LMFDB - Embedded newform 169.4.c.l.22.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} + 62 x^{16} - 106 x^{15} + 2016 x^{14} - 2731 x^{13} + 39895 x^{12} - 21896 x^{11} + \cdots + 16777216 $ x^18 - 4x^17 + 62x^16 - 106x^15 + 2016x^14 - 2731x^13 + 39895x^12 - 21896x^11 + 490851x^10 - 318018x^9 + 3391249x^8 - 990441x^7 + 13815033x^6 - 7349264x^5 + 28218112x^4 - 9093120x^3 + 32440320x^2 - 14680064*x + 16777216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.4
Root			$0.695058 + 1.20388i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.l.146.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.195058 + 0.337850i) q^{2} +(-1.80483 + 3.12606i) q^{3} +(3.92391 + 6.79640i) q^{4} +7.52136 q^{5} +(-0.704093 - 1.21953i) q^{6} +(9.77228 + 16.9261i) q^{7} -6.18247 q^{8} +(6.98515 + 12.0986i) q^{9} +O(q^{10})$	\(q+(-0.195058 + 0.337850i) q^{2} +(-1.80483 + 3.12606i) q^{3} +(3.92391 + 6.79640i) q^{4} +7.52136 q^{5} +(-0.704093 - 1.21953i) q^{6} +(9.77228 + 16.9261i) q^{7} -6.18247 q^{8} +(6.98515 + 12.0986i) q^{9} +(-1.46710 + 2.54109i) q^{10} +(22.9121 - 39.6850i) q^{11} -28.3280 q^{12} -7.62463 q^{14} +(-13.5748 + 23.5123i) q^{15} +(-30.1853 + 52.2825i) q^{16} +(-43.2600 - 74.9285i) q^{17} -5.45003 q^{18} +(74.3684 + 128.810i) q^{19} +(29.5131 + 51.1182i) q^{20} -70.5494 q^{21} +(8.93837 + 15.4817i) q^{22} +(45.7676 - 79.2718i) q^{23} +(11.1583 - 19.3268i) q^{24} -68.4292 q^{25} -147.889 q^{27} +(-76.6910 + 132.833i) q^{28} +(-129.451 + 224.215i) q^{29} +(-5.29574 - 9.17249i) q^{30} -31.2317 q^{31} +(-36.5056 - 63.2296i) q^{32} +(82.7052 + 143.250i) q^{33} +33.7528 q^{34} +(73.5008 + 127.307i) q^{35} +(-54.8181 + 94.9478i) q^{36} +(74.2180 - 128.549i) q^{37} -58.0245 q^{38} -46.5006 q^{40} +(47.9567 - 83.0635i) q^{41} +(13.7612 - 23.8351i) q^{42} +(40.4965 + 70.1420i) q^{43} +359.620 q^{44} +(52.5378 + 90.9982i) q^{45} +(17.8546 + 30.9251i) q^{46} -94.3777 q^{47} +(-108.959 - 188.722i) q^{48} +(-19.4949 + 33.7662i) q^{49} +(13.3476 - 23.1188i) q^{50} +312.308 q^{51} +493.555 q^{53} +(28.8469 - 49.9643i) q^{54} +(172.330 - 298.485i) q^{55} +(-60.4169 - 104.645i) q^{56} -536.891 q^{57} +(-50.5006 - 87.4697i) q^{58} +(-287.843 - 498.558i) q^{59} -213.065 q^{60} +(20.1432 + 34.8891i) q^{61} +(6.09199 - 10.5516i) q^{62} +(-136.522 + 236.462i) q^{63} -454.482 q^{64} -64.5291 q^{66} +(300.570 - 520.603i) q^{67} +(339.496 - 588.025i) q^{68} +(165.206 + 286.145i) q^{69} -57.3476 q^{70} +(-259.400 - 449.294i) q^{71} +(-43.1855 - 74.7995i) q^{72} +1055.21 q^{73} +(28.9536 + 50.1491i) q^{74} +(123.503 - 213.914i) q^{75} +(-583.629 + 1010.88i) q^{76} +895.615 q^{77} -320.840 q^{79} +(-227.034 + 393.235i) q^{80} +(78.3164 - 135.648i) q^{81} +(18.7087 + 32.4043i) q^{82} +32.4841 q^{83} +(-276.829 - 479.482i) q^{84} +(-325.374 - 563.564i) q^{85} -31.5966 q^{86} +(-467.274 - 809.341i) q^{87} +(-141.654 + 245.351i) q^{88} +(225.398 - 390.400i) q^{89} -40.9916 q^{90} +718.350 q^{92} +(56.3681 - 97.6324i) q^{93} +(18.4091 - 31.8855i) q^{94} +(559.352 + 968.826i) q^{95} +263.546 q^{96} +(115.871 + 200.695i) q^{97} +(-7.60526 - 13.1727i) q^{98} +640.179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.195058	+	0.337850i	−0.0689633	+	0.119448i	−0.898445	−	0.439086i	$-0.855302\pi$
$2$	−0.195058	+	0.337850i	−0.0689633	+	0.119448i	0.829482	+	0.558534i	$0.188636\pi$
$3$	−1.80483	+	3.12606i	−0.347340	+	0.601611i	−0.985776	−	0.168064i	$-0.946249\pi$
$3$	−1.80483	+	3.12606i	−0.347340	+	0.601611i	0.638436	+	0.769675i	$0.279582\pi$
$4$	3.92391	+	6.79640i	0.490488	+	0.849550i
$5$	7.52136			0.672731			0.336365	−	0.941732i	$-0.390802\pi$
$5$	7.52136			0.672731			0.336365	+	0.941732i	$0.390802\pi$
$6$	−0.704093	−	1.21953i	−0.0479075	−	0.0829782i
$7$	9.77228	+	16.9261i	0.527654	+	0.913923i	0.999480	+	0.0322315i	$0.0102614\pi$
$7$	9.77228	+	16.9261i	0.527654	+	0.913923i	−0.471827	+	0.881691i	$0.656405\pi$
$8$	−6.18247			−0.273229
$9$	6.98515	+	12.0986i	0.258709	+	0.448098i
$10$	−1.46710	+	2.54109i	−0.0463937	+	0.0803563i
$11$	22.9121	−	39.6850i	0.628024	−	1.08777i	−0.359923	−	0.932982i	$-0.617197\pi$
$11$	22.9121	−	39.6850i	0.628024	−	1.08777i	0.987948	−	0.154788i	$-0.0494695\pi$
$12$	−28.3280			−0.681465
$13$		0			0
$13$		0			0
$14$	−7.62463			−0.145555
$15$	−13.5748	+	23.5123i	−0.233667	+	0.404722i
$16$	−30.1853	+	52.2825i	−0.471645	+	0.816914i
$17$	−43.2600	−	74.9285i	−0.617182	−	1.06899i	−0.989998	−	0.141085i	$-0.954941\pi$
$17$	−43.2600	−	74.9285i	−0.617182	−	1.06899i	0.372816	−	0.927905i	$-0.378392\pi$
$18$	−5.45003			−0.0713658
$19$	74.3684	+	128.810i	0.897963	+	1.55532i	0.830095	+	0.557623i	$0.188286\pi$
$19$	74.3684	+	128.810i	0.897963	+	1.55532i	0.0678680	+	0.997694i	$0.478380\pi$
$20$	29.5131	+	51.1182i	0.329966	+	0.571519i
$21$	−70.5494			−0.733102
$22$	8.93837	+	15.4817i	0.0866212	+	0.150032i
$23$	45.7676	−	79.2718i	0.414922	−	0.718665i	−0.580499	−	0.814261i	$-0.697142\pi$
$23$	45.7676	−	79.2718i	0.414922	−	0.718665i	0.995420	+	0.0955958i	$0.0304756\pi$
$24$	11.1583	−	19.3268i	0.0949036	−	0.164378i
$25$	−68.4292			−0.547433
$26$		0			0
$27$	−147.889			−1.05412
$28$	−76.6910	+	132.833i	−0.517616	+	0.896536i
$29$	−129.451	+	224.215i	−0.828909	+	1.43571i	0.0699855	+	0.997548i	$0.477705\pi$
$29$	−129.451	+	224.215i	−0.828909	+	1.43571i	−0.898895	+	0.438165i	$0.855629\pi$
$30$	−5.29574	−	9.17249i	−0.0322288	−	0.0558220i
$31$	−31.2317			−0.180948			−0.0904739	−	0.995899i	$-0.528838\pi$
$31$	−31.2317			−0.180948			−0.0904739	+	0.995899i	$0.528838\pi$
$32$	−36.5056	−	63.2296i	−0.201667	−	0.349298i
$33$	82.7052	+	143.250i	0.436276	+	0.755653i
$34$	33.7528			0.170252
$35$	73.5008	+	127.307i	0.354969	+	0.614824i
$36$	−54.8181	+	94.9478i	−0.253788	+	0.439573i
$37$	74.2180	−	128.549i	0.329767	−	0.571173i	−0.652699	−	0.757618i	$-0.726363\pi$
$37$	74.2180	−	128.549i	0.329767	−	0.571173i	0.982465	+	0.186445i	$0.0596966\pi$
$38$	−58.0245			−0.247706
$39$		0			0
$40$	−46.5006			−0.183810
$41$	47.9567	−	83.0635i	0.182673	−	0.316399i	−0.760117	−	0.649786i	$-0.774858\pi$
$41$	47.9567	−	83.0635i	0.182673	−	0.316399i	0.942790	+	0.333388i	$0.108192\pi$
$42$	13.7612	−	23.8351i	0.0505571	−	0.0875675i
$43$	40.4965	+	70.1420i	0.143620	+	0.248757i	0.928857	−	0.370438i	$-0.120792\pi$
$43$	40.4965	+	70.1420i	0.143620	+	0.248757i	−0.785237	+	0.619195i	$0.787459\pi$
$44$	359.620			1.23215
$45$	52.5378	+	90.9982i	0.174042	+	0.301449i
$46$	17.8546	+	30.9251i	0.0572287	+	0.0991231i
$47$	−94.3777			−0.292902			−0.146451	−	0.989218i	$-0.546785\pi$
$47$	−94.3777			−0.292902			−0.146451	+	0.989218i	$0.546785\pi$
$48$	−108.959	−	188.722i	−0.327643	−	0.567494i
$49$	−19.4949	+	33.7662i	−0.0568365	+	0.0984436i
$50$	13.3476	−	23.1188i	0.0377528	−	0.0653898i
$51$	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	$0.279110\pi$
$54$	28.8469	−	49.9643i	0.0726957	−	0.125913i
$55$	172.330	−	298.485i	0.422491	−	0.731776i
$56$	−60.4169	−	104.645i	−0.144170	−	0.249710i
$57$	−536.891			−1.24759
$58$	−50.5006	−	87.4697i	−0.114329	−	0.198023i
$59$	−287.843	−	498.558i	−0.635152	−	1.10011i	−0.986483	−	0.163864i	$-0.947604\pi$
$59$	−287.843	−	498.558i	−0.635152	−	1.10011i	0.351331	−	0.936251i	$-0.385729\pi$
$60$	−213.065			−0.458443
$61$	20.1432	+	34.8891i	0.0422800	+	0.0732311i	0.886391	−	0.462937i	$-0.153205\pi$
$61$	20.1432	+	34.8891i	0.0422800	+	0.0732311i	−0.844111	+	0.536168i	$0.819871\pi$
$62$	6.09199	−	10.5516i	0.0124788	−	0.0216138i
$63$	−136.522	+	236.462i	−0.273018	+	0.472880i
$64$	−454.482			−0.887660
$65$		0			0
$66$	−64.5291			−0.120348
$67$	300.570	−	520.603i	0.548067	−	0.949280i	−0.450340	−	0.892857i	$-0.648697\pi$
$67$	300.570	−	520.603i	0.548067	−	0.949280i	0.998407	−	0.0564231i	$-0.0179696\pi$
$68$	339.496	−	588.025i	0.605441	−	1.04865i
$69$	165.206	+	286.145i	0.288238	+	0.499243i
$70$	−57.3476			−0.0979193
$71$	−259.400	−	449.294i	−0.433593	−	0.751006i	0.563586	−	0.826057i	$-0.309421\pi$
