LMFDB - Embedded newform 231.2.y.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	231.16
Dual form			231.2.y.b.130.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41978 - 0.514340i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(3.76371 + 1.67571i) q^{4} +(2.72281 + 3.02398i) q^{5} +(0.764459 - 2.35276i) q^{6} +(2.18271 - 1.49525i) q^{7} +(-4.24270 - 3.08250i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-2.41978 - 0.514340i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(3.76371 + 1.67571i) q^{4} +(2.72281 + 3.02398i) q^{5} +(0.764459 - 2.35276i) q^{6} +(2.18271 - 1.49525i) q^{7} +(-4.24270 - 3.08250i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-5.03324 - 8.71783i) q^{10} +(-2.61781 + 2.03644i) q^{11} +(-2.05994 + 3.56793i) q^{12} +(0.333422 + 1.02617i) q^{13} +(-6.05075 + 2.49552i) q^{14} +(-3.29203 + 2.39180i) q^{15} +(3.16746 + 3.51783i) q^{16} +(1.77354 - 0.376977i) q^{17} +(2.25997 + 1.00620i) q^{18} +(2.66628 - 1.18710i) q^{19} +(5.18052 + 15.9440i) q^{20} +(1.25890 + 2.32705i) q^{21} +(7.38194 - 3.58130i) q^{22} +(3.52905 - 6.11249i) q^{23} +(3.50910 - 3.89725i) q^{24} +(-1.20816 + 11.4948i) q^{25} +(-0.279009 - 2.65459i) q^{26} +(0.309017 - 0.951057i) q^{27} +(10.7207 - 1.97008i) q^{28} +(-6.62426 + 4.81280i) q^{29} +(9.19619 - 4.09441i) q^{30} +(-2.54756 + 2.82935i) q^{31} +(-0.610946 - 1.05819i) q^{32} +(-1.75165 - 2.81633i) q^{33} -4.48547 q^{34} +(10.4647 + 2.52921i) q^{35} +(-3.33306 - 2.42161i) q^{36} +(0.744182 + 7.08042i) q^{37} +(-7.06238 + 1.50116i) q^{38} +(-1.05540 + 0.224332i) q^{39} +(-2.23062 - 21.2229i) q^{40} +(-4.02479 - 2.92418i) q^{41} +(-1.84937 - 6.27846i) q^{42} -1.71446 q^{43} +(-13.2651 + 3.27788i) q^{44} +(-2.03459 - 3.52400i) q^{45} +(-11.6834 + 12.9758i) q^{46} +(2.79661 - 1.24513i) q^{47} +(-3.82964 + 2.78240i) q^{48} +(2.52847 - 6.52739i) q^{49} +(8.83573 - 27.1936i) q^{50} +(0.189527 + 1.80323i) q^{51} +(-0.464657 + 4.42091i) q^{52} +(5.76070 - 6.39790i) q^{53} +(-1.23692 + 2.14241i) q^{54} +(-13.2859 - 2.37137i) q^{55} +(-13.8697 - 0.384325i) q^{56} +(0.901898 + 2.77576i) q^{57} +(18.5047 - 8.23881i) q^{58} +(1.46356 + 0.651621i) q^{59} +(-16.3982 + 3.48554i) q^{60} +(1.54205 + 1.71262i) q^{61} +(7.61978 - 5.53610i) q^{62} +(-2.44589 + 1.00876i) q^{63} +(-1.99150 - 6.12921i) q^{64} +(-2.19527 + 3.80232i) q^{65} +(2.79005 + 7.71585i) q^{66} +(-1.62008 - 2.80606i) q^{67} +(7.30677 + 1.55310i) q^{68} +(5.71012 + 4.14864i) q^{69} +(-24.0214 - 11.5026i) q^{70} +(-1.12059 + 3.44881i) q^{71} +(3.50910 + 3.89725i) q^{72} +(-4.28406 - 1.90738i) q^{73} +(1.84099 - 17.5158i) q^{74} +(-11.3056 - 2.40307i) q^{75} +12.0243 q^{76} +(-2.66894 + 8.35923i) q^{77} +2.66922 q^{78} +(-1.25660 - 0.267098i) q^{79} +(-2.01345 + 19.1567i) q^{80} +(0.913545 + 0.406737i) q^{81} +(8.23509 + 9.14600i) q^{82} +(4.67691 - 14.3940i) q^{83} +(0.838672 + 10.8679i) q^{84} +(5.96897 + 4.33671i) q^{85} +(4.14862 + 0.881817i) q^{86} +(-4.09402 - 7.09104i) q^{87} +(17.3839 - 0.570609i) q^{88} +(4.91306 - 8.50967i) q^{89} +(3.11071 + 9.57379i) q^{90} +(2.26214 + 1.74128i) q^{91} +(23.5250 - 17.0919i) q^{92} +(-2.54756 - 2.82935i) q^{93} +(-7.40760 + 1.57453i) q^{94} +(10.8495 + 4.83052i) q^{95} +(1.11625 - 0.496989i) q^{96} +(1.46414 + 4.50617i) q^{97} +(-9.47564 + 14.4944i) q^{98} +(2.98400 - 1.44767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−2.41978	−	0.514340i	−1.71104	−	0.363694i	−0.754730	−	0.656036i	$-0.772232\pi$
$2$	−2.41978	−	0.514340i	−1.71104	−	0.363694i	−0.956314	+	0.292342i	$0.905565\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	3.76371	+	1.67571i	1.88185	+	0.837855i
$5$	2.72281	+	3.02398i	1.21768	+	1.35237i	0.917125	+	0.398601i	$0.130504\pi$
$5$	2.72281	+	3.02398i	1.21768	+	1.35237i	0.300551	+	0.953766i	$0.402829\pi$
$6$	0.764459	−	2.35276i	0.312089	−	0.960511i
$7$	2.18271	−	1.49525i	0.824988	−	0.565151i
$7$	2.18271	−	1.49525i	0.824988	−	0.565151i
$8$	−4.24270	−	3.08250i	−1.50002	−	1.08983i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−5.03324	−	8.71783i	−1.59165	−	2.75682i
$11$	−2.61781	+	2.03644i	−0.789298	+	0.614010i
$11$	−2.61781	+	2.03644i	−0.789298	+	0.614010i
$12$	−2.05994	+	3.56793i	−0.594655	+	1.02997i
$13$	0.333422	+	1.02617i	0.0924747	+	0.284608i	0.986587	−	0.163234i	$-0.0521927\pi$
$13$	0.333422	+	1.02617i	0.0924747	+	0.284608i	−0.894113	+	0.447842i	$0.852193\pi$
$14$	−6.05075	+	2.49552i	−1.61713	+	0.666955i
$15$	−3.29203	+	2.39180i	−0.849998	+	0.617560i
$16$	3.16746	+	3.51783i	0.791866	+	0.879456i
$17$	1.77354	−	0.376977i	0.430146	−	0.0914303i	0.0122494	−	0.999925i	$-0.496101\pi$
$17$	1.77354	−	0.376977i	0.430146	−	0.0914303i	0.417896	+	0.908495i	$0.362767\pi$
$18$	2.25997	+	1.00620i	0.532679	+	0.237164i
$19$	2.66628	−	1.18710i	0.611686	−	0.272340i	−0.0774226	−	0.996998i	$-0.524669\pi$
$19$	2.66628	−	1.18710i	0.611686	−	0.272340i	0.689108	+	0.724658i	$0.258002\pi$
$20$	5.18052	+	15.9440i	1.15840	+	3.56519i
$21$	1.25890	+	2.32705i	0.274715	+	0.507804i
$22$	7.38194	−	3.58130i	1.57384	−	0.763535i
$23$	3.52905	−	6.11249i	0.735857	−	1.27454i	−0.218489	−	0.975839i	$-0.570113\pi$
$23$	3.52905	−	6.11249i	0.735857	−	1.27454i	0.954346	−	0.298702i	$-0.0965538\pi$
$24$	3.50910	−	3.89725i	0.716292	−	0.795523i
$25$	−1.20816	+	11.4948i	−0.241631	+	2.29897i
$26$	−0.279009	−	2.65459i	−0.0547182	−	0.520609i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	10.7207	−	1.97008i	2.02602	−	0.372310i
$29$	−6.62426	+	4.81280i	−1.23009	+	0.893715i	−0.996897	−	0.0787145i	$-0.974918\pi$
$29$	−6.62426	+	4.81280i	−1.23009	+	0.893715i	−0.233196	+	0.972430i	$0.574918\pi$
$30$	9.19619	−	4.09441i	1.67899	−	0.747533i
$31$	−2.54756	+	2.82935i	−0.457555	+	0.508166i	−0.927137	−	0.374723i	$-0.877738\pi$
$31$	−2.54756	+	2.82935i	−0.457555	+	0.508166i	0.469582	+	0.882889i	$0.344405\pi$
$32$	−0.610946	−	1.05819i	−0.108001	−	0.187063i
$33$	−1.75165	−	2.81633i	−0.304923	−	0.490260i
$34$	−4.48547			−0.769251
$35$	10.4647	+	2.52921i	1.76886	+	0.427515i
$36$	−3.33306	−	2.42161i	−0.555510	−	0.403602i
$37$	0.744182	+	7.08042i	0.122343	+	1.16401i	0.867609	+	0.497247i	$0.165656\pi$
$37$	0.744182	+	7.08042i	0.122343	+	1.16401i	−0.745266	+	0.666767i	$0.767678\pi$
$38$	−7.06238	+	1.50116i	−1.14567	+	0.243520i
$39$	−1.05540	+	0.224332i	−0.168999	+	0.0359219i
$40$	−2.23062	−	21.2229i	−0.352692	−	3.35564i
$41$	−4.02479	−	2.92418i	−0.628567	−	0.456681i	0.227336	−	0.973816i	$-0.426998\pi$
$41$	−4.02479	−	2.92418i	−0.628567	−	0.456681i	−0.855904	+	0.517136i	$0.826998\pi$
$42$	−1.84937	−	6.27846i	−0.285364	−	0.968787i
$43$	−1.71446			−0.261453			−0.130727	−	0.991418i	$-0.541731\pi$
$43$	−1.71446			−0.261453			−0.130727	+	0.991418i	$0.541731\pi$
$44$	−13.2651	+	3.27788i	−1.99979	+	0.494158i
$45$	−2.03459	−	3.52400i	−0.303298	−	0.525328i
$46$	−11.6834	+	12.9758i	−1.72263	+	1.91317i
$47$	2.79661	−	1.24513i	0.407927	−	0.181621i	−0.192506	−	0.981296i	$-0.561661\pi$
$47$	2.79661	−	1.24513i	0.407927	−	0.181621i	0.600433	+	0.799675i	$0.294995\pi$
$48$	−3.82964	+	2.78240i	−0.552762	+	0.401605i
$49$	2.52847	−	6.52739i	0.361209	−	0.932485i
$50$	8.83573	−	27.1936i	1.24956	−	3.84575i
$51$	0.189527	+	1.80323i	0.0265390	+	0.252502i
$52$	−0.464657	+	4.42091i	−0.0644363	+	0.613070i
$53$	5.76070	−	6.39790i	0.791293	−	0.878820i	−0.203673	−	0.979039i	$-0.565288\pi$
$53$	5.76070	−	6.39790i	0.791293	−	0.878820i	0.994965	+	0.100220i	$0.0319545\pi$
$54$	−1.23692	+	2.14241i	−0.168324	+	0.291545i
$55$	−13.2859	−	2.37137i	−1.79148	−	0.319756i
$56$	−13.8697	−	0.384325i	−1.85342	−	0.0513576i
$57$	0.901898	+	2.77576i	0.119459	+	0.367658i
$58$	18.5047	−	8.23881i	2.42978	−	1.08181i
$59$	1.46356	+	0.651621i	0.190540	+	0.0848338i	0.499789	−	0.866147i	$-0.333411\pi$
$59$	1.46356	+	0.651621i	0.190540	+	0.0848338i	−0.309249	+	0.950981i	$0.600078\pi$
$60$	−16.3982	+	3.48554i	−2.11700	+	0.449981i
$61$	1.54205	+	1.71262i	0.197439	+	0.219279i	0.833732	−	0.552169i	$-0.186200\pi$
$61$	1.54205	+	1.71262i	0.197439	+	0.219279i	−0.636293	+	0.771448i	$0.719533\pi$
$62$	7.61978	−	5.53610i	0.967713	−	0.703085i
$63$	−2.44589	+	1.00876i	−0.308154	+	0.127092i
$64$	−1.99150	−	6.12921i	−0.248938	−	0.766152i
$65$	−2.19527	+	3.80232i	−0.272290	+	0.471620i
$66$	2.79005	+	7.71585i	0.343432	+	0.949756i
$67$	−1.62008	−	2.80606i	−0.197924	−	0.342815i	0.749931	−	0.661516i	$-0.230087\pi$
$67$	−1.62008	−	2.80606i	−0.197924	−	0.342815i	−0.947855	+	0.318701i	$0.896753\pi$
$68$	7.30677	+	1.55310i	0.886076	+	0.188341i
$69$	5.71012	+	4.14864i	0.687417	+	0.499438i
$70$	−24.0214	−	11.5026i	−2.87111	−	1.37482i
$71$	−1.12059	+	3.44881i	−0.132989	+	0.409298i	−0.995272	−	0.0971289i	$-0.969034\pi$
$71$	−1.12059	+	3.44881i	−0.132989	+	0.409298i	0.862283	+	0.506427i	$0.169034\pi$
$72$	3.50910	+	3.89725i	0.413551	+	0.459295i
$73$	−4.28406	−	1.90738i	−0.501411	−	0.223243i	0.140415	−	0.990093i	$-0.455156\pi$
$73$	−4.28406	−	1.90738i	−0.501411	−	0.223243i	−0.641826	+	0.766850i	$0.721823\pi$
$74$	1.84099	−	17.5158i	0.214011	−	2.03617i
$75$	−11.3056	−	2.40307i	−1.30546	−	0.277483i
$76$	12.0243			1.37928
$77$	−2.66894	+	8.35923i	−0.304153	+	0.952623i
$78$	2.66922			0.302229
$79$	−1.25660	−	0.267098i	−0.141378	−	0.0300509i	0.136679	−	0.990615i	$-0.456357\pi$
