LMFDB - Embedded newform 130.2.n.a.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(9,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.1
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	130.9
Dual form			130.2.n.a.29.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.45071 - 0.837565i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.67513 + 1.48119i) q^{5} +(0.837565 + 1.45071i) q^{6} +(-1.56410 + 0.903032i) q^{7} -1.00000i q^{8} +(-0.0969683 - 0.167954i) q^{9} +(2.19130 - 0.445186i) q^{10} +(-3.22179 + 5.58031i) q^{11} -1.67513i q^{12} +(1.98082 + 3.01270i) q^{13} +1.80606 q^{14} +(3.67072 - 0.745746i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.416726 + 0.240597i) q^{17} +0.193937i q^{18} +(-3.14363 - 5.44492i) q^{19} +(-2.12032 - 0.710109i) q^{20} +3.02539 q^{21} +(5.58031 - 3.22179i) q^{22} +(-6.16499 - 3.55936i) q^{23} +(-0.837565 + 1.45071i) q^{24} +(0.612127 - 4.96239i) q^{25} +(-0.209095 - 3.59948i) q^{26} +5.35026i q^{27} +(-1.56410 - 0.903032i) q^{28} +(1.15633 - 2.00281i) q^{29} +(-3.55181 - 1.18953i) q^{30} +3.25694 q^{31} +(0.866025 - 0.500000i) q^{32} +(9.34774 - 5.39692i) q^{33} +0.481194 q^{34} +(1.28250 - 3.82943i) q^{35} +(0.0969683 - 0.167954i) q^{36} +(2.65264 + 1.53150i) q^{37} +6.28726i q^{38} +(-0.350262 - 6.02961i) q^{39} +(1.48119 + 1.67513i) q^{40} +(-3.75329 + 6.50089i) q^{41} +(-2.62007 - 1.51270i) q^{42} +(-1.73205 + 1.00000i) q^{43} -6.44358 q^{44} +(0.411207 + 0.137716i) q^{45} +(3.55936 + 6.16499i) q^{46} -2.19394i q^{47} +(1.45071 - 0.837565i) q^{48} +(-1.86907 + 3.23732i) q^{49} +(-3.01131 + 3.99149i) q^{50} +0.806063 q^{51} +(-1.61866 + 3.22179i) q^{52} -0.906679i q^{53} +(2.67513 - 4.63346i) q^{54} +(-2.86860 - 14.1198i) q^{55} +(0.903032 + 1.56410i) q^{56} +10.5320i q^{57} +(-2.00281 + 1.15633i) q^{58} +(3.28726 + 5.69370i) q^{59} +(2.48119 + 2.80606i) q^{60} +(5.47508 + 9.48313i) q^{61} +(-2.82059 - 1.62847i) q^{62} +(0.303336 + 0.175131i) q^{63} -1.00000 q^{64} +(-7.78053 - 2.11268i) q^{65} -10.7938 q^{66} +(0.562690 + 0.324869i) q^{67} +(-0.416726 - 0.240597i) q^{68} +(5.96239 + 10.3272i) q^{69} +(-3.02539 + 2.67513i) q^{70} +(-1.83146 - 3.17217i) q^{71} +(-0.167954 + 0.0969683i) q^{72} -2.60720i q^{73} +(-1.53150 - 2.65264i) q^{74} +(-5.04434 + 6.68627i) q^{75} +(3.14363 - 5.44492i) q^{76} -11.6375i q^{77} +(-2.71147 + 5.39692i) q^{78} +2.29455 q^{79} +(-0.445186 - 2.19130i) q^{80} +(4.19029 - 7.25779i) q^{81} +(6.50089 - 3.75329i) q^{82} +13.3380i q^{83} +(1.51270 + 2.62007i) q^{84} +(0.341700 - 1.02028i) q^{85} +2.00000 q^{86} +(-3.35498 + 1.93700i) q^{87} +(5.58031 + 3.22179i) q^{88} +(-0.578163 + 1.00141i) q^{89} +(-0.287258 - 0.324869i) q^{90} +(-5.81876 - 2.92340i) q^{91} -7.11871i q^{92} +(-4.72486 - 2.72790i) q^{93} +(-1.09697 + 1.90000i) q^{94} +(13.3310 + 4.46464i) q^{95} -1.67513 q^{96} +(-11.9784 + 6.91573i) q^{97} +(3.23732 - 1.86907i) q^{98} +1.24965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{14} + 4 q^{15} - 6 q^{16} - 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 16 q^{30} + 24 q^{31} - 16 q^{34} - 6 q^{35} + 2 q^{36} + 36 q^{39} - 4 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^14 + 4 * q^15 - 6 * q^16 - 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 16 * q^30 + 24 * q^31 - 16 * q^34 - 6 * q^35 + 2 * q^36 + 36 * q^39 - 4 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 - 4 * q^49 - 8 * q^50 + 8 * q^51 + 12 * q^54 + 12 * q^55 + 10 * q^56 + 16 * q^59 + 8 * q^60 - 8 * q^61 - 12 * q^64 - 10 * q^65 - 24 * q^66 + 28 * q^69 + 24 * q^70 + 40 * q^71 - 10 * q^74 - 8 * q^75 + 26 * q^76 + 56 * q^79 + 26 * q^81 - 12 * q^84 - 16 * q^85 + 24 * q^86 + 14 * q^89 + 20 * q^90 - 38 * q^91 - 14 * q^94 - 8 * q^95 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.45071	−	0.837565i	−0.837565	−	0.483569i	0.0188705	−	0.999822i	$-0.493993\pi$
$3$	−1.45071	−	0.837565i	−0.837565	−	0.483569i	−0.856436	+	0.516253i	$0.827326\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$	0.837565	+	1.45071i	0.341935	+	0.592248i
$7$	−1.56410	+	0.903032i	−0.591173	+	0.341314i	−0.765561	−	0.643363i	$-0.777539\pi$
$7$	−1.56410	+	0.903032i	−0.591173	+	0.341314i	0.174388	+	0.984677i	$0.444205\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.0969683	−	0.167954i	−0.0323228	−	0.0559847i
$10$	2.19130	−	0.445186i	0.692951	−	0.140780i
$11$	−3.22179	+	5.58031i	−0.971407	+	1.68253i	−0.280090	+	0.959974i	$0.590364\pi$
$11$	−3.22179	+	5.58031i	−0.971407	+	1.68253i	−0.691317	+	0.722552i	$0.742969\pi$
$12$		−	1.67513i		−	0.483569i
$13$	1.98082	+	3.01270i	0.549382	+	0.835572i
$13$	1.98082	+	3.01270i	0.549382	+	0.835572i
$14$	1.80606			0.482691
$15$	3.67072	−	0.745746i	0.947776	−	0.192551i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.416726	+	0.240597i	−0.101071	+	0.0583534i	−0.549684	−	0.835373i	$-0.685252\pi$
$17$	−0.416726	+	0.240597i	−0.101071	+	0.0583534i	0.448612	+	0.893726i	$0.351918\pi$
$18$			0.193937i			0.0457113i
$19$	−3.14363	−	5.44492i	−0.721198	−	1.24915i	−0.960520	−	0.278211i	$-0.910258\pi$
$19$	−3.14363	−	5.44492i	−0.721198	−	1.24915i	0.239322	−	0.970940i	$-0.423075\pi$
$20$	−2.12032	−	0.710109i	−0.474117	−	0.158785i
$21$	3.02539			0.660195
$22$	5.58031	−	3.22179i	1.18973	−	0.686888i
$23$	−6.16499	−	3.55936i	−1.28549	−	0.742177i	−0.307642	−	0.951502i	$-0.599540\pi$
$23$	−6.16499	−	3.55936i	−1.28549	−	0.742177i	−0.977846	+	0.209325i	$0.932873\pi$
$24$	−0.837565	+	1.45071i	−0.170967	+	0.296124i
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$	−0.209095	−	3.59948i	−0.0410069	−	0.705917i
$27$			5.35026i			1.02966i
$28$	−1.56410	−	0.903032i	−0.295587	−	0.170657i
$29$	1.15633	−	2.00281i	0.214724	−	0.371913i	−0.738463	−	0.674294i	$-0.764448\pi$
$29$	1.15633	−	2.00281i	0.214724	−	0.371913i	0.953187	+	0.302381i	$0.0977814\pi$
$30$	−3.55181	−	1.18953i	−0.648469	−	0.217177i
$31$	3.25694			0.584964			0.292482	−	0.956271i	$-0.405519\pi$
$31$	3.25694			0.584964			0.292482	+	0.956271i	$0.405519\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	9.34774	−	5.39692i	1.62723	−	0.939484i
$34$	0.481194			0.0825241
$35$	1.28250	−	3.82943i	0.216782	−	0.647291i
$36$	0.0969683	−	0.167954i	0.0161614	−	0.0279923i
$37$	2.65264	+	1.53150i	0.436091	+	0.251777i	0.701938	−	0.712238i	$-0.252318\pi$
$37$	2.65264	+	1.53150i	0.436091	+	0.251777i	−0.265847	+	0.964015i	$0.585652\pi$
$38$			6.28726i			1.01993i
$39$	−0.350262	−	6.02961i	−0.0560868	−	0.965510i
$40$	1.48119	+	1.67513i	0.234197	+	0.264861i
$41$	−3.75329	+	6.50089i	−0.586166	+	1.01527i	0.408563	+	0.912730i	$0.366030\pi$
$41$	−3.75329	+	6.50089i	−0.586166	+	1.01527i	−0.994729	+	0.102539i	$0.967303\pi$
$42$	−2.62007	−	1.51270i	−0.404285	−	0.233414i
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	−0.626219	−	0.779647i	$-0.715399\pi$
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	0.362084	+	0.932145i	$0.382065\pi$
$44$	−6.44358			−0.971407
$45$	0.411207	+	0.137716i	0.0612991	+	0.0205295i
$46$	3.55936	+	6.16499i	0.524799	+	0.908978i
$47$		−	2.19394i		−	0.320019i	−0.987116	−	0.160009i	$-0.948848\pi$
$47$		−	2.19394i		−	0.320019i	0.987116	−	0.160009i	$-0.0511524\pi$
$48$	1.45071	−	0.837565i	0.209391	−	0.120892i
$49$	−1.86907	+	3.23732i	−0.267010	+	0.462474i
$50$	−3.01131	+	3.99149i	−0.425864	+	0.564482i
$51$	0.806063			0.112871
$52$	−1.61866	+	3.22179i	−0.224468	+	0.446782i
$53$		−	0.906679i		−	0.124542i	−0.998059	−	0.0622710i	$-0.980166\pi$
$53$		−	0.906679i		−	0.124542i	0.998059	−	0.0622710i	$-0.0198343\pi$
$54$	2.67513	−	4.63346i	0.364039	−	0.630534i
$55$	−2.86860	−	14.1198i	−0.386801	−	1.90392i
$56$	0.903032	+	1.56410i	0.120673	+	0.209011i
$57$			10.5320i			1.39499i
$58$	−2.00281	+	1.15633i	−0.262982	+	0.151833i
$59$	3.28726	+	5.69370i	0.427965	+	0.741256i	0.996692	−	0.0812696i	$-0.0258975\pi$
$59$	3.28726	+	5.69370i	0.427965	+	0.741256i	−0.568728	+	0.822526i	$0.692564\pi$
$60$	2.48119	+	2.80606i	0.320321	+	0.362261i
$61$	5.47508	+	9.48313i	0.701013	+	1.21419i	0.968111	+	0.250521i	$0.0806018\pi$
$61$	5.47508	+	9.48313i	0.701013	+	1.21419i	−0.267098	+	0.963669i	$0.586065\pi$
$62$	−2.82059	−	1.62847i	−0.358216	−	0.206816i
$63$	0.303336	+	0.175131i	0.0382167	+	0.0220644i
$64$	−1.00000			−0.125000
$65$	−7.78053	−	2.11268i	−0.965056	−	0.262045i
$66$	−10.7938			−1.32863
$67$	0.562690	+	0.324869i	0.0687435	+	0.0396891i	0.533978	−	0.845499i	$-0.320697\pi$
$67$	0.562690	+	0.324869i	0.0687435	+	0.0396891i	−0.465234	+	0.885188i	$0.654030\pi$
$68$	−0.416726	−	0.240597i	−0.0505355	−	0.0291767i
$69$	5.96239	+	10.3272i	0.717787	+	1.24324i
$70$	−3.02539	+	2.67513i	−0.361604	+	0.319739i
$71$	−1.83146	−	3.17217i	−0.217354	−	0.376468i	0.736644	−	0.676280i	$-0.236409\pi$
$71$	−1.83146	−	3.17217i	−0.217354	−	0.376468i	−0.953998	+	0.299812i	$0.903076\pi$
$72$	−0.167954	+	0.0969683i	−0.0197936	+	0.0114278i
$73$		−	2.60720i		−	0.305150i	−0.988292	−	0.152575i	$-0.951243\pi$
$73$		−	2.60720i		−	0.305150i	0.988292	−	0.152575i	$-0.0487566\pi$
