LMFDB - Embedded newform 169.4.c.l.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$18$
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			146.1
Root			$2.92009 - 5.05774i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.l.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42009 - 4.19172i) q^{2} +(3.09831 + 5.36643i) q^{3} +(-7.71365 + 13.3604i) q^{4} -15.2399 q^{5} +(14.9964 - 25.9745i) q^{6} +(2.15810 - 3.73794i) q^{7} +35.9495 q^{8} +(-5.69903 + 9.87102i) q^{9} +O(q^{10})$	\(q+(-2.42009 - 4.19172i) q^{2} +(3.09831 + 5.36643i) q^{3} +(-7.71365 + 13.3604i) q^{4} -15.2399 q^{5} +(14.9964 - 25.9745i) q^{6} +(2.15810 - 3.73794i) q^{7} +35.9495 q^{8} +(-5.69903 + 9.87102i) q^{9} +(36.8818 + 63.8811i) q^{10} +(12.2846 + 21.2775i) q^{11} -95.5971 q^{12} -20.8912 q^{14} +(-47.2178 - 81.7836i) q^{15} +(-25.2917 - 43.8065i) q^{16} +(63.5802 - 110.124i) q^{17} +55.1687 q^{18} +(25.8731 - 44.8135i) q^{19} +(117.555 - 203.611i) q^{20} +26.7459 q^{21} +(59.4595 - 102.987i) q^{22} +(-43.6842 - 75.6632i) q^{23} +(111.383 + 192.920i) q^{24} +107.253 q^{25} +96.6792 q^{27} +(33.2937 + 57.6664i) q^{28} +(-112.863 - 195.484i) q^{29} +(-228.542 + 395.847i) q^{30} +108.720 q^{31} +(21.3817 - 37.0342i) q^{32} +(-76.1228 + 131.849i) q^{33} -615.479 q^{34} +(-32.8892 + 56.9657i) q^{35} +(-87.9208 - 152.283i) q^{36} +(-57.8782 - 100.248i) q^{37} -250.461 q^{38} -547.865 q^{40} +(95.9425 + 166.177i) q^{41} +(-64.7274 - 112.111i) q^{42} +(61.6504 - 106.782i) q^{43} -379.036 q^{44} +(86.8524 - 150.433i) q^{45} +(-211.439 + 366.223i) q^{46} -36.7339 q^{47} +(156.723 - 271.452i) q^{48} +(162.185 + 280.913i) q^{49} +(-259.562 - 449.574i) q^{50} +787.965 q^{51} +119.162 q^{53} +(-233.972 - 405.252i) q^{54} +(-187.215 - 324.266i) q^{55} +(77.5827 - 134.377i) q^{56} +320.651 q^{57} +(-546.276 + 946.178i) q^{58} +(402.276 - 696.763i) q^{59} +1456.89 q^{60} +(-339.443 + 587.933i) q^{61} +(-263.113 - 455.725i) q^{62} +(24.5982 + 42.6053i) q^{63} -611.650 q^{64} +736.896 q^{66} +(43.7403 + 75.7604i) q^{67} +(980.872 + 1698.92i) q^{68} +(270.694 - 468.856i) q^{69} +318.379 q^{70} +(490.525 - 849.614i) q^{71} +(-204.877 + 354.858i) q^{72} +263.862 q^{73} +(-280.140 + 485.218i) q^{74} +(332.303 + 575.566i) q^{75} +(399.152 + 691.352i) q^{76} +106.045 q^{77} +321.051 q^{79} +(385.441 + 667.604i) q^{80} +(453.416 + 785.339i) q^{81} +(464.378 - 804.327i) q^{82} -1042.54 q^{83} +(-206.308 + 357.337i) q^{84} +(-968.953 + 1678.28i) q^{85} -596.798 q^{86} +(699.368 - 1211.34i) q^{87} +(441.624 + 764.915i) q^{88} +(172.373 + 298.558i) q^{89} -840.762 q^{90} +1347.86 q^{92} +(336.849 + 583.440i) q^{93} +(88.8993 + 153.978i) q^{94} +(-394.302 + 682.951i) q^{95} +264.989 q^{96} +(241.261 - 417.876i) q^{97} +(785.005 - 1359.67i) q^{98} -280.041 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.42009	−	4.19172i	−0.855630	−	1.48200i	−0.876059	−	0.482204i	$-0.839836\pi$
$2$	−2.42009	−	4.19172i	−0.855630	−	1.48200i	0.0204286	−	0.999791i	$-0.493497\pi$
$3$	3.09831	+	5.36643i	0.596270	+	1.03277i	0.993366	+	0.114993i	$0.0366845\pi$
$3$	3.09831	+	5.36643i	0.596270	+	1.03277i	−0.397097	+	0.917777i	$0.629982\pi$
$4$	−7.71365	+	13.3604i	−0.964207	+	1.67006i
$5$	−15.2399			−1.36309			−0.681547	−	0.731774i	$-0.738692\pi$
$5$	−15.2399			−1.36309			−0.681547	+	0.731774i	$0.738692\pi$
$6$	14.9964	−	25.9745i	1.02037	−	1.76734i
$7$	2.15810	−	3.73794i	0.116527	−	0.201830i	−0.801862	−	0.597509i	$-0.796157\pi$
$7$	2.15810	−	3.73794i	0.116527	−	0.201830i	0.918389	+	0.395679i	$0.129491\pi$
$8$	35.9495			1.58876
$9$	−5.69903	+	9.87102i	−0.211075	+	0.365593i
$10$	36.8818	+	63.8811i	1.16630	+	2.02010i
$11$	12.2846	+	21.2775i	0.336722	+	0.583219i	0.983814	−	0.179193i	$-0.0573485\pi$
$11$	12.2846	+	21.2775i	0.336722	+	0.583219i	−0.647092	+	0.762412i	$0.724015\pi$
$12$	−95.5971			−2.29971
$13$		0			0
$13$		0			0
$14$	−20.8912			−0.398815
$15$	−47.2178	−	81.7836i	−0.812772	−	1.40776i
$16$	−25.2917	−	43.8065i	−0.395183	−	0.684476i
$17$	63.5802	−	110.124i	0.907086	−	1.57112i	0.0889948	−	0.996032i	$-0.471635\pi$
$17$	63.5802	−	110.124i	0.907086	−	1.57112i	0.818092	−	0.575088i	$-0.195032\pi$
$18$	55.1687			0.722410
$19$	25.8731	−	44.8135i	0.312405	−	0.541101i	−0.666478	−	0.745525i	$-0.732199\pi$
$19$	25.8731	−	44.8135i	0.312405	−	0.541101i	0.978882	+	0.204424i	$0.0655321\pi$
$20$	117.555	−	203.611i	1.31430	−	2.27644i
$21$	26.7459			0.277925
$22$	59.4595	−	102.987i	0.576219	−	0.998040i
$23$	−43.6842	−	75.6632i	−0.396034	−	0.685951i	0.597199	−	0.802093i	$-0.296280\pi$
$23$	−43.6842	−	75.6632i	−0.396034	−	0.685951i	−0.993233	+	0.116142i	$0.962947\pi$
