LMFDB - Embedded newform 1053.2.e.e.352.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1053,2,Mod(352,1053)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1053, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1053.352");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not 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:	$8.40824733284$
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 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1053.352
Dual form			1053.2.e.e.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.41421 + 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} +1.58579 q^{8} +O(q^{10})$	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.41421 + 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} +1.58579 q^{8} -1.17157 q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.585786 - 1.01461i) q^{14} +(-1.50000 - 2.59808i) q^{16} -7.65685 q^{17} -2.82843 q^{19} +(2.58579 + 4.47871i) q^{20} +(0.414214 - 0.717439i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{25} +0.414214 q^{26} -5.17157 q^{28} +(1.00000 + 1.73205i) q^{29} +(0.585786 - 1.01461i) q^{31} +(2.20711 - 3.82282i) q^{32} +(-1.58579 - 2.74666i) q^{34} +8.00000 q^{35} -7.65685 q^{37} +(-0.585786 - 1.01461i) q^{38} +(-2.24264 + 3.88437i) q^{40} +(2.58579 - 4.47871i) q^{41} +(0.828427 + 1.43488i) q^{43} -3.65685 q^{44} -1.65685 q^{46} +(-5.82843 - 10.0951i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.621320 - 1.07616i) q^{50} +(-0.914214 - 1.58346i) q^{52} +2.00000 q^{53} +5.65685 q^{55} +(-2.24264 - 3.88437i) q^{56} +(-0.414214 + 0.717439i) q^{58} +(3.82843 - 6.63103i) q^{59} +(-6.65685 - 11.5300i) q^{61} +0.485281 q^{62} -4.17157 q^{64} +(1.41421 + 2.44949i) q^{65} +(-3.41421 + 5.91359i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.65685 + 2.86976i) q^{70} -2.00000 q^{71} +0.343146 q^{73} +(-1.58579 - 2.74666i) q^{74} +(-2.58579 + 4.47871i) q^{76} +(-2.82843 + 4.89898i) q^{77} +(5.65685 + 9.79796i) q^{79} +8.48528 q^{80} +2.14214 q^{82} +(1.82843 + 3.16693i) q^{83} +(10.8284 - 18.7554i) q^{85} +(-0.343146 + 0.594346i) q^{86} +(-1.58579 - 2.74666i) q^{88} -14.8284 q^{89} -2.82843 q^{91} +(3.65685 + 6.33386i) q^{92} +(2.41421 - 4.18154i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-1.82843 - 3.16693i) q^{97} -0.414214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 12 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8} - 16 q^{10} - 4 q^{11} + 2 q^{13} + 8 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 32 q^{28} + 4 q^{29} + 8 q^{31} + 6 q^{32} - 12 q^{34} + 32 q^{35} - 8 q^{37} - 8 q^{38} + 8 q^{40} + 16 q^{41} - 8 q^{43} + 8 q^{44} + 16 q^{46} - 12 q^{47} - 2 q^{49} - 6 q^{50} + 2 q^{52} + 8 q^{53} + 8 q^{56} + 4 q^{58} + 4 q^{59} - 4 q^{61} - 32 q^{62} - 28 q^{64} - 8 q^{67} - 28 q^{68} - 16 q^{70} - 8 q^{71} + 24 q^{73} - 12 q^{74} - 16 q^{76} - 48 q^{82} - 4 q^{83} + 32 q^{85} - 24 q^{86} - 12 q^{88} - 48 q^{89} - 8 q^{92} + 4 q^{94} + 16 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 12 * q^8 - 16 * q^10 - 4 * q^11 + 2 * q^13 + 8 * q^14 - 6 * q^16 - 8 * q^17 + 16 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 32 * q^28 + 4 * q^29 + 8 * q^31 + 6 * q^32 - 12 * q^34 + 32 * q^35 - 8 * q^37 - 8 * q^38 + 8 * q^40 + 16 * q^41 - 8 * q^43 + 8 * q^44 + 16 * q^46 - 12 * q^47 - 2 * q^49 - 6 * q^50 + 2 * q^52 + 8 * q^53 + 8 * q^56 + 4 * q^58 + 4 * q^59 - 4 * q^61 - 32 * q^62 - 28 * q^64 - 8 * q^67 - 28 * q^68 - 16 * q^70 - 8 * q^71 + 24 * q^73 - 12 * q^74 - 16 * q^76 - 48 * q^82 - 4 * q^83 + 32 * q^85 - 24 * q^86 - 12 * q^88 - 48 * q^89 - 8 * q^92 + 4 * q^94 + 16 * q^95 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	0.929912	−	0.367783i	$-0.119883\pi$
$2$	0.207107	+	0.358719i	0.146447	+	0.253653i	−0.783465	+	0.621436i	$0.786550\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	−	1.58346i	0.457107	−	0.791732i
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	0.354593	+	0.935021i	$0.384620\pi$
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	−0.987048	+	0.160424i	$0.948714\pi$
$6$		0			0
$7$	−1.41421	−	2.44949i	−0.534522	−	0.925820i	−0.999186	−	0.0403329i	$-0.987158\pi$
$7$	−1.41421	−	2.44949i	−0.534522	−	0.925820i	0.464664	−	0.885487i	$-0.346175\pi$
$8$	1.58579			0.560660
$9$		0			0
$10$	−1.17157			−0.370484
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.585786	−	1.01461i	0.156558	−	0.271166i
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	−7.65685			−1.85706			−0.928530	−	0.371257i	$-0.878927\pi$
$17$	−7.65685			−1.85706			−0.928530	+	0.371257i	$0.878927\pi$
$18$		0			0
$19$	−2.82843			−0.648886			−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843			−0.648886			−0.324443	+	0.945905i	$0.605177\pi$
$20$	2.58579	+	4.47871i	0.578199	+	1.00147i
$21$		0			0
$22$	0.414214	−	0.717439i	0.0883106	−	0.152958i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	0.414214			0.0812340
$27$		0			0
$28$	−5.17157			−0.977335
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$	0.585786	−	1.01461i	0.105210	−	0.182230i	−0.808614	−	0.588340i	$-0.799782\pi$
$31$	0.585786	−	1.01461i	0.105210	−	0.182230i	0.913824	+	0.406110i	$0.133115\pi$
$32$	2.20711	−	3.82282i	0.390165	−	0.675786i
$33$		0			0
$34$	−1.58579	−	2.74666i	−0.271960	−	0.471049i
$35$	8.00000			1.35225
$36$		0			0
$37$	−7.65685			−1.25878			−0.629390	−	0.777090i	$-0.716695\pi$
$37$	−7.65685			−1.25878			−0.629390	+	0.777090i	$0.716695\pi$
$38$	−0.585786	−	1.01461i	−0.0950271	−	0.164592i
$39$		0			0
$40$	−2.24264	+	3.88437i	−0.354593	+	0.614172i
$41$	2.58579	−	4.47871i	0.403832	−	0.699458i	−0.590353	−	0.807145i	$-0.701011\pi$
$41$	2.58579	−	4.47871i	0.403832	−	0.699458i	0.994185	+	0.107688i	$0.0343447\pi$
$42$		0			0
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	0.922254	−	0.386585i	$-0.126346\pi$
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	−0.795920	+	0.605402i	$0.793012\pi$
$44$	−3.65685			−0.551292
$45$		0			0
$46$	−1.65685			−0.244290
$47$	−5.82843	−	10.0951i	−0.850163	−	1.47253i	−0.881060	−	0.473004i	$-0.843170\pi$
$47$	−5.82843	−	10.0951i	−0.850163	−	1.47253i	0.0308969	−	0.999523i	$-0.490164\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.621320	−	1.07616i	0.0878680	−	0.152192i
$51$		0			0
$52$	−0.914214	−	1.58346i	−0.126779	−	0.219587i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$		0			0
$55$	5.65685			0.762770
$56$	−2.24264	−	3.88437i	−0.299685	−	0.519070i
$57$		0			0
$58$	−0.414214	+	0.717439i	−0.0543889	+	0.0942043i
$59$	3.82843	−	6.63103i	0.498419	−	0.863287i	−0.501580	−	0.865112i	$-0.667248\pi$
$59$	3.82843	−	6.63103i	0.498419	−	0.863287i	0.999998	+	0.00182490i	$0.000580884\pi$
$60$		0			0
$61$	−6.65685	−	11.5300i	−0.852323	−	1.47627i	−0.879107	−	0.476625i	$-0.841860\pi$
$61$	−6.65685	−	11.5300i	−0.852323	−	1.47627i	0.0267837	−	0.999641i	$-0.491473\pi$
$62$	0.485281			0.0616308
$63$		0			0
$64$	−4.17157			−0.521447
$65$	1.41421	+	2.44949i	0.175412	+	0.303822i
$66$		0			0
$67$	−3.41421	+	5.91359i	−0.417113	+	0.722460i	−0.995648	−	0.0931973i	$-0.970291\pi$
$67$	−3.41421	+	5.91359i	−0.417113	+	0.722460i	0.578535	+	0.815657i	$0.303625\pi$
$68$	−7.00000	+	12.1244i	−0.848875	+	1.47029i
$69$		0			0