$71$	−259.400	−	449.294i	−0.433593	−	0.751006i	−0.997180	+	0.0750515i	$0.976088\pi$
$72$	−43.1855	−	74.7995i	−0.0706869	−	0.122433i
$73$	1055.21			1.69182			0.845908	−	0.533328i	$-0.179059\pi$
$73$	1055.21			1.69182			0.845908	+	0.533328i	$0.179059\pi$
$74$	28.9536	+	50.1491i	0.0454836	+	0.0787799i
$75$	123.503	−	213.914i	0.190146	−	0.329342i
$76$	−583.629	+	1010.88i	−0.880880	+	1.52573i
$77$	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	$0.573370\pi$
$80$	−227.034	+	393.235i	−0.317290	+	0.549563i
$81$	78.3164	−	135.648i	0.107430	−	0.186074i
$82$	18.7087	+	32.4043i	0.0251954	+	0.0436398i
$83$	32.4841			0.0429590			0.0214795	−	0.999769i	$-0.493162\pi$
$83$	32.4841			0.0429590			0.0214795	+	0.999769i	$0.493162\pi$
$84$	−276.829	−	479.482i	−0.359578	−	0.622807i
$85$	−325.374	−	563.564i	−0.415197	−	0.719143i
$86$	−31.5966			−0.0396180
$87$	−467.274	−	809.341i	−0.575827	−	0.997362i
$88$	−141.654	+	245.351i	−0.171595	+	0.297211i
$89$	225.398	−	390.400i	0.268450	−	0.464970i	−0.700011	−	0.714132i	$-0.746822\pi$
$89$	225.398	−	390.400i	0.268450	−	0.464970i	0.968462	+	0.249162i	$0.0801551\pi$
$90$	−40.9916			−0.0480099
$91$		0			0
$92$	718.350			0.814057
$93$	56.3681	−	97.6324i	0.0628505	−	0.108860i
$94$	18.4091	−	31.8855i	0.0201995	−	0.0349865i
$95$	559.352	+	968.826i	0.604087	+	1.04631i
$96$	263.546			0.280189
$97$	115.871	+	200.695i	0.121288	+	0.210077i	0.920276	−	0.391270i	$-0.127964\pi$
$97$	115.871	+	200.695i	0.121288	+	0.210077i	−0.798988	+	0.601347i	$0.794631\pi$
$98$	−7.60526	−	13.1727i	−0.00783926	−	0.0135780i
$99$	640.179			0.649903
$100$	−268.510	−	465.072i	−0.268510	−	0.465072i
$101$	−285.063	+	493.743i	−0.280840	+	0.486428i	−0.971592	−	0.236663i	$-0.923946\pi$
$101$	−285.063	+	493.743i	−0.280840	+	0.486428i	0.690752	+	0.723092i	$0.257280\pi$
$102$	−60.9181	+	105.513i	−0.0591352	+	0.102425i
$103$	969.551			0.927502			0.463751	−	0.885965i	$-0.346503\pi$
$103$	969.551			0.927502			0.463751	+	0.885965i	$0.346503\pi$
$104$		0			0
$105$	−530.627			−0.493180
$106$	−96.2716	+	166.747i	−0.0882144	+	0.152792i
$107$	171.578	−	297.182i	0.155019	−	0.268502i	−0.778047	−	0.628207i	$-0.783789\pi$
$107$	171.578	−	297.182i	0.155019	−	0.268502i	0.933066	+	0.359705i	$0.117123\pi$
$108$	−580.303	−	1005.11i	−0.517034	−	0.895529i
$109$	83.1640			0.0730795			0.0365398	−	0.999332i	$-0.488366\pi$
$109$	83.1640			0.0730795			0.0365398	+	0.999332i	$0.488366\pi$
$110$	67.2287	+	116.444i	0.0582728	+	0.100931i
$111$	267.902	+	464.021i	0.229083	+	0.396783i
$112$	−1179.92			−0.995461
$113$	1058.09	+	1832.67i	0.880856	+	1.52569i	0.850391	+	0.526152i	$0.176366\pi$
$113$	1058.09	+	1832.67i	0.880856	+	1.52569i	0.0304652	+	0.999536i	$0.490301\pi$
$114$	104.725	−	181.388i	0.0860383	−	0.149023i
$115$	344.234	−	596.231i	0.279131	−	0.483468i
$116$	−2031.81			−1.62628
$117$		0			0
$118$	224.584			0.175209
$119$	845.498	−	1464.44i	0.651316	−	1.12811i
$120$	83.9259	−	145.364i	0.0638446	−	0.110582i
$121$	−384.431	−	665.855i	−0.288829	−	0.500266i
$122$	−15.7164			−0.0116631
$123$	173.108	+	299.832i	0.126899	+	0.219796i
$124$	−122.550	−	212.263i	−0.0887528	−	0.153724i
$125$	−1454.85			−1.04101
$126$	−53.2592	−	92.2476i	−0.0376564	−	0.0652228i
$127$	588.346	−	1019.04i	0.411081	−	0.712012i	−0.583928	−	0.811806i	$-0.698485\pi$
$127$	588.346	−	1019.04i	0.411081	−	0.712012i	0.995008	+	0.0997933i	$0.0318182\pi$
$128$	380.695	−	659.384i	0.262883	−	0.455327i
$129$	−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	$0.416754\pi$
$132$	−649.055	+	1124.20i	−0.427977	+	0.741278i
$133$	−1453.50	+	2517.53i	−0.947626	+	1.64134i
$134$	117.257	+	203.095i	0.0755931	+	0.130931i
$135$	−1112.33			−0.709140
$136$	267.454	+	463.243i	0.168632	+	0.292079i
$137$	1271.31	+	2201.98i	0.792814	+	1.37319i	0.924218	+	0.381865i	$0.124718\pi$
$137$	1271.31	+	2201.98i	0.792814	+	1.37319i	−0.131404	+	0.991329i	$0.541948\pi$
$138$	−128.899			−0.0795114
$139$	143.158	+	247.958i	0.0873564	+	0.151306i	0.906393	−	0.422436i	$-0.138825\pi$
$139$	143.158	+	247.958i	0.0873564	+	0.151306i	−0.819036	+	0.573741i	$0.805491\pi$
$140$	−576.821	+	999.082i	−0.348216	+	0.603128i
$141$	170.336	−	295.031i	0.101737	−	0.176213i
$142$	202.392			0.119608
$143$		0			0
$144$	−843.395			−0.488076
$145$	−973.644	+	1686.40i	−0.557633	+	0.965848i
$146$	−205.826	+	356.501i	−0.116673	+	0.202084i
$147$	−70.3701	−	121.885i	−0.0394832	−	0.0683869i
$148$	1164.90			0.646987
$149$	1177.06	+	2038.73i	0.647173	+	1.12094i	0.983795	+	0.179297i	$0.0573824\pi$
$149$	1177.06	+	2038.73i	0.647173	+	1.12094i	−0.336622	+	0.941640i	$0.609284\pi$
$150$	48.1805	+	83.4511i	0.0262261	+	0.0454250i
$151$	165.158			0.0890089			0.0445045	−	0.999009i	$-0.485829\pi$
$151$	165.158			0.0890089			0.0445045	+	0.999009i	$0.485829\pi$
$152$	−459.781	−	796.364i	−0.245350	−	0.424958i
$153$	604.355	−	1046.77i	0.319341	−	0.553115i
$154$	−174.697	+	302.583i	−0.0914120	+	0.158330i
$155$	−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	$0.788281\pi$
$158$	62.5823	−	108.396i	0.0315113	−	0.0545791i
$159$	−890.784	+	1542.88i	−0.444301	+	0.769551i
$160$	−274.572	−	475.573i	−0.135668	−	0.234983i
$161$	1789.01			0.875740
$162$	30.5524	+	52.9183i	0.0148174	+	0.0256646i
$163$	−149.655	−	259.210i	−0.0719134	−	0.124558i	0.827826	−	0.560984i	$-0.189577\pi$
$163$	−149.655	−	259.210i	−0.0719134	−	0.124558i	−0.899740	+	0.436427i	$0.856244\pi$
$164$	752.711			0.358395
$165$	622.055	+	1077.43i	0.293497	+	0.508351i
$166$	−6.33628	+	10.9748i	−0.00296259	+	0.00513136i
$167$	1502.59	−	2602.55i	0.696249	−	1.20594i	−0.273509	−	0.961869i	$-0.588184\pi$
$167$	1502.59	−	2602.55i	0.696249	−	1.20594i	0.969758	−	0.244069i	$-0.0784823\pi$
$168$	436.170			0.200305
$169$		0			0
$170$	253.867			0.114533
$171$	−1038.95	+	1799.51i	−0.464622	+	0.804750i
$172$	−317.809	+	550.461i	−0.140888	+	0.244025i
$173$	−227.926	−	394.780i	−0.100167	−	0.173495i	0.811586	−	0.584233i	$-0.198604\pi$
$173$	−227.926	−	394.780i	−0.100167	−	0.173495i	−0.911753	+	0.410738i	$0.865271\pi$
$174$	364.581			0.158844
$175$	−668.709	−	1158.24i	−0.288855	−	0.500312i
$176$	1383.22	+	2395.81i	0.592409	+	1.02608i
$177$	2078.03			0.882455
$178$	87.9310	+	152.301i	0.0370265	+	0.0641317i
$179$	−682.097	+	1181.43i	−0.284818	+	0.493318i	−0.972565	−	0.232632i	$-0.925266\pi$
$179$	−682.097	+	1181.43i	−0.284818	+	0.493318i	0.687747	+	0.725950i	$0.258600\pi$
$180$	−412.307	+	714.136i	−0.170731	+	0.295714i
$181$	−2026.11			−0.832041			−0.416021	−	0.909355i	$-0.636576\pi$
$181$	−2026.11			−0.832041			−0.416021	+	0.909355i	$0.636576\pi$
$182$		0			0
$183$	−145.421			−0.0587422
$184$	−282.957	+	490.096i	−0.113369	+	0.196360i
$185$	558.220	−	966.866i	0.221844	−	0.384246i
$186$	21.9901	+	38.0879i	0.00866876	+	0.0150147i
$187$	−3964.71			−1.55042
$188$	−370.329	−	641.429i	−0.143665	−	0.248835i
$189$	−1445.21	−	2503.18i	−0.556211	−	0.963386i
$190$	−436.423			−0.166639
$191$	−1080.53	−	1871.54i	−0.409343	−	0.709003i	0.585473	−	0.810692i	$-0.300909\pi$
$191$	−1080.53	−	1871.54i	−0.409343	−	0.709003i	−0.994816	+	0.101689i	$0.967575\pi$
$192$	820.265	−	1420.74i	0.308320	−	0.534026i
$193$	−603.938	+	1046.05i	−0.225246	+	0.390137i	−0.956393	−	0.292083i	$-0.905652\pi$
$193$	−603.938	+	1046.05i	−0.225246	+	0.390137i	0.731147	+	0.682219i	$0.238985\pi$
$194$	−90.4063			−0.0334577
$195$		0			0
$196$	−305.985			−0.111510
$197$	2463.38	−	4266.70i	0.890906	−	1.54309i	0.0521154	−	0.998641i	$-0.483404\pi$
$197$	2463.38	−	4266.70i	0.890906	−	1.54309i	0.838791	−	0.544454i	$-0.183263\pi$
$198$	−124.872	+	216.284i	−0.0448194	+	0.0776295i
$199$	−504.727	−	874.212i	−0.179795	−	0.311413i	0.762016	−	0.647559i	$-0.224210\pi$
$199$	−504.727	−	874.212i	−0.179795	−	0.311413i	−0.941810	+	0.336145i	$0.890877\pi$
$200$	423.061			0.149575
$201$	1084.96	+	1879.20i	0.380732	+	0.659447i
$202$	−111.207	−	192.617i	−0.0387352	−	0.0670914i
$203$	−5060.11			−1.74951
$204$	1225.47	+	2122.57i	0.420588	+	0.728480i
