LMFDB - Embedded newform 252.2.l.b.205.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(193,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("252.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.l (of order $3$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			205.7
Root			$1.68442 + 0.403398i$ of defining polynomial
Character	$\chi$	$=$	252.205
Dual form			252.2.l.b.193.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68442 + 0.403398i) q^{3} +3.60346 q^{5} +(-1.60302 + 2.10483i) q^{7} +(2.67454 + 1.35898i) q^{9} +O(q^{10})$	\(q+(1.68442 + 0.403398i) q^{3} +3.60346 q^{5} +(-1.60302 + 2.10483i) q^{7} +(2.67454 + 1.35898i) q^{9} -6.02669 q^{11} +(-2.55639 - 4.42780i) q^{13} +(6.06973 + 1.45363i) q^{15} +(0.111006 + 0.192269i) q^{17} +(1.71161 - 2.96460i) q^{19} +(-3.54925 + 2.89876i) q^{21} -1.01976 q^{23} +7.98490 q^{25} +(3.95684 + 3.36800i) q^{27} +(-2.83679 + 4.91347i) q^{29} +(2.52322 - 4.37035i) q^{31} +(-10.1515 - 2.43115i) q^{33} +(-5.77642 + 7.58467i) q^{35} +(1.68526 - 2.91896i) q^{37} +(-2.51987 - 8.48952i) q^{39} +(0.0955808 + 0.165551i) q^{41} +(1.71161 - 2.96460i) q^{43} +(9.63759 + 4.89704i) q^{45} +(1.03506 + 1.79278i) q^{47} +(-1.86064 - 6.74819i) q^{49} +(0.109421 + 0.368641i) q^{51} +(-2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(4.07899 - 4.30318i) q^{57} +(-3.79814 + 6.57858i) q^{59} +(-0.891408 - 1.54396i) q^{61} +(-7.14778 + 3.45098i) q^{63} +(-9.21184 - 15.9554i) q^{65} +(-6.49235 + 11.2451i) q^{67} +(-1.71770 - 0.411369i) q^{69} +5.89560 q^{71} +(6.30519 + 10.9209i) q^{73} +(13.4499 + 3.22109i) q^{75} +(9.66091 - 12.6852i) q^{77} +(-6.30763 - 10.9251i) q^{79} +(5.30633 + 7.26931i) q^{81} +(-3.59946 + 6.23444i) q^{83} +(0.400007 + 0.692832i) q^{85} +(-6.76043 + 7.13199i) q^{87} +(-4.44697 + 7.70238i) q^{89} +(13.4177 + 1.71709i) q^{91} +(6.01316 - 6.34364i) q^{93} +(6.16773 - 10.6828i) q^{95} +(-2.72991 + 4.72835i) q^{97} +(-16.1186 - 8.19016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	$ 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.68442	+	0.403398i	0.972500	+	0.232902i
$3$	1.68442	+	0.403398i	0.972500	+	0.232902i
$4$		0			0
$5$	3.60346			1.61151			0.805757	−	0.592246i	$-0.201759\pi$
$5$	3.60346			1.61151			0.805757	+	0.592246i	$0.201759\pi$
$6$		0			0
$7$	−1.60302	+	2.10483i	−0.605886	+	0.795552i
$7$	−1.60302	+	2.10483i	−0.605886	+	0.795552i
$8$		0			0
$9$	2.67454	+	1.35898i	0.891513	+	0.452994i
$10$		0			0
$11$	−6.02669			−1.81711			−0.908557	−	0.417761i	$-0.862815\pi$
$11$	−6.02669			−1.81711			−0.908557	+	0.417761i	$0.862815\pi$
$12$		0			0
$13$	−2.55639	−	4.42780i	−0.709015	−	1.22805i	−0.965223	−	0.261429i	$-0.915806\pi$
$13$	−2.55639	−	4.42780i	−0.709015	−	1.22805i	0.256207	−	0.966622i	$-0.417527\pi$
$14$		0			0
$15$	6.06973	+	1.45363i	1.56720	+	0.375325i
$16$		0			0
$17$	0.111006	+	0.192269i	0.0269230	+	0.0466320i	0.879173	−	0.476503i	$-0.158096\pi$
$17$	0.111006	+	0.192269i	0.0269230	+	0.0466320i	−0.852250	+	0.523135i	$0.824762\pi$
$18$		0			0
$19$	1.71161	−	2.96460i	0.392671	−	0.680127i	−0.600130	−	0.799903i	$-0.704884\pi$
$19$	1.71161	−	2.96460i	0.392671	−	0.680127i	0.992801	+	0.119776i	$0.0382177\pi$
$20$		0			0
$21$	−3.54925	+	2.89876i	−0.774509	+	0.632562i
$22$		0			0
$23$	−1.01976			−0.212634			−0.106317	−	0.994332i	$-0.533906\pi$
$23$	−1.01976			−0.212634			−0.106317	+	0.994332i	$0.533906\pi$
$24$		0			0
$25$	7.98490			1.59698
$26$		0			0
$27$	3.95684	+	3.36800i	0.761494	+	0.648172i
$28$		0			0
$29$	−2.83679	+	4.91347i	−0.526779	+	0.912408i	0.472734	+	0.881205i	$0.343267\pi$
$29$	−2.83679	+	4.91347i	−0.526779	+	0.912408i	−0.999513	+	0.0312031i	$0.990066\pi$
$30$		0			0
$31$	2.52322	−	4.37035i	0.453184	−	0.784938i	−0.545398	−	0.838177i	$-0.683621\pi$
$31$	2.52322	−	4.37035i	0.453184	−	0.784938i	0.998582	+	0.0532395i	$0.0169547\pi$
$32$		0			0
$33$	−10.1515	−	2.43115i	−1.76714	−	0.423209i
$34$		0			0
$35$	−5.77642	+	7.58467i	−0.976394	+	1.28204i
$36$		0			0
$37$	1.68526	−	2.91896i	0.277055	−	0.479874i	−0.693596	−	0.720364i	$-0.743975\pi$
$37$	1.68526	−	2.91896i	0.277055	−	0.479874i	0.970652	+	0.240490i	$0.0773082\pi$
$38$		0			0
$39$	−2.51987	−	8.48952i	−0.403502	−	1.35941i
$40$		0			0
$41$	0.0955808	+	0.165551i	0.0149272	+	0.0258547i	0.873393	−	0.487017i	$-0.161915\pi$
$41$	0.0955808	+	0.165551i	0.0149272	+	0.0258547i	−0.858465	+	0.512872i	$0.828582\pi$
$42$		0			0
$43$	1.71161	−	2.96460i	0.261019	−	0.452098i	−0.705494	−	0.708716i	$-0.749275\pi$
$43$	1.71161	−	2.96460i	0.261019	−	0.452098i	0.966513	+	0.256618i	$0.0826082\pi$
$44$		0			0
$45$	9.63759	+	4.89704i	1.43669	+	0.730007i
$46$		0			0
$47$	1.03506	+	1.79278i	0.150980	+	0.261504i	0.931588	−	0.363516i	$-0.118424\pi$
$47$	1.03506	+	1.79278i	0.150980	+	0.261504i	−0.780608	+	0.625021i	$0.785091\pi$
$48$		0			0
$49$	−1.86064	−	6.74819i	−0.265805	−	0.964027i
$50$		0			0
$51$	0.109421	+	0.368641i	0.0153219	+	0.0516201i
$52$		0			0
$53$	−2.65207	−	4.59353i	−0.364290	−	0.630969i	0.624372	−	0.781127i	$-0.285355\pi$
$53$	−2.65207	−	4.59353i	−0.364290	−	0.630969i	−0.988662	+	0.150158i	$0.952022\pi$
$54$		0			0
$55$	−21.7169			−2.92831
$56$		0			0
$57$	4.07899	−	4.30318i	0.540276	−	0.569969i
$58$		0			0
$59$	−3.79814	+	6.57858i	−0.494476	+	0.856458i	−0.999980	−	0.00636650i	$-0.997973\pi$
$59$	−3.79814	+	6.57858i	−0.494476	+	0.856458i	0.505503	+	0.862825i	$0.331307\pi$
$60$		0			0
$61$	−0.891408	−	1.54396i	−0.114133	−	0.197684i	0.803300	−	0.595575i	$-0.203076\pi$
$61$	−0.891408	−	1.54396i	−0.114133	−	0.197684i	−0.917433	+	0.397891i	$0.869742\pi$
$62$		0			0
$63$	−7.14778	+	3.45098i	−0.900536	+	0.434782i
$64$		0			0
$65$	−9.21184	−	15.9554i	−1.14259	−	1.97902i
$66$		0			0
$67$	−6.49235	+	11.2451i	−0.793167	+	1.37380i	0.130830	+	0.991405i	$0.458236\pi$
$67$	−6.49235	+	11.2451i	−0.793167	+	1.37380i	−0.923997	+	0.382400i	$0.875098\pi$
$68$		0			0
$69$	−1.71770	−	0.411369i	−0.206787	−	0.0495230i
$70$		0			0
$71$	5.89560			0.699679			0.349839	−	0.936810i	$-0.386236\pi$
$71$	5.89560			0.699679			0.349839	+	0.936810i	$0.386236\pi$
$72$		0			0
$73$	6.30519	+	10.9209i	0.737967	+	1.27820i	0.953409	+	0.301680i	$0.0975473\pi$
$73$	6.30519	+	10.9209i	0.737967	+	1.27820i	−0.215442	+	0.976517i	$0.569119\pi$
$74$		0			0
$75$	13.4499	+	3.22109i	1.55306	+	0.371940i
$76$		0			0
$77$	9.66091	−	12.6852i	1.10096	−	1.44561i
$78$		0			0
$79$	−6.30763	−	10.9251i	−0.709664	−	1.22917i	−0.964982	−	0.262317i	$-0.915514\pi$
$79$	−6.30763	−	10.9251i	−0.709664	−	1.22917i	0.255318	−	0.966857i	$-0.417820\pi$
$80$		0			0
$81$	5.30633	+	7.26931i	0.589592	+	0.807701i
$82$		0			0
$83$	−3.59946	+	6.23444i	−0.395092	+	0.684319i	−0.993113	−	0.117161i	$-0.962621\pi$
$83$	−3.59946	+	6.23444i	−0.395092	+	0.684319i	0.598021	+	0.801480i	$0.295954\pi$
$84$		0			0
$85$	0.400007	+	0.692832i	0.0433868	+	0.0751482i
$86$		0			0
$87$	−6.76043	+	7.13199i	−0.724794	+	0.764629i