$24$	111.383	+	192.920i	0.947328	+	1.64082i
$25$	107.253			0.858024
$26$		0			0
$27$	96.6792			0.689108
$28$	33.2937	+	57.6664i	0.224711	+	0.389212i
$29$	−112.863	−	195.484i	−0.722693	−	1.25174i	−0.959917	−	0.280286i	$-0.909571\pi$
$29$	−112.863	−	195.484i	−0.722693	−	1.25174i	0.237223	−	0.971455i	$-0.423763\pi$
$30$	−228.542	+	395.847i	−1.39086	+	2.40905i
$31$	108.720			0.629895			0.314948	−	0.949109i	$-0.398013\pi$
$31$	108.720			0.629895			0.314948	+	0.949109i	$0.398013\pi$
$32$	21.3817	−	37.0342i	0.118118	−	0.204587i
$33$	−76.1228	+	131.849i	−0.401554	+	0.695512i
$34$	−615.479			−3.10452
$35$	−32.8892	+	56.9657i	−0.158837	+	0.275113i
$36$	−87.9208	−	152.283i	−0.407041	−	0.705015i
$37$	−57.8782	−	100.248i	−0.257165	−	0.445423i	0.708316	−	0.705895i	$-0.249455\pi$
$37$	−57.8782	−	100.248i	−0.257165	−	0.445423i	−0.965481	+	0.260472i	$0.916122\pi$
$38$	−250.461			−1.06921
$39$		0			0
$40$	−547.865			−2.16563
$41$	95.9425	+	166.177i	0.365456	+	0.632988i	0.988849	−	0.148920i	$-0.0475797\pi$
$41$	95.9425	+	166.177i	0.365456	+	0.632988i	−0.623393	+	0.781908i	$0.714246\pi$
$42$	−64.7274	−	112.111i	−0.237801	−	0.411884i
$43$	61.6504	−	106.782i	0.218642	−	0.378699i	−0.735751	−	0.677252i	$-0.763171\pi$
$43$	61.6504	−	106.782i	0.218642	−	0.378699i	0.954393	+	0.298553i	$0.0965040\pi$
$44$	−379.036			−1.29868
$45$	86.8524	−	150.433i	0.287715	−	0.498338i
$46$	−211.439	+	366.223i	−0.677717	+	1.17384i
$47$	−36.7339			−0.114004			−0.0570020	−	0.998374i	$-0.518154\pi$
$47$	−36.7339			−0.114004			−0.0570020	+	0.998374i	$0.518154\pi$
$48$	156.723	−	271.452i	0.471271	−	0.816265i
$49$	162.185	+	280.913i	0.472843	+	0.818988i
$50$	−259.562	−	449.574i	−0.734152	−	1.27159i
$51$	787.965			2.16347
$52$		0			0
$53$	119.162			0.308833			0.154416	−	0.988006i	$-0.450650\pi$
$53$	119.162			0.308833			0.154416	+	0.988006i	$0.450650\pi$
$54$	−233.972	−	405.252i	−0.589622	−	1.02126i
$55$	−187.215	−	324.266i	−0.458983	−	0.794982i
$56$	77.5827	−	134.377i	0.185132	−	0.320659i
$57$	320.651			0.745110
$58$	−546.276	+	946.178i	−1.23672	+	2.14206i
$59$	402.276	−	696.763i	0.887660	−	1.53747i	0.0450253	−	0.998986i	$-0.485663\pi$
$59$	402.276	−	696.763i	0.887660	−	1.53747i	0.842634	−	0.538486i	$-0.181003\pi$
$60$	1456.89			3.13472
$61$	−339.443	+	587.933i	−0.712479	+	1.23405i	0.251444	+	0.967872i	$0.419094\pi$
$61$	−339.443	+	587.933i	−0.712479	+	1.23405i	−0.963924	+	0.266179i	$0.914239\pi$
$62$	−263.113	−	455.725i	−0.538957	−	0.933502i
$63$	24.5982	+	42.6053i	0.0491918	+	0.0852027i
$64$	−611.650			−1.19463
$65$		0			0
$66$	736.896			1.37433
$67$	43.7403	+	75.7604i	0.0797571	+	0.138143i	0.903145	−	0.429335i	$-0.141252\pi$
$67$	43.7403	+	75.7604i	0.0797571	+	0.138143i	−0.823388	+	0.567479i	$0.807919\pi$
$68$	980.872	+	1698.92i	1.74924	+	3.02977i
$69$	270.694	−	468.856i	0.472286	−	0.818024i
$70$	318.379			0.543622
$71$	490.525	−	849.614i	0.819923	−	1.42015i	−0.0858146	−	0.996311i	$-0.527349\pi$
$71$	490.525	−	849.614i	0.819923	−	1.42015i	0.905738	−	0.423838i	$-0.139317\pi$
$72$	−204.877	+	354.858i	−0.335348	+	0.580839i
$73$	263.862			0.423051			0.211526	−	0.977372i	$-0.432157\pi$
$73$	263.862			0.423051			0.211526	+	0.977372i	$0.432157\pi$
$74$	−280.140	+	485.218i	−0.440077	+	0.762235i
$75$	332.303	+	575.566i	0.511614	+	0.886141i
$76$	399.152	+	691.352i	0.602446	+	1.04347i
$77$	106.045			0.156948
$78$		0			0
$79$	321.051			0.457228			0.228614	−	0.973517i	$-0.426581\pi$
$79$	321.051			0.457228			0.228614	+	0.973517i	$0.426581\pi$
$80$	385.441	+	667.604i	0.538671	+	0.933005i
$81$	453.416	+	785.339i	0.621970	+	1.07728i
$82$	464.378	−	804.327i	0.625390	−	1.08321i
$83$	−1042.54			−1.37872			−0.689362	−	0.724417i	$-0.742109\pi$
$83$	−1042.54			−1.37872			−0.689362	+	0.724417i	$0.742109\pi$
$84$	−206.308	+	357.337i	−0.267977	+	0.464150i
$85$	−968.953	+	1678.28i	−1.23644	+	2.14158i
$86$	−596.798			−0.748307
$87$	699.368	−	1211.34i	0.861840	−	1.49275i
$88$	441.624	+	764.915i	0.534969	+	0.926594i
$89$	172.373	+	298.558i	0.205298	+	0.355586i	0.950227	−	0.311557i	$-0.100850\pi$
$89$	172.373	+	298.558i	0.205298	+	0.355586i	−0.744930	+	0.667143i	$0.767517\pi$
$90$	−840.762			−0.984712
$91$		0			0
$92$	1347.86			1.52743
$93$	336.849	+	583.440i	0.375587	+	0.650537i
$94$	88.8993	+	153.978i	0.0975453	+	0.168953i
$95$	−394.302	+	682.951i	−0.425837	+	0.737572i
$96$	264.989			0.281722
$97$	241.261	−	417.876i	0.252539	−	0.437411i	−0.711685	−	0.702499i	$-0.752068\pi$
$97$	241.261	−	417.876i	0.252539	−	0.437411i	0.964224	+	0.265088i	$0.0854010\pi$
$98$	785.005	−	1359.67i	0.809158	−	1.40150i
$99$	−280.041			−0.284295
