LMFDB - Embedded newform 169.4.c.f.146.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.f.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28078 - 3.95042i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-6.40388 + 11.0918i) q^{4} -2.80776 q^{5} +(-19.8078 + 34.3081i) q^{6} +(4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})$	\(q+(-2.28078 - 3.95042i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-6.40388 + 11.0918i) q^{4} -2.80776 q^{5} +(-19.8078 + 34.3081i) q^{6} +(4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(-24.2116 + 41.9358i) q^{9} +(6.40388 + 11.0918i) q^{10} +(19.7116 + 34.1416i) q^{11} +111.231 q^{12} -43.6155 q^{14} +(12.1922 + 21.1176i) q^{15} +(1.21165 + 2.09863i) q^{16} +(-1.00758 + 1.74518i) q^{17} +220.885 q^{18} +(-30.0961 + 52.1280i) q^{19} +(17.9806 - 31.1433i) q^{20} -83.0388 q^{21} +(89.9157 - 155.739i) q^{22} +(-2.23438 - 3.87006i) q^{23} +(-95.2311 - 164.945i) q^{24} -117.116 q^{25} +186.054 q^{27} +(61.2311 + 106.055i) q^{28} +(-70.3466 - 121.844i) q^{29} +(55.6155 - 96.3289i) q^{30} -136.155 q^{31} +(93.2505 - 161.515i) q^{32} +(171.189 - 296.508i) q^{33} +9.19224 q^{34} +(-13.4233 + 23.2498i) q^{35} +(-310.097 - 537.104i) q^{36} +(-92.8542 - 160.828i) q^{37} +274.570 q^{38} -61.5767 q^{40} +(155.116 + 268.668i) q^{41} +(189.393 + 328.038i) q^{42} +(-213.735 + 370.200i) q^{43} -504.924 q^{44} +(67.9806 - 117.746i) q^{45} +(-10.1922 + 17.6535i) q^{46} +258.617 q^{47} +(10.5227 - 18.2259i) q^{48} +(125.788 + 217.872i) q^{49} +(267.116 + 462.659i) q^{50} +17.5009 q^{51} +612.656 q^{53} +(-424.348 - 734.991i) q^{54} +(-55.3457 - 95.8615i) q^{55} +(104.847 - 181.600i) q^{56} +522.749 q^{57} +(-320.890 + 555.797i) q^{58} +(-258.943 + 448.502i) q^{59} -312.311 q^{60} +(80.6553 - 139.699i) q^{61} +(310.540 + 537.871i) q^{62} +(231.501 + 400.971i) q^{63} -831.348 q^{64} -1561.77 q^{66} +(-24.9493 - 43.2135i) q^{67} +(-12.9048 - 22.3518i) q^{68} +(-19.4048 + 33.6101i) q^{69} +122.462 q^{70} +(139.982 - 242.455i) q^{71} +(-530.982 + 919.689i) q^{72} -467.732 q^{73} +(-423.559 + 733.626i) q^{74} +(508.558 + 880.849i) q^{75} +(-385.464 - 667.643i) q^{76} +376.948 q^{77} +37.5379 q^{79} +(-3.40202 - 5.89247i) q^{80} +(-154.193 - 267.070i) q^{81} +(707.568 - 1225.54i) q^{82} +76.1553 q^{83} +(531.771 - 921.054i) q^{84} +(2.82904 - 4.90004i) q^{85} +1949.93 q^{86} +(-610.936 + 1058.17i) q^{87} +(432.294 + 748.754i) q^{88} +(101.403 + 175.635i) q^{89} -620.194 q^{90} +57.2348 q^{92} +(591.231 + 1024.04i) q^{93} +(-589.848 - 1021.65i) q^{94} +(84.5028 - 146.363i) q^{95} -1619.70 q^{96} +(-587.184 + 1017.03i) q^{97} +(573.790 - 993.834i) q^{98} -1909.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9} + 5 q^{10} + 17 q^{11} + 280 q^{12} - 92 q^{14} + 90 q^{15} - 57 q^{16} - 70 q^{17} + 430 q^{18} - 141 q^{19} + 175 q^{20} - 126 q^{21} + 170 q^{22} - 145 q^{23} - 216 q^{24} + 150 q^{25} + 670 q^{27} + 80 q^{28} - 34 q^{29} + 140 q^{30} + 280 q^{31} + 105 q^{32} + 425 q^{33} + 78 q^{34} + 70 q^{35} - 725 q^{36} - 190 q^{37} + 620 q^{38} - 370 q^{40} + 538 q^{41} + 370 q^{42} - 455 q^{43} - 1360 q^{44} + 375 q^{45} - 82 q^{46} - 120 q^{47} + 240 q^{48} + 565 q^{49} + 450 q^{50} - 466 q^{51} + 1090 q^{53} - 914 q^{54} - 510 q^{55} + 172 q^{56} + 450 q^{57} - 595 q^{58} - 809 q^{59} + 400 q^{60} - 502 q^{61} + 500 q^{62} + 390 q^{63} - 2542 q^{64} - 3196 q^{66} - 475 q^{67} + 505 q^{68} + 479 q^{69} + 160 q^{70} + 127 q^{71} - 1155 q^{72} - 1170 q^{73} - 849 q^{74} + 1725 q^{75} - 140 q^{76} + 510 q^{77} + 480 q^{79} - 1065 q^{80} - 122 q^{81} + 1515 q^{82} - 520 q^{83} + 1220 q^{84} - 1205 q^{85} + 3924 q^{86} - 1615 q^{87} + 1020 q^{88} + 921 q^{89} - 1450 q^{90} - 2080 q^{92} + 2200 q^{93} - 1040 q^{94} - 1270 q^{95} - 3840 q^{96} - 415 q^{97} + 1285 q^{98} - 4420 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9 + 5 * q^10 + 17 * q^11 + 280 * q^12 - 92 * q^14 + 90 * q^15 - 57 * q^16 - 70 * q^17 + 430 * q^18 - 141 * q^19 + 175 * q^20 - 126 * q^21 + 170 * q^22 - 145 * q^23 - 216 * q^24 + 150 * q^25 + 670 * q^27 + 80 * q^28 - 34 * q^29 + 140 * q^30 + 280 * q^31 + 105 * q^32 + 425 * q^33 + 78 * q^34 + 70 * q^35 - 725 * q^36 - 190 * q^37 + 620 * q^38 - 370 * q^40 + 538 * q^41 + 370 * q^42 - 455 * q^43 - 1360 * q^44 + 375 * q^45 - 82 * q^46 - 120 * q^47 + 240 * q^48 + 565 * q^49 + 450 * q^50 - 466 * q^51 + 1090 * q^53 - 914 * q^54 - 510 * q^55 + 172 * q^56 + 450 * q^57 - 595 * q^58 - 809 * q^59 + 400 * q^60 - 502 * q^61 + 500 * q^62 + 390 * q^63 - 2542 * q^64 - 3196 * q^66 - 475 * q^67 + 505 * q^68 + 479 * q^69 + 160 * q^70 + 127 * q^71 - 1155 * q^72 - 1170 * q^73 - 849 * q^74 + 1725 * q^75 - 140 * q^76 + 510 * q^77 + 480 * q^79 - 1065 * q^80 - 122 * q^81 + 1515 * q^82 - 520 * q^83 + 1220 * q^84 - 1205 * q^85 + 3924 * q^86 - 1615 * q^87 + 1020 * q^88 + 921 * q^89 - 1450 * q^90 - 2080 * q^92 + 2200 * q^93 - 1040 * q^94 - 1270 * q^95 - 3840 * q^96 - 415 * q^97 + 1285 * q^98 - 4420 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.28078	−	3.95042i	−0.806376	−	1.39668i	−0.915358	−	0.402641i	$-0.868092\pi$
$2$	−2.28078	−	3.95042i	−0.806376	−	1.39668i	0.108982	−	0.994044i	$-0.465241\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	−0.893474	−	0.449114i	$-0.851740\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	0.0577926	−	0.998329i	$-0.481594\pi$
$4$	−6.40388	+	11.0918i	−0.800485	+	1.38648i
$5$	−2.80776			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−2.80776			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$	−19.8078	+	34.3081i	−1.34775	+	2.33437i
$7$	4.78078	−	8.28055i	0.258138	−	0.447108i	−0.707605	−	0.706608i	$-0.750225\pi$
$7$	4.78078	−	8.28055i	0.258138	−	0.447108i	0.965743	+	0.259500i	$0.0835579\pi$
$8$	21.9309			0.969217
$9$	−24.2116	+	41.9358i	−0.896728	+	1.55318i
$10$	6.40388	+	11.0918i	0.202509	+	0.350755i
$11$	19.7116	+	34.1416i	0.540299	+	0.935825i	0.998887	+	0.0471757i	$0.0150221\pi$
$11$	19.7116	+	34.1416i	0.540299	+	0.935825i	−0.458588	+	0.888649i	$0.651645\pi$
$12$	111.231			2.67580
$13$		0			0
$13$		0			0
$14$	−43.6155			−0.832624
$15$	12.1922	+	21.1176i	0.209868	+	0.363502i
$16$	1.21165	+	2.09863i	0.0189320	+	0.0327911i
$17$	−1.00758	+	1.74518i	−0.0143749	+	0.0248981i	−0.873123	−	0.487499i	$-0.837909\pi$
$17$	−1.00758	+	1.74518i	−0.0143749	+	0.0248981i	0.858748	+	0.512397i	$0.171242\pi$
$18$	220.885			2.89240
$19$	−30.0961	+	52.1280i	−0.363396	+	0.629420i	−0.988517	−	0.151107i	$-0.951716\pi$
$19$	−30.0961	+	52.1280i	−0.363396	+	0.629420i	0.625121	+	0.780528i	$0.285049\pi$
$20$	17.9806	−	31.1433i	0.201029	−	0.348193i
$21$	−83.0388			−0.862884
$22$	89.9157	−	155.739i	0.871368	−	1.50925i
$23$	−2.23438	−	3.87006i	−0.0202565	−	0.0350853i	0.855719	−	0.517440i	$-0.173115\pi$
$23$	−2.23438	−	3.87006i	−0.0202565	−	0.0350853i	−0.875976	+	0.482355i	$0.839782\pi$
$24$	−95.2311	−	164.945i	−0.809957	−	1.40289i
$25$	−117.116			−0.936932
$26$		0			0
$27$	186.054			1.32615
$28$	61.2311	+	106.055i	0.413271	+	0.715806i
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	0.547964	−	0.836502i	$-0.315403\pi$
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	−0.998414	+	0.0563003i	$0.982070\pi$
$30$	55.6155	−	96.3289i	0.338465	−	0.586239i
$31$	−136.155			−0.788845			−0.394423	−	0.918929i	$-0.629055\pi$
$31$	−136.155			−0.788845			−0.394423	+	0.918929i	$0.629055\pi$
$32$	93.2505	−	161.515i	0.515141	−	0.892250i
$33$	171.189	−	296.508i	0.903035	−	1.56410i
$34$	9.19224			0.0463663
$35$	−13.4233	+	23.2498i	−0.0648272	+	0.112284i
$36$	−310.097	−	537.104i	−1.43563	−	2.48659i
$37$	−92.8542	−	160.828i	−0.412571	−	0.714594i	0.582599	−	0.812760i	$-0.302036\pi$
$37$	−92.8542	−	160.828i	−0.412571	−	0.714594i	−0.995170	+	0.0981657i	$0.968702\pi$
$38$	274.570			1.17214
$39$		0			0
$40$	−61.5767			−0.243403
$41$	155.116	+	268.668i	0.590853	+	1.02339i	0.994118	+	0.108304i	$0.0345420\pi$
$41$	155.116	+	268.668i	0.590853	+	1.02339i	−0.403265	+	0.915083i	$0.632125\pi$
$42$	189.393	+	328.038i	0.695809	+	1.20518i
$43$	−213.735	+	370.200i	−0.758008	+	1.31291i	0.185857	+	0.982577i	$0.440494\pi$
$43$	−213.735	+	370.200i	−0.758008	+	1.31291i	−0.943865	+	0.330331i	$0.892840\pi$
$44$	−504.924			−1.73000
$45$	67.9806	−	117.746i	0.225199	−	0.390056i
$46$	−10.1922	+	17.6535i	−0.0326688	+	0.0565840i
$47$	258.617			0.802622			0.401311	−	0.915942i	$-0.368555\pi$
$47$	258.617			0.802622			0.401311	+	0.915942i	$0.368555\pi$
$48$	10.5227	−	18.2259i	0.0316422	−	0.0548059i
$49$	125.788	+	217.872i	0.366730	+	0.635195i
$50$	267.116	+	462.659i	0.755519	+	1.30860i
$51$	17.5009			0.0480514
$52$		0			0
