LMFDB - Embedded newform 252.2.i.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (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			121.3
Root			$1.68442 - 0.403398i$ of defining polynomial
Character	$\chi$	$=$	252.121
Dual form			252.2.i.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.492857 + 1.66045i) q^{3} +(-1.80173 - 3.12069i) q^{5} +(-1.02133 - 2.44067i) q^{7} +(-2.51418 - 1.63673i) q^{9} +O(q^{10})$	\(q+(-0.492857 + 1.66045i) q^{3} +(-1.80173 - 3.12069i) q^{5} +(-1.02133 - 2.44067i) q^{7} +(-2.51418 - 1.63673i) q^{9} +(3.01334 - 5.21926i) q^{11} +(-2.55639 + 4.42780i) q^{13} +(6.06973 - 1.45363i) q^{15} +(0.111006 + 0.192269i) q^{17} +(1.71161 - 2.96460i) q^{19} +(4.55598 - 0.492957i) q^{21} +(0.509880 + 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} +(3.95684 - 3.36800i) q^{27} +(-2.83679 - 4.91347i) q^{29} -5.04645 q^{31} +(7.18117 + 7.57585i) q^{33} +(-5.77642 + 7.58467i) q^{35} +(1.68526 - 2.91896i) q^{37} +(-6.09220 - 6.42703i) q^{39} +(0.0955808 - 0.165551i) q^{41} +(1.71161 + 2.96460i) q^{43} +(-0.577838 + 10.7949i) q^{45} -2.07013 q^{47} +(-4.91378 + 4.98545i) q^{49} +(-0.373963 + 0.0895595i) q^{51} +(-2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(4.07899 + 4.30318i) q^{57} +7.59629 q^{59} +1.78282 q^{61} +(-1.42692 + 7.80794i) q^{63} +18.4237 q^{65} +12.9847 q^{67} +(-1.71770 + 0.411369i) q^{69} +5.89560 q^{71} +(6.30519 + 10.9209i) q^{73} +(-9.51451 - 10.0374i) q^{75} +(-15.8161 - 2.02402i) q^{77} +12.6153 q^{79} +(3.64224 + 8.23007i) q^{81} +(-3.59946 - 6.23444i) q^{83} +(0.400007 - 0.692832i) q^{85} +(9.55670 - 2.28871i) q^{87} +(-4.44697 + 7.70238i) q^{89} +(13.4177 + 1.71709i) q^{91} +(2.48718 - 8.37937i) q^{93} -12.3355 q^{95} +(-2.72991 - 4.72835i) q^{97} +(-16.1186 + 8.19016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.492857	+	1.66045i	−0.284551	+	0.958661i
$3$	−0.492857	+	1.66045i	−0.284551	+	0.958661i
$4$		0			0
$5$	−1.80173	−	3.12069i	−0.805757	−	1.39561i	−0.915779	−	0.401684i	$-0.868425\pi$
$5$	−1.80173	−	3.12069i	−0.805757	−	1.39561i	0.110021	−	0.993929i	$-0.464908\pi$
$6$		0			0
$7$	−1.02133	−	2.44067i	−0.386025	−	0.922488i
$7$	−1.02133	−	2.44067i	−0.386025	−	0.922488i
$8$		0			0
$9$	−2.51418	−	1.63673i	−0.838061	−	0.545576i
$10$		0			0
$11$	3.01334	−	5.21926i	0.908557	−	1.57367i	0.0924872	−	0.995714i	$-0.470518\pi$
$11$	3.01334	−	5.21926i	0.908557	−	1.57367i	0.816070	−	0.577953i	$-0.196148\pi$
$12$		0			0
$13$	−2.55639	+	4.42780i	−0.709015	+	1.22805i	0.256207	+	0.966622i	$0.417527\pi$
$13$	−2.55639	+	4.42780i	−0.709015	+	1.22805i	−0.965223	+	0.261429i	$0.915806\pi$
$14$		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
$21$	4.55598	−	0.492957i	0.994197	−	0.107572i
$22$		0			0
$23$	0.509880	+	0.883137i	0.106317	+	0.184147i	0.914276	−	0.405093i	$-0.132761\pi$
$23$	0.509880	+	0.883137i	0.106317	+	0.184147i	−0.807958	+	0.589240i	$0.799427\pi$
$24$		0			0
$25$	−3.99245	+	6.91513i	−0.798490	+	1.38303i
$26$		0			0
$27$	3.95684	−	3.36800i	0.761494	−	0.648172i
$28$		0			0
$29$	−2.83679	−	4.91347i	−0.526779	−	0.912408i	−0.999513	−	0.0312031i	$-0.990066\pi$
$29$	−2.83679	−	4.91347i	−0.526779	−	0.912408i	0.472734	−	0.881205i	$-0.343267\pi$
$30$		0			0
$31$	−5.04645			−0.906368			−0.453184	−	0.891417i	$-0.649712\pi$
$31$	−5.04645			−0.906368			−0.453184	+	0.891417i	$0.649712\pi$
$32$		0			0
$33$	7.18117	+	7.57585i	1.25008	+	1.31879i
$34$		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
$39$	−6.09220	−	6.42703i	−0.975533	−	1.02915i
$40$		0			0
$41$	0.0955808	−	0.165551i	0.0149272	−	0.0258547i	−0.858465	−	0.512872i	$-0.828582\pi$
$41$	0.0955808	−	0.165551i	0.0149272	−	0.0258547i	0.873393	+	0.487017i	$0.161915\pi$
$42$		0			0
$43$	1.71161	+	2.96460i	0.261019	+	0.452098i	0.966513	−	0.256618i	$-0.0826082\pi$
$43$	1.71161	+	2.96460i	0.261019	+	0.452098i	−0.705494	+	0.708716i	$0.749275\pi$
$44$		0			0
$45$	−0.577838	+	10.7949i	−0.0861390	+	1.60921i
$46$		0			0
$47$	−2.07013			−0.301959			−0.150980	−	0.988537i	$-0.548243\pi$
$47$	−2.07013			−0.301959			−0.150980	+	0.988537i	$0.548243\pi$
$48$		0			0
$49$	−4.91378	+	4.98545i	−0.701969	+	0.712207i
$50$		0			0
$51$	−0.373963	+	0.0895595i	−0.0523653	+	0.0125408i
$52$		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
$59$	7.59629			0.988953			0.494476	−	0.869191i	$-0.335360\pi$
$59$	7.59629			0.988953			0.494476	+	0.869191i	$0.335360\pi$
$60$		0			0
$61$	1.78282			0.228266			0.114133	−	0.993465i	$-0.463591\pi$
$61$	1.78282			0.228266			0.114133	+	0.993465i	$0.463591\pi$
$62$		0			0
$63$	−1.42692	+	7.80794i	−0.179775	+	0.983708i
$64$		0			0
$65$	18.4237			2.28518
$66$		0			0
$67$	12.9847			1.58633			0.793167	−	0.609005i	$-0.208431\pi$
$67$	12.9847			1.58633			0.793167	+	0.609005i	$0.208431\pi$
$68$		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
$75$	−9.51451	−	10.0374i	−1.09864	−	1.15902i
$76$		0			0
