LMFDB - Embedded newform 231.2.be.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, 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:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65113 - 1.83377i) q^{2} +(1.72117 - 0.193857i) q^{3} +(-0.427411 + 4.06654i) q^{4} +(-0.660086 + 3.10546i) q^{5} +(-3.19736 - 2.83614i) q^{6} +(-2.64526 - 0.0509795i) q^{7} +(4.17018 - 3.02981i) q^{8} +(2.92484 - 0.667320i) q^{9} +O(q^{10})$	\(q+(-1.65113 - 1.83377i) q^{2} +(1.72117 - 0.193857i) q^{3} +(-0.427411 + 4.06654i) q^{4} +(-0.660086 + 3.10546i) q^{5} +(-3.19736 - 2.83614i) q^{6} +(-2.64526 - 0.0509795i) q^{7} +(4.17018 - 3.02981i) q^{8} +(2.92484 - 0.667320i) q^{9} +(6.78458 - 3.91708i) q^{10} +(1.59544 + 2.90767i) q^{11} +(0.0526802 + 7.08206i) q^{12} +(3.10017 + 1.00731i) q^{13} +(4.27419 + 4.93497i) q^{14} +(-0.534105 + 5.47298i) q^{15} +(-4.44231 - 0.944242i) q^{16} +(-1.34360 + 1.49222i) q^{17} +(-6.05300 - 4.26164i) q^{18} +(3.03669 - 0.319169i) q^{19} +(-12.3463 - 4.01157i) q^{20} +(-4.56282 + 0.425057i) q^{21} +(2.69771 - 7.72662i) q^{22} +(3.96399 + 2.28861i) q^{23} +(6.59023 - 6.02323i) q^{24} +(-4.64043 - 2.06605i) q^{25} +(-3.27162 - 7.34818i) q^{26} +(4.90478 - 1.71557i) q^{27} +(1.33792 - 10.7353i) q^{28} +(-0.587971 - 0.427186i) q^{29} +(10.9180 - 8.05719i) q^{30} +(-6.15387 + 1.30804i) q^{31} +(0.448694 + 0.777160i) q^{32} +(3.30970 + 4.69531i) q^{33} +4.95486 q^{34} +(1.90441 - 8.18110i) q^{35} +(1.46358 + 12.1792i) q^{36} +(-5.78617 + 2.57617i) q^{37} +(-5.59926 - 5.04160i) q^{38} +(5.53118 + 1.13275i) q^{39} +(6.65628 + 14.9502i) q^{40} +(-4.67387 + 3.39576i) q^{41} +(8.31327 + 7.66533i) q^{42} -7.93800i q^{43} +(-12.5061 + 5.24517i) q^{44} +(0.141689 + 9.52346i) q^{45} +(-2.34829 - 11.0478i) q^{46} +(1.66312 - 0.174801i) q^{47} +(-7.82901 - 0.764028i) q^{48} +(6.99480 + 0.269708i) q^{49} +(3.87331 + 11.9208i) q^{50} +(-2.02329 + 2.82883i) q^{51} +(-5.42130 + 12.1764i) q^{52} +(-2.51646 - 11.8390i) q^{53} +(-11.2444 - 6.16159i) q^{54} +(-10.0828 + 3.03527i) q^{55} +(-11.1857 + 7.80205i) q^{56} +(5.16478 - 1.13803i) q^{57} +(0.187458 + 1.78354i) q^{58} +(1.79703 + 0.188876i) q^{59} +(-22.0278 - 4.51117i) q^{60} +(-2.45975 + 11.5722i) q^{61} +(12.5595 + 9.12501i) q^{62} +(-7.77098 + 1.61613i) q^{63} +(-2.12255 + 6.53255i) q^{64} +(-5.17452 + 8.96254i) q^{65} +(3.14535 - 13.8218i) q^{66} +(-4.24004 - 7.34397i) q^{67} +(-5.49391 - 6.10161i) q^{68} +(7.26636 + 3.17064i) q^{69} +(-18.1467 + 10.0158i) q^{70} +(12.2766 - 3.98891i) q^{71} +(10.1752 - 11.6446i) q^{72} +(8.75397 + 0.920080i) q^{73} +(14.2778 + 6.35689i) q^{74} +(-8.38749 - 2.65645i) q^{75} +12.4852i q^{76} +(-4.07213 - 7.77288i) q^{77} +(-7.05551 - 12.0132i) q^{78} +(1.08133 - 0.973634i) q^{79} +(5.86461 - 13.1721i) q^{80} +(8.10937 - 3.90361i) q^{81} +(13.9442 + 2.96393i) q^{82} +(-0.462585 - 1.42369i) q^{83} +(0.221687 - 18.7366i) q^{84} +(-3.74714 - 5.15750i) q^{85} +(-14.5564 + 13.1067i) q^{86} +(-1.09481 - 0.621277i) q^{87} +(15.4630 + 7.29162i) q^{88} +(-0.0765504 - 0.0441964i) q^{89} +(17.2299 - 15.9843i) q^{90} +(-8.14940 - 2.82263i) q^{91} +(-11.0010 + 15.1416i) q^{92} +(-10.3383 + 3.44433i) q^{93} +(-3.06658 - 2.76116i) q^{94} +(-1.01331 + 9.64100i) q^{95} +(0.922935 + 1.25064i) q^{96} +(5.31125 - 16.3463i) q^{97} +(-11.0548 - 13.2722i) q^{98} +(6.60676 + 7.43980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.65113	−	1.83377i	−1.16753	−	1.29667i	−0.946980	−	0.321293i	$-0.895883\pi$
$2$	−1.65113	−	1.83377i	−1.16753	−	1.29667i	−0.220547	−	0.975376i	$-0.570784\pi$
$3$	1.72117	−	0.193857i	0.993717	−	0.111923i
$3$	1.72117	−	0.193857i	0.993717	−	0.111923i
$4$	−0.427411	+	4.06654i	−0.213705	+	2.03327i
$5$	−0.660086	+	3.10546i	−0.295199	+	1.38880i	0.541297	+	0.840831i	$0.317933\pi$
$5$	−0.660086	+	3.10546i	−0.295199	+	1.38880i	−0.836497	+	0.547972i	$0.815400\pi$
$6$	−3.19736	−	2.83614i	−1.30532	−	1.15785i
$7$	−2.64526	−	0.0509795i	−0.999814	−	0.0192684i
$7$	−2.64526	−	0.0509795i	−0.999814	−	0.0192684i
$8$	4.17018	−	3.02981i	1.47438	−	1.07120i
$9$	2.92484	−	0.667320i	0.974946	−	0.222440i
$10$	6.78458	−	3.91708i	2.14547	−	1.23869i
$11$	1.59544	+	2.90767i	0.481044	+	0.876696i
$11$	1.59544	+	2.90767i	0.481044	+	0.876696i
$12$	0.0526802	+	7.08206i	0.0152075	+	2.04441i
$13$	3.10017	+	1.00731i	0.859832	+	0.279376i	0.705558	−	0.708652i	$-0.250696\pi$
$13$	3.10017	+	1.00731i	0.859832	+	0.279376i	0.154274	+	0.988028i	$0.450696\pi$
$14$	4.27419	+	4.93497i	1.14232	+	1.31893i
$15$	−0.534105	+	5.47298i	−0.137905	+	1.41312i
$16$	−4.44231	−	0.944242i	−1.11058	−	0.236060i
$17$	−1.34360	+	1.49222i	−0.325872	+	0.361917i	−0.883712	−	0.468031i	$-0.844964\pi$
$17$	−1.34360	+	1.49222i	−0.325872	+	0.361917i	0.557840	+	0.829948i	$0.311630\pi$
$18$	−6.05300	−	4.26164i	−1.42671	−	1.00448i
$19$	3.03669	−	0.319169i	0.696665	−	0.0732224i	0.250425	−	0.968136i	$-0.419430\pi$
$19$	3.03669	−	0.319169i	0.696665	−	0.0732224i	0.446240	+	0.894914i	$0.352763\pi$
$20$	−12.3463	−	4.01157i	−2.76073	−	0.897015i
$21$	−4.56282	+	0.425057i	−0.995689	+	0.0927550i
$22$	2.69771	−	7.72662i	0.575153	−	1.64732i
$23$	3.96399	+	2.28861i	0.826550	+	0.477209i	0.852670	−	0.522450i	$-0.174982\pi$
$23$	3.96399	+	2.28861i	0.826550	+	0.477209i	−0.0261201	+	0.999659i	$0.508315\pi$
$24$	6.59023	−	6.02323i	1.34522	−	1.22949i
$25$	−4.64043	−	2.06605i	−0.928087	−	0.413211i
$26$	−3.27162	−	7.34818i	−0.641618	−	1.44110i
$27$	4.90478	−	1.71557i	0.943925	−	0.330161i
$28$	1.33792	−	10.7353i	0.252844	−	2.02878i
$29$	−0.587971	−	0.427186i	−0.109183	−	0.0793264i	0.531854	−	0.846836i	$-0.321496\pi$
$29$	−0.587971	−	0.427186i	−0.109183	−	0.0793264i	−0.641037	+	0.767510i	$0.721496\pi$
$30$	10.9180	−	8.05719i	1.99335	−	1.47103i
$31$	−6.15387	+	1.30804i	−1.10527	+	0.234932i	−0.724182	−	0.689608i	$-0.757783\pi$
$31$	−6.15387	+	1.30804i	−1.10527	+	0.234932i	−0.381085	+	0.924540i	$0.624449\pi$
$32$	0.448694	+	0.777160i	0.0793186	+	0.137384i
$33$	3.30970	+	4.69531i	0.576145	+	0.817348i
$34$	4.95486			0.849751
$35$	1.90441	−	8.18110i	0.321905	−	1.38286i
$36$	1.46358	+	12.1792i	0.243929	+	2.02987i
$37$	−5.78617	+	2.57617i	−0.951240	+	0.423519i	−0.822884	−	0.568209i	$-0.807637\pi$
$37$	−5.78617	+	2.57617i	−0.951240	+	0.423519i	−0.128356	+	0.991728i	$0.540970\pi$
$38$	−5.59926	−	5.04160i	−0.908320	−	0.817855i
$39$	5.53118	+	1.13275i	0.885698	+	0.181386i
$40$	6.65628	+	14.9502i	1.05245	+	2.36384i
$41$	−4.67387	+	3.39576i	−0.729936	+	0.530329i	−0.889543	−	0.456851i	$-0.848977\pi$
$41$	−4.67387	+	3.39576i	−0.729936	+	0.530329i	0.159607	+	0.987181i	$0.448977\pi$
$42$	8.31327	+	7.66533i	1.28277	+	1.18279i
$43$		−	7.93800i		−	1.21053i	−0.796023	−	0.605266i	$-0.793067\pi$
$43$		−	7.93800i		−	1.21053i	0.796023	−	0.605266i	$-0.206933\pi$
$44$	−12.5061	+	5.24517i	−1.88536	+	0.790739i
$45$	0.141689	+	9.52346i	0.0211218	+	1.41967i
$46$	−2.34829	−	11.0478i	−0.346237	−	1.62892i
$47$	1.66312	−	0.174801i	0.242591	−	0.0254973i	0.0175474	−	0.999846i	$-0.494414\pi$
$47$	1.66312	−	0.174801i	0.242591	−	0.0254973i	0.225044	+	0.974349i	$0.427748\pi$
$48$	−7.82901	−	0.764028i	−1.13002	−	0.110278i
$49$	6.99480	+	0.269708i	0.999257	+	0.0385297i
$50$	3.87331	+	11.9208i	0.547768	+	1.68586i
$51$	−2.02329	+	2.82883i	−0.283317	+	0.396116i
$52$	−5.42130	+	12.1764i	−0.751798	+	1.68857i
$53$	−2.51646	−	11.8390i	−0.345662	−	1.62621i	−0.716552	−	0.697534i	$-0.754281\pi$
$53$	−2.51646	−	11.8390i	−0.345662	−	1.62621i	0.370890	−	0.928677i	$-0.379053\pi$
$54$	−11.2444	−	6.16159i	−1.53017	−	0.838486i
$55$	−10.0828	+	3.03527i	−1.35956	+	0.409276i
$56$	−11.1857	+	7.80205i	−1.49475	+	1.04259i
$57$	5.16478	−	1.13803i	0.684092	−	0.150735i
$58$	0.187458	+	1.78354i	0.0246144	+	0.234191i
$59$	1.79703	+	0.188876i	0.233954	+	0.0245895i	0.220780	−	0.975324i	$-0.429140\pi$
$59$	1.79703	+	0.188876i	0.233954	+	0.0245895i	0.0131739	+	0.999913i	$0.495806\pi$
$60$	−22.0278	−	4.51117i	−2.84378	−	0.582389i
$61$	−2.45975	+	11.5722i	−0.314938	+	1.48167i	0.481231	+	0.876594i	$0.340190\pi$
$61$	−2.45975	+	11.5722i	−0.314938	+	1.48167i	−0.796169	+	0.605074i	$0.793143\pi$
$62$	12.5595	+	9.12501i	1.59506	+	1.15888i
$63$	−7.77098	+	1.61613i	−0.979051	+	0.203613i
$64$	−2.12255	+	6.53255i	−0.265319	+	0.816569i
$65$	−5.17452	+	8.96254i	−0.641821	+	1.11167i
$66$	3.14535	−	13.8218i	0.387166	−	1.70134i
$67$	−4.24004	−	7.34397i	−0.518004	−	0.897209i	−0.999781	−	0.0209150i	$-0.993342\pi$
$67$	−4.24004	−	7.34397i	−0.518004	−	0.897209i	0.481778	−	0.876293i	$-0.339991\pi$
$68$	−5.49391	−	6.10161i	−0.666235	−	0.739929i
$69$	7.26636	+	3.17064i	0.874767	+	0.381700i
$70$	−18.1467	+	10.0158i	−2.16894	+	1.19712i
$71$	12.2766	−	3.98891i	1.45697	−	0.473397i	0.529824	−	0.848107i	$-0.322258\pi$
$71$	12.2766	−	3.98891i	1.45697	−	0.473397i	0.927142	+	0.374710i	$0.122258\pi$
$72$	10.1752	−	11.6446i	1.19916	−	1.37232i
$73$	8.75397	+	0.920080i	1.02457	+	0.107687i	0.601881	−	0.798585i	$-0.294418\pi$
$73$	8.75397	+	0.920080i	1.02457	+	0.107687i	0.422694	+	0.906273i	$0.361085\pi$
$74$	14.2778	+	6.35689i	1.65976	+	0.738974i
$75$	−8.38749	−	2.65645i	−0.968503	−	0.306740i
$76$			12.4852i			1.43216i
$77$	−4.07213	−	7.77288i	−0.464063	−	0.885802i
$78$	−7.05551	−	12.0132i	−0.798879	−	1.36023i
$79$	1.08133	−	0.973634i	0.121659	−	0.109542i	−0.606056	−	0.795422i	$-0.707249\pi$
