LMFDB - Embedded newform 169.4.e.h.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.337850 - 0.195058i) q^{2} +(-1.80483 - 3.12606i) q^{3} +(-3.92391 + 6.79640i) q^{4} +7.52136i q^{5} +(-1.21953 - 0.704093i) q^{6} +(-16.9261 - 9.77228i) q^{7} +6.18247i q^{8} +(6.98515 - 12.0986i) q^{9} +O(q^{10})$	\(q+(0.337850 - 0.195058i) q^{2} +(-1.80483 - 3.12606i) q^{3} +(-3.92391 + 6.79640i) q^{4} +7.52136i q^{5} +(-1.21953 - 0.704093i) q^{6} +(-16.9261 - 9.77228i) q^{7} +6.18247i q^{8} +(6.98515 - 12.0986i) q^{9} +(1.46710 + 2.54109i) q^{10} +(39.6850 - 22.9121i) q^{11} +28.3280 q^{12} -7.62463 q^{14} +(23.5123 - 13.5748i) q^{15} +(-30.1853 - 52.2825i) q^{16} +(43.2600 - 74.9285i) q^{17} -5.45003i q^{18} +(128.810 + 74.3684i) q^{19} +(-51.1182 - 29.5131i) q^{20} +70.5494i q^{21} +(8.93837 - 15.4817i) q^{22} +(-45.7676 - 79.2718i) q^{23} +(19.3268 - 11.1583i) q^{24} +68.4292 q^{25} -147.889 q^{27} +(132.833 - 76.6910i) q^{28} +(-129.451 - 224.215i) q^{29} +(5.29574 - 9.17249i) q^{30} -31.2317i q^{31} +(-63.2296 - 36.5056i) q^{32} +(-143.250 - 82.7052i) q^{33} -33.7528i q^{34} +(73.5008 - 127.307i) q^{35} +(54.8181 + 94.9478i) q^{36} +(128.549 - 74.2180i) q^{37} +58.0245 q^{38} -46.5006 q^{40} +(-83.0635 + 47.9567i) q^{41} +(13.7612 + 23.8351i) q^{42} +(-40.4965 + 70.1420i) q^{43} +359.620i q^{44} +(90.9982 + 52.5378i) q^{45} +(-30.9251 - 17.8546i) q^{46} +94.3777i q^{47} +(-108.959 + 188.722i) q^{48} +(19.4949 + 33.7662i) q^{49} +(23.1188 - 13.3476i) q^{50} -312.308 q^{51} +493.555 q^{53} +(-49.9643 + 28.8469i) q^{54} +(172.330 + 298.485i) q^{55} +(60.4169 - 104.645i) q^{56} -536.891i q^{57} +(-87.4697 - 50.5006i) q^{58} +(498.558 + 287.843i) q^{59} +213.065i q^{60} +(20.1432 - 34.8891i) q^{61} +(-6.09199 - 10.5516i) q^{62} +(-236.462 + 136.522i) q^{63} +454.482 q^{64} -64.5291 q^{66} +(-520.603 + 300.570i) q^{67} +(339.496 + 588.025i) q^{68} +(-165.206 + 286.145i) q^{69} -57.3476i q^{70} +(-449.294 - 259.400i) q^{71} +(74.7995 + 43.1855i) q^{72} -1055.21i q^{73} +(28.9536 - 50.1491i) q^{74} +(-123.503 - 213.914i) q^{75} +(-1010.88 + 583.629i) q^{76} -895.615 q^{77} -320.840 q^{79} +(393.235 - 227.034i) q^{80} +(78.3164 + 135.648i) q^{81} +(-18.7087 + 32.4043i) q^{82} +32.4841i q^{83} +(-479.482 - 276.829i) q^{84} +(563.564 + 325.374i) q^{85} +31.5966i q^{86} +(-467.274 + 809.341i) q^{87} +(141.654 + 245.351i) q^{88} +(390.400 - 225.398i) q^{89} +40.9916 q^{90} +718.350 q^{92} +(-97.6324 + 56.3681i) q^{93} +(18.4091 + 31.8855i) q^{94} +(-559.352 + 968.826i) q^{95} +263.546i q^{96} +(200.695 + 115.871i) q^{97} +(13.1727 + 7.60526i) q^{98} -640.179i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.337850	−	0.195058i	0.119448	−	0.0689633i	−0.439086	−	0.898445i	$-0.644698\pi$
$2$	0.337850	−	0.195058i	0.119448	−	0.0689633i	0.558534	+	0.829482i	$0.311364\pi$
$3$	−1.80483	−	3.12606i	−0.347340	−	0.601611i	0.638436	−	0.769675i	$-0.279582\pi$
$3$	−1.80483	−	3.12606i	−0.347340	−	0.601611i	−0.985776	+	0.168064i	$0.946249\pi$
$4$	−3.92391	+	6.79640i	−0.490488	+	0.849550i
$5$			7.52136i			0.672731i	0.941732	+	0.336365i	$0.109198\pi$
$5$			7.52136i			0.672731i	−0.941732	+	0.336365i	$0.890802\pi$
$6$	−1.21953	−	0.704093i	−0.0829782	−	0.0479075i
$7$	−16.9261	−	9.77228i	−0.913923	−	0.527654i	−0.0322315	−	0.999480i	$-0.510261\pi$
$7$	−16.9261	−	9.77228i	−0.913923	−	0.527654i	−0.881691	+	0.471827i	$0.843595\pi$
$8$			6.18247i			0.273229i
$9$	6.98515	−	12.0986i	0.258709	−	0.448098i
$10$	1.46710	+	2.54109i	0.0463937	+	0.0803563i
$11$	39.6850	−	22.9121i	1.08777	−	0.628024i	0.154788	−	0.987948i	$-0.450531\pi$
$11$	39.6850	−	22.9121i	1.08777	−	0.628024i	0.932982	+	0.359923i	$0.117197\pi$
$12$	28.3280			0.681465
$13$		0			0
$13$		0			0
$14$	−7.62463			−0.145555
$15$	23.5123	−	13.5748i	0.404722	−	0.233667i
$16$	−30.1853	−	52.2825i	−0.471645	−	0.816914i
$17$	43.2600	−	74.9285i	0.617182	−	1.06899i	−0.372816	−	0.927905i	$-0.621608\pi$
$17$	43.2600	−	74.9285i	0.617182	−	1.06899i	0.989998	−	0.141085i	$-0.0450590\pi$
$18$		−	5.45003i		−	0.0713658i
$19$	128.810	+	74.3684i	1.55532	+	0.897963i	0.997694	+	0.0678680i	$0.0216197\pi$
$19$	128.810	+	74.3684i	1.55532	+	0.897963i	0.557623	+	0.830095i	$0.311714\pi$
$20$	−51.1182	−	29.5131i	−0.571519	−	0.329966i
$21$			70.5494i			0.733102i
$22$	8.93837	−	15.4817i	0.0866212	−	0.150032i
$23$	−45.7676	−	79.2718i	−0.414922	−	0.718665i	0.580499	−	0.814261i	$-0.302858\pi$
$23$	−45.7676	−	79.2718i	−0.414922	−	0.718665i	−0.995420	+	0.0955958i	$0.969524\pi$
$24$	19.3268	−	11.1583i	0.164378	−	0.0949036i
$25$	68.4292			0.547433
$26$		0			0
$27$	−147.889			−1.05412
$28$	132.833	−	76.6910i	0.896536	−	0.517616i
$29$	−129.451	−	224.215i	−0.828909	−	1.43571i	−0.898895	−	0.438165i	$-0.855629\pi$
$29$	−129.451	−	224.215i	−0.828909	−	1.43571i	0.0699855	−	0.997548i	$-0.477705\pi$
$30$	5.29574	−	9.17249i	0.0322288	−	0.0558220i
$31$		−	31.2317i		−	0.180948i	−0.995899	−	0.0904739i	$-0.971162\pi$
$31$		−	31.2317i		−	0.180948i	0.995899	−	0.0904739i	$-0.0288382\pi$
$32$	−63.2296	−	36.5056i	−0.349298	−	0.201667i
$33$	−143.250	−	82.7052i	−0.755653	−	0.436276i
$34$		−	33.7528i		−	0.170252i
$35$	73.5008	−	127.307i	0.354969	−	0.614824i
$36$	54.8181	+	94.9478i	0.253788	+	0.439573i
$37$	128.549	−	74.2180i	0.571173	−	0.329767i	−0.186445	−	0.982465i	$-0.559697\pi$
$37$	128.549	−	74.2180i	0.571173	−	0.329767i	0.757618	+	0.652699i	$0.226363\pi$
$38$	58.0245			0.247706
$39$		0			0
$40$	−46.5006			−0.183810
$41$	−83.0635	+	47.9567i	−0.316399	+	0.182673i	−0.649786	−	0.760117i	$-0.725142\pi$
$41$	−83.0635	+	47.9567i	−0.316399	+	0.182673i	0.333388	+	0.942790i	$0.391808\pi$
$42$	13.7612	+	23.8351i	0.0505571	+	0.0875675i
$43$	−40.4965	+	70.1420i	−0.143620	+	0.248757i	−0.928857	−	0.370438i	$-0.879208\pi$
$43$	−40.4965	+	70.1420i	−0.143620	+	0.248757i	0.785237	+	0.619195i	$0.212541\pi$
$44$			359.620i			1.23215i
$45$	90.9982	+	52.5378i	0.301449	+	0.174042i
$46$	−30.9251	−	17.8546i	−0.0991231	−	0.0572287i
$47$			94.3777i			0.292902i	0.989218	+	0.146451i	$0.0467851\pi$
$47$			94.3777i			0.292902i	−0.989218	+	0.146451i	$0.953215\pi$
$48$	−108.959	+	188.722i	−0.327643	+	0.567494i
$49$	19.4949	+	33.7662i	0.0568365	+	0.0984436i
$50$	23.1188	−	13.3476i	0.0653898	−	0.0377528i
$51$	−312.308			−0.857489
$52$		0			0
$53$	493.555			1.27915			0.639575	−	0.768729i	$-0.279110\pi$
$53$	493.555			1.27915			0.639575	+	0.768729i	$0.279110\pi$
$54$	−49.9643	+	28.8469i	−0.125913	+	0.0726957i
$55$	172.330	+	298.485i	0.422491	+	0.731776i
$56$	60.4169	−	104.645i	0.144170	−	0.249710i
$57$		−	536.891i		−	1.24759i
$58$	−87.4697	−	50.5006i	−0.198023	−	0.114329i
$59$	498.558	+	287.843i	1.10011	+	0.635152i	0.936251	−	0.351331i	$-0.114271\pi$
$59$	498.558	+	287.843i	1.10011	+	0.635152i	0.163864	+	0.986483i	$0.447604\pi$
$60$			213.065i			0.458443i
$61$	20.1432	−	34.8891i	0.0422800	−	0.0732311i	−0.844111	−	0.536168i	$-0.819871\pi$
$61$	20.1432	−	34.8891i	0.0422800	−	0.0732311i	0.886391	+	0.462937i	$0.153205\pi$
$62$	−6.09199	−	10.5516i	−0.0124788	−	0.0216138i
$63$	−236.462	+	136.522i	−0.472880	+	0.273018i
$64$	454.482			0.887660
$65$		0			0
$66$	−64.5291			−0.120348
$67$	−520.603	+	300.570i	−0.949280	+	0.548067i	−0.892857	−	0.450340i	$-0.851303\pi$
$67$	−520.603	+	300.570i	−0.949280	+	0.548067i	−0.0564231	+	0.998407i	$0.517970\pi$
$68$	339.496	+	588.025i	0.605441	+	1.04865i
$69$	−165.206	+	286.145i	−0.288238	+	0.499243i
$70$		−	57.3476i		−	0.0979193i
$71$	−449.294	−	259.400i	−0.751006	−	0.433593i	0.0750515	−	0.997180i	$-0.476088\pi$
$71$	−449.294	−	259.400i	−0.751006	−	0.433593i	−0.826057	+	0.563586i	$0.809421\pi$
$72$	74.7995	+	43.1855i	0.122433	+	0.0706869i
$73$		−	1055.21i		−	1.69182i	−0.533328	−	0.845908i	$-0.679059\pi$
$73$		−	1055.21i		−	1.69182i	0.533328	−	0.845908i	$-0.320941\pi$
$74$	28.9536	−	50.1491i	0.0454836	−	0.0787799i
$75$	−123.503	−	213.914i	−0.190146	−	0.329342i
$76$	−1010.88	+	583.629i	−1.52573	+	0.880880i
$77$	−895.615			−1.32552
$78$		0			0
$79$	−320.840			−0.456928			−0.228464	−	0.973552i	$-0.573370\pi$
$79$	−320.840			−0.456928			−0.228464	+	0.973552i	$0.573370\pi$
$80$	393.235	−	227.034i	0.549563	−	0.317290i
