LMFDB - Embedded newform 297.2.f.c.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 35x^{12} + 108x^{10} + 589x^{8} + 792x^{6} + 465x^{4} + 22x^{2} + 121 $ x^16 + 8x^14 + 35x^12 + 108x^10 + 589x^8 + 792x^6 + 465x^4 + 22*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.4
Root			$0.723396 + 2.22638i$ of defining polynomial
Character	$\chi$	$=$	297.136
Dual form			297.2.f.c.190.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89387 + 1.37598i) q^{2} +(1.07540 + 3.30976i) q^{4} +(-2.90288 + 2.10907i) q^{5} +(0.355620 + 1.09448i) q^{7} +(-1.07069 + 3.29523i) q^{8} +O(q^{10})$	\(q+(1.89387 + 1.37598i) q^{2} +(1.07540 + 3.30976i) q^{4} +(-2.90288 + 2.10907i) q^{5} +(0.355620 + 1.09448i) q^{7} +(-1.07069 + 3.29523i) q^{8} -8.39974 q^{10} +(-1.63261 - 2.88697i) q^{11} +(5.13089 + 3.72781i) q^{13} +(-0.832490 + 2.56214i) q^{14} +(-0.931024 + 0.676429i) q^{16} +(3.16415 - 2.29889i) q^{17} +(0.457371 - 1.40764i) q^{19} +(-10.1023 - 7.33973i) q^{20} +(0.880448 - 7.71399i) q^{22} -1.24720 q^{23} +(2.43348 - 7.48948i) q^{25} +(4.58787 + 14.1200i) q^{26} +(-3.24004 + 2.35403i) q^{28} +(1.74091 + 5.35798i) q^{29} +(2.60209 + 1.89053i) q^{31} +4.23563 q^{32} +9.15572 q^{34} +(-3.34067 - 2.42714i) q^{35} +(-3.09812 - 9.53502i) q^{37} +(2.80309 - 2.03656i) q^{38} +(-3.84179 - 11.8238i) q^{40} +(-0.600044 + 1.84675i) q^{41} -9.18338 q^{43} +(7.79944 - 8.50820i) q^{44} +(-2.36205 - 1.71613i) q^{46} +(0.0767256 - 0.236137i) q^{47} +(4.59169 - 3.33606i) q^{49} +(14.9141 - 10.8357i) q^{50} +(-6.82036 + 20.9909i) q^{52} +(-4.71073 - 3.42255i) q^{53} +(10.8281 + 4.93724i) q^{55} -3.98734 q^{56} +(-4.07540 + 12.5428i) q^{58} +(-2.04158 - 6.28333i) q^{59} +(2.66709 - 1.93776i) q^{61} +(2.32670 + 7.16085i) q^{62} +(9.88379 + 7.18099i) q^{64} -22.7566 q^{65} -14.0761 q^{67} +(11.0115 + 8.00032i) q^{68} +(-2.98711 - 9.19338i) q^{70} +(-4.25711 + 3.09297i) q^{71} +(0.683585 + 2.10386i) q^{73} +(7.25256 - 22.3211i) q^{74} +5.15081 q^{76} +(2.57915 - 2.81353i) q^{77} +(2.40070 + 1.74421i) q^{79} +(1.27602 - 3.92719i) q^{80} +(-3.67749 + 2.67186i) q^{82} +(9.46937 - 6.87990i) q^{83} +(-4.33664 + 13.3468i) q^{85} +(-17.3922 - 12.6361i) q^{86} +(11.2612 - 2.28880i) q^{88} +8.93456 q^{89} +(-2.25539 + 6.94137i) q^{91} +(-1.34125 - 4.12794i) q^{92} +(0.470228 - 0.341641i) q^{94} +(1.64112 + 5.05085i) q^{95} +(-7.99937 - 5.81188i) q^{97} +13.2864 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 2 * q^4 + 8 * q^7	$ 16 q + 2 q^{4} + 8 q^{7} - 12 q^{10} + 8 q^{13} - 2 q^{16} + 10 q^{19} - 24 q^{22} - 16 q^{25} - 30 q^{28} - 6 q^{31} + 32 q^{34} + 12 q^{37} - 40 q^{40} - 80 q^{43} - 12 q^{46} + 40 q^{49} + 12 q^{52} + 56 q^{55} - 50 q^{58} - 6 q^{61} + 6 q^{64} + 64 q^{67} + 74 q^{70} - 32 q^{73} + 52 q^{76} - 4 q^{79} + 4 q^{82} + 70 q^{85} + 56 q^{88} - 94 q^{91} - 46 q^{94}+O(q^{100}) $ 16 * q + 2 * q^4 + 8 * q^7 - 12 * q^10 + 8 * q^13 - 2 * q^16 + 10 * q^19 - 24 * q^22 - 16 * q^25 - 30 * q^28 - 6 * q^31 + 32 * q^34 + 12 * q^37 - 40 * q^40 - 80 * q^43 - 12 * q^46 + 40 * q^49 + 12 * q^52 + 56 * q^55 - 50 * q^58 - 6 * q^61 + 6 * q^64 + 64 * q^67 + 74 * q^70 - 32 * q^73 + 52 * q^76 - 4 * q^79 + 4 * q^82 + 70 * q^85 + 56 * q^88 - 94 * q^91 - 46 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.89387	+	1.37598i	1.33917	+	0.972965i	0.999474	+	0.0324303i	$0.0103247\pi$
$2$	1.89387	+	1.37598i	1.33917	+	0.972965i	0.339697	+	0.940535i	$0.389675\pi$
$3$		0			0
$3$		0			0
$4$	1.07540	+	3.30976i	0.537702	+	1.65488i
$5$	−2.90288	+	2.10907i	−1.29821	+	0.943204i	−0.999936	−	0.0112765i	$-0.996411\pi$
$5$	−2.90288	+	2.10907i	−1.29821	+	0.943204i	−0.298273	+	0.954481i	$0.596411\pi$
$6$		0			0
$7$	0.355620	+	1.09448i	0.134412	+	0.413676i	0.995498	−	0.0947823i	$-0.0302155\pi$
$7$	0.355620	+	1.09448i	0.134412	+	0.413676i	−0.861086	+	0.508459i	$0.830215\pi$
$8$	−1.07069	+	3.29523i	−0.378544	+	1.16504i
$9$		0			0
$10$	−8.39974			−2.65623
$11$	−1.63261	−	2.88697i	−0.492251	−	0.870453i
$11$	−1.63261	−	2.88697i	−0.492251	−	0.870453i
$12$		0			0
$13$	5.13089	+	3.72781i	1.42305	+	1.03391i	0.991258	+	0.131937i	$0.0421197\pi$
$13$	5.13089	+	3.72781i	1.42305	+	1.03391i	0.431795	+	0.901972i	$0.357880\pi$
$14$	−0.832490	+	2.56214i	−0.222492	+	0.684761i
$15$		0			0
$16$	−0.931024	+	0.676429i	−0.232756	+	0.169107i
$17$	3.16415	−	2.29889i	0.767418	−	0.557562i	−0.133758	−	0.991014i	$-0.542705\pi$
$17$	3.16415	−	2.29889i	0.767418	−	0.557562i	0.901177	+	0.433452i	$0.142705\pi$
$18$		0			0
$19$	0.457371	−	1.40764i	0.104928	−	0.322935i	−0.884786	−	0.465998i	$-0.845695\pi$
$19$	0.457371	−	1.40764i	0.104928	−	0.322935i	0.989714	+	0.143063i	$0.0456952\pi$
$20$	−10.1023	−	7.33973i	−2.25894	−	1.64121i
$21$		0			0
$22$	0.880448	−	7.71399i	0.187712	−	1.64463i
$23$	−1.24720			−0.260060			−0.130030	−	0.991510i	$-0.541507\pi$
$23$	−1.24720			−0.260060			−0.130030	+	0.991510i	$0.541507\pi$
$24$		0			0
$25$	2.43348	−	7.48948i	0.486696	−	1.49790i
$26$	4.58787	+	14.1200i	0.899755	+	2.76916i
$27$		0			0
$28$	−3.24004	+	2.35403i	−0.612310	+	0.444869i
$29$	1.74091	+	5.35798i	0.323280	+	0.994952i	0.972211	+	0.234105i	$0.0752161\pi$
$29$	1.74091	+	5.35798i	0.323280	+	0.994952i	−0.648932	+	0.760847i	$0.724784\pi$
$30$		0			0
$31$	2.60209	+	1.89053i	0.467349	+	0.339549i	0.796407	−	0.604761i	$-0.206731\pi$
$31$	2.60209	+	1.89053i	0.467349	+	0.339549i	−0.329058	+	0.944310i	$0.606731\pi$
$32$	4.23563			0.748760
$33$		0			0
$34$	9.15572			1.57019
$35$	−3.34067	−	2.42714i	−0.564676	−	0.410261i
$36$		0			0
$37$	−3.09812	−	9.53502i	−0.509327	−	1.56755i	−0.793372	−	0.608737i	$-0.791676\pi$
$37$	−3.09812	−	9.53502i	−0.509327	−	1.56755i	0.284045	−	0.958811i	$-0.408324\pi$
$38$	2.80309	−	2.03656i	0.454721	−	0.330374i
$39$		0			0
$40$	−3.84179	−	11.8238i	−0.607441	−	1.86951i
$41$	−0.600044	+	1.84675i	−0.0937111	+	0.288413i	−0.986916	−	0.161237i	$-0.948452\pi$
$41$	−0.600044	+	1.84675i	−0.0937111	+	0.288413i	0.893205	+	0.449651i	$0.148452\pi$
$42$		0			0
$43$	−9.18338			−1.40045			−0.700226	−	0.713921i	$-0.746917\pi$
$43$	−9.18338			−1.40045			−0.700226	+	0.713921i	$0.746917\pi$
$44$	7.79944	−	8.50820i	1.17581	−	1.28266i
$45$		0			0
$46$	−2.36205	−	1.71613i	−0.348265	−	0.253029i
$47$	0.0767256	−	0.236137i	0.0111916	−	0.0344441i	−0.945305	−	0.326188i	$-0.894236\pi$
$47$	0.0767256	−	0.236137i	0.0111916	−	0.0344441i	0.956496	+	0.291744i	$0.0942356\pi$
$48$		0			0
$49$	4.59169	−	3.33606i	0.655955	−	0.476579i
$50$	14.9141	−	10.8357i	2.10917	−	1.53240i
$51$		0			0
$52$	−6.82036	+	20.9909i	−0.945813	+	2.91091i
$53$	−4.71073	−	3.42255i	−0.647069	−	0.470123i	0.215203	−	0.976569i	$-0.430959\pi$
$53$	−4.71073	−	3.42255i	−0.647069	−	0.470123i	−0.862271	+	0.506446i	$0.830959\pi$
$54$		0			0
$55$	10.8281	+	4.93724i	1.46006	+	0.665737i
$56$	−3.98734			−0.532830
$57$		0			0
$58$	−4.07540	+	12.5428i	−0.535127	+	1.64695i
$59$	−2.04158	−	6.28333i	−0.265791	−	0.818020i	−0.991510	−	0.130029i	$-0.958493\pi$
$59$	−2.04158	−	6.28333i	−0.265791	−	0.818020i	0.725719	−	0.687991i	$-0.241507\pi$
$60$		0			0
$61$	2.66709	−	1.93776i	0.341486	−	0.248104i	−0.403802	−	0.914846i	$-0.632312\pi$
$61$	2.66709	−	1.93776i	0.341486	−	0.248104i	0.745289	+	0.666742i	$0.232312\pi$
$62$	2.32670	+	7.16085i	0.295491	+	0.909429i
$63$		0			0
$64$	9.88379	+	7.18099i	1.23547	+	0.897624i
$65$	−22.7566			−2.82261
$66$		0			0
$67$	−14.0761			−1.71966			−0.859832	−	0.510578i	$-0.829432\pi$
$67$	−14.0761			−1.71966			−0.859832	+	0.510578i	$0.829432\pi$
$68$	11.0115	+	8.00032i	1.33534	+	0.970181i
$69$		0			0