$205$	360.700	−	624.751i	0.122890	−	0.212851i
$206$	−189.118	+	327.563i	−0.0639636	+	0.110788i
$207$	1278.77			0.429376
$208$		0			0
$209$	6815.76			2.25577
$210$	103.503	−	179.272i	0.0340113	−	0.0589093i
$211$	2455.66	−	4253.33i	0.801206	−	1.38773i	−0.117616	−	0.993059i	$-0.537525\pi$
$211$	2455.66	−	4253.33i	0.801206	−	1.38773i	0.918823	−	0.394671i	$-0.129141\pi$
$212$	1936.66	+	3354.40i	0.627408	+	1.08670i
$213$	1872.70			0.602418
$214$	66.9353	+	115.935i	0.0213813	+	0.0370335i
$215$	304.589	+	527.563i	0.0966176	+	0.167347i
$216$	914.321			0.288017
$217$	−305.205	−	528.631i	−0.0954778	−	0.165372i
$218$	−16.2218	+	28.0969i	−0.00503980	+	0.00872920i
$219$	−1904.47	+	3298.64i	−0.587636	+	1.01782i
$220$	2704.83			0.828908
$221$		0			0
$222$	−209.026			−0.0631932
$223$	−682.289	+	1181.76i	−0.204885	+	0.354872i	−0.950096	−	0.311957i	$-0.899016\pi$
$223$	−682.289	+	1181.76i	−0.204885	+	0.354872i	0.745211	+	0.666829i	$0.232349\pi$
$224$	713.487	−	1235.80i	0.212821	−	0.368616i
$225$	−477.988	−	827.899i	−0.141626	−	0.245303i
$226$	−825.554			−0.242987
$227$	−2084.94	−	3611.22i	−0.609614	−	1.05588i	−0.991304	−	0.131592i	$-0.957991\pi$
$227$	−2084.94	−	3611.22i	−0.609614	−	1.05588i	0.381690	−	0.924290i	$-0.375342\pi$
$228$	−2106.71	−	3648.93i	−0.611931	−	1.05989i
$229$	3506.89			1.01197			0.505987	−	0.862541i	$-0.331128\pi$
$229$	3506.89			1.01197			0.505987	+	0.862541i	$0.331128\pi$
$230$	134.291	+	232.599i	0.0384995	+	0.0666831i
$231$	−1616.44	+	2799.75i	−0.460406	+	0.797446i
$232$	800.325	−	1386.20i	0.226482	−	0.392279i
$233$	−570.253			−0.160337			−0.0801684	−	0.996781i	$-0.525546\pi$
$233$	−570.253			−0.160337			−0.0801684	+	0.996781i	$0.525546\pi$
$234$		0			0
$235$	−709.848			−0.197044
$236$	2258.94	−	3912.59i	0.623069	−	1.07919i
$237$	579.063	−	1002.97i	0.158710	−	0.274893i
$238$	329.842	+	571.302i	0.0898338	+	0.155597i
$239$	231.056			0.0625347			0.0312674	−	0.999511i	$-0.490046\pi$
$239$	231.056			0.0625347			0.0312674	+	0.999511i	$0.490046\pi$
$240$	−819.519	−	1419.45i	−0.220416	−	0.381771i
$241$	−1544.25	−	2674.72i	−0.412754	−	0.714911i	0.582436	−	0.812877i	$-0.302100\pi$
$241$	−1544.25	−	2674.72i	−0.412754	−	0.714911i	−0.995190	+	0.0979656i	$0.968766\pi$
$242$	299.945			0.0796744
$243$	−1713.81	−	2968.40i	−0.452431	−	0.783634i
$244$	−158.080	+	273.803i	−0.0414756	+	0.0718379i
$245$	−146.628	+	253.968i	−0.0382356	+	0.0662261i
$246$	−135.064			−0.0350056
$247$		0			0
$248$	193.089			0.0494403
$249$	−58.6285	+	101.547i	−0.0149214	+	0.0258446i
$250$	283.780	−	491.521i	0.0717912	−	0.124346i
$251$	1222.82	+	2117.98i	0.307504	+	0.532613i	0.977816	−	0.209467i	$-0.0671728\pi$
$251$	1222.82	+	2117.98i	0.307504	+	0.532613i	−0.670311	+	0.742080i	$0.733839\pi$
$252$	−2142.79			−0.535648
$253$	−2097.27	−	3632.57i	−0.521162	−	0.902679i
$254$	229.523	+	397.545i	0.0566989	+	0.0982054i
$255$	2348.98			0.576859
$256$	−1669.41	−	2891.51i	−0.407572	−	0.705935i
$257$	−1637.00	+	2835.36i	−0.397327	+	0.688191i	−0.993395	−	0.114743i	$-0.963396\pi$
$257$	−1637.00	+	2835.36i	−0.397327	+	0.688191i	0.596068	+	0.802934i	$0.296729\pi$
$258$	57.0266	−	98.7731i	0.0137609	−	0.0238347i
$259$	2901.12			0.696010
$260$		0			0
$261$	−3616.93			−0.857786
$262$	−151.235	+	261.947i	−0.0356616	+	0.0617678i
$263$	2315.64	−	4010.80i	0.542921	−	0.940367i	−0.455813	−	0.890075i	$-0.650652\pi$
$263$	2315.64	−	4010.80i	0.542921	−	0.940367i	0.998735	−	0.0502918i	$-0.0160151\pi$
$264$	−511.323	−	885.637i	−0.119204	−	0.206467i
$265$	3712.20			0.860524
$266$	−567.032	−	982.128i	−0.130703	−	0.226384i
$267$	813.610	+	1409.21i	0.186487	+	0.323006i
$268$	4717.64			1.07528
$269$	1419.26	+	2458.23i	0.321686	+	0.557177i	0.980836	−	0.194835i	$-0.0624170\pi$
$269$	1419.26	+	2458.23i	0.321686	+	0.557177i	−0.659150	+	0.752012i	$0.729084\pi$
$270$	216.968	−	375.800i	0.0489046	−	0.0847053i
$271$	−3526.16	+	6107.48i	−0.790401	+	1.36902i	0.135317	+	0.990802i	$0.456795\pi$
$271$	−3526.16	+	6107.48i	−0.790401	+	1.36902i	−0.925719	+	0.378213i	$0.876539\pi$
$272$	5223.26			1.16436
$273$		0			0
$274$	−991.917			−0.218700
$275$	−1567.86	+	2715.61i	−0.343801	+	0.595481i
$276$	−1296.50	+	2245.61i	−0.282755	+	0.489746i
$277$	969.154	+	1678.62i	0.210220	+	0.364111i	0.951783	−	0.306772i	$-0.0992488\pi$
$277$	969.154	+	1678.62i	0.210220	+	0.364111i	−0.741564	+	0.670883i	$0.765915\pi$
$278$	−111.697			−0.0240975
$279$	−218.158	−	377.861i	−0.0468129	−	0.0810823i
$280$	−454.417	−	787.073i	−0.0969879	−	0.167988i
$281$	−3290.74			−0.698609			−0.349305	−	0.937009i	$-0.613582\pi$
$281$	−3290.74			−0.698609			−0.349305	+	0.937009i	$0.613582\pi$
$282$	66.4507	+	115.096i	0.0140322	+	0.0243045i
$283$	3959.04	−	6857.26i	0.831592	−	1.44036i	−0.0651839	−	0.997873i	$-0.520763\pi$
$283$	3959.04	−	6857.26i	0.831592	−	1.44036i	0.896776	−	0.442486i	$-0.145903\pi$
$284$	2035.72	−	3525.98i	0.425345	−	0.736719i
$285$	−4038.15			−0.839296
$286$		0			0
$287$	1874.59			0.385552
$288$	509.995	−	883.337i	0.104346	−	0.180733i
$289$	−1286.35	+	2228.03i	−0.261827	+	0.453497i
$290$	−379.833	−	657.891i	−0.0769124	−	0.133216i
$291$	−836.514			−0.168513
$292$	4140.53	+	7171.61i	0.829816	+	1.43728i
$293$	−2837.71	−	4915.07i	−0.565806	−	0.980004i	−0.996974	−	0.0777327i	$-0.975232\pi$
$293$	−2837.71	−	4915.07i	−0.565806	−	0.980004i	0.431169	−	0.902271i	$-0.358101\pi$
$294$	54.9049			0.0108916
$295$	−2164.97	−	3749.84i	−0.427286	−	0.740081i
$296$	−458.851	+	794.753i	−0.0901019	+	0.156061i
$297$	−3388.46	+	5868.98i	−0.662014	+	1.14664i
$298$	−918.381			−0.178525
$299$		0			0
$300$	1938.46			0.373057
$301$	−791.487	+	1370.89i	−0.151563	+	0.262515i
$302$	−32.2153	+	55.7985i	−0.00613835	+	0.0106319i
$303$	−1028.98	−	1782.25i	−0.195094	−	0.337913i
$304$	−8979.33			−1.69408
$305$	151.505	+	262.414i	0.0284430	+	0.0492648i
$306$	235.768	+	408.362i	0.0440456	+	0.0762893i
$307$	−4338.86			−0.806618			−0.403309	−	0.915064i	$-0.632140\pi$
$307$	−4338.86			−0.806618			−0.403309	+	0.915064i	$0.632140\pi$
$308$	3514.31	+	6086.96i	0.650150	+	1.12609i
$309$	−1749.88	+	3030.88i	−0.322159	+	0.557996i
$310$	45.8200	−	79.3626i	0.00839485	−	0.0145403i
$311$	−5234.75			−0.954454			−0.477227	−	0.878780i	$-0.658358\pi$
$311$	−5234.75			−0.954454			−0.477227	+	0.878780i	$0.658358\pi$
$312$		0			0
$313$	2167.86			0.391484			0.195742	−	0.980655i	$-0.437288\pi$
$313$	2167.86			0.391484			0.195742	+	0.980655i	$0.437288\pi$
$314$	603.844	−	1045.89i	0.108525	−	0.187971i
$315$	−1026.83	+	1778.52i	−0.183667	+	0.318121i
$316$	−1258.95	−	2180.56i	−0.224118	−	0.388184i
$317$	4863.71			0.861744			0.430872	−	0.902413i	$-0.358206\pi$
$317$	4863.71			0.861744			0.430872	+	0.902413i	$0.358206\pi$
$318$	−347.509	−	601.902i	−0.0612809	−	0.106142i
$319$	5931.98	+	10274.5i	1.04115	+	1.80332i
$320$	−3418.32			−0.597156
$321$	619.340	+	1072.73i	0.107689	+	0.186523i
$322$	−348.961	+	604.418i	−0.0603939	+	0.104605i
$323$	6434.36	−	11144.6i	1.10841	−	1.91983i
$324$	1229.22			0.210772
$325$		0			0
$326$	116.765			0.0198375
$327$	−150.097	+	259.976i	−0.0253835	+	0.0439655i
$328$	−296.491	+	513.538i	−0.0499116	+	0.0864494i
$329$	−922.285	−	1597.44i	−0.154551	−	0.267690i
$330$	−485.347			−0.0809620
$331$	1342.63	+	2325.51i	0.222954	+	0.386167i	0.955704	−	0.294331i	$-0.0950968\pi$
$331$	1342.63	+	2325.51i	0.222954	+	0.386167i	−0.732750	+	0.680498i	$0.761763\pi$
$332$	127.465	+	220.775i	0.0210709	+	0.0364958i
$333$	2073.70			0.341255
$334$	586.182	+	1015.30i	0.0960312	+	0.166331i
$335$	2260.70	−	3915.64i	0.368702	−	0.638610i
$336$	2129.55	−	3688.50i	0.345764	−	0.598881i
$337$	−6518.36			−1.05364			−0.526821	−	0.849976i	$-0.676616\pi$
$337$	−6518.36			−1.05364			−0.526821	+	0.849976i	$0.676616\pi$
$338$		0			0
$339$	−7638.71			−1.22383
$340$	2553.47	−	4422.74i	0.407299	−	0.705462i
$341$	−715.585	+	1239.43i	−0.113640	+	0.196830i
$342$	−405.310	−	702.017i	−0.0640838	−	0.110996i
$343$	5941.75			0.935347
$344$	−250.369	−	433.651i	−0.0392412	−	0.0679677i