$77$	−15.8161	−	2.02402i	−1.80242	−	0.230658i
$78$		0			0
$79$	12.6153			1.41933			0.709664	−	0.704541i	$-0.248847\pi$
$79$	12.6153			1.41933			0.709664	+	0.704541i	$0.248847\pi$
$80$		0			0
$81$	3.64224	+	8.23007i	0.404693	+	0.914452i
$82$		0			0
$83$	−3.59946	−	6.23444i	−0.395092	−	0.684319i	0.598021	−	0.801480i	$-0.295954\pi$
$83$	−3.59946	−	6.23444i	−0.395092	−	0.684319i	−0.993113	+	0.117161i	$0.962621\pi$
$84$		0			0
$85$	0.400007	−	0.692832i	0.0433868	−	0.0751482i
$86$		0			0
$87$	9.55670	−	2.28871i	1.02459	−	0.245376i
$88$		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
$93$	2.48718	−	8.37937i	0.257908	−	0.868900i
$94$		0			0
$95$	−12.3355			−1.26559
$96$		0			0
$97$	−2.72991	−	4.72835i	−0.277181	−	0.480091i	0.693502	−	0.720454i	$-0.256067\pi$
$97$	−2.72991	−	4.72835i	−0.277181	−	0.480091i	−0.970683	+	0.240364i	$0.922733\pi$
$98$		0			0
$99$	−16.1186	+	8.19016i	−1.61998	+	0.823142i
$100$		0			0
$101$	1.98645	−	3.44063i	0.197659	−	0.342355i	−0.750110	−	0.661313i	$-0.769999\pi$
$101$	1.98645	−	3.44063i	0.197659	−	0.342355i	0.947769	+	0.318958i	$0.103333\pi$
$102$		0			0
$103$	−1.77894	−	3.08121i	−0.175284	−	0.303601i	0.764975	−	0.644059i	$-0.222751\pi$
$103$	−1.77894	−	3.08121i	−0.175284	−	0.303601i	−0.940260	+	0.340458i	$0.889418\pi$
$104$		0			0
$105$	−9.74701	−	13.3296i	−0.951211	−	1.30084i
$106$		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	−0.650863	−	0.759195i	$-0.725593\pi$
$113$	3.52974	−	6.11370i	0.332050	−	0.575128i	0.982914	+	0.184067i	$0.0589263\pi$
$114$		0			0
$115$	1.83733	−	3.18235i	0.171332	−	0.296755i
$116$		0			0
$117$	13.6743	−	6.94818i	1.26419	−	0.642360i
$118$		0			0
$119$	0.355892	−	0.467300i	0.0326245	−	0.0428373i
$120$		0			0
$121$	−12.6605	−	21.9286i	−1.15095	−	1.99351i
$122$		0			0
$123$	0.227781	+	0.240300i	0.0205383	+	0.0216671i
$124$		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
$129$	−5.76616	+	1.38092i	−0.507682	+	0.121584i
$130$		0			0
$131$	−4.22748	−	7.32221i	−0.369357	−	0.639744i	0.620108	−	0.784516i	$-0.287089\pi$
$131$	−4.22748	−	7.32221i	−0.369357	−	0.639744i	−0.989465	+	0.144772i	$0.953755\pi$
$132$		0			0
$133$	−8.98375	−	1.14967i	−0.778990	−	0.0996886i
$134$		0			0
$135$	−17.6396	−	6.27982i	−1.51818	−	0.540481i
$136$		0			0
$137$	−9.04286	+	15.6627i	−0.772584	+	1.33815i	0.163559	+	0.986534i	$0.447703\pi$
$137$	−9.04286	+	15.6627i	−0.772584	+	1.33815i	−0.936143	+	0.351621i	$0.885631\pi$
$138$		0			0
$139$	6.00936	−	10.4085i	0.509707	−	0.882839i	−0.490230	−	0.871593i	$-0.663087\pi$
$139$	6.00936	−	10.4085i	0.509707	−	0.882839i	0.999937	−	0.0112454i	$-0.00357959\pi$
$140$		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
$147$	−5.85630	−	10.6162i	−0.483019	−	0.875610i
$148$		0			0
$149$	2.49026	+	4.31325i	0.204010	+	0.353355i	0.949817	−	0.312807i	$-0.101269\pi$
$149$	2.49026	+	4.31325i	0.204010	+	0.353355i	−0.745807	+	0.666162i	$0.767936\pi$
$150$		0			0
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	−0.862250	−	0.506483i	$-0.830945\pi$
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	0.869752	+	0.493489i	$0.164279\pi$
$152$		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
$157$	4.33396			0.345888			0.172944	−	0.984932i	$-0.444672\pi$
$157$	4.33396			0.345888			0.172944	+	0.984932i	$0.444672\pi$
$158$		0			0
$159$	8.93441	−	2.13968i	0.708545	−	0.169688i
$160$		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
$165$	10.7033	−	36.0598i	0.833253	−	2.80725i
$166$		0			0
$167$	1.59445	−	2.76166i	0.123382	−	0.213704i	−0.797717	−	0.603032i	$-0.793959\pi$
$167$	1.59445	−	2.76166i	0.123382	−	0.213704i	0.921099	+	0.389328i	$0.127293\pi$
$168$		0			0
$169$	−6.57027	−	11.3800i	−0.505405	−	0.875388i
$170$		0			0
$171$	−9.15556	+	4.65211i	−0.700144	+	0.355756i
$172$		0			0
$173$	21.3060			1.61986			0.809932	−	0.586523i	$-0.199504\pi$
$173$	21.3060			1.61986			0.809932	+	0.586523i	$0.199504\pi$
$174$		0			0
$175$	20.9552	+	2.68167i	1.58406	+	0.202715i
$176$		0			0
$177$	−3.74389	+	12.6133i	−0.281408	+	0.948070i
$178$		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
$185$	−12.1455			−0.892957
$186$		0			0
$187$	1.33800			0.0978443
$188$		0			0
$189$	−12.2614	−	6.21752i	−0.891887	−	0.452258i
$190$		0			0
$191$	−7.88932			−0.570851			−0.285425	−	0.958401i	$-0.592135\pi$
$191$	−7.88932			−0.570851			−0.285425	+	0.958401i	$0.592135\pi$
$192$		0			0
$193$	19.0102			1.36838			0.684190	−	0.729303i	$-0.260156\pi$
$193$	19.0102			1.36838			0.684190	+	0.729303i	$0.260156\pi$
$194$		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
$201$	−6.39960	+	21.5604i	−0.451393	+	1.52076i
$202$		0			0
$203$	−9.09489	+	11.9419i	−0.638336	+	0.838160i
$204$		0			0
$205$	−0.688843			−0.0481109
$206$		0			0
$207$	0.163525	−	3.05490i	0.0113658	−	0.212330i
$208$		0			0
$209$	−10.3154	−	17.8667i	−0.713529	−	1.23587i
$210$		0			0
$211$	−8.75173	+	15.1584i	−0.602494	+	1.04355i	0.389948	+	0.920837i	$0.372493\pi$
