LMFDB - Embedded newform 693.2.i.f.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, 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("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.f.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 - 2.44949i) q^{7} +1.58579 q^{8} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 - 2.44949i) q^{7} +1.58579 q^{8} +(0.414214 + 0.717439i) q^{10} +(0.500000 + 0.866025i) q^{11} +4.82843 q^{13} +(-0.671573 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.792893 - 1.37333i) q^{17} +(0.621320 - 1.07616i) q^{19} -3.65685 q^{20} +0.414214 q^{22} +(-3.50000 + 6.06218i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +(4.79289 - 0.655892i) q^{28} +5.24264 q^{29} +(2.82843 + 4.89898i) q^{31} +(2.20711 + 3.82282i) q^{32} -0.656854 q^{34} +(3.24264 + 4.18154i) q^{35} +(-3.74264 + 6.48244i) q^{37} +(-0.257359 - 0.445759i) q^{38} +(-1.58579 + 2.74666i) q^{40} +6.82843 q^{41} -11.2426 q^{43} +(-0.914214 + 1.58346i) q^{44} +(1.44975 + 2.51104i) q^{46} +(2.08579 - 3.61269i) q^{47} +(-5.00000 - 4.89898i) q^{49} +0.414214 q^{50} +(4.41421 + 7.64564i) q^{52} +(-6.41421 - 11.1097i) q^{53} -2.00000 q^{55} +(1.58579 - 3.88437i) q^{56} +(1.08579 - 1.88064i) q^{58} +(1.32843 + 2.30090i) q^{59} +(2.00000 - 3.46410i) q^{61} +2.34315 q^{62} -4.17157 q^{64} +(-4.82843 + 8.36308i) q^{65} +(4.41421 + 7.64564i) q^{67} +(1.44975 - 2.51104i) q^{68} +(2.17157 - 0.297173i) q^{70} +9.82843 q^{71} +(-5.82843 - 10.0951i) q^{73} +(1.55025 + 2.68512i) q^{74} +2.27208 q^{76} +(2.62132 - 0.358719i) q^{77} +(4.65685 - 8.06591i) q^{79} +(-3.00000 - 5.19615i) q^{80} +(1.41421 - 2.44949i) q^{82} -2.82843 q^{83} +3.17157 q^{85} +(-2.32843 + 4.03295i) q^{86} +(0.792893 + 1.37333i) q^{88} +(7.07107 - 12.2474i) q^{89} +(4.82843 - 11.8272i) q^{91} -12.7990 q^{92} +(-0.863961 - 1.49642i) q^{94} +(1.24264 + 2.15232i) q^{95} +5.48528 q^{97} +(-2.79289 + 0.778985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} - 4 q^{10} + 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{16} - 6 q^{17} - 6 q^{19} + 8 q^{20} - 4 q^{22} - 14 q^{23} + 2 q^{25} + 4 q^{26} + 22 q^{28} + 4 q^{29} + 6 q^{32} + 20 q^{34} - 4 q^{35} + 2 q^{37} - 18 q^{38} - 12 q^{40} + 16 q^{41} - 28 q^{43} + 2 q^{44} - 14 q^{46} + 14 q^{47} - 20 q^{49} - 4 q^{50} + 12 q^{52} - 20 q^{53} - 8 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 8 q^{61} + 32 q^{62} - 28 q^{64} - 8 q^{65} + 12 q^{67} - 14 q^{68} + 20 q^{70} + 28 q^{71} - 12 q^{73} + 26 q^{74} + 60 q^{76} + 2 q^{77} - 4 q^{79} - 12 q^{80} + 24 q^{85} + 2 q^{86} + 6 q^{88} + 8 q^{91} + 28 q^{92} + 22 q^{94} - 12 q^{95} - 12 q^{97} - 14 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 - 4 * q^10 + 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^16 - 6 * q^17 - 6 * q^19 + 8 * q^20 - 4 * q^22 - 14 * q^23 + 2 * q^25 + 4 * q^26 + 22 * q^28 + 4 * q^29 + 6 * q^32 + 20 * q^34 - 4 * q^35 + 2 * q^37 - 18 * q^38 - 12 * q^40 + 16 * q^41 - 28 * q^43 + 2 * q^44 - 14 * q^46 + 14 * q^47 - 20 * q^49 - 4 * q^50 + 12 * q^52 - 20 * q^53 - 8 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 8 * q^61 + 32 * q^62 - 28 * q^64 - 8 * q^65 + 12 * q^67 - 14 * q^68 + 20 * q^70 + 28 * q^71 - 12 * q^73 + 26 * q^74 + 60 * q^76 + 2 * q^77 - 4 * q^79 - 12 * q^80 + 24 * q^85 + 2 * q^86 + 6 * q^88 + 8 * q^91 + 28 * q^92 + 22 * q^94 - 12 * q^95 - 12 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	−0.783465	−	0.621436i	$-0.786550\pi$
$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	0.929912	+	0.367783i	$0.119883\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	1.58579			0.560660
$9$		0			0
$10$	0.414214	+	0.717439i	0.130986	+	0.226874i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	4.82843			1.33916			0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843			1.33916			0.669582	+	0.742738i	$0.266473\pi$
$14$	−0.671573	−	0.866025i	−0.179485	−	0.231455i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.792893	−	1.37333i	−0.192305	−	0.333082i	0.753709	−	0.657209i	$-0.228263\pi$
$17$	−0.792893	−	1.37333i	−0.192305	−	0.333082i	−0.946014	+	0.324127i	$0.894930\pi$
$18$		0			0
$19$	0.621320	−	1.07616i	0.142541	−	0.246888i	−0.785912	−	0.618338i	$-0.787806\pi$
$19$	0.621320	−	1.07616i	0.142541	−	0.246888i	0.928453	+	0.371451i	$0.121139\pi$
$20$	−3.65685			−0.817697
$21$		0			0
$22$	0.414214			0.0883106
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		0			0
$28$	4.79289	−	0.655892i	0.905772	−	0.123952i
$29$	5.24264			0.973534			0.486767	−	0.873532i	$-0.338176\pi$
$29$	5.24264			0.973534			0.486767	+	0.873532i	$0.338176\pi$
$30$		0			0
$31$	2.82843	+	4.89898i	0.508001	+	0.879883i	0.999957	+	0.00926296i	$0.00294853\pi$
$31$	2.82843	+	4.89898i	0.508001	+	0.879883i	−0.491957	+	0.870620i	$0.663718\pi$
$32$	2.20711	+	3.82282i	0.390165	+	0.675786i
$33$		0			0
$34$	−0.656854			−0.112650
$35$	3.24264	+	4.18154i	0.548106	+	0.706809i
$36$		0			0
$37$	−3.74264	+	6.48244i	−0.615286	+	1.06571i	0.375048	+	0.927005i	$0.377626\pi$
$37$	−3.74264	+	6.48244i	−0.615286	+	1.06571i	−0.990334	+	0.138702i	$0.955707\pi$
$38$	−0.257359	−	0.445759i	−0.0417492	−	0.0723117i
$39$		0			0
$40$	−1.58579	+	2.74666i	−0.250735	+	0.434286i
$41$	6.82843			1.06642			0.533211	−	0.845983i	$-0.320985\pi$
$41$	6.82843			1.06642			0.533211	+	0.845983i	$0.320985\pi$
$42$		0			0
$43$	−11.2426			−1.71449			−0.857243	−	0.514912i	$-0.827825\pi$
$43$	−11.2426			−1.71449			−0.857243	+	0.514912i	$0.827825\pi$
$44$	−0.914214	+	1.58346i	−0.137823	+	0.238716i
$45$		0			0
$46$	1.44975	+	2.51104i	0.213754	+	0.370232i
$47$	2.08579	−	3.61269i	0.304243	−	0.526965i	−0.672849	−	0.739780i	$-0.734930\pi$
$47$	2.08579	−	3.61269i	0.304243	−	0.526965i	0.977093	+	0.212815i	$0.0682631\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$	0.414214			0.0585786
$51$		0			0
$52$	4.41421	+	7.64564i	0.612141	+	1.06026i
$53$	−6.41421	−	11.1097i	−0.881060	−	1.52604i	−0.850164	−	0.526518i	$-0.823497\pi$
$53$	−6.41421	−	11.1097i	−0.881060	−	1.52604i	−0.0308961	−	0.999523i	$-0.509836\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	1.58579	−	3.88437i	0.211910	−	0.519070i
$57$		0			0
$58$	1.08579	−	1.88064i	0.142571	−	0.246940i
$59$	1.32843	+	2.30090i	0.172946	+	0.299552i	0.939449	−	0.342690i	$-0.111338\pi$
$59$	1.32843	+	2.30090i	0.172946	+	0.299552i	−0.766502	+	0.642242i	$0.778005\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	2.34315			0.297580
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−4.82843	+	8.36308i	−0.598893	+	1.03731i
$66$		0			0
$67$	4.41421	+	7.64564i	0.539282	+	0.934064i	0.998943	+	0.0459693i	$0.0146376\pi$
$67$	4.41421	+	7.64564i	0.539282	+	0.934064i	−0.459661	+	0.888095i	$0.652029\pi$
$68$	1.44975	−	2.51104i	0.175808	−	0.304508i
$69$		0			0
$70$	2.17157	−	0.297173i	0.259553	−	0.0355190i
$71$	9.82843			1.16642			0.583210	−	0.812322i	$-0.301797\pi$
$71$	9.82843			1.16642			0.583210	+	0.812322i	$0.301797\pi$
$72$		0			0
$73$	−5.82843	−	10.0951i	−0.682166	−	1.18155i	−0.974319	−	0.225174i	$-0.927705\pi$
$73$	−5.82843	−	10.0951i	−0.682166	−	1.18155i	0.292153	−	0.956372i	$-0.405628\pi$
$74$	1.55025	+	2.68512i	0.180213	+	0.312138i