$81$	78.3164	+	135.648i	0.107430	+	0.186074i
$82$	−18.7087	+	32.4043i	−0.0251954	+	0.0436398i
$83$			32.4841i			0.0429590i	0.999769	+	0.0214795i	$0.00683766\pi$
$83$			32.4841i			0.0429590i	−0.999769	+	0.0214795i	$0.993162\pi$
$84$	−479.482	−	276.829i	−0.622807	−	0.359578i
$85$	563.564	+	325.374i	0.719143	+	0.415197i
$86$			31.5966i			0.0396180i
$87$	−467.274	+	809.341i	−0.575827	+	0.997362i
$88$	141.654	+	245.351i	0.171595	+	0.297211i
$89$	390.400	−	225.398i	0.464970	−	0.268450i	−0.249162	−	0.968462i	$-0.580155\pi$
$89$	390.400	−	225.398i	0.464970	−	0.268450i	0.714132	+	0.700011i	$0.246822\pi$
$90$	40.9916			0.0480099
$91$		0			0
$92$	718.350			0.814057
$93$	−97.6324	+	56.3681i	−0.108860	+	0.0628505i
$94$	18.4091	+	31.8855i	0.0201995	+	0.0349865i
$95$	−559.352	+	968.826i	−0.604087	+	1.04631i
$96$			263.546i			0.280189i
$97$	200.695	+	115.871i	0.210077	+	0.121288i	0.601347	−	0.798988i	$-0.294631\pi$
$97$	200.695	+	115.871i	0.210077	+	0.121288i	−0.391270	+	0.920276i	$0.627964\pi$
$98$	13.1727	+	7.60526i	0.0135780	+	0.00783926i
$99$		−	640.179i		−	0.649903i
$100$	−268.510	+	465.072i	−0.268510	+	0.465072i
$101$	285.063	+	493.743i	0.280840	+	0.486428i	0.971592	−	0.236663i	$-0.0760538\pi$
$101$	285.063	+	493.743i	0.280840	+	0.486428i	−0.690752	+	0.723092i	$0.742720\pi$
$102$	−105.513	+	60.9181i	−0.102425	+	0.0591352i
$103$	−969.551			−0.927502			−0.463751	−	0.885965i	$-0.653497\pi$
$103$	−969.551			−0.927502			−0.463751	+	0.885965i	$0.653497\pi$
$104$		0			0
$105$	−530.627			−0.493180
$106$	166.747	−	96.2716i	0.152792	−	0.0882144i
$107$	171.578	+	297.182i	0.155019	+	0.268502i	0.933066	−	0.359705i	$-0.117123\pi$
$107$	171.578	+	297.182i	0.155019	+	0.268502i	−0.778047	+	0.628207i	$0.783789\pi$
$108$	580.303	−	1005.11i	0.517034	−	0.895529i
$109$			83.1640i			0.0730795i	0.999332	+	0.0365398i	$0.0116336\pi$
$109$			83.1640i			0.0730795i	−0.999332	+	0.0365398i	$0.988366\pi$
$110$	116.444	+	67.2287i	0.100931	+	0.0582728i
$111$	−464.021	−	267.902i	−0.396783	−	0.229083i
$112$			1179.92i			0.995461i
$113$	1058.09	−	1832.67i	0.880856	−	1.52569i	0.0304652	−	0.999536i	$-0.490301\pi$
$113$	1058.09	−	1832.67i	0.880856	−	1.52569i	0.850391	−	0.526152i	$-0.176366\pi$
$114$	−104.725	−	181.388i	−0.0860383	−	0.149023i
$115$	596.231	−	344.234i	0.483468	−	0.279131i
$116$	2031.81			1.62628
$117$		0			0
$118$	224.584			0.175209
$119$	−1464.44	+	845.498i	−1.12811	+	0.651316i
$120$	83.9259	+	145.364i	0.0638446	+	0.110582i
$121$	384.431	−	665.855i	0.288829	−	0.500266i
$122$		−	15.7164i		−	0.0116631i
$123$	299.832	+	173.108i	0.219796	+	0.126899i
$124$	212.263	+	122.550i	0.153724	+	0.0887528i
$125$			1454.85i			1.04101i
$126$	−53.2592	+	92.2476i	−0.0376564	+	0.0652228i
$127$	−588.346	−	1019.04i	−0.411081	−	0.712012i	0.583928	−	0.811806i	$-0.301515\pi$
$127$	−588.346	−	1019.04i	−0.411081	−	0.712012i	−0.995008	+	0.0997933i	$0.968182\pi$
$128$	659.384	−	380.695i	0.455327	−	0.262883i
$129$	292.358			0.199540
$130$		0			0
$131$	775.336			0.517110			0.258555	−	0.965996i	$-0.416754\pi$
$131$	775.336			0.517110			0.258555	+	0.965996i	$0.416754\pi$
$132$	1124.20	−	649.055i	0.741278	−	0.427977i
$133$	−1453.50	−	2517.53i	−0.947626	−	1.64134i
$134$	−117.257	+	203.095i	−0.0755931	+	0.130931i
$135$		−	1112.33i		−	0.709140i
$136$	463.243	+	267.454i	0.292079	+	0.168632i
$137$	−2201.98	−	1271.31i	−1.37319	−	0.792814i	−0.381865	−	0.924218i	$-0.624718\pi$
$137$	−2201.98	−	1271.31i	−1.37319	−	0.792814i	−0.991329	+	0.131404i	$0.958052\pi$
$138$			128.899i			0.0795114i
$139$	143.158	−	247.958i	0.0873564	−	0.151306i	−0.819036	−	0.573741i	$-0.805491\pi$
$139$	143.158	−	247.958i	0.0873564	−	0.151306i	0.906393	+	0.422436i	$0.138825\pi$
$140$	576.821	+	999.082i	0.348216	+	0.603128i
$141$	295.031	−	170.336i	0.176213	−	0.101737i
$142$	−202.392			−0.119608
$143$		0			0
$144$	−843.395			−0.488076
$145$	1686.40	−	973.644i	0.965848	−	0.557633i
$146$	−205.826	−	356.501i	−0.116673	−	0.202084i
$147$	70.3701	−	121.885i	0.0394832	−	0.0683869i
$148$			1164.90i			0.646987i
$149$	2038.73	+	1177.06i	1.12094	+	0.647173i	0.941640	−	0.336622i	$-0.109284\pi$
$149$	2038.73	+	1177.06i	1.12094	+	0.647173i	0.179297	+	0.983795i	$0.442618\pi$
$150$	−83.4511	−	48.1805i	−0.0454250	−	0.0262261i
$151$		−	165.158i		−	0.0890089i	−0.999009	−	0.0445045i	$-0.985829\pi$
$151$		−	165.158i		−	0.0890089i	0.999009	−	0.0445045i	$-0.0141709\pi$
$152$	−459.781	+	796.364i	−0.245350	+	0.424958i
$153$	−604.355	−	1046.77i	−0.319341	−	0.553115i
$154$	−302.583	+	174.697i	−0.158330	+	0.0914120i
$155$	234.905			0.121729
$156$		0			0
$157$	−3095.72			−1.57367			−0.786833	−	0.617166i	$-0.788281\pi$
$157$	−3095.72			−1.57367			−0.786833	+	0.617166i	$0.788281\pi$
$158$	−108.396	+	62.5823i	−0.0545791	+	0.0315113i
$159$	−890.784	−	1542.88i	−0.444301	−	0.769551i
$160$	274.572	−	475.573i	0.135668	−	0.234983i
$161$			1789.01i			0.875740i
$162$	52.9183	+	30.5524i	0.0256646	+	0.0148174i
$163$	259.210	+	149.655i	0.124558	+	0.0719134i	0.560984	−	0.827826i	$-0.310423\pi$
$163$	259.210	+	149.655i	0.124558	+	0.0719134i	−0.436427	+	0.899740i	$0.643756\pi$
$164$		−	752.711i		−	0.358395i
$165$	622.055	−	1077.43i	0.293497	−	0.508351i
$166$	6.33628	+	10.9748i	0.00296259	+	0.00513136i
$167$	2602.55	−	1502.59i	1.20594	−	0.696249i	0.244069	−	0.969758i	$-0.421518\pi$
$167$	2602.55	−	1502.59i	1.20594	−	0.696249i	0.961869	+	0.273509i	$0.0881844\pi$
$168$	−436.170			−0.200305
$169$		0			0
$170$	253.867			0.114533
$171$	1799.51	−	1038.95i	0.804750	−	0.464622i
$172$	−317.809	−	550.461i	−0.140888	−	0.244025i
$173$	227.926	−	394.780i	0.100167	−	0.173495i	−0.811586	−	0.584233i	$-0.801396\pi$
$173$	227.926	−	394.780i	0.100167	−	0.173495i	0.911753	+	0.410738i	$0.134729\pi$
$174$			364.581i			0.158844i
$175$	−1158.24	−	668.709i	−0.500312	−	0.288855i
$176$	−2395.81	−	1383.22i	−1.02608	−	0.592409i
$177$		−	2078.03i		−	0.882455i
$178$	87.9310	−	152.301i	0.0370265	−	0.0641317i
$179$	682.097	+	1181.43i	0.284818	+	0.493318i	0.972565	−	0.232632i	$-0.0747337\pi$
$179$	682.097	+	1181.43i	0.284818	+	0.493318i	−0.687747	+	0.725950i	$0.741400\pi$
$180$	−714.136	+	412.307i	−0.295714	+	0.170731i
$181$	2026.11			0.832041			0.416021	−	0.909355i	$-0.363424\pi$
$181$	2026.11			0.832041			0.416021	+	0.909355i	$0.363424\pi$
$182$		0			0
$183$	−145.421			−0.0587422
$184$	490.096	−	282.957i	0.196360	−	0.113369i
$185$	558.220	+	966.866i	0.221844	+	0.384246i
$186$	−21.9901	+	38.0879i	−0.00866876	+	0.0150147i
$187$		−	3964.71i		−	1.55042i
$188$	−641.429	−	370.329i	−0.248835	−	0.143665i
$189$	2503.18	+	1445.21i	0.963386	+	0.556211i
$190$			436.423i			0.166639i
$191$	−1080.53	+	1871.54i	−0.409343	+	0.709003i	−0.994816	−	0.101689i	$-0.967575\pi$
$191$	−1080.53	+	1871.54i	−0.409343	+	0.709003i	0.585473	+	0.810692i	$0.300909\pi$
$192$	−820.265	−	1420.74i	−0.308320	−	0.534026i
$193$	−1046.05	+	603.938i	−0.390137	+	0.225246i	−0.682219	−	0.731147i	$-0.738985\pi$
$193$	−1046.05	+	603.938i	−0.390137	+	0.225246i	0.292083	+	0.956393i	$0.405652\pi$
$194$	90.4063			0.0334577
$195$		0			0
$196$	−305.985			−0.111510
$197$	−4266.70	+	2463.38i	−1.54309	+	0.890906i	−0.544454	+	0.838791i	$0.683263\pi$
$197$	−4266.70	+	2463.38i	−1.54309	+	0.890906i	−0.998641	+	0.0521154i	$0.983404\pi$
$198$	−124.872	−	216.284i	−0.0448194	−	0.0776295i
$199$	504.727	−	874.212i	0.179795	−	0.311413i	−0.762016	−	0.647559i	$-0.775790\pi$
$199$	504.727	−	874.212i	0.179795	−	0.311413i	0.941810	+	0.336145i	$0.109123\pi$
$200$			423.061i			0.149575i
$201$	1879.20	+	1084.96i	0.659447	+	0.380732i
$202$	192.617	+	111.207i	0.0670914	+	0.0387352i
$203$			5060.11i			1.74951i
$204$	1225.47	−	2122.57i	0.420588	−	0.728480i
$205$	−360.700	−	624.751i	−0.122890	−	0.212851i
$206$	−327.563	+	189.118i	−0.110788	+	0.0639636i
$207$	−1278.77			−0.429376
$208$		0			0
$209$	6815.76			2.25577
$210$	−179.272	+	103.503i	−0.0589093	+	0.0340113i
$211$	2455.66	+	4253.33i	0.801206	+	1.38773i	0.918823	+	0.394671i	$0.129141\pi$
$211$	2455.66	+	4253.33i	0.801206	+	1.38773i	−0.117616	+	0.993059i	$0.537525\pi$
$212$	−1936.66	+	3354.40i	−0.627408	+	1.08670i
