LMFDB - Embedded newform 231.2.bc.a.185.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(5,231)]

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, 25, 12]))

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

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

chi := DirichletCharacter("231.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.bc (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			185.13
Character	$\chi$	$=$	231.185
Dual form			231.2.bc.a.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0876680 - 0.412446i) q^{2} +(1.04792 + 1.37908i) q^{3} +(1.66467 - 0.741157i) q^{4} +(-0.908673 + 1.00918i) q^{5} +(0.476926 - 0.553112i) q^{6} +(0.442873 + 2.60842i) q^{7} +(-0.947316 - 1.30387i) q^{8} +(-0.803721 + 2.89033i) q^{9} +O(q^{10})$	\(q+(-0.0876680 - 0.412446i) q^{2} +(1.04792 + 1.37908i) q^{3} +(1.66467 - 0.741157i) q^{4} +(-0.908673 + 1.00918i) q^{5} +(0.476926 - 0.553112i) q^{6} +(0.442873 + 2.60842i) q^{7} +(-0.947316 - 1.30387i) q^{8} +(-0.803721 + 2.89033i) q^{9} +(0.495895 + 0.286305i) q^{10} +(2.95381 - 1.50832i) q^{11} +(2.76655 + 1.51903i) q^{12} +(-3.13548 - 1.01878i) q^{13} +(1.03701 - 0.411336i) q^{14} +(-2.34396 - 0.195587i) q^{15} +(1.98386 - 2.20330i) q^{16} +(-2.94112 - 0.625154i) q^{17} +(1.26257 + 0.0781011i) q^{18} +(0.465506 - 1.04554i) q^{19} +(-0.764673 + 2.35342i) q^{20} +(-3.13312 + 3.34418i) q^{21} +(-0.881055 - 1.08605i) q^{22} +(3.33269 - 1.92413i) q^{23} +(0.805425 - 2.67277i) q^{24} +(0.329878 + 3.13858i) q^{25} +(-0.145310 + 1.38253i) q^{26} +(-4.82824 + 1.92045i) q^{27} +(2.67048 + 4.01391i) q^{28} +(3.79249 - 5.21991i) q^{29} +(0.124821 + 0.983903i) q^{30} +(3.22991 - 2.90822i) q^{31} +(-3.87415 - 2.23674i) q^{32} +(5.17545 + 2.49293i) q^{33} +1.26786i q^{34} +(-3.03480 - 1.92326i) q^{35} +(0.804265 + 5.40712i) q^{36} +(0.662661 - 6.30480i) q^{37} +(-0.472040 - 0.100335i) q^{38} +(-1.88076 - 5.39168i) q^{39} +(2.17664 + 0.228774i) q^{40} +(-4.28689 + 3.11461i) q^{41} +(1.65397 + 0.999066i) q^{42} -6.25696 q^{43} +(3.79919 - 4.70008i) q^{44} +(-2.18656 - 3.43747i) q^{45} +(-1.08577 - 1.20587i) q^{46} +(-5.02926 - 2.23917i) q^{47} +(5.11745 + 0.427015i) q^{48} +(-6.60773 + 2.31040i) q^{49} +(1.26557 - 0.411209i) q^{50} +(-2.21992 - 4.71115i) q^{51} +(-5.97460 + 0.627956i) q^{52} +(-0.249480 + 0.224633i) q^{53} +(1.21536 + 1.82302i) q^{54} +(-1.16187 + 4.35150i) q^{55} +(2.98150 - 3.04845i) q^{56} +(1.92970 - 0.453678i) q^{57} +(-2.48541 - 1.10658i) q^{58} +(3.27672 - 1.45889i) q^{59} +(-4.04687 + 1.41166i) q^{60} +(0.873372 + 0.786387i) q^{61} +(-1.48264 - 1.07720i) q^{62} +(-7.89516 - 0.816390i) q^{63} +(1.24947 - 3.84547i) q^{64} +(3.87726 - 2.23854i) q^{65} +(0.574476 - 2.35314i) q^{66} +(-7.25299 + 12.5625i) q^{67} +(-5.35931 + 1.13916i) q^{68} +(6.14593 + 2.57971i) q^{69} +(-0.527185 + 1.42030i) q^{70} +(-4.80261 + 1.56046i) q^{71} +(4.52999 - 1.69011i) q^{72} +(-3.55869 - 7.99295i) q^{73} +(-2.65848 + 0.279417i) q^{74} +(-3.98266 + 3.74391i) q^{75} -2.08549i q^{76} +(5.24250 + 7.03677i) q^{77} +(-2.05889 + 1.24839i) q^{78} +(-0.650943 + 0.138362i) q^{79} +(0.420853 + 4.00415i) q^{80} +(-7.70807 - 4.64604i) q^{81} +(1.66043 + 1.49506i) q^{82} +(-5.45930 - 16.8020i) q^{83} +(-2.73704 + 7.88907i) q^{84} +(3.30341 - 2.40007i) q^{85} +(0.548535 + 2.58065i) q^{86} +(11.1729 - 0.239916i) q^{87} +(-4.76484 - 2.42252i) q^{88} +(8.26950 + 14.3232i) q^{89} +(-1.22608 + 1.20319i) q^{90} +(1.26879 - 8.62984i) q^{91} +(4.12174 - 5.67308i) q^{92} +(7.39536 + 1.40671i) q^{93} +(-0.482631 + 2.27060i) q^{94} +(0.632153 + 1.41984i) q^{95} +(-0.975162 - 7.68670i) q^{96} +(3.82461 + 1.24269i) q^{97} +(1.53220 + 2.52278i) q^{98} +(1.98552 + 9.74975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9}+O(q^{10}) $ 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9	$ 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9} - 60 q^{10} - 12 q^{12} - 36 q^{15} + 18 q^{16} + 13 q^{18} - 18 q^{19} - 6 q^{21} + 20 q^{22} - 51 q^{24} - 18 q^{25} - 26 q^{28} - 15 q^{30} - 36 q^{31} + 60 q^{33} - 32 q^{36} - 10 q^{37} + 9 q^{39} - 114 q^{42} - 96 q^{43} + 24 q^{45} - 54 q^{46} - 56 q^{49} - 29 q^{51} - 30 q^{52} - 96 q^{54} + 68 q^{57} - 64 q^{58} + 125 q^{60} - 18 q^{61} - 26 q^{63} + 56 q^{64} + 135 q^{66} + 48 q^{67} - 44 q^{70} + 19 q^{72} + 30 q^{73} + 63 q^{75} + 28 q^{78} + 30 q^{79} + 31 q^{81} + 54 q^{82} + 99 q^{84} - 248 q^{85} + 102 q^{87} + 82 q^{88} - 144 q^{91} + 34 q^{93} + 162 q^{94} - 87 q^{96} - 100 q^{99}+O(q^{100}) $ 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9 - 60 * q^10 - 12 * q^12 - 36 * q^15 + 18 * q^16 + 13 * q^18 - 18 * q^19 - 6 * q^21 + 20 * q^22 - 51 * q^24 - 18 * q^25 - 26 * q^28 - 15 * q^30 - 36 * q^31 + 60 * q^33 - 32 * q^36 - 10 * q^37 + 9 * q^39 - 114 * q^42 - 96 * q^43 + 24 * q^45 - 54 * q^46 - 56 * q^49 - 29 * q^51 - 30 * q^52 - 96 * q^54 + 68 * q^57 - 64 * q^58 + 125 * q^60 - 18 * q^61 - 26 * q^63 + 56 * q^64 + 135 * q^66 + 48 * q^67 - 44 * q^70 + 19 * q^72 + 30 * q^73 + 63 * q^75 + 28 * q^78 + 30 * q^79 + 31 * q^81 + 54 * q^82 + 99 * q^84 - 248 * q^85 + 102 * q^87 + 82 * q^88 - 144 * q^91 + 34 * q^93 + 162 * q^94 - 87 * q^96 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.0876680	−	0.412446i	−0.0619906	−	0.291643i	0.936222	−	0.351410i	$-0.114298\pi$
$2$	−0.0876680	−	0.412446i	−0.0619906	−	0.291643i	−0.998212	+	0.0597668i	$0.980964\pi$
$3$	1.04792	+	1.37908i	0.605018	+	0.796212i
$3$	1.04792	+	1.37908i	0.605018	+	0.796212i
$4$	1.66467	−	0.741157i	0.832333	−	0.370578i
$5$	−0.908673	+	1.00918i	−0.406371	+	0.451320i	−0.911240	−	0.411875i	$-0.864874\pi$
$5$	−0.908673	+	1.00918i	−0.406371	+	0.451320i	0.504870	+	0.863196i	$0.331541\pi$
$6$	0.476926	−	0.553112i	0.194704	−	0.225807i
$7$	0.442873	+	2.60842i	0.167390	+	0.985891i
$7$	0.442873	+	2.60842i	0.167390	+	0.985891i
$8$	−0.947316	−	1.30387i	−0.334927	−	0.460987i
$9$	−0.803721	+	2.89033i	−0.267907	+	0.963445i
$10$	0.495895	+	0.286305i	0.156816	+	0.0905375i
$11$	2.95381	−	1.50832i	0.890606	−	0.454776i
$11$	2.95381	−	1.50832i	0.890606	−	0.454776i
$12$	2.76655	+	1.51903i	0.798635	+	0.438507i
$13$	−3.13548	−	1.01878i	−0.869626	−	0.282558i	−0.159982	−	0.987120i	$-0.551144\pi$
$13$	−3.13548	−	1.01878i	−0.869626	−	0.282558i	−0.709643	+	0.704561i	$0.751144\pi$
$14$	1.03701	−	0.411336i	0.277152	−	0.109934i
$15$	−2.34396	−	0.195587i	−0.605208	−	0.0505003i
$16$	1.98386	−	2.20330i	0.495965	−	0.550824i
$17$	−2.94112	−	0.625154i	−0.713326	−	0.151622i	−0.163065	−	0.986615i	$-0.552138\pi$
$17$	−2.94112	−	0.625154i	−0.713326	−	0.151622i	−0.550260	+	0.834993i	$0.685471\pi$
$18$	1.26257	+	0.0781011i	0.297590	+	0.0184086i
$19$	0.465506	−	1.04554i	0.106794	−	0.239864i	−0.852242	−	0.523148i	$-0.824757\pi$
$19$	0.465506	−	1.04554i	0.106794	−	0.239864i	0.959036	+	0.283284i	$0.0914240\pi$
$20$	−0.764673	+	2.35342i	−0.170986	+	0.526241i
$21$	−3.13312	+	3.34418i	−0.683704	+	0.729760i
$22$	−0.881055	−	1.08605i	−0.187841	−	0.231547i
$23$	3.33269	−	1.92413i	0.694915	−	0.401209i	−0.110536	−	0.993872i	$-0.535257\pi$
$23$	3.33269	−	1.92413i	0.694915	−	0.401209i	0.805451	+	0.592663i	$0.201923\pi$
$24$	0.805425	−	2.67277i	0.164407	−	0.545578i
$25$	0.329878	+	3.13858i	0.0659755	+	0.627715i
$26$	−0.145310	+	1.38253i	−0.0284976	+	0.271136i
$27$	−4.82824	+	1.92045i	−0.929195	+	0.369591i
$28$	2.67048	+	4.01391i	0.504674	+	0.758558i
$29$	3.79249	−	5.21991i	0.704247	−	0.969313i	−0.295655	−	0.955295i	$-0.595538\pi$
$29$	3.79249	−	5.21991i	0.704247	−	0.969313i	0.999902	−	0.0140181i	$-0.00446226\pi$
$30$	0.124821	+	0.983903i	0.0227892	+	0.179635i
$31$	3.22991	−	2.90822i	0.580108	−	0.522332i	−0.326004	−	0.945368i	$-0.605702\pi$
$31$	3.22991	−	2.90822i	0.580108	−	0.522332i	0.906113	+	0.423036i	$0.139036\pi$
$32$	−3.87415	−	2.23674i	−0.684860	−	0.395404i
$33$	5.17545	+	2.49293i	0.900931	+	0.433963i
$34$			1.26786i			0.217436i
$35$	−3.03480	−	1.92326i	−0.512975	−	0.325090i
$36$	0.804265	+	5.40712i	0.134044	+	0.901187i
$37$	0.662661	−	6.30480i	0.108941	−	1.03650i	−0.794346	−	0.607465i	$-0.792186\pi$
$37$	0.662661	−	6.30480i	0.108941	−	1.03650i	0.903287	−	0.429037i	$-0.141147\pi$
$38$	−0.472040	−	0.100335i	−0.0765750	−	0.0162765i
$39$	−1.88076	−	5.39168i	−0.301163	−	0.863359i
$40$	2.17664	+	0.228774i	0.344157	+	0.0361724i
$41$	−4.28689	+	3.11461i	−0.669500	+	0.486421i	−0.869858	−	0.493302i	$-0.835790\pi$
$41$	−4.28689	+	3.11461i	−0.669500	+	0.486421i	0.200357	+	0.979723i	$0.435790\pi$
$42$	1.65397	+	0.999066i	0.255213	+	0.154159i
$43$	−6.25696			−0.954177			−0.477088	−	0.878855i	$-0.658308\pi$
$43$	−6.25696			−0.954177			−0.477088	+	0.878855i	$0.658308\pi$
$44$	3.79919	−	4.70008i	0.572750	−	0.708564i
$45$	−2.18656	−	3.43747i	−0.325953	−	0.512428i
$46$	−1.08577	−	1.20587i	−0.160088	−	0.177796i
$47$	−5.02926	−	2.23917i	−0.733593	−	0.326617i	0.00571512	−	0.999984i	$-0.498181\pi$
$47$	−5.02926	−	2.23917i	−0.733593	−	0.326617i	−0.739309	+	0.673367i	$0.764847\pi$
$48$	5.11745	+	0.427015i	0.738640	+	0.0616343i
$49$	−6.60773	+	2.31040i	−0.943961	+	0.330057i
$50$	1.26557	−	0.411209i	0.178979	−	0.0581538i
$51$	−2.21992	−	4.71115i	−0.310851	−	0.659692i
$52$	−5.97460	+	0.627956i	−0.828528	+	0.0870818i
$53$	−0.249480	+	0.224633i	−0.0342687	+	0.0308557i	−0.686087	−	0.727519i	$-0.740673\pi$
$53$	−0.249480	+	0.224633i	−0.0342687	+	0.0308557i	0.651818	+	0.758375i	$0.274006\pi$
$54$	1.21536	+	1.82302i	0.165390	+	0.248082i
$55$	−1.16187	+	4.35150i	−0.156666	+	0.586756i
$56$	2.98150	−	3.04845i	0.398419	−	0.407366i
$57$	1.92970	−	0.453678i	0.255595	−	0.0600911i
$58$	−2.48541	−	1.10658i	−0.326350	−	0.145300i
$59$	3.27672	−	1.45889i	0.426593	−	0.189931i	−0.182199	−	0.983262i	$-0.558321\pi$
$59$	3.27672	−	1.45889i	0.426593	−	0.189931i	0.608791	+	0.793330i	$0.291655\pi$
