LMFDB - Embedded newform 208.4.i.e.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(81,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("208.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.i (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:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.2
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.4.i.e.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.34233 + 7.52113i) q^{3} +2.80776 q^{5} +(4.78078 - 8.28055i) q^{7} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})$	\(q+(4.34233 + 7.52113i) q^{3} +2.80776 q^{5} +(4.78078 - 8.28055i) q^{7} +(-24.2116 + 41.9358i) q^{9} +(19.7116 + 34.1416i) q^{11} +(40.5270 + 23.5492i) q^{13} +(12.1922 + 21.1176i) q^{15} +(-1.00758 + 1.74518i) q^{17} +(-30.0961 + 52.1280i) q^{19} +83.0388 q^{21} +(2.23438 + 3.87006i) q^{23} -117.116 q^{25} -186.054 q^{27} +(-70.3466 - 121.844i) q^{29} -136.155 q^{31} +(-171.189 + 296.508i) q^{33} +(13.4233 - 23.2498i) q^{35} +(92.8542 + 160.828i) q^{37} +(-1.13494 + 407.067i) q^{39} +(-155.116 - 268.668i) q^{41} +(213.735 - 370.200i) q^{43} +(-67.9806 + 117.746i) q^{45} +258.617 q^{47} +(125.788 + 217.872i) q^{49} -17.5009 q^{51} +612.656 q^{53} +(55.3457 + 95.8615i) q^{55} -522.749 q^{57} +(-258.943 + 448.502i) q^{59} +(80.6553 - 139.699i) q^{61} +(231.501 + 400.971i) q^{63} +(113.790 + 66.1205i) q^{65} +(-24.9493 - 43.2135i) q^{67} +(-19.4048 + 33.6101i) q^{69} +(139.982 - 242.455i) q^{71} +467.732 q^{73} +(-508.558 - 880.849i) q^{75} +376.948 q^{77} -37.5379 q^{79} +(-154.193 - 267.070i) q^{81} +76.1553 q^{83} +(-2.82904 + 4.90004i) q^{85} +(610.936 - 1058.17i) q^{87} +(-101.403 - 175.635i) q^{89} +(388.750 - 223.002i) q^{91} +(-591.231 - 1024.04i) q^{93} +(-84.5028 + 146.363i) q^{95} +(587.184 - 1017.03i) q^{97} -1909.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{3} - 30 q^{5} + 15 q^{7} - 35 q^{9}+O(q^{10}) $ 4 * q + 5 * q^3 - 30 * q^5 + 15 * q^7 - 35 * q^9	$ 4 q + 5 q^{3} - 30 q^{5} + 15 q^{7} - 35 q^{9} + 17 q^{11} + 125 q^{13} + 90 q^{15} - 70 q^{17} - 141 q^{19} + 126 q^{21} + 145 q^{23} + 150 q^{25} - 670 q^{27} - 34 q^{29} + 280 q^{31} - 425 q^{33} - 70 q^{35} + 190 q^{37} + 181 q^{39} - 538 q^{41} + 455 q^{43} - 375 q^{45} - 120 q^{47} + 565 q^{49} + 466 q^{51} + 1090 q^{53} + 510 q^{55} - 450 q^{57} - 809 q^{59} - 502 q^{61} + 390 q^{63} - 555 q^{65} - 475 q^{67} + 479 q^{69} + 127 q^{71} + 1170 q^{73} - 1725 q^{75} + 510 q^{77} - 480 q^{79} - 122 q^{81} - 520 q^{83} + 1205 q^{85} + 1615 q^{87} - 921 q^{89} + 1287 q^{91} - 2200 q^{93} + 1270 q^{95} + 415 q^{97} - 4420 q^{99}+O(q^{100}) $ 4 * q + 5 * q^3 - 30 * q^5 + 15 * q^7 - 35 * q^9 + 17 * q^11 + 125 * q^13 + 90 * q^15 - 70 * q^17 - 141 * q^19 + 126 * q^21 + 145 * q^23 + 150 * q^25 - 670 * q^27 - 34 * q^29 + 280 * q^31 - 425 * q^33 - 70 * q^35 + 190 * q^37 + 181 * q^39 - 538 * q^41 + 455 * q^43 - 375 * q^45 - 120 * q^47 + 565 * q^49 + 466 * q^51 + 1090 * q^53 + 510 * q^55 - 450 * q^57 - 809 * q^59 - 502 * q^61 + 390 * q^63 - 555 * q^65 - 475 * q^67 + 479 * q^69 + 127 * q^71 + 1170 * q^73 - 1725 * q^75 + 510 * q^77 - 480 * q^79 - 122 * q^81 - 520 * q^83 + 1205 * q^85 + 1615 * q^87 - 921 * q^89 + 1287 * q^91 - 2200 * q^93 + 1270 * q^95 + 415 * q^97 - 4420 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	4.34233	+	7.52113i	0.835682	+	1.44744i	0.893474	+	0.449114i	$0.148260\pi$
$3$	4.34233	+	7.52113i	0.835682	+	1.44744i	−0.0577926	+	0.998329i	$0.518406\pi$
$4$		0			0
$5$	2.80776			0.251134			0.125567	−	0.992085i	$-0.459925\pi$
$5$	2.80776			0.251134			0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	4.78078	−	8.28055i	0.258138	−	0.447108i	−0.707605	−	0.706608i	$-0.750225\pi$
$7$	4.78078	−	8.28055i	0.258138	−	0.447108i	0.965743	+	0.259500i	$0.0835579\pi$
$8$		0			0
$9$	−24.2116	+	41.9358i	−0.896728	+	1.55318i
$10$		0			0
$11$	19.7116	+	34.1416i	0.540299	+	0.935825i	0.998887	+	0.0471757i	$0.0150221\pi$
$11$	19.7116	+	34.1416i	0.540299	+	0.935825i	−0.458588	+	0.888649i	$0.651645\pi$
$12$		0			0
$13$	40.5270	+	23.5492i	0.864628	+	0.502413i
$13$	40.5270	+	23.5492i	0.864628	+	0.502413i
$14$		0			0
$15$	12.1922	+	21.1176i	0.209868	+	0.363502i
$16$		0			0
$17$	−1.00758	+	1.74518i	−0.0143749	+	0.0248981i	−0.873123	−	0.487499i	$-0.837909\pi$
$17$	−1.00758	+	1.74518i	−0.0143749	+	0.0248981i	0.858748	+	0.512397i	$0.171242\pi$
$18$		0			0
$19$	−30.0961	+	52.1280i	−0.363396	+	0.629420i	−0.988517	−	0.151107i	$-0.951716\pi$
$19$	−30.0961	+	52.1280i	−0.363396	+	0.629420i	0.625121	+	0.780528i	$0.285049\pi$
$20$		0			0
$21$	83.0388			0.862884
$22$		0			0
$23$	2.23438	+	3.87006i	0.0202565	+	0.0350853i	0.875976	−	0.482355i	$-0.160218\pi$
$23$	2.23438	+	3.87006i	0.0202565	+	0.0350853i	−0.855719	+	0.517440i	$0.826885\pi$
$24$		0			0
$25$	−117.116			−0.936932
$26$		0			0
$27$	−186.054			−1.32615
$28$		0			0
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	0.547964	−	0.836502i	$-0.315403\pi$
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	−0.998414	+	0.0563003i	$0.982070\pi$
$30$		0			0
$31$	−136.155			−0.788845			−0.394423	−	0.918929i	$-0.629055\pi$
$31$	−136.155			−0.788845			−0.394423	+	0.918929i	$0.629055\pi$
$32$		0			0
$33$	−171.189	+	296.508i	−0.903035	+	1.56410i
$34$		0			0
$35$	13.4233	−	23.2498i	0.0648272	−	0.112284i
$36$		0			0
$37$	92.8542	+	160.828i	0.412571	+	0.714594i	0.995170	−	0.0981657i	$-0.0312975\pi$
$37$	92.8542	+	160.828i	0.412571	+	0.714594i	−0.582599	+	0.812760i	$0.697964\pi$
$38$		0			0
$39$	−1.13494	+	407.067i	−0.00465989	+	1.67136i
$40$		0			0
$41$	−155.116	−	268.668i	−0.590853	−	1.02339i	−0.994118	−	0.108304i	$-0.965458\pi$
$41$	−155.116	−	268.668i	−0.590853	−	1.02339i	0.403265	−	0.915083i	$-0.367875\pi$
$42$		0			0
$43$	213.735	−	370.200i	0.758008	−	1.31291i	−0.185857	−	0.982577i	$-0.559506\pi$
$43$	213.735	−	370.200i	0.758008	−	1.31291i	0.943865	−	0.330331i	$-0.107160\pi$
$44$		0			0
$45$	−67.9806	+	117.746i	−0.225199	+	0.390056i
$46$		0			0
$47$	258.617			0.802622			0.401311	−	0.915942i	$-0.368555\pi$
$47$	258.617			0.802622			0.401311	+	0.915942i	$0.368555\pi$
$48$		0			0
$49$	125.788	+	217.872i	0.366730	+	0.635195i
$50$		0			0
$51$	−17.5009			−0.0480514
$52$		0			0
$53$	612.656			1.58783			0.793913	−	0.608031i	$-0.208040\pi$
$53$	612.656			1.58783			0.793913	+	0.608031i	$0.208040\pi$
$54$		0			0
$55$	55.3457	+	95.8615i	0.135687	+	0.235017i
$56$		0			0
$57$	−522.749			−1.21473
$58$		0			0
$59$	−258.943	+	448.502i	−0.571381	+	0.989661i	0.425044	+	0.905173i	$0.360259\pi$
$59$	−258.943	+	448.502i	−0.571381	+	0.989661i	−0.996425	+	0.0844878i	$0.973075\pi$
$60$		0			0
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	−0.768879	−	0.639395i	$-0.779185\pi$
