LMFDB - Embedded newform 1386.2.bu.a.701.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.8
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.943712 - 1.29891i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.943712 - 1.29891i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +1.60554i q^{10} +(1.01598 - 3.15718i) q^{11} +(-1.22145 - 1.68118i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.11180 - 2.98740i) q^{17} +(-6.93138 + 2.25214i) q^{19} +(-0.943712 - 1.29891i) q^{20} +(1.03380 + 3.15139i) q^{22} +0.571166i q^{23} +(0.748515 + 2.30369i) q^{25} +(1.97634 + 0.642153i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(0.282021 - 0.867972i) q^{29} +(-5.53777 + 4.02343i) q^{31} +1.00000 q^{32} +5.08246 q^{34} +(-1.29891 + 0.943712i) q^{35} +(-0.0690715 + 0.212580i) q^{37} +(4.28383 - 5.89618i) q^{38} +(1.52696 + 0.496139i) q^{40} +(-0.429183 - 1.32089i) q^{41} +7.30788i q^{43} +(-2.68870 - 1.94188i) q^{44} +(-0.335723 - 0.462083i) q^{46} +(2.53888 - 0.824934i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-1.95964 - 1.42376i) q^{50} +(-1.97634 + 0.642153i) q^{52} +(-1.49449 - 2.05698i) q^{53} +(-3.14210 - 4.29913i) q^{55} -1.00000i q^{56} +(0.282021 + 0.867972i) q^{58} +(-2.53310 - 0.823054i) q^{59} +(-4.63195 + 6.37533i) q^{61} +(2.11524 - 6.51004i) q^{62} +(-0.809017 + 0.587785i) q^{64} -3.33639 q^{65} +1.07517 q^{67} +(-4.11180 + 2.98740i) q^{68} +(0.496139 - 1.52696i) q^{70} +(-1.60190 + 2.20483i) q^{71} +(-8.42993 - 2.73905i) q^{73} +(-0.0690715 - 0.212580i) q^{74} +7.28808i q^{76} +(-1.94188 + 2.68870i) q^{77} +(-1.22498 - 1.68603i) q^{79} +(-1.52696 + 0.496139i) q^{80} +(1.12362 + 0.816355i) q^{82} +(-2.76635 - 2.00987i) q^{83} +(-7.76070 + 2.52161i) q^{85} +(-4.29546 - 5.91220i) q^{86} +(3.31661 - 0.00936955i) q^{88} +1.76110i q^{89} +(0.642153 + 1.97634i) q^{91} +(0.543211 + 0.176500i) q^{92} +(-1.56912 + 2.15970i) q^{94} +(-3.61590 + 11.1286i) q^{95} +(5.45418 - 3.96269i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.943712	−	1.29891i	0.422041	−	0.580889i	−0.544063	−	0.839045i	$-0.683115\pi$
$5$	0.943712	−	1.29891i	0.422041	−	0.580889i	0.966103	+	0.258155i	$0.0831146\pi$
$6$		0			0
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$			1.60554i			0.507716i
$11$	1.01598	−	3.15718i	0.306329	−	0.951926i
$11$	1.01598	−	3.15718i	0.306329	−	0.951926i
$12$		0			0
$13$	−1.22145	−	1.68118i	−0.338768	−	0.466275i	0.605313	−	0.795988i	$-0.293048\pi$
$13$	−1.22145	−	1.68118i	−0.338768	−	0.466275i	−0.944081	+	0.329713i	$0.893048\pi$
$14$	0.951057	−	0.309017i	0.254181	−	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.11180	−	2.98740i	−0.997257	−	0.724550i	−0.0357590	−	0.999360i	$-0.511385\pi$
$17$	−4.11180	−	2.98740i	−0.997257	−	0.724550i	−0.961498	+	0.274811i	$0.911385\pi$
$18$		0			0
$19$	−6.93138	+	2.25214i	−1.59017	+	0.516677i	−0.964650	−	0.263534i	$-0.915112\pi$
$19$	−6.93138	+	2.25214i	−1.59017	+	0.516677i	−0.625517	+	0.780211i	$0.715112\pi$
$20$	−0.943712	−	1.29891i	−0.211020	−	0.290445i
$21$		0			0
$22$	1.03380	+	3.15139i	0.220407	+	0.671879i
$23$			0.571166i			0.119096i	0.998225	+	0.0595482i	$0.0189660\pi$
$23$			0.571166i			0.119096i	−0.998225	+	0.0595482i	$0.981034\pi$
$24$		0			0
$25$	0.748515	+	2.30369i	0.149703	+	0.460739i
$26$	1.97634	+	0.642153i	0.387593	+	0.125936i
$27$		0			0
$28$	−0.587785	+	0.809017i	−0.111081	+	0.152890i
$29$	0.282021	−	0.867972i	0.0523700	−	0.161178i	−0.921451	−	0.388495i	$-0.872995\pi$
$29$	0.282021	−	0.867972i	0.0523700	−	0.161178i	0.973821	+	0.227316i	$0.0729952\pi$
$30$		0			0
$31$	−5.53777	+	4.02343i	−0.994613	+	0.722629i	−0.960926	−	0.276804i	$-0.910725\pi$
$31$	−5.53777	+	4.02343i	−0.994613	+	0.722629i	−0.0336866	+	0.999432i	$0.510725\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.08246			0.871635
$35$	−1.29891	+	0.943712i	−0.219556	+	0.159516i
$36$		0			0
$37$	−0.0690715	+	0.212580i	−0.0113553	+	0.0349480i	−0.956574	−	0.291491i	$-0.905849\pi$
$37$	−0.0690715	+	0.212580i	−0.0113553	+	0.0349480i	0.945218	+	0.326439i	$0.105849\pi$
$38$	4.28383	−	5.89618i	0.694928	−	0.956487i
$39$		0			0
$40$	1.52696	+	0.496139i	0.241433	+	0.0784464i
$41$	−0.429183	−	1.32089i	−0.0670272	−	0.206288i	0.911933	−	0.410338i	$-0.134589\pi$
$41$	−0.429183	−	1.32089i	−0.0670272	−	0.206288i	−0.978960	+	0.204050i	$0.934589\pi$
$42$		0			0
$43$			7.30788i			1.11444i	0.830365	+	0.557221i	$0.188132\pi$
$43$			7.30788i			1.11444i	−0.830365	+	0.557221i	$0.811868\pi$
$44$	−2.68870	−	1.94188i	−0.405337	−	0.292749i
$45$		0			0
$46$	−0.335723	−	0.462083i	−0.0494997	−	0.0681304i
$47$	2.53888	−	0.824934i	0.370334	−	0.120329i	−0.117936	−	0.993021i	$-0.537628\pi$
$47$	2.53888	−	0.824934i	0.370334	−	0.120329i	0.488271	+	0.872692i	$0.337628\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−1.95964	−	1.42376i	−0.277135	−	0.201350i
$51$		0			0
$52$	−1.97634	+	0.642153i	−0.274069	+	0.0890505i
$53$	−1.49449	−	2.05698i	−0.205283	−	0.282548i	0.693945	−	0.720028i	$-0.255871\pi$
$53$	−1.49449	−	2.05698i	−0.205283	−	0.282548i	−0.899228	+	0.437480i	$0.855871\pi$
$54$		0			0
$55$	−3.14210	−	4.29913i	−0.423680	−	0.579695i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	0.282021	+	0.867972i	0.0370312	+	0.113970i
$59$	−2.53310	−	0.823054i	−0.329781	−	0.107152i	0.139446	−	0.990230i	$-0.455468\pi$
$59$	−2.53310	−	0.823054i	−0.329781	−	0.107152i	−0.469228	+	0.883077i	$0.655468\pi$
$60$		0			0
$61$	−4.63195	+	6.37533i	−0.593060	+	0.816277i	−0.995051	−	0.0993663i	$-0.968318\pi$
$61$	−4.63195	+	6.37533i	−0.593060	+	0.816277i	0.401991	+	0.915644i	$0.368318\pi$
$62$	2.11524	−	6.51004i	0.268636	−	0.826776i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.33639			−0.413828
$66$		0			0
$67$	1.07517			0.131353			0.0656765	−	0.997841i	$-0.479079\pi$
$67$	1.07517			0.131353			0.0656765	+	0.997841i	$0.479079\pi$
$68$	−4.11180	+	2.98740i	−0.498629	+	0.362275i
$69$		0			0
$70$	0.496139	−	1.52696i	0.0592999	−	0.182506i
$71$	−1.60190	+	2.20483i	−0.190111	+	0.261665i	−0.893423	−	0.449216i	$-0.851703\pi$
$71$	−1.60190	+	2.20483i	−0.190111	+	0.261665i	0.703313	+	0.710881i	$0.251703\pi$
$72$		0			0
$73$	−8.42993	−	2.73905i	−0.986649	−	0.320582i	−0.229131	−	0.973396i	$-0.573588\pi$
$73$	−8.42993	−	2.73905i	−0.986649	−	0.320582i	−0.757518	+	0.652814i	$0.773588\pi$
$74$	−0.0690715	−	0.212580i	−0.00802939	−	0.0247119i
$75$		0			0
$76$			7.28808i			0.836000i
$77$	−1.94188	+	2.68870i	−0.221297	+	0.306406i
$78$		0			0
$79$	−1.22498	−	1.68603i	−0.137820	−	0.189694i	0.734528	−	0.678579i	$-0.237404\pi$
$79$	−1.22498	−	1.68603i	−0.137820	−	0.189694i	−0.872348	+	0.488885i	$0.837404\pi$
$80$	−1.52696	+	0.496139i	−0.170719	+	0.0554700i
$81$		0			0
$82$	1.12362	+	0.816355i	0.124083	+	0.0901513i
$83$	−2.76635	−	2.00987i	−0.303647	−	0.220612i	0.425519	−	0.904950i	$-0.360092\pi$
$83$	−2.76635	−	2.00987i	−0.303647	−	0.220612i	−0.729166	+	0.684337i	$0.760092\pi$
$84$		0			0
$85$	−7.76070	+	2.52161i	−0.841767	+	0.273507i
$86$	−4.29546	−	5.91220i	−0.463192	−	0.637529i
$87$		0			0
$88$	3.31661	−	0.00936955i	0.353552	−	0.000998797i
$89$			1.76110i			0.186676i	0.995634	+	0.0933381i	$0.0297538\pi$
$89$			1.76110i			0.186676i	−0.995634	+	0.0933381i	$0.970246\pi$
$90$		0			0
