LMFDB - Embedded newform 693.2.i.l.298.6

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11 x^{10} - 4 x^{9} + 88 x^{8} - 32 x^{7} + 325 x^{6} - 154 x^{5} + 878 x^{4} - 246 x^{3} + \cdots + 441 $ x^12 + 11x^10 - 4x^9 + 88x^8 - 32x^7 + 325x^6 - 154x^5 + 878x^4 - 246x^3 + 793x^2 + 210x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.6
Root			$1.21005 - 2.09587i$ of defining polynomial
Character	$\chi$	$=$	693.298
Dual form			693.2.i.l.100.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21005 + 2.09587i) q^{2} +(-1.92845 + 3.34017i) q^{4} +(1.42845 + 2.47414i) q^{5} +(2.03688 + 1.68852i) q^{7} -4.49387 q^{8} +O(q^{10})$	\(q+(1.21005 + 2.09587i) q^{2} +(-1.92845 + 3.34017i) q^{4} +(1.42845 + 2.47414i) q^{5} +(2.03688 + 1.68852i) q^{7} -4.49387 q^{8} +(-3.45699 + 5.98768i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.62045 q^{13} +(-1.07419 + 6.31224i) q^{14} +(-1.58092 - 2.73823i) q^{16} +(4.05716 - 7.02721i) q^{17} +(0.602807 + 1.04409i) q^{19} -11.0187 q^{20} +2.42010 q^{22} +(-3.12308 - 5.40934i) q^{23} +(-1.58092 + 2.73823i) q^{25} +(-1.96083 - 3.39625i) q^{26} +(-9.56796 + 3.54731i) q^{28} +2.28468 q^{29} +(-3.07257 + 5.32185i) q^{31} +(-0.667886 + 1.15681i) q^{32} +19.6375 q^{34} +(-1.26806 + 7.45150i) q^{35} +(-4.31772 - 7.47851i) q^{37} +(-1.45886 + 2.52681i) q^{38} +(-6.41925 - 11.1185i) q^{40} -8.09333 q^{41} +6.81225 q^{43} +(1.92845 + 3.34017i) q^{44} +(7.55818 - 13.0912i) q^{46} +(-3.88015 - 6.72062i) q^{47} +(1.29779 + 6.87864i) q^{49} -7.65197 q^{50} +(3.12495 - 5.41258i) q^{52} +(0.784319 - 1.35848i) q^{53} +2.85689 q^{55} +(-9.15349 - 7.58799i) q^{56} +(2.76458 + 4.78839i) q^{58} +(-0.123084 + 0.213188i) q^{59} +(-1.60988 - 2.78839i) q^{61} -14.8719 q^{62} -9.55638 q^{64} +(-2.31473 - 4.00923i) q^{65} +(6.95314 - 12.0432i) q^{67} +(15.6480 + 27.1032i) q^{68} +(-17.1518 + 6.35901i) q^{70} +10.0713 q^{71} +(-5.24011 + 9.07614i) q^{73} +(10.4493 - 18.0988i) q^{74} -4.64993 q^{76} +(2.48074 - 0.919733i) q^{77} +(6.61960 + 11.4655i) q^{79} +(4.51652 - 7.82283i) q^{80} +(-9.79335 - 16.9626i) q^{82} -3.59930 q^{83} +23.1817 q^{85} +(8.24317 + 14.2776i) q^{86} +(-2.24694 + 3.89181i) q^{88} +(2.19320 + 3.79873i) q^{89} +(-3.30067 - 2.73617i) q^{91} +24.0908 q^{92} +(9.39036 - 16.2646i) q^{94} +(-1.72216 + 2.98286i) q^{95} -1.69506 q^{97} +(-12.8463 + 11.0435i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 4 q^{5} + 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 + 4 * q^5 + 6 * q^7 + 12 * q^8	$ 12 q - 10 q^{4} + 4 q^{5} + 6 q^{7} + 12 q^{8} + 6 q^{10} + 6 q^{11} - 4 q^{13} - 6 q^{14} - 2 q^{16} + 8 q^{17} - 6 q^{19} - 72 q^{20} - 2 q^{23} - 2 q^{25} + 8 q^{26} - 28 q^{28} + 4 q^{29} - 4 q^{31} - 12 q^{32} + 28 q^{34} - 26 q^{35} + 6 q^{37} + 10 q^{38} + 18 q^{40} - 60 q^{41} - 24 q^{43} + 10 q^{44} + 4 q^{46} + 14 q^{47} - 12 q^{49} + 48 q^{50} + 22 q^{52} + 16 q^{53} + 8 q^{55} - 60 q^{56} - 2 q^{58} + 34 q^{59} + 2 q^{61} - 52 q^{62} + 4 q^{64} - 20 q^{65} + 20 q^{67} + 18 q^{68} - 24 q^{70} + 12 q^{71} - 26 q^{73} + 14 q^{74} - 8 q^{76} + 6 q^{77} - 2 q^{79} + 44 q^{80} + 4 q^{82} - 16 q^{83} + 20 q^{85} + 78 q^{86} + 6 q^{88} + 20 q^{89} + 20 q^{91} + 60 q^{92} + 10 q^{94} - 10 q^{95} - 28 q^{97} - 90 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 4 * q^5 + 6 * q^7 + 12 * q^8 + 6 * q^10 + 6 * q^11 - 4 * q^13 - 6 * q^14 - 2 * q^16 + 8 * q^17 - 6 * q^19 - 72 * q^20 - 2 * q^23 - 2 * q^25 + 8 * q^26 - 28 * q^28 + 4 * q^29 - 4 * q^31 - 12 * q^32 + 28 * q^34 - 26 * q^35 + 6 * q^37 + 10 * q^38 + 18 * q^40 - 60 * q^41 - 24 * q^43 + 10 * q^44 + 4 * q^46 + 14 * q^47 - 12 * q^49 + 48 * q^50 + 22 * q^52 + 16 * q^53 + 8 * q^55 - 60 * q^56 - 2 * q^58 + 34 * q^59 + 2 * q^61 - 52 * q^62 + 4 * q^64 - 20 * q^65 + 20 * q^67 + 18 * q^68 - 24 * q^70 + 12 * q^71 - 26 * q^73 + 14 * q^74 - 8 * q^76 + 6 * q^77 - 2 * q^79 + 44 * q^80 + 4 * q^82 - 16 * q^83 + 20 * q^85 + 78 * q^86 + 6 * q^88 + 20 * q^89 + 20 * q^91 + 60 * q^92 + 10 * q^94 - 10 * q^95 - 28 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.21005	+	2.09587i	0.855635	+	1.48200i	0.876054	+	0.482212i	$0.160167\pi$
$2$	1.21005	+	2.09587i	0.855635	+	1.48200i	−0.0204193	+	0.999792i	$0.506500\pi$
$3$		0			0
$3$		0			0
$4$	−1.92845	+	3.34017i	−0.964223	+	1.67008i
$5$	1.42845	+	2.47414i	0.638821	+	1.10647i	0.985692	+	0.168557i	$0.0539108\pi$
$5$	1.42845	+	2.47414i	0.638821	+	1.10647i	−0.346871	+	0.937913i	$0.612756\pi$
$6$		0			0
$7$	2.03688	+	1.68852i	0.769870	+	0.638201i
$7$	2.03688	+	1.68852i	0.769870	+	0.638201i
$8$	−4.49387			−1.58882
$9$		0			0
$10$	−3.45699	+	5.98768i	−1.09319	+	1.89347i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−1.62045			−0.449432			−0.224716	−	0.974424i	$-0.572145\pi$
$13$	−1.62045			−0.449432			−0.224716	+	0.974424i	$0.572145\pi$
$14$	−1.07419	+	6.31224i	−0.287088	+	1.68702i
$15$		0			0
$16$	−1.58092	−	2.73823i	−0.395230	−	0.684558i
$17$	4.05716	−	7.02721i	0.984006	−	1.70435i	0.337733	−	0.941242i	$-0.390340\pi$
$17$	4.05716	−	7.02721i	0.984006	−	1.70435i	0.646273	−	0.763107i	$-0.276327\pi$
$18$		0			0
$19$	0.602807	+	1.04409i	0.138294	+	0.239531i	0.926851	−	0.375430i	$-0.122505\pi$
$19$	0.602807	+	1.04409i	0.138294	+	0.239531i	−0.788557	+	0.614961i	$0.789172\pi$
$20$	−11.0187			−2.46386
$21$		0			0
$22$	2.42010			0.515967
$23$	−3.12308	−	5.40934i	−0.651208	−	1.12793i	−0.982830	−	0.184513i	$-0.940929\pi$
$23$	−3.12308	−	5.40934i	−0.651208	−	1.12793i	0.331622	−	0.943412i	$-0.392404\pi$
$24$		0			0
$25$	−1.58092	+	2.73823i	−0.316184	+	0.547646i
$26$	−1.96083	−	3.39625i	−0.384550	−	0.666060i
$27$		0			0
$28$	−9.56796	+	3.54731i	−1.80818	+	0.670379i
$29$	2.28468			0.424254			0.212127	−	0.977242i	$-0.431961\pi$
$29$	2.28468			0.424254			0.212127	+	0.977242i	$0.431961\pi$
$30$		0			0
$31$	−3.07257	+	5.32185i	−0.551851	+	0.955833i	0.446291	+	0.894888i	$0.352745\pi$
$31$	−3.07257	+	5.32185i	−0.551851	+	0.955833i	−0.998141	+	0.0609451i	$0.980589\pi$
$32$	−0.667886	+	1.15681i	−0.118067	+	0.204497i
$33$		0			0
$34$	19.6375			3.36780
$35$	−1.26806	+	7.45150i	−0.214341	+	1.25953i
$36$		0			0
$37$	−4.31772	−	7.47851i	−0.709829	−	1.22946i	−0.964920	−	0.262543i	$-0.915439\pi$
$37$	−4.31772	−	7.47851i	−0.709829	−	1.22946i	0.255091	−	0.966917i	$-0.417894\pi$
$38$	−1.45886	+	2.52681i	−0.236658	+	0.409903i
$39$		0			0
$40$	−6.41925	−	11.1185i	−1.01497	−	1.75798i
$41$	−8.09333			−1.26397			−0.631983	−	0.774982i	$-0.717759\pi$
$41$	−8.09333			−1.26397			−0.631983	+	0.774982i	$0.717759\pi$
$42$		0			0
$43$	6.81225			1.03886			0.519429	−	0.854513i	$-0.326144\pi$
$43$	6.81225			1.03886			0.519429	+	0.854513i	$0.326144\pi$
$44$	1.92845	+	3.34017i	0.290724	+	0.503549i
$45$		0			0
$46$	7.55818	−	13.0912i	1.11439	−	1.93019i
$47$	−3.88015	−	6.72062i	−0.565978	−	0.980303i	−0.996958	−	0.0779415i	$-0.975165\pi$
$47$	−3.88015	−	6.72062i	−0.565978	−	0.980303i	0.430980	−	0.902362i	$-0.358168\pi$
$48$		0			0
$49$	1.29779	+	6.87864i	0.185399	+	0.982663i
$50$	−7.65197			−1.08215
$51$		0			0
$52$	3.12495	−	5.41258i	0.433353	−	0.750590i
$53$	0.784319	−	1.35848i	0.107734	−	0.186602i	−0.807118	−	0.590391i	$-0.798974\pi$
$53$	0.784319	−	1.35848i	0.107734	−	0.186602i	0.914852	+	0.403789i	$0.132307\pi$
$54$		0			0
$55$	2.85689			0.385223
$56$	−9.15349	−	7.58799i	−1.22319	−	1.01399i
$57$		0			0
$58$	2.76458	+	4.78839i	0.363007	+	0.628747i
