LMFDB - Embedded newform 130.2.n.a.9.6

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)

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")

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);

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			9.6
Root			$-0.147520 + 0.550552i$ of defining polynomial
Character	$\chi$	$=$	130.9
Dual form			130.2.n.a.29.6

$q$-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} +(-0.710109 - 2.12032i) q^{10} +(-3.22179 + 5.58031i) q^{11} +1.67513i q^{12} +(-1.98082 - 3.01270i) q^{13} +1.80606 q^{14} +(-1.18953 - 3.55181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.416726 - 0.240597i) q^{17} -0.193937i q^{18} +(-3.14363 - 5.44492i) q^{19} +(0.445186 - 2.19130i) 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} +(0.745746 - 3.67072i) q^{30} +3.25694 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-9.34774 + 5.39692i) q^{33} +0.481194 q^{34} +(-3.95763 - 0.804035i) 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} +(-0.0863379 + 0.424974i) q^{45} +(3.55936 + 6.16499i) q^{46} +2.19394i q^{47} +(-1.45071 + 0.837565i) q^{48} +(-1.86907 + 3.23732i) q^{49} +(-1.95108 + 4.60362i) q^{50} +0.806063 q^{51} +(1.61866 - 3.22179i) q^{52} +0.906679i q^{53} +(2.67513 - 4.63346i) q^{54} +(13.6624 - 4.57564i) 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} +(-1.14425 + 7.98064i) 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} +(-3.26831 + 7.71166i) q^{75} +(3.14363 - 5.44492i) q^{76} +11.6375i q^{77} +(2.71147 - 5.39692i) q^{78} +2.29455 q^{79} +(2.12032 - 0.710109i) q^{80} +(4.19029 - 7.25779i) q^{81} +(-6.50089 + 3.75329i) q^{82} -13.3380i q^{83} +(1.51270 + 2.62007i) q^{84} +(-1.05444 - 0.214221i) 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} +(-2.79900 + 13.7773i) 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	0.856436	−	0.516253i	$-0.172674\pi$
$3$	1.45071	+	0.837565i	0.837565	+	0.483569i	−0.0188705	+	0.999822i	$0.506007\pi$
$4$	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	−0.174388	−	0.984677i	$-0.555795\pi$
$7$	1.56410	−	0.903032i	0.591173	−	0.341314i	0.765561	+	0.643363i	$0.222461\pi$
$8$			1.00000i			0.353553i
$9$	−0.0969683	−	0.167954i	−0.0323228	−	0.0559847i
$10$	−0.710109	−	2.12032i	−0.224556	−	0.670503i
$11$	−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
$15$	−1.18953	−	3.55181i	−0.307134	−	0.917073i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.416726	−	0.240597i	0.101071	−	0.0583534i	−0.448612	−	0.893726i	$-0.648082\pi$
$17$	0.416726	−	0.240597i	0.101071	−	0.0583534i	0.549684	+	0.835373i	$0.314748\pi$
$18$		−	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	$-0.423075\pi$
$20$	0.445186	−	2.19130i	0.0995467	−	0.489990i
$21$	3.02539			0.660195
$22$	−5.58031	+	3.22179i	−1.18973	+	0.686888i
$23$	6.16499	+	3.55936i	1.28549	+	0.742177i	0.977846	−	0.209325i	$-0.0671266\pi$
$23$	6.16499	+	3.55936i	1.28549	+	0.742177i	0.307642	+	0.951502i	$0.400460\pi$
$24$	−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	$0.0977814\pi$
$30$	0.745746	−	3.67072i	0.136154	−	0.670179i
$31$	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
$35$	−3.95763	−	0.804035i	−0.668962	−	0.135907i
$36$	0.0969683	−	0.167954i	0.0161614	−	0.0279923i
$37$	−2.65264	−	1.53150i	−0.436091	−	0.251777i	0.265847	−	0.964015i	$-0.414348\pi$
$37$	−2.65264	−	1.53150i	−0.436091	−	0.251777i	−0.701938	+	0.712238i	$0.747682\pi$
$38$		−	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	−0.362084	−	0.932145i	$-0.617935\pi$
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	0.626219	+	0.779647i	$0.284601\pi$
$44$	−6.44358			−0.971407
$45$	−0.0863379	+	0.424974i	−0.0128705	+	0.0633514i
$46$	3.55936	+	6.16499i	0.524799	+	0.908978i
$47$			2.19394i			0.320019i	0.987116	+	0.160009i	$0.0511524\pi$
$47$			2.19394i			0.320019i	−0.987116	+	0.160009i	$0.948848\pi$
$48$	−1.45071	+	0.837565i	−0.209391	+	0.120892i
$49$	−1.86907	+	3.23732i	−0.267010	+	0.462474i
$50$	−1.95108	+	4.60362i	−0.275924	+	0.651050i
$51$	0.806063			0.112871
$52$	1.61866	−	3.22179i	0.224468	−	0.446782i
$53$			0.906679i			0.124542i	0.998059	+	0.0622710i	$0.0198343\pi$
$53$			0.906679i			0.124542i	−0.998059	+	0.0622710i	$0.980166\pi$
$54$	2.67513	−	4.63346i	0.364039	−	0.630534i
$55$	13.6624	−	4.57564i	1.84224	−	0.616980i
$56$	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
$65$	−1.14425	+	7.98064i	−0.141927	+	0.989877i
$66$	−10.7938			−1.32863
$67$	−0.562690	−	0.324869i	−0.0687435	−	0.0396891i	0.465234	−	0.885188i	$-0.345970\pi$
$67$	−0.562690	−	0.324869i	−0.0687435	−	0.0396891i	−0.533978	+	0.845499i	$0.679303\pi$
