LMFDB - Embedded newform 1000.2.m.b.801.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(201,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1000.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.m (of order $5$, degree $4$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.2
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	1000.801
Dual form			1000.2.m.b.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 - 0.587785i) q^{3} +0.833366 q^{7} +(2.11803 + 1.53884i) q^{9} +(1.45608 - 1.05790i) q^{11} +(-0.892334 - 0.648319i) q^{13} +(0.642383 + 1.97705i) q^{17} +(1.28187 + 3.94520i) q^{19} +(0.159159 - 0.489840i) q^{21} +(2.07411 - 1.50693i) q^{23} +(2.80902 - 2.04087i) q^{27} +(-0.740748 + 2.27979i) q^{29} +(-2.74075 - 8.43516i) q^{31} +(-0.343734 - 1.05790i) q^{33} +(8.69331 + 6.31606i) q^{37} +(-0.551493 + 0.400683i) q^{39} +(-1.51037 - 1.09735i) q^{41} +11.0324 q^{43} +(-0.628402 + 1.93402i) q^{47} -6.30550 q^{49} +1.28477 q^{51} +(2.08052 - 6.40319i) q^{53} +2.56375 q^{57} +(10.8178 + 7.85956i) q^{59} +(-0.601258 + 0.436839i) q^{61} +(1.76510 + 1.28242i) q^{63} +(-1.37160 - 4.22134i) q^{67} +(-0.489632 - 1.50693i) q^{69} +(3.32523 - 10.2340i) q^{71} +(3.01794 - 2.19266i) q^{73} +(1.21345 - 0.881621i) q^{77} +(3.96818 - 12.2128i) q^{79} +(1.76393 + 5.42882i) q^{81} +(-2.49532 - 7.67980i) q^{83} +(1.19856 + 0.870802i) q^{87} +(-8.54813 + 6.21058i) q^{89} +(-0.743641 - 0.540287i) q^{91} -5.48150 q^{93} +(-3.03299 + 9.33458i) q^{97} +4.71197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 4 q^{7} + 8 q^{9} - 2 q^{11} - 8 q^{13} - 10 q^{17} + 3 q^{19} - 3 q^{21} - 6 q^{23} + 18 q^{27} + 6 q^{29} - 10 q^{31} + 16 q^{33} + 2 q^{37} - q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47}+ \cdots - 22 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - 4 * q^7 + 8 * q^9 - 2 * q^11 - 8 * q^13 - 10 * q^17 + 3 * q^19 - 3 * q^21 - 6 * q^23 + 18 * q^27 + 6 * q^29 - 10 * q^31 + 16 * q^33 + 2 * q^37 - q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 - 20 * q^51 + 13 * q^53 + 6 * q^57 + 29 * q^59 + 15 * q^61 - 4 * q^63 - 28 * q^67 - 12 * q^69 - 16 * q^71 - q^73 + 11 * q^77 + 23 * q^79 + 32 * q^81 - 14 * q^83 - 3 * q^87 - 7 * q^89 + 29 * q^91 - 20 * q^93 + 3 * q^97 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	−0.880666	−	0.473738i	$-0.842904\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	0.990930	+	0.134380i	$0.0429043\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.833366			0.314983			0.157491	−	0.987520i	$-0.449659\pi$
$7$	0.833366			0.314983			0.157491	+	0.987520i	$0.449659\pi$
$8$		0			0
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$		0			0
$11$	1.45608	−	1.05790i	0.439025	−	0.318970i	−0.346223	−	0.938152i	$-0.612536\pi$
$11$	1.45608	−	1.05790i	0.439025	−	0.318970i	0.785247	+	0.619182i	$0.212536\pi$
$12$		0			0
$13$	−0.892334	−	0.648319i	−0.247489	−	0.179811i	0.457124	−	0.889403i	$-0.348879\pi$
$13$	−0.892334	−	0.648319i	−0.247489	−	0.179811i	−0.704613	+	0.709592i	$0.748879\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.642383	+	1.97705i	0.155801	+	0.479505i	0.998241	−	0.0592843i	$-0.0188818\pi$
$17$	0.642383	+	1.97705i	0.155801	+	0.479505i	−0.842440	+	0.538789i	$0.818882\pi$
$18$		0			0
$19$	1.28187	+	3.94520i	0.294082	+	0.905091i	0.983528	+	0.180754i	$0.0578538\pi$
$19$	1.28187	+	3.94520i	0.294082	+	0.905091i	−0.689447	+	0.724337i	$0.742146\pi$
$20$		0			0
$21$	0.159159	−	0.489840i	0.0347313	−	0.106892i
$22$		0			0
$23$	2.07411	−	1.50693i	0.432483	−	0.314217i	−0.350158	−	0.936691i	$-0.613872\pi$
$23$	2.07411	−	1.50693i	0.432483	−	0.314217i	0.782641	+	0.622474i	$0.213872\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$		0			0
$29$	−0.740748	+	2.27979i	−0.137553	+	0.423346i	−0.995978	−	0.0895931i	$-0.971443\pi$
$29$	−0.740748	+	2.27979i	−0.137553	+	0.423346i	0.858425	+	0.512939i	$0.171443\pi$
$30$		0			0
$31$	−2.74075	−	8.43516i	−0.492253	−	1.51500i	−0.821195	−	0.570648i	$-0.806692\pi$
$31$	−2.74075	−	8.43516i	−0.492253	−	1.51500i	0.328942	−	0.944350i	$-0.393308\pi$
$32$		0			0
$33$	−0.343734	−	1.05790i	−0.0598364	−	0.184157i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.69331	+	6.31606i	1.42917	+	1.03835i	0.990170	+	0.139868i	$0.0446678\pi$
$37$	8.69331	+	6.31606i	1.42917	+	1.03835i	0.439002	+	0.898486i	$0.355332\pi$
$38$		0			0
$39$	−0.551493	+	0.400683i	−0.0883095	+	0.0641606i
$40$		0			0
$41$	−1.51037	−	1.09735i	−0.235880	−	0.171377i	0.463566	−	0.886062i	$-0.346570\pi$
$41$	−1.51037	−	1.09735i	−0.235880	−	0.171377i	−0.699446	+	0.714686i	$0.746570\pi$
$42$		0			0
$43$	11.0324			1.68243			0.841215	−	0.540701i	$-0.181841\pi$
$43$	11.0324			1.68243			0.841215	+	0.540701i	$0.181841\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.628402	+	1.93402i	−0.0916619	+	0.282106i	−0.986369	−	0.164546i	$-0.947384\pi$
$47$	−0.628402	+	1.93402i	−0.0916619	+	0.282106i	0.894707	+	0.446653i	$0.147384\pi$
$48$		0			0
$49$	−6.30550			−0.900786
$50$		0			0
$51$	1.28477			0.179903
$52$		0			0
$53$	2.08052	−	6.40319i	0.285782	−	0.879545i	−0.700382	−	0.713769i	$-0.746987\pi$
$53$	2.08052	−	6.40319i	0.285782	−	0.879545i	0.986163	−	0.165777i	$-0.0530132\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.56375			0.339576
$58$		0			0
$59$	10.8178	+	7.85956i	1.40835	+	1.02323i	0.993560	+	0.113311i	$0.0361457\pi$
$59$	10.8178	+	7.85956i	1.40835	+	1.02323i	0.414792	+	0.909916i	$0.363854\pi$
$60$		0			0
$61$	−0.601258	+	0.436839i	−0.0769832	+	0.0559316i	−0.625611	−	0.780135i	$-0.715150\pi$
$61$	−0.601258	+	0.436839i	−0.0769832	+	0.0559316i	0.548628	+	0.836067i	$0.315150\pi$
$62$		0			0
$63$	1.76510	+	1.28242i	0.222381	+	0.161569i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.37160	−	4.22134i	−0.167567	−	0.515719i	0.831649	−	0.555302i	$-0.187397\pi$
$67$	−1.37160	−	4.22134i	−0.167567	−	0.515719i	−0.999216	+	0.0395825i	$0.987397\pi$
$68$		0			0
$69$	−0.489632	−	1.50693i	−0.0589447	−	0.181413i
$70$		0			0
$71$	3.32523	−	10.2340i	0.394632	−	1.21455i	−0.534615	−	0.845095i	$-0.679544\pi$
$71$	3.32523	−	10.2340i	0.394632	−	1.21455i	0.929248	−	0.369458i	$-0.120456\pi$
$72$		0			0
$73$	3.01794	−	2.19266i	0.353223	−	0.256632i	−0.396997	−	0.917820i	$-0.629948\pi$
$73$	3.01794	−	2.19266i	0.353223	−	0.256632i	0.750220	+	0.661188i	$0.229948\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.21345	−	0.881621i	0.138285	−	0.100470i
