LMFDB - Embedded newform 352.2.m.d.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(97,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$352 = 2^{5} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	352.m (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,14,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121$ x^8 - x^6 + 16x^4 - 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			257.1
Root			$-1.26313 - 1.73855i$ of defining polynomial
Character	$\chi$	$=$	352.257
Dual form			352.2.m.d.289.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780656 + 2.40261i) q^{3} +(2.30902 - 1.67760i) q^{5} +(0.780656 + 2.40261i) q^{7} +(-2.73607 - 1.98787i) q^{9} +(2.52626 - 2.14896i) q^{11} +(3.92705 + 2.85317i) q^{13} +(2.22807 + 6.85730i) q^{15} +(-4.54508 + 3.30220i) q^{17} +(0.780656 - 2.40261i) q^{19} -6.38197 q^{21} -8.17513 q^{23} +(0.972136 - 2.99193i) q^{25} +(0.780656 - 0.567180i) q^{27} +(0.427051 + 1.31433i) q^{29} +(5.35069 + 3.88751i) q^{31} +(3.19098 + 7.74721i) q^{33} +(5.83317 + 4.23804i) q^{35} +(-0.190983 - 0.587785i) q^{37} +(-9.92073 + 7.20783i) q^{39} +(2.66312 - 8.19624i) q^{41} +3.12262 q^{43} -9.65248 q^{45} +(-0.184288 + 0.567180i) q^{47} +(0.500000 - 0.363271i) q^{49} +(-4.38575 - 13.4980i) q^{51} +(-0.309017 - 0.224514i) q^{53} +(2.22807 - 9.20003i) q^{55} +(5.16312 + 3.75123i) q^{57} +(-3.30691 - 10.1776i) q^{59} +(2.92705 - 2.12663i) q^{61} +(2.64015 - 8.12555i) q^{63} +13.8541 q^{65} -13.2276 q^{67} +(6.38197 - 19.6417i) q^{69} +(9.43826 - 6.85730i) q^{71} +(1.33688 + 4.11450i) q^{73} +(6.42953 + 4.67133i) q^{75} +(7.13525 + 4.39201i) q^{77} +(-2.82444 - 2.05208i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(9.43826 - 6.85730i) q^{83} +(-4.95492 + 15.2497i) q^{85} -3.49120 q^{87} -7.23607 q^{89} +(-3.78938 + 11.6625i) q^{91} +(-13.5172 + 9.82084i) q^{93} +(-2.22807 - 6.85730i) q^{95} +(-14.3992 - 10.4616i) q^{97} +(-11.1839 + 0.857837i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 14 q^{5} - 4 q^{9} + 18 q^{13} - 14 q^{17} - 60 q^{21} - 28 q^{25} - 10 q^{29} + 30 q^{33} - 6 q^{37} - 10 q^{41} + 48 q^{45} + 4 q^{49} + 2 q^{53} + 10 q^{57} + 10 q^{61} + 84 q^{65} + 60 q^{69}+ \cdots - 66 q^{97}+O(q^{100})$ 8 * q + 14 * q^5 - 4 * q^9 + 18 * q^13 - 14 * q^17 - 60 * q^21 - 28 * q^25 - 10 * q^29 + 30 * q^33 - 6 * q^37 - 10 * q^41 + 48 * q^45 + 4 * q^49 + 2 * q^53 + 10 * q^57 + 10 * q^61 + 84 * q^65 + 60 * q^69 + 42 * q^73 - 10 * q^77 - 28 * q^81 - 62 * q^85 - 40 * q^89 - 50 * q^93 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$ .

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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

)

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

$2$		0			0
$2$		0			0
$3$	−0.780656	+	2.40261i	−0.450712	+	1.38715i	0.425385	+	0.905013i	$0.360139\pi$
$3$	−0.780656	+	2.40261i	−0.450712	+	1.38715i	−0.876096	+	0.482136i	$0.839861\pi$
$4$		0			0
$5$	2.30902	−	1.67760i	1.03262	−	0.750245i	0.0637916	−	0.997963i	$-0.479681\pi$
$5$	2.30902	−	1.67760i	1.03262	−	0.750245i	0.968832	+	0.247718i	$0.0796807\pi$
$6$		0			0
$7$	0.780656	+	2.40261i	0.295060	+	0.908102i	0.983201	+	0.182525i	$0.0584270\pi$
$7$	0.780656	+	2.40261i	0.295060	+	0.908102i	−0.688141	+	0.725577i	$0.741573\pi$
$8$		0			0
$9$	−2.73607	−	1.98787i	−0.912023	−	0.662623i
$10$		0			0
$11$	2.52626	−	2.14896i	0.761695	−	0.647936i
$11$	2.52626	−	2.14896i	0.761695	−	0.647936i
$12$		0			0
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.979259	−	0.202615i	$-0.0649439\pi$
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.109909	+	0.993942i	$0.464944\pi$
$14$		0			0
$15$	2.22807	+	6.85730i	0.575286	+	1.77055i
$16$		0			0
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.981441	−	0.191764i	$-0.938579\pi$
$17$	−4.54508	+	3.30220i	−1.10235	+	0.800901i	−0.120904	+	0.992664i	$0.538579\pi$
$18$		0			0
$19$	0.780656	−	2.40261i	0.179095	−	0.551197i	−0.820702	−	0.571356i	$-0.806417\pi$
$19$	0.780656	−	2.40261i	0.179095	−	0.551197i	0.999797	+	0.0201595i	$0.00641741\pi$
$20$		0			0
$21$	−6.38197			−1.39266
$22$		0			0
$23$	−8.17513			−1.70463			−0.852317	−	0.523026i	$-0.824803\pi$
$23$	−8.17513			−1.70463			−0.852317	+	0.523026i	$0.824803\pi$
$24$		0			0
$25$	0.972136	−	2.99193i	0.194427	−	0.598385i
$26$		0			0
$27$	0.780656	−	0.567180i	0.150237	−	0.109154i
$28$		0			0
$29$	0.427051	+	1.31433i	0.0793014	+	0.244065i	0.982846	−	0.184430i	$-0.0590440\pi$
$29$	0.427051	+	1.31433i	0.0793014	+	0.244065i	−0.903544	+	0.428495i	$0.859044\pi$
$30$		0			0
$31$	5.35069	+	3.88751i	0.961013	+	0.698217i	0.953386	−	0.301754i	$-0.0975721\pi$
$31$	5.35069	+	3.88751i	0.961013	+	0.698217i	0.00762731	+	0.999971i	$0.497572\pi$
$32$		0			0
$33$	3.19098	+	7.74721i	0.555479	+	1.34862i
$34$		0			0
$35$	5.83317	+	4.23804i	0.985985	+	0.716360i
$36$		0			0
$37$	−0.190983	−	0.587785i	−0.0313974	−	0.0966313i	0.934130	−	0.356934i	$-0.116178\pi$
$37$	−0.190983	−	0.587785i	−0.0313974	−	0.0966313i	−0.965527	+	0.260302i	$0.916178\pi$
$38$		0			0
$39$	−9.92073	+	7.20783i	−1.58859	+	1.15418i
$40$		0			0
$41$	2.66312	−	8.19624i	0.415909	−	1.28004i	−0.495526	−	0.868593i	$-0.665025\pi$
$41$	2.66312	−	8.19624i	0.415909	−	1.28004i	0.911435	−	0.411444i	$-0.134975\pi$
$42$		0			0
$43$	3.12262			0.476196			0.238098	−	0.971241i	$-0.423476\pi$
$43$	3.12262			0.476196			0.238098	+	0.971241i	$0.423476\pi$
$44$		0			0
$45$	−9.65248			−1.43891
$46$		0			0
$47$	−0.184288	+	0.567180i	−0.0268811	+	0.0827317i	−0.963597	−	0.267359i	$-0.913849\pi$
$47$	−0.184288	+	0.567180i	−0.0268811	+	0.0827317i	0.936716	+	0.350090i	$0.113849\pi$
$48$		0			0
$49$	0.500000	−	0.363271i	0.0714286	−	0.0518959i
$50$		0			0
$51$	−4.38575	−	13.4980i	−0.614128	−	1.89009i
$52$		0			0
$53$	−0.309017	−	0.224514i	−0.0424467	−	0.0308394i	0.566360	−	0.824158i	$-0.308351\pi$
$53$	−0.309017	−	0.224514i	−0.0424467	−	0.0308394i	−0.608806	+	0.793319i	$0.708351\pi$
$54$		0			0
$55$	2.22807	−	9.20003i	0.300433	−	1.24053i
$56$		0			0
$57$	5.16312	+	3.75123i	0.683872	+	0.496862i
$58$		0			0
$59$	−3.30691	−	10.1776i	−0.430523	−	1.32501i	−0.897605	−	0.440800i	$-0.854695\pi$
$59$	−3.30691	−	10.1776i	−0.430523	−	1.32501i	0.467082	−	0.884214i	$-0.345305\pi$
$60$		0			0
$61$	2.92705	−	2.12663i	0.374770	−	0.272287i	−0.384416	−	0.923160i	$-0.625597\pi$
$61$	2.92705	−	2.12663i	0.374770	−	0.272287i	0.759186	+	0.650873i	$0.225597\pi$
$62$		0			0
$63$	2.64015	−	8.12555i	0.332628	−	1.02372i
$64$		0			0
$65$	13.8541			1.71839
$66$		0			0