$91$	0.642153	+	1.97634i	0.0673159	+	0.207177i
$92$	0.543211	+	0.176500i	0.0566337	+	0.0184014i
$93$		0			0
$94$	−1.56912	+	2.15970i	−0.161842	+	0.222756i
$95$	−3.61590	+	11.1286i	−0.370983	+	1.14177i
$96$		0			0
$97$	5.45418	−	3.96269i	0.553788	−	0.402350i	−0.275392	−	0.961332i	$-0.588808\pi$
$97$	5.45418	−	3.96269i	0.553788	−	0.402350i	0.829180	+	0.558982i	$0.188808\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	2.42225			0.242225
$101$	0.340172	−	0.247150i	0.0338484	−	0.0245923i	−0.570732	−	0.821136i	$-0.693341\pi$
$101$	0.340172	−	0.247150i	0.0338484	−	0.0245923i	0.604581	+	0.796544i	$0.293341\pi$
$102$		0			0
$103$	−3.44768	+	10.6109i	−0.339710	+	1.04552i	0.624645	+	0.780909i	$0.285244\pi$
$103$	−3.44768	+	10.6109i	−0.339710	+	1.04552i	−0.964355	+	0.264612i	$0.914756\pi$
$104$	1.22145	−	1.68118i	0.119773	−	0.164853i
$105$		0			0
$106$	2.41813	+	0.785698i	0.234869	+	0.0763137i
$107$	−4.31669	−	13.2854i	−0.417310	−	1.28435i	−0.910169	−	0.414238i	$-0.864048\pi$
$107$	−4.31669	−	13.2854i	−0.417310	−	1.28435i	0.492859	−	0.870109i	$-0.335952\pi$
$108$		0			0
$109$		−	13.6880i		−	1.31108i	−0.755162	−	0.655538i	$-0.772442\pi$
$109$		−	13.6880i		−	1.31108i	0.755162	−	0.655538i	$-0.227558\pi$
$110$	5.06897	+	1.63119i	0.483308	+	0.155528i
$111$		0			0
$112$	0.587785	+	0.809017i	0.0555405	+	0.0764449i
$113$	−8.23239	+	2.67487i	−0.774438	+	0.251630i	−0.669464	−	0.742845i	$-0.733476\pi$
$113$	−8.23239	+	2.67487i	−0.774438	+	0.251630i	−0.104974	+	0.994475i	$0.533476\pi$
$114$		0			0
$115$	0.741892	+	0.539016i	0.0691818	+	0.0502635i
$116$	−0.738341	−	0.536436i	−0.0685532	−	0.0498068i
$117$		0			0
$118$	2.53310	−	0.823054i	0.233191	−	0.0757683i
$119$	2.98740	+	4.11180i	0.273854	+	0.376928i
$120$		0			0
$121$	−8.93558	−	6.41525i	−0.812325	−	0.583205i
$122$		−	7.88034i		−	0.713453i
$123$		0			0
$124$	2.11524	+	6.51004i	0.189954	+	0.584619i
$125$	11.3335	+	3.68246i	1.01370	+	0.329370i
$126$		0			0
$127$	10.8611	−	14.9490i	0.963764	−	1.32651i	0.0186291	−	0.999826i	$-0.494070\pi$
$127$	10.8611	−	14.9490i	0.963764	−	1.32651i	0.945135	−	0.326681i	$-0.105930\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	2.69919	−	1.96108i	0.236735	−	0.171998i
$131$	4.71091			0.411594			0.205797	−	0.978595i	$-0.434021\pi$
$131$	4.71091			0.411594			0.205797	+	0.978595i	$0.434021\pi$
$132$		0			0
$133$	7.28808			0.631957
$134$	−0.869831	+	0.631969i	−0.0751420	+	0.0545938i
$135$		0			0
$136$	1.57057	−	4.83371i	0.134675	−	0.414487i
$137$	2.19929	−	3.02706i	0.187898	−	0.258619i	−0.704667	−	0.709538i	$-0.748904\pi$
$137$	2.19929	−	3.02706i	0.187898	−	0.258619i	0.892565	+	0.450919i	$0.148904\pi$
$138$		0			0
$139$	−12.9725	−	4.21504i	−1.10032	−	0.357515i	−0.298093	−	0.954537i	$-0.596350\pi$
$139$	−12.9725	−	4.21504i	−1.10032	−	0.357515i	−0.802225	+	0.597022i	$0.796350\pi$
$140$	0.496139	+	1.52696i	0.0419314	+	0.129051i
$141$		0			0
$142$		−	2.72532i		−	0.228703i
$143$	−6.54874	+	2.14829i	−0.547633	+	0.179649i
$144$		0			0
$145$	−0.861269	−	1.18543i	−0.0715245	−	0.0984450i
$146$	8.42993	−	2.73905i	0.697666	−	0.226685i
$147$		0			0
$148$	0.180831	+	0.131382i	0.0148643	+	0.0107995i
$149$	−16.0965	−	11.6948i	−1.31868	−	0.958076i	−0.999948	−	0.0102304i	$-0.996744\pi$
$149$	−16.0965	−	11.6948i	−1.31868	−	0.958076i	−0.318731	−	0.947845i	$-0.603256\pi$
$150$		0			0
$151$	−18.8190	+	6.11465i	−1.53146	+	0.497603i	−0.949006	−	0.315257i	$-0.897909\pi$
$151$	−18.8190	+	6.11465i	−1.53146	+	0.497603i	−0.582459	+	0.812860i	$0.697909\pi$
$152$	−4.28383	−	5.89618i	−0.347464	−	0.478243i
$153$		0			0
$154$	−0.00936955	−	3.31661i	−0.000755020	−	0.267260i
$155$			10.9900i			0.882739i
$156$		0			0
$157$	−3.62718	−	11.1633i	−0.289480	−	0.890929i	−0.985020	−	0.172441i	$-0.944835\pi$
$157$	−3.62718	−	11.1633i	−0.289480	−	0.890929i	0.695539	−	0.718488i	$-0.255165\pi$
$158$	1.98205	+	0.644008i	0.157684	+	0.0512345i
$159$		0			0
$160$	0.943712	−	1.29891i	0.0746070	−	0.102688i
$161$	0.176500	−	0.543211i	0.0139102	−	0.0428111i
$162$		0			0
$163$	12.1028	−	8.79321i	0.947966	−	0.688738i	−0.00235891	−	0.999997i	$-0.500751\pi$
$163$	12.1028	−	8.79321i	0.947966	−	0.688738i	0.950325	+	0.311260i	$0.100751\pi$
$164$	−1.38887			−0.108452
$165$		0			0
$166$	3.41940			0.265397
$167$	−7.01083	+	5.09367i	−0.542514	+	0.394160i	−0.825018	−	0.565107i	$-0.808835\pi$
$167$	−7.01083	+	5.09367i	−0.542514	+	0.394160i	0.282504	+	0.959266i	$0.408835\pi$
$168$		0			0
$169$	2.68280	−	8.25680i	0.206369	−	0.635138i
$170$	4.79638	−	6.60165i	0.367865	−	0.506323i
$171$		0			0
$172$	6.95021	+	2.25826i	0.529948	+	0.172191i
$173$	−5.00409	−	15.4010i	−0.380454	−	1.17092i	−0.939725	−	0.341932i	$-0.888919\pi$
$173$	−5.00409	−	15.4010i	−0.380454	−	1.17092i	0.559271	−	0.828985i	$-0.311081\pi$
$174$		0			0
$175$		−	2.42225i		−	0.183105i
$176$	−2.67769	+	1.95704i	−0.201838	+	0.147517i
$177$		0			0
$178$	−1.03515	−	1.42476i	−0.0775877	−	0.106790i
$179$	−15.1656	+	4.92761i	−1.13353	+	0.368307i	−0.814917	−	0.579577i	$-0.803218\pi$
$179$	−15.1656	+	4.92761i	−1.13353	+	0.368307i	−0.318615	+	0.947884i	$0.603218\pi$
$180$		0			0
$181$	0.0502214	+	0.0364880i	0.00373293	+	0.00271213i	0.589650	−	0.807659i	$-0.299266\pi$
$181$	0.0502214	+	0.0364880i	0.00373293	+	0.00271213i	−0.585917	+	0.810371i	$0.699266\pi$
$182$	−1.68118	−	1.22145i	−0.124617	−	0.0905397i
$183$		0			0
$184$	−0.543211	+	0.176500i	−0.0400461	+	0.0130118i
$185$	0.210938	+	0.290332i	0.0155085	+	0.0213456i
$186$		0			0
$187$	−13.6092	+	9.94656i	−0.995207	+	0.727364i
$188$		−	2.66954i		−	0.194696i
$189$		0			0
$190$	−3.61590	−	11.1286i	−0.262325	−	0.807353i
$191$	2.45043	+	0.796192i	0.177307	+	0.0576105i	0.396325	−	0.918110i	$-0.370285\pi$
$191$	2.45043	+	0.796192i	0.177307	+	0.0576105i	−0.219018	+	0.975721i	$0.570285\pi$
$192$		0			0
$193$	11.9830	−	16.4931i	0.862553	−	1.18720i	−0.118402	−	0.992966i	$-0.537777\pi$
$193$	11.9830	−	16.4931i	0.862553	−	1.18720i	0.980955	−	0.194236i	$-0.0622229\pi$
$194$	−2.08331	+	6.41177i	−0.149573	+	0.460338i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	21.5481			1.53524			0.767620	−	0.640905i	$-0.221441\pi$
$197$	21.5481			1.53524			0.767620	+	0.640905i	$0.221441\pi$
$198$		0			0
$199$	−4.92565			−0.349170			−0.174585	−	0.984642i	$-0.555858\pi$
$199$	−4.92565			−0.349170			−0.174585	+	0.984642i	$0.555858\pi$
$200$	−1.95964	+	1.42376i	−0.138567	+	0.100675i
$201$		0			0
$202$	−0.129934	+	0.399897i	−0.00914214	+	0.0281366i
$203$	−0.536436	+	0.738341i	−0.0376504	+	0.0518214i
$204$		0			0
$205$	−2.12074	−	0.689070i	−0.148119	−	0.0481267i
$206$	−3.44768	−	10.6109i	−0.240211	−	0.739295i
$207$		0			0
$208$			2.07805i			0.144087i
$209$	0.0682860	+	24.1717i	0.00472344	+	1.67199i
$210$		0			0
$211$	15.7707	+	21.7065i	1.08570	+	1.49434i	0.853089	+	0.521765i	$0.174726\pi$
$211$	15.7707	+	21.7065i	1.08570	+	1.49434i	0.232609	+	0.972570i	$0.425274\pi$
$212$	−2.41813	+	0.785698i	−0.166078	+	0.0539619i
$213$		0			0
$214$	11.3012	+	8.21082i	0.772536	+	0.561280i
$215$	9.49226	+	6.89653i	0.647367	+	0.470340i
$216$		0			0
$217$	6.51004	−	2.11524i	0.441930	−	0.143592i
$218$	8.04563	+	11.0739i	0.544919	+	0.750017i
$219$		0			0
$220$	−5.05968	+	1.65981i	−0.341123	+	0.111904i
