LMFDB - Embedded newform 693.2.i.k.100.1

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			100.1
Root			$1.21005 + 2.09587i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.k.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21005 + 2.09587i) q^{2} +(-1.92845 - 3.34017i) q^{4} +(-1.42845 + 2.47414i) q^{5} +(2.03688 - 1.68852i) q^{7} +4.49387 q^{8} +O(q^{10})$	\(q+(-1.21005 + 2.09587i) q^{2} +(-1.92845 - 3.34017i) q^{4} +(-1.42845 + 2.47414i) q^{5} +(2.03688 - 1.68852i) q^{7} +4.49387 q^{8} +(-3.45699 - 5.98768i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.62045 q^{13} +(1.07419 + 6.31224i) q^{14} +(-1.58092 + 2.73823i) q^{16} +(-4.05716 - 7.02721i) q^{17} +(0.602807 - 1.04409i) q^{19} +11.0187 q^{20} +2.42010 q^{22} +(3.12308 - 5.40934i) q^{23} +(-1.58092 - 2.73823i) q^{25} +(1.96083 - 3.39625i) q^{26} +(-9.56796 - 3.54731i) q^{28} -2.28468 q^{29} +(-3.07257 - 5.32185i) q^{31} +(0.667886 + 1.15681i) q^{32} +19.6375 q^{34} +(1.26806 + 7.45150i) q^{35} +(-4.31772 + 7.47851i) q^{37} +(1.45886 + 2.52681i) q^{38} +(-6.41925 + 11.1185i) q^{40} +8.09333 q^{41} +6.81225 q^{43} +(-1.92845 + 3.34017i) q^{44} +(7.55818 + 13.0912i) q^{46} +(3.88015 - 6.72062i) q^{47} +(1.29779 - 6.87864i) q^{49} +7.65197 q^{50} +(3.12495 + 5.41258i) q^{52} +(-0.784319 - 1.35848i) q^{53} +2.85689 q^{55} +(9.15349 - 7.58799i) q^{56} +(2.76458 - 4.78839i) q^{58} +(0.123084 + 0.213188i) q^{59} +(-1.60988 + 2.78839i) q^{61} +14.8719 q^{62} -9.55638 q^{64} +(2.31473 - 4.00923i) q^{65} +(6.95314 + 12.0432i) q^{67} +(-15.6480 + 27.1032i) q^{68} +(-17.1518 - 6.35901i) q^{70} -10.0713 q^{71} +(-5.24011 - 9.07614i) q^{73} +(-10.4493 - 18.0988i) q^{74} -4.64993 q^{76} +(-2.48074 - 0.919733i) q^{77} +(6.61960 - 11.4655i) q^{79} +(-4.51652 - 7.82283i) q^{80} +(-9.79335 + 16.9626i) q^{82} +3.59930 q^{83} +23.1817 q^{85} +(-8.24317 + 14.2776i) q^{86} +(-2.24694 - 3.89181i) q^{88} +(-2.19320 + 3.79873i) q^{89} +(-3.30067 + 2.73617i) q^{91} -24.0908 q^{92} +(9.39036 + 16.2646i) q^{94} +(1.72216 + 2.98286i) q^{95} -1.69506 q^{97} +(12.8463 + 11.0435i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.21005	+	2.09587i	−0.855635	+	1.48200i	0.0204193	+	0.999792i	$0.493500\pi$
$2$	−1.21005	+	2.09587i	−0.855635	+	1.48200i	−0.876054	+	0.482212i	$0.839833\pi$
$3$		0			0
$3$		0			0
$4$	−1.92845	−	3.34017i	−0.964223	−	1.67008i
$5$	−1.42845	+	2.47414i	−0.638821	+	1.10647i	0.346871	+	0.937913i	$0.387244\pi$
$5$	−1.42845	+	2.47414i	−0.638821	+	1.10647i	−0.985692	+	0.168557i	$0.946089\pi$
$6$		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	−0.646273	−	0.763107i	$-0.723673\pi$
$17$	−4.05716	−	7.02721i	−0.984006	−	1.70435i	−0.337733	−	0.941242i	$-0.609660\pi$
$18$		0			0
$19$	0.602807	−	1.04409i	0.138294	−	0.239531i	−0.788557	−	0.614961i	$-0.789172\pi$
$19$	0.602807	−	1.04409i	0.138294	−	0.239531i	0.926851	+	0.375430i	$0.122505\pi$
$20$	11.0187			2.46386
$21$		0			0
$22$	2.42010			0.515967
$23$	3.12308	−	5.40934i	0.651208	−	1.12793i	−0.331622	−	0.943412i	$-0.607596\pi$
$23$	3.12308	−	5.40934i	0.651208	−	1.12793i	0.982830	−	0.184513i	$-0.0590708\pi$
$24$		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	$-0.568039\pi$
$29$	−2.28468			−0.424254			−0.212127	+	0.977242i	$0.568039\pi$
$30$		0			0