$88$		0			0
$89$	−4.44697	+	7.70238i	−0.471378	+	0.816451i	−0.999464	−	0.0327404i	$-0.989577\pi$
$89$	−4.44697	+	7.70238i	−0.471378	+	0.816451i	0.528086	+	0.849191i	$0.322910\pi$
$90$		0			0
$91$	13.4177	+	1.71709i	1.40656	+	0.180000i
$92$		0			0
$93$	6.01316	−	6.34364i	0.623535	−	0.657805i
$94$		0			0
$95$	6.16773	−	10.6828i	0.632796	−	1.09603i
$96$		0			0
$97$	−2.72991	+	4.72835i	−0.277181	+	0.480091i	−0.970683	−	0.240364i	$-0.922733\pi$
$97$	−2.72991	+	4.72835i	−0.277181	+	0.480091i	0.693502	+	0.720454i	$0.256067\pi$
$98$		0			0
$99$	−16.1186	−	8.19016i	−1.61998	−	0.823142i
$100$		0			0
$101$	−3.97289			−0.395318			−0.197659	−	0.980271i	$-0.563334\pi$
$101$	−3.97289			−0.395318			−0.197659	+	0.980271i	$0.563334\pi$
$102$		0			0
$103$	3.55788			0.350568			0.175284	−	0.984518i	$-0.443916\pi$
$103$	3.55788			0.350568			0.175284	+	0.984518i	$0.443916\pi$
$104$		0			0
$105$	−12.7896	+	10.4456i	−1.24813	+	1.01938i
$106$		0			0
$107$	−1.23035	+	2.13102i	−0.118942	+	0.206014i	−0.919349	−	0.393444i	$-0.871284\pi$
$107$	−1.23035	+	2.13102i	−0.118942	+	0.206014i	0.800407	+	0.599457i	$0.204617\pi$
$108$		0			0
$109$	−2.97628	−	5.15506i	−0.285075	−	0.493765i	0.687552	−	0.726135i	$-0.258685\pi$
$109$	−2.97628	−	5.15506i	−0.285075	−	0.493765i	−0.972627	+	0.232370i	$0.925352\pi$
$110$		0			0
$111$	4.01619	−	4.23692i	0.381200	−	0.402150i
$112$		0			0
$113$	3.52974	+	6.11370i	0.332050	+	0.575128i	0.982914	−	0.184067i	$-0.0589263\pi$
$113$	3.52974	+	6.11370i	0.332050	+	0.575128i	−0.650863	+	0.759195i	$0.725593\pi$
$114$		0			0
$115$	−3.67466			−0.342664
$116$		0			0
$117$	−0.819868	−	15.3164i	−0.0757968	−	1.41600i
$118$		0			0
$119$	−0.582639	−	0.0745613i	−0.0534104	−	0.00683502i
$120$		0			0
$121$	25.3209			2.30190
$122$		0			0
$123$	0.0942154	+	0.317414i	0.00849511	+	0.0286203i
$124$		0			0
$125$	10.7560			0.962042
$126$		0			0
$127$	2.76393			0.245259			0.122629	−	0.992453i	$-0.460867\pi$
$127$	2.76393			0.245259			0.122629	+	0.992453i	$0.460867\pi$
$128$		0			0
$129$	4.07899	−	4.30318i	0.359135	−	0.378873i
$130$		0			0
$131$	8.45496			0.738713			0.369357	−	0.929288i	$-0.379578\pi$
$131$	8.45496			0.738713			0.369357	+	0.929288i	$0.379578\pi$
$132$		0			0
$133$	3.49624	+	8.35499i	0.303162	+	0.724469i
$134$		0			0
$135$	14.2583	+	12.1364i	1.22716	+	1.04454i
$136$		0			0
$137$	18.0857			1.54517			0.772584	−	0.634913i	$-0.218964\pi$
$137$	18.0857			1.54517			0.772584	+	0.634913i	$0.218964\pi$
$138$		0			0
$139$	6.00936	+	10.4085i	0.509707	+	0.882839i	0.999937	+	0.0112454i	$0.00357959\pi$
$139$	6.00936	+	10.4085i	0.509707	+	0.882839i	−0.490230	+	0.871593i	$0.663087\pi$
$140$		0			0
$141$	1.02028	+	3.43734i	0.0859229	+	0.289477i
$142$		0			0
$143$	15.4066	+	26.6850i	1.28836	+	2.23151i
$144$		0			0
$145$	−10.2223	+	17.7055i	−0.848912	+	1.47036i
$146$		0			0
$147$	−0.411888	−	12.1174i	−0.0339719	−	0.999423i
$148$		0			0
$149$	−4.98051			−0.408019			−0.204010	−	0.978969i	$-0.565397\pi$
$149$	−4.98051			−0.408019			−0.204010	+	0.978969i	$0.565397\pi$
$150$		0			0
$151$	−0.184381			−0.0150047			−0.00750237	−	0.999972i	$-0.502388\pi$
$151$	−0.184381			−0.0150047			−0.00750237	+	0.999972i	$0.502388\pi$
$152$		0			0
$153$	0.0356012	+	0.665086i	0.00287819	+	0.0537690i
$154$		0			0
$155$	9.09232	−	15.7484i	0.730313	−	1.26494i
$156$		0			0
$157$	−2.16698	+	3.75332i	−0.172944	+	0.299548i	−0.939448	−	0.342692i	$-0.888661\pi$
$157$	−2.16698	+	3.75332i	−0.172944	+	0.299548i	0.766504	+	0.642240i	$0.221995\pi$
$158$		0			0
$159$	−2.61419	−	8.80727i	−0.207319	−	0.698462i
$160$		0			0
$161$	1.63470	−	2.14642i	0.128832	−	0.169162i
$162$		0			0
$163$	11.8652	−	20.5511i	0.929353	−	1.60969i	0.144946	−	0.989440i	$-0.453699\pi$
$163$	11.8652	−	20.5511i	0.929353	−	1.60969i	0.784407	−	0.620247i	$-0.212967\pi$
$164$		0			0
$165$	−36.5804	−	8.76055i	−2.84778	−	0.682008i
$166$		0			0
$167$	1.59445	+	2.76166i	0.123382	+	0.213704i	0.921099	−	0.389328i	$-0.127293\pi$
$167$	1.59445	+	2.76166i	0.123382	+	0.213704i	−0.797717	+	0.603032i	$0.793959\pi$
$168$		0			0
$169$	−6.57027	+	11.3800i	−0.505405	+	0.875388i
$170$		0			0
$171$	8.60663	−	5.60290i	0.658165	−	0.428464i
$172$		0			0
$173$	−10.6530	−	18.4515i	−0.809932	−	1.40284i	−0.912910	−	0.408160i	$-0.866170\pi$
$173$	−10.6530	−	18.4515i	−0.809932	−	1.40284i	0.102978	−	0.994684i	$-0.467163\pi$
$174$		0			0
$175$	−12.8000	+	16.8069i	−0.967587	+	1.27048i
$176$		0			0
$177$	−9.05146	+	9.54893i	−0.680349	+	0.717741i
$178$		0			0
$179$	0.250143	+	0.433260i	0.0186965	+	0.0323833i	0.875222	−	0.483721i	$-0.160715\pi$
$179$	0.250143	+	0.433260i	0.0186965	+	0.0323833i	−0.856526	+	0.516104i	$0.827382\pi$
$180$		0			0
$181$	5.88424			0.437372			0.218686	−	0.975795i	$-0.429823\pi$
$181$	5.88424			0.437372			0.218686	+	0.975795i	$0.429823\pi$
$182$		0			0
$183$	−0.878674	−	2.96028i	−0.0649534	−	0.218830i
$184$		0			0
$185$	6.07276	−	10.5183i	0.446478	−	0.773323i
$186$		0			0
$187$	−0.669001	−	1.15874i	−0.0489222	−	0.0847357i
$188$		0			0
$189$	−13.4320	+	2.92950i	−0.977033	+	0.213090i
$190$		0			0
$191$	3.94466	+	6.83235i	0.285425	+	0.494371i	0.972712	−	0.232015i	$-0.0745318\pi$
$191$	3.94466	+	6.83235i	0.285425	+	0.494371i	−0.687287	+	0.726386i	$0.741198\pi$
$192$		0			0
$193$	−9.50508	+	16.4633i	−0.684190	+	1.18505i	0.289500	+	0.957178i	$0.406511\pi$
$193$	−9.50508	+	16.4633i	−0.684190	+	1.18505i	−0.973691	+	0.227875i	$0.926822\pi$
$194$		0			0
$195$	−9.08025	−	30.5916i	−0.650250	−	2.19071i
$196$		0			0
$197$	−9.72107			−0.692597			−0.346299	−	0.938124i	$-0.612562\pi$
$197$	−9.72107			−0.692597			−0.346299	+	0.938124i	$0.612562\pi$
$198$		0			0
$199$	−7.54581	−	13.0697i	−0.534908	−	0.926489i	−0.999168	−	0.0407893i	$-0.987013\pi$
$199$	−7.54581	−	13.0697i	−0.534908	−	0.926489i	0.464259	−	0.885699i	$-0.346321\pi$
$200$		0			0
$201$	−15.4721	+	16.3224i	−1.09132	+	1.15130i
$202$		0			0
$203$	−5.79458	−	13.8474i	−0.406700	−	0.971895i
$204$		0			0
$205$	0.344421	+	0.596555i	0.0240554	+	0.0416652i
$206$		0			0
$207$	−2.72739	−	1.38583i	−0.189566	−	0.0963222i
$208$		0			0
$209$	−10.3154	+	17.8667i	−0.713529	+	1.23587i
$210$		0			0
$211$	−8.75173	−	15.1584i	−0.602494	−	1.04355i	−0.992442	−	0.122713i	$-0.960840\pi$
$211$	−8.75173	−	15.1584i	−0.602494	−	1.04355i	0.389948	−	0.920837i	$-0.372493\pi$
$212$		0			0
$213$	9.93066	+	2.37827i	0.680438	+	0.162957i
$214$		0			0
$215$	6.16773	−	10.6828i	0.420636	−	0.728562i
$216$		0			0
$217$	5.15407	+	12.3167i	0.349881	+	0.836114i
$218$		0			0
$219$	6.21512	+	20.9389i	0.419979	+	1.41492i
$220$		0			0
$221$	0.567551	−	0.983028i	0.0381776	−	0.0661256i
$222$		0			0
$223$	5.00337	−	8.66610i	0.335051	−	0.580325i	−0.648444	−	0.761262i	$-0.724580\pi$
$223$	5.00337	−	8.66610i	0.335051	−	0.580325i	0.983495	+	0.180938i	$0.0579132\pi$
$224$		0			0
$225$	21.3559	+	10.8513i	1.42373	+	0.723423i
$226$		0			0