$100$	−827.313	+	1432.95i	−0.827313	+	1.43295i
$101$	−419.890	−	727.270i	−0.413669	−	0.716496i	0.581619	−	0.813462i	$-0.302420\pi$
$101$	−419.890	−	727.270i	−0.413669	−	0.716496i	−0.995288	+	0.0969656i	$0.969086\pi$
$102$	−1906.94	−	3302.92i	−1.85113	−	3.20626i
$103$	159.823			0.152892			0.0764459	−	0.997074i	$-0.475643\pi$
$103$	159.823			0.152892			0.0764459	+	0.997074i	$0.475643\pi$
$104$		0			0
$105$	−407.603			−0.378838
$106$	−288.382	−	499.493i	−0.264247	−	0.457689i
$107$	−537.812	−	931.518i	−0.485909	−	0.841619i	0.513960	−	0.857814i	$-0.328178\pi$
$107$	−537.812	−	931.518i	−0.485909	−	0.841619i	−0.999869	+	0.0161950i	$0.994845\pi$
$108$	−745.750	+	1291.68i	−0.664443	+	1.15085i
$109$	−1161.67			−1.02080			−0.510401	−	0.859936i	$-0.670503\pi$
$109$	−1161.67			−1.02080			−0.510401	+	0.859936i	$0.670503\pi$
$110$	−906.154	+	1569.50i	−0.785440	+	1.36042i
$111$	358.649	−	621.198i	0.306680	−	0.531185i
$112$	−218.328			−0.184197
$113$	731.742	−	1267.41i	0.609172	−	1.05512i	−0.382205	−	0.924078i	$-0.624835\pi$
$113$	731.742	−	1267.41i	0.609172	−	1.05512i	0.991377	−	0.131040i	$-0.0418316\pi$
$114$	−776.004	−	1344.08i	−0.637539	−	1.10425i
$115$	665.740	+	1153.10i	0.539831	+	0.935015i
$116$	3482.34			2.78730
$117$		0			0
$118$	−3894.18			−3.03803
$119$	−274.425	−	475.319i	−0.211399	−	0.366154i
$120$	−1697.45	−	2940.08i	−1.29130	−	2.23659i
$121$	363.678	−	629.910i	0.273237	−	0.473260i
$122$	3285.93			2.43848
$123$	−594.519	+	1029.74i	−0.435821	+	0.754864i
$124$	−838.631	+	1452.55i	−0.607349	+	1.05196i
$125$	270.461			0.193526
$126$	119.060	−	206.217i	0.0841800	−	0.145804i
$127$	−144.962	−	251.081i	−0.101285	−	0.175432i	0.810929	−	0.585145i	$-0.198962\pi$
$127$	−144.962	−	251.081i	−0.101285	−	0.175432i	−0.912215	+	0.409713i	$0.865629\pi$
$128$	1309.19	+	2267.59i	0.904042	+	1.56585i
$129$	764.048			0.521478
$130$		0			0
$131$	−1201.97			−0.801653			−0.400826	−	0.916154i	$-0.631277\pi$
$131$	−1201.97			−0.801653			−0.400826	+	0.916154i	$0.631277\pi$
$132$	−1174.37	−	2034.07i	−0.774362	−	1.34123i
$133$	−111.674	−	193.424i	−0.0728069	−	0.126105i
$134$	211.711	−	366.694i	0.136485	−	0.236399i
$135$	−1473.38			−0.939319
$136$	2285.68	−	3958.91i	1.44114	−	2.49613i
$137$	−389.810	+	675.171i	−0.243093	+	0.421049i	−0.961594	−	0.274477i	$-0.911495\pi$
$137$	−389.810	+	675.171i	−0.243093	+	0.421049i	0.718501	+	0.695526i	$0.244829\pi$
$138$	−2620.41			−1.61641
$139$	−1015.74	+	1759.32i	−0.619814	+	1.07355i	0.369706	+	0.929149i	$0.379459\pi$
$139$	−1015.74	+	1759.32i	−0.619814	+	1.07355i	−0.989519	+	0.144400i	$0.953875\pi$
$140$	−507.391	−	878.827i	−0.306303	−	0.530532i
$141$	−113.813	−	197.130i	−0.0679772	−	0.117740i
$142$	−4748.45			−2.80621
$143$		0			0
$144$	576.553			0.333653
$145$	1720.01	+	2979.15i	0.985098	+	1.70624i
$146$	−638.570	−	1106.04i	−0.361976	−	0.626960i
$147$	−1005.00	+	1740.71i	−0.563884	+	0.976676i
$148$	1785.81			0.991841
$149$	−1301.80	+	2254.79i	−0.715757	+	1.23973i	0.246910	+	0.969038i	$0.420585\pi$
$149$	−1301.80	+	2254.79i	−0.715757	+	1.23973i	−0.962667	+	0.270688i	$0.912749\pi$
$150$	1608.41	−	2785.84i	0.875505	−	1.51642i
$151$	206.776			0.111438			0.0557192	−	0.998446i	$-0.482255\pi$
$151$	206.776			0.111438			0.0557192	+	0.998446i	$0.482255\pi$
$152$	930.124	−	1611.02i	0.496336	−	0.859679i
$153$	724.692	+	1255.20i	0.382927	+	0.663249i
$154$	−256.639	−	444.513i	−0.134290	−	0.232596i
$155$	−1656.88			−0.858606
$156$		0			0
$157$	699.208			0.355433			0.177716	−	0.984082i	$-0.443129\pi$
$157$	699.208			0.355433			0.177716	+	0.984082i	$0.443129\pi$
$158$	−776.971	−	1345.75i	−0.391218	−	0.677610i
$159$	369.200	+	639.474i	0.184148	+	0.318953i
$160$	−325.854	+	564.396i	−0.161006	+	0.278871i
$161$	−377.100			−0.184594
$162$	2194.61	−	3801.18i	1.06435	−	1.84351i
$163$	1472.07	−	2549.70i	0.707371	−	1.22520i	−0.258458	−	0.966023i	$-0.583214\pi$
$163$	1472.07	−	2549.70i	0.707371	−	1.22520i	0.965829	−	0.259180i	$-0.0834524\pi$
$164$	−2960.27			−1.40950
$165$	1160.10	−	2009.35i	0.547356	−	0.948048i
$166$	2523.05	+	4370.05i	1.17968	+	2.04326i
$167$	1370.41	+	2373.62i	0.635002	+	1.09986i	0.986515	+	0.163673i	$0.0523341\pi$
$167$	1370.41	+	2373.62i	0.635002	+	1.09986i	−0.351513	+	0.936183i	$0.614333\pi$
$168$	961.500			0.441556
$169$		0			0
$170$	9379.81			4.23176
$171$	294.903	+	510.787i	0.131882	+	0.228426i
$172$	951.100	+	1647.35i	0.421632	+	0.730288i
$173$	−169.406	+	293.420i	−0.0744491	+	0.128950i	−0.900847	−	0.434138i	$-0.857053\pi$
$173$	−169.406	+	293.420i	−0.0744491	+	0.128950i	0.826397	+	0.563087i	$0.190386\pi$
$174$	−6770.13			−2.94967
$175$	231.463	−	400.906i	0.0999826	−	0.173175i