$75$		0			0
$76$	2.27208			0.260625
$77$	2.62132	−	0.358719i	0.298727	−	0.0408799i
$78$		0			0
$79$	4.65685	−	8.06591i	0.523937	−	0.907486i	−0.475675	−	0.879621i	$-0.657796\pi$
$79$	4.65685	−	8.06591i	0.523937	−	0.907486i	0.999612	−	0.0278643i	$-0.00887063\pi$
$80$	−3.00000	−	5.19615i	−0.335410	−	0.580948i
$81$		0			0
$82$	1.41421	−	2.44949i	0.156174	−	0.270501i
$83$	−2.82843			−0.310460			−0.155230	−	0.987878i	$-0.549612\pi$
$83$	−2.82843			−0.310460			−0.155230	+	0.987878i	$0.549612\pi$
$84$		0			0
$85$	3.17157			0.344005
$86$	−2.32843	+	4.03295i	−0.251081	+	0.434885i
$87$		0			0
$88$	0.792893	+	1.37333i	0.0845227	+	0.146398i
$89$	7.07107	−	12.2474i	0.749532	−	1.29823i	−0.198516	−	0.980098i	$-0.563612\pi$
$89$	7.07107	−	12.2474i	0.749532	−	1.29823i	0.948047	−	0.318129i	$-0.103055\pi$
$90$		0			0
$91$	4.82843	−	11.8272i	0.506157	−	1.23983i
$92$	−12.7990			−1.33439
$93$		0			0
$94$	−0.863961	−	1.49642i	−0.0891108	−	0.154344i
$95$	1.24264	+	2.15232i	0.127492	+	0.220823i
$96$		0			0
$97$	5.48528			0.556946			0.278473	−	0.960444i	$-0.410172\pi$
$97$	5.48528			0.556946			0.278473	+	0.960444i	$0.410172\pi$
$98$	−2.79289	+	0.778985i	−0.282125	+	0.0786894i
$99$		0			0
$100$	−0.914214	+	1.58346i	−0.0914214	+	0.158346i
$101$	−7.44975	−	12.9033i	−0.741278	−	1.28393i	−0.951914	−	0.306366i	$-0.900887\pi$
$101$	−7.44975	−	12.9033i	−0.741278	−	1.28393i	0.210636	−	0.977565i	$-0.432446\pi$
$102$		0			0
$103$	2.24264	−	3.88437i	0.220974	−	0.382738i	−0.734130	−	0.679009i	$-0.762410\pi$
$103$	2.24264	−	3.88437i	0.220974	−	0.382738i	0.955104	+	0.296271i	$0.0957431\pi$
$104$	7.65685			0.750816
$105$		0			0
$106$	−5.31371			−0.516113
$107$	−0.828427	+	1.43488i	−0.0800871	+	0.138715i	−0.903287	−	0.429036i	$-0.858853\pi$
$107$	−0.828427	+	1.43488i	−0.0800871	+	0.138715i	0.823200	+	0.567751i	$0.192187\pi$
$108$		0			0
$109$	0.585786	+	1.01461i	0.0561082	+	0.0971822i	0.892715	−	0.450621i	$-0.148797\pi$
$109$	0.585786	+	1.01461i	0.0561082	+	0.0971822i	−0.836607	+	0.547803i	$0.815464\pi$
$110$	−0.414214	+	0.717439i	−0.0394937	+	0.0684051i
$111$		0			0
$112$	4.86396	+	6.27231i	0.459601	+	0.592678i
$113$	−3.65685			−0.344008			−0.172004	−	0.985096i	$-0.555024\pi$
$113$	−3.65685			−0.344008			−0.172004	+	0.985096i	$0.555024\pi$
$114$		0			0
$115$	−7.00000	−	12.1244i	−0.652753	−	1.13060i
$116$	4.79289	+	8.30153i	0.445009	+	0.770778i
$117$		0			0
$118$	1.10051			0.101310
$119$	−4.15685	+	0.568852i	−0.381058	+	0.0521466i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−0.828427	−	1.43488i	−0.0750023	−	0.129908i
$123$		0			0
$124$	−5.17157	+	8.95743i	−0.464421	+	0.804401i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−1.92893			−0.171165			−0.0855825	−	0.996331i	$-0.527275\pi$
$127$	−1.92893			−0.171165			−0.0855825	+	0.996331i	$0.527275\pi$
$128$	−5.27817	+	9.14207i	−0.466529	+	0.808052i
$129$		0			0
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−5.41421	+	9.37769i	−0.473042	+	0.819333i	−0.999524	−	0.0308535i	$-0.990177\pi$
$131$	−5.41421	+	9.37769i	−0.473042	+	0.819333i	0.526482	+	0.850186i	$0.323511\pi$
$132$		0			0
$133$	−2.01472	−	2.59808i	−0.174698	−	0.225282i
$134$	3.65685			0.315904
$135$		0			0
$136$	−1.25736	−	2.17781i	−0.107818	−	0.186746i
$137$	−8.24264	−	14.2767i	−0.704216	−	1.21974i	−0.966974	−	0.254876i	$-0.917965\pi$
$137$	−8.24264	−	14.2767i	−0.704216	−	1.21974i	0.262757	−	0.964862i	$-0.415368\pi$
$138$		0			0
$139$	5.58579			0.473780			0.236890	−	0.971536i	$-0.423872\pi$
$139$	5.58579			0.473780			0.236890	+	0.971536i	$0.423872\pi$
$140$	−3.65685	+	8.95743i	−0.309061	+	0.757041i
$141$		0			0
$142$	2.03553	−	3.52565i	0.170818	−	0.295866i
$143$	2.41421	+	4.18154i	0.201887	+	0.349678i
$144$		0			0
$145$	−5.24264	+	9.08052i	−0.435378	+	0.754096i
$146$	−4.82843			−0.399603
$147$		0			0
$148$	−13.6863			−1.12501
$149$	10.1066	−	17.5051i	0.827965	−	1.43408i	−0.0716669	−	0.997429i	$-0.522832\pi$
$149$	10.1066	−	17.5051i	0.827965	−	1.43408i	0.899632	−	0.436649i	$-0.143835\pi$
$150$		0			0
$151$	−0.449747	−	0.778985i	−0.0365999	−	0.0633929i	0.847145	−	0.531361i	$-0.178319\pi$
$151$	−0.449747	−	0.778985i	−0.0365999	−	0.0633929i	−0.883745	+	0.467969i	$0.844986\pi$
$152$	0.985281	−	1.70656i	0.0799169	−	0.138420i
$153$		0			0
$154$	0.414214	−	1.01461i	0.0333783	−	0.0817598i
$155$	−11.3137			−0.908739
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	−1.92893	−	3.34101i	−0.153458	−	0.265796i
$159$		0			0
$160$	−8.82843			−0.697948
$161$	11.3492	+	14.6354i	0.894446	+	1.15343i
$162$		0			0
$163$	−6.48528	+	11.2328i	−0.507966	+	0.879824i	0.491991	+	0.870600i	$0.336269\pi$
$163$	−6.48528	+	11.2328i	−0.507966	+	0.879824i	−0.999957	+	0.00922341i	$0.997064\pi$
$164$	6.24264	+	10.8126i	0.487468	+	0.844320i
$165$		0			0
$166$	−0.585786	+	1.01461i	−0.0454658	+	0.0787492i
$167$	−10.8284			−0.837929			−0.418964	−	0.908003i	$-0.637607\pi$
$167$	−10.8284			−0.837929			−0.418964	+	0.908003i	$0.637607\pi$
$168$		0			0
$169$	10.3137			0.793362
$170$	0.656854	−	1.13770i	0.0503784	−	0.0872580i
$171$		0			0
$172$	−10.2782	−	17.8023i	−0.783703	−	1.35741i
$173$	−4.58579	+	7.94282i	−0.348651	+	0.603881i	−0.986010	−	0.166686i	$-0.946693\pi$
$173$	−4.58579	+	7.94282i	−0.348651	+	0.603881i	0.637359	+	0.770567i	$0.280027\pi$
$174$		0			0
$175$	2.62132	−	0.358719i	0.198153	−	0.0271166i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	−2.92893	−	5.07306i	−0.219533	−	0.380242i
$179$	6.08579	+	10.5409i	0.454873	+	0.787863i	0.998681	−	0.0513465i	$-0.0163513\pi$
$179$	6.08579	+	10.5409i	0.454873	+	0.787863i	−0.543808	+	0.839210i	$0.683018\pi$
$180$		0			0
$181$	−0.343146			−0.0255058			−0.0127529	−	0.999919i	$-0.504059\pi$
$181$	−0.343146			−0.0255058			−0.0127529	+	0.999919i	$0.504059\pi$
$182$	−3.24264	−	4.18154i	−0.240361	−	0.309956i
$183$		0			0
$184$	−5.55025	+	9.61332i	−0.409170	+	0.708703i
$185$	−7.48528	−	12.9649i	−0.550329	−	0.953197i
$186$		0			0
$187$	0.792893	−	1.37333i	0.0579821	−	0.100428i
$188$	7.62742			0.556287
$189$		0			0
$190$	1.02944			0.0746832
$191$	−5.17157	+	8.95743i	−0.374202	+	0.648137i	−0.990207	−	0.139605i	$-0.955417\pi$
$191$	−5.17157	+	8.95743i	−0.374202	+	0.648137i	0.616005	+	0.787742i	$0.288750\pi$
$192$		0			0
$193$	−8.07107	−	13.9795i	−0.580968	−	1.00627i	−0.995365	−	0.0961701i	$-0.969341\pi$
$193$	−8.07107	−	13.9795i	−0.580968	−	1.00627i	0.414397	−	0.910096i	$-0.363993\pi$
$194$	1.13604	−	1.96768i	0.0815628	−	0.141271i
$195$		0			0
$196$	3.18629	−	12.3960i	0.227592	−	0.885431i
$197$	13.5858			0.967947			0.483974	−	0.875083i	$-0.339193\pi$
$197$	13.5858			0.967947			0.483974	+	0.875083i	$0.339193\pi$
$198$		0			0
$199$	−9.89949	−	17.1464i	−0.701757	−	1.21548i	−0.967849	−	0.251531i	$-0.919066\pi$
$199$	−9.89949	−	17.1464i	−0.701757	−	1.21548i	0.266093	−	0.963947i	$-0.414267\pi$
$200$	0.792893	+	1.37333i	0.0560660	+	0.0971092i
$201$		0			0
$202$	−6.17157			−0.434230
$203$	5.24264	−	12.8418i	0.367961	−	0.901317i
$204$		0			0
$205$	−6.82843	+	11.8272i	−0.476918	+	0.826046i
$206$	−0.928932	−	1.60896i	−0.0647218	−	0.112101i
$207$		0			0
$208$	−7.24264	+	12.5446i	−0.502187	+	0.869813i
$209$	1.24264			0.0859553