$227$	−2.26633			−0.150422			−0.0752110	−	0.997168i	$-0.523963\pi$
$227$	−2.26633			−0.150422			−0.0752110	+	0.997168i	$0.523963\pi$
$228$		0			0
$229$	−5.02456			−0.332032			−0.166016	−	0.986123i	$-0.553090\pi$
$229$	−5.02456			−0.332032			−0.166016	+	0.986123i	$0.553090\pi$
$230$		0			0
$231$	21.3902	−	17.4699i	1.40737	−	1.14944i
$232$		0			0
$233$	−7.72393	+	13.3782i	−0.506011	+	0.876438i	0.493964	+	0.869482i	$0.335547\pi$
$233$	−7.72393	+	13.3782i	−0.506011	+	0.876438i	−0.999976	+	0.00695541i	$0.997786\pi$
$234$		0			0
$235$	3.72981	+	6.46022i	0.243306	+	0.421418i
$236$		0			0
$237$	−6.21752	−	20.9470i	−0.403871	−	1.36065i
$238$		0			0
$239$	−4.62691	−	8.01404i	−0.299290	−	0.518385i	0.676684	−	0.736274i	$-0.263416\pi$
$239$	−4.62691	−	8.01404i	−0.299290	−	0.518385i	−0.975974	+	0.217889i	$0.930083\pi$
$240$		0			0
$241$	−16.3277			−1.05176			−0.525881	−	0.850558i	$-0.676264\pi$
$241$	−16.3277			−1.05176			−0.525881	+	0.850558i	$0.676264\pi$
$242$		0			0
$243$	6.00567	+	14.3851i	0.385264	+	0.922807i
$244$		0			0
$245$	−6.70472	−	24.3168i	−0.428349	−	1.55354i
$246$		0			0
$247$	−17.5022			−1.11364
$248$		0			0
$249$	−8.57796	+	9.04941i	−0.543606	+	0.573483i
$250$		0			0
$251$	7.54803			0.476427			0.238214	−	0.971213i	$-0.423438\pi$
$251$	7.54803			0.476427			0.238214	+	0.971213i	$0.423438\pi$
$252$		0			0
$253$	6.14577			0.386381
$254$		0			0
$255$	0.394292	+	1.32838i	0.0246915	+	0.0831865i
$256$		0			0
$257$	25.2926			1.57771			0.788856	−	0.614579i	$-0.210674\pi$
$257$	25.2926			1.57771			0.788856	+	0.614579i	$0.210674\pi$
$258$		0			0
$259$	3.44240	+	8.22634i	0.213901	+	0.511160i
$260$		0			0
$261$	−14.2644	+	9.28612i	−0.882946	+	0.574796i
$262$		0			0
$263$	23.4980			1.44895			0.724474	−	0.689302i	$-0.242083\pi$
$263$	23.4980			1.44895			0.724474	+	0.689302i	$0.242083\pi$
$264$		0			0
$265$	−9.55663	−	16.5526i	−0.587059	−	1.01682i
$266$		0			0
$267$	−10.5977	+	11.1801i	−0.648568	+	0.684214i
$268$		0			0
$269$	−13.9078	−	24.0891i	−0.847975	−	1.46874i	−0.883013	−	0.469349i	$-0.844488\pi$
$269$	−13.9078	−	24.0891i	−0.847975	−	1.46874i	0.0350378	−	0.999386i	$-0.488845\pi$
$270$		0			0
$271$	−9.57834	+	16.5902i	−0.581843	+	1.00778i	0.413418	+	0.910541i	$0.364335\pi$
$271$	−9.57834	+	16.5902i	−0.581843	+	1.00778i	−0.995261	+	0.0972397i	$0.968999\pi$
$272$		0			0
$273$	21.9084	+	8.30498i	1.32596	+	0.502640i
$274$		0			0
$275$	−48.1225			−2.90190
$276$		0			0
$277$	27.5811			1.65719			0.828593	−	0.559852i	$-0.189142\pi$
$277$	27.5811			1.65719			0.828593	+	0.559852i	$0.189142\pi$
$278$		0			0
$279$	12.6877	−	8.25966i	0.759592	−	0.494493i
$280$		0			0
$281$	0.192591	−	0.333577i	0.0114890	−	0.0198995i	−0.860224	−	0.509917i	$-0.829676\pi$
$281$	0.192591	−	0.333577i	0.0114890	−	0.0198995i	0.871713	+	0.490017i	$0.163010\pi$
$282$		0			0
$283$	7.49904	−	12.9887i	0.445772	−	0.772099i	−0.552334	−	0.833623i	$-0.686263\pi$
$283$	7.49904	−	12.9887i	0.445772	−	0.772099i	0.998106	+	0.0615239i	$0.0195960\pi$
$284$		0			0
$285$	14.6985	−	15.5063i	0.870662	−	0.918514i
$286$		0			0
$287$	−0.501675	−	0.0642002i	−0.0296129	−	0.00378962i
$288$		0			0
$289$	8.47536	−	14.6797i	0.498550	−	0.863514i
$290$		0			0
$291$	−6.50572	+	6.86328i	−0.381372	+	0.402333i
$292$		0			0
$293$	11.2323	+	19.4550i	0.656200	+	1.13657i	0.981592	+	0.190992i	$0.0611704\pi$
$293$	11.2323	+	19.4550i	0.656200	+	1.13657i	−0.325392	+	0.945579i	$0.605496\pi$
$294$		0			0
$295$	−13.6865	+	23.7056i	−0.796856	+	1.38019i
$296$		0			0
$297$	−23.8466	−	20.2979i	−1.38372	−	1.17780i
$298$		0			0
$299$	2.60690	+	4.51529i	0.150761	+	0.261126i
$300$		0			0
$301$	3.49624	+	8.35499i	0.201520	+	0.481574i
$302$		0			0
$303$	−6.69202	−	1.60266i	−0.384447	−	0.0920703i
$304$		0			0
$305$	−3.21215	−	5.56361i	−0.183927	−	0.318571i
$306$		0			0
$307$	6.90792			0.394256			0.197128	−	0.980378i	$-0.436839\pi$
$307$	6.90792			0.394256			0.197128	+	0.980378i	$0.436839\pi$
$308$		0			0
$309$	5.99296	+	1.43524i	0.340928	+	0.0816480i
$310$		0			0
$311$	−11.5890	+	20.0727i	−0.657152	+	1.13822i	0.324198	+	0.945989i	$0.394906\pi$
$311$	−11.5890	+	20.0727i	−0.657152	+	1.13822i	−0.981350	+	0.192231i	$0.938428\pi$
$312$		0			0
$313$	−8.21883	−	14.2354i	−0.464556	−	0.804635i	0.534625	−	0.845089i	$-0.320453\pi$
$313$	−8.21883	−	14.2354i	−0.464556	−	0.804635i	−0.999181	+	0.0404546i	$0.987119\pi$
$314$		0			0
$315$	−25.7567	+	12.4354i	−1.45123	+	0.700658i
$316$		0			0
$317$	7.18401	+	12.4431i	0.403494	+	0.698873i	0.994145	−	0.108055i	$-0.0344622\pi$
$317$	7.18401	+	12.4431i	0.403494	+	0.698873i	−0.590651	+	0.806927i	$0.701129\pi$
$318$		0			0
$319$	17.0965	−	29.6119i	0.957218	−	1.65795i
$320$		0			0
$321$	−2.93207	+	3.09322i	−0.163652	+	0.172646i
$322$		0			0
$323$	0.760001			0.0422876
$324$		0			0
$325$	−20.4125	−	35.3555i	−1.13228	−	1.96117i
$326$		0			0
$327$	−2.93376	−	9.88391i	−0.162237	−	0.546581i
$328$		0			0
$329$	−5.43274	−	0.695237i	−0.299517	−	0.0383297i
$330$		0			0
$331$	−1.87582	−	3.24902i	−0.103105	−	0.178582i	0.809858	−	0.586626i	$-0.199544\pi$
$331$	−1.87582	−	3.24902i	−0.103105	−	0.178582i	−0.912962	+	0.408044i	$0.866211\pi$
$332$		0			0
$333$	8.47411	−	5.51663i	0.464378	−	0.302309i
$334$		0			0
$335$	−23.3949	+	40.5211i	−1.27820	+	2.21391i
$336$		0			0
$337$	−2.77171	−	4.80074i	−0.150984	−	0.261513i	0.780605	−	0.625024i	$-0.214911\pi$
$337$	−2.77171	−	4.80074i	−0.150984	−	0.261513i	−0.931590	+	0.363512i	$0.881578\pi$
$338$		0			0
$339$	3.47932	+	11.7219i	0.188971	+	0.636647i
$340$		0			0
$341$	−15.2067	+	26.3387i	−0.823487	+	1.42632i
$342$		0			0
$343$	17.1864	+	6.90117i	0.927981	+	0.372628i
$344$		0			0
$345$	−6.18967	−	1.48235i	−0.333240	−	0.0798070i
$346$		0			0
$347$	−3.77609	+	6.54037i	−0.202711	+	0.351106i	−0.949401	−	0.314066i	$-0.898309\pi$
$347$	−3.77609	+	6.54037i	−0.202711	+	0.351106i	0.746690	+	0.665172i	$0.231642\pi$
$348$		0			0
$349$	−9.10179	+	15.7648i	−0.487207	+	0.843868i	−0.999892	−	0.0147092i	$-0.995318\pi$
$349$	−9.10179	+	15.7648i	−0.487207	+	0.843868i	0.512684	+	0.858577i	$0.328651\pi$
$350$		0			0
$351$	4.79761	−	26.1300i	0.256077	−	1.39472i
$352$		0			0
$353$	−0.532449			−0.0283394			−0.0141697	−	0.999900i	$-0.504511\pi$
$353$	−0.532449			−0.0283394			−0.0141697	+	0.999900i	$0.504511\pi$
$354$		0			0
$355$	21.2445			1.12754
$356$		0			0
$357$	−0.951331	−	0.360628i	−0.0503498	−	0.0190865i
$358$		0			0
$359$	13.0550	−	22.6118i	0.689014	−	1.19341i	−0.283143	−	0.959078i	$-0.591377\pi$
$359$	13.0550	−	22.6118i	0.689014	−	1.19341i	0.972157	−	0.234330i	$-0.0752895\pi$
$360$		0			0
$361$	3.64075	+	6.30597i	0.191618	+	0.331893i
$362$		0			0
$363$	42.6511	+	10.2144i	2.23860	+	0.536118i
$364$		0			0
$365$	22.7205	+	39.3530i	1.18924	+	2.05983i
$366$		0			0
$367$	21.1842			1.10581			0.552904	−	0.833245i	$-0.313520\pi$
$367$	21.1842			1.10581			0.552904	+	0.833245i	$0.313520\pi$
$368$		0			0
$369$	0.0306540	+	0.572665i	0.00159578	+	0.0298117i