$67$	−13.2276			−1.61601			−0.808007	−	0.589173i	$-0.799454\pi$
$67$	−13.2276			−1.61601			−0.808007	+	0.589173i	$0.799454\pi$
$68$		0			0
$69$	6.38197	−	19.6417i	0.768298	−	2.36458i
$70$		0			0
$71$	9.43826	−	6.85730i	1.12012	−	0.813812i	0.135889	−	0.990724i	$-0.456611\pi$
$71$	9.43826	−	6.85730i	1.12012	−	0.813812i	0.984227	+	0.176912i	$0.0566109\pi$
$72$		0			0
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	0.998307	−	0.0581668i	$-0.0185255\pi$
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	−0.841837	+	0.539732i	$0.818526\pi$
$74$		0			0
$75$	6.42953	+	4.67133i	0.742419	+	0.539399i
$76$		0			0
$77$	7.13525	+	4.39201i	0.813138	+	0.500516i
$78$		0			0
$79$	−2.82444	−	2.05208i	−0.317774	−	0.230877i	0.417451	−	0.908699i	$-0.362924\pi$
$79$	−2.82444	−	2.05208i	−0.317774	−	0.230877i	−0.735225	+	0.677823i	$0.762924\pi$
$80$		0			0
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$		0			0
$83$	9.43826	−	6.85730i	1.03598	−	0.752686i	0.0664863	−	0.997787i	$-0.478821\pi$
$83$	9.43826	−	6.85730i	1.03598	−	0.752686i	0.969498	+	0.245101i	$0.0788211\pi$
$84$		0			0
$85$	−4.95492	+	15.2497i	−0.537436	+	1.65406i
$86$		0			0
$87$	−3.49120			−0.374296
$88$		0			0
$89$	−7.23607			−0.767022			−0.383511	−	0.923536i	$-0.625285\pi$
$89$	−7.23607			−0.767022			−0.383511	+	0.923536i	$0.625285\pi$
$90$		0			0
$91$	−3.78938	+	11.6625i	−0.397235	+	1.22256i
$92$		0			0
$93$	−13.5172	+	9.82084i	−1.40167	+	1.01837i
$94$		0			0
$95$	−2.22807	−	6.85730i	−0.228595	−	0.703544i
$96$		0			0
$97$	−14.3992	−	10.4616i	−1.46202	−	1.06222i	−0.982832	−	0.184502i	$-0.940933\pi$
$97$	−14.3992	−	10.4616i	−1.46202	−	1.06222i	−0.479184	−	0.877715i	$-0.659067\pi$
$98$		0			0
$99$	−11.1839	+	0.857837i	−1.12402	+	0.0862159i
$100$		0			0
$101$	6.78115	+	4.92680i	0.674750	+	0.490235i	0.871612	−	0.490197i	$-0.163075\pi$
$101$	6.78115	+	4.92680i	0.674750	+	0.490235i	−0.196862	+	0.980431i	$0.563075\pi$
$102$		0			0
$103$	1.74560	+	5.37240i	0.171999	+	0.529359i	0.999484	−	0.0321297i	$-0.0102290\pi$
$103$	1.74560	+	5.37240i	0.171999	+	0.529359i	−0.827485	+	0.561488i	$0.810229\pi$
$104$		0			0
$105$	−14.7361	+	10.7064i	−1.43809	+	1.04484i
$106$		0			0
$107$	5.23680	−	16.1172i	0.506260	−	1.55811i	−0.292381	−	0.956302i	$-0.594447\pi$
$107$	5.23680	−	16.1172i	0.506260	−	1.55811i	0.798641	−	0.601807i	$-0.205553\pi$
$108$		0			0
$109$	10.4721			1.00305			0.501524	−	0.865144i	$-0.332773\pi$
$109$	10.4721			1.00305			0.501524	+	0.865144i	$0.332773\pi$
$110$		0			0
$111$	1.56131			0.148193
$112$		0			0
$113$	−2.51722	+	7.74721i	−0.236800	+	0.728796i	0.760077	+	0.649833i	$0.225161\pi$
$113$	−2.51722	+	7.74721i	−0.236800	+	0.728796i	−0.996878	+	0.0789635i	$0.974839\pi$
$114$		0			0
$115$	−18.8765	+	13.7146i	−1.76024	+	1.27889i
$116$		0			0
$117$	−5.07295	−	15.6129i	−0.468994	−	1.44342i
$118$		0			0
$119$	−11.4820	−	8.34219i	−1.05256	−	0.764728i
$120$		0			0
$121$	1.76393	−	10.8576i	0.160357	−	0.987059i
$122$		0			0
$123$	17.6134	+	12.7969i	1.58815	+	1.15386i
$124$		0			0
$125$	1.63525	+	5.03280i	0.146262	+	0.450147i
$126$		0			0
$127$	3.78938	−	2.75315i	0.336253	−	0.244302i	−0.406826	−	0.913506i	$-0.633364\pi$
$127$	3.78938	−	2.75315i	0.336253	−	0.244302i	0.743079	+	0.669203i	$0.233364\pi$
$128$		0			0
$129$	−2.43769	+	7.50245i	−0.214627	+	0.660554i
$130$		0			0
$131$	−1.92989			−0.168615			−0.0843075	−	0.996440i	$-0.526868\pi$
$131$	−1.92989			−0.168615			−0.0843075	+	0.996440i	$0.526868\pi$
$132$		0			0
$133$	6.38197			0.553387
$134$		0			0
$135$	0.851048	−	2.61925i	0.0732465	−	0.225430i
$136$		0			0
$137$	−8.01722	+	5.82485i	−0.684957	+	0.497651i	−0.874999	−	0.484125i	$-0.839138\pi$
$137$	−8.01722	+	5.82485i	−0.684957	+	0.497651i	0.190041	+	0.981776i	$0.439138\pi$
$138$		0			0
$139$	4.27185	+	13.1474i	0.362334	+	1.11515i	0.951634	+	0.307235i	$0.0994037\pi$
$139$	4.27185	+	13.1474i	0.362334	+	1.11515i	−0.589300	+	0.807915i	$0.700596\pi$
$140$		0			0
$141$	−1.21885	−	0.885544i	−0.102645	−	0.0745763i
$142$		0			0
$143$	16.0521	−	1.23125i	1.34234	−	0.102962i
$144$		0			0
$145$	3.19098	+	2.31838i	0.264997	+	0.192531i
$146$		0			0
$147$	0.482472	+	1.48490i	0.0397936	+	0.122472i
$148$		0			0
$149$	−7.54508	+	5.48183i	−0.618117	+	0.449089i	−0.852263	−	0.523113i	$-0.824771\pi$
$149$	−7.54508	+	5.48183i	−0.618117	+	0.449089i	0.234146	+	0.972201i	$0.424771\pi$
$150$		0			0
$151$	−3.30691	+	10.1776i	−0.269113	+	0.828243i	0.721605	+	0.692305i	$0.243405\pi$
$151$	−3.30691	+	10.1776i	−0.269113	+	0.828243i	−0.990717	+	0.135938i	$0.956595\pi$
$152$		0			0
$153$	19.0000			1.53606
$154$		0			0
$155$	18.8765			1.51620
$156$		0			0
$157$	6.04508	−	18.6049i	0.482450	−	1.48483i	−0.353190	−	0.935552i	$-0.614903\pi$
$157$	6.04508	−	18.6049i	0.482450	−	1.48483i	0.835640	−	0.549278i	$-0.185097\pi$
$158$		0			0
$159$	0.780656	−	0.567180i	0.0619100	−	0.0449803i
$160$		0			0
$161$	−6.38197	−	19.6417i	−0.502969	−	1.54798i
$162$		0			0
$163$	−9.43826	−	6.85730i	−0.739262	−	0.537105i	0.153218	−	0.988192i	$-0.451036\pi$
$163$	−9.43826	−	6.85730i	−0.739262	−	0.537105i	−0.892480	+	0.451087i	$0.851036\pi$
$164$		0			0
$165$	20.3647	+	12.5352i	1.58539	+	0.975868i
$166$		0			0
$167$	−5.35069	−	3.88751i	−0.414049	−	0.300824i	0.361190	−	0.932492i	$-0.382371\pi$
$167$	−5.35069	−	3.88751i	−0.414049	−	0.300824i	−0.775239	+	0.631668i	$0.782371\pi$
$168$		0			0
$169$	3.26393	+	10.0453i	0.251072	+	0.772719i
$170$		0			0
$171$	−6.91201	+	5.02187i	−0.528574	+	0.384032i
$172$		0			0
$173$	5.48278	−	16.8743i	0.416848	−	1.28293i	−0.493740	−	0.869610i	$-0.664370\pi$
$173$	5.48278	−	16.8743i	0.416848	−	1.28293i	0.910588	−	0.413316i	$-0.135630\pi$
$174$		0			0
$175$	7.94734			0.600763
$176$		0			0
$177$	27.0344			2.03203
$178$		0			0
$179$	−0.780656	+	2.40261i	−0.0583490	+	0.179580i	−0.975983	−	0.217847i	$-0.930097\pi$
$179$	−0.780656	+	2.40261i	−0.0583490	+	0.179580i	0.917634	+	0.397427i	$0.130097\pi$
$180$		0			0
$181$	−15.3992	+	11.1882i	−1.14461	+	0.831610i	−0.987755	−	0.156012i	$-0.950136\pi$
$181$	−15.3992	+	11.1882i	−1.14461	+	0.831610i	−0.156857	+	0.987621i	$0.550136\pi$
$182$		0			0
$183$	2.82444	+	8.69273i	0.208789	+	0.642585i
$184$		0			0
$185$	−1.42705	−	1.03681i	−0.104919	−	0.0762280i
$186$		0			0
$187$	−4.38575	+	18.1094i	−0.320718	+	1.32429i
$188$		0			0
$189$	1.97214	+	1.43284i	0.143452	+	0.104224i
$190$		0			0
$191$	−0.184288	−	0.567180i	−0.0133346	−	0.0410397i	0.944168	−	0.329465i	$-0.106868\pi$
$191$	−0.184288	−	0.567180i	−0.0133346	−	0.0410397i	−0.957502	+	0.288425i	$0.906868\pi$