$221$			10.5616i			0.710451i
$222$		0			0
$223$	1.36723	+	4.20791i	0.0915568	+	0.281783i	0.986341	−	0.164716i	$-0.0526707\pi$
$223$	1.36723	+	4.20791i	0.0915568	+	0.281783i	−0.894784	+	0.446499i	$0.852671\pi$
$224$	−0.951057	−	0.309017i	−0.0635451	−	0.0206471i
$225$		0			0
$226$	5.08790	−	7.00289i	0.338442	−	0.465825i
$227$	9.16703	−	28.2132i	0.608437	−	1.87258i	0.137266	−	0.990534i	$-0.456168\pi$
$227$	9.16703	−	28.2132i	0.608437	−	1.87258i	0.471170	−	0.882042i	$-0.343832\pi$
$228$		0			0
$229$	14.0808	−	10.2303i	0.930488	−	0.676039i	−0.0156243	−	0.999878i	$-0.504974\pi$
$229$	14.0808	−	10.2303i	0.930488	−	0.676039i	0.946112	+	0.323839i	$0.104974\pi$
$230$	−0.917029			−0.0604671
$231$		0			0
$232$	0.912640			0.0599177
$233$	−11.6050	+	8.43156i	−0.760272	+	0.552370i	−0.898994	−	0.437961i	$-0.855701\pi$
$233$	−11.6050	+	8.43156i	−0.760272	+	0.552370i	0.138722	+	0.990331i	$0.455701\pi$
$234$		0			0
$235$	1.32446	−	4.07628i	0.0863984	−	0.265907i
$236$	−1.56554	+	2.15478i	−0.101908	+	0.140264i
$237$		0			0
$238$	−4.83371	−	1.57057i	−0.313323	−	0.101805i
$239$	7.06213	+	21.7350i	0.456811	+	1.40592i	0.868996	+	0.494820i	$0.164766\pi$
$239$	7.06213	+	21.7350i	0.456811	+	1.40592i	−0.412185	+	0.911100i	$0.635234\pi$
$240$		0			0
$241$			6.48724i			0.417880i	0.977928	+	0.208940i	$0.0670014\pi$
$241$			6.48724i			0.417880i	−0.977928	+	0.208940i	$0.932999\pi$
$242$	10.9998	−	0.0621503i	0.707095	−	0.00399517i
$243$		0			0
$244$	4.63195	+	6.37533i	0.296530	+	0.408139i
$245$	1.52696	−	0.496139i	0.0975538	−	0.0316971i
$246$		0			0
$247$	12.2526	+	8.90200i	0.779611	+	0.566421i
$248$	−5.53777	−	4.02343i	−0.351649	−	0.255488i
$249$		0			0
$250$	−11.3335	+	3.68246i	−0.716791	+	0.232899i
$251$	10.2279	+	14.0776i	0.645582	+	0.888568i	0.998898	−	0.0469364i	$-0.0149458\pi$
$251$	10.2279	+	14.0776i	0.645582	+	0.888568i	−0.353316	+	0.935504i	$0.614946\pi$
$252$		0			0
$253$	1.80327	+	0.580293i	0.113371	+	0.0364827i
$254$			18.4780i			1.15941i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.783543	−	0.254589i	−0.0488761	−	0.0158808i	0.284477	−	0.958683i	$-0.408180\pi$
$257$	−0.783543	−	0.254589i	−0.0488761	−	0.0158808i	−0.333353	+	0.942802i	$0.608180\pi$
$258$		0			0
$259$	0.131382	−	0.180831i	0.00816366	−	0.0112363i
$260$	−1.03100	+	3.17309i	−0.0639399	+	0.196787i
$261$		0			0
$262$	−3.81121	+	2.76900i	−0.235457	+	0.171070i
$263$	20.2355			1.24777			0.623886	−	0.781515i	$-0.285553\pi$
$263$	20.2355			1.24777			0.623886	+	0.781515i	$0.285553\pi$
$264$		0			0
$265$	−4.08220			−0.250767
$266$	−5.89618	+	4.28383i	−0.361518	+	0.262658i
$267$		0			0
$268$	0.332246	−	1.02255i	0.0202952	−	0.0624621i
$269$	16.2777	−	22.4043i	0.992469	−	1.36602i	0.0626360	−	0.998036i	$-0.480049\pi$
$269$	16.2777	−	22.4043i	0.992469	−	1.36602i	0.929833	−	0.367981i	$-0.119951\pi$
$270$		0			0
$271$	−6.68788	−	2.17302i	−0.406260	−	0.132002i	0.0987566	−	0.995112i	$-0.468513\pi$
$271$	−6.68788	−	2.17302i	−0.406260	−	0.132002i	−0.505016	+	0.863110i	$0.668513\pi$
$272$	1.57057	+	4.83371i	0.0952296	+	0.293087i
$273$		0			0
$274$			3.74165i			0.226041i
$275$	8.03365	−	0.0226954i	0.484447	−	0.00136858i
$276$		0			0
$277$	−9.26240	−	12.7486i	−0.556524	−	0.765989i	0.434356	−	0.900741i	$-0.356976\pi$
$277$	−9.26240	−	12.7486i	−0.556524	−	0.765989i	−0.990879	+	0.134752i	$0.956976\pi$
$278$	12.9725	−	4.21504i	0.778042	−	0.252801i
$279$		0			0
$280$	−1.29891	−	0.943712i	−0.0776246	−	0.0563976i
$281$	−3.33411	−	2.42238i	−0.198897	−	0.144507i	0.483879	−	0.875135i	$-0.339227\pi$
$281$	−3.33411	−	2.42238i	−0.198897	−	0.144507i	−0.682776	+	0.730628i	$0.739227\pi$
$282$		0			0
$283$	−24.4279	+	7.93710i	−1.45209	+	0.471812i	−0.925643	−	0.378398i	$-0.876475\pi$
$283$	−24.4279	+	7.93710i	−1.45209	+	0.471812i	−0.526444	+	0.850210i	$0.676475\pi$
$284$	1.60190	+	2.20483i	0.0950553	+	0.130832i
$285$		0			0
$286$	4.03531	−	5.58726i	0.238613	−	0.330381i
$287$			1.38887i			0.0819822i
$288$		0			0
$289$	2.72906	+	8.39917i	0.160533	+	0.494069i
$290$	1.39356	+	0.452796i	0.0818328	+	0.0265891i
$291$		0			0
$292$	−5.20998	+	7.17093i	−0.304891	+	0.419647i
$293$	−7.12947	+	21.9422i	−0.416508	+	1.28188i	0.494387	+	0.869242i	$0.335392\pi$
$293$	−7.12947	+	21.9422i	−0.416508	+	1.28188i	−0.910895	+	0.412638i	$0.864608\pi$
$294$		0			0
$295$	−3.45959	+	2.51354i	−0.201425	+	0.146344i
$296$	−0.223520			−0.0129918
$297$		0			0
$298$	19.8964			1.15257
$299$	0.960232	−	0.697649i	0.0555316	−	0.0403461i
$300$		0			0
$301$	2.25826	−	6.95021i	0.130164	−	0.400603i
$302$	11.6308	−	16.0084i	0.669275	−	0.921178i
$303$		0			0
$304$	6.93138	+	2.25214i	0.397542	+	0.129169i
$305$	3.90974	+	12.0330i	0.223871	+	0.689005i
$306$		0			0
$307$			11.4639i			0.654281i	0.944976	+	0.327141i	$0.106085\pi$
$307$			11.4639i			0.654281i	−0.944976	+	0.327141i	$0.893915\pi$
$308$	1.95704	+	2.67769i	0.111512	+	0.152575i
$309$		0			0
$310$	−6.45977	−	8.89110i	−0.366890	−	0.504981i
$311$	−31.9383	+	10.3774i	−1.81105	+	0.588447i	−0.811060	+	0.584963i	$0.801109\pi$
$311$	−31.9383	+	10.3774i	−1.81105	+	0.588447i	−0.999994	+	0.00348429i	$0.998891\pi$
$312$		0			0
$313$	12.6362	+	9.18072i	0.714239	+	0.518925i	0.884538	−	0.466467i	$-0.154474\pi$
$313$	12.6362	+	9.18072i	0.714239	+	0.518925i	−0.170299	+	0.985392i	$0.554474\pi$
$314$	9.49608	+	6.89931i	0.535895	+	0.389350i
$315$		0			0
$316$	−1.98205	+	0.644008i	−0.111499	+	0.0362283i
$317$	0.148748	+	0.204734i	0.00835453	+	0.0114990i	0.813174	−	0.582021i	$-0.197738\pi$
$317$	0.148748	+	0.204734i	0.00835453	+	0.0114990i	−0.804819	+	0.593520i	$0.797738\pi$
$318$		0			0
$319$	−2.45382	−	1.77223i	−0.137387	−	0.0992260i
$320$			1.60554i			0.0897523i
$321$		0			0
$322$	0.176500	+	0.543211i	0.00983596	+	0.0302720i
$323$	35.2285	+	11.4464i	1.96016	+	0.636896i
$324$		0			0
$325$	2.95865	−	4.07223i	0.164116	−	0.225886i
$326$	−4.62287	+	14.2277i	−0.256037	+	0.788000i
$327$		0			0
$328$	1.12362	−	0.816355i	0.0620413	−	0.0450757i
$329$	−2.66954			−0.147177
$330$		0			0
$331$	−12.7547			−0.701060			−0.350530	−	0.936551i	$-0.613999\pi$
$331$	−12.7547			−0.701060			−0.350530	+	0.936551i	$0.613999\pi$
$332$	−2.76635	+	2.00987i	−0.151823	+	0.110306i
$333$		0			0
$334$	2.67790	−	8.24172i	0.146528	−	0.450967i
$335$	1.01465	−	1.39655i	0.0554363	−	0.0763015i
$336$		0			0
$337$	17.8760	+	5.80827i	0.973769	+	0.316397i	0.752337	−	0.658779i	$-0.228927\pi$
$337$	17.8760	+	5.80827i	0.973769	+	0.316397i	0.221433	+	0.975176i	$0.428927\pi$
$338$	2.68280	+	8.25680i	0.145925	+	0.449111i
$339$		0			0
$340$			8.16009i			0.442543i
$341$	7.07643	+	21.5715i	0.383210	+	1.16816i
$342$		0			0
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	−6.95021	+	2.25826i	−0.374730	+	0.121757i
$345$		0			0
$346$	13.1009	+	9.51834i	0.704307	+	0.511709i
$347$	10.8112	+	7.85476i	0.580373	+	0.421666i	0.838859	−	0.544349i	$-0.183223\pi$
$347$	10.8112	+	7.85476i	0.580373	+	0.421666i	−0.258485	+	0.966015i	$0.583223\pi$
$348$		0			0
$349$	17.0593	−	5.54290i	0.913162	−	0.296704i	0.185503	−	0.982644i	$-0.440608\pi$
$349$	17.0593	−	5.54290i	0.913162	−	0.296704i	0.727659	+	0.685939i	$0.240608\pi$
$350$	1.42376	+	1.95964i	0.0761032	+	0.104747i
$351$		0			0
$352$	1.01598	−	3.15718i	0.0541518	−	0.168278i
