LMFDB - Embedded newform 1386.2.k.s.793.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("1386.793");

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.k (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1386.793
Dual form			1386.2.k.s.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(-0.822876 - 1.42526i) q^{10} +(0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(2.82288 - 4.88936i) q^{19} +1.64575 q^{20} -1.00000 q^{22} +(0.822876 - 1.42526i) q^{23} +(1.14575 + 1.98450i) q^{25} +(-2.50000 + 4.33013i) q^{26} +2.64575 q^{28} -6.29150 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(-2.17712 - 3.77089i) q^{35} +(-1.82288 + 3.15731i) q^{37} +(2.82288 + 4.88936i) q^{38} +(-0.822876 + 1.42526i) q^{40} -10.9373 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.822876 + 1.42526i) q^{46} +(1.35425 - 2.34563i) q^{47} +(-3.50000 - 6.06218i) q^{49} -2.29150 q^{50} +(-2.50000 - 4.33013i) q^{52} +(0.822876 + 1.42526i) q^{53} -1.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +(3.14575 - 5.44860i) q^{58} +(2.32288 + 4.02334i) q^{59} +(-7.14575 + 12.3768i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-4.11438 + 7.12631i) q^{65} +(5.96863 + 10.3380i) q^{67} +(3.00000 - 5.19615i) q^{68} +4.35425 q^{70} -4.35425 q^{71} +(-0.177124 - 0.306788i) q^{73} +(-1.82288 - 3.15731i) q^{74} -5.64575 q^{76} -2.64575 q^{77} +(1.32288 - 2.29129i) q^{79} +(-0.822876 - 1.42526i) q^{80} +(5.46863 - 9.47194i) q^{82} -2.70850 q^{83} -9.87451 q^{85} +(2.00000 - 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.29150 - 5.70105i) q^{89} +(-6.61438 + 11.4564i) q^{91} -1.64575 q^{92} +(1.35425 + 2.34563i) q^{94} +(4.64575 + 8.04668i) q^{95} -16.2915 q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} + 2 q^{11} + 20 q^{13} - 2 q^{16} + 12 q^{17} + 6 q^{19} - 4 q^{20} - 4 q^{22} - 2 q^{23} - 6 q^{25} - 10 q^{26} - 4 q^{29} + 8 q^{31} - 2 q^{32} - 24 q^{34} - 14 q^{35} - 2 q^{37} + 6 q^{38} + 2 q^{40} - 12 q^{41} - 16 q^{43} + 2 q^{44} - 2 q^{46} + 16 q^{47} - 14 q^{49} + 12 q^{50} - 10 q^{52} - 2 q^{53} + 4 q^{55} + 2 q^{58} + 4 q^{59} - 18 q^{61} - 16 q^{62} + 4 q^{64} + 10 q^{65} + 8 q^{67} + 12 q^{68} + 28 q^{70} - 28 q^{71} - 6 q^{73} - 2 q^{74} - 12 q^{76} + 2 q^{80} + 6 q^{82} - 32 q^{83} + 24 q^{85} + 8 q^{86} + 2 q^{88} - 8 q^{89} + 4 q^{92} + 16 q^{94} + 8 q^{95} - 44 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 + 2 * q^11 + 20 * q^13 - 2 * q^16 + 12 * q^17 + 6 * q^19 - 4 * q^20 - 4 * q^22 - 2 * q^23 - 6 * q^25 - 10 * q^26 - 4 * q^29 + 8 * q^31 - 2 * q^32 - 24 * q^34 - 14 * q^35 - 2 * q^37 + 6 * q^38 + 2 * q^40 - 12 * q^41 - 16 * q^43 + 2 * q^44 - 2 * q^46 + 16 * q^47 - 14 * q^49 + 12 * q^50 - 10 * q^52 - 2 * q^53 + 4 * q^55 + 2 * q^58 + 4 * q^59 - 18 * q^61 - 16 * q^62 + 4 * q^64 + 10 * q^65 + 8 * q^67 + 12 * q^68 + 28 * q^70 - 28 * q^71 - 6 * q^73 - 2 * q^74 - 12 * q^76 + 2 * q^80 + 6 * q^82 - 32 * q^83 + 24 * q^85 + 8 * q^86 + 2 * q^88 - 8 * q^89 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 44 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.822876	+	1.42526i	−0.368001	+	0.637397i	−0.989253	−	0.146214i	$-0.953291\pi$
$5$	−0.822876	+	1.42526i	−0.368001	+	0.637397i	0.621252	+	0.783611i	$0.286624\pi$
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.822876	−	1.42526i	−0.260216	−	0.450708i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	2.82288	−	4.88936i	0.647612	−	1.12170i	−0.336080	−	0.941834i	$-0.609101\pi$
$19$	2.82288	−	4.88936i	0.647612	−	1.12170i	0.983692	−	0.179863i	$-0.0575656\pi$
$20$	1.64575			0.368001
$21$		0			0
$22$	−1.00000			−0.213201
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	−0.767391	−	0.641179i	$-0.778446\pi$
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	0.938973	+	0.343991i	$0.111779\pi$
$24$		0			0
$25$	1.14575	+	1.98450i	0.229150	+	0.396900i
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$		0			0
$28$	2.64575			0.500000
$29$	−6.29150			−1.16830			−0.584151	−	0.811645i	$-0.698573\pi$
$29$	−6.29150			−1.16830			−0.584151	+	0.811645i	$0.698573\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$	−2.17712	−	3.77089i	−0.368001	−	0.637397i
$36$		0			0
$37$	−1.82288	+	3.15731i	−0.299679	+	0.519059i	−0.976062	−	0.217491i	$-0.930213\pi$
$37$	−1.82288	+	3.15731i	−0.299679	+	0.519059i	0.676384	+	0.736550i	$0.263546\pi$
$38$	2.82288	+	4.88936i	0.457931	+	0.793160i
$39$		0			0
$40$	−0.822876	+	1.42526i	−0.130108	+	0.225354i
$41$	−10.9373			−1.70811			−0.854056	−	0.520181i	$-0.825864\pi$
$41$	−10.9373			−1.70811			−0.854056	+	0.520181i	$0.825864\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	0.822876	+	1.42526i	0.121326	+	0.210143i
$47$	1.35425	−	2.34563i	0.197537	−	0.342145i	−0.750192	−	0.661220i	$-0.770039\pi$
$47$	1.35425	−	2.34563i	0.197537	−	0.342145i	0.947729	+	0.319075i	$0.103372\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	−2.29150			−0.324067
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	0.822876	+	1.42526i	0.113031	+	0.195775i	0.916991	−	0.398908i	$-0.130611\pi$
$53$	0.822876	+	1.42526i	0.113031	+	0.195775i	−0.803960	+	0.594683i	$0.797278\pi$
$54$		0			0
$55$	−1.64575			−0.221913
$56$	−1.32288	+	2.29129i	−0.176777	+	0.306186i
$57$		0			0
$58$	3.14575	−	5.44860i	0.413057	−	0.715436i
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	0.976682	−	0.214692i	$-0.0688746\pi$
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	−0.674269	+	0.738486i	$0.735541\pi$
$60$		0			0
$61$	−7.14575	+	12.3768i	−0.914920	+	1.58469i	−0.107901	+	0.994162i	$0.534413\pi$
$61$	−7.14575	+	12.3768i	−0.914920	+	1.58469i	−0.807019	+	0.590526i	$0.798920\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.11438	+	7.12631i	−0.510326	+	0.883910i
$66$		0			0
$67$	5.96863	+	10.3380i	0.729184	+	1.26298i	0.957229	+	0.289333i	$0.0934334\pi$
$67$	5.96863	+	10.3380i	0.729184	+	1.26298i	−0.228045	+	0.973651i	$0.573233\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$	4.35425			0.520432
$71$	−4.35425			−0.516754			−0.258377	−	0.966044i	$-0.583188\pi$
$71$	−4.35425			−0.516754			−0.258377	+	0.966044i	$0.583188\pi$
$72$		0			0
$73$	−0.177124	−	0.306788i	−0.0207308	−	0.0359069i	0.855474	−	0.517846i	$-0.173266\pi$
$73$	−0.177124	−	0.306788i	−0.0207308	−	0.0359069i	−0.876205	+	0.481939i	$0.839933\pi$
$74$	−1.82288	−	3.15731i	−0.211905	−	0.367030i
$75$		0			0
$76$	−5.64575			−0.647612
$77$	−2.64575			−0.301511
$78$		0			0
$79$	1.32288	−	2.29129i	0.148835	−	0.257790i	−0.781962	−	0.623326i	$-0.785781\pi$
$79$	1.32288	−	2.29129i	0.148835	−	0.257790i	0.930797	+	0.365536i	$0.119114\pi$
$80$	−0.822876	−	1.42526i	−0.0920003	−	0.159349i
$81$		0			0
$82$	5.46863	−	9.47194i	0.603909	−	1.04600i
$83$	−2.70850			−0.297296			−0.148648	−	0.988890i	$-0.547492\pi$
$83$	−2.70850			−0.297296			−0.148648	+	0.988890i	$0.547492\pi$