$192$		0			0
$193$	−9.16312	+	6.65740i	−0.659576	+	0.479210i	−0.866520	−	0.499143i	$-0.833648\pi$
$193$	−9.16312	+	6.65740i	−0.659576	+	0.479210i	0.206944	+	0.978353i	$0.433648\pi$
$194$		0			0
$195$	−10.8153	+	33.2860i	−0.774499	+	2.38366i
$196$		0			0
$197$	−12.6525			−0.901452			−0.450726	−	0.892662i	$-0.648835\pi$
$197$	−12.6525			−0.901452			−0.450726	+	0.892662i	$0.648835\pi$
$198$		0			0
$199$	−3.12262			−0.221357			−0.110678	−	0.993856i	$-0.535302\pi$
$199$	−3.12262			−0.221357			−0.110678	+	0.993856i	$0.535302\pi$
$200$		0			0
$201$	10.3262	−	31.7809i	0.728357	−	2.24165i
$202$		0			0
$203$	−2.82444	+	2.05208i	−0.198237	+	0.144027i
$204$		0			0
$205$	−7.60081	−	23.3929i	−0.530864	−	1.63383i
$206$		0			0
$207$	22.3677	+	16.2511i	1.55466	+	1.12953i
$208$		0			0
$209$	−3.19098	−	7.74721i	−0.220725	−	0.535886i
$210$		0			0
$211$	−2.82444	−	2.05208i	−0.194442	−	0.141271i	0.486304	−	0.873789i	$-0.338345\pi$
$211$	−2.82444	−	2.05208i	−0.194442	−	0.141271i	−0.680747	+	0.732519i	$0.738345\pi$
$212$		0			0
$213$	9.10739	+	28.0297i	0.624028	+	1.92056i
$214$		0			0
$215$	7.21019	−	5.23851i	0.491731	−	0.357263i
$216$		0			0
$217$	−5.16312	+	15.8904i	−0.350495	+	1.07871i
$218$		0			0
$219$	−10.9292			−0.738526
$220$		0			0
$221$	−27.2705			−1.83441
$222$		0			0
$223$	5.46459	−	16.8183i	0.365936	−	1.12624i	−0.583457	−	0.812144i	$-0.698300\pi$
$223$	5.46459	−	16.8183i	0.365936	−	1.12624i	0.949393	−	0.314091i	$-0.101700\pi$
$224$		0			0
$225$	−8.60739	+	6.25364i	−0.573826	+	0.416909i
$226$		0			0
$227$	0.184288	+	0.567180i	0.0122316	+	0.0376450i	0.956986	−	0.290134i	$-0.0936999\pi$
$227$	0.184288	+	0.567180i	0.0122316	+	0.0376450i	−0.944754	+	0.327779i	$0.893700\pi$
$228$		0			0
$229$	2.07295	+	1.50609i	0.136984	+	0.0995249i	0.654167	−	0.756350i	$-0.273019\pi$
$229$	2.07295	+	1.50609i	0.136984	+	0.0995249i	−0.517183	+	0.855875i	$0.673019\pi$
$230$		0			0
$231$	−16.1225	+	13.7146i	−1.06078	+	0.902354i
$232$		0			0
$233$	15.6353	+	11.3597i	1.02430	+	0.744197i	0.967160	−	0.254169i	$-0.0818019\pi$
$233$	15.6353	+	11.3597i	1.02430	+	0.744197i	0.0571398	+	0.998366i	$0.481802\pi$
$234$		0			0
$235$	0.525976	+	1.61879i	0.0343109	+	0.105598i
$236$		0			0
$237$	7.13525	−	5.18407i	0.463485	−	0.336741i
$238$		0			0
$239$	−3.30691	+	10.1776i	−0.213906	+	0.658336i	0.785323	+	0.619086i	$0.212497\pi$
$239$	−3.30691	+	10.1776i	−0.213906	+	0.658336i	−0.999229	+	0.0392498i	$0.987503\pi$
$240$		0			0
$241$	3.41641			0.220070			0.110035	−	0.993928i	$-0.464904\pi$
$241$	3.41641			0.220070			0.110035	+	0.993928i	$0.464904\pi$
$242$		0			0
$243$	22.3677			1.43489
$244$		0			0
$245$	0.545085	−	1.67760i	0.0348242	−	0.107178i
$246$		0			0
$247$	9.92073	−	7.20783i	0.631241	−	0.458624i
$248$		0			0
$249$	9.10739	+	28.0297i	0.577157	+	1.77631i
$250$		0			0
$251$	−0.298184	−	0.216643i	−0.0188212	−	0.0136744i	0.578335	−	0.815799i	$-0.303703\pi$
$251$	−0.298184	−	0.216643i	−0.0188212	−	0.0136744i	−0.597156	+	0.802125i	$0.703703\pi$
$252$		0			0
$253$	−20.6525	+	17.5680i	−1.29841	+	1.10449i
$254$		0			0
$255$	−32.7709	−	23.8095i	−2.05220	−	1.49101i
$256$		0			0
$257$	−2.24671	−	6.91467i	−0.140146	−	0.431325i	0.856209	−	0.516630i	$-0.172814\pi$
$257$	−2.24671	−	6.91467i	−0.140146	−	0.431325i	−0.996355	+	0.0853047i	$0.972814\pi$
$258$		0			0
$259$	1.26313	−	0.917716i	0.0784869	−	0.0570241i
$260$		0			0
$261$	1.44427	−	4.44501i	0.0893982	−	0.275139i
$262$		0			0
$263$	6.98240			0.430553			0.215277	−	0.976553i	$-0.430935\pi$
$263$	6.98240			0.430553			0.215277	+	0.976553i	$0.430935\pi$
$264$		0			0
$265$	−1.09017			−0.0669686
$266$		0			0
$267$	5.64888	−	17.3855i	0.345706	−	1.06397i
$268$		0			0
$269$	3.30902	−	2.40414i	0.201754	−	0.146583i	−0.482321	−	0.875995i	$-0.660206\pi$
$269$	3.30902	−	2.40414i	0.201754	−	0.146583i	0.684075	+	0.729412i	$0.260206\pi$
$270$		0			0
$271$	8.35942	+	25.7277i	0.507799	+	1.56284i	0.796014	+	0.605278i	$0.206938\pi$
$271$	8.35942	+	25.7277i	0.507799	+	1.56284i	−0.288215	+	0.957566i	$0.593062\pi$
$272$		0			0
$273$	−25.0623	−	18.2088i	−1.51684	−	1.10205i
$274$		0			0
$275$	−3.97367	−	9.64745i	−0.239621	−	0.581763i
$276$		0			0
$277$	−13.1631	−	9.56357i	−0.790895	−	0.574619i	0.117334	−	0.993093i	$-0.462565\pi$
$277$	−13.1631	−	9.56357i	−0.790895	−	0.574619i	−0.908229	+	0.418474i	$0.862565\pi$
$278$		0			0
$279$	−6.91201	−	21.2730i	−0.413811	−	1.27358i
$280$		0			0
$281$	−19.6353	+	14.2658i	−1.17134	+	0.851029i	−0.991169	−	0.132606i	$-0.957666\pi$
$281$	−19.6353	+	14.2658i	−1.17134	+	0.851029i	−0.180172	+	0.983635i	$0.557666\pi$
$282$		0			0
$283$	4.49965	−	13.8485i	0.267476	−	0.823207i	−0.723636	−	0.690181i	$-0.757531\pi$
$283$	4.49965	−	13.8485i	0.267476	−	0.823207i	0.991113	−	0.133026i	$-0.0424693\pi$
$284$		0			0
$285$	18.2148			1.07895
$286$		0			0
$287$	21.7714			1.28512
$288$		0			0
$289$	4.50000	−	13.8496i	0.264706	−	0.814681i
$290$		0			0
$291$	36.3760	−	26.4287i	2.13240	−	1.54928i
$292$		0			0
$293$	0.246711	+	0.759299i	0.0144130	+	0.0443587i	0.958004	−	0.286754i	$-0.0925761\pi$
$293$	0.246711	+	0.759299i	0.0144130	+	0.0443587i	−0.943591	+	0.331112i	$0.892576\pi$
$294$		0			0
$295$	−24.7097	−	17.9526i	−1.43865	−	1.04524i
$296$		0			0
$297$	0.753289	−	3.11044i	0.0437103	−	0.180486i
$298$		0			0
$299$	−32.1042	−	23.3250i	−1.85663	−	1.34892i
$300$		0			0
$301$	2.43769	+	7.50245i	0.140506	+	0.432434i
$302$		0			0
$303$	−17.1309	+	12.4463i	−0.984146	+	0.715024i
$304$		0			0
$305$	3.19098	−	9.82084i	0.182715	−	0.562339i
$306$		0			0
$307$	−1.92989			−0.110144			−0.0550722	−	0.998482i	$-0.517539\pi$
$307$	−1.92989			−0.110144			−0.0550722	+	0.998482i	$0.517539\pi$
$308$		0			0
$309$	−14.2705			−0.811821
$310$		0			0
$311$	2.34197	−	7.20783i	0.132801	−	0.408719i	−0.862441	−	0.506158i	$-0.831065\pi$
$311$	2.34197	−	7.20783i	0.132801	−	0.408719i	0.995241	+	0.0974394i	$0.0310652\pi$
$312$		0			0
$313$	−3.30902	+	2.40414i	−0.187037	+	0.135890i	−0.677363	−	0.735649i	$-0.736877\pi$
$313$	−3.30902	+	2.40414i	−0.187037	+	0.135890i	0.490327	+	0.871539i	$0.336877\pi$
$314$		0			0
$315$	−7.53526	−	23.1912i	−0.424564	−	1.30667i
$316$		0			0
$317$	4.07295	+	2.95917i	0.228760	+	0.166204i	0.696261	−	0.717789i	$-0.254846\pi$
$317$	4.07295	+	2.95917i	0.228760	+	0.166204i	−0.467501	+	0.883992i	$0.654846\pi$
$318$		0			0
$319$	3.90328	+	2.40261i	0.218542	+	0.134520i
$320$		0			0
$321$	34.6353	+	25.1640i	1.93315	+	1.40452i
$322$		0			0
$323$	4.38575	+	13.4980i	0.244030	+	0.751046i
$324$		0			0
