LMFDB - Embedded newform 153.2.f.b.64.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(55,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.4
Root			$2.06644i$ of defining polynomial
Character	$\chi$	$=$	153.64
Dual form			153.2.f.b.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.06644i q^{2} -2.27016 q^{4} +(0.245916 + 0.245916i) q^{5} +(-3.06644 + 3.06644i) q^{7} -0.558268i q^{8} +(-0.508169 + 0.508169i) q^{10} +(-0.516075 + 0.516075i) q^{11} +5.40303 q^{13} +(-6.33660 - 6.33660i) q^{14} -3.38669 q^{16} +(4.09068 - 0.516075i) q^{17} -3.27016i q^{19} +(-0.558268 - 0.558268i) q^{20} +(-1.06644 - 1.06644i) q^{22} +(2.51608 - 2.51608i) q^{23} -4.87905i q^{25} +11.1650i q^{26} +(6.96130 - 6.96130i) q^{28} +(3.09859 + 3.09859i) q^{29} +(2.33660 + 2.33660i) q^{31} -8.11492i q^{32} +(1.06644 + 8.45313i) q^{34} -1.50817 q^{35} +(2.03215 + 2.03215i) q^{37} +6.75758 q^{38} +(0.137287 - 0.137287i) q^{40} +(-8.37879 + 8.37879i) q^{41} +3.74618i q^{43} +(1.17157 - 1.17157i) q^{44} +(5.19931 + 5.19931i) q^{46} +0.476019 q^{47} -11.8061i q^{49} +10.0822 q^{50} -12.2657 q^{52} -10.1329i q^{53} -0.253822 q^{55} +(1.71189 + 1.71189i) q^{56} +(-6.40303 + 6.40303i) q^{58} -5.29790i q^{59} +(2.50817 - 2.50817i) q^{61} +(-4.82843 + 4.82843i) q^{62} +9.99559 q^{64} +(1.32869 + 1.32869i) q^{65} -1.55666 q^{67} +(-9.28650 + 1.17157i) q^{68} -3.11654i q^{70} +(-6.33660 - 6.33660i) q^{71} +(-2.89486 - 2.89486i) q^{73} +(-4.19931 + 4.19931i) q^{74} +7.42378i q^{76} -3.16502i q^{77} +(-0.574605 + 0.574605i) q^{79} +(-0.832841 - 0.832841i) q^{80} +(-17.3142 - 17.3142i) q^{82} +7.21351i q^{83} +(1.13287 + 0.879051i) q^{85} -7.74124 q^{86} +(0.288108 + 0.288108i) q^{88} -9.77391 q^{89} +(-16.5681 + 16.5681i) q^{91} +(-5.71189 + 5.71189i) q^{92} +0.983662i q^{94} +(0.804183 - 0.804183i) q^{95} +(-1.25382 - 1.25382i) q^{97} +24.3965 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) $ 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			2.06644i			1.46119i	0.682810	+	0.730596i	$0.260757\pi$
$2$			2.06644i			1.46119i	−0.682810	+	0.730596i	$0.739243\pi$
$3$		0			0
$3$		0			0
$4$	−2.27016			−1.13508
$5$	0.245916	+	0.245916i	0.109977	+	0.109977i	0.759954	−	0.649977i	$-0.225222\pi$
$5$	0.245916	+	0.245916i	0.109977	+	0.109977i	−0.649977	+	0.759954i	$0.725222\pi$
$6$		0			0
$7$	−3.06644	+	3.06644i	−1.15900	+	1.15900i	−0.174314	+	0.984690i	$0.555771\pi$
$7$	−3.06644	+	3.06644i	−1.15900	+	1.15900i	−0.984690	+	0.174314i	$0.944229\pi$
$8$		−	0.558268i		−	0.197377i
$9$		0			0
$10$	−0.508169	+	0.508169i	−0.160697	+	0.160697i
$11$	−0.516075	+	0.516075i	−0.155603	+	0.155603i	−0.780615	−	0.625012i	$-0.785094\pi$
$11$	−0.516075	+	0.516075i	−0.155603	+	0.155603i	0.625012	+	0.780615i	$0.285094\pi$
$12$		0			0
$13$	5.40303			1.49853			0.749266	−	0.662269i	$-0.230407\pi$
$13$	5.40303			1.49853			0.749266	+	0.662269i	$0.230407\pi$
$14$	−6.33660	−	6.33660i	−1.69353	−	1.69353i
$15$		0			0
$16$	−3.38669			−0.846674
$17$	4.09068	−	0.516075i	0.992136	−	0.125167i
$17$	4.09068	−	0.516075i	0.992136	−	0.125167i
$18$		0			0
$19$		−	3.27016i		−	0.750226i	−0.926979	−	0.375113i	$-0.877604\pi$
$19$		−	3.27016i		−	0.750226i	0.926979	−	0.375113i	$-0.122396\pi$
$20$	−0.558268	−	0.558268i	−0.124832	−	0.124832i
$21$		0			0
$22$	−1.06644	−	1.06644i	−0.227365	−	0.227365i
$23$	2.51608	−	2.51608i	0.524638	−	0.524638i	−0.394331	−	0.918969i	$-0.629024\pi$
$23$	2.51608	−	2.51608i	0.524638	−	0.524638i	0.918969	+	0.394331i	$0.129024\pi$
$24$		0			0
$25$		−	4.87905i		−	0.975810i
$26$			11.1650i			2.18964i
$27$		0			0
$28$	6.96130	−	6.96130i	1.31556	−	1.31556i
$29$	3.09859	+	3.09859i	0.575393	+	0.575393i	0.933631	−	0.358237i	$-0.116622\pi$
$29$	3.09859	+	3.09859i	0.575393	+	0.575393i	−0.358237	+	0.933631i	$0.616622\pi$
$30$		0			0
$31$	2.33660	+	2.33660i	0.419665	+	0.419665i	0.885088	−	0.465423i	$-0.154098\pi$
$31$	2.33660	+	2.33660i	0.419665	+	0.419665i	−0.465423	+	0.885088i	$0.654098\pi$
$32$		−	8.11492i		−	1.43453i
$33$		0			0
$34$	1.06644	+	8.45313i	0.182892	+	1.44970i
$35$	−1.50817			−0.254927
$36$		0			0
$37$	2.03215	+	2.03215i	0.334083	+	0.334083i	0.854135	−	0.520051i	$-0.174087\pi$
$37$	2.03215	+	2.03215i	0.334083	+	0.334083i	−0.520051	+	0.854135i	$0.674087\pi$
$38$	6.75758			1.09622
$39$		0			0
$40$	0.137287	−	0.137287i	0.0217069	−	0.0217069i
$41$	−8.37879	+	8.37879i	−1.30855	+	1.30855i	−0.386083	+	0.922464i	$0.626172\pi$
$41$	−8.37879	+	8.37879i	−1.30855	+	1.30855i	−0.922464	+	0.386083i	$0.873828\pi$
$42$		0			0
$43$			3.74618i			0.571287i	0.958336	+	0.285643i	$0.0922073\pi$
$43$			3.74618i			0.571287i	−0.958336	+	0.285643i	$0.907793\pi$
$44$	1.17157	−	1.17157i	0.176621	−	0.176621i
$45$		0			0
$46$	5.19931	+	5.19931i	0.766596	+	0.766596i
$47$	0.476019			0.0694345			0.0347172	−	0.999397i	$-0.488947\pi$
$47$	0.476019			0.0694345			0.0347172	+	0.999397i	$0.488947\pi$
$48$		0			0
$49$		−	11.8061i		−	1.68658i
$50$	10.0822			1.42585
$51$		0			0
$52$	−12.2657			−1.70095
$53$		−	10.1329i		−	1.39186i	−0.718111	−	0.695929i	$-0.754993\pi$
$53$		−	10.1329i		−	1.39186i	0.718111	−	0.695929i	$-0.245007\pi$
$54$		0			0
$55$	−0.253822			−0.0342253
$56$	1.71189	+	1.71189i	0.228761	+	0.228761i
$57$		0			0
$58$	−6.40303	+	6.40303i	−0.840759	+	0.840759i
$59$		−	5.29790i		−	0.689727i	−0.938653	−	0.344864i	$-0.887925\pi$
$59$		−	5.29790i		−	0.689727i	0.938653	−	0.344864i	$-0.112075\pi$
$60$		0			0
$61$	2.50817	−	2.50817i	0.321138	−	0.321138i	−0.528066	−	0.849204i	$-0.677082\pi$
$61$	2.50817	−	2.50817i	0.321138	−	0.321138i	0.849204	+	0.528066i	$0.177082\pi$
$62$	−4.82843	+	4.82843i	−0.613211	+	0.613211i
$63$		0			0
$64$	9.99559			1.24945
$65$	1.32869	+	1.32869i	0.164804	+	0.164804i
$66$		0			0
$67$	−1.55666			−0.190176			−0.0950880	−	0.995469i	$-0.530313\pi$
$67$	−1.55666			−0.190176			−0.0950880	+	0.995469i	$0.530313\pi$
$68$	−9.28650	+	1.17157i	−1.12615	+	0.142074i
$69$		0			0
$70$		−	3.11654i		−	0.372497i
$71$	−6.33660	−	6.33660i	−0.752016	−	0.752016i	0.222840	−	0.974855i	$-0.428467\pi$
$71$	−6.33660	−	6.33660i	−0.752016	−	0.752016i	−0.974855	+	0.222840i	$0.928467\pi$
$72$		0			0
$73$	−2.89486	−	2.89486i	−0.338818	−	0.338818i	0.517104	−	0.855922i	$-0.327010\pi$
$73$	−2.89486	−	2.89486i	−0.338818	−	0.338818i	−0.855922	+	0.517104i	$0.827010\pi$
$74$	−4.19931	+	4.19931i	−0.488160	+	0.488160i
$75$		0			0
$76$			7.42378i			0.851566i
$77$		−	3.16502i		−	0.360688i
$78$		0			0
$79$	−0.574605	+	0.574605i	−0.0646481	+	0.0646481i	−0.738692	−	0.674044i	$-0.764556\pi$
$79$	−0.574605	+	0.574605i	−0.0646481	+	0.0646481i	0.674044	+	0.738692i	$0.264556\pi$
$80$	−0.832841	−	0.832841i	−0.0931144	−	0.0931144i
$81$		0			0
$82$	−17.3142	−	17.3142i	−1.91204	−	1.91204i
$83$			7.21351i			0.791786i	0.918297	+	0.395893i	$0.129565\pi$