$74$	−1.53150	−	2.65264i	−0.178033	−	0.308363i
$75$	−5.04434	+	6.68627i	−0.582470	+	0.772064i
$76$	3.14363	−	5.44492i	0.360599	−	0.624576i
$77$		−	11.6375i		−	1.32622i
$78$	−2.71147	+	5.39692i	−0.307013	+	0.611081i
$79$	2.29455			0.258157			0.129079	−	0.991634i	$-0.458798\pi$
$79$	2.29455			0.258157			0.129079	+	0.991634i	$0.458798\pi$
$80$	−0.445186	−	2.19130i	−0.0497734	−	0.244995i
$81$	4.19029	−	7.25779i	0.465588	−	0.806422i
$82$	6.50089	−	3.75329i	0.717904	−	0.414482i
$83$			13.3380i			1.46404i	0.681283	+	0.732020i	$0.261422\pi$
$83$			13.3380i			1.46404i	−0.681283	+	0.732020i	$0.738578\pi$
$84$	1.51270	+	2.62007i	0.165049	+	0.285873i
$85$	0.341700	−	1.02028i	0.0370626	−	0.110665i
$86$	2.00000			0.215666
$87$	−3.35498	+	1.93700i	−0.359691	+	0.207668i
$88$	5.58031	+	3.22179i	0.594863	+	0.343444i
$89$	−0.578163	+	1.00141i	−0.0612851	+	0.106149i	−0.895040	−	0.445986i	$-0.852853\pi$
$89$	−0.578163	+	1.00141i	−0.0612851	+	0.106149i	0.833755	+	0.552135i	$0.186187\pi$
$90$	−0.287258	−	0.324869i	−0.0302796	−	0.0342442i
$91$	−5.81876	−	2.92340i	−0.609972	−	0.306456i
$92$		−	7.11871i		−	0.742177i
$93$	−4.72486	−	2.72790i	−0.489945	−	0.282870i
$94$	−1.09697	+	1.90000i	−0.113144	+	0.195971i
$95$	13.3310	+	4.46464i	1.36773	+	0.458062i
$96$	−1.67513			−0.170967
$97$	−11.9784	+	6.91573i	−1.21622	+	0.702186i	−0.964108	−	0.265512i	$-0.914459\pi$
$97$	−11.9784	+	6.91573i	−1.21622	+	0.702186i	−0.252114	+	0.967698i	$0.581126\pi$
$98$	3.23732	−	1.86907i	0.327019	−	0.188804i
$99$	1.24965			0.125594
$100$	4.60362	−	1.95108i	0.460362	−	0.195108i
$101$	4.79995	−	8.31376i	0.477613	−	0.827250i	−0.522057	−	0.852910i	$-0.674835\pi$
$101$	4.79995	−	8.31376i	0.477613	−	0.827250i	0.999671	+	0.0256599i	$0.00816868\pi$
$102$	−0.698071	−	0.403032i	−0.0691194	−	0.0399061i
$103$			3.07522i			0.303011i	0.988456	+	0.151505i	$0.0484121\pi$
$103$			3.07522i			0.303011i	−0.988456	+	0.151505i	$0.951588\pi$
$104$	3.01270	−	1.98082i	0.295419	−	0.194236i
$105$	−5.06793	+	4.48119i	−0.494579	+	0.437320i
$106$	−0.453339	+	0.785207i	−0.0440322	+	0.0762660i
$107$	−1.45071	−	0.837565i	−0.140245	−	0.0809705i	0.428236	−	0.903667i	$-0.359135\pi$
$107$	−1.45071	−	0.837565i	−0.140245	−	0.0809705i	−0.568481	+	0.822697i	$0.692469\pi$
$108$	−4.63346	+	2.67513i	−0.445855	+	0.257415i
$109$	−10.8872			−1.04280			−0.521401	−	0.853312i	$-0.674590\pi$
$109$	−10.8872			−1.04280			−0.521401	+	0.853312i	$0.674590\pi$
$110$	−4.57564	+	13.6624i	−0.436271	+	1.30266i
$111$	−2.56547	−	4.44352i	−0.243503	−	0.421760i
$112$		−	1.80606i		−	0.170657i
$113$	12.1244	−	7.00000i	1.14056	−	0.658505i	0.193993	−	0.981003i	$-0.437856\pi$
$113$	12.1244	−	7.00000i	1.14056	−	0.658505i	0.946570	+	0.322498i	$0.104523\pi$
$114$	5.26599	−	9.12096i	0.493205	−	0.854256i
$115$	15.5993	−	3.16915i	1.45464	−	0.295525i
$116$	2.31265			0.214724
$117$	0.313917	−	0.624823i	0.0290217	−	0.0577649i
$118$		−	6.57452i		−	0.605233i
$119$	0.434534	−	0.752634i	0.0398336	−	0.0689939i
$120$	−0.745746	−	3.67072i	−0.0680769	−	0.335089i
$121$	−15.2599	−	26.4309i	−1.38726	−	2.40281i
$122$		−	10.9502i		−	0.991382i
$123$	10.8898	−	6.28726i	0.981905	−	0.566903i
$124$	1.62847	+	2.82059i	0.146241	+	0.253297i
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$	−0.175131	−	0.303336i	−0.0156019	−	0.0270233i
$127$	−4.49176	−	2.59332i	−0.398580	−	0.230120i	0.287291	−	0.957843i	$-0.407245\pi$
$127$	−4.49176	−	2.59332i	−0.398580	−	0.230120i	−0.685871	+	0.727723i	$0.740579\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.35026			0.294974
$130$	5.68180	+	5.71989i	0.498326	+	0.501668i
$131$	−10.8011			−0.943700			−0.471850	−	0.881679i	$-0.656414\pi$
$131$	−10.8011			−0.943700			−0.471850	+	0.881679i	$0.656414\pi$
$132$	9.34774	+	5.39692i	0.813617	+	0.469742i
$133$	9.83388	+	5.67759i	0.852706	+	0.492310i
$134$	−0.324869	−	0.562690i	−0.0280644	−	0.0486090i
$135$	−7.92478	−	8.96239i	−0.682056	−	0.771360i
$136$	0.240597	+	0.416726i	0.0206310	+	0.0357340i
$137$	5.32095	−	3.07205i	0.454600	−	0.262463i	−0.255171	−	0.966896i	$-0.582132\pi$
$137$	5.32095	−	3.07205i	0.454600	−	0.262463i	0.709771	+	0.704433i	$0.248798\pi$
$138$		−	11.9248i		−	1.01510i
$139$	5.16902	+	8.95301i	0.438431	+	0.759384i	0.997569	−	0.0696904i	$-0.0222011\pi$
$139$	5.16902	+	8.95301i	0.438431	+	0.759384i	−0.559138	+	0.829075i	$0.688868\pi$
$140$	3.95763	−	0.804035i	0.334481	−	0.0679534i
$141$	−1.83757	+	3.18276i	−0.154751	+	0.268036i
$142$			3.66291i			0.307385i
$143$	−23.1936	+	1.34732i	−1.93954	+	0.112669i
$144$	0.193937			0.0161614
$145$	1.02956	+	5.06772i	0.0855004	+	0.420851i
$146$	−1.30360	+	2.25790i	−0.107887	+	0.186865i
$147$	5.42293	−	3.13093i	0.447276	−	0.258235i
$148$			3.06300i			0.251777i
$149$	−8.02539	−	13.9004i	−0.657466	−	1.13876i	−0.981270	−	0.192640i	$-0.938295\pi$
$149$	−8.02539	−	13.9004i	−0.657466	−	1.13876i	0.323804	−	0.946124i	$-0.395038\pi$
$150$	7.71166	−	3.26831i	0.629655	−	0.266856i
$151$	9.31757			0.758253			0.379127	−	0.925345i	$-0.376224\pi$
$151$	9.31757			0.758253			0.379127	+	0.925345i	$0.376224\pi$
$152$	−5.44492	+	3.14363i	−0.441642	+	0.254982i
$153$	0.0808185	+	0.0466606i	0.00653379	+	0.00377228i
$154$	−5.81876	+	10.0784i	−0.468889	+	0.812140i
$155$	−5.45580	+	4.82416i	−0.438221	+	0.387486i
$156$	5.04666	−	3.31814i	0.404056	−	0.265664i
$157$			14.7562i			1.17768i	0.808251	+	0.588838i	$0.200414\pi$
$157$			14.7562i			1.17768i	−0.808251	+	0.588838i	$0.799586\pi$
$158$	−1.98714	−	1.14728i	−0.158088	−	0.0912724i
$159$	−0.759403	+	1.31532i	−0.0602246	+	0.104312i
$160$	−0.710109	+	2.12032i	−0.0561390	+	0.167626i
$161$	12.8568			1.01326
$162$	−7.25779	+	4.19029i	−0.570226	+	0.329220i
$163$	−11.7127	+	6.76234i	−0.917411	+	0.529668i	−0.882808	−	0.469734i	$-0.844350\pi$
$163$	−11.7127	+	6.76234i	−0.917411	+	0.529668i	−0.0346029	+	0.999401i	$0.511017\pi$
$164$	−7.50659			−0.586166
$165$	−7.66480	+	22.8864i	−0.596704	+	1.78170i
$166$	6.66902	−	11.5511i	0.517616	−	0.896538i
$167$	20.2858	+	11.7120i	1.56977	+	0.906304i	0.996195	+	0.0871479i	$0.0277753\pi$
$167$	20.2858	+	11.7120i	1.56977	+	0.906304i	0.573570	+	0.819157i	$0.305558\pi$
$168$		−	3.02539i		−	0.233414i
$169$	−5.15268	+	11.9352i	−0.396360	+	0.918095i
$170$	−0.806063	+	0.712742i	−0.0618222	+	0.0546648i
$171$	−0.609665	+	1.05597i	−0.0466222	+	0.0807520i
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	−4.00480	+	2.31217i	−0.304479	+	0.175791i	−0.644453	−	0.764644i	$-0.722915\pi$
$173$	−4.00480	+	2.31217i	−0.304479	+	0.175791i	0.339974	+	0.940435i	$0.389582\pi$
$174$	3.87399			0.293687
$175$	3.52377	+	8.31443i	0.266372	+	0.628512i
$176$	−3.22179	−	5.58031i	−0.242852	−	0.420631i
$177$		−	11.0132i		−	0.827801i
$178$	1.00141	−	0.578163i	0.0750586	−	0.0433351i
$179$	−4.15633	+	7.19897i	−0.310658	+	0.538076i	−0.978505	−	0.206223i	$-0.933883\pi$
$179$	−4.15633	+	7.19897i	−0.310658	+	0.538076i	0.667847	+	0.744299i	$0.267216\pi$
$180$	0.0863379	+	0.424974i	0.00643525	+	0.0316757i
$181$	−1.02539			−0.0762168			−0.0381084	−	0.999274i	$-0.512133\pi$
$181$	−1.02539			−0.0762168			−0.0381084	+	0.999274i	$0.512133\pi$
$182$	3.57749	+	5.44112i	0.265181	+	0.403323i
$183$		−	18.3430i		−	1.35595i
$184$	−3.55936	+	6.16499i	−0.262399	+	0.454489i
$185$	−6.71197	+	1.36361i	−0.493474	+	0.100254i
$186$	2.72790	+	4.72486i	0.200019	+	0.346444i
$187$		−	3.10062i		−	0.226739i
$188$	1.90000	−	1.09697i	0.138572	−	0.0800046i
$189$	−4.83146	−	8.36833i	−0.351437	−	0.608706i
$190$	−9.31265	−	10.5320i	−0.675611	−	0.764070i
$191$	−0.177593	−	0.307600i	−0.0128502	−	0.0222572i	0.859529	−	0.511087i	$-0.170757\pi$
$191$	−0.177593	−	0.307600i	−0.0128502	−	0.0222572i	−0.872379	+	0.488830i	$0.837424\pi$
$192$	1.45071	+	0.837565i	0.104696	+	0.0604461i
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.868255	+	0.496119i	$0.834758\pi$
$194$	13.8315			0.993041
$195$	9.51775	+	9.58157i	0.681580	+	0.686151i
$196$	−3.73813			−0.267010
$197$	−12.2166	−	7.05325i	−0.870396	−	0.502523i	−0.00291585	−	0.999996i	$-0.500928\pi$
$197$	−12.2166	−	7.05325i	−0.870396	−	0.502523i	−0.867480	+	0.497473i	$0.834261\pi$
$198$	−1.08223	−	0.624823i	−0.0769104	−	0.0444042i
$199$	−1.57452	−	2.72714i	−0.111614	−	0.193322i	0.804807	−	0.593537i	$-0.202269\pi$
$199$	−1.57452	−	2.72714i	−0.111614	−	0.193322i	−0.916421	+	0.400215i	$0.868935\pi$
$200$	−4.96239	−	0.612127i	−0.350894	−	0.0432839i
$201$	−0.544198	−	0.942579i	−0.0383848	−	0.0664844i
$202$	−8.31376	+	4.79995i	−0.584954	+	0.337724i
$203$			4.17679i			0.293153i
$204$	0.403032	+	0.698071i	0.0282179	+	0.0488748i
$205$	−3.34183	−	16.4492i	−0.233404	−	1.14886i
$206$	1.53761	−	2.66322i	0.107130	−	0.185555i
$207$			1.38058i			0.0959569i
$208$	−3.59948	+	0.209095i	−0.249579	+	0.0144981i
$209$	40.5125			2.80231
$210$	6.62955	−	1.34686i	0.457483	−	0.0929424i
$211$	−1.54666	+	2.67889i	−0.106477	+	0.184423i	−0.914340	−	0.404946i	$-0.867290\pi$
$211$	−1.54666	+	2.67889i	−0.106477	+	0.184423i	0.807864	+	0.589369i	$0.200624\pi$
$212$	0.785207	−	0.453339i	0.0539282	−	0.0311355i