$213$			1872.70i			0.602418i
$214$	115.935	+	66.9353i	0.0370335	+	0.0213813i
$215$	−527.563	−	304.589i	−0.167347	−	0.0966176i
$216$		−	914.321i		−	0.288017i
$217$	−305.205	+	528.631i	−0.0954778	+	0.165372i
$218$	16.2218	+	28.0969i	0.00503980	+	0.00872920i
$219$	−3298.64	+	1904.47i	−1.01782	+	0.587636i
$220$	−2704.83			−0.828908
$221$		0			0
$222$	−209.026			−0.0631932
$223$	1181.76	−	682.289i	0.354872	−	0.204885i	−0.311957	−	0.950096i	$-0.600984\pi$
$223$	1181.76	−	682.289i	0.354872	−	0.204885i	0.666829	+	0.745211i	$0.267651\pi$
$224$	713.487	+	1235.80i	0.212821	+	0.368616i
$225$	477.988	−	827.899i	0.141626	−	0.245303i
$226$		−	825.554i		−	0.242987i
$227$	−3611.22	−	2084.94i	−1.05588	−	0.609614i	−0.131592	−	0.991304i	$-0.542009\pi$
$227$	−3611.22	−	2084.94i	−1.05588	−	0.609614i	−0.924290	+	0.381690i	$0.875342\pi$
$228$	3648.93	+	2106.71i	1.05989	+	0.611931i
$229$		−	3506.89i		−	1.01197i	−0.862541	−	0.505987i	$-0.831128\pi$
$229$		−	3506.89i		−	1.01197i	0.862541	−	0.505987i	$-0.168872\pi$
$230$	134.291	−	232.599i	0.0384995	−	0.0666831i
$231$	1616.44	+	2799.75i	0.460406	+	0.797446i
$232$	1386.20	−	800.325i	0.392279	−	0.226482i
$233$	570.253			0.160337			0.0801684	−	0.996781i	$-0.474454\pi$
$233$	570.253			0.160337			0.0801684	+	0.996781i	$0.474454\pi$
$234$		0			0
$235$	−709.848			−0.197044
$236$	−3912.59	+	2258.94i	−1.07919	+	0.623069i
$237$	579.063	+	1002.97i	0.158710	+	0.274893i
$238$	−329.842	+	571.302i	−0.0898338	+	0.155597i
$239$			231.056i			0.0625347i	0.999511	+	0.0312674i	$0.00995433\pi$
$239$			231.056i			0.0625347i	−0.999511	+	0.0312674i	$0.990046\pi$
$240$	−1419.45	−	819.519i	−0.381771	−	0.220416i
$241$	2674.72	+	1544.25i	0.714911	+	0.412754i	0.812877	−	0.582436i	$-0.197900\pi$
$241$	2674.72	+	1544.25i	0.714911	+	0.412754i	−0.0979656	+	0.995190i	$0.531234\pi$
$242$		−	299.945i		−	0.0796744i
$243$	−1713.81	+	2968.40i	−0.452431	+	0.783634i
$244$	158.080	+	273.803i	0.0414756	+	0.0718379i
$245$	−253.968	+	146.628i	−0.0662261	+	0.0382356i
$246$	135.064			0.0350056
$247$		0			0
$248$	193.089			0.0494403
$249$	101.547	−	58.6285i	0.0258446	−	0.0149214i
$250$	283.780	+	491.521i	0.0717912	+	0.124346i
$251$	−1222.82	+	2117.98i	−0.307504	+	0.532613i	−0.977816	−	0.209467i	$-0.932827\pi$
$251$	−1222.82	+	2117.98i	−0.307504	+	0.532613i	0.670311	+	0.742080i	$0.266161\pi$
$252$		−	2142.79i		−	0.535648i
$253$	−3632.57	−	2097.27i	−0.902679	−	0.521162i
$254$	−397.545	−	229.523i	−0.0982054	−	0.0566989i
$255$		−	2348.98i		−	0.576859i
$256$	−1669.41	+	2891.51i	−0.407572	+	0.705935i
$257$	1637.00	+	2835.36i	0.397327	+	0.688191i	0.993395	−	0.114743i	$-0.0366045\pi$
$257$	1637.00	+	2835.36i	0.397327	+	0.688191i	−0.596068	+	0.802934i	$0.703271\pi$
$258$	98.7731	−	57.0266i	0.0238347	−	0.0137609i
$259$	−2901.12			−0.696010
$260$		0			0
$261$	−3616.93			−0.857786
$262$	261.947	−	151.235i	0.0617678	−	0.0356616i
$263$	2315.64	+	4010.80i	0.542921	+	0.940367i	0.998735	+	0.0502918i	$0.0160151\pi$
$263$	2315.64	+	4010.80i	0.542921	+	0.940367i	−0.455813	+	0.890075i	$0.650652\pi$
$264$	511.323	−	885.637i	0.119204	−	0.206467i
$265$			3712.20i			0.860524i
$266$	−982.128	−	567.032i	−0.226384	−	0.130703i
$267$	−1409.21	−	813.610i	−0.323006	−	0.186487i
$268$		−	4717.64i		−	1.07528i
$269$	1419.26	−	2458.23i	0.321686	−	0.557177i	−0.659150	−	0.752012i	$-0.729084\pi$
$269$	1419.26	−	2458.23i	0.321686	−	0.557177i	0.980836	+	0.194835i	$0.0624170\pi$
$270$	−216.968	−	375.800i	−0.0489046	−	0.0847053i
$271$	−6107.48	+	3526.16i	−1.36902	+	0.790401i	−0.990802	−	0.135317i	$-0.956795\pi$
$271$	−6107.48	+	3526.16i	−1.36902	+	0.790401i	−0.378213	+	0.925719i	$0.623461\pi$
$272$	−5223.26			−1.16436
$273$		0			0
$274$	−991.917			−0.218700
$275$	2715.61	−	1567.86i	0.595481	−	0.343801i
$276$	−1296.50	−	2245.61i	−0.282755	−	0.489746i
$277$	−969.154	+	1678.62i	−0.210220	+	0.364111i	−0.951783	−	0.306772i	$-0.900751\pi$
$277$	−969.154	+	1678.62i	−0.210220	+	0.364111i	0.741564	+	0.670883i	$0.234085\pi$
$278$		−	111.697i		−	0.0240975i
$279$	−377.861	−	218.158i	−0.0810823	−	0.0468129i
$280$	787.073	+	454.417i	0.167988	+	0.0969879i
$281$			3290.74i			0.698609i	0.937009	+	0.349305i	$0.113582\pi$
$281$			3290.74i			0.698609i	−0.937009	+	0.349305i	$0.886418\pi$
$282$	66.4507	−	115.096i	0.0140322	−	0.0243045i
$283$	−3959.04	−	6857.26i	−0.831592	−	1.44036i	−0.896776	−	0.442486i	$-0.854097\pi$
$283$	−3959.04	−	6857.26i	−0.831592	−	1.44036i	0.0651839	−	0.997873i	$-0.479237\pi$
$284$	3525.98	−	2035.72i	0.736719	−	0.425345i
$285$	4038.15			0.839296
$286$		0			0
$287$	1874.59			0.385552
$288$	−883.337	+	509.995i	−0.180733	+	0.104346i
$289$	−1286.35	−	2228.03i	−0.261827	−	0.453497i
$290$	379.833	−	657.891i	0.0769124	−	0.133216i
$291$		−	836.514i		−	0.168513i
$292$	7171.61	+	4140.53i	1.43728	+	0.829816i
$293$	4915.07	+	2837.71i	0.980004	+	0.565806i	0.902271	−	0.431169i	$-0.141899\pi$
$293$	4915.07	+	2837.71i	0.980004	+	0.565806i	0.0777327	+	0.996974i	$0.475232\pi$
$294$		−	54.9049i		−	0.0108916i
$295$	−2164.97	+	3749.84i	−0.427286	+	0.740081i
$296$	458.851	+	794.753i	0.0901019	+	0.156061i
$297$	−5868.98	+	3388.46i	−1.14664	+	0.662014i
$298$	918.381			0.178525
$299$		0			0
$300$	1938.46			0.373057
$301$	1370.89	−	791.487i	0.262515	−	0.151563i
$302$	−32.2153	−	55.7985i	−0.00613835	−	0.0106319i
$303$	1028.98	−	1782.25i	0.195094	−	0.337913i
$304$		−	8979.33i		−	1.69408i
$305$	262.414	+	151.505i	0.0492648	+	0.0284430i
$306$	−408.362	−	235.768i	−0.0762893	−	0.0440456i
$307$			4338.86i			0.806618i	0.915064	+	0.403309i	$0.132140\pi$
$307$			4338.86i			0.806618i	−0.915064	+	0.403309i	$0.867860\pi$
$308$	3514.31	−	6086.96i	0.650150	−	1.12609i
$309$	1749.88	+	3030.88i	0.322159	+	0.557996i
$310$	79.3626	−	45.8200i	0.0145403	−	0.00839485i
$311$	5234.75			0.954454			0.477227	−	0.878780i	$-0.341642\pi$
$311$	5234.75			0.954454			0.477227	+	0.878780i	$0.341642\pi$
$312$		0			0
$313$	2167.86			0.391484			0.195742	−	0.980655i	$-0.437288\pi$
$313$	2167.86			0.391484			0.195742	+	0.980655i	$0.437288\pi$
$314$	−1045.89	+	603.844i	−0.187971	+	0.108525i
$315$	−1026.83	−	1778.52i	−0.183667	−	0.318121i
$316$	1258.95	−	2180.56i	0.224118	−	0.388184i
$317$			4863.71i			0.861744i	0.902413	+	0.430872i	$0.141794\pi$
$317$			4863.71i			0.861744i	−0.902413	+	0.430872i	$0.858206\pi$
$318$	−601.902	−	347.509i	−0.106142	−	0.0612809i
$319$	−10274.5	−	5931.98i	−1.80332	−	1.04115i
$320$			3418.32i			0.597156i
$321$	619.340	−	1072.73i	0.107689	−	0.186523i
$322$	348.961	+	604.418i	0.0603939	+	0.104605i
$323$	11144.6	−	6434.36i	1.91983	−	1.10841i
$324$	−1229.22			−0.210772
$325$		0			0
$326$	116.765			0.0198375
$327$	259.976	−	150.097i	0.0439655	−	0.0253835i
$328$	−296.491	−	513.538i	−0.0499116	−	0.0864494i
$329$	922.285	−	1597.44i	0.154551	−	0.267690i
$330$		−	485.347i		−	0.0809620i
$331$	2325.51	+	1342.63i	0.386167	+	0.222954i	0.680498	−	0.732750i	$-0.261763\pi$
$331$	2325.51	+	1342.63i	0.386167	+	0.222954i	−0.294331	+	0.955704i	$0.595097\pi$
$332$	−220.775	−	127.465i	−0.0364958	−	0.0210709i
$333$		−	2073.70i		−	0.341255i
$334$	586.182	−	1015.30i	0.0960312	−	0.166331i
$335$	−2260.70	−	3915.64i	−0.368702	−	0.638610i
$336$	3688.50	−	2129.55i	0.598881	−	0.345764i
$337$	6518.36			1.05364			0.526821	−	0.849976i	$-0.323384\pi$
$337$	6518.36			1.05364			0.526821	+	0.849976i	$0.323384\pi$
$338$		0			0
$339$	−7638.71			−1.22383
$340$	−4422.74	+	2553.47i	−0.705462	+	0.407299i
$341$	−715.585	−	1239.43i	−0.113640	−	0.196830i
$342$	405.310	−	702.017i	0.0640838	−	0.110996i
$343$			5941.75i			0.935347i
$344$	−433.651	−	250.369i	−0.0679677	−	0.0392412i
$345$	−2152.20	−	1242.57i	−0.335856	−	0.193907i
$346$		−	177.835i		−	0.0276314i
$347$	−37.8982	+	65.6415i	−0.00586305	+	0.0101551i	−0.868942	−	0.494914i	$-0.835200\pi$
$347$	−37.8982	+	65.6415i	−0.00586305	+	0.0101551i	0.863079	+	0.505069i	$0.168533\pi$
$348$	−3667.07	−	6351.56i	−0.564873	−	0.978389i
$349$	3188.78	−	1841.04i	0.489088	−	0.282375i	−0.235108	−	0.971969i	$-0.575544\pi$
$349$	3188.78	−	1841.04i	0.489088	−	0.282375i	0.724196	+	0.689594i	$0.242211\pi$
$350$	−521.747			−0.0796816
$351$		0			0
$352$	−3345.69			−0.506607
