LMFDB - Embedded newform 539.2.f.d.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			295.2
Root			$1.43801 + 1.04478i$ of defining polynomial
Character	$\chi$	$=$	539.295
Dual form			539.2.f.d.148.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.549273 - 1.69049i) q^{2} +(0.500000 - 0.363271i) q^{3} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(-0.339469 - 1.04478i) q^{6} +(1.20872 - 0.878189i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})$	\(q+(0.549273 - 1.69049i) q^{2} +(0.500000 - 0.363271i) q^{3} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(-0.339469 - 1.04478i) q^{6} +(1.20872 - 0.878189i) q^{8} +(-0.809017 + 2.48990i) q^{9} +4.93693 q^{10} +(1.14849 + 3.11143i) q^{11} -0.716580 q^{12} +(1.32676 - 4.08334i) q^{13} +(1.38874 + 1.00898i) q^{15} +(-1.53723 - 4.73110i) q^{16} +(0.851514 + 2.62069i) q^{17} +(3.76477 + 2.73527i) q^{18} +(1.56876 - 1.13977i) q^{19} +(0.995144 - 3.06274i) q^{20} +(5.89066 - 0.232480i) q^{22} +4.37009 q^{23} +(0.285341 - 0.878189i) q^{24} +(-2.19601 + 1.59550i) q^{25} +(-6.17408 - 4.48573i) q^{26} +(1.07295 + 3.30220i) q^{27} +(-6.98027 - 5.07146i) q^{29} +(2.46847 - 1.79345i) q^{30} +(0.0619850 - 0.190770i) q^{31} -5.85410 q^{32} +(1.70454 + 1.13850i) q^{33} +4.89796 q^{34} +(2.45576 - 1.78421i) q^{36} +(-0.837721 - 0.608640i) q^{37} +(-1.06509 - 3.27802i) q^{38} +(-0.819981 - 2.52364i) q^{39} +(3.35721 + 2.43916i) q^{40} +(7.77155 - 5.64636i) q^{41} -4.70820 q^{43} +(1.04316 - 3.70127i) q^{44} -7.27155 q^{45} +(2.40037 - 7.38759i) q^{46} +(-10.5541 + 7.66797i) q^{47} +(-2.48729 - 1.80712i) q^{48} +(1.49096 + 4.58869i) q^{50} +(1.37778 + 1.00101i) q^{51} +(-4.02734 + 2.92604i) q^{52} +(-1.20520 + 3.70923i) q^{53} +6.17167 q^{54} +(-7.23324 + 5.70428i) q^{55} +(0.370334 - 1.13977i) q^{57} +(-12.4073 + 9.01445i) q^{58} +(-6.92286 - 5.02975i) q^{59} +(-0.615033 - 1.89288i) q^{60} +(0.305497 + 0.940223i) q^{61} +(-0.288448 - 0.209570i) q^{62} +(-0.141042 + 0.434084i) q^{64} +11.9251 q^{65} +(2.86088 - 2.25615i) q^{66} -5.41745 q^{67} +(0.987288 - 3.03856i) q^{68} +(2.18505 - 1.58753i) q^{69} +(-0.623302 - 1.91833i) q^{71} +(1.20872 + 3.72007i) q^{72} +(-8.06677 - 5.86085i) q^{73} +(-1.48904 + 1.08185i) q^{74} +(-0.518408 + 1.59550i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(1.94479 - 5.98545i) q^{79} +(11.1780 - 8.12131i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-5.27640 - 16.2391i) q^{82} +(0.531960 + 1.63720i) q^{83} +(-6.19182 + 4.49862i) q^{85} +(-2.58609 + 7.95916i) q^{86} -5.33245 q^{87} +(4.12062 + 2.75227i) q^{88} +15.3035 q^{89} +(-3.99406 + 12.2925i) q^{90} +(-4.09921 - 2.97825i) q^{92} +(-0.0383089 - 0.117903i) q^{93} +(7.16556 + 22.0533i) q^{94} +(4.35721 + 3.16570i) q^{95} +(-2.92705 + 2.12663i) q^{96} +(-3.58961 + 11.0477i) q^{97} +(-8.67628 + 0.342417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.549273	−	1.69049i	0.388395	−	1.19536i	−0.545593	−	0.838050i	$-0.683696\pi$
$2$	0.549273	−	1.69049i	0.388395	−	1.19536i	0.933988	−	0.357305i	$-0.116304\pi$
$3$	0.500000	−	0.363271i	0.288675	−	0.209735i	−0.434017	−	0.900905i	$-0.642904\pi$
$3$	0.500000	−	0.363271i	0.288675	−	0.209735i	0.722692	+	0.691170i	$0.242904\pi$
$4$	−0.938015	−	0.681508i	−0.469007	−	0.340754i
$5$	0.858290	+	2.64154i	0.383839	+	1.18133i	0.937319	+	0.348472i	$0.113299\pi$
$5$	0.858290	+	2.64154i	0.383839	+	1.18133i	−0.553480	+	0.832862i	$0.686701\pi$
$6$	−0.339469	−	1.04478i	−0.138588	−	0.426529i
$7$		0			0
$7$		0			0
$8$	1.20872	−	0.878189i	0.427348	−	0.310487i
$9$	−0.809017	+	2.48990i	−0.269672	+	0.829966i
$10$	4.93693			1.56120
$11$	1.14849	+	3.11143i	0.346282	+	0.938131i
$11$	1.14849	+	3.11143i	0.346282	+	0.938131i
$12$	−0.716580			−0.206859
$13$	1.32676	−	4.08334i	0.367976	−	1.13251i	−0.580120	−	0.814531i	$-0.696994\pi$
$13$	1.32676	−	4.08334i	0.367976	−	1.13251i	0.948096	−	0.317983i	$-0.103006\pi$
$14$		0			0
$15$	1.38874	+	1.00898i	0.358572	+	0.260518i
$16$	−1.53723	−	4.73110i	−0.384307	−	1.18278i
$17$	0.851514	+	2.62069i	0.206522	+	0.635611i	0.999647	+	0.0265518i	$0.00845268\pi$
$17$	0.851514	+	2.62069i	0.206522	+	0.635611i	−0.793125	+	0.609059i	$0.791547\pi$
$18$	3.76477	+	2.73527i	0.887365	+	0.644709i
$19$	1.56876	−	1.13977i	0.359898	−	0.261482i	−0.393111	−	0.919491i	$-0.628601\pi$
$19$	1.56876	−	1.13977i	0.359898	−	0.261482i	0.753010	+	0.658009i	$0.228601\pi$
$20$	0.995144	−	3.06274i	0.222521	−	0.684849i
$21$		0			0
$22$	5.89066	−	0.232480i	1.25589	−	0.0495649i
$23$	4.37009			0.911228			0.455614	−	0.890178i	$-0.349420\pi$
$23$	4.37009			0.911228			0.455614	+	0.890178i	$0.349420\pi$
$24$	0.285341	−	0.878189i	0.0582450	−	0.179260i
$25$	−2.19601	+	1.59550i	−0.439202	+	0.319099i
$26$	−6.17408	−	4.48573i	−1.21084	−	0.879725i
$27$	1.07295	+	3.30220i	0.206489	+	0.635508i
$28$		0			0
$29$	−6.98027	−	5.07146i	−1.29620	−	0.941747i	−0.296293	−	0.955097i	$-0.595750\pi$
$29$	−6.98027	−	5.07146i	−1.29620	−	0.941747i	−0.999911	+	0.0133499i	$0.995750\pi$
$30$	2.46847	−	1.79345i	0.450678	−	0.327437i
$31$	0.0619850	−	0.190770i	0.0111328	−	0.0342634i	−0.945336	−	0.326099i	$-0.894266\pi$
$31$	0.0619850	−	0.190770i	0.0111328	−	0.0342634i	0.956469	+	0.291835i	$0.0942659\pi$
$32$	−5.85410			−1.03487
$33$	1.70454	+	1.13850i	0.296721	+	0.198188i
$34$	4.89796			0.839993
$35$		0			0
$36$	2.45576	−	1.78421i	0.409293	−	0.297368i
$37$	−0.837721	−	0.608640i	−0.137720	−	0.100060i	0.516792	−	0.856111i	$-0.327126\pi$
$37$	−0.837721	−	0.608640i	−0.137720	−	0.100060i	−0.654512	+	0.756051i	$0.727126\pi$
$38$	−1.06509	−	3.27802i	−0.172781	−	0.531765i
$39$	−0.819981	−	2.52364i	−0.131302	−	0.404106i
$40$	3.35721	+	2.43916i	0.530821	+	0.385664i
$41$	7.77155	−	5.64636i	1.21371	−	0.881813i	0.218149	−	0.975915i	$-0.429998\pi$
$41$	7.77155	−	5.64636i	1.21371	−	0.881813i	0.995563	+	0.0941021i	$0.0299980\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	1.04316	−	3.70127i	0.157263	−	0.557987i
$45$	−7.27155			−1.08398
$46$	2.40037	−	7.38759i	0.353916	−	1.08924i
$47$	−10.5541	+	7.66797i	−1.53947	+	1.11849i	−0.588800	+	0.808279i	$0.700399\pi$
$47$	−10.5541	+	7.66797i	−1.53947	+	1.11849i	−0.950668	+	0.310210i	$0.899601\pi$
$48$	−2.48729	−	1.80712i	−0.359009	−	0.260835i
$49$		0			0
$50$	1.49096	+	4.58869i	0.210853	+	0.648939i
$51$	1.37778	+	1.00101i	0.192928	+	0.140170i
$52$	−4.02734	+	2.92604i	−0.558492	+	0.405768i
$53$	−1.20520	+	3.70923i	−0.165547	+	0.509502i	−0.999076	−	0.0429735i	$-0.986317\pi$
$53$	−1.20520	+	3.70923i	−0.165547	+	0.509502i	0.833529	+	0.552476i	$0.186317\pi$
$54$	6.17167			0.839857
$55$	−7.23324	+	5.70428i	−0.975330	+	0.769165i
$56$		0			0
$57$	0.370334	−	1.13977i	0.0490520	−	0.150966i
$58$	−12.4073	+	9.01445i	−1.62916	+	1.18365i
$59$	−6.92286	−	5.02975i	−0.901280	−	0.654818i	0.0375144	−	0.999296i	$-0.488056\pi$
$59$	−6.92286	−	5.02975i	−0.901280	−	0.654818i	−0.938794	+	0.344478i	$0.888056\pi$
$60$	−0.615033	−	1.89288i	−0.0794004	−	0.244369i
$61$	0.305497	+	0.940223i	0.0391149	+	0.120383i	0.968707	−	0.248206i	$-0.0798410\pi$
$61$	0.305497	+	0.940223i	0.0391149	+	0.120383i	−0.929592	+	0.368589i	$0.879841\pi$
$62$	−0.288448	−	0.209570i	−0.0366330	−	0.0266154i
$63$		0			0
$64$	−0.141042	+	0.434084i	−0.0176303	+	0.0542605i
$65$	11.9251			1.47912
$66$	2.86088	−	2.25615i	0.352150	−	0.277713i
$67$	−5.41745			−0.661846			−0.330923	−	0.943658i	$-0.607360\pi$
$67$	−5.41745			−0.661846			−0.330923	+	0.943658i	$0.607360\pi$
$68$	0.987288	−	3.03856i	0.119726	−	0.368479i
$69$	2.18505	−	1.58753i	0.263049	−	0.191116i
$70$		0			0
$71$	−0.623302	−	1.91833i	−0.0739724	−	0.227664i	0.907234	−	0.420627i	$-0.138190\pi$
$71$	−0.623302	−	1.91833i	−0.0739724	−	0.227664i	−0.981206	+	0.192964i	$0.938190\pi$
$72$	1.20872	+	3.72007i	0.142449	+	0.438414i
$73$	−8.06677	−	5.86085i	−0.944144	−	0.685961i	0.00527037	−	0.999986i	$-0.498322\pi$
$73$	−8.06677	−	5.86085i	−0.944144	−	0.685961i	−0.949415	+	0.314025i	$0.898322\pi$
$74$	−1.48904	+	1.08185i	−0.173097	+	0.125762i
$75$	−0.518408	+	1.59550i	−0.0598606	+	0.184232i
$76$	−2.24828			−0.257896
$77$		0			0
$78$	−4.71658			−0.534047
$79$	1.94479	−	5.98545i	0.218806	−	0.673416i	−0.780055	−	0.625711i	$-0.784809\pi$
$79$	1.94479	−	5.98545i	0.218806	−	0.673416i	0.998861	−	0.0477054i	$-0.0151909\pi$
$80$	11.1780	−	8.12131i	1.24974	−	0.907991i