$68$	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	$0.0487566\pi$
$73$			2.60720i			0.305150i	−0.988292	+	0.152575i	$0.951243\pi$
$74$	−1.53150	−	2.65264i	−0.178033	−	0.308363i
$75$	−3.26831	+	7.71166i	−0.377392	+	0.890466i
$76$	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	$0.458798\pi$
$80$	2.12032	−	0.710109i	0.237059	−	0.0793926i
$81$	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	$-0.738578\pi$
$83$		−	13.3380i		−	1.46404i	0.681283	−	0.732020i	$-0.261422\pi$
$84$	1.51270	+	2.62007i	0.165049	+	0.285873i
$85$	−1.05444	−	0.214221i	−0.114370	−	0.0232356i
$86$	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
$95$	−2.79900	+	13.7773i	−0.287172	+	1.41352i
$96$	−1.67513			−0.170967
$97$	11.9784	−	6.91573i	1.21622	−	0.702186i	0.252114	−	0.967698i	$-0.418874\pi$
$97$	11.9784	−	6.91573i	1.21622	−	0.702186i	0.964108	+	0.265512i	$0.0855409\pi$
$98$	−3.23732	+	1.86907i	−0.327019	+	0.188804i
$99$	1.24965			0.125594
$100$	−3.99149	+	3.01131i	−0.399149	+	0.301131i
$101$	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	$-0.951588\pi$
$103$		−	3.07522i		−	0.303011i	0.988456	−	0.151505i	$-0.0484121\pi$
$104$	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	0.568481	−	0.822697i	$-0.307531\pi$
$107$	1.45071	+	0.837565i	0.140245	+	0.0809705i	−0.428236	+	0.903667i	$0.640865\pi$
$108$	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	$0.674590\pi$
$110$	14.1198	+	2.86860i	1.34627	+	0.273510i
$111$	−2.56547	−	4.44352i	−0.243503	−	0.421760i
$112$			1.80606i			0.170657i
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.193993	+	0.981003i	$0.562144\pi$
$114$	5.26599	−	9.12096i	0.493205	−	0.854256i
$115$	−5.05506	−	15.0939i	−0.471387	−	1.40752i
$116$	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
$120$	3.55181	−	1.18953i	0.324234	−	0.108588i
$121$	−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	0.685871	−	0.727723i	$-0.259421\pi$
$127$	4.49176	+	2.59332i	0.398580	+	0.230120i	−0.287291	+	0.957843i	$0.592755\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.35026			0.294974
$130$	−4.98127	+	6.33932i	−0.436886	+	0.555995i
$131$	−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	−0.709771	−	0.704433i	$-0.751202\pi$
$137$	−5.32095	+	3.07205i	−0.454600	+	0.262463i	0.255171	+	0.966896i	$0.417868\pi$
$138$			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	$0.688868\pi$
$140$	−1.28250	−	3.82943i	−0.108391	−	0.323646i
$141$	−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
$145$	−4.90355	+	1.64223i	−0.407218	+	0.136380i
$146$	−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	$-0.395038\pi$
$150$	−6.68627	+	5.04434i	−0.545932	+	0.411869i
$151$	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	$-0.799586\pi$
$157$		−	14.7562i		−	1.17768i	0.808251	−	0.588838i	$-0.200414\pi$
$158$	1.98714	+	1.14728i	0.158088	+	0.0912724i
$159$	−0.759403	+	1.31532i	−0.0602246	+	0.104312i
$160$	2.19130	+	0.445186i	0.173238	+	0.0351951i
$161$	12.8568			1.01326
$162$	7.25779	−	4.19029i	0.570226	−	0.329220i
$163$	11.7127	−	6.76234i	0.917411	−	0.529668i	0.0346029	−	0.999401i	$-0.488983\pi$
$163$	11.7127	−	6.76234i	0.917411	−	0.529668i	0.882808	+	0.469734i	$0.155650\pi$
$164$	−7.50659			−0.586166
$165$	23.6526	+	4.80527i	1.84135	+	0.374090i
$166$	6.66902	−	11.5511i	0.517616	−	0.896538i
$167$	−20.2858	−	11.7120i	−1.56977	−	0.906304i	−0.996195	−	0.0871479i	$-0.972225\pi$
$167$	−20.2858	−	11.7120i	−1.56977	−	0.906304i	−0.573570	−	0.819157i	$-0.694442\pi$
$168$			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	−0.339974	−	0.940435i	$-0.610418\pi$
$173$	4.00480	−	2.31217i	0.304479	−	0.175791i	0.644453	+	0.764644i	$0.277085\pi$
$174$	3.87399			0.293687
$175$	5.43862	+	7.20889i	0.411121	+	0.544941i
$176$	−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	$0.267216\pi$
$180$	−0.411207	+	0.137716i	−0.0306496	+	0.0102647i
$181$	−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
$185$	2.17507	+	6.49454i	0.159914	+	0.477488i
$186$	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	0.868255	−	0.496119i	$-0.165242\pi$
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.00447566	+	0.999990i	$0.498575\pi$
$194$	13.8315			0.993041
$195$	−8.34428	+	10.6192i	−0.597547	+	0.760456i
$196$	−3.73813			−0.267010
$197$	12.2166	+	7.05325i	0.870396	+	0.502523i	0.867480	−	0.497473i	$-0.165739\pi$
$197$	12.2166	+	7.05325i	0.870396	+	0.502523i	0.00291585	+	0.999996i	$0.499072\pi$
$198$	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
$205$	15.9163	−	5.33049i	1.11165	−	0.372298i
$206$	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
$210$	−2.14836	−	6.41479i	−0.148251	−	0.442663i