$70$	1.65685	+	2.86976i	0.198032	+	0.343001i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	0.343146			0.0401622			0.0200811	−	0.999798i	$-0.493608\pi$
$73$	0.343146			0.0401622			0.0200811	+	0.999798i	$0.493608\pi$
$74$	−1.58579	−	2.74666i	−0.184344	−	0.319293i
$75$		0			0
$76$	−2.58579	+	4.47871i	−0.296610	+	0.513744i
$77$	−2.82843	+	4.89898i	−0.322329	+	0.558291i
$78$		0			0
$79$	5.65685	+	9.79796i	0.636446	+	1.10236i	0.986207	+	0.165518i	$0.0529295\pi$
$79$	5.65685	+	9.79796i	0.636446	+	1.10236i	−0.349761	+	0.936839i	$0.613737\pi$
$80$	8.48528			0.948683
$81$		0			0
$82$	2.14214			0.236559
$83$	1.82843	+	3.16693i	0.200696	+	0.347616i	0.948753	−	0.316019i	$-0.102346\pi$
$83$	1.82843	+	3.16693i	0.200696	+	0.347616i	−0.748057	+	0.663635i	$0.769013\pi$
$84$		0			0
$85$	10.8284	−	18.7554i	1.17451	−	2.03431i
$86$	−0.343146	+	0.594346i	−0.0370024	+	0.0640900i
$87$		0			0
$88$	−1.58579	−	2.74666i	−0.169045	−	0.292795i
$89$	−14.8284			−1.57181			−0.785905	−	0.618347i	$-0.787803\pi$
$89$	−14.8284			−1.57181			−0.785905	+	0.618347i	$0.787803\pi$
$90$		0			0
$91$	−2.82843			−0.296500
$92$	3.65685	+	6.33386i	0.381253	+	0.660350i
$93$		0			0
$94$	2.41421	−	4.18154i	0.249007	−	0.431293i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	−1.82843	−	3.16693i	−0.185649	−	0.321553i	0.758146	−	0.652085i	$-0.226105\pi$
$97$	−1.82843	−	3.16693i	−0.185649	−	0.321553i	−0.943795	+	0.330532i	$0.892772\pi$
$98$	−0.414214			−0.0418419
$99$		0			0
$100$	−5.48528			−0.548528
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	0.991197	−	0.132393i	$-0.0422662\pi$
$101$	3.82843	+	6.63103i	0.380943	+	0.659812i	−0.610255	+	0.792205i	$0.708933\pi$
$102$		0			0
$103$	−1.17157	+	2.02922i	−0.115439	+	0.199945i	−0.917955	−	0.396685i	$-0.870161\pi$
$103$	−1.17157	+	2.02922i	−0.115439	+	0.199945i	0.802516	+	0.596630i	$0.203494\pi$
$104$	0.792893	−	1.37333i	0.0777496	−	0.134666i
$105$		0			0
$106$	0.414214	+	0.717439i	0.0402320	+	0.0696838i
$107$	11.3137			1.09374			0.546869	−	0.837218i	$-0.315820\pi$
$107$	11.3137			1.09374			0.546869	+	0.837218i	$0.315820\pi$
$108$		0			0
$109$	5.31371			0.508961			0.254480	−	0.967078i	$-0.418096\pi$
$109$	5.31371			0.508961			0.254480	+	0.967078i	$0.418096\pi$
$110$	1.17157	+	2.02922i	0.111705	+	0.193479i
$111$		0			0
$112$	−4.24264	+	7.34847i	−0.400892	+	0.694365i
$113$	−2.65685	+	4.60181i	−0.249936	+	0.432902i	−0.963508	−	0.267680i	$-0.913743\pi$
$113$	−2.65685	+	4.60181i	−0.249936	+	0.432902i	0.713572	+	0.700582i	$0.247076\pi$
$114$		0			0
$115$	−5.65685	−	9.79796i	−0.527504	−	0.913664i
$116$	3.65685			0.339530
$117$		0			0
$118$	3.17157			0.291967
$119$	10.8284	+	18.7554i	0.992640	+	1.71930i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	2.75736	−	4.77589i	0.249640	−	0.432388i
$123$		0			0
$124$	−1.07107	−	1.85514i	−0.0961847	−	0.166597i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	5.65685			0.501965			0.250982	−	0.967992i	$-0.419246\pi$
$127$	5.65685			0.501965			0.250982	+	0.967992i	$0.419246\pi$
$128$	−5.27817	−	9.14207i	−0.466529	−	0.808052i
$129$		0			0
$130$	−0.585786	+	1.01461i	−0.0513769	+	0.0889873i
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	−0.986157	−	0.165812i	$-0.946976\pi$
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	0.636676	+	0.771132i	$0.280309\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	−2.82843			−0.244339
$135$		0			0
$136$	−12.1421			−1.04118
$137$	−5.41421	−	9.37769i	−0.462567	−	0.801190i	0.536521	−	0.843887i	$-0.319738\pi$
$137$	−5.41421	−	9.37769i	−0.462567	−	0.801190i	−0.999088	+	0.0426968i	$0.986405\pi$
$138$		0			0
$139$	3.65685	−	6.33386i	0.310170	−	0.537231i	−0.668229	−	0.743956i	$-0.732947\pi$
$139$	3.65685	−	6.33386i	0.310170	−	0.537231i	0.978399	+	0.206725i	$0.0662806\pi$
$140$	7.31371	−	12.6677i	0.618121	−	1.07062i
$141$		0			0
$142$	−0.414214	−	0.717439i	−0.0347600	−	0.0602061i
$143$	−2.00000			−0.167248
$144$		0			0
$145$	−5.65685			−0.469776
$146$	0.0710678	+	0.123093i	0.00588161	+	0.0101873i
$147$		0			0
$148$	−7.00000	+	12.1244i	−0.575396	+	0.996616i
$149$	−4.58579	+	7.94282i	−0.375682	+	0.650701i	−0.990429	−	0.138024i	$-0.955925\pi$
$149$	−4.58579	+	7.94282i	−0.375682	+	0.650701i	0.614747	+	0.788725i	$0.289258\pi$
$150$		0			0
$151$	1.75736	+	3.04384i	0.143012	+	0.247704i	0.928629	−	0.371009i	$-0.120988\pi$
$151$	1.75736	+	3.04384i	0.143012	+	0.247704i	−0.785618	+	0.618712i	$0.787655\pi$
$152$	−4.48528			−0.363804
$153$		0			0
$154$	−2.34315			−0.188816
$155$	1.65685	+	2.86976i	0.133082	+	0.230504i
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	−2.34315	+	4.05845i	−0.186411	+	0.322873i
$159$		0			0
$160$	6.24264	+	10.8126i	0.493524	+	0.854809i
$161$	11.3137			0.891645
$162$		0			0
$163$	18.8284			1.47476			0.737378	−	0.675480i	$-0.236064\pi$
$163$	18.8284			1.47476			0.737378	+	0.675480i	$0.236064\pi$
$164$	−4.72792	−	8.18900i	−0.369189	−	0.639454i
$165$		0			0
$166$	−0.757359	+	1.31178i	−0.0587825	+	0.101814i
$167$	−1.82843	+	3.16693i	−0.141488	+	0.245064i	−0.928057	−	0.372438i	$-0.878522\pi$
$167$	−1.82843	+	3.16693i	−0.141488	+	0.245064i	0.786569	+	0.617502i	$0.211855\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	8.97056			0.688011
$171$		0			0
$172$	3.02944			0.230992
$173$	−5.82843	−	10.0951i	−0.443127	−	0.767519i	0.554793	−	0.831989i	$-0.312798\pi$
$173$	−5.82843	−	10.0951i	−0.443127	−	0.767519i	−0.997920	+	0.0644701i	$0.979464\pi$
$174$		0			0
$175$	−4.24264	+	7.34847i	−0.320713	+	0.555492i
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$		0			0
$178$	−3.07107	−	5.31925i	−0.230186	−	0.398694i
$179$	23.3137			1.74255			0.871274	−	0.490797i	$-0.163294\pi$
$179$	23.3137			1.74255			0.871274	+	0.490797i	$0.163294\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	−0.585786	−	1.01461i	−0.0434214	−	0.0752080i
$183$		0			0
$184$	−3.17157	+	5.49333i	−0.233811	+	0.404973i
$185$	10.8284	−	18.7554i	0.796122	−	1.37892i
$186$		0			0
$187$	7.65685	+	13.2621i	0.559925	+	0.969818i
$188$	−21.3137			−1.55446
$189$		0			0
$190$	3.31371			0.240402
$191$	1.65685	+	2.86976i	0.119886	+	0.207648i	0.919722	−	0.392570i	$-0.128414\pi$
$191$	1.65685	+	2.86976i	0.119886	+	0.207648i	−0.799836	+	0.600218i	$0.795081\pi$
$192$		0			0
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	−0.945663	−	0.325149i	$-0.894586\pi$
$193$	−2.65685	+	4.60181i	−0.191245	+	0.331245i	0.754418	+	0.656394i	$0.227919\pi$
$194$	0.757359	−	1.31178i	0.0543752	−	0.0941807i
$195$		0			0
$196$	0.914214	+	1.58346i	0.0653010	+	0.113105i
$197$	−0.485281			−0.0345749			−0.0172874	−	0.999851i	$-0.505503\pi$
$197$	−0.485281			−0.0345749			−0.0172874	+	0.999851i	$0.505503\pi$
$198$		0			0
$199$	21.6569			1.53521			0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569			1.53521			0.767607	+	0.640921i	$0.221447\pi$
$200$	−2.37868	−	4.11999i	−0.168198	−	0.291328i
$201$		0			0
$202$	−1.58579	+	2.74666i	−0.111576	+	0.193255i
$203$	2.82843	−	4.89898i	0.198517	−	0.343841i
$204$		0			0
$205$	7.31371	+	12.6677i	0.510812	+	0.884752i
$206$	−0.970563			−0.0676223
$207$		0			0
$208$	−3.00000			−0.208013
$209$	2.82843	+	4.89898i	0.195646	+	0.338869i
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	1.82843	−	3.16693i	0.125577	−	0.217506i