$79$	1.08133	−	0.973634i	0.121659	−	0.109542i	0.727715	+	0.685880i	$0.240582\pi$
$80$	5.86461	−	13.1721i	0.655683	−	1.47269i
$81$	8.10937	−	3.90361i	0.901041	−	0.433734i
$82$	13.9442	+	2.96393i	1.53988	+	0.327312i
$83$	−0.462585	−	1.42369i	−0.0507753	−	0.156270i	0.922454	−	0.386108i	$-0.126181\pi$
$83$	−0.462585	−	1.42369i	−0.0507753	−	0.156270i	−0.973229	+	0.229837i	$0.926181\pi$
$84$	0.221687	−	18.7366i	0.0241880	−	2.04433i
$85$	−3.74714	−	5.15750i	−0.406435	−	0.559410i
$86$	−14.5564	+	13.1067i	−1.56966	+	1.41333i
$87$	−1.09481	−	0.621277i	−0.117376	−	0.0666078i
$88$	15.4630	+	7.29162i	1.64836	+	0.777289i
$89$	−0.0765504	−	0.0441964i	−0.00811433	−	0.00468481i	0.495937	−	0.868358i	$-0.334825\pi$
$89$	−0.0765504	−	0.0441964i	−0.00811433	−	0.00468481i	−0.504052	+	0.863673i	$0.668158\pi$
$90$	17.2299	−	15.9843i	1.81619	−	1.68489i
$91$	−8.14940	−	2.82263i	−0.854289	−	0.295892i
$92$	−11.0010	+	15.1416i	−1.14693	+	1.57862i
$93$	−10.3383	+	3.44433i	−1.07203	+	0.357161i
$94$	−3.06658	−	2.76116i	−0.316293	−	0.284792i
$95$	−1.01331	+	9.64100i	−0.103963	+	0.989146i
$96$	0.922935	+	1.25064i	0.0941966	+	0.127643i
$97$	5.31125	−	16.3463i	0.539276	−	1.65972i	−0.194949	−	0.980813i	$-0.562454\pi$
$97$	5.31125	−	16.3463i	0.539276	−	1.65972i	0.734224	−	0.678907i	$-0.237546\pi$
$98$	−11.0548	−	13.2722i	−1.11670	−	1.34069i
$99$	6.60676	+	7.43980i	0.664005	+	0.747728i
$100$	10.3851	−	17.9875i	1.03851	−	1.79875i
$101$	3.20778	−	0.681834i	0.319186	−	0.0678450i	−0.0455328	−	0.998963i	$-0.514499\pi$
$101$	3.20778	−	0.681834i	0.319186	−	0.0678450i	0.364719	+	0.931118i	$0.381165\pi$
$102$	8.52814	−	0.960532i	0.844412	−	0.0951068i
$103$	12.5759	−	5.59914i	1.23914	−	0.551700i	0.320669	−	0.947191i	$-0.396092\pi$
$103$	12.5759	−	5.59914i	1.23914	−	0.551700i	0.918470	+	0.395491i	$0.129426\pi$
$104$	15.9802	−	5.19228i	1.56699	−	0.509145i
$105$	1.69186	−	14.4502i	0.165108	−	1.41020i
$106$	−17.5550	+	24.1623i	−1.70509	+	2.34685i
$107$	−0.968173	−	9.21155i	−0.0935968	−	0.890514i	−0.936079	−	0.351790i	$-0.885573\pi$
$107$	−0.968173	−	9.21155i	−0.0935968	−	0.890514i	0.842482	−	0.538724i	$-0.181094\pi$
$108$	4.88008	+	20.6787i	0.469586	+	1.98981i
$109$	−4.86102	+	2.80651i	−0.465602	+	0.268815i	−0.714397	−	0.699741i	$-0.753299\pi$
$109$	−4.86102	+	2.80651i	−0.465602	+	0.268815i	0.248795	+	0.968556i	$0.419965\pi$
$110$	22.2140	+	13.4779i	2.11802	+	1.28506i
$111$	−9.45956	+	5.55570i	−0.897861	+	0.527324i
$112$	11.7029	+	2.72423i	1.10582	+	0.257416i
$113$	−1.59674	−	2.19772i	−0.150208	−	0.206744i	0.727282	−	0.686339i	$-0.240783\pi$
$113$	−1.59674	−	2.19772i	−0.150208	−	0.206744i	−0.877490	+	0.479595i	$0.840783\pi$
$114$	−10.6146	−	7.59198i	−0.994150	−	0.711054i
$115$	−9.72377	+	10.7993i	−0.906746	+	1.00704i
$116$	1.98847	−	2.20842i	0.184625	−	0.205047i
$117$	9.73969	+	0.877404i	0.900435	+	0.0811160i
$118$	−2.62078	−	3.60720i	−0.241263	−	0.332070i
$119$	3.63025	−	3.87882i	0.332785	−	0.355571i
$120$	14.3548	+	24.4415i	1.31041	+	2.23120i
$121$	−5.90912	+	9.27806i	−0.537193	+	0.843460i
$122$	25.2821	−	14.5966i	2.28893	−	1.32152i
$123$	−7.38622	+	6.75074i	−0.665993	+	0.608694i
$124$	−2.68899	−	25.5840i	−0.241478	−	2.29751i
$125$	0.148521	−	0.204421i	0.0132841	−	0.0182840i
$126$	15.7945	+	11.5817i	1.40709	+	1.03178i
$127$	2.26092	−	0.734619i	0.200625	−	0.0651869i	−0.206981	−	0.978345i	$-0.566364\pi$
$127$	2.26092	−	0.734619i	0.200625	−	0.0651869i	0.407606	+	0.913158i	$0.366364\pi$
$128$	17.1234	−	7.62383i	1.51351	−	0.673858i
$129$	−1.53883	−	13.6626i	−0.135487	−	1.20293i
$130$	24.9790	−	5.30946i	2.19081	−	0.465670i
$131$	5.29879	−	9.17777i	0.462957	−	0.801866i	−0.536149	−	0.844123i	$-0.680122\pi$
$131$	5.29879	−	9.17777i	0.462957	−	0.801866i	0.999107	+	0.0422573i	$0.0134549\pi$
$132$	−20.5083	+	11.4522i	−1.78501	+	0.996786i
$133$	−8.04911	+	0.689476i	−0.697946	+	0.0597852i
$134$	−6.46626	+	19.9011i	−0.558600	+	1.71919i
$135$	2.09006	+	16.3640i	0.179883	+	1.40839i
$136$	−1.08191	+	10.2937i	−0.0927731	+	0.882677i
$137$	2.07812	+	1.87115i	0.177546	+	0.159863i	0.753112	−	0.657892i	$-0.228552\pi$
$137$	2.07812	+	1.87115i	0.177546	+	0.159863i	−0.575566	+	0.817755i	$0.695218\pi$
$138$	−6.18350	−	18.5600i	−0.526375	−	1.57993i
$139$	9.50847	−	13.0873i	0.806498	−	1.11005i	−0.185356	−	0.982671i	$-0.559344\pi$
$139$	9.50847	−	13.0873i	0.806498	−	1.11005i	0.991854	−	0.127378i	$-0.0406561\pi$
$140$	32.4548	+	11.2411i	2.74293	+	0.950043i
$141$	2.82862	−	0.623269i	0.238213	−	0.0524887i
$142$	−27.5851	−	15.9262i	−2.31489	−	1.33650i
$143$	2.01723	+	10.6214i	0.168689	+	0.888204i
$144$	−13.6231	+	0.202684i	−1.13526	+	0.0168904i
$145$	1.71472	−	1.54394i	0.142400	−	0.128217i
$146$	−12.7668	−	17.5719i	−1.05658	−	1.45426i
$147$	12.0915	−	0.891776i	0.997291	−	0.0735524i
$148$	−8.00302	−	24.6308i	−0.657844	−	2.02464i
$149$	−15.8231	−	3.36331i	−1.29628	−	0.275533i	−0.492423	−	0.870356i	$-0.663889\pi$
$149$	−15.8231	−	3.36331i	−1.29628	−	0.275533i	−0.803857	+	0.594823i	$0.797222\pi$
$150$	8.97754	+	19.7668i	0.733013	+	1.61396i
$151$	−1.31634	+	2.95654i	−0.107122	+	0.240600i	−0.959151	−	0.282895i	$-0.908705\pi$
$151$	−1.31634	+	2.95654i	−0.107122	+	0.240600i	0.852029	+	0.523495i	$0.175372\pi$
$152$	11.6965	−	10.5316i	0.948713	−	0.854225i
$153$	−2.93403	+	5.26113i	−0.237203	+	0.425337i
$154$	−7.53004	+	20.3014i	−0.606788	+	1.63593i
$155$		−	19.9740i		−	1.60435i
$156$	−6.97048	+	22.0086i	−0.558085	+	1.76210i
$157$	−8.93280	−	3.97714i	−0.712915	−	0.317410i	0.0180388	−	0.999837i	$-0.494258\pi$
$157$	−8.93280	−	3.97714i	−0.712915	−	0.317410i	−0.730954	+	0.682427i	$0.760924\pi$
$158$	−3.57084	−	0.375310i	−0.284080	−	0.0298581i
$159$	−6.62631	−	19.8891i	−0.525501	−	1.57731i
$160$	−2.70961	+	0.880407i	−0.214214	+	0.0696023i
$161$	−10.3691	−	6.25606i	−0.817201	−	0.493047i
$162$	−20.5479	−	8.42533i	−1.61440	−	0.661957i
$163$	12.6199	+	14.0159i	0.988469	+	1.09781i	0.995203	+	0.0978289i	$0.0311898\pi$
$163$	12.6199	+	14.0159i	0.988469	+	1.09781i	−0.00673409	+	0.999977i	$0.502144\pi$
$164$	−11.8114	−	20.4579i	−0.922312	−	1.59749i
$165$	−16.7658	+	7.17883i	−1.30521	+	0.558871i
$166$	−1.84693	+	3.19898i	−0.143350	+	0.248289i
$167$	−3.17746	+	9.77922i	−0.245879	+	0.756739i	0.749611	+	0.661878i	$0.230240\pi$
$167$	−3.17746	+	9.77922i	−0.245879	+	0.756739i	−0.995491	+	0.0948603i	$0.969760\pi$
$168$	−17.7399	+	15.5970i	−1.36867	+	1.20334i
$169$	−1.92084	−	1.39557i	−0.147757	−	0.107352i
$170$	−3.27063	+	15.3871i	−0.250846	+	1.18014i
$171$	8.66885	−	2.95996i	0.662923	−	0.226354i
$172$	32.2802	+	3.39278i	2.46134	+	0.258697i
$173$	0.639309	+	6.08262i	0.0486057	+	0.462453i	0.991571	+	0.129562i	$0.0413572\pi$
$173$	0.639309	+	6.08262i	0.0486057	+	0.462453i	−0.942966	+	0.332890i	$0.891976\pi$
$174$	0.668398	+	3.03344i	0.0506711	+	0.229964i
$175$	12.1698	+	5.70182i	0.919953	+	0.431017i
$176$	−4.34191	−	14.4233i	−0.327284	−	1.08719i
$177$	3.12961	−	0.0232798i	0.235236	−	0.00174981i
$178$	0.0453489	+	0.213350i	0.00339904	+	0.0159912i
$179$	−2.37993	+	5.34541i	−0.177884	+	0.399535i	−0.980378	−	0.197126i	$-0.936839\pi$
$179$	−2.37993	+	5.34541i	−0.177884	+	0.399535i	0.802494	+	0.596660i	$0.203506\pi$
$180$	−38.7881	−	3.49424i	−2.89109	−	0.260445i
$181$	−0.316236	−	0.973274i	−0.0235056	−	0.0723429i	0.938616	−	0.344965i	$-0.112109\pi$
$181$	−0.316236	−	0.973274i	−0.0235056	−	0.0723429i	−0.962121	+	0.272622i	$0.912109\pi$
$182$	8.27968	+	19.6046i	0.613731	+	1.45319i
$183$	−1.99029	+	20.3945i	−0.147126	+	1.50761i
$184$	23.4646	−	2.46623i	1.72983	−	0.181813i
$185$	−4.18082	−	19.6692i	−0.307380	−	1.44611i
$186$	23.3859	+	13.2709i	1.71474	+	0.973072i
$187$	−6.48254	−	1.52600i	−0.474050	−	0.111592i
$188$			6.83786i			0.498702i
$189$	−13.0619	+	4.28808i	−0.950111	+	0.311912i
$190$	19.3525	−	14.0604i	1.40397	−	1.02005i
$191$	−7.09110	−	15.9269i	−0.513094	−	1.15243i	−0.965449	−	0.260590i	$-0.916083\pi$
$191$	−7.09110	−	15.9269i	−0.513094	−	1.15243i	0.452355	−	0.891838i	$-0.350584\pi$
$192$	−2.38689	+	11.6551i	−0.172259	+	0.841134i
$193$	−8.16993	−	7.35624i	−0.588084	−	0.529513i	0.320482	−	0.947255i	$-0.396155\pi$
$193$	−8.16993	−	7.35624i	−0.588084	−	0.529513i	−0.908566	+	0.417741i	$0.862822\pi$
$194$	−38.7450	+	17.2504i	−2.78173	+	1.23850i
$195$	−7.16878	+	16.4292i	−0.513367	+	1.17652i
$196$	−4.08643	+	28.3294i	−0.291888	+	2.02353i
$197$	−12.1203			−0.863533			−0.431766	−	0.901986i	$-0.642109\pi$
$197$	−12.1203			−0.863533			−0.431766	+	0.901986i	$0.642109\pi$
$198$	2.73423	−	24.3994i	0.194314	−	1.73399i
$199$	10.4774	+	18.1474i	0.742725	+	1.28644i	0.951250	+	0.308420i	$0.0998002\pi$
$199$	10.4774	+	18.1474i	0.742725	+	1.28644i	−0.208526	+	0.978017i	$0.566866\pi$
$200$	−25.6112	+	5.44383i	−1.81098	+	0.384937i
$201$	−8.72150	−	11.8182i	−0.615167	−	0.833595i
$202$	−6.54679	−	4.75652i	−0.460630	−	0.334668i
$203$	1.53356	+	1.15999i	0.107635	+	0.0814155i
$204$	−10.6388	−	9.43687i	−0.744864	−	0.660713i
$205$	−7.46025	−	16.7560i	−0.521047	−	1.17029i
$206$	−31.0320	−	13.8163i	−2.16210	−	0.962629i
$207$	13.1213	+	4.04857i	0.911992	+	0.281395i
$208$	−12.8208	−	7.40207i	−0.888960	−	0.513241i
$209$	5.77291	+	8.32049i	0.399320	+	0.575540i
$210$	−29.2918	+	20.7568i	−2.02133	+	1.43235i
$211$	11.9477	+	3.88203i	0.822511	+	0.267250i	0.689887	−	0.723917i	$-0.257660\pi$