$81$	−4.61803	−	3.35520i	−0.513115	−	0.372800i
$82$	−5.27640	−	16.2391i	−0.582681	−	1.79331i
$83$	0.531960	+	1.63720i	0.0583902	+	0.179707i	0.975998	−	0.217781i	$-0.0698820\pi$
$83$	0.531960	+	1.63720i	0.0583902	+	0.179707i	−0.917607	+	0.397488i	$0.869882\pi$
$84$		0			0
$85$	−6.19182	+	4.49862i	−0.671598	+	0.487944i
$86$	−2.58609	+	7.95916i	−0.278865	+	0.858259i
$87$	−5.33245			−0.571699
$88$	4.12062	+	2.75227i	0.439260	+	0.293393i
$89$	15.3035			1.62217			0.811086	−	0.584928i	$-0.198877\pi$
$89$	15.3035			1.62217			0.811086	+	0.584928i	$0.198877\pi$
$90$	−3.99406	+	12.2925i	−0.421011	+	1.29574i
$91$		0			0
$92$	−4.09921	−	2.97825i	−0.427373	−	0.310504i
$93$	−0.0383089	−	0.117903i	−0.00397244	−	0.0122259i
$94$	7.16556	+	22.0533i	0.739071	+	2.27463i
$95$	4.35721	+	3.16570i	0.447040	+	0.324794i
$96$	−2.92705	+	2.12663i	−0.298741	+	0.217048i
$97$	−3.58961	+	11.0477i	−0.364470	+	1.12172i	0.585843	+	0.810425i	$0.300764\pi$
$97$	−3.58961	+	11.0477i	−0.364470	+	1.12172i	−0.950313	+	0.311297i	$0.899236\pi$
$98$		0			0
$99$	−8.67628	+	0.342417i	−0.871999	+	0.0344142i
$100$	3.14723			0.314723
$101$	−1.05430	+	3.24480i	−0.104907	+	0.322870i	−0.989709	−	0.143098i	$-0.954294\pi$
$101$	−1.05430	+	3.24480i	−0.104907	+	0.322870i	0.884802	+	0.465968i	$0.154294\pi$
$102$	2.44898	−	1.77929i	0.242485	−	0.176176i
$103$	−14.7100	−	10.6875i	−1.44942	−	1.05307i	−0.985966	−	0.166945i	$-0.946610\pi$
$103$	−14.7100	−	10.6875i	−1.44942	−	1.05307i	−0.463455	−	0.886121i	$-0.653390\pi$
$104$	−1.98226	−	6.10077i	−0.194377	−	0.598230i
$105$		0			0
$106$	5.60843	+	4.07476i	0.544739	+	0.395776i
$107$	−2.62725	+	1.90881i	−0.253986	+	0.184532i	−0.707491	−	0.706722i	$-0.750173\pi$
$107$	−2.62725	+	1.90881i	−0.253986	+	0.184532i	0.453506	+	0.891253i	$0.350173\pi$
$108$	1.24403	−	3.82873i	0.119707	−	0.368420i
$109$	12.6912			1.21559			0.607796	−	0.794093i	$-0.292054\pi$
$109$	12.6912			1.21559			0.607796	+	0.794093i	$0.292054\pi$
$110$	5.67000	+	15.3609i	0.540613	+	1.46461i
$111$	−0.639962			−0.0607425
$112$		0			0
$113$	14.9248	−	10.8435i	1.40401	−	1.02007i	0.409845	−	0.912155i	$-0.365583\pi$
$113$	14.9248	−	10.8435i	1.40401	−	1.02007i	0.994160	−	0.107915i	$-0.0344173\pi$
$114$	−1.72336	−	1.25209i	−0.161407	−	0.117269i
$115$	3.75081	+	11.5438i	0.349765	+	1.07646i
$116$	3.09136	+	9.51422i	0.287025	+	0.883373i
$117$	9.09373	+	6.60698i	0.840715	+	0.610816i
$118$	−12.3053	+	8.94031i	−1.13279	+	0.823022i
$119$		0			0
$120$	2.56468			0.234122
$121$	−8.36196	+	7.14686i	−0.760178	+	0.649715i
$122$	1.75724			0.159093
$123$	1.83461	−	5.64636i	0.165422	−	0.509115i
$124$	−0.188154	+	0.136702i	−0.0168968	+	0.0122762i
$125$	5.13577	+	3.73136i	0.459358	+	0.333743i
$126$		0			0
$127$	6.02870	+	18.5544i	0.534961	+	1.64644i	0.743733	+	0.668476i	$0.233053\pi$
$127$	6.02870	+	18.5544i	0.534961	+	1.64644i	−0.208772	+	0.977964i	$0.566947\pi$
$128$	−8.81579	−	6.40505i	−0.779213	−	0.566132i
$129$	−2.35410	+	1.71036i	−0.207267	+	0.150588i
$130$	6.55011	−	20.1592i	0.574483	−	1.76808i
$131$	6.89796			0.602677			0.301339	−	0.953517i	$-0.402567\pi$
$131$	6.89796			0.602677			0.301339	+	0.953517i	$0.402567\pi$
$132$	−0.822982	−	2.22959i	−0.0716314	−	0.194061i
$133$		0			0
$134$	−2.97566	+	9.15813i	−0.257058	+	0.791142i
$135$	−7.80200	+	5.66849i	−0.671489	+	0.487866i
$136$	3.33070	+	2.41990i	0.285606	+	0.207505i
$137$	−0.806750	−	2.48292i	−0.0689253	−	0.212130i	0.910661	−	0.413154i	$-0.135573\pi$
$137$	−0.806750	−	2.48292i	−0.0689253	−	0.212130i	−0.979586	+	0.201024i	$0.935573\pi$
$138$	−1.48351	−	4.56578i	−0.126285	−	0.388665i
$139$	−0.810097	−	0.588570i	−0.0687116	−	0.0499219i	0.552899	−	0.833248i	$-0.313521\pi$
$139$	−0.810097	−	0.588570i	−0.0687116	−	0.0499219i	−0.621611	+	0.783326i	$0.713521\pi$
$140$		0			0
$141$	−2.49148	+	7.66797i	−0.209820	+	0.645760i
$142$	−3.58527			−0.300869
$143$	14.2288	−	0.561550i	1.18987	−	0.0469592i
$144$	13.0236			1.08530
$145$	7.40540	−	22.7915i	0.614985	−	1.89273i
$146$	−14.3386	+	10.4176i	−1.18667	+	0.862165i
$147$		0			0
$148$	0.371002	+	1.14183i	0.0304962	+	0.0938576i
$149$	−4.60273	−	14.1658i	−0.377071	−	1.16050i	−0.942071	−	0.335413i	$-0.891124\pi$
$149$	−4.60273	−	14.1658i	−0.377071	−	1.16050i	0.565000	−	0.825091i	$-0.308876\pi$
$150$	2.41242	+	1.75272i	0.196973	+	0.143109i
$151$	−12.7862	+	9.28970i	−1.04052	+	0.755985i	−0.970388	−	0.241552i	$-0.922344\pi$
$151$	−12.7862	+	9.28970i	−1.04052	+	0.755985i	−0.0701368	+	0.997537i	$0.522344\pi$
$152$	0.895263	−	2.75534i	0.0726154	−	0.223487i
$153$	−7.21414			−0.583229
$154$		0			0
$155$	0.557129			0.0447497
$156$	−0.950727	+	2.92604i	−0.0761191	+	0.234270i
$157$	3.71438	−	2.69866i	0.296440	−	0.215376i	−0.429616	−	0.903011i	$-0.641351\pi$
$157$	3.71438	−	2.69866i	0.296440	−	0.215376i	0.726056	+	0.687635i	$0.241351\pi$
$158$	−9.05011	−	6.57529i	−0.719988	−	0.523102i
$159$	0.744856	+	2.29243i	0.0590710	+	0.181802i
$160$	−5.02452	−	15.4639i	−0.397223	−	1.22253i
$161$		0			0
$162$	−8.20848	+	5.96381i	−0.644919	+	0.468561i
$163$	2.48377	−	7.64425i	0.194544	−	0.598744i	−0.805438	−	0.592680i	$-0.798070\pi$
$163$	2.48377	−	7.64425i	0.194544	−	0.598744i	0.999982	−	0.00606379i	$-0.00193018\pi$
$164$	−11.1379			−0.869721
$165$	−1.54442	+	5.47977i	−0.120233	+	0.426600i
$166$	3.05987			0.237492
$167$	4.14296	−	12.7507i	0.320592	−	0.986681i	−0.652799	−	0.757531i	$-0.726405\pi$
$167$	4.14296	−	12.7507i	0.320592	−	0.986681i	0.973391	−	0.229150i	$-0.0735946\pi$
$168$		0			0
$169$	−4.39615	−	3.19399i	−0.338165	−	0.245691i
$170$	4.20387	+	12.9382i	0.322422	+	0.992313i
$171$	1.56876	+	4.82815i	0.119966	+	0.369218i
$172$	4.41637	+	3.20868i	0.336745	+	0.244659i
$173$	−16.6512	+	12.0978i	−1.26597	+	0.919782i	−0.999035	−	0.0439325i	$-0.986011\pi$
$173$	−16.6512	+	12.0978i	−1.26597	+	0.919782i	−0.266936	+	0.963714i	$0.586011\pi$
$174$	−2.92897	+	9.01445i	−0.222045	+	0.683383i
$175$		0			0
$176$	12.9550	−	10.2166i	0.976520	−	0.770104i
$177$	−5.28860			−0.397515
$178$	8.40581	−	25.8704i	0.630042	−	1.93907i
$179$	3.00566	−	2.18374i	0.224653	−	0.163220i	−0.469765	−	0.882791i	$-0.655662\pi$
$179$	3.00566	−	2.18374i	0.224653	−	0.163220i	0.694419	+	0.719571i	$0.255662\pi$
$180$	6.82082	+	4.95562i	0.508394	+	0.369370i
$181$	−1.47458	−	4.53828i	−0.109604	−	0.337327i	0.881179	−	0.472783i	$-0.156750\pi$
$181$	−1.47458	−	4.53828i	−0.109604	−	0.337327i	−0.990783	+	0.135455i	$0.956750\pi$
$182$		0			0
$183$	0.494304	+	0.359133i	0.0365400	+	0.0265479i
$184$	5.28223	−	3.83777i	0.389411	−	0.282924i
$185$	0.888742	−	2.73527i	0.0653416	−	0.201101i
$186$	−0.220355			−0.0161572
$187$	−7.17613	+	5.65925i	−0.524771	+	0.413845i
$188$	15.1257			1.10315
$189$		0			0
$190$	7.74487	−	5.62698i	0.561872	−	0.408224i
$191$	0.670803	+	0.487367i	0.0485376	+	0.0352646i	0.611790	−	0.791021i	$-0.290450\pi$
$191$	0.670803	+	0.487367i	0.0485376	+	0.0352646i	−0.563252	+	0.826285i	$0.690450\pi$
$192$	0.0871690	+	0.268279i	0.00629088	+	0.0193613i
$193$	−2.08216	−	6.40824i	−0.149878	−	0.461276i	0.847728	−	0.530430i	$-0.177970\pi$
$193$	−2.08216	−	6.40824i	−0.149878	−	0.461276i	−0.997606	+	0.0691550i	$0.977970\pi$
$194$	16.7043	+	12.1364i	1.19930	+	0.871341i
$195$	5.96253	−	4.33203i	0.426986	−	0.310223i
$196$		0			0
$197$	−10.9216			−0.778129			−0.389065	−	0.921210i	$-0.627202\pi$
$197$	−10.9216			−0.778129			−0.389065	+	0.921210i	$0.627202\pi$
$198$	−4.18680	+	14.8552i	−0.297543	+	1.05572i
$199$	−20.9746			−1.48685			−0.743424	−	0.668820i	$-0.766800\pi$
$199$	−20.9746			−1.48685			−0.743424	+	0.668820i	$0.766800\pi$
$200$	−1.25322	+	3.85702i	−0.0886163	+	0.272733i
$201$	−2.70872	+	1.96800i	−0.191059	+	0.138812i
$202$	4.90620	+	3.56457i	0.345199	+	0.250802i
$203$		0			0
$204$	−0.610177	−	1.87793i	−0.0427210	−	0.131482i
$205$	21.5854	+	15.6827i	1.50759	+	1.09533i
$206$	−26.1468	+	18.9968i	−1.82174	+	1.32357i
$207$	−3.53548	+	10.8811i	−0.245733	+	0.756288i
$208$	−21.3582			−1.48093
$209$	5.34802	+	3.57207i	0.369930	+	0.247086i
$210$		0			0
$211$	−1.86140	+	5.72879i	−0.128144	+	0.394386i	−0.994461	−	0.105109i	$-0.966481\pi$
$211$	−1.86140	+	5.72879i	−0.128144	+	0.394386i	0.866317	+	0.499495i	$0.166481\pi$
$212$	3.65837	−	2.65796i	0.251258	−	0.182550i
$213$	−1.00852	−	0.732736i	−0.0691029	−	0.0502062i
$214$	1.78374	+	5.48979i	0.121934	+	0.375274i
$215$	−4.04100	−	12.4369i	−0.275594	−	0.848192i
