LMFDB - Embedded newform 169.4.c.l.22.6

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			22.6
Root			$-0.613994 - 1.06347i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.l.146.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11399 - 1.92949i) q^{2} +(4.87434 - 8.44260i) q^{3} +(1.51803 + 2.62931i) q^{4} +8.20685 q^{5} +(-10.8600 - 18.8100i) q^{6} +(4.17747 + 7.23560i) q^{7} +24.5882 q^{8} +(-34.0183 - 58.9214i) q^{9} +O(q^{10})$	\(q+(1.11399 - 1.92949i) q^{2} +(4.87434 - 8.44260i) q^{3} +(1.51803 + 2.62931i) q^{4} +8.20685 q^{5} +(-10.8600 - 18.8100i) q^{6} +(4.17747 + 7.23560i) q^{7} +24.5882 q^{8} +(-34.0183 - 58.9214i) q^{9} +(9.14239 - 15.8351i) q^{10} +(-4.84949 + 8.39957i) q^{11} +29.5976 q^{12} +18.6147 q^{14} +(40.0030 - 69.2872i) q^{15} +(15.2469 - 26.4084i) q^{16} +(-22.3109 - 38.6437i) q^{17} -151.585 q^{18} +(43.8709 + 75.9867i) q^{19} +(12.4583 + 21.5784i) q^{20} +81.4497 q^{21} +(10.8046 + 18.7141i) q^{22} +(-53.5263 + 92.7102i) q^{23} +(119.851 - 207.589i) q^{24} -57.6475 q^{25} -400.052 q^{27} +(-12.6831 + 21.9678i) q^{28} +(7.02150 - 12.1616i) q^{29} +(-89.1261 - 154.371i) q^{30} -171.090 q^{31} +(64.3831 + 111.515i) q^{32} +(47.2761 + 81.8846i) q^{33} -99.4170 q^{34} +(34.2839 + 59.3815i) q^{35} +(103.282 - 178.890i) q^{36} +(-206.977 + 358.495i) q^{37} +195.488 q^{38} +201.792 q^{40} +(129.141 - 223.678i) q^{41} +(90.7344 - 157.157i) q^{42} +(-30.5359 - 52.8897i) q^{43} -29.4468 q^{44} +(-279.183 - 483.560i) q^{45} +(119.256 + 206.557i) q^{46} +68.7115 q^{47} +(-148.637 - 257.446i) q^{48} +(136.597 - 236.594i) q^{49} +(-64.2190 + 111.231i) q^{50} -435.004 q^{51} +328.701 q^{53} +(-445.656 + 771.899i) q^{54} +(-39.7991 + 68.9340i) q^{55} +(102.717 + 177.911i) q^{56} +855.367 q^{57} +(-15.6438 - 27.0959i) q^{58} +(73.5721 + 127.431i) q^{59} +242.904 q^{60} +(48.9041 + 84.7045i) q^{61} +(-190.593 + 330.117i) q^{62} +(284.221 - 492.286i) q^{63} +530.839 q^{64} +210.661 q^{66} +(338.799 - 586.817i) q^{67} +(67.7376 - 117.325i) q^{68} +(521.810 + 903.802i) q^{69} +152.768 q^{70} +(393.383 + 681.360i) q^{71} +(-836.450 - 1448.77i) q^{72} -997.675 q^{73} +(461.142 + 798.722i) q^{74} +(-280.994 + 486.695i) q^{75} +(-133.195 + 230.701i) q^{76} -81.0345 q^{77} +383.897 q^{79} +(125.129 - 216.729i) q^{80} +(-1031.50 + 1786.60i) q^{81} +(-287.724 - 498.353i) q^{82} -519.718 q^{83} +(123.643 + 214.157i) q^{84} +(-183.103 - 317.143i) q^{85} -136.067 q^{86} +(-68.4503 - 118.559i) q^{87} +(-119.240 + 206.530i) q^{88} +(341.611 - 591.687i) q^{89} -1244.03 q^{90} -325.019 q^{92} +(-833.950 + 1444.44i) q^{93} +(76.5442 - 132.578i) q^{94} +(360.042 + 623.612i) q^{95} +1255.30 q^{96} +(-173.647 - 300.765i) q^{97} +(-304.337 - 527.128i) q^{98} +659.886 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 $

$2$	1.11399	−	1.92949i	0.393856	−	0.682179i	−0.599098	−	0.800676i	$-0.704474\pi$
$2$	1.11399	−	1.92949i	0.393856	−	0.682179i	0.992954	+	0.118496i	$0.0378074\pi$
$3$	4.87434	−	8.44260i	0.938066	−	1.62478i	0.168994	−	0.985617i	$-0.445948\pi$
$3$	4.87434	−	8.44260i	0.938066	−	1.62478i	0.769072	−	0.639162i	$-0.220719\pi$
$4$	1.51803	+	2.62931i	0.189754	+	0.328664i
$5$	8.20685			0.734043			0.367022	−	0.930212i	$-0.380377\pi$
$5$	8.20685			0.734043			0.367022	+	0.930212i	$0.380377\pi$
$6$	−10.8600	−	18.8100i	−0.738927	−	1.27986i
$7$	4.17747	+	7.23560i	0.225562	+	0.390686i	0.956488	−	0.291772i	$-0.0942447\pi$
$7$	4.17747	+	7.23560i	0.225562	+	0.390686i	−0.730926	+	0.682457i	$0.760911\pi$
$8$	24.5882			1.08666
$9$	−34.0183	−	58.9214i	−1.25994	−	2.18228i
$10$	9.14239	−	15.8351i	0.289108	−	0.500749i
$11$	−4.84949	+	8.39957i	−0.132925	+	0.230233i	−0.924803	−	0.380446i	$-0.875770\pi$
$11$	−4.84949	+	8.39957i	−0.132925	+	0.230233i	0.791878	+	0.610680i	$0.209104\pi$
$12$	29.5976			0.712009
$13$		0			0
$13$		0			0
$14$	18.6147			0.355357
$15$	40.0030	−	69.2872i	0.688581	−	1.19266i
$16$	15.2469	−	26.4084i	0.238232	−	0.412630i
$17$	−22.3109	−	38.6437i	−0.318306	−	0.551322i	0.661829	−	0.749655i	$-0.269781\pi$
$17$	−22.3109	−	38.6437i	−0.318306	−	0.551322i	−0.980135	+	0.198333i	$0.936447\pi$
$18$	−151.585			−1.98494
$19$	43.8709	+	75.9867i	0.529720	+	0.917502i	0.999399	+	0.0346647i	$0.0110363\pi$
$19$	43.8709	+	75.9867i	0.529720	+	0.917502i	−0.469679	+	0.882837i	$0.655630\pi$
$20$	12.4583	+	21.5784i	0.139288	+	0.241254i
$21$	81.4497			0.846370
$22$	10.8046	+	18.7141i	0.104707	+	0.181358i
$23$	−53.5263	+	92.7102i	−0.485261	+	0.840496i	−0.999857	−	0.0169365i	$-0.994609\pi$
$23$	−53.5263	+	92.7102i	−0.485261	+	0.840496i	0.514596	+	0.857433i	$0.327942\pi$
$24$	119.851	−	207.589i	1.01936	−	1.76558i
$25$	−57.6475			−0.461180
$26$		0			0
$27$	−400.052			−2.85149
$28$	−12.6831	+	21.9678i	−0.0856029	+	0.148269i
$29$	7.02150	−	12.1616i	0.0449607	−	0.0778742i	−0.842669	−	0.538431i	$-0.819017\pi$
$29$	7.02150	−	12.1616i	0.0449607	−	0.0778742i	0.887630	+	0.460557i	$0.152350\pi$
$30$	−89.1261	−	154.371i	−0.542404	−	0.939472i
$31$	−171.090			−0.991247			−0.495624	−	0.868537i	$-0.665060\pi$
$31$	−171.090			−0.991247			−0.495624	+	0.868537i	$0.665060\pi$
$32$	64.3831	+	111.515i	0.355670	+	0.616038i
$33$	47.2761	+	81.8846i	0.249385	+	0.431948i
$34$	−99.4170			−0.501467
$35$	34.2839	+	59.3815i	0.165573	+	0.286780i
$36$	103.282	−	178.890i	0.478157	−	0.828192i
$37$	−206.977	+	358.495i	−0.919643	+	1.59287i	−0.119686	+	0.992812i	$0.538189\pi$
$37$	−206.977	+	358.495i	−0.919643	+	1.59287i	−0.799957	+	0.600057i	$0.795144\pi$
$38$	195.488			0.834534
$39$		0			0
$40$	201.792			0.797653
$41$	129.141	−	223.678i	0.491912	−	0.852017i	−0.508044	−	0.861331i	$-0.669631\pi$
$41$	129.141	−	223.678i	0.491912	−	0.852017i	0.999957	+	0.00931374i	$0.00296470\pi$
$42$	90.7344	−	157.157i	0.333348	−	0.577376i
$43$	−30.5359	−	52.8897i	−0.108295	−	0.187572i	0.806785	−	0.590845i	$-0.201206\pi$
$43$	−30.5359	−	52.8897i	−0.108295	−	0.187572i	−0.915080	+	0.403273i	$0.867872\pi$
$44$	−29.4468			−0.100892
$45$	−279.183	−	483.560i	−0.924849	−	1.60188i
$46$	119.256	+	206.557i	0.382246	+	0.662070i
$47$	68.7115			0.213247			0.106623	−	0.994299i	$-0.465996\pi$
$47$	68.7115			0.213247			0.106623	+	0.994299i	$0.465996\pi$
$48$	−148.637	−	257.446i	−0.446955	−	0.774150i
$49$	136.597	−	236.594i	0.398243	−	0.689777i
$50$	−64.2190	+	111.231i	−0.181639	+	0.314608i
$51$	−435.004			−1.19437
$52$		0			0
$53$	328.701			0.851896			0.425948	−	0.904748i	$-0.359941\pi$
$53$	328.701			0.851896			0.425948	+	0.904748i	$0.359941\pi$
$54$	−445.656	+	771.899i	−1.12308	+	1.94522i
$55$	−39.7991	+	68.9340i	−0.0975728	+	0.169001i
$56$	102.717	+	177.911i	0.245109	+	0.424541i
$57$	855.367			1.98765
$58$	−15.6438	−	27.0959i	−0.0354161	−	0.0613425i
$59$	73.5721	+	127.431i	0.162344	+	0.281187i	0.935709	−	0.352773i	$-0.114761\pi$
$59$	73.5721	+	127.431i	0.162344	+	0.281187i	−0.773365	+	0.633961i	$0.781428\pi$
$60$	242.904			0.522645
$61$	48.9041	+	84.7045i	0.102648	+	0.177792i	0.912775	−	0.408463i	$-0.133935\pi$
$61$	48.9041	+	84.7045i	0.102648	+	0.177792i	−0.810127	+	0.586255i	$0.800602\pi$
$62$	−190.593	+	330.117i	−0.390409	+	0.676208i
$63$	284.221	−	492.286i	0.568389	−	0.984479i
$64$	530.839			1.03680
$65$		0			0
$66$	210.661			0.392888
$67$	338.799	−	586.817i	0.617774	−	1.07002i	−0.372117	−	0.928186i	$-0.621368\pi$
$67$	338.799	−	586.817i	0.617774	−	1.07002i	0.989891	−	0.141830i	$-0.0452986\pi$
$68$	67.7376	−	117.325i	0.120800	−	0.209231i
$69$	521.810	+	903.802i	0.910414	+	1.57688i
$70$	152.768			0.260847
$71$	393.383	+	681.360i	0.657549	+	1.13891i	0.981248	+	0.192749i	$0.0617403\pi$
$71$	393.383	+	681.360i	0.657549	+	1.13891i	−0.323699	+	0.946160i	$0.604926\pi$
$72$	−836.450	−	1448.77i	−1.36912	−	2.37138i
$73$	−997.675			−1.59958			−0.799788	−	0.600282i	$-0.795055\pi$
$73$	−997.675			−1.59958			−0.799788	+	0.600282i	$0.795055\pi$
$74$	461.142	+	798.722i	0.724415	+	1.25472i
$75$	−280.994	+	486.695i	−0.432618	+	0.749316i
$76$	−133.195	+	230.701i	−0.201033	+	0.348200i
$77$	−81.0345			−0.119932
$78$		0			0
