LMFDB - Embedded newform 392.2.e.d.195.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(195,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.195"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,-4,0,0,0,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1212153856.10
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 $ x^8 - 4x^6 + 10x^4 - 16*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.4
Root			$-1.07072 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	392.195
Dual form			392.2.e.d.195.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 + 1.39897i) q^{2} +0.765367i q^{3} +(-1.91421 - 0.579471i) q^{4} +3.02846 q^{5} +(-1.07072 - 0.158513i) q^{6} +(1.20711 - 2.55791i) q^{8} +2.41421 q^{9} +(-0.627215 + 4.23671i) q^{10} +4.24264 q^{11} +(0.443508 - 1.46508i) q^{12} -3.02846 q^{13} +2.31788i q^{15} +(3.32843 + 2.21846i) q^{16} -4.46088i q^{17} +(-0.500000 + 3.37740i) q^{18} +3.37849i q^{19} +(-5.79712 - 1.75490i) q^{20} +(-0.878680 + 5.93531i) q^{22} +5.59587i q^{23} +(1.95774 + 0.923880i) q^{24} +4.17157 q^{25} +(0.627215 - 4.23671i) q^{26} +4.14386i q^{27} -5.59587i q^{29} +(-3.24264 - 0.480049i) q^{30} -10.3398 q^{31} +(-3.79289 + 4.19690i) q^{32} +3.24718i q^{33} +(6.24063 + 0.923880i) q^{34} +(-4.62132 - 1.39897i) q^{36} -2.31788i q^{37} +(-4.72640 - 0.699709i) q^{38} -2.31788i q^{39} +(3.65568 - 7.74652i) q^{40} +7.07401i q^{41} +2.58579 q^{43} +(-8.12132 - 2.45849i) q^{44} +7.31135 q^{45} +(-7.82843 - 1.15894i) q^{46} -6.05692 q^{47} +(-1.69794 + 2.54747i) q^{48} +(-0.863961 + 5.83589i) q^{50} +3.41421 q^{51} +(5.79712 + 1.75490i) q^{52} -3.27798i q^{53} +(-5.79712 - 0.858221i) q^{54} +12.8487 q^{55} -2.58579 q^{57} +(7.82843 + 1.15894i) q^{58} -10.7695i q^{59} +(1.34315 - 4.43692i) q^{60} +7.31135 q^{61} +(2.14144 - 14.4650i) q^{62} +(-5.08579 - 6.17534i) q^{64} -9.17157 q^{65} +(-4.54269 - 0.672512i) q^{66} -2.00000 q^{67} +(-2.58495 + 8.53909i) q^{68} -4.28289 q^{69} +14.4697i q^{71} +(2.91421 - 6.17534i) q^{72} +3.37849i q^{73} +(3.24264 + 0.480049i) q^{74} +3.19278i q^{75} +(1.95774 - 6.46716i) q^{76} +(3.24264 + 0.480049i) q^{78} -11.1917i q^{79} +(10.0800 + 6.71852i) q^{80} +4.07107 q^{81} +(-9.89630 - 1.46508i) q^{82} -9.23880i q^{83} -13.5096i q^{85} +(-0.535534 + 3.61743i) q^{86} +4.28289 q^{87} +(5.12132 - 10.8523i) q^{88} +2.48181i q^{89} +(-1.51423 + 10.2283i) q^{90} +(3.24264 - 10.7117i) q^{92} -7.91375i q^{93} +(1.25443 - 8.47343i) q^{94} +10.2316i q^{95} +(-3.21217 - 2.90295i) q^{96} -6.88830i q^{97} +10.2426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 8 q^{9} + 4 q^{16} - 4 q^{18} - 24 q^{22} + 56 q^{25} + 8 q^{30} - 36 q^{32} - 20 q^{36} + 32 q^{43} - 48 q^{44} - 40 q^{46} + 44 q^{50} + 16 q^{51} - 32 q^{57} + 40 q^{58}+ \cdots + 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 8 * q^9 + 4 * q^16 - 4 * q^18 - 24 * q^22 + 56 * q^25 + 8 * q^30 - 36 * q^32 - 20 * q^36 + 32 * q^43 - 48 * q^44 - 40 * q^46 + 44 * q^50 + 16 * q^51 - 32 * q^57 + 40 * q^58 + 56 * q^60 - 52 * q^64 - 96 * q^65 - 16 * q^67 + 12 * q^72 - 8 * q^74 - 8 * q^78 - 24 * q^81 + 24 * q^86 + 24 * q^88 - 8 * q^92 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.207107	+	1.39897i	−0.146447	+	0.989219i
$2$	−0.207107	+	1.39897i	−0.146447	+	0.989219i
$3$			0.765367i			0.441885i	0.975287	+	0.220942i	$0.0709133\pi$
$3$			0.765367i			0.441885i	−0.975287	+	0.220942i	$0.929087\pi$
$4$	−1.91421	−	0.579471i	−0.957107	−	0.289735i
$5$	3.02846			1.35437			0.677184	−	0.735813i	$-0.263200\pi$
$5$	3.02846			1.35437			0.677184	+	0.735813i	$0.263200\pi$
$6$	−1.07072	−	0.158513i	−0.437121	−	0.0647125i
$7$		0			0
$7$		0			0
$8$	1.20711	−	2.55791i	0.426777	−	0.904357i
$9$	2.41421			0.804738
$10$	−0.627215	+	4.23671i	−0.198343	+	1.33977i
$11$	4.24264			1.27920			0.639602	−	0.768706i	$-0.279099\pi$
$11$	4.24264			1.27920			0.639602	+	0.768706i	$0.279099\pi$
$12$	0.443508	−	1.46508i	0.128030	−	0.422931i
$13$	−3.02846			−0.839944			−0.419972	−	0.907537i	$-0.637960\pi$
$13$	−3.02846			−0.839944			−0.419972	+	0.907537i	$0.637960\pi$
$14$		0			0
$15$			2.31788i			0.598475i
$16$	3.32843	+	2.21846i	0.832107	+	0.554615i
$17$		−	4.46088i		−	1.08192i	−0.841047	−	0.540962i	$-0.818060\pi$
$17$		−	4.46088i		−	1.08192i	0.841047	−	0.540962i	$-0.181940\pi$
$18$	−0.500000	+	3.37740i	−0.117851	+	0.796062i
$19$			3.37849i			0.775079i	0.921853	+	0.387540i	$0.126675\pi$
$19$			3.37849i			0.775079i	−0.921853	+	0.387540i	$0.873325\pi$
$20$	−5.79712	−	1.75490i	−1.29628	−	0.392409i
$21$		0			0
$22$	−0.878680	+	5.93531i	−0.187335	+	1.26541i
$23$			5.59587i			1.16682i	0.812178	+	0.583409i	$0.198282\pi$
$23$			5.59587i			1.16682i	−0.812178	+	0.583409i	$0.801718\pi$
$24$	1.95774	+	0.923880i	0.399622	+	0.188586i
$25$	4.17157			0.834315
$26$	0.627215	−	4.23671i	0.123007	−	0.830888i
$27$			4.14386i			0.797486i
$28$		0			0
$29$		−	5.59587i		−	1.03913i	−0.854432	−	0.519563i	$-0.826095\pi$
$29$		−	5.59587i		−	1.03913i	0.854432	−	0.519563i	$-0.173905\pi$
$30$	−3.24264	−	0.480049i	−0.592022	−	0.0876446i
$31$	−10.3398			−1.85708			−0.928542	−	0.371226i	$-0.878937\pi$
$31$	−10.3398			−1.85708			−0.928542	+	0.371226i	$0.878937\pi$
$32$	−3.79289	+	4.19690i	−0.670495	+	0.741914i
$33$			3.24718i			0.565261i
$34$	6.24063	+	0.923880i	1.07026	+	0.158444i
$35$		0			0
$36$	−4.62132	−	1.39897i	−0.770220	−	0.233161i
$37$		−	2.31788i		−	0.381058i	−0.981682	−	0.190529i	$-0.938980\pi$
$37$		−	2.31788i		−	0.381058i	0.981682	−	0.190529i	$-0.0610203\pi$
$38$	−4.72640	−	0.699709i	−0.766723	−	0.113508i
$39$		−	2.31788i		−	0.371158i
$40$	3.65568	−	7.74652i	0.578013	−	1.22483i
$41$			7.07401i			1.10477i	0.833587	+	0.552387i	$0.186283\pi$
$41$			7.07401i			1.10477i	−0.833587	+	0.552387i	$0.813717\pi$
$42$		0			0
$43$	2.58579			0.394329			0.197164	−	0.980370i	$-0.436827\pi$
$43$	2.58579			0.394329			0.197164	+	0.980370i	$0.436827\pi$
$44$	−8.12132	−	2.45849i	−1.22434	−	0.370631i
$45$	7.31135			1.08991
$46$	−7.82843	−	1.15894i	−1.15424	−	0.170877i
$47$	−6.05692			−0.883493			−0.441746	−	0.897140i	$-0.645641\pi$
$47$	−6.05692			−0.883493			−0.441746	+	0.897140i	$0.645641\pi$
$48$	−1.69794	+	2.54747i	−0.245076	+	0.367695i
$49$		0			0
$50$	−0.863961	+	5.83589i	−0.122183	+	0.825319i
$51$	3.41421			0.478086
$52$	5.79712	+	1.75490i	0.803916	+	0.243361i
$53$		−	3.27798i		−	0.450265i	−0.974328	−	0.225133i	$-0.927718\pi$
$53$		−	3.27798i		−	0.450265i	0.974328	−	0.225133i	$-0.0722816\pi$
$54$	−5.79712	−	0.858221i	−0.788888	−	0.116789i
$55$	12.8487			1.73251
$56$		0			0
$57$	−2.58579			−0.342496
$58$	7.82843	+	1.15894i	1.02792	+	0.152176i
$59$		−	10.7695i		−	1.40207i	−0.713125	−	0.701037i	$-0.752721\pi$
$59$		−	10.7695i		−	1.40207i	0.713125	−	0.701037i	$-0.247279\pi$
$60$	1.34315	−	4.43692i	0.173399	−	0.572804i
$61$	7.31135			0.936122			0.468061	−	0.883696i	$-0.344953\pi$
$61$	7.31135			0.936122			0.468061	+	0.883696i	$0.344953\pi$
$62$	2.14144	−	14.4650i	0.271964	−	1.83706i
$63$		0			0
$64$	−5.08579	−	6.17534i	−0.635723	−	0.771917i
$65$	−9.17157			−1.13759
$66$	−4.54269	−	0.672512i	−0.559167	−	0.0827805i
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−2.58495	+	8.53909i	−0.313472	+	1.03552i
$69$	−4.28289			−0.515599
$70$		0			0
$71$			14.4697i			1.71724i	0.512613	+	0.858619i	$0.328677\pi$
$71$			14.4697i			1.71724i	−0.512613	+	0.858619i	$0.671323\pi$