$78$		0			0
$79$	3.96818	−	12.2128i	0.446455	−	1.37405i	−0.434426	−	0.900708i	$-0.643049\pi$
$79$	3.96818	−	12.2128i	0.446455	−	1.37405i	0.880881	−	0.473339i	$-0.156951\pi$
$80$		0			0
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$		0			0
$83$	−2.49532	−	7.67980i	−0.273897	−	0.842968i	−0.989509	−	0.144470i	$-0.953852\pi$
$83$	−2.49532	−	7.67980i	−0.273897	−	0.842968i	0.715612	−	0.698498i	$-0.246148\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.19856	+	0.870802i	0.128499	+	0.0933597i
$88$		0			0
$89$	−8.54813	+	6.21058i	−0.906100	+	0.658321i	−0.940026	−	0.341104i	$-0.889199\pi$
$89$	−8.54813	+	6.21058i	−0.906100	+	0.658321i	0.0339252	+	0.999424i	$0.489199\pi$
$90$		0			0
$91$	−0.743641	−	0.540287i	−0.0779547	−	0.0566374i
$92$		0			0
$93$	−5.48150			−0.568405
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.03299	+	9.33458i	−0.307953	+	0.947783i	0.670605	+	0.741814i	$0.266034\pi$
$97$	−3.03299	+	9.33458i	−0.307953	+	0.947783i	−0.978559	+	0.205969i	$0.933966\pi$
$98$		0			0
$99$	4.71197			0.473571
$100$		0			0
$101$	−4.87628			−0.485208			−0.242604	−	0.970125i	$-0.578002\pi$
$101$	−4.87628			−0.485208			−0.242604	+	0.970125i	$0.578002\pi$
$102$		0			0
$103$	−3.87845	+	11.9366i	−0.382155	+	1.17615i	0.556368	+	0.830936i	$0.312194\pi$
$103$	−3.87845	+	11.9366i	−0.382155	+	1.17615i	−0.938523	+	0.345216i	$0.887806\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.1540			−1.46499			−0.732497	−	0.680770i	$-0.761645\pi$
$107$	−15.1540			−1.46499			−0.732497	+	0.680770i	$0.761645\pi$
$108$		0			0
$109$	10.6005	+	7.70174i	1.01535	+	0.737693i	0.965324	−	0.261055i	$-0.0840704\pi$
$109$	10.6005	+	7.70174i	1.01535	+	0.737693i	0.0500235	+	0.998748i	$0.484070\pi$
$110$		0			0
$111$	5.37276	−	3.90354i	0.509960	−	0.370508i
$112$		0			0
$113$	−7.25589	−	5.27172i	−0.682577	−	0.495921i	0.191635	−	0.981466i	$-0.438621\pi$
$113$	−7.25589	−	5.27172i	−0.682577	−	0.495921i	−0.874212	+	0.485545i	$0.838621\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.892334	−	2.74632i	−0.0824963	−	0.253898i
$118$		0			0
$119$	0.535340	+	1.64761i	0.0490745	+	0.151036i
$120$		0			0
$121$	−2.39818	+	7.38084i	−0.218016	+	0.670985i
$122$		0			0
$123$	−0.933459	+	0.678198i	−0.0841671	+	0.0611510i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.2785	−	7.46778i	0.912071	−	0.662658i	−0.0294670	−	0.999566i	$-0.509381\pi$
$127$	10.2785	−	7.46778i	0.912071	−	0.662658i	0.941538	+	0.336908i	$0.109381\pi$
$128$		0			0
$129$	2.10701	−	6.48470i	0.185512	−	0.570946i
$130$		0			0
$131$	2.04046	+	6.27990i	0.178276	+	0.548678i	0.999768	−	0.0215426i	$-0.00685777\pi$
$131$	2.04046	+	6.27990i	0.178276	+	0.548678i	−0.821492	+	0.570220i	$0.806858\pi$
$132$		0			0
$133$	1.06827	+	3.28779i	0.0926307	+	0.285088i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.548854	−	0.398766i	−0.0468918	−	0.0340689i	0.564092	−	0.825712i	$-0.309226\pi$
$137$	−0.548854	−	0.398766i	−0.0468918	−	0.0340689i	−0.610984	+	0.791643i	$0.709226\pi$
$138$		0			0
$139$	−1.85573	+	1.34827i	−0.157401	+	0.114359i	−0.663698	−	0.748001i	$-0.731014\pi$
$139$	−1.85573	+	1.34827i	−0.157401	+	0.114359i	0.506297	+	0.862359i	$0.331014\pi$
$140$		0			0
$141$	1.01678	+	0.738731i	0.0856280	+	0.0622124i
$142$		0			0
$143$	−1.98517			−0.166008
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.20424	+	3.70628i	−0.0993243	+	0.305689i
$148$		0			0
$149$	−23.5046			−1.92557			−0.962784	−	0.270271i	$-0.912887\pi$
$149$	−23.5046			−1.92557			−0.962784	+	0.270271i	$0.912887\pi$
$150$		0			0
$151$	−0.497767			−0.0405077			−0.0202539	−	0.999795i	$-0.506447\pi$
$151$	−0.497767			−0.0405077			−0.0202539	+	0.999795i	$0.506447\pi$
$152$		0			0
$153$	−1.68178	+	5.17599i	−0.135964	+	0.418454i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.32045			−0.584236			−0.292118	−	0.956382i	$-0.594360\pi$
$157$	−7.32045			−0.584236			−0.292118	+	0.956382i	$0.594360\pi$
$158$		0			0
$159$	−3.36635	−	2.44580i	−0.266969	−	0.193965i
$160$		0			0
$161$	1.72850	−	1.25583i	0.136225	−	0.0989729i
$162$		0			0
$163$	14.2778	+	10.3734i	1.11832	+	0.812509i	0.983954	−	0.178422i	$-0.0570992\pi$
$163$	14.2778	+	10.3734i	1.11832	+	0.812509i	0.134369	+	0.990931i	$0.457099\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.11524	−	18.8208i	−0.473211	−	1.45639i	−0.848355	−	0.529428i	$-0.822407\pi$
$167$	−6.11524	−	18.8208i	−0.473211	−	1.45639i	0.375143	−	0.926967i	$-0.377593\pi$
$168$		0			0
$169$	−3.64128	−	11.2067i	−0.280098	−	0.862054i
$170$		0			0
$171$	−3.35599	+	10.3287i	−0.256639	+	0.789853i
$172$		0			0
$173$	−2.58169	+	1.87571i	−0.196282	+	0.142607i	−0.681585	−	0.731739i	$-0.738709\pi$
$173$	−2.58169	+	1.87571i	−0.196282	+	0.142607i	0.485303	+	0.874346i	$0.338709\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.68574	−	4.85747i	0.502531	−	0.365110i
$178$		0			0
$179$	5.10054	−	15.6978i	0.381232	−	1.17331i	−0.557945	−	0.829878i	$-0.688410\pi$
$179$	5.10054	−	15.6978i	0.381232	−	1.17331i	0.939177	−	0.343434i	$-0.111590\pi$
$180$		0			0
$181$	3.29585	+	10.1436i	0.244979	+	0.753967i	0.995640	+	0.0932799i	$0.0297351\pi$
$181$	3.29585	+	10.1436i	0.244979	+	0.753967i	−0.750661	+	0.660687i	$0.770265\pi$
$182$		0			0
$183$	0.141938	+	0.436839i	0.0104923	+	0.0322921i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.02689	+	2.19916i	0.221348	+	0.160819i
$188$		0			0
$189$	2.34094	−	1.70079i	0.170278	−	0.123714i
$190$		0			0
$191$	−0.398022	−	0.289180i	−0.0287999	−	0.0209243i	0.573292	−	0.819351i	$-0.305666\pi$
$191$	−0.398022	−	0.289180i	−0.0287999	−	0.0209243i	−0.602092	+	0.798427i	$0.705666\pi$
$192$		0			0
$193$	−16.6968			−1.20186			−0.600932	−	0.799300i	$-0.705204\pi$
$193$	−16.6968			−1.20186			−0.600932	+	0.799300i	$0.705204\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.32005	+	10.2180i	−0.236543	+	0.728006i	0.760370	+	0.649491i	$0.225018\pi$
$197$	−3.32005	+	10.2180i	−0.236543	+	0.728006i	−0.996913	+	0.0785151i	$0.974982\pi$
$198$		0			0
$199$	−12.8786			−0.912940			−0.456470	−	0.889739i	$-0.650886\pi$
$199$	−12.8786			−0.912940			−0.456470	+	0.889739i	$0.650886\pi$
$200$		0			0
$201$	−2.74320			−0.193490
$202$		0			0
$203$	−0.617314	+	1.89990i	−0.0433270	+	0.133347i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.71197			0.466514
