LMFDB - Embedded newform 390.2.f.a.259.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(259,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.f (of order $2$, degree $1$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.4
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	390.259
Dual form			390.2.f.a.259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.17009 + 0.539189i) q^{10} -3.07838i q^{11} +1.00000i q^{12} +(2.87936 - 2.17009i) q^{13} +0.630898 q^{14} +(0.539189 - 2.17009i) q^{15} +1.00000 q^{16} -3.70928i q^{17} +1.00000 q^{18} -0.290725i q^{19} +(-2.17009 - 0.539189i) q^{20} -0.630898i q^{21} +3.07838i q^{22} -1.70928i q^{23} -1.00000i q^{24} +(4.41855 + 2.34017i) q^{25} +(-2.87936 + 2.17009i) q^{26} -1.00000i q^{27} -0.630898 q^{28} +0.447480 q^{29} +(-0.539189 + 2.17009i) q^{30} -6.68035i q^{31} -1.00000 q^{32} +3.07838 q^{33} +3.70928i q^{34} +(1.36910 + 0.340173i) q^{35} -1.00000 q^{36} +5.07838 q^{37} +0.290725i q^{38} +(2.17009 + 2.87936i) q^{39} +(2.17009 + 0.539189i) q^{40} -1.41855i q^{41} +0.630898i q^{42} -5.75872i q^{43} -3.07838i q^{44} +(2.17009 + 0.539189i) q^{45} +1.70928i q^{46} -2.73820 q^{47} +1.00000i q^{48} -6.60197 q^{49} +(-4.41855 - 2.34017i) q^{50} +3.70928 q^{51} +(2.87936 - 2.17009i) q^{52} -14.0989i q^{53} +1.00000i q^{54} +(-1.65983 + 6.68035i) q^{55} +0.630898 q^{56} +0.290725 q^{57} -0.447480 q^{58} +9.02052i q^{59} +(0.539189 - 2.17009i) q^{60} -3.26180 q^{61} +6.68035i q^{62} +0.630898 q^{63} +1.00000 q^{64} +(-7.41855 + 3.15676i) q^{65} -3.07838 q^{66} -7.75872 q^{67} -3.70928i q^{68} +1.70928 q^{69} +(-1.36910 - 0.340173i) q^{70} +1.65983i q^{71} +1.00000 q^{72} +15.3112 q^{73} -5.07838 q^{74} +(-2.34017 + 4.41855i) q^{75} -0.290725i q^{76} +1.94214i q^{77} +(-2.17009 - 2.87936i) q^{78} -10.6537 q^{79} +(-2.17009 - 0.539189i) q^{80} +1.00000 q^{81} +1.41855i q^{82} -3.23513 q^{83} -0.630898i q^{84} +(-2.00000 + 8.04945i) q^{85} +5.75872i q^{86} +0.447480i q^{87} +3.07838i q^{88} +12.3402i q^{89} +(-2.17009 - 0.539189i) q^{90} +(-1.81658 + 1.36910i) q^{91} -1.70928i q^{92} +6.68035 q^{93} +2.73820 q^{94} +(-0.156755 + 0.630898i) q^{95} -1.00000i q^{96} -8.20620 q^{97} +6.60197 q^{98} +3.07838i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35} - 6 q^{36} + 24 q^{37} + 2 q^{39} + 2 q^{40} + 2 q^{45} - 32 q^{47} - 2 q^{49} + 2 q^{50} + 8 q^{51} - 8 q^{52} - 32 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} - 4 q^{61} - 4 q^{63} + 6 q^{64} - 16 q^{65} - 12 q^{66} + 4 q^{67} - 4 q^{69} - 16 q^{70} + 6 q^{72} + 40 q^{73} - 24 q^{74} + 8 q^{75} - 2 q^{78} - 16 q^{79} - 2 q^{80} + 6 q^{81} - 12 q^{85} - 2 q^{90} - 20 q^{91} - 4 q^{93} + 32 q^{94} + 12 q^{95} + 2 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + 2 * q^10 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 6 * q^18 - 2 * q^20 - 2 * q^25 + 8 * q^26 + 4 * q^28 + 4 * q^29 - 6 * q^32 + 12 * q^33 + 16 * q^35 - 6 * q^36 + 24 * q^37 + 2 * q^39 + 2 * q^40 + 2 * q^45 - 32 * q^47 - 2 * q^49 + 2 * q^50 + 8 * q^51 - 8 * q^52 - 32 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 - 4 * q^61 - 4 * q^63 + 6 * q^64 - 16 * q^65 - 12 * q^66 + 4 * q^67 - 4 * q^69 - 16 * q^70 + 6 * q^72 + 40 * q^73 - 24 * q^74 + 8 * q^75 - 2 * q^78 - 16 * q^79 - 2 * q^80 + 6 * q^81 - 12 * q^85 - 2 * q^90 - 20 * q^91 - 4 * q^93 + 32 * q^94 + 12 * q^95 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$6$		−	1.00000i		−	0.408248i
$7$	−0.630898			−0.238457			−0.119228	−	0.992867i	$-0.538042\pi$
$7$	−0.630898			−0.238457			−0.119228	+	0.992867i	$0.538042\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	2.17009	+	0.539189i	0.686242	+	0.170506i
$11$		−	3.07838i		−	0.928166i	−0.885792	−	0.464083i	$-0.846384\pi$
$11$		−	3.07838i		−	0.928166i	0.885792	−	0.464083i	$-0.153616\pi$
$12$			1.00000i			0.288675i
$13$	2.87936	−	2.17009i	0.798591	−	0.601874i
$13$	2.87936	−	2.17009i	0.798591	−	0.601874i
$14$	0.630898			0.168614
$15$	0.539189	−	2.17009i	0.139218	−	0.560314i
$16$	1.00000			0.250000
$17$		−	3.70928i		−	0.899631i	−0.893121	−	0.449816i	$-0.851490\pi$
$17$		−	3.70928i		−	0.899631i	0.893121	−	0.449816i	$-0.148510\pi$
$18$	1.00000			0.235702
$19$		−	0.290725i		−	0.0666968i	−0.999444	−	0.0333484i	$-0.989383\pi$
$19$		−	0.290725i		−	0.0666968i	0.999444	−	0.0333484i	$-0.0106171\pi$
$20$	−2.17009	−	0.539189i	−0.485246	−	0.120566i
$21$		−	0.630898i		−	0.137673i
$22$			3.07838i			0.656312i
$23$		−	1.70928i		−	0.356409i	−0.983994	−	0.178204i	$-0.942971\pi$
$23$		−	1.70928i		−	0.356409i	0.983994	−	0.178204i	$-0.0570288\pi$
$24$		−	1.00000i		−	0.204124i
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	−2.87936	+	2.17009i	−0.564689	+	0.425589i
$27$		−	1.00000i		−	0.192450i
$28$	−0.630898			−0.119228
$29$	0.447480			0.0830950			0.0415475	−	0.999137i	$-0.486771\pi$
$29$	0.447480			0.0830950			0.0415475	+	0.999137i	$0.486771\pi$
$30$	−0.539189	+	2.17009i	−0.0984420	+	0.396202i
$31$		−	6.68035i		−	1.19983i	−0.800065	−	0.599913i	$-0.795202\pi$
$31$		−	6.68035i		−	1.19983i	0.800065	−	0.599913i	$-0.204798\pi$
$32$	−1.00000			−0.176777
$33$	3.07838			0.535877
$34$			3.70928i			0.636135i
$35$	1.36910	+	0.340173i	0.231421	+	0.0574997i
$36$	−1.00000			−0.166667
$37$	5.07838			0.834880			0.417440	−	0.908704i	$-0.362927\pi$
$37$	5.07838			0.834880			0.417440	+	0.908704i	$0.362927\pi$
$38$			0.290725i			0.0471618i
$39$	2.17009	+	2.87936i	0.347492	+	0.461067i
$40$	2.17009	+	0.539189i	0.343121	+	0.0852532i
$41$		−	1.41855i		−	0.221540i	−0.993846	−	0.110770i	$-0.964668\pi$
$41$		−	1.41855i		−	0.221540i	0.993846	−	0.110770i	$-0.0353318\pi$
$42$			0.630898i			0.0973496i
$43$		−	5.75872i		−	0.878197i	−0.898439	−	0.439099i	$-0.855298\pi$
$43$		−	5.75872i		−	0.878197i	0.898439	−	0.439099i	$-0.144702\pi$
$44$		−	3.07838i		−	0.464083i
$45$	2.17009	+	0.539189i	0.323497	+	0.0803775i
$46$			1.70928i			0.252019i
$47$	−2.73820			−0.399408			−0.199704	−	0.979856i	$-0.563998\pi$
$47$	−2.73820			−0.399408			−0.199704	+	0.979856i	$0.563998\pi$
$48$			1.00000i			0.144338i
$49$	−6.60197			−0.943138
$50$	−4.41855	−	2.34017i	−0.624877	−	0.330950i
$51$	3.70928			0.519402
$52$	2.87936	−	2.17009i	0.399296	−	0.300937i
$53$		−	14.0989i		−	1.93663i	−0.249727	−	0.968316i	$-0.580341\pi$
$53$		−	14.0989i		−	1.93663i	0.249727	−	0.968316i	$-0.419659\pi$
$54$			1.00000i			0.136083i
$55$	−1.65983	+	6.68035i	−0.223811	+	0.900778i
$56$	0.630898			0.0843072
$57$	0.290725			0.0385074
$58$	−0.447480			−0.0587570
$59$			9.02052i			1.17437i	0.809452	+	0.587186i	$0.199764\pi$
$59$			9.02052i			1.17437i	−0.809452	+	0.587186i	$0.800236\pi$
$60$	0.539189	−	2.17009i	0.0696090	−	0.280157i
$61$	−3.26180			−0.417630			−0.208815	−	0.977955i	$-0.566961\pi$
$61$	−3.26180			−0.417630			−0.208815	+	0.977955i	$0.566961\pi$
$62$			6.68035i			0.848405i
$63$	0.630898			0.0794856
$64$	1.00000			0.125000
$65$	−7.41855	+	3.15676i	−0.920158	+	0.391547i
$66$	−3.07838			−0.378922
$67$	−7.75872			−0.947879			−0.473939	−	0.880557i	$-0.657168\pi$
$67$	−7.75872			−0.947879			−0.473939	+	0.880557i	$0.657168\pi$
$68$		−	3.70928i		−	0.449816i
$69$	1.70928			0.205773
$70$	−1.36910	−	0.340173i	−0.163639	−	0.0406584i
$71$			1.65983i			0.196985i	0.995138	+	0.0984926i	$0.0314021\pi$
$71$			1.65983i			0.196985i	−0.995138	+	0.0984926i	$0.968598\pi$