$325$	12.3541	−	8.97578i	0.685282	−	0.497887i
$326$		0			0
$327$	−8.17513	+	25.1605i	−0.452086	+	1.39138i
$328$		0			0
$329$	−1.50658			−0.0830603
$330$		0			0
$331$	6.24525			0.343270			0.171635	−	0.985161i	$-0.445095\pi$
$331$	6.24525			0.343270			0.171635	+	0.985161i	$0.445095\pi$
$332$		0			0
$333$	−0.645898	+	1.98787i	−0.0353950	+	0.108935i
$334$		0			0
$335$	−30.5429	+	22.1907i	−1.66873	+	1.21241i
$336$		0			0
$337$	3.10081	+	9.54332i	0.168912	+	0.519858i	0.999303	−	0.0373230i	$-0.0118830\pi$
$337$	3.10081	+	9.54332i	0.168912	+	0.519858i	−0.830391	+	0.557181i	$0.811883\pi$
$338$		0			0
$339$	−16.6485	−	12.0958i	−0.904220	−	0.656954i
$340$		0			0
$341$	21.8713	−	1.67760i	1.18440	−	0.0908471i
$342$		0			0
$343$	15.5696	+	11.3120i	0.840680	+	0.610790i
$344$		0			0
$345$	−18.2148	−	56.0593i	−0.980651	−	3.01813i
$346$		0			0
$347$	14.4908	−	10.5282i	0.777905	−	0.565181i	−0.126444	−	0.991974i	$-0.540356\pi$
$347$	14.4908	−	10.5282i	0.777905	−	0.565181i	0.904350	+	0.426792i	$0.140356\pi$
$348$		0			0
$349$	1.28115	−	3.94298i	0.0685785	−	0.211063i	−0.910894	−	0.412640i	$-0.864607\pi$
$349$	1.28115	−	3.94298i	0.0685785	−	0.211063i	0.979473	+	0.201577i	$0.0646067\pi$
$350$		0			0
$351$	4.68393			0.250010
$352$		0			0
$353$	−7.70820			−0.410266			−0.205133	−	0.978734i	$-0.565763\pi$
$353$	−7.70820			−0.410266			−0.205133	+	0.978734i	$0.565763\pi$
$354$		0			0
$355$	10.2893	−	31.6672i	0.546100	−	1.68072i
$356$		0			0
$357$	29.0066	−	21.0745i	1.53519	−	1.11538i
$358$		0			0
$359$	0.184288	+	0.567180i	0.00972634	+	0.0299346i	0.955802	−	0.294011i	$-0.0949904\pi$
$359$	0.184288	+	0.567180i	0.00972634	+	0.0299346i	−0.946076	+	0.323946i	$0.894990\pi$
$360$		0			0
$361$	10.2082	+	7.41669i	0.537274	+	0.390352i
$362$		0			0
$363$	24.7097	+	12.7141i	1.29692	+	0.667319i
$364$		0			0
$365$	9.98936	+	7.25769i	0.522867	+	0.379885i
$366$		0			0
$367$	−1.14923	−	3.53697i	−0.0599894	−	0.184628i	0.916571	−	0.399872i	$-0.130945\pi$
$367$	−1.14923	−	3.53697i	−0.0599894	−	0.184628i	−0.976560	+	0.215244i	$0.930945\pi$
$368$		0			0
$369$	−23.5795	+	17.1315i	−1.22750	+	0.891832i
$370$		0			0
$371$	0.298184	−	0.917716i	0.0154809	−	0.0476454i
$372$		0			0
$373$	9.12461			0.472454			0.236227	−	0.971698i	$-0.424089\pi$
$373$	9.12461			0.472454			0.236227	+	0.971698i	$0.424089\pi$
$374$		0			0
$375$	−13.3684			−0.690343
$376$		0			0
$377$	−2.07295	+	6.37988i	−0.106762	+	0.328581i
$378$		0			0
$379$	−17.0170	+	12.3636i	−0.874106	+	0.635075i	−0.931686	−	0.363266i	$-0.881662\pi$
$379$	−17.0170	+	12.3636i	−0.874106	+	0.635075i	0.0575796	+	0.998341i	$0.481662\pi$
$380$		0			0
$381$	3.65654	+	11.2537i	0.187330	+	0.576543i
$382$		0			0
$383$	−26.1571	−	19.0042i	−1.33657	−	0.971072i	−0.999563	−	0.0295682i	$-0.990587\pi$
$383$	−26.1571	−	19.0042i	−1.33657	−	0.971072i	−0.337003	−	0.941504i	$-0.609413\pi$
$384$		0			0
$385$	23.8435	−	1.82887i	1.21518	−	0.0932077i
$386$		0			0
$387$	−8.54371	−	6.20737i	−0.434301	−	0.315538i
$388$		0			0
$389$	−1.01064	−	3.11044i	−0.0512416	−	0.157706i	0.922161	−	0.386806i	$-0.126422\pi$
$389$	−1.01064	−	3.11044i	−0.0512416	−	0.157706i	−0.973403	+	0.229100i	$0.926422\pi$
$390$		0			0
$391$	37.1567	−	26.9959i	1.87909	−	1.36524i
$392$		0			0
$393$	1.50658	−	4.63677i	0.0759968	−	0.233894i
$394$		0			0
$395$	−9.96424			−0.501355
$396$		0			0
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$		0			0
$399$	−4.98212	+	15.3334i	−0.249418	+	0.767629i
$400$		0			0
$401$	8.01722	−	5.82485i	0.400361	−	0.290879i	−0.369327	−	0.929299i	$-0.620412\pi$
$401$	8.01722	−	5.82485i	0.400361	−	0.290879i	0.769688	+	0.638420i	$0.220412\pi$
$402$		0			0
$403$	9.92073	+	30.5329i	0.494187	+	1.52095i
$404$		0			0
$405$	−17.7984	−	12.9313i	−0.884408	−	0.642560i
$406$		0			0
$407$	−1.74560	−	1.07448i	−0.0865262	−	0.0532600i
$408$		0			0
$409$	−30.9615	−	22.4948i	−1.53095	−	1.11230i	−0.955709	−	0.294312i	$-0.904909\pi$
$409$	−30.9615	−	22.4948i	−1.53095	−	1.11230i	−0.575238	−	0.817986i	$-0.695091\pi$
$410$		0			0
$411$	−7.73617	−	23.8095i	−0.381597	−	1.17443i
$412$		0			0
$413$	21.8713	−	15.8904i	1.07622	−	0.781918i
$414$		0			0
$415$	10.2893	−	31.6672i	0.505082	−	1.55448i
$416$		0			0
$417$	−34.9230			−1.71019
$418$		0			0
$419$	−8.17513			−0.399381			−0.199691	−	0.979859i	$-0.563994\pi$
$419$	−8.17513			−0.399381			−0.199691	+	0.979859i	$0.563994\pi$
$420$		0			0
$421$	−7.13525	+	21.9601i	−0.347751	+	1.07027i	0.612343	+	0.790592i	$0.290227\pi$
$421$	−7.13525	+	21.9601i	−0.347751	+	1.07027i	−0.960094	+	0.279676i	$0.909773\pi$
$422$		0			0
$423$	1.63170	−	1.18550i	0.0793361	−	0.0576411i
$424$		0			0
$425$	5.46149	+	16.8087i	0.264921	+	0.815344i
$426$		0			0
$427$	7.39448	+	5.37240i	0.357844	+	0.259989i
$428$		0			0
$429$	−9.57295	+	39.5281i	−0.462186	+	1.90843i
$430$		0			0
$431$	22.6659	+	16.4677i	1.09178	+	0.793223i	0.979699	−	0.200476i	$-0.0642488\pi$
$431$	22.6659	+	16.4677i	1.09178	+	0.793223i	0.112080	+	0.993699i	$0.464249\pi$
$432$		0			0
$433$	−3.86475	−	11.8945i	−0.185728	−	0.571611i	0.814232	−	0.580539i	$-0.197158\pi$
$433$	−3.86475	−	11.8945i	−0.185728	−	0.571611i	−0.999960	+	0.00892775i	$0.997158\pi$
$434$		0			0
$435$	−8.06124	+	5.85683i	−0.386507	+	0.280814i
$436$		0			0
$437$	−6.38197	+	19.6417i	−0.305291	+	0.939589i
$438$		0			0
$439$	−28.3852			−1.35475			−0.677375	−	0.735638i	$-0.736883\pi$
$439$	−28.3852			−1.35475			−0.677375	+	0.735638i	$0.736883\pi$
$440$		0			0
$441$	−2.09017			−0.0995319
$442$		0			0
$443$	1.37702	−	4.23804i	0.0654244	−	0.201356i	−0.913000	−	0.407958i	$-0.866241\pi$
$443$	1.37702	−	4.23804i	0.0654244	−	0.201356i	0.978425	+	0.206603i	$0.0662408\pi$
$444$		0			0
$445$	−16.7082	+	12.1392i	−0.792045	+	0.575454i
$446$		0			0
$447$	−7.28058	−	22.4073i	−0.344360	−	1.05983i
$448$		0			0
$449$	17.0172	+	12.3637i	0.803092	+	0.583481i	0.911820	−	0.410591i	$-0.134678\pi$
$449$	17.0172	+	12.3637i	0.803092	+	0.583481i	−0.108727	+	0.994072i	$0.534678\pi$
$450$		0			0
$451$	−10.8857	−	26.4287i	−0.512587	−	1.24448i
$452$		0			0
$453$	−21.8713	−	15.8904i	−1.02760	−	0.746598i
$454$		0			0
$455$	10.8153	+	33.2860i	0.507028	+	1.56047i
$456$		0			0
$457$	−4.01722	+	2.91868i	−0.187918	+	0.136530i	−0.677766	−	0.735277i	$-0.737052\pi$
$457$	−4.01722	+	2.91868i	−0.187918	+	0.136530i	0.489849	+	0.871807i	$0.337052\pi$
$458$		0			0
$459$	−1.67521	+	5.15576i	−0.0781920	+	0.240650i
$460$		0			0
$461$	−38.1803			−1.77824			−0.889118	−	0.457678i	$-0.848681\pi$
$461$	−38.1803			−1.77824			−0.889118	+	0.457678i	$0.848681\pi$