$31$	−3.07257	−	5.32185i	−0.551851	−	0.955833i	−0.998141	−	0.0609451i	$-0.980589\pi$
$31$	−3.07257	−	5.32185i	−0.551851	−	0.955833i	0.446291	−	0.894888i	$-0.352745\pi$
$32$	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	0.255091	+	0.966917i	$0.417894\pi$
$37$	−4.31772	+	7.47851i	−0.709829	+	1.22946i	−0.964920	+	0.262543i	$0.915439\pi$
$38$	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	$-0.282241\pi$
$41$	8.09333			1.26397			0.631983	+	0.774982i	$0.282241\pi$
$42$		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	−0.430980	−	0.902362i	$-0.641832\pi$
$47$	3.88015	−	6.72062i	0.565978	−	0.980303i	0.996958	−	0.0779415i	$-0.0248347\pi$
$48$		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	$-0.201026\pi$
$53$	−0.784319	−	1.35848i	−0.107734	−	0.186602i	−0.914852	+	0.403789i	$0.867693\pi$
$54$		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	$-0.161566\pi$
$59$	0.123084	+	0.213188i	0.0160242	+	0.0277547i	−0.857902	+	0.513813i	$0.828232\pi$
$60$		0			0
$61$	−1.60988	+	2.78839i	−0.206124	+	0.357016i	−0.950490	−	0.310755i	$-0.899418\pi$
$61$	−1.60988	+	2.78839i	−0.206124	+	0.357016i	0.744367	+	0.667771i	$0.232752\pi$
$62$	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	0.881689	+	0.471830i	$0.156406\pi$
$67$	6.95314	+	12.0432i	0.849462	+	1.47131i	−0.0322277	+	0.999481i	$0.510260\pi$
$68$	−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	$-0.703889\pi$
$71$	−10.0713			−1.19525			−0.597625	+	0.801776i	$0.703889\pi$
$72$		0			0
$73$	−5.24011	−	9.07614i	−0.613309	−	1.06228i	−0.990679	−	0.136219i	$-0.956505\pi$
$73$	−5.24011	−	9.07614i	−0.613309	−	1.06228i	0.377370	−	0.926063i	$-0.376828\pi$
$74$	−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	−0.205542	−	0.978648i	$-0.565896\pi$
$79$	6.61960	−	11.4655i	0.744763	−	1.28997i	0.950305	−	0.311320i	$-0.100771\pi$
$80$	−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	$-0.436706\pi$
$83$	3.59930			0.395075			0.197537	+	0.980295i	$0.436706\pi$
$84$		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	$-0.908017\pi$
$89$	−2.19320	+	3.79873i	−0.232479	+	0.402665i	0.726058	+	0.687633i	$0.241350\pi$
$90$		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	$-0.170557\pi$
$101$	−0.122831	−	0.212749i	−0.0122221	−	0.0211693i	−0.872072	+	0.489378i	$0.837224\pi$
$102$		0			0
$103$	4.04241	−	7.00165i	0.398310	−	0.689893i	−0.595207	−	0.803572i	$-0.702930\pi$
$103$	4.04241	−	7.00165i	0.398310	−	0.689893i	0.993518	+	0.113679i	$0.0362634\pi$
$104$	−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	$-0.907244\pi$
$107$	−2.38034	+	4.12287i	−0.230116	+	0.398573i	0.727726	+	0.685868i	$0.240577\pi$
$108$		0			0
$109$	−6.42538	−	11.1291i	−0.615440	−	1.06597i	−0.990307	−	0.138895i	$-0.955645\pi$
$109$	−6.42538	−	11.1291i	−0.615440	−	1.06597i	0.374867	−	0.927078i	$-0.377688\pi$
$110$	−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	$-0.638249\pi$
$113$	−8.94622			−0.841589			−0.420795	+	0.907156i	$0.638249\pi$
$114$		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	$-0.783840\pi$
$131$	1.77249	−	3.07005i	0.154863	−	0.268231i	0.933009	+	0.359852i	$0.117173\pi$
$132$		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	$-0.110691\pi$
$137$	2.04770	+	3.54673i	0.174947	+	0.303017i	−0.765196	+	0.643798i	$0.777358\pi$
