LMFDB - Embedded newform 231.2.ba.a.40.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			40.4
Character	$\chi$	$=$	231.40
Dual form			231.2.ba.a.52.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737298 - 1.65600i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-0.860460 + 0.955638i) q^{4} +(-3.08737 + 0.324496i) q^{5} +(1.46652 - 1.06549i) q^{6} +(-0.0887369 - 2.64426i) q^{7} +(-1.23104 - 0.399989i) q^{8} +(-0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.737298 - 1.65600i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-0.860460 + 0.955638i) q^{4} +(-3.08737 + 0.324496i) q^{5} +(1.46652 - 1.06549i) q^{6} +(-0.0887369 - 2.64426i) q^{7} +(-1.23104 - 0.399989i) q^{8} +(-0.913545 + 0.406737i) q^{9} +(2.81368 + 4.87343i) q^{10} +(0.0719126 + 3.31585i) q^{11} +(-1.11365 - 0.642969i) q^{12} +(-3.84177 - 2.79121i) q^{13} +(-4.31347 + 2.09656i) q^{14} +(-0.959305 - 2.95244i) q^{15} +(0.514096 + 4.89130i) q^{16} +(-5.88792 - 2.62147i) q^{17} +(1.34711 + 1.21294i) q^{18} +(-0.586402 - 0.651266i) q^{19} +(2.34646 - 3.22962i) q^{20} +(2.56803 - 0.636571i) q^{21} +(5.43801 - 2.56385i) q^{22} +(-1.09184 + 1.89111i) q^{23} +(0.135301 - 1.28730i) q^{24} +(4.53583 - 0.964120i) q^{25} +(-1.78971 + 8.41991i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.60331 + 2.19048i) q^{28} +(6.49150 - 2.10922i) q^{29} +(-4.18194 + 3.76543i) q^{30} +(1.02234 + 0.107453i) q^{31} +(5.47898 - 3.16329i) q^{32} +(-3.22843 + 0.759744i) q^{33} +11.6832i q^{34} +(1.13202 + 8.13503i) q^{35} +(0.397376 - 1.22300i) q^{36} +(-0.897052 - 0.190674i) q^{37} +(-0.646142 + 1.45126i) q^{38} +(1.93147 - 4.33814i) q^{39} +(3.93047 + 0.835448i) q^{40} +(2.43424 - 7.49181i) q^{41} +(-2.94756 - 3.78331i) q^{42} +1.01167i q^{43} +(-3.23062 - 2.78443i) q^{44} +(2.68847 - 1.55219i) q^{45} +(3.93669 + 0.413763i) q^{46} +(5.62244 - 5.06247i) q^{47} +(-4.67752 + 1.51982i) q^{48} +(-6.98425 + 0.469288i) q^{49} +(-4.94083 - 6.80047i) q^{50} +(1.34002 - 6.30429i) q^{51} +(5.97307 - 1.26962i) q^{52} +(0.587084 - 5.58573i) q^{53} +(-0.906358 + 1.56986i) q^{54} +(-1.29800 - 10.2139i) q^{55} +(-0.948438 + 3.29069i) q^{56} +(0.515114 - 0.708994i) q^{57} +(-8.27903 - 9.19479i) q^{58} +(-9.77112 - 8.79796i) q^{59} +(3.64690 + 1.62371i) q^{60} +(0.925348 + 8.80410i) q^{61} +(-0.575831 - 1.77222i) q^{62} +(1.15658 + 2.37956i) q^{63} +(-1.32017 - 0.959157i) q^{64} +(12.7667 + 7.37086i) q^{65} +(3.63845 + 4.78612i) q^{66} +(2.64393 + 4.57942i) q^{67} +(7.57150 - 3.37105i) q^{68} +(-2.07679 - 0.674792i) q^{69} +(12.6370 - 7.87255i) q^{70} +(0.0539502 - 0.0391971i) q^{71} +(1.28730 - 0.135301i) q^{72} +(-8.65088 + 9.60778i) q^{73} +(0.345638 + 1.62610i) q^{74} +(1.88610 + 4.23626i) q^{75} +1.12695 q^{76} +(8.76158 - 0.484394i) q^{77} -8.60802 q^{78} +(-6.22817 - 13.9887i) q^{79} +(-3.17441 - 14.9344i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-14.2012 + 1.49260i) q^{82} +(6.26756 - 4.55365i) q^{83} +(-1.60136 + 3.00185i) q^{84} +(19.0289 + 6.18285i) q^{85} +(1.67532 - 0.745899i) q^{86} +(3.41278 + 5.91111i) q^{87} +(1.23778 - 4.11070i) q^{88} +(-0.849198 - 0.490285i) q^{89} +(-4.55262 - 3.30767i) q^{90} +(-7.03978 + 10.4063i) q^{91} +(-0.867740 - 2.67063i) q^{92} +(0.107453 + 1.02234i) q^{93} +(-12.5289 - 5.57820i) q^{94} +(2.02177 + 1.82041i) q^{95} +(4.23331 + 4.70157i) q^{96} +(1.62607 - 2.23809i) q^{97} +(5.92661 + 11.2199i) q^{98} +(-1.41437 - 2.99993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.737298	−	1.65600i	−0.521348	−	1.17097i	−0.961940	−	0.273260i	$-0.911898\pi$
$2$	−0.737298	−	1.65600i	−0.521348	−	1.17097i	0.440592	−	0.897707i	$-0.354769\pi$
$3$	0.207912	+	0.978148i	0.120038	+	0.564734i
$3$	0.207912	+	0.978148i	0.120038	+	0.564734i
$4$	−0.860460	+	0.955638i	−0.430230	+	0.477819i
$5$	−3.08737	+	0.324496i	−1.38071	+	0.145119i	−0.765599	−	0.643318i	$-0.777557\pi$
$5$	−3.08737	+	0.324496i	−1.38071	+	0.145119i	−0.615115	+	0.788437i	$0.710891\pi$
$6$	1.46652	−	1.06549i	0.598703	−	0.434983i
$7$	−0.0887369	−	2.64426i	−0.0335394	−	0.999437i
$7$	−0.0887369	−	2.64426i	−0.0335394	−	0.999437i
$8$	−1.23104	−	0.399989i	−0.435239	−	0.141418i
$9$	−0.913545	+	0.406737i	−0.304515	+	0.135579i
$10$	2.81368	+	4.87343i	0.889763	+	1.54111i
$11$	0.0719126	+	3.31585i	0.0216825	+	0.999765i
$11$	0.0719126	+	3.31585i	0.0216825	+	0.999765i
$12$	−1.11365	−	0.642969i	−0.321484	−	0.185609i
$13$	−3.84177	−	2.79121i	−1.06551	−	0.774142i	−0.0904142	−	0.995904i	$-0.528819\pi$
$13$	−3.84177	−	2.79121i	−1.06551	−	0.774142i	−0.975101	+	0.221762i	$0.928819\pi$
$14$	−4.31347	+	2.09656i	−1.15282	+	0.560329i
$15$	−0.959305	−	2.95244i	−0.247692	−	0.762316i
$16$	0.514096	+	4.89130i	0.128524	+	1.22282i
$17$	−5.88792	−	2.62147i	−1.42803	−	0.635800i	−0.460295	−	0.887766i	$-0.652256\pi$
$17$	−5.88792	−	2.62147i	−1.42803	−	0.635800i	−0.967736	+	0.251966i	$0.918923\pi$
$18$	1.34711	+	1.21294i	0.317517	+	0.285893i
$19$	−0.586402	−	0.651266i	−0.134530	−	0.149411i	0.672115	−	0.740446i	$-0.265386\pi$
$19$	−0.586402	−	0.651266i	−0.134530	−	0.149411i	−0.806645	+	0.591036i	$0.798719\pi$
$20$	2.34646	−	3.22962i	0.524684	−	0.722166i
$21$	2.56803	−	0.636571i	0.560390	−	0.138911i
$22$	5.43801	−	2.56385i	1.15939	−	0.546615i
$23$	−1.09184	+	1.89111i	−0.227663	+	0.394325i	−0.957115	−	0.289708i	$-0.906442\pi$
$23$	−1.09184	+	1.89111i	−0.227663	+	0.394325i	0.729452	+	0.684032i	$0.239775\pi$
$24$	0.135301	−	1.28730i	0.0276182	−	0.262769i
$25$	4.53583	−	0.964120i	0.907165	−	0.192824i
$26$	−1.78971	+	8.41991i	−0.350991	+	1.65128i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	2.60331	+	2.19048i	0.491980	+	0.413962i
$29$	6.49150	−	2.10922i	1.20544	−	0.391672i	0.363681	−	0.931523i	$-0.381520\pi$
$29$	6.49150	−	2.10922i	1.20544	−	0.391672i	0.841760	+	0.539852i	$0.181520\pi$
$30$	−4.18194	+	3.76543i	−0.763514	+	0.687471i
$31$	1.02234	+	0.107453i	0.183618	+	0.0192991i	0.195891	−	0.980626i	$-0.437240\pi$
$31$	1.02234	+	0.107453i	0.183618	+	0.0192991i	−0.0122729	+	0.999925i	$0.503907\pi$
$32$	5.47898	−	3.16329i	0.968556	−	0.559196i
$33$	−3.22843	+	0.759744i	−0.561998	+	0.132254i
$34$			11.6832i			2.00365i
$35$	1.13202	+	8.13503i	0.191346	+	1.37507i
$36$	0.397376	−	1.22300i	0.0662294	−	0.203833i
$37$	−0.897052	−	0.190674i	−0.147474	−	0.0313467i	0.133583	−	0.991038i	$-0.457352\pi$
$37$	−0.897052	−	0.190674i	−0.147474	−	0.0313467i	−0.281057	+	0.959691i	$0.590685\pi$
$38$	−0.646142	+	1.45126i	−0.104818	+	0.235425i
$39$	1.93147	−	4.33814i	0.309282	−	0.694659i
$40$	3.93047	+	0.835448i	0.621463	+	0.132096i
$41$	2.43424	−	7.49181i	0.380164	−	1.17002i	−0.559764	−	0.828652i	$-0.689108\pi$
$41$	2.43424	−	7.49181i	0.380164	−	1.17002i	0.939928	−	0.341373i	$-0.110892\pi$
$42$	−2.94756	−	3.78331i	−0.454819	−	0.583777i
$43$			1.01167i			0.154278i	0.997020	+	0.0771388i	$0.0245785\pi$
$43$			1.01167i			0.154278i	−0.997020	+	0.0771388i	$0.975422\pi$
$44$	−3.23062	−	2.78443i	−0.487035	−	0.419769i
$45$	2.68847	−	1.55219i	0.400773	−	0.231387i
$46$	3.93669	+	0.413763i	0.580433	+	0.0610060i
$47$	5.62244	−	5.06247i	0.820117	−	0.738437i	−0.147986	−	0.988990i	$-0.547279\pi$
$47$	5.62244	−	5.06247i	0.820117	−	0.738437i	0.968103	+	0.250553i	$0.0806123\pi$
$48$	−4.67752	+	1.51982i	−0.675142	+	0.219367i
$49$	−6.98425	+	0.469288i	−0.997750	+	0.0670411i
$50$	−4.94083	−	6.80047i	−0.698739	−	0.961732i
$51$	1.34002	−	6.30429i	0.187640	−	0.882777i
$52$	5.97307	−	1.26962i	0.828316	−	0.176064i
$53$	0.587084	−	5.58573i	0.0806422	−	0.767259i	−0.877231	−	0.480068i	$-0.840612\pi$
$53$	0.587084	−	5.58573i	0.0806422	−	0.767259i	0.957873	−	0.287191i	$-0.0927214\pi$
$54$	−0.906358	+	1.56986i	−0.123340	+	0.213631i
$55$	−1.29800	−	10.2139i	−0.175022	−	1.37724i
$56$	−0.948438	+	3.29069i	−0.126740	+	0.439737i
$57$	0.515114	−	0.708994i	0.0682285	−	0.0939085i
$58$	−8.27903	−	9.19479i	−1.08709	−	1.20734i
$59$	−9.77112	−	8.79796i	−1.27209	−	1.14540i	−0.982098	−	0.188368i	$-0.939680\pi$
$59$	−9.77112	−	8.79796i	−1.27209	−	1.14540i	−0.289994	−	0.957029i	$-0.593653\pi$
$60$	3.64690	+	1.62371i	0.470813	+	0.209620i
$61$	0.925348	+	8.80410i	0.118479	+	1.12725i	0.878630	+	0.477503i	$0.158458\pi$
$61$	0.925348	+	8.80410i	0.118479	+	1.12725i	−0.760151	+	0.649746i	$0.774875\pi$
$62$	−0.575831	−	1.77222i	−0.0731306	−	0.225073i
$63$	1.15658	+	2.37956i	0.145716	+	0.299797i
$64$	−1.32017	−	0.959157i	−0.165021	−	0.119895i
$65$	12.7667	+	7.37086i	1.58351	+	0.914242i
$66$	3.63845	+	4.78612i	0.447863	+	0.589131i
$67$	2.64393	+	4.57942i	0.323007	+	0.559465i	0.981107	−	0.193466i	$-0.0619728\pi$
$67$	2.64393	+	4.57942i	0.323007	+	0.559465i	−0.658100	+	0.752931i	$0.728639\pi$
$68$	7.57150	−	3.37105i	0.918179	−	0.408800i
$69$	−2.07679	−	0.674792i	−0.250017	−	0.0812354i
$70$	12.6370	−	7.87255i	1.51040	−	0.940950i
$71$	0.0539502	−	0.0391971i	0.00640271	−	0.00465184i	−0.584579	−	0.811337i	$-0.698740\pi$
$71$	0.0539502	−	0.0391971i	0.00640271	−	0.00465184i	0.590982	+	0.806685i	$0.298740\pi$
$72$	1.28730	−	0.135301i	0.151710	−	0.0159454i
$73$	−8.65088	+	9.60778i	−1.01251	+	1.12451i	−0.0203164	+	0.999794i	$0.506467\pi$
$73$	−8.65088	+	9.60778i	−1.01251	+	1.12451i	−0.992193	+	0.124712i	$0.960199\pi$
$74$	0.345638	+	1.62610i	0.0401796	+	0.189030i
$75$	1.88610	+	4.23626i	0.217788	+	0.489161i
$76$	1.12695			0.129270
$77$	8.76158	−	0.484394i	0.998475	−	0.0552018i