$72$	1.00000			0.117851
$73$	15.3112			1.79205			0.896023	−	0.444008i	$-0.146444\pi$
$73$	15.3112			1.79205			0.896023	+	0.444008i	$0.146444\pi$
$74$	−5.07838			−0.590349
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$		−	0.290725i		−	0.0333484i
$77$			1.94214i			0.221328i
$78$	−2.17009	−	2.87936i	−0.245714	−	0.326024i
$79$	−10.6537			−1.19863			−0.599317	−	0.800512i	$-0.704561\pi$
$79$	−10.6537			−1.19863			−0.599317	+	0.800512i	$0.704561\pi$
$80$	−2.17009	−	0.539189i	−0.242623	−	0.0602831i
$81$	1.00000			0.111111
$82$			1.41855i			0.156653i
$83$	−3.23513			−0.355102			−0.177551	−	0.984112i	$-0.556817\pi$
$83$	−3.23513			−0.355102			−0.177551	+	0.984112i	$0.556817\pi$
$84$		−	0.630898i		−	0.0688366i
$85$	−2.00000	+	8.04945i	−0.216930	+	0.873085i
$86$			5.75872i			0.620979i
$87$			0.447480i			0.0479749i
$88$			3.07838i			0.328156i
$89$			12.3402i			1.30806i	0.756470	+	0.654028i	$0.226922\pi$
$89$			12.3402i			1.30806i	−0.756470	+	0.654028i	$0.773078\pi$
$90$	−2.17009	−	0.539189i	−0.228747	−	0.0568355i
$91$	−1.81658	+	1.36910i	−0.190430	+	0.143521i
$92$		−	1.70928i		−	0.178204i
$93$	6.68035			0.692720
$94$	2.73820			0.282424
$95$	−0.156755	+	0.630898i	−0.0160828	+	0.0647287i
$96$		−	1.00000i		−	0.102062i
$97$	−8.20620			−0.833214			−0.416607	−	0.909087i	$-0.636781\pi$
$97$	−8.20620			−0.833214			−0.416607	+	0.909087i	$0.636781\pi$
$98$	6.60197			0.666899
$99$			3.07838i			0.309389i
$100$	4.41855	+	2.34017i	0.441855	+	0.234017i
$101$	3.86603			0.384684			0.192342	−	0.981328i	$-0.438392\pi$
$101$	3.86603			0.384684			0.192342	+	0.981328i	$0.438392\pi$
$102$	−3.70928			−0.367273
$103$			7.84324i			0.772818i	0.922328	+	0.386409i	$0.126285\pi$
$103$			7.84324i			0.772818i	−0.922328	+	0.386409i	$0.873715\pi$
$104$	−2.87936	+	2.17009i	−0.282345	+	0.212794i
$105$	−0.340173	+	1.36910i	−0.0331975	+	0.133611i
$106$			14.0989i			1.36941i
$107$			15.7321i			1.52088i	0.649411	+	0.760438i	$0.275016\pi$
$107$			15.7321i			1.52088i	−0.649411	+	0.760438i	$0.724984\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	12.2329i		−	1.17170i	−0.810421	−	0.585848i	$-0.800762\pi$
$109$		−	12.2329i		−	1.17170i	0.810421	−	0.585848i	$-0.199238\pi$
$110$	1.65983	−	6.68035i	0.158258	−	0.636946i
$111$			5.07838i			0.482018i
$112$	−0.630898			−0.0596142
$113$		−	3.12783i		−	0.294241i	−0.989119	−	0.147121i	$-0.952999\pi$
$113$		−	3.12783i		−	0.294241i	0.989119	−	0.147121i	$-0.0470005\pi$
$114$	−0.290725			−0.0272289
$115$	−0.921622	+	3.70928i	−0.0859417	+	0.345892i
$116$	0.447480			0.0415475
$117$	−2.87936	+	2.17009i	−0.266197	+	0.200625i
$118$		−	9.02052i		−	0.830406i
$119$			2.34017i			0.214523i
$120$	−0.539189	+	2.17009i	−0.0492210	+	0.198101i
$121$	1.52359			0.138508
$122$	3.26180			0.295309
$123$	1.41855			0.127906
$124$		−	6.68035i		−	0.599913i
$125$	−8.32684	−	7.46081i	−0.744775	−	0.667315i
$126$	−0.630898			−0.0562048
$127$			20.6225i			1.82995i	0.403511	+	0.914975i	$0.367790\pi$
$127$			20.6225i			1.82995i	−0.403511	+	0.914975i	$0.632210\pi$
$128$	−1.00000			−0.0883883
$129$	5.75872			0.507027
$130$	7.41855	−	3.15676i	0.650650	−	0.276866i
$131$	6.81432			0.595369			0.297685	−	0.954664i	$-0.403786\pi$
$131$	6.81432			0.595369			0.297685	+	0.954664i	$0.403786\pi$
$132$	3.07838			0.267938
$133$			0.183417i			0.0159043i
$134$	7.75872			0.670252
$135$	−0.539189	+	2.17009i	−0.0464060	+	0.186771i
$136$			3.70928i			0.318068i
$137$	−0.424694			−0.0362840			−0.0181420	−	0.999835i	$-0.505775\pi$
$137$	−0.424694			−0.0362840			−0.0181420	+	0.999835i	$0.505775\pi$
$138$	−1.70928			−0.145503
$139$	−14.2557			−1.20915			−0.604574	−	0.796549i	$-0.706657\pi$
$139$	−14.2557			−1.20915			−0.604574	+	0.796549i	$0.706657\pi$
$140$	1.36910	+	0.340173i	0.115710	+	0.0287499i
$141$		−	2.73820i		−	0.230598i
$142$		−	1.65983i		−	0.139290i
$143$	−6.68035	−	8.86376i	−0.558639	−	0.741225i
$144$	−1.00000			−0.0833333
$145$	−0.971071	−	0.241276i	−0.0806430	−	0.0200369i
$146$	−15.3112			−1.26717
$147$		−	6.60197i		−	0.544521i
$148$	5.07838			0.417440
$149$		−	11.0205i		−	0.902836i	−0.892313	−	0.451418i	$-0.850918\pi$
$149$		−	11.0205i		−	0.902836i	0.892313	−	0.451418i	$-0.149082\pi$
$150$	2.34017	−	4.41855i	0.191074	−	0.360773i
$151$		−	13.7321i		−	1.11750i	−0.829336	−	0.558750i	$-0.811281\pi$
$151$		−	13.7321i		−	1.11750i	0.829336	−	0.558750i	$-0.188719\pi$
$152$			0.290725i			0.0235809i
$153$			3.70928i			0.299877i
$154$		−	1.94214i		−	0.156502i
$155$	−3.60197	+	14.4969i	−0.289317	+	1.16442i
$156$	2.17009	+	2.87936i	0.173746	+	0.230533i
$157$		−	20.8371i		−	1.66298i	−0.555538	−	0.831491i	$-0.687488\pi$
$157$		−	20.8371i		−	1.66298i	0.555538	−	0.831491i	$-0.312512\pi$
$158$	10.6537			0.847562
$159$	14.0989			1.11812
$160$	2.17009	+	0.539189i	0.171560	+	0.0426266i
$161$			1.07838i			0.0849881i
$162$	−1.00000			−0.0785674
$163$	5.23513			0.410047			0.205024	−	0.978757i	$-0.434273\pi$
$163$	5.23513			0.410047			0.205024	+	0.978757i	$0.434273\pi$
$164$		−	1.41855i		−	0.110770i
$165$	−6.68035	−	1.65983i	−0.520064	−	0.129217i
$166$	3.23513			0.251095
$167$	3.41855			0.264535			0.132268	−	0.991214i	$-0.457774\pi$
$167$	3.41855			0.264535			0.132268	+	0.991214i	$0.457774\pi$
$168$			0.630898i			0.0486748i
$169$	3.58145	−	12.4969i	0.275496	−	0.961302i
$170$	2.00000	−	8.04945i	0.153393	−	0.617365i
$171$			0.290725i			0.0222323i
$172$		−	5.75872i		−	0.439099i
$173$		−	8.83710i		−	0.671872i	−0.941885	−	0.335936i	$-0.890947\pi$
$173$		−	8.83710i		−	0.671872i	0.941885	−	0.335936i	$-0.109053\pi$
$174$		−	0.447480i		−	0.0339234i
$175$	−2.78765	−	1.47641i	−0.210727	−	0.111606i
$176$		−	3.07838i		−	0.232041i
$177$	−9.02052			−0.678024
$178$		−	12.3402i		−	0.924935i
$179$	21.3835			1.59828			0.799138	−	0.601147i	$-0.205290\pi$
$179$	21.3835			1.59828			0.799138	+	0.601147i	$0.205290\pi$
$180$	2.17009	+	0.539189i	0.161749	+	0.0401888i
$181$	10.9939			0.817167			0.408583	−	0.912721i	$-0.366023\pi$
$181$	10.9939			0.817167			0.408583	+	0.912721i	$0.366023\pi$
$182$	1.81658	−	1.36910i	0.134654	−	0.101485i
$183$		−	3.26180i		−	0.241119i
$184$			1.70928i			0.126009i
$185$	−11.0205	−	2.73820i	−0.810245	−	0.201317i
$186$	−6.68035			−0.489827
$187$	−11.4186			−0.835007
$188$	−2.73820			−0.199704
$189$			0.630898i			0.0458910i
$190$	0.156755	−	0.630898i	0.0113722	−	0.0457701i
$191$	13.9421			1.00882			0.504409	−	0.863465i	$-0.331710\pi$
$191$	13.9421			1.00882			0.504409	+	0.863465i	$0.331710\pi$
$192$			1.00000i			0.0721688i
$193$	−3.79380			−0.273083			−0.136542	−	0.990634i	$-0.543599\pi$
$193$	−3.79380			−0.273083			−0.136542	+	0.990634i	$0.543599\pi$
$194$	8.20620			0.589171
$195$	−3.15676	−	7.41855i	−0.226060	−	0.531253i
$196$	−6.60197			−0.471569
$197$	21.5174			1.53305			0.766527	−	0.642212i	$-0.221983\pi$
$197$	21.5174			1.53305			0.766527	+	0.642212i	$0.221983\pi$
$198$		−	3.07838i		−	0.218771i
$199$	−17.8576			−1.26589			−0.632947	−	0.774195i	$-0.718155\pi$
$199$	−17.8576			−1.26589			−0.632947	+	0.774195i	$0.718155\pi$
$200$	−4.41855	−	2.34017i	−0.312439	−	0.165475i
$201$		−	7.75872i		−	0.547258i
$202$	−3.86603			−0.272013
$203$	−0.282314			−0.0198146
$204$	3.70928			0.259701
$205$	−0.764867	+	3.07838i	−0.0534206	+	0.215003i
$206$		−	7.84324i		−	0.546465i
$207$			1.70928i			0.118803i