$79$	383.897			0.546731			0.273366	−	0.961910i	$-0.411863\pi$
$79$	383.897			0.546731			0.273366	+	0.961910i	$0.411863\pi$
$80$	125.129	−	216.729i	0.174873	−	0.302889i
$81$	−1031.50	+	1786.60i	−1.41495	+	2.45076i
$82$	−287.724	−	498.353i	−0.387486	−	0.671145i
$83$	−519.718			−0.687307			−0.343654	−	0.939096i	$-0.611665\pi$
$83$	−519.718			−0.687307			−0.343654	+	0.939096i	$0.611665\pi$
$84$	123.643	+	214.157i	0.160602	+	0.278171i
$85$	−183.103	−	317.143i	−0.233650	−	0.404694i
$86$	−136.067			−0.170610
$87$	−68.4503	−	118.559i	−0.0843522	−	0.146102i
$88$	−119.240	+	206.530i	−0.144444	+	0.250184i
$89$	341.611	−	591.687i	0.406862	−	0.704705i	−0.587675	−	0.809097i	$-0.699956\pi$
$89$	341.611	−	591.687i	0.406862	−	0.704705i	0.994536	+	0.104393i	$0.0332898\pi$
$90$	−1244.03			−1.45703
$91$		0			0
$92$	−325.019			−0.368321
$93$	−833.950	+	1444.44i	−0.929856	+	1.61056i
$94$	76.5442	−	132.578i	0.0839887	−	0.145473i
$95$	360.042	+	623.612i	0.388837	+	0.673486i
$96$	1255.30			1.33457
$97$	−173.647	−	300.765i	−0.181765	−	0.314826i	0.760717	−	0.649084i	$-0.224848\pi$
$97$	−173.647	−	300.765i	−0.181765	−	0.314826i	−0.942482	+	0.334258i	$0.891514\pi$
$98$	−304.337	−	527.128i	−0.313701	−	0.543346i
$99$	659.886			0.669909
$100$	−87.5110	−	151.573i	−0.0875110	−	0.151573i
$101$	−277.397	+	480.466i	−0.273288	+	0.473348i	−0.969702	−	0.244292i	$-0.921444\pi$
$101$	−277.397	+	480.466i	−0.273288	+	0.473348i	0.696414	+	0.717640i	$0.254778\pi$
$102$	−484.592	+	839.338i	−0.470409	+	0.814773i
$103$	1137.13			1.08781			0.543905	−	0.839147i	$-0.316945\pi$
$103$	1137.13			1.08781			0.543905	+	0.839147i	$0.316945\pi$
$104$		0			0
$105$	668.445			0.621272
$106$	366.171	−	634.226i	0.335525	−	0.581146i
$107$	778.069	−	1347.66i	0.702980	−	1.21760i	−0.264436	−	0.964403i	$-0.585186\pi$
$107$	778.069	−	1347.66i	0.702980	−	1.21760i	0.967416	−	0.253193i	$-0.0814808\pi$
$108$	−607.293	−	1051.86i	−0.541082	−	0.937181i
$109$	71.6448			0.0629572			0.0314786	−	0.999504i	$-0.489978\pi$
$109$	71.6448			0.0629572			0.0314786	+	0.999504i	$0.489978\pi$
$110$	88.6719	+	153.584i	0.0768594	+	0.133124i
$111$	2017.75	+	3494.85i	1.72537	+	2.98843i
$112$	254.774			0.214945
$113$	490.436	+	849.460i	0.408286	+	0.707173i	0.994698	−	0.102841i	$-0.0327931\pi$
$113$	490.436	+	849.460i	0.408286	+	0.707173i	−0.586411	+	0.810013i	$0.699460\pi$
$114$	952.873	−	1650.42i	0.782849	−	1.35593i
$115$	−439.282	+	760.859i	−0.356203	+	0.616961i
$116$	42.6355			0.0341259
$117$		0			0
$118$	327.836			0.255760
$119$	186.407	−	322.866i	0.143596	−	0.248715i
$120$	983.602	−	1703.65i	0.748252	−	1.29601i
$121$	618.465	+	1071.21i	0.464662	+	0.804818i
$122$	217.916			0.161714
$123$	−1258.95	−	2180.57i	−0.922893	−	1.59850i
$124$	−259.720	−	449.849i	−0.188093	−	0.325787i
$125$	−1498.96			−1.07257
$126$	−633.241	−	1096.81i	−0.447727	−	0.775486i
$127$	1088.65	−	1885.60i	0.760649	−	1.31748i	−0.181868	−	0.983323i	$-0.558214\pi$
$127$	1088.65	−	1885.60i	0.760649	−	1.31748i	0.942517	−	0.334159i	$-0.108452\pi$
$128$	76.2873	−	132.133i	0.0526790	−	0.0912426i
$129$	−595.369			−0.406351
$130$		0			0
$131$	−1919.81			−1.28041			−0.640207	−	0.768202i	$-0.721152\pi$
$131$	−1919.81			−1.28041			−0.640207	+	0.768202i	$0.721152\pi$
$132$	−143.534	+	248.607i	−0.0946438	+	0.163928i
$133$	−366.539	+	634.865i	−0.238970	+	0.413908i
$134$	−754.839	−	1307.42i	−0.486628	−	0.842865i
$135$	−3283.17			−2.09311
$136$	−548.587	−	950.180i	−0.345889	−	0.599098i
$137$	−372.006	−	644.334i	−0.231990	−	0.401819i	0.726404	−	0.687268i	$-0.241190\pi$
$137$	−372.006	−	644.334i	−0.231990	−	0.401819i	−0.958394	+	0.285450i	$0.907857\pi$
$138$	2325.17			1.43429
$139$	−1410.00	−	2442.19i	−0.860392	−	1.49024i	−0.871551	−	0.490304i	$-0.836886\pi$
$139$	−1410.00	−	2442.19i	−0.860392	−	1.49024i	0.0111596	−	0.999938i	$-0.496448\pi$
$140$	−104.088	+	180.286i	−0.0628362	+	0.108836i
$141$	334.923	−	580.104i	0.200040	−	0.346479i
$142$	1752.91			1.03592
$143$		0			0
$144$	−2074.69			−1.20063
$145$	57.6244	−	99.8084i	0.0330031	−	0.0571630i
$146$	−1111.40	+	1925.01i	−0.630003	+	1.09120i
$147$	−1331.64	−	2306.47i	−0.747157	−	1.29411i
$148$	−1256.79			−0.698025
$149$	1447.30	+	2506.80i	0.795755	+	1.37829i	0.922359	+	0.386335i	$0.126259\pi$
$149$	1447.30	+	2506.80i	0.795755	+	1.37829i	−0.126604	+	0.991953i	$0.540408\pi$
$150$	626.050	+	1084.35i	0.340779	+	0.590246i
$151$	−494.004			−0.266235			−0.133118	−	0.991100i	$-0.542499\pi$
$151$	−494.004			−0.266235			−0.133118	+	0.991100i	$0.542499\pi$
$152$	1078.71	+	1868.38i	0.575624	+	0.997010i
$153$	−1517.96	+	2629.19i	−0.802091	+	1.38926i
$154$	−90.2720	+	156.356i	−0.0472359	+	0.0818149i
$155$	−1404.11			−0.727618
$156$		0			0
$157$	50.7450			0.0257955			0.0128977	−	0.999917i	$-0.495894\pi$
$157$	50.7450			0.0257955			0.0128977	+	0.999917i	$0.495894\pi$
$158$	427.659	−	740.727i	0.215334	−	0.372969i
$159$	1602.20	−	2775.09i	0.799135	−	1.38414i
$160$	528.383	+	915.185i	0.261077	+	0.452199i
$161$	−894.419			−0.437826
$162$	2298.16	+	3980.53i	1.11457	+	1.93049i
$163$	−375.900	−	651.079i	−0.180631	−	0.312861i	0.761465	−	0.648206i	$-0.224481\pi$
$163$	−375.900	−	651.079i	−0.180631	−	0.312861i	−0.942095	+	0.335345i	$0.891147\pi$
$164$	784.161			0.373370
$165$	387.988	+	672.015i	0.183060	+	0.317069i
$166$	−578.963	+	1002.79i	−0.270700	+	0.468867i
$167$	1487.16	−	2575.84i	0.689102	−	1.19356i	−0.283027	−	0.959112i	$-0.591338\pi$
$167$	1487.16	−	2575.84i	0.689102	−	1.19356i	0.972129	−	0.234448i	$-0.0753282\pi$
$168$	2002.70			0.919714
$169$		0			0
$170$	−815.901			−0.368099
$171$	2984.83	−	5169.88i	1.33483	−	2.31199i
$172$	92.7090	−	160.577i	0.0410988	−	0.0711852i
$173$	−816.869	−	1414.86i	−0.358991	−	0.621790i	0.628802	−	0.777566i	$-0.283546\pi$
$173$	−816.869	−	1414.86i	−0.358991	−	0.621790i	−0.987792	+	0.155775i	$0.950212\pi$
$174$	−305.013			−0.132891
$175$	−240.821	−	417.114i	−0.104025	−	0.180177i
$176$	147.879	+	256.134i	0.0633341	+	0.109698i
$177$	1434.46			0.609156
$178$	−761.105	−	1318.27i	−0.320490	−	0.555105i
$179$	−1696.32	+	2938.12i	−0.708320	+	1.22685i	0.257160	+	0.966369i	$0.417213\pi$
$179$	−1696.32	+	2938.12i	−0.708320	+	1.22685i	−0.965480	+	0.260477i	$0.916120\pi$
$180$	847.620	−	1468.12i	0.350988	−	0.607929i
$181$	−3801.07			−1.56095			−0.780473	−	0.625190i	$-0.785021\pi$
$181$	−3801.07			−1.56095			−0.780473	+	0.625190i	$0.785021\pi$
$182$		0			0
$183$	953.501			0.385163
$184$	−1316.12	+	2279.58i	−0.527312	+	0.913331i
$185$	−1698.63	+	2942.11i	−0.675058	+	1.16924i
$186$	1858.03	+	3218.20i	0.732459	+	1.26866i
$187$	432.787			0.169243
$188$	104.306	+	180.664i	0.0404645	+	0.0700866i
$189$	−1671.21	−	2894.62i	−0.643188	−	1.11403i
$190$	1604.34			0.612584
$191$	−632.755	−	1095.96i	−0.239710	−	0.415189i	0.720921	−	0.693017i	$-0.243719\pi$
$191$	−632.755	−	1095.96i	−0.239710	−	0.415189i	−0.960631	+	0.277828i	$0.910386\pi$
$192$	2587.49	−	4481.66i	0.972583	−	1.68456i
$193$	−1106.16	+	1915.92i	−0.412555	+	0.714565i	−0.995168	−	0.0981838i	$-0.968697\pi$
$193$	−1106.16	+	1915.92i	−0.412555	+	0.714565i	0.582614	+	0.812749i	$0.302030\pi$
$194$	−773.767			−0.286357
$195$		0			0
$196$	829.438			0.302273
$197$	−2178.63	+	3773.49i	−0.787923	+	1.36472i	0.139315	+	0.990248i	$0.455510\pi$
$197$	−2178.63	+	3773.49i	−0.787923	+	1.36472i	−0.927238	+	0.374474i	$0.877823\pi$
$198$	735.109	−	1273.25i	0.263848	−	0.456998i
$199$	−545.316	−	944.516i	−0.194254	−	0.336457i	0.752402	−	0.658704i	$-0.228895\pi$
$199$	−545.316	−	944.516i	−0.194254	−	0.336457i	−0.946656	+	0.322247i	$0.895562\pi$
$200$	−1417.45			−0.501145
$201$	−3302.84	−	5720.68i	−1.15903	−	2.00749i
$202$	618.038	+	1070.47i	0.215272	+	0.372862i
$203$	117.329			0.0405658
$204$	−660.351	−	1143.76i	−0.226636	−	0.392546i
$205$	1059.84	−	1835.70i	0.361085	−	0.625418i
$206$	1266.75	−	2194.08i	0.428441	−	0.742081i
$207$	7283.49			2.44559
$208$		0			0
$209$	−851.007			−0.281652
$210$	744.644	−	1289.76i	0.244692	−	0.423819i
$211$	363.724	−	629.989i	0.118672	−	0.205546i	−0.800570	−	0.599240i	$-0.795470\pi$
