LMFDB - Embedded newform 351.2.i.b.161.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(161,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 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("351.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 184x^{12} + 600x^{10} + 894x^{8} + 600x^{6} + 184x^{4} + 24x^{2} + 1 $ x^16 + 24x^14 + 184x^12 + 600x^10 + 894x^8 + 600x^6 + 184x^4 + 24*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.5
Root			$-0.743961i$ of defining polynomial
Character	$\chi$	$=$	351.161
Dual form			351.2.i.b.242.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04406 + 1.04406i) q^{2} +0.180117i q^{4} +(-1.27342 - 1.27342i) q^{5} +(2.33225 + 2.33225i) q^{7} +(1.90006 - 1.90006i) q^{8} -2.65906i q^{10} +(3.47906 - 3.47906i) q^{11} +(0.619491 + 3.55193i) q^{13} +4.87000i q^{14} +4.32779 q^{16} +3.61673 q^{17} +(-4.11256 + 4.11256i) q^{19} +(0.229366 - 0.229366i) q^{20} +7.26469 q^{22} -7.41685 q^{23} -1.75678i q^{25} +(-3.06164 + 4.35521i) q^{26} +(-0.420078 + 0.420078i) q^{28} +0.458732i q^{29} +(4.25926 - 4.25926i) q^{31} +(0.718341 + 0.718341i) q^{32} +(3.77607 + 3.77607i) q^{34} -5.93988i q^{35} +(-3.35154 - 3.35154i) q^{37} -8.58751 q^{38} -4.83918 q^{40} +(-3.47906 - 3.47906i) q^{41} +4.90348i q^{43} +(0.626640 + 0.626640i) q^{44} +(-7.74363 - 7.74363i) q^{46} +(-8.36921 + 8.36921i) q^{47} +3.87875i q^{49} +(1.83418 - 1.83418i) q^{50} +(-0.639765 + 0.111581i) q^{52} +8.48673i q^{53} -8.86065 q^{55} +8.86284 q^{56} +(-0.478943 + 0.478943i) q^{58} +(-0.117519 + 0.117519i) q^{59} -6.49307 q^{61} +8.89383 q^{62} -7.15560i q^{64} +(3.73424 - 5.31200i) q^{65} +(-2.08783 + 2.08783i) q^{67} +0.651435i q^{68} +(6.20158 - 6.20158i) q^{70} +(-8.69028 - 8.69028i) q^{71} +(2.50367 + 2.50367i) q^{73} -6.99841i q^{74} +(-0.740744 - 0.740744i) q^{76} +16.2281 q^{77} +4.07914 q^{79} +(-5.51112 - 5.51112i) q^{80} -7.26469i q^{82} +(8.79106 + 8.79106i) q^{83} +(-4.60563 - 4.60563i) q^{85} +(-5.11952 + 5.11952i) q^{86} -13.2209i q^{88} +(2.66437 - 2.66437i) q^{89} +(-6.83918 + 9.72879i) q^{91} -1.33590i q^{92} -17.4759 q^{94} +10.4741 q^{95} +(-2.72336 + 2.72336i) q^{97} +(-4.04964 + 4.04964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.04406	+	1.04406i	0.738261	+	0.738261i	0.972241	−	0.233980i	$-0.0751751\pi$
$2$	1.04406	+	1.04406i	0.738261	+	0.738261i	−0.233980	+	0.972241i	$0.575175\pi$
$3$		0			0
$3$		0			0
$4$			0.180117i			0.0900587i
$5$	−1.27342	−	1.27342i	−0.569493	−	0.569493i	0.362493	−	0.931986i	$-0.381926\pi$
$5$	−1.27342	−	1.27342i	−0.569493	−	0.569493i	−0.931986	+	0.362493i	$0.881926\pi$
$6$		0			0
$7$	2.33225	+	2.33225i	0.881506	+	0.881506i	0.993688	−	0.112181i	$-0.0357838\pi$
$7$	2.33225	+	2.33225i	0.881506	+	0.881506i	−0.112181	+	0.993688i	$0.535784\pi$
$8$	1.90006	−	1.90006i	0.671774	−	0.671774i
$9$		0			0
$10$		−	2.65906i		−	0.840869i
$11$	3.47906	−	3.47906i	1.04898	−	1.04898i	0.0502392	−	0.998737i	$-0.484002\pi$
$11$	3.47906	−	3.47906i	1.04898	−	1.04898i	0.998737	−	0.0502392i	$-0.0159984\pi$
$12$		0			0
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$14$			4.87000i			1.30156i
$15$		0			0
$16$	4.32779			1.08195
$17$	3.61673			0.877185			0.438592	−	0.898686i	$-0.355477\pi$
$17$	3.61673			0.877185			0.438592	+	0.898686i	$0.355477\pi$
$18$		0			0
$19$	−4.11256	+	4.11256i	−0.943486	+	0.943486i	−0.998486	−	0.0550004i	$-0.982484\pi$
$19$	−4.11256	+	4.11256i	−0.943486	+	0.943486i	0.0550004	+	0.998486i	$0.482484\pi$
$20$	0.229366	−	0.229366i	0.0512878	−	0.0512878i
$21$		0			0
$22$	7.26469			1.54884
$23$	−7.41685			−1.54652			−0.773261	−	0.634088i	$-0.781376\pi$
$23$	−7.41685			−1.54652			−0.773261	+	0.634088i	$0.781376\pi$
$24$		0			0
$25$		−	1.75678i		−	0.351356i
$26$	−3.06164	+	4.35521i	−0.600437	+	0.854127i
$27$		0			0
$28$	−0.420078	+	0.420078i	−0.0793873	+	0.0793873i
$29$			0.458732i			0.0851844i	0.999093	+	0.0425922i	$0.0135616\pi$
$29$			0.458732i			0.0851844i	−0.999093	+	0.0425922i	$0.986438\pi$
$30$		0			0
$31$	4.25926	−	4.25926i	0.764985	−	0.764985i	−0.212234	−	0.977219i	$-0.568074\pi$
$31$	4.25926	−	4.25926i	0.764985	−	0.764985i	0.977219	+	0.212234i	$0.0680739\pi$
$32$	0.718341	+	0.718341i	0.126986	+	0.126986i
$33$		0			0
$34$	3.77607	+	3.77607i	0.647591	+	0.647591i
$35$		−	5.93988i		−	1.00402i
$36$		0			0
$37$	−3.35154	−	3.35154i	−0.550990	−	0.550990i	0.375736	−	0.926727i	$-0.377390\pi$
$37$	−3.35154	−	3.35154i	−0.550990	−	0.550990i	−0.926727	+	0.375736i	$0.877390\pi$
$38$	−8.58751			−1.39308
$39$		0			0
$40$	−4.83918			−0.765141
$41$	−3.47906	−	3.47906i	−0.543338	−	0.543338i	0.381168	−	0.924506i	$-0.375522\pi$
$41$	−3.47906	−	3.47906i	−0.543338	−	0.543338i	−0.924506	+	0.381168i	$0.875522\pi$
$42$		0			0
$43$			4.90348i			0.747773i	0.927474	+	0.373886i	$0.121975\pi$
$43$			4.90348i			0.747773i	−0.927474	+	0.373886i	$0.878025\pi$
$44$	0.626640	+	0.626640i	0.0944695	+	0.0944695i
$45$		0			0
$46$	−7.74363	−	7.74363i	−1.14174	−	1.14174i
$47$	−8.36921	+	8.36921i	−1.22077	+	1.22077i	−0.253418	+	0.967357i	$0.581555\pi$
$47$	−8.36921	+	8.36921i	−1.22077	+	1.22077i	−0.967357	+	0.253418i	$0.918445\pi$
$48$		0			0
$49$			3.87875i			0.554107i
$50$	1.83418	−	1.83418i	0.259392	−	0.259392i
$51$		0			0
$52$	−0.639765	+	0.111581i	−0.0887195	+	0.0154735i
$53$			8.48673i			1.16574i	0.812565	+	0.582871i	$0.198071\pi$
$53$			8.48673i			1.16574i	−0.812565	+	0.582871i	$0.801929\pi$
$54$		0			0
$55$	−8.86065			−1.19477
$56$	8.86284			1.18435
$57$		0			0
$58$	−0.478943	+	0.478943i	−0.0628883	+	0.0628883i
$59$	−0.117519	+	0.117519i	−0.0152997	+	0.0152997i	−0.714715	−	0.699416i	$-0.753444\pi$
$59$	−0.117519	+	0.117519i	−0.0152997	+	0.0152997i	0.699416	+	0.714715i	$0.253444\pi$
$60$		0			0
$61$	−6.49307			−0.831352			−0.415676	−	0.909513i	$-0.636455\pi$
$61$	−6.49307			−0.831352			−0.415676	+	0.909513i	$0.636455\pi$
$62$	8.89383			1.12952
$63$		0			0
$64$		−	7.15560i		−	0.894451i
$65$	3.73424	−	5.31200i	0.463176	−	0.658872i
$66$		0			0
$67$	−2.08783	+	2.08783i	−0.255069	+	0.255069i	−0.823045	−	0.567976i	$-0.807727\pi$
$67$	−2.08783	+	2.08783i	−0.255069	+	0.255069i	0.567976	+	0.823045i	$0.307727\pi$
$68$			0.651435i			0.0789981i
$69$		0			0
$70$	6.20158	−	6.20158i	0.741231	−	0.741231i
$71$	−8.69028	−	8.69028i	−1.03135	−	1.03135i	−0.999493	−	0.0318539i	$-0.989859\pi$
$71$	−8.69028	−	8.69028i	−1.03135	−	1.03135i	−0.0318539	−	0.999493i	$-0.510141\pi$
$72$		0			0
$73$	2.50367	+	2.50367i	0.293033	+	0.293033i	0.838277	−	0.545245i	$-0.183563\pi$
$73$	2.50367	+	2.50367i	0.293033	+	0.293033i	−0.545245	+	0.838277i	$0.683563\pi$
$74$		−	6.99841i		−	0.813549i
$75$		0			0
$76$	−0.740744	−	0.740744i	−0.0849691	−	0.0849691i