$208$		0			0
$209$	6.04015	+	4.38843i	0.417806	+	0.303554i
$210$		0			0
$211$	−21.4185	+	15.5615i	−1.47451	+	1.07130i	−0.495240	+	0.868756i	$0.664920\pi$
$211$	−21.4185	+	15.5615i	−1.47451	+	1.07130i	−0.979274	+	0.202540i	$0.935080\pi$
$212$		0			0
$213$	−5.38034	−	3.90904i	−0.368655	−	0.267843i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.28405	−	7.02957i	−0.155051	−	0.477198i
$218$		0			0
$219$	−0.712439	−	2.19266i	−0.0481422	−	0.148166i
$220$		0			0
$221$	0.708539	−	2.18066i	0.0476615	−	0.146687i
$222$		0			0
$223$	−16.4494	+	11.9512i	−1.10153	+	0.800309i	−0.981309	−	0.192438i	$-0.938361\pi$
$223$	−16.4494	+	11.9512i	−1.10153	+	0.800309i	−0.120222	+	0.992747i	$0.538361\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.5859	+	9.14419i	−0.835356	+	0.606921i	−0.921069	−	0.389398i	$-0.872683\pi$
$227$	−12.5859	+	9.14419i	−0.835356	+	0.606921i	0.0857138	+	0.996320i	$0.472683\pi$
$228$		0			0
$229$	6.37276	−	19.6133i	0.421124	−	1.29609i	−0.485533	−	0.874218i	$-0.661374\pi$
$229$	6.37276	−	19.6133i	0.421124	−	1.29609i	0.906657	−	0.421868i	$-0.138626\pi$
$230$		0			0
$231$	−0.286456	−	0.881621i	−0.0188474	−	0.0580064i
$232$		0			0
$233$	6.73211	+	20.7193i	0.441035	+	1.35737i	0.886774	+	0.462203i	$0.152941\pi$
$233$	6.73211	+	20.7193i	0.441035	+	1.35737i	−0.445739	+	0.895163i	$0.647059\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.42064	−	4.66487i	−0.417066	−	0.303016i
$238$		0			0
$239$	−19.2533	+	13.9883i	−1.24539	+	0.904830i	−0.997945	−	0.0640715i	$-0.979591\pi$
$239$	−19.2533	+	13.9883i	−1.24539	+	0.904830i	−0.247446	+	0.968902i	$0.579591\pi$
$240$		0			0
$241$	9.80377	+	7.12286i	0.631517	+	0.458824i	0.856925	−	0.515441i	$-0.172372\pi$
$241$	9.80377	+	7.12286i	0.631517	+	0.458824i	−0.225409	+	0.974264i	$0.572372\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.41389	−	4.35150i	0.0899635	−	0.276879i
$248$		0			0
$249$	−4.99064			−0.316269
$250$		0			0
$251$	7.11071			0.448824			0.224412	−	0.974494i	$-0.427954\pi$
$251$	7.11071			0.448824			0.224412	+	0.974494i	$0.427954\pi$
$252$		0			0
$253$	1.42589	−	4.38843i	0.0896447	−	0.275898i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−25.6564			−1.60040			−0.800202	−	0.599730i	$-0.795275\pi$
$257$	−25.6564			−1.60040			−0.800202	+	0.599730i	$0.795275\pi$
$258$		0			0
$259$	7.24471	+	5.26359i	0.450164	+	0.327063i
$260$		0			0
$261$	−5.07716	+	3.68878i	−0.314269	+	0.228329i
$262$		0			0
$263$	−20.1357	−	14.6294i	−1.24162	−	0.902089i	−0.243913	−	0.969797i	$-0.578431\pi$
$263$	−20.1357	−	14.6294i	−1.24162	−	0.902089i	−0.997705	+	0.0677085i	$0.978431\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.01794	+	6.21058i	0.123496	+	0.380082i
$268$		0			0
$269$	0.748944	+	2.30501i	0.0456639	+	0.140539i	0.971289	−	0.237903i	$-0.0764600\pi$
$269$	0.748944	+	2.30501i	0.0456639	+	0.140539i	−0.925625	+	0.378442i	$0.876460\pi$
$270$		0			0
$271$	−2.44851	+	7.53573i	−0.148736	+	0.457763i	−0.997473	−	0.0710533i	$-0.977364\pi$
$271$	−2.44851	+	7.53573i	−0.148736	+	0.457763i	0.848736	+	0.528816i	$0.177364\pi$
$272$		0			0
$273$	−0.459595	+	0.333915i	−0.0278160	+	0.0202095i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.36259	−	4.62269i	0.382291	−	0.277750i	−0.379998	−	0.924987i	$-0.624075\pi$
$277$	6.36259	−	4.62269i	0.382291	−	0.277750i	0.762289	+	0.647237i	$0.224075\pi$
$278$		0			0
$279$	7.17537	−	22.0835i	0.429578	−	1.32211i
$280$		0			0
$281$	−3.84952	−	11.8476i	−0.229643	−	0.706769i	−0.997787	−	0.0664914i	$-0.978819\pi$
$281$	−3.84952	−	11.8476i	−0.229643	−	0.706769i	0.768144	−	0.640277i	$-0.221181\pi$
$282$		0			0
$283$	−4.28071	−	13.1747i	−0.254462	−	0.783153i	−0.993935	−	0.109967i	$-0.964926\pi$
$283$	−4.28071	−	13.1747i	−0.254462	−	0.783153i	0.739474	−	0.673186i	$-0.235074\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.25869	−	0.914491i	−0.0742981	−	0.0539807i
$288$		0			0
$289$	10.2572	−	7.45230i	0.603366	−	0.438371i
$290$		0			0
$291$	4.90748	+	3.56549i	0.287682	+	0.209013i
$292$		0			0
$293$	−9.26026			−0.540990			−0.270495	−	0.962721i	$-0.587187\pi$
$293$	−9.26026			−0.540990			−0.270495	+	0.962721i	$0.587187\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.93111	−	5.94334i	0.112054	−	0.344868i
$298$		0			0
$299$	−2.82777			−0.163534
$300$		0			0
$301$	9.19405			0.529936
$302$		0			0
$303$	−0.931286	+	2.86620i	−0.0535010	+	0.164659i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−22.6968			−1.29538			−0.647688	−	0.761906i	$-0.724264\pi$
$307$	−22.6968			−1.29538			−0.647688	+	0.761906i	$0.724264\pi$
$308$		0			0
$309$	6.27546	+	4.55939i	0.356999	+	0.259375i
$310$		0			0
$311$	8.39548	−	6.09967i	0.476064	−	0.345881i	−0.323736	−	0.946148i	$-0.604939\pi$
$311$	8.39548	−	6.09967i	0.476064	−	0.345881i	0.799800	+	0.600267i	$0.204939\pi$
$312$		0			0
$313$	13.7311	+	9.97621i	0.776126	+	0.563889i	0.903814	−	0.427926i	$-0.140755\pi$
$313$	13.7311	+	9.97621i	0.776126	+	0.563889i	−0.127688	+	0.991814i	$0.540755\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.99658	−	18.4556i	−0.336802	−	1.03657i	−0.965828	−	0.259185i	$-0.916546\pi$
$317$	−5.99658	−	18.4556i	−0.336802	−	1.03657i	0.629026	−	0.777384i	$-0.283454\pi$
$318$		0			0
$319$	1.33321	+	4.10319i	0.0746454	+	0.229735i
$320$		0			0
$321$	−2.89416	+	8.90731i	−0.161536	+	0.497157i
$322$		0			0
$323$	−6.97641	+	5.06865i	−0.388178	+	0.282028i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.55149	−	4.75994i	0.362298	−	0.263225i
$328$		0			0
$329$	−0.523689	+	1.61175i	−0.0288719	+	0.0888586i
$330$		0			0
$331$	2.56085	+	7.88150i	0.140757	+	0.433206i	0.996441	−	0.0842928i	$-0.0268631\pi$
$331$	2.56085	+	7.88150i	0.140757	+	0.433206i	−0.855684	+	0.517499i	$0.826863\pi$
$332$		0			0
$333$	8.69331	+	26.7553i	0.476391	+	1.46618i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.66048	+	4.83912i	0.362819	+	0.263604i	0.754227	−	0.656614i	$-0.228012\pi$
$337$	6.66048	+	4.83912i	0.362819	+	0.263604i	−0.391408	+	0.920217i	$0.628012\pi$
$338$		0			0
$339$	−4.48439	+	3.25810i	−0.243559	+	0.176956i
$340$		0			0
$341$	−12.9143	−	9.38281i	−0.699350	−	0.508108i
$342$		0			0
$343$	−11.0883			−0.598715
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.16394	+	18.9706i	−0.330897	+	1.01840i	0.637810	+	0.770193i	$0.279840\pi$