$211$	363.724	−	629.989i	0.118672	−	0.205546i	0.919242	+	0.393694i	$0.128803\pi$
$212$	498.979	+	864.257i	0.161651	+	0.279988i
$213$	7669.93			2.46730
$214$	−1733.53	−	3002.56i	−0.553746	−	0.959116i
$215$	−250.603	−	434.058i	−0.0794931	−	0.137686i
$216$	−9836.58			−3.09859
$217$	−714.724	−	1237.94i	−0.223588	−	0.387266i
$218$	79.8119	−	138.238i	0.0247961	−	0.0429481i
$219$	−4863.01	+	8422.97i	−1.50051	+	2.59896i
$220$	−241.665			−0.0740595
$221$		0			0
$222$	8991.05			2.71820
$223$	−507.725	+	879.405i	−0.152465	+	0.264078i	−0.932133	−	0.362116i	$-0.882055\pi$
$223$	−507.725	+	879.405i	−0.152465	+	0.264078i	0.779668	+	0.626193i	$0.215388\pi$
$224$	−537.917	+	931.700i	−0.160451	+	0.277910i
$225$	1961.07	+	3396.68i	0.581058	+	1.00642i
$226$	2185.37			0.643225
$227$	2646.29	+	4583.51i	0.773747	+	1.34017i	0.935496	+	0.353338i	$0.114953\pi$
$227$	2646.29	+	4583.51i	0.773747	+	1.34017i	−0.161748	+	0.986832i	$0.551713\pi$
$228$	1298.48	+	2249.03i	0.377165	+	0.653269i
$229$	3010.03			0.868597			0.434298	−	0.900769i	$-0.356996\pi$
$229$	3010.03			0.868597			0.434298	+	0.900769i	$0.356996\pi$
$230$	978.716	+	1695.19i	0.280585	+	0.485988i
$231$	−394.989	+	684.142i	−0.112504	+	0.194862i
$232$	172.646	−	299.032i	0.0488568	−	0.0846225i
$233$	−2373.96			−0.667482			−0.333741	−	0.942665i	$-0.608311\pi$
$233$	−2373.96			−0.667482			−0.333741	+	0.942665i	$0.608311\pi$
$234$		0			0
$235$	563.905			0.156532
$236$	−223.370	+	386.888i	−0.0616108	+	0.106713i
$237$	1871.24	−	3241.09i	0.512870	−	0.888318i
$238$	−415.312	−	719.342i	−0.113112	−	0.195916i
$239$	783.439			0.212035			0.106018	−	0.994364i	$-0.466190\pi$
$239$	783.439			0.212035			0.106018	+	0.994364i	$0.466190\pi$
$240$	−1219.84	−	2112.82i	−0.328085	−	0.568259i
$241$	1758.70	+	3046.16i	0.470074	+	0.814192i	0.999414	−	0.0342172i	$-0.0108938\pi$
$241$	1758.70	+	3046.16i	0.470074	+	0.814192i	−0.529340	+	0.848410i	$0.677560\pi$
$242$	2755.86			0.732040
$243$	4655.01	+	8062.71i	1.22888	+	2.12849i
$244$	−148.476	+	257.169i	−0.0389558	+	0.0674735i
$245$	1121.04	−	1941.69i	0.292328	−	0.506327i
$246$	−5609.86			−1.45395
$247$		0			0
$248$	−4206.80			−1.07715
$249$	−2533.28	+	4387.77i	−0.644740	+	1.11672i
$250$	−1669.83	+	2892.24i	−0.422438	+	0.731685i
$251$	−708.480	−	1227.12i	−0.178163	−	0.308587i	0.763088	−	0.646294i	$-0.223682\pi$
$251$	−708.480	−	1227.12i	−0.178163	−	0.308587i	−0.941251	+	0.337707i	$0.890349\pi$
$252$	1725.83			0.431417
$253$	−519.150	−	899.195i	−0.129007	−	0.223446i
$254$	−2425.51	−	4201.10i	−0.599173	−	1.03780i
$255$	−3570.02			−0.876718
$256$	1953.39	+	3383.37i	0.476902	+	0.826018i
$257$	741.317	−	1284.00i	0.179930	−	0.311648i	−0.761926	−	0.647664i	$-0.775746\pi$
$257$	741.317	−	1284.00i	0.179930	−	0.311648i	0.941856	+	0.336015i	$0.109079\pi$
$258$	−663.237	+	1148.76i	−0.160044	+	0.277204i
$259$	−3458.56			−0.829748
$260$		0			0
$261$	−955.438			−0.226591
$262$	−2138.65	+	3704.26i	−0.504300	+	0.873473i
$263$	−3614.82	+	6261.05i	−0.847526	+	1.46796i	0.0358825	+	0.999356i	$0.488576\pi$
$263$	−3614.82	+	6261.05i	−0.847526	+	1.46796i	−0.883409	+	0.468603i	$0.844758\pi$
$264$	1162.44	+	2013.40i	0.270996	+	0.469379i
$265$	2697.60			0.625329
$266$	816.645	+	1414.47i	0.188240	+	0.326041i
$267$	−3330.25	−	5768.17i	−0.763326	−	1.32212i
$268$	2057.23			0.468901
$269$	247.452	+	428.599i	0.0560870	+	0.0971456i	0.892706	−	0.450640i	$-0.148804\pi$
$269$	247.452	+	428.599i	0.0560870	+	0.0971456i	−0.836619	+	0.547786i	$0.815471\pi$
$270$	−3657.43	+	6334.86i	−0.824387	+	1.42788i
$271$	2102.79	−	3642.14i	0.471348	−	0.816399i	−0.528115	−	0.849173i	$-0.677101\pi$
$271$	2102.79	−	3642.14i	0.471348	−	0.816399i	0.999463	+	0.0327741i	$0.0104342\pi$
$272$	−1360.69			−0.303323
$273$		0			0
$274$	−1657.65			−0.365483
$275$	279.561	−	484.214i	0.0613025	−	0.106179i
$276$	−1584.25	+	2744.00i	−0.345510	+	0.598441i
$277$	−2104.27	−	3644.71i	−0.456439	−	0.790575i	0.542331	−	0.840165i	$-0.317542\pi$
$277$	−2104.27	−	3644.71i	−0.456439	−	0.790575i	−0.998770	+	0.0495898i	$0.984209\pi$
$278$	−6282.92			−1.35548
$279$	5820.19	+	10080.9i	1.24891	+	2.16317i
$280$	842.981	+	1460.09i	0.179921	+	0.311632i
$281$	−4740.83			−1.00646			−0.503228	−	0.864153i	$-0.667855\pi$
$281$	−4740.83			−1.00646			−0.503228	+	0.864153i	$0.667855\pi$
$282$	−746.205	−	1292.46i	−0.157574	−	0.272926i
$283$	1871.41	−	3241.38i	0.393088	−	0.680848i	−0.599767	−	0.800175i	$-0.704740\pi$
$283$	1871.41	−	3241.38i	0.393088	−	0.680848i	0.992855	+	0.119326i	$0.0380735\pi$
$284$	−1194.34	+	2068.66i	−0.249546	+	0.432226i
$285$	7019.87			1.45902
$286$		0			0
$287$	2157.93			0.443828
$288$	4380.41	−	7587.09i	0.896243	−	1.55234i
$289$	1460.94	−	2530.43i	0.297363	−	0.515047i
$290$	−128.387	−	222.372i	−0.0259970	−	0.0450280i
$291$	−3385.66			−0.682030
$292$	−1514.51	−	2623.20i	−0.303526	−	0.525723i
$293$	−2627.49	−	4550.94i	−0.523889	−	0.907402i	−0.999613	−	0.0278075i	$-0.991147\pi$
$293$	−2627.49	−	4550.94i	−0.523889	−	0.907402i	0.475725	−	0.879594i	$-0.342186\pi$
$294$	−5933.77			−1.17709
$295$	603.795	+	1045.80i	0.119167	+	0.206404i
$296$	−5089.20	+	8814.75i	−0.999337	+	1.73090i
$297$	1940.05	−	3360.27i	0.379034	−	0.656507i
$298$	6449.14			1.25365
$299$		0			0
$300$	−1706.23			−0.328364
$301$	255.126	−	441.891i	0.0488545	−	0.0846185i
$302$	−550.318	+	953.179i	−0.104858	+	0.181620i
$303$	2704.25	+	4683.91i	0.512724	+	0.888064i
$304$	2675.58			0.504786
$305$	401.349	+	695.157i	0.0753482	+	0.130507i
$306$	3382.00	+	5857.79i	0.631817	+	1.09434i
$307$	−252.464			−0.0469344			−0.0234672	−	0.999725i	$-0.507471\pi$
$307$	−252.464			−0.0469344			−0.0234672	+	0.999725i	$0.507471\pi$
$308$	−123.013	−	213.065i	−0.0227576	−	0.0394172i
$309$	5542.74	−	9600.30i	1.02044	−	1.76745i
$310$	−1564.17	+	2709.22i	−0.286577	+	0.496366i
$311$	2561.20			0.466986			0.233493	−	0.972359i	$-0.424984\pi$
$311$	2561.20			0.466986			0.233493	+	0.972359i	$0.424984\pi$
$312$		0			0
$313$	−695.893			−0.125668			−0.0628342	−	0.998024i	$-0.520014\pi$
$313$	−695.893			−0.125668			−0.0628342	+	0.998024i	$0.520014\pi$
$314$	56.5296	−	97.9122i	0.0101597	−	0.0175971i
$315$	2332.56	−	4040.12i	0.417222	−	0.722650i
$316$	582.769	+	1009.39i	0.103745	+	0.179691i
$317$	−5747.37			−1.01831			−0.509155	−	0.860675i	$-0.670042\pi$
$317$	−5747.37			−1.01831			−0.509155	+	0.860675i	$0.670042\pi$
$318$	−3569.68	−	6182.86i	−0.629489	−	1.09031i
$319$	68.1014	+	117.955i	0.0119528	+	0.0207029i
$320$	4356.52			0.761053
$321$	−7585.14	−	13137.9i	−1.31888	−	2.28437i
$322$	−996.377	+	1725.78i	−0.172441	+	0.298676i
$323$	1957.60	−	3390.67i	0.337226	−	0.584092i
$324$	−6263.39			−1.07397
$325$		0			0
$326$	−1675.00			−0.284570
$327$	349.221	−	604.869i	0.0590580	−	0.102291i
$328$	3175.34	−	5499.86i	0.534540	−	0.925850i
$329$	287.041	+	497.169i	0.0481005	+	0.0833125i
$330$	1728.87			0.288397
$331$	−2122.38	−	3676.07i	−0.352437	−	0.610438i	0.634239	−	0.773137i	$-0.281314\pi$
$331$	−2122.38	−	3676.07i	−0.352437	−	0.610438i	−0.986676	+	0.162699i	$0.947980\pi$
$332$	−788.950	−	1366.50i	−0.130419	−	0.225893i
$333$	28164.0			4.63477
$334$	−3313.38	−	5738.94i	−0.542815	−	0.940182i
$335$	2780.47	−	4815.92i	0.453473	−	0.785438i
$336$	1241.85	−	2150.95i	0.201633	−	0.349238i
$337$	−7122.49			−1.15130			−0.575648	−	0.817698i	$-0.695250\pi$
$337$	−7122.49			−1.15130			−0.575648	+	0.817698i	$0.695250\pi$
$338$		0			0
$339$	9562.20			1.53200
$340$	555.912	−	962.868i	0.0886723	−	0.153585i
$341$	829.699	−	1437.08i	0.131762	−	0.228218i
$342$	−6650.16	−	11518.4i	−1.05146	−	1.82118i
$343$	5148.28			0.810440
$344$	−750.823	−	1300.46i	−0.117679	−	0.203827i
$345$	4282.42	+	7417.37i	0.668283	+	1.15750i
$346$	−3639.95			−0.565563
$347$	1683.95	+	2916.69i	0.260517	+	0.451228i	0.966379	−	0.257121i	$-0.0827738\pi$
$347$	1683.95	+	2916.69i	0.260517	+	0.451228i	−0.705863	+	0.708349i	$0.749440\pi$
$348$	207.820	−	359.954i	0.0320124	−	0.0554471i
$349$	3039.86	−	5265.18i	0.466246	−	0.807561i	−0.533011	−	0.846108i	$-0.678940\pi$
$349$	3039.86	−	5265.18i	0.466246	−	0.807561i	0.999257	+	0.0385471i	$0.0122729\pi$
