LMFDB - Embedded newform 169.4.c.l.22.8

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			22.8
Root			$-1.91278 - 3.31303i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.l.146.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41278 - 4.17905i) q^{2} +(-2.22176 + 3.84820i) q^{3} +(-7.64299 - 13.2380i) q^{4} +12.7712 q^{5} +(10.7212 + 18.5697i) q^{6} +(13.0936 + 22.6787i) q^{7} -35.1589 q^{8} +(3.62756 + 6.28312i) q^{9} +O(q^{10})$	\(q+(2.41278 - 4.17905i) q^{2} +(-2.22176 + 3.84820i) q^{3} +(-7.64299 - 13.2380i) q^{4} +12.7712 q^{5} +(10.7212 + 18.5697i) q^{6} +(13.0936 + 22.6787i) q^{7} -35.1589 q^{8} +(3.62756 + 6.28312i) q^{9} +(30.8140 - 53.3715i) q^{10} +(21.1715 - 36.6701i) q^{11} +67.9236 q^{12} +126.367 q^{14} +(-28.3745 + 49.1461i) q^{15} +(-23.6866 + 41.0265i) q^{16} +(13.6665 + 23.6711i) q^{17} +35.0100 q^{18} +(-6.55981 - 11.3619i) q^{19} +(-97.6101 - 169.066i) q^{20} -116.363 q^{21} +(-102.164 - 176.954i) q^{22} +(14.3988 - 24.9394i) q^{23} +(78.1146 - 135.298i) q^{24} +38.1033 q^{25} -152.213 q^{27} +(200.148 - 346.666i) q^{28} +(70.8138 - 122.653i) q^{29} +(136.923 + 237.157i) q^{30} +56.0144 q^{31} +(-26.3343 - 45.6124i) q^{32} +(94.0761 + 162.945i) q^{33} +131.897 q^{34} +(167.220 + 289.634i) q^{35} +(55.4508 - 96.0437i) q^{36} +(-156.991 + 271.916i) q^{37} -63.3095 q^{38} -449.021 q^{40} +(176.187 - 305.165i) q^{41} +(-280.758 + 486.287i) q^{42} +(160.338 + 277.714i) q^{43} -647.255 q^{44} +(46.3283 + 80.2430i) q^{45} +(-69.4822 - 120.347i) q^{46} -339.339 q^{47} +(-105.252 - 182.302i) q^{48} +(-171.382 + 296.843i) q^{49} +(91.9347 - 159.236i) q^{50} -121.455 q^{51} +349.461 q^{53} +(-367.257 + 636.108i) q^{54} +(270.385 - 468.321i) q^{55} +(-460.355 - 797.358i) q^{56} +58.2973 q^{57} +(-341.716 - 591.869i) q^{58} +(129.371 + 224.077i) q^{59} +867.465 q^{60} +(-325.366 - 563.550i) q^{61} +(135.150 - 234.087i) q^{62} +(-94.9954 + 164.537i) q^{63} -633.142 q^{64} +907.938 q^{66} +(-447.498 + 775.089i) q^{67} +(208.906 - 361.836i) q^{68} +(63.9813 + 110.819i) q^{69} +1613.86 q^{70} +(370.734 + 642.131i) q^{71} +(-127.541 - 220.908i) q^{72} -820.643 q^{73} +(757.569 + 1312.15i) q^{74} +(-84.6563 + 146.629i) q^{75} +(-100.273 + 173.678i) q^{76} +1108.84 q^{77} -199.372 q^{79} +(-302.507 + 523.957i) q^{80} +(240.237 - 416.103i) q^{81} +(-850.201 - 1472.59i) q^{82} -541.696 q^{83} +(889.361 + 1540.42i) q^{84} +(174.538 + 302.308i) q^{85} +1547.44 q^{86} +(314.663 + 545.012i) q^{87} +(-744.367 + 1289.28i) q^{88} +(190.307 - 329.622i) q^{89} +447.119 q^{90} -440.199 q^{92} +(-124.451 + 215.555i) q^{93} +(-818.749 + 1418.12i) q^{94} +(-83.7766 - 145.105i) q^{95} +234.034 q^{96} +(-715.250 - 1238.85i) q^{97} +(827.015 + 1432.43i) q^{98} +307.204 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 $

$2$	2.41278	−	4.17905i	0.853046	−	1.47752i	−0.0254008	−	0.999677i	$-0.508086\pi$
$2$	2.41278	−	4.17905i	0.853046	−	1.47752i	0.878446	−	0.477841i	$-0.158580\pi$
$3$	−2.22176	+	3.84820i	−0.427578	+	0.740587i	−0.996657	−	0.0816959i	$-0.973966\pi$
$3$	−2.22176	+	3.84820i	−0.427578	+	0.740587i	0.569079	+	0.822283i	$0.307300\pi$
$4$	−7.64299	−	13.2380i	−0.955374	−	1.65476i
$5$	12.7712			1.14229			0.571145	−	0.820849i	$-0.306499\pi$
$5$	12.7712			1.14229			0.571145	+	0.820849i	$0.306499\pi$
$6$	10.7212	+	18.5697i	0.729487	+	1.26351i
$7$	13.0936	+	22.6787i	0.706986	+	1.22453i	0.965970	+	0.258654i	$0.0832788\pi$
$7$	13.0936	+	22.6787i	0.706986	+	1.22453i	−0.258985	+	0.965881i	$0.583388\pi$
$8$	−35.1589			−1.55382
$9$	3.62756	+	6.28312i	0.134354	+	0.232708i
$10$	30.8140	−	53.3715i	0.974425	−	1.68775i
$11$	21.1715	−	36.6701i	0.580314	−	1.00513i	−0.415128	−	0.909763i	$-0.636263\pi$
$11$	21.1715	−	36.6701i	0.580314	−	1.00513i	0.995442	−	0.0953700i	$-0.0304034\pi$
$12$	67.9236			1.63399
$13$		0			0
$13$		0			0
$14$	126.367			2.41236
$15$	−28.3745	+	49.1461i	−0.488418	+	0.845965i
$16$	−23.6866	+	41.0265i	−0.370104	+	0.641039i
$17$	13.6665	+	23.6711i	0.194978	+	0.337711i	0.946893	−	0.321548i	$-0.104203\pi$
$17$	13.6665	+	23.6711i	0.194978	+	0.337711i	−0.751915	+	0.659259i	$0.770870\pi$
$18$	35.0100			0.458441
$19$	−6.55981	−	11.3619i	−0.0792065	−	0.137190i	0.823701	−	0.567024i	$-0.191905\pi$
$19$	−6.55981	−	11.3619i	−0.0792065	−	0.137190i	−0.902908	+	0.429834i	$0.858572\pi$
$20$	−97.6101	−	169.066i	−1.09131	−	1.89021i
$21$	−116.363			−1.20917
$22$	−102.164	−	176.954i	−0.990068	−	1.71485i
$23$	14.3988	−	24.9394i	0.130537	−	0.226097i	−0.793347	−	0.608770i	$-0.791663\pi$
$23$	14.3988	−	24.9394i	0.130537	−	0.226097i	0.923884	+	0.382673i	$0.124996\pi$
$24$	78.1146	−	135.298i	0.664378	−	1.15074i
$25$	38.1033			0.304826
$26$		0			0
$27$	−152.213			−1.08494
$28$	200.148	−	346.666i	1.35087	−	2.33978i
$29$	70.8138	−	122.653i	0.453441	−	0.785383i	−0.545156	−	0.838335i	$-0.683530\pi$
$29$	70.8138	−	122.653i	0.453441	−	0.785383i	0.998597	+	0.0529515i	$0.0168629\pi$
$30$	136.923	+	237.157i	0.833286	+	1.44329i
$31$	56.0144			0.324532			0.162266	−	0.986747i	$-0.448120\pi$
$31$	56.0144			0.324532			0.162266	+	0.986747i	$0.448120\pi$
$32$	−26.3343	−	45.6124i	−0.145478	−	0.251975i
$33$	94.0761	+	162.945i	0.496259	+	0.859545i
$34$	131.897			0.665300
$35$	167.220	+	289.634i	0.807582	+	1.39877i
$36$	55.4508	−	96.0437i	0.256717	−	0.444647i
$37$	−156.991	+	271.916i	−0.697545	+	1.20818i	0.271770	+	0.962362i	$0.412391\pi$
$37$	−156.991	+	271.916i	−0.697545	+	1.20818i	−0.969315	+	0.245821i	$0.920942\pi$
$38$	−63.3095			−0.270267
$39$		0			0
$40$	−449.021			−1.77491
$41$	176.187	−	305.165i	0.671118	−	1.16241i	−0.306470	−	0.951880i	$-0.599148\pi$
$41$	176.187	−	305.165i	0.671118	−	1.16241i	0.977587	−	0.210530i	$-0.0675188\pi$
$42$	−280.758	+	486.287i	−1.03147	+	1.78656i
$43$	160.338	+	277.714i	0.568636	+	0.984907i	0.996701	+	0.0811587i	$0.0258621\pi$
$43$	160.338	+	277.714i	0.568636	+	0.984907i	−0.428065	+	0.903748i	$0.640805\pi$
$44$	−647.255			−2.21767
$45$	46.3283	+	80.2430i	0.153471	+	0.265820i
$46$	−69.4822	−	120.347i	−0.222708	−	0.385742i
$47$	−339.339			−1.05314			−0.526571	−	0.850131i	$-0.676523\pi$
$47$	−339.339			−1.05314			−0.526571	+	0.850131i	$0.676523\pi$
$48$	−105.252	−	182.302i	−0.316496	−	0.548188i
$49$	−171.382	+	296.843i	−0.499657	+	0.865432i
$50$	91.9347	−	159.236i	0.260031	−	0.450386i
$51$	−121.455			−0.333473
$52$		0			0
$53$	349.461			0.905701			0.452851	−	0.891586i	$-0.350407\pi$
$53$	349.461			0.905701			0.452851	+	0.891586i	$0.350407\pi$
$54$	−367.257	+	636.108i	−0.925506	+	1.60302i
$55$	270.385	−	468.321i	0.662887	−	1.14815i
$56$	−460.355	−	797.358i	−1.09853	−	1.90270i
$57$	58.2973			0.135468
$58$	−341.716	−	591.869i	−0.773612	−	1.33994i
$59$	129.371	+	224.077i	0.285469	+	0.494446i	0.972723	−	0.231971i	$-0.0745174\pi$
$59$	129.371	+	224.077i	0.285469	+	0.494446i	−0.687254	+	0.726417i	$0.741184\pi$
$60$	867.465			1.86649
$61$	−325.366	−	563.550i	−0.682932	−	1.18287i	−0.974082	−	0.226195i	$-0.927371\pi$
$61$	−325.366	−	563.550i	−0.682932	−	1.18287i	0.291150	−	0.956677i	$-0.405962\pi$
$62$	135.150	−	234.087i	0.276840	−	0.479502i
$63$	−94.9954	+	164.537i	−0.189973	+	0.329043i
$64$	−633.142			−1.23661
$65$		0			0
$66$	907.938			1.69333
$67$	−447.498	+	775.089i	−0.815979	+	1.41332i	0.0926446	+	0.995699i	$0.470468\pi$
$67$	−447.498	+	775.089i	−0.815979	+	1.41332i	−0.908623	+	0.417617i	$0.862865\pi$
$68$	208.906	−	361.836i	0.372553	−	0.645281i
$69$	63.9813	+	110.819i	0.111630	+	0.193348i
$70$	1613.86			2.75562
$71$	370.734	+	642.131i	0.619691	+	1.07334i	0.989542	+	0.144245i	$0.0460754\pi$
$71$	370.734	+	642.131i	0.619691	+	1.07334i	−0.369851	+	0.929091i	$0.620591\pi$
$72$	−127.541	−	220.908i	−0.208762	−	0.361586i
$73$	−820.643			−1.31574			−0.657870	−	0.753131i	$-0.728542\pi$
$73$	−820.643			−1.31574			−0.657870	+	0.753131i	$0.728542\pi$
$74$	757.569	+	1312.15i	1.19008	+	2.06127i
$75$	−84.6563	+	146.629i	−0.130337	+	0.225750i
$76$	−100.273	+	173.678i	−0.151344	+	0.262135i
$77$	1108.84			1.64109
$78$		0			0