$211$	−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
$215$	−4.38261	−	0.890373i	−0.298891	−	0.0607229i
$216$	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	0.978136	−	0.207966i	$-0.0666842\pi$
$223$	19.2205	+	11.0970i	1.28710	+	0.743108i	0.308965	+	0.951074i	$0.400018\pi$
$224$	−0.903032	+	1.56410i	−0.0603363	+	0.104506i
$225$	0.774096	−	0.584003i	0.0516064	−	0.0389336i
$226$	−14.0000			−0.931266
$227$	−11.5490	+	6.66784i	−0.766536	+	0.442560i	−0.831638	−	0.555319i	$-0.812596\pi$
$227$	−11.5490	+	6.66784i	−0.766536	+	0.442560i	0.0651014	+	0.997879i	$0.479263\pi$
$228$	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	$0.832572\pi$
$230$	3.16915	−	15.5993i	0.208968	−	1.02858i
$231$	−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	$-0.760418\pi$
$233$		−	20.8691i		−	1.36718i	0.729867	−	0.683589i	$-0.239582\pi$
$234$	−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	$0.335309\pi$
$240$	3.67072	+	0.745746i	0.236944	+	0.0481377i
$241$	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
$245$	7.92603	−	2.65448i	0.506376	−	0.169589i
$246$	−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
$250$	10.0872	−	4.82174i	0.637968	−	0.304954i
$251$	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	−0.0960955	−	0.995372i	$-0.530635\pi$
$257$	−16.1300	−	9.31265i	−1.00616	−	0.580907i	−0.910065	+	0.414465i	$0.863969\pi$
$258$	2.90141	+	1.67513i	0.180634	+	0.104289i
$259$	−5.53198			−0.343740
$260$	−7.48357	+	2.99937i	−0.464111	+	0.186013i
$261$	−0.448507			−0.0277619
$262$	−9.35406	−	5.40057i	−0.577896	−	0.333648i
$263$	−19.9363	−	11.5102i	−1.22933	−	0.709751i	−0.262437	−	0.964949i	$-0.584526\pi$
$263$	−19.9363	−	11.5102i	−1.22933	−	0.709751i	−0.966889	+	0.255198i	$0.917859\pi$
$264$	−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	$0.968070\pi$
$270$	−11.3443	+	3.79927i	−0.690389	+	0.231216i
$271$	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
$275$	−29.6638	−	12.5719i	−1.78879	−	0.758116i
$276$	−5.96239	+	10.3272i	−0.358894	+	0.621622i
$277$	7.35125	−	4.24424i	0.441694	−	0.255012i	−0.262622	−	0.964899i	$-0.584587\pi$
$277$	7.35125	−	4.24424i	0.441694	−	0.255012i	0.704316	+	0.709887i	$0.251254\pi$
$278$			10.3380i			0.620035i
$279$	−0.315820	−	0.547016i	−0.0189076	−	0.0327490i
$280$	0.804035	−	3.95763i	0.0480503	−	0.236514i
$281$	−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	0.539038	−	0.842282i	$-0.318788\pi$
$283$	1.33100	+	0.768452i	0.0791196	+	0.0456797i	−0.459918	+	0.887961i	$0.652121\pi$
$284$	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
$290$	−5.06772	−	1.02956i	−0.297587	−	0.0604579i
$291$	23.1695			1.35822
$292$	−2.25790	+	1.30360i	−0.132134	+	0.0762875i
$293$	−5.13527	+	2.96485i	−0.300006	+	0.173208i	−0.642446	−	0.766331i	$-0.722080\pi$
$293$	−5.13527	+	2.96485i	−0.300006	+	0.173208i	0.342440	+	0.939540i	$0.388747\pi$
$294$	−6.26187			−0.365199
$295$	2.92689	−	14.4068i	0.170410	−	0.838794i
$296$	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
$305$	4.87487	−	23.9951i	0.279134	−	1.37396i
$306$	−0.0466606	−	0.0808185i	−0.00266741	−	0.00462009i
$307$			17.9756i			1.02592i	0.858413	+	0.512960i	$0.171451\pi$
$307$			17.9756i			1.02592i	−0.858413	+	0.512960i	$0.828549\pi$
$308$	−10.0784	+	5.81876i	−0.574269	+	0.331555i
$309$	2.57570	−	4.46124i	0.146526	−	0.253791i
$310$	−2.31278	−	6.90575i	−0.131357	−	0.392220i
$311$	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	$-0.769548\pi$
$313$		−	23.4372i		−	1.32475i	0.749172	−	0.662376i	$-0.230452\pi$
$314$	7.37812	−	12.7793i	0.416371	−	0.721176i
$315$	0.248724	+	0.742666i	0.0140140	+	0.0418445i
$316$	1.14728	+	1.98714i	0.0645393	+	0.111785i
$317$			20.6507i			1.15986i	0.814667	+	0.579929i	$0.196920\pi$
$317$			20.6507i			1.15986i	−0.814667	+	0.579929i	$0.803080\pi$
$318$	−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
$325$	13.7377	−	11.6738i	0.762028	−	0.647544i
$326$	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
$335$	0.461385	+	1.37765i	0.0252081	+	0.0752691i
$336$	−1.51270	+	2.62007i	−0.0825243	+	0.142936i
$337$			8.40597i			0.457902i	0.973438	+	0.228951i	$0.0735296\pi$
$337$			8.40597i			0.457902i	−0.973438	+	0.228951i	$0.926470\pi$
$338$	−10.4300	+	7.75988i	−0.567316	+	0.422082i
$339$	−23.4518			−1.27373
$340$	−0.341700	−	1.02028i	−0.0185313	−	0.0553327i
$341$	−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
$345$	5.30875	−	26.1308i	0.285813	−	1.40684i
$346$	4.62435			0.248606
$347$	18.3177	−	10.5757i	0.983343	−	0.567733i	0.0800652	−	0.996790i	$-0.474487\pi$
$347$	18.3177	−	10.5757i	0.983343	−	0.567733i	0.903278	+	0.429056i	$0.141154\pi$