$60$	−4.04687	+	1.41166i	−0.522449	+	0.182244i
$61$	0.873372	+	0.786387i	0.111824	+	0.100687i	0.723146	−	0.690695i	$-0.242695\pi$
$61$	0.873372	+	0.786387i	0.111824	+	0.100687i	−0.611322	+	0.791382i	$0.709362\pi$
$62$	−1.48264	−	1.07720i	−0.188296	−	0.136805i
$63$	−7.89516	−	0.816390i	−0.994696	−	0.102856i
$64$	1.24947	−	3.84547i	0.156184	−	0.480684i
$65$	3.87726	−	2.23854i	0.480915	−	0.277656i
$66$	0.574476	−	2.35314i	0.0707131	−	0.289652i
$67$	−7.25299	+	12.5625i	−0.886094	+	1.53476i	−0.0416384	+	0.999133i	$0.513258\pi$
$67$	−7.25299	+	12.5625i	−0.886094	+	1.53476i	−0.844455	+	0.535626i	$0.820076\pi$
$68$	−5.35931	+	1.13916i	−0.649912	+	0.138143i
$69$	6.14593	+	2.57971i	0.739883	+	0.310561i
$70$	−0.527185	+	1.42030i	−0.0630107	+	0.169758i
$71$	−4.80261	+	1.56046i	−0.569965	+	0.185193i	−0.579800	−	0.814759i	$-0.696869\pi$
$71$	−4.80261	+	1.56046i	−0.569965	+	0.185193i	0.00983534	+	0.999952i	$0.496869\pi$
$72$	4.52999	−	1.69011i	0.533865	−	0.199182i
$73$	−3.55869	−	7.99295i	−0.416513	−	0.935504i	−0.992969	−	0.118376i	$-0.962231\pi$
$73$	−3.55869	−	7.99295i	−0.416513	−	0.935504i	0.576456	−	0.817128i	$-0.304435\pi$
$74$	−2.65848	+	0.279417i	−0.309042	+	0.0324816i
$75$	−3.98266	+	3.74391i	−0.459878	+	0.432309i
$76$		−	2.08549i		−	0.239223i
$77$	5.24250	+	7.03677i	0.597438	+	0.801915i
$78$	−2.05889	+	1.24839i	−0.233123	+	0.141352i
$79$	−0.650943	+	0.138362i	−0.0732368	+	0.0155670i	−0.244384	−	0.969678i	$-0.578586\pi$
$79$	−0.650943	+	0.138362i	−0.0732368	+	0.0155670i	0.171148	+	0.985245i	$0.445253\pi$
$80$	0.420853	+	4.00415i	0.0470528	+	0.447678i
$81$	−7.70807	−	4.64604i	−0.856452	−	0.516227i
$82$	1.66043	+	1.49506i	0.183364	+	0.165102i
$83$	−5.45930	−	16.8020i	−0.599236	−	1.84426i	−0.532397	−	0.846495i	$-0.678709\pi$
$83$	−5.45930	−	16.8020i	−0.599236	−	1.84426i	−0.0668387	−	0.997764i	$-0.521291\pi$
$84$	−2.73704	+	7.88907i	−0.298636	+	0.860769i
$85$	3.30341	−	2.40007i	0.358305	−	0.260324i
$86$	0.548535	+	2.58065i	0.0591500	+	0.278279i
$87$	11.1729	−	0.239916i	1.19786	−	0.0257217i
$88$	−4.76484	−	2.42252i	−0.507933	−	0.258241i
$89$	8.26950	+	14.3232i	0.876565	+	1.51826i	0.855086	+	0.518486i	$0.173504\pi$
$89$	8.26950	+	14.3232i	0.876565	+	1.51826i	0.0214790	+	0.999769i	$0.493163\pi$
$90$	−1.22608	+	1.20319i	−0.129240	+	0.126828i
$91$	1.26879	−	8.62984i	0.133005	−	0.904653i
$92$	4.12174	−	5.67308i	0.429721	−	0.591460i
$93$	7.39536	+	1.40671i	0.766863	+	0.145869i
$94$	−0.482631	+	2.27060i	−0.0497796	+	0.234195i
$95$	0.632153	+	1.41984i	0.0648575	+	0.145672i
$96$	−0.975162	−	7.68670i	−0.0995271	−	0.784521i
$97$	3.82461	+	1.24269i	0.388331	+	0.126176i	0.496674	−	0.867937i	$-0.334555\pi$
$97$	3.82461	+	1.24269i	0.388331	+	0.126176i	−0.108343	+	0.994114i	$0.534555\pi$
$98$	1.53220	+	2.52278i	0.154776	+	0.254839i
$99$	1.98552	+	9.74975i	0.199552	+	0.979887i
$100$	2.87531	+	4.98019i	0.287531	+	0.498019i
$101$	7.10562	+	7.89159i	0.707036	+	0.785243i	0.984480	−	0.175499i	$-0.0561539\pi$
$101$	7.10562	+	7.89159i	0.707036	+	0.785243i	−0.277444	+	0.960742i	$0.589487\pi$
$102$	−1.74847	+	1.32861i	−0.173125	+	0.131552i
$103$	19.6329	+	2.06350i	1.93448	+	0.203322i	0.991556	−	0.129678i	$-0.0413944\pi$
$103$	19.6329	+	2.06350i	1.93448	+	0.203322i	0.942927	+	0.333001i	$0.108061\pi$
$104$	1.64193	+	5.05336i	0.161005	+	0.495522i
$105$	−0.527905	−	6.20066i	−0.0515182	−	0.605122i
$106$	0.114520	+	0.0832038i	0.0111232	+	0.00808147i
$107$	−3.20998	+	7.20974i	−0.310321	+	0.696992i	−0.999622	−	0.0274829i	$-0.991251\pi$
$107$	−3.20998	+	7.20974i	−0.310321	+	0.696992i	0.689302	+	0.724474i	$0.257917\pi$
$108$	−6.61404	+	6.77539i	−0.636437	+	0.651962i
$109$	1.82125	−	3.15449i	0.174444	−	0.302145i	−0.765525	−	0.643406i	$-0.777521\pi$
$109$	1.82125	−	3.15449i	0.174444	−	0.302145i	0.939969	+	0.341261i	$0.110854\pi$
$110$	1.89662	+	0.0977204i	0.180835	+	0.00931727i
$111$	9.38923	−	5.69307i	0.891187	−	0.540362i
$112$	6.62573	+	4.19896i	0.626072	+	0.396764i
$113$	−1.27793	−	1.75891i	−0.120217	−	0.165465i	0.744667	−	0.667436i	$-0.232608\pi$
$113$	−1.27793	−	1.75891i	−0.120217	−	0.165465i	−0.864884	+	0.501971i	$0.832608\pi$
$114$	−0.356291	−	0.756124i	−0.0333697	−	0.0708175i
$115$	−1.08653	+	5.11170i	−0.101319	+	0.476669i
$116$	2.44445	−	11.5002i	0.226961	−	1.06777i
$117$	5.46466	−	8.24377i	0.505208	−	0.762137i
$118$	−0.888976	−	1.22357i	−0.0818369	−	0.112639i
$119$	0.328123	−	7.94854i	0.0300789	−	0.728641i
$120$	1.96545	+	3.24150i	0.179420	+	0.295907i
$121$	6.44993	−	8.91058i	0.586357	−	0.810052i
$122$	0.247775	−	0.429159i	0.0224325	−	0.0388543i
$123$	−8.78763	−	2.64810i	−0.792354	−	0.238771i
$124$	3.22127	−	7.23508i	0.289278	−	0.649730i
$125$	−8.96033	−	6.51006i	−0.801436	−	0.582278i
$126$	0.355436	+	3.32789i	0.0316648	+	0.296472i
$127$	2.72311	+	8.38087i	0.241637	+	0.743682i	0.996171	+	0.0874216i	$0.0278627\pi$
$127$	2.72311	+	8.38087i	0.241637	+	0.743682i	−0.754534	+	0.656260i	$0.772137\pi$
$128$	−10.5936	−	1.11343i	−0.936346	−	0.0984140i
$129$	−6.55680	−	8.62884i	−0.577294	−	0.759727i
$130$	−1.26319	−	1.40291i	−0.110789	−	0.123043i
$131$	6.51430	+	11.2831i	0.569157	+	0.985809i	0.996650	+	0.0817902i	$0.0260638\pi$
$131$	6.51430	+	11.2831i	0.569157	+	0.985809i	−0.427492	+	0.904019i	$0.640603\pi$
$132$	10.4630	+	0.314072i	0.910691	+	0.0273365i
$133$	2.93338	+	0.751193i	0.254356	+	0.0651367i
$134$	5.81722	+	1.89013i	0.502531	+	0.163282i
$135$	2.44920	−	6.61763i	0.210794	−	0.569555i
$136$	1.97105	+	4.42705i	0.169016	+	0.379616i
$137$	−3.53336	+	16.6231i	−0.301875	+	1.42021i	0.521760	+	0.853092i	$0.325276\pi$
$137$	−3.53336	+	16.6231i	−0.301875	+	1.42021i	−0.823636	+	0.567119i	$0.808058\pi$
$138$	0.525189	−	2.76102i	0.0447070	−	0.235034i
$139$	−5.00893	+	6.89420i	−0.424852	+	0.584759i	−0.966762	−	0.255678i	$-0.917701\pi$
$139$	−5.00893	+	6.89420i	−0.424852	+	0.584759i	0.541910	+	0.840437i	$0.317701\pi$
$140$	−6.47737	−	0.952322i	−0.547437	−	0.0804859i
$141$	−2.18228	−	9.28223i	−0.183781	−	0.781705i
$142$	1.06464	+	1.84401i	0.0893426	+	0.154746i
$143$	−10.7982	+	1.72004i	−0.902994	+	0.143837i
$144$	4.77380	+	7.50485i	0.397817	+	0.625404i
$145$	1.82172	+	8.57050i	0.151285	+	0.711742i
$146$	−2.98467	+	2.16849i	−0.247013	+	0.179466i
$147$	−10.1106	−	6.69146i	−0.833909	−	0.551903i
$148$	−3.56973	−	10.9865i	−0.293430	−	0.903086i
$149$	16.8045	+	15.1308i	1.37668	+	1.23956i	0.940540	+	0.339683i	$0.110320\pi$
$149$	16.8045	+	15.1308i	1.37668	+	1.23956i	0.436136	+	0.899881i	$0.356347\pi$
$150$	1.89331	+	1.31441i	0.154588	+	0.107321i
$151$	−1.59640	−	15.1888i	−0.129913	−	1.23604i	−0.844138	−	0.536126i	$-0.819887\pi$
$151$	−1.59640	−	15.1888i	−0.129913	−	1.23604i	0.714224	−	0.699917i	$-0.246780\pi$
$152$	−1.80423	+	0.383501i	−0.146343	+	0.0311061i
$153$	4.17074	−	7.99836i	0.337184	−	0.646629i
$154$	2.44269	−	2.77915i	0.196837	−	0.223950i
$155$			5.90219i			0.474075i
$156$	−7.12691	−	7.58140i	−0.570610	−	0.606998i
$157$	8.63308	−	0.907374i	0.688995	−	0.0724163i	0.246441	−	0.969158i	$-0.420739\pi$
$157$	8.63308	−	0.907374i	0.688995	−	0.0724163i	0.442554	+	0.896742i	$0.354072\pi$
$158$	0.114134	+	0.256349i	0.00908000	+	0.0203940i
$159$	−0.571222	−	0.108655i	−0.0453008	−	0.00861691i
$160$	5.77762	−	1.87726i	0.456761	−	0.148411i
$161$	6.49491	+	7.84093i	0.511871	+	0.617952i
$162$	−1.24049	+	3.58647i	−0.0974620	+	0.281779i
$163$	−6.91268	+	1.46934i	−0.541443	+	0.115087i	−0.470511	−	0.882394i	$-0.655931\pi$
$163$	−6.91268	+	1.46934i	−0.541443	+	0.115087i	−0.0709315	+	0.997481i	$0.522597\pi$
$164$	−4.82783	+	8.36205i	−0.376990	+	0.652966i
$165$	−7.21861	+	2.95772i	−0.561968	+	0.230258i
$166$	−6.45130	+	3.72466i	−0.500718	+	0.289090i
$167$	−6.83342	+	21.0311i	−0.528786	+	1.62744i	0.227919	+	0.973680i	$0.426808\pi$
$167$	−6.83342	+	21.0311i	−0.528786	+	1.62744i	−0.756705	+	0.653756i	$0.773192\pi$
$168$	7.32842	+	0.917188i	0.565400	+	0.0707626i
$169$	−1.72390	−	1.25249i	−0.132608	−	0.0963452i
$170$	−1.27950	−	1.15207i	−0.0981331	−	0.0883594i
$171$	2.64783	+	2.18579i	0.202485	+	0.167152i
$172$	−10.4157	+	4.63739i	−0.794193	+	0.353597i
$173$	9.15192	+	4.07470i	0.695808	+	0.309794i	0.723991	−	0.689809i	$-0.242306\pi$
$173$	9.15192	+	4.07470i	0.695808	+	0.309794i	−0.0281834	+	0.999603i	$0.508972\pi$
$174$	−1.07846	−	4.58718i	−0.0817577	−	0.347753i
$175$	−8.04063	+	2.25045i	−0.607815	+	0.170118i
$176$	2.53665	−	9.50041i	0.191207	−	0.716120i
$177$	5.44567	+	2.99006i	0.409322	+	0.224746i
$178$	5.18257	−	4.66640i	0.388450	−	0.349762i
$179$	11.0715	−	1.16367i	0.827526	−	0.0869764i	0.318710	−	0.947852i	$-0.396750\pi$
$179$	11.0715	−	1.16367i	0.827526	−	0.0869764i	0.508815	+	0.860876i	$0.330084\pi$
$180$	−6.18759	−	4.10165i	−0.461196	−	0.305719i
$181$	−2.53533	+	0.823778i	−0.188449	+	0.0612309i	−0.401721	−	0.915762i	$-0.631588\pi$
$181$	−2.53533	+	0.823778i	−0.188449	+	0.0612309i	0.213272	+	0.976993i	$0.431588\pi$
$182$	−3.67057	+	0.233256i	−0.272081	+	0.0172901i
$183$	−0.169266	+	2.02852i	−0.0125125	+	0.149953i
$184$	−5.66593	−	2.52263i	−0.417698	−	0.185971i
$185$	5.76055	+	6.39774i	0.423524	+	0.470371i
$186$	−0.0681448	−	3.17351i	−0.00499662	−	0.232693i
$187$	−9.63042	+	2.58957i	−0.704246	+	0.189368i
$188$	−10.0316			−0.731631
$189$	−7.14764	−	11.7436i	−0.519914	−	0.854218i
$190$	0.530186	−	0.385203i	0.0384638	−	0.0279456i
$191$	−25.8401	−	2.71591i	−1.86973	−	0.196516i	−0.899205	−	0.437527i	$-0.855854\pi$
$191$	−25.8401	−	2.71591i	−1.86973	−	0.196516i	−0.970522	+	0.241011i	$0.922521\pi$
$192$	6.61256	−	2.30664i	0.477220	−	0.166467i
$193$	13.1952	+	2.80472i	0.949811	+	0.201889i	0.656668	−	0.754180i	$-0.271965\pi$
$193$	13.1952	+	2.80472i	0.949811	+	0.201889i	0.293143	+	0.956069i	$0.405299\pi$
$194$	0.177247	−	1.68639i	0.0127256	−	0.121076i
$195$	7.15018	+	3.00124i	0.512035	+	0.214923i
$196$	−9.28728	+	8.74340i	−0.663377	+	0.624529i