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	0.938171	+	0.346171i	$0.112518\pi$
$62$		0			0
$63$	231.501	+	400.971i	0.462958	+	0.801867i
$64$		0			0
$65$	113.790	+	66.1205i	0.217138	+	0.126173i
$66$		0			0
$67$	−24.9493	−	43.2135i	−0.0454933	−	0.0787966i	0.842382	−	0.538881i	$-0.181153\pi$
$67$	−24.9493	−	43.2135i	−0.0454933	−	0.0787966i	−0.887875	+	0.460084i	$0.847819\pi$
$68$		0			0
$69$	−19.4048	+	33.6101i	−0.0338560	+	0.0586403i
$70$		0			0
$71$	139.982	−	242.455i	0.233982	−	0.405269i	−0.724994	−	0.688755i	$-0.758158\pi$
$71$	139.982	−	242.455i	0.233982	−	0.405269i	0.958976	+	0.283486i	$0.0914909\pi$
$72$		0			0
$73$	467.732			0.749916			0.374958	−	0.927042i	$-0.377657\pi$
$73$	467.732			0.749916			0.374958	+	0.927042i	$0.377657\pi$
$74$		0			0
$75$	−508.558	−	880.849i	−0.782977	−	1.35616i
$76$		0			0
$77$	376.948			0.557886
$78$		0			0
$79$	−37.5379			−0.0534600			−0.0267300	−	0.999643i	$-0.508509\pi$
$79$	−37.5379			−0.0534600			−0.0267300	+	0.999643i	$0.508509\pi$
$80$		0			0
$81$	−154.193	−	267.070i	−0.211513	−	0.366352i
$82$		0			0
$83$	76.1553			0.100712			0.0503562	−	0.998731i	$-0.483964\pi$
$83$	76.1553			0.100712			0.0503562	+	0.998731i	$0.483964\pi$
$84$		0			0
$85$	−2.82904	+	4.90004i	−0.00361003	+	0.00625275i
$86$		0			0
$87$	610.936	−	1058.17i	0.752865	−	1.30400i
$88$		0			0
$89$	−101.403	−	175.635i	−0.120772	−	0.209183i	0.799300	−	0.600932i	$-0.205204\pi$
$89$	−101.403	−	175.635i	−0.120772	−	0.209183i	−0.920072	+	0.391749i	$0.871870\pi$
$90$		0			0
$91$	388.750	−	223.002i	0.447826	−	0.256890i
$92$		0			0
$93$	−591.231	−	1024.04i	−0.659224	−	1.14181i
$94$		0			0
$95$	−84.5028	+	146.363i	−0.0912611	+	0.158069i
$96$		0			0
$97$	587.184	−	1017.03i	0.614634	−	1.06458i	−0.375814	−	0.926695i	$-0.622637\pi$
$97$	587.184	−	1017.03i	0.614634	−	1.06458i	0.990449	−	0.137883i	$-0.0440297\pi$
$98$		0			0
$99$	−1909.01			−1.93800
$100$		0			0
$101$	−485.348	−	840.648i	−0.478158	−	0.828194i	0.521528	−	0.853234i	$-0.325362\pi$
$101$	−485.348	−	840.648i	−0.478158	−	0.828194i	−0.999686	+	0.0250397i	$0.992029\pi$
$102$		0			0
$103$	1899.70			1.81731			0.908654	−	0.417550i	$-0.137111\pi$
$103$	1899.70			1.81731			0.908654	+	0.417550i	$0.137111\pi$
$104$		0			0
$105$	233.153			0.216699
$106$		0			0
$107$	−953.247	−	1651.07i	−0.861251	−	1.49173i	−0.870722	−	0.491775i	$-0.836348\pi$
$107$	−953.247	−	1651.07i	−0.861251	−	1.49173i	0.00947163	−	0.999955i	$-0.496985\pi$
$108$		0			0
$109$	−896.004			−0.787354			−0.393677	−	0.919249i	$-0.628797\pi$
$109$	−896.004			−0.787354			−0.393677	+	0.919249i	$0.628797\pi$
$110$		0			0
$111$	−806.407	+	1396.74i	−0.689556	+	1.19435i
$112$		0			0
$113$	167.441	−	290.017i	0.139394	−	0.241438i	−0.787873	−	0.615837i	$-0.788818\pi$
$113$	167.441	−	290.017i	0.139394	−	0.241438i	0.927267	+	0.374400i	$0.122151\pi$
$114$		0			0
$115$	6.27361	+	10.8662i	0.00508710	+	0.00881112i
$116$		0			0
$117$	−1968.78	+	1129.37i	−1.55567	+	0.892394i
$118$		0			0
$119$	9.63401	+	16.6866i	0.00742141	+	0.0128543i
$120$		0			0
$121$	−111.598	+	193.293i	−0.0838452	+	0.145224i
$122$		0			0
$123$	1347.13	−	2333.29i	0.987530	−	1.71045i
$124$		0			0
$125$	−679.806			−0.486430
$126$		0			0
$127$	310.447	+	537.709i	0.216911	+	0.375701i	0.953862	−	0.300245i	$-0.0970686\pi$
$127$	310.447	+	537.709i	0.216911	+	0.375701i	−0.736951	+	0.675946i	$0.763735\pi$
$128$		0			0
$129$	3712.44			2.53381
$130$		0			0
$131$	1331.70			0.888180			0.444090	−	0.895982i	$-0.353527\pi$
$131$	1331.70			0.888180			0.444090	+	0.895982i	$0.353527\pi$
$132$		0			0
$133$	287.766	+	498.425i	0.187612	+	0.324954i
$134$		0			0
$135$	−522.396			−0.333042
$136$		0			0
$137$	−311.008	+	538.681i	−0.193950	+	0.335932i	−0.946556	−	0.322540i	$-0.895463\pi$
$137$	−311.008	+	538.681i	−0.193950	+	0.335932i	0.752606	+	0.658471i	$0.228797\pi$
$138$		0			0
$139$	165.290	−	286.291i	0.100861	−	0.174697i	−0.811178	−	0.584799i	$-0.801173\pi$
$139$	165.290	−	286.291i	0.100861	−	0.174697i	0.912040	+	0.410102i	$0.134507\pi$
$140$		0			0
$141$	1123.00	+	1945.10i	0.670736	+	1.16175i
$142$		0			0
$143$	−5.15196	+	1847.85i	−0.00301279	+	1.08059i
$144$		0			0
$145$	−197.517	−	342.109i	−0.113123	−	0.195935i
$146$		0			0
$147$	−1092.43	+	1892.14i	−0.612939	+	1.06164i
$148$		0			0
$149$	905.269	−	1567.97i	0.497735	−	0.862102i	−0.502262	−	0.864716i	$-0.667499\pi$
$149$	905.269	−	1567.97i	0.497735	−	0.862102i	0.999997	+	0.00261337i	$0.000831864\pi$
$150$		0			0
$151$	423.239			0.228097			0.114049	−	0.993475i	$-0.463618\pi$
$151$	423.239			0.228097			0.114049	+	0.993475i	$0.463618\pi$
$152$		0			0
$153$	−48.7902	−	84.5071i	−0.0257808	−	0.0446536i
$154$		0			0
$155$	−382.292			−0.198106
$156$		0			0
$157$	1322.17			0.672105			0.336052	−	0.941843i	$-0.390908\pi$
$157$	1322.17			0.672105			0.336052	+	0.941843i	$0.390908\pi$
$158$		0			0
$159$	2660.35	+	4607.87i	1.32692	+	2.29829i
$160$		0			0
$161$	42.7283			0.0209159
$162$		0			0
$163$	−1803.20	+	3123.23i	−0.866486	+	1.50080i	−0.000922205		1.00000i	$0.500294\pi$
$163$	−1803.20	+	3123.23i	−0.866486	+	1.50080i	−0.865564	+	0.500798i	$0.833040\pi$
$164$		0			0
$165$	−480.658	+	832.524i	−0.226783	+	0.392800i
$166$		0			0
$167$	−1707.72	−	2957.85i	−0.791300	−	1.37057i	−0.925162	−	0.379571i	$-0.876071\pi$
$167$	−1707.72	−	2957.85i	−0.791300	−	1.37057i	0.133863	−	0.991000i	$-0.457262\pi$
$168$		0			0
$169$	1087.87	+	1908.75i	0.495163	+	0.868800i
$170$		0			0
$171$	−1457.35	−	2524.21i	−0.651734	−	1.12884i
$172$		0			0
$173$	−1171.11	+	2028.43i	−0.514671	+	0.891436i	0.485184	+	0.874412i	$0.338753\pi$
$173$	−1171.11	+	2028.43i	−0.514671	+	0.891436i	−0.999855	+	0.0170243i	$0.994581\pi$
$174$		0			0
$175$	−559.908	+	969.788i	−0.241857	+	0.418909i
$176$		0			0
$177$	−4497.66			−1.90997
$178$		0			0
$179$	−333.446	−	577.545i	−0.139234	−	0.241160i	0.787973	−	0.615710i	$-0.211131\pi$
$179$	−333.446	−	577.545i	−0.139234	−	0.241160i	−0.927207	+	0.374550i	$0.877797\pi$
$180$		0			0
$181$	−701.037			−0.287888			−0.143944	−	0.989586i	$-0.545978\pi$
$181$	−701.037			−0.287888			−0.143944	+	0.989586i	$0.545978\pi$
$182$		0			0
$183$	1400.93			0.565899
$184$		0			0
$185$	260.713	+	451.567i	0.103611	+	0.179459i
$186$		0			0
$187$	−79.4440			−0.0310670
$188$		0			0
$189$	−889.482	+	1540.63i	−0.342330	+	0.592933i
$190$		0			0
$191$	650.440	−	1126.59i	0.246409	−	0.426793i	−0.716118	−	0.697980i	$-0.754083\pi$
$191$	650.440	−	1126.59i	0.246409	−	0.426793i	0.962527	+	0.271186i	$0.0874159\pi$
$192$		0			0
$193$	259.667	+	449.756i	0.0968457	+	0.167742i	0.910377	−	0.413779i	$-0.135791\pi$
$193$	259.667	+	449.756i	0.0968457	+	0.167742i	−0.813532	+	0.581521i	$0.802458\pi$
$194$		0			0
$195$	−3.18664	+	1142.95i	−0.00117026	+	0.419735i
$196$		0			0
$197$	−1560.52	−	2702.91i	−0.564379	−	0.977534i	−0.997107	−	0.0760091i	$-0.975782\pi$