$79$	−199.372			−0.283938			−0.141969	−	0.989871i	$-0.545343\pi$
$79$	−199.372			−0.283938			−0.141969	+	0.989871i	$0.545343\pi$
$80$	−302.507	+	523.957i	−0.422766	+	0.732252i
$81$	240.237	−	416.103i	0.329544	−	0.570786i
$82$	−850.201	−	1472.59i	−1.14499	−	1.98318i
$83$	−541.696			−0.716372			−0.358186	−	0.933650i	$-0.616605\pi$
$83$	−541.696			−0.716372			−0.358186	+	0.933650i	$0.616605\pi$
$84$	889.361	+	1540.42i	1.15521	+	2.00087i
$85$	174.538	+	302.308i	0.222721	+	0.385764i
$86$	1547.44			1.94029
$87$	314.663	+	545.012i	0.387763	+	0.671625i
$88$	−744.367	+	1289.28i	−0.901702	+	1.56179i
$89$	190.307	−	329.622i	0.226658	−	0.392583i	−0.730158	−	0.683279i	$-0.760553\pi$
$89$	190.307	−	329.622i	0.226658	−	0.392583i	0.956815	+	0.290696i	$0.0938868\pi$
$90$	447.119			0.523672
$91$		0			0
$92$	−440.199			−0.498847
$93$	−124.451	+	215.555i	−0.138763	+	0.240344i
$94$	−818.749	+	1418.12i	−0.898378	+	1.55604i
$95$	−83.7766	−	145.105i	−0.0904768	−	0.156710i
$96$	234.034			0.248813
$97$	−715.250	−	1238.85i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$97$	−715.250	−	1238.85i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$98$	827.015	+	1432.43i	0.852461	+	1.47651i
$99$	307.204			0.311870
$100$	−291.223	−	504.413i	−0.291223	−	0.504413i
$101$	400.598	−	693.856i	0.394663	−	0.683576i	−0.598395	−	0.801201i	$-0.704195\pi$
$101$	400.598	−	693.856i	0.394663	−	0.683576i	0.993058	+	0.117625i	$0.0375280\pi$
$102$	−293.044	+	507.567i	−0.284467	+	0.492712i
$103$	−745.805			−0.713459			−0.356730	−	0.934208i	$-0.616108\pi$
$103$	−745.805			−0.713459			−0.356730	+	0.934208i	$0.616108\pi$
$104$		0			0
$105$	−1486.09			−1.38122
$106$	843.172	−	1460.42i	0.772605	−	1.33819i
$107$	67.2730	−	116.520i	0.0607806	−	0.105275i	−0.834034	−	0.551713i	$-0.813974\pi$
$107$	67.2730	−	116.520i	0.0607806	−	0.105275i	0.894815	+	0.446438i	$0.147308\pi$
$108$	1163.36	+	2015.01i	1.03653	+	1.79532i
$109$	−293.245			−0.257686			−0.128843	−	0.991665i	$-0.541126\pi$
$109$	−293.245			−0.257686			−0.128843	+	0.991665i	$0.541126\pi$
$110$	−1304.76	−	2259.91i	−1.13094	−	1.95885i
$111$	−697.593	−	1208.27i	−0.596510	−	1.03319i
$112$	−1240.57			−1.04663
$113$	−852.689	−	1476.90i	−0.709861	−	1.22951i	−0.964909	−	0.262586i	$-0.915425\pi$
$113$	−852.689	−	1476.90i	−0.709861	−	1.22951i	0.255048	−	0.966928i	$-0.417909\pi$
$114$	140.658	−	243.628i	0.115560	−	0.200156i
$115$	183.890	−	318.506i	0.149111	−	0.258268i
$116$	−2164.92			−1.73282
$117$		0			0
$118$	1248.57			0.974071
$119$	−357.887	+	619.879i	−0.275693	+	0.477514i
$120$	997.616	−	1727.92i	0.758913	−	1.31448i
$121$	−230.966	−	400.045i	−0.173528	−	0.300560i
$122$	−3140.14			−2.33029
$123$	782.892	+	1356.01i	0.573910	+	0.994042i
$124$	−428.118	−	741.521i	−0.310049	−	0.537021i
$125$	−1109.77			−0.794090
$126$	458.405	+	793.982i	0.324111	+	0.561377i
$127$	−746.589	+	1293.13i	−0.521646	+	0.903517i	0.478037	+	0.878340i	$0.341348\pi$
$127$	−746.589	+	1293.13i	−0.521646	+	0.903517i	−0.999683	+	0.0251776i	$0.991985\pi$
$128$	−1316.96	+	2281.03i	−0.909403	+	1.57513i
$129$	−1424.93			−0.972545
$130$		0			0
$131$	−459.112			−0.306205			−0.153102	−	0.988210i	$-0.548926\pi$
$131$	−459.112			−0.306205			−0.153102	+	0.988210i	$0.548926\pi$
$132$	1438.04	−	2490.77i	0.948225	−	1.64237i
$133$	171.783	−	297.536i	0.111996	−	0.193982i
$134$	2159.43	+	3740.23i	1.39213	+	2.41125i
$135$	−1943.95			−1.23932
$136$	−480.500	−	832.251i	−0.302960	−	0.524742i
$137$	−1251.53	−	2167.72i	−0.780478	−	1.35183i	−0.931663	−	0.363323i	$-0.881642\pi$
$137$	−1251.53	−	2167.72i	−0.780478	−	1.35183i	0.151185	−	0.988506i	$-0.451691\pi$
$138$	617.491			0.380901
$139$	−901.867	−	1562.08i	−0.550326	−	0.953193i	−0.998251	−	0.0591216i	$-0.981170\pi$
$139$	−901.867	−	1562.08i	−0.550326	−	0.953193i	0.447925	−	0.894071i	$-0.352163\pi$
$140$	2556.13	−	4427.34i	1.54309	−	2.67270i
$141$	753.930	−	1305.84i	0.450300	−	0.779943i
$142$	3578.00			2.11450
$143$		0			0
$144$	−343.699			−0.198900
$145$	904.377	−	1566.43i	0.517961	−	0.897135i
$146$	−1980.03	+	3429.51i	−1.12239	+	1.94403i
$147$	−761.541	−	1319.03i	−0.427285	−	0.740079i
$148$	4799.52			2.66566
$149$	1462.72	+	2533.50i	0.804232	+	1.39297i	0.916808	+	0.399327i	$0.130756\pi$
$149$	1462.72	+	2533.50i	0.804232	+	1.39297i	−0.112577	+	0.993643i	$0.535910\pi$
$150$	408.514	+	707.567i	0.222367	+	0.385150i
$151$	1769.28			0.953524			0.476762	−	0.879032i	$-0.341810\pi$
$151$	1769.28			0.953524			0.476762	+	0.879032i	$0.341810\pi$
$152$	230.636	+	399.473i	0.123073	+	0.213168i
$153$	−99.1524	+	171.737i	−0.0523921	+	0.0907459i
$154$	2675.39	−	4633.91i	1.39993	−	2.42475i
$155$	715.371			0.370709
$156$		0			0
$157$	−1157.24			−0.588265			−0.294132	−	0.955765i	$-0.595031\pi$
$157$	−1157.24			−0.588265			−0.294132	+	0.955765i	$0.595031\pi$
$158$	−481.039	+	833.185i	−0.242212	+	0.419523i
$159$	−776.419	+	1344.80i	−0.387258	+	0.670751i
$160$	−336.321	−	582.525i	−0.166178	−	0.287829i
$161$	754.126			0.369152
$162$	−1159.28	−	2007.93i	−0.562232	−	0.973814i
$163$	1454.60	+	2519.45i	0.698977	+	1.21066i	0.968821	+	0.247760i	$0.0796945\pi$
$163$	1454.60	+	2519.45i	0.698977	+	1.21066i	−0.269844	+	0.962904i	$0.586972\pi$
$164$	−5386.39			−2.56467
$165$	1201.46	+	2081.00i	0.566871	+	0.981850i
$166$	−1306.99	+	2263.78i	−0.611098	+	1.05845i
$167$	−636.079	+	1101.72i	−0.294738	+	0.510502i	−0.974924	−	0.222538i	$-0.928566\pi$
$167$	−636.079	+	1101.72i	−0.294738	+	0.510502i	0.680186	+	0.733040i	$0.261899\pi$
$168$	4091.19			1.87882
$169$		0			0
$170$	1684.48			0.759965
$171$	47.5923	−	82.4322i	0.0212835	−	0.0368640i
$172$	2450.93	−	4245.13i	1.08652	−	1.88191i
$173$	−1185.90	−	2054.04i	−0.521169	−	0.902692i	−0.999697	−	0.0246191i	$-0.992163\pi$
$173$	−1185.90	−	2054.04i	−0.521169	−	0.902692i	0.478528	−	0.878072i	$-0.341171\pi$
$174$	3036.84			1.32312
$175$	498.907	+	864.133i	0.215508	+	0.373270i
$176$	1002.96	+	1737.19i	0.429553	+	0.744007i
$177$	−1149.72			−0.488240
$178$	−918.338	−	1590.61i	−0.386699	−	0.669782i
$179$	−363.591	+	629.759i	−0.151822	+	0.262963i	−0.931897	−	0.362722i	$-0.881847\pi$
$179$	−363.591	+	629.759i	−0.151822	+	0.262963i	0.780075	+	0.625685i	$0.215181\pi$
$180$	708.173	−	1226.59i	0.293245	−	0.507915i
$181$	3874.20			1.59098			0.795488	−	0.605969i	$-0.207215\pi$
$181$	3874.20			1.59098			0.795488	+	0.605969i	$0.207215\pi$
$182$		0			0
$183$	2891.54			1.16803
$184$	−506.246	+	876.843i	−0.202831	+	0.351314i
$185$	−2004.96	+	3472.70i	−0.796799	+	1.38010i
$186$	600.543	+	1040.17i	0.236742	+	0.410049i
$187$	1157.36			0.452593
$188$	2593.56	+	4492.18i	1.00614	+	1.74269i
$189$	−1993.01	−	3452.00i	−0.767039	−	1.32855i
$190$	−808.537			−0.308723
$191$	−1001.89	−	1735.32i	−0.379549	−	0.657399i	0.611447	−	0.791285i	$-0.290588\pi$
$191$	−1001.89	−	1735.32i	−0.379549	−	0.657399i	−0.990997	+	0.133886i	$0.957254\pi$
$192$	1406.69	−	2436.46i	0.528745	−	0.915813i
$193$	−513.124	+	888.757i	−0.191376	+	0.331472i	−0.945706	−	0.325022i	$-0.894628\pi$
$193$	−513.124	+	888.757i	−0.191376	+	0.331472i	0.754331	+	0.656495i	$0.227962\pi$
$194$	−6902.96			−2.55466
$195$		0			0
$196$	5239.50			1.90944
$197$	−654.095	+	1132.93i	−0.236560	+	0.409734i	−0.959725	−	0.280941i	$-0.909353\pi$
$197$	−654.095	+	1132.93i	−0.236560	+	0.409734i	0.723165	+	0.690675i	$0.242687\pi$
$198$	741.215	−	1283.82i	0.266040	−	0.460794i
$199$	142.560	+	246.921i	0.0507830	+	0.0879587i	0.890299	−	0.455376i	$-0.150495\pi$
$199$	142.560	+	246.921i	0.0507830	+	0.0879587i	−0.839516	+	0.543334i	$0.817162\pi$
$200$	−1339.67			−0.473644
$201$	−1988.47	−	3444.12i	−0.697789	−	1.20861i
$202$	−1933.11	−	3348.24i	−0.673331	−	1.16624i
$203$	3708.82			1.28231
$204$	928.280	+	1607.83i	0.318591	+	0.551816i
$205$	2250.12	−	3897.32i	0.766611	−	1.32781i
$206$	−1799.46	+	3116.76i	−0.608613	+	1.05415i
$207$	208.930			0.0701529
$208$		0			0
$209$	−555.525			−0.183859
$210$	−3585.61	+	6210.46i	−1.17824	+	2.04077i
$211$	1406.95	−	2436.92i	0.459046	−	0.795091i	−0.539865	−	0.841752i	$-0.681525\pi$
