LMFDB - Embedded newform 378.2.u.c.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			295.2
Character	$\chi$	$=$	378.295
Dual form			378.2.u.c.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.49215 - 0.879480i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.11377 + 1.77366i) q^{5} +(1.12523 - 1.31676i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.45303 + 2.62463i) q^{9} +(-1.37966 - 2.38965i) q^{10} +(-0.597316 - 0.501208i) q^{11} +(1.10136 + 1.33679i) q^{12} +(-0.677616 - 3.84295i) q^{13} +(0.173648 + 0.984808i) q^{14} +(4.71396 - 0.787553i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.34766 - 4.06627i) q^{17} +(-2.83708 + 0.975191i) q^{18} +(3.82914 - 6.63227i) q^{19} +(2.59292 - 0.943745i) q^{20} +(-1.70296 - 0.316096i) q^{21} +(0.597316 - 0.501208i) q^{22} +(3.02510 + 1.10105i) q^{23} +(-1.50773 + 0.852500i) q^{24} +(0.453897 - 2.57418i) q^{25} +3.90223 q^{26} +(0.140177 - 5.19426i) q^{27} -1.00000 q^{28} +(0.791941 - 4.49132i) q^{29} +(-0.0429819 + 4.77910i) q^{30} +(1.85900 + 0.676621i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.450483 + 1.27321i) q^{33} +(4.41216 - 1.60589i) q^{34} +(-1.37966 + 2.38965i) q^{35} +(-0.467722 - 2.96332i) q^{36} +(-4.95084 - 8.57511i) q^{37} +(5.86659 + 4.92265i) q^{38} +(-2.36869 + 6.33021i) q^{39} +(0.479152 + 2.71741i) q^{40} +(0.497172 + 2.81961i) q^{41} +(0.607010 - 1.62220i) q^{42} +(2.61760 + 2.19643i) q^{43} +(0.389870 + 0.675275i) q^{44} +(-7.72658 - 2.97069i) q^{45} +(-1.60962 + 2.78795i) q^{46} +(-7.88268 + 2.86906i) q^{47} +(-0.577735 - 1.63286i) q^{48} +(0.766044 - 0.642788i) q^{49} +(2.45625 + 0.894002i) q^{50} +(-0.0731388 + 8.13221i) q^{51} +(-0.677616 + 3.84295i) q^{52} +1.58204 q^{53} +(5.09101 + 1.04002i) q^{54} +2.15156 q^{55} +(0.173648 - 0.984808i) q^{56} +(-11.5466 + 6.52869i) q^{57} +(4.28557 + 1.55982i) q^{58} +(2.53250 - 2.12502i) q^{59} +(-4.69903 - 0.872211i) q^{60} +(-10.1860 + 3.70741i) q^{61} +(-0.989154 + 1.71326i) q^{62} +(2.26308 + 1.96939i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(8.24841 + 6.92124i) q^{65} +(-1.33209 + 0.222550i) q^{66} +(1.20144 + 6.81369i) q^{67} +(0.815334 + 4.62399i) q^{68} +(-3.54555 - 4.30344i) q^{69} +(-2.11377 - 1.77366i) q^{70} +(-0.570055 - 0.987364i) q^{71} +(2.99951 + 0.0539579i) q^{72} +(7.89053 - 13.6668i) q^{73} +(9.30454 - 3.38658i) q^{74} +(-2.94122 + 3.44186i) q^{75} +(-5.86659 + 4.92265i) q^{76} +(-0.732716 - 0.266687i) q^{77} +(-5.82272 - 3.43194i) q^{78} +(0.445866 - 2.52863i) q^{79} -2.75933 q^{80} +(-4.77742 + 7.62734i) q^{81} -2.86310 q^{82} +(2.26691 - 12.8563i) q^{83} +(1.49215 + 0.879480i) q^{84} +(12.1746 + 4.43119i) q^{85} +(-2.61760 + 2.19643i) q^{86} +(-5.13172 + 6.00523i) q^{87} +(-0.732716 + 0.266687i) q^{88} +(-5.93824 + 10.2853i) q^{89} +(4.26726 - 7.09334i) q^{90} +(-1.95112 - 3.37943i) q^{91} +(-2.46608 - 2.06929i) q^{92} +(-2.17884 - 2.64458i) q^{93} +(-1.45666 - 8.26113i) q^{94} +(3.66948 + 20.8107i) q^{95} +(1.70837 - 0.285415i) q^{96} +(-8.85066 - 7.42659i) q^{97} +(0.500000 + 0.866025i) q^{98} +(0.447570 - 2.29601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29}+ \cdots - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−1.49215	−	0.879480i	−0.861494	−	0.507768i
$3$	−1.49215	−	0.879480i	−0.861494	−	0.507768i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−2.11377	+	1.77366i	−0.945305	+	0.793205i	−0.978501	−	0.206243i	$-0.933876\pi$
$5$	−2.11377	+	1.77366i	−0.945305	+	0.793205i	0.0331953	+	0.999449i	$0.489432\pi$
$6$	1.12523	−	1.31676i	0.459373	−	0.537566i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.45303	+	2.62463i	0.484343	+	0.874878i
$10$	−1.37966	−	2.38965i	−0.436288	−	0.755673i
$11$	−0.597316	−	0.501208i	−0.180098	−	0.151120i	0.548282	−	0.836293i	$-0.315282\pi$
$11$	−0.597316	−	0.501208i	−0.180098	−	0.151120i	−0.728380	+	0.685174i	$0.759726\pi$
$12$	1.10136	+	1.33679i	0.317936	+	0.385897i
$13$	−0.677616	−	3.84295i	−0.187937	−	1.06584i	−0.922124	−	0.386895i	$-0.873548\pi$
$13$	−0.677616	−	3.84295i	−0.187937	−	1.06584i	0.734187	−	0.678947i	$-0.237564\pi$
$14$	0.173648	+	0.984808i	0.0464094	+	0.263201i
$15$	4.71396	−	0.787553i	1.21714	−	0.203345i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.34766	−	4.06627i	−0.569391	−	0.986215i	−0.996626	−	0.0820741i	$-0.973846\pi$
$17$	−2.34766	−	4.06627i	−0.569391	−	0.986215i	0.427235	−	0.904141i	$-0.359488\pi$
$18$	−2.83708	+	0.975191i	−0.668705	+	0.229855i
$19$	3.82914	−	6.63227i	0.878465	−	1.52155i	0.0254404	−	0.999676i	$-0.491901\pi$
$19$	3.82914	−	6.63227i	0.878465	−	1.52155i	0.853025	−	0.521870i	$-0.174765\pi$
$20$	2.59292	−	0.943745i	0.579794	−	0.211028i
$21$	−1.70296	−	0.316096i	−0.371617	−	0.0689777i
$22$	0.597316	−	0.501208i	0.127348	−	0.106858i
$23$	3.02510	+	1.10105i	0.630777	+	0.229584i	0.637569	−	0.770393i	$-0.279940\pi$
$23$	3.02510	+	1.10105i	0.630777	+	0.229584i	−0.00679270	+	0.999977i	$0.502162\pi$
$24$	−1.50773	+	0.852500i	−0.307764	+	0.174016i
$25$	0.453897	−	2.57418i	0.0907793	−	0.514835i
$26$	3.90223			0.765291
$27$	0.140177	−	5.19426i	0.0269772	−	0.999636i
$28$	−1.00000			−0.188982
$29$	0.791941	−	4.49132i	0.147060	−	0.834017i	−0.818630	−	0.574321i	$-0.805266\pi$
$29$	0.791941	−	4.49132i	0.147060	−	0.834017i	0.965690	−	0.259697i	$-0.0836226\pi$
$30$	−0.0429819	+	4.77910i	−0.00784738	+	0.872541i
$31$	1.85900	+	0.676621i	0.333886	+	0.121525i	0.503523	−	0.863982i	$-0.332037\pi$
$31$	1.85900	+	0.676621i	0.333886	+	0.121525i	−0.169636	+	0.985507i	$0.554259\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	0.450483	+	1.27321i	0.0784191	+	0.221637i
$34$	4.41216	−	1.60589i	0.756679	−	0.275409i
$35$	−1.37966	+	2.38965i	−0.233206	+	0.403924i
$36$	−0.467722	−	2.96332i	−0.0779537	−	0.493886i
$37$	−4.95084	−	8.57511i	−0.813914	−	1.40974i	−0.910105	−	0.414377i	$-0.863999\pi$
$37$	−4.95084	−	8.57511i	−0.813914	−	1.40974i	0.0961916	−	0.995363i	$-0.469334\pi$
$38$	5.86659	+	4.92265i	0.951686	+	0.798559i
$39$	−2.36869	+	6.33021i	−0.379295	+	1.01365i
$40$	0.479152	+	2.71741i	0.0757606	+	0.429660i
$41$	0.497172	+	2.81961i	0.0776453	+	0.440348i	0.998703	+	0.0509214i	$0.0162158\pi$
$41$	0.497172	+	2.81961i	0.0776453	+	0.440348i	−0.921057	+	0.389427i	$0.872673\pi$
$42$	0.607010	−	1.62220i	0.0936637	−	0.250311i
$43$	2.61760	+	2.19643i	0.399180	+	0.334952i	0.820177	−	0.572110i	$-0.193875\pi$
$43$	2.61760	+	2.19643i	0.399180	+	0.334952i	−0.420996	+	0.907062i	$0.638320\pi$
$44$	0.389870	+	0.675275i	0.0587752	+	0.101802i
$45$	−7.72658	−	2.97069i	−1.15181	−	0.442844i
$46$	−1.60962	+	2.78795i	−0.237326	+	0.411060i
$47$	−7.88268	+	2.86906i	−1.14981	+	0.418495i	−0.845446	−	0.534062i	$-0.820665\pi$
$47$	−7.88268	+	2.86906i	−1.14981	+	0.418495i	−0.304361	+	0.952557i	$0.598443\pi$
$48$	−0.577735	−	1.63286i	−0.0833888	−	0.235683i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	2.45625	+	0.894002i	0.347366	+	0.126431i
$51$	−0.0731388	+	8.13221i	−0.0102415	+	1.13874i
$52$	−0.677616	+	3.84295i	−0.0939684	+	0.532921i
$53$	1.58204			0.217310			0.108655	−	0.994079i	$-0.465346\pi$
$53$	1.58204			0.217310			0.108655	+	0.994079i	$0.465346\pi$
$54$	5.09101	+	1.04002i	0.692798	+	0.141529i
$55$	2.15156			0.290116
$56$	0.173648	−	0.984808i	0.0232047	−	0.131600i
$57$	−11.5466	+	6.52869i	−1.52939	+	0.864746i
$58$	4.28557	+	1.55982i	0.562723	+	0.204814i
$59$	2.53250	−	2.12502i	0.329703	−	0.276654i	−0.462876	−	0.886423i	$-0.653182\pi$
$59$	2.53250	−	2.12502i	0.329703	−	0.276654i	0.792579	+	0.609769i	$0.208738\pi$
$60$	−4.69903	−	0.872211i	−0.606642	−	0.112602i
$61$	−10.1860	+	3.70741i	−1.30419	+	0.474685i	−0.898358	−	0.439264i	$-0.855239\pi$
$61$	−10.1860	+	3.70741i	−1.30419	+	0.474685i	−0.405829	+	0.913949i	$0.633017\pi$
$62$	−0.989154	+	1.71326i	−0.125623	+	0.217585i
$63$	2.26308	+	1.96939i	0.285121	+	0.248119i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	8.24841	+	6.92124i	1.02309	+	0.858474i
$66$	−1.33209	+	0.222550i	−0.163969	+	0.0273940i
$67$	1.20144	+	6.81369i	0.146779	+	0.832424i	0.965922	+	0.258835i	$0.0833385\pi$
$67$	1.20144	+	6.81369i	0.146779	+	0.832424i	−0.819143	+	0.573590i	$0.805550\pi$
$68$	0.815334	+	4.62399i	0.0988738	+	0.560741i
$69$	−3.54555	−	4.30344i	−0.426835	−	0.518073i
$70$	−2.11377	−	1.77366i	−0.252644	−	0.211993i
$71$	−0.570055	−	0.987364i	−0.0676531	−	0.117179i	0.830215	−	0.557444i	$-0.188218\pi$
$71$	−0.570055	−	0.987364i	−0.0676531	−	0.117179i	−0.897868	+	0.440265i	$0.854884\pi$
$72$	2.99951	+	0.0539579i	0.353496	+	0.00635901i
$73$	7.89053	−	13.6668i	0.923517	−	1.59958i	0.129588	−	0.991568i	$-0.458635\pi$
$73$	7.89053	−	13.6668i	0.923517	−	1.59958i	0.793929	−	0.608010i	$-0.208032\pi$
$74$	9.30454	−	3.38658i	1.08163	−	0.393682i
$75$	−2.94122	+	3.44186i	−0.339623	+	0.397432i
$76$	−5.86659	+	4.92265i	−0.672943	+	0.564667i
$77$	−0.732716	−	0.266687i	−0.0835008	−	0.0303918i
$78$	−5.82272	−	3.43194i	−0.659293	−	0.388591i
$79$	0.445866	−	2.52863i	0.0501638	−	0.284493i	−0.949399	−	0.314074i	$-0.898306\pi$
$79$	0.445866	−	2.52863i	0.0501638	−	0.284493i	0.999562	+	0.0295806i	$0.00941718\pi$
$80$	−2.75933			−0.308502
