LMFDB - Embedded newform 231.2.w.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725588 - 0.235758i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.14714 - 0.833444i) q^{4} +(0.666245 - 0.216476i) q^{5} +(-0.235758 - 0.725588i) q^{6} +(0.612583 + 2.57386i) q^{7} +(1.53273 + 2.10963i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.725588 - 0.235758i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.14714 - 0.833444i) q^{4} +(0.666245 - 0.216476i) q^{5} +(-0.235758 - 0.725588i) q^{6} +(0.612583 + 2.57386i) q^{7} +(1.53273 + 2.10963i) q^{8} +(-0.309017 + 0.951057i) q^{9} -0.534456 q^{10} +(2.57267 + 2.09317i) q^{11} -1.41794i q^{12} +(1.70619 - 5.25111i) q^{13} +(0.162324 - 2.01198i) q^{14} +(0.566742 + 0.411762i) q^{15} +(0.261562 + 0.805005i) q^{16} +(1.76715 + 5.43872i) q^{17} +(0.448438 - 0.617222i) q^{18} +(3.61440 - 2.62601i) q^{19} +(-0.944696 - 0.306950i) q^{20} +(-1.72223 + 2.00847i) q^{21} +(-1.37322 - 2.12531i) q^{22} +3.20630 q^{23} +(-0.805806 + 2.48002i) q^{24} +(-3.64806 + 2.65047i) q^{25} +(-2.47598 + 3.40789i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.44245 - 3.46312i) q^{28} +(-4.48702 + 6.17586i) q^{29} +(-0.314145 - 0.432384i) q^{30} +(2.02030 + 0.656435i) q^{31} -5.86106i q^{32} +(-0.181228 + 3.31167i) q^{33} -4.36289i q^{34} +(0.965309 + 1.58221i) q^{35} +(1.14714 - 0.833444i) q^{36} +(-7.37635 - 5.35923i) q^{37} +(-3.24167 + 1.05328i) q^{38} +(5.25111 - 1.70619i) q^{39} +(1.47786 + 1.07373i) q^{40} +(5.14482 - 3.73793i) q^{41} +(1.72314 - 1.05129i) q^{42} -7.53186i q^{43} +(-1.20667 - 4.54533i) q^{44} +0.700532i q^{45} +(-2.32645 - 0.755910i) q^{46} +(-3.45258 - 4.75207i) q^{47} +(-0.497521 + 0.684778i) q^{48} +(-6.24948 + 3.15340i) q^{49} +(3.27186 - 1.06309i) q^{50} +(-3.36131 + 4.62645i) q^{51} +(-6.33373 + 4.60173i) q^{52} +(-0.0857105 + 0.263790i) q^{53} +0.762929 q^{54} +(2.16715 + 0.837640i) q^{55} +(-4.49096 + 5.23736i) q^{56} +(4.24898 + 1.38058i) q^{57} +(4.71174 - 3.42328i) q^{58} +(-6.14452 + 8.45720i) q^{59} +(-0.306950 - 0.944696i) q^{60} +(-2.65139 - 8.16013i) q^{61} +(-1.31114 - 0.952603i) q^{62} +(-2.63718 - 0.212765i) q^{63} +(-0.858667 + 2.64270i) q^{64} -3.86787i q^{65} +(0.912250 - 2.36018i) q^{66} -10.3638 q^{67} +(2.50571 - 7.71177i) q^{68} +(1.88461 + 2.59395i) q^{69} +(-0.327398 - 1.37561i) q^{70} +(-2.23595 - 6.88155i) q^{71} +(-2.48002 + 0.805806i) q^{72} +(7.88877 + 5.73153i) q^{73} +(4.08871 + 5.62763i) q^{74} +(-4.28856 - 1.39344i) q^{75} -6.33485 q^{76} +(-3.81154 + 7.90393i) q^{77} -4.21239 q^{78} +(10.6292 + 3.45362i) q^{79} +(0.348529 + 0.479709i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.61427 + 1.49927i) q^{82} +(-4.35552 - 13.4049i) q^{83} +(3.64957 - 0.868605i) q^{84} +(2.35471 + 3.24097i) q^{85} +(-1.77569 + 5.46503i) q^{86} -7.63378 q^{87} +(-0.472579 + 8.63566i) q^{88} +1.46930i q^{89} +(0.165156 - 0.508298i) q^{90} +(14.5608 + 1.17475i) q^{91} +(-3.67806 - 2.67227i) q^{92} +(0.656435 + 2.02030i) q^{93} +(1.38481 + 4.26202i) q^{94} +(1.83961 - 2.53200i) q^{95} +(4.74169 - 3.44504i) q^{96} +(7.42547 + 2.41268i) q^{97} +(5.27799 - 0.814706i) q^{98} +(-2.78572 + 1.79993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.725588	−	0.235758i	−0.513068	−	0.166706i	0.0410288	−	0.999158i	$-0.486936\pi$
$2$	−0.725588	−	0.235758i	−0.513068	−	0.166706i	−0.554097	+	0.832452i	$0.686936\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	−1.14714	−	0.833444i	−0.573569	−	0.416722i
$5$	0.666245	−	0.216476i	0.297954	−	0.0968111i	−0.156225	−	0.987721i	$-0.549933\pi$
$5$	0.666245	−	0.216476i	0.297954	−	0.0968111i	0.454179	+	0.890910i	$0.349933\pi$
$6$	−0.235758	−	0.725588i	−0.0962478	−	0.296220i
$7$	0.612583	+	2.57386i	0.231535	+	0.972827i
$7$	0.612583	+	2.57386i	0.231535	+	0.972827i
$8$	1.53273	+	2.10963i	0.541904	+	0.745866i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−0.534456			−0.169010
$11$	2.57267	+	2.09317i	0.775690	+	0.631114i
$11$	2.57267	+	2.09317i	0.775690	+	0.631114i
$12$		−	1.41794i		−	0.409324i
$13$	1.70619	−	5.25111i	0.473211	−	1.45639i	−0.375144	−	0.926967i	$-0.622407\pi$
$13$	1.70619	−	5.25111i	0.473211	−	1.45639i	0.848355	−	0.529428i	$-0.177593\pi$
$14$	0.162324	−	2.01198i	0.0433830	−	0.537725i
$15$	0.566742	+	0.411762i	0.146332	+	0.106317i
$16$	0.261562	+	0.805005i	0.0653905	+	0.201251i
$17$	1.76715	+	5.43872i	0.428596	+	1.31908i	0.899509	+	0.436903i	$0.143925\pi$
$17$	1.76715	+	5.43872i	0.428596	+	1.31908i	−0.470913	+	0.882180i	$0.656075\pi$
$18$	0.448438	−	0.617222i	0.105698	−	0.145481i
$19$	3.61440	−	2.62601i	0.829200	−	0.602449i	−0.0901331	−	0.995930i	$-0.528729\pi$
$19$	3.61440	−	2.62601i	0.829200	−	0.602449i	0.919333	+	0.393481i	$0.128729\pi$
$20$	−0.944696	−	0.306950i	−0.211240	−	0.0686362i
$21$	−1.72223	+	2.00847i	−0.375821	+	0.438283i
$22$	−1.37322	−	2.12531i	−0.292772	−	0.453117i
$23$	3.20630			0.668559			0.334279	−	0.942474i	$-0.391507\pi$
$23$	3.20630			0.668559			0.334279	+	0.942474i	$0.391507\pi$
$24$	−0.805806	+	2.48002i	−0.164485	+	0.506231i
$25$	−3.64806	+	2.65047i	−0.729613	+	0.530095i
$26$	−2.47598	+	3.40789i	−0.485580	+	0.668343i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.44245	−	3.46312i	0.272597	−	0.654468i
$29$	−4.48702	+	6.17586i	−0.833219	+	1.14683i	0.154096	+	0.988056i	$0.450753\pi$
$29$	−4.48702	+	6.17586i	−0.833219	+	1.14683i	−0.987315	+	0.158772i	$0.949247\pi$
$30$	−0.314145	−	0.432384i	−0.0573548	−	0.0789421i
$31$	2.02030	+	0.656435i	0.362856	+	0.117899i	0.484770	−	0.874642i	$-0.338903\pi$
$31$	2.02030	+	0.656435i	0.362856	+	0.117899i	−0.121914	+	0.992541i	$0.538903\pi$
$32$		−	5.86106i		−	1.03610i
$33$	−0.181228	+	3.31167i	−0.0315478	+	0.576488i
$34$		−	4.36289i		−	0.748229i
$35$	0.965309	+	1.58221i	0.163167	+	0.267442i
$36$	1.14714	−	0.833444i	0.191190	−	0.138907i
$37$	−7.37635	−	5.35923i	−1.21266	−	0.881053i	−0.217195	−	0.976128i	$-0.569691\pi$
$37$	−7.37635	−	5.35923i	−1.21266	−	0.881053i	−0.995470	+	0.0950756i	$0.969691\pi$
$38$	−3.24167	+	1.05328i	−0.525868	+	0.170865i
$39$	5.25111	−	1.70619i	0.840850	−	0.273209i
$40$	1.47786	+	1.07373i	0.233670	+	0.169772i
$41$	5.14482	−	3.73793i	0.803486	−	0.583767i	−0.108449	−	0.994102i	$-0.534588\pi$
$41$	5.14482	−	3.73793i	0.803486	−	0.583767i	0.911935	+	0.410335i	$0.134588\pi$
$42$	1.72314	−	1.05129i	0.265886	−	0.162218i
$43$		−	7.53186i		−	1.14860i	−0.818646	−	0.574299i	$-0.805275\pi$
$43$		−	7.53186i		−	1.14860i	0.818646	−	0.574299i	$-0.194725\pi$
$44$	−1.20667	−	4.54533i	−0.181913	−	0.685234i
$45$			0.700532i			0.104429i
$46$	−2.32645	−	0.755910i	−0.343016	−	0.111453i
$47$	−3.45258	−	4.75207i	−0.503611	−	0.693161i	0.479215	−	0.877698i	$-0.340922\pi$
$47$	−3.45258	−	4.75207i	−0.503611	−	0.693161i	−0.982826	+	0.184537i	$0.940922\pi$
$48$	−0.497521	+	0.684778i	−0.0718109	+	0.0988392i
$49$	−6.24948	+	3.15340i	−0.892784	+	0.450486i
$50$	3.27186	−	1.06309i	0.462711	−	0.150344i
$51$	−3.36131	+	4.62645i	−0.470678	+	0.647832i
$52$	−6.33373	+	4.60173i	−0.878331	+	0.638145i
$53$	−0.0857105	+	0.263790i	−0.0117732	+	0.0362343i	−0.956771	−	0.290844i	$-0.906064\pi$
$53$	−0.0857105	+	0.263790i	−0.0117732	+	0.0362343i	0.944997	+	0.327078i	$0.106064\pi$
$54$	0.762929			0.103821
$55$	2.16715	+	0.837640i	0.292219	+	0.112947i
$56$	−4.49096	+	5.23736i	−0.600129	+	0.699872i
$57$	4.24898	+	1.38058i	0.562791	+	0.182862i
$58$	4.71174	−	3.42328i	0.618681	−	0.449498i
$59$	−6.14452	+	8.45720i	−0.799948	+	1.10103i	0.192849	+	0.981228i	$0.438227\pi$
$59$	−6.14452	+	8.45720i	−0.799948	+	1.10103i	−0.992797	+	0.119806i	$0.961773\pi$
$60$	−0.306950	−	0.944696i	−0.0396271	−	0.121960i
$61$	−2.65139	−	8.16013i	−0.339475	−	1.04480i	−0.964475	−	0.264173i	$-0.914901\pi$
$61$	−2.65139	−	8.16013i	−0.339475	−	1.04480i	0.625000	−	0.780625i	$-0.285099\pi$
$62$	−1.31114	−	0.952603i	−0.166516	−	0.120981i
$63$	−2.63718	−	0.212765i	−0.332254	−	0.0268059i
$64$	−0.858667	+	2.64270i	−0.107333	+	0.330338i
$65$		−	3.86787i		−	0.479751i
$66$	0.912250	−	2.36018i	0.112290	−	0.290518i
$67$	−10.3638			−1.26613			−0.633067	−	0.774097i	$-0.718204\pi$
$67$	−10.3638			−1.26613			−0.633067	+	0.774097i	$0.718204\pi$
$68$	2.50571	−	7.71177i	0.303862	−	0.935190i
$69$	1.88461	+	2.59395i	0.226881	+	0.312275i
$70$	−0.327398	−	1.37561i	−0.0391316	−	0.164417i
$71$	−2.23595	−	6.88155i	−0.265359	−	0.816690i	−0.991611	−	0.129261i	$-0.958739\pi$
$71$	−2.23595	−	6.88155i	−0.265359	−	0.816690i	0.726252	−	0.687429i	$-0.241261\pi$
$72$	−2.48002	+	0.805806i	−0.292273	+	0.0949652i
$73$	7.88877	+	5.73153i	0.923311	+	0.670825i	0.944346	−	0.328954i	$-0.106696\pi$
$73$	7.88877	+	5.73153i	0.923311	+	0.670825i	−0.0210349	+	0.999779i	$0.506696\pi$
$74$	4.08871	+	5.62763i	0.475303	+	0.654199i
$75$	−4.28856	−	1.39344i	−0.495200	−	0.160900i
$76$	−6.33485			−0.726657
$77$	−3.81154	+	7.90393i	−0.434365	+	0.900737i
$78$	−4.21239			−0.476959
$79$	10.6292	+	3.45362i	1.19587	+	0.388563i	0.838241	−	0.545300i	$-0.183584\pi$