$347$	−6.16394	+	18.9706i	−0.330897	+	1.01840i	−0.968708	+	0.248204i	$0.920160\pi$
$348$		0			0
$349$	4.67641			0.250322			0.125161	−	0.992136i	$-0.460055\pi$
$349$	4.67641			0.250322			0.125161	+	0.992136i	$0.460055\pi$
$350$		0			0
$351$	−3.82972			−0.204415
$352$		0			0
$353$	7.67782	−	23.6299i	0.408649	−	1.25769i	−0.509160	−	0.860672i	$-0.670044\pi$
$353$	7.67782	−	23.6299i	0.408649	−	1.25769i	0.917810	−	0.397021i	$-0.129956\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.07068			0.0566664
$358$		0			0
$359$	−15.2461	−	11.0770i	−0.804660	−	0.584620i	0.107618	−	0.994192i	$-0.465678\pi$
$359$	−15.2461	−	11.0770i	−0.804660	−	0.584620i	−0.912277	+	0.409573i	$0.865678\pi$
$360$		0			0
$361$	1.44993	−	1.05343i	0.0763119	−	0.0554438i
$362$		0			0
$363$	3.88034	+	2.81923i	0.203665	+	0.147971i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.00893	−	9.26053i	−0.157065	−	0.483396i	0.841299	−	0.540569i	$-0.181791\pi$
$367$	−3.00893	−	9.26053i	−0.157065	−	0.483396i	−0.998364	+	0.0571736i	$0.981791\pi$
$368$		0			0
$369$	−1.51037	−	4.64844i	−0.0786266	−	0.241988i
$370$		0			0
$371$	1.73384	−	5.33620i	0.0900162	−	0.277042i
$372$		0			0
$373$	23.5821	−	17.1334i	1.22104	−	0.887135i	0.224851	−	0.974393i	$-0.427811\pi$
$373$	23.5821	−	17.1334i	1.22104	−	0.887135i	0.996186	+	0.0872583i	$0.0278105\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.13902	−	1.55409i	0.110165	−	0.0800398i
$378$		0			0
$379$	1.87942	−	5.78426i	0.0965394	−	0.297118i	−0.891112	−	0.453783i	$-0.850074\pi$
$379$	1.87942	−	5.78426i	0.0965394	−	0.297118i	0.987652	+	0.156665i	$0.0500743\pi$
$380$		0			0
$381$	−2.42643	−	7.46778i	−0.124310	−	0.382586i
$382$		0			0
$383$	−9.76498	−	30.0535i	−0.498967	−	1.53566i	−0.810682	−	0.585487i	$-0.800903\pi$
$383$	−9.76498	−	30.0535i	−0.498967	−	1.53566i	0.311715	−	0.950176i	$-0.399097\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	23.3671	+	16.9772i	1.18781	+	0.862997i
$388$		0			0
$389$	−4.83362	+	3.51183i	−0.245074	+	0.178057i	−0.703541	−	0.710655i	$-0.748399\pi$
$389$	−4.83362	+	3.51183i	−0.245074	+	0.178057i	0.458467	+	0.888712i	$0.348399\pi$
$390$		0			0
$391$	4.31166	+	3.13260i	0.218050	+	0.158422i
$392$		0			0
$393$	4.08093			0.205856
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.501105	−	1.54224i	0.0251497	−	0.0774029i	−0.937694	−	0.347462i	$-0.887043\pi$
$397$	0.501105	−	1.54224i	0.0251497	−	0.0774029i	0.962844	+	0.270060i	$0.0870434\pi$
$398$		0			0
$399$	2.13654			0.106961
$400$		0			0
$401$	−5.63644			−0.281470			−0.140735	−	0.990047i	$-0.544947\pi$
$401$	−5.63644			−0.281470			−0.140735	+	0.990047i	$0.544947\pi$
$402$		0			0
$403$	−3.02301	+	9.30386i	−0.150587	+	0.463458i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	19.3399			0.958645
$408$		0			0
$409$	26.8187	+	19.4849i	1.32610	+	0.963468i	0.999835	+	0.0181896i	$0.00579024\pi$
$409$	26.8187	+	19.4849i	1.32610	+	0.963468i	0.326265	+	0.945278i	$0.394210\pi$
$410$		0			0
$411$	−0.339211	+	0.246451i	−0.0167320	+	0.0121565i
$412$		0			0
$413$	9.01515	+	6.54989i	0.443606	+	0.322299i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.438079	+	1.34827i	0.0214528	+	0.0660250i
$418$		0			0
$419$	7.32237	+	22.5360i	0.357721	+	1.10095i	0.954415	+	0.298484i	$0.0964809\pi$
$419$	7.32237	+	22.5360i	0.357721	+	1.10095i	−0.596693	+	0.802469i	$0.703519\pi$
$420$		0			0
$421$	3.01571	−	9.28140i	0.146977	−	0.452348i	−0.850283	−	0.526325i	$-0.823569\pi$
$421$	3.01571	−	9.28140i	0.146977	−	0.452348i	0.997260	+	0.0739778i	$0.0235694\pi$
$422$		0			0
$423$	−4.30713	+	3.12931i	−0.209420	+	0.152152i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.501068	+	0.364047i	−0.0242484	+	0.0176175i
$428$		0			0
$429$	−0.379133	+	1.16685i	−0.0183047	+	0.0563362i
$430$		0			0
$431$	−4.37321	−	13.4593i	−0.210650	−	0.648314i	−0.999434	−	0.0336434i	$-0.989289\pi$
$431$	−4.37321	−	13.4593i	−0.210650	−	0.648314i	0.788784	−	0.614671i	$-0.210711\pi$
$432$		0			0
$433$	0.156266	+	0.480938i	0.00750967	+	0.0231124i	0.954741	−	0.297438i	$-0.0961322\pi$
$433$	0.156266	+	0.480938i	0.00750967	+	0.0231124i	−0.947231	+	0.320550i	$0.896132\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.60390	+	6.25110i	0.411580	+	0.299031i
$438$		0			0
$439$	−29.9702	+	21.7746i	−1.43040	+	1.03925i	−0.440457	+	0.897774i	$0.645184\pi$
$439$	−29.9702	+	21.7746i	−1.43040	+	1.03925i	−0.989942	+	0.141472i	$0.954816\pi$
$440$		0			0
$441$	−13.3553	−	9.70317i	−0.635965	−	0.462056i
$442$		0			0
$443$	20.7271			0.984775			0.492388	−	0.870376i	$-0.336124\pi$
$443$	20.7271			0.984775			0.492388	+	0.870376i	$0.336124\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.48897	+	13.8156i	−0.212321	+	0.653457i
$448$		0			0
$449$	−6.56029			−0.309599			−0.154800	−	0.987946i	$-0.549473\pi$
$449$	−6.56029			−0.309599			−0.154800	+	0.987946i	$0.549473\pi$
$450$		0			0
$451$	−3.36010			−0.158221
$452$		0			0
$453$	−0.0950651	+	0.292580i	−0.00446655	+	0.0137466i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	28.9369			1.35361			0.676805	−	0.736163i	$-0.263364\pi$
$457$	28.9369			1.35361			0.676805	+	0.736163i	$0.263364\pi$
$458$		0			0
$459$	5.83937	+	4.24255i	0.272558	+	0.198025i
$460$		0			0
$461$	27.5079	−	19.9856i	1.28117	−	0.930824i	0.281581	−	0.959537i	$-0.409141\pi$
$461$	27.5079	−	19.9856i	1.28117	−	0.930824i	0.999588	+	0.0287136i	$0.00914107\pi$
$462$		0			0
$463$	−2.13334	−	1.54996i	−0.0991445	−	0.0720327i	0.537108	−	0.843513i	$-0.319517\pi$
$463$	−2.13334	−	1.54996i	−0.0991445	−	0.0720327i	−0.636253	+	0.771480i	$0.719517\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.9619	+	36.8148i	0.553529	+	1.70359i	0.699796	+	0.714342i	$0.253274\pi$
$467$	11.9619	+	36.8148i	0.553529	+	1.70359i	−0.146267	+	0.989245i	$0.546726\pi$
$468$		0			0
$469$	−1.14304	−	3.51792i	−0.0527808	−	0.162443i
$470$		0			0
$471$	−1.39808	+	4.30285i	−0.0644202	+	0.198265i
$472$		0			0
$473$	16.0641	−	11.6712i	0.738628	−	0.536645i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	14.2601	−	10.3606i	0.652925	−	0.474378i
$478$		0			0
$479$	−2.49231	+	7.67054i	−0.113877	+	0.350476i	−0.991711	−	0.128488i	$-0.958988\pi$
$479$	−2.49231	+	7.67054i	−0.113877	+	0.350476i	0.877835	+	0.478964i	$0.158988\pi$
$480$		0			0
$481$	−3.66252	−	11.2721i	−0.166996	−	0.513962i
$482$		0			0
