LMFDB - Embedded newform 45.3.g.b.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(28,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.28"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	45.37
Dual form			45.3.g.b.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.224745 - 0.224745i) q^{2} -3.89898i q^{4} +(4.67423 - 1.77526i) q^{5} +(3.44949 + 3.44949i) q^{7} +(-1.77526 + 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} -11.3485 q^{11} +(-5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 + 17.3485i) q^{17} +8.69694i q^{19} +(-6.92168 - 18.2247i) q^{20} +(2.55051 + 2.55051i) q^{22} +(-11.5505 + 11.5505i) q^{23} +(18.6969 - 16.5959i) q^{25} +2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 + 10.4268i) q^{32} -7.79796i q^{34} +(22.2474 + 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(1.95459 - 1.95459i) q^{38} +(-5.14643 + 11.4495i) q^{40} -0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 - 44.2474i) q^{47} -25.2020i q^{49} +(-7.93189 - 0.472194i) q^{50} +(21.6413 + 21.6413i) q^{52} +(0.696938 - 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} -12.2474 q^{56} +(-7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 - 2.40408i) q^{62} +54.5051i q^{64} +(-16.0908 + 35.7980i) q^{65} +(-45.1010 - 45.1010i) q^{67} +(67.6413 - 67.6413i) q^{68} +(-2.75255 - 7.24745i) q^{70} +68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 - 39.1464i) q^{77} -24.4949i q^{79} +(-69.1691 + 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(-13.1464 + 13.1464i) q^{83} +(111.889 + 50.2929i) q^{85} +11.9092 q^{86} +(20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 + 45.0352i) q^{92} +19.8888i q^{94} +(15.4393 + 40.6515i) q^{95} +(-24.5959 - 24.5959i) q^{97} +(-5.66403 + 5.66403i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + 4 q^{10} - 16 q^{11} - 32 q^{13} - 20 q^{16} + 40 q^{17} + 36 q^{20} + 20 q^{22} - 56 q^{23} + 16 q^{25} - 88 q^{26} + 44 q^{28} - 16 q^{31} + 76 q^{32} + 40 q^{35}+ \cdots + 188 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8 + 4 * q^10 - 16 * q^11 - 32 * q^13 - 20 * q^16 + 40 * q^17 + 36 * q^20 + 20 * q^22 - 56 * q^23 + 16 * q^25 - 88 * q^26 + 44 * q^28 - 16 * q^31 + 76 * q^32 + 40 * q^35 + 64 * q^37 + 96 * q^38 + 48 * q^40 + 56 * q^41 - 8 * q^43 - 136 * q^46 - 128 * q^47 - 164 * q^50 - 80 * q^52 - 56 * q^53 - 124 * q^55 - 12 * q^58 + 200 * q^61 - 88 * q^62 + 112 * q^65 - 200 * q^67 + 104 * q^68 - 60 * q^70 + 272 * q^71 + 76 * q^73 + 312 * q^76 - 88 * q^77 - 164 * q^80 + 128 * q^82 + 16 * q^83 + 232 * q^85 + 224 * q^86 + 12 * q^88 - 16 * q^91 - 104 * q^92 - 144 * q^95 - 20 * q^97 + 188 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.224745	−	0.224745i	−0.112372	−	0.112372i	0.648685	−	0.761057i	$-0.275319\pi$
$2$	−0.224745	−	0.224745i	−0.112372	−	0.112372i	−0.761057	+	0.648685i	$0.775319\pi$
$3$		0			0
$3$		0			0
$4$		−	3.89898i		−	0.974745i
$5$	4.67423	−	1.77526i	0.934847	−	0.355051i
$5$	4.67423	−	1.77526i	0.934847	−	0.355051i
$6$		0			0
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	0.909182	−	0.416398i	$-0.136708\pi$
$7$	3.44949	+	3.44949i	0.492784	+	0.492784i	−0.416398	+	0.909182i	$0.636708\pi$
$8$	−1.77526	+	1.77526i	−0.221907	+	0.221907i
$9$		0			0
$10$	−1.44949	−	0.651531i	−0.144949	−	0.0651531i
$11$	−11.3485			−1.03168			−0.515840	−	0.856685i	$-0.672520\pi$
$11$	−11.3485			−1.03168			−0.515840	+	0.856685i	$0.672520\pi$
$12$		0			0
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	−0.887592	−	0.460630i	$-0.847624\pi$
$13$	−5.55051	+	5.55051i	−0.426962	+	0.426962i	0.460630	+	0.887592i	$0.347624\pi$
$14$		−	1.55051i		−	0.110751i
$15$		0			0
$16$	−14.7980			−0.924872
$17$	17.3485	+	17.3485i	1.02050	+	1.02050i	0.999785	+	0.0207127i	$0.00659354\pi$
$17$	17.3485	+	17.3485i	1.02050	+	1.02050i	0.0207127	+	0.999785i	$0.493406\pi$
$18$		0			0
$19$			8.69694i			0.457734i	0.973458	+	0.228867i	$0.0735020\pi$
$19$			8.69694i			0.457734i	−0.973458	+	0.228867i	$0.926498\pi$
$20$	−6.92168	−	18.2247i	−0.346084	−	0.911237i
$21$		0			0
$22$	2.55051	+	2.55051i	0.115932	+	0.115932i
$23$	−11.5505	+	11.5505i	−0.502196	+	0.502196i	−0.912120	−	0.409924i	$-0.865555\pi$
$23$	−11.5505	+	11.5505i	−0.502196	+	0.502196i	0.409924	+	0.912120i	$0.365555\pi$
$24$		0			0
$25$	18.6969	−	16.5959i	0.747878	−	0.663837i
$26$	2.49490			0.0959576
$27$		0			0
$28$	13.4495	−	13.4495i	0.480339	−	0.480339i
$29$		−	35.1464i		−	1.21195i	−0.795485	−	0.605973i	$-0.792784\pi$
$29$		−	35.1464i		−	1.21195i	0.795485	−	0.605973i	$-0.207216\pi$
$30$		0			0
$31$	10.6969			0.345063			0.172531	−	0.985004i	$-0.444805\pi$
$31$	10.6969			0.345063			0.172531	+	0.985004i	$0.444805\pi$
$32$	10.4268	+	10.4268i	0.325837	+	0.325837i
$33$		0			0
$34$		−	7.79796i		−	0.229352i
$35$	22.2474	+	10.0000i	0.635641	+	0.285714i
$36$		0			0
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	0.620677	−	0.784066i	$-0.286858\pi$
$37$	−6.04541	−	6.04541i	−0.163389	−	0.163389i	−0.784066	+	0.620677i	$0.786858\pi$
$38$	1.95459	−	1.95459i	0.0514366	−	0.0514366i
$39$		0			0
$40$	−5.14643	+	11.4495i	−0.128661	+	0.286237i
$41$	−0.696938			−0.0169985			−0.00849925	−	0.999964i	$-0.502705\pi$
$41$	−0.696938			−0.0169985			−0.00849925	+	0.999964i	$0.502705\pi$
$42$		0			0
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	−0.944544	−	0.328384i	$-0.893496\pi$
$43$	−26.4949	+	26.4949i	−0.616160	+	0.616160i	0.328384	+	0.944544i	$0.393496\pi$
$44$			44.2474i			1.00562i
$45$		0			0
$46$	5.19184			0.112866
$47$	−44.2474	−	44.2474i	−0.941435	−	0.941435i	0.0569424	−	0.998377i	$-0.481865\pi$
$47$	−44.2474	−	44.2474i	−0.941435	−	0.941435i	−0.998377	+	0.0569424i	$0.981865\pi$
$48$		0			0
$49$		−	25.2020i		−	0.514327i
$50$	−7.93189	−	0.472194i	−0.158638	−	0.00944387i
$51$		0			0
$52$	21.6413	+	21.6413i	0.416179	+	0.416179i
$53$	0.696938	−	0.696938i	0.0131498	−	0.0131498i	−0.700501	−	0.713651i	$-0.747040\pi$
$53$	0.696938	−	0.696938i	0.0131498	−	0.0131498i	0.713651	+	0.700501i	$0.247040\pi$
$54$		0			0
$55$	−53.0454	+	20.1464i	−0.964462	+	0.366299i
$56$	−12.2474			−0.218704
$57$		0			0
$58$	−7.89898	+	7.89898i	−0.136189	+	0.136189i
$59$			39.9342i			0.676851i	0.940993	+	0.338425i	$0.109894\pi$
$59$			39.9342i			0.676851i	−0.940993	+	0.338425i	$0.890106\pi$
$60$		0			0
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$	−2.40408	−	2.40408i	−0.0387755	−	0.0387755i
$63$		0			0
$64$			54.5051i			0.851642i
$65$	−16.0908	+	35.7980i	−0.247551	+	0.550738i
$66$		0			0
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	0.285291	−	0.958441i	$-0.407910\pi$
$67$	−45.1010	−	45.1010i	−0.673150	−	0.673150i	−0.958441	+	0.285291i	$0.907910\pi$
$68$	67.6413	−	67.6413i	0.994725	−	0.994725i
$69$		0			0
$70$	−2.75255	−	7.24745i	−0.0393222	−	0.103535i
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.0678931	−	0.997693i	$-0.478372\pi$
$73$	77.7878	−	77.7878i	1.06559	−	1.06559i	0.997693	−	0.0678931i	$-0.0216277\pi$
$74$			2.71735i			0.0367209i
$75$		0			0
$76$	33.9092			0.446173