$59$	−0.123084	+	0.213188i	−0.0160242	+	0.0277547i	−0.873926	−	0.486058i	$-0.838434\pi$
$59$	−0.123084	+	0.213188i	−0.0160242	+	0.0277547i	0.857902	+	0.513813i	$0.171768\pi$
$60$		0			0
$61$	−1.60988	−	2.78839i	−0.206124	−	0.357016i	0.744367	−	0.667771i	$-0.232752\pi$
$61$	−1.60988	−	2.78839i	−0.206124	−	0.357016i	−0.950490	+	0.310755i	$0.899418\pi$
$62$	−14.8719			−1.88873
$63$		0			0
$64$	−9.55638			−1.19455
$65$	−2.31473	−	4.00923i	−0.287107	−	0.497283i
$66$		0			0
$67$	6.95314	−	12.0432i	0.849462	−	1.47131i	−0.0322277	−	0.999481i	$-0.510260\pi$
$67$	6.95314	−	12.0432i	0.849462	−	1.47131i	0.881689	−	0.471830i	$-0.156406\pi$
$68$	15.6480	+	27.1032i	1.89760	+	3.28674i
$69$		0			0
$70$	−17.1518	+	6.35901i	−2.05003	+	0.760047i
$71$	10.0713			1.19525			0.597625	−	0.801776i	$-0.296111\pi$
$71$	10.0713			1.19525			0.597625	+	0.801776i	$0.296111\pi$
$72$		0			0
$73$	−5.24011	+	9.07614i	−0.613309	+	1.06228i	0.377370	+	0.926063i	$0.376828\pi$
$73$	−5.24011	+	9.07614i	−0.613309	+	1.06228i	−0.990679	+	0.136219i	$0.956505\pi$
$74$	10.4493	−	18.0988i	1.21471	−	2.10394i
$75$		0			0
$76$	−4.64993			−0.533383
$77$	2.48074	−	0.919733i	0.282707	−	0.104813i
$78$		0			0
$79$	6.61960	+	11.4655i	0.744763	+	1.28997i	0.950305	+	0.311320i	$0.100771\pi$
$79$	6.61960	+	11.4655i	0.744763	+	1.28997i	−0.205542	+	0.978648i	$0.565896\pi$
$80$	4.51652	−	7.82283i	0.504962	−	0.874620i
$81$		0			0
$82$	−9.79335	−	16.9626i	−1.08149	−	1.87320i
$83$	−3.59930			−0.395075			−0.197537	−	0.980295i	$-0.563294\pi$
$83$	−3.59930			−0.395075			−0.197537	+	0.980295i	$0.563294\pi$
$84$		0			0
$85$	23.1817			2.51441
$86$	8.24317	+	14.2776i	0.888884	+	1.53959i
$87$		0			0
$88$	−2.24694	+	3.89181i	−0.239524	+	0.414868i
$89$	2.19320	+	3.79873i	0.232479	+	0.402665i	0.958537	−	0.284968i	$-0.0919831\pi$
$89$	2.19320	+	3.79873i	0.232479	+	0.402665i	−0.726058	+	0.687633i	$0.758650\pi$
$90$		0			0
$91$	−3.30067	−	2.73617i	−0.346004	−	0.286828i
$92$	24.0908			2.51164
$93$		0			0
$94$	9.39036	−	16.2646i	0.968542	−	1.67756i
$95$	−1.72216	+	2.98286i	−0.176690	+	0.306035i
$96$		0			0
$97$	−1.69506			−0.172107			−0.0860534	−	0.996291i	$-0.527426\pi$
$97$	−1.69506			−0.172107			−0.0860534	+	0.996291i	$0.527426\pi$
$98$	−12.8463	+	11.0435i	−1.29768	+	1.11556i
$99$		0			0
$100$	−6.09743	−	10.5611i	−0.609743	−	1.05611i
$101$	0.122831	−	0.212749i	0.0122221	−	0.0211693i	−0.859850	−	0.510547i	$-0.829443\pi$
$101$	0.122831	−	0.212749i	0.0122221	−	0.0211693i	0.872072	+	0.489378i	$0.162776\pi$
$102$		0			0
$103$	4.04241	+	7.00165i	0.398310	+	0.689893i	0.993518	−	0.113679i	$-0.0362634\pi$
$103$	4.04241	+	7.00165i	0.398310	+	0.689893i	−0.595207	+	0.803572i	$0.702930\pi$
$104$	7.28210			0.714068
$105$		0			0
$106$	3.79626			0.368726
$107$	2.38034	+	4.12287i	0.230116	+	0.398573i	0.957842	−	0.287295i	$-0.0927560\pi$
$107$	2.38034	+	4.12287i	0.230116	+	0.398573i	−0.727726	+	0.685868i	$0.759423\pi$
$108$		0			0
$109$	−6.42538	+	11.1291i	−0.615440	+	1.06597i	0.374867	+	0.927078i	$0.377688\pi$
$109$	−6.42538	+	11.1291i	−0.615440	+	1.06597i	−0.990307	+	0.138895i	$0.955645\pi$
$110$	3.45699	+	5.98768i	0.329611	+	0.570902i
$111$		0			0
$112$	1.40341	−	8.24688i	0.132610	−	0.779256i
$113$	8.94622			0.841589			0.420795	−	0.907156i	$-0.361751\pi$
$113$	8.94622			0.841589			0.420795	+	0.907156i	$0.361751\pi$
$114$		0			0
$115$	8.92232	−	15.4539i	0.832010	−	1.44108i
$116$	−4.40588	+	7.63121i	−0.409076	+	0.708540i
$117$		0			0
$118$	−0.595751			−0.0548434
$119$	20.1296	−	7.46301i	1.84527	−	0.684133i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.89606	−	6.74818i	0.352733	−	0.610952i
$123$		0			0
$124$	−11.8506	−	20.5258i	−1.06421	−	1.84327i
$125$	5.25143			0.469702
$126$		0			0
$127$	15.3288			1.36021			0.680106	−	0.733114i	$-0.261934\pi$
$127$	15.3288			1.36021			0.680106	+	0.733114i	$0.261934\pi$
$128$	−10.2279	−	17.7153i	−0.904030	−	1.56583i
$129$		0			0
$130$	5.60188	−	9.70274i	0.491317	−	0.850986i
$131$	−1.77249	−	3.07005i	−0.154863	−	0.268231i	0.778146	−	0.628084i	$-0.216160\pi$
$131$	−1.77249	−	3.07005i	−0.154863	−	0.268231i	−0.933009	+	0.359852i	$0.882827\pi$
$132$		0			0
$133$	−0.535124	+	3.14455i	−0.0464012	+	0.272667i
$134$	33.6546			2.90732
$135$		0			0
$136$	−18.2324	+	31.5794i	−1.56341	+	2.70791i
$137$	−2.04770	+	3.54673i	−0.174947	+	0.303017i	−0.940143	−	0.340780i	$-0.889309\pi$
$137$	−2.04770	+	3.54673i	−0.174947	+	0.303017i	0.765196	+	0.643798i	$0.222642\pi$
$138$		0			0
$139$	−21.0198			−1.78287			−0.891437	−	0.453145i	$-0.850302\pi$
$139$	−21.0198			−1.78287			−0.891437	+	0.453145i	$0.850302\pi$
$140$	−22.4439	−	18.6054i	−1.89685	−	1.57244i
$141$		0			0
$142$	12.1868	+	21.1082i	1.02270	+	1.77136i
$143$	−0.810226	+	1.40335i	−0.0677545	+	0.117354i
$144$		0			0
$145$	3.26354	+	5.65262i	0.271022	+	0.469425i
$146$	−25.3632			−2.09907
$147$		0			0
$148$	33.3060			2.73773
$149$	−9.75348	−	16.8935i	−0.799036	−	1.38397i	−0.920244	−	0.391344i	$-0.872010\pi$
$149$	−9.75348	−	16.8935i	−0.799036	−	1.38397i	0.121208	−	0.992627i	$-0.461323\pi$
$150$		0			0
$151$	4.48441	−	7.76723i	0.364936	−	0.632088i	−0.623830	−	0.781560i	$-0.714424\pi$
$151$	4.48441	−	7.76723i	0.364936	−	0.632088i	0.988766	+	0.149472i	$0.0477574\pi$
$152$	−2.70894	−	4.69202i	−0.219724	−	0.380573i
$153$		0			0
$154$	4.92947	+	4.08639i	0.397228	+	0.329291i
$155$	−17.5560			−1.41013
$156$		0			0
$157$	−6.52929	+	11.3091i	−0.521094	+	0.902562i	0.478605	+	0.878030i	$0.341143\pi$
$157$	−6.52929	+	11.3091i	−0.521094	+	0.902562i	−0.999699	+	0.0245313i	$0.992191\pi$
$158$	−16.0201	+	27.7476i	−1.27449	+	2.20748i
$159$		0			0
$160$	−3.81616			−0.301694
$161$	2.77242	−	16.2916i	0.218498	−	1.28396i
$162$		0			0
$163$	7.15876	+	12.3993i	0.560717	+	0.971191i	0.997434	+	0.0715917i	$0.0228079\pi$
$163$	7.15876	+	12.3993i	0.560717	+	0.971191i	−0.436717	+	0.899599i	$0.643859\pi$
$164$	15.6076	−	27.0331i	1.21875	−	2.11093i
$165$		0			0
$166$	−4.35534	−	7.54367i	−0.338040	−	0.585502i
$167$	−2.14432			−0.165932			−0.0829661	−	0.996552i	$-0.526439\pi$
$167$	−2.14432			−0.165932			−0.0829661	+	0.996552i	$0.526439\pi$
$168$		0			0
$169$	−10.3741			−0.798011
$170$	28.0511	+	48.5859i	2.15142	+	3.72637i
$171$		0			0
$172$	−13.1371	+	22.7541i	−1.00169	+	1.73498i
$173$	−10.0442	−	17.3970i	−0.763646	−	1.32267i	−0.940960	−	0.338519i	$-0.890074\pi$
$173$	−10.0442	−	17.3970i	−0.763646	−	1.32267i	0.177314	−	0.984154i	$-0.443259\pi$
$174$		0			0
$175$	−7.84371	+	2.90805i	−0.592929	+	0.219828i
$176$	−3.16184			−0.238332
$177$		0			0
$178$	−5.30776	+	9.19332i	−0.397834	+	0.689068i
$179$	6.50348	−	11.2644i	0.486093	−	0.841938i	−0.513779	−	0.857922i	$-0.671755\pi$
$179$	6.50348	−	11.2644i	0.486093	−	0.841938i	0.999872	+	0.0159848i	$0.00508833\pi$
$180$		0			0
$181$	−8.64048			−0.642241			−0.321121	−	0.947038i	$-0.604060\pi$
$181$	−8.64048			−0.642241			−0.321121	+	0.947038i	$0.604060\pi$
$182$	1.74067	−	10.2287i	0.129027	−	0.758200i
$183$		0			0
$184$	14.0347	+	24.3089i	1.03465	+	1.79207i
$185$	12.3353	−	21.3653i	0.906907	−	1.57081i
$186$		0			0
$187$	−4.05716	−	7.02721i	−0.296689	−	0.513880i
$188$	29.9307			2.18292
$189$		0			0
$190$	−8.33559			−0.604727
$191$	9.91397	+	17.1715i	0.717350	+	1.24249i	0.962046	+	0.272887i	$0.0879784\pi$
$191$	9.91397	+	17.1715i	0.717350	+	1.24249i	−0.244696	+	0.969600i	$0.578688\pi$
$192$		0			0
$193$	3.63698	−	6.29943i	0.261795	−	0.453443i	−0.704924	−	0.709283i	$-0.749019\pi$