$345$	1242.57	+	2152.20i	0.193907	+	0.335856i
$346$	177.835			0.0276314
$347$	−37.8982	−	65.6415i	−0.00586305	−	0.0101551i	0.863079	−	0.505069i	$-0.168533\pi$
$347$	−37.8982	−	65.6415i	−0.00586305	−	0.0101551i	−0.868942	+	0.494914i	$0.835200\pi$
$348$	3667.07	−	6351.56i	0.564873	−	0.978389i
$349$	1841.04	−	3188.78i	0.282375	−	0.489088i	−0.689594	−	0.724196i	$-0.742211\pi$
$349$	1841.04	−	3188.78i	0.282375	−	0.489088i	0.971969	+	0.235108i	$0.0755445\pi$
$350$	521.747			0.0796816
$351$		0			0
$352$	−3345.69			−0.506607
$353$	−5015.77	+	8687.58i	−0.756268	+	1.30990i	0.188473	+	0.982078i	$0.439646\pi$
$353$	−5015.77	+	8687.58i	−0.756268	+	1.30990i	−0.944741	+	0.327817i	$0.893687\pi$
$354$	−405.336	+	702.063i	−0.0608570	+	0.105407i
$355$	−1951.04	−	3379.30i	−0.291692	−	0.505225i
$356$	3537.75			0.526687
$357$	3051.97	+	5286.16i	0.452457	+	0.783678i
$358$	−266.097	−	460.893i	−0.0392839	−	0.0680417i
$359$	−6869.76			−1.00995			−0.504975	−	0.863134i	$-0.668498\pi$
$359$	−6869.76			−1.00995			−0.504975	+	0.863134i	$0.668498\pi$
$360$	−324.814	−	562.594i	−0.0475533	−	0.0823647i
$361$	−7631.83	+	13218.7i	−1.11267	+	1.92721i
$362$	395.208	−	684.520i	0.0573803	−	0.0993856i
$363$	2775.34			0.401288
$364$		0			0
$365$	7936.59			1.13814
$366$	28.3654	−	49.1304i	0.00405105	−	0.00701663i
$367$	−4441.64	+	7693.15i	−0.631749	+	1.09422i	0.355445	+	0.934697i	$0.384329\pi$
$367$	−4441.64	+	7693.15i	−0.631749	+	1.09422i	−0.987194	+	0.159524i	$0.949004\pi$
$368$	2763.02	+	4785.68i	0.391392	+	0.677910i
$369$	1339.94			0.189037
$370$	217.770	+	377.189i	0.0305982	+	0.0529977i
$371$	4823.15	+	8353.95i	0.674948	+	1.16904i
$372$	884.732			0.123310
$373$	2727.25	+	4723.73i	0.378583	+	0.655725i	0.990856	−	0.134921i	$-0.0430780\pi$
$373$	2727.25	+	4723.73i	0.378583	+	0.655725i	−0.612273	+	0.790646i	$0.709745\pi$
$374$	773.348	−	1339.48i	0.106922	−	0.185195i
$375$	2625.76	−	4547.95i	0.361584	−	0.626281i
$376$	583.487			0.0800294
$377$		0			0
$378$	1127.60			0.153433
$379$	−3321.07	+	5752.27i	−0.450111	+	0.779615i	−0.998392	−	0.0566786i	$-0.981949\pi$
$379$	−3321.07	+	5752.27i	−0.450111	+	0.779615i	0.548281	+	0.836294i	$0.315282\pi$
$380$	−4389.69	+	7603.16i	−0.592595	+	1.02640i
$381$	2123.73	+	3678.41i	0.285570	+	0.494621i
$382$	843.064			0.112919
$383$	−631.167	−	1093.21i	−0.0842066	−	0.145850i	0.820846	−	0.571149i	$-0.193502\pi$
$383$	−631.167	−	1093.21i	−0.0842066	−	0.145850i	−0.905053	+	0.425299i	$0.860169\pi$
$384$	1374.18	+	2380.16i	0.182620	+	0.316307i
$385$	6736.24			0.891716
$386$	−235.605	−	408.081i	−0.0310674	−	0.0538102i
$387$	−565.748	+	979.905i	−0.0743116	+	0.128712i
$388$	−909.336	+	1575.02i	−0.118981	+	0.206081i
$389$	−2793.42			−0.364093			−0.182046	−	0.983290i	$-0.558272\pi$
$389$	−2793.42			−0.364093			−0.182046	+	0.983290i	$0.558272\pi$
$390$		0			0
$391$	−7919.62			−1.02433
$392$	120.527	−	208.758i	0.0155294	−	0.0268977i
$393$	−1399.35	+	2423.75i	−0.179613	+	0.311099i
$394$	961.002	+	1664.50i	0.122880	+	0.212834i
$395$	−2413.15			−0.307390
$396$	2512.00	+	4350.91i	0.318770	+	0.552125i
$397$	−3424.45	−	5931.33i	−0.432918	−	0.749836i	0.564205	−	0.825635i	$-0.309183\pi$
$397$	−3424.45	−	5931.33i	−0.432918	−	0.749836i	−0.997123	+	0.0757988i	$0.975849\pi$
$398$	393.803			0.0495969
$399$	−5246.65	−	9087.46i	−0.658298	−	1.14021i
$400$	2065.55	−	3577.65i	0.258194	−	0.447206i
$401$	−5512.25	+	9547.50i	−0.686456	+	1.18898i	0.286521	+	0.958074i	$0.407501\pi$
$401$	−5512.25	+	9547.50i	−0.686456	+	1.18898i	−0.972977	+	0.230903i	$0.925832\pi$
$402$	−846.518			−0.105026
$403$		0			0
$404$	−4474.24			−0.550994
$405$	589.046	−	1020.26i	0.0722714	−	0.125178i
$406$	987.013	−	1709.56i	0.120652	−	0.208975i
$407$	−3400.99	−	5890.68i	−0.414203	−	0.717421i
$408$	−1930.84			−0.234291
$409$	−1765.28	−	3057.55i	−0.213417	−	0.369648i	0.739365	−	0.673305i	$-0.235126\pi$
$409$	−1765.28	−	3057.55i	−0.213417	−	0.369648i	−0.952782	+	0.303656i	$0.901793\pi$
$410$	140.715	+	243.725i	0.0169497	+	0.0293578i
$411$	−9178.03			−1.10151
$412$	3804.43	+	6589.46i	0.454929	+	0.787960i
$413$	5625.76	−	9744.11i	0.670280	−	1.16096i
$414$	−249.434	+	432.033i	−0.0296112	+	0.0512881i
$415$	244.325			0.0288998
$416$		0			0
$417$	−1033.51			−0.121370
$418$	−1329.47	+	2302.70i	−0.155565	+	0.269447i
$419$	2089.61	−	3619.31i	0.243637	−	0.421992i	−0.718110	−	0.695929i	$-0.754993\pi$
$419$	2089.61	−	3619.31i	0.243637	−	0.421992i	0.961748	+	0.273937i	$0.0883260\pi$
$420$	−2082.13	−	3606.36i	−0.241899	−	0.418981i
$421$	−6209.31			−0.718820			−0.359410	−	0.933180i	$-0.617022\pi$
$421$	−6209.31			−0.718820			−0.359410	+	0.933180i	$0.617022\pi$
$422$	957.990	+	1659.29i	0.110508	+	0.191405i
$423$	−659.242	−	1141.84i	−0.0757765	−	0.131249i
$424$	−3051.39			−0.349501
$425$	2960.24	+	5127.29i	0.337866	+	0.585201i
$426$	−365.284	+	632.690i	−0.0415447	+	0.0719576i
$427$	−393.691	+	681.893i	−0.0446183	+	0.0772812i
$428$	2693.03			0.304141
$429$		0			0
$430$	−237.650			−0.0266523
$431$	5940.11	−	10288.6i	0.663864	−	1.14985i	−0.315729	−	0.948850i	$-0.602249\pi$
$431$	5940.11	−	10288.6i	0.663864	−	1.14985i	0.979592	−	0.200996i	$-0.0644178\pi$
$432$	4464.08	−	7732.01i	0.497172	−	0.861126i
$433$	−4362.86	−	7556.69i	−0.484216	−	0.838686i	0.515620	−	0.856818i	$-0.327562\pi$
$433$	−4362.86	−	7556.69i	−0.484216	−	0.838686i	−0.999836	+	0.0181311i	$0.994228\pi$
$434$	238.130			0.0263378
$435$	−3514.53	−	6087.35i	−0.387377	−	0.670956i
$436$	326.328	+	565.216i	0.0358446	+	0.0620847i
$437$	13614.7			1.49034
$438$	−742.964	−	1286.85i	−0.0810507	−	0.140384i
$439$	600.187	−	1039.55i	0.0652514	−	0.113019i	−0.831554	−	0.555444i	$-0.812548\pi$
$439$	600.187	−	1039.55i	0.0652514	−	0.113019i	0.896805	+	0.442425i	$0.145882\pi$
$440$	−1065.43	+	1845.37i	−0.115437	+	0.199943i
$441$	−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	$0.461348\pi$
$444$	−2102.45	+	3641.55i	−0.224725	+	0.389235i
$445$	1695.30	−	2936.34i	0.180595	−	0.312800i
$446$	−266.171	−	461.022i	−0.0282591	−	0.0489463i
$447$	−8497.62			−0.899158
$448$	−4441.33	−	7692.60i	−0.468377	−	0.811253i
$449$	−7331.22	−	12698.0i	−0.770561	−	1.33465i	−0.937256	−	0.348642i	$-0.886643\pi$
$449$	−7331.22	−	12698.0i	−0.770561	−	1.33465i	0.166695	−	0.986008i	$-0.446690\pi$
$450$	372.941			0.0390680
$451$	−2197.58	−	3806.32i	−0.229446	−	0.397412i
$452$	−8303.69	+	14382.4i	−0.864099	+	1.49666i
$453$	−298.082	+	516.294i	−0.0309164	+	0.0535488i
$454$	1626.73			0.168164
$455$		0			0
$456$	3319.31			0.340879
$457$	4667.47	−	8084.29i	0.477757	−	0.827500i	−0.521918	−	0.852996i	$-0.674783\pi$
$457$	4667.47	−	8084.29i	0.477757	−	0.827500i	0.999675	+	0.0254962i	$0.00811657\pi$
$458$	−684.046	+	1184.80i	−0.0697891	+	0.120878i
$459$	6397.68	+	11081.1i	0.650585	+	1.12685i
$460$	5402.97			0.547641
$461$	5368.43	+	9298.39i	0.542370	+	0.939413i	0.998767	+	0.0496365i	$0.0158063\pi$
$461$	5368.43	+	9298.39i	0.542370	+	0.939413i	−0.456397	+	0.889776i	$0.650860\pi$
$462$	−630.597	−	1092.23i	−0.0635022	−	0.109989i
$463$	−10650.0			−1.06900			−0.534501	−	0.845168i	$-0.679501\pi$
$463$	−10650.0			−1.06900			−0.534501	+	0.845168i	$0.679501\pi$
$464$	−7815.01	−	13536.0i	−0.781902	−	1.35429i
$465$	423.965	−	734.328i	0.0422815	−	0.0732337i
$466$	111.232	−	192.660i	0.0110574	−	0.0191519i
$467$	−2638.11			−0.261407			−0.130703	−	0.991422i	$-0.541724\pi$
$467$	−2638.11			−0.261407			−0.130703	+	0.991422i	$0.541724\pi$
$468$		0			0
$469$	11749.0			1.15676
$470$	138.461	−	239.822i	0.0135888	−	0.0235365i
$471$	5587.26	−	9677.43i	0.546598	−	0.946735i
$472$	1779.58	+	3082.32i	0.173542	+	0.300584i
$473$	3711.45			0.360787
$474$	225.901	+	391.273i	0.0218903	+	0.0379151i
$475$	−5088.97	−	8814.35i	−0.491575	−	0.851432i
$476$	13270.6			1.27785
$477$	3447.55	+	5971.34i	0.330928	+	0.573184i
$478$	−45.0693	+	78.0623i	−0.00431260	+	0.00746964i
$479$	−1612.66	+	2793.20i	−0.153829	+	0.266440i	−0.932632	−	0.360829i	$-0.882494\pi$