$208$	2.87936	−	2.17009i	0.199648	−	0.150468i
$209$	−0.894960			−0.0619057
$210$	0.340173	−	1.36910i	0.0234742	−	0.0944770i
$211$	16.7792			1.15513			0.577565	−	0.816344i	$-0.304003\pi$
$211$	16.7792			1.15513			0.577565	+	0.816344i	$0.304003\pi$
$212$		−	14.0989i		−	0.968316i
$213$	−1.65983			−0.113729
$214$		−	15.7321i		−	1.07542i
$215$	−3.10504	+	12.4969i	−0.211762	+	0.852283i
$216$			1.00000i			0.0680414i
$217$			4.21461i			0.286107i
$218$			12.2329i			0.828514i
$219$			15.3112i			1.03464i
$220$	−1.65983	+	6.68035i	−0.111906	+	0.450389i
$221$	−8.04945	−	10.6803i	−0.541464	−	0.718438i
$222$		−	5.07838i		−	0.340838i
$223$	−20.3630			−1.36360			−0.681802	−	0.731536i	$-0.738804\pi$
$223$	−20.3630			−1.36360			−0.681802	+	0.731536i	$0.738804\pi$
$224$	0.630898			0.0421536
$225$	−4.41855	−	2.34017i	−0.294570	−	0.156012i
$226$			3.12783i			0.208060i
$227$	14.8371			0.984773			0.492387	−	0.870377i	$-0.336125\pi$
$227$	14.8371			0.984773			0.492387	+	0.870377i	$0.336125\pi$
$228$	0.290725			0.0192537
$229$		−	12.6453i		−	0.835623i	−0.908534	−	0.417812i	$-0.862797\pi$
$229$		−	12.6453i		−	0.835623i	0.908534	−	0.417812i	$-0.137203\pi$
$230$	0.921622	−	3.70928i	0.0607700	−	0.244582i
$231$	−1.94214			−0.127784
$232$	−0.447480			−0.0293785
$233$			25.3835i			1.66293i	0.555579	+	0.831463i	$0.312496\pi$
$233$			25.3835i			1.66293i	−0.555579	+	0.831463i	$0.687504\pi$
$234$	2.87936	−	2.17009i	0.188230	−	0.141863i
$235$	5.94214	+	1.47641i	0.387623	+	0.0963103i
$236$			9.02052i			0.587186i
$237$		−	10.6537i		−	0.692031i
$238$		−	2.34017i		−	0.151691i
$239$		−	9.84324i		−	0.636707i	−0.947972	−	0.318353i	$-0.896870\pi$
$239$		−	9.84324i		−	0.636707i	0.947972	−	0.318353i	$-0.103130\pi$
$240$	0.539189	−	2.17009i	0.0348045	−	0.140078i
$241$			15.7854i			1.01683i	0.861113	+	0.508413i	$0.169768\pi$
$241$			15.7854i			1.01683i	−0.861113	+	0.508413i	$0.830232\pi$
$242$	−1.52359			−0.0979401
$243$			1.00000i			0.0641500i
$244$	−3.26180			−0.208815
$245$	14.3268	+	3.55971i	0.915308	+	0.227421i
$246$	−1.41855			−0.0904435
$247$	−0.630898	−	0.837101i	−0.0401431	−	0.0532635i
$248$			6.68035i			0.424202i
$249$		−	3.23513i		−	0.205018i
$250$	8.32684	+	7.46081i	0.526636	+	0.471863i
$251$	10.1340			0.639650			0.319825	−	0.947477i	$-0.396376\pi$
$251$	10.1340			0.639650			0.319825	+	0.947477i	$0.396376\pi$
$252$	0.630898			0.0397428
$253$	−5.26180			−0.330806
$254$		−	20.6225i		−	1.29397i
$255$	−8.04945	−	2.00000i	−0.504076	−	0.125245i
$256$	1.00000			0.0625000
$257$			28.7565i			1.79378i	0.442255	+	0.896889i	$0.354179\pi$
$257$			28.7565i			1.79378i	−0.442255	+	0.896889i	$0.645821\pi$
$258$	−5.75872			−0.358522
$259$	−3.20394			−0.199083
$260$	−7.41855	+	3.15676i	−0.460079	+	0.195774i
$261$	−0.447480			−0.0276983
$262$	−6.81432			−0.420990
$263$			7.28458i			0.449187i	0.974453	+	0.224593i	$0.0721053\pi$
$263$			7.28458i			0.449187i	−0.974453	+	0.224593i	$0.927895\pi$
$264$	−3.07838			−0.189461
$265$	−7.60197	+	30.5958i	−0.466985	+	1.87949i
$266$		−	0.183417i		−	0.0112460i
$267$	−12.3402			−0.755206
$268$	−7.75872			−0.473939
$269$	21.9071			1.33570			0.667849	−	0.744297i	$-0.267215\pi$
$269$	21.9071			1.33570			0.667849	+	0.744297i	$0.267215\pi$
$270$	0.539189	−	2.17009i	0.0328140	−	0.132067i
$271$		−	9.10504i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$271$		−	9.10504i		−	0.553092i	0.961001	−	0.276546i	$-0.0891898\pi$
$272$		−	3.70928i		−	0.224908i
$273$	−1.36910	−	1.81658i	−0.0828618	−	0.109945i
$274$	0.424694			0.0256567
$275$	7.20394	−	13.6020i	0.434414	−	0.820230i
$276$	1.70928			0.102886
$277$		−	25.2039i		−	1.51436i	−0.653208	−	0.757179i	$-0.726577\pi$
$277$		−	25.2039i		−	1.51436i	0.653208	−	0.757179i	$-0.273423\pi$
$278$	14.2557			0.854997
$279$			6.68035i			0.399942i
$280$	−1.36910	−	0.340173i	−0.0818195	−	0.0203292i
$281$		−	15.5441i		−	0.927284i	−0.886023	−	0.463642i	$-0.846542\pi$
$281$		−	15.5441i		−	0.927284i	0.886023	−	0.463642i	$-0.153458\pi$
$282$			2.73820i			0.163058i
$283$			13.2762i			0.789186i	0.918856	+	0.394593i	$0.129114\pi$
$283$			13.2762i			0.789186i	−0.918856	+	0.394593i	$0.870886\pi$
$284$			1.65983i			0.0984926i
$285$	−0.630898	−	0.156755i	−0.0373711	−	0.00928539i
$286$	6.68035	+	8.86376i	0.395017	+	0.524125i
$287$			0.894960i			0.0528278i
$288$	1.00000			0.0589256
$289$	3.24128			0.190663
$290$	0.971071	+	0.241276i	0.0570232	+	0.0141682i
$291$		−	8.20620i		−	0.481056i
$292$	15.3112			0.896023
$293$	9.31965			0.544460			0.272230	−	0.962232i	$-0.412239\pi$
$293$	9.31965			0.544460			0.272230	+	0.962232i	$0.412239\pi$
$294$			6.60197i			0.385035i
$295$	4.86376	−	19.5753i	0.283179	−	1.13972i
$296$	−5.07838			−0.295175
$297$	−3.07838			−0.178626
$298$			11.0205i			0.638402i
$299$	−3.70928	−	4.92162i	−0.214513	−	0.284625i
$300$	−2.34017	+	4.41855i	−0.135110	+	0.255105i
$301$			3.63317i			0.209412i
$302$			13.7321i			0.790191i
$303$			3.86603i			0.222098i
$304$		−	0.290725i		−	0.0166742i
$305$	7.07838	+	1.75872i	0.405307	+	0.100704i
$306$		−	3.70928i		−	0.212045i
$307$	7.54411			0.430565			0.215283	−	0.976552i	$-0.430933\pi$
$307$	7.54411			0.430565			0.215283	+	0.976552i	$0.430933\pi$
$308$			1.94214i			0.110664i
$309$	−7.84324			−0.446187
$310$	3.60197	−	14.4969i	0.204578	−	0.823370i
$311$	−29.9421			−1.69786			−0.848932	−	0.528503i	$-0.822754\pi$
$311$	−29.9421			−1.69786			−0.848932	+	0.528503i	$0.822754\pi$
$312$	−2.17009	−	2.87936i	−0.122857	−	0.163012i
$313$		−	6.52359i		−	0.368735i	−0.982857	−	0.184368i	$-0.940976\pi$
$313$		−	6.52359i		−	0.368735i	0.982857	−	0.184368i	$-0.0590237\pi$
$314$			20.8371i			1.17591i
$315$	−1.36910	−	0.340173i	−0.0771402	−	0.0191666i
$316$	−10.6537			−0.599317
$317$	6.49693			0.364904			0.182452	−	0.983215i	$-0.441597\pi$
$317$	6.49693			0.364904			0.182452	+	0.983215i	$0.441597\pi$
$318$	−14.0989			−0.790627
$319$		−	1.37751i		−	0.0771259i
$320$	−2.17009	−	0.539189i	−0.121312	−	0.0301416i
$321$	−15.7321			−0.878078
$322$		−	1.07838i		−	0.0600956i
$323$	−1.07838			−0.0600025
$324$	1.00000			0.0555556
$325$	17.8010	−	2.85043i	0.987421	−	0.158114i
$326$	−5.23513			−0.289947
$327$	12.2329			0.676479
$328$			1.41855i			0.0783264i
$329$	1.72753			0.0952416
$330$	6.68035	+	1.65983i	0.367741	+	0.0913705i
$331$			14.8143i			0.814268i	0.913368	+	0.407134i	$0.133472\pi$
$331$			14.8143i			0.814268i	−0.913368	+	0.407134i	$0.866528\pi$
$332$	−3.23513			−0.177551
$333$	−5.07838			−0.278293
$334$	−3.41855			−0.187055
$335$	16.8371	+	4.18342i	0.919909	+	0.228565i
$336$		−	0.630898i		−	0.0344183i
$337$			6.25565i			0.340767i	0.985378	+	0.170384i	$0.0545007\pi$
$337$			6.25565i			0.340767i	−0.985378	+	0.170384i	$0.945499\pi$
$338$	−3.58145	+	12.4969i	−0.194805	+	0.679743i
$339$	3.12783			0.169880
$340$	−2.00000	+	8.04945i	−0.108465	+	0.436543i
$341$	−20.5646			−1.11364
$342$		−	0.290725i		−	0.0157206i
$343$	8.58145			0.463355
$344$			5.75872i			0.310490i
$345$	−3.70928	−	0.921622i	−0.199701	−	0.0496185i
$346$			8.83710i			0.475086i
$347$		−	8.41241i		−	0.451602i	−0.974173	−	0.225801i	$-0.927500\pi$
$347$		−	8.41241i		−	0.451602i	0.974173	−	0.225801i	$-0.0724999\pi$
$348$			0.447480i			0.0239875i
$349$			23.5525i			1.26074i	0.776296	+	0.630369i	$0.217096\pi$
$349$			23.5525i			1.26074i	−0.776296	+	0.630369i	$0.782904\pi$