$81$	−4.77742	+	7.62734i	−0.530824	+	0.847482i
$82$	−2.86310			−0.316177
$83$	2.26691	−	12.8563i	0.248826	−	1.41116i	−0.562611	−	0.826721i	$-0.690203\pi$
$83$	2.26691	−	12.8563i	0.248826	−	1.41116i	0.811437	−	0.584440i	$-0.198686\pi$
$84$	1.49215	+	0.879480i	0.162807	+	0.0959592i
$85$	12.1746	+	4.43119i	1.32052	+	0.480630i
$86$	−2.61760	+	2.19643i	−0.282263	+	0.236847i
$87$	−5.13172	+	6.00523i	−0.550179	+	0.643828i
$88$	−0.732716	+	0.266687i	−0.0781078	+	0.0284289i
$89$	−5.93824	+	10.2853i	−0.629452	+	1.09024i	0.358210	+	0.933641i	$0.383387\pi$
$89$	−5.93824	+	10.2853i	−0.629452	+	1.09024i	−0.987662	+	0.156602i	$0.949946\pi$
$90$	4.26726	−	7.09334i	0.449809	−	0.747704i
$91$	−1.95112	−	3.37943i	−0.204533	−	0.354261i
$92$	−2.46608	−	2.06929i	−0.257107	−	0.215738i
$93$	−2.17884	−	2.64458i	−0.225935	−	0.274230i
$94$	−1.45666	−	8.26113i	−0.150243	−	0.852070i
$95$	3.66948	+	20.8107i	0.376481	+	2.13513i
$96$	1.70837	−	0.285415i	0.174360	−	0.0291300i
$97$	−8.85066	−	7.42659i	−0.898648	−	0.754056i	0.0712773	−	0.997457i	$-0.477292\pi$
$97$	−8.85066	−	7.42659i	−0.898648	−	0.754056i	−0.969926	+	0.243401i	$0.921737\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	0.447570	−	2.29601i	0.0449825	−	0.230757i
$100$	−1.30694	+	2.26369i	−0.130694	+	0.226369i
$101$	17.2973	−	6.29571i	1.72115	−	0.626447i	0.723210	−	0.690628i	$-0.242666\pi$
$101$	17.2973	−	6.29571i	1.72115	−	0.626447i	0.997938	+	0.0641816i	$0.0204437\pi$
$102$	−7.99596	−	1.48417i	−0.791718	−	0.146955i
$103$	−8.61717	+	7.23067i	−0.849075	+	0.712459i	−0.959586	−	0.281416i	$-0.909196\pi$
$103$	−8.61717	+	7.23067i	−0.849075	+	0.712459i	0.110511	+	0.993875i	$0.464751\pi$
$104$	−3.66690	−	1.33464i	−0.359569	−	0.130872i
$105$	4.16031	−	2.35233i	0.406005	−	0.229564i
$106$	−0.274719	+	1.55801i	−0.0266831	+	0.151327i
$107$	0.869353			0.0840435			0.0420218	−	0.999117i	$-0.486620\pi$
$107$	0.869353			0.0840435			0.0420218	+	0.999117i	$0.486620\pi$
$108$	−1.90827	+	4.83307i	−0.183623	+	0.465062i
$109$	−9.99597			−0.957440			−0.478720	−	0.877968i	$-0.658899\pi$
$109$	−9.99597			−0.957440			−0.478720	+	0.877968i	$0.658899\pi$
$110$	−0.373614	+	2.11887i	−0.0356227	+	0.202027i
$111$	−0.154238	+	17.1495i	−0.0146396	+	1.62776i
$112$	0.939693	+	0.342020i	0.0887926	+	0.0323179i
$113$	−8.50125	+	7.13339i	−0.799730	+	0.671053i	−0.948133	−	0.317874i	$-0.897031\pi$
$113$	−8.50125	+	7.13339i	−0.799730	+	0.671053i	0.148403	+	0.988927i	$0.452587\pi$
$114$	−4.42446	−	12.5049i	−0.414388	−	1.17119i
$115$	−8.34724	+	3.03815i	−0.778384	+	0.283309i
$116$	−2.28030	+	3.94960i	−0.211721	+	0.366711i
$117$	9.10175	−	7.36241i	0.841457	−	0.680655i
$118$	1.65297	+	2.86303i	0.152168	+	0.263563i
$119$	−3.59682	−	3.01809i	−0.329720	−	0.276668i
$120$	1.67494	−	4.47619i	0.152900	−	0.408618i
$121$	−1.80455	−	10.2341i	−0.164050	−	0.930375i
$122$	−1.88230	−	10.6751i	−0.170416	−	0.966475i
$123$	1.73793	−	4.64453i	0.156704	−	0.418783i
$124$	−1.51547	−	1.27163i	−0.136093	−	0.114196i
$125$	−3.29203	−	5.70197i	−0.294449	−	0.510000i
$126$	−2.33245	+	1.88672i	−0.207791	+	0.168082i
$127$	3.54082	−	6.13289i	0.314197	−	0.544206i	−0.665069	−	0.746782i	$-0.731598\pi$
$127$	3.54082	−	6.13289i	0.314197	−	0.544206i	0.979267	+	0.202576i	$0.0649313\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−1.97414	−	5.57953i	−0.173813	−	0.491250i
$130$	−8.24841	+	6.92124i	−0.723434	+	0.607033i
$131$	−15.9805	−	5.81641i	−1.39622	−	0.508182i	−0.469165	−	0.883110i	$-0.655445\pi$
$131$	−15.9805	−	5.81641i	−1.39622	−	0.508182i	−0.927054	+	0.374928i	$0.877667\pi$
$132$	0.0121460	−	1.35050i	0.00105717	−	0.117546i
$133$	1.32985	−	7.54194i	0.115312	−	0.653969i
$134$	−6.91880			−0.597693
$135$	8.91656	+	11.2281i	0.767415	+	0.966360i
$136$	−4.69532			−0.402621
$137$	2.04044	−	11.5719i	0.174327	−	0.988657i	−0.764591	−	0.644516i	$-0.777059\pi$
$137$	2.04044	−	11.5719i	0.174327	−	0.988657i	0.938918	−	0.344141i	$-0.111830\pi$
$138$	4.85374	−	2.74441i	0.413178	−	0.233619i
$139$	15.9663	+	5.81126i	1.35424	+	0.492904i	0.914270	−	0.405106i	$-0.132765\pi$
$139$	15.9663	+	5.81126i	1.35424	+	0.492904i	0.439974	+	0.898011i	$0.354988\pi$
$140$	2.11377	−	1.77366i	0.178646	−	0.149902i
$141$	14.2854	+	2.65159i	1.20305	+	0.223304i
$142$	1.07135	−	0.389940i	0.0899059	−	0.0327231i
$143$	−1.52137	+	2.63508i	−0.127223	+	0.220357i
$144$	−0.573998	+	2.94458i	−0.0478332	+	0.245381i
$145$	6.29210	+	10.8982i	0.522531	+	0.905050i
$146$	12.0890	+	10.1439i	1.00049	+	0.839513i
$147$	−1.70837	+	0.285415i	−0.140904	+	0.0235406i
$148$	1.71941	+	9.75126i	0.141335	+	0.801549i
$149$	0.306702	+	1.73939i	0.0251260	+	0.142497i	0.994790	−	0.101945i	$-0.0325065\pi$
$149$	0.306702	+	1.73939i	0.0251260	+	0.142497i	−0.969664	+	0.244441i	$0.921395\pi$
$150$	−2.87884	−	3.49421i	−0.235056	−	0.285301i
$151$	13.1555	+	11.0388i	1.07058	+	0.898326i	0.995105	−	0.0988213i	$-0.0315072\pi$
$151$	13.1555	+	11.0388i	1.07058	+	0.898326i	0.0754782	+	0.997147i	$0.475952\pi$
$152$	−3.82914	−	6.63227i	−0.310584	−	0.537948i
$153$	7.26125	−	12.0702i	0.587037	−	0.975814i
$154$	0.389870	−	0.675275i	0.0314166	−	0.0544152i
$155$	−5.12959	+	1.86702i	−0.412019	+	0.149963i
$156$	4.39090	−	5.13831i	0.351554	−	0.411394i
$157$	−1.65369	+	1.38761i	−0.131979	+	0.110743i	−0.706388	−	0.707825i	$-0.749676\pi$
$157$	−1.65369	+	1.38761i	−0.131979	+	0.110743i	0.574409	+	0.818569i	$0.305232\pi$
$158$	2.41279	+	0.878184i	0.191951	+	0.0698646i
$159$	−2.36065	−	1.39138i	−0.187212	−	0.110343i
$160$	0.479152	−	2.71741i	0.0378803	−	0.214830i
$161$	3.21924			0.253712
$162$	−6.68187	−	6.02931i	−0.524977	−	0.473707i
$163$	14.8069			1.15977			0.579883	−	0.814700i	$-0.303098\pi$
$163$	14.8069			1.15977			0.579883	+	0.814700i	$0.303098\pi$
$164$	0.497172	−	2.81961i	0.0388226	−	0.220174i
$165$	−3.21045	−	1.89225i	−0.249933	−	0.147312i
$166$	12.2673	+	4.46494i	0.952129	+	0.346547i
$167$	2.38711	−	2.00302i	0.184720	−	0.154999i	−0.545738	−	0.837956i	$-0.683751\pi$
$167$	2.38711	−	2.00302i	0.184720	−	0.154999i	0.730459	+	0.682957i	$0.239306\pi$
$168$	−1.12523	+	1.31676i	−0.0868133	+	0.101590i
$169$	−2.09310	+	0.761826i	−0.161008	+	0.0586020i
$170$	−6.47796	+	11.2202i	−0.496837	+	0.860547i
$171$	22.9711	+	0.413225i	1.75665	+	0.0316001i
$172$	−1.70852	−	2.95924i	−0.130273	−	0.225640i
$173$	−10.5056	−	8.81522i	−0.798724	−	0.670209i	0.149164	−	0.988812i	$-0.452342\pi$
$173$	−10.5056	−	8.81522i	−0.798724	−	0.670209i	−0.947888	+	0.318603i	$0.896786\pi$
$174$	−5.02288	−	6.09656i	−0.380784	−	0.462179i
$175$	−0.453897	−	2.57418i	−0.0343114	−	0.194589i
$176$	−0.135401	−	0.767895i	−0.0102062	−	0.0578822i
$177$	−5.64778	+	0.943565i	−0.424513	+	0.0709227i
$178$	−9.09791	−	7.63405i	−0.681917	−	0.572196i
$179$	4.15313	+	7.19343i	0.310419	+	0.537662i	0.978453	−	0.206469i	$-0.0661972\pi$
$179$	4.15313	+	7.19343i	0.310419	+	0.537662i	−0.668034	+	0.744131i	$0.732864\pi$
$180$	6.24457	+	5.43418i	0.465443	+	0.405040i
$181$	−9.09324	+	15.7500i	−0.675896	+	1.17069i	0.300311	+	0.953841i	$0.402910\pi$
$181$	−9.09324	+	15.7500i	−0.675896	+	1.17069i	−0.976206	+	0.216844i	$0.930424\pi$
$182$	3.66690	−	1.33464i	0.271809	−	0.0989303i
$183$	18.4597	+	3.42639i	1.36458	+	0.253286i
$184$	2.46608	−	2.06929i	0.181802	−	0.152550i
$185$	25.6743	+	9.34467i	1.88761	+	0.687034i
$186$	2.98275	−	1.68651i	0.218706	−	0.123661i
$187$	−0.635749	+	3.60551i	−0.0464906	+	0.263661i
$188$	8.38857			0.611799
$189$	−1.64482	−	4.92895i	−0.119643	−	0.358529i
$190$	−21.1317			−1.53306
$191$	1.41188	−	8.00719i	0.102160	−	0.579380i	−0.890156	−	0.455655i	$-0.849405\pi$
$191$	1.41188	−	8.00719i	0.102160	−	0.579380i	0.992317	−	0.123725i	$-0.0394839\pi$
$192$	−0.0155769	+	1.73198i	−0.00112417	+	0.124995i
$193$	11.0481	+	4.02118i	0.795260	+	0.289451i	0.707521	−	0.706692i	$-0.249814\pi$
$193$	11.0481	+	4.02118i	0.795260	+	0.289451i	0.0877394	+	0.996143i	$0.472036\pi$
$194$	8.85066	−	7.42659i	0.635440	−	0.533198i
$195$	−6.22078	−	17.5819i	−0.445479	−	1.25906i
$196$	−0.939693	+	0.342020i	−0.0671209	+	0.0244300i
$197$	11.7726	−	20.3907i	0.838760	−	1.45277i	−0.0521720	−	0.998638i	$-0.516614\pi$
$197$	11.7726	−	20.3907i	0.838760	−	1.45277i	0.890932	−	0.454137i	$-0.150052\pi$
$198$	2.18340	+	0.839467i	0.155168	+	0.0596584i
$199$	9.96441	+	17.2589i	0.706359	+	1.22345i	0.966199	+	0.257797i	$0.0829967\pi$
$199$	9.96441	+	17.2589i	0.706359	+	1.22345i	−0.259840	+	0.965652i	$0.583670\pi$
$200$	−2.00235	−	1.68017i	−0.141588	−	0.118806i
$201$	4.19978	−	11.2237i	0.296230	−	0.791658i
$202$	3.19642	+	18.1278i	0.224899	+	1.27547i
$203$	−0.791941	−	4.49132i	−0.0555834	−	0.315229i
$204$	2.85011	−	7.61676i	0.199547	−	0.533280i
$205$	−6.05193	−	5.07817i	−0.422685	−	0.354675i
$206$	−5.62446	−	9.74185i	−0.391875	−	0.678747i
$207$	1.50571	+	9.53963i	0.104654	+	0.663050i
$208$	1.95112	−	3.37943i	0.135286	−	0.234322i
$209$	−5.61135	+	2.04236i	−0.388145	+	0.141273i
$210$	1.59416	+	4.50559i	0.110007	+	0.310915i
$211$	4.69293	−	3.93784i	0.323075	−	0.271092i	−0.466796	−	0.884365i	$-0.654592\pi$
$211$	4.69293	−	3.93784i	0.323075	−	0.271092i	0.789871	+	0.613273i	$0.210147\pi$
