LMFDB - Embedded newform 560.4.q.i.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	560.401
Dual form			560.4.q.i.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.62132 - 4.54026i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(5.10660 + 17.8023i) q^{7} +(-0.242641 + 0.420266i) q^{9} +(14.0711 + 24.3718i) q^{11} -3.85786 q^{13} +26.2132 q^{15} +(-19.1838 - 33.2273i) q^{17} +(58.3848 - 101.125i) q^{19} +(67.4411 - 69.8509i) q^{21} +(-88.2315 + 152.821i) q^{23} +(-12.5000 - 21.6506i) q^{25} -139.007 q^{27} -209.853 q^{29} +(-103.711 - 179.632i) q^{31} +(73.7696 - 127.773i) q^{33} +(-89.8528 - 22.3936i) q^{35} +(7.83348 - 13.5680i) q^{37} +(10.1127 + 17.5157i) q^{39} -10.5736 q^{41} +325.929 q^{43} +(-1.21320 - 2.10133i) q^{45} +(-94.2548 + 163.254i) q^{47} +(-290.845 + 181.819i) q^{49} +(-100.574 + 174.199i) q^{51} +(137.591 + 238.314i) q^{53} -140.711 q^{55} -612.181 q^{57} +(21.9096 + 37.9485i) q^{59} +(-427.551 + 740.540i) q^{61} +(-8.72078 - 2.17344i) q^{63} +(9.64466 - 16.7050i) q^{65} +(-272.710 - 472.347i) q^{67} +925.132 q^{69} -1026.97 q^{71} +(126.439 + 218.998i) q^{73} +(-65.5330 + 113.507i) q^{75} +(-362.019 + 374.955i) q^{77} +(-461.321 + 799.031i) q^{79} +(370.934 + 642.476i) q^{81} +960.071 q^{83} +191.838 q^{85} +(550.091 + 952.786i) q^{87} +(66.6026 - 115.359i) q^{89} +(-19.7006 - 68.6789i) q^{91} +(-543.718 + 941.747i) q^{93} +(291.924 + 505.627i) q^{95} -1021.11 q^{97} -13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 10 q^{5} - 22 q^{7} + 16 q^{9} + 28 q^{11} - 72 q^{13} + 20 q^{15} + 76 q^{17} + 160 q^{19} + 134 q^{21} - 22 q^{23} - 50 q^{25} + 4 q^{27} - 500 q^{29} - 132 q^{31} + 148 q^{33} - 20 q^{35}+ \cdots - 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 10 * q^5 - 22 * q^7 + 16 * q^9 + 28 * q^11 - 72 * q^13 + 20 * q^15 + 76 * q^17 + 160 * q^19 + 134 * q^21 - 22 * q^23 - 50 * q^25 + 4 * q^27 - 500 * q^29 - 132 * q^31 + 148 * q^33 - 20 * q^35 + 416 * q^37 - 84 * q^39 - 212 * q^41 + 1332 * q^43 + 80 * q^45 - 196 * q^47 - 230 * q^49 - 572 * q^51 + 952 * q^53 - 280 * q^55 - 944 * q^57 + 840 * q^59 - 98 * q^61 - 544 * q^63 + 180 * q^65 - 1286 * q^67 + 2852 * q^69 - 2128 * q^71 + 172 * q^73 - 50 * q^75 - 724 * q^77 - 1240 * q^79 + 754 * q^81 + 3812 * q^83 - 760 * q^85 + 970 * q^87 - 650 * q^89 + 996 * q^91 - 1332 * q^93 + 800 * q^95 - 1256 * q^97 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.62132	−	4.54026i	−0.504473	−	0.873773i	−0.999987	−	0.00517309i	$-0.998353\pi$
$3$	−2.62132	−	4.54026i	−0.504473	−	0.873773i	0.495513	−	0.868600i	$-0.334980\pi$
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	5.10660	+	17.8023i	0.275731	+	0.961235i
$7$	5.10660	+	17.8023i	0.275731	+	0.961235i
$8$		0			0
$9$	−0.242641	+	0.420266i	−0.00898669	+	0.0155654i
$10$		0			0
$11$	14.0711	+	24.3718i	0.385690	+	0.668034i	0.991865	−	0.127297i	$-0.0406302\pi$
$11$	14.0711	+	24.3718i	0.385690	+	0.668034i	−0.606175	+	0.795331i	$0.707297\pi$
$12$		0			0
$13$	−3.85786			−0.0823061			−0.0411530	−	0.999153i	$-0.513103\pi$
$13$	−3.85786			−0.0823061			−0.0411530	+	0.999153i	$0.513103\pi$
$14$		0			0
$15$	26.2132			0.451215
$16$		0			0
$17$	−19.1838	−	33.2273i	−0.273691	−	0.474047i	0.696113	−	0.717932i	$-0.254911\pi$
$17$	−19.1838	−	33.2273i	−0.273691	−	0.474047i	−0.969804	+	0.243885i	$0.921578\pi$
$18$		0			0
$19$	58.3848	−	101.125i	0.704968	−	1.22104i	−0.261735	−	0.965140i	$-0.584295\pi$
$19$	58.3848	−	101.125i	0.704968	−	1.22104i	0.966703	−	0.255900i	$-0.0823719\pi$
$20$		0			0
$21$	67.4411	−	69.8509i	0.700803	−	0.725843i
$22$		0			0
$23$	−88.2315	+	152.821i	−0.799893	+	1.38546i	0.119792	+	0.992799i	$0.461777\pi$
$23$	−88.2315	+	152.821i	−0.799893	+	1.38546i	−0.919685	+	0.392656i	$0.871556\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	−139.007			−0.990812
$28$		0			0
$29$	−209.853			−1.34375			−0.671874	−	0.740666i	$-0.734510\pi$
$29$	−209.853			−1.34375			−0.671874	+	0.740666i	$0.734510\pi$
$30$		0			0
$31$	−103.711	−	179.632i	−0.600871	−	1.04074i	−0.992690	−	0.120696i	$-0.961487\pi$
$31$	−103.711	−	179.632i	−0.600871	−	1.04074i	0.391819	−	0.920042i	$-0.371846\pi$
$32$		0			0
$33$	73.7696	−	127.773i	0.389140	−	0.674011i
$34$		0			0
$35$	−89.8528	−	22.3936i	−0.433940	−	0.108149i
$36$		0			0
$37$	7.83348	−	13.5680i	0.0348058	−	0.0602855i	−0.848098	−	0.529840i	$-0.822252\pi$
$37$	7.83348	−	13.5680i	0.0348058	−	0.0602855i	0.882904	+	0.469554i	$0.155585\pi$
$38$		0			0
$39$	10.1127	+	17.5157i	0.0415212	+	0.0719169i
$40$		0			0
$41$	−10.5736			−0.0402760			−0.0201380	−	0.999797i	$-0.506411\pi$
$41$	−10.5736			−0.0402760			−0.0201380	+	0.999797i	$0.506411\pi$
$42$		0			0
$43$	325.929			1.15590			0.577950	−	0.816072i	$-0.303853\pi$
$43$	325.929			1.15590			0.577950	+	0.816072i	$0.303853\pi$
$44$		0			0
$45$	−1.21320	−	2.10133i	−0.00401897	−	0.00696106i
$46$		0			0
$47$	−94.2548	+	163.254i	−0.292521	+	0.506661i	−0.974405	−	0.224799i	$-0.927827\pi$
$47$	−94.2548	+	163.254i	−0.292521	+	0.506661i	0.681884	+	0.731460i	$0.261161\pi$
$48$		0			0
$49$	−290.845	+	181.819i	−0.847945	+	0.530084i
$50$		0			0
$51$	−100.574	+	174.199i	−0.276140	+	0.478288i
$52$		0			0
$53$	137.591	+	238.314i	0.356595	+	0.617641i	0.987390	−	0.158309i	$-0.0506041\pi$
$53$	137.591	+	238.314i	0.356595	+	0.617641i	−0.630794	+	0.775950i	$0.717271\pi$
$54$		0			0
$55$	−140.711			−0.344971
$56$		0			0
$57$	−612.181			−1.42255
$58$		0			0
$59$	21.9096	+	37.9485i	0.0483455	+	0.0837369i	0.889186	−	0.457547i	$-0.151272\pi$
$59$	21.9096	+	37.9485i	0.0483455	+	0.0837369i	−0.840840	+	0.541284i	$0.817938\pi$
$60$		0			0
$61$	−427.551	+	740.540i	−0.897414	+	1.55437i	−0.0666267	+	0.997778i	$0.521224\pi$
$61$	−427.551	+	740.540i	−0.897414	+	1.55437i	−0.830788	+	0.556589i	$0.812110\pi$
$62$		0			0
$63$	−8.72078	−	2.17344i	−0.0174399	−	0.00434646i
$64$		0			0
$65$	9.64466	−	16.7050i	0.0184042	−	0.0318770i
$66$		0			0
$67$	−272.710	−	472.347i	−0.497265	−	0.861289i	0.502730	−	0.864444i	$-0.332329\pi$
$67$	−272.710	−	472.347i	−0.497265	−	0.861289i	−0.999995	+	0.00315473i	$0.998996\pi$
$68$		0			0
$69$	925.132			1.61410
$70$		0			0
$71$	−1026.97			−1.71661			−0.858306	−	0.513138i	$-0.828483\pi$
$71$	−1026.97			−1.71661			−0.858306	+	0.513138i	$0.828483\pi$
$72$		0			0
$73$	126.439	+	218.998i	0.202719	+	0.351120i	0.949404	−	0.314058i	$-0.101689\pi$
$73$	126.439	+	218.998i	0.202719	+	0.351120i	−0.746684	+	0.665179i	$0.768355\pi$
$74$		0			0
$75$	−65.5330	+	113.507i	−0.100895	+	0.174755i
$76$		0			0
$77$	−362.019	+	374.955i	−0.535791	+	0.554936i
$78$		0			0