$77$	−39.1464	−	39.1464i	−0.508395	−	0.508395i
$78$		0			0
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$	−69.1691	+	26.2702i	−0.864614	+	0.328377i
$81$		0			0
$82$	0.156633	+	0.156633i	0.00191016	+	0.00191016i
$83$	−13.1464	+	13.1464i	−0.158391	+	0.158391i	−0.781853	−	0.623463i	$-0.785725\pi$
$83$	−13.1464	+	13.1464i	−0.158391	+	0.158391i	0.623463	+	0.781853i	$0.285725\pi$
$84$		0			0
$85$	111.889	+	50.2929i	1.31634	+	0.591681i
$86$	11.9092			0.138479
$87$		0			0
$88$	20.1464	−	20.1464i	0.228937	−	0.228937i
$89$		−	82.1816i		−	0.923389i	−0.887039	−	0.461695i	$-0.847242\pi$
$89$		−	82.1816i		−	0.923389i	0.887039	−	0.461695i	$-0.152758\pi$
$90$		0			0
$91$	−38.2929			−0.420801
$92$	45.0352	+	45.0352i	0.489513	+	0.489513i
$93$		0			0
$94$			19.8888i			0.211583i
$95$	15.4393	+	40.6515i	0.162519	+	0.427911i
$96$		0			0
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	0.568865	−	0.822431i	$-0.307383\pi$
$97$	−24.5959	−	24.5959i	−0.253566	−	0.253566i	−0.822431	+	0.568865i	$0.807383\pi$
$98$	−5.66403	+	5.66403i	−0.0577962	+	0.0577962i
$99$		0			0
$100$	−64.7071	−	72.8990i	−0.647071	−	0.728990i
$101$	105.621			1.04575			0.522876	−	0.852409i	$-0.324859\pi$
$101$	105.621			1.04575			0.522876	+	0.852409i	$0.324859\pi$
$102$		0			0
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	−0.992081	−	0.125601i	$-0.959914\pi$
$103$	−89.2474	+	89.2474i	−0.866480	+	0.866480i	0.125601	+	0.992081i	$0.459914\pi$
$104$		−	19.7071i		−	0.189492i
$105$		0			0
$106$	−0.313267			−0.00295535
$107$	−68.7423	−	68.7423i	−0.642452	−	0.642452i	0.308706	−	0.951158i	$-0.400104\pi$
$107$	−68.7423	−	68.7423i	−0.642452	−	0.642452i	−0.951158	+	0.308706i	$0.900104\pi$
$108$		0			0
$109$			68.6969i			0.630247i	0.949051	+	0.315124i	$0.102046\pi$
$109$			68.6969i			0.630247i	−0.949051	+	0.315124i	$0.897954\pi$
$110$	16.4495	+	7.39388i	0.149541	+	0.0672171i
$111$		0			0
$112$	−51.0454	−	51.0454i	−0.455763	−	0.455763i
$113$	−97.6413	+	97.6413i	−0.864083	+	0.864083i	−0.991809	−	0.127727i	$-0.959232\pi$
$113$	−97.6413	+	97.6413i	−0.864083	+	0.864083i	0.127727	+	0.991809i	$0.459232\pi$
$114$		0			0
$115$	−33.4847	+	74.4949i	−0.291171	+	0.647782i
$116$	−137.035			−1.18134
$117$		0			0
$118$	8.97500	−	8.97500i	0.0760593	−	0.0760593i
$119$			119.687i			1.00577i
$120$		0			0
$121$	7.78775			0.0643616
$122$	−1.32806	−	1.32806i	−0.0108857	−	0.0108857i
$123$		0			0
$124$		−	41.7071i		−	0.336348i
$125$	57.9319	−	110.765i	0.463455	−	0.886120i
$126$		0			0
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.930865	+	0.365362i	$0.119055\pi$
$127$	164.621	+	164.621i	1.29623	+	1.29623i	0.365362	+	0.930865i	$0.380945\pi$
$128$	53.9569	−	53.9569i	0.421538	−	0.421538i
$129$		0			0
$130$	11.6617	−	4.42908i	0.0897057	−	0.0340698i
$131$	−106.136			−0.810200			−0.405100	−	0.914272i	$-0.632763\pi$
$131$	−106.136			−0.810200			−0.405100	+	0.914272i	$0.632763\pi$
$132$		0			0
$133$	−30.0000	+	30.0000i	−0.225564	+	0.225564i
$134$			20.2724i			0.151287i
$135$		0			0
$136$	−61.5959			−0.452911
$137$	166.631	+	166.631i	1.21629	+	1.21629i	0.968923	+	0.247363i	$0.0795639\pi$
$137$	166.631	+	166.631i	1.21629	+	1.21629i	0.247363	+	0.968923i	$0.420436\pi$
$138$		0			0
$139$		−	191.171i		−	1.37533i	−0.726026	−	0.687667i	$-0.758635\pi$
$139$		−	191.171i		−	1.37533i	0.726026	−	0.687667i	$-0.241365\pi$
$140$	38.9898	−	86.7423i	0.278499	−	0.619588i
$141$		0			0
$142$	−15.2827	−	15.2827i	−0.107624	−	0.107624i
$143$	62.9898	−	62.9898i	0.440488	−	0.440488i
$144$		0			0
$145$	−62.3939	−	164.283i	−0.430303	−	1.13298i
$146$	−34.9648			−0.239485
$147$		0			0
$148$	−23.5709	+	23.5709i	−0.159263	+	0.159263i
$149$		−	84.8536i		−	0.569487i	−0.958604	−	0.284744i	$-0.908092\pi$
$149$		−	84.8536i		−	0.569487i	0.958604	−	0.284744i	$-0.0919084\pi$
$150$		0			0
$151$	148.969			0.986552			0.493276	−	0.869873i	$-0.335799\pi$
$151$	148.969			0.986552			0.493276	+	0.869873i	$0.335799\pi$
$152$	−15.4393	−	15.4393i	−0.101574	−	0.101574i
$153$		0			0
$154$			17.5959i			0.114259i
$155$	50.0000	−	18.9898i	0.322581	−	0.122515i
$156$		0			0
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	0.758741	−	0.651393i	$-0.225815\pi$
$157$	16.8536	+	16.8536i	0.107348	+	0.107348i	−0.651393	+	0.758741i	$0.725815\pi$
$158$	−5.50510	+	5.50510i	−0.0348424	+	0.0348424i
$159$		0			0
$160$	67.2474	+	30.2270i	0.420297	+	0.188919i
$161$	−79.6867			−0.494949
$162$		0			0
$163$	130.606	−	130.606i	0.801265	−	0.801265i	−0.182029	−	0.983293i	$-0.558266\pi$
$163$	130.606	−	130.606i	0.801265	−	0.801265i	0.983293	+	0.182029i	$0.0582664\pi$
$164$			2.71735i			0.0165692i
$165$		0			0
$166$	5.90918			0.0355975
$167$	45.0352	+	45.0352i	0.269672	+	0.269672i	0.828968	−	0.559296i	$-0.188929\pi$
$167$	45.0352	+	45.0352i	0.269672	+	0.269672i	−0.559296	+	0.828968i	$0.688929\pi$
$168$		0			0
$169$			107.384i			0.635406i
$170$	−13.8434	−	36.4495i	−0.0814316	−	0.214409i
$171$		0			0
$172$	103.303	+	103.303i	0.600599	+	0.600599i
$173$	−146.631	+	146.631i	−0.847579	+	0.847579i	−0.989831	−	0.142252i	$-0.954566\pi$
$173$	−146.631	+	146.631i	−0.847579	+	0.847579i	0.142252	+	0.989831i	$0.454566\pi$
$174$		0			0
$175$	121.742	+	7.24745i	0.695671	+	0.0414140i
$176$	167.934			0.954171
$177$		0			0
$178$	−18.4699	+	18.4699i	−0.103763	+	0.103763i
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$	8.60612	+	8.60612i	0.0472864	+	0.0472864i
$183$		0			0
$184$		−	41.0102i		−	0.222882i
$185$	−38.9898	−	17.5255i	−0.210756	−	0.0947325i
$186$		0			0
$187$	−196.879	−	196.879i	−1.05283	−	1.05283i
$188$	−172.520	+	172.520i	−0.917659	+	0.917659i
$189$		0			0
$190$	5.66632	−	12.6061i	0.0298228	−	0.0663480i
$191$	−48.0908			−0.251784			−0.125892	−	0.992044i	$-0.540179\pi$
$191$	−48.0908			−0.251784			−0.125892	+	0.992044i	$0.540179\pi$
$192$		0			0
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.413809	+	0.910364i	$0.635802\pi$
$193$	−255.565	+	255.565i	−1.32417	+	1.32417i	−0.910364	+	0.413809i	$0.864198\pi$
$194$			11.0556i			0.0569877i
$195$		0			0
$196$	−98.2622			−0.501338
$197$	96.6969	+	96.6969i	0.490847	+	0.490847i	0.908573	−	0.417726i	$-0.137173\pi$
$197$	96.6969	+	96.6969i	0.490847	+	0.490847i	−0.417726	+	0.908573i	$0.637173\pi$
$198$		0			0
$199$			192.606i			0.967870i	0.875104	+	0.483935i	$0.160793\pi$
$199$			192.606i			0.967870i	−0.875104	+	0.483935i	$0.839207\pi$
$200$	−3.72985	+	62.6538i	−0.0186492	+	0.313269i
$201$		0			0
$202$	−23.7378	−	23.7378i	−0.117514	−	0.117514i
$203$	121.237	−	121.237i	0.597228	−	0.597228i
$204$		0			0
$205$	−3.25765	+	1.23724i	−0.0158910	+	0.00603533i
$206$	40.1158			0.194737
$207$		0			0
$208$	82.1362	−	82.1362i	0.394886	−	0.394886i
$209$		−	98.6969i		−	0.472234i
$210$		0			0
$211$	147.212			0.697688			0.348844	−	0.937181i	$-0.386574\pi$
$211$	147.212			0.697688			0.348844	+	0.937181i	$0.386574\pi$
$212$	−2.71735	−	2.71735i	−0.0128177	−	0.0128177i
$213$		0			0
$214$			30.8990i			0.144388i
$215$	−76.8082	+	170.879i	−0.357247	+	0.794784i
$216$		0			0
$217$	36.8990	+	36.8990i	0.170041	+	0.170041i