$53$	612.656			1.58783			0.793913	−	0.608031i	$-0.208040\pi$
$53$	612.656			1.58783			0.793913	+	0.608031i	$0.208040\pi$
$54$	−424.348	−	734.991i	−1.06938	−	1.85222i
$55$	−55.3457	−	95.8615i	−0.135687	−	0.235017i
$56$	104.847	−	181.600i	0.250191	−	0.433344i
$57$	522.749			1.21473
$58$	−320.890	+	555.797i	−0.726463	+	1.25827i
$59$	−258.943	+	448.502i	−0.571381	+	0.989661i	0.425044	+	0.905173i	$0.360259\pi$
$59$	−258.943	+	448.502i	−0.571381	+	0.989661i	−0.996425	+	0.0844878i	$0.973075\pi$
$60$	−312.311			−0.671985
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	−0.768879	−	0.639395i	$-0.779185\pi$
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	0.938171	+	0.346171i	$0.112518\pi$
$62$	310.540	+	537.871i	0.636106	+	1.10177i
$63$	231.501	+	400.971i	0.462958	+	0.801867i
$64$	−831.348			−1.62373
$65$		0			0
$66$	−1561.77			−2.91274
$67$	−24.9493	−	43.2135i	−0.0454933	−	0.0787966i	0.842382	−	0.538881i	$-0.181153\pi$
$67$	−24.9493	−	43.2135i	−0.0454933	−	0.0787966i	−0.887875	+	0.460084i	$0.847819\pi$
$68$	−12.9048	−	22.3518i	−0.0230138	−	0.0398611i
$69$	−19.4048	+	33.6101i	−0.0338560	+	0.0586403i
$70$	122.462			0.209100
$71$	139.982	−	242.455i	0.233982	−	0.405269i	−0.724994	−	0.688755i	$-0.758158\pi$
$71$	139.982	−	242.455i	0.233982	−	0.405269i	0.958976	+	0.283486i	$0.0914909\pi$
$72$	−530.982	+	919.689i	−0.869123	+	1.50537i
$73$	−467.732			−0.749916			−0.374958	−	0.927042i	$-0.622343\pi$
$73$	−467.732			−0.749916			−0.374958	+	0.927042i	$0.622343\pi$
$74$	−423.559	+	733.626i	−0.665375	+	1.15246i
$75$	508.558	+	880.849i	0.782977	+	1.35616i
$76$	−385.464	−	667.643i	−0.581786	−	1.00768i
$77$	376.948			0.557886
$78$		0			0
$79$	37.5379			0.0534600			0.0267300	−	0.999643i	$-0.491491\pi$
$79$	37.5379			0.0534600			0.0267300	+	0.999643i	$0.491491\pi$
$80$	−3.40202	−	5.89247i	−0.00475446	−	0.00823497i
$81$	−154.193	−	267.070i	−0.211513	−	0.366352i
$82$	707.568	−	1225.54i	0.952900	−	1.65047i
$83$	76.1553			0.100712			0.0503562	−	0.998731i	$-0.483964\pi$
$83$	76.1553			0.100712			0.0503562	+	0.998731i	$0.483964\pi$
$84$	531.771	−	921.054i	0.690726	−	1.19637i
$85$	2.82904	−	4.90004i	0.00361003	−	0.00625275i
$86$	1949.93			2.44496
$87$	−610.936	+	1058.17i	−0.752865	+	1.30400i
$88$	432.294	+	748.754i	0.523666	+	0.907017i
$89$	101.403	+	175.635i	0.120772	+	0.209183i	0.920072	−	0.391749i	$-0.128130\pi$
$89$	101.403	+	175.635i	0.120772	+	0.209183i	−0.799300	+	0.600932i	$0.794796\pi$
$90$	−620.194			−0.726380
$91$		0			0
$92$	57.2348			0.0648602
$93$	591.231	+	1024.04i	0.659224	+	1.14181i
$94$	−589.848	−	1021.65i	−0.647215	−	1.12101i
$95$	84.5028	−	146.363i	0.0912611	−	0.158069i
$96$	−1619.70			−1.72198
$97$	−587.184	+	1017.03i	−0.614634	+	1.06458i	0.375814	+	0.926695i	$0.377363\pi$
$97$	−587.184	+	1017.03i	−0.614634	+	1.06458i	−0.990449	+	0.137883i	$0.955970\pi$
$98$	573.790	−	993.834i	0.591445	−	1.02441i
$99$	−1909.01			−1.93800
$100$	750.000	−	1299.04i	0.750000	−	1.29904i
$101$	−485.348	−	840.648i	−0.478158	−	0.828194i	0.521528	−	0.853234i	$-0.325362\pi$
$101$	−485.348	−	840.648i	−0.478158	−	0.828194i	−0.999686	+	0.0250397i	$0.992029\pi$
$102$	−39.9157	−	69.1360i	−0.0387475	−	0.0671126i
$103$	−1899.70			−1.81731			−0.908654	−	0.417550i	$-0.862889\pi$
$103$	−1899.70			−1.81731			−0.908654	+	0.417550i	$0.862889\pi$
$104$		0			0
$105$	233.153			0.216699
$106$	−1397.33	−	2420.25i	−1.28039	−	2.21769i
$107$	953.247	+	1651.07i	0.861251	+	1.49173i	0.870722	+	0.491775i	$0.163652\pi$
$107$	953.247	+	1651.07i	0.861251	+	1.49173i	−0.00947163	+	0.999955i	$0.503015\pi$
$108$	−1191.47	+	2063.68i	−1.06157	+	1.83868i
$109$	896.004			0.787354			0.393677	−	0.919249i	$-0.371203\pi$
$109$	896.004			0.787354			0.393677	+	0.919249i	$0.371203\pi$
$110$	−252.462	+	437.277i	−0.218830	+	0.379025i
$111$	−806.407	+	1396.74i	−0.689556	+	1.19435i
$112$	23.1704			0.0195482
$113$	167.441	−	290.017i	0.139394	−	0.241438i	−0.787873	−	0.615837i	$-0.788818\pi$
$113$	167.441	−	290.017i	0.139394	−	0.241438i	0.927267	+	0.374400i	$0.122151\pi$
$114$	−1192.27	−	2065.08i	−0.979532	−	1.69660i
$115$	6.27361	+	10.8662i	0.00508710	+	0.00881112i
$116$	1801.96			1.44231
$117$		0			0
$118$	2362.36			1.84299
$119$	9.63401	+	16.6866i	0.00742141	+	0.0128543i
$120$	267.386	+	463.127i	0.203408	+	0.352312i
$121$	−111.598	+	193.293i	−0.0838452	+	0.145224i
$122$	−735.827			−0.546054
$123$	1347.13	−	2333.29i	0.987530	−	1.71045i
$124$	871.922	−	1510.21i	0.631459	−	1.09372i
$125$	679.806			0.486430
$126$	1056.00	−	1829.05i	0.746637	−	1.29321i
$127$	−310.447	−	537.709i	−0.216911	−	0.375701i	0.736951	−	0.675946i	$-0.236265\pi$
$127$	−310.447	−	537.709i	−0.216911	−	0.375701i	−0.953862	+	0.300245i	$0.902931\pi$
$128$	1150.11	+	1992.06i	0.794193	+	1.37558i
$129$	3712.44			2.53381
$130$		0			0
$131$	−1331.70			−0.888180			−0.444090	−	0.895982i	$-0.646473\pi$
$131$	−1331.70			−0.888180			−0.444090	+	0.895982i	$0.646473\pi$
$132$	2192.55	+	3797.60i	1.44573	+	2.50408i
$133$	287.766	+	498.425i	0.187612	+	0.324954i
$134$	−113.808	+	197.121i	−0.0733694	+	0.127079i
$135$	−522.396			−0.333042
$136$	−22.0971	+	38.2732i	−0.0139324	+	0.0241316i
$137$	311.008	−	538.681i	0.193950	−	0.335932i	−0.752606	−	0.658471i	$-0.771203\pi$
$137$	311.008	−	538.681i	0.193950	−	0.335932i	0.946556	+	0.322540i	$0.104537\pi$
$138$	177.032			0.109203
$139$	−165.290	+	286.291i	−0.100861	+	0.174697i	−0.912040	−	0.410102i	$-0.865493\pi$
$139$	−165.290	+	286.291i	−0.100861	+	0.174697i	0.811178	+	0.584799i	$0.198827\pi$
$140$	−171.922	−	297.778i	−0.103786	−	0.179763i
$141$	−1123.00	−	1945.10i	−0.670736	−	1.16175i
$142$	−1277.07			−0.754711
$143$		0			0
$144$	−117.344			−0.0679073
$145$	197.517	+	342.109i	0.113123	+	0.195935i
$146$	1066.79	+	1847.74i	0.604715	+	1.04740i
$147$	1092.43	−	1892.14i	0.612939	−	1.06164i
$148$	2378.51			1.32103
$149$	−905.269	+	1567.97i	−0.497735	+	0.862102i	−0.999997	−	0.00261337i	$-0.999168\pi$
$149$	−905.269	+	1567.97i	−0.497735	+	0.862102i	0.502262	+	0.864716i	$0.332501\pi$
$150$	2319.82	−	4018.04i	1.26275	−	2.18714i
$151$	423.239			0.228097			0.114049	−	0.993475i	$-0.463618\pi$
$151$	423.239			0.228097			0.114049	+	0.993475i	$0.463618\pi$
$152$	−660.034	+	1143.21i	−0.352209	+	0.610045i
$153$	−48.7902	−	84.5071i	−0.0257808	−	0.0446536i
$154$	−859.734	−	1489.10i	−0.449866	−	0.779190i
$155$	382.292			0.198106
$156$		0			0
$157$	1322.17			0.672105			0.336052	−	0.941843i	$-0.390908\pi$
$157$	1322.17			0.672105			0.336052	+	0.941843i	$0.390908\pi$
$158$	−85.6155	−	148.290i	−0.0431089	−	0.0746668i
$159$	−2660.35	−	4607.87i	−1.32692	−	2.29829i
$160$	−261.825	+	453.495i	−0.129369	+	0.224074i
$161$	−42.7283			−0.0209159
$162$	−703.360	+	1218.26i	−0.341119	+	0.590835i
$163$	−1803.20	+	3123.23i	−0.866486	+	1.50080i	−0.000922205		1.00000i	$0.500294\pi$
$163$	−1803.20	+	3123.23i	−0.866486	+	1.50080i	−0.865564	+	0.500798i	$0.833040\pi$
$164$	−3973.37			−1.89188
$165$	−480.658	+	832.524i	−0.226783	+	0.392800i
$166$	−173.693	−	300.845i	−0.0812121	−	0.140663i
$167$	−1707.72	−	2957.85i	−0.791300	−	1.37057i	−0.925162	−	0.379571i	$-0.876071\pi$
$167$	−1707.72	−	2957.85i	−0.791300	−	1.37057i	0.133863	−	0.991000i	$-0.457262\pi$
$168$	−1821.11			−0.836321
$169$		0			0
$170$	−25.8096			−0.0116442
$171$	−1457.35	−	2524.21i	−0.651734	−	1.12884i
$172$	−2737.47	−	4741.44i	−1.21355	−	2.10193i
$173$	−1171.11	+	2028.43i	−0.514671	+	0.891436i	0.485184	+	0.874412i	$0.338753\pi$
$173$	−1171.11	+	2028.43i	−0.514671	+	0.891436i	−0.999855	+	0.0170243i	$0.994581\pi$
$174$	5573.63			2.42837
$175$	−559.908	+	969.788i	−0.241857	+	0.418909i
$176$	−47.7671	+	82.7350i	−0.0204578	+	0.0354340i
$177$	4497.66			1.90997
$178$	462.555	−	801.169i	0.194775	−	0.337360i
$179$	333.446	+	577.545i	0.139234	+	0.241160i	0.927207	−	0.374550i	$-0.122203\pi$
$179$	333.446	+	577.545i	0.139234	+	0.241160i	−0.787973	+	0.615710i	$0.788869\pi$
$180$	870.679	+	1508.06i	0.360537	+	0.624468i
$181$	−701.037			−0.287888			−0.143944	−	0.989586i	$-0.545978\pi$
$181$	−701.037			−0.287888			−0.143944	+	0.989586i	$0.545978\pi$
$182$		0			0
$183$	−1400.93			−0.565899
$184$	−49.0019	−	84.8737i	−0.0196330	−	0.0340053i
$185$	260.713	+	451.567i	0.103611	+	0.179459i
$186$	2696.93	−	4671.22i	1.06316	−	1.84146i
$187$	−79.4440			−0.0310670
$188$	−1656.16	+	2868.55i	−0.642487	+	1.11282i
$189$	889.482	−	1540.63i	0.342330	−	0.592933i
$190$	−770.928			−0.294363
$191$	−650.440	+	1126.59i	−0.246409	+	0.426793i	−0.962527	−	0.271186i	$-0.912584\pi$
$191$	−650.440	+	1126.59i	−0.246409	+	0.426793i	0.716118	+	0.697980i	$0.245917\pi$
$192$	3609.98	+	6252.68i	1.35692	+	2.35025i
$193$	−259.667	−	449.756i	−0.0968457	−	0.167742i	0.813532	−	0.581521i	$-0.197542\pi$