$138$		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	−0.121208	−	0.992627i	$-0.538677\pi$
$149$	9.75348	−	16.8935i	0.799036	−	1.38397i	0.920244	−	0.391344i	$-0.127990\pi$
$150$		0			0
$151$	4.48441	+	7.76723i	0.364936	+	0.632088i	0.988766	−	0.149472i	$-0.0477574\pi$
$151$	4.48441	+	7.76723i	0.364936	+	0.632088i	−0.623830	+	0.781560i	$0.714424\pi$
$152$	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	−0.999699	−	0.0245313i	$-0.992191\pi$
$157$	−6.52929	−	11.3091i	−0.521094	−	0.902562i	0.478605	−	0.878030i	$-0.341143\pi$
$158$	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	−0.436717	−	0.899599i	$-0.643859\pi$
$163$	7.15876	−	12.3993i	0.560717	−	0.971191i	0.997434	−	0.0715917i	$-0.0228079\pi$
$164$	−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	$-0.473561\pi$
$167$	2.14432			0.165932			0.0829661	+	0.996552i	$0.473561\pi$
$168$		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	−0.177314	−	0.984154i	$-0.556741\pi$
$173$	10.0442	−	17.3970i	0.763646	−	1.32267i	0.940960	−	0.338519i	$-0.109926\pi$
$174$		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	$-0.328245\pi$
$179$	−6.50348	−	11.2644i	−0.486093	−	0.841938i	−0.999872	+	0.0159848i	$0.994912\pi$
$180$		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	0.244696	+	0.969600i	$0.421312\pi$
$191$	−9.91397	+	17.1715i	−0.717350	+	1.24249i	−0.962046	+	0.272887i	$0.912022\pi$
$192$		0			0
$193$	3.63698	+	6.29943i	0.261795	+	0.453443i	0.966719	−	0.255840i	$-0.0823521\pi$
$193$	3.63698	+	6.29943i	0.261795	+	0.453443i	−0.704924	+	0.709283i	$0.749019\pi$
$194$	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	$-0.350715\pi$
$197$	12.6879			0.903974			0.451987	+	0.892025i	$0.350715\pi$
$198$		0			0
$199$	−11.6049	−	20.1003i	−0.822651	−	1.42487i	−0.903702	−	0.428163i	$-0.859161\pi$
$199$	−11.6049	−	20.1003i	−0.822651	−	1.42487i	0.0810507	−	0.996710i	$-0.474172\pi$
$200$	−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	$-0.327152\pi$
$227$	−7.27847	−	12.6067i	−0.483089	−	0.836735i	−0.999811	+	0.0194181i	$0.993819\pi$
$228$		0			0
$229$	7.28110	−	12.6112i	0.481149	−	0.833374i	−0.518617	−	0.855007i	$-0.673553\pi$
$229$	7.28110	−	12.6112i	0.481149	−	0.833374i	0.999766	+	0.0216322i	$0.00688629\pi$
$230$	−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	$-0.754199\pi$
$233$	3.75588	−	6.50538i	0.246056	−	0.426182i	0.962428	+	0.271537i	$0.0875319\pi$
$234$		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	$-0.554182\pi$
$239$	−5.23765			−0.338795			−0.169398	+	0.985548i	$0.554182\pi$
$240$		0			0
$241$	12.1752	+	21.0881i	0.784275	+	1.35840i	0.929431	+	0.368995i	$0.120298\pi$
$241$	12.1752	+	21.0881i	0.784275	+	1.35840i	−0.145156	+	0.989409i	$0.546369\pi$
$242$	−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	$-0.638238\pi$
$251$	−13.3323			−0.841528			−0.420764	+	0.907170i	$0.638238\pi$
$252$		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	$-0.800841\pi$
$257$	1.63357	−	2.82942i	0.101899	−	0.176494i	0.912467	+	0.409150i	$0.134175\pi$
$258$		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	0.994665	+	0.103160i	$0.0328954\pi$
$263$	9.51422	+	16.4791i	0.586672	+	1.01615i	−0.407993	+	0.912985i	$0.633771\pi$