$210$		0			0
$211$	−18.9706			−1.30599			−0.652994	−	0.757363i	$-0.726487\pi$
$211$	−18.9706			−1.30599			−0.652994	+	0.757363i	$0.726487\pi$
$212$	11.7279	−	20.3134i	0.805477	−	1.39513i
$213$		0			0
$214$	0.343146	+	0.594346i	0.0234570	+	0.0406286i
$215$	11.2426	−	19.4728i	0.766742	−	1.32804i
$216$		0			0
$217$	14.8284	−	2.02922i	1.00662	−	0.137753i
$218$	0.485281			0.0328674
$219$		0			0
$220$	−1.82843	−	3.16693i	−0.123273	−	0.213514i
$221$	−3.82843	−	6.63103i	−0.257528	−	0.446051i
$222$		0			0
$223$	10.9706			0.734643			0.367322	−	0.930094i	$-0.380275\pi$
$223$	10.9706			0.734643			0.367322	+	0.930094i	$0.380275\pi$
$224$	11.5711	−	1.58346i	0.773124	−	0.105800i
$225$		0			0
$226$	−0.757359	+	1.31178i	−0.0503788	+	0.0872586i
$227$	−9.48528	−	16.4290i	−0.629560	−	1.09043i	−0.987640	−	0.156739i	$-0.949902\pi$
$227$	−9.48528	−	16.4290i	−0.629560	−	1.09043i	0.358080	−	0.933691i	$-0.383432\pi$
$228$		0			0
$229$	2.17157	−	3.76127i	0.143502	−	0.248552i	−0.785311	−	0.619101i	$-0.787497\pi$
$229$	2.17157	−	3.76127i	0.143502	−	0.248552i	0.928813	+	0.370549i	$0.120830\pi$
$230$	−5.79899			−0.382374
$231$		0			0
$232$	8.31371			0.545822
$233$	3.79289	−	6.56948i	0.248481	−	0.430381i	−0.714624	−	0.699509i	$-0.753402\pi$
$233$	3.79289	−	6.56948i	0.248481	−	0.430381i	0.963104	+	0.269128i	$0.0867354\pi$
$234$		0			0
$235$	4.17157	+	7.22538i	0.272123	+	0.471332i
$236$	−2.42893	+	4.20703i	−0.158110	+	0.273855i
$237$		0			0
$238$	−0.656854	+	1.60896i	−0.0425775	+	0.104293i
$239$	−10.4853			−0.678236			−0.339118	−	0.940744i	$-0.610129\pi$
$239$	−10.4853			−0.678236			−0.339118	+	0.940744i	$0.610129\pi$
$240$		0			0
$241$	7.65685	+	13.2621i	0.493221	+	0.854284i	0.999970	−	0.00780972i	$-0.00248593\pi$
$241$	7.65685	+	13.2621i	0.493221	+	0.854284i	−0.506748	+	0.862094i	$0.669153\pi$
$242$	0.207107	+	0.358719i	0.0133133	+	0.0230594i
$243$		0			0
$244$	7.31371			0.468212
$245$	13.4853	−	3.76127i	0.861543	−	0.240299i
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$	4.48528	+	7.76874i	0.284816	+	0.493315i
$249$		0			0
$250$	−2.48528	+	4.30463i	−0.157183	+	0.272249i
$251$	19.4853			1.22990			0.614950	−	0.788566i	$-0.289176\pi$
$251$	19.4853			1.22990			0.614950	+	0.788566i	$0.289176\pi$
$252$		0			0
$253$	−7.00000			−0.440086
$254$	−0.399495	+	0.691946i	−0.0250665	+	0.0434165i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	−14.7279	+	25.5095i	−0.918703	+	1.59124i	−0.117314	+	0.993095i	$0.537429\pi$
$257$	−14.7279	+	25.5095i	−0.918703	+	1.59124i	−0.801388	+	0.598145i	$0.795905\pi$
$258$		0			0
$259$	12.1360	+	15.6500i	0.754097	+	0.972444i
$260$	−17.6569			−1.09503
$261$		0			0
$262$	2.24264	+	3.88437i	0.138551	+	0.239977i
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$	25.6569			1.57609
$266$	−1.34924	+	0.184640i	−0.0827274	+	0.0113210i
$267$		0			0
$268$	−8.07107	+	13.9795i	−0.493019	+	0.853934i
$269$	5.89949	+	10.2182i	0.359699	+	0.623016i	0.987910	−	0.155026i	$-0.0495462\pi$
$269$	5.89949	+	10.2182i	0.359699	+	0.623016i	−0.628212	+	0.778042i	$0.716213\pi$
$270$		0			0
$271$	−5.48528	+	9.50079i	−0.333207	+	0.577132i	−0.983139	−	0.182861i	$-0.941464\pi$
$271$	−5.48528	+	9.50079i	−0.333207	+	0.577132i	0.649932	+	0.759993i	$0.274798\pi$
$272$	4.75736			0.288457
$273$		0			0
$274$	−6.82843			−0.412520
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$		0			0
$277$	7.17157	+	12.4215i	0.430898	+	0.746337i	0.996951	−	0.0780316i	$-0.0248635\pi$
$277$	7.17157	+	12.4215i	0.430898	+	0.746337i	−0.566053	+	0.824369i	$0.691530\pi$
$278$	1.15685	−	2.00373i	0.0693835	−	0.120176i
$279$		0			0
$280$	5.14214	+	6.63103i	0.307301	+	0.396280i
$281$	−11.5858			−0.691150			−0.345575	−	0.938391i	$-0.612316\pi$
$281$	−11.5858			−0.691150			−0.345575	+	0.938391i	$0.612316\pi$
$282$		0			0
$283$	−15.8284	−	27.4156i	−0.940902	−	1.62969i	−0.763755	−	0.645506i	$-0.776646\pi$
$283$	−15.8284	−	27.4156i	−0.940902	−	1.62969i	−0.177147	−	0.984184i	$-0.556687\pi$
$284$	8.98528	+	15.5630i	0.533178	+	0.923492i
$285$		0			0
$286$	2.00000			0.118262
$287$	6.82843	−	16.7262i	0.403069	−	0.987314i
$288$		0			0
$289$	7.24264	−	12.5446i	0.426038	−	0.737919i
$290$	2.17157	+	3.76127i	0.127519	+	0.220870i
$291$		0			0
$292$	10.6569	−	18.4582i	0.623645	−	1.08019i
$293$	19.7279			1.15252			0.576259	−	0.817267i	$-0.304512\pi$
$293$	19.7279			1.15252			0.576259	+	0.817267i	$0.304512\pi$
$294$		0			0
$295$	−5.31371			−0.309376
$296$	−5.93503	+	10.2798i	−0.344967	+	0.597500i
$297$		0			0
$298$	−4.18629	−	7.25087i	−0.242505	−	0.420032i
$299$	−16.8995	+	29.2708i	−0.977323	+	1.69277i
$300$		0			0
$301$	−11.2426	+	27.5387i	−0.648015	+	1.58731i
$302$	−0.372583			−0.0214397
$303$		0			0
$304$	1.86396	+	3.22848i	0.106905	+	0.185166i
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$		0			0
$307$	5.31371			0.303269			0.151635	−	0.988437i	$-0.451546\pi$
$307$	5.31371			0.303269			0.151635	+	0.988437i	$0.451546\pi$
$308$	2.96447	+	3.82282i	0.168916	+	0.217825i
$309$		0			0
$310$	−2.34315	+	4.05845i	−0.133082	+	0.230504i
$311$	−7.81371	−	13.5337i	−0.443075	−	0.767428i	0.554841	−	0.831956i	$-0.312779\pi$
$311$	−7.81371	−	13.5337i	−0.443075	−	0.767428i	−0.997916	+	0.0645283i	$0.979446\pi$
$312$		0			0
$313$	17.3995	−	30.1368i	0.983478	−	1.70343i	0.334962	−	0.942232i	$-0.391276\pi$
$313$	17.3995	−	30.1368i	0.983478	−	1.70343i	0.648515	−	0.761202i	$-0.275390\pi$
$314$	−2.89949			−0.163628
$315$		0			0
$316$	17.0294			0.957981
$317$	−1.34315	+	2.32640i	−0.0754386	+	0.130663i	−0.901277	−	0.433243i	$-0.857369\pi$
$317$	−1.34315	+	2.32640i	−0.0754386	+	0.130663i	0.825838	+	0.563907i	$0.190702\pi$
$318$		0			0
$319$	2.62132	+	4.54026i	0.146766	+	0.254206i
$320$	4.17157	−	7.22538i	0.233198	−	0.403911i
$321$		0			0
$322$	7.60051	−	1.04011i	0.423560	−	0.0579628i
$323$	−1.97056			−0.109645
$324$		0			0
$325$	2.41421	+	4.18154i	0.133916	+	0.231950i
$326$	2.68629	+	4.65279i	0.148780	+	0.257694i
$327$		0			0
$328$	10.8284			0.597900
$329$	−6.76346	−	8.72180i	−0.372881	−	0.480848i
$330$		0			0
$331$	−2.75736	+	4.77589i	−0.151558	+	0.262506i	−0.931800	−	0.362971i	$-0.881762\pi$
$331$	−2.75736	+	4.77589i	−0.151558	+	0.262506i	0.780242	+	0.625477i	$0.215096\pi$
$332$	−2.58579	−	4.47871i	−0.141913	−	0.245801i
$333$		0			0
$334$	−2.24264	+	3.88437i	−0.122712	+	0.212543i
$335$	−17.6569			−0.964697
$336$		0			0
$337$	32.1421			1.75089			0.875447	−	0.483314i	$-0.160567\pi$
$337$	32.1421			1.75089			0.875447	+	0.483314i	$0.160567\pi$
$338$	2.13604	−	3.69973i	0.116185	−	0.201239i
$339$		0			0
$340$	2.89949	+	5.02207i	0.157247	+	0.272360i
$341$	−2.82843	+	4.89898i	−0.153168	+	0.265295i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−17.8284			−0.961244
$345$		0			0
$346$	1.89949	+	3.29002i	0.102117	+	0.176873i
$347$	−9.48528	−	16.4290i	−0.509197	−	0.881954i	−0.999943	−	0.0106521i	$-0.996609\pi$
$347$	−9.48528	−	16.4290i	−0.509197	−	0.881954i	0.490747	−	0.871302i	$-0.336724\pi$
$348$		0			0
$349$	−22.9706			−1.22959			−0.614793	−	0.788688i	$-0.710760\pi$
$349$	−22.9706			−1.22959			−0.614793	+	0.788688i	$0.710760\pi$
$350$	0.414214	−	1.01461i	0.0221406	−	0.0542333i
$351$		0			0