$193$	3.63698	−	6.29943i	0.261795	−	0.453443i	0.966719	+	0.255840i	$0.0823521\pi$
$194$	−2.05110	−	3.55262i	−0.147261	−	0.255063i
$195$		0			0
$196$	−25.4785	−	8.93025i	−1.81990	−	0.637875i
$197$	−12.6879			−0.903974			−0.451987	−	0.892025i	$-0.649285\pi$
$197$	−12.6879			−0.903974			−0.451987	+	0.892025i	$0.649285\pi$
$198$		0			0
$199$	−11.6049	+	20.1003i	−0.822651	+	1.42487i	0.0810507	+	0.996710i	$0.474172\pi$
$199$	−11.6049	+	20.1003i	−0.822651	+	1.42487i	−0.903702	+	0.428163i	$0.859161\pi$
$200$	7.10444	−	12.3053i	0.502360	−	0.870113i
$201$		0			0
$202$	0.594525			0.0418306
$203$	4.65363	+	3.85773i	0.326621	+	0.270760i
$204$		0			0
$205$	−11.5609	−	20.0241i	−0.807448	−	1.39854i
$206$	−9.78304	+	16.9447i	−0.681616	+	1.18059i
$207$		0			0
$208$	2.56180	+	4.43717i	0.177629	+	0.307662i
$209$	1.20561			0.0833941
$210$		0			0
$211$	−11.7680			−0.810142			−0.405071	−	0.914285i	$-0.632753\pi$
$211$	−11.7680			−0.810142			−0.405071	+	0.914285i	$0.632753\pi$
$212$	3.02503	+	5.23951i	0.207760	+	0.359851i
$213$		0			0
$214$	−5.76067	+	9.97777i	−0.393791	+	0.682066i
$215$	9.73094	+	16.8545i	0.663645	+	1.14947i
$216$		0			0
$217$	−15.2445	+	5.65190i	−1.03487	+	0.383676i
$218$	−31.1001			−2.10637
$219$		0			0
$220$	−5.50937	+	9.54250i	−0.371441	+	0.643355i
$221$	−6.57443	+	11.3872i	−0.442244	+	0.765989i
$222$		0			0
$223$	9.69505			0.649229			0.324614	−	0.945846i	$-0.394766\pi$
$223$	9.69505			0.649229			0.324614	+	0.945846i	$0.394766\pi$
$224$	−3.31371	+	1.22855i	−0.221406	+	0.0820862i
$225$		0			0
$226$	10.8254	+	18.7501i	0.720094	+	1.24724i
$227$	7.27847	−	12.6067i	0.483089	−	0.836735i	−0.516722	−	0.856153i	$-0.672848\pi$
$227$	7.27847	−	12.6067i	0.483089	−	0.836735i	0.999811	+	0.0194181i	$0.00618136\pi$
$228$		0			0
$229$	7.28110	+	12.6112i	0.481149	+	0.833374i	0.999766	−	0.0216322i	$-0.00688629\pi$
$229$	7.28110	+	12.6112i	0.481149	+	0.833374i	−0.518617	+	0.855007i	$0.673553\pi$
$230$	43.1858			2.84759
$231$		0			0
$232$	−10.2671			−0.674065
$233$	−3.75588	−	6.50538i	−0.246056	−	0.426182i	0.716372	−	0.697719i	$-0.245801\pi$
$233$	−3.75588	−	6.50538i	−0.246056	−	0.426182i	−0.962428	+	0.271537i	$0.912468\pi$
$234$		0			0
$235$	11.0852	−	19.2001i	0.723117	−	1.25248i
$236$	−0.474722	−	0.822242i	−0.0309017	−	0.0535234i
$237$		0			0
$238$	39.9993	+	33.1583i	2.59277	+	2.14933i
$239$	5.23765			0.338795			0.169398	−	0.985548i	$-0.445818\pi$
$239$	5.23765			0.338795			0.169398	+	0.985548i	$0.445818\pi$
$240$		0			0
$241$	12.1752	−	21.0881i	0.784275	−	1.35840i	−0.145156	−	0.989409i	$-0.546369\pi$
$241$	12.1752	−	21.0881i	0.784275	−	1.35840i	0.929431	−	0.368995i	$-0.120298\pi$
$242$	1.21005	−	2.09587i	0.0777850	−	0.134728i
$243$		0			0
$244$	12.4182			0.794996
$245$	−15.1649	+	13.0367i	−0.968851	+	0.832884i
$246$		0			0
$247$	−0.976820	−	1.69190i	−0.0621536	−	0.107653i
$248$	13.8077	−	23.9157i	0.876793	−	1.51865i
$249$		0			0
$250$	6.35450	+	11.0063i	0.401894	+	0.696101i
$251$	13.3323			0.841528			0.420764	−	0.907170i	$-0.361762\pi$
$251$	13.3323			0.841528			0.420764	+	0.907170i	$0.361762\pi$
$252$		0			0
$253$	−6.24617			−0.392693
$254$	18.5486	+	32.1272i	1.16385	+	2.01584i
$255$		0			0
$256$	15.1963	−	26.3207i	0.949766	−	1.64504i
$257$	−1.63357	−	2.82942i	−0.101899	−	0.176494i	0.810568	−	0.585645i	$-0.199159\pi$
$257$	−1.63357	−	2.82942i	−0.101899	−	0.176494i	−0.912467	+	0.409150i	$0.865825\pi$
$258$		0			0
$259$	3.83293	−	22.5234i	0.238167	−	1.39954i
$260$	17.8553			1.10734
$261$		0			0
$262$	4.28961	−	7.42983i	0.265013	−	0.459016i
$263$	−9.51422	+	16.4791i	−0.586672	+	1.01615i	0.407993	+	0.912985i	$0.366229\pi$
$263$	−9.51422	+	16.4791i	−0.586672	+	1.01615i	−0.994665	+	0.103160i	$0.967105\pi$
$264$		0			0
$265$	4.48143			0.275292
$266$	−7.23809	+	2.68351i	−0.443796	+	0.164537i
$267$		0			0
$268$	26.8175	+	46.4493i	1.63814	+	2.83734i
$269$	−6.49114	+	11.2430i	−0.395772	+	0.685497i	−0.993199	−	0.116426i	$-0.962856\pi$
$269$	−6.49114	+	11.2430i	−0.395772	+	0.685497i	0.597427	+	0.801923i	$0.296190\pi$
$270$		0			0
$271$	−2.36814	−	4.10174i	−0.143854	−	0.249163i	0.785091	−	0.619381i	$-0.212616\pi$
$271$	−2.36814	−	4.10174i	−0.143854	−	0.249163i	−0.928945	+	0.370218i	$0.879283\pi$
$272$	−25.6562			−1.55563
$273$		0			0
$274$	−9.91130			−0.598764
$275$	1.58092	+	2.73823i	0.0953330	+	0.165122i
$276$		0			0
$277$	5.77086	−	9.99543i	0.346738	−	0.600567i	−0.638930	−	0.769265i	$-0.720623\pi$
$277$	5.77086	−	9.99543i	0.346738	−	0.600567i	0.985668	+	0.168697i	$0.0539561\pi$
$278$	−25.4350	−	44.0547i	−1.52549	−	2.64223i
$279$		0			0
$280$	5.69850	−	33.4861i	0.340550	−	2.00118i
$281$	−25.8579			−1.54255			−0.771277	−	0.636500i	$-0.780381\pi$
$281$	−25.8579			−1.54255			−0.771277	+	0.636500i	$0.780381\pi$
$282$		0			0
$283$	−5.29353	+	9.16867i	−0.314668	+	0.545021i	−0.979367	−	0.202091i	$-0.935226\pi$
$283$	−5.29353	+	9.16867i	−0.314668	+	0.545021i	0.664699	+	0.747111i	$0.268560\pi$
$284$	−19.4221	+	33.6400i	−1.15249	+	1.99617i
$285$		0			0
$286$	−3.92166			−0.231892
$287$	−16.4852	−	13.6658i	−0.973090	−	0.806665i
$288$		0			0
$289$	−24.4211	−	42.2986i	−1.43654	−	2.48815i
$290$	−7.89811	+	13.6799i	−0.463793	+	0.803313i
$291$		0			0
$292$	−20.2105	−	35.0057i	−1.18273	−	2.04855i
$293$	−5.61873			−0.328250			−0.164125	−	0.986440i	$-0.552480\pi$
$293$	−5.61873			−0.328250			−0.164125	+	0.986440i	$0.552480\pi$
$294$		0			0
$295$	−0.703275			−0.0409463
$296$	19.4033	+	33.6075i	1.12779	+	1.95339i
$297$		0			0
$298$	23.6044	−	40.8840i	1.36737	−	2.36835i
$299$	5.06081	+	8.76557i	0.292674	+	0.506926i
$300$		0			0
$301$	13.8758	+	11.5026i	0.799786	+	0.663001i
$302$	21.7055			1.24901
$303$		0			0
$304$	1.90598	−	3.30125i	0.109315	−	0.189340i
$305$	4.59924	−	7.96612i	0.263352	−	0.456139i
$306$		0			0
$307$	−16.5271			−0.943251			−0.471625	−	0.881799i	$-0.656332\pi$
$307$	−16.5271			−0.943251			−0.471625	+	0.881799i	$0.656332\pi$
$308$	−1.71192	+	10.0598i	−0.0975457	+	0.573208i
$309$		0			0
$310$	−21.2437	−	36.7952i	−1.20656	−	2.08982i
$311$	8.77366	−	15.1964i	0.497509	−	0.861711i	−0.502487	−	0.864585i	$-0.667582\pi$
$311$	8.77366	−	15.1964i	0.497509	−	0.861711i	0.999996	+	0.00287417i	$0.000914879\pi$
$312$		0			0
$313$	−6.22809	−	10.7874i	−0.352033	−	0.609739i	0.634573	−	0.772863i	$-0.281176\pi$
$313$	−6.22809	−	10.7874i	−0.352033	−	0.609739i	−0.986605	+	0.163125i	$0.947843\pi$
$314$	−31.6031			−1.78347
$315$		0			0
$316$	−51.0622			−2.87247
$317$	3.59131	+	6.22033i	0.201708	+	0.349368i	0.949079	−	0.315039i	$-0.102017\pi$
$317$	3.59131	+	6.22033i	0.201708	+	0.349368i	−0.747371	+	0.664407i	$0.768684\pi$
$318$		0			0
$319$	1.14234	−	1.97859i	0.0639588	−	0.110780i
$320$	−13.6508	−	23.6438i	−0.763102	−	1.32173i
$321$		0			0
$322$	37.4998	−	13.9030i	2.08978	−	0.774785i
$323$	9.78275			0.544327
$324$		0			0
$325$	2.56180	−	4.43717i	0.142103	−	0.246130i
$326$	−17.3249	+	30.0076i	−0.959539	+	1.66197i
$327$		0			0
$328$	36.3704			2.00822
$329$	3.44449	−	20.2408i	0.189901	−	1.11591i
$330$		0			0
$331$	−15.3116	−	26.5204i	−0.841599	−	1.45769i	−0.888542	−	0.458795i	$-0.848281\pi$
$331$	−15.3116	−	26.5204i	−0.841599	−	1.45769i	0.0469432	−	0.998898i	$-0.485052\pi$
$332$	6.94106	−	12.0223i	0.380940	−	0.659808i
$333$		0			0
$334$	−2.59473	−	4.49421i	−0.141977	−	0.245912i
$335$	39.7288			2.17061
$336$		0			0
$337$	8.16699			0.444884			0.222442	−	0.974946i	$-0.428597\pi$
$337$	8.16699			0.444884			0.222442	+	0.974946i	$0.428597\pi$