$79$	10.6292	+	3.45362i	1.19587	+	0.388563i	0.357632	+	0.933863i	$0.383584\pi$
$80$	0.348529	+	0.479709i	0.0389667	+	0.0536331i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−4.61427	+	1.49927i	−0.509561	+	0.165566i
$83$	−4.35552	−	13.4049i	−0.478081	−	1.47138i	−0.841757	−	0.539856i	$-0.818479\pi$
$83$	−4.35552	−	13.4049i	−0.478081	−	1.47138i	0.363677	−	0.931525i	$-0.381521\pi$
$84$	3.64957	−	0.868605i	0.398201	−	0.0947726i
$85$	2.35471	+	3.24097i	0.255404	+	0.351533i
$86$	−1.77569	+	5.46503i	−0.191478	+	0.589309i
$87$	−7.63378			−0.818427
$88$	−0.472579	+	8.63566i	−0.0503771	+	0.920564i
$89$			1.46930i			0.155745i	0.996963	+	0.0778725i	$0.0248127\pi$
$89$			1.46930i			0.155745i	−0.996963	+	0.0778725i	$0.975187\pi$
$90$	0.165156	−	0.508298i	0.0174090	−	0.0535793i
$91$	14.5608	+	1.17475i	1.52638	+	0.123147i
$92$	−3.67806	−	2.67227i	−0.383464	−	0.278603i
$93$	0.656435	+	2.02030i	0.0680691	+	0.209495i
$94$	1.38481	+	4.26202i	0.142833	+	0.439594i
$95$	1.83961	−	2.53200i	0.188740	−	0.259778i
$96$	4.74169	−	3.44504i	0.483947	−	0.351608i
$97$	7.42547	+	2.41268i	0.753942	+	0.244971i	0.660676	−	0.750671i	$-0.270270\pi$
$97$	7.42547	+	2.41268i	0.753942	+	0.244971i	0.0932653	+	0.995641i	$0.470270\pi$
$98$	5.27799	−	0.814706i	0.533158	−	0.0822977i
$99$	−2.78572	+	1.79993i	−0.279975	+	0.180900i
$100$	6.39385			0.639385
$101$	3.53206	−	10.8706i	0.351453	−	1.08166i	−0.606585	−	0.795019i	$-0.707461\pi$
$101$	3.53206	−	10.8706i	0.351453	−	1.08166i	0.958038	−	0.286642i	$-0.0925389\pi$
$102$	3.52965	−	2.56444i	0.349488	−	0.253918i
$103$	2.02928	−	2.79306i	0.199951	−	0.275208i	−0.697253	−	0.716825i	$-0.745595\pi$
$103$	2.02928	−	2.79306i	0.199951	−	0.275208i	0.897204	+	0.441616i	$0.145595\pi$
$104$	13.6930	−	4.44913i	1.34271	−	0.436273i
$105$	−0.712641	+	1.71095i	−0.0695466	+	0.166972i
$106$	0.124381	−	0.171196i	0.0120810	−	0.0166280i
$107$	2.15697	+	2.96882i	0.208522	+	0.287006i	0.900449	−	0.434961i	$-0.143238\pi$
$107$	2.15697	+	2.96882i	0.208522	+	0.287006i	−0.691927	+	0.721968i	$0.743238\pi$
$108$	1.34854	+	0.438167i	0.129763	+	0.0421627i
$109$			7.16195i			0.685990i	0.939337	+	0.342995i	$0.111441\pi$
$109$			7.16195i			0.685990i	−0.939337	+	0.342995i	$0.888559\pi$
$110$	−1.37498	−	1.11871i	−0.131099	−	0.106664i
$111$		−	9.11767i		−	0.865411i
$112$	−1.91174	+	1.16636i	−0.180642	+	0.110210i
$113$	−5.46133	+	3.96789i	−0.513759	+	0.373268i	−0.814248	−	0.580518i	$-0.802850\pi$
$113$	−5.46133	+	3.96789i	−0.513759	+	0.373268i	0.300489	+	0.953785i	$0.402850\pi$
$114$	−2.75753	−	2.00346i	−0.258266	−	0.187641i
$115$	2.13618	−	0.694087i	0.199200	−	0.0647239i
$116$	10.2945	−	3.34487i	0.955817	−	0.310564i
$117$	4.46686	+	3.24536i	0.412961	+	0.300034i
$118$	6.45224	−	4.68783i	0.593977	−	0.431550i
$119$	−12.9160	+	7.88005i	−1.18400	+	0.722363i
$120$			1.82674i			0.166758i
$121$	2.23730	+	10.7701i	0.203391	+	0.979098i
$122$			6.54598i			0.592645i
$123$	6.04810	+	1.96515i	0.545339	+	0.177191i
$124$	−1.77046	−	2.43683i	−0.158992	−	0.218833i
$125$	−3.91555	+	5.38929i	−0.350218	+	0.482033i
$126$	1.86335	+	0.776116i	0.166000	+	0.0691419i
$127$	2.80259	−	0.910616i	0.248689	−	0.0808041i	−0.182020	−	0.983295i	$-0.558263\pi$
$127$	2.80259	−	0.910616i	0.248689	−	0.0808041i	0.430709	+	0.902491i	$0.358263\pi$
$128$	−5.64401	+	7.76831i	−0.498865	+	0.686628i
$129$	6.09340	−	4.42711i	0.536494	−	0.389786i
$130$	−0.911882	+	2.80648i	−0.0799773	+	0.246145i
$131$	12.3849			1.08207			0.541037	−	0.840999i	$-0.318032\pi$
$131$	12.3849			1.08207			0.541037	+	0.840999i	$0.318032\pi$
$132$	2.96799	−	3.64790i	0.258330	−	0.317509i
$133$	8.97310	+	7.69429i	0.778067	+	0.667180i
$134$	7.51982	+	2.44334i	0.649613	+	0.211072i
$135$	−0.566742	+	0.411762i	−0.0487774	+	0.0354388i
$136$	−8.76511	+	12.0641i	−0.751602	+	1.03449i
$137$	−2.25693	−	6.94613i	−0.192823	−	0.593448i	−0.999995	−	0.00313182i	$-0.999003\pi$
$137$	−2.25693	−	6.94613i	−0.192823	−	0.593448i	0.807172	−	0.590316i	$-0.200997\pi$
$138$	−0.755910	−	2.32645i	−0.0643473	−	0.198041i
$139$	−7.84744	−	5.70150i	−0.665611	−	0.483595i	0.202942	−	0.979191i	$-0.434950\pi$
$139$	−7.84744	−	5.70150i	−0.665611	−	0.483595i	−0.868553	+	0.495596i	$0.834950\pi$
$140$	0.211342	−	2.61954i	0.0178616	−	0.221392i
$141$	1.81513	−	5.58640i	0.152862	−	0.470459i
$142$			5.52032i			0.463255i
$143$	15.3809	−	9.93804i	1.28622	−	0.831061i
$144$	−0.846432			−0.0705360
$145$	−1.65253	+	5.08597i	−0.137235	+	0.422367i
$146$	−4.37275	−	6.01857i	−0.361891	−	0.498101i
$147$	−6.22451	−	3.20242i	−0.513389	−	0.264131i
$148$	3.99507	+	12.2956i	0.328393	+	1.01069i
$149$	8.28708	−	2.69264i	0.678904	−	0.220589i	0.0507887	−	0.998709i	$-0.483826\pi$
$149$	8.28708	−	2.69264i	0.678904	−	0.220589i	0.628116	+	0.778120i	$0.283826\pi$
$150$	2.78321	+	2.02212i	0.227248	+	0.165106i
$151$	−3.00424	−	4.13498i	−0.244482	−	0.336500i	0.669087	−	0.743184i	$-0.266685\pi$
$151$	−3.00424	−	4.13498i	−0.244482	−	0.336500i	−0.913569	+	0.406683i	$0.866685\pi$
$152$	11.0798	+	3.60005i	0.898693	+	0.292003i
$153$	−5.71861			−0.462322
$154$	4.62902	−	4.83640i	0.373017	−	0.389728i
$155$	1.48812			0.119528
$156$	−7.44575	−	2.41927i	−0.596137	−	0.193697i
$157$	−8.67530	−	11.9405i	−0.692365	−	0.952958i	−0.999999	−	0.00145341i	$-0.999537\pi$
$157$	−8.67530	−	11.9405i	−0.692365	−	0.952958i	0.307634	−	0.951505i	$-0.400463\pi$
$158$	−6.89817	−	5.01181i	−0.548789	−	0.398718i
$159$	−0.263790	+	0.0857105i	−0.0209199	+	0.00679728i
$160$	−1.26878	−	3.90490i	−0.100306	−	0.308710i
$161$	1.96412	+	8.25255i	0.154794	+	0.650392i
$162$	0.448438	+	0.617222i	0.0352326	+	0.0484936i
$163$	5.65736	−	17.4115i	0.443118	−	1.36378i	−0.441416	−	0.897303i	$-0.645524\pi$
$163$	5.65736	−	17.4115i	0.443118	−	1.36378i	0.884534	−	0.466475i	$-0.154476\pi$
$164$	−9.01718			−0.704123
$165$	0.596155	+	2.24562i	0.0464106	+	0.174821i
$166$			10.7533i			0.834618i
$167$	−3.52118	+	10.8371i	−0.272477	+	0.838599i	0.717399	+	0.696663i	$0.245333\pi$
$167$	−3.52118	+	10.8371i	−0.272477	+	0.838599i	−0.989876	+	0.141936i	$0.954667\pi$
$168$	−6.87683	−	0.554815i	−0.530559	−	0.0428049i
$169$	−14.1458	−	10.2775i	−1.08814	−	0.790579i
$170$	−0.944462	−	2.90675i	−0.0724369	−	0.222938i
$171$	1.38058	+	4.24898i	0.105575	+	0.324928i
$172$	−6.27738	+	8.64007i	−0.478646	+	0.658799i
$173$	−17.9719	+	13.0573i	−1.36638	+	0.992730i	−0.368365	+	0.929681i	$0.620082\pi$
$173$	−17.9719	+	13.0573i	−1.36638	+	0.992730i	−0.998010	+	0.0630484i	$0.979918\pi$
$174$	5.53898	+	1.79972i	0.419909	+	0.136437i
$175$	−9.05668	−	7.76596i	−0.684621	−	0.587052i
$176$	−1.01210	+	2.61851i	−0.0762897	+	0.197378i
$177$	−10.4537			−0.785746
$178$	0.346398	−	1.06610i	0.0259636	−	0.0799079i
$179$	8.77885	−	6.37821i	0.656162	−	0.476729i	−0.209203	−	0.977872i	$-0.567087\pi$
$179$	8.77885	−	6.37821i	0.656162	−	0.476729i	0.865365	+	0.501143i	$0.167087\pi$
$180$	0.583854	−	0.803606i	0.0435179	−	0.0598973i
$181$	−2.80870	+	0.912602i	−0.208769	+	0.0678332i	−0.411535	−	0.911394i	$-0.635007\pi$
$181$	−2.80870	+	0.912602i	−0.208769	+	0.0678332i	0.202766	+	0.979227i	$0.435007\pi$
$182$	−10.2882	−	4.28520i	−0.762610	−	0.317640i
$183$	5.04324	−	6.94142i	0.372807	−	0.513124i
$184$	4.91440	+	6.76409i	0.362295	+	0.498656i
$185$	−6.07461	−	1.97376i	−0.446614	−	0.145114i
$186$		−	1.62066i		−	0.118833i
$187$	−6.83785	+	17.6910i	−0.500033	+	1.29369i
$188$			8.32881i			0.607441i
$189$	−1.37797	−	2.25859i	−0.100232	−	0.164288i
$190$	−1.93174	+	1.40349i	−0.140143	+	0.101820i
$191$	−1.45788	−	1.05922i	−0.105489	−	0.0766421i	0.533790	−	0.845617i	$-0.320767\pi$
$191$	−1.45788	−	1.05922i	−0.105489	−	0.0766421i	−0.639279	+	0.768975i	$0.720767\pi$
$192$	−2.64270	+	0.858667i	−0.190721	+	0.0619689i
$193$	−15.8913	+	5.16340i	−1.14388	+	0.371669i	−0.818835	−	0.574029i	$-0.805380\pi$
$193$	−15.8913	+	5.16340i	−1.14388	+	0.371669i	−0.325046	+	0.945698i	$0.605380\pi$
$194$	−4.81902	−	3.50123i	−0.345986	−	0.251373i
$195$	3.12917	−	2.27348i	0.224085	−	0.162807i
$196$	9.79720	+	1.59121i	0.699800	+	0.113658i
$197$		−	8.02318i		−	0.571628i	−0.958285	−	0.285814i	$-0.907736\pi$
$197$		−	8.02318i		−	0.571628i	0.958285	−	0.285814i	$-0.0922639\pi$
$198$	2.44564	−	0.649255i	0.173804	−	0.0461406i
$199$		−	18.8821i		−	1.33852i	−0.743029	−	0.669259i	$-0.766612\pi$
$199$		−	18.8821i		−	1.33852i	0.743029	−	0.669259i	$-0.233388\pi$
$200$	−11.1830	−	3.63359i	−0.790760	−	0.256933i
$201$	−6.09166	−	8.38445i	−0.429673	−	0.591394i
$202$	−5.12564	+	7.05483i	−0.360639	+	0.496376i
$203$	−18.6444	−	7.76573i	−1.30858	−	0.545047i
$204$	7.71177	−	2.50571i	0.539932	−	0.175435i
$205$	2.61854	−	3.60411i	0.182887	−	0.251722i
$206$	−2.13090	+	1.54819i	−0.148467	+	0.107868i
$207$	−0.990800	+	3.04937i	−0.0688654	+	0.211946i
$208$	4.67344			0.324045
$209$	14.7954	+	0.809663i	1.02342	+	0.0560056i
$210$	0.920454	−	1.07344i	0.0635174	−	0.0740741i
$211$	12.1721	+	3.95495i	0.837961	+	0.272270i	0.696395	−	0.717659i	$-0.254786\pi$
$211$	12.1721	+	3.95495i	0.837961	+	0.272270i	0.141566	+	0.989929i	$0.454786\pi$