$83$			7.21351i			0.791786i	−0.918297	+	0.395893i	$0.870435\pi$
$84$		0			0
$85$	1.13287	+	0.879051i	0.122877	+	0.0953465i
$86$	−7.74124			−0.834759
$87$		0			0
$88$	0.288108	+	0.288108i	0.0307124	+	0.0307124i
$89$	−9.77391			−1.03603			−0.518016	−	0.855371i	$-0.673329\pi$
$89$	−9.77391			−1.03603			−0.518016	+	0.855371i	$0.673329\pi$
$90$		0			0
$91$	−16.5681	+	16.5681i	−1.73680	+	1.73680i
$92$	−5.71189	+	5.71189i	−0.595506	+	0.595506i
$93$		0			0
$94$			0.983662i			0.101457i
$95$	0.804183	−	0.804183i	0.0825074	−	0.0825074i
$96$		0			0
$97$	−1.25382	−	1.25382i	−0.127306	−	0.127306i	0.640583	−	0.767889i	$-0.278693\pi$
$97$	−1.25382	−	1.25382i	−0.127306	−	0.127306i	−0.767889	+	0.640583i	$0.778693\pi$
$98$	24.3965			2.46442
$99$		0			0
$100$			11.0762i			1.10762i
$101$	14.6089			1.45364			0.726820	−	0.686828i	$-0.240998\pi$
$101$	14.6089			1.45364			0.726820	+	0.686828i	$0.240998\pi$
$102$		0			0
$103$	2.86271			0.282072			0.141036	−	0.990005i	$-0.454957\pi$
$103$	2.86271			0.282072			0.141036	+	0.990005i	$0.454957\pi$
$104$		−	3.01634i		−	0.295776i
$105$		0			0
$106$	20.9389			2.03377
$107$	4.46759	+	4.46759i	0.431898	+	0.431898i	0.889274	−	0.457376i	$-0.151211\pi$
$107$	4.46759	+	4.46759i	0.431898	+	0.431898i	−0.457376	+	0.889274i	$0.651211\pi$
$108$		0			0
$109$	−3.32239	+	3.32239i	−0.318228	+	0.318228i	−0.848086	−	0.529858i	$-0.822245\pi$
$109$	−3.32239	+	3.32239i	−0.318228	+	0.318228i	0.529858	+	0.848086i	$0.322245\pi$
$110$		−	0.524507i		−	0.0500097i
$111$		0			0
$112$	10.3851	−	10.3851i	0.981298	−	0.981298i
$113$	8.78623	−	8.78623i	0.826539	−	0.826539i	−0.160497	−	0.987036i	$-0.551310\pi$
$113$	8.78623	−	8.78623i	0.826539	−	0.826539i	0.987036	+	0.160497i	$0.0513097\pi$
$114$		0			0
$115$	1.23748			0.115396
$116$	−7.03429	−	7.03429i	−0.653117	−	0.653117i
$117$		0			0
$118$	10.9478			1.00782
$119$	−10.9613	+	14.1263i	−1.00482	+	1.29496i
$120$		0			0
$121$			10.4673i			0.951576i
$122$	5.18297	+	5.18297i	0.469244	+	0.469244i
$123$		0			0
$124$	−5.30445	−	5.30445i	−0.476353	−	0.476353i
$125$	2.42941	−	2.42941i	0.217293	−	0.217293i
$126$		0			0
$127$		−	1.81048i		−	0.160654i	−0.996769	−	0.0803270i	$-0.974404\pi$
$127$		−	1.81048i		−	0.160654i	0.996769	−	0.0803270i	$-0.0255965\pi$
$128$			4.42539i			0.391153i
$129$		0			0
$130$	−2.74565	+	2.74565i	−0.240810	+	0.240810i
$131$	−4.51608	−	4.51608i	−0.394571	−	0.394571i	0.481742	−	0.876313i	$-0.340004\pi$
$131$	−4.51608	−	4.51608i	−0.394571	−	0.394571i	−0.876313	+	0.481742i	$0.840004\pi$
$132$		0			0
$133$	10.0277	+	10.0277i	0.869515	+	0.869515i
$134$		−	3.21673i		−	0.277883i
$135$		0			0
$136$	−0.288108	−	2.28369i	−0.0247051	−	0.195825i
$137$	2.28156			0.194927			0.0974633	−	0.995239i	$-0.468927\pi$
$137$	2.28156			0.194927			0.0974633	+	0.995239i	$0.468927\pi$
$138$		0			0
$139$	−11.7554	−	11.7554i	−0.997083	−	0.997083i	0.00291227	−	0.999996i	$-0.499073\pi$
$139$	−11.7554	−	11.7554i	−0.997083	−	0.997083i	−0.999996	+	0.00291227i	$0.999073\pi$
$140$	3.42378			0.289363
$141$		0			0
$142$	13.0942	−	13.0942i	1.09884	−	1.09884i
$143$	−2.78837	+	2.78837i	−0.233175	+	0.233175i
$144$		0			0
$145$			1.52398i			0.126560i
$146$	5.98205	−	5.98205i	0.495078	−	0.495078i
$147$		0			0
$148$	−4.61331	−	4.61331i	−0.379211	−	0.379211i
$149$	−12.1814			−0.997936			−0.498968	−	0.866620i	$-0.666287\pi$
$149$	−12.1814			−0.997936			−0.498968	+	0.866620i	$0.666287\pi$
$150$		0			0
$151$		−	19.3823i		−	1.57731i	−0.614837	−	0.788654i	$-0.710778\pi$
$151$		−	19.3823i		−	1.57731i	0.614837	−	0.788654i	$-0.289222\pi$
$152$	−1.82562			−0.148078
$153$		0			0
$154$	6.54032			0.527034
$155$			1.14921i			0.0923068i
$156$		0			0
$157$	−1.81475			−0.144833			−0.0724164	−	0.997374i	$-0.523071\pi$
$157$	−1.81475			−0.144833			−0.0724164	+	0.997374i	$0.523071\pi$
$158$	−1.18739	−	1.18739i	−0.0944633	−	0.0944633i
$159$		0			0
$160$	1.99559	−	1.99559i	0.157765	−	0.157765i
$161$			15.4308i			1.21611i
$162$		0			0
$163$	−10.4009	+	10.4009i	−0.814661	+	0.814661i	−0.985329	−	0.170668i	$-0.945408\pi$
$163$	−10.4009	+	10.4009i	−0.814661	+	0.814661i	0.170668	+	0.985329i	$0.445408\pi$
$164$	19.0212	−	19.0212i	1.48531	−	1.48531i
$165$		0			0
$166$	−14.9063			−1.15695
$167$	5.68110	+	5.68110i	0.439617	+	0.439617i	0.891883	−	0.452266i	$-0.149384\pi$
$167$	5.68110	+	5.68110i	0.439617	+	0.439617i	−0.452266	+	0.891883i	$0.649384\pi$
$168$		0			0
$169$	16.1928			1.24560
$170$	−1.81650	+	2.34101i	−0.139319	+	0.179547i
$171$		0			0
$172$		−	8.50442i		−	0.648456i
$173$	−8.51166	−	8.51166i	−0.647130	−	0.647130i	0.305169	−	0.952298i	$-0.401287\pi$
$173$	−8.51166	−	8.51166i	−0.647130	−	0.647130i	−0.952298	+	0.305169i	$0.901287\pi$
$174$		0			0
$175$	14.9613	+	14.9613i	1.13097	+	1.13097i
$176$	1.74779	−	1.74779i	0.131745	−	0.131745i
$177$		0			0
$178$		−	20.1972i		−	1.51384i
$179$			9.05223i			0.676596i	0.941039	+	0.338298i	$0.109851\pi$
$179$			9.05223i			0.676596i	−0.941039	+	0.338298i	$0.890149\pi$
$180$		0			0
$181$	−6.78973	+	6.78973i	−0.504676	+	0.504676i	−0.912888	−	0.408211i	$-0.866153\pi$
$181$	−6.78973	+	6.78973i	−0.504676	+	0.504676i	0.408211	+	0.912888i	$0.366153\pi$
$182$	−34.2368	−	34.2368i	−2.53780	−	2.53780i
$183$		0			0
$184$	−1.40464	−	1.40464i	−0.103552	−	0.103552i
$185$			0.999475i			0.0734828i
$186$		0			0
$187$	−1.84476	+	2.37743i	−0.134903	+	0.173855i
$188$	−1.08064			−0.0788136
$189$		0			0
$190$	1.66179	+	1.66179i	0.120559	+	0.120559i
$191$	18.9231			1.36923			0.684615	−	0.728905i	$-0.259971\pi$
$191$	18.9231			1.36923			0.684615	+	0.728905i	$0.259971\pi$
$192$		0			0
$193$	17.5681	−	17.5681i	1.26458	−	1.26458i	0.315726	−	0.948850i	$-0.397752\pi$
$193$	17.5681	−	17.5681i	1.26458	−	1.26458i	0.948850	−	0.315726i	$-0.102248\pi$
$194$	2.59094	−	2.59094i	0.186019	−	0.186019i
$195$		0			0
$196$			26.8017i			1.91440i
$197$	7.90277	−	7.90277i	0.563049	−	0.563049i	−0.367123	−	0.930172i	$-0.619657\pi$
$197$	7.90277	−	7.90277i	0.563049	−	0.563049i	0.930172	+	0.367123i	$0.119657\pi$
$198$		0			0
$199$	−12.1105	−	12.1105i	−0.858491	−	0.858491i	0.132669	−	0.991160i	$-0.457645\pi$
$199$	−12.1105	−	12.1105i	−0.858491	−	0.858491i	−0.991160	+	0.132669i	$0.957645\pi$
$200$	−2.72382			−0.192603
$201$		0			0
$202$			30.1883i			2.12404i
$203$	−19.0032			−1.33377
$204$		0			0
$205$	−4.12095			−0.287820
$206$			5.91562i			0.412160i
$207$		0			0
$208$	−18.2984			−1.26877
$209$	1.68765	+	1.68765i	0.116737	+	0.116737i
$210$		0			0
$211$	3.25596	−	3.25596i	0.224149	−	0.224149i	−0.586094	−	0.810243i	$-0.699335\pi$
$211$	3.25596	−	3.25596i	0.224149	−	0.224149i	0.810243	+	0.586094i	$0.199335\pi$
$212$			23.0032i			1.57987i
$213$		0			0
$214$	−9.23198	+	9.23198i	−0.631085	+	0.631085i
$215$	−0.921244	+	0.921244i	−0.0628283	+	0.0628283i
$216$		0			0
$217$	−14.3300			−0.972787