$72$	2.91421	−	6.17534i	0.343443	−	0.727770i
$73$			3.37849i			0.395423i	0.980260	+	0.197711i	$0.0633509\pi$
$73$			3.37849i			0.395423i	−0.980260	+	0.197711i	$0.936649\pi$
$74$	3.24264	+	0.480049i	0.376949	+	0.0558046i
$75$			3.19278i			0.368671i
$76$	1.95774	−	6.46716i	0.224568	−	0.741834i
$77$		0			0
$78$	3.24264	+	0.480049i	0.367157	+	0.0543549i
$79$		−	11.1917i		−	1.25917i	−0.776932	−	0.629584i	$-0.783225\pi$
$79$		−	11.1917i		−	1.25917i	0.776932	−	0.629584i	$-0.216775\pi$
$80$	10.0800	+	6.71852i	1.12698	+	0.751154i
$81$	4.07107			0.452341
$82$	−9.89630	−	1.46508i	−1.09286	−	0.161791i
$83$		−	9.23880i		−	1.01409i	−0.861920	−	0.507045i	$-0.830738\pi$
$83$		−	9.23880i		−	1.01409i	0.861920	−	0.507045i	$-0.169262\pi$
$84$		0			0
$85$		−	13.5096i		−	1.46532i
$86$	−0.535534	+	3.61743i	−0.0577481	+	0.390077i
$87$	4.28289			0.459174
$88$	5.12132	−	10.8523i	0.545935	−	1.15686i
$89$			2.48181i			0.263071i	0.991311	+	0.131536i	$0.0419908\pi$
$89$			2.48181i			0.263071i	−0.991311	+	0.131536i	$0.958009\pi$
$90$	−1.51423	+	10.2283i	−0.159614	+	1.07816i
$91$		0			0
$92$	3.24264	−	10.7117i	0.338069	−	1.11677i
$93$		−	7.91375i		−	0.820618i
$94$	1.25443	−	8.47343i	0.129385	−	0.873967i
$95$			10.2316i			1.04974i
$96$	−3.21217	−	2.90295i	−0.327840	−	0.296282i
$97$		−	6.88830i		−	0.699401i	−0.936862	−	0.349701i	$-0.886283\pi$
$97$		−	6.88830i		−	0.699401i	0.936862	−	0.349701i	$-0.113717\pi$
$98$		0			0
$99$	10.2426			1.02942
$100$	−7.98528	−	2.41730i	−0.798528	−	0.241730i
$101$	11.5942			1.15367			0.576835	−	0.816861i	$-0.304288\pi$
$101$	11.5942			1.15367			0.576835	+	0.816861i	$0.304288\pi$
$102$	−0.707107	+	4.77637i	−0.0700140	+	0.472931i
$103$	−4.28289			−0.422006			−0.211003	−	0.977485i	$-0.567673\pi$
$103$	−4.28289			−0.422006			−0.211003	+	0.977485i	$0.567673\pi$
$104$	−3.65568	+	7.74652i	−0.358468	+	0.759609i
$105$		0			0
$106$	4.58579	+	0.678892i	0.445411	+	0.0659398i
$107$	−3.31371			−0.320348			−0.160174	−	0.987089i	$-0.551206\pi$
$107$	−3.31371			−0.320348			−0.160174	+	0.987089i	$0.551206\pi$
$108$	2.40125	−	7.93223i	0.231060	−	0.763279i
$109$		−	5.59587i		−	0.535987i	−0.963421	−	0.267993i	$-0.913639\pi$
$109$		−	5.59587i		−	0.535987i	0.963421	−	0.267993i	$-0.0863605\pi$
$110$	−2.66105	+	17.9749i	−0.253721	+	1.71384i
$111$	1.77403			0.168384
$112$		0			0
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$	0.535534	−	3.61743i	0.0501573	−	0.338803i
$115$			16.9469i			1.58030i
$116$	−3.24264	+	10.7117i	−0.301072	+	0.994555i
$117$	−7.31135			−0.675935
$118$	15.0662	+	2.23044i	1.38696	+	0.205329i
$119$		0			0
$120$	5.92893	+	2.79793i	0.541235	+	0.255415i
$121$	7.00000			0.636364
$122$	−1.51423	+	10.2283i	−0.137092	+	0.926030i
$123$	−5.41421			−0.488183
$124$	19.7926	+	5.99162i	1.77743	+	0.538063i
$125$	−2.50886			−0.224399
$126$		0			0
$127$		−	0.960099i		−	0.0851950i	−0.999092	−	0.0425975i	$-0.986437\pi$
$127$		−	0.960099i		−	0.0851950i	0.999092	−	0.0425975i	$-0.0135633\pi$
$128$	9.69239	−	5.83589i	0.856694	−	0.515825i
$129$			1.97908i			0.174248i
$130$	1.89949	−	12.8307i	0.166597	−	1.12533i
$131$		−	6.88830i		−	0.601834i	−0.953650	−	0.300917i	$-0.902707\pi$
$131$		−	6.88830i		−	0.601834i	0.953650	−	0.300917i	$-0.0972927\pi$
$132$	1.88164	−	6.21579i	0.163776	−	0.541015i
$133$		0			0
$134$	0.414214	−	2.79793i	0.0357826	−	0.241705i
$135$			12.5495i			1.08009i
$136$	−11.4105	−	5.38476i	−0.978445	−	0.461740i
$137$	−19.5563			−1.67081			−0.835406	−	0.549634i	$-0.814767\pi$
$137$	−19.5563			−1.67081			−0.835406	+	0.549634i	$0.814767\pi$
$138$	0.887016	−	5.99162i	0.0755078	−	0.510040i
$139$			1.66205i			0.140973i	0.997513	+	0.0704866i	$0.0224552\pi$
$139$			1.66205i			0.140973i	−0.997513	+	0.0704866i	$0.977545\pi$
$140$		0			0
$141$		−	4.63577i		−	0.390402i
$142$	−20.2426	−	2.99678i	−1.69872	−	0.251484i
$143$	−12.8487			−1.07446
$144$	8.03553	+	5.35584i	0.669628	+	0.446320i
$145$		−	16.9469i		−	1.40736i
$146$	−4.72640	−	0.699709i	−0.391159	−	0.0579083i
$147$		0			0
$148$	−1.34315	+	4.43692i	−0.110406	+	0.364713i
$149$			4.63577i			0.379777i	0.981806	+	0.189888i	$0.0608126\pi$
$149$			4.63577i			0.379777i	−0.981806	+	0.189888i	$0.939187\pi$
$150$	−4.46660	−	0.661247i	−0.364696	−	0.0539906i
$151$		−	10.2316i		−	0.832638i	−0.909219	−	0.416319i	$-0.863320\pi$
$151$		−	10.2316i		−	0.832638i	0.909219	−	0.416319i	$-0.136680\pi$
$152$	8.64187	+	4.07820i	0.700949	+	0.330786i
$153$		−	10.7695i		−	0.870665i
$154$		0			0
$155$	−31.3137			−2.51518
$156$	−1.34315	+	4.43692i	−0.107538	+	0.355238i
$157$	−7.31135			−0.583509			−0.291755	−	0.956493i	$-0.594239\pi$
$157$	−7.31135			−0.583509			−0.291755	+	0.956493i	$0.594239\pi$
$158$	15.6569	+	2.31788i	1.24559	+	0.184401i
$159$	2.50886			0.198965
$160$	−11.4866	+	12.7101i	−0.908098	+	1.00483i
$161$		0			0
$162$	−0.843146	+	5.69529i	−0.0662438	+	0.447464i
$163$	−5.41421			−0.424074			−0.212037	−	0.977262i	$-0.568010\pi$
$163$	−5.41421			−0.424074			−0.212037	+	0.977262i	$0.568010\pi$
$164$	4.09918	−	13.5412i	0.320092	−	1.05739i
$165$			9.83395i			0.765572i
$166$	12.9248	+	1.91342i	1.00316	+	0.148510i
$167$	−8.56578			−0.662840			−0.331420	−	0.943483i	$-0.607528\pi$
$167$	−8.56578			−0.662840			−0.331420	+	0.943483i	$0.607528\pi$
$168$		0			0
$169$	−3.82843			−0.294494
$170$	18.8995	+	2.79793i	1.44953	+	0.214592i
$171$			8.15640i			0.623736i
$172$	−4.94975	−	1.49839i	−0.377415	−	0.114251i
$173$	−9.82021			−0.746617			−0.373308	−	0.927707i	$-0.621777\pi$
$173$	−9.82021			−0.746617			−0.373308	+	0.927707i	$0.621777\pi$
$174$	−0.887016	+	5.99162i	−0.0672445	+	0.454223i
$175$		0			0
$176$	14.1213	+	9.41214i	1.06443	+	0.709466i
$177$	8.24264			0.619555
$178$	−3.47197	−	0.514000i	−0.260235	−	0.0385259i
$179$	2.34315			0.175135			0.0875675	−	0.996159i	$-0.472091\pi$
$179$	2.34315			0.175135			0.0875675	+	0.996159i	$0.472091\pi$
$180$	−13.9955	−	4.23671i	−1.04316	−	0.315786i
$181$	−9.08538			−0.675311			−0.337656	−	0.941270i	$-0.609634\pi$
$181$	−9.08538			−0.675311			−0.337656	+	0.941270i	$0.609634\pi$
$182$		0			0
$183$			5.59587i			0.413658i
$184$	14.3137	+	6.75481i	1.05522	+	0.497971i
$185$		−	7.01962i		−	0.516093i
$186$	11.0711	+	1.63899i	0.811770	+	0.120177i
$187$		−	18.9259i		−	1.38400i
$188$	11.5942	+	3.50981i	0.845597	+	0.255979i
$189$		0			0
$190$	−14.3137	−	2.11904i	−1.03843	−	0.153731i
$191$			3.27798i			0.237186i	0.992943	+	0.118593i	$0.0378384\pi$
$191$			3.27798i			0.237186i	−0.992943	+	0.118593i	$0.962162\pi$
$192$	4.72640	−	3.89249i	0.341098	−	0.280916i
$193$	−9.41421			−0.677650			−0.338825	−	0.940849i	$-0.610029\pi$
$193$	−9.41421			−0.677650			−0.338825	+	0.940849i	$0.610029\pi$
$194$	9.63650	+	1.42661i	0.691861	+	0.102425i
$195$		−	7.01962i		−	0.502685i
$196$		0			0
$197$			19.1055i			1.36121i	0.732651	+	0.680605i	$0.238283\pi$
$197$			19.1055i			1.36121i	−0.732651	+	0.680605i	$0.761717\pi$
$198$	−2.12132	+	14.3291i	−0.150756	+	1.01833i
$199$	16.3967			1.16233			0.581167	−	0.813784i	$-0.302596\pi$
$199$	16.3967			1.16233			0.581167	+	0.813784i	$0.302596\pi$
$200$	5.03553	−	10.6705i	0.356066	−	0.754518i
$201$		−	1.53073i		−	0.107970i
$202$	−2.40125	+	16.2200i	−0.168951	+	1.14123i
$203$		0			0
$204$	−6.53553	−	1.97844i	−0.457579	−	0.138518i
$205$			21.4234i			1.49627i
$206$	0.887016	−	5.99162i	0.0618013	−	0.417456i
$207$			13.5096i			0.938983i