$211$	−8.75173	+	15.1584i	−0.602494	+	1.04355i	−0.992442	+	0.122713i	$0.960840\pi$
$212$		0			0
$213$	−2.90569	+	9.78934i	−0.199094	+	0.670755i
$214$		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
$219$	−21.2412	+	5.08700i	−1.43535	+	0.343748i
$220$		0			0
$221$	−1.13510			−0.0763553
$222$		0			0
$223$	5.00337	+	8.66610i	0.335051	+	0.580325i	0.983495	−	0.180938i	$-0.0579132\pi$
$223$	5.00337	+	8.66610i	0.335051	+	0.580325i	−0.648444	+	0.761262i	$0.724580\pi$
$224$		0			0
$225$	21.3559	−	10.8513i	1.42373	−	0.723423i
$226$		0			0
$227$	1.13317	−	1.96270i	0.0752110	−	0.130269i	−0.825967	−	0.563718i	$-0.809370\pi$
$227$	1.13317	−	1.96270i	0.0752110	−	0.130269i	0.901178	+	0.433449i	$0.142704\pi$
$228$		0			0
$229$	2.51228	+	4.35140i	0.166016	+	0.287549i	0.937016	−	0.349287i	$-0.113576\pi$
$229$	2.51228	+	4.35140i	0.166016	+	0.287549i	−0.770999	+	0.636836i	$0.780243\pi$
$230$		0			0
$231$	11.1559	−	25.2643i	0.734002	−	1.66227i
$232$		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	−0.975974	−	0.217889i	$-0.930083\pi$
$239$	−4.62691	+	8.01404i	−0.299290	+	0.518385i	0.676684	+	0.736274i	$0.263416\pi$
$240$		0			0
$241$	8.16387	−	14.1402i	0.525881	−	0.910853i	−0.473664	−	0.880705i	$-0.657069\pi$
$241$	8.16387	−	14.1402i	0.525881	−	0.910853i	0.999545	−	0.0301474i	$-0.00959768\pi$
$242$		0			0
$243$	−15.4607	+	1.99151i	−0.991806	+	0.127755i
$244$		0			0
$245$	24.4113	+	6.35194i	1.55958	+	0.405811i
$246$		0			0
$247$	8.75111	+	15.1574i	0.556820	+	0.964440i
$248$		0			0
$249$	12.1260	−	2.90403i	0.768454	−	0.184035i
$250$		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
$255$	0.953266	+	1.00566i	0.0596958	+	0.0629767i
$256$		0			0
$257$	−12.6463	−	21.9041i	−0.788856	−	1.36634i	−0.926668	−	0.375880i	$-0.877341\pi$
$257$	−12.6463	−	21.9041i	−0.788856	−	1.36634i	0.137813	−	0.990458i	$-0.455993\pi$
$258$		0			0
$259$	−8.84543	−	1.13196i	−0.549628	−	0.0703368i
$260$		0			0
$261$	−0.909797	+	16.9964i	−0.0563150	+	1.05205i
$262$		0			0
$263$	−11.7490	+	20.3499i	−0.724474	+	1.25483i	0.234716	+	0.972064i	$0.424584\pi$
$263$	−11.7490	+	20.3499i	−0.724474	+	1.25483i	−0.959190	+	0.282762i	$0.908749\pi$
$264$		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
$273$	−9.46416	+	21.4332i	−0.572797	+	1.29719i
$274$		0			0
$275$	24.0612	+	41.6753i	1.45095	+	2.51312i
$276$		0			0
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	0.0705495	+	0.997508i	$0.477525\pi$
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	−0.899142	+	0.437657i	$0.855809\pi$
$278$		0			0
$279$	12.6877	+	8.25966i	0.759592	+	0.494493i
$280$		0			0
$281$	0.192591	+	0.333577i	0.0114890	+	0.0198995i	0.871713	−	0.490017i	$-0.163010\pi$
$281$	0.192591	+	0.333577i	0.0114890	+	0.0198995i	−0.860224	+	0.509917i	$0.829676\pi$
$282$		0			0
$283$	−14.9981			−0.891543			−0.445772	−	0.895147i	$-0.647071\pi$
$283$	−14.9981			−0.891543			−0.445772	+	0.895147i	$0.647071\pi$
$284$		0			0
$285$	6.07962	−	20.4824i	0.360126	−	1.21327i
$286$		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
$291$	9.19664	−	2.20248i	0.539116	−	0.129112i
$292$		0			0
$293$	11.2323	−	19.4550i	0.656200	−	1.13657i	−0.325392	−	0.945579i	$-0.605496\pi$
$293$	11.2323	−	19.4550i	0.656200	−	1.13657i	0.981592	−	0.190992i	$-0.0611704\pi$
$294$		0			0
$295$	−13.6865	−	23.7056i	−0.796856	−	1.38019i
$296$		0			0
$297$	−5.65518	−	30.8007i	−0.328147	−	1.78724i
$298$		0			0
$299$	−5.21381			−0.301522
$300$		0			0
$301$	5.48751	−	7.20532i	0.316295	−	0.415308i
$302$		0			0
$303$	4.73395	+	4.99413i	0.271958	+	0.286905i
$304$		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
$311$	23.1780			1.31430			0.657152	−	0.753758i	$-0.271761\pi$
$311$	23.1780			1.31430			0.657152	+	0.753758i	$0.271761\pi$
$312$		0			0
$313$	16.4377			0.929112			0.464556	−	0.885544i	$-0.346214\pi$
$313$	16.4377			0.929112			0.464556	+	0.885544i	$0.346214\pi$
$314$		0			0
$315$	26.9370	−	9.61482i	1.51773	−	0.541734i
$316$		0			0
$317$	−14.3680			−0.806989			−0.403494	−	0.914982i	$-0.632205\pi$
$317$	−14.3680			−0.806989			−0.403494	+	0.914982i	$0.632205\pi$
$318$		0			0
$319$	−34.1929			−1.91444
$320$		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
$327$	10.0266	−	2.40125i	0.554472	−	0.132789i
$328$		0			0
$329$	2.11428	+	5.05251i	0.116564	+	0.278554i
$330$		0			0
$331$	3.75165			0.206209			0.103105	−	0.994671i	$-0.467122\pi$
$331$	3.75165			0.206209			0.103105	+	0.994671i	$0.467122\pi$
$332$		0			0
$333$	−9.01459	+	4.58048i	−0.493997	+	0.251009i
$334$		0			0
$335$	−23.3949	−	40.5211i	−1.27820	−	2.21391i
$336$		0			0
$337$	−2.77171	+	4.80074i	−0.150984	+	0.261513i	−0.931590	−	0.363512i	$-0.881578\pi$
$337$	−2.77171	+	4.80074i	−0.150984	+	0.261513i	0.780605	+	0.625024i	$0.214911\pi$
$338$		0			0
$339$	8.41182	+	8.87414i	0.456868	+	0.481977i
$340$		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
$345$	4.37859	+	4.61923i	0.235735	+	0.248691i