$218$	−6.86552	−	6.86552i	−0.464991	−	0.464991i
$219$		0			0
$220$	0.576216			0.0388485
$221$	22.1021	−	2.78837i	1.48675	−	0.187566i
$222$		0			0
$223$			4.04355i			0.270776i	0.990793	+	0.135388i	$0.0432281\pi$
$223$			4.04355i			0.270776i	−0.990793	+	0.135388i	$0.956772\pi$
$224$	24.8839	+	24.8839i	1.66263	+	1.66263i
$225$		0			0
$226$	18.1562	+	18.1562i	1.20773	+	1.20773i
$227$	−12.2742	+	12.2742i	−0.814666	+	0.814666i	−0.985329	−	0.170664i	$-0.945409\pi$
$227$	−12.2742	+	12.2742i	−0.814666	+	0.814666i	0.170664	+	0.985329i	$0.445409\pi$
$228$		0			0
$229$			18.7418i			1.23849i	0.785198	+	0.619245i	$0.212561\pi$
$229$			18.7418i			1.23849i	−0.785198	+	0.619245i	$0.787439\pi$
$230$			2.55718i			0.168616i
$231$		0			0
$232$	1.72984	−	1.72984i	0.113570	−	0.113570i
$233$	6.91911	+	6.91911i	0.453286	+	0.453286i	0.896444	−	0.443158i	$-0.146142\pi$
$233$	6.91911	+	6.91911i	0.453286	+	0.453286i	−0.443158	+	0.896444i	$0.646142\pi$
$234$		0			0
$235$	0.117060	+	0.117060i	0.00763618	+	0.00763618i
$236$			12.0271i			0.782896i
$237$		0			0
$238$	−29.1911	−	22.6508i	−1.89218	−	1.46824i
$239$	14.2984			0.924888			0.462444	−	0.886648i	$-0.346973\pi$
$239$	14.2984			0.924888			0.462444	+	0.886648i	$0.346973\pi$
$240$		0			0
$241$	−4.50817	−	4.50817i	−0.290397	−	0.290397i	0.546840	−	0.837237i	$-0.315830\pi$
$241$	−4.50817	−	4.50817i	−0.290397	−	0.290397i	−0.837237	+	0.546840i	$0.815830\pi$
$242$	−21.6301			−1.39043
$243$		0			0
$244$	−5.69394	+	5.69394i	−0.364517	+	0.364517i
$245$	2.90330	−	2.90330i	0.185485	−	0.185485i
$246$		0			0
$247$		−	17.6688i		−	1.12424i
$248$	1.30445	−	1.30445i	0.0828324	−	0.0828324i
$249$		0			0
$250$	5.02023	+	5.02023i	0.317507	+	0.317507i
$251$	−27.4308			−1.73141			−0.865707	−	0.500550i	$-0.833131\pi$
$251$	−27.4308			−1.73141			−0.865707	+	0.500550i	$0.833131\pi$
$252$		0			0
$253$			2.59697i			0.163270i
$254$	3.74124			0.234746
$255$		0			0
$256$	10.8464			0.677898
$257$			0.657380i			0.0410062i	0.999790	+	0.0205031i	$0.00652680\pi$
$257$			0.657380i			0.0410062i	−0.999790	+	0.0205031i	$0.993473\pi$
$258$		0			0
$259$	−12.4629			−0.774408
$260$	−3.01634	−	3.01634i	−0.187065	−	0.187065i
$261$		0			0
$262$	9.33218	−	9.33218i	0.576544	−	0.576544i
$263$			9.50817i			0.586299i	0.956067	+	0.293149i	$0.0947033\pi$
$263$			9.50817i			0.586299i	−0.956067	+	0.293149i	$0.905297\pi$
$264$		0			0
$265$	2.49183	−	2.49183i	0.153072	−	0.153072i
$266$	−20.7217	+	20.7217i	−1.27053	+	1.27053i
$267$		0			0
$268$	3.53386			0.215865
$269$	−12.2170	−	12.2170i	−0.744884	−	0.744884i	0.228630	−	0.973513i	$-0.426576\pi$
$269$	−12.2170	−	12.2170i	−0.744884	−	0.744884i	−0.973513	+	0.228630i	$0.926576\pi$
$270$		0			0
$271$	21.2897			1.29326			0.646630	−	0.762804i	$-0.276178\pi$
$271$	21.2897			1.29326			0.646630	+	0.762804i	$0.276178\pi$
$272$	−13.8539	+	1.74779i	−0.840015	+	0.105975i
$273$		0			0
$274$			4.71470i			0.284825i
$275$	2.51796	+	2.51796i	0.151839	+	0.151839i
$276$		0			0
$277$	−8.01140	−	8.01140i	−0.481358	−	0.481358i	0.424207	−	0.905565i	$-0.360553\pi$
$277$	−8.01140	−	8.01140i	−0.481358	−	0.481358i	−0.905565	+	0.424207i	$0.860553\pi$
$278$	24.2919	−	24.2919i	1.45693	−	1.45693i
$279$		0			0
$280$			0.841962i			0.0503168i
$281$		−	19.0233i		−	1.13484i	−0.823430	−	0.567418i	$-0.807942\pi$
$281$		−	19.0233i		−	1.13484i	0.823430	−	0.567418i	$-0.192058\pi$
$282$		0			0
$283$	−8.30003	+	8.30003i	−0.493386	+	0.493386i	−0.909371	−	0.415986i	$-0.863437\pi$
$283$	−8.30003	+	8.30003i	−0.493386	+	0.493386i	0.415986	+	0.909371i	$0.363437\pi$
$284$	14.3851	+	14.3851i	0.853598	+	0.853598i
$285$		0			0
$286$	−5.76199	−	5.76199i	−0.340714	−	0.340714i
$287$		−	51.3860i		−	3.03322i
$288$		0			0
$289$	16.4673	−	4.22220i	0.968667	−	0.248365i
$290$	−3.14921			−0.184928
$291$		0			0
$292$	6.57180	+	6.57180i	0.384586	+	0.384586i
$293$	−20.9548			−1.22419			−0.612095	−	0.790784i	$-0.709673\pi$
$293$	−20.9548			−1.22419			−0.612095	+	0.790784i	$0.709673\pi$
$294$		0			0
$295$	1.30284	−	1.30284i	0.0758540	−	0.0758540i
$296$	1.13448	−	1.13448i	0.0659405	−	0.0659405i
$297$		0			0
$298$		−	25.1720i		−	1.45818i
$299$	13.5944	−	13.5944i	0.786187	−	0.786187i
$300$		0			0
$301$	−11.4874	−	11.4874i	−0.662124	−	0.662124i
$302$	40.0523			2.30475
$303$		0			0
$304$			11.0750i			0.635197i
$305$	1.23360			0.0706355
$306$		0			0
$307$	33.4019			1.90634			0.953172	−	0.302428i	$-0.0977971\pi$
$307$	33.4019			1.90634			0.953172	+	0.302428i	$0.0977971\pi$
$308$			7.18511i			0.409409i
$309$		0			0
$310$	−2.37477			−0.134878
$311$	11.4858	+	11.4858i	0.651300	+	0.651300i	0.953306	−	0.302006i	$-0.0976562\pi$
$311$	11.4858	+	11.4858i	0.651300	+	0.651300i	−0.302006	+	0.953306i	$0.597656\pi$
$312$		0			0
$313$	−5.59697	+	5.59697i	−0.316359	+	0.316359i	−0.847367	−	0.531008i	$-0.821814\pi$
$313$	−5.59697	+	5.59697i	−0.316359	+	0.316359i	0.531008	+	0.847367i	$0.321814\pi$
$314$		−	3.75007i		−	0.211629i
$315$		0			0
$316$	1.30445	−	1.30445i	0.0733808	−	0.0733808i
$317$	−7.63891	+	7.63891i	−0.429044	+	0.429044i	−0.888303	−	0.459259i	$-0.848115\pi$
$317$	−7.63891	+	7.63891i	−0.429044	+	0.429044i	0.459259	+	0.888303i	$0.348115\pi$
$318$		0			0
$319$	−3.19821			−0.179065
$320$	2.45807	+	2.45807i	0.137410	+	0.137410i
$321$		0			0
$322$	−31.8867			−1.77698
$323$	−1.68765	−	13.3772i	−0.0939032	−	0.744326i
$324$		0			0
$325$		−	26.3617i		−	1.46228i
$326$	−21.4928	−	21.4928i	−1.19038	−	1.19038i
$327$		0			0
$328$	4.67761	+	4.67761i	0.258278	+	0.258278i
$329$	−1.45968	+	1.45968i	−0.0804748	+	0.0804748i
$330$		0			0
$331$			22.4389i			1.23336i	0.787215	+	0.616678i	$0.211522\pi$
$331$			22.4389i			1.23336i	−0.787215	+	0.616678i	$0.788478\pi$
$332$		−	16.3758i		−	0.898740i
$333$		0			0
$334$	−11.7396	+	11.7396i	−0.642364	+	0.642364i
$335$	−0.382806	−	0.382806i	−0.0209149	−	0.0209149i
$336$		0			0
$337$	11.6405	+	11.6405i	0.634099	+	0.634099i	0.949094	−	0.314994i	$-0.102003\pi$
$337$	11.6405	+	11.6405i	0.634099	+	0.634099i	−0.314994	+	0.949094i	$0.602003\pi$
$338$			33.4613i			1.82006i
$339$		0			0
$340$	−2.57180	−	1.99559i	−0.139476	−	0.108226i
$341$	−2.41172			−0.130602
$342$		0			0
$343$	14.7375	+	14.7375i	0.795750	+	0.795750i
$344$	2.09137			0.112759
$345$		0			0
$346$	17.5888	−	17.5888i	0.945580	−	0.945580i
$347$	15.0457	−	15.0457i	0.807695	−	0.807695i	−0.176590	−	0.984285i	$-0.556507\pi$
$347$	15.0457	−	15.0457i	0.807695	−	0.807695i	0.984285	+	0.176590i	$0.0565066\pi$
$348$		0			0
$349$			6.41832i			0.343565i	0.985135	+	0.171782i	$0.0549526\pi$
$349$			6.41832i			0.343565i	−0.985135	+	0.171782i	$0.945047\pi$
$350$	−30.9166	+	30.9166i	−1.65256	+	1.65256i
$351$		0			0
$352$	4.18791	+	4.18791i	0.223216	+	0.223216i
$353$	−10.0201			−0.533315			−0.266658	−	0.963791i	$-0.585919\pi$
$353$	−10.0201			−0.533315			−0.266658	+	0.963791i	$0.585919\pi$