$370$		0			0
$371$	13.9199	+	1.78136i	0.722687	+	0.0924835i
$372$		0			0
$373$	18.0085			0.932447			0.466223	−	0.884667i	$-0.345614\pi$
$373$	18.0085			0.932447			0.466223	+	0.884667i	$0.345614\pi$
$374$		0			0
$375$	18.1176	+	4.33893i	0.935586	+	0.224061i
$376$		0			0
$377$	29.0078			1.49398
$378$		0			0
$379$	−15.9120			−0.817343			−0.408672	−	0.912681i	$-0.634008\pi$
$379$	−15.9120			−0.817343			−0.408672	+	0.912681i	$0.634008\pi$
$380$		0			0
$381$	4.65561	+	1.11496i	0.238514	+	0.0571212i
$382$		0			0
$383$	−0.308586			−0.0157680			−0.00788400	−	0.999969i	$-0.502510\pi$
$383$	−0.308586			−0.0157680			−0.00788400	+	0.999969i	$0.502510\pi$
$384$		0			0
$385$	34.8127	−	45.7104i	1.77422	−	2.32962i
$386$		0			0
$387$	8.60663	−	5.60290i	0.437499	−	0.284811i
$388$		0			0
$389$	4.77506			0.242105			0.121053	−	0.992646i	$-0.461373\pi$
$389$	4.77506			0.242105			0.121053	+	0.992646i	$0.461373\pi$
$390$		0			0
$391$	−0.113200	−	0.196068i	−0.00572476	−	0.00991557i
$392$		0			0
$393$	14.2417	+	3.41071i	0.718399	+	0.172048i
$394$		0			0
$395$	−22.7293	−	39.3683i	−1.14363	−	1.98083i
$396$		0			0
$397$	−4.75029	+	8.22774i	−0.238410	+	0.412939i	−0.960258	−	0.279113i	$-0.909960\pi$
$397$	−4.75029	+	8.22774i	−0.238410	+	0.412939i	0.721848	+	0.692052i	$0.243293\pi$
$398$		0			0
$399$	2.51874	+	15.4837i	0.126095	+	0.775154i
$400$		0			0
$401$	−19.3418			−0.965882			−0.482941	−	0.875653i	$-0.660431\pi$
$401$	−19.3418			−0.965882			−0.482941	+	0.875653i	$0.660431\pi$
$402$		0			0
$403$	−25.8014			−1.28526
$404$		0			0
$405$	19.1211	+	26.1946i	0.950137	+	1.30162i
$406$		0			0
$407$	−10.1565	+	17.5916i	−0.503441	+	0.871985i
$408$		0			0
$409$	5.34036	−	9.24977i	0.264064	−	0.457372i	−0.703254	−	0.710939i	$-0.748270\pi$
$409$	5.34036	−	9.24977i	0.264064	−	0.457372i	0.967318	+	0.253567i	$0.0816037\pi$
$410$		0			0
$411$	30.4639	+	7.29574i	1.50268	+	0.359872i
$412$		0			0
$413$	−7.75829	−	18.5401i	−0.381761	−	0.912297i
$414$		0			0
$415$	−12.9705	+	22.4655i	−0.636696	+	1.10279i
$416$		0			0
$417$	5.92351	+	19.9565i	0.290076	+	0.977273i
$418$		0			0
$419$	−17.5274	−	30.3583i	−0.856267	−	1.48310i	−0.875464	−	0.483283i	$-0.839444\pi$
$419$	−17.5274	−	30.3583i	−0.856267	−	1.48310i	0.0191966	−	0.999816i	$-0.493889\pi$
$420$		0			0
$421$	15.8653	−	27.4795i	0.773226	−	1.33927i	−0.162560	−	0.986699i	$-0.551975\pi$
$421$	15.8653	−	27.4795i	0.773226	−	1.33927i	0.935786	−	0.352568i	$-0.114692\pi$
$422$		0			0
$423$	0.331959	+	6.20151i	0.0161404	+	0.301528i
$424$		0			0
$425$	0.886375	+	1.53525i	0.0429955	+	0.0744704i
$426$		0			0
$427$	4.67873	+	0.598745i	0.226420	+	0.0289753i
$428$		0			0
$429$	15.1865	+	51.1636i	0.733210	+	2.47020i
$430$		0			0
$431$	−17.4768	−	30.2707i	−0.841829	−	1.45809i	−0.888347	−	0.459172i	$-0.848146\pi$
$431$	−17.4768	−	30.2707i	−0.841829	−	1.45809i	0.0465186	−	0.998917i	$-0.485187\pi$
$432$		0			0
$433$	−28.3369			−1.36178			−0.680891	−	0.732385i	$-0.738407\pi$
$433$	−28.3369			−1.36178			−0.680891	+	0.732385i	$0.738407\pi$
$434$		0			0
$435$	−24.3609	+	25.6998i	−1.16802	+	1.23221i
$436$		0			0
$437$	−1.74543	+	3.02318i	−0.0834955	+	0.144618i
$438$		0			0
$439$	4.85457	+	8.40837i	0.231696	+	0.401310i	0.958307	−	0.285739i	$-0.0922391\pi$
$439$	4.85457	+	8.40837i	0.231696	+	0.401310i	−0.726611	+	0.687049i	$0.758906\pi$
$440$		0			0
$441$	4.19432	−	20.5769i	0.199730	−	0.979851i
$442$		0			0
$443$	5.03961	+	8.72885i	0.239439	+	0.414720i	0.960553	−	0.278096i	$-0.0897032\pi$
$443$	5.03961	+	8.72885i	0.239439	+	0.414720i	−0.721114	+	0.692816i	$0.756370\pi$
$444$		0			0
$445$	−16.0245	+	27.7552i	−0.759633	+	1.31572i
$446$		0			0
$447$	−8.38927	−	2.00913i	−0.396799	−	0.0950285i
$448$		0			0
$449$	−28.9202			−1.36483			−0.682414	−	0.730966i	$-0.739070\pi$
$449$	−28.9202			−1.36483			−0.682414	+	0.730966i	$0.739070\pi$
$450$		0			0
$451$	−0.576035	−	0.997723i	−0.0271245	−	0.0469809i
$452$		0			0
$453$	−0.310575	−	0.0743790i	−0.0145921	−	0.00349463i
$454$		0			0
$455$	48.3502	+	6.18746i	2.26669	+	0.290072i
$456$		0			0
$457$	4.10680	+	7.11318i	0.192108	+	0.332741i	0.945949	−	0.324317i	$-0.105134\pi$
$457$	4.10680	+	7.11318i	0.192108	+	0.332741i	−0.753841	+	0.657057i	$0.771801\pi$
$458$		0			0
$459$	−0.208327	+	1.13465i	−0.00972387	+	0.0529607i
$460$		0			0
$461$	14.0516	−	24.3381i	0.654448	−	1.13354i	−0.327584	−	0.944822i	$-0.606234\pi$
$461$	14.0516	−	24.3381i	0.654448	−	1.13354i	0.982032	−	0.188715i	$-0.0604323\pi$
$462$		0			0
$463$	1.54897	+	2.68289i	0.0719866	+	0.124684i	0.899772	−	0.436361i	$-0.143733\pi$
$463$	1.54897	+	2.68289i	0.0719866	+	0.124684i	−0.827785	+	0.561045i	$0.810399\pi$
$464$		0			0
$465$	21.6681	−	22.8590i	1.00484	−	1.06006i
$466$		0			0
$467$	5.75954	−	9.97582i	0.266520	−	0.461626i	−0.701441	−	0.712728i	$-0.747460\pi$
$467$	5.75954	−	9.97582i	0.266520	−	0.461626i	0.967961	+	0.251102i	$0.0807929\pi$
$468$		0			0
$469$	−13.2616	−	31.6914i	−0.612365	−	1.46337i
$470$		0			0
$471$	−5.16419	+	5.44801i	−0.237953	+	0.251031i
$472$		0			0
$473$	−10.3154	+	17.8667i	−0.474301	+	0.821513i
$474$		0			0
$475$	13.6671	−	23.6721i	0.627088	−	1.08615i
$476$		0			0
$477$	−0.850555	−	15.8897i	−0.0389442	−	0.727539i
$478$		0			0
$479$	−40.7084			−1.86001			−0.930007	−	0.367541i	$-0.880200\pi$
$479$	−40.7084			−1.86001			−0.930007	+	0.367541i	$0.880200\pi$
$480$		0			0
$481$	−17.2327			−0.785745
$482$		0			0
$483$	3.61938	−	2.95604i	0.164687	−	0.134505i
$484$		0			0
$485$	−9.83712	+	17.0384i	−0.446681	+	0.773673i
$486$		0			0
$487$	16.7955	+	29.0907i	0.761077	+	1.31822i	0.942296	+	0.334781i	$0.108662\pi$
$487$	16.7955	+	29.0907i	0.761077	+	1.31822i	−0.181219	+	0.983443i	$0.558004\pi$
$488$		0			0
$489$	28.2762	−	29.8303i	1.27869	−	1.34897i
$490$		0			0
$491$	−3.22990	−	5.59435i	−0.145763	−	0.252469i	0.783894	−	0.620894i	$-0.213230\pi$
$491$	−3.22990	−	5.59435i	−0.145763	−	0.252469i	−0.929657	+	0.368425i	$0.879897\pi$
$492$		0			0
$493$	−1.25961			−0.0567299
$494$		0			0
$495$	−58.0827	−	29.5129i	−2.61062	−	1.32651i
$496$		0			0
$497$	−9.45078	+	12.4092i	−0.423925	+	0.556631i
$498$		0			0
$499$	−12.0117			−0.537717			−0.268859	−	0.963180i	$-0.586646\pi$
$499$	−12.0117			−0.537717			−0.268859	+	0.963180i	$0.586646\pi$
$500$		0			0
$501$	1.57167	+	5.29500i	0.0702170	+	0.236563i
$502$		0			0
$503$	34.3935			1.53353			0.766765	−	0.641928i	$-0.221865\pi$
$503$	34.3935			1.53353			0.766765	+	0.641928i	$0.221865\pi$
$504$		0			0
$505$	−14.3162			−0.637060
$506$		0			0
$507$	−15.6578	+	16.5183i	−0.695386	+	0.733605i
$508$		0			0
$509$	−31.5046			−1.39642			−0.698208	−	0.715895i	$-0.746019\pi$
$509$	−31.5046			−1.39642			−0.698208	+	0.715895i	$0.746019\pi$
$510$		0			0
$511$	−33.0941	−	4.23510i	−1.46399	−	0.187350i
$512$		0			0
$513$	16.7574	−	5.96574i	0.739856	−	0.263394i
$514$		0			0
$515$	12.8207			0.564946
$516$		0			0
$517$	−6.23801	−	10.8045i	−0.274347	−	0.475183i