$197$	−1560.52	−	2702.91i	−0.564379	−	0.977534i	0.432728	−	0.901525i	$-0.357551\pi$
$198$		0			0
$199$	618.529	−	1071.32i	0.220333	−	0.381629i	−0.734576	−	0.678527i	$-0.762619\pi$
$199$	618.529	−	1071.32i	0.220333	−	0.381629i	0.954909	+	0.296898i	$0.0959521\pi$
$200$		0			0
$201$	216.677	−	375.295i	0.0760358	−	0.131698i
$202$		0			0
$203$	−1345.25			−0.465112
$204$		0			0
$205$	−435.528	−	754.356i	−0.148383	−	0.257007i
$206$		0			0
$207$	−216.392			−0.0726584
$208$		0			0
$209$	−2372.98			−0.785369
$210$		0			0
$211$	−1265.83	−	2192.49i	−0.413003	−	0.715342i	0.582214	−	0.813036i	$-0.302187\pi$
$211$	−1265.83	−	2192.49i	−0.413003	−	0.715342i	−0.995217	+	0.0976940i	$0.968853\pi$
$212$		0			0
$213$	2431.38			0.782139
$214$		0			0
$215$	600.118	−	1039.44i	0.190362	−	0.329716i
$216$		0			0
$217$	−650.928	+	1127.44i	−0.203631	+	0.352699i
$218$		0			0
$219$	2031.05	+	3517.88i	0.626691	+	1.08546i
$220$		0			0
$221$	−81.9315	+	46.9991i	−0.0249381	+	0.0143054i
$222$		0			0
$223$	−597.766	−	1035.36i	−0.179504	−	0.310910i	0.762207	−	0.647333i	$-0.224116\pi$
$223$	−597.766	−	1035.36i	−0.179504	−	0.310910i	−0.941711	+	0.336424i	$0.890783\pi$
$224$		0			0
$225$	2835.58	−	4911.37i	0.840173	−	1.45522i
$226$		0			0
$227$	−434.596	+	752.742i	−0.127071	+	0.220094i	−0.922541	−	0.385900i	$-0.873891\pi$
$227$	−434.596	+	752.742i	−0.127071	+	0.220094i	0.795469	+	0.605994i	$0.207224\pi$
$228$		0			0
$229$	4684.64			1.35183			0.675916	−	0.736978i	$-0.263748\pi$
$229$	4684.64			1.35183			0.675916	+	0.736978i	$0.263748\pi$
$230$		0			0
$231$	1636.83	+	2835.08i	0.466215	+	0.807508i
$232$		0			0
$233$	−4868.99			−1.36900			−0.684502	−	0.729011i	$-0.739980\pi$
$233$	−4868.99			−1.36900			−0.684502	+	0.729011i	$0.739980\pi$
$234$		0			0
$235$	726.137			0.201566
$236$		0			0
$237$	−163.002	−	282.328i	−0.0446756	−	0.0773803i
$238$		0			0
$239$	−4807.53			−1.30114			−0.650572	−	0.759444i	$-0.725471\pi$
$239$	−4807.53			−1.30114			−0.650572	+	0.759444i	$0.725471\pi$
$240$		0			0
$241$	−2937.98	+	5088.73i	−0.785278	+	1.36014i	0.143555	+	0.989642i	$0.454147\pi$
$241$	−2937.98	+	5088.73i	−0.785278	+	1.36014i	−0.928833	+	0.370499i	$0.879187\pi$
$242$		0			0
$243$	−1172.61	+	2031.03i	−0.309561	+	0.536175i
$244$		0			0
$245$	353.184	+	611.733i	0.0920984	+	0.159519i
$246$		0			0
$247$	−2447.28	+	1403.85i	−0.630431	+	0.361640i
$248$		0			0
$249$	330.691	+	572.774i	0.0841635	+	0.145775i
$250$		0			0
$251$	2903.13	−	5028.38i	0.730057	−	1.26450i	−0.226802	−	0.973941i	$-0.572827\pi$
$251$	2903.13	−	5028.38i	0.730057	−	1.26450i	0.956858	−	0.290554i	$-0.0938397\pi$
$252$		0			0
$253$	−88.0866	+	152.570i	−0.0218891	+	0.0379131i
$254$		0			0
$255$	−49.1385			−0.0120673
$256$		0			0
$257$	597.930	+	1035.65i	0.145128	+	0.251369i	0.929421	−	0.369022i	$-0.120307\pi$
$257$	597.930	+	1035.65i	0.145128	+	0.251369i	−0.784293	+	0.620391i	$0.786974\pi$
$258$		0			0
$259$	1775.66			0.426001
$260$		0			0
$261$	6812.83			1.61572
$262$		0			0
$263$	117.092	+	202.810i	0.0274533	+	0.0475505i	0.879426	−	0.476036i	$-0.157927\pi$
$263$	117.092	+	202.810i	0.0274533	+	0.0475505i	−0.851972	+	0.523587i	$0.824594\pi$
$264$		0			0
$265$	1720.19			0.398757
$266$		0			0
$267$	880.650	−	1525.33i	0.201854	−	0.349621i
$268$		0			0
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	−0.674285	−	0.738471i	$-0.735548\pi$
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	0.976677	+	0.214712i	$0.0688813\pi$
$270$		0			0
$271$	2850.64	+	4937.45i	0.638982	+	1.10675i	0.985657	+	0.168763i	$0.0539774\pi$
$271$	2850.64	+	4937.45i	0.638982	+	1.10675i	−0.346675	+	0.937985i	$0.612689\pi$
$272$		0			0
$273$	3365.31	+	1955.50i	0.746073	+	0.433524i
$274$		0			0
$275$	−2308.56	−	3998.54i	−0.506223	−	0.876804i
$276$		0			0
$277$	3576.24	−	6194.24i	0.775725	−	1.34359i	−0.158662	−	0.987333i	$-0.550718\pi$
$277$	3576.24	−	6194.24i	0.775725	−	1.34359i	0.934386	−	0.356261i	$-0.115949\pi$
$278$		0			0
$279$	3296.54	−	5709.78i	0.707380	−	1.22522i
$280$		0			0
$281$	−6132.87			−1.30198			−0.650990	−	0.759086i	$-0.725646\pi$
$281$	−6132.87			−1.30198			−0.650990	+	0.759086i	$0.725646\pi$
$282$		0			0
$283$	1688.58	+	2924.70i	0.354683	+	0.614330i	0.987064	−	0.160328i	$-0.0512553\pi$
$283$	1688.58	+	2924.70i	0.354683	+	0.614330i	−0.632380	+	0.774658i	$0.717922\pi$
$284$		0			0
$285$	−1467.76			−0.305061
$286$		0			0
$287$	−2966.29			−0.610086
$288$		0			0
$289$	2454.47	+	4251.27i	0.499587	+	0.865310i
$290$		0			0
$291$	10199.0			2.05455
$292$		0			0
$293$	2352.38	−	4074.45i	0.469037	−	0.812395i	−0.530337	−	0.847787i	$-0.677935\pi$
$293$	2352.38	−	4074.45i	0.469037	−	0.812395i	0.999374	+	0.0353917i	$0.0112679\pi$
$294$		0			0
$295$	−727.050	+	1259.29i	−0.143493	+	0.248537i
$296$		0			0
$297$	−3667.43	−	6352.18i	−0.716518	−	1.24105i
$298$		0			0
$299$	−0.583991	+	209.460i	−0.000112953	+	0.0405129i
$300$		0			0
$301$	−2043.64	−	3539.69i	−0.391341	−	0.677822i
$302$		0			0
$303$	4215.09	−	7300.74i	0.799176	−	1.38421i
$304$		0			0
$305$	226.461	−	392.242i	0.0425151	−	0.0736384i
$306$		0			0
$307$	−5130.49			−0.953787			−0.476894	−	0.878961i	$-0.658237\pi$
$307$	−5130.49			−0.953787			−0.476894	+	0.878961i	$0.658237\pi$
$308$		0			0
$309$	8249.11	+	14287.9i	1.51869	+	2.63045i
$310$		0			0
$311$	−7948.94			−1.44933			−0.724667	−	0.689099i	$-0.758006\pi$
$311$	−7948.94			−1.44933			−0.724667	+	0.689099i	$0.758006\pi$
$312$		0			0
$313$	−8521.87			−1.53893			−0.769465	−	0.638689i	$-0.779477\pi$
$313$	−8521.87			−1.53893			−0.769465	+	0.638689i	$0.779477\pi$
$314$		0			0
$315$	650.000	+	1125.83i	0.116265	+	0.201376i
$316$		0			0
$317$	−6662.46			−1.18044			−0.590222	−	0.807241i	$-0.700960\pi$
$317$	−6662.46			−1.18044			−0.590222	+	0.807241i	$0.700960\pi$
$318$		0			0
$319$	2773.29	−	4803.49i	0.486754	−	0.843083i
$320$		0			0
$321$	8278.62	−	14339.0i	1.43946	−	2.49322i
$322$		0			0
$323$	−60.6483	−	105.046i	−0.0104476	−	0.0180957i
$324$		0			0
$325$	−4746.38	−	2758.00i	−0.810097	−	0.470726i
$326$		0			0
$327$	−3890.74	−	6738.96i	−0.657977	−	1.13965i
$328$		0			0
$329$	1236.39	−	2141.49i	0.207187	−	0.358858i
$330$		0			0
$331$	−1955.89	+	3387.69i	−0.324789	+	0.562551i	−0.981470	−	0.191618i	$-0.938627\pi$
$331$	−1955.89	+	3387.69i	−0.324789	+	0.562551i	0.656681	+	0.754169i	$0.271960\pi$
$332$		0			0
$333$	−8992.61			−1.47986
$334$		0			0
$335$	−70.0519	−	121.333i	−0.0114249	−	0.0197885i
$336$		0			0
$337$	−627.211			−0.101384			−0.0506919	−	0.998714i	$-0.516143\pi$
$337$	−627.211			−0.101384			−0.0506919	+	0.998714i	$0.516143\pi$
$338$		0			0
$339$	2908.34			0.465957
$340$		0			0
$341$	−2683.84	−	4648.56i	−0.426212	−	0.738221i
$342$		0			0
$343$	5685.08			0.894943
$344$		0			0
$345$	−54.4841	+	94.3693i	−0.00850240	+	0.0147266i