$79$	−461.321	+	799.031i	−0.656996	+	1.13795i	0.324394	+	0.945922i	$0.394840\pi$
$79$	−461.321	+	799.031i	−0.656996	+	1.13795i	−0.981390	+	0.192028i	$0.938494\pi$
$80$		0			0
$81$	370.934	+	642.476i	0.508825	+	0.881311i
$82$		0			0
$83$	960.071			1.26966			0.634828	−	0.772653i	$-0.281071\pi$
$83$	960.071			1.26966			0.634828	+	0.772653i	$0.281071\pi$
$84$		0			0
$85$	191.838			0.244797
$86$		0			0
$87$	550.091	+	952.786i	0.677885	+	1.17413i
$88$		0			0
$89$	66.6026	−	115.359i	0.0793243	−	0.137394i	−0.823634	−	0.567121i	$-0.808057\pi$
$89$	66.6026	−	115.359i	0.0793243	−	0.137394i	0.902959	+	0.429728i	$0.141390\pi$
$90$		0			0
$91$	−19.7006	−	68.6789i	−0.0226943	−	0.0791155i
$92$		0			0
$93$	−543.718	+	941.747i	−0.606246	+	1.05005i
$94$		0			0
$95$	291.924	+	505.627i	0.315271	+	0.546066i
$96$		0			0
$97$	−1021.11			−1.06884			−0.534421	−	0.845218i	$-0.679470\pi$
$97$	−1021.11			−1.06884			−0.534421	+	0.845218i	$0.679470\pi$
$98$		0			0
$99$	−13.6569			−0.0138643
$100$		0			0
$101$	−481.779	−	834.466i	−0.474642	−	0.822104i	0.524936	−	0.851141i	$-0.324089\pi$
$101$	−481.779	−	834.466i	−0.474642	−	0.822104i	−0.999578	+	0.0290376i	$0.990756\pi$
$102$		0			0
$103$	−899.150	+	1557.37i	−0.860155	+	1.48983i	0.0116248	+	0.999932i	$0.496300\pi$
$103$	−899.150	+	1557.37i	−0.860155	+	1.48983i	−0.871779	+	0.489899i	$0.837034\pi$
$104$		0			0
$105$	133.860	+	466.656i	0.124414	+	0.433723i
$106$		0			0
$107$	139.501	−	241.624i	0.126038	−	0.218305i	−0.796100	−	0.605165i	$-0.793107\pi$
$107$	139.501	−	241.624i	0.126038	−	0.218305i	0.922138	+	0.386860i	$0.126440\pi$
$108$		0			0
$109$	−390.537	−	676.429i	−0.343180	−	0.594405i	0.641841	−	0.766837i	$-0.278171\pi$
$109$	−390.537	−	676.429i	−0.343180	−	0.594405i	−0.985021	+	0.172432i	$0.944837\pi$
$110$		0			0
$111$	−82.1362			−0.0702345
$112$		0			0
$113$	−587.239			−0.488874			−0.244437	−	0.969665i	$-0.578603\pi$
$113$	−587.239			−0.488874			−0.244437	+	0.969665i	$0.578603\pi$
$114$		0			0
$115$	−441.157	−	764.107i	−0.357723	−	0.619594i
$116$		0			0
$117$	0.936075	−	1.62133i	0.000739659	−	0.00128113i
$118$		0			0
$119$	493.558	−	511.194i	0.380205	−	0.393791i
$120$		0			0
$121$	269.510	−	466.805i	0.202487	−	0.350718i
$122$		0			0
$123$	27.7168	+	48.0069i	0.0203182	+	0.0351921i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	−1559.62			−1.08972			−0.544860	−	0.838527i	$-0.683417\pi$
$127$	−1559.62			−1.08972			−0.544860	+	0.838527i	$0.683417\pi$
$128$		0			0
$129$	−854.364	−	1479.80i	−0.583121	−	1.00999i
$130$		0			0
$131$	−826.823	+	1432.10i	−0.551449	+	0.955138i	0.446721	+	0.894673i	$0.352592\pi$
$131$	−826.823	+	1432.10i	−0.551449	+	0.955138i	−0.998170	+	0.0604645i	$0.980742\pi$
$132$		0			0
$133$	2098.41	+	522.977i	1.36809	+	0.340962i
$134$		0			0
$135$	347.518	−	601.919i	0.221552	−	0.383740i
$136$		0			0
$137$	148.329	+	256.913i	0.0925007	+	0.160216i	0.908563	−	0.417748i	$-0.137181\pi$
$137$	148.329	+	256.913i	0.0925007	+	0.160216i	−0.816062	+	0.577964i	$0.803847\pi$
$138$		0			0
$139$	−237.868			−0.145149			−0.0725745	−	0.997363i	$-0.523121\pi$
$139$	−237.868			−0.145149			−0.0725745	+	0.997363i	$0.523121\pi$
$140$		0			0
$141$	988.288			0.590276
$142$		0			0
$143$	−54.2843	−	94.0231i	−0.0317446	−	0.0549833i
$144$		0			0
$145$	524.632	−	908.689i	0.300471	−	0.520431i
$146$		0			0
$147$	1587.90	+	843.908i	0.890939	+	0.473499i
$148$		0			0
$149$	−1368.56	+	2370.41i	−0.752459	+	1.30330i	0.194169	+	0.980968i	$0.437799\pi$
$149$	−1368.56	+	2370.41i	−0.752459	+	1.30330i	−0.946628	+	0.322329i	$0.895534\pi$
$150$		0			0
$151$	−1781.82	−	3086.21i	−0.960283	−	1.66326i	−0.721788	−	0.692114i	$-0.756679\pi$
$151$	−1781.82	−	3086.21i	−0.960283	−	1.66326i	−0.238495	−	0.971144i	$-0.576654\pi$
$152$		0			0
$153$	18.6190			0.00983831
$154$		0			0
$155$	1037.11			0.537435
$156$		0			0
$157$	−624.539	−	1081.73i	−0.317475	−	0.549884i	0.662485	−	0.749075i	$-0.269502\pi$
$157$	−624.539	−	1081.73i	−0.317475	−	0.549884i	−0.979961	+	0.199191i	$0.936168\pi$
$158$		0			0
$159$	721.339	−	1249.40i	0.359786	−	0.623167i
$160$		0			0
$161$	−3171.14	−	790.327i	−1.55230	−	0.386873i
$162$		0			0
$163$	−982.318	+	1701.42i	−0.472031	+	0.817582i	−0.999488	−	0.0320000i	$-0.989812\pi$
$163$	−982.318	+	1701.42i	−0.472031	+	0.817582i	0.527457	+	0.849582i	$0.323146\pi$
$164$		0			0
$165$	368.848	+	638.863i	0.174029	+	0.301427i
$166$		0			0
$167$	939.402			0.435288			0.217644	−	0.976028i	$-0.430163\pi$
$167$	939.402			0.435288			0.217644	+	0.976028i	$0.430163\pi$
$168$		0			0
$169$	−2182.12			−0.993226
$170$		0			0
$171$	28.3330	+	49.0743i	0.0126707	+	0.0219462i
$172$		0			0
$173$	1351.22	−	2340.38i	0.593821	−	1.02853i	−0.399891	−	0.916563i	$-0.630952\pi$
$173$	1351.22	−	2340.38i	0.593821	−	1.02853i	0.993712	−	0.111966i	$-0.0357147\pi$
$174$		0			0
$175$	321.599	−	333.090i	0.138918	−	0.143881i
$176$		0			0
$177$	114.864	−	198.951i	0.0487781	−	0.0844861i
$178$		0			0
$179$	−717.024	−	1241.92i	−0.299402	−	0.518579i	0.676597	−	0.736353i	$-0.263454\pi$
$179$	−717.024	−	1241.92i	−0.299402	−	0.518579i	−0.975999	+	0.217774i	$0.930120\pi$
$180$		0			0
$181$	2711.21			1.11339			0.556693	−	0.830718i	$-0.312070\pi$
$181$	2711.21			1.11339			0.556693	+	0.830718i	$0.312070\pi$
$182$		0			0
$183$	4482.99			1.81089
$184$		0			0
$185$	39.1674	+	67.8399i	0.0155656	+	0.0269605i
$186$		0			0
$187$	539.872	−	935.086i	0.211120	−	0.365670i
$188$		0			0
$189$	−709.854	−	2474.65i	−0.273197	−	0.952404i
$190$		0			0
$191$	−1747.30	+	3026.41i	−0.661938	+	1.14651i	0.318168	+	0.948034i	$0.396933\pi$
$191$	−1747.30	+	3026.41i	−0.661938	+	1.14651i	−0.980106	+	0.198476i	$0.936401\pi$
$192$		0			0
$193$	814.881	+	1411.41i	0.303919	+	0.526403i	0.977020	−	0.213147i	$-0.0683714\pi$
$193$	814.881	+	1411.41i	0.303919	+	0.526403i	−0.673101	+	0.739551i	$0.735038\pi$
$194$		0			0
$195$	−101.127			−0.0371377
$196$		0			0
$197$	693.696			0.250882			0.125441	−	0.992101i	$-0.459965\pi$
$197$	693.696			0.250882			0.125441	+	0.992101i	$0.459965\pi$
$198$		0			0
$199$	−1902.81	−	3295.76i	−0.677821	−	1.17402i	−0.975636	−	0.219397i	$-0.929591\pi$
$199$	−1902.81	−	3295.76i	−0.677821	−	1.17402i	0.297815	−	0.954624i	$-0.403742\pi$
$200$		0			0
$201$	−1429.72	+	2476.35i	−0.501714	+	0.868995i
$202$		0			0
$203$	−1071.63	−	3735.87i	−0.370512	−	1.29166i
$204$		0			0
$205$	26.4340	−	45.7850i	0.00900600	−	0.0155988i
$206$		0			0
$207$	−42.8171	−	74.1614i	−0.0143768	−	0.0249013i
$208$		0			0
$209$	3286.14			1.08760
$210$		0			0
$211$	627.239			0.204649			0.102324	−	0.994751i	$-0.467372\pi$
$211$	627.239			0.204649			0.102324	+	0.994751i	$0.467372\pi$