$350$	−1073.09			−0.163884
$351$		0			0
$352$	−1248.90			−0.189110
$353$	1615.50	−	2798.12i	0.243581	−	0.421895i	−0.718151	−	0.695888i	$-0.755011\pi$
$353$	1615.50	−	2798.12i	0.243581	−	0.421895i	0.961732	+	0.273993i	$0.0883445\pi$
$354$	1597.98	−	2767.78i	0.239920	−	0.415554i
$355$	3228.44	+	5591.82i	0.482670	+	0.836009i
$356$	2074.31			0.308815
$357$	−1817.22	−	3147.52i	−0.269405	−	0.466622i
$358$	3779.39	+	6546.10i	0.557952	+	0.966402i
$359$	−5345.81			−0.785908			−0.392954	−	0.919558i	$-0.628547\pi$
$359$	−5345.81			−0.785908			−0.392954	+	0.919558i	$0.628547\pi$
$360$	−6864.62	−	11889.9i	−1.00499	−	1.74070i
$361$	−419.816	+	727.143i	−0.0612066	+	0.106013i
$362$	−4234.37	+	7334.14i	−0.614788	+	1.06484i
$363$	12058.4			1.74353
$364$		0			0
$365$	−8187.78			−1.17416
$366$	1062.19	−	1839.77i	0.151699	−	0.262750i
$367$	6085.66	−	10540.7i	0.865583	−	1.49923i	−0.000883749	−	1.00000i	$-0.500281\pi$
$367$	6085.66	−	10540.7i	0.865583	−	1.49923i	0.866467	−	0.499234i	$-0.166385\pi$
$368$	1632.22	+	2827.08i	0.231210	+	0.400467i
$369$	−17572.6			−2.47911
$370$	3784.53	+	6554.99i	0.531752	+	0.921021i
$371$	1373.14	+	2378.35i	0.192156	+	0.332824i
$372$	−5063.86			−0.705776
$373$	2231.98	+	3865.90i	0.309832	+	0.536645i	0.978325	−	0.207073i	$-0.0663938\pi$
$373$	2231.98	+	3865.90i	0.309832	+	0.536645i	−0.668493	+	0.743718i	$0.733061\pi$
$374$	482.122	−	835.060i	0.0666576	−	0.115454i
$375$	−7306.44	+	12655.1i	−1.00614	+	1.74269i
$376$	1689.49			0.231726
$377$		0			0
$378$	−7446.87			−1.01330
$379$	2684.53	−	4649.74i	0.363839	−	0.630188i	−0.624750	−	0.780825i	$-0.714799\pi$
$379$	2684.53	−	4649.74i	0.363839	−	0.630188i	0.988589	+	0.150637i	$0.0481324\pi$
$380$	−1093.11	+	1893.33i	−0.147567	+	0.255594i
$381$	−10612.9	−	18382.1i	−1.42708	−	2.47177i
$382$	−2819.54			−0.377645
$383$	97.5419	+	168.948i	0.0130135	+	0.0225400i	0.872459	−	0.488688i	$-0.162524\pi$
$383$	97.5419	+	168.948i	0.0130135	+	0.0225400i	−0.859445	+	0.511228i	$0.829191\pi$
$384$	−743.700	−	1288.13i	−0.0988327	−	0.171183i
$385$	−665.038			−0.0880351
$386$	2464.51	+	4268.65i	0.324974	+	0.562872i
$387$	−2077.56	+	3598.44i	−0.272889	+	0.472658i
$388$	527.204	−	913.145i	0.0689813	−	0.119479i
$389$	9120.52			1.18876			0.594381	−	0.804183i	$-0.297397\pi$
$389$	9120.52			1.18876			0.594381	+	0.804183i	$0.297397\pi$
$390$		0			0
$391$	4776.89			0.617845
$392$	3358.69	−	5817.42i	0.432754	−	0.749551i
$393$	−9357.79	+	16208.2i	−1.20111	+	2.08039i
$394$	4853.95	+	8407.30i	0.620657	+	1.07501i
$395$	3150.59			0.401325
$396$	1001.73	+	1735.05i	0.127118	+	0.220175i
$397$	−3306.73	−	5727.43i	−0.418036	−	0.724059i	0.577706	−	0.816245i	$-0.303948\pi$
$397$	−3306.73	−	5727.43i	−0.418036	−	0.724059i	−0.995742	+	0.0921859i	$0.970615\pi$
$398$	−2429.92			−0.306032
$399$	3573.27	+	6189.09i	0.448339	+	0.776546i
$400$	−878.945	+	1522.38i	−0.109868	+	0.190297i
$401$	4294.63	−	7438.51i	0.534822	−	0.926338i	−0.464350	−	0.885652i	$-0.653712\pi$
$401$	4294.63	−	7438.51i	0.534822	−	0.926338i	0.999172	−	0.0406868i	$-0.0129546\pi$
$402$	−14717.4			−1.82596
$403$		0			0
$404$	−1684.39			−0.207430
$405$	−8465.34	+	14662.4i	−1.03863	+	1.79896i
$406$	130.703	−	226.385i	0.0159771	−	0.0276731i
$407$	−2007.47	−	3477.03i	−0.244487	−	0.423465i
$408$	−10696.0			−1.29787
$409$	3757.80	+	6508.70i	0.454306	+	0.786881i	0.998648	−	0.0519824i	$-0.0165540\pi$
$409$	3757.80	+	6508.70i	0.454306	+	0.786881i	−0.544342	+	0.838863i	$0.683221\pi$
$410$	−2361.31	−	4089.91i	−0.284431	−	0.492649i
$411$	−7253.14			−0.870489
$412$	1726.20	+	2989.86i	0.206417	+	0.357524i
$413$	−614.691	+	1064.68i	−0.0732372	+	0.126851i
$414$	8113.77	−	14053.5i	0.963212	−	1.66833i
$415$	−4265.25			−0.504513
$416$		0			0
$417$	−27491.2			−3.22842
$418$	−948.016	+	1642.01i	−0.110931	+	0.192137i
$419$	2278.67	−	3946.76i	0.265680	−	0.460172i	−0.702061	−	0.712117i	$-0.747737\pi$
$419$	2278.67	−	3946.76i	0.265680	−	0.460172i	0.967742	+	0.251945i	$0.0810701\pi$
$420$	1014.72	+	1757.55i	0.117889	+	0.204190i
$421$	−2225.19			−0.257599			−0.128800	−	0.991671i	$-0.541112\pi$
$421$	−2225.19			−0.257599			−0.128800	+	0.991671i	$0.541112\pi$
$422$	−810.373	−	1403.61i	−0.0934795	−	0.161911i
$423$	−2337.45	−	4048.58i	−0.268678	−	0.465363i
$424$	8082.17			0.925719
$425$	1286.17	+	2227.71i	0.146796	+	0.254259i
$426$	8544.26	−	14799.1i	0.971762	−	1.68314i
$427$	−408.592	+	707.701i	−0.0463071	+	0.0802063i
$428$	4724.54			0.533574
$429$		0			0
$430$	−1116.68			−0.125235
$431$	198.014	−	342.970i	0.0221299	−	0.0383302i	−0.854748	−	0.519043i	$-0.826289\pi$
$431$	198.014	−	342.970i	0.0221299	−	0.0383302i	0.876878	+	0.480712i	$0.159622\pi$
$432$	−6099.55	+	10564.7i	−0.679316	+	1.17661i
$433$	−2594.03	−	4492.99i	−0.287901	−	0.498659i	0.685408	−	0.728159i	$-0.259624\pi$
$433$	−2594.03	−	4492.99i	−0.287901	−	0.498659i	−0.973308	+	0.229501i	$0.926291\pi$
$434$	−3184.79			−0.352246
$435$	−561.762	−	973.000i	−0.0619182	−	0.107245i
$436$	108.759	+	188.377i	0.0119464	+	0.0206918i
$437$	−9392.99			−1.02821
$438$	10834.7	+	18766.3i	1.18197	+	2.04723i
$439$	−5664.93	+	9811.94i	−0.615882	+	1.06674i	0.374347	+	0.927289i	$0.377867\pi$
$439$	−5664.93	+	9811.94i	−0.615882	+	1.06674i	−0.990229	+	0.139450i	$0.955466\pi$
$440$	−978.589	+	1694.97i	−0.106028	+	0.183646i
$441$	−18587.2			−2.00705
$442$		0			0
$443$	15625.2			1.67579			0.837897	−	0.545828i	$-0.183785\pi$
$443$	15625.2			1.67579			0.837897	+	0.545828i	$0.183785\pi$
$444$	−6126.03	+	10610.6i	−0.654794	+	1.13414i
$445$	2803.55	−	4855.89i	0.298654	−	0.517284i
$446$	1131.20	+	1959.30i	0.120099	+	0.208017i
$447$	28218.5			2.98588
$448$	2217.57	+	3840.94i	0.233862	+	0.405061i
$449$	6843.29	+	11852.9i	0.719276	+	1.24582i	0.961287	+	0.275549i	$0.0888596\pi$
$449$	6843.29	+	11852.9i	0.719276	+	1.24582i	−0.242011	+	0.970273i	$0.577807\pi$
$450$	8738.49			0.915414
$451$	1252.53	+	2169.45i	0.130775	+	0.226509i
$452$	−1489.00	+	2579.02i	−0.154948	+	0.268378i
$453$	−2407.94	+	4170.68i	−0.249746	+	0.432573i
$454$	11791.8			1.21898
$455$		0			0
$456$	21031.9			2.15989
$457$	6336.55	−	10975.2i	0.648602	−	1.12341i	−0.334854	−	0.942270i	$-0.608687\pi$
$457$	6336.55	−	10975.2i	0.648602	−	1.12341i	0.983457	−	0.181142i	$-0.0579795\pi$
$458$	3353.16	−	5807.84i	0.342102	−	0.592539i
$459$	8925.55	+	15459.5i	0.907645	+	1.57209i
$460$	−2667.38			−0.270364
$461$	4577.43	+	7928.34i	0.462456	+	0.800996i	0.999083	−	0.0428230i	$-0.0136352\pi$
$461$	4577.43	+	7928.34i	0.462456	+	0.800996i	−0.536627	+	0.843819i	$0.680302\pi$
$462$	880.032	+	1524.26i	0.0886207	+	0.153496i
$463$	−6910.59			−0.693655			−0.346827	−	0.937929i	$-0.612741\pi$
$463$	−6910.59			−0.693655			−0.346827	+	0.937929i	$0.612741\pi$
$464$	−214.112	−	370.852i	−0.0214222	−	0.0371043i
$465$	−6844.11	+	11854.3i	−0.682554	+	1.18222i
$466$	−2644.58	+	4580.55i	−0.262892	+	0.455343i
$467$	2920.19			0.289359			0.144679	−	0.989479i	$-0.453785\pi$
$467$	2920.19			0.289359			0.144679	+	0.989479i	$0.453785\pi$
$468$		0			0
$469$	5661.29			0.557386
$470$	628.187	−	1088.05i	0.0616513	−	0.106783i
$471$	247.348	−	428.420i	0.0241979	−	0.0419120i
$472$	1809.01	+	3133.29i	0.176412	+	0.305554i
$473$	592.334			0.0575804
$474$	−4169.11	−	7221.10i	−0.403995	−	0.699739i
$475$	−2529.05	−	4380.45i	−0.244296	−	0.423134i
$476$	1131.89			0.108992
$477$	−11181.8	−	19367.5i	−1.07334	−	1.85907i
$478$	872.746	−	1511.64i	0.0835115	−	0.144646i
$479$	−8544.31	+	14799.2i	−0.815030	+	1.41167i	0.0942761	+	0.995546i	$0.469946\pi$
$479$	−8544.31	+	14799.2i	−0.815030	+	1.41167i	−0.909306	+	0.416128i	$0.863387\pi$
$480$	10302.1			0.979630
$481$		0			0
$482$	7836.73			0.740567
$483$	−4359.70	+	7551.22i	−0.410710	+	0.711371i
$484$	−1877.70	+	3252.28i	−0.176343	+	0.305435i
$485$	−1425.10	−	2468.34i	−0.133423	−	0.231096i
$486$	20742.6			1.93602
$487$	−6906.48	−	11962.4i	−0.642634	−	1.11307i	−0.984843	−	0.173450i	$-0.944508\pi$
$487$	−6906.48	−	11962.4i	−0.642634	−	1.11307i	0.342209	−	0.939624i	$-0.388825\pi$
$488$	1202.47	+	2082.73i	0.111543	+	0.193199i