$353$	8687.58	−	5015.77i	1.30990	−	0.756268i	0.327817	−	0.944741i	$-0.393687\pi$
$353$	8687.58	−	5015.77i	1.30990	−	0.756268i	0.982078	+	0.188473i	$0.0603537\pi$
$354$	−405.336	−	702.063i	−0.0608570	−	0.105407i
$355$	1951.04	−	3379.30i	0.291692	−	0.505225i
$356$			3537.75i			0.526687i
$357$	5286.16	+	3051.97i	0.783678	+	0.452457i
$358$	460.893	+	266.097i	0.0680417	+	0.0392839i
$359$			6869.76i			1.00995i	0.863134	+	0.504975i	$0.168498\pi$
$359$			6869.76i			1.00995i	−0.863134	+	0.504975i	$0.831502\pi$
$360$	−324.814	+	562.594i	−0.0475533	+	0.0823647i
$361$	7631.83	+	13218.7i	1.11267	+	1.92721i
$362$	684.520	−	395.208i	0.0993856	−	0.0573803i
$363$	−2775.34			−0.401288
$364$		0			0
$365$	7936.59			1.13814
$366$	−49.1304	+	28.3654i	−0.00701663	+	0.00405105i
$367$	−4441.64	−	7693.15i	−0.631749	−	1.09422i	−0.987194	−	0.159524i	$-0.949004\pi$
$367$	−4441.64	−	7693.15i	−0.631749	−	1.09422i	0.355445	−	0.934697i	$-0.384329\pi$
$368$	−2763.02	+	4785.68i	−0.391392	+	0.677910i
$369$			1339.94i			0.189037i
$370$	377.189	+	217.770i	0.0529977	+	0.0305982i
$371$	−8353.95	−	4823.15i	−1.16904	−	0.674948i
$372$		−	884.732i		−	0.123310i
$373$	2727.25	−	4723.73i	0.378583	−	0.655725i	−0.612273	−	0.790646i	$-0.709745\pi$
$373$	2727.25	−	4723.73i	0.378583	−	0.655725i	0.990856	+	0.134921i	$0.0430780\pi$
$374$	−773.348	−	1339.48i	−0.106922	−	0.185195i
$375$	4547.95	−	2625.76i	0.626281	−	0.361584i
$376$	−583.487			−0.0800294
$377$		0			0
$378$	1127.60			0.153433
$379$	5752.27	−	3321.07i	0.779615	−	0.450111i	−0.0566786	−	0.998392i	$-0.518051\pi$
$379$	5752.27	−	3321.07i	0.779615	−	0.450111i	0.836294	+	0.548281i	$0.184718\pi$
$380$	−4389.69	−	7603.16i	−0.592595	−	1.02640i
$381$	−2123.73	+	3678.41i	−0.285570	+	0.494621i
$382$			843.064i			0.112919i
$383$	−1093.21	−	631.167i	−0.145850	−	0.0842066i	0.425299	−	0.905053i	$-0.360169\pi$
$383$	−1093.21	−	631.167i	−0.145850	−	0.0842066i	−0.571149	+	0.820846i	$0.693502\pi$
$384$	−2380.16	−	1374.18i	−0.316307	−	0.182620i
$385$		−	6736.24i		−	0.891716i
$386$	−235.605	+	408.081i	−0.0310674	+	0.0538102i
$387$	565.748	+	979.905i	0.0743116	+	0.128712i
$388$	−1575.02	+	909.336i	−0.206081	+	0.118981i
$389$	2793.42			0.364093			0.182046	−	0.983290i	$-0.441728\pi$
$389$	2793.42			0.364093			0.182046	+	0.983290i	$0.441728\pi$
$390$		0			0
$391$	−7919.62			−1.02433
$392$	−208.758	+	120.527i	−0.0268977	+	0.0155294i
$393$	−1399.35	−	2423.75i	−0.179613	−	0.311099i
$394$	−961.002	+	1664.50i	−0.122880	+	0.212834i
$395$		−	2413.15i		−	0.307390i
$396$	4350.91	+	2512.00i	0.552125	+	0.318770i
$397$	5931.33	+	3424.45i	0.749836	+	0.432918i	0.825635	−	0.564205i	$-0.190817\pi$
$397$	5931.33	+	3424.45i	0.749836	+	0.432918i	−0.0757988	+	0.997123i	$0.524151\pi$
$398$		−	393.803i		−	0.0495969i
$399$	−5246.65	+	9087.46i	−0.658298	+	1.14021i
$400$	−2065.55	−	3577.65i	−0.258194	−	0.447206i
$401$	−9547.50	+	5512.25i	−1.18898	+	0.686456i	−0.958074	−	0.286521i	$-0.907501\pi$
$401$	−9547.50	+	5512.25i	−1.18898	+	0.686456i	−0.230903	+	0.972977i	$0.574168\pi$
$402$	846.518			0.105026
$403$		0			0
$404$	−4474.24			−0.550994
$405$	−1020.26	+	589.046i	−0.125178	+	0.0722714i
$406$	987.013	+	1709.56i	0.120652	+	0.208975i
$407$	3400.99	−	5890.68i	0.414203	−	0.717421i
$408$		−	1930.84i		−	0.234291i
$409$	−3057.55	−	1765.28i	−0.369648	−	0.213417i	0.303656	−	0.952782i	$-0.401793\pi$
$409$	−3057.55	−	1765.28i	−0.369648	−	0.213417i	−0.673305	+	0.739365i	$0.735126\pi$
$410$	−243.725	−	140.715i	−0.0293578	−	0.0169497i
$411$			9178.03i			1.10151i
$412$	3804.43	−	6589.46i	0.454929	−	0.787960i
$413$	−5625.76	−	9744.11i	−0.670280	−	1.16096i
$414$	−432.033	+	249.434i	−0.0512881	+	0.0296112i
$415$	−244.325			−0.0288998
$416$		0			0
$417$	−1033.51			−0.121370
$418$	2302.70	−	1329.47i	0.269447	−	0.155565i
$419$	2089.61	+	3619.31i	0.243637	+	0.421992i	0.961748	−	0.273937i	$-0.0883260\pi$
$419$	2089.61	+	3619.31i	0.243637	+	0.421992i	−0.718110	+	0.695929i	$0.754993\pi$
$420$	2082.13	−	3606.36i	0.241899	−	0.418981i
$421$		−	6209.31i		−	0.718820i	−0.933180	−	0.359410i	$-0.882978\pi$
$421$		−	6209.31i		−	0.718820i	0.933180	−	0.359410i	$-0.117022\pi$
$422$	1659.29	+	957.990i	0.191405	+	0.110508i
$423$	1141.84	+	659.242i	0.131249	+	0.0757765i
$424$			3051.39i			0.349501i
$425$	2960.24	−	5127.29i	0.337866	−	0.585201i
$426$	365.284	+	632.690i	0.0415447	+	0.0719576i
$427$	−681.893	+	393.691i	−0.0772812	+	0.0446183i
$428$	−2693.03			−0.304141
$429$		0			0
$430$	−237.650			−0.0266523
$431$	−10288.6	+	5940.11i	−1.14985	+	0.663864i	−0.948850	−	0.315729i	$-0.897751\pi$
$431$	−10288.6	+	5940.11i	−1.14985	+	0.663864i	−0.200996	+	0.979592i	$0.564418\pi$
$432$	4464.08	+	7732.01i	0.497172	+	0.861126i
$433$	4362.86	−	7556.69i	0.484216	−	0.838686i	−0.515620	−	0.856818i	$-0.672438\pi$
$433$	4362.86	−	7556.69i	0.484216	−	0.838686i	0.999836	+	0.0181311i	$0.00577161\pi$
$434$			238.130i			0.0263378i
$435$	−6087.35	−	3514.53i	−0.670956	−	0.387377i
$436$	−565.216	−	326.328i	−0.0620847	−	0.0358446i
$437$		−	13614.7i		−	1.49034i
$438$	−742.964	+	1286.85i	−0.0810507	+	0.140384i
$439$	−600.187	−	1039.55i	−0.0652514	−	0.113019i	0.831554	−	0.555444i	$-0.187452\pi$
$439$	−600.187	−	1039.55i	−0.0652514	−	0.113019i	−0.896805	+	0.442425i	$0.854118\pi$
$440$	−1845.37	+	1065.43i	−0.199943	+	0.115437i
$441$	544.699			0.0588165
$442$		0			0
$443$	2258.86			0.242261			0.121130	−	0.992637i	$-0.461348\pi$
$443$	2258.86			0.242261			0.121130	+	0.992637i	$0.461348\pi$
$444$	3641.55	−	2102.45i	0.389235	−	0.224725i
$445$	1695.30	+	2936.34i	0.180595	+	0.312800i
$446$	266.171	−	461.022i	0.0282591	−	0.0489463i
$447$		−	8497.62i		−	0.899158i
$448$	−7692.60	−	4441.33i	−0.811253	−	0.468377i
$449$	12698.0	+	7331.22i	1.33465	+	0.770561i	0.986008	−	0.166695i	$-0.0533096\pi$
$449$	12698.0	+	7331.22i	1.33465	+	0.770561i	0.348642	+	0.937256i	$0.386643\pi$
$450$		−	372.941i		−	0.0390680i
$451$	−2197.58	+	3806.32i	−0.229446	+	0.397412i
$452$	8303.69	+	14382.4i	0.864099	+	1.49666i
$453$	−516.294	+	298.082i	−0.0535488	+	0.0309164i
$454$	−1626.73			−0.168164
$455$		0			0
$456$	3319.31			0.340879
$457$	−8084.29	+	4667.47i	−0.827500	+	0.477757i	−0.852996	−	0.521918i	$-0.825217\pi$
$457$	−8084.29	+	4667.47i	−0.827500	+	0.477757i	0.0254962	+	0.999675i	$0.491883\pi$
$458$	−684.046	−	1184.80i	−0.0697891	−	0.120878i
$459$	−6397.68	+	11081.1i	−0.650585	+	1.12685i
$460$			5402.97i			0.547641i
$461$	9298.39	+	5368.43i	0.939413	+	0.542370i	0.889776	−	0.456397i	$-0.150860\pi$
$461$	9298.39	+	5368.43i	0.939413	+	0.542370i	0.0496365	+	0.998767i	$0.484194\pi$
$462$	1092.23	+	630.597i	0.109989	+	0.0635022i
$463$			10650.0i			1.06900i	0.845168	+	0.534501i	$0.179501\pi$
$463$			10650.0i			1.06900i	−0.845168	+	0.534501i	$0.820499\pi$
$464$	−7815.01	+	13536.0i	−0.781902	+	1.35429i
$465$	−423.965	−	734.328i	−0.0422815	−	0.0732337i
$466$	192.660	−	111.232i	0.0191519	−	0.0110574i
$467$	2638.11			0.261407			0.130703	−	0.991422i	$-0.458276\pi$
$467$	2638.11			0.261407			0.130703	+	0.991422i	$0.458276\pi$
$468$		0			0
$469$	11749.0			1.15676
$470$	−239.822	+	138.461i	−0.0235365	+	0.0135888i
$471$	5587.26	+	9677.43i	0.546598	+	0.946735i
$472$	−1779.58	+	3082.32i	−0.173542	+	0.300584i
$473$			3711.45i			0.360787i
$474$	391.273	+	225.901i	0.0379151	+	0.0218903i
$475$	8814.35	+	5088.97i	0.851432	+	0.491575i
$476$		−	13270.6i		−	1.27785i
$477$	3447.55	−	5971.34i	0.330928	−	0.573184i
$478$	45.0693	+	78.0623i	0.00431260	+	0.00746964i
$479$	−2793.20	+	1612.66i	−0.266440	+	0.153829i	−0.627269	−	0.778803i	$-0.715827\pi$
$479$	−2793.20	+	1612.66i	−0.266440	+	0.153829i	0.360829	+	0.932632i	$0.382494\pi$
$480$	−1982.23			−0.188491
$481$		0			0
$482$	1204.87			0.113860
$483$	5592.57	−	3228.87i	0.526855	−	0.304180i
$484$	3016.94	+	5225.50i	0.283334	+	0.490749i
$485$	−871.510	+	1509.50i	−0.0815943	+	0.141325i
$486$			1337.17i			0.124805i
$487$	−1295.91	−	748.196i	−0.120582	−	0.0696181i	0.438496	−	0.898733i	$-0.355511\pi$
$487$	−1295.91	−	748.196i	−0.120582	−	0.0696181i	−0.559078	+	0.829115i	$0.688845\pi$
$488$	215.701	+	124.535i	0.0200089	+	0.0115521i
$489$		−	1080.41i		−	0.0999137i