$350$	2.78765	+	1.47641i	0.149006	+	0.0789174i
$351$	−2.17009	−	2.87936i	−0.115831	−	0.153689i
$352$			3.07838i			0.164078i
$353$	−14.4124			−0.767095			−0.383548	−	0.923521i	$-0.625298\pi$
$353$	−14.4124			−0.767095			−0.383548	+	0.923521i	$0.625298\pi$
$354$	9.02052			0.479435
$355$	0.894960	−	3.60197i	0.0474996	−	0.191173i
$356$			12.3402i			0.654028i
$357$	−2.34017			−0.123855
$358$	−21.3835			−1.13015
$359$			31.3340i			1.65375i	0.562388	+	0.826873i	$0.309883\pi$
$359$			31.3340i			1.65375i	−0.562388	+	0.826873i	$0.690117\pi$
$360$	−2.17009	−	0.539189i	−0.114374	−	0.0284177i
$361$	18.9155			0.995552
$362$	−10.9939			−0.577824
$363$			1.52359i			0.0799678i
$364$	−1.81658	+	1.36910i	−0.0952148	+	0.0717605i
$365$	−33.2267	−	8.25565i	−1.73917	−	0.432121i
$366$			3.26180i			0.170497i
$367$		−	5.05172i		−	0.263697i	−0.991270	−	0.131849i	$-0.957909\pi$
$367$		−	5.05172i		−	0.263697i	0.991270	−	0.131849i	$-0.0420913\pi$
$368$		−	1.70928i		−	0.0891021i
$369$			1.41855i			0.0738468i
$370$	11.0205	+	2.73820i	0.572929	+	0.142352i
$371$			8.89496i			0.461803i
$372$	6.68035			0.346360
$373$			13.5174i			0.699907i	0.936767	+	0.349953i	$0.113803\pi$
$373$			13.5174i			0.699907i	−0.936767	+	0.349953i	$0.886197\pi$
$374$	11.4186			0.590439
$375$	7.46081	−	8.32684i	0.385275	−	0.429996i
$376$	2.73820			0.141212
$377$	1.28846	−	0.971071i	0.0663589	−	0.0500127i
$378$		−	0.630898i		−	0.0324499i
$379$		−	6.59970i		−	0.339004i	−0.985530	−	0.169502i	$-0.945784\pi$
$379$		−	6.59970i		−	0.339004i	0.985530	−	0.169502i	$-0.0542159\pi$
$380$	−0.156755	+	0.630898i	−0.00804139	+	0.0323644i
$381$	−20.6225			−1.05652
$382$	−13.9421			−0.713342
$383$	−25.9421			−1.32558			−0.662791	−	0.748805i	$-0.730628\pi$
$383$	−25.9421			−1.32558			−0.662791	+	0.748805i	$0.730628\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	1.04718	−	4.21461i	0.0533693	−	0.214797i
$386$	3.79380			0.193099
$387$			5.75872i			0.292732i
$388$	−8.20620			−0.416607
$389$	−6.75646			−0.342566			−0.171283	−	0.985222i	$-0.554791\pi$
$389$	−6.75646			−0.342566			−0.171283	+	0.985222i	$0.554791\pi$
$390$	3.15676	+	7.41855i	0.159849	+	0.375653i
$391$	−6.34017			−0.320636
$392$	6.60197			0.333450
$393$			6.81432i			0.343737i
$394$	−21.5174			−1.08403
$395$	23.1194	+	5.74435i	1.16326	+	0.289030i
$396$			3.07838i			0.154694i
$397$	33.1773			1.66512			0.832560	−	0.553935i	$-0.186874\pi$
$397$	33.1773			1.66512			0.832560	+	0.553935i	$0.186874\pi$
$398$	17.8576			0.895122
$399$	−0.183417			−0.00918236
$400$	4.41855	+	2.34017i	0.220928	+	0.117009i
$401$		−	10.8950i		−	0.544068i	−0.962288	−	0.272034i	$-0.912304\pi$
$401$		−	10.8950i		−	0.544068i	0.962288	−	0.272034i	$-0.0876964\pi$
$402$			7.75872i			0.386970i
$403$	−14.4969	−	19.2351i	−0.722143	−	0.958170i
$404$	3.86603			0.192342
$405$	−2.17009	−	0.539189i	−0.107832	−	0.0267925i
$406$	0.282314			0.0140110
$407$		−	15.6332i		−	0.774907i
$408$	−3.70928			−0.183636
$409$			5.78992i			0.286293i	0.989701	+	0.143147i	$0.0457220\pi$
$409$			5.78992i			0.286293i	−0.989701	+	0.143147i	$0.954278\pi$
$410$	0.764867	−	3.07838i	0.0377741	−	0.152030i
$411$		−	0.424694i		−	0.0209486i
$412$			7.84324i			0.386409i
$413$		−	5.69102i		−	0.280037i
$414$		−	1.70928i		−	0.0840063i
$415$	7.02052	+	1.74435i	0.344624	+	0.0856267i
$416$	−2.87936	+	2.17009i	−0.141172	+	0.106397i
$417$		−	14.2557i		−	0.698102i
$418$	0.894960			0.0437739
$419$	−40.4885			−1.97799			−0.988997	−	0.147937i	$-0.952737\pi$
$419$	−40.4885			−1.97799			−0.988997	+	0.147937i	$0.952737\pi$
$420$	−0.340173	+	1.36910i	−0.0165987	+	0.0668054i
$421$			24.3318i			1.18586i	0.805255	+	0.592929i	$0.202028\pi$
$421$			24.3318i			1.18586i	−0.805255	+	0.592929i	$0.797972\pi$
$422$	−16.7792			−0.816801
$423$	2.73820			0.133136
$424$			14.0989i			0.684703i
$425$	8.68035	−	16.3896i	0.421059	−	0.795013i
$426$	1.65983			0.0804189
$427$	2.05786			0.0995868
$428$			15.7321i			0.760438i
$429$	8.86376	−	6.68035i	0.427947	−	0.322530i
$430$	3.10504	−	12.4969i	0.149738	−	0.602655i
$431$		−	32.8781i		−	1.58368i	−0.610726	−	0.791842i	$-0.709122\pi$
$431$		−	32.8781i		−	1.58368i	0.610726	−	0.791842i	$-0.290878\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			33.4063i			1.60540i	0.596381	+	0.802701i	$0.296605\pi$
$433$			33.4063i			1.60540i	−0.596381	+	0.802701i	$0.703395\pi$
$434$		−	4.21461i		−	0.202308i
$435$	0.241276	−	0.971071i	0.0115683	−	0.0465593i
$436$		−	12.2329i		−	0.585848i
$437$	−0.496928			−0.0237713
$438$		−	15.3112i		−	0.731600i
$439$	−30.0410			−1.43378			−0.716890	−	0.697186i	$-0.754435\pi$
$439$	−30.0410			−1.43378			−0.716890	+	0.697186i	$0.754435\pi$
$440$	1.65983	−	6.68035i	0.0791291	−	0.318473i
$441$	6.60197			0.314379
$442$	8.04945	+	10.6803i	0.382873	+	0.508012i
$443$		−	4.58145i		−	0.217671i	−0.994060	−	0.108836i	$-0.965288\pi$
$443$		−	4.58145i		−	0.217671i	0.994060	−	0.108836i	$-0.0347122\pi$
$444$			5.07838i			0.241009i
$445$	6.65368	−	26.7792i	0.315415	−	1.26946i
$446$	20.3630			0.964214
$447$	11.0205			0.521253
$448$	−0.630898			−0.0298071
$449$		−	13.8166i		−	0.652045i	−0.945362	−	0.326022i	$-0.894292\pi$
$449$		−	13.8166i		−	0.652045i	0.945362	−	0.326022i	$-0.105708\pi$
$450$	4.41855	+	2.34017i	0.208292	+	0.110317i
$451$	−4.36683			−0.205626
$452$		−	3.12783i		−	0.147121i
$453$	13.7321			0.645189
$454$	−14.8371			−0.696340
$455$	4.68035	−	1.99159i	0.219418	−	0.0933672i
$456$	−0.290725			−0.0136144
$457$	−28.2062			−1.31943			−0.659715	−	0.751516i	$-0.729323\pi$
$457$	−28.2062			−1.31943			−0.659715	+	0.751516i	$0.729323\pi$
$458$			12.6453i			0.590875i
$459$	−3.70928			−0.173134
$460$	−0.921622	+	3.70928i	−0.0429709	+	0.172946i
$461$			28.3812i			1.32184i	0.750454	+	0.660922i	$0.229835\pi$
$461$			28.3812i			1.32184i	−0.750454	+	0.660922i	$0.770165\pi$
$462$	1.94214			0.0903566
$463$	39.5669			1.83883			0.919415	−	0.393289i	$-0.128663\pi$
$463$	39.5669			1.83883			0.919415	+	0.393289i	$0.128663\pi$
$464$	0.447480			0.0207737
$465$	−14.4969	−	3.60197i	−0.672279	−	0.167037i
$466$		−	25.3835i		−	1.17587i
$467$		−	36.0989i		−	1.67046i	−0.549902	−	0.835229i	$-0.685335\pi$
$467$		−	36.0989i		−	1.67046i	0.549902	−	0.835229i	$-0.314665\pi$
$468$	−2.87936	+	2.17009i	−0.133099	+	0.100312i
$469$	4.89496			0.226028
$470$	−5.94214	−	1.47641i	−0.274091	−	0.0681017i
$471$	20.8371			0.960123
$472$		−	9.02052i		−	0.415203i
$473$	−17.7275			−0.815113
$474$			10.6537i			0.489340i
$475$	0.680346	−	1.28458i	0.0312164	−	0.0589406i
$476$			2.34017i			0.107262i
$477$			14.0989i			0.645544i
$478$			9.84324i			0.450220i
$479$			37.3607i			1.70705i	0.521049	+	0.853527i	$0.325541\pi$
$479$			37.3607i			1.70705i	−0.521049	+	0.853527i	$0.674459\pi$
$480$	−0.539189	+	2.17009i	−0.0246105	+	0.0990504i
$481$	14.6225	−	11.0205i	0.666728	−	0.502492i
$482$		−	15.7854i		−	0.719005i
$483$	−1.07838			−0.0490679
$484$	1.52359			0.0692541
$485$	17.8082	+	4.42469i	0.808627	+	0.200915i
$486$		−	1.00000i		−	0.0453609i
$487$	32.0950			1.45436			0.727182	−	0.686445i	$-0.240830\pi$
$487$	32.0950			1.45436			0.727182	+	0.686445i	$0.240830\pi$
$488$	3.26180			0.147655
$489$			5.23513i			0.236741i
$490$	−14.3268	−	3.55971i	−0.647221	−	0.160811i
$491$	20.5874			0.929097			0.464549	−	0.885548i	$-0.346217\pi$
$491$	20.5874			0.929097			0.464549	+	0.885548i	$0.346217\pi$