$208$	−10.0800	−	6.71852i	−0.698923	−	0.465846i
$209$			14.3337i			0.991485i
$210$		0			0
$211$	18.9706			1.30599			0.652994	−	0.757363i	$-0.273513\pi$
$211$	18.9706			1.30599			0.652994	+	0.757363i	$0.273513\pi$
$212$	−1.89949	+	6.27476i	−0.130458	+	0.430952i
$213$	−11.0746			−0.758822
$214$	0.686292	−	4.63577i	0.0469139	−	0.316894i
$215$	7.83095			0.534066
$216$	10.5996	+	5.00208i	0.721212	+	0.340349i
$217$		0			0
$218$	7.82843	+	1.15894i	0.530208	+	0.0784934i
$219$	−2.58579			−0.174731
$220$	−24.5951	−	7.44543i	−1.65820	−	0.501971i
$221$			13.5096i			0.908755i
$222$	−0.367414	+	2.48181i	−0.0246592	+	0.166568i
$223$	−4.28289			−0.286804			−0.143402	−	0.989665i	$-0.545804\pi$
$223$	−4.28289			−0.286804			−0.143402	+	0.989665i	$0.545804\pi$
$224$		0			0
$225$	10.0711			0.671405
$226$	0.292893	−	1.97844i	0.0194830	−	0.131604i
$227$			4.72352i			0.313511i	0.987637	+	0.156755i	$0.0501034\pi$
$227$			4.72352i			0.313511i	−0.987637	+	0.156755i	$0.949897\pi$
$228$	4.94975	+	1.49839i	0.327805	+	0.0992332i
$229$	24.4429			1.61523			0.807616	−	0.589708i	$-0.200757\pi$
$229$	24.4429			1.61523			0.807616	+	0.589708i	$0.200757\pi$
$230$	−23.7081	−	3.50981i	−1.56326	−	0.231430i
$231$		0			0
$232$	−14.3137	−	6.75481i	−0.939741	−	0.443475i
$233$	−9.89949			−0.648537			−0.324269	−	0.945965i	$-0.605118\pi$
$233$	−9.89949			−0.648537			−0.324269	+	0.945965i	$0.605118\pi$
$234$	1.51423	−	10.2283i	0.0989883	−	0.668647i
$235$	−18.3431			−1.19657
$236$	−6.24063	+	20.6152i	−0.406230	+	1.34193i
$237$	8.56578			0.556407
$238$		0			0
$239$		−	18.1454i		−	1.17373i	−0.809686	−	0.586864i	$-0.800362\pi$
$239$		−	18.1454i		−	1.17373i	0.809686	−	0.586864i	$-0.199638\pi$
$240$	−5.14214	+	7.71491i	−0.331923	+	0.497995i
$241$			18.4232i			1.18674i	0.804929	+	0.593371i	$0.202203\pi$
$241$			18.4232i			1.18674i	−0.804929	+	0.593371i	$0.797797\pi$
$242$	−1.44975	+	9.79276i	−0.0931933	+	0.629503i
$243$			15.5474i			0.997369i
$244$	−13.9955	−	4.23671i	−0.895969	−	0.271228i
$245$		0			0
$246$	1.12132	−	7.57430i	0.0714928	−	0.482920i
$247$		−	10.2316i		−	0.651023i
$248$	−12.4813	+	26.4483i	−0.792561	+	1.67947i
$249$	7.07107			0.448111
$250$	0.519602	−	3.50981i	0.0328625	−	0.221980i
$251$			21.4077i			1.35124i	0.737248	+	0.675622i	$0.236125\pi$
$251$			21.4077i			1.35124i	−0.737248	+	0.675622i	$0.763875\pi$
$252$		0			0
$253$			23.7412i			1.49260i
$254$	1.34315	+	0.198843i	0.0842765	+	0.0124765i
$255$	10.3398			0.647504
$256$	6.15685	+	14.7680i	0.384803	+	0.922999i
$257$		−	10.9552i		−	0.683369i	−0.939815	−	0.341684i	$-0.889003\pi$
$257$		−	10.9552i		−	0.683369i	0.939815	−	0.341684i	$-0.110997\pi$
$258$	−2.76866	−	0.409880i	−0.172369	−	0.0255180i
$259$		0			0
$260$	17.5563	+	5.31466i	1.08880	+	0.329601i
$261$		−	13.5096i		−	0.836224i
$262$	9.63650	+	1.42661i	0.595345	+	0.0881365i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	8.30598	+	3.91969i	0.511198	+	0.241240i
$265$		−	9.92724i		−	0.609825i
$266$		0			0
$267$	−1.89949			−0.116247
$268$	3.82843	+	1.15894i	0.233858	+	0.0707936i
$269$	−5.53732			−0.337616			−0.168808	−	0.985649i	$-0.553992\pi$
$269$	−5.53732			−0.337616			−0.168808	+	0.985649i	$0.553992\pi$
$270$	−17.5563	−	2.59909i	−1.06845	−	0.158176i
$271$	1.77403			0.107765			0.0538824	−	0.998547i	$-0.482840\pi$
$271$	1.77403			0.107765			0.0538824	+	0.998547i	$0.482840\pi$
$272$	9.89630	−	14.8477i	0.600052	−	0.900276i
$273$		0			0
$274$	4.05025	−	27.3587i	0.244685	−	1.65280i
$275$	17.6985			1.06726
$276$	8.19837	+	2.48181i	0.493484	+	0.149387i
$277$		−	9.83395i		−	0.590865i	−0.955364	−	0.295432i	$-0.904536\pi$
$277$		−	9.83395i		−	0.590865i	0.955364	−	0.295432i	$-0.0954637\pi$
$278$	−2.32515	−	0.344222i	−0.139453	−	0.0206451i
$279$	−24.9625			−1.49447
$280$		0			0
$281$	−11.0711			−0.660445			−0.330222	−	0.943903i	$-0.607124\pi$
$281$	−11.0711			−0.660445			−0.330222	+	0.943903i	$0.607124\pi$
$282$	6.48528	+	0.960099i	0.386193	+	0.0571730i
$283$		−	25.8142i		−	1.53450i	−0.641350	−	0.767248i	$-0.721625\pi$
$283$		−	25.8142i		−	1.53450i	0.641350	−	0.767248i	$-0.278375\pi$
$284$	8.38478	−	27.6981i	0.497545	−	1.64358i
$285$	−7.83095			−0.463866
$286$	2.66105	−	17.9749i	0.157351	−	1.06288i
$287$		0			0
$288$	−9.15685	+	10.1322i	−0.539573	+	0.597046i
$289$	−2.89949			−0.170559
$290$	23.7081	+	3.50981i	1.39219	+	0.206103i
$291$	5.27208			0.309055
$292$	1.95774	−	6.46716i	0.114568	−	0.378462i
$293$	29.7650			1.73889			0.869445	−	0.494030i	$-0.164477\pi$
$293$	29.7650			1.73889			0.869445	+	0.494030i	$0.164477\pi$
$294$		0			0
$295$		−	32.6151i		−	1.89892i
$296$	−5.92893	−	2.79793i	−0.344612	−	0.162627i
$297$			17.5809i			1.02015i
$298$	−6.48528	−	0.960099i	−0.375682	−	0.0556170i
$299$		−	16.9469i		−	0.980062i
$300$	1.85012	−	6.11167i	0.106817	−	0.352857i
$301$		0			0
$302$	14.3137	+	2.11904i	0.823661	+	0.121937i
$303$			8.87385i			0.509789i
$304$	−7.49506	+	11.2451i	−0.429871	+	0.644949i
$305$	22.1421			1.26785
$306$	15.0662	+	2.23044i	0.861278	+	0.127506i
$307$		−	23.2011i		−	1.32416i	−0.749434	−	0.662079i	$-0.769674\pi$
$307$		−	23.2011i		−	1.32416i	0.749434	−	0.662079i	$-0.230326\pi$
$308$		0			0
$309$		−	3.27798i		−	0.186478i
$310$	6.48528	−	43.8068i	0.368339	−	2.48806i
$311$	−3.54806			−0.201192			−0.100596	−	0.994927i	$-0.532075\pi$
$311$	−3.54806			−0.201192			−0.100596	+	0.994927i	$0.532075\pi$
$312$	−5.92893	−	2.79793i	−0.335660	−	0.158402i
$313$			34.7360i			1.96340i	0.190447	+	0.981698i	$0.439006\pi$
$313$			34.7360i			1.96340i	−0.190447	+	0.981698i	$0.560994\pi$
$314$	1.51423	−	10.2283i	0.0854530	−	0.577218i
$315$		0			0
$316$	−6.48528	+	21.4234i	−0.364826	+	1.20516i
$317$		−	15.8275i		−	0.888961i	−0.895789	−	0.444480i	$-0.853388\pi$
$317$		−	15.8275i		−	0.888961i	0.895789	−	0.444480i	$-0.146612\pi$
$318$	−0.519602	+	3.50981i	−0.0291378	+	0.196820i
$319$		−	23.7412i		−	1.32925i
$320$	−15.4021	−	18.7018i	−0.861004	−	1.04546i
$321$		−	2.53620i		−	0.141557i
$322$		0			0
$323$	15.0711			0.838577
$324$	−7.79289	−	2.35907i	−0.432939	−	0.131059i
$325$	−12.6334			−0.700777
$326$	1.12132	−	7.57430i	0.0621042	−	0.419502i
$327$	4.28289			0.236844
$328$	18.0947	+	8.53909i	0.999111	+	0.471492i
$329$		0			0
$330$	−13.7574	−	2.03668i	−0.757318	−	0.112115i
$331$	−3.07107			−0.168801			−0.0844006	−	0.996432i	$-0.526898\pi$
$331$	−3.07107			−0.168801			−0.0844006	+	0.996432i	$0.526898\pi$
$332$	−5.35361	+	17.6850i	−0.293818	+	0.970592i
$333$		−	5.59587i		−	0.306652i
$334$	1.77403	−	11.9832i	0.0970707	−	0.655694i
$335$	−6.05692			−0.330925
$336$		0			0
$337$	14.1421			0.770371			0.385186	−	0.922839i	$-0.374137\pi$
$337$	14.1421			0.770371			0.385186	+	0.922839i	$0.374137\pi$
$338$	0.792893	−	5.35584i	0.0431277	−	0.291319i
$339$		−	1.08239i		−	0.0587875i
$340$	−7.82843	+	25.8603i	−0.424556	+	1.40247i
$341$	−43.8681			−2.37559
$342$	−11.4105	−	1.68925i	−0.617011	−	0.0913440i
$343$		0			0
$344$	3.12132	−	6.61420i	0.168290	−	0.356614i
$345$	−12.9706			−0.698312
$346$	2.03383	−	13.7381i	0.109339	−	0.738567i
$347$	3.75736			0.201706			0.100853	−	0.994901i	$-0.467843\pi$
$347$	3.75736			0.201706			0.100853	+	0.994901i	$0.467843\pi$
$348$	−8.19837	−	2.48181i	−0.439479	−	0.133039i
$349$	5.53732			0.296406			0.148203	−	0.988957i	$-0.452651\pi$
$349$	5.53732			0.296406			0.148203	+	0.988957i	$0.452651\pi$
$350$		0			0
$351$		−	12.5495i		−	0.669844i
$352$	−16.0919	+	17.8059i	−0.857700	+	0.949059i