$346$		0			0
$347$	7.55217			0.405422			0.202711	−	0.979239i	$-0.435025\pi$
$347$	7.55217			0.405422			0.202711	+	0.979239i	$0.435025\pi$
$348$		0			0
$349$	−9.10179	−	15.7648i	−0.487207	−	0.843868i	0.512684	−	0.858577i	$-0.328651\pi$
$349$	−9.10179	−	15.7648i	−0.487207	−	0.843868i	−0.999892	+	0.0147092i	$0.995318\pi$
$350$		0			0
$351$	4.79761	+	26.1300i	0.256077	+	1.39472i
$352$		0			0
$353$	0.266224	−	0.461114i	0.0141697	−	0.0245426i	−0.858854	−	0.512221i	$-0.828823\pi$
$353$	0.266224	−	0.461114i	0.0141697	−	0.0245426i	0.873023	+	0.487678i	$0.162156\pi$
$354$		0			0
$355$	−10.6223	−	18.3983i	−0.563771	−	0.976481i
$356$		0			0
$357$	0.600524	+	0.821252i	0.0317831	+	0.0434653i
$358$		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
$367$	−10.5921	+	18.3461i	−0.552904	+	0.957658i	0.445159	+	0.895451i	$0.353147\pi$
$367$	−10.5921	+	18.3461i	−0.552904	+	0.957658i	−0.998063	+	0.0622062i	$0.980186\pi$
$368$		0			0
$369$	−0.511269	+	0.259785i	−0.0266156	+	0.0135239i
$370$		0			0
$371$	−8.50267	+	11.1643i	−0.441437	+	0.579624i
$372$		0			0
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	0.533032	−	0.846095i	$-0.321052\pi$
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	−0.999256	+	0.0385721i	$0.987719\pi$
$374$		0			0
$375$	−5.30115	+	17.8597i	−0.273750	+	0.922272i
$376$		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
$381$	−1.36222	+	4.58936i	−0.0697887	+	0.235120i
$382$		0			0
$383$	0.154293	+	0.267243i	0.00788400	+	0.0136555i	0.869940	−	0.493157i	$-0.164157\pi$
$383$	0.154293	+	0.267243i	0.00788400	+	0.0136555i	−0.862056	+	0.506812i	$0.830824\pi$
$384$		0			0
$385$	22.1801	+	53.0039i	1.13040	+	2.70133i
$386$		0			0
$387$	0.548937	−	10.2550i	0.0279040	−	0.521291i
$388$		0			0
$389$	−2.38753	+	4.13533i	−0.121053	+	0.209669i	−0.920183	−	0.391488i	$-0.871960\pi$
$389$	−2.38753	+	4.13533i	−0.121053	+	0.209669i	0.799130	+	0.601158i	$0.205294\pi$
$390$		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
$399$	6.33667	−	14.3504i	0.317230	−	0.718421i
$400$		0			0
$401$	9.67088	+	16.7505i	0.482941	+	0.836478i	0.999808	−	0.0195874i	$-0.00623526\pi$
$401$	9.67088	+	16.7505i	0.482941	+	0.836478i	−0.516867	+	0.856066i	$0.672902\pi$
$402$		0			0
$403$	12.9007	−	22.3446i	0.642629	−	1.11307i
$404$		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
$409$	−10.6807			−0.528127			−0.264064	−	0.964505i	$-0.585063\pi$
$409$	−10.6807			−0.528127			−0.264064	+	0.964505i	$0.585063\pi$
$410$		0			0
$411$	−21.5503	−	22.7347i	−1.06300	−	1.12142i
$412$		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
$417$	14.3211	+	15.1081i	0.701305	+	0.739849i
$418$		0			0
$419$	−17.5274	+	30.3583i	−0.856267	+	1.48310i	0.0191966	+	0.999816i	$0.493889\pi$
$419$	−17.5274	+	30.3583i	−0.856267	+	1.48310i	−0.875464	+	0.483283i	$0.839444\pi$
$420$		0			0
$421$	15.8653	+	27.4795i	0.773226	+	1.33927i	0.935786	+	0.352568i	$0.114692\pi$
$421$	15.8653	+	27.4795i	0.773226	+	1.33927i	−0.162560	+	0.986699i	$0.551975\pi$
$422$		0			0
$423$	5.20468	+	3.38824i	0.253060	+	0.164742i
$424$		0			0
$425$	−1.77275			−0.0859910
$426$		0			0
$427$	−1.82084	−	4.35127i	−0.0881165	−	0.210573i
$428$		0			0
$429$	−51.9023	+	12.4300i	−2.50586	+	0.600124i
$430$		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
$437$	3.49087			0.166991
$438$		0			0
$439$	−9.70915			−0.463392			−0.231696	−	0.972788i	$-0.574428\pi$
$439$	−9.70915			−0.463392			−0.231696	+	0.972788i	$0.574428\pi$
$440$		0			0
$441$	20.5140	−	4.49181i	0.976856	−	0.213896i
$442$		0			0
$443$	−10.0792			−0.478878			−0.239439	−	0.970911i	$-0.576963\pi$
$443$	−10.0792			−0.478878			−0.239439	+	0.970911i	$0.576963\pi$
$444$		0			0
$445$	32.0489			1.51927
$446$		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
$453$	0.219702	+	0.231777i	0.0103225	+	0.0108898i
$454$		0			0
$455$	−18.8166	−	44.9662i	−0.882136	−	2.10805i
$456$		0			0
$457$	−8.21359			−0.384216			−0.192108	−	0.981374i	$-0.561532\pi$
$457$	−8.21359			−0.384216			−0.192108	+	0.981374i	$0.561532\pi$
$458$		0			0
$459$	1.08680	+	0.386906i	0.0507273	+	0.0180592i
$460$		0			0
$461$	14.0516	+	24.3381i	0.654448	+	1.13354i	0.982032	+	0.188715i	$0.0604323\pi$
$461$	14.0516	+	24.3381i	0.654448	+	1.13354i	−0.327584	+	0.944822i	$0.606234\pi$
$462$		0			0
$463$	1.54897	−	2.68289i	0.0719866	−	0.124684i	−0.827785	−	0.561045i	$-0.810399\pi$
$463$	1.54897	−	2.68289i	0.0719866	−	0.124684i	0.899772	+	0.436361i	$0.143733\pi$
$464$		0			0
$465$	−30.6306	+	7.33565i	−1.42046	+	0.340183i
$466$		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
$471$	−2.13602	+	7.19632i	−0.0984228	+	0.331589i
$472$		0			0
$473$	20.6307			0.948602
$474$		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
$479$	20.3542	−	35.2545i	0.930007	−	1.61082i	0.146704	−	0.989180i	$-0.453133\pi$
$479$	20.3542	−	35.2545i	0.930007	−	1.61082i	0.783303	−	0.621640i	$-0.213533\pi$
$480$		0			0