$70$	−2.98711	−	9.19338i	−0.357028	−	1.09882i
$71$	−4.25711	+	3.09297i	−0.505226	+	0.367068i	−0.811009	−	0.585033i	$-0.801082\pi$
$71$	−4.25711	+	3.09297i	−0.505226	+	0.367068i	0.305784	+	0.952101i	$0.401082\pi$
$72$		0			0
$73$	0.683585	+	2.10386i	0.0800075	+	0.246238i	0.983057	−	0.183298i	$-0.0586773\pi$
$73$	0.683585	+	2.10386i	0.0800075	+	0.246238i	−0.903050	+	0.429536i	$0.858677\pi$
$74$	7.25256	−	22.3211i	0.843093	−	2.59477i
$75$		0			0
$76$	5.15081			0.590838
$77$	2.57915	−	2.81353i	0.293922	−	0.320632i
$78$		0			0
$79$	2.40070	+	1.74421i	0.270100	+	0.196239i	0.714588	−	0.699546i	$-0.246614\pi$
$79$	2.40070	+	1.74421i	0.270100	+	0.196239i	−0.444488	+	0.895785i	$0.646614\pi$
$80$	1.27602	−	3.92719i	0.142663	−	0.439073i
$81$		0			0
$82$	−3.67749	+	2.67186i	−0.406111	+	0.295057i
$83$	9.46937	−	6.87990i	1.03940	−	0.755167i	0.0692306	−	0.997601i	$-0.477946\pi$
$83$	9.46937	−	6.87990i	1.03940	−	0.755167i	0.970168	+	0.242433i	$0.0779456\pi$
$84$		0			0
$85$	−4.33664	+	13.3468i	−0.470375	+	1.44766i
$86$	−17.3922	−	12.6361i	−1.87544	−	1.36259i
$87$		0			0
$88$	11.2612	−	2.28880i	1.20045	−	0.243987i
$89$	8.93456			0.947061			0.473531	−	0.880777i	$-0.342979\pi$
$89$	8.93456			0.947061			0.473531	+	0.880777i	$0.342979\pi$
$90$		0			0
$91$	−2.25539	+	6.94137i	−0.236429	+	0.727653i
$92$	−1.34125	−	4.12794i	−0.139835	−	0.430368i
$93$		0			0
$94$	0.470228	−	0.341641i	0.0485004	−	0.0352376i
$95$	1.64112	+	5.05085i	0.168375	+	0.518206i
$96$		0			0
$97$	−7.99937	−	5.81188i	−0.812213	−	0.590107i	0.102258	−	0.994758i	$-0.467393\pi$
$97$	−7.99937	−	5.81188i	−0.812213	−	0.590107i	−0.914471	+	0.404651i	$0.867393\pi$
$98$	13.2864			1.34213
$99$		0			0
$100$	27.4053			2.74053
$101$	6.41432	+	4.66028i	0.638249	+	0.463715i	0.859248	−	0.511559i	$-0.170932\pi$
$101$	6.41432	+	4.66028i	0.638249	+	0.463715i	−0.220999	+	0.975274i	$0.570932\pi$
$102$		0			0
$103$	1.99754	+	6.14781i	0.196824	+	0.605762i	0.999950	+	0.00995321i	$0.00316826\pi$
$103$	1.99754	+	6.14781i	0.196824	+	0.605762i	−0.803127	+	0.595808i	$0.796832\pi$
$104$	−17.7776	+	12.9162i	−1.74323	+	1.26653i
$105$		0			0
$106$	−4.21218	−	12.9637i	−0.409123	−	1.25915i
$107$	1.91774	−	5.90218i	0.185394	−	0.570586i	−0.814560	−	0.580079i	$-0.803022\pi$
$107$	1.91774	−	5.90218i	0.185394	−	0.570586i	0.999955	+	0.00949312i	$0.00302180\pi$
$108$		0			0
$109$	−1.74313			−0.166961			−0.0834807	−	0.996509i	$-0.526604\pi$
$109$	−1.74313			−0.166961			−0.0834807	+	0.996509i	$0.526604\pi$
$110$	13.7135	+	24.2498i	1.30753	+	2.31212i
$111$		0			0
$112$	−1.07143	−	0.778440i	−0.101241	−	0.0735557i
$113$	−5.19116	+	15.9768i	−0.488344	+	1.50297i	0.338735	+	0.940882i	$0.390001\pi$
$113$	−5.19116	+	15.9768i	−0.488344	+	1.50297i	−0.827079	+	0.562086i	$0.809999\pi$
$114$		0			0
$115$	3.62049	−	2.63044i	0.337612	−	0.245290i
$116$	−15.8614	+	11.5240i	−1.47270	+	1.06998i
$117$		0			0
$118$	4.77925	−	14.7090i	0.439965	−	1.35407i
$119$	3.64133	+	2.64558i	0.333800	+	0.242520i
$120$		0			0
$121$	−5.66916	+	9.42659i	−0.515378	+	0.856963i
$122$	7.71745			0.698705
$123$		0			0
$124$	−3.45889	+	10.6454i	−0.310617	+	0.955982i
$125$	3.18770	+	9.81075i	0.285117	+	0.877500i
$126$		0			0
$127$	−1.79273	+	1.30250i	−0.159079	+	0.115578i	−0.664477	−	0.747308i	$-0.731346\pi$
$127$	−1.79273	+	1.30250i	−0.159079	+	0.115578i	0.505398	+	0.862886i	$0.331346\pi$
$128$	6.21999	+	19.1432i	0.549775	+	1.69203i
$129$		0			0
$130$	−43.0981	−	31.3126i	−3.77996	−	2.74630i
$131$	−11.8297			−1.03357			−0.516784	−	0.856116i	$-0.672871\pi$
$131$	−11.8297			−1.03357			−0.516784	+	0.856116i	$0.672871\pi$
$132$		0			0
$133$	1.70329			0.147694
$134$	−26.6583	−	19.3684i	−2.30292	−	1.67317i
$135$		0			0
$136$	4.18756	+	12.8880i	0.359080	+	1.10513i
$137$	13.7646	−	10.0006i	1.17599	−	0.854406i	0.184275	−	0.982875i	$-0.441006\pi$
$137$	13.7646	−	10.0006i	1.17599	−	0.854406i	0.991714	+	0.128469i	$0.0410062\pi$
$138$		0			0
$139$	−2.16582	−	6.66569i	−0.183702	−	0.565377i	0.816222	−	0.577739i	$-0.196065\pi$
$139$	−2.16582	−	6.66569i	−0.183702	−	0.565377i	−0.999924	+	0.0123622i	$0.996065\pi$
$140$	4.44066	−	13.6669i	0.375304	−	1.15507i
$141$		0			0
$142$	−12.3183			−1.03373
$143$	2.38531	−	20.8988i	0.199470	−	1.74764i
$144$		0			0
$145$	−16.3540	−	11.8819i	−1.35813	−	0.986737i
$146$	−1.60024	+	4.92504i	−0.132437	+	0.407599i
$147$		0			0
$148$	28.2269	−	20.5080i	2.32023	−	1.68575i
$149$	−6.84488	+	4.97309i	−0.560754	+	0.407412i	−0.831735	−	0.555173i	$-0.812652\pi$
$149$	−6.84488	+	4.97309i	−0.560754	+	0.407412i	0.270981	+	0.962585i	$0.412652\pi$
$150$		0			0
$151$	6.74304	−	20.7530i	0.548741	−	1.68885i	−0.163183	−	0.986596i	$-0.552176\pi$
$151$	6.74304	−	20.7530i	0.548741	−	1.68885i	0.711924	−	0.702256i	$-0.247824\pi$
$152$	4.14881	+	3.01428i	0.336513	+	0.244491i
$153$		0			0
$154$	8.75595	−	1.77961i	0.705575	−	0.143405i
$155$	−11.5408			−0.926981
$156$		0			0
$157$	−2.60632	+	8.02144i	−0.208007	+	0.640181i	0.791569	+	0.611080i	$0.209264\pi$
$157$	−2.60632	+	8.02144i	−0.208007	+	0.640181i	−0.999576	+	0.0291010i	$0.990736\pi$
$158$	2.14663	+	6.60664i	0.170777	+	0.525596i
$159$		0			0
$160$	−12.2955	+	8.93322i	−0.972047	+	0.706233i
$161$	−0.443530	−	1.36505i	−0.0349551	−	0.107581i
$162$		0			0
$163$	4.69987	+	3.41465i	0.368122	+	0.267456i	0.756432	−	0.654073i	$-0.226941\pi$
$163$	4.69987	+	3.41465i	0.368122	+	0.267456i	−0.388310	+	0.921529i	$0.626941\pi$
$164$	−6.75757			−0.527677
$165$		0			0
$166$	27.4004			2.12668
$167$	−13.0668	−	9.49361i	−1.01114	−	0.734638i	−0.0466938	−	0.998909i	$-0.514868\pi$
$167$	−13.0668	−	9.49361i	−1.01114	−	0.734638i	−0.964448	+	0.264272i	$0.914868\pi$
$168$		0			0
$169$	8.41225	+	25.8903i	0.647096	+	1.99156i
$170$	−26.5780	+	19.3100i	−2.03844	+	1.48101i
$171$		0			0
$172$	−9.87584	−	30.3947i	−0.753026	−	2.31758i
$173$	−4.45601	+	13.7142i	−0.338784	+	1.04267i	0.626044	+	0.779788i	$0.284673\pi$
$173$	−4.45601	+	13.7142i	−0.338784	+	1.04267i	−0.964828	+	0.262883i	$0.915327\pi$
$174$		0			0
$175$	9.06252			0.685062
$176$	3.47283	+	1.58349i	0.261774	+	0.119360i
$177$		0			0
$178$	16.9209	+	12.2938i	1.26828	+	0.921457i
$179$	1.34424	−	4.13714i	0.100473	−	0.309224i	−0.888168	−	0.459518i	$-0.848022\pi$
$179$	1.34424	−	4.13714i	0.100473	−	0.309224i	0.988641	+	0.150294i	$0.0480220\pi$
$180$		0			0
$181$	−12.1278	+	8.81137i	−0.901453	+	0.654944i	−0.938839	−	0.344357i	$-0.888097\pi$
$181$	−12.1278	+	8.81137i	−0.901453	+	0.654944i	0.0373860	+	0.999301i	$0.488097\pi$
$182$	−13.8226	+	10.0427i	−1.02460	+	0.744415i
$183$		0			0
$184$	1.33536	−	4.10983i	0.0984443	−	0.302980i
$185$	29.1035	+	21.1449i	2.13973	+	1.55461i
$186$		0			0
$187$	−11.8026	−	5.38160i	−0.863094	−	0.393541i
$188$	0.864067			0.0630185
$189$		0			0
$190$	−3.84179	+	11.8238i	−0.278713	+	0.857790i
$191$	−3.83437	−	11.8010i	−0.277446	−	0.853890i	−0.988562	−	0.150815i	$-0.951810\pi$
$191$	−3.83437	−	11.8010i	−0.277446	−	0.853890i	0.711116	−	0.703074i	$-0.248190\pi$
$192$		0			0
$193$	8.36053	−	6.07428i	0.601804	−	0.437236i	−0.244715	−	0.969595i	$-0.578694\pi$
$193$	8.36053	−	6.07428i	0.601804	−	0.437236i	0.846519	+	0.532359i	$0.178694\pi$
$194$	−7.15277	−	22.0139i	−0.513539	−	1.58051i
$195$		0			0
$196$	15.9795	+	11.6098i	1.14139	+	0.829268i
$197$	−0.770815			−0.0549183			−0.0274591	−	0.999623i	$-0.508742\pi$
$197$	−0.770815			−0.0549183			−0.0274591	+	0.999623i	$0.508742\pi$
$198$		0			0
$199$	−3.63580			−0.257735			−0.128868	−	0.991662i	$-0.541134\pi$
$199$	−3.63580			−0.257735			−0.128868	+	0.991662i	$0.541134\pi$
$200$	22.0741	+	16.0378i	1.56087	+	1.13404i