$353$		−	21.9355i		−	1.16751i	−0.811930	−	0.583755i	$-0.801583\pi$
$353$		−	21.9355i		−	1.16751i	0.811930	−	0.583755i	$-0.198417\pi$
$354$		0			0
$355$	1.35213	+	4.16144i	0.0717638	+	0.220866i
$356$	1.67491	+	0.544210i	0.0887698	+	0.0288431i
$357$		0			0
$358$	9.37288	−	12.9007i	0.495372	−	0.681821i
$359$	3.59087	−	11.0515i	0.189519	−	0.583278i	−0.810478	−	0.585769i	$-0.800793\pi$
$359$	3.59087	−	11.0515i	0.189519	−	0.583278i	0.999997	+	0.00249036i	$0.000792708\pi$
$360$		0			0
$361$	27.6005	−	20.0530i	1.45266	−	1.05542i
$362$	−0.0620771			−0.00326270
$363$		0			0
$364$	2.07805			0.108919
$365$	−11.5132	+	8.36483i	−0.602628	+	0.437835i
$366$		0			0
$367$	7.32055	−	22.5303i	0.382130	−	1.17607i	−0.556412	−	0.830907i	$-0.687822\pi$
$367$	7.32055	−	22.5303i	0.382130	−	1.17607i	0.938541	−	0.345167i	$-0.112178\pi$
$368$	0.335723	−	0.462083i	0.0175008	−	0.0240878i
$369$		0			0
$370$	−0.341306	−	0.110897i	−0.0177436	−	0.00576525i
$371$	0.785698	+	2.41813i	0.0407914	+	0.125543i
$372$		0			0
$373$			15.1876i			0.786383i	0.919457	+	0.393191i	$0.128629\pi$
$373$			15.1876i			0.786383i	−0.919457	+	0.393191i	$0.871371\pi$
$374$	5.16367	−	16.0462i	0.267007	−	0.829732i
$375$		0			0
$376$	1.56912	+	2.15970i	0.0809210	+	0.111378i
$377$	−1.80369	+	0.586054i	−0.0928947	+	0.0301833i
$378$		0			0
$379$	5.08238	+	3.69256i	0.261064	+	0.189674i	0.710616	−	0.703580i	$-0.248416\pi$
$379$	5.08238	+	3.69256i	0.261064	+	0.189674i	−0.449552	+	0.893254i	$0.648416\pi$
$380$	9.46655	+	6.87785i	0.485624	+	0.352826i
$381$		0			0
$382$	−2.45043	+	0.796192i	−0.125375	+	0.0407367i
$383$	0.213108	+	0.293317i	0.0108893	+	0.0149878i	0.814427	−	0.580266i	$-0.197051\pi$
$383$	0.213108	+	0.293317i	0.0108893	+	0.0149878i	−0.803538	+	0.595254i	$0.797051\pi$
$384$		0			0
$385$	1.65981	+	5.05968i	0.0845916	+	0.257865i
$386$			20.3866i			1.03765i
$387$		0			0
$388$	−2.08331	−	6.41177i	−0.105764	−	0.325508i
$389$	−34.0858	−	11.0751i	−1.72822	−	0.561532i	−0.735028	−	0.678037i	$-0.762831\pi$
$389$	−34.0858	−	11.0751i	−1.72822	−	0.561532i	−0.993190	+	0.116505i	$0.962831\pi$
$390$		0			0
$391$	1.70630	−	2.34852i	0.0862913	−	0.118770i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	−17.4328	+	12.6657i	−0.878251	+	0.638087i
$395$	−3.34603			−0.168357
$396$		0			0
$397$	−2.45086			−0.123005			−0.0615025	−	0.998107i	$-0.519589\pi$
$397$	−2.45086			−0.123005			−0.0615025	+	0.998107i	$0.519589\pi$
$398$	3.98494	−	2.89523i	0.199747	−	0.145125i
$399$		0			0
$400$	0.748515	−	2.30369i	0.0374258	−	0.115185i
$401$	16.2731	−	22.3980i	0.812640	−	1.11850i	−0.178271	−	0.983981i	$-0.557050\pi$
$401$	16.2731	−	22.3980i	0.812640	−	1.11850i	0.990911	−	0.134521i	$-0.0429497\pi$
$402$		0			0
$403$	13.5282	+	4.39557i	0.673887	+	0.218959i
$404$	−0.129934	−	0.399897i	−0.00646447	−	0.0198956i
$405$		0			0
$406$		−	0.912640i		−	0.0452935i
$407$	0.600979	+	0.434048i	0.0297894	+	0.0215150i
$408$		0			0
$409$	3.01096	+	4.14423i	0.148882	+	0.204919i	0.876944	−	0.480593i	$-0.159578\pi$
$409$	3.01096	+	4.14423i	0.148882	+	0.204919i	−0.728062	+	0.685512i	$0.759578\pi$
$410$	2.12074	−	0.689070i	0.104736	−	0.0340307i
$411$		0			0
$412$	9.02615	+	6.55788i	0.444687	+	0.323084i
$413$	2.15478	+	1.56554i	0.106030	+	0.0770353i
$414$		0			0
$415$	−5.22128	+	1.69650i	−0.256303	+	0.0832778i
$416$	−1.22145	−	1.68118i	−0.0598864	−	0.0824265i
$417$		0			0
$418$	−14.2630	−	19.5152i	−0.697628	−	0.954520i
$419$		−	1.83272i		−	0.0895341i	−0.998997	−	0.0447670i	$-0.985745\pi$
$419$		−	1.83272i		−	0.0895341i	0.998997	−	0.0447670i	$-0.0142546\pi$
$420$		0			0
$421$	7.27315	+	22.3844i	0.354472	+	1.09095i	0.956315	+	0.292337i	$0.0944330\pi$
$421$	7.27315	+	22.3844i	0.354472	+	1.09095i	−0.601844	+	0.798614i	$0.705567\pi$
$422$	−25.5175	−	8.29114i	−1.24217	−	0.403606i
$423$		0			0
$424$	1.49449	−	2.05698i	0.0725787	−	0.0998960i
$425$	3.80430	−	11.7084i	0.184536	−	0.567942i
$426$		0			0
$427$	6.37533	−	4.63195i	0.308524	−	0.224156i
$428$	−13.9691			−0.675221
$429$		0			0
$430$	−11.7331			−0.565819
$431$	−11.1259	+	8.08344i	−0.535916	+	0.389366i	−0.822566	−	0.568670i	$-0.807458\pi$
$431$	−11.1259	+	8.08344i	−0.535916	+	0.389366i	0.286650	+	0.958035i	$0.407458\pi$
$432$		0			0
$433$	2.33873	−	7.19786i	0.112392	−	0.345907i	−0.879002	−	0.476818i	$-0.841790\pi$
$433$	2.33873	−	7.19786i	0.112392	−	0.345907i	0.991394	+	0.130911i	$0.0417902\pi$
$434$	−4.02343	+	5.53777i	−0.193131	+	0.265822i
$435$		0			0
$436$	−13.0181	−	4.22984i	−0.623454	−	0.202573i
$437$	−1.28635	−	3.95897i	−0.0615343	−	0.189383i
$438$		0			0
$439$			17.9761i			0.857953i	0.903316	+	0.428976i	$0.141126\pi$
$439$			17.9761i			0.857953i	−0.903316	+	0.428976i	$0.858874\pi$
$440$	3.11776	−	4.31682i	0.148633	−	0.205796i
$441$		0			0
$442$	−6.20796	−	8.54452i	−0.295282	−	0.406421i
$443$	30.6860	−	9.97049i	1.45794	−	0.473712i	0.530497	−	0.847687i	$-0.322005\pi$
$443$	30.6860	−	9.97049i	1.45794	−	0.473712i	0.927439	+	0.373975i	$0.122005\pi$
$444$		0			0
$445$	2.28751	+	1.66197i	0.108438	+	0.0787850i
$446$	−3.57947	−	2.60063i	−0.169493	−	0.123144i
$447$		0			0
$448$	0.951057	−	0.309017i	0.0449332	−	0.0145997i
$449$	2.64455	+	3.63992i	0.124804	+	0.171778i	0.866847	−	0.498574i	$-0.166143\pi$
$449$	2.64455	+	3.63992i	0.124804	+	0.171778i	−0.742043	+	0.670353i	$0.766143\pi$
$450$		0			0
$451$	−4.60633	+	0.0130130i	−0.216904	+	0.000612760i
$452$			8.65605i			0.407146i
$453$		0			0
$454$	9.16703	+	28.2132i	0.430230	+	1.32411i
$455$	3.17309	+	1.03100i	0.148757	+	0.0483341i
$456$		0			0
$457$	−19.9540	+	27.4643i	−0.933407	+	1.28472i	0.0251087	+	0.999685i	$0.492007\pi$
$457$	−19.9540	+	27.4643i	−0.933407	+	1.28472i	−0.958516	+	0.285040i	$0.907993\pi$
$458$	−5.37840	+	16.5530i	−0.251316	+	0.773472i
$459$		0			0
$460$	0.741892	−	0.539016i	0.0345909	−	0.0251318i
$461$	−16.7578			−0.780488			−0.390244	−	0.920712i	$-0.627609\pi$
$461$	−16.7578			−0.780488			−0.390244	+	0.920712i	$0.627609\pi$
$462$		0			0
$463$	2.18566			0.101576			0.0507881	−	0.998709i	$-0.483827\pi$
$463$	2.18566			0.101576			0.0507881	+	0.998709i	$0.483827\pi$
$464$	−0.738341	+	0.536436i	−0.0342766	+	0.0249034i
$465$		0			0
$466$	4.43273	−	13.6426i	0.205342	−	0.631979i
$467$	15.9417	−	21.9419i	0.737696	−	1.01535i	−0.261052	−	0.965325i	$-0.584069\pi$
$467$	15.9417	−	21.9419i	0.737696	−	1.01535i	0.998748	−	0.0500264i	$-0.0159305\pi$
$468$		0			0
$469$	−1.02255	−	0.332246i	−0.0472169	−	0.0153417i
$470$	1.32446	+	4.07628i	0.0610929	+	0.188025i
$471$		0			0
$472$		−	2.66346i		−	0.122596i
$473$	23.0723	+	7.42465i	1.06087	+	0.341386i
$474$		0			0
$475$	−10.3765	−	14.2820i	−0.476106	−	0.655303i
$476$	4.83371	−	1.57057i	0.221553	−	0.0719868i
$477$		0			0
$478$	−18.4889	−	13.4330i	−0.845662	−	0.614410i
$479$	−14.8834	−	10.8134i	−0.680039	−	0.494077i	0.193332	−	0.981133i	$-0.438071\pi$
$479$	−14.8834	−	10.8134i	−0.680039	−	0.494077i	−0.873371	+	0.487056i	$0.838071\pi$
$480$		0			0
$481$	0.441752	−	0.143534i	0.0201422	−	0.00654458i
$482$	−3.81311	−	5.24829i	−0.173682	−	0.239053i
$483$		0			0
$484$	−8.86251	+	6.51582i	−0.402842	+	0.296173i
$485$		−	10.8241i		−	0.491498i
$486$		0			0
$487$	0.196381	+	0.604400i	0.00889889	+	0.0273880i	0.955407	−	0.295291i	$-0.0954166\pi$