$481$	8.61637	+	14.9240i	0.392873	+	0.680475i
$482$		0			0
$483$	2.75835	+	3.77221i	0.125509	+	0.171642i
$484$		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	−0.929657	−	0.368425i	$-0.879897\pi$
$491$	−3.22990	+	5.59435i	−0.145763	+	0.252469i	0.783894	+	0.620894i	$0.213230\pi$
$492$		0			0
$493$	0.629804	−	1.09085i	0.0283650	−	0.0491295i
$494$		0			0
$495$	54.6003	+	35.5447i	2.45410	+	1.59761i
$496$		0			0
$497$	−6.02133	−	14.3892i	−0.270094	−	0.645445i
$498$		0			0
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	0.968567	−	0.248752i	$-0.0800203\pi$
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	−0.699709	+	0.714428i	$0.746687\pi$
$500$		0			0
$501$	3.79977	+	4.00860i	0.169761	+	0.179091i
$502$		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
$507$	22.1342	−	5.30087i	0.983014	−	0.235420i
$508$		0			0
$509$	15.7523	+	27.2838i	0.698208	+	1.20933i	0.969087	+	0.246718i	$0.0793522\pi$
$509$	15.7523	+	27.2838i	0.698208	+	1.20933i	−0.270879	+	0.962613i	$0.587314\pi$
$510$		0			0
$511$	20.2147	−	26.5427i	0.894247	−	1.17418i
$512$		0			0
$513$	−3.21221	−	17.4952i	−0.141822	−	0.772431i
$514$		0			0
$515$	−6.41033	+	11.1030i	−0.282473	+	0.489258i
$516$		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
$525$	−14.7807	+	33.4733i	−0.645082	+	1.46090i
$526$		0			0
$527$	−0.560188	−	0.970273i	−0.0244022	−	0.0422658i
$528$		0			0
$529$	10.9800	−	19.0180i	0.477393	−	0.826869i
$530$		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
$535$	8.86700			0.383354
$536$		0			0
$537$	−0.842690	+	0.201814i	−0.0363648	+	0.00870891i
$538$		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
$543$	−2.90009	+	9.77048i	−0.124455	+	0.419291i
$544$		0			0
$545$	−10.7249	+	18.5760i	−0.459403	+	0.795710i
$546$		0			0
$547$	9.25785	+	16.0351i	0.395837	+	0.685610i	0.993208	−	0.116355i	$-0.0371211\pi$
$547$	9.25785	+	16.0351i	0.395837	+	0.685610i	−0.597370	+	0.801965i	$0.703788\pi$
$548$		0			0
$549$	−4.48233	−	2.91799i	−0.191301	−	0.124537i
$550$		0			0
$551$	−19.4220			−0.827404
$552$		0			0
$553$	−12.8843	−	30.7897i	−0.547896	−	1.30931i
$554$		0			0
$555$	5.98601	−	20.1670i	0.254092	−	0.856043i
$556$		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
$563$	24.7400			1.04267			0.521334	−	0.853353i	$-0.325435\pi$
$563$	24.7400			1.04267			0.521334	+	0.853353i	$0.325435\pi$
$564$		0			0
$565$	−25.4386			−1.07021
$566$		0			0
$567$	16.3670	−	17.2951i	0.687350	−	0.726327i
$568$		0			0
$569$	16.7196			0.700923			0.350462	−	0.936577i	$-0.386025\pi$
$569$	16.7196			0.700923			0.350462	+	0.936577i	$0.386025\pi$
$570$		0			0
$571$	−29.6270			−1.23985			−0.619926	−	0.784660i	$-0.712837\pi$
$571$	−29.6270			−1.23985			−0.619926	+	0.784660i	$0.712837\pi$
$572$		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
$579$	−9.36929	+	31.5654i	−0.389374	+	1.31181i
$580$		0			0
$581$	−11.5400	+	15.1525i	−0.478761	+	0.628632i
$582$		0			0
$583$	−31.9664			−1.32391
$584$		0			0
$585$	−46.3205	−	30.1546i	−1.91512	−	1.24674i
$586$		0			0
$587$	7.88611	+	13.6591i	0.325495	+	0.563773i	0.981612	−	0.190885i	$-0.0611359\pi$
$587$	7.88611	+	13.6591i	0.325495	+	0.563773i	−0.656118	+	0.754658i	$0.727803\pi$
$588$		0			0
$589$	−8.63757	+	14.9607i	−0.355905	+	0.616445i
$590$		0			0
$591$	4.79110	−	16.1413i	0.197079	−	0.663966i
$592$		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
$597$	25.4206	−	6.08793i	1.04040	−	0.249162i
$598$		0			0
$599$	32.3392			1.32135			0.660673	−	0.750674i	$-0.270271\pi$
$599$	32.3392			1.32135			0.660673	+	0.750674i	$0.270271\pi$
$600$		0			0
$601$	−14.9839	−	25.9529i	−0.611208	−	1.05864i	−0.991037	−	0.133586i	$-0.957351\pi$
$601$	−14.9839	−	25.9529i	−0.611208	−	1.05864i	0.379830	−	0.925056i	$-0.375983\pi$
$602$		0			0
$603$	−32.6459	−	21.2524i	−1.32944	−	0.865466i
$604$		0			0
$605$	−45.6215	+	79.0187i	−1.85478	+	3.21257i
$606$		0			0
$607$	10.1275	+	17.5414i	0.411064	+	0.711984i	0.995006	−	0.0998113i	$-0.0318239\pi$
$607$	10.1275	+	17.5414i	0.411064	+	0.711984i	−0.583942	+	0.811795i	$0.698491\pi$
$608$		0			0
$609$	−15.3465	−	20.9873i	−0.621872	−	0.850447i
$610$		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	0.0362561	+	0.999343i	$0.488457\pi$
$617$	−21.0472	+	36.4548i	−0.847328	+	1.46762i	−0.883584	+	0.468273i	$0.844877\pi$
$618$		0			0
$619$	7.41252	−	12.8389i	0.297934	−	0.516037i	−0.677729	−	0.735312i	$-0.737036\pi$
$619$	7.41252	−	12.8389i	0.297934	−	0.516037i	0.975663	+	0.219275i	$0.0703690\pi$
$620$		0			0
$621$	4.99192	+	1.77716i	0.200319	+	0.0713148i
$622$		0			0
$623$	23.3408	+	2.98696i	0.935130	+	0.119670i
$624$		0			0
$625$	0.582932	+	1.00967i	0.0233173	+	0.0403867i
$626$		0			0
$627$	34.7508	−	8.32239i	1.38781	−	0.332364i
$628$		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
$633$	−20.8565	−	22.0027i	−0.828970	−	0.874531i
$634$		0			0
$635$	−4.97984	−	8.62534i	−0.197619	−	0.342286i
$636$		0			0