$176$	621.395	−	1076.29i	0.266133	−	0.460956i
$177$	4985.51			2.11714
$178$	834.315	−	1445.08i	0.351318	−	0.608500i
$179$	547.199	+	947.777i	0.228489	+	0.395755i	0.957361	−	0.288896i	$-0.0932881\pi$
$179$	547.199	+	947.777i	0.228489	+	0.395755i	−0.728871	+	0.684651i	$0.759955\pi$
$180$	1339.90	+	2320.77i	0.554834	+	0.961001i
$181$	−1420.26			−0.583243			−0.291622	−	0.956534i	$-0.594195\pi$
$181$	−1420.26			−0.583243			−0.291622	+	0.956534i	$0.594195\pi$
$182$		0			0
$183$	−4206.80			−1.69932
$184$	−1570.42	−	2720.05i	−0.629202	−	1.08981i
$185$	882.054	+	1527.76i	0.350540	+	0.607153i
$186$	1630.41	−	2823.95i	0.642728	−	1.11324i
$187$	3124.22			1.22174
$188$	283.353	−	490.781i	0.109923	−	0.190393i
$189$	208.644	−	361.381i	0.0802994	−	0.139083i
$190$	3816.98			1.45744
$191$	448.390	−	776.633i	0.169866	−	0.294216i	−0.768507	−	0.639842i	$-0.779000\pi$
$191$	448.390	−	776.633i	0.169866	−	0.294216i	0.938372	+	0.345626i	$0.112333\pi$
$192$	−1895.08	−	3282.37i	−0.712321	−	1.23378i
$193$	−1294.98	−	2242.98i	−0.482980	−	0.836545i	0.516829	−	0.856088i	$-0.327112\pi$
$193$	−1294.98	−	2242.98i	−0.482980	−	0.836545i	−0.999809	+	0.0195433i	$0.993779\pi$
$194$	−2335.49			−0.864321
$195$		0			0
$196$	−5004.16			−1.82367
$197$	−740.934	−	1283.33i	−0.267966	−	0.464131i	0.700370	−	0.713780i	$-0.253018\pi$
$197$	−740.934	−	1283.33i	−0.267966	−	0.464131i	−0.968336	+	0.249649i	$0.919685\pi$
$198$	677.724	+	1173.85i	0.243251	+	0.421323i
$199$	1799.73	−	3117.22i	0.641101	−	1.11042i	−0.344086	−	0.938938i	$-0.611811\pi$
$199$	1799.73	−	3117.22i	0.641101	−	1.11042i	0.985187	−	0.171482i	$-0.0548555\pi$
$200$	3855.69			1.36319
$201$	−271.042	+	469.458i	−0.0951135	+	0.164741i
$202$	−2032.34	+	3520.12i	−0.707896	+	1.22611i
$203$	−974.278			−0.336852
$204$	−6078.09	+	10527.6i	−2.08604	+	3.61312i
$205$	−1462.15	−	2532.52i	−0.498151	−	0.862822i
$206$	−386.786	−	669.933i	−0.130819	−	0.226585i
$207$	995.830			0.334372
$208$		0			0
$209$	1271.36			0.420774
$210$	986.435	+	1708.56i	0.324145	+	0.561436i
$211$	−1525.61	−	2642.43i	−0.497759	−	0.862144i	0.502238	−	0.864730i	$-0.332510\pi$
$211$	−1525.61	−	2642.43i	−0.497759	−	0.862144i	−0.999997	+	0.00258567i	$0.999177\pi$
$212$	−919.173	+	1592.05i	−0.297779	+	0.515768i
$213$	6079.19			1.95558
$214$	−2603.11	+	4508.71i	−0.831517	+	1.44023i
$215$	−939.544	+	1627.34i	−0.298030	+	0.516202i
$216$	3475.57			1.09483
$217$	234.630	−	406.390i	0.0733995	−	0.127132i
$218$	2811.34	+	4869.38i	0.873430	+	1.51282i
$219$	817.527	+	1416.00i	0.252253	+	0.436915i
$220$	5776.45			1.77022
$221$		0			0
$222$	−3471.85			−1.04962
$223$	−1299.93	−	2251.55i	−0.390359	−	0.676121i	0.602138	−	0.798392i	$-0.294316\pi$
$223$	−1299.93	−	2251.55i	−0.390359	−	0.676121i	−0.992497	+	0.122271i	$0.960982\pi$
$224$	−92.2879	−	159.847i	−0.0275279	−	0.0476797i
$225$	−611.239	+	1058.70i	−0.181108	+	0.313688i
$226$	−7083.52			−2.08491
$227$	−496.604	+	860.144i	−0.145202	+	0.251497i	−0.929448	−	0.368953i	$-0.879716\pi$
$227$	−496.604	+	860.144i	−0.145202	+	0.251497i	0.784246	+	0.620449i	$0.213050\pi$
$228$	−2473.39	+	4284.04i	−0.718440	+	1.24438i
$229$	−437.772			−0.126327			−0.0631633	−	0.998003i	$-0.520119\pi$
$229$	−437.772			−0.126327			−0.0631633	+	0.998003i	$0.520119\pi$
$230$	3222.30	−	5581.19i	0.923792	−	1.60006i
$231$	328.562	+	569.085i	0.0935834	+	0.162091i
$232$	−4057.36	−	7027.55i	−1.14818	−	1.98871i
$233$	2933.08			0.824689			0.412344	−	0.911028i	$-0.364710\pi$
$233$	2933.08			0.824689			0.412344	+	0.911028i	$0.364710\pi$
$234$		0			0
$235$	559.819			0.155398
$236$	6206.04	+	10749.2i	1.71178	+	2.96488i
$237$	994.714	+	1722.90i	0.272631	+	0.472211i
$238$	−1328.27	+	2300.63i	−0.361759	+	0.626586i
$239$	−5813.48			−1.57340			−0.786700	−	0.617335i	$-0.788212\pi$
$239$	−5813.48			−1.57340			−0.786700	+	0.617335i	$0.788212\pi$
$240$	−2388.43	+	4136.89i	−0.642386	+	1.11265i
$241$	574.125	−	994.413i	0.153455	−	0.265792i	−0.779040	−	0.626974i	$-0.784293\pi$
$241$	574.125	−	994.413i	0.153455	−	0.265792i	0.932495	+	0.361182i	$0.117627\pi$
$242$	−3520.54			−0.935160
$243$	−1504.48	+	2605.83i	−0.397169	+	0.687918i
$244$	−5236.69	−	9070.22i	−1.37395	−	2.37976i
$245$	−2471.68	−	4281.07i	−0.644529	−	1.11636i
$246$	5755.15			1.49161
$247$		0			0
$248$	3908.44			1.00075
$249$	−3230.12	−	5594.74i	−0.822091	−	1.42390i
$250$	−654.539	−	1133.70i	−0.165587	−	0.286805i
$251$	1627.90	−	2819.60i	0.409371	−	0.709051i	−0.585449	−	0.810709i	$-0.699082\pi$
$251$	1627.90	−	2819.60i	0.409371	−	0.709051i	0.994819	+	0.101659i	$0.0324149\pi$
$252$	−758.968			−0.189724
$253$	1073.28	−	1858.98i	0.266706	−	0.461949i