$84$		0			0
$85$	−9.87451			−1.07104
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	3.29150	−	5.70105i	0.348899	−	0.604310i	−0.637156	−	0.770735i	$-0.719889\pi$
$89$	3.29150	−	5.70105i	0.348899	−	0.604310i	0.986054	+	0.166425i	$0.0532224\pi$
$90$		0			0
$91$	−6.61438	+	11.4564i	−0.693375	+	1.20096i
$92$	−1.64575			−0.171581
$93$		0			0
$94$	1.35425	+	2.34563i	0.139680	+	0.241933i
$95$	4.64575	+	8.04668i	0.476644	+	0.825572i
$96$		0			0
$97$	−16.2915			−1.65415			−0.827076	−	0.562090i	$-0.809997\pi$
$97$	−16.2915			−1.65415			−0.827076	+	0.562090i	$0.809997\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	1.14575	−	1.98450i	0.114575	−	0.198450i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	1.46863	−	2.54374i	0.144708	−	0.250642i	−0.784556	−	0.620058i	$-0.787109\pi$
$103$	1.46863	−	2.54374i	0.144708	−	0.250642i	0.929264	+	0.369416i	$0.120442\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	−1.64575			−0.159849
$107$	−5.46863	+	9.47194i	−0.528672	+	0.915687i	0.470769	+	0.882257i	$0.343977\pi$
$107$	−5.46863	+	9.47194i	−0.528672	+	0.915687i	−0.999441	+	0.0334304i	$0.989357\pi$
$108$		0			0
$109$	5.29150	+	9.16515i	0.506834	+	0.877862i	0.999969	+	0.00790932i	$0.00251764\pi$
$109$	5.29150	+	9.16515i	0.506834	+	0.877862i	−0.493135	+	0.869953i	$0.664149\pi$
$110$	0.822876	−	1.42526i	0.0784581	−	0.135893i
$111$		0			0
$112$	−1.32288	−	2.29129i	−0.125000	−	0.216506i
$113$	18.2915			1.72072			0.860360	−	0.509687i	$-0.170239\pi$
$113$	18.2915			1.72072			0.860360	+	0.509687i	$0.170239\pi$
$114$		0			0
$115$	1.35425	+	2.34563i	0.126284	+	0.218731i
$116$	3.14575	+	5.44860i	0.292076	+	0.505890i
$117$		0			0
$118$	−4.64575			−0.427676
$119$	−15.8745			−1.45521
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−7.14575	−	12.3768i	−0.646946	−	1.12054i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	15.9373			1.41420			0.707101	−	0.707112i	$-0.250002\pi$
$127$	15.9373			1.41420			0.707101	+	0.707112i	$0.250002\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.11438	−	7.12631i	−0.360855	−	0.625019i
$131$	5.17712	−	8.96704i	0.452327	−	0.783454i	−0.546203	−	0.837653i	$-0.683927\pi$
$131$	5.17712	−	8.96704i	0.452327	−	0.783454i	0.998530	+	0.0541989i	$0.0172605\pi$
$132$		0			0
$133$	7.46863	+	12.9360i	0.647612	+	1.12170i
$134$	−11.9373			−1.03122
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−6.43725	−	11.1497i	−0.549972	−	0.952579i	−0.998276	−	0.0586978i	$-0.981305\pi$
$137$	−6.43725	−	11.1497i	−0.549972	−	0.952579i	0.448304	−	0.893881i	$-0.352028\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.17712	+	3.77089i	−0.184001	+	0.318698i
$141$		0			0
$142$	2.17712	−	3.77089i	0.182700	−	0.316446i
$143$	2.50000	+	4.33013i	0.209061	+	0.362103i
$144$		0			0
$145$	5.17712	−	8.96704i	0.429937	−	0.744672i
$146$	0.354249			0.0293178
$147$		0			0
$148$	3.64575			0.299679
$149$	−7.64575	+	13.2428i	−0.626364	+	1.08489i	0.361911	+	0.932213i	$0.382124\pi$
$149$	−7.64575	+	13.2428i	−0.626364	+	1.08489i	−0.988275	+	0.152682i	$0.951209\pi$
$150$		0			0
$151$	4.32288	+	7.48744i	0.351791	+	0.609319i	0.986563	−	0.163380i	$-0.0522396\pi$
$151$	4.32288	+	7.48744i	0.351791	+	0.609319i	−0.634773	+	0.772699i	$0.718906\pi$
$152$	2.82288	−	4.88936i	0.228965	−	0.396580i
$153$		0			0
$154$	1.32288	−	2.29129i	0.106600	−	0.184637i
$155$	−6.58301			−0.528760
$156$		0			0
$157$	−10.5830	−	18.3303i	−0.844616	−	1.46292i	−0.885954	−	0.463772i	$-0.846496\pi$
$157$	−10.5830	−	18.3303i	−0.844616	−	1.46292i	0.0413387	−	0.999145i	$-0.486838\pi$
$158$	1.32288	+	2.29129i	0.105242	+	0.182285i
$159$		0			0
$160$	1.64575			0.130108
$161$	2.17712	+	3.77089i	0.171581	+	0.297188i
$162$		0			0
$163$	−0.322876	+	0.559237i	−0.0252896	+	0.0438028i	−0.878393	−	0.477939i	$-0.841384\pi$
$163$	−0.322876	+	0.559237i	−0.0252896	+	0.0438028i	0.853104	+	0.521741i	$0.174717\pi$
$164$	5.46863	+	9.47194i	0.427028	+	0.739634i
$165$		0			0
$166$	1.35425	−	2.34563i	0.105110	−	0.182056i
$167$	11.2288			0.868907			0.434454	−	0.900694i	$-0.356941\pi$
$167$	11.2288			0.868907			0.434454	+	0.900694i	$0.356941\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	4.93725	−	8.55157i	0.378670	−	0.655876i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−0.145751	+	0.252449i	−0.0110813	+	0.0191933i	−0.871513	−	0.490373i	$-0.836861\pi$
$173$	−0.145751	+	0.252449i	−0.0110813	+	0.0191933i	0.860432	+	0.509566i	$0.170194\pi$
$174$		0			0
$175$	−6.06275			−0.458301
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	3.29150	+	5.70105i	0.246709	+	0.427312i
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	−0.950153	−	0.311785i	$-0.899073\pi$
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	0.205062	−	0.978749i	$-0.434260\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−6.61438	−	11.4564i	−0.490290	−	0.849208i
$183$		0			0
$184$	0.822876	−	1.42526i	0.0606632	−	0.105072i
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−2.70850			−0.197537
$189$		0			0
$190$	−9.29150			−0.674076
$191$	−1.35425	+	2.34563i	−0.0979900	+	0.169724i	−0.910853	−	0.412732i	$-0.864575\pi$
$191$	−1.35425	+	2.34563i	−0.0979900	+	0.169724i	0.812863	+	0.582456i	$0.197908\pi$
$192$		0			0
$193$	−12.7601	−	22.1012i	−0.918494	−	1.59088i	−0.801703	−	0.597722i	$-0.796073\pi$
$193$	−12.7601	−	22.1012i	−0.918494	−	1.59088i	−0.116791	−	0.993157i	$-0.537261\pi$
$194$	8.14575	−	14.1089i	0.584831	−	1.01296i
$195$		0			0
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	12.8745			0.917271			0.458635	−	0.888625i	$-0.348338\pi$
$197$	12.8745			0.917271			0.458635	+	0.888625i	$0.348338\pi$
$198$		0			0
$199$	−2.11438	−	3.66221i	−0.149884	−	0.259607i	0.781300	−	0.624155i	$-0.214557\pi$
$199$	−2.11438	−	3.66221i	−0.149884	−	0.259607i	−0.931185	+	0.364548i	$0.881223\pi$
$200$	1.14575	+	1.98450i	0.0810169	+	0.140325i
$201$		0			0
$202$	−3.00000			−0.211079
$203$	8.32288	−	14.4156i	0.584151	−	1.01178i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	1.46863	+	2.54374i	0.102324	+	0.177231i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	5.64575			0.390525
$210$		0			0
$211$	0.937254			0.0645232			0.0322616	−	0.999479i	$-0.489729\pi$
$211$	0.937254			0.0645232			0.0322616	+	0.999479i	$0.489729\pi$
$212$	0.822876	−	1.42526i	0.0565153	−	0.0978874i
$213$		0			0
$214$	−5.46863	−	9.47194i	−0.373828	−	0.647488i
$215$	3.29150	−	5.70105i	0.224479	−	0.388808i
$216$		0			0
$217$	−10.5830			−0.718421
$218$	−10.5830			−0.716772
$219$		0			0
$220$	0.822876	+	1.42526i	0.0554783	+	0.0960912i
$221$	15.0000	+	25.9808i	1.00901	+	1.74766i
$222$		0			0
$223$	−17.6458			−1.18165			−0.590823	−	0.806801i	$-0.701197\pi$
$223$	−17.6458			−1.18165			−0.590823	+	0.806801i	$0.701197\pi$
$224$	2.64575			0.176777
$225$		0			0
$226$	−9.14575	+	15.8409i	−0.608366	+	1.05372i