$216$	4.19685	+	3.04919i	0.285560	+	0.207471i
$217$		0			0
$218$	6.97091	−	21.4542i	0.472129	−	1.45306i
$219$	−6.16247			−0.416421
$220$	10.6724	−	0.421195i	0.719533	−	0.0283970i
$221$	11.8309			0.795833
$222$	−0.351514	+	1.08185i	−0.0235921	+	0.0726089i
$223$	−3.74176	+	2.71855i	−0.250567	+	0.182048i	−0.705978	−	0.708234i	$-0.749492\pi$
$223$	−3.74176	+	2.71855i	−0.250567	+	0.182048i	0.455411	+	0.890281i	$0.349492\pi$
$224$		0			0
$225$	−2.19601	−	6.75863i	−0.146401	−	0.450575i
$226$	−10.1330	−	31.1862i	−0.674038	−	2.07448i
$227$	13.9963	+	10.1689i	0.928965	+	0.674932i	0.945739	−	0.324927i	$-0.105340\pi$
$227$	13.9963	+	10.1689i	0.928965	+	0.674932i	−0.0167745	+	0.999859i	$0.505340\pi$
$228$	−1.12414	+	0.816737i	−0.0744481	+	0.0540897i
$229$	1.36775	−	4.20949i	0.0903832	−	0.278171i	−0.895640	−	0.444780i	$-0.853282\pi$
$229$	1.36775	−	4.20949i	0.0903832	−	0.278171i	0.986023	+	0.166609i	$0.0532818\pi$
$230$	21.5749			1.42260
$231$		0			0
$232$	−12.8909			−0.846330
$233$	−3.25489	+	10.0175i	−0.213235	+	0.656269i	0.786039	+	0.618176i	$0.212128\pi$
$233$	−3.25489	+	10.0175i	−0.213235	+	0.656269i	−0.999274	+	0.0380929i	$0.987872\pi$
$234$	16.1640	−	11.7438i	1.05667	−	0.767716i
$235$	−29.3137	−	21.2977i	−1.91222	−	1.38931i
$236$	3.06593	+	9.43597i	0.199575	+	0.614229i
$237$	−1.20195	−	3.69921i	−0.0780748	−	0.240290i
$238$		0			0
$239$	7.89314	−	5.73470i	0.510565	−	0.370947i	−0.302473	−	0.953158i	$-0.597812\pi$
$239$	7.89314	−	5.73470i	0.510565	−	0.370947i	0.813038	+	0.582211i	$0.197812\pi$
$240$	2.63878	−	8.12131i	0.170332	−	0.524229i
$241$	−12.5501			−0.808422			−0.404211	−	0.914666i	$-0.632454\pi$
$241$	−12.5501			−0.808422			−0.404211	+	0.914666i	$0.632454\pi$
$242$	7.48869	+	18.0614i	0.481391	+	1.16103i
$243$	−13.9443			−0.894525
$244$	0.354208	−	1.09014i	0.0226759	−	0.0697892i
$245$		0			0
$246$	−8.53740	−	6.20278i	−0.544325	−	0.395475i
$247$	−2.57271	−	7.91798i	−0.163698	−	0.503809i
$248$	−0.0926096	−	0.285023i	−0.00588072	−	0.0180990i
$249$	0.860729	+	0.625357i	0.0545465	+	0.0396304i
$250$	9.12876	−	6.63243i	0.577353	−	0.419472i
$251$	3.39646	−	10.4532i	0.214383	−	0.659803i	−0.784814	−	0.619732i	$-0.787241\pi$
$251$	3.39646	−	10.4532i	0.214383	−	0.659803i	0.999197	−	0.0400713i	$-0.0127585\pi$
$252$		0			0
$253$	5.01899	+	13.5972i	0.315541	+	0.854850i
$254$	34.6775			2.17586
$255$	−1.46169	+	4.49862i	−0.0915346	+	0.281715i
$256$	−16.4084	+	11.9214i	−1.02553	+	0.745089i
$257$	4.31432	+	3.13454i	0.269120	+	0.195527i	0.714158	−	0.699985i	$-0.246810\pi$
$257$	4.31432	+	3.13454i	0.269120	+	0.195527i	−0.445038	+	0.895512i	$0.646810\pi$
$258$	1.59829	+	4.91903i	0.0995052	+	0.306246i
$259$		0			0
$260$	−11.1859	−	8.12702i	−0.693719	−	0.504017i
$261$	18.2746	−	13.2773i	1.13117	−	0.821842i
$262$	3.78886	−	11.6609i	0.234077	−	0.720414i
$263$	−8.18034			−0.504421			−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034			−0.504421			−0.252211	+	0.967672i	$0.581158\pi$
$264$	3.06013	−	0.120771i	0.188338	−	0.00743291i
$265$	−10.8325			−0.665436
$266$		0			0
$267$	7.65177	−	5.55933i	0.468280	−	0.340226i
$268$	5.08165	+	3.69203i	0.310411	+	0.225527i
$269$	−3.96899	−	12.2153i	−0.241993	−	0.744779i	−0.996116	−	0.0880459i	$-0.971938\pi$
$269$	−3.96899	−	12.2153i	−0.241993	−	0.744779i	0.754123	−	0.656733i	$-0.228062\pi$
$270$	5.29708	+	16.3027i	0.322370	+	0.992153i
$271$	−17.8366	−	12.9590i	−1.08349	−	0.787205i	−0.105206	−	0.994450i	$-0.533550\pi$
$271$	−17.8366	−	12.9590i	−1.08349	−	0.787205i	−0.978289	+	0.207246i	$0.933550\pi$
$272$	11.0898	−	8.05720i	0.672417	−	0.488539i
$273$		0			0
$274$	−4.64047			−0.280341
$275$	−7.48636	−	5.00032i	−0.451444	−	0.301531i
$276$	−3.13152			−0.188495
$277$	7.44019	−	22.8986i	0.447038	−	1.37584i	−0.433196	−	0.901300i	$-0.642614\pi$
$277$	7.44019	−	22.8986i	0.447038	−	1.37584i	0.880234	−	0.474541i	$-0.157386\pi$
$278$	−1.43994	+	1.04617i	−0.0863616	+	0.0627454i
$279$	0.424852	+	0.308673i	0.0254352	+	0.0184798i
$280$		0			0
$281$	4.77179	+	14.6861i	0.284661	+	0.876097i	0.986500	+	0.163761i	$0.0523626\pi$
$281$	4.77179	+	14.6861i	0.284661	+	0.876097i	−0.701839	+	0.712336i	$0.747637\pi$
$282$	11.5941	+	8.42362i	0.690420	+	0.501619i
$283$	−2.71613	+	1.97338i	−0.161457	+	0.117305i	−0.665580	−	0.746326i	$-0.731816\pi$
$283$	−2.71613	+	1.97338i	−0.161457	+	0.117305i	0.504123	+	0.863632i	$0.331816\pi$
$284$	−0.722688	+	2.22421i	−0.0428836	+	0.131982i
$285$	3.32861			0.197170
$286$	6.86618	−	24.3620i	0.406006	−	1.44056i
$287$		0			0
$288$	4.73607	−	14.5761i	0.279075	−	0.858906i
$289$	7.61035	−	5.52924i	0.447668	−	0.325250i
$290$	−34.4611	−	25.0375i	−2.02363	−	1.47025i
$291$	2.21850	+	6.82784i	0.130051	+	0.400255i
$292$	3.57254	+	10.9951i	0.209067	+	0.643442i
$293$	5.53129	+	4.01872i	0.323142	+	0.234776i	0.737515	−	0.675331i	$-0.235999\pi$
$293$	5.53129	+	4.01872i	0.323142	+	0.234776i	−0.414373	+	0.910107i	$0.635999\pi$
$294$		0			0
$295$	7.34450	−	22.6040i	0.427613	−	1.31606i
$296$	−1.54707			−0.0899218
$297$	−9.04228	+	7.13093i	−0.524686	+	0.413779i
$298$	−26.4752			−1.53367
$299$	5.79805	−	17.8446i	0.335310	−	1.03198i
$300$	1.57362	−	1.14330i	0.0908528	−	0.0660084i
$301$		0			0
$302$	8.68103	+	26.7175i	0.499537	+	1.53742i
$303$	0.651594	+	2.00540i	0.0374331	+	0.115207i
$304$	−7.80392	−	5.66988i	−0.447586	−	0.325190i
$305$	−2.22144	+	1.61397i	−0.127199	+	0.0924155i
$306$	−3.96253	+	12.1954i	−0.226523	+	0.697166i
$307$	11.7970			0.673293			0.336646	−	0.941631i	$-0.390707\pi$
$307$	11.7970			0.673293			0.336646	+	0.941631i	$0.390707\pi$
$308$		0			0
$309$	−11.2375			−0.639276
$310$	0.306016	−	0.941821i	0.0173805	−	0.0534918i
$311$	20.4794	−	14.8791i	1.16128	−	0.843718i	0.171339	−	0.985212i	$-0.445191\pi$
$311$	20.4794	−	14.8791i	1.16128	−	0.843718i	0.989939	+	0.141494i	$0.0451906\pi$
$312$	−3.20736	−	2.33029i	−0.181581	−	0.131926i
$313$	6.07352	+	18.6924i	0.343296	+	1.05656i	0.962490	+	0.271318i	$0.0874595\pi$
$313$	6.07352	+	18.6924i	0.343296	+	1.05656i	−0.619194	+	0.785238i	$0.712540\pi$
$314$	−2.52184	−	7.76141i	−0.142315	−	0.438002i
$315$		0			0
$316$	−5.90337	+	4.28905i	−0.332091	+	0.241278i
$317$	1.11572	−	3.43385i	0.0626653	−	0.192864i	−0.914822	−	0.403856i	$-0.867670\pi$
$317$	1.11572	−	3.43385i	0.0626653	−	0.192864i	0.977488	+	0.210992i	$0.0676695\pi$
$318$	4.28446			0.240261
$319$	7.76275	−	27.5431i	0.434630	−	1.54212i
$320$	−1.26771			−0.0708670
$321$	−0.620210	+	1.90881i	−0.0346167	+	0.106539i
$322$		0			0
$323$	4.32281	+	3.14071i	0.240528	+	0.174754i
$324$	2.04519	+	6.29445i	0.113622	+	0.349692i
$325$	3.60137	+	11.0839i	0.199768	+	0.614824i
$326$	−11.5582	−	8.39756i	−0.640152	−	0.465098i
$327$	6.34558	−	4.61033i	0.350911	−	0.254952i
$328$	4.43508	−	13.6498i	0.244886	−	0.753683i
$329$		0			0
$330$	8.41518	+	5.62071i	0.463240	+	0.309410i
$331$	−26.5335			−1.45841			−0.729205	−	0.684295i	$-0.760110\pi$
$331$	−26.5335			−1.45841			−0.729205	+	0.684295i	$0.760110\pi$
$332$	0.616781	−	1.89826i	0.0338503	−	0.104180i
$333$	2.19318	−	1.59344i	0.120186	−	0.0873200i
$334$	−19.2793	−	14.0073i	−1.05492	−	0.766443i
$335$	−4.64974	−	14.3104i	−0.254042	−	0.781862i
$336$		0			0
$337$	0.554969	+	0.403208i	0.0302311	+	0.0219642i	0.602798	−	0.797894i	$-0.294052\pi$
$337$	0.554969	+	0.403208i	0.0302311	+	0.0219642i	−0.572567	+	0.819858i	$0.694052\pi$
$338$	−7.81408	+	5.67726i	−0.425030	+	0.308802i
$339$	3.52326	−	10.8435i	0.191357	−	0.588938i
$340$	8.87387			0.481253
$341$	0.664757	−	0.0262352i	0.0359986	−	0.00142071i
$342$	9.02361			0.487941
$343$		0			0
$344$	−5.69091	+	4.13469i	−0.306834	+	0.222928i
$345$	6.06893	+	4.40934i	0.326740	+	0.237391i
$346$	11.3052	+	34.7937i	0.607770	+	1.87052i
$347$	6.64555	+	20.4529i	0.356752	+	1.09797i	0.954987	+	0.296649i	$0.0958690\pi$
$347$	6.64555	+	20.4529i	0.356752	+	1.09797i	−0.598235	+	0.801321i	$0.704131\pi$
$348$	5.00192	+	3.63411i	0.268131	+	0.194809i
$349$	15.7296	−	11.4282i	0.841987	−	0.611739i	−0.0809381	−	0.996719i	$-0.525792\pi$
$349$	15.7296	−	11.4282i	0.841987	−	0.611739i	0.922925	+	0.384980i	$0.125792\pi$
$350$		0			0
$351$	14.9075			0.795705
$352$	−6.72336	−	18.2146i	−0.358356	−	0.970842i
$353$	20.9307			1.11403			0.557015	−	0.830502i	$-0.311947\pi$
$353$	20.9307			1.11403			0.557015	+	0.830502i	$0.311947\pi$
$354$	−2.90488	+	8.94031i	−0.154393	+	0.475172i