$346$		0			0
$347$	−1911.51	+	3310.83i	−0.295721	+	0.512204i	−0.975152	−	0.221535i	$-0.928893\pi$
$347$	−1911.51	+	3310.83i	−0.295721	+	0.512204i	0.679431	+	0.733739i	$0.262227\pi$
$348$		0			0
$349$	−1705.33	−	2953.72i	−0.261560	−	0.453035i	0.705097	−	0.709111i	$-0.250904\pi$
$349$	−1705.33	−	2953.72i	−0.261560	−	0.453035i	−0.966657	+	0.256076i	$0.917570\pi$
$350$		0			0
$351$	−7540.21	−	4381.42i	−1.14663	−	0.666275i
$352$		0			0
$353$	2793.82	+	4839.03i	0.421246	+	0.729620i	0.996062	−	0.0886632i	$-0.0282595\pi$
$353$	2793.82	+	4839.03i	0.421246	+	0.729620i	−0.574815	+	0.818283i	$0.694926\pi$
$354$		0			0
$355$	393.035	−	680.757i	0.0587609	−	0.101777i
$356$		0			0
$357$	−83.6680	+	144.917i	−0.0124039	+	0.0214841i
$358$		0			0
$359$	−2230.14			−0.327861			−0.163931	−	0.986472i	$-0.552417\pi$
$359$	−2230.14			−0.327861			−0.163931	+	0.986472i	$0.552417\pi$
$360$		0			0
$361$	1617.95	+	2802.37i	0.235887	+	0.408568i
$362$		0			0
$363$	−1938.38			−0.280272
$364$		0			0
$365$	1313.28			0.188330
$366$		0			0
$367$	−4349.57	−	7533.68i	−0.618653	−	1.07154i	−0.989732	−	0.142938i	$-0.954345\pi$
$367$	−4349.57	−	7533.68i	−0.618653	−	1.07154i	0.371078	−	0.928602i	$-0.378988\pi$
$368$		0			0
$369$	15022.4			2.11934
$370$		0			0
$371$	2928.97	−	5073.13i	0.409878	−	0.709929i
$372$		0			0
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	0.181340	+	0.983420i	$0.441956\pi$
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	−0.942337	+	0.334665i	$0.891377\pi$
$374$		0			0
$375$	−2951.94	−	5112.91i	−0.406500	−	0.704079i
$376$		0			0
$377$	18.3862	−	6594.57i	0.00251177	−	0.900895i
$378$		0			0
$379$	6955.06	+	12046.5i	0.942631	+	1.63269i	0.760426	+	0.649425i	$0.224990\pi$
$379$	6955.06	+	12046.5i	0.942631	+	1.63269i	0.182206	+	0.983260i	$0.441676\pi$
$380$		0			0
$381$	−2696.12	+	4669.82i	−0.362537	+	0.627932i
$382$		0			0
$383$	−247.377	+	428.469i	−0.0330035	+	0.0571638i	−0.882055	−	0.471146i	$-0.843841\pi$
$383$	−247.377	+	428.469i	−0.0330035	+	0.0571638i	0.849052	+	0.528310i	$0.177174\pi$
$384$		0			0
$385$	1058.38			0.140104
$386$		0			0
$387$	10349.8	+	17926.3i	1.35945	+	2.35464i
$388$		0			0
$389$	−4140.47			−0.539666			−0.269833	−	0.962907i	$-0.586968\pi$
$389$	−4140.47			−0.539666			−0.269833	+	0.962907i	$0.586968\pi$
$390$		0			0
$391$	−9.00524			−0.00116474
$392$		0			0
$393$	5782.70	+	10015.9i	0.742236	+	1.28559i
$394$		0			0
$395$	−105.398			−0.0134256
$396$		0			0
$397$	940.896	−	1629.68i	0.118948	−	0.206023i	−0.800403	−	0.599462i	$-0.795381\pi$
$397$	940.896	−	1629.68i	0.118948	−	0.206023i	0.919351	+	0.393439i	$0.128715\pi$
$398$		0			0
$399$	−2499.15	+	4328.65i	−0.313568	+	0.543116i
$400$		0			0
$401$	−210.883	−	365.259i	−0.0262618	−	0.0454867i	0.852596	−	0.522571i	$-0.175027\pi$
$401$	−210.883	−	365.259i	−0.0262618	−	0.0454867i	−0.878858	+	0.477084i	$0.841694\pi$
$402$		0			0
$403$	−5517.96	−	3206.34i	−0.682058	−	0.396326i
$404$		0			0
$405$	−432.938	−	749.871i	−0.0531182	−	0.0920034i
$406$		0			0
$407$	−3660.62	+	6340.37i	−0.445823	+	0.772188i
$408$		0			0
$409$	−1275.11	+	2208.55i	−0.154157	+	0.267007i	−0.932752	−	0.360520i	$-0.882599\pi$
$409$	−1275.11	+	2208.55i	−0.154157	+	0.267007i	0.778595	+	0.627527i	$0.215933\pi$
$410$		0			0
$411$	−5401.99			−0.648322
$412$		0			0
$413$	2475.89	+	4288.37i	0.294990	+	0.510937i
$414$		0			0
$415$	213.826			0.0252923
$416$		0			0
$417$	2870.98			0.337152
$418$		0			0
$419$	6192.41	+	10725.6i	0.722002	+	1.25054i	0.960196	+	0.279327i	$0.0901112\pi$
$419$	6192.41	+	10725.6i	0.722002	+	1.25054i	−0.238194	+	0.971218i	$0.576555\pi$
$420$		0			0
$421$	10463.0			1.21124			0.605622	−	0.795752i	$-0.292924\pi$
$421$	10463.0			1.21124			0.605622	+	0.795752i	$0.292924\pi$
$422$		0			0
$423$	−6261.55	+	10845.3i	−0.719733	+	1.24661i
$424$		0			0
$425$	118.004	−	204.389i	0.0134683	−	0.0233278i
$426$		0			0
$427$	−771.190	−	1335.74i	−0.0874016	−	0.151384i
$428$		0			0
$429$	−13920.3	+	7985.22i	−1.56661	+	0.898671i
$430$		0			0
$431$	−1981.19	−	3431.53i	−0.221417	−	0.383506i	0.733821	−	0.679342i	$-0.237735\pi$
$431$	−1981.19	−	3431.53i	−0.221417	−	0.383506i	−0.955238	+	0.295837i	$0.904402\pi$
$432$		0			0
$433$	4197.07	−	7269.54i	0.465816	−	0.806817i	−0.533422	−	0.845849i	$-0.679094\pi$
$433$	4197.07	−	7269.54i	0.465816	−	0.806817i	0.999238	+	0.0390321i	$0.0124275\pi$
$434$		0			0
$435$	1715.36	−	2971.10i	0.189070	−	0.327479i
$436$		0			0
$437$	−268.984			−0.0294446
$438$		0			0
$439$	5087.26	+	8811.39i	0.553079	+	0.957960i	0.998050	+	0.0624156i	$0.0198804\pi$
$439$	5087.26	+	8811.39i	0.553079	+	0.957960i	−0.444972	+	0.895545i	$0.646786\pi$
$440$		0			0
$441$	−12182.2			−1.31543
$442$		0			0
$443$	5880.74			0.630705			0.315353	−	0.948975i	$-0.397877\pi$
$443$	5880.74			0.630705			0.315353	+	0.948975i	$0.397877\pi$
$444$		0			0
$445$	−284.716	−	493.142i	−0.0303299	−	0.0525330i
$446$		0			0
$447$	15723.9			1.66379
$448$		0			0
$449$	−5332.43	+	9236.05i	−0.560475	+	0.970771i	0.436980	+	0.899471i	$0.356048\pi$
$449$	−5332.43	+	9236.05i	−0.560475	+	0.970771i	−0.997455	+	0.0712996i	$0.977285\pi$
$450$		0			0
$451$	6115.16	−	10591.8i	0.638474	−	1.10587i
$452$		0			0
$453$	1837.84	+	3183.23i	0.190617	+	0.330158i
$454$		0			0
$455$	1091.52	−	626.138i	0.112464	−	0.0645138i
$456$		0			0
$457$	7414.43	+	12842.2i	0.758933	+	1.31451i	0.943395	+	0.331671i	$0.107612\pi$
$457$	7414.43	+	12842.2i	0.758933	+	1.31451i	−0.184462	+	0.982840i	$0.559054\pi$
$458$		0			0
$459$	187.464	−	324.697i	0.0190633	−	0.0330186i
$460$		0			0
$461$	4855.85	−	8410.58i	0.490585	−	0.849717i	−0.509357	−	0.860555i	$-0.670117\pi$
$461$	4855.85	−	8410.58i	0.490585	−	0.849717i	0.999941	+	0.0108381i	$0.00344995\pi$
$462$		0			0
$463$	−11353.5			−1.13962			−0.569809	−	0.821777i	$-0.692983\pi$
$463$	−11353.5			−1.13962			−0.569809	+	0.821777i	$0.692983\pi$
$464$		0			0
$465$	−1660.04	−	2875.27i	−0.165554	−	0.286747i
$466$		0			0
$467$	−6451.31			−0.639252			−0.319626	−	0.947544i	$-0.603557\pi$
$467$	−6451.31			−0.639252			−0.319626	+	0.947544i	$0.603557\pi$
$468$		0			0
$469$	−477.109			−0.0469741
$470$		0			0
$471$	5741.29	+	9944.20i	0.561666	+	0.972833i
$472$		0			0
$473$	16852.3			1.63820
$474$		0			0
$475$	3524.75	−	6105.05i	0.340477	−	0.589724i
$476$		0			0
$477$	−14833.4	+	25692.2i	−1.42385	+	2.46618i
$478$		0			0
$479$	−4783.23	−	8284.79i	−0.456266	−	0.790275i	0.542494	−	0.840059i	$-0.317480\pi$
$479$	−4783.23	−	8284.79i	−0.456266	−	0.790275i	−0.998760	+	0.0497842i	$0.984147\pi$
$480$		0			0
$481$	−24.2689	+	8704.52i	−0.00230056	+	0.825139i
$482$		0			0
$483$	185.540	+	321.365i	0.0174790	+	0.0302746i
$484$		0			0
$485$	1648.67	−	2855.59i	0.154356	−	0.267352i
$486$		0			0
$487$	2458.56	−	4258.35i	0.228764	−	0.396230i	−0.728678	−	0.684856i	$-0.759865\pi$
