LMFDB - Embedded newform 231.2.j.g.190.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.3
Root			$0.383242 + 0.278442i$ of defining polynomial
Character	$\chi$	$=$	231.190
Dual form			231.2.j.g.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.383242 + 0.278442i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.548689 + 1.68869i) q^{4} +(-3.04094 - 2.20937i) q^{5} +(-0.383242 - 0.278442i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.552692 - 1.70101i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.78060 q^{10} +(-2.47012 + 2.21326i) q^{11} -1.77560 q^{12} +(-2.19061 + 1.59157i) q^{13} +(-0.146385 - 0.450528i) q^{14} +(1.16154 - 3.57484i) q^{15} +(-2.18753 - 1.58933i) q^{16} +(-2.00865 - 1.45937i) q^{17} +(0.146385 - 0.450528i) q^{18} +(-0.539130 - 1.65927i) q^{19} +(5.39949 - 3.92296i) q^{20} -1.00000 q^{21} +(0.330389 - 1.53600i) q^{22} +3.79843 q^{23} +(1.44697 - 1.05128i) q^{24} +(2.82092 + 8.68189i) q^{25} +(0.396374 - 1.21991i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.43649 - 1.04367i) q^{28} +(-1.79248 + 5.51669i) q^{29} +(0.550235 + 1.69345i) q^{30} +(-1.81837 + 1.32112i) q^{31} +4.85799 q^{32} +(-2.86824 - 1.66529i) q^{33} +1.17615 q^{34} +(3.04094 - 2.20937i) q^{35} +(-0.548689 - 1.68869i) q^{36} +(-2.36494 + 7.27854i) q^{37} +(0.668627 + 0.485786i) q^{38} +(-2.19061 - 1.59157i) q^{39} +(-2.07747 + 6.39378i) q^{40} +(-1.29324 - 3.98017i) q^{41} +(0.383242 - 0.278442i) q^{42} +7.75162 q^{43} +(-2.38219 - 5.38566i) q^{44} +3.75881 q^{45} +(-1.45572 + 1.05764i) q^{46} +(3.83399 + 11.7998i) q^{47} +(0.835561 - 2.57159i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.49849 - 2.54180i) q^{50} +(0.767235 - 2.36131i) q^{51} +(-1.48571 - 4.57254i) q^{52} +(-7.15135 + 5.19576i) q^{53} +0.473713 q^{54} +(12.4014 - 1.27298i) q^{55} +1.78855 q^{56} +(1.41146 - 1.02549i) q^{57} +(-0.849122 - 2.61333i) q^{58} +(1.40345 - 4.31938i) q^{59} +(5.39949 + 3.92296i) q^{60} +(9.28955 + 6.74925i) q^{61} +(0.329020 - 1.01262i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(2.51327 - 1.82600i) q^{64} +10.1779 q^{65} +(1.56292 - 0.160431i) q^{66} -12.2041 q^{67} +(3.56655 - 2.59125i) q^{68} +(1.17378 + 3.61253i) q^{69} +(-0.550235 + 1.69345i) q^{70} +(-6.27787 - 4.56114i) q^{71} +(1.44697 + 1.05128i) q^{72} +(4.84526 - 14.9122i) q^{73} +(-1.12030 - 3.44794i) q^{74} +(-7.38525 + 5.36570i) q^{75} +3.09781 q^{76} +(-1.34163 - 3.03316i) q^{77} +1.28269 q^{78} +(5.70664 - 4.14612i) q^{79} +(3.14072 + 9.66614i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.60387 + 1.16528i) q^{82} +(-9.62766 - 6.99490i) q^{83} +(0.548689 - 1.68869i) q^{84} +(2.88389 + 8.87571i) q^{85} +(-2.97075 + 2.15837i) q^{86} -5.80060 q^{87} +(5.12999 + 2.97845i) q^{88} -1.69179 q^{89} +(-1.44053 + 1.04661i) q^{90} +(-0.836738 - 2.57522i) q^{91} +(-2.08416 + 6.41439i) q^{92} +(-1.81837 - 1.32112i) q^{93} +(-4.75491 - 3.45464i) q^{94} +(-2.02649 + 6.23689i) q^{95} +(1.50120 + 4.62022i) q^{96} +(-5.66019 + 4.11237i) q^{97} +0.473713 q^{98} +(0.697445 - 3.24246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25}+ \cdots - q^{99}+O(q^{100}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.383242	+	0.278442i	−0.270993	+	0.196888i	−0.714979	−	0.699146i	$-0.753564\pi$
$2$	−0.383242	+	0.278442i	−0.270993	+	0.196888i	0.443986	+	0.896034i	$0.353564\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.548689	+	1.68869i	−0.274345	+	0.844346i
$5$	−3.04094	−	2.20937i	−1.35995	−	0.988062i	−0.998448	−	0.0556917i	$-0.982264\pi$
$5$	−3.04094	−	2.20937i	−1.35995	−	0.988062i	−0.361503	−	0.932371i	$-0.617736\pi$
$6$	−0.383242	−	0.278442i	−0.156458	−	0.113673i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	−0.552692	−	1.70101i	−0.195406	−	0.601398i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.78060			0.563075
$11$	−2.47012	+	2.21326i	−0.744768	+	0.667323i
$11$	−2.47012	+	2.21326i	−0.744768	+	0.667323i
$12$	−1.77560			−0.512570
$13$	−2.19061	+	1.59157i	−0.607566	+	0.441422i	−0.848556	−	0.529105i	$-0.822528\pi$
$13$	−2.19061	+	1.59157i	−0.607566	+	0.441422i	0.240991	+	0.970527i	$0.422528\pi$
$14$	−0.146385	−	0.450528i	−0.0391231	−	0.120409i
$15$	1.16154	−	3.57484i	0.299908	−	0.923021i
$16$	−2.18753	−	1.58933i	−0.546882	−	0.397333i
$17$	−2.00865	−	1.45937i	−0.487169	−	0.353949i	0.316926	−	0.948450i	$-0.397349\pi$
$17$	−2.00865	−	1.45937i	−0.487169	−	0.353949i	−0.804094	+	0.594502i	$0.797349\pi$
$18$	0.146385	−	0.450528i	0.0345034	−	0.106190i
$19$	−0.539130	−	1.65927i	−0.123685	−	0.380663i	0.869974	−	0.493097i	$-0.164135\pi$
$19$	−0.539130	−	1.65927i	−0.123685	−	0.380663i	−0.993659	+	0.112434i	$0.964135\pi$
$20$	5.39949	−	3.92296i	1.20736	−	0.877200i
$21$	−1.00000			−0.218218
$22$	0.330389	−	1.53600i	0.0704391	−	0.327476i
$23$	3.79843			0.792028			0.396014	−	0.918244i	$-0.370393\pi$
$23$	3.79843			0.792028			0.396014	+	0.918244i	$0.370393\pi$
$24$	1.44697	−	1.05128i	0.295361	−	0.214592i
$25$	2.82092	+	8.68189i	0.564183	+	1.73638i
$26$	0.396374	−	1.21991i	0.0777353	−	0.239245i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.43649	−	1.04367i	−0.271471	−	0.197235i
$29$	−1.79248	+	5.51669i	−0.332856	+	1.02442i	0.634913	+	0.772584i	$0.281036\pi$
$29$	−1.79248	+	5.51669i	−0.332856	+	1.02442i	−0.967769	+	0.251841i	$0.918964\pi$
$30$	0.550235	+	1.69345i	0.100459	+	0.309180i
$31$	−1.81837	+	1.32112i	−0.326589	+	0.237281i	−0.738982	−	0.673725i	$-0.764693\pi$
$31$	−1.81837	+	1.32112i	−0.326589	+	0.237281i	0.412393	+	0.911006i	$0.364693\pi$
$32$	4.85799			0.858779
$33$	−2.86824	−	1.66529i	−0.499297	−	0.289889i
$34$	1.17615			0.201707
$35$	3.04094	−	2.20937i	0.514013	−	0.373453i
$36$	−0.548689	−	1.68869i	−0.0914482	−	0.281449i
$37$	−2.36494	+	7.27854i	−0.388794	+	1.19658i	0.544897	+	0.838503i	$0.316569\pi$
$37$	−2.36494	+	7.27854i	−0.388794	+	1.19658i	−0.933690	+	0.358081i	$0.883431\pi$
$38$	0.668627	+	0.485786i	0.108466	+	0.0788049i
$39$	−2.19061	−	1.59157i	−0.350778	−	0.254855i
$40$	−2.07747	+	6.39378i	−0.328476	+	1.01095i
$41$	−1.29324	−	3.98017i	−0.201969	−	0.621598i	−0.999824	−	0.0187483i	$-0.994032\pi$
$41$	−1.29324	−	3.98017i	−0.201969	−	0.621598i	0.797855	−	0.602850i	$-0.205968\pi$
$42$	0.383242	−	0.278442i	0.0591355	−	0.0429645i
$43$	7.75162			1.18211			0.591056	−	0.806631i	$-0.298711\pi$
$43$	7.75162			1.18211			0.591056	+	0.806631i	$0.298711\pi$
$44$	−2.38219	−	5.38566i	−0.359128	−	0.811919i
$45$	3.75881			0.560331
$46$	−1.45572	+	1.05764i	−0.214634	+	0.155941i
$47$	3.83399	+	11.7998i	0.559246	+	1.72118i	0.684459	+	0.729051i	$0.260038\pi$
$47$	3.83399	+	11.7998i	0.559246	+	1.72118i	−0.125214	+	0.992130i	$0.539962\pi$
$48$	0.835561	−	2.57159i	0.120603	−	0.371178i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−3.49849	−	2.54180i	−0.494761	−	0.359465i
$51$	0.767235	−	2.36131i	0.107434	−	0.330649i
$52$	−1.48571	−	4.57254i	−0.206031	−	0.634098i
$53$	−7.15135	+	5.19576i	−0.982314	+	0.713693i	−0.958225	−	0.286017i	$-0.907669\pi$
$53$	−7.15135	+	5.19576i	−0.982314	+	0.713693i	−0.0240892	+	0.999710i	$0.507669\pi$
$54$	0.473713			0.0644642
$55$	12.4014	−	1.27298i	1.67221	−	0.171649i
$56$	1.78855			0.239005
$57$	1.41146	−	1.02549i	0.186953	−	0.135829i
$58$	−0.849122	−	2.61333i	−0.111495	−	0.343147i
$59$	1.40345	−	4.31938i	0.182714	−	0.562335i	−0.817188	−	0.576371i	$-0.804468\pi$
$59$	1.40345	−	4.31938i	0.182714	−	0.562335i	0.999901	+	0.0140367i	$0.00446815\pi$
$60$	5.39949	+	3.92296i	0.697071	+	0.506452i
$61$	9.28955	+	6.74925i	1.18940	+	0.864153i	0.993201	−	0.116410i	$-0.0371386\pi$
$61$	9.28955	+	6.74925i	1.18940	+	0.864153i	0.196204	+	0.980563i	$0.437139\pi$
$62$	0.329020	−	1.01262i	0.0417856	−	0.128603i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	2.51327	−	1.82600i	0.314159	−	0.228250i
$65$	10.1779			1.26241
$66$	1.56292	−	0.160431i	0.192382	−	0.0197477i
$67$	−12.2041			−1.49096			−0.745481	−	0.666527i	$-0.767780\pi$
$67$	−12.2041			−1.49096			−0.745481	+	0.666527i	$0.767780\pi$
$68$	3.56655	−	2.59125i	0.432507	−	0.314235i
$69$	1.17378	+	3.61253i	0.141307	+	0.434897i
$70$	−0.550235	+	1.69345i	−0.0657657	+	0.202406i
$71$	−6.27787	−	4.56114i	−0.745047	−	0.541308i	0.149241	−	0.988801i	$-0.452317\pi$
$71$	−6.27787	−	4.56114i	−0.745047	−	0.541308i	−0.894288	+	0.447493i	$0.852317\pi$
$72$	1.44697	+	1.05128i	0.170527	+	0.123895i
$73$	4.84526	−	14.9122i	0.567095	−	1.74534i	−0.0945471	−	0.995520i	$-0.530140\pi$
$73$	4.84526	−	14.9122i	0.567095	−	1.74534i	0.661642	−	0.749820i	$-0.269860\pi$
$74$	−1.12030	−	3.44794i	−0.130233	−	0.400815i
$75$	−7.38525	+	5.36570i	−0.852776	+	0.619578i
$76$	3.09781			0.355344
$77$	−1.34163	−	3.03316i	−0.152893	−	0.345660i
$78$	1.28269			0.145236
$79$	5.70664	−	4.14612i	0.642048	−	0.466475i	−0.218505	−	0.975836i	$-0.570118\pi$
$79$	5.70664	−	4.14612i	0.642048	−	0.466475i	0.860553	+	0.509361i	$0.170118\pi$