$490$	−57.2019	+	99.0766i	−0.00527371	+	0.00913434i
$491$	−259.204	−	448.955i	−0.0238243	−	0.0412648i	0.853867	−	0.520491i	$-0.174251\pi$
$491$	−259.204	−	448.955i	−0.0238243	−	0.0412648i	−0.877692	+	0.479226i	$0.840918\pi$
$492$	−2353.02	+	1358.52i	−0.215615	+	0.124485i
$493$	−22400.1			−2.04635
$494$		0			0
$495$	4815.01			0.437210
$496$	−1632.87	+	942.739i	−0.147819	+	0.0853432i
$497$	5069.86	+	8781.26i	0.457574	+	0.792542i
$498$	22.8719	−	39.6152i	0.00205806	−	0.00356466i
$499$			2405.01i			0.215757i	0.994164	+	0.107879i	$0.0344058\pi$
$499$			2405.01i			0.215757i	−0.994164	+	0.107879i	$0.965594\pi$
$500$	−9887.75	−	5708.69i	−0.884387	−	0.510601i
$501$	−9394.36	−	5423.83i	−0.837742	−	0.483671i
$502$			954.080i			0.0848260i
$503$	−1206.88	+	2090.38i	−0.106983	+	0.185299i	−0.914546	−	0.404481i	$-0.867452\pi$
$503$	−1206.88	+	2090.38i	−0.106983	+	0.185299i	0.807564	+	0.589780i	$0.200786\pi$
$504$	−844.041	−	1461.92i	−0.0745964	−	0.129205i
$505$	−3713.62	+	2144.06i	−0.327235	+	0.188929i
$506$	−1636.35			−0.143764
$507$		0			0
$508$	9234.45			0.806520
$509$	−13577.8	+	7839.15i	−1.18237	+	0.682641i	−0.956561	−	0.291531i	$-0.905835\pi$
$509$	−13577.8	+	7839.15i	−1.18237	+	0.682641i	−0.225807	+	0.974172i	$0.572502\pi$
$510$	−458.187	−	793.604i	−0.0397821	−	0.0689046i
$511$	−10311.8	+	17860.5i	−0.892693	+	1.54619i
$512$			7393.65i			0.638196i
$513$	−19049.6	−	10998.3i	−1.63949	−	0.946562i
$514$	1106.12	+	638.618i	0.0949198	+	0.0548020i
$515$		−	7292.34i		−	0.623959i
$516$	−1147.18	+	1986.98i	−0.0978721	+	0.169519i
$517$	2162.39	+	3745.37i	0.183950	+	0.318610i
$518$	−980.142	+	565.885i	−0.0831370	+	0.0479992i
$519$	−1645.48			−0.139168
$520$		0			0
$521$	−11691.5			−0.983135			−0.491568	−	0.870839i	$-0.663576\pi$
$521$	−11691.5			−0.983135			−0.491568	+	0.870839i	$0.663576\pi$
$522$	−1221.98	+	705.509i	−0.102461	+	0.0591557i
$523$	1939.48	+	3359.27i	0.162156	+	0.280862i	0.935642	−	0.352952i	$-0.114822\pi$
$523$	1939.48	+	3359.27i	0.162156	+	0.280862i	−0.773486	+	0.633814i	$0.781489\pi$
$524$	−3042.35	+	5269.50i	−0.253637	+	0.439311i
$525$			4827.63i			0.401324i
$526$	1564.67	+	903.365i	0.129702	+	0.0748833i
$527$	−2340.15	−	1351.08i	−0.193431	−	0.111678i
$528$			9985.92i			0.823071i
$529$	1894.16	−	3280.78i	0.155680	−	0.269646i
$530$	724.093	+	1254.17i	0.0593445	+	0.102788i
$531$	6965.01	−	4021.25i	0.569220	−	0.328639i
$532$	22813.6			1.85920
$533$		0			0
$534$	−634.804			−0.0514431
$535$	−2235.21	+	1290.50i	−0.180629	+	0.104286i
$536$	−1858.27	−	3218.61i	−0.149748	−	0.259371i
$537$	2462.14	−	4264.56i	0.197857	−	0.342699i
$538$		−	1107.35i		−	0.0887382i
$539$	1547.31	+	893.340i	0.123650	+	0.0713894i
$540$	7559.83	+	4364.67i	0.602450	+	0.347825i
$541$		−	16353.0i		−	1.29958i	−0.760115	−	0.649788i	$-0.774858\pi$
$541$		−	16353.0i		−	1.29958i	0.760115	−	0.649788i	$-0.225142\pi$
$542$	−1375.61	+	2382.62i	−0.109017	+	0.188824i
$543$	−3656.79	−	6333.75i	−0.289002	−	0.500565i
$544$	−5470.63	+	3158.47i	−0.431160	+	0.248930i
$545$	−625.506			−0.0491628
$546$		0			0
$547$	2748.67			0.214853			0.107426	−	0.994213i	$-0.465739\pi$
$547$	2748.67			0.214853			0.107426	+	0.994213i	$0.465739\pi$
$548$	17280.7	−	9977.02i	1.34707	−	0.777732i
$549$	−281.407	−	487.411i	−0.0218764	−	0.0378911i
$550$	611.645	−	1059.40i	0.0474193	−	0.0821327i
$551$		−	38508.1i		−	2.97732i
$552$	−1769.08	−	1021.38i	−0.136408	−	0.0787551i
$553$	5430.57	+	3135.34i	0.417597	+	0.241100i
$554$			756.163i			0.0579897i
$555$	2014.99	−	3490.07i	0.154111	−	0.266928i
$556$	1123.48	+	1945.93i	0.0856946	+	0.148427i
$557$	−14519.4	+	8382.81i	−1.10450	+	0.637686i	−0.937400	−	0.348254i	$-0.886775\pi$
$557$	−14519.4	+	8382.81i	−1.10450	+	0.637686i	−0.167104	+	0.985939i	$0.553442\pi$
$558$	−170.214			−0.0129135
$559$		0			0
$560$	−8874.58			−0.669677
$561$	−12394.0	+	7155.65i	−0.932750	+	0.538524i
$562$	641.884	+	1111.78i	0.0481784	+	0.0834474i
$563$	9246.21	−	16014.9i	0.692151	−	1.19884i	−0.278980	−	0.960297i	$-0.589996\pi$
$563$	9246.21	−	16014.9i	0.692151	−	1.19884i	0.971132	−	0.238545i	$-0.0766703\pi$
$564$			2673.53i			0.199603i
$565$	13784.1	+	7958.27i	1.02638	+	0.592579i
$566$	−2675.12	−	1544.48i	−0.198664	−	0.114699i
$567$		−	3061.32i		−	0.226743i
$568$	1603.73	−	2777.75i	0.118470	−	0.205197i
$569$	781.639	+	1353.84i	0.0575888	+	0.0997467i	0.893383	−	0.449297i	$-0.148325\pi$
$569$	781.639	+	1353.84i	0.0575888	+	0.0997467i	−0.835794	+	0.549044i	$0.814992\pi$
$570$	1364.29	−	787.672i	0.100252	−	0.0578806i
$571$	−9165.98			−0.671776			−0.335888	−	0.941902i	$-0.609036\pi$
$571$	−9165.98			−0.671776			−0.335888	+	0.941902i	$0.609036\pi$
$572$		0			0
$573$	7800.72			0.568726
$574$	633.329	−	365.652i	0.0460534	−	0.0265889i
$575$	−3131.84	−	5424.50i	−0.227142	−	0.393421i
$576$	3174.62	−	5498.61i	0.229646	−	0.397758i
$577$			18762.5i			1.35372i	0.736114	+	0.676858i	$0.236659\pi$
$577$			18762.5i			1.35372i	−0.736114	+	0.676858i	$0.763341\pi$
$578$	−869.189	−	501.826i	−0.0625493	−	0.0361128i
$579$	3775.90	+	2180.02i	0.271021	+	0.156474i
$580$			15281.9i			1.09405i
$581$	317.444	−	549.829i	0.0226675	−	0.0392612i
$582$	−163.168	−	282.616i	−0.0116212	−	0.0201285i
$583$	19586.7	−	11308.4i	1.39142	−	0.803337i
$584$	6523.79			0.462254
$585$		0			0
$586$	2214.07			0.156079
$587$	10952.0	−	6323.14i	0.770080	−	0.444606i	−0.0628229	−	0.998025i	$-0.520010\pi$
$587$	10952.0	−	6323.14i	0.770080	−	0.444606i	0.832903	+	0.553419i	$0.186677\pi$
$588$	552.252	+	956.528i	0.0387321	+	0.0670859i
$589$	2322.65	−	4022.96i	0.162484	−	0.281431i
$590$			1689.18i			0.117868i
$591$	15401.4	+	8891.98i	1.07196	+	0.618896i
$592$	−7760.60	−	4480.59i	−0.538782	−	0.311066i
$593$			9662.74i			0.669142i	0.942371	+	0.334571i	$0.108591\pi$
$593$			9662.74i			0.669142i	−0.942371	+	0.334571i	$0.891409\pi$
$594$	−1321.89	+	2289.58i	−0.0913093	+	0.158152i
$595$	−6359.29	−	11014.6i	−0.438161	−	0.758916i
$596$	−15999.6	+	9237.37i	−1.09961	+	0.634862i
$597$	−3643.79			−0.249800
$598$		0			0
$599$	−26968.7			−1.83959			−0.919794	−	0.392402i	$-0.871644\pi$
$599$	−26968.7			−1.83959			−0.919794	+	0.392402i	$0.871644\pi$
$600$	1322.52	−	763.556i	0.0899859	−	0.0519534i
$601$	−5640.06	−	9768.87i	−0.382800	−	0.663029i	0.608661	−	0.793430i	$-0.291707\pi$
$601$	−5640.06	−	9768.87i	−0.382800	−	0.663029i	−0.991461	+	0.130401i	$0.958373\pi$
$602$	308.771	−	534.807i	0.0209046	−	0.0362078i
$603$			8398.11i			0.567160i
$604$	1122.48	+	648.063i	0.0756175	+	0.0436578i
$605$	5008.13	+	2891.45i	0.336545	+	0.194304i
$606$		−	802.843i		−	0.0538173i
$607$	−6026.30	+	10437.9i	−0.402965	+	0.697957i	−0.994082	−	0.108629i	$-0.965354\pi$
$607$	−6026.30	+	10437.9i	−0.402965	+	0.697957i	0.591117	+	0.806586i	$0.298687\pi$
$608$	−5429.73	−	9404.58i	−0.362179	−	0.627312i
$609$	15818.2	−	9132.66i	1.05252	−	0.607675i
$610$	118.208			0.00784610
$611$		0			0
$612$	9485.73			0.626532
$613$	9751.17	−	5629.84i	0.642489	−	0.370941i	−0.143083	−	0.989711i	$-0.545702\pi$
$613$	9751.17	−	5629.84i	0.642489	−	0.370941i	0.785573	+	0.618769i	$0.212368\pi$
$614$	846.327	+	1465.88i	0.0556270	+	0.0963488i
$615$	−1302.01	+	2255.14i	−0.0853691	+	0.147864i
$616$		−	5537.12i		−	0.362170i
$617$	20835.0	+	12029.1i	1.35946	+	0.784882i	0.989550	−	0.144187i	$-0.0460566\pi$
$617$	20835.0	+	12029.1i	1.35946	+	0.784882i	0.369906	+	0.929069i	$0.379390\pi$
$618$	1182.39	+	682.655i	0.0769625	+	0.0444343i
$619$			2793.41i			0.181384i	0.995879	+	0.0906919i	$0.0289079\pi$
$619$			2793.41i			0.181384i	−0.995879	+	0.0906919i	$0.971092\pi$
$620$	−921.745	+	1596.51i	−0.0597067	+	0.103415i
$621$	6768.53	+	11723.4i	0.437378	+	0.757561i
$622$	1768.56	−	1021.08i	0.114008	−	0.0658223i
$623$	−8810.59			−0.566595
$624$		0			0
$625$	−2388.81			−0.152884
$626$	732.410	−	422.857i	0.0467619	−	0.0269980i
$627$	−12301.3	−	21306.5i	−0.783520	−	1.35710i
$628$	12147.3	−	21039.8i	0.771864	−	1.33691i
$629$		−	12842.7i		−	0.814104i
$630$	−693.827	−	400.581i	−0.0438774	−	0.0253326i
$631$	−21520.7	−	12425.0i	−1.35773	−	0.783883i	−0.368409	−	0.929664i	$-0.620097\pi$
$631$	−21520.7	−	12425.0i	−1.35773	−	0.783883i	−0.989317	+	0.145780i	$0.953431\pi$