$518$		0			0
$519$	−10.5008	−	35.3775i	−0.460934	−	1.55290i
$520$		0			0
$521$	13.3195	+	23.0701i	0.583539	+	1.01072i	0.995056	+	0.0993168i	$0.0316657\pi$
$521$	13.3195	+	23.0701i	0.583539	+	1.01072i	−0.411517	+	0.911402i	$0.635001\pi$
$522$		0			0
$523$	15.2006	−	26.3282i	0.664676	−	1.15125i	−0.314697	−	0.949192i	$-0.601903\pi$
$523$	15.2006	−	26.3282i	0.664676	−	1.15125i	0.979373	−	0.202060i	$-0.0647637\pi$
$524$		0			0
$525$	−28.3404	+	23.1463i	−1.23688	+	1.01019i
$526$		0			0
$527$	1.12038			0.0488043
$528$		0			0
$529$	−21.9601			−0.954787
$530$		0			0
$531$	−19.0985	+	12.4331i	−0.828803	+	0.539549i
$532$		0			0
$533$	0.488684	−	0.846425i	0.0211672	−	0.0366627i
$534$		0			0
$535$	−4.43350	+	7.67904i	−0.191677	+	0.331994i
$536$		0			0
$537$	0.246569	+	0.830698i	0.0106402	+	0.0358473i
$538$		0			0
$539$	11.2135	+	40.6692i	0.482998	+	1.75175i
$540$		0			0
$541$	−1.25855	+	2.17988i	−0.0541094	+	0.0937202i	−0.891811	−	0.452407i	$-0.850565\pi$
$541$	−1.25855	+	2.17988i	−0.0541094	+	0.0937202i	0.837702	+	0.546128i	$0.183899\pi$
$542$		0			0
$543$	9.91153	+	2.37369i	0.425344	+	0.101865i
$544$		0			0
$545$	−10.7249	−	18.5760i	−0.459403	−	0.795710i
$546$		0			0
$547$	9.25785	−	16.0351i	0.395837	−	0.685610i	−0.597370	−	0.801965i	$-0.703788\pi$
$547$	9.25785	−	16.0351i	0.395837	−	0.685610i	0.993208	+	0.116355i	$0.0371211\pi$
$548$		0			0
$549$	−0.285886	−	5.34080i	−0.0122013	−	0.227940i
$550$		0			0
$551$	9.71099	+	16.8199i	0.413702	+	0.716553i
$552$		0			0
$553$	33.1068	+	4.23674i	1.40785	+	0.180164i
$554$		0			0
$555$	14.4722	−	15.2676i	0.614309	−	0.648071i
$556$		0			0
$557$	−12.2124	−	21.1524i	−0.517454	−	0.896257i	−0.999794	−	0.0202733i	$-0.993546\pi$
$557$	−12.2124	−	21.1524i	−0.517454	−	0.896257i	0.482340	−	0.875984i	$-0.339787\pi$
$558$		0			0
$559$	−17.5022			−0.740265
$560$		0			0
$561$	−0.659443	−	2.22168i	−0.0278417	−	0.0937995i
$562$		0			0
$563$	−12.3700	+	21.4255i	−0.521334	+	0.902976i	0.478359	+	0.878165i	$0.341232\pi$
$563$	−12.3700	+	21.4255i	−0.521334	+	0.902976i	−0.999692	+	0.0248116i	$0.992101\pi$
$564$		0			0
$565$	12.7193	+	22.0304i	0.535104	+	0.926828i
$566$		0			0
$567$	−23.8068	−	0.483930i	−0.999793	−	0.0203231i
$568$		0			0
$569$	−8.35982	−	14.4796i	−0.350462	−	0.607018i	0.635869	−	0.771797i	$-0.280642\pi$
$569$	−8.35982	−	14.4796i	−0.350462	−	0.607018i	−0.986330	+	0.164780i	$0.947309\pi$
$570$		0			0
$571$	14.8135	−	25.6578i	0.619926	−	1.07374i	−0.369573	−	0.929202i	$-0.620496\pi$
$571$	14.8135	−	25.6578i	0.619926	−	1.07374i	0.989499	−	0.144542i	$-0.0461708\pi$
$572$		0			0
$573$	3.88831	+	13.0998i	0.162436	+	0.547252i
$574$		0			0
$575$	−8.14267			−0.339573
$576$		0			0
$577$	15.3341	+	26.5594i	0.638367	+	1.10568i	0.985791	+	0.167976i	$0.0537230\pi$
$577$	15.3341	+	26.5594i	0.638367	+	1.10568i	−0.347425	+	0.937708i	$0.612944\pi$
$578$		0			0
$579$	−22.6518	+	23.8967i	−0.941376	+	0.993115i
$580$		0			0
$581$	−7.35244	−	17.5702i	−0.305031	−	0.728935i
$582$		0			0
$583$	15.9832	+	27.6837i	0.661957	+	1.14654i
$584$		0			0
$585$	−2.95436	−	55.1921i	−0.122148	−	2.28191i
$586$		0			0
$587$	7.88611	−	13.6591i	0.325495	−	0.563773i	−0.656118	−	0.754658i	$-0.727803\pi$
$587$	7.88611	−	13.6591i	0.325495	−	0.563773i	0.981612	+	0.190885i	$0.0611359\pi$
$588$		0			0
$589$	−8.63757	−	14.9607i	−0.355905	−	0.616445i
$590$		0			0
$591$	−16.3744	−	3.92146i	−0.673551	−	0.161307i
$592$		0			0
$593$	−1.53339	+	2.65591i	−0.0629688	+	0.109065i	−0.895791	−	0.444475i	$-0.853390\pi$
$593$	−1.53339	+	2.65591i	−0.0629688	+	0.109065i	0.832822	+	0.553540i	$0.186724\pi$
$594$		0			0
$595$	−2.09951	−	0.268678i	−0.0860717	−	0.0110147i
$596$		0			0
$597$	−7.43801	−	25.0589i	−0.304418	−	1.02559i
$598$		0			0
$599$	−16.1696	+	28.0066i	−0.660673	+	1.14432i	0.319766	+	0.947496i	$0.396396\pi$
$599$	−16.1696	+	28.0066i	−0.660673	+	1.14432i	−0.980439	+	0.196822i	$0.936938\pi$
$600$		0			0
$601$	−14.9839	+	25.9529i	−0.611208	+	1.05864i	0.379830	+	0.925056i	$0.375983\pi$
$601$	−14.9839	+	25.9529i	−0.611208	+	1.05864i	−0.991037	+	0.133586i	$0.957351\pi$
$602$		0			0
$603$	−32.6459	+	21.2524i	−1.32944	+	0.865466i
$604$		0			0
$605$	91.2429			3.70955
$606$		0			0
$607$	−20.2551			−0.822128			−0.411064	−	0.911606i	$-0.634843\pi$
$607$	−20.2551			−0.822128			−0.411064	+	0.911606i	$0.634843\pi$
$608$		0			0
$609$	−4.17451	−	25.6623i	−0.169160	−	1.03989i
$610$		0			0
$611$	5.29206	−	9.16611i	0.214094	−	0.370821i
$612$		0			0
$613$	12.5419	+	21.7233i	0.506564	+	0.877395i	0.999971	+	0.00759665i	$0.00241811\pi$
$613$	12.5419	+	21.7233i	0.506564	+	0.877395i	−0.493407	+	0.869799i	$0.664249\pi$
$614$		0			0
$615$	0.339501	+	1.14379i	0.0136900	+	0.0461220i
$616$		0			0
$617$	−21.0472	−	36.4548i	−0.847328	−	1.46762i	−0.883584	−	0.468273i	$-0.844877\pi$
$617$	−21.0472	−	36.4548i	−0.847328	−	1.46762i	0.0362561	−	0.999343i	$-0.488457\pi$
$618$		0			0
$619$	−14.8250			−0.595869			−0.297934	−	0.954586i	$-0.596298\pi$
$619$	−14.8250			−0.595869			−0.297934	+	0.954586i	$0.596298\pi$
$620$		0			0
$621$	−4.03502	−	3.43455i	−0.161920	−	0.137824i
$622$		0			0
$623$	−9.08362	−	21.7072i	−0.363928	−	0.869681i
$624$		0			0
$625$	−1.16586			−0.0466345
$626$		0			0
$627$	−24.5828	+	25.9339i	−0.981743	+	1.03570i
$628$		0			0
$629$	0.748299			0.0298366
$630$		0			0
$631$	20.6414			0.821722			0.410861	−	0.911698i	$-0.365228\pi$
$631$	20.6414			0.821722			0.410861	+	0.911698i	$0.365228\pi$
$632$		0			0
$633$	−8.62670	−	29.0636i	−0.342881	−	1.15517i
$634$		0			0
$635$	9.95969			0.395238
$636$		0			0
$637$	−25.1231	+	25.4895i	−0.995414	+	1.00993i
$638$		0			0
$639$	15.7680	+	8.01202i	0.623773	+	0.316950i
$640$		0			0
$641$	1.55327			0.0613503			0.0306752	−	0.999529i	$-0.490234\pi$
$641$	1.55327			0.0613503			0.0306752	+	0.999529i	$0.490234\pi$
$642$		0			0
$643$	−10.7061	−	18.5435i	−0.422206	−	0.731282i	0.573949	−	0.818891i	$-0.305411\pi$
$643$	−10.7061	−	18.5435i	−0.422206	−	0.731282i	−0.996155	+	0.0876087i	$0.972077\pi$
$644$		0			0
$645$	14.6985	−	15.5063i	0.578752	−	0.610560i
$646$		0			0
$647$	−14.7637	−	25.5715i	−0.580422	−	1.00532i	−0.995429	−	0.0955019i	$-0.969554\pi$
$647$	−14.7637	−	25.5715i	−0.580422	−	1.00532i	0.415008	−	0.909818i	$-0.363779\pi$
$648$		0			0
$649$	22.8902	−	39.6470i	0.898520	−	1.55628i
$650$		0			0
$651$	3.71307	+	22.8257i	0.145527	+	0.894609i
$652$		0			0
$653$	16.0608			0.628508			0.314254	−	0.949339i	$-0.398246\pi$
$653$	16.0608			0.628508			0.314254	+	0.949339i	$0.398246\pi$
$654$		0			0
$655$	30.4671			1.19045
$656$		0			0
$657$	2.02216	+	37.7771i	0.0788919	+	1.47382i
$658$		0			0
$659$	14.2100	−	24.6124i	0.553543	−	0.958764i	−0.444473	−	0.895792i	$-0.646609\pi$
$659$	14.2100	−	24.6124i	0.553543	−	0.958764i	0.998015	−	0.0629717i	$-0.0200578\pi$
$660$		0			0
$661$	−16.9884	+	29.4248i	−0.660773	+	1.14449i	0.319640	+	0.947539i	$0.396438\pi$