$212$	−1.48663	−	0.541091i	−0.102102	−	0.0371623i
$213$	−0.0177594	+	1.97465i	−0.00121686	+	0.135301i
$214$	−0.150962	+	0.856145i	−0.0103195	+	0.0585249i
$215$	−9.42872			−0.643033
$216$	−4.42827	−	2.71853i	−0.301306	−	0.184972i
$217$	1.97831			0.134296
$218$	1.73578	−	9.84411i	0.117562	−	0.666727i
$219$	−23.7935	+	13.4534i	−1.60782	+	0.909094i
$220$	−2.02180	−	0.735877i	−0.136310	−	0.0496128i
$221$	−14.0357	+	11.7773i	−0.944140	+	0.792228i
$222$	−16.8622	−	3.12988i	−1.13172	−	0.210064i
$223$	−3.33973	+	1.21556i	−0.223645	+	0.0814000i	−0.451412	−	0.892316i	$-0.649080\pi$
$223$	−3.33973	+	1.21556i	−0.223645	+	0.0814000i	0.227768	+	0.973716i	$0.426857\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	7.41579	−	2.54904i	0.494386	−	0.169936i
$226$	−5.54879	−	9.61079i	−0.369100	−	0.639300i
$227$	0.667139	+	0.559796i	0.0442796	+	0.0371550i	0.664659	−	0.747147i	$-0.268577\pi$
$227$	0.667139	+	0.559796i	0.0442796	+	0.0371550i	−0.620379	+	0.784302i	$0.713021\pi$
$228$	13.0832	−	2.18579i	0.866456	−	0.144757i
$229$	3.24950	+	18.4288i	0.214733	+	1.21781i	0.881370	+	0.472427i	$0.156622\pi$
$229$	3.24950	+	18.4288i	0.214733	+	1.21781i	−0.666637	+	0.745383i	$0.732267\pi$
$230$	−1.54251	−	8.74799i	−0.101710	−	0.576825i
$231$	0.858778	+	1.04235i	0.0565034	+	0.0685814i
$232$	−3.49363	−	2.93150i	−0.229368	−	0.192462i
$233$	−5.77682	−	10.0058i	−0.378452	−	0.655499i	0.612385	−	0.790560i	$-0.290210\pi$
$233$	−5.77682	−	10.0058i	−0.378452	−	0.655499i	−0.990837	+	0.135061i	$0.956877\pi$
$234$	5.67006	+	10.2419i	0.370663	+	0.669537i
$235$	11.5734	−	20.0457i	0.754965	−	1.30764i
$236$	−3.10657	+	1.13070i	−0.202220	+	0.0736022i
$237$	−2.88918	+	3.38097i	−0.187672	+	0.219617i
$238$	3.59682	−	3.01809i	0.233148	−	0.195634i
$239$	−26.3234	−	9.58092i	−1.70272	−	0.619738i	−0.706586	−	0.707627i	$-0.749766\pi$
$239$	−26.3234	−	9.58092i	−1.70272	−	0.619738i	−0.996130	+	0.0878888i	$0.971988\pi$
$240$	4.11733	+	2.42677i	0.265773	+	0.156648i
$241$	−4.00121	+	22.6920i	−0.257741	+	1.46172i	0.531198	+	0.847248i	$0.321742\pi$
$241$	−4.00121	+	22.6920i	−0.257741	+	1.46172i	−0.788939	+	0.614472i	$0.789369\pi$
$242$	10.3920			0.668023
$243$	13.8367	−	7.17949i	0.887626	−	0.460565i
$244$	10.8397			0.693943
$245$	−0.479152	+	2.71741i	−0.0306119	+	0.173609i
$246$	4.27218	+	2.51804i	0.272384	+	0.160545i
$247$	−28.0822	−	10.2211i	−1.78683	−	0.650351i
$248$	1.51547	−	1.27163i	0.0962326	−	0.0807487i
$249$	−14.6894	+	17.1898i	−0.930905	+	1.08936i
$250$	6.18700	−	2.25188i	0.391300	−	0.142422i
$251$	2.99675	−	5.19052i	0.189153	−	0.327623i	−0.755815	−	0.654785i	$-0.772759\pi$
$251$	2.99675	−	5.19052i	0.189153	−	0.327623i	0.944968	+	0.327162i	$0.106092\pi$
$252$	−1.45303	−	2.62463i	−0.0915322	−	0.165336i
$253$	−1.25509	−	2.17387i	−0.0789066	−	0.136670i
$254$	5.42486	+	4.55200i	0.340386	+	0.285618i
$255$	−14.2692	−	17.3193i	−0.893571	−	1.08458i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.68209	−	9.53963i	−0.104926	−	0.595066i	−0.991250	−	0.132000i	$-0.957860\pi$
$257$	−1.68209	−	9.53963i	−0.104926	−	0.595066i	0.886324	−	0.463066i	$-0.153251\pi$
$258$	5.83757	−	0.975273i	0.363431	−	0.0607178i
$259$	−7.58513	−	6.36468i	−0.471317	−	0.395482i
$260$	−5.38377	−	9.32496i	−0.333887	−	0.578310i
$261$	12.9388	−	4.44746i	0.800891	−	0.275291i
$262$	8.50302	−	14.7277i	0.525319	−	0.909879i
$263$	−8.25635	+	3.00507i	−0.509108	+	0.185300i	−0.583786	−	0.811907i	$-0.698429\pi$
$263$	−8.25635	+	3.00507i	−0.509108	+	0.185300i	0.0746779	+	0.997208i	$0.476207\pi$
$264$	1.32787	+	0.246473i	0.0817247	+	0.0151693i
$265$	−3.34407	+	2.80601i	−0.205425	+	0.172372i
$266$	7.19643	+	2.61929i	0.441242	+	0.160599i
$267$	17.9065	−	10.1247i	1.09586	−	0.619621i
$268$	1.20144	−	6.81369i	0.0733894	−	0.416212i
$269$	−16.6709			−1.01645			−0.508223	−	0.861226i	$-0.669697\pi$
$269$	−16.6709			−1.01645			−0.508223	+	0.861226i	$0.669697\pi$
$270$	−12.6059	+	6.83136i	−0.767168	+	0.415743i
$271$	26.4275			1.60536			0.802678	−	0.596412i	$-0.203408\pi$
$271$	26.4275			1.60536			0.802678	+	0.596412i	$0.203408\pi$
$272$	0.815334	−	4.62399i	0.0494369	−	0.280371i
$273$	−0.0607849	+	6.75859i	−0.00367887	+	0.409049i
$274$	11.0418	+	4.01889i	0.667060	+	0.242790i
$275$	−1.56132	+	1.31010i	−0.0941509	+	0.0790020i
$276$	1.85987	+	5.25656i	0.111951	+	0.316408i
$277$	−14.3084	+	5.20785i	−0.859711	+	0.312909i	−0.733993	−	0.679157i	$-0.762346\pi$
$277$	−14.3084	+	5.20785i	−0.859711	+	0.312909i	−0.125718	+	0.992066i	$0.540123\pi$
$278$	−8.49549	+	14.7146i	−0.509526	+	0.882524i
$279$	0.925298	+	5.86235i	0.0553962	+	0.350970i
$280$	1.37966	+	2.38965i	0.0824507	+	0.142809i
$281$	17.8914	+	15.0126i	1.06731	+	0.895579i	0.994806	−	0.101790i	$-0.0324568\pi$
$281$	17.8914	+	15.0126i	1.06731	+	0.895579i	0.0725031	+	0.997368i	$0.476901\pi$
$282$	−5.09194	+	13.6080i	−0.303221	+	0.810342i
$283$	−3.90198	−	22.1292i	−0.231949	−	1.31545i	−0.848945	−	0.528481i	$-0.822762\pi$
$283$	−3.90198	−	22.1292i	−0.231949	−	1.31545i	0.616997	−	0.786966i	$-0.288349\pi$
$284$	0.197978	+	1.12279i	0.0117478	+	0.0666253i
$285$	12.8272	−	34.2799i	0.759815	−	2.03057i
$286$	−2.33087	−	1.95583i	−0.137827	−	0.115651i
$287$	1.43155	+	2.47952i	0.0845018	+	0.146361i
$288$	−2.80017	−	1.07660i	−0.165001	−	0.0634392i
$289$	−2.52302	+	4.37000i	−0.148413	+	0.257059i
$290$	−11.8253	+	4.30405i	−0.694405	+	0.252743i
$291$	6.67498	+	18.8656i	0.391294	+	1.10592i
$292$	−12.0890	+	10.1439i	−0.707455	+	0.593625i
$293$	7.50671	+	2.73222i	0.438547	+	0.159618i	0.551852	−	0.833942i	$-0.313921\pi$
$293$	7.50671	+	2.73222i	0.438547	+	0.159618i	−0.113305	+	0.993560i	$0.536144\pi$
$294$	0.0155769	−	1.73198i	0.000908466	−	0.101011i
$295$	−1.58405	+	8.98358i	−0.0922269	+	0.523044i
$296$	−9.90169			−0.575524
$297$	−2.68713	+	3.03236i	−0.155923	+	0.175955i
$298$	−1.76623			−0.102315
$299$	2.18141	−	12.3714i	0.126154	−	0.715456i
$300$	3.94103	−	2.22834i	0.227535	−	0.128653i
$301$	3.21096	+	1.16869i	0.185077	+	0.0673624i
$302$	−13.1555	+	11.0388i	−0.757017	+	0.635213i
$303$	−31.3472	−	5.81851i	−1.80085	−	0.334265i
$304$	7.19643	−	2.61929i	0.412744	−	0.150226i
$305$	14.9552	−	25.9032i	0.856332	−	1.48321i
$306$	10.6259	+	9.24690i	0.607441	+	0.528610i
$307$	−2.04697	−	3.54545i	−0.116827	−	0.202350i	0.801682	−	0.597751i	$-0.203939\pi$
$307$	−2.04697	−	3.54545i	−0.116827	−	0.202350i	−0.918508	+	0.395401i	$0.870606\pi$
$308$	0.597316	+	0.501208i	0.0340352	+	0.0285590i
$309$	19.2174	−	3.21061i	1.09324	−	0.182645i
$310$	−0.947910	−	5.37587i	−0.0538377	−	0.305329i
$311$	0.958212	+	5.43429i	0.0543352	+	0.308150i	0.999848	−	0.0174347i	$-0.00554992\pi$
$311$	0.958212	+	5.43429i	0.0543352	+	0.308150i	−0.945513	+	0.325585i	$0.894439\pi$
$312$	4.29778	+	5.21646i	0.243314	+	0.295324i
$313$	17.3818	+	14.5850i	0.982475	+	0.824395i	0.984461	−	0.175603i	$-0.0561877\pi$
$313$	17.3818	+	14.5850i	0.982475	+	0.824395i	−0.00198580	+	0.999998i	$0.500632\pi$
$314$	−1.07937	−	1.86952i	−0.0609123	−	0.105503i
$315$	−8.27664	−	0.148888i	−0.466336	−	0.00838887i
$316$	−1.28382	+	2.22364i	−0.0722205	+	0.125090i
$317$	−28.3251	+	10.3095i	−1.59090	+	0.579039i	−0.977537	−	0.210764i	$-0.932405\pi$
$317$	−28.3251	+	10.3095i	−1.59090	+	0.579039i	−0.613360	+	0.789803i	$0.710183\pi$
$318$	1.78016	−	2.08317i	0.0998264	−	0.116819i
$319$	−2.72412	+	2.28581i	−0.152522	+	0.127981i
$320$	2.59292	+	0.943745i	0.144949	+	0.0527570i
$321$	−1.29721	−	0.764579i	−0.0724029	−	0.0426746i
$322$	−0.559016	+	3.17033i	−0.0311527	+	0.176676i
$323$	−35.9581			−2.00076
$324$	7.09801	−	5.53338i	0.394334	−	0.307410i
$325$	−10.2000			−0.565794
$326$	−2.57119	+	14.5819i	−0.142405	+	0.807619i
$327$	14.9155	+	8.79126i	0.824829	+	0.486158i
$328$	2.69044	+	0.979239i	0.148554	+	0.0540694i
$329$	−6.42602	+	5.39207i	−0.354278	+	0.297274i
$330$	2.42100	−	2.83309i	0.133271	−	0.155957i
$331$	−12.4800	+	4.54236i	−0.685965	+	0.249671i	−0.661406	−	0.750028i	$-0.730040\pi$
$331$	−12.4800	+	4.54236i	−0.685965	+	0.249671i	−0.0245582	+	0.999698i	$0.507818\pi$
$332$	−6.52731	+	11.3056i	−0.358233	+	0.620477i
$333$	15.3128	−	25.4540i	0.839138	−	1.39487i
$334$	1.55808	+	2.69867i	0.0852541	+	0.147664i
$335$	−14.6247	−	12.2716i	−0.799034	−	0.670469i
$336$	−1.10136	−	1.33679i	−0.0600843	−	0.0729277i
$337$	−5.62939	−	31.9259i	−0.306652	−	1.73911i	−0.615623	−	0.788041i	$-0.711095\pi$
$337$	−5.62939	−	31.9259i	−0.306652	−	1.73911i	0.308970	−	0.951072i	$-0.400016\pi$
$338$	−0.386789	−	2.19359i	−0.0210386	−	0.119316i
$339$	18.9588	−	3.16742i	1.02970	−	0.172031i
$340$	−9.92482	−	8.32791i	−0.538249	−	0.451644i
$341$	−0.771284	−	1.33590i	−0.0417673	−	0.0723432i
$342$	−4.39584	+	22.5504i	−0.237700	+	1.21939i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	3.21096	−	1.16869i	0.173123	−	0.0630118i
$345$	15.1273	+	2.80786i	0.814428	+	0.151170i
$346$	10.5056	−	8.81522i	0.564783	−	0.473909i
$347$	19.5975	+	7.13289i	1.05205	+	0.382914i	0.809435	−	0.587210i	$-0.199774\pi$
$347$	19.5975	+	7.13289i	1.05205	+	0.382914i	0.242612	+	0.970123i	$0.421996\pi$
$348$	6.87615	−	3.88792i	0.368600	−	0.208414i
$349$	−5.09749	+	28.9093i	−0.272862	+	1.54748i	0.472809	+	0.881165i	$0.343240\pi$