$213$			6.13586i			0.420422i
$214$	0.837565	+	1.45071i	0.0572548	+	0.0991682i
$215$	1.42022	−	4.24063i	0.0968580	−	0.289209i
$216$	5.35026			0.364039
$217$	−5.09417	+	2.94112i	−0.345815	+	0.199656i
$218$	9.42856	+	5.44358i	0.638583	+	0.368686i
$219$	−2.18370	+	3.78228i	−0.147561	+	0.255583i
$220$	10.7938	−	9.54420i	0.727721	−	0.643470i
$221$	−1.55031	−	0.778890i	−0.104285	−	0.0523938i
$222$			5.13093i			0.344366i
$223$	−19.2205	−	11.0970i	−1.28710	−	0.743108i	−0.308965	−	0.951074i	$-0.599982\pi$
$223$	−19.2205	−	11.0970i	−1.28710	−	0.743108i	−0.978136	+	0.207966i	$0.933316\pi$
$224$	−0.903032	+	1.56410i	−0.0603363	+	0.104506i
$225$	−0.892810	+	0.378385i	−0.0595207	+	0.0252257i
$226$	−14.0000			−0.931266
$227$	11.5490	−	6.66784i	0.766536	−	0.442560i	−0.0651014	−	0.997879i	$-0.520737\pi$
$227$	11.5490	−	6.66784i	0.766536	−	0.442560i	0.831638	+	0.555319i	$0.187404\pi$
$228$	−9.12096	+	5.26599i	−0.604050	+	0.348749i
$229$	−26.1744			−1.72965			−0.864827	−	0.502069i	$-0.832572\pi$
$229$	−26.1744			−1.72965			−0.864827	+	0.502069i	$0.832572\pi$
$230$	−15.0939	−	5.05506i	−0.995264	−	0.333321i
$231$	−9.74718	+	16.8826i	−0.641318	+	1.11079i
$232$	−2.00281	−	1.15633i	−0.131491	−	0.0759165i
$233$			20.8691i			1.36718i	0.729867	+	0.683589i	$0.239582\pi$
$233$			20.8691i			1.36718i	−0.729867	+	0.683589i	$0.760418\pi$
$234$	−0.584272	+	0.384154i	−0.0381951	+	0.0251129i
$235$	3.24965	+	3.67513i	0.211984	+	0.239739i
$236$	−3.28726	+	5.69370i	−0.213982	+	0.370628i
$237$	−3.32872	−	1.92184i	−0.216224	−	0.124837i
$238$	−0.752634	+	0.434534i	−0.0487860	+	0.0281666i
$239$	15.2931			0.989231			0.494615	−	0.869112i	$-0.335309\pi$
$239$	15.2931			0.989231			0.494615	+	0.869112i	$0.335309\pi$
$240$	−1.18953	+	3.55181i	−0.0767835	+	0.229268i
$241$	6.38423	+	11.0578i	0.411244	+	0.712296i	0.995026	−	0.0996147i	$-0.0317610\pi$
$241$	6.38423	+	11.0578i	0.411244	+	0.712296i	−0.583782	+	0.811910i	$0.698428\pi$
$242$			30.5198i			1.96188i
$243$	1.74263	−	1.00611i	0.111790	−	0.0645419i
$244$	−5.47508	+	9.48313i	−0.350506	+	0.607095i
$245$	−1.66417	−	8.19139i	−0.106320	−	0.523328i
$246$	−12.5745			−0.801722
$247$	10.1769	−	20.2562i	0.647543	−	1.28887i
$248$		−	3.25694i		−	0.206816i
$249$	11.1715	−	19.3496i	0.707964	−	1.22623i
$250$	−0.867833	−	11.1466i	−0.0548866	−	0.704973i
$251$	2.10602	+	3.64773i	0.132931	+	0.230243i	0.924805	−	0.380441i	$-0.124228\pi$
$251$	2.10602	+	3.64773i	0.132931	+	0.230243i	−0.791874	+	0.610684i	$0.790895\pi$
$252$			0.350262i			0.0220644i
$253$	39.7246	−	22.9350i	2.49746	−	1.44191i
$254$	2.59332	+	4.49176i	0.162719	+	0.281838i
$255$	−1.35026	+	1.19394i	−0.0845567	+	0.0747672i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.1300	+	9.31265i	1.00616	+	0.580907i	0.910065	−	0.414465i	$-0.136031\pi$
$257$	16.1300	+	9.31265i	1.00616	+	0.580907i	0.0960955	+	0.995372i	$0.469365\pi$
$258$	−2.90141	−	1.67513i	−0.180634	−	0.104289i
$259$	−5.53198			−0.343740
$260$	−2.06063	−	7.79447i	−0.127795	−	0.483393i
$261$	−0.448507			−0.0277619
$262$	9.35406	+	5.40057i	0.577896	+	0.333648i
$263$	19.9363	+	11.5102i	1.22933	+	0.709751i	0.966889	−	0.255198i	$-0.0821406\pi$
$263$	19.9363	+	11.5102i	1.22933	+	0.709751i	0.262437	+	0.964949i	$0.415474\pi$
$264$	−5.39692	−	9.34774i	−0.332158	−	0.575314i
$265$	1.34297	+	1.51881i	0.0824978	+	0.0932995i
$266$	−5.67759	−	9.83388i	−0.348116	−	0.602954i
$267$	1.67749	−	0.968498i	0.102661	−	0.0592711i
$268$			0.649738i			0.0396891i
$269$	−6.73695	−	11.6687i	−0.410759	−	0.711456i	0.584214	−	0.811600i	$-0.301403\pi$
$269$	−6.73695	−	11.6687i	−0.410759	−	0.711456i	−0.994973	+	0.100144i	$0.968070\pi$
$270$	2.38186	+	11.7240i	0.144956	+	0.713503i
$271$	8.95017	−	15.5021i	0.543684	−	0.941688i	−0.455004	−	0.890489i	$-0.650362\pi$
$271$	8.95017	−	15.5021i	0.543684	−	0.941688i	0.998688	−	0.0511993i	$-0.0163044\pi$
$272$		−	0.481194i		−	0.0291767i
$273$	5.99277	+	9.11459i	0.362699	+	0.551640i
$274$	−6.14411			−0.371179
$275$	25.7195	+	19.4036i	1.55094	+	1.17008i
$276$	−5.96239	+	10.3272i	−0.358894	+	0.621622i
$277$	−7.35125	+	4.24424i	−0.441694	+	0.255012i	−0.704316	−	0.709887i	$-0.748746\pi$
$277$	−7.35125	+	4.24424i	−0.441694	+	0.255012i	0.262622	+	0.964899i	$0.415413\pi$
$278$		−	10.3380i		−	0.620035i
$279$	−0.315820	−	0.547016i	−0.0189076	−	0.0327490i
$280$	−3.82943	−	1.28250i	−0.228852	−	0.0766441i
$281$	−16.5296			−0.986074			−0.493037	−	0.870008i	$-0.664113\pi$
$281$	−16.5296			−0.986074			−0.493037	+	0.870008i	$0.664113\pi$
$282$	3.18276	−	1.83757i	0.189530	−	0.109425i
$283$	−1.33100	−	0.768452i	−0.0791196	−	0.0456797i	0.459918	−	0.887961i	$-0.347879\pi$
$283$	−1.33100	−	0.768452i	−0.0791196	−	0.0456797i	−0.539038	+	0.842282i	$0.681212\pi$
$284$	1.83146	−	3.17217i	0.108677	−	0.188234i
$285$	−15.5999	−	17.6424i	−0.924059	−	1.04505i
$286$	20.7599	+	10.4300i	1.22756	+	0.616737i
$287$		−	13.5574i		−	0.800266i
$288$	−0.167954	−	0.0969683i	−0.00989678	−	0.00571391i
$289$	−8.38423	+	14.5219i	−0.493190	+	0.854230i
$290$	1.64223	−	4.90355i	0.0964353	−	0.287947i
$291$	23.1695			1.35822
$292$	2.25790	−	1.30360i	0.132134	−	0.0762875i
$293$	5.13527	−	2.96485i	0.300006	−	0.173208i	−0.342440	−	0.939540i	$-0.611253\pi$
$293$	5.13527	−	2.96485i	0.300006	−	0.173208i	0.642446	+	0.766331i	$0.277920\pi$
$294$	−6.26187			−0.365199
$295$	−13.9401	−	4.66862i	−0.811622	−	0.271818i
$296$	1.53150	−	2.65264i	0.0890167	−	0.154182i
$297$	−29.8561	−	17.2374i	−1.73243	−	1.00022i
$298$			16.0508i			0.929797i
$299$	−1.48849	−	25.6237i	−0.0860815	−	1.48186i
$300$	−8.31265	−	1.02539i	−0.479931	−	0.0592011i
$301$	1.80606	−	3.12819i	0.104100	−	0.180306i
$302$	−8.06926	−	4.65879i	−0.464334	−	0.268083i
$303$	−13.9266	+	8.04055i	−0.800065	+	0.461918i
$304$	6.28726			0.360599
$305$	−23.2178	−	7.77581i	−1.32945	−	0.445242i
$306$	−0.0466606	−	0.0808185i	−0.00266741	−	0.00462009i
$307$		−	17.9756i		−	1.02592i	−0.858413	−	0.512960i	$-0.828549\pi$
$307$		−	17.9756i		−	1.02592i	0.858413	−	0.512960i	$-0.171451\pi$
$308$	10.0784	−	5.81876i	0.574269	−	0.331555i
$309$	2.57570	−	4.46124i	0.146526	−	0.253791i
$310$	7.13694	−	1.44995i	0.405351	−	0.0823514i
$311$	15.9575			0.904865			0.452432	−	0.891799i	$-0.350556\pi$
$311$	15.9575			0.904865			0.452432	+	0.891799i	$0.350556\pi$
$312$	−6.02961	+	0.350262i	−0.341359	+	0.0198297i
$313$			23.4372i			1.32475i	0.749172	+	0.662376i	$0.230452\pi$
$313$			23.4372i			1.32475i	−0.749172	+	0.662376i	$0.769548\pi$
$314$	7.37812	−	12.7793i	0.416371	−	0.721176i
$315$	−0.767530	+	0.155932i	−0.0432454	+	0.00878576i
$316$	1.14728	+	1.98714i	0.0645393	+	0.111785i
$317$		−	20.6507i		−	1.15986i	−0.814667	−	0.579929i	$-0.803080\pi$
$317$		−	20.6507i		−	1.15986i	0.814667	−	0.579929i	$-0.196920\pi$
$318$	1.31532	−	0.759403i	0.0737597	−	0.0425852i
$319$	7.45088	+	12.9053i	0.417169	+	0.722558i
$320$	1.67513	−	1.48119i	0.0936427	−	0.0828013i
$321$	1.40303	+	2.43012i	0.0783096	+	0.135636i
$322$	−11.1344	−	6.42842i	−0.620493	−	0.358242i
$323$	2.62007	+	1.51270i	0.145784	+	0.0841687i
$324$	8.38058			0.465588
$325$	16.1627	−	7.98546i	0.896544	−	0.442954i
$326$	13.5247			0.749063
$327$	15.7941	+	9.11871i	0.873414	+	0.504266i
$328$	6.50089	+	3.75329i	0.358952	+	0.207241i
$329$	1.98119	+	3.43153i	0.109227	+	0.189186i
$330$	18.0811	−	15.9878i	0.995332	−	0.880098i
$331$	13.3380	+	23.1022i	0.733125	+	1.26981i	0.955541	+	0.294858i	$0.0952724\pi$
$331$	13.3380	+	23.1022i	0.733125	+	1.26981i	−0.222416	+	0.974952i	$0.571394\pi$
$332$	−11.5511	+	6.66902i	−0.633948	+	0.366010i
$333$		−	0.594028i		−	0.0325526i
$334$	−11.7120	−	20.2858i	−0.640854	−	1.10999i
$335$	−1.42377	+	0.289255i	−0.0777891	+	0.0158037i
$336$	−1.51270	+	2.62007i	−0.0825243	+	0.142936i
$337$		−	8.40597i		−	0.457902i	−0.973438	−	0.228951i	$-0.926470\pi$
$337$		−	8.40597i		−	0.457902i	0.973438	−	0.228951i	$-0.0735296\pi$
$338$	10.4300	−	7.75988i	0.567316	−	0.422082i
$339$	−23.4518			−1.27373
$340$	1.05444	−	0.214221i	0.0571852	−	0.0116178i
$341$	−10.4932	+	18.1747i	−0.568238	+	0.984217i
$342$	1.05597	−	0.609665i	0.0571003	−	0.0329669i
$343$		−	19.3938i		−	1.04716i
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	−25.2843	−	8.46789i	−1.36126	−	0.455896i
$346$	4.62435			0.248606
$347$	−18.3177	+	10.5757i	−0.983343	+	0.567733i	−0.903278	−	0.429056i	$-0.858846\pi$
$347$	−18.3177	+	10.5757i	−0.983343	+	0.567733i	−0.0800652	+	0.996790i	$0.525513\pi$
$348$	−3.35498	−	1.93700i	−0.179846	−	0.103834i
$349$	2.73695	−	4.74054i	0.146506	−	0.253755i	−0.783428	−	0.621482i	$-0.786531\pi$
$349$	2.73695	−	4.74054i	0.146506	−	0.253755i	0.929934	+	0.367727i	$0.119864\pi$
$350$	1.10554	−	8.96239i	0.0590936	−	0.479060i
$351$	−16.1187	+	10.5979i	−0.860353	+	0.565675i
$352$			6.44358i			0.343444i
$353$	−26.1056	−	15.0721i	−1.38946	−	0.802204i	−0.396205	−	0.918162i	$-0.629673\pi$
$353$	−26.1056	−	15.0721i	−1.38946	−	0.802204i	−0.993254	+	0.115958i	$0.963006\pi$
$354$	−5.50659	+	9.53769i	−0.292672	+	0.506922i