$79$	−1.25660	−	0.267098i	−0.141378	−	0.0300509i	−0.278057	+	0.960565i	$0.589690\pi$
$80$	−2.01345	+	19.1567i	−0.225111	+	2.14179i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	8.23509	+	9.14600i	0.909414	+	1.01001i
$83$	4.67691	−	14.3940i	0.513357	−	1.57995i	−0.272895	−	0.962044i	$-0.587981\pi$
$83$	4.67691	−	14.3940i	0.513357	−	1.57995i	0.786252	−	0.617907i	$-0.212019\pi$
$84$	0.838672	+	10.8679i	0.0915067	+	1.18578i
$85$	5.96897	+	4.33671i	0.647426	+	0.470382i
$86$	4.14862	+	0.881817i	0.447358	+	0.0950888i
$87$	−4.09402	−	7.09104i	−0.438924	−	0.760240i
$88$	17.3839	−	0.570609i	1.85313	−	0.0608272i
$89$	4.91306	−	8.50967i	0.520784	−	0.902024i	−0.478924	−	0.877856i	$-0.658973\pi$
$89$	4.91306	−	8.50967i	0.520784	−	0.902024i	0.999708	−	0.0241675i	$-0.00769350\pi$
$90$	3.11071	+	9.57379i	0.327898	+	1.00917i
$91$	2.26214	+	1.74128i	0.237137	+	0.182536i
$92$	23.5250	−	17.0919i	2.45265	−	1.78196i
$93$	−2.54756	−	2.82935i	−0.264169	−	0.293390i
$94$	−7.40760	+	1.57453i	−0.764036	+	0.162401i
$95$	10.8495	+	4.83052i	1.11314	+	0.495601i
$96$	1.11625	−	0.496989i	0.113927	−	0.0507237i
$97$	1.46414	+	4.50617i	0.148661	+	0.457532i	0.997464	−	0.0711781i	$-0.0226759\pi$
$97$	1.46414	+	4.50617i	0.148661	+	0.457532i	−0.848802	+	0.528710i	$0.822676\pi$
$98$	−9.47564	+	14.4944i	−0.957184	+	1.46415i
$99$	2.98400	−	1.44767i	0.299903	−	0.145496i
$100$	−23.8091	+	41.2386i	−2.38091	+	4.12386i
$101$	−7.02269	+	7.79948i	−0.698783	+	0.776078i	−0.983182	−	0.182629i	$-0.941539\pi$
$101$	−7.02269	+	7.79948i	−0.698783	+	0.776078i	0.284399	+	0.958706i	$0.408206\pi$
$102$	0.468859	−	4.46089i	0.0464239	−	0.441694i
$103$	−0.175141	−	1.66636i	−0.0172572	−	0.164191i	0.982499	−	0.186267i	$-0.0596390\pi$
$103$	−0.175141	−	1.66636i	−0.0172572	−	0.164191i	−0.999756	+	0.0220761i	$0.992972\pi$
$104$	1.74855	−	5.38150i	0.171460	−	0.527699i
$105$	−3.60922	+	10.1430i	−0.352224	+	0.989856i
$106$	−17.2303	+	12.5186i	−1.67356	+	1.21591i
$107$	6.80379	−	3.02924i	0.657747	−	0.292848i	−0.0505926	−	0.998719i	$-0.516111\pi$
$107$	6.80379	−	3.02924i	0.657747	−	0.292848i	0.708340	+	0.705871i	$0.249444\pi$
$108$	2.75674	−	3.06167i	0.265268	−	0.294610i
$109$	−2.21467	−	3.83591i	−0.212126	−	0.367414i	0.740253	−	0.672328i	$-0.234706\pi$
$109$	−2.21467	−	3.83591i	−0.212126	−	0.367414i	−0.952380	+	0.304914i	$0.901372\pi$
$110$	30.9294	+	12.5717i	2.94900	+	1.19866i
$111$	−7.11942			−0.675746
$112$	12.1737	+	2.94226i	1.15031	+	0.278017i
$113$	−8.89696	−	6.46402i	−0.836955	−	0.608084i	0.0845632	−	0.996418i	$-0.473051\pi$
$113$	−8.89696	−	6.46402i	−0.836955	−	0.608084i	−0.921518	+	0.388335i	$0.873051\pi$
$114$	−0.754712	−	7.18061i	−0.0706853	−	0.672525i
$115$	28.0930	−	5.97134i	2.61968	−	0.556831i
$116$	−32.9966	+	7.01364i	−3.06366	+	0.651201i
$117$	−0.112784	−	1.07307i	−0.0104269	−	0.0992050i
$118$	−3.20635	−	2.32955i	−0.295168	−	0.214452i
$119$	3.30745	−	3.47471i	0.303193	−	0.318526i
$120$	21.3398			1.94805
$121$	2.70582	−	10.6620i	0.245984	−	0.969274i
$122$	−2.85056	−	4.93731i	−0.258077	−	0.447003i
$123$	3.32887	−	3.69708i	0.300154	−	0.333355i
$124$	−14.3294	+	6.37987i	−1.28682	+	0.572929i
$125$	−21.5896	+	15.6858i	−1.93103	+	1.40298i
$126$	6.43738	−	1.18296i	0.573487	−	0.105387i
$127$	1.02802	−	3.16391i	0.0912218	−	0.280752i	−0.895029	−	0.446008i	$-0.852845\pi$
$127$	1.02802	−	3.16391i	0.0912218	−	0.280752i	0.986251	+	0.165256i	$0.0528452\pi$
$128$	1.92194	+	18.2861i	0.169877	+	1.61627i
$129$	0.179210	−	1.70507i	0.0157786	−	0.150123i
$130$	7.26776	−	8.07167i	0.637425	−	0.707932i
$131$	−3.62341	+	6.27594i	−0.316579	+	0.548331i	−0.979772	−	0.200117i	$-0.935868\pi$
$131$	−3.62341	+	6.27594i	−0.316579	+	0.548331i	0.663193	+	0.748449i	$0.269201\pi$
$132$	−1.87334	−	13.5351i	−0.163053	−	1.17808i
$133$	4.04470	−	6.57785i	0.350720	−	0.570372i
$134$	2.47697	+	7.62332i	0.213977	+	0.658554i
$135$	3.71737	−	1.65508i	0.319940	−	0.142447i
$136$	−8.68662	−	3.86753i	−0.744871	−	0.331638i
$137$	6.31368	−	1.34201i	0.539414	−	0.114656i	0.0698550	−	0.997557i	$-0.477746\pi$
$137$	6.31368	−	1.34201i	0.539414	−	0.114656i	0.469559	+	0.882901i	$0.344413\pi$
$138$	−11.6834	−	12.9758i	−0.994559	−	1.10457i
$139$	12.7048	−	9.23059i	1.07761	−	0.782929i	0.100344	−	0.994953i	$-0.468006\pi$
$139$	12.7048	−	9.23059i	1.07761	−	0.782929i	0.977264	+	0.212024i	$0.0680055\pi$
$140$	35.1478	+	27.0550i	2.97054	+	2.28657i
$141$	0.945984	+	2.91144i	0.0796662	+	0.245187i
$142$	4.48543	−	7.76900i	0.376409	−	0.651960i
$143$	−2.96256	−	2.00732i	−0.247742	−	0.167860i
$144$	−2.36685	−	4.09951i	−0.197238	−	0.341625i
$145$	−32.5904	−	6.92730i	−2.70649	−	0.575281i
$146$	9.38544	+	6.81892i	0.776744	+	0.564338i
$147$	6.22734	+	3.19691i	0.513622	+	0.263677i
$148$	−9.06385	+	27.8957i	−0.745044	+	2.29301i
$149$	5.85332	+	6.50077i	0.479523	+	0.532564i	0.933561	−	0.358418i	$-0.116684\pi$
$149$	5.85332	+	6.50077i	0.479523	+	0.532564i	−0.454038	+	0.890982i	$0.650017\pi$
$150$	26.1210	+	11.6298i	2.13277	+	0.949571i
$151$	0.881301	−	8.38502i	0.0717193	−	0.682363i	−0.898308	−	0.439367i	$-0.855203\pi$
$151$	0.881301	−	8.38502i	0.0717193	−	0.682363i	0.970027	−	0.242997i	$-0.0781304\pi$
$152$	−14.9715	−	3.18228i	−1.21435	−	0.258117i
$153$	−1.81316			−0.146585
$154$	10.7577	−	18.8548i	0.866883	−	1.51936i
$155$	−15.4924			−1.24438
$156$	−4.34812	−	0.924222i	−0.348129	−	0.0739970i
$157$	0.819453	−	7.79658i	0.0653995	−	0.622235i	−0.911906	−	0.410399i	$-0.865389\pi$
$157$	0.819453	−	7.79658i	0.0653995	−	0.622235i	0.977305	−	0.211835i	$-0.0679440\pi$
$158$	2.90331	+	1.29264i	0.230975	+	0.102837i
$159$	5.76070	+	6.39790i	0.456853	+	0.507387i
$160$	1.53646	−	4.72874i	0.121468	−	0.373840i
$161$	−1.43679	−	18.6186i	−0.113235	−	1.46735i
$162$	−2.00138	−	1.45409i	−0.157243	−	0.114244i
$163$	9.10245	+	1.93479i	0.712959	+	0.151544i	0.550092	−	0.835104i	$-0.314593\pi$
$163$	9.10245	+	1.93479i	0.712959	+	0.151544i	0.162867	+	0.986648i	$0.447926\pi$
$164$	−10.2481	−	17.7501i	−0.800238	−	1.38605i
$165$	3.74714	−	12.9653i	0.291714	−	1.00935i
$166$	−18.7205	+	32.4249i	−1.45299	+	2.51666i
$167$	−7.10521	−	21.8676i	−0.549818	−	1.69217i	−0.709250	−	0.704957i	$-0.750966\pi$
$167$	−7.10521	−	21.8676i	−0.549818	−	1.69217i	0.159432	−	0.987209i	$-0.449034\pi$
$168$	1.83200	−	13.7535i	0.141342	−	1.06111i
$169$	9.57537	−	6.95691i	0.736567	−	0.535147i
$170$	−12.2131	−	13.5640i	−0.936699	−	1.04031i
$171$	−2.85482	+	0.606812i	−0.218314	+	0.0464041i
$172$	−6.45273	−	2.87294i	−0.492016	−	0.219060i
$173$	−10.7453	+	4.78411i	−0.816948	+	0.363729i	−0.772287	−	0.635273i	$-0.780887\pi$
$173$	−10.7453	+	4.78411i	−0.816948	+	0.363729i	−0.0446610	+	0.999002i	$0.514221\pi$
$174$	6.25941	+	19.2645i	0.474525	+	1.46044i
$175$	14.5506	+	26.8964i	1.09992	+	2.03318i
$176$	−15.4557	−	2.75864i	−1.16501	−	0.207940i
$177$	−0.801035	+	1.38743i	−0.0602095	+	0.104286i
$178$	−16.2654	+	18.0646i	−1.21914	+	1.35400i
$179$	−0.396630	+	3.77368i	−0.0296455	+	0.282058i	0.969649	+	0.244501i	$0.0786242\pi$
$179$	−0.396630	+	3.77368i	−0.0296455	+	0.282058i	−0.999294	+	0.0375568i	$0.988042\pi$
$180$	−1.75237	−	16.6727i	−0.130614	−	1.24271i
$181$	−7.22075	+	22.2232i	−0.536714	+	1.65184i	0.203202	+	0.979137i	$0.434865\pi$
$181$	−7.22075	+	22.2232i	−0.536714	+	1.65184i	−0.739916	+	0.672699i	$0.765135\pi$
$182$	−4.57827	−	5.37703i	−0.339364	−	0.398572i
$183$	−1.86443	+	1.35459i	−0.137822	+	0.100134i
$184$	−33.8144	+	15.0552i	−2.49283	+	1.10988i
$185$	−19.3848	+	21.5290i	−1.42520	+	1.58284i
$186$	4.70928	+	8.15672i	0.345301	+	0.598080i
$187$	−3.87509	+	4.59855i	−0.283374	+	0.336280i
$188$	12.6121			0.919831
$189$	−0.747570	−	2.53794i	−0.0543777	−	0.184608i
$190$	−23.7690	−	17.2692i	−1.72438	−	1.25284i
$191$	−2.59894	−	24.7273i	−0.188053	−	1.78920i	−0.528496	−	0.848936i	$-0.677244\pi$
$191$	−2.59894	−	24.7273i	−0.188053	−	1.78920i	0.340443	−	0.940265i	$-0.389423\pi$
$192$	6.30380	−	1.33991i	0.454938	−	0.0967000i
$193$	3.43477	−	0.730083i	0.247240	−	0.0525525i	−0.0826246	−	0.996581i	$-0.526330\pi$
$193$	3.43477	−	0.730083i	0.247240	−	0.0525525i	0.329865	+	0.944028i	$0.392997\pi$
$194$	−1.22520	−	11.6570i	−0.0879643	−	0.836924i
$195$	−3.55202	−	2.58070i	−0.254366	−	0.184807i
$196$	20.4544	−	20.3302i	1.46103	−	1.45216i
$197$	25.5993			1.82388			0.911938	−	0.410327i	$-0.134586\pi$
$197$	25.5993			1.82388			0.911938	+	0.410327i	$0.134586\pi$
$198$	−7.96522	+	1.96824i	−0.566064	+	0.139877i
$199$	−2.61658	−	4.53206i	−0.185485	−	0.321269i	0.758255	−	0.651958i	$-0.226052\pi$
$199$	−2.61658	−	4.53206i	−0.185485	−	0.321269i	−0.943740	+	0.330689i	$0.892719\pi$
$200$	40.5587	−	45.0450i	2.86793	−	3.18516i
$201$	2.96003	−	1.31789i	0.208784	−	0.0929568i
$202$	21.0050	−	15.2610i	1.47790	−	1.07376i
$203$	−7.26251	+	20.4099i	−0.509728	+	1.43249i
$204$	−2.30836	+	7.10440i	−0.161618	+	0.497408i
$205$	−2.11605	−	20.1329i	−0.147792	−	1.40614i
$206$	−0.433272	+	4.12231i	−0.0301875	+	0.287215i
$207$	−4.72279	+	5.24518i	−0.328256	+	0.364566i
$208$	−2.55378	+	4.42327i	−0.177073	+	0.306699i
$209$	−4.56233	+	8.53732i	−0.315583	+	0.590539i
$210$	13.9505	−	22.6875i	0.962674	−	1.56559i
$211$	−1.27198	−	3.91474i	−0.0875665	−	0.269502i	0.897679	−	0.440651i	$-0.145252\pi$
$211$	−1.27198	−	3.91474i	−0.0875665	−	0.269502i	−0.985245	+	0.171149i	$0.945252\pi$