$349$	−5.09749	+	28.9093i	−0.272862	+	1.54748i	−0.745671	+	0.666314i	$0.767871\pi$
$350$	2.61389			0.139718
$351$	−20.0563	+	2.98102i	−1.07052	+	0.159115i
$352$	0.779741			0.0415603
$353$	−5.08214	+	28.8222i	−0.270495	+	1.53405i	0.482423	+	0.875938i	$0.339757\pi$
$353$	−5.08214	+	28.8222i	−0.270495	+	1.53405i	−0.752918	+	0.658114i	$0.771354\pi$
$354$	0.0514965	−	5.72582i	0.00273701	−	0.304324i
$355$	2.95621	+	1.07597i	0.156899	+	0.0571067i
$356$	9.09791	−	7.63405i	0.482188	−	0.404604i
$357$	2.71265	+	7.66679i	0.143569	+	0.405770i
$358$	−7.80533	+	2.84091i	−0.412524	+	0.150147i
$359$	13.6452	−	23.6341i	0.720164	−	1.24736i	−0.240769	−	0.970582i	$-0.577400\pi$
$359$	13.6452	−	23.6341i	0.720164	−	1.24736i	0.960934	−	0.276779i	$-0.0892669\pi$
$360$	−6.43598	+	5.20607i	−0.339206	+	0.274384i
$361$	−19.8247	−	34.3373i	−1.04340	−	1.80723i
$362$	−13.9317	−	11.6900i	−0.732232	−	0.614415i
$363$	−6.30805	+	16.8579i	−0.331087	+	0.884812i
$364$	0.677616	+	3.84295i	0.0355167	+	0.201425i
$365$	7.56153	+	42.8836i	0.395789	+	2.24463i
$366$	−6.57983	+	17.5842i	−0.343933	+	0.919143i
$367$	3.55966	+	2.98691i	0.185813	+	0.155915i	0.730949	−	0.682432i	$-0.239078\pi$
$367$	3.55966	+	2.98691i	0.185813	+	0.155915i	−0.545136	+	0.838347i	$0.683522\pi$
$368$	1.60962	+	2.78795i	0.0839073	+	0.145332i
$369$	−6.67803	+	5.40186i	−0.347644	+	0.281210i
$370$	−13.6610	+	23.6615i	−0.710201	+	1.23010i
$371$	1.48663	−	0.541091i	0.0771822	−	0.0280920i
$372$	1.14294	+	3.23029i	0.0592585	+	0.167483i
$373$	−13.8092	+	11.5873i	−0.715014	+	0.599968i	−0.926001	−	0.377521i	$-0.876777\pi$
$373$	−13.8092	+	11.5873i	−0.715014	+	0.599968i	0.210987	+	0.977489i	$0.432332\pi$
$374$	−3.44034	−	1.25218i	−0.177896	−	0.0647487i
$375$	−0.102560	+	11.4035i	−0.00529616	+	0.588873i
$376$	−1.45666	+	8.26113i	−0.0751215	+	0.426035i
$377$	−17.7966			−0.916569
$378$	5.13969	−	0.763926i	0.264357	−	0.0392921i
$379$	−5.38304			−0.276508			−0.138254	−	0.990397i	$-0.544149\pi$
$379$	−5.38304			−0.276508			−0.138254	+	0.990397i	$0.544149\pi$
$380$	3.66948	−	20.8107i	0.188240	−	1.06756i
$381$	−10.6772	+	6.03711i	−0.547009	+	0.309290i
$382$	7.64037	+	2.78087i	0.390915	+	0.142282i
$383$	−1.35064	+	1.13332i	−0.0690146	+	0.0579101i	−0.676642	−	0.736312i	$-0.736566\pi$
$383$	−1.35064	+	1.13332i	−0.0690146	+	0.0579101i	0.607628	+	0.794222i	$0.292121\pi$
$384$	−1.70296	−	0.316096i	−0.0869040	−	0.0161307i
$385$	2.02180	−	0.735877i	0.103041	−	0.0375037i
$386$	−5.87858	+	10.1820i	−0.299212	+	0.518250i
$387$	−1.96137	+	10.0617i	−0.0997022	+	0.511466i
$388$	5.77686	+	10.0058i	0.293276	+	0.507968i
$389$	−8.02873	−	6.73690i	−0.407073	−	0.341575i	0.416147	−	0.909297i	$-0.363380\pi$
$389$	−8.02873	−	6.73690i	−0.407073	−	0.341575i	−0.823220	+	0.567723i	$0.807825\pi$
$390$	18.3950	−	3.07322i	0.931466	−	0.155618i
$391$	−2.62476	−	14.8857i	−0.132740	−	0.752804i
$392$	−0.173648	−	0.984808i	−0.00877056	−	0.0497403i
$393$	18.7298	+	22.7335i	0.944795	+	1.14675i
$394$	18.0366	+	15.1345i	0.908671	+	0.762466i
$395$	3.54248	+	6.13575i	0.178241	+	0.308723i
$396$	−1.20586	+	2.00446i	−0.0605967	+	0.100728i
$397$	−13.8098	+	23.9193i	−0.693095	+	1.20048i	0.277724	+	0.960661i	$0.410420\pi$
$397$	−13.8098	+	23.9193i	−0.693095	+	1.20048i	−0.970819	+	0.239815i	$0.922913\pi$
$398$	−18.7270	+	6.81606i	−0.938698	+	0.341658i
$399$	−8.61732	+	10.0841i	−0.431405	+	0.504838i
$400$	2.00235	−	1.68017i	0.100118	−	0.0840087i
$401$	19.4536	+	7.08052i	0.971465	+	0.353584i	0.778516	−	0.627624i	$-0.215973\pi$
$401$	19.4536	+	7.08052i	0.971465	+	0.353584i	0.192949	+	0.981209i	$0.438195\pi$
$402$	10.3239	+	6.08495i	0.514909	+	0.303490i
$403$	1.34053	−	7.60254i	0.0667767	−	0.378709i
$404$	−18.4074			−0.915804
$405$	−3.42997	−	24.5959i	−0.170436	−	1.22218i
$406$	4.56061			0.226339
$407$	−1.34069	+	7.60345i	−0.0664557	+	0.376889i
$408$	7.00613	+	4.12944i	0.346855	+	0.204438i
$409$	10.9038	+	3.96867i	0.539159	+	0.196238i	0.597223	−	0.802075i	$-0.296271\pi$
$409$	10.9038	+	3.96867i	0.539159	+	0.196238i	−0.0580641	+	0.998313i	$0.518493\pi$
$410$	6.05193	−	5.07817i	0.298884	−	0.250793i
$411$	−13.2219	+	15.4725i	−0.652190	+	0.763204i
$412$	10.5705	−	3.84736i	0.520773	−	0.189546i
$413$	1.65297	−	2.86303i	0.0813373	−	0.140880i
$414$	−9.65616	−	0.173704i	−0.474575	−	0.00853707i
$415$	18.0110	+	31.1959i	0.884124	+	1.53135i
$416$	2.98928	+	2.50831i	0.146562	+	0.122980i
$417$	−18.7132	−	22.7133i	−0.916391	−	1.11228i
$418$	−1.03694	−	5.88075i	−0.0507182	−	0.287637i
$419$	−2.78421	−	15.7900i	−0.136018	−	0.771394i	−0.974146	−	0.225921i	$-0.927461\pi$
$419$	−2.78421	−	15.7900i	−0.136018	−	0.771394i	0.838128	−	0.545473i	$-0.183650\pi$
$420$	−4.71396	+	0.787553i	−0.230018	+	0.0384287i
$421$	2.45710	+	2.06175i	0.119752	+	0.100484i	0.700697	−	0.713459i	$-0.252872\pi$
$421$	2.45710	+	2.06175i	0.119752	+	0.100484i	−0.580945	+	0.813943i	$0.697317\pi$
$422$	3.06310	+	5.30544i	0.149109	+	0.258265i
$423$	−18.9840	−	16.5203i	−0.923033	−	0.803245i
$424$	0.791022	−	1.37009i	0.0384154	−	0.0665375i
$425$	−11.5329	+	4.19763i	−0.559427	+	0.203615i
$426$	−1.94156	−	0.360384i	−0.0940691	−	0.0174606i
$427$	−8.30372	+	6.96765i	−0.401845	+	0.337188i
$428$	−0.816924	−	0.297336i	−0.0394875	−	0.0143723i
$429$	4.58761	−	2.59393i	0.221492	−	0.125236i
$430$	1.63728	−	9.28547i	0.0789566	−	0.447785i
$431$	27.0136			1.30120			0.650600	−	0.759421i	$-0.274518\pi$
$431$	27.0136			1.30120			0.650600	+	0.759421i	$0.274518\pi$
$432$	3.44619	−	3.88893i	0.165805	−	0.187106i
$433$	16.6075			0.798106			0.399053	−	0.916928i	$-0.369339\pi$
$433$	16.6075			0.798106			0.399053	+	0.916928i	$0.369339\pi$
$434$	−0.343530	+	1.94825i	−0.0164899	+	0.0935191i
$435$	0.196023	−	21.7956i	0.00939861	−	1.04502i
$436$	9.39314	+	3.41882i	0.449850	+	0.163732i
$437$	18.8860	−	15.8472i	0.903438	−	0.758074i
$438$	−9.11727	−	25.7682i	−0.435640	−	1.23125i
$439$	1.80543	−	0.657124i	0.0861687	−	0.0313628i	−0.298576	−	0.954386i	$-0.596512\pi$
$439$	1.80543	−	0.657124i	0.0861687	−	0.0313628i	0.384745	+	0.923023i	$0.374289\pi$
$440$	1.07578	−	1.86331i	0.0512858	−	0.0888296i
$441$	2.80017	+	1.07660i	0.133341	+	0.0512666i
$442$	−9.16112	−	15.8675i	−0.435750	−	0.754741i
$443$	26.0063	+	21.8219i	1.23560	+	1.03679i	0.997855	+	0.0654600i	$0.0208515\pi$
$443$	26.0063	+	21.8219i	1.23560	+	1.03679i	0.237741	+	0.971329i	$0.423593\pi$
$444$	6.01042	−	16.0625i	0.285242	−	0.762294i
$445$	−5.69064	−	32.2732i	−0.269762	−	1.52990i
$446$	−0.617157	−	3.50007i	−0.0292232	−	0.165733i
$447$	1.07212	−	2.86518i	0.0507094	−	0.135518i
$448$	−0.766044	−	0.642788i	−0.0361922	−	0.0303689i
$449$	−2.98834	−	5.17596i	−0.141028	−	0.244269i	0.786856	−	0.617137i	$-0.211708\pi$
$449$	−2.98834	−	5.17596i	−0.141028	−	0.244269i	−0.927884	+	0.372869i	$0.878374\pi$
$450$	1.22257	+	7.74577i	0.0576326	+	0.365139i
$451$	1.11624	−	1.93338i	0.0525616	−	0.0910394i
$452$	10.4283	−	3.79560i	0.490507	−	0.178530i
$453$	−9.92164	−	28.0416i	−0.466159	−	1.31751i
$454$	−0.667139	+	0.559796i	−0.0313104	+	0.0262725i
$455$	10.1182	+	3.68272i	0.474347	+	0.172648i
$456$	−0.119293	+	13.2640i	−0.00558639	+	0.621144i
$457$	1.98819	−	11.2756i	0.0930034	−	0.527449i	−0.902337	−	0.431030i	$-0.858150\pi$
$457$	1.98819	−	11.2756i	0.0930034	−	0.527449i	0.995341	−	0.0964184i	$-0.0307387\pi$
$458$	−18.7131			−0.874406
$459$	−21.4503	+	11.6244i	−1.00122	+	0.542579i
$460$	8.88294			0.414169
$461$	−2.94807	+	16.7193i	−0.137305	+	0.778697i	0.835921	+	0.548849i	$0.184934\pi$
$461$	−2.94807	+	16.7193i	−0.137305	+	0.778697i	−0.973227	+	0.229848i	$0.926177\pi$
$462$	−1.17564	+	0.664729i	−0.0546956	+	0.0309260i
$463$	27.1767	+	9.89150i	1.26301	+	0.459697i	0.884777	−	0.466015i	$-0.154311\pi$
$463$	27.1767	+	9.89150i	1.26301	+	0.459697i	0.378230	+	0.925712i	$0.376533\pi$
$464$	3.49363	−	2.93150i	0.162188	−	0.136092i
$465$	9.29613	+	1.72550i	0.431098	+	0.0800182i
$466$	10.8569	−	3.95158i	0.502935	−	0.183053i
$467$	14.3139	−	24.7923i	0.662366	−	1.14725i	−0.317626	−	0.948216i	$-0.602886\pi$
$467$	14.3139	−	24.7923i	0.662366	−	1.14725i	0.979992	−	0.199036i	$-0.0637811\pi$
$468$	−11.0709	+	3.80542i	−0.511754	+	0.175906i
$469$	3.45940	+	5.99185i	0.159740	+	0.276678i
$470$	17.7315	+	14.8785i	0.817892	+	0.686293i
$471$	3.68793	−	0.616136i	0.169931	−	0.0283900i
$472$	−0.574070	−	3.25572i	−0.0264237	−	0.149856i
$473$	−0.462668	−	2.62392i	−0.0212735	−	0.120648i
$474$	−2.82790	−	3.43239i	−0.129890	−	0.157655i
$475$	−15.3346	−	12.8672i	−0.703599	−	0.590390i
$476$	2.34766	+	4.06627i	0.107605	+	0.186377i
$477$	2.29875	+	4.15229i	0.105253	+	0.190120i
$478$	14.0064	−	24.2597i	0.640636	−	1.10961i
$479$	33.3692	−	12.1454i	1.52468	−	0.554938i	0.562368	−	0.826887i	$-0.309890\pi$
$479$	33.3692	−	12.1454i	1.52468	−	0.554938i	0.962312	+	0.271949i	$0.0876682\pi$
$480$	−3.10487	+	3.63338i	−0.141717	+	0.165840i
$481$	−29.5990	+	24.8365i	−1.34960	+	1.13245i
$482$	−21.6524	−	7.88085i	−0.986242	−	0.358963i
$483$	−4.80360	−	2.83126i	−0.218571	−	0.128827i
$484$	−1.80455	+	10.2341i	−0.0820251	+	0.465188i
$485$	31.8805			1.44762
$486$	4.66770	+	14.8732i	0.211731	+	0.674663i