$489$	−7329.06			−0.677774
$490$	−2497.65	−	4326.06i	−0.230270	−	0.398840i
$491$	5924.21	−	10261.0i	0.544513	−	0.943125i	−0.454124	−	0.890938i	$-0.650048\pi$
$491$	5924.21	−	10261.0i	0.544513	−	0.943125i	0.998637	−	0.0521862i	$-0.0166189\pi$
$492$	3822.26	−	6620.35i	0.350246	−	0.606644i
$493$	−626.625			−0.0572450
$494$		0			0
$495$	5415.59			0.491743
$496$	−2608.59	+	4518.20i	−0.236147	+	0.409019i
$497$	−3286.70	+	5692.73i	−0.296637	+	0.513790i
$498$	5644.12	+	9775.90i	0.507870	+	0.879656i
$499$	5224.46			0.468696			0.234348	−	0.972153i	$-0.424705\pi$
$499$	5224.46			0.468696			0.234348	+	0.972153i	$0.424705\pi$
$500$	−2275.48	−	3941.24i	−0.203525	−	0.352515i
$501$	−14497.9	−	25111.0i	−1.29285	−	2.23928i
$502$	−3156.97			−0.280682
$503$	−3942.20	−	6828.08i	−0.349451	−	0.605267i	0.636701	−	0.771111i	$-0.280299\pi$
$503$	−3942.20	−	6828.08i	−0.349451	−	0.605267i	−0.986152	+	0.165844i	$0.946965\pi$
$504$	6988.50	−	12104.4i	0.617644	−	1.06979i
$505$	−2276.56	+	3943.11i	−0.200605	+	0.347458i
$506$	−2313.32			−0.203241
$507$		0			0
$508$	6610.45			0.577345
$509$	−2013.28	+	3487.10i	−0.175318	+	0.303660i	−0.940271	−	0.340426i	$-0.889429\pi$
$509$	−2013.28	+	3487.10i	−0.175318	+	0.303660i	0.764953	+	0.644086i	$0.222762\pi$
$510$	−3976.98	+	6888.33i	−0.345301	+	0.598079i
$511$	−4167.76	−	7218.78i	−0.360804	−	0.624931i
$512$	9924.86			0.856681
$513$	−17550.7	−	30398.7i	−1.51049	−	2.61624i
$514$	−1651.65	−	2860.73i	−0.141733	−	0.245489i
$515$	9332.23			0.798499
$516$	−903.790	−	1565.41i	−0.0771068	−	0.133553i
$517$	−333.216	+	577.147i	−0.0283459	+	0.0490965i
$518$	−3852.82	+	6673.28i	−0.326802	+	0.566037i
$519$	−15926.8			−1.34703
$520$		0			0
$521$	6196.12			0.521030			0.260515	−	0.965470i	$-0.416108\pi$
$521$	6196.12			0.521030			0.260515	+	0.965470i	$0.416108\pi$
$522$	−1064.35	+	1843.51i	−0.0892441	+	0.154575i
$523$	−3949.69	+	6841.07i	−0.330226	+	0.571968i	−0.982556	−	0.185967i	$-0.940458\pi$
$523$	−3949.69	+	6841.07i	−0.330226	+	0.571968i	0.652330	+	0.757935i	$0.273792\pi$
$524$	−2914.33	−	5047.77i	−0.242964	−	0.420826i
$525$	−4695.37			−0.390329
$526$	8053.78	+	13949.6i	0.667607	+	1.15633i
$527$	3817.18	+	6611.55i	0.315520	+	0.546496i
$528$	2883.25			0.237646
$529$	353.376	+	612.065i	0.0290438	+	0.0503053i
$530$	3005.11	−	5205.00i	0.246290	−	0.426586i
$531$	5005.60	−	8669.95i	0.409085	−	0.708557i
$532$	−2225.68			−0.181382
$533$		0			0
$534$	−14839.5			−1.20256
$535$	6385.50	−	11060.0i	0.516017	−	0.893768i
$536$	8330.46	−	14428.8i	0.671308	−	1.16274i
$537$	16536.9	+	28642.8i	1.32890	+	2.30173i
$538$	1102.64			0.0883609
$539$	1324.86	+	2294.72i	0.105873	+	0.183378i
$540$	−4983.97	−	8632.49i	−0.397178	−	0.687932i
$541$	6146.22			0.488441			0.244220	−	0.969720i	$-0.421468\pi$
$541$	6146.22			0.488441			0.244220	+	0.969720i	$0.421468\pi$
$542$	−4684.99	−	8114.64i	−0.371287	−	0.643088i
$543$	−18527.7	+	32090.9i	−1.46427	+	2.53619i
$544$	2872.89	−	4976.00i	0.226423	−	0.392177i
$545$	587.979			0.0462133
$546$		0			0
$547$	5555.49			0.434252			0.217126	−	0.976144i	$-0.430332\pi$
$547$	5555.49			0.434252			0.217126	+	0.976144i	$0.430332\pi$
$548$	1129.44	−	1956.24i	0.0880422	−	0.152494i
$549$	3327.27	−	5763.00i	0.258660	−	0.448013i
$550$	−622.859	−	1078.82i	−0.0482887	−	0.0836385i
$551$	1232.16			0.0952663
$552$	12830.4	+	22222.9i	0.989307	+	1.71353i
$553$	1603.72	+	2777.72i	0.123322	+	0.213600i
$554$	−9376.59			−0.719085
$555$	16559.4	+	28681.7i	1.26650	+	2.19364i
$556$	4280.85	−	7414.65i	0.326526	−	0.565560i
$557$	3790.35	−	6565.08i	0.288335	−	0.499410i	−0.685078	−	0.728470i	$-0.740232\pi$
$557$	3790.35	−	6565.08i	0.288335	−	0.499410i	0.973412	+	0.229060i	$0.0735651\pi$
$558$	25934.6			1.96756
$559$		0			0
$560$	2090.89			0.157779
$561$	2109.55	−	3653.85i	0.158762	−	0.274983i
$562$	−5281.26	+	9147.41i	−0.396399	+	0.686584i
$563$	6797.30	+	11773.3i	0.508831	+	0.881322i	0.999948	+	0.0102278i	$0.00325567\pi$
$563$	6797.30	+	11773.3i	0.508831	+	0.881322i	−0.491116	+	0.871094i	$0.663411\pi$
$564$	2033.70			0.151834
$565$	4024.94	+	6971.40i	0.299700	+	0.519095i
$566$	−4169.48	−	7221.76i	−0.309640	−	0.536313i
$567$	−17236.2			−1.27664
$568$	9672.60	+	16753.4i	0.714530	+	1.23760i
$569$	−2825.07	+	4893.16i	−0.208143	+	0.360513i	−0.951129	−	0.308793i	$-0.900075\pi$
$569$	−2825.07	+	4893.16i	−0.208143	+	0.360513i	0.742987	+	0.669306i	$0.233408\pi$
$570$	7820.09	−	13544.8i	0.574645	−	0.995314i
$571$	6297.53			0.461547			0.230773	−	0.973008i	$-0.425874\pi$
$571$	6297.53			0.461547			0.230773	+	0.973008i	$0.425874\pi$
$572$		0			0
$573$	−12337.0			−0.899454
$574$	2403.92	−	4163.71i	0.174804	−	0.302770i
$575$	3085.66	−	5344.52i	0.223793	−	0.387620i
$576$	−18058.3	−	31277.8i	−1.30630	−	2.26257i
$577$	−17838.9			−1.28707			−0.643537	−	0.765415i	$-0.722534\pi$
$577$	−17838.9			−1.28707			−0.643537	+	0.765415i	$0.722534\pi$
$578$	−3254.96	−	5637.76i	−0.234236	−	0.405709i
$579$	10783.6	+	18677.7i	0.774007	+	1.34062i
$580$	349.903			0.0250499
$581$	−2171.11	−	3760.47i	−0.155031	−	0.268521i
$582$	−3771.60	+	6532.60i	−0.268622	+	0.465266i
$583$	−1594.03	+	2760.94i	−0.113238	+	0.196135i
$584$	−24531.1			−1.73819
$585$		0			0
$586$	−11708.0			−0.825348
$587$	−227.545	+	394.120i	−0.0159997	+	0.0277122i	−0.873914	−	0.486080i	$-0.838426\pi$
$587$	−227.545	+	394.120i	−0.0159997	+	0.0277122i	0.857915	+	0.513792i	$0.171760\pi$
$588$	4042.96	−	7002.61i	0.283553	−	0.491127i
$589$	−7505.87	−	13000.6i	−0.525083	−	0.909471i
$590$	2690.50			0.187739
$591$	21238.7	+	36786.5i	1.47825	+	2.56040i
$592$	6311.50	+	10931.8i	0.438178	+	0.758946i
$593$	16240.6			1.12466			0.562330	−	0.826913i	$-0.309905\pi$
$593$	16240.6			1.12466			0.562330	+	0.826913i	$0.309905\pi$
$594$	−4322.41	−	7486.63i	−0.298570	−	0.517139i
$595$	1529.81	−	2649.71i	0.105405	−	0.182568i
$596$	−4394.10	+	7610.81i	−0.301996	+	0.523072i
$597$	−10632.2			−0.728891
$598$		0			0
$599$	−6704.05			−0.457296			−0.228648	−	0.973509i	$-0.573430\pi$
$599$	−6704.05			−0.457296			−0.228648	+	0.973509i	$0.573430\pi$
$600$	−6909.13	+	11967.0i	−0.470107	+	0.814249i
$601$	−13206.6	+	22874.5i	−0.896354	+	1.55253i	−0.0642341	+	0.997935i	$0.520460\pi$
$601$	−13206.6	+	22874.5i	−0.896354	+	1.55253i	−0.832120	+	0.554596i	$0.812873\pi$
$602$	−568.417	−	984.527i	−0.0384833	−	0.0666550i
$603$	−46101.4			−3.11343
$604$	−749.916	−	1298.89i	−0.0505193	−	0.0875019i
$605$	5075.65	+	8791.29i	0.341082	+	0.590771i
$606$	12050.1			0.807758
$607$	1663.19	+	2880.72i	0.111214	+	0.192628i	0.916260	−	0.400584i	$-0.131193\pi$
$607$	1663.19	+	2880.72i	0.111214	+	0.192628i	−0.805046	+	0.593212i	$0.797860\pi$
$608$	−5649.09	+	9784.51i	−0.376811	+	0.652655i
$609$	571.899	−	990.558i	0.0380534	−	0.0659104i
$610$	1788.40			0.118705
$611$		0			0
$612$	−9217.27			−0.608801
$613$	−13129.3	+	22740.7i	−0.865072	+	1.49835i	0.00190303	+	0.999998i	$0.499394\pi$
$613$	−13129.3	+	22740.7i	−0.865072	+	1.49835i	−0.866975	+	0.498351i	$0.833939\pi$
$614$	−281.243	+	487.127i	−0.0184854	+	0.0320177i
$615$	−10332.0	−	17895.6i	−0.677443	−	1.17337i
$616$	−1992.50			−0.130325
$617$	−13676.4	−	23688.3i	−0.892370	−	1.54563i	−0.837026	−	0.547163i	$-0.815708\pi$
$617$	−13676.4	−	23688.3i	−0.892370	−	1.54563i	−0.0553441	−	0.998467i	$-0.517626\pi$
$618$	−12349.1	−	21389.4i	−0.803812	−	1.39224i
$619$	−13056.5			−0.847795			−0.423897	−	0.905710i	$-0.639338\pi$
$619$	−13056.5			−0.847795			−0.423897	+	0.905710i	$0.639338\pi$
$620$	−2131.49	−	3691.85i	−0.138069	−	0.239142i
$621$	21413.3	−	37089.0i	1.38371	−	2.39666i
$622$	2853.17	−	4941.83i	0.183925	−	0.318568i
$623$	5708.28			0.367091
$624$		0			0
$625$	−5095.82			−0.326132
$626$	−775.220	+	1342.72i	−0.0494953	+	0.0857283i
$627$	−4148.09	+	7184.71i	−0.264209	+	0.457623i
$628$	77.0326	+	133.424i	0.00489480	+	0.00847805i
$629$	18471.4			1.17091
$630$	−5196.92	−	9001.33i	−0.328651	−	0.569241i
$631$	−3276.46	−	5674.99i	−0.206709	−	0.358031i	0.743967	−	0.668217i	$-0.232942\pi$
$631$	−3276.46	−	5674.99i	−0.206709	−	0.358031i	−0.950676	+	0.310186i	$0.899609\pi$