$193$	−259.667	−	449.756i	−0.0968457	−	0.167742i	−0.910377	+	0.413779i	$0.864209\pi$
$194$	5356.94			1.98251
$195$		0			0
$196$	−3222.14			−1.17425
$197$	1560.52	+	2702.91i	0.564379	+	0.977534i	0.997107	+	0.0760091i	$0.0242178\pi$
$197$	1560.52	+	2702.91i	0.564379	+	0.977534i	−0.432728	+	0.901525i	$0.642449\pi$
$198$	4354.01	+	7541.38i	1.56276	+	2.70678i
$199$	−618.529	+	1071.32i	−0.220333	+	0.381629i	−0.954909	−	0.296898i	$-0.904048\pi$
$199$	−618.529	+	1071.32i	−0.220333	+	0.381629i	0.734576	+	0.678527i	$0.237381\pi$
$200$	−2568.47			−0.908090
$201$	−216.677	+	375.295i	−0.0760358	+	0.131698i
$202$	−2213.94	+	3834.66i	−0.771151	+	1.33567i
$203$	−1345.25			−0.465112
$204$	−112.074	+	194.118i	−0.0384644	+	0.0666223i
$205$	−435.528	−	754.356i	−0.148383	−	0.257007i
$206$	4332.78	+	7504.60i	1.46543	+	2.53821i
$207$	216.392			0.0726584
$208$		0			0
$209$	−2372.98			−0.785369
$210$	−531.771	−	921.054i	−0.174741	−	0.302661i
$211$	1265.83	+	2192.49i	0.413003	+	0.715342i	0.995217	−	0.0976940i	$-0.0311466\pi$
$211$	1265.83	+	2192.49i	0.413003	+	0.715342i	−0.582214	+	0.813036i	$0.697813\pi$
$212$	−3923.38	+	6795.49i	−1.27103	+	2.20149i
$213$	−2431.38			−0.782139
$214$	4348.28	−	7531.45i	1.38898	−	2.40579i
$215$	600.118	−	1039.44i	0.190362	−	0.329716i
$216$	4080.33			1.28533
$217$	−650.928	+	1127.44i	−0.203631	+	0.352699i
$218$	−2043.58	−	3539.59i	−0.634904	−	1.09969i
$219$	2031.05	+	3517.88i	0.626691	+	1.08546i
$220$	1417.71			0.434463
$221$		0			0
$222$	7356.93			2.22417
$223$	−597.766	−	1035.36i	−0.179504	−	0.310910i	0.762207	−	0.647333i	$-0.224116\pi$
$223$	−597.766	−	1035.36i	−0.179504	−	0.310910i	−0.941711	+	0.336424i	$0.890783\pi$
$224$	−891.619	−	1544.33i	−0.265955	−	0.460647i
$225$	2835.58	−	4911.37i	0.840173	−	1.45522i
$226$	−1527.58			−0.449617
$227$	−434.596	+	752.742i	−0.127071	+	0.220094i	−0.922541	−	0.385900i	$-0.873891\pi$
$227$	−434.596	+	752.742i	−0.127071	+	0.220094i	0.795469	+	0.605994i	$0.207224\pi$
$228$	−3347.62	+	5798.25i	−0.972376	+	1.68420i
$229$	−4684.64			−1.35183			−0.675916	−	0.736978i	$-0.736252\pi$
$229$	−4684.64			−1.35183			−0.675916	+	0.736978i	$0.736252\pi$
$230$	28.6174	−	49.5668i	0.00820424	−	0.0142102i
$231$	−1636.83	−	2835.08i	−0.466215	−	0.807508i
$232$	−1542.76	−	2672.14i	−0.436583	−	0.756184i
$233$	−4868.99			−1.36900			−0.684502	−	0.729011i	$-0.739980\pi$
$233$	−4868.99			−1.36900			−0.684502	+	0.729011i	$0.739980\pi$
$234$		0			0
$235$	−726.137			−0.201566
$236$	−3316.48	−	5744.31i	−0.914764	−	1.58442i
$237$	−163.002	−	282.328i	−0.0446756	−	0.0773803i
$238$	43.9460	−	76.1167i	0.0119689	−	0.0207307i
$239$	−4807.53			−1.30114			−0.650572	−	0.759444i	$-0.725471\pi$
$239$	−4807.53			−1.30114			−0.650572	+	0.759444i	$0.725471\pi$
$240$	−29.5454	+	51.1740i	−0.00794643	+	0.0137636i
$241$	2937.98	−	5088.73i	0.785278	−	1.36014i	−0.143555	−	0.989642i	$-0.545853\pi$
$241$	2937.98	−	5088.73i	0.785278	−	1.36014i	0.928833	−	0.370499i	$-0.120813\pi$
$242$	1018.12			0.270443
$243$	1172.61	−	2031.03i	0.309561	−	0.536175i
$244$	1033.01	+	1789.23i	0.271033	+	0.469442i
$245$	−353.184	−	611.733i	−0.0920984	−	0.159519i
$246$	−12290.0			−3.18528
$247$		0			0
$248$	−2986.00			−0.764562
$249$	−330.691	−	572.774i	−0.0841635	−	0.145775i
$250$	−1550.49	−	2685.52i	−0.392245	−	0.679389i
$251$	−2903.13	+	5028.38i	−0.730057	+	1.26450i	0.226802	+	0.973941i	$0.427173\pi$
$251$	−2903.13	+	5028.38i	−0.730057	+	1.26450i	−0.956858	+	0.290554i	$0.906160\pi$
$252$	−5930.02			−1.48237
$253$	88.0866	−	152.570i	0.0218891	−	0.0379131i
$254$	−1416.12	+	2452.79i	−0.349823	+	0.605912i
$255$	−49.1385			−0.0120673
$256$	1920.92	−	3327.12i	0.468974	−	0.812286i
$257$	597.930	+	1035.65i	0.145128	+	0.251369i	0.929421	−	0.369022i	$-0.120307\pi$
$257$	597.930	+	1035.65i	0.145128	+	0.251369i	−0.784293	+	0.620391i	$0.786974\pi$
$258$	−8467.24	−	14665.7i	−2.04321	−	3.53894i
$259$	−1775.66			−0.426001
$260$		0			0
$261$	6812.83			1.61572
$262$	3037.32	+	5260.79i	0.716207	+	1.24051i
$263$	−117.092	−	202.810i	−0.0274533	−	0.0475505i	0.851972	−	0.523587i	$-0.175406\pi$
$263$	−117.092	−	202.810i	−0.0274533	−	0.0475505i	−0.879426	+	0.476036i	$0.842073\pi$
$264$	3754.32	−	6502.68i	0.875237	−	1.51595i
$265$	−1720.19			−0.398757
$266$	1312.66	−	2273.59i	0.302572	−	0.524071i
$267$	880.650	−	1525.33i	0.201854	−	0.349621i
$268$	639.091			0.145667
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	−0.674285	−	0.738471i	$-0.735548\pi$
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	0.976677	+	0.214712i	$0.0688813\pi$
$270$	1191.47	+	2063.68i	0.268557	+	0.465155i
$271$	2850.64	+	4937.45i	0.638982	+	1.10675i	0.985657	+	0.168763i	$0.0539774\pi$
$271$	2850.64	+	4937.45i	0.638982	+	1.10675i	−0.346675	+	0.937985i	$0.612689\pi$
$272$	−4.88331			−0.00108858
$273$		0			0
$274$	−2837.35			−0.625587
$275$	−2308.56	−	3998.54i	−0.506223	−	0.876804i
$276$	−248.532	−	430.471i	−0.0542025	−	0.0938815i
$277$	3576.24	−	6194.24i	0.775725	−	1.34359i	−0.158662	−	0.987333i	$-0.550718\pi$
$277$	3576.24	−	6194.24i	0.775725	−	1.34359i	0.934386	−	0.356261i	$-0.115949\pi$
$278$	1507.96			0.325329
$279$	3296.54	−	5709.78i	0.707380	−	1.22522i
$280$	−294.384	+	509.889i	−0.0628316	+	0.108827i
$281$	6132.87			1.30198			0.650990	−	0.759086i	$-0.274354\pi$
$281$	6132.87			1.30198			0.650990	+	0.759086i	$0.274354\pi$
$282$	−5122.63	+	8872.66i	−1.08173	+	1.87361i
$283$	−1688.58	−	2924.70i	−0.354683	−	0.614330i	0.632380	−	0.774658i	$-0.282078\pi$
$283$	−1688.58	−	2924.70i	−0.354683	−	0.614330i	−0.987064	+	0.160328i	$0.948745\pi$
$284$	1792.85	+	3105.31i	0.374599	+	0.648824i
$285$	−1467.76			−0.305061
$286$		0			0
$287$	2966.29			0.610086
$288$	4515.49	+	7821.07i	0.923882	+	1.60021i
$289$	2454.47	+	4251.27i	0.499587	+	0.865310i
$290$	900.982	−	1560.55i	0.182440	−	0.315995i
$291$	10199.0			2.05455
$292$	2995.30	−	5188.01i	0.600297	−	1.03974i
$293$	−2352.38	+	4074.45i	−0.469037	+	0.812395i	−0.999374	−	0.0353917i	$-0.988732\pi$
$293$	−2352.38	+	4074.45i	−0.469037	+	0.812395i	0.530337	+	0.847787i	$0.322065\pi$
$294$	−9966.34			−1.97704
$295$	727.050	−	1259.29i	0.143493	−	0.248537i
$296$	−2036.37	−	3527.10i	−0.399871	−	0.692596i
$297$	3667.43	+	6352.18i	0.716518	+	1.24105i
$298$	8258.86			1.60545
$299$		0			0
$300$	−13027.0			−2.50704
$301$	2043.64	+	3539.69i	0.391341	+	0.677822i
$302$	−965.312	−	1671.97i	−0.183932	−	0.318580i
$303$	−4215.09	+	7300.74i	−0.799176	+	1.38421i
$304$	−145.863			−0.0275192
$305$	−226.461	+	392.242i	−0.0425151	+	0.0736384i
$306$	−222.559	+	385.484i	−0.0415780	+	0.0720152i
$307$	−5130.49			−0.953787			−0.476894	−	0.878961i	$-0.658237\pi$
$307$	−5130.49			−0.953787			−0.476894	+	0.878961i	$0.658237\pi$
$308$	−2413.93	+	4181.05i	−0.446579	+	0.773498i
$309$	8249.11	+	14287.9i	1.51869	+	2.63045i
$310$	−871.922	−	1510.21i	−0.159748	−	0.276692i
$311$	7948.94			1.44933			0.724667	−	0.689099i	$-0.241994\pi$
$311$	7948.94			1.44933			0.724667	+	0.689099i	$0.241994\pi$
$312$		0			0
$313$	−8521.87			−1.53893			−0.769465	−	0.638689i	$-0.779477\pi$
$313$	−8521.87			−1.53893			−0.769465	+	0.638689i	$0.779477\pi$
$314$	−3015.57	−	5223.12i	−0.541969	−	0.938718i
$315$	−650.000	−	1125.83i	−0.116265	−	0.201376i
$316$	−240.388	+	416.365i	−0.0427940	+	0.0741213i
$317$	6662.46			1.18044			0.590222	−	0.807241i	$-0.299040\pi$
$317$	6662.46			1.18044			0.590222	+	0.807241i	$0.299040\pi$
$318$	−12135.3	+	21019.0i	−2.13999	+	3.70657i
$319$	2773.29	−	4803.49i	0.486754	−	0.843083i
$320$	2334.23			0.407773
$321$	8278.62	−	14339.0i	1.43946	−	2.49322i
$322$	97.4536	+	168.795i	0.0168661	+	0.0292129i
$323$	−60.6483	−	105.046i	−0.0104476	−	0.0180957i
$324$	3949.74			0.677253
$325$		0			0
$326$	16450.8			2.79486
$327$	−3890.74	−	6738.96i	−0.657977	−	1.13965i
$328$	3401.82	+	5892.12i	0.572665	+	0.991884i
$329$	1236.39	−	2141.49i	0.207187	−	0.358858i
$330$	4385.09			0.731489
$331$	−1955.89	+	3387.69i	−0.324789	+	0.562551i	−0.981470	−	0.191618i	$-0.938627\pi$
$331$	−1955.89	+	3387.69i	−0.324789	+	0.562551i	0.656681	+	0.754169i	$0.271960\pi$
$332$	−487.689	+	844.703i	−0.0806188	+	0.139636i
$333$	8992.61			1.47986
$334$	−7789.84	+	13492.4i	−1.27617	+	2.21039i
$335$	70.0519	+	121.333i	0.0114249	+	0.0197885i
$336$	−100.614	−	174.268i	−0.0163361	−	0.0282949i
$337$	−627.211			−0.101384			−0.0506919	−	0.998714i	$-0.516143\pi$
$337$	−627.211			−0.101384			−0.0506919	+	0.998714i	$0.516143\pi$
$338$		0			0
$339$	−2908.34			−0.465957
$340$	36.2337	+	62.7586i	0.00577955	+	0.0100105i
$341$	−2683.84	−	4648.56i	−0.426212	−	0.738221i
$342$	−6647.79	+	11514.3i	−1.05109	+	1.82053i
$343$	5685.08			0.894943