$78$	−8.60802			−0.974666
$79$	−6.22817	−	13.9887i	−0.700724	−	1.57385i	−0.814380	−	0.580331i	$-0.802923\pi$
$79$	−6.22817	−	13.9887i	−0.700724	−	1.57385i	0.113657	−	0.993520i	$-0.463744\pi$
$80$	−3.17441	−	14.9344i	−0.354910	−	1.66972i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−14.2012	+	1.49260i	−1.56826	+	0.164831i
$83$	6.26756	−	4.55365i	0.687954	−	0.499828i	−0.188033	−	0.982163i	$-0.560211\pi$
$83$	6.26756	−	4.55365i	0.687954	−	0.499828i	0.875987	+	0.482335i	$0.160211\pi$
$84$	−1.60136	+	3.00185i	−0.174722	+	0.327529i
$85$	19.0289	+	6.18285i	2.06397	+	0.670624i
$86$	1.67532	−	0.745899i	0.180654	−	0.0804323i
$87$	3.41278	+	5.91111i	0.365889	+	0.633738i
$88$	1.23778	−	4.11070i	0.131947	−	0.438203i
$89$	−0.849198	−	0.490285i	−0.0900148	−	0.0519701i	0.454317	−	0.890840i	$-0.349883\pi$
$89$	−0.849198	−	0.490285i	−0.0900148	−	0.0519701i	−0.544332	+	0.838870i	$0.683217\pi$
$90$	−4.55262	−	3.30767i	−0.479889	−	0.348660i
$91$	−7.03978	+	10.4063i	−0.737970	+	1.09088i
$92$	−0.867740	−	2.67063i	−0.0904681	−	0.278432i
$93$	0.107453	+	1.02234i	0.0111423	+	0.106012i
$94$	−12.5289	−	5.57820i	−1.29225	−	0.575348i
$95$	2.02177	+	1.82041i	0.207430	+	0.186771i
$96$	4.23331	+	4.70157i	0.432060	+	0.479852i
$97$	1.62607	−	2.23809i	0.165102	−	0.227244i	−0.718447	−	0.695581i	$-0.755147\pi$
$97$	1.62607	−	2.23809i	0.165102	−	0.227244i	0.883550	+	0.468337i	$0.155147\pi$
$98$	5.92661	+	11.2199i	0.598678	+	1.13338i
$99$	−1.41437	−	2.99993i	−0.142150	−	0.301504i
$100$	−2.98155	+	5.16419i	−0.298155	+	0.516419i
$101$	−1.60408	+	15.2618i	−0.159612	+	1.51861i	0.562480	+	0.826811i	$0.309847\pi$
$101$	−1.60408	+	15.2618i	−0.159612	+	1.51861i	−0.722092	+	0.691797i	$0.756819\pi$
$102$	−11.4279	+	2.42907i	−1.13153	+	0.240514i
$103$	1.60002	−	7.52748i	0.157654	−	0.741705i	−0.826292	−	0.563241i	$-0.809554\pi$
$103$	1.60002	−	7.52748i	0.157654	−	0.741705i	0.983947	−	0.178463i	$-0.0571125\pi$
$104$	3.61292	+	4.97276i	0.354276	+	0.487619i
$105$	−7.72190	+	2.79865i	−0.753580	+	0.273120i
$106$	−9.68282	+	3.14614i	−0.940478	+	0.305580i
$107$	−12.5211	+	11.2741i	−1.21046	+	1.08991i	−0.216951	+	0.976182i	$0.569611\pi$
$107$	−12.5211	+	11.2741i	−1.21046	+	1.08991i	−0.993512	+	0.113724i	$0.963722\pi$
$108$	1.27889	+	0.134417i	0.123062	+	0.0129343i
$109$	1.96765	−	1.13602i	0.188466	−	0.108811i	−0.402798	−	0.915289i	$-0.631962\pi$
$109$	1.96765	−	1.13602i	0.188466	−	0.108811i	0.591264	+	0.806478i	$0.298629\pi$
$110$	−15.9572	+	9.68018i	−1.52146	+	0.922969i
$111$		−	0.917093i		−	0.0870466i
$112$	12.8883	−	1.79344i	1.21783	−	0.169465i
$113$	−4.99757	+	15.3810i	−0.470132	+	1.44692i	0.382279	+	0.924047i	$0.375139\pi$
$113$	−4.99757	+	15.3810i	−0.470132	+	1.44692i	−0.852412	+	0.522871i	$0.824861\pi$
$114$	−1.55388	−	0.330288i	−0.145535	−	0.0309343i
$115$	2.75724	−	6.19287i	0.257114	−	0.577488i
$116$	−3.57003	+	8.01842i	−0.331469	+	0.744491i
$117$	4.64492	+	0.987308i	0.429423	+	0.0912766i
$118$	−7.36518	+	22.6677i	−0.678019	+	2.08673i
$119$	−6.40938	+	15.8018i	−0.587547	+	1.44855i
$120$			4.01828i			0.366817i
$121$	−10.9897	+	0.476902i	−0.999060	+	0.0433548i
$122$	13.8973	−	8.02362i	1.25820	−	0.726424i
$123$	7.83421	+	0.823408i	0.706387	+	0.0742442i
$124$	−0.982372	+	0.884532i	−0.0882196	+	0.0794333i
$125$	1.07127	−	0.348076i	0.0958170	−	0.0311328i
$126$	3.08780	−	3.66975i	0.275083	−	0.326927i
$127$	−3.38091	−	4.65342i	−0.300007	−	0.412925i	0.632225	−	0.774785i	$-0.282142\pi$
$127$	−3.38091	−	4.65342i	−0.300007	−	0.412925i	−0.932232	+	0.361860i	$0.882142\pi$
$128$	2.01573	−	9.48329i	0.178167	−	0.838212i
$129$	−0.989558	+	0.210337i	−0.0871258	+	0.0185192i
$130$	2.79327	−	26.5761i	0.244986	−	2.33088i
$131$	0.955159	−	1.65438i	0.0834526	−	0.144544i	−0.821278	−	0.570528i	$-0.806739\pi$
$131$	0.955159	−	1.65438i	0.0834526	−	0.144544i	0.904731	+	0.425984i	$0.140072\pi$
$132$	2.05190	−	3.73894i	0.178595	−	0.325433i
$133$	−1.67008	+	1.60839i	−0.144815	+	0.139465i
$134$	5.63415	−	7.75474i	0.486716	−	0.669907i
$135$	2.07723	+	2.30700i	0.178780	+	0.198555i
$136$	6.19971	+	5.58225i	0.531621	+	0.478674i
$137$	−15.0653	−	6.70752i	−1.28712	−	0.573062i	−0.354882	−	0.934911i	$-0.615479\pi$
$137$	−15.0653	−	6.70752i	−1.28712	−	0.573062i	−0.932237	+	0.361849i	$0.882146\pi$
$138$	0.413763	+	3.93669i	0.0352218	+	0.335113i
$139$	4.11965	+	12.6790i	0.349424	+	1.07542i	0.959172	+	0.282822i	$0.0912705\pi$
$139$	4.11965	+	12.6790i	0.349424	+	1.07542i	−0.609748	+	0.792595i	$0.708729\pi$
$140$	−8.74819	−	5.91807i	−0.739357	−	0.500168i
$141$	6.12081	+	4.44703i	0.515465	+	0.374508i
$142$	−0.104688	−	0.0604415i	−0.00878520	−	0.00507214i
$143$	8.97894	−	12.9394i	0.750857	−	1.08205i
$144$	−2.45912	−	4.25932i	−0.204927	−	0.354943i
$145$	−19.3572	+	8.61840i	−1.60753	+	0.715719i
$146$	22.2887	+	7.24205i	1.84463	+	0.599356i
$147$	−1.91114	−	6.73406i	−0.157628	−	0.555416i
$148$	0.954093	−	0.693189i	0.0784260	−	0.0569798i
$149$	6.66954	−	0.700997i	0.546390	−	0.0574279i	0.172688	−	0.984977i	$-0.444755\pi$
$149$	6.66954	−	0.700997i	0.546390	−	0.0574279i	0.373702	+	0.927549i	$0.378088\pi$
$150$	5.62461	−	6.24676i	0.459248	−	0.510046i
$151$	−4.14785	−	19.5141i	−0.337547	−	1.58803i	−0.740009	−	0.672597i	$-0.765179\pi$
$151$	−4.14785	−	19.5141i	−0.337547	−	1.58803i	0.402462	−	0.915437i	$-0.368154\pi$
$152$	0.461386	+	1.03629i	0.0374233	+	0.0840542i
$153$	6.44513			0.521058
$154$	−7.26205	−	14.1520i	−0.585193	−	1.14040i
$155$	−3.19122			−0.256325
$156$	2.48374	+	5.57858i	0.198859	+	0.446644i
$157$	−0.814001	−	3.82957i	−0.0649643	−	0.305633i	0.933654	−	0.358175i	$-0.116601\pi$
$157$	−0.814001	−	3.82957i	−0.0649643	−	0.305633i	−0.998619	+	0.0525421i	$0.983268\pi$
$158$	−18.5732	+	20.6277i	−1.47761	+	1.64105i
$159$	5.58573	−	0.587084i	0.442977	−	0.0465588i
$160$	−15.8892	+	11.5442i	−1.25615	+	0.912646i
$161$	5.09749	+	2.71929i	0.401739	+	0.214310i
$162$	−1.72399	−	0.560160i	−0.135450	−	0.0440103i
$163$	4.19904	−	1.86953i	0.328894	−	0.146433i	−0.235645	−	0.971839i	$-0.575720\pi$
$163$	4.19904	−	1.86953i	0.328894	−	0.146433i	0.564540	+	0.825406i	$0.309054\pi$
$164$	5.06489	+	8.77265i	0.395502	+	0.685029i
$165$	9.72084	−	3.39323i	0.756767	−	0.264162i
$166$	−12.1619	−	7.02167i	−0.943945	−	0.544987i
$167$	−1.66678	−	1.21098i	−0.128979	−	0.0937088i	0.521425	−	0.853297i	$-0.325401\pi$
$167$	−1.66678	−	1.21098i	−0.128979	−	0.0937088i	−0.650404	+	0.759588i	$0.725401\pi$
$168$	−3.41597	−	0.243540i	−0.263548	−	0.0187895i
$169$	2.95112	+	9.08262i	0.227009	+	0.698663i
$170$	−3.79115	−	36.0704i	−0.290768	−	2.76647i
$171$	0.800599	+	0.356450i	0.0612233	+	0.0272584i
$172$	−0.966786	−	0.870498i	−0.0737167	−	0.0663748i
$173$	5.07848	+	5.64022i	0.386110	+	0.428818i	0.904597	−	0.426267i	$-0.140172\pi$
$173$	5.07848	+	5.64022i	0.386110	+	0.428818i	−0.518488	+	0.855085i	$0.673505\pi$
$174$	7.27256	−	10.0098i	0.551331	−	0.758842i
$175$	−2.95188	−	11.9084i	−0.223141	−	0.900188i
$176$	−16.1818	+	2.05641i	−1.21975	+	0.155008i
$177$	6.57417	−	11.3868i	0.494145	−	0.855884i
$178$	−0.185799	+	1.76776i	−0.0139262	+	0.132499i
$179$	−10.8250	+	2.30092i	−0.809098	+	0.171979i	−0.593845	−	0.804579i	$-0.702391\pi$
$179$	−10.8250	+	2.30092i	−0.809098	+	0.171979i	−0.215253	+	0.976558i	$0.569057\pi$
$180$	−0.829991	+	3.90480i	−0.0618638	+	0.291047i
$181$	6.97751	+	9.60372i	0.518634	+	0.713839i	0.985345	−	0.170571i	$-0.0545613\pi$
$181$	6.97751	+	9.60372i	0.518634	+	0.713839i	−0.466711	+	0.884410i	$0.654561\pi$
$182$	22.4233	+	3.98530i	1.66212	+	0.295410i
$183$	−8.41932	+	2.73560i	−0.622374	+	0.202222i
$184$	2.10052	−	1.89132i	0.154852	−	0.139430i
$185$	2.83141	+	0.297593i	0.208169	+	0.0218795i
$186$	1.61378	−	0.931714i	0.118328	−	0.0683166i
$187$	8.26898	−	19.7120i	0.604688	−	1.44148i
$188$			9.72907i			0.709565i
$189$	−2.08710	+	1.62605i	−0.151814	+	0.118278i
$190$	1.52395	−	4.69024i	0.110559	−	0.340266i
$191$	−12.2834	−	2.61092i	−0.888798	−	0.188920i	−0.259184	−	0.965828i	$-0.583454\pi$
$191$	−12.2834	−	2.61092i	−0.888798	−	0.188920i	−0.629614	+	0.776908i	$0.716787\pi$
$192$	0.663719	−	1.49074i	0.0478998	−	0.107585i
$193$	2.50336	−	5.62263i	0.180196	−	0.404726i	−0.800753	−	0.598995i	$-0.795567\pi$
$193$	2.50336	−	5.62263i	0.180196	−	0.404726i	0.980948	+	0.194269i	$0.0622335\pi$
$194$	−4.90518	−	1.04263i	−0.352171	−	0.0748563i
$195$	−4.55544	+	14.0202i	−0.326222	+	1.00401i
$196$	5.56120	−	7.07822i	0.397229	−	0.505587i
$197$		−	23.0266i		−	1.64057i	−0.571952	−	0.820287i	$-0.693814\pi$
$197$		−	23.0266i		−	1.64057i	0.571952	−	0.820287i	$-0.306186\pi$
$198$	−3.92506	+	4.55403i	−0.278942	+	0.323641i
$199$	−6.57469	+	3.79590i	−0.466068	+	0.269084i	−0.714592	−	0.699541i	$-0.753388\pi$
$199$	−6.57469	+	3.79590i	−0.466068	+	0.269084i	0.248524	+	0.968626i	$0.420054\pi$
$200$	−5.96942	−	0.627412i	−0.422102	−	0.0443647i
$201$	−3.92965	+	3.53827i	−0.277176	+	0.249570i
$202$	26.4562	−	8.59615i	1.86145	−	0.604823i
$203$	−6.15336	−	16.9781i	−0.431881	−	1.19163i
$204$	4.87159	+	6.70516i	0.341079	+	0.469455i
$205$	−5.08433	+	23.9199i	−0.355105	+	1.67064i
$206$	−13.6452	+	2.90037i	−0.950705	+	0.202078i
$207$	0.228256	−	2.17171i	0.0158649	−	0.150944i
$208$	11.6776	−	20.2262i	0.809695	−	1.40243i
$209$	2.11733	−	1.99125i	0.146459	−	0.137738i
$210$	10.3279	+	10.7240i	0.712692	+	0.740027i
$211$	7.58407	−	10.4386i	0.522109	−	0.718621i	−0.463793	−	0.885943i	$-0.653512\pi$
