LMFDB - Embedded newform 1456.2.r.p.417.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			417.4
Root			$1.50426 + 2.60546i$ of defining polynomial
Character	$\chi$	$=$	1456.417
Dual form			1456.2.r.p.625.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.879528 - 1.52339i) q^{3} +(-0.452861 - 0.784378i) q^{5} +(-0.237709 + 2.63505i) q^{7} +(-0.0471392 - 0.0816475i) q^{9} +(0.358181 - 0.620387i) q^{11} +1.00000 q^{13} -1.59322 q^{15} +(-1.17614 + 2.03713i) q^{17} +(3.31796 + 5.74687i) q^{19} +(3.80513 + 2.67972i) q^{21} +(1.87953 + 3.25544i) q^{23} +(2.08983 - 3.61970i) q^{25} +5.11133 q^{27} +3.25799 q^{29} +(0.785250 - 1.36009i) q^{31} +(-0.630060 - 1.09130i) q^{33} +(2.17452 - 1.00686i) q^{35} +(-2.60441 - 4.51098i) q^{37} +(0.879528 - 1.52339i) q^{39} +4.92168 q^{41} +9.43766 q^{43} +(-0.0426950 + 0.0739499i) q^{45} +(-4.15993 - 7.20521i) q^{47} +(-6.88699 - 1.25275i) q^{49} +(2.06889 + 3.58342i) q^{51} +(-7.04163 + 12.1965i) q^{53} -0.648824 q^{55} +11.6729 q^{57} +(0.358181 - 0.620387i) q^{59} +(5.82633 + 10.0915i) q^{61} +(0.226351 - 0.104806i) q^{63} +(-0.452861 - 0.784378i) q^{65} +(4.69587 - 8.13349i) q^{67} +6.61239 q^{69} -10.9914 q^{71} +(1.73650 - 3.00771i) q^{73} +(-3.67614 - 6.36725i) q^{75} +(1.54961 + 1.09130i) q^{77} +(6.50408 + 11.2654i) q^{79} +(4.63697 - 8.03147i) q^{81} -3.54083 q^{83} +2.13050 q^{85} +(2.86550 - 4.96318i) q^{87} +(-6.02503 - 10.4357i) q^{89} +(-0.237709 + 2.63505i) q^{91} +(-1.38130 - 2.39248i) q^{93} +(3.00514 - 5.20506i) q^{95} +7.43766 q^{97} -0.0675374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) $ 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.879528	−	1.52339i	0.507796	−	0.879528i	−0.492164	−	0.870503i	$-0.663794\pi$
$3$	0.879528	−	1.52339i	0.507796	−	0.879528i	0.999959	−	0.00902528i	$-0.00287288\pi$
$4$		0			0
$5$	−0.452861	−	0.784378i	−0.202526	−	0.350784i	0.746816	−	0.665031i	$-0.231582\pi$
$5$	−0.452861	−	0.784378i	−0.202526	−	0.350784i	−0.949342	+	0.314246i	$0.898248\pi$
$6$		0			0
$7$	−0.237709	+	2.63505i	−0.0898454	+	0.995956i
$7$	−0.237709	+	2.63505i	−0.0898454	+	0.995956i
$8$		0			0
$9$	−0.0471392	−	0.0816475i	−0.0157131	−	0.0272158i
$10$		0			0
$11$	0.358181	−	0.620387i	0.107996	−	0.187054i	−0.806963	−	0.590603i	$-0.798890\pi$
$11$	0.358181	−	0.620387i	0.107996	−	0.187054i	0.914958	+	0.403549i	$0.132223\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−1.59322			−0.411366
$16$		0			0
$17$	−1.17614	+	2.03713i	−0.285255	+	0.494076i	−0.972671	−	0.232188i	$-0.925412\pi$
$17$	−1.17614	+	2.03713i	−0.285255	+	0.494076i	0.687416	+	0.726264i	$0.258745\pi$
$18$		0			0
$19$	3.31796	+	5.74687i	0.761191	+	1.31842i	0.942237	+	0.334947i	$0.108718\pi$
$19$	3.31796	+	5.74687i	0.761191	+	1.31842i	−0.181046	+	0.983475i	$0.557948\pi$
$20$		0			0
$21$	3.80513	+	2.67972i	0.830348	+	0.584764i
$22$		0			0
$23$	1.87953	+	3.25544i	0.391909	+	0.678806i	0.992701	−	0.120599i	$-0.0384816\pi$
$23$	1.87953	+	3.25544i	0.391909	+	0.678806i	−0.600793	+	0.799405i	$0.705148\pi$
$24$		0			0
$25$	2.08983	−	3.61970i	0.417967	−	0.723940i
$26$		0			0
$27$	5.11133			0.983675
$28$		0			0
$29$	3.25799			0.604994			0.302497	−	0.953150i	$-0.402180\pi$
$29$	3.25799			0.604994			0.302497	+	0.953150i	$0.402180\pi$
$30$		0			0
$31$	0.785250	−	1.36009i	0.141035	−	0.244280i	−0.786852	−	0.617142i	$-0.788290\pi$
$31$	0.785250	−	1.36009i	0.141035	−	0.244280i	0.927887	+	0.372862i	$0.121624\pi$
$32$		0			0
$33$	−0.630060	−	1.09130i	−0.109679	−	0.189970i
$34$		0			0
$35$	2.17452	−	1.00686i	0.367562	−	0.170190i
$36$		0			0
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	0.568547	−	0.822651i	$-0.307506\pi$
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	−0.996710	+	0.0810508i	$0.974172\pi$
$38$		0			0
$39$	0.879528	−	1.52339i	0.140837	−	0.243937i
$40$		0			0
$41$	4.92168			0.768637			0.384318	−	0.923201i	$-0.374437\pi$
$41$	4.92168			0.768637			0.384318	+	0.923201i	$0.374437\pi$
$42$		0			0
$43$	9.43766			1.43923			0.719615	−	0.694373i	$-0.244318\pi$
$43$	9.43766			1.43923			0.719615	+	0.694373i	$0.244318\pi$
$44$		0			0
$45$	−0.0426950	+	0.0739499i	−0.00636459	+	0.0110238i
$46$		0			0
$47$	−4.15993	−	7.20521i	−0.606788	−	1.05099i	−0.991766	−	0.128062i	$-0.959124\pi$
$47$	−4.15993	−	7.20521i	−0.606788	−	1.05099i	0.384978	−	0.922926i	$-0.374209\pi$
$48$		0			0
$49$	−6.88699	−	1.25275i	−0.983856	−	0.178964i
$50$		0			0
$51$	2.06889	+	3.58342i	0.289702	+	0.501779i
$52$		0			0
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.263777	+	0.964584i	$0.584968\pi$
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.703465	+	0.710729i	$0.748365\pi$
$54$		0			0
$55$	−0.648824			−0.0874874
$56$		0			0
$57$	11.6729			1.54612
$58$		0			0
$59$	0.358181	−	0.620387i	0.0466311	−	0.0807675i	−0.841768	−	0.539840i	$-0.818485\pi$
$59$	0.358181	−	0.620387i	0.0466311	−	0.0807675i	0.888399	+	0.459072i	$0.151818\pi$
$60$		0			0
$61$	5.82633	+	10.0915i	0.745986	+	1.29208i	0.949733	+	0.313061i	$0.101355\pi$
$61$	5.82633	+	10.0915i	0.745986	+	1.29208i	−0.203747	+	0.979024i	$0.565312\pi$
$62$		0			0
$63$	0.226351	−	0.104806i	0.0285175	−	0.0132043i
$64$		0			0
$65$	−0.452861	−	0.784378i	−0.0561705	−	0.0972901i
$66$		0			0
$67$	4.69587	−	8.13349i	0.573692	−	0.993664i	−0.422490	−	0.906367i	$-0.638844\pi$
$67$	4.69587	−	8.13349i	0.573692	−	0.993664i	0.996182	−	0.0872964i	$-0.0278227\pi$
$68$		0			0
$69$	6.61239			0.796038
$70$		0			0
$71$	−10.9914			−1.30444			−0.652220	−	0.758030i	$-0.726162\pi$
$71$	−10.9914			−1.30444			−0.652220	+	0.758030i	$0.726162\pi$
$72$		0			0
$73$	1.73650	−	3.00771i	0.203242	−	0.352025i	−0.746329	−	0.665577i	$-0.768186\pi$
$73$	1.73650	−	3.00771i	0.203242	−	0.352025i	0.949571	+	0.313552i	$0.101519\pi$
$74$		0			0
$75$	−3.67614	−	6.36725i	−0.424484	−	0.735227i
$76$		0			0
$77$	1.54961	+	1.09130i	0.176594	+	0.124365i
$78$		0			0
$79$	6.50408	+	11.2654i	0.731766	+	1.26746i	0.956128	+	0.292950i	$0.0946370\pi$
$79$	6.50408	+	11.2654i	0.731766	+	1.26746i	−0.224361	+	0.974506i	$0.572030\pi$
$80$		0			0
$81$	4.63697	−	8.03147i	0.515219	−	0.892386i
$82$		0			0
$83$	−3.54083			−0.388656			−0.194328	−	0.980937i	$-0.562253\pi$
$83$	−3.54083			−0.388656			−0.194328	+	0.980937i	$0.562253\pi$
$84$		0			0
$85$	2.13050			0.231085
$86$		0			0
$87$	2.86550	−	4.96318i	0.307213	−	0.532109i
$88$		0			0
$89$	−6.02503	−	10.4357i	−0.638651	−	1.10618i	−0.985729	−	0.168340i	$-0.946159\pi$