$227$	−1.35425	−	2.34563i	−0.0898846	−	0.155685i	0.817578	−	0.575818i	$-0.195317\pi$
$227$	−1.35425	−	2.34563i	−0.0898846	−	0.155685i	−0.907462	+	0.420134i	$0.861983\pi$
$228$		0			0
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$	−2.70850			−0.178593
$231$		0			0
$232$	−6.29150			−0.413057
$233$	0.531373	−	0.920365i	0.0348114	−	0.0602951i	−0.848095	−	0.529845i	$-0.822250\pi$
$233$	0.531373	−	0.920365i	0.0348114	−	0.0602951i	0.882906	+	0.469549i	$0.155584\pi$
$234$		0			0
$235$	2.22876	+	3.86032i	0.145388	+	0.251819i
$236$	2.32288	−	4.02334i	0.151206	−	0.261897i
$237$		0			0
$238$	7.93725	−	13.7477i	0.514496	−	0.891133i
$239$	17.2288			1.11444			0.557218	−	0.830366i	$-0.311869\pi$
$239$	17.2288			1.11444			0.557218	+	0.830366i	$0.311869\pi$
$240$		0			0
$241$	12.4059	+	21.4876i	0.799133	+	1.38414i	0.920181	+	0.391492i	$0.128041\pi$
$241$	12.4059	+	21.4876i	0.799133	+	1.38414i	−0.121048	+	0.992647i	$0.538626\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$		0			0
$244$	14.2915			0.914920
$245$	11.5203			0.736002
$246$		0			0
$247$	14.1144	−	24.4468i	0.898076	−	1.55551i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	3.29150			0.207758			0.103879	−	0.994590i	$-0.466875\pi$
$251$	3.29150			0.207758			0.103879	+	0.994590i	$0.466875\pi$
$252$		0			0
$253$	1.64575			0.103467
$254$	−7.96863	+	13.8021i	−0.499996	+	0.866019i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.7915	+	18.6914i	−0.673155	+	1.16594i	0.303849	+	0.952720i	$0.401728\pi$
$257$	−10.7915	+	18.6914i	−0.673155	+	1.16594i	−0.977004	+	0.213219i	$0.931605\pi$
$258$		0			0
$259$	−4.82288	−	8.35347i	−0.299679	−	0.519059i
$260$	8.22876			0.510326
$261$		0			0
$262$	5.17712	+	8.96704i	0.319844	+	0.553986i
$263$	9.96863	+	17.2662i	0.614692	+	1.06468i	0.990438	+	0.137955i	$0.0440530\pi$
$263$	9.96863	+	17.2662i	0.614692	+	1.06468i	−0.375747	+	0.926722i	$0.622614\pi$
$264$		0			0
$265$	−2.70850			−0.166382
$266$	−14.9373			−0.915862
$267$		0			0
$268$	5.96863	−	10.3380i	0.364592	−	0.631492i
$269$	2.70850	+	4.69126i	0.165140	+	0.286031i	0.936705	−	0.350120i	$-0.113859\pi$
$269$	2.70850	+	4.69126i	0.165140	+	0.286031i	−0.771565	+	0.636151i	$0.780526\pi$
$270$		0			0
$271$	1.03137	−	1.78639i	0.0626514	−	0.108515i	−0.832998	−	0.553275i	$-0.813378\pi$
$271$	1.03137	−	1.78639i	0.0626514	−	0.108515i	0.895650	+	0.444760i	$0.146711\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	12.8745			0.777777
$275$	−1.14575	+	1.98450i	−0.0690914	+	0.119670i
$276$		0			0
$277$	11.1458	+	19.3050i	0.669683	+	1.15993i	0.977993	+	0.208639i	$0.0669035\pi$
$277$	11.1458	+	19.3050i	0.669683	+	1.15993i	−0.308309	+	0.951286i	$0.599763\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$		0			0
$280$	−2.17712	−	3.77089i	−0.130108	−	0.225354i
$281$	22.9373			1.36832			0.684161	−	0.729331i	$-0.260169\pi$
$281$	22.9373			1.36832			0.684161	+	0.729331i	$0.260169\pi$
$282$		0			0
$283$	1.17712	+	2.03884i	0.0699728	+	0.121196i	0.898889	−	0.438176i	$-0.144375\pi$
$283$	1.17712	+	2.03884i	0.0699728	+	0.121196i	−0.828916	+	0.559373i	$0.811042\pi$
$284$	2.17712	+	3.77089i	0.129189	+	0.223761i
$285$		0			0
$286$	−5.00000			−0.295656
$287$	14.4686	−	25.0604i	0.854056	−	1.47927i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	5.17712	+	8.96704i	0.304011	+	0.526563i
$291$		0			0
$292$	−0.177124	+	0.306788i	−0.0103654	+	0.0179534i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	−7.64575			−0.445153
$296$	−1.82288	+	3.15731i	−0.105952	+	0.183515i
$297$		0			0
$298$	−7.64575	−	13.2428i	−0.442906	−	0.767137i
$299$	4.11438	−	7.12631i	0.237941	−	0.412125i
$300$		0			0
$301$	5.29150	−	9.16515i	0.304997	−	0.528271i
$302$	−8.64575			−0.497507
$303$		0			0
$304$	2.82288	+	4.88936i	0.161903	+	0.280424i
$305$	−11.7601	−	20.3691i	−0.673383	−	1.16633i
$306$		0			0
$307$	22.2288			1.26866			0.634331	−	0.773062i	$-0.281276\pi$
$307$	22.2288			1.26866			0.634331	+	0.773062i	$0.281276\pi$
$308$	1.32288	+	2.29129i	0.0753778	+	0.130558i
$309$		0			0
$310$	3.29150	−	5.70105i	0.186945	−	0.323798i
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	0.880698	−	0.473678i	$-0.157074\pi$
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	−0.850566	+	0.525868i	$0.823741\pi$
$312$		0			0
$313$	−11.7915	+	20.4235i	−0.666495	+	1.15440i	0.312382	+	0.949956i	$0.398873\pi$
$313$	−11.7915	+	20.4235i	−0.666495	+	1.15440i	−0.978878	+	0.204447i	$0.934460\pi$
$314$	21.1660			1.19447
$315$		0			0
$316$	−2.64575			−0.148835
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$		0			0
$319$	−3.14575	−	5.44860i	−0.176128	−	0.305063i
$320$	−0.822876	+	1.42526i	−0.0460001	+	0.0796746i
$321$		0			0
$322$	−4.35425			−0.242653
$323$	33.8745			1.88483
$324$		0			0
$325$	5.72876	+	9.92250i	0.317774	+	0.550401i
$326$	−0.322876	−	0.559237i	−0.0178824	−	0.0309733i
$327$		0			0
$328$	−10.9373			−0.603909
$329$	3.58301	+	6.20595i	0.197537	+	0.342145i
$330$		0			0
$331$	10.3229	−	17.8797i	0.567397	−	0.982760i	−0.429426	−	0.903102i	$-0.641284\pi$
$331$	10.3229	−	17.8797i	0.567397	−	0.982760i	0.996822	−	0.0796575i	$-0.0253827\pi$
$332$	1.35425	+	2.34563i	0.0743241	+	0.128733i
$333$		0			0
$334$	−5.61438	+	9.72439i	−0.307205	+	0.532095i
$335$	−19.6458			−1.07336
$336$		0			0
$337$	9.06275			0.493679			0.246840	−	0.969056i	$-0.420608\pi$
$337$	9.06275			0.493679			0.246840	+	0.969056i	$0.420608\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$	4.93725	+	8.55157i	0.267760	+	0.463774i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$	18.5203			1.00000
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−0.145751	−	0.252449i	−0.00783564	−	0.0135717i
$347$	−10.4059	−	18.0235i	−0.558617	−	0.967553i	−0.997612	−	0.0690636i	$-0.977999\pi$
$347$	−10.4059	−	18.0235i	−0.558617	−	0.967553i	0.438995	−	0.898489i	$-0.355334\pi$
$348$		0			0
$349$	−1.87451			−0.100340			−0.0501701	−	0.998741i	$-0.515976\pi$
$349$	−1.87451			−0.100340			−0.0501701	+	0.998741i	$0.515976\pi$
$350$	3.03137	−	5.25049i	0.162034	−	0.280651i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	3.58301	+	6.20595i	0.190704	+	0.330309i	0.945484	−	0.325669i	$-0.105590\pi$
$353$	3.58301	+	6.20595i	0.190704	+	0.330309i	−0.754780	+	0.655978i	$0.772256\pi$
$354$		0			0
$355$	3.58301	−	6.20595i	0.190166	−	0.329377i
$356$	−6.58301			−0.348899
$357$		0			0
$358$	19.9373			1.05372
$359$	−12.9686	+	22.4623i	−0.684458	+	1.18552i	0.289149	+	0.957284i	$0.406628\pi$
$359$	−12.9686	+	22.4623i	−0.684458	+	1.18552i	−0.973607	+	0.228232i	$0.926706\pi$
$360$		0			0
$361$	−6.43725	−	11.1497i	−0.338803	−	0.586824i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$		0			0
$364$	13.2288			0.693375
$365$	0.583005			0.0305159
$366$		0			0
$367$	18.1144	+	31.3750i	0.945563	+	1.63776i	0.754620	+	0.656162i	$0.227821\pi$
$367$	18.1144	+	31.3750i	0.945563	+	1.63776i	0.190943	+	0.981601i	$0.438846\pi$