$211$	1406.95	−	2436.92i	0.459046	−	0.795091i	0.998911	+	0.0466607i	$0.0148580\pi$
$212$	−2670.93	−	4626.18i	−0.865283	−	1.49871i
$213$	−3294.73			−1.05986
$214$	−324.630	−	562.275i	−0.103697	−	0.179609i
$215$	2047.71	+	3546.74i	0.649547	+	1.12505i
$216$	5351.65			1.68580
$217$	733.428	+	1270.33i	0.229439	+	0.397401i
$218$	−707.534	+	1225.48i	−0.219818	+	0.380735i
$219$	1823.27	−	3158.00i	0.562581	−	0.974420i
$220$	−8266.21			−2.53322
$221$		0			0
$222$	−6732.55			−2.03540
$223$	754.932	−	1307.58i	0.226699	−	0.392655i	−0.730129	−	0.683310i	$-0.760540\pi$
$223$	754.932	−	1307.58i	0.226699	−	0.392655i	0.956828	+	0.290655i	$0.0938732\pi$
$224$	689.620	−	1194.46i	0.205702	−	0.356286i
$225$	138.222	+	239.408i	0.0409547	+	0.0709356i
$226$	−8229.40			−2.42217
$227$	−321.561	−	556.960i	−0.0940209	−	0.162849i	0.815179	−	0.579210i	$-0.196639\pi$
$227$	−321.561	−	556.960i	−0.0940209	−	0.162849i	−0.909200	+	0.416361i	$0.863305\pi$
$228$	−445.566	−	771.742i	−0.129422	−	0.224166i
$229$	−154.009			−0.0444420			−0.0222210	−	0.999753i	$-0.507074\pi$
$229$	−154.009			−0.0444420			−0.0222210	+	0.999753i	$0.507074\pi$
$230$	−887.370	−	1536.97i	−0.254398	−	0.440630i
$231$	−2463.58	+	4267.05i	−0.701696	+	1.21537i
$232$	−2489.73	+	4312.35i	−0.704565	+	1.22034i
$233$	−261.668			−0.0735726			−0.0367863	−	0.999323i	$-0.511712\pi$
$233$	−261.668			−0.0735726			−0.0367863	+	0.999323i	$0.511712\pi$
$234$		0			0
$235$	−4333.76			−1.20299
$236$	1977.56	−	3425.23i	0.545458	−	0.944762i
$237$	442.956	−	767.222i	0.121405	−	0.210280i
$238$	1727.00	+	2991.26i	0.470357	+	0.814683i
$239$	2495.09			0.675288			0.337644	−	0.941274i	$-0.390370\pi$
$239$	2495.09			0.675288			0.337644	+	0.941274i	$0.390370\pi$
$240$	−1344.19	−	2328.21i	−0.361531	−	0.626190i
$241$	1917.85	+	3321.81i	0.512612	+	0.887870i	0.999893	+	0.0146247i	$0.00465534\pi$
$241$	1917.85	+	3321.81i	0.512612	+	0.887870i	−0.487281	+	0.873245i	$0.662011\pi$
$242$	−2229.08			−0.592110
$243$	−987.381	−	1710.19i	−0.260660	−	0.451477i
$244$	−4973.54	+	8614.42i	−1.30491	+	2.26017i
$245$	−2188.76	+	3791.04i	−0.570753	+	0.988574i
$246$	7555.77			1.95829
$247$		0			0
$248$	−1969.40			−0.504263
$249$	1203.52	−	2084.56i	0.306305	−	0.530536i
$250$	−2677.64	+	4637.81i	−0.677395	+	1.17328i
$251$	1988.79	+	3444.69i	0.500126	+	0.866243i	1.00000		0.000145339i	$4.62628e-5\pi$
$251$	1988.79	+	3444.69i	0.500126	+	0.866243i	−0.499874	+	0.866098i	$0.666620\pi$
$252$	2904.19			0.725980
$253$	−609.689	−	1056.01i	−0.151505	−	0.262415i
$254$	3602.70	+	6240.07i	0.889976	+	1.54148i
$255$	−1551.13			−0.380923
$256$	3822.47	+	6620.72i	0.933221	+	1.61639i
$257$	60.7431	−	105.210i	0.0147434	−	0.0255363i	−0.858560	−	0.512714i	$-0.828640\pi$
$257$	60.7431	−	105.210i	0.0147434	−	0.0255363i	0.873303	+	0.487178i	$0.161974\pi$
$258$	−3438.04	+	5954.87i	−0.829625	+	1.43695i
$259$	−8222.29			−1.97262
$260$		0			0
$261$	1027.53			0.243687
$262$	−1107.73	+	1918.65i	−0.261206	+	0.452423i
$263$	−587.708	+	1017.94i	−0.137793	+	0.238665i	−0.926661	−	0.375898i	$-0.877334\pi$
$263$	−587.708	+	1017.94i	−0.137793	+	0.238665i	0.788868	+	0.614563i	$0.210668\pi$
$264$	−3307.61	−	5728.95i	−0.771096	−	1.33558i
$265$	4463.03			1.03457
$266$	−828.946	−	1435.78i	−0.191075	−	0.330952i
$267$	845.634	+	1464.68i	0.193828	+	0.335719i
$268$	13680.9			3.11826
$269$	4159.83	+	7205.04i	0.942860	+	1.63308i	0.759981	+	0.649946i	$0.225208\pi$
$269$	4159.83	+	7205.04i	0.942860	+	1.63308i	0.182879	+	0.983135i	$0.441458\pi$
$270$	−4690.31	+	8123.85i	−1.05720	+	1.83112i
$271$	1964.28	−	3402.23i	0.440301	−	0.762623i	−0.557411	−	0.830237i	$-0.688205\pi$
$271$	1964.28	−	3402.23i	0.440301	−	0.762623i	0.997712	+	0.0676135i	$0.0215385\pi$
$272$	−1294.86			−0.288648
$273$		0			0
$274$	−12078.7			−2.66313
$275$	806.704	−	1397.25i	0.176895	−	0.306391i
$276$	978.017	−	1693.98i	0.213296	−	0.369440i
$277$	3011.30	+	5215.73i	0.653183	+	1.13135i	0.982346	+	0.187073i	$0.0599001\pi$
$277$	3011.30	+	5215.73i	0.653183	+	1.13135i	−0.329163	+	0.944273i	$0.606767\pi$
$278$	−8704.01			−1.87781
$279$	203.196	+	351.946i	0.0436022	+	0.0755212i
$280$	−5879.28	−	10183.2i	−1.25484	−	2.17344i
$281$	2183.71			0.463592			0.231796	−	0.972764i	$-0.425540\pi$
$281$	2183.71			0.463592			0.231796	+	0.972764i	$0.425540\pi$
$282$	−3638.13	−	6301.43i	−0.768253	−	1.33065i
$283$	4066.62	−	7043.60i	0.854190	−	1.47950i	−0.0232048	−	0.999731i	$-0.507387\pi$
$283$	4066.62	−	7043.60i	0.854190	−	1.47950i	0.877395	−	0.479769i	$-0.159280\pi$
$284$	5667.04	−	9815.59i	1.18407	−	2.05087i
$285$	744.526			0.154744
$286$		0			0
$287$	9227.67			1.89788
$288$	191.059	−	330.924i	0.0390912	−	0.0677079i
$289$	2082.95	−	3607.78i	0.423967	−	0.734333i
$290$	−4364.12	−	7558.88i	−0.883689	−	1.53059i
$291$	6356.46			1.28049
$292$	6272.17	+	10863.7i	1.25702	+	2.17723i
$293$	−1591.28	−	2756.17i	−0.317281	−	0.549547i	0.662639	−	0.748939i	$-0.269436\pi$
$293$	−1591.28	−	2756.17i	−0.317281	−	0.549547i	−0.979920	+	0.199392i	$0.936103\pi$
$294$	−7349.72			−1.45797
$295$	1652.22	+	2861.73i	0.326088	+	0.564801i
$296$	5519.63	−	9560.28i	1.08386	−	1.87730i
$297$	−3222.59	+	5581.68i	−0.629608	+	1.09051i
$298$	14116.9			2.74419
$299$		0			0
$300$	2588.11			0.498082
$301$	−4198.80	+	7272.53i	−0.804035	+	1.39263i
$302$	4268.88	−	7393.93i	0.813400	−	1.40885i
$303$	1780.06	+	3083.16i	0.337498	+	0.584564i
$304$	621.520			0.117259
$305$	−4155.31	−	7197.21i	−0.780106	−	1.35118i
$306$	478.465	+	828.726i	0.0893858	+	0.154821i
$307$	−1230.21			−0.228703			−0.114352	−	0.993440i	$-0.536479\pi$
$307$	−1230.21			−0.228703			−0.114352	+	0.993440i	$0.536479\pi$
$308$	−8474.86	−	14678.9i	−1.56786	−	2.71561i
$309$	1657.00	−	2870.01i	0.305060	−	0.528379i
$310$	1726.03	−	2989.57i	0.316232	−	0.547730i
$311$	−5881.49			−1.07237			−0.536187	−	0.844099i	$-0.680136\pi$
$311$	−5881.49			−1.07237			−0.536187	+	0.844099i	$0.680136\pi$
$312$		0			0
$313$	6800.24			1.22803			0.614013	−	0.789296i	$-0.289554\pi$
$313$	6800.24			1.22803			0.614013	+	0.789296i	$0.289554\pi$
$314$	−2792.15	+	4836.15i	−0.501816	+	0.869172i
$315$	−1213.20	+	2101.33i	−0.217004	+	0.375862i
$316$	1523.80	+	2639.29i	0.271266	+	0.469847i
$317$	−2212.50			−0.392008			−0.196004	−	0.980603i	$-0.562796\pi$
$317$	−2212.50			−0.392008			−0.196004	+	0.980603i	$0.562796\pi$
$318$	3746.65	+	6489.39i	0.660697	+	1.14436i
$319$	−2998.47	−	5193.50i	−0.526276	−	0.911537i
$320$	−8085.97			−1.41256
$321$	298.929	+	517.760i	0.0519769	+	0.0900267i
$322$	1819.54	−	3151.53i	0.314903	−	0.545428i
$323$	179.300	−	310.556i	0.0308870	−	0.0534979i
$324$	−7344.53			−1.25935
$325$		0			0
$326$	14038.5			2.38504
$327$	651.519	−	1128.46i	0.110181	−	0.190839i
$328$	−6194.55	+	10729.3i	−1.04279	+	1.80617i
$329$	−4443.15	−	7695.77i	−0.744556	−	1.28961i
$330$	11595.5			1.93427
$331$	−872.069	−	1510.47i	−0.144814	−	0.250824i	0.784490	−	0.620142i	$-0.212925\pi$
$331$	−872.069	−	1510.47i	−0.144814	−	0.250824i	−0.929303	+	0.369317i	$0.879592\pi$
$332$	4140.18	+	7171.00i	0.684403	+	1.18542i
$333$	−2277.98			−0.374872
$334$	3069.43	+	5316.42i	0.502850	+	0.870962i
$335$	−5715.08	+	9898.81i	−0.932084	+	1.61442i
$336$	2756.25	−	4773.96i	0.447517	−	0.775122i
$337$	8805.54			1.42335			0.711674	−	0.702510i	$-0.247937\pi$
$337$	8805.54			1.42335			0.711674	+	0.702510i	$0.247937\pi$
$338$		0			0
$339$	7577.88			1.21408
$340$	2667.98	−	4621.08i	0.425564	−	0.737098i
$341$	1185.91	−	2054.06i	0.188330	−	0.326198i
$342$	−229.659	−	397.781i	−0.0363115	−	0.0628934i
$343$	6.15700			0.000969232
$344$	−5637.31	−	9764.11i	−0.883557	−	1.53037i
$345$	817.118	+	1415.29i	0.127513	+	0.220860i
$346$	−11445.2			−1.77832
$347$	971.576	+	1682.82i	0.150308	+	0.260342i	0.931341	−	0.364149i	$-0.118640\pi$
$347$	971.576	+	1682.82i	0.150308	+	0.260342i	−0.781033	+	0.624490i	$0.785307\pi$
$348$	4809.93	−	8331.04i	0.740917	−	1.28331i
$349$	−2658.46	+	4604.58i	−0.407748	+	0.706240i	−0.994637	−	0.103427i	$-0.967019\pi$
$349$	−2658.46	+	4604.58i	−0.407748	+	0.706240i	0.586889	+	0.809667i	$0.300352\pi$