$344$	−4687.40	+	8118.82i	−0.734674	+	1.27249i
$345$	54.4841	−	94.3693i	0.00850240	−	0.0147266i
$346$	10684.2			1.66007
$347$	1911.51	−	3310.83i	0.295721	−	0.512204i	−0.679431	−	0.733739i	$-0.737773\pi$
$347$	1911.51	−	3310.83i	0.295721	−	0.512204i	0.975152	+	0.221535i	$0.0711068\pi$
$348$	−7824.72	−	13552.8i	−1.20531	−	2.08767i
$349$	1705.33	+	2953.72i	0.261560	+	0.453035i	0.966657	−	0.256076i	$-0.0824298\pi$
$349$	1705.33	+	2953.72i	0.261560	+	0.453035i	−0.705097	+	0.709111i	$0.749096\pi$
$350$	5108.10			0.780112
$351$		0			0
$352$	7352.48			1.11332
$353$	−2793.82	−	4839.03i	−0.421246	−	0.729620i	0.574815	−	0.818283i	$-0.305074\pi$
$353$	−2793.82	−	4839.03i	−0.421246	−	0.729620i	−0.996062	+	0.0886632i	$0.971741\pi$
$354$	−10258.2	−	17767.6i	−1.54015	−	2.66763i
$355$	−393.035	+	680.757i	−0.0587609	+	0.101777i
$356$	−2597.49			−0.386704
$357$	83.6680	−	144.917i	0.0124039	−	0.0214841i
$358$	1521.03	−	2634.50i	0.224550	−	0.388932i
$359$	−2230.14			−0.327861			−0.163931	−	0.986472i	$-0.552417\pi$
$359$	−2230.14			−0.327861			−0.163931	+	0.986472i	$0.552417\pi$
$360$	1490.87	−	2582.27i	0.218266	−	0.378049i
$361$	1617.95	+	2802.37i	0.235887	+	0.408568i
$362$	1598.91	+	2769.39i	0.232146	+	0.402088i
$363$	1938.38			0.280272
$364$		0			0
$365$	1313.28			0.188330
$366$	3195.20	+	5534.25i	0.456327	+	0.790382i
$367$	4349.57	+	7533.68i	0.618653	+	1.07154i	0.989732	+	0.142938i	$0.0456548\pi$
$367$	4349.57	+	7533.68i	0.618653	+	1.07154i	−0.371078	+	0.928602i	$0.621012\pi$
$368$	5.41455	−	9.37828i	0.000766992	−	0.00132847i
$369$	−15022.4			−2.11934
$370$	1189.25	−	2059.85i	0.167098	−	0.289423i
$371$	2928.97	−	5073.13i	0.409878	−	0.709929i
$372$	−15144.7			−2.11080
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	0.181340	+	0.983420i	$0.441956\pi$
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	−0.942337	+	0.334665i	$0.891377\pi$
$374$	181.194	+	313.837i	0.0250517	+	0.0433908i
$375$	−2951.94	−	5112.91i	−0.406500	−	0.704079i
$376$	5671.70			0.777914
$377$		0			0
$378$	−8114.84			−1.10419
$379$	6955.06	+	12046.5i	0.942631	+	1.63269i	0.760426	+	0.649425i	$0.224990\pi$
$379$	6955.06	+	12046.5i	0.942631	+	1.63269i	0.182206	+	0.983260i	$0.441676\pi$
$380$	1082.29	+	1874.58i	0.146106	+	0.253064i
$381$	−2696.12	+	4669.82i	−0.362537	+	0.627932i
$382$	5934.03			0.794794
$383$	−247.377	+	428.469i	−0.0330035	+	0.0571638i	−0.882055	−	0.471146i	$-0.843841\pi$
$383$	−247.377	+	428.469i	−0.0330035	+	0.0571638i	0.849052	+	0.528310i	$0.177174\pi$
$384$	9988.35	−	17300.3i	1.32738	−	2.29910i
$385$	−1058.38			−0.140104
$386$	−1184.48	+	2051.59i	−0.156188	+	0.270526i
$387$	−10349.8	−	17926.3i	−1.35945	−	2.35464i
$388$	−7520.52	−	13025.9i	−0.984011	−	1.70436i
$389$	−4140.47			−0.539666			−0.269833	−	0.962907i	$-0.586968\pi$
$389$	−4140.47			−0.539666			−0.269833	+	0.962907i	$0.586968\pi$
$390$		0			0
$391$	9.00524			0.00116474
$392$	2758.65	+	4778.12i	0.355441	+	0.615641i
$393$	5782.70	+	10015.9i	0.742236	+	1.28559i
$394$	7118.41	−	12329.5i	0.910204	−	1.57652i
$395$	−105.398			−0.0134256
$396$	12225.0	−	21174.4i	1.55134	−	2.68700i
$397$	−940.896	+	1629.68i	−0.118948	+	0.206023i	−0.919351	−	0.393439i	$-0.871285\pi$
$397$	−940.896	+	1629.68i	−0.118948	+	0.206023i	0.800403	+	0.599462i	$0.204619\pi$
$398$	5642.90			0.710686
$399$	2499.15	−	4328.65i	0.313568	−	0.543116i
$400$	−141.904	−	245.784i	−0.0177380	−	0.0307231i
$401$	210.883	+	365.259i	0.0262618	+	0.0454867i	0.878858	−	0.477084i	$-0.158306\pi$
$401$	210.883	+	365.259i	0.0262618	+	0.0454867i	−0.852596	+	0.522571i	$0.824973\pi$
$402$	1976.76			0.245254
$403$		0			0
$404$	12432.5			1.53103
$405$	432.938	+	749.871i	0.0531182	+	0.0920034i
$406$	3068.20	+	5314.28i	0.375055	+	0.649615i
$407$	3660.62	−	6340.37i	0.445823	−	0.772188i
$408$	383.811			0.0465722
$409$	1275.11	−	2208.55i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$409$	1275.11	−	2208.55i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$410$	−1986.68	+	3441.04i	−0.239306	+	0.414489i
$411$	−5401.99			−0.648322
$412$	12165.4	−	21071.2i	1.45473	−	2.51966i
$413$	2475.89	+	4288.37i	0.294990	+	0.510937i
$414$	−493.542	−	854.839i	−0.0585900	−	0.101481i
$415$	−213.826			−0.0252923
$416$		0			0
$417$	2870.98			0.337152
$418$	5412.23	+	9374.25i	0.633303	+	1.09691i
$419$	−6192.41	−	10725.6i	−0.722002	−	1.25054i	−0.960196	−	0.279327i	$-0.909889\pi$
$419$	−6192.41	−	10725.6i	−0.722002	−	1.25054i	0.238194	−	0.971218i	$-0.423445\pi$
$420$	−1493.09	+	2586.10i	−0.173465	+	0.300450i
$421$	−10463.0			−1.21124			−0.605622	−	0.795752i	$-0.707076\pi$
$421$	−10463.0			−1.21124			−0.605622	+	0.795752i	$0.707076\pi$
$422$	5774.17	−	10001.2i	0.666071	−	1.15367i
$423$	−6261.55	+	10845.3i	−0.719733	+	1.24661i
$424$	13436.1			1.53895
$425$	118.004	−	204.389i	0.0134683	−	0.0233278i
$426$	5545.44	+	9604.99i	0.630698	+	1.09240i
$427$	−771.190	−	1335.74i	−0.0874016	−	0.151384i
$428$	−24417.9			−2.75767
$429$		0			0
$430$	−5474.94			−0.614012
$431$	−1981.19	−	3431.53i	−0.221417	−	0.383506i	0.733821	−	0.679342i	$-0.237735\pi$
$431$	−1981.19	−	3431.53i	−0.221417	−	0.383506i	−0.955238	+	0.295837i	$0.904402\pi$
$432$	225.432	+	390.459i	0.0251067	+	0.0434860i
$433$	4197.07	−	7269.54i	0.465816	−	0.806817i	−0.533422	−	0.845849i	$-0.679094\pi$
$433$	4197.07	−	7269.54i	0.465816	−	0.806817i	0.999238	+	0.0390321i	$0.0124275\pi$
$434$	5938.48			0.656812
$435$	1715.36	−	2971.10i	0.189070	−	0.327479i
$436$	−5737.90	+	9938.34i	−0.630265	+	1.09165i
$437$	268.984			0.0294446
$438$	9264.72	−	16047.0i	1.01070	−	1.75058i
$439$	−5087.26	−	8811.39i	−0.553079	−	0.957960i	−0.998050	−	0.0624156i	$-0.980120\pi$
$439$	−5087.26	−	8811.39i	−0.553079	−	0.957960i	0.444972	−	0.895545i	$-0.353214\pi$
$440$	−1213.78	−	2102.33i	−0.131510	−	0.227783i
$441$	−12182.2			−1.31543
$442$		0			0
$443$	−5880.74			−0.630705			−0.315353	−	0.948975i	$-0.602123\pi$
$443$	−5880.74			−0.630705			−0.315353	+	0.948975i	$0.602123\pi$
$444$	−10328.3	−	17889.1i	−1.10396	−	1.91211i
$445$	−284.716	−	493.142i	−0.0303299	−	0.0525330i
$446$	−2726.74	+	4722.85i	−0.289495	+	0.501420i
$447$	15723.9			1.66379
$448$	−3974.49	+	6884.01i	−0.419145	+	0.725980i
$449$	5332.43	−	9236.05i	0.560475	−	0.970771i	−0.436980	−	0.899471i	$-0.643952\pi$
$449$	5332.43	−	9236.05i	0.560475	−	0.970771i	0.997455	−	0.0712996i	$-0.0227146\pi$
$450$	−25869.3			−2.70998
$451$	−6115.16	+	10591.8i	−0.638474	+	1.10587i
$452$	2144.55	+	3714.47i	0.223166	+	0.386535i
$453$	−1837.84	−	3183.23i	−0.190617	−	0.330158i
$454$	3964.87			0.409869
$455$		0			0
$456$	11464.3			1.17734
$457$	−7414.43	−	12842.2i	−0.758933	−	1.31451i	−0.943395	−	0.331671i	$-0.892388\pi$
$457$	−7414.43	−	12842.2i	−0.758933	−	1.31451i	0.184462	−	0.982840i	$-0.440946\pi$
$458$	10684.6	+	18506.3i	1.09009	+	1.88808i
$459$	−187.464	+	324.697i	−0.0190633	+	0.0330186i
$460$	−160.702			−0.0162886
$461$	−4855.85	+	8410.58i	−0.490585	+	0.849717i	−0.999941	−	0.0108381i	$-0.996550\pi$
$461$	−4855.85	+	8410.58i	−0.490585	+	0.849717i	0.509357	+	0.860555i	$0.329883\pi$
$462$	−7466.49	+	12932.3i	−0.751889	+	1.30231i
$463$	−11353.5			−1.13962			−0.569809	−	0.821777i	$-0.692983\pi$
$463$	−11353.5			−1.13962			−0.569809	+	0.821777i	$0.692983\pi$
$464$	170.470	−	295.263i	0.0170558	−	0.0295415i
$465$	−1660.04	−	2875.27i	−0.165554	−	0.286747i
$466$	11105.1	+	19234.6i	1.10393	+	1.91207i
$467$	6451.31			0.639252			0.319626	−	0.947544i	$-0.396443\pi$
$467$	6451.31			0.639252			0.319626	+	0.947544i	$0.396443\pi$
$468$		0			0
$469$	−477.109			−0.0469741
$470$	1656.16	+	2868.55i	0.162538	+	0.281524i
$471$	−5741.29	−	9944.20i	−0.561666	−	0.972833i
$472$	−5678.84	+	9836.04i	−0.553792	+	0.959196i
$473$	−16852.3			−1.63820
$474$	−743.542	+	1287.85i	−0.0720506	+	0.124795i
$475$	3524.75	−	6105.05i	0.340477	−	0.589724i
$476$	−246.780			−0.0237629
$477$	−14833.4	+	25692.2i	−1.42385	+	2.46618i
$478$	10964.9	+	18991.8i	1.04921	+	1.81729i
$479$	−4783.23	−	8284.79i	−0.456266	−	0.790275i	0.542494	−	0.840059i	$-0.317480\pi$
$479$	−4783.23	−	8284.79i	−0.456266	−	0.790275i	−0.998760	+	0.0497842i	$0.984147\pi$
$480$	4547.73			0.432447
$481$		0			0
$482$	−26803.5			−2.53292
$483$	185.540	+	321.365i	0.0174790	+	0.0302746i
$484$	−1429.32	−	2475.66i	−0.134234	−	0.232500i
$485$	1648.67	−	2855.59i	0.154356	−	0.267352i
$486$	−10697.9			−0.998489
$487$	2458.56	−	4258.35i	0.228764	−	0.396230i	−0.728678	−	0.684856i	$-0.759865\pi$
$487$	2458.56	−	4258.35i	0.228764	−	0.396230i	0.957442	+	0.288626i	$0.0931984\pi$
$488$	1768.84	−	3063.72i	0.164081	−	0.284197i
$489$	31320.3			2.89643
$490$	−1611.07	+	2790.45i	−0.148532	+	0.257265i