$80$	3.14072	+	9.66614i	0.351143	+	1.08071i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.60387	+	1.16528i	0.177117	+	0.128683i
$83$	−9.62766	−	6.99490i	−1.05677	−	0.767790i	−0.0832842	−	0.996526i	$-0.526541\pi$
$83$	−9.62766	−	6.99490i	−1.05677	−	0.767790i	−0.973489	+	0.228735i	$0.926541\pi$
$84$	0.548689	−	1.68869i	0.0598669	−	0.184251i
$85$	2.88389	+	8.87571i	0.312802	+	0.962706i
$86$	−2.97075	+	2.15837i	−0.320344	+	0.232743i
$87$	−5.80060			−0.621889
$88$	5.12999	+	2.97845i	0.546859	+	0.317503i
$89$	−1.69179			−0.179329			−0.0896647	−	0.995972i	$-0.528580\pi$
$89$	−1.69179			−0.179329			−0.0896647	+	0.995972i	$0.528580\pi$
$90$	−1.44053	+	1.04661i	−0.151846	+	0.110322i
$91$	−0.836738	−	2.57522i	−0.0877140	−	0.269956i
$92$	−2.08416	+	6.41439i	−0.217289	+	0.668746i
$93$	−1.81837	−	1.32112i	−0.188556	−	0.136994i
$94$	−4.75491	−	3.45464i	−0.490431	−	0.356319i
$95$	−2.02649	+	6.23689i	−0.207913	+	0.639892i
$96$	1.50120	+	4.62022i	0.153216	+	0.471549i
$97$	−5.66019	+	4.11237i	−0.574706	+	0.417548i	−0.836812	−	0.547491i	$-0.815583\pi$
$97$	−5.66019	+	4.11237i	−0.574706	+	0.417548i	0.262106	+	0.965039i	$0.415583\pi$
$98$	0.473713			0.0478522
$99$	0.697445	−	3.24246i	0.0700959	−	0.325880i
$100$	−16.2088			−1.62088
$101$	−2.19796	+	1.59691i	−0.218705	+	0.158899i	−0.691744	−	0.722143i	$-0.743157\pi$
$101$	−2.19796	+	1.59691i	−0.218705	+	0.158899i	0.473038	+	0.881042i	$0.343157\pi$
$102$	0.363449	+	1.11858i	0.0359868	+	0.110756i
$103$	−0.0790429	+	0.243269i	−0.00778833	+	0.0239700i	−0.954875	−	0.297007i	$-0.904011\pi$
$103$	−0.0790429	+	0.243269i	−0.00778833	+	0.0239700i	0.947087	+	0.320977i	$0.104011\pi$
$104$	3.91801	+	2.84660i	0.384193	+	0.279132i
$105$	3.04094	+	2.20937i	0.296766	+	0.215613i
$106$	1.29398	−	3.98247i	0.125683	−	0.386811i
$107$	3.66517	+	11.2802i	0.354326	+	1.09050i	0.956399	+	0.292062i	$0.0943414\pi$
$107$	3.66517	+	11.2802i	0.354326	+	1.09050i	−0.602074	+	0.798441i	$0.705659\pi$
$108$	1.43649	−	1.04367i	0.138226	−	0.100427i
$109$	−15.8720			−1.52026			−0.760129	−	0.649772i	$-0.774864\pi$
$109$	−15.8720			−1.52026			−0.760129	+	0.649772i	$0.774864\pi$
$110$	−4.39829	+	3.94093i	−0.419360	+	0.375753i
$111$	−7.65311			−0.726401
$112$	2.18753	−	1.58933i	0.206702	−	0.150178i
$113$	−1.58109	−	4.86608i	−0.148736	−	0.457763i	0.848736	−	0.528816i	$-0.177364\pi$
$113$	−1.58109	−	4.86608i	−0.148736	−	0.457763i	−0.997473	+	0.0710535i	$0.977364\pi$
$114$	−0.255393	+	0.786019i	−0.0239197	+	0.0736174i
$115$	−11.5508	−	8.39217i	−1.07712	−	0.782573i
$116$	−8.33248	−	6.05390i	−0.773652	−	0.562091i
$117$	0.836738	−	2.57522i	0.0773565	−	0.238079i
$118$	0.664833	+	2.04614i	0.0612028	+	0.188363i
$119$	2.00865	−	1.45937i	0.184132	−	0.133780i
$120$	−6.72282			−0.613707
$121$	1.20296	−	10.9340i	0.109360	−	0.994002i
$122$	−5.43942			−0.492462
$123$	3.38573	−	2.45988i	0.305281	−	0.221800i
$124$	−1.23325	−	3.79556i	−0.110749	−	0.340851i
$125$	4.79561	−	14.7594i	0.428932	−	1.32012i
$126$	0.383242	+	0.278442i	0.0341419	+	0.0248055i
$127$	−0.164504	−	0.119519i	−0.0145974	−	0.0106056i	0.580463	−	0.814287i	$-0.302872\pi$
$127$	−0.164504	−	0.119519i	−0.0145974	−	0.0106056i	−0.595060	+	0.803681i	$0.702872\pi$
$128$	−3.45716	+	10.6400i	−0.305572	+	0.940455i
$129$	2.39538	+	7.37223i	0.210902	+	0.649089i
$130$	−3.90060	+	2.83395i	−0.342105	+	0.248554i
$131$	−10.2788			−0.898067			−0.449034	−	0.893515i	$-0.648232\pi$
$131$	−10.2788			−0.898067			−0.449034	+	0.893515i	$0.648232\pi$
$132$	4.38593	−	3.92986i	0.381746	−	0.342050i
$133$	1.74466			0.151281
$134$	4.67710	−	3.39812i	0.404040	−	0.293552i
$135$	1.16154	+	3.57484i	0.0999692	+	0.307674i
$136$	−1.37224	+	4.22331i	−0.117668	+	0.362146i
$137$	13.8420	+	10.0568i	1.18260	+	0.859209i	0.992463	−	0.122549i	$-0.0391068\pi$
$137$	13.8420	+	10.0568i	1.18260	+	0.859209i	0.190137	+	0.981758i	$0.439107\pi$
$138$	−1.45572	−	1.05764i	−0.123919	−	0.0900324i
$139$	6.02612	−	18.5465i	0.511129	−	1.57309i	−0.279089	−	0.960265i	$-0.590032\pi$
$139$	6.02612	−	18.5465i	0.511129	−	1.57309i	0.790217	−	0.612827i	$-0.209968\pi$
$140$	2.06242	+	6.34748i	0.174306	+	0.536460i
$141$	−10.0375	+	7.29269i	−0.845312	+	0.614155i
$142$	3.67596			0.308479
$143$	1.88850	−	8.77976i	0.157924	−	0.734200i
$144$	2.70393			0.225328
$145$	17.6393	−	12.8157i	1.46486	−	1.06429i
$146$	2.29526	+	7.06410i	0.189957	+	0.584629i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−10.9936	−	7.98731i	−0.903668	−	0.656553i
$149$	8.00148	+	5.81342i	0.655507	+	0.476254i	0.865143	−	0.501526i	$-0.167228\pi$
$149$	8.00148	+	5.81342i	0.655507	+	0.476254i	−0.209636	+	0.977780i	$0.567228\pi$
$150$	1.33630	−	4.11272i	0.109109	−	0.335802i
$151$	−4.79018	−	14.7427i	−0.389819	−	1.19974i	−0.932923	−	0.360075i	$-0.882751\pi$
$151$	−4.79018	−	14.7427i	−0.389819	−	1.19974i	0.543104	−	0.839666i	$-0.317249\pi$
$152$	−2.52447	+	1.83413i	−0.204761	+	0.148768i
$153$	2.48283			0.200725
$154$	1.35872	+	0.788868i	0.109489	+	0.0635688i
$155$	8.44843			0.678594
$156$	3.88964	−	2.82599i	0.311420	−	0.226260i
$157$	5.23896	+	16.1238i	0.418114	+	1.28682i	0.909436	+	0.415845i	$0.136514\pi$
$157$	5.23896	+	16.1238i	0.418114	+	1.28682i	−0.491321	+	0.870978i	$0.663486\pi$
$158$	−1.03257	+	3.17793i	−0.0821471	+	0.252823i
$159$	−7.15135	−	5.19576i	−0.567139	−	0.412051i
$160$	−14.7729	−	10.7331i	−1.16790	−	0.848527i
$161$	−1.17378	+	3.61253i	−0.0925069	+	0.284707i
$162$	0.146385	+	0.450528i	0.0115011	+	0.0353968i
$163$	−16.1592	+	11.7403i	−1.26569	+	0.919574i	−0.999022	−	0.0442152i	$-0.985921\pi$
$163$	−16.1592	+	11.7403i	−1.26569	+	0.919574i	−0.266664	+	0.963790i	$0.585921\pi$
$164$	7.43086			0.580253
$165$	5.04293	+	11.4011i	0.392591	+	0.887572i
$166$	5.63739			0.437547
$167$	−14.1186	+	10.2578i	−1.09253	+	0.793771i	−0.979825	−	0.199858i	$-0.935952\pi$
$167$	−14.1186	+	10.2578i	−1.09253	+	0.793771i	−0.112706	+	0.993628i	$0.535952\pi$
$168$	0.552692	+	1.70101i	0.0426411	+	0.131236i
$169$	−1.75155	+	5.39071i	−0.134735	+	0.414670i
$170$	−3.57660	−	2.59855i	−0.274312	−	0.199300i
$171$	1.41146	+	1.02549i	0.107937	+	0.0784209i
$172$	−4.25323	+	13.0901i	−0.324306	+	0.998111i
$173$	−2.89223	−	8.90136i	−0.219892	−	0.676758i	−0.998770	−	0.0495825i	$-0.984211\pi$
$173$	−2.89223	−	8.90136i	−0.219892	−	0.676758i	0.778878	−	0.627175i	$-0.215789\pi$
$174$	2.22303	−	1.61513i	0.168528	−	0.122442i
$175$	−9.12868			−0.690063
$176$	8.92106	−	0.915732i	0.672450	−	0.0690259i
$177$	4.54166			0.341372
$178$	0.648365	−	0.471064i	0.0485970	−	0.0353078i
$179$	1.69758	+	5.22460i	0.126883	+	0.390505i	0.994239	−	0.107182i	$-0.0341827\pi$
$179$	1.69758	+	5.22460i	0.126883	+	0.390505i	−0.867357	+	0.497687i	$0.834183\pi$
$180$	−2.06242	+	6.34748i	−0.153724	+	0.473113i
$181$	9.04839	+	6.57404i	0.672562	+	0.488645i	0.870882	−	0.491493i	$-0.163549\pi$
$181$	9.04839	+	6.57404i	0.672562	+	0.488645i	−0.198320	+	0.980137i	$0.563549\pi$
$182$	1.03772	+	0.753948i	0.0769209	+	0.0558863i
$183$	−3.54829	+	10.9205i	−0.262297	+	0.807268i
$184$	−2.09936	−	6.46118i	−0.154767	−	0.476324i
$185$	23.2727	−	16.9086i	1.71104	−	1.24314i
$186$	1.06473			0.0780699
$187$	8.19156	−	0.840850i	0.599026	−	0.0614891i
$188$	−22.0299			−1.60670
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−0.959974	−	2.95450i	−0.0696438	−	0.214342i
$191$	−1.77939	+	5.47639i	−0.128752	+	0.396258i	−0.994566	−	0.104108i	$-0.966801\pi$
$191$	−1.77939	+	5.47639i	−0.128752	+	0.396258i	0.865814	+	0.500366i	$0.166801\pi$
$192$	2.51327	+	1.82600i	0.181380	+	0.131780i
$193$	12.0419	+	8.74893i	0.866793	+	0.629762i	0.929725	−	0.368256i	$-0.120045\pi$
$193$	12.0419	+	8.74893i	0.866793	+	0.629762i	−0.0629313	+	0.998018i	$0.520045\pi$
$194$	1.02417	−	3.15207i	0.0735310	−	0.226305i
$195$	3.14514	+	9.67975i	0.225228	+	0.693182i
$196$	1.43649	−	1.04367i	0.102606	−	0.0745478i
$197$	12.5476			0.893978			0.446989	−	0.894540i	$-0.352496\pi$
$197$	12.5476			0.893978			0.446989	+	0.894540i	$0.352496\pi$
$198$	0.635546	+	1.43685i	0.0451663	+	0.102112i
$199$	0.834418			0.0591503			0.0295752	−	0.999563i	$-0.490585\pi$
$199$	0.834418			0.0591503			0.0295752	+	0.999563i	$0.490585\pi$
$200$	13.2089	−	9.59682i	0.934009	−	0.678598i
$201$	−3.77126	−	11.6067i	−0.266004	−	0.818677i
$202$	0.397704	−	1.22401i	0.0279824	−	0.0861209i
$203$	−4.69278	−	3.40950i	−0.329369	−	0.239300i
$204$	3.56655	+	2.59125i	0.249708	+	0.181424i
$205$	−4.86103	+	14.9607i	−0.339509	+	1.04490i
$206$	−0.0374437	−	0.115240i	−0.00260882	−	0.00802913i
$207$	−3.07300	+	2.23266i	−0.213588	+	0.155181i
$208$	7.32155			0.507658
$209$	5.00411	+	2.90536i	0.346142	+	0.200968i
$210$	−1.78060			−0.122873
$211$	21.7385	−	15.7940i	1.49654	−	1.08730i	0.524809	−	0.851220i	$-0.324137\pi$
$211$	21.7385	−	15.7940i	1.49654	−	1.08730i	0.971733	−	0.236082i	$-0.0758633\pi$
$212$	−4.85017	−	14.9273i	−0.333111	−	1.02521i