$632$		−	1983.59i		−	0.124846i
$633$	8864.11	−	15353.1i	0.556583	−	0.964030i
$634$	948.703	+	1643.20i	0.0594287	+	0.102934i
$635$	7664.60	−	4425.16i	0.478993	−	0.276547i
$636$	13981.4			0.871696
$637$		0			0
$638$	−4628.31			−0.287205
$639$	−6276.77	+	3623.90i	−0.388584	+	0.224349i
$640$	2863.35	+	4959.46i	0.176850	+	0.306312i
$641$	−3897.35	+	6750.41i	−0.240150	+	0.415952i	−0.960757	−	0.277392i	$-0.910530\pi$
$641$	−3897.35	+	6750.41i	−0.240150	+	0.415952i	0.720607	+	0.693344i	$0.243863\pi$
$642$		−	483.228i		−	0.0297064i
$643$	−23997.5	−	13854.9i	−1.47180	−	0.849744i	−0.472302	−	0.881437i	$-0.656577\pi$
$643$	−23997.5	−	13854.9i	−1.47180	−	0.849744i	−0.999498	+	0.0316924i	$0.989910\pi$
$644$	−12158.9	−	7019.92i	−0.743985	−	0.429540i
$645$			2198.93i			0.134237i
$646$	2510.14	−	4347.69i	0.152880	−	0.264795i
$647$	5575.47	+	9656.99i	0.338786	+	0.586794i	0.984205	−	0.177035i	$-0.0566505\pi$
$647$	5575.47	+	9656.99i	0.338786	+	0.586794i	−0.645419	+	0.763829i	$0.723317\pi$
$648$	−838.640	+	484.189i	−0.0508409	+	0.0293530i
$649$	26380.4			1.59556
$650$		0			0
$651$	2203.38			0.132653
$652$	−2034.23	+	1174.46i	−0.122188	+	0.0705453i
$653$	−14568.7	−	25233.8i	−0.873077	−	1.51221i	−0.858797	−	0.512315i	$-0.828788\pi$
$653$	−14568.7	−	25233.8i	−0.873077	−	1.51221i	−0.0142794	−	0.999898i	$-0.504545\pi$
$654$	58.5552	−	101.421i	0.00350106	−	0.00606401i
$655$			5831.58i			0.347876i
$656$	5014.59	+	2895.18i	0.298456	+	0.172314i
$657$	−12766.6	−	7370.78i	−0.758099	−	0.437689i
$658$		−	719.595i		−	0.0426333i
$659$	2650.06	−	4590.04i	0.156649	−	0.271324i	−0.777009	−	0.629489i	$-0.783264\pi$
$659$	2650.06	−	4590.04i	0.156649	−	0.271324i	0.933658	+	0.358165i	$0.116598\pi$
$660$	4881.77	+	8455.48i	0.287913	+	0.498680i
$661$	23739.9	−	13706.3i	1.39694	−	0.806523i	0.402868	−	0.915258i	$-0.368013\pi$
$661$	23739.9	−	13706.3i	1.39694	−	0.806523i	0.994071	+	0.108735i	$0.0346800\pi$
$662$	1047.56			0.0615025
$663$		0			0
$664$	−200.832			−0.0117377
$665$	18935.3	−	10932.3i	1.10418	−	0.637497i
$666$	−404.490	−	700.598i	−0.0235341	−	0.0407622i
$667$	−11849.3	+	20523.5i	−0.687865	+	1.19142i
$668$			23584.0i			1.36601i
$669$	−4265.76	−	2462.84i	−0.246523	−	0.142330i
$670$	−1527.55	−	881.933i	−0.0880813	−	0.0508538i
$671$		−	1846.10i		−	0.106211i
$672$	2575.45	−	4460.81i	0.147842	−	0.256071i
$673$	−10641.0	−	18430.8i	−0.609482	−	1.05565i	−0.991326	−	0.131427i	$-0.958044\pi$
$673$	−10641.0	−	18430.8i	−0.609482	−	1.05565i	0.381844	−	0.924227i	$-0.375289\pi$
$674$	2202.22	−	1271.46i	0.125855	−	0.0726626i
$675$	−10119.9			−0.577061
$676$		0			0
$677$	−13544.2			−0.768904			−0.384452	−	0.923145i	$-0.625610\pi$
$677$	−13544.2			−0.768904			−0.384452	+	0.923145i	$0.625610\pi$
$678$	−2580.74	+	1489.99i	−0.146184	+	0.0843992i
$679$	−2264.65	−	3922.49i	−0.127996	−	0.221696i
$680$	−2011.62	+	3484.22i	−0.113444	+	0.196491i
$681$			15051.9i			0.846974i
$682$	−483.521	−	279.161i	−0.0271480	−	0.0156739i
$683$	8963.48	+	5175.06i	0.502164	+	0.289924i	0.729607	−	0.683867i	$-0.239703\pi$
$683$	8963.48	+	5175.06i	0.502164	+	0.289924i	−0.227443	+	0.973791i	$0.573037\pi$
$684$			16307.0i			0.911567i
$685$	9562.00	−	16561.9i	0.533350	−	0.923790i
$686$	1158.98	+	2007.42i	0.0645046	+	0.111725i
$687$	−10962.8	+	6329.36i	−0.608815	+	0.351499i
$688$	4889.60			0.270951
$689$		0			0
$690$	−969.492			−0.0534898
$691$	−22269.7	+	12857.4i	−1.22602	+	0.707843i	−0.966195	−	0.257813i	$-0.916998\pi$
$691$	−22269.7	+	12857.4i	−1.22602	+	0.707843i	−0.259825	+	0.965656i	$0.583665\pi$
$692$	1788.72	+	3098.16i	0.0982617	+	0.170194i
$693$	−6256.00	+	10835.7i	−0.342923	+	0.593961i
$694$			29.5693i			0.00161734i
$695$	1864.98	+	1076.75i	0.101788	+	0.0587674i
$696$	−5003.73	−	2888.91i	−0.272509	−	0.157333i
$697$			8298.43i			0.450969i
$698$	718.219	−	1243.99i	0.0389470	−	0.0674582i
$699$	−1029.21	−	1782.65i	−0.0556915	−	0.0964605i
$700$	9089.63	−	5247.90i	0.490794	−	0.283360i
$701$	−7431.30			−0.400394			−0.200197	−	0.979756i	$-0.564158\pi$
$701$	−7431.30			−0.400394			−0.200197	+	0.979756i	$0.564158\pi$
$702$		0			0
$703$	22077.9			1.18447
$704$	18036.1	−	10413.2i	0.965570	−	0.557472i
$705$	1281.16	+	2219.03i	0.0684414	+	0.118544i
$706$	1956.73	−	3389.16i	0.104310	−	0.180669i
$707$		−	11142.8i		−	0.592744i
$708$	14123.2	+	8154.01i	0.749690	+	0.432834i
$709$	−17309.1	−	9993.40i	−0.916863	−	0.529351i	−0.0342303	−	0.999414i	$-0.510898\pi$
$709$	−17309.1	−	9993.40i	−0.916863	−	0.529351i	−0.882633	+	0.470063i	$0.844231\pi$
$710$		−	1522.26i		−	0.0804641i
$711$	−2241.12	+	3881.73i	−0.118212	+	0.204748i
$712$	1393.51	+	2413.64i	0.0733485	+	0.127043i
$713$	−2475.79	+	1429.40i	−0.130041	+	0.0750792i
$714$	2381.24			0.124812
$715$		0			0
$716$	−10705.9			−0.558798
$717$	722.297	−	417.018i	0.0376216	−	0.0217208i
$718$	1340.00	+	2320.95i	0.0696495	+	0.120636i
$719$	18050.9	−	31265.1i	0.936281	−	1.62169i	0.163948	−	0.986469i	$-0.447577\pi$
$719$	18050.9	−	31265.1i	0.936281	−	1.62169i	0.772333	−	0.635218i	$-0.219090\pi$
$720$		−	6343.48i		−	0.328344i
$721$	16410.7	+	9474.73i	0.847665	+	0.489400i
$722$	5156.82	+	2977.29i	0.265813	+	0.153467i
$723$		−	11148.4i		−	0.573465i
$724$	−7950.26	+	13770.2i	−0.408106	+	0.706861i
$725$	−8858.19	−	15342.8i	−0.453772	−	0.785957i
$726$	−937.648	+	541.351i	−0.0479330	+	0.0276741i
$727$	1751.90			0.0893735			0.0446868	−	0.999001i	$-0.485771\pi$
$727$	1751.90			0.0893735			0.0446868	+	0.999001i	$0.485771\pi$
$728$		0			0
$729$	16601.6			0.843451
$730$	2681.37	−	1548.09i	0.135948	−	0.0784897i
$731$	3503.76	+	6068.69i	0.177279	+	0.307057i
$732$	570.618	−	988.339i	0.0288123	−	0.0499044i
$733$		−	20031.3i		−	1.00938i	−0.863302	−	0.504688i	$-0.831607\pi$
$733$		−	20031.3i		−	1.00938i	0.863302	−	0.504688i	$-0.168393\pi$
$734$	−3001.22	−	1732.75i	−0.150922	−	0.0871350i
$735$	916.738	+	529.279i	0.0460060	+	0.0265616i
$736$			6683.10i			0.334704i
$737$	−13773.4	+	23856.2i	−0.688399	+	1.19234i
$738$	261.366	+	452.698i	0.0130366	+	0.0225800i
$739$	−16136.6	+	9316.47i	−0.803240	+	0.463751i	−0.844603	−	0.535393i	$-0.820163\pi$
$739$	−16136.6	+	9316.47i	−0.803240	+	0.463751i	0.0413627	+	0.999144i	$0.486830\pi$
$740$	−8761.62			−0.435248
$741$		0			0
$742$	−3763.17			−0.186187
$743$	4250.19	−	2453.85i	0.209858	−	0.121161i	−0.391388	−	0.920226i	$-0.628005\pi$
$743$	4250.19	−	2453.85i	0.209858	−	0.121161i	0.601245	+	0.799065i	$0.294671\pi$
$744$	−348.494	−	603.610i	−0.0171726	−	0.0297438i
$745$	−8853.12	+	15334.1i	−0.435373	+	0.754089i
$746$		−	2127.88i		−	0.104433i
$747$	393.014	+	226.906i	0.0192498	+	0.0111139i
$748$	26945.8	+	15557.2i	1.31716	+	0.760463i
$749$		−	6706.84i		−	0.327186i
$750$	1024.35	−	1774.23i	0.0498720	−	0.0863808i
$751$	15578.4	+	26982.7i	0.756945	+	1.31107i	0.944402	+	0.328794i	$0.106642\pi$
$751$	15578.4	+	26982.7i	0.756945	+	1.31107i	−0.187457	+	0.982273i	$0.560024\pi$
$752$	4934.30	−	2848.82i	0.239276	−	0.138146i
$753$	8827.93			0.427235
$754$		0			0
$755$	1242.21			0.0598790
$756$	−19644.5	+	11341.8i	−0.945058	+	0.545630i
$757$	5523.49	+	9566.97i	0.265198	+	0.459336i	0.967615	−	0.252429i	$-0.0812294\pi$
$757$	5523.49	+	9566.97i	0.265198	+	0.459336i	−0.702418	+	0.711765i	$0.747896\pi$
$758$	1295.60	−	2244.05i	0.0620823	−	0.107530i
$759$			15140.9i			0.724082i
$760$	−5989.74	−	3458.18i	−0.285882	−	0.165054i
$761$	23907.6	+	13803.0i	1.13883	+	0.657503i	0.946140	−	0.323757i	$-0.104946\pi$
$761$	23907.6	+	13803.0i	1.13883	+	0.657503i	0.192688	+	0.981260i	$0.438279\pi$
$762$			1657.00i			0.0787753i
$763$	812.702	−	1407.64i	0.0385607	−	0.0667890i
$764$	−8479.81	−	14687.5i	−0.401556	−	0.695515i
$765$	7873.16	−	4545.57i	0.372098	−	0.214831i
$766$	−492.456			−0.0232287
$767$		0			0
$768$	12052.1			0.566264
$769$	−3199.72	+	1847.36i	−0.150045	+	0.0866287i	−0.573143	−	0.819455i	$-0.694276\pi$
$769$	−3199.72	+	1847.36i	−0.150045	+	0.0866287i	0.423098	+	0.906084i	$0.360943\pi$
$770$	−1313.96	−	2275.84i	−0.0614957	−	0.106514i
$771$	5909.02	−	10234.7i	0.276016	−	0.478073i
$772$		−	9479.18i		−	0.441921i
$773$	−17154.2	−	9904.01i	−0.798183	−	0.460831i	0.0446525	−	0.999003i	$-0.485782\pi$