$211$	11.9477	+	3.88203i	0.822511	+	0.267250i	0.132623	+	0.991167i	$0.457660\pi$
$212$	49.2193	−	5.17316i	3.38040	−	0.355294i
$213$	20.3568	−	9.24550i	1.39483	−	0.633491i
$214$	−15.2933	+	16.9849i	−1.04543	+	1.16106i
$215$	24.6511	+	5.23976i	1.68119	+	0.357348i
$216$	15.2559	−	22.0148i	1.03803	−	1.49792i
$217$	16.3453	−	3.14640i	1.10959	−	0.213591i
$218$	13.1727	+	4.28006i	0.892167	+	0.289882i
$219$	15.2454	−	0.113404i	1.03019	−	0.00766312i
$220$	−8.03357	−	42.2994i	−0.541623	−	2.85182i
$221$	−5.66852	+	3.27272i	−0.381306	+	0.220147i
$222$	25.8068	+	8.17343i	1.73204	+	0.548565i
$223$	2.36846	−	1.72079i	0.158604	−	0.115233i	−0.505653	−	0.862737i	$-0.668748\pi$
$223$	2.36846	−	1.72079i	0.158604	−	0.115233i	0.664257	+	0.747505i	$0.268748\pi$
$224$	−1.14729	−	2.07866i	−0.0766567	−	0.138887i
$225$	−14.9512	−	2.94622i	−0.996750	−	0.196415i
$226$	−1.39368	+	6.55676i	−0.0927064	+	0.436149i
$227$	−1.15222	+	10.9626i	−0.0764755	+	0.727616i	0.887353	+	0.461092i	$0.152542\pi$
$227$	−1.15222	+	10.9626i	−0.0764755	+	0.727616i	−0.963828	+	0.266525i	$0.914125\pi$
$228$	2.42035	+	21.4892i	0.160291	+	1.42316i
$229$	0.486184	+	0.539962i	0.0321279	+	0.0356817i	0.758995	−	0.651097i	$-0.225691\pi$
$229$	0.486184	+	0.539962i	0.0321279	+	0.0356817i	−0.726867	+	0.686779i	$0.759024\pi$
$230$	35.8587			2.36445
$231$	−8.51565	−	12.5890i	−0.560289	−	0.828297i
$232$	−3.74624			−0.245952
$233$	11.2448	+	12.4886i	0.736669	+	0.818154i	0.988754	−	0.149551i	$-0.0477829\pi$
$233$	11.2448	+	12.4886i	0.736669	+	0.818154i	−0.252085	+	0.967705i	$0.581116\pi$
$234$	−14.4726	−	19.3090i	−0.946101	−	1.26227i
$235$	−0.554965	+	5.28013i	−0.0362019	+	0.344438i
$236$	−1.53614	+	7.22698i	−0.0999943	+	0.470436i
$237$	1.67241	−	1.88541i	0.108634	−	0.122471i
$238$	−13.1069	−	0.252596i	−0.849593	−	0.0163734i
$239$	−0.0661616	+	0.0480692i	−0.00427964	+	0.00310934i	−0.589923	−	0.807459i	$-0.700842\pi$
$239$	−0.0661616	+	0.0480692i	−0.00427964	+	0.00310934i	0.585643	+	0.810569i	$0.300842\pi$
$240$	7.54047	−	23.8083i	0.486735	−	1.53682i
$241$	12.2168	−	7.05339i	0.786955	−	0.454349i	−0.0519345	−	0.998650i	$-0.516539\pi$
$241$	12.2168	−	7.05339i	0.786955	−	0.454349i	0.838889	+	0.544302i	$0.183205\pi$
$242$	26.7705	−	4.48334i	1.72087	−	0.288200i
$243$	13.2008	−	8.29082i	0.846835	−	0.531856i
$244$	−46.0075	−	14.9487i	−2.94533	−	0.956995i
$245$	−5.45474	+	21.5440i	−0.348490	+	1.37640i
$246$	24.5749	+	2.39825i	1.56684	+	0.152907i
$247$	9.73576	+	2.06940i	0.619471	+	0.131673i
$248$	−21.6996	+	24.0998i	−1.37792	+	1.53034i
$249$	−1.07218	−	2.36074i	−0.0679466	−	0.149606i
$250$	−0.620089	+	0.0651740i	−0.0392179	+	0.00412196i
$251$	0.148587	+	0.0482788i	0.00937871	+	0.00304733i	0.313703	−	0.949521i	$-0.398431\pi$
$251$	0.148587	+	0.0482788i	0.00937871	+	0.00304733i	−0.304324	+	0.952569i	$0.598431\pi$
$252$	−3.25065	−	32.2918i	−0.204772	−	2.03419i
$253$	−0.330207	+	15.1773i	−0.0207600	+	0.954192i
$254$	−5.08020	−	2.93306i	−0.318760	−	0.184036i
$255$	−7.44928	−	8.15052i	−0.466492	−	0.510405i
$256$	−29.7035	−	13.2249i	−1.85647	−	0.826554i
$257$	0.894121	+	2.00823i	0.0557737	+	0.125270i	0.939283	−	0.343145i	$-0.111492\pi$
$257$	0.894121	+	2.00823i	0.0557737	+	0.125270i	−0.883509	+	0.468414i	$0.844825\pi$
$258$	−22.5133	+	25.3807i	−1.40161	+	1.58013i
$259$	15.4372	−	6.51966i	0.959224	−	0.405112i
$260$	−34.2349	−	24.8731i	−2.12316	−	1.54256i
$261$	−2.00479	−	0.857085i	−0.124093	−	0.0530523i
$262$	−25.5789	+	5.43696i	−1.58027	+	0.335897i
$263$	−5.10914	−	8.84928i	−0.315043	−	0.545670i	0.664404	−	0.747374i	$-0.268686\pi$
$263$	−5.10914	−	8.84928i	−0.315043	−	0.545670i	−0.979447	+	0.201704i	$0.935352\pi$
$264$	28.0279	+	9.55250i	1.72500	+	0.587915i
$265$	38.4266			2.36053
$266$	14.5545	+	13.6218i	0.892392	+	0.835205i
$267$	−0.140324	−	0.0612296i	−0.00858768	−	0.00374719i
$268$	31.6768	−	14.1034i	1.93497	−	0.861503i
$269$	7.31315	+	6.58479i	0.445891	+	0.401482i	0.861255	−	0.508173i	$-0.169679\pi$
$269$	7.31315	+	6.58479i	0.445891	+	0.401482i	−0.415364	+	0.909655i	$0.636346\pi$
$270$	26.5568	−	30.8518i	1.61620	−	1.87758i
$271$	−1.54165	−	3.46260i	−0.0936485	−	0.210338i	0.860647	−	0.509201i	$-0.170059\pi$
$271$	−1.54165	−	3.46260i	−0.0936485	−	0.210338i	−0.954296	+	0.298863i	$0.903392\pi$
$272$	7.37772	−	5.36023i	0.447340	−	0.325012i
$273$	−14.5737	−	3.27841i	−0.882039	−	0.198418i
$274$		−	6.90031i		−	0.416863i
$275$	−1.39614	−	16.7891i	−0.0841906	−	1.01242i
$276$	−15.9993	+	28.1938i	−0.963042	+	1.69707i
$277$	−1.80040	−	8.47023i	−0.108176	−	0.508927i	−0.998557	−	0.0537105i	$-0.982895\pi$
$277$	−1.80040	−	8.47023i	−0.108176	−	0.508927i	0.890381	−	0.455217i	$-0.150438\pi$
$278$	−39.6988	+	4.17251i	−2.38097	+	0.250251i
$279$	−17.1262	+	7.93242i	−1.02532	+	0.474901i
$280$	−16.8454	−	39.8866i	−1.00671	−	2.38368i
$281$	−7.68597	−	23.6550i	−0.458507	−	1.41114i	−0.866968	−	0.498363i	$-0.833935\pi$
$281$	−7.68597	−	23.6550i	−0.458507	−	1.41114i	0.408462	−	0.912775i	$-0.366065\pi$
$282$	−5.81336	−	4.15794i	−0.346181	−	0.247602i
$283$	6.55287	−	14.7180i	0.389528	−	0.874894i	−0.607237	−	0.794521i	$-0.707722\pi$
$283$	6.55287	−	14.7180i	0.389528	−	0.874894i	0.996765	−	0.0803730i	$-0.0256111\pi$
$284$	10.9739	+	51.6283i	0.651183	+	3.06357i
$285$	0.124895	+	16.7902i	0.00739814	+	0.994567i
$286$	16.1464	−	21.2364i	0.954758	−	1.25574i
$287$	12.5367	−	8.74441i	0.740019	−	0.516166i
$288$	1.83097	+	1.97365i	0.107891	+	0.116298i
$289$	1.35553	+	12.8970i	0.0797368	+	0.758645i
$290$	−5.66246	−	0.595148i	−0.332511	−	0.0349483i
$291$	5.97271	−	29.1644i	0.350126	−	1.70965i
$292$	−7.48308	+	35.2051i	−0.437914	+	2.06022i
$293$	9.60738	+	6.98017i	0.561269	+	0.407786i	0.831923	−	0.554891i	$-0.187240\pi$
$293$	9.60738	+	6.98017i	0.561269	+	0.407786i	−0.270654	+	0.962677i	$0.587240\pi$
$294$	−21.6000	−	20.7006i	−1.25974	−	1.20728i
$295$	−1.77274	+	5.45594i	−0.103213	+	0.317657i
$296$	−16.3240	+	28.2741i	−0.948815	+	1.64340i
$297$	12.8136	+	11.5244i	0.743521	+	0.668713i
$298$	19.9585	+	34.5692i	1.15617	+	2.00254i
$299$	9.98372	+	11.0880i	0.577373	+	0.641238i
$300$	14.3875	−	32.9727i	0.830660	−	1.90368i
$301$	−0.404675	+	20.9981i	−0.0233251	+	1.21031i
$302$	7.59506	−	2.46779i	0.437047	−	0.142005i
$303$	5.38895	−	1.79540i	0.309587	−	0.103143i
$304$	−13.7913	−	1.44952i	−0.790985	−	0.0831358i
$305$	−34.3133	−	15.2773i	−1.96478	−	0.874775i
$306$	14.4922	−	3.30647i	0.828462	−	0.189019i
$307$			19.3716i			1.10559i	0.833316	+	0.552797i	$0.186440\pi$
$307$			19.3716i			1.10559i	−0.833316	+	0.552797i	$0.813560\pi$
$308$	33.3492	−	13.2373i	1.90025	−	0.754264i
$309$	20.5598	−	12.0750i	1.16960	−	0.686922i
$310$	−36.6277	+	32.9797i	−2.08031	+	1.87312i
$311$	4.17317	−	9.37310i	0.236639	−	0.531500i	−0.755718	−	0.654897i	$-0.772712\pi$
$311$	4.17317	−	9.37310i	0.236639	−	0.531500i	0.992357	+	0.123397i	$0.0393788\pi$
$312$	26.4981	−	12.0347i	1.50016	−	0.681328i
$313$	−23.7565	−	5.04960i	−1.34280	−	0.285420i	−0.520199	−	0.854045i	$-0.674142\pi$
$313$	−23.7565	−	5.04960i	−1.34280	−	0.285420i	−0.822597	+	0.568625i	$0.807476\pi$
$314$	7.45608	+	22.9475i	0.420771	+	1.29500i
$315$	0.110696	−	25.1992i	0.00623700	−	1.41982i
$316$	3.49715	+	4.81341i	0.196730	+	0.270776i
$317$	7.26809	−	6.54421i	0.408216	−	0.367560i	−0.439290	−	0.898345i	$-0.644770\pi$
$317$	7.26809	−	6.54421i	0.408216	−	0.367560i	0.847506	+	0.530786i	$0.178103\pi$
$318$	−25.5310	+	44.9906i	−1.43171	+	2.52295i
$319$	0.304042	−	2.39118i	0.0170231	−	0.133880i
$320$	−18.8855	−	10.9035i	−1.05573	−	0.609527i
$321$	−3.45211	−	15.6669i	−0.192678	−	0.874443i
$322$	5.64863	+	29.3441i	0.314786	+	1.63528i
$323$	−3.60384	+	4.96026i	−0.200523	+	0.275996i
$324$	12.4081	+	34.6455i	0.689341	+	1.92475i
$325$	−12.3050	−	11.0795i	−0.682558	−	0.614578i
$326$	4.86465	−	46.2840i	0.269428	−	2.56344i
$327$	−7.82258	+	5.77282i	−0.432589	+	0.319238i
$328$	−9.20234	+	28.3219i	−0.508114	+	1.56381i
$329$	−4.40830	+	0.377609i	−0.243037	+	0.0208183i
$330$	40.8468	+	18.8913i	2.24854	+	1.03993i
$331$	−2.91094	+	5.04190i	−0.160000	+	0.277128i	−0.934868	−	0.354995i	$-0.884483\pi$
$331$	−2.91094	+	5.04190i	−0.160000	+	0.277128i	0.774869	+	0.632122i	$0.217816\pi$
$332$	5.98721	−	1.27262i	0.328591	−	0.0698442i
$333$	−15.2045	+	11.3961i	−0.833200	+	0.624502i
$334$	23.1792	−	10.3201i	1.26831	−	0.564688i
$335$	25.6052	−	8.31963i	1.39896	−	0.454550i
$336$	20.6708	+	2.42017i	1.12769	+	0.132031i
$337$	−7.90657	+	10.8825i	−0.430698	+	0.592805i	−0.968113	−	0.250513i	$-0.919401\pi$
$337$	−7.90657	+	10.8825i	−0.430698	+	0.592805i	0.537415	+	0.843318i	$0.319401\pi$
$338$	0.612406	+	5.82665i	0.0333105	+	0.316928i
$339$	−3.17429	−	3.47310i	−0.172404	−	0.188633i
$340$	22.5748	−	13.0335i	1.22429	−	0.706843i
$341$	−13.6215	−	15.8065i	−0.737646	−	0.855971i
$342$	−19.7413	−	11.0094i	−1.06749	−	0.595318i
$343$	−18.4893	−	1.07004i	−0.998330	−	0.0577767i
$344$	−24.0506	−	33.1028i	−1.29672	−	1.78479i
$345$	−14.6427	+	20.4725i	−0.788337	+	1.10220i
$346$	10.0985	−	11.2155i	0.542900	−	0.602951i
$347$	7.02681	−	7.80407i	0.377219	−	0.418944i	−0.524402	−	0.851471i	$-0.675711\pi$
$347$	7.02681	−	7.80407i	0.377219	−	0.418944i	0.901621	+	0.432527i	$0.142378\pi$
$348$	2.99438	−	4.18655i	0.160516	−	0.224422i
$349$	−1.43360	−	1.97317i	−0.0767386	−	0.105622i	0.768922	−	0.639342i	$-0.220793\pi$