$348$	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	0.993254	−	0.115958i	$-0.0369937\pi$
$353$	26.1056	+	15.0721i	1.38946	+	0.802204i	0.396205	+	0.918162i	$0.370327\pi$
$354$	−5.50659	+	9.53769i	−0.292672	+	0.506922i
$355$	−1.63068	+	8.02655i	−0.0865474	+	0.426005i
$356$	−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	$0.428954\pi$
$360$	−0.424974	−	0.0863379i	−0.0223981	−	0.00455041i
$361$	−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	−0.0107388	−	0.999942i	$-0.503418\pi$
$367$	−16.8983	−	9.75623i	−0.882084	−	0.509271i	−0.871345	+	0.490671i	$0.836752\pi$
$368$	−6.16499	+	3.55936i	−0.321372	+	0.185544i
$369$	1.45580			0.0757860
$370$	−1.36361	+	6.71197i	−0.0708906	+	0.348939i
$371$	0.818760	+	1.41813i	0.0425079	+	0.0736258i
$372$			5.45580i			0.282870i
$373$	−7.37324	+	4.25694i	−0.381772	+	0.220416i	−0.678589	−	0.734518i	$-0.737408\pi$
$373$	−7.37324	+	4.25694i	−0.381772	+	0.220416i	0.296817	+	0.954934i	$0.404075\pi$
$374$	−1.55031	+	2.68521i	−0.0801645	+	0.138849i
$375$	16.8973	−	8.07704i	0.872574	−	0.417097i
$376$	−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	$0.997628\pi$
$380$	−13.3310	+	4.46464i	−0.683865	+	0.229031i
$381$	4.34415	+	7.52429i	0.222558	+	0.385481i
$382$		−	0.355186i		−	0.0181729i
$383$	24.0059	−	13.8598i	1.22664	−	0.708202i	0.260316	−	0.965523i	$-0.416173\pi$
$383$	24.0059	−	13.8598i	1.22664	−	0.708202i	0.966326	+	0.257321i	$0.0828399\pi$
$384$	−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	$0.574526\pi$
$390$	−12.5360	+	5.02434i	−0.634783	+	0.254417i
$391$	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	−0.530764	−	0.847520i	$-0.678095\pi$
$397$	−1.23877	+	0.715205i	−0.0621721	+	0.0358951i	0.468592	+	0.883415i	$0.344762\pi$
$398$		−	3.14903i		−	0.157847i
$399$	−9.51071	−	16.4730i	−0.476131	−	0.824683i
$400$	−4.60362	−	1.95108i	−0.230181	−	0.0975538i
$401$	−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
$405$	−17.7695	+	5.95112i	−0.882973	+	0.295714i
$406$	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	$0.761253\pi$
$410$	16.4492	+	3.34183i	0.812368	+	0.165041i
$411$	−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	$0.290625\pi$
$420$	1.34686	−	6.62955i	0.0657202	−	0.323489i
$421$	−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
$425$	1.44903	+	1.92068i	0.0702881	+	0.0931668i
$426$	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	−0.796279	−	0.604930i	$-0.793201\pi$
$433$	−13.9529	+	8.05571i	−0.670534	+	0.387133i	0.125745	+	0.992063i	$0.459868\pi$
$434$	5.88224			0.282357
$435$	−8.48909	−	1.72465i	−0.407021	−	0.0826906i
$436$	−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	$0.167301\pi$
$440$	4.57564	+	13.6624i	0.218135	+	0.651331i
$441$	0.724961			0.0345220
$442$	−0.953161	−	1.44969i	−0.0453372	−	0.0689548i
$443$			40.9135i			1.94386i	0.235271	+	0.971930i	$0.424402\pi$
$443$			40.9135i			1.94386i	−0.235271	+	0.971930i	$0.575598\pi$
$444$	2.56547	−	4.44352i	0.121752	−	0.210880i
$445$	2.45178	−	0.821117i	0.116225	−	0.0389247i
$446$	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
$455$	5.41706	+	13.5158i	0.253956	+	0.633630i
$456$	10.5320			0.493205
$457$	−28.2912	−	16.3339i	−1.32341	−	0.764068i	−0.339135	−	0.940738i	$-0.610134\pi$
$457$	−28.2912	−	16.3339i	−1.32341	−	0.764068i	−0.984270	+	0.176669i	$0.943468\pi$
$458$	−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	$0.0617196\pi$
$463$			8.29218i			0.385370i	−0.981261	+	0.192685i	$0.938280\pi$
$464$	1.15633	+	2.00281i	0.0536810	+	0.0929783i
$465$	−3.87421	−	11.5680i	−0.179662	−	0.536455i
$466$	10.4345	−	18.0731i	0.483370	−	0.837222i
$467$			23.5369i			1.08916i	0.838710	+	0.544579i	$0.183311\pi$
$467$			23.5369i			1.08916i	−0.838710	+	0.544579i	$0.816689\pi$
$468$	−0.698071	+	0.0405512i	−0.0322684	+	0.00187448i
$469$	−1.17347			−0.0541857
$470$	4.65184	−	1.55793i	0.214573	−	0.0718621i
$471$	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
$475$	25.0955	−	18.9329i	1.15146	−	0.868701i
$476$	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
$485$	−30.3089	−	6.15758i	−1.37626	−	0.279601i
$486$	−2.01222			−0.0912761
$487$	11.7432	−	6.77996i	0.532137	−	0.307229i	−0.209749	−	0.977755i	$-0.567265\pi$
$487$	11.7432	−	6.77996i	0.532137	−	0.307229i	0.741886	+	0.670526i	$0.233931\pi$
$488$	−9.48313	+	5.47508i	−0.429281	+	0.247845i
$489$	22.6556			1.02452
$490$	8.19139	+	1.66417i	0.370049	+	0.0751794i
$491$	−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	$0.399519\pi$
$500$	11.1466	+	0.867833i	0.498491	+	0.0388107i
$501$	−19.6192	−	33.9814i	−0.876521	−	1.51818i
$502$			4.21203i			0.187992i