$637$	−9.51303	−	34.5020i	−0.376920	−	1.36702i
$638$		0			0
$639$	−14.8226	−	9.64949i	−0.586374	−	0.381728i
$640$		0			0
$641$	−0.776633	+	1.34517i	−0.0306752	+	0.0531309i	−0.880955	−	0.473199i	$-0.843099\pi$
$641$	−0.776633	+	1.34517i	−0.0306752	+	0.0531309i	0.850280	+	0.526330i	$0.176432\pi$
$642$		0			0
$643$	−10.7061	+	18.5435i	−0.422206	+	0.731282i	−0.996155	−	0.0876087i	$-0.972077\pi$
$643$	−10.7061	+	18.5435i	−0.422206	+	0.731282i	0.573949	+	0.818891i	$0.305411\pi$
$644$		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
$651$	−22.9915	+	2.48768i	−0.901109	+	0.0975000i
$652$		0			0
$653$	−8.03041	−	13.9091i	−0.314254	−	0.544304i	0.665025	−	0.746822i	$-0.268421\pi$
$653$	−8.03041	−	13.9091i	−0.314254	−	0.544304i	−0.979279	+	0.202517i	$0.935088\pi$
$654$		0			0
$655$	−15.2335	+	26.3853i	−0.595224	+	1.03096i
$656$		0			0
$657$	2.02216	−	37.7771i	0.0788919	−	1.47382i
$658$		0			0
$659$	14.2100	+	24.6124i	0.553543	+	0.958764i	0.998015	+	0.0629717i	$0.0200578\pi$
$659$	14.2100	+	24.6124i	0.553543	+	0.958764i	−0.444473	+	0.895792i	$0.646609\pi$
$660$		0			0
$661$	33.9768			1.32155			0.660773	−	0.750586i	$-0.270229\pi$
$661$	33.9768			1.32155			0.660773	+	0.750586i	$0.270229\pi$
$662$		0			0
$663$	0.559444	−	1.88478i	0.0217270	−	0.0731988i
$664$		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
$669$	−16.8556	+	4.03670i	−0.651674	+	0.156068i
$670$		0			0
$671$	5.37224	−	9.30499i	0.207393	−	0.359215i
$672$		0			0
$673$	−0.807019	−	1.39780i	−0.0311083	−	0.0538812i	0.850052	−	0.526699i	$-0.176570\pi$
$673$	−0.807019	−	1.39780i	−0.0311083	−	0.0538812i	−0.881160	+	0.472817i	$0.843237\pi$
$674$		0			0
$675$	7.49268	+	40.8086i	0.288393	+	1.57072i
$676$		0			0
$677$	−26.6958			−1.02600			−0.513002	−	0.858387i	$-0.671467\pi$
$677$	−26.6958			−1.02600			−0.513002	+	0.858387i	$0.671467\pi$
$678$		0			0
$679$	−8.75222	+	11.4920i	−0.335879	+	0.441023i
$680$		0			0
$681$	2.70048	+	2.84890i	0.103483	+	0.109170i
$682$		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
$689$	27.1190			1.03315
$690$		0			0
$691$	−28.7807			−1.09487			−0.547435	−	0.836848i	$-0.684396\pi$
$691$	−28.7807			−1.09487			−0.547435	+	0.836848i	$0.684396\pi$
$692$		0			0
$693$	36.4519	+	30.9755i	1.38469	+	1.17666i
$694$		0			0
$695$	−43.3089			−1.64280
$696$		0			0
$697$	0.0424403			0.00160754
$698$		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
$705$	−12.5651	+	3.00919i	−0.473230	+	0.113333i
$706$		0			0
$707$	−10.4263	−	1.33427i	−0.392120	−	0.0501803i
$708$		0			0
$709$	45.6421			1.71413			0.857063	−	0.515211i	$-0.172287\pi$
$709$	45.6421			1.71413			0.857063	+	0.515211i	$0.172287\pi$
$710$		0			0
$711$	−31.7171	−	20.6478i	−1.18948	−	0.774351i
$712$		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
$717$	−11.0265	−	11.6325i	−0.411792	−	0.434424i
$718$		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
$723$	19.4555	+	20.5248i	0.723559	+	0.763326i
$724$		0			0
$725$	45.3030			1.68251
$726$		0			0
$727$	−18.3031	−	31.7019i	−0.678824	−	1.17576i	−0.975335	−	0.220728i	$-0.929157\pi$
$727$	−18.3031	−	31.7019i	−0.678824	−	1.17576i	0.296512	−	0.955029i	$-0.404177\pi$
$728$		0			0
$729$	4.31313	−	26.6533i	0.159746	−	0.987158i
$730$		0			0
$731$	−0.380000	+	0.658180i	−0.0140548	+	0.0243437i
$732$		0			0
$733$	19.9734	+	34.5950i	0.737736	+	1.27780i	0.953513	+	0.301353i	$0.0974383\pi$
$733$	19.9734	+	34.5950i	0.737736	+	1.27780i	−0.215777	+	0.976443i	$0.569228\pi$
$734$		0			0
$735$	−22.5784	+	37.4032i	−0.832816	+	1.37964i
$736$		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	−0.911953	−	0.410295i	$-0.865426\pi$
$743$	−2.74353	+	4.75194i	−0.100651	+	0.174332i	0.811302	+	0.584627i	$0.198759\pi$
$744$		0			0
$745$	8.97353	−	15.5426i	0.328765	−	0.569437i
$746$		0			0
$747$	−1.15439	+	21.5659i	−0.0422370	+	0.789054i
$748$		0			0
$749$	6.45771	+	0.826405i	0.235960	+	0.0301962i
$750$		0			0
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	0.999983	−	0.00589323i	$-0.00187588\pi$
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	−0.505095	+	0.863064i	$0.668543\pi$
$752$		0			0
$753$	−3.72010	+	12.5331i	−0.135568	+	0.456732i
$754$		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
$759$	−3.02899	+	10.2047i	−0.109945	+	0.370408i
$760$		0			0
$761$	−26.4394	−	45.7944i	−0.958429	−	1.66005i	−0.726319	−	0.687358i	$-0.758770\pi$
$761$	−26.4394	−	45.7944i	−0.958429	−	1.66005i	−0.232110	−	0.972690i	$-0.574563\pi$
$762$		0			0
$763$	−9.54207	+	12.5291i	−0.345446	+	0.453585i
$764$		0			0
$765$	−2.13967	+	1.08720i	−0.0773599	+	0.0393080i
$766$		0			0
$767$	−19.4191	+	33.6348i	−0.701183	+	1.21448i
$768$		0			0
$769$	22.9381	−	39.7299i	0.827169	−	1.43270i	−0.0730816	−	0.997326i	$-0.523283\pi$
$769$	22.9381	−	39.7299i	0.827169	−	1.43270i	0.900250	−	0.435372i	$-0.143383\pi$
$770$		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
$777$	6.23910	−	14.1295i	0.223826	−	0.506892i
$778$		0			0