$353$		−	21.8561i		−	1.16328i	−0.813446	−	0.581641i	$-0.802411\pi$
$353$		−	21.8561i		−	1.16328i	0.813446	−	0.581641i	$-0.197589\pi$
$354$	−1.70711	+	11.5312i	−0.0907317	+	0.612875i
$355$			43.8210i			2.32577i
$356$	1.43814	−	4.75071i	0.0762211	−	0.251787i
$357$		0			0
$358$	−0.485281	+	3.27798i	−0.0256479	+	0.173247i
$359$		−	18.1454i		−	0.957677i	−0.877903	−	0.478838i	$-0.841058\pi$
$359$		−	18.1454i		−	0.957677i	0.877903	−	0.478838i	$-0.158942\pi$
$360$	8.82558	−	18.7018i	0.465149	−	0.985669i
$361$	7.58579			0.399252
$362$	1.88164	−	12.7101i	0.0988970	−	0.668030i
$363$			5.35757i			0.281199i
$364$		0			0
$365$			10.2316i			0.535548i
$366$	−7.82843	−	1.15894i	−0.409198	−	0.0605789i
$367$	36.0372			1.88112			0.940562	−	0.339622i	$-0.110299\pi$
$367$	36.0372			1.88112			0.940562	+	0.339622i	$0.110299\pi$
$368$	−12.4142	+	18.6254i	−0.647136	+	0.970918i
$369$			17.0782i			0.889054i
$370$	9.82021	+	1.45381i	0.510528	+	0.0755800i
$371$		0			0
$372$	−4.58579	+	15.1486i	−0.237762	+	0.785419i
$373$			31.6550i			1.63903i	0.573055	+	0.819517i	$0.305758\pi$
$373$			31.6550i			1.63903i	−0.573055	+	0.819517i	$0.694242\pi$
$374$	26.4767	+	3.91969i	1.36908	+	0.202682i
$375$		−	1.92020i		−	0.0991586i
$376$	−7.31135	+	15.4930i	−0.377054	+	0.798993i
$377$			16.9469i			0.872808i
$378$		0			0
$379$	−26.3848			−1.35529			−0.677647	−	0.735387i	$-0.737000\pi$
$379$	−26.3848			−1.35529			−0.677647	+	0.735387i	$0.737000\pi$
$380$	5.92893	−	19.5855i	0.304148	−	1.00472i
$381$	0.734828			0.0376464
$382$	−4.58579	−	0.678892i	−0.234629	−	0.0347352i
$383$	9.60498			0.490792			0.245396	−	0.969423i	$-0.421082\pi$
$383$	9.60498			0.490792			0.245396	+	0.969423i	$0.421082\pi$
$384$	4.46660	+	7.41823i	0.227935	+	0.378560i
$385$		0			0
$386$	1.94975	−	13.1702i	0.0992395	−	0.670344i
$387$	6.24264			0.317331
$388$	−3.99157	+	13.1857i	−0.202641	+	0.669402i
$389$			0.960099i			0.0486789i	0.999704	+	0.0243395i	$0.00774826\pi$
$389$			0.960099i			0.0486789i	−0.999704	+	0.0243395i	$0.992252\pi$
$390$	9.82021	+	1.45381i	0.497266	+	0.0736166i
$391$	24.9625			1.26241
$392$		0			0
$393$	5.27208			0.265941
$394$	−26.7279	−	3.95687i	−1.34653	−	0.199344i
$395$		−	33.8937i		−	1.70538i
$396$	−19.6066	−	5.93531i	−0.985269	−	0.298261i
$397$	3.76329			0.188874			0.0944370	−	0.995531i	$-0.469895\pi$
$397$	3.76329			0.188874			0.0944370	+	0.995531i	$0.469895\pi$
$398$	−3.39587	+	22.9385i	−0.170220	+	1.14980i
$399$		0			0
$400$	13.8848	+	9.25448i	0.694239	+	0.462724i
$401$	16.1421			0.806100			0.403050	−	0.915178i	$-0.367950\pi$
$401$	16.1421			0.806100			0.403050	+	0.915178i	$0.367950\pi$
$402$	2.14144	+	0.317025i	0.106806	+	0.0158118i
$403$	31.3137			1.55985
$404$	−22.1939	−	6.71852i	−1.10419	−	0.334259i
$405$	12.3291			0.612636
$406$		0			0
$407$		−	9.83395i		−	0.487451i
$408$	4.12132	−	8.73324i	0.204036	−	0.432360i
$409$		−	25.7373i		−	1.27263i	−0.771430	−	0.636314i	$-0.780458\pi$
$409$		−	25.7373i		−	1.27263i	0.771430	−	0.636314i	$-0.219542\pi$
$410$	−29.9706	−	4.43692i	−1.48014	−	0.219124i
$411$		−	14.9678i		−	0.738306i
$412$	8.19837	+	2.48181i	0.403904	+	0.122270i
$413$		0			0
$414$	−18.8995	−	2.79793i	−0.928860	−	0.137511i
$415$		−	27.9793i		−	1.37345i
$416$	11.4866	−	12.7101i	0.563178	−	0.623166i
$417$	−1.27208			−0.0622939
$418$	−20.0524	−	2.96861i	−0.980795	−	0.145200i
$419$			24.0209i			1.17350i	0.809770	+	0.586748i	$0.199592\pi$
$419$			24.0209i			1.17350i	−0.809770	+	0.586748i	$0.800408\pi$
$420$		0			0
$421$			30.2972i			1.47660i	0.674475	+	0.738298i	$0.264370\pi$
$421$			30.2972i			1.47660i	−0.674475	+	0.738298i	$0.735630\pi$
$422$	−3.92893	+	26.5392i	−0.191257	+	1.29191i
$423$	−14.6227			−0.710980
$424$	−8.38478	−	3.95687i	−0.407201	−	0.192163i
$425$		−	18.6089i		−	0.902665i
$426$	2.29363	−	15.4930i	0.111127	−	0.750641i
$427$		0			0
$428$	6.34315	+	1.92020i	0.306608	+	0.0928162i
$429$		−	9.83395i		−	0.474787i
$430$	−1.62184	+	10.9552i	−0.0782122	+	0.528308i
$431$		−	20.0656i		−	0.966525i	−0.875476	−	0.483262i	$-0.839452\pi$
$431$		−	20.0656i		−	0.966525i	0.875476	−	0.483262i	$-0.160548\pi$
$432$	−9.19299	+	13.7925i	−0.442298	+	0.663594i
$433$		−	3.19278i		−	0.153435i	−0.997053	−	0.0767177i	$-0.975556\pi$
$433$		−	3.19278i		−	0.153435i	0.997053	−	0.0767177i	$-0.0244440\pi$
$434$		0			0
$435$	12.9706			0.621891
$436$	−3.24264	+	10.7117i	−0.155294	+	0.512996i
$437$	−18.9056			−0.904377
$438$	0.535534	−	3.61743i	0.0255888	−	0.172847i
$439$	−5.32209			−0.254010			−0.127005	−	0.991902i	$-0.540536\pi$
$439$	−5.32209			−0.254010			−0.127005	+	0.991902i	$0.540536\pi$
$440$	15.5097	−	32.8657i	0.739397	−	1.56681i
$441$		0			0
$442$	−18.8995	−	2.79793i	−0.898957	−	0.133084i
$443$	−34.9706			−1.66150			−0.830751	−	0.556645i	$-0.812089\pi$
$443$	−34.9706			−1.66150			−0.830751	+	0.556645i	$0.812089\pi$
$444$	−3.39587	−	1.02800i	−0.161161	−	0.0487867i
$445$			7.51606i			0.356296i
$446$	0.887016	−	5.99162i	0.0420014	−	0.283711i
$447$	−3.54806			−0.167818
$448$		0			0
$449$	−20.2843			−0.957274			−0.478637	−	0.878013i	$-0.658869\pi$
$449$	−20.2843			−0.957274			−0.478637	+	0.878013i	$0.658869\pi$
$450$	−2.08579	+	14.0891i	−0.0983249	+	0.664166i
$451$			30.0125i			1.41323i
$452$	2.70711	+	0.819496i	0.127332	+	0.0385458i
$453$	7.83095			0.367930
$454$	−6.60804	−	0.978272i	−0.310131	−	0.0459126i
$455$		0			0
$456$	−3.12132	+	6.61420i	−0.146169	+	0.309738i
$457$	24.0416			1.12462			0.562310	−	0.826927i	$-0.309913\pi$
$457$	24.0416			1.12462			0.562310	+	0.826927i	$0.309913\pi$
$458$	−5.06229	+	34.1948i	−0.236545	+	1.59782i
$459$	18.4853			0.862819
$460$	9.82021	−	32.4399i	0.457870	−	1.51252i
$461$	14.1031			0.656847			0.328423	−	0.944531i	$-0.393483\pi$
$461$	14.1031			0.656847			0.328423	+	0.944531i	$0.393483\pi$
$462$		0			0
$463$			23.7412i			1.10335i	0.834059	+	0.551675i	$0.186011\pi$
$463$			23.7412i			1.10335i	−0.834059	+	0.551675i	$0.813989\pi$
$464$	12.4142	−	18.6254i	0.576315	−	0.864664i
$465$		−	23.9665i		−	1.11142i
$466$	2.05025	−	13.8491i	0.0949761	−	0.641545i
$467$			5.28064i			0.244359i	0.992508	+	0.122180i	$0.0389884\pi$
$467$			5.28064i			0.244359i	−0.992508	+	0.122180i	$0.961012\pi$
$468$	13.9955	+	4.23671i	0.646942	+	0.195842i
$469$		0			0
$470$	3.79899	−	25.6614i	0.175234	−	1.18367i
$471$		−	5.59587i		−	0.257844i
$472$	−27.5475	−	13.0000i	−1.26797	−	0.598372i
$473$	10.9706			0.504427
$474$	−1.77403	+	11.9832i	−0.0814839	+	0.550408i
$475$			14.0936i			0.646660i
$476$		0			0
$477$		−	7.91375i		−	0.362346i
$478$	25.3848	+	3.75803i	1.16107	+	0.171888i
$479$	18.9056			0.863818			0.431909	−	0.901917i	$-0.357840\pi$
$479$	18.9056			0.863818			0.431909	+	0.901917i	$0.357840\pi$
$480$	−9.72792	−	8.79148i	−0.444017	−	0.401275i
$481$			7.01962i			0.320067i
$482$	−25.7734	−	3.81557i	−1.17395	−	0.173794i
$483$		0			0
$484$	−13.3995	−	4.05630i	−0.609068	−	0.184377i
$485$		−	20.8609i		−	0.947247i
$486$	−21.7503	−	3.21998i	−0.986616	−	0.146061i
$487$			33.9729i			1.53946i	0.638371	+	0.769729i	$0.279609\pi$
$487$			33.9729i			1.53946i	−0.638371	+	0.769729i	$0.720391\pi$
$488$	8.82558	−	18.7018i	0.399515	−	0.846589i
$489$		−	4.14386i		−	0.187392i
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	10.3640	+	3.13738i	0.467243	+	0.141444i
$493$	−24.9625			−1.12425
$494$	14.3137	+	2.11904i	0.644004	+	0.0953401i
$495$	31.0194			1.39422