$338$	−12.5532	−	21.7428i	−0.682806	−	1.18265i
$339$		0			0
$340$	−44.7048	+	77.4309i	−2.42446	+	4.19928i
$341$	3.07257	+	5.32185i	0.166389	+	0.288195i
$342$		0			0
$343$	−8.97128	+	16.2024i	−0.484403	+	0.874845i
$344$	−30.6134			−1.65056
$345$		0			0
$346$	24.3080	−	42.1026i	1.30680	−	2.26345i
$347$	−10.1197	+	17.5278i	−0.543252	+	0.940939i	0.455463	+	0.890255i	$0.349474\pi$
$347$	−10.1197	+	17.5278i	−0.543252	+	0.940939i	−0.998715	+	0.0506848i	$0.983860\pi$
$348$		0			0
$349$	−29.7317			−1.59150			−0.795749	−	0.605626i	$-0.792923\pi$
$349$	−29.7317			−1.59150			−0.795749	+	0.605626i	$0.792923\pi$
$350$	−15.5862	−	12.9205i	−0.833116	−	0.690630i
$351$		0			0
$352$	0.667886	+	1.15681i	0.0355984	+	0.0616583i
$353$	−10.8938	+	18.8687i	−0.579820	+	1.00428i	0.415679	+	0.909511i	$0.363544\pi$
$353$	−10.8938	+	18.8687i	−0.579820	+	1.00428i	−0.995500	+	0.0947668i	$0.969789\pi$
$354$		0			0
$355$	14.3864	+	24.9179i	0.763550	+	1.32251i
$356$	−16.9179			−0.896645
$357$		0			0
$358$	31.4782			1.66367
$359$	2.13699	+	3.70138i	0.112786	+	0.195351i	0.916893	−	0.399134i	$-0.130689\pi$
$359$	2.13699	+	3.70138i	0.112786	+	0.195351i	−0.804106	+	0.594485i	$0.797356\pi$
$360$		0			0
$361$	8.77325	−	15.1957i	0.461750	−	0.799774i
$362$	−10.4554	−	18.1093i	−0.549524	−	0.951804i
$363$		0			0
$364$	15.5044	−	5.74825i	0.812652	−	0.301290i
$365$	−29.9409			−1.56718
$366$		0			0
$367$	1.50270	−	2.60276i	0.0784405	−	0.135863i	−0.824137	−	0.566391i	$-0.808339\pi$
$367$	1.50270	−	2.60276i	0.0784405	−	0.135863i	0.902577	+	0.430528i	$0.141673\pi$
$368$	−9.87468	+	17.1035i	−0.514753	+	0.891579i
$369$		0			0
$370$	59.7052			3.10393
$371$	3.89139	−	1.44273i	0.202031	−	0.0749027i
$372$		0			0
$373$	−0.127209	−	0.220333i	−0.00658665	−	0.0114084i	0.862713	−	0.505693i	$-0.168763\pi$
$373$	−0.127209	−	0.220333i	−0.00658665	−	0.0114084i	−0.869300	+	0.494285i	$0.835430\pi$
$374$	9.81874	−	17.0066i	0.507715	−	0.879388i
$375$		0			0
$376$	17.4369	+	30.2016i	0.899239	+	1.55753i
$377$	−3.70221			−0.190674
$378$		0			0
$379$	−2.87695			−0.147779			−0.0738895	−	0.997266i	$-0.523541\pi$
$379$	−2.87695			−0.147779			−0.0738895	+	0.997266i	$0.523541\pi$
$380$	−6.64217	−	11.5046i	−0.340736	−	0.590173i
$381$		0			0
$382$	−23.9928	+	41.5568i	−1.22758	+	2.12623i
$383$	17.5038	+	30.3175i	0.894404	+	1.54915i	0.834540	+	0.550947i	$0.185733\pi$
$383$	17.5038	+	30.3175i	0.894404	+	1.54915i	0.0598643	+	0.998207i	$0.480933\pi$
$384$		0			0
$385$	5.81916	+	4.82392i	0.296572	+	0.245850i
$386$	17.6037			0.896005
$387$		0			0
$388$	3.26882	−	5.66177i	0.165949	−	0.287433i
$389$	18.9738	−	32.8636i	0.962009	−	1.66625i	0.244565	−	0.969633i	$-0.421355\pi$
$389$	18.9738	−	32.8636i	0.962009	−	1.66625i	0.717444	−	0.696616i	$-0.245312\pi$
$390$		0			0
$391$	−50.6834			−2.56317
$392$	−5.83212	−	30.9117i	−0.294566	−	1.56128i
$393$		0			0
$394$	−15.3530	−	26.5921i	−0.773472	−	1.33969i
$395$	−18.9115	+	32.7557i	−0.951541	+	1.64812i
$396$		0			0
$397$	−0.633041	−	1.09646i	−0.0317714	−	0.0550297i	0.849702	−	0.527262i	$-0.176782\pi$
$397$	−0.633041	−	1.09646i	−0.0317714	−	0.0550297i	−0.881474	+	0.472233i	$0.843448\pi$
$398$	−56.1702			−2.81556
$399$		0			0
$400$	9.99722			0.499861
$401$	−11.9416	−	20.6834i	−0.596334	−	1.03288i	−0.993357	−	0.115072i	$-0.963290\pi$
$401$	−11.9416	−	20.6834i	−0.596334	−	1.03288i	0.397023	−	0.917809i	$-0.370043\pi$
$402$		0			0
$403$	4.97896	−	8.62381i	0.248019	−	0.429582i
$404$	0.473744	+	0.820549i	0.0235697	+	0.0408238i
$405$		0			0
$406$	−2.45417	+	14.4214i	−0.121798	+	0.715724i
$407$	−8.63544			−0.428043
$408$		0			0
$409$	9.69789	−	16.7972i	0.479530	−	0.830570i	−0.520195	−	0.854048i	$-0.674141\pi$
$409$	9.69789	−	16.7972i	0.479530	−	0.830570i	0.999724	+	0.0234779i	$0.00747394\pi$
$410$	27.9785	−	48.4603i	1.38176	−	2.39328i
$411$		0			0
$412$	−31.1823			−1.53624
$413$	−0.610680	+	0.226409i	−0.0300496	+	0.0111408i
$414$		0			0
$415$	−5.14141	−	8.90518i	−0.252382	−	0.437138i
$416$	1.08228	−	1.87456i	0.0530630	−	0.0919077i
$417$		0			0
$418$	1.45886	+	2.52681i	0.0713550	+	0.123590i
$419$	7.86765			0.384360			0.192180	−	0.981360i	$-0.438444\pi$
$419$	7.86765			0.384360			0.192180	+	0.981360i	$0.438444\pi$
$420$		0			0
$421$	23.7578			1.15788			0.578942	−	0.815369i	$-0.303466\pi$
$421$	23.7578			1.15788			0.578942	+	0.815369i	$0.303466\pi$
$422$	−14.2399	−	24.6642i	−0.693186	−	1.20063i
$423$		0			0
$424$	−3.52463	+	6.10483i	−0.171171	+	0.296477i
$425$	12.8281	+	22.2189i	0.622253	+	1.07777i
$426$		0			0
$427$	1.42912	−	8.39793i	0.0691599	−	0.406404i
$428$	−18.3614			−0.887534
$429$		0			0
$430$	−23.5499	+	40.7896i	−1.13568	+	1.96705i
$431$	0.963605	−	1.66901i	0.0464152	−	0.0803935i	−0.841884	−	0.539658i	$-0.818554\pi$
$431$	0.963605	−	1.66901i	0.0464152	−	0.0803935i	0.888300	+	0.459264i	$0.151887\pi$
$432$		0			0
$433$	8.35461			0.401497			0.200748	−	0.979643i	$-0.435663\pi$
$433$	8.35461			0.401497			0.200748	+	0.979643i	$0.435663\pi$
$434$	−30.2923	−	25.1115i	−1.45408	−	1.20539i
$435$		0			0
$436$	−24.7820	−	42.9237i	−1.18684	−	2.05567i
$437$	3.76524	−	6.52158i	0.180116	−	0.311970i
$438$		0			0
$439$	7.19283	+	12.4583i	0.343295	+	0.594604i	0.985042	−	0.172312i	$-0.0551236\pi$
$439$	7.19283	+	12.4583i	0.343295	+	0.594604i	−0.641748	+	0.766916i	$0.721790\pi$
$440$	−12.8385			−0.612052
$441$		0			0
$442$	−31.8216			−1.51360
$443$	4.29019	+	7.43082i	0.203833	+	0.353049i	0.949760	−	0.312978i	$-0.101327\pi$
$443$	4.29019	+	7.43082i	0.203833	+	0.353049i	−0.745927	+	0.666027i	$0.767993\pi$
$444$		0			0
$445$	−6.26573	+	10.8526i	−0.297024	+	0.514461i
$446$	11.7315	+	20.3196i	0.555503	+	0.962159i
$447$		0			0
$448$	−19.4652	−	16.1361i	−0.919646	−	0.762361i
$449$	18.2061			0.859200			0.429600	−	0.903019i	$-0.358655\pi$
$449$	18.2061			0.859200			0.429600	+	0.903019i	$0.358655\pi$
$450$		0			0
$451$	−4.04667	+	7.00903i	−0.190550	+	0.330042i
$452$	−17.2523	+	29.8819i	−0.811480	+	1.40552i
$453$		0			0
$454$	35.2293			1.65339
$455$	2.05483	−	12.0748i	0.0963319	−	0.566075i
$456$		0			0
$457$	20.2286	+	35.0370i	0.946255	+	1.63896i	0.753218	+	0.657771i	$0.228501\pi$
$457$	20.2286	+	35.0370i	0.946255	+	1.63896i	0.193037	+	0.981191i	$0.438166\pi$
$458$	−17.6210	+	30.5205i	−0.823376	+	1.42613i
$459$		0			0
$460$	34.4124	+	59.6041i	1.60449	+	2.77905i
$461$	−40.7664			−1.89868			−0.949341	−	0.314247i	$-0.898248\pi$
$461$	−40.7664			−1.89868			−0.949341	+	0.314247i	$0.898248\pi$
$462$		0			0
$463$	−24.5461			−1.14076			−0.570378	−	0.821382i	$-0.693203\pi$
$463$	−24.5461			−1.14076			−0.570378	+	0.821382i	$0.693203\pi$
$464$	−3.61189	−	6.25598i	−0.167678	−	0.290427i
$465$		0			0
$466$	9.08962	−	15.7437i	0.421069	−	0.729312i
$467$	−6.73926	−	11.6727i	−0.311856	−	0.540150i	0.666908	−	0.745140i	$-0.267617\pi$
$467$	−6.73926	−	11.6727i	−0.311856	−	0.540150i	−0.978764	+	0.204990i	$0.934284\pi$
$468$		0			0
$469$	34.4979	−	12.7901i	1.59297	−	0.590591i
$470$	53.6545			2.47490
$471$		0			0
$472$	0.553123	−	0.958038i	0.0254596	−	0.0440973i
$473$	3.40613	−	5.89959i	0.156614	−	0.271263i
$474$		0			0
$475$	−3.81196			−0.174905
$476$	−13.8911	+	81.6281i	−0.636696	+	3.74142i
$477$		0			0
$478$	6.33782	+	10.9774i	0.289885	+	0.502096i
$479$	10.1375	−	17.5586i	0.463193	−	0.802273i	−0.535925	−	0.844265i	$-0.680037\pi$
$479$	10.1375	−	17.5586i	0.463193	−	0.802273i	0.999118	+	0.0419924i	$0.0133705\pi$
$480$		0			0