$77$	16.2281			1.84936
$78$		0			0
$79$	4.07914			0.458939			0.229469	−	0.973316i	$-0.426301\pi$
$79$	4.07914			0.458939			0.229469	+	0.973316i	$0.426301\pi$
$80$	−5.51112	−	5.51112i	−0.616162	−	0.616162i
$81$		0			0
$82$		−	7.26469i		−	0.802251i
$83$	8.79106	+	8.79106i	0.964944	+	0.964944i	0.999406	−	0.0344622i	$-0.0109718\pi$
$83$	8.79106	+	8.79106i	0.964944	+	0.964944i	−0.0344622	+	0.999406i	$0.510972\pi$
$84$		0			0
$85$	−4.60563	−	4.60563i	−0.499551	−	0.499551i
$86$	−5.11952	+	5.11952i	−0.552052	+	0.552052i
$87$		0			0
$88$		−	13.2209i		−	1.40935i
$89$	2.66437	−	2.66437i	0.282422	−	0.282422i	−0.551652	−	0.834074i	$-0.686002\pi$
$89$	2.66437	−	2.66437i	0.282422	−	0.282422i	0.834074	+	0.551652i	$0.186002\pi$
$90$		0			0
$91$	−6.83918	+	9.72879i	−0.716941	+	1.01985i
$92$		−	1.33590i		−	0.139278i
$93$		0			0
$94$	−17.4759			−1.80250
$95$	10.4741			1.07462
$96$		0			0
$97$	−2.72336	+	2.72336i	−0.276515	+	0.276515i	−0.831716	−	0.555201i	$-0.812641\pi$
$97$	−2.72336	+	2.72336i	−0.276515	+	0.276515i	0.555201	+	0.831716i	$0.312641\pi$
$98$	−4.04964	+	4.04964i	−0.409075	+	0.409075i
$99$		0			0
$100$	0.316426			0.0316426
$101$	−7.45715			−0.742014			−0.371007	−	0.928630i	$-0.620987\pi$
$101$	−7.45715			−0.742014			−0.371007	+	0.928630i	$0.620987\pi$
$102$		0			0
$103$		−	2.36758i		−	0.233284i	−0.993174	−	0.116642i	$-0.962787\pi$
$103$		−	2.36758i		−	0.233284i	0.993174	−	0.116642i	$-0.0372131\pi$
$104$	7.92598	+	5.57183i	0.777206	+	0.546363i
$105$		0			0
$106$	−8.86065	+	8.86065i	−0.860622	+	0.860622i
$107$			5.66455i			0.547613i	0.961785	+	0.273806i	$0.0882828\pi$
$107$			5.66455i			0.547613i	−0.961785	+	0.273806i	$0.911717\pi$
$108$		0			0
$109$	−4.30752	+	4.30752i	−0.412585	+	0.412585i	−0.882638	−	0.470053i	$-0.844235\pi$
$109$	−4.30752	+	4.30752i	−0.412585	+	0.412585i	0.470053	+	0.882638i	$0.344235\pi$
$110$	−9.25103	−	9.25103i	−0.882052	−	0.882052i
$111$		0			0
$112$	10.0935	+	10.0935i	0.953744	+	0.953744i
$113$		−	12.5622i		−	1.18175i	−0.806763	−	0.590876i	$-0.798782\pi$
$113$		−	12.5622i		−	1.18175i	0.806763	−	0.590876i	$-0.201218\pi$
$114$		0			0
$115$	9.44481	+	9.44481i	0.880733	+	0.880733i
$116$	−0.0826256			−0.00767160
$117$		0			0
$118$	−0.245393			−0.0225903
$119$	8.43510	+	8.43510i	0.773244	+	0.773244i
$120$		0			0
$121$		−	13.2077i		−	1.20070i
$122$	−6.77915	−	6.77915i	−0.613755	−	0.613755i
$123$		0			0
$124$	0.767166	+	0.767166i	0.0688936	+	0.0688936i
$125$	−8.60425	+	8.60425i	−0.769587	+	0.769587i
$126$		0			0
$127$		−	8.03631i		−	0.713107i	−0.934275	−	0.356554i	$-0.883952\pi$
$127$		−	8.03631i		−	0.713107i	0.934275	−	0.356554i	$-0.116048\pi$
$128$	8.90755	−	8.90755i	0.787324	−	0.787324i
$129$		0			0
$130$	9.44481	−	1.64726i	0.828364	−	0.144475i
$131$		−	8.77091i		−	0.766318i	−0.923682	−	0.383159i	$-0.874836\pi$
$131$		−	8.77091i		−	0.766318i	0.923682	−	0.383159i	$-0.125164\pi$
$132$		0			0
$133$	−19.1830			−1.66338
$134$	−4.35964			−0.376615
$135$		0			0
$136$	6.87201	−	6.87201i	0.589270	−	0.589270i
$137$	−7.19656	+	7.19656i	−0.614844	+	0.614844i	−0.944204	−	0.329360i	$-0.893167\pi$
$137$	−7.19656	+	7.19656i	−0.614844	+	0.614844i	0.329360	+	0.944204i	$0.393167\pi$
$138$		0			0
$139$	17.4714			1.48191			0.740954	−	0.671555i	$-0.234374\pi$
$139$	17.4714			1.48191			0.740954	+	0.671555i	$0.234374\pi$
$140$	1.06988			0.0904210
$141$		0			0
$142$		−	18.1463i		−	1.52281i
$143$	14.5126	+	10.2021i	1.21361	+	0.853146i
$144$		0			0
$145$	0.584161	−	0.584161i	0.0485119	−	0.0485119i
$146$			5.22796i			0.432669i
$147$		0			0
$148$	0.603671	−	0.603671i	0.0496215	−	0.0496215i
$149$	0.341213	+	0.341213i	0.0279533	+	0.0279533i	0.720945	−	0.692992i	$-0.243708\pi$
$149$	0.341213	+	0.341213i	0.0279533	+	0.0279533i	−0.692992	+	0.720945i	$0.743708\pi$
$150$		0			0
$151$	11.6365	+	11.6365i	0.946965	+	0.946965i	0.998663	−	0.0516975i	$-0.0164632\pi$
$151$	11.6365	+	11.6365i	0.946965	+	0.946965i	−0.0516975	+	0.998663i	$0.516463\pi$
$152$			15.6283i			1.26762i
$153$		0			0
$154$	16.9430	+	16.9430i	1.36531	+	1.36531i
$155$	−10.8477			−0.871307
$156$		0			0
$157$	2.46410			0.196657			0.0983284	−	0.995154i	$-0.468650\pi$
$157$	2.46410			0.196657			0.0983284	+	0.995154i	$0.468650\pi$
$158$	4.25886	+	4.25886i	0.338817	+	0.338817i
$159$		0			0
$160$		−	1.82951i		−	0.144635i
$161$	−17.2979	−	17.2979i	−1.36327	−	1.36327i
$162$		0			0
$163$	16.3043	+	16.3043i	1.27705	+	1.27705i	0.942312	+	0.334736i	$0.108647\pi$
$163$	16.3043	+	16.3043i	1.27705	+	1.27705i	0.334736	+	0.942312i	$0.391353\pi$
$164$	0.626640	−	0.626640i	0.0489323	−	0.0489323i
$165$		0			0
$166$			18.3568i			1.42476i
$167$	−16.8191	+	16.8191i	−1.30150	+	1.30150i	−0.374115	+	0.927382i	$0.622054\pi$
$167$	−16.8191	+	16.8191i	−1.30150	+	1.30150i	−0.927382	+	0.374115i	$0.877946\pi$
$168$		0			0
$169$	−12.2325	+	4.40078i	−0.940959	+	0.338522i
$170$		−	9.61709i		−	0.737597i
$171$		0			0
$172$	−0.883201			−0.0673435
$173$	6.62231			0.503485			0.251742	−	0.967794i	$-0.418996\pi$
$173$	6.62231			0.503485			0.251742	+	0.967794i	$0.418996\pi$
$174$		0			0
$175$	4.09724	−	4.09724i	0.309722	−	0.309722i
$176$	15.0567	−	15.0567i	1.13494	−	1.13494i
$177$		0			0
$178$	5.56351			0.417003
$179$	0.407097			0.0304279			0.0152139	−	0.999884i	$-0.495157\pi$
$179$	0.407097			0.0304279			0.0152139	+	0.999884i	$0.495157\pi$
$180$		0			0
$181$		−	8.61008i		−	0.639982i	−0.947421	−	0.319991i	$-0.896320\pi$
$181$		−	8.61008i		−	0.639982i	0.947421	−	0.319991i	$-0.103680\pi$
$182$	−17.2979	+	3.01693i	−1.28221	+	0.223629i
$183$		0			0
$184$	−14.0925	+	14.0925i	−1.03891	+	1.03891i
$185$			8.53587i			0.627570i
$186$		0			0
$187$	12.5828	−	12.5828i	0.920146	−	0.920146i
$188$	−1.50744	−	1.50744i	−0.109941	−	0.109941i
$189$		0			0
$190$	10.9355	+	10.9355i	0.793348	+	0.793348i
$191$		−	18.6520i		−	1.34961i	−0.737996	−	0.674805i	$-0.764228\pi$
$191$		−	18.6520i		−	1.34961i	0.737996	−	0.674805i	$-0.235772\pi$
$192$		0			0
$193$	−18.8315	−	18.8315i	−1.35552	−	1.35552i	−0.879359	−	0.476159i	$-0.842029\pi$
$193$	−18.8315	−	18.8315i	−1.35552	−	1.35552i	−0.476159	−	0.879359i	$-0.657971\pi$
$194$	−5.68669			−0.408281
$195$		0			0
$196$	−0.698630			−0.0499021
$197$	−7.07564	−	7.07564i	−0.504119	−	0.504119i	0.408597	−	0.912715i	$-0.366018\pi$
$197$	−7.07564	−	7.07564i	−0.504119	−	0.504119i	−0.912715	+	0.408597i	$0.866018\pi$
$198$		0			0
$199$		−	0.971033i		−	0.0688347i	−0.999408	−	0.0344174i	$-0.989042\pi$
$199$		−	0.971033i		−	0.0688347i	0.999408	−	0.0344174i	$-0.0109575\pi$
$200$	−3.33799	−	3.33799i	−0.236032	−	0.236032i
$201$		0			0
$202$	−7.78570	−	7.78570i	−0.547800	−	0.547800i
$203$	−1.06988	+	1.06988i	−0.0750906	+	0.0750906i
$204$		0			0