$492$	1.41855			0.0639532
$493$		−	1.65983i		−	0.0747548i
$494$	0.630898	+	0.837101i	0.0283854	+	0.0376630i
$495$	1.65983	−	6.68035i	0.0746037	−	0.300259i
$496$		−	6.68035i		−	0.299956i
$497$		−	1.04718i		−	0.0469725i
$498$			3.23513i			0.144970i
$499$		−	31.7093i		−	1.41950i	−0.704453	−	0.709751i	$-0.748807\pi$
$499$		−	31.7093i		−	1.41950i	0.704453	−	0.709751i	$-0.251193\pi$
$500$	−8.32684	−	7.46081i	−0.372388	−	0.333658i
$501$			3.41855i			0.152730i
$502$	−10.1340			−0.452301
$503$		−	1.70928i		−	0.0762128i	−0.999274	−	0.0381064i	$-0.987867\pi$
$503$		−	1.70928i		−	0.0762128i	0.999274	−	0.0381064i	$-0.0121326\pi$
$504$	−0.630898			−0.0281024
$505$	−8.38962	−	2.08452i	−0.373333	−	0.0927600i
$506$	5.26180			0.233915
$507$	12.4969	+	3.58145i	0.555008	+	0.159058i
$508$			20.6225i			0.914975i
$509$		−	15.6475i		−	0.693565i	−0.937946	−	0.346783i	$-0.887274\pi$
$509$		−	15.6475i		−	0.693565i	0.937946	−	0.346783i	$-0.112726\pi$
$510$	8.04945	+	2.00000i	0.356436	+	0.0885615i
$511$	−9.65983			−0.427326
$512$	−1.00000			−0.0441942
$513$	−0.290725			−0.0128358
$514$		−	28.7565i		−	1.26839i
$515$	4.22899	−	17.0205i	0.186352	−	0.750014i
$516$	5.75872			0.253514
$517$			8.42923i			0.370717i
$518$	3.20394			0.140773
$519$	8.83710			0.387906
$520$	7.41855	−	3.15676i	0.325325	−	0.138433i
$521$	−3.67420			−0.160970			−0.0804849	−	0.996756i	$-0.525647\pi$
$521$	−3.67420			−0.160970			−0.0804849	+	0.996756i	$0.525647\pi$
$522$	0.447480			0.0195857
$523$			20.6803i			0.904288i	0.891945	+	0.452144i	$0.149341\pi$
$523$			20.6803i			0.904288i	−0.891945	+	0.452144i	$0.850659\pi$
$524$	6.81432			0.297685
$525$	1.47641	−	2.78765i	0.0644358	−	0.121663i
$526$		−	7.28458i		−	0.317623i
$527$	−24.7792			−1.07940
$528$	3.07838			0.133969
$529$	20.0784			0.872973
$530$	7.60197	−	30.5958i	0.330208	−	1.32900i
$531$		−	9.02052i		−	0.391457i
$532$			0.183417i			0.00795216i
$533$	−3.07838	−	4.08452i	−0.133339	−	0.176920i
$534$	12.3402			0.534012
$535$	8.48255	−	34.1399i	0.366733	−	1.47600i
$536$	7.75872			0.335126
$537$			21.3835i			0.922765i
$538$	−21.9071			−0.944481
$539$			20.3234i			0.875389i
$540$	−0.539189	+	2.17009i	−0.0232030	+	0.0933857i
$541$		−	8.13397i		−	0.349707i	−0.984594	−	0.174853i	$-0.944055\pi$
$541$		−	8.13397i		−	0.349707i	0.984594	−	0.174853i	$-0.0559451\pi$
$542$			9.10504i			0.391095i
$543$			10.9939i			0.471792i
$544$			3.70928i			0.159034i
$545$	−6.59583	+	26.5464i	−0.282534	+	1.13712i
$546$	1.36910	+	1.81658i	0.0585922	+	0.0777426i
$547$		−	10.8371i		−	0.463361i	−0.972792	−	0.231680i	$-0.925578\pi$
$547$		−	10.8371i		−	0.463361i	0.972792	−	0.231680i	$-0.0744224\pi$
$548$	−0.424694			−0.0181420
$549$	3.26180			0.139210
$550$	−7.20394	+	13.6020i	−0.307177	+	0.579990i
$551$		−	0.130094i		−	0.00554217i
$552$	−1.70928			−0.0727516
$553$	6.72138			0.285822
$554$			25.2039i			1.07081i
$555$	2.73820	−	11.0205i	0.116230	−	0.467795i
$556$	−14.2557			−0.604574
$557$	−1.18956			−0.0504033			−0.0252016	−	0.999682i	$-0.508023\pi$
$557$	−1.18956			−0.0504033			−0.0252016	+	0.999682i	$0.508023\pi$
$558$		−	6.68035i		−	0.282802i
$559$	−12.4969	−	16.5814i	−0.528564	−	0.701321i
$560$	1.36910	+	0.340173i	0.0578551	+	0.0143749i
$561$		−	11.4186i		−	0.482092i
$562$			15.5441i			0.655689i
$563$			7.47187i			0.314902i	0.987527	+	0.157451i	$0.0503276\pi$
$563$			7.47187i			0.314902i	−0.987527	+	0.157451i	$0.949672\pi$
$564$		−	2.73820i		−	0.115299i
$565$	−1.68649	+	6.78765i	−0.0709511	+	0.285559i
$566$		−	13.2762i		−	0.558039i
$567$	−0.630898			−0.0264952
$568$		−	1.65983i		−	0.0696448i
$569$	31.0472			1.30157			0.650783	−	0.759264i	$-0.274441\pi$
$569$	31.0472			1.30157			0.650783	+	0.759264i	$0.274441\pi$
$570$	0.630898	+	0.156755i	0.0264254	+	0.00656577i
$571$	6.73820			0.281985			0.140993	−	0.990011i	$-0.454971\pi$
$571$	6.73820			0.281985			0.140993	+	0.990011i	$0.454971\pi$
$572$	−6.68035	−	8.86376i	−0.279319	−	0.370613i
$573$			13.9421i			0.582441i
$574$		−	0.894960i		−	0.0373549i
$575$	4.00000	−	7.55252i	0.166812	−	0.314962i
$576$	−1.00000			−0.0416667
$577$	−4.47414			−0.186261			−0.0931305	−	0.995654i	$-0.529687\pi$
$577$	−4.47414			−0.186261			−0.0931305	+	0.995654i	$0.529687\pi$
$578$	−3.24128			−0.134819
$579$		−	3.79380i		−	0.157665i
$580$	−0.971071	−	0.241276i	−0.0403215	−	0.0100185i
$581$	2.04104			0.0846765
$582$			8.20620i			0.340158i
$583$	−43.4017			−1.79752
$584$	−15.3112			−0.633584
$585$	7.41855	−	3.15676i	0.306719	−	0.130516i
$586$	−9.31965			−0.384991
$587$	−36.0288			−1.48707			−0.743533	−	0.668699i	$-0.766851\pi$
$587$	−36.0288			−1.48707			−0.743533	+	0.668699i	$0.766851\pi$
$588$		−	6.60197i		−	0.272261i
$589$	−1.94214			−0.0800245
$590$	−4.86376	+	19.5753i	−0.200238	+	0.805903i
$591$			21.5174i			0.885110i
$592$	5.07838			0.208720
$593$	−39.1917			−1.60941			−0.804704	−	0.593676i	$-0.797676\pi$
$593$	−39.1917			−1.60941			−0.804704	+	0.593676i	$0.797676\pi$
$594$	3.07838			0.126307
$595$	1.26180	−	5.07838i	0.0517286	−	0.208193i
$596$		−	11.0205i		−	0.451418i
$597$		−	17.8576i		−	0.730864i
$598$	3.70928	+	4.92162i	0.151684	+	0.201260i
$599$	5.10957			0.208772			0.104386	−	0.994537i	$-0.466712\pi$
$599$	5.10957			0.208772			0.104386	+	0.994537i	$0.466712\pi$
$600$	2.34017	−	4.41855i	0.0955372	−	0.180387i
$601$	19.4452			0.793187			0.396593	−	0.917994i	$-0.370192\pi$
$601$	19.4452			0.793187			0.396593	+	0.917994i	$0.370192\pi$
$602$		−	3.63317i		−	0.148077i
$603$	7.75872			0.315960
$604$		−	13.7321i		−	0.558750i
$605$	−3.30632	−	0.821503i	−0.134421	−	0.0333988i
$606$		−	3.86603i		−	0.157047i
$607$			20.6225i			0.837041i	0.908207	+	0.418520i	$0.137451\pi$
$607$			20.6225i			0.837041i	−0.908207	+	0.418520i	$0.862549\pi$
$608$			0.290725i			0.0117904i
$609$		−	0.282314i		−	0.0114399i
$610$	−7.07838	−	1.75872i	−0.286595	−	0.0712086i
$611$	−7.88428	+	5.94214i	−0.318964	+	0.240393i
$612$			3.70928i			0.149939i
$613$	4.71154			0.190297			0.0951487	−	0.995463i	$-0.469667\pi$
$613$	4.71154			0.190297			0.0951487	+	0.995463i	$0.469667\pi$
$614$	−7.54411			−0.304455
$615$	−3.07838	−	0.764867i	−0.124132	−	0.0308424i
$616$		−	1.94214i		−	0.0782511i
$617$	−13.6332			−0.548851			−0.274425	−	0.961608i	$-0.588488\pi$
$617$	−13.6332			−0.548851			−0.274425	+	0.961608i	$0.588488\pi$
$618$	7.84324			0.315502
$619$			37.4368i			1.50471i	0.658757	+	0.752356i	$0.271083\pi$
$619$			37.4368i			1.50471i	−0.658757	+	0.752356i	$0.728917\pi$
$620$	−3.60197	+	14.4969i	−0.144659	+	0.582211i
$621$	−1.70928			−0.0685909
$622$	29.9421			1.20057
$623$		−	7.78539i		−	0.311915i
$624$	2.17009	+	2.87936i	0.0868730	+	0.115267i
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$			6.52359i			0.260735i
$627$		−	0.894960i		−	0.0357413i
$628$		−	20.8371i		−	0.831491i
$629$		−	18.8371i		−	0.751084i
$630$	1.36910	+	0.340173i	0.0545463	+	0.0135528i
$631$			8.05786i			0.320778i	0.987054	+	0.160389i	$0.0512749\pi$
$631$			8.05786i			0.320778i	−0.987054	+	0.160389i	$0.948725\pi$
$632$	10.6537			0.423781
$633$			16.7792i			0.666915i
$634$	−6.49693			−0.258026
$635$	11.1194	−	44.7526i	0.441261	−	1.77595i
$636$	14.0989			0.559058
$637$	−19.0095	+	14.3268i	−0.753182	+	0.567650i
$638$			1.37751i			0.0545363i
$639$		−	1.65983i		−	0.0656617i
$640$	2.17009	+	0.539189i	0.0857802	+	0.0213133i