$354$		0			0
$355$		−	3.11654i		−	0.165409i
$356$	22.1883			1.17598
$357$		0			0
$358$	−18.7059			−0.988636
$359$		−	30.1366i		−	1.59055i	−0.606248	−	0.795275i	$-0.707326\pi$
$359$		−	30.1366i		−	1.59055i	0.606248	−	0.795275i	$-0.292674\pi$
$360$		0			0
$361$	8.30606			0.437161
$362$	−14.0305	−	14.0305i	−0.737429	−	0.737429i
$363$		0			0
$364$	37.6121	−	37.6121i	1.97141	−	1.97141i
$365$		−	1.42378i		−	0.0745243i
$366$		0			0
$367$	17.5620	−	17.5620i	0.916731	−	0.916731i	−0.0800595	−	0.996790i	$-0.525511\pi$
$367$	17.5620	−	17.5620i	0.916731	−	0.916731i	0.996790	+	0.0800595i	$0.0255110\pi$
$368$	−8.52118	+	8.52118i	−0.444197	+	0.444197i
$369$		0			0
$370$	−2.06535			−0.107372
$371$	31.0718	+	31.0718i	1.61317	+	1.61317i
$372$		0			0
$373$	−6.09593			−0.315635			−0.157818	−	0.987468i	$-0.550446\pi$
$373$	−6.09593			−0.315635			−0.157818	+	0.987468i	$0.550446\pi$
$374$	−4.91281	−	3.81209i	−0.254035	−	0.197118i
$375$		0			0
$376$		−	0.265746i		−	0.0137048i
$377$	16.7418	+	16.7418i	0.862245	+	0.862245i
$378$		0			0
$379$	−19.7723	−	19.7723i	−1.01564	−	1.01564i	−0.999876	−	0.0157592i	$-0.994983\pi$
$379$	−19.7723	−	19.7723i	−1.01564	−	1.01564i	−0.0157592	−	0.999876i	$-0.505017\pi$
$380$	−1.82562	+	1.82562i	−0.0936525	+	0.0936525i
$381$		0			0
$382$			39.1034i			2.00071i
$383$			36.1155i			1.84542i	0.385500	+	0.922708i	$0.374029\pi$
$383$			36.1155i			1.84542i	−0.385500	+	0.922708i	$0.625971\pi$
$384$		0			0
$385$	0.778328	−	0.778328i	0.0396673	−	0.0396673i
$386$	36.3033	+	36.3033i	1.84779	+	1.84779i
$387$		0			0
$388$	2.84638	+	2.84638i	0.144503	+	0.144503i
$389$			23.1246i			1.17246i	0.810144	+	0.586231i	$0.199389\pi$
$389$			23.1246i			1.17246i	−0.810144	+	0.586231i	$0.800611\pi$
$390$		0			0
$391$	8.99398	−	11.5909i	0.454845	−	0.586179i
$392$	−6.59094			−0.332893
$393$		0			0
$394$	16.3306	+	16.3306i	0.822722	+	0.822722i
$395$	−0.282609			−0.0142196
$396$		0			0
$397$	2.97925	−	2.97925i	0.149524	−	0.149524i	−0.628381	−	0.777905i	$-0.716282\pi$
$397$	2.97925	−	2.97925i	0.149524	−	0.149524i	0.777905	+	0.628381i	$0.216282\pi$
$398$	25.0256	−	25.0256i	1.25442	−	1.25442i
$399$		0			0
$400$			16.5239i			0.826193i
$401$	−4.37879	+	4.37879i	−0.218666	+	0.218666i	−0.807936	−	0.589270i	$-0.799415\pi$
$401$	−4.37879	+	4.37879i	−0.218666	+	0.218666i	0.589270	+	0.807936i	$0.299415\pi$
$402$		0			0
$403$	12.6247	+	12.6247i	0.628881	+	0.628881i
$404$	−33.1645			−1.65000
$405$		0			0
$406$		−	39.2690i		−	1.94889i
$407$	−2.09748			−0.103968
$408$		0			0
$409$	−34.6034			−1.71103			−0.855515	−	0.517778i	$-0.826759\pi$
$409$	−34.6034			−1.71103			−0.855515	+	0.517778i	$0.826759\pi$
$410$		−	8.51568i		−	0.420559i
$411$		0			0
$412$	−6.49882			−0.320174
$413$	16.2457	+	16.2457i	0.799397	+	0.799397i
$414$		0			0
$415$	−1.77391	+	1.77391i	−0.0870780	+	0.0870780i
$416$		−	43.8452i		−	2.14969i
$417$		0			0
$418$	−3.48742	+	3.48742i	−0.170575	+	0.170575i
$419$	−4.12632	+	4.12632i	−0.201584	+	0.201584i	−0.800678	−	0.599094i	$-0.795527\pi$
$419$	−4.12632	+	4.12632i	−0.201584	+	0.201584i	0.599094	+	0.800678i	$0.295527\pi$
$420$		0			0
$421$	−27.0152			−1.31664			−0.658319	−	0.752739i	$-0.728732\pi$
$421$	−27.0152			−1.31664			−0.658319	+	0.752739i	$0.728732\pi$
$422$	6.72823	+	6.72823i	0.327525	+	0.327525i
$423$		0			0
$424$	−5.65685			−0.274721
$425$	−2.51796	−	19.9586i	−0.122139	−	0.968136i
$426$		0			0
$427$			15.3823i			0.744401i
$428$	−10.1421	−	10.1421i	−0.490239	−	0.490239i
$429$		0			0
$430$	−1.90369	−	1.90369i	−0.0918041	−	0.0918041i
$431$	12.2592	−	12.2592i	0.590505	−	0.590505i	−0.347263	−	0.937768i	$-0.612889\pi$
$431$	12.2592	−	12.2592i	0.590505	−	0.590505i	0.937768	+	0.347263i	$0.112889\pi$
$432$		0			0
$433$			3.97603i			0.191076i	0.995426	+	0.0955378i	$0.0304571\pi$
$433$			3.97603i			0.191076i	−0.995426	+	0.0955378i	$0.969543\pi$
$434$		−	29.6121i		−	1.42143i
$435$		0			0
$436$	7.54236	−	7.54236i	0.361214	−	0.361214i
$437$	−8.22797	−	8.22797i	−0.393597	−	0.393597i
$438$		0			0
$439$	−1.97764	−	1.97764i	−0.0943875	−	0.0943875i	0.658336	−	0.752724i	$-0.271260\pi$
$439$	−1.97764	−	1.97764i	−0.0943875	−	0.0943875i	−0.752724	+	0.658336i	$0.771260\pi$
$440$			0.141700i			0.00675531i
$441$		0			0
$442$	5.76199	+	45.6725i	0.274070	+	2.17242i
$443$	−9.88565			−0.469682			−0.234841	−	0.972034i	$-0.575457\pi$
$443$	−9.88565			−0.469682			−0.234841	+	0.972034i	$0.575457\pi$
$444$		0			0
$445$	−2.40356	−	2.40356i	−0.113940	−	0.113940i
$446$	−8.35574			−0.395656
$447$		0			0
$448$	−30.6508	+	30.6508i	−1.44812	+	1.44812i
$449$	−28.3191	+	28.3191i	−1.33646	+	1.33646i	−0.436997	+	0.899463i	$0.643958\pi$
$449$	−28.3191	+	28.3191i	−1.33646	+	1.33646i	−0.899463	+	0.436997i	$0.856042\pi$
$450$		0			0
$451$		−	8.64817i		−	0.407226i
$452$	−19.9462	+	19.9462i	−0.938188	+	0.938188i
$453$		0			0
$454$	−25.3638	−	25.3638i	−1.19038	−	1.19038i
$455$	−8.14869			−0.382016
$456$		0			0
$457$			0.452046i			0.0211458i	0.999944	+	0.0105729i	$0.00336552\pi$
$457$			0.452046i			0.0211458i	−0.999944	+	0.0105729i	$0.996634\pi$
$458$	−38.7287			−1.80967
$459$		0			0
$460$	−2.80929			−0.130984
$461$			11.5310i			0.537051i	0.963273	+	0.268525i	$0.0865363\pi$
$461$			11.5310i			0.537051i	−0.963273	+	0.268525i	$0.913464\pi$
$462$		0			0
$463$	−4.41067			−0.204981			−0.102491	−	0.994734i	$-0.532681\pi$
$463$	−4.41067			−0.204981			−0.102491	+	0.994734i	$0.532681\pi$
$464$	−10.4940	−	10.4940i	−0.487170	−	0.487170i
$465$		0			0
$466$	−14.2979	+	14.2979i	−0.662337	+	0.662337i
$467$		−	8.34586i		−	0.386200i	−0.981179	−	0.193100i	$-0.938146\pi$
$467$		−	8.34586i		−	0.386200i	0.981179	−	0.193100i	$-0.0618542\pi$
$468$		0			0
$469$	4.77339	−	4.77339i	0.220415	−	0.220415i
$470$	−0.241898	+	0.241898i	−0.0111579	+	0.0111579i
$471$		0			0
$472$	−2.95764			−0.136137
$473$	−1.93331	−	1.93331i	−0.0888937	−	0.0888937i
$474$		0			0
$475$	−15.9553			−0.732078
$476$	24.8839	−	32.0690i	1.14055	−	1.46988i
$477$		0			0
$478$			29.5468i			1.35144i
$479$	−9.02477	−	9.02477i	−0.412352	−	0.412352i	0.470205	−	0.882557i	$-0.344180\pi$
$479$	−9.02477	−	9.02477i	−0.412352	−	0.412352i	−0.882557	+	0.470205i	$0.844180\pi$
$480$		0			0
$481$	10.9798	+	10.9798i	0.500635	+	0.500635i
$482$	9.31584	−	9.31584i	0.424325	−	0.424325i
$483$		0			0
$484$		−	23.7625i		−	1.08011i
$485$		−	0.616669i		−	0.0280015i
$486$		0			0
$487$	9.08225	−	9.08225i	0.411556	−	0.411556i	−0.470724	−	0.882280i	$-0.656007\pi$
$487$	9.08225	−	9.08225i	0.411556	−	0.411556i	0.882280	+	0.470724i	$0.156007\pi$
$488$	−1.40023	−	1.40023i	−0.0633854	−	0.0633854i
$489$		0			0
$490$	5.99947	+	5.99947i	0.271029	+	0.271029i
$491$		−	20.4629i		−	0.923479i	−0.887016	−	0.461739i	$-0.847226\pi$
$491$		−	20.4629i		−	0.923479i	0.887016	−	0.461739i	$-0.152774\pi$
$492$		0			0