$212$	0.318176	−	0.231168i	0.0218524	−	0.0158767i
$213$	4.25303	−	5.85380i	0.291413	−	0.401096i
$214$	−0.865152	−	2.66266i	−0.0591405	−	0.182016i
$215$	−1.63047	−	5.01806i	−0.111197	−	0.342229i
$216$	−2.10963	−	1.53273i	−0.143542	−	0.104289i
$217$	−0.451969	+	5.60208i	−0.0306817	+	0.380294i
$218$	1.68849	−	5.19663i	0.114359	−	0.351960i
$219$			9.75106i			0.658916i
$220$	−1.78790	−	2.76709i	−0.120540	−	0.186557i
$221$	31.5744			2.12392
$222$	−2.14956	+	6.61568i	−0.144269	+	0.444015i
$223$	4.80928	+	6.61940i	0.322053	+	0.443268i	0.939093	−	0.343664i	$-0.111668\pi$
$223$	4.80928	+	6.61940i	0.322053	+	0.443268i	−0.617040	+	0.786932i	$0.711668\pi$
$224$	15.0855	−	3.59038i	1.00794	−	0.239893i
$225$	−1.39344	−	4.28856i	−0.0928958	−	0.285904i
$226$	4.89814	−	1.59150i	0.325819	−	0.105865i
$227$	−2.06157	−	1.49782i	−0.136831	−	0.0994136i	0.517264	−	0.855826i	$-0.326950\pi$
$227$	−2.06157	−	1.49782i	−0.136831	−	0.0994136i	−0.654095	+	0.756412i	$0.726950\pi$
$228$	−3.72353	−	5.12500i	−0.246597	−	0.339411i
$229$	11.7466	+	3.81670i	0.776237	+	0.252215i	0.670233	−	0.742151i	$-0.266194\pi$
$229$	11.7466	+	3.81670i	0.776237	+	0.252215i	0.106004	+	0.994366i	$0.466194\pi$
$230$	−1.71362			−0.112993
$231$	−8.63478	+	1.56222i	−0.568127	+	0.102786i
$232$	−19.9062			−1.30690
$233$	−10.5097	−	3.41482i	−0.688516	−	0.223712i	−0.0561958	−	0.998420i	$-0.517897\pi$
$233$	−10.5097	−	3.41482i	−0.688516	−	0.223712i	−0.632320	+	0.774707i	$0.717897\pi$
$234$	−2.47598	−	3.40789i	−0.161860	−	0.222781i
$235$	−3.32898	−	2.41864i	−0.217159	−	0.157775i
$236$	14.0972	−	4.58046i	0.917650	−	0.298163i
$237$	3.45362	+	10.6292i	0.224337	+	0.690438i
$238$	11.2295	−	2.67263i	0.727897	−	0.173241i
$239$	0.658287	+	0.906054i	0.0425810	+	0.0586078i	0.829777	−	0.558096i	$-0.188468\pi$
$239$	0.658287	+	0.906054i	0.0425810	+	0.0586078i	−0.787196	+	0.616703i	$0.788468\pi$
$240$	−0.183232	+	0.563932i	−0.0118276	+	0.0364016i
$241$	1.27864			0.0823644			0.0411822	−	0.999152i	$-0.486888\pi$
$241$	1.27864			0.0823644			0.0411822	+	0.999152i	$0.486888\pi$
$242$	0.915771	−	8.34210i	0.0588680	−	0.536251i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.75951	+	11.5706i	−0.240678	+	0.740730i
$245$	−3.48105	+	3.45380i	−0.222396	+	0.220655i
$246$	−3.92513	−	2.85178i	−0.250257	−	0.181823i
$247$	−7.62263	−	23.4601i	−0.485017	−	1.49273i
$248$	1.71175	+	5.26822i	0.108696	+	0.334532i
$249$	8.28470	−	11.4029i	0.525021	−	0.722630i
$250$	4.11165	−	2.98729i	0.260043	−	0.188933i
$251$	−20.7714	−	6.74905i	−1.31108	−	0.425996i	−0.431658	−	0.902037i	$-0.642071\pi$
$251$	−20.7714	−	6.74905i	−1.31108	−	0.425996i	−0.879423	+	0.476041i	$0.842071\pi$
$252$	2.84788	+	2.44201i	0.179400	+	0.153832i
$253$	8.24875	+	6.71131i	0.518595	+	0.421937i
$254$	−2.24821			−0.141065
$255$	−1.23794	+	3.80999i	−0.0775229	+	0.238591i
$256$	10.4227	−	7.57254i	0.651419	−	0.473284i
$257$	−11.4514	+	15.7615i	−0.714320	+	0.983177i	0.285374	+	0.958416i	$0.407882\pi$
$257$	−11.4514	+	15.7615i	−0.714320	+	0.983177i	−0.999693	+	0.0247603i	$0.992118\pi$
$258$	−5.46503	+	1.77569i	−0.340238	+	0.110550i
$259$	9.27528	−	22.2687i	0.576338	−	1.38371i
$260$	−3.22366	+	4.43698i	−0.199923	+	0.275170i
$261$	−4.48702	−	6.17586i	−0.277740	−	0.382276i
$262$	−8.98635	−	2.91984i	−0.555178	−	0.180388i
$263$			20.2701i			1.24991i	0.780662	+	0.624953i	$0.214882\pi$
$263$			20.2701i			1.24991i	−0.780662	+	0.624953i	$0.785118\pi$
$264$	−7.26417	+	4.69359i	−0.447079	+	0.288870i
$265$			0.194303i			0.0119359i
$266$	−4.69679	−	7.69837i	−0.287979	−	0.472017i
$267$	−1.18869	+	0.863630i	−0.0727464	+	0.0528533i
$268$	11.8886	+	8.63761i	0.726215	+	0.527626i
$269$	18.9413	−	6.15440i	1.15487	−	0.375241i	0.331895	−	0.943316i	$-0.392312\pi$
$269$	18.9413	−	6.15440i	1.15487	−	0.375241i	0.822976	+	0.568076i	$0.192312\pi$
$270$	0.508298	−	0.165156i	0.0309340	−	0.0100511i
$271$	2.25879	+	1.64111i	0.137212	+	0.0996902i	0.654274	−	0.756258i	$-0.272974\pi$
$271$	2.25879	+	1.64111i	0.137212	+	0.0996902i	−0.517062	+	0.855948i	$0.672974\pi$
$272$	−3.91598	+	2.84512i	−0.237441	+	0.172511i
$273$	7.60822	+	12.4704i	0.460470	+	0.754744i
$274$			5.57212i			0.336624i
$275$	−14.9332	−	0.817205i	−0.900504	−	0.0492793i
$276$		−	4.54633i		−	0.273657i
$277$	−9.51488	−	3.09157i	−0.571694	−	0.185754i	0.00888246	−	0.999961i	$-0.497173\pi$
$277$	−9.51488	−	3.09157i	−0.571694	−	0.185754i	−0.580576	+	0.814206i	$0.697173\pi$
$278$	4.34984	+	5.98704i	0.260886	+	0.359079i
$279$	−1.24861	+	1.71857i	−0.0747525	+	0.102888i
$280$	−1.85831	+	4.46155i	−0.111055	+	0.266629i
$281$	−14.9570	+	4.85981i	−0.892258	+	0.289912i	−0.719038	−	0.694971i	$-0.755417\pi$
$281$	−14.9570	+	4.85981i	−0.892258	+	0.289912i	−0.173220	+	0.984883i	$0.555417\pi$
$282$	−2.63407	+	3.62549i	−0.156857	+	0.215895i
$283$	9.88803	−	7.18407i	0.587782	−	0.427049i	−0.253739	−	0.967273i	$-0.581660\pi$
$283$	9.88803	−	7.18407i	0.587782	−	0.427049i	0.841521	+	0.540224i	$0.181660\pi$
$284$	−3.17044	+	9.75763i	−0.188131	+	0.579009i
$285$	3.12972			0.185389
$286$	−13.5032	+	3.58476i	−0.798460	+	0.211971i
$287$	12.7725	+	10.9522i	0.753939	+	0.646491i
$288$	5.57420	+	1.81117i	0.328463	+	0.106724i
$289$	−12.7035	+	9.22967i	−0.747267	+	0.542922i
$290$	2.39811	−	3.30072i	0.140822	−	0.193825i
$291$	2.41268	+	7.42547i	0.141434	+	0.435288i
$292$	−4.27260	−	13.1497i	−0.250035	−	0.769528i
$293$	−8.03255	−	5.83599i	−0.469267	−	0.340942i	0.327889	−	0.944716i	$-0.393663\pi$
$293$	−8.03255	−	5.83599i	−0.469267	−	0.340942i	−0.797155	+	0.603774i	$0.793663\pi$
$294$	3.76144	+	3.79111i	0.219371	+	0.221102i
$295$	−2.26297	+	6.96471i	−0.131755	+	0.405501i
$296$		−	23.7757i		−	1.38193i
$297$	−3.09358	−	1.19572i	−0.179508	−	0.0693827i
$298$	−6.64782			−0.385098
$299$	5.47054	−	16.8366i	0.316370	−	0.973685i
$300$	3.75821	+	5.17274i	0.216980	+	0.298648i
$301$	19.3859	−	4.61389i	1.11739	−	0.265940i
$302$	1.20499	+	3.70857i	0.0693392	+	0.213404i
$303$	10.8706	−	3.53206i	0.624497	−	0.202911i
$304$	3.05934	+	2.22274i	0.175465	+	0.127483i
$305$	−3.53295	−	4.86268i	−0.202296	−	0.278436i
$306$	4.14935	+	1.34821i	0.237203	+	0.0770718i
$307$	3.82351			0.218219			0.109110	−	0.994030i	$-0.465200\pi$
$307$	3.82351			0.218219			0.109110	+	0.994030i	$0.465200\pi$
$308$	10.9598	−	5.89019i	0.624495	−	0.335625i
$309$	3.45241			0.196401
$310$	−1.07976	−	0.350835i	−0.0613262	−	0.0199261i
$311$	−8.65762	−	11.9162i	−0.490929	−	0.675705i	0.489630	−	0.871930i	$-0.337132\pi$
$311$	−8.65762	−	11.9162i	−0.490929	−	0.675705i	−0.980559	+	0.196225i	$0.937132\pi$
$312$	11.6480	+	8.46275i	0.659437	+	0.479109i
$313$	−19.1659	+	6.22739i	−1.08332	+	0.351993i	−0.795663	−	0.605740i	$-0.792877\pi$
$313$	−19.1659	+	6.22739i	−1.08332	+	0.351993i	−0.287660	+	0.957733i	$0.592877\pi$
$314$	3.47962	+	10.7092i	0.196367	+	0.604354i
$315$	−1.80307	+	0.429134i	−0.101591	+	0.0241789i
$316$	−9.31470	−	12.8206i	−0.523993	−	0.721214i
$317$	−5.69570	+	17.5296i	−0.319902	+	0.984559i	0.653787	+	0.756679i	$0.273179\pi$
$317$	−5.69570	+	17.5296i	−0.319902	+	0.984559i	−0.973689	+	0.227880i	$0.926821\pi$
$318$	0.211610			0.0118665
$319$	−24.4707	+	6.49637i	−1.37010	+	0.363727i
$320$			1.94657i			0.108817i
$321$	−1.13399	+	3.49005i	−0.0632930	+	0.194796i
$322$	0.520460	−	6.45101i	0.0290041	−	0.359501i
$323$	20.6693	+	15.0171i	1.15007	+	0.835576i
$324$	0.438167	+	1.34854i	0.0243426	+	0.0749189i
$325$	7.69363	+	23.6786i	0.426766	+	1.31345i
$326$	−8.20982	+	11.2999i	−0.454700	+	0.625841i
$327$	−5.79414	+	4.20969i	−0.320417	+	0.232796i
$328$	15.7713	+	5.12441i	0.870824	+	0.282948i
$329$	10.1162	−	11.7975i	0.557722	−	0.650417i
$330$	0.0968585	−	1.76994i	0.00533189	−	0.0974320i
$331$	8.95658			0.492298			0.246149	−	0.969232i	$-0.420835\pi$
$331$	8.95658			0.492298			0.246149	+	0.969232i	$0.420835\pi$
$332$	−6.17587	+	19.0074i	−0.338945	+	1.04316i
$333$	7.37635	−	5.35923i	0.404222	−	0.293684i
$334$	5.10986	−	7.03312i	0.279599	−	0.384835i
$335$	−6.90480	+	2.24351i	−0.377249	+	0.122576i
$336$	−2.06729	−	0.861064i	−0.112780	−	0.0469749i
$337$	−1.64749	+	2.26758i	−0.0897446	+	0.123523i	−0.851528	−	0.524308i	$-0.824324\pi$
$337$	−1.64749	+	2.26758i	−0.0897446	+	0.123523i	0.761784	+	0.647831i	$0.224324\pi$
$338$	7.84102	+	10.7922i	0.426495	+	0.587021i
$339$	−6.42018	−	2.08604i	−0.348696	−	0.113298i
$340$		−	5.68036i		−	0.308061i
$341$	3.82354	+	5.91761i	0.207056	+	0.320457i
$342$		−	3.40849i		−	0.184310i
$343$	−11.9447	−	14.1536i	−0.644955	−	0.764221i
$344$	15.8894	−	11.5443i	0.856700	−	0.622429i
$345$	1.81714	+	1.32023i	0.0978317	+	0.0710789i
$346$	16.1185	−	5.23723i	0.866538	−	0.281555i
$347$	−4.73756	+	1.53933i	−0.254326	+	0.0826354i	−0.433405	−	0.901199i	$-0.642688\pi$
$347$	−4.73756	+	1.53933i	−0.254326	+	0.0826354i	0.179079	+	0.983835i	$0.442688\pi$
$348$	8.75699	+	6.36233i	0.469424	+	0.341056i
$349$	6.14513	−	4.46470i	0.328941	−	0.238990i	−0.411040	−	0.911617i	$-0.634834\pi$
$349$	6.14513	−	4.46470i	0.328941	−	0.238990i	0.739981	+	0.672627i	$0.234834\pi$