$641$	46.2967			1.82861			0.914305	−	0.405027i	$-0.132738\pi$
$641$	46.2967			1.82861			0.914305	+	0.405027i	$0.132738\pi$
$642$	15.7321			0.620895
$643$	21.4329			0.845232			0.422616	−	0.906309i	$-0.361112\pi$
$643$	21.4329			0.845232			0.422616	+	0.906309i	$0.361112\pi$
$644$			1.07838i			0.0424940i
$645$	−12.4969	−	3.10504i	−0.492066	−	0.122261i
$646$	1.07838			0.0424282
$647$		−	26.5874i		−	1.04526i	−0.852560	−	0.522630i	$-0.824951\pi$
$647$		−	26.5874i		−	1.04526i	0.852560	−	0.522630i	$-0.175049\pi$
$648$	−1.00000			−0.0392837
$649$	27.7686			1.09001
$650$	−17.8010	+	2.85043i	−0.698212	+	0.111803i
$651$	−4.21461			−0.165184
$652$	5.23513			0.205024
$653$			1.53427i			0.0600406i	0.999549	+	0.0300203i	$0.00955719\pi$
$653$			1.53427i			0.0600406i	−0.999549	+	0.0300203i	$0.990443\pi$
$654$	−12.2329			−0.478343
$655$	−14.7877	−	3.67420i	−0.577801	−	0.143563i
$656$		−	1.41855i		−	0.0553851i
$657$	−15.3112			−0.597349
$658$	−1.72753			−0.0673460
$659$	−14.3318			−0.558286			−0.279143	−	0.960250i	$-0.590050\pi$
$659$	−14.3318			−0.558286			−0.279143	+	0.960250i	$0.590050\pi$
$660$	−6.68035	−	1.65983i	−0.260032	−	0.0646087i
$661$			38.1049i			1.48211i	0.671446	+	0.741054i	$0.265674\pi$
$661$			38.1049i			1.48211i	−0.671446	+	0.741054i	$0.734326\pi$
$662$		−	14.8143i		−	0.575775i
$663$	10.6803	−	8.04945i	0.414790	−	0.312615i
$664$	3.23513			0.125548
$665$	0.0988967	−	0.398032i	0.00383505	−	0.0154350i
$666$	5.07838			0.196783
$667$		−	0.764867i		−	0.0296158i
$668$	3.41855			0.132268
$669$		−	20.3630i		−	0.787277i
$670$	−16.8371	−	4.18342i	−0.650474	−	0.161620i
$671$			10.0410i			0.387630i
$672$			0.630898i			0.0243374i
$673$		−	28.4657i		−	1.09727i	−0.836061	−	0.548637i	$-0.815147\pi$
$673$		−	28.4657i		−	1.09727i	0.836061	−	0.548637i	$-0.184853\pi$
$674$		−	6.25565i		−	0.240959i
$675$	2.34017	−	4.41855i	0.0900733	−	0.170070i
$676$	3.58145	−	12.4969i	0.137748	−	0.480651i
$677$		−	0.424694i		−	0.0163223i	−0.999967	−	0.00816115i	$-0.997402\pi$
$677$		−	0.424694i		−	0.0163223i	0.999967	−	0.00816115i	$-0.00259780\pi$
$678$	−3.12783			−0.120123
$679$	5.17727			0.198686
$680$	2.00000	−	8.04945i	0.0766965	−	0.308682i
$681$			14.8371i			0.568559i
$682$	20.5646			0.787460
$683$	−4.28231			−0.163858			−0.0819291	−	0.996638i	$-0.526108\pi$
$683$	−4.28231			−0.163858			−0.0819291	+	0.996638i	$0.526108\pi$
$684$			0.290725i			0.0111161i
$685$	0.921622	+	0.228990i	0.0352134	+	0.00874926i
$686$	−8.58145			−0.327641
$687$	12.6453			0.482447
$688$		−	5.75872i		−	0.219549i
$689$	−30.5958	−	40.5958i	−1.16561	−	1.54658i
$690$	3.70928	+	0.921622i	0.141210	+	0.0350856i
$691$		−	38.5464i		−	1.46637i	−0.680027	−	0.733187i	$-0.738032\pi$
$691$		−	38.5464i		−	1.46637i	0.680027	−	0.733187i	$-0.261968\pi$
$692$		−	8.83710i		−	0.335936i
$693$		−	1.94214i		−	0.0737758i
$694$			8.41241i			0.319331i
$695$	30.9360	+	7.68649i	1.17347	+	0.291565i
$696$		−	0.447480i		−	0.0169617i
$697$	−5.26180			−0.199305
$698$		−	23.5525i		−	0.891476i
$699$	−25.3835			−0.960091
$700$	−2.78765	−	1.47641i	−0.105363	−	0.0558030i
$701$	−47.4824			−1.79338			−0.896692	−	0.442654i	$-0.854037\pi$
$701$	−47.4824			−1.79338			−0.896692	+	0.442654i	$0.854037\pi$
$702$	2.17009	+	2.87936i	0.0819046	+	0.108675i
$703$		−	1.47641i		−	0.0556838i
$704$		−	3.07838i		−	0.116021i
$705$	−1.47641	+	5.94214i	−0.0556048	+	0.223794i
$706$	14.4124			0.542418
$707$	−2.43907			−0.0917307
$708$	−9.02052			−0.339012
$709$		−	35.4824i		−	1.33257i	−0.745698	−	0.666284i	$-0.767884\pi$
$709$		−	35.4824i		−	1.33257i	0.745698	−	0.666284i	$-0.232116\pi$
$710$	−0.894960	+	3.60197i	−0.0335873	+	0.135179i
$711$	10.6537			0.399544
$712$		−	12.3402i		−	0.462468i
$713$	−11.4186			−0.427628
$714$	2.34017			0.0875788
$715$	9.71769	+	22.8371i	0.363421	+	0.854059i
$716$	21.3835			0.799138
$717$	9.84324			0.367603
$718$		−	31.3340i		−	1.16938i
$719$	32.8781			1.22615			0.613074	−	0.790026i	$-0.289933\pi$
$719$	32.8781			1.22615			0.613074	+	0.790026i	$0.289933\pi$
$720$	2.17009	+	0.539189i	0.0808743	+	0.0200944i
$721$		−	4.94828i		−	0.184284i
$722$	−18.9155			−0.703961
$723$	−15.7854			−0.587065
$724$	10.9939			0.408583
$725$	1.97721	+	1.04718i	0.0734319	+	0.0388913i
$726$		−	1.52359i		−	0.0565457i
$727$		−	26.9939i		−	1.00115i	−0.865694	−	0.500573i	$-0.833123\pi$
$727$		−	26.9939i		−	1.00115i	0.865694	−	0.500573i	$-0.166877\pi$
$728$	1.81658	−	1.36910i	0.0673270	−	0.0507423i
$729$	−1.00000			−0.0370370
$730$	33.2267	+	8.25565i	1.22978	+	0.305555i
$731$	−21.3607			−0.790054
$732$		−	3.26180i		−	0.120559i
$733$	23.3340			0.861862			0.430931	−	0.902385i	$-0.358185\pi$
$733$	23.3340			0.861862			0.430931	+	0.902385i	$0.358185\pi$
$734$			5.05172i			0.186462i
$735$	−3.55971	+	14.3268i	−0.131302	+	0.528454i
$736$			1.70928i			0.0630047i
$737$			23.8843i			0.879789i
$738$		−	1.41855i		−	0.0522176i
$739$			45.3835i			1.66946i	0.550661	+	0.834729i	$0.314376\pi$
$739$			45.3835i			1.66946i	−0.550661	+	0.834729i	$0.685624\pi$
$740$	−11.0205	−	2.73820i	−0.405122	−	0.100658i
$741$	0.837101	−	0.630898i	0.0307517	−	0.0231766i
$742$		−	8.89496i		−	0.326544i
$743$	10.8904			0.399531			0.199765	−	0.979844i	$-0.435982\pi$
$743$	10.8904			0.399531			0.199765	+	0.979844i	$0.435982\pi$
$744$	−6.68035			−0.244913
$745$	−5.94214	+	23.9155i	−0.217703	+	0.876195i
$746$		−	13.5174i		−	0.494909i
$747$	3.23513			0.118367
$748$	−11.4186			−0.417504
$749$		−	9.92532i		−	0.362663i
$750$	−7.46081	+	8.32684i	−0.272430	+	0.304053i
$751$	−33.1917			−1.21118			−0.605590	−	0.795777i	$-0.707063\pi$
$751$	−33.1917			−1.21118			−0.605590	+	0.795777i	$0.707063\pi$
$752$	−2.73820			−0.0998521
$753$			10.1340i			0.369302i
$754$	−1.28846	+	0.971071i	−0.0469228	+	0.0353643i
$755$	−7.40417	+	29.7998i	−0.269466	+	1.08452i
$756$			0.630898i			0.0229455i
$757$			7.54411i			0.274195i	0.990558	+	0.137098i	$0.0437774\pi$
$757$			7.54411i			0.274195i	−0.990558	+	0.137098i	$0.956223\pi$
$758$			6.59970i			0.239712i
$759$		−	5.26180i		−	0.190991i
$760$	0.156755	−	0.630898i	0.00568612	−	0.0228851i
$761$			35.8264i			1.29871i	0.760487	+	0.649353i	$0.224960\pi$
$761$			35.8264i			1.29871i	−0.760487	+	0.649353i	$0.775040\pi$
$762$	20.6225			0.747074
$763$			7.71769i			0.279399i
$764$	13.9421			0.504409
$765$	2.00000	−	8.04945i	0.0723102	−	0.291028i
$766$	25.9421			0.937328
$767$	19.5753	+	25.9733i	0.706823	+	0.937843i
$768$			1.00000i			0.0360844i
$769$			36.3135i			1.30950i	0.755846	+	0.654749i	$0.227226\pi$
$769$			36.3135i			1.30950i	−0.755846	+	0.654749i	$0.772774\pi$
$770$	−1.04718	+	4.21461i	−0.0377378	+	0.151884i
$771$	−28.7565			−1.03564
$772$	−3.79380			−0.136542
$773$	−2.99386			−0.107682			−0.0538408	−	0.998550i	$-0.517146\pi$
$773$	−2.99386			−0.107682			−0.0538408	+	0.998550i	$0.517146\pi$
$774$		−	5.75872i		−	0.206993i
$775$	15.6332	−	29.5174i	0.561560	−	1.06030i
$776$	8.20620			0.294586
$777$		−	3.20394i		−	0.114941i
$778$	6.75646			0.242231
$779$	−0.412408			−0.0147760
$780$	−3.15676	−	7.41855i	−0.113030	−	0.265627i
$781$	5.10957			0.182835
$782$	6.34017			0.226724
$783$		−	0.447480i		−	0.0159916i
$784$	−6.60197			−0.235785
$785$	−11.2351	+	45.2183i	−0.400999	+	1.61391i
$786$		−	6.81432i		−	0.243059i
$787$	38.9627			1.38887			0.694434	−	0.719556i	$-0.255655\pi$
$787$	38.9627			1.38887			0.694434	+	0.719556i	$0.255655\pi$