$462$		0			0
$463$	33.4377			1.55398			0.776991	−	0.629512i	$-0.216745\pi$
$463$	33.4377			1.55398			0.776991	+	0.629512i	$0.216745\pi$
$464$		0			0
$465$	−14.7361	+	45.3530i	−0.683369	+	2.10319i
$466$		0			0
$467$	8.47332	−	6.15623i	0.392098	−	0.284876i	−0.374216	−	0.927341i	$-0.622088\pi$
$467$	8.47332	−	6.15623i	0.392098	−	0.284876i	0.766315	+	0.642465i	$0.222088\pi$
$468$		0			0
$469$	−10.3262	−	31.7809i	−0.476821	−	1.46751i
$470$		0			0
$471$	39.9811	+	29.0480i	1.84223	+	1.33846i
$472$		0			0
$473$	7.88854	−	6.71040i	0.362716	−	0.308544i
$474$		0			0
$475$	−6.42953	−	4.67133i	−0.295007	−	0.214335i
$476$		0			0
$477$	0.399187	+	1.22857i	0.0182775	+	0.0562524i
$478$		0			0
$479$	−20.1397	+	14.6323i	−0.920204	+	0.668567i	−0.943575	−	0.331159i	$-0.892560\pi$
$479$	−20.1397	+	14.6323i	−0.920204	+	0.668567i	0.0233707	+	0.999727i	$0.492560\pi$
$480$		0			0
$481$	0.927051	−	2.85317i	0.0422699	−	0.130093i
$482$		0			0
$483$	52.1734			2.37397
$484$		0			0
$485$	−50.7984			−2.30664
$486$		0			0
$487$	−13.0434	+	40.1433i	−0.591051	+	1.81907i	−0.0175746	+	0.999846i	$0.505594\pi$
$487$	−13.0434	+	40.1433i	−0.591051	+	1.81907i	−0.573476	+	0.819222i	$0.694406\pi$
$488$		0			0
$489$	23.8435	−	17.3233i	1.07824	−	0.783386i
$490$		0			0
$491$	11.2543	+	34.6370i	0.507897	+	1.56315i	0.795845	+	0.605501i	$0.207027\pi$
$491$	11.2543	+	34.6370i	0.507897	+	1.56315i	−0.287947	+	0.957646i	$0.592973\pi$
$492$		0			0
$493$	−6.28115	−	4.56352i	−0.282889	−	0.205531i
$494$		0			0
$495$	−24.3846	+	20.7428i	−1.09601	+	0.932319i
$496$		0			0
$497$	23.8435	+	17.3233i	1.06953	+	0.777056i
$498$		0			0
$499$	3.30691	+	10.1776i	0.148038	+	0.455613i	0.997389	−	0.0722146i	$-0.0230067\pi$
$499$	3.30691	+	10.1776i	0.148038	+	0.455613i	−0.849351	+	0.527828i	$0.823007\pi$
$500$		0			0
$501$	13.5172	−	9.82084i	0.603905	−	0.438763i
$502$		0			0
$503$	−4.27185	+	13.1474i	−0.190473	+	0.586214i	−1.00000		0.000868244i	$-0.999724\pi$
$503$	−4.27185	+	13.1474i	−0.190473	+	0.586214i	0.809527	+	0.587083i	$0.199724\pi$
$504$		0			0
$505$	23.9230			1.06456
$506$		0			0
$507$	−26.6831			−1.18504
$508$		0			0
$509$	6.48278	−	19.9519i	0.287344	−	0.884354i	−0.698342	−	0.715764i	$-0.746079\pi$
$509$	6.48278	−	19.9519i	0.287344	−	0.884354i	0.985686	−	0.168590i	$-0.0539214\pi$
$510$		0			0
$511$	−8.84189	+	6.42401i	−0.391142	+	0.284182i
$512$		0			0
$513$	−0.753289	−	2.31838i	−0.0332585	−	0.102359i
$514$		0			0
$515$	13.0434	+	9.47655i	0.574759	+	0.417587i
$516$		0			0
$517$	0.753289	+	1.82887i	0.0331296	+	0.0804335i
$518$		0			0
$519$	36.2621	+	26.3460i	1.59173	+	1.15646i
$520$		0			0
$521$	6.71885	+	20.6785i	0.294358	+	0.905941i	0.983436	+	0.181254i	$0.0580156\pi$
$521$	6.71885	+	20.6785i	0.294358	+	0.905941i	−0.689078	+	0.724687i	$0.741984\pi$
$522$		0			0
$523$	−23.6308	+	17.1688i	−1.03330	+	0.750740i	−0.968967	−	0.247188i	$-0.920493\pi$
$523$	−23.6308	+	17.1688i	−1.03330	+	0.750740i	−0.0643374	+	0.997928i	$0.520493\pi$
$524$		0			0
$525$	−6.20414	+	19.0944i	−0.270771	+	0.833347i
$526$		0			0
$527$	−37.1567			−1.61857
$528$		0			0
$529$	43.8328			1.90577
$530$		0			0
$531$	−11.1839	+	34.4204i	−0.485338	+	1.49372i
$532$		0			0
$533$	33.8435	−	24.5887i	1.46592	−	1.06506i
$534$		0			0
$535$	−14.9464	−	46.0002i	−0.646187	−	1.98876i
$536$		0			0
$537$	−5.16312	−	3.75123i	−0.222805	−	0.161877i
$538$		0			0
$539$	0.482472	−	1.99220i	0.0207815	−	0.0858100i
$540$		0			0
$541$	14.5451	+	10.5676i	0.625342	+	0.454338i	0.854783	−	0.518985i	$-0.173690\pi$
$541$	14.5451	+	10.5676i	0.625342	+	0.454338i	−0.229441	+	0.973322i	$0.573690\pi$
$542$		0			0
$543$	−14.8593	−	45.7324i	−0.637676	−	1.96256i
$544$		0			0
$545$	24.1803	−	17.5680i	1.03577	−	0.752532i
$546$		0			0
$547$	−3.67549	+	11.3120i	−0.157152	+	0.483666i	−0.998373	−	0.0570272i	$-0.981838\pi$
$547$	−3.67549	+	11.3120i	−0.157152	+	0.483666i	0.841220	+	0.540693i	$0.181838\pi$
$548$		0			0
$549$	−12.2361			−0.522223
$550$		0			0
$551$	3.49120			0.148730
$552$		0			0
$553$	2.72542	−	8.38800i	0.115897	−	0.356694i
$554$		0			0
$555$	3.60510	−	2.61925i	0.153028	−	0.111181i
$556$		0			0
$557$	3.10081	+	9.54332i	0.131386	+	0.404364i	0.995010	−	0.0997718i	$-0.0318113\pi$
$557$	3.10081	+	9.54332i	0.131386	+	0.404364i	−0.863625	+	0.504135i	$0.831811\pi$
$558$		0			0
$559$	12.2627	+	8.90937i	0.518657	+	0.376826i
$560$		0			0
$561$	−40.0861	−	24.6745i	−1.69244	−	1.04176i
$562$		0			0
$563$	34.3322	+	24.9438i	1.44693	+	1.05126i	0.986536	+	0.163543i	$0.0522923\pi$
$563$	34.3322	+	24.9438i	1.44693	+	1.05126i	0.460395	+	0.887714i	$0.347708\pi$
$564$		0			0
$565$	7.18441	+	22.1113i	0.302250	+	0.930230i
$566$		0			0
$567$	15.7539	−	11.4459i	0.661602	−	0.480682i
$568$		0			0
$569$	3.33688	−	10.2699i	0.139889	−	0.430535i	−0.856429	−	0.516265i	$-0.827322\pi$
$569$	3.33688	−	10.2699i	0.139889	−	0.430535i	0.996318	+	0.0857295i	$0.0273221\pi$
$570$		0			0
$571$	−4.31536			−0.180592			−0.0902961	−	0.995915i	$-0.528781\pi$
$571$	−4.31536			−0.180592			−0.0902961	+	0.995915i	$0.528781\pi$
$572$		0			0
$573$	1.50658			0.0629382
$574$		0			0
$575$	−7.94734	+	24.4594i	−0.331427	+	1.02003i
$576$		0			0
$577$	−22.9615	+	16.6825i	−0.955899	+	0.694502i	−0.952195	−	0.305492i	$-0.901179\pi$
$577$	−22.9615	+	16.6825i	−0.955899	+	0.694502i	−0.00370466	+	0.999993i	$0.501179\pi$
$578$		0			0
$579$	−8.84189	−	27.2126i	−0.367457	−	1.13092i
$580$		0			0
$581$	23.8435	+	17.3233i	0.989193	+	0.718691i
$582$		0			0
$583$	−1.26313	+	0.0968859i	−0.0523134	+	0.00401260i
$584$		0			0
$585$	−37.9058	−	27.5402i	−1.56721	−	1.13865i
$586$		0			0
$587$	10.8857	+	33.5027i	0.449300	+	1.38280i	0.877699	+	0.479213i	$0.159078\pi$
$587$	10.8857	+	33.5027i	0.449300	+	1.38280i	−0.428399	+	0.903590i	$0.640922\pi$
$588$		0			0
$589$	13.5172	−	9.82084i	0.556967	−	0.404660i
$590$		0			0
$591$	9.87723	−	30.3990i	0.406295	−	1.25045i
$592$		0			0
$593$	2.29180			0.0941128			0.0470564	−	0.998892i	$-0.485016\pi$
$593$	2.29180			0.0941128			0.0470564	+	0.998892i	$0.485016\pi$
$594$		0			0
$595$	−40.5071			−1.66063
$596$		0			0
$597$	2.43769	−	7.50245i	0.0997682	−	0.307055i
$598$		0			0
$599$	−0.298184	+	0.216643i	−0.0121835	+	0.00885181i	−0.593860	−	0.804568i	$-0.702397\pi$
$599$	−0.298184	+	0.216643i	−0.0121835	+	0.00885181i	0.581677	+	0.813420i	$0.302397\pi$
$600$		0			0
$601$	5.95492	+	18.3273i	0.242906	+	0.747588i	0.995974	+	0.0896450i	$0.0285732\pi$
$601$	5.95492	+	18.3273i	0.242906	+	0.747588i	−0.753068	+	0.657943i	$0.771427\pi$
$602$		0			0