$205$			8.86065i			0.618854i
$206$	2.47189	−	2.47189i	0.172225	−	0.172225i
$207$		0			0
$208$	2.68103	+	15.3720i	0.185896	+	1.06586i
$209$			28.6157i			1.97939i
$210$		0			0
$211$	8.97103			0.617591			0.308796	−	0.951128i	$-0.400074\pi$
$211$	8.97103			0.617591			0.308796	+	0.951128i	$0.400074\pi$
$212$	−1.52861			−0.104985
$213$		0			0
$214$	−5.91413	+	5.91413i	−0.404281	+	0.404281i
$215$	6.24421	−	6.24421i	0.425851	−	0.425851i
$216$		0			0
$217$	19.8673			1.34868
$218$	−8.99461			−0.609192
$219$		0			0
$220$		−	1.59596i		−	0.107599i
$221$	2.24053	+	12.8464i	0.150714	+	0.864140i
$222$		0			0
$223$	3.85945	−	3.85945i	0.258448	−	0.258448i	−0.565975	−	0.824423i	$-0.691500\pi$
$223$	3.85945	−	3.85945i	0.258448	−	0.258448i	0.824423	+	0.565975i	$0.191500\pi$
$224$			3.35070i			0.223878i
$225$		0			0
$226$	13.1157	−	13.1157i	0.872441	−	0.872441i
$227$	16.0245	+	16.0245i	1.06358	+	1.06358i	0.997836	+	0.0657477i	$0.0209432\pi$
$227$	16.0245	+	16.0245i	1.06358	+	1.06358i	0.0657477	+	0.997836i	$0.479057\pi$
$228$		0			0
$229$	10.8305	+	10.8305i	0.715699	+	0.715699i	0.967721	−	0.252023i	$-0.0810958\pi$
$229$	10.8305	+	10.8305i	0.715699	+	0.715699i	−0.252023	+	0.967721i	$0.581096\pi$
$230$			19.7219i			1.30042i
$231$		0			0
$232$	0.871620	+	0.871620i	0.0572247	+	0.0572247i
$233$	12.4393			0.814924			0.407462	−	0.913222i	$-0.366414\pi$
$233$	12.4393			0.814924			0.407462	+	0.913222i	$0.366414\pi$
$234$		0			0
$235$	21.3151			1.39045
$236$	−0.0211672	−	0.0211672i	−0.00137787	−	0.00137787i
$237$		0			0
$238$			17.6135i			1.14171i
$239$	−8.94887	−	8.94887i	−0.578854	−	0.578854i	0.355733	−	0.934587i	$-0.384231\pi$
$239$	−8.94887	−	8.94887i	−0.578854	−	0.578854i	−0.934587	+	0.355733i	$0.884231\pi$
$240$		0			0
$241$	−14.0618	−	14.0618i	−0.905797	−	0.905797i	0.0901326	−	0.995930i	$-0.471271\pi$
$241$	−14.0618	−	14.0618i	−0.905797	−	0.905797i	−0.995930	+	0.0901326i	$0.971271\pi$
$242$	13.7896	−	13.7896i	0.886432	−	0.886432i
$243$		0			0
$244$		−	1.16951i		−	0.0748705i
$245$	4.93929	−	4.93929i	0.315560	−	0.315560i
$246$		0			0
$247$	−17.1552	−	12.0598i	−1.09156	−	0.767349i
$248$		−	16.1857i		−	1.02779i
$249$		0			0
$250$	−17.9667			−1.13631
$251$	17.5216			1.10596			0.552978	−	0.833196i	$-0.313491\pi$
$251$	17.5216			1.10596			0.552978	+	0.833196i	$0.313491\pi$
$252$		0			0
$253$	−25.8037	+	25.8037i	−1.62226	+	1.62226i
$254$	8.39038	−	8.39038i	0.526459	−	0.526459i
$255$		0			0
$256$	4.28881			0.268051
$257$	6.22406			0.388246			0.194123	−	0.980977i	$-0.437814\pi$
$257$	6.22406			0.388246			0.194123	+	0.980977i	$0.437814\pi$
$258$		0			0
$259$		−	15.6332i		−	0.971403i
$260$	0.956783	+	0.672603i	0.0593372	+	0.0417130i
$261$		0			0
$262$	9.15735	−	9.15735i	0.565743	−	0.565743i
$263$		−	22.8504i		−	1.40901i	−0.709697	−	0.704507i	$-0.751168\pi$
$263$		−	22.8504i		−	1.40901i	0.709697	−	0.704507i	$-0.248832\pi$
$264$		0			0
$265$	10.8072	−	10.8072i	0.663882	−	0.663882i
$266$	−20.0282	−	20.0282i	−1.22801	−	1.22801i
$267$		0			0
$268$	−0.376055	−	0.376055i	−0.0229712	−	0.0229712i
$269$			16.6042i			1.01237i	0.862424	+	0.506187i	$0.168945\pi$
$269$			16.6042i			1.01237i	−0.862424	+	0.506187i	$0.831055\pi$
$270$		0			0
$271$	12.6268	+	12.6268i	0.767025	+	0.767025i	0.977582	−	0.210556i	$-0.0675275\pi$
$271$	12.6268	+	12.6268i	0.767025	+	0.767025i	−0.210556	+	0.977582i	$0.567528\pi$
$272$	15.6524			0.949068
$273$		0			0
$274$	−15.0273			−0.907831
$275$	−6.11194	−	6.11194i	−0.368564	−	0.368564i
$276$		0			0
$277$		−	20.9529i		−	1.25894i	−0.777025	−	0.629470i	$-0.783272\pi$
$277$		−	20.9529i		−	1.25894i	0.777025	−	0.629470i	$-0.216728\pi$
$278$	18.2412	+	18.2412i	1.09404	+	1.09404i
$279$		0			0
$280$	−11.2862	−	11.2862i	−0.674477	−	0.674477i
$281$	13.7127	−	13.7127i	0.818031	−	0.818031i	−0.167792	−	0.985822i	$-0.553664\pi$
$281$	13.7127	−	13.7127i	0.818031	−	0.818031i	0.985822	+	0.167792i	$0.0536636\pi$
$282$		0			0
$283$		−	14.8077i		−	0.880224i	−0.897943	−	0.440112i	$-0.854939\pi$
$283$		−	14.8077i		−	0.880224i	0.897943	−	0.440112i	$-0.145061\pi$
$284$	1.56527	−	1.56527i	0.0928817	−	0.0928817i
$285$		0			0
$286$	4.50041	+	25.8037i	0.266115	+	1.52580i
$287$		−	16.2281i		−	0.957912i
$288$		0			0
$289$	−3.91930			−0.230547
$290$	1.21980			0.0716289
$291$		0			0
$292$	−0.450955	+	0.450955i	−0.0263901	+	0.0263901i
$293$	−3.53070	+	3.53070i	−0.206265	+	0.206265i	−0.802678	−	0.596413i	$-0.796592\pi$
$293$	−3.53070	+	3.53070i	−0.206265	+	0.206265i	0.596413	+	0.802678i	$0.296592\pi$
$294$		0			0
$295$	0.299303			0.0174261
$296$	−12.7363			−0.740282
$297$		0			0
$298$			0.712493i			0.0412736i
$299$	−4.59468	−	26.3442i	−0.265717	−	1.52352i
$300$		0			0
$301$	−11.4361	+	11.4361i	−0.659167	+	0.659167i
$302$			24.2984i			1.39822i
$303$		0			0
$304$	−17.7983	+	17.7983i	−1.02080	+	1.02080i
$305$	8.26843	+	8.26843i	0.473449	+	0.473449i
$306$		0			0
$307$	−9.78222	−	9.78222i	−0.558301	−	0.558301i	0.370523	−	0.928823i	$-0.379179\pi$
$307$	−9.78222	−	9.78222i	−0.558301	−	0.558301i	−0.928823	+	0.370523i	$0.879179\pi$
$308$			2.92296i			0.166551i
$309$		0			0
$310$	−11.3256	−	11.3256i	−0.643252	−	0.643252i
$311$	15.3106			0.868184			0.434092	−	0.900869i	$-0.357069\pi$
$311$	15.3106			0.868184			0.434092	+	0.900869i	$0.357069\pi$
$312$		0			0
$313$	−9.33322			−0.527545			−0.263773	−	0.964585i	$-0.584967\pi$
$313$	−9.33322			−0.527545			−0.263773	+	0.964585i	$0.584967\pi$
$314$	2.57267	+	2.57267i	0.145184	+	0.145184i
$315$		0			0
$316$			0.734724i			0.0413315i
$317$	12.8498	+	12.8498i	0.721715	+	0.721715i	0.968954	−	0.247239i	$-0.0795234\pi$
$317$	12.8498	+	12.8498i	0.721715	+	0.721715i	−0.247239	+	0.968954i	$0.579523\pi$
$318$		0			0
$319$	1.59596	+	1.59596i	0.0893564	+	0.0893564i
$320$	−9.11212	+	9.11212i	−0.509383	+	0.509383i
$321$		0			0
$322$		−	36.1201i		−	2.01290i
$323$	−14.8740	+	14.8740i	−0.827611	+	0.827611i
$324$		0			0
$325$	6.23996	−	1.08831i	0.346131	−	0.0603685i
$326$			34.0452i			1.88559i
$327$		0			0
$328$	−13.2209			−0.730001
$329$	−39.0381			−2.15224
$330$		0			0
$331$	−14.5529	+	14.5529i	−0.799898	+	0.799898i	−0.983079	−	0.183181i	$-0.941360\pi$
$331$	−14.5529	+	14.5529i	−0.799898	+	0.799898i	0.183181	+	0.983079i	$0.441360\pi$
$332$	−1.58342	+	1.58342i	−0.0869016	+	0.0869016i
$333$		0			0
$334$	−35.1202			−1.92169
$335$	5.31739			0.290520
$336$		0			0
$337$		−	18.3900i		−	1.00177i	−0.865514	−	0.500884i	$-0.833008\pi$
$337$		−	18.3900i		−	1.00177i	0.865514	−	0.500884i	$-0.166992\pi$
$338$	−17.3661	−	8.17673i	−0.944590	−	0.444756i
$339$		0			0
$340$	0.829554	−	0.829554i	0.0449889	−	0.0449889i
$341$		−	29.6364i		−	1.60490i
$342$		0			0
$343$	7.27953	−	7.27953i	0.393058	−	0.393058i