$350$	4.74054	+	7.77008i	0.253392	+	0.415328i
$351$			5.52134i			0.294707i
$352$	12.2682	−	15.0786i	0.653896	−	0.803691i
$353$		−	14.4322i		−	0.768147i	−0.923302	−	0.384074i	$-0.874521\pi$
$353$		−	14.4322i		−	0.768147i	0.923302	−	0.384074i	$-0.125479\pi$
$354$	7.58507	+	2.46454i	0.403142	+	0.130989i
$355$	−2.97938	−	4.10077i	−0.158129	−	0.217646i
$356$	1.22458	−	1.68548i	0.0649024	−	0.0893305i
$357$	−13.9669	−	5.81745i	−0.739207	−	0.307892i
$358$	−7.87354	+	2.55827i	−0.416130	+	0.135209i
$359$	11.4175	−	15.7149i	0.602594	−	0.829399i	−0.393349	−	0.919389i	$-0.628684\pi$
$359$	11.4175	−	15.7149i	0.602594	−	0.829399i	0.995943	+	0.0899901i	$0.0286835\pi$
$360$	−1.47786	+	1.07373i	−0.0778902	+	0.0565905i
$361$	0.296601	−	0.912843i	0.0156106	−	0.0480444i
$362$	2.25311			0.118421
$363$	−7.39812	+	8.14050i	−0.388301	+	0.427266i
$364$	−15.7241	−	13.4832i	−0.824168	−	0.706711i
$365$	6.49660	+	2.11087i	0.340047	+	0.110488i
$366$	−5.29581	+	3.84763i	−0.276816	+	0.201119i
$367$	21.3963	−	29.4495i	1.11688	−	1.53725i	0.306009	−	0.952029i	$-0.401006\pi$
$367$	21.3963	−	29.4495i	1.11688	−	1.53725i	0.810871	−	0.585225i	$-0.198994\pi$
$368$	0.838645	+	2.58108i	0.0437174	+	0.134548i
$369$	1.96515	+	6.04810i	0.102301	+	0.314852i
$370$	3.94233	+	2.86427i	0.204952	+	0.148906i
$371$	−0.731462	−	0.0590135i	−0.0379756	−	0.00306383i
$372$	0.930785	−	2.86466i	0.0482589	−	0.148526i
$373$			4.09492i			0.212027i	0.994365	+	0.106014i	$0.0338087\pi$
$373$			4.09492i			0.212027i	−0.994365	+	0.106014i	$0.966191\pi$
$374$	9.13226	−	11.2243i	0.472218	−	0.580394i
$375$	−6.66153			−0.344000
$376$	4.73321	−	14.5673i	0.244097	−	0.751253i
$377$	24.7744	+	34.0990i	1.27594	+	1.75619i
$378$	0.467357	+	1.96367i	0.0240383	+	0.101000i
$379$	6.28296	+	19.3370i	0.322734	+	0.993273i	0.972453	+	0.233099i	$0.0748865\pi$
$379$	6.28296	+	19.3370i	0.322734	+	0.993273i	−0.649719	+	0.760174i	$0.725113\pi$
$380$	−4.22056	+	1.37134i	−0.216510	+	0.0703484i
$381$	2.38402	+	1.73209i	0.122137	+	0.0887379i
$382$	0.808106	+	1.11226i	0.0413463	+	0.0569083i
$383$	5.35563	+	1.74015i	0.273660	+	0.0889175i	0.442632	−	0.896703i	$-0.354045\pi$
$383$	5.35563	+	1.74015i	0.273660	+	0.0889175i	−0.168972	+	0.985621i	$0.554045\pi$
$384$	−9.60216			−0.490008
$385$	−0.828406	+	6.09107i	−0.0422195	+	0.310429i
$386$	12.7479			0.648849
$387$	7.16322	+	2.32747i	0.364127	+	0.118312i
$388$	−6.50719	−	8.95639i	−0.330353	−	0.454692i
$389$	7.31625	+	5.31557i	0.370949	+	0.269510i	0.757604	−	0.652714i	$-0.226370\pi$
$389$	7.31625	+	5.31557i	0.370949	+	0.269510i	−0.386656	+	0.922224i	$0.626370\pi$
$390$	−2.80648	+	0.911882i	−0.142112	+	0.0461749i
$391$	5.66599	+	17.4381i	0.286542	+	0.881884i
$392$	−16.2313	−	8.35076i	−0.819805	−	0.421777i
$393$	7.27967	+	10.0196i	0.367211	+	0.505422i
$394$	−1.89153	+	5.82153i	−0.0952938	+	0.293284i
$395$	7.82925			0.393932
$396$	4.69575	+	0.256971i	0.235970	+	0.0129133i
$397$		−	31.7609i		−	1.59403i	−0.603958	−	0.797016i	$-0.706411\pi$
$397$		−	31.7609i		−	1.59403i	0.603958	−	0.797016i	$-0.293589\pi$
$398$	−4.45161	+	13.7007i	−0.223139	+	0.686752i
$399$	−0.950557	+	11.7820i	−0.0475874	+	0.589837i
$400$	−3.08784	−	2.24345i	−0.154392	−	0.112172i
$401$	10.1128	+	31.1241i	0.505010	+	1.55426i	0.800754	+	0.598994i	$0.204433\pi$
$401$	10.1128	+	31.1241i	0.505010	+	1.55426i	−0.295744	+	0.955267i	$0.595567\pi$
$402$	2.44334	+	7.51982i	0.121863	+	0.375054i
$403$	6.89401	−	9.48880i	0.343415	−	0.472671i
$404$	−13.1117	+	9.52624i	−0.652334	+	0.473948i
$405$	−0.666245	−	0.216476i	−0.0331060	−	0.0107568i
$406$	11.6974	+	10.0303i	0.580530	+	0.497795i
$407$	−7.75918	−	29.2275i	−0.384608	−	1.44875i
$408$	−14.9121			−0.738258
$409$	−4.00330	+	12.3209i	−0.197950	+	0.609229i	0.801979	+	0.597352i	$0.203780\pi$
$409$	−4.00330	+	12.3209i	−0.197950	+	0.609229i	−0.999929	+	0.0118765i	$0.996220\pi$
$410$	−2.74968	+	1.99776i	−0.135797	+	0.0986623i
$411$	4.29294	−	5.90873i	0.211755	−	0.291456i
$412$	−4.65572	+	1.51273i	−0.229371	+	0.0745271i
$413$	−25.5317	−	10.6344i	−1.25633	−	0.523283i
$414$	1.43783	−	1.97900i	0.0706653	−	0.0972624i
$415$	−5.80369	−	7.98810i	−0.284892	−	0.392120i
$416$	−30.7770	−	10.0001i	−1.50897	−	0.490293i
$417$		−	9.69997i		−	0.475009i
$418$	−10.5445	−	4.07560i	−0.515746	−	0.199344i
$419$			27.3872i			1.33795i	0.743283	+	0.668977i	$0.233268\pi$
$419$			27.3872i			1.33795i	−0.743283	+	0.668977i	$0.766732\pi$
$420$	2.24348	−	1.36875i	0.109471	−	0.0667882i
$421$	−7.81949	+	5.68119i	−0.381099	+	0.276884i	−0.761798	−	0.647814i	$-0.775683\pi$
$421$	−7.81949	+	5.68119i	−0.381099	+	0.276884i	0.380700	+	0.924699i	$0.375683\pi$
$422$	−7.89951	−	5.73933i	−0.384542	−	0.279386i
$423$	5.58640	−	1.81513i	0.271620	−	0.0882546i
$424$	−0.687870	+	0.223502i	−0.0334059	+	0.0108542i
$425$	−20.8618	−	15.1570i	−1.01195	−	0.735223i
$426$	−4.46603	+	3.24476i	−0.216380	+	0.157209i
$427$	19.3788	−	11.8230i	0.937806	−	0.572157i
$428$		−	5.20336i		−	0.251514i
$429$	17.0807	+	6.60198i	0.824665	+	0.318747i
$430$			4.02544i			0.194124i
$431$	−5.69014	−	1.84884i	−0.274085	−	0.0890555i	0.168750	−	0.985659i	$-0.446027\pi$
$431$	−5.69014	−	1.84884i	−0.274085	−	0.0890555i	−0.442834	+	0.896603i	$0.646027\pi$
$432$	−0.497521	−	0.684778i	−0.0239370	−	0.0329464i
$433$	−4.08205	+	5.61846i	−0.196171	+	0.270006i	−0.895759	−	0.444541i	$-0.853367\pi$
$433$	−4.08205	+	5.61846i	−0.196171	+	0.270006i	0.699588	+	0.714547i	$0.253367\pi$
$434$	1.64868	−	3.95825i	0.0791391	−	0.190002i
$435$	−5.08597	+	1.65253i	−0.243853	+	0.0792328i
$436$	5.96909	−	8.21574i	0.285867	−	0.393463i
$437$	11.5888	−	8.41978i	0.554369	−	0.402773i
$438$	2.29889	−	7.07526i	0.109845	−	0.338069i
$439$	26.5247			1.26596			0.632978	−	0.774170i	$-0.281832\pi$
$439$	26.5247			1.26596			0.632978	+	0.774170i	$0.281832\pi$
$440$	1.55456	+	5.85577i	0.0741108	+	0.279163i
$441$	−1.06787	−	6.91807i	−0.0508508	−	0.329432i
$442$	−22.9100	−	7.44391i	−1.08972	−	0.354070i
$443$	−10.9623	+	7.96460i	−0.520836	+	0.378410i	−0.816919	−	0.576753i	$-0.804320\pi$
$443$	−10.9623	+	7.96460i	−0.520836	+	0.378410i	0.296082	+	0.955162i	$0.404320\pi$
$444$	−7.59907	+	10.4592i	−0.360636	+	0.496373i
$445$	0.318068	+	0.978911i	0.0150778	+	0.0464048i
$446$	−1.92898	−	5.93679i	−0.0913398	−	0.281115i
$447$	7.04941	+	5.12170i	0.333426	+	0.242248i
$448$	−7.32795	−	0.591210i	−0.346213	−	0.0279321i
$449$	4.62536	−	14.2354i	0.218284	−	0.671810i	−0.780620	−	0.625006i	$-0.785096\pi$
$449$	4.62536	−	14.2354i	0.218284	−	0.671810i	0.998904	−	0.0468037i	$-0.0149035\pi$
$450$			3.44024i			0.162174i
$451$	21.0601	+	1.15249i	0.991680	+	0.0542688i
$452$	9.57191			0.450225
$453$	1.57942	−	4.86097i	0.0742078	−	0.228388i
$454$	1.14273	+	1.57283i	0.0536308	+	0.0738165i
$455$	9.95535	−	2.36939i	0.466714	−	0.111079i
$456$	3.60005	+	11.0798i	0.168588	+	0.518860i
$457$	−19.1162	+	6.21123i	−0.894218	+	0.290549i	−0.719848	−	0.694131i	$-0.755789\pi$
$457$	−19.1162	+	6.21123i	−0.894218	+	0.290549i	−0.174369	+	0.984680i	$0.555789\pi$
$458$	−7.62337	−	5.53871i	−0.356217	−	0.258807i
$459$	−3.36131	−	4.62645i	−0.156893	−	0.215944i
$460$	−3.02897	−	0.984173i	−0.141227	−	0.0458873i
$461$	−9.04514			−0.421274			−0.210637	−	0.977564i	$-0.567554\pi$
$461$	−9.04514			−0.421274			−0.210637	+	0.977564i	$0.567554\pi$
$462$	6.63360	+	0.902193i	0.308623	+	0.0419738i
$463$	5.44904			0.253238			0.126619	−	0.991951i	$-0.459587\pi$
$463$	5.44904			0.253238			0.126619	+	0.991951i	$0.459587\pi$
$464$	−6.14523	−	1.99671i	−0.285285	−	0.0926948i
$465$	0.874693	+	1.20391i	0.0405629	+	0.0558301i
$466$	6.82067	+	4.95551i	0.315961	+	0.229559i
$467$	−14.4674	+	4.70075i	−0.669472	+	0.217525i	−0.623980	−	0.781440i	$-0.714485\pi$
$467$	−14.4674	+	4.70075i	−0.669472	+	0.217525i	−0.0454918	+	0.998965i	$0.514485\pi$
$468$	−2.41927	−	7.44575i	−0.111831	−	0.344180i
$469$	−6.34866	−	26.6748i	−0.293154	−	1.23173i
$470$	1.84525	+	2.53977i	0.0851152	+	0.117151i
$471$	4.56088	−	14.0369i	0.210154	−	0.646788i
$472$	−27.2595			−1.25472
$473$	15.7654	−	19.3770i	0.724895	−	0.890956i
$474$		−	8.52661i		−	0.391640i
$475$	−6.22537	+	19.1597i	−0.285640	+	0.879109i
$476$	21.3840	+	1.72523i	0.980132	+	0.0790759i
$477$	−0.224393	−	0.163031i	−0.0102742	−	0.00746468i
$478$	−0.264036	−	0.812619i	−0.0120767	−	0.0371683i
$479$	9.64046	+	29.6703i	0.440484	+	1.35567i	0.887361	+	0.461075i	$0.152536\pi$
$479$	9.64046	+	29.6703i	0.440484	+	1.35567i	−0.446877	+	0.894595i	$0.647464\pi$
$480$	2.41336	−	3.32171i	0.110154	−	0.151615i
$481$	−40.7273	+	29.5901i	−1.85701	+	1.34919i
$482$	−0.927766	−	0.301449i	−0.0422586	−	0.0137306i
$483$	−5.52197	+	6.43973i	−0.251258	+	0.293018i
$484$	6.40976	−	14.2194i	0.291353	−	0.646337i
$485$	5.46947			0.248356
$486$	−0.235758	+	0.725588i	−0.0106942	+	0.0329134i
$487$	−7.16706	+	5.20718i	−0.324771	+	0.235960i	−0.738208	−	0.674573i	$-0.764328\pi$
$487$	−7.16706	+	5.20718i	−0.324771	+	0.235960i	0.413438	+	0.910532i	$0.364328\pi$
$488$	13.1510	−	18.1008i	0.595316	−	0.819383i
$489$	17.4115	−	5.65736i	0.787377	−	0.255834i