$211$	7.58407	−	10.4386i	0.522109	−	0.718621i	0.985902	+	0.167322i	$0.0535120\pi$
$212$	4.83277	+	5.36734i	0.331916	+	0.368630i
$213$	0.0495575	+	0.0446217i	0.00339562	+	0.00305743i
$214$	27.9017	+	12.4226i	1.90732	+	0.849193i
$215$	−0.328281	−	3.12339i	−0.0223886	−	0.213013i
$216$	0.399989	+	1.23104i	0.0272158	+	0.0837617i
$217$	0.193413	−	2.71288i	0.0131298	−	0.184162i
$218$	−3.33199	−	2.42083i	−0.225671	−	0.163959i
$219$	−11.1964	−	6.46427i	−0.756586	−	0.436815i
$220$	10.8777	+	7.54824i	0.733372	+	0.508902i
$221$	15.3030	+	26.5055i	1.02939	+	1.78295i
$222$	−1.51870	+	0.676171i	−0.101929	+	0.0453816i
$223$	−10.0401	−	3.26221i	−0.672332	−	0.218454i	−0.0470966	−	0.998890i	$-0.514997\pi$
$223$	−10.0401	−	3.26221i	−0.672332	−	0.218454i	−0.625235	+	0.780437i	$0.714997\pi$
$224$	−8.85076	−	14.2072i	−0.591366	−	0.949256i
$225$	−3.75154	+	2.72565i	−0.250103	+	0.181710i
$226$	29.1555	−	3.06437i	1.93940	−	0.203839i
$227$	−4.77862	+	5.30719i	−0.317168	+	0.352251i	−0.880556	−	0.473942i	$-0.842831\pi$
$227$	−4.77862	+	5.30719i	−0.317168	+	0.352251i	0.563388	+	0.826192i	$0.309497\pi$
$228$	0.234306	+	1.10232i	0.0155173	+	0.0730031i
$229$	5.60571	+	12.5906i	0.370436	+	0.832013i	0.998547	+	0.0538889i	$0.0171617\pi$
$229$	5.60571	+	12.5906i	0.370436	+	0.832013i	−0.628111	+	0.778124i	$0.716172\pi$
$230$	−12.2883			−0.810266
$231$	2.29544	+	8.46941i	0.151029	+	0.557246i
$232$	−8.83497			−0.580044
$233$	2.34118	+	5.25838i	0.153376	+	0.344488i	0.973849	−	0.227198i	$-0.0729563\pi$
$233$	2.34118	+	5.25838i	0.153376	+	0.344488i	−0.820473	+	0.571686i	$0.806290\pi$
$234$	−1.78971	−	8.41991i	−0.116997	−	0.550427i
$235$	−15.7158	+	17.4542i	−1.02519	+	1.13859i
$236$	16.8153	−	1.76736i	1.09458	−	0.115045i
$237$	12.3881	−	9.00048i	0.804694	−	0.584644i
$238$	30.8934	−	1.03673i	2.00252	−	0.0672013i
$239$	−1.05336	−	0.342257i	−0.0681361	−	0.0221388i	0.274751	−	0.961516i	$-0.411405\pi$
$239$	−1.05336	−	0.342257i	−0.0681361	−	0.0221388i	−0.342887	+	0.939377i	$0.611405\pi$
$240$	13.9481	−	6.21008i	0.900345	−	0.400859i
$241$	−10.9061	−	18.8899i	−0.702522	−	1.21680i	−0.967578	−	0.252571i	$-0.918724\pi$
$241$	−10.9061	−	18.8899i	−0.702522	−	1.21680i	0.265057	−	0.964233i	$-0.414609\pi$
$242$	8.89240	+	17.8472i	0.571625	+	1.14726i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−9.20975	−	6.69128i	−0.589594	−	0.428365i
$245$	21.4107	−	3.71523i	1.36788	−	0.237357i
$246$	−4.41258	−	13.5805i	−0.281336	−	0.865863i
$247$	0.435004	+	4.13878i	0.0276786	+	0.263345i
$248$	−1.21557	−	0.541205i	−0.0771886	−	0.0343666i
$249$	5.75724	+	5.18384i	0.364850	+	0.328512i
$250$	−1.36625	−	1.51738i	−0.0864095	−	0.0959675i
$251$	−3.01407	+	4.14851i	−0.190246	+	0.261851i	−0.893476	−	0.449111i	$-0.851741\pi$
$251$	−3.01407	+	4.14851i	−0.190246	+	0.261851i	0.703230	+	0.710963i	$0.251741\pi$
$252$	−3.26919	−	0.942243i	−0.205940	−	0.0593557i
$253$	−6.34916	−	3.48436i	−0.399168	−	0.219060i
$254$	−5.21332	+	9.02974i	−0.327113	+	0.566576i
$255$	−2.09142	+	19.8985i	−0.130970	+	1.24609i
$256$	−20.3828	+	4.33250i	−1.27393	+	0.270781i
$257$	−0.801407	+	3.77032i	−0.0499904	+	0.235186i	−0.996049	−	0.0888106i	$-0.971693\pi$
$257$	−0.801407	+	3.77032i	−0.0499904	+	0.235186i	0.946058	+	0.323997i	$0.105027\pi$
$258$	1.07792	+	1.48363i	0.0671082	+	0.0923665i
$259$	−0.424591	+	2.38896i	−0.0263828	+	0.148443i
$260$	−18.0291	+	5.85801i	−1.11812	+	0.363298i
$261$	−5.07239	+	4.56720i	−0.313973	+	0.282702i
$262$	−3.44389	−	0.361968i	−0.212764	−	0.0223624i
$263$	15.6267	−	9.02210i	0.963586	−	0.556326i	0.0663110	−	0.997799i	$-0.478877\pi$
$263$	15.6267	−	9.02210i	0.963586	−	0.556326i	0.897275	+	0.441473i	$0.145544\pi$
$264$	4.27822	+	0.356063i	0.263306	+	0.0219142i
$265$			17.4357i			1.07107i
$266$	3.89484	+	1.57979i	0.238808	+	0.0968630i
$267$	0.303013	−	0.932577i	0.0185441	−	0.0570728i
$268$	−6.65126	−	1.41377i	−0.406291	−	0.0863597i
$269$	1.34550	−	3.02205i	0.0820368	−	0.184258i	−0.867870	−	0.496792i	$-0.834511\pi$
$269$	1.34550	−	3.02205i	0.0820368	−	0.184258i	0.949906	+	0.312534i	$0.101178\pi$
$270$	2.28885	−	5.14084i	0.139295	−	0.312862i
$271$	−18.0021	−	3.82647i	−1.09355	−	0.232442i	−0.374381	−	0.927275i	$-0.622145\pi$
$271$	−18.0021	−	3.82647i	−1.09355	−	0.232442i	−0.719171	+	0.694833i	$0.755478\pi$
$272$	9.79544	−	30.1473i	0.593936	−	1.82795i
$273$	−11.6426	−	4.72235i	−0.704641	−	0.285809i
$274$			29.8936i			1.80594i
$275$	3.52305	+	14.9708i	0.212448	+	0.902771i
$276$	2.43185	−	1.40403i	0.146380	−	0.0845128i
$277$	−17.4677	−	1.83593i	−1.04953	−	0.110310i	−0.435973	−	0.899960i	$-0.643596\pi$
$277$	−17.4677	−	1.83593i	−1.04953	−	0.110310i	−0.613558	+	0.789650i	$0.710262\pi$
$278$	17.9590	−	16.1703i	1.07711	−	0.969831i
$279$	−0.977663	+	0.317662i	−0.0585311	+	0.0190179i
$280$	1.86037	−	10.4673i	0.111178	−	0.625543i
$281$	7.26763	+	10.0030i	0.433550	+	0.596731i	0.968764	−	0.247986i	$-0.0797687\pi$
$281$	7.26763	+	10.0030i	0.433550	+	0.596731i	−0.535213	+	0.844717i	$0.679769\pi$
$282$	2.85141	−	13.4148i	0.169799	−	0.798842i
$283$	−14.8212	+	3.15033i	−0.881026	+	0.187268i	−0.626147	−	0.779705i	$-0.715369\pi$
$283$	−14.8212	+	3.15033i	−0.881026	+	0.187268i	−0.254879	+	0.966973i	$0.582036\pi$
$284$	−0.00896375	+	0.0852844i	−0.000531901	+	0.00506070i
$285$	−1.36028	+	2.35608i	−0.0805762	+	0.139562i
$286$	−28.0478	−	5.32890i	−1.65850	−	0.315104i
$287$	−20.0263	−	5.77196i	−1.18212	−	0.340708i
$288$	−3.71867	+	5.11831i	−0.219125	+	0.301600i
$289$	16.4203	+	18.2366i	0.965900	+	1.07274i
$290$	28.5441	+	25.7012i	1.67617	+	1.50923i
$291$	2.52727	+	1.12521i	0.148151	+	0.0659610i
$292$	−1.73782	−	16.5342i	−0.101698	−	0.967592i
$293$	−0.321046	−	0.988079i	−0.0187557	−	0.0577242i	0.941241	−	0.337737i	$-0.109661\pi$
$293$	−0.321046	−	0.988079i	−0.0187557	−	0.0577242i	−0.959996	+	0.280013i	$0.909661\pi$
$294$	−9.74251	+	8.12985i	−0.568195	+	0.474143i
$295$	33.0220	+	23.9919i	1.92261	+	1.39686i
$296$	1.02804	+	0.593539i	0.0597536	+	0.0344988i
$297$	2.64031	−	2.00718i	0.153206	−	0.116469i
$298$	−6.07828	−	10.5279i	−0.352106	−	0.609865i
$299$	9.47308	−	4.21769i	0.547842	−	0.243915i
$300$	−5.67124	−	1.84270i	−0.327429	−	0.106388i
$301$	2.67511	−	0.0897721i	0.154191	−	0.00517438i
$302$	−29.2571	+	21.2565i	−1.68356	+	1.22317i
$303$	−15.2618	+	1.60408i	−0.876769	+	0.0921521i
$304$	2.88407	−	3.20308i	0.165413	−	0.183709i
$305$	−5.71379	−	26.8812i	−0.327170	−	1.53922i
$306$	−4.75198	−	10.6731i	−0.271653	−	0.610142i
$307$	−16.0421			−0.915572			−0.457786	−	0.889062i	$-0.651357\pi$
$307$	−16.0421			−0.915572			−0.457786	+	0.889062i	$0.651357\pi$
$308$	−7.07609	+	8.78970i	−0.403197	+	0.500840i
$309$	7.69565			0.437790
$310$	2.35288	+	5.28466i	0.133635	+	0.300149i
$311$	−2.06333	−	9.70721i	−0.117001	−	0.550445i	−0.997130	−	0.0757109i	$-0.975877\pi$
$311$	−2.06333	−	9.70721i	−0.117001	−	0.550445i	0.880129	−	0.474735i	$-0.157456\pi$
$312$	−4.11292	+	4.56786i	−0.232848	+	0.258604i
$313$	11.7377	−	1.23368i	0.663453	−	0.0697318i	0.233185	−	0.972433i	$-0.425085\pi$
$313$	11.7377	−	1.23368i	0.663453	−	0.0697318i	0.430269	+	0.902701i	$0.358419\pi$
$314$	−5.74160	+	4.17152i	−0.324017	+	0.235412i
$315$	−4.34296	−	6.97128i	−0.244698	−	0.392787i
$316$	18.7272	+	6.08484i	1.05349	+	0.342299i
$317$	25.9239	−	11.5420i	1.45603	−	0.648266i	0.482306	−	0.876003i	$-0.339799\pi$
$317$	25.9239	−	11.5420i	1.45603	−	0.648266i	0.973723	+	0.227737i	$0.0731327\pi$
$318$	−5.09056	−	8.81710i	−0.285464	−	0.494439i
$319$	7.46066	+	21.3731i	0.417717	+	1.19667i
$320$	4.38709	+	2.53289i	0.245246	+	0.141593i
$321$	−13.6310	−	9.90350i	−0.760808	−	0.552760i
$322$	0.744768	−	10.4464i	0.0415043	−	0.582153i
$323$	1.74542	+	5.37184i	0.0971176	+	0.298897i
$324$	0.134417	+	1.27889i	0.00746761	+	0.0710496i
$325$	−20.1167	−	8.95651i	−1.11587	−	0.496818i
$326$	−6.19189	−	5.57520i	−0.342937	−	0.308782i
$327$	1.52029	+	1.68846i	0.0840724	+	0.0933718i
$328$	−5.99329	+	8.24906i	−0.330924	+	0.455478i
$329$	−13.8854	−	14.4180i	−0.765528	−	0.794889i
$330$	−12.7863	−	13.5959i	−0.703864	−	0.748428i
$331$	17.5054	−	30.3202i	0.962184	−	1.66655i	0.245185	−	0.969476i	$-0.421151\pi$
$331$	17.5054	−	30.3202i	0.962184	−	1.66655i	0.716999	−	0.697074i	$-0.245515\pi$
$332$	−1.04135	+	9.90774i	−0.0571513	+	0.543758i
$333$	0.897052	−	0.190674i	0.0491582	−	0.0104489i
$334$	−0.776476	+	3.65303i	−0.0424869	+	0.199885i
$335$	−9.64880	−	13.2804i	−0.527170	−	0.725587i
$336$	4.43387	+	12.2337i	0.241888	+	0.667405i
$337$	−8.30747	+	2.69926i	−0.452537	+	0.147038i	−0.526413	−	0.850229i	$-0.676463\pi$
$337$	−8.30747	+	2.69926i	−0.452537	+	0.147038i	0.0738756	+	0.997267i	$0.476463\pi$
$338$	12.8649	−	11.5836i	0.699761	−	0.630067i
$339$	−16.0839	−	1.69049i	−0.873557	−	0.0918146i
$340$	−22.2821	+	12.8646i	−1.20842	+	0.697681i
$341$	−0.282777	+	3.39766i	−0.0153132	+	0.183994i
$342$		−	1.58860i		−	0.0859016i
$343$	1.86068	+	18.4266i	0.100467	+	0.994940i
$344$	0.404655	−	1.24540i	0.0218176	−	0.0671476i
$345$	6.63080	+	1.40942i	0.356990	+	0.0758807i
$346$	5.59585	−	12.5685i	0.300835	−	0.675685i
$347$	3.11025	−	6.98574i	0.166967	−	0.375014i	−0.810612	−	0.585584i	$-0.800865\pi$
$347$	3.11025	−	6.98574i	0.166967	−	0.375014i	0.977579	+	0.210570i	$0.0675319\pi$
$348$	−8.58545	−	1.82489i	−0.460228	−	0.0978245i
$349$	5.39096	−	16.5917i	0.288572	−	0.888132i	−0.696734	−	0.717330i	$-0.745364\pi$