$344$	9.31692	+	9.31692i	0.502335	+	0.502335i
$345$		0			0
$346$	6.91408	+	6.91408i	0.371703	+	0.371703i
$347$			9.86293i			0.529470i	0.964321	+	0.264735i	$0.0852844\pi$
$347$			9.86293i			0.529470i	−0.964321	+	0.264735i	$0.914716\pi$
$348$		0			0
$349$	−10.3582	−	10.3582i	−0.554460	−	0.554460i	0.373265	−	0.927725i	$-0.378238\pi$
$349$	−10.3582	−	10.3582i	−0.554460	−	0.554460i	−0.927725	+	0.373265i	$0.878238\pi$
$350$	8.55552			0.457312
$351$		0			0
$352$	4.99831			0.266411
$353$	−20.5184	−	20.5184i	−1.09208	−	1.09208i	−0.995306	−	0.0967786i	$-0.969146\pi$
$353$	−20.5184	−	20.5184i	−1.09208	−	1.09208i	−0.0967786	−	0.995306i	$-0.530854\pi$
$354$		0			0
$355$			22.1328i			1.17469i
$356$	0.479899	+	0.479899i	0.0254346	+	0.0254346i
$357$		0			0
$358$	0.425034	+	0.425034i	0.0224637	+	0.0224637i
$359$	−8.17991	+	8.17991i	−0.431719	+	0.431719i	−0.889213	−	0.457494i	$-0.848747\pi$
$359$	−8.17991	+	8.17991i	−0.431719	+	0.431719i	0.457494	+	0.889213i	$0.348747\pi$
$360$		0			0
$361$		−	14.8263i		−	0.780331i
$362$	8.98943	−	8.98943i	0.472474	−	0.472474i
$363$		0			0
$364$	−1.75232	−	1.23186i	−0.0918468	−	0.0645668i
$365$		−	6.37647i		−	0.333760i
$366$		0			0
$367$	21.3695			1.11548			0.557740	−	0.830016i	$-0.311669\pi$
$367$	21.3695			1.11548			0.557740	+	0.830016i	$0.311669\pi$
$368$	−32.0986			−1.67326
$369$		0			0
$370$	−8.91195	+	8.91195i	−0.463310	+	0.463310i
$371$	−19.7931	+	19.7931i	−1.02761	+	1.02761i
$372$		0			0
$373$	37.4336			1.93824			0.969118	−	0.246596i	$-0.0793121\pi$
$373$	37.4336			1.93824			0.969118	+	0.246596i	$0.0793121\pi$
$374$	26.2744			1.35862
$375$		0			0
$376$			31.8041i			1.64017i
$377$	−1.62939	+	0.284180i	−0.0839176	+	0.0146360i
$378$		0			0
$379$	−9.52938	+	9.52938i	−0.489491	+	0.489491i	−0.908146	−	0.418654i	$-0.862502\pi$
$379$	−9.52938	+	9.52938i	−0.489491	+	0.489491i	0.418654	+	0.908146i	$0.362502\pi$
$380$			1.88656i			0.0967786i
$381$		0			0
$382$	19.4738	−	19.4738i	0.996365	−	0.996365i
$383$	11.7824	+	11.7824i	0.602052	+	0.602052i	0.940857	−	0.338805i	$-0.110023\pi$
$383$	11.7824	+	11.7824i	0.602052	+	0.602052i	−0.338805	+	0.940857i	$0.610023\pi$
$384$		0			0
$385$	−20.6652	−	20.6652i	−1.05320	−	1.05320i
$386$		−	39.3223i		−	2.00145i
$387$		0			0
$388$	−0.490524	−	0.490524i	−0.0249026	−	0.0249026i
$389$	−35.5335			−1.80162			−0.900811	−	0.434212i	$-0.857027\pi$
$389$	−35.5335			−1.80162			−0.900811	+	0.434212i	$0.857027\pi$
$390$		0			0
$391$	−26.8247			−1.35658
$392$	7.36987	+	7.36987i	0.372235	+	0.372235i
$393$		0			0
$394$		−	14.7748i		−	0.744342i
$395$	−5.19448	−	5.19448i	−0.261362	−	0.261362i
$396$		0			0
$397$	−3.22719	−	3.22719i	−0.161968	−	0.161968i	0.621470	−	0.783438i	$-0.286536\pi$
$397$	−3.22719	−	3.22719i	−0.161968	−	0.161968i	−0.783438	+	0.621470i	$0.786536\pi$
$398$	1.01382	−	1.01382i	0.0508180	−	0.0508180i
$399$		0			0
$400$		−	7.60297i		−	0.380149i
$401$	−4.79278	+	4.79278i	−0.239340	+	0.239340i	−0.816577	−	0.577237i	$-0.804131\pi$
$401$	−4.79278	+	4.79278i	−0.239340	+	0.239340i	0.577237	+	0.816577i	$0.304131\pi$
$402$		0			0
$403$	17.7672	+	12.4900i	0.885046	+	0.622172i
$404$		−	1.34316i		−	0.0668248i
$405$		0			0
$406$	−2.23403			−0.110873
$407$	−23.3204			−1.15595
$408$		0			0
$409$	17.1630	−	17.1630i	0.848655	−	0.848655i	−0.141310	−	0.989965i	$-0.545131\pi$
$409$	17.1630	−	17.1630i	0.848655	−	0.848655i	0.989965	+	0.141310i	$0.0451314\pi$
$410$	−9.25103	+	9.25103i	−0.456876	+	0.456876i
$411$		0			0
$412$	0.426442			0.0210093
$413$	−0.548166			−0.0269735
$414$		0			0
$415$		−	22.3895i		−	1.09906i
$416$	−2.10649	+	2.99651i	−0.103279	+	0.146916i
$417$		0			0
$418$	−29.8765	+	29.8765i	−1.46131	+	1.46131i
$419$		−	15.7718i		−	0.770504i	−0.922811	−	0.385252i	$-0.874115\pi$
$419$		−	15.7718i		−	0.770504i	0.922811	−	0.385252i	$-0.125885\pi$
$420$		0			0
$421$	−0.367362	+	0.367362i	−0.0179041	+	0.0179041i	−0.716002	−	0.698098i	$-0.754030\pi$
$421$	−0.367362	+	0.367362i	−0.0179041	+	0.0179041i	0.698098	+	0.716002i	$0.254030\pi$
$422$	9.36629	+	9.36629i	0.455944	+	0.455944i
$423$		0			0
$424$	16.1253	+	16.1253i	0.783115	+	0.783115i
$425$		−	6.35379i		−	0.308204i
$426$		0			0
$427$	−15.1434	−	15.1434i	−0.732842	−	0.732842i
$428$	−1.02028			−0.0493173
$429$		0			0
$430$	13.0386			0.628779
$431$	17.4155	+	17.4155i	0.838873	+	0.838873i	0.988711	−	0.149838i	$-0.0478752\pi$
$431$	17.4155	+	17.4155i	0.838873	+	0.838873i	−0.149838	+	0.988711i	$0.547875\pi$
$432$		0			0
$433$		−	10.2954i		−	0.494763i	−0.968918	−	0.247381i	$-0.920430\pi$
$433$		−	10.2954i		−	0.494763i	0.968918	−	0.247381i	$-0.0795701\pi$
$434$	20.7426	+	20.7426i	0.995677	+	0.995677i
$435$		0			0
$436$	−0.775859	−	0.775859i	−0.0371569	−	0.0371569i
$437$	30.5023	−	30.5023i	1.45912	−	1.45912i
$438$		0			0
$439$			33.6000i			1.60364i	0.597564	+	0.801821i	$0.296135\pi$
$439$			33.6000i			1.60364i	−0.597564	+	0.801821i	$0.703865\pi$
$440$	−16.8358	+	16.8358i	−0.802615	+	0.802615i
$441$		0			0
$442$	−11.0731	+	15.7516i	−0.526695	+	0.749228i
$443$		−	23.1680i		−	1.10075i	−0.834919	−	0.550373i	$-0.814485\pi$
$443$		−	23.1680i		−	1.10075i	0.834919	−	0.550373i	$-0.185515\pi$
$444$		0			0
$445$	−6.78575			−0.321675
$446$	8.05899			0.381604
$447$		0			0
$448$	16.6886	−	16.6886i	0.788464	−	0.788464i
$449$	0.344617	−	0.344617i	0.0162635	−	0.0162635i	−0.698928	−	0.715192i	$-0.746339\pi$
$449$	0.344617	−	0.344617i	0.0162635	−	0.0162635i	0.715192	+	0.698928i	$0.246339\pi$
$450$		0			0
$451$	−24.2077			−1.13990
$452$	2.26267			0.106427
$453$		0			0
$454$			33.4611i			1.57041i
$455$	21.0981	−	3.67970i	0.989092	−	0.172507i
$456$		0			0
$457$	17.0160	−	17.0160i	0.795977	−	0.795977i	−0.186482	−	0.982458i	$-0.559709\pi$
$457$	17.0160	−	17.0160i	0.795977	−	0.795977i	0.982458	+	0.186482i	$0.0597086\pi$
$458$			22.6153i			1.05674i
$459$		0			0
$460$	−1.70117	+	1.70117i	−0.0793177	+	0.0793177i
$461$	11.7622	+	11.7622i	0.547822	+	0.547822i	0.925810	−	0.377988i	$-0.123384\pi$
$461$	11.7622	+	11.7622i	0.547822	+	0.547822i	−0.377988	+	0.925810i	$0.623384\pi$
$462$		0			0
$463$	18.9537	+	18.9537i	0.880853	+	0.880853i	0.993621	−	0.112768i	$-0.0359718\pi$
$463$	18.9537	+	18.9537i	0.880853	+	0.880853i	−0.112768	+	0.993621i	$0.535972\pi$
$464$			1.98530i			0.0921651i
$465$		0			0
$466$	12.9873	+	12.9873i	0.601626	+	0.601626i
$467$	−15.6685			−0.725054			−0.362527	−	0.931973i	$-0.618086\pi$
$467$	−15.6685			−0.725054			−0.362527	+	0.931973i	$0.618086\pi$
$468$		0			0
$469$	−9.73868			−0.449690
$470$	22.2542	+	22.2542i	1.02651	+	1.02651i
$471$		0			0
$472$			0.446587i			0.0205558i
$473$	17.0595	+	17.0595i	0.784396	+	0.784396i
$474$		0			0
$475$	7.22486	+	7.22486i	0.331499	+	0.331499i