$218$	15.4393	−	15.4393i	0.0708224	−	0.0708224i
$219$		0			0
$220$	78.5505	+	206.823i	0.357048	+	0.940104i
$221$	−192.586			−0.871429
$222$		0			0
$223$	167.429	−	167.429i	0.750803	−	0.750803i	−0.223826	−	0.974629i	$-0.571855\pi$
$223$	167.429	−	167.429i	0.750803	−	0.750803i	0.974629	+	0.223826i	$0.0718548\pi$
$224$			71.9342i			0.321135i
$225$		0			0
$226$	43.8888			0.194198
$227$	−253.171	−	253.171i	−1.11529	−	1.11529i	−0.992423	−	0.122870i	$-0.960790\pi$
$227$	−253.171	−	253.171i	−1.11529	−	1.11529i	−0.122870	−	0.992423i	$-0.539210\pi$
$228$		0			0
$229$		−	224.202i		−	0.979048i	−0.871990	−	0.489524i	$-0.837171\pi$
$229$		−	224.202i		−	0.979048i	0.871990	−	0.489524i	$-0.162829\pi$
$230$	24.2679	−	9.21683i	0.105512	−	0.0400732i
$231$		0			0
$232$	62.3939	+	62.3939i	0.268939	+	0.268939i
$233$	205.712	−	205.712i	0.882883	−	0.882883i	−0.110944	−	0.993827i	$-0.535387\pi$
$233$	205.712	−	205.712i	0.882883	−	0.882883i	0.993827	+	0.110944i	$0.0353873\pi$
$234$		0			0
$235$	−285.373	−	128.272i	−1.21436	−	0.545840i
$236$	155.703			0.659757
$237$		0			0
$238$	26.8990	−	26.8990i	0.113021	−	0.113021i
$239$			345.798i			1.44685i	0.690401	+	0.723427i	$0.257434\pi$
$239$			345.798i			1.44685i	−0.690401	+	0.723427i	$0.742566\pi$
$240$		0			0
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$	−1.75026	−	1.75026i	−0.00723247	−	0.00723247i
$243$		0			0
$244$		−	23.0398i		−	0.0944254i
$245$	−44.7401	−	117.800i	−0.182612	−	0.480817i
$246$		0			0
$247$	−48.2724	−	48.2724i	−0.195435	−	0.195435i
$248$	−18.9898	+	18.9898i	−0.0765718	+	0.0765718i
$249$		0			0
$250$	−37.9138	+	11.8740i	−0.151655	+	0.0474959i
$251$	331.258			1.31975			0.659876	−	0.751375i	$-0.270609\pi$
$251$	331.258			1.31975			0.659876	+	0.751375i	$0.270609\pi$
$252$		0			0
$253$	131.081	−	131.081i	0.518105	−	0.518105i
$254$		−	73.9954i		−	0.291321i
$255$		0			0
$256$	193.767			0.756904
$257$	−33.2372	−	33.2372i	−0.129328	−	0.129328i	0.639480	−	0.768808i	$-0.279150\pi$
$257$	−33.2372	−	33.2372i	−0.129328	−	0.129328i	−0.768808	+	0.639480i	$0.779150\pi$
$258$		0			0
$259$		−	41.7071i		−	0.161031i
$260$	139.576	+	62.7378i	0.536829	+	0.241299i
$261$		0			0
$262$	23.8536	+	23.8536i	0.0910442	+	0.0910442i
$263$	278.157	−	278.157i	1.05763	−	1.05763i	0.0593952	−	0.998235i	$-0.481083\pi$
$263$	278.157	−	278.157i	1.05763	−	1.05763i	0.998235	−	0.0593952i	$-0.0189172\pi$
$264$		0			0
$265$	2.02041	−	4.49490i	0.00762419	−	0.0169619i
$266$	13.4847			0.0506943
$267$		0			0
$268$	−175.848	+	175.848i	−0.656149	+	0.656149i
$269$			488.499i			1.81598i	0.418988	+	0.907992i	$0.362385\pi$
$269$			488.499i			1.81598i	−0.418988	+	0.907992i	$0.637615\pi$
$270$		0			0
$271$	131.576			0.485518			0.242759	−	0.970087i	$-0.421947\pi$
$271$	131.576			0.485518			0.242759	+	0.970087i	$0.421947\pi$
$272$	−256.722	−	256.722i	−0.943831	−	0.943831i
$273$		0			0
$274$		−	74.8990i		−	0.273354i
$275$	−212.182	+	188.338i	−0.771570	+	0.684866i
$276$		0			0
$277$	101.510	+	101.510i	0.366461	+	0.366461i	0.866185	−	0.499724i	$-0.166565\pi$
$277$	101.510	+	101.510i	0.366461	+	0.366461i	−0.499724	+	0.866185i	$0.666565\pi$
$278$	−42.9648	+	42.9648i	−0.154550	+	0.154550i
$279$		0			0
$280$	−57.2474	+	21.7423i	−0.204455	+	0.0776512i
$281$	−343.303			−1.22172			−0.610860	−	0.791739i	$-0.709176\pi$
$281$	−343.303			−1.22172			−0.610860	+	0.791739i	$0.709176\pi$
$282$		0			0
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	−0.704998	−	0.709209i	$-0.749052\pi$
$283$	1.19184	−	1.19184i	0.00421143	−	0.00421143i	0.709209	+	0.704998i	$0.249052\pi$
$284$		−	265.131i		−	0.933558i
$285$		0			0
$286$	−28.3133			−0.0989974
$287$	−2.40408	−	2.40408i	−0.00837659	−	0.00837659i
$288$		0			0
$289$			312.939i			1.08283i
$290$	−22.8990	+	50.9444i	−0.0789620	+	0.175670i
$291$		0			0
$292$	−303.293	−	303.293i	−1.03867	−	1.03867i
$293$	−96.5653	+	96.5653i	−0.329574	+	0.329574i	−0.852425	−	0.522850i	$-0.824869\pi$
$293$	−96.5653	+	96.5653i	−0.329574	+	0.329574i	0.522850	+	0.852425i	$0.324869\pi$
$294$		0			0
$295$	70.8934	+	186.662i	0.240316	+	0.632752i
$296$	21.4643			0.0725145
$297$		0			0
$298$	−19.0704	+	19.0704i	−0.0639946	+	0.0639946i
$299$		−	128.222i		−	0.428838i
$300$		0			0
$301$	−182.788			−0.607268
$302$	−33.4801	−	33.4801i	−0.110861	−	0.110861i
$303$		0			0
$304$		−	128.697i		−	0.423345i
$305$	27.6209	−	10.4903i	0.0905604	−	0.0343945i
$306$		0			0
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	0.473648	−	0.880714i	$-0.342937\pi$
$307$	−124.969	−	124.969i	−0.407066	−	0.407066i	−0.880714	+	0.473648i	$0.842937\pi$
$308$	−152.631	+	152.631i	−0.495556	+	0.495556i
$309$		0			0
$310$	−15.5051	−	6.96938i	−0.0500165	−	0.0224819i
$311$	586.302			1.88522			0.942608	−	0.333902i	$-0.108365\pi$
$311$	586.302			1.88522			0.942608	+	0.333902i	$0.108365\pi$
$312$		0			0
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	−0.851472	−	0.524400i	$-0.824290\pi$
$313$	−102.373	+	102.373i	−0.327072	+	0.327072i	0.524400	+	0.851472i	$0.324290\pi$
$314$		−	7.57551i		−	0.0241258i
$315$		0			0
$316$	−95.5051			−0.302231
$317$	108.783	+	108.783i	0.343165	+	0.343165i	0.857556	−	0.514391i	$-0.171982\pi$
$317$	108.783	+	108.783i	0.343165	+	0.343165i	−0.514391	+	0.857556i	$0.671982\pi$
$318$		0			0
$319$			398.858i			1.25034i
$320$	96.7605	+	254.770i	0.302376	+	0.796155i
$321$		0			0
$322$	17.9092	+	17.9092i	0.0556186	+	0.0556186i
$323$	−150.879	+	150.879i	−0.467116	+	0.467116i
$324$		0			0
$325$	−11.6617	+	195.893i	−0.0358823	+	0.602749i
$326$	−58.7061			−0.180080
$327$		0			0
$328$	1.23724	−	1.23724i	0.00377208	−	0.00377208i
$329$		−	305.262i		−	0.927849i
$330$		0			0
$331$	−245.423			−0.741461			−0.370730	−	0.928741i	$-0.620893\pi$
$331$	−245.423			−0.741461			−0.370730	+	0.928741i	$0.620893\pi$
$332$	51.2577	+	51.2577i	0.154391	+	0.154391i
$333$		0			0
$334$		−	20.2429i		−	0.0606074i
$335$	−290.879	−	130.747i	−0.868294	−	0.390289i
$336$		0			0
$337$	213.808	+	213.808i	0.634446	+	0.634446i	0.949180	−	0.314734i	$-0.101915\pi$
$337$	213.808	+	213.808i	0.634446	+	0.634446i	−0.314734	+	0.949180i	$0.601915\pi$
$338$	24.1339	−	24.1339i	0.0714022	−	0.0714022i
$339$		0			0
$340$	196.091	−	436.252i	0.576738	−	1.28309i
$341$	−121.394			−0.355994
$342$		0			0
$343$	255.959	−	255.959i	0.746237	−	0.746237i
$344$		−	94.0704i		−	0.273460i
$345$		0			0
$346$	65.9092			0.190489
$347$	160.050	+	160.050i	0.461239	+	0.461239i	0.899062	−	0.437822i	$-0.144250\pi$
$347$	160.050	+	160.050i	0.461239	+	0.461239i	−0.437822	+	0.899062i	$0.644250\pi$
$348$		0			0
$349$		−	298.009i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$349$		−	298.009i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$350$	−25.7321	−	28.9898i	−0.0735204	−	0.0828280i
$351$		0			0
$352$	−118.328	−	118.328i	−0.336159	−	0.336159i
$353$	22.5199	−	22.5199i	0.0637957	−	0.0637957i	−0.674489	−	0.738285i	$-0.735636\pi$
$353$	22.5199	−	22.5199i	0.0637957	−	0.0637957i	0.738285	+	0.674489i	$0.235636\pi$
$354$		0			0