$503$	−2.98650	+	1.72425i	−0.133161	+	0.0768807i	−0.565101	−	0.825022i	$-0.691163\pi$
$503$	−2.98650	+	1.72425i	−0.133161	+	0.0768807i	0.431940	+	0.901903i	$0.357829\pi$
$504$	0.175131	−	0.303336i	0.00780095	−	0.0135116i
$505$	−20.3549	+	6.81698i	−0.905779	+	0.303352i
$506$	−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	$0.925948\pi$
$510$	−0.572393	−	1.70911i	−0.0253460	−	0.0756807i
$511$	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
$520$	−7.98064	−	1.14425i	−0.349974	−	0.0501787i
$521$	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	0.287537	−	0.957769i	$-0.407163\pi$
$523$	−9.10529	−	5.25694i	−0.398146	−	0.229870i	−0.685684	+	0.727899i	$0.740497\pi$
$524$	−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
$530$	1.92245	−	0.643841i	0.0835058	−	0.0279666i
$531$	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
$535$	−1.18953	−	3.55181i	−0.0514277	−	0.153558i
$536$	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
$540$	−11.7240	−	2.38186i	−0.504523	−	0.102499i
$541$	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	$-0.832047\pi$
$547$		−	23.5515i		−	1.00699i	0.863998	−	0.503495i	$-0.167953\pi$
$548$	−5.32095	−	3.07205i	−0.227300	−	0.131232i
$549$	1.06182	−	1.83912i	0.0453173	−	0.0784919i
$550$	−19.4036	−	25.7195i	−0.827374	−	1.09668i
$551$	−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
$555$	−2.28422	+	11.2434i	−0.0969598	+	0.477257i
$556$	−5.16902	+	8.95301i	−0.219215	+	0.379692i
$557$	−17.3602	−	10.0229i	−0.735576	−	0.424685i	0.0848824	−	0.996391i	$-0.472949\pi$
$557$	−17.3602	−	10.0229i	−0.735576	−	0.424685i	−0.820459	+	0.571706i	$0.806282\pi$
$558$		−	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	−0.252651	−	0.967557i	$-0.581303\pi$
$563$	10.8898	−	6.28726i	0.458952	−	0.264976i	0.711604	+	0.702581i	$0.247969\pi$
$564$	−3.67513			−0.154751
$565$	30.6782	+	6.23261i	1.29064	+	0.262208i
$566$	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	$0.138007\pi$
$570$	−22.3311	+	7.47885i	−0.935348	+	0.313255i
$571$	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
$575$	−13.8892	+	32.7718i	−0.579218	+	1.36668i
$576$	0.0969683	+	0.167954i	0.00404035	+	0.00699808i
$577$			37.8169i			1.57434i	0.616738	+	0.787168i	$0.288454\pi$
$577$			37.8169i			1.57434i	−0.616738	+	0.787168i	$0.711546\pi$
$578$	−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
$585$	1.45134	−	0.581688i	0.0600054	−	0.0240498i
$586$	−5.92970			−0.244954
$587$	19.5289	+	11.2750i	0.806046	+	0.465371i	0.845581	−	0.533848i	$-0.179254\pi$
$587$	19.5289	+	11.2750i	0.806046	+	0.465371i	−0.0395351	+	0.999218i	$0.512588\pi$
$588$	−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	$0.0550954\pi$
$593$			8.38787i			0.344449i	−0.985058	+	0.172224i	$0.944905\pi$
$594$	17.2374	+	29.8561i	0.707260	+	1.22501i
$595$	−1.84270	+	0.617132i	−0.0755433	+	0.0253000i
$596$	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	$0.702555\pi$
$600$	−7.71166	−	3.26831i	−0.314827	−	0.133428i
$601$	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
$605$	−13.5870	+	66.8780i	−0.552389	+	2.71898i
$606$	16.0811			0.653250
$607$	−18.8372	+	10.8757i	−0.764578	+	0.441429i	−0.830937	−	0.556367i	$-0.812195\pi$
$607$	−18.8372	+	10.8757i	−0.764578	+	0.441429i	0.0663591	+	0.997796i	$0.478862\pi$
$608$	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	−0.147488	−	0.989064i	$-0.547119\pi$
$613$	−26.6848	−	15.4064i	−1.07779	−	0.622261i	−0.930299	+	0.366803i	$0.880452\pi$
$614$	−8.98778	+	15.5673i	−0.362717	+	0.628245i
$615$	27.5546	+	5.59800i	1.11111	+	0.225733i
$616$	−11.6375			−0.468889
$617$	39.9125	−	23.0435i	1.60682	−	0.927696i	0.616740	−	0.787167i	$-0.288453\pi$
$617$	39.9125	−	23.0435i	1.60682	−	0.927696i	0.990077	−	0.140529i	$-0.0448804\pi$
$618$	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	$0.412170\pi$
$620$	1.44995	−	7.13694i	0.0582312	−	0.286627i
$621$	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
$630$	−0.155932	+	0.767530i	−0.00621247	+	0.0305791i
$631$	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
$635$	−3.68308	−	10.9973i	−0.146159	−	0.436416i
$636$	−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
$640$	0.710109	+	2.12032i	0.0280695	+	0.0838129i
$641$	−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	−0.290119	−	0.956991i	$-0.593695\pi$
$643$	9.98067	−	5.76234i	0.393599	−	0.227245i	0.683718	+	0.729746i	$0.260362\pi$
$644$	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	0.436217	−	0.899841i	$-0.356318\pi$
$647$	−3.17849	−	1.83510i	−0.124959	−	0.0721453i	−0.561177	+	0.827696i	$0.689651\pi$
$648$	7.25779	+	4.19029i	0.285113	+	0.164610i
$649$	−42.3634			−1.66291