$349$	5.39096	−	16.5917i	0.288572	−	0.888132i	0.985305	−	0.170802i	$-0.0546359\pi$
$350$	−17.5438	+	13.6683i	−0.937756	+	0.730602i
$351$			4.74869i			0.253466i
$352$	10.8830	+	17.9400i	0.580066	+	0.956204i
$353$	28.0874	−	16.2163i	1.49494	−	0.863106i	0.494960	−	0.868916i	$-0.335183\pi$
$353$	28.0874	−	16.2163i	1.49494	−	0.863106i	0.999983	+	0.00581017i	$0.00184944\pi$
$354$	−23.7036	−	2.49135i	−1.25983	−	0.132414i
$355$	−0.153845	+	0.138523i	−0.00816525	+	0.00735202i
$356$	1.19924	−	0.389655i	0.0635593	−	0.0206517i
$357$	−16.7891	−	2.98394i	−0.888574	−	0.157927i
$358$	11.7916	+	16.2297i	0.623203	+	0.857766i
$359$	−4.37973	+	20.6050i	−0.231153	+	1.08749i	0.697512	+	0.716573i	$0.254290\pi$
$359$	−4.37973	+	20.6050i	−0.231153	+	1.08749i	−0.928666	+	0.370918i	$0.879043\pi$
$360$	−3.93047	+	0.835448i	−0.207154	+	0.0440320i
$361$	1.90576	−	18.1321i	0.100303	−	0.954321i
$362$	10.7592	−	18.6355i	0.565493	−	0.979462i
$363$	−2.75136	−	10.6504i	−0.144409	−	0.558999i
$364$	−3.88723	−	15.6817i	−0.203746	−	0.821945i
$365$	23.5908	−	32.4700i	1.23480	−	1.69956i
$366$	10.7377	+	11.9254i	0.561268	+	0.623352i
$367$	21.8694	+	19.6913i	1.14157	+	1.02788i	0.999276	+	0.0380546i	$0.0121161\pi$
$367$	21.8694	+	19.6913i	1.14157	+	1.02788i	0.142299	+	0.989824i	$0.454551\pi$
$368$	−9.81131	−	4.36828i	−0.511450	−	0.227712i
$369$	0.823408	+	7.83421i	0.0428649	+	0.407832i
$370$	−1.59478	−	4.90822i	−0.0829085	−	0.255166i
$371$	−14.8222	−	1.05674i	−0.769532	−	0.0548634i
$372$	−1.06945	−	0.777000i	−0.0554484	−	0.0402856i
$373$	−3.70494	−	2.13905i	−0.191835	−	0.110756i	0.401007	−	0.916075i	$-0.368660\pi$
$373$	−3.70494	−	2.13905i	−0.191835	−	0.110756i	−0.592841	+	0.805319i	$0.701994\pi$
$374$	−38.7397	+	0.840169i	−2.00318	+	0.0434441i
$375$	0.563198	+	0.975488i	0.0290834	+	0.0503740i
$376$	−8.94639	+	3.98319i	−0.461375	+	0.205417i
$377$	−30.8261	−	10.0160i	−1.58763	−	0.515851i
$378$	4.23154	+	2.25734i	0.217647	+	0.116105i
$379$	18.1321	−	13.1737i	0.931381	−	0.676688i	−0.0149492	−	0.999888i	$-0.504759\pi$
$379$	18.1321	−	13.1737i	0.931381	−	0.676688i	0.946331	+	0.323200i	$0.104759\pi$
$380$	−3.47931	+	0.365690i	−0.178485	+	0.0187595i
$381$	3.84880	−	4.27453i	0.197180	−	0.218991i
$382$	4.73286	+	22.2664i	0.242154	+	1.13925i
$383$	4.86430	+	10.9254i	0.248554	+	0.558261i	0.994134	−	0.108155i	$-0.0344942\pi$
$383$	4.86430	+	10.9254i	0.248554	+	0.558261i	−0.745580	+	0.666416i	$0.767828\pi$
$384$	9.69515			0.494754
$385$	−26.8931	+	4.33860i	−1.37060	+	0.221116i
$386$	−11.1568			−0.567866
$387$	−0.411481	−	0.924203i	−0.0209168	−	0.0469799i
$388$	0.739638	+	3.47972i	0.0375494	+	0.176656i
$389$	−1.18302	+	1.31388i	−0.0599816	+	0.0666164i	−0.772389	−	0.635150i	$-0.780938\pi$
$389$	−1.18302	+	1.31388i	−0.0599816	+	0.0666164i	0.712407	+	0.701766i	$0.247605\pi$
$390$	26.5761	−	2.79327i	1.34574	−	0.141443i
$391$	11.3861	−	8.27252i	0.575822	−	0.418359i
$392$	8.78561	+	2.21591i	0.443740	+	0.111921i
$393$	1.81682	+	0.590320i	0.0916464	+	0.0297777i
$394$	−38.1319	+	16.9774i	−1.92106	+	0.855311i
$395$	23.7679	+	41.1673i	1.19590	+	2.07135i
$396$	4.08385	+	1.22969i	0.205221	+	0.0617942i
$397$	19.7046	+	11.3764i	0.988945	+	0.570967i	0.904959	−	0.425500i	$-0.139902\pi$
$397$	19.7046	+	11.3764i	0.988945	+	0.570967i	0.0839859	+	0.996467i	$0.473235\pi$
$398$	11.1335	+	8.08897i	0.558073	+	0.405463i
$399$	−1.92048	−	1.29918i	−0.0961440	−	0.0650405i
$400$	7.04765	+	21.6904i	0.352382	+	1.08452i
$401$	0.672272	+	6.39624i	0.0335717	+	0.319413i	0.998401	+	0.0565347i	$0.0180052\pi$
$401$	0.672272	+	6.39624i	0.0335717	+	0.319413i	−0.964829	+	0.262878i	$0.915328\pi$
$402$	8.75669	+	3.89873i	0.436744	+	0.194451i
$403$	−3.62769	−	3.26638i	−0.180708	−	0.162710i
$404$	−13.2045	−	14.6651i	−0.656950	−	0.729617i
$405$	−1.82471	+	2.51149i	−0.0906704	+	0.124797i
$406$	−23.5788	+	22.7078i	−1.17020	+	1.12697i
$407$	0.567737	−	2.98820i	0.0281417	−	0.148120i
$408$	−4.17127	+	7.22485i	−0.206509	+	0.357683i
$409$	−1.58954	+	15.1234i	−0.0785976	+	0.747806i	0.882260	+	0.470763i	$0.156021\pi$
$409$	−1.58954	+	15.1234i	−0.0785976	+	0.747806i	−0.960857	+	0.277043i	$0.910645\pi$
$410$	43.3600	−	9.21645i	2.14140	−	0.455168i
$411$	3.42869	−	16.1307i	0.169125	−	0.795669i
$412$	5.81679	+	8.00613i	0.286573	+	0.394434i
$413$	−22.3971	+	26.6181i	−1.10209	+	1.30979i
$414$	−3.76464	+	1.22321i	−0.185022	+	0.0601172i
$415$	−17.8726	+	16.0926i	−0.877333	+	0.789954i
$416$	−29.8784	−	3.14035i	−1.46491	−	0.153968i
$417$	−11.5454	+	6.66573i	−0.565380	+	0.326422i
$418$	−4.85861	−	2.03814i	−0.237642	−	0.0996888i
$419$		−	22.4641i		−	1.09744i	−0.836005	−	0.548722i	$-0.815115\pi$
$419$		−	22.4641i		−	1.09744i	0.836005	−	0.548722i	$-0.184885\pi$
$420$	3.96989	−	9.78746i	0.193711	−	0.477579i
$421$	−1.79190	+	5.51490i	−0.0873319	+	0.268780i	−0.985180	−	0.171526i	$-0.945130\pi$
$421$	−1.79190	+	5.51490i	−0.0873319	+	0.268780i	0.897848	+	0.440306i	$0.145130\pi$
$422$	−22.8780	−	4.86287i	−1.11368	−	0.236721i
$423$	−3.07726	+	6.91165i	−0.149622	+	0.336056i
$424$	−2.95696	+	6.64144i	−0.143603	+	0.322537i
$425$	−29.2340	−	6.21388i	−1.41806	−	0.301417i
$426$	0.0373549	−	0.114967i	0.00180985	−	0.00557015i
$427$	23.1982	−	3.22811i	1.12264	−	0.156219i
$428$		−	21.6666i		−	1.04729i
$429$	14.5235	+	6.09247i	0.701201	+	0.294147i
$430$	−4.93028	+	2.84650i	−0.237759	+	0.137270i
$431$	−3.35420	−	0.352541i	−0.161566	−	0.0169813i	0.0233999	−	0.999726i	$-0.492551\pi$
$431$	−3.35420	−	0.352541i	−0.161566	−	0.0169813i	−0.184966	+	0.982745i	$0.559218\pi$
$432$	3.65496	−	3.29094i	0.175850	−	0.158336i
$433$	5.50027	−	1.78715i	0.264326	−	0.0858847i	−0.173856	−	0.984771i	$-0.555623\pi$
$433$	5.50027	−	1.78715i	0.264326	−	0.0858847i	0.438182	+	0.898886i	$0.355623\pi$
$434$	−4.63513	+	1.67991i	−0.222493	+	0.0806382i
$435$	−12.4547	−	17.1424i	−0.597155	−	0.821914i
$436$	−0.607456	+	2.85786i	−0.0290919	+	0.136867i
$437$	1.87187	−	0.397879i	0.0895439	−	0.0190331i
$438$	−2.44971	+	23.3074i	−0.117051	+	1.11367i
$439$	12.7375	−	22.0620i	0.607929	−	1.05296i	−0.383652	−	0.923478i	$-0.625334\pi$
$439$	12.7375	−	22.0620i	0.607929	−	1.05296i	0.991581	−	0.129486i	$-0.0413328\pi$
$440$	−2.48757	+	13.0929i	−0.118590	+	0.624181i
$441$	6.18955	−	3.26947i	0.294741	−	0.155689i
$442$	32.6102	−	44.8841i	1.55111	−	2.13492i
$443$	11.5718	+	12.8517i	0.549791	+	0.610605i	0.952431	−	0.304753i	$-0.0985741\pi$
$443$	11.5718	+	12.8517i	0.549791	+	0.610605i	−0.402640	+	0.915358i	$0.631907\pi$
$444$	0.876409	+	0.789122i	0.0415925	+	0.0374501i
$445$	2.78088	+	1.23813i	0.131827	+	0.0586930i
$446$	2.00029	+	19.0315i	0.0947167	+	0.901169i
$447$	2.07235	+	6.37805i	0.0980189	+	0.301671i
$448$	−2.41912	+	3.57598i	−0.114293	+	0.168949i
$449$	18.7703	+	13.6374i	0.885826	+	0.643590i	0.934786	−	0.355210i	$-0.115591\pi$
$449$	18.7703	+	13.6374i	0.885826	+	0.643590i	−0.0489601	+	0.998801i	$0.515591\pi$
$450$	7.27968	+	4.20292i	0.343167	+	0.198128i
$451$	25.0167	+	7.53280i	1.17799	+	0.354706i
$452$	−10.3984	−	18.0106i	−0.489100	−	0.847146i
$453$	18.2253	−	8.11441i	0.856298	−	0.381248i
$454$	12.3120	+	4.00040i	0.577829	+	0.187748i
$455$	18.3576	−	34.4126i	0.860618	−	1.61329i
$456$	−0.917716	+	0.666760i	−0.0429760	+	0.0312239i
$457$	39.0534	−	4.10468i	1.82684	−	0.192009i	0.872075	−	0.489372i	$-0.162774\pi$
$457$	39.0534	−	4.10468i	1.82684	−	0.192009i	0.954764	+	0.297363i	$0.0961072\pi$
$458$	16.7170	−	18.5661i	0.781134	−	0.867537i
$459$	1.34002	+	6.30429i	0.0625467	+	0.294259i
$460$	3.54564	+	7.96364i	0.165316	+	0.371307i
$461$	−19.7204			−0.918469			−0.459235	−	0.888315i	$-0.651876\pi$
$461$	−19.7204			−0.918469			−0.459235	+	0.888315i	$0.651876\pi$
$462$	12.3329	−	10.0457i	0.573779	−	0.467370i
$463$	−29.7766			−1.38384			−0.691918	−	0.721976i	$-0.743234\pi$
$463$	−29.7766			−1.38384			−0.691918	+	0.721976i	$0.743234\pi$
$464$	13.6541	+	30.6675i	0.633874	+	1.42370i
$465$	−0.663493	−	3.12149i	−0.0307687	−	0.144756i
$466$	6.98172	−	7.75399i	0.323422	−	0.359197i
$467$	−0.377076	+	0.0396323i	−0.0174490	+	0.00183396i	−0.113249	−	0.993567i	$-0.536126\pi$
$467$	−0.377076	+	0.0396323i	−0.0174490	+	0.00183396i	0.0957999	+	0.995401i	$0.469459\pi$
$468$	−4.94027	+	3.58932i	−0.228364	+	0.165916i
$469$	11.8746	−	7.39761i	0.548317	−	0.341590i
$470$	40.4913	+	13.1564i	1.86773	+	0.606861i
$471$	3.57665	−	1.59243i	0.164803	−	0.0733751i
$472$	8.50956	+	14.7390i	0.391684	+	0.678417i
$473$	−3.35453	+	0.0727516i	−0.154241	+	0.00334512i
$474$	−24.0385	−	13.8786i	−1.10412	−	0.637467i
$475$	−3.28772	−	2.38867i	−0.150851	−	0.109600i
$476$	−9.58581	−	19.7219i	−0.439365	−	0.903952i
$477$	1.73559	+	5.34161i	0.0794674	+	0.244575i
$478$	0.209862	+	1.99671i	0.00959887	+	0.0913272i
$479$	−2.54920	−	1.13498i	−0.116476	−	0.0518585i	0.347671	−	0.937616i	$-0.386973\pi$
$479$	−2.54920	−	1.13498i	−0.116476	−	0.0518585i	−0.464147	+	0.885758i	$0.653639\pi$
$480$	−14.5954	−	13.1418i	−0.666188	−	0.599838i
$481$	2.91406	+	3.23639i	0.132870	+	0.147567i
$482$	−23.2406	+	31.9879i	−1.05858	+	1.45701i
$483$	−1.60004	+	5.55147i	−0.0728042	+	0.252601i
$484$	9.00041	−	10.9125i	0.409110	−	0.496022i
$485$	−4.29403	+	7.43748i	−0.194982	+	0.337719i
$486$	0.189480	−	1.80279i	0.00859500	−	0.0817760i
$487$	2.39590	−	0.509263i	0.108568	−	0.0230769i	−0.153307	−	0.988179i	$-0.548992\pi$
$487$	2.39590	−	0.509263i	0.108568	−	0.0230769i	0.261875	+	0.965102i	$0.415659\pi$