$212$		0			0
$213$	2692.03	+	4662.73i	0.865985	+	1.49993i
$214$		0			0
$215$	−814.822	+	1411.31i	−0.258467	+	0.447678i
$216$		0			0
$217$	2668.26	−	2763.60i	0.834716	−	0.864541i
$218$		0			0
$219$	662.872	−	1148.13i	0.204533	−	0.354262i
$220$		0			0
$221$	74.0084	+	128.186i	0.0225264	+	0.0390169i
$222$		0			0
$223$	2000.99			0.600878			0.300439	−	0.953801i	$-0.402867\pi$
$223$	2000.99			0.600878			0.300439	+	0.953801i	$0.402867\pi$
$224$		0			0
$225$	12.1320			0.00359468
$226$		0			0
$227$	−796.121	−	1378.92i	−0.232777	−	0.403182i	0.725847	−	0.687856i	$-0.241448\pi$
$227$	−796.121	−	1378.92i	−0.232777	−	0.403182i	−0.958624	+	0.284674i	$0.908115\pi$
$228$		0			0
$229$	1962.58	−	3399.29i	0.566336	−	0.980923i	−0.430588	−	0.902549i	$-0.641694\pi$
$229$	1962.58	−	3399.29i	0.566336	−	0.980923i	0.996924	−	0.0783742i	$-0.0249729\pi$
$230$		0			0
$231$	2651.36	+	660.785i	0.755181	+	0.188210i
$232$		0			0
$233$	−1084.88	+	1879.06i	−0.305032	+	0.528331i	−0.977269	−	0.212005i	$-0.932001\pi$
$233$	−1084.88	+	1879.06i	−0.305032	+	0.528331i	0.672236	+	0.740337i	$0.265334\pi$
$234$		0			0
$235$	−471.274	−	816.271i	−0.130819	−	0.226586i
$236$		0			0
$237$	4837.08			1.32575
$238$		0			0
$239$	−1057.70			−0.286262			−0.143131	−	0.989704i	$-0.545717\pi$
$239$	−1057.70			−0.286262			−0.143131	+	0.989704i	$0.545717\pi$
$240$		0			0
$241$	−1199.62	−	2077.80i	−0.320640	−	0.555365i	0.659980	−	0.751283i	$-0.270565\pi$
$241$	−1199.62	−	2077.80i	−0.320640	−	0.555365i	−0.980620	+	0.195918i	$0.937231\pi$
$242$		0			0
$243$	68.0749	−	117.909i	0.0179712	−	0.0311271i
$244$		0			0
$245$	−60.1851	−	1713.94i	−0.0156942	−	0.446938i
$246$		0			0
$247$	−225.241	+	390.128i	−0.0580231	+	0.100499i
$248$		0			0
$249$	−2516.65	−	4358.97i	−0.640508	−	1.10939i
$250$		0			0
$251$	3812.95			0.958848			0.479424	−	0.877583i	$-0.340846\pi$
$251$	3812.95			0.958848			0.479424	+	0.877583i	$0.340846\pi$
$252$		0			0
$253$	−4966.05			−1.23404
$254$		0			0
$255$	−502.868	−	870.993i	−0.123493	−	0.213897i
$256$		0			0
$257$	−1745.08	+	3022.57i	−0.423561	+	0.733629i	−0.996285	−	0.0861194i	$-0.972553\pi$
$257$	−1745.08	+	3022.57i	−0.423561	+	0.733629i	0.572724	+	0.819748i	$0.305887\pi$
$258$		0			0
$259$	281.544	+	70.1678i	0.0675455	+	0.0168340i
$260$		0			0
$261$	50.9188	−	88.1940i	0.0120758	−	0.0209160i
$262$		0			0
$263$	3562.28	+	6170.05i	0.835207	+	1.44662i	0.893862	+	0.448343i	$0.147986\pi$
$263$	3562.28	+	6170.05i	0.835207	+	1.44662i	−0.0586547	+	0.998278i	$0.518681\pi$
$264$		0			0
$265$	−1375.91			−0.318949
$266$		0			0
$267$	−698.347			−0.160068
$268$		0			0
$269$	213.971	+	370.609i	0.0484984	+	0.0840017i	0.889256	−	0.457411i	$-0.151223\pi$
$269$	213.971	+	370.609i	0.0484984	+	0.0840017i	−0.840757	+	0.541412i	$0.817890\pi$
$270$		0			0
$271$	4094.29	−	7091.52i	0.917751	−	1.58959i	0.114927	−	0.993374i	$-0.463337\pi$
$271$	4094.29	−	7091.52i	0.917751	−	1.58959i	0.802824	−	0.596217i	$-0.203330\pi$
$272$		0			0
$273$	−260.179	+	269.475i	−0.0576803	+	0.0597413i
$274$		0			0
$275$	351.777	−	609.295i	0.0771379	−	0.133607i
$276$		0			0
$277$	2084.98	+	3611.29i	0.452254	+	0.783326i	0.998526	−	0.0542815i	$-0.0172868\pi$
$277$	2084.98	+	3611.29i	0.452254	+	0.783326i	−0.546272	+	0.837608i	$0.683954\pi$
$278$		0			0
$279$	100.658			0.0215994
$280$		0			0
$281$	1284.60			0.272714			0.136357	−	0.990660i	$-0.456461\pi$
$281$	1284.60			0.272714			0.136357	+	0.990660i	$0.456461\pi$
$282$		0			0
$283$	2394.67	+	4147.70i	0.502998	+	0.871219i	0.999994	+	0.00346581i	$0.00110320\pi$
$283$	2394.67	+	4147.70i	0.502998	+	0.871219i	−0.496996	+	0.867753i	$0.665563\pi$
$284$		0			0
$285$	1530.45	−	2650.82i	0.318092	−	0.550951i
$286$		0			0
$287$	−53.9951	−	188.234i	−0.0111053	−	0.0387147i
$288$		0			0
$289$	1720.47	−	2979.93i	0.350186	−	0.606541i
$290$		0			0
$291$	2676.65	+	4636.09i	0.539202	+	0.933926i
$292$		0			0
$293$	6983.27			1.39238			0.696189	−	0.717858i	$-0.254877\pi$
$293$	6983.27			1.39238			0.696189	+	0.717858i	$0.254877\pi$
$294$		0			0
$295$	−219.096			−0.0432416
$296$		0			0
$297$	−1955.98	−	3387.85i	−0.382146	−	0.661897i
$298$		0			0
$299$	340.385	−	589.564i	0.0658361	−	0.114031i
$300$		0			0
$301$	1664.39	+	5802.29i	0.318717	+	1.11109i
$302$		0			0
$303$	−2525.80	+	4374.81i	−0.478888	+	0.829459i
$304$		0			0
$305$	−2137.75	−	3702.70i	−0.401336	−	0.695134i
$306$		0			0
$307$	2069.43			0.384719			0.192359	−	0.981325i	$-0.438386\pi$
$307$	2069.43			0.384719			0.192359	+	0.981325i	$0.438386\pi$
$308$		0			0
$309$	9427.84			1.73570
$310$		0			0
$311$	1060.98	+	1837.67i	0.193449	+	0.335064i	0.946391	−	0.323023i	$-0.104699\pi$
$311$	1060.98	+	1837.67i	0.193449	+	0.335064i	−0.752942	+	0.658087i	$0.771366\pi$
$312$		0			0
$313$	−764.398	+	1323.98i	−0.138039	+	0.239091i	−0.926754	−	0.375668i	$-0.877413\pi$
$313$	−764.398	+	1323.98i	−0.138039	+	0.239091i	0.788715	+	0.614759i	$0.210747\pi$
$314$		0			0
$315$	31.2132	−	32.3285i	0.00558306	−	0.00578255i
$316$		0			0
$317$	−2571.22	+	4453.49i	−0.455565	+	0.789062i	−0.998721	−	0.0505699i	$-0.983896\pi$
$317$	−2571.22	+	4453.49i	−0.455565	+	0.789062i	0.543155	+	0.839632i	$0.317230\pi$
$318$		0			0
$319$	−2952.85	−	5114.49i	−0.518270	−	0.897669i
$320$		0			0
$321$	−1462.71			−0.254332
$322$		0			0
$323$	−4480.16			−0.771773
$324$		0			0
$325$	48.2233	+	83.5252i	0.00823061	+	0.0142558i
$326$		0			0
$327$	−2047.44	+	3546.28i	−0.346250	+	0.599723i
$328$		0			0
$329$	−3387.62	−	844.281i	−0.567677	−	0.141479i
$330$		0			0
$331$	−2887.02	+	5000.47i	−0.479411	+	0.830364i	−0.999721	−	0.0236134i	$-0.992483\pi$
$331$	−2887.02	+	5000.47i	−0.479411	+	0.830364i	0.520310	+	0.853977i	$0.325816\pi$
$332$		0			0
$333$	3.80144	+	6.58429i	0.000625579	+	0.00108353i
$334$		0			0
$335$	2727.10			0.444768
$336$		0			0
$337$	−484.761			−0.0783579			−0.0391790	−	0.999232i	$-0.512474\pi$
$337$	−484.761			−0.0783579			−0.0391790	+	0.999232i	$0.512474\pi$
$338$		0			0
$339$	1539.34	+	2666.22i	0.246624	+	0.427165i
$340$		0			0
$341$	2918.64	−	5055.23i	0.463499	−	0.802804i
$342$		0			0
$343$	−4722.03	−	4249.24i	−0.743339	−	0.668914i
$344$		0			0
$345$	−2312.83	+	4005.94i	−0.360923	+	0.625138i
$346$		0			0
$347$	−3899.11	−	6753.45i	−0.603213	−	1.04480i	−0.992331	−	0.123608i	$-0.960553\pi$
$347$	−3899.11	−	6753.45i	−0.603213	−	1.04480i	0.389118	−	0.921188i	$-0.372780\pi$
$348$		0			0
$349$	−662.157			−0.101560			−0.0507800	−	0.998710i	$-0.516171\pi$
$349$	−662.157			−0.101560			−0.0507800	+	0.998710i	$0.516171\pi$
$350$		0			0
$351$	536.271			0.0815499
$352$		0			0