$491$	−1475.41	−	2555.49i	−0.135610	−	0.234883i	0.790220	−	0.612823i	$-0.209966\pi$
$491$	−1475.41	−	2555.49i	−0.135610	−	0.234883i	−0.925830	+	0.377940i	$0.876633\pi$
$492$	17253.7	+	29884.2i	1.58101	+	2.73838i
$493$	283.519			0.0259007
$494$		0			0
$495$	5360.04			0.486699
$496$	−164.972	−	285.740i	−0.0149344	−	0.0258671i
$497$	−1338.44	−	2318.25i	−0.120799	−	0.209231i
$498$	−1508.47	+	2612.74i	−0.135735	+	0.235100i
$499$	−13430.1			−1.20484			−0.602418	−	0.798180i	$-0.705796\pi$
$499$	−13430.1			−1.20484			−0.602418	+	0.798180i	$0.705796\pi$
$500$	−4353.40	+	7540.30i	−0.389380	+	0.674425i
$501$	−14830.9	+	25687.9i	−1.32255	+	2.29072i
$502$	26485.6			2.35480
$503$	−660.143	+	1143.40i	−0.0585175	+	0.101355i	−0.893800	−	0.448466i	$-0.851971\pi$
$503$	−660.143	+	1143.40i	−0.0585175	+	0.101355i	0.835283	+	0.549821i	$0.185304\pi$
$504$	5077.02	+	8793.65i	0.448707	+	0.777183i
$505$	1362.74	+	2360.34i	0.120082	+	0.207988i
$506$	−803.623			−0.0706036
$507$		0			0
$508$	7952.25			0.694536
$509$	10458.2	+	18114.2i	0.910713	+	1.57740i	0.813060	+	0.582180i	$0.197800\pi$
$509$	10458.2	+	18114.2i	0.910713	+	1.57740i	0.0976524	+	0.995221i	$0.468867\pi$
$510$	112.074	+	194.118i	0.00973082	+	0.0168543i
$511$	−2236.12	+	3873.08i	−0.193582	+	0.335293i
$512$	877.105			0.0757089
$513$	−5599.50	+	9698.62i	−0.481918	+	0.834707i
$514$	2727.49	−	4724.15i	0.234055	−	0.405396i
$515$	5333.90			0.456388
$516$	−23774.0	+	41177.8i	−2.02828	+	3.51308i
$517$	5097.77	+	8829.60i	0.433655	+	0.751113i
$518$	4049.88	+	7014.60i	0.343517	+	0.594988i
$519$	20341.4			1.72040
$520$		0			0
$521$	−10104.2			−0.849661			−0.424831	−	0.905273i	$-0.639666\pi$
$521$	−10104.2			−0.849661			−0.424831	+	0.905273i	$0.639666\pi$
$522$	−15538.5	−	26913.5i	−1.30288	−	2.25665i
$523$	−3565.61	−	6175.82i	−0.298113	−	0.516347i	0.677591	−	0.735439i	$-0.263024\pi$
$523$	−3565.61	−	6175.82i	−0.298113	−	0.516347i	−0.975704	+	0.219092i	$0.929691\pi$
$524$	8528.08	−	14771.1i	0.710975	−	1.23144i
$525$	9725.21			0.808463
$526$	−534.122	+	925.127i	−0.0442753	+	0.0766871i
$527$	137.187	−	237.615i	0.0113396	−	0.0196407i
$528$	829.682			0.0683849
$529$	6073.52	−	10519.6i	0.499179	−	0.864604i
$530$	3923.38	+	6795.49i	0.321548	+	0.556938i
$531$	−12538.9	−	21717.9i	−1.02475	−	1.77491i
$532$	−7371.27			−0.600724
$533$		0			0
$534$	−8034.26			−0.651080
$535$	−2676.49	−	4635.82i	−0.216289	−	0.374624i
$536$	−547.161	−	947.710i	−0.0440928	−	0.0763710i
$537$	2895.86	−	5015.78i	0.232711	−	0.403067i
$538$	−12171.5			−0.975369
$539$	−4958.99	+	8589.22i	−0.396287	+	0.686390i
$540$	3345.36	−	5794.33i	0.266595	−	0.461756i
$541$	−16831.7			−1.33762			−0.668809	−	0.743435i	$-0.733195\pi$
$541$	−16831.7			−1.33762			−0.668809	+	0.743435i	$0.733195\pi$
$542$	13003.3	−	22522.5i	1.03052	−	1.78491i
$543$	3044.13	+	5272.59i	0.240582	+	0.416701i
$544$	187.914	+	325.477i	0.0148102	+	0.0256520i
$545$	−2515.77			−0.197731
$546$		0			0
$547$	−9560.55			−0.747312			−0.373656	−	0.927567i	$-0.621896\pi$
$547$	−9560.55			−0.747312			−0.373656	+	0.927567i	$0.621896\pi$
$548$	3983.31	+	6899.30i	0.310508	+	0.537816i
$549$	3905.59	+	6764.69i	0.303619	+	0.525883i
$550$	−10530.6	+	18239.6i	−0.816412	+	1.41407i
$551$	8468.64			0.654766
$552$	−425.564	+	737.099i	−0.0328138	+	0.0568352i
$553$	179.460	−	310.834i	0.0138000	−	0.0239024i
$554$	−32626.5			−2.50210
$555$	2264.20	−	3921.71i	0.173171	−	0.299941i
$556$	−2117.00	−	3666.75i	−0.161476	−	0.279685i
$557$	−11414.0	−	19769.5i	−0.868267	−	1.50388i	−0.863766	−	0.503893i	$-0.831901\pi$
$557$	−11414.0	−	19769.5i	−0.868267	−	1.50388i	−0.00450060	−	0.999990i	$-0.501433\pi$
$558$	−30074.7			−2.28166
$559$		0			0
$560$	−65.0571			−0.00490922
$561$	344.972	+	597.509i	0.0259621	+	0.0449677i
$562$	−13987.7	−	24227.4i	−1.04989	−	1.81846i
$563$	−10814.9	+	18731.9i	−0.809578	+	1.40223i	0.103579	+	0.994621i	$0.466971\pi$
$563$	−10814.9	+	18731.9i	−0.809578	+	1.40223i	−0.913157	+	0.407609i	$0.866363\pi$
$564$	28766.3			2.14766
$565$	−470.136	+	814.299i	−0.0350066	+	0.0606333i
$566$	−7702.53	+	13341.2i	−0.572016	+	0.990761i
$567$	−2948.65			−0.218398
$568$	3069.92	−	5317.25i	0.226780	−	0.392794i
$569$	5294.93	+	9171.09i	0.390114	+	0.675698i	0.992464	−	0.122534i	$-0.0391022\pi$
$569$	5294.93	+	9171.09i	0.390114	+	0.675698i	−0.602350	+	0.798232i	$0.705769\pi$
$570$	3347.62	+	5798.25i	0.245994	+	0.426074i
$571$	−1757.27			−0.128791			−0.0643954	−	0.997924i	$-0.520512\pi$
$571$	−1757.27			−0.128791			−0.0643954	+	0.997924i	$0.520512\pi$
$572$		0			0
$573$	11297.7			0.823679
$574$	−6765.45	−	11718.1i	−0.491959	−	0.852097i
$575$	261.683	+	453.247i	0.0189790	+	0.0328726i
$576$	20128.3	−	34863.2i	1.45604	−	2.52193i
$577$	13580.6			0.979840			0.489920	−	0.871767i	$-0.337026\pi$
$577$	13580.6			0.979840			0.489920	+	0.871767i	$0.337026\pi$
$578$	11196.2	−	19392.4i	0.805710	−	1.39553i
$579$	−2255.12	+	3905.98i	−0.161864	+	0.280357i
$580$	−5059.49			−0.362214
$581$	364.081	−	630.607i	0.0259977	−	0.0450293i
$582$	−23261.6	−	40290.3i	−1.65674	−	2.86956i
$583$	12076.5	+	20917.0i	0.857900	+	1.48593i
$584$	−10257.8			−0.726831
$585$		0			0
$586$	21461.0			1.51288
$587$	−478.663	−	829.068i	−0.0336568	−	0.0582952i	0.848706	−	0.528864i	$-0.177382\pi$
$587$	−478.663	−	829.068i	−0.0336568	−	0.0582952i	−0.882363	+	0.470569i	$0.844049\pi$
$588$	13991.6	+	24234.1i	0.981297	+	1.69966i
$589$	4097.75	−	7097.50i	0.286663	−	0.496515i
$590$	−6632.95			−0.462838
$591$	13552.6	−	23473.8i	0.943283	−	1.63381i
$592$	225.013	−	389.734i	0.0156216	−	0.0270573i
$593$	−6729.49			−0.466015			−0.233007	−	0.972475i	$-0.574857\pi$
$593$	−6729.49			−0.466015			−0.233007	+	0.972475i	$0.574857\pi$
$594$	16729.2	−	28975.8i	1.15557	−	2.00150i
$595$	−27.0500	−	46.8520i	−0.00186377	−	0.00322814i
$596$	−11594.5	−	20082.2i	−0.796859	−	1.38020i
$597$	10743.4			0.736514
$598$		0			0
$599$	2281.52			0.155626			0.0778132	−	0.996968i	$-0.475206\pi$
$599$	2281.52			0.155626			0.0778132	+	0.996968i	$0.475206\pi$
$600$	11153.1	+	19317.8i	0.758874	+	1.31441i
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	0.736725	−	0.676192i	$-0.236371\pi$
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	−0.953962	+	0.299926i	$0.903038\pi$
$602$	9322.18	−	16146.5i	0.631136	−	1.09316i
$603$	2416.26			0.163180
$604$	−2710.37	+	4694.50i	−0.182588	+	0.316252i
$605$	313.341	−	542.722i	0.0210564	−	0.0364707i
$606$	38454.7			2.57775
$607$	−1389.62	+	2406.89i	−0.0929207	+	0.160943i	−0.908739	−	0.417365i	$-0.862954\pi$
$607$	−1389.62	+	2406.89i	−0.0929207	+	0.160943i	0.815818	+	0.578308i	$0.196287\pi$
$608$	5612.95	+	9721.92i	0.374400	+	0.648480i
$609$	5841.50	+	10117.8i	0.388685	+	0.673223i
$610$	2066.03			0.137133
$611$		0			0
$612$	1249.79			0.0825485
$613$	11310.4	+	19590.2i	0.745226	+	1.29077i	0.950089	+	0.311979i	$0.100992\pi$
$613$	11310.4	+	19590.2i	0.745226	+	1.29077i	−0.204863	+	0.978791i	$0.565675\pi$
$614$	11701.5	+	20267.6i	0.769111	+	1.33214i
$615$	−3782.41	+	6551.33i	−0.248002	+	0.429553i
$616$	8266.80			0.540712
$617$	10987.0	−	19030.1i	0.716889	−	1.24169i	−0.245337	−	0.969438i	$-0.578899\pi$
$617$	10987.0	−	19030.1i	0.716889	−	1.24169i	0.962226	−	0.272250i	$-0.0877679\pi$
$618$	37628.7	−	65174.9i	2.44927	−	4.24226i
$619$	−7145.19			−0.463957			−0.231979	−	0.972721i	$-0.574520\pi$
$619$	−7145.19			−0.463957			−0.231979	+	0.972721i	$0.574520\pi$
$620$	−2448.15	+	4240.32i	−0.158581	+	0.274670i
$621$	−415.715	−	720.040i	−0.0268632	−	0.0465285i
$622$	−18129.8	−	31401.7i	−1.16871	−	2.02426i
$623$	1939.14			0.124703
$624$		0			0
$625$	12730.8			0.814773
$626$	19436.5	+	33665.0i	1.24096	+	2.14940i
$627$	10304.2	+	17847.5i	0.656319	+	1.13678i
$628$	−8467.00	+	14665.3i	−0.538010	+	0.931861i
$629$	374.231			0.0237227
$630$	−2965.01	+	5135.55i	−0.187506	+	0.324770i
$631$	−9441.62	+	16353.4i	−0.595666	+	1.03172i	0.397787	+	0.917478i	$0.369778\pi$
$631$	−9441.62	+	16353.4i	−0.595666	+	1.03172i	−0.993453	+	0.114245i	$0.963555\pi$
$632$	823.239			0.0518144
$633$	10993.3	−	19041.0i	0.690278	−	1.19560i
$634$	−15195.6	−	26319.5i	−0.951882	−	1.64871i
$635$	871.661	+	1509.76i	0.0544737	+	0.0943512i
$636$	68146.4			4.24871
$637$		0			0
$638$	−25301.1			−1.57003
$639$	6778.37	+	11740.5i	0.419637	+	0.726833i
$640$	−3229.25	−	5593.22i	−0.199449	−	0.345456i
$641$	1815.54	−	3144.61i	0.111871	−	0.193767i	−0.804653	−	0.593745i	$-0.797649\pi$
$641$	1815.54	−	3144.61i	0.111871	−	0.193767i	0.916525	+	0.399978i	$0.130982\pi$
$642$	−75526.7			−4.64299
$643$	−5385.98	+	9328.78i	−0.330330	+	0.572148i	−0.982576	−	0.185859i	$-0.940493\pi$
$643$	−5385.98	+	9328.78i	−0.330330	+	0.572148i	0.652247	+	0.758007i	$0.273827\pi$