$479$	−1612.66	+	2793.20i	−0.153829	+	0.266440i	0.778803	+	0.627269i	$0.215827\pi$
$480$	1982.23			0.188491
$481$		0			0
$482$	1204.87			0.113860
$483$	−3228.87	+	5592.57i	−0.304180	+	0.526855i
$484$	3016.94	−	5225.50i	0.283334	−	0.490749i
$485$	871.510	+	1509.50i	0.0815943	+	0.141325i
$486$	1337.17			0.124805
$487$	−748.196	−	1295.91i	−0.0696181	−	0.120582i	0.829115	−	0.559078i	$-0.188845\pi$
$487$	−748.196	−	1295.91i	−0.0696181	−	0.120582i	−0.898733	+	0.438496i	$0.855511\pi$
$488$	−124.535	−	215.701i	−0.0115521	−	0.0200089i
$489$	1080.41			0.0999137
$490$	−57.2019	−	99.0766i	−0.00527371	−	0.00913434i
$491$	259.204	−	448.955i	0.0238243	−	0.0412648i	−0.853867	−	0.520491i	$-0.825749\pi$
$491$	259.204	−	448.955i	0.0238243	−	0.0412648i	0.877692	+	0.479226i	$0.159082\pi$
$492$	−1358.52	+	2353.02i	−0.124485	+	0.215615i
$493$	22400.1			2.04635
$494$		0			0
$495$	4815.01			0.437210
$496$	942.739	−	1632.87i	0.0853432	−	0.147819i
$497$	5069.86	−	8781.26i	0.457574	−	0.792542i
$498$	−22.8719	−	39.6152i	−0.00205806	−	0.00356466i
$499$	2405.01			0.215757			0.107879	−	0.994164i	$-0.465594\pi$
$499$	2405.01			0.215757			0.107879	+	0.994164i	$0.465594\pi$
$500$	−5708.69	−	9887.75i	−0.510601	−	0.884387i
$501$	5423.83	+	9394.36i	0.483671	+	0.837742i
$502$	−954.080			−0.0848260
$503$	−1206.88	−	2090.38i	−0.106983	−	0.185299i	0.807564	−	0.589780i	$-0.200786\pi$
$503$	−1206.88	−	2090.38i	−0.106983	−	0.185299i	−0.914546	+	0.404481i	$0.867452\pi$
$504$	844.041	−	1461.92i	0.0745964	−	0.129205i
$505$	−2144.06	+	3713.62i	−0.188929	+	0.327235i
$506$	1636.35			0.143764
$507$		0			0
$508$	9234.45			0.806520
$509$	7839.15	−	13577.8i	0.682641	−	1.18237i	−0.291531	−	0.956561i	$-0.594165\pi$
$509$	7839.15	−	13577.8i	0.682641	−	1.18237i	0.974172	−	0.225807i	$-0.0725019\pi$
$510$	−458.187	+	793.604i	−0.0397821	+	0.0689046i
$511$	10311.8	+	17860.5i	0.892693	+	1.54619i
$512$	7393.65			0.638196
$513$	−10998.3	−	19049.6i	−0.946562	−	1.63949i
$514$	−638.618	−	1106.12i	−0.0548020	−	0.0949198i
$515$	7292.34			0.623959
$516$	−1147.18	−	1986.98i	−0.0978721	−	0.169519i
$517$	−2162.39	+	3745.37i	−0.183950	+	0.318610i
$518$	−565.885	+	980.142i	−0.0479992	+	0.0831370i
$519$	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	$0.663576\pi$
$522$	705.509	−	1221.98i	0.0591557	−	0.102461i
$523$	1939.48	−	3359.27i	0.162156	−	0.280862i	−0.773486	−	0.633814i	$-0.781489\pi$
$523$	1939.48	−	3359.27i	0.162156	−	0.280862i	0.935642	+	0.352952i	$0.114822\pi$
$524$	3042.35	+	5269.50i	0.253637	+	0.439311i
$525$	4827.63			0.401324
$526$	903.365	+	1564.67i	0.0748833	+	0.129702i
$527$	1351.08	+	2340.15i	0.111678	+	0.193431i
$528$	−9985.92			−0.823071
$529$	1894.16	+	3280.78i	0.155680	+	0.269646i
$530$	−724.093	+	1254.17i	−0.0593445	+	0.102788i
$531$	4021.25	−	6965.01i	0.328639	−	0.569220i
$532$	−22813.6			−1.85920
$533$		0			0
$534$	−634.804			−0.0514431
$535$	1290.50	−	2235.21i	0.104286	−	0.180629i
$536$	−1858.27	+	3218.61i	−0.149748	+	0.259371i
$537$	−2462.14	−	4264.56i	−0.197857	−	0.342699i
$538$	−1107.35			−0.0887382
$539$	893.340	+	1547.31i	0.0713894	+	0.123650i
$540$	−4364.67	−	7559.83i	−0.347825	−	0.602450i
$541$	16353.0			1.29958			0.649788	−	0.760115i	$-0.274858\pi$
$541$	16353.0			1.29958			0.649788	+	0.760115i	$0.274858\pi$
$542$	−1375.61	−	2382.62i	−0.109017	−	0.188824i
$543$	3656.79	−	6333.75i	0.289002	−	0.500565i
$544$	−3158.47	+	5470.63i	−0.248930	+	0.431160i
$545$	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	$0.465739\pi$
$548$	−9977.02	+	17280.7i	−0.777732	+	1.34707i
$549$	−281.407	+	487.411i	−0.0218764	+	0.0378911i
$550$	−611.645	−	1059.40i	−0.0474193	−	0.0821327i
$551$	−38508.1			−2.97732
$552$	−1021.38	−	1769.08i	−0.0787551	−	0.136408i
$553$	−3135.34	−	5430.57i	−0.241100	−	0.417597i
$554$	−756.163			−0.0579897
$555$	2014.99	+	3490.07i	0.154111	+	0.266928i
$556$	−1123.48	+	1945.93i	−0.0856946	+	0.148427i
$557$	−8382.81	+	14519.4i	−0.637686	+	1.10450i	0.348254	+	0.937400i	$0.386775\pi$
$557$	−8382.81	+	14519.4i	−0.637686	+	1.10450i	−0.985939	+	0.167104i	$0.946558\pi$
$558$	170.214			0.0129135
$559$		0			0
$560$	−8874.58			−0.669677
$561$	7155.65	−	12394.0i	0.538524	−	0.932750i
$562$	641.884	−	1111.78i	0.0481784	−	0.0834474i
$563$	−9246.21	−	16014.9i	−0.692151	−	1.19884i	−0.971132	−	0.238545i	$-0.923330\pi$
$563$	−9246.21	−	16014.9i	−0.692151	−	1.19884i	0.278980	−	0.960297i	$-0.410004\pi$
$564$	2673.53			0.199603
$565$	7958.27	+	13784.1i	0.592579	+	1.02638i
$566$	1544.48	+	2675.12i	0.114699	+	0.198664i
$567$	3061.32			0.226743
$568$	1603.73	+	2777.75i	0.118470	+	0.205197i
$569$	−781.639	+	1353.84i	−0.0575888	+	0.0997467i	−0.893383	−	0.449297i	$-0.851675\pi$
$569$	−781.639	+	1353.84i	−0.0575888	+	0.0997467i	0.835794	+	0.549044i	$0.185008\pi$
$570$	787.672	−	1364.29i	0.0578806	−	0.100252i
$571$	9165.98			0.671776			0.335888	−	0.941902i	$-0.390964\pi$
$571$	9165.98			0.671776			0.335888	+	0.941902i	$0.390964\pi$
$572$		0			0
$573$	7800.72			0.568726
$574$	−365.652	+	633.329i	−0.0265889	+	0.0460534i
$575$	−3131.84	+	5424.50i	−0.227142	+	0.393421i
$576$	−3174.62	−	5498.61i	−0.229646	−	0.397758i
$577$	18762.5			1.35372			0.676858	−	0.736114i	$-0.263341\pi$
$577$	18762.5			1.35372			0.676858	+	0.736114i	$0.263341\pi$
$578$	−501.826	−	869.189i	−0.0361128	−	0.0625493i
$579$	−2180.02	−	3775.90i	−0.156474	−	0.271021i
$580$	−15281.9			−1.09405
$581$	317.444	+	549.829i	0.0226675	+	0.0392612i
$582$	163.168	−	282.616i	0.0116212	−	0.0201285i
$583$	11308.4	−	19586.7i	0.803337	−	1.39142i
$584$	−6523.79			−0.462254
$585$		0			0
$586$	2214.07			0.156079
$587$	−6323.14	+	10952.0i	−0.444606	+	0.770080i	−0.998025	−	0.0628229i	$-0.979990\pi$
$587$	−6323.14	+	10952.0i	−0.444606	+	0.770080i	0.553419	+	0.832903i	$0.313323\pi$
$588$	552.252	−	956.528i	0.0387321	−	0.0670859i
$589$	−2322.65	−	4022.96i	−0.162484	−	0.281431i
$590$	1689.18			0.117868
$591$	8891.98	+	15401.4i	0.618896	+	1.07196i
$592$	4480.59	+	7760.60i	0.311066	+	0.538782i
$593$	−9662.74			−0.669142			−0.334571	−	0.942371i	$-0.608591\pi$
$593$	−9662.74			−0.669142			−0.334571	+	0.942371i	$0.608591\pi$
$594$	−1321.89	−	2289.58i	−0.0913093	−	0.158152i
$595$	6359.29	−	11014.6i	0.438161	−	0.758916i
$596$	−9237.37	+	15999.6i	−0.634862	+	1.09961i
$597$	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	$0.871644\pi$
$600$	−763.556	+	1322.52i	−0.0519534	+	0.0899859i
$601$	−5640.06	+	9768.87i	−0.382800	+	0.663029i	−0.991461	−	0.130401i	$-0.958373\pi$
$601$	−5640.06	+	9768.87i	−0.382800	+	0.663029i	0.608661	+	0.793430i	$0.291707\pi$
$602$	−308.771	−	534.807i	−0.0209046	−	0.0362078i
$603$	8398.11			0.567160
$604$	648.063	+	1122.48i	0.0436578	+	0.0756175i
$605$	−2891.45	−	5008.13i	−0.194304	−	0.336545i
$606$	802.843			0.0538173
$607$	−6026.30	−	10437.9i	−0.402965	−	0.697957i	0.591117	−	0.806586i	$-0.298687\pi$
$607$	−6026.30	−	10437.9i	−0.402965	−	0.697957i	−0.994082	+	0.108629i	$0.965354\pi$
$608$	5429.73	−	9404.58i	0.362179	−	0.627312i
$609$	9132.66	−	15818.2i	0.607675	−	1.05252i
$610$	−118.208			−0.00784610
$611$		0			0
$612$	9485.73			0.626532
$613$	−5629.84	+	9751.17i	−0.370941	+	0.642489i	−0.989711	−	0.143083i	$-0.954298\pi$
$613$	−5629.84	+	9751.17i	−0.370941	+	0.642489i	0.618769	+	0.785573i	$0.287632\pi$
$614$	846.327	−	1465.88i	0.0556270	−	0.0963488i
$615$	1302.01	+	2255.14i	0.0853691	+	0.147864i
$616$	−5537.12			−0.362170
$617$	12029.1	+	20835.0i	0.784882	+	1.35946i	0.929069	+	0.369906i	$0.120610\pi$
$617$	12029.1	+	20835.0i	0.784882	+	1.35946i	−0.144187	+	0.989550i	$0.546057\pi$
$618$	−682.655	−	1182.39i	−0.0444343	−	0.0769625i
$619$	−2793.41			−0.181384			−0.0906919	−	0.995879i	$-0.528908\pi$
$619$	−2793.41			−0.181384			−0.0906919	+	0.995879i	$0.528908\pi$
$620$	−921.745	−	1596.51i	−0.0597067	−	0.103415i
$621$	−6768.53	+	11723.4i	−0.437378	+	0.757561i
$622$	1021.08	−	1768.56i	0.0658223	−	0.114008i
$623$	8810.59			0.566595
$624$		0			0
$625$	−2388.81			−0.152884