$350$	4815.01			0.735352
$351$		0			0
$352$	−2230.15			−0.337692
$353$	2506.84	−	4341.97i	0.377976	−	0.654673i	−0.612792	−	0.790244i	$-0.709954\pi$
$353$	2506.84	−	4341.97i	0.377976	−	0.654673i	0.990768	+	0.135571i	$0.0432870\pi$
$354$	−2774.03	+	4804.76i	−0.416491	+	0.721384i
$355$	4734.72	+	8200.77i	0.707867	+	1.22606i
$356$	−5818.07			−0.866171
$357$	−1590.28	−	2754.44i	−0.235760	−	0.408349i
$358$	1754.53	+	3038.93i	0.259022	+	0.448639i
$359$	−8143.55			−1.19722			−0.598608	−	0.801042i	$-0.704279\pi$
$359$	−8143.55			−1.19722			−0.598608	+	0.801042i	$0.704279\pi$
$360$	−1628.85	−	2821.25i	−0.238467	−	0.413036i
$361$	3343.44	−	5791.00i	0.487453	−	0.844293i
$362$	9347.57	−	16190.5i	1.35718	−	2.35070i
$363$	2052.60			0.296787
$364$		0			0
$365$	−10480.6			−1.50296
$366$	6976.64	−	12083.9i	0.996380	−	1.72578i
$367$	−3258.92	+	5644.62i	−0.463527	+	0.802852i	−0.999134	−	0.0416152i	$-0.986750\pi$
$367$	−3258.92	+	5644.62i	−0.463527	+	0.802852i	0.535607	+	0.844468i	$0.320083\pi$
$368$	682.118	+	1181.46i	0.0966247	+	0.167359i
$369$	2556.52			0.360670
$370$	9675.06	+	16757.7i	1.35941	+	2.35457i
$371$	4575.69	+	7925.33i	0.640318	+	1.10906i
$372$	3804.70			0.530281
$373$	−3623.78	−	6276.58i	−0.503036	−	0.871284i	−0.999994	−	0.00350906i	$-0.998883\pi$
$373$	−3623.78	−	6276.58i	−0.503036	−	0.871284i	0.496958	−	0.867775i	$-0.334450\pi$
$374$	2792.46	−	4836.69i	0.386082	−	0.668714i
$375$	2465.65	−	4270.64i	0.339535	−	0.588093i
$376$	11930.8			1.63639
$377$		0			0
$378$	−19234.8			−2.61728
$379$	−3274.63	+	5671.82i	−0.443816	+	0.768712i	−0.997969	−	0.0637031i	$-0.979709\pi$
$379$	−3274.63	+	5671.82i	−0.443816	+	0.768712i	0.554153	+	0.832415i	$0.313042\pi$
$380$	−1280.61	+	2218.08i	−0.172878	+	0.299434i
$381$	−3317.48	−	5746.05i	−0.446089	−	0.772648i
$382$	−9669.31			−1.29509
$383$	4015.16	+	6954.47i	0.535679	+	0.927824i	0.999130	+	0.0417013i	$0.0132778\pi$
$383$	4015.16	+	6954.47i	0.535679	+	0.927824i	−0.463451	+	0.886123i	$0.653389\pi$
$384$	−5851.92	−	10135.8i	−0.777681	−	1.34698i
$385$	14161.2			1.87460
$386$	2476.11	+	4288.75i	0.326504	+	0.565522i
$387$	−1163.27	+	2014.85i	−0.152797	+	0.264653i
$388$	−10933.3	+	18937.0i	−1.43055	+	2.47779i
$389$	481.389			0.0627440			0.0313720	−	0.999508i	$-0.490012\pi$
$389$	481.389			0.0627440			0.0313720	+	0.999508i	$0.490012\pi$
$390$		0			0
$391$	787.126			0.101807
$392$	6025.62	−	10436.7i	0.776376	−	1.34472i
$393$	1020.04	−	1766.76i	0.130926	−	0.226771i
$394$	3156.37	+	5466.99i	0.403593	+	0.699044i
$395$	−2546.21			−0.324339
$396$	−2347.96	−	4066.78i	−0.297953	−	0.516069i
$397$	1401.04	+	2426.66i	0.177118	+	0.306778i	0.940892	−	0.338706i	$-0.109989\pi$
$397$	1401.04	+	2426.66i	0.177118	+	0.306778i	−0.763774	+	0.645484i	$0.776656\pi$
$398$	1375.86			0.173281
$399$	763.319	+	1322.11i	0.0957738	+	0.165885i
$400$	−902.539	+	1563.24i	−0.112817	+	0.195405i
$401$	−2188.39	+	3790.41i	−0.272527	+	0.472030i	−0.969508	−	0.245059i	$-0.921193\pi$
$401$	−2188.39	+	3790.41i	−0.272527	+	0.472030i	0.696981	+	0.717089i	$0.254526\pi$
$402$	−19190.9			−2.38098
$403$		0			0
$404$	−12247.1			−1.50820
$405$	3068.12	−	5314.13i	0.376434	−	0.652004i
$406$	8948.55	−	15499.3i	1.09387	−	1.89463i
$407$	6647.48	+	11513.8i	0.809590	+	1.40225i
$408$	4270.22			0.518156
$409$	−6484.49	−	11231.5i	−0.783954	−	1.35785i	−0.929622	−	0.368515i	$-0.879866\pi$
$409$	−6484.49	−	11231.5i	−0.783954	−	1.35785i	0.145668	−	0.989334i	$-0.453467\pi$
$410$	−10858.1	−	18806.7i	−1.30791	−	2.26536i
$411$	11122.4			1.33486
$412$	5700.18	+	9873.00i	0.681620	+	1.18060i
$413$	−3387.85	+	5867.93i	−0.403644	+	0.699133i
$414$	504.102	−	873.130i	0.0598436	−	0.103652i
$415$	−6918.10			−0.818304
$416$		0			0
$417$	8014.93			0.941229
$418$	−1340.36	+	2321.57i	−0.156840	+	0.271654i
$419$	−3839.52	+	6650.25i	−0.447668	+	0.775384i	−0.998234	−	0.0594078i	$-0.981079\pi$
$419$	−3839.52	+	6650.25i	−0.447668	+	0.775384i	0.550566	+	0.834792i	$0.314412\pi$
$420$	11358.2	+	19673.0i	1.31958	+	2.28558i
$421$	−2963.10			−0.343022			−0.171511	−	0.985182i	$-0.554865\pi$
$421$	−2963.10			−0.343022			−0.171511	+	0.985182i	$0.554865\pi$
$422$	−6789.33	−	11759.5i	−0.783174	−	1.35650i
$423$	−1230.97	−	2132.11i	−0.141494	−	0.245075i
$424$	−12286.7			−1.40730
$425$	520.740	+	901.948i	0.0594343	+	0.102943i
$426$	−7949.45	+	13768.9i	−0.904113	+	1.56597i
$427$	8520.39	−	14757.8i	0.965646	−	1.67255i
$428$	−2056.67			−0.232273
$429$		0			0
$430$	19762.7			2.21637
$431$	7101.31	−	12299.8i	0.793639	−	1.37462i	−0.130061	−	0.991506i	$-0.541517\pi$
$431$	7101.31	−	12299.8i	0.793639	−	1.37462i	0.923700	−	0.383116i	$-0.125149\pi$
$432$	3605.42	−	6244.78i	0.401542	−	0.695491i
$433$	−5059.09	−	8762.60i	−0.561488	−	0.972526i	−0.997367	−	0.0725204i	$-0.976896\pi$
$433$	−5059.09	−	8762.60i	−0.561488	−	0.972526i	0.435879	−	0.900005i	$-0.356438\pi$
$434$	7078.39			0.782889
$435$	4018.62	+	6960.45i	0.442938	+	0.767191i
$436$	2241.27	+	3881.99i	0.246186	+	0.426407i
$437$	−377.814			−0.0413576
$438$	−8798.30	−	15239.1i	−0.959815	−	1.66245i
$439$	8092.17	−	14016.0i	0.879768	−	1.52380i	0.0281722	−	0.999603i	$-0.491031\pi$
$439$	8092.17	−	14016.0i	0.879768	−	1.52380i	0.851596	−	0.524199i	$-0.175635\pi$
$440$	−9506.45	+	16465.7i	−1.03000	+	1.78402i
$441$	−2486.80			−0.268524
$442$		0			0
$443$	−10025.2			−1.07519			−0.537596	−	0.843203i	$-0.680667\pi$
$443$	−10025.2			−1.07519			−0.537596	+	0.843203i	$0.680667\pi$
$444$	−10663.4	+	18469.5i	−1.13978	+	1.97416i
$445$	2430.45	−	4209.66i	0.258909	−	0.448443i
$446$	−3642.97	−	6309.80i	−0.386770	−	0.669905i
$447$	−12999.2			−1.37549
$448$	−8290.08	−	14358.8i	−0.874262	−	1.51427i
$449$	−5214.14	−	9031.16i	−0.548041	−	0.949236i	−0.998409	−	0.0563922i	$-0.982040\pi$
$449$	−5214.14	−	9031.16i	−0.548041	−	0.949236i	0.450367	−	0.892843i	$-0.351293\pi$
$450$	1334.00			0.139745
$451$	−7460.30	−	12921.6i	−0.778918	−	1.34913i
$452$	−13034.2	+	22575.9i	−1.35636	+	2.34929i
$453$	−3930.92	+	6808.56i	−0.407706	+	0.706167i
$454$	−3103.42			−0.320816
$455$		0			0
$456$	−2049.67			−0.210492
$457$	−6131.91	+	10620.8i	−0.627656	+	1.08713i	0.360365	+	0.932811i	$0.382652\pi$
$457$	−6131.91	+	10620.8i	−0.627656	+	1.08713i	−0.988021	+	0.154320i	$0.950681\pi$
$458$	−371.590	+	643.613i	−0.0379110	+	0.0656639i
$459$	−2080.23	−	3603.06i	−0.211540	−	0.366398i
$460$	−5621.87			−0.569828
$461$	2023.99	+	3505.66i	0.204483	+	0.354175i	0.949968	−	0.312348i	$-0.101115\pi$
$461$	2023.99	+	3505.66i	0.204483	+	0.354175i	−0.745485	+	0.666523i	$0.767782\pi$
$462$	11888.1	+	20590.9i	1.19716	+	2.07354i
$463$	10473.9			1.05133			0.525663	−	0.850693i	$-0.323817\pi$
$463$	10473.9			1.05133			0.525663	+	0.850693i	$0.323817\pi$
$464$	3354.68	+	5810.48i	0.335641	+	0.581347i
$465$	−1589.38	+	2752.89i	−0.158507	+	0.274543i
$466$	−631.346	+	1093.52i	−0.0627608	+	0.108705i
$467$	4906.17			0.486146			0.243073	−	0.970008i	$-0.421845\pi$
$467$	4906.17			0.486146			0.243073	+	0.970008i	$0.421845\pi$
$468$		0			0
$469$	−23437.4			−2.30754
$470$	−10456.4	+	18111.0i	−1.02621	+	1.77744i
$471$	2571.10	−	4453.28i	0.251529	−	0.435661i
$472$	−4548.53	−	7878.29i	−0.443566	−	0.768279i
$473$	13578.4			1.31995
$474$	−2137.51	−	3702.27i	−0.207129	−	0.358757i
$475$	−249.950	−	432.927i	−0.0241442	−	0.0418190i
$476$	10941.3			1.05356
$477$	1267.69	+	2195.71i	0.121685	+	0.210764i
$478$	6020.09	−	10427.1i	0.576051	−	0.997750i
$479$	−624.709	+	1082.03i	−0.0595902	+	0.103213i	−0.894281	−	0.447505i	$-0.852313\pi$
$479$	−624.709	+	1082.03i	−0.0595902	+	0.103213i	0.834691	+	0.550718i	$0.185646\pi$
$480$	2988.90			0.284216
$481$		0			0
$482$	18509.4			1.74913
$483$	−1675.49	+	2902.03i	−0.157841	+	0.273389i
$484$	−3530.54	+	6115.07i	−0.331568	+	0.574293i
$485$	−9134.59	−	15821.6i	−0.855218	−	1.48128i
$486$	−9529.32			−0.889421
$487$	9645.12	+	16705.8i	0.897458	+	1.55444i	0.830733	+	0.556672i	$0.187922\pi$
$487$	9645.12	+	16705.8i	0.897458	+	1.55444i	0.0667254	+	0.997771i	$0.478745\pi$