$476$	−1.51931	+	1.51931i	−0.0696374	+	0.0696374i
$477$		0			0
$478$		−	18.6863i		−	0.854691i
$479$	7.12478	−	7.12478i	0.325540	−	0.325540i	−0.525348	−	0.850888i	$-0.676065\pi$
$479$	7.12478	−	7.12478i	0.325540	−	0.325540i	0.850888	+	0.525348i	$0.176065\pi$
$480$		0			0
$481$	9.82820	−	13.9807i	0.448127	−	0.637465i
$482$		−	29.3626i		−	1.33743i
$483$		0			0
$484$	2.37894			0.108134
$485$	6.93598			0.314947
$486$		0			0
$487$	8.26795	−	8.26795i	0.374657	−	0.374657i	−0.494513	−	0.869170i	$-0.664654\pi$
$487$	8.26795	−	8.26795i	0.374657	−	0.374657i	0.869170	+	0.494513i	$0.164654\pi$
$488$	−12.3372	+	12.3372i	−0.558481	+	0.558481i
$489$		0			0
$490$	10.3138			0.465931
$491$	−7.00976			−0.316346			−0.158173	−	0.987411i	$-0.550560\pi$
$491$	−7.00976			−0.316346			−0.158173	+	0.987411i	$0.550560\pi$
$492$		0			0
$493$			1.65911i			0.0747225i
$494$	−5.31989	−	30.5023i	−0.239353	−	1.37236i
$495$		0			0
$496$	18.4332	−	18.4332i	0.827674	−	0.827674i
$497$		−	40.5357i		−	1.81828i
$498$		0			0
$499$	−0.277836	+	0.277836i	−0.0124376	+	0.0124376i	−0.713298	−	0.700861i	$-0.752799\pi$
$499$	−0.277836	+	0.277836i	−0.0124376	+	0.0124376i	0.700861	+	0.713298i	$0.252799\pi$
$500$	−1.54978	−	1.54978i	−0.0693081	−	0.0693081i
$501$		0			0
$502$	18.2936	+	18.2936i	0.816484	+	0.816484i
$503$			20.0463i			0.893822i	0.894578	+	0.446911i	$0.147476\pi$
$503$			20.0463i			0.893822i	−0.894578	+	0.446911i	$0.852524\pi$
$504$		0			0
$505$	9.49611	+	9.49611i	0.422572	+	0.422572i
$506$	−53.8811			−2.39531
$507$		0			0
$508$	1.44748			0.0642215
$509$	−3.36495	−	3.36495i	−0.149149	−	0.149149i	0.628589	−	0.777738i	$-0.283633\pi$
$509$	−3.36495	−	3.36495i	−0.149149	−	0.149149i	−0.777738	+	0.628589i	$0.783633\pi$
$510$		0			0
$511$			11.6784i			0.516620i
$512$	−13.3373	−	13.3373i	−0.589433	−	0.589433i
$513$		0			0
$514$	6.49829	+	6.49829i	0.286627	+	0.286627i
$515$	−3.01493	+	3.01493i	−0.132854	+	0.132854i
$516$		0			0
$517$			58.2340i			2.56113i
$518$	16.3220	−	16.3220i	0.717149	−	0.717149i
$519$		0			0
$520$	−2.99783	−	17.1884i	−0.131463	−	0.753763i
$521$			9.35106i			0.409678i	0.978796	+	0.204839i	$0.0656670\pi$
$521$			9.35106i			0.409678i	−0.978796	+	0.204839i	$0.934333\pi$
$522$		0			0
$523$	4.54324			0.198662			0.0993310	−	0.995054i	$-0.468330\pi$
$523$	4.54324			0.198662			0.0993310	+	0.995054i	$0.468330\pi$
$524$	1.57979			0.0690136
$525$		0			0
$526$	23.8571	−	23.8571i	1.04022	−	1.04022i
$527$	15.4046	−	15.4046i	0.671033	−	0.671033i
$528$		0			0
$529$	32.0097			1.39173
$530$	22.5667			0.980236
$531$		0			0
$532$		−	3.45519i		−	0.149802i
$533$	10.2021	−	14.5126i	0.441904	−	0.628612i
$534$		0			0
$535$	7.21338	−	7.21338i	0.311862	−	0.311862i
$536$			7.93403i			0.342698i
$537$		0			0
$538$	−17.3357	+	17.3357i	−0.747396	+	0.747396i
$539$	13.4944	+	13.4944i	0.581245	+	0.581245i
$540$		0			0
$541$	−12.0375	−	12.0375i	−0.517533	−	0.517533i	0.399291	−	0.916824i	$-0.369256\pi$
$541$	−12.0375	−	12.0375i	−0.517533	−	0.517533i	−0.916824	+	0.399291i	$0.869256\pi$
$542$			26.3663i			1.13253i
$543$		0			0
$544$	2.59804	+	2.59804i	0.111390	+	0.111390i
$545$	10.9706			0.469929
$546$		0			0
$547$	29.7830			1.27343			0.636716	−	0.771099i	$-0.280293\pi$
$547$	29.7830			1.27343			0.636716	+	0.771099i	$0.280293\pi$
$548$	−1.29623	−	1.29623i	−0.0553721	−	0.0553721i
$549$		0			0
$550$		−	12.7625i		−	0.544193i
$551$	−1.88656	−	1.88656i	−0.0803703	−	0.0803703i
$552$		0			0
$553$	9.51356	+	9.51356i	0.404558	+	0.404558i
$554$	21.8761	−	21.8761i	0.929426	−	0.929426i
$555$		0			0
$556$			3.14691i			0.133459i
$557$	−15.7659	+	15.7659i	−0.668023	+	0.668023i	−0.957258	−	0.289235i	$-0.906599\pi$
$557$	−15.7659	+	15.7659i	−0.668023	+	0.668023i	0.289235	+	0.957258i	$0.406599\pi$
$558$		0			0
$559$	−17.4168	+	3.03766i	−0.736653	+	0.128479i
$560$		−	25.7066i		−	1.08630i
$561$		0			0
$562$	28.6337			1.20784
$563$	−2.77304			−0.116870			−0.0584348	−	0.998291i	$-0.518611\pi$
$563$	−2.77304			−0.116870			−0.0584348	+	0.998291i	$0.518611\pi$
$564$		0			0
$565$	−15.9970	+	15.9970i	−0.672999	+	0.672999i
$566$	15.4601	−	15.4601i	0.649835	−	0.649835i
$567$		0			0
$568$	−33.0242			−1.38566
$569$	7.09919			0.297614			0.148807	−	0.988866i	$-0.452457\pi$
$569$	7.09919			0.297614			0.148807	+	0.988866i	$0.452457\pi$
$570$		0			0
$571$		−	29.1877i		−	1.22147i	−0.791837	−	0.610733i	$-0.790875\pi$
$571$		−	29.1877i		−	1.22147i	0.791837	−	0.610733i	$-0.209125\pi$
$572$	−1.83758	+	2.61398i	−0.0768333	+	0.109296i
$573$		0			0
$574$	16.9430	−	16.9430i	0.707189	−	0.707189i
$575$			13.0298i			0.543379i
$576$		0			0
$577$	−33.3512	+	33.3512i	−1.38843	+	1.38843i	−0.559799	+	0.828629i	$0.689122\pi$
$577$	−33.3512	+	33.3512i	−1.38843	+	1.38843i	−0.828629	+	0.559799i	$0.810878\pi$
$578$	−4.09197	−	4.09197i	−0.170204	−	0.170204i
$579$		0			0
$580$	0.105218	+	0.105218i	0.00436892	+	0.00436892i
$581$			41.0058i			1.70121i
$582$		0			0
$583$	29.5259	+	29.5259i	1.22284	+	1.22284i
$584$	9.51427			0.393703
$585$		0			0
$586$	−7.37251			−0.304555
$587$	22.1645	+	22.1645i	0.914828	+	0.914828i	0.996647	−	0.0818190i	$-0.0260729\pi$
$587$	22.1645	+	22.1645i	0.914828	+	0.914828i	−0.0818190	+	0.996647i	$0.526073\pi$
$588$		0			0
$589$			35.0329i			1.44351i
$590$	0.312490	+	0.312490i	0.0128650	+	0.0128650i
$591$		0			0
$592$	−14.5048	−	14.5048i	−0.596143	−	0.596143i
$593$	16.8963	−	16.8963i	0.693847	−	0.693847i	−0.269229	−	0.963076i	$-0.586769\pi$
$593$	16.8963	−	16.8963i	0.693847	−	0.693847i	0.963076	+	0.269229i	$0.0867689\pi$
$594$		0			0
$595$		−	21.4829i		−	0.880714i
$596$	−0.0614584	+	0.0614584i	−0.00251744	+	0.00251744i
$597$		0			0
$598$	22.7078	−	32.3020i	0.928589	−	1.32093i
$599$			33.7920i			1.38070i	0.723473	+	0.690352i	$0.242544\pi$
$599$			33.7920i			1.38070i	−0.723473	+	0.690352i	$0.757456\pi$
$600$		0			0
$601$	−3.50041			−0.142785			−0.0713924	−	0.997448i	$-0.522744\pi$
$601$	−3.50041			−0.142785			−0.0713924	+	0.997448i	$0.522744\pi$
$602$	−23.8799			−0.973274
$603$		0			0
$604$	−2.09594	+	2.09594i	−0.0852825	+	0.0852825i
$605$	−16.8191	+	16.8191i	−0.683792	+	0.683792i
$606$		0			0
$607$	−11.0285			−0.447635			−0.223817	−	0.974631i	$-0.571852\pi$
$607$	−11.0285			−0.447635			−0.223817	+	0.974631i	$0.571852\pi$
$608$	−5.90844			−0.239619
$609$		0			0
$610$			17.2655i			0.699058i
$611$	−34.9115	−	24.5422i	−1.41237	−	0.992872i
$612$		0			0
$613$	−0.260607	+	0.260607i	−0.0105258	+	0.0105258i	−0.712350	−	0.701824i	$-0.752369\pi$
$613$	−0.260607	+	0.260607i	−0.0105258	+	0.0105258i	0.701824	+	0.712350i	$0.252369\pi$
$614$		−	20.4264i		−	0.824344i
$615$		0			0
$616$	30.8344	−	30.8344i	1.24235	−	1.24235i