$368$	0.822876	+	1.42526i	0.0428954	+	0.0742969i
$369$		0			0
$370$	6.00000			0.311925
$371$	−4.35425			−0.226061
$372$		0			0
$373$	−10.4373	+	18.0779i	−0.540421	+	0.936036i	0.458459	+	0.888715i	$0.348402\pi$
$373$	−10.4373	+	18.0779i	−0.540421	+	0.936036i	−0.998880	+	0.0473204i	$0.984932\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	1.35425	−	2.34563i	0.0698400	−	0.120967i
$377$	−31.4575			−1.62014
$378$		0			0
$379$	6.06275			0.311422			0.155711	−	0.987803i	$-0.450233\pi$
$379$	6.06275			0.311422			0.155711	+	0.987803i	$0.450233\pi$
$380$	4.64575	−	8.04668i	0.238322	−	0.412786i
$381$		0			0
$382$	−1.35425	−	2.34563i	−0.0692894	−	0.120013i
$383$	12.0516	−	20.8740i	0.615810	−	1.06661i	−0.374432	−	0.927254i	$-0.622162\pi$
$383$	12.0516	−	20.8740i	0.615810	−	1.06661i	0.990242	−	0.139359i	$-0.0445043\pi$
$384$		0			0
$385$	2.17712	−	3.77089i	0.110957	−	0.192182i
$386$	25.5203			1.29895
$387$		0			0
$388$	8.14575	+	14.1089i	0.413538	+	0.716269i
$389$	13.4059	+	23.2197i	0.679705	+	1.17728i	0.975070	+	0.221899i	$0.0712256\pi$
$389$	13.4059	+	23.2197i	0.679705	+	1.17728i	−0.295364	+	0.955385i	$0.595441\pi$
$390$		0			0
$391$	9.87451			0.499375
$392$	−3.50000	−	6.06218i	−0.176777	−	0.306186i
$393$		0			0
$394$	−6.43725	+	11.1497i	−0.324304	+	0.561711i
$395$	2.17712	+	3.77089i	0.109543	+	0.189734i
$396$		0			0
$397$	5.58301	−	9.67005i	0.280203	−	0.485326i	−0.691232	−	0.722633i	$-0.742932\pi$
$397$	5.58301	−	9.67005i	0.280203	−	0.485326i	0.971435	+	0.237307i	$0.0762649\pi$
$398$	4.22876			0.211968
$399$		0			0
$400$	−2.29150			−0.114575
$401$	10.7915	−	18.6914i	0.538902	−	0.933406i	−0.460062	−	0.887887i	$-0.652173\pi$
$401$	10.7915	−	18.6914i	0.538902	−	0.933406i	0.998963	−	0.0455185i	$-0.0144940\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		0			0
$406$	8.32288	+	14.4156i	0.413057	+	0.715436i
$407$	−3.64575			−0.180713
$408$		0			0
$409$	−1.53137	−	2.65242i	−0.0757215	−	0.131154i	0.825678	−	0.564141i	$-0.190793\pi$
$409$	−1.53137	−	2.65242i	−0.0757215	−	0.131154i	−0.901400	+	0.432988i	$0.857459\pi$
$410$	9.00000	+	15.5885i	0.444478	+	0.769859i
$411$		0			0
$412$	−2.93725			−0.144708
$413$	−12.2915			−0.604825
$414$		0			0
$415$	2.22876	−	3.86032i	0.109405	−	0.189496i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$		0			0
$418$	−2.82288	+	4.88936i	−0.138071	+	0.239147i
$419$	9.87451			0.482401			0.241201	−	0.970475i	$-0.422459\pi$
$419$	9.87451			0.482401			0.241201	+	0.970475i	$0.422459\pi$
$420$		0			0
$421$	9.16601			0.446724			0.223362	−	0.974736i	$-0.428297\pi$
$421$	9.16601			0.446724			0.223362	+	0.974736i	$0.428297\pi$
$422$	−0.468627	+	0.811686i	−0.0228124	+	0.0395122i
$423$		0			0
$424$	0.822876	+	1.42526i	0.0399624	+	0.0692169i
$425$	−6.87451	+	11.9070i	−0.333463	+	0.577574i
$426$		0			0
$427$	−18.9059	−	32.7459i	−0.914920	−	1.58469i
$428$	10.9373			0.528672
$429$		0			0
$430$	3.29150	+	5.70105i	0.158730	+	0.274929i
$431$	14.6144	+	25.3128i	0.703950	+	1.21928i	0.967069	+	0.254514i	$0.0819154\pi$
$431$	14.6144	+	25.3128i	0.703950	+	1.21928i	−0.263119	+	0.964763i	$0.584751\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	5.29150	−	9.16515i	0.254000	−	0.439941i
$435$		0			0
$436$	5.29150	−	9.16515i	0.253417	−	0.438931i
$437$	−4.64575	−	8.04668i	−0.222236	−	0.384925i
$438$		0			0
$439$	−1.96863	+	3.40976i	−0.0939574	+	0.162739i	−0.909173	−	0.416419i	$-0.863285\pi$
$439$	−1.96863	+	3.40976i	−0.0939574	+	0.162739i	0.815216	+	0.579158i	$0.196618\pi$
$440$	−1.64575			−0.0784581
$441$		0			0
$442$	−30.0000			−1.42695
$443$	17.2288	−	29.8411i	0.818563	−	1.41779i	−0.0881781	−	0.996105i	$-0.528104\pi$
$443$	17.2288	−	29.8411i	0.818563	−	1.41779i	0.906741	−	0.421688i	$-0.138562\pi$
$444$		0			0
$445$	5.41699	+	9.38251i	0.256790	+	0.444774i
$446$	8.82288	−	15.2817i	0.417775	−	0.723608i
$447$		0			0
$448$	−1.32288	+	2.29129i	−0.0625000	+	0.108253i
$449$	21.8745			1.03232			0.516161	−	0.856492i	$-0.327361\pi$
$449$	21.8745			1.03232			0.516161	+	0.856492i	$0.327361\pi$
$450$		0			0
$451$	−5.46863	−	9.47194i	−0.257508	−	0.446016i
$452$	−9.14575	−	15.8409i	−0.430180	−	0.745094i
$453$		0			0
$454$	2.70850			0.127116
$455$	−10.8856	−	18.8544i	−0.510326	−	0.883910i
$456$		0			0
$457$	−1.58301	+	2.74185i	−0.0740499	+	0.128258i	−0.900673	−	0.434498i	$-0.856926\pi$
$457$	−1.58301	+	2.74185i	−0.0740499	+	0.128258i	0.826623	+	0.562756i	$0.190259\pi$
$458$	8.00000	+	13.8564i	0.373815	+	0.647467i
$459$		0			0
$460$	1.35425	−	2.34563i	0.0631422	−	0.109365i
$461$	−10.1660			−0.473478			−0.236739	−	0.971573i	$-0.576079\pi$
$461$	−10.1660			−0.473478			−0.236739	+	0.971573i	$0.576079\pi$
$462$		0			0
$463$	30.4575			1.41548			0.707740	−	0.706473i	$-0.249715\pi$
$463$	30.4575			1.41548			0.707740	+	0.706473i	$0.249715\pi$
$464$	3.14575	−	5.44860i	0.146038	−	0.252945i
$465$		0			0
$466$	0.531373	+	0.920365i	0.0246154	+	0.0426351i
$467$	10.6458	−	18.4390i	0.492627	−	0.853254i	−0.507337	−	0.861748i	$-0.669370\pi$
$467$	10.6458	−	18.4390i	0.492627	−	0.853254i	0.999964	+	0.00849322i	$0.00270351\pi$
$468$		0			0
$469$	−31.5830			−1.45837
$470$	−4.45751			−0.205610
$471$		0			0
$472$	2.32288	+	4.02334i	0.106919	+	0.185189i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$		0			0
$475$	12.9373			0.593602
$476$	7.93725	+	13.7477i	0.363803	+	0.630126i
$477$		0			0
$478$	−8.61438	+	14.9205i	−0.394012	+	0.682450i
$479$	−5.03137	−	8.71459i	−0.229889	−	0.398180i	0.727886	−	0.685698i	$-0.240503\pi$
$479$	−5.03137	−	8.71459i	−0.229889	−	0.398180i	−0.957775	+	0.287518i	$0.907170\pi$
$480$		0			0
$481$	−9.11438	+	15.7866i	−0.415580	+	0.719805i
$482$	−24.8118			−1.13014
$483$		0			0
$484$	1.00000			0.0454545
$485$	13.4059	−	23.2197i	0.608730	−	1.05435i
$486$		0			0
$487$	4.70850	+	8.15536i	0.213362	+	0.369554i	0.952765	−	0.303709i	$-0.0982252\pi$
$487$	4.70850	+	8.15536i	0.213362	+	0.369554i	−0.739402	+	0.673264i	$0.764892\pi$
$488$	−7.14575	+	12.3768i	−0.323473	+	0.560272i
$489$		0			0
$490$	−5.76013	+	9.97684i	−0.260216	+	0.450708i
$491$	−21.2915			−0.960872			−0.480436	−	0.877030i	$-0.659522\pi$
$491$	−21.2915			−0.960872			−0.480436	+	0.877030i	$0.659522\pi$
$492$		0			0
$493$	−18.8745	−	32.6916i	−0.850065	−	1.47236i
$494$	14.1144	+	24.4468i	0.635036	+	1.09991i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	5.76013	−	9.97684i	0.258377	−	0.447522i
$498$		0			0
$499$	6.93725	−	12.0157i	0.310554	−	0.537896i	−0.667928	−	0.744226i	$-0.732819\pi$
$499$	6.93725	−	12.0157i	0.310554	−	0.537896i	0.978482	+	0.206330i	$0.0661521\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	−1.64575	+	2.85052i	−0.0734535	+	0.127225i
$503$	4.06275			0.181149			0.0905744	−	0.995890i	$-0.471130\pi$
$503$	4.06275			0.181149			0.0905744	+	0.995890i	$0.471130\pi$
$504$		0			0
$505$	−4.93725			−0.219705