$349$	−1.43360	−	1.97317i	−0.0767386	−	0.105622i	−0.845661	+	0.533721i	$0.820793\pi$
$350$	−9.63818	−	31.7311i	−0.515183	−	1.69610i
$351$	16.9337	−	0.377943i	0.903856	−	0.0201731i
$352$	−1.54386	+	2.54457i	−0.0822881	+	0.135626i
$353$	−15.9167	+	9.18952i	−0.847161	+	0.489109i	−0.859692	−	0.510813i	$-0.829344\pi$
$353$	−15.9167	+	9.18952i	−0.847161	+	0.489109i	0.0125310	+	0.999921i	$0.496011\pi$
$354$	−5.21009	−	5.70054i	−0.276913	−	0.302980i
$355$	4.28379	+	40.7576i	0.227360	+	2.16319i
$356$	0.212445	−	0.292405i	0.0112596	−	0.0154974i
$357$	5.49634	−	7.37985i	0.290897	−	0.390583i
$358$	13.7318	−	4.46174i	0.725749	−	0.235810i
$359$	−19.7115	+	8.77612i	−1.04033	+	0.463186i	−0.854531	−	0.519401i	$-0.826155\pi$
$359$	−19.7115	+	8.77612i	−1.04033	+	0.463186i	−0.185802	+	0.982587i	$0.559488\pi$
$360$	29.4451	+	39.2852i	1.55190	+	2.07051i
$361$	−9.46518	+	2.01189i	−0.498167	+	0.105889i
$362$	−1.26261	+	2.18691i	−0.0663614	+	0.114941i
$363$	−8.37197	+	17.1146i	−0.439415	+	0.898284i
$364$	14.9615	−	31.9334i	0.784195	−	1.67377i
$365$	−8.63564	+	26.5778i	−0.452010	+	1.39114i
$366$	40.6851	−	30.0243i	2.12664	−	1.56940i
$367$	−1.19091	+	11.3308i	−0.0621652	+	0.591462i	0.918453	+	0.395531i	$0.129439\pi$
$367$	−1.19091	+	11.3308i	−0.0621652	+	0.591462i	−0.980618	+	0.195931i	$0.937227\pi$
$368$	−15.4483	−	13.9097i	−0.805297	−	0.725093i
$369$	−11.4043	+	13.0510i	−0.593682	+	0.679409i
$370$	−29.1656	+	40.1431i	−1.51625	+	2.08694i
$371$	6.05314	+	31.4455i	0.314263	+	1.63257i
$372$	−9.58783	−	43.5131i	−0.497106	−	2.25605i
$373$	−24.0259	−	13.8713i	−1.24401	−	0.718230i	−0.274103	−	0.961700i	$-0.588381\pi$
$373$	−24.0259	−	13.8713i	−1.24401	−	0.718230i	−0.969908	+	0.243470i	$0.921714\pi$
$374$	7.90520	+	14.4071i	0.408768	+	0.744973i
$375$	0.216001	−	0.380635i	0.0111542	−	0.0196559i
$376$	6.40589	−	5.76789i	0.330359	−	0.297456i
$377$	−1.39250	−	1.91661i	−0.0717175	−	0.0987107i
$378$	29.4302	+	16.8722i	1.51373	+	0.867814i
$379$	−7.71162	−	23.7339i	−0.396119	−	1.21913i	−0.928086	−	0.372365i	$-0.878547\pi$
$379$	−7.71162	−	23.7339i	−0.396119	−	1.21913i	0.531967	−	0.846765i	$-0.321453\pi$
$380$	−38.7724	−	8.24133i	−1.98898	−	0.422771i
$381$	3.74902	−	1.70270i	0.192068	−	0.0872318i
$382$	−17.4978	+	39.3008i	−0.895268	+	2.01080i
$383$	9.87857	−	8.89471i	0.504772	−	0.454498i	−0.376974	−	0.926224i	$-0.623035\pi$
$383$	9.87857	−	8.89471i	0.504772	−	0.454498i	0.881745	+	0.471726i	$0.156369\pi$
$384$	27.9943	−	16.4414i	1.42858	−	0.839021i
$385$	26.8263	−	7.51507i	1.36720	−	0.383003i
$386$			27.1279i			1.38077i
$387$	−5.29718	−	23.2174i	−0.269271	−	1.18020i
$388$	64.2030	+	28.5850i	3.25941	+	1.45118i
$389$	−2.89427	−	0.304200i	−0.146745	−	0.0154236i	0.0308709	−	0.999523i	$-0.490172\pi$
$389$	−2.89427	−	0.304200i	−0.146745	−	0.0154236i	−0.177616	+	0.984100i	$0.556839\pi$
$390$	41.9638	−	13.9808i	2.12492	−	0.707946i
$391$	−8.74116	+	2.84017i	−0.442059	+	0.143634i
$392$	29.9867	−	20.0682i	1.51456	−	1.01360i
$393$	7.34094	−	16.8237i	0.370301	−	0.848643i
$394$	20.0121	+	22.2257i	1.00820	+	1.11972i
$395$	2.30981	+	4.00071i	0.116219	+	0.201297i
$396$	−33.0781	+	23.6868i	−1.66224	+	1.19031i
$397$	4.99690	−	8.65489i	0.250787	−	0.434377i	−0.712955	−	0.701209i	$-0.752644\pi$
$397$	4.99690	−	8.65489i	0.250787	−	0.434377i	0.963743	+	0.266833i	$0.0859771\pi$
$398$	15.9786	−	49.1769i	0.800933	−	2.46502i
$399$	−13.7202	+	2.74708i	−0.686870	+	0.137526i
$400$	18.6634	+	13.5597i	0.933169	+	0.677987i
$401$	−4.24800	+	19.9853i	−0.212135	+	0.998017i	0.735219	+	0.677829i	$0.237079\pi$
$401$	−4.24800	+	19.9853i	−0.212135	+	0.998017i	−0.947354	+	0.320187i	$0.896254\pi$
$402$	−7.27156	+	35.5067i	−0.362673	+	1.77091i
$403$	−20.3956	−	2.14367i	−1.01598	−	0.106784i
$404$	1.40167	+	13.3360i	0.0697356	+	0.663490i
$405$	6.76961	+	27.7600i	0.336385	+	1.37941i
$406$	−0.404951	−	4.72749i	−0.0200974	−	0.234621i
$407$	−16.7222	−	12.7141i	−0.828886	−	0.630217i
$408$	0.133350	+	17.9269i	0.00660183	+	0.887515i
$409$	6.93357	+	32.6199i	0.342843	+	1.61295i	0.724930	+	0.688823i	$0.241872\pi$
$409$	6.93357	+	32.6199i	0.342843	+	1.61295i	−0.382087	+	0.924126i	$0.624795\pi$
$410$	−18.4088	+	41.3467i	−0.909144	+	2.04197i
$411$	3.93953	+	2.81770i	0.194323	+	0.138987i
$412$	17.3941	+	53.5335i	0.856945	+	2.63740i
$413$	−4.74399	−	0.591237i	−0.233436	−	0.0290929i
$414$	−14.2408	−	30.7461i	−0.699898	−	1.51109i
$415$	4.72656	−	0.496782i	0.232018	−	0.0243860i
$416$	0.608188	+	2.86130i	0.0298189	+	0.140287i
$417$	13.8286	−	24.3687i	0.677190	−	1.19334i
$418$	5.72601	−	24.3244i	0.280068	−	1.18975i
$419$		−	25.4753i		−	1.24455i	−0.782799	−	0.622274i	$-0.786209\pi$
$419$		−	25.4753i		−	1.24455i	0.782799	−	0.622274i	$-0.213791\pi$
$420$	58.0393	+	13.0562i	2.83203	+	0.637076i
$421$	11.4099	−	8.28981i	0.556086	−	0.404020i	−0.273938	−	0.961747i	$-0.588326\pi$
$421$	11.4099	−	8.28981i	0.556086	−	0.404020i	0.830025	+	0.557727i	$0.188326\pi$
$422$	−12.6084	−	28.3190i	−0.613768	−	1.37855i
$423$	4.74771	−	1.62110i	0.230842	−	0.0788205i
$424$	−46.3640	−	41.7463i	−2.25163	−	2.02738i
$425$	9.31792	−	4.14860i	0.451985	−	0.201237i
$426$	−50.5659	−	22.0642i	−2.44993	−	1.06901i
$427$	7.09661	−	30.4861i	0.343429	−	1.47532i
$428$	37.8729			1.83066
$429$	5.53101	+	17.8901i	0.267040	+	0.863743i
$430$	−31.0937	−	53.8560i	−1.49947	−	2.59716i
$431$	22.3798	−	4.75697i	1.07800	−	0.229135i	0.365500	−	0.930812i	$-0.380898\pi$
$431$	22.3798	−	4.75697i	1.07800	−	0.229135i	0.712496	+	0.701677i	$0.247565\pi$
$432$	−23.4084	+	2.98979i	−1.12624	+	0.143846i
$433$	−7.71307	−	5.60387i	−0.370666	−	0.269305i	0.386821	−	0.922155i	$-0.373573\pi$
$433$	−7.71307	−	5.60387i	−0.370666	−	0.269305i	−0.757487	+	0.652850i	$0.773573\pi$
$434$	−32.7579	−	24.7783i	−1.57243	−	1.18940i
$435$	2.65202	−	2.98979i	0.127154	−	0.143349i
$436$	−9.33515	−	20.9671i	−0.447072	−	1.00414i
$437$	12.7679	+	5.68463i	0.610770	+	0.271933i
$438$	−25.3802	−	27.7693i	−1.21271	−	1.32687i
$439$	3.84769	+	2.22146i	0.183640	+	0.106025i	0.589002	−	0.808132i	$-0.299521\pi$
$439$	3.84769	+	2.22146i	0.183640	+	0.106025i	−0.405362	+	0.914156i	$0.632854\pi$
$440$	−32.8507	+	43.2066i	−1.56610	+	2.05979i
$441$	20.6387	−	3.87892i	0.982793	−	0.184710i
$442$	15.3609	+	4.99106i	0.730643	+	0.237400i
$443$	−16.4999	+	1.73421i	−0.783934	+	0.0823948i	−0.488035	−	0.872824i	$-0.662286\pi$
$443$	−16.4999	+	1.73421i	−0.783934	+	0.0823948i	−0.295899	+	0.955219i	$0.595619\pi$
$444$	−18.5494	−	40.8422i	−0.880314	−	1.93829i
$445$	0.187780	−	0.208551i	0.00890162	−	0.00988625i
$446$	−7.06617	−	1.50196i	−0.334593	−	0.0711199i
$447$	−27.8862	−	2.72140i	−1.31897	−	0.128718i
$448$	5.94773	−	17.1721i	0.281004	−	0.811305i
$449$	7.14191	+	2.32055i	0.337047	+	0.109513i	0.472651	−	0.881250i	$-0.343297\pi$
$449$	7.14191	+	2.32055i	0.337047	+	0.109513i	−0.135603	+	0.990763i	$0.543297\pi$
$450$	19.2838	+	32.2817i	0.909046	+	1.52177i
$451$	−17.3307	−	8.17233i	−0.816069	−	0.384820i
$452$	9.61957	−	5.55386i	0.452467	−	0.261232i
$453$	−1.69249	+	5.34389i	−0.0795203	+	0.251078i
$454$	22.0054	−	15.9879i	1.03276	−	0.750348i
$455$	14.1449	−	23.4444i	0.663122	−	1.09909i
$456$	18.0901	−	20.3941i	0.847144	−	0.955041i
$457$	1.87816	−	8.83605i	0.0878566	−	0.413333i	−0.912137	−	0.409885i	$-0.865569\pi$
$457$	1.87816	−	8.83605i	0.0878566	−	0.413333i	0.999994	−	0.00344844i	$-0.00109767\pi$
$458$	0.187411	−	1.78310i	0.00875714	−	0.0833187i
$459$	−4.03006	+	9.62406i	−0.188107	+	0.449213i
$460$	−39.7599	−	44.1579i	−1.85382	−	2.05887i
$461$	−1.81796			−0.0846711			−0.0423355	−	0.999103i	$-0.513480\pi$
$461$	−1.81796			−0.0846711			−0.0423355	+	0.999103i	$0.513480\pi$
$462$	−9.02490	+	36.4019i	−0.419876	+	1.69357i
$463$	7.46535			0.346944			0.173472	−	0.984839i	$-0.444501\pi$
$463$	7.46535			0.346944			0.173472	+	0.984839i	$0.444501\pi$
$464$	2.20858	+	2.45288i	0.102531	+	0.113872i
$465$	−3.87209	−	34.3786i	−0.179564	−	1.59427i
$466$	4.33456	−	41.2406i	0.200795	−	1.91043i
$467$	−5.83090	+	27.4322i	−0.269822	+	1.26941i	0.609347	+	0.792904i	$0.291432\pi$
$467$	−5.83090	+	27.4322i	−0.269822	+	1.26941i	−0.879169	+	0.476510i	$0.841902\pi$
$468$	−7.73085	+	39.2318i	−0.357359	+	1.81349i
$469$	10.8416	+	19.6429i	0.500620	+	0.907023i
$470$	10.5989	−	7.70052i	0.488889	−	0.355199i
$471$	−16.1458	−	5.11364i	−0.743961	−	0.235624i
$472$	8.06620	−	4.65702i	0.371277	−	0.214357i
$473$	23.0811	−	12.6646i	1.06127	−	0.582320i
$474$	−6.21877	+	0.0462586i	−0.285637	+	0.00212473i
$475$	−14.7510	−	4.79289i	−0.676822	−	0.219913i
$476$	14.2218	+	16.4204i	0.651854	+	0.752629i
$477$	−15.2606	−	32.9479i	−0.698736	−	1.50858i
$478$	0.197389	+	0.0419564i	0.00902837	+	0.00191904i
$479$	−18.9928	+	21.0936i	−0.867802	+	0.963792i	−0.999622	−	0.0274816i	$-0.991251\pi$
$479$	−18.9928	+	21.0936i	−0.867802	+	0.963792i	0.131820	+	0.991274i	$0.457918\pi$
$480$	−4.49303	+	2.04061i	−0.205078	+	0.0931405i
$481$	−20.5331	+	2.15811i	−0.936228	+	0.0984015i
$482$	−33.1059	−	10.7567i	−1.50793	−	0.489956i
$483$	−19.0598	−	8.75761i	−0.867250	−	0.398485i
$484$	−35.2040	−	27.9952i	−1.60018	−	1.27251i
$485$	47.2570	+	27.2839i	2.14583	+	1.23890i
$486$	−36.9998	−	10.5181i	−1.67834	−	0.477109i
$487$	−17.1051	−	7.61568i	−0.775106	−	0.345100i	−0.0192309	−	0.999815i	$-0.506122\pi$
$487$	−17.1051	−	7.61568i	−0.775106	−	0.345100i	−0.755875	+	0.654716i	$0.772788\pi$
$488$	24.8040	+	55.7107i	1.12282	+	2.52190i