$496$	−34.4153	−	22.9385i	−1.54529	−	1.02997i
$497$		0			0
$498$	−1.46447	+	9.89219i	−0.0656243	+	0.443279i
$499$	4.62742			0.207152			0.103576	−	0.994622i	$-0.466972\pi$
$499$	4.62742			0.207152			0.103576	+	0.994622i	$0.466972\pi$
$500$	4.80249	+	1.45381i	0.214774	+	0.0650164i
$501$		−	6.55596i		−	0.292899i
$502$	−29.9487	−	4.43369i	−1.33668	−	0.197885i
$503$	−15.3575			−0.684758			−0.342379	−	0.939562i	$-0.611233\pi$
$503$	−15.3575			−0.684758			−0.342379	+	0.939562i	$0.611233\pi$
$504$		0			0
$505$	35.1127			1.56249
$506$	−33.2132	−	4.91697i	−1.47651	−	0.218586i
$507$		−	2.93015i		−	0.130133i
$508$	−0.556349	+	1.83783i	−0.0246840	+	0.0815407i
$509$	13.3683			0.592538			0.296269	−	0.955105i	$-0.404257\pi$
$509$	13.3683			0.592538			0.296269	+	0.955105i	$0.404257\pi$
$510$	−2.14144	+	14.4650i	−0.0948248	+	0.640523i
$511$		0			0
$512$	−21.9350	+	5.55468i	−0.969400	+	0.245485i
$513$	−14.0000			−0.618115
$514$	15.3260	+	2.26890i	0.676001	+	0.100077i
$515$	−12.9706			−0.571551
$516$	1.14682	−	3.78837i	0.0504858	−	0.166774i
$517$	−25.6973			−1.13017
$518$		0			0
$519$		−	7.51606i		−	0.329919i
$520$	−11.0711	+	23.4600i	−0.485498	+	1.02879i
$521$			10.2124i			0.447413i	0.974657	+	0.223707i	$0.0718158\pi$
$521$			10.2124i			0.447413i	−0.974657	+	0.223707i	$0.928184\pi$
$522$	18.8995	+	2.79793i	0.827208	+	0.122462i
$523$			5.99162i			0.261995i	0.991383	+	0.130998i	$0.0418180\pi$
$523$			5.99162i			0.261995i	−0.991383	+	0.130998i	$0.958182\pi$
$524$	−3.99157	+	13.1857i	−0.174373	+	0.576019i
$525$		0			0
$526$		0			0
$527$			46.1247i			2.00922i
$528$	−7.20374	+	10.8080i	−0.313502	+	0.470357i
$529$	−8.31371			−0.361466
$530$	13.8879	+	2.05600i	0.603251	+	0.0893069i
$531$		−	25.9999i		−	1.12830i
$532$		0			0
$533$		−	21.4234i		−	0.927949i
$534$	0.393398	−	2.65733i	0.0170240	−	0.114994i
$535$	−10.0354			−0.433870
$536$	−2.41421	+	5.11582i	−0.104278	+	0.220970i
$537$			1.79337i			0.0773895i
$538$	1.14682	−	7.74652i	0.0494428	−	0.333976i
$539$		0			0
$540$	7.27208	−	24.0225i	0.312940	−	1.03376i
$541$			30.2972i			1.30258i	0.758829	+	0.651289i	$0.225772\pi$
$541$			30.2972i			1.30258i	−0.758829	+	0.651289i	$0.774228\pi$
$542$	−0.367414	+	2.48181i	−0.0157818	+	0.106603i
$543$		−	6.95365i		−	0.298410i
$544$	18.7219	+	16.9197i	0.802694	+	0.725424i
$545$		−	16.9469i		−	0.725924i
$546$		0			0
$547$	34.5858			1.47878			0.739391	−	0.673277i	$-0.235114\pi$
$547$	34.5858			1.47878			0.739391	+	0.673277i	$0.235114\pi$
$548$	37.4350	+	11.3323i	1.59915	+	0.484093i
$549$	17.6512			0.753333
$550$	−3.66548	+	24.7596i	−0.156296	+	1.05575i
$551$	18.9056			0.805405
$552$	−5.16991	+	10.9552i	−0.220046	+	0.466286i
$553$		0			0
$554$	13.7574	+	2.03668i	0.584494	+	0.0865301i
$555$	5.37258			0.228053
$556$	0.963109	−	3.18152i	0.0408449	−	0.134926i
$557$		−	30.2972i		−	1.28373i	−0.766816	−	0.641867i	$-0.778160\pi$
$557$		−	30.2972i		−	1.28373i	0.766816	−	0.641867i	$-0.221840\pi$
$558$	5.16991	−	34.9217i	0.218860	−	1.47835i
$559$	−7.83095			−0.331214
$560$		0			0
$561$	14.4853			0.611569
$562$	2.29289	−	15.4881i	0.0967199	−	0.653324i
$563$			24.8406i			1.04691i	0.852054	+	0.523454i	$0.175357\pi$
$563$			24.8406i			1.04691i	−0.852054	+	0.523454i	$0.824643\pi$
$564$	−2.68629	+	8.87385i	−0.113113	+	0.373656i
$565$	−4.28289			−0.180183
$566$	36.1132	+	5.34630i	1.51795	+	0.224722i
$567$		0			0
$568$	37.0122	+	17.4665i	1.55300	+	0.732878i
$569$	18.8284			0.789329			0.394664	−	0.918825i	$-0.370861\pi$
$569$	18.8284			0.789329			0.394664	+	0.918825i	$0.370861\pi$
$570$	1.62184	−	10.9552i	0.0679315	−	0.458864i
$571$	2.38478			0.0997998			0.0498999	−	0.998754i	$-0.484110\pi$
$571$	2.38478			0.0997998			0.0498999	+	0.998754i	$0.484110\pi$
$572$	24.5951	+	7.44543i	1.02837	+	0.311309i
$573$	−2.50886			−0.104809
$574$		0			0
$575$			23.3436i			0.973494i
$576$	−12.2782	−	14.9086i	−0.511591	−	0.621191i
$577$			32.4943i			1.35276i	0.736555	+	0.676378i	$0.236451\pi$
$577$			32.4943i			1.35276i	−0.736555	+	0.676378i	$0.763549\pi$
$578$	0.600505	−	4.05630i	0.0249777	−	0.168720i
$579$		−	7.20533i		−	0.299443i
$580$	−9.82021	+	32.4399i	−0.407762	+	1.34699i
$581$		0			0
$582$	−1.09188	+	7.37546i	−0.0452600	+	0.305723i
$583$		−	13.9073i		−	0.575982i
$584$	8.64187	+	4.07820i	0.357603	+	0.168757i
$585$	−22.1421			−0.915465
$586$	−6.16453	+	41.6402i	−0.254655	+	1.72014i
$587$			38.8799i			1.60474i	0.596824	+	0.802372i	$0.296429\pi$
$587$			38.8799i			1.60474i	−0.596824	+	0.802372i	$0.703571\pi$
$588$		0			0
$589$		−	34.9330i		−	1.43939i
$590$	45.6274	+	6.75481i	1.87845	+	0.278091i
$591$	−14.6227			−0.601498
$592$	5.14214	−	7.71491i	0.211340	−	0.317081i
$593$			19.1660i			0.787055i	0.919313	+	0.393527i	$0.128745\pi$
$593$			19.1660i			0.787055i	−0.919313	+	0.393527i	$0.871255\pi$
$594$	−24.5951	−	3.64113i	−1.00915	−	0.149397i
$595$		0			0
$596$	2.68629	−	8.87385i	0.110035	−	0.363487i
$597$			12.5495i			0.513617i
$598$	23.7081	+	3.50981i	0.969496	+	0.143527i
$599$			30.2972i			1.23791i	0.785426	+	0.618955i	$0.212444\pi$
$599$			30.2972i			1.23791i	−0.785426	+	0.618955i	$0.787556\pi$
$600$	8.16685	+	3.85403i	0.333410	+	0.157340i
$601$			43.5809i			1.77770i	0.458198	+	0.888850i	$0.348495\pi$
$601$			43.5809i			1.77770i	−0.458198	+	0.888850i	$0.651505\pi$
$602$		0			0
$603$	−4.82843			−0.196629
$604$	−5.92893	+	19.5855i	−0.241245	+	0.796924i
$605$	21.1992			0.861871
$606$	−12.4142	−	1.83783i	−0.504293	−	0.0746569i
$607$	−40.3200			−1.63654			−0.818270	−	0.574834i	$-0.805067\pi$
$607$	−40.3200			−1.63654			−0.818270	+	0.574834i	$0.805067\pi$
$608$	−14.1792	−	12.8143i	−0.575042	−	0.519687i
$609$		0			0
$610$	−4.58579	+	30.9761i	−0.185673	+	1.25419i
$611$	18.3431			0.742084
$612$	−6.24063	+	20.6152i	−0.252262	+	0.833319i
$613$			42.4490i			1.71450i	0.514900	+	0.857250i	$0.327829\pi$
$613$			42.4490i			1.71450i	−0.514900	+	0.857250i	$0.672171\pi$
$614$	32.4576	+	4.80511i	1.30988	+	0.193918i
$615$	−16.3967			−0.661180
$616$		0			0
$617$	−28.8284			−1.16059			−0.580294	−	0.814407i	$-0.697063\pi$
$617$	−28.8284			−1.16059			−0.580294	+	0.814407i	$0.697063\pi$
$618$	4.58579	+	0.678892i	0.184467	+	0.0273091i
$619$		−	20.4023i		−	0.820037i	−0.912077	−	0.410018i	$-0.865522\pi$
$619$		−	20.4023i		−	0.820037i	0.912077	−	0.410018i	$-0.134478\pi$
$620$	59.9411	+	18.1454i	2.40729	+	0.728736i
$621$	−23.1885			−0.930522
$622$	0.734828	−	4.96362i	0.0294639	−	0.199023i
$623$		0			0
$624$	5.14214	−	7.71491i	0.205850	−	0.308843i
$625$	−28.4558			−1.13823
$626$	−48.5945	−	7.19406i	−1.94223	−	0.287533i
$627$	−10.9706			−0.438122
$628$	13.9955	+	4.23671i	0.558481	+	0.169063i
$629$	−10.3398			−0.412275
$630$		0			0
$631$		−	17.1853i		−	0.684135i	−0.939675	−	0.342068i	$-0.888873\pi$
$631$		−	17.1853i		−	0.684135i	0.939675	−	0.342068i	$-0.111127\pi$
$632$	−28.6274	−	13.5096i	−1.13874	−	0.537384i
$633$			14.5194i			0.577096i
$634$	22.1421	+	3.27798i	0.879377	+	0.130185i
$635$		−	2.90762i		−	0.115385i
$636$	−4.80249	−	1.45381i	−0.190431	−	0.0576473i
$637$		0			0
$638$	33.2132	+	4.91697i	1.31492	+	0.194665i
$639$			34.9330i			1.38193i
$640$	29.3530	−	17.6738i	1.16028	−	0.698617i
$641$	−6.14214			−0.242600			−0.121300	−	0.992616i	$-0.538706\pi$
$641$	−6.14214			−0.242600			−0.121300	+	0.992616i	$0.538706\pi$
$642$	3.54806	+	0.525265i	0.140031	+	0.0207305i
$643$		−	49.3324i		−	1.94548i	−0.231901	−	0.972739i	$-0.574495\pi$