$788$	21.5174			0.766527
$789$	−7.28458			−0.259338
$790$	−23.1194	−	5.74435i	−0.822552	−	0.204375i
$791$			1.97334i			0.0701638i
$792$		−	3.07838i		−	0.109385i
$793$	−9.39189	+	7.07838i	−0.333516	+	0.251361i
$794$	−33.1773			−1.17742
$795$	−30.5958	−	7.60197i	−1.08512	−	0.269614i
$796$	−17.8576			−0.632947
$797$		−	14.9405i		−	0.529221i	−0.964355	−	0.264610i	$-0.914757\pi$
$797$		−	14.9405i		−	0.529221i	0.964355	−	0.264610i	$-0.0852434\pi$
$798$	0.183417			0.00649291
$799$			10.1568i			0.359320i
$800$	−4.41855	−	2.34017i	−0.156219	−	0.0827376i
$801$		−	12.3402i		−	0.436019i
$802$			10.8950i			0.384714i
$803$		−	47.1338i		−	1.66332i
$804$		−	7.75872i		−	0.273629i
$805$	0.581449	−	2.34017i	0.0204934	−	0.0824803i
$806$	14.4969	+	19.2351i	0.510633	+	0.677529i
$807$			21.9071i			0.771165i
$808$	−3.86603			−0.136006
$809$	−8.05786			−0.283299			−0.141650	−	0.989917i	$-0.545241\pi$
$809$	−8.05786			−0.283299			−0.141650	+	0.989917i	$0.545241\pi$
$810$	2.17009	+	0.539189i	0.0762491	+	0.0189452i
$811$			22.7610i			0.799246i	0.916679	+	0.399623i	$0.130859\pi$
$811$			22.7610i			0.799246i	−0.916679	+	0.399623i	$0.869141\pi$
$812$	−0.282314			−0.00990728
$813$	9.10504			0.319328
$814$			15.6332i			0.547942i
$815$	−11.3607	−	2.82273i	−0.397948	−	0.0988758i
$816$	3.70928			0.129851
$817$	−1.67420			−0.0585729
$818$		−	5.78992i		−	0.202440i
$819$	1.81658	−	1.36910i	0.0634765	−	0.0478403i
$820$	−0.764867	+	3.07838i	−0.0267103	+	0.107502i
$821$			36.8925i			1.28756i	0.765212	+	0.643779i	$0.222634\pi$
$821$			36.8925i			1.28756i	−0.765212	+	0.643779i	$0.777366\pi$
$822$			0.424694i			0.0148129i
$823$			14.0000i			0.488009i	0.969774	+	0.244005i	$0.0784612\pi$
$823$			14.0000i			0.488009i	−0.969774	+	0.244005i	$0.921539\pi$
$824$		−	7.84324i		−	0.273232i
$825$	13.6020	+	7.20394i	0.473560	+	0.250809i
$826$			5.69102i			0.198016i
$827$	−23.4329			−0.814843			−0.407421	−	0.913240i	$-0.633572\pi$
$827$	−23.4329			−0.814843			−0.407421	+	0.913240i	$0.633572\pi$
$828$			1.70928i			0.0594014i
$829$	24.4079			0.847720			0.423860	−	0.905728i	$-0.360675\pi$
$829$	24.4079			0.847720			0.423860	+	0.905728i	$0.360675\pi$
$830$	−7.02052	−	1.74435i	−0.243686	−	0.0605472i
$831$	25.2039			0.874315
$832$	2.87936	−	2.17009i	0.0998239	−	0.0752342i
$833$			24.4885i			0.848477i
$834$			14.2557i			0.493633i
$835$	−7.41855	−	1.84324i	−0.256730	−	0.0637881i
$836$	−0.894960			−0.0309528
$837$	−6.68035			−0.230907
$838$	40.4885			1.39865
$839$		−	7.00614i		−	0.241879i	−0.992660	−	0.120939i	$-0.961409\pi$
$839$		−	7.00614i		−	0.241879i	0.992660	−	0.120939i	$-0.0385907\pi$
$840$	0.340173	−	1.36910i	0.0117371	−	0.0472385i
$841$	−28.7998			−0.993095
$842$		−	24.3318i		−	0.838528i
$843$	15.5441			0.535368
$844$	16.7792			0.577565
$845$	−14.5103	+	25.1883i	−0.499168	+	0.866505i
$846$	−2.73820			−0.0941414
$847$	−0.961230			−0.0330282
$848$		−	14.0989i		−	0.484158i
$849$	−13.2762			−0.455637
$850$	−8.68035	+	16.3896i	−0.297733	+	0.562159i
$851$		−	8.68035i		−	0.297558i
$852$	−1.65983			−0.0568647
$853$	16.9171			0.579230			0.289615	−	0.957143i	$-0.406473\pi$
$853$	16.9171			0.579230			0.289615	+	0.957143i	$0.406473\pi$
$854$	−2.05786			−0.0704185
$855$	0.156755	−	0.630898i	0.00536092	−	0.0215762i
$856$		−	15.7321i		−	0.537711i
$857$			12.3363i			0.421400i	0.977551	+	0.210700i	$0.0675743\pi$
$857$			12.3363i			0.421400i	−0.977551	+	0.210700i	$0.932426\pi$
$858$	−8.86376	+	6.68035i	−0.302604	+	0.228063i
$859$	21.4596			0.732192			0.366096	−	0.930577i	$-0.380694\pi$
$859$	21.4596			0.732192			0.366096	+	0.930577i	$0.380694\pi$
$860$	−3.10504	+	12.4969i	−0.105881	+	0.426142i
$861$	−0.894960			−0.0305002
$862$			32.8781i			1.11983i
$863$	27.9832			0.952558			0.476279	−	0.879294i	$-0.341985\pi$
$863$	27.9832			0.952558			0.476279	+	0.879294i	$0.341985\pi$
$864$			1.00000i			0.0340207i
$865$	−4.76487	+	19.1773i	−0.162010	+	0.652047i
$866$		−	33.4063i		−	1.13519i
$867$			3.24128i			0.110080i
$868$			4.21461i			0.143053i
$869$			32.7961i			1.11253i
$870$	−0.241276	+	0.971071i	−0.00818003	+	0.0329224i
$871$	−22.3402	+	16.8371i	−0.756968	+	0.570503i
$872$			12.2329i			0.414257i
$873$	8.20620			0.277738
$874$	0.496928			0.0168089
$875$	5.25338	+	4.70701i	0.177597	+	0.159126i
$876$			15.3112i			0.517319i
$877$	−39.2183			−1.32431			−0.662154	−	0.749368i	$-0.730358\pi$
$877$	−39.2183			−1.32431			−0.662154	+	0.749368i	$0.730358\pi$
$878$	30.0410			1.01384
$879$			9.31965i			0.314344i
$880$	−1.65983	+	6.68035i	−0.0559528	+	0.225194i
$881$	−36.8827			−1.24261			−0.621304	−	0.783569i	$-0.713397\pi$
$881$	−36.8827			−1.24261			−0.621304	+	0.783569i	$0.713397\pi$
$882$	−6.60197			−0.222300
$883$		−	24.9939i		−	0.841110i	−0.907267	−	0.420555i	$-0.861835\pi$
$883$		−	24.9939i		−	0.841110i	0.907267	−	0.420555i	$-0.138165\pi$
$884$	−8.04945	−	10.6803i	−0.270732	−	0.359219i
$885$	19.5753	+	4.86376i	0.658017	+	0.163494i
$886$			4.58145i			0.153917i
$887$		−	11.3547i		−	0.381254i	−0.981663	−	0.190627i	$-0.938948\pi$
$887$		−	11.3547i		−	0.381254i	0.981663	−	0.190627i	$-0.0610522\pi$
$888$		−	5.07838i		−	0.170419i
$889$		−	13.0107i		−	0.436364i
$890$	−6.65368	+	26.7792i	−0.223032	+	0.897642i
$891$		−	3.07838i		−	0.103130i
$892$	−20.3630			−0.681802
$893$			0.796064i			0.0266393i
$894$	−11.0205			−0.368581
$895$	−46.4040	−	11.5297i	−1.55111	−	0.385396i
$896$	0.630898			0.0210768
$897$	4.92162	−	3.70928i	0.164328	−	0.123849i
$898$			13.8166i			0.461065i
$899$		−	2.98932i		−	0.0996995i
$900$	−4.41855	−	2.34017i	−0.147285	−	0.0780058i
$901$	−52.2967			−1.74226
$902$	4.36683			0.145400
$903$	−3.63317			−0.120904
$904$			3.12783i			0.104030i
$905$	−23.8576	−	5.92777i	−0.793054	−	0.197046i
$906$	−13.7321			−0.456217
$907$		−	9.81205i		−	0.325804i	−0.986642	−	0.162902i	$-0.947915\pi$
$907$		−	9.81205i		−	0.325804i	0.986642	−	0.162902i	$-0.0520854\pi$
$908$	14.8371			0.492387
$909$	−3.86603			−0.128228
$910$	−4.68035	+	1.99159i	−0.155152	+	0.0660205i
$911$	33.3074			1.10352			0.551761	−	0.834002i	$-0.313956\pi$
$911$	33.3074			1.10352			0.551761	+	0.834002i	$0.313956\pi$
$912$	0.290725			0.00962685
$913$			9.95896i			0.329594i
$914$	28.2062			0.932978
$915$	−1.75872	+	7.07838i	−0.0581416	+	0.234004i
$916$		−	12.6453i		−	0.417812i
$917$	−4.29914			−0.141970
$918$	3.70928			0.122424
$919$	−20.4826			−0.675657			−0.337829	−	0.941208i	$-0.609692\pi$
$919$	−20.4826			−0.675657			−0.337829	+	0.941208i	$0.609692\pi$
$920$	0.921622	−	3.70928i	0.0303850	−	0.122291i
$921$			7.54411i			0.248587i
$922$		−	28.3812i		−	0.934685i
$923$	3.60197	+	4.77924i	0.118560	+	0.157311i
$924$	−1.94214			−0.0638918
$925$	22.4391	+	11.8843i	0.737792	+	0.390753i
$926$	−39.5669			−1.30025
$927$		−	7.84324i		−	0.257606i
$928$	−0.447480			−0.0146893
$929$		−	35.6886i		−	1.17090i	−0.810707	−	0.585452i	$-0.800917\pi$
$929$		−	35.6886i		−	1.17090i	0.810707	−	0.585452i	$-0.199083\pi$
$930$	14.4969	+	3.60197i	0.475373	+	0.118113i
$931$			1.91935i			0.0629043i
$932$			25.3835i			0.831463i
$933$		−	29.9421i		−	0.980262i
$934$			36.0989i			1.18119i
$935$	24.7792	+	6.15676i	0.810368	+	0.201347i
$936$	2.87936	−	2.17009i	0.0941149	−	0.0709315i
$937$			35.2495i			1.15155i	0.817608	+	0.575776i	$0.195300\pi$
$937$			35.2495i			1.15155i	−0.817608	+	0.575776i	$0.804700\pi$