$626$	−422.857	+	732.410i	−0.0269980	+	0.0467619i
$627$	−12301.3	+	21306.5i	−0.783520	+	1.35710i
$628$	−12147.3	−	21039.8i	−0.771864	−	1.33691i
$629$	−12842.7			−0.814104
$630$	−400.581	−	693.827i	−0.0253326	−	0.0438774i
$631$	12425.0	+	21520.7i	0.783883	+	1.35773i	0.929664	+	0.368409i	$0.120097\pi$
$631$	12425.0	+	21520.7i	0.783883	+	1.35773i	−0.145780	+	0.989317i	$0.546569\pi$
$632$	1983.59			0.124846
$633$	8864.11	+	15353.1i	0.556583	+	0.964030i
$634$	−948.703	+	1643.20i	−0.0594287	+	0.102934i
$635$	4425.16	−	7664.60i	0.276547	−	0.478993i
$636$	−13981.4			−0.871696
$637$		0			0
$638$	−4628.31			−0.287205
$639$	3623.90	−	6276.77i	0.224349	−	0.388584i
$640$	2863.35	−	4959.46i	0.176850	−	0.306312i
$641$	3897.35	+	6750.41i	0.240150	+	0.415952i	0.960757	−	0.277392i	$-0.0894700\pi$
$641$	3897.35	+	6750.41i	0.240150	+	0.415952i	−0.720607	+	0.693344i	$0.756137\pi$
$642$	−483.228			−0.0297064
$643$	−13854.9	−	23997.5i	−0.849744	−	1.47180i	−0.881437	−	0.472302i	$-0.843423\pi$
$643$	−13854.9	−	23997.5i	−0.849744	−	1.47180i	0.0316924	−	0.999498i	$-0.489910\pi$
$644$	7019.92	+	12158.9i	0.429540	+	0.743985i
$645$	−2198.93			−0.134237
$646$	2510.14	+	4347.69i	0.152880	+	0.264795i
$647$	−5575.47	+	9656.99i	−0.338786	+	0.586794i	−0.984205	−	0.177035i	$-0.943349\pi$
$647$	−5575.47	+	9656.99i	−0.338786	+	0.586794i	0.645419	+	0.763829i	$0.276683\pi$
$648$	−484.189	+	838.640i	−0.0293530	+	0.0508409i
$649$	−26380.4			−1.59556
$650$		0			0
$651$	2203.38			0.132653
$652$	1174.46	−	2034.23i	0.0705453	−	0.122188i
$653$	−14568.7	+	25233.8i	−0.873077	+	1.51221i	−0.0142794	+	0.999898i	$0.504545\pi$
$653$	−14568.7	+	25233.8i	−0.873077	+	1.51221i	−0.858797	+	0.512315i	$0.828788\pi$
$654$	−58.5552	−	101.421i	−0.00350106	−	0.00606401i
$655$	5831.58			0.347876
$656$	2895.18	+	5014.59i	0.172314	+	0.298456i
$657$	7370.78	+	12766.6i	0.437689	+	0.758099i
$658$	719.595			0.0426333
$659$	2650.06	+	4590.04i	0.156649	+	0.271324i	0.933658	−	0.358165i	$-0.116598\pi$
$659$	2650.06	+	4590.04i	0.156649	+	0.271324i	−0.777009	+	0.629489i	$0.783264\pi$
$660$	−4881.77	+	8455.48i	−0.287913	+	0.498680i
$661$	13706.3	−	23739.9i	0.806523	−	1.39694i	−0.108735	−	0.994071i	$-0.534680\pi$
$661$	13706.3	−	23739.9i	0.806523	−	1.39694i	0.915258	−	0.402868i	$-0.131987\pi$
$662$	−1047.56			−0.0615025
$663$		0			0
$664$	−200.832			−0.0117377
$665$	−10932.3	+	18935.3i	−0.637497	+	1.10418i
$666$	−404.490	+	700.598i	−0.0235341	+	0.0407622i
$667$	11849.3	+	20523.5i	0.687865	+	1.19142i
$668$	23584.0			1.36601
$669$	−2462.84	−	4265.76i	−0.142330	−	0.246523i
$670$	881.933	+	1527.55i	0.0508538	+	0.0880813i
$671$	1846.10			0.106211
$672$	2575.45	+	4460.81i	0.147842	+	0.256071i
$673$	10641.0	−	18430.8i	0.609482	−	1.05565i	−0.381844	−	0.924227i	$-0.624711\pi$
$673$	10641.0	−	18430.8i	0.609482	−	1.05565i	0.991326	−	0.131427i	$-0.0419560\pi$
$674$	1271.46	−	2202.22i	0.0726626	−	0.125855i
$675$	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	$0.625610\pi$
$678$	1489.99	−	2580.74i	0.0843992	−	0.146184i
$679$	−2264.65	+	3922.49i	−0.127996	+	0.221696i
$680$	2011.62	+	3484.22i	0.113444	+	0.196491i
$681$	15051.9			0.846974
$682$	−279.161	−	483.521i	−0.0156739	−	0.0271480i
$683$	−5175.06	−	8963.48i	−0.289924	−	0.502164i	0.683867	−	0.729607i	$-0.260297\pi$
$683$	−5175.06	−	8963.48i	−0.289924	−	0.502164i	−0.973791	+	0.227443i	$0.926963\pi$
$684$	−16307.0			−0.911567
$685$	9562.00	+	16561.9i	0.533350	+	0.923790i
$686$	−1158.98	+	2007.42i	−0.0645046	+	0.111725i
$687$	−6329.36	+	10962.8i	−0.351499	+	0.608815i
$688$	−4889.60			−0.270951
$689$		0			0
$690$	−969.492			−0.0534898
$691$	12857.4	−	22269.7i	0.707843	−	1.22602i	−0.257813	−	0.966195i	$-0.583002\pi$
$691$	12857.4	−	22269.7i	0.707843	−	1.22602i	0.965656	−	0.259825i	$-0.0836648\pi$
$692$	1788.72	−	3098.16i	0.0982617	−	0.170194i
$693$	6256.00	+	10835.7i	0.342923	+	0.593961i
$694$	29.5693			0.00161734
$695$	1076.75	+	1864.98i	0.0587674	+	0.101788i
$696$	2888.91	+	5003.73i	0.157333	+	0.272509i
$697$	−8298.43			−0.450969
$698$	718.219	+	1243.99i	0.0389470	+	0.0674582i
$699$	1029.21	−	1782.65i	0.0556915	−	0.0964605i
$700$	5247.90	−	9089.63i	0.283360	−	0.490794i
$701$	7431.30			0.400394			0.200197	−	0.979756i	$-0.435842\pi$
$701$	7431.30			0.400394			0.200197	+	0.979756i	$0.435842\pi$
$702$		0			0
$703$	22077.9			1.18447
$704$	−10413.2	+	18036.1i	−0.557472	+	0.965570i
$705$	1281.16	−	2219.03i	0.0684414	−	0.118544i
$706$	−1956.73	−	3389.16i	−0.104310	−	0.180669i
$707$	−11142.8			−0.592744
$708$	8154.01	+	14123.2i	0.432834	+	0.749690i
$709$	9993.40	+	17309.1i	0.529351	+	0.916863i	0.999414	+	0.0342303i	$0.0108980\pi$
$709$	9993.40	+	17309.1i	0.529351	+	0.916863i	−0.470063	+	0.882633i	$0.655769\pi$
$710$	1522.26			0.0804641
$711$	−2241.12	−	3881.73i	−0.118212	−	0.204748i
$712$	−1393.51	+	2413.64i	−0.0733485	+	0.127043i
$713$	−1429.40	+	2475.79i	−0.0750792	+	0.130041i
$714$	−2381.24			−0.124812
$715$		0			0
$716$	−10705.9			−0.558798
$717$	−417.018	+	722.297i	−0.0217208	+	0.0376216i
$718$	1340.00	−	2320.95i	0.0696495	−	0.120636i
$719$	−18050.9	−	31265.1i	−0.936281	−	1.62169i	−0.772333	−	0.635218i	$-0.780910\pi$
$719$	−18050.9	−	31265.1i	−0.936281	−	1.62169i	−0.163948	−	0.986469i	$-0.552423\pi$
$720$	−6343.48			−0.328344
$721$	9474.73	+	16410.7i	0.489400	+	0.847665i
$722$	−2977.29	−	5156.82i	−0.153467	−	0.265813i
$723$	11148.4			0.573465
$724$	−7950.26	−	13770.2i	−0.408106	−	0.706861i
$725$	8858.19	−	15342.8i	0.453772	−	0.785957i
$726$	−541.351	+	937.648i	−0.0276741	+	0.0479330i
$727$	−1751.90			−0.0893735			−0.0446868	−	0.999001i	$-0.514229\pi$
$727$	−1751.90			−0.0893735			−0.0446868	+	0.999001i	$0.514229\pi$
$728$		0			0
$729$	16601.6			0.843451
$730$	−1548.09	+	2681.37i	−0.0784897	+	0.135948i
$731$	3503.76	−	6068.69i	0.177279	−	0.307057i
$732$	−570.618	−	988.339i	−0.0288123	−	0.0499044i
$733$	−20031.3			−1.00938			−0.504688	−	0.863302i	$-0.668393\pi$
$733$	−20031.3			−1.00938			−0.504688	+	0.863302i	$0.668393\pi$
$734$	−1732.75	−	3001.22i	−0.0871350	−	0.150922i
$735$	−529.279	−	916.738i	−0.0265616	−	0.0460060i
$736$	−6683.10			−0.334704
$737$	−13773.4	−	23856.2i	−0.688399	−	1.19234i
$738$	−261.366	+	452.698i	−0.0130366	+	0.0225800i
$739$	−9316.47	+	16136.6i	−0.463751	+	0.803240i	−0.999144	−	0.0413627i	$-0.986830\pi$
$739$	−9316.47	+	16136.6i	−0.463751	+	0.803240i	0.535393	+	0.844603i	$0.320163\pi$
$740$	8761.62			0.435248
$741$		0			0
$742$	−3763.17			−0.186187
$743$	−2453.85	+	4250.19i	−0.121161	+	0.209858i	−0.920226	−	0.391388i	$-0.871995\pi$
$743$	−2453.85	+	4250.19i	−0.121161	+	0.209858i	0.799065	+	0.601245i	$0.205329\pi$
$744$	−348.494	+	603.610i	−0.0171726	+	0.0297438i
$745$	8853.12	+	15334.1i	0.435373	+	0.754089i
$746$	−2127.88			−0.104433
$747$	226.906	+	393.014i	0.0111139	+	0.0192498i
$748$	−15557.2	−	26945.8i	−0.760463	−	1.31716i
$749$	6706.84			0.327186
$750$	1024.35	+	1774.23i	0.0498720	+	0.0863808i
$751$	−15578.4	+	26982.7i	−0.756945	+	1.31107i	0.187457	+	0.982273i	$0.439976\pi$
$751$	−15578.4	+	26982.7i	−0.756945	+	1.31107i	−0.944402	+	0.328794i	$0.893358\pi$
$752$	2848.82	−	4934.30i	0.138146	−	0.239276i
$753$	−8827.93			−0.427235
$754$		0			0
$755$	1242.21			0.0598790
$756$	11341.8	−	19644.5i	0.545630	−	0.945058i
$757$	5523.49	−	9566.97i	0.265198	−	0.459336i	−0.702418	−	0.711765i	$-0.747896\pi$
$757$	5523.49	−	9566.97i	0.265198	−	0.459336i	0.967615	+	0.252429i	$0.0812294\pi$
$758$	−1295.60	−	2244.05i	−0.0620823	−	0.107530i
$759$	15140.9			0.724082
$760$	−3458.18	−	5989.74i	−0.165054	−	0.285882i
$761$	−13803.0	−	23907.6i	−0.657503	−	1.13883i	−0.981260	−	0.192688i	$-0.938279\pi$
$761$	−13803.0	−	23907.6i	−0.657503	−	1.13883i	0.323757	−	0.946140i	$-0.395054\pi$
$762$	−1657.00			−0.0787753
$763$	812.702	+	1407.64i	0.0385607	+	0.0667890i
$764$	8479.81	−	14687.5i	0.401556	−	0.695515i
$765$	4545.57	−	7873.16i	0.214831	−	0.372098i
$766$	492.456			0.0232287
$767$		0			0
$768$	12052.1			0.566264