$254$	−701.639	+	1215.28i	−0.173326	+	0.300209i
$255$	−12008.5			−2.94902
$256$	3890.12	−	6737.89i	0.949737	−	1.64499i
$257$	−3160.45	−	5474.06i	−0.767095	−	1.32865i	−0.939132	−	0.343557i	$-0.888368\pi$
$257$	−3160.45	−	5474.06i	−0.767095	−	1.32865i	0.172037	−	0.985090i	$-0.444965\pi$
$258$	−1849.06	−	3202.67i	−0.446193	−	0.772829i
$259$	−499.628			−0.119866
$260$		0			0
$261$	2572.84			0.610171
$262$	2908.87	+	5038.31i	0.685919	+	1.18805i
$263$	3084.49	+	5342.50i	0.723187	+	1.25260i	0.959716	+	0.280972i	$0.0906567\pi$
$263$	3084.49	+	5342.50i	0.723187	+	1.25260i	−0.236529	+	0.971624i	$0.576010\pi$
$264$	−2736.58	+	4739.89i	−0.637972	+	1.10500i
$265$	−1816.01			−0.420968
$266$	−540.520	+	936.207i	−0.124592	+	0.215799i
$267$	−1068.13	+	1850.05i	−0.244825	+	0.424050i
$268$	−1349.59			−0.307609
$269$	−421.799	+	730.578i	−0.0956043	+	0.165591i	−0.909861	−	0.414914i	$-0.863812\pi$
$269$	−421.799	+	730.578i	−0.0956043	+	0.165591i	0.814256	+	0.580505i	$0.197145\pi$
$270$	3565.70	+	6175.98i	0.803710	+	1.39207i
$271$	−1031.53	−	1786.66i	−0.231221	−	0.400486i	0.726947	−	0.686694i	$-0.240939\pi$
$271$	−1031.53	−	1786.66i	−0.231221	−	0.400486i	−0.958168	+	0.286208i	$0.907605\pi$
$272$	−6432.20			−1.43386
$273$		0			0
$274$	3773.50			0.831990
$275$	1317.56	+	2282.08i	0.288915	+	0.500416i
$276$	4176.08	+	7233.19i	0.910763	+	1.57749i
$277$	−3291.24	+	5700.60i	−0.713905	+	1.23652i	0.249475	+	0.968381i	$0.419742\pi$
$277$	−3291.24	+	5700.60i	−0.713905	+	1.23652i	−0.963380	+	0.268139i	$0.913591\pi$
$278$	9832.74			2.12133
$279$	−619.601	+	1073.18i	−0.132955	+	0.230285i
$280$	−1182.35	+	2047.89i	−0.252353	+	0.437088i
$281$	935.025			0.198502			0.0992508	−	0.995062i	$-0.468355\pi$
$281$	935.025			0.198502			0.0992508	+	0.995062i	$0.468355\pi$
$282$	−550.875	+	954.143i	−0.116327	+	0.201484i
$283$	2669.38	+	4623.51i	0.560701	+	0.971163i	0.997435	+	0.0715723i	$0.0228017\pi$
$283$	2669.38	+	4623.51i	0.560701	+	0.971163i	−0.436734	+	0.899591i	$0.643865\pi$
$284$	7567.47	+	13107.3i	1.58115	+	2.73863i
$285$	−4886.68			−1.01566
$286$		0			0
$287$	828.215			0.170341
$288$	243.710	+	422.119i	0.0498638	+	0.0863666i
$289$	−5628.39	−	9748.66i	−1.14561	−	1.98426i
$290$	8325.16	−	14419.6i	1.68576	−	2.91982i
$291$	2990.00			0.602326
$292$	−2035.34	+	3525.32i	−0.407909	+	0.706519i
$293$	−881.882	+	1527.46i	−0.175837	+	0.304558i	−0.940450	−	0.339931i	$-0.889596\pi$
$293$	−881.882	+	1527.46i	−0.175837	+	0.304558i	0.764614	+	0.644489i	$0.222930\pi$
$294$	9728.75			1.92991
$295$	−6130.63	+	10618.6i	−1.20996	+	2.09572i
$296$	−2080.69	−	3603.86i	−0.408573	−	0.707669i
$297$	1187.66	+	2057.09i	0.232038	+	0.401901i
$298$	12601.9			2.44969
$299$		0			0
$300$	−10253.1			−1.97321
$301$	−266.096	−	460.892i	−0.0509552	−	0.0882570i
$302$	−500.416	−	866.747i	−0.0953501	−	0.165151i
$303$	2601.90	−	4506.62i	0.493317	−	0.854450i
$304$	−2617.50			−0.493828
$305$	5173.06	−	8960.01i	0.971176	−	1.68213i
$306$	3507.64	−	6075.40i	0.655288	−	1.13499i
$307$	4736.59			0.880558			0.440279	−	0.897861i	$-0.354879\pi$
$307$	4736.59			0.880558			0.440279	+	0.897861i	$0.354879\pi$
$308$	−817.998	+	1416.81i	−0.151330	+	0.262112i
$309$	495.182	+	857.680i	0.0911647	+	0.157902i
$310$	4009.80	+	6945.18i	0.734649	+	1.27245i
$311$	−4746.90			−0.865505			−0.432753	−	0.901513i	$-0.642458\pi$
$311$	−4746.90			−0.865505			−0.432753	+	0.901513i	$0.642458\pi$
$312$		0			0
$313$	10115.9			1.82679			0.913393	−	0.407078i	$-0.133452\pi$
$313$	10115.9			1.82679			0.913393	+	0.407078i	$0.133452\pi$
$314$	−1692.15	−	2930.88i	−0.304119	−	0.526749i
$315$	−374.873	−	649.299i	−0.0670530	−	0.116139i
$316$	−2476.47	+	4289.38i	−0.440862	+	0.763596i
$317$	5906.13			1.04644			0.523219	−	0.852198i	$-0.324731\pi$
$317$	5906.13			1.04644			0.523219	+	0.852198i	$0.324731\pi$
$318$	1786.99	−	3095.16i	0.315125	−	0.545812i
$319$	2772.94	−	4802.88i	0.486693	−	0.842977i
$320$	9321.45			1.62839
$321$	3332.62	−	5772.26i	0.579466	−	1.00366i
$322$	912.615	+	1580.69i	0.157944	+	0.273567i
$323$	−3290.03	−	5698.51i	−0.566757	−	0.981651i
$324$	−13990.0			−2.39883
$325$		0			0
$326$	−14250.2			−2.42099
$327$	−3599.20	−	6234.00i	−0.608674	−	1.05425i
$328$	3449.08	+	5973.98i	0.580621	+	1.00567i
$329$	−79.2755	+	137.309i	−0.0132845	+	0.0230094i
$330$	−11230.2			−1.87334
$331$	−1401.41	+	2427.32i	−0.232715	+	0.403074i	−0.958606	−	0.284736i	$-0.908094\pi$
$331$	−1401.41	+	2427.32i	−0.232715	+	0.403074i	0.725891	+	0.687809i	$0.241427\pi$
$332$	8041.82	−	13928.8i	1.32937	−	2.30254i
$333$	1319.40			0.217125
$334$	6633.02	−	11488.7i	1.08665	−	1.88214i
$335$	−666.596	−	1154.58i	−0.108716	−	0.188302i