$352$	−2.20711	+	3.82282i	−0.117639	+	0.203757i
$353$	−4.65685	−	8.06591i	−0.247859	−	0.429305i	0.715072	−	0.699051i	$-0.246394\pi$
$353$	−4.65685	−	8.06591i	−0.247859	−	0.429305i	−0.962932	+	0.269746i	$0.913060\pi$
$354$		0			0
$355$	−9.82843	+	17.0233i	−0.521639	+	0.903505i
$356$	25.8579			1.37046
$357$		0			0
$358$	5.04163			0.266458
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	−0.952063	−	0.305903i	$-0.901042\pi$
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	0.740951	+	0.671559i	$0.234375\pi$
$360$		0			0
$361$	8.72792	+	15.1172i	0.459364	+	0.795642i
$362$	−0.0710678	+	0.123093i	−0.00373524	+	0.00646963i
$363$		0			0
$364$	23.1421	−	3.16693i	1.21298	−	0.165992i
$365$	23.3137			1.22030
$366$		0			0
$367$	−12.0711	−	20.9077i	−0.630105	−	1.09137i	−0.987530	−	0.157431i	$-0.949679\pi$
$367$	−12.0711	−	20.9077i	−0.630105	−	1.09137i	0.357425	−	0.933942i	$-0.383655\pi$
$368$	−10.5000	−	18.1865i	−0.547350	−	0.948039i
$369$		0			0
$370$	−6.20101			−0.322375
$371$	−33.6274	+	4.60181i	−1.74585	+	0.238914i
$372$		0			0
$373$	−4.82843	+	8.36308i	−0.250006	+	0.433024i	−0.963527	−	0.267610i	$-0.913766\pi$
$373$	−4.82843	+	8.36308i	−0.250006	+	0.433024i	0.713521	+	0.700634i	$0.247099\pi$
$374$	−0.328427	−	0.568852i	−0.0169826	−	0.0294147i
$375$		0			0
$376$	3.30761	−	5.72895i	0.170577	−	0.295448i
$377$	25.3137			1.30372
$378$		0			0
$379$	13.1716			0.676578			0.338289	−	0.941042i	$-0.390152\pi$
$379$	13.1716			0.676578			0.338289	+	0.941042i	$0.390152\pi$
$380$	−2.27208	+	3.93535i	−0.116555	+	0.201879i
$381$		0			0
$382$	2.14214	+	3.71029i	0.109601	+	0.189835i
$383$	−10.1569	+	17.5922i	−0.518991	+	0.898919i	0.480765	+	0.876849i	$0.340359\pi$
$383$	−10.1569	+	17.5922i	−0.518991	+	0.898919i	−0.999756	+	0.0220695i	$0.992974\pi$
$384$		0			0
$385$	−2.00000	+	4.89898i	−0.101929	+	0.249675i
$386$	−6.68629			−0.340323
$387$		0			0
$388$	5.01472	+	8.68575i	0.254584	+	0.440952i
$389$	13.8995	+	24.0746i	0.704732	+	1.22063i	0.966788	+	0.255580i	$0.0822663\pi$
$389$	13.8995	+	24.0746i	0.704732	+	1.22063i	−0.262056	+	0.965053i	$0.584400\pi$
$390$		0			0
$391$	11.1005			0.561377
$392$	−7.92893	−	7.76874i	−0.400472	−	0.392380i
$393$		0			0
$394$	2.81371	−	4.87349i	0.141753	−	0.245523i
$395$	9.31371	+	16.1318i	0.468624	+	0.811680i
$396$		0			0
$397$	−0.257359	+	0.445759i	−0.0129165	+	0.0223720i	−0.872411	−	0.488772i	$-0.837445\pi$
$397$	−0.257359	+	0.445759i	−0.0129165	+	0.0223720i	0.859495	+	0.511144i	$0.170778\pi$
$398$	−8.20101			−0.411079
$399$		0			0
$400$	−3.00000			−0.150000
$401$	12.2426	−	21.2049i	0.611368	−	1.05892i	−0.379642	−	0.925134i	$-0.623953\pi$
$401$	12.2426	−	21.2049i	0.611368	−	1.05892i	0.991010	−	0.133787i	$-0.0427139\pi$
$402$		0			0
$403$	13.6569	+	23.6544i	0.680296	+	1.17831i
$404$	13.6213	−	23.5928i	0.677686	−	1.17379i
$405$		0			0
$406$	−3.52082	−	4.54026i	−0.174735	−	0.225329i
$407$	−7.48528			−0.371032
$408$		0			0
$409$	−15.8995	−	27.5387i	−0.786179	−	1.36170i	−0.928292	−	0.371852i	$-0.878723\pi$
$409$	−15.8995	−	27.5387i	−0.786179	−	1.36170i	0.142113	−	0.989851i	$-0.454611\pi$
$410$	2.82843	+	4.89898i	0.139686	+	0.241943i
$411$		0			0
$412$	8.20101			0.404035
$413$	6.96447	−	0.953065i	0.342699	−	0.0468973i
$414$		0			0
$415$	2.82843	−	4.89898i	0.138842	−	0.240481i
$416$	10.6569	+	18.4582i	0.522495	+	0.904988i
$417$		0			0
$418$	0.257359	−	0.445759i	0.0125879	−	0.0218028i
$419$	24.7990			1.21151			0.605755	−	0.795651i	$-0.292871\pi$
$419$	24.7990			1.21151			0.605755	+	0.795651i	$0.292871\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	−3.92893	+	6.80511i	−0.191257	+	0.331268i
$423$		0			0
$424$	−10.1716	−	17.6177i	−0.493975	−	0.855590i
$425$	0.792893	−	1.37333i	0.0384610	−	0.0666164i
$426$		0			0
$427$	−6.48528	−	8.36308i	−0.313845	−	0.404718i
$428$	−3.02944			−0.146433
$429$		0			0
$430$	−4.65685	−	8.06591i	−0.224573	−	0.388973i
$431$	−13.4853	−	23.3572i	−0.649563	−	1.12508i	−0.983227	−	0.182384i	$-0.941618\pi$
$431$	−13.4853	−	23.3572i	−0.649563	−	1.12508i	0.333664	−	0.942692i	$-0.391715\pi$
$432$		0			0
$433$	29.1421			1.40048			0.700241	−	0.713907i	$-0.253076\pi$
$433$	29.1421			1.40048			0.700241	+	0.713907i	$0.253076\pi$
$434$	2.34315	−	5.73951i	0.112475	−	0.275505i
$435$		0			0
$436$	−1.07107	+	1.85514i	−0.0512948	+	0.0888453i
$437$	4.34924	+	7.53311i	0.208052	+	0.360357i
$438$		0			0
$439$	−5.55025	+	9.61332i	−0.264899	+	0.458819i	−0.967537	−	0.252729i	$-0.918672\pi$
$439$	−5.55025	+	9.61332i	−0.264899	+	0.458819i	0.702638	+	0.711547i	$0.252005\pi$
$440$	−3.17157			−0.151199
$441$		0			0
$442$	−3.17157			−0.150856
$443$	−5.81371	+	10.0696i	−0.276218	+	0.478423i	−0.970442	−	0.241336i	$-0.922414\pi$
$443$	−5.81371	+	10.0696i	−0.276218	+	0.478423i	0.694224	+	0.719759i	$0.255748\pi$
$444$		0			0
$445$	14.1421	+	24.4949i	0.670402	+	1.16117i
$446$	2.27208	−	3.93535i	0.107586	−	0.186344i
$447$		0			0
$448$	−4.17157	+	10.2182i	−0.197088	+	0.482766i
$449$	4.00000			0.188772			0.0943858	−	0.995536i	$-0.469911\pi$
$449$	4.00000			0.188772			0.0943858	+	0.995536i	$0.469911\pi$
$450$		0			0
$451$	3.41421	+	5.91359i	0.160769	+	0.278460i
$452$	−3.34315	−	5.79050i	−0.157248	−	0.272362i
$453$		0			0
$454$	−7.85786			−0.368788
$455$	15.6569	+	20.1903i	0.734005	+	0.946534i
$456$		0			0
$457$	−6.58579	+	11.4069i	−0.308070	+	0.533593i	−0.977940	−	0.208885i	$-0.933016\pi$
$457$	−6.58579	+	11.4069i	−0.308070	+	0.533593i	0.669870	+	0.742478i	$0.266350\pi$
$458$	−0.899495	−	1.55797i	−0.0420306	−	0.0727992i
$459$		0			0
$460$	12.7990	−	22.1685i	0.596756	−	1.03361i
$461$	−15.2426			−0.709921			−0.354960	−	0.934881i	$-0.615506\pi$
$461$	−15.2426			−0.709921			−0.354960	+	0.934881i	$0.615506\pi$
$462$		0			0
$463$	−26.6274			−1.23748			−0.618741	−	0.785595i	$-0.712357\pi$
$463$	−26.6274			−1.23748			−0.618741	+	0.785595i	$0.712357\pi$
$464$	−7.86396	+	13.6208i	−0.365075	+	0.632329i
$465$		0			0
$466$	−1.57107	−	2.72117i	−0.0727783	−	0.126056i
$467$	7.15685	−	12.3960i	0.331180	−	0.573620i	−0.651564	−	0.758594i	$-0.725887\pi$
$467$	7.15685	−	12.3960i	0.331180	−	0.573620i	0.982743	+	0.184974i	$0.0592200\pi$
$468$		0			0
$469$	23.1421	−	3.16693i	1.06860	−	0.146235i
$470$	3.45584			0.159406
$471$		0			0
$472$	2.10660	+	3.64874i	0.0969642	+	0.167947i
$473$	−5.62132	−	9.73641i	−0.258469	−	0.447681i
$474$		0			0
$475$	1.24264			0.0570163
$476$	−4.70101	−	6.06218i	−0.215470	−	0.277859i
$477$		0			0
$478$	−2.17157	+	3.76127i	−0.0993254	+	0.172037i
$479$	7.00000	+	12.1244i	0.319838	+	0.553976i	0.980454	−	0.196748i	$-0.0630381\pi$
$479$	7.00000	+	12.1244i	0.319838	+	0.553976i	−0.660616	+	0.750724i	$0.729705\pi$
$480$		0			0
$481$	−18.0711	+	31.3000i	−0.823970	+	1.42716i
$482$	6.34315			0.288922
$483$		0			0
$484$	−1.82843			−0.0831103
$485$	−5.48528	+	9.50079i	−0.249074	+	0.431408i
$486$		0			0
$487$	−6.31371	−	10.9357i	−0.286101	−	0.495542i	0.686774	−	0.726871i	$-0.259026\pi$
$487$	−6.31371	−	10.9357i	−0.286101	−	0.495542i	−0.972876	+	0.231329i	$0.925693\pi$
$488$	3.17157	−	5.49333i	0.143570	−	0.248671i
$489$		0			0
$490$	1.44365	−	5.61642i	0.0652175	−	0.253724i
$491$	18.4853			0.834229			0.417115	−	0.908854i	$-0.363041\pi$