$489$	24.4381	+	21.6772i	1.10513	+	0.980276i
$490$	48.5133	−	25.5693i	2.19161	−	1.15510i
$491$	32.0011	+	23.2502i	1.44419	+	1.04927i	0.987146	+	0.159823i	$0.0510923\pi$
$491$	32.0011	+	23.2502i	1.44419	+	1.04927i	0.457045	+	0.889443i	$0.348908\pi$
$492$	−24.2952	−	32.9217i	−1.09531	−	1.48423i
$493$	1.42746	−	0.303415i	0.0642894	−	0.0136651i
$494$	−12.2802	−	21.2700i	−0.552513	−	0.956981i
$495$	−27.4650	+	15.6061i	−1.23446	+	0.701443i
$496$	28.5725			1.28294
$497$	−32.6782	+	9.92586i	−1.46582	+	0.445236i
$498$	−2.55873	+	5.86402i	−0.114660	+	0.262773i
$499$	−4.12716	+	1.83753i	−0.184757	+	0.0822592i	−0.497030	−	0.867733i	$-0.665576\pi$
$499$	−4.12716	+	1.83753i	−0.184757	+	0.0822592i	0.312273	+	0.949992i	$0.398910\pi$
$500$	0.767809	+	0.691338i	0.0343374	+	0.0309176i
$501$	−3.57318	+	17.4476i	−0.159638	+	0.779503i
$502$	−0.156804	−	0.352188i	−0.00699852	−	0.0157189i
$503$	−15.4089	+	11.1952i	−0.687048	+	0.499170i	−0.875688	−	0.482877i	$-0.839592\pi$
$503$	−15.4089	+	11.1952i	−0.687048	+	0.499170i	0.188640	+	0.982046i	$0.439592\pi$
$504$	−27.5098	+	30.2841i	−1.22538	+	1.34896i
$505$			10.4117i			0.463314i
$506$	28.3769	−	24.4543i	1.26151	−	1.08713i
$507$	−3.57663	−	2.02965i	−0.158844	−	0.0901398i
$508$	2.02101	+	9.50812i	0.0896680	+	0.421855i
$509$	22.0304	−	2.31549i	0.976482	−	0.102632i	0.397176	−	0.917742i	$-0.369990\pi$
$509$	22.0304	−	2.31549i	0.976482	−	0.102632i	0.579306	+	0.815110i	$0.303324\pi$
$510$	−2.64641	+	27.1178i	−0.117185	+	1.20080i
$511$	−23.1096	−	2.88012i	−1.02231	−	0.127409i
$512$	13.2088	+	40.6524i	0.583750	+	1.79660i
$513$	14.3467	−	6.77511i	0.633424	−	0.299128i
$514$	2.20631	−	4.95546i	0.0973163	−	0.218576i
$515$	9.08675	+	42.7498i	0.400410	+	1.88378i
$516$	56.2173	−	0.418176i	2.47483	−	0.0184092i
$517$	3.16168	+	4.55692i	0.139050	+	0.200413i
$518$	−37.4445	−	17.5435i	−1.64522	−	0.770818i
$519$	2.27951	+	10.3453i	0.100060	+	0.454107i
$520$	5.57612	+	53.0532i	0.244529	+	2.32654i
$521$	−3.62868	−	0.381390i	−0.158975	−	0.0167090i	0.0247064	−	0.999695i	$-0.492135\pi$
$521$	−3.62868	−	0.381390i	−0.158975	−	0.0167090i	−0.183682	+	0.982986i	$0.558802\pi$
$522$	1.73848	+	5.09148i	0.0760911	+	0.222848i
$523$	−8.33689	+	39.2220i	−0.364547	+	1.71506i	0.288277	+	0.957547i	$0.406918\pi$
$523$	−8.33689	+	39.2220i	−0.364547	+	1.71506i	−0.652823	+	0.757510i	$0.726416\pi$
$524$	35.0570	+	25.4704i	1.53147	+	1.11268i
$525$	22.0517	+	7.45459i	0.962413	+	0.325345i
$526$	−7.79167	+	23.9803i	−0.339733	+	1.04559i
$527$	6.31646	−	10.9404i	0.275149	−	0.476573i
$528$	−10.2692	−	23.9831i	−0.446909	−	1.04373i
$529$	−1.02450	−	1.77449i	−0.0445436	−	0.0771517i
$530$	−63.4474	−	70.4654i	−2.75598	−	3.06082i
$531$	5.38207	−	0.646764i	0.233562	−	0.0280672i
$532$	0.636491	−	33.0267i	0.0275954	−	1.43189i
$533$	−17.9104	+	5.81943i	−0.775784	+	0.252067i
$534$	0.119412	+	0.358420i	0.00516748	+	0.0155103i
$535$	29.2452	+	3.07379i	1.26438	+	0.132892i
$536$	−39.9326	−	17.7791i	−1.72482	−	0.767941i
$537$	−3.06002	+	9.66171i	−0.132049	+	0.416934i
$538$		−	24.2830i		−	1.04691i
$539$	10.3756	+	20.7689i	0.446908	+	0.894580i
$540$	−67.4382	+	1.50515i	−2.90208	+	0.0647713i
$541$	28.7781	−	25.9119i	1.23727	−	1.11404i	0.247870	−	0.968793i	$-0.420269\pi$
$541$	28.7781	−	25.9119i	1.23727	−	1.11404i	0.989396	−	0.145246i	$-0.0463973\pi$
$542$	−3.80414	+	8.54423i	−0.163402	+	0.367006i
$543$	−0.732971	−	1.61386i	−0.0314548	−	0.0692575i
$544$	−1.76256	−	0.374644i	−0.0755692	−	0.0160627i
$545$	−5.50682	−	16.9482i	−0.235886	−	0.725983i
$546$	18.0512	+	32.1378i	0.772521	+	1.37537i
$547$	3.79738	+	5.22664i	0.162364	+	0.223475i	0.882446	−	0.470415i	$-0.155896\pi$
$547$	3.79738	+	5.22664i	0.162364	+	0.223475i	−0.720081	+	0.693890i	$0.755896\pi$
$548$	−8.49731	+	7.65102i	−0.362987	+	0.326835i
$549$	0.527992	+	35.4883i	0.0225341	+	1.51460i
$550$	−28.4822	+	30.2813i	−1.21448	+	1.29120i
$551$	−1.92183	−	1.10957i	−0.0818727	−	0.0472692i
$552$	39.9085	−	8.79357i	1.69862	−	0.374279i
$553$	−2.91003	+	2.52039i	−0.123747	+	0.107178i
$554$	−12.5597	+	17.2870i	−0.533612	+	0.734454i
$555$	−11.0089	−	33.0435i	−0.467301	−	1.40262i
$556$	49.1560	+	44.2602i	2.08468	+	1.87705i
$557$	−3.91604	+	37.2586i	−0.165928	+	1.57870i	0.522018	+	0.852935i	$0.325179\pi$
$557$	−3.91604	+	37.2586i	−0.165928	+	1.57870i	−0.687945	+	0.725762i	$0.741487\pi$
$558$	42.8238	+	18.3080i	1.81288	+	0.775039i
$559$	7.99599	−	24.6091i	0.338194	−	1.04086i
$560$	−16.1849	+	34.5447i	−0.683938	+	1.45978i
$561$	−11.4534	−	1.36982i	−0.483561	−	0.0578339i
$562$	−30.6872	+	53.1518i	−1.29446	+	2.24207i
$563$	30.8429	−	6.55587i	1.29987	−	0.276297i	0.494560	−	0.869144i	$-0.335329\pi$
$563$	30.8429	−	6.55587i	1.29987	−	0.276297i	0.805315	+	0.592847i	$0.201996\pi$
$564$	1.32556	+	11.7691i	0.0558163	+	0.495569i
$565$	7.87891	−	3.50791i	0.331468	−	0.147579i
$566$	−37.8090	+	12.2849i	−1.58923	+	0.516373i
$567$	−21.6504	+	9.91264i	−0.909231	+	0.416292i
$568$	39.1100	−	53.8303i	1.64102	−	2.25867i
$569$	−1.15424	−	10.9818i	−0.0483881	−	0.460382i	−0.991709	−	0.128501i	$-0.958983\pi$
$569$	−1.15424	−	10.9818i	−0.0483881	−	0.460382i	0.943321	−	0.331881i	$-0.107683\pi$
$570$	30.5831	−	27.9519i	1.28099	−	1.17078i
$571$	−17.9351	+	10.3548i	−0.750559	+	0.433335i	−0.825896	−	0.563823i	$-0.809330\pi$
$571$	−17.9351	+	10.3548i	−0.750559	+	0.433335i	0.0753369	+	0.997158i	$0.475997\pi$
$572$	−44.0544	+	3.66346i	−1.84201	+	0.153177i
$573$	−15.2925	−	26.0382i	−0.638854	−	1.08776i
$574$	−36.7350	−	8.55125i	−1.53329	−	0.356922i
$575$	−13.6663	−	18.8100i	−0.569922	−	0.784431i
$576$	−1.84883	+	20.5231i	−0.0770346	+	0.855129i
$577$	−8.50794	+	9.44902i	−0.354190	+	0.393368i	−0.893740	−	0.448586i	$-0.851928\pi$
$577$	−8.50794	+	9.44902i	−0.354190	+	0.393368i	0.539550	+	0.841954i	$0.318595\pi$
$578$	21.4119	−	23.7803i	0.890617	−	0.989130i
$579$	−15.4879	−	11.0775i	−0.643654	−	0.460366i
$580$	5.54561	+	7.63287i	0.230269	+	0.316938i
$581$	1.15108	+	3.78962i	0.0477548	+	0.157220i
$582$	−63.3425	+	37.2018i	−2.62563	+	1.54206i
$583$	30.4091	−	26.2055i	1.25941	−	1.08532i
$584$	39.2933	−	22.6860i	1.62597	−	0.938753i
$585$	−9.15377	+	29.6670i	−0.378462	+	1.22658i
$586$	−3.06304	−	29.1429i	−0.126533	−	1.20388i
$587$	−17.9006	+	24.6380i	−0.738836	+	1.01692i	0.259849	+	0.965649i	$0.416327\pi$
$587$	−17.9006	+	24.6380i	−0.738836	+	1.01692i	−0.998685	+	0.0512707i	$0.983673\pi$
$588$	−1.54160	+	49.5518i	−0.0635745	+	2.04348i
$589$	−18.2699	+	5.93625i	−0.752798	+	0.244599i
$590$	12.9319	−	5.75767i	0.532400	−	0.237040i
$591$	−20.8610	+	2.34959i	−0.858107	+	0.0966493i
$592$	28.1365	−	5.98059i	1.15640	−	0.245801i
$593$	11.5346	−	19.9785i	0.473668	−	0.820417i	−0.525878	−	0.850560i	$-0.676263\pi$
$593$	11.5346	−	19.9785i	0.473668	−	0.820417i	0.999546	+	0.0301434i	$0.00959638\pi$
$594$	−0.0239031	−	42.5255i	−0.000980755	−	1.74484i
$595$	9.64924	+	13.8340i	0.395580	+	0.567137i
$596$	20.4400	−	62.9078i	0.837255	−	2.57681i
$597$	21.5514	+	29.2037i	0.882040	+	1.19523i
$598$	3.84846	−	36.6156i	0.157375	−	1.49732i
$599$	−6.76996	−	6.09570i	−0.276613	−	0.249063i	0.519134	−	0.854693i	$-0.326255\pi$
$599$	−6.76996	−	6.09570i	−0.276613	−	0.249063i	−0.795747	+	0.605630i	$0.792921\pi$
$600$	−43.0258	+	14.3346i	−1.75652	+	0.585209i
$601$	6.88617	−	9.47801i	0.280893	−	0.386616i	−0.645136	−	0.764067i	$-0.723199\pi$
$601$	6.88617	−	9.47801i	0.280893	−	0.386616i	0.926029	+	0.377451i	$0.123199\pi$
$602$	39.1737	−	33.9285i	1.59660	−	1.38282i
$603$	−17.3022	−	18.6505i	−0.704601	−	0.759506i
$604$	−11.4603	−	6.61660i	−0.466313	−	0.269226i
$605$	−24.9121	−	24.4748i	−1.01282	−	0.995044i
$606$	−12.1902	−	6.91763i	−0.495193	−	0.281010i
$607$	11.0582	−	9.95687i	0.448839	−	0.404137i	−0.413471	−	0.910517i	$-0.635684\pi$
$607$	11.0582	−	9.95687i	0.448839	−	0.404137i	0.862310	+	0.506381i	$0.169017\pi$
$608$	1.61059	+	2.21679i	0.0653180	+	0.0899025i
$609$	2.86438	+	1.69925i	0.116071	+	0.0688571i
$610$	28.6409	+	88.1475i	1.15963	+	3.56899i
$611$	5.33203	+	1.13336i	0.215711	+	0.0458508i
$612$	−20.1405	−	14.1800i	−0.814133	−	0.573194i
$613$	13.3114	−	29.8979i	0.537642	−	1.20756i	−0.416754	−	0.909019i	$-0.636832\pi$
$613$	13.3114	−	29.8979i	0.537642	−	1.20756i	0.954396	−	0.298544i	$-0.0965010\pi$
$614$	35.5230	−	31.9850i	1.43359	−	1.29081i
$615$	−16.0886	−	27.3937i	−0.648755	−	1.10462i
$616$	−40.5319	−	20.0765i	−1.63308	−	0.808906i
$617$			5.43939i			0.218982i	0.993988	+	0.109491i	$0.0349220\pi$
$617$			5.43939i			0.218982i	−0.993988	+	0.109491i	$0.965078\pi$
$618$	−56.0896	−	17.7645i	−2.25626	−	0.714591i
$619$	−2.73595	−	1.21812i	−0.109967	−	0.0489605i	0.351016	−	0.936370i	$-0.385836\pi$
$619$	−2.73595	−	1.21812i	−0.109967	−	0.0489605i	−0.460983	+	0.887409i	$0.652503\pi$
$620$	81.2251	+	8.53710i	3.26208	+	0.342858i
$621$	23.3688	+	4.42463i	0.937757	+	0.177554i
$622$	−24.0785	+	7.82359i	−0.965462	+	0.313698i
$623$	0.200243	+	0.120813i	0.00802255	+	0.00484029i
$624$	−23.5016	−	10.2548i	−0.940818	−	0.410521i
$625$	−16.4578	−	18.2782i	−0.658310	−	0.731127i
$626$	29.9653	+	51.9014i	1.19765	+	2.07440i
$627$	11.5491	+	13.2018i	0.461228	+	0.527231i
$628$	19.9912	−	34.6257i	0.797734	−	1.38172i
$629$	3.93010	−	12.0956i	0.156703	−	0.482283i
$630$	−46.3923	+	41.4043i	−1.84831	+	1.64959i
$631$	28.1921	+	20.4827i	1.12231	+	0.815405i	0.984557	−	0.175062i	$-0.0560125\pi$