$355$	7.76654	+	2.60107i	0.412205	+	0.138050i
$356$	−1.15633			−0.0612851
$357$	−1.26076	+	0.727901i	−0.0667266	+	0.0385246i
$358$	7.19897	−	4.15633i	0.380477	−	0.219669i
$359$	8.38787			0.442695			0.221348	−	0.975195i	$-0.428954\pi$
$359$	8.38787			0.442695			0.221348	+	0.975195i	$0.428954\pi$
$360$	0.137716	−	0.411207i	0.00725827	−	0.0216725i
$361$	−10.2648	+	17.7792i	−0.540253	+	0.935745i
$362$	0.888016	+	0.512696i	0.0466731	+	0.0269467i
$363$			51.1246i			2.68335i
$364$	−0.377639	−	6.50089i	−0.0197937	−	0.340739i
$365$	3.86177	+	4.36741i	0.202134	+	0.228600i
$366$	−9.17148	+	15.8855i	−0.479401	+	0.830347i
$367$	16.8983	+	9.75623i	0.882084	+	0.509271i	0.871345	−	0.490671i	$-0.163248\pi$
$367$	16.8983	+	9.75623i	0.882084	+	0.509271i	0.0107388	+	0.999942i	$0.496582\pi$
$368$	6.16499	−	3.55936i	0.321372	−	0.185544i
$369$	1.45580			0.0757860
$370$	6.49454	+	2.17507i	0.337635	+	0.113076i
$371$	0.818760	+	1.41813i	0.0425079	+	0.0736258i
$372$		−	5.45580i		−	0.282870i
$373$	7.37324	−	4.25694i	0.381772	−	0.220416i	−0.296817	−	0.954934i	$-0.595925\pi$
$373$	7.37324	−	4.25694i	0.381772	−	0.220416i	0.678589	+	0.734518i	$0.262592\pi$
$374$	−1.55031	+	2.68521i	−0.0801645	+	0.138849i
$375$	−1.45373	−	18.6720i	−0.0750705	−	0.964219i
$376$	−2.19394			−0.113144
$377$	8.32435	−	0.483564i	0.428726	−	0.0249048i
$378$			9.66291i			0.497007i
$379$	−9.85931	+	17.0768i	−0.506439	+	0.877178i	0.493533	+	0.869727i	$0.335705\pi$
$379$	−9.85931	+	17.0768i	−0.506439	+	0.877178i	−0.999972	+	0.00745089i	$0.997628\pi$
$380$	2.79900	+	13.7773i	0.143586	+	0.706760i
$381$	4.34415	+	7.52429i	0.222558	+	0.385481i
$382$			0.355186i			0.0181729i
$383$	−24.0059	+	13.8598i	−1.22664	+	0.708202i	−0.966326	−	0.257321i	$-0.917160\pi$
$383$	−24.0059	+	13.8598i	−1.22664	+	0.708202i	−0.260316	+	0.965523i	$0.583827\pi$
$384$	−0.837565	−	1.45071i	−0.0427418	−	0.0740310i
$385$	17.2374	+	19.4944i	0.878501	+	0.993525i
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	0.335908	+	0.193937i	0.0170752	+	0.00985835i
$388$	−11.9784	−	6.91573i	−0.608111	−	0.351093i
$389$	−9.15140			−0.463994			−0.231997	−	0.972716i	$-0.574526\pi$
$389$	−9.15140			−0.463994			−0.231997	+	0.972716i	$0.574526\pi$
$390$	−3.45183	−	13.0568i	−0.174790	−	0.661155i
$391$	3.42548			0.173234
$392$	3.23732	+	1.86907i	0.163509	+	0.0944022i
$393$	15.6693	+	9.04666i	0.790410	+	0.456344i
$394$	7.05325	+	12.2166i	0.355337	+	0.615463i
$395$	−3.84367	+	3.39868i	−0.193396	+	0.171006i
$396$	0.624823	+	1.08223i	0.0313985	+	0.0543839i
$397$	1.23877	−	0.715205i	0.0621721	−	0.0358951i	−0.468592	−	0.883415i	$-0.655238\pi$
$397$	1.23877	−	0.715205i	0.0621721	−	0.0358951i	0.530764	+	0.847520i	$0.321905\pi$
$398$			3.14903i			0.157847i
$399$	−9.51071	−	16.4730i	−0.476131	−	0.824683i
$400$	3.99149	+	3.01131i	0.199575	+	0.150566i
$401$	−10.8351	+	18.7669i	−0.541079	+	0.937177i	0.457763	+	0.889074i	$0.348651\pi$
$401$	−10.8351	+	18.7669i	−0.541079	+	0.937177i	−0.998842	+	0.0481025i	$0.984683\pi$
$402$			1.08840i			0.0542843i
$403$	6.45142	+	9.81217i	0.321368	+	0.488779i
$404$	9.59991			0.477613
$405$	3.73092	+	18.3644i	0.185391	+	0.912534i
$406$	2.08840	−	3.61721i	0.103645	−	0.179519i
$407$	−17.0925	+	9.86836i	−0.847244	+	0.489156i
$408$		−	0.806063i		−	0.0399061i
$409$	4.54055	+	7.86447i	0.224516	+	0.388873i	0.956174	−	0.292799i	$-0.0945866\pi$
$409$	4.54055	+	7.86447i	0.224516	+	0.388873i	−0.731658	+	0.681672i	$0.761253\pi$
$410$	−5.33049	+	15.9163i	−0.263254	+	0.786052i
$411$	−10.2922			−0.507676
$412$	−2.66322	+	1.53761i	−0.131207	+	0.0757527i
$413$	−10.2832	−	5.93700i	−0.506002	−	0.292140i
$414$	0.690289	−	1.19562i	0.0339259	−	0.0587613i
$415$	−19.7562	−	22.3430i	−0.969795	−	1.09677i
$416$	3.22179	+	1.61866i	0.157961	+	0.0793613i
$417$		−	17.3176i		−	0.848045i
$418$	−35.0848	−	20.2562i	−1.71605	−	0.990765i
$419$	−7.77139	+	13.4604i	−0.379657	+	0.657586i	−0.991012	−	0.133771i	$-0.957291\pi$
$419$	−7.77139	+	13.4604i	−0.379657	+	0.657586i	0.611355	+	0.791356i	$0.290625\pi$
$420$	−6.41479	−	2.14836i	−0.313010	−	0.104829i
$421$	−4.96476			−0.241968			−0.120984	−	0.992654i	$-0.538605\pi$
$421$	−4.96476			−0.241968			−0.120984	+	0.992654i	$0.538605\pi$
$422$	2.67889	−	1.54666i	0.130407	−	0.0752903i
$423$	−0.368480	+	0.212742i	−0.0179161	+	0.0103439i
$424$	−0.906679			−0.0440322
$425$	0.938847	+	2.21523i	0.0455408	+	0.107455i
$426$	3.06793	−	5.31381i	0.148642	−	0.257455i
$427$	−17.1271	−	9.88835i	−0.828840	−	0.478531i
$428$		−	1.67513i		−	0.0809705i
$429$	34.7755	+	17.4716i	1.67898	+	0.843535i
$430$	−3.35026	+	2.96239i	−0.161564	+	0.142859i
$431$	16.4853	−	28.5534i	0.794070	−	1.37537i	−0.129358	−	0.991598i	$-0.541292\pi$
$431$	16.4853	−	28.5534i	0.794070	−	1.37537i	0.923428	−	0.383771i	$-0.125375\pi$
$432$	−4.63346	−	2.67513i	−0.222928	−	0.128707i
$433$	13.9529	−	8.05571i	0.670534	−	0.387133i	−0.125745	−	0.992063i	$-0.540132\pi$
$433$	13.9529	−	8.05571i	0.670534	−	0.387133i	0.796279	+	0.604930i	$0.206799\pi$
$434$	5.88224			0.282357
$435$	2.75096	−	8.21409i	0.131898	−	0.393836i
$436$	−5.44358	−	9.42856i	−0.260700	−	0.451546i
$437$			44.7572i			2.14103i
$438$	3.78228	−	2.18370i	0.180725	−	0.104341i
$439$	−0.0417360	+	0.0722889i	−0.00199195	+	0.00345016i	−0.867020	−	0.498274i	$-0.833967\pi$
$439$	−0.0417360	+	0.0722889i	−0.00199195	+	0.00345016i	0.865028	+	0.501724i	$0.167301\pi$
$440$	−14.1198	+	2.86860i	−0.673137	+	0.136755i
$441$	0.724961			0.0345220
$442$	0.953161	+	1.44969i	0.0453372	+	0.0689548i
$443$		−	40.9135i		−	1.94386i	−0.235271	−	0.971930i	$-0.575598\pi$
$443$		−	40.9135i		−	1.94386i	0.235271	−	0.971930i	$-0.424402\pi$
$444$	2.56547	−	4.44352i	0.121752	−	0.210880i
$445$	−0.514780	−	2.53386i	−0.0244029	−	0.120116i
$446$	11.0970	+	19.2205i	0.525457	+	0.910118i
$447$			26.8872i			1.27172i
$448$	1.56410	−	0.903032i	0.0738966	−	0.0426642i
$449$	−14.5659	−	25.2290i	−0.687409	−	1.19063i	−0.972673	−	0.232179i	$-0.925415\pi$
$449$	−14.5659	−	25.2290i	−0.687409	−	1.19063i	0.285264	−	0.958449i	$-0.407919\pi$
$450$	0.962389	+	0.118714i	0.0453674	+	0.00559622i
$451$	−24.1847	−	41.8891i	−1.13881	−	1.97248i
$452$	12.1244	+	7.00000i	0.570282	+	0.329252i
$453$	−13.5171	−	7.80408i	−0.635087	−	0.366668i
$454$	−13.3357			−0.625874
$455$	14.0773	−	3.72163i	0.659955	−	0.174473i
$456$	10.5320			0.493205
$457$	28.2912	+	16.3339i	1.32341	+	0.764068i	0.984270	−	0.176669i	$-0.0565323\pi$
$457$	28.2912	+	16.3339i	1.32341	+	0.764068i	0.339135	+	0.940738i	$0.389866\pi$
$458$	22.6677	+	13.0872i	1.05919	+	0.611525i
$459$	−1.28726	−	2.22960i	−0.0600840	−	0.104069i
$460$	10.5442	+	11.9248i	0.491626	+	0.555996i
$461$	9.55031	+	16.5416i	0.444802	+	0.770420i	0.998038	−	0.0626044i	$-0.0199407\pi$
$461$	9.55031	+	16.5416i	0.444802	+	0.770420i	−0.553236	+	0.833024i	$0.686607\pi$
$462$	16.8826	−	9.74718i	0.785450	−	0.453480i
$463$		−	8.29218i		−	0.385370i	−0.981261	−	0.192685i	$-0.938280\pi$
$463$		−	8.29218i		−	0.385370i	0.981261	−	0.192685i	$-0.0617196\pi$
$464$	1.15633	+	2.00281i	0.0536810	+	0.0929783i
$465$	11.9553	−	2.42885i	0.554414	−	0.112635i
$466$	10.4345	−	18.0731i	0.483370	−	0.837222i
$467$		−	23.5369i		−	1.08916i	−0.838710	−	0.544579i	$-0.816689\pi$
$467$		−	23.5369i		−	1.08916i	0.838710	−	0.544579i	$-0.183311\pi$
$468$	0.698071	−	0.0405512i	0.0322684	−	0.00187448i
$469$	−1.17347			−0.0541857
$470$	−0.976711	−	4.80758i	−0.0450523	−	0.221757i
$471$	12.3593	−	21.4070i	0.569487	−	0.986380i
$472$	5.69370	−	3.28726i	0.262074	−	0.151308i
$473$		−	12.8872i		−	0.592553i
$474$	1.92184	+	3.32872i	0.0882729	+	0.152893i
$475$	−28.9441	+	12.2669i	−1.32805	+	0.562845i
$476$	0.869067			0.0398336
$477$	−0.152280	+	0.0879191i	−0.00697244	+	0.00402554i
$478$	−13.2442	−	7.64657i	−0.605778	−	0.349746i
$479$	3.27821	−	5.67802i	0.149785	−	0.259436i	−0.781363	−	0.624077i	$-0.785475\pi$
$479$	3.27821	−	5.67802i	0.149785	−	0.259436i	0.931148	+	0.364642i	$0.118808\pi$
$480$	2.80606	−	2.48119i	0.128079	−	0.113251i
$481$	0.640459	+	11.0252i	0.0292024	+	0.502707i
$482$		−	12.7685i		−	0.581587i
$483$	−18.6515	−	10.7685i	−0.848673	−	0.489982i
$484$	15.2599	−	26.4309i	0.693631	−	1.20140i
$485$	9.82184	−	29.3271i	0.445987	−	1.33167i
$486$	−2.01222			−0.0912761
$487$	−11.7432	+	6.77996i	−0.532137	+	0.307229i	−0.741886	−	0.670526i	$-0.766069\pi$
$487$	−11.7432	+	6.77996i	−0.532137	+	0.307229i	0.209749	+	0.977755i	$0.432735\pi$
$488$	9.48313	−	5.47508i	0.429281	−	0.247845i
$489$	22.6556			1.02452
$490$	−2.65448	+	7.92603i	−0.119917	+	0.358062i
$491$	−2.47873	+	4.29329i	−0.111864	+	0.193753i	−0.916522	−	0.399985i	$-0.869015\pi$
$491$	−2.47873	+	4.29329i	−0.111864	+	0.193753i	0.804658	+	0.593739i	$0.202349\pi$
$492$	10.8898	+	6.28726i	0.490952	+	0.283451i
$493$			1.11283i			0.0501195i
$494$	−18.9416	+	12.4539i	−0.852223	+	0.560330i
$495$	−2.09332	+	1.85097i	−0.0940878	+	0.0831949i
$496$	−1.62847	+	2.82059i	−0.0731205	+	0.126648i
$497$	5.72915	+	3.30773i	0.256987	+	0.148372i
$498$	−19.3496	+	11.1715i	−0.867075	+	0.500606i