$938$	−4.89496			−0.159826
$939$	6.52359			0.212889
$940$	5.94214	+	1.47641i	0.193811	+	0.0481552i
$941$			37.2228i			1.21343i	0.794919	+	0.606715i	$0.207513\pi$
$941$			37.2228i			1.21343i	−0.794919	+	0.606715i	$0.792487\pi$
$942$	−20.8371			−0.678909
$943$	−2.42469			−0.0789589
$944$			9.02052i			0.293593i
$945$	0.340173	−	1.36910i	0.0110658	−	0.0445369i
$946$	17.7275			0.576372
$947$	2.24128			0.0728317			0.0364158	−	0.999337i	$-0.488406\pi$
$947$	2.24128			0.0728317			0.0364158	+	0.999337i	$0.488406\pi$
$948$		−	10.6537i		−	0.346016i
$949$	44.0866	−	33.2267i	1.43111	−	1.07859i
$950$	−0.680346	+	1.28458i	−0.0220733	+	0.0416773i
$951$			6.49693i			0.210677i
$952$		−	2.34017i		−	0.0758454i
$953$		−	11.6391i		−	0.377028i	−0.982070	−	0.188514i	$-0.939633\pi$
$953$		−	11.6391i		−	0.377028i	0.982070	−	0.188514i	$-0.0603672\pi$
$954$		−	14.0989i		−	0.456469i
$955$	−30.2557	−	7.51745i	−0.979050	−	0.243259i
$956$		−	9.84324i		−	0.318353i
$957$	1.37751			0.0445287
$958$		−	37.3607i		−	1.20707i
$959$	0.267938			0.00865218
$960$	0.539189	−	2.17009i	0.0174022	−	0.0700392i
$961$	−13.6270			−0.439581
$962$	−14.6225	+	11.0205i	−0.471448	+	0.355316i
$963$		−	15.7321i		−	0.506959i
$964$			15.7854i			0.508413i
$965$	8.23287	+	2.04557i	0.265025	+	0.0658493i
$966$	1.07838			0.0346962
$967$	10.0449			0.323023			0.161511	−	0.986871i	$-0.448363\pi$
$967$	10.0449			0.323023			0.161511	+	0.986871i	$0.448363\pi$
$968$	−1.52359			−0.0489701
$969$		−	1.07838i		−	0.0346425i
$970$	−17.8082	−	4.42469i	−0.571786	−	0.142068i
$971$	−28.0060			−0.898754			−0.449377	−	0.893342i	$-0.648354\pi$
$971$	−28.0060			−0.898754			−0.449377	+	0.893342i	$0.648354\pi$
$972$			1.00000i			0.0320750i
$973$	8.99386			0.288330
$974$	−32.0950			−1.02839
$975$	2.85043	+	17.8010i	0.0912869	+	0.570088i
$976$	−3.26180			−0.104408
$977$	29.4641			0.942641			0.471320	−	0.881962i	$-0.343778\pi$
$977$	29.4641			0.942641			0.471320	+	0.881962i	$0.343778\pi$
$978$		−	5.23513i		−	0.167401i
$979$	37.9877			1.21409
$980$	14.3268	+	3.55971i	0.457654	+	0.113711i
$981$			12.2329i			0.390565i
$982$	−20.5874			−0.656971
$983$	15.0349			0.479539			0.239769	−	0.970830i	$-0.422928\pi$
$983$	15.0349			0.479539			0.239769	+	0.970830i	$0.422928\pi$
$984$	−1.41855			−0.0452217
$985$	−46.6947	−	11.6020i	−1.48782	−	0.369669i
$986$			1.65983i			0.0528597i
$987$			1.72753i			0.0549878i
$988$	−0.630898	−	0.837101i	−0.0200715	−	0.0266317i
$989$	−9.84324			−0.312997
$990$	−1.65983	+	6.68035i	−0.0527528	+	0.212315i
$991$	21.3463			0.678088			0.339044	−	0.940771i	$-0.389896\pi$
$991$	21.3463			0.678088			0.339044	+	0.940771i	$0.389896\pi$
$992$			6.68035i			0.212101i
$993$	−14.8143			−0.470118
$994$			1.04718i			0.0332146i
$995$	38.7526	+	9.62863i	1.22854	+	0.305248i
$996$		−	3.23513i		−	0.102509i
$997$		−	3.10957i		−	0.0984812i	−0.998787	−	0.0492406i	$-0.984320\pi$
$997$		−	3.10957i		−	0.0984812i	0.998787	−	0.0492406i	$-0.0156801\pi$
$998$			31.7093i			1.00374i
$999$		−	5.07838i		−	0.160673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.f.a.259.4	yes	6
3.2	odd	2		1170.2.f.d.649.6		6
4.3	odd	2		3120.2.r.g.2209.1		6
5.2	odd	4		1950.2.b.m.1351.2		6
5.3	odd	4		1950.2.b.l.1351.5		6
5.4	even	2		390.2.f.b.259.3	yes	6
13.12	even	2		390.2.f.b.259.6	yes	6
15.14	odd	2		1170.2.f.c.649.2		6
20.19	odd	2		3120.2.r.h.2209.6		6
39.38	odd	2		1170.2.f.c.649.1		6
52.51	odd	2		3120.2.r.h.2209.3		6
65.12	odd	4		1950.2.b.m.1351.5		6
65.38	odd	4		1950.2.b.l.1351.2		6
65.64	even	2	inner	390.2.f.a.259.1	✓	6
195.194	odd	2		1170.2.f.d.649.5		6
260.259	odd	2		3120.2.r.g.2209.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.f.a.259.1	✓	6	65.64	even	2	inner
390.2.f.a.259.4	yes	6	1.1	even	1	trivial
390.2.f.b.259.3	yes	6	5.4	even	2
390.2.f.b.259.6	yes	6	13.12	even	2
1170.2.f.c.649.1		6	39.38	odd	2
1170.2.f.c.649.2		6	15.14	odd	2
1170.2.f.d.649.5		6	195.194	odd	2
1170.2.f.d.649.6		6	3.2	odd	2
1950.2.b.l.1351.2		6	65.38	odd	4
1950.2.b.l.1351.5		6	5.3	odd	4
1950.2.b.m.1351.2		6	5.2	odd	4
1950.2.b.m.1351.5		6	65.12	odd	4
3120.2.r.g.2209.1		6	4.3	odd	2
3120.2.r.g.2209.4		6	260.259	odd	2
3120.2.r.h.2209.3		6	52.51	odd	2
3120.2.r.h.2209.6		6	20.19	odd	2

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.17009 + 0.539189i) q^{10} -3.07838i q^{11} +1.00000i q^{12} +(2.87936 - 2.17009i) q^{13} +0.630898 q^{14} +(0.539189 - 2.17009i) q^{15} +1.00000 q^{16} -3.70928i q^{17} +1.00000 q^{18} -0.290725i q^{19} +(-2.17009 - 0.539189i) q^{20} -0.630898i q^{21} +3.07838i q^{22} -1.70928i q^{23} -1.00000i q^{24} +(4.41855 + 2.34017i) q^{25} +(-2.87936 + 2.17009i) q^{26} -1.00000i q^{27} -0.630898 q^{28} +0.447480 q^{29} +(-0.539189 + 2.17009i) q^{30} -6.68035i q^{31} -1.00000 q^{32} +3.07838 q^{33} +3.70928i q^{34} +(1.36910 + 0.340173i) q^{35} -1.00000 q^{36} +5.07838 q^{37} +0.290725i q^{38} +(2.17009 + 2.87936i) q^{39} +(2.17009 + 0.539189i) q^{40} -1.41855i q^{41} +0.630898i q^{42} -5.75872i q^{43} -3.07838i q^{44} +(2.17009 + 0.539189i) q^{45} +1.70928i q^{46} -2.73820 q^{47} +1.00000i q^{48} -6.60197 q^{49} +(-4.41855 - 2.34017i) q^{50} +3.70928 q^{51} +(2.87936 - 2.17009i) q^{52} -14.0989i q^{53} +1.00000i q^{54} +(-1.65983 + 6.68035i) q^{55} +0.630898 q^{56} +0.290725 q^{57} -0.447480 q^{58} +9.02052i q^{59} +(0.539189 - 2.17009i) q^{60} -3.26180 q^{61} +6.68035i q^{62} +0.630898 q^{63} +1.00000 q^{64} +(-7.41855 + 3.15676i) q^{65} -3.07838 q^{66} -7.75872 q^{67} -3.70928i q^{68} +1.70928 q^{69} +(-1.36910 - 0.340173i) q^{70} +1.65983i q^{71} +1.00000 q^{72} +15.3112 q^{73} -5.07838 q^{74} +(-2.34017 + 4.41855i) q^{75} -0.290725i q^{76} +1.94214i q^{77} +(-2.17009 - 2.87936i) q^{78} -10.6537 q^{79} +(-2.17009 - 0.539189i) q^{80} +1.00000 q^{81} +1.41855i q^{82} -3.23513 q^{83} -0.630898i q^{84} +(-2.00000 + 8.04945i) q^{85} +5.75872i q^{86} +0.447480i q^{87} +3.07838i q^{88} +12.3402i q^{89} +(-2.17009 - 0.539189i) q^{90} +(-1.81658 + 1.36910i) q^{91} -1.70928i q^{92} +6.68035 q^{93} +2.73820 q^{94} +(-0.156755 + 0.630898i) q^{95} -1.00000i q^{96} -8.20620 q^{97} +6.60197 q^{98} +3.07838i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35} - 6 q^{36} + 24 q^{37} + 2 q^{39} + 2 q^{40} + 2 q^{45} - 32 q^{47} - 2 q^{49} + 2 q^{50} + 8 q^{51} - 8 q^{52} - 32 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} - 4 q^{61} - 4 q^{63} + 6 q^{64} - 16 q^{65} - 12 q^{66} + 4 q^{67} - 4 q^{69} - 16 q^{70} + 6 q^{72} + 40 q^{73} - 24 q^{74} + 8 q^{75} - 2 q^{78} - 16 q^{79} - 2 q^{80} + 6 q^{81} - 12 q^{85} - 2 q^{90} - 20 q^{91} - 4 q^{93} + 32 q^{94} + 12 q^{95} + 2 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + 2 * q^10 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 6 * q^18 - 2 * q^20 - 2 * q^25 + 8 * q^26 + 4 * q^28 + 4 * q^29 - 6 * q^32 + 12 * q^33 + 16 * q^35 - 6 * q^36 + 24 * q^37 + 2 * q^39 + 2 * q^40 + 2 * q^45 - 32 * q^47 - 2 * q^49 + 2 * q^50 + 8 * q^51 - 8 * q^52 - 32 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 - 4 * q^61 - 4 * q^63 + 6 * q^64 - 16 * q^65 - 12 * q^66 + 4 * q^67 - 4 * q^69 - 16 * q^70 + 6 * q^72 + 40 * q^73 - 24 * q^74 + 8 * q^75 - 2 * q^78 - 16 * q^79 - 2 * q^80 + 6 * q^81 - 12 * q^85 - 2 * q^90 - 20 * q^91 - 4 * q^93 + 32 * q^94 + 12 * q^95 + 2 * q^98

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