$197$		−	22.8743i		−	1.62972i	−0.579655	−	0.814862i	$-0.696813\pi$
$197$		−	22.8743i		−	1.62972i	0.579655	−	0.814862i	$-0.303187\pi$
$198$	3.84718	−	1.67366i	0.273407	−	0.118942i
$199$	−3.99450	−	2.30622i	−0.283162	−	0.163484i	0.351692	−	0.936116i	$-0.385607\pi$
$199$	−3.99450	−	2.30622i	−0.283162	−	0.163484i	−0.634854	+	0.772632i	$0.718940\pi$
$200$	3.77979	−	3.40334i	0.267272	−	0.240652i
$201$	−24.9253	+	3.16211i	−1.75810	+	0.223038i
$202$	2.63192	−	3.62252i	0.185181	−	0.254880i
$203$	15.2953	+	7.58065i	1.07352	+	0.532057i
$204$	−7.18713	−	6.19717i	−0.503199	−	0.433889i
$205$	0.752170	−	7.15642i	0.0525339	−	0.499826i
$206$	−0.870093	−	8.27839i	−0.0606223	−	0.576783i
$207$	2.88283	+	11.1791i	0.200371	+	0.776999i
$208$	−8.46502	+	4.88728i	−0.586944	+	0.338872i
$209$	−0.202002	−	3.79047i	−0.0139728	−	0.262192i
$210$	−2.51115	+	0.761331i	−0.173286	+	0.0525369i
$211$	−5.40686	+	16.6406i	−0.372224	+	1.14559i	0.573109	+	0.819479i	$0.305737\pi$
$211$	−5.40686	+	16.6406i	−0.372224	+	1.14559i	−0.945333	+	0.326108i	$0.894263\pi$
$212$	−0.248812	+	0.558842i	−0.0170885	+	0.0383814i
$213$	−7.18476	−	4.98793i	−0.492291	−	0.341768i
$214$	3.25504	+	0.691879i	0.222510	+	0.0472959i
$215$	5.68552	−	6.31441i	0.387750	−	0.430639i
$216$	7.07788	+	4.47611i	0.481588	+	0.304561i
$217$	9.01631	+	7.13699i	0.612067	+	0.484490i
$218$	−1.46072	−	0.474617i	−0.0989325	−	0.0321451i
$219$	7.29368	−	13.2837i	0.492861	−	0.897629i
$220$	1.29102	+	8.10492i	0.0870406	+	0.546434i
$221$	8.58492	+	4.95650i	0.577484	+	0.333411i
$222$	−3.17122	−	3.37345i	−0.212838	−	0.226411i
$223$	−9.14143	−	12.5821i	−0.612155	−	0.842559i	0.384597	−	0.923084i	$-0.374340\pi$
$223$	−9.14143	−	12.5821i	−0.612155	−	0.842559i	−0.996753	+	0.0805251i	$0.974340\pi$
$224$	4.11861	−	11.0960i	0.275186	−	0.741384i
$225$	−9.33666	−	1.56908i	−0.622444	−	0.104605i
$226$	−0.613423	+	0.681275i	−0.0408043	+	0.0453178i
$227$	−2.64760	+	1.17879i	−0.175727	+	0.0782387i	−0.492715	−	0.870191i	$-0.663995\pi$
$227$	−2.64760	+	1.17879i	−0.175727	+	0.0782387i	0.316988	+	0.948430i	$0.397329\pi$
$228$	2.87606	−	2.18543i	0.190472	−	0.144734i
$229$	−4.22319	−	19.8686i	−0.279076	−	1.31295i	−0.864668	−	0.502344i	$-0.832471\pi$
$229$	−4.22319	−	19.8686i	−0.279076	−	1.31295i	0.585591	−	0.810607i	$-0.300862\pi$
$230$	2.20355			0.145298
$231$	−4.21054	+	14.6038i	−0.277033	+	0.960860i
$232$	−10.3988			−0.682712
$233$	−0.745162	−	3.50571i	−0.0488172	−	0.229667i	0.946975	−	0.321307i	$-0.104122\pi$
$233$	−0.745162	−	3.50571i	−0.0488172	−	0.229667i	−0.995792	+	0.0916405i	$0.970789\pi$
$234$	−3.87918	−	1.53116i	−0.253590	−	0.100095i
$235$	6.82969	−	3.04077i	0.445520	−	0.198358i
$236$	4.37338	−	4.85713i	0.284683	−	0.316172i
$237$	−0.872950	−	0.752710i	−0.0567042	−	0.0488938i
$238$	−3.30710	+	0.561500i	−0.214368	+	0.0363966i
$239$	−6.08758	−	8.37884i	−0.393773	−	0.541982i	0.565395	−	0.824821i	$-0.308724\pi$
$239$	−6.08758	−	8.37884i	−0.393773	−	0.541982i	−0.959168	+	0.282839i	$0.908724\pi$
$240$	−5.08102	+	4.77643i	−0.327979	+	0.308317i
$241$	−3.89479	−	2.24866i	−0.250886	−	0.144849i	0.369284	−	0.929317i	$-0.379603\pi$
$241$	−3.89479	−	2.24866i	−0.250886	−	0.144849i	−0.620170	+	0.784468i	$0.712936\pi$
$242$	−4.24058	−	1.87907i	−0.272595	−	0.120791i
$243$	−1.67019	−	15.4987i	−0.107143	−	0.994244i
$244$	2.03671	+	0.661767i	0.130387	+	0.0423653i
$245$	3.67264	−	8.76780i	0.234637	−	0.560154i
$246$	−0.321803	+	3.85657i	−0.0205174	+	0.245886i
$247$	−2.52476	+	2.80403i	−0.160647	+	0.178416i
$248$	−6.85168	−	1.45637i	−0.435082	−	0.0924795i
$249$	17.4504	−	25.1360i	1.10587	−	1.59293i
$250$	−1.89951	+	4.26637i	−0.120136	+	0.269829i
$251$	8.19822	−	25.2315i	0.517467	−	1.59260i	−0.261281	−	0.965263i	$-0.584145\pi$
$251$	8.19822	−	25.2315i	0.517467	−	1.59260i	0.778748	−	0.627337i	$-0.215855\pi$
$252$	−13.7479	+	4.49253i	−0.866034	+	0.283003i
$253$	6.94192	−	10.7103i	0.436435	−	0.673350i
$254$	3.21792	−	1.85787i	0.201910	−	0.116573i
$255$	6.77159	+	2.04058i	0.424054	+	0.127786i
$256$	−0.375807	−	3.57556i	−0.0234879	−	0.223473i
$257$	−0.922608	+	8.77803i	−0.0575507	+	0.547558i	0.927320	+	0.374269i	$0.122106\pi$
$257$	−0.922608	+	8.77803i	−0.0575507	+	0.547558i	−0.984871	+	0.173289i	$0.944560\pi$
$258$	−2.98410	+	3.46080i	−0.185782	+	0.215460i
$259$	16.7390	−	1.06373i	1.04011	−	0.0660968i
$260$	4.79523	−	6.60007i	0.297388	−	0.409319i
$261$	12.0392	+	15.1569i	0.745207	+	0.938189i
$262$	4.08257	−	3.67596i	0.252222	−	0.227102i
$263$	3.61114	+	2.08489i	0.222672	+	0.128560i	0.607187	−	0.794559i	$-0.292298\pi$
$263$	3.61114	+	2.08489i	0.222672	+	0.128560i	−0.384515	+	0.923119i	$0.625631\pi$
$264$	−1.65233	−	9.10970i	−0.101694	−	0.560663i
$265$		−	0.455888i		−	0.0280050i
$266$	0.0526626	−	1.27571i	0.00322895	−	0.0782191i
$267$	−11.0870	+	26.4139i	−0.678515	+	1.61650i
$268$	−2.76298	+	26.2880i	−0.168776	+	1.60580i
$269$	−4.08769	−	0.868866i	−0.249231	−	0.0529757i	0.0816020	−	0.996665i	$-0.473996\pi$
$269$	−4.08769	−	0.868866i	−0.249231	−	0.0529757i	−0.330833	+	0.943689i	$0.607330\pi$
$270$	−2.94413	−	0.430007i	−0.179174	−	0.0261694i
$271$	−19.9154	−	2.09319i	−1.20977	−	0.127152i	−0.521916	−	0.852997i	$-0.674782\pi$
$271$	−19.9154	−	2.09319i	−1.20977	−	0.127152i	−0.687859	+	0.725845i	$0.741449\pi$
$272$	−7.21216	+	5.23994i	−0.437301	+	0.317718i
$273$	13.2308	−	7.29364i	0.800766	−	0.441431i
$274$	7.16591			0.432908
$275$	5.70838	+	8.77318i	0.344228	+	0.529043i
$276$	12.1429	−	0.260745i	0.730916	−	0.0156950i
$277$	15.8893	+	17.6468i	0.954694	+	1.06030i	0.998123	+	0.0612386i	$0.0195050\pi$
$277$	15.8893	+	17.6468i	0.954694	+	1.06030i	−0.0434292	+	0.999057i	$0.513828\pi$
$278$	3.28261	+	1.46151i	0.196878	+	0.0876556i
$279$	5.80979	+	11.6729i	0.347823	+	0.698839i
$280$	0.367236	+	5.77892i	0.0219466	+	0.345356i
$281$	−12.2348	+	3.97534i	−0.729869	+	0.237149i	−0.650297	−	0.759680i	$-0.725355\pi$
$281$	−12.2348	+	3.97534i	−0.729869	+	0.237149i	−0.0795724	+	0.996829i	$0.525355\pi$
$282$	−3.63710	+	1.71383i	−0.216586	+	0.102057i
$283$	6.32626	−	0.664917i	0.376057	−	0.0395252i	0.0853853	−	0.996348i	$-0.472788\pi$
$283$	6.32626	−	0.664917i	0.376057	−	0.0395252i	0.290672	+	0.956823i	$0.406121\pi$
$284$	−6.83819	+	6.15713i	−0.405772	+	0.365358i
$285$	−1.29562	+	2.35967i	−0.0767461	+	0.139775i
$286$	1.65608	+	4.30289i	0.0979262	+	0.254435i
$287$	−10.0228	−	9.80265i	−0.591625	−	0.578632i
$288$	9.57868	−	9.39989i	0.564429	−	0.553894i
$289$	−7.27092	−	3.23722i	−0.427701	−	0.190425i
$290$	3.37516	−	1.50272i	0.198196	−	0.0882426i
$291$	2.29412	+	6.57669i	0.134484	+	0.385532i
$292$	−11.8481	−	10.6680i	−0.693355	−	0.624300i
$293$	13.1261	+	9.53664i	0.766832	+	0.557136i	0.900998	−	0.433823i	$-0.142836\pi$
$293$	13.1261	+	9.53664i	0.766832	+	0.557136i	−0.134166	+	0.990959i	$0.542836\pi$
$294$	−1.87349	+	4.75670i	−0.109264	+	0.277416i
$295$	−1.50518	+	4.63247i	−0.0876349	+	0.269713i
$296$	−8.84837	+	5.10861i	−0.514301	+	0.296932i
$297$	−11.3650	+	12.9552i	−0.659465	+	0.751735i
$298$	4.76742	−	8.25741i	0.276169	−	0.478339i
$299$	−12.4099	+	2.63780i	−0.717681	+	0.152548i
$300$	−3.85497	+	9.18413i	−0.222567	+	0.530246i
$301$	−2.77104	−	16.3208i	−0.159720	−	0.940714i
$302$	−6.12458	+	1.99000i	−0.352430	+	0.114511i
$303$	−3.43700	+	18.0690i	−0.197450	+	1.03804i
$304$	−1.38015	−	3.09986i	−0.0791568	−	0.177789i
$305$	−1.58722	+	0.166823i	−0.0908838	+	0.00955228i
$306$	−3.66453	−	1.01900i	−0.209487	−	0.0582525i
$307$			18.6366i			1.06365i	0.846856	+	0.531823i	$0.178493\pi$
$307$			18.6366i			1.06365i	−0.846856	+	0.531823i	$0.821507\pi$
$308$	13.9424	+	7.82836i	0.794440	+	0.446062i
$309$	17.7280	+	29.2377i	1.00851	+	1.66327i
$310$	2.43433	−	0.517433i	0.138261	−	0.0293882i
$311$	0.982471	+	9.34758i	0.0557108	+	0.530053i	0.986414	+	0.164278i	$0.0525294\pi$
$311$	0.982471	+	9.34758i	0.0557108	+	0.530053i	−0.930703	+	0.365775i	$0.880804\pi$
$312$	−5.24836	+	7.55988i	−0.297130	+	0.427994i
$313$	−5.07897	−	4.57313i	−0.287081	−	0.258488i	0.512990	−	0.858395i	$-0.328538\pi$
$313$	−5.07897	−	4.57313i	−0.287081	−	0.258488i	−0.800070	+	0.599906i	$0.795205\pi$
$314$	−1.13109	−	3.48113i	−0.0638310	−	0.196451i
$315$	7.99800	−	7.22583i	0.450636	−	0.407129i
$316$	−0.981055	+	0.712778i	−0.0551886	+	0.0400969i
$317$	−0.988195	−	4.64909i	−0.0555025	−	0.261119i	0.941644	−	0.336611i	$-0.109281\pi$
$317$	−0.988195	−	4.64909i	−0.0555025	−	0.261119i	−0.997146	+	0.0754919i	$0.975947\pi$
$318$	0.00526354	+	0.245123i	0.000295165	+	0.0137458i
$319$	3.32896	−	21.1389i	0.186386	−	1.18355i
$320$	2.74543	+	4.75522i	0.153474	+	0.265825i
$321$	−13.3066	+	3.12842i	−0.742703	+	0.174611i
$322$	2.66456	−	3.36619i	0.148490	−	0.187591i
$323$	−2.02273	+	2.78405i	−0.112548	+	0.154909i
$324$	−16.2748	−	2.02122i	−0.904155	−	0.112290i
$325$	2.16319	−	10.1770i	0.119992	−	0.564519i
$326$	1.21204	+	2.72229i	0.0671288	+	0.150774i
$327$	6.25882	−	0.794016i	0.346113	−	0.0439092i
$328$	8.12208	+	2.63902i	0.448467	+	0.145716i
$329$	3.61338	−	14.1101i	0.199212	−	0.777915i
$330$	1.85274	+	2.71799i	0.101990	+	0.149620i
$331$	6.56985	+	11.3793i	0.361112	+	0.625464i	0.988144	−	0.153529i	$-0.0490640\pi$
$331$	6.56985	+	11.3793i	0.361112	+	0.625464i	−0.627032	+	0.778993i	$0.715731\pi$
$332$	−21.5408	−	23.9235i	−1.18221	−	1.31297i
$333$	17.6904	+	6.98261i	0.969427	+	0.382644i
$334$	9.27326	+	0.974659i	0.507410	+	0.0533310i
$335$	−6.08732	−	18.7348i	−0.332586	−	1.02359i
$336$	1.15255	+	13.5376i	0.0628766	+	0.738536i
$337$	20.2676	+	14.7253i	1.10405	+	0.802138i	0.981716	−	0.190351i	$-0.0609627\pi$
$337$	20.2676	+	14.7253i	1.10405	+	0.802138i	0.122332	+	0.992489i	$0.460963\pi$
$338$	−0.365452	+	0.820818i	−0.0198780	+	0.0446466i
$339$	1.08652	−	3.60557i	0.0590115	−	0.195827i
$340$	3.72024	−	6.44365i	0.201758	−	0.349456i
$341$	5.15398	−	13.4621i	0.279104	−	0.729011i