$483$	−0.408042	−	1.25583i	−0.0185666	−	0.0571420i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.04666	+	4.39316i	0.274000	+	0.199073i	0.716296	−	0.697796i	$-0.245836\pi$
$487$	6.04666	+	4.39316i	0.274000	+	0.199073i	−0.442296	+	0.896869i	$0.645836\pi$
$488$		0			0
$489$	8.82416	−	6.41113i	0.399042	−	0.289921i
$490$		0			0
$491$	−5.51407	−	4.00621i	−0.248847	−	0.180798i	0.456369	−	0.889791i	$-0.349150\pi$
$491$	−5.51407	−	4.00621i	−0.248847	−	0.180798i	−0.705216	+	0.708993i	$0.749150\pi$
$492$		0			0
$493$	−4.98310			−0.224428
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.77113	−	8.52867i	0.124302	−	0.382563i
$498$		0			0
$499$	19.5176			0.873727			0.436863	−	0.899528i	$-0.356089\pi$
$499$	19.5176			0.873727			0.436863	+	0.899528i	$0.356089\pi$
$500$		0			0
$501$	−12.2305			−0.546417
$502$		0			0
$503$	4.30626	−	13.2533i	0.192007	−	0.590935i	−0.807992	−	0.589194i	$-0.799446\pi$
$503$	4.30626	−	13.2533i	0.192007	−	0.590935i	0.999998	−	0.00174190i	$-0.000554465\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.28256			−0.323430
$508$		0			0
$509$	18.8189	+	13.6727i	0.834134	+	0.606034i	0.920726	−	0.390210i	$-0.127598\pi$
$509$	18.8189	+	13.6727i	0.834134	+	0.606034i	−0.0865919	+	0.996244i	$0.527598\pi$
$510$		0			0
$511$	2.51505	−	1.82729i	0.111259	−	0.0808345i
$512$		0			0
$513$	11.6524	+	8.46599i	0.514468	+	0.373783i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.13101	+	3.48088i	0.0497416	+	0.153089i
$518$		0			0
$519$	0.609454	+	1.87571i	0.0267520	+	0.0823343i
$520$		0			0
$521$	13.4660	−	41.4440i	0.589955	−	1.81570i	0.0115690	−	0.999933i	$-0.496317\pi$
$521$	13.4660	−	41.4440i	0.589955	−	1.81570i	0.578386	−	0.815763i	$-0.303683\pi$
$522$		0			0
$523$	6.31766	−	4.59005i	0.276252	−	0.200709i	−0.441029	−	0.897493i	$-0.645386\pi$
$523$	6.31766	−	4.59005i	0.276252	−	0.200709i	0.717281	+	0.696784i	$0.245386\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.9161	−	10.8372i	0.649756	−	0.472076i
$528$		0			0
$529$	−5.07629	+	15.6232i	−0.220708	+	0.679270i
$530$		0			0
$531$	10.8178	+	33.2936i	0.469451	+	1.44482i
$532$		0			0
$533$	0.636323	+	1.95840i	0.0275622	+	0.0848277i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.25284	−	5.99604i	−0.356137	−	0.258748i
$538$		0			0
$539$	−9.18131	+	6.67061i	−0.395467	+	0.287324i
$540$		0			0
$541$	20.8579	+	15.1541i	0.896749	+	0.651526i	0.937629	−	0.347638i	$-0.113016\pi$
$541$	20.8579	+	15.1541i	0.896749	+	0.651526i	−0.0408799	+	0.999164i	$0.513016\pi$
$542$		0			0
$543$	6.59171			0.282877
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.40053	−	22.7765i	0.316424	−	0.973852i	−0.658741	−	0.752370i	$-0.728911\pi$
$547$	7.40053	−	22.7765i	0.316424	−	0.973852i	0.975164	−	0.221482i	$-0.0710895\pi$
$548$		0			0
$549$	−1.94571			−0.0830410
$550$		0			0
$551$	−9.94376			−0.423619
$552$		0			0
$553$	3.30694	−	10.1777i	0.140625	−	0.432801i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.4185			−0.949904			−0.474952	−	0.880012i	$-0.657535\pi$
$557$	−22.4185			−0.949904			−0.474952	+	0.880012i	$0.657535\pi$
$558$		0			0
$559$	−9.84461	−	7.15253i	−0.416383	−	0.302520i
$560$		0			0
$561$	1.87072	−	1.35916i	0.0789819	−	0.0573837i
$562$		0			0
$563$	−8.17248	−	5.93765i	−0.344429	−	0.250242i	0.402099	−	0.915596i	$-0.368281\pi$
$563$	−8.17248	−	5.93765i	−0.344429	−	0.250242i	−0.746528	+	0.665354i	$0.768281\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.47000	+	4.52420i	0.0617342	+	0.189998i
$568$		0			0
$569$	3.48538	+	10.7269i	0.146115	+	0.449695i	0.997153	−	0.0754091i	$-0.0240263\pi$
$569$	3.48538	+	10.7269i	0.146115	+	0.449695i	−0.851038	+	0.525104i	$0.824026\pi$
$570$		0			0
$571$	1.62957	−	5.01529i	0.0681953	−	0.209883i	−0.911151	−	0.412072i	$-0.864805\pi$
$571$	1.62957	−	5.01529i	0.0681953	−	0.209883i	0.979347	+	0.202188i	$0.0648053\pi$
$572$		0			0
$573$	−0.245991	+	0.178723i	−0.0102764	+	0.00746626i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.8012	+	10.0272i	−0.574553	+	0.417437i	−0.836756	−	0.547576i	$-0.815551\pi$
$577$	−13.8012	+	10.0272i	−0.574553	+	0.417437i	0.262203	+	0.965013i	$0.415551\pi$
$578$		0			0
$579$	−3.18881	+	9.81415i	−0.132522	+	0.407862i
$580$		0			0
$581$	−2.07951	−	6.40009i	−0.0862728	−	0.265520i
$582$		0			0
$583$	−3.74455	−	11.5245i	−0.155083	−	0.477298i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.82680	−	1.32725i	−0.0754001	−	0.0547814i	0.549447	−	0.835529i	$-0.314839\pi$
$587$	−1.82680	−	1.32725i	−0.0754001	−	0.0547814i	−0.624847	+	0.780747i	$0.714839\pi$
$588$		0			0
$589$	29.7651	−	21.6256i	1.22645	−	0.891067i
$590$		0			0
$591$	5.37195	+	3.90295i	0.220972	+	0.160546i
$592$		0			0
$593$	−27.9744			−1.14877			−0.574385	−	0.818585i	$-0.694759\pi$
$593$	−27.9744			−1.14877			−0.574385	+	0.818585i	$0.694759\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.45960	+	7.56986i	−0.100665	+	0.309814i
$598$		0			0
$599$	−5.13906			−0.209976			−0.104988	−	0.994473i	$-0.533480\pi$
$599$	−5.13906			−0.209976			−0.104988	+	0.994473i	$0.533480\pi$
$600$		0			0
$601$	37.9217			1.54686			0.773429	−	0.633882i	$-0.218540\pi$
$601$	37.9217			1.54686			0.773429	+	0.633882i	$0.218540\pi$
$602$		0			0
$603$	3.59089	−	11.0516i	0.146232	−	0.450057i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	39.0728			1.58592			0.792959	−	0.609275i	$-0.208539\pi$
$607$	39.0728			1.58592			0.792959	+	0.609275i	$0.208539\pi$
$608$		0			0
$609$	0.998835	+	0.725696i	0.0404748	+	0.0294067i
$610$		0			0
$611$	1.81461	−	1.31839i	0.0734112	−	0.0533363i
$612$		0			0
$613$	−1.53761	−	1.11714i	−0.0621035	−	0.0451208i	0.556300	−	0.830981i	$-0.312220\pi$
$613$	−1.53761	−	1.11714i	−0.0621035	−	0.0451208i	−0.618404	+	0.785860i	$0.712220\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.39305	−	13.5204i	−0.176858	−	0.544312i	0.822856	−	0.568250i	$-0.192379\pi$
$617$	−4.39305	−	13.5204i	−0.176858	−	0.544312i	−0.999713	+	0.0239383i	$0.992379\pi$
$618$		0			0
$619$	6.80529	+	20.9445i	0.273528	+	0.841831i	0.989605	+	0.143811i	$0.0459356\pi$
$619$	6.80529	+	20.9445i	0.273528	+	0.841831i	−0.716078	+	0.698021i	$0.754064\pi$
$620$		0			0
$621$	2.75077	−	8.46599i	0.110385	−	0.339729i
$622$		0			0
$623$	−7.12372	+	5.17569i	−0.285406	+	0.207360i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.73302	−	2.71220i	0.149082	−	0.108315i
$628$		0			0
$629$	−6.90274	+	21.2444i	−0.275230	+	0.847072i