$89$	−6.02503	−	10.4357i	−0.638651	−	1.10618i	0.347077	−	0.937836i	$-0.387174\pi$
$90$		0			0
$91$	−0.237709	+	2.63505i	−0.0249186	+	0.276228i
$92$		0			0
$93$	−1.38130	−	2.39248i	−0.143234	−	0.248088i
$94$		0			0
$95$	3.00514	−	5.20506i	0.308321	−	0.534028i
$96$		0			0
$97$	7.43766			0.755180			0.377590	−	0.925973i	$-0.376753\pi$
$97$	7.43766			0.755180			0.377590	+	0.925973i	$0.376753\pi$
$98$		0			0
$99$	−0.0675374			−0.00678776
$100$		0			0
$101$	0.599526	−	1.03841i	0.0596551	−	0.103326i	−0.834656	−	0.550772i	$-0.814333\pi$
$101$	0.599526	−	1.03841i	0.0596551	−	0.103326i	0.894311	+	0.447447i	$0.147667\pi$
$102$		0			0
$103$	−7.20615	−	12.4814i	−0.710043	−	1.22983i	−0.964840	−	0.262837i	$-0.915342\pi$
$103$	−7.20615	−	12.4814i	−0.710043	−	1.22983i	0.254797	−	0.966995i	$-0.417991\pi$
$104$		0			0
$105$	0.378721	−	4.19820i	0.0369594	−	0.409703i
$106$		0			0
$107$	6.79661	+	11.7721i	0.657053	+	1.13805i	0.981375	+	0.192102i	$0.0615305\pi$
$107$	6.79661	+	11.7721i	0.657053	+	1.13805i	−0.324322	+	0.945947i	$0.605136\pi$
$108$		0			0
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	−0.324013	−	0.946053i	$-0.605032\pi$
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	0.981312	−	0.192423i	$-0.0616346\pi$
$110$		0			0
$111$	−9.16262			−0.869677
$112$		0			0
$113$	−3.25799			−0.306486			−0.153243	−	0.988189i	$-0.548972\pi$
$113$	−3.25799			−0.306486			−0.153243	+	0.988189i	$0.548972\pi$
$114$		0			0
$115$	1.70233	−	2.94852i	0.158743	−	0.274951i
$116$		0			0
$117$	−0.0471392	−	0.0816475i	−0.00435802	−	0.00754831i
$118$		0			0
$119$	−5.08836	−	3.58342i	−0.466449	−	0.328492i
$120$		0			0
$121$	5.24341	+	9.08186i	0.476674	+	0.825623i
$122$		0			0
$123$	4.32875	−	7.49762i	0.390310	−	0.676037i
$124$		0			0
$125$	−8.31422			−0.743647
$126$		0			0
$127$	0.950834			0.0843729			0.0421865	−	0.999110i	$-0.486568\pi$
$127$	0.950834			0.0843729			0.0421865	+	0.999110i	$0.486568\pi$
$128$		0			0
$129$	8.30069	−	14.3772i	0.730835	−	1.26584i
$130$		0			0
$131$	−9.40980	−	16.2983i	−0.822138	−	1.42399i	−0.904087	−	0.427349i	$-0.859448\pi$
$131$	−9.40980	−	16.2983i	−0.822138	−	1.42399i	0.0819487	−	0.996637i	$-0.473886\pi$
$132$		0			0
$133$	−15.9320	+	7.37690i	−1.38148	+	0.639658i
$134$		0			0
$135$	−2.31472	−	4.00921i	−0.199219	−	0.345058i
$136$		0			0
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	−0.967320	−	0.253557i	$-0.918399\pi$
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	0.703247	+	0.710945i	$0.251733\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−14.6351			−1.23250
$142$		0			0
$143$	0.358181	−	0.620387i	0.0299526	−	0.0518794i
$144$		0			0
$145$	−1.47542	−	2.55550i	−0.122527	−	0.212223i
$146$		0			0
$147$	−7.96572	+	9.38972i	−0.657002	+	0.774451i
$148$		0			0
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	0.868675	+	0.495382i	$0.164972\pi$
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	−0.00532425	+	0.999986i	$0.501695\pi$
$150$		0			0
$151$	−7.86171	+	13.6169i	−0.639777	+	1.10813i	0.345704	+	0.938344i	$0.387640\pi$
$151$	−7.86171	+	13.6169i	−0.639777	+	1.10813i	−0.985481	+	0.169783i	$0.945693\pi$
$152$		0			0
$153$	0.221768			0.0179289
$154$		0			0
$155$	−1.42244			−0.114253
$156$		0			0
$157$	3.89250	−	6.74200i	0.310655	−	0.538070i	−0.667849	−	0.744297i	$-0.732785\pi$
$157$	3.89250	−	6.74200i	0.310655	−	0.538070i	0.978504	+	0.206226i	$0.0661183\pi$
$158$		0			0
$159$	12.3866	+	21.4543i	0.982323	+	1.70143i
$160$		0			0
$161$	−9.02503	+	4.17881i	−0.711272	+	0.329336i
$162$		0			0
$163$	0.844956	+	1.46351i	0.0661820	+	0.114631i	0.897218	−	0.441588i	$-0.145585\pi$
$163$	0.844956	+	1.46351i	0.0661820	+	0.114631i	−0.831036	+	0.556219i	$0.812252\pi$
$164$		0			0
$165$	−0.570659	+	0.988410i	−0.0444257	+	0.0769476i
$166$		0			0
$167$	21.8667			1.69210			0.846049	−	0.533105i	$-0.178975\pi$
$167$	21.8667			1.69210			0.846049	+	0.533105i	$0.178975\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	0.312812	−	0.541805i	0.0239213	−	0.0414329i
$172$		0			0
$173$	−2.92061	−	5.05865i	−0.222050	−	0.384602i	0.733380	−	0.679819i	$-0.237942\pi$
$173$	−2.92061	−	5.05865i	−0.222050	−	0.384602i	−0.955430	+	0.295217i	$0.904608\pi$
$174$		0			0
$175$	9.04132	+	6.36725i	0.683460	+	0.481319i
$176$		0			0
$177$	−0.630060	−	1.09130i	−0.0473582	−	0.0820268i
$178$		0			0
$179$	1.26714	−	2.19475i	0.0947103	−	0.164043i	−0.814777	−	0.579774i	$-0.803141\pi$
$179$	1.26714	−	2.19475i	0.0947103	−	0.164043i	0.909488	+	0.415731i	$0.136474\pi$
$180$		0			0
$181$	−10.7248			−0.797169			−0.398585	−	0.917132i	$-0.630498\pi$
$181$	−10.7248			−0.797169			−0.398585	+	0.917132i	$0.630498\pi$
$182$		0			0
$183$	20.4977			1.51523
$184$		0			0
$185$	−2.35887	+	4.08569i	−0.173428	+	0.300386i
$186$		0			0
$187$	0.842538	+	1.45932i	0.0616125	+	0.106716i
$188$		0			0
$189$	−1.21501	+	13.4686i	−0.0883787	+	0.979697i
$190$		0			0
$191$	−0.839303	−	1.45371i	−0.0607298	−	0.105187i	0.834062	−	0.551671i	$-0.186009\pi$
$191$	−0.839303	−	1.45371i	−0.0607298	−	0.105187i	−0.894792	+	0.446484i	$0.852676\pi$
$192$		0			0
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	−0.726344	−	0.687331i	$-0.758782\pi$
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	0.958418	+	0.285367i	$0.0921154\pi$
$194$		0			0
$195$	−1.59322			−0.114093
$196$		0			0
$197$	1.87251			0.133411			0.0667054	−	0.997773i	$-0.478751\pi$
$197$	1.87251			0.133411			0.0667054	+	0.997773i	$0.478751\pi$
$198$		0			0
$199$	−5.69833	+	9.86979i	−0.403944	+	0.699651i	−0.994198	−	0.107566i	$-0.965694\pi$
$199$	−5.69833	+	9.86979i	−0.403944	+	0.699651i	0.590254	+	0.807217i	$0.299028\pi$
$200$		0			0
$201$	−8.26030	−	14.3073i	−0.582637	−	1.00916i
$202$		0			0
$203$	−0.774453	+	8.58498i	−0.0543559	+	0.602547i
$204$		0			0
$205$	−2.22883	−	3.86045i	−0.155669	−	0.269626i
$206$		0			0
$207$	0.177199	−	0.306918i	0.0123162	−	0.0213322i
$208$		0			0
$209$	4.75371			0.328821
$210$		0			0
$211$	−7.53599			−0.518799			−0.259400	−	0.965770i	$-0.583525\pi$
$211$	−7.53599			−0.518799			−0.259400	+	0.965770i	$0.583525\pi$
$212$		0			0
$213$	−9.66725	+	16.7442i	−0.662389	+	1.14729i
$214$		0			0
$215$	−4.27395	−	7.40269i	−0.291481	−	0.504859i
$216$		0			0
$217$	3.39725	+	2.39248i	0.230621	+	0.162412i
$218$		0			0
$219$	−3.05460	−	5.29072i	−0.206411	−	0.357514i
$220$		0			0
$221$	−1.17614	+	2.03713i	−0.0791154	+	0.137032i
$222$		0			0
$223$	−17.6349			−1.18092			−0.590459	−	0.807067i	$-0.701053\pi$
$223$	−17.6349			−1.18092			−0.590459	+	0.807067i	$0.701053\pi$