$264$		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	$-0.0371438\pi$
$269$	6.49114	+	11.2430i	0.395772	+	0.685497i	−0.597427	+	0.801923i	$0.703810\pi$
$270$		0			0
$271$	−2.36814	+	4.10174i	−0.143854	+	0.249163i	−0.928945	−	0.370218i	$-0.879283\pi$
$271$	−2.36814	+	4.10174i	−0.143854	+	0.249163i	0.785091	+	0.619381i	$0.212616\pi$
$272$	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	0.985668	−	0.168697i	$-0.0539561\pi$
$277$	5.77086	+	9.99543i	0.346738	+	0.600567i	−0.638930	+	0.769265i	$0.720623\pi$
$278$	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	$-0.219619\pi$
$281$	25.8579			1.54255			0.771277	+	0.636500i	$0.219619\pi$
$282$		0			0
$283$	−5.29353	−	9.16867i	−0.314668	−	0.545021i	0.664699	−	0.747111i	$-0.268560\pi$
$283$	−5.29353	−	9.16867i	−0.314668	−	0.545021i	−0.979367	+	0.202091i	$0.935226\pi$
$284$	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	$-0.447520\pi$
$293$	5.61873			0.328250			0.164125	+	0.986440i	$0.447520\pi$
$294$		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	$-0.332418\pi$
$311$	−8.77366	−	15.1964i	−0.497509	−	0.861711i	−0.999996	+	0.00287417i	$0.999085\pi$
$312$		0			0
$313$	−6.22809	+	10.7874i	−0.352033	+	0.609739i	−0.986605	−	0.163125i	$-0.947843\pi$
$313$	−6.22809	+	10.7874i	−0.352033	+	0.609739i	0.634573	+	0.772863i	$0.281176\pi$
$314$	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	$-0.897983\pi$
$317$	−3.59131	+	6.22033i	−0.201708	+	0.349368i	0.747371	+	0.664407i	$0.231316\pi$
$318$		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	0.0469432	+	0.998898i	$0.485052\pi$
$331$	−15.3116	+	26.5204i	−0.841599	+	1.45769i	−0.888542	+	0.458795i	$0.848281\pi$
$332$	−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	0.998715	+	0.0506848i	$0.0161404\pi$
$347$	10.1197	+	17.5278i	0.543252	+	0.940939i	−0.455463	+	0.890255i	$0.650526\pi$
$348$		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	0.995500	+	0.0947668i	$0.0302105\pi$
$353$	10.8938	+	18.8687i	0.579820	+	1.00428i	−0.415679	+	0.909511i	$0.636456\pi$
$354$		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	$-0.869311\pi$
$359$	−2.13699	+	3.70138i	−0.112786	+	0.195351i	0.804106	+	0.594485i	$0.202644\pi$
$360$		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	0.902577	−	0.430528i	$-0.141673\pi$
$367$	1.50270	+	2.60276i	0.0784405	+	0.135863i	−0.824137	+	0.566391i	$0.808339\pi$
$368$	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	−0.869300	−	0.494285i	$-0.835430\pi$
$373$	−0.127209	+	0.220333i	−0.00658665	+	0.0114084i	0.862713	+	0.505693i	$0.168763\pi$
$374$	−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	−0.0598643	+	0.998207i	$0.519067\pi$
$383$	−17.5038	+	30.3175i	−0.894404	+	1.54915i	−0.834540	+	0.550947i	$0.814267\pi$
$384$		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	−0.717444	−	0.696616i	$-0.754688\pi$
$389$	−18.9738	−	32.8636i	−0.962009	−	1.66625i	−0.244565	−	0.969633i	$-0.578645\pi$
$390$		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	−0.881474	−	0.472233i	$-0.843448\pi$
$397$	−0.633041	+	1.09646i	−0.0317714	+	0.0550297i	0.849702	+	0.527262i	$0.176782\pi$
$398$	56.1702			2.81556
$399$		0			0
$400$	9.99722			0.499861
$401$	11.9416	−	20.6834i	0.596334	−	1.03288i	−0.397023	−	0.917809i	$-0.629957\pi$