$773$	−17154.2	−	9904.01i	−0.798183	−	0.460831i	−0.842835	+	0.538172i	$0.819115\pi$
$774$	382.276	+	220.707i	0.0177527	+	0.0102496i
$775$		−	2137.16i		−	0.0990569i
$776$	−716.371	+	1240.79i	−0.0331395	+	0.0573992i
$777$	5236.04	+	9069.08i	0.241753	+	0.418728i
$778$	943.757	−	544.878i	0.0434901	−	0.0251090i
$779$	−14265.9			−0.656133
$780$		0			0
$781$	−23773.6			−1.08923
$782$	−2675.64	+	1544.78i	−0.122354	+	0.0706411i
$783$	19144.3	+	33159.0i	0.873771	+	1.51342i
$784$	1176.92	−	2038.48i	0.0536133	−	0.0928610i
$785$		−	23284.0i		−	1.05865i
$786$	−945.542	−	545.909i	−0.0429089	−	0.0247735i
$787$	−3565.24	−	2058.39i	−0.161483	−	0.0932322i	0.417081	−	0.908869i	$-0.363053\pi$
$787$	−3565.24	−	2058.39i	−0.161483	−	0.0932322i	−0.578564	+	0.815637i	$0.696387\pi$
$788$		−	38664.3i		−	1.74792i
$789$	8358.68	−	14477.7i	0.377157	−	0.653255i
$790$	−470.704	−	815.284i	−0.0211986	−	0.0367171i
$791$	−35818.6	+	20679.9i	−1.61007	+	0.929574i
$792$	3957.89			0.177572
$793$		0			0
$794$	2671.86			0.119422
$795$	11604.6	−	6699.91i	0.517701	−	0.298895i
$796$	3961.00	+	6860.65i	0.176374	+	0.305489i
$797$	12679.6	−	21961.8i	0.563533	−	0.976068i	−0.433652	−	0.901081i	$-0.642775\pi$
$797$	12679.6	−	21961.8i	0.563533	−	0.976068i	0.997185	−	0.0749871i	$-0.0238916\pi$
$798$			4093.59i			0.181594i
$799$	7071.58	+	4082.78i	0.313109	+	0.180774i
$800$	−4326.75	−	2498.05i	−0.191217	−	0.110399i
$801$		−	6297.74i		−	0.277802i
$802$	−2150.41	+	3724.63i	−0.0946805	+	0.163991i
$803$	−24177.0	−	41875.9i	−1.06250	−	1.84031i
$804$	−14747.6	+	8514.55i	−0.646902	+	0.373489i
$805$	−13455.8			−0.589137
$806$		0			0
$807$	−10246.1			−0.446939
$808$	−3052.55	+	1762.39i	−0.132906	+	0.0767336i
$809$	2779.37	+	4814.00i	0.120788	+	0.209211i	0.920079	−	0.391734i	$-0.128125\pi$
$809$	2779.37	+	4814.00i	0.120788	+	0.209211i	−0.799291	+	0.600944i	$0.794791\pi$
$810$	−229.796	+	398.018i	−0.00996815	+	0.0172653i
$811$			15021.4i			0.650399i	0.945646	+	0.325199i	$0.105431\pi$
$811$			15021.4i			0.650399i	−0.945646	+	0.325199i	$0.894569\pi$
$812$	−34390.5	−	19855.4i	−1.48629	−	0.858113i
$813$	22046.0	+	12728.3i	0.951029	+	0.549077i
$814$		−	2653.55i		−	0.114259i
$815$	−1125.61	+	1949.61i	−0.0483784	+	0.0837938i
$816$	9427.12	+	16328.3i	0.404431	+	0.700494i
$817$	−10432.7	+	6023.32i	−0.446749	+	0.257931i
$818$	−1377.32			−0.0588717
$819$		0			0
$820$	5661.41			0.241104
$821$	−13771.2	+	7950.78i	−0.585404	+	0.337983i	−0.763278	−	0.646070i	$-0.776411\pi$
$821$	−13771.2	+	7950.78i	−0.585404	+	0.337983i	0.177874	+	0.984053i	$0.443078\pi$
$822$	1790.24	+	3100.80i	0.0759635	+	0.131573i
$823$	−20139.6	+	34882.9i	−0.853006	+	1.47745i	0.0254768	+	0.999675i	$0.491890\pi$
$823$	−20139.6	+	34882.9i	−0.853006	+	1.47745i	−0.878483	+	0.477774i	$0.841444\pi$
$824$		−	5994.23i		−	0.253421i
$825$	−9802.45	−	5659.45i	−0.413670	−	0.238832i
$826$	−3801.32	−	2194.70i	−0.160127	−	0.0924494i
$827$			5251.09i			0.220796i	0.993887	+	0.110398i	$0.0352125\pi$
$827$			5251.09i			0.220796i	−0.993887	+	0.110398i	$0.964787\pi$
$828$	5017.78	−	8691.06i	0.210604	−	0.364777i
$829$	16982.2	+	29414.0i	0.711479	+	1.23232i	0.964302	+	0.264805i	$0.0853075\pi$
$829$	16982.2	+	29414.0i	0.711479	+	1.23232i	−0.252823	+	0.967512i	$0.581359\pi$
$830$	−82.5451	+	47.6574i	−0.00345203	+	0.00199303i
$831$	6996.65			0.292071
$832$		0			0
$833$	3373.40			0.140314
$834$	−349.171	+	201.594i	−0.0144974	+	0.00837005i
$835$	11301.5	+	19574.7i	0.468388	+	0.811272i
$836$	−26744.4	+	46322.6i	−1.10643	+	1.91639i
$837$			4618.83i			0.190741i
$838$	1411.95	+	815.188i	0.0582039	+	0.0336041i
$839$	13410.4	+	7742.49i	0.551821	+	0.318594i	0.749856	−	0.661601i	$-0.230123\pi$
$839$	13410.4	+	7742.49i	0.551821	+	0.318594i	−0.198035	+	0.980195i	$0.563456\pi$
$840$		−	3280.59i		−	0.134751i
$841$	−21320.4	+	36928.0i	−0.874181	+	1.51413i
$842$	−1211.17	−	2097.81i	−0.0495722	−	0.0858615i
$843$	10287.1	−	5939.24i	0.420291	−	0.242655i
$844$	−38543.1			−1.57193
$845$		0			0
$846$	514.361			0.0209032
$847$	−13013.8	+	7513.54i	−0.527935	+	0.304803i
$848$	−14898.1	−	25804.3i	−0.603305	−	1.04496i
$849$	−14290.8	+	24752.4i	−0.577691	+	1.00059i
$850$		−	2309.67i		−	0.0932014i
$851$	−11766.8	−	6793.56i	−0.473984	−	0.273655i
$852$	−12727.6	−	7348.28i	−0.511784	−	0.295479i
$853$			20057.8i			0.805118i	0.915394	+	0.402559i	$0.131879\pi$
$853$			20057.8i			0.805118i	−0.915394	+	0.402559i	$0.868121\pi$
$854$	−153.585	+	266.017i	−0.00615406	+	0.0106591i
$855$	7814.31	+	13534.8i	0.312566	+	0.541380i
$856$	−1837.32	+	1060.78i	−0.0733625	+	0.0423559i
$857$	8066.23			0.321514			0.160757	−	0.986994i	$-0.448606\pi$
$857$	8066.23			0.321514			0.160757	+	0.986994i	$0.448606\pi$
$858$		0			0
$859$	39719.0			1.57764			0.788821	−	0.614623i	$-0.210692\pi$
$859$	39719.0			1.57764			0.788821	+	0.614623i	$0.210692\pi$
$860$	4140.22	−	2390.36i	0.164163	−	0.0947796i
$861$	−3383.32	−	5860.08i	−0.133918	−	0.231952i
$862$	−2317.33	+	4013.73i	−0.0915644	+	0.158594i
$863$			24473.8i			0.965351i	0.875799	+	0.482676i	$0.160335\pi$
$863$			24473.8i			0.965351i	−0.875799	+	0.482676i	$0.839665\pi$
$864$	9350.98	+	5398.79i	0.368202	+	0.212582i
$865$	2969.28	+	1714.32i	0.116715	+	0.0673856i
$866$		−	3404.03i		−	0.133572i
$867$	−4643.31	+	8042.45i	−0.181886	+	0.315036i
$868$	−2395.19	−	4148.60i	−0.0936614	−	0.162226i
$869$	−12732.5	+	7351.13i	−0.497033	+	0.286962i
$870$	−2742.15			−0.106859
$871$		0			0
$872$	−514.159			−0.0199675
$873$	2803.77	−	1618.76i	0.108698	−	0.0627567i
$874$	−2655.64	−	4599.71i	−0.102779	−	0.178018i
$875$	14217.2	−	24624.9i	0.549290	−	0.951399i
$876$		−	29891.9i		−	1.15291i
$877$	−21933.5	−	12663.3i	−0.844515	−	0.487581i	0.0142811	−	0.999898i	$-0.495454\pi$
$877$	−21933.5	−	12663.3i	−0.844515	−	0.487581i	−0.858797	+	0.512317i	$0.828787\pi$
$878$	−405.546	−	234.142i	−0.0155883	−	0.00899990i
$879$		−	20486.4i		−	0.786109i
$880$	10403.7	−	18019.7i	0.398532	−	0.690278i
$881$	663.719	+	1149.59i	0.0253817	+	0.0439624i	0.878437	−	0.477858i	$-0.158587\pi$
$881$	663.719	+	1149.59i	0.0253817	+	0.0439624i	−0.853056	+	0.521820i	$0.825253\pi$
$882$	184.027	−	106.248i	0.00702551	−	0.00405618i
$883$	2112.05			0.0804941			0.0402470	−	0.999190i	$-0.487186\pi$
$883$	2112.05			0.0804941			0.0402470	+	0.999190i	$0.487186\pi$
$884$		0			0
$885$	15629.6			0.593655
$886$	763.154	−	440.607i	0.0289375	−	0.0167071i
$887$	20467.7	+	35451.1i	0.774790	+	1.34197i	0.934913	+	0.354878i	$0.115478\pi$
$887$	20467.7	+	35451.1i	0.774790	+	1.34197i	−0.160123	+	0.987097i	$0.551189\pi$
$888$	1656.30	−	2868.80i	0.0625921	−	0.108413i
$889$			22997.9i			0.867632i
$890$	1145.51	+	661.361i	0.0431434	+	0.0249088i
$891$	6215.97	+	3588.79i	0.233718	+	0.134937i
$892$			10708.9i			0.401975i
$893$	−7018.72	+	12156.8i	−0.263015	+	0.455555i
$894$	−1657.53	−	2870.92i	−0.0620089	−	0.107403i
$895$	−8885.94	+	5130.30i	−0.331871	+	0.191606i
$896$	−14881.0			−0.554845
$897$		0			0
$898$	5720.04			0.212562
$899$	−7002.62	+	4042.96i	−0.259789	+	0.149989i
$900$	3751.16	+	6497.20i	0.138932	+	0.240637i
$901$	21351.2	−	36981.3i	0.789468	−	1.36740i
$902$			1714.62i			0.0632934i
$903$	−4948.48	−	2857.00i	−0.182364	−	0.105288i
$904$	11330.4	+	6541.61i	0.416862	+	0.240676i
$905$			15239.1i			0.559740i
$906$	−116.286	+	201.414i	−0.00426419	+	0.00738580i
$907$	76.9840	+	133.340i	0.00281831	+	0.00488146i	0.867431	−	0.497557i	$-0.165770\pi$
$907$	76.9840	+	133.340i	0.00281831	+	0.00488146i	−0.864613	+	0.502439i	$0.832436\pi$
$908$	28340.2	−	16362.2i	1.03580	−	0.598017i
$909$	7964.82			0.290623
$910$		0			0
$911$	−733.607			−0.0266800			−0.0133400	−	0.999911i	$-0.504246\pi$
$911$	−733.607			−0.0266800			−0.0133400	+	0.999911i	$0.504246\pi$
$912$	−28070.0	+	16206.2i	−1.01918	+	0.588422i
$913$	744.280	+	1289.13i	0.0269793	+	0.0467295i
$914$	−1820.85	+	3153.81i	−0.0658954	+	0.114134i
$915$		−	1093.76i		−	0.0395177i
$916$	23834.3	+	13760.7i	0.859723	+	0.496361i
$917$	−13123.4	−	7576.80i	−0.472599	−	0.272855i
$918$			4991.67i			0.179466i
$919$	25553.2	−	44259.4i	0.917216	−	1.58867i	0.113592	−	0.993527i	$-0.463764\pi$
$919$	25553.2	−	44259.4i	0.917216	−	1.58867i	0.803624	−	0.595138i	$-0.202902\pi$