$353$	−3313.07	−	5738.40i	−0.499538	−	0.865225i	0.500462	−	0.865759i	$-0.333164\pi$
$353$	−3313.07	−	5738.40i	−0.499538	−	0.865225i	−1.00000		0.000533475i	$0.999830\pi$
$354$		0			0
$355$	2567.44	−	4446.93i	0.383846	−	0.664841i
$356$		0			0
$357$	−3614.73	−	900.881i	−0.535887	−	0.133556i
$358$		0			0
$359$	5199.03	−	9004.98i	0.764329	−	1.32386i	−0.176272	−	0.984342i	$-0.556404\pi$
$359$	5199.03	−	9004.98i	0.764329	−	1.32386i	0.940601	−	0.339515i	$-0.110263\pi$
$360$		0			0
$361$	−3388.06	−	5868.30i	−0.493959	−	0.855562i
$362$		0			0
$363$	−2825.89			−0.408597
$364$		0			0
$365$	−1264.39			−0.181318
$366$		0			0
$367$	1123.15	+	1945.36i	0.159750	+	0.276694i	0.934778	−	0.355232i	$-0.115598\pi$
$367$	1123.15	+	1945.36i	0.159750	+	0.276694i	−0.775029	+	0.631926i	$0.782265\pi$
$368$		0			0
$369$	2.56558	−	4.44372i	0.000361948	−	0.000626913i
$370$		0			0
$371$	−3539.93	+	3666.41i	−0.495374	+	0.513075i
$372$		0			0
$373$	−96.0126	+	166.299i	−0.0133280	+	0.0230848i	−0.872612	−	0.488413i	$-0.837576\pi$
$373$	−96.0126	+	166.299i	−0.0133280	+	0.0230848i	0.859284	+	0.511498i	$0.170909\pi$
$374$		0			0
$375$	−327.665	−	567.533i	−0.0451215	−	0.0781527i
$376$		0			0
$377$	809.584			0.110599
$378$		0			0
$379$	4565.76			0.618805			0.309403	−	0.950931i	$-0.399871\pi$
$379$	4565.76			0.618805			0.309403	+	0.950931i	$0.399871\pi$
$380$		0			0
$381$	4088.28	+	7081.10i	0.549734	+	0.952168i
$382$		0			0
$383$	693.535	−	1201.24i	0.0925273	−	0.160262i	−0.816047	−	0.577986i	$-0.803839\pi$
$383$	693.535	−	1201.24i	0.0925273	−	0.160262i	0.908574	+	0.417724i	$0.137172\pi$
$384$		0			0
$385$	−718.553	−	2504.98i	−0.0951191	−	0.331599i
$386$		0			0
$387$	−79.0836	+	136.977i	−0.0103877	+	0.0179921i
$388$		0			0
$389$	−2291.50	−	3969.00i	−0.298673	−	0.517317i	0.677160	−	0.735836i	$-0.263211\pi$
$389$	−2291.50	−	3969.00i	−0.298673	−	0.517317i	−0.975833	+	0.218519i	$0.929877\pi$
$390$		0			0
$391$	6770.45			0.875694
$392$		0			0
$393$	8669.47			1.11277
$394$		0			0
$395$	−2306.60	−	3995.16i	−0.293817	−	0.508907i
$396$		0			0
$397$	4480.53	−	7760.50i	0.566426	−	0.981079i	−0.430489	−	0.902596i	$-0.641659\pi$
$397$	4480.53	−	7760.50i	0.566426	−	0.981079i	0.996915	−	0.0784836i	$-0.0250078\pi$
$398$		0			0
$399$	−3126.16	−	10898.2i	−0.392240	−	1.36740i
$400$		0			0
$401$	−5814.64	+	10071.2i	−0.724113	+	1.25420i	0.235225	+	0.971941i	$0.424417\pi$
$401$	−5814.64	+	10071.2i	−0.724113	+	1.25420i	−0.959338	+	0.282259i	$0.908916\pi$
$402$		0			0
$403$	400.102	+	692.997i	0.0494553	+	0.0856591i
$404$		0			0
$405$	−3709.34			−0.455107
$406$		0			0
$407$	440.902			0.0536970
$408$		0			0
$409$	−2160.07	−	3741.34i	−0.261145	−	0.452317i	0.705401	−	0.708808i	$-0.250767\pi$
$409$	−2160.07	−	3741.34i	−0.261145	−	0.452317i	−0.966546	+	0.256491i	$0.917433\pi$
$410$		0			0
$411$	777.635	−	1346.90i	0.0933282	−	0.161649i
$412$		0			0
$413$	−563.688	+	583.830i	−0.0671605	+	0.0695602i
$414$		0			0
$415$	−2400.18	+	4157.23i	−0.283904	+	0.491736i
$416$		0			0
$417$	623.528	+	1079.98i	0.0732238	+	0.126827i
$418$		0			0
$419$	−7824.02			−0.912240			−0.456120	−	0.889918i	$-0.650761\pi$
$419$	−7824.02			−0.912240			−0.456120	+	0.889918i	$0.650761\pi$
$420$		0			0
$421$	6944.28			0.803904			0.401952	−	0.915661i	$-0.368332\pi$
$421$	6944.28			0.803904			0.401952	+	0.915661i	$0.368332\pi$
$422$		0			0
$423$	−45.7401	−	79.2242i	−0.00525759	−	0.00910641i
$424$		0			0
$425$	−479.594	+	830.681i	−0.0547382	+	0.0948093i
$426$		0			0
$427$	−15366.7	−	3829.76i	−1.74156	−	0.434039i
$428$		0			0
$429$	−284.593	+	492.929i	−0.0320286	+	0.0554752i
$430$		0			0
$431$	1628.68	+	2820.96i	0.182020	+	0.315268i	0.942568	−	0.334013i	$-0.108403\pi$
$431$	1628.68	+	2820.96i	0.182020	+	0.315268i	−0.760548	+	0.649282i	$0.775070\pi$
$432$		0			0
$433$	−16857.1			−1.87090			−0.935449	−	0.353461i	$-0.885005\pi$
$433$	−16857.1			−1.87090			−0.935449	+	0.353461i	$0.885005\pi$
$434$		0			0
$435$	−5500.91			−0.606319
$436$		0			0
$437$	10302.8	+	17844.9i	1.12780	+	1.95340i
$438$		0			0
$439$	3976.51	−	6887.52i	0.432320	−	0.748800i	−0.564753	−	0.825260i	$-0.691028\pi$
$439$	3976.51	−	6887.52i	0.432320	−	0.748800i	0.997073	+	0.0764599i	$0.0243617\pi$
$440$		0			0
$441$	−5.84134	−	166.349i	−0.000630746	−	0.0179623i
$442$		0			0
$443$	−4854.88	+	8408.90i	−0.520683	+	0.901849i	0.479028	+	0.877800i	$0.340989\pi$
$443$	−4854.88	+	8408.90i	−0.520683	+	0.901849i	−0.999711	+	0.0240492i	$0.992344\pi$
$444$		0			0
$445$	333.013	+	576.795i	0.0354749	+	0.0614443i
$446$		0			0
$447$	14349.7			1.51838
$448$		0			0
$449$	−11758.3			−1.23588			−0.617938	−	0.786227i	$-0.712032\pi$
$449$	−11758.3			−1.23588			−0.617938	+	0.786227i	$0.712032\pi$
$450$		0			0
$451$	−148.782	−	257.698i	−0.0155341	−	0.0269058i
$452$		0			0
$453$	−9341.46	+	16179.9i	−0.968874	+	1.67814i
$454$		0			0
$455$	346.640	+	86.3913i	0.0357159	+	0.00890129i
$456$		0			0
$457$	−1375.09	+	2381.72i	−0.140753	+	0.243791i	−0.927780	−	0.373127i	$-0.878286\pi$
$457$	−1375.09	+	2381.72i	−0.140753	+	0.243791i	0.787028	+	0.616918i	$0.211619\pi$
$458$		0			0
$459$	2666.68	+	4618.83i	0.271176	+	0.469691i
$460$		0			0
$461$	−3041.43			−0.307275			−0.153637	−	0.988127i	$-0.549099\pi$
$461$	−3041.43			−0.307275			−0.153637	+	0.988127i	$0.549099\pi$
$462$		0			0
$463$	−5422.89			−0.544327			−0.272163	−	0.962251i	$-0.587739\pi$
$463$	−5422.89			−0.544327			−0.272163	+	0.962251i	$0.587739\pi$
$464$		0			0
$465$	−2718.59	−	4708.73i	−0.271122	−	0.469596i
$466$		0			0
$467$	−2773.80	+	4804.36i	−0.274853	+	0.476059i	−0.970098	−	0.242714i	$-0.921962\pi$
$467$	−2773.80	+	4804.36i	−0.274853	+	0.476059i	0.695245	+	0.718772i	$0.255296\pi$
$468$		0			0
$469$	7016.25	−	7266.95i	0.690790	−	0.715473i
$470$		0			0
$471$	−3274.23	+	5671.14i	−0.320316	+	0.554803i
$472$		0			0
$473$	4586.17	+	7943.48i	0.445819	+	0.772181i
$474$		0			0
$475$	−2919.24			−0.281987
$476$		0			0
$477$	−133.541			−0.0128185
$478$		0			0
$479$	564.275	+	977.353i	0.0538254	+	0.0932284i	0.891683	−	0.452661i	$-0.149525\pi$
$479$	564.275	+	977.353i	0.0538254	+	0.0932284i	−0.837857	+	0.545889i	$0.816192\pi$
$480$		0			0
$481$	−30.2205	+	52.3434i	−0.00286473	+	0.00496186i
$482$		0			0
$483$	4724.28	+	16469.5i	0.445056	+	1.55153i
$484$		0			0
$485$	2552.77	−	4421.52i	0.239000	−	0.413961i
$486$		0			0
$487$	2403.09	+	4162.27i	0.223602	+	0.387291i	0.955899	−	0.293695i	$-0.0948850\pi$
$487$	2403.09	+	4162.27i	0.223602	+	0.387291i	−0.732297	+	0.680986i	$0.761552\pi$
$488$		0			0
$489$	10299.9			0.952508
$490$		0			0
$491$	12452.1			1.14451			0.572255	−	0.820076i	$-0.306069\pi$