$212$	32.4026	−	14.4266i	2.22542	−	0.990820i
$213$	−3.31278	−	1.47495i	−0.226988	−	0.101062i
$214$	−18.0218	+	3.83064i	−1.23194	+	0.261857i
$215$	−4.66815	−	5.18451i	−0.318365	−	0.353580i
$216$	−4.24270	+	3.08250i	−0.288679	+	0.209738i
$217$	−1.33001	+	9.98489i	−0.0902867	+	0.677818i
$218$	3.38604	+	10.4212i	0.229332	+	0.705810i
$219$	2.34474	−	4.06121i	0.158443	−	0.274431i
$220$	−46.0306	−	31.1885i	−3.10338	−	2.10273i
$221$	0.978178	+	1.69425i	0.0657994	+	0.113968i
$222$	17.2274	+	3.66181i	1.15623	+	0.245764i
$223$	−15.7360	−	11.4329i	−1.05376	−	0.765604i	−0.0808386	−	0.996727i	$-0.525760\pi$
$223$	−15.7360	−	11.4329i	−1.05376	−	0.765604i	−0.972924	+	0.231124i	$0.925760\pi$
$224$	−2.91578	−	1.39621i	−0.194819	−	0.0932881i
$225$	3.57166	−	10.9925i	0.238111	−	0.732830i
$226$	18.2040	+	20.2176i	1.21091	+	1.34485i
$227$	−11.2558	−	5.01141i	−0.747075	−	0.332619i	−0.00235575	−	0.999997i	$-0.500750\pi$
$227$	−11.2558	−	5.01141i	−0.747075	−	0.332619i	−0.744719	+	0.667378i	$0.767417\pi$
$228$	−1.25688	+	11.9584i	−0.0832391	+	0.791968i
$229$	9.17629	+	1.95048i	0.606386	+	0.128891i	0.500865	−	0.865526i	$-0.333015\pi$
$229$	9.17629	+	1.95048i	0.606386	+	0.128891i	0.105522	+	0.994417i	$0.466349\pi$
$230$	−71.0501			−4.68491
$231$	−8.03446	−	3.52809i	−0.528629	−	0.232131i
$232$	42.9402			2.81916
$233$	−7.83681	−	1.66577i	−0.513407	−	0.109128i	−0.0560792	−	0.998426i	$-0.517860\pi$
$233$	−7.83681	−	1.66577i	−0.513407	−	0.109128i	−0.457328	+	0.889298i	$0.651193\pi$
$234$	−0.279009	+	2.65459i	−0.0182394	+	0.173536i
$235$	11.3799	+	5.06665i	0.742341	+	0.330512i
$236$	4.41650	+	4.90502i	0.287489	+	0.319289i
$237$	0.396985	−	1.22179i	0.0257869	−	0.0793640i
$238$	−9.79048	+	6.70688i	−0.634623	+	0.434743i
$239$	11.0064	+	7.99662i	0.711945	+	0.517258i	0.883800	−	0.467864i	$-0.154976\pi$
$239$	11.0064	+	7.99662i	0.711945	+	0.517258i	−0.171856	+	0.985122i	$0.554976\pi$
$240$	−18.8413	−	4.00484i	−1.21620	−	0.258512i
$241$	−2.22026	−	3.84560i	−0.143020	−	0.247717i	0.785613	−	0.618718i	$-0.212348\pi$
$241$	−2.22026	−	3.84560i	−0.143020	−	0.247717i	−0.928632	+	0.371001i	$0.879015\pi$
$242$	−12.0314	+	24.4080i	−0.773408	+	1.56901i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.93397	+	9.02983i	0.187828	+	0.578076i
$245$	26.6232	−	10.1268i	1.70090	−	0.646977i
$246$	−9.95670	+	7.23396i	−0.634816	+	0.461221i
$247$	2.10716	+	2.34024i	0.134076	+	0.148906i
$248$	19.5300	−	4.15123i	1.24016	−	0.263603i
$249$	13.8263	+	6.15587i	0.876207	+	0.390112i
$250$	60.3100	−	26.8517i	3.81434	−	1.69825i
$251$	−3.73760	−	11.5031i	−0.235915	−	0.726072i	−0.996999	−	0.0774180i	$-0.975332\pi$
$251$	−3.73760	−	11.5031i	−0.235915	−	0.726072i	0.761084	−	0.648654i	$-0.224668\pi$
$252$	−10.8960	−	0.301925i	−0.686385	−	0.0190195i
$253$	3.20935	+	23.1880i	0.201770	+	1.45782i
$254$	−4.11491	+	7.12723i	−0.258192	+	0.447202i
$255$	−4.93688	+	5.48296i	−0.309159	+	0.343356i
$256$	3.40728	−	32.4181i	0.212955	−	2.02613i
$257$	1.83456	+	17.4546i	0.114437	+	1.08879i	0.889509	+	0.456918i	$0.151047\pi$
$257$	1.83456	+	17.4546i	0.114437	+	1.08879i	−0.775072	+	0.631873i	$0.782287\pi$
$258$	−1.31064	+	4.03372i	−0.0815966	+	0.251129i
$259$	12.2113	+	14.3418i	0.758775	+	0.891155i
$260$	−14.6339	+	10.6322i	−0.907558	+	0.659379i
$261$	7.48014	−	3.33037i	0.463009	−	0.206145i
$262$	11.9958	−	13.3227i	0.741105	−	0.823081i
$263$	14.9662	+	25.9222i	0.922853	+	1.59843i	0.794978	+	0.606638i	$0.207482\pi$
$263$	14.9662	+	25.9222i	0.922853	+	1.59843i	0.127875	+	0.991790i	$0.459184\pi$
$264$	−1.24963	+	17.3483i	−0.0769093	+	1.06771i
$265$	35.0324			2.15202
$266$	−13.1705	+	13.8366i	−0.807538	+	0.848377i
$267$	7.94950	+	5.77565i	0.486502	+	0.353464i
$268$	−1.39536	−	13.2760i	−0.0852351	−	0.810958i
$269$	24.1994	−	5.14375i	1.47547	−	0.313620i	0.601212	−	0.799089i	$-0.294685\pi$
$269$	24.1994	−	5.14375i	1.47547	−	0.313620i	0.874254	+	0.485469i	$0.161351\pi$
$270$	−9.84650	+	2.09294i	−0.599239	+	0.127372i
$271$	1.25179	+	11.9100i	0.0760411	+	0.723482i	0.964421	+	0.264373i	$0.0851649\pi$
$271$	1.25179	+	11.9100i	0.0760411	+	0.723482i	−0.888380	+	0.459110i	$0.848168\pi$
$272$	6.94375	+	5.04493i	0.421027	+	0.305894i
$273$	−1.96820	+	2.06773i	−0.119121	+	0.125145i
$274$	−15.9680			−0.964660
$275$	−20.2458	−	32.5516i	−1.22087	−	1.96293i
$276$	14.5393	+	25.1828i	0.875161	+	1.51582i
$277$	4.56847	−	5.07381i	0.274493	−	0.304855i	−0.590098	−	0.807332i	$-0.700911\pi$
$277$	4.56847	−	5.07381i	0.274493	−	0.304855i	0.864591	+	0.502476i	$0.167578\pi$
$278$	−35.4906	+	15.8014i	−2.12858	+	0.947706i
$279$	3.08014	−	2.23785i	0.184403	−	0.133977i
$280$	−36.6023	−	42.9882i	−2.18741	−	2.56903i
$281$	−0.00220983	+	0.00680115i	−0.000131827	+	0.000405723i	−0.951122	−	0.308814i	$-0.900068\pi$
$281$	−0.00220983	+	0.00680115i	−0.000131827	+	0.000405723i	0.950991	+	0.309220i	$0.100068\pi$
$282$	−0.791604	−	7.53161i	−0.0471393	−	0.448501i
$283$	−1.74819	+	16.6329i	−0.103919	+	0.988722i	0.810990	+	0.585061i	$0.198929\pi$
$283$	−1.74819	+	16.6329i	−0.103919	+	0.988722i	−0.914908	+	0.403661i	$0.867737\pi$
$284$	−9.99675	+	11.1025i	−0.593198	+	0.658813i
$285$	−5.93815	+	10.2852i	−0.351745	+	0.609241i
$286$	6.13631	+	6.38103i	0.362848	+	0.377318i
$287$	−13.1573	−	0.364586i	−0.776654	−	0.0215208i
$288$	0.377586	+	1.16209i	0.0222494	+	0.0684768i
$289$	−12.5270	+	5.57736i	−0.736879	+	0.328080i
$290$	75.2987	+	33.5251i	4.42169	+	1.96866i
$291$	−4.63453	+	0.985099i	−0.271681	+	0.0577475i
$292$	−12.9277	−	14.3577i	−0.756537	−	0.840219i
$293$	1.05136	−	0.763859i	0.0614212	−	0.0446251i	−0.556651	−	0.830746i	$-0.687914\pi$
$293$	1.05136	−	0.763859i	0.0614212	−	0.0446251i	0.618072	+	0.786121i	$0.287914\pi$
$294$	−13.4245	−	10.9388i	−0.782933	−	0.637964i
$295$	2.01451	+	6.20003i	0.117289	+	0.360980i
$296$	18.6681	−	32.3340i	1.08506	−	1.87938i
$297$	1.12782	+	3.11898i	0.0654429	+	0.180981i
$298$	−10.8202	−	18.7411i	−0.626794	−	1.08564i
$299$	7.44910	+	1.58336i	0.430793	+	0.0915678i
$300$	−38.5240	−	27.9893i	−2.22418	−	1.61596i
$301$	−3.74218	+	2.56355i	−0.215696	+	0.147760i
$302$	−6.44531	+	19.8366i	−0.370886	+	1.14147i
$303$	−7.02269	−	7.79948i	−0.403443	−	0.448069i
$304$	12.6214	+	5.61939i	0.723885	+	0.322294i
$305$	−0.980231	+	9.32627i	−0.0561279	+	0.534021i
$306$	4.38745	+	0.932581i	0.250814	+	0.0533121i
$307$	3.91996			0.223724			0.111862	−	0.993724i	$-0.464319\pi$
$307$	3.91996			0.223724			0.111862	+	0.993724i	$0.464319\pi$
$308$	−24.0527	+	26.9893i	−1.37053	+	1.53786i
$309$	1.67554			0.0953180
$310$	37.4883	+	7.96837i	2.12919	+	0.452573i
$311$	0.0782997	−	0.744972i	0.00443997	−	0.0422435i	−0.992078	−	0.125627i	$-0.959906\pi$
$311$	0.0782997	−	0.744972i	0.00443997	−	0.0422435i	0.996518	+	0.0833832i	$0.0265725\pi$
$312$	5.16924	+	2.30150i	0.292651	+	0.130297i
$313$	−17.4460	−	19.3758i	−0.986107	−	1.09518i	−0.995456	−	0.0952265i	$-0.969642\pi$
$313$	−17.4460	−	19.3758i	−0.986107	−	1.09518i	0.00934864	−	0.999956i	$-0.497024\pi$
$314$	−5.99299	+	18.4445i	−0.338204	+	1.04089i
$315$	−9.71018	−	4.64968i	−0.547106	−	0.261980i
$316$	−4.28188	−	3.11097i	−0.240875	−	0.175006i
$317$	−11.1823	−	2.37686i	−0.628058	−	0.133498i	−0.117123	−	0.993117i	$-0.537367\pi$
$317$	−11.1823	−	2.37686i	−0.628058	−	0.133498i	−0.510935	+	0.859620i	$0.670701\pi$
$318$	−10.6489	−	18.4445i	−0.597162	−	1.03432i
$319$	7.54004	−	26.0889i	0.422161	−	1.46070i
$320$	13.1122	−	22.7109i	0.732992	−	1.26958i
$321$	2.30146	+	7.08316i	0.128455	+	0.395344i
$322$	−6.09957	+	45.7919i	−0.339916	+	2.55189i
$323$	4.28123	−	3.11050i	0.238214	−	0.173073i
$324$	2.75674	+	3.06167i	0.153152	+	0.170093i
$325$	−12.1985	+	2.59286i	−0.676648	+	0.143826i
$326$	−21.0308	−	9.36352i	−1.16479	−	0.518597i
$327$	4.04640	−	1.80157i	0.223766	−	0.0996271i
$328$	8.06219	+	24.8129i	0.445160	+	1.37006i
$329$	4.24241	−	6.89938i	0.233892	−	0.380375i
$330$	−15.7358	+	29.4458i	−0.866229	+	1.62094i
$331$	−1.41995	+	2.45943i	−0.0780476	+	0.135182i	−0.902408	−	0.430884i	$-0.858202\pi$
$331$	−1.41995	+	2.45943i	−0.0780476	+	0.135182i	0.824360	+	0.566066i	$0.191535\pi$
$332$	41.7227	−	46.3378i	2.28983	−	2.54312i
$333$	0.744182	−	7.08042i	0.0407809	−	0.388005i
$334$	5.94567	+	56.5693i	0.325333	+	3.09533i
$335$	4.07431	−	12.5394i	0.222603	−	0.685103i
$336$	−4.19863	+	11.7994i	−0.229054	+	0.643713i
$337$	−13.5927	+	9.87565i	−0.740439	+	0.537961i	−0.892849	−	0.450357i	$-0.851297\pi$
$337$	−13.5927	+	9.87565i	−0.740439	+	0.537961i	0.152409	+	0.988317i	$0.451297\pi$
$338$	−26.7485	+	11.9092i	−1.45493	+	0.647776i
$339$	7.35859	−	8.17254i	0.399664	−	0.443872i
$340$	15.1984	+	26.3244i	0.824248	+	1.42764i
$341$	0.907213	−	12.5946i	0.0491284	−	0.682038i
$342$	7.22016			0.390422
$343$	−4.24116	−	18.0281i	−0.229001	−	0.973426i
$344$	7.27395	+	5.28483i	0.392185	+	0.284939i
$345$	3.00212	+	28.5632i	0.161629	+	1.53779i
$346$	28.4619	−	6.04976i	1.53012	−	0.325237i
$347$	−35.0297	+	7.44579i	−1.88049	+	0.399711i	−0.997562	−	0.0697915i	$-0.977767\pi$
$347$	−35.0297	+	7.44579i	−1.88049	+	0.399711i	−0.882931	+	0.469503i	$0.844433\pi$
$348$	−3.52614	−	33.5490i	−0.189021	−	1.79841i
$349$	−20.5870	−	14.9573i	−1.10200	−	0.800648i	−0.120613	−	0.992700i	$-0.538486\pi$