$491$	18.4853			0.834229			0.417115	+	0.908854i	$0.363041\pi$
$492$		0			0
$493$	−4.15685	−	7.19988i	−0.187215	−	0.324266i
$494$	−1.24264	−	2.15232i	−0.0559090	−	0.0968373i
$495$		0			0
$496$	−16.9706			−0.762001
$497$	9.82843	−	24.0746i	0.440865	−	1.07989i
$498$		0			0
$499$	−3.89949	+	6.75412i	−0.174565	+	0.302356i	−0.940011	−	0.341145i	$-0.889185\pi$
$499$	−3.89949	+	6.75412i	−0.174565	+	0.302356i	0.765445	+	0.643501i	$0.222519\pi$
$500$	−10.9706	−	19.0016i	−0.490618	−	0.849776i
$501$		0			0
$502$	4.03553	−	6.98975i	0.180115	−	0.311968i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	29.7990			1.32604
$506$	−1.44975	+	2.51104i	−0.0644491	+	0.111629i
$507$		0			0
$508$	−1.76346	−	3.05440i	−0.0782407	−	0.135517i
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	−0.967811	−	0.251679i	$-0.919017\pi$
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	0.701866	+	0.712309i	$0.252351\pi$
$510$		0			0
$511$	−30.5563	+	4.18154i	−1.35173	+	0.184980i
$512$	−22.7574			−1.00574
$513$		0			0
$514$	6.10051	+	10.5664i	0.269082	+	0.466063i
$515$	4.48528	+	7.76874i	0.197645	+	0.342331i
$516$		0			0
$517$	4.17157			0.183466
$518$	8.12742	−	1.11221i	0.357098	−	0.0488678i
$519$		0			0
$520$	−7.65685	+	13.2621i	−0.335775	+	0.581580i
$521$	18.4142	+	31.8944i	0.806741	+	1.39732i	0.915109	+	0.403206i	$0.132104\pi$
$521$	18.4142	+	31.8944i	0.806741	+	1.39732i	−0.108368	+	0.994111i	$0.534562\pi$
$522$		0			0
$523$	−17.1421	+	29.6910i	−0.749573	+	1.29830i	0.198454	+	0.980110i	$0.436408\pi$
$523$	−17.1421	+	29.6910i	−0.749573	+	1.29830i	−0.948027	+	0.318189i	$0.896925\pi$
$524$	−19.7990			−0.864923
$525$		0			0
$526$	7.45584			0.325090
$527$	4.48528	−	7.76874i	0.195382	−	0.338411i
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$	5.31371	−	9.20361i	0.230813	−	0.399779i
$531$		0			0
$532$	2.27208	−	5.56543i	0.0985071	−	0.241292i
$533$	32.9706			1.42811
$534$		0			0
$535$	−1.65685	−	2.86976i	−0.0716321	−	0.124070i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$		0			0
$538$	4.88730			0.210707
$539$	1.74264	−	6.77962i	0.0750608	−	0.292019i
$540$		0			0
$541$	−4.17157	+	7.22538i	−0.179350	+	0.310643i	−0.941658	−	0.336571i	$-0.890733\pi$
$541$	−4.17157	+	7.22538i	−0.179350	+	0.310643i	0.762308	+	0.647214i	$0.224066\pi$
$542$	2.27208	+	3.93535i	0.0975941	+	0.169038i
$543$		0			0
$544$	3.50000	−	6.06218i	0.150061	−	0.259914i
$545$	−2.34315			−0.100369
$546$		0			0
$547$	18.2132			0.778740			0.389370	−	0.921081i	$-0.372693\pi$
$547$	18.2132			0.778740			0.389370	+	0.921081i	$0.372693\pi$
$548$	15.0711	−	26.1039i	0.643804	−	1.11510i
$549$		0			0
$550$	0.207107	+	0.358719i	0.00883106	+	0.0152958i
$551$	3.25736	−	5.64191i	0.138768	−	0.240354i
$552$		0			0
$553$	−15.1005	−	19.4728i	−0.642139	−	0.828069i
$554$	5.94113			0.252414
$555$		0			0
$556$	5.10660	+	8.84489i	0.216568	+	0.375107i
$557$	11.2782	+	19.5344i	0.477872	+	0.827698i	0.999678	−	0.0253659i	$-0.00807509\pi$
$557$	11.2782	+	19.5344i	0.477872	+	0.827698i	−0.521807	+	0.853064i	$0.674742\pi$
$558$		0			0
$559$	−54.2843			−2.29598
$560$	−15.7279	+	2.15232i	−0.664626	+	0.0909520i
$561$		0			0
$562$	−2.39949	+	4.15605i	−0.101217	+	0.175312i
$563$	9.58579	+	16.6031i	0.403993	+	0.699736i	0.994204	−	0.107513i	$-0.0342888\pi$
$563$	9.58579	+	16.6031i	0.403993	+	0.699736i	−0.590211	+	0.807249i	$0.700955\pi$
$564$		0			0
$565$	3.65685	−	6.33386i	0.153845	−	0.266467i
$566$	−13.1127			−0.551168
$567$		0			0
$568$	15.5858			0.653965
$569$	−3.62132	+	6.27231i	−0.151814	+	0.262949i	−0.931894	−	0.362730i	$-0.881845\pi$
$569$	−3.62132	+	6.27231i	−0.151814	+	0.262949i	0.780081	+	0.625679i	$0.215178\pi$
$570$		0			0
$571$	9.03553	+	15.6500i	0.378125	+	0.654932i	0.990790	−	0.135411i	$-0.0432355\pi$
$571$	9.03553	+	15.6500i	0.378125	+	0.654932i	−0.612664	+	0.790343i	$0.709902\pi$
$572$	−4.41421	+	7.64564i	−0.184568	+	0.319680i
$573$		0			0
$574$	−4.58579	−	5.91359i	−0.191407	−	0.246829i
$575$	−7.00000			−0.291920
$576$		0			0
$577$	1.82843	+	3.16693i	0.0761184	+	0.131841i	0.901572	−	0.432629i	$-0.142414\pi$
$577$	1.82843	+	3.16693i	0.0761184	+	0.131841i	−0.825454	+	0.564470i	$0.809081\pi$
$578$	−3.00000	−	5.19615i	−0.124784	−	0.216131i
$579$		0			0
$580$	−19.1716			−0.796056
$581$	−2.82843	+	6.92820i	−0.117343	+	0.287430i
$582$		0			0
$583$	6.41421	−	11.1097i	0.265650	−	0.460119i
$584$	−9.24264	−	16.0087i	−0.382463	−	0.662446i
$585$		0			0
$586$	4.08579	−	7.07679i	0.168782	−	0.292339i
$587$	−31.3137			−1.29246			−0.646228	−	0.763145i	$-0.723654\pi$
$587$	−31.3137			−1.29246			−0.646228	+	0.763145i	$0.723654\pi$
$588$		0			0
$589$	7.02944			0.289643
$590$	−1.10051	+	1.90613i	−0.0453071	+	0.0784742i
$591$		0			0
$592$	−11.2279	−	19.4473i	−0.461465	−	0.799280i
$593$	−23.8640	+	41.3336i	−0.979975	+	1.69737i	−0.317546	+	0.948243i	$0.602859\pi$
$593$	−23.8640	+	41.3336i	−0.979975	+	1.69737i	−0.662429	+	0.749124i	$0.730475\pi$
$594$		0			0
$595$	3.17157	−	7.76874i	0.130022	−	0.318487i
$596$	36.9584			1.51387
$597$		0			0
$598$	7.00000	+	12.1244i	0.286251	+	0.495802i
$599$	−23.3137	−	40.3805i	−0.952572	−	1.64990i	−0.739828	−	0.672796i	$-0.765093\pi$
$599$	−23.3137	−	40.3805i	−0.952572	−	1.64990i	−0.212744	−	0.977108i	$-0.568240\pi$
$600$		0			0
$601$	2.48528			0.101377			0.0506884	−	0.998715i	$-0.483858\pi$
$601$	2.48528			0.101377			0.0506884	+	0.998715i	$0.483858\pi$
$602$	7.55025	+	9.73641i	0.307725	+	0.396827i
$603$		0			0
$604$	0.822330	−	1.42432i	0.0334602	−	0.0579547i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	20.6569	−	35.7787i	0.838436	−	1.45221i	−0.0527662	−	0.998607i	$-0.516804\pi$
$607$	20.6569	−	35.7787i	0.838436	−	1.45221i	0.891202	−	0.453607i	$-0.149863\pi$
$608$	5.48528			0.222458
$609$		0			0
$610$	3.31371			0.134168
$611$	10.0711	−	17.4436i	0.407432	−	0.705693i
$612$		0			0
$613$	−15.4142	−	26.6982i	−0.622574	−	1.07833i	−0.989005	−	0.147885i	$-0.952754\pi$
$613$	−15.4142	−	26.6982i	−0.622574	−	1.07833i	0.366430	−	0.930445i	$-0.380580\pi$
$614$	1.10051	−	1.90613i	0.0444128	−	0.0769252i
$615$		0			0
$616$	4.15685	−	0.568852i	0.167484	−	0.0229197i
$617$	−18.8284			−0.758004			−0.379002	−	0.925396i	$-0.623733\pi$
$617$	−18.8284			−0.758004			−0.379002	+	0.925396i	$0.623733\pi$
$618$		0			0
$619$	5.31371	+	9.20361i	0.213576	+	0.369924i	0.952831	−	0.303501i	$-0.0981556\pi$
$619$	5.31371	+	9.20361i	0.213576	+	0.369924i	−0.739255	+	0.673425i	$0.764822\pi$
$620$	−10.3431	−	17.9149i	−0.415391	−	0.719478i
$621$		0			0
$622$	−6.47309			−0.259547
$623$	−22.9289	−	29.5680i	−0.918628	−	1.18462i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−7.20711	−	12.4831i	−0.288054	−	0.498924i
$627$		0			0
$628$	6.39949	−	11.0843i	0.255368	−	0.442310i
$629$	11.8701			0.473290
$630$		0			0
$631$	−30.2843			−1.20560			−0.602799	−	0.797893i	$-0.705948\pi$
$631$	−30.2843			−1.20560			−0.602799	+	0.797893i	$0.705948\pi$
$632$	7.38478	−	12.7908i	0.293751	−	0.508791i
$633$		0			0
$634$	0.556349	+	0.963625i	0.0220954	+	0.0382704i
$635$	1.92893	−	3.34101i	0.0765473	−	0.132584i
$636$		0			0
$637$	−24.1421	−	23.6544i	−0.956546	−	0.937220i
$638$	2.17157			0.0859734
$639$		0			0