$779$	−0.327195	−	0.566718i	−0.0117230	−	0.0203048i
$780$		0			0
$781$	17.7655	−	30.7707i	0.635698	−	1.10106i
$782$		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
$787$	21.1235			0.752970			0.376485	−	0.926423i	$-0.377133\pi$
$787$	21.1235			0.752970			0.376485	+	0.926423i	$0.377133\pi$
$788$		0			0
$789$	−27.9993	−	29.5382i	−0.996802	−	1.05159i
$790$		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
$795$	−22.7747	−	24.0264i	−0.807734	−	0.852127i
$796$		0			0
$797$	−27.0532	+	46.8575i	−0.958272	+	1.65978i	−0.231577	+	0.972817i	$0.574389\pi$
$797$	−27.0532	+	46.8575i	−0.958272	+	1.65978i	−0.726695	+	0.686960i	$0.758945\pi$
$798$		0			0
$799$	−0.229798	−	0.398021i	−0.00812965	−	0.0140810i
$800$		0			0
$801$	23.7872	−	12.0867i	0.840480	−	0.427063i
$802$		0			0
$803$	75.9988			2.68194
$804$		0			0
$805$	−9.64359	−	1.23411i	−0.339892	−	0.0434965i
$806$		0			0
$807$	46.8532	−	11.2208i	1.64931	−	0.394990i
$808$		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
$815$	−85.5113			−2.99533
$816$		0			0
$817$	11.7185			0.409978
$818$		0			0
$819$	−30.9242	−	26.2783i	−1.08058	−	0.918236i
$820$		0			0
$821$	35.4603			1.23757			0.618787	−	0.785559i	$-0.287625\pi$
$821$	35.4603			1.23757			0.618787	+	0.785559i	$0.287625\pi$
$822$		0			0
$823$	7.91451			0.275883			0.137941	−	0.990440i	$-0.455951\pi$
$823$	7.91451			0.275883			0.137941	+	0.990440i	$0.455951\pi$
$824$		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
$831$	−32.8646	−	34.6708i	−1.14006	−	1.20272i
$832$		0			0
$833$	−1.50401	−	0.391350i	−0.0521108	−	0.0135595i
$834$		0			0
$835$	−11.4910			−0.397664
$836$		0			0
$837$	−19.9680	+	16.9964i	−0.690194	+	0.587483i
$838$		0			0
$839$	−10.3598	−	17.9437i	−0.357660	−	0.619485i	0.629910	−	0.776668i	$-0.283092\pi$
$839$	−10.3598	−	17.9437i	−0.357660	−	0.619485i	−0.987569	+	0.157183i	$0.949759\pi$
$840$		0			0
$841$	−1.59479	+	2.76225i	−0.0549926	+	0.0952500i
$842$		0			0
$843$	−0.648808	+	0.155381i	−0.0223461	+	0.00535162i
$844$		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
$849$	7.39191	−	24.9035i	0.253690	−	0.854688i
$850$		0			0
$851$	3.43712			0.117823
$852$		0			0
$853$	7.75942	+	13.4397i	0.265678	+	0.460167i	0.967741	−	0.251947i	$-0.0810710\pi$
$853$	7.75942	+	13.4397i	0.265678	+	0.460167i	−0.702063	+	0.712115i	$0.747738\pi$
$854$		0			0
$855$	31.0136	+	20.1898i	1.06064	+	0.690476i
$856$		0			0
$857$	−1.24091	+	2.14933i	−0.0423888	+	0.0734196i	−0.886441	−	0.462841i	$-0.846830\pi$
$857$	−1.24091	+	2.14933i	−0.0423888	+	0.0734196i	0.844053	+	0.536260i	$0.180163\pi$
$858$		0			0
$859$	−17.5198	−	30.3452i	−0.597768	−	1.03537i	−0.993150	−	0.116848i	$-0.962721\pi$
$859$	−17.5198	−	30.3452i	−0.597768	−	1.03537i	0.395382	−	0.918517i	$-0.370612\pi$
$860$		0			0
$861$	0.353855	−	0.801364i	0.0120594	−	0.0273104i
$862$		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
$871$	−33.1940	+	57.4936i	−1.12473	+	1.94810i
$872$		0			0
$873$	−0.875519	+	16.3561i	−0.0296318	+	0.553569i
$874$		0			0
$875$	−10.9853	−	26.2518i	−0.371373	−	0.887473i
$876$		0			0
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	0.651876	−	0.758325i	$-0.273982\pi$
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	−0.982667	+	0.185379i	$0.940649\pi$
$878$		0			0
$879$	26.7680	+	28.2392i	0.902864	+	0.952486i
$880$		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
$885$	46.1075	−	11.0422i	1.54989	−	0.371178i
$886$		0			0
$887$	6.31301	+	10.9345i	0.211970	+	0.367143i	0.952331	−	0.305066i	$-0.0986787\pi$
$887$	6.31301	+	10.9345i	0.211970	+	0.367143i	−0.740361	+	0.672210i	$0.765345\pi$
$888$		0			0
$889$	−2.82287	−	6.74584i	−0.0946760	−	0.226248i
$890$		0			0
$891$	53.9302	+	5.79022i	1.80673	+	0.193980i
$892$		0			0
$893$	−3.54326	+	6.13711i	−0.118571	+	0.205371i
$894$		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
$903$	9.25951	+	12.6629i	0.308137	+	0.421396i
$904$		0			0
$905$	−10.6018	−	18.3629i	−0.352416	−	0.610402i
$906$		0			0
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	−0.772147	−	0.635445i	$-0.780817\pi$
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	0.936384	+	0.350976i	$0.114150\pi$
$908$		0			0
$909$	−10.6257	+	5.39910i	−0.352431	+	0.179077i
$910$		0			0
$911$	29.8185	+	51.6472i	0.987932	+	1.71115i	0.628104	+	0.778130i	$0.283831\pi$
$911$	29.8185	+	51.6472i	0.987932	+	1.71115i	0.359828	+	0.933019i	$0.382835\pi$
$912$		0			0
$913$	−43.3856			−1.43585
$914$		0			0
$915$	10.8212	−	2.59155i	0.357739	−	0.0856740i
$916$		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
$921$	−3.40462	+	11.4703i	−0.112186	+	0.377958i
$922$		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
$927$	−0.570529	+	10.6584i	−0.0187386	+	0.350067i
$928$		0			0
$929$	27.6715			0.907872			0.453936	−	0.891034i	$-0.350019\pi$
$929$	27.6715			0.907872			0.453936	+	0.891034i	$0.350019\pi$
$930$		0			0
$931$	6.36938	+	23.1006i	0.208748	+	0.757091i