$631$	28.1921	+	20.4827i	1.12231	+	0.815405i	0.137751	+	0.990467i	$0.456013\pi$
$632$	1.55941	−	7.33645i	0.0620300	−	0.291828i
$633$	21.3165	+	4.36549i	0.847254	+	0.173513i
$634$	−24.0011	−	2.52262i	−0.953207	−	0.100186i
$635$	0.788925	+	7.50612i	0.0313075	+	0.297871i
$636$	83.7119	−	18.4454i	3.31939	−	0.731406i
$637$	21.4134	+	7.88205i	0.848429	+	0.312298i
$638$	−4.88688	+	3.39061i	−0.193473	+	0.134235i
$639$	33.2452	−	19.8594i	1.31516	−	0.785624i
$640$	12.3726	+	58.2084i	0.489069	+	2.30089i
$641$	−1.14366	+	2.56871i	−0.0451720	+	0.101458i	−0.934722	−	0.355380i	$-0.884351\pi$
$641$	−1.14366	+	2.56871i	−0.0451720	+	0.101458i	0.889550	+	0.456838i	$0.151018\pi$
$642$	−23.0296	+	32.1985i	−0.908907	+	1.27078i
$643$	−13.4713	−	41.4604i	−0.531256	−	1.63504i	−0.751602	−	0.659617i	$-0.770719\pi$
$643$	−13.4713	−	41.4604i	−0.531256	−	1.63504i	0.220346	−	0.975422i	$-0.429281\pi$
$644$	29.8724	−	39.4926i	1.17714	−	1.55622i
$645$	43.4445	+	4.23972i	1.71062	+	0.166939i
$646$	15.0464	−	1.58144i	0.591992	−	0.0622208i
$647$	−3.02606	−	14.2365i	−0.118967	−	0.559695i	−0.996744	−	0.0806263i	$-0.974308\pi$
$647$	−3.02606	−	14.2365i	−0.118967	−	0.559695i	0.877778	−	0.479068i	$-0.159025\pi$
$648$	21.9903	−	40.8486i	0.863861	−	1.60468i
$649$	2.31788	+	5.52652i	0.0909846	+	0.216935i
$650$			40.8581i			1.60259i
$651$	27.5230	−	8.58411i	1.07871	−	0.336438i
$652$	−62.3899	+	45.3289i	−2.44338	+	1.77522i
$653$	7.08547	+	15.9142i	0.277276	+	0.622772i	0.997477	−	0.0709939i	$-0.0226171\pi$
$653$	7.08547	+	15.9142i	0.277276	+	0.622772i	−0.720201	+	0.693765i	$0.755950\pi$
$654$	23.5021	+	4.81310i	0.919006	+	0.188207i
$655$	25.0035	+	22.5133i	0.976969	+	0.879667i
$656$	23.9692	−	10.6718i	0.935840	−	0.416663i
$657$	26.2179	−	3.15061i	1.02286	−	0.122917i
$658$	7.97113	+	7.46031i	0.310747	+	0.290833i
$659$	−38.4798			−1.49896			−0.749481	−	0.662026i	$-0.769697\pi$
$659$	−38.4798			−1.49896			−0.749481	+	0.662026i	$0.769697\pi$
$660$	−22.0271	−	71.2470i	−0.857405	−	2.77328i
$661$	−23.8500	−	41.3094i	−0.927658	−	1.60675i	−0.787230	−	0.616660i	$-0.788485\pi$
$661$	−23.8500	−	41.3094i	−0.927658	−	1.60675i	−0.140428	−	0.990091i	$-0.544848\pi$
$662$	14.0520	−	2.98685i	0.546147	−	0.116087i
$663$	−9.12204	+	6.73179i	−0.354271	+	0.261441i
$664$	−6.24258	−	4.53550i	−0.242259	−	0.176012i
$665$	3.17196	−	25.4513i	0.123003	−	0.986959i
$666$	46.0024	+	9.06502i	1.78256	+	0.351262i
$667$	−1.35305	−	3.03900i	−0.0523903	−	0.117671i
$668$	−38.4095	−	17.1010i	−1.48611	−	0.661658i
$669$	3.74294	−	3.42091i	0.144710	−	0.132260i
$670$	−57.5338	−	33.2172i	−2.22272	−	1.28329i
$671$	−37.5725	+	11.3107i	−1.45047	+	0.436643i
$672$	−2.37765	−	3.35532i	−0.0917197	−	0.129434i
$673$	3.55641	+	1.15555i	0.137090	+	0.0445431i	0.376758	−	0.926312i	$-0.377039\pi$
$673$	3.55641	+	1.15555i	0.137090	+	0.0445431i	−0.239669	+	0.970855i	$0.577039\pi$
$674$	33.0107	−	3.46956i	1.27152	−	0.133643i
$675$	−26.3047	−	2.17255i	−1.01247	−	0.0836215i
$676$	6.49614	−	7.21469i	0.249852	−	0.277488i
$677$	−0.531444	−	0.112962i	−0.0204250	−	0.00434148i	0.197688	−	0.980265i	$-0.436657\pi$
$677$	−0.531444	−	0.112962i	−0.0204250	−	0.00434148i	−0.218113	+	0.975924i	$0.569990\pi$
$678$	−1.12769	+	11.5555i	−0.0433087	+	0.443785i
$679$	−14.8830	+	42.9696i	−0.571156	+	1.64902i
$680$	−31.2525	−	10.1546i	−1.19848	−	0.389409i
$681$	0.142016	+	19.0919i	0.00544207	+	0.731604i
$682$	−6.49456	+	51.0773i	−0.248690	+	1.95585i
$683$	0.986505	−	0.569559i	0.0377476	−	0.0217936i	−0.481007	−	0.876717i	$-0.659729\pi$
$683$	0.986505	−	0.569559i	0.0377476	−	0.0217936i	0.518755	+	0.854923i	$0.326396\pi$
$684$	8.33165	+	36.5173i	0.318569	+	1.39628i
$685$	−7.18251	+	5.21840i	−0.274430	+	0.199385i
$686$	28.5661	+	35.6719i	1.09066	+	1.36196i
$687$	0.941480	+	0.835115i	0.0359197	+	0.0318616i
$688$	−7.49539	+	35.2630i	−0.285759	+	1.34439i
$689$	4.12405	−	39.2377i	0.157114	−	1.49484i
$690$	61.7189	−	6.95145i	2.34960	−	0.264637i
$691$	2.11661	+	2.35073i	0.0805196	+	0.0894260i	0.782058	−	0.623205i	$-0.214170\pi$
$691$	2.11661	+	2.35073i	0.0805196	+	0.0894260i	−0.701539	+	0.712631i	$0.747503\pi$
$692$	−25.0085			−0.950679
$693$	−17.0973	−	20.0170i	−0.649474	−	0.760384i
$694$	−25.9130			−0.983645
$695$	34.3656	+	38.1669i	1.30356	+	1.44775i
$696$	−6.44790	+	0.726232i	−0.244407	+	0.0275278i
$697$	1.21259	−	11.5370i	0.0459301	−	0.436996i
$698$	−1.25129	+	5.88685i	−0.0473620	+	0.222821i
$699$	21.7751	+	19.3151i	0.823611	+	0.730563i
$700$	−28.3882	+	47.0521i	−1.07297	+	1.77840i
$701$	24.6292	−	17.8942i	0.930234	−	0.675854i	−0.0158163	−	0.999875i	$-0.505035\pi$
$701$	24.6292	−	17.8942i	0.930234	−	0.675854i	0.946050	+	0.324021i	$0.105035\pi$
$702$	−28.6529	−	30.4285i	−1.08143	−	1.14845i
$703$	−16.7486	+	9.66979i	−0.631684	+	0.364703i
$704$	−22.3809	+	4.25062i	−0.843513	+	0.160201i
$705$	0.0684018	+	9.19558i	0.00257616	+	0.346326i
$706$	43.1320	+	14.0144i	1.62329	+	0.527440i
$707$	−8.52016	+	1.64010i	−0.320434	+	0.0616822i
$708$	−1.24296	+	12.7366i	−0.0467133	+	0.478672i
$709$	18.1761	+	3.86345i	0.682619	+	0.145095i	0.536153	−	0.844121i	$-0.319877\pi$
$709$	18.1761	+	3.86345i	0.682619	+	0.145095i	0.146465	+	0.989216i	$0.453210\pi$
$710$	67.6668	−	75.1516i	2.53949	−	2.82039i
$711$	2.51299	−	3.56931i	0.0942445	−	0.133860i
$712$	−0.453135	+	0.0476265i	−0.0169820	+	0.00178488i
$713$	−27.3875	−	8.89874i	−1.02567	−	0.333260i
$714$	−22.6081	+	2.10610i	−0.846088	+	0.0788187i
$715$	−34.3158	−	0.746595i	−1.28334	−	0.0279211i
$716$	−20.7201	−	11.9628i	−0.774347	−	0.447069i
$717$	−0.104557	+	0.0955610i	−0.00390474	+	0.00356879i
$718$	48.6396	+	21.6558i	1.81522	+	0.808186i
$719$	−10.0264	−	22.5196i	−0.373920	−	0.839839i	−0.998276	−	0.0586983i	$-0.981305\pi$
$719$	−10.0264	−	22.5196i	−0.373920	−	0.839839i	0.624356	−	0.781140i	$-0.285362\pi$
$720$	8.36302	−	42.4399i	0.311671	−	1.58164i
$721$	−33.5519	+	14.1701i	−1.24954	+	0.527721i
$722$	19.3176	+	14.0351i	0.718926	+	0.522331i
$723$	19.6599	−	14.5084i	0.731158	−	0.539572i
$724$	4.09302	−	0.869999i	0.152116	−	0.0323332i
$725$	1.84585	+	3.19711i	0.0685532	+	0.118738i
$726$	45.2075	−	12.9062i	1.67781	−	0.478995i
$727$	−24.7737			−0.918804			−0.459402	−	0.888229i	$-0.651936\pi$
$727$	−24.7737			−0.918804			−0.459402	+	0.888229i	$0.651936\pi$
$728$	−42.5365	+	12.9203i	−1.57651	+	0.478857i
$729$	21.1136	−	16.8290i	0.781987	−	0.623295i
$730$	62.9960	−	28.0476i	2.33159	−	1.03809i
$731$	11.8453	+	10.6655i	0.438113	+	0.394478i
$732$	−82.0845	−	16.8104i	−3.03393	−	0.621332i
$733$	3.50413	+	7.87040i	0.129428	+	0.290700i	0.966622	−	0.256205i	$-0.0824724\pi$
$733$	3.50413	+	7.87040i	0.129428	+	0.290700i	−0.837194	+	0.546905i	$0.815806\pi$
$734$	22.7444	−	16.5248i	0.839510	−	0.609940i
$735$	−5.21206	+	38.1384i	−0.192250	+	1.40675i
$736$			4.10754i			0.151406i
$737$	14.5891	−	24.0455i	0.537397	−	0.885729i
$738$	42.7625	−	0.636217i	1.57411	−	0.0234195i
$739$	−0.892636	−	4.19952i	−0.0328362	−	0.154482i	0.958675	−	0.284503i	$-0.0918287\pi$
$739$	−0.892636	−	4.19952i	−0.0328362	−	0.154482i	−0.991511	+	0.130021i	$0.958495\pi$
$740$	81.7725	−	8.59463i	3.00602	−	0.315945i
$741$	17.1580	+	1.67444i	0.630316	+	0.0615122i
$742$	47.6692	−	63.0207i	1.74999	−	2.31356i
$743$	5.38781	+	16.5820i	0.197659	+	0.608333i	0.999935	+	0.0113797i	$0.00362236\pi$
$743$	5.38781	+	16.5820i	0.197659	+	0.608333i	−0.802276	+	0.596954i	$0.796378\pi$
$744$	−32.6767	+	45.6865i	−1.19799	+	1.67495i
$745$	20.8892	−	46.9180i	0.765322	−	1.71894i
$746$	14.2330	+	66.9612i	0.521109	+	2.45162i
$747$	−2.30305	−	3.85538i	−0.0842640	−	0.141061i
$748$	8.97625	−	25.7093i	0.328204	−	0.940024i
$749$	2.09147	+	24.4163i	0.0764206	+	0.892152i
$750$	−1.05464	+	0.232384i	−0.0385101	+	0.00848545i
$751$	−3.85099	−	36.6397i	−0.140525	−	1.33700i	−0.806591	−	0.591110i	$-0.798690\pi$
$751$	−3.85099	−	36.6397i	−0.140525	−	1.33700i	0.666067	−	0.745892i	$-0.267977\pi$
$752$	−7.55315	−	0.793868i	−0.275435	−	0.0289494i
$753$	0.265102	+	0.0542913i	0.00966085	+	0.00197849i
$754$	−1.21542	+	5.71811i	−0.0442630	+	0.208241i
$755$	−8.31253	−	6.03941i	−0.302524	−	0.219797i
$756$	−11.8549	−	54.9494i	−0.431158	−	1.99849i
$757$	−13.3240	+	41.0072i	−0.484270	+	1.49043i	0.348765	+	0.937210i	$0.386601\pi$
$757$	−13.3240	+	41.0072i	−0.484270	+	1.49043i	−0.833035	+	0.553220i	$0.813399\pi$
$758$	−30.7896	+	53.3292i	−1.11833	+	1.93700i
$759$	2.37389	+	26.1868i	0.0861666	+	0.950520i
$760$	24.9847	+	43.2748i	0.906291	+	1.56974i
$761$	12.4433	+	13.8196i	0.451068	+	0.500962i	0.925194	−	0.379496i	$-0.123902\pi$
$761$	12.4433	+	13.8196i	0.451068	+	0.500962i	−0.474126	+	0.880457i	$0.657236\pi$
$762$	−9.31248	−	4.06345i	−0.337355	−	0.147203i
$763$	13.0017	−	7.17614i	0.470695	−	0.259794i
$764$	67.7981	−	22.0289i	2.45285	−	0.796979i
$765$	−14.4015	−	12.5843i	−0.520687	−	0.454987i
$766$	−32.6217	−	3.42867i	−1.17867	−	0.123883i
$767$	5.38085	+	2.39571i	0.194291	+	0.0865040i
$768$	−53.6885	−	17.0040i	−1.93732	−	0.613579i
$769$			29.3645i			1.05891i	0.848338	+	0.529456i	$0.177604\pi$
$769$			29.3645i			1.05891i	−0.848338	+	0.529456i	$0.822396\pi$
$770$	−58.0747	−	36.7849i	−2.09287	−	1.32564i
$771$	1.92824	+	3.28317i	0.0694439	+	0.118240i
$772$	33.4063	−	30.0792i	1.20232	−	1.08257i
$773$	−19.7282	+	44.3103i	−0.709574	+	1.59373i	0.0919475	+	0.995764i	$0.470691\pi$