$213$		0			0
$214$	2.34315	+	4.05845i	0.160174	+	0.277430i
$215$	−4.68629			−0.319602
$216$		0			0
$217$	−3.31371			−0.224949
$218$	1.10051	+	1.90613i	0.0745356	+	0.129099i
$219$		0			0
$220$	5.17157	−	8.95743i	0.348667	−	0.603910i
$221$	−3.82843	+	6.63103i	−0.257528	+	0.446051i
$222$		0			0
$223$	6.24264	+	10.8126i	0.418038	+	0.724063i	0.995742	−	0.0921831i	$-0.0293845\pi$
$223$	6.24264	+	10.8126i	0.418038	+	0.724063i	−0.577704	+	0.816246i	$0.696051\pi$
$224$	−12.4853			−0.834208
$225$		0			0
$226$	−2.20101			−0.146409
$227$	−8.65685	−	14.9941i	−0.574576	−	0.995194i	−0.996088	−	0.0883713i	$-0.971834\pi$
$227$	−8.65685	−	14.9941i	−0.574576	−	0.995194i	0.421512	−	0.906823i	$-0.361500\pi$
$228$		0			0
$229$	0.656854	−	1.13770i	0.0434062	−	0.0751817i	−0.843506	−	0.537120i	$-0.819512\pi$
$229$	0.656854	−	1.13770i	0.0434062	−	0.0751817i	0.886912	+	0.461938i	$0.152846\pi$
$230$	2.34315	−	4.05845i	0.154502	−	0.267606i
$231$		0			0
$232$	1.58579	+	2.74666i	0.104112	+	0.180327i
$233$	−6.97056			−0.456657			−0.228328	−	0.973584i	$-0.573326\pi$
$233$	−6.97056			−0.456657			−0.228328	+	0.973584i	$0.573326\pi$
$234$		0			0
$235$	32.9706			2.15076
$236$	−7.00000	−	12.1244i	−0.455661	−	0.789228i
$237$		0			0
$238$	−4.48528	+	7.76874i	−0.290738	+	0.503572i
$239$	1.00000	−	1.73205i	0.0646846	−	0.112037i	−0.831869	−	0.554971i	$-0.812729\pi$
$239$	1.00000	−	1.73205i	0.0646846	−	0.112037i	0.896554	+	0.442934i	$0.146063\pi$
$240$		0			0
$241$	−0.171573	−	0.297173i	−0.0110520	−	0.0191426i	0.860447	−	0.509541i	$-0.170185\pi$
$241$	−0.171573	−	0.297173i	−0.0110520	−	0.0191426i	−0.871499	+	0.490398i	$0.836851\pi$
$242$	2.89949			0.186387
$243$		0			0
$244$	−24.3431			−1.55841
$245$	−1.41421	−	2.44949i	−0.0903508	−	0.156492i
$246$		0			0
$247$	−1.41421	+	2.44949i	−0.0899843	+	0.155857i
$248$	0.928932	−	1.60896i	0.0589873	−	0.102169i
$249$		0			0
$250$	−1.17157	−	2.02922i	−0.0740968	−	0.128339i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	1.17157	+	2.02922i	0.0735110	+	0.127325i
$255$		0			0
$256$	−1.98528	+	3.43861i	−0.124080	+	0.214913i
$257$	−2.17157	+	3.76127i	−0.135459	+	0.234622i	−0.925773	−	0.378081i	$-0.876584\pi$
$257$	−2.17157	+	3.76127i	−0.135459	+	0.234622i	0.790314	+	0.612702i	$0.209918\pi$
$258$		0			0
$259$	10.8284	+	18.7554i	0.672846	+	1.16540i
$260$	5.17157			0.320727
$261$		0			0
$262$	−3.31371			−0.204722
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	−2.82843	+	4.89898i	−0.173749	+	0.300942i
$266$	−1.65685	+	2.86976i	−0.101588	+	0.175956i
$267$		0			0
$268$	6.24264	+	10.8126i	0.381330	+	0.660483i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$	−27.7990			−1.68867			−0.844334	−	0.535817i	$-0.820004\pi$
$271$	−27.7990			−1.68867			−0.844334	+	0.535817i	$0.820004\pi$
$272$	11.4853	+	19.8931i	0.696397	+	1.20620i
$273$		0			0
$274$	2.24264	−	3.88437i	0.135483	−	0.234663i
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	3.02944			0.181694
$279$		0			0
$280$	12.6863			0.758151
$281$	10.5858	+	18.3351i	0.631495	+	1.09378i	0.987246	+	0.159201i	$0.0508917\pi$
$281$	10.5858	+	18.3351i	0.631495	+	1.09378i	−0.355751	+	0.934581i	$0.615775\pi$
$282$		0			0
$283$	−14.4853	+	25.0892i	−0.861061	+	1.49140i	0.00984565	+	0.999952i	$0.496866\pi$
$283$	−14.4853	+	25.0892i	−0.861061	+	1.49140i	−0.870906	+	0.491449i	$0.836467\pi$
$284$	−1.82843	+	3.16693i	−0.108497	+	0.187923i
$285$		0			0
$286$	−0.414214	−	0.717439i	−0.0244930	−	0.0424231i
$287$	−14.6274			−0.863429
$288$		0			0
$289$	41.6274			2.44867
$290$	−1.17157	−	2.02922i	−0.0687971	−	0.119160i
$291$		0			0
$292$	0.313708	−	0.543359i	0.0183584	−	0.0317977i
$293$	1.07107	−	1.85514i	0.0625724	−	0.108379i	−0.833042	−	0.553210i	$-0.813403\pi$
$293$	1.07107	−	1.85514i	0.0625724	−	0.108379i	0.895615	+	0.444831i	$0.146736\pi$
$294$		0			0
$295$	10.8284	+	18.7554i	0.630455	+	1.09198i
$296$	−12.1421			−0.705747
$297$		0			0
$298$	−3.79899			−0.220070
$299$	2.00000	+	3.46410i	0.115663	+	0.200334i
$300$		0			0
$301$	2.34315	−	4.05845i	0.135057	−	0.233925i
$302$	−0.727922	+	1.26080i	−0.0418872	+	0.0725508i
$303$		0			0
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$	37.6569			2.15623
$306$		0			0
$307$	−22.8284			−1.30289			−0.651444	−	0.758697i	$-0.725836\pi$
$307$	−22.8284			−1.30289			−0.651444	+	0.758697i	$0.725836\pi$
$308$	5.17157	+	8.95743i	0.294678	+	0.510397i
$309$		0			0
$310$	−0.686292	+	1.18869i	−0.0389787	+	0.0675132i
$311$	−5.31371	+	9.20361i	−0.301313	+	0.521889i	−0.976434	−	0.215818i	$-0.930758\pi$
$311$	−5.31371	+	9.20361i	−0.301313	+	0.521889i	0.675121	+	0.737707i	$0.264091\pi$
$312$		0			0
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	0.768699	−	0.639611i	$-0.220905\pi$
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	−0.938269	+	0.345907i	$0.887571\pi$
$314$	4.14214			0.233754
$315$		0			0
$316$	20.6863			1.16369
$317$	4.24264	+	7.34847i	0.238290	+	0.412731i	0.960224	−	0.279231i	$-0.0900797\pi$
$317$	4.24264	+	7.34847i	0.238290	+	0.412731i	−0.721933	+	0.691963i	$0.756746\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	5.89949	−	10.2182i	0.329792	−	0.571216i
$321$		0			0
$322$	2.34315	+	4.05845i	0.130578	+	0.226168i
$323$	21.6569			1.20502
$324$		0			0
$325$	−3.00000			−0.166410
$326$	3.89949	+	6.75412i	0.215973	+	0.374076i
$327$		0			0
$328$	4.10051	−	7.10228i	0.226413	−	0.392158i
$329$	−16.4853	+	28.5533i	−0.908863	+	1.57420i
$330$		0			0
$331$	−13.0711	−	22.6398i	−0.718451	−	1.24439i	−0.961613	−	0.274408i	$-0.911518\pi$
$331$	−13.0711	−	22.6398i	−0.718451	−	1.24439i	0.243163	−	0.969986i	$-0.421815\pi$
$332$	6.68629			0.366958
$333$		0			0
$334$	−1.51472			−0.0828817
$335$	−9.65685	−	16.7262i	−0.527610	−	0.913848i
$336$		0			0
$337$	−4.65685	+	8.06591i	−0.253675	+	0.439378i	−0.964535	−	0.263956i	$-0.914973\pi$
$337$	−4.65685	+	8.06591i	−0.253675	+	0.439378i	0.710860	+	0.703334i	$0.248306\pi$
$338$	0.207107	−	0.358719i	0.0112651	−	0.0195118i
$339$		0			0
$340$	−19.7990	−	34.2929i	−1.07375	−	1.85979i
$341$	−2.34315			−0.126888
$342$		0			0
$343$	−16.9706			−0.916324
$344$	1.31371	+	2.27541i	0.0708304	+	0.122682i
$345$		0			0
$346$	2.41421	−	4.18154i	0.129789	−	0.224801i
$347$	−4.34315	+	7.52255i	−0.233152	+	0.403832i	−0.958734	−	0.284304i	$-0.908237\pi$
$347$	−4.34315	+	7.52255i	−0.233152	+	0.403832i	0.725582	+	0.688136i	$0.241571\pi$
$348$		0			0
$349$	−1.82843	−	3.16693i	−0.0978735	−	0.169522i	0.812931	−	0.582360i	$-0.197871\pi$
$349$	−1.82843	−	3.16693i	−0.0978735	−	0.169522i	−0.910804	+	0.412839i	$0.864537\pi$
$350$	−3.51472			−0.187870
$351$		0			0
$352$	−8.82843			−0.470557
$353$	−16.7279	−	28.9736i	−0.890337	−	1.54211i	−0.839471	−	0.543404i	$-0.817135\pi$
$353$	−16.7279	−	28.9736i	−0.890337	−	1.54211i	−0.0508663	−	0.998705i	$-0.516198\pi$
$354$		0			0
$355$	2.82843	−	4.89898i	0.150117	−	0.260011i
$356$	−13.5563	+	23.4803i	−0.718485	+	1.24445i
$357$		0			0
$358$	4.82843	+	8.36308i	0.255190	+	0.442003i
$359$	−34.9706			−1.84568			−0.922838	−	0.385189i	$-0.874136\pi$
$359$	−34.9706			−1.84568			−0.922838	+	0.385189i	$0.874136\pi$
$360$		0			0
$361$	−11.0000			−0.578947
$362$	2.89949	+	5.02207i	0.152394	+	0.263954i
$363$		0			0
$364$	−2.58579	+	4.47871i	−0.135532	+	0.234748i
$365$	−0.485281	+	0.840532i	−0.0254008	+	0.0439955i