$201$		0			0
$202$	5.73547	+	17.6520i	0.403546	+	1.24199i
$203$	−5.24512	+	3.81081i	−0.368136	+	0.267466i
$204$		0			0
$205$	−2.15306	−	6.62642i	−0.150376	−	0.462809i
$206$	−4.67617	+	14.3918i	−0.325804	+	1.00272i
$207$		0			0
$208$	−7.29858			−0.506066
$209$	−4.81053	+	0.977719i	−0.332751	+	0.0676302i
$210$		0			0
$211$	−12.8992	−	9.37181i	−0.888017	−	0.645182i	0.0473435	−	0.998879i	$-0.484924\pi$
$211$	−12.8992	−	9.37181i	−0.888017	−	0.645182i	−0.935360	+	0.353697i	$0.884924\pi$
$212$	6.26185	−	19.2720i	0.430066	−	1.32361i
$213$		0			0
$214$	11.7532	−	8.53923i	0.803435	−	0.583730i
$215$	26.6583	−	19.3684i	1.81808	−	1.32091i
$216$		0			0
$217$	−1.14380	+	3.52026i	−0.0776462	+	0.238971i
$218$	−3.30127	−	2.39851i	−0.223590	−	0.162448i
$219$		0			0
$220$	−4.69647	+	41.1479i	−0.316636	+	2.77419i
$221$	24.8047			1.66855
$222$		0			0
$223$	−1.77548	+	5.46437i	−0.118895	+	0.365921i	−0.992739	−	0.120284i	$-0.961619\pi$
$223$	−1.77548	+	5.46437i	−0.118895	+	0.365921i	0.873844	+	0.486206i	$0.161619\pi$
$224$	1.50627	+	4.63583i	0.100642	+	0.309744i
$225$		0			0
$226$	−31.8151	+	23.1150i	−2.11631	+	1.53759i
$227$	5.76936	+	17.7563i	0.382926	+	1.17852i	0.937974	+	0.346706i	$0.112700\pi$
$227$	5.76936	+	17.7563i	0.382926	+	1.17852i	−0.555048	+	0.831818i	$0.687300\pi$
$228$		0			0
$229$	1.38776	+	1.00827i	0.0917060	+	0.0666283i	0.632693	−	0.774402i	$-0.281949\pi$
$229$	1.38776	+	1.00827i	0.0917060	+	0.0666283i	−0.540987	+	0.841031i	$0.681949\pi$
$230$	10.4762			0.690779
$231$		0			0
$232$	−19.5198			−1.28153
$233$	−5.81874	−	4.22756i	−0.381198	−	0.276957i	0.380641	−	0.924723i	$-0.375703\pi$
$233$	−5.81874	−	4.22756i	−0.381198	−	0.276957i	−0.761839	+	0.647766i	$0.775703\pi$
$234$		0			0
$235$	0.275304	+	0.847298i	0.0179588	+	0.0552716i
$236$	18.6008	−	13.5142i	1.21081	−	0.879702i
$237$		0			0
$238$	3.25595	+	10.0208i	0.211052	+	0.649552i
$239$	2.97991	−	9.17123i	0.192755	−	0.593237i	−0.807241	−	0.590222i	$-0.799040\pi$
$239$	2.97991	−	9.17123i	0.192755	−	0.593237i	0.999995	−	0.00301535i	$-0.000959817\pi$
$240$		0			0
$241$	2.97674			0.191748			0.0958742	−	0.995393i	$-0.469435\pi$
$241$	2.97674			0.191748			0.0958742	+	0.995393i	$0.469435\pi$
$242$	−23.7075	+	10.0521i	−1.52397	+	0.646176i
$243$		0			0
$244$	9.28170	+	6.74355i	0.594200	+	0.431712i
$245$	−6.29316	+	19.3684i	−0.402056	+	1.23740i
$246$		0			0
$247$	7.59414	−	5.51747i	0.483204	−	0.351068i
$248$	−9.01575	+	6.55032i	−0.572501	+	0.415946i
$249$		0			0
$250$	−7.46228	+	22.9665i	−0.471956	+	1.45253i
$251$	13.0518	+	9.48268i	0.823821	+	0.598541i	0.917805	−	0.397032i	$-0.129960\pi$
$251$	13.0518	+	9.48268i	0.823821	+	0.598541i	−0.0939831	+	0.995574i	$0.529960\pi$
$252$		0			0
$253$	2.03620	+	3.60064i	0.128015	+	0.226370i
$254$	−5.18742			−0.325488
$255$		0			0
$256$	−7.01019	+	21.5752i	−0.438137	+	1.34845i
$257$	1.32222	+	4.06939i	0.0824781	+	0.253841i	0.983789	−	0.179332i	$-0.0573937\pi$
$257$	1.32222	+	4.06939i	0.0824781	+	0.253841i	−0.901310	+	0.433174i	$0.857394\pi$
$258$		0			0
$259$	9.33418	−	6.78168i	0.579998	−	0.421393i
$260$	−24.4725	−	75.3188i	−1.51772	−	4.67107i
$261$		0			0
$262$	−22.4040	−	16.2775i	−1.38412	−	1.00563i
$263$	26.8429			1.65521			0.827603	−	0.561314i	$-0.189704\pi$
$263$	26.8429			1.65521			0.827603	+	0.561314i	$0.189704\pi$
$264$		0			0
$265$	20.8931			1.28345
$266$	3.22582	+	2.34370i	0.197788	+	0.143701i
$267$		0			0
$268$	−15.1375	−	46.5883i	−0.924667	−	2.84583i
$269$	−1.43046	+	1.03929i	−0.0872166	+	0.0633666i	−0.630539	−	0.776158i	$-0.717166\pi$
$269$	−1.43046	+	1.03929i	−0.0872166	+	0.0633666i	0.543322	+	0.839524i	$0.317166\pi$
$270$		0			0
$271$	−5.99637	−	18.4549i	−0.364253	−	1.12106i	−0.950447	−	0.310886i	$-0.899374\pi$
$271$	−5.99637	−	18.4549i	−0.364253	−	1.12106i	0.586194	−	0.810171i	$-0.300626\pi$
$272$	−1.39086	+	4.28064i	−0.0843335	+	0.259552i
$273$		0			0
$274$	39.8290			2.40616
$275$	−25.5948	+	5.20204i	−1.54343	+	0.313695i
$276$		0			0
$277$	2.79710	+	2.03221i	0.168061	+	0.122104i	0.668637	−	0.743589i	$-0.266878\pi$
$277$	2.79710	+	2.03221i	0.168061	+	0.122104i	−0.500575	+	0.865693i	$0.666878\pi$
$278$	5.07008	−	15.6041i	0.304083	−	0.935872i
$279$		0			0
$280$	11.5748	−	8.40957i	0.691725	−	0.502568i
$281$	0.948127	−	0.688854i	0.0565605	−	0.0410936i	−0.559146	−	0.829069i	$-0.688871\pi$
$281$	0.948127	−	0.688854i	0.0565605	−	0.0410936i	0.615706	+	0.787976i	$0.288871\pi$
$282$		0			0
$283$	−1.26884	+	3.90510i	−0.0754249	+	0.232134i	−0.981660	−	0.190640i	$-0.938944\pi$
$283$	−1.26884	+	3.90510i	−0.0754249	+	0.232134i	0.906235	+	0.422774i	$0.138944\pi$
$284$	−14.8151	−	10.7638i	−0.879113	−	0.638713i
$285$		0			0
$286$	33.2738	−	36.2975i	1.96752	−	2.14632i
$287$	−2.23462			−0.131906
$288$		0			0
$289$	−0.526346	+	1.61993i	−0.0309616	+	0.0952899i
$290$	−14.6232	−	45.0056i	−0.858705	−	2.64282i
$291$		0			0
$292$	−6.22812	+	4.52500i	−0.364473	+	0.264805i
$293$	−1.84922	−	5.69130i	−0.108032	−	0.332489i	0.882398	−	0.470504i	$-0.155928\pi$
$293$	−1.84922	−	5.69130i	−0.108032	−	0.332489i	−0.990430	+	0.138015i	$0.955928\pi$
$294$		0			0
$295$	19.1784	+	13.9339i	1.11661	+	0.811266i
$296$	34.7372			2.01906
$297$		0			0
$298$	−19.8062			−1.14734
$299$	−6.39927	−	4.64934i	−0.370079	−	0.268878i
$300$		0			0
$301$	−3.26579	−	10.0511i	−0.188237	−	0.579334i
$302$	41.3261	−	30.0252i	2.37805	−	1.72776i
$303$		0			0
$304$	0.526346	+	1.61993i	0.0301880	+	0.0929092i
$305$	−3.65540	+	11.2502i	−0.209308	+	0.644182i
$306$		0			0
$307$	4.70930			0.268774			0.134387	−	0.990929i	$-0.457093\pi$
$307$	4.70930			0.268774			0.134387	+	0.990929i	$0.457093\pi$
$308$	12.0857	+	5.51068i	0.688648	+	0.314000i
$309$		0			0
$310$	−21.8569	−	15.8799i	−1.24139	−	0.901920i
$311$	6.54171	−	20.1333i	0.370947	−	1.14166i	−0.575226	−	0.817994i	$-0.695086\pi$
$311$	6.54171	−	20.1333i	0.370947	−	1.14166i	0.946173	−	0.323662i	$-0.104914\pi$
$312$		0			0
$313$	−17.3590	+	12.6121i	−0.981189	+	0.712876i	−0.957974	−	0.286855i	$-0.907390\pi$
$313$	−17.3590	+	12.6121i	−0.981189	+	0.712876i	−0.0232153	+	0.999730i	$0.507390\pi$
$314$	−15.9734	+	11.6053i	−0.901431	+	0.654928i
$315$		0			0
$316$	−3.19119	+	9.82148i	−0.179519	+	0.552501i
$317$	0.897839	+	0.652318i	0.0504276	+	0.0366378i	0.612714	−	0.790305i	$-0.290078\pi$
$317$	0.897839	+	0.652318i	0.0504276	+	0.0366378i	−0.562286	+	0.826943i	$0.690078\pi$
$318$		0			0
$319$	12.6261	−	13.7735i	0.706925	−	0.771166i
$320$	−43.8367			−2.45055
$321$		0			0
$322$	1.03829	−	3.19551i	0.0578614	−	0.178079i
$323$	−1.78882	−	5.50543i	−0.0995328	−	0.306330i
$324$		0			0
$325$	40.4053	−	29.3562i	2.24128	−	1.62839i
$326$	4.20246	+	12.9339i	0.232753	+	0.716340i
$327$		0			0
$328$	−5.44300	−	3.95457i	−0.300539	−	0.218354i
$329$	0.285733			0.0157530
$330$		0			0
$331$	−5.93868			−0.326420			−0.163210	−	0.986591i	$-0.552185\pi$
$331$	−5.93868			−0.326420			−0.163210	+	0.986591i	$0.552185\pi$
$332$	32.9542	+	23.9426i	1.80860	+	1.31402i
$333$		0			0
$334$	−11.6839	−	35.9594i	−0.639316	−	1.96761i
$335$	40.8611	−	29.6874i	2.23248	−	1.62199i
$336$		0			0
$337$	−9.58204	−	29.4905i	−0.521967	−	1.60645i	−0.770236	−	0.637759i	$-0.779862\pi$
$337$	−9.58204	−	29.4905i	−0.521967	−	1.60645i	0.248269	−	0.968691i	$-0.420138\pi$
$338$	−19.6927	+	60.6080i	−1.07114	+	3.29664i
$339$		0			0
$340$	−48.8383			−2.64863
$341$	1.20969	−	10.5986i	0.0655085	−	0.573949i
$342$		0			0
$343$	11.8013	+	8.57417i	0.637212	+	0.462961i
$344$	9.83250	−	30.2613i	0.530133	−	1.63158i
$345$		0			0
$346$	−27.3096	+	19.8416i	−1.46817	+	1.06669i