$481$	6.99666	+	12.1186i	0.319020	+	0.552559i
$482$	58.9305			2.68421
$483$		0			0
$484$	3.85689			0.175313
$485$	−2.42130	−	4.19381i	−0.109945	−	0.190431i
$486$		0			0
$487$	0.497918	−	0.862418i	0.0225628	−	0.0390799i	−0.854524	−	0.519413i	$-0.826151\pi$
$487$	0.497918	−	0.862418i	0.0225628	−	0.0390799i	0.877086	+	0.480333i	$0.159484\pi$
$488$	7.23457	+	12.5307i	0.327494	+	0.567236i
$489$		0			0
$490$	−45.6735	−	16.0086i	−2.06332	−	0.723195i
$491$	−22.1296			−0.998693			−0.499346	−	0.866402i	$-0.666426\pi$
$491$	−22.1296			−0.998693			−0.499346	+	0.866402i	$0.666426\pi$
$492$		0			0
$493$	9.26931	−	16.0549i	0.417469	−	0.723077i
$494$	2.36400	−	4.09457i	0.106362	−	0.184224i
$495$		0			0
$496$	19.4300			0.872431
$497$	20.5142	+	17.0057i	0.920186	+	0.762809i
$498$		0			0
$499$	4.35177	+	7.53749i	0.194812	+	0.337424i	0.946839	−	0.321708i	$-0.104257\pi$
$499$	4.35177	+	7.53749i	0.194812	+	0.337424i	−0.752027	+	0.659132i	$0.770924\pi$
$500$	−10.1271	+	17.5407i	−0.452898	+	0.784442i
$501$		0			0
$502$	16.1328	+	27.9428i	0.720041	+	1.24715i
$503$	25.3699			1.13119			0.565595	−	0.824683i	$-0.308647\pi$
$503$	25.3699			1.13119			0.565595	+	0.824683i	$0.308647\pi$
$504$		0			0
$505$	0.701827			0.0312309
$506$	−7.55818	−	13.0912i	−0.336002	−	0.581973i
$507$		0			0
$508$	−29.5608	+	51.2008i	−1.31155	+	2.27167i
$509$	17.7756	+	30.7883i	0.787891	+	1.36467i	0.927257	+	0.374426i	$0.122160\pi$
$509$	17.7756	+	30.7883i	0.787891	+	1.36467i	−0.139366	+	0.990241i	$0.544506\pi$
$510$		0			0
$511$	−25.9987	+	9.63900i	−1.15012	+	0.426404i
$512$	32.6413			1.44255
$513$		0			0
$514$	3.95339	−	6.84748i	0.174377	−	0.302029i
$515$	−11.5487	+	20.0030i	−0.508898	+	0.881436i
$516$		0			0
$517$	−7.76030			−0.341298
$518$	51.8442	−	19.2212i	2.27790	−	0.844530i
$519$		0			0
$520$	10.4021	+	18.0169i	0.456162	+	0.790095i
$521$	−0.963877	+	1.66948i	−0.0422282	+	0.0731414i	−0.886367	−	0.462983i	$-0.846779\pi$
$521$	−0.963877	+	1.66948i	−0.0422282	+	0.0731414i	0.844139	+	0.536125i	$0.180112\pi$
$522$		0			0
$523$	17.4771	+	30.2712i	0.764218	+	1.32367i	0.940659	+	0.339354i	$0.110208\pi$
$523$	17.4771	+	30.2712i	0.764218	+	1.32367i	−0.176440	+	0.984311i	$0.556458\pi$
$524$	13.6726			0.597292
$525$		0			0
$526$	−46.0507			−2.00791
$527$	24.9319	+	43.1832i	1.08605	+	1.88109i
$528$		0			0
$529$	−8.00731	+	13.8691i	−0.348144	+	0.603003i
$530$	5.42276	+	9.39249i	0.235550	+	0.407984i
$531$		0			0
$532$	−9.47136	−	7.85150i	−0.410636	−	0.340406i
$533$	13.1149			0.568067
$534$		0			0
$535$	−6.80038	+	11.7786i	−0.294006	+	0.509233i
$536$	−31.2465	+	54.1206i	−1.34964	+	2.33765i
$537$		0			0
$538$	−31.4184			−1.35455
$539$	6.60598	+	2.31540i	0.284540	+	0.0997313i
$540$		0			0
$541$	3.97367	+	6.88260i	0.170842	+	0.295906i	0.938714	−	0.344696i	$-0.112018\pi$
$541$	3.97367	+	6.88260i	0.170842	+	0.295906i	−0.767873	+	0.640602i	$0.778685\pi$
$542$	5.73114	−	9.92662i	0.246173	−	0.426385i
$543$		0			0
$544$	5.41944	+	9.38674i	0.232357	+	0.402453i
$545$	−36.7132			−1.57262
$546$		0			0
$547$	−3.68742			−0.157663			−0.0788313	−	0.996888i	$-0.525119\pi$
$547$	−3.68742			−0.157663			−0.0788313	+	0.996888i	$0.525119\pi$
$548$	−7.89777	−	13.6793i	−0.337376	−	0.584353i
$549$		0			0
$550$	−3.82598	+	6.62680i	−0.163141	+	0.282568i
$551$	1.37722	+	2.38542i	0.0586716	+	0.101622i
$552$		0			0
$553$	−5.87635	+	34.5312i	−0.249888	+	1.46842i
$554$	27.9322			1.18672
$555$		0			0
$556$	40.5355	−	70.2096i	1.71909	−	2.97755i
$557$	6.75066	−	11.6925i	0.286035	−	0.495426i	−0.686825	−	0.726823i	$-0.740996\pi$
$557$	6.75066	−	11.6925i	0.286035	−	0.495426i	0.972860	+	0.231396i	$0.0743294\pi$
$558$		0			0
$559$	−11.0389			−0.466897
$560$	22.4086	−	8.30798i	0.946938	−	0.351076i
$561$		0			0
$562$	−31.2894	−	54.1948i	−1.31986	−	2.28607i
$563$	−13.9826	+	24.2186i	−0.589296	+	1.02069i	0.405029	+	0.914304i	$0.367262\pi$
$563$	−13.9826	+	24.2186i	−0.589296	+	1.02069i	−0.994325	+	0.106387i	$0.966072\pi$
$564$		0			0
$565$	12.7792	+	22.1342i	0.537625	+	0.931193i
$566$	−25.6218			−1.07696
$567$		0			0
$568$	−45.2593			−1.89904
$569$	−6.32317	−	10.9520i	−0.265081	−	0.459134i	0.702504	−	0.711680i	$-0.252065\pi$
$569$	−6.32317	−	10.9520i	−0.265081	−	0.459134i	−0.967585	+	0.252546i	$0.918732\pi$
$570$		0			0
$571$	9.54081	−	16.5252i	0.399270	−	0.691556i	−0.594366	−	0.804195i	$-0.702597\pi$
$571$	9.54081	−	16.5252i	0.399270	−	0.691556i	0.993636	+	0.112638i	$0.0359302\pi$
$572$	−3.12495	−	5.41258i	−0.130661	−	0.226311i
$573$		0			0
$574$	8.69375	−	51.0871i	0.362870	−	2.13233i
$575$	19.7494			0.823606
$576$		0			0
$577$	19.7954	−	34.2866i	0.824093	−	1.42737i	−0.0785173	−	0.996913i	$-0.525019\pi$
$577$	19.7954	−	34.2866i	0.824093	−	1.42737i	0.902610	−	0.430458i	$-0.141648\pi$
$578$	59.1016	−	102.367i	2.45830	−	4.25790i
$579$		0			0
$580$	−25.1743			−1.04530
$581$	−7.33136	−	6.07750i	−0.304156	−	0.252137i
$582$		0			0
$583$	−0.784319	−	1.35848i	−0.0324832	−	0.0562625i
$584$	23.5484	−	40.7870i	0.974439	−	1.68778i
$585$		0			0
$586$	−6.79895	−	11.7761i	−0.280862	−	0.486467i
$587$	−30.9761			−1.27852			−0.639261	−	0.768990i	$-0.720760\pi$
$587$	−30.9761			−1.27852			−0.639261	+	0.768990i	$0.720760\pi$
$588$		0			0
$589$	−7.40868			−0.305269
$590$	−0.850999	−	1.47397i	−0.0350351	−	0.0606825i
$591$		0			0
$592$	−13.6519	+	23.6458i	−0.561091	+	0.971838i
$593$	−18.2848	−	31.6703i	−0.750868	−	1.30054i	−0.947403	−	0.320044i	$-0.896302\pi$
$593$	−18.2848	−	31.6703i	−0.750868	−	1.30054i	0.196535	−	0.980497i	$-0.437031\pi$
$594$		0			0
$595$	47.2185	+	39.1429i	1.93577	+	1.60470i
$596$	75.2362			3.08180
$597$		0			0
$598$	−12.2477	+	21.2136i	−0.500844	+	0.867488i
$599$	−7.91908	+	13.7163i	−0.323565	+	0.560431i	−0.981221	−	0.192888i	$-0.938215\pi$
$599$	−7.91908	+	13.7163i	−0.323565	+	0.560431i	0.657656	+	0.753318i	$0.271548\pi$
$600$		0			0
$601$	−3.42710			−0.139794			−0.0698971	−	0.997554i	$-0.522267\pi$
$601$	−3.42710			−0.139794			−0.0698971	+	0.997554i	$0.522267\pi$
$602$	−7.31763	+	43.0006i	−0.298244	+	1.75257i
$603$		0			0
$604$	17.2959	+	29.9574i	0.703760	+	1.21895i
$605$	1.42845	−	2.47414i	0.0580746	−	0.100588i
$606$		0			0
$607$	4.64070	+	8.03793i	0.188360	+	0.326250i	0.944704	−	0.327925i	$-0.106349\pi$
$607$	4.64070	+	8.03793i	0.188360	+	0.326250i	−0.756343	+	0.654175i	$0.773016\pi$
$608$	−1.61043			−0.0653114
$609$		0			0
$610$	22.2613			0.901333
$611$	6.28760	+	10.8904i	0.254369	+	0.440580i
$612$		0			0
$613$	−7.89667	+	13.6774i	−0.318943	+	0.552426i	−0.980268	−	0.197674i	$-0.936661\pi$
$613$	−7.89667	+	13.6774i	−0.318943	+	0.552426i	0.661324	+	0.750100i	$0.269995\pi$
$614$	−19.9986	−	34.6386i	−0.807078	−	1.39790i
$615$		0			0
$616$	−11.1481	+	4.13316i	−0.449171	+	0.166530i
$617$	−46.6541			−1.87823			−0.939113	−	0.343610i	$-0.888350\pi$
$617$	−46.6541			−1.87823			−0.939113	+	0.343610i	$0.888350\pi$
$618$		0			0
$619$	19.2083	−	33.2698i	0.772048	−	1.33723i	−0.164390	−	0.986395i	$-0.552566\pi$
$619$	19.2083	−	33.2698i	0.772048	−	1.33723i	0.936439	−	0.350832i	$-0.114101\pi$
$620$	33.8559	−	58.6401i	1.35968	−	2.35504i
$621$		0			0
$622$	42.4663			1.70274
$623$	−1.94695	+	11.4408i	−0.0780028	+	0.458368i
$624$		0			0
$625$	15.4060	+	26.6839i	0.616239	+	1.06736i
$626$	15.0726	−	26.1065i	0.602423	−	1.04343i
$627$		0			0
$628$	−25.1828	−	43.6179i	−1.00490	−	1.74054i
$629$	−70.0708			−2.79390
$630$		0			0
$631$	29.9006			1.19032			0.595162	−	0.803606i	$-0.297088\pi$