$499$	13.8700			0.620907			0.310454	−	0.950588i	$-0.399519\pi$
$499$	13.8700			0.620907			0.310454	+	0.950588i	$0.399519\pi$
$500$	−4.82174	+	10.0872i	−0.215635	+	0.451112i
$501$	−19.6192	−	33.9814i	−0.876521	−	1.51818i
$502$		−	4.21203i		−	0.187992i
$503$	2.98650	−	1.72425i	0.133161	−	0.0768807i	−0.431940	−	0.901903i	$-0.642171\pi$
$503$	2.98650	−	1.72425i	0.133161	−	0.0768807i	0.565101	+	0.825022i	$0.308837\pi$
$504$	0.175131	−	0.303336i	0.00780095	−	0.0135116i
$505$	4.27375	+	21.0363i	0.190179	+	0.936103i
$506$	−45.8700			−2.03917
$507$	17.4716	−	12.9988i	0.775939	−	0.577298i
$508$		−	5.18664i		−	0.230120i
$509$	−15.4812	+	26.8142i	−0.686192	+	1.18852i	0.286869	+	0.957970i	$0.407386\pi$
$509$	−15.4812	+	26.8142i	−0.686192	+	1.18852i	−0.973061	+	0.230549i	$0.925948\pi$
$510$	1.76633	−	0.358849i	0.0782144	−	0.0158901i
$511$	2.35439	+	4.07792i	0.104152	+	0.180396i
$512$			1.00000i			0.0441942i
$513$	29.1318	−	16.8192i	1.28620	−	0.742587i
$514$	−9.31265	−	16.1300i	−0.410763	−	0.711463i
$515$	−4.55500	−	5.15140i	−0.200717	−	0.226998i
$516$	1.67513	+	2.90141i	0.0737435	+	0.127728i
$517$	12.2428	+	7.06841i	0.538439	+	0.310868i
$518$	4.79083	+	2.76599i	0.210497	+	0.121531i
$519$	7.74638			0.340029
$520$	−2.11268	+	7.78053i	−0.0926470	+	0.341199i
$521$	14.2506			0.624330			0.312165	−	0.950028i	$-0.398946\pi$
$521$	14.2506			0.624330			0.312165	+	0.950028i	$0.398946\pi$
$522$	0.388419	+	0.224254i	0.0170006	+	0.00981532i
$523$	9.10529	+	5.25694i	0.398146	+	0.229870i	0.685684	−	0.727899i	$-0.259503\pi$
$523$	9.10529	+	5.25694i	0.398146	+	0.229870i	−0.287537	+	0.957769i	$0.592837\pi$
$524$	−5.40057	−	9.35406i	−0.235925	−	0.408634i
$525$	1.85192	−	15.0132i	0.0808246	−	0.655229i
$526$	−11.5102	−	19.9363i	−0.501870	−	0.869264i
$527$	−1.35725	+	0.783611i	−0.0591229	+	0.0341346i
$528$			10.7938i			0.469742i
$529$	13.8380	+	23.9682i	0.601654	+	1.04210i
$530$	−0.403641	−	1.98681i	−0.0175331	−	0.0863014i
$531$	0.637519	−	1.10422i	0.0276660	−	0.0479189i
$532$			11.3552i			0.492310i
$533$	−27.0198	+	1.56959i	−1.17036	+	0.0679865i
$534$	−1.93700			−0.0838220
$535$	3.67072	−	0.745746i	0.158699	−	0.0322414i
$536$	0.324869	−	0.562690i	0.0140322	−	0.0243045i
$537$	12.0592	−	6.96239i	0.520393	−	0.300449i
$538$			13.4739i			0.580901i
$539$	−12.0435	−	20.8599i	−0.518750	−	0.898501i
$540$	3.79927	−	11.3443i	0.163494	−	0.488179i
$541$	15.5345			0.667882			0.333941	−	0.942594i	$-0.391621\pi$
$541$	15.5345			0.667882			0.333941	+	0.942594i	$0.391621\pi$
$542$	−15.5021	+	8.95017i	−0.665874	+	0.384443i
$543$	1.48754	+	0.858833i	0.0638366	+	0.0368561i
$544$	−0.240597	+	0.416726i	−0.0103155	+	0.0178670i
$545$	18.2374	−	16.1260i	0.781206	−	0.690762i
$546$	−0.632595	−	10.8898i	−0.0270726	−	0.466043i
$547$			23.5515i			1.00699i	0.863998	+	0.503495i	$0.167953\pi$
$547$			23.5515i			1.00699i	−0.863998	+	0.503495i	$0.832047\pi$
$548$	5.32095	+	3.07205i	0.227300	+	0.131232i
$549$	1.06182	−	1.83912i	0.0453173	−	0.0784919i
$550$	−12.5719	−	29.6638i	−0.536069	−	1.26487i
$551$	−14.5402			−0.619435
$552$	10.3272	−	5.96239i	0.439553	−	0.253776i
$553$	−3.58890	+	2.07205i	−0.152616	+	0.0881127i
$554$	8.48849			0.360641
$555$	10.8792	+	3.64352i	0.461797	+	0.154659i
$556$	−5.16902	+	8.95301i	−0.219215	+	0.379692i
$557$	17.3602	+	10.0229i	0.735576	+	0.424685i	0.820459	−	0.571706i	$-0.193718\pi$
$557$	17.3602	+	10.0229i	0.735576	+	0.424685i	−0.0848824	+	0.996391i	$0.527051\pi$
$558$			0.631640i			0.0267394i
$559$	−6.44358	−	3.23732i	−0.272535	−	0.136924i
$560$	2.67513	+	3.02539i	0.113045	+	0.127846i
$561$	−2.59697	+	4.49808i	−0.109644	+	0.189909i
$562$	14.3151	+	8.26480i	0.603844	+	0.348630i
$563$	−10.8898	+	6.28726i	−0.458952	+	0.264976i	−0.711604	−	0.702581i	$-0.752031\pi$
$563$	−10.8898	+	6.28726i	−0.458952	+	0.264976i	0.252651	+	0.967557i	$0.418697\pi$
$564$	−3.67513			−0.154751
$565$	−9.94152	+	29.6844i	−0.418243	+	1.24883i
$566$	0.768452	+	1.33100i	0.0323004	+	0.0559460i
$567$			15.1359i			0.635646i
$568$	−3.17217	+	1.83146i	−0.133102	+	0.0768462i
$569$	2.14481	−	3.71493i	0.0899153	−	0.155738i	−0.817560	−	0.575844i	$-0.804674\pi$
$569$	2.14481	−	3.71493i	0.0899153	−	0.155738i	0.907475	+	0.420106i	$0.138007\pi$
$570$	4.68869	+	23.0788i	0.196388	+	0.966663i
$571$	6.39280			0.267530			0.133765	−	0.991013i	$-0.457293\pi$
$571$	6.39280			0.267530			0.133765	+	0.991013i	$0.457293\pi$
$572$	−12.7636	−	19.4126i	−0.533673	−	0.811680i
$573$			0.594984i			0.0248558i
$574$	−6.77869	+	11.7410i	−0.282937	+	0.490061i
$575$	−21.4367	+	28.4143i	−0.893971	+	1.18496i
$576$	0.0969683	+	0.167954i	0.00404035	+	0.00699808i
$577$		−	37.8169i		−	1.57434i	−0.616738	−	0.787168i	$-0.711546\pi$
$577$		−	37.8169i		−	1.57434i	0.616738	−	0.787168i	$-0.288454\pi$
$578$	14.5219	−	8.38423i	0.604032	−	0.348738i
$579$	11.7259	+	20.3099i	0.487312	+	0.844050i
$580$	−3.87399	+	3.42548i	−0.160859	+	0.142236i
$581$	−12.0447	−	20.8620i	−0.499697	−	0.865501i
$582$	−20.0654	−	11.5847i	−0.831737	−	0.480203i
$583$	5.05955	+	2.92113i	0.209545	+	0.120981i
$584$	−2.60720			−0.107887
$585$	0.399632	+	1.51163i	0.0165227	+	0.0624983i
$586$	−5.92970			−0.244954
$587$	−19.5289	−	11.2750i	−0.806046	−	0.465371i	0.0395351	−	0.999218i	$-0.487412\pi$
$587$	−19.5289	−	11.2750i	−0.806046	−	0.465371i	−0.845581	+	0.533848i	$0.820746\pi$
$588$	5.42293	+	3.13093i	0.223638	+	0.129117i
$589$	−10.2386	−	17.7338i	−0.421875	−	0.730708i
$590$	9.73813	+	11.0132i	0.400913	+	0.453405i
$591$	11.8151	+	20.4644i	0.486009	+	0.841792i
$592$	−2.65264	+	1.53150i	−0.109023	+	0.0629443i
$593$		−	8.38787i		−	0.344449i	−0.985058	−	0.172224i	$-0.944905\pi$
$593$		−	8.38787i		−	0.344449i	0.985058	−	0.172224i	$-0.0550954\pi$
$594$	17.2374	+	29.8561i	0.707260	+	1.22501i
$595$	0.386897	+	1.90439i	0.0158612	+	0.0780724i
$596$	8.02539	−	13.9004i	0.328733	−	0.569382i
$597$			5.27504i			0.215893i
$598$	−11.5228	+	22.9350i	−0.471201	+	0.937882i
$599$	−29.0884			−1.18852			−0.594260	−	0.804273i	$-0.702555\pi$
$599$	−29.0884			−1.18852			−0.594260	+	0.804273i	$0.702555\pi$
$600$	6.68627	+	5.04434i	0.272966	+	0.205934i
$601$	21.5059	−	37.2493i	0.877243	−	1.51943i	0.0228892	−	0.999738i	$-0.492713\pi$
$601$	21.5059	−	37.2493i	0.877243	−	1.51943i	0.854354	−	0.519692i	$-0.173953\pi$
$602$	−3.12819	+	1.80606i	−0.127496	+	0.0736097i
$603$		−	0.126008i		−	0.00513144i
$604$	4.65879	+	8.06926i	0.189563	+	0.328333i
$605$	64.7116	+	21.6723i	2.63090	+	0.881106i
$606$	16.0811			0.653250
$607$	18.8372	−	10.8757i	0.764578	−	0.441429i	−0.0663591	−	0.997796i	$-0.521138\pi$
$607$	18.8372	−	10.8757i	0.764578	−	0.441429i	0.830937	+	0.556367i	$0.187805\pi$
$608$	−5.44492	−	3.14363i	−0.220821	−	0.127491i
$609$	3.49834	−	6.05930i	0.141760	−	0.245535i
$610$	16.2193	+	18.3430i	0.656701	+	0.742685i
$611$	6.60966	−	4.34580i	0.267398	−	0.175812i
$612$			0.0933212i			0.00377228i
$613$	26.6848	+	15.4064i	1.07779	+	0.622261i	0.930299	−	0.366803i	$-0.119548\pi$
$613$	26.6848	+	15.4064i	1.07779	+	0.622261i	0.147488	+	0.989064i	$0.452881\pi$
$614$	−8.98778	+	15.5673i	−0.362717	+	0.628245i
$615$	−8.92927	+	26.6620i	−0.360063	+	1.07511i
$616$	−11.6375			−0.468889
$617$	−39.9125	+	23.0435i	−1.60682	+	0.927696i	−0.616740	+	0.787167i	$0.711547\pi$
$617$	−39.9125	+	23.0435i	−1.60682	+	0.927696i	−0.990077	+	0.140529i	$0.955120\pi$
$618$	−4.46124	+	2.57570i	−0.179458	+	0.103610i
$619$	13.5564			0.544878			0.272439	−	0.962173i	$-0.412170\pi$
$619$	13.5564			0.544878			0.272439	+	0.962173i	$0.412170\pi$
$620$	−6.90575	−	2.31278i	−0.277341	−	0.0928836i
$621$	19.0435	−	32.9843i	0.764189	−	1.32361i
$622$	−13.8196	−	7.97873i	−0.554114	−	0.319918i
$623$		−	2.08840i		−	0.0836698i
$624$	5.39692	+	2.71147i	0.216050	+	0.108546i
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	11.7186	−	20.2972i	0.468370	−	0.811241i
$627$	−58.7717	−	33.9318i	−2.34711	−	1.35511i
$628$	−12.7793	+	7.37812i	−0.509949	+	0.294419i
$629$	−1.47390			−0.0587682
$630$	0.742666	+	0.248724i	0.0295885	+	0.00990940i
$631$	2.67513	+	4.63346i	0.106495	+	0.184455i	0.914348	−	0.404929i	$-0.132704\pi$
$631$	2.67513	+	4.63346i	0.106495	+	0.184455i	−0.807853	+	0.589384i	$0.799370\pi$
$632$		−	2.29455i		−	0.0912724i
$633$	4.48750	−	2.59086i	0.178362	−	0.102977i
$634$	−10.3253	+	17.8840i	−0.410072	+	0.710265i
$635$	11.3655	−	2.30902i	0.451026	−	0.0916308i
$636$	−1.51881			−0.0602246
$637$	−13.4554	+	0.781626i	−0.533121	+	0.0309691i
$638$		−	14.9018i		−	0.589966i
$639$	−0.355186	+	0.615201i	−0.0140510	+	0.0243370i
$640$	−2.19130	+	0.445186i	−0.0866189	+	0.0175975i
$641$	−6.19029	−	10.7219i	−0.244502	−	0.423489i	0.717490	−	0.696569i	$-0.245291\pi$
$641$	−6.19029	−	10.7219i	−0.244502	−	0.423489i	−0.961991	+	0.273080i	$0.911958\pi$
$642$		−	2.80606i		−	0.110746i
$643$	−9.98067	+	5.76234i	−0.393599	+	0.227245i	−0.683718	−	0.729746i	$-0.739638\pi$
$643$	−9.98067	+	5.76234i	−0.393599	+	0.227245i	0.290119	+	0.956991i	$0.406305\pi$
$644$	6.42842	+	11.1344i	0.253315	+	0.438755i
$645$	−5.61213	+	4.96239i	−0.220977	+	0.195394i