$506$	−0.822876	+	1.42526i	−0.0365813	+	0.0633606i
$507$		0			0
$508$	−7.96863	−	13.8021i	−0.353551	−	0.612368i
$509$	−0.291503	+	0.504897i	−0.0129206	+	0.0223792i	−0.872413	−	0.488769i	$-0.837446\pi$
$509$	−0.291503	+	0.504897i	−0.0129206	+	0.0223792i	0.859493	+	0.511148i	$0.170780\pi$
$510$		0			0
$511$	0.937254			0.0414617
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.7915	−	18.6914i	−0.475993	−	0.824444i
$515$	2.41699	+	4.18636i	0.106506	+	0.184473i
$516$		0			0
$517$	2.70850			0.119120
$518$	9.64575			0.423810
$519$		0			0
$520$	−4.11438	+	7.12631i	−0.180427	+	0.312509i
$521$	−16.9373	−	29.3362i	−0.742035	−	1.28524i	−0.951567	−	0.307440i	$-0.900528\pi$
$521$	−16.9373	−	29.3362i	−0.742035	−	1.28524i	0.209533	−	0.977802i	$-0.432806\pi$
$522$		0			0
$523$	10.7601	−	18.6371i	0.470508	−	0.814943i	−0.528923	−	0.848670i	$-0.677404\pi$
$523$	10.7601	−	18.6371i	0.470508	−	0.814943i	0.999431	+	0.0337264i	$0.0107375\pi$
$524$	−10.3542			−0.452327
$525$		0			0
$526$	−19.9373			−0.869306
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$	1.35425	−	2.34563i	0.0588248	−	0.101888i
$531$		0			0
$532$	7.46863	−	12.9360i	0.323806	−	0.560849i
$533$	−54.6863			−2.36873
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$	5.96863	+	10.3380i	0.257805	+	0.446532i
$537$		0			0
$538$	−5.41699			−0.233543
$539$	3.50000	−	6.06218i	0.150756	−	0.261116i
$540$		0			0
$541$	−1.14575	+	1.98450i	−0.0492597	+	0.0853203i	−0.889604	−	0.456733i	$-0.849020\pi$
$541$	−1.14575	+	1.98450i	−0.0492597	+	0.0853203i	0.840344	+	0.542053i	$0.182353\pi$
$542$	1.03137	+	1.78639i	0.0443013	+	0.0767320i
$543$		0			0
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−17.4170			−0.746062
$546$		0			0
$547$	−9.52026			−0.407057			−0.203528	−	0.979069i	$-0.565241\pi$
$547$	−9.52026			−0.407057			−0.203528	+	0.979069i	$0.565241\pi$
$548$	−6.43725	+	11.1497i	−0.274986	+	0.476289i
$549$		0			0
$550$	−1.14575	−	1.98450i	−0.0488550	−	0.0846193i
$551$	−17.7601	+	30.7614i	−0.756607	+	1.31048i
$552$		0			0
$553$	3.50000	+	6.06218i	0.148835	+	0.257790i
$554$	−22.2915			−0.947075
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−15.8745	−	27.4955i	−0.672624	−	1.16502i	−0.977157	−	0.212518i	$-0.931834\pi$
$557$	−15.8745	−	27.4955i	−0.672624	−	1.16502i	0.304533	−	0.952502i	$-0.401500\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	4.35425			0.184001
$561$		0			0
$562$	−11.4686	+	19.8642i	−0.483775	+	0.837923i
$563$	14.4686	+	25.0604i	0.609780	+	1.05617i	0.991276	+	0.131800i	$0.0420755\pi$
$563$	14.4686	+	25.0604i	0.609780	+	1.05617i	−0.381496	+	0.924370i	$0.624591\pi$
$564$		0			0
$565$	−15.0516	+	26.0702i	−0.633227	+	1.09678i
$566$	−2.35425			−0.0989565
$567$		0			0
$568$	−4.35425			−0.182700
$569$	0.583005	−	1.00979i	0.0244409	−	0.0423328i	−0.853546	−	0.521017i	$-0.825553\pi$
$569$	0.583005	−	1.00979i	0.0244409	−	0.0423328i	0.877987	+	0.478684i	$0.158886\pi$
$570$		0			0
$571$	14.5314	+	25.1691i	0.608119	+	1.05329i	0.991550	+	0.129724i	$0.0414090\pi$
$571$	14.5314	+	25.1691i	0.608119	+	1.05329i	−0.383431	+	0.923569i	$0.625258\pi$
$572$	2.50000	−	4.33013i	0.104530	−	0.181052i
$573$		0			0
$574$	14.4686	+	25.0604i	0.603909	+	1.04600i
$575$	3.77124			0.157272
$576$		0			0
$577$	−13.7288	−	23.7789i	−0.571536	−	0.989929i	−0.996409	−	0.0846757i	$-0.973015\pi$
$577$	−13.7288	−	23.7789i	−0.571536	−	0.989929i	0.424873	−	0.905253i	$-0.360319\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	−10.3542			−0.429937
$581$	3.58301	−	6.20595i	0.148648	−	0.257466i
$582$		0			0
$583$	−0.822876	+	1.42526i	−0.0340800	+	0.0590283i
$584$	−0.177124	−	0.306788i	−0.00732946	−	0.0126950i
$585$		0			0
$586$	6.00000	−	10.3923i	0.247858	−	0.429302i
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$		0			0
$589$	22.5830			0.930517
$590$	3.82288	−	6.62141i	0.157385	−	0.272599i
$591$		0			0
$592$	−1.82288	−	3.15731i	−0.0749197	−	0.129765i
$593$	3.53137	−	6.11652i	0.145016	−	0.251175i	−0.784363	−	0.620302i	$-0.787010\pi$
$593$	3.53137	−	6.11652i	0.145016	−	0.251175i	0.929379	+	0.369127i	$0.120343\pi$
$594$		0			0
$595$	13.0627	−	22.6253i	0.535520	−	0.927549i
$596$	15.2915			0.626364
$597$		0			0
$598$	4.11438	+	7.12631i	0.168249	+	0.291417i
$599$	21.8745	+	37.8878i	0.893768	+	1.54805i	0.835322	+	0.549761i	$0.185281\pi$
$599$	21.8745	+	37.8878i	0.893768	+	1.54805i	0.0584464	+	0.998291i	$0.481385\pi$
$600$		0			0
$601$	−3.41699			−0.139382			−0.0696911	−	0.997569i	$-0.522201\pi$
$601$	−3.41699			−0.139382			−0.0696911	+	0.997569i	$0.522201\pi$
$602$	5.29150	+	9.16515i	0.215666	+	0.373544i
$603$		0			0
$604$	4.32288	−	7.48744i	0.175895	−	0.304660i
$605$	−0.822876	−	1.42526i	−0.0334547	−	0.0579452i
$606$		0			0
$607$	−5.35425	+	9.27383i	−0.217322	+	0.376413i	−0.953988	−	0.299843i	$-0.903066\pi$
$607$	−5.35425	+	9.27383i	−0.217322	+	0.376413i	0.736666	+	0.676257i	$0.236399\pi$
$608$	−5.64575			−0.228965
$609$		0			0
$610$	23.5203			0.952307
$611$	6.77124	−	11.7281i	0.273935	−	0.474470i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−11.1144	+	19.2507i	−0.448540	+	0.776894i
$615$		0			0
$616$	−2.64575			−0.106600
$617$	5.70850			0.229815			0.114908	−	0.993376i	$-0.463343\pi$
$617$	5.70850			0.229815			0.114908	+	0.993376i	$0.463343\pi$
$618$		0			0
$619$	−6.70850	−	11.6195i	−0.269637	−	0.467025i	0.699131	−	0.714994i	$-0.253570\pi$
$619$	−6.70850	−	11.6195i	−0.269637	−	0.467025i	−0.968768	+	0.247968i	$0.920237\pi$
$620$	3.29150	+	5.70105i	0.132190	+	0.228960i
$621$		0			0
$622$	−1.06275			−0.0426122
$623$	8.70850	+	15.0836i	0.348899	+	0.604310i
$624$		0			0
$625$	4.14575	−	7.18065i	0.165830	−	0.287226i
$626$	−11.7915	−	20.4235i	−0.471283	−	0.816286i
$627$		0			0
$628$	−10.5830	+	18.3303i	−0.422308	+	0.731459i
$629$	−21.8745			−0.872194
$630$		0			0
$631$	−12.8118			−0.510028			−0.255014	−	0.966937i	$-0.582080\pi$
$631$	−12.8118			−0.510028			−0.255014	+	0.966937i	$0.582080\pi$
$632$	1.32288	−	2.29129i	0.0526212	−	0.0911425i
$633$		0			0
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−13.1144	+	22.7148i	−0.520428	+	0.901408i
$636$		0			0
$637$	−17.5000	−	30.3109i	−0.693375	−	1.20096i
$638$	6.29150			0.249083
$639$		0			0
$640$	−0.822876	−	1.42526i	−0.0325270	−	0.0563384i
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	0.964693	−	0.263376i	$-0.0848360\pi$
$641$	6.43725	+	11.1497i	0.254256	+	0.440385i	−0.710437	+	0.703761i	$0.751503\pi$
$642$		0			0
$643$	−30.5203			−1.20360			−0.601801	−	0.798646i	$-0.705550\pi$
$643$	−30.5203			−1.20360			−0.601801	+	0.798646i	$0.705550\pi$
$644$	2.17712	−	3.77089i	0.0857907	−	0.148594i
$645$		0			0
$646$	−16.9373	+	29.3362i	−0.666387	+	1.15422i
$647$	−4.40588	−	7.63121i	−0.173213	−	0.300014i	0.766328	−	0.642449i	$-0.222082\pi$
$647$	−4.40588	−	7.63121i	−0.173213	−	0.300014i	−0.939541	+	0.342435i	$0.888748\pi$