$631$	29.9006			1.19032			0.595162	+	0.803606i	$0.297088\pi$
$632$	−29.7476	−	51.5244i	−1.18330	−	2.04953i
$633$		0			0
$634$	−8.69133	+	15.0538i	−0.345177	+	0.597864i
$635$	21.8964	+	37.9256i	0.868931	+	1.50503i
$636$		0			0
$637$	−2.10301	−	11.1465i	−0.0833244	−	0.441641i
$638$	5.52916			0.218901
$639$		0			0
$640$	29.2201	−	50.6107i	1.15503	−	2.00056i
$641$	3.30800	−	5.72962i	0.130658	−	0.226306i	−0.793272	−	0.608867i	$-0.791624\pi$
$641$	3.30800	−	5.72962i	0.130658	−	0.226306i	0.923930	+	0.382561i	$0.124958\pi$
$642$		0			0
$643$	12.5670			0.495594			0.247797	−	0.968812i	$-0.420293\pi$
$643$	12.5670			0.495594			0.247797	+	0.968812i	$0.420293\pi$
$644$	49.0702	+	40.6778i	1.93364	+	1.60293i
$645$		0			0
$646$	11.8376	+	20.5034i	0.465745	+	0.806694i
$647$	8.63760	−	14.9608i	0.339579	−	0.588168i	−0.644775	−	0.764373i	$-0.723049\pi$
$647$	8.63760	−	14.9608i	0.339579	−	0.588168i	0.984354	+	0.176205i	$0.0563821\pi$
$648$		0			0
$649$	0.123084	+	0.213188i	0.00483147	+	0.00836835i
$650$	12.3996			0.486354
$651$		0			0
$652$	−55.2211			−2.16263
$653$	−2.16810	−	3.75526i	−0.0848444	−	0.146955i	0.820480	−	0.571675i	$-0.193706\pi$
$653$	−2.16810	−	3.75526i	−0.0848444	−	0.146955i	−0.905325	+	0.424720i	$0.860373\pi$
$654$		0			0
$655$	5.06382	−	8.77080i	0.197860	−	0.342703i
$656$	12.7949	+	22.1614i	0.499557	+	0.865258i
$657$		0			0
$658$	46.5902	−	17.2733i	1.81627	−	0.673381i
$659$	−36.6318			−1.42697			−0.713486	−	0.700669i	$-0.752885\pi$
$659$	−36.6318			−1.42697			−0.713486	+	0.700669i	$0.752885\pi$
$660$		0			0
$661$	−13.4383	+	23.2759i	−0.522691	+	0.905328i	0.476960	+	0.878925i	$0.341739\pi$
$661$	−13.4383	+	23.2759i	−0.522691	+	0.905328i	−0.999651	+	0.0264027i	$0.991595\pi$
$662$	37.0555	−	64.1820i	1.44020	−	2.49451i
$663$		0			0
$664$	16.1748			0.627704
$665$	−8.54446	+	3.16785i	−0.331340	+	0.122844i
$666$		0			0
$667$	−7.13525	−	12.3586i	−0.276278	−	0.478527i
$668$	4.13520	−	7.16238i	0.159996	−	0.277121i
$669$		0			0
$670$	48.0738	+	83.2663i	1.85725	+	3.21686i
$671$	−3.21975			−0.124297
$672$		0			0
$673$	0.0568409			0.00219105			0.00109553	−	0.999999i	$-0.499651\pi$
$673$	0.0568409			0.00219105			0.00109553	+	0.999999i	$0.499651\pi$
$674$	9.88247	+	17.1169i	0.380659	+	0.659320i
$675$		0			0
$676$	20.0060	−	34.6514i	0.769460	−	1.33274i
$677$	16.9862	+	29.4210i	0.652833	+	1.13074i	0.982432	+	0.186619i	$0.0597531\pi$
$677$	16.9862	+	29.4210i	0.652833	+	1.13074i	−0.329599	+	0.944121i	$0.606914\pi$
$678$		0			0
$679$	−3.45263	−	2.86214i	−0.132500	−	0.109839i
$680$	−104.176			−3.99496
$681$		0			0
$682$	−7.43594	+	12.8794i	−0.284737	+	0.493179i
$683$	3.66698	−	6.35140i	0.140313	−	0.243030i	−0.787301	−	0.616568i	$-0.788522\pi$
$683$	3.66698	−	6.35140i	0.140313	−	0.243030i	0.927615	+	0.373539i	$0.121856\pi$
$684$		0			0
$685$	−11.7001			−0.447039
$686$	−44.8137	+	0.803044i	−1.71100	+	0.0306603i
$687$		0			0
$688$	−10.7696	−	18.6535i	−0.410588	−	0.711159i
$689$	−1.27095	+	2.20135i	−0.0484194	+	0.0838648i
$690$		0			0
$691$	−0.116710	−	0.202147i	−0.00443985	−	0.00769004i	0.863797	−	0.503840i	$-0.168080\pi$
$691$	−0.116710	−	0.202147i	−0.00443985	−	0.00769004i	−0.868237	+	0.496150i	$0.834747\pi$
$692$	77.4787			2.94530
$693$		0			0
$694$	−48.9812			−1.85930
$695$	−30.0256	−	52.0059i	−1.13894	−	1.97270i
$696$		0			0
$697$	−32.8360	+	56.8736i	−1.24375	+	2.15424i
$698$	−35.9768	−	62.3137i	−1.36174	−	2.35861i
$699$		0			0
$700$	5.41281	−	31.8073i	0.204585	−	1.20220i
$701$	34.8430			1.31600			0.658001	−	0.753017i	$-0.271402\pi$
$701$	34.8430			1.31600			0.658001	+	0.753017i	$0.271402\pi$
$702$		0			0
$703$	5.20551	−	9.01621i	0.196329	−	0.340053i
$704$	−4.77819	+	8.27607i	−0.180085	+	0.311916i
$705$		0			0
$706$	−52.7284			−1.98446
$707$	0.609422	−	0.225943i	0.0229197	−	0.00849744i
$708$		0			0
$709$	0.960460	+	1.66357i	0.0360708	+	0.0624765i	0.883497	−	0.468436i	$-0.155182\pi$
$709$	0.960460	+	1.66357i	0.0360708	+	0.0624765i	−0.847426	+	0.530913i	$0.821849\pi$
$710$	−34.8165	+	60.3040i	−1.30664	+	2.26317i
$711$		0			0
$712$	−9.85595	−	17.0710i	−0.369367	−	0.639763i
$713$	38.3836			1.43748
$714$		0			0
$715$	−4.62946			−0.173132
$716$	25.0832	+	43.4454i	0.937404	+	1.62363i
$717$		0			0
$718$	−5.17174	+	8.95772i	−0.193008	+	0.334299i
$719$	9.95207	+	17.2375i	0.371149	+	0.642850i	0.989743	−	0.142862i	$-0.0456304\pi$
$719$	9.95207	+	17.2375i	0.371149	+	0.642850i	−0.618593	+	0.785711i	$0.712297\pi$
$720$		0			0
$721$	−3.58853	+	21.0872i	−0.133644	+	0.785330i
$722$	42.4643			1.58036
$723$		0			0
$724$	16.6627	−	28.8606i	0.619264	−	1.07260i
$725$	−3.61189	+	6.25598i	−0.134142	+	0.232341i
$726$		0			0
$727$	45.7396			1.69639			0.848195	−	0.529685i	$-0.177690\pi$
$727$	45.7396			1.69639			0.848195	+	0.529685i	$0.177690\pi$
$728$	14.8328	+	12.2960i	0.549740	+	0.455719i
$729$		0			0
$730$	−36.2300	−	62.7522i	−1.34093	−	2.32256i
$731$	27.6384	−	47.8711i	1.02224	−	1.77058i
$732$		0			0
$733$	−23.8129	−	41.2452i	−0.879550	−	1.52342i	−0.851836	−	0.523809i	$-0.824511\pi$
$733$	−23.8129	−	41.2452i	−0.879550	−	1.52342i	−0.0277140	−	0.999616i	$-0.508823\pi$
$734$	7.27339			0.268466
$735$		0			0
$736$	8.34345			0.307544
$737$	−6.95314	−	12.0432i	−0.256122	−	0.443617i
$738$		0			0
$739$	7.42678	−	12.8636i	0.273199	−	0.473194i	−0.696481	−	0.717576i	$-0.745252\pi$
$739$	7.42678	−	12.8636i	0.273199	−	0.473194i	0.969679	+	0.244382i	$0.0785851\pi$
$740$	47.5758	+	82.4037i	1.74892	+	3.02922i
$741$		0			0
$742$	7.73255	+	6.41007i	0.283871	+	0.235321i
$743$	5.27520			0.193528			0.0967641	−	0.995307i	$-0.469151\pi$
$743$	5.27520			0.193528			0.0967641	+	0.995307i	$0.469151\pi$
$744$		0			0
$745$	27.8646	−	48.2630i	1.02088	−	1.76822i
$746$	0.307860	−	0.533229i	0.0112715	−	0.0195229i
$747$		0			0
$748$	31.2961			1.14430
$749$	−2.11308	+	12.4171i	−0.0772101	+	0.453710i
$750$		0			0
$751$	−9.44109	−	16.3524i	−0.344510	−	0.596709i	0.640754	−	0.767746i	$-0.278622\pi$
$751$	−9.44109	−	16.3524i	−0.344510	−	0.596709i	−0.985265	+	0.171037i	$0.945288\pi$
$752$	−12.2684	+	21.2495i	−0.447383	+	0.774890i
$753$		0			0
$754$	−4.47986	−	7.75935i	−0.163147	−	0.282579i
$755$	25.6230			0.932516
$756$		0			0
$757$	43.0350			1.56413			0.782067	−	0.623194i	$-0.214165\pi$
$757$	43.0350			1.56413			0.782067	+	0.623194i	$0.214165\pi$
$758$	−3.48125	−	6.02971i	−0.126445	−	0.219009i
$759$		0			0
$760$	7.73915	−	13.4046i	0.280728	−	0.486236i
$761$	9.40117	+	16.2833i	0.340792	+	0.590270i	0.984580	−	0.174934i	$-0.0559714\pi$
$761$	9.40117	+	16.2833i	0.340792	+	0.590270i	−0.643788	+	0.765204i	$0.722638\pi$
$762$		0			0
$763$	−31.8794	+	11.8193i	−1.15411	+	0.427886i
$764$	−76.4743			−2.76674
$765$		0			0
$766$	−42.3611	+	73.3715i	−1.53057	+	2.65102i
$767$	0.199452	−	0.345460i	0.00720178	−	0.0124738i
$768$		0			0
$769$	−28.8942			−1.04195			−0.520975	−	0.853572i	$-0.674432\pi$
$769$	−28.8942			−1.04195			−0.520975	+	0.853572i	$0.674432\pi$
$770$	−3.06884	+	18.0334i	−0.110593	+	0.649878i
$771$		0			0
$772$	14.0274	+	24.2962i	0.504858	+	0.874440i
$773$	13.9634	−	24.1853i	0.502227	−	0.869883i	−0.497769	−	0.867309i	$-0.665847\pi$
$773$	13.9634	−	24.1853i	0.502227	−	0.869883i	0.999997	−	0.00257386i	$-0.000819286\pi$
$774$		0			0
$775$	−9.71498	−	16.8268i	−0.348972	−	0.604438i
$776$	7.61736			0.273447
$777$		0			0
$778$	91.8370			3.29252
$779$	−4.87872	−	8.45020i	−0.174798	−	0.302760i
$780$		0			0