$632$	9439.35			0.594109
$633$	−3545.83	−	6141.55i	−0.222645	−	0.385632i
$634$	−6402.54	+	11089.5i	−0.401068	+	0.694671i
$635$	8934.42	−	15474.9i	0.558349	−	0.967089i
$636$	9728.76			0.606557
$637$		0			0
$638$	303.458			0.0188308
$639$	26764.5	−	46357.4i	1.65694	−	2.86991i
$640$	626.079	−	1084.40i	0.0386686	−	0.0669760i
$641$	2882.38	+	4992.44i	0.177609	+	0.307628i	0.941061	−	0.338237i	$-0.109830\pi$
$641$	2882.38	+	4992.44i	0.177609	+	0.307628i	−0.763452	+	0.645864i	$0.776497\pi$
$642$	−33799.2			−2.07780
$643$	−6139.75	−	10634.4i	−0.376560	−	0.652221i	0.613999	−	0.789307i	$-0.289560\pi$
$643$	−6139.75	−	10634.4i	−0.376560	−	0.652221i	−0.990559	+	0.137086i	$0.956226\pi$
$644$	−1357.76	−	2351.71i	−0.0830795	−	0.143898i
$645$	−4886.10			−0.298279
$646$	−4361.52	−	7554.37i	−0.265637	−	0.460097i
$647$	14512.1	−	25135.8i	0.881810	−	1.52734i	0.0324826	−	0.999472i	$-0.489659\pi$
$647$	14512.1	−	25135.8i	0.881810	−	1.52734i	0.849327	−	0.527867i	$-0.177008\pi$
$648$	−25362.7	+	43929.4i	−1.53756	+	2.66313i
$649$	−1427.15			−0.0863182
$650$		0			0
$651$	−13935.2			−0.838962
$652$	1141.26	−	1976.72i	0.0685509	−	0.118734i
$653$	8583.57	−	14867.2i	0.514396	−	0.890961i	−0.485464	−	0.874257i	$-0.661349\pi$
$653$	8583.57	−	14867.2i	0.514396	−	0.890961i	0.999860	−	0.0167042i	$-0.00531736\pi$
$654$	−778.060	−	1347.64i	−0.0465207	−	0.0805763i
$655$	−15755.6			−0.939880
$656$	−3937.99	−	6820.79i	−0.234379	−	0.405956i
$657$	33939.2	+	58784.5i	2.01537	+	3.49072i
$658$	1279.05			0.0757787
$659$	−9156.49	−	15859.5i	−0.541254	−	0.937479i	−0.998832	−	0.0483096i	$-0.984617\pi$
$659$	−9156.49	−	15859.5i	−0.541254	−	0.937479i	0.457579	−	0.889169i	$-0.348717\pi$
$660$	−1177.96	+	2040.28i	−0.0694727	+	0.120330i
$661$	−3442.65	+	5962.85i	−0.202577	+	0.350874i	−0.949358	−	0.314196i	$-0.898265\pi$
$661$	−3442.65	+	5962.85i	−0.202577	+	0.350874i	0.746781	+	0.665070i	$0.231598\pi$
$662$	−9457.28			−0.555238
$663$		0			0
$664$	−12779.0			−0.746867
$665$	−3008.13	+	5210.24i	−0.175414	+	0.303826i
$666$	31374.6	−	54342.3i	1.82543	−	3.16175i
$667$	751.669	+	1301.93i	0.0436353	+	0.0755786i
$668$	9030.25			0.523040
$669$	4949.64	+	8573.03i	0.286045	+	0.495445i
$670$	−6194.86	−	10729.8i	−0.357206	−	0.618699i
$671$	−948.641			−0.0545781
$672$	5243.98	+	9082.84i	0.301028	+	0.521396i
$673$	−3119.13	+	5402.50i	−0.178653	+	0.309437i	−0.941420	−	0.337238i	$-0.890507\pi$
$673$	−3119.13	+	5402.50i	−0.178653	+	0.309437i	0.762766	+	0.646674i	$0.223841\pi$
$674$	−7934.41	+	13742.8i	−0.453445	+	0.785390i
$675$	23062.0			1.31505
$676$		0			0
$677$	25482.4			1.44663			0.723316	−	0.690517i	$-0.242617\pi$
$677$	25482.4			1.44663			0.723316	+	0.690517i	$0.242617\pi$
$678$	10652.2	−	18450.2i	0.603388	−	1.04510i
$679$	1450.81	−	2512.88i	0.0819986	−	0.142026i
$680$	−4502.17	−	7797.99i	−0.253898	−	0.439764i
$681$	51595.7			2.90331
$682$	−1848.56	−	3201.80i	−0.103790	−	0.179770i
$683$	13713.2	+	23752.0i	0.768261	+	1.33067i	0.938505	+	0.345266i	$0.112211\pi$
$683$	13713.2	+	23752.0i	0.768261	+	1.33067i	−0.170243	+	0.985402i	$0.554455\pi$
$684$	18124.3			1.01316
$685$	−3053.00	−	5287.95i	−0.170291	−	0.294952i
$686$	5735.15	−	9933.57i	0.319197	−	0.552865i
$687$	14671.9	−	25412.5i	0.814802	−	1.41128i
$688$	−1862.31			−0.103197
$689$		0			0
$690$	19082.4			1.05283
$691$	−6943.15	+	12025.9i	−0.382243	+	0.662064i	−0.991383	−	0.130999i	$-0.958182\pi$
$691$	−6943.15	+	12025.9i	−0.382243	+	0.662064i	0.609140	+	0.793063i	$0.291515\pi$
$692$	2480.07	−	4295.61i	0.136240	−	0.235975i
$693$	2756.66	+	4774.67i	0.151106	+	0.261724i
$694$	7503.65			0.410425
$695$	−11571.6	−	20042.7i	−0.631565	−	1.09390i
$696$	−1683.07	−	2915.17i	−0.0916619	−	0.158763i
$697$	−11525.0			−0.626314
$698$	−6772.76	−	11730.8i	−0.367268	−	0.636126i
$699$	−11571.5	+	20042.4i	−0.626143	+	1.08451i
$700$	731.150	−	1266.39i	0.0394784	−	0.0683785i
$701$	15744.4			0.848301			0.424151	−	0.905592i	$-0.360573\pi$
$701$	15744.4			0.848301			0.424151	+	0.905592i	$0.360573\pi$
$702$		0			0
$703$	−36321.1			−1.94861
$704$	−2574.30	+	4458.82i	−0.137816	+	0.238705i
$705$	2748.66	−	4760.83i	0.146838	−	0.254331i
$706$	−3599.30	−	6234.18i	−0.191872	−	0.332332i
$707$	−4635.28			−0.246574
$708$	2177.56	+	3771.65i	0.115590	+	0.200208i
$709$	−14344.6	−	24845.5i	−0.759833	−	1.31607i	−0.942935	−	0.332976i	$-0.891947\pi$
$709$	−14344.6	−	24845.5i	−0.759833	−	1.31607i	0.183102	−	0.983094i	$-0.441386\pi$
$710$	14385.9			0.760410
$711$	−13059.5	−	22619.8i	−0.688847	−	1.19312i
$712$	8399.61	−	14548.5i	0.442119	−	0.765772i
$713$	9157.81	−	15861.8i	0.481013	−	0.833140i
$714$	−8097.48			−0.424427
$715$		0			0
$716$	−10300.3			−0.537627
$717$	3818.75	−	6614.26i	0.198903	−	0.344511i
$718$	−5955.20	+	10314.7i	−0.309535	+	0.536130i
$719$	6309.54	+	10928.4i	0.327269	+	0.566846i	0.981969	−	0.189043i	$-0.0605384\pi$
$719$	6309.54	+	10928.4i	0.327269	+	0.566846i	−0.654700	+	0.755889i	$0.727205\pi$
$720$	−17026.7			−0.881315
$721$	4750.32	+	8227.79i	0.245369	+	0.424991i
$722$	935.345	+	1620.07i	0.0482132	+	0.0835078i
$723$	34290.0			1.76384
$724$	−5770.15	−	9994.19i	−0.296196	−	0.513027i
$725$	−404.772	+	701.086i	−0.0207350	+	0.0359140i
$726$	13433.0	−	23266.7i	0.686702	−	1.18940i
$727$	−12644.5			−0.645061			−0.322531	−	0.946559i	$-0.604534\pi$
$727$	−12644.5			−0.645061			−0.322531	+	0.946559i	$0.604534\pi$
$728$		0			0
$729$	35059.5			1.78121
$730$	−9121.13	+	15798.3i	−0.462450	+	0.800986i
$731$	−1362.57	+	2360.04i	−0.0689418	+	0.119411i
$732$	1447.45	+	2507.05i	0.0730863	+	0.126589i
$733$	−19109.0			−0.962903			−0.481451	−	0.876473i	$-0.659890\pi$
$733$	−19109.0			−0.962903			−0.481451	+	0.876473i	$0.659890\pi$
$734$	−13558.8	−	23484.5i	−0.681831	−	1.18097i
$735$	−10928.6	−	18928.9i	−0.548446	−	0.949936i
$736$	−13784.7			−0.690370
$737$	3286.00	+	5691.52i	0.164235	+	0.284464i
$738$	−19575.8	+	33906.2i	−0.976415	+	1.69120i
$739$	−7046.78	+	12205.4i	−0.350771	+	0.607554i	−0.986385	−	0.164454i	$-0.947414\pi$
$739$	−7046.78	+	12205.4i	−0.350771	+	0.607554i	0.635614	+	0.772007i	$0.280747\pi$
$740$	−10314.3			−0.512381
$741$		0			0
$742$	6118.67			0.302727
$743$	−8793.70	+	15231.1i	−0.434198	+	0.752054i	−0.997230	−	0.0743817i	$-0.976302\pi$
$743$	−8793.70	+	15231.1i	−0.434198	+	0.752054i	0.563031	+	0.826436i	$0.309635\pi$
$744$	−20505.4	+	35516.3i	−1.01043	+	1.75012i
$745$	11877.8	+	20572.9i	0.584119	+	1.01172i
$746$	9945.63			0.488117
$747$	17679.9	+	30622.5i	0.865964	+	1.49989i
$748$	656.985	+	1137.93i	0.0321147	+	0.0556242i
$749$	13001.5			0.634263
$750$	16278.7	+	28195.5i	0.792551	+	1.37274i
$751$	8293.48	−	14364.7i	0.402974	−	0.697971i	−0.591109	−	0.806591i	$-0.701310\pi$
$751$	8293.48	−	14364.7i	0.402974	−	0.697971i	0.994083	+	0.108620i	$0.0346432\pi$
$752$	1047.64	−	1814.56i	0.0508023	−	0.0879922i
$753$	−13813.5			−0.668514
$754$		0			0
$755$	−4054.22			−0.195428
$756$	5073.91	−	8788.26i	0.244095	−	0.422786i
$757$	−16909.7	+	29288.5i	−0.811882	+	1.40622i	0.0996637	+	0.995021i	$0.468223\pi$
$757$	−16909.7	+	29288.5i	−0.811882	+	1.40622i	−0.911545	+	0.411199i	$0.865110\pi$
$758$	−5981.10	−	10359.6i	−0.286601	−	0.496407i
$759$	−10122.1			−0.484068
$760$	8852.80	+	15333.5i	0.422533	+	0.731848i
$761$	−14065.6	−	24362.4i	−0.670011	−	1.16049i	−0.977901	−	0.209071i	$-0.932956\pi$
$761$	−14065.6	−	24362.4i	−0.670011	−	1.16049i	0.307890	−	0.951422i	$-0.400377\pi$
$762$	−47290.9			−2.24825
$763$	299.295	+	518.393i	0.0142008	+	0.0245965i
$764$	1921.09	−	3327.42i	0.0909719	−	0.157568i
$765$	−12457.7	+	21577.3i	−0.588769	+	1.01978i
$766$	434.645			0.0205018
$767$		0			0
$768$	38085.9			1.78946
$769$	11867.5	−	20555.1i	0.556506	−	0.963897i	−0.441279	−	0.897370i	$-0.645475\pi$
$769$	11867.5	−	20555.1i	0.556506	−	0.963897i	0.997785	−	0.0665267i	$-0.0211917\pi$
$770$	−740.849	+	1283.19i	−0.0346732	+	0.0600557i
$771$	−7226.86	−	12517.3i	−0.337573	−	0.584694i
$772$	−6716.75			−0.313136
$773$	4768.13	+	8258.64i	0.221860	+	0.384272i	0.955373	−	0.295403i	$-0.0954540\pi$