$355$	4.53237	−	3.29296i	0.240553	−	0.174772i
$356$	−14.3549	−	10.4295i	−0.760810	−	0.552761i
$357$		0			0
$358$	−2.04066	−	6.28050i	−0.107852	−	0.331935i
$359$	−7.90512	−	5.74341i	−0.417216	−	0.303125i	0.359300	−	0.933222i	$-0.383015\pi$
$359$	−7.90512	−	5.74341i	−0.417216	−	0.303125i	−0.776517	+	0.630096i	$0.783015\pi$
$360$	−8.78929	+	6.38579i	−0.463236	+	0.336561i
$361$	−4.70939	+	14.4940i	−0.247863	+	0.762843i
$362$	−8.48185			−0.445796
$363$	−1.58473	+	6.61109i	−0.0831767	+	0.346992i
$364$		0			0
$365$	8.55808	−	26.3390i	0.447950	−	1.37865i
$366$	0.878618	−	0.638353i	0.0459261	−	0.0333673i
$367$	8.00901	+	5.81889i	0.418067	+	0.303744i	0.776860	−	0.629674i	$-0.216811\pi$
$367$	8.00901	+	5.81889i	0.418067	+	0.303744i	−0.358793	+	0.933417i	$0.616811\pi$
$368$	−6.71783	−	20.6754i	−0.350191	−	1.07778i
$369$	7.77155	+	23.9184i	0.404571	+	1.24514i
$370$	−4.13577	−	3.00482i	−0.215009	−	0.156213i
$371$		0			0
$372$	−0.0444172	+	0.136702i	−0.00230293	+	0.00708768i
$373$	−4.27475			−0.221338			−0.110669	−	0.993857i	$-0.535299\pi$
$373$	−4.27475			−0.221338			−0.110669	+	0.993857i	$0.535299\pi$
$374$	5.62524	+	15.2396i	0.290874	+	0.788023i
$375$	3.92338			0.202603
$376$	−6.02301	+	18.5369i	−0.310613	+	0.955968i
$377$	−29.9696	+	21.7742i	−1.54351	+	1.12143i
$378$		0			0
$379$	1.33679	+	4.11421i	0.0686662	+	0.211333i	0.979501	−	0.201437i	$-0.0645612\pi$
$379$	1.33679	+	4.11421i	0.0686662	+	0.211333i	−0.910835	+	0.412770i	$0.864561\pi$
$380$	−1.92968	−	5.93894i	−0.0989905	−	0.304661i
$381$	9.75465	+	7.08717i	0.499746	+	0.363087i
$382$	1.19234	−	0.866287i	0.0610055	−	0.0443231i
$383$	0.408551	−	1.25739i	0.0208760	−	0.0642497i	−0.940076	−	0.340966i	$-0.889246\pi$
$383$	0.408551	−	1.25739i	0.0208760	−	0.0642497i	0.960952	+	0.276716i	$0.0892461\pi$
$384$	−6.73467			−0.343677
$385$		0			0
$386$	−11.9767			−0.609600
$387$	3.80902	−	11.7229i	0.193623	−	0.595911i
$388$	10.8962	−	7.91654i	0.553170	−	0.401902i
$389$	31.1546	+	22.6351i	1.57960	+	1.14765i	0.917152	+	0.398537i	$0.130482\pi$
$389$	31.1546	+	22.6351i	1.57960	+	1.14765i	0.662447	+	0.749109i	$0.269518\pi$
$390$	−4.04819	−	12.4591i	−0.204988	−	0.630889i
$391$	3.72119	+	11.4527i	0.188189	+	0.579186i
$392$		0			0
$393$	3.44898	−	2.50583i	0.173978	−	0.126402i
$394$	−5.99892	+	18.4628i	−0.302221	+	0.930141i
$395$	17.4800			0.879516
$396$	8.37184	+	5.59176i	0.420701	+	0.280997i
$397$	0.410109			0.0205828			0.0102914	−	0.999947i	$-0.496724\pi$
$397$	0.410109			0.0205828			0.0102914	+	0.999947i	$0.496724\pi$
$398$	−11.5208	+	35.4573i	−0.577484	+	1.77731i
$399$		0			0
$400$	10.9242	+	7.93691i	0.546211	+	0.396846i
$401$	−0.484180	−	1.49015i	−0.0241788	−	0.0744147i	0.938239	−	0.345988i	$-0.112456\pi$
$401$	−0.484180	−	1.49015i	−0.0241788	−	0.0744147i	−0.962418	+	0.271573i	$0.912456\pi$
$402$	1.83906	+	5.66003i	0.0917238	+	0.282297i
$403$	−0.696741	−	0.506212i	−0.0347071	−	0.0252162i
$404$	3.20031	−	2.32516i	0.159221	−	0.115681i
$405$	4.89929	−	15.0785i	0.243448	−	0.749255i
$406$		0			0
$407$	0.931628	−	3.30552i	0.0461791	−	0.163849i
$408$	2.54443			0.125968
$409$	2.09468	−	6.44676i	0.103575	−	0.318772i	−0.885818	−	0.464032i	$-0.846402\pi$
$409$	2.09468	−	6.44676i	0.103575	−	0.318772i	0.989393	+	0.145261i	$0.0464021\pi$
$410$	38.3676	−	27.8757i	1.89484	−	1.37668i
$411$	−1.30535	−	0.948391i	−0.0643881	−	0.0467807i
$412$	6.51463	+	20.0500i	0.320953	+	0.987792i
$413$		0			0
$414$	16.4524	+	11.9534i	0.808592	+	0.587476i
$415$	−3.86817	+	2.81039i	−0.189881	+	0.137957i
$416$	−7.76697	+	23.9043i	−0.380807	+	1.17200i
$417$	−0.618859			−0.0303057
$418$	8.97607	−	7.07872i	0.439034	−	0.346231i
$419$	−28.7218			−1.40315			−0.701577	−	0.712594i	$-0.747520\pi$
$419$	−28.7218			−1.40315			−0.701577	+	0.712594i	$0.747520\pi$
$420$		0			0
$421$	−9.89070	+	7.18601i	−0.482043	+	0.350225i	−0.802116	−	0.597168i	$-0.796293\pi$
$421$	−9.89070	+	7.18601i	−0.482043	+	0.350225i	0.320073	+	0.947393i	$0.396293\pi$
$422$	8.66204	+	6.29334i	0.421661	+	0.306355i
$423$	−10.5541	−	32.4821i	−0.513156	−	1.57933i
$424$	1.80065	+	5.54183i	0.0874473	+	0.269135i
$425$	−6.05123	−	4.39648i	−0.293528	−	0.213260i
$426$	−1.79264	+	1.30243i	−0.0868535	+	0.0631028i
$427$		0			0
$428$	3.76527			0.182001
$429$	6.91039	−	5.44968i	0.333637	−	0.263113i
$430$	−23.2441			−1.12093
$431$	1.14067	−	3.51063i	0.0549442	−	0.169101i	−0.919819	−	0.392344i	$-0.871664\pi$
$431$	1.14067	−	3.51063i	0.0549442	−	0.169101i	0.974763	+	0.223243i	$0.0716643\pi$
$432$	13.9737	−	10.1525i	0.672308	−	0.488461i
$433$	23.5221	+	17.0898i	1.13040	+	0.821283i	0.985753	−	0.168201i	$-0.0537957\pi$
$433$	23.5221	+	17.0898i	1.13040	+	0.821283i	0.144646	+	0.989483i	$0.453796\pi$
$434$		0			0
$435$	−4.57679	−	14.0859i	−0.219440	−	0.675368i
$436$	−11.9045	−	8.64912i	−0.570122	−	0.414218i
$437$	6.85563	−	4.98091i	0.327949	−	0.238269i
$438$	−3.38488	+	10.4176i	−0.161736	+	0.497771i
$439$	14.2017			0.677811			0.338905	−	0.940820i	$-0.389943\pi$
$439$	14.2017			0.677811			0.338905	+	0.940820i	$0.389943\pi$
$440$	−3.73355	+	13.2470i	−0.177990	+	0.631528i
$441$		0			0
$442$	6.49840	−	20.0000i	0.309097	−	0.951304i
$443$	−22.0341	+	16.0087i	−1.04687	+	0.760595i	−0.971615	−	0.236569i	$-0.923977\pi$
$443$	−22.0341	+	16.0087i	−1.04687	+	0.760595i	−0.0752548	+	0.997164i	$0.523977\pi$
$444$	0.600294	+	0.436139i	0.0284887	+	0.0206982i
$445$	13.1349	+	40.4250i	0.622652	+	1.91633i
$446$	2.54043	+	7.81863i	0.120293	+	0.370223i
$447$	−7.44738	−	5.41084i	−0.352249	−	0.255924i
$448$		0			0
$449$	−12.9527	+	39.8644i	−0.611277	+	1.88132i	−0.165389	+	0.986228i	$0.552888\pi$
$449$	−12.9527	+	39.8644i	−0.611277	+	1.88132i	−0.445888	+	0.895089i	$0.647112\pi$
$450$	−12.6316			−0.595459
$451$	26.4938	+	17.6958i	1.24754	+	0.833265i
$452$	−21.3896			−1.00608
$453$	−3.01841	+	9.28970i	−0.141817	+	0.436468i
$454$	24.8781	−	18.0750i	1.16759	−	0.848303i
$455$		0			0
$456$	−0.553303	−	1.70289i	−0.0259108	−	0.0797452i
$457$	6.02512	+	18.5434i	0.281843	+	0.867424i	0.987327	+	0.158698i	$0.0507296\pi$
$457$	6.02512	+	18.5434i	0.281843	+	0.867424i	−0.705484	+	0.708726i	$0.749270\pi$
$458$	−6.36483	−	4.62432i	−0.297409	−	0.216080i
$459$	−7.74040	+	5.62373i	−0.361291	+	0.262493i
$460$	4.34887	−	13.3845i	0.202767	−	0.624054i
$461$	−12.2251			−0.569380			−0.284690	−	0.958620i	$-0.591891\pi$
$461$	−12.2251			−0.569380			−0.284690	+	0.958620i	$0.591891\pi$
$462$		0			0
$463$	13.8550			0.643894			0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550			0.643894			0.321947	+	0.946758i	$0.395663\pi$
$464$	−13.2633	+	40.8204i	−0.615735	+	1.89504i
$465$	0.278565	−	0.202389i	0.0129181	−	0.00938557i
$466$	15.1467	+	11.0047i	0.701656	+	0.509783i
$467$	5.07428	+	15.6170i	0.234810	+	0.722671i	0.997147	+	0.0754899i	$0.0240521\pi$
$467$	5.07428	+	15.6170i	0.234810	+	0.722671i	−0.762337	+	0.647181i	$0.775948\pi$
$468$	−4.02734	−	12.3949i	−0.186164	−	0.572954i
$469$		0			0
$470$	−52.1047	+	37.8563i	−2.40341	+	1.74618i
$471$	0.876846	−	2.69866i	0.0404029	−	0.124347i
$472$	−12.7849			−0.588473
$473$	−5.40731	−	14.6492i	−0.248628	−	0.673572i
$474$	−6.91367			−0.317555
$475$	−1.62652	+	5.00590i	−0.0746297	+	0.229687i
$476$		0			0
$477$	−8.26058	−	6.00167i	−0.378226	−	0.274797i
$478$	−5.35896	−	16.4932i	−0.245113	−	0.754380i
$479$	7.66096	+	23.5780i	0.350038	+	1.07731i	0.958831	+	0.283977i	$0.0916540\pi$
$479$	7.66096	+	23.5780i	0.350038	+	1.07731i	−0.608793	+	0.793329i	$0.708346\pi$
$480$	−8.12984	−	5.90667i	−0.371075	−	0.269602i
$481$	−3.59674	+	2.61318i	−0.163997	+	0.119151i
$482$	−6.89342	+	21.2158i	−0.313987	+	0.966352i
$483$		0			0
$484$	12.7143	−	1.00512i	0.577922	−	0.0456875i
$485$	−32.2639			−1.46503
$486$	−7.65921	+	23.5726i	−0.347429	+	1.06928i
$487$	11.5966	−	8.42542i	0.525492	−	0.381792i	−0.293177	−	0.956058i	$-0.594712\pi$
$487$	11.5966	−	8.42542i	0.525492	−	0.381792i	0.818669	+	0.574266i	$0.194712\pi$
$488$	1.19495	+	0.868185i	0.0540930	+	0.0393009i
$489$	−1.53505	−	4.72441i	−0.0694175	−	0.213645i
$490$		0			0
$491$	17.8140	+	12.9426i	0.803935	+	0.584093i	0.912066	−	0.410044i	$-0.134486\pi$
$491$	17.8140	+	12.9426i	0.803935	+	0.584093i	−0.108131	+	0.994137i	$0.534486\pi$
$492$	−5.56893	+	4.04607i	−0.251067	+	0.182411i
$493$	7.34694	−	22.6115i	0.330889	−	1.01837i
$494$	−14.7984			−0.665810
$495$	−8.35127	−	22.6249i	−0.375362	−	1.01691i