$213$	2.39793	−	7.38008i	0.164304	−	0.505675i
$214$	−4.54554	−	3.30253i	−0.310727	−	0.225756i
$215$	−23.5722	−	17.1262i	−1.60761	−	1.16800i
$216$	−0.552692	+	1.70101i	−0.0376059	+	0.115739i
$217$	−0.694556	−	2.13762i	−0.0471495	−	0.145111i
$218$	6.08280	−	4.41941i	0.411979	−	0.299320i
$219$	15.6796			1.05953
$220$	−4.65484	+	21.6406i	−0.313829	+	1.45901i
$221$	6.72285			0.452228
$222$	2.93299	−	2.13094i	0.196849	−	0.143020i
$223$	1.24199	+	3.82247i	0.0831701	+	0.255971i	0.983991	−	0.178221i	$-0.0570340\pi$
$223$	1.24199	+	3.82247i	0.0831701	+	0.255971i	−0.900820	+	0.434192i	$0.857034\pi$
$224$	−1.50120	+	4.62022i	−0.100303	+	0.308701i
$225$	−7.38525	−	5.36570i	−0.492350	−	0.357713i
$226$	1.96086	+	1.42465i	0.130434	+	0.0947661i
$227$	−3.61612	+	11.1293i	−0.240010	+	0.738676i	0.756407	+	0.654102i	$0.226953\pi$
$227$	−3.61612	+	11.1293i	−0.240010	+	0.738676i	−0.996417	+	0.0845746i	$0.973047\pi$
$228$	0.957277	+	2.94620i	0.0633972	+	0.195117i
$229$	5.29505	−	3.84708i	0.349906	−	0.254222i	−0.398923	−	0.916984i	$-0.630616\pi$
$229$	5.29505	−	3.84708i	0.349906	−	0.254222i	0.748830	+	0.662762i	$0.230616\pi$
$230$	6.76349			0.445971
$231$	2.47012	−	2.21326i	0.162522	−	0.145622i
$232$	10.3746			0.681129
$233$	−0.139610	+	0.101432i	−0.00914614	+	0.00664506i	−0.592349	−	0.805682i	$-0.701799\pi$
$233$	−0.139610	+	0.101432i	−0.00914614	+	0.00664506i	0.583203	+	0.812327i	$0.301799\pi$
$234$	0.396374	+	1.21991i	0.0259118	+	0.0797482i
$235$	14.4113	−	44.3533i	0.940088	−	2.89329i
$236$	6.52404	+	4.73999i	0.424679	+	0.308547i
$237$	5.70664	+	4.14612i	0.370686	+	0.269319i
$238$	−0.363449	+	1.11858i	−0.0235589	+	0.0725069i
$239$	−3.22936	−	9.93895i	−0.208890	−	0.642897i	−0.999531	−	0.0306176i	$-0.990253\pi$
$239$	−3.22936	−	9.93895i	−0.208890	−	0.642897i	0.790641	−	0.612280i	$-0.209747\pi$
$240$	−8.22251	+	5.97400i	−0.530761	+	0.385620i
$241$	−3.41821			−0.220186			−0.110093	−	0.993921i	$-0.535115\pi$
$241$	−3.41821			−0.220186			−0.110093	+	0.993921i	$0.535115\pi$
$242$	2.58346	+	4.52533i	0.166071	+	0.290899i
$243$	1.00000			0.0641500
$244$	−16.4945	+	11.9839i	−1.05595	+	0.767194i
$245$	1.16154	+	3.57484i	0.0742079	+	0.228388i
$246$	−0.612622	+	1.88546i	−0.0390594	+	0.120212i
$247$	3.82187	+	2.77675i	0.243180	+	0.176681i
$248$	3.25225	+	2.36290i	0.206518	+	0.150044i
$249$	3.67744	−	11.3180i	0.233048	−	0.717249i
$250$	2.27174	+	6.99171i	0.143678	+	0.442194i
$251$	−10.2544	+	7.45026i	−0.647252	+	0.470256i	−0.862334	−	0.506340i	$-0.830998\pi$
$251$	−10.2544	+	7.45026i	−0.647252	+	0.470256i	0.215082	+	0.976596i	$0.430998\pi$
$252$	1.77560			0.111852
$253$	−9.38258	+	8.40692i	−0.589878	+	0.528539i
$254$	0.0963238			0.00604389
$255$	−7.55013	+	5.48549i	−0.472808	+	0.343515i
$256$	0.282269	+	0.868734i	0.0176418	+	0.0542959i
$257$	−5.61954	+	17.2952i	−0.350538	+	1.07884i	0.608014	+	0.793926i	$0.291966\pi$
$257$	−5.61954	+	17.2952i	−0.350538	+	1.07884i	−0.958552	+	0.284918i	$0.908034\pi$
$258$	−2.97075	−	2.15837i	−0.184951	−	0.134374i
$259$	−6.19149	−	4.49838i	−0.384721	−	0.279516i
$260$	−5.58450	+	17.1873i	−0.346336	+	1.06591i
$261$	−1.79248	−	5.51669i	−0.110952	−	0.341475i
$262$	3.93929	−	2.86206i	0.243370	−	0.176819i
$263$	15.7837			0.973264			0.486632	−	0.873607i	$-0.338225\pi$
$263$	15.7837			0.973264			0.486632	+	0.873607i	$0.338225\pi$
$264$	−1.24741	+	5.79930i	−0.0767731	+	0.356923i
$265$	33.2262			2.04107
$266$	−0.668627	+	0.485786i	−0.0409962	+	0.0297855i
$267$	−0.522792	−	1.60899i	−0.0319943	−	0.0984684i
$268$	6.69623	−	20.6089i	0.409038	−	1.25889i
$269$	−18.5990	−	13.5130i	−1.13400	−	0.823900i	−0.147728	−	0.989028i	$-0.547196\pi$
$269$	−18.5990	−	13.5130i	−1.13400	−	0.823900i	−0.986272	+	0.165128i	$0.947196\pi$
$270$	−1.44053	−	1.04661i	−0.0876681	−	0.0636946i
$271$	2.88628	−	8.88306i	0.175329	−	0.539608i	−0.824319	−	0.566125i	$-0.808442\pi$
$271$	2.88628	−	8.88306i	0.175329	−	0.539608i	0.999648	+	0.0265176i	$0.00844182\pi$
$272$	2.07455	+	6.38482i	0.125788	+	0.387136i
$273$	2.19061	−	1.59157i	0.132582	−	0.0963263i
$274$	−8.10505			−0.489644
$275$	−26.1833	−	15.2019i	−1.57891	−	0.916706i
$276$	−6.74448			−0.405970
$277$	−15.7246	+	11.4246i	−0.944799	+	0.686437i	−0.949571	−	0.313552i	$-0.898481\pi$
$277$	−15.7246	+	11.4246i	−0.944799	+	0.686437i	0.00477176	+	0.999989i	$0.498481\pi$
$278$	2.85465	+	8.78571i	0.171211	+	0.526932i
$279$	0.694556	−	2.13762i	0.0415820	−	0.127976i
$280$	−5.43888	−	3.95157i	−0.325035	−	0.236152i
$281$	3.59493	+	2.61187i	0.214456	+	0.155811i	0.689827	−	0.723974i	$-0.257686\pi$
$281$	3.59493	+	2.61187i	0.214456	+	0.155811i	−0.475372	+	0.879785i	$0.657686\pi$
$282$	1.81621	−	5.58973i	0.108154	−	0.332864i
$283$	4.27947	+	13.1708i	0.254388	+	0.782925i	0.993950	+	0.109837i	$0.0350328\pi$
$283$	4.27947	+	13.1708i	0.254388	+	0.782925i	−0.739562	+	0.673089i	$0.764967\pi$
$284$	11.1470	−	8.09875i	0.661451	−	0.480572i
$285$	−6.55786			−0.388454
$286$	1.72090	+	3.89061i	0.101759	+	0.230056i
$287$	4.18500			0.247033
$288$	−3.93019	+	2.85545i	−0.231589	+	0.168259i
$289$	−3.34838	−	10.3052i	−0.196963	−	0.606191i
$290$	−3.19169	+	9.82302i	−0.187423	+	0.576828i
$291$	−5.66019	−	4.11237i	−0.331806	−	0.241071i
$292$	22.5236	+	16.3643i	1.31809	+	0.957649i
$293$	−5.94422	+	18.2944i	−0.347265	+	1.06877i	0.613095	+	0.790009i	$0.289924\pi$
$293$	−5.94422	+	18.2944i	−0.347265	+	1.06877i	−0.960360	+	0.278763i	$0.910076\pi$
$294$	0.146385	+	0.450528i	0.00853737	+	0.0262753i
$295$	−13.8109	+	10.0342i	−0.804104	+	0.584215i
$296$	13.6880			0.795596
$297$	3.29929	−	0.338667i	0.191444	−	0.0196514i
$298$	−4.68520			−0.271406
$299$	−8.32089	+	6.04548i	−0.481209	+	0.349619i
$300$	−5.00881	−	15.4155i	−0.289184	−	0.890016i
$301$	−2.39538	+	7.37223i	−0.138068	+	0.424928i
$302$	5.94077	+	4.31622i	0.341853	+	0.248371i
$303$	−2.19796	−	1.59691i	−0.126270	−	0.0917402i
$304$	−1.45777	+	4.48656i	−0.0836089	+	0.257322i
$305$	−13.3374	−	41.0482i	−0.763695	−	2.35041i
$306$	−0.951523	+	0.691322i	−0.0543949	+	0.0395202i
$307$	2.24474			0.128114			0.0640571	−	0.997946i	$-0.479596\pi$
$307$	2.24474			0.128114			0.0640571	+	0.997946i	$0.479596\pi$
$308$	5.85820	−	0.601335i	0.333802	−	0.0342643i
$309$	−0.255788			−0.0145513
$310$	−3.23779	+	2.35239i	−0.183894	+	0.133607i
$311$	3.90260	+	12.0110i	0.221296	+	0.681080i	0.998646	+	0.0520116i	$0.0165633\pi$
$311$	3.90260	+	12.0110i	0.221296	+	0.681080i	−0.777350	+	0.629068i	$0.783437\pi$
$312$	−1.49655	+	4.60590i	−0.0847253	+	0.260758i
$313$	−0.862781	−	0.626847i	−0.0487673	−	0.0354315i	0.563135	−	0.826365i	$-0.309595\pi$
$313$	−0.862781	−	0.626847i	−0.0487673	−	0.0354315i	−0.611902	+	0.790934i	$0.709595\pi$
$314$	−6.49734	−	4.72059i	−0.366666	−	0.266398i
$315$	−1.16154	+	3.57484i	−0.0654452	+	0.201420i
$316$	3.87035	+	11.9117i	0.217724	+	0.670085i
$317$	20.3638	−	14.7951i	1.14374	−	0.830978i	0.156106	−	0.987740i	$-0.450106\pi$
$317$	20.3638	−	14.7951i	1.14374	−	0.830978i	0.987636	+	0.156763i	$0.0501058\pi$
$318$	4.18741			0.234818
$319$	−7.78224	−	17.5941i	−0.435722	−	0.985081i
$320$	−11.6770			−0.652766
$321$	−9.59555	+	6.97158i	−0.535571	+	0.389115i
$322$	−0.556035	−	1.71130i	−0.0309866	−	0.0953670i
$323$	−1.33857	+	4.11968i	−0.0744798	+	0.229225i
$324$	1.43649	+	1.04367i	0.0798049	+	0.0579816i
$325$	−19.9974	−	14.5289i	−1.10925	−	0.805920i
$326$	2.92388	−	8.99878i	0.161939	−	0.498396i
$327$	−4.90471	−	15.0951i	−0.271231	−	0.834763i
$328$	−6.05555	+	4.39961i	−0.334362	+	0.242928i
$329$	−12.4071			−0.684024
$330$	−5.10719	−	2.96521i	−0.281142	−	0.163229i
$331$	−8.53640			−0.469203			−0.234601	−	0.972092i	$-0.575378\pi$
$331$	−8.53640			−0.469203			−0.234601	+	0.972092i	$0.575378\pi$
$332$	17.0948	−	12.4201i	0.938201	−	0.681643i
$333$	−2.36494	−	7.27854i	−0.129598	−	0.398861i
$334$	2.55465	−	7.86242i	0.139784	−	0.430212i
$335$	37.1118	+	26.9633i	2.02764	+	1.47316i
$336$	2.18753	+	1.58933i	0.119339	+	0.0867052i
$337$	−5.33254	+	16.4119i	−0.290482	+	0.894012i	0.694219	+	0.719763i	$0.255750\pi$
$337$	−5.33254	+	16.4119i	−0.290482	+	0.894012i	−0.984702	+	0.174249i	$0.944250\pi$
$338$	−0.829732	−	2.55365i	−0.0451315	−	0.138900i
$339$	4.13934	−	3.00741i	0.224818	−	0.163340i
$340$	−16.5707			−0.898673
$341$	1.56760	−	7.28786i	0.0848903	−	0.394660i
$342$	−0.826469			−0.0446903
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−4.28426	−	13.1856i	−0.230992	−	0.710920i
$345$	4.41202	−	13.5788i	0.237535	−	0.731058i
$346$	3.58693	+	2.60606i	0.192835	+	0.140103i
$347$	−3.36307	−	2.44341i	−0.180539	−	0.131169i	0.493845	−	0.869550i	$-0.335591\pi$
$347$	−3.36307	−	2.44341i	−0.180539	−	0.131169i	−0.674384	+	0.738380i	$0.735591\pi$
$348$	3.18273	−	9.79542i	0.170612	−	0.525090i
$349$	2.38186	+	7.33060i	0.127498	+	0.392398i	0.994348	−	0.106171i	$-0.0338590\pi$
$349$	2.38186	+	7.33060i	0.127498	+	0.392398i	−0.866850	+	0.498569i	$0.833859\pi$