$773$	4768.13	+	8258.64i	0.221860	+	0.384272i	−0.733513	+	0.679675i	$0.762121\pi$
$774$	4628.77	+	8017.27i	0.214958	+	0.372319i
$775$	9862.92			0.457144
$776$	−4269.67	−	7395.29i	−0.197516	−	0.342108i
$777$	−16858.2	+	29199.3i	−0.778359	+	1.34816i
$778$	10160.2	−	17598.0i	0.468202	−	0.810949i
$779$	22662.1			1.04230
$780$		0			0
$781$	−7630.84			−0.349619
$782$	5321.42	−	9216.98i	0.243342	−	0.421481i
$783$	−2808.97	+	4865.28i	−0.128205	+	0.222057i
$784$	−4165.37	−	7214.62i	−0.189749	−	0.328655i
$785$	416.457			0.0189350
$786$	20849.0	+	36111.6i	0.946133	+	1.63875i
$787$	−8848.10	−	15325.4i	−0.400763	−	0.694143i	0.593055	−	0.805162i	$-0.297922\pi$
$787$	−8848.10	−	15325.4i	−0.400763	−	0.694143i	−0.993818	+	0.111019i	$0.964588\pi$
$788$	−13228.9			−0.598047
$789$	35239.7	+	61037.0i	1.59007	+	2.75409i
$790$	3509.73	−	6079.04i	0.158064	−	0.273775i
$791$	−4097.57	+	7097.20i	−0.184188	+	0.319023i
$792$	16225.4			0.727961
$793$		0			0
$794$	−14734.7			−0.658584
$795$	13149.0	−	22774.7i	0.586600	−	1.01602i
$796$	1655.62	−	2867.61i	0.0737209	−	0.127688i
$797$	16283.4	+	28203.6i	0.723696	+	1.25348i	0.959508	+	0.281680i	$0.0908917\pi$
$797$	16283.4	+	28203.6i	0.723696	+	1.25348i	−0.235812	+	0.971799i	$0.575775\pi$
$798$	15922.4			0.706325
$799$	−1533.02	−	2655.27i	−0.0678777	−	0.117568i
$800$	−3711.53	−	6428.55i	−0.164028	−	0.284105i
$801$	−46484.1			−2.05048
$802$	−9568.38	−	16572.9i	−0.421286	−	0.729689i
$803$	4838.22	−	8380.04i	0.212624	−	0.368275i
$804$	10027.6	−	17368.4i	0.439860	−	0.761860i
$805$	−7340.36			−0.321384
$806$		0			0
$807$	4824.66			0.210453
$808$	−6820.71	+	11813.8i	−0.296970	+	0.514367i
$809$	−5811.13	+	10065.2i	−0.252544	+	0.437420i	−0.964226	−	0.265083i	$-0.914601\pi$
$809$	−5811.13	+	10065.2i	−0.252544	+	0.437420i	0.711681	+	0.702502i	$0.247934\pi$
$810$	18860.7	+	32667.6i	0.818144	+	1.41707i
$811$	6494.39			0.281195			0.140597	−	0.990067i	$-0.455098\pi$
$811$	6494.39			0.281195			0.140597	+	0.990067i	$0.455098\pi$
$812$	178.109	+	308.493i	0.00769753	+	0.0133325i
$813$	−20499.4	−	35506.0i	−0.884312	−	1.53167i
$814$	−8945.22			−0.385172
$815$	−3084.96	−	5343.31i	−0.132591	−	0.229654i
$816$	−6632.45	+	11487.7i	−0.284537	+	0.492833i
$817$	2679.27	−	4640.64i	0.114732	−	0.198721i
$818$	16744.7			0.715725
$819$		0			0
$820$	6435.49			0.274070
$821$	−17448.9	+	30222.4i	−0.741743	+	1.28474i	0.209959	+	0.977710i	$0.432667\pi$
$821$	−17448.9	+	30222.4i	−0.741743	+	1.28474i	−0.951701	+	0.307026i	$0.900666\pi$
$822$	−8079.95	+	13994.9i	−0.342847	+	0.593829i
$823$	−751.307	−	1301.30i	−0.0318213	−	0.0551161i	0.849676	−	0.527305i	$-0.176797\pi$
$823$	−751.307	−	1301.30i	−0.0318213	−	0.0551161i	−0.881497	+	0.472189i	$0.843464\pi$
$824$	27959.9			1.18208
$825$	−2725.35	−	4720.45i	−0.115012	−	0.199206i
$826$	1369.52	+	2372.09i	0.0576899	+	0.0999218i
$827$	27887.8			1.17262			0.586308	−	0.810088i	$-0.300581\pi$
$827$	27887.8			1.17262			0.586308	+	0.810088i	$0.300581\pi$
$828$	11056.6	+	19150.6i	0.464062	+	0.803779i
$829$	−15421.8	+	26711.4i	−0.646107	+	1.11909i	0.337938	+	0.941168i	$0.390271\pi$
$829$	−15421.8	+	26711.4i	−0.646107	+	1.11909i	−0.984045	+	0.177922i	$0.943063\pi$
$830$	−4751.47	+	8229.78i	−0.198706	+	0.344168i
$831$	−41027.8			−1.71268
$832$		0			0
$833$	−12190.5			−0.507053
$834$	−30625.0	+	53044.1i	−1.27153	+	2.20236i
$835$	12204.9	−	21139.5i	0.505831	−	0.876125i
$836$	−1291.86	−	2237.56i	−0.0534448	−	0.0925690i
$837$	68445.0			2.82653
$838$	−5076.84	−	8793.35i	−0.209280	−	0.362483i
$839$	18299.4	+	31695.5i	0.752997	+	1.30423i	0.946364	+	0.323103i	$0.104726\pi$
$839$	18299.4	+	31695.5i	0.752997	+	1.30423i	−0.193366	+	0.981127i	$0.561941\pi$
$840$	16435.9			0.675110
$841$	12095.9	+	20950.7i	0.495957	+	0.859023i
$842$	−2478.85	+	4293.50i	−0.101457	+	0.175729i
$843$	−23108.4	+	40024.9i	−0.944123	+	1.63527i
$844$	2208.58			0.0900741
$845$		0			0
$846$	−10415.6			−0.423282
$847$	−5167.24	+	8949.93i	−0.209620	+	0.363073i
$848$	5011.66	−	8680.44i	0.202949	−	0.351518i
$849$	−18243.8	−	31599.2i	−0.737485	−	1.27736i
$850$	5731.15			0.231267
$851$	−22157.4	−	38377.8i	−0.892534	−	1.54591i
$852$	11643.2	+	20166.6i	0.468181	+	0.810913i
$853$	21578.4			0.866155			0.433077	−	0.901357i	$-0.357428\pi$
$853$	21578.4			0.866155			0.433077	+	0.901357i	$0.357428\pi$
$854$	910.337	+	1576.75i	0.0364767	+	0.0631795i
$855$	24496.1	−	42428.4i	0.979822	−	1.69710i
$856$	19131.4	−	33136.5i	0.763897	−	1.32311i
$857$	−31199.6			−1.24359			−0.621795	−	0.783180i	$-0.713596\pi$
$857$	−31199.6			−1.24359			−0.621795	+	0.783180i	$0.713596\pi$
$858$		0			0
$859$	8035.71			0.319179			0.159590	−	0.987183i	$-0.448983\pi$
$859$	8035.71			0.319179			0.159590	+	0.987183i	$0.448983\pi$
$860$	760.849	−	1317.83i	0.0301683	−	0.0522531i
$861$	10518.5	−	18218.5i	0.416340	−	0.721122i
$862$	−441.173	−	764.134i	−0.0174320	−	0.0301932i
$863$	−8741.47			−0.344801			−0.172400	−	0.985027i	$-0.555152\pi$
$863$	−8741.47			−0.344801			−0.172400	+	0.985027i	$0.555152\pi$
$864$	−25756.6	−	44611.8i	−1.01419	−	1.75662i
$865$	−6703.93	−	11611.5i	−0.263515	−	0.456421i
$866$	−11558.9			−0.453566
$867$	−14242.3	−	24668.3i	−0.557892	−	0.966297i
$868$	2169.95	−	3758.47i	0.0848536	−	0.146971i
$869$	−1861.71	+	3224.57i	−0.0726744	+	0.125876i
$870$	−2503.20			−0.0975475
$871$		0			0
$872$	1761.62			0.0684128
$873$	−11814.4	+	20463.1i	−0.458024	+	0.793321i
$874$	−10463.7	+	18123.7i	−0.404967	+	0.701423i
$875$	−6261.87	−	10845.9i	−0.241931	−	0.419038i
$876$	−29528.8			−1.13891
$877$	872.066	+	1510.46i	0.0335776	+	0.0581582i	0.882326	−	0.470639i	$-0.155977\pi$
$877$	872.066	+	1510.46i	0.0335776	+	0.0581582i	−0.848748	+	0.528797i	$0.822643\pi$
$878$	12621.4	+	21860.9i	0.485138	+	0.840284i
$879$	−51229.0			−1.96577
$880$	1213.62	+	2102.06i	0.0464900	+	0.0805230i
$881$	2844.40	−	4926.65i	0.108775	−	0.188403i	−0.806500	−	0.591235i	$-0.798641\pi$
$881$	2844.40	−	4926.65i	0.108775	−	0.188403i	0.915274	+	0.402832i	$0.131974\pi$
$882$	−20706.1	+	35864.0i	−0.790488	+	1.36916i
$883$	−3940.14			−0.150165			−0.0750827	−	0.997177i	$-0.523922\pi$
$883$	−3940.14			−0.150165			−0.0750827	+	0.997177i	$0.523922\pi$
$884$		0			0
$885$	11772.4			0.447147
$886$	17406.4	−	30148.8i	0.660022	−	1.14319i
$887$	18440.2	−	31939.3i	0.698039	−	1.20904i	−0.271106	−	0.962549i	$-0.587389\pi$
$887$	18440.2	−	31939.3i	0.698039	−	1.20904i	0.969145	−	0.246490i	$-0.0792772\pi$
$888$	49612.9	+	85932.1i	1.87489	+	3.24740i
$889$	18191.3			0.686295
$890$	−6246.28	−	10818.9i	−0.235254	−	0.407471i
$891$	−10004.5	−	17328.2i	−0.376164	−	0.651535i
$892$	−3082.97			−0.115724
$893$	3014.44	+	5221.16i	0.112961	+	0.195654i
$894$	31435.3	−	54447.5i	1.17601	−	2.03691i
$895$	−13921.5	+	24112.7i	−0.519937	+	0.900558i
$896$	1274.75			0.0475296
$897$		0			0
$898$	30493.5			1.13317
$899$	−1201.31	+	2080.73i	−0.0445671	+	0.0771926i
$900$	−5953.95	+	10312.5i	−0.220517	+	0.381946i
$901$	−7333.62	−	12702.2i	−0.271164	−	0.469669i
$902$	5581.26			0.206026
$903$	−2487.14	−	4307.85i	−0.0916575	−	0.158755i
$904$	12059.0	+	20886.7i	0.443667	+	0.768454i
$905$	−31194.8			−1.14580
$906$	5364.87	+	9292.23i	0.196728	+	0.340743i
$907$	−8955.99	+	15512.2i	−0.327871	+	0.567889i	−0.982089	−	0.188417i	$-0.939664\pi$
$907$	−8955.99	+	15512.2i	−0.327871	+	0.567889i	0.654219	+	0.756306i	$0.272998\pi$
$908$	−8034.33	+	13915.9i	−0.293644	+	0.508606i
$909$	37746.3			1.37730
$910$		0			0
$911$	51246.0			1.86373			0.931864	−	0.362807i	$-0.118181\pi$
$911$	51246.0			1.86373			0.931864	+	0.362807i	$0.118181\pi$
$912$	13041.7	−	22588.8i	0.473523	−	0.820165i
$913$	2520.37	−	4365.41i	0.0913604	−	0.158241i
$914$	−14117.8	−	24452.7i	−0.510912	−	0.884926i
$915$	7825.24			0.282726
$916$	4569.34	+	7914.32i	0.164820	+	0.285477i
$917$	−8019.95	−	13891.0i	−0.288814	−	0.500240i
$918$	39772.0			1.42993
$919$	−12748.3	−	22080.6i	−0.457591	−	0.792571i	0.541242	−	0.840867i	$-0.317954\pi$
$919$	−12748.3	−	22080.6i	−0.457591	−	0.792571i	−0.998833	+	0.0482959i	$0.984621\pi$
$920$	−10801.2	+	18708.2i	−0.387070	+	0.670425i