$648$		0			0
$649$	−2.32288	+	4.02334i	−0.0911808	+	0.157930i
$650$	−11.4575			−0.449401
$651$		0			0
$652$	0.645751			0.0252896
$653$	3.82288	−	6.62141i	0.149601	−	0.259116i	−0.781479	−	0.623931i	$-0.785535\pi$
$653$	3.82288	−	6.62141i	0.149601	−	0.259116i	0.931080	+	0.364815i	$0.118868\pi$
$654$		0			0
$655$	8.52026	+	14.7575i	0.332914	+	0.576624i
$656$	5.46863	−	9.47194i	0.213514	−	0.369817i
$657$		0			0
$658$	−7.16601			−0.279360
$659$	6.58301			0.256437			0.128219	−	0.991746i	$-0.459074\pi$
$659$	6.58301			0.256437			0.128219	+	0.991746i	$0.459074\pi$
$660$		0			0
$661$	−3.70850	−	6.42331i	−0.144244	−	0.249838i	0.784847	−	0.619690i	$-0.212742\pi$
$661$	−3.70850	−	6.42331i	−0.144244	−	0.249838i	−0.929091	+	0.369852i	$0.879408\pi$
$662$	10.3229	+	17.8797i	0.401210	+	0.694916i
$663$		0			0
$664$	−2.70850			−0.105110
$665$	−24.5830			−0.953288
$666$		0			0
$667$	−5.17712	+	8.96704i	−0.200459	+	0.347205i
$668$	−5.61438	−	9.72439i	−0.217227	−	0.376248i
$669$		0			0
$670$	9.82288	−	17.0137i	0.379491	−	0.657297i
$671$	−14.2915			−0.551717
$672$		0			0
$673$	0.937254			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$673$	0.937254			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$674$	−4.53137	+	7.84857i	−0.174542	+	0.302316i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−16.9373	+	29.3362i	−0.650952	+	1.12748i	0.331941	+	0.943300i	$0.392297\pi$
$677$	−16.9373	+	29.3362i	−0.650952	+	1.12748i	−0.982892	+	0.184181i	$0.941037\pi$
$678$		0			0
$679$	21.5516	−	37.3285i	0.827076	−	1.43254i
$680$	−9.87451			−0.378670
$681$		0			0
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	0.968627	+	1.67771i	0.0370635	+	0.0641958i	0.883962	−	0.467559i	$-0.154866\pi$
$683$	0.968627	+	1.67771i	0.0370635	+	0.0641958i	−0.846899	+	0.531754i	$0.821533\pi$
$684$		0			0
$685$	21.1882			0.809561
$686$	−9.26013	+	16.0390i	−0.353553	+	0.612372i
$687$		0			0
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	4.11438	+	7.12631i	0.156745	+	0.271491i
$690$		0			0
$691$	22.6144	−	39.1693i	0.860291	−	1.49007i	−0.0113561	−	0.999936i	$-0.503615\pi$
$691$	22.6144	−	39.1693i	0.860291	−	1.49007i	0.871648	−	0.490133i	$-0.163052\pi$
$692$	0.291503			0.0110813
$693$		0			0
$694$	20.8118			0.790004
$695$	3.29150	−	5.70105i	0.124854	−	0.216253i
$696$		0			0
$697$	−32.8118	−	56.8316i	−1.24283	−	2.15265i
$698$	0.937254	−	1.62337i	0.0354756	−	0.0614455i
$699$		0			0
$700$	3.03137	+	5.25049i	0.114575	+	0.198450i
$701$	−24.8745			−0.939497			−0.469749	−	0.882800i	$-0.655655\pi$
$701$	−24.8745			−0.939497			−0.469749	+	0.882800i	$0.655655\pi$
$702$		0			0
$703$	10.2915	+	17.8254i	0.388151	+	0.672298i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	−7.16601			−0.269696
$707$	−7.93725			−0.298511
$708$		0			0
$709$	−20.4059	+	35.3440i	−0.766359	+	1.32737i	0.173166	+	0.984893i	$0.444600\pi$
$709$	−20.4059	+	35.3440i	−0.766359	+	1.32737i	−0.939525	+	0.342480i	$0.888733\pi$
$710$	3.58301	+	6.20595i	0.134468	+	0.232905i
$711$		0			0
$712$	3.29150	−	5.70105i	0.123354	−	0.213656i
$713$	6.58301			0.246535
$714$		0			0
$715$	−8.22876			−0.307738
$716$	−9.96863	+	17.2662i	−0.372545	+	0.645267i
$717$		0			0
$718$	−12.9686	−	22.4623i	−0.483985	−	0.838286i
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	−0.479964	−	0.877288i	$-0.659350\pi$
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	0.999736	−	0.0229831i	$-0.00731639\pi$
$720$		0			0
$721$	3.88562	+	6.73009i	0.144708	+	0.250642i
$722$	12.8745			0.479140
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−7.20850	−	12.4855i	−0.267717	−	0.463699i
$726$		0			0
$727$	−6.70850			−0.248804			−0.124402	−	0.992232i	$-0.539701\pi$
$727$	−6.70850			−0.248804			−0.124402	+	0.992232i	$0.539701\pi$
$728$	−6.61438	+	11.4564i	−0.245145	+	0.424604i
$729$		0			0
$730$	−0.291503	+	0.504897i	−0.0107890	+	0.0186871i
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	5.72876	−	9.92250i	0.211596	−	0.366496i	−0.740618	−	0.671926i	$-0.765467\pi$
$733$	5.72876	−	9.92250i	0.211596	−	0.366496i	0.952214	+	0.305431i	$0.0988004\pi$
$734$	−36.2288			−1.33723
$735$		0			0
$736$	−1.64575			−0.0606632
$737$	−5.96863	+	10.3380i	−0.219857	+	0.380804i
$738$		0			0
$739$	−11.9373	−	20.6759i	−0.439119	−	0.760576i	0.558503	−	0.829503i	$-0.311376\pi$
$739$	−11.9373	−	20.6759i	−0.439119	−	0.760576i	−0.997622	+	0.0689263i	$0.978043\pi$
$740$	−3.00000	+	5.19615i	−0.110282	+	0.191014i
$741$		0			0
$742$	2.17712	−	3.77089i	0.0799247	−	0.138434i
$743$	45.2915			1.66158			0.830792	−	0.556583i	$-0.187888\pi$
$743$	45.2915			1.66158			0.830792	+	0.556583i	$0.187888\pi$
$744$		0			0
$745$	−12.5830	−	21.7944i	−0.461006	−	0.798485i
$746$	−10.4373	−	18.0779i	−0.382135	−	0.661877i
$747$		0			0
$748$	6.00000			0.219382
$749$	−14.4686	−	25.0604i	−0.528672	−	0.915687i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	1.35425	+	2.34563i	0.0493844	+	0.0855362i
$753$		0			0
$754$	15.7288	−	27.2430i	0.572808	−	0.992132i
$755$	−14.2288			−0.517837
$756$		0			0
$757$	−23.1660			−0.841983			−0.420991	−	0.907065i	$-0.638318\pi$
$757$	−23.1660			−0.841983			−0.420991	+	0.907065i	$0.638318\pi$
$758$	−3.03137	+	5.25049i	−0.110104	+	0.190706i
$759$		0			0
$760$	4.64575	+	8.04668i	0.168519	+	0.291884i
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$		0			0
$763$	−28.0000			−1.01367
$764$	2.70850			0.0979900
$765$		0			0
$766$	12.0516	+	20.8740i	0.435443	+	0.754210i
$767$	11.6144	+	20.1167i	0.419371	+	0.726372i
$768$		0			0
$769$	27.1660			0.979631			0.489816	−	0.871826i	$-0.337064\pi$
$769$	27.1660			0.979631			0.489816	+	0.871826i	$0.337064\pi$
$770$	2.17712	+	3.77089i	0.0784581	+	0.135893i
$771$		0			0
$772$	−12.7601	+	22.1012i	−0.459247	+	0.795439i
$773$	−9.29150	−	16.0934i	−0.334192	−	0.578838i	0.649137	−	0.760671i	$-0.275130\pi$
$773$	−9.29150	−	16.0934i	−0.334192	−	0.578838i	−0.983329	+	0.181834i	$0.941797\pi$
$774$		0			0
$775$	−4.58301	+	7.93800i	−0.164626	+	0.285141i
$776$	−16.2915			−0.584831
$777$		0			0
$778$	−26.8118			−0.961248
$779$	−30.8745	+	53.4762i	−1.10619	+	1.91598i
$780$		0			0
$781$	−2.17712	−	3.77089i	−0.0779036	−	0.134933i
$782$	−4.93725	+	8.55157i	−0.176556	+	0.305804i
$783$		0			0
$784$	7.00000			0.250000
$785$	34.8340			1.24328
$786$		0			0
$787$	−23.4059	−	40.5402i	−0.834330	−	1.44510i	−0.894575	−	0.446918i	$-0.852522\pi$
$787$	−23.4059	−	40.5402i	−0.834330	−	1.44510i	0.0602456	−	0.998184i	$-0.480812\pi$
$788$	−6.43725	−	11.1497i	−0.229318	−	0.397190i
$789$		0			0
$790$	−4.35425			−0.154917
$791$	−24.1974	+	41.9111i	−0.860360	+	1.49019i
$792$		0			0
$793$	−35.7288	+	61.8840i	−1.26877	+	2.19757i
$794$	5.58301	+	9.67005i	0.198133	+	0.343177i
$795$		0			0
$796$	−2.11438	+	3.66221i	−0.0749422	+	0.129804i
$797$	−7.16601			−0.253833			−0.126917	−	0.991913i	$-0.540508\pi$