$493$	14.2744	+	11.0762i	0.642888	+	0.498848i
$494$	36.5114			1.64273
$495$		0			0
$496$	−7.91334	−	7.91334i	−0.355319	−	0.355319i
$497$	38.8615			1.74318
$498$		0			0
$499$	−5.00979	+	5.00979i	−0.224269	+	0.224269i	−0.810293	−	0.586024i	$-0.800692\pi$
$499$	−5.00979	+	5.00979i	−0.224269	+	0.224269i	0.586024	+	0.810293i	$0.300692\pi$
$500$	−5.51515	+	5.51515i	−0.246645	+	0.246645i
$501$		0			0
$502$		−	56.6839i		−	2.52993i
$503$	−12.9594	+	12.9594i	−0.577832	+	0.577832i	−0.934305	−	0.356474i	$-0.883979\pi$
$503$	−12.9594	+	12.9594i	−0.577832	+	0.577832i	0.356474	+	0.934305i	$0.383979\pi$
$504$		0			0
$505$	3.59255	+	3.59255i	0.159867	+	0.159867i
$506$	−5.36647			−0.238569
$507$		0			0
$508$			4.11008i			0.182355i
$509$	−9.62950			−0.426820			−0.213410	−	0.976963i	$-0.568457\pi$
$509$	−9.62950			−0.426820			−0.213410	+	0.976963i	$0.568457\pi$
$510$		0			0
$511$	17.7538			0.785383
$512$			31.2641i			1.38169i
$513$		0			0
$514$	−1.35843			−0.0599179
$515$	0.703986	+	0.703986i	0.0310213	+	0.0310213i
$516$		0			0
$517$	−0.245661	+	0.245661i	−0.0108042	+	0.0108042i
$518$		−	25.7538i		−	1.13156i
$519$		0			0
$520$	0.741764	−	0.741764i	0.0325285	−	0.0325285i
$521$	−2.29440	+	2.29440i	−0.100520	+	0.100520i	−0.755578	−	0.655059i	$-0.772644\pi$
$521$	−2.29440	+	2.29440i	−0.100520	+	0.100520i	0.655059	+	0.755578i	$0.272644\pi$
$522$		0			0
$523$	6.77444			0.296226			0.148113	−	0.988970i	$-0.452680\pi$
$523$	6.77444			0.296226			0.148113	+	0.988970i	$0.452680\pi$
$524$	10.2522	+	10.2522i	0.447870	+	0.447870i
$525$		0			0
$526$	−19.6480			−0.856695
$527$	10.7641	+	8.35241i	0.468893	+	0.363837i
$528$		0			0
$529$			10.3387i			0.449510i
$530$	5.14921	+	5.14921i	0.223667	+	0.223667i
$531$		0			0
$532$	−22.7646	−	22.7646i	−0.986969	−	0.986969i
$533$	−45.2709	+	45.2709i	−1.96090	+	1.96090i
$534$		0			0
$535$			2.19730i			0.0949975i
$536$			0.869031i			0.0375364i
$537$		0			0
$538$	25.2457	−	25.2457i	1.08842	−	1.08842i
$539$	6.09282	+	6.09282i	0.262436	+	0.262436i
$540$		0			0
$541$	17.4144	+	17.4144i	0.748705	+	0.748705i	0.974236	−	0.225531i	$-0.0724117\pi$
$541$	17.4144	+	17.4144i	0.748705	+	0.748705i	−0.225531	+	0.974236i	$0.572412\pi$
$542$			43.9939i			1.88970i
$543$		0			0
$544$	−4.18791	−	33.1956i	−0.179555	−	1.42325i
$545$	−1.63406			−0.0699953
$546$		0			0
$547$	−22.7233	−	22.7233i	−0.971578	−	0.971578i	0.0280293	−	0.999607i	$-0.491077\pi$
$547$	−22.7233	−	22.7233i	−0.971578	−	0.971578i	−0.999607	+	0.0280293i	$0.991077\pi$
$548$	−5.17950			−0.221257
$549$		0			0
$550$	−5.20320	+	5.20320i	−0.221865	+	0.221865i
$551$	10.1329	−	10.1329i	0.431675	−	0.431675i
$552$		0			0
$553$		−	3.52398i		−	0.149855i
$554$	16.5550	−	16.5550i	0.703357	−	0.703357i
$555$		0			0
$556$	26.6867	+	26.6867i	1.13177	+	1.13177i
$557$	43.4415			1.84068			0.920338	−	0.391124i	$-0.127914\pi$
$557$	43.4415			1.84068			0.920338	+	0.391124i	$0.127914\pi$
$558$		0			0
$559$			20.2407i			0.856091i
$560$	5.10771			0.215840
$561$		0			0
$562$	39.3105			1.65821
$563$			14.3986i			0.606829i	0.952859	+	0.303415i	$0.0981267\pi$
$563$			14.3986i			0.606829i	−0.952859	+	0.303415i	$0.901873\pi$
$564$		0			0
$565$	4.32134			0.181800
$566$	−17.1515	−	17.1515i	−0.720931	−	0.720931i
$567$		0			0
$568$	−3.53752	+	3.53752i	−0.148431	+	0.148431i
$569$		−	16.8103i		−	0.704726i	−0.935863	−	0.352363i	$-0.885378\pi$
$569$		−	16.8103i		−	0.704726i	0.935863	−	0.352363i	$-0.114622\pi$
$570$		0			0
$571$	−16.0462	+	16.0462i	−0.671513	+	0.671513i	−0.958065	−	0.286552i	$-0.907491\pi$
$571$	−16.0462	+	16.0462i	−0.671513	+	0.671513i	0.286552	+	0.958065i	$0.407491\pi$
$572$	6.33005	−	6.33005i	0.264673	−	0.264673i
$573$		0			0
$574$	106.186			4.43212
$575$	−12.2761	−	12.2761i	−0.511947	−	0.511947i
$576$		0			0
$577$	−20.5881			−0.857095			−0.428548	−	0.903519i	$-0.640975\pi$
$577$	−20.5881			−0.857095			−0.428548	+	0.903519i	$0.640975\pi$
$578$	8.72490	+	34.0287i	0.362908	+	1.41541i
$579$		0			0
$580$		−	3.45968i		−	0.143655i
$581$	−22.1198	−	22.1198i	−0.917683	−	0.917683i
$582$		0			0
$583$	5.22932	+	5.22932i	0.216576	+	0.216576i
$584$	−1.61611	+	1.61611i	−0.0668750	+	0.0668750i
$585$		0			0
$586$		−	43.3017i		−	1.78878i
$587$		−	10.5119i		−	0.433873i	−0.976186	−	0.216937i	$-0.930394\pi$
$587$		−	10.5119i		−	0.433873i	0.976186	−	0.216937i	$-0.0696065\pi$
$588$		0			0
$589$	7.64104	−	7.64104i	0.314844	−	0.314844i
$590$	2.69223	+	2.69223i	0.110837	+	0.110837i
$591$		0			0
$592$	−6.88227	−	6.88227i	−0.282860	−	0.282860i
$593$			7.79428i			0.320073i	0.987111	+	0.160036i	$0.0511612\pi$
$593$			7.79428i			0.320073i	−0.987111	+	0.160036i	$0.948839\pi$
$594$		0			0
$595$	−6.16944	+	0.778328i	−0.252922	+	0.0319084i
$596$	27.6536			1.13274
$597$		0			0
$598$	28.0920	+	28.0920i	1.14877	+	1.14877i
$599$	16.8503			0.688484			0.344242	−	0.938881i	$-0.388136\pi$
$599$	16.8503			0.688484			0.344242	+	0.938881i	$0.388136\pi$
$600$		0			0
$601$	−21.4721	+	21.4721i	−0.875866	+	0.875866i	−0.993104	−	0.117237i	$-0.962596\pi$
$601$	−21.4721	+	21.4721i	−0.875866	+	0.875866i	0.117237	+	0.993104i	$0.462596\pi$
$602$	23.7380	−	23.7380i	0.967489	−	0.967489i
$603$		0			0
$604$			44.0009i			1.79037i
$605$	−2.57408	+	2.57408i	−0.104651	+	0.104651i
$606$		0			0
$607$	17.7107	+	17.7107i	0.718856	+	0.718856i	0.968371	−	0.249515i	$-0.0802712\pi$
$607$	17.7107	+	17.7107i	0.718856	+	0.718856i	−0.249515	+	0.968371i	$0.580271\pi$
$608$	−26.5371			−1.07622
$609$		0			0
$610$			2.54915i			0.103212i
$611$	2.57194			0.104050
$612$		0			0
$613$	−31.5000			−1.27227			−0.636137	−	0.771576i	$-0.719469\pi$
$613$	−31.5000			−1.27227			−0.636137	+	0.771576i	$0.719469\pi$
$614$			69.0228i			2.78553i
$615$		0			0
$616$	−1.76693			−0.0711916
$617$	−8.17040	−	8.17040i	−0.328928	−	0.328928i	0.523251	−	0.852179i	$-0.324719\pi$
$617$	−8.17040	−	8.17040i	−0.328928	−	0.328928i	−0.852179	+	0.523251i	$0.824719\pi$
$618$		0			0
$619$	−16.7761	+	16.7761i	−0.674286	+	0.674286i	−0.958701	−	0.284415i	$-0.908201\pi$
$619$	−16.7761	+	16.7761i	−0.674286	+	0.674286i	0.284415	+	0.958701i	$0.408201\pi$
$620$		−	2.60889i		−	0.104776i
$621$		0			0
$622$	−23.7347	+	23.7347i	−0.951674	+	0.951674i
$623$	29.9711	−	29.9711i	1.20077	−	1.20077i
$624$		0			0
$625$	−23.2004			−0.928016
$626$	−11.5658	−	11.5658i	−0.462261	−	0.462261i
$627$		0			0
$628$	4.11977			0.164397
$629$	9.36162	+	7.26414i	0.373272	+	0.289640i
$630$		0			0
$631$		−	36.8092i		−	1.46535i	−0.680579	−	0.732675i	$-0.738272\pi$
$631$		−	36.8092i		−	1.46535i	0.680579	−	0.732675i	$-0.261728\pi$
$632$	0.320784	+	0.320784i	0.0127601	+	0.0127601i
$633$		0			0
$634$	−15.7853	−	15.7853i	−0.626915	−	0.626915i
$635$	0.445225	−	0.445225i	0.0176682	−	0.0176682i
$636$		0			0
$637$		−	63.7886i		−	2.52739i
$638$		−	6.60889i		−	0.261649i
$639$		0			0
$640$	−1.08827	+	1.08827i	−0.0430178	+	0.0430178i