$487$	1.43005			0.0648017			0.0324009	−	0.999475i	$-0.489685\pi$
$487$	1.43005			0.0648017			0.0324009	+	0.999475i	$0.489685\pi$
$488$	−1.88230	+	10.6751i	−0.0852078	+	0.483237i
$489$	−22.0941	−	13.0224i	−0.999131	−	0.588892i
$490$	−2.59292	−	0.943745i	−0.117136	−	0.0426341i
$491$	−8.40168	+	7.04984i	−0.379162	+	0.318155i	−0.812374	−	0.583137i	$-0.801825\pi$
$491$	−8.40168	+	7.04984i	−0.379162	+	0.318155i	0.433211	+	0.901292i	$0.357380\pi$
$492$	−3.22164	+	3.77002i	−0.145243	+	0.169966i
$493$	−20.1221	+	7.32385i	−0.906255	+	0.329850i
$494$	14.9422	−	25.8807i	0.672282	−	1.16443i
$495$	3.12628	+	5.64706i	0.140516	+	0.253816i
$496$	0.989154	+	1.71326i	0.0444143	+	0.0769279i
$497$	−0.873375	−	0.732848i	−0.0391762	−	0.0328727i
$498$	−14.3779	−	17.4512i	−0.644288	−	0.782009i
$499$	−5.74112	−	32.5595i	−0.257008	−	1.45756i	−0.790866	−	0.611989i	$-0.790369\pi$
$499$	−5.74112	−	32.5595i	−0.257008	−	1.45756i	0.533858	−	0.845574i	$-0.320742\pi$
$500$	1.14331	+	6.48404i	0.0511304	+	0.289975i
$501$	−5.32355	+	0.889397i	−0.237839	+	0.0397353i
$502$	4.59128	+	3.85254i	0.204919	+	0.171947i
$503$	17.8246	+	30.8731i	0.794758	+	1.37656i	0.922993	+	0.384817i	$0.125736\pi$
$503$	17.8246	+	30.8731i	0.794758	+	1.37656i	−0.128235	+	0.991744i	$0.540931\pi$
$504$	2.83708	−	0.975191i	0.126373	−	0.0434384i
$505$	−25.3961	+	43.9873i	−1.13011	+	1.95741i
$506$	2.35879	−	0.858530i	0.104861	−	0.0381663i
$507$	3.79323	+	0.704081i	0.168463	+	0.0312693i
$508$	−5.42486	+	4.55200i	−0.240689	+	0.201962i
$509$	11.7951	+	4.29305i	0.522807	+	0.190286i	0.589924	−	0.807459i	$-0.299158\pi$
$509$	11.7951	+	4.29305i	0.522807	+	0.190286i	−0.0671168	+	0.997745i	$0.521380\pi$
$510$	19.5340	−	11.0449i	0.864981	−	0.489078i
$511$	2.74035	−	15.5413i	0.121226	−	0.687507i
$512$	−1.00000			−0.0441942
$513$	−33.9130	−	20.8193i	−1.49729	−	0.919193i
$514$	9.68680			0.427266
$515$	5.38994	−	30.5679i	0.237509	−	1.34698i
$516$	−0.0532270	+	5.91824i	−0.00234319	+	0.260536i
$517$	6.14644	+	2.23712i	0.270320	+	0.0983885i
$518$	7.58513	−	6.36468i	0.333272	−	0.279648i
$519$	7.92309	+	22.3931i	0.347785	+	0.982948i
$520$	10.1182	−	3.68272i	0.443711	−	0.161498i
$521$	6.78139	−	11.7457i	0.297098	−	0.514589i	−0.678373	−	0.734718i	$-0.737314\pi$
$521$	6.78139	−	11.7457i	0.297098	−	0.514589i	0.975471	+	0.220129i	$0.0706478\pi$
$522$	2.13310	+	13.5145i	0.0933631	+	0.591514i
$523$	0.292579	+	0.506762i	0.0127936	+	0.0221592i	0.872351	−	0.488879i	$-0.162594\pi$
$523$	0.292579	+	0.506762i	0.0127936	+	0.0221592i	−0.859558	+	0.511039i	$0.829261\pi$
$524$	13.0274	+	10.9313i	0.569104	+	0.477535i
$525$	−1.58665	+	4.24025i	−0.0692473	+	0.185060i
$526$	−1.52571	−	8.65274i	−0.0665242	−	0.377277i
$527$	−1.61298	−	9.14767i	−0.0702626	−	0.398479i
$528$	−0.473310	+	1.26490i	−0.0205982	+	0.0550476i
$529$	−9.68010	−	8.12257i	−0.420874	−	0.353155i
$530$	−2.18269	−	3.78053i	−0.0948099	−	0.164216i
$531$	9.25718	+	3.55917i	0.401728	+	0.154455i
$532$	−3.82914	+	6.63227i	−0.166014	+	0.287545i
$533$	10.4987	−	3.82122i	0.454750	−	0.165515i
$534$	6.86145	+	19.3926i	0.296924	+	0.839199i
$535$	−1.83761	+	1.54194i	−0.0794468	+	0.0666638i
$536$	6.50154	+	2.36637i	0.280824	+	0.102212i
$537$	0.129386	−	14.3863i	0.00558342	−	0.620814i
$538$	2.89488	−	16.4177i	0.124807	−	0.707816i
$539$	−0.779741			−0.0335858
$540$	−4.53859	−	13.6006i	−0.195310	−	0.585276i
$541$	1.53837			0.0661396			0.0330698	−	0.999453i	$-0.489472\pi$
$541$	1.53837			0.0661396			0.0330698	+	0.999453i	$0.489472\pi$
$542$	−4.58909	+	26.0260i	−0.197118	+	1.11791i
$543$	27.4203	−	15.5040i	1.17672	−	0.665340i
$544$	4.41216	+	1.60589i	0.189170	+	0.0688522i
$545$	21.1291	−	17.7295i	0.905073	−	0.759447i
$546$	−6.64536	−	1.23348i	−0.284395	−	0.0527880i
$547$	3.98672	−	1.45105i	0.170460	−	0.0620424i	−0.255380	−	0.966841i	$-0.582201\pi$
$547$	3.98672	−	1.45105i	0.170460	−	0.0620424i	0.425840	+	0.904798i	$0.359978\pi$
$548$	−5.87523	+	10.1762i	−0.250977	+	0.434705i
$549$	−24.5312	−	21.3476i	−1.04697	−	0.911094i
$550$	−1.01908	−	1.76509i	−0.0434536	−	0.0752638i
$551$	−26.7552	−	22.4503i	−1.13981	−	0.956413i
$552$	−5.49967	+	0.918820i	−0.234081	+	0.0391076i
$553$	−0.445866	−	2.52863i	−0.0189601	−	0.107528i
$554$	−2.64409	−	14.9954i	−0.112337	−	0.637094i
$555$	−30.0914	−	36.5237i	−1.27731	−	1.55034i
$556$	−13.0158	−	10.9216i	−0.551995	−	0.463179i
$557$	11.9217	+	20.6490i	0.505138	+	0.874925i	0.999982	+	0.00594293i	$0.00189171\pi$
$557$	11.9217	+	20.6490i	0.505138	+	0.874925i	−0.494844	+	0.868982i	$0.664775\pi$
$558$	−5.93396	−	0.106745i	−0.251205	−	0.00451889i
$559$	6.66703	−	11.5476i	0.281986	−	0.488413i
$560$	−2.59292	+	0.943745i	−0.109571	+	0.0398805i
$561$	4.11961	−	4.82084i	0.173930	−	0.203536i
$562$	−17.8914	+	15.0126i	−0.754701	+	0.633270i
$563$	−36.4057	−	13.2506i	−1.53432	−	0.558446i	−0.569643	−	0.821892i	$-0.692919\pi$
$563$	−36.4057	−	13.2506i	−1.53432	−	0.558446i	−0.964674	+	0.263446i	$0.915141\pi$
$564$	−12.5170	−	7.37758i	−0.527061	−	0.310652i
$565$	5.31743	−	30.1567i	0.223706	−	1.26870i
$566$	22.4706			0.944510
$567$	−1.88060	+	8.80133i	−0.0789778	+	0.369621i
$568$	−1.14011			−0.0478379
$569$	−0.118334	+	0.671107i	−0.00496083	+	0.0281343i	−0.987188	−	0.159563i	$-0.948991\pi$
$569$	−0.118334	+	0.671107i	−0.00496083	+	0.0281343i	0.982227	+	0.187698i	$0.0601025\pi$
$570$	31.5317	+	18.5849i	1.32072	+	0.778437i
$571$	−20.0003	−	7.27950i	−0.836985	−	0.304638i	−0.112263	−	0.993679i	$-0.535810\pi$
$571$	−20.0003	−	7.27950i	−0.836985	−	0.304638i	−0.724723	+	0.689041i	$0.758032\pi$
$572$	2.33087	−	1.95583i	0.0974584	−	0.0817773i
$573$	−9.14891	+	10.7062i	−0.382201	+	0.447258i
$574$	−2.69044	+	0.979239i	−0.112297	+	0.0408726i
$575$	4.20737	−	7.28737i	0.175459	−	0.303904i
$576$	1.54649	−	2.57068i	0.0644369	−	0.107112i
$577$	−8.68065	−	15.0353i	−0.361380	−	0.625929i	0.626808	−	0.779174i	$-0.284361\pi$
$577$	−8.68065	−	15.0353i	−0.361380	−	0.625929i	−0.988188	+	0.153245i	$0.951028\pi$
$578$	−3.86549	−	3.24353i	−0.160783	−	0.134913i
$579$	−12.9489	−	15.7168i	−0.538138	−	0.653168i
$580$	−2.18522	−	12.3930i	−0.0907365	−	0.514592i
$581$	−2.26691	−	12.8563i	−0.0940473	−	0.533369i
$582$	−19.7381	+	3.29760i	−0.818169	+	0.136690i
$583$	−0.944980	−	0.792932i	−0.0391371	−	0.0328399i
$584$	−7.89053	−	13.6668i	−0.326513	−	0.565536i
$585$	−6.18055	+	31.7058i	−0.255534	+	1.31087i
$586$	−3.99424	+	6.91822i	−0.165000	+	0.285789i
$587$	−16.6993	+	6.07805i	−0.689254	+	0.250868i	−0.662816	−	0.748783i	$-0.730639\pi$
$587$	−16.6993	+	6.07805i	−0.689254	+	0.250868i	−0.0264380	+	0.999650i	$0.508416\pi$
$588$	1.70296	+	0.316096i	0.0702290	+	0.0130356i
$589$	11.6059	−	9.73852i	0.478213	−	0.401269i
$590$	−8.57204	−	3.11997i	−0.352905	−	0.128447i
$591$	−35.4996	+	20.0722i	−1.46026	+	0.825661i
$592$	1.71941	−	9.75126i	0.0706673	−	0.400774i
$593$	9.15244			0.375846			0.187923	−	0.982184i	$-0.439825\pi$
$593$	9.15244			0.375846			0.187923	+	0.982184i	$0.439825\pi$
$594$	−2.51967	−	3.17287i	−0.103383	−	0.130185i
$595$	12.9559			0.531141
$596$	0.306702	−	1.73939i	0.0125630	−	0.0712484i
$597$	0.310430	−	34.5163i	0.0127051	−	1.41266i
$598$	11.8046	+	4.29654i	0.482728	+	0.175699i
$599$	−2.86989	+	2.40812i	−0.117260	+	0.0983932i	−0.699532	−	0.714601i	$-0.746608\pi$
$599$	−2.86989	+	2.40812i	−0.117260	+	0.0983932i	0.582272	+	0.812994i	$0.302164\pi$
$600$	1.51013	+	4.26810i	0.0616509	+	0.174245i
$601$	14.3262	−	5.21430i	0.584376	−	0.212696i	−0.0328779	−	0.999459i	$-0.510467\pi$
$601$	14.3262	−	5.21430i	0.584376	−	0.212696i	0.617254	+	0.786764i	$0.288245\pi$
$602$	−1.70852	+	2.95924i	−0.0696340	+	0.120610i
$603$	−16.1377	+	13.0538i	−0.657179	+	0.531592i
$604$	−8.58667	−	14.8726i	−0.349387	−	0.605156i
$605$	21.9663	+	18.4319i	0.893056	+	0.749363i
$606$	11.1735	−	29.8606i	0.453892	−	1.21300i
$607$	−3.43822	−	19.4991i	−0.139553	−	0.791445i	−0.971580	−	0.236710i	$-0.923931\pi$
$607$	−3.43822	−	19.4991i	−0.139553	−	0.791445i	0.832027	−	0.554735i	$-0.187180\pi$
$608$	1.32985	+	7.54194i	0.0539324	+	0.305866i
$609$	−2.76833	+	7.39822i	−0.112179	+	0.299791i
$610$	22.9127	+	19.2260i	0.927708	+	0.778439i
$611$	16.3671	+	28.3486i	0.662141	+	1.14686i
$612$	−10.9516	+	8.85874i	−0.442691	+	0.358093i
$613$	6.52536	−	11.3023i	0.263557	−	0.456494i	−0.703628	−	0.710569i	$-0.748438\pi$
$613$	6.52536	−	11.3023i	0.263557	−	0.456494i	0.967184	+	0.254075i	$0.0817710\pi$
$614$	3.84704	−	1.40021i	0.155254	−	0.0565078i
$615$	4.56424	+	12.9000i	0.184048	+	0.520176i
$616$	−0.597316	+	0.501208i	−0.0240665	+	0.0201942i
$617$	3.22069	+	1.17223i	0.129660	+	0.0471923i	0.406035	−	0.913857i	$-0.366911\pi$
$617$	3.22069	+	1.17223i	0.129660	+	0.0471923i	−0.276375	+	0.961050i	$0.589133\pi$
$618$	−0.175224	+	19.4829i	−0.00704854	+	0.783718i
$619$	−3.86058	+	21.8944i	−0.155170	+	0.880012i	0.803460	+	0.595358i	$0.202990\pi$
$619$	−3.86058	+	21.8944i	−0.155170	+	0.880012i	−0.958630	+	0.284654i	$0.908121\pi$
$620$	5.45880			0.219231
$621$	6.14317	−	15.5588i	0.246517	−	0.624353i
$622$	−5.51812			−0.221256
$623$	−2.06233	+	11.6960i	−0.0826254	+	0.468592i
$624$	−5.88351	+	3.32666i	−0.235529	+	0.133173i