$797$	−7.16601			−0.253833			−0.126917	+	0.991913i	$0.540508\pi$
$798$		0			0
$799$	16.2510			0.574918
$800$	1.14575	−	1.98450i	0.0405084	−	0.0701627i
$801$		0			0
$802$	10.7915	+	18.6914i	0.381061	+	0.660017i
$803$	0.177124	−	0.306788i	0.00625058	−	0.0108263i
$804$		0			0
$805$	−7.16601			−0.252569
$806$	−20.0000			−0.704470
$807$		0			0
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	14.7085	+	25.4759i	0.517123	+	0.895684i	0.999802	+	0.0198864i	$0.00633045\pi$
$809$	14.7085	+	25.4759i	0.517123	+	0.895684i	−0.482679	+	0.875797i	$0.660336\pi$
$810$		0			0
$811$	−35.7490			−1.25532			−0.627659	−	0.778489i	$-0.715987\pi$
$811$	−35.7490			−1.25532			−0.627659	+	0.778489i	$0.715987\pi$
$812$	−16.6458			−0.584151
$813$		0			0
$814$	1.82288	−	3.15731i	0.0638918	−	0.110664i
$815$	−0.531373	−	0.920365i	−0.0186132	−	0.0322390i
$816$		0			0
$817$	−11.2915	+	19.5575i	−0.395040	+	0.684229i
$818$	3.06275			0.107086
$819$		0			0
$820$	−18.0000			−0.628587
$821$	−9.14575	+	15.8409i	−0.319189	+	0.552851i	−0.980319	−	0.197420i	$-0.936744\pi$
$821$	−9.14575	+	15.8409i	−0.319189	+	0.552851i	0.661130	+	0.750271i	$0.270077\pi$
$822$		0			0
$823$	6.06275	+	10.5010i	0.211334	+	0.366041i	0.952132	−	0.305686i	$-0.0988859\pi$
$823$	6.06275	+	10.5010i	0.211334	+	0.366041i	−0.740798	+	0.671728i	$0.765553\pi$
$824$	1.46863	−	2.54374i	0.0511620	−	0.0886153i
$825$		0			0
$826$	6.14575	−	10.6448i	0.213838	−	0.370378i
$827$	−33.3948			−1.16125			−0.580625	−	0.814171i	$-0.697192\pi$
$827$	−33.3948			−1.16125			−0.580625	+	0.814171i	$0.697192\pi$
$828$		0			0
$829$	12.6974	+	21.9925i	0.440998	+	0.763832i	0.997764	−	0.0668382i	$-0.0212911\pi$
$829$	12.6974	+	21.9925i	0.440998	+	0.763832i	−0.556765	+	0.830670i	$0.687958\pi$
$830$	2.22876	+	3.86032i	0.0773613	+	0.133994i
$831$		0			0
$832$	5.00000			0.173344
$833$	21.0000	−	36.3731i	0.727607	−	1.26025i
$834$		0			0
$835$	−9.23987	+	16.0039i	−0.319759	+	0.553839i
$836$	−2.82288	−	4.88936i	−0.0976312	−	0.169102i
$837$		0			0
$838$	−4.93725	+	8.55157i	−0.170555	+	0.295409i
$839$	3.87451			0.133763			0.0668814	−	0.997761i	$-0.478695\pi$
$839$	3.87451			0.133763			0.0668814	+	0.997761i	$0.478695\pi$
$840$		0			0
$841$	10.5830			0.364931
$842$	−4.58301	+	7.93800i	−0.157941	+	0.273561i
$843$		0			0
$844$	−0.468627	−	0.811686i	−0.0161308	−	0.0279394i
$845$	−9.87451	+	17.1031i	−0.339693	+	0.588366i
$846$		0			0
$847$	−1.32288	−	2.29129i	−0.0454545	−	0.0787296i
$848$	−1.64575			−0.0565153
$849$		0			0
$850$	−6.87451	−	11.9070i	−0.235794	−	0.408407i
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		0			0
$853$	39.1660			1.34102			0.670509	−	0.741901i	$-0.266076\pi$
$853$	39.1660			1.34102			0.670509	+	0.741901i	$0.266076\pi$
$854$	37.8118			1.29389
$855$		0			0
$856$	−5.46863	+	9.47194i	−0.186914	+	0.323744i
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	0.990408	+	0.138177i	$0.0441242\pi$
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	−0.375539	+	0.926806i	$0.622542\pi$
$858$		0			0
$859$	4.90588	−	8.49723i	0.167386	−	0.289922i	−0.770114	−	0.637907i	$-0.779801\pi$
$859$	4.90588	−	8.49723i	0.167386	−	0.289922i	0.937500	+	0.347985i	$0.113134\pi$
$860$	−6.58301			−0.224479
$861$		0			0
$862$	−29.2288			−0.995535
$863$	−6.23987	+	10.8078i	−0.212408	+	0.367901i	−0.952468	−	0.304640i	$-0.901464\pi$
$863$	−6.23987	+	10.8078i	−0.212408	+	0.367901i	0.740060	+	0.672541i	$0.234797\pi$
$864$		0			0
$865$	−0.239870	−	0.415468i	−0.00815584	−	0.0141263i
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$		0			0
$868$	5.29150	+	9.16515i	0.179605	+	0.311086i
$869$	2.64575			0.0897510
$870$		0			0
$871$	29.8431	+	51.6898i	1.01120	+	1.75144i
$872$	5.29150	+	9.16515i	0.179193	+	0.310371i
$873$		0			0
$874$	9.29150			0.314290
$875$	15.8745	−	27.4955i	0.536656	−	0.929516i
$876$		0			0
$877$	11.4373	−	19.8099i	0.386209	−	0.668933i	−0.605727	−	0.795672i	$-0.707118\pi$
$877$	11.4373	−	19.8099i	0.386209	−	0.668933i	0.991936	+	0.126739i	$0.0404511\pi$
$878$	−1.96863	−	3.40976i	−0.0664379	−	0.115074i
$879$		0			0
$880$	0.822876	−	1.42526i	0.0277391	−	0.0480456i
$881$	24.8745			0.838043			0.419022	−	0.907976i	$-0.362373\pi$
$881$	24.8745			0.838043			0.419022	+	0.907976i	$0.362373\pi$
$882$		0			0
$883$	21.9373			0.738247			0.369124	−	0.929380i	$-0.379658\pi$
$883$	21.9373			0.738247			0.369124	+	0.929380i	$0.379658\pi$
$884$	15.0000	−	25.9808i	0.504505	−	0.873828i
$885$		0			0
$886$	17.2288	+	29.8411i	0.578811	+	1.00253i
$887$	22.5516	−	39.0606i	0.757210	−	1.31153i	−0.187059	−	0.982349i	$-0.559895\pi$
$887$	22.5516	−	39.0606i	0.757210	−	1.31153i	0.944268	−	0.329177i	$-0.106771\pi$
$888$		0			0
$889$	−21.0830	+	36.5168i	−0.707101	+	1.22474i
$890$	−10.8340			−0.363156
$891$		0			0
$892$	8.82288	+	15.2817i	0.295412	+	0.511668i
$893$	−7.64575	−	13.2428i	−0.255855	−	0.443154i
$894$		0			0
$895$	32.8118			1.09678
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$		0			0
$898$	−10.9373	+	18.9439i	−0.364981	+	0.632165i
$899$	−12.5830	−	21.7944i	−0.419667	−	0.726884i
$900$		0			0
$901$	−4.93725	+	8.55157i	−0.164484	+	0.284894i
$902$	10.9373			0.364171
$903$		0			0
$904$	18.2915			0.608366
$905$	8.22876	−	14.2526i	0.273533	−	0.473773i
$906$		0			0
$907$	−21.2288	−	36.7693i	−0.704889	−	1.22090i	−0.966731	−	0.255793i	$-0.917663\pi$
$907$	−21.2288	−	36.7693i	−0.704889	−	1.22090i	0.261842	−	0.965111i	$-0.415670\pi$
$908$	−1.35425	+	2.34563i	−0.0449423	+	0.0778424i
$909$		0			0
$910$	21.7712			0.721710
$911$	−9.29150			−0.307841			−0.153921	−	0.988083i	$-0.549190\pi$
$911$	−9.29150			−0.307841			−0.153921	+	0.988083i	$0.549190\pi$
$912$		0			0
$913$	−1.35425	−	2.34563i	−0.0448191	−	0.0776289i
$914$	−1.58301	−	2.74185i	−0.0523612	−	0.0906922i
$915$		0			0
$916$	−16.0000			−0.528655
$917$	13.6974	+	23.7246i	0.452327	+	0.783454i
$918$		0			0
$919$	12.3542	−	21.3982i	0.407529	−	0.705861i	−0.587083	−	0.809527i	$-0.699724\pi$
$919$	12.3542	−	21.3982i	0.407529	−	0.705861i	0.994612	+	0.103666i	$0.0330572\pi$
$920$	1.35425	+	2.34563i	0.0446483	+	0.0773330i
$921$		0			0
$922$	5.08301	−	8.80402i	0.167400	−	0.289945i
$923$	−21.7712			−0.716609
$924$		0			0
$925$	−8.35425			−0.274686
$926$	−15.2288	+	26.3770i	−0.500448	+	0.866801i
$927$		0			0
$928$	3.14575	+	5.44860i	0.103264	+	0.178859i
$929$	7.20850	−	12.4855i	0.236503	−	0.409635i	−0.723205	−	0.690633i	$-0.757332\pi$
$929$	7.20850	−	12.4855i	0.236503	−	0.409635i	0.959708	+	0.280998i	$0.0906653\pi$
$930$		0			0
$931$	−39.5203			−1.29522
$932$	−1.06275			−0.0348114
$933$		0			0
$934$	10.6458	+	18.4390i	0.348340	+	0.603342i
$935$	−4.93725	−	8.55157i	−0.161465	−	0.279666i
$936$		0			0
$937$	32.6863			1.06781			0.533907	−	0.845543i	$-0.320723\pi$
$937$	32.6863			1.06781			0.533907	+	0.845543i	$0.320723\pi$
$938$	15.7915	−	27.3517i	0.515611	−	0.893064i
$939$		0			0