$646$	−1.51270	−	2.62007i	−0.0595162	−	0.103085i
$647$	3.17849	+	1.83510i	0.124959	+	0.0721453i	0.561177	−	0.827696i	$-0.310349\pi$
$647$	3.17849	+	1.83510i	0.124959	+	0.0721453i	−0.436217	+	0.899841i	$0.643682\pi$
$648$	−7.25779	−	4.19029i	−0.285113	−	0.164610i
$649$	−42.3634			−1.66291
$650$	−17.9900	−	1.16573i	−0.705627	−	0.0457237i
$651$	9.85352			0.386190
$652$	−11.7127	−	6.76234i	−0.458706	−	0.264834i
$653$	−7.02043	−	4.05325i	−0.274731	−	0.158616i	0.356305	−	0.934370i	$-0.384036\pi$
$653$	−7.02043	−	4.05325i	−0.274731	−	0.158616i	−0.631036	+	0.775754i	$0.717370\pi$
$654$	−9.11871	−	15.7941i	−0.356570	−	0.617597i
$655$	18.0933	−	15.9986i	0.706965	−	0.625116i
$656$	−3.75329	−	6.50089i	−0.146541	−	0.253817i
$657$	−0.437890	+	0.252816i	−0.0170837	+	0.00986329i
$658$		−	3.96239i		−	0.154470i
$659$	9.27210	+	16.0597i	0.361190	+	0.625599i	0.988157	−	0.153447i	$-0.0490373\pi$
$659$	9.27210	+	16.0597i	0.361190	+	0.625599i	−0.626967	+	0.779046i	$0.715704\pi$
$660$	−23.6526	+	4.80527i	−0.920676	+	0.187045i
$661$	−23.2059	+	40.1938i	−0.902606	+	1.56336i	−0.0785068	+	0.996914i	$0.525015\pi$
$661$	−23.2059	+	40.1938i	−0.902606	+	1.56336i	−0.824099	+	0.566446i	$0.808318\pi$
$662$		−	26.6761i		−	1.03680i
$663$	1.59667	+	2.42842i	0.0620095	+	0.0943122i
$664$	13.3380			0.517616
$665$	−24.8827	+	5.05518i	−0.964908	+	0.196031i
$666$	−0.297014	+	0.514444i	−0.0115091	+	0.0199343i
$667$	−14.2575	+	8.23155i	−0.552051	+	0.318727i
$668$			23.4241i			0.906304i
$669$	18.5889	+	32.1969i	0.718687	+	1.24480i
$670$	1.37765	+	0.461385i	0.0532233	+	0.0178249i
$671$	−70.5583			−2.72387
$672$	2.62007	−	1.51270i	0.101071	−	0.0583535i
$673$	34.9956	+	20.2047i	1.34898	+	0.778836i	0.988105	−	0.153778i	$-0.0491440\pi$
$673$	34.9956	+	20.2047i	1.34898	+	0.778836i	0.360877	+	0.932613i	$0.382477\pi$
$674$	−4.20299	+	7.27978i	−0.161893	+	0.280407i
$675$	26.5501	+	3.27504i	1.02191	+	0.126056i
$676$	−12.9126	+	1.50527i	−0.496637	+	0.0578950i
$677$			14.2473i			0.547567i	0.961791	+	0.273784i	$0.0882752\pi$
$677$			14.2473i			0.547567i	−0.961791	+	0.273784i	$0.911725\pi$
$678$	20.3099	+	11.7259i	0.779996	+	0.450331i
$679$	12.4902	−	21.6337i	0.479332	−	0.830227i
$680$	−1.02028	−	0.341700i	−0.0391261	−	0.0131036i
$681$	−22.3390			−0.856032
$682$	18.1747	−	10.4932i	0.695946	−	0.401805i
$683$	5.02599	−	2.90175i	0.192314	−	0.111033i	−0.400751	−	0.916187i	$-0.631251\pi$
$683$	5.02599	−	2.90175i	0.192314	−	0.111033i	0.593065	+	0.805154i	$0.297918\pi$
$684$	−1.21933			−0.0466222
$685$	−4.36298	+	13.0275i	−0.166701	+	0.497753i
$686$	−9.69688	+	16.7955i	−0.370228	+	0.641255i
$687$	37.9714	+	21.9228i	1.44870	+	0.836407i
$688$		−	2.00000i		−	0.0762493i
$689$	2.73155	−	1.79597i	0.104064	−	0.0684210i
$690$	17.6629	+	19.9756i	0.672416	+	0.760457i
$691$	9.61990	−	16.6622i	0.365958	−	0.633858i	−0.622971	−	0.782245i	$-0.714075\pi$
$691$	9.61990	−	16.6622i	0.365958	−	0.633858i	0.988929	+	0.148387i	$0.0474080\pi$
$692$	−4.00480	−	2.31217i	−0.152240	−	0.0878956i
$693$	−1.95457	+	1.12847i	−0.0742479	+	0.0428670i
$694$	21.1514			0.802896
$695$	−21.9199	−	7.34113i	−0.831470	−	0.278465i
$696$	1.93700	+	3.35498i	0.0734216	+	0.127170i
$697$		−	3.61213i		−	0.136819i
$698$	−4.74054	+	2.73695i	−0.179432	+	0.103595i
$699$	17.4792	−	30.2749i	0.661124	−	1.14510i
$700$	−5.43862	+	7.20889i	−0.205561	+	0.272470i
$701$	45.3742			1.71376			0.856881	−	0.515515i	$-0.172399\pi$
$701$	45.3742			1.71376			0.856881	+	0.515515i	$0.172399\pi$
$702$	19.2582	−	1.11871i	0.726853	−	0.0422231i
$703$		−	19.2579i		−	0.726325i
$704$	3.22179	−	5.58031i	0.121426	−	0.210316i
$705$	−1.63612	−	8.05333i	−0.0616198	−	0.303306i
$706$	15.0721	+	26.1056i	0.567244	+	0.982496i
$707$			17.3380i			0.652064i
$708$	9.53769	−	5.50659i	0.358448	−	0.206950i
$709$	1.98660	+	3.44089i	0.0746082	+	0.129225i	0.900916	−	0.433994i	$-0.142896\pi$
$709$	1.98660	+	3.44089i	0.0746082	+	0.129225i	−0.826308	+	0.563219i	$0.809563\pi$
$710$	−5.42548	−	6.13586i	−0.203615	−	0.230275i
$711$	−0.222499	−	0.385379i	−0.00834436	−	0.0144528i
$712$	1.00141	+	0.578163i	0.0375293	+	0.0216676i
$713$	−20.0790	−	11.5926i	−0.751964	−	0.434147i
$714$	1.45580			0.0544820
$715$	36.8566	−	36.6111i	1.37836	−	1.36918i
$716$	−8.31265			−0.310658
$717$	−22.1858	−	12.8090i	−0.828546	−	0.478361i
$718$	−7.26411	−	4.19394i	−0.271094	−	0.156516i
$719$	22.8496	+	39.5766i	0.852145	+	1.47596i	0.879269	+	0.476326i	$0.158032\pi$
$719$	22.8496	+	39.5766i	0.852145	+	1.47596i	−0.0271244	+	0.999632i	$0.508635\pi$
$720$	−0.324869	+	0.287258i	−0.0121072	+	0.0107055i
$721$	−2.77702	−	4.80995i	−0.103422	−	0.179132i
$722$	17.7792	−	10.2648i	0.661672	−	0.382016i
$723$		−	21.3888i		−	0.795459i
$724$	−0.512696	−	0.888016i	−0.0190542	−	0.0330029i
$725$	−9.23092	−	6.96411i	−0.342828	−	0.258641i
$726$	25.5623	−	44.2752i	0.948706	−	1.64321i
$727$			24.7948i			0.919588i	0.888026	+	0.459794i	$0.152077\pi$
$727$			24.7948i			0.919588i	−0.888026	+	0.459794i	$0.847923\pi$
$728$	−2.92340	+	5.81876i	−0.108349	+	0.215658i
$729$	−28.5125			−1.05602
$730$	−1.16069	−	5.71317i	−0.0429591	−	0.211454i
$731$	0.481194	−	0.833453i	0.0177976	−	0.0308264i
$732$	15.8855	−	9.17148i	0.587144	−	0.338988i
$733$			45.8651i			1.69407i	0.531540	+	0.847033i	$0.321613\pi$
$733$			45.8651i			1.69407i	−0.531540	+	0.847033i	$0.678387\pi$
$734$	−9.75623	−	16.8983i	−0.360109	−	0.623727i
$735$	−4.44661	+	13.2771i	−0.164016	+	0.489735i
$736$	−7.11871			−0.262399
$737$	−3.62574	+	2.09332i	−0.133556	+	0.0771085i
$738$	−1.26076	−	0.727901i	−0.0464093	−	0.0267944i
$739$	17.4817	−	30.2791i	0.643074	−	1.11384i	−0.341669	−	0.939820i	$-0.610992\pi$
$739$	17.4817	−	30.2791i	0.643074	−	1.11384i	0.984743	−	0.174016i	$-0.0556744\pi$
$740$	−4.53690	−	5.13093i	−0.166780	−	0.188617i
$741$	−31.7297	+	20.8620i	−1.16562	+	0.766384i
$742$		−	1.63752i		−	0.0601152i
$743$	5.94673	+	3.43335i	0.218165	+	0.125957i	0.605100	−	0.796149i	$-0.293133\pi$
$743$	5.94673	+	3.43335i	0.218165	+	0.125957i	−0.386936	+	0.922107i	$0.626466\pi$
$744$	−2.72790	+	4.72486i	−0.100010	+	0.173222i
$745$	34.0328	+	11.3978i	1.24686	+	0.417583i
$746$	−8.51388			−0.311715
$747$	2.24018	−	1.29337i	0.0819638	−	0.0473218i
$748$	2.68521	−	1.55031i	0.0981811	−	0.0566849i
$749$	3.02539			0.110545
$750$	−8.07704	+	16.8973i	−0.294932	+	0.617003i
$751$	−2.40009	+	4.15708i	−0.0875806	+	0.151694i	−0.906488	−	0.422232i	$-0.861247\pi$
$751$	−2.40009	+	4.15708i	−0.0875806	+	0.151694i	0.818907	+	0.573926i	$0.194580\pi$
$752$	1.90000	+	1.09697i	0.0692860	+	0.0400023i
$753$		−	7.05571i		−	0.257124i
$754$	−7.45088	−	3.74339i	−0.271345	−	0.136326i
$755$	−15.6082	+	13.8011i	−0.568039	+	0.502275i
$756$	4.83146	−	8.36833i	0.175718	−	0.304353i
$757$	−24.0541	−	13.8876i	−0.874261	−	0.504755i	−0.00549931	−	0.999985i	$-0.501750\pi$
$757$	−24.0541	−	13.8876i	−0.874261	−	0.504755i	−0.868762	+	0.495230i	$0.835084\pi$
$758$	17.0768	−	9.85931i	0.620258	−	0.358106i
$759$	−76.8383			−2.78905
$760$	4.46464	−	13.3310i	0.161949	−	0.483566i
$761$	1.58110	+	2.73855i	0.0573149	+	0.0992723i	0.893259	−	0.449542i	$-0.148413\pi$
$761$	1.58110	+	2.73855i	0.0573149	+	0.0992723i	−0.835944	+	0.548814i	$0.815079\pi$
$762$		−	8.68830i		−	0.314744i
$763$	17.0286	−	9.83146i	0.616476	−	0.355923i
$764$	0.177593	−	0.307600i	0.00642509	−	0.0111286i
$765$	−0.204495	+	0.0415453i	−0.00739353	+	0.00150207i
$766$	27.7196			1.00155
$767$	−10.6419	+	21.1817i	−0.384257	+	0.764828i
$768$			1.67513i			0.0604461i
$769$	4.07816	−	7.06358i	0.147062	−	0.254719i	−0.783078	−	0.621923i	$-0.786352\pi$
$769$	4.07816	−	7.06358i	0.147062	−	0.254719i	0.930140	+	0.367204i	$0.119685\pi$
$770$	−5.18087	−	25.5013i	−0.186705	−	0.919004i
$771$	−15.5999	−	27.0198i	−0.561817	−	0.973096i
$772$		−	14.0000i		−	0.503871i
$773$	5.09129	−	2.93946i	0.183121	−	0.105725i	−0.405637	−	0.914034i	$-0.632950\pi$
$773$	5.09129	−	2.93946i	0.183121	−	0.105725i	0.588758	+	0.808309i	$0.299617\pi$
$774$	−0.193937	−	0.335908i	−0.00697091	−	0.0120740i
$775$	1.99366	−	16.1622i	0.0716144	−	0.580564i
$776$	6.91573	+	11.9784i	0.248260	+	0.429999i
$777$	8.02528	+	4.63339i	0.287905	+	0.166222i
$778$	7.92535	+	4.57570i	0.284137	+	0.164047i
$779$	47.1958			1.69097
$780$	−3.53901	+	13.0334i	−0.126717	+	0.466671i
$781$	23.6023			0.844556
$782$	−2.96656	−	1.71274i	−0.106084	−	0.0612475i
$783$	10.7156	+	6.18664i	0.382944	+	0.221093i
$784$	−1.86907	−	3.23732i	−0.0667524	−	0.115619i
$785$	−21.8568	−	24.7186i	−0.780104	−	0.882245i
$786$	−9.04666	−	15.6693i	−0.322684	−	0.558905i
$787$	−20.5261	+	11.8507i	−0.731676	+	0.422433i	−0.819035	−	0.573744i	$-0.805491\pi$
$787$	−20.5261	+	11.8507i	−0.731676	+	0.422433i	0.0873591	+	0.996177i	$0.472157\pi$
$788$		−	14.1065i		−	0.502523i
$789$	−19.2811	−	33.3959i	−0.686427	−	1.18893i
$790$	5.02806	−	1.02150i	0.178890	−	0.0363435i
$791$	−12.6424	+	21.8974i	−0.449514	+	0.778580i
$792$		−	1.24965i		−	0.0444042i
$793$	−17.7246	+	35.2792i	−0.629419	+	1.25280i
$794$	−1.43041			−0.0507633