$603$	36.1917	+	26.2948i	1.47384	+	1.07081i
$604$		0			0
$605$	−14.1418	−	28.0297i	−0.574947	−	1.13957i
$606$		0			0
$607$	11.3681	+	8.25944i	0.461419	+	0.335240i	0.794088	−	0.607803i	$-0.207949\pi$
$607$	11.3681	+	8.25944i	0.461419	+	0.335240i	−0.332669	+	0.943044i	$0.607949\pi$
$608$		0			0
$609$	−2.72542	−	8.38800i	−0.110440	−	0.339899i
$610$		0			0
$611$	−2.34197	+	1.70154i	−0.0947459	+	0.0688369i
$612$		0			0
$613$	11.2254	−	34.5483i	0.453391	−	1.39539i	−0.419624	−	0.907698i	$-0.637838\pi$
$613$	11.2254	−	34.5483i	0.453391	−	1.39539i	0.873014	−	0.487695i	$-0.162162\pi$
$614$		0			0
$615$	62.1377			2.50563
$616$		0			0
$617$	17.1246			0.689411			0.344705	−	0.938711i	$-0.387979\pi$
$617$	17.1246			0.689411			0.344705	+	0.938711i	$0.387979\pi$
$618$		0			0
$619$	−3.67549	+	11.3120i	−0.147730	+	0.454667i	−0.997352	−	0.0727255i	$-0.976830\pi$
$619$	−3.67549	+	11.3120i	−0.147730	+	0.454667i	0.849622	+	0.527393i	$0.176830\pi$
$620$		0			0
$621$	−6.38197	+	4.63677i	−0.256099	+	0.186067i
$622$		0			0
$623$	−5.64888	−	17.3855i	−0.226318	−	0.696534i
$624$		0			0
$625$	24.9443	+	18.1231i	0.997771	+	0.724923i
$626$		0			0
$627$	21.1046	−	1.61879i	0.842836	−	0.0646482i
$628$		0			0
$629$	2.80902	+	2.04087i	0.112003	+	0.0813748i
$630$		0			0
$631$	3.67549	+	11.3120i	0.146319	+	0.450323i	0.997178	−	0.0750704i	$-0.0239182\pi$
$631$	3.67549	+	11.3120i	0.146319	+	0.450323i	−0.850859	+	0.525393i	$0.823918\pi$
$632$		0			0
$633$	7.13525	−	5.18407i	0.283601	−	0.206048i
$634$		0			0
$635$	4.13107	−	12.7141i	0.163937	−	0.504545i
$636$		0			0
$637$	3.00000			0.118864
$638$		0			0
$639$	−39.4551			−1.56082
$640$		0			0
$641$	−10.4271	+	32.0912i	−0.411844	+	1.26752i	0.503200	+	0.864170i	$0.332156\pi$
$641$	−10.4271	+	32.0912i	−0.411844	+	1.26752i	−0.915044	+	0.403355i	$0.867844\pi$
$642$		0			0
$643$	7.87695	−	5.72294i	0.310637	−	0.225691i	−0.421533	−	0.906813i	$-0.638508\pi$
$643$	7.87695	−	5.72294i	0.310637	−	0.225691i	0.732170	+	0.681122i	$0.238508\pi$
$644$		0			0
$645$	6.95743	+	21.4128i	0.273948	+	0.843127i
$646$		0			0
$647$	−15.4557	−	11.2292i	−0.607627	−	0.441467i	0.240951	−	0.970537i	$-0.422541\pi$
$647$	−15.4557	−	11.2292i	−0.607627	−	0.441467i	−0.848578	+	0.529071i	$0.822541\pi$
$648$		0			0
$649$	−30.2254	−	18.6049i	−1.18645	−	0.730305i
$650$		0			0
$651$	−34.1480	−	24.8099i	−1.33836	−	0.972378i
$652$		0			0
$653$	−3.33688	−	10.2699i	−0.130582	−	0.401891i	0.864295	−	0.502986i	$-0.167765\pi$
$653$	−3.33688	−	10.2699i	−0.130582	−	0.401891i	−0.994877	+	0.101095i	$0.967765\pi$
$654$		0			0
$655$	−4.45614	+	3.23758i	−0.174116	+	0.126503i
$656$		0			0
$657$	4.52129	−	13.9151i	0.176392	−	0.542879i
$658$		0			0
$659$	−1.92989			−0.0751777			−0.0375889	−	0.999293i	$-0.511968\pi$
$659$	−1.92989			−0.0751777			−0.0375889	+	0.999293i	$0.511968\pi$
$660$		0			0
$661$	25.5279			0.992919			0.496459	−	0.868060i	$-0.334633\pi$
$661$	25.5279			0.992919			0.496459	+	0.868060i	$0.334633\pi$
$662$		0			0
$663$	21.2889	−	65.5204i	0.826792	−	2.54460i
$664$		0			0
$665$	14.7361	−	10.7064i	0.571440	−	0.415176i
$666$		0			0
$667$	−3.49120	−	10.7448i	−0.135180	−	0.416041i
$668$		0			0
$669$	36.1418	+	26.2586i	1.39732	+	1.01522i
$670$		0			0
$671$	2.82444	−	11.6625i	0.109036	−	0.450227i
$672$		0			0
$673$	−32.3435	−	23.4989i	−1.24675	−	0.905816i	−0.248720	−	0.968575i	$-0.580010\pi$
$673$	−32.3435	−	23.4989i	−1.24675	−	0.905816i	−0.998029	+	0.0627595i	$0.980010\pi$
$674$		0			0
$675$	−0.938056	−	2.88704i	−0.0361058	−	0.111122i
$676$		0			0
$677$	−32.8156	+	23.8419i	−1.26121	+	0.916320i	−0.998816	−	0.0486424i	$-0.984511\pi$
$677$	−32.8156	+	23.8419i	−1.26121	+	0.916320i	−0.262390	+	0.964962i	$0.584511\pi$
$678$		0			0
$679$	13.8944	−	42.7626i	0.533218	−	1.64108i
$680$		0			0
$681$	−1.50658			−0.0577322
$682$		0			0
$683$	−42.8056			−1.63791			−0.818955	−	0.573858i	$-0.805446\pi$
$683$	−42.8056			−1.63791			−0.818955	+	0.573858i	$0.805446\pi$
$684$		0			0
$685$	−8.74013	+	26.8994i	−0.333943	+	1.02777i
$686$		0			0
$687$	−5.23680	+	3.80476i	−0.199796	+	0.145161i
$688$		0			0
$689$	−0.572949	−	1.76336i	−0.0218276	−	0.0671785i
$690$		0			0
$691$	−23.6308	−	17.1688i	−0.898960	−	0.653133i	0.0392387	−	0.999230i	$-0.487507\pi$
$691$	−23.6308	−	17.1688i	−0.898960	−	0.653133i	−0.938199	+	0.346097i	$0.887507\pi$
$692$		0			0
$693$	−10.7918	−	26.2008i	−0.409946	−	0.995286i
$694$		0			0
$695$	31.9199	+	23.1912i	1.21079	+	0.879690i
$696$		0			0
$697$	14.9615	+	46.0467i	0.566707	+	1.74414i
$698$		0			0
$699$	−39.4986	+	28.6974i	−1.49398	+	1.08544i
$700$		0			0
$701$	3.71885	−	11.4454i	0.140459	−	0.432288i	−0.855940	−	0.517075i	$-0.827021\pi$
$701$	3.71885	−	11.4454i	0.140459	−	0.432288i	0.996399	+	0.0847867i	$0.0270209\pi$
$702$		0			0
$703$	−1.56131			−0.0588860
$704$		0			0
$705$	−4.29993			−0.161945
$706$		0			0
$707$	−6.54343	+	20.1386i	−0.246091	+	0.757390i
$708$		0			0
$709$	−42.1976	+	30.6583i	−1.58476	+	1.15140i	−0.673796	+	0.738917i	$0.735337\pi$
$709$	−42.1976	+	30.6583i	−1.58476	+	1.15140i	−0.910967	+	0.412480i	$0.864663\pi$
$710$		0			0
$711$	3.64860	+	11.2292i	0.136833	+	0.421129i
$712$		0			0
$713$	−43.7426	−	31.7809i	−1.63817	−	1.19020i
$714$		0			0
$715$	34.9990	−	29.7719i	1.30889	−	1.11341i
$716$		0			0
$717$	−21.8713	−	15.8904i	−0.816800	−	0.593440i
$718$		0			0
$719$	−5.09602	−	15.6839i	−0.190049	−	0.584912i	0.809949	−	0.586500i	$-0.199494\pi$
$719$	−5.09602	−	15.6839i	−0.190049	−	0.584912i	−0.999999	+	0.00158811i	$0.999494\pi$
$720$		0			0
$721$	−11.5451	+	8.38800i	−0.429961	+	0.312385i
$722$		0			0
$723$	−2.66704	+	8.20830i	−0.0991882	+	0.305270i
$724$		0			0
$725$	4.34752			0.161463
$726$		0			0
$727$	6.24525			0.231623			0.115812	−	0.993271i	$-0.463053\pi$
$727$	6.24525			0.231623			0.115812	+	0.993271i	$0.463053\pi$
$728$		0			0
$729$	−10.3156	+	31.7481i	−0.382059	+	1.17586i
$730$		0			0
$731$	−14.1926	+	10.3115i	−0.524932	+	0.381385i
$732$		0			0
$733$	−5.04508	−	15.5272i	−0.186344	−	0.573509i	0.813624	−	0.581391i	$-0.197491\pi$
$733$	−5.04508	−	15.5272i	−0.186344	−	0.573509i	−0.999969	+	0.00788146i	$0.997491\pi$
$734$		0			0
$735$	3.60510	+	2.61925i	0.132976	+	0.0966127i
$736$		0			0
$737$	−33.4164	+	28.4257i	−1.23091	+	1.04707i
$738$		0			0
$739$	5.35069	+	3.88751i	0.196828	+	0.143004i	0.681834	−	0.731507i	$-0.261183\pi$
$739$	5.35069	+	3.88751i	0.196828	+	0.143004i	−0.485006	+	0.874511i	$0.661183\pi$
$740$		0			0
$741$	9.57295	+	29.4625i	0.351671	+	1.08233i
$742$		0			0