$641$	−25.3135	−	25.3135i	−0.999821	−	0.999821i	0.000178651	−	1.00000i	$-0.499943\pi$
$641$	−25.3135	−	25.3135i	−0.999821	−	0.999821i	−1.00000		0.000178651i	$0.999943\pi$
$642$		0			0
$643$	−11.7990	−	11.7990i	−0.465307	−	0.465307i	0.435083	−	0.900390i	$-0.356719\pi$
$643$	−11.7990	−	11.7990i	−0.465307	−	0.465307i	−0.900390	+	0.435083i	$0.856719\pi$
$644$		−	35.0303i		−	1.38039i
$645$		0			0
$646$	27.6431	−	3.48742i	1.08760	−	0.137211i
$647$	−19.2205			−0.755636			−0.377818	−	0.925880i	$-0.623325\pi$
$647$	−19.2205			−0.755636			−0.377818	+	0.925880i	$0.623325\pi$
$648$		0			0
$649$	2.73411	+	2.73411i	0.107323	+	0.107323i
$650$	54.4747			2.13667
$651$		0			0
$652$	23.6117	−	23.6117i	0.924705	−	0.924705i
$653$	19.8412	−	19.8412i	0.776445	−	0.776445i	−0.202779	−	0.979225i	$-0.564997\pi$
$653$	19.8412	−	19.8412i	0.776445	−	0.776445i	0.979225	+	0.202779i	$0.0649973\pi$
$654$		0			0
$655$		−	2.22115i		−	0.0867874i
$656$	28.3764	−	28.3764i	1.10791	−	1.10791i
$657$		0			0
$658$	−3.01634	−	3.01634i	−0.117589	−	0.117589i
$659$	−27.6727			−1.07797			−0.538987	−	0.842314i	$-0.681193\pi$
$659$	−27.6727			−1.07797			−0.538987	+	0.842314i	$0.681193\pi$
$660$		0			0
$661$			13.8137i			0.537291i	0.963239	+	0.268645i	$0.0865760\pi$
$661$			13.8137i			0.537291i	−0.963239	+	0.268645i	$0.913424\pi$
$662$	−46.3687			−1.80217
$663$		0			0
$664$	4.02707			0.156281
$665$			4.93195i			0.191253i
$666$		0			0
$667$	15.5926			0.603746
$668$	−12.8970	−	12.8970i	−0.499000	−	0.499000i
$669$		0			0
$670$	0.791045	−	0.791045i	0.0305607	−	0.0305607i
$671$			2.58881i			0.0999398i
$672$		0			0
$673$	−13.8338	+	13.8338i	−0.533254	+	0.533254i	−0.921539	−	0.388285i	$-0.873067\pi$
$673$	−13.8338	+	13.8338i	−0.533254	+	0.533254i	0.388285	+	0.921539i	$0.373067\pi$
$674$	−24.0544	+	24.0544i	−0.926540	+	0.926540i
$675$		0			0
$676$	−36.7601			−1.41385
$677$	24.0683	+	24.0683i	0.925021	+	0.925021i	0.997379	−	0.0723581i	$-0.0230524\pi$
$677$	24.0683	+	24.0683i	0.925021	+	0.925021i	−0.0723581	+	0.997379i	$0.523052\pi$
$678$		0			0
$679$	7.68953			0.295097
$680$	0.490746	−	0.632446i	0.0188192	−	0.0242532i
$681$		0			0
$682$		−	4.98366i		−	0.190834i
$683$	−4.72635	−	4.72635i	−0.180849	−	0.180849i	0.610877	−	0.791726i	$-0.290817\pi$
$683$	−4.72635	−	4.72635i	−0.180849	−	0.180849i	−0.791726	+	0.610877i	$0.790817\pi$
$684$		0			0
$685$	0.561071	+	0.561071i	0.0214374	+	0.0214374i
$686$	−30.4541	+	30.4541i	−1.16274	+	1.16274i
$687$		0			0
$688$		−	12.6872i		−	0.483694i
$689$		−	54.7482i		−	2.08574i
$690$		0			0
$691$	24.7880	−	24.7880i	0.942979	−	0.942979i	−0.0554808	−	0.998460i	$-0.517669\pi$
$691$	24.7880	−	24.7880i	0.942979	−	0.942979i	0.998460	+	0.0554808i	$0.0176691\pi$
$692$	19.3228	+	19.3228i	0.734544	+	0.734544i
$693$		0			0
$694$	31.0910	+	31.0910i	1.18020	+	1.18020i
$695$		−	5.78169i		−	0.219312i
$696$		0			0
$697$	−29.9509	+	38.5990i	−1.13447	+	1.46204i
$698$	−13.2630			−0.502014
$699$		0			0
$700$	−33.9645	−	33.9645i	−1.28374	−	1.28374i
$701$	−39.3006			−1.48436			−0.742182	−	0.670199i	$-0.766209\pi$
$701$	−39.3006			−1.48436			−0.742182	+	0.670199i	$0.766209\pi$
$702$		0			0
$703$	6.64546	−	6.64546i	0.250638	−	0.250638i
$704$	−5.15847	+	5.15847i	−0.194417	+	0.194417i
$705$		0			0
$706$		−	20.7059i		−	0.779276i
$707$	−44.7972	+	44.7972i	−1.68477	+	1.68477i
$708$		0			0
$709$	8.63339	+	8.63339i	0.324234	+	0.324234i	0.850389	−	0.526155i	$-0.176367\pi$
$709$	8.63339	+	8.63339i	0.324234	+	0.324234i	−0.526155	+	0.850389i	$0.676367\pi$
$710$	6.44012			0.241693
$711$		0			0
$712$			5.45646i			0.204489i
$713$	11.7581			0.440344
$714$		0			0
$715$	−1.37141			−0.0512877
$716$		−	20.5500i		−	0.767990i
$717$		0			0
$718$	62.2754			2.32410
$719$	−22.0885	−	22.0885i	−0.823764	−	0.823764i	0.162882	−	0.986646i	$-0.447921\pi$
$719$	−22.0885	−	22.0885i	−0.823764	−	0.823764i	−0.986646	+	0.162882i	$0.947921\pi$
$720$		0			0
$721$	−8.77833	+	8.77833i	−0.326922	+	0.326922i
$722$			17.1639i			0.638776i
$723$		0			0
$724$	15.4138	−	15.4138i	0.572848	−	0.572848i
$725$	15.1182	−	15.1182i	0.561474	−	0.561474i
$726$		0			0
$727$	36.9344			1.36982			0.684910	−	0.728627i	$-0.259841\pi$
$727$	36.9344			1.36982			0.684910	+	0.728627i	$0.259841\pi$
$728$	9.24941	+	9.24941i	0.342806	+	0.342806i
$729$		0			0
$730$	2.94216			0.108894
$731$	1.93331	+	15.3244i	0.0715060	+	0.566794i
$732$		0			0
$733$		−	8.29737i		−	0.306470i	−0.988190	−	0.153235i	$-0.951031\pi$
$733$		−	8.29737i		−	0.306470i	0.988190	−	0.153235i	$-0.0489692\pi$
$734$	36.2908	+	36.2908i	1.33952	+	1.33952i
$735$		0			0
$736$	−20.4178	−	20.4178i	−0.752609	−	0.752609i
$737$	0.803352	−	0.803352i	0.0295918	−	0.0295918i
$738$		0			0
$739$		−	21.2613i		−	0.782111i	−0.920367	−	0.391055i	$-0.872110\pi$
$739$		−	21.2613i		−	0.782111i	0.920367	−	0.391055i	$-0.127890\pi$
$740$		−	2.26897i		−	0.0834089i
$741$		0			0
$742$	−64.2079	+	64.2079i	−2.35715	+	2.35715i
$743$	34.2118	+	34.2118i	1.25511	+	1.25511i	0.953401	+	0.301707i	$0.0975564\pi$
$743$	34.2118	+	34.2118i	1.25511	+	1.25511i	0.301707	+	0.953401i	$0.402444\pi$
$744$		0			0
$745$	−2.99559	−	2.99559i	−0.109750	−	0.109750i
$746$		−	12.5968i		−	0.461203i
$747$		0			0
$748$	4.18791	−	5.39715i	0.153125	−	0.197339i
$749$	−27.3991			−1.00114
$750$		0			0
$751$	−20.6666	−	20.6666i	−0.754136	−	0.754136i	0.221112	−	0.975248i	$-0.429031\pi$
$751$	−20.6666	−	20.6666i	−0.754136	−	0.754136i	−0.975248	+	0.221112i	$0.929031\pi$
$752$	−1.61213			−0.0587883
$753$		0			0
$754$	−34.5958	+	34.5958i	−1.25990	+	1.25990i
$755$	4.76640	−	4.76640i	0.173467	−	0.173467i
$756$		0			0
$757$			42.3932i			1.54081i	0.637557	+	0.770403i	$0.279945\pi$
$757$			42.3932i			1.54081i	−0.637557	+	0.770403i	$0.720055\pi$
$758$	40.8582	−	40.8582i	1.48404	−	1.48404i
$759$		0			0
$760$	−0.448949	−	0.448949i	−0.0162851	−	0.0162851i
$761$	−15.1503			−0.549197			−0.274598	−	0.961559i	$-0.588545\pi$
$761$	−15.1503			−0.549197			−0.274598	+	0.961559i	$0.588545\pi$
$762$		0			0
$763$		−	20.3758i		−	0.737654i
$764$	−42.9585			−1.55418
$765$		0			0
$766$	−74.6304			−2.69651
$767$		−	28.6247i		−	1.03358i
$768$		0			0
$769$	−28.3540			−1.02247			−0.511236	−	0.859440i	$-0.670812\pi$
$769$	−28.3540			−1.02247			−0.511236	+	0.859440i	$0.670812\pi$
$770$	1.60837	+	1.60837i	0.0579615	+	0.0579615i
$771$		0			0
$772$	−39.8823	+	39.8823i	−1.43540	+	1.43540i
$773$			21.2004i			0.762526i	0.924467	+	0.381263i	$0.124511\pi$
$773$			21.2004i			0.762526i	−0.924467	+	0.381263i	$0.875489\pi$
$774$		0			0
$775$	11.4004	−	11.4004i	0.409513	−	0.409513i
$776$	−0.699968	+	0.699968i	−0.0251274	+	0.0251274i
$777$		0			0
$778$	−47.7855			−1.71319
$779$	27.4000	+	27.4000i	0.981706	+	0.981706i
$780$		0			0
$781$	6.54032			0.234031
$782$	23.9519	+	18.5855i	0.856520	+	0.664615i