$401$	11.9416	−	20.6834i	0.596334	−	1.03288i	0.993357	−	0.115072i	$-0.0367100\pi$
$402$		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	0.999724	−	0.0234779i	$-0.00747394\pi$
$409$	9.69789	+	16.7972i	0.479530	+	0.830570i	−0.520195	+	0.854048i	$0.674141\pi$
$410$	−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	$-0.561556\pi$
$419$	−7.86765			−0.384360			−0.192180	+	0.981360i	$0.561556\pi$
$420$		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	$-0.181446\pi$
$431$	−0.963605	−	1.66901i	−0.0464152	−	0.0803935i	−0.888300	+	0.459264i	$0.848113\pi$
$432$		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	−0.641748	−	0.766916i	$-0.721790\pi$
$439$	7.19283	−	12.4583i	0.343295	−	0.594604i	0.985042	+	0.172312i	$0.0551236\pi$
$440$	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	$-0.898673\pi$
$443$	−4.29019	+	7.43082i	−0.203833	+	0.353049i	0.745927	+	0.666027i	$0.232007\pi$
$444$		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	$-0.641345\pi$
$449$	−18.2061			−0.859200			−0.429600	+	0.903019i	$0.641345\pi$
$450$		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	0.193037	−	0.981191i	$-0.438166\pi$
$457$	20.2286	−	35.0370i	0.946255	−	1.63896i	0.753218	−	0.657771i	$-0.228501\pi$
$458$	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	$-0.101752\pi$
$461$	40.7664			1.89868			0.949341	+	0.314247i	$0.101752\pi$
$462$		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	$-0.732383\pi$
$467$	6.73926	−	11.6727i	0.311856	−	0.540150i	0.978764	+	0.204990i	$0.0657161\pi$
$468$		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	$-0.319963\pi$
$479$	−10.1375	−	17.5586i	−0.463193	−	0.802273i	−0.999118	+	0.0419924i	$0.986629\pi$
$480$		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	0.877086	−	0.480333i	$-0.159484\pi$
$487$	0.497918	+	0.862418i	0.0225628	+	0.0390799i	−0.854524	+	0.519413i	$0.826151\pi$
$488$	−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	$-0.333574\pi$
$491$	22.1296			0.998693			0.499346	+	0.866402i	$0.333574\pi$
$492$		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	−0.752027	−	0.659132i	$-0.770924\pi$
$499$	4.35177	−	7.53749i	0.194812	−	0.337424i	0.946839	+	0.321708i	$0.104257\pi$
$500$	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	$-0.691353\pi$
$503$	−25.3699			−1.13119			−0.565595	+	0.824683i	$0.691353\pi$
$504$		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	0.139366	+	0.990241i	$0.455494\pi$
$509$	−17.7756	+	30.7883i	−0.787891	+	1.36467i	−0.927257	+	0.374426i	$0.877840\pi$
$510$		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	$-0.153221\pi$
$521$	0.963877	+	1.66948i	0.0422282	+	0.0731414i	−0.844139	+	0.536125i	$0.819888\pi$
$522$		0			0
$523$	17.4771	−	30.2712i	0.764218	−	1.32367i	−0.176440	−	0.984311i	$-0.556458\pi$
$523$	17.4771	−	30.2712i	0.764218	−	1.32367i	0.940659	−	0.339354i	$-0.110208\pi$
$524$	−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	−0.767873	−	0.640602i	$-0.778685\pi$
$541$	3.97367	−	6.88260i	0.170842	−	0.295906i	0.938714	+	0.344696i	$0.112018\pi$
$542$	−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	$-0.259004\pi$
$557$	−6.75066	−	11.6925i	−0.286035	−	0.495426i	−0.972860	+	0.231396i	$0.925671\pi$
$558$		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	0.994325	+	0.106387i	$0.0339282\pi$