$355$	317.848	−	120.717i	0.895346	−	0.340049i
$356$	−320.424			−0.900069
$357$		0			0
$358$	−41.2883	+	41.2883i	−0.115330	+	0.115330i
$359$		−	48.2724i		−	0.134464i	−0.997737	−	0.0672318i	$-0.978583\pi$
$359$		−	48.2724i		−	0.134464i	0.997737	−	0.0672318i	$-0.0214167\pi$
$360$		0			0
$361$	285.363			0.790480
$362$	64.3383	+	64.3383i	0.177730	+	0.177730i
$363$		0			0
$364$			149.303i			0.410173i
$365$	225.505	−	501.691i	0.617822	−	1.37450i
$366$		0			0
$367$	146.510	+	146.510i	0.399209	+	0.399209i	0.877954	−	0.478745i	$-0.158908\pi$
$367$	146.510	+	146.510i	0.399209	+	0.399209i	−0.478745	+	0.877954i	$0.658908\pi$
$368$	170.924	−	170.924i	0.464467	−	0.464467i
$369$		0			0
$370$	4.82399	+	12.7015i	0.0130378	+	0.0343284i
$371$	4.80816			0.0129600
$372$		0			0
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	−0.582042	−	0.813159i	$-0.697746\pi$
$373$	86.2066	−	86.2066i	0.231117	−	0.231117i	0.813159	+	0.582042i	$0.197746\pi$
$374$			88.4949i			0.236617i
$375$		0			0
$376$	157.101			0.417822
$377$	195.081	+	195.081i	0.517455	+	0.517455i
$378$		0			0
$379$		−	210.000i		−	0.554090i	−0.960857	−	0.277045i	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$	158.499	−	60.1975i	0.417104	−	0.158414i
$381$		0			0
$382$	10.8082	+	10.8082i	0.0282936	+	0.0282936i
$383$	10.6311	−	10.6311i	0.0277575	−	0.0277575i	−0.693092	−	0.720849i	$-0.743752\pi$
$383$	10.6311	−	10.6311i	0.0277575	−	0.0277575i	0.720849	+	0.693092i	$0.243752\pi$
$384$		0			0
$385$	−252.474	−	113.485i	−0.655778	−	0.294765i
$386$	114.874			0.297601
$387$		0			0
$388$	−95.8990	+	95.8990i	−0.247162	+	0.247162i
$389$			535.337i			1.37619i	0.725621	+	0.688094i	$0.241552\pi$
$389$			535.337i			1.37619i	−0.725621	+	0.688094i	$0.758448\pi$
$390$		0			0
$391$	−400.767			−1.02498
$392$	44.7401	+	44.7401i	0.114133	+	0.114133i
$393$		0			0
$394$		−	43.4643i		−	0.110315i
$395$	−43.4847	−	114.495i	−0.110088	−	0.289860i
$396$		0			0
$397$	118.742	+	118.742i	0.299099	+	0.299099i	0.840661	−	0.541562i	$-0.182167\pi$
$397$	118.742	+	118.742i	0.299099	+	0.299099i	−0.541562	+	0.840661i	$0.682167\pi$
$398$	43.2872	−	43.2872i	0.108762	−	0.108762i
$399$		0			0
$400$	−276.677	+	245.586i	−0.691691	+	0.613964i
$401$	−420.302			−1.04813			−0.524067	−	0.851677i	$-0.675586\pi$
$401$	−420.302			−1.04813			−0.524067	+	0.851677i	$0.675586\pi$
$402$		0			0
$403$	−59.3735	+	59.3735i	−0.147329	+	0.147329i
$404$		−	411.814i		−	1.01934i
$405$		0			0
$406$	−54.4949			−0.134224
$407$	68.6061	+	68.6061i	0.168565	+	0.168565i
$408$		0			0
$409$		−	515.110i		−	1.25944i	−0.776823	−	0.629719i	$-0.783170\pi$
$409$		−	515.110i		−	1.25944i	0.776823	−	0.629719i	$-0.216830\pi$
$410$	1.01021	+	0.454077i	0.00246391	+	0.00110750i
$411$		0			0
$412$	347.974	+	347.974i	0.844597	+	0.844597i
$413$	−137.753	+	137.753i	−0.333541	+	0.333541i
$414$		0			0
$415$	−38.1112	+	84.7878i	−0.0918343	+	0.204308i
$416$	−115.748			−0.278240
$417$		0			0
$418$	−22.1816	+	22.1816i	−0.0530661	+	0.0530661i
$419$			88.6015i			0.211460i	0.994395	+	0.105730i	$0.0337178\pi$
$419$			88.6015i			0.211460i	−0.994395	+	0.105730i	$0.966282\pi$
$420$		0			0
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$	−33.0852	−	33.0852i	−0.0784009	−	0.0784009i
$423$		0			0
$424$			2.47449i			0.00583605i
$425$	612.277	+	36.4495i	1.44065	+	0.0857635i
$426$		0			0
$427$	20.3837	+	20.3837i	0.0477369	+	0.0477369i
$428$	−268.025	+	268.025i	−0.626227	+	0.626227i
$429$		0			0
$430$	55.6663	−	21.1418i	0.129457	−	0.0491671i
$431$	−804.636			−1.86690			−0.933452	−	0.358702i	$-0.883219\pi$
$431$	−804.636			−1.86690			−0.933452	+	0.358702i	$0.883219\pi$
$432$		0			0
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	−0.982528	−	0.186113i	$-0.940411\pi$
$433$	−344.848	+	344.848i	−0.796416	+	0.796416i	0.186113	+	0.982528i	$0.440411\pi$
$434$		−	16.5857i		−	0.0382159i
$435$		0			0
$436$	267.848			0.614330
$437$	−100.454	−	100.454i	−0.229872	−	0.229872i
$438$		0			0
$439$			432.929i			0.986170i	0.869981	+	0.493085i	$0.164131\pi$
$439$			432.929i			0.986170i	−0.869981	+	0.493085i	$0.835869\pi$
$440$	58.4041	−	129.934i	0.132737	−	0.295305i
$441$		0			0
$442$	43.2827	+	43.2827i	0.0979246	+	0.0979246i
$443$	−245.131	+	245.131i	−0.553342	+	0.553342i	−0.927404	−	0.374062i	$-0.877965\pi$
$443$	−245.131	+	245.131i	−0.553342	+	0.553342i	0.374062	+	0.927404i	$0.377965\pi$
$444$		0			0
$445$	−145.893	−	384.136i	−0.327850	−	0.863227i
$446$	−75.2577			−0.168739
$447$		0			0
$448$	−188.015	+	188.015i	−0.419676	+	0.419676i
$449$		−	386.091i		−	0.859890i	−0.902855	−	0.429945i	$-0.858533\pi$
$449$		−	386.091i		−	0.859890i	0.902855	−	0.429945i	$-0.141467\pi$
$450$		0			0
$451$	7.90918			0.0175370
$452$	380.702	+	380.702i	0.842260	+	0.842260i
$453$		0			0
$454$			113.798i			0.250656i
$455$	−178.990	+	67.9796i	−0.393384	+	0.149406i
$456$		0			0
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	0.418580	−	0.908180i	$-0.362528\pi$
$457$	−223.747	−	223.747i	−0.489599	−	0.489599i	−0.908180	+	0.418580i	$0.862528\pi$
$458$	−50.3883	+	50.3883i	−0.110018	+	0.110018i
$459$		0			0
$460$	290.454	+	130.556i	0.631422	+	0.283818i
$461$	722.620			1.56751			0.783753	−	0.621073i	$-0.213303\pi$
$461$	722.620			1.56751			0.783753	+	0.621073i	$0.213303\pi$
$462$		0			0
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	−0.833162	−	0.553029i	$-0.813472\pi$
$463$	−129.702	+	129.702i	−0.280133	+	0.280133i	0.553029	+	0.833162i	$0.313472\pi$
$464$			520.095i			1.12090i
$465$		0			0
$466$	−92.4653			−0.198423
$467$	−415.258	−	415.258i	−0.889203	−	0.889203i	0.105244	−	0.994446i	$-0.466438\pi$
$467$	−415.258	−	415.258i	−0.889203	−	0.889203i	−0.994446	+	0.105244i	$0.966438\pi$
$468$		0			0
$469$		−	311.151i		−	0.663435i
$470$	35.3076	+	92.9648i	0.0751227	+	0.197797i
$471$		0			0
$472$	−70.8934	−	70.8934i	−0.150198	−	0.150198i
$473$	300.677	−	300.677i	0.635680	−	0.635680i
$474$		0			0
$475$	144.334	+	162.606i	0.303860	+	0.342329i
$476$	466.656			0.980370
$477$		0			0
$478$	77.7163	−	77.7163i	0.162586	−	0.162586i
$479$		−	304.949i		−	0.636637i	−0.947984	−	0.318318i	$-0.896882\pi$
$479$		−	304.949i		−	0.636637i	0.947984	−	0.318318i	$-0.103118\pi$
$480$		0			0
$481$	67.1102			0.139522
$482$	−22.8286	−	22.8286i	−0.0473622	−	0.0473622i
$483$		0			0
$484$		−	30.3643i		−	0.0627361i
$485$	−158.631	−	71.3031i	−0.327074	−	0.147017i
$486$		0			0
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	0.112137	−	0.993693i	$-0.464231\pi$
$487$	−429.318	−	429.318i	−0.881556	−	0.881556i	−0.993693	+	0.112137i	$0.964231\pi$
$488$	−10.4903	+	10.4903i	−0.0214965	+	0.0214965i
$489$		0			0
$490$	−16.4199	+	36.5301i	−0.0335100	+	0.0745512i
$491$	414.318			0.843825			0.421912	−	0.906637i	$-0.361359\pi$
$491$	414.318			0.843825			0.421912	+	0.906637i	$0.361359\pi$
$492$		0			0
$493$	609.737	−	609.737i	1.23679	−	1.23679i
$494$			21.6980i			0.0439230i
$495$		0			0
$496$	−158.293			−0.319139
$497$	234.565	+	234.565i	0.471962	+	0.471962i
$498$		0			0
$499$			367.585i			0.736643i	0.929699	+	0.368321i	$0.120067\pi$