$650$	17.7340	−	3.24095i	0.695586	−	0.127121i
$651$	9.85352			0.386190
$652$	11.7127	+	6.76234i	0.458706	+	0.264834i
$653$	7.02043	+	4.05325i	0.274731	+	0.158616i	0.631036	−	0.775754i	$-0.282630\pi$
$653$	7.02043	+	4.05325i	0.274731	+	0.158616i	−0.356305	+	0.934370i	$0.615964\pi$
$654$	−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	$0.715704\pi$
$660$	7.66480	+	22.8864i	0.298352	+	0.890851i
$661$	−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
$665$	8.06342	+	24.0766i	0.312686	+	0.933650i
$666$	−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
$670$	−0.289255	+	1.42377i	−0.0111749	+	0.0550052i
$671$	−70.5583			−2.72387
$672$	−2.62007	+	1.51270i	−0.101071	+	0.0583535i
$673$	−34.9956	−	20.2047i	−1.34898	−	0.778836i	−0.360877	−	0.932613i	$-0.617523\pi$
$673$	−34.9956	−	20.2047i	−1.34898	−	0.778836i	−0.988105	+	0.153778i	$0.950856\pi$
$674$	−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	$-0.911725\pi$
$677$		−	14.2473i		−	0.547567i	0.961791	−	0.273784i	$-0.0882752\pi$
$678$	−20.3099	−	11.7259i	−0.779996	−	0.450331i
$679$	12.4902	−	21.6337i	0.479332	−	0.830227i
$680$	0.214221	−	1.05444i	0.00821501	−	0.0404360i
$681$	−22.3390			−0.856032
$682$	−18.1747	+	10.4932i	−0.695946	+	0.401805i
$683$	−5.02599	+	2.90175i	−0.192314	+	0.111033i	−0.593065	−	0.805154i	$-0.702082\pi$
$683$	−5.02599	+	2.90175i	−0.192314	+	0.111033i	0.400751	+	0.916187i	$0.368749\pi$
$684$	−1.21933			−0.0466222
$685$	13.4636	+	2.73527i	0.514418	+	0.104509i
$686$	−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
$695$	4.60236	−	22.6538i	0.174577	−	0.859307i
$696$	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
$700$	−3.52377	+	8.31443i	−0.133186	+	0.314256i
$701$	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
$705$	7.79244	−	2.60974i	0.293480	−	0.0982886i
$706$	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
$715$	−40.8479	−	32.0972i	−1.52763	−	1.20037i
$716$	−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
$725$	10.6466	+	4.51216i	0.395403	+	0.167577i
$726$	25.5623	−	44.2752i	0.948706	−	1.64321i
$727$		−	24.7948i		−	0.919588i	−0.888026	−	0.459794i	$-0.847923\pi$
$727$		−	24.7948i		−	0.919588i	0.888026	−	0.459794i	$-0.152077\pi$
$728$	2.92340	−	5.81876i	0.108349	−	0.215658i
$729$	−28.5125			−1.05602
$730$	5.52810	−	1.85140i	0.204604	−	0.0685233i
$731$	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	$-0.678387\pi$
$733$		−	45.8651i		−	1.69407i	0.531540	−	0.847033i	$-0.321613\pi$
$734$	−9.75623	−	16.8983i	−0.360109	−	0.623727i
$735$	13.7216	+	2.78770i	0.506130	+	0.102826i
$736$	−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	0.386936	−	0.922107i	$-0.373534\pi$
$743$	−5.94673	−	3.43335i	−0.218165	−	0.125957i	−0.605100	+	0.796149i	$0.706867\pi$
$744$	−2.72790	+	4.72486i	−0.100010	+	0.173222i
$745$	−7.14559	+	35.1721i	−0.261794	+	1.28861i
$746$	−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
$750$	18.6720	+	1.45373i	0.681806	+	0.0530828i
$751$	−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	0.868762	−	0.495230i	$-0.164916\pi$
$757$	24.0541	+	13.8876i	0.874261	+	0.504755i	0.00549931	+	0.999985i	$0.498250\pi$
$758$	−17.0768	+	9.85931i	−0.620258	+	0.358106i
$759$	−76.8383			−2.78905
$760$	−13.7773	−	2.79900i	−0.499755	−	0.101530i
$761$	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
$765$	0.0662682	+	0.197870i	0.00239593	+	0.00715402i
$766$	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	$0.119685\pi$
$770$	24.6752	−	8.26390i	0.889234	−	0.297810i
$771$	−15.5999	−	27.0198i	−0.561817	−	0.973096i
$772$			14.0000i			0.503871i
$773$	−5.09129	+	2.93946i	−0.183121	+	0.105725i	−0.588758	−	0.808309i	$-0.700383\pi$
$773$	−5.09129	+	2.93946i	−0.183121	+	0.105725i	0.405637	+	0.914034i	$0.367050\pi$
$774$	−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
$780$	−13.3686	−	1.91677i	−0.478674	−	0.0686313i
$781$	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	−0.0873591	−	0.996177i	$-0.527843\pi$
$787$	20.5261	−	11.8507i	0.731676	−	0.422433i	0.819035	+	0.573744i	$0.194509\pi$
$788$			14.1065i			0.502523i
$789$	−19.2811	−	33.3959i	−0.686427	−	1.18893i
$790$	−1.62938	−	4.86518i	−0.0579708	−	0.173095i
$791$	−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
$795$	3.22035	−	1.07852i	0.114214	−	0.0382511i
$796$	1.57452	−	2.72714i	0.0558072	−	0.0966609i
$797$	−42.0193	+	24.2599i	−1.48840	+	0.859329i	−0.999912	−	0.0132409i	$-0.995785\pi$
$797$	−42.0193	+	24.2599i	−1.48840	+	0.859329i	−0.488489	+	0.872570i	$0.662452\pi$
$798$		−	19.0214i		−	0.673351i
$799$	0.527855	+	0.914271i	0.0186742	+	0.0323446i
$800$	−3.01131	−	3.99149i	−0.106466	−	0.141121i