$491$	12452.1			1.14451			0.572255	+	0.820076i	$0.306069\pi$
$492$		0			0
$493$	4025.77	+	6972.83i	0.367772	+	0.636999i
$494$		0			0
$495$	34.1421	−	59.1359i	0.00310015	−	0.00536962i
$496$		0			0
$497$	−5244.35	−	18282.5i	−0.473323	−	1.65007i
$498$		0			0
$499$	−5898.68	+	10216.8i	−0.529180	+	0.916567i	0.470240	+	0.882538i	$0.344167\pi$
$499$	−5898.68	+	10216.8i	−0.529180	+	0.916567i	−0.999421	+	0.0340289i	$0.989166\pi$
$500$		0			0
$501$	−2462.47	−	4265.13i	−0.219591	−	0.380343i
$502$		0			0
$503$	−2900.55			−0.257116			−0.128558	−	0.991702i	$-0.541035\pi$
$503$	−2900.55			−0.257116			−0.128558	+	0.991702i	$0.541035\pi$
$504$		0			0
$505$	4817.79			0.424533
$506$		0			0
$507$	5720.03	+	9907.38i	0.501056	+	0.867854i
$508$		0			0
$509$	−4743.42	+	8215.85i	−0.413062	+	0.715444i	−0.995223	−	0.0976294i	$-0.968874\pi$
$509$	−4743.42	+	8215.85i	−0.413062	+	0.715444i	0.582161	+	0.813074i	$0.302207\pi$
$510$		0			0
$511$	−3253.00	+	3369.24i	−0.281613	+	0.291676i
$512$		0			0
$513$	−8115.90	+	14057.2i	−0.698491	+	1.20982i
$514$		0			0
$515$	−4495.75	−	7786.87i	−0.384673	−	0.666273i
$516$		0			0
$517$	−5305.06			−0.451289
$518$		0			0
$519$	−14167.9			−1.19827
$520$		0			0
$521$	10176.5	+	17626.2i	0.855740	+	1.48219i	0.875957	+	0.482390i	$0.160231\pi$
$521$	10176.5	+	17626.2i	0.855740	+	1.48219i	−0.0202163	+	0.999796i	$0.506435\pi$
$522$		0			0
$523$	4614.44	−	7992.45i	0.385804	−	0.668232i	−0.606076	−	0.795407i	$-0.707257\pi$
$523$	4614.44	−	7992.45i	0.385804	−	0.668232i	0.991880	+	0.127174i	$0.0405907\pi$
$524$		0			0
$525$	−2355.33	−	587.007i	−0.195800	−	0.0487983i
$526$		0			0
$527$	−3979.12	+	6892.04i	−0.328906	+	0.569681i
$528$		0			0
$529$	−9486.09	−	16430.4i	−0.779658	−	1.35041i
$530$		0			0
$531$	−21.2646			−0.00173787
$532$		0			0
$533$	40.7915			0.00331496
$534$		0			0
$535$	697.507	+	1208.12i	0.0563661	+	0.0976290i
$536$		0			0
$537$	−3759.10	+	6510.95i	−0.302080	+	0.523219i
$538$		0			0
$539$	−8523.75	−	4530.04i	−0.681158	−	0.362009i
$540$		0			0
$541$	348.637	−	603.857i	0.0277062	−	0.0479886i	−0.851840	−	0.523802i	$-0.824513\pi$
$541$	348.637	−	603.857i	0.0277062	−	0.0479886i	0.879546	+	0.475814i	$0.157846\pi$
$542$		0			0
$543$	−7106.96	−	12309.6i	−0.561674	−	0.972847i
$544$		0			0
$545$	3905.37			0.306950
$546$		0			0
$547$	8032.62			0.627879			0.313940	−	0.949443i	$-0.398351\pi$
$547$	8032.62			0.627879			0.313940	+	0.949443i	$0.398351\pi$
$548$		0			0
$549$	−207.482	−	359.370i	−0.0161296	−	0.0279372i
$550$		0			0
$551$	−12252.2	+	21221.4i	−0.947299	+	1.64077i
$552$		0			0
$553$	−16580.4	−	4132.25i	−1.27499	−	0.317760i
$554$		0			0
$555$	205.341	−	355.660i	0.0157049	−	0.0272017i
$556$		0			0
$557$	−6793.37	−	11766.5i	−0.516776	−	0.895083i	−0.999810	−	0.0194814i	$-0.993798\pi$
$557$	−6793.37	−	11766.5i	−0.516776	−	0.895083i	0.483034	−	0.875602i	$-0.339535\pi$
$558$		0			0
$559$	−1257.39			−0.0951376
$560$		0			0
$561$	−5660.71			−0.426017
$562$		0			0
$563$	8607.90	+	14909.3i	0.644369	+	1.11608i	0.984447	+	0.175683i	$0.0562133\pi$
$563$	8607.90	+	14909.3i	0.644369	+	1.11608i	−0.340078	+	0.940397i	$0.610453\pi$
$564$		0			0
$565$	1468.10	−	2542.82i	0.109316	−	0.189340i
$566$		0			0
$567$	−9543.35	+	9884.35i	−0.706848	+	0.732105i
$568$		0			0
$569$	9220.75	−	15970.8i	0.679357	−	1.17668i	−0.295818	−	0.955244i	$-0.595592\pi$
$569$	9220.75	−	15970.8i	0.679357	−	1.17668i	0.975175	−	0.221437i	$-0.0710746\pi$
$570$		0			0
$571$	−5390.17	−	9336.04i	−0.395046	−	0.684240i	0.598061	−	0.801451i	$-0.295938\pi$
$571$	−5390.17	−	9336.04i	−0.395046	−	0.684240i	−0.993107	+	0.117210i	$0.962605\pi$
$572$		0			0
$573$	18320.9			1.33572
$574$		0			0
$575$	4411.57			0.319957
$576$		0			0
$577$	6481.49	+	11226.3i	0.467640	+	0.809975i	0.999316	−	0.0369719i	$-0.0117712\pi$
$577$	6481.49	+	11226.3i	0.467640	+	0.809975i	−0.531677	+	0.846947i	$0.678438\pi$
$578$		0			0
$579$	4272.13	−	7399.54i	0.306638	−	0.531113i
$580$		0			0
$581$	4902.70	+	17091.5i	0.350083	+	1.22044i
$582$		0			0
$583$	−3872.10	+	6706.67i	−0.275070	+	0.476436i
$584$		0			0
$585$	4.68037	+	8.10665i	0.000330786	+	0.000572938i
$586$		0			0
$587$	16181.8			1.13781			0.568905	−	0.822403i	$-0.307367\pi$
$587$	16181.8			1.13781			0.568905	+	0.822403i	$0.307367\pi$
$588$		0			0
$589$	−24220.5			−1.69438
$590$		0			0
$591$	−1818.40	−	3149.56i	−0.126563	−	0.219214i
$592$		0			0
$593$	−373.815	+	647.467i	−0.0258866	+	0.0448369i	−0.878678	−	0.477414i	$-0.841574\pi$
$593$	−373.815	+	647.467i	−0.0258866	+	0.0448369i	0.852792	+	0.522251i	$0.174908\pi$
$594$		0			0
$595$	979.639	+	3415.16i	0.0674979	+	0.235307i
$596$		0			0
$597$	−9975.73	+	17278.5i	−0.683885	+	1.18452i
$598$		0			0
$599$	1924.93	+	3334.08i	0.131303	+	0.227424i	0.924179	−	0.381959i	$-0.124751\pi$
$599$	1924.93	+	3334.08i	0.131303	+	0.227424i	−0.792876	+	0.609383i	$0.791417\pi$
$600$		0			0
$601$	1808.82			0.122768			0.0613838	−	0.998114i	$-0.480449\pi$
$601$	1808.82			0.122768			0.0613838	+	0.998114i	$0.480449\pi$
$602$		0			0
$603$	264.682			0.0178751
$604$		0			0
$605$	1347.55	+	2334.03i	0.0905549	+	0.156846i
$606$		0			0
$607$	268.046	−	464.270i	0.0179237	−	0.0310447i	−0.856924	−	0.515442i	$-0.827628\pi$
$607$	268.046	−	464.270i	0.0179237	−	0.0310447i	0.874848	+	0.484397i	$0.160961\pi$
$608$		0			0
$609$	−14152.7	+	14658.4i	−0.941702	+	0.975351i
$610$		0			0
$611$	363.622	−	629.812i	0.0240762	−	0.0417013i
$612$		0			0
$613$	−7367.99	−	12761.7i	−0.485465	−	0.840851i	0.514395	−	0.857553i	$-0.328016\pi$
$613$	−7367.99	−	12761.7i	−0.485465	−	0.840851i	−0.999861	+	0.0167026i	$0.994683\pi$
$614$		0			0
$615$	−277.168			−0.0181731
$616$		0			0
$617$	9604.91			0.626709			0.313354	−	0.949636i	$-0.398547\pi$
$617$	9604.91			0.626709			0.313354	+	0.949636i	$0.398547\pi$
$618$		0			0
$619$	−4297.11	−	7442.81i	−0.279023	−	0.483283i	0.692119	−	0.721783i	$-0.256677\pi$
$619$	−4297.11	−	7442.81i	−0.279023	−	0.483283i	−0.971142	+	0.238501i	$0.923344\pi$
$620$		0			0
$621$	12264.8	−	21243.3i	0.792544	−	1.37273i
$622$		0			0
$623$	2393.77	+	596.588i	0.153940	+	0.0383656i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−8614.04	−	14920.0i	−0.548663	−	0.950312i
$628$		0			0
$629$	−601.102			−0.0381042
$630$		0			0
$631$	14803.3			0.933933			0.466966	−	0.884275i	$-0.345347\pi$
$631$	14803.3			0.933933			0.466966	+	0.884275i	$0.345347\pi$
$632$		0			0
$633$	−1644.19	−	2847.83i	−0.103240	−	0.178817i
$634$		0			0
$635$	3899.06	−	6753.37i	0.243669	−	0.422046i
$636$		0			0
$637$	1122.04	−	701.432i	0.0697911	−	0.0436291i
$638$		0			0
$639$	249.186	−	431.603i	0.0154267	−	0.0267198i