$488$	11439.5	+	19813.8i	1.06115	+	1.83797i
$489$	−12927.1			−1.19547
$490$	10562.0	+	18293.9i	0.973757	+	1.68660i
$491$	4190.58	−	7258.30i	0.385170	−	0.667134i	−0.606623	−	0.794990i	$-0.707476\pi$
$491$	4190.58	−	7258.30i	0.385170	−	0.667134i	0.991793	+	0.127856i	$0.0408096\pi$
$492$	11967.3	−	20727.9i	1.09660	−	1.89936i
$493$	3871.12			0.353644
$494$		0			0
$495$	3923.36			0.356246
$496$	−1326.79	+	2298.07i	−0.120110	+	0.208037i
$497$	−9708.46	+	16815.5i	−0.876225	+	1.51767i
$498$	−5807.65	−	10059.1i	−0.522584	−	0.905142i
$499$	−199.025			−0.0178549			−0.00892743	−	0.999960i	$-0.502842\pi$
$499$	−199.025			−0.0178549			−0.00892743	+	0.999960i	$0.502842\pi$
$500$	8481.99	+	14691.2i	0.758653	+	1.31402i
$501$	−2826.43	−	4895.52i	−0.252047	−	0.436558i
$502$	19194.1			1.70652
$503$	3783.95	+	6554.00i	0.335424	+	0.580971i	0.983566	−	0.180548i	$-0.0577872\pi$
$503$	3783.95	+	6554.00i	0.335424	+	0.580971i	−0.648142	+	0.761519i	$0.724454\pi$
$504$	3339.93	−	5784.93i	0.295183	−	0.511273i
$505$	5116.11	−	8861.36i	0.450820	−	0.780842i
$506$	−5884.17			−0.516963
$507$		0			0
$508$	22824.7			1.99347
$509$	2999.11	−	5194.61i	0.261166	−	0.452352i	−0.705386	−	0.708823i	$-0.749226\pi$
$509$	2999.11	−	5194.61i	0.261166	−	0.452352i	0.966552	+	0.256471i	$0.0825598\pi$
$510$	−3742.52	+	6482.24i	−0.324944	+	0.562820i
$511$	−10745.1	−	18611.1i	−0.930209	−	1.61117i
$512$	15819.8			1.36552
$513$	998.491	+	1729.44i	0.0859346	+	0.148843i
$514$	−293.119	−	507.697i	−0.0251536	−	0.0435672i
$515$	−9524.81			−0.814977
$516$	10890.7	+	18863.3i	0.929144	+	1.60932i
$517$	−7184.32	+	12443.6i	−0.611153	+	1.05855i
$518$	−19838.5	+	34361.4i	−1.68273	+	2.91458i
$519$	10539.1			0.891362
$520$		0			0
$521$	−2863.99			−0.240833			−0.120416	−	0.992723i	$-0.538423\pi$
$521$	−2863.99			−0.240833			−0.120416	+	0.992723i	$0.538423\pi$
$522$	2479.19	−	4294.09i	0.207876	−	0.360052i
$523$	1264.54	−	2190.25i	0.105726	−	0.183123i	−0.808309	−	0.588759i	$-0.799617\pi$
$523$	1264.54	−	2190.25i	0.105726	−	0.183123i	0.914035	+	0.405636i	$0.132950\pi$
$524$	3508.99	+	6077.74i	0.292540	+	0.506694i
$525$	−4433.81			−0.368585
$526$	2836.02	+	4912.12i	0.235088	+	0.407184i
$527$	765.523	+	1325.92i	0.0632765	+	0.109598i
$528$	−8913.38			−0.734669
$529$	5668.85	+	9818.74i	0.465920	+	0.806997i
$530$	10768.3	−	18651.3i	0.882539	−	1.52860i
$531$	−938.602	+	1625.71i	−0.0767078	+	0.132862i
$532$	−5251.73			−0.427991
$533$		0			0
$534$	8161.31			0.661375
$535$	859.156	−	1488.10i	0.0694291	−	0.120255i
$536$	15733.5	−	27251.3i	1.26788	−	2.19604i
$537$	−1615.63	−	2798.35i	−0.129831	−	0.224874i
$538$	40147.0			3.21721
$539$	7256.85	+	12569.2i	0.579916	+	1.00444i
$540$	14857.6	+	25734.0i	1.18401	+	2.05077i
$541$	−22053.6			−1.75260			−0.876302	−	0.481762i	$-0.839997\pi$
$541$	−22053.6			−1.75260			−0.876302	+	0.481762i	$0.839997\pi$
$542$	−9478.74	−	16417.7i	−0.751193	−	1.30110i
$543$	−8607.53	+	14908.7i	−0.680266	+	1.17826i
$544$	719.798	−	1246.73i	0.0567299	−	0.0982591i
$545$	−3745.08			−0.294352
$546$		0			0
$547$	−2821.80			−0.220569			−0.110285	−	0.993900i	$-0.535176\pi$
$547$	−2821.80			−0.220569			−0.110285	+	0.993900i	$0.535176\pi$
$548$	−19130.9	+	33135.7i	−1.49130	+	2.58300i
$549$	2360.57	−	4088.63i	0.183509	−	0.317848i
$550$	−3892.79	−	6742.52i	−0.301799	−	0.522731i
$551$	−1858.10			−0.143662
$552$	−2249.51	−	3896.27i	−0.173452	−	0.300428i
$553$	−2610.48	−	4521.49i	−0.200740	−	0.347691i
$554$	29062.4			2.22878
$555$	−8909.09	−	15431.0i	−0.681387	−	1.18020i
$556$	−13785.9	+	23877.9i	−1.05153	+	1.82131i
$557$	918.583	−	1591.03i	0.0698772	−	0.121031i	−0.828970	−	0.559293i	$-0.811073\pi$
$557$	918.583	−	1591.03i	0.0698772	−	0.121031i	0.898847	+	0.438262i	$0.144406\pi$
$558$	1961.07			0.148779
$559$		0			0
$560$	−15843.6			−1.19556
$561$	−2571.39	+	4453.77i	−0.193519	+	0.335184i
$562$	5268.81	−	9125.85i	0.395465	−	0.684966i
$563$	12438.9	+	21544.9i	0.931152	+	1.61280i	0.781356	+	0.624086i	$0.214528\pi$
$563$	12438.9	+	21544.9i	0.931152	+	1.61280i	0.149796	+	0.988717i	$0.452138\pi$
$564$	−23049.1			−1.72082
$565$	−10889.9	−	18861.8i	−0.810867	−	1.40446i
$566$	−19623.7	−	33989.3i	−1.45733	−	2.52416i
$567$	12582.2			0.931931
$568$	−13034.6	−	22576.6i	−0.962887	−	1.66777i
$569$	3555.86	−	6158.93i	0.261985	−	0.453771i	−0.704785	−	0.709421i	$-0.748956\pi$
$569$	3555.86	−	6158.93i	0.261985	−	0.453771i	0.966769	+	0.255651i	$0.0822897\pi$
$570$	1796.38	−	3111.41i	0.132003	−	0.228636i
$571$	−11919.4			−0.873578			−0.436789	−	0.899564i	$-0.643884\pi$
$571$	−11919.4			−0.873578			−0.436789	+	0.899564i	$0.643884\pi$
$572$		0			0
$573$	8903.80			0.649148
$574$	22264.3	−	38562.9i	1.61898	−	2.80416i
$575$	548.641	−	950.274i	0.0397912	−	0.0689203i
$576$	−2296.76	−	3978.11i	−0.166143	−	0.287768i
$577$	−11600.6			−0.836984			−0.418492	−	0.908220i	$-0.637441\pi$
$577$	−11600.6			−0.836984			−0.418492	+	0.908220i	$0.637441\pi$
$578$	−10051.4	−	17409.5i	−0.723327	−	1.25284i
$579$	−2280.08	−	3949.21i	−0.163656	−	0.283461i
$580$	−27648.6			−1.97939
$581$	−7092.73	−	12285.0i	−0.506465	−	0.877222i
$582$	15336.7	−	26564.0i	1.09232	−	1.89195i
$583$	7398.62	−	12814.8i	0.525591	−	0.910350i
$584$	28852.9			2.04442
$585$		0			0
$586$	−15357.6			−1.08262
$587$	−5170.84	+	8956.16i	−0.363583	+	0.629745i	−0.988548	−	0.150908i	$-0.951780\pi$
$587$	−5170.84	+	8956.16i	−0.363583	+	0.629745i	0.624964	+	0.780653i	$0.285114\pi$
$588$	−11640.9	+	20162.6i	−0.816433	+	1.41410i
$589$	−367.444	−	636.432i	−0.0257050	−	0.0445224i
$590$	15945.8			1.11267
$591$	−2906.48	−	5034.18i	−0.202296	−	0.350387i
$592$	−7437.18	−	12881.6i	−0.516328	−	0.894307i
$593$	2782.21			0.192668			0.0963338	−	0.995349i	$-0.469288\pi$
$593$	2782.21			0.192668			0.0963338	+	0.995349i	$0.469288\pi$
$594$	15550.8	+	26934.7i	1.07417	+	1.86051i
$595$	−4570.64	+	7916.59i	−0.314921	+	0.545460i
$596$	22359.1	−	38727.1i	1.53668	−	2.66161i
$597$	−1266.94			−0.0868547
$598$		0			0
$599$	10560.6			0.720359			0.360179	−	0.932883i	$-0.382715\pi$
$599$	10560.6			0.720359			0.360179	+	0.932883i	$0.382715\pi$
$600$	2976.42	−	5155.31i	0.202520	−	0.350775i
$601$	−1923.43	+	3331.47i	−0.130546	+	0.226112i	−0.923887	−	0.382665i	$-0.875006\pi$
$601$	−1923.43	+	3331.47i	−0.130546	+	0.226112i	0.793341	+	0.608777i	$0.208340\pi$
$602$	20261.5	+	35094.0i	1.37176	+	2.37595i
$603$	−6493.31			−0.438520
$604$	−13522.6	−	23421.8i	−0.910972	−	1.57785i
$605$	−2949.71	−	5109.05i	−0.198219	−	0.343326i
$606$	17179.6			1.15161
$607$	−3247.75	−	5625.27i	−0.217170	−	0.376149i	0.736772	−	0.676142i	$-0.236349\pi$
$607$	−3247.75	−	5625.27i	−0.217170	−	0.376149i	−0.953942	+	0.299992i	$0.903016\pi$
$608$	−345.496	+	598.417i	−0.0230456	+	0.0399162i
$609$	−8240.11	+	14272.3i	−0.548286	+	0.949659i
$610$	−40103.4			−2.66186
$611$		0			0
$612$	3031.28			0.200216
$613$	−1766.30	+	3059.33i	−0.116379	+	0.201574i	−0.918330	−	0.395815i	$-0.870462\pi$
$613$	−1766.30	+	3059.33i	−0.116379	+	0.201574i	0.801951	+	0.597390i	$0.203795\pi$
$614$	−2968.23	+	5141.13i	−0.195094	+	0.337914i
$615$	9998.46	+	17317.8i	0.655572	+	1.13548i
$616$	−38985.6			−2.54996
$617$	8148.97	+	14114.4i	0.531710	+	0.920949i	0.999315	+	0.0370116i	$0.0117838\pi$
$617$	8148.97	+	14114.4i	0.531710	+	0.920949i	−0.467604	+	0.883938i	$0.654883\pi$
$618$	−7995.94	−	13849.4i	−0.520459	−	0.901462i
$619$	9123.86			0.592438			0.296219	−	0.955120i	$-0.404274\pi$
$619$	9123.86			0.592438			0.296219	+	0.955120i	$0.404274\pi$
$620$	−5467.57	−	9470.11i	−0.354166	−	0.613434i
$621$	−2191.69	+	3796.12i	−0.141626	+	0.245303i
$622$	−14190.7	+	24579.0i	−0.914785	+	1.58445i
$623$	9967.20			0.640975
$624$		0			0
$625$	−18936.0			−1.21191
$626$	16407.5	−	28418.6i	1.04756	−	1.81443i
$627$	1234.24	−	2137.77i	0.0786139	−	0.136163i
$628$	8844.75	+	15319.6i	0.562012	+	0.973434i
$629$	−8582.09			−0.544023
$630$	5854.38	+	10140.1i	0.370229	+	0.641255i
$631$	11625.4	+	20135.8i	0.733438	+	1.27035i	0.955405	+	0.295298i	$0.0954189\pi$
$631$	11625.4	+	20135.8i	0.733438	+	1.27035i	−0.221967	+	0.975054i	$0.571248\pi$