$644$	273.627	−	473.935i	0.0167429	−	0.0289995i
$645$	−10423.6			−0.636327
$646$	−276.651	+	479.173i	−0.0168493	+	0.0291839i
$647$	−7574.14	−	13118.8i	−0.460232	−	0.797146i	0.538740	−	0.842472i	$-0.318901\pi$
$647$	−7574.14	−	13118.8i	−0.460232	−	0.797146i	−0.998972	+	0.0453265i	$0.985567\pi$
$648$	−3381.59	−	5857.09i	−0.205002	−	0.355074i
$649$	−20416.7			−1.23487
$650$		0			0
$651$	11306.2			0.680682
$652$	−23094.9	−	40001.6i	−1.38722	−	2.40273i
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	0.734458	−	0.678654i	$-0.237436\pi$
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	−0.954961	+	0.296733i	$0.904103\pi$
$654$	−17747.8	+	30740.1i	−1.06115	+	1.83797i
$655$	3739.11			0.223052
$656$	−375.890	+	651.061i	−0.0223720	+	0.0387495i
$657$	11324.6	−	19614.7i	0.672471	−	1.16475i
$658$	−11279.7			−0.668282
$659$	−14166.6	+	24537.3i	−0.837411	+	1.45044i	0.0546414	+	0.998506i	$0.482598\pi$
$659$	−14166.6	+	24537.3i	−0.837411	+	1.45044i	−0.892052	+	0.451932i	$0.850735\pi$
$660$	−6156.16	−	10662.8i	−0.363073	−	0.628860i
$661$	554.842	+	961.014i	0.0326488	+	0.0565493i	0.881888	−	0.471459i	$-0.156272\pi$
$661$	554.842	+	961.014i	0.0326488	+	0.0565493i	−0.849239	+	0.528008i	$0.822939\pi$
$662$	17843.8			1.04761
$663$		0			0
$664$	1670.15			0.0976121
$665$	−807.978	−	1399.46i	−0.0471159	−	0.0816071i
$666$	−20510.1	−	35524.6i	−1.19332	−	2.06689i
$667$	−314.362	+	544.491i	−0.0182491	+	0.0316083i
$668$	43744.1			2.53369
$669$	−5191.39	+	8991.75i	−0.300016	+	0.519643i
$670$	319.545	−	553.469i	0.0184255	−	0.0319140i
$671$	6359.39			0.365874
$672$	−7743.41	+	13412.0i	−0.444507	+	0.769908i
$673$	−10489.5	−	18168.4i	−0.600806	−	1.04063i	−0.992699	−	0.120616i	$-0.961513\pi$
$673$	−10489.5	−	18168.4i	−0.600806	−	1.04063i	0.391893	−	0.920011i	$-0.371820\pi$
$674$	1430.53	+	2477.75i	0.0817535	+	0.141601i
$675$	−21790.0			−1.24251
$676$		0			0
$677$	30941.9			1.75656			0.878282	−	0.478142i	$-0.158690\pi$
$677$	30941.9			1.75656			0.878282	+	0.478142i	$0.158690\pi$
$678$	6633.27	+	11489.2i	0.375736	+	0.650795i
$679$	5614.39	+	9724.41i	0.317320	+	0.549615i
$680$	62.0433	−	107.462i	0.00349890	−	0.00606027i
$681$	7548.64			0.424764
$682$	−12242.5	+	21204.6i	−0.687375	+	1.19057i
$683$	2713.11	−	4699.24i	0.151997	−	0.263267i	−0.779964	−	0.625824i	$-0.784763\pi$
$683$	2713.11	−	4699.24i	0.151997	−	0.263267i	0.931962	+	0.362557i	$0.118096\pi$
$684$	37330.9			2.08682
$685$	−873.236	+	1512.49i	−0.0487075	+	0.0843638i
$686$	−12966.4	−	22458.4i	−0.721660	−	1.24995i
$687$	20342.2	+	35233.8i	1.12970	+	1.95670i
$688$	−1035.89			−0.0574023
$689$		0			0
$690$	−497.065			−0.0274245
$691$	−16896.3	−	29265.3i	−0.930199	−	1.61115i	−0.782979	−	0.622048i	$-0.786301\pi$
$691$	−16896.3	−	29265.3i	−0.930199	−	1.61115i	−0.147219	−	0.989104i	$-0.547032\pi$
$692$	−14999.3	−	25979.6i	−0.823973	−	1.42716i
$693$	−9126.53	+	15807.6i	−0.500272	+	0.866496i
$694$	−17438.9			−0.953849
$695$	464.096	−	803.838i	0.0253297	−	0.0438724i
$696$	−13398.4	+	23206.6i	−0.729689	+	1.26386i
$697$	−625.164			−0.0339738
$698$	7778.97	−	13473.6i	0.421831	−	0.730633i
$699$	21142.8	+	36620.3i	1.14405	+	1.98156i
$700$	−7171.16	−	12420.8i	−0.387206	−	0.670661i
$701$	6905.96			0.372089			0.186045	−	0.982541i	$-0.440433\pi$
$701$	6905.96			0.372089			0.186045	+	0.982541i	$0.440433\pi$
$702$		0			0
$703$	11178.2			0.599707
$704$	−16387.2	−	28383.5i	−0.877297	−	1.51952i
$705$	3153.12	+	5461.37i	0.168445	+	0.291755i
$706$	−12744.1	+	22073.5i	−0.679366	+	1.17670i
$707$	−9281.37			−0.493723
$708$	−28802.5	+	49887.3i	−1.52890	+	2.64814i
$709$	−1003.56	+	1738.22i	−0.0531589	+	0.0920739i	−0.891380	−	0.453256i	$-0.850262\pi$
$709$	−1003.56	+	1738.22i	−0.0531589	+	0.0920739i	0.838221	+	0.545330i	$0.183596\pi$
$710$	3585.70			0.189534
$711$	−908.854	+	1574.18i	−0.0479391	+	0.0830329i
$712$	2223.85	+	3851.83i	0.117054	+	0.202744i
$713$	304.222	+	526.929i	0.0159793	+	0.0276769i
$714$	−763.312			−0.0400088
$715$		0			0
$716$	−8541.38			−0.445819
$717$	20875.9	+	36158.1i	1.08734	+	1.88333i
$718$	5086.44	+	8809.98i	0.264379	+	0.457918i
$719$	6393.72	−	11074.3i	0.331635	−	0.574409i	−0.651198	−	0.758908i	$-0.725733\pi$
$719$	6393.72	−	11074.3i	0.331635	−	0.574409i	0.982833	+	0.184499i	$0.0590664\pi$
$720$	329.474			0.0170538
$721$	−9082.03	+	15730.5i	−0.469116	+	0.812532i
$722$	7380.35	−	12783.1i	0.380427	−	0.658919i
$723$	−51030.7			−2.62497
$724$	4489.36	−	7775.80i	0.230450	−	0.399151i
$725$	8238.74	+	14269.9i	0.422040	+	0.730995i
$726$	−4421.01	−	7657.42i	−0.226004	−	0.391451i
$727$	−6090.70			−0.310717			−0.155359	−	0.987858i	$-0.549653\pi$
$727$	−6090.70			−0.310717			−0.155359	+	0.987858i	$0.549653\pi$
$728$		0			0
$729$	−28693.9			−1.45780
$730$	−2995.30	−	5188.01i	−0.151864	−	0.263037i
$731$	−430.710	−	746.011i	−0.0217926	−	0.0377459i
$732$	8971.37	−	15538.9i	0.452994	−	0.784608i
$733$	38846.5			1.95747			0.978737	−	0.205117i	$-0.0657574\pi$
$733$	38846.5			1.95747			0.978737	+	0.205117i	$0.0657574\pi$
$734$	19840.8	−	34365.3i	0.997735	−	1.72813i
$735$	−3067.28	+	5312.69i	−0.153930	+	0.266614i
$736$	−833.427			−0.0417399
$737$	983.585	−	1703.62i	0.0491599	−	0.0851474i
$738$	34262.8	+	59344.8i	1.70898	+	2.96005i
$739$	7228.77	+	12520.6i	0.359830	+	0.623245i	0.987932	−	0.154887i	$-0.0495012\pi$
$739$	7228.77	+	12520.6i	0.359830	+	0.623245i	−0.628102	+	0.778131i	$0.716168\pi$
$740$	−6678.29			−0.331755
$741$		0			0
$742$	−26721.3			−1.32206
$743$	−638.901	−	1106.61i	−0.0315464	−	0.0546400i	0.849821	−	0.527071i	$-0.176710\pi$
$743$	−638.901	−	1106.61i	−0.0315464	−	0.0546400i	−0.881368	+	0.472431i	$0.843377\pi$
$744$	12966.2	+	22458.1i	0.638931	+	1.10666i
$745$	2541.78	−	4402.49i	0.124998	−	0.216503i
$746$	50013.7			2.45460
$747$	−1843.84	+	3193.63i	−0.0903116	+	0.156424i
$748$	508.750	−	881.181i	0.0248687	−	0.0430738i
$749$	18229.0			0.889285
$750$	−13465.4	+	23322.8i	−0.655584	+	1.13551i
$751$	6503.93	+	11265.1i	0.316021	+	0.547364i	0.979654	−	0.200694i	$-0.0643197\pi$
$751$	6503.93	+	11265.1i	0.316021	+	0.547364i	−0.663633	+	0.748058i	$0.730986\pi$
$752$	313.353	+	542.743i	0.0151952	+	0.0263189i
$753$	50425.5			2.44038
$754$		0			0
$755$	−1188.35			−0.0572829
$756$	11392.3	+	19732.0i	0.548060	+	0.949268i
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	0.965551	−	0.260212i	$-0.0837926\pi$
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	−0.708126	+	0.706086i	$0.750459\pi$
$758$	31725.9	−	54950.8i	1.52023	−	2.63312i
$759$	−1530.00			−0.0731694
$760$	1853.22	−	3209.87i	0.0884518	−	0.153203i
$761$	6810.90	−	11796.8i	0.324435	−	0.561938i	−0.656963	−	0.753923i	$-0.728159\pi$
$761$	6810.90	−	11796.8i	0.324435	−	0.561938i	0.981398	+	0.191985i	$0.0614925\pi$
$762$	24597.0			1.16936
$763$	4283.59	−	7419.40i	0.203246	−	0.352032i
$764$	−8330.68	−	14429.2i	−0.394494	−	0.683284i
$765$	136.991	+	237.276i	0.00647443	+	0.0112140i
$766$	2256.84			0.106453
$767$		0			0
$768$	−33365.0			−1.56765
$769$	−4247.57	−	7357.01i	−0.199183	−	0.344994i	0.749081	−	0.662478i	$-0.230495\pi$
$769$	−4247.57	−	7357.01i	−0.199183	−	0.344994i	−0.948264	+	0.317484i	$0.897162\pi$
$770$	2413.93	+	4181.05i	0.112977	+	0.195681i
$771$	5192.82	−	8994.22i	0.242561	−	0.420128i
$772$	6651.50			0.310094
$773$	17131.3	−	29672.2i	0.797113	−	1.38064i	−0.124375	−	0.992235i	$-0.539693\pi$
$773$	17131.3	−	29672.2i	0.797113	−	1.38064i	0.921489	−	0.388405i	$-0.126974\pi$
$774$	−47211.0	+	81771.9i	−2.19246	+	3.79745i
$775$	15946.0			0.739094
$776$	−12877.5	+	22304.4i	−0.595714	+	1.03181i
$777$	7710.50	+	13355.0i	0.356001	+	0.616612i
$778$	9443.48	+	16356.6i	0.435174	+	0.753743i
$779$	−18673.5			−0.858854
$780$		0			0
$781$	11037.1			0.505681
$782$	−20.5389	−	35.5745i	−0.000939221	−	0.00162678i
$783$	−13088.3	−	22669.5i	−0.597364	−	1.03467i
$784$	−304.822	+	527.967i	−0.0138858	+	0.0240510i
$785$	−3712.33			−0.168788
$786$	26378.1	−	45688.2i	1.19704	−	2.07334i
$787$	−6321.29	+	10948.8i	−0.286315	+	0.495912i	−0.972927	−	0.231112i	$-0.925764\pi$
$787$	−6321.29	+	10948.8i	−0.286315	+	0.495912i	0.686612	+	0.727024i	$0.259097\pi$
$788$	−39973.6			−1.80711
$789$	−1016.91	+	1761.33i	−0.0458844	+	0.0794741i
$790$	240.388	+	416.365i	0.0108261	+	0.0187514i
$791$	−1601.00	−	2773.01i	−0.0719658	−	0.124648i
$792$	−41866.2			−1.87834
$793$		0			0
$794$	8583.89			0.383666
$795$	7469.65	+	12937.8i	0.333234	+	0.577178i
$796$	−7921.97	−	13721.3i	−0.352747	−	0.610976i
$797$	−9542.18	+	16527.5i	−0.424092	+	0.734549i	−0.996335	−	0.0855350i	$-0.972740\pi$
$797$	−9542.18	+	16527.5i	−0.424092	+	0.734549i	0.572243	+	0.820084i	$0.306073\pi$
$798$	−22800.0			−1.01142
$799$	−260.577	+	451.333i	−0.0115376	+	0.0199837i