$661$	−16.9884	+	29.4248i	−0.660773	+	1.14449i	−0.980413	+	0.196953i	$0.936895\pi$
$662$		0			0
$663$	1.35255	−	1.42688i	0.0525285	−	0.0554155i
$664$		0			0
$665$	12.5985	+	30.1068i	0.488550	+	1.16749i
$666$		0			0
$667$	2.89285	−	5.01055i	0.112011	−	0.194009i
$668$		0			0
$669$	11.9237	−	12.5790i	0.460996	−	0.486332i
$670$		0			0
$671$	5.37224	+	9.30499i	0.207393	+	0.359215i
$672$		0			0
$673$	−0.807019	+	1.39780i	−0.0311083	+	0.0538812i	−0.881160	−	0.472817i	$-0.843237\pi$
$673$	−0.807019	+	1.39780i	−0.0311083	+	0.0538812i	0.850052	+	0.526699i	$0.176570\pi$
$674$		0			0
$675$	31.5950	+	26.8932i	1.21609	+	1.03512i
$676$		0			0
$677$	13.3479	+	23.1193i	0.513002	+	0.888545i	0.999886	+	0.0150790i	$0.00479996\pi$
$677$	13.3479	+	23.1193i	0.513002	+	0.888545i	−0.486884	+	0.873466i	$0.661867\pi$
$678$		0			0
$679$	−5.57626	−	13.3257i	−0.213997	−	0.511392i
$680$		0			0
$681$	−3.81746	−	0.914235i	−0.146285	−	0.0350335i
$682$		0			0
$683$	−17.6183	−	30.5158i	−0.674146	−	1.16765i	−0.976718	−	0.214528i	$-0.931179\pi$
$683$	−17.6183	−	30.5158i	−0.674146	−	1.16765i	0.302572	−	0.953126i	$-0.402155\pi$
$684$		0			0
$685$	65.1711			2.49006
$686$		0			0
$687$	−8.46347	−	2.02690i	−0.322902	−	0.0773310i
$688$		0			0
$689$	−13.5595	+	23.4857i	−0.516575	+	0.894734i
$690$		0			0
$691$	14.3904	+	24.9248i	0.547435	+	0.948185i	0.998449	+	0.0556685i	$0.0177290\pi$
$691$	14.3904	+	24.9248i	0.547435	+	0.948185i	−0.451014	+	0.892517i	$0.648938\pi$
$692$		0			0
$693$	43.0774	−	20.7980i	1.63638	−	0.790049i
$694$		0			0
$695$	21.6545	+	37.5066i	0.821401	+	1.42271i
$696$		0			0
$697$	−0.0212202	+	0.0367544i	−0.000803771	+	0.00139217i
$698$		0			0
$699$	−18.4071	+	19.4188i	−0.696220	+	0.734485i
$700$		0			0
$701$	17.2044			0.649800			0.324900	−	0.945748i	$-0.394669\pi$
$701$	17.2044			0.649800			0.324900	+	0.945748i	$0.394669\pi$
$702$		0			0
$703$	−5.76903	−	9.99226i	−0.217583	−	0.376865i
$704$		0			0
$705$	3.67653	+	12.3863i	0.138466	+	0.466496i
$706$		0			0
$707$	6.36864	−	8.36228i	0.239517	−	0.314496i
$708$		0			0
$709$	−22.8211	−	39.5272i	−0.857063	−	1.48448i	−0.874718	−	0.484633i	$-0.838953\pi$
$709$	−22.8211	−	39.5272i	−0.857063	−	1.48448i	0.0176546	−	0.999844i	$-0.494380\pi$
$710$		0			0
$711$	−2.02294	−	37.7917i	−0.0758662	−	1.41730i
$712$		0			0
$713$	−2.57308	+	4.45670i	−0.0963626	+	0.166905i
$714$		0			0
$715$	55.5169	+	96.1581i	2.07621	+	3.59611i
$716$		0			0
$717$	−4.56081	−	15.3655i	−0.170326	−	0.573834i
$718$		0			0
$719$	11.1857	−	19.3741i	0.417155	−	0.722533i	−0.578497	−	0.815684i	$-0.696361\pi$
$719$	11.1857	−	19.3741i	0.417155	−	0.722533i	0.995652	+	0.0931513i	$0.0296940\pi$
$720$		0			0
$721$	−5.70336	+	7.48874i	−0.212404	+	0.278895i
$722$		0			0
$723$	−27.5028	−	6.58658i	−1.02284	−	0.244957i
$724$		0			0
$725$	−22.6515	+	39.2336i	−0.841256	+	1.45710i
$726$		0			0
$727$	−18.3031	+	31.7019i	−0.678824	+	1.17576i	0.296512	+	0.955029i	$0.404177\pi$
$727$	−18.3031	+	31.7019i	−0.678824	+	1.17576i	−0.975335	+	0.220728i	$0.929157\pi$
$728$		0			0
$729$	4.31313	+	26.6533i	0.159746	+	0.987158i
$730$		0			0
$731$	0.760001			0.0281096
$732$		0			0
$733$	−39.9469			−1.47547			−0.737736	−	0.675090i	$-0.764105\pi$
$733$	−39.9469			−1.47547			−0.737736	+	0.675090i	$0.764105\pi$
$734$		0			0
$735$	−1.48422	−	43.6644i	−0.0547463	−	1.61058i
$736$		0			0
$737$	39.1273	−	67.7706i	1.44127	−	2.49636i
$738$		0			0
$739$	5.42140	+	9.39015i	0.199430	+	0.345422i	0.948344	−	0.317245i	$-0.102758\pi$
$739$	5.42140	+	9.39015i	0.199430	+	0.345422i	−0.748914	+	0.662667i	$0.769424\pi$
$740$		0			0
$741$	−29.4811	−	7.06036i	−1.08302	−	0.259369i
$742$		0			0
$743$	−2.74353	−	4.75194i	−0.100651	−	0.174332i	0.811302	−	0.584627i	$-0.198759\pi$
$743$	−2.74353	−	4.75194i	−0.100651	−	0.174332i	−0.911953	+	0.410295i	$0.865426\pi$
$744$		0			0
$745$	−17.9471			−0.657529
$746$		0			0
$747$	−18.0994	+	11.7827i	−0.662222	+	0.431105i
$748$		0			0
$749$	−2.51317	−	6.00575i	−0.0918292	−	0.219445i
$750$		0			0
$751$	−27.1242			−0.989775			−0.494888	−	0.868957i	$-0.664791\pi$
$751$	−27.1242			−0.989775			−0.494888	+	0.868957i	$0.664791\pi$
$752$		0			0
$753$	12.7140	+	3.04486i	0.463326	+	0.110961i
$754$		0			0
$755$	−0.664410			−0.0241804
$756$		0			0
$757$	−36.5294			−1.32768			−0.663842	−	0.747872i	$-0.731075\pi$
$757$	−36.5294			−1.32768			−0.663842	+	0.747872i	$0.731075\pi$
$758$		0			0
$759$	10.3521	+	2.47919i	0.375756	+	0.0899889i
$760$		0			0
$761$	52.8789			1.91686			0.958429	−	0.285332i	$-0.0921037\pi$
$761$	52.8789			1.91686			0.958429	+	0.285332i	$0.0921037\pi$
$762$		0			0
$763$	15.6216	+	1.99912i	0.565539	+	0.0723730i
$764$		0			0
$765$	0.128287	+	2.39661i	0.00463824	+	0.0866496i
$766$		0			0
$767$	38.8382			1.40237
$768$		0			0
$769$	22.9381	+	39.7299i	0.827169	+	1.43270i	0.900250	+	0.435372i	$0.143383\pi$
$769$	22.9381	+	39.7299i	0.827169	+	1.43270i	−0.0730816	+	0.997326i	$0.523283\pi$
$770$		0			0
$771$	42.6034	+	10.2030i	1.53432	+	0.367452i
$772$		0			0
$773$	7.61224	+	13.1848i	0.273793	+	0.474224i	0.969830	−	0.243782i	$-0.0783883\pi$
$773$	7.61224	+	13.1848i	0.273793	+	0.474224i	−0.696037	+	0.718006i	$0.745055\pi$
$774$		0			0
$775$	20.1477	−	34.8968i	0.723726	−	1.25353i
$776$		0			0
$777$	2.47996	+	15.2453i	0.0889681	+	0.546921i
$778$		0			0
$779$	0.654390			0.0234460
$780$		0			0
$781$	−35.5309			−1.27140
$782$		0			0
$783$	−27.7733	+	9.88748i	−0.992537	+	0.353350i
$784$		0			0
$785$	−7.80862	+	13.5249i	−0.278702	+	0.482725i
$786$		0			0
$787$	−10.5617	+	18.2935i	−0.376485	+	0.652091i	−0.990548	−	0.137166i	$-0.956201\pi$
$787$	−10.5617	+	18.2935i	−0.376485	+	0.652091i	0.614063	+	0.789257i	$0.289534\pi$
$788$		0			0
$789$	39.5805	+	9.47904i	1.40910	+	0.337463i
$790$		0			0
$791$	−18.5266	−	2.37088i	−0.658729	−	0.0842986i
$792$		0			0
$793$	−4.55758	+	7.89395i	−0.161844	+	0.280322i
$794$		0			0
$795$	−9.42011	−	31.7366i	−0.334097	−	1.12558i
$796$		0			0
$797$	−27.0532	−	46.8575i	−0.958272	−	1.65978i	−0.726695	−	0.686960i	$-0.758945\pi$
$797$	−27.0532	−	46.8575i	−0.958272	−	1.65978i	−0.231577	−	0.972817i	$-0.574389\pi$
$798$		0			0
$799$	−0.229798	+	0.398021i	−0.00812965	+	0.0140810i
$800$		0			0
$801$	−22.3610	+	14.5570i	−0.790087	+	0.514345i
$802$		0			0
$803$	−37.9994	−	65.8169i	−1.34097	−	2.32263i
$804$		0			0
$805$	5.89056	−	7.73454i	0.207615	−	0.272607i
$806$		0			0
$807$	−13.7091	−	46.1865i	−0.482584	−	1.62584i
$808$		0			0
$809$	27.3280	+	47.3335i	0.960803	+	1.66416i	0.720493	+	0.693463i	$0.243916\pi$
$809$	27.3280	+	47.3335i	0.960803	+	1.66416i	0.240310	+	0.970696i	$0.422751\pi$
$810$		0			0
$811$	−12.7853			−0.448954			−0.224477	−	0.974479i	$-0.572067\pi$
$811$	−12.7853			−0.448954			−0.224477	+	0.974479i	$0.572067\pi$
$812$		0			0
$813$	−22.8264	+	24.0809i	−0.800556	+	0.844555i
$814$		0			0
$815$	42.7557	−	74.0550i	1.49767	−	2.59403i
$816$		0			0
$817$	−5.85925	−	10.1485i	−0.204989	−	0.355052i