$769$	1847.36	−	3199.72i	0.0866287	−	0.150045i	−0.819455	−	0.573143i	$-0.805724\pi$
$769$	1847.36	−	3199.72i	0.0866287	−	0.150045i	0.906084	+	0.423098i	$0.139057\pi$
$770$	−1313.96	+	2275.84i	−0.0614957	+	0.106514i
$771$	−5909.02	−	10234.7i	−0.276016	−	0.478073i
$772$	−9479.18			−0.441921
$773$	−9904.01	−	17154.2i	−0.460831	−	0.798183i	0.538172	−	0.842835i	$-0.319115\pi$
$773$	−9904.01	−	17154.2i	−0.460831	−	0.798183i	−0.999003	+	0.0446525i	$0.985782\pi$
$774$	−220.707	−	382.276i	−0.0102496	−	0.0177527i
$775$	2137.16			0.0990569
$776$	−716.371	−	1240.79i	−0.0331395	−	0.0573992i
$777$	−5236.04	+	9069.08i	−0.241753	+	0.418728i
$778$	544.878	−	943.757i	0.0251090	−	0.0434901i
$779$	14265.9			0.656133
$780$		0			0
$781$	−23773.6			−1.08923
$782$	1544.78	−	2675.64i	0.0706411	−	0.122354i
$783$	19144.3	−	33159.0i	0.873771	−	1.51342i
$784$	−1176.92	−	2038.48i	−0.0536133	−	0.0928610i
$785$	−23284.0			−1.05865
$786$	−545.909	−	945.542i	−0.0247735	−	0.0429089i
$787$	2058.39	+	3565.24i	0.0932322	+	0.161483i	0.908869	−	0.417081i	$-0.136947\pi$
$787$	2058.39	+	3565.24i	0.0932322	+	0.161483i	−0.815637	+	0.578564i	$0.803613\pi$
$788$	38664.3			1.74792
$789$	8358.68	+	14477.7i	0.377157	+	0.653255i
$790$	470.704	−	815.284i	0.0211986	−	0.0367171i
$791$	−20679.9	+	35818.6i	−0.929574	+	1.61007i
$792$	−3957.89			−0.177572
$793$		0			0
$794$	2671.86			0.119422
$795$	−6699.91	+	11604.6i	−0.298895	+	0.517701i
$796$	3961.00	−	6860.65i	0.176374	−	0.305489i
$797$	−12679.6	−	21961.8i	−0.563533	−	0.976068i	−0.997185	−	0.0749871i	$-0.976108\pi$
$797$	−12679.6	−	21961.8i	−0.563533	−	0.976068i	0.433652	−	0.901081i	$-0.357225\pi$
$798$	4093.59			0.181594
$799$	4082.78	+	7071.58i	0.180774	+	0.313109i
$800$	2498.05	+	4326.75i	0.110399	+	0.191217i
$801$	6297.74			0.277802
$802$	−2150.41	−	3724.63i	−0.0946805	−	0.163991i
$803$	24177.0	−	41875.9i	1.06250	−	1.84031i
$804$	−8514.55	+	14747.6i	−0.373489	+	0.646902i
$805$	13455.8			0.589137
$806$		0			0
$807$	−10246.1			−0.446939
$808$	1762.39	−	3052.55i	0.0767336	−	0.132906i
$809$	2779.37	−	4814.00i	0.120788	−	0.209211i	−0.799291	−	0.600944i	$-0.794791\pi$
$809$	2779.37	−	4814.00i	0.120788	−	0.209211i	0.920079	+	0.391734i	$0.128125\pi$
$810$	229.796	+	398.018i	0.00996815	+	0.0172653i
$811$	15021.4			0.650399			0.325199	−	0.945646i	$-0.394569\pi$
$811$	15021.4			0.650399			0.325199	+	0.945646i	$0.394569\pi$
$812$	−19855.4	−	34390.5i	−0.858113	−	1.48629i
$813$	−12728.3	−	22046.0i	−0.549077	−	0.951029i
$814$	2653.55			0.114259
$815$	−1125.61	−	1949.61i	−0.0483784	−	0.0837938i
$816$	−9427.12	+	16328.3i	−0.404431	+	0.700494i
$817$	−6023.32	+	10432.7i	−0.257931	+	0.446749i
$818$	1377.32			0.0588717
$819$		0			0
$820$	5661.41			0.241104
$821$	7950.78	−	13771.2i	0.337983	−	0.585404i	−0.646070	−	0.763278i	$-0.723589\pi$
$821$	7950.78	−	13771.2i	0.337983	−	0.585404i	0.984053	+	0.177874i	$0.0569220\pi$
$822$	1790.24	−	3100.80i	0.0759635	−	0.131573i
$823$	20139.6	+	34882.9i	0.853006	+	1.47745i	0.878483	+	0.477774i	$0.158556\pi$
$823$	20139.6	+	34882.9i	0.853006	+	1.47745i	−0.0254768	+	0.999675i	$0.508110\pi$
$824$	−5994.23			−0.253421
$825$	−5659.45	−	9802.45i	−0.238832	−	0.413670i
$826$	2194.70	+	3801.32i	0.0924494	+	0.160127i
$827$	−5251.09			−0.220796			−0.110398	−	0.993887i	$-0.535213\pi$
$827$	−5251.09			−0.220796			−0.110398	+	0.993887i	$0.535213\pi$
$828$	5017.78	+	8691.06i	0.210604	+	0.364777i
$829$	−16982.2	+	29414.0i	−0.711479	+	1.23232i	0.252823	+	0.967512i	$0.418641\pi$
$829$	−16982.2	+	29414.0i	−0.711479	+	1.23232i	−0.964302	+	0.264805i	$0.914692\pi$
$830$	−47.6574	+	82.5451i	−0.00199303	+	0.00345203i
$831$	−6996.65			−0.292071
$832$		0			0
$833$	3373.40			0.140314
$834$	201.594	−	349.171i	0.00837005	−	0.0144974i
$835$	11301.5	−	19574.7i	0.468388	−	0.811272i
$836$	26744.4	+	46322.6i	1.10643	+	1.91639i
$837$	4618.83			0.190741
$838$	815.188	+	1411.95i	0.0336041	+	0.0582039i
$839$	−7742.49	−	13410.4i	−0.318594	−	0.551821i	0.661601	−	0.749856i	$-0.269877\pi$
$839$	−7742.49	−	13410.4i	−0.318594	−	0.551821i	−0.980195	+	0.198035i	$0.936544\pi$
$840$	3280.59			0.134751
$841$	−21320.4	−	36928.0i	−0.874181	−	1.51413i
$842$	1211.17	−	2097.81i	0.0495722	−	0.0858615i
$843$	5939.24	−	10287.1i	0.242655	−	0.420291i
$844$	38543.1			1.57193
$845$		0			0
$846$	514.361			0.0209032
$847$	7513.54	−	13013.8i	0.304803	−	0.527935i
$848$	−14898.1	+	25804.3i	−0.603305	+	1.04496i
$849$	14290.8	+	24752.4i	0.577691	+	1.00059i
$850$	−2309.67			−0.0932014
$851$	−6793.56	−	11766.8i	−0.273655	−	0.473984i
$852$	7348.28	+	12727.6i	0.295479	+	0.511784i
$853$	−20057.8			−0.805118			−0.402559	−	0.915394i	$-0.631879\pi$
$853$	−20057.8			−0.805118			−0.402559	+	0.915394i	$0.631879\pi$
$854$	−153.585	−	266.017i	−0.00615406	−	0.0106591i
$855$	−7814.31	+	13534.8i	−0.312566	+	0.541380i
$856$	−1060.78	+	1837.32i	−0.0423559	+	0.0733625i
$857$	−8066.23			−0.321514			−0.160757	−	0.986994i	$-0.551394\pi$
$857$	−8066.23			−0.321514			−0.160757	+	0.986994i	$0.551394\pi$
$858$		0			0
$859$	39719.0			1.57764			0.788821	−	0.614623i	$-0.210692\pi$
$859$	39719.0			1.57764			0.788821	+	0.614623i	$0.210692\pi$
$860$	−2390.36	+	4140.22i	−0.0947796	+	0.164163i
$861$	−3383.32	+	5860.08i	−0.133918	+	0.231952i
$862$	2317.33	+	4013.73i	0.0915644	+	0.158594i
$863$	24473.8			0.965351			0.482676	−	0.875799i	$-0.339665\pi$
$863$	24473.8			0.965351			0.482676	+	0.875799i	$0.339665\pi$
$864$	5398.79	+	9350.98i	0.212582	+	0.368202i
$865$	−1714.32	−	2969.28i	−0.0673856	−	0.116715i
$866$	3404.03			0.133572
$867$	−4643.31	−	8042.45i	−0.181886	−	0.315036i
$868$	2395.19	−	4148.60i	0.0936614	−	0.162226i
$869$	−7351.13	+	12732.5i	−0.286962	+	0.497033i
$870$	2742.15			0.106859
$871$		0			0
$872$	−514.159			−0.0199675
$873$	−1618.76	+	2803.77i	−0.0627567	+	0.108698i
$874$	−2655.64	+	4599.71i	−0.102779	+	0.178018i
$875$	−14217.2	−	24624.9i	−0.549290	−	0.951399i
$876$	−29891.9			−1.15291
$877$	−12663.3	−	21933.5i	−0.487581	−	0.844515i	0.512317	−	0.858797i	$-0.328787\pi$
$877$	−12663.3	−	21933.5i	−0.487581	−	0.844515i	−0.999898	+	0.0142811i	$0.995454\pi$
$878$	234.142	+	405.546i	0.00899990	+	0.0155883i
$879$	20486.4			0.786109
$880$	10403.7	+	18019.7i	0.398532	+	0.690278i
$881$	−663.719	+	1149.59i	−0.0253817	+	0.0439624i	−0.878437	−	0.477858i	$-0.841413\pi$
$881$	−663.719	+	1149.59i	−0.0253817	+	0.0439624i	0.853056	+	0.521820i	$0.174747\pi$
$882$	106.248	−	184.027i	0.00405618	−	0.00702551i
$883$	−2112.05			−0.0804941			−0.0402470	−	0.999190i	$-0.512814\pi$
$883$	−2112.05			−0.0804941			−0.0402470	+	0.999190i	$0.512814\pi$
$884$		0			0
$885$	15629.6			0.593655
$886$	−440.607	+	763.154i	−0.0167071	+	0.0289375i
$887$	20467.7	−	35451.1i	0.774790	−	1.34197i	−0.160123	−	0.987097i	$-0.551189\pi$
$887$	20467.7	−	35451.1i	0.774790	−	1.34197i	0.934913	−	0.354878i	$-0.115478\pi$
$888$	−1656.30	−	2868.80i	−0.0625921	−	0.108413i
$889$	22997.9			0.867632
$890$	661.361	+	1145.51i	0.0249088	+	0.0431434i
$891$	−3588.79	−	6215.97i	−0.134937	−	0.233718i
$892$	−10708.9			−0.401975
$893$	−7018.72	−	12156.8i	−0.263015	−	0.455555i
$894$	1657.53	−	2870.92i	0.0620089	−	0.107403i
$895$	−5130.30	+	8885.94i	−0.191606	+	0.331871i
$896$	14881.0			0.554845
$897$		0			0
$898$	5720.04			0.212562
$899$	4042.96	−	7002.62i	0.149989	−	0.259789i
$900$	3751.16	−	6497.20i	0.138932	−	0.240637i
$901$	−21351.2	−	36981.3i	−0.789468	−	1.36740i
$902$	1714.62			0.0632934
$903$	−2857.00	−	4948.48i	−0.105288	−	0.182364i
$904$	−6541.61	−	11330.4i	−0.240676	−	0.416862i
$905$	−15239.1			−0.559740
$906$	−116.286	−	201.414i	−0.00426419	−	0.00738580i
$907$	−76.9840	+	133.340i	−0.00281831	+	0.00488146i	−0.867431	−	0.497557i	$-0.834230\pi$
$907$	−76.9840	+	133.340i	−0.00281831	+	0.00488146i	0.864613	+	0.502439i	$0.167564\pi$
$908$	16362.2	−	28340.2i	0.598017	−	1.03580i
$909$	−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	$0.504246\pi$
$912$	16206.2	−	28070.0i	0.588422	−	1.01918i