$800$	−10921.2	+	18916.0i	−0.482652	+	0.835978i
$801$	−9820.53			−0.433198
$802$	961.952	−	1666.15i	0.0423538	−	0.0733589i
$803$	−9219.77	−	15969.1i	−0.405179	−	0.701790i
$804$	−2775.14	−	4806.69i	−0.121731	−	0.210844i
$805$	119.971			0.00525269
$806$		0			0
$807$	−23173.0			−1.01082
$808$	−10644.1	−	18436.1i	−0.463439	−	0.802700i
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	0.711874	−	0.702307i	$-0.247847\pi$
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	−0.964153	+	0.265347i	$0.914513\pi$
$810$	1974.87	−	3420.57i	0.0856665	−	0.148379i
$811$	−9613.36			−0.416240			−0.208120	−	0.978103i	$-0.566734\pi$
$811$	−9613.36			−0.416240			−0.208120	+	0.978103i	$0.566734\pi$
$812$	8614.79	−	14921.3i	0.372315	−	0.644869i
$813$	24756.8	−	42880.1i	1.06797	−	1.84978i
$814$	−33396.2			−1.43800
$815$	5062.95	−	8769.29i	0.217604	−	0.376901i
$816$	21.2049	+	36.7280i	0.000909707	+	0.00157566i
$817$	−12865.2	−	22283.2i	−0.550914	−	0.954211i
$818$	−11632.9			−0.497233
$819$		0			0
$820$	11156.3			0.475115
$821$	−13240.7	−	22933.6i	−0.562856	−	0.974895i	−0.997246	−	0.0741699i	$-0.976369\pi$
$821$	−13240.7	−	22933.6i	−0.562856	−	0.974895i	0.434390	−	0.900725i	$-0.356964\pi$
$822$	12320.7	+	21340.1i	0.522792	+	0.905502i
$823$	−6907.25	+	11963.7i	−0.292553	+	0.506718i	−0.974413	−	0.224766i	$-0.927838\pi$
$823$	−6907.25	+	11963.7i	−0.292553	+	0.506718i	0.681859	+	0.731483i	$0.261172\pi$
$824$	−41662.0			−1.76136
$825$	−20049.0	+	34726.0i	−0.846082	+	1.46546i
$826$	11293.9	−	19561.6i	0.475746	−	0.824015i
$827$	44401.0			1.86696			0.933479	−	0.358633i	$-0.116757\pi$
$827$	44401.0			1.86696			0.933479	+	0.358633i	$0.116757\pi$
$828$	−1385.75	+	2400.19i	−0.0581619	+	0.100739i
$829$	−12168.7	−	21076.8i	−0.509815	−	0.883025i	−0.999935	−	0.0113707i	$-0.996381\pi$
$829$	−12168.7	−	21076.8i	−0.509815	−	0.883025i	0.490120	−	0.871655i	$-0.336953\pi$
$830$	487.689	+	844.703i	0.0203951	+	0.0353254i
$831$	−62116.9			−2.59303
$832$		0			0
$833$	−506.966			−0.0210868
$834$	−6548.06	−	11341.6i	−0.271871	−	0.470895i
$835$	4794.86	+	8304.95i	0.198722	+	0.344197i
$836$	15196.3	−	26320.7i	0.628677	−	1.08890i
$837$	−25332.2			−1.04613
$838$	−28247.0	+	48925.2i	−1.16441	+	2.01682i
$839$	−12340.0	+	21373.6i	−0.507778	+	0.879497i	0.492181	+	0.870493i	$0.336200\pi$
$839$	−12340.0	+	21373.6i	−0.507778	+	0.879497i	−0.999959	+	0.00900472i	$0.997134\pi$
$840$	5113.26			0.210029
$841$	2297.22	−	3978.90i	0.0941907	−	0.163143i
$842$	23863.7	+	41333.1i	0.976719	+	1.69173i
$843$	−26631.0	−	46126.2i	−1.08804	−	1.88454i
$844$	−32425.0			−1.32241
$845$		0			0
$846$	57124.8			2.32150
$847$	1067.05	+	1848.18i	0.0432872	+	0.0749757i
$848$	742.323	+	1285.74i	0.0300607	+	0.0520666i
$849$	−14664.7	+	25400.0i	−0.592805	+	1.02677i
$850$	−1076.56			−0.0434421
$851$	−414.943	+	718.702i	−0.0167145	+	0.0289504i
$852$	15570.3	−	26968.5i	0.626091	−	1.08442i
$853$	10151.7			0.407490			0.203745	−	0.979024i	$-0.434689\pi$
$853$	10151.7			0.407490			0.203745	+	0.979024i	$0.434689\pi$
$854$	−3517.82	+	6093.05i	−0.140957	+	0.244145i
$855$	4091.90	+	7087.39i	0.163673	+	0.283489i
$856$	20905.5	+	36209.4i	0.834739	+	1.44581i
$857$	2028.92			0.0808713			0.0404357	−	0.999182i	$-0.487125\pi$
$857$	2028.92			0.0808713			0.0404357	+	0.999182i	$0.487125\pi$
$858$		0			0
$859$	6655.76			0.264367			0.132184	−	0.991225i	$-0.457801\pi$
$859$	6655.76			0.264367			0.132184	+	0.991225i	$0.457801\pi$
$860$	7686.17	+	13312.8i	0.304763	+	0.527865i
$861$	−12880.6	−	22309.9i	−0.509837	−	0.883064i
$862$	−9037.32	+	15653.1i	−0.357091	+	0.618500i
$863$	−45690.8			−1.80224			−0.901121	−	0.433568i	$-0.857254\pi$
$863$	−45690.8			−1.80224			−0.901121	+	0.433568i	$0.857254\pi$
$864$	17349.6	−	30050.4i	0.683155	−	1.18326i
$865$	3288.21	−	5695.35i	0.129251	−	0.223870i
$866$	−38290.3			−1.50249
$867$	21316.2	−	36920.8i	0.834991	−	1.44625i
$868$	−8336.93	−	14440.0i	−0.326007	−	0.564660i
$869$	739.934	+	1281.60i	0.0288844	+	0.0500292i
$870$	−15649.4			−0.609846
$871$		0			0
$872$	19650.1			0.763117
$873$	−28433.4	−	49248.1i	−1.10232	−	1.90927i
$874$	−613.493	−	1062.60i	−0.0237434	−	0.0411248i
$875$	3250.00	−	5629.17i	0.125566	−	0.217486i
$876$	−52026.3			−2.00663
$877$	15223.8	−	26368.3i	0.586168	−	1.01527i	−0.408560	−	0.912731i	$-0.633969\pi$
$877$	15223.8	−	26368.3i	0.586168	−	1.01527i	0.994729	−	0.102542i	$-0.0326976\pi$
$878$	−23205.8	+	40193.6i	−0.891979	+	1.54495i
$879$	40859.3			1.56786
$880$	134.119	−	232.300i	0.00513766	−	0.00889869i
$881$	−16271.0	−	28182.2i	−0.622230	−	1.07773i	−0.989070	−	0.147450i	$-0.952894\pi$
$881$	−16271.0	−	28182.2i	−0.622230	−	1.07773i	0.366840	−	0.930284i	$-0.380440\pi$
$882$	27784.8	+	48124.7i	1.06073	+	1.83724i
$883$	27641.9			1.05348			0.526741	−	0.850026i	$-0.323414\pi$
$883$	27641.9			1.05348			0.526741	+	0.850026i	$0.323414\pi$
$884$		0			0
$885$	−12628.4			−0.479658
$886$	13412.7	+	23231.4i	0.508586	+	0.880896i
$887$	−20050.0	−	34727.5i	−0.758976	−	1.31458i	−0.943373	−	0.331733i	$-0.892367\pi$
$887$	−20050.0	−	34727.5i	−0.758976	−	1.31458i	0.184397	−	0.982852i	$-0.440967\pi$
$888$	−17685.2	+	30631.7i	−0.668329	+	1.15758i
$889$	−5936.70			−0.223971
$890$	−1298.75	+	2249.49i	−0.0489146	+	0.0847226i
$891$	6078.80	−	10528.8i	0.228561	−	0.395879i
$892$	15312.1			0.574761
$893$	−7783.38	+	13481.2i	−0.291670	+	0.505186i
$894$	−35862.7	−	62116.0i	−1.34164	−	2.32379i
$895$	−936.236	−	1621.61i	−0.0349664	−	0.0605636i
$896$	21993.8			0.820044
$897$		0			0
$898$	−48648.4			−1.80781
$899$	9578.06	+	16589.7i	0.355335	+	0.615458i
$900$	36317.5	+	62903.7i	1.34509	+	2.32977i
$901$	−617.299	+	1069.19i	−0.0228249	+	0.0395338i
$902$	55789.3			2.05940
$903$	17748.3	−	30741.0i	0.654072	−	1.13289i
$904$	3672.13	−	6360.32i	0.135103	−	0.234006i
$905$	1968.35			0.0722984
$906$	−8383.41	+	14520.5i	−0.307417	+	0.532462i
$907$	18412.4	+	31891.3i	0.674062	+	1.16751i	0.976742	+	0.214418i	$0.0687855\pi$
$907$	18412.4	+	31891.3i	0.674062	+	1.16751i	−0.302679	+	0.953092i	$0.597881\pi$
$908$	−5566.20	−	9640.95i	−0.203437	−	0.352363i
$909$	47004.3			1.71511
$910$		0			0
$911$	34520.5			1.25545			0.627725	−	0.778435i	$-0.283986\pi$
$911$	34520.5			1.25545			0.627725	+	0.778435i	$0.283986\pi$
$912$	633.387	+	1097.06i	0.0229973	+	0.0398325i
$913$	1501.15	+	2600.06i	0.0544148	+	0.0942491i
$914$	−33821.3	+	58580.2i	−1.22397	+	2.11998i
$915$	3933.47			0.142117
$916$	29999.9	−	51961.3i	1.08212	−	1.87429i
$917$	−6366.58	+	11027.2i	−0.229273	+	0.397112i
$918$	1710.25			0.0614888
$919$	−11761.4	+	20371.3i	−0.422168	+	0.731216i	−0.996151	−	0.0876506i	$-0.972064\pi$
$919$	−11761.4	+	20371.3i	−0.422168	+	0.731216i	0.573983	+	0.818867i	$0.305397\pi$
$920$	137.586	+	238.305i	0.00493051	+	0.00853989i
$921$	22278.3	+	38587.1i	0.797062	+	1.38055i
$922$	44300.4			1.58238
$923$		0			0
$924$	41928.3			1.49279
$925$	10874.8	+	18835.6i	0.386551	+	0.669526i
$926$	25894.8	+	44851.2i	0.918961	+	1.59169i
$927$	45994.8	−	79665.3i	1.62963	−	2.82260i
$928$	−26239.4			−0.928180
$929$	−12281.6	+	21272.3i	−0.433741	+	0.751262i	−0.997192	−	0.0748880i	$-0.976140\pi$
$929$	−12281.6	+	21272.3i	−0.433741	+	0.751262i	0.563451	+	0.826150i	$0.309473\pi$
$930$	−7572.35	+	13115.7i	−0.266997	+	0.462452i
$931$	−15143.0			−0.533073
$932$	31180.4	−	54006.1i	1.09587	−	1.89810i
$933$	−34516.9	−	59785.0i	−1.21118	−	2.09783i
$934$	−14714.0	−	25485.4i	−0.515478	−	0.892834i
$935$	223.060			0.00780197
$936$		0			0
$937$	−12115.6			−0.422411			−0.211206	−	0.977442i	$-0.567739\pi$
$937$	−12115.6			−0.422411			−0.211206	+	0.977442i	$0.567739\pi$
$938$	1088.18	+	1884.78i	0.0378788	+	0.0656080i
$939$	37004.8	+	64094.2i	1.28605	+	2.22751i
$940$	4650.09	−	8054.20i	0.161350	−	0.279467i
$941$	−14898.3			−0.516123			−0.258062	−	0.966128i	$-0.583084\pi$
$941$	−14898.3			−0.516123			−0.258062	+	0.966128i	$0.583084\pi$
$942$	−26189.2	+	45361.0i	−0.905828	+	1.56894i
$943$	693.174	−	1200.61i	0.0239373	−	0.0414606i
$944$	−1254.99			−0.0432695
$945$	−2497.46	+	4325.72i	−0.0859707	+	0.148906i
$946$	38436.3	+	66573.7i	1.32101	+	2.28805i
$947$	3717.16	+	6438.31i	0.127552	+	0.220926i	0.922727	−	0.385453i	$-0.125955\pi$
$947$	3717.16	+	6438.31i	0.127552	+	0.220926i	−0.795176	+	0.606379i	$0.792621\pi$
$948$	4175.38			0.143049
$949$		0			0
$950$	−32156.7			−1.09821
$951$	−28930.6	−	50109.2i	−0.986476	−	1.70863i
$952$	211.282	+	365.951i	0.00719295	+	0.0124586i
$953$	11764.3	−	20376.3i	0.399877	−	0.692607i	−0.593833	−	0.804588i	$-0.702386\pi$
$953$	11764.3	−	20376.3i	0.399877	−	0.692607i	0.993710	+	0.111981i	$0.0357195\pi$
$954$	135327.			4.59263
$955$	1826.28	−	3163.21i	0.0618818	−	0.107182i