$795$	−0.676152	−	3.32816i	−0.0239806	−	0.118038i
$796$	1.57452	−	2.72714i	0.0558072	−	0.0966609i
$797$	42.0193	−	24.2599i	1.48840	−	0.859329i	0.488489	−	0.872570i	$-0.337548\pi$
$797$	42.0193	−	24.2599i	1.48840	−	0.859329i	0.999912	+	0.0132409i	$0.00421482\pi$
$798$			19.0214i			0.673351i
$799$	0.527855	+	0.914271i	0.0186742	+	0.0323446i
$800$	−1.95108	−	4.60362i	−0.0689810	−	0.162762i
$801$	0.224254			0.00792362
$802$	18.7669	−	10.8351i	0.662684	−	0.382601i
$803$	14.5490	+	8.39986i	0.513423	+	0.296425i
$804$	0.544198	−	0.942579i	0.0191924	−	0.0332422i
$805$	−21.5369	+	19.0435i	−0.759076	+	0.671195i
$806$	−0.681010	−	11.7233i	−0.0239876	−	0.412936i
$807$			22.5705i			0.794521i
$808$	−8.31376	−	4.79995i	−0.292477	−	0.168862i
$809$	−8.55936	+	14.8252i	−0.300931	+	0.521228i	−0.976347	−	0.216209i	$-0.930631\pi$
$809$	−8.55936	+	14.8252i	−0.300931	+	0.521228i	0.675416	+	0.737437i	$0.263964\pi$
$810$	5.95112	−	17.7695i	0.209101	−	0.624356i
$811$	−7.67372			−0.269461			−0.134730	−	0.990882i	$-0.543017\pi$
$811$	−7.67372			−0.269461			−0.134730	+	0.990882i	$0.543017\pi$
$812$	−3.61721	+	2.08840i	−0.126939	+	0.0732884i
$813$	−25.9681	+	14.9927i	−0.910742	+	0.525817i
$814$	19.7367			0.691772
$815$	9.60400	−	28.6766i	0.336413	−	1.00450i
$816$	−0.403032	+	0.698071i	−0.0141089	+	0.0244374i
$817$	10.8898	+	6.28726i	0.380988	+	0.219963i
$818$		−	9.08110i		−	0.317513i
$819$	0.0732380	+	1.26076i	0.00255914	+	0.0440546i
$820$	12.5745	−	11.1187i	0.439121	−	0.388282i
$821$	26.8933	−	46.5805i	0.938582	−	1.62567i	0.170463	−	0.985364i	$-0.445474\pi$
$821$	26.8933	−	46.5805i	0.938582	−	1.62567i	0.768119	−	0.640307i	$-0.221193\pi$
$822$	8.91329	+	5.14609i	0.310887	+	0.179491i
$823$	8.46604	−	4.88787i	0.295108	−	0.170381i	−0.345135	−	0.938553i	$-0.612167\pi$
$823$	8.46604	−	4.88787i	0.295108	−	0.170381i	0.640243	+	0.768172i	$0.278834\pi$
$824$	3.07522			0.107130
$825$	−21.0596	−	49.6907i	−0.733202	−	1.73001i
$826$	5.93700	+	10.2832i	0.206575	+	0.357798i
$827$		−	28.1598i		−	0.979213i	−0.871943	−	0.489607i	$-0.837140\pi$
$827$		−	28.1598i		−	0.979213i	0.871943	−	0.489607i	$-0.162860\pi$
$828$	−1.19562	+	0.690289i	−0.0415505	+	0.0239892i
$829$	10.1065	−	17.5050i	0.351013	−	0.607972i	−0.635414	−	0.772172i	$-0.719171\pi$
$829$	10.1065	−	17.5050i	0.351013	−	0.607972i	0.986427	+	0.164199i	$0.0525039\pi$
$830$	5.93792	+	29.2277i	0.206108	+	1.01451i
$831$	14.2193			0.493263
$832$	−1.98082	−	3.01270i	−0.0686727	−	0.104446i
$833$		−	1.79877i		−	0.0623237i
$834$	−8.65879	+	14.9975i	−0.299829	+	0.519320i
$835$	−51.3292	+	10.4281i	−1.77632	+	0.360879i
$836$	20.2562	+	35.0848i	0.700576	+	1.21343i
$837$			17.4255i			0.602313i
$838$	13.4604	−	7.77139i	0.464983	−	0.268458i
$839$	6.29631	+	10.9055i	0.217373	+	0.376500i	0.954004	−	0.299794i	$-0.0969180\pi$
$839$	6.29631	+	10.9055i	0.217373	+	0.376500i	−0.736631	+	0.676295i	$0.763585\pi$
$840$	4.48119	+	5.06793i	0.154616	+	0.174860i
$841$	11.8258	+	20.4829i	0.407787	+	0.706308i
$842$	4.29961	+	2.48238i	0.148174	+	0.0855484i
$843$	23.9796	+	13.8446i	0.825901	+	0.476834i
$844$	−3.09332			−0.106477
$845$	−9.04700	−	27.6252i	−0.311226	−	0.950336i
$846$	0.425485			0.0146285
$847$	47.7359	+	27.5603i	1.64022	+	0.946984i
$848$	0.785207	+	0.453339i	0.0269641	+	0.0155677i
$849$	1.28726	+	2.22960i	0.0441786	+	0.0765195i
$850$	0.294552	−	2.38787i	0.0101030	−	0.0819034i
$851$	−10.9023	−	18.8834i	−0.373727	−	0.647314i
$852$	−5.31381	+	3.06793i	−0.182048	+	0.105106i
$853$		−	45.7704i		−	1.56715i	−0.621299	−	0.783574i	$-0.713395\pi$
$853$		−	45.7704i		−	1.56715i	0.621299	−	0.783574i	$-0.286605\pi$
$854$	9.88835	+	17.1271i	0.338372	+	0.586078i
$855$	−0.542829	−	2.67192i	−0.0185644	−	0.0913777i
$856$	−0.837565	+	1.45071i	−0.0286274	+	0.0495841i
$857$			27.8169i			0.950206i	0.879930	+	0.475103i	$0.157589\pi$
$857$			27.8169i			0.950206i	−0.879930	+	0.475103i	$0.842411\pi$
$858$	−21.3807	−	32.5186i	−0.729925	−	1.11017i
$859$	−25.9706			−0.886107			−0.443053	−	0.896495i	$-0.646105\pi$
$859$	−25.9706			−0.886107			−0.443053	+	0.896495i	$0.646105\pi$
$860$	4.38261	−	0.890373i	0.149446	−	0.0303615i
$861$	−11.3552	+	19.6678i	−0.386984	+	0.670275i
$862$	−28.5534	+	16.4853i	−0.972533	+	0.561492i
$863$			18.7210i			0.637270i	0.947877	+	0.318635i	$0.103224\pi$
$863$			18.7210i			0.637270i	−0.947877	+	0.318635i	$0.896776\pi$
$864$	2.67513	+	4.63346i	0.0910098	+	0.157634i
$865$	3.28379	−	9.80508i	0.111652	−	0.333383i
$866$	−16.1114			−0.547488
$867$	24.3261	−	14.0447i	0.826157	−	0.476982i
$868$	−5.09417	−	2.94112i	−0.172907	−	0.0998281i
$869$	−7.39257	+	12.8043i	−0.250776	+	0.434356i
$870$	−6.48944	+	5.73813i	−0.220013	+	0.194541i
$871$	0.135857	+	2.33872i	0.00460334	+	0.0792446i
$872$			10.8872i			0.368686i
$873$	2.32305	+	1.34121i	0.0786233	+	0.0453932i
$874$	22.3786	−	38.7609i	0.756967	−	1.31111i
$875$	−18.2181	−	8.70837i	−0.615883	−	0.294397i
$876$	−4.36741			−0.147561
$877$	19.6466	−	11.3430i	0.663418	−	0.383025i	−0.130160	−	0.991493i	$-0.541549\pi$
$877$	19.6466	−	11.3430i	0.663418	−	0.383025i	0.793578	+	0.608468i	$0.208216\pi$
$878$	0.0722889	−	0.0417360i	0.00243963	−	0.00140852i
$879$	−9.93303			−0.335033
$880$	13.6624	+	4.57564i	0.460561	+	0.154245i
$881$	1.23813	−	2.14451i	0.0417138	−	0.0722505i	−0.844415	−	0.535690i	$-0.820052\pi$
$881$	1.23813	−	2.14451i	0.0417138	−	0.0722505i	0.886129	+	0.463440i	$0.153385\pi$
$882$	−0.627835	−	0.362481i	−0.0211403	−	0.0122054i
$883$		−	31.4641i		−	1.05885i	−0.848357	−	0.529425i	$-0.822408\pi$
$883$		−	31.4641i		−	1.05885i	0.848357	−	0.529425i	$-0.177592\pi$
$884$	−0.100615	−	1.73205i	−0.00338406	−	0.0582552i
$885$	16.3127	+	18.4485i	0.548344	+	0.620140i
$886$	−20.4568	+	35.4321i	−0.687258	+	1.19037i
$887$	34.3953	+	19.8581i	1.15488	+	0.666771i	0.950072	−	0.312031i	$-0.101009\pi$
$887$	34.3953	+	19.8581i	1.15488	+	0.666771i	0.204809	+	0.978802i	$0.434343\pi$
$888$	−4.44352	+	2.56547i	−0.149115	+	0.0860914i
$889$	9.36741			0.314173
$890$	−0.821117	+	2.45178i	−0.0275239	+	0.0821837i
$891$	27.0005	+	46.7662i	0.904550	+	1.56673i
$892$		−	22.1939i		−	0.743108i
$893$	−11.9458	+	6.89692i	−0.399752	+	0.230797i
$894$	13.4436	−	23.2850i	0.449621	−	0.778766i
$895$	−3.70068	−	18.2155i	−0.123700	−	0.608878i
$896$	−1.80606			−0.0603363
$897$	−19.3022	+	38.4191i	−0.644480	+	1.28278i
$898$			29.1319i			0.972144i
$899$	3.76608	−	6.52305i	0.125606	−	0.217556i
$900$	−0.774096	−	0.584003i	−0.0258032	−	0.0194668i
$901$	0.218144	+	0.377837i	0.00726744	+	0.0125876i
$902$			48.3693i			1.61052i
$903$	−5.24013	+	3.02539i	−0.174381	+	0.100679i
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	1.71767	−	1.51881i	0.0570972	−	0.0504868i
$906$	7.80408	+	13.5171i	0.259273	+	0.449074i
$907$	−46.3977	−	26.7877i	−1.54061	−	0.889472i	−0.998800	−	0.0489717i	$-0.984406\pi$
$907$	−46.3977	−	26.7877i	−1.54061	−	0.889472i	−0.541811	−	0.840500i	$-0.682261\pi$
$908$	11.5490	+	6.66784i	0.383268	+	0.221280i
$909$	−1.86177			−0.0617511
$910$	−14.0521	−	3.81563i	−0.465823	−	0.126487i
$911$	14.6253			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$911$	14.6253			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$912$	−9.12096	−	5.26599i	−0.302025	−	0.174374i
$913$	−74.4304	−	42.9724i	−2.46329	−	1.42218i
$914$	−16.3339	−	28.2912i	−0.540278	−	0.935789i
$915$	27.1695	+	30.7269i	0.898196	+	1.01580i
$916$	−13.0872	−	22.6677i	−0.432414	−	0.748962i
$917$	16.8940	−	9.75377i	0.557890	−	0.322098i
$918$			2.57452i			0.0849717i
$919$	26.5247	+	45.9421i	0.874969	+	1.51549i	0.856796	+	0.515655i	$0.172451\pi$
$919$	26.5247	+	45.9421i	0.874969	+	1.51549i	0.0181725	+	0.999835i	$0.494215\pi$
$920$	−3.16915	−	15.5993i	−0.104484	−	0.514292i
$921$	−15.0557	+	26.0773i	−0.496103	+	0.859275i
$922$		−	19.1006i		−	0.629045i
$923$	5.92901	−	11.8011i	0.195156	−	0.388439i
$924$	−19.4944			−0.641318
$925$	9.22366	−	12.2260i	0.303272	−	0.401987i
$926$	−4.14609	+	7.18124i	−0.136249	+	0.235990i
$927$	0.516496	−	0.298199i	0.0169640	−	0.00979414i
$928$		−	2.31265i		−	0.0759165i
$929$	−5.22521	−	9.05033i	−0.171434	−	0.296932i	0.767488	−	0.641064i	$-0.221507\pi$
$929$	−5.22521	−	9.05033i	−0.171434	−	0.296932i	−0.938921	+	0.344132i	$0.888173\pi$
$930$	−11.5680	−	3.87421i	−0.379331	−	0.127040i
$931$	23.5026			0.770267
$932$	−18.0731	+	10.4345i	−0.592005	+	0.341795i
$933$	−23.1496	−	13.3654i	−0.757883	−	0.437564i
$934$	−11.7685	+	20.3836i	−0.385076	+	0.666970i
$935$	4.59261	+	5.19394i	0.150195	+	0.169860i
$936$	−0.624823	−	0.313917i	−0.0204230	−	0.0102607i
$937$		−	10.5745i		−	0.345454i	−0.984970	−	0.172727i	$-0.944742\pi$
$937$		−	10.5745i		−	0.345454i	0.984970	−	0.172727i	$-0.0552579\pi$
$938$	1.01625	+	0.586734i	0.0331819	+	0.0191576i
$939$	19.6302	−	34.0005i	0.640608	−	1.10957i
$940$	−1.55793	+	4.65184i	−0.0508142	+	0.151726i
$941$	−16.6107			−0.541494			−0.270747	−	0.962651i	$-0.587271\pi$
$941$	−16.6107			−0.541494			−0.270747	+	0.962651i	$0.587271\pi$
$942$	−21.4070	+	12.3593i	−0.697476	+	0.402688i