$499$			367.585i			0.736643i	−0.929699	+	0.368321i	$0.879933\pi$
$500$	−431.871	−	225.875i	−0.863741	−	0.451750i
$501$		0			0
$502$	−74.4485	−	74.4485i	−0.148304	−	0.148304i
$503$	9.59133	−	9.59133i	0.0190683	−	0.0190683i	−0.697508	−	0.716577i	$-0.745708\pi$
$503$	9.59133	−	9.59133i	0.0190683	−	0.0190683i	0.716577	+	0.697508i	$0.245708\pi$
$504$		0			0
$505$	493.697	−	187.504i	0.977618	−	0.371295i
$506$	−58.9194			−0.116441
$507$		0			0
$508$	641.854	−	641.854i	1.26349	−	1.26349i
$509$		−	777.489i		−	1.52748i	−0.645522	−	0.763742i	$-0.723360\pi$
$509$		−	777.489i		−	1.52748i	0.645522	−	0.763742i	$-0.276640\pi$
$510$		0			0
$511$	536.656			1.05021
$512$	−259.376	−	259.376i	−0.506593	−	0.506593i
$513$		0			0
$514$			14.9398i			0.0290658i
$515$	−258.727	+	575.601i	−0.502382	+	1.11767i
$516$		0			0
$517$	502.141	+	502.141i	0.971259	+	0.971259i
$518$	−9.37347	+	9.37347i	−0.0180955	+	0.0180955i
$519$		0			0
$520$	−34.9852	−	92.1158i	−0.0672792	−	0.177146i
$521$	−321.605			−0.617284			−0.308642	−	0.951178i	$-0.599875\pi$
$521$	−321.605			−0.617284			−0.308642	+	0.951178i	$0.599875\pi$
$522$		0			0
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.121030	+	0.992649i	$0.538620\pi$
$523$	−582.454	+	582.454i	−1.11368	+	1.11368i	−0.992649	+	0.121030i	$0.961380\pi$
$524$			413.823i			0.789738i
$525$		0			0
$526$	−125.029			−0.237697
$527$	185.576	+	185.576i	0.352136	+	0.352136i
$528$		0			0
$529$			262.171i			0.495598i
$530$	−1.46428	+	0.556128i	−0.00276280	+	0.00104930i
$531$		0			0
$532$	116.969	+	116.969i	0.219867	+	0.219867i
$533$	3.86836	−	3.86836i	0.00725772	−	0.00725772i
$534$		0			0
$535$	−443.353	−	199.283i	−0.828697	−	0.372491i
$536$	160.132			0.298753
$537$		0			0
$538$	109.788	−	109.788i	0.204066	−	0.204066i
$539$			286.005i			0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$	−29.5709	−	29.5709i	−0.0545589	−	0.0545589i
$543$		0			0
$544$			361.778i			0.665032i
$545$	121.955	+	321.106i	0.223770	+	0.589185i
$546$		0			0
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.971081	−	0.238750i	$-0.923262\pi$
$547$	−661.778	−	661.778i	−1.20983	−	1.20983i	−0.238750	−	0.971081i	$-0.576738\pi$
$548$	649.691	−	649.691i	1.18557	−	1.18557i
$549$		0			0
$550$	90.0148	+	5.35867i	0.163663	+	0.00974304i
$551$	305.666			0.554748
$552$		0			0
$553$	84.4949	−	84.4949i	0.152794	−	0.152794i
$554$		−	45.6276i		−	0.0823602i
$555$		0			0
$556$	−745.373			−1.34060
$557$	−125.909	−	125.909i	−0.226049	−	0.226049i	0.584991	−	0.811040i	$-0.301098\pi$
$557$	−125.909	−	125.909i	−0.226049	−	0.226049i	−0.811040	+	0.584991i	$0.801098\pi$
$558$		0			0
$559$		−	294.120i		−	0.526155i
$560$	−329.217	−	147.980i	−0.587887	−	0.264249i
$561$		0			0
$562$	77.1556	+	77.1556i	0.137288	+	0.137288i
$563$	200.009	−	200.009i	0.355256	−	0.355256i	−0.506805	−	0.862061i	$-0.669174\pi$
$563$	200.009	−	200.009i	0.355256	−	0.355256i	0.862061	+	0.506805i	$0.169174\pi$
$564$		0			0
$565$	−283.060	+	629.737i	−0.500992	+	1.11458i
$566$	−0.535718			−0.000946498
$567$		0			0
$568$	−120.717	+	120.717i	−0.212531	+	0.212531i
$569$			599.839i			1.05420i	0.849804	+	0.527099i	$0.176720\pi$
$569$			599.839i			1.05420i	−0.849804	+	0.527099i	$0.823280\pi$
$570$		0			0
$571$	−247.970			−0.434274			−0.217137	−	0.976141i	$-0.569672\pi$
$571$	−247.970			−0.434274			−0.217137	+	0.976141i	$0.569672\pi$
$572$	−245.596	−	245.596i	−0.429363	−	0.429363i
$573$		0			0
$574$			1.08061i			0.00188260i
$575$	−24.2679	+	407.650i	−0.0422050	+	0.708957i
$576$		0			0
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	0.407105	−	0.913381i	$-0.366538\pi$
$577$	−292.121	−	292.121i	−0.506276	−	0.506276i	−0.913381	+	0.407105i	$0.866538\pi$
$578$	70.3314	−	70.3314i	0.121681	−	0.121681i
$579$		0			0
$580$	−640.535	+	243.272i	−1.10437	+	0.419435i
$581$	−90.6969			−0.156105
$582$		0			0
$583$	−7.90918	+	7.90918i	−0.0135664	+	0.0135664i
$584$			276.186i			0.472922i
$585$		0			0
$586$	43.4051			0.0740702
$587$	−611.217	−	611.217i	−1.04126	−	1.04126i	−0.999112	−	0.0421437i	$-0.986581\pi$
$587$	−611.217	−	611.217i	−1.04126	−	1.04126i	−0.0421437	−	0.999112i	$-0.513419\pi$
$588$		0			0
$589$			93.0306i			0.157947i
$590$	26.0183	−	57.8842i	0.0440989	−	0.0981088i
$591$		0			0
$592$	89.4597	+	89.4597i	0.151114	+	0.151114i
$593$	−524.742	+	524.742i	−0.884894	+	0.884894i	−0.994027	−	0.109133i	$-0.965193\pi$
$593$	−524.742	+	524.742i	−0.884894	+	0.884894i	0.109133	+	0.994027i	$0.465193\pi$
$594$		0			0
$595$	212.474	+	559.444i	0.357100	+	0.940242i
$596$	−330.842			−0.555105
$597$		0			0
$598$	−28.8173	+	28.8173i	−0.0481895	+	0.0481895i
$599$			368.858i			0.615790i	0.951420	+	0.307895i	$0.0996245\pi$
$599$			368.858i			0.615790i	−0.951420	+	0.307895i	$0.900375\pi$
$600$		0			0
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$	41.0806	+	41.0806i	0.0682402	+	0.0682402i
$603$		0			0
$604$		−	580.829i		−	0.961637i
$605$	36.4018	−	13.8252i	0.0601682	−	0.0228517i
$606$		0			0
$607$	513.611	+	513.611i	0.846146	+	0.846146i	0.989650	−	0.143504i	$-0.0458369\pi$
$607$	513.611	+	513.611i	0.846146	+	0.846146i	−0.143504	+	0.989650i	$0.545837\pi$
$608$	−90.6811	+	90.6811i	−0.149147	+	0.149147i
$609$		0			0
$610$	−8.56530	−	3.85002i	−0.0140415	−	0.00631150i
$611$	491.192			0.803915
$612$		0			0
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.00373821	+	0.999993i	$0.501190\pi$
$613$	−615.287	+	615.287i	−1.00373	+	1.00373i	−0.999993	+	0.00373821i	$0.998810\pi$
$614$			56.1725i			0.0914861i
$615$		0			0
$616$	138.990			0.225633
$617$	−546.752	−	546.752i	−0.886145	−	0.886145i	0.108005	−	0.994150i	$-0.465554\pi$
$617$	−546.752	−	546.752i	−0.886145	−	0.886145i	−0.994150	+	0.108005i	$0.965554\pi$
$618$		0			0
$619$			152.869i			0.246962i	0.992347	+	0.123481i	$0.0394058\pi$
$619$			152.869i			0.246962i	−0.992347	+	0.123481i	$0.960594\pi$
$620$	−74.0408	−	194.949i	−0.119421	−	0.314434i
$621$		0			0
$622$	−131.768	−	131.768i	−0.211846	−	0.211846i
$623$	283.485	−	283.485i	0.455032	−	0.455032i
$624$		0			0
$625$	74.1510	−	620.586i	0.118642	−	0.992937i
$626$	46.0158			0.0735077
$627$		0			0
$628$	65.7117	−	65.7117i	0.104637	−	0.104637i
$629$		−	209.757i		−	0.333477i
$630$		0			0
$631$	−41.4847			−0.0657444			−0.0328722	−	0.999460i	$-0.510465\pi$
$631$	−41.4847			−0.0657444			−0.0328722	+	0.999460i	$0.510465\pi$
$632$	43.4847	+	43.4847i	0.0688049	+	0.0688049i
$633$		0			0
$634$		−	48.8969i		−	0.0771245i
$635$	1061.72	+	477.233i	1.67200	+	0.751547i
$636$		0			0
$637$	139.884	+	139.884i	0.219598	+	0.219598i
$638$	89.6413	−	89.6413i	0.140504	−	0.140504i
$639$		0			0
$640$	156.420	−	347.994i	0.244406	−	0.543741i
$641$	−47.2122			−0.0736541			−0.0368270	−	0.999322i	$-0.511725\pi$
$641$	−47.2122			−0.0736541			−0.0368270	+	0.999322i	$0.511725\pi$
$642$		0			0
$643$	460.372	−	460.372i	0.715976	−	0.715976i	−0.251803	−	0.967779i	$-0.581023\pi$
$643$	460.372	−	460.372i	0.715976	−	0.715976i	0.967779	+	0.251803i	$0.0810234\pi$
$644$			310.697i			0.482449i
$645$		0			0
$646$	67.8184			0.104982