$625$	29.3532	+	10.6837i	1.17413	+	0.427348i
$626$	−17.3818	+	14.5850i	−0.694715	+	0.582935i
$627$	10.1692	+	1.88756i	0.406119	+	0.0753818i
$628$	2.02855	−	0.738332i	0.0809479	−	0.0294626i
$629$	−23.2458	+	40.2629i	−0.926871	+	1.60539i
$630$	1.58385	−	8.12505i	0.0631021	−	0.323710i
$631$	6.18153	+	10.7067i	0.246083	+	0.426228i	0.962435	−	0.271510i	$-0.0875232\pi$
$631$	6.18153	+	10.7067i	0.246083	+	0.426228i	−0.716353	+	0.697738i	$0.754190\pi$
$632$	−1.96693	−	1.65045i	−0.0782401	−	0.0656512i
$633$	−10.4658	+	1.74851i	−0.415979	+	0.0694969i
$634$	−5.23427	−	29.6850i	−0.207879	−	1.17894i
$635$	3.39319	+	19.2437i	0.134655	+	0.763664i
$636$	1.74240	+	2.11486i	0.0690908	+	0.0838595i
$637$	−2.98928	−	2.50831i	−0.118440	−	0.0993828i
$638$	−1.77804	−	3.07966i	−0.0703935	−	0.121925i
$639$	1.76316	−	2.93085i	0.0697497	−	0.115943i
$640$	−1.37966	+	2.38965i	−0.0545360	+	0.0944591i
$641$	17.7167	−	6.44835i	0.699768	−	0.254695i	0.0324559	−	0.999473i	$-0.489667\pi$
$641$	17.7167	−	6.44835i	0.699768	−	0.254695i	0.667312	+	0.744779i	$0.267445\pi$
$642$	0.978220	−	1.14473i	0.0386073	−	0.0451789i
$643$	−7.92897	+	6.65320i	−0.312688	+	0.262377i	−0.785602	−	0.618732i	$-0.787647\pi$
$643$	−7.92897	+	6.65320i	−0.312688	+	0.262377i	0.472914	+	0.881109i	$0.343202\pi$
$644$	−3.02510	−	1.10105i	−0.119206	−	0.0433873i
$645$	14.0691	+	8.29237i	0.553969	+	0.326512i
$646$	6.24406	−	35.4118i	0.245669	−	1.39326i
$647$	43.0279			1.69160			0.845800	−	0.533500i	$-0.179123\pi$
$647$	43.0279			1.69160			0.845800	+	0.533500i	$0.179123\pi$
$648$	4.21676	+	7.95103i	0.165650	+	0.312346i
$649$	−2.57778			−0.101187
$650$	1.77121	−	10.0450i	0.0694726	−	0.393999i
$651$	−2.95193	−	1.73988i	−0.115695	−	0.0681914i
$652$	−13.9139	−	5.06426i	−0.544912	−	0.198332i
$653$	6.93049	−	5.81537i	0.271211	−	0.227573i	−0.497031	−	0.867733i	$-0.665576\pi$
$653$	6.93049	−	5.81537i	0.271211	−	0.227573i	0.768242	+	0.640160i	$0.221132\pi$
$654$	−11.2477	+	13.1623i	−0.439822	+	0.514687i
$655$	44.0953	−	16.0494i	1.72295	−	0.627101i
$656$	−1.43155	+	2.47952i	−0.0558927	+	0.0968090i
$657$	47.3355	+	0.851514i	1.84674	+	0.0332207i
$658$	−4.19428	−	7.26471i	−0.163510	−	0.283208i
$659$	−5.38899	−	4.52190i	−0.209925	−	0.176148i	0.531762	−	0.846894i	$-0.321530\pi$
$659$	−5.38899	−	4.52190i	−0.209925	−	0.176148i	−0.741688	+	0.670745i	$0.765974\pi$
$660$	2.36965	+	2.87618i	0.0922384	+	0.111955i
$661$	4.52572	+	25.6666i	0.176030	+	0.998316i	0.936948	+	0.349468i	$0.113638\pi$
$661$	4.52572	+	25.6666i	0.176030	+	0.998316i	−0.760918	+	0.648848i	$0.775251\pi$
$662$	−2.30622	−	13.0792i	−0.0896337	−	0.508338i
$663$	31.3012	−	5.22944i	1.21564	−	0.203095i
$664$	−10.0004	−	8.39135i	−0.388091	−	0.325647i
$665$	10.5659	+	18.3006i	0.409726	+	0.709667i
$666$	22.4083	+	19.5002i	0.868304	+	0.755619i
$667$	7.34085	−	12.7147i	0.284239	−	0.492316i
$668$	−2.92823	+	1.06579i	−0.113296	+	0.0412365i
$669$	6.05244	+	1.12342i	0.234001	+	0.0434341i
$670$	14.6247	−	12.2716i	0.565003	−	0.474093i
$671$	7.94246	+	2.89082i	0.306615	+	0.111599i
$672$	1.50773	−	0.852500i	0.0581619	−	0.0328859i
$673$	−2.37229	+	13.4539i	−0.0914449	+	0.518610i	0.904334	+	0.426825i	$0.140368\pi$
$673$	−2.37229	+	13.4539i	−0.0914449	+	0.518610i	−0.995779	+	0.0917843i	$0.970743\pi$
$674$	32.4184			1.24871
$675$	−13.3073	−	2.71850i	−0.512199	−	0.104635i
$676$	2.22743			0.0856704
$677$	−2.72767	+	15.4694i	−0.104833	+	0.594538i	0.886454	+	0.462817i	$0.153161\pi$
$677$	−2.72767	+	15.4694i	−0.104833	+	0.594538i	−0.991287	+	0.131721i	$0.957950\pi$
$678$	−0.172867	+	19.2208i	−0.00663890	+	0.738171i
$679$	−10.8569	−	3.95160i	−0.416651	−	0.151649i
$680$	9.92482	−	8.32791i	0.380599	−	0.319361i
$681$	−0.503143	−	1.42204i	−0.0192805	−	0.0544926i
$682$	1.44954	−	0.527589i	0.0555057	−	0.0202024i
$683$	−12.8766	+	22.3028i	−0.492708	+	0.853395i	−0.999965	−	0.00840008i	$-0.997326\pi$
$683$	−12.8766	+	22.3028i	−0.492708	+	0.853395i	0.507257	+	0.861795i	$0.330659\pi$
$684$	−21.4445	−	8.24489i	−0.819950	−	0.315251i
$685$	16.2117	+	28.0794i	0.619416	+	1.07286i
$686$	0.766044	+	0.642788i	0.0292477	+	0.0245417i
$687$	11.3590	−	30.3564i	0.433374	−	1.15817i
$688$	0.593362	+	3.36512i	0.0226217	+	0.128294i
$689$	−1.07202	−	6.07972i	−0.0408406	−	0.231619i
$690$	−5.39203	+	14.4099i	−0.205271	+	0.548577i
$691$	3.87609	+	3.25242i	0.147453	+	0.123728i	0.713530	−	0.700624i	$-0.247095\pi$
$691$	3.87609	+	3.25242i	0.147453	+	0.123728i	−0.566077	+	0.824352i	$0.691540\pi$
$692$	6.85703	+	11.8767i	0.260665	+	0.451485i
$693$	−0.364702	−	2.31062i	−0.0138539	−	0.0877731i
$694$	−10.4276	+	18.0611i	−0.395826	+	0.685590i
$695$	−44.0562	+	16.0352i	−1.67115	+	0.608248i
$696$	2.63482	+	7.44682i	0.0998726	+	0.282271i
$697$	10.2981	−	8.64111i	0.390068	−	0.327306i
$698$	−27.5849	−	10.0401i	−1.04410	−	0.380023i
$699$	−0.179971	+	20.0107i	−0.00680711	+	0.756874i
$700$	−0.453897	+	2.57418i	−0.0171557	+	0.0972947i
$701$	16.0484			0.606139			0.303069	−	0.952968i	$-0.401989\pi$
$701$	16.0484			0.606139			0.303069	+	0.952968i	$0.401989\pi$
$702$	0.547005	−	20.2692i	0.0206454	−	0.765013i
$703$	−75.8299			−2.85998
$704$	−0.135401	+	0.767895i	−0.00510310	+	0.0289411i
$705$	−34.8991	+	19.7327i	−1.31438	+	0.743175i
$706$	−27.5019	−	10.0099i	−1.03505	−	0.376726i
$707$	14.1009	−	11.8321i	0.530319	−	0.444991i
$708$	5.62989	+	1.04499i	0.211584	+	0.0392732i
$709$	17.4772	−	6.36117i	0.656369	−	0.238899i	0.00770119	−	0.999970i	$-0.497549\pi$
$709$	17.4772	−	6.36117i	0.656369	−	0.238899i	0.648668	+	0.761071i	$0.275326\pi$
$710$	−1.57297	+	2.72446i	−0.0590324	+	0.102247i
$711$	7.28459	−	2.50394i	0.273193	−	0.0939050i
$712$	5.93824	+	10.2853i	0.222545	+	0.385459i
$713$	4.87867	+	4.09369i	0.182708	+	0.153310i
$714$	−8.02136	+	1.34012i	−0.300192	+	0.0501526i
$715$	−1.45793	−	8.26834i	−0.0545235	−	0.309218i
$716$	−1.44237	−	8.18007i	−0.0539038	−	0.305703i
$717$	30.8522	+	37.4471i	1.15220	+	1.39849i
$718$	20.9056	+	17.5419i	0.780190	+	0.654657i
$719$	24.5686	+	42.5540i	0.916253	+	1.58700i	0.805056	+	0.593199i	$0.202135\pi$
$719$	24.5686	+	42.5540i	0.916253	+	1.58700i	0.111197	+	0.993798i	$0.464531\pi$
$720$	−4.00938	−	7.24223i	−0.149421	−	0.269902i
$721$	−5.62446	+	9.74185i	−0.209466	+	0.362805i
$722$	37.2582	−	13.5609i	1.38660	−	0.504683i
$723$	25.9276	−	30.3409i	0.964257	−	1.12839i
$724$	13.9317	−	11.6900i	0.517766	−	0.434457i
$725$	−11.2020	−	4.07719i	−0.416031	−	0.151423i
$726$	−15.5064	−	9.13956i	−0.575498	−	0.339201i
$727$	2.11570	−	11.9988i	0.0784671	−	0.445009i	−0.920109	−	0.391663i	$-0.871900\pi$
$727$	2.11570	−	11.9988i	0.0784671	−	0.445009i	0.998576	−	0.0533466i	$-0.0169888\pi$
$728$	−3.90223			−0.144626
$729$	−26.9607	−	1.45624i	−0.998544	−	0.0539347i
$730$	−43.5451			−1.61168
$731$	2.78602	−	15.8003i	0.103045	−	0.584396i
$732$	−16.1745	−	9.53334i	−0.597828	−	0.352362i
$733$	−26.7290	−	9.72856i	−0.987258	−	0.359332i	−0.202600	−	0.979262i	$-0.564939\pi$
$733$	−26.7290	−	9.72856i	−0.987258	−	0.359332i	−0.784658	+	0.619929i	$0.787161\pi$
$734$	−3.55966	+	2.98691i	−0.131389	+	0.110249i
$735$	3.10487	−	3.63338i	0.114525	−	0.134019i
$736$	−3.02510	+	1.10105i	−0.111507	+	0.0405851i
$737$	2.69743	−	4.67209i	0.0993613	−	0.172099i
$738$	−4.16017	−	7.51460i	−0.153138	−	0.276616i
$739$	−15.3964	−	26.6673i	−0.566364	−	0.980971i	−0.996921	−	0.0784080i	$-0.975016\pi$
$739$	−15.3964	−	26.6673i	−0.566364	−	0.980971i	0.430557	−	0.902563i	$-0.358317\pi$
$740$	−20.9299	−	17.5622i	−0.769397	−	0.645601i
$741$	32.9136	+	39.9491i	1.20911	+	1.46757i
$742$	0.274719	+	1.55801i	0.0100853	+	0.0571963i
$743$	−1.52612	−	8.65508i	−0.0559881	−	0.317524i	0.943932	−	0.330139i	$-0.107096\pi$
$743$	−1.52612	−	8.65508i	−0.0559881	−	0.317524i	−0.999920	+	0.0126148i	$0.995984\pi$
$744$	−3.37969	+	0.564639i	−0.123905	+	0.0207007i
$745$	−3.73339	−	3.13269i	−0.136781	−	0.114773i
$746$	−9.01332	−	15.6115i	−0.330001	−	0.571579i
$747$	37.0369	−	12.7307i	1.35511	−	0.465793i
$748$	1.83057	−	3.17063i	0.0669321	−	0.115930i
$749$	0.816924	−	0.297336i	0.0298498	−	0.0108644i
$750$	−11.2124	−	2.08120i	−0.409420	−	0.0759945i
$751$	−5.64843	+	4.73960i	−0.206114	+	0.172950i	−0.740001	−	0.672605i	$-0.765175\pi$
$751$	−5.64843	+	4.73960i	−0.206114	+	0.172950i	0.533887	+	0.845556i	$0.320731\pi$
$752$	−7.88268	−	2.86906i	−0.287452	−	0.104624i
$753$	−9.03656	+	5.10946i	−0.329311	+	0.186199i
$754$	3.09034	−	17.5262i	0.112544	−	0.638266i
$755$	−47.3869			−1.72459
$756$	−0.140177	+	5.19426i	−0.00509820	+	0.188913i
$757$	−15.3306			−0.557198			−0.278599	−	0.960407i	$-0.589870\pi$
$757$	−15.3306			−0.557198			−0.278599	+	0.960407i	$0.589870\pi$
$758$	0.934754	−	5.30125i	0.0339518	−	0.192550i
$759$	−0.0391008	+	4.34757i	−0.00141927	+	0.157807i
$760$	19.8573	+	7.22747i	0.720300	+	0.262168i
$761$	30.5250	−	25.6135i	1.10653	−	0.928488i	0.108682	−	0.994077i	$-0.465337\pi$
$761$	30.5250	−	25.6135i	1.10653	−	0.928488i	0.997847	+	0.0655887i	$0.0208925\pi$
$762$	−4.09131	−	11.5633i	−0.148213	−	0.418895i
$763$	−9.39314	+	3.41882i	−0.340054	+	0.123770i
$764$	−4.06536	+	7.04141i	−0.147079	+	0.254749i
$765$	6.05977	+	38.3925i	0.219092	+	1.38808i