$349$	−20.5870	−	14.9573i	−1.10200	−	0.800648i	−0.981385	+	0.192051i	$0.938486\pi$
$350$	−21.3753	−	72.5674i	−1.14256	−	3.87889i
$351$	1.07898			0.0575915
$352$	3.75428	+	1.52598i	0.200104	+	0.0813351i
$353$	12.5493	+	21.7361i	0.667933	+	1.15689i	0.978481	+	0.206337i	$0.0661542\pi$
$353$	12.5493	+	21.7361i	0.667933	+	1.15689i	−0.310548	+	0.950558i	$0.600512\pi$
$354$	2.65194	−	2.94528i	0.140949	−	0.156540i
$355$	−13.4803	+	6.00180i	−0.715459	+	0.318543i
$356$	32.7511	−	23.7950i	1.73580	−	1.26113i
$357$	3.10995	+	3.65253i	0.164596	+	0.193313i
$358$	2.90071	−	8.92747i	0.153307	−	0.471832i
$359$	3.28576	+	31.2619i	0.173416	+	1.64994i	0.642133	+	0.766593i	$0.278050\pi$
$359$	3.28576	+	31.2619i	0.173416	+	1.64994i	−0.468717	+	0.883348i	$0.655284\pi$
$360$	−2.23062	+	21.2229i	−0.117564	+	1.11855i
$361$	−7.01366	+	7.78946i	−0.369140	+	0.409972i
$362$	28.9029	−	50.0613i	1.51910	−	2.63116i
$363$	10.3208	+	3.80549i	0.541700	+	0.199736i
$364$	5.59615	+	10.3444i	0.293318	+	0.542192i
$365$	−5.89676	−	18.1484i	−0.308650	−	0.949928i
$366$	5.20823	−	2.31885i	0.272238	−	0.121208i
$367$	−26.3116	−	11.7147i	−1.37345	−	0.611501i	−0.418489	−	0.908222i	$-0.637440\pi$
$367$	−26.3116	−	11.7147i	−1.37345	−	0.611501i	−0.954964	+	0.296721i	$0.904107\pi$
$368$	32.6808	−	6.94652i	1.70360	−	0.362112i
$369$	3.32887	+	3.69708i	0.173294	+	0.192463i
$370$	57.9802	−	42.1251i	3.01425	−	2.18998i
$371$	3.00749	−	22.5785i	0.156141	−	1.17221i
$372$	−4.84709	−	14.9178i	−0.251310	−	0.773452i
$373$	−5.98199	+	10.3611i	−0.309736	+	0.536478i	−0.978304	−	0.207172i	$-0.933574\pi$
$373$	−5.98199	+	10.3611i	−0.309736	+	0.536478i	0.668569	+	0.743650i	$0.266907\pi$
$374$	11.7421	−	9.13438i	0.607169	−	0.472328i
$375$	−13.3431	−	23.1109i	−0.689035	−	1.19344i
$376$	−15.7033	−	3.33784i	−0.809835	−	0.172136i
$377$	−7.14742	−	5.19290i	−0.368111	−	0.267448i
$378$	0.503592	+	6.52577i	0.0259020	+	0.335649i
$379$	−4.51983	+	13.9106i	−0.232168	+	0.714539i	0.765317	+	0.643654i	$0.222582\pi$
$379$	−4.51983	+	13.9106i	−0.232168	+	0.714539i	−0.997484	+	0.0708852i	$0.977418\pi$
$380$	32.7399	+	36.3613i	1.67952	+	1.86530i
$381$	3.03912	+	1.35311i	0.155699	+	0.0693217i
$382$	−6.42936	+	61.1713i	−0.328955	+	3.12980i
$383$	13.6004	+	2.89086i	0.694950	+	0.147716i	0.541826	−	0.840491i	$-0.317733\pi$
$383$	13.6004	+	2.89086i	0.694950	+	0.147716i	0.153124	+	0.988207i	$0.451067\pi$
$384$	−18.3868			−0.938297
$385$	−32.5452	+	14.6898i	−1.65866	+	0.748659i
$386$	−8.68690			−0.442152
$387$	1.67700	+	0.356457i	0.0852466	+	0.0181197i
$388$	−2.04043	+	19.4134i	−0.103587	+	0.985564i
$389$	−12.2835	−	5.46895i	−0.622796	−	0.277287i	0.0709796	−	0.997478i	$-0.477387\pi$
$389$	−12.2835	−	5.46895i	−0.622796	−	0.277287i	−0.693776	+	0.720191i	$0.744054\pi$
$390$	7.26776	+	8.07167i	0.368017	+	0.408725i
$391$	3.95463	−	12.1711i	0.199994	−	0.615518i
$392$	−30.8482	+	19.8998i	−1.55807	+	1.00509i
$393$	−5.86281	−	4.25958i	−0.295739	−	0.214867i
$394$	−61.9448	−	13.1668i	−3.12073	−	0.663332i
$395$	−2.61377	−	4.52718i	−0.131513	−	0.227787i
$396$	13.6568	−	0.448270i	0.686278	−	0.0225264i
$397$	13.6057	−	23.5658i	0.682853	−	1.18274i	−0.291254	−	0.956646i	$-0.594072\pi$
$397$	13.6057	−	23.5658i	0.682853	−	1.18274i	0.974106	−	0.226090i	$-0.0725944\pi$
$398$	4.00054	+	12.3124i	0.200529	+	0.617165i
$399$	6.11903	+	4.71012i	0.306335	+	0.235801i
$400$	−44.2636	+	32.1594i	−2.21318	+	1.60797i
$401$	9.69869	+	10.7715i	0.484330	+	0.537903i	0.934934	−	0.354821i	$-0.115458\pi$
$401$	9.69869	+	10.7715i	0.484330	+	0.537903i	−0.450605	+	0.892724i	$0.648792\pi$
$402$	−7.84047	+	1.66654i	−0.391047	+	0.0831196i
$403$	−3.75280	−	1.67085i	−0.186940	−	0.0832312i
$404$	−39.5010	+	17.5870i	−1.96525	+	0.874985i
$405$	1.25744	+	3.87001i	0.0624828	+	0.192302i
$406$	28.0713	−	45.6520i	1.39316	−	2.26567i
$407$	−16.3670	−	17.0197i	−0.811281	−	0.843635i
$408$	4.75434	−	8.23476i	0.235375	−	0.407682i
$409$	3.21259	−	3.56794i	0.158852	−	0.176423i	−0.658465	−	0.752612i	$-0.728794\pi$
$409$	3.21259	−	3.56794i	0.158852	−	0.176423i	0.817317	+	0.576188i	$0.195461\pi$
$410$	−5.23478	+	49.8056i	−0.258527	+	2.45972i
$411$	0.674703	+	6.41937i	0.0332806	+	0.316644i
$412$	2.13315	−	6.56517i	0.105093	−	0.323443i
$413$	4.16887	−	0.766091i	0.205137	−	0.0376969i
$414$	14.1259	−	10.2631i	0.694251	−	0.504403i
$415$	56.2616	−	25.0493i	2.76177	−	1.22962i
$416$	0.882178	−	0.979758i	0.0432523	−	0.0480366i
$417$	7.85201	+	13.6001i	0.384515	+	0.665999i
$418$	15.4309	−	18.3119i	0.754752	−	0.895662i
$419$	−22.3303			−1.09091			−0.545454	−	0.838140i	$-0.683643\pi$
$419$	−22.3303			−1.09091			−0.545454	+	0.838140i	$0.683643\pi$
$420$	−30.5808	+	32.1273i	−1.49219	+	1.56765i
$421$	−8.21090	−	5.96557i	−0.400175	−	0.290744i	0.369437	−	0.929256i	$-0.379550\pi$
$421$	−8.21090	−	5.96557i	−0.400175	−	0.290744i	−0.769612	+	0.638512i	$0.779550\pi$
$422$	1.06440	+	10.1271i	0.0518140	+	0.492977i
$423$	−2.99437	+	0.636474i	−0.145591	+	0.0309464i
$424$	−44.1625	+	9.38702i	−2.14472	+	0.455874i
$425$	2.19058	+	20.8420i	0.106259	+	1.01098i
$426$	7.25758	+	5.27294i	0.351631	+	0.255475i
$427$	5.92665	+	1.43241i	0.286811	+	0.0693192i
$428$	30.6836			1.48315
$429$	2.30599	−	2.73651i	0.111334	−	0.132120i
$430$	8.62930	+	14.9464i	0.416142	+	0.720779i
$431$	−8.54785	+	9.49335i	−0.411736	+	0.457279i	−0.912966	−	0.408035i	$-0.866214\pi$
$431$	−8.54785	+	9.49335i	−0.411736	+	0.457279i	0.501231	+	0.865314i	$0.332881\pi$
$432$	4.32445	−	1.92537i	0.208060	−	0.0926344i
$433$	20.7731	−	15.0925i	0.998290	−	0.725300i	0.0365690	−	0.999331i	$-0.488357\pi$
$433$	20.7731	−	15.0925i	0.998290	−	0.725300i	0.961721	+	0.274031i	$0.0883571\pi$
$434$	8.35395	−	23.4772i	0.401003	−	1.12694i
$435$	10.2960	−	31.6878i	0.493654	−	1.51931i
$436$	−1.90747	−	18.1484i	−0.0913513	−	0.869150i
$437$	2.15326	−	20.4869i	0.103004	−	0.980022i
$438$	−7.76261	+	8.62125i	−0.370912	+	0.411939i
$439$	−7.22934	+	12.5216i	−0.345038	+	0.597623i	−0.985361	−	0.170483i	$-0.945467\pi$
$439$	−7.22934	+	12.5216i	−0.345038	+	0.597623i	0.640323	+	0.768106i	$0.278801\pi$
$440$	49.0585	+	51.0150i	2.33877	+	2.43204i
$441$	−3.83033	+	5.85906i	−0.182397	+	0.279003i
$442$	−1.49555	−	4.60284i	−0.0711362	−	0.218935i
$443$	−17.0330	+	7.58359i	−0.809263	+	0.360307i	−0.769295	−	0.638894i	$-0.779392\pi$
$443$	−17.0330	+	7.58359i	−0.809263	+	0.360307i	−0.0399682	+	0.999201i	$0.512726\pi$
$444$	−26.7954	−	11.9301i	−1.27165	−	0.566177i
$445$	39.1104	−	8.31318i	1.85401	−	0.394082i
$446$	32.1974	+	35.7588i	1.52459	+	1.69323i
$447$	−7.07700	+	5.14174i	−0.334731	+	0.243196i
$448$	−13.5116	−	10.4005i	−0.638362	−	0.491378i
$449$	10.1590	+	31.2661i	0.479431	+	1.47554i	0.839887	+	0.542761i	$0.182621\pi$
$449$	10.1590	+	31.2661i	0.479431	+	1.47554i	−0.360457	+	0.932776i	$0.617379\pi$
$450$	−14.2965	+	24.7623i	−0.673944	+	1.16731i
$451$	16.4911	−	0.541303i	0.776533	−	0.0254890i
$452$	−22.6537	−	39.2374i	−1.06554	−	1.84557i
$453$	8.24697	+	1.75295i	0.387476	+	0.0823606i
$454$	24.6590	+	17.9158i	1.15731	+	0.840832i
$455$	0.893768	+	11.5818i	0.0419005	+	0.542965i
$456$	4.72979	−	14.5568i	0.221493	−	0.681685i
$457$	23.6055	+	26.2166i	1.10422	+	1.22636i	0.971960	+	0.235147i	$0.0755570\pi$
$457$	23.6055	+	26.2166i	1.10422	+	1.22636i	0.132261	+	0.991215i	$0.457776\pi$
$458$	−21.2014	−	9.43948i	−0.990677	−	0.441078i
$459$	0.189527	−	1.80323i	0.00884635	−	0.0841674i
$460$	115.740	+	24.6013i	5.39640	+	1.14704i
$461$	34.5060			1.60710			0.803552	−	0.595234i	$-0.202941\pi$
$461$	34.5060			1.60710			0.803552	+	0.595234i	$0.202941\pi$
$462$	17.6270	+	12.6697i	0.820082	+	0.589446i
$463$	4.72008			0.219361			0.109680	−	0.993967i	$-0.465017\pi$
$463$	4.72008			0.219361			0.109680	+	0.993967i	$0.465017\pi$
$464$	−37.9127	−	8.05859i	−1.76005	−	0.374111i
$465$	1.61940	−	15.4075i	0.0750978	−	0.714508i
$466$	18.1066	+	8.06158i	0.838772	+	0.373445i
$467$	−20.3208	−	22.5686i	−0.940336	−	1.04435i	−0.998938	−	0.0460680i	$-0.985331\pi$
$467$	−20.3208	−	22.5686i	−0.940336	−	1.04435i	0.0586018	−	0.998281i	$-0.481336\pi$
$468$	1.37366	−	4.22770i	0.0634976	−	0.195425i
$469$	−7.73192	−	3.70240i	−0.357027	−	0.170961i
$470$	−24.9308	−	18.1133i	−1.14997	−	0.835505i
$471$	7.66821	+	1.62993i	0.353332	+	0.0751031i
$472$	−4.20084	−	7.27607i	−0.193359	−	0.334908i
$473$	4.48813	−	3.49140i	0.206365	−	0.160535i
$474$	−1.58903	+	2.75229i	−0.0729868	+	0.126417i
$475$	10.4243	+	32.0826i	0.478298	+	1.47205i
$476$	18.2709	−	7.53546i	0.837443	−	0.345387i
$477$	−6.96501	+	5.06038i	−0.318906	+	0.231699i
$478$	−22.5201	−	25.0111i	−1.03004	−	1.14398i
$479$	−8.03386	+	1.70765i	−0.367077	+	0.0780245i	−0.387757	−	0.921762i	$-0.626750\pi$
$479$	−8.03386	+	1.70765i	−0.367077	+	0.0780245i	0.0206805	+	0.999786i	$0.493417\pi$
$480$	4.54223	+	2.02233i	0.207323	+	0.0923064i
$481$	−7.01757	+	3.12443i	−0.319974	+	0.142462i
$482$	3.39460	+	10.4475i	0.154620	+	0.475870i
$483$	18.6668	+	0.517251i	0.849368	+	0.0235358i
$484$	28.0504	−	35.5945i	1.27502	−	1.61793i
$485$	−9.64000	+	16.6970i	−0.437730	+	0.758170i
$486$	1.65532	−	1.83842i	0.0750870	−	0.0833925i
$487$	3.17409	−	30.1995i	0.143832	−	1.36847i	−0.649816	−	0.760091i	$-0.725154\pi$
$487$	3.17409	−	30.1995i	0.143832	−	1.36847i	0.793648	−	0.608377i	$-0.208179\pi$
$488$	−1.26330	−	12.0195i	−0.0571870	−	0.544098i