$487$	0.196381	+	0.604400i	0.00889889	+	0.0273880i	−0.946508	+	0.322679i	$0.895417\pi$
$488$	−7.49465	−	2.43516i	−0.339267	−	0.110234i
$489$		0			0
$490$	−0.943712	+	1.29891i	−0.0426326	+	0.0586787i
$491$	−8.69472	+	26.7596i	−0.392387	+	1.20764i	0.538590	+	0.842568i	$0.318957\pi$
$491$	−8.69472	+	26.7596i	−0.392387	+	1.20764i	−0.930978	+	0.365076i	$0.881043\pi$
$492$		0			0
$493$	−3.75259	+	2.72642i	−0.169008	+	0.122792i
$494$	−15.1450			−0.681405
$495$		0			0
$496$	6.84506			0.307352
$497$	2.20483	−	1.60190i	0.0989000	−	0.0718550i
$498$		0			0
$499$	4.34898	−	13.3848i	0.194687	−	0.599185i	−0.805293	−	0.592877i	$-0.797992\pi$
$499$	4.34898	−	13.3848i	0.194687	−	0.599185i	0.999980	−	0.00630793i	$-0.00200789\pi$
$500$	7.00446	−	9.64081i	0.313249	−	0.431150i
$501$		0			0
$502$	−16.5492	−	5.37715i	−0.738625	−	0.239994i
$503$	5.55098	+	17.0842i	0.247506	+	0.761745i	0.995214	+	0.0977174i	$0.0311541\pi$
$503$	5.55098	+	17.0842i	0.247506	+	0.761745i	−0.747708	+	0.664027i	$0.768846\pi$
$504$		0			0
$505$		−	0.675091i		−	0.0300411i
$506$	−1.79997	+	0.590472i	−0.0800183	+	0.0262497i
$507$		0			0
$508$	−10.8611	−	14.9490i	−0.481882	−	0.663254i
$509$	7.76443	−	2.52281i	0.344152	−	0.111822i	−0.131841	−	0.991271i	$-0.542089\pi$
$509$	7.76443	−	2.52281i	0.344152	−	0.111822i	0.475993	+	0.879449i	$0.342089\pi$
$510$		0			0
$511$	7.17093	+	5.20998i	0.317223	+	0.230476i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	0.783543	−	0.254589i	0.0345606	−	0.0112294i
$515$	10.5289	+	14.4918i	0.463960	+	0.638586i
$516$		0			0
$517$	−0.0250124	−	8.85383i	−0.00110004	−	0.389391i
$518$			0.223520i			0.00982090i
$519$		0			0
$520$	−1.03100	−	3.17309i	−0.0452124	−	0.139149i
$521$	−20.3926	−	6.62596i	−0.893416	−	0.290289i	−0.173899	−	0.984763i	$-0.555637\pi$
$521$	−20.3926	−	6.62596i	−0.893416	−	0.290289i	−0.719517	+	0.694475i	$0.755637\pi$
$522$		0			0
$523$	20.3474	−	28.0057i	0.889728	−	1.22461i	−0.0839025	−	0.996474i	$-0.526738\pi$
$523$	20.3474	−	28.0057i	0.889728	−	1.22461i	0.973630	−	0.228131i	$-0.0732616\pi$
$524$	1.45575	−	4.48034i	0.0635948	−	0.195725i
$525$		0			0
$526$	−16.3708	+	11.8941i	−0.713802	+	0.518608i
$527$	34.7898			1.51547
$528$		0			0
$529$	22.6738			0.985816
$530$	3.30257	−	2.39945i	0.143454	−	0.104226i
$531$		0			0
$532$	2.25214	−	6.93138i	0.0976427	−	0.300513i
$533$	−1.69643	+	2.33493i	−0.0734804	+	0.101137i
$534$		0			0
$535$	−21.3302	−	6.93060i	−0.922185	−	0.299636i
$536$	0.332246	+	1.02255i	0.0143508	+	0.0441673i
$537$		0			0
$538$			27.6933i			1.19394i
$539$	2.67769	−	1.95704i	0.115336	−	0.0842955i
$540$		0			0
$541$	−13.5577	−	18.6606i	−0.582892	−	0.802282i	0.411117	−	0.911583i	$-0.365139\pi$
$541$	−13.5577	−	18.6606i	−0.582892	−	0.802282i	−0.994009	+	0.109301i	$0.965139\pi$
$542$	6.68788	−	2.17302i	0.287269	−	0.0933393i
$543$		0			0
$544$	−4.11180	−	2.98740i	−0.176292	−	0.128084i
$545$	−17.7795	−	12.9176i	−0.761591	−	0.553328i
$546$		0			0
$547$	−27.3382	+	8.88272i	−1.16890	+	0.379798i	−0.828231	−	0.560386i	$-0.810653\pi$
$547$	−27.3382	+	8.88272i	−1.16890	+	0.379798i	−0.340666	+	0.940184i	$0.610653\pi$
$548$	−2.19929	−	3.02706i	−0.0939489	−	0.129310i
$549$		0			0
$550$	−6.48602	+	4.74042i	−0.276565	+	0.202132i
$551$			6.65139i			0.283359i
$552$		0			0
$553$	0.644008	+	1.98205i	0.0273860	+	0.0842854i
$554$	14.9869	+	4.86953i	0.636731	+	0.206887i
$555$		0			0
$556$	−8.01748	+	11.0351i	−0.340017	+	0.467993i
$557$	0.691501	−	2.12822i	0.0292999	−	0.0901757i	−0.935337	−	0.353757i	$-0.884904\pi$
$557$	0.691501	−	2.12822i	0.0292999	−	0.0901757i	0.964637	+	0.263582i	$0.0849039\pi$
$558$		0			0
$559$	12.2858	−	8.92619i	0.519636	−	0.377537i
$560$	1.60554			0.0678464
$561$		0			0
$562$	4.12119			0.173842
$563$	17.2047	−	12.5000i	0.725092	−	0.526810i	−0.162915	−	0.986640i	$-0.552090\pi$
$563$	17.2047	−	12.5000i	0.725092	−	0.526810i	0.888007	+	0.459830i	$0.152090\pi$
$564$		0			0
$565$	−4.29460	+	13.2174i	−0.180675	+	0.556061i
$566$	15.0973	−	20.7796i	0.634585	−	0.873432i
$567$		0			0
$568$	−2.59193	−	0.842169i	−0.108755	−	0.0353366i
$569$	−7.82027	−	24.0683i	−0.327843	−	1.00900i	−0.970141	−	0.242541i	$-0.922019\pi$
$569$	−7.82027	−	24.0683i	−0.327843	−	1.00900i	0.642298	−	0.766455i	$-0.277981\pi$
$570$		0			0
$571$			37.4910i			1.56895i	0.620160	+	0.784476i	$0.287068\pi$
$571$			37.4910i			1.56895i	−0.620160	+	0.784476i	$0.712932\pi$
$572$	0.0194704	+	6.89208i	0.000814098	+	0.288172i
$573$		0			0
$574$	−0.816355	−	1.12362i	−0.0340740	−	0.0468988i
$575$	−1.31579	+	0.427527i	−0.0548723	+	0.0178291i
$576$		0			0
$577$	−3.60687	−	2.62055i	−0.150156	−	0.109095i	0.510171	−	0.860073i	$-0.329582\pi$
$577$	−3.60687	−	2.62055i	−0.150156	−	0.109095i	−0.660327	+	0.750978i	$0.729582\pi$
$578$	−7.14476	−	5.19098i	−0.297183	−	0.215916i
$579$		0			0
$580$	−1.39356	+	0.452796i	−0.0578645	+	0.0188013i
$581$	2.00987	+	2.76635i	0.0833836	+	0.114768i
$582$		0			0
$583$	−8.01263	+	2.62851i	−0.331849	+	0.108862i
$584$		−	8.86375i		−	0.366785i
$585$		0			0
$586$	−7.12947	−	21.9422i	−0.294515	−	0.906425i
$587$	−13.9104	−	4.51976i	−0.574143	−	0.186550i	0.00753197	−	0.999972i	$-0.497602\pi$
$587$	−13.9104	−	4.51976i	−0.574143	−	0.186550i	−0.581675	+	0.813421i	$0.697602\pi$
$588$		0			0
$589$	29.3231	−	40.3597i	1.20824	−	1.66299i
$590$	1.32144	−	4.06699i	0.0544030	−	0.167435i
$591$		0			0
$592$	0.180831	−	0.131382i	0.00743213	−	0.00539976i
$593$	−3.46567			−0.142318			−0.0711591	−	0.997465i	$-0.522670\pi$
$593$	−3.46567			−0.142318			−0.0711591	+	0.997465i	$0.522670\pi$
$594$		0			0
$595$	8.16009			0.334531
$596$	−16.0965	+	11.6948i	−0.659339	+	0.479038i
$597$		0			0
$598$	−0.366776	+	1.12882i	−0.0149986	+	0.0461609i
$599$	−10.8009	+	14.8662i	−0.441313	+	0.607415i	−0.970503	−	0.241088i	$-0.922496\pi$
$599$	−10.8009	+	14.8662i	−0.441313	+	0.607415i	0.529190	+	0.848503i	$0.322496\pi$
$600$		0			0
$601$	−14.4255	−	4.68713i	−0.588428	−	0.191192i	−0.000355338	−	1.00000i	$-0.500113\pi$
$601$	−14.4255	−	4.68713i	−0.588428	−	0.191192i	−0.588073	+	0.808808i	$0.700113\pi$
$602$	2.25826	+	6.95021i	0.0920398	+	0.283269i
$603$		0			0
$604$			19.7874i			0.805139i
$605$	−16.7654	+	5.55234i	−0.681612	+	0.225735i
$606$		0			0
$607$	25.8387	+	35.5639i	1.04876	+	1.44349i	0.889880	+	0.456194i	$0.150788\pi$
$607$	25.8387	+	35.5639i	1.04876	+	1.44349i	0.158878	+	0.987298i	$0.449212\pi$
$608$	−6.93138	+	2.25214i	−0.281104	+	0.0913364i
$609$		0			0
$610$	−10.2358	−	7.43677i	−0.414437	−	0.301106i
$611$	−4.48797	−	3.26070i	−0.181564	−	0.131914i
$612$		0			0
$613$	6.70962	−	2.18009i	0.270999	−	0.0880530i	−0.170365	−	0.985381i	$-0.554495\pi$
$613$	6.70962	−	2.18009i	0.270999	−	0.0880530i	0.441364	+	0.897328i	$0.354495\pi$
$614$	−6.73833	−	9.27452i	−0.271937	−	0.374289i
$615$		0			0
$616$	−3.15718	−	1.01598i	−0.127206	−	0.0409349i
$617$		−	31.9516i		−	1.28632i	−0.765731	−	0.643161i	$-0.777623\pi$
$617$		−	31.9516i		−	1.28632i	0.765731	−	0.643161i	$-0.222377\pi$
$618$		0			0
$619$	11.9229	+	36.6951i	0.479224	+	1.47490i	0.840176	+	0.542314i	$0.182452\pi$
$619$	11.9229	+	36.6951i	0.479224	+	1.47490i	−0.360952	+	0.932584i	$0.617548\pi$
$620$	10.4521	+	3.39610i	0.419767	+	0.136391i
$621$		0			0
$622$	19.7389	−	27.1683i	0.791460	−	1.08935i