$336$	−676.448	−	1171.64i	−0.109831	−	0.190233i
$337$	−244.919			−0.0395892			−0.0197946	−	0.999804i	$-0.506301\pi$
$337$	−244.919			−0.0395892			−0.0197946	+	0.999804i	$0.506301\pi$
$338$		0			0
$339$	9068.65			1.45292
$340$	−14948.3	−	25891.3i	−2.38438	−	4.12986i
$341$	1335.58	+	2313.30i	0.212099	+	0.367367i
$342$	1427.38	−	2472.30i	0.225684	−	0.390897i
$343$	2880.51			0.453448
$344$	2216.30	−	3838.75i	0.347369	−	0.601661i
$345$	−4125.34	+	7145.30i	−0.643770	+	1.11504i
$346$	1639.91			0.254804
$347$	−5178.41	+	8969.27i	−0.801129	+	1.38760i	0.117745	+	0.993044i	$0.462434\pi$
$347$	−5178.41	+	8969.27i	−0.801129	+	1.38760i	−0.918874	+	0.394552i	$0.870900\pi$
$348$	10789.4	+	18687.7i	1.66198	+	2.87864i
$349$	−4216.79	−	7303.69i	−0.646761	−	1.12022i	−0.983892	−	0.178765i	$-0.942790\pi$
$349$	−4216.79	−	7303.69i	−0.646761	−	1.12022i	0.337131	−	0.941458i	$-0.390544\pi$
$350$	−2240.64			−0.342193
$351$		0			0
$352$	1050.66			0.159092
$353$	2366.86	+	4099.52i	0.356871	+	0.618118i	0.987436	−	0.158018i	$-0.0505104\pi$
$353$	2366.86	+	4099.52i	0.356871	+	0.618118i	−0.630566	+	0.776136i	$0.717177\pi$
$354$	−12065.4	−	20897.8i	−1.81149	−	3.13759i
$355$	−7475.52	+	12948.0i	−1.11763	+	1.93580i
$356$	−5318.50			−0.791797
$357$	1700.51	−	2945.37i	0.252102	−	0.436654i
$358$	2648.54	−	4587.41i	0.391005	−	0.677240i
$359$	−7561.34			−1.11162			−0.555811	−	0.831309i	$-0.687592\pi$
$359$	−7561.34			−1.11162			−0.555811	+	0.831309i	$0.687592\pi$
$360$	3122.30	−	5407.98i	0.457110	−	0.791738i
$361$	2090.67	+	3621.14i	0.304806	+	0.527940i
$362$	3437.15	+	5953.32i	0.499041	+	0.864364i
$363$	4507.15			0.651692
$364$		0			0
$365$	−4021.22			−0.576659
$366$	10180.8	+	17633.7i	1.45399	+	2.51838i
$367$	5969.99	+	10340.3i	0.849130	+	1.47074i	0.881986	+	0.471276i	$0.156206\pi$
$367$	5969.99	+	10340.3i	0.849130	+	1.47074i	−0.0328557	+	0.999460i	$0.510460\pi$
$368$	−2209.69	+	3827.30i	−0.313011	+	0.542152i
$369$	−2187.12			−0.308555
$370$	4269.30	−	7394.64i	0.599866	−	1.03900i
$371$	257.164	−	445.420i	0.0359872	−	0.0623317i
$372$	−10393.4			−1.44858
$373$	2898.56	−	5020.46i	0.402364	−	0.696915i	−0.591647	−	0.806197i	$-0.701522\pi$
$373$	2898.56	−	5020.46i	0.402364	−	0.696915i	0.994011	+	0.109282i	$0.0348552\pi$
$374$	−7560.90	−	13095.9i	−1.04536	−	1.81062i
$375$	837.971	+	1451.41i	0.115394	+	0.199868i
$376$	−1320.56			−0.181125
$377$		0			0
$378$	−2019.74			−0.274826
$379$	4423.15	+	7661.13i	0.599478	+	1.03833i	0.992898	+	0.118968i	$0.0379585\pi$
$379$	4423.15	+	7661.13i	0.599478	+	1.03833i	−0.393420	+	0.919359i	$0.628708\pi$
$380$	−6083.02	−	10536.1i	−0.821190	−	1.42234i
$381$	898.271	−	1555.85i	0.120787	−	0.209209i
$382$	−4340.57			−0.581369
$383$	523.805	−	907.256i	0.0698830	−	0.121041i	−0.828967	−	0.559298i	$-0.811071\pi$
$383$	523.805	−	907.256i	0.0698830	−	0.121041i	0.898850	+	0.438257i	$0.144404\pi$
$384$	−8112.56	+	14051.4i	−1.07811	+	1.86733i
$385$	−1616.12			−0.213935
$386$	−6267.96	+	10856.4i	−0.826504	+	1.43155i
$387$	702.696	+	1217.11i	0.0922999	+	0.159868i
$388$	3722.00	+	6446.70i	0.487000	+	0.843509i
$389$	−11858.4			−1.54562			−0.772808	−	0.634640i	$-0.781148\pi$
$389$	−11858.4			−1.54562			−0.772808	+	0.634640i	$0.781148\pi$
$390$		0			0
$391$	−11109.8			−1.43695
$392$	5830.47	+	10098.7i	0.751233	+	1.30117i
$393$	−3724.07	−	6450.28i	−0.478001	−	0.827923i
$394$	−3586.25	+	6211.57i	−0.458560	+	0.794249i
$395$	−4892.76			−0.623245
$396$	2160.14	−	3741.47i	0.274119	−	0.474788i
$397$	5240.17	−	9076.25i	0.662460	−	1.14741i	−0.317507	−	0.948256i	$-0.602846\pi$
$397$	5240.17	−	9076.25i	0.662460	−	1.14741i	0.979967	−	0.199159i	$-0.0638210\pi$
$398$	−17422.0			−2.19418
$399$	691.998	−	1198.58i	0.0868252	−	0.150386i
$400$	−2712.61	−	4698.38i	−0.339076	−	0.587297i
$401$	3968.20	+	6873.12i	0.494171	+	0.855929i	0.999977	−	0.00671803i	$-0.00213843\pi$
$401$	3968.20	+	6873.12i	0.494171	+	0.855929i	−0.505807	+	0.862647i	$0.668805\pi$
$402$	2623.78			0.325528
$403$		0			0
$404$	12955.5			1.59545
$405$	−6909.99	−	11968.5i	−0.847803	−	1.46844i
$406$	2357.84	+	4083.90i	0.288221	+	0.499213i
$407$	1422.02	−	2463.01i	0.173186	−	0.299967i
$408$	28326.9			3.43723
$409$	−2917.84	+	5053.85i	−0.352758	+	0.610994i	−0.986732	−	0.162360i	$-0.948089\pi$
$409$	−2917.84	+	5053.85i	−0.352758	+	0.610994i	0.633974	+	0.773355i	$0.281423\pi$
$410$	−7077.06	+	12257.8i	−0.852466	+	1.47651i
$411$	−4831.01			−0.579796
$412$	−1232.82	+	2135.31i	−0.147419	+	0.255338i
$413$	−1736.31	−	3007.37i	−0.206872	−	0.358313i
$414$	−2410.00	−	4174.24i	−0.286099	−	0.495538i
$415$	15888.2			1.87933
$416$		0			0
$417$	−12588.3			−1.47830