$366$		0			0
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	12.0000			0.625543
$369$		0			0
$370$	8.97056			0.466357
$371$	−2.82843	−	4.89898i	−0.146845	−	0.254342i
$372$		0			0
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	−3.17157	+	5.49333i	−0.163998	+	0.284053i
$375$		0			0
$376$	−9.24264	−	16.0087i	−0.476653	−	0.825587i
$377$	2.00000			0.103005
$378$		0			0
$379$	0.485281			0.0249272			0.0124636	−	0.999922i	$-0.496033\pi$
$379$	0.485281			0.0249272			0.0124636	+	0.999922i	$0.496033\pi$
$380$	−7.31371	−	12.6677i	−0.375185	−	0.649840i
$381$		0			0
$382$	−0.686292	+	1.18869i	−0.0351137	+	0.0608188i
$383$	15.4853	−	26.8213i	0.791261	−	1.37050i	−0.133926	−	0.990991i	$-0.542758\pi$
$383$	15.4853	−	26.8213i	0.791261	−	1.37050i	0.925187	−	0.379513i	$-0.123908\pi$
$384$		0			0
$385$	−8.00000	−	13.8564i	−0.407718	−	0.706188i
$386$	−2.20101			−0.112028
$387$		0			0
$388$	−6.68629			−0.339445
$389$	−13.4853	−	23.3572i	−0.683731	−	1.18426i	−0.973834	−	0.227261i	$-0.927023\pi$
$389$	−13.4853	−	23.3572i	−0.683731	−	1.18426i	0.290103	−	0.956995i	$-0.406310\pi$
$390$		0			0
$391$	15.3137	−	26.5241i	0.774448	−	1.34138i
$392$	−0.792893	+	1.37333i	−0.0400472	+	0.0693637i
$393$		0			0
$394$	−0.100505	−	0.174080i	−0.00506337	−	0.00877002i
$395$	−32.0000			−1.61009
$396$		0			0
$397$	30.9706			1.55437			0.777184	−	0.629273i	$-0.216647\pi$
$397$	30.9706			1.55437			0.777184	+	0.629273i	$0.216647\pi$
$398$	4.48528	+	7.76874i	0.224827	+	0.389412i
$399$		0			0
$400$	−4.50000	+	7.79423i	−0.225000	+	0.389711i
$401$	13.0711	−	22.6398i	0.652738	−	1.13058i	−0.329718	−	0.944080i	$-0.606954\pi$
$401$	13.0711	−	22.6398i	0.652738	−	1.13058i	0.982456	−	0.186496i	$-0.0597131\pi$
$402$		0			0
$403$	−0.585786	−	1.01461i	−0.0291801	−	0.0505414i
$404$	14.0000			0.696526
$405$		0			0
$406$	2.34315			0.116288
$407$	7.65685	+	13.2621i	0.379536	+	0.657376i
$408$		0			0
$409$	17.4853	−	30.2854i	0.864592	−	1.49752i	−0.00286068	−	0.999996i	$-0.500911\pi$
$409$	17.4853	−	30.2854i	0.864592	−	1.49752i	0.867452	−	0.497521i	$-0.165756\pi$
$410$	−3.02944	+	5.24714i	−0.149613	+	0.259138i
$411$		0			0
$412$	2.14214	+	3.71029i	0.105535	+	0.182793i
$413$	−21.6569			−1.06566
$414$		0			0
$415$	−10.3431			−0.507725
$416$	−2.20711	−	3.82282i	−0.108212	−	0.187429i
$417$		0			0
$418$	−1.17157	+	2.02922i	−0.0573035	+	0.0992526i
$419$	7.31371	−	12.6677i	0.357298	−	0.618858i	−0.630210	−	0.776424i	$-0.717031\pi$
$419$	7.31371	−	12.6677i	0.357298	−	0.618858i	0.987508	+	0.157566i	$0.0503647\pi$
$420$		0			0
$421$	−18.6569	−	32.3146i	−0.909279	−	1.57492i	−0.815067	−	0.579366i	$-0.803300\pi$
$421$	−18.6569	−	32.3146i	−0.909279	−	1.57492i	−0.0942120	−	0.995552i	$-0.530033\pi$
$422$	4.97056			0.241963
$423$		0			0
$424$	3.17157			0.154025
$425$	11.4853	+	19.8931i	0.557118	+	0.964957i
$426$		0			0
$427$	−18.8284	+	32.6118i	−0.911171	+	1.57820i
$428$	10.3431	−	17.9149i	0.499955	−	0.865947i
$429$		0			0
$430$	−0.970563	−	1.68106i	−0.0468047	−	0.0810681i
$431$	−8.34315			−0.401875			−0.200938	−	0.979604i	$-0.564399\pi$
$431$	−8.34315			−0.401875			−0.200938	+	0.979604i	$0.564399\pi$
$432$		0			0
$433$	−21.3137			−1.02427			−0.512136	−	0.858905i	$-0.671146\pi$
$433$	−21.3137			−1.02427			−0.512136	+	0.858905i	$0.671146\pi$
$434$	−0.686292	−	1.18869i	−0.0329430	−	0.0570590i
$435$		0			0
$436$	4.85786	−	8.41407i	0.232650	−	0.402961i
$437$	5.65685	−	9.79796i	0.270604	−	0.468700i
$438$		0			0
$439$	−8.48528	−	14.6969i	−0.404980	−	0.701447i	0.589339	−	0.807886i	$-0.299388\pi$
$439$	−8.48528	−	14.6969i	−0.404980	−	0.701447i	−0.994319	+	0.106439i	$0.966055\pi$
$440$	8.97056			0.427655
$441$		0			0
$442$	−3.17157			−0.150856
$443$	−12.9706	−	22.4657i	−0.616250	−	1.06738i	−0.990164	−	0.139913i	$-0.955318\pi$
$443$	−12.9706	−	22.4657i	−0.616250	−	1.06738i	0.373914	−	0.927463i	$-0.378016\pi$
$444$		0			0
$445$	20.9706	−	36.3221i	0.994100	−	1.72183i
$446$	−2.58579	+	4.47871i	−0.122441	+	0.212073i
$447$		0			0
$448$	5.89949	+	10.2182i	0.278725	+	0.482766i
$449$	31.7990			1.50069			0.750344	−	0.661048i	$-0.229888\pi$
$449$	31.7990			1.50069			0.750344	+	0.661048i	$0.229888\pi$
$450$		0			0
$451$	−10.3431			−0.487040
$452$	4.85786	+	8.41407i	0.228495	+	0.395764i
$453$		0			0
$454$	3.58579	−	6.21076i	0.168289	−	0.291486i
$455$	4.00000	−	6.92820i	0.187523	−	0.324799i
$456$		0			0
$457$	3.82843	+	6.63103i	0.179086	+	0.310187i	0.941568	−	0.336823i	$-0.109353\pi$
$457$	3.82843	+	6.63103i	0.179086	+	0.310187i	−0.762482	+	0.647010i	$0.776019\pi$
$458$	0.544156			0.0254267
$459$		0			0
$460$	−20.6863			−0.964503
$461$	2.58579	+	4.47871i	0.120432	+	0.208594i	0.919938	−	0.392064i	$-0.128239\pi$
$461$	2.58579	+	4.47871i	0.120432	+	0.208594i	−0.799506	+	0.600658i	$0.794905\pi$
$462$		0			0
$463$	12.2426	−	21.2049i	0.568964	−	0.985474i	−0.427705	−	0.903918i	$-0.640678\pi$
$463$	12.2426	−	21.2049i	0.568964	−	0.985474i	0.996669	−	0.0815558i	$-0.0259889\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	−1.44365	−	2.50048i	−0.0668758	−	0.115832i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	19.3137			0.891824
$470$	6.82843	+	11.8272i	0.314972	+	0.545547i
$471$		0			0
$472$	6.07107	−	10.5154i	0.279444	−	0.484010i
$473$	1.65685	−	2.86976i	0.0761822	−	0.131952i
$474$		0			0
$475$	4.24264	+	7.34847i	0.194666	+	0.337171i
$476$	39.5980			1.81497
$477$		0			0
$478$	0.828427			0.0378914
$479$	12.6569	+	21.9223i	0.578306	+	1.00166i	0.995674	+	0.0929182i	$0.0296195\pi$
$479$	12.6569	+	21.9223i	0.578306	+	1.00166i	−0.417367	+	0.908738i	$0.637047\pi$
$480$		0			0
$481$	−3.82843	+	6.63103i	−0.174561	+	0.302349i
$482$	0.0710678	−	0.123093i	0.00323705	−	0.00560674i
$483$		0			0
$484$	−6.39949	−	11.0843i	−0.290886	−	0.503830i
$485$	10.3431			0.469658
$486$		0			0
$487$	−7.79899			−0.353406			−0.176703	−	0.984264i	$-0.556543\pi$
$487$	−7.79899			−0.353406			−0.176703	+	0.984264i	$0.556543\pi$
$488$	−10.5563	−	18.2841i	−0.477863	−	0.827684i
$489$		0			0
$490$	0.585786	−	1.01461i	0.0264631	−	0.0458355i
$491$	15.3137	−	26.5241i	0.691098	−	1.19702i	−0.280380	−	0.959889i	$-0.590461\pi$
$491$	15.3137	−	26.5241i	0.691098	−	1.19702i	0.971478	−	0.237128i	$-0.0762060\pi$
$492$		0			0
$493$	−7.65685	−	13.2621i	−0.344847	−	0.597293i
$494$	−1.17157			−0.0527116
$495$		0			0
$496$	−3.51472			−0.157816
$497$	2.82843	+	4.89898i	0.126872	+	0.219749i
$498$		0			0
$499$	−13.0711	+	22.6398i	−0.585141	+	1.01349i	0.409716	+	0.912213i	$0.365628\pi$
$499$	−13.0711	+	22.6398i	−0.585141	+	1.01349i	−0.994858	+	0.101282i	$0.967706\pi$
$500$	−5.17157	+	8.95743i	−0.231280	+	0.400588i
$501$		0			0
$502$		0			0
$503$	7.31371			0.326102			0.163051	−	0.986618i	$-0.447866\pi$
$503$	7.31371			0.326102			0.163051	+	0.986618i	$0.447866\pi$
$504$		0			0
$505$	−21.6569			−0.963717
$506$	1.65685	+	2.86976i	0.0736562	+	0.127576i
$507$		0			0
$508$	5.17157	−	8.95743i	0.229451	−	0.397422i
$509$	5.89949	−	10.2182i	0.261491	−	0.452915i	−0.705148	−	0.709060i	$-0.749119\pi$
$509$	5.89949	−	10.2182i	0.261491	−	0.452915i	0.966638	+	0.256146i	$0.0824527\pi$
$510$		0			0
$511$	−0.485281	−	0.840532i	−0.0214676	−	0.0371829i
$512$	−22.7574			−1.00574
$513$		0			0
$514$	−1.79899			−0.0793500
$515$	−3.31371	−	5.73951i	−0.146019	−	0.252913i