$490$	3.34007	−	1.68535i	0.150889	−	0.0761365i
$491$	−20.0756	+	27.6317i	−0.906001	+	1.24700i	0.0625135	+	0.998044i	$0.480088\pi$
$491$	−20.0756	+	27.6317i	−0.906001	+	1.24700i	−0.968514	+	0.248959i	$0.919912\pi$
$492$	−5.30016	−	7.29505i	−0.238950	−	0.328886i
$493$	−41.5180	−	13.4900i	−1.86987	−	0.607559i
$494$			18.8194i			0.846727i
$495$	−1.46633	+	1.80224i	−0.0659066	+	0.0810046i
$496$			1.79805i			0.0807348i
$497$	16.3424	−	9.97054i	0.733058	−	0.447240i
$498$	−8.69961	+	6.32063i	−0.389839	+	0.283234i
$499$	7.17883	+	5.21572i	0.321368	+	0.233488i	0.736759	−	0.676155i	$-0.236355\pi$
$499$	7.17883	+	5.21572i	0.321368	+	0.233488i	−0.415391	+	0.909643i	$0.636355\pi$
$500$	8.98335	−	2.91887i	0.401748	−	0.130536i
$501$	−10.8371	+	3.52118i	−0.484165	+	0.157315i
$502$	13.4804	+	9.79406i	0.601658	+	0.437130i
$503$	15.2517	−	11.0810i	0.680038	−	0.494077i	−0.193332	−	0.981133i	$-0.561929\pi$
$503$	15.2517	−	11.0810i	0.680038	−	0.494077i	0.873370	+	0.487057i	$0.161929\pi$
$504$	−3.59325	−	5.88959i	−0.160056	−	0.262343i
$505$		−	8.00706i		−	0.356309i
$506$	−4.40295	−	6.81436i	−0.195735	−	0.302935i
$507$		−	17.4852i		−	0.776544i
$508$	−3.97390	−	1.29120i	−0.176313	−	0.0572877i
$509$	4.41596	+	6.07805i	0.195734	+	0.269405i	0.895591	−	0.444878i	$-0.146753\pi$
$509$	4.41596	+	6.07805i	0.195734	+	0.269405i	−0.699857	+	0.714283i	$0.746753\pi$
$510$	1.79647	−	2.47263i	0.0795491	−	0.109490i
$511$	−9.91961	+	23.8156i	−0.438818	+	1.05354i
$512$	8.91651	−	2.89715i	0.394058	−	0.128037i
$513$	−2.62601	+	3.61440i	−0.115941	+	0.159580i
$514$	12.0249	−	8.73661i	0.530396	−	0.385355i
$515$	0.747365	−	2.30015i	0.0329328	−	0.101357i
$516$	−10.6797			−0.470148
$517$	1.06451	−	19.4524i	0.0468173	−	0.855514i
$518$	−11.9800	+	13.9712i	−0.526373	+	0.613857i
$519$	−21.1272	−	6.86464i	−0.927381	−	0.301324i
$520$	8.15978	−	5.92842i	0.357830	−	0.259979i
$521$	−12.2503	+	16.8611i	−0.536694	+	0.738696i	−0.988132	−	0.153606i	$-0.950911\pi$
$521$	−12.2503	+	16.8611i	−0.536694	+	0.738696i	0.451438	+	0.892302i	$0.350911\pi$
$522$	1.79972	+	5.53898i	0.0787718	+	0.242435i
$523$	8.22843	+	25.3245i	0.359804	+	1.10736i	0.953171	+	0.302432i	$0.0977984\pi$
$523$	8.22843	+	25.3245i	0.359804	+	1.10736i	−0.593367	+	0.804932i	$0.702202\pi$
$524$	−14.2072	−	10.3221i	−0.620644	−	0.450924i
$525$	0.959411	−	11.8917i	0.0418721	−	0.518998i
$526$	4.77883	−	14.7077i	0.208367	−	0.641287i
$527$			12.1478i			0.529168i
$528$	−2.71331	+	0.720317i	−0.118082	+	0.0313478i
$529$	−12.7197			−0.553029
$530$	0.0458085	−	0.140984i	0.00198979	−	0.00612395i
$531$	−6.14452	−	8.45720i	−0.266649	−	0.367011i
$532$	−3.88062	−	16.3050i	−0.168246	−	0.706911i
$533$	−10.8502	−	33.3936i	−0.469976	−	1.44644i
$534$	1.06610	−	0.346398i	0.0461348	−	0.0149901i
$535$	2.07975	+	1.51103i	0.0899155	+	0.0653274i
$536$	−15.8849	−	21.8637i	−0.686122	−	0.944366i
$537$	10.3202	+	3.35322i	0.445347	+	0.144702i
$538$	−15.1945			−0.655083
$539$	−22.6785	−	4.96854i	−0.976831	−	0.214010i
$540$	0.993312			0.0427453
$541$	21.4695	+	6.97586i	0.923045	+	0.299916i	0.731715	−	0.681610i	$-0.238720\pi$
$541$	21.4695	+	6.97586i	0.923045	+	0.299916i	0.191330	+	0.981526i	$0.438720\pi$
$542$	−1.25205	−	1.72330i	−0.0537801	−	0.0740219i
$543$	−2.38922	−	1.73587i	−0.102531	−	0.0744934i
$544$	31.8766	−	10.3573i	1.36670	−	0.444067i
$545$	1.55039	+	4.77162i	0.0664115	+	0.204394i
$546$	−2.58044	−	10.8421i	−0.110432	−	0.463998i
$547$	−0.510685	−	0.702897i	−0.0218353	−	0.0300537i	0.797960	−	0.602711i	$-0.205913\pi$
$547$	−0.510685	−	0.702897i	−0.0218353	−	0.0300537i	−0.819795	+	0.572657i	$0.805913\pi$
$548$	−3.20020	+	9.84919i	−0.136706	+	0.420737i
$549$	8.58006			0.366188
$550$	10.6427	+	4.11357i	0.453805	+	0.175403i
$551$			34.1050i			1.45292i
$552$	−2.58365	+	7.95167i	−0.109968	+	0.338446i
$553$	−2.37789	+	29.4735i	−0.101118	+	1.25334i
$554$	6.17502	+	4.48642i	0.262352	+	0.190610i
$555$	−1.97376	−	6.07461i	−0.0837814	−	0.257853i
$556$	4.25021	+	13.0808i	0.180249	+	0.554750i
$557$	12.0067	−	16.5258i	0.508740	−	0.700220i	−0.474966	−	0.880004i	$-0.657540\pi$
$557$	12.0067	−	16.5258i	0.508740	−	0.700220i	0.983706	+	0.179784i	$0.0575398\pi$
$558$	1.31114	−	0.952603i	0.0555052	−	0.0403269i
$559$	−39.5506	−	12.8508i	−1.67281	−	0.543529i
$560$	−1.02120	+	1.19093i	−0.0431536	+	0.0503258i
$561$	−18.3315	+	4.86656i	−0.773956	+	0.205466i
$562$	11.9983			0.506120
$563$	1.15998	−	3.57005i	0.0488873	−	0.150459i	−0.923633	−	0.383278i	$-0.874795\pi$
$563$	1.15998	−	3.57005i	0.0488873	−	0.150459i	0.972520	+	0.232819i	$0.0747950\pi$
$564$	−6.73815	+	4.89555i	−0.283727	+	0.206140i
$565$	−2.77963	+	3.82584i	−0.116940	+	0.160954i
$566$	−8.86834	+	2.88150i	−0.372764	+	0.121118i
$567$	1.01729	−	2.44236i	0.0427220	−	0.102570i
$568$	11.0904	−	15.2646i	0.465343	−	0.640489i
$569$	−4.64729	−	6.39644i	−0.194824	−	0.268153i	0.700417	−	0.713733i	$-0.252997\pi$
$569$	−4.64729	−	6.39644i	−0.194824	−	0.268153i	−0.895242	+	0.445581i	$0.852997\pi$
$570$	−2.27089	−	0.737857i	−0.0951172	−	0.0309054i
$571$			10.7489i			0.449826i	0.974379	+	0.224913i	$0.0722098\pi$
$571$			10.7489i			0.449826i	−0.974379	+	0.224913i	$0.927790\pi$
$572$	−25.9268	−	1.41882i	−1.08405	−	0.0593240i
$573$		−	1.80204i		−	0.0752815i
$574$	−6.68552	−	10.9580i	−0.279048	−	0.457380i
$575$	−11.6968	+	8.49820i	−0.487789	+	0.354400i
$576$	−2.24802	−	1.63328i	−0.0936674	−	0.0680534i
$577$	2.55518	−	0.830228i	0.106373	−	0.0345628i	−0.255347	−	0.966850i	$-0.582190\pi$
$577$	2.55518	−	0.830228i	0.106373	−	0.0345628i	0.361720	+	0.932287i	$0.382190\pi$
$578$	11.3935	−	3.70198i	0.473908	−	0.153982i
$579$	−13.5179	−	9.82136i	−0.561787	−	0.408162i
$580$	6.13455	−	4.45701i	0.254723	−	0.185067i
$581$	31.8342	−	19.4221i	1.32071	−	0.805765i
$582$		−	5.95664i		−	0.246911i
$583$	−0.772661	+	0.499239i	−0.0320004	+	0.0206763i
$584$			25.4273i			1.05219i
$585$	3.67857	+	1.19524i	0.152090	+	0.0494170i
$586$	4.45245	+	6.12827i	0.183929	+	0.253156i
$587$	2.79277	−	3.84392i	0.115270	−	0.158655i	−0.747483	−	0.664280i	$-0.768738\pi$
$587$	2.79277	−	3.84392i	0.115270	−	0.158655i	0.862753	+	0.505625i	$0.168738\pi$
$588$	4.47133	+	8.86139i	0.184395	+	0.365438i
$589$	9.02597	−	2.93271i	0.371908	−	0.120840i
$590$	3.28397	−	4.52000i	0.135199	−	0.186085i
$591$	6.49089	−	4.71591i	0.266999	−	0.193986i
$592$	2.38484	−	7.33977i	0.0980162	−	0.301663i
$593$	37.4883			1.53946			0.769731	−	0.638369i	$-0.220391\pi$
$593$	37.4883			1.53946			0.769731	+	0.638369i	$0.220391\pi$
$594$	1.96277	+	1.59694i	0.0805333	+	0.0655231i
$595$	−6.89935	+	8.04604i	−0.282846	+	0.329856i
$596$	−11.7506	−	3.81800i	−0.481323	−	0.156391i
$597$	15.2760	−	11.0986i	0.625203	−	0.454237i
$598$	−7.93872	+	10.9267i	−0.324639	+	0.446827i
$599$	−4.19965	−	12.9252i	−0.171593	−	0.528109i	0.827868	−	0.560922i	$-0.189553\pi$
$599$	−4.19965	−	12.9252i	−0.171593	−	0.528109i	−0.999462	+	0.0328131i	$0.989553\pi$
$600$	−3.63359	−	11.1830i	−0.148341	−	0.456545i
$601$	−0.401756	−	0.291893i	−0.0163880	−	0.0119066i	0.579561	−	0.814929i	$-0.303224\pi$
$601$	−0.401756	−	0.291893i	−0.0163880	−	0.0119066i	−0.595949	+	0.803022i	$0.703224\pi$
$602$	−15.1540	−	1.22260i	−0.617629	−	0.0498296i
$603$	3.20257	−	9.85651i	0.130419	−	0.401388i
$604$			7.24726i			0.294887i
$605$	3.82206	+	6.69119i	0.155389	+	0.272035i
$606$	−8.72026			−0.354236
$607$	2.86258	−	8.81011i	0.116188	−	0.357591i	−0.876005	−	0.482303i	$-0.839801\pi$
$607$	2.86258	−	8.81011i	0.116188	−	0.357591i	0.992193	+	0.124711i	$0.0398005\pi$
$608$	−15.3912	−	21.1842i	−0.624196	−	0.859132i
$609$	−4.67632	−	19.6483i	−0.189494	−	0.796187i
$610$	1.41705	+	4.36123i	0.0573746	+	0.176581i
$611$	−30.8444	+	10.0219i	−1.24783	+	0.405445i
$612$	6.56003	+	4.76614i	0.265173	+	0.192660i
$613$	12.4694	+	17.1626i	0.503633	+	0.693191i	0.982829	−	0.184516i	$-0.0590718\pi$
$613$	12.4694	+	17.1626i	0.503633	+	0.693191i	−0.479196	+	0.877708i	$0.659072\pi$
$614$	−2.77429	−	0.901423i	−0.111961	−	0.0363785i
$615$	4.45493			0.179640
$616$	−22.5164	+	4.07370i	−0.907213	+	0.164134i
$617$	4.96377			0.199834			0.0999169	−	0.994996i	$-0.468142\pi$
$617$	4.96377			0.199834			0.0999169	+	0.994996i	$0.468142\pi$
$618$	−2.50503	−	0.813933i	−0.100767	−	0.0327412i
$619$	18.5359	+	25.5125i	0.745022	+	1.02544i	0.998314	+	0.0580454i	$0.0184868\pi$
$619$	18.5359	+	25.5125i	0.745022	+	1.02544i	−0.253292	+	0.967390i	$0.581513\pi$
$620$	−1.70707	−	1.24026i	−0.0685577	−	0.0498101i
$621$	−3.04937	+	0.990800i	−0.122367	+	0.0397594i
$622$	3.47253	+	10.6874i	0.139236	+	0.428524i
$623$	−3.78176	+	0.900065i	−0.151513	+	0.0360604i
$624$	2.74698	+	3.78089i	0.109967	+	0.151357i
$625$	5.52512	−	17.0046i	0.221005	−	0.680183i
$626$	15.3747			0.614498
$627$	8.04146	+	12.4456i	0.321145	+	0.497029i
$628$			20.9278i			0.835110i
$629$	16.1123	−	49.5884i	0.642438	−	1.97722i
$630$	1.40946	+	0.113713i	0.0561541	+	0.00453045i
$631$	11.9820	+	8.70541i	0.476995	+	0.346557i	0.800161	−	0.599785i	$-0.204747\pi$