$773$	−19.7282	+	44.3103i	−0.709574	+	1.59373i	−0.801522	+	0.597966i	$0.795976\pi$
$774$	−33.8289	+	48.0487i	−1.21595	+	1.72708i
$775$	31.2591	+	6.64433i	1.12286	+	0.238671i
$776$	−27.3775	−	84.2593i	−0.982795	−	3.02473i
$777$	25.3062	−	14.2140i	0.907855	−	0.509926i
$778$	4.22099	+	5.80970i	0.151330	+	0.208288i
$779$	−13.1093	+	11.8036i	−0.469688	+	0.422909i
$780$	−63.7458	−	36.1741i	−2.28247	−	1.29524i
$781$	31.1851	+	29.3323i	1.11589	+	1.04959i
$782$	19.6410	+	11.3397i	0.702362	+	0.405509i
$783$	−3.61673	−	1.08655i	−0.129251	−	0.0388300i
$784$	−30.8184	−	7.80291i	−1.10066	−	0.278675i
$785$	18.2472	−	25.1152i	0.651272	−	0.896399i
$786$	−42.9716	+	14.3166i	−1.53275	+	0.510655i
$787$	−39.5937	−	35.6503i	−1.41136	−	1.27080i	−0.915455	−	0.402421i	$-0.868169\pi$
$787$	−39.5937	−	35.6503i	−1.41136	−	1.27080i	−0.495907	−	0.868375i	$-0.665164\pi$
$788$	5.18033	−	49.2875i	0.184542	−	1.75580i
$789$	−10.5092	−	14.2407i	−0.374136	−	0.506981i
$790$	3.52257	−	10.8413i	0.125327	−	0.385718i
$791$	4.11174	+	5.89494i	0.146197	+	0.209600i
$792$	50.0926	+	11.0081i	1.77996	+	0.391154i
$793$	−19.2824	+	33.3980i	−0.684737	+	1.18600i
$794$	−24.1216	+	5.12721i	−0.856044	+	0.181958i
$795$	66.1386	−	7.44925i	2.34570	−	0.264198i
$796$	−78.2754	+	34.8505i	−2.77440	+	1.23524i
$797$	32.9378	−	10.7021i	1.16672	−	0.379089i	0.339300	−	0.940678i	$-0.389810\pi$
$797$	32.9378	−	10.7021i	1.16672	−	0.379089i	0.827416	+	0.561589i	$0.189810\pi$
$798$	27.6914	+	20.6239i	0.980264	+	0.730078i
$799$	−1.97373	+	2.71661i	−0.0698256	+	0.0961067i
$800$	−0.476478	−	4.53339i	−0.0168460	−	0.160279i
$801$	−0.253391	−	0.0781838i	−0.00895312	−	0.00276249i
$802$	43.6624	−	25.2085i	1.54177	−	0.890142i
$803$	11.2912	+	26.9216i	0.398457	+	0.950043i
$804$	51.7870	−	30.4151i	1.82639	−	1.07266i
$805$	26.2724	−	28.0713i	0.925982	−	0.989385i
$806$	29.7449	+	40.9403i	1.04772	+	1.44206i
$807$	13.8637	+	9.91583i	0.488024	+	0.349054i
$808$	11.3112	−	12.5623i	0.397926	−	0.441941i
$809$	−14.0246	+	15.5759i	−0.493079	+	0.547620i	−0.937403	−	0.348247i	$-0.886777\pi$
$809$	−14.0246	+	15.5759i	−0.493079	+	0.547620i	0.444324	+	0.895866i	$0.353444\pi$
$810$	39.7279	−	58.2494i	1.39590	−	2.04667i
$811$	14.4208	+	19.8485i	0.506382	+	0.696975i	0.983304	−	0.181971i	$-0.0582476\pi$
$811$	14.4208	+	19.8485i	0.506382	+	0.696975i	−0.476922	+	0.878946i	$0.658248\pi$
$812$	−5.37261	+	5.74048i	−0.188542	+	0.201451i
$813$	−3.32468	−	5.66086i	−0.116602	−	0.198535i
$814$	4.29569	+	51.6573i	0.150564	+	1.81059i
$815$	−51.8559	+	29.9390i	−1.81643	+	1.04872i
$816$	11.6592	−	10.6561i	0.408153	−	0.373037i
$817$	−2.53356	−	24.1052i	−0.0886381	−	0.843336i
$818$	48.3690	−	66.5743i	1.69118	−	2.32771i
$819$	−25.7193	−	2.81749i	−0.898704	−	0.0984510i
$820$	71.3276	−	23.1757i	2.49087	−	0.809332i
$821$	−42.5068	+	18.9252i	−1.48350	+	0.660495i	−0.979174	−	0.203021i	$-0.934924\pi$
$821$	−42.5068	+	18.9252i	−1.48350	+	0.660495i	−0.504322	+	0.863516i	$0.668257\pi$
$822$	−1.33767	−	11.8766i	−0.0466566	−	0.414244i
$823$	17.0990	−	3.63451i	0.596035	−	0.126691i	0.0999908	−	0.994988i	$-0.468119\pi$
$823$	17.0990	−	3.63451i	0.596035	−	0.126691i	0.496044	+	0.868297i	$0.334785\pi$
$824$	35.4793	−	61.4520i	1.23598	−	2.14078i
$825$	−5.65768	−	28.6263i	−0.196975	−	0.996639i
$826$	6.74876	+	9.67558i	0.234819	+	0.336657i
$827$	9.76910	−	30.0662i	0.339705	−	1.04550i	−0.624653	−	0.780902i	$-0.714760\pi$
$827$	9.76910	−	30.0662i	0.339705	−	1.04550i	0.964358	−	0.264601i	$-0.0852404\pi$
$828$	−22.0719	+	51.6278i	−0.767050	+	1.79419i
$829$	−4.43835	+	42.2281i	−0.154150	+	1.46664i	0.594724	+	0.803930i	$0.297261\pi$
$829$	−4.43835	+	42.2281i	−0.154150	+	1.46664i	−0.748874	+	0.662712i	$0.769405\pi$
$830$	−8.71516	−	7.84716i	−0.302508	−	0.272379i
$831$	−4.74081	−	14.2297i	−0.164457	−	0.493622i
$832$	−13.1606	+	18.1139i	−0.456260	+	0.627988i
$833$	−9.80071	+	10.0754i	−0.339574	+	0.349093i
$834$	−67.5194	+	14.8775i	−2.33801	+	0.515164i
$835$	−28.2716	−	16.3226i	−0.978378	−	0.564867i
$836$	−36.3030	+	19.9195i	−1.25557	+	0.688930i
$837$	−27.9393	+	16.9730i	−0.965723	+	0.586674i
$838$	−46.7157	+	42.0630i	−1.61377	+	1.45304i
$839$	−7.30058	−	10.0484i	−0.252044	−	0.346909i	0.664182	−	0.747571i	$-0.268780\pi$
$839$	−7.30058	−	10.0484i	−0.252044	−	0.346909i	−0.916226	+	0.400662i	$0.868780\pi$
$840$	−36.7261	−	65.3860i	−1.26717	−	2.25603i
$841$	−8.79827	−	27.0783i	−0.303389	−	0.933734i
$842$	−34.0409	−	7.23561i	−1.17313	−	0.249356i
$843$	−17.8145	−	39.2242i	−0.613565	−	1.35095i
$844$	−20.8930	+	46.9264i	−0.719166	+	1.61527i
$845$	5.60181	−	5.04389i	0.192708	−	0.173515i
$846$	−10.8118	−	6.02955i	−0.371718	−	0.207300i
$847$	16.1041	−	24.2416i	0.553345	−	0.832952i
$848$			54.9686i			1.88763i
$849$	8.42541	−	26.6025i	0.289159	−	0.912994i
$850$	−22.9927	−	10.2370i	−0.788643	−	0.351126i
$851$	−28.8322	−	3.03038i	−0.988354	−	0.103880i
$852$	28.8965	+	86.7336i	0.989976	+	2.97144i
$853$	−32.0592	+	10.4167i	−1.09769	+	0.356660i	−0.801212	−	0.598380i	$-0.795811\pi$
$853$	−32.0592	+	10.4167i	−1.09769	+	0.356660i	−0.296475	+	0.955041i	$0.595811\pi$
$854$	−67.6218	+	37.3230i	−2.31397	+	1.27717i
$855$	3.46986	+	28.8746i	0.118667	+	0.987489i
$856$	−31.9467	−	35.4804i	−1.09192	−	1.21270i
$857$	8.86743	+	15.3588i	0.302906	+	0.524648i	0.976793	−	0.214186i	$-0.0687099\pi$
$857$	8.86743	+	15.3588i	0.302906	+	0.524648i	−0.673887	+	0.738834i	$0.735377\pi$
$858$	23.6739	−	39.6815i	0.808213	−	1.35471i
$859$	−0.200010	+	0.346427i	−0.00682424	+	0.0118199i	−0.869417	−	0.494078i	$-0.835506\pi$
$859$	−0.200010	+	0.346427i	−0.00682424	+	0.0118199i	0.862593	+	0.505898i	$0.168839\pi$
$860$	−31.8438	+	98.0052i	−1.08587	+	3.34195i
$861$	19.8826	−	17.4809i	0.677598	−	0.595748i
$862$	−45.6751	−	33.1849i	−1.55570	−	1.13028i
$863$	9.32825	−	43.8860i	0.317537	−	1.49390i	−0.472770	−	0.881186i	$-0.656746\pi$
$863$	9.32825	−	43.8860i	0.317537	−	1.49390i	0.790308	−	0.612710i	$-0.209921\pi$
$864$	3.53401	+	3.04203i	0.120230	+	0.103492i
$865$	−19.3113	−	2.02970i	−0.656604	−	0.0690119i
$866$	2.45909	+	23.3967i	0.0835634	+	0.795052i
$867$	4.83325	+	21.9351i	0.164146	+	0.744954i
$868$	5.80881	+	67.8135i	0.197164	+	2.30174i
$869$	4.55621	+	1.59078i	0.154559	+	0.0539633i
$870$	−9.86141	+	0.0733546i	−0.334333	+	0.00248695i
$871$	−5.74722	−	27.0386i	−0.194737	−	0.916167i
$872$	−11.7681	+	26.4316i	−0.398519	+	0.895088i
$873$	4.62631	−	51.3547i	0.156577	−	1.73809i
$874$	−10.6572	−	32.7994i	−0.360484	−	1.10946i
$875$	−0.403298	+	0.533176i	−0.0136339	+	0.0180246i
$876$	−6.05489	+	62.0446i	−0.204576	+	2.09629i
$877$	−50.6275	+	5.32116i	−1.70957	+	0.179683i	−0.908214	−	0.418506i	$-0.862554\pi$
$877$	−50.6275	+	5.32116i	−1.70957	+	0.179683i	−0.801355	+	0.598189i	$0.795887\pi$
$878$	−2.27939	−	10.7237i	−0.0769257	−	0.361907i
$879$	17.8891	+	10.1516i	0.603384	+	0.342405i
$880$	47.6569	−	3.96303i	1.60651	−	0.133594i
$881$			49.8429i			1.67925i	0.543167	+	0.839625i	$0.317225\pi$
$881$			49.8429i			1.67925i	−0.543167	+	0.839625i	$0.682775\pi$
$882$	−41.1902	−	31.4419i	−1.38695	−	1.05870i
$883$	−37.5807	+	27.3040i	−1.26469	+	0.918851i	−0.998978	−	0.0452009i	$-0.985607\pi$
$883$	−37.5807	+	27.3040i	−1.26469	+	0.918851i	−0.265713	+	0.964052i	$0.585607\pi$
$884$	−10.8859	−	24.4501i	−0.366132	−	0.822345i
$885$	−1.99352	+	9.73424i	−0.0670113	+	0.327213i
$886$	30.4237	+	27.3936i	1.02210	+	0.920305i
$887$	26.8142	−	11.9385i	0.900334	−	0.400855i	0.0962410	−	0.995358i	$-0.469318\pi$
$887$	26.8142	−	11.9385i	0.900334	−	0.400855i	0.804093	+	0.594504i	$0.202651\pi$
$888$	−22.6153	+	51.8289i	−0.758920	+	1.73927i
$889$	−6.01818	+	1.82800i	−0.201843	+	0.0613091i
$890$	−0.692483			−0.0232121
$891$	24.2884	+	17.3514i	0.813694	+	0.581294i
$892$	5.98535	+	10.3669i	0.200404	+	0.347111i
$893$	4.99459	−	1.06163i	0.167138	−	0.0355262i
$894$	41.0534	+	55.6303i	1.37303	+	1.86055i
$895$	−15.0290	−	10.9192i	−0.502364	−	0.364989i
$896$	−45.6845	+	19.2941i	−1.52621	+	0.644570i
$897$	19.3331	+	17.1490i	0.645515	+	0.572587i
$898$	−7.53689	−	16.9281i	−0.251509	−	0.564899i
$899$	4.17707	+	1.85975i	0.139313	+	0.0620262i
$900$	18.3713	−	59.5406i	0.612375	−	1.98469i
$901$	21.0475	+	12.1518i	0.701195	+	0.404835i
$902$	13.6291	+	45.2740i	0.453798	+	1.50746i
$903$	3.37410	+	36.2196i	0.112283	+	1.20531i
$904$	−13.3173	−	4.32707i	−0.442928	−	0.143916i
$905$	3.23121	−	0.339613i	0.107409	−	0.0112891i
$906$	12.5940	−	5.71983i	0.418407	−	0.190029i
$907$	−22.9775	+	25.5191i	−0.762954	+	0.847346i	−0.992022	−	0.126064i	$-0.959765\pi$
$907$	−22.9775	+	25.5191i	−0.762954	+	0.847346i	0.229068	+	0.973410i	$0.426432\pi$
$908$	−44.0876	−	9.37110i	−1.46310	−	0.310991i
$909$	8.92723	−	4.13487i	0.296098	−	0.137145i
$910$	−66.3467	+	12.7715i	−2.19937	+	0.423370i
$911$	50.1968	+	16.3099i	1.66310	+	0.540372i	0.981517	−	0.191373i	$-0.0612940\pi$
$911$	50.1968	+	16.3099i	1.66310	+	0.540372i	0.681578	+	0.731745i	$0.261294\pi$
$912$	−24.0181	+	0.178660i	−0.795320	+	0.00591603i
$913$	3.40160	−	3.61647i	0.112577	−	0.119688i
$914$	−19.3044	+	11.1454i	−0.638531	+	0.368656i
$915$	−62.0206	−	19.6429i	−2.05034	−	0.649374i
$916$	−2.40358	+	1.74630i	−0.0794164	+	0.0576994i
$917$	−14.4846	+	24.0075i	−0.478322	+	0.792797i
$918$	24.3025	−	8.50040i	0.802101	−	0.280555i
$919$	3.63032	−	17.0793i	0.119753	−	0.563394i	−0.876830	−	0.480800i	$-0.840346\pi$