$920$	2128.22	+	3686.18i	0.0762667	+	0.132098i
$921$	13563.5	−	7830.92i	0.485270	−	0.280171i
$922$	4188.61			0.149615
$923$		0			0
$924$	−25371.0			−0.903294
$925$	8796.53	−	5078.68i	0.312679	−	0.180525i
$926$	2077.37	+	3598.10i	0.0737219	+	0.127690i
$927$	−6772.46	+	11730.2i	−0.239953	+	0.415611i
$928$			18902.7i			0.668655i
$929$	26539.5	+	15322.6i	0.937280	+	0.541139i	0.889107	−	0.457700i	$-0.151327\pi$
$929$	26539.5	+	15322.6i	0.937280	+	0.541139i	0.0481735	+	0.998839i	$0.484660\pi$
$930$	−286.473	−	165.395i	−0.0101009	−	0.00583174i
$931$			5799.22i			0.204148i
$932$	−2237.62	+	3875.67i	−0.0786433	+	0.136214i
$933$	−9447.85	−	16364.2i	−0.331520	−	0.574210i
$934$	891.284	−	514.583i	0.0312245	−	0.0180275i
$935$	29820.0			1.04302
$936$		0			0
$937$	−24422.2			−0.851482			−0.425741	−	0.904845i	$-0.639987\pi$
$937$	−24422.2			−0.851482			−0.425741	+	0.904845i	$0.639987\pi$
$938$	3969.41	−	2291.74i	0.138172	−	0.0797739i
$939$	−3912.62	−	6776.86i	−0.135978	−	0.235521i
$940$	2785.38	−	4824.41i	0.0966479	−	0.167399i
$941$		−	16475.9i		−	0.570774i	−0.958412	−	0.285387i	$-0.907878\pi$
$941$		−	16475.9i		−	0.570774i	0.958412	−	0.285387i	$-0.0921221\pi$
$942$	3775.31	+	2179.68i	0.130580	+	0.0753904i
$943$	7603.23	+	4389.73i	0.262561	+	0.151590i
$944$		−	34754.5i		−	1.19827i
$945$	−10870.0	+	18827.4i	−0.374180	+	0.648099i
$946$	723.946	+	1253.91i	0.0248811	+	0.0430953i
$947$	8765.97	−	5061.03i	0.300798	−	0.173666i	−0.342003	−	0.939699i	$-0.611105\pi$
$947$	8765.97	−	5061.03i	0.300798	−	0.173666i	0.642801	+	0.766033i	$0.277772\pi$
$948$	−9088.76			−0.311381
$949$		0			0
$950$	3970.57			0.135602
$951$	15204.3	−	8778.18i	0.518435	−	0.299319i
$952$	−5227.27	−	9053.89i	−0.177959	−	0.308233i
$953$	19048.6	−	32993.1i	0.647475	−	1.12146i	−0.336248	−	0.941773i	$-0.609158\pi$
$953$	19048.6	−	32993.1i	0.647475	−	1.12146i	0.983724	−	0.179687i	$-0.0575085\pi$
$954$		−	2689.89i		−	0.0912875i
$955$	−14076.5	−	8127.07i	−0.476968	−	0.275378i
$956$	−1570.35	−	906.643i	−0.0531264	−	0.0306725i
$957$			42824.9i			1.44653i
$958$	−629.121	+	1089.67i	−0.0212171	+	0.0367491i
$959$	24847.2	+	43036.7i	0.836662	+	1.44914i
$960$	10685.9	−	6169.50i	0.359256	−	0.207417i
$961$	28815.6			0.967258
$962$		0			0
$963$	4794.00			0.160420
$964$	−20990.7	+	12119.0i	−0.701311	+	0.404902i
$965$	−4542.43	−	7867.73i	−0.151530	−	0.262457i
$966$	1259.63	−	2181.75i	0.0419545	−	0.0726673i
$967$		−	44515.5i		−	1.48037i	−0.672401	−	0.740187i	$-0.734737\pi$
$967$		−	44515.5i		−	1.48037i	0.672401	−	0.740187i	$-0.265263\pi$
$968$	4116.63	+	2376.74i	0.136687	+	0.0789165i
$969$	−40228.4	−	23225.9i	−1.33367	−	0.769993i
$970$			679.978i			0.0225080i
$971$	12722.2	−	22035.4i	0.420467	−	0.728270i	−0.575518	−	0.817789i	$-0.695200\pi$
$971$	12722.2	−	22035.4i	0.420467	−	0.728270i	0.995985	+	0.0895186i	$0.0285329\pi$
$972$	−13449.6	−	23295.5i	−0.443824	−	0.768726i
$973$	−4846.22	+	2797.97i	−0.159674	+	0.0921878i
$974$	−583.765			−0.0192044
$975$		0			0
$976$	−2432.12			−0.0797646
$977$	34180.2	−	19734.0i	1.11927	−	0.646208i	0.178052	−	0.984021i	$-0.443020\pi$
$977$	34180.2	−	19734.0i	1.11927	−	0.646208i	0.941213	+	0.337813i	$0.109687\pi$
$978$	−210.742	−	365.016i	−0.00689038	−	0.0119345i
$979$	10328.7	−	17889.8i	0.337187	−	0.584025i
$980$		−	2301.42i		−	0.0750165i
$981$	1006.17	+	580.913i	0.0327467	+	0.0189063i
$982$	−175.144	−	101.119i	−0.00569152	−	0.00328600i
$983$			14970.4i			0.485740i	0.970059	+	0.242870i	$0.0780888\pi$
$983$			14970.4i			0.485740i	−0.970059	+	0.242870i	$0.921911\pi$
$984$	−1070.24	+	1853.70i	−0.0346726	+	0.0600547i
$985$	−18528.0	−	32091.4i	−0.599340	−	1.03809i
$986$	−7567.88	+	4369.31i	−0.244432	+	0.141123i
$987$	−6658.28			−0.214727
$988$		0			0
$989$	7413.71			0.238364
$990$	1626.75	−	939.205i	0.0522238	−	0.0301514i
$991$	−29211.2	−	50595.3i	−0.936352	−	1.62181i	−0.772206	−	0.635373i	$-0.780846\pi$
$991$	−29211.2	−	50595.3i	−0.936352	−	1.62181i	−0.164146	−	0.986436i	$-0.552487\pi$
$992$	−1140.13	+	1974.77i	−0.0364912	+	0.0632047i
$993$		−	9692.91i		−	0.309763i
$994$	3425.70	+	1977.83i	0.109313	+	0.0631116i
$995$	6575.26	+	3796.23i	0.209497	+	0.120953i
$996$			920.210i			0.0292751i
$997$	−10065.8	+	17434.5i	−0.319746	+	0.553817i	−0.980435	−	0.196843i	$-0.936931\pi$
$997$	−10065.8	+	17434.5i	−0.319746	+	0.553817i	0.660689	+	0.750660i	$0.270264\pi$
$998$	469.115	+	812.531i	0.0148793	+	0.0257718i
$999$	−19011.1	+	10976.0i	−0.602086	+	0.347614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.11		36
13.2	odd	12		169.4.a.k.1.6	✓	9
13.3	even	3		169.4.b.g.168.11		18
13.4	even	6	inner	169.4.e.h.147.11		36
13.5	odd	4		169.4.c.l.146.4		18
13.6	odd	12		169.4.c.l.22.4		18
13.7	odd	12		169.4.c.k.22.6		18
13.8	odd	4		169.4.c.k.146.6		18
13.9	even	3	inner	169.4.e.h.147.8		36
13.10	even	6		169.4.b.g.168.8		18
13.11	odd	12		169.4.a.l.1.4	yes	9
13.12	even	2	inner	169.4.e.h.23.8		36
39.2	even	12		1521.4.a.bh.1.4		9
39.11	even	12		1521.4.a.bg.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.6	✓	9	13.2	odd	12
169.4.a.l.1.4	yes	9	13.11	odd	12
169.4.b.g.168.8		18	13.10	even	6
169.4.b.g.168.11		18	13.3	even	3
169.4.c.k.22.6		18	13.7	odd	12
169.4.c.k.146.6		18	13.8	odd	4
169.4.c.l.22.4		18	13.6	odd	12
169.4.c.l.146.4		18	13.5	odd	4
169.4.e.h.23.8		36	13.12	even	2	inner
169.4.e.h.23.11		36	1.1	even	1	trivial
169.4.e.h.147.8		36	13.9	even	3	inner
169.4.e.h.147.11		36	13.4	even	6	inner
1521.4.a.bg.1.6		9	39.11	even	12
1521.4.a.bh.1.4		9	39.2	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.337850 - 0.195058i) q^{2} +(-1.80483 - 3.12606i) q^{3} +(-3.92391 + 6.79640i) q^{4} +7.52136i q^{5} +(-1.21953 - 0.704093i) q^{6} +(-16.9261 - 9.77228i) q^{7} +6.18247i q^{8} +(6.98515 - 12.0986i) q^{9} +O(q^{10})\)	\(q+(0.337850 - 0.195058i) q^{2} +(-1.80483 - 3.12606i) q^{3} +(-3.92391 + 6.79640i) q^{4} +7.52136i q^{5} +(-1.21953 - 0.704093i) q^{6} +(-16.9261 - 9.77228i) q^{7} +6.18247i q^{8} +(6.98515 - 12.0986i) q^{9} +(1.46710 + 2.54109i) q^{10} +(39.6850 - 22.9121i) q^{11} +28.3280 q^{12} -7.62463 q^{14} +(23.5123 - 13.5748i) q^{15} +(-30.1853 - 52.2825i) q^{16} +(43.2600 - 74.9285i) q^{17} -5.45003i q^{18} +(128.810 + 74.3684i) q^{19} +(-51.1182 - 29.5131i) q^{20} +70.5494i q^{21} +(8.93837 - 15.4817i) q^{22} +(-45.7676 - 79.2718i) q^{23} +(19.3268 - 11.1583i) q^{24} +68.4292 q^{25} -147.889 q^{27} +(132.833 - 76.6910i) q^{28} +(-129.451 - 224.215i) q^{29} +(5.29574 - 9.17249i) q^{30} -31.2317i q^{31} +(-63.2296 - 36.5056i) q^{32} +(-143.250 - 82.7052i) q^{33} -33.7528i q^{34} +(73.5008 - 127.307i) q^{35} +(54.8181 + 94.9478i) q^{36} +(128.549 - 74.2180i) q^{37} +58.0245 q^{38} -46.5006 q^{40} +(-83.0635 + 47.9567i) q^{41} +(13.7612 + 23.8351i) q^{42} +(-40.4965 + 70.1420i) q^{43} +359.620i q^{44} +(90.9982 + 52.5378i) q^{45} +(-30.9251 - 17.8546i) q^{46} +94.3777i q^{47} +(-108.959 + 188.722i) q^{48} +(19.4949 + 33.7662i) q^{49} +(23.1188 - 13.3476i) q^{50} -312.308 q^{51} +493.555 q^{53} +(-49.9643 + 28.8469i) q^{54} +(172.330 + 298.485i) q^{55} +(60.4169 - 104.645i) q^{56} -536.891i q^{57} +(-87.4697 - 50.5006i) q^{58} +(498.558 + 287.843i) q^{59} +213.065i q^{60} +(20.1432 - 34.8891i) q^{61} +(-6.09199 - 10.5516i) q^{62} +(-236.462 + 136.522i) q^{63} +454.482 q^{64} -64.5291 q^{66} +(-520.603 + 300.570i) q^{67} +(339.496 + 588.025i) q^{68} +(-165.206 + 286.145i) q^{69} -57.3476i q^{70} +(-449.294 - 259.400i) q^{71} +(74.7995 + 43.1855i) q^{72} -1055.21i q^{73} +(28.9536 - 50.1491i) q^{74} +(-123.503 - 213.914i) q^{75} +(-1010.88 + 583.629i) q^{76} -895.615 q^{77} -320.840 q^{79} +(393.235 - 227.034i) q^{80} +(78.3164 + 135.648i) q^{81} +(-18.7087 + 32.4043i) q^{82} +32.4841i q^{83} +(-479.482 - 276.829i) q^{84} +(563.564 + 325.374i) q^{85} +31.5966i q^{86} +(-467.274 + 809.341i) q^{87} +(141.654 + 245.351i) q^{88} +(390.400 - 225.398i) q^{89} +40.9916 q^{90} +718.350 q^{92} +(-97.6324 + 56.3681i) q^{93} +(18.4091 + 31.8855i) q^{94} +(-559.352 + 968.826i) q^{95} +263.546i q^{96} +(200.695 + 115.871i) q^{97} +(13.1727 + 7.60526i) q^{98} -640.179i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more