$224$		0			0
$225$	−0.394052			−0.0262702
$226$		0			0
$227$	−2.66452	+	4.61509i	−0.176851	+	0.306314i	−0.940800	−	0.338962i	$-0.889924\pi$
$227$	−2.66452	+	4.61509i	−0.176851	+	0.306314i	0.763950	+	0.645276i	$0.223258\pi$
$228$		0			0
$229$	4.25950	+	7.37767i	0.281476	+	0.487530i	0.971748	−	0.236019i	$-0.0758428\pi$
$229$	4.25950	+	7.37767i	0.281476	+	0.487530i	−0.690273	+	0.723549i	$0.742509\pi$
$230$		0			0
$231$	3.02539	−	1.40083i	0.199056	−	0.0921678i
$232$		0			0
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	0.777605	−	0.628752i	$-0.216434\pi$
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	−0.933318	+	0.359050i	$0.883101\pi$
$234$		0			0
$235$	−3.76774	+	6.52592i	−0.245780	+	0.425704i
$236$		0			0
$237$	22.8821			1.48635
$238$		0			0
$239$	−14.8314			−0.959365			−0.479682	−	0.877442i	$-0.659248\pi$
$239$	−14.8314			−0.959365			−0.479682	+	0.877442i	$0.659248\pi$
$240$		0			0
$241$	3.06066	−	5.30121i	0.197154	−	0.341481i	−0.750450	−	0.660927i	$-0.770163\pi$
$241$	3.06066	−	5.30121i	0.197154	−	0.341481i	0.947605	+	0.319446i	$0.103497\pi$
$242$		0			0
$243$	−0.489705	−	0.848195i	−0.0314146	−	0.0544117i
$244$		0			0
$245$	2.13622	+	5.96932i	0.136478	+	0.381366i
$246$		0			0
$247$	3.31796	+	5.74687i	0.211116	+	0.365664i
$248$		0			0
$249$	−3.11426	+	5.39405i	−0.197358	+	0.341834i
$250$		0			0
$251$	13.9708			0.881832			0.440916	−	0.897548i	$-0.354654\pi$
$251$	13.9708			0.881832			0.440916	+	0.897548i	$0.354654\pi$
$252$		0			0
$253$	2.69284			0.169298
$254$		0			0
$255$	1.87384	−	3.24558i	0.117344	−	0.203246i
$256$		0			0
$257$	−8.63253	−	14.9520i	−0.538482	−	0.932679i	−0.998986	−	0.0450210i	$-0.985665\pi$
$257$	−8.63253	−	14.9520i	−0.538482	−	0.932679i	0.460504	−	0.887658i	$-0.347669\pi$
$258$		0			0
$259$	12.5057	−	5.79047i	0.777069	−	0.359802i
$260$		0			0
$261$	−0.153579	−	0.266007i	−0.00950631	−	0.0164654i
$262$		0			0
$263$	−1.30336	+	2.25749i	−0.0803687	+	0.139203i	−0.903408	−	0.428781i	$-0.858943\pi$
$263$	−1.30336	+	2.25749i	−0.0803687	+	0.139203i	0.823040	+	0.567984i	$0.192276\pi$
$264$		0			0
$265$	12.7555			0.783565
$266$		0			0
$267$	−21.1967			−1.29722
$268$		0			0
$269$	7.24477	−	12.5483i	0.441721	−	0.765084i	−0.556096	−	0.831118i	$-0.687701\pi$
$269$	7.24477	−	12.5483i	0.441721	−	0.765084i	0.997817	+	0.0660343i	$0.0210347\pi$
$270$		0			0
$271$	−4.31796	−	7.47892i	−0.262297	−	0.454312i	0.704555	−	0.709650i	$-0.251147\pi$
$271$	−4.31796	−	7.47892i	−0.262297	−	0.454312i	−0.966852	+	0.255338i	$0.917813\pi$
$272$		0			0
$273$	3.80513	+	2.67972i	0.230297	+	0.162184i
$274$		0			0
$275$	−1.49708	−	2.59301i	−0.0902771	−	0.156364i
$276$		0			0
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	−0.989146	−	0.146935i	$-0.953059\pi$
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	0.621822	+	0.783158i	$0.286393\pi$
$278$		0			0
$279$	−0.148064			−0.00886437
$280$		0			0
$281$	−24.1822			−1.44259			−0.721293	−	0.692630i	$-0.756452\pi$
$281$	−24.1822			−1.44259			−0.721293	+	0.692630i	$0.756452\pi$
$282$		0			0
$283$	−15.3842	+	26.6461i	−0.914493	+	1.58395i	−0.106851	+	0.994275i	$0.534077\pi$
$283$	−15.3842	+	26.6461i	−0.914493	+	1.58395i	−0.807642	+	0.589674i	$0.799256\pi$
$284$		0			0
$285$	−5.28622	−	9.15599i	−0.313128	−	0.542354i
$286$		0			0
$287$	−1.16992	+	12.9689i	−0.0690585	+	0.765528i
$288$		0			0
$289$	5.73341	+	9.93056i	0.337259	+	0.584150i
$290$		0			0
$291$	6.54163	−	11.3304i	0.383477	−	0.664202i
$292$		0			0
$293$	−31.8295			−1.85950			−0.929749	−	0.368193i	$-0.879976\pi$
$293$	−31.8295			−1.85950			−0.929749	+	0.368193i	$0.879976\pi$
$294$		0			0
$295$	−0.648824			−0.0377760
$296$		0			0
$297$	1.83078	−	3.17100i	0.106233	−	0.184000i
$298$		0			0
$299$	1.87953	+	3.25544i	0.108696	+	0.188267i
$300$		0			0
$301$	−2.24341	+	24.8687i	−0.129308	+	1.43341i
$302$		0			0
$303$	−1.05460	−	1.82662i	−0.0605852	−	0.104937i
$304$		0			0
$305$	5.27704	−	9.14010i	0.302162	−	0.523360i
$306$		0			0
$307$	−28.7884			−1.64304			−0.821520	−	0.570179i	$-0.806874\pi$
$307$	−28.7884			−1.64304			−0.821520	+	0.570179i	$0.806874\pi$
$308$		0			0
$309$	−25.3521			−1.44223
$310$		0			0
$311$	2.75931	−	4.77927i	0.156466	−	0.271007i	−0.777126	−	0.629345i	$-0.783323\pi$
$311$	2.75931	−	4.77927i	0.156466	−	0.271007i	0.933592	+	0.358338i	$0.116656\pi$
$312$		0			0
$313$	2.42399	+	4.19848i	0.137012	+	0.237312i	0.926364	−	0.376629i	$-0.122917\pi$
$313$	2.42399	+	4.19848i	0.137012	+	0.237312i	−0.789352	+	0.613941i	$0.789583\pi$
$314$		0			0
$315$	−0.184713	−	0.130082i	−0.0104074	−	0.00732929i
$316$		0			0
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	0.953265	−	0.302134i	$-0.0976990\pi$
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	−0.738288	+	0.674485i	$0.764366\pi$
$318$		0			0
$319$	1.16695	−	2.02122i	0.0653366	−	0.113166i
$320$		0			0
$321$	23.9112			1.33459
$322$		0			0
$323$	−15.6095			−0.868534
$324$		0			0
$325$	2.08983	−	3.61970i	0.115923	−	0.200785i
$326$		0			0
$327$	−12.0714	−	20.9082i	−0.667548	−	1.15623i
$328$		0			0
$329$	19.9750	−	9.24889i	1.10125	−	0.509908i
$330$		0			0
$331$	5.67159	+	9.82348i	0.311739	+	0.539947i	0.978739	−	0.205110i	$-0.0657553\pi$
$331$	5.67159	+	9.82348i	0.311739	+	0.539947i	−0.667000	+	0.745058i	$0.732422\pi$
$332$		0			0
$333$	−0.245540	+	0.425288i	−0.0134555	+	0.0233056i
$334$		0			0
$335$	−8.50631			−0.464749
$336$		0			0
$337$	1.74149			0.0948649			0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149			0.0948649			0.0474324	+	0.998874i	$0.484896\pi$
$338$		0			0
$339$	−2.86550	+	4.96318i	−0.155632	+	0.269563i
$340$		0			0
$341$	−0.562522	−	0.974317i	−0.0304623	−	0.0527622i
$342$		0			0
$343$	4.93815	−	17.8498i	0.266635	−	0.963798i
$344$		0			0
$345$	−2.99449	−	5.18661i	−0.161218	−	0.279238i
$346$		0			0
$347$	10.5251	−	18.2301i	0.565019	−	0.978641i	−0.432029	−	0.901860i	$-0.642202\pi$
$347$	10.5251	−	18.2301i	0.565019	−	0.978641i	0.997048	−	0.0767814i	$-0.0244643\pi$
$348$		0			0
$349$	−8.35601			−0.447287			−0.223643	−	0.974671i	$-0.571795\pi$
$349$	−8.35601			−0.447287			−0.223643	+	0.974671i	$0.571795\pi$
$350$		0			0
$351$	5.11133			0.272822
$352$		0			0
$353$	4.26677	−	7.39027i	0.227097	−	0.393344i	−0.729849	−	0.683608i	$-0.760410\pi$
$353$	4.26677	−	7.39027i	0.227097	−	0.393344i	0.956947	+	0.290264i	$0.0937431\pi$
$354$		0			0
$355$	4.97758	+	8.62141i	0.264182	+	0.457577i
$356$		0			0
$357$	−9.93429	+	4.59982i	−0.525778	+	0.243448i