$350$	3.49849	−	2.54180i	0.187002	−	0.135865i
$351$	2.70774			0.144529
$352$	−11.9998	+	10.7520i	−0.639591	+	0.573083i
$353$	−4.84242			−0.257736			−0.128868	−	0.991662i	$-0.541134\pi$
$353$	−4.84242			−0.257736			−0.128868	+	0.991662i	$0.541134\pi$
$354$	−1.74055	+	1.26459i	−0.0925094	+	0.0672120i
$355$	9.01339	+	27.7404i	0.478381	+	1.47231i
$356$	0.928267	−	2.85691i	0.0491980	−	0.151416i
$357$	2.00865	+	1.45937i	0.106309	+	0.0772379i
$358$	−2.10533	−	1.52961i	−0.111270	−	0.0808425i
$359$	1.36534	−	4.20209i	0.0720600	−	0.221778i	−0.908540	−	0.417798i	$-0.862802\pi$
$359$	1.36534	−	4.20209i	0.0720600	−	0.221778i	0.980600	+	0.196020i	$0.0628019\pi$
$360$	−2.07747	−	6.39378i	−0.109492	−	0.336982i
$361$	12.9088	−	9.37879i	0.679411	−	0.493621i
$362$	−5.29821			−0.278468
$363$	10.7706	−	2.23472i	0.565310	−	0.117292i
$364$	4.80786			0.252000
$365$	−47.6808	+	34.6421i	−2.49573	+	1.81325i
$366$	−1.68087	−	5.17319i	−0.0878606	−	0.270407i
$367$	−9.12574	+	28.0861i	−0.476360	+	1.46608i	0.367756	+	0.929922i	$0.380126\pi$
$367$	−9.12574	+	28.0861i	−0.476360	+	1.46608i	−0.844115	+	0.536161i	$0.819874\pi$
$368$	−8.30918	−	6.03697i	−0.433146	−	0.314699i
$369$	3.38573	+	2.45988i	0.176254	+	0.128056i
$370$	−4.21101	+	12.9602i	−0.218920	+	0.673766i
$371$	−2.73157	−	8.40692i	−0.141816	−	0.436465i
$372$	3.22869	−	2.34578i	0.167400	−	0.121623i
$373$	7.64965			0.396084			0.198042	−	0.980194i	$-0.436542\pi$
$373$	7.64965			0.396084			0.198042	+	0.980194i	$0.436542\pi$
$374$	−2.90522	+	2.60312i	−0.150225	+	0.134604i
$375$	15.5189			0.801394
$376$	17.9526	−	13.0433i	0.925835	−	0.672659i
$377$	−4.85358	−	14.9378i	−0.249972	−	0.769335i
$378$	−0.146385	+	0.450528i	−0.00752925	+	0.0231727i
$379$	9.06860	+	6.58872i	0.465823	+	0.338440i	0.795811	−	0.605545i	$-0.207045\pi$
$379$	9.06860	+	6.58872i	0.465823	+	0.338440i	−0.329988	+	0.943985i	$0.607045\pi$
$380$	−9.42028	−	6.84423i	−0.483250	−	0.351102i
$381$	0.0628349	−	0.193386i	0.00321913	−	0.00990746i
$382$	−0.842919	−	2.59424i	−0.0431275	−	0.132733i
$383$	20.0189	−	14.5446i	1.02292	−	0.743194i	0.0560396	−	0.998429i	$-0.482153\pi$
$383$	20.0189	−	14.5446i	1.02292	−	0.743194i	0.966879	+	0.255235i	$0.0821527\pi$
$384$	−11.1876			−0.570915
$385$	−2.62157	+	12.1878i	−0.133607	+	0.621149i
$386$	−7.05102			−0.358887
$387$	−6.27119	+	4.55629i	−0.318783	+	0.231609i
$388$	−3.83884	−	11.8147i	−0.194888	−	0.599802i
$389$	−8.97223	+	27.6137i	−0.454910	+	1.40007i	0.416331	+	0.909213i	$0.363316\pi$
$389$	−8.97223	+	27.6137i	−0.454910	+	1.40007i	−0.871241	+	0.490856i	$0.836684\pi$
$390$	−3.90060	−	2.83395i	−0.197514	−	0.143503i
$391$	−7.62972	−	5.54331i	−0.385851	−	0.280337i
$392$	−0.552692	+	1.70101i	−0.0279152	+	0.0859140i
$393$	−3.17634	−	9.77577i	−0.160225	−	0.493122i
$394$	−4.80876	+	3.49377i	−0.242262	+	0.176013i
$395$	−26.5139			−1.33406
$396$	5.09284	+	2.95688i	0.255925	+	0.148589i
$397$	−8.27461			−0.415291			−0.207645	−	0.978204i	$-0.566580\pi$
$397$	−8.27461			−0.415291			−0.207645	+	0.978204i	$0.566580\pi$
$398$	−0.319784	+	0.232337i	−0.0160293	+	0.0116460i
$399$	0.539130	+	1.65927i	0.0269903	+	0.0830675i
$400$	7.62757	−	23.4752i	0.381378	−	1.17376i
$401$	21.6323	+	15.7168i	1.08027	+	0.784860i	0.977729	−	0.209869i	$-0.0673038\pi$
$401$	21.6323	+	15.7168i	1.08027	+	0.784860i	0.102538	+	0.994729i	$0.467304\pi$
$402$	4.67710	+	3.39812i	0.233273	+	0.169483i
$403$	1.88068	−	5.78814i	0.0936833	−	0.288328i
$404$	−1.49070	−	4.58789i	−0.0741649	−	0.228256i
$405$	−3.04094	+	2.20937i	−0.151106	+	0.109785i
$406$	2.74782			0.136372
$407$	−10.2676	−	23.2131i	−0.508947	−	1.15063i
$408$	−4.44065			−0.219845
$409$	−28.0590	+	20.3861i	−1.38743	+	1.00803i	−0.391288	+	0.920268i	$0.627970\pi$
$409$	−28.0590	+	20.3861i	−1.38743	+	1.00803i	−0.996142	+	0.0877586i	$0.972030\pi$
$410$	−2.30273	−	7.08708i	−0.113724	−	0.350006i
$411$	−5.28716	+	16.2722i	−0.260797	+	0.802649i
$412$	−0.367437	−	0.266958i	−0.0181023	−	0.0131521i
$413$	3.67428	+	2.66952i	0.180800	+	0.131359i
$414$	0.556035	−	1.71130i	0.0273276	−	0.0841058i
$415$	13.8228	+	42.5422i	0.678535	+	2.08832i
$416$	−10.6419	+	7.73183i	−0.521764	+	0.379084i
$417$	19.5009			0.954964
$418$	−2.72676	+	0.279897i	−0.133370	+	0.0136902i
$419$	−4.34546			−0.212290			−0.106145	−	0.994351i	$-0.533851\pi$
$419$	−4.34546			−0.212290			−0.106145	+	0.994351i	$0.533851\pi$
$420$	−5.39949	+	3.92296i	−0.263468	+	0.191421i
$421$	−1.46425	−	4.50649i	−0.0713631	−	0.219633i	0.909014	−	0.416767i	$-0.136837\pi$
$421$	−1.46425	−	4.50649i	−0.0713631	−	0.219633i	−0.980377	+	0.197133i	$0.936837\pi$
$422$	−3.93342	+	12.1058i	−0.191476	+	0.589302i
$423$	−10.0375	−	7.29269i	−0.488041	−	0.354583i
$424$	12.7905	+	9.29287i	0.621164	+	0.451302i
$425$	7.00384	−	21.5556i	0.339736	−	1.04560i
$426$	1.13593	+	3.49604i	0.0550361	+	0.169384i
$427$	−9.28955	+	6.74925i	−0.449553	+	0.326619i
$428$	−21.0599			−1.01797
$429$	8.93362	−	0.917022i	0.431319	−	0.0442742i
$430$	13.8025			0.665617
$431$	24.1590	−	17.5526i	1.16370	−	0.845478i	0.173459	−	0.984841i	$-0.444506\pi$
$431$	24.1590	−	17.5526i	1.16370	−	0.845478i	0.990241	+	0.139363i	$0.0445056\pi$
$432$	0.835561	+	2.57159i	0.0402010	+	0.123726i
$433$	−6.71306	+	20.6607i	−0.322609	+	0.992889i	0.649899	+	0.760020i	$0.274811\pi$
$433$	−6.71306	+	20.6607i	−0.322609	+	0.992889i	−0.972508	+	0.232868i	$0.925189\pi$
$434$	0.861386	+	0.625834i	0.0413479	+	0.0300410i
$435$	17.6393	+	12.8157i	0.845739	+	0.614465i
$436$	8.70878	−	26.8029i	0.417075	−	1.28362i
$437$	−2.04785	−	6.30263i	−0.0979620	−	0.301496i
$438$	−6.00908	+	4.36585i	−0.287125	+	0.208609i
$439$	−40.3447			−1.92555			−0.962773	−	0.270313i	$-0.912873\pi$
$439$	−40.3447			−1.92555			−0.962773	+	0.270313i	$0.912873\pi$
$440$	−9.01952	−	20.3914i	−0.429989	−	0.972120i
$441$	1.00000			0.0476190
$442$	−2.57648	+	1.87192i	−0.122551	+	0.0890382i
$443$	−4.28883	−	13.1996i	−0.203768	−	0.627134i	−0.999762	−	0.0218290i	$-0.993051\pi$
$443$	−4.28883	−	13.1996i	−0.203768	−	0.627134i	0.795993	−	0.605305i	$-0.206949\pi$
$444$	4.19918	−	12.9237i	0.199284	−	0.613334i
$445$	5.14464	+	3.73780i	0.243879	+	0.177189i
$446$	−1.54032	−	1.11911i	−0.0729361	−	0.0529912i
$447$	−3.05629	+	9.40630i	−0.144558	+	0.444903i
$448$	0.959985	+	2.95453i	0.0453550	+	0.139588i
$449$	11.5708	−	8.40666i	0.546059	−	0.396735i	−0.280272	−	0.959921i	$-0.590425\pi$
$449$	11.5708	−	8.40666i	0.546059	−	0.396735i	0.826330	+	0.563186i	$0.190425\pi$
$450$	4.32437			0.203853
$451$	12.0036	+	6.96922i	0.565227	+	0.328168i
$452$	9.08484			0.427315
$453$	12.5409	−	9.11147i	0.589221	−	0.428094i
$454$	−1.71300	−	5.27208i	−0.0803953	−	0.247431i
$455$	−3.14514	+	9.67975i	−0.147447	+	0.453794i
$456$	−2.52447	−	1.83413i	−0.118219	−	0.0858911i
$457$	11.4296	+	8.30410i	0.534655	+	0.388449i	0.822096	−	0.569349i	$-0.192805\pi$
$457$	11.4296	+	8.30410i	0.534655	+	0.388449i	−0.287441	+	0.957798i	$0.592805\pi$
$458$	−0.958097	+	2.94872i	−0.0447690	+	0.137785i
$459$	0.767235	+	2.36131i	0.0358115	+	0.110216i
$460$	20.5096	−	14.9011i	0.956265	−	0.694767i
$461$	−0.966736			−0.0450254			−0.0225127	−	0.999747i	$-0.507167\pi$
$461$	−0.966736			−0.0450254			−0.0225127	+	0.999747i	$0.507167\pi$
$462$	−0.330389	+	1.53600i	−0.0153711	+	0.0714611i
$463$	31.8119			1.47842			0.739212	−	0.673473i	$-0.235198\pi$
$463$	31.8119			1.47842			0.739212	+	0.673473i	$0.235198\pi$
$464$	12.6890	−	9.21907i	0.589070	−	0.427985i
$465$	2.61071	+	8.03493i	0.121069	+	0.372611i
$466$	0.0252613	−	0.0777463i	0.00117021	−	0.00360153i
$467$	23.9576	+	17.4062i	1.10863	+	0.805465i	0.982447	−	0.186543i	$-0.0597282\pi$
$467$	23.9576	+	17.4062i	1.10863	+	0.805465i	0.126180	+	0.992007i	$0.459728\pi$
$468$	3.88964	+	2.82599i	0.179799	+	0.130631i
$469$	3.77126	−	11.6067i	0.174141	−	0.535950i
$470$	6.82681	+	21.0107i	0.314897	+	0.969153i
$471$	−13.7158	+	9.96509i	−0.631989	+	0.459167i
$472$	−8.12298			−0.373891
$473$	−19.1474	+	17.1564i	−0.880399	+	0.788850i
$474$	−3.34148			−0.153479
$475$	12.8848	−	9.36133i	0.591194	−	0.429527i
$476$	1.36230	+	4.19273i	0.0624409	+	0.192173i
$477$	2.73157	−	8.40692i	0.125070	−	0.384926i
$478$	4.00504	+	2.90983i	0.183186	+	0.133093i
$479$	21.5079	+	15.6264i	0.982723	+	0.713990i	0.958316	−	0.285712i	$-0.0922301\pi$
$479$	21.5079	+	15.6264i	0.982723	+	0.713990i	0.0244075	+	0.999702i	$0.492230\pi$
$480$	5.64273	−	17.3665i	0.257554	−	0.792670i
$481$	−6.40365	−	19.7084i	−0.291981	−	0.898626i
$482$	1.31000	−	0.951771i	0.0596689	−	0.0433520i
$483$	−3.79843			−0.172835
$484$	17.8042	+	8.03081i	0.809280	+	0.365037i
$485$	26.2981			1.19414
$486$	−0.383242	+	0.278442i	−0.0173842	+	0.0126304i
$487$	4.36774	+	13.4425i	0.197921	+	0.609138i	0.999930	+	0.0118263i	$0.00376451\pi$
$487$	4.36774	+	13.4425i	0.197921	+	0.609138i	−0.802009	+	0.597312i	$0.796235\pi$