$801$	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	$0.263964\pi$
$810$	−18.3644	−	3.73092i	−0.645259	−	0.131091i
$811$	−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
$815$	−29.6367	−	6.02101i	−1.03813	−	0.210907i
$816$	−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	−0.640243	−	0.768172i	$-0.721166\pi$
$823$	−8.46604	+	4.88787i	−0.295108	+	0.170381i	0.345135	+	0.938553i	$0.387833\pi$
$824$	3.07522			0.107130
$825$	−32.5036	−	43.0835i	−1.13163	−	1.49998i
$826$	5.93700	+	10.2832i	0.206575	+	0.357798i
$827$			28.1598i			0.979213i	0.871943	+	0.489607i	$0.162860\pi$
$827$			28.1598i			0.979213i	−0.871943	+	0.489607i	$0.837140\pi$
$828$	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	$0.0525039\pi$
$830$	−28.2809	+	9.47146i	−0.981644	+	0.328759i
$831$	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
$835$	16.6336	+	49.6665i	0.575631	+	1.71878i
$836$	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
$845$	26.3098	−	12.3610i	0.905085	−	0.425230i
$846$	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	$0.286605\pi$
$853$			45.7704i			1.56715i	−0.621299	+	0.783574i	$0.713395\pi$
$854$	9.88835	+	17.1271i	0.338372	+	0.586078i
$855$	2.58536	−	0.865856i	0.0884176	−	0.0296117i
$856$	−0.837565	+	1.45071i	−0.0286274	+	0.0495841i
$857$		−	27.8169i		−	0.950206i	−0.879930	−	0.475103i	$-0.842411\pi$
$857$		−	27.8169i		−	0.950206i	0.879930	−	0.475103i	$-0.157589\pi$
$858$	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	$0.646105\pi$
$860$	−1.42022	−	4.24063i	−0.0484290	−	0.144604i
$861$	−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	$-0.896776\pi$
$863$		−	18.7210i		−	0.637270i	0.947877	−	0.318635i	$-0.103224\pi$
$864$	2.67513	+	4.63346i	0.0910098	+	0.157634i
$865$	−10.1333	−	2.05870i	−0.344544	−	0.0699978i
$866$	−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
$875$	1.56736	−	20.1315i	0.0529865	−	0.680568i
$876$	−4.36741			−0.147561
$877$	−19.6466	+	11.3430i	−0.663418	+	0.383025i	−0.793578	−	0.608468i	$-0.791784\pi$
$877$	−19.6466	+	11.3430i	−0.663418	+	0.383025i	0.130160	+	0.991493i	$0.458451\pi$
$878$	−0.0722889	+	0.0417360i	−0.00243963	+	0.00140852i
$879$	−9.93303			−0.335033
$880$	−2.86860	+	14.1198i	−0.0967003	+	0.475980i
$881$	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	$0.177592\pi$
$883$			31.4641i			1.05885i	−0.848357	+	0.529425i	$0.822408\pi$
$884$	−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	−0.204809	−	0.978802i	$-0.565657\pi$
$887$	−34.3953	−	19.8581i	−1.15488	−	0.666771i	−0.950072	+	0.312031i	$0.898991\pi$
$888$	4.44352	−	2.56547i	0.149115	−	0.0860914i
$889$	9.36741			0.314173
$890$	2.53386	+	0.514780i	0.0849351	+	0.0172555i
$891$	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
$895$	17.6255	−	5.90289i	0.589154	−	0.197312i
$896$	−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
$900$	0.892810	+	0.378385i	0.0297603	+	0.0126128i
$901$	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	$0.0155944\pi$
$907$	46.3977	+	26.7877i	1.54061	+	0.889472i	0.541811	+	0.840500i	$0.317739\pi$
$908$	−11.5490	−	6.66784i	−0.383268	−	0.221280i
$909$	−1.86177			−0.0617511
$910$	−2.06659	+	14.4136i	−0.0685067	+	0.477805i
$911$	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	$0.494215\pi$
$920$	15.0939	−	5.05506i	0.497632	−	0.166660i
$921$	−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
$925$	5.97616	−	14.1009i	0.196495	−	0.463635i
$926$	−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	$0.888173\pi$
$930$	2.42885	−	11.9553i	0.0796451	−	0.392030i
$931$	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	$0.0552579\pi$
$937$			10.5745i			0.345454i	−0.984970	+	0.172727i	$0.944742\pi$
$938$	−1.01625	−	0.586734i	−0.0331819	−	0.0191576i
$939$	19.6302	−	34.0005i	0.640608	−	1.10957i
$940$	4.80758	+	0.976711i	0.156806	+	0.0318568i
$941$	−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
$945$	−4.30180	+	21.1744i	−0.139937	+	0.688802i
$946$	−6.44358	+	11.1606i	−0.209499	+	0.362863i
$947$	36.7949	+	21.2435i	1.19567	+	0.690322i	0.959588	−	0.281410i	$-0.0908021\pi$
$947$	36.7949	+	21.2435i	1.19567	+	0.690322i	0.236086	+	0.971732i	$0.424135\pi$
$948$			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	0.289346	−	0.957224i	$-0.406562\pi$
$953$	38.9897	−	22.5107i	1.26300	−	0.729193i	0.973654	+	0.228031i	$0.0732288\pi$
$954$	0.175838			0.00569297
$955$	−0.158124	+	0.778321i	−0.00511678	+	0.0251859i
$956$	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
$960$	1.18953	+	3.55181i	0.0383918	+	0.114634i
$961$	−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
$965$	−9.94152	−	29.6844i	−0.320029	−	0.955576i