$489$	−2.87565	+	8.85035i	−0.130042	+	0.400227i
$490$	−69.6311	+	10.8112i	−3.14561	+	0.488401i
$491$	−12.7215	+	9.24269i	−0.574112	+	0.417117i	−0.836597	−	0.547819i	$-0.815458\pi$
$491$	−12.7215	+	9.24269i	−0.574112	+	0.417117i	0.262485	+	0.964936i	$0.415458\pi$
$492$	18.7241	−	8.33652i	0.844149	−	0.375839i
$493$	−9.93405	+	11.0329i	−0.447407	+	0.496896i
$494$	−3.89519	−	6.74667i	−0.175253	−	0.303547i
$495$	12.5026	+	5.08185i	0.561949	+	0.228412i
$496$	−18.0225			−0.809232
$497$	2.71091	+	9.20331i	0.121601	+	0.412825i
$498$	−30.2904	−	22.0073i	−1.35735	−	0.986170i
$499$	−0.669333	−	6.36828i	−0.0299635	−	0.285083i	−0.999236	−	0.0390924i	$-0.987553\pi$
$499$	−0.669333	−	6.36828i	−0.0299635	−	0.285083i	0.969272	−	0.245991i	$-0.0791133\pi$
$500$	−107.542	+	22.8587i	−4.80941	+	1.02227i
$501$	22.4905	−	4.78050i	1.00480	−	0.213577i
$502$	3.12764	+	29.7575i	0.139593	+	1.32814i
$503$	9.91316	+	7.20234i	0.442006	+	0.321136i	0.786432	−	0.617677i	$-0.211926\pi$
$503$	9.91316	+	7.20234i	0.442006	+	0.321136i	−0.344425	+	0.938814i	$0.611926\pi$
$504$	13.4867	+	3.25960i	0.600746	+	0.145194i
$505$	−42.7069			−1.90043
$506$	4.16059	−	57.7606i	0.184961	−	2.56777i
$507$	5.91790	+	10.2501i	0.262823	+	0.455223i
$508$	9.17096	−	10.1854i	0.406895	−	0.451903i
$509$	36.5327	−	16.2654i	1.61929	−	0.720952i	0.621250	−	0.783612i	$-0.286625\pi$
$509$	36.5327	−	16.2654i	1.61929	−	0.720952i	0.998035	+	0.0626601i	$0.0199584\pi$
$510$	14.7663	−	10.7283i	0.653862	−	0.475058i
$511$	−12.2029	+	2.24246i	−0.539824	+	0.0992004i
$512$	−13.5552	+	41.7186i	−0.599060	+	1.84372i
$513$	−0.305077	−	2.90261i	−0.0134695	−	0.128154i
$514$	4.53840	−	43.1800i	0.200180	−	1.90459i
$515$	4.56216	−	5.06680i	0.201033	−	0.223270i
$516$	3.53170	−	6.11708i	0.155474	−	0.269289i
$517$	−4.78535	+	8.95464i	−0.210459	+	0.393824i
$518$	−22.1722	−	40.9848i	−0.974189	−	1.80077i
$519$	−3.63471	−	11.1865i	−0.159546	−	0.491032i
$520$	21.0345	−	9.36518i	0.922425	−	0.410690i
$521$	−26.5749	−	11.8319i	−1.16427	−	0.518366i	−0.268672	−	0.963232i	$-0.586585\pi$
$521$	−26.5749	−	11.8319i	−1.16427	−	0.518366i	−0.895597	+	0.444866i	$0.853251\pi$
$522$	−19.8132	+	4.21143i	−0.867202	+	0.184329i
$523$	−8.15874	−	9.06120i	−0.356757	−	0.396218i	0.537874	−	0.843025i	$-0.319228\pi$
$523$	−8.15874	−	9.06120i	−0.356757	−	0.396218i	−0.894630	+	0.446807i	$0.852561\pi$
$524$	−24.1541	+	17.5490i	−1.05518	+	0.766631i
$525$	−28.2700	+	11.6594i	−1.23380	+	0.508859i
$526$	−22.8820	−	70.4236i	−0.997704	−	3.07062i
$527$	−3.45159	+	5.97833i	−0.150354	+	0.260420i
$528$	4.35908	−	15.0826i	0.189705	−	0.656387i
$529$	−13.4083	−	23.2239i	−0.582971	−	1.00974i
$530$	−84.7708	−	18.0186i	−3.68221	−	0.782677i
$531$	−1.29610	−	0.941673i	−0.0562460	−	0.0408651i
$532$	26.2456	−	17.9793i	1.13789	−	0.779503i
$533$	1.65875	−	5.10510i	0.0718484	−	0.221127i
$534$	−16.2654	−	18.0646i	−0.703873	−	0.781730i
$535$	27.6858	+	12.3265i	1.19696	+	0.532921i
$536$	−1.77617	+	16.8992i	−0.0767190	+	0.729932i
$537$	−3.71155	−	0.788913i	−0.160165	−	0.0340441i
$538$	−61.2030			−2.63865
$539$	6.67361	+	22.2365i	0.287453	+	0.957795i
$540$	16.7645			0.721430
$541$	−33.4908	−	7.11870i	−1.43988	−	0.306057i	−0.579195	−	0.815189i	$-0.696633\pi$
$541$	−33.4908	−	7.11870i	−1.43988	−	0.306057i	−0.860688	+	0.509132i	$0.829966\pi$
$542$	3.09674	−	29.4635i	0.133016	−	1.26557i
$543$	−21.3467	−	9.50415i	−0.916073	−	0.407862i
$544$	−1.48245	−	1.64643i	−0.0635595	−	0.0705900i
$545$	5.56963	−	17.1416i	0.238577	−	0.734264i
$546$	5.82613	−	3.99114i	0.249335	−	0.170805i
$547$	13.8722	+	10.0787i	0.593130	+	0.430935i	0.843434	−	0.537233i	$-0.180530\pi$
$547$	13.8722	+	10.0787i	0.593130	+	0.430935i	−0.250303	+	0.968167i	$0.580530\pi$
$548$	26.0116	+	5.52894i	1.11116	+	0.236185i
$549$	−1.15228	−	1.99581i	−0.0491781	−	0.0851790i
$550$	32.2479	+	89.1810i	1.37505	+	3.80269i
$551$	−11.9488	+	20.6959i	−0.509036	+	0.881677i
$552$	−11.4381	−	35.2029i	−0.486838	−	1.49833i
$553$	−3.14217	+	1.29593i	−0.133619	+	0.0551084i
$554$	−13.6644	+	9.92775i	−0.580544	+	0.421790i
$555$	−19.3848	−	21.5290i	−0.822839	−	0.913856i
$556$	63.2850	−	13.4516i	2.68388	−	0.570477i
$557$	9.19292	+	4.09295i	0.389516	+	0.173424i	0.592144	−	0.805832i	$-0.298282\pi$
$557$	9.19292	+	4.09295i	0.389516	+	0.173424i	−0.202628	+	0.979256i	$0.564948\pi$
$558$	−8.60429	+	3.83088i	−0.364249	+	0.162174i
$559$	−0.571640	−	1.75933i	−0.0241778	−	0.0744116i
$560$	24.2493	+	44.8242i	1.02472	+	1.89417i
$561$	−4.16831	−	4.33454i	−0.175986	−	0.183004i
$562$	0.00884540	−	0.0153207i	0.000373121	−	0.000646264i
$563$	−5.79431	+	6.43524i	−0.244201	+	0.271213i	−0.852768	−	0.522290i	$-0.825078\pi$
$563$	−5.79431	+	6.43524i	−0.244201	+	0.271213i	0.608567	+	0.793503i	$0.291745\pi$
$564$	−1.31832	+	12.5430i	−0.0555114	+	0.528155i
$565$	−4.67761	−	44.5045i	−0.196789	−	1.87232i
$566$	12.7852	−	39.3488i	0.537402	−	1.65395i
$567$	2.60218	−	0.478188i	0.109281	−	0.0200820i
$568$	15.3853	−	11.1780i	0.645551	−	0.469021i
$569$	−17.4822	+	7.78359i	−0.732893	+	0.326305i	−0.739027	−	0.673676i	$-0.764714\pi$
$569$	−17.4822	+	7.78359i	−0.732893	+	0.326305i	0.00613360	+	0.999981i	$0.498048\pi$
$570$	19.6591	−	21.8336i	0.823429	−	0.914510i
$571$	9.36356	+	16.2182i	0.391853	+	0.678709i	0.992694	−	0.120660i	$-0.0385009\pi$
$571$	9.36356	+	16.2182i	0.391853	+	0.678709i	−0.600841	+	0.799368i	$0.705168\pi$
$572$	−7.78654	−	12.5193i	−0.325572	−	0.523460i
$573$	24.8635			1.03869
$574$	31.6504	+	7.64957i	1.32106	+	0.319287i
$575$	65.9984	+	47.9506i	2.75232	+	1.99968i
$576$	0.673648	+	6.40933i	0.0280687	+	0.267055i
$577$	−12.1008	+	2.57210i	−0.503762	+	0.107078i	−0.452781	−	0.891622i	$-0.649568\pi$
$577$	−12.1008	+	2.57210i	−0.503762	+	0.107078i	−0.0509811	+	0.998700i	$0.516235\pi$
$578$	33.1811	−	7.05287i	1.38015	−	0.293361i
$579$	0.367052	+	3.49227i	0.0152542	+	0.145134i
$580$	−111.053	−	80.6844i	−4.61120	−	3.35024i
$581$	−11.3143	−	38.4112i	−0.469397	−	1.59356i
$582$	11.7212			0.485860
$583$	−2.05145	+	28.4798i	−0.0849623	+	1.17951i
$584$	12.2964	+	21.2981i	0.508831	+	0.881321i
$585$	2.93785	−	3.26281i	0.121465	−	0.134900i
$586$	−2.93695	+	1.30761i	−0.121324	+	0.0540170i
$587$	−21.3881	+	15.5393i	−0.882780	+	0.641377i	−0.933986	−	0.357311i	$-0.883694\pi$
$587$	−21.3881	+	15.5393i	−0.882780	+	0.641377i	0.0512055	+	0.998688i	$0.483694\pi$
$588$	18.0808	+	22.4674i	0.745638	+	0.926542i
$589$	−3.43376	+	10.5680i	−0.141486	+	0.435449i
$590$	−1.68575	−	16.0389i	−0.0694013	−	0.660309i
$591$	−2.67586	+	25.4591i	−0.110070	+	1.04725i
$592$	−22.5505	+	25.0449i	−0.926821	+	1.02934i
$593$	−8.34955	+	14.4618i	−0.342875	+	0.593877i	−0.984965	−	0.172752i	$-0.944734\pi$
$593$	−8.34955	+	14.4618i	−0.342875	+	0.593877i	0.642091	+	0.766629i	$0.278067\pi$
$594$	−1.12487	−	8.12733i	−0.0461539	−	0.333468i
$595$	19.5130	+	0.540700i	0.799955	+	0.0221665i
$596$	11.1368	+	34.2755i	0.456180	+	1.40398i
$597$	4.78074	−	2.12852i	0.195663	−	0.0871146i
$598$	−17.2108	−	7.66275i	−0.703802	−	0.313353i
$599$	33.9152	−	7.20889i	1.38574	−	0.294547i	0.546111	−	0.837713i	$-0.316108\pi$
$599$	33.9152	−	7.20889i	1.38574	−	0.294547i	0.839626	+	0.543165i	$0.182774\pi$
$600$	40.5587	+	45.0450i	1.65580	+	1.83895i
$601$	−20.6424	+	14.9976i	−0.842022	+	0.611765i	−0.922935	−	0.384956i	$-0.874217\pi$
$601$	−20.6424	+	14.9976i	−0.842022	+	0.611765i	0.0809127	+	0.996721i	$0.474217\pi$
$602$	10.3738	−	4.27847i	0.422804	−	0.174377i
$603$	1.00126	+	3.08157i	0.0407746	+	0.125491i
$604$	17.3678	−	30.0819i	0.706686	−	1.22402i
$605$	39.6092	−	20.8482i	1.61034	−	0.847601i
$606$	12.9818	+	22.4851i	0.527349	+	0.913394i
$607$	1.51057	+	0.321081i	0.0613121	+	0.0130323i	0.238466	−	0.971151i	$-0.423356\pi$
$607$	1.51057	+	0.321081i	0.0613121	+	0.0130323i	−0.177154	+	0.984183i	$0.556689\pi$
$608$	−2.88513	−	2.09617i	−0.117008	−	0.0850110i
$609$	−19.5389	−	9.35614i	−0.791757	−	0.379130i
$610$	7.16882	−	22.0634i	0.290257	−	0.893320i
$611$	2.21016	+	2.45464i	0.0894137	+	0.0993039i
$612$	−6.82419	−	3.03833i	−0.275852	−	0.122817i
$613$	−0.512468	+	4.87581i	−0.0206984	+	0.196932i	−0.999985	−	0.00554890i	$-0.998234\pi$
$613$	−0.512468	+	4.87581i	−0.0206984	+	0.196932i	0.979286	+	0.202481i	$0.0649004\pi$
$614$	−9.48543	−	2.01619i	−0.382801	−	0.0813669i
$615$	20.2438			0.816308
$616$	37.0908	−	27.2387i	1.49443	−	1.09748i
$617$	16.4856			0.663686			0.331843	−	0.943335i	$-0.392330\pi$
$617$	16.4856			0.663686			0.331843	+	0.943335i	$0.392330\pi$
$618$	−4.05443	−	0.861796i	−0.163093	−	0.0346665i
$619$	1.95090	−	18.5616i	0.0784134	−	0.746054i	−0.882707	−	0.469924i	$-0.844281\pi$
$619$	1.95090	−	18.5616i	0.0784134	−	0.746054i	0.961120	−	0.276130i	$-0.0890520\pi$
$620$	−58.3089	−	25.9608i	−2.34174	−	1.04261i
$621$	−4.72279	−	5.24518i	−0.189519	−	0.210482i
$622$	−0.572637	+	1.76240i	−0.0229607	+	0.0706656i
$623$	−2.00027	−	25.9204i	−0.0801392	−	1.03848i
$624$	−4.13210	−	3.00215i	−0.165416	−	0.120182i
$625$	−49.6899	−	10.5619i	−1.98760	−	0.422477i
$626$	32.2498	+	55.8583i	1.28896	+	2.23255i
$627$	−8.01366	−	5.42973i	−0.320035	−	0.216843i
$628$	16.1490	−	27.9708i	0.644414	−	1.11616i
$629$	3.98899	+	12.2768i	0.159051	+	0.489510i
$630$	21.1050	+	16.2455i	0.840843	+	0.647238i
$631$	−17.2078	+	12.5022i	−0.685031	+	0.497704i	−0.875023	−	0.484081i	$-0.839154\pi$