$630$		0			0
$631$	−9.56547	−	29.4395i	−0.380795	−	1.17197i	−0.939485	−	0.342591i	$-0.888696\pi$
$631$	−9.56547	−	29.4395i	−0.380795	−	1.17197i	0.558689	−	0.829377i	$-0.311304\pi$
$632$		0			0
$633$	5.05623	+	15.5615i	0.200967	+	0.618514i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.62661	+	4.08797i	0.222935	+	0.161971i
$638$		0			0
$639$	22.7915	−	16.5590i	0.901616	−	0.655063i
$640$		0			0
$641$	−16.2639	−	11.8164i	−0.642385	−	0.466720i	0.218284	−	0.975885i	$-0.429954\pi$
$641$	−16.2639	−	11.8164i	−0.642385	−	0.466720i	−0.860669	+	0.509166i	$0.829954\pi$
$642$		0			0
$643$	17.9165			0.706558			0.353279	−	0.935518i	$-0.385067\pi$
$643$	17.9165			0.706558			0.353279	+	0.935518i	$0.385067\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.64211	+	23.5200i	−0.300442	+	0.924666i	0.680897	+	0.732380i	$0.261590\pi$
$647$	−7.64211	+	23.5200i	−0.300442	+	0.924666i	−0.981339	+	0.192287i	$0.938410\pi$
$648$		0			0
$649$	24.0662			0.944680
$650$		0			0
$651$	−4.56809			−0.179038
$652$		0			0
$653$	0.918758	−	2.82765i	0.0359538	−	0.110654i	−0.931469	−	0.363821i	$-0.881472\pi$
$653$	0.918758	−	2.82765i	0.0359538	−	0.110654i	0.967423	+	0.253166i	$0.0814720\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.76626			0.381018
$658$		0			0
$659$	−15.3181	−	11.1293i	−0.596709	−	0.433534i	0.248001	−	0.968760i	$-0.420227\pi$
$659$	−15.3181	−	11.1293i	−0.596709	−	0.433534i	−0.844709	+	0.535226i	$0.820227\pi$
$660$		0			0
$661$	−31.7914	+	23.0978i	−1.23654	+	0.898401i	−0.997363	−	0.0725749i	$-0.976878\pi$
$661$	−31.7914	+	23.0978i	−1.23654	+	0.898401i	−0.239179	+	0.970975i	$0.576878\pi$
$662$		0			0
$663$	−1.14644	−	0.832937i	−0.0445240	−	0.0323486i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.89909	+	5.84480i	0.0735331	+	0.226311i
$668$		0			0
$669$	3.88317	+	11.9512i	0.150132	+	0.462059i
$670$		0			0
$671$	−0.413345	+	1.27215i	−0.0159570	+	0.0491107i
$672$		0			0
$673$	19.9660	−	14.5061i	0.769632	−	0.559170i	−0.132217	−	0.991221i	$-0.542210\pi$
$673$	19.9660	−	14.5061i	0.769632	−	0.559170i	0.901850	+	0.432050i	$0.142210\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−35.2934	+	25.6421i	−1.35643	+	0.985508i	−0.357772	+	0.933809i	$0.616464\pi$
$677$	−35.2934	+	25.6421i	−1.35643	+	0.985508i	−0.998663	+	0.0516988i	$0.983536\pi$
$678$		0			0
$679$	−2.52759	+	7.77912i	−0.0970000	+	0.298535i
$680$		0			0
$681$	2.97113	+	9.14419i	0.113854	+	0.350406i
$682$		0			0
$683$	−6.81741	−	20.9818i	−0.260861	−	0.802847i	−0.992618	−	0.121282i	$-0.961300\pi$
$683$	−6.81741	−	20.9818i	−0.260861	−	0.802847i	0.731757	−	0.681565i	$-0.238700\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−10.3113	−	7.49163i	−0.393402	−	0.285824i
$688$		0			0
$689$	−6.00783	+	4.36494i	−0.228880	+	0.166291i
$690$		0			0
$691$	−14.7311	−	10.7028i	−0.560397	−	0.407152i	0.271207	−	0.962521i	$-0.412577\pi$
$691$	−14.7311	−	10.7028i	−0.560397	−	0.407152i	−0.831604	+	0.555369i	$0.812577\pi$
$692$		0			0
$693$	3.92680			0.149167
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.19928	−	3.69099i	0.0454258	−	0.139806i
$698$		0			0
$699$	13.4642			0.509263
$700$		0			0
$701$	1.95162			0.0737115			0.0368558	−	0.999321i	$-0.488266\pi$
$701$	1.95162			0.0737115			0.0368558	+	0.999321i	$0.488266\pi$
$702$		0			0
$703$	−13.7744	+	42.3932i	−0.519511	+	1.59889i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.06372			−0.152832
$708$		0			0
$709$	−27.8786	−	20.2550i	−1.04700	−	0.760692i	−0.0753622	−	0.997156i	$-0.524011\pi$
$709$	−27.8786	−	20.2550i	−1.04700	−	0.760692i	−0.971640	+	0.236465i	$0.924011\pi$
$710$		0			0
$711$	27.1983	−	19.7607i	1.02002	−	0.741084i
$712$		0			0
$713$	−18.3958	−	13.3654i	−0.688929	−	0.500536i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.54508	+	13.9883i	0.169739	+	0.522404i
$718$		0			0
$719$	−5.09724	−	15.6877i	−0.190095	−	0.585052i	0.809904	−	0.586562i	$-0.199519\pi$
$719$	−5.09724	−	15.6877i	−0.190095	−	0.585052i	−0.999999	+	0.00151058i	$0.999519\pi$
$720$		0			0
$721$	−3.23217	+	9.94759i	−0.120372	+	0.370468i
$722$		0			0
$723$	6.05907	−	4.40217i	0.225339	−	0.163718i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−6.01184	+	4.36786i	−0.222967	+	0.161995i	−0.693661	−	0.720301i	$-0.744003\pi$
$727$	−6.01184	+	4.36786i	−0.222967	+	0.161995i	0.470694	+	0.882296i	$0.344003\pi$
$728$		0			0
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$		0			0
$731$	7.08704	+	21.8117i	0.262124	+	0.806734i
$732$		0			0
$733$	1.21919	+	3.75230i	0.0450320	+	0.138594i	0.971045	−	0.238898i	$-0.0767863\pi$
$733$	1.21919	+	3.75230i	0.0450320	+	0.138594i	−0.926013	+	0.377493i	$0.876786\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.46293	−	4.69560i	−0.238065	−	0.172964i
$738$		0			0
$739$	8.04823	−	5.84738i	0.296059	−	0.215099i	−0.429833	−	0.902909i	$-0.641427\pi$
$739$	8.04823	−	5.84738i	0.296059	−	0.215099i	0.725892	+	0.687809i	$0.241427\pi$
$740$		0			0
$741$	−2.28772	−	1.66212i	−0.0840414	−	0.0610597i
$742$		0			0
$743$	29.7044			1.08975			0.544875	−	0.838517i	$-0.316577\pi$
$743$	29.7044			1.08975			0.544875	+	0.838517i	$0.316577\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.53283	−	20.1060i	0.239024	−	0.735640i
$748$		0			0
$749$	−12.6288			−0.461448
$750$		0			0
$751$	−3.82521			−0.139584			−0.0697919	−	0.997562i	$-0.522234\pi$
$751$	−3.82521			−0.139584			−0.0697919	+	0.997562i	$0.522234\pi$
$752$		0			0
$753$	1.35803	−	4.17957i	0.0494892	−	0.152312i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	19.8075			0.719917			0.359959	−	0.932968i	$-0.382791\pi$
$757$	19.8075			0.719917			0.359959	+	0.932968i	$0.382791\pi$
$758$		0			0
$759$	−2.30713	−	1.67623i	−0.0837436	−	0.0608433i
$760$		0			0
$761$	−2.24147	+	1.62852i	−0.0812532	+	0.0590339i	−0.627670	−	0.778479i	$-0.715991\pi$
$761$	−2.24147	+	1.62852i	−0.0812532	+	0.0590339i	0.546417	+	0.837513i	$0.315991\pi$
$762$		0			0
$763$	8.83412	+	6.41837i	0.319817	+	0.232360i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.55755	−	14.0267i	−0.164564	−	0.506475i
$768$		0			0
$769$	−15.1222	−	46.5413i	−0.545320	−	1.67832i	−0.720228	−	0.693738i	$-0.755963\pi$
$769$	−15.1222	−	46.5413i	−0.545320	−	1.67832i	0.174908	−	0.984585i	$-0.444037\pi$
$770$		0			0
$771$	−4.89994	+	15.0805i	−0.176467	+	0.543110i
$772$		0			0
$773$	−8.69890	+	6.32012i	−0.312878	+	0.227319i	−0.733130	−	0.680088i	$-0.761941\pi$