$966$	10.7685	+	18.6515i	0.346469	+	0.600102i
$967$			24.4763i			0.787104i	0.919302	+	0.393552i	$0.128754\pi$
$967$			24.4763i			0.787104i	−0.919302	+	0.393552i	$0.871246\pi$
$968$	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
$975$	29.7068	−	5.42902i	0.951380	−	0.173868i
$976$	−10.9502			−0.350506
$977$	−11.7021	−	6.75623i	−0.374385	−	0.216151i	0.300988	−	0.953628i	$-0.402684\pi$
$977$	−11.7021	−	6.75623i	−0.374385	−	0.216151i	−0.675372	+	0.737477i	$0.736017\pi$
$978$	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	$-0.840521\pi$
$983$		−	30.1187i		−	0.960638i	0.877094	−	0.480319i	$-0.159479\pi$
$984$	−6.28726	−	10.8898i	−0.200430	−	0.347156i
$985$	−10.0171	−	29.9102i	−0.319173	−	0.953020i
$986$	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
$990$	−0.887385	−	2.64965i	−0.0282029	−	0.0842113i
$991$	−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
$995$	−1.40191	+	6.90048i	−0.0444434	+	0.218760i
$996$	22.3430			0.707964
$997$	14.5638	−	8.40843i	0.461241	−	0.266298i	−0.251325	−	0.967903i	$-0.580866\pi$
$997$	14.5638	−	8.40843i	0.461241	−	0.266298i	0.712566	+	0.701605i	$0.247533\pi$
$998$	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.9.6	yes	12
3.2	odd	2		1170.2.bp.h.919.3		12
4.3	odd	2		1040.2.dh.b.529.2		12
5.2	odd	4		650.2.e.j.451.3		6
5.3	odd	4		650.2.e.k.451.1		6
5.4	even	2	inner	130.2.n.a.9.1	✓	12
13.3	even	3	inner	130.2.n.a.29.1	yes	12
13.4	even	6		1690.2.b.b.339.4		6
13.6	odd	12		1690.2.c.b.1689.2		6
13.7	odd	12		1690.2.c.c.1689.2		6
13.9	even	3		1690.2.b.c.339.1		6
15.14	odd	2		1170.2.bp.h.919.6		12
20.19	odd	2		1040.2.dh.b.529.5		12
39.29	odd	6		1170.2.bp.h.289.6		12
52.3	odd	6		1040.2.dh.b.289.5		12
65.3	odd	12		650.2.e.k.601.1		6
65.4	even	6		1690.2.b.b.339.3		6
65.9	even	6		1690.2.b.c.339.6		6
65.17	odd	12		8450.2.a.bt.1.1		3
65.19	odd	12		1690.2.c.c.1689.5		6
65.22	odd	12		8450.2.a.cb.1.1		3
65.29	even	6	inner	130.2.n.a.29.6	yes	12
65.42	odd	12		650.2.e.j.601.3		6
65.43	odd	12		8450.2.a.ca.1.3		3
65.48	odd	12		8450.2.a.bu.1.3		3
65.59	odd	12		1690.2.c.b.1689.5		6
195.29	odd	6		1170.2.bp.h.289.3		12
260.159	odd	6		1040.2.dh.b.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	5.4	even	2	inner
130.2.n.a.9.6	yes	12	1.1	even	1	trivial
130.2.n.a.29.1	yes	12	13.3	even	3	inner
130.2.n.a.29.6	yes	12	65.29	even	6	inner
650.2.e.j.451.3		6	5.2	odd	4
650.2.e.j.601.3		6	65.42	odd	12
650.2.e.k.451.1		6	5.3	odd	4
650.2.e.k.601.1		6	65.3	odd	12
1040.2.dh.b.289.2		12	260.159	odd	6
1040.2.dh.b.289.5		12	52.3	odd	6
1040.2.dh.b.529.2		12	4.3	odd	2
1040.2.dh.b.529.5		12	20.19	odd	2
1170.2.bp.h.289.3		12	195.29	odd	6
1170.2.bp.h.289.6		12	39.29	odd	6
1170.2.bp.h.919.3		12	3.2	odd	2
1170.2.bp.h.919.6		12	15.14	odd	2
1690.2.b.b.339.3		6	65.4	even	6
1690.2.b.b.339.4		6	13.4	even	6
1690.2.b.c.339.1		6	13.9	even	3
1690.2.b.c.339.6		6	65.9	even	6
1690.2.c.b.1689.2		6	13.6	odd	12
1690.2.c.b.1689.5		6	65.59	odd	12
1690.2.c.c.1689.2		6	13.7	odd	12
1690.2.c.c.1689.5		6	65.19	odd	12
8450.2.a.bt.1.1		3	65.17	odd	12
8450.2.a.bu.1.3		3	65.48	odd	12
8450.2.a.ca.1.3		3	65.43	odd	12
8450.2.a.cb.1.1		3	65.22	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} +(-0.710109 - 2.12032i) q^{10} +(-3.22179 + 5.58031i) q^{11} +1.67513i q^{12} +(-1.98082 - 3.01270i) q^{13} +1.80606 q^{14} +(-1.18953 - 3.55181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.416726 - 0.240597i) q^{17} -0.193937i q^{18} +(-3.14363 - 5.44492i) q^{19} +(0.445186 - 2.19130i) 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} +(0.745746 - 3.67072i) q^{30} +3.25694 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-9.34774 + 5.39692i) q^{33} +0.481194 q^{34} +(-3.95763 - 0.804035i) 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} +(-0.0863379 + 0.424974i) q^{45} +(3.55936 + 6.16499i) q^{46} +2.19394i q^{47} +(-1.45071 + 0.837565i) q^{48} +(-1.86907 + 3.23732i) q^{49} +(-1.95108 + 4.60362i) q^{50} +0.806063 q^{51} +(1.61866 - 3.22179i) q^{52} +0.906679i q^{53} +(2.67513 - 4.63346i) q^{54} +(13.6624 - 4.57564i) 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} +(-1.14425 + 7.98064i) 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} +(-3.26831 + 7.71166i) q^{75} +(3.14363 - 5.44492i) q^{76} +11.6375i q^{77} +(2.71147 - 5.39692i) q^{78} +2.29455 q^{79} +(2.12032 - 0.710109i) q^{80} +(4.19029 - 7.25779i) q^{81} +(-6.50089 + 3.75329i) q^{82} -13.3380i q^{83} +(1.51270 + 2.62007i) q^{84} +(-1.05444 - 0.214221i) 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} +(-2.79900 + 13.7773i) 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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