$640$	−10.5563	−	18.2841i	−0.417276	−	0.722744i
$641$	2.24264	+	3.88437i	0.0885790	+	0.153423i	0.906911	−	0.421323i	$-0.138434\pi$
$641$	2.24264	+	3.88437i	0.0885790	+	0.153423i	−0.818332	+	0.574746i	$0.805101\pi$
$642$		0			0
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$	−12.7990	+	31.3510i	−0.504351	+	1.23540i
$645$		0			0
$646$	−0.408117	+	0.706879i	−0.0160571	+	0.0278118i
$647$	1.65685	+	2.86976i	0.0651377	+	0.112822i	0.896755	−	0.442527i	$-0.145918\pi$
$647$	1.65685	+	2.86976i	0.0651377	+	0.112822i	−0.831617	+	0.555349i	$0.812585\pi$
$648$		0			0
$649$	−1.32843	+	2.30090i	−0.0521453	+	0.0903184i
$650$	2.00000			0.0784465
$651$		0			0
$652$	−23.7157			−0.928780
$653$	−15.5563	+	26.9444i	−0.608767	+	1.05442i	0.382677	+	0.923882i	$0.375002\pi$
$653$	−15.5563	+	26.9444i	−0.608767	+	1.05442i	−0.991444	+	0.130533i	$0.958331\pi$
$654$		0			0
$655$	−10.8284	−	18.7554i	−0.423102	−	0.732834i
$656$	−10.2426	+	17.7408i	−0.399908	+	0.692661i
$657$		0			0
$658$	−4.52944	+	0.619839i	−0.176576	+	0.0241639i
$659$	−17.5147			−0.682277			−0.341138	−	0.940013i	$-0.610812\pi$
$659$	−17.5147			−0.682277			−0.341138	+	0.940013i	$0.610812\pi$
$660$		0			0
$661$	10.9853	+	19.0271i	0.427278	+	0.740067i	0.996630	−	0.0820266i	$-0.0261393\pi$
$661$	10.9853	+	19.0271i	0.427278	+	0.740067i	−0.569352	+	0.822094i	$0.692806\pi$
$662$	1.14214	+	1.97824i	0.0443904	+	0.0768864i
$663$		0			0
$664$	−4.48528			−0.174063
$665$	6.51472	−	0.891519i	0.252630	−	0.0345716i
$666$		0			0
$667$	−18.3492	+	31.7818i	−0.710486	+	1.23060i
$668$	−9.89949	−	17.1464i	−0.383023	−	0.663415i
$669$		0			0
$670$	−3.65685	+	6.33386i	−0.141277	+	0.244698i
$671$	4.00000			0.154418
$672$		0			0
$673$	32.8284			1.26544			0.632721	−	0.774379i	$-0.281938\pi$
$673$	32.8284			1.26544			0.632721	+	0.774379i	$0.281938\pi$
$674$	6.65685	−	11.5300i	0.256412	−	0.444119i
$675$		0			0
$676$	9.42893	+	16.3314i	0.362651	+	0.628130i
$677$	25.0061	−	43.3118i	0.961062	−	1.66461i	0.241221	−	0.970470i	$-0.422452\pi$
$677$	25.0061	−	43.3118i	0.961062	−	1.66461i	0.719841	−	0.694139i	$-0.244215\pi$
$678$		0			0
$679$	5.48528	−	13.4361i	0.210506	−	0.515632i
$680$	5.02944			0.192870
$681$		0			0
$682$	1.17157	+	2.02922i	0.0448618	+	0.0777030i
$683$	21.3995	+	37.0650i	0.818829	+	1.41825i	0.906546	+	0.422108i	$0.138710\pi$
$683$	21.3995	+	37.0650i	0.818829	+	1.41825i	−0.0877167	+	0.996145i	$0.527957\pi$
$684$		0			0
$685$	32.9706			1.25974
$686$	−0.884776	+	7.62015i	−0.0337809	+	0.290939i
$687$		0			0
$688$	16.8640	−	29.2092i	0.642932	−	1.11359i
$689$	−30.9706	−	53.6426i	−1.17988	−	2.04362i
$690$		0			0
$691$	−19.7279	+	34.1698i	−0.750486	+	1.29988i	0.197102	+	0.980383i	$0.436847\pi$
$691$	−19.7279	+	34.1698i	−0.750486	+	1.29988i	−0.947588	+	0.319496i	$0.896486\pi$
$692$	−16.7696			−0.637483
$693$		0			0
$694$	−7.85786			−0.298280
$695$	−5.58579	+	9.67487i	−0.211881	+	0.366989i
$696$		0			0
$697$	−5.41421	−	9.37769i	−0.205078	−	0.355205i
$698$	−4.75736	+	8.23999i	−0.180069	+	0.311888i
$699$		0			0
$700$	2.96447	+	3.82282i	0.112046	+	0.144489i
$701$	−16.8995			−0.638285			−0.319143	−	0.947707i	$-0.603395\pi$
$701$	−16.8995			−0.638285			−0.319143	+	0.947707i	$0.603395\pi$
$702$		0			0
$703$	4.65076	+	8.05535i	0.175407	+	0.303813i
$704$	−2.08579	−	3.61269i	−0.0786110	−	0.136158i
$705$		0			0
$706$	−3.85786			−0.145193
$707$	−39.0563	+	5.34474i	−1.46887	+	0.201010i
$708$		0			0
$709$	23.8848	−	41.3696i	0.897012	−	1.55367i	0.0657165	−	0.997838i	$-0.479067\pi$
$709$	23.8848	−	41.3696i	0.897012	−	1.55367i	0.831295	−	0.555831i	$-0.187600\pi$
$710$	4.07107	+	7.05130i	0.152784	+	0.264630i
$711$		0			0
$712$	11.2132	−	19.4218i	0.420233	−	0.727864i
$713$	−39.5980			−1.48296
$714$		0			0
$715$	−9.65685			−0.361146
$716$	−11.1274	+	19.2733i	−0.415851	+	0.720275i
$717$		0			0
$718$	1.65685	+	2.86976i	0.0618333	+	0.107098i
$719$	25.3995	−	43.9932i	0.947241	−	1.64067i	0.196041	−	0.980596i	$-0.437191\pi$
$719$	25.3995	−	43.9932i	0.947241	−	1.64067i	0.751200	−	0.660074i	$-0.229475\pi$
$720$		0			0
$721$	−7.27208	−	9.37769i	−0.270826	−	0.349244i
$722$	7.23045			0.269089
$723$		0			0
$724$	−0.313708	−	0.543359i	−0.0116589	−	0.0201938i
$725$	2.62132	+	4.54026i	0.0973534	+	0.168621i
$726$		0			0
$727$	−50.0833			−1.85749			−0.928743	−	0.370725i	$-0.879109\pi$
$727$	−50.0833			−1.85749			−0.928743	+	0.370725i	$0.879109\pi$
$728$	7.65685	−	18.7554i	0.283782	−	0.695121i
$729$		0			0
$730$	4.82843	−	8.36308i	0.178708	−	0.309532i
$731$	8.91421	+	15.4399i	0.329704	+	0.571064i
$732$		0			0
$733$	0.828427	−	1.43488i	0.0305987	−	0.0529984i	−0.850321	−	0.526265i	$-0.823592\pi$
$733$	0.828427	−	1.43488i	0.0305987	−	0.0529984i	0.880919	+	0.473267i	$0.156925\pi$
$734$	−10.0000			−0.369107
$735$		0			0
$736$	−30.8995			−1.13897
$737$	−4.41421	+	7.64564i	−0.162600	+	0.281631i
$738$		0			0
$739$	14.1716	+	24.5459i	0.521310	+	0.902935i	0.999693	+	0.0247837i	$0.00788971\pi$
$739$	14.1716	+	24.5459i	0.521310	+	0.902935i	−0.478383	+	0.878151i	$0.658777\pi$
$740$	13.6863	−	23.7054i	0.503118	−	0.871426i
$741$		0			0
$742$	−5.31371	+	13.0159i	−0.195072	+	0.477828i
$743$	5.79899			0.212744			0.106372	−	0.994326i	$-0.466077\pi$
$743$	5.79899			0.212744			0.106372	+	0.994326i	$0.466077\pi$
$744$		0			0
$745$	20.2132	+	35.0103i	0.740554	+	1.28268i
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$		0			0
$748$	2.89949			0.106016
$749$	2.68629	+	3.46410i	0.0981550	+	0.126576i
$750$		0			0
$751$	3.34315	−	5.79050i	0.121993	−	0.211298i	−0.798560	−	0.601915i	$-0.794405\pi$
$751$	3.34315	−	5.79050i	0.121993	−	0.211298i	0.920554	+	0.390616i	$0.127738\pi$
$752$	6.25736	+	10.8381i	0.228182	+	0.395224i
$753$		0			0
$754$	5.24264	−	9.08052i	0.190926	−	0.330693i
$755$	1.79899			0.0654719
$756$		0			0
$757$	−30.3137			−1.10177			−0.550885	−	0.834581i	$-0.685710\pi$
$757$	−30.3137			−1.10177			−0.550885	+	0.834581i	$0.685710\pi$
$758$	2.72792	−	4.72490i	0.0990826	−	0.171616i
$759$		0			0
$760$	1.97056	+	3.41311i	0.0714798	+	0.123807i
$761$	−19.8995	+	34.4669i	−0.721356	+	1.24943i	0.239100	+	0.970995i	$0.423148\pi$
$761$	−19.8995	+	34.4669i	−0.721356	+	1.24943i	−0.960456	+	0.278431i	$0.910186\pi$
$762$		0			0
$763$	3.07107	−	0.420266i	0.111180	−	0.0152147i
$764$	−18.9117			−0.684201
$765$		0			0
$766$	4.20711	+	7.28692i	0.152009	+	0.263287i
$767$	6.41421	+	11.1097i	0.231604	+	0.401150i
$768$		0			0
$769$	−5.79899			−0.209117			−0.104558	−	0.994519i	$-0.533343\pi$
$769$	−5.79899			−0.209117			−0.104558	+	0.994519i	$0.533343\pi$
$770$	1.34315	+	1.73205i	0.0484036	+	0.0624188i
$771$		0			0
$772$	14.7574	−	25.5605i	0.531129	−	0.919942i
$773$	−20.1716	−	34.9382i	−0.725521	−	1.25664i	−0.958759	−	0.284220i	$-0.908265\pi$
$773$	−20.1716	−	34.9382i	−0.725521	−	1.25664i	0.233238	−	0.972420i	$-0.425068\pi$
$774$		0			0
$775$	−2.82843	+	4.89898i	−0.101600	+	0.175977i
$776$	8.69848			0.312257
$777$		0			0
$778$	11.5147			0.412823
$779$	4.24264	−	7.34847i	0.152008	−	0.263286i
$780$		0			0
$781$	4.91421	+	8.51167i	0.175844	+	0.304571i
$782$	2.29899	−	3.98197i	0.0822117	−	0.142395i
$783$		0			0
$784$	20.2279	−	5.64191i	0.722426	−	0.201497i
$785$	14.0000			0.499681