$563$	13.9826	+	24.2186i	0.589296	+	1.02069i	−0.405029	+	0.914304i	$0.632738\pi$
$564$		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	$-0.747935\pi$
$569$	6.32317	−	10.9520i	0.265081	−	0.459134i	0.967585	+	0.252546i	$0.0812680\pi$
$570$		0			0
$571$	9.54081	+	16.5252i	0.399270	+	0.691556i	0.993636	−	0.112638i	$-0.0359302\pi$
$571$	9.54081	+	16.5252i	0.399270	+	0.691556i	−0.594366	+	0.804195i	$0.702597\pi$
$572$	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	0.902610	+	0.430458i	$0.141648\pi$
$577$	19.7954	+	34.2866i	0.824093	+	1.42737i	−0.0785173	+	0.996913i	$0.525019\pi$
$578$	−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	$-0.279240\pi$
$587$	30.9761			1.27852			0.639261	+	0.768990i	$0.279240\pi$
$588$		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	−0.196535	−	0.980497i	$-0.562969\pi$
$593$	18.2848	−	31.6703i	0.750868	−	1.30054i	0.947403	−	0.320044i	$-0.103698\pi$
$594$		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	$-0.0617853\pi$
$599$	7.91908	+	13.7163i	0.323565	+	0.560431i	−0.657656	+	0.753318i	$0.728452\pi$
$600$		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	−0.756343	−	0.654175i	$-0.773016\pi$
$607$	4.64070	−	8.03793i	0.188360	−	0.326250i	0.944704	+	0.327925i	$0.106349\pi$
$608$	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	0.661324	−	0.750100i	$-0.269995\pi$
$613$	−7.89667	−	13.6774i	−0.318943	−	0.552426i	−0.980268	+	0.197674i	$0.936661\pi$
$614$	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	$-0.111650\pi$
$617$	46.6541			1.87823			0.939113	+	0.343610i	$0.111650\pi$
$618$		0			0
$619$	19.2083	+	33.2698i	0.772048	+	1.33723i	0.936439	+	0.350832i	$0.114101\pi$
$619$	19.2083	+	33.2698i	0.772048	+	1.33723i	−0.164390	+	0.986395i	$0.552566\pi$
$620$	−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	$-0.208376\pi$
$641$	−3.30800	−	5.72962i	−0.130658	−	0.226306i	−0.923930	+	0.382561i	$0.875042\pi$
$642$		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	$-0.276951\pi$
$647$	−8.63760	−	14.9608i	−0.339579	−	0.588168i	−0.984354	+	0.176205i	$0.943618\pi$
$648$		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	$-0.806294\pi$
$653$	2.16810	−	3.75526i	0.0848444	−	0.146955i	0.905325	+	0.424720i	$0.139627\pi$
$654$		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	$-0.247115\pi$
$659$	36.6318			1.42697			0.713486	+	0.700669i	$0.247115\pi$
$660$		0			0
$661$	−13.4383	−	23.2759i	−0.522691	−	0.905328i	−0.999651	−	0.0264027i	$-0.991595\pi$
$661$	−13.4383	−	23.2759i	−0.522691	−	0.905328i	0.476960	−	0.878925i	$-0.341739\pi$
$662$	−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	0.329599	+	0.944121i	$0.393086\pi$
$677$	−16.9862	+	29.4210i	−0.652833	+	1.13074i	−0.982432	+	0.186619i	$0.940247\pi$
$678$		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	$-0.211478\pi$
$683$	−3.66698	−	6.35140i	−0.140313	−	0.243030i	−0.927615	+	0.373539i	$0.878144\pi$
$684$		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	−0.868237	−	0.496150i	$-0.834747\pi$
$691$	−0.116710	+	0.202147i	−0.00443985	+	0.00769004i	0.863797	+	0.503840i	$0.168080\pi$
$692$	−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	$-0.728598\pi$
$701$	−34.8430			−1.31600			−0.658001	+	0.753017i	$0.728598\pi$