$418$	−3076.80	−	5329.18i	−0.360027	−	0.623585i
$419$	4272.14	+	7399.57i	0.498109	+	0.862751i	0.999998	−	0.00218165i	$-0.000694441\pi$
$419$	4272.14	+	7399.57i	0.498109	+	0.862751i	−0.501888	+	0.864933i	$0.667361\pi$
$420$	3144.11	−	5445.76i	0.365278	−	0.632680i
$421$	16524.6			1.91297			0.956484	−	0.291786i	$-0.0942496\pi$
$421$	16524.6			1.91297			0.956484	+	0.291786i	$0.0942496\pi$
$422$	−7384.21	+	12789.8i	−0.851796	+	1.47535i
$423$	209.348	−	362.601i	0.0240634	−	0.0416791i
$424$	4283.81			0.490661
$425$	6819.17	−	11811.2i	0.778302	−	1.34806i
$426$	−14712.2	−	25482.2i	−1.67326	−	2.89816i
$427$	1465.11	+	2537.64i	0.166046	+	0.287599i
$428$	16594.0			1.87407
$429$		0			0
$430$	9095.11			1.02001
$431$	−3418.29	−	5920.65i	−0.382026	−	0.661689i	0.609326	−	0.792920i	$-0.291440\pi$
$431$	−3418.29	−	5920.65i	−0.382026	−	0.661689i	−0.991352	+	0.131231i	$0.958107\pi$
$432$	−2445.18	−	4235.18i	−0.272324	−	0.471678i
$433$	3145.32	−	5447.86i	0.349087	−	0.604636i	−0.637001	−	0.770863i	$-0.719825\pi$
$433$	3145.32	−	5447.86i	0.349087	−	0.604636i	0.986088	+	0.166227i	$0.0531585\pi$
$434$	−2271.30			−0.251211
$435$	−10658.3	+	18460.6i	−1.17477	+	2.03476i
$436$	8960.70	−	15520.4i	0.984265	−	1.70480i
$437$	−4520.98			−0.494892
$438$	3956.97	−	6853.68i	0.431670	−	0.747675i
$439$	−4434.30	−	7680.43i	−0.482090	−	0.835004i	0.517699	−	0.855563i	$-0.326789\pi$
$439$	−4434.30	−	7680.43i	−0.482090	−	0.835004i	−0.999789	+	0.0205589i	$0.993455\pi$
$440$	−6730.28	−	11657.2i	−0.729213	−	1.26303i
$441$	−3697.20			−0.399222
$442$		0			0
$443$	−4310.67			−0.462316			−0.231158	−	0.972916i	$-0.574251\pi$
$443$	−4310.67			−0.462316			−0.231158	+	0.972916i	$0.574251\pi$
$444$	5532.98	+	9583.41i	0.591405	+	1.02434i
$445$	−2626.94	−	4549.99i	−0.279840	−	0.484697i
$446$	−6291.91	+	10897.9i	−0.668006	+	1.15702i
$447$	−16133.5			−1.70714
$448$	−1320.00	+	2286.31i	−0.139206	+	0.241112i
$449$	−2302.24	+	3987.59i	−0.241981	+	0.419123i	−0.961278	−	0.275579i	$-0.911130\pi$
$449$	−2302.24	+	3987.59i	−0.241981	+	0.419123i	0.719298	+	0.694702i	$0.244464\pi$
$450$	5917.01			0.619845
$451$	−2357.22	+	4082.83i	−0.246114	+	0.426282i
$452$	11288.8	+	19552.8i	1.17474	+	2.03470i
$453$	640.656	+	1109.65i	0.0664474	+	0.115090i
$454$	4807.30			0.496956
$455$		0			0
$456$	11527.2			1.18380
$457$	8189.62	+	14184.8i	0.838281	+	1.45195i	0.891331	+	0.453353i	$0.149772\pi$
$457$	8189.62	+	14184.8i	0.838281	+	1.45195i	−0.0530498	+	0.998592i	$0.516894\pi$
$458$	1059.45	+	1835.02i	0.108089	+	0.187215i
$459$	6146.89	−	10646.7i	0.625081	−	1.08267i
$460$	−20541.2			−2.08204
$461$	4815.76	−	8341.13i	0.486534	−	0.842701i	−0.513346	−	0.858182i	$-0.671594\pi$
$461$	4815.76	−	8341.13i	0.486534	−	0.842701i	0.999880	+	0.0154801i	$0.00492768\pi$
$462$	1590.30	−	2754.47i	0.160146	−	0.277380i
$463$	17855.0			1.79220			0.896102	−	0.443848i	$-0.146387\pi$
$463$	17855.0			1.79220			0.896102	+	0.443848i	$0.146387\pi$
$464$	−5708.98	+	9888.25i	−0.571191	+	0.989332i
$465$	−5133.53	−	8891.54i	−0.511961	−	0.886742i
$466$	−7098.31	−	12294.6i	−0.705629	−	1.22219i
$467$	8220.28			0.814538			0.407269	−	0.913308i	$-0.366481\pi$
$467$	8220.28			0.814538			0.407269	+	0.913308i	$0.366481\pi$
$468$		0			0
$469$	377.584			0.0371753
$470$	−1354.81	−	2346.60i	−0.132963	−	0.230299i
$471$	2166.36	+	3752.25i	0.211934	+	0.367080i
$472$	14461.6	−	25048.3i	1.41028	−	2.44267i
$473$	3029.40			0.294486
$474$	4814.59	−	8339.12i	0.466543	−	0.808077i
$475$	2774.97	−	4806.38i	0.268051	−	0.464278i
$476$	8467.29			0.815331
$477$	−679.108	+	1176.25i	−0.0651870	+	0.112907i
$478$	14069.1	+	24368.5i	1.34625	+	2.33177i
$479$	−1582.05	−	2740.19i	−0.150909	−	0.261383i	0.780653	−	0.624965i	$-0.214887\pi$
$479$	−1582.05	−	2740.19i	−0.150909	−	0.261383i	−0.931562	+	0.363582i	$0.881554\pi$
$480$	−4038.39			−0.384013
$481$		0			0
$482$	−5557.73			−0.525203
$483$	−1168.37	−	2023.68i	−0.110068	−	0.190643i
$484$	5610.58	+	9717.81i	0.526914	+	0.912642i
$485$	−3676.78	+	6368.36i	−0.344235	+	0.596232i
$486$	14563.9			1.35932
$487$	−3743.99	+	6484.79i	−0.348371	+	0.603396i	−0.985960	−	0.166981i	$-0.946598\pi$
$487$	−3743.99	+	6484.79i	−0.348371	+	0.603396i	0.637590	+	0.770376i	$0.279932\pi$
$488$	−12202.8	+	21135.9i	−1.13196	+	1.96061i
$489$	18243.7			1.68714
$490$	−11963.4	+	20721.1i	−1.10296	+	1.91038i
$491$	8006.83	+	13868.2i	0.735933	+	1.27467i	0.954313	+	0.298809i	$0.0965895\pi$
$491$	8006.83	+	13868.2i	0.735933	+	1.27467i	−0.218380	+	0.975864i	$0.570077\pi$
$492$	−9171.82	−	15886.1i	−0.840443	−	1.45569i
$493$	−28703.4			−2.62218
$494$		0			0
$495$	4267.78			0.387520