$773$	−8.69890	+	6.32012i	−0.312878	+	0.227319i	0.420253	+	0.907407i	$0.361941\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	4.47748	−	3.25308i	0.160629	−	0.116703i
$778$		0			0
$779$	2.39315	−	7.36536i	0.0857435	−	0.263891i
$780$		0			0
$781$	−5.98479	−	18.4193i	−0.214153	−	0.659095i
$782$		0			0
$783$	2.57198	+	7.91574i	0.0919150	+	0.282885i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−19.3427	−	14.0533i	−0.689492	−	0.500945i	0.187001	−	0.982360i	$-0.440123\pi$
$787$	−19.3427	−	14.0533i	−0.689492	−	0.500945i	−0.876493	+	0.481415i	$0.840123\pi$
$788$		0			0
$789$	−12.4445	+	9.04148i	−0.443037	+	0.321885i
$790$		0			0
$791$	−6.04681	−	4.39327i	−0.215000	−	0.156207i
$792$		0			0
$793$	0.819734			0.0291096
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.9085	−	39.7284i	0.457244	−	1.40725i	−0.411236	−	0.911529i	$-0.634903\pi$
$797$	12.9085	−	39.7284i	0.457244	−	1.40725i	0.868480	−	0.495724i	$-0.165097\pi$
$798$		0			0
$799$	−4.22734			−0.149552
$800$		0			0
$801$	−27.6623			−0.977401
$802$		0			0
$803$	2.07474	−	6.38538i	0.0732159	−	0.225335i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.49789			0.0527281
$808$		0			0
$809$	−21.8310	−	15.8612i	−0.767538	−	0.557649i	0.133675	−	0.991025i	$-0.457322\pi$
$809$	−21.8310	−	15.8612i	−0.767538	−	0.557649i	−0.901213	+	0.433376i	$0.857322\pi$
$810$		0			0
$811$	−30.8555	+	22.4178i	−1.08348	+	0.787196i	−0.978287	−	0.207256i	$-0.933547\pi$
$811$	−30.8555	+	22.4178i	−1.08348	+	0.787196i	−0.105195	+	0.994452i	$0.533547\pi$
$812$		0			0
$813$	3.96177	+	2.87839i	0.138945	+	0.100950i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	14.1422	+	43.5251i	0.494772	+	1.52275i
$818$		0			0
$819$	−0.743641	−	2.28869i	−0.0259849	−	0.0799733i
$820$		0			0
$821$	−14.3480	+	44.1587i	−0.500750	+	1.54115i	0.307049	+	0.951694i	$0.400658\pi$
$821$	−14.3480	+	44.1587i	−0.500750	+	1.54115i	−0.807800	+	0.589457i	$0.799342\pi$
$822$		0			0
$823$	−34.2286	+	24.8685i	−1.19313	+	0.866862i	−0.993592	−	0.113028i	$-0.963945\pi$
$823$	−34.2286	+	24.8685i	−1.19313	+	0.866862i	−0.199541	+	0.979889i	$0.563945\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.6821	+	10.6671i	−0.510546	+	0.370933i	−0.813030	−	0.582221i	$-0.802184\pi$
$827$	−14.6821	+	10.6671i	−0.510546	+	0.370933i	0.302485	+	0.953154i	$0.402184\pi$
$828$		0			0
$829$	−3.34078	+	10.2819i	−0.116030	+	0.357104i	−0.992160	−	0.124970i	$-0.960116\pi$
$829$	−3.34078	+	10.2819i	−0.116030	+	0.357104i	0.876130	+	0.482074i	$0.160116\pi$
$830$		0			0
$831$	−1.50200	−	4.62269i	−0.0521039	−	0.160359i
$832$		0			0
$833$	−4.05055	−	12.4663i	−0.140343	−	0.431932i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−24.9139	−	18.1010i	−0.861149	−	0.625662i
$838$		0			0
$839$	24.0000	−	17.4370i	0.828571	−	0.601992i	−0.0905835	−	0.995889i	$-0.528873\pi$
$839$	24.0000	−	17.4370i	0.828571	−	0.601992i	0.919155	+	0.393897i	$0.128873\pi$
$840$		0			0
$841$	18.8128	+	13.6683i	0.648716	+	0.471320i
$842$		0			0
$843$	−7.69904			−0.265169
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.99856	+	6.15094i	−0.0686713	+	0.211349i
$848$		0			0
$849$	−8.56142			−0.293827
$850$		0			0
$851$	27.5488			0.944361
$852$		0			0
$853$	−3.00414	+	9.24579i	−0.102860	+	0.316570i	−0.989222	−	0.146422i	$-0.953224\pi$
$853$	−3.00414	+	9.24579i	−0.102860	+	0.316570i	0.886362	+	0.462992i	$0.153224\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.25560			0.0428905			0.0214452	−	0.999770i	$-0.493173\pi$
$857$	1.25560			0.0428905			0.0214452	+	0.999770i	$0.493173\pi$
$858$		0			0
$859$	−22.5900	−	16.4126i	−0.770761	−	0.559991i	0.131431	−	0.991325i	$-0.458043\pi$
$859$	−22.5900	−	16.4126i	−0.770761	−	0.559991i	−0.902192	+	0.431334i	$0.858043\pi$
$860$		0			0
$861$	−0.777913	+	0.565187i	−0.0265112	+	0.0192615i
$862$		0			0
$863$	15.8484	+	11.5145i	0.539484	+	0.391958i	0.823894	−	0.566745i	$-0.191797\pi$
$863$	15.8484	+	11.5145i	0.539484	+	0.391958i	−0.284409	+	0.958703i	$0.591797\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.42140	−	7.45230i	−0.0822351	−	0.253093i
$868$		0			0
$869$	−7.14198	−	21.9807i	−0.242275	−	0.745646i
$870$		0			0
$871$	−1.51285	+	4.65608i	−0.0512611	+	0.157765i
$872$		0			0
$873$	−20.7884	+	15.1037i	−0.703581	+	0.511182i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	24.5200	−	17.8148i	0.827980	−	0.601563i	−0.0910069	−	0.995850i	$-0.529009\pi$
$877$	24.5200	−	17.8148i	0.827980	−	0.601563i	0.918987	+	0.394287i	$0.129009\pi$
$878$		0			0
$879$	−1.76855	+	5.44304i	−0.0596518	+	0.183589i
$880$		0			0
$881$	6.74593	+	20.7618i	0.227276	+	0.699484i	0.998053	+	0.0623785i	$0.0198686\pi$
$881$	6.74593	+	20.7618i	0.227276	+	0.699484i	−0.770776	+	0.637106i	$0.780131\pi$
$882$		0			0
$883$	7.88167	+	24.2573i	0.265239	+	0.816323i	0.991638	+	0.129049i	$0.0411925\pi$
$883$	7.88167	+	24.2573i	0.265239	+	0.816323i	−0.726399	+	0.687273i	$0.758807\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−34.0788	−	24.7597i	−1.14425	−	0.831349i	−0.156547	−	0.987671i	$-0.550036\pi$
$887$	−34.0788	−	24.7597i	−1.14425	−	0.831349i	−0.987706	+	0.156322i	$0.950036\pi$
$888$		0			0
$889$	8.56576	−	6.22339i	0.287286	−	0.208726i
$890$		0			0
$891$	8.31160	+	6.03873i	0.278449	+	0.202305i
$892$		0			0
$893$	−8.43564			−0.282288
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.540057	+	1.66212i	−0.0180320	+	0.0554967i
$898$		0			0
$899$	21.2606			0.709080
$900$		0			0
$901$	13.9959			0.466272
$902$		0			0
$903$	1.75591	−	5.40412i	0.0584329	−	0.179838i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−48.7145			−1.61754			−0.808769	−	0.588126i	$-0.799866\pi$
$907$	−48.7145			−1.61754			−0.808769	+	0.588126i	$0.799866\pi$
$908$		0			0
$909$	−10.3281	−	7.50382i	−0.342562	−	0.248886i
$910$		0			0
$911$	14.7336	−	10.7046i	0.488147	−	0.354659i	−0.316324	−	0.948651i	$-0.602449\pi$
$911$	14.7336	−	10.7046i	0.488147	−	0.354659i	0.804471	+	0.593992i	$0.202449\pi$
$912$		0			0
$913$	−11.7579	−	8.54260i	−0.389129	−	0.282719i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.70045	+	5.23346i	0.0561539	+	0.172824i
$918$		0			0
$919$	−3.09130	−	9.51404i	−0.101973	−	0.313839i	0.887035	−	0.461701i	$-0.152761\pi$
$919$	−3.09130	−	9.51404i	−0.101973	−	0.313839i	−0.989008	+	0.147862i	$0.952761\pi$
$920$		0			0