$640$		0			0
$641$	4645.16	+	8045.65i	0.286229	+	0.495763i	0.972906	−	0.231199i	$-0.0742649\pi$
$641$	4645.16	+	8045.65i	0.286229	+	0.495763i	−0.686678	+	0.726962i	$0.740932\pi$
$642$		0			0
$643$	1861.78			0.114186			0.0570928	−	0.998369i	$-0.481817\pi$
$643$	1861.78			0.114186			0.0570928	+	0.998369i	$0.481817\pi$
$644$		0			0
$645$	8543.64			0.521559
$646$		0			0
$647$	14763.7	+	25571.5i	0.897095	+	1.55381i	0.831190	+	0.555989i	$0.187660\pi$
$647$	14763.7	+	25571.5i	0.897095	+	1.55381i	0.0659057	+	0.997826i	$0.479006\pi$
$648$		0			0
$649$	−616.583	+	1067.95i	−0.0372927	+	0.0645929i
$650$		0			0
$651$	−19541.8	−	4870.31i	−1.17650	−	0.293214i
$652$		0			0
$653$	−2596.28	+	4496.88i	−0.155590	+	0.269489i	−0.933274	−	0.359166i	$-0.883061\pi$
$653$	−2596.28	+	4496.88i	−0.155590	+	0.269489i	0.777684	+	0.628656i	$0.216394\pi$
$654$		0			0
$655$	−4134.11	−	7160.49i	−0.246615	−	0.427151i
$656$		0			0
$657$	−122.717			−0.00728711
$658$		0			0
$659$	11740.1			0.693976			0.346988	−	0.937870i	$-0.387205\pi$
$659$	11740.1			0.693976			0.346988	+	0.937870i	$0.387205\pi$
$660$		0			0
$661$	−4396.25	−	7614.53i	−0.258690	−	0.448065i	0.707201	−	0.707013i	$-0.249958\pi$
$661$	−4396.25	−	7614.53i	−0.258690	−	0.448065i	−0.965891	+	0.258948i	$0.916624\pi$
$662$		0			0
$663$	387.999	−	672.034i	0.0227280	−	0.0393660i
$664$		0			0
$665$	−7510.59	+	7778.96i	−0.437967	+	0.453617i
$666$		0			0
$667$	18515.6	−	32070.0i	1.07485	−	1.86170i
$668$		0			0
$669$	−5245.22	−	9084.99i	−0.303127	−	0.525032i
$670$		0			0
$671$	−24064.4			−1.38449
$672$		0			0
$673$	30366.5			1.73929			0.869646	−	0.493676i	$-0.164347\pi$
$673$	30366.5			1.73929			0.869646	+	0.493676i	$0.164347\pi$
$674$		0			0
$675$	1737.59	+	3009.59i	0.0990812	+	0.171614i
$676$		0			0
$677$	8708.45	−	15083.5i	0.494377	−	0.856286i	−0.505602	−	0.862767i	$-0.668730\pi$
$677$	8708.45	−	15083.5i	0.494377	−	0.856286i	0.999979	+	0.00648104i	$0.00206299\pi$
$678$		0			0
$679$	−5214.39	−	18178.1i	−0.294712	−	1.02741i
$680$		0			0
$681$	−4173.78	+	7229.19i	−0.234860	+	0.406789i
$682$		0			0
$683$	4414.16	+	7645.55i	0.247296	+	0.428329i	0.962775	−	0.270305i	$-0.0871246\pi$
$683$	4414.16	+	7645.55i	0.247296	+	0.428329i	−0.715479	+	0.698635i	$0.753791\pi$
$684$		0			0
$685$	−1483.29			−0.0827351
$686$		0			0
$687$	−20578.2			−1.14281
$688$		0			0
$689$	−530.807	−	919.384i	−0.0293500	−	0.0508356i
$690$		0			0
$691$	5315.51	−	9206.74i	0.292636	−	0.506861i	−0.681796	−	0.731542i	$-0.738801\pi$
$691$	5315.51	−	9206.74i	0.292636	−	0.506861i	0.974432	+	0.224681i	$0.0721342\pi$
$692$		0			0
$693$	−69.7401	−	243.124i	−0.00382281	−	0.0133268i
$694$		0			0
$695$	594.670	−	1030.00i	0.0324563	−	0.0562159i
$696$		0			0
$697$	202.841	+	351.332i	0.0110232	+	0.0190927i
$698$		0			0
$699$	11375.2			0.615523
$700$		0			0
$701$	30120.7			1.62289			0.811443	−	0.584431i	$-0.198682\pi$
$701$	30120.7			1.62289			0.811443	+	0.584431i	$0.198682\pi$
$702$		0			0
$703$	−914.712	−	1584.33i	−0.0490740	−	0.0849986i
$704$		0			0
$705$	−2470.72	+	4279.41i	−0.131990	+	0.228613i
$706$		0			0
$707$	12395.2	−	12838.1i	0.659362	−	0.682921i
$708$		0			0
$709$	−2207.47	+	3823.45i	−0.116930	+	0.202529i	−0.918550	−	0.395306i	$-0.870639\pi$
$709$	−2207.47	+	3823.45i	−0.116930	+	0.202529i	0.801620	+	0.597834i	$0.203972\pi$
$710$		0			0
$711$	−223.870	−	387.755i	−0.0118084	−	0.0204528i
$712$		0			0
$713$	36602.2			1.92253
$714$		0			0
$715$	542.843			0.0283932
$716$		0			0
$717$	2772.56	+	4802.21i	0.144412	+	0.250128i
$718$		0			0
$719$	8567.98	−	14840.2i	0.444411	−	0.769743i	−0.553600	−	0.832783i	$-0.686746\pi$
$719$	8567.98	−	14840.2i	0.444411	−	0.769743i	0.998011	+	0.0630401i	$0.0200796\pi$
$720$		0			0
$721$	−32316.5	−	8054.07i	−1.66925	−	0.416019i
$722$		0			0
$723$	−6289.18	+	10893.2i	−0.323509	+	0.560334i
$724$		0			0
$725$	2623.16	+	4543.45i	0.134375	+	0.232744i
$726$		0			0
$727$	3271.77			0.166909			0.0834546	−	0.996512i	$-0.473405\pi$
$727$	3271.77			0.166909			0.0834546	+	0.996512i	$0.473405\pi$
$728$		0			0
$729$	19316.6			0.981386
$730$		0			0
$731$	−6252.54	−	10829.7i	−0.316359	−	0.547951i
$732$		0			0
$733$	−2234.92	+	3870.99i	−0.112618	+	0.195059i	−0.916825	−	0.399290i	$-0.869257\pi$
$733$	−2234.92	+	3870.99i	−0.112618	+	0.195059i	0.804207	+	0.594349i	$0.202590\pi$
$734$		0			0
$735$	−7623.99	+	4766.05i	−0.382605	+	0.239182i
$736$		0			0
$737$	7674.63	−	13292.9i	0.383580	−	0.664381i
$738$		0			0
$739$	−1237.60	−	2143.58i	−0.0616046	−	0.106702i	0.833578	−	0.552401i	$-0.186288\pi$
$739$	−1237.60	−	2143.58i	−0.0616046	−	0.106702i	−0.895183	+	0.445699i	$0.852955\pi$
$740$		0			0
$741$	2361.71			0.117084
$742$		0			0
$743$	−9240.48			−0.456259			−0.228129	−	0.973631i	$-0.573261\pi$
$743$	−9240.48			−0.456259			−0.228129	+	0.973631i	$0.573261\pi$
$744$		0			0
$745$	−6842.78	−	11852.0i	−0.336510	−	0.582852i
$746$		0			0
$747$	−232.952	+	403.485i	−0.0114100	+	0.0197627i
$748$		0			0
$749$	5013.84	+	1249.57i	0.244595	+	0.0609592i
$750$		0			0
$751$	2526.23	−	4375.57i	0.122748	−	0.212605i	−0.798103	−	0.602522i	$-0.794163\pi$
$751$	2526.23	−	4375.57i	0.122748	−	0.212605i	0.920850	+	0.389916i	$0.127496\pi$
$752$		0			0
$753$	−9994.95	−	17311.8i	−0.483713	−	0.837816i
$754$		0			0
$755$	17818.2			0.858903
$756$		0			0
$757$	−37779.2			−1.81388			−0.906942	−	0.421256i	$-0.861589\pi$
$757$	−37779.2			−1.81388			−0.906942	+	0.421256i	$0.861589\pi$
$758$		0			0
$759$	13017.6	+	22547.1i	0.622541	+	1.07827i
$760$		0			0
$761$	−3751.35	+	6497.52i	−0.178694	+	0.309507i	−0.941434	−	0.337199i	$-0.890521\pi$
$761$	−3751.35	+	6497.52i	−0.178694	+	0.309507i	0.762739	+	0.646706i	$0.223854\pi$
$762$		0			0
$763$	10047.7	−	10406.7i	0.476738	−	0.493772i
$764$		0			0
$765$	−46.5476	+	80.6228i	−0.00219991	+	0.00381036i
$766$		0			0
$767$	−84.5243	−	146.400i	−0.00397913	−	0.00689206i
$768$		0			0
$769$	24209.4			1.13526			0.567628	−	0.823285i	$-0.307861\pi$
$769$	24209.4			1.13526			0.567628	+	0.823285i	$0.307861\pi$
$770$		0			0
$771$	18297.7			0.854701
$772$		0			0
$773$	−3760.50	−	6513.37i	−0.174975	−	0.303065i	0.765178	−	0.643819i	$-0.222651\pi$
$773$	−3760.50	−	6513.37i	−0.174975	−	0.303065i	−0.940153	+	0.340754i	$0.889318\pi$
$774$		0			0
$775$	−2592.77	+	4490.80i	−0.120174	+	0.208148i
$776$		0			0
$777$	−419.437	−	1462.22i	−0.0193658	−	0.0675118i
$778$		0			0
$779$	−617.337	+	1069.26i	−0.0283933	+	0.0491787i
$780$		0			0
$781$	−14450.6	−	25029.2i	−0.662080	−	1.14676i
$782$		0			0
$783$	29171.0			1.33140
$784$		0			0
$785$	6245.39			0.283959
$786$		0			0