$786$		0			0
$787$	17.7635	+	30.7672i	0.633199	+	1.09673i	0.986894	+	0.161372i	$0.0515918\pi$
$787$	17.7635	+	30.7672i	0.633199	+	1.09673i	−0.353695	+	0.935361i	$0.615075\pi$
$788$	12.4203	+	21.5126i	0.442455	+	0.766355i
$789$		0			0
$790$	7.71573			0.274513
$791$	−3.65685	+	8.95743i	−0.130023	+	0.318489i
$792$		0			0
$793$	9.65685	−	16.7262i	0.342925	−	0.593963i
$794$	0.106602	+	0.184640i	0.00378315	+	0.00655261i
$795$		0			0
$796$	18.1005	−	31.3510i	0.641555	−	1.11121i
$797$	−16.8284			−0.596093			−0.298047	−	0.954551i	$-0.596335\pi$
$797$	−16.8284			−0.596093			−0.298047	+	0.954551i	$0.596335\pi$
$798$		0			0
$799$	−6.61522			−0.234030
$800$	−2.20711	+	3.82282i	−0.0780330	+	0.135157i
$801$		0			0
$802$	−5.07107	−	8.78335i	−0.179066	−	0.310151i
$803$	5.82843	−	10.0951i	0.205681	−	0.356249i
$804$		0			0
$805$	−36.6985	+	5.02207i	−1.29345	+	0.177005i
$806$	11.3137			0.398508
$807$		0			0
$808$	−11.8137	−	20.4619i	−0.415605	−	0.719849i
$809$	2.58579	+	4.47871i	0.0909114	+	0.157463i	0.907895	−	0.419198i	$-0.137689\pi$
$809$	2.58579	+	4.47871i	0.0909114	+	0.157463i	−0.816983	+	0.576661i	$0.804355\pi$
$810$		0			0
$811$	−18.9706			−0.666147			−0.333073	−	0.942901i	$-0.608086\pi$
$811$	−18.9706			−0.666147			−0.333073	+	0.942901i	$0.608086\pi$
$812$	25.1274	−	3.43861i	0.881799	−	0.120671i
$813$		0			0
$814$	−1.55025	+	2.68512i	−0.0543363	+	0.0941133i
$815$	−12.9706	−	22.4657i	−0.454339	−	0.786938i
$816$		0			0
$817$	−6.98528	+	12.0989i	−0.244384	+	0.423286i
$818$	−13.1716			−0.460533
$819$		0			0
$820$	−24.9706			−0.872010
$821$	16.5858	−	28.7274i	0.578848	−	1.00259i	−0.416764	−	0.909015i	$-0.636836\pi$
$821$	16.5858	−	28.7274i	0.578848	−	1.00259i	0.995612	−	0.0935793i	$-0.0298309\pi$
$822$		0			0
$823$	19.4142	+	33.6264i	0.676737	+	1.17214i	0.975958	+	0.217959i	$0.0699399\pi$
$823$	19.4142	+	33.6264i	0.676737	+	1.17214i	−0.299221	+	0.954184i	$0.596727\pi$
$824$	3.55635	−	6.15978i	0.123891	−	0.214586i
$825$		0			0
$826$	1.10051	−	2.69568i	0.0382915	−	0.0937946i
$827$	14.6863			0.510692			0.255346	−	0.966850i	$-0.417811\pi$
$827$	14.6863			0.510692			0.255346	+	0.966850i	$0.417811\pi$
$828$		0			0
$829$	5.91421	+	10.2437i	0.205409	+	0.355779i	0.950263	−	0.311449i	$-0.100814\pi$
$829$	5.91421	+	10.2437i	0.205409	+	0.355779i	−0.744854	+	0.667228i	$0.767481\pi$
$830$	−1.17157	−	2.02922i	−0.0406659	−	0.0704354i
$831$		0			0
$832$	−20.1421			−0.698303
$833$	−2.76346	+	10.7510i	−0.0957481	+	0.372501i
$834$		0			0
$835$	10.8284	−	18.7554i	0.374733	−	0.649057i
$836$	1.13604	+	1.96768i	0.0392907	+	0.0680535i
$837$		0			0
$838$	5.13604	−	8.89588i	0.177422	−	0.307303i
$839$	24.9706			0.862080			0.431040	−	0.902333i	$-0.358147\pi$
$839$	24.9706			0.862080			0.431040	+	0.902333i	$0.358147\pi$
$840$		0			0
$841$	−1.51472			−0.0522317
$842$	−1.44975	+	2.51104i	−0.0499616	+	0.0865360i
$843$		0			0
$844$	−17.3431	−	30.0392i	−0.596976	−	1.03399i
$845$	−10.3137	+	17.8639i	−0.354802	+	0.614536i
$846$		0			0
$847$	1.62132	+	2.09077i	0.0557092	+	0.0718397i
$848$	38.4853			1.32159
$849$		0			0
$850$	−0.328427	−	0.568852i	−0.0112650	−	0.0195115i
$851$	−26.1985	−	45.3771i	−0.898072	−	1.55551i
$852$		0			0
$853$	4.48528			0.153573			0.0767866	−	0.997048i	$-0.475534\pi$
$853$	4.48528			0.153573			0.0767866	+	0.997048i	$0.475534\pi$
$854$	−4.34315	+	0.594346i	−0.148619	+	0.0203381i
$855$		0			0
$856$	−1.31371	+	2.27541i	−0.0449016	+	0.0777719i
$857$	13.1777	+	22.8244i	0.450141	+	0.779666i	0.998394	−	0.0566456i	$-0.0180405\pi$
$857$	13.1777	+	22.8244i	0.450141	+	0.779666i	−0.548254	+	0.836312i	$0.684707\pi$
$858$		0			0
$859$	3.75736	−	6.50794i	0.128199	−	0.222048i	−0.794780	−	0.606898i	$-0.792414\pi$
$859$	3.75736	−	6.50794i	0.128199	−	0.222048i	0.922979	+	0.384850i	$0.125747\pi$
$860$	41.1127			1.40193
$861$		0			0
$862$	−11.1716			−0.380505
$863$	−21.3137	+	36.9164i	−0.725527	+	1.25665i	0.233230	+	0.972422i	$0.425071\pi$
$863$	−21.3137	+	36.9164i	−0.725527	+	1.25665i	−0.958757	+	0.284228i	$0.908263\pi$
$864$		0			0
$865$	−9.17157	−	15.8856i	−0.311843	−	0.540128i
$866$	6.03553	−	10.4539i	0.205096	−	0.355236i
$867$		0			0
$868$	16.7696	+	21.6251i	0.569196	+	0.734005i
$869$	9.31371			0.315946
$870$		0			0
$871$	21.3137	+	36.9164i	0.722187	+	1.25087i
$872$	0.928932	+	1.60896i	0.0314576	+	0.0544862i
$873$		0			0
$874$	3.60303			0.121874
$875$	−12.0000	+	29.3939i	−0.405674	+	0.993694i
$876$		0			0
$877$	7.24264	−	12.5446i	0.244567	−	0.423602i	−0.717443	−	0.696617i	$-0.754688\pi$
$877$	7.24264	−	12.5446i	0.244567	−	0.423602i	0.962010	+	0.273015i	$0.0880210\pi$
$878$	2.29899	+	3.98197i	0.0775872	+	0.134385i
$879$		0			0
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−39.3137			−1.32451			−0.662256	−	0.749277i	$-0.730401\pi$
$881$	−39.3137			−1.32451			−0.662256	+	0.749277i	$0.730401\pi$
$882$		0			0
$883$	28.3431			0.953823			0.476911	−	0.878951i	$-0.341756\pi$
$883$	28.3431			0.953823			0.476911	+	0.878951i	$0.341756\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$		0			0
$886$	2.40812	+	4.17098i	0.0809023	+	0.140127i
$887$	4.65685	−	8.06591i	0.156362	−	0.270827i	−0.777192	−	0.629263i	$-0.783357\pi$
$887$	4.65685	−	8.06591i	0.156362	−	0.270827i	0.933554	+	0.358437i	$0.116690\pi$
$888$		0			0
$889$	−1.92893	+	4.72490i	−0.0646943	+	0.158468i
$890$	11.7157			0.392712
$891$		0			0
$892$	10.0294	+	17.3715i	0.335810	+	0.581641i
$893$	−2.59188	−	4.48927i	−0.0867341	−	0.150228i
$894$		0			0
$895$	−24.3431			−0.813702
$896$	17.1152	+	22.0709i	0.571779	+	0.737337i
$897$		0			0
$898$	0.828427	−	1.43488i	0.0276450	−	0.0478825i
$899$	14.8284	+	25.6836i	0.494556	+	0.856596i
$900$		0			0
$901$	−10.1716	+	17.6177i	−0.338864	+	0.586930i
$902$	2.82843			0.0941763
$903$		0			0
$904$	−5.79899			−0.192872
$905$	0.343146	−	0.594346i	0.0114066	−	0.0197567i
$906$		0			0
$907$	17.2426	+	29.8651i	0.572532	+	0.991655i	0.996305	+	0.0858867i	$0.0273723\pi$
$907$	17.2426	+	29.8651i	0.572532	+	0.991655i	−0.423772	+	0.905769i	$0.639294\pi$
$908$	17.3431	−	30.0392i	0.575553	−	0.996886i
$909$		0			0
$910$	10.4853	−	1.43488i	0.347584	−	0.0475657i
$911$	21.4853			0.711839			0.355920	−	0.934517i	$-0.384168\pi$
$911$	21.4853			0.711839			0.355920	+	0.934517i	$0.384168\pi$
$912$		0			0
$913$	−1.41421	−	2.44949i	−0.0468036	−	0.0810663i
$914$	2.72792	+	4.72490i	0.0902316	+	0.156286i
$915$		0			0
$916$	7.94113			0.262382
$917$	17.5563	+	22.6398i	0.579762	+	0.747631i
$918$		0			0
$919$	7.17767	−	12.4321i	0.236769	−	0.410097i	−0.723016	−	0.690831i	$-0.757245\pi$
$919$	7.17767	−	12.4321i	0.236769	−	0.410097i	0.959785	+	0.280735i	$0.0905781\pi$
$920$	−11.1005	−	19.2266i	−0.365973	−	0.633884i
$921$		0			0
$922$	−3.15685	+	5.46783i	−0.103965	+	0.180073i
$923$	47.4558			1.56203
$924$		0			0
$925$	−7.48528			−0.246115
$926$	−5.51472	+	9.55177i	−0.181225	+	0.313891i
$927$		0			0
$928$	11.5711	+	20.0417i	0.379839	+	0.657900i
$929$	−8.58579	+	14.8710i	−0.281691	+	0.487902i	−0.971801	−	0.235802i	$-0.924228\pi$
$929$	−8.58579	+	14.8710i	−0.281691	+	0.487902i	0.690111	+	0.723704i	$0.257562\pi$
$930$		0			0
$931$	−8.37868	+	2.33696i	−0.274600	+	0.0765907i
$932$	13.8701			0.454329