$488$	6.34629	−	19.5319i	0.287283	−	0.884167i
$489$	−16.1592	−	11.7403i	−0.730744	−	0.530917i
$490$	−1.44053	−	1.04661i	−0.0650767	−	0.0472810i
$491$	4.76461	−	14.6639i	0.215024	−	0.661775i	−0.784128	−	0.620599i	$-0.786890\pi$
$491$	4.76461	−	14.6639i	0.215024	−	0.661775i	0.999152	−	0.0411759i	$-0.0131104\pi$
$492$	2.29626	+	7.06717i	0.103524	+	0.318613i
$493$	11.6514	−	8.46520i	0.524751	−	0.381254i
$494$	−2.23786			−0.100686
$495$	−9.28471	+	8.31923i	−0.417317	+	0.373922i
$496$	6.07744			0.272885
$497$	6.27787	−	4.56114i	0.281601	−	0.204595i
$498$	1.74205	+	5.36148i	0.0780631	+	0.240254i
$499$	9.48757	−	29.1997i	0.424722	−	1.30716i	−0.478538	−	0.878067i	$-0.658833\pi$
$499$	9.48757	−	29.1997i	0.424722	−	1.30716i	0.903260	−	0.429093i	$-0.141167\pi$
$500$	22.2927	+	16.1966i	0.996961	+	0.724335i
$501$	−14.1186	−	10.2578i	−0.630773	−	0.458284i
$502$	1.85545	−	5.71050i	0.0828130	−	0.254872i
$503$	−5.62070	−	17.2987i	−0.250614	−	0.771312i	−0.994662	−	0.103185i	$-0.967096\pi$
$503$	−5.62070	−	17.2987i	−0.250614	−	0.771312i	0.744048	−	0.668127i	$-0.232904\pi$
$504$	−1.44697	+	1.05128i	−0.0644530	+	0.0468279i
$505$	10.2121			0.454431
$506$	1.25496	−	5.83438i	0.0557898	−	0.259370i
$507$	−5.66813			−0.251731
$508$	0.292092	−	0.212217i	0.0129595	−	0.00941563i
$509$	−9.94245	−	30.5997i	−0.440691	−	1.35631i	−0.887140	−	0.461499i	$-0.847312\pi$
$509$	−9.94245	−	30.5997i	−0.440691	−	1.35631i	0.446449	−	0.894809i	$-0.352688\pi$
$510$	1.36614	−	4.20454i	0.0604936	−	0.186180i
$511$	12.6851	+	9.21624i	0.561154	+	0.407702i
$512$	−18.4520	−	13.4061i	−0.815470	−	0.592474i
$513$	−0.539130	+	1.65927i	−0.0238032	+	0.0732586i
$514$	−2.66205	−	8.19295i	−0.117418	−	0.361376i
$515$	0.777838	−	0.565132i	0.0342756	−	0.0249027i
$516$	−13.7637			−0.605915
$517$	−35.5865	−	20.6613i	−1.56509	−	0.908684i
$518$	3.62538			0.159290
$519$	7.57195	−	5.50134i	0.332372	−	0.241482i
$520$	−5.62524	−	17.3127i	−0.246683	−	0.759213i
$521$	−8.59801	+	26.4620i	−0.376686	+	1.15932i	0.565648	+	0.824646i	$0.308626\pi$
$521$	−8.59801	+	26.4620i	−0.376686	+	1.15932i	−0.942334	+	0.334673i	$0.891374\pi$
$522$	2.22303	+	1.61513i	0.0972994	+	0.0706922i
$523$	15.4751	+	11.2433i	0.676677	+	0.491635i	0.872254	−	0.489054i	$-0.162658\pi$
$523$	15.4751	+	11.2433i	0.676677	+	0.491635i	−0.195577	+	0.980688i	$0.562658\pi$
$524$	5.63990	−	17.3578i	0.246380	−	0.758280i
$525$	−2.82092	−	8.68189i	−0.123115	−	0.378909i
$526$	−6.04897	+	4.39483i	−0.263748	+	0.191624i
$527$	5.58048			0.243089
$528$	3.62767	+	8.20145i	0.157874	+	0.356922i
$529$	−8.57190			−0.372691
$530$	−12.7337	+	9.25156i	−0.553116	+	0.401862i
$531$	1.40345	+	4.31938i	0.0609045	+	0.187445i
$532$	−0.957277	+	2.94620i	−0.0415032	+	0.127734i
$533$	9.16769	+	6.66072i	0.397097	+	0.288508i
$534$	0.648365	+	0.471064i	0.0280575	+	0.0203850i
$535$	13.7767	−	42.4003i	0.595619	−	1.83313i
$536$	6.74508	+	20.7592i	0.291343	+	0.896662i
$537$	−4.44431	+	3.22898i	−0.191786	+	0.139341i
$538$	10.8905			0.469522
$539$	3.29929	−	0.338667i	0.142110	−	0.0145874i
$540$	−6.67413			−0.287209
$541$	−34.5304	+	25.0878i	−1.48458	+	1.07861i	−0.508534	+	0.861042i	$0.669813\pi$
$541$	−34.5304	+	25.0878i	−1.48458	+	1.07861i	−0.976045	+	0.217569i	$0.930187\pi$
$542$	1.36727	+	4.20802i	0.0587293	+	0.180750i
$543$	−3.45618	+	10.6370i	−0.148319	+	0.456478i
$544$	−9.75798	−	7.08959i	−0.418370	−	0.303964i
$545$	48.2657	+	35.0671i	2.06748	+	1.50211i
$546$	−0.396374	+	1.21991i	−0.0169632	+	0.0522075i
$547$	−7.76134	−	23.8869i	−0.331851	−	1.02133i	−0.968253	−	0.249974i	$-0.919578\pi$
$547$	−7.76134	−	23.8869i	−0.331851	−	1.02133i	0.636402	−	0.771358i	$-0.280422\pi$
$548$	−24.5778	+	17.8568i	−1.04991	+	0.762804i
$549$	−11.4825			−0.490062
$550$	14.2674	−	1.46452i	0.608362	−	0.0624474i
$551$	10.1201			0.431130
$552$	5.49621	−	3.99323i	0.233934	−	0.169963i
$553$	2.17974	+	6.70856i	0.0926922	+	0.285277i
$554$	2.84524	−	8.75676i	0.120883	−	0.372039i
$555$	23.2727	+	16.9086i	0.987870	+	0.717730i
$556$	28.0128	+	20.3525i	1.18801	+	0.863139i
$557$	−1.31555	+	4.04884i	−0.0557415	+	0.171555i	−0.975051	−	0.221980i	$-0.928748\pi$
$557$	−1.31555	+	4.04884i	−0.0557415	+	0.171555i	0.919310	+	0.393535i	$0.128748\pi$
$558$	0.329020	+	1.01262i	0.0139285	+	0.0428676i
$559$	−16.9808	+	12.3373i	−0.718210	+	0.521810i
$560$	−10.1636			−0.429490
$561$	3.33103	+	7.53080i	0.140636	+	0.317950i
$562$	−2.10498			−0.0887933
$563$	6.01677	−	4.37144i	0.253577	−	0.184234i	−0.453734	−	0.891137i	$-0.649908\pi$
$563$	6.01677	−	4.37144i	0.253577	−	0.184234i	0.707310	+	0.706903i	$0.249908\pi$
$564$	−6.80763	−	20.9517i	−0.286653	−	0.882226i
$565$	−5.94301	+	18.2907i	−0.250024	+	0.769496i
$566$	−5.30738	−	3.85604i	−0.223086	−	0.162081i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	−4.28882	+	13.1996i	−0.179955	+	0.553845i
$569$	13.4822	+	41.4939i	0.565203	+	1.73952i	0.667348	+	0.744746i	$0.267430\pi$
$569$	13.4822	+	41.4939i	0.565203	+	1.73952i	−0.102145	+	0.994770i	$0.532570\pi$
$570$	2.51325	−	1.82598i	0.105268	−	0.0764819i
$571$	−34.1074			−1.42735			−0.713676	−	0.700476i	$-0.752971\pi$
$571$	−34.1074			−1.42735			−0.713676	+	0.700476i	$0.752971\pi$
$572$	13.7901	+	8.00646i	0.576593	+	0.334767i
$573$	−5.75822			−0.240553
$574$	−1.60387	+	1.16528i	−0.0669441	+	0.0486377i
$575$	10.7151	+	32.9776i	0.446849	+	1.37526i
$576$	−0.959985	+	2.95453i	−0.0399994	+	0.123105i
$577$	−22.7175	−	16.5052i	−0.945743	−	0.687122i	0.00405352	−	0.999992i	$-0.498710\pi$
$577$	−22.7175	−	16.5052i	−0.945743	−	0.687122i	−0.949796	+	0.312870i	$0.898710\pi$
$578$	4.15265	+	3.01707i	0.172727	+	0.125494i
$579$	−4.59959	+	14.1561i	−0.191152	+	0.588306i
$580$	11.9633	+	36.8192i	0.496748	+	1.52883i
$581$	9.62766	−	6.99490i	0.399423	−	0.290198i
$582$	3.31428			0.137381
$583$	6.16511	−	28.6619i	0.255333	−	1.18706i
$584$	−28.0437			−1.16046
$585$	−8.23409	+	5.98242i	−0.340438	+	0.247343i
$586$	−2.81585	−	8.66631i	−0.116322	−	0.358002i
$587$	−2.07887	+	6.39809i	−0.0858040	+	0.264078i	−0.984748	−	0.173986i	$-0.944335\pi$
$587$	−2.07887	+	6.39809i	−0.0858040	+	0.264078i	0.898944	+	0.438063i	$0.144335\pi$
$588$	1.43649	+	1.04367i	0.0592397	+	0.0430402i
$589$	3.17244	+	2.30491i	0.130718	+	0.0949724i
$590$	2.49898	−	7.69107i	0.102881	−	0.316636i
$591$	3.87741	+	11.9335i	0.159495	+	0.490877i
$592$	16.7414	−	12.1633i	0.688067	−	0.499910i
$593$	20.8442			0.855969			0.427984	−	0.903786i	$-0.359224\pi$
$593$	20.8442			0.855969			0.427984	+	0.903786i	$0.359224\pi$
$594$	−1.17013	+	1.04845i	−0.0480109	+	0.0430184i
$595$	−9.33248			−0.382594
$596$	−14.2074	+	10.3223i	−0.581958	+	0.422817i
$597$	0.257849	+	0.793579i	0.0105531	+	0.0324790i
$598$	1.50560	−	4.63376i	0.0615686	−	0.189489i
$599$	−0.146169	−	0.106198i	−0.00597231	−	0.00433913i	0.584795	−	0.811181i	$-0.301175\pi$
$599$	−0.146169	−	0.106198i	−0.00597231	−	0.00433913i	−0.590767	+	0.806842i	$0.701175\pi$
$600$	13.2089	+	9.59682i	0.539251	+	0.391788i
$601$	8.53019	−	26.2532i	0.347954	−	1.07089i	−0.612030	−	0.790835i	$-0.709647\pi$
$601$	8.53019	−	26.2532i	0.347954	−	1.07089i	0.959984	−	0.280056i	$-0.0903532\pi$
$602$	−1.13472	−	3.49232i	−0.0462479	−	0.142336i
$603$	9.87329	−	7.17336i	0.402071	−	0.292122i
$604$	27.5241			1.11994
$605$	−27.8155	+	30.5920i	−1.13086	+	1.24374i
$606$	1.28700			0.0522807
$607$	−18.8727	+	13.7118i	−0.766021	+	0.556547i	−0.900751	−	0.434336i	$-0.856983\pi$
$607$	−18.8727	+	13.7118i	−0.766021	+	0.556547i	0.134730	+	0.990882i	$0.456983\pi$
$608$	−2.61909	−	8.06072i	−0.106218	−	0.326905i
$609$	1.79248	−	5.51669i	0.0726351	−	0.223548i
$610$	16.5410	+	12.0177i	0.669724	+	0.486583i
$611$	−27.1790	−	19.7467i	−1.09955	−	0.798867i
$612$	−1.36230	+	4.19273i	−0.0550677	+	0.169481i
$613$	−6.02591	−	18.5459i	−0.243384	−	0.749060i	−0.995898	−	0.0904833i	$-0.971159\pi$
$613$	−6.02591	−	18.5459i	−0.243384	−	0.749060i	0.752514	−	0.658577i	$-0.228841\pi$
$614$	−0.860279	+	0.625029i	−0.0347180	+	0.0252241i
$615$	−15.7306			−0.634320
$616$	−4.41793	+	3.95852i	−0.178003	+	0.159493i
$617$	−23.2566			−0.936276			−0.468138	−	0.883655i	$-0.655075\pi$
$617$	−23.2566			−0.936276			−0.468138	+	0.883655i	$0.655075\pi$
$618$	0.0980288	−	0.0712221i	0.00394330	−	0.00286497i
$619$	−8.82217	−	27.1518i	−0.354593	−	1.09132i	−0.956245	−	0.292566i	$-0.905491\pi$
$619$	−8.82217	−	27.1518i	−0.354593	−	1.09132i	0.601652	−	0.798758i	$-0.294509\pi$
$620$	−4.63556	+	14.2668i	−0.186169	+	0.572968i
$621$	−3.07300	−	2.23266i	−0.123315	−	0.0895937i
$622$	−4.83999	−	3.51646i	−0.194066	−	0.140997i
$623$	0.522792	−	1.60899i	0.0209452	−	0.0644627i
$624$	2.26248	+	6.96321i	0.0905719	+	0.278752i
$625$	−10.2659	+	7.45861i	−0.410636	+	0.298344i
$626$	0.505194			0.0201916
$627$	−1.21681	+	5.65700i	−0.0485945	+	0.225919i
$628$	−30.1028			−1.20123
$629$	15.3724	−	11.1687i	0.612938	−	0.445325i
$630$	−0.550235	−	1.69345i	−0.0219219	−	0.0674687i