$632$	7009.68			0.441187
$633$	6251.83	+	10828.5i	0.392556	+	0.679927i
$634$	−5338.27	+	9246.16i	−0.334400	+	0.579198i
$635$	−9534.83	+	16514.8i	−0.595871	+	1.03208i
$636$	23736.6			1.47990
$637$		0			0
$638$	−28938.6			−1.79575
$639$	−2689.72	+	4658.74i	−0.166516	+	0.288414i
$640$	−16819.1	+	29131.5i	−1.03880	+	1.79926i
$641$	3739.22	+	6476.52i	0.230406	+	0.399075i	0.957928	−	0.287010i	$-0.0926612\pi$
$641$	3739.22	+	6476.52i	0.230406	+	0.399075i	−0.727522	+	0.686085i	$0.759328\pi$
$642$	2885.00			0.177355
$643$	4163.99	+	7212.24i	0.255384	+	0.442338i	0.965000	−	0.262251i	$-0.0844648\pi$
$643$	4163.99	+	7212.24i	0.255384	+	0.442338i	−0.709616	+	0.704589i	$0.751132\pi$
$644$	−5763.77	−	9983.15i	−0.352678	−	0.610856i
$645$	−18198.1			−1.11093
$646$	−865.221	−	1498.61i	−0.0526961	−	0.0912723i
$647$	−3139.37	+	5437.55i	−0.190760	+	0.330405i	−0.945502	−	0.325616i	$-0.894428\pi$
$647$	−3139.37	+	5437.55i	−0.190760	+	0.330405i	0.754743	+	0.656021i	$0.227762\pi$
$648$	−8446.48	+	14629.7i	−0.512051	+	0.886898i
$649$	10955.9			0.662645
$650$		0			0
$651$	−6518.01			−0.392413
$652$	22235.0	−	38512.2i	1.33557	−	2.31327i
$653$	13581.7	−	23524.3i	0.813928	−	1.40976i	−0.0961676	−	0.995365i	$-0.530658\pi$
$653$	13581.7	−	23524.3i	0.813928	−	1.40976i	0.910095	−	0.414399i	$-0.136008\pi$
$654$	−3143.94	−	5445.47i	−0.187978	−	0.325588i
$655$	−5863.41			−0.349774
$656$	8346.57	+	14456.7i	0.496766	+	0.860425i
$657$	−2976.93	−	5156.20i	−0.176775	−	0.306184i
$658$	−42881.4			−2.54056
$659$	5175.99	+	8965.09i	0.305961	+	0.529940i	0.977475	−	0.211052i	$-0.0676890\pi$
$659$	5175.99	+	8965.09i	0.305961	+	0.529940i	−0.671514	+	0.740992i	$0.734356\pi$
$660$	18365.5	−	31810.0i	1.08315	−	1.87607i
$661$	3135.23	−	5430.37i	0.184487	−	0.319542i	−0.758916	−	0.651188i	$-0.774271\pi$
$661$	3135.23	−	5430.37i	0.184487	−	0.319542i	0.943404	+	0.331647i	$0.107604\pi$
$662$	−8416.44			−0.494130
$663$		0			0
$664$	19045.4			1.11311
$665$	2193.87	−	3799.89i	0.127932	−	0.221584i
$666$	−5496.26	+	9519.80i	−0.319783	+	0.553881i
$667$	−2039.27	−	3532.11i	−0.118382	−	0.205043i
$668$	19446.2			1.12634
$669$	3354.56	+	5810.26i	0.193863	+	0.335781i
$670$	27578.4	+	47767.2i	1.59022	+	2.75434i
$671$	−27554.0			−1.58526
$672$	3064.34	+	5307.59i	0.175907	+	0.304680i
$673$	15150.9	−	26242.2i	0.867794	−	1.50306i	0.00354882	−	0.999994i	$-0.498870\pi$
$673$	15150.9	−	26242.2i	0.867794	−	1.50306i	0.864246	−	0.503070i	$-0.167796\pi$
$674$	21245.8	−	36798.8i	1.21418	−	2.10302i
$675$	−5799.83			−0.330719
$676$		0			0
$677$	−10223.3			−0.580375			−0.290188	−	0.956970i	$-0.593718\pi$
$677$	−10223.3			−0.580375			−0.290188	+	0.956970i	$0.593718\pi$
$678$	18283.7	−	31668.4i	1.03567	−	1.79383i
$679$	18730.3	−	32441.9i	1.05862	−	1.83359i
$680$	−6136.56	−	10628.8i	−0.346068	−	0.599407i
$681$	2857.72			0.160805
$682$	−5722.67	−	9911.96i	−0.321309	−	0.556523i
$683$	8488.99	+	14703.4i	0.475582	+	0.823732i	0.999609	−	0.0279701i	$-0.00890431\pi$
$683$	8488.99	+	14703.4i	0.475582	+	0.823732i	−0.524027	+	0.851702i	$0.675571\pi$
$684$	−1454.99			−0.0813346
$685$	−15983.5	−	27684.3i	−0.891533	−	1.54418i
$686$	14.8555	−	25.7304i	0.000826799	−	0.00143206i
$687$	342.172	−	592.659i	0.0190024	−	0.0329132i
$688$	−15191.5			−0.841818
$689$		0			0
$690$	7886.09			0.435099
$691$	3967.67	−	6872.20i	0.218433	−	0.378337i	−0.735896	−	0.677094i	$-0.763239\pi$
$691$	3967.67	−	6872.20i	0.218433	−	0.378337i	0.954329	+	0.298758i	$0.0965722\pi$
$692$	−18127.6	+	31398.0i	−0.995823	+	1.72482i
$693$	4022.39	+	6966.99i	0.220488	+	0.381896i
$694$	9376.79			0.512879
$695$	−11517.9	−	19949.6i	−0.628632	−	1.08882i
$696$	−11063.2	−	19162.0i	−0.602513	−	1.04358i
$697$	9631.48			0.523412
$698$	12828.5	+	22219.7i	0.695655	+	1.20491i
$699$	581.363	−	1006.95i	0.0314580	−	0.0544869i
$700$	7626.29	−	13209.1i	0.411781	−	0.713225i
$701$	18557.3			0.999857			0.499928	−	0.866067i	$-0.333360\pi$
$701$	18557.3			0.999857			0.499928	+	0.866067i	$0.333360\pi$
$702$		0			0
$703$	4119.33			0.221001
$704$	−13404.6	+	23217.4i	−0.717619	+	1.24295i
$705$	9628.58	−	16677.2i	0.514374	−	0.890921i
$706$	−12096.9	−	20952.4i	−0.644861	−	1.11693i
$707$	20981.0			1.11608
$708$	8787.33	+	15220.1i	0.466452	+	0.807918i
$709$	7081.86	+	12266.1i	0.375127	+	0.649738i	0.990346	−	0.138618i	$-0.0442659\pi$
$709$	7081.86	+	12266.1i	0.375127	+	0.649738i	−0.615219	+	0.788356i	$0.710933\pi$
$710$	45695.3			2.41537
$711$	−723.233	−	1252.68i	−0.0381482	−	0.0660746i
$712$	−6690.99	+	11589.1i	−0.352185	+	0.610002i
$713$	806.540	−	1396.97i	0.0423635	−	0.0733757i
$714$	−15348.0			−0.804458
$715$		0			0
$716$	11115.7			0.580186
$717$	−5543.49	+	9601.60i	−0.288738	+	0.500109i
$718$	−19648.6	+	34032.3i	−1.02128	+	1.76891i
$719$	−12418.3	−	21509.2i	−0.644125	−	1.11566i	−0.984503	−	0.175368i	$-0.943888\pi$
$719$	−12418.3	−	21509.2i	−0.644125	−	1.11566i	0.340378	−	0.940289i	$-0.389445\pi$
$720$	−4389.45			−0.227201
$721$	−9765.24	−	16913.9i	−0.504406	−	0.873656i
$722$	−16133.9	−	27944.8i	−0.831639	−	1.44044i
$723$	−17044.0			−0.876726
$724$	−29610.4	−	51286.8i	−1.51998	−	2.63268i
$725$	2698.24	−	4673.49i	0.138221	−	0.239405i
$726$	4952.48	−	8577.94i	0.253173	−	0.438509i
$727$	−10641.0			−0.542852			−0.271426	−	0.962459i	$-0.587495\pi$
$727$	−10641.0			−0.542852			−0.271426	+	0.962459i	$0.587495\pi$
$728$		0			0
$729$	21747.7			1.10490
$730$	−25287.3	+	43798.9i	−1.28209	+	2.22065i
$731$	−4382.54	+	7590.78i	−0.221743	+	0.384070i
$732$	−22100.0	−	38278.3i	−1.11590	−	1.93280i
$733$	22429.1			1.13020			0.565102	−	0.825021i	$-0.308837\pi$
$733$	22429.1			1.13020			0.565102	+	0.825021i	$0.308837\pi$
$734$	15726.1	+	27238.4i	0.790819	+	1.36974i
$735$	−9725.79	−	16845.6i	−0.488083	−	0.845385i
$736$	−1516.73			−0.0759612
$737$	18948.4	+	32819.6i	0.947047	+	1.64033i
$738$	6168.32	−	10683.8i	0.307668	−	0.532896i
$739$	−16712.9	+	28947.6i	−0.831928	+	1.44094i	0.0645796	+	0.997913i	$0.479429\pi$
$739$	−16712.9	+	28947.6i	−0.831928	+	1.44094i	−0.896507	+	0.443029i	$0.853904\pi$
$740$	61295.6			3.04496
$741$		0			0
$742$	44160.5			2.18488
$743$	−6568.14	+	11376.4i	−0.324309	+	0.561720i	−0.981372	−	0.192115i	$-0.938465\pi$
$743$	−6568.14	+	11376.4i	−0.324309	+	0.561720i	0.657063	+	0.753836i	$0.271799\pi$
$744$	4375.55	−	7578.67i	0.215612	−	0.373451i
$745$	18680.7	+	32355.8i	0.918666	+	1.59118i
$746$	−34973.5			−1.71645
$747$	−1965.04	−	3403.54i	−0.0962476	−	0.166706i
$748$	−8845.73	−	15321.2i	−0.432395	−	0.748931i
$749$	3523.37			0.171884
$750$	−11898.1	−	20608.2i	−0.579278	−	1.00334i
$751$	−10344.1	+	17916.5i	−0.502612	+	0.870549i	0.497384	+	0.867531i	$0.334294\pi$
$751$	−10344.1	+	17916.5i	−0.502612	+	0.870549i	−0.999995	+	0.00301848i	$0.999039\pi$
$752$	8037.80	−	13921.9i	0.389772	−	0.675105i
$753$	−17674.5			−0.855371
$754$		0			0
$755$	22595.8			1.08920
$756$	−30465.2	+	52767.2i	−1.46562	+	2.53853i
$757$	3072.92	−	5322.46i	0.147539	−	0.255546i	−0.782778	−	0.622301i	$-0.786198\pi$
$757$	3072.92	−	5322.46i	0.147539	−	0.255546i	0.930317	+	0.366755i	$0.119531\pi$
$758$	15801.9	+	27369.7i	0.757191	+	1.31149i
$759$	5418.33			0.259121
$760$	2945.49	+	5101.74i	0.140584	+	0.243499i
$761$	8244.25	+	14279.5i	0.392712	+	0.680197i	0.992806	−	0.119732i	$-0.0382036\pi$
$761$	8244.25	+	14279.5i	0.392712	+	0.680197i	−0.600094	+	0.799929i	$0.704870\pi$
$762$	−32017.4			−1.52214
$763$	−3839.61	−	6650.41i	−0.182180	−	0.315545i
$764$	−15314.8	+	26526.0i	−0.725223	+	1.25612i
$765$	−1266.29	+	2193.29i	−0.0598470	+	0.103658i
$766$	38750.8			1.82784
$767$		0			0
$768$	−33970.5			−1.59610
$769$	3900.85	−	6756.48i	0.182924	−	0.316833i	−0.759951	−	0.649980i	$-0.774777\pi$
$769$	3900.85	−	6756.48i	0.182924	−	0.316833i	0.942875	+	0.333147i	$0.108111\pi$
$770$	34167.9	−	59180.5i	1.59912	−	2.76976i
$771$	269.913	+	467.503i	0.0126079	+	0.0218375i
$772$	15687.2			0.731341
$773$	13650.6	+	23643.6i	0.635161	+	1.10013i	0.986481	+	0.163875i	$0.0523995\pi$