$921$	−4.33471	+	13.3409i	−0.142833	+	0.439596i
$922$		0			0
$923$	−9.60211	+	6.97634i	−0.316057	+	0.229629i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−26.5833	+	19.3139i	−0.873110	+	0.634352i
$928$		0			0
$929$	−14.5855	+	44.8895i	−0.478534	+	1.47278i	0.362597	+	0.931946i	$0.381890\pi$
$929$	−14.5855	+	44.8895i	−0.478534	+	1.47278i	−0.841131	+	0.540831i	$0.818110\pi$
$930$		0			0
$931$	−8.08285	−	24.8765i	−0.264905	−	0.815293i
$932$		0			0
$933$	−1.98190	−	6.09967i	−0.0648846	−	0.199694i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.30953	+	0.951426i	0.0427803	+	0.0310817i	0.608970	−	0.793193i	$-0.291583\pi$
$937$	1.30953	+	0.951426i	0.0427803	+	0.0310817i	−0.566190	+	0.824275i	$0.691583\pi$
$938$		0			0
$939$	8.48627	−	6.16564i	0.276939	−	0.201208i
$940$		0			0
$941$	11.2661	+	8.18530i	0.367265	+	0.266833i	0.756076	−	0.654484i	$-0.227114\pi$
$941$	11.2661	+	8.18530i	0.367265	+	0.266833i	−0.388811	+	0.921317i	$0.627114\pi$
$942$		0			0
$943$	−4.78630			−0.155863
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.1131	−	40.3580i	0.426119	−	1.31146i	−0.475801	−	0.879553i	$-0.657842\pi$
$947$	13.1131	−	40.3580i	0.426119	−	1.31146i	0.901919	−	0.431905i	$-0.142158\pi$
$948$		0			0
$949$	−4.11456			−0.133564
$950$		0			0
$951$	−11.9932			−0.388905
$952$		0			0
$953$	−16.4010	+	50.4771i	−0.531281	+	1.63511i	0.220270	+	0.975439i	$0.429306\pi$
$953$	−16.4010	+	50.4771i	−0.531281	+	1.63511i	−0.751550	+	0.659676i	$0.770694\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.66642			0.0861930
$958$		0			0
$959$	−0.457396	−	0.332318i	−0.0147701	−	0.0107311i
$960$		0			0
$961$	−38.5606	+	28.0159i	−1.24389	+	0.903740i
$962$		0			0
$963$	−32.0967	−	23.3196i	−1.03430	−	0.751464i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−8.32828	−	25.6318i	−0.267819	−	0.824263i	−0.991030	−	0.133636i	$-0.957335\pi$
$967$	−8.32828	−	25.6318i	−0.267819	−	0.824263i	0.723211	−	0.690627i	$-0.242665\pi$
$968$		0			0
$969$	1.64691	+	5.06865i	0.0529062	+	0.162829i
$970$		0			0
$971$	8.41468	−	25.8977i	0.270040	−	0.831097i	−0.720449	−	0.693508i	$-0.756064\pi$
$971$	8.41468	−	25.8977i	0.270040	−	0.831097i	0.990489	−	0.137590i	$-0.0439356\pi$
$972$		0			0
$973$	−1.54650	+	1.12360i	−0.0495786	+	0.0360210i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.8970	+	15.1826i	−0.668554	+	0.485733i	−0.869541	−	0.493861i	$-0.835585\pi$
$977$	−20.8970	+	15.1826i	−0.668554	+	0.485733i	0.200987	+	0.979594i	$0.435585\pi$
$978$		0			0
$979$	−5.87657	+	18.0862i	−0.187816	+	0.578038i
$980$		0			0
$981$	10.6005	+	32.6251i	0.338449	+	1.04164i
$982$		0			0
$983$	4.09840	+	12.6136i	0.130719	+	0.402311i	0.994900	−	0.100870i	$-0.0321628\pi$
$983$	4.09840	+	12.6136i	0.130719	+	0.402311i	−0.864181	+	0.503181i	$0.832163\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.847346	+	0.615633i	0.0269713	+	0.0195958i
$988$		0			0
$989$	22.8825	−	16.6251i	0.727621	−	0.528648i
$990$		0			0
$991$	19.3656	+	14.0700i	0.615170	+	0.446947i	0.851231	−	0.524791i	$-0.175857\pi$
$991$	19.3656	+	14.0700i	0.615170	+	0.446947i	−0.236061	+	0.971738i	$0.575857\pi$
$992$		0			0
$993$	5.12171			0.162532
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.1968	+	46.7710i	−0.481288	+	1.48125i	0.355999	+	0.934487i	$0.384141\pi$
$997$	−15.1968	+	46.7710i	−0.481288	+	1.48125i	−0.837286	+	0.546765i	$0.815859\pi$
$998$		0			0
$999$	37.3099			1.18043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.m.b.801.2		8
5.2	odd	4		1000.2.q.b.449.2		16
5.3	odd	4		1000.2.q.b.449.3		16
5.4	even	2		200.2.m.b.161.2	yes	8
20.19	odd	2		400.2.u.e.161.2		8
25.4	even	10		5000.2.a.i.1.1		4
25.9	even	10		200.2.m.b.41.2	✓	8
25.12	odd	20		1000.2.q.b.49.4		16
25.13	odd	20		1000.2.q.b.49.1		16
25.16	even	5	inner	1000.2.m.b.201.2		8
25.21	even	5		5000.2.a.f.1.4		4
100.59	odd	10		400.2.u.e.241.2		8
100.71	odd	10		10000.2.a.z.1.1		4
100.79	odd	10		10000.2.a.q.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.b.41.2	✓	8	25.9	even	10
200.2.m.b.161.2	yes	8	5.4	even	2
400.2.u.e.161.2		8	20.19	odd	2
400.2.u.e.241.2		8	100.59	odd	10
1000.2.m.b.201.2		8	25.16	even	5	inner
1000.2.m.b.801.2		8	1.1	even	1	trivial
1000.2.q.b.49.1		16	25.13	odd	20
1000.2.q.b.49.4		16	25.12	odd	20
1000.2.q.b.449.2		16	5.2	odd	4
1000.2.q.b.449.3		16	5.3	odd	4
5000.2.a.f.1.4		4	25.21	even	5
5000.2.a.i.1.1		4	25.4	even	10
10000.2.a.q.1.4		4	100.79	odd	10
10000.2.a.z.1.1		4	100.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{3} +0.833366 q^{7} +(2.11803 + 1.53884i) q^{9} +(1.45608 - 1.05790i) q^{11} +(-0.892334 - 0.648319i) q^{13} +(0.642383 + 1.97705i) q^{17} +(1.28187 + 3.94520i) q^{19} +(0.159159 - 0.489840i) q^{21} +(2.07411 - 1.50693i) q^{23} +(2.80902 - 2.04087i) q^{27} +(-0.740748 + 2.27979i) q^{29} +(-2.74075 - 8.43516i) q^{31} +(-0.343734 - 1.05790i) q^{33} +(8.69331 + 6.31606i) q^{37} +(-0.551493 + 0.400683i) q^{39} +(-1.51037 - 1.09735i) q^{41} +11.0324 q^{43} +(-0.628402 + 1.93402i) q^{47} -6.30550 q^{49} +1.28477 q^{51} +(2.08052 - 6.40319i) q^{53} +2.56375 q^{57} +(10.8178 + 7.85956i) q^{59} +(-0.601258 + 0.436839i) q^{61} +(1.76510 + 1.28242i) q^{63} +(-1.37160 - 4.22134i) q^{67} +(-0.489632 - 1.50693i) q^{69} +(3.32523 - 10.2340i) q^{71} +(3.01794 - 2.19266i) q^{73} +(1.21345 - 0.881621i) q^{77} +(3.96818 - 12.2128i) q^{79} +(1.76393 + 5.42882i) q^{81} +(-2.49532 - 7.67980i) q^{83} +(1.19856 + 0.870802i) q^{87} +(-8.54813 + 6.21058i) q^{89} +(-0.743641 - 0.540287i) q^{91} -5.48150 q^{93} +(-3.03299 + 9.33458i) q^{97} +4.71197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 4 q^{7} + 8 q^{9} - 2 q^{11} - 8 q^{13} - 10 q^{17} + 3 q^{19} - 3 q^{21} - 6 q^{23} + 18 q^{27} + 6 q^{29} - 10 q^{31} + 16 q^{33} + 2 q^{37} - q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47}+ \cdots - 22 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - 4 * q^7 + 8 * q^9 - 2 * q^11 - 8 * q^13 - 10 * q^17 + 3 * q^19 - 3 * q^21 - 6 * q^23 + 18 * q^27 + 6 * q^29 - 10 * q^31 + 16 * q^33 + 2 * q^37 - q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 - 20 * q^51 + 13 * q^53 + 6 * q^57 + 29 * q^59 + 15 * q^61 - 4 * q^63 - 28 * q^67 - 12 * q^69 - 16 * q^71 - q^73 + 11 * q^77 + 23 * q^79 + 32 * q^81 - 14 * q^83 - 3 * q^87 - 7 * q^89 + 29 * q^91 - 20 * q^93 + 3 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more