$617$	2.51785	+	2.51785i	0.101365	+	0.101365i	0.755971	−	0.654606i	$-0.227165\pi$
$617$	2.51785	+	2.51785i	0.101365	+	0.101365i	−0.654606	+	0.755971i	$0.727165\pi$
$618$		0			0
$619$	−16.5287	−	16.5287i	−0.664343	−	0.664343i	0.292058	−	0.956401i	$-0.405660\pi$
$619$	−16.5287	−	16.5287i	−0.664343	−	0.664343i	−0.956401	+	0.292058i	$0.905660\pi$
$620$		−	1.95386i		−	0.0784688i
$621$		0			0
$622$	15.9852	+	15.9852i	0.640946	+	0.640946i
$623$	12.4279			0.497914
$624$		0			0
$625$	13.1298			0.525193
$626$	−9.74444	−	9.74444i	−0.389466	−	0.389466i
$627$		0			0
$628$			0.443828i			0.0177107i
$629$	−12.1216	−	12.1216i	−0.483320	−	0.483320i
$630$		0			0
$631$	10.3527	+	10.3527i	0.412136	+	0.412136i	0.882482	−	0.470346i	$-0.155871\pi$
$631$	10.3527	+	10.3527i	0.412136	+	0.412136i	−0.470346	+	0.882482i	$0.655871\pi$
$632$	7.75063	−	7.75063i	0.308303	−	0.308303i
$633$		0			0
$634$			26.8318i			1.06563i
$635$	−10.2336	+	10.2336i	−0.406109	+	0.406109i
$636$		0			0
$637$	−13.7771	+	2.40285i	−0.545867	+	0.0952044i
$638$			3.33255i			0.131937i
$639$		0			0
$640$	−22.6862			−0.896751
$641$	43.5723			1.72100			0.860502	−	0.509448i	$-0.170150\pi$
$641$	43.5723			1.72100			0.860502	+	0.509448i	$0.170150\pi$
$642$		0			0
$643$	−29.2937	+	29.2937i	−1.15523	+	1.15523i	−0.169743	+	0.985488i	$0.554294\pi$
$643$	−29.2937	+	29.2937i	−1.15523	+	1.15523i	−0.985488	+	0.169743i	$0.945706\pi$
$644$	3.11566	−	3.11566i	0.122774	−	0.122774i
$645$		0			0
$646$	−31.0587			−1.22199
$647$	−31.4069			−1.23473			−0.617366	−	0.786676i	$-0.711800\pi$
$647$	−31.4069			−1.23473			−0.617366	+	0.786676i	$0.711800\pi$
$648$		0			0
$649$			0.817711i			0.0320980i
$650$	7.65114	+	5.37863i	0.300103	+	0.210967i
$651$		0			0
$652$	−2.93668	+	2.93668i	−0.115009	+	0.115009i
$653$		−	10.7985i		−	0.422580i	−0.977423	−	0.211290i	$-0.932234\pi$
$653$		−	10.7985i		−	0.422580i	0.977423	−	0.211290i	$-0.0677664\pi$
$654$		0			0
$655$	−11.1691	+	11.1691i	−0.436413	+	0.436413i
$656$	−15.0567	−	15.0567i	−0.587864	−	0.587864i
$657$		0			0
$658$	−40.7581	−	40.7581i	−1.58892	−	1.58892i
$659$			32.9975i			1.28540i	0.766118	+	0.642699i	$0.222186\pi$
$659$			32.9975i			1.28540i	−0.766118	+	0.642699i	$0.777814\pi$
$660$		0			0
$661$	−19.5480	−	19.5480i	−0.760327	−	0.760327i	0.216054	−	0.976381i	$-0.430681\pi$
$661$	−19.5480	−	19.5480i	−0.760327	−	0.760327i	−0.976381	+	0.216054i	$0.930681\pi$
$662$	−30.3881			−1.18107
$663$		0			0
$664$	33.4071			1.29645
$665$	24.4281	+	24.4281i	0.947282	+	0.947282i
$666$		0			0
$667$		−	3.40235i		−	0.131739i
$668$	−3.02941	−	3.02941i	−0.117211	−	0.117211i
$669$		0			0
$670$	5.55167	+	5.55167i	0.214480	+	0.214480i
$671$	−22.5898	+	22.5898i	−0.872069	+	0.872069i
$672$		0			0
$673$		−	4.03703i		−	0.155616i	−0.996968	−	0.0778079i	$-0.975208\pi$
$673$		−	4.03703i		−	0.155616i	0.996968	−	0.0778079i	$-0.0247921\pi$
$674$	19.2003	−	19.2003i	0.739567	−	0.739567i
$675$		0			0
$676$	−0.792658	−	2.20328i	−0.0304868	−	0.0847415i
$677$		−	11.1860i		−	0.429913i	−0.976624	−	0.214956i	$-0.931039\pi$
$677$		−	11.1860i		−	0.429913i	0.976624	−	0.214956i	$-0.0689609\pi$
$678$		0			0
$679$	−12.7031			−0.487500
$680$	−17.5020			−0.671170
$681$		0			0
$682$	30.9422	−	30.9422i	1.18484	−	1.18484i
$683$	6.34498	−	6.34498i	0.242784	−	0.242784i	−0.575217	−	0.818001i	$-0.695082\pi$
$683$	6.34498	−	6.34498i	0.242784	−	0.242784i	0.818001	+	0.575217i	$0.195082\pi$
$684$		0			0
$685$	18.3286			0.700299
$686$	15.2005			0.580358
$687$		0			0
$688$			21.2212i			0.809052i
$689$	−30.1443	+	5.25745i	−1.14841	+	0.200293i
$690$		0			0
$691$	8.78270	−	8.78270i	0.334110	−	0.334110i	−0.520035	−	0.854145i	$-0.674081\pi$
$691$	8.78270	−	8.78270i	0.334110	−	0.334110i	0.854145	+	0.520035i	$0.174081\pi$
$692$			1.19279i			0.0453432i
$693$		0			0
$694$	−10.2975	+	10.2975i	−0.390887	+	0.390887i
$695$	−22.2486	−	22.2486i	−0.843936	−	0.843936i
$696$		0			0
$697$	−12.5828	−	12.5828i	−0.476608	−	0.476608i
$698$		−	21.6291i		−	0.818672i
$699$		0			0
$700$	0.737985	+	0.737985i	0.0278932	+	0.0278932i
$701$	11.1875			0.422546			0.211273	−	0.977427i	$-0.432239\pi$
$701$	11.1875			0.422546			0.211273	+	0.977427i	$0.432239\pi$
$702$		0			0
$703$	27.5668			1.03970
$704$	−24.8948	−	24.8948i	−0.938258	−	0.938258i
$705$		0			0
$706$		−	42.8448i		−	1.61249i
$707$	−17.3919	−	17.3919i	−0.654090	−	0.654090i
$708$		0			0
$709$	20.1446	+	20.1446i	0.756547	+	0.756547i	0.975692	−	0.219145i	$-0.0703267\pi$
$709$	20.1446	+	20.1446i	0.756547	+	0.756547i	−0.219145	+	0.975692i	$0.570327\pi$
$710$	−23.1080	+	23.1080i	−0.867227	+	0.867227i
$711$		0			0
$712$		−	10.1249i		−	0.379448i
$713$	−31.5903	+	31.5903i	−1.18307	+	1.18307i
$714$		0			0
$715$	−5.48909	−	31.4724i	−0.205280	−	1.17700i
$716$			0.0733253i			0.00274030i
$717$		0			0
$718$	−17.0806			−0.637443
$719$	2.02763			0.0756179			0.0378089	−	0.999285i	$-0.487962\pi$
$719$	2.02763			0.0756179			0.0378089	+	0.999285i	$0.487962\pi$
$720$		0			0
$721$	5.52177	−	5.52177i	0.205642	−	0.205642i
$722$	15.4795	−	15.4795i	0.576088	−	0.576088i
$723$		0			0
$724$	1.55083			0.0576360
$725$	0.805891			0.0299300
$726$		0			0
$727$		−	32.2360i		−	1.19557i	−0.801658	−	0.597783i	$-0.796048\pi$
$727$		−	32.2360i		−	1.19557i	0.801658	−	0.597783i	$-0.203952\pi$
$728$	5.49045	+	31.4802i	0.203490	+	1.16673i
$729$		0			0
$730$	6.65741	−	6.65741i	0.246402	−	0.246402i
$731$			17.7345i			0.655935i
$732$		0			0
$733$	−34.7310	+	34.7310i	−1.28282	+	1.28282i	−0.343760	+	0.939058i	$0.611701\pi$
$733$	−34.7310	+	34.7310i	−1.28282	+	1.28282i	−0.939058	+	0.343760i	$0.888299\pi$
$734$	22.3110	+	22.3110i	0.823516	+	0.823516i
$735$		0			0
$736$	−5.32783	−	5.32783i	−0.196386	−	0.196386i
$737$			14.5274i			0.535123i
$738$		0			0
$739$	−15.7879	−	15.7879i	−0.580766	−	0.580766i	0.354348	−	0.935114i	$-0.384703\pi$
$739$	−15.7879	−	15.7879i	−0.580766	−	0.580766i	−0.935114	+	0.354348i	$0.884703\pi$
$740$	−1.53746			−0.0565181
$741$		0			0
$742$	−41.3304			−1.51729
$743$	−13.4998	−	13.4998i	−0.495260	−	0.495260i	0.414699	−	0.909959i	$-0.363887\pi$
$743$	−13.4998	−	13.4998i	−0.495260	−	0.495260i	−0.909959	+	0.414699i	$0.863887\pi$
$744$		0			0
$745$		−	0.869019i		−	0.0318384i
$746$	39.0828	+	39.0828i	1.43092	+	1.43092i
$747$		0			0
$748$	2.26638	+	2.26638i	0.0828672	+	0.0828672i
$749$	−13.2111	+	13.2111i	−0.482724	+	0.482724i
$750$		0			0
$751$			37.2744i			1.36016i	0.733136	+	0.680082i	$0.238056\pi$
$751$			37.2744i			1.36016i	−0.733136	+	0.680082i	$0.761944\pi$
$752$	−36.2202	+	36.2202i	−1.32082	+	1.32082i
$753$		0			0
$754$	−1.99788	−	1.40447i	−0.0727583	−	0.0511479i
$755$		−	29.6364i		−	1.07858i
$756$		0			0
$757$	13.7807			0.500867			0.250433	−	0.968134i	$-0.419427\pi$