$342$	0.669390	−	1.28371i	0.0361965	−	0.0694152i
$343$	−8.95288	−	16.2125i	−0.483410	−	0.875394i
$344$	5.92731	+	8.15824i	0.319579	+	0.439863i
$345$	−8.18804	+	3.85826i	−0.440829	+	0.207722i
$346$	0.878261	−	4.13189i	0.0472156	−	0.222132i
$347$	−2.10314	+	9.89450i	−0.112903	+	0.531165i	0.884951	+	0.465684i	$0.154192\pi$
$347$	−2.10314	+	9.89450i	−0.112903	+	0.531165i	−0.997854	+	0.0654810i	$0.979142\pi$
$348$	18.4213	−	8.68025i	0.987487	−	0.465310i
$349$	−14.0704	−	19.3662i	−0.753169	−	1.03665i	−0.997752	−	0.0670199i	$-0.978651\pi$
$349$	−14.0704	−	19.3662i	−0.753169	−	1.03665i	0.244582	−	0.969628i	$-0.421349\pi$
$350$	1.63309	+	3.11903i	0.0872926	+	0.166719i
$351$	17.0954	−	1.10262i	0.912482	−	0.0588537i
$352$	−14.8172	−	0.763436i	−0.789761	−	0.0406913i
$353$	12.2572	−	21.2302i	0.652387	−	1.12997i	−0.330155	−	0.943927i	$-0.607101\pi$
$353$	12.2572	−	21.2302i	0.652387	−	1.12997i	0.982542	−	0.186041i	$-0.0595657\pi$
$354$	0.755824	−	2.50818i	0.0401716	−	0.133308i
$355$	2.78921	−	6.26466i	0.148036	−	0.332494i
$356$	24.3817	+	17.7143i	1.29223	+	0.938857i
$357$	11.3055	−	7.87694i	0.598351	−	0.416892i
$358$	−1.45057	−	4.46439i	−0.0766649	−	0.235950i
$359$	−21.9356	−	2.30553i	−1.15772	−	0.121681i	−0.493861	−	0.869541i	$-0.664415\pi$
$359$	−21.9356	−	2.30553i	−1.15772	−	0.121681i	−0.663857	+	0.747860i	$0.731082\pi$
$360$	−2.41065	+	6.10735i	−0.127052	+	0.321886i
$361$	11.8370	+	13.1463i	0.623001	+	0.691913i
$362$	0.562030	+	0.973465i	0.0295397	+	0.0511642i
$363$	19.0474	−	0.442617i	0.999730	−	0.0232314i
$364$	−4.28396	−	15.3062i	−0.224541	−	0.802261i
$365$	11.3000	+	3.67160i	0.591471	+	0.192181i
$366$	0.851494	−	0.108024i	0.0445083	−	0.00564648i
$367$	0.423524	+	0.951251i	0.0221078	+	0.0496549i	0.924262	−	0.381759i	$-0.124682\pi$
$367$	0.423524	+	0.951251i	0.0221078	+	0.0496549i	−0.902154	+	0.431414i	$0.858015\pi$
$368$	2.37216	−	11.1601i	0.123657	−	0.581762i
$369$	−5.55680	−	14.8938i	−0.289276	−	0.775342i
$370$	2.13370	−	2.93679i	0.110926	−	0.152677i
$371$	−0.696425	−	0.551265i	−0.0361566	−	0.0286203i
$372$	13.3534	−	3.13942i	0.692341	−	0.162771i
$373$	14.8606	+	25.7393i	0.769452	+	1.33273i	0.937860	+	0.347013i	$0.112804\pi$
$373$	14.8606	+	25.7393i	0.769452	+	1.33273i	−0.168408	+	0.985717i	$0.553863\pi$
$374$	1.91234	+	3.74500i	0.0988845	+	0.193649i
$375$	−0.411832	−	19.1790i	−0.0212669	−	0.990402i
$376$	1.84471	+	8.67870i	0.0951339	+	0.447570i
$377$	−17.2092	+	12.5032i	−0.886319	+	0.643948i
$378$	−4.21696	+	3.97755i	−0.216897	+	0.204583i
$379$	7.09953	+	21.8501i	0.364678	+	1.12236i	0.950182	+	0.311695i	$0.100897\pi$
$379$	7.09953	+	21.8501i	0.364678	+	1.12236i	−0.585504	+	0.810669i	$0.699103\pi$
$380$	2.10464	+	1.89503i	0.107966	+	0.0972130i
$381$	−8.70428	+	12.5379i	−0.445934	+	0.642335i
$382$	1.14519	+	10.8958i	0.0585930	+	0.557475i
$383$	−16.0890	+	3.41983i	−0.822111	+	0.174745i	−0.599717	−	0.800212i	$-0.704720\pi$
$383$	−16.0890	+	3.41983i	−0.822111	+	0.174745i	−0.222393	+	0.974957i	$0.571387\pi$
$384$	−9.56571	−	15.7761i	−0.488148	−	0.805072i
$385$	−11.8651	−	1.10348i	−0.604702	−	0.0562386i
$386$		−	5.68818i		−	0.289521i
$387$	5.02884	−	18.0847i	0.255631	−	0.919297i
$388$	7.28773	−	0.765971i	0.369978	−	0.0388863i
$389$	7.34867	+	16.5054i	0.372592	+	0.836856i	0.998382	+	0.0568639i	$0.0181101\pi$
$389$	7.34867	+	16.5054i	0.372592	+	0.836856i	−0.625790	+	0.779992i	$0.715223\pi$
$390$	0.611005	−	3.21217i	0.0309394	−	0.162655i
$391$	−11.0047	+	3.57565i	−0.556533	+	0.180828i
$392$	9.27206	+	6.42693i	0.468310	+	0.324609i
$393$	−8.73382	+	20.8075i	−0.440563	+	1.04960i
$394$	−9.43439	+	2.00534i	−0.475298	+	0.101028i
$395$	0.451861	−	0.782647i	0.0227356	−	0.0393792i
$396$	10.5313	+	14.7585i	0.529219	+	0.741642i
$397$	−4.08822	+	2.36034i	−0.205182	+	0.118462i	−0.599070	−	0.800696i	$-0.704463\pi$
$397$	−4.08822	+	2.36034i	−0.205182	+	0.118462i	0.393888	+	0.919158i	$0.371130\pi$
$398$	−0.601002	+	1.84969i	−0.0301255	+	0.0927168i
$399$	2.03800	+	4.83255i	0.102027	+	0.241930i
$400$	7.56965	+	5.49967i	0.378482	+	0.274984i
$401$	−3.62151	−	3.26083i	−0.180850	−	0.162838i	0.573734	−	0.819042i	$-0.305494\pi$
$401$	−3.62151	−	3.26083i	−0.180850	−	0.162838i	−0.754584	+	0.656204i	$0.772161\pi$
$402$	3.48935	+	10.0031i	0.174033	+	0.498910i
$403$	−13.0901	+	5.82811i	−0.652066	+	0.290319i
$404$	17.6774	+	7.87048i	0.879483	+	0.391571i
$405$	11.6928	−	3.55712i	0.581021	−	0.176755i
$406$	1.78569	−	6.97307i	0.0886225	−	0.346067i
$407$	−7.55229	−	19.6226i	−0.374353	−	0.972659i
$408$	−4.03974	+	7.35743i	−0.199997	+	0.364247i
$409$	−17.9448	+	16.1575i	−0.887311	+	0.798939i	−0.980461	−	0.196713i	$-0.936973\pi$
$409$	−17.9448	+	16.1575i	−0.887311	+	0.798939i	0.0931497	+	0.995652i	$0.470306\pi$
$410$	−3.01758	+	0.317160i	−0.149027	+	0.0156634i
$411$	−26.6273	+	12.5470i	−1.31343	+	0.618897i
$412$	34.2115	−	11.1160i	1.68548	−	0.547646i
$413$	5.25657	+	7.90097i	0.258659	+	0.388781i
$414$	4.35802	−	2.16906i	0.214185	−	0.106603i
$415$	21.9170	+	9.75808i	1.07586	+	0.479005i
$416$	9.86858	+	10.9602i	0.483847	+	0.537367i
$417$	−14.7566	+	0.316869i	−0.722635	+	0.0155172i
$418$	−1.54565	+	0.415617i	−0.0756003	+	0.0203285i
$419$	−40.2712			−1.96738			−0.983688	−	0.179886i	$-0.942427\pi$
$419$	−40.2712			−1.96738			−0.983688	+	0.179886i	$0.942427\pi$
$420$	−5.47444	−	9.93076i	−0.267126	−	0.484572i
$421$	21.9870	−	15.9745i	1.07158	−	0.778548i	0.0953843	−	0.995441i	$-0.469592\pi$
$421$	21.9870	−	15.9745i	1.07158	−	0.778548i	0.976196	+	0.216892i	$0.0695920\pi$
$422$	7.33735	+	0.771187i	0.357177	+	0.0375408i
$423$	10.5141	−	12.7366i	0.511212	−	0.619274i
$424$	0.529228	+	0.112491i	0.0257016	+	0.00546304i
$425$	0.991884	−	9.43714i	0.0481134	−	0.457769i
$426$	−1.42738	+	3.40060i	−0.0691567	+	0.164760i
$427$	−1.66444	+	2.62639i	−0.0805478	+	0.127100i
$428$			14.3809i			0.695127i
$429$	−13.6878	−	13.0892i	−0.660852	−	0.631951i
$430$	−3.10279	−	1.79140i	−0.149630	−	0.0863888i
$431$	20.1764	−	18.1669i	0.971865	−	0.875071i	−0.0203270	−	0.999793i	$-0.506471\pi$
$431$	20.1764	−	18.1669i	0.971865	−	0.875071i	0.992192	+	0.124723i	$0.0398041\pi$
$432$	−5.34722	+	14.4479i	−0.257268	+	0.695127i
$433$	5.28451	−	7.27351i	0.253957	−	0.349542i	−0.662935	−	0.748677i	$-0.730689\pi$
$433$	5.28451	−	7.27351i	0.253957	−	0.349542i	0.916892	+	0.399135i	$0.130689\pi$
$434$	2.15318	−	4.34442i	0.103356	−	0.208539i
$435$	−9.91039	+	11.4935i	−0.475167	+	0.551071i
$436$	0.693793	−	6.60100i	0.0332267	−	0.316131i
$437$	−0.460375	−	4.38017i	−0.0220227	−	0.209532i
$438$	−6.11823	−	1.84369i	−0.292340	−	0.0880950i
$439$	7.73048	−	4.46320i	0.368956	−	0.213017i	−0.304046	−	0.952657i	$-0.598338\pi$
$439$	7.73048	−	4.46320i	0.368956	−	0.213017i	0.673002	+	0.739641i	$0.265004\pi$
$440$	6.77444	−	2.60732i	0.322959	−	0.124299i
$441$	−1.36706	−	20.9555i	−0.0650982	−	0.997879i
$442$	1.29167	−	3.97534i	0.0614383	−	0.189088i
$443$	9.93326	−	22.3105i	0.471944	−	1.06000i	−0.508114	−	0.861290i	$-0.669657\pi$
$443$	9.93326	−	22.3105i	0.471944	−	1.06000i	0.980058	−	0.198713i	$-0.0636761\pi$
$444$	11.4105	−	16.4360i	0.541517	−	0.780016i
$445$	−21.9690	−	4.66965i	−1.04143	−	0.221363i
$446$	−4.38802	+	4.87339i	−0.207779	+	0.230762i
$447$	−3.25683	+	39.0306i	−0.154043	+	1.84608i
$448$	10.5840	+	1.55609i	0.500046	+	0.0735182i
$449$	−16.7594	−	5.44545i	−0.790924	−	0.256987i	−0.114426	−	0.993432i	$-0.536503\pi$
$449$	−16.7594	−	5.44545i	−0.790924	−	0.256987i	−0.676497	+	0.736445i	$0.736503\pi$
$450$	0.171366	+	3.98842i	0.00807827	+	0.188016i
$451$	−7.96482	+	15.6660i	−0.375049	+	0.737682i
$452$	−3.43095	−	1.98086i	−0.161378	−	0.0931718i
$453$	19.2736	−	18.1182i	0.905553	−	0.851267i
$454$	0.718294	+	0.988647i	0.0337112	+	0.0463995i
$455$	7.55618	+	9.12214i	0.354239	+	0.427652i
$456$	−2.41957	−	2.08630i	−0.113307	−	0.0977000i
$457$	−2.86109	+	3.17756i	−0.133836	+	0.148640i	−0.806337	−	0.591456i	$-0.798553\pi$
$457$	−2.86109	+	3.17756i	−0.133836	+	0.148640i	0.672501	+	0.740096i	$0.265220\pi$
$458$	−7.82446	+	3.48367i	−0.365613	+	0.162781i
$459$	15.4010	−	2.62988i	0.718856	−	0.122752i
$460$	1.97987	+	9.31456i	0.0923120	+	0.434294i
$461$	−7.87785			−0.366908			−0.183454	−	0.983028i	$-0.558728\pi$
$461$	−7.87785			−0.366908			−0.183454	+	0.983028i	$0.558728\pi$
$462$	6.39241	+	0.456332i	0.297402	+	0.0212305i
$463$	−36.9233			−1.71597			−0.857986	−	0.513673i	$-0.828285\pi$
$463$	−36.9233			−1.71597			−0.857986	+	0.513673i	$0.828285\pi$
$464$	−3.97726	−	18.7115i	−0.184640	−	0.868662i
$465$	−8.13959	+	6.18503i	−0.377464	+	0.286824i
$466$	−1.38059	+	0.614678i	−0.0639546	+	0.0284744i
$467$	22.6736	−	25.1816i	1.04921	−	1.16527i	0.0632999	−	0.997995i	$-0.479838\pi$
$467$	22.6736	−	25.1816i	1.04921	−	1.16527i	0.985911	−	0.167272i	$-0.0534958\pi$
$468$	2.98691	−	17.7733i	0.138070	−	0.821571i
$469$	−35.9806	−	13.3552i	−1.66143	−	0.616688i
$470$	−1.85290	−	2.55030i	−0.0854678	−	0.117636i
$471$	10.2981	+	10.9549i	0.474513	+	0.504773i
$472$	−5.00629	−	2.89038i	−0.230433	−	0.133041i
$473$	−18.4818	+	9.43750i	−0.849795	+	0.433937i
$474$	−0.233922	+	0.426033i	−0.0107444	+	0.0195683i
$475$	3.43508	+	1.11612i	0.157612	+	0.0512113i
$476$	−5.34490	−	13.4748i	−0.244983	−	0.617618i
$477$	−0.448752	−	0.901622i	−0.0205469	−	0.0412825i
$478$	−2.92213	+	3.24535i	−0.133655	+	0.148439i
$479$	13.5439	+	2.87884i	0.618835	+	0.131538i	0.506653	−	0.862150i	$-0.330883\pi$
$479$	13.5439	+	2.87884i	0.618835	+	0.131538i	0.112182	+	0.993688i	$0.464216\pi$
$480$	8.64339	+	6.00058i	0.394515	+	0.273888i
$481$	−8.50095	+	19.0935i	−0.387610	+	0.870587i
$482$	−0.586001	+	1.80353i	−0.0266916	+	0.0821484i
$483$	−4.00710	+	17.1737i	−0.182330	+	0.781429i
$484$	4.13284	−	19.6135i	0.187857	−	0.891524i
$485$	−4.72942	+	2.73053i	−0.214752	+	0.123987i
$486$	−6.24596	+	2.04760i	−0.283322	+	0.0928812i