$488$	2.38240	−	11.2083i	0.107846	−	0.507377i
$489$	2.70171	+	3.71859i	0.122176	+	0.168160i
$490$	−21.9385	−	32.7168i	−0.991079	−	1.47800i
$491$	26.1156	−	8.48546i	1.17858	−	0.382943i	0.346740	−	0.937961i	$-0.387289\pi$
$491$	26.1156	−	8.48546i	1.17858	−	0.382943i	0.831838	+	0.555018i	$0.187289\pi$
$492$	−7.52790	+	6.77815i	−0.339384	+	0.305583i
$493$	−43.7507	−	4.59838i	−1.97043	−	0.207101i
$494$	6.53309	−	3.77188i	0.293938	−	0.169705i
$495$	5.34015	+	8.80293i	0.240022	+	0.395662i
$496$			5.05583i			0.227013i
$497$	−0.108435	−	0.139180i	−0.00486397	−	0.00624309i
$498$	4.33963	−	13.3560i	0.194463	−	0.598497i
$499$	−1.00937	−	0.214547i	−0.0451854	−	0.00960446i	0.185264	−	0.982689i	$-0.440686\pi$
$499$	−1.00937	−	0.214547i	−0.0451854	−	0.00960446i	−0.230449	+	0.973084i	$0.574019\pi$
$500$	−0.589148	+	1.32325i	−0.0263475	+	0.0591774i
$501$	0.837979	−	1.88213i	0.0374381	−	0.0840874i
$502$	9.09218	+	1.93260i	0.405804	+	0.0862563i
$503$	12.9177	−	39.7565i	0.575971	−	1.77266i	−0.0568778	−	0.998381i	$-0.518115\pi$
$503$	12.9177	−	39.7565i	0.575971	−	1.77266i	0.632849	−	0.774275i	$-0.281885\pi$
$504$	−0.472002	−	3.39196i	−0.0210247	−	0.151090i
$505$		−	47.6394i		−	2.11993i
$506$	−1.08888	+	13.0832i	−0.0484064	+	0.581620i
$507$	−8.27057	+	4.77502i	−0.367309	+	0.212066i
$508$	7.35612	+	0.773160i	0.326375	+	0.0343034i
$509$	−25.1442	+	22.6399i	−1.11450	+	1.00350i	−0.114548	+	0.993418i	$0.536542\pi$
$509$	−25.1442	+	22.6399i	−1.11450	+	1.00350i	−0.999949	+	0.0100801i	$0.996791\pi$
$510$	34.4939	−	11.2077i	1.52742	−	0.496288i
$511$	26.1731	+	22.0226i	1.15783	+	0.974225i
$512$	10.8055	+	14.8725i	0.477539	+	0.657277i
$513$	−0.182206	+	0.857214i	−0.00804461	+	0.0378469i
$514$	6.83452	−	1.45272i	0.301458	−	0.0640768i
$515$	−2.49721	+	23.7593i	−0.110040	+	1.04696i
$516$	0.650469	−	1.12665i	0.0286353	−	0.0495978i
$517$	17.1907	+	18.2791i	0.756046	+	0.803913i
$518$	4.26917	−	1.05825i	0.187576	−	0.0464970i
$519$	−4.46109	+	6.14017i	−0.195820	+	0.269524i
$520$	−12.7681	−	14.1804i	−0.559917	−	0.621850i
$521$	−26.5133	−	23.8726i	−1.16157	−	1.04588i	−0.998240	−	0.0593074i	$-0.981111\pi$
$521$	−26.5133	−	23.8726i	−1.16157	−	1.04588i	−0.163327	−	0.986572i	$-0.552223\pi$
$522$	11.3031	+	5.03248i	0.494724	+	0.220265i
$523$	1.39519	+	13.2744i	0.0610075	+	0.580448i	0.981737	+	0.190245i	$0.0609283\pi$
$523$	1.39519	+	13.2744i	0.0610075	+	0.580448i	−0.920729	+	0.390202i	$0.872405\pi$
$524$	0.759115	+	2.33632i	0.0331621	+	0.102062i
$525$	11.0344	−	5.36326i	0.481581	−	0.234072i
$526$	−26.4621	−	19.2259i	−1.15380	−	0.838288i
$527$	−5.73780	−	3.31272i	−0.249942	−	0.144304i
$528$	−5.37586	−	15.4007i	−0.233954	−	0.670227i
$529$	9.11579	+	15.7890i	0.396339	+	0.686479i
$530$	28.8735	−	12.8553i	1.25419	−	0.558400i
$531$	12.5048	+	4.06306i	0.542663	+	0.176322i
$532$	−0.100002	−	2.97995i	−0.00433564	−	0.129197i
$533$	−30.2630	+	21.9873i	−1.31084	+	0.952378i
$534$	−1.76776	+	0.185799i	−0.0764983	+	0.00804029i
$535$	34.9990	−	38.8703i	1.51314	−	1.68051i
$536$	−1.42307	−	6.69500i	−0.0614671	−	0.289180i
$537$	−4.50128	−	10.1100i	−0.194245	−	0.436281i
$538$	−5.99654			−0.258529
$539$	−2.05834	−	23.1249i	−0.0886590	−	0.996062i
$540$	−3.99203			−0.171790
$541$	−9.03179	−	20.2857i	−0.388307	−	0.872151i	−0.996901	−	0.0786696i	$-0.974933\pi$
$541$	−9.03179	−	20.2857i	−0.388307	−	0.872151i	0.608594	−	0.793482i	$-0.291734\pi$
$542$	6.93631	+	32.6328i	0.297940	+	1.40170i
$543$	−7.94315	+	8.82176i	−0.340873	+	0.378578i
$544$	−40.5523	+	4.26222i	−1.73867	+	0.182741i
$545$	−5.70622	+	4.14581i	−0.244428	+	0.177587i
$546$	0.763849	+	22.7619i	0.0326897	+	0.974118i
$547$	−3.84507	−	1.24934i	−0.164403	−	0.0534178i	0.225659	−	0.974206i	$-0.427546\pi$
$547$	−3.84507	−	1.24934i	−0.164403	−	0.0534178i	−0.390062	+	0.920789i	$0.627546\pi$
$548$	19.3731	−	8.62545i	0.827577	−	0.368461i
$549$	−4.42630	−	7.66657i	−0.188910	−	0.327201i
$550$	22.1940	−	16.8721i	0.946356	−	0.719428i
$551$	−5.18029	−	2.99084i	−0.220688	−	0.127414i
$552$	2.28671	+	1.66139i	0.0973288	+	0.0707135i
$553$	−36.4371	+	17.7102i	−1.54946	+	0.753116i
$554$	9.83859	+	30.2801i	0.418001	+	1.28648i
$555$	0.297593	+	2.83141i	0.0126321	+	0.120187i
$556$	−15.6613	−	6.97286i	−0.664187	−	0.295715i
$557$	−5.41118	−	4.87225i	−0.229279	−	0.206444i	0.546482	−	0.837471i	$-0.315967\pi$
$557$	−5.41118	−	4.87225i	−0.229279	−	0.206444i	−0.775761	+	0.631027i	$0.782634\pi$
$558$	1.24688	+	1.38480i	0.0527845	+	0.0586231i
$559$	2.82377	−	3.88659i	0.119433	−	0.164385i
$560$	−39.2089	+	9.71921i	−1.65688	+	0.410712i
$561$	21.0004	+	3.98994i	0.886638	+	0.168455i
$562$	11.2066	−	19.4104i	0.472722	−	0.818778i
$563$	−1.96289	+	18.6756i	−0.0827259	+	0.787084i	0.871982	+	0.489538i	$0.162835\pi$
$563$	−1.96289	+	18.6756i	−0.0827259	+	0.787084i	−0.954708	+	0.297546i	$0.903832\pi$
$564$	−9.51646	+	2.02279i	−0.400715	+	0.0851747i
$565$	10.4383	−	49.1084i	0.439143	−	2.06601i
$566$	16.1446	+	22.2211i	0.678606	+	0.934021i
$567$	−2.02445	−	1.70341i	−0.0850188	−	0.0715366i
$568$	−0.0820933	+	0.0266737i	−0.00344456	+	0.00111921i
$569$	−14.8753	+	13.3938i	−0.623606	+	0.561498i	−0.919188	−	0.393820i	$-0.871153\pi$
$569$	−14.8753	+	13.3938i	−0.623606	+	0.561498i	0.295581	+	0.955318i	$0.404487\pi$
$570$	4.90460	+	0.515494i	0.205431	+	0.0215917i
$571$	−27.2074	+	15.7082i	−1.13859	+	0.657367i	−0.946082	−	0.323928i	$-0.894997\pi$
$571$	−27.2074	+	15.7082i	−1.13859	+	0.657367i	−0.192512	+	0.981295i	$0.561663\pi$
$572$	4.63939	+	19.7145i	0.193983	+	0.824304i
$573$		−	12.5578i		−	0.524612i
$574$	5.20701	+	37.4192i	0.217336	+	1.56185i
$575$	−3.12912	+	9.63043i	−0.130493	+	0.401617i
$576$	1.59616	+	0.339274i	0.0665065	+	0.0141364i
$577$	−0.123846	+	0.278163i	−0.00515577	+	0.0115801i	−0.916105	−	0.400938i	$-0.868684\pi$
$577$	−0.123846	+	0.278163i	−0.00515577	+	0.0115801i	0.910949	+	0.412519i	$0.135351\pi$
$578$	18.0931	−	40.6378i	0.752574	−	1.69031i
$579$	6.02024	+	1.27964i	0.250193	+	0.0531801i
$580$	8.42006	−	25.9143i	0.349624	−	1.07603i
$581$	−12.5972	−	16.1690i	−0.522620	−	0.670803i
$582$		−	5.01476i		−	0.207869i
$583$	18.5636	+	1.54499i	0.768827	+	0.0639872i
$584$	14.4926	−	8.36731i	0.599708	−	0.346242i
$585$	−14.6610	−	1.54093i	−0.606156	−	0.0637096i
$586$	−1.39955	+	1.26016i	−0.0578149	+	0.0520567i
$587$	−12.5764	+	4.08633i	−0.519084	+	0.168661i	−0.556830	−	0.830627i	$-0.687982\pi$
$587$	−12.5764	+	4.08633i	−0.519084	+	0.168661i	0.0377454	+	0.999287i	$0.487982\pi$
$588$	8.07978	+	3.96803i	0.333204	+	0.163639i
$589$	−0.529525	−	0.728828i	−0.0218187	−	0.0300308i
$590$	15.3835	−	72.3735i	0.633327	−	2.97957i
$591$	22.5234	−	4.78749i	0.926488	−	0.196931i
$592$	0.471474	−	4.48577i	0.0193775	−	0.184364i
$593$	−19.9072	+	34.4803i	−0.817490	+	1.41593i	0.0900360	+	0.995939i	$0.471302\pi$
$593$	−19.9072	+	34.4803i	−0.817490	+	1.41593i	−0.907526	+	0.419996i	$0.862032\pi$
$594$	−5.27058	−	2.89245i	−0.216255	−	0.118679i
$595$	14.6605	−	50.8660i	0.601023	−	2.08530i
$596$	−5.06897	+	6.97684i	−0.207633	+	0.285782i
$597$	−5.07991	−	5.64181i	−0.207907	−	0.230904i
$598$	−13.9690	−	12.5777i	−0.571233	−	0.514341i
$599$	15.1772	+	6.75730i	0.620122	+	0.276096i	0.692654	−	0.721270i	$-0.256441\pi$
$599$	15.1772	+	6.75730i	0.620122	+	0.276096i	−0.0725323	+	0.997366i	$0.523108\pi$
$600$	−0.627412	−	5.96942i	−0.0256140	−	0.243701i
$601$	−3.19577	−	9.83556i	−0.130358	−	0.401201i	0.864481	−	0.502665i	$-0.167647\pi$
$601$	−3.19577	−	9.83556i	−0.130358	−	0.401201i	−0.994839	+	0.101464i	$0.967647\pi$
$602$	−2.12101	−	4.36379i	−0.0864461	−	0.177855i
$603$	−4.27797	−	3.10813i	−0.174212	−	0.126573i
$604$	22.2174	+	12.8272i	0.904015	+	0.521933i
$605$	33.7744	−	5.03847i	1.37312	−	0.204843i
$606$	13.9089	+	24.0909i	0.565009	+	0.978625i
$607$	13.5436	−	6.02998i	0.549716	−	0.244749i	−0.113033	−	0.993591i	$-0.536056\pi$
$607$	13.5436	−	6.02998i	0.549716	−	0.244749i	0.662749	+	0.748842i	$0.269390\pi$
$608$	−5.27303	−	1.71331i	−0.213850	−	0.0694840i
$609$	15.3277	−	9.54883i	0.621110	−	0.386938i
$610$	−40.3025	+	29.2815i	−1.63180	+	1.18557i
$611$	−35.7305	+	3.75543i	−1.44550	+	0.151928i
$612$	−5.54578	+	6.15921i	−0.224175	+	0.248971i
$613$	4.52599	+	21.2931i	0.182803	+	0.860020i	0.969959	+	0.243267i	$0.0782190\pi$
$613$	4.52599	+	21.2931i	0.182803	+	0.860020i	−0.787157	+	0.616753i	$0.788448\pi$
$614$	11.8278	+	26.5657i	0.477332	+	1.07210i
$615$	−24.4543			−0.986092
$616$	−10.9796	−	2.90823i	−0.442381	−	0.117176i
$617$	−11.6663			−0.469669			−0.234835	−	0.972035i	$-0.575455\pi$
$617$	−11.6663			−0.469669			−0.234835	+	0.972035i	$0.575455\pi$
$618$	−5.67398	−	12.7440i	−0.228241	−	0.512638i
$619$	−1.58579	−	7.46057i	−0.0637384	−	0.299866i	0.934719	−	0.355388i	$-0.115651\pi$
$619$	−1.58579	−	7.46057i	−0.0637384	−	0.299866i	−0.998457	+	0.0555218i	$0.982318\pi$
$620$	2.74592	−	3.04965i	0.110279	−	0.122477i
$621$	2.17171	−	0.228256i	0.0871477	−	0.00915959i
$622$	−14.5538	+	10.5740i	−0.583556	+	0.423978i
$623$	−1.22109	+	2.28901i	−0.0489218	+	0.0917072i
$624$	22.2121	+	7.21715i	0.889196	+	0.288917i
$625$	−24.3757	+	10.8528i	−0.975029	+	0.434111i
$626$	−10.6971	−	18.5280i	−0.427544	−	0.740528i
$627$	2.38796	+	1.65705i	0.0953658	+	0.0661763i
$628$	4.36010	+	2.51730i	0.173987	+	0.100451i
$629$	4.78193	+	3.47427i	0.190668	+	0.138528i
$630$	−8.34238	+	12.3318i	−0.332368	+	0.491313i