$757$	13.7807			0.500867			0.250433	+	0.968134i	$0.419427\pi$
$758$	−19.8985			−0.722745
$759$		0			0
$760$	19.9014	−	19.9014i	0.721900	−	0.721900i
$761$	−0.763058	+	0.763058i	−0.0276608	+	0.0276608i	−0.720802	−	0.693141i	$-0.756226\pi$
$761$	−0.763058	+	0.763058i	−0.0276608	+	0.0276608i	0.693141	+	0.720802i	$0.256226\pi$
$762$		0			0
$763$	−20.0924			−0.727393
$764$	3.35955			0.121544
$765$		0			0
$766$			24.6030i			0.888943i
$767$	−0.490221	−	0.344617i	−0.0177009	−	0.0124434i
$768$		0			0
$769$	−16.3676	+	16.3676i	−0.590230	+	0.590230i	−0.937693	−	0.347464i	$-0.887043\pi$
$769$	−16.3676	+	16.3676i	−0.590230	+	0.590230i	0.347464	+	0.937693i	$0.387043\pi$
$770$		−	43.1514i		−	1.55507i
$771$		0			0
$772$	3.39187	−	3.39187i	0.122076	−	0.122076i
$773$	13.4811	+	13.4811i	0.484880	+	0.484880i	0.906686	−	0.421806i	$-0.138604\pi$
$773$	13.4811	+	13.4811i	0.484880	+	0.484880i	−0.421806	+	0.906686i	$0.638604\pi$
$774$		0			0
$775$	−7.48257	−	7.48257i	−0.268782	−	0.268782i
$776$			10.3491i			0.371511i
$777$		0			0
$778$	−37.0991	−	37.0991i	−1.33007	−	1.33007i
$779$	28.6157			1.02526
$780$		0			0
$781$	−60.4680			−2.16372
$782$	−28.0066	−	28.0066i	−1.00151	−	1.00151i
$783$		0			0
$784$			16.7864i			0.599515i
$785$	−3.13785	−	3.13785i	−0.111995	−	0.111995i
$786$		0			0
$787$	5.92918	+	5.92918i	0.211353	+	0.211353i	0.804842	−	0.593489i	$-0.202250\pi$
$787$	5.92918	+	5.92918i	0.211353	+	0.211353i	−0.593489	+	0.804842i	$0.702250\pi$
$788$	1.27445	−	1.27445i	0.0454003	−	0.0454003i
$789$		0			0
$790$		−	10.8467i		−	0.385907i
$791$	29.2981	−	29.2981i	1.04172	−	1.04172i
$792$		0			0
$793$	−4.02240	−	23.0629i	−0.142840	−	0.818989i
$794$		−	6.73874i		−	0.239149i
$795$		0			0
$796$	0.174900			0.00619917
$797$	−12.3247			−0.436562			−0.218281	−	0.975886i	$-0.570045\pi$
$797$	−12.3247			−0.436562			−0.218281	+	0.975886i	$0.570045\pi$
$798$		0			0
$799$	−30.2691	+	30.2691i	−1.07085	+	1.07085i
$800$	1.26197	−	1.26197i	0.0446172	−	0.0446172i
$801$		0			0
$802$	−10.0079			−0.353391
$803$	17.4208			0.614768
$804$		0			0
$805$			44.0552i			1.55274i
$806$	5.50965	+	31.5903i	0.194069	+	1.11272i
$807$		0			0
$808$	−14.1691	+	14.1691i	−0.498466	+	0.498466i
$809$		−	6.98762i		−	0.245672i	−0.992427	−	0.122836i	$-0.960801\pi$
$809$		−	6.98762i		−	0.245672i	0.992427	−	0.122836i	$-0.0391988\pi$
$810$		0			0
$811$	−23.4230	+	23.4230i	−0.822492	+	0.822492i	−0.986465	−	0.163973i	$-0.947569\pi$
$811$	−23.4230	+	23.4230i	−0.822492	+	0.822492i	0.163973	+	0.986465i	$0.447569\pi$
$812$	−0.192703	−	0.192703i	−0.00676256	−	0.00676256i
$813$		0			0
$814$	−24.3479	−	24.3479i	−0.853394	−	0.853394i
$815$		−	41.5245i		−	1.45454i
$816$		0			0
$817$	−20.1658	−	20.1658i	−0.705513	−	0.705513i
$818$	35.8383			1.25306
$819$		0			0
$820$	−1.59596			−0.0557332
$821$	5.70144	+	5.70144i	0.198982	+	0.198982i	0.799563	−	0.600582i	$-0.205064\pi$
$821$	5.70144	+	5.70144i	0.198982	+	0.198982i	−0.600582	+	0.799563i	$0.705064\pi$
$822$		0			0
$823$		−	12.9939i		−	0.452939i	−0.974018	−	0.226470i	$-0.927282\pi$
$823$		−	12.9939i		−	0.452939i	0.974018	−	0.226470i	$-0.0727184\pi$
$824$	−4.49855	−	4.49855i	−0.156714	−	0.156714i
$825$		0			0
$826$	−0.572317	−	0.572317i	−0.0199135	−	0.0199135i
$827$	27.8359	−	27.8359i	0.967949	−	0.967949i	−0.0315532	−	0.999502i	$-0.510045\pi$
$827$	27.8359	−	27.8359i	0.967949	−	0.967949i	0.999502	+	0.0315532i	$0.0100454\pi$
$828$		0			0
$829$		−	1.92467i		−	0.0668466i	−0.999441	−	0.0334233i	$-0.989359\pi$
$829$		−	1.92467i		−	0.0668466i	0.999441	−	0.0334233i	$-0.0106409\pi$
$830$	23.3760	−	23.3760i	0.811391	−	0.811391i
$831$		0			0
$832$	25.4162	−	4.43283i	0.881149	−	0.153681i
$833$			14.0284i			0.486054i
$834$		0			0
$835$	42.8356			1.48239
$836$	−5.15419			−0.178261
$837$		0			0
$838$	16.4667	−	16.4667i	0.568833	−	0.568833i
$839$	16.6780	−	16.6780i	0.575788	−	0.575788i	−0.357952	−	0.933740i	$-0.616525\pi$
$839$	16.6780	−	16.6780i	0.575788	−	0.575788i	0.933740	+	0.357952i	$0.116525\pi$
$840$		0			0
$841$	28.7896			0.992744
$842$	−0.767095			−0.0264358
$843$		0			0
$844$			1.61584i			0.0556195i
$845$	21.1812	+	9.97305i	0.728655	+	0.343083i
$846$		0			0
$847$	30.8037	−	30.8037i	1.05843	−	1.05843i
$848$			36.7288i			1.26127i
$849$		0			0
$850$	6.63373	−	6.63373i	0.227535	−	0.227535i
$851$	24.8579	+	24.8579i	0.852118	+	0.852118i
$852$		0			0
$853$	−13.4161	−	13.4161i	−0.459357	−	0.459357i	0.439087	−	0.898444i	$-0.355302\pi$
$853$	−13.4161	−	13.4161i	−0.459357	−	0.459357i	−0.898444	+	0.439087i	$0.855302\pi$
$854$		−	31.6213i		−	1.08206i
$855$		0			0
$856$	10.7630	+	10.7630i	0.367872	+	0.367872i
$857$	48.5839			1.65960			0.829798	−	0.558064i	$-0.188456\pi$
$857$	48.5839			1.65960			0.829798	+	0.558064i	$0.188456\pi$
$858$		0			0
$859$	−29.8410			−1.01816			−0.509081	−	0.860719i	$-0.670014\pi$
$859$	−29.8410			−1.01816			−0.509081	+	0.860719i	$0.670014\pi$
$860$	1.12469	+	1.12469i	0.0383516	+	0.0383516i
$861$		0			0
$862$			36.3655i			1.23861i
$863$	8.26503	+	8.26503i	0.281345	+	0.281345i	0.833645	−	0.552300i	$-0.186250\pi$
$863$	8.26503	+	8.26503i	0.281345	+	0.281345i	−0.552300	+	0.833645i	$0.686250\pi$
$864$		0			0
$865$	−8.43301	−	8.43301i	−0.286731	−	0.286731i
$866$	10.7490	−	10.7490i	0.365264	−	0.365264i
$867$		0			0
$868$			3.57844i			0.121460i
$869$	14.1916	−	14.1916i	0.481416	−	0.481416i
$870$		0			0
$871$	−8.70923	−	6.12245i	−0.295101	−	0.207451i
$872$			16.3691i			0.554329i
$873$		0			0
$874$	63.6923			2.15442
$875$	−40.1345			−1.35679
$876$		0			0
$877$	17.4338	−	17.4338i	0.588699	−	0.588699i	−0.348580	−	0.937279i	$-0.613336\pi$
$877$	17.4338	−	17.4338i	0.588699	−	0.588699i	0.937279	+	0.348580i	$0.113336\pi$
$878$	−35.0804	+	35.0804i	−1.18391	+	1.18391i
$879$		0			0
$880$	−38.3470			−1.29268
$881$	−29.2200			−0.984448			−0.492224	−	0.870469i	$-0.663816\pi$
$881$	−29.2200			−0.984448			−0.492224	+	0.870469i	$0.663816\pi$
$882$		0			0
$883$			18.5571i			0.624496i	0.950001	+	0.312248i	$0.101082\pi$
$883$			18.5571i			0.624496i	−0.950001	+	0.312248i	$0.898918\pi$
$884$	−2.31385	+	0.403558i	−0.0778234	+	0.0135731i
$885$		0			0
$886$	24.1888	−	24.1888i	0.812638	−	0.812638i
$887$			25.6013i			0.859606i	0.902923	+	0.429803i	$0.141417\pi$
$887$			25.6013i			0.859606i	−0.902923	+	0.429803i	$0.858583\pi$
$888$		0			0
$889$	18.7427	−	18.7427i	0.628608	−	0.628608i
$890$	−7.08472	−	7.08472i	−0.237480	−	0.237480i
$891$		0			0
$892$	0.695155	+	0.695155i	0.0232755	+	0.0232755i
$893$		−	68.8378i		−	2.30357i
$894$		0			0
$895$	−0.518408	−	0.518408i	−0.0173285	−	0.0173285i
$896$	41.5492			1.38806
$897$		0			0
$898$	0.719601			0.0240134
$899$	1.95386	+	1.95386i	0.0651648	+	0.0651648i
$900$		0			0