$783$		0			0
$784$			39.9835i			1.42798i
$785$	−0.446275	−	0.446275i	−0.0159283	−	0.0159283i
$786$		0			0
$787$	25.4689	+	25.4689i	0.907870	+	0.907870i	0.996100	−	0.0882303i	$-0.0281211\pi$
$787$	25.4689	+	25.4689i	0.907870	+	0.907870i	−0.0882303	+	0.996100i	$0.528121\pi$
$788$	−17.9405	+	17.9405i	−0.639106	+	0.639106i
$789$		0			0
$790$		−	0.583993i		−	0.0207775i
$791$			53.8849i			1.91593i
$792$		0			0
$793$	13.5517	−	13.5517i	0.481236	−	0.481236i
$794$	6.15643	+	6.15643i	0.218483	+	0.218483i
$795$		0			0
$796$	27.4928	+	27.4928i	0.974456	+	0.974456i
$797$		−	0.536047i		−	0.0189878i	−0.999955	−	0.00949388i	$-0.996978\pi$
$797$		−	0.536047i		−	0.0189878i	0.999955	−	0.00949388i	$-0.00302204\pi$
$798$		0			0
$799$	1.94724	−	0.245661i	0.0688884	−	0.00869087i
$800$	−39.5931			−1.39983
$801$		0			0
$802$	−9.04849	−	9.04849i	−0.319513	−	0.319513i
$803$	2.98793			0.105442
$804$		0			0
$805$	−3.79467	+	3.79467i	−0.133744	+	0.133744i
$806$	−26.0881	+	26.0881i	−0.918916	+	0.918916i
$807$		0			0
$808$		−	8.15567i		−	0.286915i
$809$	3.50842	−	3.50842i	0.123350	−	0.123350i	−0.642737	−	0.766087i	$-0.722201\pi$
$809$	3.50842	−	3.50842i	0.123350	−	0.123350i	0.766087	+	0.642737i	$0.222201\pi$
$810$		0			0
$811$	32.8997	+	32.8997i	1.15527	+	1.15527i	0.985481	+	0.169784i	$0.0543069\pi$
$811$	32.8997	+	32.8997i	1.15527	+	1.15527i	0.169784	+	0.985481i	$0.445693\pi$
$812$	43.1404			1.51393
$813$		0			0
$814$		−	4.33432i		−	0.151918i
$815$	−5.11548			−0.179188
$816$		0			0
$817$	12.2506			0.428594
$818$		−	71.5058i		−	2.50014i
$819$		0			0
$820$	9.35521			0.326698
$821$	22.1358	+	22.1358i	0.772546	+	0.772546i	0.978551	−	0.206005i	$-0.0660463\pi$
$821$	22.1358	+	22.1358i	0.772546	+	0.772546i	−0.206005	+	0.978551i	$0.566046\pi$
$822$		0			0
$823$	32.2842	−	32.2842i	1.12536	−	1.12536i	0.134435	−	0.990922i	$-0.457078\pi$
$823$	32.2842	−	32.2842i	1.12536	−	1.12536i	0.990922	−	0.134435i	$-0.0429218\pi$
$824$		−	1.59816i		−	0.0556745i
$825$		0			0
$826$	−33.5706	+	33.5706i	−1.16807	+	1.16807i
$827$	0.516075	−	0.516075i	0.0179457	−	0.0179457i	−0.698077	−	0.716023i	$-0.745961\pi$
$827$	0.516075	−	0.516075i	0.0179457	−	0.0179457i	0.716023	+	0.698077i	$0.245961\pi$
$828$		0			0
$829$	24.0881			0.836616			0.418308	−	0.908305i	$-0.362623\pi$
$829$	24.0881			0.836616			0.418308	+	0.908305i	$0.362623\pi$
$830$	−3.66568	−	3.66568i	−0.127238	−	0.127238i
$831$		0			0
$832$	54.0065			1.87234
$833$	−6.09282	−	48.2948i	−0.211104	−	1.67332i
$834$		0			0
$835$			2.79414i			0.0966952i
$836$	−3.83123	−	3.83123i	−0.132506	−	0.132506i
$837$		0			0
$838$	−8.52678	−	8.52678i	−0.294553	−	0.294553i
$839$	23.0760	−	23.0760i	0.796671	−	0.796671i	−0.185898	−	0.982569i	$-0.559519\pi$
$839$	23.0760	−	23.0760i	0.796671	−	0.796671i	0.982569	+	0.185898i	$0.0595194\pi$
$840$		0			0
$841$		−	9.79752i		−	0.337846i
$842$		−	55.8251i		−	1.92386i
$843$		0			0
$844$	−7.39154	+	7.39154i	−0.254427	+	0.254427i
$845$	3.98205	+	3.98205i	0.136987	+	0.136987i
$846$		0			0
$847$	−32.0974	−	32.0974i	−1.10288	−	1.10288i
$848$			34.3169i			1.17845i
$849$		0			0
$850$	41.2433	−	5.20320i	1.41463	−	0.178468i
$851$	10.2261			0.350546
$852$		0			0
$853$	16.8181	+	16.8181i	0.575842	+	0.575842i	0.933755	−	0.357913i	$-0.116512\pi$
$853$	16.8181	+	16.8181i	0.575842	+	0.575842i	−0.357913	+	0.933755i	$0.616512\pi$
$854$	−31.7865			−1.08771
$855$		0			0
$856$	2.49411	−	2.49411i	0.0852469	−	0.0852469i
$857$	−30.4123	+	30.4123i	−1.03886	+	1.03886i	−0.0396506	+	0.999214i	$0.512624\pi$
$857$	−30.4123	+	30.4123i	−1.03886	+	1.03886i	−0.999214	+	0.0396506i	$0.987376\pi$
$858$		0			0
$859$			5.99573i			0.204572i	0.994755	+	0.102286i	$0.0326156\pi$
$859$			5.99573i			0.204572i	−0.994755	+	0.102286i	$0.967384\pi$
$860$	2.09137	−	2.09137i	0.0713151	−	0.0713151i
$861$		0			0
$862$	25.3328	+	25.3328i	0.862840	+	0.862840i
$863$	54.1552			1.84346			0.921732	−	0.387828i	$-0.126775\pi$
$863$	54.1552			1.84346			0.921732	+	0.387828i	$0.126775\pi$
$864$		0			0
$865$		−	4.18630i		−	0.142338i
$866$	−8.21621			−0.279198
$867$		0			0
$868$	32.5315			1.10419
$869$		−	0.593079i		−	0.0201188i
$870$		0			0
$871$	−8.41067			−0.284985
$872$	1.85478	+	1.85478i	0.0628109	+	0.0628109i
$873$		0			0
$874$	17.0026	−	17.0026i	0.575121	−	0.575121i
$875$			14.8993i			0.503688i
$876$		0			0
$877$	18.8910	−	18.8910i	0.637903	−	0.637903i	−0.312135	−	0.950038i	$-0.601044\pi$
$877$	18.8910	−	18.8910i	0.637903	−	0.637903i	0.950038	+	0.312135i	$0.101044\pi$
$878$	4.08666	−	4.08666i	0.137918	−	0.137918i
$879$		0			0
$880$	0.859617			0.0289777
$881$	8.57086	+	8.57086i	0.288760	+	0.288760i	0.836590	−	0.547830i	$-0.184546\pi$
$881$	8.57086	+	8.57086i	0.288760	+	0.288760i	−0.547830	+	0.836590i	$0.684546\pi$
$882$		0			0
$883$	−44.5718			−1.49996			−0.749981	−	0.661460i	$-0.769937\pi$
$883$	−44.5718			−1.49996			−0.749981	+	0.661460i	$0.769937\pi$
$884$	−50.1752	+	6.33005i	−1.68758	+	0.212902i
$885$		0			0
$886$		−	20.4281i		−	0.686295i
$887$	15.5520	+	15.5520i	0.522185	+	0.522185i	0.918231	−	0.396046i	$-0.129618\pi$
$887$	15.5520	+	15.5520i	0.522185	+	0.522185i	−0.396046	+	0.918231i	$0.629618\pi$
$888$		0			0
$889$	5.55172	+	5.55172i	0.186199	+	0.186199i
$890$	4.96680	−	4.96680i	0.166487	−	0.166487i
$891$		0			0
$892$		−	9.17950i		−	0.307352i
$893$		−	1.55666i		−	0.0520915i
$894$		0			0
$895$	−2.22609	+	2.22609i	−0.0744098	+	0.0744098i
$896$	−13.5702	−	13.5702i	−0.453348	−	0.453348i
$897$		0			0
$898$	−58.5196	−	58.5196i	−1.95282	−	1.95282i
$899$			14.4803i			0.482945i
$900$		0			0
$901$	−5.22932	−	41.4503i	−0.174214	−	1.38091i
$902$	17.8709			0.595036
$903$		0			0
$904$	−4.90507	−	4.90507i	−0.163140	−	0.163140i
$905$	−3.33940			−0.111005
$906$		0			0
$907$	−11.2925	+	11.2925i	−0.374962	+	0.374962i	−0.869281	−	0.494319i	$-0.835418\pi$
$907$	−11.2925	+	11.2925i	−0.374962	+	0.374962i	0.494319	+	0.869281i	$0.335418\pi$
$908$	27.8643	−	27.8643i	0.924711	−	0.924711i
$909$		0			0
$910$		−	16.8387i		−	0.558199i
$911$	−26.8989	+	26.8989i	−0.891200	+	0.891200i	−0.994636	−	0.103436i	$-0.967016\pi$
$911$	−26.8989	+	26.8989i	−0.891200	+	0.891200i	0.103436	+	0.994636i	$0.467016\pi$
$912$		0			0
$913$	−3.72271	−	3.72271i	−0.123204	−	0.123204i
$914$	−0.934124			−0.0308981
$915$		0			0
$916$		−	42.5468i		−	1.40579i
$917$	27.6965			0.914619
$918$		0			0
$919$	7.23321			0.238602			0.119301	−	0.992858i	$-0.461935\pi$
$919$	7.23321			0.238602			0.119301	+	0.992858i	$0.461935\pi$
$920$		−	0.690847i		−	0.0227766i
$921$		0			0
$922$	−23.8280			−0.784734
$923$	−34.2368	−	34.2368i	−1.12692	−	1.12692i
$924$		0			0
$925$	9.91496	−	9.91496i	0.326002	−	0.326002i
$926$		−	9.11436i		−	0.299517i
$927$		0			0
$928$	25.1448	−	25.1448i	0.825418	−	0.825418i
$929$	31.2492	−	31.2492i	1.02525	−	1.02525i	0.0255787	−	0.999673i	$-0.491857\pi$