$496$	−0.997839			−0.0448043
$497$		0			0
$498$	1.52993	−	1.11156i	0.0685579	−	0.0498103i
$499$	20.4776	+	14.8779i	0.916704	+	0.666024i	0.942701	−	0.333638i	$-0.108276\pi$
$499$	20.4776	+	14.8779i	0.916704	+	0.666024i	−0.0259975	+	0.999662i	$0.508276\pi$
$500$	−2.27448	−	7.00014i	−0.101718	−	0.313056i
$501$	−2.56049	−	7.88038i	−0.114394	−	0.352070i
$502$	−15.8055	−	11.4834i	−0.705434	−	0.512528i
$503$	−21.0518	+	15.2950i	−0.938653	+	0.681971i	−0.948096	−	0.317984i	$-0.896994\pi$
$503$	−21.0518	+	15.2950i	−0.938653	+	0.681971i	0.00944301	+	0.999955i	$0.496994\pi$
$504$		0			0
$505$	−9.47619			−0.421685
$506$	25.7427	−	1.01596i	1.14440	−	0.0451649i
$507$	−3.35836			−0.149150
$508$	6.98998	−	21.5130i	0.310130	−	0.954483i
$509$	30.8453	−	22.4104i	1.36719	−	0.993325i	0.369244	−	0.929333i	$-0.379617\pi$
$509$	30.8453	−	22.4104i	1.36719	−	0.993325i	0.997950	−	0.0639922i	$-0.0203833\pi$
$510$	6.80200	+	4.94194i	0.301198	+	0.218833i
$511$		0			0
$512$	4.40566	+	13.5592i	0.194704	+	0.599238i
$513$	5.44695	+	3.95744i	0.240489	+	0.174725i
$514$	7.66864	−	5.57159i	0.338249	−	0.245753i
$515$	15.6059	−	48.0301i	0.687679	−	2.11646i
$516$	3.37380			0.148523
$517$	−35.9795	−	24.0316i	−1.58238	−	1.05691i
$518$		0			0
$519$	−3.93083	+	12.0978i	−0.172544	+	0.531036i
$520$	14.4141	−	10.4725i	0.632100	−	0.459248i
$521$	−21.0684	−	15.3071i	−0.923024	−	0.670616i	0.0212509	−	0.999774i	$-0.493235\pi$
$521$	−21.0684	−	15.3071i	−0.923024	−	0.670616i	−0.944275	+	0.329158i	$0.893235\pi$
$522$	−12.4073	−	38.1858i	−0.543054	−	1.67135i
$523$	−5.90933	−	18.1870i	−0.258397	−	0.795263i	−0.993141	−	0.116920i	$-0.962698\pi$
$523$	−5.90933	−	18.1870i	−0.258397	−	0.795263i	0.734745	−	0.678344i	$-0.237302\pi$
$524$	−6.47039	−	4.70101i	−0.282660	−	0.205365i
$525$		0			0
$526$	−4.49324	+	13.8288i	−0.195915	+	0.602963i
$527$	0.552731			0.0240773
$528$	2.76611	−	9.81447i	0.120379	−	0.427120i
$529$	−3.90228			−0.169664
$530$	−5.95001	+	18.3122i	−0.258452	+	0.795433i
$531$	18.1243	−	13.1681i	0.786527	−	0.571445i
$532$		0			0
$533$	−12.7450	−	39.2252i	−0.552049	−	1.69903i
$534$	−5.19508	−	15.9888i	−0.224813	−	0.691903i
$535$	−7.29714	−	5.30169i	−0.315483	−	0.229212i
$536$	−6.54819	+	4.75754i	−0.282839	+	0.205494i
$537$	0.709539	−	2.18374i	0.0306189	−	0.0942352i
$538$	−22.8298			−0.984265
$539$		0			0
$540$	11.1815			0.481176
$541$	3.36397	−	10.3532i	0.144628	−	0.445120i	−0.852335	−	0.522997i	$-0.824814\pi$
$541$	3.36397	−	10.3532i	0.144628	−	0.445120i	0.996963	+	0.0778764i	$0.0248139\pi$
$542$	−31.7042	+	23.0345i	−1.36181	+	0.989415i
$543$	−2.38591	−	1.73347i	−0.102389	−	0.0743902i
$544$	−4.98485	−	15.3418i	−0.213724	−	0.657774i
$545$	10.8927	+	33.5243i	0.466592	+	1.43602i
$546$		0			0
$547$	10.4436	−	7.58775i	0.446538	−	0.324429i	−0.341689	−	0.939813i	$-0.610999\pi$
$547$	10.4436	−	7.58775i	0.446538	−	0.324429i	0.788227	+	0.615384i	$0.210999\pi$
$548$	−0.935386	+	2.87882i	−0.0399577	+	0.122977i
$549$	−2.58821			−0.110462
$550$	−12.5650	+	9.90905i	−0.535775	+	0.422523i
$551$	−16.7307			−0.712751
$552$	1.24697	−	3.83777i	0.0530744	−	0.163346i
$553$		0			0
$554$	−34.6230	−	25.1551i	−1.47099	−	1.06874i
$555$	−0.549273	−	1.69049i	−0.0233153	−	0.0717572i
$556$	0.358768	+	1.10418i	0.0152152	+	0.0468275i
$557$	0.616977	+	0.448260i	0.0261422	+	0.0189934i	0.600780	−	0.799415i	$-0.294857\pi$
$557$	0.616977	+	0.448260i	0.0261422	+	0.0189934i	−0.574637	+	0.818408i	$0.694857\pi$
$558$	0.755167	−	0.548661i	0.0319688	−	0.0232267i
$559$	−6.24664	+	19.2252i	−0.264205	+	0.813139i
$560$		0			0
$561$	−1.53222	+	5.43651i	−0.0646906	+	0.229530i
$562$	27.4476			1.15781
$563$	6.86886	−	21.1402i	0.289488	−	0.890953i	−0.695529	−	0.718498i	$-0.744830\pi$
$563$	6.86886	−	21.1402i	0.289488	−	0.890953i	0.985017	−	0.172455i	$-0.0551700\pi$
$564$	7.56283	−	5.49471i	0.318452	−	0.231369i
$565$	41.4534	+	30.1176i	1.74396	+	1.26706i
$566$	1.84408	+	5.67551i	0.0775127	+	0.238559i
$567$		0			0
$568$	−2.43805	−	1.77135i	−0.102298	−	0.0743242i
$569$	16.5955	−	12.0573i	0.695719	−	0.505469i	−0.182816	−	0.983147i	$-0.558521\pi$
$569$	16.5955	−	12.0573i	0.695719	−	0.505469i	0.878535	+	0.477678i	$0.158521\pi$
$570$	1.82832	−	5.62698i	0.0765797	−	0.235688i
$571$	−19.5654			−0.818785			−0.409393	−	0.912358i	$-0.634259\pi$
$571$	−19.5654			−0.818785			−0.409393	+	0.912358i	$0.634259\pi$
$572$	−13.7295	−	9.17028i	−0.574059	−	0.383429i
$573$	0.512448			0.0214078
$574$		0			0
$575$	−9.59677	+	6.97246i	−0.400213	+	0.290772i
$576$	−0.966719	−	0.702362i	−0.0402800	−	0.0292651i
$577$	6.04795	+	18.6137i	0.251780	+	0.774898i	0.994447	+	0.105237i	$0.0335603\pi$
$577$	6.04795	+	18.6137i	0.251780	+	0.774898i	−0.742668	+	0.669660i	$0.766440\pi$
$578$	−5.16696	−	15.9023i	−0.214917	−	0.661447i
$579$	−3.36901	−	2.44773i	−0.140011	−	0.101724i
$580$	−22.4790	+	16.3319i	−0.933388	+	0.678146i
$581$		0			0
$582$	12.7609			0.528958
$583$	−12.9252	+	0.510102i	−0.535306	+	0.0211263i
$584$	−14.8974			−0.616460
$585$	−9.64758	+	29.6922i	−0.398878	+	1.22762i
$586$	9.83178	−	7.14321i	0.406147	−	0.295083i
$587$	1.27071	+	0.923224i	0.0524477	+	0.0381055i	0.613700	−	0.789539i	$-0.289680\pi$
$587$	1.27071	+	0.923224i	0.0524477	+	0.0381055i	−0.561253	+	0.827645i	$0.689680\pi$
$588$		0			0
$589$	−0.120195	−	0.369922i	−0.00495254	−	0.0152424i
$590$	−34.1777	−	24.8316i	−1.40707	−	1.02230i
$591$	−5.46078	+	3.96749i	−0.224627	+	0.163201i
$592$	−1.59177	+	4.89896i	−0.0654213	+	0.201346i
$593$	30.1230			1.23700			0.618502	−	0.785783i	$-0.287740\pi$
$593$	30.1230			1.23700			0.618502	+	0.785783i	$0.287740\pi$
$594$	7.08807	+	19.2027i	0.290827	+	0.787896i
$595$		0			0
$596$	−5.33664	+	16.4245i	−0.218597	+	0.672773i
$597$	−10.4873	+	7.61946i	−0.429216	+	0.311844i
$598$	−26.9813	−	19.6031i	−1.10335	−	0.801629i
$599$	1.78547	+	5.49513i	0.0729525	+	0.224525i	0.980884	−	0.194594i	$-0.0623390\pi$
$599$	1.78547	+	5.49513i	0.0729525	+	0.224525i	−0.907931	+	0.419119i	$0.862339\pi$
$600$	0.774534	+	2.38377i	0.0316202	+	0.0973171i
$601$	36.8625	+	26.7822i	1.50365	+	1.09247i	0.968898	+	0.247460i	$0.0795958\pi$
$601$	36.8625	+	26.7822i	1.50365	+	1.09247i	0.534754	+	0.845008i	$0.320404\pi$
$602$		0			0
$603$	4.38281	−	13.4889i	0.178482	−	0.549310i
$604$	18.3246			0.745619
$605$	−26.0557	−	15.9544i	−1.05932	−	0.648639i
$606$	3.74801			0.152252
$607$	−10.7294	+	33.0217i	−0.435493	+	1.34031i	0.457088	+	0.889421i	$0.348892\pi$
$607$	−10.7294	+	33.0217i	−0.435493	+	1.34031i	−0.892581	+	0.450887i	$0.851108\pi$
$608$	−9.18369	+	6.67234i	−0.372448	+	0.270599i
$609$		0			0
$610$	1.50822	+	4.64182i	0.0610660	+	0.187942i
$611$	17.3083	+	53.2693i	0.700217	+	2.15505i
$612$	6.76697	+	4.91649i	0.273539	+	0.198737i
$613$	19.5315	−	14.1905i	0.788870	−	0.573148i	−0.118758	−	0.992923i	$-0.537891\pi$
$613$	19.5315	−	14.1905i	0.788870	−	0.573148i	0.907628	+	0.419776i	$0.137891\pi$
$614$	6.47979	−	19.9428i	0.261503	−	0.804824i
$615$	16.4897			0.664931
$616$		0			0
$617$	−13.4967			−0.543358			−0.271679	−	0.962388i	$-0.587579\pi$
$617$	−13.4967			−0.543358			−0.271679	+	0.962388i	$0.587579\pi$
$618$	−6.17243	+	18.9968i	−0.248291	+	0.764162i
$619$	−35.1806	+	25.5602i	−1.41403	+	1.02735i	−0.421307	+	0.906918i	$0.638428\pi$
$619$	−35.1806	+	25.5602i	−1.41403	+	1.02735i	−0.992721	+	0.120433i	$0.961572\pi$
$620$	−0.522596	−	0.379688i	−0.0209879	−	0.0152486i
$621$	4.68889	+	14.4309i	0.188159	+	0.579093i
$622$	−13.9042	−	42.7928i	−0.557509	−	1.71584i
$623$		0			0
$624$	−10.6791	+	7.75883i	−0.427507	+	0.310602i
$625$	−9.64257	+	29.6768i	−0.385703	+	1.18707i
$626$	34.9353			1.39629
$627$	3.97164	−	0.156744i	0.158612	−	0.00625975i
$628$	−5.32330			−0.212423
$629$	0.881726	−	2.71367i	0.0351567	−	0.108201i
$630$		0			0
$631$	−5.19398	−	3.77365i	−0.206769	−	0.150227i	0.479581	−	0.877497i	$-0.340788\pi$
$631$	−5.19398	−	3.77365i	−0.206769	−	0.150227i	−0.686351	+	0.727271i	$0.740788\pi$
$632$	−2.90564	−	8.94265i	−0.115580	−	0.355719i
$633$	1.15041	+	3.54059i	0.0457246	+	0.140726i
$634$	−5.19204	−	3.77224i	−0.206202	−	0.149815i
$635$	−43.8380	+	31.8502i	−1.73966	+	1.26394i
$636$	0.863624	−	2.65796i	0.0342449	−	0.105395i
$637$		0			0
$638$	−42.2974	−	28.2515i	−1.67457	−	1.11849i
$639$	5.28070			0.208901
$640$	9.35272	−	28.7847i	0.369699	−	1.13782i
$641$	5.17447	−	3.75947i	0.204379	−	0.148490i	−0.480888	−	0.876782i	$-0.659686\pi$