$487$	2458.56	−	4258.35i	0.228764	−	0.396230i	0.957442	+	0.288626i	$0.0931984\pi$
$488$		0			0
$489$	−31320.3			−2.89643
$490$		0			0
$491$	1475.41	+	2555.49i	0.135610	+	0.234883i	0.925830	−	0.377940i	$-0.123367\pi$
$491$	1475.41	+	2555.49i	0.135610	+	0.234883i	−0.790220	+	0.612823i	$0.790034\pi$
$492$		0			0
$493$	283.519			0.0259007
$494$		0			0
$495$	−5360.04			−0.486699
$496$		0			0
$497$	−1338.44	−	2318.25i	−0.120799	−	0.209231i
$498$		0			0
$499$	−13430.1			−1.20484			−0.602418	−	0.798180i	$-0.705796\pi$
$499$	−13430.1			−1.20484			−0.602418	+	0.798180i	$0.705796\pi$
$500$		0			0
$501$	14830.9	−	25687.9i	1.32255	−	2.29072i
$502$		0			0
$503$	660.143	−	1143.40i	0.0585175	−	0.101355i	−0.835283	−	0.549821i	$-0.814696\pi$
$503$	660.143	−	1143.40i	0.0585175	−	0.101355i	0.893800	+	0.448466i	$0.148029\pi$
$504$		0			0
$505$	−1362.74	−	2360.34i	−0.120082	−	0.207988i
$506$		0			0
$507$	−9632.09	+	16470.5i	−0.843740	+	1.44276i
$508$		0			0
$509$	−10458.2	−	18114.2i	−0.910713	−	1.57740i	−0.813060	−	0.582180i	$-0.802200\pi$
$509$	−10458.2	−	18114.2i	−0.910713	−	1.57740i	−0.0976524	−	0.995221i	$-0.531133\pi$
$510$		0			0
$511$	2236.12	−	3873.08i	0.193582	−	0.335293i
$512$		0			0
$513$	5599.50	−	9698.62i	0.481918	−	0.834707i
$514$		0			0
$515$	5333.90			0.456388
$516$		0			0
$517$	5097.77	+	8829.60i	0.433655	+	0.751113i
$518$		0			0
$519$	−20341.4			−1.72040
$520$		0			0
$521$	−10104.2			−0.849661			−0.424831	−	0.905273i	$-0.639666\pi$
$521$	−10104.2			−0.849661			−0.424831	+	0.905273i	$0.639666\pi$
$522$		0			0
$523$	3565.61	+	6175.82i	0.298113	+	0.516347i	0.975704	−	0.219092i	$-0.0703093\pi$
$523$	3565.61	+	6175.82i	0.298113	+	0.516347i	−0.677591	+	0.735439i	$0.736976\pi$
$524$		0			0
$525$	−9725.21			−0.808463
$526$		0			0
$527$	137.187	−	237.615i	0.0113396	−	0.0196407i
$528$		0			0
$529$	6073.52	−	10519.6i	0.499179	−	0.864604i
$530$		0			0
$531$	−12538.9	−	21717.9i	−1.02475	−	1.77491i
$532$		0			0
$533$	40.5420	−	14541.1i	0.00329469	−	1.18170i
$534$		0			0
$535$	−2676.49	−	4635.82i	−0.216289	−	0.374624i
$536$		0			0
$537$	2895.86	−	5015.78i	0.232711	−	0.403067i
$538$		0			0
$539$	−4958.99	+	8589.22i	−0.396287	+	0.686390i
$540$		0			0
$541$	16831.7			1.33762			0.668809	−	0.743435i	$-0.266805\pi$
$541$	16831.7			1.33762			0.668809	+	0.743435i	$0.266805\pi$
$542$		0			0
$543$	−3044.13	−	5272.59i	−0.240582	−	0.416701i
$544$		0			0
$545$	−2515.77			−0.197731
$546$		0			0
$547$	9560.55			0.747312			0.373656	−	0.927567i	$-0.378104\pi$
$547$	9560.55			0.747312			0.373656	+	0.927567i	$0.378104\pi$
$548$		0			0
$549$	3905.59	+	6764.69i	0.303619	+	0.525883i
$550$		0			0
$551$	8468.64			0.654766
$552$		0			0
$553$	−179.460	+	310.834i	−0.0138000	+	0.0239024i
$554$		0			0
$555$	−2264.20	+	3921.71i	−0.173171	+	0.299941i
$556$		0			0
$557$	11414.0	+	19769.5i	0.868267	+	1.50388i	0.863766	+	0.503893i	$0.168099\pi$
$557$	11414.0	+	19769.5i	0.868267	+	1.50388i	0.00450060	+	0.999990i	$0.498567\pi$
$558$		0			0
$559$	17380.0	−	9969.82i	1.31502	−	0.754344i
$560$		0			0
$561$	−344.972	−	597.509i	−0.0259621	−	0.0449677i
$562$		0			0
$563$	10814.9	−	18731.9i	0.809578	−	1.40223i	−0.103579	−	0.994621i	$-0.533029\pi$
$563$	10814.9	−	18731.9i	0.809578	−	1.40223i	0.913157	−	0.407609i	$-0.133637\pi$
$564$		0			0
$565$	470.136	−	814.299i	0.0350066	−	0.0606333i
$566$		0			0
$567$	−2948.65			−0.218398
$568$		0			0
$569$	5294.93	+	9171.09i	0.390114	+	0.675698i	0.992464	−	0.122534i	$-0.0391022\pi$
$569$	5294.93	+	9171.09i	0.390114	+	0.675698i	−0.602350	+	0.798232i	$0.705769\pi$
$570$		0			0
$571$	1757.27			0.128791			0.0643954	−	0.997924i	$-0.479488\pi$
$571$	1757.27			0.128791			0.0643954	+	0.997924i	$0.479488\pi$
$572$		0			0
$573$	11297.7			0.823679
$574$		0			0
$575$	−261.683	−	453.247i	−0.0189790	−	0.0328726i
$576$		0			0
$577$	−13580.6			−0.979840			−0.489920	−	0.871767i	$-0.662974\pi$
$577$	−13580.6			−0.979840			−0.489920	+	0.871767i	$0.662974\pi$
$578$		0			0
$579$	−2255.12	+	3905.98i	−0.161864	+	0.280357i
$580$		0			0
$581$	364.081	−	630.607i	0.0259977	−	0.0450293i
$582$		0			0
$583$	12076.5	+	20917.0i	0.857900	+	1.48593i
$584$		0			0
$585$	−5527.86	+	3171.00i	−0.390682	+	0.224110i
$586$		0			0
$587$	−478.663	−	829.068i	−0.0336568	−	0.0582952i	0.848706	−	0.528864i	$-0.177382\pi$
$587$	−478.663	−	829.068i	−0.0336568	−	0.0582952i	−0.882363	+	0.470569i	$0.844049\pi$
$588$		0			0
$589$	4097.75	−	7097.50i	0.286663	−	0.496515i
$590$		0			0
$591$	13552.6	−	23473.8i	0.943283	−	1.63381i
$592$		0			0
$593$	6729.49			0.466015			0.233007	−	0.972475i	$-0.425143\pi$
$593$	6729.49			0.466015			0.233007	+	0.972475i	$0.425143\pi$
$594$		0			0
$595$	27.0500	+	46.8520i	0.00186377	+	0.00322814i
$596$		0			0
$597$	10743.4			0.736514
$598$		0			0
$599$	−2281.52			−0.155626			−0.0778132	−	0.996968i	$-0.524794\pi$
$599$	−2281.52			−0.155626			−0.0778132	+	0.996968i	$0.524794\pi$
$600$		0			0
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	0.736725	−	0.676192i	$-0.236371\pi$
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	−0.953962	+	0.299926i	$0.903038\pi$
$602$		0			0
$603$	2416.26			0.163180
$604$		0			0
$605$	−313.341	+	542.722i	−0.0210564	+	0.0364707i
$606$		0			0
$607$	1389.62	−	2406.89i	0.0929207	−	0.160943i	−0.815818	−	0.578308i	$-0.803713\pi$
$607$	1389.62	−	2406.89i	0.0929207	−	0.160943i	0.908739	+	0.417365i	$0.137046\pi$
$608$		0			0
$609$	−5841.50	−	10117.8i	−0.388685	−	0.673223i
$610$		0			0
$611$	10481.0	+	6090.22i	0.693969	+	0.403247i
$612$		0			0
$613$	−11310.4	−	19590.2i	−0.745226	−	1.29077i	−0.950089	−	0.311979i	$-0.899008\pi$
$613$	−11310.4	−	19590.2i	−0.745226	−	1.29077i	0.204863	−	0.978791i	$-0.434325\pi$
$614$		0			0
$615$	3782.41	−	6551.33i	0.248002	−	0.429553i
$616$		0			0
$617$	−10987.0	+	19030.1i	−0.716889	+	1.24169i	0.245337	+	0.969438i	$0.421101\pi$
$617$	−10987.0	+	19030.1i	−0.716889	+	1.24169i	−0.962226	+	0.272250i	$0.912232\pi$
$618$		0			0
$619$	−7145.19			−0.463957			−0.231979	−	0.972721i	$-0.574520\pi$
$619$	−7145.19			−0.463957			−0.231979	+	0.972721i	$0.574520\pi$
$620$		0			0
$621$	−415.715	−	720.040i	−0.0268632	−	0.0465285i
$622$		0			0
$623$	−1939.14			−0.124703
$624$		0			0
$625$	12730.8			0.814773
$626$		0			0
$627$	−10304.2	−	17847.5i	−0.656319	−	1.13678i
$628$		0			0
$629$	−374.231			−0.0237227
$630$		0			0
$631$	−9441.62	+	16353.4i	−0.595666	+	1.03172i	0.397787	+	0.917478i	$0.369778\pi$
$631$	−9441.62	+	16353.4i	−0.595666	+	1.03172i	−0.993453	+	0.114245i	$0.963555\pi$
$632$		0			0
$633$	10993.3	−	19041.0i	0.690278	−	1.19560i
$634$		0			0
$635$	871.661	+	1509.76i	0.0544737	+	0.0943512i
$636$		0			0
$637$	−32.8768	+	11791.9i	−0.00204494	+	0.733457i
$638$		0			0
$639$	6778.37	+	11740.5i	0.419637	+	0.726833i