$956$	30786.9	−	53324.4i	1.04155	−	1.80401i
$957$	−48170.2			−1.62709
$958$	−21818.9	+	37791.5i	−0.735844	+	1.27452i
$959$	−2973.72	−	5150.63i	−0.100132	−	0.173433i
$960$	−10136.0	−	17556.0i	−0.340768	−	0.590228i
$961$	−11252.7			−0.377723
$962$		0			0
$963$	−92318.7			−3.08923
$964$	37629.0	+	65175.3i	1.25721	+	2.17755i
$965$	729.083	+	1262.81i	0.0243213	+	0.0421256i
$966$	846.351	−	1465.92i	0.0281893	−	0.0488254i
$967$	−23558.0			−0.783427			−0.391713	−	0.920087i	$-0.628118\pi$
$967$	−23558.0			−0.783427			−0.391713	+	0.920087i	$0.628118\pi$
$968$	−2447.44	+	4239.09i	−0.0812642	+	0.140754i
$969$	−526.710	+	912.289i	−0.0174617	+	0.0302445i
$970$	−15041.0			−0.497875
$971$	131.169	−	227.191i	0.00433513	−	0.00750866i	−0.863850	−	0.503750i	$-0.831953\pi$
$971$	131.169	−	227.191i	0.00433513	−	0.00750866i	0.868185	+	0.496241i	$0.165287\pi$
$972$	15018.6	+	26012.9i	0.495597	+	0.858400i
$973$	1580.43	+	2737.39i	0.0520722	+	0.0901918i
$974$	−22429.7			−0.737878
$975$		0			0
$976$	390.903			0.0128202
$977$	16572.2	+	28703.9i	0.542673	+	0.939936i	0.998749	+	0.0499960i	$0.0159209\pi$
$977$	16572.2	+	28703.9i	0.542673	+	0.939936i	−0.456077	+	0.889940i	$0.650746\pi$
$978$	−71434.6	−	123728.i	−2.33561	−	4.04539i
$979$	−3997.64	+	6924.11i	−0.130506	+	0.226042i
$980$	9047.00			0.294894
$981$	−21693.7	+	37574.6i	−0.706042	+	1.22290i
$982$	−6730.17	+	11657.0i	−0.218705	+	0.378808i
$983$	4866.80			0.157911			0.0789557	−	0.996878i	$-0.474841\pi$
$983$	4866.80			0.157911			0.0789557	+	0.996878i	$0.474841\pi$
$984$	29543.6	−	51171.1i	0.957131	−	1.65780i
$985$	−4381.58	−	7589.12i	−0.141735	−	0.245492i
$986$	−646.642	−	1120.02i	−0.0208857	−	0.0361751i
$987$	−21475.3			−0.692569
$988$		0			0
$989$	1910.26			0.0614184
$990$	−12225.0	−	21174.4i	−0.392462	−	0.679764i
$991$	−6266.97	−	10854.7i	−0.200885	−	0.347943i	0.747929	−	0.663779i	$-0.231048\pi$
$991$	−6266.97	−	10854.7i	−0.200885	−	0.347943i	−0.948814	+	0.315836i	$0.897715\pi$
$992$	−12696.5	+	21991.1i	−0.406367	+	0.703848i
$993$	33972.4			1.08568
$994$	−6105.37	+	10574.8i	−0.194819	+	0.337437i
$995$	1736.68	−	3008.02i	0.0553332	−	0.0958399i
$996$	8470.83			0.269487
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	−0.836361	−	0.548180i	$-0.815321\pi$
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	0.892918	+	0.450220i	$0.148654\pi$
$998$	30631.0	+	53054.5i	0.971552	+	1.68278i
$999$	−17275.9	−	29922.7i	−0.547132	−	0.947660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.f.146.1		4
13.2	odd	12		169.4.b.e.168.1		4
13.3	even	3		169.4.a.j.1.2		2
13.4	even	6		13.4.c.b.9.2	yes	4
13.5	odd	4		169.4.e.g.23.1		8
13.6	odd	12		169.4.e.g.147.4		8
13.7	odd	12		169.4.e.g.147.1		8
13.8	odd	4		169.4.e.g.23.4		8
13.9	even	3	inner	169.4.c.f.22.1		4
13.10	even	6		169.4.a.f.1.1		2
13.11	odd	12		169.4.b.e.168.4		4
13.12	even	2		13.4.c.b.3.2	✓	4
39.17	odd	6		117.4.g.d.100.1		4
39.23	odd	6		1521.4.a.t.1.2		2
39.29	odd	6		1521.4.a.l.1.1		2
39.38	odd	2		117.4.g.d.55.1		4
52.43	odd	6		208.4.i.e.113.2		4
52.51	odd	2		208.4.i.e.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.b.3.2	✓	4	13.12	even	2
13.4.c.b.9.2	yes	4	13.4	even	6
117.4.g.d.55.1		4	39.38	odd	2
117.4.g.d.100.1		4	39.17	odd	6
169.4.a.f.1.1		2	13.10	even	6
169.4.a.j.1.2		2	13.3	even	3
169.4.b.e.168.1		4	13.2	odd	12
169.4.b.e.168.4		4	13.11	odd	12
169.4.c.f.22.1		4	13.9	even	3	inner
169.4.c.f.146.1		4	1.1	even	1	trivial
169.4.e.g.23.1		8	13.5	odd	4
169.4.e.g.23.4		8	13.8	odd	4
169.4.e.g.147.1		8	13.7	odd	12
169.4.e.g.147.4		8	13.6	odd	12
208.4.i.e.81.2		4	52.51	odd	2
208.4.i.e.113.2		4	52.43	odd	6
1521.4.a.l.1.1		2	39.29	odd	6
1521.4.a.t.1.2		2	39.23	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)

\(f(q)\)	\(=\)	\(q+(-2.28078 - 3.95042i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-6.40388 + 11.0918i) q^{4} -2.80776 q^{5} +(-19.8078 + 34.3081i) q^{6} +(4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})\)	\(q+(-2.28078 - 3.95042i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(-6.40388 + 11.0918i) q^{4} -2.80776 q^{5} +(-19.8078 + 34.3081i) q^{6} +(4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(-24.2116 + 41.9358i) q^{9} +(6.40388 + 11.0918i) q^{10} +(19.7116 + 34.1416i) q^{11} +111.231 q^{12} -43.6155 q^{14} +(12.1922 + 21.1176i) q^{15} +(1.21165 + 2.09863i) q^{16} +(-1.00758 + 1.74518i) q^{17} +220.885 q^{18} +(-30.0961 + 52.1280i) q^{19} +(17.9806 - 31.1433i) q^{20} -83.0388 q^{21} +(89.9157 - 155.739i) q^{22} +(-2.23438 - 3.87006i) q^{23} +(-95.2311 - 164.945i) q^{24} -117.116 q^{25} +186.054 q^{27} +(61.2311 + 106.055i) q^{28} +(-70.3466 - 121.844i) q^{29} +(55.6155 - 96.3289i) q^{30} -136.155 q^{31} +(93.2505 - 161.515i) q^{32} +(171.189 - 296.508i) q^{33} +9.19224 q^{34} +(-13.4233 + 23.2498i) q^{35} +(-310.097 - 537.104i) q^{36} +(-92.8542 - 160.828i) q^{37} +274.570 q^{38} -61.5767 q^{40} +(155.116 + 268.668i) q^{41} +(189.393 + 328.038i) q^{42} +(-213.735 + 370.200i) q^{43} -504.924 q^{44} +(67.9806 - 117.746i) q^{45} +(-10.1922 + 17.6535i) q^{46} +258.617 q^{47} +(10.5227 - 18.2259i) q^{48} +(125.788 + 217.872i) q^{49} +(267.116 + 462.659i) q^{50} +17.5009 q^{51} +612.656 q^{53} +(-424.348 - 734.991i) q^{54} +(-55.3457 - 95.8615i) q^{55} +(104.847 - 181.600i) q^{56} +522.749 q^{57} +(-320.890 + 555.797i) q^{58} +(-258.943 + 448.502i) q^{59} -312.311 q^{60} +(80.6553 - 139.699i) q^{61} +(310.540 + 537.871i) q^{62} +(231.501 + 400.971i) q^{63} -831.348 q^{64} -1561.77 q^{66} +(-24.9493 - 43.2135i) q^{67} +(-12.9048 - 22.3518i) q^{68} +(-19.4048 + 33.6101i) q^{69} +122.462 q^{70} +(139.982 - 242.455i) q^{71} +(-530.982 + 919.689i) q^{72} -467.732 q^{73} +(-423.559 + 733.626i) q^{74} +(508.558 + 880.849i) q^{75} +(-385.464 - 667.643i) q^{76} +376.948 q^{77} +37.5379 q^{79} +(-3.40202 - 5.89247i) q^{80} +(-154.193 - 267.070i) q^{81} +(707.568 - 1225.54i) q^{82} +76.1553 q^{83} +(531.771 - 921.054i) q^{84} +(2.82904 - 4.90004i) q^{85} +1949.93 q^{86} +(-610.936 + 1058.17i) q^{87} +(432.294 + 748.754i) q^{88} +(101.403 + 175.635i) q^{89} -620.194 q^{90} +57.2348 q^{92} +(591.231 + 1024.04i) q^{93} +(-589.848 - 1021.65i) q^{94} +(84.5028 - 146.363i) q^{95} -1619.70 q^{96} +(-587.184 + 1017.03i) q^{97} +(573.790 - 993.834i) q^{98} -1909.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9} + 5 q^{10} + 17 q^{11} + 280 q^{12} - 92 q^{14} + 90 q^{15} - 57 q^{16} - 70 q^{17} + 430 q^{18} - 141 q^{19} + 175 q^{20} - 126 q^{21} + 170 q^{22} - 145 q^{23} - 216 q^{24} + 150 q^{25} + 670 q^{27} + 80 q^{28} - 34 q^{29} + 140 q^{30} + 280 q^{31} + 105 q^{32} + 425 q^{33} + 78 q^{34} + 70 q^{35} - 725 q^{36} - 190 q^{37} + 620 q^{38} - 370 q^{40} + 538 q^{41} + 370 q^{42} - 455 q^{43} - 1360 q^{44} + 375 q^{45} - 82 q^{46} - 120 q^{47} + 240 q^{48} + 565 q^{49} + 450 q^{50} - 466 q^{51} + 1090 q^{53} - 914 q^{54} - 510 q^{55} + 172 q^{56} + 450 q^{57} - 595 q^{58} - 809 q^{59} + 400 q^{60} - 502 q^{61} + 500 q^{62} + 390 q^{63} - 2542 q^{64} - 3196 q^{66} - 475 q^{67} + 505 q^{68} + 479 q^{69} + 160 q^{70} + 127 q^{71} - 1155 q^{72} - 1170 q^{73} - 849 q^{74} + 1725 q^{75} - 140 q^{76} + 510 q^{77} + 480 q^{79} - 1065 q^{80} - 122 q^{81} + 1515 q^{82} - 520 q^{83} + 1220 q^{84} - 1205 q^{85} + 3924 q^{86} - 1615 q^{87} + 1020 q^{88} + 921 q^{89} - 1450 q^{90} - 2080 q^{92} + 2200 q^{93} - 1040 q^{94} - 1270 q^{95} - 3840 q^{96} - 415 q^{97} + 1285 q^{98} - 4420 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9 + 5 * q^10 + 17 * q^11 + 280 * q^12 - 92 * q^14 + 90 * q^15 - 57 * q^16 - 70 * q^17 + 430 * q^18 - 141 * q^19 + 175 * q^20 - 126 * q^21 + 170 * q^22 - 145 * q^23 - 216 * q^24 + 150 * q^25 + 670 * q^27 + 80 * q^28 - 34 * q^29 + 140 * q^30 + 280 * q^31 + 105 * q^32 + 425 * q^33 + 78 * q^34 + 70 * q^35 - 725 * q^36 - 190 * q^37 + 620 * q^38 - 370 * q^40 + 538 * q^41 + 370 * q^42 - 455 * q^43 - 1360 * q^44 + 375 * q^45 - 82 * q^46 - 120 * q^47 + 240 * q^48 + 565 * q^49 + 450 * q^50 - 466 * q^51 + 1090 * q^53 - 914 * q^54 - 510 * q^55 + 172 * q^56 + 450 * q^57 - 595 * q^58 - 809 * q^59 + 400 * q^60 - 502 * q^61 + 500 * q^62 + 390 * q^63 - 2542 * q^64 - 3196 * q^66 - 475 * q^67 + 505 * q^68 + 479 * q^69 + 160 * q^70 + 127 * q^71 - 1155 * q^72 - 1170 * q^73 - 849 * q^74 + 1725 * q^75 - 140 * q^76 + 510 * q^77 + 480 * q^79 - 1065 * q^80 - 122 * q^81 + 1515 * q^82 - 520 * q^83 + 1220 * q^84 - 1205 * q^85 + 3924 * q^86 - 1615 * q^87 + 1020 * q^88 + 921 * q^89 - 1450 * q^90 - 2080 * q^92 + 2200 * q^93 - 1040 * q^94 - 1270 * q^95 - 3840 * q^96 - 415 * q^97 + 1285 * q^98 - 4420 * q^99

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