$347$	−20.0950	+	14.5998i	−1.07875	+	0.783761i	−0.977465	−	0.211096i	$-0.932297\pi$
$347$	−20.0950	+	14.5998i	−1.07875	+	0.783761i	−0.101289	+	0.994857i	$0.532297\pi$
$348$		0			0
$349$	−3.73395	+	11.4919i	−0.199874	+	0.615148i	0.800011	+	0.599985i	$0.204827\pi$
$349$	−3.73395	+	11.4919i	−0.199874	+	0.615148i	−0.999885	+	0.0151633i	$0.995173\pi$
$350$	17.1633	+	12.4698i	0.917415	+	0.666541i
$351$		0			0
$352$	−6.91513	−	12.2281i	−0.368578	−	0.651760i
$353$	−8.73656			−0.465000			−0.232500	−	0.972596i	$-0.574691\pi$
$353$	−8.73656			−0.465000			−0.232500	+	0.972596i	$0.574691\pi$
$354$		0			0
$355$	5.83460	−	17.9571i	0.309669	−	0.953062i
$356$	9.60826	+	29.5712i	0.509237	+	1.56727i
$357$		0			0
$358$	8.23844	−	5.98558i	0.435415	−	0.316348i
$359$	4.65359	+	14.3223i	0.245607	+	0.755901i	0.995536	+	0.0943824i	$0.0300876\pi$
$359$	4.65359	+	14.3223i	0.245607	+	0.755901i	−0.749929	+	0.661518i	$0.769912\pi$
$360$		0			0
$361$	13.5991	+	9.88029i	0.715740	+	0.520015i
$362$	−35.0928			−1.84444
$363$		0			0
$364$	−25.3997			−1.33130
$365$	−6.42155	−	4.66553i	−0.336119	−	0.244205i
$366$		0			0
$367$	6.40104	+	19.7004i	0.334132	+	1.02835i	0.967148	+	0.254213i	$0.0818166\pi$
$367$	6.40104	+	19.7004i	0.334132	+	1.02835i	−0.633016	+	0.774138i	$0.718183\pi$
$368$	1.16118	−	0.843645i	0.0605306	−	0.0439780i
$369$		0			0
$370$	26.0234	+	80.0917i	1.35289	+	4.16377i
$371$	2.07070	−	6.37295i	0.107505	−	0.330867i
$372$		0			0
$373$	−12.0439			−0.623610			−0.311805	−	0.950146i	$-0.600934\pi$
$373$	−12.0439			−0.623610			−0.311805	+	0.950146i	$0.600934\pi$
$374$	−14.9477	−	26.4323i	−0.772929	−	1.36678i
$375$		0			0
$376$	0.695977	+	0.505657i	0.0358923	+	0.0260773i
$377$	−11.0411	+	33.9810i	−0.568646	+	1.75011i
$378$		0			0
$379$	8.75138	−	6.35825i	0.449528	−	0.326601i	−0.339881	−	0.940468i	$-0.610387\pi$
$379$	8.75138	−	6.35825i	0.449528	−	0.326601i	0.789409	+	0.613867i	$0.210387\pi$
$380$	−14.9522	+	10.8634i	−0.767032	+	0.557281i
$381$		0			0
$382$	8.97611	−	27.6256i	0.459258	−	1.41345i
$383$	24.8994	+	18.0905i	1.27230	+	0.924381i	0.999292	−	0.0376296i	$-0.0119807\pi$
$383$	24.8994	+	18.0905i	1.27230	+	0.924381i	0.273010	+	0.962011i	$0.411981\pi$
$384$		0			0
$385$	−1.55305	+	13.6070i	−0.0791508	+	0.693475i
$386$	24.1919			1.23133
$387$		0			0
$388$	10.6333	−	32.7261i	0.539826	−	1.66141i
$389$	−0.416722	−	1.28254i	−0.0211287	−	0.0650273i	0.939936	−	0.341350i	$-0.110884\pi$
$389$	−0.416722	−	1.28254i	−0.0211287	−	0.0650273i	−0.961065	+	0.276323i	$0.910884\pi$
$390$		0			0
$391$	−3.94634	+	2.86718i	−0.199575	+	0.145000i
$392$	6.07682	+	18.7025i	0.306926	+	0.944621i
$393$		0			0
$394$	−1.45983	−	1.06063i	−0.0735450	−	0.0534336i
$395$	−10.6476			−0.535741
$396$		0			0
$397$	−1.13262			−0.0568446			−0.0284223	−	0.999596i	$-0.509048\pi$
$397$	−1.13262			−0.0568446			−0.0284223	+	0.999596i	$0.509048\pi$
$398$	−6.88575	−	5.00279i	−0.345152	−	0.250767i
$399$		0			0
$400$	2.80047	+	8.61896i	0.140024	+	0.430948i
$401$	26.7475	−	19.4332i	1.33571	−	0.970447i	0.336115	−	0.941821i	$-0.390887\pi$
$401$	26.7475	−	19.4332i	1.33571	−	0.970447i	0.999590	−	0.0286260i	$-0.00911319\pi$
$402$		0			0
$403$	6.30351	+	19.4002i	0.314000	+	0.966393i
$404$	−8.52638	+	26.2415i	−0.424203	+	1.30556i
$405$		0			0
$406$	−15.1772			−0.753232
$407$	−22.4693	+	24.5111i	−1.11376	+	1.21497i
$408$		0			0
$409$	1.28288	+	0.932067i	0.0634343	+	0.0460877i	0.619051	−	0.785351i	$-0.287518\pi$
$409$	1.28288	+	0.932067i	0.0634343	+	0.0460877i	−0.555616	+	0.831439i	$0.687518\pi$
$410$	5.04021	−	15.5122i	0.248918	−	0.766092i
$411$		0			0
$412$	−18.1996	+	13.2228i	−0.896629	+	0.651439i
$413$	6.15098	−	4.46895i	0.302670	−	0.219903i
$414$		0			0
$415$	−12.9783	+	39.9431i	−0.637080	+	1.96073i
$416$	21.7325	+	15.7896i	1.06553	+	0.774149i
$417$		0			0
$418$	−10.4559	−	4.76751i	−0.511412	−	0.233187i
$419$	−3.23928			−0.158249			−0.0791245	−	0.996865i	$-0.525212\pi$
$419$	−3.23928			−0.158249			−0.0791245	+	0.996865i	$0.525212\pi$
$420$		0			0
$421$	11.3884	−	35.0499i	0.555036	−	1.70823i	−0.140811	−	0.990037i	$-0.544971\pi$
$421$	11.3884	−	35.0499i	0.555036	−	1.70823i	0.695847	−	0.718190i	$-0.255029\pi$
$422$	−11.5340	−	35.4981i	−0.561467	−	1.72802i
$423$		0			0
$424$	16.3218	−	11.8585i	0.792656	−	0.575899i
$425$	−9.51758	−	29.2921i	−0.461671	−	1.42088i
$426$		0			0
$427$	3.06931	+	2.22999i	0.148535	+	0.107917i
$428$	21.5971			1.04394
$429$		0			0
$430$	77.1379			3.71992
$431$	4.37531	+	3.17885i	0.210751	+	0.153120i	0.688154	−	0.725565i	$-0.258422\pi$
$431$	4.37531	+	3.17885i	0.210751	+	0.153120i	−0.477402	+	0.878685i	$0.658422\pi$
$432$		0			0
$433$	9.71285	+	29.8931i	0.466770	+	1.43657i	0.856743	+	0.515744i	$0.172484\pi$
$433$	9.71285	+	29.8931i	0.466770	+	1.43657i	−0.389973	+	0.920826i	$0.627516\pi$
$434$	−7.01002	+	5.09308i	−0.336492	+	0.244476i
$435$		0			0
$436$	−1.87457	−	5.76933i	−0.0897755	−	0.276301i
$437$	−0.570435	+	1.75562i	−0.0272876	+	0.0839826i
$438$		0			0
$439$	−26.8081			−1.27948			−0.639740	−	0.768591i	$-0.720958\pi$
$439$	−26.8081			−1.27948			−0.639740	+	0.768591i	$0.720958\pi$
$440$	−27.8628	+	30.3948i	−1.32831	+	1.44902i
$441$		0			0
$442$	46.9770	+	34.1308i	2.23447	+	1.62344i
$443$	−5.89130	+	18.1316i	−0.279904	+	0.861457i	0.707976	+	0.706237i	$0.249609\pi$
$443$	−5.89130	+	18.1316i	−0.279904	+	0.861457i	−0.987880	+	0.155220i	$0.950391\pi$
$444$		0			0
$445$	−25.9360	+	18.8436i	−1.22948	+	0.893272i
$446$	−10.8814	+	7.90580i	−0.515249	+	0.374351i
$447$		0			0
$448$	−4.34462	+	13.3714i	−0.205264	+	0.631737i
$449$	−22.4771	−	16.3306i	−1.06076	−	0.770687i	−0.0865311	−	0.996249i	$-0.527578\pi$
$449$	−22.4771	−	16.3306i	−1.06076	−	0.770687i	−0.974229	+	0.225562i	$0.927578\pi$
$450$		0			0
$451$	6.31113	−	1.28271i	0.297180	−	0.0604005i
$452$	−58.4618			−2.74981
$453$		0			0
$454$	−13.5058	+	41.5666i	−0.633859	+	1.95082i
$455$	−8.09269	−	24.9067i	−0.379391	−	1.16765i
$456$		0			0
$457$	−15.1643	+	11.0175i	−0.709354	+	0.515376i	−0.882965	−	0.469438i	$-0.844456\pi$
$457$	−15.1643	+	11.0175i	−0.709354	+	0.515376i	0.173611	+	0.984814i	$0.444456\pi$
$458$	1.24089	+	3.81907i	0.0579831	+	0.178454i
$459$		0			0
$460$	12.5996	+	9.15415i	0.587459	+	0.426814i
$461$	−18.1064			−0.843297			−0.421649	−	0.906759i	$-0.638548\pi$
$461$	−18.1064			−0.843297			−0.421649	+	0.906759i	$0.638548\pi$
$462$		0			0
$463$	−24.5770			−1.14219			−0.571096	−	0.820883i	$-0.693482\pi$
$463$	−24.5770			−1.14219			−0.571096	+	0.820883i	$0.693482\pi$
$464$	−5.24512	−	3.81081i	−0.243499	−	0.176912i
$465$		0			0
$466$	−5.20292	−	16.0129i	−0.241021	−	0.741786i
$467$	−12.5464	+	9.11548i	−0.580578	+	0.421814i	−0.838932	−	0.544236i	$-0.816820\pi$
$467$	−12.5464	+	9.11548i	−0.580578	+	0.421814i	0.258355	+	0.966050i	$0.416820\pi$
$468$		0			0
$469$	−5.00572	−	15.4060i	−0.231143	−	0.711384i
$470$	−0.644474	+	1.98349i	−0.0297274	+	0.0914915i
$471$		0			0
$472$	22.8909			1.05364
$473$	14.9929	+	26.5121i	0.689374	+	1.21903i
$474$		0			0
$475$	−9.42951	−	6.85094i	−0.432655	−	0.314343i
$476$	−4.84032	+	14.8970i	−0.221856	+	0.682802i
$477$		0			0
$478$	18.2630	−	13.2689i	0.835331	−	0.606903i
$479$	7.79546	−	5.66373i	0.356184	−	0.258783i	−0.395275	−	0.918563i	$-0.629351\pi$
$479$	7.79546	−	5.66373i	0.356184	−	0.258783i	0.751459	+	0.659780i	$0.229351\pi$
$480$		0			0
$481$	19.6487	−	60.4724i	0.895902	−	2.75730i
$482$	5.63756	+	4.09593i	0.256784	+	0.186564i
$483$		0			0
$484$	−37.2964	−	8.62612i	−1.69529	−	0.392097i
$485$	35.4789			1.61101
$486$		0			0
$487$	10.6077	−	32.6472i	0.480681	−	1.47938i	−0.357458	−	0.933929i	$-0.616357\pi$