$358$		0			0
$359$	−8.08565	−	14.0047i	−0.426744	−	0.739142i	0.569837	−	0.821757i	$-0.307006\pi$
$359$	−8.08565	−	14.0047i	−0.426744	−	0.739142i	−0.996582	+	0.0826150i	$0.973673\pi$
$360$		0			0
$361$	−12.5177	+	21.6812i	−0.658824	+	1.14112i
$362$		0			0
$363$	18.4469			0.968212
$364$		0			0
$365$	−3.14557			−0.164647
$366$		0			0
$367$	14.0770	−	24.3821i	0.734813	−	1.27273i	−0.219992	−	0.975502i	$-0.570603\pi$
$367$	14.0770	−	24.3821i	0.734813	−	1.27273i	0.954805	−	0.297232i	$-0.0960636\pi$
$368$		0			0
$369$	−0.232004	−	0.401842i	−0.0120776	−	0.0209191i
$370$		0			0
$371$	−30.4644	−	21.4543i	−1.58164	−	1.11385i
$372$		0			0
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	0.953425	+	0.301630i	$0.0975308\pi$
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	−0.215493	+	0.976505i	$0.569136\pi$
$374$		0			0
$375$	−7.31259	+	12.6658i	−0.377621	+	0.654058i
$376$		0			0
$377$	3.25799			0.167795
$378$		0			0
$379$	7.26263			0.373056			0.186528	−	0.982450i	$-0.440276\pi$
$379$	7.26263			0.373056			0.186528	+	0.982450i	$0.440276\pi$
$380$		0			0
$381$	0.836286	−	1.44849i	0.0428442	−	0.0742083i
$382$		0			0
$383$	6.46627	+	11.1999i	0.330411	+	0.572289i	0.982592	−	0.185774i	$-0.0594793\pi$
$383$	6.46627	+	11.1999i	0.330411	+	0.572289i	−0.652181	+	0.758063i	$0.726146\pi$
$384$		0			0
$385$	0.154231	−	1.70968i	0.00786034	−	0.0871336i
$386$		0			0
$387$	−0.444884	−	0.770561i	−0.0226147	−	0.0391698i
$388$		0			0
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	−0.463312	−	0.886195i	$-0.653339\pi$
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	0.999124	−	0.0418574i	$-0.0133275\pi$
$390$		0			0
$391$	−8.84232			−0.447175
$392$		0			0
$393$	−33.1047			−1.66991
$394$		0			0
$395$	5.89089	−	10.2033i	0.296403	−	0.513384i
$396$		0			0
$397$	−9.60366	−	16.6340i	−0.481994	−	0.834838i	0.517792	−	0.855506i	$-0.326754\pi$
$397$	−9.60366	−	16.6340i	−0.481994	−	0.834838i	−0.999786	+	0.0206683i	$0.993421\pi$
$398$		0			0
$399$	−2.77476	+	30.7588i	−0.138912	+	1.53987i
$400$		0			0
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	0.579344	−	0.815083i	$-0.303309\pi$
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	−0.995555	+	0.0941856i	$0.969975\pi$
$402$		0			0
$403$	0.785250	−	1.36009i	0.0391161	−	0.0677510i
$404$		0			0
$405$	−8.39961			−0.417380
$406$		0			0
$407$	−3.73140			−0.184959
$408$		0			0
$409$	−6.17416	+	10.6940i	−0.305293	+	0.528782i	−0.977326	−	0.211738i	$-0.932088\pi$
$409$	−6.17416	+	10.6940i	−0.305293	+	0.528782i	0.672034	+	0.740520i	$0.265421\pi$
$410$		0			0
$411$	5.43706	+	9.41727i	0.268190	+	0.464520i
$412$		0			0
$413$	1.54961	+	1.09130i	0.0762513	+	0.0536991i
$414$		0			0
$415$	1.60350	+	2.77735i	0.0787128	+	0.136335i
$416$		0			0
$417$	3.51811	−	6.09355i	0.172283	−	0.298402i
$418$		0			0
$419$	−4.35934			−0.212968			−0.106484	−	0.994314i	$-0.533959\pi$
$419$	−4.35934			−0.212968			−0.106484	+	0.994314i	$0.533959\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	−0.392192	+	0.679296i	−0.0190690	+	0.0330285i
$424$		0			0
$425$	4.91586	+	8.51451i	0.238454	+	0.413015i
$426$		0			0
$427$	−27.9766	+	12.9538i	−1.35388	+	0.626881i
$428$		0			0
$429$	−0.630060	−	1.09130i	−0.0304196	−	0.0526882i
$430$		0			0
$431$	−11.6813	+	20.2326i	−0.562667	+	0.974569i	0.434595	+	0.900626i	$0.356891\pi$
$431$	−11.6813	+	20.2326i	−0.562667	+	0.974569i	−0.997262	+	0.0739426i	$0.976442\pi$
$432$		0			0
$433$	−2.71285			−0.130371			−0.0651856	−	0.997873i	$-0.520764\pi$
$433$	−2.71285			−0.130371			−0.0651856	+	0.997873i	$0.520764\pi$
$434$		0			0
$435$	−5.19068			−0.248874
$436$		0			0
$437$	−12.4724	+	21.6028i	−0.596635	+	1.03340i
$438$		0			0
$439$	−4.41760	−	7.65150i	−0.210840	−	0.365186i	0.741137	−	0.671353i	$-0.234287\pi$
$439$	−4.41760	−	7.65150i	−0.210840	−	0.365186i	−0.951978	+	0.306167i	$0.900953\pi$
$440$		0			0
$441$	0.222363	+	0.621359i	0.0105887	+	0.0295885i
$442$		0			0
$443$	−1.45279	−	2.51630i	−0.0690240	−	0.119553i	0.829448	−	0.558584i	$-0.188655\pi$
$443$	−1.45279	−	2.51630i	−0.0690240	−	0.119553i	−0.898472	+	0.439031i	$0.855322\pi$
$444$		0			0
$445$	−5.45700	+	9.45179i	−0.258686	+	0.448058i
$446$		0			0
$447$	37.0758			1.75362
$448$		0			0
$449$	−15.2777			−0.720998			−0.360499	−	0.932760i	$-0.617394\pi$
$449$	−15.2777			−0.720998			−0.360499	+	0.932760i	$0.617394\pi$
$450$		0			0
$451$	1.76285	−	3.05334i	0.0830093	−	0.143776i
$452$		0			0
$453$	13.8292	+	23.9529i	0.649752	+	1.12540i
$454$		0			0
$455$	2.17452	−	1.00686i	0.101943	−	0.0472022i
$456$		0			0
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	−0.998027	−	0.0627815i	$-0.980003\pi$
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	0.444643	−	0.895708i	$-0.353330\pi$
$458$		0			0
$459$	−6.01161	+	10.4124i	−0.280598	+	0.486010i
$460$		0			0
$461$	−26.6170			−1.23968			−0.619839	−	0.784729i	$-0.712802\pi$
$461$	−26.6170			−1.23968			−0.619839	+	0.784729i	$0.712802\pi$
$462$		0			0
$463$	1.44250			0.0670385			0.0335193	−	0.999438i	$-0.489328\pi$
$463$	1.44250			0.0670385			0.0335193	+	0.999438i	$0.489328\pi$
$464$		0			0
$465$	−1.25107	+	2.16692i	−0.0580171	+	0.100488i
$466$		0			0
$467$	−4.19480	−	7.26560i	−0.194112	−	0.336212i	0.752497	−	0.658596i	$-0.228849\pi$
$467$	−4.19480	−	7.26560i	−0.194112	−	0.336212i	−0.946609	+	0.322384i	$0.895516\pi$
$468$		0			0
$469$	20.3159	+	14.3073i	0.938102	+	0.660648i
$470$		0			0
$471$	−6.84712	−	11.8596i	−0.315499	−	0.546460i
$472$		0			0
$473$	3.38039	−	5.85500i	0.155430	−	0.269213i
$474$		0			0
$475$	27.7359			1.27261
$476$		0			0
$477$	1.32775			0.0607934
$478$		0			0
$479$	6.30608	−	10.9225i	0.288132	−	0.499060i	−0.685232	−	0.728325i	$-0.740299\pi$
$479$	6.30608	−	10.9225i	0.288132	−	0.499060i	0.973364	+	0.229265i	$0.0736324\pi$
$480$		0			0
$481$	−2.60441	−	4.51098i	−0.118751	−	0.205683i
$482$		0			0
$483$	−1.57182	+	17.4240i	−0.0715204	+	0.792819i
$484$		0			0
$485$	−3.36823	−	5.83394i	−0.152943	−	0.264905i
$486$		0			0
$487$	10.7840	−	18.6785i	0.488671	−	0.846403i	−0.511244	−	0.859435i	$-0.670815\pi$
$487$	10.7840	−	18.6785i	0.488671	−	0.846403i	0.999915	+	0.0130329i	$0.00414861\pi$
$488$		0			0
$489$	2.97265			0.134428
$490$		0			0
$491$	−39.2347			−1.77064			−0.885318	−	0.464987i	$-0.846059\pi$
$491$	−39.2347			−1.77064			−0.885318	+	0.464987i	$0.846059\pi$
$492$		0			0
$493$	−3.83184	+	6.63694i	−0.172577	+	0.298913i
$494$		0			0
$495$	0.0305850	+	0.0529748i	0.00137469	+	0.00238104i