$818$		0			0
$819$	33.5528	+	22.8269i	1.17243	+	0.797636i
$820$		0			0
$821$	−17.7302	−	30.7095i	−0.618787	−	1.07177i	−0.989707	−	0.143105i	$-0.954291\pi$
$821$	−17.7302	−	30.7095i	−0.618787	−	1.07177i	0.370921	−	0.928664i	$-0.379042\pi$
$822$		0			0
$823$	−3.95726	+	6.85417i	−0.137941	+	0.238921i	−0.926717	−	0.375760i	$-0.877382\pi$
$823$	−3.95726	+	6.85417i	−0.137941	+	0.238921i	0.788776	+	0.614681i	$0.210715\pi$
$824$		0			0
$825$	−81.0585	−	19.4125i	−2.82209	−	0.675857i
$826$		0			0
$827$	45.6562			1.58762			0.793811	−	0.608164i	$-0.208094\pi$
$827$	45.6562			1.58762			0.793811	+	0.608164i	$0.208094\pi$
$828$		0			0
$829$	21.0443	+	36.4498i	0.730898	+	1.26595i	0.956500	+	0.291733i	$0.0942318\pi$
$829$	21.0443	+	36.4498i	0.730898	+	1.26595i	−0.225602	+	0.974220i	$0.572435\pi$
$830$		0			0
$831$	46.4581	+	11.1261i	1.61161	+	0.385962i
$832$		0			0
$833$	1.09092	−	1.10683i	0.0377982	−	0.0383495i
$834$		0			0
$835$	5.74552	+	9.95154i	0.198832	+	0.344387i
$836$		0			0
$837$	24.7033	−	8.79455i	0.853872	−	0.303984i
$838$		0			0
$839$	−10.3598	+	17.9437i	−0.357660	+	0.619485i	−0.987569	−	0.157183i	$-0.949759\pi$
$839$	−10.3598	+	17.9437i	−0.357660	+	0.619485i	0.629910	+	0.776668i	$0.283092\pi$
$840$		0			0
$841$	−1.59479	−	2.76225i	−0.0549926	−	0.0952500i
$842$		0			0
$843$	0.458968	−	0.484193i	0.0158077	−	0.0166765i
$844$		0			0
$845$	−23.6757	+	41.0075i	−0.814468	+	1.41070i
$846$		0			0
$847$	−40.5901	+	53.2963i	−1.39469	+	1.83128i
$848$		0			0
$849$	17.8712	−	18.8534i	0.613336	−	0.647045i
$850$		0			0
$851$	−1.71856	+	2.97663i	−0.0589115	+	0.102038i
$852$		0			0
$853$	7.75942	−	13.4397i	0.265678	−	0.460167i	−0.702063	−	0.712115i	$-0.747738\pi$
$853$	7.75942	−	13.4397i	0.265678	−	0.460167i	0.967741	+	0.251947i	$0.0810710\pi$
$854$		0			0
$855$	31.0136	−	20.1898i	1.06064	−	0.690476i
$856$		0			0
$857$	2.48183			0.0847777			0.0423888	−	0.999101i	$-0.486503\pi$
$857$	2.48183			0.0847777			0.0423888	+	0.999101i	$0.486503\pi$
$858$		0			0
$859$	35.0396			1.19554			0.597768	−	0.801669i	$-0.296054\pi$
$859$	35.0396			1.19554			0.597768	+	0.801669i	$0.296054\pi$
$860$		0			0
$861$	−0.819133	−	0.310515i	−0.0279160	−	0.0105823i
$862$		0			0
$863$	−14.4778	+	25.0763i	−0.492831	+	0.853608i	−0.999966	−	0.00825876i	$-0.997371\pi$
$863$	−14.4778	+	25.0763i	−0.492831	+	0.853608i	0.507135	+	0.861866i	$0.330704\pi$
$864$		0			0
$865$	−38.3876	−	66.4893i	−1.30522	−	2.26070i
$866$		0			0
$867$	20.1978	−	21.3079i	0.685954	−	0.723655i
$868$		0			0
$869$	38.0141	+	65.8424i	1.28954	+	2.23355i
$870$		0			0
$871$	66.3879			2.24947
$872$		0			0
$873$	−13.7270	+	8.93625i	−0.464589	+	0.302446i
$874$		0			0
$875$	−17.2421	+	22.6395i	−0.582888	+	0.765355i
$876$		0			0
$877$	19.5922			0.661582			0.330791	−	0.943704i	$-0.392684\pi$
$877$	19.5922			0.661582			0.330791	+	0.943704i	$0.392684\pi$
$878$		0			0
$879$	11.0719	+	37.3014i	0.373445	+	1.25815i
$880$		0			0
$881$	−15.9010			−0.535717			−0.267858	−	0.963458i	$-0.586316\pi$
$881$	−15.9010			−0.535717			−0.267858	+	0.963458i	$0.586316\pi$
$882$		0			0
$883$	0.329844			0.0111001			0.00555007	−	0.999985i	$-0.498233\pi$
$883$	0.329844			0.0111001			0.00555007	+	0.999985i	$0.498233\pi$
$884$		0			0
$885$	−32.6165	+	34.4091i	−1.09639	+	1.15665i
$886$		0			0
$887$	−12.6260			−0.423940			−0.211970	−	0.977276i	$-0.567988\pi$
$887$	−12.6260			−0.423940			−0.211970	+	0.977276i	$0.567988\pi$
$888$		0			0
$889$	−4.43064	+	5.81760i	−0.148599	+	0.195116i
$890$		0			0
$891$	−31.9796	−	43.8098i	−1.07136	−	1.46768i
$892$		0			0
$893$	7.08653			0.237142
$894$		0			0
$895$	0.901378	+	1.56123i	0.0301297	+	0.0521862i
$896$		0			0
$897$	2.56966	+	8.65726i	0.0857985	+	0.289057i
$898$		0			0
$899$	14.3157	+	24.7956i	0.477456	+	0.826978i
$900$		0			0
$901$	0.588794	−	1.01982i	0.0196156	−	0.0339752i
$902$		0			0
$903$	2.51874	+	15.4837i	0.0838185	+	0.515265i
$904$		0			0
$905$	21.2036			0.704831
$906$		0			0
$907$	−9.89252			−0.328476			−0.164238	−	0.986421i	$-0.552516\pi$
$907$	−9.89252			−0.328476			−0.164238	+	0.986421i	$0.552516\pi$
$908$		0			0
$909$	−10.6257	−	5.39910i	−0.352431	−	0.179077i
$910$		0			0
$911$	29.8185	−	51.6472i	0.987932	−	1.71115i	0.359828	−	0.933019i	$-0.382835\pi$
$911$	29.8185	−	51.6472i	0.987932	−	1.71115i	0.628104	−	0.778130i	$-0.283831\pi$
$912$		0			0
$913$	21.6928	−	37.5730i	0.717927	−	1.24349i
$914$		0			0
$915$	−3.16626	−	10.6672i	−0.104673	−	0.352648i
$916$		0			0
$917$	−13.5535	+	17.7963i	−0.447576	+	0.587685i
$918$		0			0
$919$	3.84759	−	6.66423i	0.126920	−	0.219833i	−0.795562	−	0.605873i	$-0.792824\pi$
$919$	3.84759	−	6.66423i	0.126920	−	0.219833i	0.922482	+	0.386040i	$0.126157\pi$
$920$		0			0
$921$	11.6358	+	2.78664i	0.383414	+	0.0918229i
$922$		0			0
$923$	−15.0715	−	26.1045i	−0.496083	−	0.859241i
$924$		0			0
$925$	13.4566	−	23.3076i	0.442452	−	0.766349i
$926$		0			0
$927$	9.51569	+	4.83510i	0.312536	+	0.158805i
$928$		0			0
$929$	−13.8357	−	23.9642i	−0.453936	−	0.786240i	0.544690	−	0.838637i	$-0.316647\pi$
$929$	−13.8357	−	23.9642i	−0.453936	−	0.786240i	−0.998626	+	0.0523969i	$0.983314\pi$
$930$		0			0
$931$	−23.1904	−	6.03425i	−0.760034	−	0.197765i
$932$		0			0
$933$	−27.6180	+	29.1359i	−0.904174	+	0.953867i
$934$		0			0
$935$	−2.41071	−	4.17548i	−0.0788388	−	0.136553i
$936$		0			0
$937$	44.7712			1.46261			0.731305	−	0.682051i	$-0.238912\pi$
$937$	44.7712			1.46261			0.731305	+	0.682051i	$0.238912\pi$
$938$		0			0
$939$	−8.10142	−	27.2939i	−0.264380	−	0.890703i
$940$		0			0
$941$	−20.0046	+	34.6490i	−0.652132	+	1.12953i	0.330472	+	0.943816i	$0.392792\pi$
$941$	−20.0046	+	34.6490i	−0.652132	+	1.12953i	−0.982605	+	0.185710i	$0.940541\pi$
$942$		0			0
$943$	−0.0974694	−	0.168822i	−0.00317404	−	0.00549760i
$944$		0			0
$945$	−48.4016	+	10.5563i	−1.57450	+	0.343397i
$946$		0			0
$947$	22.4634	+	38.9078i	0.729963	+	1.26433i	0.956898	+	0.290423i	$0.0937961\pi$
$947$	22.4634	+	38.9078i	0.729963	+	1.26433i	−0.226935	+	0.973910i	$0.572871\pi$
$948$		0			0
$949$	32.2371	−	55.8362i	1.04646	−	1.81252i
$950$		0			0
$951$	7.08138	+	23.8574i	0.229630	+	0.773629i
$952$		0			0
$953$	−40.8038			−1.32176			−0.660882	−	0.750490i	$-0.729818\pi$
$953$	−40.8038			−1.32176			−0.660882	+	0.750490i	$0.729818\pi$
$954$		0			0
$955$	14.2144	+	24.6201i	0.459967	+	0.796687i
$956$		0			0
$957$	40.7430	−	42.9823i	1.31703	−	1.38942i
$958$		0			0
$959$	−28.9918	+	38.0674i	−0.936195	+	1.22926i
$960$		0			0
$961$	2.76670	+	4.79206i	0.0892483	+	0.154583i
$962$		0			0
$963$	−6.18663	+	4.02748i	−0.199361	+	0.129784i
$964$		0			0
$965$	−34.2511	+	59.3247i	−1.10258	+	1.90973i
$966$		0			0
$967$	−9.63289	−	16.6847i	−0.309773	−	0.536542i	0.668540	−	0.743677i	$-0.266920\pi$
$967$	−9.63289	−	16.6847i	−0.309773	−	0.536542i	−0.978313	+	0.207134i	$0.933586\pi$
$968$		0			0
$969$	1.28016	+	0.306583i	0.0411247	+	0.00984885i
$970$		0			0