$487$	−0.969085	−	9.22023i	−0.0439134	−	0.417808i	−0.994290	−	0.106708i	$-0.965969\pi$
$487$	−0.969085	−	9.22023i	−0.0439134	−	0.417808i	0.950377	−	0.311101i	$-0.100698\pi$
$488$	0.197987	−	1.88372i	0.00896244	−	0.0852719i
$489$	−9.27028	−	7.99339i	−0.419216	−	0.361473i
$490$	−3.93821	−	0.746109i	−0.177910	−	0.0337058i
$491$	11.2368	−	15.4661i	0.507108	−	0.697974i	−0.476320	−	0.879272i	$-0.658030\pi$
$491$	11.2368	−	15.4661i	0.507108	−	0.697974i	0.983428	+	0.181298i	$0.0580297\pi$
$492$	−16.5911	+	2.10481i	−0.747985	+	0.0948921i
$493$	−14.4174	+	12.9815i	−0.649327	+	0.584656i
$494$	1.37785	+	0.795503i	0.0619925	+	0.0357914i
$495$	−11.6435	−	6.85558i	−0.523335	−	0.308135i
$496$		−	12.8859i		−	0.578596i
$497$	−6.19729	−	11.8361i	−0.277986	−	0.530923i
$498$	−11.8971	−	4.99371i	−0.533120	−	0.223773i
$499$	2.23875	−	21.3003i	0.100220	−	0.953531i	−0.822683	−	0.568500i	$-0.807524\pi$
$499$	2.23875	−	21.3003i	0.100220	−	0.953531i	0.922903	−	0.385031i	$-0.125809\pi$
$500$	−19.7409	−	4.19606i	−0.882841	−	0.187654i
$501$	−36.1645	+	12.6151i	−1.61571	+	0.563602i
$502$	−11.1254	−	1.16932i	−0.496549	−	0.0521894i
$503$	21.0872	−	15.3208i	0.940232	−	0.683119i	−0.00824425	−	0.999966i	$-0.502624\pi$
$503$	21.0872	−	15.3208i	0.940232	−	0.683119i	0.948477	+	0.316847i	$0.102624\pi$
$504$	6.41474	+	11.0676i	0.285735	+	0.492991i
$505$	−14.4207			−0.641715
$506$	−5.02599	−	1.92421i	−0.223433	−	0.0855418i
$507$	−0.0792334	−	3.68990i	−0.00351888	−	0.163874i
$508$	10.7446	+	11.9331i	0.476715	+	0.529445i
$509$	−10.9232	−	4.86330i	−0.484160	−	0.215562i	0.150116	−	0.988668i	$-0.452035\pi$
$509$	−10.9232	−	4.86330i	−0.484160	−	0.215562i	−0.634276	+	0.773106i	$0.718702\pi$
$510$	0.247976	−	2.97181i	0.0109806	−	0.131594i
$511$	19.2729	−	12.8224i	0.852584	−	0.567231i
$512$	−21.7029	+	7.05170i	−0.959142	+	0.311644i
$513$	−0.239660	+	5.94211i	−0.0105812	+	0.262351i
$514$	3.70134	−	0.389027i	0.163259	−	0.0171592i
$515$	−19.9223	+	17.9381i	−0.877881	+	0.790447i
$516$	−17.3102	−	9.50451i	−0.762039	−	0.418413i
$517$	−18.2329	+	0.971667i	−0.801880	+	0.0427339i
$518$	−1.90621	−	6.81069i	−0.0837540	−	0.299245i
$519$	3.97117	+	16.8912i	0.174315	+	0.741441i
$520$	−6.59174	−	2.93483i	−0.289067	−	0.128701i
$521$	7.48198	−	3.33119i	0.327792	−	0.145942i	−0.236242	−	0.971694i	$-0.575916\pi$
$521$	7.48198	−	3.33119i	0.327792	−	0.145942i	0.564033	+	0.825752i	$0.309249\pi$
$522$	5.19595	−	6.29428i	0.227420	−	0.275493i
$523$	−5.69938	−	5.13174i	−0.249216	−	0.224395i	0.535049	−	0.844821i	$-0.320293\pi$
$523$	−5.69938	−	5.13174i	−0.249216	−	0.224395i	−0.784265	+	0.620426i	$0.786960\pi$
$524$	19.2067	+	13.9545i	0.839048	+	0.609604i
$525$	−11.5295	−	8.73038i	−0.503189	−	0.381025i
$526$	0.543323	−	1.67218i	0.0236900	−	0.0729104i
$527$	−11.3176	+	6.53423i	−0.493003	+	0.284636i
$528$	15.7600	−	6.45744i	0.685867	−	0.281024i
$529$	−4.09543	+	7.09350i	−0.178062	+	0.308413i
$530$	−0.188029	+	0.0399668i	−0.00816747	+	0.00173605i
$531$	1.58311	+	10.6434i	0.0687012	+	0.461882i
$532$	5.43985	−	0.923609i	0.235847	−	0.0400435i
$533$	16.6146	−	5.39840i	0.719657	−	0.233831i
$534$	11.8663	+	2.25715i	0.513503	+	0.0976762i
$535$	−4.35912	−	9.79075i	−0.188461	−	0.423291i
$536$	23.2508	−	2.44375i	1.00428	−	0.105554i
$537$	13.2069	+	14.0491i	0.569919	+	0.606263i
$538$			1.76212i			0.0759705i
$539$	−16.0331	+	16.7910i	−0.690595	+	0.723242i
$540$	−0.827604	−	12.8314i	−0.0356144	−	0.552175i
$541$	8.39203	−	1.78378i	0.360801	−	0.0766907i	−0.0239444	−	0.999713i	$-0.507622\pi$
$541$	8.39203	−	1.78378i	0.360801	−	0.0766907i	0.384746	+	0.923023i	$0.374289\pi$
$542$	0.882615	+	8.39752i	0.0379116	+	0.360705i
$543$	−3.79288	−	2.63316i	−0.162768	−	0.113000i
$544$	9.99603	+	9.00047i	0.428576	+	0.385892i
$545$	1.52854	+	4.70437i	0.0654756	+	0.201513i
$546$	−4.16815	−	4.81758i	−0.178380	−	0.206173i
$547$	−1.09951	+	0.798839i	−0.0470116	+	0.0341559i	−0.611043	−	0.791597i	$-0.709250\pi$
$547$	−1.09951	+	0.798839i	−0.0470116	+	0.0341559i	0.564031	+	0.825753i	$0.309250\pi$
$548$	6.43850	+	30.2908i	0.275039	+	1.29396i
$549$	−2.97487	+	1.89230i	−0.126964	+	0.0807614i
$550$	3.11802	−	3.12352i	0.132953	−	0.133187i
$551$	−3.69222	−	6.39511i	−0.157294	−	0.272441i
$552$	−2.45854	−	10.4573i	−0.104642	−	0.445092i
$553$	−0.649192	−	1.63666i	−0.0276065	−	0.0695978i
$554$	5.88537	−	8.10052i	0.250046	−	0.344158i
$555$	−2.78639	+	14.6486i	−0.118276	+	0.621798i
$556$	−3.22851	+	15.1889i	−0.136919	+	0.644155i
$557$	−2.18804	−	4.91441i	−0.0927101	−	0.208230i	0.861238	−	0.508202i	$-0.169690\pi$
$557$	−2.18804	−	4.91441i	−0.0927101	−	0.208230i	−0.953948	+	0.299971i	$0.903023\pi$
$558$	4.30511	−	3.41956i	0.182250	−	0.144762i
$559$	19.6186	+	6.37446i	0.829777	+	0.269611i
$560$	−10.2581	+	2.87109i	−0.433485	+	0.121326i
$561$	−13.6631	−	10.5674i	−0.576858	−	0.446158i
$562$	2.71222	+	4.69769i	0.114408	+	0.198160i
$563$	15.2340	+	16.9190i	0.642035	+	0.713052i	0.973055	−	0.230571i	$-0.0740595\pi$
$563$	15.2340	+	16.9190i	0.642035	+	0.713052i	−0.331020	+	0.943624i	$0.607393\pi$
$564$	−10.5123	−	13.8344i	−0.442650	−	0.582533i
$565$	2.93628	+	0.308616i	0.123530	+	0.0129836i
$566$	−0.828852	−	2.55095i	−0.0348393	−	0.107224i
$567$	8.70514	−	22.1635i	0.365582	−	0.930779i
$568$	6.58422	+	4.78372i	0.276268	+	0.200720i
$569$	12.2642	−	27.5459i	0.514142	−	1.15478i	−0.450873	−	0.892588i	$-0.648887\pi$
$569$	12.2642	−	27.5459i	0.514142	−	1.15478i	0.965015	−	0.262194i	$-0.0844460\pi$
$570$	1.08682	+	0.327507i	0.0455218	+	0.0137177i
$571$	9.77351	−	16.9282i	0.409009	−	0.708424i	−0.585770	−	0.810477i	$-0.699208\pi$
$571$	9.77351	−	16.9282i	0.409009	−	0.708424i	0.994779	+	0.102053i	$0.0325413\pi$
$572$	−16.7006	+	10.8665i	−0.698289	+	0.454350i
$573$	−23.3330	−	38.4817i	−0.974750	−	1.60760i
$574$	−3.16438	+	4.99323i	−0.132079	+	0.208413i
$575$	7.13842	+	9.82519i	0.297692	+	0.409739i
$576$	10.1105	+	6.70207i	0.421270	+	0.279253i
$577$	−6.36614	+	29.9503i	−0.265026	+	1.24685i	0.621221	+	0.783635i	$0.286637\pi$
$577$	−6.36614	+	29.9503i	−0.265026	+	1.24685i	−0.886247	+	0.463213i	$0.846696\pi$
$578$	−0.697751	+	3.28266i	−0.0290226	+	0.136541i
$579$	9.95959	+	21.1364i	0.413906	+	0.878397i
$580$	9.38463	+	12.9168i	0.389676	+	0.536343i
$581$	41.4089	−	21.6813i	1.71793	−	0.899492i
$582$	2.51141	−	1.52277i	0.104101	−	0.0631207i
$583$	−0.398097	+	1.03982i	−0.0164875	+	0.0430648i
$584$	−7.05055	+	12.2119i	−0.291754	+	0.505332i
$585$	3.35389	+	13.0057i	0.138666	+	0.537721i
$586$	2.78261	−	6.24984i	0.114949	−	0.258179i
$587$	−16.3273	−	11.8625i	−0.673900	−	0.489617i	0.197428	−	0.980317i	$-0.436741\pi$
$587$	−16.3273	−	11.8625i	−0.673900	−	0.489617i	−0.871329	+	0.490700i	$0.836741\pi$
$588$	−21.7902	−	3.64550i	−0.898613	−	0.150338i
$589$	−1.53713	−	4.73080i	−0.0633364	−	0.194929i
$590$	2.04260	+	0.214685i	0.0840923	+	0.00883846i
$591$	31.5454	−	23.9704i	1.29761	−	0.986012i
$592$	−12.5767	−	13.9679i	−0.516900	−	0.574076i
$593$	−4.31511	−	7.47400i	−0.177201	−	0.306920i	0.763720	−	0.645548i	$-0.223371\pi$
$593$	−4.31511	−	7.47400i	−0.177201	−	0.306920i	−0.940921	+	0.338627i	$0.890037\pi$
$594$	6.33965	+	3.55170i	0.260119	+	0.145728i
$595$	7.72337	+	7.55375i	0.316627	+	0.309674i
$596$	39.1881	+	12.7330i	1.60521	+	0.521564i
$597$	−1.00545	−	7.92547i	−0.0411505	−	0.324368i
$598$	2.17590	+	4.88714i	0.0889790	+	0.199850i
$599$	2.24091	−	10.5427i	0.0915611	−	0.430761i	−0.908360	−	0.418189i	$-0.862665\pi$
$599$	2.24091	−	10.5427i	0.0915611	−	0.430761i	0.999921	−	0.0125718i	$-0.00400183\pi$
$600$	8.65440	+	1.64620i	0.353314	+	0.0672058i
$601$	−7.11614	+	9.79453i	−0.290274	+	0.399527i	−0.929103	−	0.369821i	$-0.879419\pi$
$601$	−7.11614	+	9.79453i	−0.290274	+	0.399527i	0.638829	+	0.769348i	$0.279419\pi$
$602$	−6.48850	+	2.57371i	−0.264452	+	0.104897i
$603$	−30.4806	−	31.0603i	−1.24127	−	1.26487i
$604$	−13.9147	−	24.1010i	−0.566182	−	0.980656i
$605$	3.13153	+	14.6060i	0.127315	+	0.593817i
$606$	7.75379	−	0.166497i	0.314976	−	0.00676349i
$607$	1.12936	+	5.31323i	0.0458394	+	0.215657i	0.995106	−	0.0988159i	$-0.0315055\pi$
$607$	1.12936	+	5.31323i	0.0458394	+	0.215657i	−0.949266	+	0.314473i	$0.898172\pi$
$608$	−4.14206	+	3.00938i	−0.167983	+	0.122046i
$609$	5.57398	+	29.0374i	0.225869	+	1.17665i
$610$	0.207954	+	0.640016i	0.00841980	+	0.0259135i
$611$	13.4879	+	12.1446i	0.545663	+	0.491317i
$612$	1.01484	−	16.4058i	0.0410227	−	0.663164i
$613$	1.14766	+	10.9193i	0.0463536	+	0.441025i	0.992944	+	0.118586i	$0.0378361\pi$
$613$	1.14766	+	10.9193i	0.0463536	+	0.441025i	−0.946590	+	0.322439i	$0.895497\pi$
$614$	7.68658	−	1.63383i	0.310205	−	0.0659361i
$615$	10.6575	−	6.46207i	0.429752	−	0.260576i
$616$	4.20872	−	13.5016i	0.169574	−	0.543994i
$617$			27.3242i			1.10003i	0.835154	+	0.550015i	$0.185378\pi$
$617$			27.3242i			1.10003i	−0.835154	+	0.550015i	$0.814622\pi$
$618$	10.5048	−	9.87503i	0.422564	−	0.397232i
$619$	40.9453	−	4.30353i	1.64573	−	0.172973i	0.764161	−	0.645026i	$-0.223153\pi$
$619$	40.9453	−	4.30353i	1.64573	−	0.172973i	0.881570	+	0.472053i	$0.156487\pi$
$620$	4.37445	+	9.82517i	0.175682	+	0.394588i
$621$	−12.3958	+	15.6904i	−0.497428	+	0.629636i
$622$	3.76924	−	1.22470i	0.151133	−	0.0491060i
$623$	−33.6986	+	27.9137i	−1.35011	+	1.11834i
$624$	−15.6106	−	6.55245i	−0.624925	−	0.262308i
$625$	−0.722651	+	0.153604i	−0.0289060	+	0.00614417i
$626$	−1.44090	+	2.49572i	−0.0575901	+	0.0997489i
$627$	5.01567	−	4.25069i	0.200307	−	0.169756i
$628$	13.6987	−	7.90894i	0.546637	−	0.315601i
$629$	−5.89043	+	18.1289i	−0.234867	+	0.722846i
$630$	−3.68143	−	2.66527i	−0.146672	−	0.106187i
$631$	−1.95104	−	1.41751i	−0.0776696	−	0.0564303i	0.548273	−	0.836300i	$-0.315286\pi$
$631$	−1.95104	−	1.41751i	−0.0776696	−	0.0564303i	−0.625942	+	0.779869i	$0.715286\pi$
$632$	0.797055	+	0.717671i	0.0317051	+	0.0285474i
$633$	−28.6147	+	9.98156i	−1.13733	+	0.396732i