$496$		0			0
$497$	2.61275	−	28.9629i	0.117198	−	1.29916i
$498$		0			0
$499$	4.58407	+	7.93984i	0.205211	+	0.355436i	0.950200	−	0.311641i	$-0.100879\pi$
$499$	4.58407	+	7.93984i	0.205211	+	0.355436i	−0.744989	+	0.667077i	$0.767545\pi$
$500$		0			0
$501$	19.2324	−	33.3115i	0.859240	−	1.48825i
$502$		0			0
$503$	−24.9370			−1.11188			−0.555942	−	0.831221i	$-0.687642\pi$
$503$	−24.9370			−1.11188			−0.555942	+	0.831221i	$0.687642\pi$
$504$		0			0
$505$	−1.08601			−0.0483267
$506$		0			0
$507$	0.879528	−	1.52339i	0.0390612	−	0.0676560i
$508$		0			0
$509$	−2.94904	−	5.10788i	−0.130714	−	0.226403i	0.793238	−	0.608912i	$-0.208394\pi$
$509$	−2.94904	−	5.10788i	−0.130714	−	0.226403i	−0.923952	+	0.382509i	$0.875060\pi$
$510$		0			0
$511$	7.51268	+	5.29072i	0.332341	+	0.234048i
$512$		0			0
$513$	16.9592	+	29.3741i	0.748765	+	1.29690i
$514$		0			0
$515$	−6.52677	+	11.3047i	−0.287604	+	0.498144i
$516$		0			0
$517$	−5.96003			−0.262122
$518$		0			0
$519$	−10.2750			−0.451024
$520$		0			0
$521$	18.5948	−	32.2071i	0.814652	−	1.41102i	−0.0949259	−	0.995484i	$-0.530261\pi$
$521$	18.5948	−	32.2071i	0.814652	−	1.41102i	0.909578	−	0.415534i	$-0.136405\pi$
$522$		0			0
$523$	−2.54540	−	4.40876i	−0.111303	−	0.192782i	0.804993	−	0.593284i	$-0.202169\pi$
$523$	−2.54540	−	4.40876i	−0.111303	−	0.192782i	−0.916296	+	0.400502i	$0.868836\pi$
$524$		0			0
$525$	17.6519	−	8.17325i	0.770392	−	0.356710i
$526$		0			0
$527$	1.84712	+	3.19931i	0.0804618	+	0.139364i
$528$		0			0
$529$	4.43475	−	7.68121i	0.192815	−	0.333966i
$530$		0			0
$531$	−0.0675374			−0.00293087
$532$		0			0
$533$	4.92168			0.213181
$534$		0			0
$535$	6.15583	−	10.6622i	0.266140	−	0.460968i
$536$		0			0
$537$	−2.22897	−	3.86068i	−0.0961870	−	0.166601i
$538$		0			0
$539$	−3.24397	+	3.82389i	−0.139728	+	0.164707i
$540$		0			0
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	0.874150	−	0.485656i	$-0.161419\pi$
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	−0.857665	+	0.514208i	$0.828086\pi$
$542$		0			0
$543$	−9.43277	+	16.3380i	−0.404799	+	0.701133i
$544$		0			0
$545$	−12.4309			−0.532480
$546$		0			0
$547$	−14.1428			−0.604702			−0.302351	−	0.953197i	$-0.597771\pi$
$547$	−14.1428			−0.604702			−0.302351	+	0.953197i	$0.597771\pi$
$548$		0			0
$549$	0.549297	−	0.951411i	0.0234434	−	0.0406052i
$550$		0			0
$551$	10.8099	+	18.7233i	0.460516	+	0.797637i
$552$		0			0
$553$	−31.2310	+	14.4607i	−1.32808	+	0.614932i
$554$		0			0
$555$	4.14939	+	7.18696i	0.176132	+	0.305069i
$556$		0			0
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	−0.472782	−	0.881180i	$-0.656750\pi$
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	0.999515	−	0.0311490i	$-0.00991664\pi$
$558$		0			0
$559$	9.43766			0.399171
$560$		0			0
$561$	2.96414			0.125146
$562$		0			0
$563$	22.0047	−	38.1133i	0.927388	−	1.60628i	0.139713	−	0.990192i	$-0.455382\pi$
$563$	22.0047	−	38.1133i	0.927388	−	1.60628i	0.787675	−	0.616091i	$-0.211285\pi$
$564$		0			0
$565$	1.47542	+	2.55550i	0.0620713	+	0.107511i
$566$		0			0
$567$	20.0611	+	14.1278i	0.842487	+	0.593312i
$568$		0			0
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	0.969434	+	0.245353i	$0.0789040\pi$
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	−0.272235	+	0.962231i	$0.587763\pi$
$570$		0			0
$571$	−6.17699	+	10.6989i	−0.258499	+	0.447734i	−0.965840	−	0.259139i	$-0.916561\pi$
$571$	−6.17699	+	10.6989i	−0.258499	+	0.447734i	0.707341	+	0.706873i	$0.249895\pi$
$572$		0			0
$573$	−2.95276			−0.123353
$574$		0			0
$575$	15.7116			0.655219
$576$		0			0
$577$	12.9829	−	22.4871i	0.540486	−	0.936150i	−0.458390	−	0.888751i	$-0.651574\pi$
$577$	12.9829	−	22.4871i	0.540486	−	0.936150i	0.998876	−	0.0473984i	$-0.0150930\pi$
$578$		0			0
$579$	−5.67133	−	9.82304i	−0.235693	−	0.408232i
$580$		0			0
$581$	0.841685	−	9.33026i	0.0349190	−	0.387085i
$582$		0			0
$583$	5.04435	+	8.73707i	0.208916	+	0.361853i
$584$		0			0
$585$	−0.0426950	+	0.0739499i	−0.00176522	+	0.00305745i
$586$		0			0
$587$	23.9747			0.989543			0.494771	−	0.869023i	$-0.335252\pi$
$587$	23.9747			0.989543			0.494771	+	0.869023i	$0.335252\pi$
$588$		0			0
$589$	10.4217			0.429418
$590$		0			0
$591$	1.64693	−	2.85256i	0.0677454	−	0.117339i
$592$		0			0
$593$	−23.5240	−	40.7448i	−0.966015	−	1.67319i	−0.706862	−	0.707352i	$-0.749890\pi$
$593$	−23.5240	−	40.7448i	−0.966015	−	1.67319i	−0.259154	−	0.965836i	$-0.583444\pi$
$594$		0			0
$595$	−0.506439	+	5.61398i	−0.0207620	+	0.230151i
$596$		0			0
$597$	10.0237	+	17.3615i	0.410242	+	0.710560i
$598$		0			0
$599$	10.0868	−	17.4708i	0.412135	−	0.713840i	−0.582988	−	0.812481i	$-0.698116\pi$
$599$	10.0868	−	17.4708i	0.412135	−	0.713840i	0.995123	+	0.0986415i	$0.0314497\pi$
$600$		0			0
$601$	29.5773			1.20648			0.603242	−	0.797558i	$-0.293875\pi$
$601$	29.5773			1.20648			0.603242	+	0.797558i	$0.293875\pi$
$602$		0			0
$603$	−0.885439			−0.0360579
$604$		0			0
$605$	4.74907	−	8.22564i	0.193077	−	0.334420i
$606$		0			0
$607$	−7.72099	−	13.3732i	−0.313385	−	0.542799i	0.665708	−	0.746213i	$-0.268130\pi$
$607$	−7.72099	−	13.3732i	−0.313385	−	0.542799i	−0.979093	+	0.203413i	$0.934796\pi$
$608$		0			0
$609$	12.3971	+	8.73052i	0.502356	+	0.353779i
$610$		0			0
$611$	−4.15993	−	7.20521i	−0.168293	−	0.291492i
$612$		0			0
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	−0.885465	−	0.464706i	$-0.846160\pi$
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	0.845180	+	0.534482i	$0.179493\pi$
$614$		0			0
$615$	−7.84129			−0.316191
$616$		0			0
$617$	−2.85584			−0.114972			−0.0574858	−	0.998346i	$-0.518308\pi$
$617$	−2.85584			−0.114972			−0.0574858	+	0.998346i	$0.518308\pi$
$618$		0			0
$619$	15.9911	−	27.6975i	0.642738	−	1.11326i	−0.342080	−	0.939671i	$-0.611132\pi$
$619$	15.9911	−	27.6975i	0.642738	−	1.11326i	0.984819	−	0.173585i	$-0.0555351\pi$
$620$		0			0
$621$	9.60688	+	16.6396i	0.385511	+	0.667725i
$622$		0			0
$623$	28.9307	−	13.3956i	1.15908	−	0.536684i
$624$		0			0
$625$	−6.68398	−	11.5770i	−0.267359	−	0.463080i
$626$		0			0
$627$	4.18102	−	7.24174i	0.166974	−	0.289207i
$628$		0			0
$629$	12.2526			0.488542
$630$		0			0
$631$	−32.1115			−1.27834			−0.639169	−	0.769066i	$-0.720722\pi$
$631$	−32.1115			−1.27834			−0.639169	+	0.769066i	$0.720722\pi$
$632$		0			0
$633$	−6.62812	+	11.4802i	−0.263444	+	0.456298i
$634$		0			0
$635$	−0.430596	−	0.745814i	−0.0170877	−	0.0295967i
$636$		0			0
$637$	−6.88699	−	1.25275i	−0.272872	−	0.0496357i
$638$		0			0