$781$	5.03567	−	8.72204i	0.180191	−	0.312099i
$782$	−61.3295	−	106.226i	−2.19314	−	3.79863i
$783$		0			0
$784$	16.7836	−	14.4282i	0.599415	−	0.515294i
$785$	−37.3070			−1.33154
$786$		0			0
$787$	7.54412	−	13.0668i	0.268919	−	0.465781i	−0.699664	−	0.714472i	$-0.746667\pi$
$787$	7.54412	−	13.0668i	0.268919	−	0.465781i	0.968583	+	0.248691i	$0.0800003\pi$
$788$	24.4679	−	42.3796i	0.871633	−	1.50971i
$789$		0			0
$790$	−91.5355			−3.25669
$791$	18.2224	+	15.1059i	0.647914	+	0.537103i
$792$		0			0
$793$	2.60873	+	4.51845i	0.0926386	+	0.160455i
$794$	1.53202	−	2.65354i	0.0543695	−	0.0941707i
$795$		0			0
$796$	−44.7589	−	77.5247i	−1.58644	−	2.74779i
$797$	22.7824			0.806993			0.403496	−	0.914981i	$-0.367795\pi$
$797$	22.7824			0.806993			0.403496	+	0.914981i	$0.367795\pi$
$798$		0			0
$799$	−62.9696			−2.22770
$800$	−2.11175	−	3.65765i	−0.0746615	−	0.129318i
$801$		0			0
$802$	28.8998	−	50.0560i	1.02049	−	1.76754i
$803$	5.24011	+	9.07614i	0.184919	+	0.320290i
$804$		0			0
$805$	44.2680	−	16.4123i	1.56024	−	0.578457i
$806$	24.0992			0.848857
$807$		0			0
$808$	−0.551984	+	0.956065i	−0.0194187	+	0.0336342i
$809$	−28.1855	+	48.8187i	−0.990949	+	1.71637i	−0.379221	+	0.925306i	$0.623808\pi$
$809$	−28.1855	+	48.8187i	−0.990949	+	1.71637i	−0.611728	+	0.791068i	$0.709525\pi$
$810$		0			0
$811$	38.7478			1.36062			0.680310	−	0.732924i	$-0.261845\pi$
$811$	38.7478			1.36062			0.680310	+	0.732924i	$0.261845\pi$
$812$	−21.8597	+	8.10447i	−0.767126	+	0.284411i
$813$		0			0
$814$	−10.4493	−	18.0988i	−0.366249	−	0.634361i
$815$	−20.4518	+	35.4236i	−0.716396	+	1.24083i
$816$		0			0
$817$	4.10648	+	7.11263i	0.143667	+	0.248839i
$818$	46.9398			1.64121
$819$		0			0
$820$	89.1783			3.11424
$821$	18.0448	+	31.2544i	0.629766	+	1.09079i	0.987598	+	0.157001i	$0.0501827\pi$
$821$	18.0448	+	31.2544i	0.629766	+	1.09079i	−0.357832	+	0.933786i	$0.616484\pi$
$822$		0			0
$823$	0.928769	−	1.60867i	0.0323748	−	0.0560749i	−0.849384	−	0.527775i	$-0.823026\pi$
$823$	0.928769	−	1.60867i	0.0323748	−	0.0560749i	0.881759	+	0.471700i	$0.156360\pi$
$824$	−18.1661	−	31.4645i	−0.632844	−	1.09612i
$825$		0			0
$826$	−1.21348	−	1.00594i	−0.0422223	−	0.0350011i
$827$	3.54179			0.123160			0.0615801	−	0.998102i	$-0.480386\pi$
$827$	3.54179			0.123160			0.0615801	+	0.998102i	$0.480386\pi$
$828$		0			0
$829$	−18.9435	+	32.8111i	−0.657934	+	1.13957i	0.323216	+	0.946325i	$0.395236\pi$
$829$	−18.9435	+	32.8111i	−0.657934	+	1.13957i	−0.981150	+	0.193250i	$0.938097\pi$
$830$	12.4427	−	21.5514i	0.431894	−	0.748062i
$831$		0			0
$832$	15.4856			0.536868
$833$	53.6030	+	18.7879i	1.85723	+	0.650962i
$834$		0			0
$835$	−3.06304	−	5.30535i	−0.106001	−	0.183599i
$836$	−2.32496	+	4.02696i	−0.0804106	+	0.139275i
$837$		0			0
$838$	9.52026	+	16.4896i	0.328872	+	0.569623i
$839$	−15.0661			−0.520140			−0.260070	−	0.965590i	$-0.583746\pi$
$839$	−15.0661			−0.520140			−0.260070	+	0.965590i	$0.583746\pi$
$840$		0			0
$841$	−23.7802			−0.820008
$842$	28.7481	+	49.7933i	0.990727	+	1.71599i
$843$		0			0
$844$	22.6939	−	39.3070i	0.781157	−	1.35300i
$845$	−14.8189	−	25.6671i	−0.509786	−	0.882975i
$846$		0			0
$847$	0.443860	−	2.60825i	0.0152512	−	0.0896207i
$848$	−4.95978			−0.170319
$849$		0			0
$850$	−31.0453	+	53.7720i	−1.06484	+	1.84436i
$851$	−26.9692	+	46.7120i	−0.924493	+	1.60127i
$852$		0			0
$853$	−38.8605			−1.33056			−0.665278	−	0.746595i	$-0.731687\pi$
$853$	−38.8605			−1.33056			−0.665278	+	0.746595i	$0.731687\pi$
$854$	19.3303	−	7.16668i	0.661469	−	0.245239i
$855$		0			0
$856$	−10.6969	−	18.5276i	−0.365614	−	0.633262i
$857$	11.6059	−	20.1021i	0.396452	−	0.686674i	−0.596834	−	0.802365i	$-0.703575\pi$
$857$	11.6059	−	20.1021i	0.396452	−	0.686674i	0.993285	+	0.115691i	$0.0369081\pi$
$858$		0			0
$859$	13.8157	+	23.9294i	0.471384	+	0.816461i	0.999464	−	0.0327332i	$-0.0104212\pi$
$859$	13.8157	+	23.9294i	0.471384	+	0.816461i	−0.528080	+	0.849195i	$0.677088\pi$
$860$	−75.0624			−2.55961
$861$		0			0
$862$	4.66404			0.158858
$863$	−3.15926	−	5.47200i	−0.107543	−	0.186269i	0.807232	−	0.590235i	$-0.200965\pi$
$863$	−3.15926	−	5.47200i	−0.107543	−	0.186269i	−0.914774	+	0.403966i	$0.867632\pi$
$864$		0			0
$865$	28.6952	−	49.7015i	0.975665	−	1.68990i
$866$	10.1095	+	17.5102i	0.343535	+	0.595020i
$867$		0			0
$868$	10.5200	−	61.8187i	0.357072	−	2.09826i
$869$	13.2392			0.449109
$870$		0			0
$871$	−11.2672	+	19.5154i	−0.381776	+	0.661255i
$872$	28.8748	−	50.0127i	0.977825	−	1.69364i
$873$		0			0
$874$	18.2245			0.616453
$875$	10.6966	+	8.86716i	0.361610	+	0.299765i
$876$		0			0
$877$	5.40380	+	9.35966i	0.182473	+	0.316053i	0.942722	−	0.333579i	$-0.108256\pi$
$877$	5.40380	+	9.35966i	0.182473	+	0.316053i	−0.760249	+	0.649632i	$0.774923\pi$
$878$	−17.4074	+	30.1505i	−0.587470	+	1.01753i
$879$		0			0
$880$	−4.51652	−	7.82283i	−0.152252	−	0.263708i
$881$	32.9475			1.11003			0.555015	−	0.831841i	$-0.312713\pi$
$881$	32.9475			1.11003			0.555015	+	0.831841i	$0.312713\pi$
$882$		0			0
$883$	−13.9550			−0.469622			−0.234811	−	0.972041i	$-0.575447\pi$
$883$	−13.9550			−0.469622			−0.234811	+	0.972041i	$0.575447\pi$
$884$	−25.3569	−	43.9194i	−0.852844	−	1.47717i
$885$		0			0
$886$	−10.3827	+	17.9833i	−0.348813	+	0.604162i
$887$	4.37577	+	7.57906i	0.146924	+	0.254480i	0.930089	−	0.367334i	$-0.119729\pi$
$887$	4.37577	+	7.57906i	0.146924	+	0.254480i	−0.783165	+	0.621814i	$0.786396\pi$
$888$		0			0
$889$	31.2230	+	25.8830i	1.04719	+	0.868088i
$890$	−30.3274			−1.01658
$891$		0			0
$892$	−18.6964	+	32.3831i	−0.626001	+	1.08427i
$893$	4.67797	−	8.10248i	0.156542	−	0.271139i
$894$		0			0
$895$	37.1595			1.24210
$896$	9.07954	−	53.3541i	0.303326	−	1.78244i
$897$		0			0
$898$	22.0303	+	38.1577i	0.735162	+	1.27334i
$899$	−7.01985	+	12.1587i	−0.234125	+	0.405516i
$900$		0			0
$901$	−6.36422	−	11.0231i	−0.212023	−	0.367234i
$902$	−19.5867			−0.652166
$903$		0			0
$904$	−40.2031			−1.33714
$905$	−12.3425	−	21.3778i	−0.410277	−	0.710621i
$906$		0			0
$907$	−0.264221	+	0.457644i	−0.00877330	+	0.0151958i	−0.870379	−	0.492383i	$-0.836126\pi$
$907$	−0.264221	+	0.457644i	−0.00877330	+	0.0151958i	0.861605	+	0.507579i	$0.169459\pi$
$908$	28.0723	+	48.6226i	0.931612	+	1.61360i
$909$		0			0
$910$	27.7936	−	10.3045i	0.921350	−	0.341590i
$911$	36.6894			1.21557			0.607787	−	0.794100i	$-0.292057\pi$
$911$	36.6894			1.21557			0.607787	+	0.794100i	$0.292057\pi$
$912$		0			0
$913$	−1.79965	+	3.11709i	−0.0595597	+	0.103161i
$914$	−48.9553	+	84.7931i	−1.61930	+	2.80471i
$915$		0			0
$916$	−56.1649			−1.85574
$917$	1.57348	−	9.24622i	0.0519608	−	0.305337i
$918$		0			0
$919$	11.3790	+	19.7090i	0.375358	+	0.650140i	0.990381	−	0.138370i	$-0.0441863\pi$
$919$	11.3790	+	19.7090i	0.375358	+	0.650140i	−0.615022	+	0.788510i	$0.710853\pi$
$920$	−40.0957	+	69.4478i	−1.32192	+	2.28963i
$921$		0			0
$922$	−49.3295	−	85.4412i	−1.62458	−	2.81385i
$923$	−16.3201			−0.537184
$924$		0			0
$925$	27.3039			0.897746
$926$	−29.7021	−	51.4455i	−0.976071	−	1.69060i
$927$		0			0
$928$	−1.52590	+	2.64294i	−0.0500903	+	0.0867589i
$929$	−6.25497	−	10.8339i	−0.205219	−	0.355450i	0.744984	−	0.667083i	$-0.232457\pi$
$929$	−6.25497	−	10.8339i	−0.205219	−	0.355450i	−0.950202	+	0.311633i	$0.899124\pi$
$930$		0			0
$931$	−6.39962	+	5.50152i	−0.209739	+	0.180305i
$932$	28.9721			0.949012
$933$		0			0
$934$	16.3097	−	28.2492i	0.533670	−	0.924343i
$935$	11.5909	−	20.0760i	0.379062	−	0.656555i
$936$		0			0