$634$	−1.83086	+	0.815153i	−0.0727129	+	0.0323739i
$635$	−10.9322	−	4.86735i	−0.433833	−	0.193155i
$636$	−1.03142	+	0.242490i	−0.0408986	+	0.00961537i
$637$	23.0722	−	0.512398i	0.914153	−	0.0203020i
$638$	−9.01048	+	0.480188i	−0.356728	+	0.0190108i
$639$	−0.650302	−	15.1353i	−0.0257255	−	0.598744i
$640$	10.7497	−	9.67909i	0.424920	−	0.382600i
$641$	−11.9628	+	1.25734i	−0.472501	+	0.0496619i	−0.337787	−	0.941223i	$-0.609678\pi$
$641$	−11.9628	+	1.25734i	−0.472501	+	0.0496619i	−0.134714	+	0.990884i	$0.543012\pi$
$642$	2.45687	+	5.21399i	0.0969648	+	0.205780i
$643$	20.0587	−	6.51748i	0.791040	−	0.257024i	0.114493	−	0.993424i	$-0.463476\pi$
$643$	20.0587	−	6.51748i	0.791040	−	0.257024i	0.676547	+	0.736400i	$0.263476\pi$
$644$	16.6232	+	8.23877i	0.655046	+	0.324653i
$645$	14.6661	+	1.22378i	0.577476	+	0.0481862i
$646$	1.32560	+	0.590195i	0.0521550	+	0.0232209i
$647$	−7.73868	−	8.59467i	−0.304239	−	0.337892i	0.571567	−	0.820556i	$-0.306336\pi$
$647$	−7.73868	−	8.59467i	−0.304239	−	0.337892i	−0.875806	+	0.482664i	$0.839669\pi$
$648$	1.24415	+	14.4516i	0.0488746	+	0.567711i
$649$	7.47832	−	9.25163i	0.293550	−	0.363158i
$650$	−4.38711			−0.172076
$651$	−0.394089	+	19.9132i	−0.0154456	+	0.780460i
$652$	−10.4183	+	7.56933i	−0.408012	+	0.296438i
$653$	−0.0477949	−	0.00502345i	−0.00187036	−	0.000196583i	0.103593	−	0.994620i	$-0.466966\pi$
$653$	−0.0477949	−	0.00502345i	−0.00187036	−	0.000196583i	−0.105464	+	0.994423i	$0.533633\pi$
$654$	−0.876186	−	2.51181i	−0.0342616	−	0.0982196i
$655$	−17.3061	−	3.67852i	−0.676205	−	0.143732i
$656$	−1.64218	+	15.6243i	−0.0641162	+	0.610025i
$657$	25.9625	−	3.86171i	1.01289	−	0.150660i
$658$	−6.13643	−	0.253317i	−0.239223	−	0.00987533i
$659$			13.2804i			0.517331i	0.965967	+	0.258665i	$0.0832827\pi$
$659$			13.2804i			0.517331i	−0.965967	+	0.258665i	$0.916717\pi$
$660$	−9.82444	+	10.2737i	−0.382416	+	0.399905i
$661$	12.5289	+	7.23356i	0.487318	+	0.281353i	0.723461	−	0.690365i	$-0.242550\pi$
$661$	12.5289	+	7.23356i	0.487318	+	0.281353i	−0.236143	+	0.971718i	$0.575883\pi$
$662$	4.11738	−	3.70731i	0.160027	−	0.144089i
$663$	2.16091	+	17.0333i	0.0839227	+	0.661519i
$664$	−16.7359	+	23.0350i	−0.649479	+	0.893931i
$665$	−3.42357	+	2.27773i	−0.132760	+	0.0883265i
$666$	1.32906	−	7.90847i	0.0515002	−	0.306447i
$667$	2.59540	−	24.6936i	0.100494	−	0.956141i
$668$	4.21199	+	40.0744i	0.162967	+	1.55053i
$669$	7.77221	−	25.7918i	0.300491	−	0.997169i
$670$	−7.19343	+	4.15313i	−0.277907	+	0.160449i
$671$	3.76590	+	1.00551i	0.145381	+	0.0388173i
$672$	19.6183	−	5.94787i	0.756792	−	0.229444i
$673$	−7.69340	+	23.6778i	−0.296559	+	0.912714i	0.686135	+	0.727474i	$0.259306\pi$
$673$	−7.69340	+	23.6778i	−0.296559	+	0.912714i	−0.982693	+	0.185239i	$0.940694\pi$
$674$	4.29656	−	9.65023i	0.165497	−	0.371713i
$675$	−7.62020	−	14.5203i	−0.293302	−	0.558886i
$676$	−3.79801	−	0.807291i	−0.146077	−	0.0310497i
$677$	−15.5731	+	17.2956i	−0.598521	+	0.664725i	−0.963940	−	0.266118i	$-0.914259\pi$
$677$	−15.5731	+	17.2956i	−0.598521	+	0.664725i	0.365419	+	0.930843i	$0.380926\pi$
$678$	−1.58235	−	0.132036i	−0.0607699	−	0.00507081i
$679$	−1.54765	+	10.5266i	−0.0593932	+	0.403972i
$680$	−6.25874	−	2.03359i	−0.240012	−	0.0779845i
$681$	−4.40011	−	2.41597i	−0.168613	−	0.0925802i
$682$	−6.00421	−	0.945546i	−0.229913	−	0.0362068i
$683$	−17.1801	−	9.91892i	−0.657377	−	0.379537i	0.133900	−	0.990995i	$-0.457250\pi$
$683$	−17.1801	−	9.91892i	−0.657377	−	0.379537i	−0.791277	+	0.611458i	$0.790583\pi$
$684$	6.02777	+	1.67615i	0.230478	+	0.0640894i
$685$	−13.5651	−	18.6708i	−0.518297	−	0.713375i
$686$	−5.90190	+	5.11390i	−0.225336	+	0.195249i
$687$	22.9747	−	26.6448i	0.876541	−	1.01656i
$688$	−12.4129	+	13.7859i	−0.473238	+	0.525584i
$689$	1.01109	−	0.450166i	0.0385195	−	0.0171500i
$690$	2.30915	+	3.03888i	0.0879079	+	0.115688i
$691$	−2.32478	−	10.9372i	−0.0884388	−	0.416072i	−0.999988	−	0.00488097i	$-0.998446\pi$
$691$	−2.32478	−	10.9372i	−0.0884388	−	0.416072i	0.911549	−	0.411191i	$-0.134887\pi$
$692$	18.2549			0.693946
$693$	−24.5521	+	9.49698i	−0.932659	+	0.360760i
$694$	4.26532			0.161909
$695$	−2.40603	−	11.3195i	−0.0912661	−	0.429373i
$696$	−10.8971	−	14.3407i	−0.413053	−	0.543583i
$697$	14.5554	−	6.48047i	0.551324	−	0.245465i
$698$	−6.75398	+	7.50105i	−0.255642	+	0.283919i
$699$	4.05379	−	4.70135i	0.153328	−	0.177821i
$700$	−11.7170	+	9.70562i	−0.442862	+	0.366838i
$701$	23.1316	+	31.8379i	0.873668	+	1.20250i	0.978135	+	0.207973i	$0.0666866\pi$
$701$	23.1316	+	31.8379i	0.873668	+	1.20250i	−0.104466	+	0.994528i	$0.533313\pi$
$702$	−1.95349	−	6.95424i	−0.0737296	−	0.262471i
$703$	−6.28347	−	3.62776i	−0.236986	−	0.136824i
$704$	−2.10952	−	13.2434i	−0.0795055	−	0.499129i
$705$	11.3504	+	6.23219i	0.427482	+	0.234718i
$706$	−9.83085	−	3.19424i	−0.369989	−	0.120217i
$707$	−17.4377	+	22.0294i	−0.655813	+	0.828502i
$708$	11.2813	+	0.941346i	0.423978	+	0.0353780i
$709$	14.5697	−	16.1813i	0.547178	−	0.607703i	−0.404599	−	0.914494i	$-0.632589\pi$
$709$	14.5697	−	16.1813i	0.547178	−	0.607703i	0.951777	+	0.306791i	$0.0992554\pi$
$710$	−2.82835	−	0.601185i	−0.106146	−	0.0225621i
$711$	0.123263	−	1.99265i	0.00462273	−	0.0747302i
$712$	10.8417	−	24.3509i	0.406311	−	0.912589i
$713$	5.16849	−	15.9070i	0.193562	−	0.595721i
$714$	−4.23994	−	3.97235i	−0.158676	−	0.148662i
$715$	8.07623	−	12.4604i	0.302034	−	0.465991i
$716$	17.5679	−	10.1429i	0.656545	−	0.379056i
$717$	5.17577	−	17.1756i	0.193293	−	0.641435i
$718$	0.972148	+	9.24937i	0.0362803	+	0.345184i
$719$	0.813652	−	7.74138i	0.0303441	−	0.288705i	−0.968818	−	0.247774i	$-0.920301\pi$
$719$	0.813652	−	7.74138i	0.0303441	−	0.288705i	0.999162	−	0.0409308i	$-0.0130323\pi$
$720$	−11.9116	−	2.00181i	−0.443919	−	0.0746032i
$721$	3.31240	+	52.1246i	0.123360	+	1.94122i
$722$	4.38442	−	6.03464i	0.163171	−	0.224586i
$723$	−0.980357	−	7.72765i	−0.0364599	−	0.287394i
$724$	−3.60992	+	3.25039i	−0.134162	+	0.120800i
$725$	17.6341	+	10.1811i	0.654916	+	0.378116i
$726$	−1.85240	−	7.81722i	−0.0687492	−	0.290124i
$727$		−	8.89125i		−	0.329758i	−0.986314	−	0.164879i	$-0.947277\pi$
$727$		−	8.89125i		−	0.329758i	0.986314	−	0.164879i	$-0.0527234\pi$
$728$	−12.4541	+	6.52085i	−0.461580	+	0.241679i
$729$	19.6237	−	18.5448i	0.726805	−	0.686843i
$730$	0.523685	−	4.98253i	0.0193825	−	0.184412i
$731$	18.4024	+	3.91156i	0.680639	+	0.144674i
$732$	1.22168	+	3.50226i	0.0451547	+	0.129447i
$733$	28.9136	+	3.03894i	1.06795	+	0.112246i	0.622157	−	0.782892i	$-0.286256\pi$
$733$	28.9136	+	3.03894i	1.06795	+	0.112246i	0.445789	+	0.895138i	$0.352923\pi$
$734$	0.355210	−	0.258075i	0.0131110	−	0.00952572i
$735$	15.9401	−	4.12310i	0.587961	−	0.152083i
$736$	−17.2152			−0.634559
$737$	−2.47556	+	48.0471i	−0.0911884	+	1.76984i
$738$	−5.65574	+	3.59759i	−0.208191	+	0.132429i
$739$	−4.43605	−	4.92674i	−0.163183	−	0.181233i	0.656008	−	0.754754i	$-0.272244\pi$
$739$	−4.43605	−	4.92674i	−0.163183	−	0.181233i	−0.819191	+	0.573521i	$0.805577\pi$
$740$	14.3311	+	6.38063i	0.526823	+	0.234556i
$741$	−6.51274	−	0.543442i	−0.239251	−	0.0199638i
$742$	−0.166313	+	0.335566i	−0.00610553	+	0.0123190i
$743$	−0.878181	+	0.285338i	−0.0322173	+	0.0104681i	−0.325081	−	0.945686i	$-0.605392\pi$
$743$	−0.878181	+	0.285338i	−0.0322173	+	0.0104681i	0.292864	+	0.956154i	$0.405392\pi$
$744$	−5.17157	−	10.9752i	−0.189599	−	0.402369i
$745$	−30.5395	+	3.20983i	−1.11888	+	0.117599i
$746$	9.31326	−	8.38570i	0.340983	−	0.307022i
$747$	52.9511	−	2.27509i	1.93738	−	0.0832412i
$748$	−14.1121	+	11.4484i	−0.515991	+	0.418595i
$749$	−20.2276	−	5.17999i	−0.739102	−	0.189273i
$750$	−7.87421	+	1.85125i	−0.287525	+	0.0675980i
$751$	17.6996	+	7.88035i	0.645866	+	0.287558i	0.703409	−	0.710785i	$-0.251660\pi$
$751$	17.6996	+	7.88035i	0.645866	+	0.287558i	−0.0575435	+	0.998343i	$0.518327\pi$
$752$	−14.9109	+	6.63876i	−0.543745	+	0.242091i
$753$	43.3874	−	15.1347i	1.58112	−	0.551538i
$754$	6.66559	+	6.00173i	0.242747	+	0.218570i
$755$	16.7788	+	12.1905i	0.610645	+	0.443659i
$756$	−20.6022	−	14.2516i	−0.749296	−	0.518325i
$757$	10.1592	−	31.2669i	0.369243	−	1.13641i	−0.578038	−	0.816010i	$-0.696182\pi$
$757$	10.1592	−	31.2669i	0.369243	−	1.13641i	0.947281	−	0.320404i	$-0.103818\pi$
$758$	8.38957	−	4.84372i	0.304723	−	0.175932i
$759$	22.0449	−	1.65008i	0.800180	−	0.0598941i
$760$	1.25243	−	2.16928i	0.0454305	−	0.0786880i
$761$	18.7636	−	3.98832i	0.680178	−	0.144576i	0.145149	−	0.989410i	$-0.453634\pi$
$761$	18.7636	−	3.98832i	0.680178	−	0.144576i	0.535029	+	0.844833i	$0.320301\pi$
$762$	5.93428	+	2.49087i	0.214976	+	0.0902347i
$763$	9.03482	+	3.35354i	0.327083	+	0.121406i
$764$	−45.0281	+	14.6305i	−1.62906	+	0.529314i
$765$	4.28198	+	11.4769i	0.154815	+	0.414949i
$766$	2.82099	+	6.33604i	0.101926	+	0.228930i
$767$	−11.7604	+	1.23607i	−0.424643	+	0.0446317i
$768$	4.53717	−	4.26518i	0.163721	−	0.153906i
$769$			42.3186i			1.52605i	0.646370	+	0.763024i	$0.276286\pi$
$769$			42.3186i			1.52605i	−0.646370	+	0.763024i	$0.723714\pi$
$770$	0.585064	+	4.99045i	0.0210843	+	0.179843i
$771$	−13.0724	+	7.92633i	−0.470792	+	0.285460i
$772$	24.0443	−	5.11078i	0.865374	−	0.183941i
$773$	−3.32683	−	31.6527i	−0.119658	−	1.13847i	−0.875333	−	0.483521i	$-0.839358\pi$
$773$	−3.32683	−	31.6527i	−0.119658	−	1.13847i	0.755675	−	0.654947i	$-0.227309\pi$
$774$	−7.89982	−	0.488675i	−0.283953	−	0.0175651i
$775$	10.1931	+	9.17795i	0.366149	+	0.329682i
$776$	−2.00281	−	6.16401i	−0.0718967	−	0.221275i
$777$	19.0082	+	21.9698i	0.681914	+	0.788161i
$778$	6.16332	−	4.47792i	0.220966	−	0.160541i
$779$	1.26089	+	5.93201i	0.0451760	+	0.212536i
$780$	14.1270	−	0.303351i	0.505829	−	0.0108617i
$781$	−11.8323	+	11.8532i	−0.423393	+	0.424140i
$782$	2.43952	+	4.22538i	0.0872372	+	0.151099i
$783$	−8.28645	+	32.4862i	−0.296134	+	1.16096i
$784$	−8.01829	+	19.1423i	−0.286368	+	0.683653i