$639$	0.518126	+	0.897420i	0.0204967	+	0.0355014i
$640$		0			0
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	0.330387	+	0.943845i	$0.392821\pi$
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	−0.982588	+	0.185799i	$0.940513\pi$
$642$		0			0
$643$	−15.7942			−0.622863			−0.311432	−	0.950269i	$-0.600808\pi$
$643$	−15.7942			−0.622863			−0.311432	+	0.950269i	$0.600808\pi$
$644$		0			0
$645$	−15.0362			−0.592051
$646$		0			0
$647$	−2.32036	+	4.01898i	−0.0912227	+	0.158002i	−0.908026	−	0.418914i	$-0.862411\pi$
$647$	−2.32036	+	4.01898i	−0.0912227	+	0.158002i	0.816803	+	0.576916i	$0.195744\pi$
$648$		0			0
$649$	−0.256587	−	0.444421i	−0.0100719	−	0.0174451i
$650$		0			0
$651$	6.63265	−	3.07108i	0.259954	−	0.120365i
$652$		0			0
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	−0.999578	−	0.0290430i	$-0.990754\pi$
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	0.474637	−	0.880182i	$-0.342579\pi$
$654$		0			0
$655$	−8.52266	+	14.7617i	−0.333008	+	0.576787i
$656$		0			0
$657$	−0.327429			−0.0127742
$658$		0			0
$659$	42.9889			1.67461			0.837306	−	0.546735i	$-0.184129\pi$
$659$	42.9889			1.67461			0.837306	+	0.546735i	$0.184129\pi$
$660$		0			0
$661$	14.7349	−	25.5216i	0.573122	−	0.992676i	−0.423121	−	0.906073i	$-0.639066\pi$
$661$	14.7349	−	25.5216i	0.573122	−	0.992676i	0.996243	−	0.0866030i	$-0.0276012\pi$
$662$		0			0
$663$	2.06889	+	3.58342i	0.0803490	+	0.139169i
$664$		0			0
$665$	13.0013	+	9.15599i	0.504167	+	0.355054i
$666$		0			0
$667$	6.12349	+	10.6062i	0.237102	+	0.410673i
$668$		0			0
$669$	−15.5104	+	26.8647i	−0.599666	+	1.03865i
$670$		0			0
$671$	8.34752			0.322252
$672$		0			0
$673$	−20.1702			−0.777504			−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702			−0.777504			−0.388752	+	0.921342i	$0.627094\pi$
$674$		0			0
$675$	10.6818	−	18.5015i	0.411144	−	0.712122i
$676$		0			0
$677$	3.10241	+	5.37353i	0.119235	+	0.206521i	0.919465	−	0.393172i	$-0.128622\pi$
$677$	3.10241	+	5.37353i	0.119235	+	0.206521i	−0.800230	+	0.599694i	$0.795289\pi$
$678$		0			0
$679$	−1.76800	+	19.5986i	−0.0678495	+	0.752126i
$680$		0			0
$681$	4.68704	+	8.11820i	0.179608	+	0.311090i
$682$		0			0
$683$	−0.884758	+	1.53245i	−0.0338543	+	0.0586374i	−0.882456	−	0.470395i	$-0.844112\pi$
$683$	−0.884758	+	1.53245i	−0.0338543	+	0.0586374i	0.848602	+	0.529032i	$0.177445\pi$
$684$		0			0
$685$	5.59899			0.213926
$686$		0			0
$687$	14.9854			0.571729
$688$		0			0
$689$	−7.04163	+	12.1965i	−0.268265	+	0.464648i
$690$		0			0
$691$	22.4658	+	38.9120i	0.854641	+	1.48028i	0.876977	+	0.480531i	$0.159556\pi$
$691$	22.4658	+	38.9120i	0.854641	+	1.48028i	−0.0223363	+	0.999751i	$0.507110\pi$
$692$		0			0
$693$	0.0160542	−	0.177964i	0.000609849	−	0.00676031i
$694$		0			0
$695$	−1.81144	−	3.13751i	−0.0687120	−	0.119013i
$696$		0			0
$697$	−5.78856	+	10.0261i	−0.219257	+	0.379765i
$698$		0			0
$699$	−8.36204			−0.316281
$700$		0			0
$701$	38.5707			1.45679			0.728397	−	0.685156i	$-0.240266\pi$
$701$	38.5707			1.45679			0.728397	+	0.685156i	$0.240266\pi$
$702$		0			0
$703$	17.2827	−	29.9344i	0.651828	−	1.12900i
$704$		0			0
$705$	6.62767	+	11.4795i	0.249612	+	0.432341i
$706$		0			0
$707$	2.59375	+	1.82662i	0.0975480	+	0.0686972i
$708$		0			0
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	0.771772	−	0.635900i	$-0.219371\pi$
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	−0.936591	+	0.350424i	$0.886037\pi$
$710$		0			0
$711$	0.613194	−	1.06208i	0.0229966	−	0.0398312i
$712$		0			0
$713$	5.90360			0.221091
$714$		0			0
$715$	−0.648824			−0.0242646
$716$		0			0
$717$	−13.0447	+	22.5940i	−0.487161	+	0.843788i
$718$		0			0
$719$	2.10218	+	3.64109i	0.0783982	+	0.135790i	0.902559	−	0.430566i	$-0.141686\pi$
$719$	2.10218	+	3.64109i	0.0783982	+	0.135790i	−0.824161	+	0.566356i	$0.808353\pi$
$720$		0			0
$721$	34.6022	−	16.0216i	1.28865	−	0.596677i
$722$		0			0
$723$	−5.38386	−	9.32513i	−0.200228	−	0.346805i
$724$		0			0
$725$	6.80866	−	11.7930i	0.252867	−	0.437979i
$726$		0			0
$727$	28.9856			1.07502			0.537509	−	0.843258i	$-0.319366\pi$
$727$	28.9856			1.07502			0.537509	+	0.843258i	$0.319366\pi$
$728$		0			0
$729$	26.0990			0.966630
$730$		0			0
$731$	−11.1000	+	19.2257i	−0.410547	+	0.711089i
$732$		0			0
$733$	12.0172	+	20.8145i	0.443867	+	0.768800i	0.997972	−	0.0636467i	$-0.0202731\pi$
$733$	12.0172	+	20.8145i	0.443867	+	0.768800i	−0.554106	+	0.832446i	$0.686940\pi$
$734$		0			0
$735$	10.9725	+	1.99590i	0.404725	+	0.0736198i
$736$		0			0
$737$	−3.36394	−	5.82652i	−0.123912	−	0.214622i
$738$		0			0
$739$	5.90276	−	10.2239i	0.217136	−	0.376091i	−0.736795	−	0.676116i	$-0.763662\pi$
$739$	5.90276	−	10.2239i	0.217136	−	0.376091i	0.953931	+	0.300025i	$0.0969950\pi$
$740$		0			0
$741$	11.6729			0.428816
$742$		0			0
$743$	−47.2786			−1.73448			−0.867241	−	0.497888i	$-0.834109\pi$
$743$	−47.2786			−1.73448			−0.867241	+	0.497888i	$0.834109\pi$
$744$		0			0
$745$	9.54499	−	16.5324i	0.349701	−	0.605700i
$746$		0			0
$747$	0.166912	+	0.289100i	0.00610698	+	0.0105776i
$748$		0			0
$749$	−32.6356	+	15.1111i	−1.19248	+	0.552147i
$750$		0			0
$751$	2.73850	+	4.74322i	0.0999294	+	0.173083i	0.911655	−	0.410956i	$-0.134805\pi$
$751$	2.73850	+	4.74322i	0.0999294	+	0.173083i	−0.811726	+	0.584039i	$0.801472\pi$
$752$		0			0
$753$	12.2877	−	21.2830i	0.447790	−	0.775596i
$754$		0			0
$755$	14.2410			0.518285
$756$		0			0
$757$	10.7453			0.390546			0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453			0.390546			0.195273	+	0.980749i	$0.437441\pi$
$758$		0			0
$759$	2.36843	−	4.10224i	0.0859686	−	0.148902i
$760$		0			0
$761$	16.5200	+	28.6134i	0.598848	+	1.03724i	0.992991	+	0.118186i	$0.0377080\pi$
$761$	16.5200	+	28.6134i	0.598848	+	1.03724i	−0.394143	+	0.919049i	$0.628959\pi$
$762$		0			0
$763$	29.6891	+	20.9082i	1.07482	+	0.756928i
$764$		0			0
$765$	−0.100430	−	0.173950i	−0.00363106	−	0.00628918i
$766$		0			0
$767$	0.358181	−	0.620387i	0.0129332	−	0.0224009i
$768$		0			0
$769$	2.98332			0.107581			0.0537907	−	0.998552i	$-0.482870\pi$
$769$	2.98332			0.107581			0.0537907	+	0.998552i	$0.482870\pi$
$770$		0			0
$771$	−30.3702			−1.09376
$772$		0			0
$773$	10.9543	−	18.9733i	0.393998	−	0.682424i	−0.598975	−	0.800768i	$-0.704425\pi$
$773$	10.9543	−	18.9733i	0.393998	−	0.682424i	0.992973	+	0.118344i	$0.0377585\pi$
$774$		0			0
$775$	−3.28208	−	5.68473i	−0.117896	−	0.204202i
$776$		0			0
$777$	2.17803	−	24.1440i	0.0781365	−	0.866160i
$778$		0			0