$743$	−8.84189	+	6.42401i	−0.324378	+	0.235674i	−0.738041	−	0.674756i	$-0.764249\pi$
$743$	−8.84189	+	6.42401i	−0.324378	+	0.235674i	0.413664	+	0.910430i	$0.364249\pi$
$744$		0			0
$745$	−8.22542	+	25.3153i	−0.301356	+	0.927479i
$746$		0			0
$747$	−39.4551			−1.44359
$748$		0			0
$749$	42.8115			1.56430
$750$		0			0
$751$	−7.76305	+	23.8922i	−0.283278	+	0.871840i	0.703632	+	0.710565i	$0.251561\pi$
$751$	−7.76305	+	23.8922i	−0.283278	+	0.871840i	−0.986910	+	0.161275i	$0.948439\pi$
$752$		0			0
$753$	0.753289	−	0.547296i	0.0274514	−	0.0199446i
$754$		0			0
$755$	9.43826	+	29.0480i	0.343494	+	1.05716i
$756$		0			0
$757$	31.1074	+	22.6008i	1.13062	+	0.821442i	0.985785	−	0.168015i	$-0.0537356\pi$
$757$	31.1074	+	22.6008i	1.13062	+	0.821442i	0.144833	+	0.989456i	$0.453736\pi$
$758$		0			0
$759$	−26.0867	−	63.3345i	−0.946888	−	2.29890i
$760$		0			0
$761$	−18.4894	−	13.4333i	−0.670239	−	0.486957i	0.199866	−	0.979823i	$-0.435949\pi$
$761$	−18.4894	−	13.4333i	−0.670239	−	0.486957i	−0.870105	+	0.492866i	$0.835949\pi$
$762$		0			0
$763$	8.17513	+	25.1605i	0.295960	+	0.910870i
$764$		0			0
$765$	43.8713	−	31.8744i	1.58617	−	1.15242i
$766$		0			0
$767$	16.0521	−	49.4032i	0.579607	−	1.78385i
$768$		0			0
$769$	16.1803			0.583478			0.291739	−	0.956498i	$-0.405766\pi$
$769$	16.1803			0.583478			0.291739	+	0.956498i	$0.405766\pi$
$770$		0			0
$771$	18.3672			0.661477
$772$		0			0
$773$	0.572949	−	1.76336i	0.0206075	−	0.0634235i	−0.940224	−	0.340557i	$-0.889384\pi$
$773$	0.572949	−	1.76336i	0.0206075	−	0.0634235i	0.960831	+	0.277133i	$0.0893844\pi$
$774$		0			0
$775$	16.8327	−	12.2297i	0.604650	−	0.439304i
$776$		0			0
$777$	1.21885	+	3.75123i	0.0437259	+	0.134574i
$778$		0			0
$779$	−17.6134	−	12.7969i	−0.631065	−	0.458496i
$780$		0			0
$781$	9.10739	−	37.6057i	0.325888	−	1.34564i
$782$		0			0
$783$	1.07884	+	0.783823i	0.0385546	+	0.0280115i
$784$		0			0
$785$	−17.2533	−	53.1002i	−0.615796	−	1.89523i
$786$		0			0
$787$	42.5074	−	30.8834i	1.51522	−	1.10087i	0.551432	−	0.834220i	$-0.314082\pi$
$787$	42.5074	−	30.8834i	1.51522	−	1.10087i	0.963792	−	0.266655i	$-0.0859185\pi$
$788$		0			0
$789$	−5.45085	+	16.7760i	−0.194055	+	0.597241i
$790$		0			0
$791$	−20.5786			−0.731691
$792$		0			0
$793$	17.5623			0.623656
$794$		0			0
$795$	0.851048	−	2.61925i	0.0301835	−	0.0928954i
$796$		0			0
$797$	−19.0172	+	13.8168i	−0.673625	+	0.489417i	−0.871237	−	0.490863i	$-0.836681\pi$
$797$	−19.0172	+	13.8168i	−0.673625	+	0.489417i	0.197612	+	0.980280i	$0.436681\pi$
$798$		0			0
$799$	−1.03534	−	3.18643i	−0.0366275	−	0.112728i
$800$		0			0
$801$	19.7984	+	14.3844i	0.699541	+	0.508246i
$802$		0			0
$803$	12.2192	+	7.52136i	0.431206	+	0.265423i
$804$		0			0
$805$	−47.6869	−	34.6466i	−1.68074	−	1.22113i
$806$		0			0
$807$	3.19302	+	9.82709i	0.112399	+	0.345930i
$808$		0			0
$809$	7.39919	−	5.37582i	0.260142	−	0.189004i	−0.450068	−	0.892994i	$-0.648600\pi$
$809$	7.39919	−	5.37582i	0.260142	−	0.189004i	0.710209	+	0.703990i	$0.248600\pi$
$810$		0			0
$811$	6.42953	−	19.7881i	0.225771	−	0.694853i	−0.772441	−	0.635087i	$-0.780964\pi$
$811$	6.42953	−	19.7881i	0.225771	−	0.694853i	0.998212	−	0.0597665i	$-0.0190356\pi$
$812$		0			0
$813$	−68.3394			−2.39677
$814$		0			0
$815$	−33.2969			−1.16634
$816$		0			0
$817$	2.43769	−	7.50245i	0.0852841	−	0.262478i
$818$		0			0
$819$	33.5516	−	24.3767i	1.17239	−	0.851789i
$820$		0			0
$821$	3.51722	+	10.8249i	0.122752	+	0.377791i	0.993485	−	0.113965i	$-0.0363551\pi$
$821$	3.51722	+	10.8249i	0.122752	+	0.377791i	−0.870733	+	0.491756i	$0.836355\pi$
$822$		0			0
$823$	−20.1397	−	14.6323i	−0.702024	−	0.510050i	0.178567	−	0.983928i	$-0.442854\pi$
$823$	−20.1397	−	14.6323i	−0.702024	−	0.510050i	−0.880591	+	0.473877i	$0.842854\pi$
$824$		0			0
$825$	26.2812	−	2.01585i	0.914992	−	0.0701828i
$826$		0			0
$827$	−31.8060	−	23.1084i	−1.10600	−	0.803558i	−0.123973	−	0.992286i	$-0.539564\pi$
$827$	−31.8060	−	23.1084i	−1.10600	−	0.803558i	−0.982029	+	0.188728i	$0.939564\pi$
$828$		0			0
$829$	−10.2467	−	31.5361i	−0.355883	−	1.09530i	−0.955496	−	0.295005i	$-0.904679\pi$
$829$	−10.2467	−	31.5361i	−0.355883	−	1.09530i	0.599613	−	0.800290i	$-0.295321\pi$
$830$		0			0
$831$	33.2534	−	24.1600i	1.15355	−	0.838101i
$832$		0			0
$833$	−1.07295	+	3.30220i	−0.0371755	+	0.114414i
$834$		0			0
$835$	−18.8765			−0.653249
$836$		0			0
$837$	6.38197			0.220593
$838$		0			0
$839$	−9.32437	+	28.6974i	−0.321913	+	0.990746i	0.650902	+	0.759162i	$0.274391\pi$
$839$	−9.32437	+	28.6974i	−0.321913	+	0.990746i	−0.972815	+	0.231584i	$0.925609\pi$
$840$		0			0
$841$	21.9164	−	15.9232i	0.755738	−	0.549076i
$842$		0			0
$843$	−18.9469	−	58.3126i	−0.652566	−	2.00839i
$844$		0			0
$845$	24.3885	+	17.7193i	0.838991	+	0.609563i
$846$		0			0
$847$	27.4637	−	4.23804i	0.943665	−	0.145621i
$848$		0			0
$849$	29.7599	+	21.6218i	1.02136	+	0.742059i
$850$		0			0
$851$	1.56131	+	4.80522i	0.0535211	+	0.164721i
$852$		0			0
$853$	24.2533	−	17.6210i	0.830417	−	0.603333i	−0.0892604	−	0.996008i	$-0.528450\pi$
$853$	24.2533	−	17.6210i	0.830417	−	0.603333i	0.919677	+	0.392675i	$0.128450\pi$
$854$		0			0
$855$	−7.53526	+	23.1912i	−0.257701	+	0.793121i
$856$		0			0
$857$	19.7082			0.673219			0.336610	−	0.941644i	$-0.390720\pi$
$857$	19.7082			0.673219			0.336610	+	0.941644i	$0.390720\pi$
$858$		0			0
$859$	26.4553			0.902643			0.451321	−	0.892361i	$-0.350953\pi$
$859$	26.4553			0.902643			0.451321	+	0.892361i	$0.350953\pi$
$860$		0			0
$861$	−16.9959	+	52.3081i	−0.579220	+	1.78266i
$862$		0			0
$863$	−7.50837	+	5.45515i	−0.255588	+	0.185696i	−0.708200	−	0.706012i	$-0.750492\pi$
$863$	−7.50837	+	5.45515i	−0.255588	+	0.185696i	0.452612	+	0.891708i	$0.350492\pi$
$864$		0			0
$865$	−15.6484	−	48.1609i	−0.532062	−	1.63752i
$866$		0			0
$867$	29.7622	+	21.6235i	1.01078	+	0.734373i
$868$		0			0
$869$	−11.5451	+	0.885544i	−0.391640	+	0.0300400i
$870$		0			0
$871$	−51.9456	−	37.7407i	−1.76011	−	1.27880i
$872$		0			0
$873$	18.6008	+	57.2474i	0.629542	+	1.93753i
$874$		0			0
$875$	−10.8153	+	7.85776i	−0.365623	+	0.265641i
$876$		0			0
$877$	−7.24671	+	22.3031i	−0.244704	+	0.753122i	0.750981	+	0.660324i	$0.229581\pi$
$877$	−7.24671	+	22.3031i	−0.244704	+	0.753122i	−0.995685	+	0.0927977i	$0.970419\pi$
$878$		0			0
$879$	−2.01690			−0.0680282
$880$		0			0
$881$	−20.6525			−0.695800			−0.347900	−	0.937532i	$-0.613105\pi$
$881$	−20.6525			−0.695800			−0.347900	+	0.937532i	$0.613105\pi$
$882$		0			0
$883$	15.2010	−	46.7840i	0.511556	−	1.57441i	−0.277907	−	0.960608i	$-0.589641\pi$