$487$	10.6077	−	32.6472i	0.480681	−	1.47938i	0.838140	−	0.545456i	$-0.183643\pi$
$488$	3.52974	+	10.8634i	0.159784	+	0.491763i
$489$		0			0
$490$	−38.5690	+	28.0220i	−1.74237	+	1.26590i
$491$	−5.41835	−	16.6760i	−0.244527	−	0.752576i	−0.995714	−	0.0924868i	$-0.970518\pi$
$491$	−5.41835	−	16.6760i	−0.244527	−	0.752576i	0.751187	−	0.660089i	$-0.229482\pi$
$492$		0			0
$493$	17.8259	+	12.9513i	0.802838	+	0.583296i
$494$	21.9743			0.988670
$495$		0			0
$496$	−3.70142			−0.166199
$497$	−4.89912	−	3.55942i	−0.219755	−	0.159662i
$498$		0			0
$499$	7.45891	+	22.9562i	0.333907	+	1.02766i	0.967258	+	0.253795i	$0.0816787\pi$
$499$	7.45891	+	22.9562i	0.333907	+	1.02766i	−0.633352	+	0.773864i	$0.718321\pi$
$500$	−29.0431	+	21.1010i	−1.29885	+	0.943667i
$501$		0			0
$502$	11.6705	+	35.9180i	0.520878	+	1.60310i
$503$	6.51381	−	20.0474i	0.290436	−	0.893872i	−0.694280	−	0.719705i	$-0.744277\pi$
$503$	6.51381	−	20.0474i	0.290436	−	0.893872i	0.984716	−	0.174166i	$-0.0557230\pi$
$504$		0			0
$505$	−28.4489			−1.26596
$506$	−1.09810	+	9.62093i	−0.0488165	+	0.427702i
$507$		0			0
$508$	−6.23886	−	4.53280i	−0.276805	−	0.201110i
$509$	−10.1551	+	31.2543i	−0.450119	+	1.38532i	0.426653	+	0.904416i	$0.359693\pi$
$509$	−10.1551	+	31.2543i	−0.450119	+	1.38532i	−0.876771	+	0.480907i	$0.840307\pi$
$510$		0			0
$511$	−2.05954	+	1.49635i	−0.0911088	+	0.0661944i
$512$	−10.3951	+	7.55249i	−0.459404	+	0.333776i
$513$		0			0
$514$	−3.09527	+	9.52626i	−0.136527	+	0.420186i
$515$	−18.7648	−	13.6334i	−0.826876	−	0.600760i
$516$		0			0
$517$	−0.806983	+	0.164016i	−0.0354911	+	0.00721341i
$518$	27.0092			1.18672
$519$		0			0
$520$	24.3652	−	74.9882i	1.06848	−	3.28845i
$521$	7.10565	+	21.8689i	0.311304	+	0.958096i	0.977249	+	0.212095i	$0.0680286\pi$
$521$	7.10565	+	21.8689i	0.311304	+	0.958096i	−0.665945	+	0.746001i	$0.731971\pi$
$522$		0			0
$523$	−22.7327	+	16.5163i	−0.994031	+	0.722206i	−0.960800	−	0.277242i	$-0.910580\pi$
$523$	−22.7327	+	16.5163i	−0.994031	+	0.722206i	−0.0332309	+	0.999448i	$0.510580\pi$
$524$	−12.7217	−	39.1535i	−0.555752	−	1.71043i
$525$		0			0
$526$	50.8371	+	36.9353i	2.21660	+	1.61046i
$527$	12.5795			0.547972
$528$		0			0
$529$	−21.4445			−0.932369
$530$	39.5689	+	28.7485i	1.71876	+	1.24875i
$531$		0			0
$532$	1.83173	+	5.63748i	0.0794155	+	0.244416i
$533$	−9.96308	+	7.23860i	−0.431549	+	0.313539i
$534$		0			0
$535$	6.88115	+	21.1780i	0.297498	+	0.915604i
$536$	15.0710	−	46.3838i	0.650969	−	2.00348i
$537$		0			0
$538$	−4.13915			−0.178451
$539$	−17.1275	−	7.80957i	−0.737735	−	0.336382i
$540$		0			0
$541$	10.2202	+	7.42539i	0.439400	+	0.319243i	0.785396	−	0.618993i	$-0.212459\pi$
$541$	10.2202	+	7.42539i	0.439400	+	0.319243i	−0.345997	+	0.938236i	$0.612459\pi$
$542$	14.0372	−	43.2022i	0.602951	−	1.85569i
$543$		0			0
$544$	13.4021	−	9.73722i	0.574612	−	0.417480i
$545$	5.06010	−	3.67638i	0.216751	−	0.157479i
$546$		0			0
$547$	−6.91799	+	21.2914i	−0.295792	+	0.910353i	0.687163	+	0.726504i	$0.258856\pi$
$547$	−6.91799	+	21.2914i	−0.295792	+	0.910353i	−0.982954	+	0.183850i	$0.941144\pi$
$548$	47.9019	+	34.8028i	2.04627	+	1.48670i
$549$		0			0
$550$	−55.6313	−	25.3660i	−2.37213	−	1.08161i
$551$	8.33836			0.355226
$552$		0			0
$553$	−1.05528	+	3.24781i	−0.0448750	+	0.138111i
$554$	2.50107	+	7.69750i	0.106260	+	0.327036i
$555$		0			0
$556$	19.7327	−	14.3366i	0.836852	−	0.608009i
$557$	−1.64815	−	5.07249i	−0.0698344	−	0.214928i	0.910048	−	0.414502i	$-0.136044\pi$
$557$	−1.64815	−	5.07249i	−0.0698344	−	0.214928i	−0.979883	+	0.199574i	$0.936044\pi$
$558$		0			0
$559$	−47.1189	−	34.2339i	−1.99292	−	1.44794i
$560$	4.75203			0.200810
$561$		0			0
$562$	2.74348			0.115727
$563$	−36.8747	−	26.7910i	−1.55408	−	1.12911i	−0.940658	−	0.339355i	$-0.889791\pi$
$563$	−36.8747	−	26.7910i	−1.55408	−	1.12911i	−0.613425	−	0.789753i	$-0.710209\pi$
$564$		0			0
$565$	−18.6267	−	57.3272i	−0.783633	−	2.41177i
$566$	−7.77637	+	5.64986i	−0.326865	+	0.237481i
$567$		0			0
$568$	−5.63402	−	17.3397i	−0.236398	−	0.727560i
$569$	−7.98042	+	24.5612i	−0.334557	+	1.02966i	0.632383	+	0.774656i	$0.282077\pi$
$569$	−7.98042	+	24.5612i	−0.334557	+	1.02966i	−0.966940	+	0.255004i	$0.917923\pi$
$570$		0			0
$571$	−21.7759			−0.911295			−0.455648	−	0.890160i	$-0.650592\pi$
$571$	−21.7759			−0.911295			−0.455648	+	0.890160i	$0.650592\pi$
$572$	71.7350	−	14.5798i	2.99939	−	0.609614i
$573$		0			0
$574$	−4.23209	−	3.07480i	−0.176644	−	0.128340i
$575$	−3.03505	+	9.34091i	−0.126570	+	0.389543i
$576$		0			0
$577$	27.6324	−	20.0761i	1.15035	−	0.835780i	0.161825	−	0.986819i	$-0.448262\pi$
$577$	27.6324	−	20.0761i	1.15035	−	0.835780i	0.988528	+	0.151039i	$0.0482620\pi$
$578$	−3.22582	+	2.34370i	−0.134177	+	0.0974850i
$579$		0			0
$580$	21.7390	−	66.9056i	0.902661	−	2.77811i
$581$	10.8974	+	7.91745i	0.452102	+	0.328471i
$582$		0			0
$583$	−2.18998	+	19.1874i	−0.0906999	+	0.794662i
$584$	−7.66460			−0.317163
$585$		0			0
$586$	4.32893	−	13.3231i	0.178827	−	0.550372i
$587$	9.03764	+	27.8150i	0.373023	+	1.14805i	0.944803	+	0.327640i	$0.106253\pi$
$587$	9.03764	+	27.8150i	0.373023	+	1.14805i	−0.571779	+	0.820408i	$0.693747\pi$
$588$		0			0
$589$	3.85131	−	2.79814i	0.158690	−	0.115295i
$590$	17.1487	+	52.7783i	0.706001	+	2.17285i
$591$		0			0
$592$	9.33418	+	6.78168i	0.383633	+	0.278725i
$593$	−6.12062			−0.251344			−0.125672	−	0.992072i	$-0.540109\pi$
$593$	−6.12062			−0.251344			−0.125672	+	0.992072i	$0.540109\pi$
$594$		0			0
$595$	−16.1501			−0.662088
$596$	−23.8207	−	17.3068i	−0.975735	−	0.708913i
$597$		0			0
$598$	−5.72201	−	17.6105i	−0.233990	−	0.720149i
$599$	−15.8456	+	11.5125i	−0.647433	+	0.470387i	−0.862396	−	0.506235i	$-0.831037\pi$
$599$	−15.8456	+	11.5125i	−0.647433	+	0.470387i	0.214963	+	0.976622i	$0.431037\pi$
$600$		0			0
$601$	3.62705	+	11.1629i	0.147950	+	0.455345i	0.997379	−	0.0723596i	$-0.0230529\pi$
$601$	3.62705	+	11.1629i	0.147950	+	0.455345i	−0.849428	+	0.527704i	$0.823053\pi$
$602$	7.64507	−	23.5291i	0.311590	−	0.958975i
$603$		0			0
$604$	75.9387			3.08990
$605$	−3.42442	−	39.3209i	−0.139223	−	1.59862i
$606$		0			0
$607$	−5.59025	−	4.06156i	−0.226901	−	0.164853i	0.468526	−	0.883449i	$-0.344785\pi$
$607$	−5.59025	−	4.06156i	−0.226901	−	0.164853i	−0.695428	+	0.718596i	$0.744785\pi$
$608$	1.93725	−	5.96224i	0.0785659	−	0.241801i
$609$		0			0
$610$	−22.4029	+	16.2766i	−0.907066	+	0.659022i
$611$	1.27394	−	0.925575i	0.0515383	−	0.0374448i
$612$		0			0
$613$	−4.52119	+	13.9148i	−0.182609	+	0.562014i	−0.999899	−	0.0142134i	$-0.995476\pi$
$613$	−4.52119	+	13.9148i	−0.182609	+	0.562014i	0.817290	+	0.576227i	$0.195476\pi$
$614$	8.91882	+	6.47990i	0.359934	+	0.261508i
$615$		0			0
$616$	6.50977	+	11.5113i	0.262286	+	0.463804i
$617$	−19.6654			−0.791699			−0.395850	−	0.918315i	$-0.629550\pi$
$617$	−19.6654			−0.791699			−0.395850	+	0.918315i	$0.629550\pi$
$618$		0			0
$619$	1.88924	−	5.81447i	0.0759348	−	0.233703i	−0.905883	−	0.423527i	$-0.860792\pi$
$619$	1.88924	−	5.81447i	0.0759348	−	0.233703i	0.981818	+	0.189824i	$0.0607918\pi$
$620$	−12.4111	−	38.1973i	−0.498440	−	1.53404i
$621$		0			0
$622$	40.0923	−	29.1287i	1.60755	−	1.16796i
$623$	3.17730	+	9.77874i	0.127296	+	0.391777i
$624$		0			0
$625$	1.90959	+	1.38740i	0.0763836	+	0.0554959i
$626$	−50.2297			−2.00758
$627$		0			0
$628$	−29.3519			−1.17127
$629$	−31.7228	−	23.0480i	−1.26487	−	0.918984i
$630$		0			0
$631$	3.27739	+	10.0868i	0.130471	+	0.401548i	0.994858	−	0.101279i	$-0.0322934\pi$
$631$	3.27739	+	10.0868i	0.130471	+	0.401548i	−0.864387	+	0.502827i	$0.832293\pi$