$971$	−29.8684	+	51.7336i	−0.958523	+	1.66021i	−0.232430	+	0.972613i	$0.574668\pi$
$971$	−29.8684	+	51.7336i	−0.958523	+	1.66021i	−0.726093	+	0.687597i	$0.758666\pi$
$972$		0			0
$973$	−31.5413	−	4.03640i	−1.01117	−	0.129401i
$974$		0			0
$975$	−20.1209	−	67.7879i	−0.644385	−	2.17095i
$976$		0			0
$977$	29.7758	−	51.5732i	0.952613	−	1.64997i	0.212873	−	0.977080i	$-0.431718\pi$
$977$	29.7758	−	51.5732i	0.952613	−	1.64997i	0.739739	−	0.672893i	$-0.234949\pi$
$978$		0			0
$979$	26.8005	−	46.4198i	0.856548	−	1.48358i
$980$		0			0
$981$	−0.954530	−	17.8321i	−0.0304758	−	0.569336i
$982$		0			0
$983$	−8.12829			−0.259252			−0.129626	−	0.991563i	$-0.541378\pi$
$983$	−8.12829			−0.259252			−0.129626	+	0.991563i	$0.541378\pi$
$984$		0			0
$985$	−35.0294			−1.11613
$986$		0			0
$987$	−8.87056	−	3.36263i	−0.282353	−	0.107034i
$988$		0			0
$989$	−1.74543	+	3.02318i	−0.0555016	+	0.0961316i
$990$		0			0
$991$	−27.6811	−	47.9451i	−0.879320	−	1.52303i	−0.852089	−	0.523397i	$-0.824665\pi$
$991$	−27.6811	−	47.9451i	−0.879320	−	1.52303i	−0.0272305	−	0.999629i	$-0.508669\pi$
$992$		0			0
$993$	−1.84903	−	6.22942i	−0.0586770	−	0.197685i
$994$		0			0
$995$	−27.1910	−	47.0962i	−0.862013	−	1.49305i
$996$		0			0
$997$	−9.66374			−0.306054			−0.153027	−	0.988222i	$-0.548902\pi$
$997$	−9.66374			−0.306054			−0.153027	+	0.988222i	$0.548902\pi$
$998$		0			0
$999$	16.4994	−	5.87388i	0.522016	−	0.185841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.l.b.205.7	yes	14
3.2	odd	2		756.2.l.b.289.2		14
4.3	odd	2		1008.2.t.j.961.1		14
7.2	even	3		1764.2.j.g.1177.2		14
7.3	odd	6		1764.2.i.i.1537.5		14
7.4	even	3		252.2.i.b.25.3	✓	14
7.5	odd	6		1764.2.j.h.1177.6		14
7.6	odd	2		1764.2.l.i.961.1		14
9.2	odd	6		2268.2.k.f.1297.6		14
9.4	even	3		252.2.i.b.121.3	yes	14
9.5	odd	6		756.2.i.b.37.6		14
9.7	even	3		2268.2.k.e.1297.2		14
12.11	even	2		3024.2.t.j.289.2		14
21.2	odd	6		5292.2.j.h.3529.6		14
21.5	even	6		5292.2.j.g.3529.2		14
21.11	odd	6		756.2.i.b.613.6		14
21.17	even	6		5292.2.i.i.2125.2		14
21.20	even	2		5292.2.l.i.3313.6		14
28.11	odd	6		1008.2.q.j.529.5		14
36.23	even	6		3024.2.q.j.2305.6		14
36.31	odd	6		1008.2.q.j.625.5		14
63.4	even	3	inner	252.2.l.b.193.7	yes	14
63.5	even	6		5292.2.j.g.1765.2		14
63.11	odd	6		2268.2.k.f.1621.6		14
63.13	odd	6		1764.2.i.i.373.5		14
63.23	odd	6		5292.2.j.h.1765.6		14
63.25	even	3		2268.2.k.e.1621.2		14
63.31	odd	6		1764.2.l.i.949.1		14
63.32	odd	6		756.2.l.b.361.2		14
63.40	odd	6		1764.2.j.h.589.6		14
63.41	even	6		5292.2.i.i.1549.2		14
63.58	even	3		1764.2.j.g.589.2		14
63.59	even	6		5292.2.l.i.361.6		14
84.11	even	6		3024.2.q.j.2881.6		14
252.67	odd	6		1008.2.t.j.193.1		14
252.95	even	6		3024.2.t.j.1873.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.3	✓	14	7.4	even	3
252.2.i.b.121.3	yes	14	9.4	even	3
252.2.l.b.193.7	yes	14	63.4	even	3	inner
252.2.l.b.205.7	yes	14	1.1	even	1	trivial
756.2.i.b.37.6		14	9.5	odd	6
756.2.i.b.613.6		14	21.11	odd	6
756.2.l.b.289.2		14	3.2	odd	2
756.2.l.b.361.2		14	63.32	odd	6
1008.2.q.j.529.5		14	28.11	odd	6
1008.2.q.j.625.5		14	36.31	odd	6
1008.2.t.j.193.1		14	252.67	odd	6
1008.2.t.j.961.1		14	4.3	odd	2
1764.2.i.i.373.5		14	63.13	odd	6
1764.2.i.i.1537.5		14	7.3	odd	6
1764.2.j.g.589.2		14	63.58	even	3
1764.2.j.g.1177.2		14	7.2	even	3
1764.2.j.h.589.6		14	63.40	odd	6
1764.2.j.h.1177.6		14	7.5	odd	6
1764.2.l.i.949.1		14	63.31	odd	6
1764.2.l.i.961.1		14	7.6	odd	2
2268.2.k.e.1297.2		14	9.7	even	3
2268.2.k.e.1621.2		14	63.25	even	3
2268.2.k.f.1297.6		14	9.2	odd	6
2268.2.k.f.1621.6		14	63.11	odd	6
3024.2.q.j.2305.6		14	36.23	even	6
3024.2.q.j.2881.6		14	84.11	even	6
3024.2.t.j.289.2		14	12.11	even	2
3024.2.t.j.1873.2		14	252.95	even	6
5292.2.i.i.1549.2		14	63.41	even	6
5292.2.i.i.2125.2		14	21.17	even	6
5292.2.j.g.1765.2		14	63.5	even	6
5292.2.j.g.3529.2		14	21.5	even	6
5292.2.j.h.1765.6		14	63.23	odd	6
5292.2.j.h.3529.6		14	21.2	odd	6
5292.2.l.i.361.6		14	63.59	even	6
5292.2.l.i.3313.6		14	21.20	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68442 + 0.403398i) q^{3} +3.60346 q^{5} +(-1.60302 + 2.10483i) q^{7} +(2.67454 + 1.35898i) q^{9} +O(q^{10})\)	\(q+(1.68442 + 0.403398i) q^{3} +3.60346 q^{5} +(-1.60302 + 2.10483i) q^{7} +(2.67454 + 1.35898i) q^{9} -6.02669 q^{11} +(-2.55639 - 4.42780i) q^{13} +(6.06973 + 1.45363i) q^{15} +(0.111006 + 0.192269i) q^{17} +(1.71161 - 2.96460i) q^{19} +(-3.54925 + 2.89876i) q^{21} -1.01976 q^{23} +7.98490 q^{25} +(3.95684 + 3.36800i) q^{27} +(-2.83679 + 4.91347i) q^{29} +(2.52322 - 4.37035i) q^{31} +(-10.1515 - 2.43115i) q^{33} +(-5.77642 + 7.58467i) q^{35} +(1.68526 - 2.91896i) q^{37} +(-2.51987 - 8.48952i) q^{39} +(0.0955808 + 0.165551i) q^{41} +(1.71161 - 2.96460i) q^{43} +(9.63759 + 4.89704i) q^{45} +(1.03506 + 1.79278i) q^{47} +(-1.86064 - 6.74819i) q^{49} +(0.109421 + 0.368641i) q^{51} +(-2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(4.07899 - 4.30318i) q^{57} +(-3.79814 + 6.57858i) q^{59} +(-0.891408 - 1.54396i) q^{61} +(-7.14778 + 3.45098i) q^{63} +(-9.21184 - 15.9554i) q^{65} +(-6.49235 + 11.2451i) q^{67} +(-1.71770 - 0.411369i) q^{69} +5.89560 q^{71} +(6.30519 + 10.9209i) q^{73} +(13.4499 + 3.22109i) q^{75} +(9.66091 - 12.6852i) q^{77} +(-6.30763 - 10.9251i) q^{79} +(5.30633 + 7.26931i) q^{81} +(-3.59946 + 6.23444i) q^{83} +(0.400007 + 0.692832i) q^{85} +(-6.76043 + 7.13199i) q^{87} +(-4.44697 + 7.70238i) q^{89} +(13.4177 + 1.71709i) q^{91} +(6.01316 - 6.34364i) q^{93} +(6.16773 - 10.6828i) q^{95} +(-2.72991 + 4.72835i) q^{97} +(-16.1186 - 8.19016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9}+O(q^{10}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9	\( 14 q + 4 q^{5} - 3 q^{7} + 10 q^{9} - 4 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 2 q^{21} - 22 q^{23} + 18 q^{25} + 9 q^{27} + q^{29} - q^{31} + 5 q^{33} - 19 q^{35} + 10 q^{37} - 20 q^{39} - 33 q^{41} + 7 q^{43} + 5 q^{45} - 3 q^{47} - 13 q^{49} + 20 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} - 14 q^{59} - 10 q^{61} - 39 q^{63} + 15 q^{65} + 6 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} + q^{75} + 19 q^{77} - 10 q^{79} + 22 q^{81} - 25 q^{83} + 8 q^{85} - 2 q^{87} - 6 q^{89} + 2 q^{91} + 16 q^{93} - 28 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 4 * q^5 - 3 * q^7 + 10 * q^9 - 4 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 2 * q^21 - 22 * q^23 + 18 * q^25 + 9 * q^27 + q^29 - q^31 + 5 * q^33 - 19 * q^35 + 10 * q^37 - 20 * q^39 - 33 * q^41 + 7 * q^43 + 5 * q^45 - 3 * q^47 - 13 * q^49 + 20 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 - 14 * q^59 - 10 * q^61 - 39 * q^63 + 15 * q^65 + 6 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 + q^75 + 19 * q^77 - 10 * q^79 + 22 * q^81 - 25 * q^83 + 8 * q^85 - 2 * q^87 - 6 * q^89 + 2 * q^91 + 16 * q^93 - 28 * q^95 - 18 * q^97 + 7 * q^99

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