$773$	13650.6	+	23643.6i	0.635161	+	1.10013i	−0.351320	+	0.936255i	$0.614267\pi$
$774$	5613.44	+	9722.77i	0.260686	+	0.451522i
$775$	2134.33			0.0989258
$776$	25147.4	+	43556.6i	1.16332	+	2.01494i
$777$	18267.9	−	31641.0i	0.843448	−	1.46089i
$778$	1161.49	−	2011.75i	0.0535235	−	0.0927054i
$779$	−4623.02			−0.212628
$780$		0			0
$781$	31396.0			1.43846
$782$	1899.16	−	3289.44i	0.0868464	−	0.150422i
$783$	−10778.8	+	18669.4i	−0.491958	+	0.852096i
$784$	−8118.95	−	14062.4i	−0.369850	−	0.640599i
$785$	−14779.3			−0.671969
$786$	−4922.24	−	8525.58i	−0.223372	−	0.386892i
$787$	−13008.0	−	22530.5i	−0.589181	−	1.02049i	−0.994340	−	0.106246i	$-0.966117\pi$
$787$	−13008.0	−	22530.5i	−0.589181	−	1.02049i	0.405159	−	0.914246i	$-0.367216\pi$
$788$	19997.0			0.904013
$789$	−2611.49	−	4523.24i	−0.117835	−	0.204096i
$790$	−6143.45	+	10640.8i	−0.276676	+	0.479217i
$791$	22329.5	−	38675.8i	1.00372	−	1.73850i
$792$	−10800.9			−0.484590
$793$		0			0
$794$	13521.5			0.604360
$795$	−9915.79	+	17174.7i	−0.442361	+	0.766192i
$796$	2179.17	−	3774.43i	0.0970334	−	0.168067i
$797$	−4089.08	−	7082.50i	−0.181735	−	0.314774i	0.760737	−	0.649061i	$-0.224838\pi$
$797$	−4089.08	−	7082.50i	−0.181735	−	0.314774i	−0.942471	+	0.334287i	$0.891505\pi$
$798$	7366.88			0.326798
$799$	−4637.59	−	8032.54i	−0.205339	−	0.355658i
$800$	−1003.42	−	1737.98i	−0.0443455	−	0.0768087i
$801$	2761.41			0.121810
$802$	10560.2	+	18290.8i	0.464955	+	0.805326i
$803$	−17374.3	+	30093.1i	−0.763542	+	1.32249i
$804$	−30395.6	+	52646.8i	−1.33330	+	2.30934i
$805$	9631.08			0.421678
$806$		0			0
$807$	−36968.6			−1.61258
$808$	−14084.6	+	24395.2i	−0.613234	+	1.06215i
$809$	−8081.00	+	13996.7i	−0.351190	+	0.608279i	−0.986458	−	0.164013i	$-0.947556\pi$
$809$	−8081.00	+	13996.7i	−0.351190	+	0.608279i	0.635268	+	0.772292i	$0.280890\pi$
$810$	−14805.4	−	25643.6i	−0.642232	−	1.11238i
$811$	24714.6			1.07009			0.535046	−	0.844823i	$-0.320294\pi$
$811$	24714.6			1.07009			0.535046	+	0.844823i	$0.320294\pi$
$812$	−28346.5	−	49097.5i	−1.22508	−	2.12190i
$813$	8728.32	+	15117.9i	0.376526	+	0.652162i
$814$	64155.5			2.76247
$815$	18577.0	+	32176.3i	0.798435	+	1.38293i
$816$	2876.86	−	4982.87i	0.123420	−	0.213769i
$817$	2103.58	−	3643.50i	0.0900794	−	0.156022i
$818$	−62582.5			−2.67499
$819$		0			0
$820$	−68790.6			−2.92960
$821$	14282.6	−	24738.3i	0.607147	−	1.05161i	−0.384561	−	0.923100i	$-0.625647\pi$
$821$	14282.6	−	24738.3i	0.607147	−	1.05161i	0.991708	−	0.128510i	$-0.0410195\pi$
$822$	26835.9	−	46481.1i	1.13870	−	1.97228i
$823$	−4638.01	−	8033.26i	−0.196441	−	0.340245i	0.750931	−	0.660380i	$-0.229605\pi$
$823$	−4638.01	−	8033.26i	−0.196441	−	0.340245i	−0.947372	+	0.320135i	$0.896272\pi$
$824$	26221.7			1.10859
$825$	3584.61	+	6208.72i	0.151273	+	0.262012i
$826$	16348.2	+	28316.0i	0.688654	+	1.19278i
$827$	−36.2767			−0.00152535			−0.000762676	−	1.00000i	$-0.500243\pi$
$827$	−36.2767			−0.00152535			−0.000762676		1.00000i	$0.500243\pi$
$828$	−1596.85	−	2765.83i	−0.0670222	−	0.116086i
$829$	−8382.21	+	14518.4i	−0.351177	+	0.608257i	−0.986456	−	0.164026i	$-0.947552\pi$
$829$	−8382.21	+	14518.4i	−0.351177	+	0.608257i	0.635279	+	0.772283i	$0.280885\pi$
$830$	−16691.8	+	28911.1i	−0.698051	+	1.20906i
$831$	−26761.6			−1.11715
$832$		0			0
$833$	−9368.82			−0.389688
$834$	19338.2	−	33494.8i	0.802912	−	1.39068i
$835$	−8123.49	+	14070.3i	−0.336676	+	0.583141i
$836$	4245.87	+	7354.06i	0.175654	+	0.304241i
$837$	−8526.14			−0.352099
$838$	18527.8	+	32091.1i	0.763763	+	1.32288i
$839$	22658.3	+	39245.4i	0.932363	+	1.61490i	0.779271	+	0.626687i	$0.215590\pi$
$839$	22658.3	+	39245.4i	0.932363	+	1.61490i	0.153092	+	0.988212i	$0.451077\pi$
$840$	52249.4			2.14616
$841$	2165.31	+	3750.42i	0.0887821	+	0.153775i
$842$	−7149.29	+	12382.9i	−0.292614	+	0.506822i
$843$	−4851.69	+	8403.37i	−0.198222	+	0.343330i
$844$	−43013.3			−1.75424
$845$		0			0
$846$	−11880.3			−0.482803
$847$	6048.33	−	10476.0i	0.245364	−	0.424982i
$848$	−8277.56	+	14337.2i	−0.335204	+	0.580590i
$849$	18070.1	+	31298.4i	0.730465	+	1.26520i
$850$	5025.72			0.202801
$851$	4520.96	+	7830.54i	0.182111	+	0.315426i
$852$	25181.6	+	43615.8i	1.01257	+	1.75382i
$853$	−17557.7			−0.704766			−0.352383	−	0.935856i	$-0.614629\pi$
$853$	−17557.7			−0.704766			−0.352383	+	0.935856i	$0.614629\pi$
$854$	−41115.6	−	71214.4i	−1.64748	−	2.85352i
$855$	607.810	−	1052.76i	0.0243119	−	0.0421094i
$856$	−2365.24	+	4096.72i	−0.0944420	+	0.163578i
$857$	37943.6			1.51240			0.756201	−	0.654339i	$-0.227053\pi$
$857$	37943.6			1.51240			0.756201	+	0.654339i	$0.227053\pi$
$858$		0			0
$859$	−12833.2			−0.509735			−0.254867	−	0.966976i	$-0.582032\pi$
$859$	−12833.2			−0.509735			−0.254867	+	0.966976i	$0.582032\pi$
$860$	31301.3	−	54215.4i	1.24112	−	2.14968i
$861$	−20501.7	+	35509.9i	−0.811493	+	1.40555i
$862$	−34267.8	−	59353.5i	−1.35402	−	2.34523i
$863$	−24264.0			−0.957076			−0.478538	−	0.878067i	$-0.658833\pi$
$863$	−24264.0			−0.957076			−0.478538	+	0.878067i	$0.658833\pi$
$864$	4008.44	+	6942.82i	0.157835	+	0.273379i
$865$	−15145.3	−	26232.5i	−0.595326	−	1.03114i
$866$	−48825.8			−1.91590
$867$	9255.64	+	16031.2i	0.362558	+	0.627969i
$868$	11211.2	−	19418.3i	0.438401	−	0.759332i
$869$	−4221.00	+	7310.99i	−0.164773	+	0.285395i
$870$	38784.1			1.51138
$871$		0			0
$872$	10310.2			0.400397
$873$	5189.23	−	8988.01i	0.201178	−	0.348451i
$874$	−911.580	+	1578.90i	−0.0352799	+	0.0611066i
$875$	−14530.9	−	25168.2i	−0.561410	−	0.972391i
$876$	−55741.0			−2.14990
$877$	2049.34	+	3549.56i	0.0789069	+	0.136671i	0.902779	−	0.430106i	$-0.141524\pi$
$877$	2049.34	+	3549.56i	0.0789069	+	0.136671i	−0.823872	+	0.566776i	$0.808190\pi$
$878$	−39049.2	−	67635.2i	−1.50096	−	2.59975i
$879$	14141.7			0.542649
$880$	12809.0	+	22185.9i	0.490674	+	0.849872i
$881$	−23382.0	+	40498.8i	−0.894164	+	1.54874i	−0.0593281	+	0.998239i	$0.518896\pi$
$881$	−23382.0	+	40498.8i	−0.894164	+	1.54874i	−0.834836	+	0.550499i	$0.814438\pi$
$882$	−6000.10	+	10392.5i	−0.229063	+	0.396749i
$883$	−27183.9			−1.03603			−0.518013	−	0.855373i	$-0.673328\pi$
$883$	−27183.9			−1.03603			−0.518013	+	0.855373i	$0.673328\pi$
$884$		0			0
$885$	−14683.3			−0.557712
$886$	−24188.5	+	41895.7i	−0.917188	+	1.58862i
$887$	10591.0	−	18344.1i	0.400914	−	0.694403i	−0.592923	−	0.805259i	$-0.702026\pi$
$887$	10591.0	−	18344.1i	0.400914	−	0.694403i	0.993836	+	0.110856i	$0.0353594\pi$
$888$	24526.6	+	42481.3i	0.926868	+	1.60538i
$889$	−39102.0			−1.47518
$890$	−11728.3	−	20314.0i	−0.441722	−	0.765085i
$891$	−10172.4	−	17619.1i	−0.382478	−	0.662471i
$892$	−23079.7			−0.866331
$893$	2226.00	+	3855.54i	0.0834157	+	0.144480i
$894$	−31364.3	+	54324.5i	−1.17335	+	2.03231i
$895$	−4643.49	+	8042.77i	−0.173424	+	0.300380i
$896$	−68974.5			−2.57174
$897$		0			0
$898$	−50322.3			−1.87002
$899$	3966.60	−	6870.34i	0.147156	−	0.254882i
$900$	2112.86	−	3659.58i	0.0782540	−	0.135540i
$901$	4775.92	+	8272.14i	0.176592	+	0.305866i
$902$	−72000.2			−2.65781
$903$	−18657.4	−	32315.6i	−0.687575	−	1.19092i
$904$	29979.6	+	51926.2i	1.10299	+	1.91044i
$905$	49478.1			1.81736
$906$	18968.9	+	32855.1i	0.695584	+	1.20479i
$907$	25405.1	−	44003.0i	0.930060	−	1.61091i	0.146844	−	0.989160i	$-0.453088\pi$
$907$	25405.1	−	44003.0i	0.930060	−	1.61091i	0.783215	−	0.621751i	$-0.213578\pi$
$908$	−4915.37	+	8513.68i	−0.179650	+	0.311163i
$909$	5812.77			0.212099
$910$		0			0
$911$	−7309.10			−0.265819			−0.132910	−	0.991128i	$-0.542432\pi$
$911$	−7309.10			−0.265819			−0.132910	+	0.991128i	$0.542432\pi$
$912$	−1380.87	+	2391.73i	−0.0501372	+	0.0868401i
$913$	−11468.5	+	19864.1i	−0.415720	+	0.720049i
$914$	29589.9	+	51251.1i	1.07084	+	1.85475i
$915$	36928.4			1.33422
$916$	1177.09	+	2038.78i	0.0424587	+	0.0735406i
$917$	−6011.41	−	10412.1i	−0.216482	−	0.374958i
$918$	−20076.5			−0.721812
$919$	−1754.98	−	3039.71i	−0.0629939	−	0.109109i	0.832808	−	0.553561i	$-0.186732\pi$
$919$	−1754.98	−	3039.71i	−0.0629939	−	0.109109i	−0.895802	+	0.444453i	$0.853398\pi$
$920$	−6465.36	+	11198.3i	−0.231692	+	0.401302i