$631$	1.63814	−	5.04166i	0.0652131	−	0.200705i	−0.913141	−	0.407645i	$-0.866350\pi$
$631$	1.63814	−	5.04166i	0.0652131	−	0.200705i	0.978354	+	0.206939i	$0.0663502\pi$
$632$	−10.2066	−	7.41554i	−0.405997	−	0.294974i
$633$	21.7385	+	15.7940i	0.864029	+	0.627754i
$634$	−3.68466	+	11.3402i	−0.146337	+	0.450378i
$635$	0.236185	+	0.726901i	0.00937270	+	0.0288462i
$636$	12.6979	−	9.22557i	0.503505	−	0.365818i
$637$	2.70774			0.107285
$638$	7.88141	+	4.57590i	0.312028	+	0.181162i
$639$	7.75988			0.306976
$640$	34.0209	−	24.7176i	1.34479	−	0.977049i
$641$	−9.23593	−	28.4253i	−0.364797	−	1.12273i	−0.950108	−	0.311922i	$-0.899027\pi$
$641$	−9.23593	−	28.4253i	−0.364797	−	1.12273i	0.585310	−	0.810809i	$-0.300973\pi$
$642$	1.73624	−	5.34360i	0.0685240	−	0.210895i
$643$	−31.0989	−	22.5946i	−1.22642	−	0.891046i	−0.229803	−	0.973237i	$-0.573808\pi$
$643$	−31.0989	−	22.5946i	−1.22642	−	0.891046i	−0.996617	+	0.0821916i	$0.973808\pi$
$644$	−5.45640	−	3.96431i	−0.215012	−	0.156216i
$645$	9.00380	−	27.7108i	0.354524	−	1.09111i
$646$	−0.634096	−	1.95155i	−0.0249482	−	0.0767826i
$647$	26.1799	−	19.0208i	1.02924	−	0.747786i	0.0610828	−	0.998133i	$-0.480545\pi$
$647$	26.1799	−	19.0208i	1.02924	−	0.747786i	0.968156	+	0.250347i	$0.0805446\pi$
$648$	−1.78855			−0.0702608
$649$	6.09322	+	13.7756i	0.239180	+	0.540738i
$650$	11.7093			0.459276
$651$	1.81837	−	1.32112i	0.0712676	−	0.0517789i
$652$	−10.9594	−	33.7297i	−0.429205	−	1.32096i
$653$	7.38692	−	22.7346i	0.289073	−	0.889674i	−0.696076	−	0.717969i	$-0.745072\pi$
$653$	7.38692	−	22.7346i	0.289073	−	0.889674i	0.985148	−	0.171706i	$-0.0549278\pi$
$654$	6.08280	+	4.41941i	0.237856	+	0.172813i
$655$	31.2574	+	22.7098i	1.22133	+	0.887347i
$656$	−3.49682	+	10.7621i	−0.136528	+	0.420190i
$657$	4.84526	+	14.9122i	0.189032	+	0.581780i
$658$	4.75491	−	3.45464i	0.185366	−	0.134676i
$659$	34.5124			1.34441			0.672205	−	0.740365i	$-0.265347\pi$
$659$	34.5124			1.34441			0.672205	+	0.740365i	$0.265347\pi$
$660$	−22.0199	+	2.26031i	−0.857123	+	0.0879823i
$661$	−2.56237			−0.0996647			−0.0498324	−	0.998758i	$-0.515869\pi$
$661$	−2.56237			−0.0996647			−0.0498324	+	0.998758i	$0.515869\pi$
$662$	3.27150	−	2.37689i	0.127151	−	0.0923803i
$663$	2.07748	+	6.39381i	0.0806824	+	0.248315i
$664$	−6.57728	+	20.2428i	−0.255248	+	0.785572i
$665$	−5.30542	−	3.85461i	−0.205735	−	0.149475i
$666$	2.93299	+	2.13094i	0.113651	+	0.0825724i
$667$	−6.80863	+	20.9548i	−0.263631	+	0.811373i
$668$	−9.57549	−	29.4703i	−0.370487	−	1.14024i
$669$	−3.25158	+	2.36241i	−0.125713	+	0.0913362i
$670$	−21.7305			−0.839523
$671$	−37.8841	+	3.88875i	−1.46250	+	0.150123i
$672$	−4.85799			−0.187401
$673$	−29.6642	+	21.5523i	−1.14347	+	0.830781i	−0.987599	−	0.156996i	$-0.949819\pi$
$673$	−29.6642	+	21.5523i	−1.14347	+	0.830781i	−0.155872	+	0.987777i	$0.549819\pi$
$674$	−2.52610	−	7.77452i	−0.0973016	−	0.299463i
$675$	2.82092	−	8.68189i	0.108577	−	0.334166i
$676$	−8.14220	−	5.91566i	−0.313162	−	0.227525i
$677$	−25.8733	−	18.7981i	−0.994392	−	0.722468i	−0.0335138	−	0.999438i	$-0.510670\pi$
$677$	−25.8733	−	18.7981i	−0.994392	−	0.722468i	−0.960879	+	0.276970i	$0.910670\pi$
$678$	−0.748981	+	2.30513i	−0.0287645	+	0.0885279i
$679$	−2.16200	−	6.65396i	−0.0829700	−	0.255355i
$680$	13.5038	−	9.81107i	0.517846	−	0.376237i
$681$	−11.7020			−0.448422
$682$	1.42847	+	3.22950i	0.0546991	+	0.123664i
$683$	6.96871			0.266650			0.133325	−	0.991072i	$-0.457435\pi$
$683$	6.96871			0.266650			0.133325	+	0.991072i	$0.457435\pi$
$684$	−2.50618	+	1.82085i	−0.0958263	+	0.0696219i
$685$	−19.8735	−	61.1642i	−0.759326	−	2.33696i
$686$	−0.146385	+	0.450528i	−0.00558902	+	0.0172012i
$687$	5.29505	+	3.84708i	0.202019	+	0.146775i
$688$	−16.9569	−	12.3199i	−0.646475	−	0.469692i
$689$	7.39640	−	22.7638i	0.281780	−	0.867230i
$690$	2.09003	+	6.43246i	0.0795662	+	0.244879i
$691$	4.10336	−	2.98127i	0.156099	−	0.113413i	−0.506994	−	0.861950i	$-0.669243\pi$
$691$	4.10336	−	2.98127i	0.156099	−	0.113413i	0.663093	+	0.748537i	$0.269243\pi$
$692$	16.6186			0.631744
$693$	2.86824	+	1.66529i	0.108956	+	0.0632590i
$694$	1.96922			0.0747505
$695$	−59.3012	+	43.0848i	−2.24942	+	1.63430i
$696$	3.20594	+	9.86688i	0.121521	+	0.374003i
$697$	−3.21088	+	9.88206i	−0.121621	+	0.374310i
$698$	−2.95397	−	2.14619i	−0.111809	−	0.0812344i
$699$	−0.139610	−	0.101432i	−0.00528052	−	0.00383653i
$700$	5.00881	−	15.4155i	0.189315	−	0.582652i
$701$	0.129238	+	0.397753i	0.00488125	+	0.0150229i	0.953467	−	0.301496i	$-0.0974860\pi$
$701$	0.129238	+	0.397753i	0.00488125	+	0.0150229i	−0.948586	+	0.316519i	$0.897486\pi$
$702$	−1.03772	+	0.753948i	−0.0391662	+	0.0284559i
$703$	13.3521			0.503583
$704$	−2.16667	+	10.0730i	−0.0816593	+	0.379639i
$705$	46.6358			1.75641
$706$	1.85582	−	1.34833i	0.0698447	−	0.0507451i
$707$	−0.839547	−	2.58386i	−0.0315744	−	0.0971760i
$708$	−2.49196	+	7.66947i	−0.0936536	+	0.288236i
$709$	2.91783	+	2.11993i	0.109582	+	0.0796157i	0.641226	−	0.767352i	$-0.278426\pi$
$709$	2.91783	+	2.11993i	0.109582	+	0.0796157i	−0.531645	+	0.846967i	$0.678426\pi$
$710$	−11.1784	−	8.12156i	−0.419517	−	0.304797i
$711$	−2.17974	+	6.70856i	−0.0817468	+	0.251591i
$712$	0.935039	+	2.87775i	0.0350420	+	0.107848i
$713$	−6.90697	+	5.01820i	−0.258668	+	0.187933i
$714$	−1.17615			−0.0440162
$715$	−25.1406	+	22.5263i	−0.940205	+	0.842437i
$716$	−9.75419			−0.364531
$717$	8.45458	−	6.14261i	0.315742	−	0.229400i
$718$	0.646781	+	1.99059i	0.0241376	+	0.0742880i
$719$	−5.55293	+	17.0902i	−0.207089	+	0.637356i	0.792532	+	0.609831i	$0.208763\pi$
$719$	−5.55293	+	17.0902i	−0.207089	+	0.637356i	−0.999621	+	0.0275250i	$0.991237\pi$
$720$	−8.22251	−	5.97400i	−0.306435	−	0.222638i
$721$	−0.206937	−	0.150349i	−0.00770674	−	0.00559928i
$722$	−2.33575	+	7.18869i	−0.0869275	+	0.267535i
$723$	−1.05628	−	3.25091i	−0.0392836	−	0.120903i
$724$	−16.0663	+	11.6728i	−0.597099	+	0.433818i
$725$	−52.9518			−1.96658
$726$	−3.50551	+	3.85542i	−0.130102	+	0.143088i
$727$	10.0774			0.373752			0.186876	−	0.982384i	$-0.440164\pi$
$727$	10.0774			0.373752			0.186876	+	0.982384i	$0.440164\pi$
$728$	−3.91801	+	2.84660i	−0.145211	+	0.105502i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	8.62747	−	26.5526i	0.319317	−	0.982757i
$731$	−15.5703	−	11.3125i	−0.575888	−	0.418407i
$732$	−16.4945	−	11.9839i	−0.609654	−	0.442939i
$733$	−3.77849	+	11.6290i	−0.139562	+	0.429527i	−0.996272	−	0.0862717i	$-0.972505\pi$
$733$	−3.77849	+	11.6290i	−0.139562	+	0.429527i	0.856710	+	0.515799i	$0.172505\pi$
$734$	−4.32298	−	13.3048i	−0.159564	−	0.491088i
$735$	−3.04094	+	2.20937i	−0.112167	+	0.0814940i
$736$	18.4527			0.680177
$737$	30.1454	−	27.0107i	1.11042	−	0.994954i
$738$	−1.98249			−0.0729764
$739$	−2.83011	+	2.05620i	−0.104107	+	0.0756385i	−0.638621	−	0.769521i	$-0.720495\pi$
$739$	−2.83011	+	2.05620i	−0.104107	+	0.0756385i	0.534514	+	0.845160i	$0.320495\pi$
$740$	15.7839	+	48.5779i	0.580229	+	1.78576i
$741$	−1.45983	+	4.49288i	−0.0536280	+	0.165050i
$742$	3.38769	+	2.46130i	0.124366	+	0.0903571i
$743$	−2.21381	−	1.60843i	−0.0812167	−	0.0590074i	0.546436	−	0.837501i	$-0.315984\pi$
$743$	−2.21381	−	1.60843i	−0.0812167	−	0.0590074i	−0.627653	+	0.778493i	$0.715984\pi$
$744$	−1.24225	+	3.82325i	−0.0455430	+	0.140167i
$745$	−11.4880	−	35.3565i	−0.420889	−	1.29536i
$746$	−2.93166	+	2.12998i	−0.107336	+	0.0779841i
$747$	11.9004			0.435414
$748$	−3.07468	+	14.2944i	−0.112422	+	0.522654i
$749$	−11.8608			−0.433382
$750$	−5.94750	+	4.32111i	−0.217172	+	0.157785i
$751$	−3.10499	−	9.55617i	−0.113303	−	0.348710i	0.878287	−	0.478135i	$-0.158687\pi$
$751$	−3.10499	−	9.55617i	−0.113303	−	0.348710i	−0.991589	+	0.129425i	$0.958687\pi$
$752$	10.3669	−	31.9059i	0.378041	−	1.16349i
$753$	−10.2544	−	7.45026i	−0.373691	−	0.271502i
$754$	6.01940	+	4.37335i	0.219213	+	0.159268i
$755$	−18.0054	+	55.4149i	−0.655283	+	2.01676i
$756$	0.548689	+	1.68869i	0.0199556	+	0.0614171i
$757$	−12.2558	+	8.90436i	−0.445445	+	0.323634i	−0.787795	−	0.615938i	$-0.788777\pi$
$757$	−12.2558	+	8.90436i	−0.445445	+	0.323634i	0.342350	+	0.939573i	$0.388777\pi$
$758$	−5.31004			−0.192869
$759$	−10.8948	−	6.32548i	−0.395457	−	0.229600i
$760$	11.7290			0.425457
$761$	−28.6726	+	20.8319i	−1.03938	+	0.755154i	−0.970165	−	0.242447i	$-0.922050\pi$
$761$	−28.6726	+	20.8319i	−1.03938	+	0.755154i	−0.0692162	+	0.997602i	$0.522050\pi$
$762$	0.0297657	+	0.0916094i	0.00107830	+	0.00331866i
$763$	4.90471	−	15.0951i	0.177562	−	0.546481i
$764$	−8.27161	−	6.00967i	−0.299256	−	0.217422i
$765$	−7.55013	−	5.48549i	−0.272976	−	0.198328i
$766$	−3.62227	+	11.1482i	−0.130878	+	0.402801i
$767$	3.80018	+	11.6958i	0.137217	+	0.422309i
$768$	−0.738989	+	0.536907i	−0.0266660	+	0.0193740i
$769$	38.7592			1.39769			0.698845	−	0.715273i	$-0.253698\pi$
$769$	38.7592			1.39769			0.698845	+	0.715273i	$0.253698\pi$