$641$	5.17447	−	3.75947i	0.204379	−	0.148490i	0.685267	+	0.728292i	$0.259686\pi$
$642$	2.88615	+	2.09691i	0.113907	+	0.0827586i
$643$	−0.201683	−	0.620716i	−0.00795360	−	0.0244787i	0.947001	−	0.321231i	$-0.104097\pi$
$643$	−0.201683	−	0.620716i	−0.00795360	−	0.0244787i	−0.954955	+	0.296752i	$0.904097\pi$
$644$		0			0
$645$	−6.53848	−	4.75048i	−0.257452	−	0.187050i
$646$	7.68373	−	5.58255i	0.302312	−	0.219643i
$647$	−5.55061	+	17.0830i	−0.218217	+	0.671603i	0.780693	+	0.624915i	$0.214866\pi$
$647$	−5.55061	+	17.0830i	−0.218217	+	0.671603i	−0.998910	+	0.0466874i	$0.985134\pi$
$648$	−8.52842			−0.335028
$649$	7.69890	−	27.3166i	0.302208	−	1.07227i
$650$	20.7153			0.812522
$651$		0			0
$652$	−7.53943	+	5.47771i	−0.295267	+	0.214524i
$653$	13.6870	+	9.94419i	0.535614	+	0.389146i	0.822454	−	0.568832i	$-0.192605\pi$
$653$	13.6870	+	9.94419i	0.535614	+	0.389146i	−0.286840	+	0.957979i	$0.592605\pi$
$654$	−4.30826	−	13.2595i	−0.168466	−	0.518486i
$655$	5.92045	+	18.2213i	0.231331	+	0.711964i
$656$	−38.6602	−	28.0882i	−1.50943	−	1.09666i
$657$	21.1191	−	15.3439i	0.823934	−	0.598623i
$658$		0			0
$659$	23.6249			0.920297			0.460148	−	0.887842i	$-0.347796\pi$
$659$	23.6249			0.920297			0.460148	+	0.887842i	$0.347796\pi$
$660$	5.18319	−	4.08757i	0.201755	−	0.159109i
$661$	20.9819			0.816103			0.408051	−	0.912959i	$-0.366208\pi$
$661$	20.9819			0.816103			0.408051	+	0.912959i	$0.366208\pi$
$662$	−14.5741	+	44.8545i	−0.566439	+	1.74332i
$663$	5.91546	−	4.29783i	0.229737	−	0.166914i
$664$	2.08077	+	1.51177i	0.0807494	+	0.0586679i
$665$		0			0
$666$	−1.48904	−	4.58278i	−0.0576990	−	0.177579i
$667$	−30.5044	−	22.1628i	−1.18114	−	0.858146i
$668$	−12.5759	+	9.13691i	−0.486575	+	0.353518i
$669$	−0.883311	+	2.71855i	−0.0341508	+	0.105105i
$670$	−26.7456			−1.03327
$671$	−2.57458	+	2.03036i	−0.0993904	+	0.0783813i
$672$		0			0
$673$	3.73868	−	11.5065i	0.144116	−	0.443542i	−0.852781	−	0.522269i	$-0.825086\pi$
$673$	3.73868	−	11.5065i	0.144116	−	0.443542i	0.996896	+	0.0787272i	$0.0250856\pi$
$674$	0.986448	−	0.716696i	0.0379965	−	0.0276061i
$675$	−7.62485	−	5.53978i	−0.293481	−	0.213226i
$676$	1.94692	+	5.99202i	0.0748817	+	0.230462i
$677$	2.91399	+	8.96834i	0.111994	+	0.344681i	0.991308	−	0.131560i	$-0.0419987\pi$
$677$	2.91399	+	8.96834i	0.111994	+	0.344681i	−0.879314	+	0.476242i	$0.841999\pi$
$678$	−16.3956	−	11.9121i	−0.629668	−	0.457480i
$679$		0			0
$680$	−3.53356	+	10.8752i	−0.135506	+	0.417044i
$681$	10.6922			0.409726
$682$	0.320783	−	1.13817i	0.0122834	−	0.0435829i
$683$	−15.2986			−0.585385			−0.292692	−	0.956207i	$-0.594551\pi$
$683$	−15.2986			−0.585385			−0.292692	+	0.956207i	$0.594551\pi$
$684$	1.81890	−	5.59800i	0.0695474	−	0.214045i
$685$	5.86632	−	4.26213i	0.224141	−	0.162848i
$686$		0			0
$687$	−0.845314	−	2.60161i	−0.0322507	−	0.0992575i
$688$	7.23758	+	22.2750i	0.275930	+	0.849226i
$689$	13.5470	+	9.84250i	0.516101	+	0.374970i
$690$	10.7874	−	7.83753i	0.410671	−	0.298370i
$691$	−7.05154	+	21.7024i	−0.268253	+	0.825599i	0.722673	+	0.691190i	$0.242913\pi$
$691$	−7.05154	+	21.7024i	−0.268253	+	0.825599i	−0.990926	+	0.134408i	$0.957087\pi$
$692$	23.8639			0.907169
$693$		0			0
$694$	38.2256			1.45102
$695$	0.859436	−	2.64507i	0.0326003	−	0.100333i
$696$	−6.44546	+	4.68290i	−0.244314	+	0.177505i
$697$	21.4149	+	15.5589i	0.811149	+	0.589334i
$698$	−10.6794	−	32.8679i	−0.404223	−	1.24407i
$699$	2.01163	+	6.19117i	0.0760869	+	0.234171i
$700$		0			0
$701$	26.1508	−	18.9997i	0.987702	−	0.717607i	0.0282853	−	0.999600i	$-0.490995\pi$
$701$	26.1508	−	18.9997i	0.987702	−	0.717607i	0.959417	+	0.281992i	$0.0909953\pi$
$702$	8.18830	−	25.2010i	0.309048	−	0.951151i
$703$	−2.00789			−0.0757292
$704$	−1.51261	+	0.0596962i	−0.0570085	+	0.00224989i
$705$	−22.3937			−0.843396
$706$	11.4967	−	35.3831i	0.432683	−	1.33166i
$707$		0			0
$708$	4.96078	+	3.60422i	0.186438	+	0.135455i
$709$	4.49922	+	13.8472i	0.168972	+	0.520041i	0.999307	−	0.0372228i	$-0.0118511\pi$
$709$	4.49922	+	13.8472i	0.168972	+	0.520041i	−0.830335	+	0.557264i	$0.811851\pi$
$710$	−3.07720	−	9.47066i	−0.115485	−	0.355427i
$711$	13.3298	+	9.68466i	0.499906	+	0.363203i
$712$	18.4977	−	13.4394i	0.693232	−	0.503662i
$713$	0.270880	−	0.833684i	0.0101446	−	0.0312217i
$714$		0			0
$715$	13.6958	+	37.1040i	0.512193	+	1.38761i
$716$	−4.30759			−0.160982
$717$	1.86332	−	5.73470i	0.0695869	−	0.214166i
$718$	−14.0512	+	10.2088i	−0.524387	+	0.380990i
$719$	36.2926	+	26.3682i	1.35349	+	0.983366i	0.998829	+	0.0483700i	$0.0154027\pi$
$719$	36.2926	+	26.3682i	1.35349	+	0.983366i	0.354658	+	0.934996i	$0.384597\pi$
$720$	11.1780	+	34.4024i	0.416581	+	1.28210i
$721$		0			0
$722$	21.9152	+	15.9223i	0.815600	+	0.592568i
$723$	−6.27504	+	4.55909i	−0.233371	+	0.169554i
$724$	−1.70970	+	5.26191i	−0.0635404	+	0.195557i
$725$	23.4202			0.869806
$726$	10.3055	+	6.31026i	0.382474	+	0.234196i
$727$	−28.3582			−1.05175			−0.525874	−	0.850562i	$-0.676262\pi$
$727$	−28.3582			−1.05175			−0.525874	+	0.850562i	$0.676262\pi$
$728$		0			0
$729$	6.88197	−	5.00004i	0.254888	−	0.185187i
$730$	−39.8251	−	28.9346i	−1.47399	−	1.07092i
$731$	−4.00910	−	12.3387i	−0.148282	−	0.456365i
$732$	−0.218913	−	0.673744i	−0.00809125	−	0.0249023i
$733$	5.06199	+	3.67775i	0.186969	+	0.135841i	0.677332	−	0.735677i	$-0.263136\pi$
$733$	5.06199	+	3.67775i	0.186969	+	0.135841i	−0.490364	+	0.871518i	$0.663136\pi$
$734$	14.2359	−	10.3430i	0.525456	−	0.381766i
$735$		0			0
$736$	−25.5830			−0.943001
$737$	−6.22186	−	16.8560i	−0.229185	−	0.620898i
$738$	44.7024			1.64552
$739$	2.88993	−	8.89429i	0.106308	−	0.327182i	−0.883727	−	0.468002i	$-0.844974\pi$
$739$	2.88993	−	8.89429i	0.106308	−	0.327182i	0.990035	+	0.140820i	$0.0449740\pi$
$740$	−2.69776	+	1.96004i	−0.0991716	+	0.0720524i
$741$	−4.16273	−	3.02440i	−0.152922	−	0.111104i
$742$		0			0
$743$	7.78926	+	23.9729i	0.285760	+	0.879480i	0.986170	+	0.165739i	$0.0530008\pi$
$743$	7.78926	+	23.9729i	0.285760	+	0.879480i	−0.700409	+	0.713741i	$0.746999\pi$
$744$	−0.149845	−	0.108869i	−0.00549360	−	0.00399134i
$745$	33.4690	−	24.3167i	1.22621	−	0.890893i
$746$	−2.34800	+	7.22641i	−0.0859665	+	0.264578i
$747$	−4.50684			−0.164897
$748$	10.5881	−	0.417870i	0.387141	−	0.0152788i
$749$		0			0
$750$	2.15501	−	6.63243i	0.0786897	−	0.242182i
$751$	28.1128	−	20.4251i	1.02585	−	0.745323i	0.0583755	−	0.998295i	$-0.481408\pi$
$751$	28.1128	−	20.4251i	1.02585	−	0.745323i	0.967474	+	0.252972i	$0.0814079\pi$
$752$	52.5020	+	38.1449i	1.91455	+	1.39100i
$753$	−2.09913	−	6.46046i	−0.0764966	−	0.235432i
$754$	20.3475	+	62.6233i	0.741014	+	2.28061i
$755$	−35.5134	−	25.8020i	−1.29247	−	0.939031i
$756$		0			0
$757$	10.7526	−	33.0930i	0.390808	−	1.20278i	−0.541370	−	0.840784i	$-0.682094\pi$
$757$	10.7526	−	33.0930i	0.390808	−	1.20278i	0.932178	−	0.362000i	$-0.117906\pi$
$758$	7.68929			0.279288
$759$	7.44898	+	4.97536i	0.270381	+	0.180594i
$760$	8.04674			0.291886
$761$	3.77787	−	11.6271i	0.136948	−	0.421482i	−0.858940	−	0.512076i	$-0.828877\pi$
$761$	3.77787	−	11.6271i	0.136948	−	0.421482i	0.995888	+	0.0905941i	$0.0288766\pi$
$762$	17.3387	−	12.5973i	0.628116	−	0.456353i
$763$		0			0
$764$	−0.297079	−	0.914315i	−0.0107479	−	0.0330788i
$765$	−6.19182	−	19.0565i	−0.223866	−	0.688988i
$766$	−1.90120	−	1.38130i	−0.0686931	−	0.0499085i
$767$	−29.7231	+	21.5951i	−1.07324	+	0.779755i
$768$	−3.87351	+	11.9214i	−0.139773	+	0.430178i
$769$	2.61946			0.0944603			0.0472301	−	0.998884i	$-0.484961\pi$
$769$	2.61946			0.0944603			0.0472301	+	0.998884i	$0.484961\pi$
$770$		0			0
$771$	3.29585			0.118697
$772$	−2.41417	+	7.43004i	−0.0868878	+	0.267413i
$773$	−0.172162	+	0.125083i	−0.00619225	+	0.00449894i	−0.590877	−	0.806762i	$-0.701218\pi$
$773$	−0.172162	+	0.125083i	−0.00619225	+	0.00449894i	0.584685	+	0.811261i	$0.301218\pi$
$774$	−17.7253	−	12.8782i	−0.637123	−	0.462897i
$775$	0.168253	+	0.517831i	0.00604384	+	0.0186010i
$776$	5.36310	+	16.5059i	0.192524	+	0.592529i
$777$		0			0
$778$	55.3767	−	40.2336i	1.98535	−	1.44244i
$779$	5.75614	−	17.7156i	0.206235	−	0.634727i
$780$	−8.54526			−0.305969
$781$	5.25288	−	4.14253i	0.187963	−	0.148231i
$782$	21.4045			0.765425
$783$	9.25750	−	28.4917i	0.330836	−	1.01821i
$784$		0			0
$785$	10.3166	+	7.49547i	0.368216	+	0.267525i
$786$	−2.34164	−	7.20684i	−0.0835237	−	0.257060i