$933$		0			0
$934$	−2.96447	−	5.13461i	−0.0970003	−	0.168009i
$935$	1.58579	+	2.74666i	0.0518608	+	0.0898255i
$936$		0			0
$937$	34.1421			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$937$	34.1421			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$938$	3.65685	−	8.95743i	0.119401	−	0.292470i
$939$		0			0
$940$	−7.62742	+	13.2111i	−0.248779	+	0.430898i
$941$	1.03553	+	1.79360i	0.0337574	+	0.0584696i	0.882411	−	0.470480i	$-0.155919\pi$
$941$	1.03553	+	1.79360i	0.0337574	+	0.0584696i	−0.848653	+	0.528950i	$0.822586\pi$
$942$		0			0
$943$	−23.8995	+	41.3951i	−0.778275	+	1.34801i
$944$	−7.97056			−0.259420
$945$		0			0
$946$	−4.65685			−0.151407
$947$	10.2574	−	17.7663i	0.333319	−	0.577326i	−0.649841	−	0.760070i	$-0.725165\pi$
$947$	10.2574	−	17.7663i	0.333319	−	0.577326i	0.983161	+	0.182744i	$0.0584979\pi$
$948$		0			0
$949$	−28.1421	−	48.7436i	−0.913532	−	1.58228i
$950$	0.257359	−	0.445759i	0.00834984	−	0.0144623i
$951$		0			0
$952$	−6.59188	+	0.902079i	−0.213644	+	0.0292365i
$953$	−14.1421			−0.458109			−0.229054	−	0.973414i	$-0.573563\pi$
$953$	−14.1421			−0.458109			−0.229054	+	0.973414i	$0.573563\pi$
$954$		0			0
$955$	−10.3431	−	17.9149i	−0.334696	−	0.579711i
$956$	−9.58579	−	16.6031i	−0.310026	−	0.536982i
$957$		0			0
$958$	5.79899			0.187357
$959$	−43.2132	+	5.91359i	−1.39543	+	0.190960i
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.0161290	+	0.0279363i
$962$	7.48528	+	12.9649i	0.241335	+	0.418005i
$963$		0			0
$964$	−14.0000	+	24.2487i	−0.450910	+	0.780998i
$965$	32.2843			1.03927
$966$		0			0
$967$	27.0416			0.869600			0.434800	−	0.900527i	$-0.356819\pi$
$967$	27.0416			0.869600			0.434800	+	0.900527i	$0.356819\pi$
$968$	−0.792893	+	1.37333i	−0.0254846	+	0.0441405i
$969$		0			0
$970$	2.27208	+	3.93535i	0.0729520	+	0.126357i
$971$	−14.4853	+	25.0892i	−0.464855	+	0.805152i	−0.999195	−	0.0401174i	$-0.987227\pi$
$971$	−14.4853	+	25.0892i	−0.464855	+	0.805152i	0.534340	+	0.845270i	$0.320560\pi$
$972$		0			0
$973$	5.58579	−	13.6823i	0.179072	−	0.438635i
$974$	−5.23045			−0.167594
$975$		0			0
$976$	6.00000	+	10.3923i	0.192055	+	0.332650i
$977$	−3.58579	−	6.21076i	−0.114719	−	0.198700i	0.802948	−	0.596049i	$-0.203264\pi$
$977$	−3.58579	−	6.21076i	−0.114719	−	0.198700i	−0.917668	+	0.397349i	$0.869930\pi$
$978$		0			0
$979$	14.1421			0.451985
$980$	18.2843	+	17.9149i	0.584070	+	0.572269i
$981$		0			0
$982$	3.82843	−	6.63103i	0.122170	−	0.211605i
$983$	−17.9853	−	31.1514i	−0.573641	−	0.993576i	−0.996188	−	0.0872347i	$-0.972197\pi$
$983$	−17.9853	−	31.1514i	−0.573641	−	0.993576i	0.422546	−	0.906341i	$-0.361136\pi$
$984$		0			0
$985$	−13.5858	+	23.5313i	−0.432879	+	0.749769i
$986$	−3.44365			−0.109668
$987$		0			0
$988$	10.9706			0.349020
$989$	39.3492	−	68.1549i	1.25123	−	2.16720i
$990$		0			0
$991$	23.6569	+	40.9749i	0.751485	+	1.30161i	0.947103	+	0.320930i	$0.103995\pi$
$991$	23.6569	+	40.9749i	0.751485	+	1.30161i	−0.195618	+	0.980680i	$0.562671\pi$
$992$	−12.4853	+	21.6251i	−0.396408	+	0.686599i
$993$		0			0
$994$	−6.60051	−	8.51167i	−0.209355	−	0.269974i
$995$	39.5980			1.25534
$996$		0			0
$997$	−19.0711	−	33.0321i	−0.603987	−	1.04614i	−0.992211	−	0.124571i	$-0.960245\pi$
$997$	−19.0711	−	33.0321i	−0.603987	−	1.04614i	0.388224	−	0.921565i	$-0.373089\pi$
$998$	1.61522	+	2.79765i	0.0511290	+	0.0885580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.f.100.2		4
3.2	odd	2		231.2.i.d.100.1	yes	4
7.2	even	3		4851.2.a.be.1.1		2
7.4	even	3	inner	693.2.i.f.298.2		4
7.5	odd	6		4851.2.a.bd.1.1		2
21.2	odd	6		1617.2.a.n.1.2		2
21.5	even	6		1617.2.a.m.1.2		2
21.11	odd	6		231.2.i.d.67.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.d.67.1	✓	4	21.11	odd	6
231.2.i.d.100.1	yes	4	3.2	odd	2
693.2.i.f.100.2		4	1.1	even	1	trivial
693.2.i.f.298.2		4	7.4	even	3	inner
1617.2.a.m.1.2		2	21.5	even	6
1617.2.a.n.1.2		2	21.2	odd	6
4851.2.a.bd.1.1		2	7.5	odd	6
4851.2.a.be.1.1		2	7.2	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 - 2.44949i) q^{7} +1.58579 q^{8} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 - 2.44949i) q^{7} +1.58579 q^{8} +(0.414214 + 0.717439i) q^{10} +(0.500000 + 0.866025i) q^{11} +4.82843 q^{13} +(-0.671573 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.792893 - 1.37333i) q^{17} +(0.621320 - 1.07616i) q^{19} -3.65685 q^{20} +0.414214 q^{22} +(-3.50000 + 6.06218i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +(4.79289 - 0.655892i) q^{28} +5.24264 q^{29} +(2.82843 + 4.89898i) q^{31} +(2.20711 + 3.82282i) q^{32} -0.656854 q^{34} +(3.24264 + 4.18154i) q^{35} +(-3.74264 + 6.48244i) q^{37} +(-0.257359 - 0.445759i) q^{38} +(-1.58579 + 2.74666i) q^{40} +6.82843 q^{41} -11.2426 q^{43} +(-0.914214 + 1.58346i) q^{44} +(1.44975 + 2.51104i) q^{46} +(2.08579 - 3.61269i) q^{47} +(-5.00000 - 4.89898i) q^{49} +0.414214 q^{50} +(4.41421 + 7.64564i) q^{52} +(-6.41421 - 11.1097i) q^{53} -2.00000 q^{55} +(1.58579 - 3.88437i) q^{56} +(1.08579 - 1.88064i) q^{58} +(1.32843 + 2.30090i) q^{59} +(2.00000 - 3.46410i) q^{61} +2.34315 q^{62} -4.17157 q^{64} +(-4.82843 + 8.36308i) q^{65} +(4.41421 + 7.64564i) q^{67} +(1.44975 - 2.51104i) q^{68} +(2.17157 - 0.297173i) q^{70} +9.82843 q^{71} +(-5.82843 - 10.0951i) q^{73} +(1.55025 + 2.68512i) q^{74} +2.27208 q^{76} +(2.62132 - 0.358719i) q^{77} +(4.65685 - 8.06591i) q^{79} +(-3.00000 - 5.19615i) q^{80} +(1.41421 - 2.44949i) q^{82} -2.82843 q^{83} +3.17157 q^{85} +(-2.32843 + 4.03295i) q^{86} +(0.792893 + 1.37333i) q^{88} +(7.07107 - 12.2474i) q^{89} +(4.82843 - 11.8272i) q^{91} -12.7990 q^{92} +(-0.863961 - 1.49642i) q^{94} +(1.24264 + 2.15232i) q^{95} +5.48528 q^{97} +(-2.79289 + 0.778985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{7} + 12 q^{8} - 4 q^{10} + 2 q^{11} + 8 q^{13} - 14 q^{14} - 6 q^{16} - 6 q^{17} - 6 q^{19} + 8 q^{20} - 4 q^{22} - 14 q^{23} + 2 q^{25} + 4 q^{26} + 22 q^{28} + 4 q^{29} + 6 q^{32} + 20 q^{34} - 4 q^{35} + 2 q^{37} - 18 q^{38} - 12 q^{40} + 16 q^{41} - 28 q^{43} + 2 q^{44} - 14 q^{46} + 14 q^{47} - 20 q^{49} - 4 q^{50} + 12 q^{52} - 20 q^{53} - 8 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 8 q^{61} + 32 q^{62} - 28 q^{64} - 8 q^{65} + 12 q^{67} - 14 q^{68} + 20 q^{70} + 28 q^{71} - 12 q^{73} + 26 q^{74} + 60 q^{76} + 2 q^{77} - 4 q^{79} - 12 q^{80} + 24 q^{85} + 2 q^{86} + 6 q^{88} + 8 q^{91} + 28 q^{92} + 22 q^{94} - 12 q^{95} - 12 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^7 + 12 * q^8 - 4 * q^10 + 2 * q^11 + 8 * q^13 - 14 * q^14 - 6 * q^16 - 6 * q^17 - 6 * q^19 + 8 * q^20 - 4 * q^22 - 14 * q^23 + 2 * q^25 + 4 * q^26 + 22 * q^28 + 4 * q^29 + 6 * q^32 + 20 * q^34 - 4 * q^35 + 2 * q^37 - 18 * q^38 - 12 * q^40 + 16 * q^41 - 28 * q^43 + 2 * q^44 - 14 * q^46 + 14 * q^47 - 20 * q^49 - 4 * q^50 + 12 * q^52 - 20 * q^53 - 8 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 8 * q^61 + 32 * q^62 - 28 * q^64 - 8 * q^65 + 12 * q^67 - 14 * q^68 + 20 * q^70 + 28 * q^71 - 12 * q^73 + 26 * q^74 + 60 * q^76 + 2 * q^77 - 4 * q^79 - 12 * q^80 + 24 * q^85 + 2 * q^86 + 6 * q^88 + 8 * q^91 + 28 * q^92 + 22 * q^94 - 12 * q^95 - 12 * q^97 - 14 * q^98

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