$785$	−6.92894	+	9.53687i	−0.247304	+	0.340385i
$786$	9.34766	+	1.77807i	0.333420	+	0.0634216i
$787$	9.79574	−	46.0853i	0.349181	−	1.64277i	−0.356544	−	0.934279i	$-0.616045\pi$
$787$	9.79574	−	46.0853i	0.349181	−	1.64277i	0.705724	−	0.708487i	$-0.250622\pi$
$788$	−16.9534	−	38.0780i	−0.603940	−	1.35647i
$789$	0.908959	+	7.16486i	0.0323598	+	0.255076i
$790$	−0.362413	−	0.117755i	−0.0128941	−	0.00418954i
$791$	4.02203	−	4.11235i	0.143007	−	0.146218i
$792$	10.8315	−	11.8249i	0.384880	−	0.420181i
$793$	−1.93728	−	3.35547i	−0.0687950	−	0.119156i
$794$	1.33192	+	1.47924i	0.0472679	+	0.0524963i
$795$	0.628706	−	0.477735i	0.0222979	−	0.0169435i
$796$	−8.35877	−	0.878542i	−0.296269	−	0.0311391i
$797$	−3.04666	−	9.37666i	−0.107918	−	0.332138i	0.882486	−	0.470339i	$-0.155868\pi$
$797$	−3.04666	−	9.37666i	−0.107918	−	0.332138i	−0.990404	+	0.138200i	$0.955868\pi$
$798$	1.81450	−	1.26422i	0.0642326	−	0.0447530i
$799$	13.3918	+	9.72973i	0.473769	+	0.344213i
$800$	5.74219	−	12.8972i	0.203017	−	0.455984i
$801$	−48.0452	+	12.3898i	−1.69759	+	0.437771i
$802$	−1.02742	+	1.77955i	−0.0362795	+	0.0628380i
$803$	−22.5676	−	18.2420i	−0.796394	−	0.643745i
$804$	−39.1487	+	23.7374i	−1.38067	+	0.837154i
$805$	−13.8147	−	0.570282i	−0.486903	−	0.0200998i
$806$	3.55136	+	4.88803i	0.125091	+	0.172174i
$807$	−3.08535	−	6.54776i	−0.108609	−	0.230492i
$808$	3.55833	−	16.7406i	0.125182	−	0.588933i
$809$	−4.87085	+	22.9155i	−0.171250	+	0.805667i	0.805721	+	0.592295i	$0.201778\pi$
$809$	−4.87085	+	22.9155i	−0.171250	+	0.805667i	−0.976971	+	0.213372i	$0.931555\pi$
$810$	−2.49220	−	4.51080i	−0.0875671	−	0.158493i
$811$	−20.2283	−	27.8419i	−0.710312	−	0.977660i	−0.999790	−	0.0204759i	$-0.993482\pi$
$811$	−20.2283	−	27.8419i	−0.710312	−	0.977660i	0.289478	−	0.957185i	$-0.406518\pi$
$812$	31.0800	+	1.28301i	1.09070	+	0.0450249i
$813$	−17.9831	−	29.6584i	−0.630695	−	1.04017i
$814$	−7.43118	+	4.83519i	−0.260463	+	0.169473i
$815$	4.79853	−	8.31130i	0.168085	−	0.291132i
$816$	−14.7841	−	4.45509i	−0.517546	−	0.155959i
$817$	−2.91265	+	6.54192i	−0.101901	+	0.228873i
$818$	8.23728	+	5.98474i	0.288010	+	0.209251i
$819$	23.9234	+	10.6032i	0.835951	+	0.370506i
$820$	−4.05192	−	12.4705i	−0.141499	−	0.435490i
$821$	−22.2599	−	2.33960i	−0.776874	−	0.0816528i	−0.292211	−	0.956354i	$-0.594391\pi$
$821$	−22.2599	−	2.33960i	−0.776874	−	0.0816528i	−0.484663	+	0.874701i	$0.661058\pi$
$822$	7.50931	+	9.88235i	0.261917	+	0.344687i
$823$	−4.19666	−	4.66086i	−0.146286	−	0.162467i	0.665548	−	0.746355i	$-0.268198\pi$
$823$	−4.19666	−	4.66086i	−0.146286	−	0.162467i	−0.811835	+	0.583887i	$0.801531\pi$
$824$	−15.9080	−	27.5534i	−0.554181	−	0.959869i
$825$	−6.11698	+	17.0659i	−0.212966	+	0.594159i
$826$	2.79789	−	2.86071i	0.0973509	−	0.0995369i
$827$	−3.81674	−	1.24013i	−0.132721	−	0.0431237i	0.241903	−	0.970300i	$-0.422228\pi$
$827$	−3.81674	−	1.24013i	−0.132721	−	0.0431237i	−0.374624	+	0.927177i	$0.622228\pi$
$828$	13.0844	+	16.4728i	0.454714	+	0.572468i
$829$	2.07183	+	4.65341i	0.0719577	+	0.161620i	0.945943	−	0.324332i	$-0.105140\pi$
$829$	2.07183	+	4.65341i	0.0719577	+	0.161620i	−0.873985	+	0.485952i	$0.838473\pi$
$830$	2.10326	−	9.89504i	0.0730051	−	0.343462i
$831$	−7.68566	+	40.4051i	−0.266613	+	1.40164i
$832$	−7.83537	+	10.7845i	−0.271643	+	0.373884i
$833$	20.8784	−	2.66431i	0.723395	−	0.0923129i
$834$	1.42438	+	6.05852i	0.0493221	+	0.209790i
$835$	−15.0149	−	26.0066i	−0.519612	−	0.899994i
$836$	−3.14559	−	6.16014i	−0.108793	−	0.213053i
$837$	−10.0097	+	20.2445i	−0.345985	+	0.699751i
$838$	3.53049	+	16.6097i	0.121959	+	0.573771i
$839$	6.31171	−	4.58572i	0.217904	−	0.158317i	−0.473478	−	0.880805i	$-0.657002\pi$
$839$	6.31171	−	4.58572i	0.217904	−	0.158317i	0.691383	+	0.722489i	$0.257002\pi$
$840$	−7.58475	+	6.56230i	−0.261699	+	0.226421i
$841$	−3.90302	−	12.0122i	−0.134587	−	0.414215i
$842$	−8.51616	−	7.66798i	−0.293486	−	0.264256i
$843$	−18.3035	−	12.7070i	−0.630405	−	0.437651i
$844$	3.33268	+	31.7084i	0.114716	+	1.09145i
$845$	2.83045	−	0.601631i	0.0973704	−	0.0206967i
$846$	−6.17490	−	3.21989i	−0.212297	−	0.110702i
$847$	26.0990	+	12.8779i	0.896774	+	0.442489i
$848$			0.995318i			0.0341794i
$849$	7.54640	+	8.02763i	0.258992	+	0.275508i
$850$	−3.97926	+	0.418237i	−0.136488	+	0.0143454i
$851$	−9.92282	−	22.2870i	−0.340150	−	0.763989i
$852$	−15.6571	−	2.97821i	−0.536402	−	0.102032i
$853$	27.6452	−	8.98245i	0.946552	−	0.307553i	0.205238	−	0.978712i	$-0.434203\pi$
$853$	27.6452	−	8.98245i	0.946552	−	0.307553i	0.741314	+	0.671159i	$0.234203\pi$
$854$	1.22916	+	0.456239i	0.0420610	+	0.0156122i
$855$	−4.61188	+	0.685979i	−0.157723	+	0.0234600i
$856$	12.4414	−	2.64450i	0.425239	−	0.0903873i
$857$	17.2926	−	29.9517i	0.590704	−	1.02313i	−0.403433	−	0.915009i	$-0.632183\pi$
$857$	17.2926	−	29.9517i	0.590704	−	1.02313i	0.994138	−	0.108121i	$-0.0344834\pi$
$858$	−4.19859	+	6.79296i	−0.143337	+	0.231908i
$859$	9.32795	−	5.38550i	0.318266	−	0.183751i	−0.332354	−	0.943155i	$-0.607843\pi$
$859$	9.32795	−	5.38550i	0.318266	−	0.183751i	0.650619	+	0.759404i	$0.274509\pi$
$860$	4.78452	−	14.7253i	0.163151	−	0.502127i
$861$	3.01556	−	24.0946i	0.102770	−	0.821142i
$862$	−9.26170	−	6.72902i	−0.315455	−	0.229191i
$863$	37.9813	+	34.1986i	1.29290	+	1.16413i	0.976503	+	0.215505i	$0.0691399\pi$
$863$	37.9813	+	34.1986i	1.29290	+	1.16413i	0.316397	+	0.948627i	$0.397527\pi$
$864$	23.0009	+	3.35941i	0.782506	+	0.114290i
$865$	−12.4282	+	5.53340i	−0.422572	+	0.188141i
$866$	−3.46321	−	1.54192i	−0.117685	−	0.0523966i
$867$	−3.15497	−	13.4195i	−0.107148	−	0.455751i
$868$	20.2988	+	5.19820i	0.688985	+	0.176438i
$869$	−1.71407	+	1.39053i	−0.0581457	+	0.0471704i
$870$	5.60927	+	3.07988i	0.190172	+	0.104418i
$871$	35.5401	−	32.0004i	1.20423	−	1.08429i
$872$	−5.83833	+	0.613634i	−0.197711	+	0.0207803i
$873$	−6.66572	+	10.0556i	−0.225600	+	0.340332i
$874$	−1.76622	+	0.573881i	−0.0597434	+	0.0194118i
$875$	13.0127	−	26.2555i	0.439909	−	0.887596i
$876$	2.29624	−	27.5187i	0.0775827	−	0.929770i
$877$	−36.1410	−	16.0910i	−1.22039	−	0.543355i	−0.307499	−	0.951548i	$-0.599492\pi$
$877$	−36.1410	−	16.0910i	−1.22039	−	0.543355i	−0.912895	+	0.408194i	$0.866159\pi$
$878$	−2.51854	−	2.79712i	−0.0849966	−	0.0943983i
$879$	0.603296	+	28.0955i	0.0203487	+	0.947639i
$880$	7.28267	+	11.1927i	0.245499	+	0.377306i
$881$	12.6694			0.426844			0.213422	−	0.976960i	$-0.431539\pi$
$881$	12.6694			0.426844			0.213422	+	0.976960i	$0.431539\pi$
$882$	−8.52314	+	2.40096i	−0.286989	+	0.0808446i
$883$	−26.0636	+	18.9363i	−0.877112	+	0.637259i	−0.932486	−	0.361207i	$-0.882365\pi$
$883$	−26.0636	+	18.9363i	−0.877112	+	0.637259i	0.0553742	+	0.998466i	$0.482365\pi$
$884$	17.9646	+	1.88815i	0.604214	+	0.0635054i
$885$	−7.96585	+	2.77870i	−0.267769	+	0.0934049i
$886$	−10.0727	−	2.14102i	−0.338398	−	0.0719288i
$887$	0.211299	−	2.01037i	0.00709472	−	0.0675017i	−0.990402	−	0.138219i	$-0.955862\pi$
$887$	0.211299	−	2.01037i	0.00709472	−	0.0675017i	0.997496	+	0.0707174i	$0.0225288\pi$
$888$	−16.3176	−	6.84919i	−0.547582	−	0.229844i
$889$	−20.6549	+	10.8147i	−0.692742	+	0.362713i
$890$			9.47039i			0.317448i
$891$	−29.7759	−	2.09726i	−0.997529	−	0.0702609i
$892$	−24.5427	−	14.1697i	−0.821751	−	0.474438i
$893$	−4.68231	+	4.21597i	−0.156687	+	0.141082i
$894$	16.3835	−	2.07847i	0.547947	−	0.0695145i
$895$	−8.88605	+	12.2306i	−0.297028	+	0.408824i
$896$	−1.78731	−	28.1256i	−0.0597099	−	0.939609i
$897$	−16.6423	−	14.3500i	−0.555670	−	0.479132i
$898$	−0.776691	+	7.38972i	−0.0259185	+	0.246598i
$899$	−2.93128	−	27.8892i	−0.0977635	−	0.930158i
$900$	−16.7054	+	4.30794i	−0.556845	+	0.143598i
$901$	0.874179	−	0.504708i	0.0291231	−	0.0168143i
$902$	7.15962	+	1.91165i	0.238389	+	0.0636509i
$903$	19.6038	−	20.9244i	0.652374	−	0.696320i
$904$	−1.08279	+	3.33249i	−0.0360132	+	0.110837i
$905$	1.47244	−	3.30715i	0.0489455	−	0.109933i
$906$	−9.16245	−	6.36092i	−0.304402	−	0.211328i
$907$	−29.4043	−	6.25008i	−0.976355	−	0.207531i	−0.308011	−	0.951383i	$-0.599663\pi$
$907$	−29.4043	−	6.25008i	−0.976355	−	0.207531i	−0.668344	+	0.743852i	$0.732997\pi$
$908$	−3.53370	+	3.92457i	−0.117270	+	0.130241i
$909$	−28.5203	+	14.1950i	−0.945958	+	0.470818i
$910$	3.09995	−	3.91623i	0.102762	−	0.129822i
$911$	−37.7726	−	12.2731i	−1.25146	−	0.406625i	−0.393018	−	0.919531i	$-0.628569\pi$
$911$	−37.7726	−	12.2731i	−1.25146	−	0.406625i	−0.858445	+	0.512906i	$0.828569\pi$
$912$	2.82867	−	5.15174i	0.0936665	−	0.170591i
$913$	−41.4685	−	41.3954i	−1.37241	−	1.36999i
$914$	1.56140	+	0.901473i	0.0516464	+	0.0298181i
$915$	−1.89334	−	2.01408i	−0.0625920	−	0.0665835i
$916$	−21.7559	−	29.9444i	−0.718836	−	0.989392i
$917$	−26.5461	+	21.9890i	−0.876629	+	0.726142i
$918$	−2.43485	−	6.12151i	−0.0803622	−	0.202040i
$919$	−2.19058	+	2.43289i	−0.0722607	+	0.0802536i	−0.778191	−	0.628028i	$-0.783862\pi$
$919$	−2.19058	+	2.43289i	−0.0722607	+	0.0802536i	0.705930	+	0.708281i	$0.250529\pi$
$920$	7.69427	−	3.42571i	0.253673	−	0.112942i
$921$	−25.7013	+	19.5297i	−0.846888	+	0.643525i
$922$	0.690635	+	3.24918i	0.0227449	+	0.107006i
$923$	16.6482			0.547983
$924$	3.81457	+	27.4311i	0.125490	+	0.902418i
$925$	20.0067			0.657816
$926$	3.23699	+	15.2289i	0.106374	+	0.500451i
$927$	−21.7435	+	55.0870i	−0.714151	+	1.80930i
$928$	−26.3683	+	11.7399i	−0.865581	+	0.385382i
$929$	−33.4078	+	37.1031i	−1.09607	+	1.21731i	−0.121654	+	0.992573i	$0.538820\pi$
$929$	−33.4078	+	37.1031i	−1.09607	+	1.21731i	−0.974419	+	0.224740i	$0.927847\pi$
$930$	3.26457	+	2.81491i	0.107049	+	0.0923044i
$931$	−0.660313	+	7.98417i	−0.0216409	+	0.261671i
$932$	−3.83873	−	5.28356i	−0.125742	−	0.173069i
$933$	−11.8615	+	11.1504i	−0.388328	+	0.365049i
$934$	−12.3738	−	7.14402i	−0.404883	−	0.233759i
$935$	6.13755	−	12.0719i	0.200719	−	0.394794i
$936$	−15.9255	+	0.684255i	−0.520543	+	0.0223656i