$623$	0.544210	−	1.67491i	0.0218033	−	0.0671037i
$624$		0			0
$625$	5.68051	−	4.12713i	0.227220	−	0.165085i
$626$	−15.6192			−0.624268
$627$		0			0
$628$	−11.7378			−0.468389
$629$	0.919069	−	0.667743i	0.0366457	−	0.0266246i
$630$		0			0
$631$	8.41915	−	25.9115i	0.335161	−	1.03152i	−0.631481	−	0.775391i	$-0.717553\pi$
$631$	8.41915	−	25.9115i	0.335161	−	1.03152i	0.966643	−	0.256129i	$-0.0824472\pi$
$632$	1.22498	−	1.68603i	0.0487269	−	0.0670668i
$633$		0			0
$634$	−0.240680	−	0.0782016i	−0.00955861	−	0.00310578i
$635$	−9.16763	−	28.2151i	−0.363806	−	1.11968i
$636$		0			0
$637$		−	2.07805i		−	0.0823353i
$638$	3.02687	−	0.00855102i	0.119835	−	0.000338538i
$639$		0			0
$640$	−0.943712	−	1.29891i	−0.0373035	−	0.0513438i
$641$	−24.9374	+	8.10265i	−0.984968	+	0.320036i	−0.756843	−	0.653596i	$-0.773259\pi$
$641$	−24.9374	+	8.10265i	−0.984968	+	0.320036i	−0.228125	+	0.973632i	$0.573259\pi$
$642$		0			0
$643$	13.9281	+	10.1194i	0.549273	+	0.399070i	0.827517	−	0.561440i	$-0.189753\pi$
$643$	13.9281	+	10.1194i	0.549273	+	0.399070i	−0.278245	+	0.960510i	$0.589753\pi$
$644$	−0.462083	−	0.335723i	−0.0182086	−	0.0132293i
$645$		0			0
$646$	−35.2285	+	11.4464i	−1.38605	+	0.450353i
$647$	−27.7069	−	38.1352i	−1.08927	−	1.49925i	−0.848889	−	0.528571i	$-0.822728\pi$
$647$	−27.7069	−	38.1352i	−1.08927	−	1.49925i	−0.240379	−	0.970679i	$-0.577272\pi$
$648$		0			0
$649$	−5.17210	+	7.16125i	−0.203023	+	0.281104i
$650$			5.03355i			0.197432i
$651$		0			0
$652$	−4.62287	−	14.2277i	−0.181045	−	0.557200i
$653$	−23.4336	−	7.61404i	−0.917028	−	0.297961i	−0.187781	−	0.982211i	$-0.560130\pi$
$653$	−23.4336	−	7.61404i	−0.917028	−	0.297961i	−0.729247	+	0.684250i	$0.760130\pi$
$654$		0			0
$655$	4.44574	−	6.11904i	0.173710	−	0.239091i
$656$	−0.429183	+	1.32089i	−0.0167568	+	0.0515721i
$657$		0			0
$658$	2.15970	−	1.56912i	0.0841940	−	0.0611705i
$659$	37.5368			1.46222			0.731112	−	0.682257i	$-0.239002\pi$
$659$	37.5368			1.46222			0.731112	+	0.682257i	$0.239002\pi$
$660$		0			0
$661$	−48.6994			−1.89419			−0.947093	−	0.320958i	$-0.895995\pi$
$661$	−48.6994			−1.89419			−0.947093	+	0.320958i	$0.895995\pi$
$662$	10.3187	−	7.49701i	0.401049	−	0.291379i
$663$		0			0
$664$	1.05665	−	3.25205i	0.0410061	−	0.126204i
$665$	6.87785	−	9.46655i	0.266711	−	0.367097i
$666$		0			0
$667$	0.495756	+	0.161081i	0.0191958	+	0.00623708i
$668$	2.67790	+	8.24172i	0.103611	+	0.318882i
$669$		0			0
$670$			1.72623i			0.0666900i
$671$	15.4221	+	21.1011i	0.595364	+	0.814599i
$672$		0			0
$673$	14.8705	+	20.4675i	0.573216	+	0.788964i	0.992931	−	0.118692i	$-0.0378701\pi$
$673$	14.8705	+	20.4675i	0.573216	+	0.788964i	−0.419715	+	0.907656i	$0.637870\pi$
$674$	−17.8760	+	5.80827i	−0.688559	+	0.223726i
$675$		0			0
$676$	−7.02365	−	5.10298i	−0.270140	−	0.196269i
$677$	−31.9902	−	23.2422i	−1.22948	−	0.893271i	−0.232631	−	0.972565i	$-0.574733\pi$
$677$	−31.9902	−	23.2422i	−1.22948	−	0.893271i	−0.996851	+	0.0792943i	$0.974733\pi$
$678$		0			0
$679$	−6.41177	+	2.08331i	−0.246061	+	0.0799501i
$680$	−4.79638	−	6.60165i	−0.183933	−	0.253162i
$681$		0			0
$682$	−18.4043	−	13.2923i	−0.704738	−	0.508987i
$683$		−	24.4657i		−	0.936152i	−0.883688	−	0.468076i	$-0.844947\pi$
$683$		−	24.4657i		−	0.936152i	0.883688	−	0.468076i	$-0.155053\pi$
$684$		0			0
$685$	−1.85638	−	5.71334i	−0.0709285	−	0.218296i
$686$	0.951057	+	0.309017i	0.0363115	+	0.0117983i
$687$		0			0
$688$	4.29546	−	5.91220i	0.163763	−	0.225400i
$689$	−1.63272	+	5.02499i	−0.0622016	+	0.191437i
$690$		0			0
$691$	11.9547	−	8.68557i	0.454777	−	0.330414i	−0.336702	−	0.941611i	$-0.609312\pi$
$691$	11.9547	−	8.68557i	0.454777	−	0.330414i	0.791479	+	0.611197i	$0.209312\pi$
$692$	−16.1936			−0.615587
$693$		0			0
$694$	−13.3633			−0.507265
$695$	−17.7173	+	12.8724i	−0.672055	+	0.488277i
$696$		0			0
$697$	−2.18131	+	6.71337i	−0.0826229	+	0.254287i
$698$	−10.5432	+	14.5115i	−0.399067	+	0.549268i
$699$		0			0
$700$	−2.30369	−	0.748515i	−0.0870714	−	0.0282912i
$701$	−11.8624	−	36.5086i	−0.448035	−	1.37891i	−0.879120	−	0.476600i	$-0.841869\pi$
$701$	−11.8624	−	36.5086i	−0.448035	−	1.37891i	0.431085	−	0.902311i	$-0.358131\pi$
$702$		0			0
$703$		−	1.62903i		−	0.0614401i
$704$	1.03380	+	3.15139i	0.0389628	+	0.118772i
$705$		0			0
$706$	12.8934	+	17.7462i	0.485249	+	0.667888i
$707$	−0.399897	+	0.129934i	−0.0150397	+	0.00488668i
$708$		0			0
$709$	42.0538	+	30.5539i	1.57937	+	1.14748i	0.917417	+	0.397926i	$0.130270\pi$
$709$	42.0538	+	30.5539i	1.57937	+	1.14748i	0.661948	+	0.749550i	$0.269730\pi$
$710$	−3.53993	−	2.57191i	−0.132851	−	0.0965222i
$711$		0			0
$712$	−1.67491	+	0.544210i	−0.0627698	+	0.0203951i
$713$	−2.29805	−	3.16299i	−0.0860625	−	0.118455i
$714$		0			0
$715$	−3.38970	+	10.5336i	−0.126768	+	0.393934i
$716$			15.9461i			0.595933i
$717$		0			0
$718$	3.59087	+	11.0515i	0.134010	+	0.412440i
$719$	−32.7633	−	10.6454i	−1.22186	−	0.397008i	−0.374103	−	0.927387i	$-0.622049\pi$
$719$	−32.7633	−	10.6454i	−1.22186	−	0.397008i	−0.847760	+	0.530380i	$0.822049\pi$
$720$		0			0
$721$	6.55788	−	9.02615i	0.244228	−	0.336151i
$722$	−10.5425	+	32.4464i	−0.392350	+	1.20753i
$723$		0			0
$724$	0.0502214	−	0.0364880i	0.00186646	−	0.00135607i
$725$	2.21064			0.0821010
$726$		0			0
$727$	−49.2737			−1.82746			−0.913731	−	0.406320i	$-0.866812\pi$
$727$	−49.2737			−1.82746			−0.913731	+	0.406320i	$0.866812\pi$
$728$	−1.68118	+	1.22145i	−0.0623086	+	0.0452698i
$729$		0			0
$730$	4.39765	−	13.5346i	0.162764	−	0.500937i
$731$	21.8315	−	30.0485i	0.807468	−	1.11138i
$732$		0			0
$733$	−20.6563	−	6.71165i	−0.762959	−	0.247900i	−0.0984110	−	0.995146i	$-0.531376\pi$
$733$	−20.6563	−	6.71165i	−0.762959	−	0.247900i	−0.664548	+	0.747245i	$0.731376\pi$
$734$	7.32055	+	22.5303i	0.270206	+	0.831610i
$735$		0			0
$736$			0.571166i			0.0210535i
$737$	1.09235	−	3.39451i	0.0402372	−	0.125038i
$738$		0			0
$739$	−10.1893	−	14.0244i	−0.374819	−	0.515894i	0.579384	−	0.815055i	$-0.303293\pi$
$739$	−10.1893	−	14.0244i	−0.374819	−	0.515894i	−0.954203	+	0.299161i	$0.903293\pi$
$740$	0.341306	−	0.110897i	0.0125466	−	0.00407665i
$741$		0			0
$742$	−2.05698	−	1.49449i	−0.0755142	−	0.0548643i
$743$	−11.0479	−	8.02674i	−0.405307	−	0.294473i	0.366392	−	0.930460i	$-0.380593\pi$
$743$	−11.0479	−	8.02674i	−0.405307	−	0.294473i	−0.771699	+	0.635988i	$0.780593\pi$
$744$		0			0
$745$	−30.3809	+	9.87137i	−1.11307	+	0.361659i
$746$	−8.92703	−	12.2870i	−0.326842	−	0.449859i
$747$		0			0
$748$	5.25425	+	16.0168i	0.192114	+	0.585633i
$749$			13.9691i			0.510419i
$750$		0			0
$751$	2.82437	+	8.69251i	0.103063	+	0.317194i	0.989271	−	0.146093i	$-0.0466698\pi$
$751$	2.82437	+	8.69251i	0.103063	+	0.317194i	−0.886208	+	0.463287i	$0.846670\pi$
$752$	−2.53888	−	0.824934i	−0.0925836	−	0.0300822i
$753$		0			0
$754$	1.11474	−	1.53431i	0.0405965	−	0.0558762i
$755$	−9.81730	+	30.2146i	−0.357288	+	1.09962i
$756$		0			0
$757$	39.2757	−	28.5355i	1.42750	−	1.03714i	0.437024	−	0.899450i	$-0.356032\pi$
$757$	39.2757	−	28.5355i	1.42750	−	1.03714i	0.990475	−	0.137689i	$-0.0439676\pi$
$758$	−6.28216			−0.228178
$759$		0			0
$760$	−11.7013			−0.424451
$761$	30.8448	−	22.4100i	1.11812	−	0.812363i	0.134199	−	0.990954i	$-0.457154\pi$
$761$	30.8448	−	22.4100i	1.11812	−	0.812363i	0.983923	+	0.178591i	$0.0571540\pi$