$901$			30.6942i			1.02257i
$902$	−25.2743	−	25.2743i	−0.841542	−	0.841542i
$903$		0			0
$904$	−23.8690	−	23.8690i	−0.793870	−	0.793870i
$905$	−10.9643	+	10.9643i	−0.364465	+	0.364465i
$906$		0			0
$907$		−	43.1271i		−	1.43201i	−0.698094	−	0.716006i	$-0.745968\pi$
$907$		−	43.1271i		−	1.43201i	0.698094	−	0.716006i	$-0.254032\pi$
$908$	−2.88629	+	2.88629i	−0.0957850	+	0.0957850i
$909$		0			0
$910$	25.8694	+	18.1858i	0.857564	+	0.602853i
$911$			40.7929i			1.35153i	0.737117	+	0.675765i	$0.236187\pi$
$911$			40.7929i			1.35153i	−0.737117	+	0.675765i	$0.763813\pi$
$912$		0			0
$913$	61.1692			2.02441
$914$	35.5315			1.17528
$915$		0			0
$916$	−1.95076	+	1.95076i	−0.0644549	+	0.0644549i
$917$	20.4559	−	20.4559i	0.675514	−	0.675514i
$918$		0			0
$919$	−49.5429			−1.63427			−0.817135	−	0.576446i	$-0.804439\pi$
$919$	−49.5429			−1.63427			−0.817135	+	0.576446i	$0.804439\pi$
$920$	35.8915			1.18331
$921$		0			0
$922$			24.5609i			0.808872i
$923$	25.4837	−	36.2508i	0.838808	−	1.19321i
$924$		0			0
$925$	−5.88792	+	5.88792i	−0.193594	+	0.193594i
$926$			39.5775i			1.30060i
$927$		0			0
$928$	−0.329526	+	0.329526i	−0.0108172	+	0.0108172i
$929$	−18.4873	−	18.4873i	−0.606549	−	0.606549i	0.335493	−	0.942043i	$-0.391097\pi$
$929$	−18.4873	−	18.4873i	−0.606549	−	0.606549i	−0.942043	+	0.335493i	$0.891097\pi$
$930$		0			0
$931$	−15.9516	−	15.9516i	−0.522792	−	0.522792i
$932$			2.24053i			0.0733910i
$933$		0			0
$934$	−16.3589	−	16.3589i	−0.535279	−	0.535279i
$935$	−32.0465			−1.04803
$936$		0			0
$937$	38.1244			1.24547			0.622734	−	0.782433i	$-0.286022\pi$
$937$	38.1244			1.24547			0.622734	+	0.782433i	$0.286022\pi$
$938$	−10.1678	−	10.1678i	−0.331989	−	0.331989i
$939$		0			0
$940$			3.83923i			0.125222i
$941$	−27.4933	−	27.4933i	−0.896255	−	0.896255i	0.0988476	−	0.995103i	$-0.468484\pi$
$941$	−27.4933	−	27.4933i	−0.896255	−	0.896255i	−0.995103	+	0.0988476i	$0.968484\pi$
$942$		0			0
$943$	25.8037	+	25.8037i	0.840284	+	0.840284i
$944$	−0.508597	+	0.508597i	−0.0165534	+	0.0165534i
$945$		0			0
$946$			35.6222i			1.15818i
$947$	−7.01266	+	7.01266i	−0.227881	+	0.227881i	−0.811807	−	0.583926i	$-0.801516\pi$
$947$	−7.01266	+	7.01266i	−0.227881	+	0.227881i	0.583926	+	0.811807i	$0.301516\pi$
$948$		0			0
$949$	−7.34187	+	10.4439i	−0.238327	+	0.339023i
$950$			15.0864i			0.489466i
$951$		0			0
$952$	32.0544			1.03889
$953$	9.79596			0.317322			0.158661	−	0.987333i	$-0.449282\pi$
$953$	9.79596			0.317322			0.158661	+	0.987333i	$0.449282\pi$
$954$		0			0
$955$	−23.7519	+	23.7519i	−0.768594	+	0.768594i
$956$	1.61185	−	1.61185i	0.0521309	−	0.0521309i
$957$		0			0
$958$	14.8774			0.480667
$959$	−33.5683			−1.08398
$960$		0			0
$961$		−	5.28253i		−	0.170404i
$962$	24.8579	−	4.33546i	0.801451	−	0.139781i
$963$		0			0
$964$	2.53277	−	2.53277i	0.0815749	−	0.0815749i
$965$			47.9609i			1.54392i
$966$		0			0
$967$	−30.9773	+	30.9773i	−0.996162	+	0.996162i	−0.999993	−	0.00383028i	$-0.998781\pi$
$967$	−30.9773	+	30.9773i	−0.996162	+	0.996162i	0.00383028	+	0.999993i	$0.498781\pi$
$968$	−25.0955	−	25.0955i	−0.806601	−	0.806601i
$969$		0			0
$970$	7.24157	+	7.24157i	0.232513	+	0.232513i
$971$			26.8727i			0.862386i	0.902260	+	0.431193i	$0.141907\pi$
$971$			26.8727i			0.862386i	−0.902260	+	0.431193i	$0.858093\pi$
$972$		0			0
$973$	40.7477	+	40.7477i	1.30631	+	1.30631i
$974$	17.2644			0.553189
$975$		0			0
$976$	−28.1007			−0.899480
$977$	−4.62616	−	4.62616i	−0.148004	−	0.148004i	0.629222	−	0.777226i	$-0.283374\pi$
$977$	−4.62616	−	4.62616i	−0.148004	−	0.148004i	−0.777226	+	0.629222i	$0.783374\pi$
$978$		0			0
$979$		−	18.5390i		−	0.592509i
$980$	0.889653	+	0.889653i	0.0284189	+	0.0284189i
$981$		0			0
$982$	−7.31860	−	7.31860i	−0.233546	−	0.233546i
$983$	5.15759	−	5.15759i	0.164502	−	0.164502i	−0.620056	−	0.784558i	$-0.712890\pi$
$983$	5.15759	−	5.15759i	0.164502	−	0.164502i	0.784558	+	0.620056i	$0.212890\pi$
$984$		0			0
$985$			18.0206i			0.574184i
$986$	−1.73221	+	1.73221i	−0.0551647	+	0.0551647i
$987$		0			0
$988$	2.17219	−	3.08996i	0.0691065	−	0.0983046i
$989$		−	36.3684i		−	1.15645i
$990$		0			0
$991$	28.5734			0.907662			0.453831	−	0.891088i	$-0.350057\pi$
$991$	28.5734			0.907662			0.453831	+	0.891088i	$0.350057\pi$
$992$	6.11920			0.194285
$993$		0			0
$994$	42.3217	−	42.3217i	1.34236	−	1.34236i
$995$	−1.23654	+	1.23654i	−0.0392009	+	0.0392009i
$996$		0			0
$997$	−31.8638			−1.00914			−0.504569	−	0.863371i	$-0.668349\pi$
$997$	−31.8638			−1.00914			−0.504569	+	0.863371i	$0.668349\pi$
$998$	−0.580153			−0.0183644
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.i.b.161.5	yes	16
3.2	odd	2	inner	351.2.i.b.161.4	✓	16
13.8	odd	4	inner	351.2.i.b.242.4	yes	16
39.8	even	4	inner	351.2.i.b.242.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.i.b.161.4	✓	16	3.2	odd	2	inner
351.2.i.b.161.5	yes	16	1.1	even	1	trivial
351.2.i.b.242.4	yes	16	13.8	odd	4	inner
351.2.i.b.242.5	yes	16	39.8	even	4	inner

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04406 + 1.04406i) q^{2} +0.180117i q^{4} +(-1.27342 - 1.27342i) q^{5} +(2.33225 + 2.33225i) q^{7} +(1.90006 - 1.90006i) q^{8} -2.65906i q^{10} +(3.47906 - 3.47906i) q^{11} +(0.619491 + 3.55193i) q^{13} +4.87000i q^{14} +4.32779 q^{16} +3.61673 q^{17} +(-4.11256 + 4.11256i) q^{19} +(0.229366 - 0.229366i) q^{20} +7.26469 q^{22} -7.41685 q^{23} -1.75678i q^{25} +(-3.06164 + 4.35521i) q^{26} +(-0.420078 + 0.420078i) q^{28} +0.458732i q^{29} +(4.25926 - 4.25926i) q^{31} +(0.718341 + 0.718341i) q^{32} +(3.77607 + 3.77607i) q^{34} -5.93988i q^{35} +(-3.35154 - 3.35154i) q^{37} -8.58751 q^{38} -4.83918 q^{40} +(-3.47906 - 3.47906i) q^{41} +4.90348i q^{43} +(0.626640 + 0.626640i) q^{44} +(-7.74363 - 7.74363i) q^{46} +(-8.36921 + 8.36921i) q^{47} +3.87875i q^{49} +(1.83418 - 1.83418i) q^{50} +(-0.639765 + 0.111581i) q^{52} +8.48673i q^{53} -8.86065 q^{55} +8.86284 q^{56} +(-0.478943 + 0.478943i) q^{58} +(-0.117519 + 0.117519i) q^{59} -6.49307 q^{61} +8.89383 q^{62} -7.15560i q^{64} +(3.73424 - 5.31200i) q^{65} +(-2.08783 + 2.08783i) q^{67} +0.651435i q^{68} +(6.20158 - 6.20158i) q^{70} +(-8.69028 - 8.69028i) q^{71} +(2.50367 + 2.50367i) q^{73} -6.99841i q^{74} +(-0.740744 - 0.740744i) q^{76} +16.2281 q^{77} +4.07914 q^{79} +(-5.51112 - 5.51112i) q^{80} -7.26469i q^{82} +(8.79106 + 8.79106i) q^{83} +(-4.60563 - 4.60563i) q^{85} +(-5.11952 + 5.11952i) q^{86} -13.2209i q^{88} +(2.66437 - 2.66437i) q^{89} +(-6.83918 + 9.72879i) q^{91} -1.33590i q^{92} -17.4759 q^{94} +10.4741 q^{95} +(-2.72336 + 2.72336i) q^{97} +(-4.04964 + 4.04964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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