$932$		0			0
$933$	−11.4234	+	38.4859i	−0.373987	+	1.25997i
$934$		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
$941$	40.0093			1.30426			0.652132	−	0.758105i	$-0.273875\pi$
$941$	40.0093			1.30426			0.652132	+	0.758105i	$0.273875\pi$
$942$		0			0
$943$	0.194939			0.00634808
$944$		0			0
$945$	2.68881	+	49.4663i	0.0874671	+	1.60914i
$946$		0			0
$947$	−44.9268			−1.45993			−0.729963	−	0.683487i	$-0.760463\pi$
$947$	−44.9268			−1.45993			−0.729963	+	0.683487i	$0.760463\pi$
$948$		0			0
$949$	−64.4741			−2.09292
$950$		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
$957$	16.8522	−	56.7756i	0.544755	−	1.83529i
$958$		0			0
$959$	47.4633	+	6.07395i	1.53267	+	0.196138i
$960$		0			0
$961$	−5.53339			−0.178497
$962$		0			0
$963$	6.58122	−	3.34404i	0.212077	−	0.107760i
$964$		0			0
$965$	−34.2511	−	59.3247i	−1.10258	−	1.90973i
$966$		0			0
$967$	−9.63289	+	16.6847i	−0.309773	+	0.536542i	−0.978313	−	0.207134i	$-0.933586\pi$
$967$	−9.63289	+	16.6847i	−0.309773	+	0.536542i	0.668540	+	0.743677i	$0.266920\pi$
$968$		0			0
$969$	−0.374572	+	1.26194i	−0.0120330	+	0.0405394i
$970$		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
$975$	68.7665	−	16.4687i	2.20229	−	0.527422i
$976$		0			0
$977$	−59.5516			−1.90523			−0.952613	−	0.304186i	$-0.901615\pi$
$977$	−59.5516			−1.90523			−0.952613	+	0.304186i	$0.901615\pi$
$978$		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
$983$	4.06414	−	7.03930i	0.129626	−	0.224519i	−0.793906	−	0.608041i	$-0.791956\pi$
$983$	4.06414	−	7.03930i	0.129626	−	0.224519i	0.923532	+	0.383522i	$0.125289\pi$
$984$		0			0
$985$	17.5147	+	30.3364i	0.558066	+	0.966598i
$986$		0			0
$987$	−9.43147	+	1.02049i	−0.300207	+	0.0324824i
$988$		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
$997$	4.83187	−	8.36904i	0.153027	−	0.265050i	−0.779312	−	0.626636i	$-0.784431\pi$
$997$	4.83187	−	8.36904i	0.153027	−	0.265050i	0.932339	+	0.361586i	$0.117765\pi$
$998$		0			0
$999$	−3.16275	−	17.2258i	−0.100065	−	0.545000i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.3	✓	14	63.25	even	3	inner
252.2.i.b.121.3	yes	14	1.1	even	1	trivial
252.2.l.b.193.7	yes	14	7.4	even	3
252.2.l.b.205.7	yes	14	9.7	even	3
756.2.i.b.37.6		14	3.2	odd	2
756.2.i.b.613.6		14	63.11	odd	6
756.2.l.b.289.2		14	9.2	odd	6
756.2.l.b.361.2		14	21.11	odd	6
1008.2.q.j.529.5		14	252.151	odd	6
1008.2.q.j.625.5		14	4.3	odd	2
1008.2.t.j.193.1		14	28.11	odd	6
1008.2.t.j.961.1		14	36.7	odd	6
1764.2.i.i.373.5		14	7.6	odd	2
1764.2.i.i.1537.5		14	63.52	odd	6
1764.2.j.g.589.2		14	7.2	even	3
1764.2.j.g.1177.2		14	63.16	even	3
1764.2.j.h.589.6		14	7.5	odd	6
1764.2.j.h.1177.6		14	63.61	odd	6
1764.2.l.i.949.1		14	7.3	odd	6
1764.2.l.i.961.1		14	63.34	odd	6
2268.2.k.e.1297.2		14	9.4	even	3
2268.2.k.e.1621.2		14	63.4	even	3
2268.2.k.f.1297.6		14	9.5	odd	6
2268.2.k.f.1621.6		14	63.32	odd	6
3024.2.q.j.2305.6		14	12.11	even	2
3024.2.q.j.2881.6		14	252.11	even	6
3024.2.t.j.289.2		14	36.11	even	6
3024.2.t.j.1873.2		14	84.11	even	6
5292.2.i.i.1549.2		14	21.20	even	2
5292.2.i.i.2125.2		14	63.38	even	6
5292.2.j.g.1765.2		14	21.5	even	6
5292.2.j.g.3529.2		14	63.47	even	6
5292.2.j.h.1765.6		14	21.2	odd	6
5292.2.j.h.3529.6		14	63.2	odd	6
5292.2.l.i.361.6		14	21.17	even	6
5292.2.l.i.3313.6		14	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.492857 + 1.66045i) q^{3} +(-1.80173 - 3.12069i) q^{5} +(-1.02133 - 2.44067i) q^{7} +(-2.51418 - 1.63673i) q^{9} +O(q^{10})\)	\(q+(-0.492857 + 1.66045i) q^{3} +(-1.80173 - 3.12069i) q^{5} +(-1.02133 - 2.44067i) q^{7} +(-2.51418 - 1.63673i) q^{9} +(3.01334 - 5.21926i) q^{11} +(-2.55639 + 4.42780i) q^{13} +(6.06973 - 1.45363i) q^{15} +(0.111006 + 0.192269i) q^{17} +(1.71161 - 2.96460i) q^{19} +(4.55598 - 0.492957i) q^{21} +(0.509880 + 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} +(3.95684 - 3.36800i) q^{27} +(-2.83679 - 4.91347i) q^{29} -5.04645 q^{31} +(7.18117 + 7.57585i) q^{33} +(-5.77642 + 7.58467i) q^{35} +(1.68526 - 2.91896i) q^{37} +(-6.09220 - 6.42703i) q^{39} +(0.0955808 - 0.165551i) q^{41} +(1.71161 + 2.96460i) q^{43} +(-0.577838 + 10.7949i) q^{45} -2.07013 q^{47} +(-4.91378 + 4.98545i) q^{49} +(-0.373963 + 0.0895595i) q^{51} +(-2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(4.07899 + 4.30318i) q^{57} +7.59629 q^{59} +1.78282 q^{61} +(-1.42692 + 7.80794i) q^{63} +18.4237 q^{65} +12.9847 q^{67} +(-1.71770 + 0.411369i) q^{69} +5.89560 q^{71} +(6.30519 + 10.9209i) q^{73} +(-9.51451 - 10.0374i) q^{75} +(-15.8161 - 2.02402i) q^{77} +12.6153 q^{79} +(3.64224 + 8.23007i) q^{81} +(-3.59946 - 6.23444i) q^{83} +(0.400007 - 0.692832i) q^{85} +(9.55670 - 2.28871i) q^{87} +(-4.44697 + 7.70238i) q^{89} +(13.4177 + 1.71709i) q^{91} +(2.48718 - 8.37937i) q^{93} -12.3355 q^{95} +(-2.72991 - 4.72835i) q^{97} +(-16.1186 + 8.19016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

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