$631$	11.9820	+	8.70541i	0.476995	+	0.346557i	−0.323166	+	0.946342i	$0.604747\pi$
$632$	9.00581	+	27.7170i	0.358232	+	1.10252i
$633$	3.95495	+	12.1721i	0.157195	+	0.483797i
$634$	8.26547	−	11.3764i	0.328264	−	0.451816i
$635$	1.67008	−	1.21339i	0.0662753	−	0.0481518i
$636$	0.374038	+	0.121532i	0.0148316	+	0.00481907i
$637$	5.89605	+	38.1970i	0.233610	+	1.51342i
$638$	19.2873	+	1.05548i	0.763590	+	0.0417868i
$639$	7.23569			0.286240
$640$	−2.07864	+	6.39739i	−0.0821654	+	0.252879i
$641$	−31.7035	+	23.0340i	−1.25221	+	0.909787i	−0.998348	−	0.0574528i	$-0.981702\pi$
$641$	−31.7035	+	23.0340i	−1.25221	+	0.909787i	−0.253866	+	0.967239i	$0.581702\pi$
$642$	1.64562	−	2.26500i	0.0649473	−	0.0893923i
$643$	10.7860	−	3.50458i	0.425358	−	0.138207i	−0.0885122	−	0.996075i	$-0.528211\pi$
$643$	10.7860	−	3.50458i	0.425358	−	0.138207i	0.513870	+	0.857868i	$0.328211\pi$
$644$	4.62492	−	11.1038i	0.182247	−	0.437551i
$645$	3.10133	−	4.26862i	0.122115	−	0.168077i
$646$	−11.4570	−	15.7692i	−0.450770	−	0.620431i
$647$	−23.2236	−	7.54581i	−0.913015	−	0.296657i	−0.185417	−	0.982660i	$-0.559363\pi$
$647$	−23.2236	−	7.54581i	−0.913015	−	0.296657i	−0.727598	+	0.686004i	$0.759363\pi$
$648$		−	2.60764i		−	0.102438i
$649$	−33.5102	+	8.89612i	−1.31539	+	0.349203i
$650$		−	18.9947i		−	0.745035i
$651$	−4.79784	+	2.92717i	−0.188042	+	0.114725i
$652$	−21.0013	+	15.2583i	−0.822475	+	0.597563i
$653$	28.8895	+	20.9895i	1.13053	+	0.821381i	0.985772	−	0.168085i	$-0.0537583\pi$
$653$	28.8895	+	20.9895i	1.13053	+	0.821381i	0.144762	+	0.989466i	$0.453758\pi$
$654$	5.19663	−	1.68849i	0.203204	−	0.0660251i
$655$	8.25139	−	2.68104i	0.322408	−	0.104757i
$656$	4.35474	+	3.16391i	0.170024	+	0.123530i
$657$	−7.88877	+	5.73153i	−0.307770	+	0.223608i
$658$	−10.1215	+	6.17516i	−0.394578	+	0.240733i
$659$			27.4016i			1.06742i	0.845669	+	0.533708i	$0.179202\pi$
$659$			27.4016i			1.06742i	−0.845669	+	0.533708i	$0.820798\pi$
$660$	1.18772	−	3.07289i	0.0462321	−	0.119612i
$661$		−	23.7536i		−	0.923909i	−0.886904	−	0.461955i	$-0.847148\pi$
$661$		−	23.7536i		−	0.923909i	0.886904	−	0.461955i	$-0.152852\pi$
$662$	−6.49879	−	2.11159i	−0.252583	−	0.0820691i
$663$	18.5589	+	25.5442i	0.720770	+	0.992054i
$664$	21.6035	−	29.7347i	0.838380	−	1.15393i
$665$	7.64392	+	3.18382i	0.296418	+	0.123463i
$666$	−6.61568	+	2.14956i	−0.256352	+	0.0832939i
$667$	−14.3867	+	19.8016i	−0.557056	+	0.766722i
$668$	13.0714	−	9.49692i	0.505747	−	0.367447i
$669$	−2.52839	+	7.78157i	−0.0977531	+	0.300853i
$670$	5.53897			0.213989
$671$	10.2594	−	26.5431i	0.396058	−	1.02469i
$672$	11.7717	+	10.0941i	0.454104	+	0.389387i
$673$	45.8440	+	14.8956i	1.76716	+	0.574184i	0.997901	−	0.0647555i	$-0.0206267\pi$
$673$	45.8440	+	14.8956i	1.76716	+	0.574184i	0.769257	+	0.638940i	$0.220627\pi$
$674$	1.73000	−	1.25692i	0.0666372	−	0.0484147i
$675$	2.65047	−	3.64806i	0.102017	−	0.140414i
$676$	7.66144	+	23.5795i	0.294671	+	0.906903i
$677$	−11.0364	−	33.9667i	−0.424165	−	1.30545i	−0.903792	−	0.427973i	$-0.859228\pi$
$677$	−11.0364	−	33.9667i	−0.424165	−	1.30545i	0.479627	−	0.877473i	$-0.340772\pi$
$678$	4.16661	+	3.02722i	0.160018	+	0.116260i
$679$	−1.66118	+	20.5901i	−0.0637503	+	0.790174i
$680$	−3.22811	+	9.93511i	−0.123792	+	0.380994i
$681$		−	2.54824i		−	0.0976487i
$682$	−1.37919	−	5.19518i	−0.0528120	−	0.198934i
$683$	−6.29521			−0.240879			−0.120440	−	0.992721i	$-0.538430\pi$
$683$	−6.29521			−0.240879			−0.120440	+	0.992721i	$0.538430\pi$
$684$	1.95758	−	6.02480i	0.0748498	−	0.230364i
$685$	−3.00734	−	4.13925i	−0.114905	−	0.158153i
$686$	5.33014	+	13.0857i	0.203506	+	0.499615i
$687$	3.81670	+	11.7466i	0.145616	+	0.448161i
$688$	6.06318	−	1.97005i	0.231157	−	0.0751073i
$689$	1.23895	+	0.900150i	0.0472002	+	0.0342930i
$690$	−1.00724	−	1.38635i	−0.0383451	−	0.0527775i
$691$	34.7683	+	11.2969i	1.32265	+	0.429754i	0.883403	−	0.468614i	$-0.155246\pi$
$691$	34.7683	+	11.2969i	1.32265	+	0.429754i	0.439244	+	0.898368i	$0.355246\pi$
$692$	31.4987			1.19740
$693$	−6.33926	−	6.06744i	−0.240808	−	0.230483i
$694$	3.80043			0.144262
$695$	−6.46256	−	2.09981i	−0.245139	−	0.0796504i
$696$	−11.7006	−	16.1044i	−0.443508	−	0.610437i
$697$	29.4212	+	21.3758i	1.11441	+	0.809665i
$698$	−5.51142	+	1.79077i	−0.208610	+	0.0677817i
$699$	−3.41482	−	10.5097i	−0.129160	−	0.397515i
$700$	3.91676	+	16.4569i	0.148040	+	0.622011i
$701$	−1.24793	−	1.71763i	−0.0471337	−	0.0648740i	0.784800	−	0.619750i	$-0.212766\pi$
$701$	−1.24793	−	1.71763i	−0.0471337	−	0.0648740i	−0.831933	+	0.554876i	$0.812766\pi$
$702$	1.30170	−	4.00622i	0.0491295	−	0.151205i
$703$	−40.7345			−1.53633
$704$	−7.74069	+	5.00148i	−0.291738	+	0.188500i
$705$		−	4.11484i		−	0.154974i
$706$	−3.40250	+	10.4718i	−0.128055	+	0.394112i
$707$	30.1429	+	2.43190i	1.13364	+	0.0914609i
$708$	11.9918	+	8.71255i	0.450680	+	0.327438i
$709$	−1.48801	−	4.57961i	−0.0558832	−	0.171991i	0.919219	−	0.393747i	$-0.128821\pi$
$709$	−1.48801	−	4.57961i	−0.0558832	−	0.171991i	−0.975102	+	0.221756i	$0.928821\pi$
$710$	1.19502	+	3.67789i	0.0448482	+	0.138029i
$711$	−6.56918	+	9.04170i	−0.246363	+	0.339090i
$712$	−3.09967	+	2.25204i	−0.116165	+	0.0843988i
$713$	6.47767	+	2.10472i	0.242591	+	0.0788225i
$714$	8.76271	+	7.51389i	0.327936	+	0.281200i
$715$	8.09611	−	9.95077i	0.302777	−	0.372138i
$716$	−15.3864			−0.575018
$717$	−0.346082	+	1.06513i	−0.0129247	+	0.0397780i
$718$	−11.9893	+	8.71076i	−0.447438	+	0.325083i
$719$	16.2358	−	22.3466i	0.605493	−	0.833389i	−0.390704	−	0.920516i	$-0.627769\pi$
$719$	16.2358	−	22.3466i	0.605493	−	0.833389i	0.996197	+	0.0871269i	$0.0277685\pi$
$720$	−0.563932	+	0.183232i	−0.0210165	+	0.00682867i
$721$	8.43204	+	3.51209i	0.314025	+	0.130797i
$722$	−0.430420	+	0.592422i	−0.0160186	+	0.0220477i
$723$	0.751566	+	1.03444i	0.0279510	+	0.0384713i
$724$	3.98257	+	1.29401i	0.148011	+	0.0480917i
$725$		−	34.4226i		−	1.27843i
$726$	7.28718	−	4.16249i	0.270453	−	0.154484i
$727$			6.08929i			0.225839i	0.993604	+	0.112920i	$0.0360203\pi$
$727$			6.08929i			0.225839i	−0.993604	+	0.112920i	$0.963980\pi$
$728$	19.8395	+	32.5184i	0.735302	+	1.20521i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−4.21620	−	3.06325i	−0.156049	−	0.113376i
$731$	40.9636	−	13.3099i	1.51509	−	0.492284i
$732$	−11.5706	+	3.75951i	−0.427660	+	0.138955i
$733$	−18.0281	−	13.0982i	−0.665882	−	0.483791i	0.202762	−	0.979228i	$-0.435008\pi$
$733$	−18.0281	−	13.0982i	−0.665882	−	0.483791i	−0.868644	+	0.495437i	$0.835008\pi$
$734$	−22.4679	+	16.3239i	−0.829305	+	0.602526i
$735$	−4.84030	−	0.786136i	−0.178537	−	0.0289971i
$736$		−	18.7923i		−	0.692693i
$737$	−26.6625	−	21.6931i	−0.982128	−	0.799074i
$738$		−	4.85173i		−	0.178595i
$739$	19.3080	+	6.27356i	0.710258	+	0.230777i	0.641794	−	0.766877i	$-0.278190\pi$
$739$	19.3080	+	6.27356i	0.710258	+	0.230777i	0.0684635	+	0.997654i	$0.478190\pi$
$740$	5.32339	+	7.32702i	0.195692	+	0.269347i
$741$	14.4991	−	19.9563i	0.532638	−	0.733114i
$742$	0.516827	+	0.215268i	0.0189733	+	0.00790272i
$743$	−14.2196	+	4.62024i	−0.521667	+	0.169500i	−0.558002	−	0.829840i	$-0.688432\pi$
$743$	−14.2196	+	4.62024i	−0.521667	+	0.169500i	0.0363345	+	0.999340i	$0.488432\pi$
$744$	−3.25594	+	4.48141i	−0.119368	+	0.164297i
$745$	4.93834	−	3.58791i	0.180927	−	0.131451i
$746$	0.965411	−	2.97123i	0.0353462	−	0.108784i
$747$	14.0948			0.515701
$748$	22.5884	−	14.5950i	0.825914	−	0.533646i
$749$	−6.31999	+	7.37039i	−0.230927	+	0.269308i
$750$	4.83353	+	1.57051i	0.176496	+	0.0573469i
$751$	−7.48297	+	5.43669i	−0.273057	+	0.198388i	−0.715884	−	0.698220i	$-0.753976\pi$
$751$	−7.48297	+	5.43669i	−0.273057	+	0.198388i	0.442826	+	0.896607i	$0.353976\pi$
$752$	2.92238	−	4.02231i	0.106568	−	0.146678i
$753$	−6.74905	−	20.7714i	−0.245949	−	0.756953i
$754$	−9.93688	−	30.5826i	−0.361880	−	1.11375i
$755$	−2.89669	−	2.10457i	−0.105421	−	0.0765930i
$756$	−0.301688	+	3.73937i	−0.0109723	+	0.135999i
$757$	−14.6889	+	45.2077i	−0.533877	+	1.64310i	0.212188	+	0.977229i	$0.431941\pi$
$757$	−14.6889	+	45.2077i	−0.533877	+	1.64310i	−0.746064	+	0.665874i	$0.768059\pi$
$758$		−	15.5119i		−	0.563419i
$759$	−0.581072	+	10.6182i	−0.0210916	+	0.385416i
$760$	8.16121			0.296038
$761$	−0.748594	+	2.30394i	−0.0271365	+	0.0835176i	−0.963708	−	0.266960i	$-0.913981\pi$
$761$	−0.748594	+	2.30394i	−0.0271365	+	0.0835176i	0.936571	+	0.350478i	$0.113981\pi$
$762$	−1.32146	−	1.81884i	−0.0478716	−	0.0658896i
$763$	−18.4338	+	4.38729i	−0.667350	+	0.158830i
$764$	0.789597	+	2.43013i	0.0285666	+	0.0879190i
$765$	−3.80999	+	1.23794i	−0.137751	+	0.0447579i
$766$	−3.47573	−	2.52526i	−0.125583	−	0.0912415i
$767$	33.9260	+	46.6951i	1.22500	+	1.68606i
$768$	12.2526	+	3.98112i	0.442128	+	0.143656i
$769$	0.396165			0.0142861			0.00714303	−	0.999974i	$-0.497726\pi$
$769$	0.396165			0.0142861			0.00714303	+	0.999974i	$0.497726\pi$
$770$	2.03710	−	4.22430i	0.0734120	−	0.152233i
$771$	−19.4823			−0.701638
$772$	22.5329	+	7.32138i	0.810977	+	0.263502i
$773$	−21.3036	−	29.3219i	−0.766237	−	1.05463i	−0.996670	−	0.0815466i	$-0.974014\pi$