$787$	−9.00399	−	27.7114i	−0.320958	−	0.987806i	−0.973232	−	0.229823i	$-0.926185\pi$
$787$	−9.00399	−	27.7114i	−0.320958	−	0.987806i	0.652275	−	0.757983i	$-0.273815\pi$
$788$	10.2446	+	7.44313i	0.364948	+	0.265151i
$789$	−4.09017	+	2.97168i	−0.145614	+	0.105795i
$790$	9.60131	−	29.5498i	0.341599	−	1.05133i
$791$		0			0
$792$	−10.1865	+	8.03330i	−0.361962	+	0.285451i
$793$	4.24457			0.150729
$794$	0.225262	−	0.693284i	0.00799424	−	0.0246037i
$795$	−5.41626	+	3.93514i	−0.192095	+	0.139565i
$796$	19.6745	+	14.2943i	0.697343	+	0.506649i
$797$	−9.95913	−	30.6510i	−0.352770	−	1.08572i	−0.957291	−	0.289126i	$-0.906635\pi$
$797$	−9.95913	−	30.6510i	−0.352770	−	1.08572i	0.604521	−	0.796589i	$-0.293365\pi$
$798$		0			0
$799$	−29.0823	−	21.1295i	−1.02886	−	0.747509i
$800$	12.8557	−	9.34019i	0.454517	−	0.330226i
$801$	−12.3808	+	38.1042i	−0.437455	+	1.34635i
$802$	−2.78503			−0.0983430
$803$	8.97104	−	31.8303i	0.316581	−	1.12327i
$804$	3.88203			0.136909
$805$		0			0
$806$	−1.23845	+	0.899783i	−0.0436224	+	0.0316935i
$807$	−6.42195	−	4.66582i	−0.226064	−	0.164245i
$808$	1.57519	+	4.84794i	0.0554151	+	0.170550i
$809$	−9.06844	−	27.9098i	−0.318829	−	0.981256i	−0.974149	−	0.225905i	$-0.927466\pi$
$809$	−9.06844	−	27.9098i	−0.318829	−	0.981256i	0.655320	−	0.755351i	$-0.272534\pi$
$810$	−22.7989	−	16.5644i	−0.801073	−	0.582013i
$811$	0.840891	−	0.610943i	0.0295277	−	0.0214531i	−0.572924	−	0.819609i	$-0.694191\pi$
$811$	0.840891	−	0.610943i	0.0295277	−	0.0214531i	0.602451	+	0.798156i	$0.294191\pi$
$812$		0			0
$813$	−13.6259			−0.477882
$814$	−5.07623	−	3.39054i	−0.177922	−	0.118838i
$815$	22.3244			0.781990
$816$	2.61794	−	8.05720i	0.0916463	−	0.282058i
$817$	−7.38605	+	5.36628i	−0.258405	+	0.187742i
$818$	−9.74762	−	7.08206i	−0.340817	−	0.247618i
$819$		0			0
$820$	−9.55952	−	29.4212i	−0.333833	−	1.02743i
$821$	−23.0831	−	16.7709i	−0.805607	−	0.585308i	0.106946	−	0.994265i	$-0.465893\pi$
$821$	−23.0831	−	16.7709i	−0.805607	−	0.585308i	−0.912554	+	0.408957i	$0.865893\pi$
$822$	−2.32024	+	1.68575i	−0.0809275	+	0.0587973i
$823$	8.23767	−	25.3529i	0.287147	−	0.883748i	−0.698600	−	0.715513i	$-0.746193\pi$
$823$	8.23767	−	25.3529i	0.287147	−	0.883748i	0.985747	−	0.168235i	$-0.0538068\pi$
$824$	−27.1659			−0.946370
$825$	−5.55965	+	0.219416i	−0.193562	+	0.00763909i
$826$		0			0
$827$	0.531399	−	1.63548i	0.0184785	−	0.0568711i	−0.941392	−	0.337314i	$-0.890481\pi$
$827$	0.531399	−	1.63548i	0.0184785	−	0.0568711i	0.959871	+	0.280443i	$0.0904815\pi$
$828$	10.7319	−	7.79717i	0.372959	−	0.270970i
$829$	22.6205	+	16.4347i	0.785642	+	0.570802i	0.906667	−	0.421847i	$-0.138618\pi$
$829$	22.6205	+	16.4347i	0.785642	+	0.570802i	−0.121025	+	0.992649i	$0.538618\pi$
$830$	2.62625	+	8.08277i	0.0911585	+	0.280557i
$831$	−4.59829	−	14.1521i	−0.159513	−	0.490930i
$832$	1.58538	+	1.15185i	0.0549632	+	0.0399331i
$833$		0			0
$834$	−0.339923	+	1.04617i	−0.0117706	+	0.0362261i
$835$	37.2375			1.28866
$836$	−2.58212	−	6.99537i	−0.0893046	−	0.241940i
$837$	0.696468			0.0240735
$838$	−15.7761	+	48.5539i	−0.544977	+	1.67727i
$839$	29.0133	−	21.0794i	1.00165	−	0.727742i	0.0392091	−	0.999231i	$-0.487516\pi$
$839$	29.0133	−	21.0794i	1.00165	−	0.727742i	0.962441	+	0.271489i	$0.0875162\pi$
$840$		0			0
$841$	14.0429	+	43.2197i	0.484240	+	1.49034i
$842$	6.71518	+	20.6672i	0.231420	+	0.712239i
$843$	7.72092	+	5.60957i	0.265922	+	0.193204i
$844$	5.65023	−	4.10514i	0.194489	−	0.141305i
$845$	4.66389	−	14.3540i	0.160443	−	0.493792i
$846$	−60.7076			−2.08717
$847$		0			0
$848$	19.4014			0.666248
$849$	−0.641191	+	1.97338i	−0.0220056	+	0.0677263i
$850$	−10.7560	+	7.81467i	−0.368927	+	0.268041i
$851$	−3.66092	−	2.65981i	−0.125495	−	0.0911772i
$852$	0.446646	+	1.37463i	0.0153018	+	0.0470942i
$853$	4.67937	+	14.4016i	0.160218	+	0.493102i	0.998652	−	0.0519019i	$-0.0165283\pi$
$853$	4.67937	+	14.4016i	0.160218	+	0.493102i	−0.838434	+	0.545004i	$0.816528\pi$
$854$		0			0
$855$	−11.4073	+	8.28790i	−0.390122	+	0.283440i
$856$	−1.49932	+	4.61444i	−0.0512458	+	0.157718i
$857$	−25.3267			−0.865142			−0.432571	−	0.901600i	$-0.642394\pi$
$857$	−25.3267			−0.865142			−0.432571	+	0.901600i	$0.642394\pi$
$858$	−5.41693	−	14.6753i	−0.184931	−	0.501006i
$859$	−41.5291			−1.41696			−0.708478	−	0.705733i	$-0.750618\pi$
$859$	−41.5291			−1.41696			−0.708478	+	0.705733i	$0.750618\pi$
$860$	−4.68534	+	14.4200i	−0.159769	+	0.491718i
$861$		0			0
$862$	−5.30813	−	3.85658i	−0.180796	−	0.131356i
$863$	−7.43197	−	22.8733i	−0.252987	−	0.778615i	−0.994220	−	0.107366i	$-0.965758\pi$
$863$	−7.43197	−	22.8733i	−0.252987	−	0.778615i	0.741232	−	0.671249i	$-0.234242\pi$
$864$	−6.28115	−	19.3314i	−0.213689	−	0.657668i
$865$	−46.2486	−	33.6016i	−1.57250	−	1.14249i
$866$	41.8101	−	30.3768i	1.42077	−	1.03225i
$867$	1.79656	−	5.52924i	0.0610144	−	0.187783i
$868$		0			0
$869$	20.8569	−	0.823133i	0.707521	−	0.0279229i
$870$	−26.3260			−0.892534
$871$	−7.18764	+	22.1213i	−0.243544	+	0.749551i
$872$	15.3401	−	11.1452i	0.519481	−	0.377425i
$873$	−24.6035	−	17.8755i	−0.832704	−	0.604995i
$874$	−4.65455	−	14.3252i	−0.157443	−	0.484559i
$875$		0			0
$876$	5.78049	+	4.19977i	0.195304	+	0.141897i
$877$	−27.3490	+	19.8702i	−0.923509	+	0.670969i	−0.944395	−	0.328813i	$-0.893351\pi$
$877$	−27.3490	+	19.8702i	−0.923509	+	0.670969i	0.0208857	+	0.999782i	$0.493351\pi$
$878$	7.80061	−	24.0078i	0.263258	−	0.810225i
$879$	4.22553			0.142524
$880$	38.1067	+	25.4524i	1.28458	+	0.858001i
$881$	36.8296			1.24082			0.620410	−	0.784278i	$-0.286966\pi$
$881$	36.8296			1.24082			0.620410	+	0.784278i	$0.286966\pi$
$882$		0			0
$883$	−43.2099	+	31.3938i	−1.45413	+	1.05649i	−0.469283	+	0.883048i	$0.655488\pi$
$883$	−43.2099	+	31.3938i	−1.45413	+	1.05649i	−0.984845	+	0.173438i	$0.944512\pi$
$884$	−11.0976	−	8.06286i	−0.373252	−	0.271183i
$885$	−4.53915	−	13.9701i	−0.152582	−	0.469599i
$886$	14.9598	+	46.0414i	0.502583	+	1.54679i
$887$	9.27263	+	6.73696i	0.311344	+	0.226205i	0.732473	−	0.680796i	$-0.238366\pi$
$887$	9.27263	+	6.73696i	0.311344	+	0.226205i	−0.421129	+	0.907001i	$0.638366\pi$
$888$	−0.773537	+	0.562007i	−0.0259582	+	0.0188597i
$889$		0			0
$890$	75.5525			2.53253
$891$	5.13571	−	18.2221i	0.172053	−	0.610463i
$892$	5.36254			0.179551
$893$	−7.81706	+	24.0584i	−0.261588	+	0.805085i
$894$	−13.2376	+	9.61768i	−0.442732	+	0.321663i
$895$	8.34817	+	6.06530i	0.279048	+	0.202741i
$896$		0			0
$897$	−3.58339	−	11.0286i	−0.119646	−	0.368233i
$898$	60.2757	+	43.7929i	2.01143	+	1.46139i
$899$	−1.40016	+	1.01727i	−0.0466979	+	0.0339280i
$900$	−2.54617	+	7.83629i	−0.0848722	+	0.261210i
$901$	−10.7470			−0.358034
$902$	44.4669	−	35.0675i	1.48059	−	1.16762i
$903$		0			0
$904$	8.51730	−	26.2136i	0.283281	−	0.871850i
$905$	10.7224	−	7.79031i	0.356426	−	0.258959i
$906$	14.0462	+	10.2052i	0.466654	+	0.339044i
$907$	17.6319	+	54.2655i	0.585459	+	1.80186i	0.597419	+	0.801929i	$0.296193\pi$
$907$	17.6319	+	54.2655i	0.585459	+	1.80186i	−0.0119596	+	0.999928i	$0.503807\pi$
$908$	−6.19853	−	19.0771i	−0.205706	−	0.633097i
$909$	−7.22628	−	5.25020i	−0.239681	−	0.174138i
$910$		0			0
$911$	2.06289	−	6.34893i	0.0683467	−	0.210350i	−0.911050	−	0.412296i	$-0.864727\pi$
$911$	2.06289	−	6.34893i	0.0683467	−	0.210350i	0.979396	+	0.201947i	$0.0647268\pi$
$912$	−5.96167			−0.197410
$913$	−4.48309	+	3.53546i	−0.148369	+	0.117007i
$914$	34.6568			1.14635
$915$	−0.524410	+	1.61397i	−0.0173365	+	0.0533561i
$916$	−4.15177	+	3.01643i	−0.137178	+	0.0996658i
$917$		0			0
$918$	5.25526	+	16.1740i	0.173449	+	0.533822i
$919$	−9.00287	−	27.7080i	−0.296977	−	0.914002i	−0.982550	−	0.185998i	$-0.940448\pi$
$919$	−9.00287	−	27.7080i	−0.296977	−	0.914002i	0.685573	−	0.728004i	$-0.259552\pi$
$920$	14.6713	+	10.6593i	0.483699	+	0.351428i
$921$	5.89852	−	4.28553i	0.194363	−	0.141213i
$922$	−6.71491	+	20.6664i	−0.221144	+	0.680611i
$923$	−8.66015			−0.285052
$924$		0			0
$925$	2.81073			0.0924161
$926$	7.61015	−	23.4216i	0.250085	−	0.769683i
$927$	38.5113	−	27.9801i	1.26488	−	0.918987i
$928$	40.8632	+	29.6889i	1.34140	+	0.974585i
$929$	−0.724557	−	2.22996i	−0.0237720	−	0.0731626i	0.938467	−	0.345370i	$-0.112246\pi$
$929$	−0.724557	−	2.22996i	−0.0237720	−	0.0731626i	−0.962239	+	0.272207i	$0.912246\pi$
$930$	−0.189128	−	0.582077i	−0.00620176	−	0.0190871i
$931$		0			0
$932$	9.88015	−	7.17835i	0.323635	−	0.235135i