$647$	281.287	+	281.287i	0.434756	+	0.434756i	0.890243	−	0.455487i	$-0.150535\pi$
$647$	281.287	+	281.287i	0.434756	+	0.434756i	−0.455487	+	0.890243i	$0.650535\pi$
$648$		0			0
$649$		−	453.192i		−	0.698293i
$650$	46.6469	−	41.4051i	0.0717645	−	0.0637002i
$651$		0			0
$652$	−509.231	−	509.231i	−0.781029	−	0.781029i
$653$	−89.8230	+	89.8230i	−0.137554	+	0.137554i	−0.772531	−	0.634977i	$-0.781010\pi$
$653$	−89.8230	+	89.8230i	−0.137554	+	0.137554i	0.634977	+	0.772531i	$0.281010\pi$
$654$		0			0
$655$	−496.106	+	188.419i	−0.757413	+	0.287662i
$656$	10.3133			0.0157214
$657$		0			0
$658$	−68.6061	+	68.6061i	−0.104265	+	0.104265i
$659$		−	1081.24i		−	1.64072i	−0.571844	−	0.820362i	$-0.693772\pi$
$659$		−	1081.24i		−	1.64072i	0.571844	−	0.820362i	$-0.306228\pi$
$660$		0			0
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$	55.1577	+	55.1577i	0.0833197	+	0.0833197i
$663$		0			0
$664$		−	46.6765i		−	0.0702960i
$665$	−86.9694	+	193.485i	−0.130781	+	0.290954i
$666$		0			0
$667$	405.959	+	405.959i	0.608634	+	0.608634i
$668$	175.591	−	175.591i	0.262861	−	0.262861i
$669$		0			0
$670$	35.9888	+	94.7582i	0.0537146	+	0.141430i
$671$	−67.0602			−0.0999407
$672$		0			0
$673$	233.293	−	233.293i	0.346646	−	0.346646i	−0.512213	−	0.858859i	$-0.671174\pi$
$673$	233.293	−	233.293i	0.346646	−	0.346646i	0.858859	+	0.512213i	$0.171174\pi$
$674$		−	96.1046i		−	0.142588i
$675$		0			0
$676$	418.687			0.619359
$677$	48.3883	+	48.3883i	0.0714745	+	0.0714745i	0.741940	−	0.670466i	$-0.233906\pi$
$677$	48.3883	+	48.3883i	0.0714745	+	0.0714745i	−0.670466	+	0.741940i	$0.733906\pi$
$678$		0			0
$679$		−	169.687i		−	0.249907i
$680$	−287.914	+	109.348i	−0.423403	+	0.160807i
$681$		0			0
$682$	27.2827	+	27.2827i	0.0400039	+	0.0400039i
$683$	−213.410	+	213.410i	−0.312459	+	0.312459i	−0.845862	−	0.533402i	$-0.820913\pi$
$683$	−213.410	+	213.410i	−0.312459	+	0.312459i	0.533402	+	0.845862i	$0.320913\pi$
$684$		0			0
$685$	1074.69	+	483.060i	1.56888	+	0.705197i
$686$	−115.051			−0.167713
$687$		0			0
$688$	392.070	−	392.070i	0.569870	−	0.569870i
$689$			7.73673i			0.0112289i
$690$		0			0
$691$	151.121			0.218700			0.109350	−	0.994003i	$-0.465123\pi$
$691$	151.121			0.218700			0.109350	+	0.994003i	$0.465123\pi$
$692$	571.712	+	571.712i	0.826173	+	0.826173i
$693$		0			0
$694$		−	71.9408i		−	0.103661i
$695$	−339.378	−	893.580i	−0.488314	−	1.28573i
$696$		0			0
$697$	−12.0908	−	12.0908i	−0.0173469	−	0.0173469i
$698$	−66.9760	+	66.9760i	−0.0959542	+	0.0959542i
$699$		0			0
$700$	28.2577	−	474.671i	0.0403681	−	0.678101i
$701$	745.680			1.06374			0.531869	−	0.846827i	$-0.321490\pi$
$701$	745.680			1.06374			0.531869	+	0.846827i	$0.321490\pi$
$702$		0			0
$703$	52.5765	−	52.5765i	0.0747888	−	0.0747888i
$704$		−	618.549i		−	0.878621i
$705$		0			0
$706$	−10.1225			−0.0143378
$707$	364.338	+	364.338i	0.515330	+	0.515330i
$708$		0			0
$709$			719.049i			1.01417i	0.861895	+	0.507087i	$0.169278\pi$
$709$			719.049i			1.01417i	−0.861895	+	0.507087i	$0.830722\pi$
$710$	−98.5653	−	44.3041i	−0.138824	−	0.0624001i
$711$		0			0
$712$	145.893	+	145.893i	0.204906	+	0.204906i
$713$	−123.555	+	123.555i	−0.173289	+	0.173289i
$714$		0			0
$715$	182.606	−	406.252i	0.255393	−	0.568185i
$716$	−716.288			−1.00040
$717$		0			0
$718$	−10.8490	+	10.8490i	−0.0151100	+	0.0151100i
$719$			605.271i			0.841824i	0.907101	+	0.420912i	$0.138290\pi$
$719$			605.271i			0.841824i	−0.907101	+	0.420912i	$0.861710\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$	−64.1339	−	64.1339i	−0.0888282	−	0.0888282i
$723$		0			0
$724$			1116.17i			1.54167i
$725$	−583.287	−	657.131i	−0.804534	−	0.906387i
$726$		0			0
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	0.517271	−	0.855821i	$-0.326948\pi$
$727$	−246.126	−	246.126i	−0.338550	−	0.338550i	−0.855821	+	0.517271i	$0.826948\pi$
$728$	67.9796	−	67.9796i	0.0933786	−	0.0933786i
$729$		0			0
$730$	−163.434	+	62.0714i	−0.223882	+	0.0850294i
$731$	−919.292			−1.25758
$732$		0			0
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	−0.867255	−	0.497865i	$-0.834118\pi$
$733$	−270.763	+	270.763i	−0.369390	+	0.369390i	0.497865	+	0.867255i	$0.334118\pi$
$734$		−	65.8546i		−	0.0897202i
$735$		0			0
$736$	−240.869			−0.327268
$737$	511.828	+	511.828i	0.694474	+	0.694474i
$738$		0			0
$739$		−	515.666i		−	0.697789i	−0.937162	−	0.348895i	$-0.886557\pi$
$739$		−	515.666i		−	0.697789i	0.937162	−	0.348895i	$-0.113443\pi$
$740$	−68.3316	+	152.020i	−0.0923400	+	0.205433i
$741$		0			0
$742$	−1.08061	−	1.08061i	−0.00145635	−	0.00145635i
$743$	−420.702	+	420.702i	−0.566220	+	0.566220i	−0.931067	−	0.364847i	$-0.881121\pi$
$743$	−420.702	+	420.702i	−0.566220	+	0.566220i	0.364847	+	0.931067i	$0.381121\pi$
$744$		0			0
$745$	−150.637	−	396.626i	−0.202197	−	0.532383i
$746$	−38.7490			−0.0519424
$747$		0			0
$748$	−767.626	+	767.626i	−1.02624	+	1.02624i
$749$		−	474.252i		−	0.633180i
$750$		0			0
$751$	−859.787			−1.14486			−0.572428	−	0.819955i	$-0.693998\pi$
$751$	−859.787			−1.14486			−0.572428	+	0.819955i	$0.693998\pi$
$752$	654.772	+	654.772i	0.870707	+	0.870707i
$753$		0			0
$754$		−	87.6867i		−	0.116295i
$755$	696.318	−	264.459i	0.922275	−	0.350276i
$756$		0			0
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.949642	−	0.313337i	$-0.898553\pi$
$757$	−956.075	−	956.075i	−1.26298	−	1.26298i	−0.313337	−	0.949642i	$-0.601447\pi$
$758$	−47.1964	+	47.1964i	−0.0622644	+	0.0622644i
$759$		0			0
$760$	−99.5755	−	44.7582i	−0.131020	−	0.0588923i
$761$	322.758			0.424124			0.212062	−	0.977256i	$-0.431982\pi$
$761$	322.758			0.424124			0.212062	+	0.977256i	$0.431982\pi$
$762$		0			0
$763$	−236.969	+	236.969i	−0.310576	+	0.310576i
$764$			187.505i			0.245426i
$765$		0			0
$766$	−4.77858			−0.00623835
$767$	−221.655	−	221.655i	−0.288990	−	0.288990i
$768$		0			0
$769$			692.402i			0.900393i	0.892930	+	0.450196i	$0.148646\pi$
$769$			692.402i			0.900393i	−0.892930	+	0.450196i	$0.851354\pi$
$770$	31.2372	+	82.2474i	0.0405678	+	0.106815i
$771$		0			0
$772$	996.444	+	996.444i	1.29073	+	1.29073i
$773$	−375.226	+	375.226i	−0.485415	+	0.485415i	−0.906856	−	0.421441i	$-0.861525\pi$
$773$	−375.226	+	375.226i	−0.485415	+	0.485415i	0.421441	+	0.906856i	$0.361525\pi$
$774$		0			0
$775$	200.000	−	177.526i	0.258065	−	0.229065i
$776$	87.3281			0.112536
$777$		0			0
$778$	120.314	−	120.314i	0.154646	−	0.154646i
$779$		−	6.06123i		−	0.00778078i
$780$		0			0
$781$	−771.696			−0.988087
$782$	90.0704	+	90.0704i	0.115180	+	0.115180i
$783$		0			0
$784$			372.939i			0.475687i
$785$	108.697	+	48.8582i	0.138467	+	0.0622397i
$786$		0			0
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.985001	+	0.172546i	$0.0551993\pi$
$787$	910.990	+	910.990i	1.15755	+	1.15755i	0.172546	+	0.985001i	$0.444801\pi$
$788$	377.019	−	377.019i	0.478451	−	0.478451i
$789$		0			0
$790$	−15.9592	+	35.5051i	−0.0202015	+	0.0449432i
$791$	−673.626			−0.851613
$792$		0			0
$793$	−32.7990	+	32.7990i	−0.0413606	+	0.0413606i
$794$		−	53.3735i		−	0.0672210i
$795$		0			0