$779$	16.3299	+	28.2842i	0.585079	+	1.01339i
$780$		0			0
$781$	−3.93691	+	6.81892i	−0.140874	+	0.244000i
$782$		0			0
$783$	16.6527			0.595118
$784$		0			0
$785$	−7.05104			−0.251662
$786$		0			0
$787$	−6.68161	+	11.5729i	−0.238174	+	0.412529i	−0.960190	−	0.279347i	$-0.909882\pi$
$787$	−6.68161	+	11.5729i	−0.238174	+	0.412529i	0.722017	+	0.691876i	$0.243215\pi$
$788$		0			0
$789$	2.29269	+	3.97105i	0.0816218	+	0.141373i
$790$		0			0
$791$	0.774453	−	8.58498i	0.0275364	−	0.305247i
$792$		0			0
$793$	5.82633	+	10.0915i	0.206899	+	0.358360i
$794$		0			0
$795$	11.2188	−	19.4316i	0.397891	−	0.689167i
$796$		0			0
$797$	32.5388			1.15258			0.576292	−	0.817244i	$-0.304499\pi$
$797$	32.5388			1.15258			0.576292	+	0.817244i	$0.304499\pi$
$798$		0			0
$799$	19.5706			0.692357
$800$		0			0
$801$	−0.568030	+	0.983857i	−0.0200703	+	0.0347629i
$802$		0			0
$803$	−1.24396	−	2.15460i	−0.0438984	−	0.0760343i
$804$		0			0
$805$	7.36484	+	5.18661i	0.259577	+	0.182804i
$806$		0			0
$807$	−12.7440	−	22.0732i	−0.448608	−	0.777013i
$808$		0			0
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	−0.925656	−	0.378367i	$-0.876486\pi$
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	0.790503	+	0.612458i	$0.209819\pi$
$810$		0			0
$811$	48.3178			1.69667			0.848334	−	0.529461i	$-0.177606\pi$
$811$	48.3178			1.69667			0.848334	+	0.529461i	$0.177606\pi$
$812$		0			0
$813$	−15.1911			−0.532773
$814$		0			0
$815$	0.765295	−	1.32553i	0.0268071	−	0.0464313i
$816$		0			0
$817$	31.3137	+	54.2370i	1.09553	+	1.89751i
$818$		0			0
$819$	0.226351	−	0.104806i	0.00790933	−	0.00366221i
$820$		0			0
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	0.896768	−	0.442502i	$-0.145909\pi$
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	−0.831602	+	0.555373i	$0.812576\pi$
$822$		0			0
$823$	7.11590	−	12.3251i	0.248045	−	0.429626i	−0.714939	−	0.699187i	$-0.753545\pi$
$823$	7.11590	−	12.3251i	0.248045	−	0.429626i	0.962983	+	0.269561i	$0.0868787\pi$
$824$		0			0
$825$	−5.26688			−0.183369
$826$		0			0
$827$	−48.3016			−1.67961			−0.839805	−	0.542888i	$-0.817331\pi$
$827$	−48.3016			−1.67961			−0.839805	+	0.542888i	$0.817331\pi$
$828$		0			0
$829$	−5.75506	+	9.96806i	−0.199882	+	0.346205i	−0.948490	−	0.316808i	$-0.897389\pi$
$829$	−5.75506	+	9.96806i	−0.199882	+	0.346205i	0.748608	+	0.663013i	$0.230722\pi$
$830$		0			0
$831$	10.7540	+	18.6264i	0.373051	+	0.646143i
$832$		0			0
$833$	10.6520	−	12.5563i	0.369071	−	0.435049i
$834$		0			0
$835$	−9.90258	−	17.1518i	−0.342693	−	0.593562i
$836$		0			0
$837$	4.01367	−	6.95188i	0.138733	−	0.240292i
$838$		0			0
$839$	−13.1103			−0.452616			−0.226308	−	0.974056i	$-0.572666\pi$
$839$	−13.1103			−0.452616			−0.226308	+	0.974056i	$0.572666\pi$
$840$		0			0
$841$	−18.3855			−0.633982
$842$		0			0
$843$	−21.2689	+	36.8388i	−0.732539	+	1.26880i
$844$		0			0
$845$	−0.452861	−	0.784378i	−0.0155789	−	0.0269834i
$846$		0			0
$847$	−25.1776	+	11.6578i	−0.865111	+	0.400568i
$848$		0			0
$849$	27.0616	+	46.8721i	0.928751	+	1.60864i
$850$		0			0
$851$	9.79014	−	16.9570i	0.335602	−	0.581279i
$852$		0			0
$853$	8.80346			0.301425			0.150712	−	0.988578i	$-0.451843\pi$
$853$	8.80346			0.301425			0.150712	+	0.988578i	$0.451843\pi$
$854$		0			0
$855$	−0.566640			−0.0193787
$856$		0			0
$857$	−8.48254	+	14.6922i	−0.289758	+	0.501876i	−0.973752	−	0.227612i	$-0.926908\pi$
$857$	−8.48254	+	14.6922i	−0.289758	+	0.501876i	0.683994	+	0.729488i	$0.260242\pi$
$858$		0			0
$859$	7.27049	+	12.5929i	0.248066	+	0.429663i	0.962989	−	0.269540i	$-0.0868717\pi$
$859$	7.27049	+	12.5929i	0.248066	+	0.429663i	−0.714923	+	0.699203i	$0.753538\pi$
$860$		0			0
$861$	18.7276	+	13.1887i	0.638236	+	0.449471i
$862$		0			0
$863$	19.5222	+	33.8135i	0.664544	+	1.15102i	0.979409	+	0.201887i	$0.0647074\pi$
$863$	19.5222	+	33.8135i	0.664544	+	1.15102i	−0.314865	+	0.949136i	$0.601959\pi$
$864$		0			0
$865$	−2.64526	+	4.58173i	−0.0899416	+	0.155783i
$866$		0			0
$867$	20.1708			0.685036
$868$		0			0
$869$	9.31854			0.316110
$870$		0			0
$871$	4.69587	−	8.13349i	0.159114	−	0.275593i
$872$		0			0
$873$	−0.350605	−	0.607266i	−0.0118662	−	0.0205529i
$874$		0			0
$875$	1.97636	−	21.9084i	0.0668133	−	0.740639i
$876$		0			0
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	−0.998252	−	0.0591051i	$-0.981175\pi$
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	0.447939	−	0.894064i	$-0.352158\pi$
$878$		0			0
$879$	−27.9949	+	48.4886i	−0.944245	+	1.63548i
$880$		0			0
$881$	−43.4141			−1.46266			−0.731330	−	0.682024i	$-0.761100\pi$
$881$	−43.4141			−1.46266			−0.731330	+	0.682024i	$0.761100\pi$
$882$		0			0
$883$	−28.2902			−0.952040			−0.476020	−	0.879434i	$-0.657921\pi$
$883$	−28.2902			−0.952040			−0.476020	+	0.879434i	$0.657921\pi$
$884$		0			0
$885$	−0.570659	+	0.988410i	−0.0191825	+	0.0332250i
$886$		0			0
$887$	−25.1325	−	43.5307i	−0.843866	−	1.46162i	−0.886602	−	0.462532i	$-0.846941\pi$
$887$	−25.1325	−	43.5307i	−0.843866	−	1.46162i	0.0427364	−	0.999086i	$-0.486392\pi$
$888$		0			0
$889$	−0.226022	+	2.50550i	−0.00758052	+	0.0840317i
$890$		0			0
$891$	−3.32175	−	5.75344i	−0.111283	−	0.192747i
$892$		0			0
$893$	27.6049	−	47.8131i	0.923764	−	1.60001i
$894$		0			0
$895$	−2.29535			−0.0767250
$896$		0			0
$897$	6.61239			0.220781
$898$		0			0
$899$	2.55834	−	4.43117i	0.0853253	−	0.147788i
$900$		0			0
$901$	−16.5638	−	28.6894i	−0.551821	−	0.955782i
$902$		0			0
$903$	35.9115	+	25.2903i	1.19506	+	0.841609i
$904$		0			0
$905$	4.85685	+	8.41231i	0.161447	+	0.279635i
$906$		0			0
$907$	13.4138	−	23.2334i	0.445399	−	0.771453i	−0.552681	−	0.833393i	$-0.686395\pi$
$907$	13.4138	−	23.2334i	0.445399	−	0.771453i	0.998080	+	0.0619394i	$0.0197286\pi$
$908$		0			0
$909$	−0.113045			−0.00374946
$910$		0			0
$911$	22.3560			0.740687			0.370344	−	0.928895i	$-0.379240\pi$
$911$	22.3560			0.740687			0.370344	+	0.928895i	$0.379240\pi$
$912$		0			0
$913$	−1.26826	+	2.19668i	−0.0419731	+	0.0726996i
$914$		0			0
$915$	−9.28260	−	16.0779i	−0.306873	−	0.531520i
$916$		0			0
$917$	45.1835	−	20.9211i	1.49209	−	0.690875i
$918$		0			0
$919$	−4.31122	−	7.46725i	−0.142214	−	0.246322i	0.786116	−	0.618079i	$-0.212089\pi$
$919$	−4.31122	−	7.46725i	−0.142214	−	0.246322i	−0.928330	+	0.371757i	$0.878755\pi$
$920$		0			0
$921$	−25.3202	+	43.8559i	−0.834329	+	1.44510i
$922$		0			0
$923$	−10.9914			−0.361786
$924$		0			0
$925$	−21.7712			−0.715832
$926$		0			0
$927$	−0.679385	+	1.17673i	−0.0223139	+	0.0386488i