$921$	2733.24	−	4734.11i	0.0977886	−	0.169375i
$922$	19533.8			0.697733
$923$		0			0
$924$	75316.5			2.68153
$925$	−5981.87	+	10360.9i	−0.212630	+	0.368286i
$926$	25271.2	−	43771.0i	0.896829	−	1.55335i
$927$	−2705.45	−	4685.98i	−0.0958563	−	0.166028i
$928$	−7459.34			−0.263863
$929$	−3312.34	−	5737.14i	−0.116980	−	0.202615i	0.801590	−	0.597875i	$-0.203988\pi$
$929$	−3312.34	−	5737.14i	−0.116980	−	0.202615i	−0.918569	+	0.395260i	$0.870655\pi$
$930$	7669.65	+	13284.2i	0.270428	+	0.468395i
$931$	4496.95			0.158304
$932$	1999.92	+	3463.97i	0.0702893	+	0.121745i
$933$	13067.3	−	22633.1i	0.458524	−	0.794187i
$934$	11837.5	−	20503.1i	0.414705	−	0.718290i
$935$	14780.9			0.516992
$936$		0			0
$937$	36109.1			1.25895			0.629473	−	0.777022i	$-0.283271\pi$
$937$	36109.1			1.25895			0.629473	+	0.777022i	$0.283271\pi$
$938$	−56549.1	+	97945.9i	−1.96844	+	3.40943i
$939$	−15108.5	+	26168.7i	−0.525077	+	0.909460i
$940$	33122.9	+	57370.5i	1.14931	+	1.99066i
$941$	47894.5			1.65921			0.829604	−	0.558352i	$-0.188566\pi$
$941$	47894.5			1.65921			0.829604	+	0.558352i	$0.188566\pi$
$942$	−12407.0	−	21489.5i	−0.429131	−	0.743277i
$943$	−5073.77	−	8788.02i	−0.175212	−	0.303476i
$944$	−12257.4			−0.422612
$945$	−25453.2	−	44086.2i	−0.876181	−	1.51759i
$946$	32761.7	−	56744.9i	1.12598	−	1.95025i
$947$	−17270.7	+	29913.7i	−0.592631	+	1.02647i	0.401246	+	0.915970i	$0.368577\pi$
$947$	−17270.7	+	29913.7i	−0.592631	+	1.02647i	−0.993877	+	0.110496i	$0.964756\pi$
$948$	−13542.0			−0.463950
$949$		0			0
$950$	−2412.30			−0.0823845
$951$	4915.64	−	8514.15i	0.167614	−	0.290316i
$952$	12582.9	−	21794.2i	0.428377	−	0.741970i
$953$	−18608.5	−	32230.9i	−0.632517	−	1.09555i	−0.987035	−	0.160503i	$-0.948688\pi$
$953$	−18608.5	−	32230.9i	−0.632517	−	1.09555i	0.354518	−	0.935049i	$-0.384645\pi$
$954$	12234.6			0.415211
$955$	−12795.3	−	22162.1i	−0.433555	−	0.750940i
$956$	−19069.9	−	33030.1i	−0.645152	−	1.11744i
$957$	26647.5			0.900097
$958$	3014.57	+	5221.38i	0.101666	+	0.176091i
$959$	32774.0	−	56766.2i	1.10357	−	1.91145i
$960$	17965.1	−	31116.5i	0.603980	−	1.04612i
$961$	−26653.4			−0.894679
$962$		0			0
$963$	976.148			0.0326645
$964$	29316.2	−	50777.1i	0.979472	−	1.69649i
$965$	−6553.21	+	11350.5i	−0.218606	+	0.378637i
$966$	8085.15	+	14003.9i	0.269291	+	0.466426i
$967$	−19683.1			−0.654567			−0.327283	−	0.944926i	$-0.606133\pi$
$967$	−19683.1			−0.654567			−0.327283	+	0.944926i	$0.606133\pi$
$968$	8120.50	+	14065.1i	0.269631	+	0.467015i
$969$	796.722	+	1379.96i	0.0264132	+	0.0457490i
$970$	−88159.0			−2.91816
$971$	−16875.2	−	29228.8i	−0.557726	−	0.966010i	−0.997686	−	0.0679926i	$-0.978341\pi$
$971$	−16875.2	−	29228.8i	−0.557726	−	0.966010i	0.439960	−	0.898018i	$-0.354993\pi$
$972$	−15093.1	+	26142.0i	−0.498056	+	0.862659i
$973$	23617.3	−	40906.3i	0.778145	−	1.34779i
$974$	93086.1			3.06229
$975$		0			0
$976$	30827.3			1.01102
$977$	11972.6	−	20737.2i	0.392055	−	0.679059i	−0.600665	−	0.799500i	$-0.705098\pi$
$977$	11972.6	−	20737.2i	0.392055	−	0.679059i	0.992720	+	0.120441i	$0.0384310\pi$
$978$	−31190.3	+	54023.1i	−1.01979	+	1.76633i
$979$	−8058.19	−	13957.2i	−0.263065	−	0.455642i
$980$	66914.6			2.18113
$981$	−1063.76	−	1842.49i	−0.0346211	−	0.0599656i
$982$	−20221.9	−	35025.3i	−0.657135	−	1.13819i
$983$	53283.1			1.72886			0.864429	−	0.502756i	$-0.167680\pi$
$983$	53283.1			1.72886			0.864429	+	0.502756i	$0.167680\pi$
$984$	−27525.6	−	47675.7i	−0.891752	−	1.54456i
$985$	−8353.57	+	14468.8i	−0.270220	+	0.468035i
$986$	9340.14	−	16177.6i	0.301674	−	0.522515i
$987$	39486.5			1.27342
$988$		0			0
$989$	9234.71			0.296913
$990$	9466.19	−	16395.9i	0.303894	−	0.526360i
$991$	23334.7	−	40416.9i	0.747983	−	1.29555i	−0.200805	−	0.979631i	$-0.564356\pi$
$991$	23334.7	−	40416.9i	0.747983	−	1.29555i	0.948788	−	0.315914i	$-0.102311\pi$
$992$	−1475.10	−	2554.95i	−0.0472122	−	0.0817740i
$993$	7750.12			0.247676
$994$	46848.7	+	81144.3i	1.49492	+	2.58928i
$995$	1820.66	+	3153.48i	0.0580089	+	0.100474i
$996$	−36793.9			−1.17054
$997$	14146.6	+	24502.6i	0.449374	+	0.778339i	0.998345	−	0.0575025i	$-0.0183137\pi$
$997$	14146.6	+	24502.6i	0.449374	+	0.778339i	−0.548971	+	0.835841i	$0.684980\pi$
$998$	−480.203	+	831.736i	−0.0152310	+	0.0263809i
$999$	23896.1	−	41389.3i	0.756797	−	1.31081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.l.22.8		18
13.2	odd	12		169.4.e.h.23.16		36
13.3	even	3	inner	169.4.c.l.146.8		18
13.4	even	6		169.4.a.l.1.8	yes	9
13.5	odd	4		169.4.e.h.147.3		36
13.6	odd	12		169.4.b.g.168.16		18
13.7	odd	12		169.4.b.g.168.3		18
13.8	odd	4		169.4.e.h.147.16		36
13.9	even	3		169.4.a.k.1.2	✓	9
13.10	even	6		169.4.c.k.146.2		18
13.11	odd	12		169.4.e.h.23.3		36
13.12	even	2		169.4.c.k.22.2		18
39.17	odd	6		1521.4.a.bg.1.2		9
39.35	odd	6		1521.4.a.bh.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.2	✓	9	13.9	even	3
169.4.a.l.1.8	yes	9	13.4	even	6
169.4.b.g.168.3		18	13.7	odd	12
169.4.b.g.168.16		18	13.6	odd	12
169.4.c.k.22.2		18	13.12	even	2
169.4.c.k.146.2		18	13.10	even	6
169.4.c.l.22.8		18	1.1	even	1	trivial
169.4.c.l.146.8		18	13.3	even	3	inner
169.4.e.h.23.3		36	13.11	odd	12
169.4.e.h.23.16		36	13.2	odd	12
169.4.e.h.147.3		36	13.5	odd	4
169.4.e.h.147.16		36	13.8	odd	4
1521.4.a.bg.1.2		9	39.17	odd	6
1521.4.a.bh.1.8		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)

\(f(q)\)	\(=\)	\(q+(2.41278 - 4.17905i) q^{2} +(-2.22176 + 3.84820i) q^{3} +(-7.64299 - 13.2380i) q^{4} +12.7712 q^{5} +(10.7212 + 18.5697i) q^{6} +(13.0936 + 22.6787i) q^{7} -35.1589 q^{8} +(3.62756 + 6.28312i) q^{9} +O(q^{10})\)	\(q+(2.41278 - 4.17905i) q^{2} +(-2.22176 + 3.84820i) q^{3} +(-7.64299 - 13.2380i) q^{4} +12.7712 q^{5} +(10.7212 + 18.5697i) q^{6} +(13.0936 + 22.6787i) q^{7} -35.1589 q^{8} +(3.62756 + 6.28312i) q^{9} +(30.8140 - 53.3715i) q^{10} +(21.1715 - 36.6701i) q^{11} +67.9236 q^{12} +126.367 q^{14} +(-28.3745 + 49.1461i) q^{15} +(-23.6866 + 41.0265i) q^{16} +(13.6665 + 23.6711i) q^{17} +35.0100 q^{18} +(-6.55981 - 11.3619i) q^{19} +(-97.6101 - 169.066i) q^{20} -116.363 q^{21} +(-102.164 - 176.954i) q^{22} +(14.3988 - 24.9394i) q^{23} +(78.1146 - 135.298i) q^{24} +38.1033 q^{25} -152.213 q^{27} +(200.148 - 346.666i) q^{28} +(70.8138 - 122.653i) q^{29} +(136.923 + 237.157i) q^{30} +56.0144 q^{31} +(-26.3343 - 45.6124i) q^{32} +(94.0761 + 162.945i) q^{33} +131.897 q^{34} +(167.220 + 289.634i) q^{35} +(55.4508 - 96.0437i) q^{36} +(-156.991 + 271.916i) q^{37} -63.3095 q^{38} -449.021 q^{40} +(176.187 - 305.165i) q^{41} +(-280.758 + 486.287i) q^{42} +(160.338 + 277.714i) q^{43} -647.255 q^{44} +(46.3283 + 80.2430i) q^{45} +(-69.4822 - 120.347i) q^{46} -339.339 q^{47} +(-105.252 - 182.302i) q^{48} +(-171.382 + 296.843i) q^{49} +(91.9347 - 159.236i) q^{50} -121.455 q^{51} +349.461 q^{53} +(-367.257 + 636.108i) q^{54} +(270.385 - 468.321i) q^{55} +(-460.355 - 797.358i) q^{56} +58.2973 q^{57} +(-341.716 - 591.869i) q^{58} +(129.371 + 224.077i) q^{59} +867.465 q^{60} +(-325.366 - 563.550i) q^{61} +(135.150 - 234.087i) q^{62} +(-94.9954 + 164.537i) q^{63} -633.142 q^{64} +907.938 q^{66} +(-447.498 + 775.089i) q^{67} +(208.906 - 361.836i) q^{68} +(63.9813 + 110.819i) q^{69} +1613.86 q^{70} +(370.734 + 642.131i) q^{71} +(-127.541 - 220.908i) q^{72} -820.643 q^{73} +(757.569 + 1312.15i) q^{74} +(-84.6563 + 146.629i) q^{75} +(-100.273 + 173.678i) q^{76} +1108.84 q^{77} -199.372 q^{79} +(-302.507 + 523.957i) q^{80} +(240.237 - 416.103i) q^{81} +(-850.201 - 1472.59i) q^{82} -541.696 q^{83} +(889.361 + 1540.42i) q^{84} +(174.538 + 302.308i) q^{85} +1547.44 q^{86} +(314.663 + 545.012i) q^{87} +(-744.367 + 1289.28i) q^{88} +(190.307 - 329.622i) q^{89} +447.119 q^{90} -440.199 q^{92} +(-124.451 + 215.555i) q^{93} +(-818.749 + 1418.12i) q^{94} +(-83.7766 - 145.105i) q^{95} +234.034 q^{96} +(-715.250 - 1238.85i) q^{97} +(827.015 + 1432.43i) q^{98} +307.204 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

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