$632$	−8.31799	+	6.04337i	−0.330872	+	0.240392i
$633$		0			0
$634$	0.802817	+	2.47082i	0.0318839	+	0.0981287i
$635$	2.45704	−	7.56200i	0.0975047	−	0.300089i
$636$		0			0
$637$	35.9956			1.42620
$638$	42.8642	−	8.71197i	1.69701	−	0.344910i
$639$		0			0
$640$	−58.4302	−	42.4520i	−2.30966	−	1.67806i
$641$	11.6981	−	36.0029i	0.462045	−	1.42203i	−0.400615	−	0.916246i	$-0.631204\pi$
$641$	11.6981	−	36.0029i	0.462045	−	1.42203i	0.862661	−	0.505783i	$-0.168796\pi$
$642$		0			0
$643$	5.26221	−	3.82322i	0.207521	−	0.150773i	−0.479170	−	0.877722i	$-0.659062\pi$
$643$	5.26221	−	3.82322i	0.207521	−	0.150773i	0.686691	+	0.726949i	$0.259062\pi$
$644$	4.04099	−	2.93595i	0.159237	−	0.115693i
$645$		0			0
$646$	4.18756	−	12.8880i	0.164757	−	0.507071i
$647$	−19.9715	−	14.5101i	−0.785161	−	0.570453i	0.121363	−	0.992608i	$-0.461274\pi$
$647$	−19.9715	−	14.5101i	−0.785161	−	0.570453i	−0.906523	+	0.422155i	$0.861274\pi$
$648$		0			0
$649$	−14.8067	+	16.1522i	−0.581212	+	0.634029i
$650$	116.916			4.58583
$651$		0			0
$652$	−6.24741	+	19.2275i	−0.244667	+	0.753009i
$653$	−8.58310	−	26.4161i	−0.335883	−	1.03374i	−0.966286	−	0.257473i	$-0.917110\pi$
$653$	−8.58310	−	26.4161i	−0.335883	−	1.03374i	0.630403	−	0.776268i	$-0.282890\pi$
$654$		0			0
$655$	34.3403	−	24.9497i	1.34179	−	0.974866i
$656$	−0.690536	−	2.12525i	−0.0269609	−	0.0829772i
$657$		0			0
$658$	0.541143	+	0.393164i	0.0210960	+	0.0153271i
$659$	35.1489			1.36921			0.684603	−	0.728917i	$-0.259976\pi$
$659$	35.1489			1.36921			0.684603	+	0.728917i	$0.259976\pi$
$660$		0			0
$661$	−25.1379			−0.977751			−0.488875	−	0.872354i	$-0.662593\pi$
$661$	−25.1379			−0.977751			−0.488875	+	0.872354i	$0.662593\pi$
$662$	−11.2471	−	8.17151i	−0.437132	−	0.317595i
$663$		0			0
$664$	12.5321	+	38.5700i	0.486342	+	1.49681i
$665$	−4.94446	+	3.59236i	−0.191738	+	0.139306i
$666$		0			0
$667$	−2.17127	−	6.68250i	−0.0840721	−	0.258747i
$668$	17.3694	−	53.4575i	0.672042	−	2.06833i
$669$		0			0
$670$	118.235			4.56782
$671$	−9.94856	−	4.53620i	−0.384060	−	0.175118i
$672$		0			0
$673$	20.3692	+	14.7991i	0.785175	+	0.570463i	0.906528	−	0.422146i	$-0.138723\pi$
$673$	20.3692	+	14.7991i	0.785175	+	0.570463i	−0.121353	+	0.992609i	$0.538723\pi$
$674$	22.4312	−	69.0360i	0.864016	−	2.65917i
$675$		0			0
$676$	−76.6438	+	55.6850i	−2.94784	+	2.14173i
$677$	−22.6873	+	16.4833i	−0.871943	+	0.633503i	−0.931108	−	0.364745i	$-0.881156\pi$
$677$	−22.6873	+	16.4833i	−0.871943	+	0.633503i	0.0591649	+	0.998248i	$0.481156\pi$
$678$		0			0
$679$	3.51628	−	10.8220i	0.134943	−	0.415310i
$680$	−39.3376	−	28.5805i	−1.50853	−	1.09601i
$681$		0			0
$682$	16.8745	−	18.4080i	0.646159	−	0.704879i
$683$	−48.2755			−1.84721			−0.923605	−	0.383346i	$-0.874772\pi$
$683$	−48.2755			−1.84721			−0.923605	+	0.383346i	$0.874772\pi$
$684$		0			0
$685$	−18.8652	+	58.0610i	−0.720800	+	2.21840i
$686$	10.5523	+	32.4768i	0.402891	+	1.23997i
$687$		0			0
$688$	8.54995	−	6.21190i	0.325964	−	0.236826i
$689$	−11.4116	−	35.1214i	−0.434749	−	1.33802i
$690$		0			0
$691$	10.6840	+	7.76238i	0.406439	+	0.295295i	0.772158	−	0.635430i	$-0.219177\pi$
$691$	10.6840	+	7.76238i	0.406439	+	0.295295i	−0.365720	+	0.930725i	$0.619177\pi$
$692$	−50.1826			−1.90766
$693$		0			0
$694$	−58.1464			−2.20721
$695$	20.3455	+	14.7819i	0.771750	+	0.560709i
$696$		0			0
$697$	2.34683	+	7.22281i	0.0888926	+	0.273583i
$698$	−22.8843	+	16.6264i	−0.866183	+	0.629319i
$699$		0			0
$700$	9.74587	+	29.9947i	0.368359	+	1.13369i
$701$	10.0560	−	30.9490i	0.379808	−	1.16893i	−0.560369	−	0.828243i	$-0.689341\pi$
$701$	10.0560	−	30.9490i	0.379808	−	1.16893i	0.940177	−	0.340686i	$-0.110659\pi$
$702$		0			0
$703$	−14.8389			−0.559659
$704$	4.59490	−	40.2580i	0.173177	−	1.51728i
$705$		0			0
$706$	−16.5459	−	12.0213i	−0.622715	−	0.452429i
$707$	−2.81954	+	8.67766i	−0.106040	+	0.326357i
$708$		0			0
$709$	−1.61618	+	1.17422i	−0.0606968	+	0.0440988i	−0.617720	−	0.786398i	$-0.711943\pi$
$709$	−1.61618	+	1.17422i	−0.0606968	+	0.0440988i	0.557023	+	0.830497i	$0.311943\pi$
$710$	35.7586	−	25.9801i	1.34200	−	0.975017i
$711$		0			0
$712$	−9.56610	+	29.4414i	−0.358505	+	1.10336i
$713$	−3.24534	−	2.35788i	−0.121539	−	0.0883031i
$714$		0			0
$715$	37.1527	+	65.6975i	1.38943	+	2.45695i
$716$	15.1385			0.565753
$717$		0			0
$718$	−10.8939	+	33.5278i	−0.406555	+	1.25125i
$719$	14.0695	+	43.3014i	0.524703	+	1.61487i	0.764901	+	0.644147i	$0.222788\pi$
$719$	14.0695	+	43.3014i	0.524703	+	1.61487i	−0.240198	+	0.970724i	$0.577212\pi$
$720$		0			0
$721$	−6.01832	+	4.37256i	−0.224134	+	0.162843i
$722$	12.1598	+	37.4241i	0.452541	+	1.39278i
$723$		0			0
$724$	−42.2058	−	30.6643i	−1.56856	−	1.13963i
$725$	44.3650			1.64767
$726$		0			0
$727$	−34.5005			−1.27955			−0.639776	−	0.768562i	$-0.720973\pi$
$727$	−34.5005			−1.27955			−0.639776	+	0.768562i	$0.720973\pi$
$728$	−20.4586	−	14.8640i	−0.758246	−	0.550898i
$729$		0			0
$730$	−5.74193	−	17.6718i	−0.212518	−	0.654064i
$731$	−29.0575	+	21.1115i	−1.07473	+	0.780839i
$732$		0			0
$733$	3.49867	+	10.7678i	0.129226	+	0.397718i	0.994647	−	0.103327i	$-0.0329490\pi$
$733$	3.49867	+	10.7678i	0.129226	+	0.397718i	−0.865421	+	0.501045i	$0.832949\pi$
$734$	−14.9846	+	46.1178i	−0.553091	+	1.70224i
$735$		0			0
$736$	−5.28269			−0.194723
$737$	22.9807	+	40.6371i	0.846506	+	1.49689i
$738$		0			0
$739$	−5.54111	−	4.02585i	−0.203833	−	0.148093i	0.481186	−	0.876619i	$-0.340206\pi$
$739$	−5.54111	−	4.02585i	−0.203833	−	0.148093i	−0.685019	+	0.728525i	$0.740206\pi$
$740$	−38.6865	+	119.065i	−1.42214	+	4.37691i
$741$		0			0
$742$	12.6907	−	9.22033i	0.465890	−	0.338489i
$743$	14.6994	−	10.6798i	0.539270	−	0.391803i	−0.284544	−	0.958663i	$-0.591842\pi$
$743$	14.6994	−	10.6798i	0.539270	−	0.391803i	0.823814	+	0.566860i	$0.191842\pi$
$744$		0			0
$745$	9.38129	−	28.8726i	0.343704	−	1.05781i
$746$	−22.8096	−	16.5722i	−0.835120	−	0.606750i
$747$		0			0
$748$	5.11916	−	44.8512i	0.187175	−	1.63992i
$749$	7.14183			0.260957
$750$		0			0
$751$	−5.44189	+	16.7484i	−0.198578	+	0.611159i	0.801339	+	0.598211i	$0.204122\pi$
$751$	−5.44189	+	16.7484i	−0.198578	+	0.611159i	−0.999916	+	0.0129479i	$0.995878\pi$
$752$	0.0882965	+	0.271749i	0.00321984	+	0.00990965i
$753$		0			0
$754$	−67.6677	+	49.1634i	−2.46431	+	1.79043i
$755$	24.1951	+	74.4650i	0.880551	+	2.71006i
$756$		0			0
$757$	1.69987	+	1.23503i	0.0617827	+	0.0448878i	0.618248	−	0.785983i	$-0.287843\pi$
$757$	1.69987	+	1.23503i	0.0617827	+	0.0448878i	−0.556465	+	0.830871i	$0.687843\pi$
$758$	25.3228			0.919767
$759$		0			0
$760$	−18.4008			−0.667468
$761$	12.8668	+	9.34825i	0.466420	+	0.338874i	0.796044	−	0.605238i	$-0.206922\pi$
$761$	12.8668	+	9.34825i	0.466420	+	0.338874i	−0.329625	+	0.944112i	$0.606922\pi$
$762$		0			0
$763$	−0.619890	−	1.90783i	−0.0224415	−	0.0690680i
$764$	34.9349	−	25.3817i	1.26390	−	0.918277i
$765$		0			0
$766$	22.2642	+	68.5223i	0.804440	+	2.47581i
$767$	12.9479	−	39.8497i	0.467523	−	1.43889i
$768$		0			0
$769$	−6.44506			−0.232415			−0.116207	−	0.993225i	$-0.537074\pi$
$769$	−6.44506			−0.232415			−0.116207	+	0.993225i	$0.537074\pi$
$770$	−21.6642	+	23.6329i	−0.780723	+	0.851671i
$771$		0			0
$772$	29.0953	+	21.1390i	1.04716	+	0.760809i
$773$	−14.0473	+	43.2331i	−0.505246	+	1.55499i	0.295111	+	0.955463i	$0.404643\pi$
$773$	−14.0473	+	43.2331i	−0.505246	+	1.55499i	−0.800357	+	0.599524i	$0.795357\pi$
$774$		0			0
$775$	20.4912	−	14.8877i	0.736066	−	0.534783i
$776$	27.7163	−	20.1371i	0.994957	−	0.722879i
$777$		0			0
$778$	0.975530	−	3.00237i	0.0349744	−	0.107640i