$631$	−17.2078	+	12.5022i	−0.685031	+	0.497704i	0.189992	+	0.981786i	$0.439154\pi$
$632$	4.50803	+	5.00668i	0.179320	+	0.199155i
$633$	4.02626	−	0.855807i	0.160029	−	0.0340153i
$634$	25.8361	+	11.5030i	1.02608	+	0.456841i
$635$	12.3667	−	5.50602i	0.490758	−	0.218500i
$636$	10.9605	+	33.7331i	0.434614	+	1.33760i
$637$	7.54125	+	0.418253i	0.298795	+	0.0165718i
$638$	−31.6638	+	59.2513i	−1.25358	+	2.34578i
$639$	1.81315	−	3.14046i	0.0717269	−	0.124235i
$640$	−50.0637	+	55.6013i	−1.97894	+	2.19784i
$641$	−0.423473	+	4.02908i	−0.0167262	+	0.159139i	−0.999697	−	0.0246238i	$-0.992161\pi$
$641$	−0.423473	+	4.02908i	−0.0167262	+	0.159139i	0.982971	+	0.183763i	$0.0588279\pi$
$642$	−1.92587	−	18.3234i	−0.0760081	−	0.723168i
$643$	−13.0903	+	40.2879i	−0.516232	+	1.58880i	0.264796	+	0.964304i	$0.414695\pi$
$643$	−13.0903	+	40.2879i	−0.516232	+	1.58880i	−0.781029	+	0.624495i	$0.785305\pi$
$644$	25.7917	−	72.4826i	1.01634	−	2.85621i
$645$	5.64406	−	4.10065i	0.222235	−	0.161463i
$646$	−11.9595	+	5.32471i	−0.470540	+	0.209498i
$647$	−13.3579	+	14.8354i	−0.525152	+	0.583241i	−0.946112	−	0.323838i	$-0.895027\pi$
$647$	−13.3579	+	14.8354i	−0.525152	+	0.583241i	0.420960	+	0.907079i	$0.361693\pi$
$648$	−2.62213	−	4.54167i	−0.103007	−	0.178414i
$649$	−5.15831	+	1.27464i	−0.202482	+	0.0500341i
$650$	30.8512			1.21008
$651$	−9.79117	−	2.36642i	−0.383746	−	0.0927475i
$652$	31.0168	+	22.5350i	1.21471	+	0.882540i
$653$	2.32760	+	22.1456i	0.0910861	+	0.866626i	0.940704	+	0.339228i	$0.110166\pi$
$653$	2.32760	+	22.1456i	0.0910861	+	0.866626i	−0.849618	+	0.527398i	$0.823168\pi$
$654$	−10.7180	+	2.27818i	−0.419107	+	0.0890840i
$655$	−28.8442	+	6.13102i	−1.12704	+	0.239559i
$656$	−2.46162	−	23.4208i	−0.0961102	−	0.914427i
$657$	3.79387	+	2.75641i	0.148013	+	0.107538i
$658$	−13.8143	+	14.5130i	−0.538539	+	0.565774i
$659$	−38.0096			−1.48064			−0.740322	−	0.672253i	$-0.765327\pi$
$659$	−38.0096			−1.48064			−0.740322	+	0.672253i	$0.765327\pi$
$660$	35.8292	−	42.5184i	1.39465	−	1.65503i
$661$	−6.58149	−	11.3995i	−0.255990	−	0.443388i	0.709174	−	0.705034i	$-0.249068\pi$
$661$	−6.58149	−	11.3995i	−0.255990	−	0.443388i	−0.965164	+	0.261645i	$0.915735\pi$
$662$	4.70095	−	5.22094i	0.182708	−	0.202918i
$663$	−1.78722	+	0.795722i	−0.0694099	+	0.0309033i
$664$	−64.2123	+	46.6530i	−2.49192	+	1.81049i
$665$	30.9042	−	5.67910i	1.19842	−	0.220226i
$666$	−5.44251	+	16.7503i	−0.210893	+	0.649061i
$667$	6.04090	+	57.4753i	0.233904	+	2.22545i
$668$	9.90181	−	94.2095i	0.383113	−	3.64507i
$669$	13.0151	−	14.4548i	0.503194	−	0.558854i
$670$	−16.3085	+	28.2471i	−0.630052	+	1.09128i
$671$	−7.52444	−	1.34302i	−0.290478	−	0.0518466i
$672$	1.69334	−	2.75386i	0.0653221	−	0.106232i
$673$	1.52303	+	4.68739i	0.0587083	+	0.180686i	0.976110	−	0.217277i	$-0.0697174\pi$
$673$	1.52303	+	4.68739i	0.0587083	+	0.180686i	−0.917402	+	0.397962i	$0.869717\pi$
$674$	37.9707	−	16.9056i	1.46258	−	0.651181i
$675$	10.5589	+	4.70112i	0.406412	+	0.180946i
$676$	47.6966	−	10.1382i	1.83449	−	0.389932i
$677$	−15.7281	−	17.4678i	−0.604480	−	0.671343i	0.360775	−	0.932653i	$-0.382512\pi$
$677$	−15.7281	−	17.4678i	−0.604480	−	0.671343i	−0.965255	+	0.261310i	$0.915846\pi$
$678$	−22.0097	+	15.9909i	−0.845276	+	0.614129i
$679$	9.93364	+	7.64641i	0.381218	+	0.293442i
$680$	−11.9566	−	36.7987i	−0.458516	−	1.41117i
$681$	6.16051	−	10.6703i	0.236071	−	0.408888i
$682$	−8.67319	+	30.0097i	−0.332114	+	1.14913i
$683$	5.68696	+	9.85011i	0.217606	+	0.376904i	0.954075	−	0.299566i	$-0.0968420\pi$
$683$	5.68696	+	9.85011i	0.217606	+	0.376904i	−0.736470	+	0.676470i	$0.763509\pi$
$684$	−11.7616	−	2.50000i	−0.449714	−	0.0955897i
$685$	21.2491	+	15.4384i	0.811888	+	0.589871i
$686$	0.990097	+	45.8055i	0.0378021	+	1.74886i
$687$	−2.89898	+	8.92214i	−0.110603	+	0.340401i
$688$	−5.43050	−	6.03118i	−0.207036	−	0.229937i
$689$	8.48607	+	3.77824i	0.323293	+	0.143940i
$690$	7.42676	−	70.6609i	0.282732	−	2.69002i
$691$	−0.694064	−	0.147528i	−0.0264034	−	0.00561222i	0.194691	−	0.980865i	$-0.437630\pi$
$691$	−0.694064	−	0.147528i	−0.0264034	−	0.00561222i	−0.221094	+	0.975252i	$0.570963\pi$
$692$	−48.4588			−1.84213
$693$	4.34860	−	7.62166i	0.165189	−	0.289523i
$694$	88.5939			3.36298
$695$	62.5059	+	13.2860i	2.37098	+	0.503968i
$696$	−4.48847	+	42.7050i	−0.170135	+	1.61873i
$697$	−8.24047	−	3.66889i	−0.312130	−	0.138969i
$698$	42.1229	+	46.7822i	1.59438	+	1.77073i
$699$	2.47581	−	7.61976i	0.0936438	−	0.288206i
$700$	9.69350	+	125.613i	0.366380	+	4.74771i
$701$	0.294453	+	0.213932i	0.0111213	+	0.00808011i	0.593332	−	0.804958i	$-0.297812\pi$
$701$	0.294453	+	0.213932i	0.0111213	+	0.00808011i	−0.582211	+	0.813038i	$0.697812\pi$
$702$	−2.61089	−	0.554961i	−0.0985416	−	0.0209457i
$703$	10.3894	+	17.9949i	0.391843	+	0.678692i
$704$	17.6951	+	11.9895i	0.666911	+	0.451872i
$705$	−6.22841	+	10.7879i	−0.234576	+	0.406297i
$706$	−19.1869	−	59.0512i	−0.722108	−	2.22242i
$707$	−3.66634	+	27.5247i	−0.137887	+	1.03517i
$708$	−5.33980	+	3.87959i	−0.200682	+	0.145804i
$709$	−2.59417	−	2.88112i	−0.0974263	−	0.108203i	0.692460	−	0.721456i	$-0.256527\pi$
$709$	−2.59417	−	2.88112i	−0.0974263	−	0.108203i	−0.789886	+	0.613254i	$0.789860\pi$
$710$	35.7063	−	7.58961i	1.34003	−	0.284833i
$711$	1.17360	+	0.522522i	0.0440136	+	0.0195961i
$712$	−47.0757	+	20.9595i	−1.76424	+	0.785489i
$713$	8.30391	+	25.5568i	0.310984	+	0.957110i
$714$	−5.64676	−	10.4379i	−0.211325	−	0.390629i
$715$	−1.99640	−	14.4243i	−0.0746612	−	0.539437i
$716$	−7.81638	+	13.5384i	−0.292112	+	0.505953i
$717$	−9.10329	+	10.1102i	−0.339969	+	0.377573i
$718$	8.12845	−	77.3370i	0.303351	−	2.88619i
$719$	−2.32569	−	22.1274i	−0.0867334	−	0.825214i	−0.948259	−	0.317499i	$-0.897157\pi$
$719$	−2.32569	−	22.1274i	−0.0867334	−	0.825214i	0.861525	−	0.507715i	$-0.169510\pi$
$720$	5.95236	−	18.3195i	0.221831	−	0.682727i
$721$	−2.87390	−	3.37530i	−0.107030	−	0.125703i
$722$	20.9780	−	15.2414i	0.780719	−	0.567226i
$723$	4.05662	−	1.80612i	0.150867	−	0.0671704i
$724$	−64.4163	+	71.5416i	−2.39401	+	2.65882i
$725$	−47.3192	−	81.9593i	−1.75739	−	3.04389i
$726$	−23.0167	−	14.5168i	−0.854230	−	0.538770i
$727$	−19.3664			−0.718259			−0.359129	−	0.933288i	$-0.616926\pi$
$727$	−19.3664			−0.718259			−0.359129	+	0.933288i	$0.616926\pi$
$728$	−4.23008	−	14.3608i	−0.156777	−	0.532246i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	4.93443	+	46.9480i	0.182632	+	1.73762i
$731$	−3.04066	+	0.646313i	−0.112463	+	0.0239047i
$732$	−9.28705	+	1.97402i	−0.343259	+	0.0729620i
$733$	−2.10830	−	20.0592i	−0.0778720	−	0.740903i	−0.961888	−	0.273445i	$-0.911837\pi$
$733$	−2.10830	−	20.0592i	−0.0778720	−	0.740903i	0.884016	−	0.467457i	$-0.154830\pi$
$734$	57.6430	+	41.8801i	2.12764	+	1.54582i
$735$	7.28843	+	27.5359i	0.268838	+	1.01568i
$736$	−8.62423			−0.317893
$737$	9.95542	+	4.04653i	0.366713	+	0.149056i
$738$	−6.15358	−	10.6583i	−0.226516	−	0.392338i
$739$	−1.16307	+	1.29172i	−0.0427841	+	0.0475165i	−0.764157	−	0.645030i	$-0.776845\pi$
$739$	−1.16307	+	1.29172i	−0.0427841	+	0.0475165i	0.721373	+	0.692547i	$0.243511\pi$
$740$	−109.035	+	48.5455i	−4.00821	+	1.78457i
$741$	−2.54768	+	1.85100i	−0.0935913	+	0.0679981i
$742$	−18.8905	+	53.0880i	−0.693492	+	1.94892i
$743$	10.3871	−	31.9682i	0.381066	−	1.17280i	−0.558229	−	0.829687i	$-0.688519\pi$
$743$	10.3871	−	31.9682i	0.381066	−	1.17280i	0.939294	−	0.343113i	$-0.111481\pi$
$744$	2.08705	+	19.8569i	0.0765149	+	0.727990i
$745$	−3.72076	+	35.4007i	−0.136318	+	1.29698i
$746$	19.8042	−	21.9948i	0.725085	−	0.805289i
$747$	−7.56739	+	13.1071i	−0.276876	+	0.479564i
$748$	−22.2905	+	10.8141i	−0.815022	+	0.395402i
$749$	10.3212	−	16.7853i	0.377130	−	0.613322i
$750$	20.4005	+	62.7863i	0.744922	+	2.29263i
$751$	−37.5650	+	16.7250i	−1.37077	+	0.610305i	−0.954301	−	0.298847i	$-0.903398\pi$
$751$	−37.5650	+	16.7250i	−1.37077	+	0.610305i	−0.416466	+	0.909151i	$0.636731\pi$
$752$	13.2383	+	5.89407i	0.482751	+	0.214935i
$753$	11.8308	−	2.51472i	0.431139	−	0.0916413i
$754$	14.6243	+	16.2419i	0.532585	+	0.591495i
$755$	27.7558	−	20.1657i	1.01014	−	0.733907i
$756$	1.43922	−	10.8048i	0.0523438	−	0.392966i
$757$	4.74416	+	14.6010i	0.172430	+	0.530684i	0.999507	−	0.0314048i	$-0.00999810\pi$
$757$	4.74416	+	14.6010i	0.172430	+	0.530684i	−0.827077	+	0.562088i	$0.809998\pi$
$758$	18.0918	−	31.3359i	0.657123	−	1.13817i
$759$	−23.3964	+	0.767965i	−0.849237	+	0.0278754i
$760$	−31.1412	−	53.9382i	−1.12961	−	1.95654i
$761$	1.65820	+	0.352461i	0.0601097	+	0.0127767i	0.237868	−	0.971297i	$-0.423551\pi$
$761$	1.65820	+	0.352461i	0.0601097	+	0.0127767i	−0.177759	+	0.984074i	$0.556885\pi$
$762$	−6.65806	−	4.83736i	−0.241196	−	0.175239i
$763$	−10.5696	−	5.06122i	−0.382646	−	0.183228i
$764$	31.6541	−	97.4211i	1.14520	−	3.52457i
$765$	−4.93688	−	5.48296i	−0.178493	−	0.198237i
$766$	−31.4232	−	13.9905i	−1.13537	−	0.505497i
$767$	−0.180688	+	1.71913i	−0.00652425	+	0.0620741i
$768$	31.8844	+	6.77724i	1.15053	+	0.244552i
$769$	36.3988			1.31258			0.656288	−	0.754511i	$-0.272126\pi$
$769$	36.3988			1.31258			0.656288	+	0.754511i	$0.272126\pi$
$770$	86.3077	−	18.8067i	3.11032	−	0.677747i
$771$	−17.5508			−0.632076
$772$	14.1509	+	3.00786i	0.509301	+	0.108255i