$631$	−13.8240	−	42.5459i	−0.550325	−	1.69373i	−0.707981	−	0.706231i	$-0.750394\pi$
$631$	−13.8240	−	42.5459i	−0.550325	−	1.69373i	0.157656	−	0.987494i	$-0.449606\pi$
$632$	2.07180	+	19.7119i	0.0824118	+	0.784096i
$633$	11.7873	+	5.24804i	0.468503	+	0.208591i
$634$	−38.2272	−	34.4199i	−1.51820	−	1.36699i
$635$	11.9481	+	13.2698i	0.474147	+	0.526594i
$636$	−4.24526	+	5.84310i	−0.168335	+	0.231694i
$637$	28.1418	+	17.6916i	1.11502	+	0.700967i
$638$	29.8931	−	28.1132i	1.18348	−	1.11301i
$639$	−0.0333431	+	0.0577519i	−0.00131903	+	0.00228463i
$640$	−3.14604	+	29.9325i	−0.124358	+	1.18319i
$641$	47.6537	−	10.1291i	1.88221	−	0.400076i	0.884429	−	0.466676i	$-0.154548\pi$
$641$	47.6537	−	10.1291i	1.88221	−	0.400076i	0.997780	+	0.0665998i	$0.0212151\pi$
$642$	−6.35007	+	29.8747i	−0.250617	+	1.17906i
$643$	10.9067	+	15.0118i	0.430119	+	0.592008i	0.967981	−	0.251025i	$-0.0807677\pi$
$643$	10.9067	+	15.0118i	0.430119	+	0.592008i	−0.537862	+	0.843033i	$0.680768\pi$
$644$	−6.98484	+	2.53151i	−0.275241	+	0.0997557i
$645$	2.98688	−	0.970496i	0.117608	−	0.0382133i
$646$	7.60886	−	6.85105i	0.299367	−	0.269551i
$647$	19.9826	+	2.10026i	0.785598	+	0.0825696i	0.488829	−	0.872380i	$-0.337424\pi$
$647$	19.9826	+	2.10026i	0.785598	+	0.0825696i	0.296769	+	0.954949i	$0.404091\pi$
$648$	−1.12098	+	0.647196i	−0.0440361	+	0.0254243i
$649$	28.4700	−	33.0322i	1.11755	−	1.29663i
$650$			39.9167i			1.56566i
$651$	2.69381	−	0.374853i	0.105579	−	0.0146916i
$652$	−1.82651	+	5.62142i	−0.0715317	+	0.220152i
$653$	2.62340	+	0.557621i	0.102662	+	0.0218214i	0.258956	−	0.965889i	$-0.416622\pi$
$653$	2.62340	+	0.557621i	0.102662	+	0.0218214i	−0.156294	+	0.987711i	$0.549955\pi$
$654$	1.67517	−	3.76250i	0.0655044	−	0.147125i
$655$	−2.41209	+	5.41764i	−0.0942481	+	0.211685i
$656$	37.8961	+	8.05507i	1.47959	+	0.314498i
$657$	3.99514	−	12.2958i	0.155865	−	0.479704i
$658$	−13.6385	+	33.6246i	−0.531683	+	1.31082i
$659$			22.9520i			0.894082i	0.894513	+	0.447041i	$0.147522\pi$
$659$			22.9520i			0.894082i	−0.894513	+	0.447041i	$0.852478\pi$
$660$	−5.12170	+	12.2093i	−0.199362	+	0.475248i
$661$	−4.38323	+	2.53066i	−0.170488	+	0.0984312i	−0.582816	−	0.812604i	$-0.698049\pi$
$661$	−4.38323	+	2.53066i	−0.170488	+	0.0984312i	0.412328	+	0.911035i	$0.364716\pi$
$662$	−63.1169	−	6.63386i	−2.45311	−	0.257832i
$663$	−22.7446	+	20.4794i	−0.883328	+	0.795352i
$664$	−9.53703	+	3.09877i	−0.370108	+	0.120256i
$665$	4.63425	−	5.50764i	0.179708	−	0.213577i
$666$	−0.977151	−	1.34493i	−0.0378638	−	0.0521151i
$667$	−3.09888	+	14.5791i	−0.119989	+	0.564505i
$668$	2.59146	−	0.550831i	0.100266	−	0.0213123i
$669$	1.10348	−	10.4989i	0.0426630	−	0.405911i
$670$	−14.8783	+	25.7700i	−0.574800	+	0.995583i
$671$	−29.1265	+	3.70144i	−1.12442	+	0.142892i
$672$	12.0565	−	11.6112i	0.465091	−	0.447911i
$673$	−18.6232	+	25.6326i	−0.717871	+	0.988064i	0.281721	+	0.959496i	$0.409095\pi$
$673$	−18.6232	+	25.6326i	−0.717871	+	0.988064i	−0.999592	+	0.0285680i	$0.990905\pi$
$674$	10.5951	+	11.7670i	0.408106	+	0.453248i
$675$	−3.44608	−	3.10286i	−0.132640	−	0.119429i
$676$	−11.2190	−	4.99503i	−0.431501	−	0.192116i
$677$	−5.12553	−	48.7661i	−0.196990	−	1.87423i	−0.431489	−	0.902118i	$-0.642012\pi$
$677$	−5.12553	−	48.7661i	−0.196990	−	1.87423i	0.234499	−	0.972116i	$-0.424655\pi$
$678$	9.05918	+	27.8813i	0.347916	+	1.07077i
$679$	−6.06240	−	4.10116i	−0.232654	−	0.157388i
$680$	−20.9522	−	15.2227i	−0.803481	−	0.583763i
$681$	−6.18475	−	3.57077i	−0.237000	−	0.136832i
$682$	5.83501	−	2.03681i	0.223434	−	0.0779935i
$683$	−14.1467	−	24.5027i	−0.541307	−	0.937571i	−0.998829	−	0.0483729i	$-0.984596\pi$
$683$	−14.1467	−	24.5027i	−0.541307	−	0.937571i	0.457523	−	0.889198i	$-0.348737\pi$
$684$	−1.02952	+	0.458372i	−0.0393647	+	0.0175263i
$685$	48.6889	+	15.8200i	1.86031	+	0.604450i
$686$	29.1425	−	16.6671i	1.11266	−	0.636354i
$687$	−11.1500	+	8.10095i	−0.425399	+	0.309071i
$688$	−4.94836	+	0.520093i	−0.188654	+	0.0198284i
$689$	−17.8464	+	19.8204i	−0.679893	+	0.755098i
$690$	−2.55488	−	12.0198i	−0.0972626	−	0.457584i
$691$	−4.29930	−	9.65639i	−0.163553	−	0.367346i	0.813114	−	0.582104i	$-0.197770\pi$
$691$	−4.29930	−	9.65639i	−0.163553	−	0.367346i	−0.976667	+	0.214758i	$0.931104\pi$
$692$	−9.75984			−0.371013
$693$	−7.80708	+	4.00617i	−0.296567	+	0.152182i
$694$	−13.8616			−0.526177
$695$	−16.8332	−	37.8079i	−0.638518	−	1.43414i
$696$	−1.83689	−	8.64190i	−0.0696272	−	0.327570i
$697$	−33.9722	+	37.7299i	−1.28679	+	1.42912i
$698$	−31.4505	+	3.30558i	−1.19042	+	0.125118i
$699$	−4.65672	+	3.38330i	−0.176133	+	0.127968i
$700$	13.9201	+	7.42574i	0.526129	+	0.280667i
$701$	−34.1877	−	11.1083i	−1.29125	−	0.419553i	−0.418723	−	0.908114i	$-0.637522\pi$
$701$	−34.1877	−	11.1083i	−1.29125	−	0.419553i	−0.872530	+	0.488561i	$0.837522\pi$
$702$	7.86382	−	3.50120i	0.296801	−	0.132144i
$703$	0.401854	+	0.696031i	0.0151562	+	0.0262513i
$704$	3.08548	−	4.44644i	0.116288	−	0.167582i
$705$	−20.3403	−	11.7435i	−0.766059	−	0.442284i
$706$	−47.5629	−	34.5565i	−1.79005	−	1.30055i
$707$	40.4986	+	2.88733i	1.52311	+	0.108589i
$708$	5.22484	+	16.0804i	0.196362	+	0.604339i
$709$	−0.364684	−	3.46974i	−0.0136960	−	0.130309i	0.985537	−	0.169458i	$-0.0542018\pi$
$709$	−0.364684	−	3.46974i	−0.0136960	−	0.130309i	−0.999233	+	0.0391495i	$0.987535\pi$
$710$	0.342823	+	0.152635i	0.0128659	+	0.00572827i
$711$	11.3794	+	10.2461i	0.426762	+	0.384258i
$712$	0.849289	+	0.943231i	0.0318284	+	0.0353491i
$713$	−1.31944	+	1.81605i	−0.0494133	+	0.0680116i
$714$	7.43718	+	30.0028i	0.278330	+	1.12283i
$715$	−23.5225	+	42.8625i	−0.879693	+	1.60297i
$716$	7.11562	−	12.3246i	0.265923	−	0.460593i
$717$	0.115772	−	1.10150i	0.00432360	−	0.0411363i
$718$	37.3510	−	7.93920i	1.39393	−	0.296288i
$719$	−9.10830	+	42.8512i	−0.339682	+	1.59808i	0.394347	+	0.918962i	$0.370971\pi$
$719$	−9.10830	+	42.8512i	−0.339682	+	1.59808i	−0.734029	+	0.679118i	$0.762362\pi$
$720$	8.97435	+	12.3521i	0.334454	+	0.460337i
$721$	−20.0466	−	3.56289i	−0.746575	−	0.132689i
$722$	−31.4318	+	10.2128i	−1.16977	+	0.380082i
$723$	16.2096	−	14.5952i	0.602841	−	0.542800i
$724$	−15.1815	−	1.59564i	−0.564217	−	0.0593016i
$725$	27.4108	−	15.8256i	1.01801	−	0.587749i
$726$	−15.6084	+	12.4087i	−0.579282	+	0.460531i
$727$		−	5.89021i		−	0.218456i	−0.994017	−	0.109228i	$-0.965162\pi$
$727$		−	5.89021i		−	0.218456i	0.994017	−	0.109228i	$-0.0348378\pi$
$728$	12.8287	−	9.99478i	0.475462	−	0.370431i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−71.1636	−	15.1263i	−2.63388	−	0.559849i
$731$	2.65205	−	5.95661i	0.0980897	−	0.220313i
$732$	4.63024	−	10.3997i	0.171139	−	0.384384i
$733$	−9.53369	−	2.02645i	−0.352135	−	0.0748486i	0.0284484	−	0.999595i	$-0.490943\pi$
$733$	−9.53369	−	2.02645i	−0.352135	−	0.0748486i	−0.380583	+	0.924747i	$0.624277\pi$
$734$	16.4845	−	50.7341i	0.608454	−	1.87263i
$735$	8.08557	+	20.1704i	0.298241	+	0.743996i
$736$			13.8152i			0.509234i
$737$	−14.9945	+	9.09618i	−0.552330	+	0.335062i
$738$	12.3663	−	7.13970i	0.455211	−	0.262816i
$739$	24.7506	+	2.60140i	0.910467	+	0.0956939i	0.548168	−	0.836368i	$-0.315325\pi$
$739$	24.7506	+	2.60140i	0.910467	+	0.0956939i	0.362299	+	0.932062i	$0.381992\pi$
$740$	−2.72070	+	2.44973i	−0.100015	+	0.0900539i
$741$	−3.95790	+	1.28600i	−0.145397	+	0.0472424i
$742$	9.17844	+	25.3247i	0.336951	+	0.929700i
$743$	−9.31265	−	12.8178i	−0.341648	−	0.470238i	0.603274	−	0.797534i	$-0.293863\pi$
$743$	−9.31265	−	12.8178i	−0.341648	−	0.470238i	−0.944922	+	0.327296i	$0.893863\pi$
$744$	0.276648	−	1.30153i	0.0101424	−	0.0477163i
$745$	−20.3639	+	4.32847i	−0.746074	+	0.158583i
$746$	−0.810615	+	7.71249i	−0.0296787	+	0.282374i
$747$	−3.87356	+	6.70921i	−0.141726	+	0.245477i
$748$	11.7224	+	24.8635i	0.428612	+	0.909099i
$749$	30.9227	+	32.1087i	1.12989	+	1.17323i
$750$	1.20016	−	1.65188i	0.0438237	−	0.0603181i
$751$	−22.1532	−	24.6036i	−0.808381	−	0.897798i	0.188054	−	0.982159i	$-0.439782\pi$
$751$	−22.1532	−	24.6036i	−0.808381	−	0.897798i	−0.996435	+	0.0843603i	$0.973115\pi$
$752$	27.6525	+	24.8984i	1.00838	+	0.907953i
$753$	−4.68451	−	2.08568i	−0.170713	−	0.0760064i
$754$	6.14153	+	58.4327i	0.223661	+	2.12800i
$755$	19.1382	+	58.9013i	0.696510	+	2.14364i
$756$	0.241949	−	3.39366i	0.00879960	−	0.123426i
$757$	8.65274	+	6.28658i	0.314489	+	0.228490i	0.733820	−	0.679344i	$-0.237735\pi$
$757$	8.65274	+	6.28658i	0.314489	+	0.228490i	−0.419331	+	0.907833i	$0.637735\pi$
$758$	−35.1844	−	20.3137i	−1.27795	−	0.737827i
$759$	2.08816	−	6.93486i	0.0757953	−	0.251719i
$760$	−1.76074	−	3.04969i	−0.0638688	−	0.110624i
$761$	−10.7544	+	4.78817i	−0.389847	+	0.173571i	−0.592294	−	0.805722i	$-0.701777\pi$
$761$	−10.7544	+	4.78817i	−0.389847	+	0.173571i	0.202447	+	0.979293i	$0.435111\pi$
$762$	−9.91633	−	3.22201i	−0.359231	−	0.116721i
$763$	−3.17854	−	5.10217i	−0.115071	−	0.184711i
$764$	13.0645	−	9.49191i	0.472657	−	0.343405i
$765$	−19.8985	+	2.09142i	−0.719433	+	0.0756154i
$766$	14.5060	−	16.1105i	0.524122	−	0.582097i
$767$	12.9815	+	61.0730i	0.468733	+	2.20522i
$768$	−8.47565	−	19.0366i	−0.305839	−	0.686925i
$769$	10.0363			0.361918			0.180959	−	0.983491i	$-0.442080\pi$
$769$	10.0363			0.361918			0.180959	+	0.983491i	$0.442080\pi$
$770$	27.0129	+	41.3360i	0.973478	+	1.48965i
$771$	−3.85455			−0.138818
$772$	3.21916	+	7.23035i	0.115860	+	0.260226i
$773$	4.98497	+	23.4524i	0.179297	+	0.843526i	0.972195	+	0.234172i	$0.0752378\pi$