$779$	2.32511	+	1.68929i	0.0833059	+	0.0605253i
$780$		0			0
$781$	15.8795	+	7.24051i	0.568213	+	0.259086i
$782$	−11.4191			−0.408345
$783$		0			0
$784$	−2.01837	+	6.21190i	−0.0720846	+	0.221854i
$785$	−9.35191	−	28.7822i	−0.333784	−	1.02728i
$786$		0			0
$787$	40.7262	−	29.5893i	1.45173	−	1.05475i	0.466311	−	0.884621i	$-0.345583\pi$
$787$	40.7262	−	29.5893i	1.45173	−	1.05475i	0.985422	−	0.170125i	$-0.0544172\pi$
$788$	−0.828938	−	2.55121i	−0.0295297	−	0.0908830i
$789$		0			0
$790$	−20.1653	−	14.6509i	−0.717449	−	0.521257i
$791$	−19.3324			−0.687381
$792$		0			0
$793$	20.9081			0.742470
$794$	−2.14504	−	1.55846i	−0.0761247	−	0.0553079i
$795$		0			0
$796$	−3.90996	−	12.0336i	−0.138585	−	0.426520i
$797$	36.1986	−	26.2998i	1.28222	−	0.931588i	0.282603	−	0.959237i	$-0.408802\pi$
$797$	36.1986	−	26.2998i	1.28222	−	0.931588i	0.999618	+	0.0276488i	$0.00880200\pi$
$798$		0			0
$799$	−0.300081	−	0.923556i	−0.0106161	−	0.0326730i
$800$	10.3073	−	31.7226i	0.364418	−	1.12156i
$801$		0			0
$802$	77.3961			2.73295
$803$	4.95774	−	5.40827i	0.174955	−	0.190854i
$804$		0			0
$805$	4.16649	+	3.02713i	0.146850	+	0.106692i
$806$	−14.7562	+	45.4150i	−0.519766	+	1.59968i
$807$		0			0
$808$	−22.2244	+	16.1470i	−0.781852	+	0.568049i
$809$	21.6493	−	15.7291i	0.761148	−	0.553006i	−0.138114	−	0.990416i	$-0.544104\pi$
$809$	21.6493	−	15.7291i	0.761148	−	0.553006i	0.899262	+	0.437410i	$0.144104\pi$
$810$		0			0
$811$	15.8989	−	48.9318i	0.558286	−	1.71823i	−0.128819	−	0.991668i	$-0.541119\pi$
$811$	15.8989	−	48.9318i	0.558286	−	1.71823i	0.687105	−	0.726559i	$-0.258881\pi$
$812$	−18.2535	−	13.2619i	−0.640571	−	0.465402i
$813$		0			0
$814$	−76.2808	+	15.5038i	−2.67364	+	0.543407i
$815$	−20.8449			−0.730165
$816$		0			0
$817$	−4.20021	+	12.9269i	−0.146947	+	0.452255i
$818$	1.14711	+	3.53044i	0.0401077	+	0.123439i
$819$		0			0
$820$	19.6164	−	14.2522i	0.685036	−	0.497707i
$821$	0.166002	+	0.510902i	0.00579352	+	0.0178306i	0.953911	−	0.300088i	$-0.0970161\pi$
$821$	0.166002	+	0.510902i	0.00579352	+	0.0178306i	−0.948118	+	0.317919i	$0.897016\pi$
$822$		0			0
$823$	−7.85190	−	5.70474i	−0.273700	−	0.198855i	0.442465	−	0.896786i	$-0.354104\pi$
$823$	−7.85190	−	5.70474i	−0.273700	−	0.198855i	−0.716165	+	0.697931i	$0.754104\pi$
$824$	−22.3972			−0.780243
$825$		0			0
$826$	17.7984			0.619285
$827$	32.2959	+	23.4643i	1.12304	+	0.815934i	0.984667	−	0.174447i	$-0.0558136\pi$
$827$	32.2959	+	23.4643i	1.12304	+	0.815934i	0.138370	+	0.990381i	$0.455814\pi$
$828$		0			0
$829$	6.01231	+	18.5040i	0.208816	+	0.642670i	0.999535	+	0.0304906i	$0.00970697\pi$
$829$	6.01231	+	18.5040i	0.208816	+	0.642670i	−0.790719	+	0.612179i	$0.790293\pi$
$830$	−79.5402	+	57.7894i	−2.76088	+	2.00590i
$831$		0			0
$832$	23.9433	+	73.6898i	0.830084	+	2.55473i
$833$	6.85956	−	21.1115i	0.237670	−	0.731472i
$834$		0			0
$835$	57.9542			2.00559
$836$	−8.40927	−	14.8702i	−0.290841	−	0.514297i
$837$		0			0
$838$	−6.13478	−	4.45718i	−0.211923	−	0.153971i
$839$	3.05596	−	9.40529i	0.105504	−	0.324707i	−0.884345	−	0.466834i	$-0.845394\pi$
$839$	3.05596	−	9.40529i	0.105504	−	0.324707i	0.989848	+	0.142128i	$0.0453944\pi$
$840$		0			0
$841$	−2.21569	+	1.60979i	−0.0764029	+	0.0555100i
$842$	69.7961	−	50.7099i	2.40533	−	1.74758i
$843$		0			0
$844$	17.1465	−	52.7716i	0.590208	−	1.81647i
$845$	−79.0241	−	57.4144i	−2.71851	−	1.97512i
$846$		0			0
$847$	−12.3333	−	2.85253i	−0.423778	−	0.0980139i
$848$	6.70091			0.230110
$849$		0			0
$850$	22.2803	−	68.5716i	0.764207	−	2.35199i
$851$	3.86398	+	11.8921i	0.132456	+	0.407657i
$852$		0			0
$853$	33.5819	−	24.3987i	1.14982	−	0.835396i	0.161366	−	0.986895i	$-0.448410\pi$
$853$	33.5819	−	24.3987i	1.14982	−	0.835396i	0.988457	+	0.151499i	$0.0484100\pi$
$854$	2.74448	+	8.44663i	0.0939141	+	0.289038i
$855$		0			0
$856$	17.3958	+	12.6388i	0.594575	+	0.431984i
$857$	−37.8305			−1.29227			−0.646133	−	0.763225i	$-0.723615\pi$
$857$	−37.8305			−1.29227			−0.646133	+	0.763225i	$0.723615\pi$
$858$		0			0
$859$	44.5423			1.51976			0.759882	−	0.650061i	$-0.225257\pi$
$859$	44.5423			1.51976			0.759882	+	0.650061i	$0.225257\pi$
$860$	92.7730	+	67.4035i	3.16353	+	2.29844i
$861$		0			0
$862$	3.91225	+	12.0407i	0.133252	+	0.410107i
$863$	−15.9320	+	11.5753i	−0.542332	+	0.394028i	−0.824951	−	0.565205i	$-0.808797\pi$
$863$	−15.9320	+	11.5753i	−0.542332	+	0.394028i	0.282618	+	0.959233i	$0.408797\pi$
$864$		0			0
$865$	−15.9889	−	49.2087i	−0.543638	−	1.67315i
$866$	−22.7374	+	69.9785i	−0.772648	+	2.37796i
$867$		0			0
$868$	−12.8812			−0.437218
$869$	1.11607	−	9.77838i	0.0378601	−	0.331709i
$870$		0			0
$871$	−72.2227	−	52.4729i	−2.44717	−	1.77797i
$872$	1.86634	−	5.74401i	0.0632023	−	0.194517i
$873$		0			0
$874$	−3.49603	+	2.54001i	−0.118255	+	0.0859172i
$875$	−9.60410	+	6.97779i	−0.324678	+	0.235892i
$876$		0			0
$877$	−12.6113	+	38.8136i	−0.425854	+	1.31064i	0.476321	+	0.879272i	$0.341970\pi$
$877$	−12.6113	+	38.8136i	−0.425854	+	1.31064i	−0.902174	+	0.431372i	$0.858030\pi$
$878$	−50.7712	−	36.8874i	−1.71344	−	1.24489i
$879$		0			0
$880$	−13.4209	+	2.72774i	−0.452419	+	0.0919522i
$881$	−37.0974			−1.24984			−0.624921	−	0.780688i	$-0.714869\pi$
$881$	−37.0974			−1.24984			−0.624921	+	0.780688i	$0.714869\pi$
$882$		0			0
$883$	12.8664	−	39.5986i	0.432988	−	1.33260i	−0.462146	−	0.886804i	$-0.652920\pi$
$883$	12.8664	−	39.5986i	0.432988	−	1.33260i	0.895134	−	0.445797i	$-0.147080\pi$
$884$	26.6751	+	82.0975i	0.897181	+	2.76124i
$885$		0			0
$886$	−36.1061	+	26.2326i	−1.21301	+	0.881301i
$887$	3.65713	+	11.2555i	0.122794	+	0.377922i	0.993493	−	0.113895i	$-0.0363328\pi$
$887$	3.65713	+	11.2555i	0.122794	+	0.377922i	−0.870698	+	0.491817i	$0.836333\pi$
$888$		0			0
$889$	−2.06309	−	1.49893i	−0.0691940	−	0.0502724i
$890$	−75.0479			−2.51561
$891$		0			0
$892$	−19.9951			−0.669485
$893$	−0.297304	−	0.216004i	−0.00994891	−	0.00722831i
$894$		0			0
$895$	4.82334	+	14.8447i	0.161227	+	0.496204i
$896$	−18.7400	+	13.6154i	−0.626058	+	0.454858i
$897$		0			0
$898$	−20.0983	−	61.8561i	−0.670688	−	2.06416i
$899$	−5.59940	+	17.2332i	−0.186751	+	0.574759i
$900$		0			0
$901$	−22.7735			−0.758695
$902$	13.7175	+	6.25470i	0.456742	+	0.208259i
$903$		0			0
$904$	−47.0890	−	34.2122i	−1.56616	−	1.13788i
$905$	16.6218	−	51.1567i	0.552529	−	1.70051i
$906$		0			0
$907$	35.6443	−	25.8971i	1.18355	−	0.859899i	0.190982	−	0.981593i	$-0.438833\pi$
$907$	35.6443	−	25.8971i	1.18355	−	0.859899i	0.992568	+	0.121694i	$0.0388327\pi$
$908$	−52.5645	+	38.1903i	−1.74441	+	1.26739i
$909$		0			0
$910$	18.9446	−	58.3056i	0.628009	−	1.93281i
$911$	21.3540	+	15.5146i	0.707491	+	0.514022i	0.882363	−	0.470569i	$-0.155951\pi$
$911$	21.3540	+	15.5146i	0.707491	+	0.514022i	−0.174872	+	0.984591i	$0.555951\pi$
$912$		0			0
$913$	−35.3219	−	16.1056i	−1.16898	−	0.533016i
$914$	−43.8790			−1.45139
$915$		0			0
$916$	−1.84472	+	5.67746i	−0.0609512	+	0.187588i
$917$	−4.20688	−	12.9475i	−0.138924	−	0.427563i
$918$		0			0
$919$	−1.55803	+	1.13197i	−0.0513945	+	0.0373403i	−0.613186	−	0.789939i	$-0.710112\pi$
$919$	−1.55803	+	1.13197i	−0.0513945	+	0.0373403i	0.561791	+	0.827279i	$0.310112\pi$
$920$	4.79150	+	14.7467i	0.157971	+	0.486185i
$921$		0			0
$922$	−34.2912	−	24.9140i	−1.12932	−	0.820499i
$923$	−33.3728			−1.09848
$924$		0			0
$925$	−78.9516			−2.59591
$926$	−46.5458	−	33.8175i	−1.52959	−	1.11131i
$927$		0			0
$928$	7.37386	+	22.6944i	0.242059	+	0.744980i
$929$	−19.9286	+	14.4789i	−0.653835	+	0.475039i	−0.864575	−	0.502503i	$-0.832412\pi$
$929$	−19.9286	+	14.4789i	−0.653835	+	0.475039i	0.210741	+	0.977542i	$0.432412\pi$