$766$	−0.881569	−	1.52692i	−0.0318524	−	0.0551699i
$767$	−9.88240	−	8.29231i	−0.356833	−	0.299418i
$768$	0.607010	−	1.62220i	0.0219036	−	0.0585362i
$769$	−4.73368	−	26.8460i	−0.170701	−	0.968092i	−0.942990	−	0.332821i	$-0.892000\pi$
$769$	−4.73368	−	26.8460i	−0.170701	−	0.968092i	0.772289	−	0.635271i	$-0.219112\pi$
$770$	0.373614	+	2.11887i	0.0134641	+	0.0763589i
$771$	−5.87998	+	15.7139i	−0.211762	+	0.565924i
$772$	−9.00650	−	7.55735i	−0.324151	−	0.271995i
$773$	19.9184	+	34.4997i	0.716416	+	1.24087i	0.962411	+	0.271598i	$0.0875521\pi$
$773$	19.9184	+	34.4997i	0.716416	+	1.24087i	−0.245995	+	0.969271i	$0.579115\pi$
$774$	−9.56827	−	3.67877i	−0.343924	−	0.132231i
$775$	2.58554	−	4.47828i	0.0928752	−	0.160865i
$776$	−10.8569	+	3.95160i	−0.389742	+	0.141854i
$777$	5.72055	+	16.1680i	0.205224	+	0.580025i
$778$	8.02873	−	6.73690i	0.287844	−	0.241530i
$779$	20.6041	+	7.49929i	0.738219	+	0.268690i
$780$	−0.167725	+	18.6492i	−0.00600553	+	0.667747i
$781$	−0.154371	+	0.875484i	−0.00552384	+	0.0313273i
$782$	15.1154			0.540525
$783$	−23.2181	−	4.74313i	−0.829746	−	0.169506i
$784$	1.00000			0.0357143
$785$	1.03436	−	5.86617i	0.0369180	−	0.209372i
$786$	−25.6405	+	14.4977i	−0.914566	+	0.517115i
$787$	31.1343	+	11.3320i	1.10982	+	0.403941i	0.830927	−	0.556382i	$-0.187811\pi$
$787$	31.1343	+	11.3320i	1.10982	+	0.403941i	0.278892	+	0.960323i	$0.410033\pi$
$788$	−18.0366	+	15.1345i	−0.642527	+	0.539145i
$789$	14.9626	+	2.77729i	0.532683	+	0.0988740i
$790$	−6.65768	+	2.42320i	−0.236870	+	0.0862135i
$791$	−5.54879	+	9.61079i	−0.197292	+	0.341720i
$792$	−1.76461	−	1.53561i	−0.0627028	−	0.0545655i
$793$	21.1496	+	36.6322i	0.751044	+	1.30085i
$794$	−21.1579	−	17.7536i	−0.750865	−	0.630050i
$795$	7.45769	−	1.24594i	0.264497	−	0.0441891i
$796$	−3.46060	−	19.6261i	−0.122658	−	0.695627i
$797$	−0.797581	−	4.52331i	−0.0282518	−	0.160224i	0.967418	−	0.253185i	$-0.0814780\pi$
$797$	−0.797581	−	4.52331i	−0.0282518	−	0.160224i	−0.995670	+	0.0929608i	$0.970367\pi$
$798$	−8.43455	−	10.2375i	−0.298580	−	0.362403i
$799$	30.1722	+	25.3175i	1.06742	+	0.895668i
$800$	1.30694	+	2.26369i	0.0462074	+	0.0800336i
$801$	−35.6237	−	0.640830i	−1.25870	−	0.0226426i
$802$	−10.3510	+	17.9285i	−0.365508	+	0.633078i
$803$	−11.5630	+	4.20860i	−0.408051	+	0.148518i
$804$	−7.78523	+	9.11041i	−0.274564	+	0.321299i
$805$	−6.80473	+	5.70985i	−0.239835	+	0.201246i
$806$	7.25426	+	2.64033i	0.255520	+	0.0930018i
$807$	24.8756	+	14.6618i	0.875661	+	0.516119i
$808$	3.19642	−	18.1278i	0.112450	−	0.637733i
$809$	−43.0247			−1.51267			−0.756334	−	0.654185i	$-0.773012\pi$
$809$	−43.0247			−1.51267			−0.756334	+	0.654185i	$0.773012\pi$
$810$	24.8179	+	0.893181i	0.872011	+	0.0313832i
$811$	29.7128			1.04336			0.521678	−	0.853142i	$-0.325306\pi$
$811$	29.7128			1.04336			0.521678	+	0.853142i	$0.325306\pi$
$812$	−0.791941	+	4.49132i	−0.0277917	+	0.157614i
$813$	−39.4338	−	23.2425i	−1.38300	−	0.815149i
$814$	−7.25513	−	2.64065i	−0.254292	−	0.0925548i
$815$	−31.2983	+	26.2624i	−1.09633	+	0.919932i
$816$	−5.28331	+	6.18262i	−0.184953	+	0.216435i
$817$	24.5905	−	8.95020i	0.860311	−	0.313128i
$818$	−5.80180	+	10.0490i	−0.202855	+	0.351356i
$819$	6.03475	−	10.0314i	0.210871	−	0.350525i
$820$	3.95012	+	6.84180i	0.137944	+	0.238926i
$821$	3.77356	+	3.16639i	0.131698	+	0.110508i	0.706257	−	0.707955i	$-0.250382\pi$
$821$	3.77356	+	3.16639i	0.131698	+	0.110508i	−0.574559	+	0.818463i	$0.694827\pi$
$822$	−12.9415	−	15.7079i	−0.451387	−	0.547874i
$823$	4.67026	+	26.4864i	0.162795	+	0.923256i	0.951309	+	0.308239i	$0.0997397\pi$
$823$	4.67026	+	26.4864i	0.162795	+	0.923256i	−0.788514	+	0.615017i	$0.789149\pi$
$824$	1.95335	+	11.0780i	0.0680483	+	0.385921i
$825$	3.48193	−	0.581719i	0.121225	−	0.0202529i
$826$	2.53250	+	2.12502i	0.0881168	+	0.0739388i
$827$	−28.4944	−	49.3538i	−0.990848	−	1.71620i	−0.612323	−	0.790608i	$-0.709765\pi$
$827$	−28.4944	−	49.3538i	−0.990848	−	1.71620i	−0.378525	−	0.925591i	$-0.623569\pi$
$828$	1.84784	−	9.47930i	0.0642169	−	0.329429i
$829$	−13.4760	+	23.3411i	−0.468041	+	0.810670i	−0.999333	−	0.0365184i	$-0.988373\pi$
$829$	−13.4760	+	23.3411i	−0.468041	+	0.810670i	0.531292	+	0.847189i	$0.321707\pi$
$830$	−33.8496	+	12.3202i	−1.17494	+	0.427642i
$831$	25.9306	+	4.81310i	0.899521	+	0.166965i
$832$	−2.98928	+	2.50831i	−0.103635	+	0.0869599i
$833$	−4.41216	−	1.60589i	−0.152872	−	0.0556409i
$834$	25.6178	−	14.4848i	0.887071	−	0.501568i
$835$	−1.49311	+	8.46785i	−0.0516712	+	0.293042i
$836$	5.97147			0.206528
$837$	3.77514	−	9.56129i	0.130488	−	0.330487i
$838$	16.0336			0.553872
$839$	−3.41774	+	19.3830i	−0.117994	+	0.669175i	0.867231	+	0.497906i	$0.165898\pi$
$839$	−3.41774	+	19.3830i	−0.117994	+	0.669175i	−0.985224	+	0.171268i	$0.945213\pi$
$840$	0.0429819	−	4.77910i	0.00148302	−	0.164895i
$841$	7.70630	+	2.80486i	0.265734	+	0.0967194i
$842$	−2.45710	+	2.06175i	−0.0846774	+	0.0710528i
$843$	−13.4933	−	38.1362i	−0.464734	−	1.31348i
$844$	−5.75674	+	2.09528i	−0.198155	+	0.0721225i
$845$	3.07310	−	5.32277i	0.105718	−	0.183109i
$846$	19.5659	−	15.8269i	0.672689	−	0.544138i
$847$	−5.19600	−	8.99974i	−0.178537	−	0.309235i
$848$	1.21192	+	1.01692i	0.0416174	+	0.0349211i
$849$	−13.6399	+	36.4519i	−0.468120	+	1.25103i
$850$	−2.13119	−	12.0866i	−0.0730992	−	0.414566i
$851$	−5.53520	−	31.3917i	−0.189744	−	1.07609i
$852$	0.692058	−	1.84949i	0.0237095	−	0.0633624i
$853$	−0.393283	−	0.330003i	−0.0134657	−	0.0112991i	0.636030	−	0.771664i	$-0.280575\pi$
$853$	−0.393283	−	0.330003i	−0.0134657	−	0.0112991i	−0.649496	+	0.760365i	$0.725020\pi$
$854$	−5.41987	−	9.38749i	−0.185464	−	0.321233i
$855$	−49.2885	+	39.8695i	−1.68563	+	1.36351i
$856$	0.434676	−	0.752882i	0.0148569	−	0.0257330i
$857$	13.3917	−	4.87418i	0.457452	−	0.166499i	−0.103008	−	0.994681i	$-0.532847\pi$
$857$	13.3917	−	4.87418i	0.457452	−	0.166499i	0.560460	+	0.828182i	$0.310624\pi$
$858$	1.75789	+	4.96834i	0.0600134	+	0.169616i
$859$	−22.1864	+	18.6166i	−0.756989	+	0.635189i	−0.937341	−	0.348413i	$-0.886721\pi$
$859$	−22.1864	+	18.6166i	−0.756989	+	0.635189i	0.180352	+	0.983602i	$0.442276\pi$
$860$	8.86010	+	3.22481i	0.302127	+	0.109965i
$861$	0.0445984	−	4.95884i	0.00151991	−	0.168997i
$862$	−4.69086	+	26.6032i	−0.159771	+	0.906109i
$863$	10.3148			0.351120			0.175560	−	0.984469i	$-0.443826\pi$
$863$	10.3148			0.351120			0.175560	+	0.984469i	$0.443826\pi$
$864$	3.23142	+	4.06914i	0.109935	+	0.138435i
$865$	37.8416			1.28665
$866$	−2.88386	+	16.3552i	−0.0979977	+	0.555773i
$867$	7.60806	−	4.30175i	0.258383	−	0.146095i
$868$	−1.85900	−	0.676621i	−0.0630986	−	0.0229660i
$869$	−1.53369	+	1.28692i	−0.0520269	+	0.0436558i
$870$	21.4304	+	3.97781i	0.726560	+	0.134860i
$871$	25.3705	−	9.23412i	0.859648	−	0.312886i
$872$	−4.99798	+	8.65676i	−0.169253	+	0.293155i
$873$	6.63182	−	34.0208i	0.224453	−	1.15143i
$874$	12.3269	+	21.3509i	0.416965	+	0.722204i
$875$	−5.04369	−	4.23216i	−0.170508	−	0.143073i
$876$	26.9599	−	4.50415i	0.910892	−	0.152181i
$877$	7.09095	+	40.2148i	0.239444	+	1.35796i	0.833049	+	0.553200i	$0.186593\pi$
$877$	7.09095	+	40.2148i	0.239444	+	1.35796i	−0.593604	+	0.804757i	$0.702296\pi$
$878$	0.333631	+	1.89211i	0.0112595	+	0.0638557i
$879$	−8.79821	−	10.6789i	−0.296756	−	0.360190i
$880$	1.64819	+	1.38300i	0.0555605	+	0.0466208i
$881$	−3.41203	−	5.90981i	−0.114954	−	0.199107i	0.802807	−	0.596239i	$-0.203339\pi$
$881$	−3.41203	−	5.90981i	−0.114954	−	0.199107i	−0.917761	+	0.397132i	$0.870005\pi$
$882$	−1.54649	+	2.57068i	−0.0520729	+	0.0865592i
$883$	22.8036	−	39.4969i	0.767401	−	1.32918i	−0.171567	−	0.985172i	$-0.554883\pi$
$883$	22.8036	−	39.4969i	0.767401	−	1.32918i	0.938968	−	0.344005i	$-0.111784\pi$
$884$	17.2173	−	6.26658i	0.579080	−	0.210768i
$885$	10.2645	−	12.0117i	0.345038	−	0.403770i
$886$	−26.0063	+	21.8219i	−0.873699	+	0.733120i
$887$	−45.9952	−	16.7409i	−1.54437	−	0.562103i	−0.577279	−	0.816547i	$-0.695885\pi$
$887$	−45.9952	−	16.7409i	−1.54437	−	0.562103i	−0.967088	+	0.254444i	$0.918108\pi$
$888$	14.7748	+	8.70834i	0.495810	+	0.292233i
$889$	1.22972	−	6.97406i	0.0412433	−	0.233903i
$890$	32.7711			1.09849
$891$	6.67651	−	2.16145i	0.223671	−	0.0724114i
$892$	3.55406			0.118999
$893$	−11.1555	+	63.2660i	−0.373305	+	2.11712i
$894$	2.63548	+	1.55336i	0.0881435	+	0.0519522i
$895$	−21.5375	−	7.83899i	−0.719918	−	0.262029i
$896$	0.766044	−	0.642788i	0.0255917	−	0.0214740i
$897$	−14.1354	+	16.5415i	−0.471967	+	0.552304i
$898$	5.61624	−	2.04415i	0.187416	−	0.0682140i
$899$	4.51114	−	7.81353i	0.150455	−	0.260596i
$900$	−7.84039	−	0.141040i	−0.261346	−	0.00470133i
$901$	−3.71410	−	6.43301i	−0.123735	−	0.214315i
$902$	1.71018	+	1.43501i	0.0569427	+	0.0477806i
$903$	−3.76340	−	4.56785i	−0.125238	−	0.152008i
$904$	1.92708	+	10.9290i	0.0640936	+	0.363493i
$905$	−8.71409	−	49.4201i	−0.289666	−	1.64278i
$906$	29.3385	−	4.90153i	0.974706	−	0.162842i
$907$	7.71934	+	6.47729i	0.256316	+	0.215075i	0.761886	−	0.647711i	$-0.224273\pi$
$907$	7.71934	+	6.47729i	0.256316	+	0.215075i	−0.505570	+	0.862785i	$0.668718\pi$
$908$	−0.435444	−	0.754212i	−0.0144507	−	0.0250294i