$773$	0.709511	−	6.75054i	0.0255193	−	0.242800i	−0.974325	−	0.225147i	$-0.927714\pi$
$773$	0.709511	−	6.75054i	0.0255193	−	0.242800i	0.999844	−	0.0176533i	$-0.00561952\pi$
$774$	−3.87463	−	1.72510i	−0.139271	−	0.0620073i
$775$	−29.4451	−	32.7020i	−1.05770	−	1.17469i
$776$	7.67835	−	23.6315i	0.275637	−	0.848323i
$777$	−15.5397	+	10.6453i	−0.557482	+	0.381898i
$778$	26.9104	+	19.5515i	0.964784	+	0.700957i
$779$	−14.2025	−	3.01884i	−0.508858	−	0.108161i
$780$	−9.04427	−	15.6651i	−0.323837	−	0.560902i
$781$	−4.08981	−	11.3103i	−0.146345	−	0.404715i
$782$	−15.8294	+	27.4174i	−0.566059	+	0.980442i
$783$	2.53024	+	7.78728i	0.0904234	+	0.278295i
$784$	30.9711	−	11.7806i	1.10611	−	0.420735i
$785$	25.8079	−	18.7506i	0.921124	−	0.669236i
$786$	11.9958	+	13.3227i	0.427877	+	0.475206i
$787$	13.0771	−	2.77962i	0.466147	−	0.0990827i	0.0311507	−	0.999515i	$-0.490083\pi$
$787$	13.0771	−	2.77962i	0.466147	−	0.0990827i	0.434997	+	0.900432i	$0.356749\pi$
$788$	96.3483	+	42.8970i	3.43227	+	1.52814i
$789$	−27.3445	+	12.1746i	−0.973491	+	0.433426i
$790$	3.99624	+	12.2992i	0.142180	+	0.437585i
$791$	−29.0848	−	0.805932i	−1.03414	−	0.0286556i
$792$	−17.1227	−	3.05618i	−0.608427	−	0.108596i
$793$	−1.24328	+	2.15343i	−0.0441503	+	0.0764705i
$794$	−45.0438	+	50.0262i	−1.59854	+	1.77536i
$795$	−3.66188	+	34.8405i	−0.129874	+	1.23567i
$796$	−2.25364	−	21.4420i	−0.0798782	−	0.759990i
$797$	14.7244	−	45.3171i	0.521565	−	1.60521i	−0.249444	−	0.968389i	$-0.580248\pi$
$797$	14.7244	−	45.3171i	0.521565	−	1.60521i	0.771010	−	0.636823i	$-0.219752\pi$
$798$	−12.3841	−	14.5447i	−0.438393	−	0.514877i
$799$	4.49050	−	3.26254i	0.158863	−	0.115420i
$800$	12.9018	−	5.74427i	0.456149	−	0.203091i
$801$	−6.57496	+	7.30223i	−0.232315	+	0.258012i
$802$	−17.9285	−	31.0531i	−0.633078	−	1.09652i
$803$	15.0991	−	3.73106i	0.532836	−	0.131666i
$804$	13.3491			0.470786
$805$	52.3902	−	55.0397i	1.84651	−	1.93989i
$806$	8.22157	+	5.97332i	0.289592	+	0.210401i
$807$	2.58604	+	24.6045i	0.0910330	+	0.866121i
$808$	53.8371	−	11.4434i	1.89398	−	0.402578i
$809$	−1.38548	+	0.294492i	−0.0487108	+	0.0103538i	−0.232203	−	0.972667i	$-0.574593\pi$
$809$	−1.38548	+	0.294492i	−0.0487108	+	0.0103538i	0.183492	+	0.983021i	$0.441260\pi$
$810$	−1.05223	−	10.0113i	−0.0369717	−	0.351762i
$811$	10.3018	+	7.48473i	0.361747	+	0.262824i	0.753780	−	0.657127i	$-0.228228\pi$
$811$	10.3018	+	7.48473i	0.361747	+	0.262824i	−0.392034	+	0.919951i	$0.628228\pi$
$812$	−61.5350	+	64.6469i	−2.15945	+	2.26866i
$813$	−11.9756			−0.420004
$814$	30.8506	+	49.6021i	1.08131	+	1.73855i
$815$	18.9335	+	32.7937i	0.663210	+	1.14871i
$816$	−5.74312	+	6.37838i	−0.201049	+	0.223288i
$817$	−4.57123	+	2.03524i	−0.159927	+	0.0712042i
$818$	−9.60889	+	6.98127i	−0.335967	+	0.244094i
$819$	−1.85067	−	2.17355i	−0.0646678	−	0.0759502i
$820$	25.7727	−	79.3202i	0.900021	−	2.76998i
$821$	−3.30439	−	31.4392i	−0.115324	−	1.09723i	−0.887176	−	0.461432i	$-0.847336\pi$
$821$	−3.30439	−	31.4392i	−0.115324	−	1.09723i	0.771852	−	0.635803i	$-0.219331\pi$
$822$	1.66911	−	15.8805i	0.0582168	−	0.553896i
$823$	−29.5381	+	32.8054i	−1.02963	+	1.14352i	−0.0401024	+	0.999196i	$0.512768\pi$
$823$	−29.5381	+	32.8054i	−1.02963	+	1.14352i	−0.989530	+	0.144327i	$0.953898\pi$
$824$	−4.39348	+	7.60973i	−0.153054	+	0.265098i
$825$	34.4895	−	16.7323i	1.20077	−	0.582545i
$826$	−10.4818	−	0.290448i	−0.364708	−	0.0101060i
$827$	−1.07765	−	3.31666i	−0.0374735	−	0.115332i	0.930570	−	0.366114i	$-0.119312\pi$
$827$	−1.07765	−	3.31666i	−0.0374735	−	0.115332i	−0.968043	+	0.250783i	$0.919312\pi$
$828$	−26.5646	+	11.8273i	−0.923183	+	0.411027i
$829$	−6.28879	−	2.79995i	−0.218419	−	0.0972463i	0.294610	−	0.955617i	$-0.404810\pi$
$829$	−6.28879	−	2.79995i	−0.218419	−	0.0972463i	−0.513029	+	0.858371i	$0.671477\pi$
$830$	−149.025	+	31.6762i	−5.17272	+	1.09950i
$831$	4.56847	+	5.07381i	0.158479	+	0.176008i
$832$	5.62559	−	4.08723i	0.195032	−	0.141699i
$833$	2.02365	−	12.5297i	0.0701153	−	0.434130i
$834$	−12.0051	−	36.9478i	−0.415702	−	1.27940i
$835$	46.7811	−	81.0273i	1.61893	−	2.80406i
$836$	−31.4773	+	24.4868i	−1.08867	+	0.846894i
$837$	1.90363	+	3.29719i	0.0657992	+	0.113968i
$838$	54.0346	+	11.4854i	1.86659	+	0.396757i
$839$	−33.2343	−	24.1461i	−1.14738	−	0.833617i	−0.159246	−	0.987239i	$-0.550906\pi$
$839$	−33.2343	−	24.1461i	−1.14738	−	0.833617i	−0.988130	+	0.153622i	$0.950906\pi$
$840$	46.5787	−	31.9083i	1.60712	−	1.10094i
$841$	11.7562	−	36.1818i	0.405386	−	1.24765i
$842$	16.8002	+	18.6586i	0.578975	+	0.643017i
$843$	−0.00653290	−	0.00290864i	−0.000225005	−	0.000100179i
$844$	1.77263	−	16.8654i	0.0610163	−	0.580531i
$845$	47.1095	+	10.0134i	1.62062	+	0.344472i
$846$	7.57309			0.260368
$847$	−10.0363	−	27.3180i	−0.344852	−	0.938657i
$848$	40.7535			1.39948
$849$	−16.3590	−	3.47722i	−0.561440	−	0.119338i
$850$	5.41914	−	51.5597i	0.185875	−	1.76848i
$851$	45.9052	+	20.4383i	1.57361	+	0.700617i
$852$	−9.99675	−	11.1025i	−0.342483	−	0.380366i
$853$	13.9067	−	42.8004i	0.476156	−	1.46546i	−0.368236	−	0.929732i	$-0.620038\pi$
$853$	13.9067	−	42.8004i	0.476156	−	1.46546i	0.844392	−	0.535726i	$-0.179962\pi$
$854$	−13.6044	−	6.51444i	−0.465535	−	0.222919i
$855$	−9.60812	−	6.98071i	−0.328591	−	0.238735i
$856$	−38.2041	−	8.12053i	−1.30579	−	0.277554i
$857$	16.7462	+	29.0052i	0.572038	+	0.990798i	0.996357	+	0.0852854i	$0.0271802\pi$
$857$	16.7462	+	29.0052i	0.572038	+	0.990798i	−0.424319	+	0.905513i	$0.639486\pi$
$858$	−6.98749	+	5.43570i	−0.238549	+	0.185572i
$859$	1.51934	−	2.63158i	0.0518393	−	0.0897883i	−0.838941	−	0.544222i	$-0.816825\pi$
$859$	1.51934	−	2.63158i	0.0518393	−	0.0897883i	0.890781	+	0.454434i	$0.150158\pi$
$860$	−8.88181	−	27.3354i	−0.302867	−	0.932130i
$861$	1.73791	−	13.0472i	0.0592277	−	0.444646i
$862$	25.5668	−	18.5753i	0.870807	−	0.632678i
$863$	16.3290	+	18.1352i	0.555846	+	0.617330i	0.953934	−	0.300018i	$-0.0969926\pi$
$863$	16.3290	+	18.1352i	0.555846	+	0.617330i	−0.398087	+	0.917348i	$0.630326\pi$
$864$	−1.19519	+	0.254046i	−0.0406612	+	0.00864281i
$865$	−43.7244	−	19.4673i	−1.48667	−	0.661909i
$866$	−58.0290	+	25.8362i	−1.97190	+	0.877949i
$867$	−4.23738	−	13.0413i	−0.143909	−	0.442906i
$868$	−21.7375	+	35.3515i	−0.737819	+	1.19991i
$869$	3.83346	−	1.85977i	0.130041	−	0.0630885i
$870$	−41.2123	+	71.3818i	−1.39723	+	2.42007i
$871$	2.33932	−	2.59807i	0.0792647	−	0.0880324i
$872$	−2.42805	+	23.1013i	−0.0822241	+	0.782310i
$873$	−0.495263	−	4.71211i	−0.0167621	−	0.159481i
$874$	−15.7477	+	48.4664i	−0.532673	+	1.63940i
$875$	−23.6698	+	66.5193i	−0.800185	+	2.24876i
$876$	15.6303	−	11.3561i	0.528100	−	0.383687i
$877$	−17.1375	+	7.63009i	−0.578691	+	0.257650i	−0.675142	−	0.737688i	$-0.735918\pi$
$877$	−17.1375	+	7.63009i	−0.578691	+	0.257650i	0.0964507	+	0.995338i	$0.469251\pi$
$878$	23.9338	−	26.5812i	0.807726	−	0.897071i
$879$	0.649777	+	1.12545i	0.0219164	+	0.0379604i
$880$	−33.7407	−	54.2489i	−1.13740	−	1.82873i
$881$	−21.8490			−0.736113			−0.368056	−	0.929804i	$-0.619977\pi$
$881$	−21.8490			−0.736113			−0.368056	+	0.929804i	$0.619977\pi$
$882$	12.2821	−	12.2075i	0.413561	−	0.411049i
$883$	5.06903	+	3.68286i	0.170586	+	0.123938i	0.669803	−	0.742539i	$-0.266379\pi$
$883$	5.06903	+	3.68286i	0.170586	+	0.123938i	−0.499216	+	0.866477i	$0.666379\pi$
$884$	0.842496	+	8.01582i	0.0283362	+	0.269601i
$885$	−6.37664	+	1.35540i	−0.214348	+	0.0455612i
$886$	45.1167	−	9.58986i	1.51573	−	0.322178i
$887$	−5.15165	−	49.0147i	−0.172976	−	1.64575i	−0.645011	−	0.764174i	$-0.723147\pi$
$887$	−5.15165	−	49.0147i	−0.172976	−	1.64575i	0.472035	−	0.881580i	$-0.343520\pi$
$888$	30.2056	+	21.9456i	1.01363	+	0.736447i
$889$	−2.48697	−	8.44305i	−0.0834103	−	0.283171i
$890$	−98.9145			−3.31562
$891$	−3.21978	+	0.795623i	−0.107867	+	0.0266544i
$892$	−40.0676	−	69.3991i	−1.34156	−	2.32365i
$893$	5.97843	−	6.63972i	0.200061	−	0.222190i
$894$	19.7694	−	8.80190i	0.661188	−	0.294380i
$895$	−12.4915	+	9.07559i	−0.417544	+	0.303364i
$896$	31.5372	+	37.0394i	1.05359	+	1.23740i
$897$	−2.35332	+	7.24279i	−0.0785752	+	0.241830i
$898$	−8.50106	−	80.8822i	−0.283684	−	2.69907i
$899$	3.25857	−	31.0032i	0.108679	−	1.03402i
$900$	31.8628	−	35.3873i	1.06209	−	1.17958i
$901$	7.80495	−	13.5186i	0.260021	−	0.450369i
$902$	−40.1832	−	7.17218i	−1.33795	−	0.238808i
$903$	−2.15834	−	3.98964i	−0.0718250	−	0.132767i
$904$	17.8218	+	54.8498i	0.592743	+	1.82428i
$905$	−86.8632	+	38.6740i	−2.88743	+	1.28557i
$906$	−19.0542	−	8.48349i	−0.633035	−	0.281845i
$907$	−48.7598	+	10.3642i	−1.61904	+	0.344138i	−0.926224	−	0.376973i	$-0.876965\pi$
$907$	−48.7598	+	10.3642i	−1.61904	+	0.344138i	−0.692819	+	0.721112i	$0.743632\pi$
$908$	−33.9659	−	37.7230i	−1.12720	−	1.25188i
$909$	8.49083	−	6.16895i	0.281623	−	0.204611i
$910$	3.79429	−	28.4852i	0.125779	−	0.944276i
$911$	12.1209	+	37.3042i	0.401582	+	1.23594i	0.923716	+	0.383079i	$0.125136\pi$
$911$	12.1209	+	37.3042i	0.401582	+	1.23594i	−0.522133	+	0.852864i	$0.674864\pi$
$912$	−6.90790	+	11.9648i	−0.228743	+	0.396195i
$913$	17.0694	+	47.2050i	0.564913	+	1.56226i
$914$	−43.6360	−	75.5798i	−1.44335	−	2.49996i
$915$	−9.17272	−	1.94972i	−0.303241	−	0.0644558i
$916$	31.2684	+	22.7178i	1.03314	+	0.750618i
$917$	1.47521	+	19.1165i	0.0487158	+	0.631281i
$918$	−1.38609	+	4.26593i	−0.0457476	+	0.140797i