$643$		−	49.3324i		−	1.94548i	0.231901	−	0.972739i	$-0.425505\pi$
$644$		0			0
$645$			5.99355i			0.235996i
$646$	−3.12132	+	21.0839i	−0.122807	+	0.829536i
$647$	−34.5675			−1.35899			−0.679494	−	0.733681i	$-0.737801\pi$
$647$	−34.5675			−1.35899			−0.679494	+	0.733681i	$0.737801\pi$
$648$	4.91421	−	10.4134i	0.193049	−	0.409078i
$649$		−	45.6912i		−	1.79354i
$650$	2.61647	−	17.6738i	0.102626	−	0.693222i
$651$		0			0
$652$	10.3640	+	3.13738i	0.405884	+	0.122869i
$653$			4.23808i			0.165849i	0.996556	+	0.0829245i	$0.0264260\pi$
$653$			4.23808i			0.165849i	−0.996556	+	0.0829245i	$0.973574\pi$
$654$	−0.887016	+	5.99162i	−0.0346851	+	0.234291i
$655$		−	20.8609i		−	0.815105i
$656$	−15.6934	+	23.5453i	−0.612725	+	0.919291i
$657$			8.15640i			0.318212i
$658$		0			0
$659$	25.6985			1.00107			0.500535	−	0.865716i	$-0.333137\pi$
$659$	25.6985			1.00107			0.500535	+	0.865716i	$0.333137\pi$
$660$	5.69848	−	18.8243i	0.221813	−	0.732734i
$661$	19.4252			0.755552			0.377776	−	0.925897i	$-0.376689\pi$
$661$	19.4252			0.755552			0.377776	+	0.925897i	$0.376689\pi$
$662$	0.636039	−	4.29632i	0.0247204	−	0.166981i
$663$	−10.3398			−0.401565
$664$	−23.6320	−	11.1522i	−0.917099	−	0.432790i
$665$		0			0
$666$	7.82843	+	1.15894i	0.303345	+	0.0449081i
$667$	31.3137			1.21247
$668$	16.3967	+	4.96362i	0.634409	+	0.192048i
$669$		−	3.27798i		−	0.126734i
$670$	1.25443	−	8.47343i	0.0484628	−	0.327357i
$671$	31.0194			1.19749
$672$		0			0
$673$	−29.8995			−1.15254			−0.576270	−	0.817259i	$-0.695492\pi$
$673$	−29.8995			−1.15254			−0.576270	+	0.817259i	$0.695492\pi$
$674$	−2.92893	+	19.7844i	−0.112818	+	0.762066i
$675$			17.2864i			0.665354i
$676$	7.32843	+	2.21846i	0.281863	+	0.0853255i
$677$	43.3485			1.66602			0.833009	−	0.553259i	$-0.186616\pi$
$677$	43.3485			1.66602			0.833009	+	0.553259i	$0.186616\pi$
$678$	1.51423	+	0.224171i	0.0581537	+	0.00860923i
$679$		0			0
$680$	−34.5563	−	16.3075i	−1.32518	−	0.625366i
$681$	−3.61522			−0.138536
$682$	9.08538	−	61.3700i	0.347897	−	2.34998i
$683$	−50.9706			−1.95033			−0.975167	−	0.221470i	$-0.928915\pi$
$683$	−50.9706			−1.95033			−0.975167	+	0.221470i	$0.928915\pi$
$684$	4.72640	−	15.6131i	0.180718	−	0.596982i
$685$	−59.2256			−2.26290
$686$		0			0
$687$			18.7078i			0.713747i
$688$	8.60660	+	5.73647i	0.328124	+	0.218701i
$689$			9.92724i			0.378198i
$690$	2.68629	−	18.1454i	0.102265	−	0.690783i
$691$		−	30.0669i		−	1.14380i	−0.820324	−	0.571899i	$-0.806207\pi$
$691$		−	30.0669i		−	1.14380i	0.820324	−	0.571899i	$-0.193793\pi$
$692$	18.7980	+	5.69052i	0.714592	+	0.216321i
$693$		0			0
$694$	−0.778175	+	5.25642i	−0.0295391	+	0.199531i
$695$			5.03345i			0.190930i
$696$	5.16991	−	10.9552i	0.195965	−	0.415257i
$697$	31.5563			1.19528
$698$	−1.14682	+	7.74652i	−0.0434076	+	0.293210i
$699$		−	7.57675i		−	0.286579i
$700$		0			0
$701$			16.7876i			0.634059i	0.948416	+	0.317029i	$0.102685\pi$
$701$			16.7876i			0.634059i	−0.948416	+	0.317029i	$0.897315\pi$
$702$	17.5563	+	2.59909i	0.662622	+	0.0980963i
$703$	7.83095			0.295350
$704$	−21.5772	−	26.1997i	−0.813220	−	0.987440i
$705$		−	14.0392i		−	0.528748i
$706$	30.5759	+	4.52654i	1.15074	+	0.170359i
$707$		0			0
$708$	−15.7782	−	4.77637i	−0.592980	−	0.179507i
$709$		−	10.7940i		−	0.405379i	−0.979243	−	0.202689i	$-0.935032\pi$
$709$		−	10.7940i		−	0.405379i	0.979243	−	0.202689i	$-0.0649682\pi$
$710$	−61.3040	−	9.07562i	−2.30070	−	0.340602i
$711$		−	27.0192i		−	1.01330i
$712$	6.34824	+	2.99581i	0.237910	+	0.112273i
$713$		−	57.8602i		−	2.16688i
$714$		0			0
$715$	−38.9117			−1.45521
$716$	−4.48528	−	1.35778i	−0.167623	−	0.0507428i
$717$	13.8879			0.518652
$718$	25.3848	+	3.75803i	0.947351	+	0.140248i
$719$	−12.1138			−0.451770			−0.225885	−	0.974154i	$-0.572527\pi$
$719$	−12.1138			−0.451770			−0.225885	+	0.974154i	$0.572527\pi$
$720$	24.3353	+	16.2200i	0.906923	+	0.604482i
$721$		0			0
$722$	−1.57107	+	10.6123i	−0.0584691	+	0.394947i
$723$	−14.1005			−0.524403
$724$	17.3914	+	5.26471i	0.646345	+	0.195662i
$725$		−	23.3436i		−	0.866958i
$726$	−7.49506	−	1.10959i	−0.278168	−	0.0411807i
$727$	38.8504			1.44088			0.720441	−	0.693517i	$-0.243940\pi$
$727$	38.8504			1.44088			0.720441	+	0.693517i	$0.243940\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$	−14.3137	−	2.11904i	−0.529774	−	0.0784292i
$731$		−	11.5349i		−	0.426634i
$732$	3.24264	−	10.7117i	0.119851	−	0.395915i
$733$	27.2561			1.00673			0.503364	−	0.864074i	$-0.332095\pi$
$733$	27.2561			1.00673			0.503364	+	0.864074i	$0.332095\pi$
$734$	−7.46354	+	50.4148i	−0.275484	+	1.86084i
$735$		0			0
$736$	−23.4853	−	21.2245i	−0.865679	−	0.782346i
$737$	−8.48528			−0.312559
$738$	−23.8918	−	3.53701i	−0.879469	−	0.130199i
$739$	−24.2426			−0.891780			−0.445890	−	0.895088i	$-0.647113\pi$
$739$	−24.2426			−0.891780			−0.445890	+	0.895088i	$0.647113\pi$
$740$	−4.06766	+	13.4370i	−0.149530	+	0.493956i
$741$	7.83095			0.287677
$742$		0			0
$743$			38.6086i			1.41641i	0.706005	+	0.708207i	$0.250496\pi$
$743$			38.6086i			1.41641i	−0.706005	+	0.708207i	$0.749504\pi$
$744$	−20.2426	−	9.55274i	−0.742131	−	0.350220i
$745$			14.0392i			0.514358i
$746$	−44.2843	−	6.55596i	−1.62136	−	0.240031i
$747$		−	22.3044i		−	0.816076i
$748$	−10.9670	+	36.2283i	−0.400994	+	1.32464i
$749$		0			0
$750$	2.68629	+	0.397686i	0.0980895	+	0.0145214i
$751$		−	37.8133i		−	1.37983i	−0.723892	−	0.689913i	$-0.757649\pi$
$751$		−	37.8133i		−	1.37983i	0.723892	−	0.689913i	$-0.242351\pi$
$752$	−20.1600	−	13.4370i	−0.735160	−	0.489999i
$753$	−16.3848			−0.597094
$754$	−23.7081	−	3.50981i	−0.863397	−	0.127820i
$755$		−	30.9861i		−	1.12770i
$756$		0			0
$757$		−	27.4169i		−	0.996485i	−0.867038	−	0.498242i	$-0.833979\pi$
$757$		−	27.4169i		−	0.996485i	0.867038	−	0.498242i	$-0.166021\pi$
$758$	5.46447	−	36.9114i	0.198478	−	1.34068i
$759$	−18.1708			−0.659557
$760$	26.1716	+	12.3507i	0.949343	+	0.448006i
$761$		−	13.9079i		−	0.504162i	−0.967706	−	0.252081i	$-0.918885\pi$
$761$		−	13.9079i		−	0.504162i	0.967706	−	0.252081i	$-0.0811149\pi$
$762$	−0.152188	+	1.02800i	−0.00551318	+	0.0372405i
$763$		0			0
$764$	1.89949	−	6.27476i	0.0687213	−	0.227013i
$765$		−	32.6151i		−	1.17920i
$766$	−1.98926	+	13.4370i	−0.0718748	+	0.485500i
$767$			32.6151i			1.17766i
$768$	−11.3029	+	4.71225i	−0.407859	+	0.170039i
$769$		−	1.21371i		−	0.0437674i	−0.999761	−	0.0218837i	$-0.993034\pi$
$769$		−	1.21371i		−	0.0437674i	0.999761	−	0.0218837i	$-0.00696636\pi$
$770$		0			0
$771$	8.38478			0.301970
$772$	18.0208	+	5.45526i	0.648583	+	0.196339i
$773$	17.6512			0.634868			0.317434	−	0.948280i	$-0.397179\pi$
$773$	17.6512			0.634868			0.317434	+	0.948280i	$0.397179\pi$
$774$	−1.29289	+	8.73324i	−0.0464721	+	0.313910i
$775$	−43.1333			−1.54939
$776$	−17.6196	−	8.31492i	−0.632508	−	0.298488i
$777$		0			0
$778$	−1.34315	−	0.198843i	−0.0481541	−	0.00712887i
$779$	−23.8995			−0.856288
$780$	−4.06766	+	13.4370i	−0.145646	+	0.481123i
$781$			61.3898i			2.19670i
$782$	−5.16991	+	34.9217i	−0.184875	+	1.24880i
$783$	23.1885			0.828689
$784$		0			0
$785$	−22.1421			−0.790287
$786$	−1.09188	+	7.37546i	−0.0389462	+	0.263074i
$787$			6.43996i			0.229560i	0.993391	+	0.114780i	$0.0366163\pi$
$787$			6.43996i			0.229560i	−0.993391	+	0.114780i	$0.963384\pi$
$788$	11.0711	−	36.5720i	0.394390	−	1.30282i
$789$		0			0
$790$	47.4162	+	7.01962i	1.68699	+	0.249747i