$773$	−21.3036	−	29.3219i	−0.766237	−	1.05463i	0.230432	−	0.973088i	$-0.425986\pi$
$774$	−4.64883	−	3.37757i	−0.167099	−	0.121404i
$775$	−9.11004	+	2.96003i	−0.327242	+	0.106327i
$776$	6.29141	+	19.3630i	0.225849	+	0.695090i
$777$	23.4676	−	5.58533i	0.841895	−	0.200373i
$778$	−4.05540	−	5.58178i	−0.145393	−	0.200116i
$779$	8.77957	−	27.0207i	0.314561	−	0.968119i
$780$	−5.48441			−0.196373
$781$	8.65187	−	22.3842i	0.309588	−	0.800970i
$782$		−	13.9887i		−	0.500235i
$783$	2.35897	−	7.26015i	0.0843026	−	0.259457i
$784$	−4.17313	−	4.20606i	−0.149040	−	0.150216i
$785$	−8.36472	−	6.07732i	−0.298550	−	0.216909i
$786$	−2.91984	−	8.98635i	−0.104147	−	0.320532i
$787$	11.1438	+	34.2972i	0.397235	+	1.22256i	0.927208	+	0.374548i	$0.122202\pi$
$787$	11.1438	+	34.2972i	0.397235	+	1.22256i	−0.529973	+	0.848015i	$0.677798\pi$
$788$	−6.68687	+	9.20369i	−0.238210	+	0.327868i
$789$	−16.3988	+	11.9144i	−0.583814	+	0.424166i
$790$	−5.68081	−	1.84581i	−0.202114	−	0.0656709i
$791$	−13.5583	−	11.6260i	−0.482078	−	0.413374i
$792$	−8.06696	−	3.11801i	−0.286647	−	0.110794i
$793$	−47.3734			−1.68228
$794$	−7.48788	+	23.0453i	−0.265735	+	0.817848i
$795$	−0.157194	+	0.114208i	−0.00557511	+	0.00405055i
$796$	−15.7372	+	21.6604i	−0.557790	+	0.767732i
$797$	8.45807	−	2.74819i	0.299600	−	0.0973460i	−0.155360	−	0.987858i	$-0.549654\pi$
$797$	8.45807	−	2.74819i	0.299600	−	0.0973460i	0.454960	+	0.890512i	$0.349654\pi$
$798$	3.46741	−	8.32477i	0.122745	−	0.294694i
$799$	19.7440	−	27.1752i	0.698491	−	0.961390i
$800$	15.5346	+	21.3815i	0.549230	+	0.755951i
$801$	−1.39738	−	0.454037i	−0.0493741	−	0.0160426i
$802$		−	24.9674i		−	0.881631i
$803$	8.29819	+	31.2579i	0.292837	+	1.10307i
$804$			14.6952i			0.518259i
$805$	3.09507	+	5.07304i	0.109087	+	0.178801i
$806$	−7.23928	+	5.25964i	−0.254993	+	0.185263i
$807$	16.1124	+	11.7064i	0.567185	+	0.412084i
$808$	28.3465	−	9.21035i	0.997227	−	0.324019i
$809$	−23.4346	+	7.61438i	−0.823918	+	0.267707i	−0.690481	−	0.723350i	$-0.742601\pi$
$809$	−23.4346	+	7.61438i	−0.823918	+	0.267707i	−0.133437	+	0.991057i	$0.542601\pi$
$810$	0.432384	+	0.314145i	0.0151924	+	0.0110379i
$811$	15.7247	−	11.4246i	0.552168	−	0.401174i	−0.276416	−	0.961038i	$-0.589147\pi$
$811$	15.7247	−	11.4246i	0.552168	−	0.401174i	0.828584	+	0.559865i	$0.189147\pi$
$812$	14.9154	+	24.4475i	0.523429	+	0.857938i
$813$			2.79202i			0.0979204i
$814$	−1.26065	+	23.0364i	−0.0441857	+	0.807426i
$815$		−	12.8250i		−	0.449242i
$816$	−4.60351	−	1.49577i	−0.161155	−	0.0523624i
$817$	−19.7788	−	27.2231i	−0.691971	−	0.952416i
$818$	5.80949	−	7.99608i	0.203124	−	0.279576i
$819$	−5.61678	+	13.4851i	−0.196266	+	0.471208i
$820$	−6.00765	+	1.95200i	−0.209796	+	0.0681669i
$821$	32.1833	−	44.2965i	1.12321	−	1.54596i	0.322835	−	0.946455i	$-0.395364\pi$
$821$	32.1833	−	44.2965i	1.12321	−	1.54596i	0.800371	−	0.599505i	$-0.204636\pi$
$822$	−4.50794	+	3.27521i	−0.157232	+	0.114236i
$823$	10.1892	−	31.3592i	0.355174	−	1.09311i	−0.600734	−	0.799449i	$-0.705125\pi$
$823$	10.1892	−	31.3592i	0.355174	−	1.09311i	0.955908	−	0.293665i	$-0.0948751\pi$
$824$	9.00266			0.313623
$825$	−8.11636	−	12.5615i	−0.282575	−	0.437336i
$826$	16.0183	+	13.7355i	0.557349	+	0.477918i
$827$	−16.9616	−	5.51115i	−0.589812	−	0.191642i	−0.00112064	−	0.999999i	$-0.500357\pi$
$827$	−16.9616	−	5.51115i	−0.589812	−	0.191642i	−0.588692	+	0.808358i	$0.700357\pi$
$828$	3.67806	−	2.67227i	0.127821	−	0.0928677i
$829$	−27.1514	+	37.3707i	−0.943008	+	1.29794i	0.0115563	+	0.999933i	$0.496321\pi$
$829$	−27.1514	+	37.3707i	−0.943008	+	1.29794i	−0.954564	+	0.298006i	$0.903679\pi$
$830$	2.32783	+	7.16434i	0.0808003	+	0.248678i
$831$	−3.09157	−	9.51488i	−0.107245	−	0.330067i
$832$	12.4121	+	9.01790i	0.430311	+	0.312639i
$833$	−28.1942	−	28.4167i	−0.976872	−	0.984579i
$834$	−2.28684	+	7.03818i	−0.0791870	+	0.243712i
$835$			7.98241i			0.276243i
$836$	−16.2975	−	13.2599i	−0.563661	−	0.458603i
$837$	−2.12427			−0.0734254
$838$	6.45676	−	19.8719i	0.223045	−	0.686462i
$839$	3.52051	+	4.84557i	0.121542	+	0.167288i	0.865452	−	0.500992i	$-0.167031\pi$
$839$	3.52051	+	4.84557i	0.121542	+	0.167288i	−0.743911	+	0.668279i	$0.767031\pi$
$840$	−4.70176	+	1.11903i	−0.162226	+	0.0386101i
$841$	−9.04633	−	27.8418i	−0.311943	−	0.960060i
$842$	7.01312	−	2.27870i	0.241688	−	0.0785292i
$843$	−12.7232	−	9.24391i	−0.438209	−	0.318377i
$844$	−10.6668	−	14.6816i	−0.367167	−	0.505362i
$845$	−11.6494	−	3.78513i	−0.400752	−	0.130212i
$846$	−4.48136			−0.154072
$847$	−26.3501	+	12.3561i	−0.905400	+	0.424559i
$848$	−0.234771			−0.00806206
$849$	11.6241	+	3.77689i	0.398937	+	0.129623i
$850$	11.5637	+	15.9161i	0.396632	+	0.545918i
$851$	−23.6508	−	17.1833i	−0.810738	−	0.589036i
$852$	−9.75763	+	3.17044i	−0.334291	+	0.108618i
$853$	−1.50828	−	4.64201i	−0.0516425	−	0.158939i	0.921909	−	0.387406i	$-0.126629\pi$
$853$	−1.50828	−	4.64201i	−0.0516425	−	0.158939i	−0.973552	+	0.228467i	$0.926629\pi$
$854$	−16.8484	+	4.00995i	−0.576541	+	0.137218i
$855$	1.83961	+	2.53200i	0.0629132	+	0.0865926i
$856$	−2.95704	+	9.10082i	−0.101069	+	0.311060i
$857$	−45.1617			−1.54269			−0.771346	−	0.636415i	$-0.780416\pi$
$857$	−45.1617			−1.54269			−0.771346	+	0.636415i	$0.780416\pi$
$858$	−10.8371	−	8.81723i	−0.369972	−	0.301015i
$859$			5.45577i			0.186148i	0.995659	+	0.0930742i	$0.0296694\pi$
$859$			5.45577i			0.186148i	−0.995659	+	0.0930742i	$0.970331\pi$
$860$	−2.31190	+	7.11531i	−0.0788353	+	0.242630i
$861$	−1.35305	+	16.7708i	−0.0461117	+	0.571546i
$862$	3.69282	+	2.68299i	0.125778	+	0.0913831i
$863$	1.37743	+	4.23929i	0.0468882	+	0.144307i	0.971760	−	0.235973i	$-0.0758277\pi$
$863$	1.37743	+	4.23929i	0.0468882	+	0.144307i	−0.924871	+	0.380280i	$0.875828\pi$
$864$	1.81117	+	5.57420i	0.0616171	+	0.189638i
$865$	−9.14707	+	12.5899i	−0.311010	+	0.428068i
$866$	4.28648	−	3.11431i	0.145661	−	0.105829i
$867$	−14.9339	−	4.85232i	−0.507182	−	0.164794i
$868$	5.18749	−	6.04966i	0.176075	−	0.205339i
$869$	20.1163	+	31.1336i	0.682400	+	1.05614i
$870$	4.07992			0.138322
$871$	−17.6825	+	54.4211i	−0.599149	+	1.84399i
$872$	−15.1091	+	10.9774i	−0.511657	+	0.371741i
$873$	−4.58919	+	6.31648i	−0.155321	+	0.213780i
$874$	−10.3937	+	3.37713i	−0.351574	+	0.114233i
$875$	−16.2699	−	6.77668i	−0.550022	−	0.229094i
$876$	8.12696	−	11.1858i	0.274585	−	0.377933i
$877$	−17.7700	−	24.4583i	−0.600051	−	0.825899i	0.395662	−	0.918396i	$-0.370515\pi$
$877$	−17.7700	−	24.4583i	−0.600051	−	0.825899i	−0.995713	+	0.0924972i	$0.970515\pi$
$878$	−19.2460	−	6.25342i	−0.649522	−	0.211043i
$879$		−	9.92878i		−	0.334890i
$880$	−0.107460	+	1.96366i	−0.00362247	+	0.0661951i
$881$		−	44.7326i		−	1.50708i	−0.657403	−	0.753539i	$-0.728345\pi$
$881$		−	44.7326i		−	1.50708i	0.657403	−	0.753539i	$-0.271655\pi$
$882$	−0.856158	+	5.27143i	−0.0288283	+	0.177498i
$883$	17.9848	−	13.0667i	0.605237	−	0.439730i	−0.242497	−	0.970152i	$-0.577966\pi$
$883$	17.9848	−	13.0667i	0.605237	−	0.439730i	0.847734	+	0.530422i	$0.177966\pi$
$884$	−36.2201	−	26.3155i	−1.21821	−	0.885085i
$885$	−6.96471	+	2.26297i	−0.234116	+	0.0760690i
$886$	9.83186	−	3.19457i	0.330308	−	0.107324i
$887$	35.8403	+	26.0395i	1.20340	+	0.874321i	0.994615	−	0.103641i	$-0.0330494\pi$
$887$	35.8403	+	26.0395i	1.20340	+	0.874321i	0.208784	+	0.977962i	$0.433049\pi$
$888$	19.2349	−	13.9750i	0.645481	−	0.468970i
$889$	4.06061	+	6.65563i	0.136189	+	0.223223i
$890$		−	0.785274i		−	0.0263224i
$891$	−0.851004	−	3.20559i	−0.0285097	−	0.107391i
$892$		−	11.6016i		−	0.388451i
$893$	−24.9580	−	8.10935i	−0.835188	−	0.271369i
$894$	−3.90749	−	5.37820i	−0.130686	−	0.179874i
$895$	4.46814	−	6.14986i	0.149353	−	0.205567i
$896$	−23.4519	−	9.76814i	−0.783475	−	0.326331i
$897$	16.8366	−	5.47054i	0.562158	−	0.182656i
$898$	−6.71222	+	9.23857i	−0.223990	+	0.308295i
$899$	−13.1192	+	9.53163i	−0.437549	+	0.317898i
$900$	−1.97581	+	6.08091i	−0.0658603	+	0.202697i
$901$	−1.58614			−0.0528420
$902$	−15.0092	−	5.80131i	−0.499753	−	0.193163i
$903$	15.1275	+	12.9716i	0.503411	+	0.431667i
$904$	−16.7415	−	5.43966i	−0.556816	−	0.180920i
$905$	−1.67373	+	1.21603i	−0.0556365	+	0.0404223i
$906$	−2.29202	+	3.15470i	−0.0761474	+	0.104808i
$907$	−16.7968	−	51.6952i	−0.557728	−	1.71651i	−0.688628	−	0.725115i	$-0.741787\pi$
$907$	−16.7968	−	51.6952i	−0.557728	−	1.71651i	0.130900	−	0.991396i	$-0.458213\pi$
$908$	1.11655	+	3.43640i	0.0370542	+	0.114041i
$909$	9.24704	+	6.71837i	0.306705	+	0.222834i
$910$	−7.78209	−	0.627850i	−0.257974	−	0.0208130i
$911$	16.3886	−	50.4388i	0.542978	−	1.67111i	−0.182773	−	0.983155i	$-0.558507\pi$
$911$	16.3886	−	50.4388i	0.542978	−	1.67111i	0.725750	−	0.687958i	$-0.241493\pi$
$912$			3.78156i			0.125220i
$913$	16.8534	−	43.6033i	0.557766	−	1.44306i
$914$	15.3348			0.507231
$915$	1.85738	−	5.71643i	0.0614031	−	0.188979i
$916$	−10.2940	−	14.1684i	−0.340122	−	0.468137i
$917$	7.58678	+	31.8770i	0.250538	+	1.05267i
$918$	1.34821	+	4.14935i	0.0444975	+	0.136949i
$919$	−18.6676	+	6.06547i	−0.615787	+	0.200081i	−0.600269	−	0.799798i	$-0.704940\pi$