$773$	4.98497	+	23.4524i	0.179297	+	0.843526i	−0.792898	+	0.609354i	$0.791429\pi$
$774$	−1.22709	+	1.36282i	−0.0441070	+	0.0489857i
$775$	4.74077	−	0.498275i	0.170294	−	0.0178986i
$776$	−2.89697	+	2.10477i	−0.103995	+	0.0755570i
$777$	−2.42503	+	0.0813800i	−0.0869976	+	0.00291949i
$778$	3.04802	+	0.990363i	0.109277	+	0.0355062i
$779$	−6.30660	+	2.80788i	−0.225958	+	0.100603i
$780$	−9.47846	−	16.4172i	−0.339383	−	0.587829i
$781$	0.133851	+	0.176072i	0.00478958	+	0.00630034i
$782$	−22.0943	−	12.7561i	−0.790089	−	0.456158i
$783$	−5.52200	−	4.01197i	−0.197340	−	0.143376i
$784$	−5.88600	−	33.9208i	−0.210214	−	1.21146i
$785$	3.75580	+	11.5592i	0.134050	+	0.412565i
$786$	−0.361968	−	3.44389i	−0.0129110	−	0.122840i
$787$	2.06262	+	0.918336i	0.0735243	+	0.0327351i	0.443169	−	0.896438i	$-0.353854\pi$
$787$	2.06262	+	0.918336i	0.0735243	+	0.0327351i	−0.369645	+	0.929173i	$0.620521\pi$
$788$	22.0050	+	19.8134i	0.783897	+	0.705824i
$789$	12.0739	+	13.4095i	0.429843	+	0.477389i
$790$	50.6489	−	69.7122i	1.80201	−	2.48025i
$791$	41.1147	+	11.8500i	1.46187	+	0.421339i
$792$	0.541210	+	4.25876i	0.0192311	+	0.151329i
$793$	21.0191	−	36.4061i	0.746410	−	1.29282i
$794$	4.31123	−	41.0186i	0.153000	−	1.45569i
$795$	−17.0547	+	3.62509i	−0.604869	+	0.128569i
$796$	2.02975	−	9.54924i	0.0719427	−	0.338464i
$797$	5.21396	+	7.17641i	0.184688	+	0.254201i	0.891315	−	0.453385i	$-0.149784\pi$
$797$	5.21396	+	7.17641i	0.184688	+	0.254201i	−0.706627	+	0.707587i	$0.749784\pi$
$798$	−0.735482	+	4.13819i	−0.0260358	+	0.146490i
$799$	−46.3756	+	15.0684i	−1.64065	+	0.533080i
$800$	21.8019	−	19.6305i	0.770814	−	0.694044i
$801$	0.975198	+	0.102497i	0.0344569	+	0.00362157i
$802$	10.0965	−	5.82922i	0.356520	−	0.205837i
$803$	−32.4800	−	27.9941i	−1.14619	−	0.987889i
$804$		−	6.79986i		−	0.239812i
$805$	−16.6202	−	6.74134i	−0.585787	−	0.237601i
$806$	−2.73444	+	8.41574i	−0.0963165	+	0.296432i
$807$	3.23576	+	0.687781i	0.113904	+	0.0242110i
$808$	8.07926	−	18.1463i	0.284227	−	0.638385i
$809$	15.4139	−	34.6201i	0.541922	−	1.21718i	−0.410350	−	0.911928i	$-0.634593\pi$
$809$	15.4139	−	34.6201i	0.541922	−	1.21718i	0.952272	−	0.305250i	$-0.0987399\pi$
$810$	5.50438	+	1.16999i	0.193404	+	0.0411093i
$811$	12.7718	−	39.3076i	0.448479	−	1.38028i	−0.430144	−	0.902760i	$-0.641537\pi$
$811$	12.7718	−	39.3076i	0.448479	−	1.38028i	0.878623	−	0.477516i	$-0.158463\pi$
$812$	21.5196	+	8.72857i	0.755190	+	0.306313i
$813$		−	18.4043i		−	0.645468i
$814$	−5.36704	+	1.26302i	−0.188115	+	0.0442688i
$815$	−12.3573	+	7.13452i	−0.432859	+	0.249911i
$816$	31.5251	+	3.31342i	1.10360	+	0.115993i
$817$	0.658863	−	0.593243i	0.0230507	−	0.0207549i
$818$	26.2164	−	8.51821i	0.916633	−	0.297832i
$819$	2.19853	−	12.3700i	0.0768227	−	0.432243i
$820$	−18.4839	−	25.4409i	−0.645486	−	0.888435i
$821$	6.95650	−	32.7277i	0.242783	−	1.14221i	−0.672720	−	0.739897i	$-0.734874\pi$
$821$	6.95650	−	32.7277i	0.242783	−	1.14221i	0.915504	−	0.402309i	$-0.131792\pi$
$822$	−29.2404	+	6.21523i	−1.01988	+	0.216781i
$823$	−0.187018	+	1.77936i	−0.00651904	+	0.0620245i	−0.997298	−	0.0734654i	$-0.976594\pi$
$823$	−0.187018	+	1.77936i	−0.00651904	+	0.0620245i	0.990779	+	0.135490i	$0.0432608\pi$
$824$	−4.98060	+	8.62664i	−0.173507	+	0.300523i
$825$	−13.9111	+	6.55866i	−0.484323	+	0.228343i
$826$	60.5929	+	17.4640i	2.10830	+	0.607650i
$827$	12.7414	−	17.5371i	0.443063	−	0.609824i	−0.527826	−	0.849352i	$-0.676993\pi$
$827$	12.7414	−	17.5371i	0.443063	−	0.609824i	0.970889	+	0.239528i	$0.0769928\pi$
$828$	1.87896	+	2.08680i	0.0652984	+	0.0725213i
$829$	−32.1041	−	28.9067i	−1.11502	−	1.00397i	−0.999944	−	0.0106129i	$-0.996622\pi$
$829$	−32.1041	−	28.9067i	−1.11502	−	1.00397i	−0.115077	−	0.993357i	$-0.536712\pi$
$830$	39.8267	+	17.7320i	1.38241	+	0.615487i
$831$	−1.83593	−	17.4677i	−0.0636876	−	0.605947i
$832$	2.39457	+	7.36972i	0.0830167	+	0.255499i
$833$	42.3530	+	15.5459i	1.46744	+	0.538633i
$834$	19.5508	+	14.2045i	0.676990	+	0.491862i
$835$	5.53892	+	3.19790i	0.191682	+	0.110668i
$836$	0.0810419	+	3.73679i	0.00280289	+	0.129240i
$837$	−0.513988	−	0.890253i	−0.0177660	−	0.0307716i
$838$	−37.2005	+	16.5627i	−1.28507	+	0.572150i
$839$	4.43378	+	1.44062i	0.153071	+	0.0497358i	0.384550	−	0.923104i	$-0.374357\pi$
$839$	4.43378	+	1.44062i	0.153071	+	0.0497358i	−0.231479	+	0.972840i	$0.574357\pi$
$840$	10.6254	−	0.356570i	0.366611	−	0.0123028i
$841$	14.2293	−	10.3382i	0.490665	−	0.356489i
$842$	10.4538	−	1.09874i	0.360263	−	0.0378651i
$843$	−8.27342	+	9.18856i	−0.284952	+	0.316471i
$844$	3.44971	+	16.2296i	0.118744	+	0.558646i
$845$	−12.0585	−	27.0838i	−0.414824	−	0.931711i
$846$	13.7145			0.471515
$847$	2.23624	+	29.0172i	0.0768383	+	0.997044i
$848$	27.6233			0.948588
$849$	−6.16298	−	13.8423i	−0.211513	−	0.475066i
$850$	11.2640	+	52.9929i	0.386352	+	1.81764i
$851$	1.34002	−	1.48824i	0.0459353	−	0.0510163i
$852$	−0.0852844	+	0.00896375i	−0.00292180	+	0.000307093i
$853$	−28.1717	+	20.4679i	−0.964580	+	0.700808i	−0.954210	−	0.299138i	$-0.903301\pi$
$853$	−28.1717	+	20.4679i	−0.964580	+	0.700808i	−0.0103697	+	0.999946i	$0.503301\pi$
$854$	−22.4498	−	36.0362i	−0.768215	−	1.23313i
$855$	−2.58741	−	0.840701i	−0.0884876	−	0.0287514i
$856$	19.9235	−	8.87053i	0.680972	−	0.303188i
$857$	−10.0546	−	17.4150i	−0.343458	−	0.594886i	0.641615	−	0.767027i	$-0.278265\pi$
$857$	−10.0546	−	17.4150i	−0.343458	−	0.594886i	−0.985072	+	0.172141i	$0.944932\pi$
$858$	−0.619025	−	28.5429i	−0.0211332	−	0.974437i
$859$	3.52413	+	2.03466i	0.120242	+	0.0694216i	0.558915	−	0.829225i	$-0.311218\pi$
$859$	3.52413	+	2.03466i	0.120242	+	0.0694216i	−0.438673	+	0.898647i	$0.644551\pi$
$860$	3.26730	+	2.37383i	0.111414	+	0.0809470i
$861$	1.48212	−	20.7888i	0.0505107	−	0.708479i
$862$	1.88924	+	5.81448i	0.0643477	+	0.198042i
$863$	0.657209	+	6.25292i	0.0223716	+	0.212852i	0.999997	+	0.00249778i	$0.000795069\pi$
$863$	0.657209	+	6.25292i	0.0223716	+	0.212852i	−0.977625	+	0.210354i	$0.932538\pi$
$864$	−5.77962	−	2.57325i	−0.196627	−	0.0875439i
$865$	−17.5094	−	15.7655i	−0.595337	−	0.536044i
$866$	−7.01484	−	7.79077i	−0.238374	−	0.264741i
$867$	−14.4241	+	19.8531i	−0.489868	+	0.674246i
$868$	2.42611	+	2.51916i	0.0823474	+	0.0855058i
$869$	45.9365	−	21.6576i	1.55829	−	0.734684i
$870$	−19.2049	+	33.2639i	−0.651108	+	1.12775i
$871$	2.62475	−	24.9728i	0.0889363	−	0.846172i
$872$	−2.87665	+	0.611450i	−0.0974156	+	0.0207063i
$873$	−0.575174	+	2.70598i	−0.0194667	+	0.0915836i
$874$	−2.03901	−	2.80646i	−0.0689707	−	0.0949300i
$875$	−1.01546	−	2.80182i	−0.0343290	−	0.0947189i
$876$	15.8116	−	5.13750i	0.534224	−	0.173580i
$877$	−22.5276	+	20.2839i	−0.760702	+	0.684939i	−0.955199	−	0.295964i	$-0.904359\pi$
$877$	−22.5276	+	20.2839i	−0.760702	+	0.684939i	0.194497	+	0.980903i	$0.437693\pi$
$878$	−45.9261	−	4.82702i	−1.54993	−	0.162904i
$879$	0.899738	−	0.519464i	0.0303474	−	0.0175211i
$880$	49.2920	−	11.5998i	1.66163	−	0.391030i
$881$			43.6699i			1.47128i	0.677375	+	0.735638i	$0.263118\pi$
$881$			43.6699i			1.47128i	−0.677375	+	0.735638i	$0.736882\pi$
$882$	−9.97777	−	7.83932i	−0.335969	−	0.263964i
$883$	5.73185	−	17.6408i	0.192892	−	0.593661i	−0.807102	−	0.590411i	$-0.798966\pi$
$883$	5.73185	−	17.6408i	0.192892	−	0.593661i	0.999995	−	0.00324990i	$-0.00103448\pi$
$884$	−38.4972	−	8.18284i	−1.29480	−	0.275219i
$885$	−16.6019	+	37.2886i	−0.558068	+	1.25344i
$886$	12.7506	−	28.6384i	0.428366	−	0.962125i
$887$	−11.7847	−	2.50492i	−0.395692	−	0.0841068i	0.00576850	−	0.999983i	$-0.498164\pi$
$887$	−11.7847	−	2.50492i	−0.395692	−	0.0841068i	−0.401460	+	0.915877i	$0.631497\pi$
$888$	−0.366827	+	1.12898i	−0.0123099	+	0.0378860i
$889$	−12.0049	+	9.35294i	−0.402630	+	0.313688i
$890$		−	5.51801i		−	0.184964i
$891$	2.51227	+	2.16529i	0.0841643	+	0.0725400i
$892$	11.7566	−	6.78765i	0.393638	−	0.227267i
$893$	−6.59403	−	0.693060i	−0.220661	−	0.0231924i
$894$	9.03409	−	8.13433i	0.302145	−	0.272053i
$895$	32.6741	−	10.6165i	1.09218	−	0.354869i
$896$	−25.2552	−	4.48862i	−0.843716	−	0.149954i
$897$	6.09508	+	8.38916i	0.203509	+	0.280106i
$898$	8.74425	−	41.1385i	0.291799	−	1.37281i
$899$	6.86319	−	1.45882i	0.228900	−	0.0486542i
$900$	0.623313	−	5.93043i	0.0207771	−	0.197681i
$901$	−18.0995	+	31.3493i	−0.602983	+	1.04440i
$902$	−5.97049	−	46.9816i	−0.198796	−	1.56432i
$903$	0.643997	+	2.59799i	0.0214309	+	0.0864556i
$904$	12.3044	−	16.9356i	0.409239	−	0.563270i
$905$	−24.6585	−	27.3861i	−0.819677	−	0.910344i
$906$	−26.8749	−	24.1983i	−0.892859	−	0.803934i
$907$	−41.8611	−	18.6377i	−1.38997	−	0.618856i	−0.431000	−	0.902352i	$-0.641839\pi$
$907$	−41.8611	−	18.6377i	−1.38997	−	0.618856i	−0.958973	+	0.283496i	$0.908506\pi$
$908$	−0.959943	−	9.13325i	−0.0318568	−	0.303098i
$909$	−4.74214	−	14.5948i	−0.157287	−	0.484079i
$910$	−70.5222	−	5.02784i	−2.33779	−	0.166671i
$911$	−3.54994	−	2.57918i	−0.117615	−	0.0854521i	0.527423	−	0.849603i	$-0.323158\pi$
$911$	−3.54994	−	2.57918i	−0.117615	−	0.0854521i	−0.645038	+	0.764151i	$0.723158\pi$
$912$	3.73272	+	2.15509i	0.123603	+	0.0713620i
$913$	15.5499	+	20.4548i	0.514627	+	0.676954i
$914$	−35.5913	−	61.6459i	−1.17726	−	2.03907i
$915$	25.1059	−	11.1779i	0.829974	−	0.369528i
$916$	−16.8556	−	5.47671i	−0.556924	−	0.180956i
$917$	−4.45938	−	2.37889i	−0.147262	−	0.0785577i
$918$	9.45190	−	6.86721i	0.311959	−	0.226652i