$913$	744.280	−	1289.13i	0.0269793	−	0.0467295i
$914$	1820.85	+	3153.81i	0.0658954	+	0.114134i
$915$	−1093.76			−0.0395177
$916$	13760.7	+	23834.3i	0.496361	+	0.859723i
$917$	7576.80	+	13123.4i	0.272855	+	0.472599i
$918$	−4991.67			−0.179466
$919$	25553.2	+	44259.4i	0.917216	+	1.58867i	0.803624	+	0.595138i	$0.202902\pi$
$919$	25553.2	+	44259.4i	0.917216	+	1.58867i	0.113592	+	0.993527i	$0.463764\pi$
$920$	−2128.22	+	3686.18i	−0.0762667	+	0.132098i
$921$	7830.92	−	13563.5i	0.280171	−	0.485270i
$922$	−4188.61			−0.149615
$923$		0			0
$924$	−25371.0			−0.903294
$925$	−5078.68	+	8796.53i	−0.180525	+	0.312679i
$926$	2077.37	−	3598.10i	0.0737219	−	0.127690i
$927$	6772.46	+	11730.2i	0.239953	+	0.415611i
$928$	18902.7			0.668655
$929$	15322.6	+	26539.5i	0.541139	+	0.937280i	0.998839	+	0.0481735i	$0.0153400\pi$
$929$	15322.6	+	26539.5i	0.541139	+	0.937280i	−0.457700	+	0.889107i	$0.651327\pi$
$930$	165.395	+	286.473i	0.00583174	+	0.0101009i
$931$	−5799.22			−0.204148
$932$	−2237.62	−	3875.67i	−0.0786433	−	0.136214i
$933$	9447.85	−	16364.2i	0.331520	−	0.574210i
$934$	514.583	−	891.284i	0.0180275	−	0.0312245i
$935$	−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	$0.639987\pi$
$938$	−2291.74	+	3969.41i	−0.0797739	+	0.138172i
$939$	−3912.62	+	6776.86i	−0.135978	+	0.235521i
$940$	−2785.38	−	4824.41i	−0.0966479	−	0.167399i
$941$	−16475.9			−0.570774			−0.285387	−	0.958412i	$-0.592122\pi$
$941$	−16475.9			−0.570774			−0.285387	+	0.958412i	$0.592122\pi$
$942$	2179.68	+	3775.31i	0.0753904	+	0.130580i
$943$	−4389.73	−	7603.23i	−0.151590	−	0.262561i
$944$	34754.5			1.19827
$945$	−10870.0	−	18827.4i	−0.374180	−	0.648099i
$946$	−723.946	+	1253.91i	−0.0248811	+	0.0430953i
$947$	5061.03	−	8765.97i	0.173666	−	0.300798i	−0.766033	−	0.642801i	$-0.777772\pi$
$947$	5061.03	−	8765.97i	0.173666	−	0.300798i	0.939699	+	0.342003i	$0.111105\pi$
$948$	9088.76			0.311381
$949$		0			0
$950$	3970.57			0.135602
$951$	−8778.18	+	15204.3i	−0.299319	+	0.518435i
$952$	−5227.27	+	9053.89i	−0.177959	+	0.308233i
$953$	−19048.6	−	32993.1i	−0.647475	−	1.12146i	−0.983724	−	0.179687i	$-0.942491\pi$
$953$	−19048.6	−	32993.1i	−0.647475	−	1.12146i	0.336248	−	0.941773i	$-0.390842\pi$
$954$	−2689.89			−0.0912875
$955$	−8127.07	−	14076.5i	−0.275378	−	0.476968i
$956$	906.643	+	1570.35i	0.0306725	+	0.0531264i
$957$	−42824.9			−1.44653
$958$	−629.121	−	1089.67i	−0.0212171	−	0.0367491i
$959$	−24847.2	+	43036.7i	−0.836662	+	1.44914i
$960$	6169.50	−	10685.9i	0.207417	−	0.359256i
$961$	−28815.6			−0.967258
$962$		0			0
$963$	4794.00			0.160420
$964$	12119.0	−	20990.7i	0.404902	−	0.701311i
$965$	−4542.43	+	7867.73i	−0.151530	+	0.262457i
$966$	−1259.63	−	2181.75i	−0.0419545	−	0.0726673i
$967$	−44515.5			−1.48037			−0.740187	−	0.672401i	$-0.765263\pi$
$967$	−44515.5			−1.48037			−0.740187	+	0.672401i	$0.765263\pi$
$968$	2376.74	+	4116.63i	0.0789165	+	0.136687i
$969$	23225.9	+	40228.4i	0.769993	+	1.33367i
$970$	−679.978			−0.0225080
$971$	12722.2	+	22035.4i	0.420467	+	0.728270i	0.995985	−	0.0895186i	$-0.0285329\pi$
$971$	12722.2	+	22035.4i	0.420467	+	0.728270i	−0.575518	+	0.817789i	$0.695200\pi$
$972$	13449.6	−	23295.5i	0.443824	−	0.768726i
$973$	−2797.97	+	4846.22i	−0.0921878	+	0.159674i
$974$	583.765			0.0192044
$975$		0			0
$976$	−2432.12			−0.0797646
$977$	−19734.0	+	34180.2i	−0.646208	+	1.11927i	0.337813	+	0.941213i	$0.390313\pi$
$977$	−19734.0	+	34180.2i	−0.646208	+	1.11927i	−0.984021	+	0.178052i	$0.943020\pi$
$978$	−210.742	+	365.016i	−0.00689038	+	0.0119345i
$979$	−10328.7	−	17889.8i	−0.337187	−	0.584025i
$980$	−2301.42			−0.0750165
$981$	580.913	+	1006.17i	0.0189063	+	0.0327467i
$982$	101.119	+	175.144i	0.00328600	+	0.00569152i
$983$	−14970.4			−0.485740			−0.242870	−	0.970059i	$-0.578089\pi$
$983$	−14970.4			−0.485740			−0.242870	+	0.970059i	$0.578089\pi$
$984$	−1070.24	−	1853.70i	−0.0346726	−	0.0600547i
$985$	18528.0	−	32091.4i	0.599340	−	1.03809i
$986$	−4369.31	+	7567.88i	−0.141123	+	0.244432i
$987$	6658.28			0.214727
$988$		0			0
$989$	7413.71			0.238364
$990$	−939.205	+	1626.75i	−0.0301514	+	0.0522238i
$991$	−29211.2	+	50595.3i	−0.936352	+	1.62181i	−0.164146	+	0.986436i	$0.552487\pi$
$991$	−29211.2	+	50595.3i	−0.936352	+	1.62181i	−0.772206	+	0.635373i	$0.780846\pi$
$992$	1140.13	+	1974.77i	0.0364912	+	0.0632047i
$993$	−9692.91			−0.309763
$994$	1977.83	+	3425.70i	0.0631116	+	0.109313i
$995$	−3796.23	−	6575.26i	−0.120953	−	0.209497i
$996$	−920.210			−0.0292751
$997$	−10065.8	−	17434.5i	−0.319746	−	0.553817i	0.660689	−	0.750660i	$-0.270264\pi$
$997$	−10065.8	−	17434.5i	−0.319746	−	0.553817i	−0.980435	+	0.196843i	$0.936931\pi$
$998$	−469.115	+	812.531i	−0.0148793	+	0.0257718i
$999$	−10976.0	+	19011.1i	−0.347614	+	0.602086i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.6	✓	9	13.9	even	3
169.4.a.l.1.4	yes	9	13.4	even	6
169.4.b.g.168.8		18	13.6	odd	12
169.4.b.g.168.11		18	13.7	odd	12
169.4.c.k.22.6		18	13.12	even	2
169.4.c.k.146.6		18	13.10	even	6
169.4.c.l.22.4		18	1.1	even	1	trivial
169.4.c.l.146.4		18	13.3	even	3	inner
169.4.e.h.23.8		36	13.2	odd	12
169.4.e.h.23.11		36	13.11	odd	12
169.4.e.h.147.8		36	13.8	odd	4
169.4.e.h.147.11		36	13.5	odd	4
1521.4.a.bg.1.6		9	39.17	odd	6
1521.4.a.bh.1.4		9	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.195058 + 0.337850i) q^{2} +(-1.80483 + 3.12606i) q^{3} +(3.92391 + 6.79640i) q^{4} +7.52136 q^{5} +(-0.704093 - 1.21953i) q^{6} +(9.77228 + 16.9261i) q^{7} -6.18247 q^{8} +(6.98515 + 12.0986i) q^{9} +O(q^{10})\)	\(q+(-0.195058 + 0.337850i) q^{2} +(-1.80483 + 3.12606i) q^{3} +(3.92391 + 6.79640i) q^{4} +7.52136 q^{5} +(-0.704093 - 1.21953i) q^{6} +(9.77228 + 16.9261i) q^{7} -6.18247 q^{8} +(6.98515 + 12.0986i) q^{9} +(-1.46710 + 2.54109i) q^{10} +(22.9121 - 39.6850i) q^{11} -28.3280 q^{12} -7.62463 q^{14} +(-13.5748 + 23.5123i) q^{15} +(-30.1853 + 52.2825i) q^{16} +(-43.2600 - 74.9285i) q^{17} -5.45003 q^{18} +(74.3684 + 128.810i) q^{19} +(29.5131 + 51.1182i) q^{20} -70.5494 q^{21} +(8.93837 + 15.4817i) q^{22} +(45.7676 - 79.2718i) q^{23} +(11.1583 - 19.3268i) q^{24} -68.4292 q^{25} -147.889 q^{27} +(-76.6910 + 132.833i) q^{28} +(-129.451 + 224.215i) q^{29} +(-5.29574 - 9.17249i) q^{30} -31.2317 q^{31} +(-36.5056 - 63.2296i) q^{32} +(82.7052 + 143.250i) q^{33} +33.7528 q^{34} +(73.5008 + 127.307i) q^{35} +(-54.8181 + 94.9478i) q^{36} +(74.2180 - 128.549i) q^{37} -58.0245 q^{38} -46.5006 q^{40} +(47.9567 - 83.0635i) q^{41} +(13.7612 - 23.8351i) q^{42} +(40.4965 + 70.1420i) q^{43} +359.620 q^{44} +(52.5378 + 90.9982i) q^{45} +(17.8546 + 30.9251i) q^{46} -94.3777 q^{47} +(-108.959 - 188.722i) q^{48} +(-19.4949 + 33.7662i) q^{49} +(13.3476 - 23.1188i) q^{50} +312.308 q^{51} +493.555 q^{53} +(28.8469 - 49.9643i) q^{54} +(172.330 - 298.485i) q^{55} +(-60.4169 - 104.645i) q^{56} -536.891 q^{57} +(-50.5006 - 87.4697i) q^{58} +(-287.843 - 498.558i) q^{59} -213.065 q^{60} +(20.1432 + 34.8891i) q^{61} +(6.09199 - 10.5516i) q^{62} +(-136.522 + 236.462i) q^{63} -454.482 q^{64} -64.5291 q^{66} +(300.570 - 520.603i) q^{67} +(339.496 - 588.025i) q^{68} +(165.206 + 286.145i) q^{69} -57.3476 q^{70} +(-259.400 - 449.294i) q^{71} +(-43.1855 - 74.7995i) q^{72} +1055.21 q^{73} +(28.9536 + 50.1491i) q^{74} +(123.503 - 213.914i) q^{75} +(-583.629 + 1010.88i) q^{76} +895.615 q^{77} -320.840 q^{79} +(-227.034 + 393.235i) q^{80} +(78.3164 - 135.648i) q^{81} +(18.7087 + 32.4043i) q^{82} +32.4841 q^{83} +(-276.829 - 479.482i) q^{84} +(-325.374 - 563.564i) q^{85} -31.5966 q^{86} +(-467.274 - 809.341i) q^{87} +(-141.654 + 245.351i) q^{88} +(225.398 - 390.400i) q^{89} -40.9916 q^{90} +718.350 q^{92} +(56.3681 - 97.6324i) q^{93} +(18.4091 - 31.8855i) q^{94} +(559.352 + 968.826i) q^{95} +263.546 q^{96} +(115.871 + 200.695i) q^{97} +(-7.60526 - 13.1727i) q^{98} +640.179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

Introduction

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