$943$	46.2780	−	26.7186i	1.50702	−	0.870078i
$944$	−6.57452			−0.213982
$945$	20.4884	+	6.86172i	0.666489	+	0.223212i
$946$	−6.44358	+	11.1606i	−0.209499	+	0.362863i
$947$	−36.7949	−	21.2435i	−1.19567	−	0.690322i	−0.236086	−	0.971732i	$-0.575865\pi$
$947$	−36.7949	−	21.2435i	−1.19567	−	0.690322i	−0.959588	+	0.281410i	$0.909198\pi$
$948$		−	3.84367i		−	0.124837i
$949$	7.85471	−	5.16441i	0.254975	−	0.167644i
$950$	31.1998	+	3.84860i	1.01226	+	0.124865i
$951$	−17.2963	+	29.9581i	−0.560871	+	0.971457i
$952$	−0.752634	−	0.434534i	−0.0243930	−	0.0140833i
$953$	−38.9897	+	22.5107i	−1.26300	+	0.729193i	−0.973654	−	0.228031i	$-0.926771\pi$
$953$	−38.9897	+	22.5107i	−1.26300	+	0.729193i	−0.289346	+	0.957224i	$0.593438\pi$
$954$	0.175838			0.00569297
$955$	0.753108	+	0.252221i	0.0243700	+	0.00816168i
$956$	7.64657	+	13.2442i	0.247308	+	0.428350i
$957$		−	24.9624i		−	0.806919i
$958$	−5.67802	+	3.27821i	−0.183449	+	0.105914i
$959$	−5.54832	+	9.60998i	−0.179165	+	0.310322i
$960$	−3.67072	+	0.745746i	−0.118472	+	0.0240688i
$961$	−20.3923			−0.657817
$962$	4.95796	−	9.86836i	0.159851	−	0.318169i
$963$			0.324869i			0.0104688i
$964$	−6.38423	+	11.0578i	−0.205622	+	0.356148i
$965$	30.6782	−	6.23261i	0.987568	−	0.200635i
$966$	10.7685	+	18.6515i	0.346469	+	0.600102i
$967$		−	24.4763i		−	0.787104i	−0.919302	−	0.393552i	$-0.871246\pi$
$967$		−	24.4763i		−	0.787104i	0.919302	−	0.393552i	$-0.128754\pi$
$968$	−26.4309	+	15.2599i	−0.849521	+	0.490471i
$969$	−2.53396	−	4.38895i	−0.0814027	−	0.140994i
$970$	−23.1695	+	20.4871i	−0.743928	+	0.657800i
$971$	28.2023	+	48.8478i	0.905054	+	1.56760i	0.820844	+	0.571152i	$0.193503\pi$
$971$	28.2023	+	48.8478i	0.905054	+	1.56760i	0.0842097	+	0.996448i	$0.473163\pi$
$972$	1.74263	+	1.00611i	0.0558950	+	0.0322710i
$973$	−16.1697	−	9.33558i	−0.518377	−	0.299285i
$974$	13.5599			0.434488
$975$	−30.1356	−	1.95275i	−0.965113	−	0.0625380i
$976$	−10.9502			−0.350506
$977$	11.7021	+	6.75623i	0.374385	+	0.216151i	0.675372	−	0.737477i	$-0.263983\pi$
$977$	11.7021	+	6.75623i	0.374385	+	0.216151i	−0.300988	+	0.953628i	$0.597316\pi$
$978$	−19.6203	−	11.3278i	−0.627389	−	0.362223i
$979$	−3.72544	−	6.45265i	−0.119066	−	0.206228i
$980$	6.26187	−	5.53690i	0.200028	−	0.176870i
$981$	1.05571	+	1.82854i	0.0337062	+	0.0583809i
$982$	4.29329	−	2.47873i	0.137004	−	0.0790995i
$983$			30.1187i			0.960638i	0.877094	+	0.480319i	$0.159479\pi$
$983$			30.1187i			0.960638i	−0.877094	+	0.480319i	$0.840521\pi$
$984$	−6.28726	−	10.8898i	−0.200430	−	0.347156i
$985$	30.9116	−	6.28002i	0.984926	−	0.200098i
$986$	0.556417	−	0.963743i	0.0177199	−	0.0306918i
$987$		−	6.63752i		−	0.211275i
$988$	22.6309	−	1.31464i	0.719984	−	0.0418241i
$989$	14.2374			0.452724
$990$	2.73835	−	0.556326i	0.0870306	−	0.0176812i
$991$	−17.6629	+	30.5931i	−0.561081	+	0.971821i	0.436322	+	0.899791i	$0.356281\pi$
$991$	−17.6629	+	30.5931i	−0.561081	+	0.971821i	−0.997402	+	0.0720298i	$0.977052\pi$
$992$	2.82059	−	1.62847i	0.0895539	−	0.0517040i
$993$		−	44.6859i		−	1.41807i
$994$	−3.30773	−	5.72915i	−0.104915	−	0.181718i
$995$	6.67694	+	2.23615i	0.211673	+	0.0708909i
$996$	22.3430			0.707964
$997$	−14.5638	+	8.40843i	−0.461241	+	0.266298i	−0.712566	−	0.701605i	$-0.752467\pi$
$997$	−14.5638	+	8.40843i	−0.461241	+	0.266298i	0.251325	+	0.967903i	$0.419134\pi$
$998$	−12.0118	−	6.93501i	−0.380227	−	0.219524i
$999$	−8.19394	+	14.1923i	−0.259245	+	0.449025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.n.a.9.1	✓	12
3.2	odd	2		1170.2.bp.h.919.6		12
4.3	odd	2		1040.2.dh.b.529.5		12
5.2	odd	4		650.2.e.k.451.1		6
5.3	odd	4		650.2.e.j.451.3		6
5.4	even	2	inner	130.2.n.a.9.6	yes	12
13.3	even	3	inner	130.2.n.a.29.6	yes	12
13.4	even	6		1690.2.b.b.339.3		6
13.6	odd	12		1690.2.c.c.1689.5		6
13.7	odd	12		1690.2.c.b.1689.5		6
13.9	even	3		1690.2.b.c.339.6		6
15.14	odd	2		1170.2.bp.h.919.3		12
20.19	odd	2		1040.2.dh.b.529.2		12
39.29	odd	6		1170.2.bp.h.289.3		12
52.3	odd	6		1040.2.dh.b.289.2		12
65.3	odd	12		650.2.e.j.601.3		6
65.4	even	6		1690.2.b.b.339.4		6
65.9	even	6		1690.2.b.c.339.1		6
65.17	odd	12		8450.2.a.ca.1.3		3
65.19	odd	12		1690.2.c.b.1689.2		6
65.22	odd	12		8450.2.a.bu.1.3		3
65.29	even	6	inner	130.2.n.a.29.1	yes	12
65.42	odd	12		650.2.e.k.601.1		6
65.43	odd	12		8450.2.a.bt.1.1		3
65.48	odd	12		8450.2.a.cb.1.1		3
65.59	odd	12		1690.2.c.c.1689.2		6
195.29	odd	6		1170.2.bp.h.289.6		12
260.159	odd	6		1040.2.dh.b.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	1.1	even	1	trivial
130.2.n.a.9.6	yes	12	5.4	even	2	inner
130.2.n.a.29.1	yes	12	65.29	even	6	inner
130.2.n.a.29.6	yes	12	13.3	even	3	inner
650.2.e.j.451.3		6	5.3	odd	4
650.2.e.j.601.3		6	65.3	odd	12
650.2.e.k.451.1		6	5.2	odd	4
650.2.e.k.601.1		6	65.42	odd	12
1040.2.dh.b.289.2		12	52.3	odd	6
1040.2.dh.b.289.5		12	260.159	odd	6
1040.2.dh.b.529.2		12	20.19	odd	2
1040.2.dh.b.529.5		12	4.3	odd	2
1170.2.bp.h.289.3		12	39.29	odd	6
1170.2.bp.h.289.6		12	195.29	odd	6
1170.2.bp.h.919.3		12	15.14	odd	2
1170.2.bp.h.919.6		12	3.2	odd	2
1690.2.b.b.339.3		6	13.4	even	6
1690.2.b.b.339.4		6	65.4	even	6
1690.2.b.c.339.1		6	65.9	even	6
1690.2.b.c.339.6		6	13.9	even	3
1690.2.c.b.1689.2		6	65.19	odd	12
1690.2.c.b.1689.5		6	13.7	odd	12
1690.2.c.c.1689.2		6	65.59	odd	12
1690.2.c.c.1689.5		6	13.6	odd	12
8450.2.a.bt.1.1		3	65.43	odd	12
8450.2.a.bu.1.3		3	65.22	odd	12
8450.2.a.ca.1.3		3	65.17	odd	12
8450.2.a.cb.1.1		3	65.48	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.45071 - 0.837565i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.67513 + 1.48119i) q^{5} +(0.837565 + 1.45071i) q^{6} +(-1.56410 + 0.903032i) q^{7} -1.00000i q^{8} +(-0.0969683 - 0.167954i) q^{9} +(2.19130 - 0.445186i) q^{10} +(-3.22179 + 5.58031i) q^{11} -1.67513i q^{12} +(1.98082 + 3.01270i) q^{13} +1.80606 q^{14} +(3.67072 - 0.745746i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.416726 + 0.240597i) q^{17} +0.193937i q^{18} +(-3.14363 - 5.44492i) q^{19} +(-2.12032 - 0.710109i) q^{20} +3.02539 q^{21} +(5.58031 - 3.22179i) q^{22} +(-6.16499 - 3.55936i) q^{23} +(-0.837565 + 1.45071i) q^{24} +(0.612127 - 4.96239i) q^{25} +(-0.209095 - 3.59948i) q^{26} +5.35026i q^{27} +(-1.56410 - 0.903032i) q^{28} +(1.15633 - 2.00281i) q^{29} +(-3.55181 - 1.18953i) q^{30} +3.25694 q^{31} +(0.866025 - 0.500000i) q^{32} +(9.34774 - 5.39692i) q^{33} +0.481194 q^{34} +(1.28250 - 3.82943i) q^{35} +(0.0969683 - 0.167954i) q^{36} +(2.65264 + 1.53150i) q^{37} +6.28726i q^{38} +(-0.350262 - 6.02961i) q^{39} +(1.48119 + 1.67513i) q^{40} +(-3.75329 + 6.50089i) q^{41} +(-2.62007 - 1.51270i) q^{42} +(-1.73205 + 1.00000i) q^{43} -6.44358 q^{44} +(0.411207 + 0.137716i) q^{45} +(3.55936 + 6.16499i) q^{46} -2.19394i q^{47} +(1.45071 - 0.837565i) q^{48} +(-1.86907 + 3.23732i) q^{49} +(-3.01131 + 3.99149i) q^{50} +0.806063 q^{51} +(-1.61866 + 3.22179i) q^{52} -0.906679i q^{53} +(2.67513 - 4.63346i) q^{54} +(-2.86860 - 14.1198i) q^{55} +(0.903032 + 1.56410i) q^{56} +10.5320i q^{57} +(-2.00281 + 1.15633i) q^{58} +(3.28726 + 5.69370i) q^{59} +(2.48119 + 2.80606i) q^{60} +(5.47508 + 9.48313i) q^{61} +(-2.82059 - 1.62847i) q^{62} +(0.303336 + 0.175131i) q^{63} -1.00000 q^{64} +(-7.78053 - 2.11268i) q^{65} -10.7938 q^{66} +(0.562690 + 0.324869i) q^{67} +(-0.416726 - 0.240597i) q^{68} +(5.96239 + 10.3272i) q^{69} +(-3.02539 + 2.67513i) q^{70} +(-1.83146 - 3.17217i) q^{71} +(-0.167954 + 0.0969683i) q^{72} -2.60720i q^{73} +(-1.53150 - 2.65264i) q^{74} +(-5.04434 + 6.68627i) q^{75} +(3.14363 - 5.44492i) q^{76} -11.6375i q^{77} +(-2.71147 + 5.39692i) q^{78} +2.29455 q^{79} +(-0.445186 - 2.19130i) q^{80} +(4.19029 - 7.25779i) q^{81} +(6.50089 - 3.75329i) q^{82} +13.3380i q^{83} +(1.51270 + 2.62007i) q^{84} +(0.341700 - 1.02028i) q^{85} +2.00000 q^{86} +(-3.35498 + 1.93700i) q^{87} +(5.58031 + 3.22179i) q^{88} +(-0.578163 + 1.00141i) q^{89} +(-0.287258 - 0.324869i) q^{90} +(-5.81876 - 2.92340i) q^{91} -7.11871i q^{92} +(-4.72486 - 2.72790i) q^{93} +(-1.09697 + 1.90000i) q^{94} +(13.3310 + 4.46464i) q^{95} -1.67513 q^{96} +(-11.9784 + 6.91573i) q^{97} +(3.23732 - 1.86907i) q^{98} +1.24965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{14} + 4 q^{15} - 6 q^{16} - 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 16 q^{30} + 24 q^{31} - 16 q^{34} - 6 q^{35} + 2 q^{36} + 36 q^{39} - 4 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^14 + 4 * q^15 - 6 * q^16 - 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 16 * q^30 + 24 * q^31 - 16 * q^34 - 6 * q^35 + 2 * q^36 + 36 * q^39 - 4 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 - 4 * q^49 - 8 * q^50 + 8 * q^51 + 12 * q^54 + 12 * q^55 + 10 * q^56 + 16 * q^59 + 8 * q^60 - 8 * q^61 - 12 * q^64 - 10 * q^65 - 24 * q^66 + 28 * q^69 + 24 * q^70 + 40 * q^71 - 10 * q^74 - 8 * q^75 + 26 * q^76 + 56 * q^79 + 26 * q^81 - 12 * q^84 - 16 * q^85 + 24 * q^86 + 14 * q^89 + 20 * q^90 - 38 * q^91 - 14 * q^94 - 8 * q^95 - 52 * q^99

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