$933$	4.83452	−	14.8791i	0.158275	−	0.487121i
$934$	29.1876			0.955047
$935$	−21.1084	−	14.0988i	−0.690317	−	0.461080i
$936$	16.7940			0.548928
$937$	−2.71558	+	8.35769i	−0.0887141	+	0.273034i	−0.985565	−	0.169300i	$-0.945849\pi$
$937$	−2.71558	+	8.35769i	−0.0887141	+	0.273034i	0.896850	+	0.442334i	$0.145849\pi$
$938$		0			0
$939$	9.82717	+	7.13986i	0.320698	+	0.233000i
$940$	12.9822	+	39.9551i	0.423432	+	1.30319i
$941$	−2.74676	−	8.45366i	−0.0895419	−	0.275582i	0.896251	−	0.443547i	$-0.146280\pi$
$941$	−2.74676	−	8.45366i	−0.0895419	−	0.275582i	−0.985793	+	0.167966i	$0.946280\pi$
$942$	−4.08042	−	2.96460i	−0.132947	−	0.0965918i
$943$	33.9624	−	24.6751i	1.10597	−	0.803533i
$944$	−13.1543	+	40.4847i	−0.428135	+	1.31766i
$945$		0			0
$946$	−27.7344	+	1.09456i	−0.901724	+	0.0355873i
$947$	−7.86275			−0.255505			−0.127752	−	0.991806i	$-0.540776\pi$
$947$	−7.86275			−0.255505			−0.127752	+	0.991806i	$0.540776\pi$
$948$	−1.39360	+	4.28905i	−0.0452620	+	0.139302i
$949$	−34.6345	+	25.1634i	−1.12428	+	0.816840i
$950$	7.56902	+	5.49921i	0.245571	+	0.178418i
$951$	−0.689556	−	2.12223i	−0.0223604	−	0.0688182i
$952$		0			0
$953$	14.1290	+	10.2653i	0.457683	+	0.332526i	0.792622	−	0.609714i	$-0.208716\pi$
$953$	14.1290	+	10.2653i	0.457683	+	0.332526i	−0.334939	+	0.942240i	$0.608716\pi$
$954$	−14.6831	+	10.6679i	−0.475382	+	0.345385i
$955$	−0.711658	+	2.19026i	−0.0230287	+	0.0708751i
$956$	−11.3121			−0.365860
$957$	−6.12425	−	16.5915i	−0.197969	−	0.536328i
$958$	44.0663			1.42372
$959$		0			0
$960$	−0.633854	+	0.460522i	−0.0204575	+	0.0148633i
$961$	25.0470	+	18.1977i	0.807967	+	0.587022i
$962$	2.44196	+	7.51559i	0.0787320	+	0.242312i
$963$	−2.62725	−	8.08584i	−0.0846619	−	0.260563i
$964$	11.7722	+	8.55298i	0.379156	+	0.275473i
$965$	15.1406	−	11.0003i	0.487392	−	0.354111i
$966$		0			0
$967$	−45.6122			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$968$	−3.83100	+	15.9820i	−0.123133	+	0.513680i
$969$	3.30233			0.106086
$970$	−17.7217	+	54.5417i	−0.569008	+	1.75123i
$971$	1.92852	−	1.40115i	0.0618892	−	0.0449651i	−0.556411	−	0.830908i	$-0.687822\pi$
$971$	1.92852	−	1.40115i	0.0618892	−	0.0449651i	0.618300	+	0.785942i	$0.287822\pi$
$972$	13.0799	+	9.50313i	0.419539	+	0.304813i
$973$		0			0
$974$	−7.87338	−	24.2318i	−0.252279	−	0.776436i
$975$	5.82715	+	4.23367i	0.186618	+	0.135586i
$976$	3.97867	−	2.89067i	0.127354	−	0.0925282i
$977$	−5.95358	+	18.3232i	−0.190472	+	0.586212i	−1.00000		0.000869450i	$-0.999723\pi$
$977$	−5.95358	+	18.3232i	−0.190472	+	0.586212i	0.809528	+	0.587082i	$0.199723\pi$
$978$	−8.82972			−0.282343
$979$	17.5759	+	47.6158i	0.561728	+	1.52181i
$980$		0			0
$981$	−10.2674	+	31.5997i	−0.327812	+	1.00890i
$982$	31.6641	−	23.0053i	1.01044	−	0.734130i
$983$	−13.1268	−	9.53718i	−0.418680	−	0.304189i	0.358426	−	0.933558i	$-0.383313\pi$
$983$	−13.1268	−	9.53718i	−0.418680	−	0.304189i	−0.777107	+	0.629369i	$0.783313\pi$
$984$	−2.74103	−	8.43602i	−0.0873808	−	0.268931i
$985$	−9.37387	−	28.8498i	−0.298676	−	0.919231i
$986$	−34.1891	−	24.8398i	−1.08880	−	0.791061i
$987$		0			0
$988$	−2.98293	+	9.18051i	−0.0948996	+	0.292071i
$989$	−20.5753			−0.654256
$990$	−42.8342	+	1.69049i	−1.36136	+	0.0537272i
$991$	−50.5214			−1.60487			−0.802433	−	0.596743i	$-0.796461\pi$
$991$	−50.5214			−1.60487			−0.802433	+	0.596743i	$0.796461\pi$
$992$	−0.362867	+	1.11679i	−0.0115210	+	0.0354581i
$993$	−13.2667	+	9.63884i	−0.421007	+	0.305879i
$994$		0			0
$995$	−18.0023	−	55.4053i	−0.570710	−	1.75647i
$996$	−0.381192	−	1.17319i	−0.0120785	−	0.0371739i
$997$	−36.4224	−	26.4625i	−1.15351	−	0.838074i	−0.164567	−	0.986366i	$-0.552623\pi$
$997$	−36.4224	−	26.4625i	−1.15351	−	0.838074i	−0.988944	+	0.148292i	$0.952623\pi$
$998$	36.3986	−	26.4452i	1.15218	−	0.837107i
$999$	1.11102	−	3.41936i	0.0351510	−	0.108184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.d.295.2		8
7.2	even	3		539.2.q.b.361.1		16
7.3	odd	6		539.2.q.c.471.2		16
7.4	even	3		539.2.q.b.471.2		16
7.5	odd	6		539.2.q.c.361.1		16
7.6	odd	2		77.2.f.a.64.2	✓	8
11.4	even	5		5929.2.a.bi.1.3		4
11.5	even	5	inner	539.2.f.d.148.2		8
11.7	odd	10		5929.2.a.bb.1.2		4
21.20	even	2		693.2.m.g.64.1		8
77.5	odd	30		539.2.q.c.214.2		16
77.6	even	10		847.2.f.q.148.1		8
77.13	even	10		847.2.f.s.729.2		8
77.16	even	15		539.2.q.b.214.2		16
77.20	odd	10		847.2.f.p.729.1		8
77.27	odd	10		77.2.f.a.71.2	yes	8
77.38	odd	30		539.2.q.c.324.1		16
77.41	even	10		847.2.f.s.323.2		8
77.48	odd	10		847.2.a.l.1.3		4
77.60	even	15		539.2.q.b.324.1		16
77.62	even	10		847.2.a.k.1.2		4
77.69	odd	10		847.2.f.p.323.1		8
77.76	even	2		847.2.f.q.372.1		8
231.62	odd	10		7623.2.a.co.1.3		4
231.104	even	10		693.2.m.g.379.1		8
231.125	even	10		7623.2.a.ch.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	7.6	odd	2
77.2.f.a.71.2	yes	8	77.27	odd	10
539.2.f.d.148.2		8	11.5	even	5	inner
539.2.f.d.295.2		8	1.1	even	1	trivial
539.2.q.b.214.2		16	77.16	even	15
539.2.q.b.324.1		16	77.60	even	15
539.2.q.b.361.1		16	7.2	even	3
539.2.q.b.471.2		16	7.4	even	3
539.2.q.c.214.2		16	77.5	odd	30
539.2.q.c.324.1		16	77.38	odd	30
539.2.q.c.361.1		16	7.5	odd	6
539.2.q.c.471.2		16	7.3	odd	6
693.2.m.g.64.1		8	21.20	even	2
693.2.m.g.379.1		8	231.104	even	10
847.2.a.k.1.2		4	77.62	even	10
847.2.a.l.1.3		4	77.48	odd	10
847.2.f.p.323.1		8	77.69	odd	10
847.2.f.p.729.1		8	77.20	odd	10
847.2.f.q.148.1		8	77.6	even	10
847.2.f.q.372.1		8	77.76	even	2
847.2.f.s.323.2		8	77.41	even	10
847.2.f.s.729.2		8	77.13	even	10
5929.2.a.bb.1.2		4	11.7	odd	10
5929.2.a.bi.1.3		4	11.4	even	5
7623.2.a.ch.1.2		4	231.125	even	10
7623.2.a.co.1.3		4	231.62	odd	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.549273 - 1.69049i) q^{2} +(0.500000 - 0.363271i) q^{3} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(-0.339469 - 1.04478i) q^{6} +(1.20872 - 0.878189i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})\)	\(q+(0.549273 - 1.69049i) q^{2} +(0.500000 - 0.363271i) q^{3} +(-0.938015 - 0.681508i) q^{4} +(0.858290 + 2.64154i) q^{5} +(-0.339469 - 1.04478i) q^{6} +(1.20872 - 0.878189i) q^{8} +(-0.809017 + 2.48990i) q^{9} +4.93693 q^{10} +(1.14849 + 3.11143i) q^{11} -0.716580 q^{12} +(1.32676 - 4.08334i) q^{13} +(1.38874 + 1.00898i) q^{15} +(-1.53723 - 4.73110i) q^{16} +(0.851514 + 2.62069i) q^{17} +(3.76477 + 2.73527i) q^{18} +(1.56876 - 1.13977i) q^{19} +(0.995144 - 3.06274i) q^{20} +(5.89066 - 0.232480i) q^{22} +4.37009 q^{23} +(0.285341 - 0.878189i) q^{24} +(-2.19601 + 1.59550i) q^{25} +(-6.17408 - 4.48573i) q^{26} +(1.07295 + 3.30220i) q^{27} +(-6.98027 - 5.07146i) q^{29} +(2.46847 - 1.79345i) q^{30} +(0.0619850 - 0.190770i) q^{31} -5.85410 q^{32} +(1.70454 + 1.13850i) q^{33} +4.89796 q^{34} +(2.45576 - 1.78421i) q^{36} +(-0.837721 - 0.608640i) q^{37} +(-1.06509 - 3.27802i) q^{38} +(-0.819981 - 2.52364i) q^{39} +(3.35721 + 2.43916i) q^{40} +(7.77155 - 5.64636i) q^{41} -4.70820 q^{43} +(1.04316 - 3.70127i) q^{44} -7.27155 q^{45} +(2.40037 - 7.38759i) q^{46} +(-10.5541 + 7.66797i) q^{47} +(-2.48729 - 1.80712i) q^{48} +(1.49096 + 4.58869i) q^{50} +(1.37778 + 1.00101i) q^{51} +(-4.02734 + 2.92604i) q^{52} +(-1.20520 + 3.70923i) q^{53} +6.17167 q^{54} +(-7.23324 + 5.70428i) q^{55} +(0.370334 - 1.13977i) q^{57} +(-12.4073 + 9.01445i) q^{58} +(-6.92286 - 5.02975i) q^{59} +(-0.615033 - 1.89288i) q^{60} +(0.305497 + 0.940223i) q^{61} +(-0.288448 - 0.209570i) q^{62} +(-0.141042 + 0.434084i) q^{64} +11.9251 q^{65} +(2.86088 - 2.25615i) q^{66} -5.41745 q^{67} +(0.987288 - 3.03856i) q^{68} +(2.18505 - 1.58753i) q^{69} +(-0.623302 - 1.91833i) q^{71} +(1.20872 + 3.72007i) q^{72} +(-8.06677 - 5.86085i) q^{73} +(-1.48904 + 1.08185i) q^{74} +(-0.518408 + 1.59550i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(1.94479 - 5.98545i) q^{79} +(11.1780 - 8.12131i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-5.27640 - 16.2391i) q^{82} +(0.531960 + 1.63720i) q^{83} +(-6.19182 + 4.49862i) q^{85} +(-2.58609 + 7.95916i) q^{86} -5.33245 q^{87} +(4.12062 + 2.75227i) q^{88} +15.3035 q^{89} +(-3.99406 + 12.2925i) q^{90} +(-4.09921 - 2.97825i) q^{92} +(-0.0383089 - 0.117903i) q^{93} +(7.16556 + 22.0533i) q^{94} +(4.35721 + 3.16570i) q^{95} +(-2.92705 + 2.12663i) q^{96} +(-3.58961 + 11.0477i) q^{97} +(-8.67628 + 0.342417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more