$516$		0			0
$517$	−11.6569	+	20.1903i	−0.512668	+	0.887967i
$518$	−4.48528	+	7.76874i	−0.197072	+	0.341339i
$519$		0			0
$520$	2.24264	+	3.88437i	0.0983463	+	0.170341i
$521$	−25.3137			−1.10901			−0.554507	−	0.832179i	$-0.687093\pi$
$521$	−25.3137			−1.10901			−0.554507	+	0.832179i	$0.687093\pi$
$522$		0			0
$523$	−15.3137			−0.669622			−0.334811	−	0.942285i	$-0.608672\pi$
$523$	−15.3137			−0.669622			−0.334811	+	0.942285i	$0.608672\pi$
$524$	7.31371	+	12.6677i	0.319501	+	0.553392i
$525$		0			0
$526$	−2.48528	+	4.30463i	−0.108363	+	0.187691i
$527$	−4.48528	+	7.76874i	−0.195382	+	0.338411i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−2.34315			−0.101780
$531$		0			0
$532$	14.6274			0.634179
$533$	−2.58579	−	4.47871i	−0.112003	−	0.193995i
$534$		0			0
$535$	−16.0000	+	27.7128i	−0.691740	+	1.19813i
$536$	−5.41421	+	9.37769i	−0.233858	+	0.405055i
$537$		0			0
$538$	−3.72792	−	6.45695i	−0.160722	−	0.278379i
$539$	2.00000			0.0861461
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$	−5.75736	−	9.97204i	−0.247300	−	0.428336i
$543$		0			0
$544$	−16.8995	+	29.2708i	−0.724560	+	1.25497i
$545$	−7.51472	+	13.0159i	−0.321895	+	0.557539i
$546$		0			0
$547$	−11.6569	−	20.1903i	−0.498411	−	0.863273i	0.501587	−	0.865107i	$-0.332750\pi$
$547$	−11.6569	−	20.1903i	−0.498411	−	0.863273i	−0.999998	+	0.00183374i	$0.999416\pi$
$548$	−19.7990			−0.845771
$549$		0			0
$550$	−2.48528			−0.105973
$551$	−2.82843	−	4.89898i	−0.120495	−	0.208704i
$552$		0			0
$553$	16.0000	−	27.7128i	0.680389	−	1.17847i
$554$	−0.414214	+	0.717439i	−0.0175982	+	0.0304811i
$555$		0			0
$556$	−6.68629	−	11.5810i	−0.283562	−	0.491144i
$557$	7.79899			0.330454			0.165227	−	0.986256i	$-0.447164\pi$
$557$	7.79899			0.330454			0.165227	+	0.986256i	$0.447164\pi$
$558$		0			0
$559$	1.65685			0.0700775
$560$	−12.0000	−	20.7846i	−0.507093	−	0.878310i
$561$		0			0
$562$	−4.38478	+	7.59466i	−0.184961	+	0.320361i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	−7.51472	−	13.0159i	−0.316147	−	0.547582i
$566$	−12.0000			−0.504398
$567$		0			0
$568$	−3.17157			−0.133076
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.826575	−	0.562827i	$-0.809714\pi$
$569$	−21.4853	−	37.2136i	−0.900710	−	1.56008i	−0.0741351	−	0.997248i	$-0.523620\pi$
$570$		0			0
$571$	6.48528	−	11.2328i	0.271401	−	0.470080i	−0.697820	−	0.716273i	$-0.745847\pi$
$571$	6.48528	−	11.2328i	0.271401	−	0.470080i	0.969221	+	0.246193i	$0.0791799\pi$
$572$	−1.82843	+	3.16693i	−0.0764504	+	0.132416i
$573$		0			0
$574$	−3.02944	−	5.24714i	−0.126446	−	0.219011i
$575$	12.0000			0.500435
$576$		0			0
$577$	−31.9411			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$577$	−31.9411			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$578$	8.62132	+	14.9326i	0.358600	+	0.621113i
$579$		0			0
$580$	−5.17157	+	8.95743i	−0.214738	+	0.371937i
$581$	5.17157	−	8.95743i	0.214553	−	0.371617i
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	0.544156			0.0225173
$585$		0			0
$586$	0.887302			0.0366541
$587$	−5.48528	−	9.50079i	−0.226402	−	0.392139i	0.730337	−	0.683087i	$-0.239363\pi$
$587$	−5.48528	−	9.50079i	−0.226402	−	0.392139i	−0.956739	+	0.290947i	$0.906030\pi$
$588$		0			0
$589$	−1.65685	+	2.86976i	−0.0682695	+	0.118246i
$590$	−4.48528	+	7.76874i	−0.184656	+	0.319834i
$591$		0			0
$592$	11.4853	+	19.8931i	0.472042	+	0.817601i
$593$	20.4853			0.841230			0.420615	−	0.907239i	$-0.361814\pi$
$593$	20.4853			0.841230			0.420615	+	0.907239i	$0.361814\pi$
$594$		0			0
$595$	−61.2548			−2.51120
$596$	8.38478	+	14.5229i	0.343454	+	0.594879i
$597$		0			0
$598$	−0.828427	+	1.43488i	−0.0338769	+	0.0586765i
$599$	−11.6569	+	20.1903i	−0.476286	+	0.824952i	−0.999631	−	0.0271693i	$-0.991351\pi$
$599$	−11.6569	+	20.1903i	−0.476286	+	0.824952i	0.523345	+	0.852121i	$0.324684\pi$
$600$		0			0
$601$	0.313708	+	0.543359i	0.0127964	+	0.0221641i	0.872353	−	0.488877i	$-0.162593\pi$
$601$	0.313708	+	0.543359i	0.0127964	+	0.0221641i	−0.859556	+	0.511041i	$0.829260\pi$
$602$	1.94113			0.0791144
$603$		0			0
$604$	6.42641			0.261487
$605$	9.89949	+	17.1464i	0.402472	+	0.697101i
$606$		0			0
$607$	−20.9706	+	36.3221i	−0.851169	+	1.47427i	0.0289853	+	0.999580i	$0.490772\pi$
$607$	−20.9706	+	36.3221i	−0.851169	+	1.47427i	−0.880154	+	0.474688i	$0.842561\pi$
$608$	−6.24264	+	10.8126i	−0.253173	+	0.438508i
$609$		0			0
$610$	7.79899	+	13.5082i	0.315772	+	0.546933i
$611$	−11.6569			−0.471586
$612$		0			0
$613$	−47.6569			−1.92484			−0.962421	−	0.271561i	$-0.912460\pi$
$613$	−47.6569			−1.92484			−0.962421	+	0.271561i	$0.912460\pi$
$614$	−4.72792	−	8.18900i	−0.190803	−	0.330481i
$615$		0			0
$616$	−4.48528	+	7.76874i	−0.180717	+	0.313011i
$617$	−17.4142	+	30.1623i	−0.701070	+	1.21429i	0.267021	+	0.963691i	$0.413961\pi$
$617$	−17.4142	+	30.1623i	−0.701070	+	1.21429i	−0.968091	+	0.250598i	$0.919373\pi$
$618$		0			0
$619$	−11.8995	−	20.6105i	−0.478281	−	0.828407i	0.521409	−	0.853307i	$-0.325407\pi$
$619$	−11.8995	−	20.6105i	−0.478281	−	0.828407i	−0.999690	+	0.0248998i	$0.992073\pi$
$620$	6.05887			0.243330
$621$		0			0
$622$	−4.40202			−0.176505
$623$	20.9706	+	36.3221i	0.840168	+	1.45521i
$624$		0			0
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	1.24264	−	2.15232i	0.0496659	−	0.0860239i
$627$		0			0
$628$	−9.14214	−	15.8346i	−0.364811	−	0.631871i
$629$	58.6274			2.33763
$630$		0			0
$631$	43.1127			1.71629			0.858145	−	0.513408i	$-0.171617\pi$
$631$	43.1127			1.71629			0.858145	+	0.513408i	$0.171617\pi$
$632$	8.97056	+	15.5375i	0.356830	+	0.618047i
$633$		0			0
$634$	−1.75736	+	3.04384i	−0.0697937	+	0.120886i
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$		0			0
$637$	0.500000	+	0.866025i	0.0198107	+	0.0343132i
$638$	1.65685			0.0655955
$639$		0			0
$640$	29.8579			1.18024
$641$	15.1421	+	26.2269i	0.598078	+	1.03590i	0.993105	+	0.117232i	$0.0374022\pi$
$641$	15.1421	+	26.2269i	0.598078	+	1.03590i	−0.395026	+	0.918670i	$0.629264\pi$
$642$		0			0
$643$	−11.4142	+	19.7700i	−0.450133	+	0.779653i	−0.998394	−	0.0566545i	$-0.981957\pi$
$643$	−11.4142	+	19.7700i	−0.450133	+	0.779653i	0.548261	+	0.836307i	$0.315290\pi$
$644$	10.3431	−	17.9149i	0.407577	−	0.705944i
$645$		0			0
$646$	4.48528	+	7.76874i	0.176471	+	0.305657i
$647$	−11.3137			−0.444788			−0.222394	−	0.974957i	$-0.571387\pi$
$647$	−11.3137			−0.444788			−0.222394	+	0.974957i	$0.571387\pi$
$648$		0			0
$649$	−15.3137			−0.601116
$650$	−0.621320	−	1.07616i	−0.0243702	−	0.0422104i
$651$		0			0
$652$	17.2132	−	29.8141i	0.674121	−	1.16761i
$653$	−12.6569	+	21.9223i	−0.495301	+	0.857886i	−0.999985	−	0.00541749i	$-0.998276\pi$
$653$	−12.6569	+	21.9223i	−0.495301	+	0.857886i	0.504684	+	0.863304i	$0.331609\pi$
$654$		0			0
$655$	−11.3137	−	19.5959i	−0.442063	−	0.765676i
$656$	−15.5147			−0.605748
$657$		0			0
$658$	−13.6569			−0.532400
$659$	−23.6569	−	40.9749i	−0.921540	−	1.59615i	−0.797033	−	0.603936i	$-0.793598\pi$
$659$	−23.6569	−	40.9749i	−0.921540	−	1.59615i	−0.124507	−	0.992219i	$-0.539735\pi$
$660$		0			0
$661$	17.4853	−	30.2854i	0.680099	−	1.17797i	−0.294852	−	0.955543i	$-0.595270\pi$
$661$	17.4853	−	30.2854i	0.680099	−	1.17797i	0.974950	−	0.222422i	$-0.0713964\pi$
$662$	5.41421	−	9.37769i	0.210429	−	0.364474i