$702$		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	−0.847426	−	0.530913i	$-0.821849\pi$
$709$	0.960460	−	1.66357i	0.0360708	−	0.0624765i	0.883497	+	0.468436i	$0.155182\pi$
$710$	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	$-0.954370\pi$
$719$	−9.95207	+	17.2375i	−0.371149	+	0.642850i	0.618593	+	0.785711i	$0.287703\pi$
$720$		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	−0.0277140	+	0.999616i	$0.508823\pi$
$733$	−23.8129	+	41.2452i	−0.879550	+	1.52342i	−0.851836	+	0.523809i	$0.824511\pi$
$734$	−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	0.969679	−	0.244382i	$-0.0785851\pi$
$739$	7.42678	+	12.8636i	0.273199	+	0.473194i	−0.696481	+	0.717576i	$0.745252\pi$
$740$	−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	$-0.530849\pi$
$743$	−5.27520			−0.193528			−0.0967641	+	0.995307i	$0.530849\pi$
$744$		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	−0.985265	−	0.171037i	$-0.945288\pi$
$751$	−9.44109	+	16.3524i	−0.344510	+	0.596709i	0.640754	+	0.767746i	$0.278622\pi$
$752$	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	$-0.944029\pi$
$761$	−9.40117	+	16.2833i	−0.340792	+	0.590270i	0.643788	+	0.765204i	$0.277362\pi$
$762$		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	−0.999997	−	0.00257386i	$-0.999181\pi$
$773$	−13.9634	−	24.1853i	−0.502227	−	0.869883i	0.497769	−	0.867309i	$-0.334153\pi$
$774$		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	0.968583	−	0.248691i	$-0.0800003\pi$
$787$	7.54412	+	13.0668i	0.268919	+	0.465781i	−0.699664	+	0.714472i	$0.746667\pi$
$788$	−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	$-0.632205\pi$
$797$	−22.7824			−0.806993			−0.403496	+	0.914981i	$0.632205\pi$
$798$		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	0.611728	+	0.791068i	$0.290475\pi$
$809$	28.1855	+	48.8187i	0.990949	+	1.71637i	0.379221	+	0.925306i	$0.376192\pi$
$810$		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	0.357832	+	0.933786i	$0.383516\pi$
$821$	−18.0448	+	31.2544i	−0.629766	+	1.09079i	−0.987598	+	0.157001i	$0.949817\pi$
$822$		0			0
$823$	0.928769	+	1.60867i	0.0323748	+	0.0560749i	0.881759	−	0.471700i	$-0.156360\pi$
$823$	0.928769	+	1.60867i	0.0323748	+	0.0560749i	−0.849384	+	0.527775i	$0.823026\pi$
$824$	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	$-0.519614\pi$
$827$	−3.54179			−0.123160			−0.0615801	+	0.998102i	$0.519614\pi$
$828$		0			0
$829$	−18.9435	−	32.8111i	−0.657934	−	1.13957i	−0.981150	−	0.193250i	$-0.938097\pi$
$829$	−18.9435	−	32.8111i	−0.657934	−	1.13957i	0.323216	−	0.946325i	$-0.395236\pi$
$830$	−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	$-0.416254\pi$
$839$	15.0661			0.520140			0.260070	+	0.965590i	$0.416254\pi$
$840$		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	$-0.296425\pi$
$857$	−11.6059	−	20.1021i	−0.396452	−	0.686674i	−0.993285	+	0.115691i	$0.963092\pi$
$858$		0			0
$859$	13.8157	−	23.9294i	0.471384	−	0.816461i	−0.528080	−	0.849195i	$-0.677088\pi$
$859$	13.8157	−	23.9294i	0.471384	−	0.816461i	0.999464	+	0.0327332i	$0.0104212\pi$
$860$	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	$-0.799035\pi$
$863$	3.15926	−	5.47200i	0.107543	−	0.186269i	0.914774	+	0.403966i	$0.132368\pi$