$640$		0			0
$641$	1815.54	−	3144.61i	0.111871	−	0.193767i	−0.804653	−	0.593745i	$-0.797649\pi$
$641$	1815.54	−	3144.61i	0.111871	−	0.193767i	0.916525	+	0.399978i	$0.130982\pi$
$642$		0			0
$643$	−5385.98	+	9328.78i	−0.330330	+	0.572148i	−0.982576	−	0.185859i	$-0.940493\pi$
$643$	−5385.98	+	9328.78i	−0.330330	+	0.572148i	0.652247	+	0.758007i	$0.273827\pi$
$644$		0			0
$645$	10423.6			0.636327
$646$		0			0
$647$	7574.14	+	13118.8i	0.460232	+	0.797146i	0.998972	−	0.0453265i	$-0.0144328\pi$
$647$	7574.14	+	13118.8i	0.460232	+	0.797146i	−0.538740	+	0.842472i	$0.681099\pi$
$648$		0			0
$649$	−20416.7			−1.23487
$650$		0			0
$651$	−11306.2			−0.680682
$652$		0			0
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	0.734458	−	0.678654i	$-0.237436\pi$
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	−0.954961	+	0.296733i	$0.904103\pi$
$654$		0			0
$655$	3739.11			0.223052
$656$		0			0
$657$	−11324.6	+	19614.7i	−0.672471	+	1.16475i
$658$		0			0
$659$	14166.6	−	24537.3i	0.837411	−	1.45044i	−0.0546414	−	0.998506i	$-0.517402\pi$
$659$	14166.6	−	24537.3i	0.837411	−	1.45044i	0.892052	−	0.451932i	$-0.149265\pi$
$660$		0			0
$661$	−554.842	−	961.014i	−0.0326488	−	0.0565493i	0.849239	−	0.528008i	$-0.177061\pi$
$661$	−554.842	−	961.014i	−0.0326488	−	0.0565493i	−0.881888	+	0.471459i	$0.843728\pi$
$662$		0			0
$663$	−709.260	−	412.132i	−0.0415466	−	0.0241416i
$664$		0			0
$665$	807.978	+	1399.46i	0.0471159	+	0.0816071i
$666$		0			0
$667$	314.362	−	544.491i	0.0182491	−	0.0316083i
$668$		0			0
$669$	5191.39	−	8991.75i	0.300016	−	0.519643i
$670$		0			0
$671$	6359.39			0.365874
$672$		0			0
$673$	−10489.5	−	18168.4i	−0.600806	−	1.04063i	−0.992699	−	0.120616i	$-0.961513\pi$
$673$	−10489.5	−	18168.4i	−0.600806	−	1.04063i	0.391893	−	0.920011i	$-0.371820\pi$
$674$		0			0
$675$	21790.0			1.24251
$676$		0			0
$677$	30941.9			1.75656			0.878282	−	0.478142i	$-0.158690\pi$
$677$	30941.9			1.75656			0.878282	+	0.478142i	$0.158690\pi$
$678$		0			0
$679$	−5614.39	−	9724.41i	−0.317320	−	0.549615i
$680$		0			0
$681$	−7548.64			−0.424764
$682$		0			0
$683$	2713.11	−	4699.24i	0.151997	−	0.263267i	−0.779964	−	0.625824i	$-0.784763\pi$
$683$	2713.11	−	4699.24i	0.151997	−	0.263267i	0.931962	+	0.362557i	$0.118096\pi$
$684$		0			0
$685$	−873.236	+	1512.49i	−0.0487075	+	0.0843638i
$686$		0			0
$687$	20342.2	+	35233.8i	1.12970	+	1.95670i
$688$		0			0
$689$	24829.1	+	14427.5i	1.37288	+	0.797744i
$690$		0			0
$691$	−16896.3	−	29265.3i	−0.930199	−	1.61115i	−0.782979	−	0.622048i	$-0.786301\pi$
$691$	−16896.3	−	29265.3i	−0.930199	−	1.61115i	−0.147219	−	0.989104i	$-0.547032\pi$
$692$		0			0
$693$	−9126.53	+	15807.6i	−0.500272	+	0.866496i
$694$		0			0
$695$	464.096	−	803.838i	0.0253297	−	0.0438724i
$696$		0			0
$697$	625.164			0.0339738
$698$		0			0
$699$	−21142.8	−	36620.3i	−1.14405	−	1.98156i
$700$		0			0
$701$	6905.96			0.372089			0.186045	−	0.982541i	$-0.440433\pi$
$701$	6905.96			0.372089			0.186045	+	0.982541i	$0.440433\pi$
$702$		0			0
$703$	−11178.2			−0.599707
$704$		0			0
$705$	3153.12	+	5461.37i	0.168445	+	0.291755i
$706$		0			0
$707$	−9281.37			−0.493723
$708$		0			0
$709$	1003.56	−	1738.22i	0.0531589	−	0.0920739i	−0.838221	−	0.545330i	$-0.816404\pi$
$709$	1003.56	−	1738.22i	0.0531589	−	0.0920739i	0.891380	+	0.453256i	$0.149738\pi$
$710$		0			0
$711$	908.854	−	1574.18i	0.0479391	−	0.0830329i
$712$		0			0
$713$	−304.222	−	526.929i	−0.0159793	−	0.0276769i
$714$		0			0
$715$	−14.4655	+	5188.32i	−0.000756613	+	0.271374i
$716$		0			0
$717$	−20875.9	−	36158.1i	−1.08734	−	1.88333i
$718$		0			0
$719$	−6393.72	+	11074.3i	−0.331635	+	0.574409i	−0.982833	−	0.184499i	$-0.940934\pi$
$719$	−6393.72	+	11074.3i	−0.331635	+	0.574409i	0.651198	+	0.758908i	$0.274267\pi$
$720$		0			0
$721$	9082.03	−	15730.5i	0.469116	−	0.812532i
$722$		0			0
$723$	−51030.7			−2.62497
$724$		0			0
$725$	8238.74	+	14269.9i	0.422040	+	0.730995i
$726$		0			0
$727$	6090.70			0.310717			0.155359	−	0.987858i	$-0.450347\pi$
$727$	6090.70			0.310717			0.155359	+	0.987858i	$0.450347\pi$
$728$		0			0
$729$	−28693.9			−1.45780
$730$		0			0
$731$	430.710	+	746.011i	0.0217926	+	0.0377459i
$732$		0			0
$733$	−38846.5			−1.95747			−0.978737	−	0.205117i	$-0.934243\pi$
$733$	−38846.5			−1.95747			−0.978737	+	0.205117i	$0.934243\pi$
$734$		0			0
$735$	−3067.28	+	5312.69i	−0.153930	+	0.266614i
$736$		0			0
$737$	983.585	−	1703.62i	0.0491599	−	0.0851474i
$738$		0			0
$739$	7228.77	+	12520.6i	0.359830	+	0.623245i	0.987932	−	0.154887i	$-0.0495012\pi$
$739$	7228.77	+	12520.6i	0.359830	+	0.623245i	−0.628102	+	0.778131i	$0.716168\pi$
$740$		0			0
$741$	−21185.4	−	12310.3i	−1.05029	−	0.610297i
$742$		0			0
$743$	−638.901	−	1106.61i	−0.0315464	−	0.0546400i	0.849821	−	0.527071i	$-0.176710\pi$
$743$	−638.901	−	1106.61i	−0.0315464	−	0.0546400i	−0.881368	+	0.472431i	$0.843377\pi$
$744$		0			0
$745$	2541.78	−	4402.49i	0.124998	−	0.216503i
$746$		0			0
$747$	−1843.84	+	3193.63i	−0.0903116	+	0.156424i
$748$		0			0
$749$	−18229.0			−0.889285
$750$		0			0
$751$	−6503.93	−	11265.1i	−0.316021	−	0.547364i	0.663633	−	0.748058i	$-0.269014\pi$
$751$	−6503.93	−	11265.1i	−0.316021	−	0.547364i	−0.979654	+	0.200694i	$0.935680\pi$
$752$		0			0
$753$	50425.5			2.44038
$754$		0			0
$755$	1188.35			0.0572829
$756$		0			0
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	0.965551	−	0.260212i	$-0.0837926\pi$
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	−0.708126	+	0.706086i	$0.750459\pi$
$758$		0			0
$759$	−1530.00			−0.0731694
$760$		0			0
$761$	−6810.90	+	11796.8i	−0.324435	+	0.561938i	−0.981398	−	0.191985i	$-0.938508\pi$
$761$	−6810.90	+	11796.8i	−0.324435	+	0.561938i	0.656963	+	0.753923i	$0.271841\pi$
$762$		0			0
$763$	−4283.59	+	7419.40i	−0.203246	+	0.352032i
$764$		0			0
$765$	−136.991	−	237.276i	−0.00647443	−	0.0112140i
$766$		0			0
$767$	−21056.0	+	12078.5i	−0.991250	+	0.568619i
$768$		0			0
$769$	4247.57	+	7357.01i	0.199183	+	0.344994i	0.948264	−	0.317484i	$-0.102838\pi$
$769$	4247.57	+	7357.01i	0.199183	+	0.344994i	−0.749081	+	0.662478i	$0.769505\pi$
$770$		0			0
$771$	−5192.82	+	8994.22i	−0.242561	+	0.420128i
$772$		0			0
$773$	−17131.3	+	29672.2i	−0.797113	+	1.38064i	0.124375	+	0.992235i	$0.460307\pi$
$773$	−17131.3	+	29672.2i	−0.797113	+	1.38064i	−0.921489	+	0.388405i	$0.873026\pi$
$774$		0			0
$775$	15946.0			0.739094
$776$		0			0
$777$	7710.50	+	13355.0i	0.356001	+	0.616612i
$778$		0			0
$779$	18673.5			0.858854
$780$		0			0
$781$	11037.1			0.505681
$782$		0			0
$783$	13088.3	+	22669.5i	0.597364	+	1.03467i
$784$		0			0
$785$	3712.33			0.168788
$786$		0			0
$787$	−6321.29	+	10948.8i	−0.286315	+	0.495912i	−0.972927	−	0.231112i	$-0.925764\pi$
$787$	−6321.29	+	10948.8i	−0.286315	+	0.495912i	0.686612	+	0.727024i	$0.259097\pi$