$663$		0			0
$664$	2.89949	+	5.02207i	0.112522	+	0.194894i
$665$	−22.6274			−0.877454
$666$		0			0
$667$	−8.00000			−0.309761
$668$	3.34315	+	5.79050i	0.129350	+	0.224041i
$669$		0			0
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	−13.3137	+	23.0600i	−0.513970	+	0.890222i
$672$		0			0
$673$	−8.31371	−	14.3998i	−0.320470	−	0.555070i	0.660115	−	0.751164i	$-0.270507\pi$
$673$	−8.31371	−	14.3998i	−0.320470	−	0.555070i	−0.980585	+	0.196094i	$0.937174\pi$
$674$	−3.85786			−0.148599
$675$		0			0
$676$	−1.82843			−0.0703241
$677$	13.3431	+	23.1110i	0.512819	+	0.888228i	0.999890	+	0.0148656i	$0.00473205\pi$
$677$	13.3431	+	23.1110i	0.512819	+	0.888228i	−0.487071	+	0.873363i	$0.661935\pi$
$678$		0			0
$679$	−5.17157	+	8.95743i	−0.198467	+	0.343754i
$680$	17.1716	−	29.7420i	0.658500	−	1.14056i
$681$		0			0
$682$	−0.485281	−	0.840532i	−0.0185824	−	0.0321856i
$683$	−47.9411			−1.83442			−0.917208	−	0.398408i	$-0.869563\pi$
$683$	−47.9411			−1.83442			−0.917208	+	0.398408i	$0.869563\pi$
$684$		0			0
$685$	30.6274			1.17021
$686$	−3.51472	−	6.08767i	−0.134193	−	0.232428i
$687$		0			0
$688$	2.48528	−	4.30463i	0.0947505	−	0.164113i
$689$	1.00000	−	1.73205i	0.0380970	−	0.0659859i
$690$		0			0
$691$	2.92893	+	5.07306i	0.111422	+	0.192988i	0.916344	−	0.400392i	$-0.131126\pi$
$691$	2.92893	+	5.07306i	0.111422	+	0.192988i	−0.804922	+	0.593381i	$0.797793\pi$
$692$	−21.3137			−0.810226
$693$		0			0
$694$	−3.59798			−0.136577
$695$	10.3431	+	17.9149i	0.392338	+	0.679549i
$696$		0			0
$697$	−19.7990	+	34.2929i	−0.749940	+	1.29893i
$698$	0.757359	−	1.31178i	0.0286665	−	0.0496518i
$699$		0			0
$700$	7.75736	+	13.4361i	0.293201	+	0.507838i
$701$	−5.02944			−0.189959			−0.0949796	−	0.995479i	$-0.530279\pi$
$701$	−5.02944			−0.189959			−0.0949796	+	0.995479i	$0.530279\pi$
$702$		0			0
$703$	21.6569			0.816804
$704$	4.17157	+	7.22538i	0.157222	+	0.272317i
$705$		0			0
$706$	6.92893	−	12.0013i	0.260774	−	0.451673i
$707$	10.8284	−	18.7554i	0.407245	−	0.705369i
$708$		0			0
$709$	2.31371	+	4.00746i	0.0868931	+	0.150503i	0.906196	−	0.422857i	$-0.138973\pi$
$709$	2.31371	+	4.00746i	0.0868931	+	0.150503i	−0.819303	+	0.573360i	$0.805639\pi$
$710$	2.34315			0.0879367
$711$		0			0
$712$	−23.5147			−0.881251
$713$	2.34315	+	4.05845i	0.0877515	+	0.151990i
$714$		0			0
$715$	2.82843	−	4.89898i	0.105777	−	0.183211i
$716$	21.3137	−	36.9164i	0.796531	−	1.37963i
$717$		0			0
$718$	−7.24264	−	12.5446i	−0.270293	−	0.468161i
$719$	29.9411			1.11662			0.558308	−	0.829634i	$-0.311451\pi$
$719$	29.9411			1.11662			0.558308	+	0.829634i	$0.311451\pi$
$720$		0			0
$721$	6.62742			0.246818
$722$	−2.27817	−	3.94591i	−0.0847849	−	0.146852i
$723$		0			0
$724$	12.7990	−	22.1685i	0.475671	−	0.823886i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	5.17157	+	8.95743i	0.191803	+	0.332213i	0.945848	−	0.324610i	$-0.105233\pi$
$727$	5.17157	+	8.95743i	0.191803	+	0.332213i	−0.754045	+	0.656823i	$0.771900\pi$
$728$	−4.48528			−0.166236
$729$		0			0
$730$	−0.402020			−0.0148794
$731$	−6.34315	−	10.9867i	−0.234610	−	0.406356i
$732$		0			0
$733$	18.3137	−	31.7203i	0.676432	−	1.17162i	−0.299616	−	0.954060i	$-0.596858\pi$
$733$	18.3137	−	31.7203i	0.676432	−	1.17162i	0.976048	−	0.217555i	$-0.0698082\pi$
$734$	−4.97056	+	8.60927i	−0.183467	+	0.317774i
$735$		0			0
$736$	8.82843	+	15.2913i	0.325420	+	0.563644i
$737$	13.6569			0.503057
$738$		0			0
$739$	−18.1421			−0.667369			−0.333685	−	0.942685i	$-0.608292\pi$
$739$	−18.1421			−0.667369			−0.333685	+	0.942685i	$0.608292\pi$
$740$	−19.7990	−	34.2929i	−0.727825	−	1.26063i
$741$		0			0
$742$	1.17157	−	2.02922i	0.0430098	−	0.0744951i
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	−0.847099	−	0.531435i	$-0.821653\pi$
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	0.883786	+	0.467892i	$0.154986\pi$
$744$		0			0
$745$	−12.9706	−	22.4657i	−0.475205	−	0.823079i
$746$	−4.14214			−0.151654
$747$		0			0
$748$	28.0000			1.02378
$749$	−16.0000	−	27.7128i	−0.584627	−	1.01260i
$750$		0			0
$751$	0.485281	−	0.840532i	0.0177082	−	0.0306714i	−0.857036	−	0.515257i	$-0.827696\pi$
$751$	0.485281	−	0.840532i	0.0177082	−	0.0306714i	0.874744	+	0.484586i	$0.161030\pi$
$752$	−17.4853	+	30.2854i	−0.637623	+	1.10439i
$753$		0			0
$754$	0.414214	+	0.717439i	0.0150848	+	0.0261276i
$755$	−9.94113			−0.361795
$756$		0			0
$757$	51.9411			1.88783			0.943916	−	0.330185i	$-0.107111\pi$
$757$	51.9411			1.88783			0.943916	+	0.330185i	$0.107111\pi$
$758$	0.100505	+	0.174080i	0.00365051	+	0.00632287i
$759$		0			0
$760$	6.34315	−	10.9867i	0.230090	−	0.398528i
$761$	16.2426	−	28.1331i	0.588795	−	1.01982i	−0.405595	−	0.914053i	$-0.632936\pi$
$761$	16.2426	−	28.1331i	0.588795	−	1.01982i	0.994391	−	0.105771i	$-0.0337309\pi$
$762$		0			0
$763$	−7.51472	−	13.0159i	−0.272051	−	0.471206i
$764$	6.05887			0.219202
$765$		0			0
$766$	12.8284			0.463510
$767$	−3.82843	−	6.63103i	−0.138236	−	0.239433i
$768$		0			0
$769$	−21.0000	+	36.3731i	−0.757279	+	1.31165i	0.186954	+	0.982369i	$0.440139\pi$
$769$	−21.0000	+	36.3731i	−0.757279	+	1.31165i	−0.944233	+	0.329278i	$0.893195\pi$
$770$	3.31371	−	5.73951i	0.119418	−	0.206838i
$771$		0			0
$772$	4.85786	+	8.41407i	0.174838	+	0.302829i
$773$	−34.1421			−1.22801			−0.614004	−	0.789303i	$-0.710442\pi$
$773$	−34.1421			−1.22801			−0.614004	+	0.789303i	$0.710442\pi$
$774$		0			0
$775$	−3.51472			−0.126252
$776$	−2.89949	−	5.02207i	−0.104086	−	0.180282i
$777$		0			0
$778$	5.58579	−	9.67487i	0.200260	−	0.346861i
$779$	−7.31371	+	12.6677i	−0.262041	+	0.453868i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	12.6863			0.453661
$783$		0			0
$784$	3.00000			0.107143
$785$	14.1421	+	24.4949i	0.504754	+	0.874260i
$786$		0			0
$787$	20.3848	−	35.3075i	0.726639	−	1.25858i	−0.231657	−	0.972798i	$-0.574415\pi$
$787$	20.3848	−	35.3075i	0.726639	−	1.25858i	0.958296	−	0.285778i	$-0.0922519\pi$
$788$	−0.443651	+	0.768426i	−0.0158044	+	0.0273740i
$789$		0			0
$790$	−6.62742	−	11.4790i	−0.235793	−	0.408405i
$791$	15.0294			0.534385
$792$		0			0
$793$	−13.3137			−0.472784
$794$	6.41421	+	11.1097i	0.227632	+	0.394270i
$795$		0			0
$796$	19.7990	−	34.2929i	0.701757	−	1.21548i
$797$	12.1716	−	21.0818i	0.431139	−	0.746755i	−0.565832	−	0.824520i	$-0.691445\pi$
$797$	12.1716	−	21.0818i	0.431139	−	0.746755i	0.996972	+	0.0777652i	$0.0247784\pi$
$798$		0			0
$799$	44.6274	+	77.2970i	1.57880	+	2.73457i
$800$	−13.2426			−0.468198
$801$		0			0
$802$	10.8284			0.382365
$803$	−0.343146	−	0.594346i	−0.0121094	−	0.0209740i
$804$		0			0
$805$	−16.0000	+	27.7128i	−0.563926	+	0.976748i
$806$	0.242641	−	0.420266i	0.00854665	−	0.0148032i
$807$		0			0
$808$	6.07107	+	10.5154i	0.213579	+	0.369930i
$809$	−18.6863			−0.656975			−0.328488	−	0.944508i	$-0.606539\pi$
$809$	−18.6863			−0.656975			−0.328488	+	0.944508i	$0.606539\pi$
$810$		0			0
$811$	−30.1421			−1.05843			−0.529217	−	0.848487i	$-0.677514\pi$
$811$	−30.1421			−1.05843			−0.529217	+	0.848487i	$0.677514\pi$
$812$	−5.17157	−	8.95743i	−0.181487	−	0.314344i
$813$		0			0
$814$	−3.17157	+	5.49333i	−0.111164	+	0.192541i
$815$	−26.6274	+	46.1200i	−0.932718	+	1.61551i
$816$		0			0
$817$	−2.34315	−	4.05845i	−0.0819763	−	0.141987i
$818$	14.4853			0.506466
$819$		0			0
$820$	26.7452			0.933982