$937$	45.8451			1.49770			0.748848	−	0.662742i	$-0.230607\pi$
$937$	45.8451			1.49770			0.748848	+	0.662742i	$0.230607\pi$
$938$	68.5506	+	56.8265i	2.23826	+	1.85545i
$939$		0			0
$940$	42.7543	+	74.0527i	1.39449	+	2.41533i
$941$	−1.63890	+	2.83866i	−0.0534266	+	0.0925376i	−0.891502	−	0.453017i	$-0.850348\pi$
$941$	−1.63890	+	2.83866i	−0.0534266	+	0.0925376i	0.838075	+	0.545555i	$0.183681\pi$
$942$		0			0
$943$	25.2762	+	43.7796i	0.823105	+	1.42566i
$944$	0.778343			0.0253329
$945$		0			0
$946$	16.4863			0.536017
$947$	−4.46335	−	7.73076i	−0.145040	−	0.251216i	0.784348	−	0.620321i	$-0.212998\pi$
$947$	−4.46335	−	7.73076i	−0.145040	−	0.251216i	−0.929388	+	0.369105i	$0.879664\pi$
$948$		0			0
$949$	8.49134	−	14.7074i	0.275641	−	0.477424i
$950$	−4.61266	−	7.98937i	−0.149655	−	0.259209i
$951$		0			0
$952$	−90.4596	+	33.5378i	−2.93181	+	1.08697i
$953$	9.92412			0.321474			0.160737	−	0.986997i	$-0.448613\pi$
$953$	9.92412			0.321474			0.160737	+	0.986997i	$0.448613\pi$
$954$		0			0
$955$	−28.3232	+	49.0571i	−0.916516	+	1.58745i
$956$	−10.1005	+	17.4946i	−0.326674	+	0.565816i
$957$		0			0
$958$	49.0674			1.58530
$959$	−10.1597	+	3.76668i	−0.328072	+	0.121632i
$960$		0			0
$961$	−3.38142	−	5.85680i	−0.109078	−	0.188929i
$962$	−16.9326	+	29.3282i	−0.545930	+	0.945578i
$963$		0			0
$964$	46.9585	+	81.3345i	1.51243	+	2.61961i
$965$	20.7809			0.668961
$966$		0			0
$967$	−17.8164			−0.572936			−0.286468	−	0.958090i	$-0.592481\pi$
$967$	−17.8164			−0.572936			−0.286468	+	0.958090i	$0.592481\pi$
$968$	2.24694	+	3.89181i	0.0722192	+	0.125087i
$969$		0			0
$970$	5.85978	−	10.1494i	0.188146	−	0.325879i
$971$	23.1360	+	40.0726i	0.742468	+	1.28599i	0.951368	+	0.308055i	$0.0996782\pi$
$971$	23.1360	+	40.0726i	0.742468	+	1.28599i	−0.208900	+	0.977937i	$0.566988\pi$
$972$		0			0
$973$	−42.8148	−	35.4923i	−1.37258	−	1.13783i
$974$	2.41002			0.0772221
$975$		0			0
$976$	−5.09017	+	8.81643i	−0.162932	+	0.282207i
$977$	15.7184	−	27.2250i	0.502876	−	0.871006i	−0.497119	−	0.867683i	$-0.665609\pi$
$977$	15.7184	−	27.2250i	0.502876	−	0.871006i	0.999994	−	0.00332380i	$-0.00105800\pi$
$978$		0			0
$979$	4.38640			0.140190
$980$	−14.3000	−	75.7939i	−0.456798	−	2.42115i
$981$		0			0
$982$	−26.7779	−	46.3807i	−0.854517	−	1.48007i
$983$	−6.77506	+	11.7347i	−0.216091	+	0.374280i	−0.953609	−	0.301046i	$-0.902664\pi$
$983$	−6.77506	+	11.7347i	−0.216091	+	0.374280i	0.737519	+	0.675327i	$0.235997\pi$
$984$		0			0
$985$	−18.1240	−	31.3916i	−0.577477	−	1.00022i
$986$	44.8654			1.42880
$987$		0			0
$988$	7.53498			0.239720
$989$	−21.2752	−	36.8498i	−0.676513	−	1.17176i
$990$		0			0
$991$	15.0202	−	26.0158i	0.477134	−	0.826420i	−0.522523	−	0.852625i	$-0.675009\pi$
$991$	15.0202	−	26.0158i	0.477134	−	0.826420i	0.999657	+	0.0262054i	$0.00834240\pi$
$992$	−4.10426	−	7.10878i	−0.130310	−	0.225704i
$993$		0			0
$994$	−10.8185	+	63.5728i	−0.343142	+	2.01641i
$995$	−66.3080			−2.10211
$996$		0			0
$997$	−9.74665	+	16.8817i	−0.308680	+	0.534649i	−0.978074	−	0.208259i	$-0.933220\pi$
$997$	−9.74665	+	16.8817i	−0.308680	+	0.534649i	0.669394	+	0.742907i	$0.266554\pi$
$998$	−10.5317	+	18.2415i	−0.333376	+	0.577424i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.l.298.6	yes	12
3.2	odd	2		693.2.i.k.298.1	yes	12
7.2	even	3	inner	693.2.i.l.100.6	yes	12
7.3	odd	6		4851.2.a.ce.1.1		6
7.4	even	3		4851.2.a.cc.1.1		6
21.2	odd	6		693.2.i.k.100.1	✓	12
21.11	odd	6		4851.2.a.cd.1.6		6
21.17	even	6		4851.2.a.cb.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.i.k.100.1	✓	12	21.2	odd	6
693.2.i.k.298.1	yes	12	3.2	odd	2
693.2.i.l.100.6	yes	12	7.2	even	3	inner
693.2.i.l.298.6	yes	12	1.1	even	1	trivial
4851.2.a.cb.1.6		6	21.17	even	6
4851.2.a.cc.1.1		6	7.4	even	3
4851.2.a.cd.1.6		6	21.11	odd	6
4851.2.a.ce.1.1		6	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.21005 + 2.09587i) q^{2} +(-1.92845 + 3.34017i) q^{4} +(1.42845 + 2.47414i) q^{5} +(2.03688 + 1.68852i) q^{7} -4.49387 q^{8} +O(q^{10})\)	\(q+(1.21005 + 2.09587i) q^{2} +(-1.92845 + 3.34017i) q^{4} +(1.42845 + 2.47414i) q^{5} +(2.03688 + 1.68852i) q^{7} -4.49387 q^{8} +(-3.45699 + 5.98768i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.62045 q^{13} +(-1.07419 + 6.31224i) q^{14} +(-1.58092 - 2.73823i) q^{16} +(4.05716 - 7.02721i) q^{17} +(0.602807 + 1.04409i) q^{19} -11.0187 q^{20} +2.42010 q^{22} +(-3.12308 - 5.40934i) q^{23} +(-1.58092 + 2.73823i) q^{25} +(-1.96083 - 3.39625i) q^{26} +(-9.56796 + 3.54731i) q^{28} +2.28468 q^{29} +(-3.07257 + 5.32185i) q^{31} +(-0.667886 + 1.15681i) q^{32} +19.6375 q^{34} +(-1.26806 + 7.45150i) q^{35} +(-4.31772 - 7.47851i) q^{37} +(-1.45886 + 2.52681i) q^{38} +(-6.41925 - 11.1185i) q^{40} -8.09333 q^{41} +6.81225 q^{43} +(1.92845 + 3.34017i) q^{44} +(7.55818 - 13.0912i) q^{46} +(-3.88015 - 6.72062i) q^{47} +(1.29779 + 6.87864i) q^{49} -7.65197 q^{50} +(3.12495 - 5.41258i) q^{52} +(0.784319 - 1.35848i) q^{53} +2.85689 q^{55} +(-9.15349 - 7.58799i) q^{56} +(2.76458 + 4.78839i) q^{58} +(-0.123084 + 0.213188i) q^{59} +(-1.60988 - 2.78839i) q^{61} -14.8719 q^{62} -9.55638 q^{64} +(-2.31473 - 4.00923i) q^{65} +(6.95314 - 12.0432i) q^{67} +(15.6480 + 27.1032i) q^{68} +(-17.1518 + 6.35901i) q^{70} +10.0713 q^{71} +(-5.24011 + 9.07614i) q^{73} +(10.4493 - 18.0988i) q^{74} -4.64993 q^{76} +(2.48074 - 0.919733i) q^{77} +(6.61960 + 11.4655i) q^{79} +(4.51652 - 7.82283i) q^{80} +(-9.79335 - 16.9626i) q^{82} -3.59930 q^{83} +23.1817 q^{85} +(8.24317 + 14.2776i) q^{86} +(-2.24694 + 3.89181i) q^{88} +(2.19320 + 3.79873i) q^{89} +(-3.30067 - 2.73617i) q^{91} +24.0908 q^{92} +(9.39036 - 16.2646i) q^{94} +(-1.72216 + 2.98286i) q^{95} -1.69506 q^{97} +(-12.8463 + 11.0435i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 4 q^{5} + 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 + 4 * q^5 + 6 * q^7 + 12 * q^8	\( 12 q - 10 q^{4} + 4 q^{5} + 6 q^{7} + 12 q^{8} + 6 q^{10} + 6 q^{11} - 4 q^{13} - 6 q^{14} - 2 q^{16} + 8 q^{17} - 6 q^{19} - 72 q^{20} - 2 q^{23} - 2 q^{25} + 8 q^{26} - 28 q^{28} + 4 q^{29} - 4 q^{31} - 12 q^{32} + 28 q^{34} - 26 q^{35} + 6 q^{37} + 10 q^{38} + 18 q^{40} - 60 q^{41} - 24 q^{43} + 10 q^{44} + 4 q^{46} + 14 q^{47} - 12 q^{49} + 48 q^{50} + 22 q^{52} + 16 q^{53} + 8 q^{55} - 60 q^{56} - 2 q^{58} + 34 q^{59} + 2 q^{61} - 52 q^{62} + 4 q^{64} - 20 q^{65} + 20 q^{67} + 18 q^{68} - 24 q^{70} + 12 q^{71} - 26 q^{73} + 14 q^{74} - 8 q^{76} + 6 q^{77} - 2 q^{79} + 44 q^{80} + 4 q^{82} - 16 q^{83} + 20 q^{85} + 78 q^{86} + 6 q^{88} + 20 q^{89} + 20 q^{91} + 60 q^{92} + 10 q^{94} - 10 q^{95} - 28 q^{97} - 90 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 4 * q^5 + 6 * q^7 + 12 * q^8 + 6 * q^10 + 6 * q^11 - 4 * q^13 - 6 * q^14 - 2 * q^16 + 8 * q^17 - 6 * q^19 - 72 * q^20 - 2 * q^23 - 2 * q^25 + 8 * q^26 - 28 * q^28 + 4 * q^29 - 4 * q^31 - 12 * q^32 + 28 * q^34 - 26 * q^35 + 6 * q^37 + 10 * q^38 + 18 * q^40 - 60 * q^41 - 24 * q^43 + 10 * q^44 + 4 * q^46 + 14 * q^47 - 12 * q^49 + 48 * q^50 + 22 * q^52 + 16 * q^53 + 8 * q^55 - 60 * q^56 - 2 * q^58 + 34 * q^59 + 2 * q^61 - 52 * q^62 + 4 * q^64 - 20 * q^65 + 20 * q^67 + 18 * q^68 - 24 * q^70 + 12 * q^71 - 26 * q^73 + 14 * q^74 - 8 * q^76 + 6 * q^77 - 2 * q^79 + 44 * q^80 + 4 * q^82 - 16 * q^83 + 20 * q^85 + 78 * q^86 + 6 * q^88 + 20 * q^89 + 20 * q^91 + 60 * q^92 + 10 * q^94 - 10 * q^95 - 28 * q^97 - 90 * q^98

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