$788$		0			0
$789$	−1016.91	+	1761.33i	−0.0458844	+	0.0794741i
$790$		0			0
$791$	−1601.00	−	2773.01i	−0.0719658	−	0.124648i
$792$		0			0
$793$	6558.51	−	3762.22i	0.293694	−	0.168474i
$794$		0			0
$795$	7469.65	+	12937.8i	0.333234	+	0.577178i
$796$		0			0
$797$	−9542.18	+	16527.5i	−0.424092	+	0.734549i	−0.996335	−	0.0855350i	$-0.972740\pi$
$797$	−9542.18	+	16527.5i	−0.424092	+	0.734549i	0.572243	+	0.820084i	$0.306073\pi$
$798$		0			0
$799$	−260.577	+	451.333i	−0.0115376	+	0.0199837i
$800$		0			0
$801$	9820.53			0.433198
$802$		0			0
$803$	9219.77	+	15969.1i	0.405179	+	0.701790i
$804$		0			0
$805$	119.971			0.00525269
$806$		0			0
$807$	23173.0			1.01082
$808$		0			0
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	0.711874	−	0.702307i	$-0.247847\pi$
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	−0.964153	+	0.265347i	$0.914513\pi$
$810$		0			0
$811$	−9613.36			−0.416240			−0.208120	−	0.978103i	$-0.566734\pi$
$811$	−9613.36			−0.416240			−0.208120	+	0.978103i	$0.566734\pi$
$812$		0			0
$813$	−24756.8	+	42880.1i	−1.06797	+	1.84978i
$814$		0			0
$815$	−5062.95	+	8769.29i	−0.217604	+	0.376901i
$816$		0			0
$817$	12865.2	+	22283.2i	0.550914	+	0.954211i
$818$		0			0
$819$	−60.5065	+	21701.8i	−0.00258153	+	0.925913i
$820$		0			0
$821$	13240.7	+	22933.6i	0.562856	+	0.974895i	0.997246	+	0.0741699i	$0.0236307\pi$
$821$	13240.7	+	22933.6i	0.562856	+	0.974895i	−0.434390	+	0.900725i	$0.643036\pi$
$822$		0			0
$823$	6907.25	−	11963.7i	0.292553	−	0.506718i	−0.681859	−	0.731483i	$-0.738828\pi$
$823$	6907.25	−	11963.7i	0.292553	−	0.506718i	0.974413	+	0.224766i	$0.0721617\pi$
$824$		0			0
$825$	20049.0	−	34726.0i	0.846082	−	1.46546i
$826$		0			0
$827$	44401.0			1.86696			0.933479	−	0.358633i	$-0.116757\pi$
$827$	44401.0			1.86696			0.933479	+	0.358633i	$0.116757\pi$
$828$		0			0
$829$	−12168.7	−	21076.8i	−0.509815	−	0.883025i	−0.999935	−	0.0113707i	$-0.996381\pi$
$829$	−12168.7	−	21076.8i	−0.509815	−	0.883025i	0.490120	−	0.871655i	$-0.336953\pi$
$830$		0			0
$831$	62116.9			2.59303
$832$		0			0
$833$	−506.966			−0.0210868
$834$		0			0
$835$	−4794.86	−	8304.95i	−0.198722	−	0.344197i
$836$		0			0
$837$	25332.2			1.04613
$838$		0			0
$839$	−12340.0	+	21373.6i	−0.507778	+	0.879497i	0.492181	+	0.870493i	$0.336200\pi$
$839$	−12340.0	+	21373.6i	−0.507778	+	0.879497i	−0.999959	+	0.00900472i	$0.997134\pi$
$840$		0			0
$841$	2297.22	−	3978.90i	0.0941907	−	0.163143i
$842$		0			0
$843$	−26631.0	−	46126.2i	−1.08804	−	1.88454i
$844$		0			0
$845$	3054.49	+	5359.33i	0.124352	+	0.218185i
$846$		0			0
$847$	1067.05	+	1848.18i	0.0432872	+	0.0749757i
$848$		0			0
$849$	−14664.7	+	25400.0i	−0.592805	+	1.02677i
$850$		0			0
$851$	−414.943	+	718.702i	−0.0167145	+	0.0289504i
$852$		0			0
$853$	−10151.7			−0.407490			−0.203745	−	0.979024i	$-0.565311\pi$
$853$	−10151.7			−0.407490			−0.203745	+	0.979024i	$0.565311\pi$
$854$		0			0
$855$	−4091.90	−	7087.39i	−0.163673	−	0.283489i
$856$		0			0
$857$	2028.92			0.0808713			0.0404357	−	0.999182i	$-0.487125\pi$
$857$	2028.92			0.0808713			0.0404357	+	0.999182i	$0.487125\pi$
$858$		0			0
$859$	−6655.76			−0.264367			−0.132184	−	0.991225i	$-0.542199\pi$
$859$	−6655.76			−0.264367			−0.132184	+	0.991225i	$0.542199\pi$
$860$		0			0
$861$	−12880.6	−	22309.9i	−0.509837	−	0.883064i
$862$		0			0
$863$	−45690.8			−1.80224			−0.901121	−	0.433568i	$-0.857254\pi$
$863$	−45690.8			−1.80224			−0.901121	+	0.433568i	$0.857254\pi$
$864$		0			0
$865$	−3288.21	+	5695.35i	−0.129251	+	0.223870i
$866$		0			0
$867$	−21316.2	+	36920.8i	−0.834991	+	1.44625i
$868$		0			0
$869$	−739.934	−	1281.60i	−0.0288844	−	0.0500292i
$870$		0			0
$871$	6.52092	−	2338.85i	0.000253677	−	0.0909861i
$872$		0			0
$873$	28433.4	+	49248.1i	1.10232	+	1.90927i
$874$		0			0
$875$	−3250.00	+	5629.17i	−0.125566	+	0.217486i
$876$		0			0
$877$	−15223.8	+	26368.3i	−0.586168	+	1.01527i	0.408560	+	0.912731i	$0.366031\pi$
$877$	−15223.8	+	26368.3i	−0.586168	+	1.01527i	−0.994729	+	0.102542i	$0.967302\pi$
$878$		0			0
$879$	40859.3			1.56786
$880$		0			0
$881$	−16271.0	−	28182.2i	−0.622230	−	1.07773i	−0.989070	−	0.147450i	$-0.952894\pi$
$881$	−16271.0	−	28182.2i	−0.622230	−	1.07773i	0.366840	−	0.930284i	$-0.380440\pi$
$882$		0			0
$883$	−27641.9			−1.05348			−0.526741	−	0.850026i	$-0.676586\pi$
$883$	−27641.9			−1.05348			−0.526741	+	0.850026i	$0.676586\pi$
$884$		0			0
$885$	−12628.4			−0.479658
$886$		0			0
$887$	20050.0	+	34727.5i	0.758976	+	1.31458i	0.943373	+	0.331733i	$0.107633\pi$
$887$	20050.0	+	34727.5i	0.758976	+	1.31458i	−0.184397	+	0.982852i	$0.559033\pi$
$888$		0			0
$889$	5936.70			0.223971
$890$		0			0
$891$	6078.80	−	10528.8i	0.228561	−	0.395879i
$892$		0			0
$893$	−7783.38	+	13481.2i	−0.291670	+	0.505186i
$894$		0			0
$895$	−936.236	−	1621.61i	−0.0349664	−	0.0605636i
$896$		0			0
$897$	−1577.91	+	905.150i	−0.0587345	+	0.0336924i
$898$		0			0
$899$	9578.06	+	16589.7i	0.355335	+	0.615458i
$900$		0			0
$901$	−617.299	+	1069.19i	−0.0228249	+	0.0395338i
$902$		0			0
$903$	17748.3	−	30741.0i	0.654072	−	1.13289i
$904$		0			0
$905$	−1968.35			−0.0722984
$906$		0			0
$907$	−18412.4	−	31891.3i	−0.674062	−	1.16751i	−0.976742	−	0.214418i	$-0.931215\pi$
$907$	−18412.4	−	31891.3i	−0.674062	−	1.16751i	0.302679	−	0.953092i	$-0.402119\pi$
$908$		0			0
$909$	47004.3			1.71511
$910$		0			0
$911$	−34520.5			−1.25545			−0.627725	−	0.778435i	$-0.716014\pi$
$911$	−34520.5			−1.25545			−0.627725	+	0.778435i	$0.716014\pi$
$912$		0			0
$913$	1501.15	+	2600.06i	0.0544148	+	0.0942491i
$914$		0			0
$915$	3933.47			0.142117
$916$		0			0
$917$	6366.58	−	11027.2i	0.229273	−	0.397112i
$918$		0			0
$919$	11761.4	−	20371.3i	0.422168	−	0.731216i	−0.573983	−	0.818867i	$-0.694603\pi$
$919$	11761.4	−	20371.3i	0.422168	−	0.731216i	0.996151	+	0.0876506i	$0.0279359\pi$
$920$		0			0
$921$	−22278.3	−	38587.1i	−0.797062	−	1.38055i
$922$		0			0
$923$	11382.6	−	6529.53i	0.405920	−	0.232852i
$924$		0			0
$925$	−10874.8	−	18835.6i	−0.386551	−	0.669526i
$926$		0			0
$927$	−45994.8	+	79665.3i	−1.62963	+	2.82260i
$928$		0			0
$929$	12281.6	−	21272.3i	0.433741	−	0.751262i	−0.563451	−	0.826150i	$-0.690527\pi$
$929$	12281.6	−	21272.3i	0.433741	−	0.751262i	0.997192	+	0.0748880i	$0.0238599\pi$
$930$		0			0
$931$	−15143.0			−0.533073
$932$		0			0
$933$	−34516.9	−	59785.0i	−1.21118	−	2.09783i
$934$		0			0
$935$	−223.060			−0.00780197
$936$		0			0
$937$	−12115.6			−0.422411			−0.211206	−	0.977442i	$-0.567739\pi$
$937$	−12115.6			−0.422411			−0.211206	+	0.977442i	$0.567739\pi$
$938$		0			0
$939$	−37004.8	−	64094.2i	−1.28605	−	2.22751i
$940$		0			0
$941$	14898.3			0.516123			0.258062	−	0.966128i	$-0.416916\pi$
$941$	14898.3			0.516123			0.258062	+	0.966128i	$0.416916\pi$
$942$		0			0
$943$	693.174	−	1200.61i	0.0239373	−	0.0414606i