$821$	−11.8995	−	20.6105i	−0.415295	−	0.719312i	0.580164	−	0.814500i	$-0.302988\pi$
$821$	−11.8995	−	20.6105i	−0.415295	−	0.719312i	−0.995459	+	0.0951871i	$0.969655\pi$
$822$		0			0
$823$	−7.51472	+	13.0159i	−0.261947	+	0.453705i	−0.966759	−	0.255689i	$-0.917698\pi$
$823$	−7.51472	+	13.0159i	−0.261947	+	0.453705i	0.704813	+	0.709394i	$0.251031\pi$
$824$	−1.85786	+	3.21792i	−0.0647218	+	0.112101i
$825$		0			0
$826$	−4.48528	−	7.76874i	−0.156063	−	0.270309i
$827$	26.0000			0.904109			0.452054	−	0.891990i	$-0.350691\pi$
$827$	26.0000			0.904109			0.452054	+	0.891990i	$0.350691\pi$
$828$		0			0
$829$	−17.3137			−0.601330			−0.300665	−	0.953730i	$-0.597209\pi$
$829$	−17.3137			−0.601330			−0.300665	+	0.953730i	$0.597209\pi$
$830$	−2.14214	−	3.71029i	−0.0743546	−	0.128786i
$831$		0			0
$832$	−2.08579	+	3.61269i	−0.0723116	+	0.125247i
$833$	3.82843	−	6.63103i	0.132647	−	0.229752i
$834$		0			0
$835$	−5.17157	−	8.95743i	−0.178970	−	0.309985i
$836$	10.3431			0.357725
$837$		0			0
$838$	6.05887			0.209300
$839$	21.6274	+	37.4598i	0.746661	+	1.29326i	0.949415	+	0.314026i	$0.101678\pi$
$839$	21.6274	+	37.4598i	0.746661	+	1.29326i	−0.202753	+	0.979230i	$0.564989\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	7.72792	−	13.3852i	0.266322	−	0.461283i
$843$		0			0
$844$	−10.9706	−	19.0016i	−0.377622	−	0.654061i
$845$	2.82843			0.0973009
$846$		0			0
$847$	−19.7990			−0.680301
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	−4.75736	+	8.23999i	−0.163176	+	0.282629i
$851$	15.3137	−	26.5241i	0.524947	−	0.909235i
$852$		0			0
$853$	−1.82843	−	3.16693i	−0.0626042	−	0.108434i	0.833025	−	0.553236i	$-0.186607\pi$
$853$	−1.82843	−	3.16693i	−0.0626042	−	0.108434i	−0.895629	+	0.444802i	$0.853274\pi$
$854$	−15.5980			−0.533752
$855$		0			0
$856$	17.9411			0.613215
$857$	−24.7990	−	42.9531i	−0.847117	−	1.46725i	−0.883770	−	0.467922i	$-0.845003\pi$
$857$	−24.7990	−	42.9531i	−0.847117	−	1.46725i	0.0366523	−	0.999328i	$-0.488331\pi$
$858$		0			0
$859$	0.343146	−	0.594346i	0.0117080	−	0.0202788i	−0.860112	−	0.510105i	$-0.829606\pi$
$859$	0.343146	−	0.594346i	0.0117080	−	0.0202788i	0.871820	+	0.489826i	$0.162940\pi$
$860$	−4.28427	+	7.42058i	−0.146092	+	0.253040i
$861$		0			0
$862$	−1.72792	−	2.99285i	−0.0588533	−	0.101937i
$863$	28.3431			0.964812			0.482406	−	0.875948i	$-0.339763\pi$
$863$	28.3431			0.964812			0.482406	+	0.875948i	$0.339763\pi$
$864$		0			0
$865$	32.9706			1.12103
$866$	−4.41421	−	7.64564i	−0.150001	−	0.259809i
$867$		0			0
$868$	−3.02944	+	5.24714i	−0.102826	+	0.178100i
$869$	11.3137	−	19.5959i	0.383791	−	0.664746i
$870$		0			0
$871$	3.41421	+	5.91359i	0.115686	+	0.200374i
$872$	8.42641			0.285354
$873$		0			0
$874$	4.68629			0.158516
$875$	8.00000	+	13.8564i	0.270449	+	0.468432i
$876$		0			0
$877$	−21.1421	+	36.6193i	−0.713919	+	1.23654i	0.249456	+	0.968386i	$0.419748\pi$
$877$	−21.1421	+	36.6193i	−0.713919	+	1.23654i	−0.963375	+	0.268158i	$0.913585\pi$
$878$	3.51472	−	6.08767i	0.118616	−	0.205449i
$879$		0			0
$880$	−8.48528	−	14.6969i	−0.286039	−	0.495434i
$881$	25.5980			0.862418			0.431209	−	0.902252i	$-0.358087\pi$
$881$	25.5980			0.862418			0.431209	+	0.902252i	$0.358087\pi$
$882$		0			0
$883$	27.5980			0.928746			0.464373	−	0.885640i	$-0.346280\pi$
$883$	27.5980			0.928746			0.464373	+	0.885640i	$0.346280\pi$
$884$	7.00000	+	12.1244i	0.235435	+	0.407786i
$885$		0			0
$886$	5.37258	−	9.30559i	0.180495	−	0.312627i
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	−0.925332	−	0.379157i	$-0.876214\pi$
$887$	−4.00000	+	6.92820i	−0.134307	+	0.232626i	0.791026	+	0.611783i	$0.209547\pi$
$888$		0			0
$889$	−8.00000	−	13.8564i	−0.268311	−	0.464729i
$890$	17.3726			0.582330
$891$		0			0
$892$	22.8284			0.764352
$893$	16.4853	+	28.5533i	0.551659	+	0.955501i
$894$		0			0
$895$	−32.9706	+	57.1067i	−1.10208	+	1.90887i
$896$	−14.9289	+	25.8577i	−0.498741	+	0.863844i
$897$		0			0
$898$	6.58579	+	11.4069i	0.219771	+	0.380654i
$899$	2.34315			0.0781483
$900$		0			0
$901$	−15.3137			−0.510174
$902$	−2.14214	−	3.71029i	−0.0713253	−	0.123539i
$903$		0			0
$904$	−4.21320	+	7.29748i	−0.140129	+	0.242711i
$905$	−19.7990	+	34.2929i	−0.658141	+	1.13993i
$906$		0			0
$907$	6.48528	+	11.2328i	0.215340	+	0.372980i	0.953378	−	0.301779i	$-0.0975806\pi$
$907$	6.48528	+	11.2328i	0.215340	+	0.372980i	−0.738038	+	0.674760i	$0.764247\pi$
$908$	−31.6569			−1.05057
$909$		0			0
$910$	3.31371			0.109848
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	−0.979922	−	0.199380i	$-0.936107\pi$
$911$	−20.0000	−	34.6410i	−0.662630	−	1.14771i	0.317293	−	0.948328i	$-0.397226\pi$
$912$		0			0
$913$	3.65685	−	6.33386i	0.121024	−	0.209620i
$914$	−1.58579	+	2.74666i	−0.0524532	+	0.0908515i
$915$		0			0
$916$	−1.20101	−	2.08021i	−0.0396825	−	0.0687321i
$917$	22.6274			0.747223
$918$		0			0
$919$	3.31371			0.109309			0.0546546	−	0.998505i	$-0.482594\pi$
$919$	3.31371			0.109309			0.0546546	+	0.998505i	$0.482594\pi$
$920$	−8.97056	−	15.5375i	−0.295751	−	0.512255i
$921$		0			0
$922$	−1.07107	+	1.85514i	−0.0352737	+	0.0610959i
$923$	−1.00000	+	1.73205i	−0.0329154	+	0.0570111i
$924$		0			0
$925$	11.4853	+	19.8931i	0.377634	+	0.654081i
$926$	10.1421			0.333291
$927$		0			0
$928$	8.82843			0.289807
$929$	5.89949	+	10.2182i	0.193556	+	0.335249i	0.946426	−	0.322920i	$-0.104664\pi$
$929$	5.89949	+	10.2182i	0.193556	+	0.335249i	−0.752870	+	0.658169i	$0.771331\pi$
$930$		0			0
$931$	1.41421	−	2.44949i	0.0463490	−	0.0802788i
$932$	−6.37258	+	11.0376i	−0.208741	+	0.361550i
$933$		0			0
$934$	1.65685	+	2.86976i	0.0542139	+	0.0939013i
$935$	−43.3137			−1.41651
$936$		0			0
$937$	−21.3137			−0.696289			−0.348144	−	0.937441i	$-0.613188\pi$
$937$	−21.3137			−0.696289			−0.348144	+	0.937441i	$0.613188\pi$
$938$	4.00000	+	6.92820i	0.130605	+	0.226214i
$939$		0			0
$940$	30.1421	−	52.2077i	0.983128	−	1.70283i
$941$	17.0711	−	29.5680i	0.556501	−	0.963888i	−0.441284	−	0.897367i	$-0.645477\pi$
$941$	17.0711	−	29.5680i	0.556501	−	0.963888i	0.997785	−	0.0665204i	$-0.0211898\pi$
$942$		0			0
$943$	10.3431	+	17.9149i	0.336819	+	0.583388i
$944$	−22.9706			−0.747628
$945$		0			0
$946$	1.37258			0.0446265
$947$	−10.5147	−	18.2120i	−0.341682	−	0.591811i	0.643063	−	0.765813i	$-0.277663\pi$
$947$	−10.5147	−	18.2120i	−0.341682	−	0.591811i	−0.984745	+	0.174002i	$0.944330\pi$
$948$		0			0
$949$	0.171573	−	0.297173i	0.00556949	−	0.00964664i
$950$	−1.75736	+	3.04384i	−0.0570163	+	0.0987551i
$951$		0			0
$952$	17.1716	+	29.7420i	0.556534	+	0.963945i
$953$	−40.3431			−1.30684			−0.653421	−	0.756994i	$-0.726667\pi$
$953$	−40.3431			−1.30684			−0.653421	+	0.756994i	$0.726667\pi$
$954$		0			0
$955$	−9.37258			−0.303290
$956$	−1.82843	−	3.16693i	−0.0591356	−	0.102426i
$957$		0			0
$958$	−5.24264	+	9.08052i	−0.169382	+	0.293378i
$959$	−15.3137	+	26.5241i	−0.494505	+	0.856509i
$960$		0			0
$961$	14.8137	+	25.6581i	0.477862	+	0.827681i
$962$	−3.17157			−0.102256
$963$		0			0
$964$	−0.627417			−0.0202077
$965$	−7.51472	−	13.0159i	−0.241907	−	0.418996i
$966$		0			0
$967$	−9.07107	+	15.7116i	−0.291706	+	0.505249i	−0.974213	−	0.225629i	$-0.927556\pi$
$967$	−9.07107	+	15.7116i	−0.291706	+	0.505249i	0.682507	+	0.730879i	$0.260890\pi$
$968$	5.55025	−	9.61332i	0.178392	−	0.308984i