$909$	41.6574	+	36.2513i	1.38169	+	1.20238i
$910$	−5.38377	+	9.32496i	−0.178470	+	0.309120i
$911$	7.50964	−	2.73328i	0.248805	−	0.0905578i	−0.214607	−	0.976700i	$-0.568847\pi$
$911$	7.50964	−	2.73328i	0.248805	−	0.0905578i	0.463412	+	0.886143i	$0.346625\pi$
$912$	−13.0418	−	2.42075i	−0.431856	−	0.0801590i
$913$	−7.79773	+	6.54307i	−0.258067	+	0.216544i
$914$	10.7590	+	3.91596i	0.355877	+	0.129529i
$915$	−45.0967	+	25.4986i	−1.49085	+	0.842958i
$916$	3.24950	−	18.4288i	0.107366	−	0.608905i
$917$	−17.0060			−0.561589
$918$	−7.72295	−	23.1430i	−0.254895	−	0.763833i
$919$	−14.6329			−0.482695			−0.241348	−	0.970439i	$-0.577589\pi$
$919$	−14.6329			−0.482695			−0.241348	+	0.970439i	$0.577589\pi$
$920$	−1.54251	+	8.74799i	−0.0508549	+	0.288413i
$921$	−0.0637710	+	7.09062i	−0.00210133	+	0.233644i
$922$	−15.9534	−	5.80656i	−0.525397	−	0.191229i
$923$	−3.40811	+	2.85975i	−0.112179	+	0.0941297i
$924$	−0.450483	−	1.27321i	−0.0148198	−	0.0418854i
$925$	−24.3210	+	8.85213i	−0.799670	+	0.291056i
$926$	−14.4604	+	25.0462i	−0.475198	+	0.823068i
$927$	−31.4989	−	12.1106i	−1.03456	−	0.397763i
$928$	2.28030	+	3.94960i	0.0748546	+	0.129652i
$929$	−35.1586	−	29.5016i	−1.15352	−	0.967915i	−0.153720	−	0.988114i	$-0.549125\pi$
$929$	−35.1586	−	29.5016i	−1.15352	−	0.967915i	−0.999796	+	0.0201995i	$0.993570\pi$
$930$	−3.31354	+	8.85527i	−0.108655	+	0.290376i
$931$	−1.32985	−	7.54194i	−0.0435840	−	0.247177i
$932$	2.00627	+	11.3781i	0.0657175	+	0.372703i
$933$	3.34955	−	8.95151i	0.109659	−	0.293059i
$934$	21.9301	+	18.4015i	0.717575	+	0.602117i
$935$	−5.05113	−	8.74882i	−0.165190	−	0.286117i
$936$	−1.82516	−	11.5635i	−0.0596573	−	0.377966i
$937$	−10.3981	+	18.0100i	−0.339691	+	0.588361i	−0.984374	−	0.176088i	$-0.943656\pi$
$937$	−10.3981	+	18.0100i	−0.339691	+	0.588361i	0.644684	+	0.764449i	$0.276989\pi$
$938$	−6.50154	+	2.36637i	−0.212283	+	0.0772647i
$939$	−13.1090	−	37.0500i	−0.427795	−	1.20908i
$940$	−17.7315	+	14.8785i	−0.578337	+	0.485282i
$941$	12.9139	+	4.70028i	0.420982	+	0.153225i	0.543820	−	0.839202i	$-0.316977\pi$
$941$	12.9139	+	4.70028i	0.420982	+	0.153225i	−0.122838	+	0.992427i	$0.539200\pi$
$942$	−0.0336265	+	3.73889i	−0.00109561	+	0.121820i
$943$	−1.60052	+	9.07699i	−0.0521201	+	0.295588i
$944$	3.30594			0.107599
$945$	12.2191	+	7.50131i	0.397486	+	0.244018i
$946$	2.66440			0.0866271
$947$	7.25260	−	41.1316i	0.235678	−	1.33660i	−0.605503	−	0.795843i	$-0.707028\pi$
$947$	7.25260	−	41.1316i	0.235678	−	1.33660i	0.841181	−	0.540753i	$-0.181861\pi$
$948$	3.87130	−	2.18891i	0.125734	−	0.0710926i
$949$	−57.8676	−	21.0621i	−1.87846	−	0.683704i
$950$	15.3346	−	12.8672i	0.497520	−	0.417469i
$951$	51.3324	+	9.52806i	1.66457	+	0.308968i
$952$	−4.41216	+	1.60589i	−0.142999	+	0.0520473i
$953$	1.05830	−	1.83303i	0.0342817	−	0.0593777i	−0.848376	−	0.529395i	$-0.822419\pi$
$953$	1.05830	−	1.83303i	0.0342817	−	0.0593777i	0.882657	+	0.470017i	$0.155752\pi$
$954$	−4.48838	+	1.54279i	−0.145317	+	0.0499498i
$955$	11.2177	+	19.4295i	0.362995	+	0.628725i
$956$	21.4590	+	18.0062i	0.694034	+	0.582363i
$957$	6.07513	−	1.01496i	0.196381	−	0.0328090i
$958$	6.16639	+	34.9713i	0.199227	+	1.12987i
$959$	−2.04044	−	11.5719i	−0.0658894	−	0.373677i
$960$	−3.03902	−	3.68863i	−0.0980840	−	0.119050i
$961$	−20.7493	−	17.4107i	−0.669333	−	0.561637i
$962$	−19.3194	−	33.4621i	−0.622881	−	1.07886i
$963$	1.26319	+	2.28173i	0.0407059	+	0.0735278i
$964$	11.5210	−	19.9550i	0.371067	−	0.642707i
$965$	−30.4853	+	11.0958i	−0.981358	+	0.357185i
$966$	3.62238	−	4.23897i	0.116548	−	0.136387i
$967$	15.7346	−	13.2029i	0.505992	−	0.424577i	−0.353724	−	0.935350i	$-0.615085\pi$
$967$	15.7346	−	13.2029i	0.505992	−	0.424577i	0.859716	+	0.510772i	$0.170640\pi$
$968$	−9.76529	−	3.55427i	−0.313868	−	0.114239i
$969$	53.6549	+	31.6244i	1.72364	+	1.01592i
$970$	−5.53599	+	31.3961i	−0.177750	+	1.00807i
$971$	48.3038			1.55014			0.775072	−	0.631873i	$-0.217714\pi$
$971$	48.3038			1.55014			0.775072	+	0.631873i	$0.217714\pi$
$972$	−15.4578	+	2.01408i	−0.495809	+	0.0646017i
$973$	16.9910			0.544706
$974$	−0.248325	+	1.40832i	−0.00795686	+	0.0451256i
$975$	15.2199	+	8.97070i	0.487428	+	0.287292i
$976$	−10.1860	−	3.70741i	−0.326047	−	0.118671i
$977$	−25.4558	+	21.3600i	−0.814404	+	0.683366i	−0.951655	−	0.307170i	$-0.900618\pi$
$977$	−25.4558	+	21.3600i	−0.814404	+	0.683366i	0.137250	+	0.990536i	$0.456173\pi$
$978$	16.6611	−	19.4972i	0.532765	−	0.623450i
$979$	8.70209	−	3.16730i	0.278120	−	0.101227i
$980$	1.37966	−	2.38965i	0.0440717	−	0.0763345i
$981$	−14.5244	−	26.2358i	−0.463729	−	0.837644i
$982$	−5.48381	−	9.49823i	−0.174995	−	0.303101i
$983$	−22.0783	−	18.5259i	−0.704187	−	0.590883i	0.218774	−	0.975776i	$-0.429794\pi$
$983$	−22.0783	−	18.5259i	−0.704187	−	0.590883i	−0.922962	+	0.384892i	$0.874239\pi$
$984$	−3.15332	−	3.82736i	−0.100524	−	0.122012i
$985$	11.2817	+	63.9817i	0.359465	+	2.03862i
$986$	−3.71842	−	21.0882i	−0.118419	−	0.671585i
$987$	14.3308	−	2.39422i	0.456154	−	0.0762090i
$988$	22.8928	+	19.2093i	0.728317	+	0.611130i
$989$	5.50013	+	9.52651i	0.174894	+	0.302925i
$990$	−6.10414	+	2.09818i	−0.194002	+	0.0666846i
$991$	−17.9557	+	31.1002i	−0.570383	+	0.987932i	0.426144	+	0.904655i	$0.359872\pi$
$991$	−17.9557	+	31.1002i	−0.570383	+	0.987932i	−0.996526	+	0.0832763i	$0.973462\pi$
$992$	−1.85900	+	0.676621i	−0.0590234	+	0.0214827i
$993$	22.6170	+	4.19806i	0.717729	+	0.133221i
$994$	0.873375	−	0.732848i	0.0277018	−	0.0232445i
$995$	−51.6738	−	18.8077i	−1.63817	−	0.596246i
$996$	19.6828	−	11.1291i	0.623674	−	0.352638i
$997$	9.29975	−	52.7415i	0.294526	−	1.67034i	−0.374596	−	0.927188i	$-0.622219\pi$
$997$	9.29975	−	52.7415i	0.294526	−	1.67034i	0.669122	−	0.743152i	$-0.266670\pi$
$998$	33.0618			1.04655
$999$	−45.2354	+	24.5139i	−1.43118	+	0.775587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.295.2	✓	24
27.13	even	9	inner	378.2.u.c.337.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.295.2	✓	24	1.1	even	1	trivial
378.2.u.c.337.2	yes	24	27.13	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.49215 - 0.879480i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-2.11377 + 1.77366i) q^{5} +(1.12523 - 1.31676i) q^{6} +(0.939693 - 0.342020i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.45303 + 2.62463i) q^{9} +(-1.37966 - 2.38965i) q^{10} +(-0.597316 - 0.501208i) q^{11} +(1.10136 + 1.33679i) q^{12} +(-0.677616 - 3.84295i) q^{13} +(0.173648 + 0.984808i) q^{14} +(4.71396 - 0.787553i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.34766 - 4.06627i) q^{17} +(-2.83708 + 0.975191i) q^{18} +(3.82914 - 6.63227i) q^{19} +(2.59292 - 0.943745i) q^{20} +(-1.70296 - 0.316096i) q^{21} +(0.597316 - 0.501208i) q^{22} +(3.02510 + 1.10105i) q^{23} +(-1.50773 + 0.852500i) q^{24} +(0.453897 - 2.57418i) q^{25} +3.90223 q^{26} +(0.140177 - 5.19426i) q^{27} -1.00000 q^{28} +(0.791941 - 4.49132i) q^{29} +(-0.0429819 + 4.77910i) q^{30} +(1.85900 + 0.676621i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.450483 + 1.27321i) q^{33} +(4.41216 - 1.60589i) q^{34} +(-1.37966 + 2.38965i) q^{35} +(-0.467722 - 2.96332i) q^{36} +(-4.95084 - 8.57511i) q^{37} +(5.86659 + 4.92265i) q^{38} +(-2.36869 + 6.33021i) q^{39} +(0.479152 + 2.71741i) q^{40} +(0.497172 + 2.81961i) q^{41} +(0.607010 - 1.62220i) q^{42} +(2.61760 + 2.19643i) q^{43} +(0.389870 + 0.675275i) q^{44} +(-7.72658 - 2.97069i) q^{45} +(-1.60962 + 2.78795i) q^{46} +(-7.88268 + 2.86906i) q^{47} +(-0.577735 - 1.63286i) q^{48} +(0.766044 - 0.642788i) q^{49} +(2.45625 + 0.894002i) q^{50} +(-0.0731388 + 8.13221i) q^{51} +(-0.677616 + 3.84295i) q^{52} +1.58204 q^{53} +(5.09101 + 1.04002i) q^{54} +2.15156 q^{55} +(0.173648 - 0.984808i) q^{56} +(-11.5466 + 6.52869i) q^{57} +(4.28557 + 1.55982i) q^{58} +(2.53250 - 2.12502i) q^{59} +(-4.69903 - 0.872211i) q^{60} +(-10.1860 + 3.70741i) q^{61} +(-0.989154 + 1.71326i) q^{62} +(2.26308 + 1.96939i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(8.24841 + 6.92124i) q^{65} +(-1.33209 + 0.222550i) q^{66} +(1.20144 + 6.81369i) q^{67} +(0.815334 + 4.62399i) q^{68} +(-3.54555 - 4.30344i) q^{69} +(-2.11377 - 1.77366i) q^{70} +(-0.570055 - 0.987364i) q^{71} +(2.99951 + 0.0539579i) q^{72} +(7.89053 - 13.6668i) q^{73} +(9.30454 - 3.38658i) q^{74} +(-2.94122 + 3.44186i) q^{75} +(-5.86659 + 4.92265i) q^{76} +(-0.732716 - 0.266687i) q^{77} +(-5.82272 - 3.43194i) q^{78} +(0.445866 - 2.52863i) q^{79} -2.75933 q^{80} +(-4.77742 + 7.62734i) q^{81} -2.86310 q^{82} +(2.26691 - 12.8563i) q^{83} +(1.49215 + 0.879480i) q^{84} +(12.1746 + 4.43119i) q^{85} +(-2.61760 + 2.19643i) q^{86} +(-5.13172 + 6.00523i) q^{87} +(-0.732716 + 0.266687i) q^{88} +(-5.93824 + 10.2853i) q^{89} +(4.26726 - 7.09334i) q^{90} +(-1.95112 - 3.37943i) q^{91} +(-2.46608 - 2.06929i) q^{92} +(-2.17884 - 2.64458i) q^{93} +(-1.45666 - 8.26113i) q^{94} +(3.66948 + 20.8107i) q^{95} +(1.70837 - 0.285415i) q^{96} +(-8.85066 - 7.42659i) q^{97} +(0.500000 + 0.866025i) q^{98} +(0.447570 - 2.29601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29}+ \cdots - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more