$762$		0			0
$763$	−4.22984	+	13.0181i	−0.153130	+	0.471287i
$764$	1.51445	−	2.08446i	0.0547908	−	0.0754131i
$765$		0			0
$766$	−0.344815	−	0.112037i	−0.0124587	−	0.00404807i
$767$	1.71035	+	5.26391i	0.0617570	+	0.190069i
$768$		0			0
$769$			3.10519i			0.111976i	0.998431	+	0.0559881i	$0.0178309\pi$
$769$			3.10519i			0.111976i	−0.998431	+	0.0559881i	$0.982169\pi$
$770$	−4.31682	−	3.11776i	−0.155567	−	0.112356i
$771$		0			0
$772$	−11.9830	−	16.4931i	−0.431276	−	0.593601i
$773$	−18.3730	+	5.96974i	−0.660830	+	0.214717i	−0.620183	−	0.784457i	$-0.712942\pi$
$773$	−18.3730	+	5.96974i	−0.660830	+	0.214717i	−0.0406465	+	0.999174i	$0.512942\pi$
$774$		0			0
$775$	−13.4138	−	9.74573i	−0.481840	−	0.350077i
$776$	5.45418	+	3.96269i	0.195794	+	0.142252i
$777$		0			0
$778$	34.0858	−	11.0751i	1.22203	−	0.397063i
$779$	5.94966	+	8.18901i	0.213169	+	0.293402i
$780$		0			0
$781$	5.33354	+	7.29754i	0.190849	+	0.261127i
$782$			2.90293i			0.103809i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−17.9231	−	5.82358i	−0.639704	−	0.207852i
$786$		0			0
$787$	−6.01883	+	8.28421i	−0.214548	+	0.295300i	−0.902703	−	0.430263i	$-0.858421\pi$
$787$	−6.01883	+	8.28421i	−0.214548	+	0.295300i	0.688155	+	0.725563i	$0.258421\pi$
$788$	6.65873	−	20.4935i	0.237208	−	0.730050i
$789$		0			0
$790$	2.70699	−	1.96674i	0.0963104	−	0.0699736i
$791$	8.65605			0.307774
$792$		0			0
$793$	16.3757			0.581520
$794$	1.98278	−	1.44058i	0.0703664	−	0.0511242i
$795$		0			0
$796$	−1.52211	+	4.68457i	−0.0539498	+	0.166040i
$797$	−8.32750	+	11.4618i	−0.294975	+	0.405999i	−0.930622	−	0.365981i	$-0.880733\pi$
$797$	−8.32750	+	11.4618i	−0.294975	+	0.405999i	0.635647	+	0.771980i	$0.280733\pi$
$798$		0			0
$799$	−12.9038	−	4.19269i	−0.456503	−	0.148327i
$800$	0.748515	+	2.30369i	0.0264640	+	0.0814479i
$801$		0			0
$802$			27.6855i			0.977607i
$803$	−17.2123	+	23.8320i	−0.607409	+	0.841013i
$804$		0			0
$805$	−0.539016	−	0.741892i	−0.0189978	−	0.0261483i
$806$	−13.5282	+	4.39557i	−0.476510	+	0.154827i
$807$		0			0
$808$	0.340172	+	0.247150i	0.0119672	+	0.00869470i
$809$	4.91362	+	3.56995i	0.172754	+	0.125513i	0.670802	−	0.741636i	$-0.265950\pi$
$809$	4.91362	+	3.56995i	0.172754	+	0.125513i	−0.498049	+	0.867149i	$0.665950\pi$
$810$		0			0
$811$	−27.6825	+	8.99460i	−0.972065	+	0.315843i	−0.751649	−	0.659563i	$-0.770741\pi$
$811$	−27.6825	+	8.99460i	−0.972065	+	0.315843i	−0.220416	+	0.975406i	$0.570741\pi$
$812$	0.536436	+	0.738341i	0.0188252	+	0.0259107i
$813$		0			0
$814$	−0.741329	+	0.00209428i	−0.0259836	+	7.34045e-5i
$815$		−	24.0187i		−	0.841339i
$816$		0			0
$817$	−16.4584	−	50.6537i	−0.575806	−	1.77215i
$818$	−4.87183	−	1.58295i	−0.170340	−	0.0553467i
$819$		0			0
$820$	−1.31069	+	1.80401i	−0.0457713	+	0.0629987i
$821$	9.59243	−	29.5225i	0.334778	−	1.03034i	−0.632053	−	0.774925i	$-0.717787\pi$
$821$	9.59243	−	29.5225i	0.334778	−	1.03034i	0.966831	−	0.255416i	$-0.0822125\pi$
$822$		0			0
$823$	−27.3996	+	19.9070i	−0.955090	+	0.693914i	−0.952005	−	0.306081i	$-0.900982\pi$
$823$	−27.3996	+	19.9070i	−0.955090	+	0.693914i	−0.00308506	+	0.999995i	$0.500982\pi$
$824$	−11.1569			−0.388670
$825$		0			0
$826$	−2.66346			−0.0926736
$827$	35.5462	−	25.8258i	1.23606	−	0.898052i	0.238734	−	0.971085i	$-0.423268\pi$
$827$	35.5462	−	25.8258i	1.23606	−	0.898052i	0.997330	+	0.0730327i	$0.0232677\pi$
$828$		0			0
$829$	3.63277	−	11.1805i	0.126171	−	0.388315i	−0.867941	−	0.496667i	$-0.834557\pi$
$829$	3.63277	−	11.1805i	0.126171	−	0.388315i	0.994113	+	0.108351i	$0.0345572\pi$
$830$	3.22693	−	4.44149i	0.112008	−	0.154166i
$831$		0			0
$832$	1.97634	+	0.642153i	0.0685173	+	0.0222626i
$833$	−1.57057	−	4.83371i	−0.0544169	−	0.167478i
$834$		0			0
$835$			13.9134i			0.481492i
$836$	23.0098	+	7.40453i	0.795810	+	0.256091i
$837$		0			0
$838$	1.07724	+	1.48270i	0.0372128	+	0.0512190i
$839$	−15.0733	+	4.89763i	−0.520390	+	0.169085i	−0.557422	−	0.830229i	$-0.688209\pi$
$839$	−15.0733	+	4.89763i	−0.520390	+	0.169085i	0.0370325	+	0.999314i	$0.488209\pi$
$840$		0			0
$841$	22.7877	+	16.5562i	0.785781	+	0.570903i
$842$	−19.0413	−	13.8343i	−0.656208	−	0.476763i
$843$		0			0
$844$	25.5175	−	8.29114i	0.878348	−	0.285393i
$845$	−8.19303	−	11.2767i	−0.281849	−	0.387932i
$846$		0			0
$847$	6.51582	+	8.86251i	0.223886	+	0.304520i
$848$			2.54257i			0.0873123i
$849$		0			0
$850$	3.80430	+	11.7084i	0.130486	+	0.401596i
$851$	−0.121419	−	0.0394513i	−0.00416218	−	0.00135237i
$852$		0			0
$853$	29.3106	−	40.3425i	1.00357	−	1.38130i	0.0804676	−	0.996757i	$-0.474359\pi$
$853$	29.3106	−	40.3425i	1.00357	−	1.38130i	0.923107	−	0.384544i	$-0.125641\pi$
$854$	−2.43516	+	7.49465i	−0.0833294	+	0.256462i
$855$		0			0
$856$	11.3012	−	8.21082i	0.386268	−	0.280640i
$857$	34.7487			1.18699			0.593497	−	0.804836i	$-0.297747\pi$
$857$	34.7487			1.18699			0.593497	+	0.804836i	$0.297747\pi$
$858$		0			0
$859$	−4.03723			−0.137749			−0.0688743	−	0.997625i	$-0.521941\pi$
$859$	−4.03723			−0.137749			−0.0688743	+	0.997625i	$0.521941\pi$
$860$	9.49226	−	6.89653i	0.323683	−	0.235170i
$861$		0			0
$862$	4.24972	−	13.0793i	0.144746	−	0.445482i
$863$	−11.2303	+	15.4572i	−0.382284	+	0.526169i	−0.956188	−	0.292754i	$-0.905428\pi$
$863$	−11.2303	+	15.4572i	−0.382284	+	0.526169i	0.573904	+	0.818923i	$0.305428\pi$
$864$		0			0
$865$	−24.7269	−	8.03426i	−0.840740	−	0.273173i
$866$	2.33873	+	7.19786i	0.0794731	+	0.244593i
$867$		0			0
$868$		−	6.84506i		−	0.232337i
$869$	−6.56766	+	2.15449i	−0.222793	+	0.0730862i
$870$		0			0
$871$	−1.31326	−	1.80755i	−0.0444982	−	0.0612466i
$872$	13.0181	−	4.22984i	0.440849	−	0.143240i
$873$		0			0
$874$	3.36770	+	2.44678i	0.113914	+	0.0827635i
$875$	−9.64081	−	7.00446i	−0.325919	−	0.236794i
$876$		0			0
$877$	−7.85467	+	2.55214i	−0.265234	+	0.0861796i	−0.438615	−	0.898675i	$-0.644531\pi$
$877$	−7.85467	+	2.55214i	−0.265234	+	0.0861796i	0.173381	+	0.984855i	$0.444531\pi$
$878$	−10.5661	−	14.5430i	−0.356588	−	0.490802i
$879$		0			0
$880$	0.0150432	+	5.32495i	0.000507105	+	0.179504i
$881$		−	23.6691i		−	0.797434i	−0.917074	−	0.398717i	$-0.869456\pi$
$881$		−	23.6691i		−	0.797434i	0.917074	−	0.398717i	$-0.130544\pi$
$882$		0			0
$883$	16.4965	+	50.7709i	0.555150	+	1.70858i	0.695547	+	0.718481i	$0.255162\pi$
$883$	16.4965	+	50.7709i	0.555150	+	1.70858i	−0.140397	+	0.990095i	$0.544838\pi$
$884$	10.0447	+	3.26372i	0.337839	+	0.109771i
$885$		0			0
$886$	−18.9650	+	26.1031i	−0.637141	+	0.876950i
$887$	10.9917	−	33.8289i	0.369064	−	1.13586i	−0.578333	−	0.815801i	$-0.696296\pi$
$887$	10.9917	−	33.8289i	0.369064	−	1.13586i	0.947397	−	0.320062i	$-0.103704\pi$
$888$		0			0
$889$	−14.9490	+	10.8611i	−0.501373	+	0.364269i
$890$	−2.82751			−0.0947785
$891$		0			0
$892$	4.42446			0.148142
$893$	−15.7401	+	11.4359i	−0.526722	+	0.382686i
$894$		0			0
$895$	−7.91147	+	24.3490i	−0.264451	+	0.813897i
$896$	−0.587785	+	0.809017i	−0.0196365	+	0.0270274i
$897$		0			0
$898$	−4.27898	−	1.39032i	−0.142791	−	0.0463957i
$899$	1.93045	+	5.94132i	0.0643842	+	0.198154i
$900$		0			0
$901$			12.9225i			0.430512i
$902$	3.71895	−	2.71806i	0.123827	−	0.0905015i
$903$		0			0
$904$	−5.08790	−	7.00289i	−0.169221	−	0.232913i
$905$	0.0947891	−	0.0307988i	0.00315090	−	0.00102379i