$930$		0			0
$931$	−2.59587	−	7.98927i	−0.0850762	−	0.261838i
$932$	7.73470	−	23.8050i	0.253358	−	0.779757i
$933$		0			0
$934$	−36.3040			−1.18790
$935$	45.6118	−	9.27041i	1.49167	−	0.303175i
$936$		0			0
$937$	44.1168	+	32.0527i	1.44123	+	1.04712i	0.987783	+	0.155835i	$0.0498068\pi$
$937$	44.1168	+	32.0527i	1.44123	+	1.04712i	0.453450	+	0.891282i	$0.350193\pi$
$938$	11.7182	−	36.0648i	0.382612	−	1.17756i
$939$		0			0
$940$	−2.50829	+	1.82238i	−0.0818112	+	0.0594393i
$941$	−22.2658	+	16.1771i	−0.725846	+	0.527358i	−0.888246	−	0.459367i	$-0.848076\pi$
$941$	−22.2658	+	16.1771i	−0.725846	+	0.527358i	0.162401	+	0.986725i	$0.448076\pi$
$942$		0			0
$943$	0.748378	−	2.30327i	0.0243705	−	0.0750048i
$944$	6.15098	+	4.46895i	0.200197	+	0.145452i
$945$		0			0
$946$	−8.08549	+	70.8405i	−0.262882	+	2.30322i
$947$	19.2088			0.624203			0.312102	−	0.950049i	$-0.398967\pi$
$947$	19.2088			0.624203			0.312102	+	0.950049i	$0.398967\pi$
$948$		0			0
$949$	−4.33538	+	13.3429i	−0.140732	+	0.433130i
$950$	−8.43155	−	25.9496i	−0.273555	−	0.841917i
$951$		0			0
$952$	−12.6165	+	9.16644i	−0.408904	+	0.297086i
$953$	8.93933	+	27.5124i	0.289573	+	0.891215i	0.984991	+	0.172608i	$0.0552195\pi$
$953$	8.93933	+	27.5124i	0.289573	+	0.891215i	−0.695417	+	0.718606i	$0.744780\pi$
$954$		0			0
$955$	36.0198	+	26.1700i	1.16557	+	0.846840i
$956$	33.5591			1.08538
$957$		0			0
$958$	22.5568			0.728777
$959$	15.8404	+	11.5087i	0.511514	+	0.371637i
$960$		0			0
$961$	−6.38276	−	19.6441i	−0.205895	−	0.633681i
$962$	120.421	−	87.4909i	3.88252	−	2.82082i
$963$		0			0
$964$	3.20120	+	9.85227i	0.103104	+	0.317320i
$965$	−11.4586	+	35.2659i	−0.368865	+	1.13525i
$966$		0			0
$967$	−13.8862			−0.446552			−0.223276	−	0.974755i	$-0.571675\pi$
$967$	−13.8862			−0.446552			−0.223276	+	0.974755i	$0.571675\pi$
$968$	−24.9929	−	28.7741i	−0.803303	−	0.924834i
$969$		0			0
$970$	67.1926	+	48.8183i	2.15742	+	1.56746i
$971$	9.80736	−	30.1840i	0.314733	−	0.968649i	−0.661131	−	0.750271i	$-0.729923\pi$
$971$	9.80736	−	30.1840i	0.314733	−	0.968649i	0.975864	−	0.218379i	$-0.0700768\pi$
$972$		0			0
$973$	6.52529	−	4.74090i	0.209191	−	0.151986i
$974$	65.0115	−	47.2337i	2.08310	−	1.51346i
$975$		0			0
$976$	−1.17237	+	3.60820i	−0.0375268	+	0.115496i
$977$	−5.26888	−	3.82806i	−0.168566	−	0.122471i	0.500304	−	0.865850i	$-0.333222\pi$
$977$	−5.26888	−	3.82806i	−0.168566	−	0.122471i	−0.668870	+	0.743379i	$0.733222\pi$
$978$		0			0
$979$	−14.5867	−	25.7938i	−0.466192	−	0.824373i
$980$	−70.8723			−2.26393
$981$		0			0
$982$	12.6841	−	39.0377i	0.404767	−	1.24574i
$983$	18.1369	+	55.8197i	0.578478	+	1.78037i	0.624019	+	0.781409i	$0.285499\pi$
$983$	18.1369	+	55.8197i	0.578478	+	1.78037i	−0.0455410	+	0.998962i	$0.514501\pi$
$984$		0			0
$985$	2.23759	−	1.62570i	0.0712954	−	0.0517991i
$986$	15.9393	+	49.0562i	0.507611	+	1.56227i
$987$		0			0
$988$	26.4282	+	19.2012i	0.840794	+	0.610873i
$989$	11.4535			0.364202
$990$		0			0
$991$	54.1267			1.71939			0.859696	−	0.510806i	$-0.170653\pi$
$991$	54.1267			1.71939			0.859696	+	0.510806i	$0.170653\pi$
$992$	11.0215	+	8.00757i	0.349932	+	0.254241i
$993$		0			0
$994$	−4.38063	−	13.4822i	−0.138945	−	0.427629i
$995$	10.5543	−	7.66816i	0.334594	−	0.243097i
$996$		0			0
$997$	−4.23734	−	13.0412i	−0.134198	−	0.413019i	0.861266	−	0.508154i	$-0.169672\pi$
$997$	−4.23734	−	13.0412i	−0.134198	−	0.413019i	−0.995464	+	0.0951346i	$0.969672\pi$
$998$	−17.4610	+	53.7394i	−0.552718	+	1.70109i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.c.136.4	yes	16
3.2	odd	2	inner	297.2.f.c.136.1	✓	16
9.2	odd	6		891.2.n.g.433.1		32
9.4	even	3		891.2.n.g.136.1		32
9.5	odd	6		891.2.n.g.136.4		32
9.7	even	3		891.2.n.g.433.4		32
11.3	even	5	inner	297.2.f.c.190.4	yes	16
11.5	even	5		3267.2.a.bg.1.1		8
11.6	odd	10		3267.2.a.bh.1.8		8
33.5	odd	10		3267.2.a.bg.1.8		8
33.14	odd	10	inner	297.2.f.c.190.1	yes	16
33.17	even	10		3267.2.a.bh.1.1		8
99.14	odd	30		891.2.n.g.784.1		32
99.25	even	15		891.2.n.g.190.1		32
99.47	odd	30		891.2.n.g.190.4		32
99.58	even	15		891.2.n.g.784.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.c.136.1	✓	16	3.2	odd	2	inner
297.2.f.c.136.4	yes	16	1.1	even	1	trivial
297.2.f.c.190.1	yes	16	33.14	odd	10	inner
297.2.f.c.190.4	yes	16	11.3	even	5	inner
891.2.n.g.136.1		32	9.4	even	3
891.2.n.g.136.4		32	9.5	odd	6
891.2.n.g.190.1		32	99.25	even	15
891.2.n.g.190.4		32	99.47	odd	30
891.2.n.g.433.1		32	9.2	odd	6
891.2.n.g.433.4		32	9.7	even	3
891.2.n.g.784.1		32	99.14	odd	30
891.2.n.g.784.4		32	99.58	even	15
3267.2.a.bg.1.1		8	11.5	even	5
3267.2.a.bg.1.8		8	33.5	odd	10
3267.2.a.bh.1.1		8	33.17	even	10
3267.2.a.bh.1.8		8	11.6	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89387 + 1.37598i) q^{2} +(1.07540 + 3.30976i) q^{4} +(-2.90288 + 2.10907i) q^{5} +(0.355620 + 1.09448i) q^{7} +(-1.07069 + 3.29523i) q^{8} +O(q^{10})\)	\(q+(1.89387 + 1.37598i) q^{2} +(1.07540 + 3.30976i) q^{4} +(-2.90288 + 2.10907i) q^{5} +(0.355620 + 1.09448i) q^{7} +(-1.07069 + 3.29523i) q^{8} -8.39974 q^{10} +(-1.63261 - 2.88697i) q^{11} +(5.13089 + 3.72781i) q^{13} +(-0.832490 + 2.56214i) q^{14} +(-0.931024 + 0.676429i) q^{16} +(3.16415 - 2.29889i) q^{17} +(0.457371 - 1.40764i) q^{19} +(-10.1023 - 7.33973i) q^{20} +(0.880448 - 7.71399i) q^{22} -1.24720 q^{23} +(2.43348 - 7.48948i) q^{25} +(4.58787 + 14.1200i) q^{26} +(-3.24004 + 2.35403i) q^{28} +(1.74091 + 5.35798i) q^{29} +(2.60209 + 1.89053i) q^{31} +4.23563 q^{32} +9.15572 q^{34} +(-3.34067 - 2.42714i) q^{35} +(-3.09812 - 9.53502i) q^{37} +(2.80309 - 2.03656i) q^{38} +(-3.84179 - 11.8238i) q^{40} +(-0.600044 + 1.84675i) q^{41} -9.18338 q^{43} +(7.79944 - 8.50820i) q^{44} +(-2.36205 - 1.71613i) q^{46} +(0.0767256 - 0.236137i) q^{47} +(4.59169 - 3.33606i) q^{49} +(14.9141 - 10.8357i) q^{50} +(-6.82036 + 20.9909i) q^{52} +(-4.71073 - 3.42255i) q^{53} +(10.8281 + 4.93724i) q^{55} -3.98734 q^{56} +(-4.07540 + 12.5428i) q^{58} +(-2.04158 - 6.28333i) q^{59} +(2.66709 - 1.93776i) q^{61} +(2.32670 + 7.16085i) q^{62} +(9.88379 + 7.18099i) q^{64} -22.7566 q^{65} -14.0761 q^{67} +(11.0115 + 8.00032i) q^{68} +(-2.98711 - 9.19338i) q^{70} +(-4.25711 + 3.09297i) q^{71} +(0.683585 + 2.10386i) q^{73} +(7.25256 - 22.3211i) q^{74} +5.15081 q^{76} +(2.57915 - 2.81353i) q^{77} +(2.40070 + 1.74421i) q^{79} +(1.27602 - 3.92719i) q^{80} +(-3.67749 + 2.67186i) q^{82} +(9.46937 - 6.87990i) q^{83} +(-4.33664 + 13.3468i) q^{85} +(-17.3922 - 12.6361i) q^{86} +(11.2612 - 2.28880i) q^{88} +8.93456 q^{89} +(-2.25539 + 6.94137i) q^{91} +(-1.34125 - 4.12794i) q^{92} +(0.470228 - 0.341641i) q^{94} +(1.64112 + 5.05085i) q^{95} +(-7.99937 - 5.81188i) q^{97} +13.2864 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 2 * q^4 + 8 * q^7	\( 16 q + 2 q^{4} + 8 q^{7} - 12 q^{10} + 8 q^{13} - 2 q^{16} + 10 q^{19} - 24 q^{22} - 16 q^{25} - 30 q^{28} - 6 q^{31} + 32 q^{34} + 12 q^{37} - 40 q^{40} - 80 q^{43} - 12 q^{46} + 40 q^{49} + 12 q^{52} + 56 q^{55} - 50 q^{58} - 6 q^{61} + 6 q^{64} + 64 q^{67} + 74 q^{70} - 32 q^{73} + 52 q^{76} - 4 q^{79} + 4 q^{82} + 70 q^{85} + 56 q^{88} - 94 q^{91} - 46 q^{94}+O(q^{100}) \) 16 * q + 2 * q^4 + 8 * q^7 - 12 * q^10 + 8 * q^13 - 2 * q^16 + 10 * q^19 - 24 * q^22 - 16 * q^25 - 30 * q^28 - 6 * q^31 + 32 * q^34 + 12 * q^37 - 40 * q^40 - 80 * q^43 - 12 * q^46 + 40 * q^49 + 12 * q^52 + 56 * q^55 - 50 * q^58 - 6 * q^61 + 6 * q^64 + 64 * q^67 + 74 * q^70 - 32 * q^73 + 52 * q^76 - 4 * q^79 + 4 * q^82 + 70 * q^85 + 56 * q^88 - 94 * q^91 - 46 * q^94

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