$791$		0			0
$792$	12.3640	−	26.1997i	0.439334	−	0.930967i
$793$	−22.1421			−0.786290
$794$	−0.779403	+	5.26471i	−0.0276600	+	0.186838i
$795$	7.59798			0.269473
$796$	−31.3868	−	9.50143i	−1.11248	−	0.336769i
$797$	23.7081			0.839783			0.419892	−	0.907574i	$-0.362068\pi$
$797$	23.7081			0.839783			0.419892	+	0.907574i	$0.362068\pi$
$798$		0			0
$799$			27.0192i			0.955872i
$800$	−15.8223	+	17.5077i	−0.559404	+	0.618990i
$801$			5.99162i			0.211703i
$802$	−3.34315	+	22.5823i	−0.118051	+	0.797409i
$803$			14.3337i			0.505826i
$804$	−0.887016	+	2.93015i	−0.0312826	+	0.103338i
$805$		0			0
$806$	−6.48528	+	43.8068i	−0.228434	+	1.54303i
$807$		−	4.23808i		−	0.149188i
$808$	13.9955	−	29.6570i	0.492359	−	1.04333i
$809$	−35.0711			−1.23303			−0.616517	−	0.787342i	$-0.711457\pi$
$809$	−35.0711			−1.23303			−0.616517	+	0.787342i	$0.711457\pi$
$810$	−2.55343	+	17.2480i	−0.0897185	+	0.606031i
$811$			32.6800i			1.14755i	0.819013	+	0.573775i	$0.194522\pi$
$811$			32.6800i			1.14755i	−0.819013	+	0.573775i	$0.805478\pi$
$812$		0			0
$813$			1.35778i			0.0476196i
$814$	13.7574	+	2.03668i	0.482195	+	0.0713855i
$815$	−16.3967			−0.574352
$816$	11.3640	+	7.57430i	0.397818	+	0.265154i
$817$			8.73606i			0.305636i
$818$	36.0056	+	5.33037i	1.25891	+	0.186372i
$819$		0			0
$820$	12.4142	−	41.0089i	0.433523	−	1.43209i
$821$		−	28.9394i		−	1.00999i	−0.863121	−	0.504996i	$-0.831494\pi$
$821$		−	28.9394i		−	1.00999i	0.863121	−	0.504996i	$-0.168506\pi$
$822$	20.9394	+	3.09993i	0.730346	+	0.108122i
$823$			25.6614i			0.894502i	0.894409	+	0.447251i	$0.147597\pi$
$823$			25.6614i			0.894502i	−0.894409	+	0.447251i	$0.852403\pi$
$824$	−5.16991	+	10.9552i	−0.180102	+	0.381644i
$825$			13.5458i			0.471605i
$826$		0			0
$827$	−1.65685			−0.0576145			−0.0288072	−	0.999585i	$-0.509171\pi$
$827$	−1.65685			−0.0576145			−0.0288072	+	0.999585i	$0.509171\pi$
$828$	7.82843	−	25.8603i	0.272057	−	0.898707i
$829$	26.9518			0.936074			0.468037	−	0.883709i	$-0.344961\pi$
$829$	26.9518			0.936074			0.468037	+	0.883709i	$0.344961\pi$
$830$	39.1421	+	5.79471i	1.35864	+	0.201137i
$831$	7.52658			0.261094
$832$	15.4021	+	18.7018i	0.533972	+	0.648367i
$833$		0			0
$834$	0.263456	−	1.77959i	0.00912273	−	0.0616223i
$835$	−25.9411			−0.897730
$836$	8.30598	−	27.4378i	0.287268	−	0.948957i
$837$		−	42.8467i		−	1.48100i
$838$	−33.6044	−	4.97488i	−1.16084	−	0.171855i
$839$	−16.3967			−0.566078			−0.283039	−	0.959108i	$-0.591343\pi$
$839$	−16.3967			−0.566078			−0.283039	+	0.959108i	$0.591343\pi$
$840$		0			0
$841$	−2.31371			−0.0797831
$842$	−42.3848	−	6.27476i	−1.46068	−	0.216242i
$843$		−	8.47343i		−	0.291840i
$844$	−36.3137	−	10.9929i	−1.24997	−	0.378391i
$845$	−11.5942			−0.398854
$846$	3.02846	−	20.4567i	0.104121	−	0.703315i
$847$		0			0
$848$	7.27208	−	10.9105i	0.249724	−	0.374669i
$849$	19.7574			0.678071
$850$	26.0332	+	3.85403i	0.892933	+	0.132192i
$851$	12.9706			0.444625
$852$	21.1992	+	6.41743i	0.726273	+	0.219858i
$853$	−19.4252			−0.665106			−0.332553	−	0.943085i	$-0.607910\pi$
$853$	−19.4252			−0.665106			−0.332553	+	0.943085i	$0.607910\pi$
$854$		0			0
$855$			24.7013i			0.844768i
$856$	−4.00000	+	8.47616i	−0.136717	+	0.289709i
$857$		−	38.6942i		−	1.32177i	−0.750488	−	0.660884i	$-0.770182\pi$
$857$		−	38.6942i		−	1.32177i	0.750488	−	0.660884i	$-0.229818\pi$
$858$	13.7574	+	2.03668i	0.469669	+	0.0695310i
$859$			3.00707i			0.102600i	0.998683	+	0.0513000i	$0.0163365\pi$
$859$			3.00707i			0.102600i	−0.998683	+	0.0513000i	$0.983664\pi$
$860$	−14.9901	−	4.53781i	−0.511159	−	0.154738i
$861$		0			0
$862$	28.0711	+	4.15572i	0.956104	+	0.141544i
$863$			33.5752i			1.14291i	0.820632	+	0.571456i	$0.193621\pi$
$863$			33.5752i			1.14291i	−0.820632	+	0.571456i	$0.806379\pi$
$864$	−17.3914	−	15.7172i	−0.591666	−	0.534711i
$865$	−29.7401			−1.01119
$866$	4.46660	+	0.661247i	0.151781	+	0.0224701i
$867$		−	2.21918i		−	0.0753672i
$868$		0			0
$869$		−	47.4825i		−	1.61073i
$870$	−2.68629	+	18.1454i	−0.0910738	+	0.615186i
$871$	6.05692			0.205231
$872$	−14.3137	−	6.75481i	−0.484723	−	0.228747i
$873$		−	16.6298i		−	0.562835i
$874$	3.91548	−	26.4483i	0.132443	−	0.894627i
$875$		0			0
$876$	4.94975	+	1.49839i	0.167236	+	0.0506258i
$877$		−	27.9793i		−	0.944795i	−0.881386	−	0.472397i	$-0.843389\pi$
$877$		−	27.9793i		−	0.944795i	0.881386	−	0.472397i	$-0.156611\pi$
$878$	1.10224	−	7.44543i	0.0371989	−	0.251271i
$879$			22.7811i			0.768389i
$880$	42.7659	+	28.5043i	1.44164	+	0.960879i
$881$		−	4.19825i		−	0.141443i	−0.997496	−	0.0707214i	$-0.977470\pi$
$881$		−	4.19825i		−	0.141443i	0.997496	−	0.0707214i	$-0.0225301\pi$
$882$		0			0
$883$	−13.6569			−0.459590			−0.229795	−	0.973239i	$-0.573806\pi$
$883$	−13.6569			−0.459590			−0.229795	+	0.973239i	$0.573806\pi$
$884$	7.82843	−	25.8603i	0.263298	−	0.869776i
$885$	24.9625			0.839106
$886$	7.24264	−	48.9226i	0.243321	−	1.64359i
$887$	−26.7365			−0.897725			−0.448863	−	0.893601i	$-0.648171\pi$
$887$	−26.7365			−0.897725			−0.448863	+	0.893601i	$0.648171\pi$
$888$	2.14144	−	4.53781i	0.0718622	−	0.152279i
$889$		0			0
$890$	−10.5147	−	1.55663i	−0.352454	−	0.0521783i
$891$	17.2721			0.578636
$892$	8.19837	+	2.48181i	0.274502	+	0.0830971i
$893$		−	20.4633i		−	0.684777i
$894$	0.734828	−	4.96362i	0.0245763	−	0.166008i
$895$	7.09612			0.237197
$896$		0			0
$897$	12.9706			0.433074
$898$	4.20101	−	28.3770i	0.140190	−	0.946953i
$899$			57.8602i			1.92975i
$900$	−19.2782	−	5.83589i	−0.642606	−	0.194530i
$901$	−14.6227			−0.487153
$902$	−41.9865	−	6.21579i	−1.39800	−	0.206963i
$903$		0			0
$904$	−1.70711	+	3.61743i	−0.0567775	+	0.120314i
$905$	−27.5147			−0.914620
$906$	−1.62184	+	10.9552i	−0.0538821	+	0.363963i
$907$	36.9706			1.22759			0.613794	−	0.789466i	$-0.289643\pi$
$907$	36.9706			1.22759			0.613794	+	0.789466i	$0.289643\pi$
$908$	2.73714	−	9.04182i	0.0908352	−	0.300063i
$909$	27.9910			0.928402
$910$		0			0
$911$		−	27.9793i		−	0.926996i	−0.886098	−	0.463498i	$-0.846594\pi$
$911$		−	27.9793i		−	0.926996i	0.886098	−	0.463498i	$-0.153406\pi$
$912$	−8.60660	−	5.73647i	−0.284993	−	0.189953i
$913$		−	39.1969i		−	1.29723i
$914$	−4.97918	+	33.6334i	−0.164697	+	1.11250i
$915$			16.9469i			0.560246i
$916$	−46.7889	−	14.1640i	−1.54595	−	0.467990i
$917$		0			0
$918$	−3.82843	+	25.8603i	−0.126357	+	0.853517i
$919$			14.4697i			0.477312i	0.971104	+	0.238656i	$0.0767068\pi$
$919$			14.4697i			0.477312i	−0.971104	+	0.238656i	$0.923293\pi$
$920$	43.3485	+	20.4567i	1.42916	+	0.674436i
$921$	17.7574			0.585125
$922$	−2.92085	+	19.7298i	−0.0961930	+	0.649765i
$923$		−	43.8210i		−	1.44238i
$924$		0			0
$925$		−	9.66922i		−	0.317922i
$926$	−33.2132	−	4.91697i	−1.09145	−	0.161582i
$927$	−10.3398			−0.339604
$928$	23.4853	+	21.2245i	0.770942	+	0.696729i
$929$		−	7.52235i		−	0.246800i	−0.992357	−	0.123400i	$-0.960620\pi$
$929$		−	7.52235i		−	0.246800i	0.992357	−	0.123400i	$-0.0393799\pi$
$930$	33.5283	+	4.96362i	1.09944	+	0.162763i
$931$		0			0
$932$	18.9497	+	5.73647i	0.620720	+	0.187904i
$933$		−	2.71557i		−	0.0889037i
$934$	−7.38744	−	1.09366i	−0.241725	−	0.0357856i
$935$		−	57.3164i		−	1.87445i
$936$	−8.82558	+	18.7018i	−0.288473	+	0.611286i
$937$		−	12.0376i		−	0.393252i	−0.980479	−	0.196626i	$-0.937001\pi$
$937$		−	12.0376i		−	0.393252i	0.980479	−	0.196626i	$-0.0629985\pi$
$938$		0			0
$939$	−26.5858			−0.867594
$940$	35.1127	+	10.6293i	1.14525	+	0.346690i