$906$		0			0
$907$	−2.90705	−	2.11209i	−0.0965270	−	0.0701309i	0.538475	−	0.842642i	$-0.319001\pi$
$907$	−2.90705	−	2.11209i	−0.0965270	−	0.0701309i	−0.635002	+	0.772511i	$0.719001\pi$
$908$	−23.9996	−	17.4367i	−0.796454	−	0.578658i
$909$		0			0
$910$	−3.17309	+	1.03100i	−0.105187	+	0.0341773i
$911$	−19.8449	−	27.3141i	−0.657490	−	0.904957i	0.341905	−	0.939734i	$-0.388928\pi$
$911$	−19.8449	−	27.3141i	−0.657490	−	0.904957i	−0.999395	+	0.0347774i	$0.988928\pi$
$912$		0			0
$913$	−9.15609	+	6.69189i	−0.303022	+	0.221469i
$914$		−	33.9477i		−	1.12289i
$915$		0			0
$916$	−5.37840	−	16.5530i	−0.177707	−	0.546927i
$917$	−4.48034	−	1.45575i	−0.147954	−	0.0480732i
$918$		0			0
$919$	−4.21408	+	5.80018i	−0.139010	+	0.191330i	−0.872846	−	0.487996i	$-0.837728\pi$
$919$	−4.21408	+	5.80018i	−0.139010	+	0.191330i	0.733836	+	0.679327i	$0.237728\pi$
$920$	−0.283378	+	0.872147i	−0.00934268	+	0.0287538i
$921$		0			0
$922$	13.5573	−	9.84998i	0.446487	−	0.324392i
$923$	5.66334			0.186411
$924$		0			0
$925$	−0.541420			−0.0178018
$926$	−1.76823	+	1.28470i	−0.0581078	+	0.0422178i
$927$		0			0
$928$	0.282021	−	0.867972i	0.00925780	−	0.0284926i
$929$	−4.89101	+	6.73190i	−0.160469	+	0.220866i	−0.881679	−	0.471850i	$-0.843586\pi$
$929$	−4.89101	+	6.73190i	−0.160469	+	0.220866i	0.721210	+	0.692717i	$0.243586\pi$
$930$		0			0
$931$	−6.93138	−	2.25214i	−0.227167	−	0.0738109i
$932$	4.43273	+	13.6426i	0.145199	+	0.446877i
$933$		0			0
$934$			27.1217i			0.887449i
$935$	0.0764563	+	27.0638i	0.00250039	+	0.885082i
$936$		0			0
$937$	−29.1895	−	40.1759i	−0.953579	−	1.31249i	−0.949919	−	0.312495i	$-0.898835\pi$
$937$	−29.1895	−	40.1759i	−0.953579	−	1.31249i	−0.00365967	−	0.999993i	$-0.501165\pi$
$938$	1.02255	−	0.332246i	0.0333874	−	0.0108482i
$939$		0			0
$940$	−3.46749	−	2.51928i	−0.113097	−	0.0821698i
$941$	41.2711	+	29.9852i	1.34540	+	0.977490i	0.999227	+	0.0393198i	$0.0125191\pi$
$941$	41.2711	+	29.9852i	1.34540	+	0.977490i	0.346173	+	0.938171i	$0.387481\pi$
$942$		0			0
$943$	0.754448	−	0.245135i	0.0245682	−	0.00798269i
$944$	1.56554	+	2.15478i	0.0509540	+	0.0701322i
$945$		0			0
$946$	−23.0300	+	7.55489i	−0.748769	+	0.245631i
$947$		−	38.0125i		−	1.23524i	−0.786477	−	0.617620i	$-0.788097\pi$
$947$		−	38.0125i		−	1.23524i	0.786477	−	0.617620i	$-0.211903\pi$
$948$		0			0
$949$	5.69188	+	17.5178i	0.184766	+	0.568652i
$950$	16.7895	+	5.45524i	0.544723	+	0.176991i
$951$		0			0
$952$	−2.98740	+	4.11180i	−0.0968221	+	0.133264i
$953$	−12.1404	+	37.3644i	−0.393267	+	1.21035i	0.537035	+	0.843560i	$0.319544\pi$
$953$	−12.1404	+	37.3644i	−0.393267	+	1.21035i	−0.930303	+	0.366793i	$0.880456\pi$
$954$		0			0
$955$	3.34668	−	2.43150i	0.108296	−	0.0786816i
$956$	22.8535			0.739136
$957$		0			0
$958$	18.3969			0.594376
$959$	−3.02706	+	2.19929i	−0.0977488	+	0.0710187i
$960$		0			0
$961$	4.89942	−	15.0789i	0.158046	−	0.486415i
$962$	−0.273018	+	0.375777i	−0.00880244	+	0.0121155i
$963$		0			0
$964$	6.16974	+	2.00467i	0.198714	+	0.0645660i
$965$	−10.1146	−	31.1295i	−0.325601	−	1.00210i
$966$		0			0
$967$		−	34.4093i		−	1.10653i	−0.833005	−	0.553265i	$-0.813382\pi$
$967$		−	34.4093i		−	1.10653i	0.833005	−	0.553265i	$-0.186618\pi$
$968$	3.34002	−	10.4807i	0.107352	−	0.336861i
$969$		0			0
$970$	6.36225	+	8.75689i	0.204280	+	0.281167i
$971$	−23.3026	+	7.57148i	−0.747816	+	0.242980i	−0.658041	−	0.752982i	$-0.728615\pi$
$971$	−23.3026	+	7.57148i	−0.747816	+	0.242980i	−0.0897751	+	0.995962i	$0.528615\pi$
$972$		0			0
$973$	11.0351	+	8.01748i	0.353769	+	0.257028i
$974$	−0.514133	−	0.373539i	−0.0164739	−	0.0119690i
$975$		0			0
$976$	7.49465	−	2.43516i	0.239898	−	0.0779476i
$977$	32.2052	+	44.3266i	1.03033	+	1.41813i	0.904696	+	0.426058i	$0.140098\pi$
$977$	32.2052	+	44.3266i	1.03033	+	1.41813i	0.125638	+	0.992076i	$0.459902\pi$
$978$		0			0
$979$	5.56011	+	1.78924i	0.177702	+	0.0571844i
$980$		−	1.60554i		−	0.0512870i
$981$		0			0
$982$	−8.69472	−	26.7596i	−0.277460	−	0.853933i
$983$	2.39431	+	0.777960i	0.0763668	+	0.0248131i	0.346951	−	0.937883i	$-0.387217\pi$
$983$	2.39431	+	0.777960i	0.0763668	+	0.0248131i	−0.270584	+	0.962696i	$0.587217\pi$
$984$		0			0
$985$	20.3352	−	27.9890i	0.647934	−	0.891804i
$986$	1.43336	−	4.41143i	0.0456475	−	0.140489i
$987$		0			0
$988$	12.2526	−	8.90200i	0.389806	−	0.283210i
$989$	−4.17401			−0.132726
$990$		0			0
$991$	−5.02938			−0.159764			−0.0798818	−	0.996804i	$-0.525454\pi$
$991$	−5.02938			−0.159764			−0.0798818	+	0.996804i	$0.525454\pi$
$992$	−5.53777	+	4.02343i	−0.175824	+	0.127744i
$993$		0			0
$994$	−0.842169	+	2.59193i	−0.0267120	+	0.0822110i
$995$	−4.64840	+	6.39797i	−0.147364	+	0.202829i
$996$		0			0
$997$	0.00314762	+	0.00102272i	9.96861e−5	+	3.23900e-5i	0.309067	−	0.951040i	$-0.399983\pi$
$997$	0.00314762	+	0.00102272i	9.96861e−5	+	3.23900e-5i	−0.308967	+	0.951073i	$0.599983\pi$
$998$	4.34898	+	13.3848i	0.137664	+	0.423688i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.8	✓	48
3.2	odd	2		1386.2.bu.b.701.5	yes	48
11.7	odd	10		1386.2.bu.b.953.5	yes	48
33.29	even	10	inner	1386.2.bu.a.953.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.8	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.8	yes	48	33.29	even	10	inner
1386.2.bu.b.701.5	yes	48	3.2	odd	2
1386.2.bu.b.953.5	yes	48	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.943712 - 1.29891i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.943712 - 1.29891i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +1.60554i q^{10} +(1.01598 - 3.15718i) q^{11} +(-1.22145 - 1.68118i) q^{13} +(0.951057 - 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.11180 - 2.98740i) q^{17} +(-6.93138 + 2.25214i) q^{19} +(-0.943712 - 1.29891i) q^{20} +(1.03380 + 3.15139i) q^{22} +0.571166i q^{23} +(0.748515 + 2.30369i) q^{25} +(1.97634 + 0.642153i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(0.282021 - 0.867972i) q^{29} +(-5.53777 + 4.02343i) q^{31} +1.00000 q^{32} +5.08246 q^{34} +(-1.29891 + 0.943712i) q^{35} +(-0.0690715 + 0.212580i) q^{37} +(4.28383 - 5.89618i) q^{38} +(1.52696 + 0.496139i) q^{40} +(-0.429183 - 1.32089i) q^{41} +7.30788i q^{43} +(-2.68870 - 1.94188i) q^{44} +(-0.335723 - 0.462083i) q^{46} +(2.53888 - 0.824934i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-1.95964 - 1.42376i) q^{50} +(-1.97634 + 0.642153i) q^{52} +(-1.49449 - 2.05698i) q^{53} +(-3.14210 - 4.29913i) q^{55} -1.00000i q^{56} +(0.282021 + 0.867972i) q^{58} +(-2.53310 - 0.823054i) q^{59} +(-4.63195 + 6.37533i) q^{61} +(2.11524 - 6.51004i) q^{62} +(-0.809017 + 0.587785i) q^{64} -3.33639 q^{65} +1.07517 q^{67} +(-4.11180 + 2.98740i) q^{68} +(0.496139 - 1.52696i) q^{70} +(-1.60190 + 2.20483i) q^{71} +(-8.42993 - 2.73905i) q^{73} +(-0.0690715 - 0.212580i) q^{74} +7.28808i q^{76} +(-1.94188 + 2.68870i) q^{77} +(-1.22498 - 1.68603i) q^{79} +(-1.52696 + 0.496139i) q^{80} +(1.12362 + 0.816355i) q^{82} +(-2.76635 - 2.00987i) q^{83} +(-7.76070 + 2.52161i) q^{85} +(-4.29546 - 5.91220i) q^{86} +(3.31661 - 0.00936955i) q^{88} +1.76110i q^{89} +(0.642153 + 1.97634i) q^{91} +(0.543211 + 0.176500i) q^{92} +(-1.56912 + 2.15970i) q^{94} +(-3.61590 + 11.1286i) q^{95} +(5.45418 - 3.96269i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more