$921$	−1230.59	+	2131.45i	−0.0440276	+	0.0762580i
$922$	20396.9			0.728564
$923$		0			0
$924$	−2398.43			−0.0853924
$925$	11931.7	−	20666.3i	0.424121	−	0.734600i
$926$	−7698.35	+	13333.9i	−0.273200	+	0.473197i
$927$	−38683.1	−	67001.1i	−1.37057	−	2.37390i
$928$	1808.26			0.0639646
$929$	22524.3	+	39013.2i	0.795477	+	1.37781i	0.922536	+	0.385912i	$0.126113\pi$
$929$	22524.3	+	39013.2i	0.795477	+	1.37781i	−0.127058	+	0.991895i	$0.540553\pi$
$930$	15248.6	+	26411.3i	0.537657	+	0.931249i
$931$	23970.6			0.843830
$932$	−3603.76	−	6241.89i	−0.126658	−	0.219378i
$933$	12484.2	−	21623.2i	0.438064	−	0.758748i
$934$	3253.08	−	5634.50i	0.113966	−	0.197394i
$935$	3551.82			0.124232
$936$		0			0
$937$	−2280.50			−0.0795099			−0.0397550	−	0.999209i	$-0.512658\pi$
$937$	−2280.50			−0.0795099			−0.0397550	+	0.999209i	$0.512658\pi$
$938$	6306.65	−	10923.4i	0.219530	−	0.380237i
$939$	−3392.02	+	5875.14i	−0.117885	+	0.204183i
$940$	856.028	+	1482.68i	0.0297027	+	0.0514466i
$941$	−31174.8			−1.07999			−0.539994	−	0.841669i	$-0.681573\pi$
$941$	−31174.8			−1.07999			−0.539994	+	0.841669i	$0.681573\pi$
$942$	−551.089	−	954.514i	−0.0190610	−	0.0330146i
$943$	13824.9	+	23945.3i	0.477412	+	0.826901i
$944$	4486.98			0.154702
$945$	−13715.4	−	23755.7i	−0.472128	−	0.817750i
$946$	659.856	−	1142.90i	0.0226784	−	0.0392802i
$947$	−14197.0	+	24589.9i	−0.487159	+	0.843784i	−0.999891	−	0.0147644i	$-0.995300\pi$
$947$	−14197.0	+	24589.9i	−0.487159	+	0.843784i	0.512732	+	0.858549i	$0.328634\pi$
$948$	11362.4			0.389277
$949$		0			0
$950$	−11269.4			−0.384871
$951$	−28014.6	+	48522.8i	−0.955243	+	1.65453i
$952$	4583.41	−	7938.71i	0.156039	−	0.270268i
$953$	16958.4	+	29372.8i	0.576429	+	0.998404i	0.995885	+	0.0906283i	$0.0288875\pi$
$953$	16958.4	+	29372.8i	0.576429	+	0.998404i	−0.419456	+	0.907776i	$0.637779\pi$
$954$	−49826.0			−1.69096
$955$	−5192.93	−	8994.42i	−0.175957	−	0.304767i
$956$	1189.29	+	2059.91i	0.0402346	+	0.0696884i
$957$	1327.80			0.0448501
$958$	19036.6	+	32972.4i	0.642010	+	1.11199i
$959$	3108.09	−	5383.38i	0.104657	−	0.181270i
$960$	21235.1	−	36780.4i	0.713918	−	1.23654i
$961$	−519.228			−0.0174290
$962$		0			0
$963$	−105874.			−3.54284
$964$	−5339.54	+	9248.35i	−0.178397	+	0.308993i
$965$	−9078.08	+	15723.7i	−0.302833	+	0.524522i
$966$	9713.35	+	16824.0i	0.323522	+	0.560356i
$967$	10792.9			0.358920			0.179460	−	0.983765i	$-0.442565\pi$
$967$	10792.9			0.358920			0.179460	+	0.983765i	$0.442565\pi$
$968$	15207.0	+	26339.2i	0.504928	+	0.874561i
$969$	−19084.0	−	33054.5i	−0.632681	−	1.09584i
$970$	−6350.19			−0.210198
$971$	−3715.56	−	6435.55i	−0.122799	−	0.212695i	0.798071	−	0.602563i	$-0.205854\pi$
$971$	−3715.56	−	6435.55i	−0.122799	−	0.212695i	−0.920871	+	0.389868i	$0.872520\pi$
$972$	−14132.9	+	24478.9i	−0.466372	+	0.807780i
$973$	11780.5	−	20404.4i	0.388144	−	0.672285i
$974$	−30775.1			−1.01242
$975$		0			0
$976$	2982.54			0.0978164
$977$	6211.30	−	10758.3i	0.203395	−	0.352291i	−0.746225	−	0.665694i	$-0.768136\pi$
$977$	6211.30	−	10758.3i	0.203395	−	0.352291i	0.949620	+	0.313403i	$0.101469\pi$
$978$	−8164.53	+	14141.4i	−0.266946	+	0.462364i
$979$	3313.28	+	5738.77i	0.108164	+	0.187346i
$980$	6807.08			0.221882
$981$	−2437.24	−	4221.42i	−0.0793221	−	0.137390i
$982$	−13199.1	−	22861.5i	−0.428920	−	0.742911i
$983$	38791.6			1.25866			0.629328	−	0.777140i	$-0.283330\pi$
$983$	38791.6			1.25866			0.629328	+	0.777140i	$0.283330\pi$
$984$	−30955.4	−	53616.3i	−1.00287	−	1.73702i
$985$	−17879.7	+	30968.5i	−0.578369	+	1.00177i
$986$	−698.057	+	1209.07i	−0.0225463	+	0.0390513i
$987$	5596.53			0.180486
$988$		0			0
$989$	6537.89			0.210205
$990$	6032.93	−	10449.3i	0.193676	−	0.335457i
$991$	533.253	−	923.621i	0.0170932	−	0.0296062i	−0.857352	−	0.514730i	$-0.827892\pi$
$991$	533.253	−	923.621i	0.0170932	−	0.0296062i	0.874445	+	0.485124i	$0.161225\pi$
$992$	−11015.3	−	19079.1i	−0.352557	−	0.610646i
$993$	−41380.8			−1.32244
$994$	7322.72	+	12683.3i	0.233665	+	0.404719i
$995$	−4475.33	−	7751.50i	−0.142590	−	0.246974i
$996$	−15382.4			−0.489369
$997$	15325.8	+	26545.0i	0.486833	+	0.843219i	0.999885	−	0.0151382i	$-0.00481881\pi$
$997$	15325.8	+	26545.0i	0.486833	+	0.843219i	−0.513053	+	0.858357i	$0.671485\pi$
$998$	5820.02	−	10080.6i	0.184599	−	0.319734i
$999$	82801.7	−	143417.i	2.62235	−	4.54204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.l.22.6		18
13.2	odd	12		169.4.e.h.23.13		36
13.3	even	3	inner	169.4.c.l.146.6		18
13.4	even	6		169.4.a.l.1.6	yes	9
13.5	odd	4		169.4.e.h.147.6		36
13.6	odd	12		169.4.b.g.168.13		18
13.7	odd	12		169.4.b.g.168.6		18
13.8	odd	4		169.4.e.h.147.13		36
13.9	even	3		169.4.a.k.1.4	✓	9
13.10	even	6		169.4.c.k.146.4		18
13.11	odd	12		169.4.e.h.23.6		36
13.12	even	2		169.4.c.k.22.4		18
39.17	odd	6		1521.4.a.bg.1.4		9
39.35	odd	6		1521.4.a.bh.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.4	✓	9	13.9	even	3
169.4.a.l.1.6	yes	9	13.4	even	6
169.4.b.g.168.6		18	13.7	odd	12
169.4.b.g.168.13		18	13.6	odd	12
169.4.c.k.22.4		18	13.12	even	2
169.4.c.k.146.4		18	13.10	even	6
169.4.c.l.22.6		18	1.1	even	1	trivial
169.4.c.l.146.6		18	13.3	even	3	inner
169.4.e.h.23.6		36	13.11	odd	12
169.4.e.h.23.13		36	13.2	odd	12
169.4.e.h.147.6		36	13.5	odd	4
169.4.e.h.147.13		36	13.8	odd	4
1521.4.a.bg.1.4		9	39.17	odd	6
1521.4.a.bh.1.6		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)

\(f(q)\)	\(=\)	\(q+(1.11399 - 1.92949i) q^{2} +(4.87434 - 8.44260i) q^{3} +(1.51803 + 2.62931i) q^{4} +8.20685 q^{5} +(-10.8600 - 18.8100i) q^{6} +(4.17747 + 7.23560i) q^{7} +24.5882 q^{8} +(-34.0183 - 58.9214i) q^{9} +O(q^{10})\)	\(q+(1.11399 - 1.92949i) q^{2} +(4.87434 - 8.44260i) q^{3} +(1.51803 + 2.62931i) q^{4} +8.20685 q^{5} +(-10.8600 - 18.8100i) q^{6} +(4.17747 + 7.23560i) q^{7} +24.5882 q^{8} +(-34.0183 - 58.9214i) q^{9} +(9.14239 - 15.8351i) q^{10} +(-4.84949 + 8.39957i) q^{11} +29.5976 q^{12} +18.6147 q^{14} +(40.0030 - 69.2872i) q^{15} +(15.2469 - 26.4084i) q^{16} +(-22.3109 - 38.6437i) q^{17} -151.585 q^{18} +(43.8709 + 75.9867i) q^{19} +(12.4583 + 21.5784i) q^{20} +81.4497 q^{21} +(10.8046 + 18.7141i) q^{22} +(-53.5263 + 92.7102i) q^{23} +(119.851 - 207.589i) q^{24} -57.6475 q^{25} -400.052 q^{27} +(-12.6831 + 21.9678i) q^{28} +(7.02150 - 12.1616i) q^{29} +(-89.1261 - 154.371i) q^{30} -171.090 q^{31} +(64.3831 + 111.515i) q^{32} +(47.2761 + 81.8846i) q^{33} -99.4170 q^{34} +(34.2839 + 59.3815i) q^{35} +(103.282 - 178.890i) q^{36} +(-206.977 + 358.495i) q^{37} +195.488 q^{38} +201.792 q^{40} +(129.141 - 223.678i) q^{41} +(90.7344 - 157.157i) q^{42} +(-30.5359 - 52.8897i) q^{43} -29.4468 q^{44} +(-279.183 - 483.560i) q^{45} +(119.256 + 206.557i) q^{46} +68.7115 q^{47} +(-148.637 - 257.446i) q^{48} +(136.597 - 236.594i) q^{49} +(-64.2190 + 111.231i) q^{50} -435.004 q^{51} +328.701 q^{53} +(-445.656 + 771.899i) q^{54} +(-39.7991 + 68.9340i) q^{55} +(102.717 + 177.911i) q^{56} +855.367 q^{57} +(-15.6438 - 27.0959i) q^{58} +(73.5721 + 127.431i) q^{59} +242.904 q^{60} +(48.9041 + 84.7045i) q^{61} +(-190.593 + 330.117i) q^{62} +(284.221 - 492.286i) q^{63} +530.839 q^{64} +210.661 q^{66} +(338.799 - 586.817i) q^{67} +(67.7376 - 117.325i) q^{68} +(521.810 + 903.802i) q^{69} +152.768 q^{70} +(393.383 + 681.360i) q^{71} +(-836.450 - 1448.77i) q^{72} -997.675 q^{73} +(461.142 + 798.722i) q^{74} +(-280.994 + 486.695i) q^{75} +(-133.195 + 230.701i) q^{76} -81.0345 q^{77} +383.897 q^{79} +(125.129 - 216.729i) q^{80} +(-1031.50 + 1786.60i) q^{81} +(-287.724 - 498.353i) q^{82} -519.718 q^{83} +(123.643 + 214.157i) q^{84} +(-183.103 - 317.143i) q^{85} -136.067 q^{86} +(-68.4503 - 118.559i) q^{87} +(-119.240 + 206.530i) q^{88} +(341.611 - 591.687i) q^{89} -1244.03 q^{90} -325.019 q^{92} +(-833.950 + 1444.44i) q^{93} +(76.5442 - 132.578i) q^{94} +(360.042 + 623.612i) q^{95} +1255.30 q^{96} +(-173.647 - 300.765i) q^{97} +(-304.337 - 527.128i) q^{98} +659.886 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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