$770$	−2.38890	−	5.40083i	−0.0860900	−	0.194633i
$771$	−18.1852			−0.654925
$772$	−21.3815	+	15.5346i	−0.769537	+	0.559102i
$773$	8.20190	+	25.2428i	0.295002	+	0.907922i	0.983221	+	0.182419i	$0.0583928\pi$
$773$	8.20190	+	25.2428i	0.295002	+	0.907922i	−0.688219	+	0.725503i	$0.741607\pi$
$774$	1.13472	−	3.49232i	0.0407868	−	0.125529i
$775$	−16.5993	−	12.0601i	−0.596265	−	0.433212i
$776$	10.1235	+	7.35518i	0.363414	+	0.264035i
$777$	2.36494	−	7.27854i	0.0848418	−	0.261116i
$778$	−4.25026	−	13.0810i	−0.152379	−	0.468975i
$779$	−5.90696	+	4.29166i	−0.211639	+	0.153765i
$780$	−18.0718			−0.647075
$781$	25.6021	−	2.62801i	0.916114	−	0.0940377i
$782$	4.46752			0.159758
$783$	4.69278	−	3.40950i	0.167706	−	0.121846i
$784$	0.835561	+	2.57159i	0.0298415	+	0.0918426i
$785$	19.6923	−	60.6065i	0.702847	−	2.16314i
$786$	3.93929	+	2.86206i	0.140510	+	0.102086i
$787$	−15.9216	−	11.5677i	−0.567545	−	0.412345i	0.266668	−	0.963788i	$-0.414077\pi$
$787$	−15.9216	−	11.5677i	−0.567545	−	0.412345i	−0.834212	+	0.551443i	$0.814077\pi$
$788$	−6.88472	+	21.1890i	−0.245258	+	0.754827i
$789$	4.87743	+	15.0112i	0.173641	+	0.534412i
$790$	10.1612	−	7.38258i	0.361521	−	0.262660i
$791$	5.11650			0.181922
$792$	−5.90094	+	0.605722i	−0.209681	+	0.0215234i
$793$	−31.0917			−1.10410
$794$	3.17118	−	2.30400i	0.112541	−	0.0817658i
$795$	10.2675	+	31.6000i	0.364150	+	1.12074i
$796$	−0.457836	+	1.40907i	−0.0162276	+	0.0499433i
$797$	20.4517	+	14.8590i	0.724435	+	0.526333i	0.887798	−	0.460233i	$-0.152234\pi$
$797$	20.4517	+	14.8590i	0.724435	+	0.526333i	−0.163363	+	0.986566i	$0.552234\pi$
$798$	−0.668627	−	0.485786i	−0.0236691	−	0.0171966i
$799$	9.51914	−	29.2969i	0.336763	−	1.03645i
$800$	13.7040	+	42.1765i	0.484509	+	1.49116i
$801$	1.36869	−	0.994409i	0.0483602	−	0.0351357i
$802$	−12.6666			−0.447274
$803$	21.0362	+	47.5587i	0.742351	+	1.67831i
$804$	21.6695			0.764223
$805$	11.5508	−	8.39217i	0.407113	−	0.295785i
$806$	0.890902	+	2.74191i	0.0313807	+	0.0965798i
$807$	7.10418	−	21.8644i	0.250079	−	0.769664i
$808$	3.93116	+	2.85616i	0.138298	+	0.100479i
$809$	28.9540	+	21.0363i	1.01797	+	0.739597i	0.965865	−	0.259045i	$-0.0834079\pi$
$809$	28.9540	+	21.0363i	1.01797	+	0.739597i	0.0521021	+	0.998642i	$0.483408\pi$
$810$	0.550235	−	1.69345i	0.0193333	−	0.0595018i
$811$	6.47127	+	19.9165i	0.227237	+	0.699364i	0.998057	+	0.0623105i	$0.0198469\pi$
$811$	6.47127	+	19.9165i	0.227237	+	0.699364i	−0.770820	+	0.637053i	$0.780153\pi$
$812$	8.33248	−	6.05390i	0.292413	−	0.212450i
$813$	9.34021			0.327575
$814$	10.3985	+	6.03729i	0.364466	+	0.211607i
$815$	75.0780			2.62987
$816$	−5.43125	+	3.94603i	−0.190132	+	0.138139i
$817$	−4.17913	−	12.8620i	−0.146209	−	0.449986i
$818$	5.07706	−	15.6256i	0.177515	−	0.546336i
$819$	2.19061	+	1.59157i	0.0765461	+	0.0556140i
$820$	−22.5968	−	16.4176i	−0.789116	−	0.573326i
$821$	−2.49273	+	7.67182i	−0.0869967	+	0.267748i	−0.985085	−	0.172066i	$-0.944956\pi$
$821$	−2.49273	+	7.67182i	−0.0869967	+	0.267748i	0.898089	+	0.439814i	$0.144956\pi$
$822$	−2.50460	−	7.70836i	−0.0873579	−	0.268860i
$823$	16.2903	−	11.8356i	0.567845	−	0.412564i	−0.266477	−	0.963841i	$-0.585860\pi$
$823$	16.2903	−	11.8356i	0.567845	−	0.412564i	0.834322	+	0.551278i	$0.185860\pi$
$824$	0.457490			0.0159374
$825$	6.36675	−	29.5994i	0.221662	−	1.03052i
$826$	−2.15144			−0.0748583
$827$	17.3276	−	12.5892i	0.602540	−	0.437771i	−0.244240	−	0.969715i	$-0.578538\pi$
$827$	17.3276	−	12.5892i	0.602540	−	0.437771i	0.846779	+	0.531944i	$0.178538\pi$
$828$	−2.08416	−	6.41439i	−0.0724296	−	0.222915i
$829$	−8.46584	+	26.0552i	−0.294031	+	0.904934i	0.689514	+	0.724272i	$0.257824\pi$
$829$	−8.46584	+	26.0552i	−0.294031	+	0.904934i	−0.983545	+	0.180662i	$0.942176\pi$
$830$	−17.1430	−	12.4551i	−0.595042	−	0.432323i
$831$	−15.7246	−	11.4246i	−0.545480	−	0.396315i
$832$	−2.59939	+	8.00010i	−0.0901177	+	0.277354i
$833$	0.767235	+	2.36131i	0.0265831	+	0.0818144i
$834$	−7.47357	+	5.42987i	−0.258789	+	0.188021i
$835$	65.5972			2.27008
$836$	−7.65196	+	6.85627i	−0.264649	+	0.237129i
$837$	2.24763			0.0776895
$838$	1.66536	−	1.20996i	0.0575290	−	0.0417972i
$839$	−6.29643	−	19.3784i	−0.217377	−	0.669017i	−0.998976	−	0.0452363i	$-0.985596\pi$
$839$	−6.29643	−	19.3784i	−0.217377	−	0.669017i	0.781600	−	0.623781i	$-0.214404\pi$
$840$	2.07747	−	6.39378i	0.0716794	−	0.220606i
$841$	−3.75943	−	2.73139i	−0.129636	−	0.0941858i
$842$	1.81596	+	1.31937i	0.0625820	+	0.0454685i
$843$	−1.37314	+	4.22610i	−0.0472935	+	0.145555i
$844$	14.7435	+	45.3757i	0.507490	+	1.56190i
$845$	17.2365	−	12.5230i	0.592953	−	0.430805i
$846$	5.87739			0.202069
$847$	10.0271	+	4.52288i	0.344537	+	0.155408i
$848$	23.9016			0.820783
$849$	−11.2038	+	8.14003i	−0.384513	+	0.279365i
$850$	3.31781	+	10.2112i	0.113800	+	0.350240i
$851$	−8.98307	+	27.6471i	−0.307936	+	0.947729i
$852$	11.1470	+	8.09875i	0.381889	+	0.277458i
$853$	6.70421	+	4.87090i	0.229548	+	0.166776i	0.696614	−	0.717446i	$-0.254689\pi$
$853$	6.70421	+	4.87090i	0.229548	+	0.166776i	−0.467066	+	0.884222i	$0.654689\pi$
$854$	1.68087	−	5.17319i	0.0575183	−	0.177023i
$855$	−2.02649	−	6.23689i	−0.0693045	−	0.213297i
$856$	17.1621	−	12.4690i	0.586589	−	0.426182i
$857$	−31.0459			−1.06051			−0.530254	−	0.847839i	$-0.677903\pi$
$857$	−31.0459			−1.06051			−0.530254	+	0.847839i	$0.677903\pi$
$858$	−3.16840	+	2.83893i	−0.108167	+	0.0969196i
$859$	−1.63124			−0.0556573			−0.0278287	−	0.999613i	$-0.508859\pi$
$859$	−1.63124			−0.0556573			−0.0278287	+	0.999613i	$0.508859\pi$
$860$	41.8548	−	30.4093i	1.42724	−	1.03695i
$861$	1.29324	+	3.98017i	0.0440733	+	0.135644i
$862$	−4.37139	+	13.4538i	−0.148890	+	0.458237i
$863$	−4.31095	−	3.13209i	−0.146746	−	0.106617i	0.511990	−	0.858992i	$-0.328909\pi$
$863$	−4.31095	−	3.13209i	−0.146746	−	0.106617i	−0.658736	+	0.752374i	$0.728909\pi$
$864$	−3.93019	−	2.85545i	−0.133708	−	0.0971445i
$865$	−10.8713	+	33.4586i	−0.369637	+	1.13762i
$866$	−3.18006	−	9.78723i	−0.108063	−	0.332584i
$867$	8.76617	−	6.36899i	0.297715	−	0.216302i
$868$	3.99088			0.135459
$869$	−4.91964	+	22.8717i	−0.166887	+	0.775869i
$870$	−10.3285			−0.350170
$871$	26.7343	−	19.4236i	0.905858	−	0.658144i
$872$	8.77231	+	26.9984i	0.297068	+	0.914281i
$873$	2.16200	−	6.65396i	0.0731727	−	0.225202i
$874$	2.53974	+	1.84523i	0.0859079	+	0.0624157i
$875$	12.5551	+	9.12179i	0.424439	+	0.308373i
$876$	−8.60323	+	26.4780i	−0.290676	+	0.894610i
$877$	−4.98344	−	15.3374i	−0.168279	−	0.517909i	0.830984	−	0.556296i	$-0.187778\pi$
$877$	−4.98344	−	15.3374i	−0.168279	−	0.517909i	−0.999263	+	0.0383874i	$0.987778\pi$
$878$	15.4618	−	11.2336i	0.521809	−	0.379117i
$879$	−19.2359			−0.648811
$880$	−29.1516	−	16.9253i	−0.982701	−	0.570551i
$881$	−35.1173			−1.18313			−0.591565	−	0.806257i	$-0.701490\pi$
$881$	−35.1173			−1.18313			−0.591565	+	0.806257i	$0.701490\pi$
$882$	−0.383242	+	0.278442i	−0.0129044	+	0.00937561i
$883$	0.148400	+	0.456727i	0.00499405	+	0.0153701i	0.953522	−	0.301322i	$-0.0974279\pi$
$883$	0.148400	+	0.456727i	0.00499405	+	0.0153701i	−0.948528	+	0.316692i	$0.897428\pi$
$884$	−3.68876	+	11.3528i	−0.124066	+	0.381837i
$885$	−13.8109	−	10.0342i	−0.464249	−	0.337297i
$886$	5.31899	+	3.86447i	0.178695	+	0.129829i
$887$	11.3483	−	34.9264i	0.381038	−	1.17271i	−0.558276	−	0.829655i	$-0.688537\pi$
$887$	11.3483	−	34.9264i	0.381038	−	1.17271i	0.939314	−	0.343059i	$-0.111463\pi$
$888$	4.22981	+	13.0180i	0.141943	+	0.436856i
$889$	0.164504	−	0.119519i	0.00551728	−	0.00400854i
$890$	−3.01240			−0.100976
$891$	1.34163	+	3.03316i	0.0449462	+	0.101615i
$892$	−7.13644			−0.238946
$893$	17.5121	−	12.7233i	0.586020	−	0.425768i
$894$	−1.44781	−	4.45589i	−0.0484219	−	0.149027i
$895$	6.38087	−	19.6383i	0.213289	−	0.656436i
$896$	−9.05096	−	6.57590i	−0.302371	−	0.219686i
$897$	−8.32089	−	6.04548i	−0.277826	−	0.201853i
$898$	−2.09364	+	6.44357i	−0.0698657	+	0.215025i
$899$	−4.02884	−	12.3995i	−0.134369	−	0.413546i
$900$	13.1132	−	9.52732i	0.437108	−	0.317577i
$901$	21.9471			0.731163
$902$	−6.54080	+	0.671402i	−0.217785	+	0.0223553i
$903$	−7.75162			−0.257958
$904$	−7.40341	+	5.37889i	−0.246234	+	0.178899i
$905$	−12.9911	−	39.9826i	−0.431840	−	1.32907i
$906$	−2.26917	+	6.98379i	−0.0753882	+	0.232021i
$907$	−9.86328	−	7.16609i	−0.327505	−	0.237946i	0.411866	−	0.911244i	$-0.364877\pi$
$907$	−9.86328	−	7.16609i	−0.327505	−	0.237946i	−0.739371	+	0.673298i	$0.764877\pi$
$908$	−16.8098	−	12.2130i	−0.557853	−	0.405304i
$909$	0.839547	−	2.58386i	0.0278460	−	0.0857012i
$910$	−1.48990	−	4.58543i	−0.0493895	−	0.152005i
$911$	6.56799	−	4.77193i	0.217607	−	0.158101i	−0.473642	−	0.880718i	$-0.657061\pi$
$911$	6.56799	−	4.77193i	0.217607	−	0.158101i	0.691249	+	0.722617i	$0.257061\pi$
$912$	−4.71745			−0.156210
$913$	39.2630	−	4.03028i	1.29942	−	0.133383i
$914$	−6.69251			−0.221369
$915$	34.9177	−	25.3692i	1.15434	−	0.838679i