$787$	−8060.68	−	13961.5i	−0.365098	−	0.632368i	0.623694	−	0.781669i	$-0.285631\pi$
$787$	−8060.68	−	13961.5i	−0.365098	−	0.632368i	−0.988792	+	0.149300i	$0.952298\pi$
$788$		0			0
$789$	18675.7	−	32347.3i	0.842679	−	1.45956i
$790$		0			0
$791$	−2998.79	−	10454.2i	−0.134798	−	0.469923i
$792$		0			0
$793$	1649.43	−	2856.90i	0.0738627	−	0.127934i
$794$		0			0
$795$	3606.70	+	6246.98i	0.160901	+	0.278689i
$796$		0			0
$797$	−32223.0			−1.43212			−0.716058	−	0.698041i	$-0.754056\pi$
$797$	−32223.0			−1.43212			−0.716058	+	0.698041i	$0.754056\pi$
$798$		0			0
$799$	7232.65			0.320241
$800$		0			0
$801$	32.3210	+	55.9816i	0.00142573	+	0.00246943i
$802$		0			0
$803$	−3558.25	+	6163.07i	−0.156374	+	0.270847i
$804$		0			0
$805$	11350.1	−	11755.6i	0.496941	−	0.514697i
$806$		0			0
$807$	1121.77	−	1942.97i	0.0489323	−	0.0847532i
$808$		0			0
$809$	12272.2	+	21256.0i	0.533334	+	0.923761i	0.999242	+	0.0389282i	$0.0123944\pi$
$809$	12272.2	+	21256.0i	0.533334	+	0.923761i	−0.465908	+	0.884833i	$0.654272\pi$
$810$		0			0
$811$	−18783.9			−0.813308			−0.406654	−	0.913582i	$-0.633305\pi$
$811$	−18783.9			−0.813308			−0.406654	+	0.913582i	$0.633305\pi$
$812$		0			0
$813$	−42929.8			−1.85192
$814$		0			0
$815$	−4911.59	−	8507.12i	−0.211099	−	0.365634i
$816$		0			0
$817$	19029.3	−	32959.7i	0.814872	−	1.41140i
$818$		0			0
$819$	33.6436	+	8.38482i	0.00143541	+	0.000357740i
$820$		0			0
$821$	−9042.53	+	15662.1i	−0.384393	+	0.665788i	−0.991685	−	0.128691i	$-0.958923\pi$
$821$	−9042.53	+	15662.1i	−0.384393	+	0.665788i	0.607292	+	0.794479i	$0.292256\pi$
$822$		0			0
$823$	3717.59	+	6439.06i	0.157457	+	0.272723i	0.933951	−	0.357401i	$-0.116337\pi$
$823$	3717.59	+	6439.06i	0.157457	+	0.272723i	−0.776494	+	0.630125i	$0.783004\pi$
$824$		0			0
$825$	−3688.48			−0.155656
$826$		0			0
$827$	−26487.2			−1.11373			−0.556863	−	0.830604i	$-0.687995\pi$
$827$	−26487.2			−1.11373			−0.556863	+	0.830604i	$0.687995\pi$
$828$		0			0
$829$	9688.53	+	16781.0i	0.405906	+	0.703051i	0.994427	−	0.105432i	$-0.0336226\pi$
$829$	9688.53	+	16781.0i	0.405906	+	0.703051i	−0.588520	+	0.808483i	$0.700289\pi$
$830$		0			0
$831$	10930.8	−	18932.7i	0.456300	−	0.790334i
$832$		0			0
$833$	11620.8	+	6176.02i	0.483359	+	0.256887i
$834$		0			0
$835$	−2348.50	+	4067.73i	−0.0973333	+	0.168586i
$836$		0			0
$837$	14416.5	+	24970.2i	0.595350	+	1.03118i
$838$		0			0
$839$	4645.97			0.191176			0.0955880	−	0.995421i	$-0.469527\pi$
$839$	4645.97			0.191176			0.0955880	+	0.995421i	$0.469527\pi$
$840$		0			0
$841$	19649.2			0.805658
$842$		0			0
$843$	−3367.35	−	5832.41i	−0.137577	−	0.238291i
$844$		0			0
$845$	5455.29	−	9448.84i	0.222092	−	0.384675i
$846$		0			0
$847$	9686.50	+	2414.12i	0.392954	+	0.0979339i
$848$		0			0
$849$	12554.4	−	21744.9i	0.507499	−	0.879013i
$850$		0			0
$851$	1382.32	+	2394.25i	0.0556819	+	0.0964438i
$852$		0			0
$853$	32566.5			1.30722			0.653609	−	0.756833i	$-0.273254\pi$
$853$	32566.5			1.30722			0.653609	+	0.756833i	$0.273254\pi$
$854$		0			0
$855$	−283.330			−0.0113330
$856$		0			0
$857$	−67.4706	−	116.862i	−0.00268932	−	0.00465805i	0.864678	−	0.502327i	$-0.167523\pi$
$857$	−67.4706	−	116.862i	−0.00268932	−	0.00465805i	−0.867367	+	0.497669i	$0.834189\pi$
$858$		0			0
$859$	−5190.45	+	8990.13i	−0.206165	+	0.357089i	−0.950503	−	0.310714i	$-0.899432\pi$
$859$	−5190.45	+	8990.13i	−0.206165	+	0.357089i	0.744338	+	0.667803i	$0.232765\pi$
$860$		0			0
$861$	−713.095	+	738.575i	−0.0282256	+	0.0292341i
$862$		0			0
$863$	12674.6	−	21953.1i	0.499941	−	0.865924i	−0.500059	−	0.865992i	$-0.666688\pi$
$863$	12674.6	−	21953.1i	0.499941	−	0.865924i	1.00000		6.76895e-5i	$2.15462e-5\pi$
$864$		0			0
$865$	6756.08	+	11701.9i	0.265565	+	0.459972i
$866$		0			0
$867$	−18039.6			−0.706639
$868$		0			0
$869$	−25965.1			−1.01359
$870$		0			0
$871$	1052.08	+	1822.25i	0.0409280	+	0.0708893i
$872$		0			0
$873$	247.762	−	429.136i	0.00960536	−	0.0166370i
$874$		0			0
$875$	638.325	+	2225.29i	0.0246621	+	0.0859755i
$876$		0			0
$877$	11259.7	−	19502.3i	0.433537	−	0.750909i	−0.563638	−	0.826022i	$-0.690599\pi$
$877$	11259.7	−	19502.3i	0.433537	−	0.750909i	0.997175	+	0.0751134i	$0.0239319\pi$
$878$		0			0
$879$	−18305.4	−	31705.9i	−0.702418	−	1.21662i
$880$		0			0
$881$	−12419.9			−0.474958			−0.237479	−	0.971393i	$-0.576321\pi$
$881$	−12419.9			−0.474958			−0.237479	+	0.971393i	$0.576321\pi$
$882$		0			0
$883$	46011.8			1.75359			0.876794	−	0.480866i	$-0.159678\pi$
$883$	46011.8			1.75359			0.876794	+	0.480866i	$0.159678\pi$
$884$		0			0
$885$	574.321	+	994.753i	0.0218142	+	0.0377833i
$886$		0			0
$887$	−14043.3	+	24323.8i	−0.531600	+	0.920759i	0.467719	+	0.883877i	$0.345076\pi$
$887$	−14043.3	+	24323.8i	−0.531600	+	0.920759i	−0.999320	+	0.0368816i	$0.988258\pi$
$888$		0			0
$889$	−7964.38	−	27764.9i	−0.300469	−	1.04748i
$890$		0			0
$891$	−10438.9	+	18080.6i	−0.392497	+	0.679825i
$892$		0			0
$893$	11006.1	+	19063.1i	0.412436	+	0.714359i
$894$		0			0
$895$	7170.24			0.267793
$896$		0			0
$897$	−3569.03			−0.132850
$898$		0			0
$899$	21764.0	+	37696.3i	0.807419	+	1.39849i
$900$		0			0
$901$	5279.02	−	9143.53i	0.195194	−	0.338086i
$902$		0			0
$903$	21981.0	−	22766.4i	0.810058	−	0.839002i
$904$		0			0
$905$	−6778.03	+	11739.9i	−0.248961	+	0.431213i
$906$		0			0
$907$	−15229.4	−	26378.1i	−0.557534	−	0.965677i	−0.997702	−	0.0677613i	$-0.978414\pi$
$907$	−15229.4	−	26378.1i	−0.557534	−	0.965677i	0.440168	−	0.897916i	$-0.354919\pi$
$908$		0			0
$909$	467.597			0.0170618
$910$		0			0
$911$	26850.4			0.976502			0.488251	−	0.872703i	$-0.337635\pi$
$911$	26850.4			0.976502			0.488251	+	0.872703i	$0.337635\pi$
$912$		0			0
$913$	13509.2	+	23398.7i	0.489693	+	0.848174i
$914$		0			0
$915$	−11207.5	+	19411.9i	−0.404927	+	0.701353i
$916$		0			0
$917$	−29716.9	−	7406.20i	−1.07016	−	0.266711i
$918$		0			0
$919$	−19047.9	+	32992.0i	−0.683714	+	1.18423i	0.290125	+	0.956989i	$0.406303\pi$
$919$	−19047.9	+	32992.0i	−0.683714	+	1.18423i	−0.973839	+	0.227238i	$0.927030\pi$
$920$		0			0
$921$	−5424.64	−	9395.76i	−0.194080	−	0.336157i
$922$		0			0
$923$	3961.93			0.141288
$924$		0			0
$925$	−391.674			−0.0139223
$926$		0			0
$927$	−436.341	−	755.765i	−0.0154599	−	0.0267773i
$928$		0			0
$929$	−18177.5	+	31484.4i	−0.641964	+	1.11191i	0.343030	+	0.939325i	$0.388547\pi$
$929$	−18177.5	+	31484.4i	−0.641964	+	1.11191i	−0.984994	+	0.172590i	$0.944786\pi$
$930$		0			0
$931$	1405.56	+	40027.3i	0.0494793	+	1.40907i
$932$		0			0
$933$	5562.34	−	9634.25i	0.195180	−	0.338061i
$934$		0			0
$935$	2699.36	+	4675.43i	0.0944155	+	0.163533i
$936$		0			0