$929$	31.2492	−	31.2492i	1.02525	−	1.02525i	0.999673	−	0.0255787i	$-0.00814283\pi$
$930$		0			0
$931$	−38.6077			−1.26532
$932$	−15.7075	−	15.7075i	−0.514516	−	0.514516i
$933$		0			0
$934$	17.2462			0.564312
$935$	−1.03830	+	0.130991i	−0.0339562	+	0.00428387i
$936$		0			0
$937$			22.5141i			0.735504i	0.929924	+	0.367752i	$0.119873\pi$
$937$			22.5141i			0.735504i	−0.929924	+	0.367752i	$0.880127\pi$
$938$	9.86391	+	9.86391i	0.322068	+	0.322068i
$939$		0			0
$940$	−0.265746	−	0.265746i	−0.00866767	−	0.00866767i
$941$	−1.57783	+	1.57783i	−0.0514357	+	0.0514357i	−0.732357	−	0.680921i	$-0.761580\pi$
$941$	−1.57783	+	1.57783i	−0.0514357	+	0.0514357i	0.680921	+	0.732357i	$0.261580\pi$
$942$		0			0
$943$			42.1633i			1.37303i
$944$			17.9424i			0.583974i
$945$		0			0
$946$	3.99506	−	3.99506i	0.129891	−	0.129891i
$947$	−9.76465	−	9.76465i	−0.317309	−	0.317309i	0.530424	−	0.847733i	$-0.322033\pi$
$947$	−9.76465	−	9.76465i	−0.317309	−	0.317309i	−0.847733	+	0.530424i	$0.822033\pi$
$948$		0			0
$949$	−15.6410	−	15.6410i	−0.507730	−	0.507730i
$950$		−	32.9706i		−	1.06971i
$951$		0			0
$952$	7.88627	+	6.11934i	0.255595	+	0.198329i
$953$	7.23736			0.234441			0.117221	−	0.993106i	$-0.462602\pi$
$953$	7.23736			0.234441			0.117221	+	0.993106i	$0.462602\pi$
$954$		0			0
$955$	4.65349	+	4.65349i	0.150583	+	0.150583i
$956$	−32.4597			−1.04982
$957$		0			0
$958$	18.6491	−	18.6491i	0.602525	−	0.602525i
$959$	−6.99625	+	6.99625i	−0.225921	+	0.225921i
$960$		0			0
$961$		−	20.0806i		−	0.647763i
$962$	−22.6890	+	22.6890i	−0.731523	+	0.731523i
$963$		0			0
$964$	10.2343	+	10.2343i	0.329623	+	0.329623i
$965$	8.64052			0.278148
$966$		0			0
$967$			10.6240i			0.341646i	0.985302	+	0.170823i	$0.0546426\pi$
$967$			10.6240i			0.341646i	−0.985302	+	0.170823i	$0.945357\pi$
$968$	5.84357			0.187820
$969$		0			0
$970$	1.27431			0.0409155
$971$		−	25.6491i		−	0.823118i	−0.911383	−	0.411559i	$-0.864984\pi$
$971$		−	25.6491i		−	0.823118i	0.911383	−	0.411559i	$-0.135016\pi$
$972$		0			0
$973$	72.0946			2.31125
$974$	18.7679	+	18.7679i	0.601362	+	0.601362i
$975$		0			0
$976$	−8.49440	+	8.49440i	−0.271899	+	0.271899i
$977$		−	17.2663i		−	0.552397i	−0.961101	−	0.276198i	$-0.910925\pi$
$977$		−	17.2663i		−	0.552397i	0.961101	−	0.276198i	$-0.0890747\pi$
$978$		0			0
$979$	5.04407	−	5.04407i	0.161209	−	0.161209i
$980$	−6.59094	+	6.59094i	−0.210540	+	0.210540i
$981$		0			0
$982$	42.2853			1.34938
$983$	−24.7459	−	24.7459i	−0.789272	−	0.789272i	0.192102	−	0.981375i	$-0.438469\pi$
$983$	−24.7459	−	24.7459i	−0.789272	−	0.789272i	−0.981375	+	0.192102i	$0.938469\pi$
$984$		0			0
$985$	3.88683			0.123845
$986$	−22.8883	+	29.4972i	−0.728912	+	0.939382i
$987$		0			0
$988$			40.1109i			1.27610i
$989$	9.42567	+	9.42567i	0.299719	+	0.299719i
$990$		0			0
$991$	16.2075	+	16.2075i	0.514848	+	0.514848i	0.916008	−	0.401160i	$-0.131393\pi$
$991$	16.2075	+	16.2075i	0.514848	+	0.514848i	−0.401160	+	0.916008i	$0.631393\pi$
$992$	18.9613	−	18.9613i	0.602022	−	0.602022i
$993$		0			0
$994$			80.3049i			2.54712i
$995$		−	5.95633i		−	0.188828i
$996$		0			0
$997$	−42.3017	+	42.3017i	−1.33971	+	1.33971i	−0.443367	+	0.896340i	$0.646216\pi$
$997$	−42.3017	+	42.3017i	−1.33971	+	1.33971i	−0.896340	+	0.443367i	$0.853784\pi$
$998$	−10.3524	−	10.3524i	−0.327700	−	0.327700i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.f.b.64.4		8
3.2	odd	2		51.2.e.a.13.1	yes	8
4.3	odd	2		2448.2.be.x.1441.2		8
12.11	even	2		816.2.bd.e.625.2		8
17.2	even	8		2601.2.a.be.1.1		4
17.4	even	4	inner	153.2.f.b.55.1		8
17.15	even	8		2601.2.a.bf.1.1		4
51.2	odd	8		867.2.a.l.1.4		4
51.5	even	16		867.2.h.k.733.3		16
51.8	odd	8		867.2.d.f.577.1		8
51.11	even	16		867.2.h.k.757.3		16
51.14	even	16		867.2.h.i.712.1		16
51.20	even	16		867.2.h.i.712.2		16
51.23	even	16		867.2.h.k.757.4		16
51.26	odd	8		867.2.d.f.577.2		8
51.29	even	16		867.2.h.k.733.4		16
51.32	odd	8		867.2.a.k.1.4		4
51.38	odd	4		51.2.e.a.4.4	✓	8
51.41	even	16		867.2.h.i.688.2		16
51.44	even	16		867.2.h.i.688.1		16
51.47	odd	4		867.2.e.g.616.4		8
51.50	odd	2		867.2.e.g.829.1		8
68.55	odd	4		2448.2.be.x.1585.2		8
204.191	even	4		816.2.bd.e.769.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.4	✓	8	51.38	odd	4
51.2.e.a.13.1	yes	8	3.2	odd	2
153.2.f.b.55.1		8	17.4	even	4	inner
153.2.f.b.64.4		8	1.1	even	1	trivial
816.2.bd.e.625.2		8	12.11	even	2
816.2.bd.e.769.2		8	204.191	even	4
867.2.a.k.1.4		4	51.32	odd	8
867.2.a.l.1.4		4	51.2	odd	8
867.2.d.f.577.1		8	51.8	odd	8
867.2.d.f.577.2		8	51.26	odd	8
867.2.e.g.616.4		8	51.47	odd	4
867.2.e.g.829.1		8	51.50	odd	2
867.2.h.i.688.1		16	51.44	even	16
867.2.h.i.688.2		16	51.41	even	16
867.2.h.i.712.1		16	51.14	even	16
867.2.h.i.712.2		16	51.20	even	16
867.2.h.k.733.3		16	51.5	even	16
867.2.h.k.733.4		16	51.29	even	16
867.2.h.k.757.3		16	51.11	even	16
867.2.h.k.757.4		16	51.23	even	16
2448.2.be.x.1441.2		8	4.3	odd	2
2448.2.be.x.1585.2		8	68.55	odd	4
2601.2.a.be.1.1		4	17.2	even	8
2601.2.a.bf.1.1		4	17.15	even	8

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.06644i q^{2} -2.27016 q^{4} +(0.245916 + 0.245916i) q^{5} +(-3.06644 + 3.06644i) q^{7} -0.558268i q^{8} +(-0.508169 + 0.508169i) q^{10} +(-0.516075 + 0.516075i) q^{11} +5.40303 q^{13} +(-6.33660 - 6.33660i) q^{14} -3.38669 q^{16} +(4.09068 - 0.516075i) q^{17} -3.27016i q^{19} +(-0.558268 - 0.558268i) q^{20} +(-1.06644 - 1.06644i) q^{22} +(2.51608 - 2.51608i) q^{23} -4.87905i q^{25} +11.1650i q^{26} +(6.96130 - 6.96130i) q^{28} +(3.09859 + 3.09859i) q^{29} +(2.33660 + 2.33660i) q^{31} -8.11492i q^{32} +(1.06644 + 8.45313i) q^{34} -1.50817 q^{35} +(2.03215 + 2.03215i) q^{37} +6.75758 q^{38} +(0.137287 - 0.137287i) q^{40} +(-8.37879 + 8.37879i) q^{41} +3.74618i q^{43} +(1.17157 - 1.17157i) q^{44} +(5.19931 + 5.19931i) q^{46} +0.476019 q^{47} -11.8061i q^{49} +10.0822 q^{50} -12.2657 q^{52} -10.1329i q^{53} -0.253822 q^{55} +(1.71189 + 1.71189i) q^{56} +(-6.40303 + 6.40303i) q^{58} -5.29790i q^{59} +(2.50817 - 2.50817i) q^{61} +(-4.82843 + 4.82843i) q^{62} +9.99559 q^{64} +(1.32869 + 1.32869i) q^{65} -1.55666 q^{67} +(-9.28650 + 1.17157i) q^{68} -3.11654i q^{70} +(-6.33660 - 6.33660i) q^{71} +(-2.89486 - 2.89486i) q^{73} +(-4.19931 + 4.19931i) q^{74} +7.42378i q^{76} -3.16502i q^{77} +(-0.574605 + 0.574605i) q^{79} +(-0.832841 - 0.832841i) q^{80} +(-17.3142 - 17.3142i) q^{82} +7.21351i q^{83} +(1.13287 + 0.879051i) q^{85} -7.74124 q^{86} +(0.288108 + 0.288108i) q^{88} -9.77391 q^{89} +(-16.5681 + 16.5681i) q^{91} +(-5.71189 + 5.71189i) q^{92} +0.983662i q^{94} +(0.804183 - 0.804183i) q^{95} +(-1.25382 - 1.25382i) q^{97} +24.3965 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) \) 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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