$919$	3.63032	−	17.0793i	0.119753	−	0.563394i	0.996583	−	0.0825938i	$-0.0263204\pi$
$920$	−7.82988	+	74.4963i	−0.258144	+	2.45607i
$921$	3.75531	+	33.3417i	0.123742	+	1.09865i
$922$	3.00170	+	3.33373i	0.0988557	+	0.109790i
$923$	42.0776			1.38500
$924$	54.8335	−	29.2485i	1.80389	−	0.962207i
$925$	32.1728			1.05784
$926$	−12.3263	−	13.6897i	−0.405066	−	0.449872i
$927$	33.0460	−	24.7687i	1.08537	−	0.813512i
$928$	0.0681730	−	0.648623i	0.00223789	−	0.0212921i
$929$	0.689623	−	3.24442i	0.0226258	−	0.106446i	−0.965386	−	0.260827i	$-0.916005\pi$
$929$	0.689623	−	3.24442i	0.0226258	−	0.106446i	0.988011	+	0.154381i	$0.0493382\pi$
$930$	−56.6490	+	63.8641i	−1.85760	+	2.09419i
$931$	21.3271	−	1.41350i	0.698969	−	0.0463257i
$932$	−55.5914	+	40.3895i	−1.82096	+	1.32300i
$933$	5.36570	−	16.9417i	0.175665	−	0.554646i
$934$	59.9320	−	34.6017i	1.96103	−	1.13220i
$935$	9.01797	−	19.1240i	0.294919	−	0.625421i
$936$	43.2746	−	25.8505i	1.41447	−	0.844950i
$937$	23.9841	+	7.79289i	0.783525	+	0.254583i	0.673345	−	0.739329i	$-0.264857\pi$
$937$	23.9841	+	7.79289i	0.783525	+	0.254583i	0.110181	+	0.993912i	$0.464857\pi$
$938$	18.1195	−	52.3140i	0.591623	−	1.70811i
$939$	−41.8678	−	4.08585i	−1.36630	−	0.133337i
$940$	−21.2347	−	4.51357i	−0.692599	−	0.147216i
$941$	23.6347	−	26.2490i	0.770469	−	0.855692i	−0.222394	−	0.974957i	$-0.571387\pi$
$941$	23.6347	−	26.2490i	0.770469	−	0.855692i	0.992863	+	0.119265i	$0.0380537\pi$
$942$	17.2817	+	38.0510i	0.563068	+	1.23977i
$943$	−26.2988	+	2.76411i	−0.856406	+	0.0900119i
$944$	−7.80463	−	2.53588i	−0.254019	−	0.0825358i
$945$	−4.69451	−	43.3936i	−0.152713	−	1.41159i
$946$	−61.3339	−	21.4144i	−1.99414	−	0.696242i
$947$	−32.6946	−	18.8762i	−1.06243	−	0.613395i	−0.136328	−	0.990664i	$-0.543530\pi$
$947$	−32.6946	−	18.8762i	−1.06243	−	0.613395i	−0.926104	+	0.377269i	$0.876863\pi$
$948$	6.95229	+	7.60675i	0.225800	+	0.247056i
$949$	26.2120	+	11.6703i	0.850877	+	0.378835i
$950$	15.5668	+	34.9636i	0.505053	+	1.13437i
$951$	11.2410	−	12.6727i	0.364513	−	0.410939i
$952$	3.38670	−	27.1744i	0.109764	−	0.880726i
$953$	−37.3328	−	27.1238i	−1.20933	−	0.878627i	−0.214157	−	0.976799i	$-0.568700\pi$
$953$	−37.3328	−	27.1238i	−1.20933	−	0.878627i	−0.995169	+	0.0981720i	$0.968700\pi$
$954$	−35.2215	+	82.3857i	−1.14034	+	2.66734i
$955$	54.1410	−	11.5080i	1.75196	−	0.372391i
$956$	−0.167197	−	0.289594i	−0.00540754	−	0.00936614i
$957$	0.0597618	−	4.17456i	0.00193183	−	0.134944i
$958$	70.0404			2.26290
$959$	−5.40178	−	5.05562i	−0.174433	−	0.163254i
$960$	−34.6188	−	15.1058i	−1.11732	−	0.487536i
$961$	7.83917	−	3.49022i	0.252877	−	0.112588i
$962$	37.8603	+	34.0896i	1.22066	+	1.09909i
$963$	−8.97880	−	26.2962i	−0.289338	−	0.847384i
$964$	23.4613	+	52.6949i	0.755637	+	1.69719i
$965$	28.2373	−	20.5156i	0.908992	−	0.660421i
$966$	15.4108	+	49.4112i	0.495834	+	1.58978i
$967$		−	41.1747i		−	1.32409i	−0.749464	−	0.662045i	$-0.769689\pi$
$967$		−	41.1747i		−	1.32409i	0.749464	−	0.662045i	$-0.230311\pi$
$968$	3.46869	+	56.5946i	0.111488	+	1.81902i
$969$	−5.24123	+	9.23606i	−0.168373	+	0.296705i
$970$	−27.9953	−	131.708i	−0.898876	−	4.22888i
$971$	−35.4300	+	3.72385i	−1.13700	+	0.119504i	−0.654268	−	0.756262i	$-0.727023\pi$
$971$	−35.4300	+	3.72385i	−1.13700	+	0.119504i	−0.482735	+	0.875766i	$0.660357\pi$
$972$	28.0728	+	57.2254i	0.900434	+	1.83550i
$973$	−25.8196	+	34.1345i	−0.827737	+	1.09430i
$974$	14.2774	+	43.9413i	0.457477	+	1.40797i
$975$	−23.3268	−	16.6842i	−0.747054	−	0.534322i
$976$	21.8539	−	49.0847i	0.699526	−	1.57116i
$977$	−12.2834	−	57.7887i	−0.392980	−	1.84882i	−0.516231	−	0.856449i	$-0.672666\pi$
$977$	−12.2834	−	57.7887i	−0.392980	−	1.84882i	0.123252	−	0.992375i	$-0.460668\pi$
$978$	−0.599589	−	80.6057i	−0.0191728	−	2.57748i
$979$	0.00637678	−	0.293096i	0.000203803	−	0.00936740i
$980$	−85.2783	−	31.3901i	−2.72412	−	1.00272i
$981$	−12.3449	+	11.4525i	−0.394141	+	0.365649i
$982$	−10.2027	−	97.0718i	−0.325580	−	3.09768i
$983$	−4.06498	−	0.427246i	−0.129653	−	0.0136270i	0.0394799	−	0.999220i	$-0.487430\pi$
$983$	−4.06498	−	0.427246i	−0.129653	−	0.0136270i	−0.169132	+	0.985593i	$0.554097\pi$
$984$	−10.3484	+	50.5307i	−0.329894	+	1.61086i
$985$	8.00041	−	37.6390i	0.254914	−	1.19928i
$986$	−2.91331	−	2.11664i	−0.0927787	−	0.0674077i
$987$	−7.51422	+	1.50451i	−0.239180	+	0.0478890i
$988$	−12.5765	+	38.7064i	−0.400110	+	1.23141i
$989$	18.1670	−	31.4662i	0.577677	−	1.00057i
$990$	73.9664	+	24.5967i	2.35081	+	0.781735i
$991$	−22.1733	−	38.4052i	−0.704357	−	1.21998i	−0.966923	−	0.255068i	$-0.917902\pi$
$991$	−22.1733	−	38.4052i	−0.704357	−	1.21998i	0.262566	−	0.964914i	$-0.415431\pi$
$992$	−3.77776	−	4.19563i	−0.119944	−	0.133211i
$993$	−4.03281	+	9.24226i	−0.127977	+	0.293294i
$994$	72.1577	+	43.5353i	2.28870	+	1.38086i
$995$	−63.2721	+	20.5583i	−2.00586	+	0.651743i
$996$	10.0583	−	3.35106i	0.318709	−	0.106182i
$997$	1.39373	+	0.146487i	0.0441399	+	0.00463929i	0.126573	−	0.991957i	$-0.459602\pi$
$997$	1.39373	+	0.146487i	0.0441399	+	0.00463929i	−0.0824328	+	0.996597i	$0.526269\pi$
$998$	10.1841	+	4.53425i	0.322372	+	0.143529i
$999$	−23.9603	+	22.5621i	−0.758069	+	0.713833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.2	✓	224
3.2	odd	2	inner	231.2.be.a.2.27	yes	224
7.4	even	3	inner	231.2.be.a.200.27	yes	224
11.6	odd	10	inner	231.2.be.a.149.2	yes	224
21.11	odd	6	inner	231.2.be.a.200.2	yes	224
33.17	even	10	inner	231.2.be.a.149.27	yes	224
77.39	odd	30	inner	231.2.be.a.116.27	yes	224
231.116	even	30	inner	231.2.be.a.116.2	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.2	✓	224	1.1	even	1	trivial
231.2.be.a.2.27	yes	224	3.2	odd	2	inner
231.2.be.a.116.2	yes	224	231.116	even	30	inner
231.2.be.a.116.27	yes	224	77.39	odd	30	inner
231.2.be.a.149.2	yes	224	11.6	odd	10	inner
231.2.be.a.149.27	yes	224	33.17	even	10	inner
231.2.be.a.200.2	yes	224	21.11	odd	6	inner
231.2.be.a.200.27	yes	224	7.4	even	3	inner

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.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65113 - 1.83377i) q^{2} +(1.72117 - 0.193857i) q^{3} +(-0.427411 + 4.06654i) q^{4} +(-0.660086 + 3.10546i) q^{5} +(-3.19736 - 2.83614i) q^{6} +(-2.64526 - 0.0509795i) q^{7} +(4.17018 - 3.02981i) q^{8} +(2.92484 - 0.667320i) q^{9} +O(q^{10})\)	\(q+(-1.65113 - 1.83377i) q^{2} +(1.72117 - 0.193857i) q^{3} +(-0.427411 + 4.06654i) q^{4} +(-0.660086 + 3.10546i) q^{5} +(-3.19736 - 2.83614i) q^{6} +(-2.64526 - 0.0509795i) q^{7} +(4.17018 - 3.02981i) q^{8} +(2.92484 - 0.667320i) q^{9} +(6.78458 - 3.91708i) q^{10} +(1.59544 + 2.90767i) q^{11} +(0.0526802 + 7.08206i) q^{12} +(3.10017 + 1.00731i) q^{13} +(4.27419 + 4.93497i) q^{14} +(-0.534105 + 5.47298i) q^{15} +(-4.44231 - 0.944242i) q^{16} +(-1.34360 + 1.49222i) q^{17} +(-6.05300 - 4.26164i) q^{18} +(3.03669 - 0.319169i) q^{19} +(-12.3463 - 4.01157i) q^{20} +(-4.56282 + 0.425057i) q^{21} +(2.69771 - 7.72662i) q^{22} +(3.96399 + 2.28861i) q^{23} +(6.59023 - 6.02323i) q^{24} +(-4.64043 - 2.06605i) q^{25} +(-3.27162 - 7.34818i) q^{26} +(4.90478 - 1.71557i) q^{27} +(1.33792 - 10.7353i) q^{28} +(-0.587971 - 0.427186i) q^{29} +(10.9180 - 8.05719i) q^{30} +(-6.15387 + 1.30804i) q^{31} +(0.448694 + 0.777160i) q^{32} +(3.30970 + 4.69531i) q^{33} +4.95486 q^{34} +(1.90441 - 8.18110i) q^{35} +(1.46358 + 12.1792i) q^{36} +(-5.78617 + 2.57617i) q^{37} +(-5.59926 - 5.04160i) q^{38} +(5.53118 + 1.13275i) q^{39} +(6.65628 + 14.9502i) q^{40} +(-4.67387 + 3.39576i) q^{41} +(8.31327 + 7.66533i) q^{42} -7.93800i q^{43} +(-12.5061 + 5.24517i) q^{44} +(0.141689 + 9.52346i) q^{45} +(-2.34829 - 11.0478i) q^{46} +(1.66312 - 0.174801i) q^{47} +(-7.82901 - 0.764028i) q^{48} +(6.99480 + 0.269708i) q^{49} +(3.87331 + 11.9208i) q^{50} +(-2.02329 + 2.82883i) q^{51} +(-5.42130 + 12.1764i) q^{52} +(-2.51646 - 11.8390i) q^{53} +(-11.2444 - 6.16159i) q^{54} +(-10.0828 + 3.03527i) q^{55} +(-11.1857 + 7.80205i) q^{56} +(5.16478 - 1.13803i) q^{57} +(0.187458 + 1.78354i) q^{58} +(1.79703 + 0.188876i) q^{59} +(-22.0278 - 4.51117i) q^{60} +(-2.45975 + 11.5722i) q^{61} +(12.5595 + 9.12501i) q^{62} +(-7.77098 + 1.61613i) q^{63} +(-2.12255 + 6.53255i) q^{64} +(-5.17452 + 8.96254i) q^{65} +(3.14535 - 13.8218i) q^{66} +(-4.24004 - 7.34397i) q^{67} +(-5.49391 - 6.10161i) q^{68} +(7.26636 + 3.17064i) q^{69} +(-18.1467 + 10.0158i) q^{70} +(12.2766 - 3.98891i) q^{71} +(10.1752 - 11.6446i) q^{72} +(8.75397 + 0.920080i) q^{73} +(14.2778 + 6.35689i) q^{74} +(-8.38749 - 2.65645i) q^{75} +12.4852i q^{76} +(-4.07213 - 7.77288i) q^{77} +(-7.05551 - 12.0132i) q^{78} +(1.08133 - 0.973634i) q^{79} +(5.86461 - 13.1721i) q^{80} +(8.10937 - 3.90361i) q^{81} +(13.9442 + 2.96393i) q^{82} +(-0.462585 - 1.42369i) q^{83} +(0.221687 - 18.7366i) q^{84} +(-3.74714 - 5.15750i) q^{85} +(-14.5564 + 13.1067i) q^{86} +(-1.09481 - 0.621277i) q^{87} +(15.4630 + 7.29162i) q^{88} +(-0.0765504 - 0.0441964i) q^{89} +(17.2299 - 15.9843i) q^{90} +(-8.14940 - 2.82263i) q^{91} +(-11.0010 + 15.1416i) q^{92} +(-10.3383 + 3.44433i) q^{93} +(-3.06658 - 2.76116i) q^{94} +(-1.01331 + 9.64100i) q^{95} +(0.922935 + 1.25064i) q^{96} +(5.31125 - 16.3463i) q^{97} +(-11.0548 - 13.2722i) q^{98} +(6.60676 + 7.43980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

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