$944$		0			0
$945$	−2497.46	+	4325.72i	−0.0859707	+	0.148906i
$946$		0			0
$947$	3717.16	+	6438.31i	0.127552	+	0.220926i	0.922727	−	0.385453i	$-0.125955\pi$
$947$	3717.16	+	6438.31i	0.127552	+	0.220926i	−0.795176	+	0.606379i	$0.792621\pi$
$948$		0			0
$949$	18955.8	+	11014.7i	0.648399	+	0.376767i
$950$		0			0
$951$	−28930.6	−	50109.2i	−0.986476	−	1.70863i
$952$		0			0
$953$	11764.3	−	20376.3i	0.399877	−	0.692607i	−0.593833	−	0.804588i	$-0.702386\pi$
$953$	11764.3	−	20376.3i	0.399877	−	0.692607i	0.993710	+	0.111981i	$0.0357195\pi$
$954$		0			0
$955$	1826.28	−	3163.21i	0.0618818	−	0.107182i
$956$		0			0
$957$	48170.2			1.62709
$958$		0			0
$959$	2973.72	+	5150.63i	0.100132	+	0.173433i
$960$		0			0
$961$	−11252.7			−0.377723
$962$		0			0
$963$	92318.7			3.08923
$964$		0			0
$965$	729.083	+	1262.81i	0.0243213	+	0.0421256i
$966$		0			0
$967$	−23558.0			−0.783427			−0.391713	−	0.920087i	$-0.628118\pi$
$967$	−23558.0			−0.783427			−0.391713	+	0.920087i	$0.628118\pi$
$968$		0			0
$969$	526.710	−	912.289i	0.0174617	−	0.0302445i
$970$		0			0
$971$	−131.169	+	227.191i	−0.00433513	+	0.00750866i	−0.868185	−	0.496241i	$-0.834713\pi$
$971$	−131.169	+	227.191i	−0.00433513	+	0.00750866i	0.863850	+	0.503750i	$0.168047\pi$
$972$		0			0
$973$	−1580.43	−	2737.39i	−0.0520722	−	0.0901918i
$974$		0			0
$975$	132.920	−	47674.3i	0.00436600	−	1.56595i
$976$		0			0
$977$	−16572.2	−	28703.9i	−0.542673	−	0.939936i	−0.998749	−	0.0499960i	$-0.984079\pi$
$977$	−16572.2	−	28703.9i	−0.542673	−	0.939936i	0.456077	−	0.889940i	$-0.349254\pi$
$978$		0			0
$979$	3997.64	−	6924.11i	0.130506	−	0.226042i
$980$		0			0
$981$	21693.7	−	37574.6i	0.706042	−	1.22290i
$982$		0			0
$983$	4866.80			0.157911			0.0789557	−	0.996878i	$-0.474841\pi$
$983$	4866.80			0.157911			0.0789557	+	0.996878i	$0.474841\pi$
$984$		0			0
$985$	−4381.58	−	7589.12i	−0.141735	−	0.245492i
$986$		0			0
$987$	21475.3			0.692569
$988$		0			0
$989$	1910.26			0.0614184
$990$		0			0
$991$	6266.97	+	10854.7i	0.200885	+	0.347943i	0.948814	−	0.315836i	$-0.102285\pi$
$991$	6266.97	+	10854.7i	0.200885	+	0.347943i	−0.747929	+	0.663779i	$0.768952\pi$
$992$		0			0
$993$	−33972.4			−1.08568
$994$		0			0
$995$	1736.68	−	3008.02i	0.0553332	−	0.0958399i
$996$		0			0
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	−0.836361	−	0.548180i	$-0.815321\pi$
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	0.892918	+	0.450220i	$0.148654\pi$
$998$		0			0
$999$	−17275.9	−	29922.7i	−0.547132	−	0.947660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.i.e.81.2		4
4.3	odd	2		13.4.c.b.3.2	✓	4
12.11	even	2		117.4.g.d.55.1		4
13.9	even	3	inner	208.4.i.e.113.2		4
52.3	odd	6		169.4.a.f.1.1		2
52.7	even	12		169.4.e.g.147.4		8
52.11	even	12		169.4.b.e.168.1		4
52.15	even	12		169.4.b.e.168.4		4
52.19	even	12		169.4.e.g.147.1		8
52.23	odd	6		169.4.a.j.1.2		2
52.31	even	4		169.4.e.g.23.4		8
52.35	odd	6		13.4.c.b.9.2	yes	4
52.43	odd	6		169.4.c.f.22.1		4
52.47	even	4		169.4.e.g.23.1		8
52.51	odd	2		169.4.c.f.146.1		4
156.23	even	6		1521.4.a.l.1.1		2
156.35	even	6		117.4.g.d.100.1		4
156.107	even	6		1521.4.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.b.3.2	✓	4	4.3	odd	2
13.4.c.b.9.2	yes	4	52.35	odd	6
117.4.g.d.55.1		4	12.11	even	2
117.4.g.d.100.1		4	156.35	even	6
169.4.a.f.1.1		2	52.3	odd	6
169.4.a.j.1.2		2	52.23	odd	6
169.4.b.e.168.1		4	52.11	even	12
169.4.b.e.168.4		4	52.15	even	12
169.4.c.f.22.1		4	52.43	odd	6
169.4.c.f.146.1		4	52.51	odd	2
169.4.e.g.23.1		8	52.47	even	4
169.4.e.g.23.4		8	52.31	even	4
169.4.e.g.147.1		8	52.19	even	12
169.4.e.g.147.4		8	52.7	even	12
208.4.i.e.81.2		4	1.1	even	1	trivial
208.4.i.e.113.2		4	13.9	even	3	inner
1521.4.a.l.1.1		2	156.23	even	6
1521.4.a.t.1.2		2	156.107	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.34233 + 7.52113i) q^{3} +2.80776 q^{5} +(4.78078 - 8.28055i) q^{7} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})\)	\(q+(4.34233 + 7.52113i) q^{3} +2.80776 q^{5} +(4.78078 - 8.28055i) q^{7} +(-24.2116 + 41.9358i) q^{9} +(19.7116 + 34.1416i) q^{11} +(40.5270 + 23.5492i) q^{13} +(12.1922 + 21.1176i) q^{15} +(-1.00758 + 1.74518i) q^{17} +(-30.0961 + 52.1280i) q^{19} +83.0388 q^{21} +(2.23438 + 3.87006i) q^{23} -117.116 q^{25} -186.054 q^{27} +(-70.3466 - 121.844i) q^{29} -136.155 q^{31} +(-171.189 + 296.508i) q^{33} +(13.4233 - 23.2498i) q^{35} +(92.8542 + 160.828i) q^{37} +(-1.13494 + 407.067i) q^{39} +(-155.116 - 268.668i) q^{41} +(213.735 - 370.200i) q^{43} +(-67.9806 + 117.746i) q^{45} +258.617 q^{47} +(125.788 + 217.872i) q^{49} -17.5009 q^{51} +612.656 q^{53} +(55.3457 + 95.8615i) q^{55} -522.749 q^{57} +(-258.943 + 448.502i) q^{59} +(80.6553 - 139.699i) q^{61} +(231.501 + 400.971i) q^{63} +(113.790 + 66.1205i) q^{65} +(-24.9493 - 43.2135i) q^{67} +(-19.4048 + 33.6101i) q^{69} +(139.982 - 242.455i) q^{71} +467.732 q^{73} +(-508.558 - 880.849i) q^{75} +376.948 q^{77} -37.5379 q^{79} +(-154.193 - 267.070i) q^{81} +76.1553 q^{83} +(-2.82904 + 4.90004i) q^{85} +(610.936 - 1058.17i) q^{87} +(-101.403 - 175.635i) q^{89} +(388.750 - 223.002i) q^{91} +(-591.231 - 1024.04i) q^{93} +(-84.5028 + 146.363i) q^{95} +(587.184 - 1017.03i) q^{97} -1909.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{3} - 30 q^{5} + 15 q^{7} - 35 q^{9}+O(q^{10}) \) 4 * q + 5 * q^3 - 30 * q^5 + 15 * q^7 - 35 * q^9	\( 4 q + 5 q^{3} - 30 q^{5} + 15 q^{7} - 35 q^{9} + 17 q^{11} + 125 q^{13} + 90 q^{15} - 70 q^{17} - 141 q^{19} + 126 q^{21} + 145 q^{23} + 150 q^{25} - 670 q^{27} - 34 q^{29} + 280 q^{31} - 425 q^{33} - 70 q^{35} + 190 q^{37} + 181 q^{39} - 538 q^{41} + 455 q^{43} - 375 q^{45} - 120 q^{47} + 565 q^{49} + 466 q^{51} + 1090 q^{53} + 510 q^{55} - 450 q^{57} - 809 q^{59} - 502 q^{61} + 390 q^{63} - 555 q^{65} - 475 q^{67} + 479 q^{69} + 127 q^{71} + 1170 q^{73} - 1725 q^{75} + 510 q^{77} - 480 q^{79} - 122 q^{81} - 520 q^{83} + 1205 q^{85} + 1615 q^{87} - 921 q^{89} + 1287 q^{91} - 2200 q^{93} + 1270 q^{95} + 415 q^{97} - 4420 q^{99}+O(q^{100}) \) 4 * q + 5 * q^3 - 30 * q^5 + 15 * q^7 - 35 * q^9 + 17 * q^11 + 125 * q^13 + 90 * q^15 - 70 * q^17 - 141 * q^19 + 126 * q^21 + 145 * q^23 + 150 * q^25 - 670 * q^27 - 34 * q^29 + 280 * q^31 - 425 * q^33 - 70 * q^35 + 190 * q^37 + 181 * q^39 - 538 * q^41 + 455 * q^43 - 375 * q^45 - 120 * q^47 + 565 * q^49 + 466 * q^51 + 1090 * q^53 + 510 * q^55 - 450 * q^57 - 809 * q^59 - 502 * q^61 + 390 * q^63 - 555 * q^65 - 475 * q^67 + 479 * q^69 + 127 * q^71 + 1170 * q^73 - 1725 * q^75 + 510 * q^77 - 480 * q^79 - 122 * q^81 - 520 * q^83 + 1205 * q^85 + 1615 * q^87 - 921 * q^89 + 1287 * q^91 - 2200 * q^93 + 1270 * q^95 + 415 * q^97 - 4420 * q^99

Introduction

L-functions

Modular forms

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