$864$		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	−0.760249	−	0.649632i	$-0.774923\pi$
$877$	5.40380	−	9.35966i	0.182473	−	0.316053i	0.942722	+	0.333579i	$0.108256\pi$
$878$	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	$-0.687287\pi$
$881$	−32.9475			−1.11003			−0.555015	+	0.831841i	$0.687287\pi$
$882$		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	$-0.880271\pi$
$887$	−4.37577	+	7.57906i	−0.146924	+	0.254480i	0.783165	+	0.621814i	$0.213604\pi$
$888$		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	0.861605	−	0.507579i	$-0.169459\pi$
$907$	−0.264221	−	0.457644i	−0.00877330	−	0.0151958i	−0.870379	+	0.492383i	$0.836126\pi$
$908$	−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	$-0.707943\pi$
$911$	−36.6894			−1.21557			−0.607787	+	0.794100i	$0.707943\pi$
$912$		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	−0.615022	−	0.788510i	$-0.710853\pi$
$919$	11.3790	−	19.7090i	0.375358	−	0.650140i	0.990381	+	0.138370i	$0.0441863\pi$
$920$	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	$-0.767543\pi$
$929$	6.25497	−	10.8339i	0.205219	−	0.355450i	0.950202	+	0.311633i	$0.100876\pi$
$930$		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	$-0.149652\pi$
$941$	1.63890	+	2.83866i	0.0534266	+	0.0925376i	−0.838075	+	0.545555i	$0.816319\pi$
$942$		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	$-0.787002\pi$
$947$	4.46335	−	7.73076i	0.145040	−	0.251216i	0.929388	+	0.369105i	$0.120336\pi$
$948$		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	$-0.551387\pi$
$953$	−9.92412			−0.321474			−0.160737	+	0.986997i	$0.551387\pi$
$954$		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	0.208900	+	0.977937i	$0.433012\pi$
$971$	−23.1360	+	40.0726i	−0.742468	+	1.28599i	−0.951368	+	0.308055i	$0.900322\pi$
$972$		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	−0.999994	−	0.00332380i	$-0.998942\pi$
$977$	−15.7184	−	27.2250i	−0.502876	−	0.871006i	0.497119	−	0.867683i	$-0.334391\pi$
$978$		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	$-0.0973359\pi$
$983$	6.77506	+	11.7347i	0.216091	+	0.374280i	−0.737519	+	0.675327i	$0.764003\pi$
$984$		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	0.999657	−	0.0262054i	$-0.00834240\pi$
$991$	15.0202	+	26.0158i	0.477134	+	0.826420i	−0.522523	+	0.852625i	$0.675009\pi$
$992$	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	0.669394	−	0.742907i	$-0.266554\pi$
$997$	−9.74665	−	16.8817i	−0.308680	−	0.534649i	−0.978074	+	0.208259i	$0.933220\pi$
$998$	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.k.100.1	✓	12
3.2	odd	2		693.2.i.l.100.6	yes	12
7.2	even	3		4851.2.a.cd.1.6		6
7.4	even	3	inner	693.2.i.k.298.1	yes	12
7.5	odd	6		4851.2.a.cb.1.6		6
21.2	odd	6		4851.2.a.cc.1.1		6
21.5	even	6		4851.2.a.ce.1.1		6
21.11	odd	6		693.2.i.l.298.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.i.k.100.1	✓	12	1.1	even	1	trivial
693.2.i.k.298.1	yes	12	7.4	even	3	inner
693.2.i.l.100.6	yes	12	3.2	odd	2
693.2.i.l.298.6	yes	12	21.11	odd	6
4851.2.a.cb.1.6		6	7.5	odd	6
4851.2.a.cc.1.1		6	21.2	odd	6
4851.2.a.cd.1.6		6	7.2	even	3
4851.2.a.ce.1.1		6	21.5	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
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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