$941$	16.6120			0.541534			0.270767	−	0.962645i	$-0.412723\pi$
$941$	16.6120			0.541534			0.270767	+	0.962645i	$0.412723\pi$
$942$	7.82843	+	1.15894i	0.255064	+	0.0377604i
$943$	−39.5852			−1.28907
$944$	23.8918	−	35.8456i	0.777612	−	1.16667i
$945$		0			0
$946$	−2.27208	+	15.3474i	−0.0738716	+	0.498989i
$947$	17.2132			0.559354			0.279677	−	0.960094i	$-0.409773\pi$
$947$	17.2132			0.559354			0.279677	+	0.960094i	$0.409773\pi$
$948$	−16.3967	−	4.96362i	−0.532541	−	0.161211i
$949$		−	10.2316i		−	0.332133i
$950$	−19.7165	−	2.91889i	−0.639688	−	0.0947012i
$951$	12.1138			0.392818
$952$		0			0
$953$	50.6274			1.63998			0.819991	−	0.572376i	$-0.193978\pi$
$953$	50.6274			1.63998			0.819991	+	0.572376i	$0.193978\pi$
$954$	11.0711	+	1.63899i	0.358439	+	0.0530643i
$955$			9.92724i			0.321238i
$956$	−10.5147	+	34.7341i	−0.340070	+	1.12338i
$957$	18.1708			0.587377
$958$	−3.91548	+	26.4483i	−0.126503	+	0.854505i
$959$		0			0
$960$	14.3137	−	11.7883i	0.461973	−	0.380464i
$961$	75.9117			2.44876
$962$	−9.82021	−	1.45381i	−0.316616	−	0.0468727i
$963$	−8.00000			−0.257796
$964$	10.6757	−	35.2659i	0.343841	−	1.13584i
$965$	−28.5106			−0.917788
$966$		0			0
$967$			16.7876i			0.539853i	0.962881	+	0.269926i	$0.0869994\pi$
$967$			16.7876i			0.539853i	−0.962881	+	0.269926i	$0.913001\pi$
$968$	8.44975	−	17.9054i	0.271585	−	0.575500i
$969$			11.5349i			0.370554i
$970$	29.1838	+	4.32044i	0.937034	+	0.138721i
$971$			1.47634i			0.0473780i	0.999719	+	0.0236890i	$0.00754115\pi$
$971$			1.47634i			0.0473780i	−0.999719	+	0.0236890i	$0.992459\pi$
$972$	9.00929	−	29.7611i	0.288973	−	0.954588i
$973$		0			0
$974$	−47.5269	−	7.03601i	−1.52286	−	0.225448i
$975$		−	9.66922i		−	0.309663i
$976$	24.3353	+	16.2200i	0.778954	+	0.519188i
$977$	12.2426			0.391677			0.195838	−	0.980636i	$-0.437257\pi$
$977$	12.2426			0.391677			0.195838	+	0.980636i	$0.437257\pi$
$978$	5.79712	+	0.858221i	0.185371	+	0.0274429i
$979$			10.5294i			0.336522i
$980$		0			0
$981$		−	13.5096i		−	0.431329i
$982$	5.38478	−	36.3731i	0.171835	−	1.16071i
$983$	10.3398			0.329789			0.164894	−	0.986311i	$-0.447272\pi$
$983$	10.3398			0.329789			0.164894	+	0.986311i	$0.447272\pi$
$984$	−6.53553	+	13.8491i	−0.208345	+	0.441492i
$985$			57.8602i			1.84358i
$986$	5.16991	−	34.9217i	0.164643	−	1.11213i
$987$		0			0
$988$	−5.92893	+	19.5855i	−0.188624	+	0.623099i
$989$			14.4697i			0.460110i
$990$	−6.42433	+	43.3951i	−0.204179	+	1.37919i
$991$		−	21.0257i		−	0.667903i	−0.942590	−	0.333951i	$-0.891618\pi$
$991$		−	21.0257i		−	0.667903i	0.942590	−	0.333951i	$-0.108382\pi$
$992$	39.2178	−	43.3951i	1.24517	−	1.37780i
$993$		−	2.35049i		−	0.0745907i
$994$		0			0
$995$	49.6569			1.57423
$996$	−13.5355	−	4.09748i	−0.428890	−	0.129834i
$997$	−26.2169			−0.830299			−0.415149	−	0.909753i	$-0.636271\pi$
$997$	−26.2169			−0.830299			−0.415149	+	0.909753i	$0.636271\pi$
$998$	−0.958369	+	6.47360i	−0.0303367	+	0.204918i
$999$	9.60498			0.303888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.e.d.195.4	yes	8
4.3	odd	2		1568.2.e.d.783.4		8
7.2	even	3		392.2.m.h.227.7		16
7.3	odd	6		392.2.m.h.19.3		16
7.4	even	3		392.2.m.h.19.4		16
7.5	odd	6		392.2.m.h.227.8		16
7.6	odd	2	inner	392.2.e.d.195.3	yes	8
8.3	odd	2	inner	392.2.e.d.195.2	yes	8
8.5	even	2		1568.2.e.d.783.3		8
28.3	even	6		1568.2.q.h.1391.6		16
28.11	odd	6		1568.2.q.h.1391.3		16
28.19	even	6		1568.2.q.h.815.4		16
28.23	odd	6		1568.2.q.h.815.5		16
28.27	even	2		1568.2.e.d.783.5		8
56.3	even	6		392.2.m.h.19.7		16
56.5	odd	6		1568.2.q.h.815.3		16
56.11	odd	6		392.2.m.h.19.8		16
56.13	odd	2		1568.2.e.d.783.6		8
56.19	even	6		392.2.m.h.227.4		16
56.27	even	2	inner	392.2.e.d.195.1	✓	8
56.37	even	6		1568.2.q.h.815.6		16
56.45	odd	6		1568.2.q.h.1391.5		16
56.51	odd	6		392.2.m.h.227.3		16
56.53	even	6		1568.2.q.h.1391.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.1	✓	8	56.27	even	2	inner
392.2.e.d.195.2	yes	8	8.3	odd	2	inner
392.2.e.d.195.3	yes	8	7.6	odd	2	inner
392.2.e.d.195.4	yes	8	1.1	even	1	trivial
392.2.m.h.19.3		16	7.3	odd	6
392.2.m.h.19.4		16	7.4	even	3
392.2.m.h.19.7		16	56.3	even	6
392.2.m.h.19.8		16	56.11	odd	6
392.2.m.h.227.3		16	56.51	odd	6
392.2.m.h.227.4		16	56.19	even	6
392.2.m.h.227.7		16	7.2	even	3
392.2.m.h.227.8		16	7.5	odd	6
1568.2.e.d.783.3		8	8.5	even	2
1568.2.e.d.783.4		8	4.3	odd	2
1568.2.e.d.783.5		8	28.27	even	2
1568.2.e.d.783.6		8	56.13	odd	2
1568.2.q.h.815.3		16	56.5	odd	6
1568.2.q.h.815.4		16	28.19	even	6
1568.2.q.h.815.5		16	28.23	odd	6
1568.2.q.h.815.6		16	56.37	even	6
1568.2.q.h.1391.3		16	28.11	odd	6
1568.2.q.h.1391.4		16	56.53	even	6
1568.2.q.h.1391.5		16	56.45	odd	6
1568.2.q.h.1391.6		16	28.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 1.39897i) q^{2} +0.765367i q^{3} +(-1.91421 - 0.579471i) q^{4} +3.02846 q^{5} +(-1.07072 - 0.158513i) q^{6} +(1.20711 - 2.55791i) q^{8} +2.41421 q^{9} +(-0.627215 + 4.23671i) q^{10} +4.24264 q^{11} +(0.443508 - 1.46508i) q^{12} -3.02846 q^{13} +2.31788i q^{15} +(3.32843 + 2.21846i) q^{16} -4.46088i q^{17} +(-0.500000 + 3.37740i) q^{18} +3.37849i q^{19} +(-5.79712 - 1.75490i) q^{20} +(-0.878680 + 5.93531i) q^{22} +5.59587i q^{23} +(1.95774 + 0.923880i) q^{24} +4.17157 q^{25} +(0.627215 - 4.23671i) q^{26} +4.14386i q^{27} -5.59587i q^{29} +(-3.24264 - 0.480049i) q^{30} -10.3398 q^{31} +(-3.79289 + 4.19690i) q^{32} +3.24718i q^{33} +(6.24063 + 0.923880i) q^{34} +(-4.62132 - 1.39897i) q^{36} -2.31788i q^{37} +(-4.72640 - 0.699709i) q^{38} -2.31788i q^{39} +(3.65568 - 7.74652i) q^{40} +7.07401i q^{41} +2.58579 q^{43} +(-8.12132 - 2.45849i) q^{44} +7.31135 q^{45} +(-7.82843 - 1.15894i) q^{46} -6.05692 q^{47} +(-1.69794 + 2.54747i) q^{48} +(-0.863961 + 5.83589i) q^{50} +3.41421 q^{51} +(5.79712 + 1.75490i) q^{52} -3.27798i q^{53} +(-5.79712 - 0.858221i) q^{54} +12.8487 q^{55} -2.58579 q^{57} +(7.82843 + 1.15894i) q^{58} -10.7695i q^{59} +(1.34315 - 4.43692i) q^{60} +7.31135 q^{61} +(2.14144 - 14.4650i) q^{62} +(-5.08579 - 6.17534i) q^{64} -9.17157 q^{65} +(-4.54269 - 0.672512i) q^{66} -2.00000 q^{67} +(-2.58495 + 8.53909i) q^{68} -4.28289 q^{69} +14.4697i q^{71} +(2.91421 - 6.17534i) q^{72} +3.37849i q^{73} +(3.24264 + 0.480049i) q^{74} +3.19278i q^{75} +(1.95774 - 6.46716i) q^{76} +(3.24264 + 0.480049i) q^{78} -11.1917i q^{79} +(10.0800 + 6.71852i) q^{80} +4.07107 q^{81} +(-9.89630 - 1.46508i) q^{82} -9.23880i q^{83} -13.5096i q^{85} +(-0.535534 + 3.61743i) q^{86} +4.28289 q^{87} +(5.12132 - 10.8523i) q^{88} +2.48181i q^{89} +(-1.51423 + 10.2283i) q^{90} +(3.24264 - 10.7117i) q^{92} -7.91375i q^{93} +(1.25443 - 8.47343i) q^{94} +10.2316i q^{95} +(-3.21217 - 2.90295i) q^{96} -6.88830i q^{97} +10.2426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 8 q^{9} + 4 q^{16} - 4 q^{18} - 24 q^{22} + 56 q^{25} + 8 q^{30} - 36 q^{32} - 20 q^{36} + 32 q^{43} - 48 q^{44} - 40 q^{46} + 44 q^{50} + 16 q^{51} - 32 q^{57} + 40 q^{58}+ \cdots + 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 8 * q^9 + 4 * q^16 - 4 * q^18 - 24 * q^22 + 56 * q^25 + 8 * q^30 - 36 * q^32 - 20 * q^36 + 32 * q^43 - 48 * q^44 - 40 * q^46 + 44 * q^50 + 16 * q^51 - 32 * q^57 + 40 * q^58 + 56 * q^60 - 52 * q^64 - 96 * q^65 - 16 * q^67 + 12 * q^72 - 8 * q^74 - 8 * q^78 - 24 * q^81 + 24 * q^86 + 24 * q^88 - 8 * q^92 + 48 * q^99

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