$937$	−27.4360	−	8.91451i	−0.896297	−	0.291224i	−0.175589	−	0.984464i	$-0.556183\pi$
$937$	−27.4360	−	8.91451i	−0.896297	−	0.291224i	−0.720708	+	0.693239i	$0.756183\pi$
$938$	−2.35396	+	16.0109i	−0.0768596	+	0.522773i
$939$	0.984341	−	11.7966i	0.0321228	−	0.384967i
$940$	9.11545	−	10.1237i	0.297313	−	0.330200i
$941$	10.4899	+	2.22970i	0.341961	+	0.0726860i	0.375691	−	0.926745i	$-0.377405\pi$
$941$	10.4899	+	2.22970i	0.341961	+	0.0726860i	−0.0337303	+	0.999431i	$0.510739\pi$
$942$	3.61546	−	5.20781i	0.117798	−	0.169680i
$943$	−8.29399	+	18.6286i	−0.270089	+	0.606631i
$944$	3.28618	−	10.1138i	0.106956	−	0.329177i
$945$	18.3463	+	3.45778i	0.596804	+	0.112481i
$946$	5.51272	+	6.79538i	0.179234	+	0.220937i
$947$	48.4236	−	27.9574i	1.57356	−	0.908493i	0.577829	−	0.816158i	$-0.303900\pi$
$947$	48.4236	−	27.9574i	1.57356	−	0.908493i	0.995728	−	0.0923356i	$-0.0294333\pi$
$948$	−2.01105	−	0.606017i	−0.0653157	−	0.0196825i
$949$	3.01515	+	28.6872i	0.0978759	+	0.931227i
$950$	0.159194	−	1.51463i	0.00516494	−	0.0491411i
$951$	5.37591	−	6.23468i	0.174326	−	0.202173i
$952$	−10.6747	+	7.10194i	−0.345968	+	0.230175i
$953$	30.3608	−	41.7880i	0.983482	−	1.35365i	0.0485492	−	0.998821i	$-0.484540\pi$
$953$	30.3608	−	41.7880i	0.983482	−	1.35365i	0.934932	−	0.354826i	$-0.115460\pi$
$954$	−0.332529	+	0.264129i	−0.0107660	+	0.00855149i
$955$	26.2211	−	23.6096i	0.848494	−	0.763988i
$956$	−16.3438	−	9.43611i	−0.528597	−	0.305186i
$957$	32.6407	−	17.5610i	1.05512	−	0.567666i
$958$		−	5.83849i		−	0.188633i
$959$	−44.9250	−	1.85454i	−1.45070	−	0.0598864i
$960$	−3.68083	+	8.76926i	−0.118798	+	0.283027i
$961$	−1.26583	+	12.0436i	−0.0408334	+	0.388503i
$962$	8.62027	+	1.83230i	0.277929	+	0.0590756i
$963$	−18.2586	−	15.0725i	−0.588376	−	0.485706i
$964$	−8.15014	−	0.856614i	−0.262498	−	0.0275897i
$965$	−14.8206	+	10.7678i	−0.477092	+	0.346627i
$966$	7.43450	+	0.147131i	0.239201	+	0.00473386i
$967$	−25.0917			−0.806896			−0.403448	−	0.915003i	$-0.632188\pi$
$967$	−25.0917			−0.806896			−0.403448	+	0.915003i	$0.632188\pi$
$968$	−17.7283	+	0.0312677i	−0.569810	+	0.00100498i
$969$	−5.95910	+	0.127960i	−0.191434	+	0.00411066i
$970$	1.54082	+	1.71125i	0.0494726	+	0.0549449i
$971$	49.2334	+	21.9201i	1.57997	+	0.703450i	0.994252	−	0.107063i	$-0.0341445\pi$
$971$	49.2334	+	21.9201i	1.57997	+	0.703450i	0.585722	+	0.810512i	$0.300811\pi$
$972$	−14.2673	−	24.5623i	−0.457623	−	0.787837i
$973$	−20.2013	−	10.0122i	−0.647624	−	0.320975i
$974$	−3.71788	+	1.20801i	−0.119129	+	0.0387072i
$975$	16.3018	−	7.68150i	0.522074	−	0.246005i
$976$	3.46529	−	0.364217i	0.110921	−	0.0116583i
$977$	9.24010	−	8.31982i	0.295617	−	0.266175i	−0.507953	−	0.861385i	$-0.669598\pi$
$977$	9.24010	−	8.31982i	0.295617	−	0.266175i	0.803570	+	0.595210i	$0.202931\pi$
$978$	−2.48413	+	4.52425i	−0.0794337	+	0.144670i
$979$	46.0305	+	29.8349i	1.47114	+	0.953526i
$980$	−0.384595	−	17.3175i	−0.0122854	−	0.553186i
$981$	7.65376	+	7.79934i	0.244366	+	0.249014i
$982$	−7.36402	−	3.27867i	−0.234995	−	0.104627i
$983$	−0.308025	+	0.137142i	−0.00982448	+	0.00437414i	−0.411643	−	0.911345i	$-0.635045\pi$
$983$	−0.308025	+	0.137142i	−0.00982448	+	0.00437414i	0.401819	+	0.915719i	$0.368378\pi$
$984$	4.87188	+	13.9665i	0.155310	+	0.445235i
$985$	23.0843	+	20.7852i	0.735528	+	0.662272i
$986$	6.61810	+	4.80833i	0.210763	+	0.153128i
$987$	23.2455	−	9.80315i	0.739912	−	0.312038i
$988$	−2.12466	+	6.53902i	−0.0675943	+	0.208034i
$989$	−20.8525	+	12.0392i	−0.663072	+	0.382825i
$990$	−1.80679	+	5.40331i	−0.0574237	+	0.171729i
$991$	−9.17437	+	15.8905i	−0.291433	+	0.504777i	−0.974149	−	0.225907i	$-0.927465\pi$
$991$	−9.17437	+	15.8905i	−0.291433	+	0.504777i	0.682716	+	0.730684i	$0.260799\pi$
$992$	−19.0181	+	4.04242i	−0.603826	+	0.128347i
$993$	−8.80829	+	20.9850i	−0.279523	+	0.665938i
$994$	−4.33846	+	3.59369i	−0.137608	+	0.113985i
$995$	5.95709	−	1.93558i	0.188852	−	0.0613619i
$996$	10.4193	−	54.7765i	0.330149	−	1.73566i
$997$	19.7450	+	44.3480i	0.625330	+	1.40451i	0.896960	+	0.442112i	$0.145771\pi$
$997$	19.7450	+	44.3480i	0.625330	+	1.40451i	−0.271630	+	0.962402i	$0.587563\pi$
$998$	−8.98147	+	0.943991i	−0.284303	+	0.0298815i
$999$	8.90856	+	31.7137i	0.281854	+	1.00338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.bc.a.185.13	yes	224
3.2	odd	2	inner	231.2.bc.a.185.16	yes	224
7.5	odd	6	inner	231.2.bc.a.152.13	yes	224
11.5	even	5	inner	231.2.bc.a.38.16	yes	224
21.5	even	6	inner	231.2.bc.a.152.16	yes	224
33.5	odd	10	inner	231.2.bc.a.38.13	yes	224
77.5	odd	30	inner	231.2.bc.a.5.16	yes	224
231.5	even	30	inner	231.2.bc.a.5.13	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.bc.a.5.13	✓	224	231.5	even	30	inner
231.2.bc.a.5.16	yes	224	77.5	odd	30	inner
231.2.bc.a.38.13	yes	224	33.5	odd	10	inner
231.2.bc.a.38.16	yes	224	11.5	even	5	inner
231.2.bc.a.152.13	yes	224	7.5	odd	6	inner
231.2.bc.a.152.16	yes	224	21.5	even	6	inner
231.2.bc.a.185.13	yes	224	1.1	even	1	trivial
231.2.bc.a.185.16	yes	224	3.2	odd	2	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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0876680 - 0.412446i) q^{2} +(1.04792 + 1.37908i) q^{3} +(1.66467 - 0.741157i) q^{4} +(-0.908673 + 1.00918i) q^{5} +(0.476926 - 0.553112i) q^{6} +(0.442873 + 2.60842i) q^{7} +(-0.947316 - 1.30387i) q^{8} +(-0.803721 + 2.89033i) q^{9} +O(q^{10})\)	\(q+(-0.0876680 - 0.412446i) q^{2} +(1.04792 + 1.37908i) q^{3} +(1.66467 - 0.741157i) q^{4} +(-0.908673 + 1.00918i) q^{5} +(0.476926 - 0.553112i) q^{6} +(0.442873 + 2.60842i) q^{7} +(-0.947316 - 1.30387i) q^{8} +(-0.803721 + 2.89033i) q^{9} +(0.495895 + 0.286305i) q^{10} +(2.95381 - 1.50832i) q^{11} +(2.76655 + 1.51903i) q^{12} +(-3.13548 - 1.01878i) q^{13} +(1.03701 - 0.411336i) q^{14} +(-2.34396 - 0.195587i) q^{15} +(1.98386 - 2.20330i) q^{16} +(-2.94112 - 0.625154i) q^{17} +(1.26257 + 0.0781011i) q^{18} +(0.465506 - 1.04554i) q^{19} +(-0.764673 + 2.35342i) q^{20} +(-3.13312 + 3.34418i) q^{21} +(-0.881055 - 1.08605i) q^{22} +(3.33269 - 1.92413i) q^{23} +(0.805425 - 2.67277i) q^{24} +(0.329878 + 3.13858i) q^{25} +(-0.145310 + 1.38253i) q^{26} +(-4.82824 + 1.92045i) q^{27} +(2.67048 + 4.01391i) q^{28} +(3.79249 - 5.21991i) q^{29} +(0.124821 + 0.983903i) q^{30} +(3.22991 - 2.90822i) q^{31} +(-3.87415 - 2.23674i) q^{32} +(5.17545 + 2.49293i) q^{33} +1.26786i q^{34} +(-3.03480 - 1.92326i) q^{35} +(0.804265 + 5.40712i) q^{36} +(0.662661 - 6.30480i) q^{37} +(-0.472040 - 0.100335i) q^{38} +(-1.88076 - 5.39168i) q^{39} +(2.17664 + 0.228774i) q^{40} +(-4.28689 + 3.11461i) q^{41} +(1.65397 + 0.999066i) q^{42} -6.25696 q^{43} +(3.79919 - 4.70008i) q^{44} +(-2.18656 - 3.43747i) q^{45} +(-1.08577 - 1.20587i) q^{46} +(-5.02926 - 2.23917i) q^{47} +(5.11745 + 0.427015i) q^{48} +(-6.60773 + 2.31040i) q^{49} +(1.26557 - 0.411209i) q^{50} +(-2.21992 - 4.71115i) q^{51} +(-5.97460 + 0.627956i) q^{52} +(-0.249480 + 0.224633i) q^{53} +(1.21536 + 1.82302i) q^{54} +(-1.16187 + 4.35150i) q^{55} +(2.98150 - 3.04845i) q^{56} +(1.92970 - 0.453678i) q^{57} +(-2.48541 - 1.10658i) q^{58} +(3.27672 - 1.45889i) q^{59} +(-4.04687 + 1.41166i) q^{60} +(0.873372 + 0.786387i) q^{61} +(-1.48264 - 1.07720i) q^{62} +(-7.89516 - 0.816390i) q^{63} +(1.24947 - 3.84547i) q^{64} +(3.87726 - 2.23854i) q^{65} +(0.574476 - 2.35314i) q^{66} +(-7.25299 + 12.5625i) q^{67} +(-5.35931 + 1.13916i) q^{68} +(6.14593 + 2.57971i) q^{69} +(-0.527185 + 1.42030i) q^{70} +(-4.80261 + 1.56046i) q^{71} +(4.52999 - 1.69011i) q^{72} +(-3.55869 - 7.99295i) q^{73} +(-2.65848 + 0.279417i) q^{74} +(-3.98266 + 3.74391i) q^{75} -2.08549i q^{76} +(5.24250 + 7.03677i) q^{77} +(-2.05889 + 1.24839i) q^{78} +(-0.650943 + 0.138362i) q^{79} +(0.420853 + 4.00415i) q^{80} +(-7.70807 - 4.64604i) q^{81} +(1.66043 + 1.49506i) q^{82} +(-5.45930 - 16.8020i) q^{83} +(-2.73704 + 7.88907i) q^{84} +(3.30341 - 2.40007i) q^{85} +(0.548535 + 2.58065i) q^{86} +(11.1729 - 0.239916i) q^{87} +(-4.76484 - 2.42252i) q^{88} +(8.26950 + 14.3232i) q^{89} +(-1.22608 + 1.20319i) q^{90} +(1.26879 - 8.62984i) q^{91} +(4.12174 - 5.67308i) q^{92} +(7.39536 + 1.40671i) q^{93} +(-0.482631 + 2.27060i) q^{94} +(0.632153 + 1.41984i) q^{95} +(-0.975162 - 7.68670i) q^{96} +(3.82461 + 1.24269i) q^{97} +(1.53220 + 2.52278i) q^{98} +(1.98552 + 9.74975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9}+O(q^{10}) \) 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9	\( 224 q - 9 q^{3} - 30 q^{4} - 16 q^{7} + 3 q^{9} - 60 q^{10} - 12 q^{12} - 36 q^{15} + 18 q^{16} + 13 q^{18} - 18 q^{19} - 6 q^{21} + 20 q^{22} - 51 q^{24} - 18 q^{25} - 26 q^{28} - 15 q^{30} - 36 q^{31} + 60 q^{33} - 32 q^{36} - 10 q^{37} + 9 q^{39} - 114 q^{42} - 96 q^{43} + 24 q^{45} - 54 q^{46} - 56 q^{49} - 29 q^{51} - 30 q^{52} - 96 q^{54} + 68 q^{57} - 64 q^{58} + 125 q^{60} - 18 q^{61} - 26 q^{63} + 56 q^{64} + 135 q^{66} + 48 q^{67} - 44 q^{70} + 19 q^{72} + 30 q^{73} + 63 q^{75} + 28 q^{78} + 30 q^{79} + 31 q^{81} + 54 q^{82} + 99 q^{84} - 248 q^{85} + 102 q^{87} + 82 q^{88} - 144 q^{91} + 34 q^{93} + 162 q^{94} - 87 q^{96} - 100 q^{99}+O(q^{100}) \) 224 * q - 9 * q^3 - 30 * q^4 - 16 * q^7 + 3 * q^9 - 60 * q^10 - 12 * q^12 - 36 * q^15 + 18 * q^16 + 13 * q^18 - 18 * q^19 - 6 * q^21 + 20 * q^22 - 51 * q^24 - 18 * q^25 - 26 * q^28 - 15 * q^30 - 36 * q^31 + 60 * q^33 - 32 * q^36 - 10 * q^37 + 9 * q^39 - 114 * q^42 - 96 * q^43 + 24 * q^45 - 54 * q^46 - 56 * q^49 - 29 * q^51 - 30 * q^52 - 96 * q^54 + 68 * q^57 - 64 * q^58 + 125 * q^60 - 18 * q^61 - 26 * q^63 + 56 * q^64 + 135 * q^66 + 48 * q^67 - 44 * q^70 + 19 * q^72 + 30 * q^73 + 63 * q^75 + 28 * q^78 + 30 * q^79 + 31 * q^81 + 54 * q^82 + 99 * q^84 - 248 * q^85 + 102 * q^87 + 82 * q^88 - 144 * q^91 + 34 * q^93 + 162 * q^94 - 87 * q^96 - 100 * q^99

Introduction

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