$919$	46.9162	−	4.93109i	1.54762	−	0.162662i	0.708150	−	0.706062i	$-0.249530\pi$
$919$	46.9162	−	4.93109i	1.54762	−	0.162662i	0.839474	+	0.543401i	$0.182864\pi$
$920$	−5.87136	+	6.52081i	−0.193573	+	0.214985i
$921$	−3.33534	−	15.6916i	−0.109903	−	0.517054i
$922$	14.5398	+	32.6569i	0.478842	+	1.07550i
$923$	−0.316672			−0.0104234
$924$	−10.0688	−	5.09398i	−0.331240	−	0.167580i
$925$	−4.25271			−0.139828
$926$	21.9542	+	49.3100i	0.721460	+	1.62043i
$927$	1.60002	+	7.52748i	0.0525514	+	0.247235i
$928$	28.8947	−	32.0909i	0.948517	−	1.05343i
$929$	15.2932	−	1.60738i	0.501753	−	0.0527364i	0.149729	−	0.988727i	$-0.452160\pi$
$929$	15.2932	−	1.60738i	0.501753	−	0.0527364i	0.352025	+	0.935991i	$0.385493\pi$
$930$	−4.67999	+	3.40021i	−0.153463	+	0.111497i
$931$	4.40121	+	4.27341i	0.144244	+	0.140055i
$932$	−7.03960	−	2.28731i	−0.230590	−	0.0749232i
$933$	9.06609	−	4.03649i	0.296811	−	0.132149i
$934$	0.343649	+	0.595217i	0.0112445	+	0.0194761i
$935$	−19.1330	+	63.5414i	−0.625715	+	2.07803i
$936$	−5.32317	−	3.07333i	−0.173993	−	0.100455i
$937$	46.4005	+	33.7119i	1.51584	+	1.10132i	0.963502	+	0.267699i	$0.0862634\pi$
$937$	46.4005	+	33.7119i	1.51584	+	1.10132i	0.552336	+	0.833622i	$0.313737\pi$
$938$	−21.0055	−	14.2100i	−0.685855	−	0.463974i
$939$	3.64713	+	11.2247i	0.119019	+	0.366304i
$940$	−3.15704	−	30.0372i	−0.102971	−	0.979707i
$941$	−6.76253	−	3.01087i	−0.220452	−	0.0981516i	0.293539	−	0.955947i	$-0.405167\pi$
$941$	−6.76253	−	3.01087i	−0.220452	−	0.0981516i	−0.513991	+	0.857796i	$0.671834\pi$
$942$	−5.27411	−	4.74883i	−0.171840	−	0.154725i
$943$	11.5101	+	12.7833i	0.374820	+	0.416280i
$944$	38.0101	−	52.3165i	1.23712	−	1.70276i
$945$	5.91599	−	5.69747i	0.192447	−	0.185339i
$946$	2.59376	+	5.50145i	0.0843305	+	0.178868i
$947$	−12.3644	+	21.4158i	−0.401790	+	0.695921i	−0.993942	−	0.109906i	$-0.964945\pi$
$947$	−12.3644	+	21.4158i	−0.401790	+	0.695921i	0.592152	+	0.805826i	$0.298278\pi$
$948$	−2.05827	+	19.5831i	−0.0668494	+	0.636029i
$949$	60.0520	−	12.7644i	1.94937	−	0.414352i
$950$	−1.53160	+	7.20561i	−0.0496917	+	0.233781i
$951$	16.6797	+	22.9576i	0.540876	+	0.744452i
$952$	14.2108	−	16.8890i	0.460574	−	0.547376i
$953$	−54.7371	+	17.7852i	−1.77311	+	0.576118i	−0.998418	−	0.0562219i	$-0.982095\pi$
$953$	−54.7371	+	17.7852i	−1.77311	+	0.576118i	−0.774691	+	0.632340i	$0.782095\pi$
$954$	7.56604	−	6.81250i	0.244960	−	0.220563i
$955$	38.7707	+	4.07497i	1.25459	+	0.131863i
$956$	1.23345	−	0.712131i	0.0398925	−	0.0230320i
$957$	−19.3549	+	11.7413i	−0.625656	+	0.379544i
$958$			5.05829i			0.163426i
$959$	−16.3996	+	40.4319i	−0.529571	+	1.30562i
$960$	−1.56541	+	4.81784i	−0.0505234	+	0.155495i
$961$	−29.2889	−	6.22556i	−0.944804	−	0.200824i
$962$	3.21092	−	7.21185i	0.103524	−	0.232519i
$963$	6.85304	−	15.3922i	0.220836	−	0.496006i
$964$	27.4361	+	5.83172i	0.883657	+	0.187827i
$965$	−5.90427	+	18.1715i	−0.190065	+	0.584961i
$966$	10.3729	−	1.44343i	0.333743	−	0.0464415i
$967$		−	52.4804i		−	1.68766i	−0.536613	−	0.843828i	$-0.680297\pi$
$967$		−	52.4804i		−	1.68766i	0.536613	−	0.843828i	$-0.319703\pi$
$968$	13.7195	+	3.80866i	0.440960	+	0.122415i
$969$	−4.89156	+	2.82414i	−0.157140	+	0.0907246i
$970$	15.4824	+	1.62727i	0.497111	+	0.0522485i
$971$	−6.96032	+	6.26710i	−0.223367	+	0.201121i	−0.773215	−	0.634144i	$-0.781353\pi$
$971$	−6.96032	+	6.26710i	−0.223367	+	0.201121i	0.549847	+	0.835265i	$0.314686\pi$
$972$	−1.22300	+	0.397376i	−0.0392277	+	0.0127459i
$973$	33.1610	−	12.0185i	1.06309	−	0.385296i
$974$	−2.60983	−	3.59212i	−0.0836243	−	0.115099i
$975$	4.57830	−	21.5392i	0.146623	−	0.689807i
$976$	−42.5877	+	9.05230i	−1.36320	+	0.289757i
$977$	1.39433	−	13.2661i	0.0446085	−	0.424421i	−0.949313	−	0.314332i	$-0.898220\pi$
$977$	1.39433	−	13.2661i	0.0446085	−	0.424421i	0.993922	−	0.110089i	$-0.0351137\pi$
$978$	4.16600	−	7.21573i	0.133214	−	0.230734i
$979$	1.56464	−	2.85107i	0.0500061	−	0.0911205i
$980$	−14.8726	+	23.6577i	−0.475089	+	0.755716i
$981$	−1.33547	+	1.83812i	−0.0426384	+	0.0586867i
$982$	−33.3068	−	36.9910i	−1.06286	−	1.18043i
$983$	21.3605	+	19.2331i	0.681294	+	0.613440i	0.935339	−	0.353752i	$-0.115094\pi$
$983$	21.3605	+	19.2331i	0.681294	+	0.613440i	−0.254045	+	0.967192i	$0.581761\pi$
$984$	−9.31487	−	4.14725i	−0.296947	−	0.132209i
$985$	7.47202	+	71.0915i	0.238078	+	2.26517i
$986$	24.6424	+	75.8415i	0.784773	+	2.41528i
$987$	11.2160	−	16.5797i	0.357008	−	0.527736i
$988$	−4.32948	−	3.14555i	−0.137739	−	0.100073i
$989$	−1.91318	−	1.10457i	−0.0608355	−	0.0351234i
$990$	10.6403	−	15.3337i	0.338172	−	0.487336i
$991$	13.6535	+	23.6486i	0.433719	+	0.751224i	0.997190	−	0.0749122i	$-0.0238676\pi$
$991$	13.6535	+	23.6486i	0.433719	+	0.751224i	−0.563471	+	0.826136i	$0.690534\pi$
$992$	5.94131	−	2.64524i	0.188637	−	0.0839865i
$993$	33.2972	+	10.8189i	1.05666	+	0.343328i
$994$	−0.150534	+	0.282185i	−0.00477463	+	0.00895037i
$995$	19.0668	−	13.8528i	0.604457	−	0.439164i
$996$	−9.90774	+	1.04135i	−0.313939	+	0.0329963i
$997$	0.901057	−	1.00073i	0.0285368	−	0.0316933i	−0.728707	−	0.684825i	$-0.759879\pi$
$997$	0.901057	−	1.00073i	0.0285368	−	0.0316933i	0.757244	+	0.653132i	$0.226545\pi$
$998$	0.388913	+	1.82969i	0.0123108	+	0.0579179i
$999$	0.373015	+	0.837806i	0.0118017	+	0.0265070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.40.4	yes	128
3.2	odd	2		693.2.cg.c.271.13		128
7.3	odd	6	inner	231.2.ba.a.73.13	yes	128
11.8	odd	10	inner	231.2.ba.a.19.13	✓	128
21.17	even	6		693.2.cg.c.73.4		128
33.8	even	10		693.2.cg.c.19.4		128
77.52	even	30	inner	231.2.ba.a.52.4	yes	128
231.206	odd	30		693.2.cg.c.514.13		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.13	✓	128	11.8	odd	10	inner
231.2.ba.a.40.4	yes	128	1.1	even	1	trivial
231.2.ba.a.52.4	yes	128	77.52	even	30	inner
231.2.ba.a.73.13	yes	128	7.3	odd	6	inner
693.2.cg.c.19.4		128	33.8	even	10
693.2.cg.c.73.4		128	21.17	even	6
693.2.cg.c.271.13		128	3.2	odd	2
693.2.cg.c.514.13		128	231.206	odd	30

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

\(f(q)\)	\(=\)	\(q+(-0.737298 - 1.65600i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-0.860460 + 0.955638i) q^{4} +(-3.08737 + 0.324496i) q^{5} +(1.46652 - 1.06549i) q^{6} +(-0.0887369 - 2.64426i) q^{7} +(-1.23104 - 0.399989i) q^{8} +(-0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.737298 - 1.65600i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-0.860460 + 0.955638i) q^{4} +(-3.08737 + 0.324496i) q^{5} +(1.46652 - 1.06549i) q^{6} +(-0.0887369 - 2.64426i) q^{7} +(-1.23104 - 0.399989i) q^{8} +(-0.913545 + 0.406737i) q^{9} +(2.81368 + 4.87343i) q^{10} +(0.0719126 + 3.31585i) q^{11} +(-1.11365 - 0.642969i) q^{12} +(-3.84177 - 2.79121i) q^{13} +(-4.31347 + 2.09656i) q^{14} +(-0.959305 - 2.95244i) q^{15} +(0.514096 + 4.89130i) q^{16} +(-5.88792 - 2.62147i) q^{17} +(1.34711 + 1.21294i) q^{18} +(-0.586402 - 0.651266i) q^{19} +(2.34646 - 3.22962i) q^{20} +(2.56803 - 0.636571i) q^{21} +(5.43801 - 2.56385i) q^{22} +(-1.09184 + 1.89111i) q^{23} +(0.135301 - 1.28730i) q^{24} +(4.53583 - 0.964120i) q^{25} +(-1.78971 + 8.41991i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.60331 + 2.19048i) q^{28} +(6.49150 - 2.10922i) q^{29} +(-4.18194 + 3.76543i) q^{30} +(1.02234 + 0.107453i) q^{31} +(5.47898 - 3.16329i) q^{32} +(-3.22843 + 0.759744i) q^{33} +11.6832i q^{34} +(1.13202 + 8.13503i) q^{35} +(0.397376 - 1.22300i) q^{36} +(-0.897052 - 0.190674i) q^{37} +(-0.646142 + 1.45126i) q^{38} +(1.93147 - 4.33814i) q^{39} +(3.93047 + 0.835448i) q^{40} +(2.43424 - 7.49181i) q^{41} +(-2.94756 - 3.78331i) q^{42} +1.01167i q^{43} +(-3.23062 - 2.78443i) q^{44} +(2.68847 - 1.55219i) q^{45} +(3.93669 + 0.413763i) q^{46} +(5.62244 - 5.06247i) q^{47} +(-4.67752 + 1.51982i) q^{48} +(-6.98425 + 0.469288i) q^{49} +(-4.94083 - 6.80047i) q^{50} +(1.34002 - 6.30429i) q^{51} +(5.97307 - 1.26962i) q^{52} +(0.587084 - 5.58573i) q^{53} +(-0.906358 + 1.56986i) q^{54} +(-1.29800 - 10.2139i) q^{55} +(-0.948438 + 3.29069i) q^{56} +(0.515114 - 0.708994i) q^{57} +(-8.27903 - 9.19479i) q^{58} +(-9.77112 - 8.79796i) q^{59} +(3.64690 + 1.62371i) q^{60} +(0.925348 + 8.80410i) q^{61} +(-0.575831 - 1.77222i) q^{62} +(1.15658 + 2.37956i) q^{63} +(-1.32017 - 0.959157i) q^{64} +(12.7667 + 7.37086i) q^{65} +(3.63845 + 4.78612i) q^{66} +(2.64393 + 4.57942i) q^{67} +(7.57150 - 3.37105i) q^{68} +(-2.07679 - 0.674792i) q^{69} +(12.6370 - 7.87255i) q^{70} +(0.0539502 - 0.0391971i) q^{71} +(1.28730 - 0.135301i) q^{72} +(-8.65088 + 9.60778i) q^{73} +(0.345638 + 1.62610i) q^{74} +(1.88610 + 4.23626i) q^{75} +1.12695 q^{76} +(8.76158 - 0.484394i) q^{77} -8.60802 q^{78} +(-6.22817 - 13.9887i) q^{79} +(-3.17441 - 14.9344i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-14.2012 + 1.49260i) q^{82} +(6.26756 - 4.55365i) q^{83} +(-1.60136 + 3.00185i) q^{84} +(19.0289 + 6.18285i) q^{85} +(1.67532 - 0.745899i) q^{86} +(3.41278 + 5.91111i) q^{87} +(1.23778 - 4.11070i) q^{88} +(-0.849198 - 0.490285i) q^{89} +(-4.55262 - 3.30767i) q^{90} +(-7.03978 + 10.4063i) q^{91} +(-0.867740 - 2.67063i) q^{92} +(0.107453 + 1.02234i) q^{93} +(-12.5289 - 5.57820i) q^{94} +(2.02177 + 1.82041i) q^{95} +(4.23331 + 4.70157i) q^{96} +(1.62607 - 2.23809i) q^{97} +(5.92661 + 11.2199i) q^{98} +(-1.41437 - 2.99993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

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