$919$	26.5070	+	29.4390i	0.874384	+	0.971102i	0.999779	−	0.0210049i	$-0.00668655\pi$
$919$	26.5070	+	29.4390i	0.874384	+	0.971102i	−0.125395	+	0.992107i	$0.540020\pi$
$920$	−137.597	−	61.2620i	−4.53643	−	2.01975i
$921$	−0.409747	+	3.89848i	−0.0135016	+	0.128459i
$922$	−83.4970	−	17.7478i	−2.74983	−	0.584493i
$923$	−3.91268			−0.128788
$924$	−24.3273	−	26.7421i	−0.800309	−	0.879751i
$925$	−82.2873			−2.70559
$926$	−11.4216	−	2.42773i	−0.375336	−	0.0797801i
$927$	−0.175141	+	1.66636i	−0.00575240	+	0.0547304i
$928$	9.13993	+	4.06936i	0.300033	+	0.133583i
$929$	22.0630	+	24.5034i	0.723864	+	0.803932i	0.986982	−	0.160832i	$-0.0514176\pi$
$929$	22.0630	+	24.5034i	0.723864	+	0.803932i	−0.263118	+	0.964764i	$0.584751\pi$
$930$	−11.8433	+	36.4500i	−0.388357	+	1.19524i
$931$	−1.00710	−	20.4054i	−0.0330063	−	0.668759i
$932$	−26.7041	−	19.4017i	−0.874722	−	0.635523i
$933$	0.732706	+	0.155742i	0.0239877	+	0.00509875i
$934$	37.5641	+	65.0629i	1.22913	+	2.12892i
$935$	−24.4571	+	0.802779i	−0.799831	+	0.0262537i
$936$	−2.82922	+	4.90035i	−0.0924760	+	0.160173i
$937$	−13.8273	−	42.5560i	−0.451718	−	1.39025i	−0.874945	−	0.484222i	$-0.839103\pi$
$937$	−13.8273	−	42.5560i	−0.451718	−	1.39025i	0.423227	−	0.906023i	$-0.360897\pi$
$938$	16.8053	+	12.9358i	0.548711	+	0.422370i
$939$	21.0932	−	15.3251i	0.688351	−	0.500117i
$940$	34.3403	+	38.1387i	1.12006	+	1.24395i
$941$	1.34499	−	0.285887i	0.0438455	−	0.00931966i	−0.185937	−	0.982562i	$-0.559532\pi$
$941$	1.34499	−	0.285887i	0.0438455	−	0.00931966i	0.229782	+	0.973242i	$0.426199\pi$
$942$	−17.7171	−	7.88814i	−0.577253	−	0.257010i
$943$	−32.0777	+	14.2819i	−1.04459	+	0.465083i
$944$	2.34350	+	7.21255i	0.0762744	+	0.234748i
$945$	5.63920	−	9.17096i	0.183443	−	0.298331i
$946$	−12.6561	+	6.14000i	−0.411484	+	0.199629i
$947$	9.15997	−	15.8655i	0.297659	−	0.515560i	−0.677941	−	0.735116i	$-0.737128\pi$
$947$	9.15997	−	15.8655i	0.297659	−	0.515560i	0.975600	+	0.219556i	$0.0704608\pi$
$948$	3.54151	−	3.93324i	0.115023	−	0.127746i
$949$	0.528898	−	5.03213i	0.0171687	−	0.163350i
$950$	−8.72307	−	82.9945i	−0.283014	−	2.69270i
$951$	3.53270	−	10.8725i	0.114556	−	0.352566i
$952$	−24.7433	+	4.54694i	−0.801935	+	0.147367i
$953$	27.6475	−	20.0871i	0.895589	−	0.650684i	−0.0417399	−	0.999129i	$-0.513290\pi$
$953$	27.6475	−	20.0871i	0.895589	−	0.650684i	0.937329	+	0.348445i	$0.113290\pi$
$954$	19.4566	−	8.66262i	0.629929	−	0.280463i
$955$	67.6984	−	75.1867i	2.19067	−	2.43298i
$956$	28.0248	+	48.5404i	0.906388	+	1.56991i
$957$	25.1578	+	10.2258i	0.813237	+	0.330552i
$958$	20.3185			0.656461
$959$	11.7743	−	12.3697i	0.380212	−	0.399440i
$960$	21.2159	+	15.4143i	0.684741	+	0.497493i
$961$	1.72521	+	16.4143i	0.0556521	+	0.529494i
$962$	18.5880	−	3.95100i	0.599302	−	0.127386i
$963$	−7.28493	+	1.54846i	−0.234754	+	0.0498984i
$964$	−1.91229	−	18.1942i	−0.0615907	−	0.585997i
$965$	11.5600	+	8.39881i	0.372129	+	0.270367i
$966$	−44.9035	−	10.8527i	−1.44475	−	0.349181i
$967$	5.06552			0.162896			0.0814480	−	0.996678i	$-0.474046\pi$
$967$	5.06552			0.162896			0.0814480	+	0.996678i	$0.474046\pi$
$968$	−44.3457	+	36.8950i	−1.42532	+	1.18585i
$969$	2.64595	+	4.58291i	0.0850000	+	0.147224i
$970$	31.9146	−	35.4448i	1.02472	−	1.13806i
$971$	27.5182	−	12.2519i	0.883101	−	0.393182i	0.0854794	−	0.996340i	$-0.472758\pi$
$971$	27.5182	−	12.2519i	0.883101	−	0.393182i	0.797622	+	0.603158i	$0.206091\pi$
$972$	−3.33306	+	2.42161i	−0.106908	+	0.0776732i
$973$	13.9289	−	39.1446i	0.446541	−	1.25492i
$974$	−23.2134	+	71.4436i	−0.743806	+	2.28920i
$975$	−1.30357	−	12.4027i	−0.0417477	−	0.397203i
$976$	−1.14031	+	10.8493i	−0.0365005	+	0.347279i
$977$	29.1683	−	32.3947i	0.933177	−	1.03640i	−0.0660782	−	0.997814i	$-0.521049\pi$
$977$	29.1683	−	32.3947i	0.933177	−	1.03640i	0.999255	−	0.0385838i	$-0.0122846\pi$
$978$	11.5105	−	19.9368i	0.368067	−	0.637510i
$979$	4.46799	+	32.2818i	0.142798	+	1.03173i
$980$	117.172	+	6.49857i	3.74291	+	0.207589i
$981$	1.36874	+	4.21254i	0.0437005	+	0.134496i
$982$	35.5371	−	15.8221i	1.13403	−	0.504904i
$983$	−32.7411	−	14.5773i	−1.04428	−	0.464943i	−0.188386	−	0.982095i	$-0.560326\pi$
$983$	−32.7411	−	14.5773i	−1.04428	−	0.464943i	−0.855894	+	0.517152i	$0.826992\pi$
$984$	−25.5197	+	5.42437i	−0.813537	+	0.172923i
$985$	69.7020	+	77.4119i	2.22089	+	2.46655i
$986$	29.7129	−	21.5877i	0.946251	−	0.687491i
$987$	6.41814	+	4.94035i	0.204292	+	0.157253i
$988$	4.00917	+	12.3390i	0.127549	+	0.392555i
$989$	−6.05042	+	10.4796i	−0.192392	+	0.333233i
$990$	−27.6397	−	18.7276i	−0.878447	−	0.595201i
$991$	12.6986	+	21.9947i	0.403386	+	0.698685i	0.994132	−	0.108173i	$-0.0344999\pi$
$991$	12.6986	+	21.9947i	0.403386	+	0.698685i	−0.590746	+	0.806857i	$0.701167\pi$
$992$	4.55041	+	0.967220i	0.144476	+	0.0307093i
$993$	−2.29753	−	1.66925i	−0.0729099	−	0.0529721i
$994$	−1.82617	−	23.6643i	−0.0579226	−	0.750587i
$995$	6.58041	−	20.2524i	0.208613	−	0.642045i
$996$	41.7227	+	46.3378i	1.32203	+	1.46827i
$997$	39.4527	+	17.5655i	1.24948	+	0.556304i	0.921499	−	0.388381i	$-0.126965\pi$
$997$	39.4527	+	17.5655i	1.24948	+	0.556304i	0.327980	+	0.944685i	$0.393632\pi$
$998$	−1.65582	+	15.7541i	−0.0524142	+	0.498688i
$999$	6.96385	+	1.48021i	0.220326	+	0.0468318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.16.1	✓	64
3.2	odd	2		693.2.by.c.478.8		64
7.4	even	3	inner	231.2.y.b.214.8	yes	64
11.9	even	5	inner	231.2.y.b.163.8	yes	64
21.11	odd	6		693.2.by.c.676.1		64
33.20	odd	10		693.2.by.c.163.1		64
77.53	even	15	inner	231.2.y.b.130.1	yes	64
231.53	odd	30		693.2.by.c.361.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.1	✓	64	1.1	even	1	trivial
231.2.y.b.130.1	yes	64	77.53	even	15	inner
231.2.y.b.163.8	yes	64	11.9	even	5	inner
231.2.y.b.214.8	yes	64	7.4	even	3	inner
693.2.by.c.163.1		64	33.20	odd	10
693.2.by.c.361.8		64	231.53	odd	30
693.2.by.c.478.8		64	3.2	odd	2
693.2.by.c.676.1		64	21.11	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41978 - 0.514340i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(3.76371 + 1.67571i) q^{4} +(2.72281 + 3.02398i) q^{5} +(0.764459 - 2.35276i) q^{6} +(2.18271 - 1.49525i) q^{7} +(-4.24270 - 3.08250i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-2.41978 - 0.514340i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(3.76371 + 1.67571i) q^{4} +(2.72281 + 3.02398i) q^{5} +(0.764459 - 2.35276i) q^{6} +(2.18271 - 1.49525i) q^{7} +(-4.24270 - 3.08250i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-5.03324 - 8.71783i) q^{10} +(-2.61781 + 2.03644i) q^{11} +(-2.05994 + 3.56793i) q^{12} +(0.333422 + 1.02617i) q^{13} +(-6.05075 + 2.49552i) q^{14} +(-3.29203 + 2.39180i) q^{15} +(3.16746 + 3.51783i) q^{16} +(1.77354 - 0.376977i) q^{17} +(2.25997 + 1.00620i) q^{18} +(2.66628 - 1.18710i) q^{19} +(5.18052 + 15.9440i) q^{20} +(1.25890 + 2.32705i) q^{21} +(7.38194 - 3.58130i) q^{22} +(3.52905 - 6.11249i) q^{23} +(3.50910 - 3.89725i) q^{24} +(-1.20816 + 11.4948i) q^{25} +(-0.279009 - 2.65459i) q^{26} +(0.309017 - 0.951057i) q^{27} +(10.7207 - 1.97008i) q^{28} +(-6.62426 + 4.81280i) q^{29} +(9.19619 - 4.09441i) q^{30} +(-2.54756 + 2.82935i) q^{31} +(-0.610946 - 1.05819i) q^{32} +(-1.75165 - 2.81633i) q^{33} -4.48547 q^{34} +(10.4647 + 2.52921i) q^{35} +(-3.33306 - 2.42161i) q^{36} +(0.744182 + 7.08042i) q^{37} +(-7.06238 + 1.50116i) q^{38} +(-1.05540 + 0.224332i) q^{39} +(-2.23062 - 21.2229i) q^{40} +(-4.02479 - 2.92418i) q^{41} +(-1.84937 - 6.27846i) q^{42} -1.71446 q^{43} +(-13.2651 + 3.27788i) q^{44} +(-2.03459 - 3.52400i) q^{45} +(-11.6834 + 12.9758i) q^{46} +(2.79661 - 1.24513i) q^{47} +(-3.82964 + 2.78240i) q^{48} +(2.52847 - 6.52739i) q^{49} +(8.83573 - 27.1936i) q^{50} +(0.189527 + 1.80323i) q^{51} +(-0.464657 + 4.42091i) q^{52} +(5.76070 - 6.39790i) q^{53} +(-1.23692 + 2.14241i) q^{54} +(-13.2859 - 2.37137i) q^{55} +(-13.8697 - 0.384325i) q^{56} +(0.901898 + 2.77576i) q^{57} +(18.5047 - 8.23881i) q^{58} +(1.46356 + 0.651621i) q^{59} +(-16.3982 + 3.48554i) q^{60} +(1.54205 + 1.71262i) q^{61} +(7.61978 - 5.53610i) q^{62} +(-2.44589 + 1.00876i) q^{63} +(-1.99150 - 6.12921i) q^{64} +(-2.19527 + 3.80232i) q^{65} +(2.79005 + 7.71585i) q^{66} +(-1.62008 - 2.80606i) q^{67} +(7.30677 + 1.55310i) q^{68} +(5.71012 + 4.14864i) q^{69} +(-24.0214 - 11.5026i) q^{70} +(-1.12059 + 3.44881i) q^{71} +(3.50910 + 3.89725i) q^{72} +(-4.28406 - 1.90738i) q^{73} +(1.84099 - 17.5158i) q^{74} +(-11.3056 - 2.40307i) q^{75} +12.0243 q^{76} +(-2.66894 + 8.35923i) q^{77} +2.66922 q^{78} +(-1.25660 - 0.267098i) q^{79} +(-2.01345 + 19.1567i) q^{80} +(0.913545 + 0.406737i) q^{81} +(8.23509 + 9.14600i) q^{82} +(4.67691 - 14.3940i) q^{83} +(0.838672 + 10.8679i) q^{84} +(5.96897 + 4.33671i) q^{85} +(4.14862 + 0.881817i) q^{86} +(-4.09402 - 7.09104i) q^{87} +(17.3839 - 0.570609i) q^{88} +(4.91306 - 8.50967i) q^{89} +(3.11071 + 9.57379i) q^{90} +(2.26214 + 1.74128i) q^{91} +(23.5250 - 17.0919i) q^{92} +(-2.54756 - 2.82935i) q^{93} +(-7.40760 + 1.57453i) q^{94} +(10.8495 + 4.83052i) q^{95} +(1.11625 - 0.496989i) q^{96} +(1.46414 + 4.50617i) q^{97} +(-9.47564 + 14.4944i) q^{98} +(2.98400 - 1.44767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

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