$796$	750.967			0.943426
$797$	7.21683	+	7.21683i	0.00905500	+	0.00905500i	0.711620	−	0.702565i	$-0.247962\pi$
$797$	7.21683	+	7.21683i	0.00905500	+	0.00905500i	−0.702565	+	0.711620i	$0.747962\pi$
$798$		0			0
$799$		−	1535.25i		−	1.92147i
$800$	367.991	+	21.9069i	0.459989	+	0.0273836i
$801$		0			0
$802$	94.4607	+	94.4607i	0.117781	+	0.117781i
$803$	−882.772	+	882.772i	−1.09934	+	1.09934i
$804$		0			0
$805$	−372.474	+	141.464i	−0.462701	+	0.175732i
$806$	26.6878			0.0331114
$807$		0			0
$808$	−187.504	+	187.504i	−0.232059	+	0.232059i
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$		0			0
$811$	1336.85			1.64839			0.824197	−	0.566304i	$-0.191627\pi$
$811$	1336.85			1.64839			0.824197	+	0.566304i	$0.191627\pi$
$812$	−472.702	−	472.702i	−0.582145	−	0.582145i
$813$		0			0
$814$		−	30.8377i		−	0.0378842i
$815$	378.624	−	842.343i	0.464570	−	1.03355i
$816$		0			0
$817$	−230.424	−	230.424i	−0.282037	−	0.282037i
$818$	−115.768	+	115.768i	−0.141526	+	0.141526i
$819$		0			0
$820$	4.82399	+	12.7015i	0.00588291	+	0.0154897i
$821$	33.8934			0.0412830			0.0206415	−	0.999787i	$-0.493429\pi$
$821$	33.8934			0.0412830			0.0206415	+	0.999787i	$0.493429\pi$
$822$		0			0
$823$	481.631	−	481.631i	0.585214	−	0.585214i	−0.351117	−	0.936331i	$-0.614198\pi$
$823$	481.631	−	481.631i	0.585214	−	0.585214i	0.936331	+	0.351117i	$0.114198\pi$
$824$		−	316.874i		−	0.384556i
$825$		0			0
$826$	61.9184			0.0749617
$827$	−350.756	−	350.756i	−0.424131	−	0.424131i	0.462492	−	0.886623i	$-0.346955\pi$
$827$	−350.756	−	350.756i	−0.424131	−	0.424131i	−0.886623	+	0.462492i	$0.846955\pi$
$828$		0			0
$829$		−	697.423i		−	0.841283i	−0.907227	−	0.420641i	$-0.861805\pi$
$829$		−	697.423i		−	0.841283i	0.907227	−	0.420641i	$-0.138195\pi$
$830$	27.6209	−	10.4903i	0.0332782	−	0.0126389i
$831$		0			0
$832$	−302.531	−	302.531i	−0.363619	−	0.363619i
$833$	437.217	−	437.217i	0.524870	−	0.524870i
$834$		0			0
$835$	290.454	+	130.556i	0.347849	+	0.156355i
$836$	−384.817			−0.460308
$837$		0			0
$838$	19.9127	−	19.9127i	0.0237622	−	0.0237622i
$839$		−	72.3724i		−	0.0862604i	−0.999069	−	0.0431302i	$-0.986267\pi$
$839$		−	72.3724i		−	0.0862604i	0.999069	−	0.0431302i	$-0.0137330\pi$
$840$		0			0
$841$	−394.271			−0.468813
$842$	57.7934	+	57.7934i	0.0686382	+	0.0686382i
$843$		0			0
$844$		−	573.978i		−	0.680068i
$845$	190.633	+	501.936i	0.225602	+	0.594008i
$846$		0			0
$847$	26.8638	+	26.8638i	0.0317164	+	0.0317164i
$848$	−10.3133	+	10.3133i	−0.0121619	+	0.0121619i
$849$		0			0
$850$	−129.414	−	145.798i	−0.152252	−	0.171527i
$851$	139.655			0.164107
$852$		0			0
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	−0.749465	−	0.662044i	$-0.769689\pi$
$853$	−74.5699	+	74.5699i	−0.0874207	+	0.0874207i	0.662044	+	0.749465i	$0.269689\pi$
$854$		−	9.16225i		−	0.0107286i
$855$		0			0
$856$	244.070			0.285129
$857$	293.176	+	293.176i	0.342096	+	0.342096i	0.857155	−	0.515059i	$-0.172230\pi$
$857$	293.176	+	293.176i	0.342096	+	0.342096i	−0.515059	+	0.857155i	$0.672230\pi$
$858$		0			0
$859$		−	786.867i		−	0.916027i	−0.888945	−	0.458014i	$-0.848561\pi$
$859$		−	786.867i		−	0.916027i	0.888945	−	0.458014i	$-0.151439\pi$
$860$	666.252	+	299.473i	0.774712	+	0.348225i
$861$		0			0
$862$	180.838	+	180.838i	0.209789	+	0.209789i
$863$	1072.68	−	1072.68i	1.24297	−	1.24297i	0.284204	−	0.958764i	$-0.408271\pi$
$863$	1072.68	−	1072.68i	1.24297	−	1.24297i	0.958764	−	0.284204i	$-0.0917292\pi$
$864$		0			0
$865$	−425.081	+	945.696i	−0.491423	+	1.09329i
$866$	155.006			0.178990
$867$		0			0
$868$	143.868	−	143.868i	0.165747	−	0.165747i
$869$			277.980i			0.319884i
$870$		0			0
$871$	500.667			0.574819
$872$	−121.955	−	121.955i	−0.139856	−	0.139856i
$873$		0			0
$874$			45.1531i			0.0516626i
$875$	581.918	−	182.247i	0.665050	−	0.208283i
$876$		0			0
$877$	239.460	+	239.460i	0.273044	+	0.273044i	0.830324	−	0.557280i	$-0.188155\pi$
$877$	239.460	+	239.460i	0.273044	+	0.273044i	−0.557280	+	0.830324i	$0.688155\pi$
$878$	97.2985	−	97.2985i	0.110818	−	0.110818i
$879$		0			0
$880$	784.964	−	298.126i	0.892004	−	0.338780i
$881$	−62.8490			−0.0713382			−0.0356691	−	0.999364i	$-0.511356\pi$
$881$	−62.8490			−0.0713382			−0.0356691	+	0.999364i	$0.511356\pi$
$882$		0			0
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	−0.790922	−	0.611917i	$-0.790399\pi$
$883$	−158.061	+	158.061i	−0.179005	+	0.179005i	0.611917	+	0.790922i	$0.290399\pi$
$884$			750.888i			0.849421i
$885$		0			0
$886$	110.184			0.124361
$887$	−30.2066	−	30.2066i	−0.0340548	−	0.0340548i	0.689874	−	0.723929i	$-0.257666\pi$
$887$	−30.2066	−	30.2066i	−0.0340548	−	0.0340548i	−0.723929	+	0.689874i	$0.757666\pi$
$888$		0			0
$889$			1135.72i			1.27752i
$890$	−53.5439	+	119.121i	−0.0601616	+	0.133844i
$891$		0			0
$892$	−652.803	−	652.803i	−0.731841	−	0.731841i
$893$	384.817	−	384.817i	0.430926	−	0.430926i
$894$		0			0
$895$	−326.135	−	858.712i	−0.364397	−	0.959454i
$896$	372.247			0.415455
$897$		0			0
$898$	−86.7719	+	86.7719i	−0.0966280	+	0.0966280i
$899$		−	375.959i		−	0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$	−1.77755	−	1.77755i	−0.00197067	−	0.00197067i
$903$		0			0
$904$		−	346.677i		−	0.383492i
$905$	−1338.10	+	508.207i	−1.47857	+	0.561554i
$906$		0			0
$907$	571.342	+	571.342i	0.629925	+	0.629925i	0.948049	−	0.318124i	$-0.103053\pi$
$907$	571.342	+	571.342i	0.629925	+	0.629925i	−0.318124	+	0.948049i	$0.603053\pi$
$908$	−987.110	+	987.110i	−1.08713	+	1.08713i
$909$		0			0
$910$	55.5051	+	24.9490i	0.0609946	+	0.0274165i
$911$	−173.362			−0.190299			−0.0951494	−	0.995463i	$-0.530333\pi$
$911$	−173.362			−0.190299			−0.0951494	+	0.995463i	$0.530333\pi$
$912$		0			0
$913$	149.192	−	149.192i	0.163408	−	0.163408i
$914$			100.572i			0.110035i
$915$		0			0
$916$	−874.159			−0.954322
$917$	−366.116	−	366.116i	−0.399254	−	0.399254i
$918$		0			0
$919$			1147.42i			1.24856i	0.781202	+	0.624278i	$0.214607\pi$
$919$			1147.42i			1.24856i	−0.781202	+	0.624278i	$0.785393\pi$
$920$	−72.8036	−	191.691i	−0.0791343	−	0.208360i
$921$		0			0
$922$	−162.405	−	162.405i	−0.176144	−	0.176144i
$923$	−377.435	+	377.435i	−0.408922	+	0.408922i
$924$		0			0
$925$	−213.360	−	12.7015i	−0.230659	−	0.0137314i
$926$	58.2995			0.0629584
$927$		0			0
$928$	366.464	−	366.464i	0.394897	−	0.394897i
$929$			220.293i			0.237129i	0.992946	+	0.118565i	$0.0378292\pi$
$929$			220.293i			0.237129i	−0.992946	+	0.118565i	$0.962171\pi$
$930$		0			0
$931$	219.181			0.235425
$932$	−802.066	−	802.066i	−0.860586	−	0.860586i
$933$		0			0
$934$			186.654i			0.199844i
$935$	−1269.77	−	570.747i	−1.35804	−	0.610425i
$936$		0			0
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	0.463418	−	0.886140i	$-0.346623\pi$
$937$	−396.090	−	396.090i	−0.422721	−	0.422721i	−0.886140	+	0.463418i	$0.846623\pi$
$938$	−69.9296	+	69.9296i	−0.0745518	+	0.0745518i
$939$		0			0
$940$	−500.132	+	1112.67i	−0.532055	+	1.18369i
$941$	−185.771			−0.197419			−0.0987093	−	0.995116i	$-0.531471\pi$
$941$	−185.771			−0.197419			−0.0987093	+	0.995116i	$0.531471\pi$