$919$	−18.6676	+	6.06547i	−0.615787	+	0.200081i	−0.0155183	+	0.999880i	$0.504940\pi$
$920$	4.73846	+	3.44269i	0.156222	+	0.113502i
$921$	2.24740	+	3.09328i	0.0740544	+	0.101927i
$922$	6.56305	+	2.13246i	0.216143	+	0.0702290i
$923$	−39.9507			−1.31499
$924$	11.2073	+	5.40453i	0.368693	+	0.177796i
$925$	41.1139			1.35182
$926$	−3.95376	−	1.28465i	−0.129928	−	0.0422163i
$927$	2.02928	+	2.79306i	0.0666502	+	0.0917361i
$928$	36.1970	+	26.2987i	1.18823	+	0.863297i
$929$	−36.7558	+	11.9427i	−1.20592	+	0.391827i	−0.841936	−	0.539578i	$-0.818584\pi$
$929$	−36.7558	+	11.9427i	−1.20592	+	0.391827i	−0.363984	+	0.931405i	$0.618584\pi$
$930$	−0.350835	−	1.07976i	−0.0115043	−	0.0354067i
$931$	−14.3072	+	27.8089i	−0.468901	+	0.911399i
$932$	9.21005	+	12.6765i	0.301685	+	0.415234i
$933$	4.55158	−	14.0083i	0.149012	−	0.458612i
$934$	11.6056			0.379748
$935$	−0.726012	+	13.2668i	−0.0237431	+	0.433870i
$936$			14.3977i			0.470603i
$937$	13.9568	−	42.9546i	0.455949	−	1.40327i	−0.414069	−	0.910246i	$-0.635893\pi$
$937$	13.9568	−	42.9546i	0.455949	−	1.40327i	0.870018	−	0.493021i	$-0.164107\pi$
$938$	−1.68229	+	20.8517i	−0.0549287	+	0.680832i
$939$	−16.3035	−	11.8452i	−0.532045	−	0.386553i
$940$	1.80299	+	5.54903i	0.0588071	+	0.180989i
$941$	14.5577	+	44.8039i	0.474567	+	1.46057i	0.846541	+	0.532323i	$0.178681\pi$
$941$	14.5577	+	44.8039i	0.474567	+	1.46057i	−0.371974	+	0.928243i	$0.621319\pi$
$942$	−6.61864	+	9.10977i	−0.215647	+	0.296812i
$943$	16.4958	−	11.9849i	0.537178	−	0.390283i
$944$	−8.41526	−	2.73428i	−0.273893	−	0.0889934i
$945$	−1.40699	−	1.20647i	−0.0457695	−	0.0392466i
$946$	−16.0075	+	10.3429i	−0.520449	+	0.336277i
$947$	59.0518			1.91892			0.959462	−	0.281837i	$-0.0909439\pi$
$947$	59.0518			1.91892			0.959462	+	0.281837i	$0.0909439\pi$
$948$	4.89703	−	15.0715i	0.159048	−	0.489499i
$949$	43.5566	−	31.6457i	1.41391	−	1.02726i
$950$	9.03412	−	12.4344i	0.293106	−	0.403425i
$951$	−17.5296	+	5.69570i	−0.568435	+	0.184696i
$952$	−36.4207	−	15.1699i	−1.18040	−	0.491658i
$953$	−3.02452	+	4.16290i	−0.0979738	+	0.134849i	−0.855189	−	0.518316i	$-0.826559\pi$
$953$	−3.02452	+	4.16290i	−0.0979738	+	0.134849i	0.757216	+	0.653165i	$0.226559\pi$
$954$	0.124381	+	0.171196i	0.00402699	+	0.00554267i
$955$	−1.20060	−	0.390100i	−0.0388506	−	0.0126233i
$956$		−	1.58801i		−	0.0513600i
$957$	−19.6392	−	15.9788i	−0.634846	−	0.516520i
$958$		−	23.8012i		−	0.768983i
$959$	16.4958	−	10.0641i	0.532677	−	0.324987i
$960$	−1.57481	+	1.14417i	−0.0508267	+	0.0369278i
$961$	−21.4288	−	15.5690i	−0.691253	−	0.502224i
$962$	36.5274	−	11.8685i	1.17769	−	0.382655i
$963$	−3.49005	+	1.13399i	−0.112465	+	0.0365422i
$964$	−1.46678	−	1.06567i	−0.0472417	−	0.0343231i
$965$	−9.46975	+	6.88017i	−0.304842	+	0.221481i
$966$	5.52490	−	3.37075i	0.177761	−	0.108452i
$967$			28.5213i			0.917182i	0.888647	+	0.458591i	$0.151646\pi$
$967$			28.5213i			0.917182i	−0.888647	+	0.458591i	$0.848354\pi$
$968$	−19.2917	+	21.2275i	−0.620058	+	0.682279i
$969$			25.5487i			0.820742i
$970$	−3.96858	−	1.28947i	−0.127424	−	0.0414024i
$971$	−27.3074	−	37.5854i	−0.876336	−	1.20617i	−0.977422	−	0.211296i	$-0.932232\pi$
$971$	−27.3074	−	37.5854i	−0.876336	−	1.20617i	0.101086	−	0.994878i	$-0.467768\pi$
$972$	−0.833444	+	1.14714i	−0.0267327	+	0.0367944i
$973$	9.86764	−	23.6908i	0.316342	−	0.759493i
$974$	6.42797	−	2.08857i	0.205965	−	0.0669222i
$975$	−14.6342	+	20.1422i	−0.468668	+	0.645067i
$976$	5.87544	−	4.26876i	0.188068	−	0.136640i
$977$	−8.18063	+	25.1774i	−0.261721	+	0.805496i	0.730709	+	0.682689i	$0.239190\pi$
$977$	−8.18063	+	25.1774i	−0.261721	+	0.805496i	−0.992431	+	0.122807i	$0.960810\pi$
$978$	−13.9674			−0.446628
$979$	−3.07548	+	3.78002i	−0.0982928	+	0.120810i
$980$	6.87180	−	1.06072i	0.219512	−	0.0338836i
$981$	−6.81142	−	2.21316i	−0.217472	−	0.0706609i
$982$	21.0810	−	15.3163i	0.672723	−	0.488762i
$983$	−17.4866	+	24.0683i	−0.557737	+	0.767660i	−0.991037	−	0.133590i	$-0.957349\pi$
$983$	−17.4866	+	24.0683i	−0.557737	+	0.767660i	0.433299	+	0.901250i	$0.357349\pi$
$984$	5.12441	+	15.7713i	0.163360	+	0.502771i
$985$	−1.73683	−	5.34540i	−0.0553399	−	0.170319i
$986$	26.9446	+	19.5764i	0.858090	+	0.623439i
$987$	15.4905	+	1.24976i	0.493068	+	0.0397802i
$988$	−10.8084	+	33.2649i	−0.343862	+	1.05830i
$989$		−	24.1494i		−	0.767905i
$990$	1.48884	−	0.961985i	0.0473186	−	0.0305739i
$991$	−1.44432			−0.0458805			−0.0229402	−	0.999737i	$-0.507303\pi$
$991$	−1.44432			−0.0458805			−0.0229402	+	0.999737i	$0.507303\pi$
$992$	3.84740	−	11.8411i	0.122155	−	0.375955i
$993$	5.26455	+	7.24603i	0.167065	+	0.229946i
$994$	−14.2085	+	3.38165i	−0.450667	+	0.107259i
$995$	−4.08753	−	12.5801i	−0.129583	−	0.398817i
$996$	−19.0074	+	6.17587i	−0.602272	+	0.195690i
$997$	−28.7296	−	20.8733i	−0.909877	−	0.661064i	0.0311066	−	0.999516i	$-0.490097\pi$
$997$	−28.7296	−	20.8733i	−0.909877	−	0.661064i	−0.940984	+	0.338452i	$0.890097\pi$
$998$	−3.97923	−	5.47693i	−0.125960	−	0.173369i
$999$	8.67142	+	2.81752i	0.274352	+	0.0891423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.13.8	yes	64
3.2	odd	2		693.2.bu.f.244.9		64
7.6	odd	2	inner	231.2.w.a.13.7	✓	64
11.6	odd	10	inner	231.2.w.a.160.7	yes	64
21.20	even	2		693.2.bu.f.244.10		64
33.17	even	10		693.2.bu.f.622.10		64
77.6	even	10	inner	231.2.w.a.160.8	yes	64
231.83	odd	10		693.2.bu.f.622.9		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.13.7	✓	64	7.6	odd	2	inner
231.2.w.a.13.8	yes	64	1.1	even	1	trivial
231.2.w.a.160.7	yes	64	11.6	odd	10	inner
231.2.w.a.160.8	yes	64	77.6	even	10	inner
693.2.bu.f.244.9		64	3.2	odd	2
693.2.bu.f.244.10		64	21.20	even	2
693.2.bu.f.622.9		64	231.83	odd	10
693.2.bu.f.622.10		64	33.17	even	10

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.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.725588 - 0.235758i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.14714 - 0.833444i) q^{4} +(0.666245 - 0.216476i) q^{5} +(-0.235758 - 0.725588i) q^{6} +(0.612583 + 2.57386i) q^{7} +(1.53273 + 2.10963i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.725588 - 0.235758i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.14714 - 0.833444i) q^{4} +(0.666245 - 0.216476i) q^{5} +(-0.235758 - 0.725588i) q^{6} +(0.612583 + 2.57386i) q^{7} +(1.53273 + 2.10963i) q^{8} +(-0.309017 + 0.951057i) q^{9} -0.534456 q^{10} +(2.57267 + 2.09317i) q^{11} -1.41794i q^{12} +(1.70619 - 5.25111i) q^{13} +(0.162324 - 2.01198i) q^{14} +(0.566742 + 0.411762i) q^{15} +(0.261562 + 0.805005i) q^{16} +(1.76715 + 5.43872i) q^{17} +(0.448438 - 0.617222i) q^{18} +(3.61440 - 2.62601i) q^{19} +(-0.944696 - 0.306950i) q^{20} +(-1.72223 + 2.00847i) q^{21} +(-1.37322 - 2.12531i) q^{22} +3.20630 q^{23} +(-0.805806 + 2.48002i) q^{24} +(-3.64806 + 2.65047i) q^{25} +(-2.47598 + 3.40789i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.44245 - 3.46312i) q^{28} +(-4.48702 + 6.17586i) q^{29} +(-0.314145 - 0.432384i) q^{30} +(2.02030 + 0.656435i) q^{31} -5.86106i q^{32} +(-0.181228 + 3.31167i) q^{33} -4.36289i q^{34} +(0.965309 + 1.58221i) q^{35} +(1.14714 - 0.833444i) q^{36} +(-7.37635 - 5.35923i) q^{37} +(-3.24167 + 1.05328i) q^{38} +(5.25111 - 1.70619i) q^{39} +(1.47786 + 1.07373i) q^{40} +(5.14482 - 3.73793i) q^{41} +(1.72314 - 1.05129i) q^{42} -7.53186i q^{43} +(-1.20667 - 4.54533i) q^{44} +0.700532i q^{45} +(-2.32645 - 0.755910i) q^{46} +(-3.45258 - 4.75207i) q^{47} +(-0.497521 + 0.684778i) q^{48} +(-6.24948 + 3.15340i) q^{49} +(3.27186 - 1.06309i) q^{50} +(-3.36131 + 4.62645i) q^{51} +(-6.33373 + 4.60173i) q^{52} +(-0.0857105 + 0.263790i) q^{53} +0.762929 q^{54} +(2.16715 + 0.837640i) q^{55} +(-4.49096 + 5.23736i) q^{56} +(4.24898 + 1.38058i) q^{57} +(4.71174 - 3.42328i) q^{58} +(-6.14452 + 8.45720i) q^{59} +(-0.306950 - 0.944696i) q^{60} +(-2.65139 - 8.16013i) q^{61} +(-1.31114 - 0.952603i) q^{62} +(-2.63718 - 0.212765i) q^{63} +(-0.858667 + 2.64270i) q^{64} -3.86787i q^{65} +(0.912250 - 2.36018i) q^{66} -10.3638 q^{67} +(2.50571 - 7.71177i) q^{68} +(1.88461 + 2.59395i) q^{69} +(-0.327398 - 1.37561i) q^{70} +(-2.23595 - 6.88155i) q^{71} +(-2.48002 + 0.805806i) q^{72} +(7.88877 + 5.73153i) q^{73} +(4.08871 + 5.62763i) q^{74} +(-4.28856 - 1.39344i) q^{75} -6.33485 q^{76} +(-3.81154 + 7.90393i) q^{77} -4.21239 q^{78} +(10.6292 + 3.45362i) q^{79} +(0.348529 + 0.479709i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.61427 + 1.49927i) q^{82} +(-4.35552 - 13.4049i) q^{83} +(3.64957 - 0.868605i) q^{84} +(2.35471 + 3.24097i) q^{85} +(-1.77569 + 5.46503i) q^{86} -7.63378 q^{87} +(-0.472579 + 8.63566i) q^{88} +1.46930i q^{89} +(0.165156 - 0.508298i) q^{90} +(14.5608 + 1.17475i) q^{91} +(-3.67806 - 2.67227i) q^{92} +(0.656435 + 2.02030i) q^{93} +(1.38481 + 4.26202i) q^{94} +(1.83961 - 2.53200i) q^{95} +(4.74169 - 3.44504i) q^{96} +(7.42547 + 2.41268i) q^{97} +(5.27799 - 0.814706i) q^{98} +(-2.78572 + 1.79993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more