$928$		0			0
$929$	−20.6930	−	35.8414i	−0.678916	−	1.17592i	−0.975308	−	0.220851i	$-0.929117\pi$
$929$	−20.6930	−	35.8414i	−0.678916	−	1.17592i	0.296391	−	0.955067i	$-0.404217\pi$
$930$		0			0
$931$	−15.6513	−	43.7352i	−0.512952	−	1.43336i
$932$		0			0
$933$	−4.85379	−	8.40700i	−0.158906	−	0.275233i
$934$		0			0
$935$	0.763105	−	1.32174i	0.0249562	−	0.0432254i
$936$		0			0
$937$	21.3818			0.698514			0.349257	−	0.937027i	$-0.386434\pi$
$937$	21.3818			0.698514			0.349257	+	0.937027i	$0.386434\pi$
$938$		0			0
$939$	8.52788			0.278297
$940$		0			0
$941$	26.5740	−	46.0275i	0.866288	−	1.50046i	0.000525658	−	1.00000i	$-0.499833\pi$
$941$	26.5740	−	46.0275i	0.866288	−	1.50046i	0.865762	−	0.500455i	$-0.166834\pi$
$942$		0			0
$943$	9.25043	+	16.0222i	0.301235	+	0.521755i
$944$		0			0
$945$	11.1147	−	5.14638i	0.361561	−	0.167412i
$946$		0			0
$947$	−4.43468	−	7.68109i	−0.144108	−	0.249602i	0.784932	−	0.619582i	$-0.212698\pi$
$947$	−4.43468	−	7.68109i	−0.144108	−	0.249602i	−0.929040	+	0.369980i	$0.879365\pi$
$948$		0			0
$949$	1.73650	−	3.00771i	0.0563692	−	0.0976343i
$950$		0			0
$951$	13.4658			0.436658
$952$		0			0
$953$	−39.8167			−1.28979			−0.644894	−	0.764272i	$-0.723099\pi$
$953$	−39.8167			−1.28979			−0.644894	+	0.764272i	$0.723099\pi$
$954$		0			0
$955$	−0.760174	+	1.31666i	−0.0245987	+	0.0426061i
$956$		0			0
$957$	−2.05273	−	3.55543i	−0.0663553	−	0.114931i
$958$		0			0
$959$	−13.3723	−	9.41727i	−0.431813	−	0.304099i
$960$		0			0
$961$	14.2668	+	24.7108i	0.460218	+	0.797121i
$962$		0			0
$963$	0.640773	−	1.10985i	0.0206486	−	0.0357645i
$964$		0			0
$965$	−5.84024			−0.188004
$966$		0			0
$967$	22.1611			0.712652			0.356326	−	0.934362i	$-0.384029\pi$
$967$	22.1611			0.712652			0.356326	+	0.934362i	$0.384029\pi$
$968$		0			0
$969$	−13.7290	+	23.7793i	−0.441038	+	0.763900i
$970$		0			0
$971$	18.0212	+	31.2136i	0.578327	+	1.00169i	0.995671	+	0.0929428i	$0.0296274\pi$
$971$	18.0212	+	31.2136i	0.578327	+	1.00169i	−0.417345	+	0.908748i	$0.637039\pi$
$972$		0			0
$973$	−0.950834	+	10.5402i	−0.0304824	+	0.337903i
$974$		0			0
$975$	−3.67614	−	6.36725i	−0.117731	−	0.203915i
$976$		0			0
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	0.472559	+	0.881299i	$0.343330\pi$
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	−0.999507	+	0.0314009i	$0.990003\pi$
$978$		0			0
$979$	−8.63219			−0.275886
$980$		0			0
$981$	−1.29395			−0.0413128
$982$		0			0
$983$	−2.09973	+	3.63683i	−0.0669709	+	0.115997i	−0.897567	−	0.440879i	$-0.854667\pi$
$983$	−2.09973	+	3.63683i	−0.0669709	+	0.115997i	0.830596	+	0.556876i	$0.188000\pi$
$984$		0			0
$985$	−0.847986	−	1.46876i	−0.0270191	−	0.0467984i
$986$		0			0
$987$	3.47889	−	38.5643i	0.110734	−	1.22751i
$988$		0			0
$989$	17.7383	+	30.7237i	0.564047	+	0.976958i
$990$		0			0
$991$	−6.70693	+	11.6167i	−0.213053	+	0.369018i	−0.952668	−	0.304011i	$-0.901674\pi$
$991$	−6.70693	+	11.6167i	−0.213053	+	0.369018i	0.739616	+	0.673029i	$0.235007\pi$
$992$		0			0
$993$	19.9533			0.633198
$994$		0			0
$995$	10.3222			0.327236
$996$		0			0
$997$	23.9434	−	41.4712i	0.758295	−	1.31341i	−0.185424	−	0.982659i	$-0.559366\pi$
$997$	23.9434	−	41.4712i	0.758295	−	1.31341i	0.943719	−	0.330747i	$-0.107301\pi$
$998$		0			0
$999$	−13.3120	−	23.0571i	−0.421173	−	0.729494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.p.417.4		10
4.3	odd	2		91.2.e.c.53.5	✓	10
7.2	even	3	inner	1456.2.r.p.625.4		10
12.11	even	2		819.2.j.h.235.1		10
28.3	even	6		637.2.a.k.1.1		5
28.11	odd	6		637.2.a.l.1.1		5
28.19	even	6		637.2.e.m.79.5		10
28.23	odd	6		91.2.e.c.79.5	yes	10
28.27	even	2		637.2.e.m.508.5		10
52.51	odd	2		1183.2.e.f.508.1		10
84.11	even	6		5733.2.a.bl.1.5		5
84.23	even	6		819.2.j.h.352.1		10
84.59	odd	6		5733.2.a.bm.1.5		5
364.51	odd	6		1183.2.e.f.170.1		10
364.207	odd	6		8281.2.a.bw.1.5		5
364.311	even	6		8281.2.a.bx.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	4.3	odd	2
91.2.e.c.79.5	yes	10	28.23	odd	6
637.2.a.k.1.1		5	28.3	even	6
637.2.a.l.1.1		5	28.11	odd	6
637.2.e.m.79.5		10	28.19	even	6
637.2.e.m.508.5		10	28.27	even	2
819.2.j.h.235.1		10	12.11	even	2
819.2.j.h.352.1		10	84.23	even	6
1183.2.e.f.170.1		10	364.51	odd	6
1183.2.e.f.508.1		10	52.51	odd	2
1456.2.r.p.417.4		10	1.1	even	1	trivial
1456.2.r.p.625.4		10	7.2	even	3	inner
5733.2.a.bl.1.5		5	84.11	even	6
5733.2.a.bm.1.5		5	84.59	odd	6
8281.2.a.bw.1.5		5	364.207	odd	6
8281.2.a.bx.1.5		5	364.311	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.879528 - 1.52339i) q^{3} +(-0.452861 - 0.784378i) q^{5} +(-0.237709 + 2.63505i) q^{7} +(-0.0471392 - 0.0816475i) q^{9} +(0.358181 - 0.620387i) q^{11} +1.00000 q^{13} -1.59322 q^{15} +(-1.17614 + 2.03713i) q^{17} +(3.31796 + 5.74687i) q^{19} +(3.80513 + 2.67972i) q^{21} +(1.87953 + 3.25544i) q^{23} +(2.08983 - 3.61970i) q^{25} +5.11133 q^{27} +3.25799 q^{29} +(0.785250 - 1.36009i) q^{31} +(-0.630060 - 1.09130i) q^{33} +(2.17452 - 1.00686i) q^{35} +(-2.60441 - 4.51098i) q^{37} +(0.879528 - 1.52339i) q^{39} +4.92168 q^{41} +9.43766 q^{43} +(-0.0426950 + 0.0739499i) q^{45} +(-4.15993 - 7.20521i) q^{47} +(-6.88699 - 1.25275i) q^{49} +(2.06889 + 3.58342i) q^{51} +(-7.04163 + 12.1965i) q^{53} -0.648824 q^{55} +11.6729 q^{57} +(0.358181 - 0.620387i) q^{59} +(5.82633 + 10.0915i) q^{61} +(0.226351 - 0.104806i) q^{63} +(-0.452861 - 0.784378i) q^{65} +(4.69587 - 8.13349i) q^{67} +6.61239 q^{69} -10.9914 q^{71} +(1.73650 - 3.00771i) q^{73} +(-3.67614 - 6.36725i) q^{75} +(1.54961 + 1.09130i) q^{77} +(6.50408 + 11.2654i) q^{79} +(4.63697 - 8.03147i) q^{81} -3.54083 q^{83} +2.13050 q^{85} +(2.86550 - 4.96318i) q^{87} +(-6.02503 - 10.4357i) q^{89} +(-0.237709 + 2.63505i) q^{91} +(-1.38130 - 2.39248i) q^{93} +(3.00514 - 5.20506i) q^{95} +7.43766 q^{97} -0.0675374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45}+ \cdots - 22 q^{99}+O(q^{100}) \) 10 * q - 2 * q^5 - q^7 - 3 * q^9 + 11 * q^11 + 10 * q^13 + 5 * q^17 + 9 * q^19 + 2 * q^21 + 10 * q^23 - 9 * q^25 - 6 * q^29 - 6 * q^31 - 8 * q^33 + 4 * q^35 - 4 * q^37 + 28 * q^41 - 4 * q^43 + 32 * q^45 + q^47 - 11 * q^49 - 8 * q^51 - 17 * q^53 - 32 * q^57 + 11 * q^59 + 11 * q^61 - 5 * q^63 - 2 * q^65 + 13 * q^67 + 36 * q^69 - 30 * q^71 - 20 * q^75 - 46 * q^77 + 2 * q^79 + 19 * q^81 - 12 * q^83 - 44 * q^85 - 8 * q^87 + 4 * q^89 - q^91 - 18 * q^93 - 12 * q^95 - 24 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

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