$940$	2.22876	−	3.86032i	0.0726940	−	0.125910i
$941$	25.3118	+	43.8413i	0.825140	+	1.42918i	0.901812	+	0.432128i	$0.142237\pi$
$941$	25.3118	+	43.8413i	0.825140	+	1.42918i	−0.0766725	+	0.997056i	$0.524430\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−4.64575			−0.151206
$945$		0			0
$946$	4.00000			0.130051
$947$	−1.06275	+	1.84073i	−0.0345346	+	0.0598157i	−0.882776	−	0.469794i	$-0.844328\pi$
$947$	−1.06275	+	1.84073i	−0.0345346	+	0.0598157i	0.848242	+	0.529610i	$0.177662\pi$
$948$		0			0
$949$	−0.885622	−	1.53394i	−0.0287485	−	0.0497939i
$950$	−6.46863	+	11.2040i	−0.209870	+	0.363505i
$951$		0			0
$952$	−15.8745			−0.514496
$953$	−11.5203			−0.373178			−0.186589	−	0.982438i	$-0.559743\pi$
$953$	−11.5203			−0.373178			−0.186589	+	0.982438i	$0.559743\pi$
$954$		0			0
$955$	−2.22876	−	3.86032i	−0.0721209	−	0.124917i
$956$	−8.61438	−	14.9205i	−0.278609	−	0.482565i
$957$		0			0
$958$	10.0627			0.325113
$959$	34.0627			1.09994
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−9.11438	−	15.7866i	−0.293859	−	0.508979i
$963$		0			0
$964$	12.4059	−	21.4876i	0.399567	−	0.692070i
$965$	42.0000			1.35203
$966$		0			0
$967$	58.3320			1.87583			0.937916	−	0.346863i	$-0.112753\pi$
$967$	58.3320			1.87583			0.937916	+	0.346863i	$0.112753\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$	13.4059	+	23.2197i	0.430437	+	0.745539i
$971$	−5.03137	+	8.71459i	−0.161464	+	0.279665i	−0.935394	−	0.353607i	$-0.884955\pi$
$971$	−5.03137	+	8.71459i	−0.161464	+	0.279665i	0.773930	+	0.633272i	$0.218288\pi$
$972$		0			0
$973$	5.29150	−	9.16515i	0.169638	−	0.293821i
$974$	−9.41699			−0.301740
$975$		0			0
$976$	−7.14575	−	12.3768i	−0.228730	−	0.396172i
$977$	−8.22876	−	14.2526i	−0.263261	−	0.455982i	0.703845	−	0.710353i	$-0.251465\pi$
$977$	−8.22876	−	14.2526i	−0.263261	−	0.455982i	−0.967107	+	0.254371i	$0.918131\pi$
$978$		0			0
$979$	6.58301			0.210394
$980$	−5.76013	−	9.97684i	−0.184001	−	0.318698i
$981$		0			0
$982$	10.6458	−	18.4390i	0.339720	−	0.588412i
$983$	−13.3542	−	23.1302i	−0.425934	−	0.737740i	0.570573	−	0.821247i	$-0.306721\pi$
$983$	−13.3542	−	23.1302i	−0.425934	−	0.737740i	−0.996507	+	0.0835070i	$0.973388\pi$
$984$		0			0
$985$	−10.5941	+	18.3496i	−0.337557	+	0.584665i
$986$	37.7490			1.20217
$987$		0			0
$988$	−28.2288			−0.898076
$989$	−3.29150	+	5.70105i	−0.104664	+	0.181283i
$990$		0			0
$991$	11.3431	+	19.6469i	0.360327	+	0.624104i	0.988014	−	0.154361i	$-0.0493319\pi$
$991$	11.3431	+	19.6469i	0.360327	+	0.624104i	−0.627688	+	0.778465i	$0.715999\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	5.76013	+	9.97684i	0.182700	+	0.316446i
$995$	6.95948			0.220630
$996$		0			0
$997$	10.7085	+	18.5477i	0.339142	+	0.587410i	0.984271	−	0.176663i	$-0.0565301\pi$
$997$	10.7085	+	18.5477i	0.339142	+	0.587410i	−0.645130	+	0.764073i	$0.723197\pi$
$998$	6.93725	+	12.0157i	0.219595	+	0.380350i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.s.793.1		4
3.2	odd	2		154.2.e.f.23.1	✓	4
7.2	even	3		9702.2.a.cz.1.2		2
7.4	even	3	inner	1386.2.k.s.991.1		4
7.5	odd	6		9702.2.a.dr.1.1		2
12.11	even	2		1232.2.q.g.177.2		4
21.2	odd	6		1078.2.a.s.1.2		2
21.5	even	6		1078.2.a.n.1.1		2
21.11	odd	6		154.2.e.f.67.1	yes	4
21.17	even	6		1078.2.e.v.67.2		4
21.20	even	2		1078.2.e.v.177.2		4
84.11	even	6		1232.2.q.g.529.2		4
84.23	even	6		8624.2.a.ca.1.1		2
84.47	odd	6		8624.2.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.1	✓	4	3.2	odd	2
154.2.e.f.67.1	yes	4	21.11	odd	6
1078.2.a.n.1.1		2	21.5	even	6
1078.2.a.s.1.2		2	21.2	odd	6
1078.2.e.v.67.2		4	21.17	even	6
1078.2.e.v.177.2		4	21.20	even	2
1232.2.q.g.177.2		4	12.11	even	2
1232.2.q.g.529.2		4	84.11	even	6
1386.2.k.s.793.1		4	1.1	even	1	trivial
1386.2.k.s.991.1		4	7.4	even	3	inner
8624.2.a.bk.1.2		2	84.47	odd	6
8624.2.a.ca.1.1		2	84.23	even	6
9702.2.a.cz.1.2		2	7.2	even	3
9702.2.a.dr.1.1		2	7.5	odd	6

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.822876 + 1.42526i) q^{5} +(-1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(-0.822876 - 1.42526i) q^{10} +(0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(2.82288 - 4.88936i) q^{19} +1.64575 q^{20} -1.00000 q^{22} +(0.822876 - 1.42526i) q^{23} +(1.14575 + 1.98450i) q^{25} +(-2.50000 + 4.33013i) q^{26} +2.64575 q^{28} -6.29150 q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.00000 q^{34} +(-2.17712 - 3.77089i) q^{35} +(-1.82288 + 3.15731i) q^{37} +(2.82288 + 4.88936i) q^{38} +(-0.822876 + 1.42526i) q^{40} -10.9373 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.822876 + 1.42526i) q^{46} +(1.35425 - 2.34563i) q^{47} +(-3.50000 - 6.06218i) q^{49} -2.29150 q^{50} +(-2.50000 - 4.33013i) q^{52} +(0.822876 + 1.42526i) q^{53} -1.64575 q^{55} +(-1.32288 + 2.29129i) q^{56} +(3.14575 - 5.44860i) q^{58} +(2.32288 + 4.02334i) q^{59} +(-7.14575 + 12.3768i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-4.11438 + 7.12631i) q^{65} +(5.96863 + 10.3380i) q^{67} +(3.00000 - 5.19615i) q^{68} +4.35425 q^{70} -4.35425 q^{71} +(-0.177124 - 0.306788i) q^{73} +(-1.82288 - 3.15731i) q^{74} -5.64575 q^{76} -2.64575 q^{77} +(1.32288 - 2.29129i) q^{79} +(-0.822876 - 1.42526i) q^{80} +(5.46863 - 9.47194i) q^{82} -2.70850 q^{83} -9.87451 q^{85} +(2.00000 - 3.46410i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.29150 - 5.70105i) q^{89} +(-6.61438 + 11.4564i) q^{91} -1.64575 q^{92} +(1.35425 + 2.34563i) q^{94} +(4.64575 + 8.04668i) q^{95} -16.2915 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} + 2 q^{11} + 20 q^{13} - 2 q^{16} + 12 q^{17} + 6 q^{19} - 4 q^{20} - 4 q^{22} - 2 q^{23} - 6 q^{25} - 10 q^{26} - 4 q^{29} + 8 q^{31} - 2 q^{32} - 24 q^{34} - 14 q^{35} - 2 q^{37} + 6 q^{38} + 2 q^{40} - 12 q^{41} - 16 q^{43} + 2 q^{44} - 2 q^{46} + 16 q^{47} - 14 q^{49} + 12 q^{50} - 10 q^{52} - 2 q^{53} + 4 q^{55} + 2 q^{58} + 4 q^{59} - 18 q^{61} - 16 q^{62} + 4 q^{64} + 10 q^{65} + 8 q^{67} + 12 q^{68} + 28 q^{70} - 28 q^{71} - 6 q^{73} - 2 q^{74} - 12 q^{76} + 2 q^{80} + 6 q^{82} - 32 q^{83} + 24 q^{85} + 8 q^{86} + 2 q^{88} - 8 q^{89} + 4 q^{92} + 16 q^{94} + 8 q^{95} - 44 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 + 2 * q^11 + 20 * q^13 - 2 * q^16 + 12 * q^17 + 6 * q^19 - 4 * q^20 - 4 * q^22 - 2 * q^23 - 6 * q^25 - 10 * q^26 - 4 * q^29 + 8 * q^31 - 2 * q^32 - 24 * q^34 - 14 * q^35 - 2 * q^37 + 6 * q^38 + 2 * q^40 - 12 * q^41 - 16 * q^43 + 2 * q^44 - 2 * q^46 + 16 * q^47 - 14 * q^49 + 12 * q^50 - 10 * q^52 - 2 * q^53 + 4 * q^55 + 2 * q^58 + 4 * q^59 - 18 * q^61 - 16 * q^62 + 4 * q^64 + 10 * q^65 + 8 * q^67 + 12 * q^68 + 28 * q^70 - 28 * q^71 - 6 * q^73 - 2 * q^74 - 12 * q^76 + 2 * q^80 + 6 * q^82 - 32 * q^83 + 24 * q^85 + 8 * q^86 + 2 * q^88 - 8 * q^89 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 44 * q^97 + 28 * q^98

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