$916$	3.59119	+	11.0526i	0.118656	+	0.365187i
$917$	3.17634	−	9.77577i	0.104892	−	0.322824i
$918$	−0.951523	−	0.691322i	−0.0314049	−	0.0228170i
$919$	40.1708	+	29.1858i	1.32511	+	0.962751i	0.999853	+	0.0171266i	$0.00545185\pi$
$919$	40.1708	+	29.1858i	1.32511	+	0.962751i	0.325260	+	0.945625i	$0.394548\pi$
$920$	−7.89112	+	24.2864i	−0.260162	+	0.800698i
$921$	0.693663	+	2.13488i	0.0228570	+	0.0703466i
$922$	0.370494	−	0.269179i	0.0122016	−	0.00886495i
$923$	21.0118			0.691610
$924$	2.38219	+	5.38566i	0.0783682	+	0.177175i
$925$	−69.8627			−2.29707
$926$	−12.1917	+	8.85775i	−0.400643	+	0.291084i
$927$	−0.0790429	−	0.243269i	−0.00259611	−	0.00799001i
$928$	−8.70786	+	26.8000i	−0.285849	+	0.879754i
$929$	0.302391	+	0.219700i	0.00992114	+	0.00720813i	0.592735	−	0.805398i	$-0.298048\pi$
$929$	0.302391	+	0.219700i	0.00992114	+	0.00720813i	−0.582814	+	0.812606i	$0.698048\pi$
$930$	−3.23779	−	2.35239i	−0.106171	−	0.0771380i
$931$	−0.539130	+	1.65927i	−0.0176693	+	0.0543804i
$932$	−0.0946857	−	0.291413i	−0.00310153	−	0.00954554i
$933$	−10.2171	+	7.42319i	−0.334494	+	0.243024i
$934$	−14.0282			−0.459016
$935$	−26.7678	−	15.5412i	−0.875401	−	0.508253i
$936$	−4.84293			−0.158296
$937$	37.2687	−	27.0773i	1.21752	−	0.884578i	0.221625	−	0.975132i	$-0.428864\pi$
$937$	37.2687	−	27.0773i	1.21752	−	0.884578i	0.995892	+	0.0905544i	$0.0288639\pi$
$938$	1.78649	+	5.49827i	0.0583311	+	0.179525i
$939$	0.329553	−	1.01426i	0.0107546	−	0.0330991i
$940$	66.9918	+	48.6724i	2.18503	+	1.58752i
$941$	15.6443	+	11.3662i	0.509988	+	0.370528i	0.812819	−	0.582516i	$-0.197932\pi$
$941$	15.6443	+	11.3662i	0.509988	+	0.370528i	−0.302831	+	0.953044i	$0.597932\pi$
$942$	2.48176	−	7.63808i	0.0808602	−	0.248862i
$943$	−4.91227	−	15.1184i	−0.159965	−	0.492323i
$944$	−9.93501	+	7.21821i	−0.323357	+	0.234933i
$945$	−3.75881			−0.122274
$946$	2.56105	−	11.9065i	0.0832669	−	0.387113i
$947$	−8.06969			−0.262230			−0.131115	−	0.991367i	$-0.541856\pi$
$947$	−8.06969			−0.262230			−0.131115	+	0.991367i	$0.541856\pi$
$948$	−10.1327	+	7.36183i	−0.329095	+	0.239101i
$949$	13.1197	+	40.3784i	0.425884	+	1.31074i
$950$	−2.33140	+	7.17531i	−0.0756406	+	0.232798i
$951$	20.3638	+	14.7951i	0.660340	+	0.479765i
$952$	−3.59256	−	2.61015i	−0.116436	−	0.0845955i
$953$	10.7030	−	32.9406i	0.346706	−	1.06705i	−0.613959	−	0.789338i	$-0.710424\pi$
$953$	10.7030	−	32.9406i	0.346706	−	1.06705i	0.960664	−	0.277712i	$-0.0895761\pi$
$954$	1.29398	+	3.98247i	0.0418942	+	0.128937i
$955$	17.5104	−	12.7221i	0.566624	−	0.411676i
$956$	18.5557			0.600136
$957$	14.3282	−	12.8382i	0.463163	−	0.415001i
$958$	−12.5938			−0.406887
$959$	−13.8420	+	10.0568i	−0.446981	+	0.324750i
$960$	−3.60840	−	11.1055i	−0.116461	−	0.358429i
$961$	−8.01842	+	24.6782i	−0.258659	+	0.796070i
$962$	7.94178	+	5.77004i	0.256053	+	0.186034i
$963$	−9.59555	−	6.97158i	−0.309212	−	0.224656i
$964$	1.87553	−	5.77230i	0.0604069	−	0.185913i
$965$	−17.2890	−	53.2100i	−0.556552	−	1.71289i
$966$	1.45572	−	1.05764i	0.0468370	−	0.0340291i
$967$	8.15074			0.262110			0.131055	−	0.991375i	$-0.458164\pi$
$967$	8.15074			0.262110			0.131055	+	0.991375i	$0.458164\pi$
$968$	−19.2638	+	3.99690i	−0.619161	+	0.128465i
$969$	−4.33169			−0.139154
$970$	−10.0785	+	7.32248i	−0.323602	+	0.235111i
$971$	10.3314	+	31.7967i	0.331549	+	1.02040i	0.968397	+	0.249414i	$0.0802380\pi$
$971$	10.3314	+	31.7967i	0.331549	+	1.02040i	−0.636848	+	0.770990i	$0.719762\pi$
$972$	−0.548689	+	1.68869i	−0.0175992	+	0.0541648i
$973$	15.7766	+	11.4624i	0.505774	+	0.367466i
$974$	−5.41685	−	3.93557i	−0.173567	−	0.126104i
$975$	7.63831	−	23.5083i	0.244622	−	0.752868i
$976$	−9.59435	−	29.5284i	−0.307108	−	0.945180i
$977$	4.43987	−	3.22575i	0.142044	−	0.103201i	−0.514494	−	0.857494i	$-0.672020\pi$
$977$	4.43987	−	3.22575i	0.142044	−	0.103201i	0.656538	+	0.754293i	$0.272020\pi$
$978$	9.46188			0.302557
$979$	4.17892	−	3.74437i	0.133559	−	0.119671i
$980$	−6.67413			−0.213197
$981$	12.8407	−	9.32931i	0.409972	−	0.297862i
$982$	2.25706	+	6.94650i	0.0720255	+	0.221672i
$983$	4.49323	−	13.8288i	0.143312	−	0.441069i	−0.853478	−	0.521129i	$-0.825511\pi$
$983$	4.49323	−	13.8288i	0.143312	−	0.441069i	0.996790	+	0.0800600i	$0.0255112\pi$
$984$	−6.05555	−	4.39961i	−0.193044	−	0.140255i
$985$	−38.1565	−	27.7223i	−1.21577	−	0.883306i
$986$	−2.10822	+	6.48844i	−0.0671395	+	0.206634i
$987$	−3.83399	−	11.7998i	−0.122037	−	0.375592i
$988$	−6.78610	+	4.93039i	−0.215895	+	0.156857i
$989$	29.4440			0.936266
$990$	1.24187	−	5.77353i	0.0394692	−	0.183495i
$991$	−9.68326			−0.307599			−0.153799	−	0.988102i	$-0.549151\pi$
$991$	−9.68326			−0.307599			−0.153799	+	0.988102i	$0.549151\pi$
$992$	−8.83362	+	6.41800i	−0.280468	+	0.203772i
$993$	−2.63789	−	8.11860i	−0.0837110	−	0.257636i
$994$	−1.13593	+	3.49604i	−0.0360296	+	0.110888i
$995$	−2.53742	−	1.84354i	−0.0804415	−	0.0584442i
$996$	17.0948	+	12.4201i	0.541671	+	0.393547i
$997$	−7.79389	+	23.9871i	−0.246835	+	0.759680i	0.748494	+	0.663141i	$0.230777\pi$
$997$	−7.79389	+	23.9871i	−0.246835	+	0.759680i	−0.995329	+	0.0965389i	$0.969223\pi$
$998$	4.49438	+	13.8323i	0.142267	+	0.437854i
$999$	6.19149	−	4.49838i	0.195890	−	0.142323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.190.3	yes	20
3.2	odd	2		693.2.m.j.190.3		20
11.2	odd	10		2541.2.a.br.1.5		10
11.4	even	5	inner	231.2.j.g.169.3	✓	20
11.9	even	5		2541.2.a.bq.1.6		10
33.2	even	10		7623.2.a.cy.1.6		10
33.20	odd	10		7623.2.a.cx.1.5		10
33.26	odd	10		693.2.m.j.631.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.3	✓	20	11.4	even	5	inner
231.2.j.g.190.3	yes	20	1.1	even	1	trivial
693.2.m.j.190.3		20	3.2	odd	2
693.2.m.j.631.3		20	33.26	odd	10
2541.2.a.bq.1.6		10	11.9	even	5
2541.2.a.br.1.5		10	11.2	odd	10
7623.2.a.cx.1.5		10	33.20	odd	10
7623.2.a.cy.1.6		10	33.2	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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.383242 + 0.278442i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.548689 + 1.68869i) q^{4} +(-3.04094 - 2.20937i) q^{5} +(-0.383242 - 0.278442i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.552692 - 1.70101i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.78060 q^{10} +(-2.47012 + 2.21326i) q^{11} -1.77560 q^{12} +(-2.19061 + 1.59157i) q^{13} +(-0.146385 - 0.450528i) q^{14} +(1.16154 - 3.57484i) q^{15} +(-2.18753 - 1.58933i) q^{16} +(-2.00865 - 1.45937i) q^{17} +(0.146385 - 0.450528i) q^{18} +(-0.539130 - 1.65927i) q^{19} +(5.39949 - 3.92296i) q^{20} -1.00000 q^{21} +(0.330389 - 1.53600i) q^{22} +3.79843 q^{23} +(1.44697 - 1.05128i) q^{24} +(2.82092 + 8.68189i) q^{25} +(0.396374 - 1.21991i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.43649 - 1.04367i) q^{28} +(-1.79248 + 5.51669i) q^{29} +(0.550235 + 1.69345i) q^{30} +(-1.81837 + 1.32112i) q^{31} +4.85799 q^{32} +(-2.86824 - 1.66529i) q^{33} +1.17615 q^{34} +(3.04094 - 2.20937i) q^{35} +(-0.548689 - 1.68869i) q^{36} +(-2.36494 + 7.27854i) q^{37} +(0.668627 + 0.485786i) q^{38} +(-2.19061 - 1.59157i) q^{39} +(-2.07747 + 6.39378i) q^{40} +(-1.29324 - 3.98017i) q^{41} +(0.383242 - 0.278442i) q^{42} +7.75162 q^{43} +(-2.38219 - 5.38566i) q^{44} +3.75881 q^{45} +(-1.45572 + 1.05764i) q^{46} +(3.83399 + 11.7998i) q^{47} +(0.835561 - 2.57159i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-3.49849 - 2.54180i) q^{50} +(0.767235 - 2.36131i) q^{51} +(-1.48571 - 4.57254i) q^{52} +(-7.15135 + 5.19576i) q^{53} +0.473713 q^{54} +(12.4014 - 1.27298i) q^{55} +1.78855 q^{56} +(1.41146 - 1.02549i) q^{57} +(-0.849122 - 2.61333i) q^{58} +(1.40345 - 4.31938i) q^{59} +(5.39949 + 3.92296i) q^{60} +(9.28955 + 6.74925i) q^{61} +(0.329020 - 1.01262i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(2.51327 - 1.82600i) q^{64} +10.1779 q^{65} +(1.56292 - 0.160431i) q^{66} -12.2041 q^{67} +(3.56655 - 2.59125i) q^{68} +(1.17378 + 3.61253i) q^{69} +(-0.550235 + 1.69345i) q^{70} +(-6.27787 - 4.56114i) q^{71} +(1.44697 + 1.05128i) q^{72} +(4.84526 - 14.9122i) q^{73} +(-1.12030 - 3.44794i) q^{74} +(-7.38525 + 5.36570i) q^{75} +3.09781 q^{76} +(-1.34163 - 3.03316i) q^{77} +1.28269 q^{78} +(5.70664 - 4.14612i) q^{79} +(3.14072 + 9.66614i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.60387 + 1.16528i) q^{82} +(-9.62766 - 6.99490i) q^{83} +(0.548689 - 1.68869i) q^{84} +(2.88389 + 8.87571i) q^{85} +(-2.97075 + 2.15837i) q^{86} -5.80060 q^{87} +(5.12999 + 2.97845i) q^{88} -1.69179 q^{89} +(-1.44053 + 1.04661i) q^{90} +(-0.836738 - 2.57522i) q^{91} +(-2.08416 + 6.41439i) q^{92} +(-1.81837 - 1.32112i) q^{93} +(-4.75491 - 3.45464i) q^{94} +(-2.02649 + 6.23689i) q^{95} +(1.50120 + 4.62022i) q^{96} +(-5.66019 + 4.11237i) q^{97} +0.473713 q^{98} +(0.697445 - 3.24246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25}+ \cdots - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more