$937$	37878.5			1.32064			0.660318	−	0.750986i	$-0.270421\pi$
$937$	37878.5			1.32064			0.660318	+	0.750986i	$0.270421\pi$
$938$		0			0
$939$	8014.93			0.278549
$940$		0			0
$941$	−27062.8	−	46874.1i	−0.937536	−	1.62386i	−0.770047	−	0.637987i	$-0.779767\pi$
$941$	−27062.8	−	46874.1i	−0.937536	−	1.62386i	−0.167489	−	0.985874i	$-0.553566\pi$
$942$		0			0
$943$	932.924	−	1615.87i	0.0322165	−	0.0558007i
$944$		0			0
$945$	12490.2	+	3112.87i	0.429953	+	0.107155i
$946$		0			0
$947$	−19172.9	+	33208.5i	−0.657906	+	1.13953i	0.323251	+	0.946313i	$0.395224\pi$
$947$	−19172.9	+	33208.5i	−0.657906	+	1.13953i	−0.981157	+	0.193213i	$0.938109\pi$
$948$		0			0
$949$	−487.783	−	844.865i	−0.0166850	−	0.0288993i
$950$		0			0
$951$	26960.0			0.919282
$952$		0			0
$953$	−15096.4			−0.513137			−0.256569	−	0.966526i	$-0.582592\pi$
$953$	−15096.4			−0.513137			−0.256569	+	0.966526i	$0.582592\pi$
$954$		0			0
$955$	−8736.50	−	15132.1i	−0.296028	−	0.512735i
$956$		0			0
$957$	−15480.7	+	26813.4i	−0.522906	+	0.905701i
$958$		0			0
$959$	−3816.19	+	3952.55i	−0.128500	+	0.133091i
$960$		0			0
$961$	−6616.31	+	11459.8i	−0.222091	+	0.384673i
$962$		0			0
$963$	67.6975	+	117.255i	0.00226534	+	0.00392368i
$964$		0			0
$965$	−8148.81			−0.271833
$966$		0			0
$967$	−6917.06			−0.230029			−0.115014	−	0.993364i	$-0.536691\pi$
$967$	−6917.06			−0.230029			−0.115014	+	0.993364i	$0.536691\pi$
$968$		0			0
$969$	11743.9	+	20341.1i	0.389339	+	0.674355i
$970$		0			0
$971$	19758.8	−	34223.3i	0.653029	−	1.13108i	−0.329355	−	0.944206i	$-0.606831\pi$
$971$	19758.8	−	34223.3i	0.653029	−	1.13108i	0.982384	−	0.186874i	$-0.0598355\pi$
$972$		0			0
$973$	−1214.70	−	4234.60i	−0.0400220	−	0.139522i
$974$		0			0
$975$	252.817	−	437.893i	0.00830424	−	0.0143834i
$976$		0			0
$977$	19429.2	+	33652.4i	0.636229	+	1.10198i	0.986253	+	0.165240i	$0.0528400\pi$
$977$	19429.2	+	33652.4i	0.636229	+	1.10198i	−0.350024	+	0.936741i	$0.613827\pi$
$978$		0			0
$979$	3748.68			0.122378
$980$		0			0
$981$	379.040			0.0123362
$982$		0			0
$983$	−255.115	−	441.872i	−0.00827762	−	0.0143373i	0.861857	−	0.507151i	$-0.169302\pi$
$983$	−255.115	−	441.872i	−0.00827762	−	0.0143373i	−0.870135	+	0.492814i	$0.835968\pi$
$984$		0			0
$985$	−1734.24	+	3003.79i	−0.0560989	+	0.0971662i
$986$		0			0
$987$	5046.80	+	17593.8i	0.162757	+	0.567394i
$988$		0			0
$989$	−28757.2	+	49808.9i	−0.924596	+	1.60145i
$990$		0			0
$991$	−18111.4	−	31369.9i	−0.580553	−	1.00555i	−0.995414	−	0.0956623i	$-0.969503\pi$
$991$	−18111.4	−	31369.9i	−0.580553	−	1.00555i	0.414861	−	0.909885i	$-0.363830\pi$
$992$		0			0
$993$	30271.2			0.967400
$994$		0			0
$995$	19028.1			0.606262
$996$		0			0
$997$	10428.0	+	18061.9i	0.331253	+	0.573747i	0.982758	−	0.184898i	$-0.0591954\pi$
$997$	10428.0	+	18061.9i	0.331253	+	0.573747i	−0.651505	+	0.758644i	$0.725862\pi$
$998$		0			0
$999$	−1088.91	+	1886.05i	−0.0344861	+	0.0597316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.4.q.i.401.1		4
4.3	odd	2		35.4.e.b.16.1	yes	4
7.4	even	3	inner	560.4.q.i.81.1		4
12.11	even	2		315.4.j.c.226.2		4
20.3	even	4		175.4.k.c.149.2		8
20.7	even	4		175.4.k.c.149.3		8
20.19	odd	2		175.4.e.c.51.2		4
28.3	even	6		245.4.e.l.116.1		4
28.11	odd	6		35.4.e.b.11.1	✓	4
28.19	even	6		245.4.a.h.1.2		2
28.23	odd	6		245.4.a.g.1.2		2
28.27	even	2		245.4.e.l.226.1		4
84.11	even	6		315.4.j.c.46.2		4
84.23	even	6		2205.4.a.bf.1.1		2
84.47	odd	6		2205.4.a.bg.1.1		2
140.19	even	6		1225.4.a.v.1.1		2
140.39	odd	6		175.4.e.c.151.2		4
140.67	even	12		175.4.k.c.74.2		8
140.79	odd	6		1225.4.a.x.1.1		2
140.123	even	12		175.4.k.c.74.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.b.11.1	✓	4	28.11	odd	6
35.4.e.b.16.1	yes	4	4.3	odd	2
175.4.e.c.51.2		4	20.19	odd	2
175.4.e.c.151.2		4	140.39	odd	6
175.4.k.c.74.2		8	140.67	even	12
175.4.k.c.74.3		8	140.123	even	12
175.4.k.c.149.2		8	20.3	even	4
175.4.k.c.149.3		8	20.7	even	4
245.4.a.g.1.2		2	28.23	odd	6
245.4.a.h.1.2		2	28.19	even	6
245.4.e.l.116.1		4	28.3	even	6
245.4.e.l.226.1		4	28.27	even	2
315.4.j.c.46.2		4	84.11	even	6
315.4.j.c.226.2		4	12.11	even	2
560.4.q.i.81.1		4	7.4	even	3	inner
560.4.q.i.401.1		4	1.1	even	1	trivial
1225.4.a.v.1.1		2	140.19	even	6
1225.4.a.x.1.1		2	140.79	odd	6
2205.4.a.bf.1.1		2	84.23	even	6
2205.4.a.bg.1.1		2	84.47	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.62132 - 4.54026i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(5.10660 + 17.8023i) q^{7} +(-0.242641 + 0.420266i) q^{9} +(14.0711 + 24.3718i) q^{11} -3.85786 q^{13} +26.2132 q^{15} +(-19.1838 - 33.2273i) q^{17} +(58.3848 - 101.125i) q^{19} +(67.4411 - 69.8509i) q^{21} +(-88.2315 + 152.821i) q^{23} +(-12.5000 - 21.6506i) q^{25} -139.007 q^{27} -209.853 q^{29} +(-103.711 - 179.632i) q^{31} +(73.7696 - 127.773i) q^{33} +(-89.8528 - 22.3936i) q^{35} +(7.83348 - 13.5680i) q^{37} +(10.1127 + 17.5157i) q^{39} -10.5736 q^{41} +325.929 q^{43} +(-1.21320 - 2.10133i) q^{45} +(-94.2548 + 163.254i) q^{47} +(-290.845 + 181.819i) q^{49} +(-100.574 + 174.199i) q^{51} +(137.591 + 238.314i) q^{53} -140.711 q^{55} -612.181 q^{57} +(21.9096 + 37.9485i) q^{59} +(-427.551 + 740.540i) q^{61} +(-8.72078 - 2.17344i) q^{63} +(9.64466 - 16.7050i) q^{65} +(-272.710 - 472.347i) q^{67} +925.132 q^{69} -1026.97 q^{71} +(126.439 + 218.998i) q^{73} +(-65.5330 + 113.507i) q^{75} +(-362.019 + 374.955i) q^{77} +(-461.321 + 799.031i) q^{79} +(370.934 + 642.476i) q^{81} +960.071 q^{83} +191.838 q^{85} +(550.091 + 952.786i) q^{87} +(66.6026 - 115.359i) q^{89} +(-19.7006 - 68.6789i) q^{91} +(-543.718 + 941.747i) q^{93} +(291.924 + 505.627i) q^{95} -1021.11 q^{97} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 10 q^{5} - 22 q^{7} + 16 q^{9} + 28 q^{11} - 72 q^{13} + 20 q^{15} + 76 q^{17} + 160 q^{19} + 134 q^{21} - 22 q^{23} - 50 q^{25} + 4 q^{27} - 500 q^{29} - 132 q^{31} + 148 q^{33} - 20 q^{35}+ \cdots - 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 10 * q^5 - 22 * q^7 + 16 * q^9 + 28 * q^11 - 72 * q^13 + 20 * q^15 + 76 * q^17 + 160 * q^19 + 134 * q^21 - 22 * q^23 - 50 * q^25 + 4 * q^27 - 500 * q^29 - 132 * q^31 + 148 * q^33 - 20 * q^35 + 416 * q^37 - 84 * q^39 - 212 * q^41 + 1332 * q^43 + 80 * q^45 - 196 * q^47 - 230 * q^49 - 572 * q^51 + 952 * q^53 - 280 * q^55 - 944 * q^57 + 840 * q^59 - 98 * q^61 - 544 * q^63 + 180 * q^65 - 1286 * q^67 + 2852 * q^69 - 2128 * q^71 + 172 * q^73 - 50 * q^75 - 724 * q^77 - 1240 * q^79 + 754 * q^81 + 3812 * q^83 - 760 * q^85 + 970 * q^87 - 650 * q^89 + 996 * q^91 - 1332 * q^93 + 800 * q^95 - 1256 * q^97 - 32 * q^99

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