$942$		0			0
$943$	8.04999	−	8.04999i	0.00853658	−	0.00853658i
$944$		−	590.944i		−	0.626000i
$945$		0			0
$946$	−135.151			−0.142866
$947$	845.190	+	845.190i	0.892492	+	0.892492i	0.994757	−	0.102265i	$-0.0326091\pi$
$947$	845.190	+	845.190i	0.892492	+	0.892492i	−0.102265	+	0.994757i	$0.532609\pi$
$948$		0			0
$949$			863.523i			0.909930i
$950$	4.10664	−	68.9831i	0.00432278	−	0.0726138i
$951$		0			0
$952$	−212.474	−	212.474i	−0.223187	−	0.223187i
$953$	630.499	−	630.499i	0.661594	−	0.661594i	−0.294161	−	0.955756i	$-0.595040\pi$
$953$	630.499	−	630.499i	0.661594	−	0.661594i	0.955756	+	0.294161i	$0.0950403\pi$
$954$		0			0
$955$	−224.788	+	85.3735i	−0.235380	+	0.0893963i
$956$	1348.26			1.41031
$957$		0			0
$958$	−68.5357	+	68.5357i	−0.0715404	+	0.0715404i
$959$			1149.58i			1.19873i
$960$		0			0
$961$	−846.576			−0.880932
$962$	−15.0827	−	15.0827i	−0.0156785	−	0.0156785i
$963$		0			0
$964$		−	396.041i		−	0.410831i
$965$	−740.879	+	1648.27i	−0.767750	+	1.70805i
$966$		0			0
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	0.481649	−	0.876364i	$-0.340038\pi$
$967$	−381.690	−	381.690i	−0.394716	−	0.394716i	−0.876364	+	0.481649i	$0.840038\pi$
$968$	−13.8252	+	13.8252i	−0.0142823	+	0.0142823i
$969$		0			0
$970$	19.6265	+	51.6765i	0.0202335	+	0.0532748i
$971$	1000.44			1.03032			0.515159	−	0.857095i	$-0.327733\pi$
$971$	1000.44			1.03032			0.515159	+	0.857095i	$0.327733\pi$
$972$		0			0
$973$	659.444	−	659.444i	0.677743	−	0.677743i
$974$			192.974i			0.198125i
$975$		0			0
$976$	−87.4439			−0.0895941
$977$	−593.662	−	593.662i	−0.607637	−	0.607637i	0.334691	−	0.942328i	$-0.391368\pi$
$977$	−593.662	−	593.662i	−0.607637	−	0.607637i	−0.942328	+	0.334691i	$0.891368\pi$
$978$		0			0
$979$			932.636i			0.952641i
$980$	−459.301	+	174.441i	−0.468674	+	0.178001i
$981$		0			0
$982$	−93.1158	−	93.1158i	−0.0948226	−	0.0948226i
$983$	1217.34	−	1217.34i	1.23839	−	1.23839i	0.277731	−	0.960659i	$-0.410418\pi$
$983$	1217.34	−	1217.34i	1.23839	−	1.23839i	0.960659	−	0.277731i	$-0.0895824\pi$
$984$		0			0
$985$	623.646	+	280.322i	0.633143	+	0.284591i
$986$	−274.070			−0.277962
$987$		0			0
$988$	−188.213	+	188.213i	−0.190499	+	0.190499i
$989$		−	612.059i		−	0.618867i
$990$		0			0
$991$	−544.061			−0.549002			−0.274501	−	0.961587i	$-0.588513\pi$
$991$	−544.061			−0.549002			−0.274501	+	0.961587i	$0.588513\pi$
$992$	111.535	+	111.535i	0.112434	+	0.112434i
$993$		0			0
$994$		−	105.435i		−	0.106071i
$995$	341.925	+	900.286i	0.343643	+	0.904810i
$996$		0			0
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	0.530192	−	0.847878i	$-0.322120\pi$
$997$	−316.733	−	316.733i	−0.317686	−	0.317686i	−0.847878	+	0.530192i	$0.822120\pi$
$998$	82.6128	−	82.6128i	0.0827783	−	0.0827783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.g.b.37.1		4
3.2	odd	2		15.3.f.a.7.2	✓	4
4.3	odd	2		720.3.bh.k.577.2		4
5.2	odd	4		225.3.g.a.118.2		4
5.3	odd	4	inner	45.3.g.b.28.1		4
5.4	even	2		225.3.g.a.82.2		4
9.2	odd	6		405.3.l.h.352.2		8
9.4	even	3		405.3.l.f.217.2		8
9.5	odd	6		405.3.l.h.217.1		8
9.7	even	3		405.3.l.f.352.1		8
12.11	even	2		240.3.bg.a.97.2		4
15.2	even	4		75.3.f.c.43.1		4
15.8	even	4		15.3.f.a.13.2	yes	4
15.14	odd	2		75.3.f.c.7.1		4
20.3	even	4		720.3.bh.k.433.2		4
24.5	odd	2		960.3.bg.i.577.2		4
24.11	even	2		960.3.bg.h.577.1		4
45.13	odd	12		405.3.l.f.298.1		8
45.23	even	12		405.3.l.h.298.2		8
45.38	even	12		405.3.l.h.28.1		8
45.43	odd	12		405.3.l.f.28.2		8
60.23	odd	4		240.3.bg.a.193.2		4
60.47	odd	4		1200.3.bg.k.193.1		4
60.59	even	2		1200.3.bg.k.1057.1		4
120.53	even	4		960.3.bg.i.193.2		4
120.83	odd	4		960.3.bg.h.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	3.2	odd	2
15.3.f.a.13.2	yes	4	15.8	even	4
45.3.g.b.28.1		4	5.3	odd	4	inner
45.3.g.b.37.1		4	1.1	even	1	trivial
75.3.f.c.7.1		4	15.14	odd	2
75.3.f.c.43.1		4	15.2	even	4
225.3.g.a.82.2		4	5.4	even	2
225.3.g.a.118.2		4	5.2	odd	4
240.3.bg.a.97.2		4	12.11	even	2
240.3.bg.a.193.2		4	60.23	odd	4
405.3.l.f.28.2		8	45.43	odd	12
405.3.l.f.217.2		8	9.4	even	3
405.3.l.f.298.1		8	45.13	odd	12
405.3.l.f.352.1		8	9.7	even	3
405.3.l.h.28.1		8	45.38	even	12
405.3.l.h.217.1		8	9.5	odd	6
405.3.l.h.298.2		8	45.23	even	12
405.3.l.h.352.2		8	9.2	odd	6
720.3.bh.k.433.2		4	20.3	even	4
720.3.bh.k.577.2		4	4.3	odd	2
960.3.bg.h.193.1		4	120.83	odd	4
960.3.bg.h.577.1		4	24.11	even	2
960.3.bg.i.193.2		4	120.53	even	4
960.3.bg.i.577.2		4	24.5	odd	2
1200.3.bg.k.193.1		4	60.47	odd	4
1200.3.bg.k.1057.1		4	60.59	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.224745 - 0.224745i) q^{2} -3.89898i q^{4} +(4.67423 - 1.77526i) q^{5} +(3.44949 + 3.44949i) q^{7} +(-1.77526 + 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} -11.3485 q^{11} +(-5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 + 17.3485i) q^{17} +8.69694i q^{19} +(-6.92168 - 18.2247i) q^{20} +(2.55051 + 2.55051i) q^{22} +(-11.5505 + 11.5505i) q^{23} +(18.6969 - 16.5959i) q^{25} +2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 + 10.4268i) q^{32} -7.79796i q^{34} +(22.2474 + 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(1.95459 - 1.95459i) q^{38} +(-5.14643 + 11.4495i) q^{40} -0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 - 44.2474i) q^{47} -25.2020i q^{49} +(-7.93189 - 0.472194i) q^{50} +(21.6413 + 21.6413i) q^{52} +(0.696938 - 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} -12.2474 q^{56} +(-7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 - 2.40408i) q^{62} +54.5051i q^{64} +(-16.0908 + 35.7980i) q^{65} +(-45.1010 - 45.1010i) q^{67} +(67.6413 - 67.6413i) q^{68} +(-2.75255 - 7.24745i) q^{70} +68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 - 39.1464i) q^{77} -24.4949i q^{79} +(-69.1691 + 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(-13.1464 + 13.1464i) q^{83} +(111.889 + 50.2929i) q^{85} +11.9092 q^{86} +(20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 + 45.0352i) q^{92} +19.8888i q^{94} +(15.4393 + 40.6515i) q^{95} +(-24.5959 - 24.5959i) q^{97} +(-5.66403 + 5.66403i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + 4 q^{10} - 16 q^{11} - 32 q^{13} - 20 q^{16} + 40 q^{17} + 36 q^{20} + 20 q^{22} - 56 q^{23} + 16 q^{25} - 88 q^{26} + 44 q^{28} - 16 q^{31} + 76 q^{32} + 40 q^{35}+ \cdots + 188 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^7 - 12 * q^8 + 4 * q^10 - 16 * q^11 - 32 * q^13 - 20 * q^16 + 40 * q^17 + 36 * q^20 + 20 * q^22 - 56 * q^23 + 16 * q^25 - 88 * q^26 + 44 * q^28 - 16 * q^31 + 76 * q^32 + 40 * q^35 + 64 * q^37 + 96 * q^38 + 48 * q^40 + 56 * q^41 - 8 * q^43 - 136 * q^46 - 128 * q^47 - 164 * q^50 - 80 * q^52 - 56 * q^53 - 124 * q^55 - 12 * q^58 + 200 * q^61 - 88 * q^62 + 112 * q^65 - 200 * q^67 + 104 * q^68 - 60 * q^70 + 272 * q^71 + 76 * q^73 + 312 * q^76 - 88 * q^77 - 164 * q^80 + 128 * q^82 + 16 * q^83 + 232 * q^85 + 224 * q^86 + 12 * q^88 - 16 * q^91 - 104 * q^92 - 144 * q^95 - 20 * q^97 + 188 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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