$883$	15.2010	−	46.7840i	0.511556	−	1.57441i	0.789463	−	0.613798i	$-0.210359\pi$
$884$		0			0
$885$	62.4230	−	45.3530i	2.09833	−	1.52452i
$886$		0			0
$887$	10.6579	+	32.8016i	0.357857	+	1.10137i	0.954334	+	0.298740i	$0.0965664\pi$
$887$	10.6579	+	32.8016i	0.357857	+	1.10137i	−0.596478	+	0.802630i	$0.703434\pi$
$888$		0			0
$889$	9.57295	+	6.95515i	0.321066	+	0.233268i
$890$		0			0
$891$	−21.7714	−	13.4011i	−0.729368	−	0.448953i
$892$		0			0
$893$	1.21885	+	0.885544i	0.0407872	+	0.0296336i
$894$		0			0
$895$	2.22807	+	6.85730i	0.0744762	+	0.229214i
$896$		0			0
$897$	81.1033	−	58.9250i	2.70796	−	1.96745i
$898$		0			0
$899$	−2.82444	+	8.69273i	−0.0942003	+	0.289919i
$900$		0			0
$901$	2.14590			0.0714902
$902$		0			0
$903$	−19.9285			−0.663178
$904$		0			0
$905$	−16.7877	+	51.6673i	−0.558043	+	1.71748i
$906$		0			0
$907$	12.5609	−	9.12602i	0.417077	−	0.303024i	−0.359383	−	0.933190i	$-0.617013\pi$
$907$	12.5609	−	9.12602i	0.417077	−	0.303024i	0.776461	+	0.630166i	$0.217013\pi$
$908$		0			0
$909$	−8.75987	−	26.9601i	−0.290546	−	0.894210i
$910$		0			0
$911$	38.4198	+	27.9136i	1.27290	+	0.924820i	0.999314	−	0.0370266i	$-0.0117886\pi$
$911$	38.4198	+	27.9136i	1.27290	+	0.924820i	0.273591	+	0.961846i	$0.411789\pi$
$912$		0			0
$913$	9.10739	−	37.6057i	0.301411	−	1.24457i
$914$		0			0
$915$	21.1046	+	15.3334i	0.697696	+	0.506906i
$916$		0			0
$917$	−1.50658	−	4.63677i	−0.0497516	−	0.153120i
$918$		0			0
$919$	−24.5958	+	17.8699i	−0.811340	+	0.589473i	−0.914219	−	0.405221i	$-0.867195\pi$
$919$	−24.5958	+	17.8699i	−0.811340	+	0.589473i	0.102879	+	0.994694i	$0.467195\pi$
$920$		0			0
$921$	1.50658	−	4.63677i	0.0496434	−	0.152787i
$922$		0			0
$923$	56.6296			1.86398
$924$		0			0
$925$	−1.94427			−0.0639273
$926$		0			0
$927$	5.90356	−	18.1693i	0.193898	−	0.596758i
$928$		0			0
$929$	27.5795	−	20.0377i	0.904855	−	0.657416i	−0.0348535	−	0.999392i	$-0.511096\pi$
$929$	27.5795	−	20.0377i	0.904855	−	0.657416i	0.939708	+	0.341977i	$0.111096\pi$
$930$		0			0
$931$	−0.482472	−	1.48490i	−0.0158124	−	0.0486655i
$932$		0			0
$933$	15.4894	+	11.2537i	0.507099	+	0.368429i
$934$		0			0
$935$	20.2535	+	49.1725i	0.662362	+	1.60811i
$936$		0			0
$937$	−18.4894	−	13.4333i	−0.604021	−	0.438847i	0.243283	−	0.969955i	$-0.421776\pi$
$937$	−18.4894	−	13.4333i	−0.604021	−	0.438847i	−0.847304	+	0.531108i	$0.821776\pi$
$938$		0			0
$939$	−3.19302	−	9.82709i	−0.104200	−	0.320695i
$940$		0			0
$941$	16.1074	−	11.7027i	0.525086	−	0.381497i	−0.293430	−	0.955980i	$-0.594797\pi$
$941$	16.1074	−	11.7027i	0.525086	−	0.381497i	0.818516	+	0.574483i	$0.194797\pi$
$942$		0			0
$943$	−21.7714	+	67.0053i	−0.708973	+	2.18199i
$944$		0			0
$945$	6.95743			0.226325
$946$		0			0
$947$	−26.4553			−0.859681			−0.429841	−	0.902905i	$-0.641430\pi$
$947$	−26.4553			−0.859681			−0.429841	+	0.902905i	$0.641430\pi$
$948$		0			0
$949$	−6.48936	+	19.9722i	−0.210653	+	0.648325i
$950$		0			0
$951$	−10.2893	+	7.47562i	−0.333654	+	0.242414i
$952$		0			0
$953$	2.60739	+	8.02472i	0.0844617	+	0.259946i	0.984364	−	0.176145i	$-0.0563626\pi$
$953$	2.60739	+	8.02472i	0.0844617	+	0.259946i	−0.899903	+	0.436091i	$0.856363\pi$
$954$		0			0
$955$	−1.37702	−	1.00047i	−0.0445594	−	0.0323743i
$956$		0			0
$957$	−8.81966	+	7.50245i	−0.285099	+	0.242520i
$958$		0			0
$959$	−20.2535	−	14.7151i	−0.654021	−	0.475174i
$960$		0			0
$961$	3.93769	+	12.1190i	0.127022	+	0.390935i
$962$		0			0
$963$	−46.3671	+	33.6877i	−1.49416	+	1.08557i
$964$		0			0
$965$	−9.98936	+	30.7441i	−0.321569	+	0.989687i
$966$		0			0
$967$	39.6829			1.27612			0.638059	−	0.769988i	$-0.279738\pi$
$967$	39.6829			1.27612			0.638059	+	0.769988i	$0.279738\pi$
$968$		0			0
$969$	−35.8541			−1.15180
$970$		0			0
$971$	−6.20174	+	19.0870i	−0.199023	+	0.612531i	0.800883	+	0.598821i	$0.204364\pi$
$971$	−6.20174	+	19.0870i	−0.199023	+	0.612531i	−0.999906	+	0.0137096i	$0.995636\pi$
$972$		0			0
$973$	−28.2533	+	20.5272i	−0.905759	+	0.658072i
$974$		0			0
$975$	11.9210	+	36.6891i	0.381778	+	1.17499i
$976$		0			0
$977$	−37.4894	−	27.2376i	−1.19939	−	0.871408i	−0.205166	−	0.978727i	$-0.565773\pi$
$977$	−37.4894	−	27.2376i	−1.19939	−	0.871408i	−0.994225	+	0.107319i	$0.965773\pi$
$978$		0			0
$979$	−18.2802	+	15.5500i	−0.584236	+	0.496981i
$980$		0			0
$981$	−28.6525	−	20.8172i	−0.914803	−	0.664643i
$982$		0			0
$983$	−4.64043	−	14.2818i	−0.148007	−	0.455518i	0.849379	−	0.527784i	$-0.176977\pi$
$983$	−4.64043	−	14.2818i	−0.148007	−	0.455518i	−0.997385	+	0.0722660i	$0.976977\pi$
$984$		0			0
$985$	−29.2148	+	21.2258i	−0.930860	+	0.676310i
$986$		0			0
$987$	1.17612	−	3.61972i	0.0374363	−	0.115217i
$988$		0			0
$989$	−25.5279			−0.811739
$990$		0			0
$991$	12.4905			0.396774			0.198387	−	0.980124i	$-0.436430\pi$
$991$	12.4905			0.396774			0.198387	+	0.980124i	$0.436430\pi$
$992$		0			0
$993$	−4.87539	+	15.0049i	−0.154716	+	0.476166i
$994$		0			0
$995$	−7.21019	+	5.23851i	−0.228578	+	0.166072i
$996$		0			0
$997$	16.6976	+	51.3898i	0.528817	+	1.62753i	0.756642	+	0.653829i	$0.226839\pi$
$997$	16.6976	+	51.3898i	0.528817	+	1.62753i	−0.227825	+	0.973702i	$0.573161\pi$
$998$		0			0
$999$	−0.482472	−	0.350536i	−0.0152647	−	0.0110905i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.d.257.1	✓	8
4.3	odd	2	inner	352.2.m.d.257.2	yes	8
8.3	odd	2		704.2.m.j.257.1		8
8.5	even	2		704.2.m.j.257.2		8
11.3	even	5	inner	352.2.m.d.289.1	yes	8
11.5	even	5		3872.2.a.bj.1.2		4
11.6	odd	10		3872.2.a.bk.1.2		4
44.3	odd	10	inner	352.2.m.d.289.2	yes	8
44.27	odd	10		3872.2.a.bj.1.3		4
44.39	even	10		3872.2.a.bk.1.3		4
88.3	odd	10		704.2.m.j.641.1		8
88.5	even	10		7744.2.a.dm.1.3		4
88.27	odd	10		7744.2.a.dm.1.2		4
88.61	odd	10		7744.2.a.dl.1.3		4
88.69	even	10		704.2.m.j.641.2		8
88.83	even	10		7744.2.a.dl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.d.257.1	✓	8	1.1	even	1	trivial
352.2.m.d.257.2	yes	8	4.3	odd	2	inner
352.2.m.d.289.1	yes	8	11.3	even	5	inner
352.2.m.d.289.2	yes	8	44.3	odd	10	inner
704.2.m.j.257.1		8	8.3	odd	2
704.2.m.j.257.2		8	8.5	even	2
704.2.m.j.641.1		8	88.3	odd	10
704.2.m.j.641.2		8	88.69	even	10
3872.2.a.bj.1.2		4	11.5	even	5
3872.2.a.bj.1.3		4	44.27	odd	10
3872.2.a.bk.1.2		4	11.6	odd	10
3872.2.a.bk.1.3		4	44.39	even	10
7744.2.a.dl.1.2		4	88.83	even	10
7744.2.a.dl.1.3		4	88.61	odd	10
7744.2.a.dm.1.2		4	88.27	odd	10
7744.2.a.dm.1.3		4	88.5	even	10

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	352.2.m.d.257.1

Level	$352$
Weight	$2$
Character	352.257
Analytic conductor	$2.811$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$