27.11	odd	18
567.2.u.a.361.18		132	21.11	odd	6
567.2.w.a.37.5		132	3.2	odd	2
567.2.w.a.46.5		132	189.11	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.337831 + 1.91594i) q^{2} +(-1.21495 - 1.23446i) q^{3} +(-1.67729 + 0.610485i) q^{4} +(0.582582 - 3.30399i) q^{5} +(1.95469 - 2.74481i) q^{6} +(0.666452 - 2.56044i) q^{7} +(0.209199 + 0.362343i) q^{8} +(-0.0477764 + 2.99962i) q^{9} +O(q^{10})\)	\(q+(0.337831 + 1.91594i) q^{2} +(-1.21495 - 1.23446i) q^{3} +(-1.67729 + 0.610485i) q^{4} +(0.582582 - 3.30399i) q^{5} +(1.95469 - 2.74481i) q^{6} +(0.666452 - 2.56044i) q^{7} +(0.209199 + 0.362343i) q^{8} +(-0.0477764 + 2.99962i) q^{9} +6.52704 q^{10} +(-0.778751 - 4.41652i) q^{11} +(2.79145 + 1.32884i) q^{12} +(2.58000 + 2.16488i) q^{13} +(5.13078 + 0.411883i) q^{14} +(-4.78645 + 3.29502i) q^{15} +(-3.35824 + 2.81790i) q^{16} -3.96521 q^{17} +(-5.76322 + 0.921828i) q^{18} +4.97740 q^{19} +(1.03987 + 5.89742i) q^{20} +(-3.97046 + 2.28811i) q^{21} +(8.19868 - 2.98408i) q^{22} +(1.70156 + 1.42778i) q^{23} +(0.193131 - 0.698477i) q^{24} +(-5.87847 - 2.13959i) q^{25} +(-3.27617 + 5.67449i) q^{26} +(3.76095 - 3.58542i) q^{27} +(0.445273 + 4.70147i) q^{28} +(-3.26643 + 2.74086i) q^{29} +(-7.93005 - 8.05737i) q^{30} +(2.19236 - 0.797953i) q^{31} +(-5.89240 - 4.94431i) q^{32} +(-4.50586 + 6.32720i) q^{33} +(-1.33957 - 7.59708i) q^{34} +(-8.07139 - 3.69362i) q^{35} +(-1.75109 - 5.06041i) q^{36} +(1.49965 + 2.59748i) q^{37} +(1.68152 + 9.53637i) q^{38} +(-0.462129 - 5.81514i) q^{39} +(1.31905 - 0.480096i) q^{40} +(0.219856 + 0.184481i) q^{41} +(-5.72521 - 6.83416i) q^{42} +(9.46658 + 3.44555i) q^{43} +(4.00242 + 6.93239i) q^{44} +(9.88287 + 1.90538i) q^{45} +(-2.16069 + 3.74243i) q^{46} +(-5.08474 - 1.85069i) q^{47} +(7.55868 + 0.721993i) q^{48} +(-6.11168 - 3.41282i) q^{49} +(2.11338 - 11.9856i) q^{50} +(4.81754 + 4.89489i) q^{51} +(-5.64906 - 2.05609i) q^{52} +(5.11933 + 8.86693i) q^{53} +(8.14000 + 5.99448i) q^{54} -15.0458 q^{55} +(1.06718 - 0.294156i) q^{56} +(-6.04730 - 6.14439i) q^{57} +(-6.35481 - 5.33232i) q^{58} +(2.56062 + 2.14861i) q^{59} +(6.01672 - 8.44877i) q^{60} +(-9.73706 - 3.54400i) q^{61} +(2.26947 + 3.93084i) q^{62} +(7.64850 + 2.12143i) q^{63} +(3.09848 - 5.36673i) q^{64} +(8.65580 - 7.26308i) q^{65} +(-13.6447 - 6.49542i) q^{66} +(-2.20525 + 12.5066i) q^{67} +(6.65082 - 2.42070i) q^{68} +(-0.304783 - 3.83519i) q^{69} +(4.34996 - 16.7121i) q^{70} +(2.77738 - 4.81056i) q^{71} +(-1.09689 + 0.610205i) q^{72} +(-2.30040 + 3.98440i) q^{73} +(-4.46997 + 3.75075i) q^{74} +(4.50084 + 9.85623i) q^{75} +(-8.34856 + 3.03863i) q^{76} +(-11.8272 - 0.949453i) q^{77} +(10.9853 - 2.84994i) q^{78} +(0.215339 + 1.22125i) q^{79} +(7.35385 + 12.7372i) q^{80} +(-8.99543 - 0.286622i) q^{81} +(-0.279180 + 0.483554i) q^{82} +(-8.72055 + 7.31741i) q^{83} +(5.26278 - 6.26174i) q^{84} +(-2.31006 + 13.1010i) q^{85} +(-3.40335 + 19.3014i) q^{86} +(7.35204 + 0.702255i) q^{87} +(1.43738 - 1.20611i) q^{88} +12.2622 q^{89} +(-0.311839 + 19.5786i) q^{90} +(7.26249 - 5.16315i) q^{91} +(-3.72566 - 1.35603i) q^{92} +(-3.64865 - 1.73690i) q^{93} +(1.82803 - 10.3673i) q^{94} +(2.89974 - 16.4453i) q^{95} +(1.05545 + 13.2810i) q^{96} +(10.3763 + 3.77665i) q^{97} +(4.47402 - 12.8625i) q^{98} +(13.2851 - 2.12495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

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