$969$		0			0
$970$	2.14214	+	3.71029i	0.0687798	+	0.119130i
$971$	15.3137			0.491440			0.245720	−	0.969341i	$-0.420976\pi$
$971$	15.3137			0.491440			0.245720	+	0.969341i	$0.420976\pi$
$972$		0			0
$973$	−20.6863			−0.663172
$974$	−1.61522	−	2.79765i	−0.0517551	−	0.0896425i
$975$		0			0
$976$	−19.9706	+	34.5900i	−0.639242	+	1.10720i
$977$	21.0711	−	36.4962i	0.674123	−	1.16762i	−0.302601	−	0.953117i	$-0.597855\pi$
$977$	21.0711	−	36.4962i	0.674123	−	1.16762i	0.976724	−	0.214498i	$-0.0688117\pi$
$978$		0			0
$979$	14.8284	+	25.6836i	0.473919	+	0.820851i
$980$	−5.17157			−0.165200
$981$		0			0
$982$	12.6863			0.404836
$983$	12.6569	+	21.9223i	0.403691	+	0.699213i	0.994168	−	0.107841i	$-0.0343938\pi$
$983$	12.6569	+	21.9223i	0.403691	+	0.699213i	−0.590477	+	0.807054i	$0.701060\pi$
$984$		0			0
$985$	0.686292	−	1.18869i	0.0218671	−	0.0378749i
$986$	3.17157	−	5.49333i	0.101003	−	0.174943i
$987$		0			0
$988$	2.58579	+	4.47871i	0.0822648	+	0.142487i
$989$	−6.62742			−0.210740
$990$		0			0
$991$	4.68629			0.148865			0.0744325	−	0.997226i	$-0.476285\pi$
$991$	4.68629			0.148865			0.0744325	+	0.997226i	$0.476285\pi$
$992$	−2.58579	−	4.47871i	−0.0820988	−	0.142199i
$993$		0			0
$994$	−1.17157	+	2.02922i	−0.0371600	+	0.0643631i
$995$	−30.6274	+	53.0482i	−0.970954	+	1.68174i
$996$		0			0
$997$	19.6274	+	33.9957i	0.621607	+	1.07665i	0.989187	+	0.146662i	$0.0468530\pi$
$997$	19.6274	+	33.9957i	0.621607	+	1.07665i	−0.367580	+	0.929992i	$0.619814\pi$
$998$	−10.8284			−0.342768
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.e.352.2		4
3.2	odd	2		1053.2.e.m.352.1		4
9.2	odd	6		1053.2.e.m.703.1		4
9.4	even	3		117.2.a.c.1.1		2
9.5	odd	6		39.2.a.b.1.2	✓	2
9.7	even	3	inner	1053.2.e.e.703.2		4
36.23	even	6		624.2.a.k.1.1		2
36.31	odd	6		1872.2.a.w.1.2		2
45.4	even	6		2925.2.a.v.1.2		2
45.13	odd	12		2925.2.c.u.2224.3		4
45.14	odd	6		975.2.a.l.1.1		2
45.22	odd	12		2925.2.c.u.2224.2		4
45.23	even	12		975.2.c.h.274.2		4
45.32	even	12		975.2.c.h.274.3		4
63.13	odd	6		5733.2.a.u.1.1		2
63.41	even	6		1911.2.a.h.1.2		2
72.5	odd	6		2496.2.a.bf.1.2		2
72.13	even	6		7488.2.a.cl.1.1		2
72.59	even	6		2496.2.a.bi.1.2		2
72.67	odd	6		7488.2.a.co.1.1		2
99.32	even	6		4719.2.a.p.1.1		2
117.5	even	12		507.2.b.e.337.2		4
117.23	odd	6		507.2.e.d.22.2		4
117.31	odd	12		1521.2.b.j.1351.3		4
117.32	even	12		507.2.j.f.361.2		8
117.41	even	12		507.2.j.f.316.3		8
117.50	even	12		507.2.j.f.316.2		8
117.59	even	12		507.2.j.f.361.3		8
117.68	odd	6		507.2.e.h.22.1		4
117.77	odd	6		507.2.a.h.1.1		2
117.86	even	12		507.2.b.e.337.3		4
117.95	odd	6		507.2.e.d.484.2		4
117.103	even	6		1521.2.a.f.1.2		2
117.112	odd	12		1521.2.b.j.1351.2		4
117.113	odd	6		507.2.e.h.484.1		4
468.311	even	6		8112.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.b.1.2	✓	2	9.5	odd	6
117.2.a.c.1.1		2	9.4	even	3
507.2.a.h.1.1		2	117.77	odd	6
507.2.b.e.337.2		4	117.5	even	12
507.2.b.e.337.3		4	117.86	even	12
507.2.e.d.22.2		4	117.23	odd	6
507.2.e.d.484.2		4	117.95	odd	6
507.2.e.h.22.1		4	117.68	odd	6
507.2.e.h.484.1		4	117.113	odd	6
507.2.j.f.316.2		8	117.50	even	12
507.2.j.f.316.3		8	117.41	even	12
507.2.j.f.361.2		8	117.32	even	12
507.2.j.f.361.3		8	117.59	even	12
624.2.a.k.1.1		2	36.23	even	6
975.2.a.l.1.1		2	45.14	odd	6
975.2.c.h.274.2		4	45.23	even	12
975.2.c.h.274.3		4	45.32	even	12
1053.2.e.e.352.2		4	1.1	even	1	trivial
1053.2.e.e.703.2		4	9.7	even	3	inner
1053.2.e.m.352.1		4	3.2	odd	2
1053.2.e.m.703.1		4	9.2	odd	6
1521.2.a.f.1.2		2	117.103	even	6
1521.2.b.j.1351.2		4	117.112	odd	12
1521.2.b.j.1351.3		4	117.31	odd	12
1872.2.a.w.1.2		2	36.31	odd	6
1911.2.a.h.1.2		2	63.41	even	6
2496.2.a.bf.1.2		2	72.5	odd	6
2496.2.a.bi.1.2		2	72.59	even	6
2925.2.a.v.1.2		2	45.4	even	6
2925.2.c.u.2224.2		4	45.22	odd	12
2925.2.c.u.2224.3		4	45.13	odd	12
4719.2.a.p.1.1		2	99.32	even	6
5733.2.a.u.1.1		2	63.13	odd	6
7488.2.a.cl.1.1		2	72.13	even	6
7488.2.a.co.1.1		2	72.67	odd	6
8112.2.a.bm.1.2		2	468.311	even	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:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.41421 + 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} +1.58579 q^{8} +O(q^{10})\)	\(q+(0.207107 + 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-1.41421 + 2.44949i) q^{5} +(-1.41421 - 2.44949i) q^{7} +1.58579 q^{8} -1.17157 q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.585786 - 1.01461i) q^{14} +(-1.50000 - 2.59808i) q^{16} -7.65685 q^{17} -2.82843 q^{19} +(2.58579 + 4.47871i) q^{20} +(0.414214 - 0.717439i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{25} +0.414214 q^{26} -5.17157 q^{28} +(1.00000 + 1.73205i) q^{29} +(0.585786 - 1.01461i) q^{31} +(2.20711 - 3.82282i) q^{32} +(-1.58579 - 2.74666i) q^{34} +8.00000 q^{35} -7.65685 q^{37} +(-0.585786 - 1.01461i) q^{38} +(-2.24264 + 3.88437i) q^{40} +(2.58579 - 4.47871i) q^{41} +(0.828427 + 1.43488i) q^{43} -3.65685 q^{44} -1.65685 q^{46} +(-5.82843 - 10.0951i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.621320 - 1.07616i) q^{50} +(-0.914214 - 1.58346i) q^{52} +2.00000 q^{53} +5.65685 q^{55} +(-2.24264 - 3.88437i) q^{56} +(-0.414214 + 0.717439i) q^{58} +(3.82843 - 6.63103i) q^{59} +(-6.65685 - 11.5300i) q^{61} +0.485281 q^{62} -4.17157 q^{64} +(1.41421 + 2.44949i) q^{65} +(-3.41421 + 5.91359i) q^{67} +(-7.00000 + 12.1244i) q^{68} +(1.65685 + 2.86976i) q^{70} -2.00000 q^{71} +0.343146 q^{73} +(-1.58579 - 2.74666i) q^{74} +(-2.58579 + 4.47871i) q^{76} +(-2.82843 + 4.89898i) q^{77} +(5.65685 + 9.79796i) q^{79} +8.48528 q^{80} +2.14214 q^{82} +(1.82843 + 3.16693i) q^{83} +(10.8284 - 18.7554i) q^{85} +(-0.343146 + 0.594346i) q^{86} +(-1.58579 - 2.74666i) q^{88} -14.8284 q^{89} -2.82843 q^{91} +(3.65685 + 6.33386i) q^{92} +(2.41421 - 4.18154i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-1.82843 - 3.16693i) q^{97} -0.414214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 12 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 12 q^{8} - 16 q^{10} - 4 q^{11} + 2 q^{13} + 8 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 32 q^{28} + 4 q^{29} + 8 q^{31} + 6 q^{32} - 12 q^{34} + 32 q^{35} - 8 q^{37} - 8 q^{38} + 8 q^{40} + 16 q^{41} - 8 q^{43} + 8 q^{44} + 16 q^{46} - 12 q^{47} - 2 q^{49} - 6 q^{50} + 2 q^{52} + 8 q^{53} + 8 q^{56} + 4 q^{58} + 4 q^{59} - 4 q^{61} - 32 q^{62} - 28 q^{64} - 8 q^{67} - 28 q^{68} - 16 q^{70} - 8 q^{71} + 24 q^{73} - 12 q^{74} - 16 q^{76} - 48 q^{82} - 4 q^{83} + 32 q^{85} - 24 q^{86} - 12 q^{88} - 48 q^{89} - 8 q^{92} + 4 q^{94} + 16 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 12 * q^8 - 16 * q^10 - 4 * q^11 + 2 * q^13 + 8 * q^14 - 6 * q^16 - 8 * q^17 + 16 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 32 * q^28 + 4 * q^29 + 8 * q^31 + 6 * q^32 - 12 * q^34 + 32 * q^35 - 8 * q^37 - 8 * q^38 + 8 * q^40 + 16 * q^41 - 8 * q^43 + 8 * q^44 + 16 * q^46 - 12 * q^47 - 2 * q^49 - 6 * q^50 + 2 * q^52 + 8 * q^53 + 8 * q^56 + 4 * q^58 + 4 * q^59 - 4 * q^61 - 32 * q^62 - 28 * q^64 - 8 * q^67 - 28 * q^68 - 16 * q^70 - 8 * q^71 + 24 * q^73 - 12 * q^74 - 16 * q^76 - 48 * q^82 - 4 * q^83 + 32 * q^85 - 24 * q^86 - 12 * q^88 - 48 * q^89 - 8 * q^92 + 4 * q^94 + 16 * q^95 + 4 * q^97 + 4 * q^98

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