$496$	−2749.72	−	4762.66i	−0.248924	−	0.431148i
$497$	−2117.20	−	3667.11i	−0.191086	−	0.330970i
$498$	−15634.4	+	27079.5i	−1.40681	+	2.43667i
$499$	−10343.2			−0.927904			−0.463952	−	0.885860i	$-0.653569\pi$
$499$	−10343.2			−0.927904			−0.463952	+	0.885860i	$0.653569\pi$
$500$	−2086.24	+	3613.48i	−0.186599	+	0.323199i
$501$	−8491.89	+	14708.4i	−0.757265	+	1.31162i
$502$	−15758.6			−1.40108
$503$	9307.63	−	16121.3i	0.825063	−	1.42905i	−0.0768077	−	0.997046i	$-0.524473\pi$
$503$	9307.63	−	16121.3i	0.825063	−	1.42905i	0.901871	−	0.432006i	$-0.142194\pi$
$504$	884.292	+	1531.64i	0.0781538	+	0.135366i
$505$	6399.06	+	11083.5i	0.563870	+	0.976651i
$506$	−10389.8			−0.912809
$507$		0			0
$508$	4472.73			0.390641
$509$	−1814.20	−	3142.29i	−0.157983	−	0.273634i	0.776158	−	0.630538i	$-0.217166\pi$
$509$	−1814.20	−	3142.29i	−0.157983	−	0.273634i	−0.934141	+	0.356904i	$0.883832\pi$
$510$	29061.5	+	50336.1i	2.52327	+	4.37043i
$511$	569.442	−	986.302i	0.0492967	−	0.0853844i
$512$	−16710.7			−1.44241
$513$	2501.39	−	4332.53i	0.215281	−	0.372877i
$514$	−15297.1	+	26495.4i	−1.31270	+	2.27366i
$515$	−2435.68			−0.208406
$516$	−5893.61	+	10208.0i	−0.502813	+	0.870898i
$517$	−451.260	−	781.606i	−0.0383876	−	0.0664893i
$518$	1209.14	+	2094.30i	0.102561	+	0.177641i
$519$	−2099.49			−0.177567
$520$		0			0
$521$	−3105.46			−0.261137			−0.130569	−	0.991439i	$-0.541680\pi$
$521$	−3105.46			−0.261137			−0.130569	+	0.991439i	$0.541680\pi$
$522$	−6226.49	−	10784.6i	−0.522081	−	0.904270i
$523$	−955.613	−	1655.17i	−0.0798969	−	0.138385i	0.823308	−	0.567594i	$-0.192126\pi$
$523$	−955.613	−	1655.17i	−0.0798969	−	0.138385i	−0.903205	+	0.429209i	$0.858792\pi$
$524$	9271.57	−	16058.8i	0.772959	−	1.33880i
$525$	2868.58			0.238467
$526$	14929.5	−	25858.6i	1.23756	−	2.14352i
$527$	6912.46	−	11972.7i	0.571369	−	0.989641i
$528$	7701.10			0.634748
$529$	2266.89	−	3926.36i	0.186314	−	0.322706i
$530$	4394.90	+	7612.19i	0.360193	+	0.623873i
$531$	4585.17	+	7941.75i	0.374726	+	0.649045i
$532$	3445.64			0.280804
$533$		0			0
$534$	10339.9			0.837920
$535$	8196.18	+	14196.2i	0.662340	+	1.14721i
$536$	1572.44	+	2723.55i	0.126715	+	0.219476i
$537$	−3390.78	+	5873.01i	−0.272483	+	0.471954i
$538$	4083.16			0.327208
$539$	−3984.75	+	6901.79i	−0.318433	+	0.551542i
$540$	11365.1	−	19685.0i	0.905698	−	1.56871i
$541$	15251.2			1.21202			0.606008	−	0.795459i	$-0.292770\pi$
$541$	15251.2			1.21202			0.606008	+	0.795459i	$0.292770\pi$
$542$	−4992.78	+	8647.74i	−0.395679	+	0.685336i
$543$	−4400.40	−	7621.72i	−0.347770	−	0.602356i
$544$	−2718.91	−	4709.29i	−0.214287	−	0.371156i
$545$	17703.6			1.39145
$546$		0			0
$547$	1838.85			0.143736			0.0718681	−	0.997414i	$-0.477104\pi$
$547$	1838.85			0.143736			0.0718681	+	0.997414i	$0.477104\pi$
$548$	−6013.72	−	10416.1i	−0.468783	−	0.811957i
$549$	−3869.00	−	6701.30i	−0.300774	−	0.520955i
$550$	6377.21	−	11045.7i	0.494410	−	0.856343i
$551$	−11680.4			−0.903091
$552$	9731.31	−	16855.1i	0.750348	−	1.29964i
$553$	692.860	−	1200.07i	0.0532792	−	0.0922823i
$554$	31860.4			2.44336
$555$	−5465.75	+	9466.96i	−0.418033	+	0.724054i
$556$	−15670.2	−	27141.5i	−1.19526	−	2.07025i
$557$	3150.64	+	5457.08i	0.239672	+	0.415123i	0.960620	−	0.277865i	$-0.0896269\pi$
$557$	3150.64	+	5457.08i	0.239672	+	0.415123i	−0.720948	+	0.692989i	$0.756294\pi$
$558$	5997.96			0.455042
$559$		0			0
$560$	3327.29			0.251078
$561$	9679.81	+	16765.9i	0.728488	+	1.26178i
$562$	−2262.84	−	3919.36i	−0.169844	−	0.294178i
$563$	−5879.92	+	10184.3i	−0.440158	+	0.762376i	−0.997701	−	0.0677720i	$-0.978411\pi$
$563$	−5879.92	+	10184.3i	−0.440158	+	0.762376i	0.557543	+	0.830148i	$0.311744\pi$
$564$	3511.66			0.262176
$565$	−11151.6	+	19315.2i	−0.830359	+	1.43822i
$566$	12920.3	−	22378.6i	0.959506	−	1.66191i
$567$	3914.07			0.289904
$568$	17634.1	−	30543.2i	1.30266	−	2.25627i
$569$	8609.71	+	14912.5i	0.634337	+	1.09870i	0.986655	+	0.162824i	$0.0520603\pi$
$569$	8609.71	+	14912.5i	0.634337	+	1.09870i	−0.352318	+	0.935880i	$0.614606\pi$
$570$	11826.2	+	20483.6i	0.869026	+	1.50520i
$571$	825.501			0.0605011			0.0302506	−	0.999542i	$-0.490369\pi$
$571$	825.501			0.0605011			0.0302506	+	0.999542i	$0.490369\pi$
$572$		0			0
$573$	5557.00			0.405143
$574$	−2004.35	−	3471.64i	−0.145749	−	0.252445i
$575$	−4685.26	−	8115.11i	−0.339807	−	0.588563i
$576$	3485.81	−	6037.60i	0.252156	−	0.436748i
$577$	−1073.19			−0.0774308			−0.0387154	−	0.999250i	$-0.512327\pi$
$577$	−1073.19			−0.0774308			−0.0387154	+	0.999250i	$0.512327\pi$
$578$	−27242.4	+	47185.2i	−1.96044	+	3.39558i
$579$	8024.53	−	13898.9i	0.575972	−	0.997613i
$580$	−53070.3			−3.79935
$581$	−2249.92	+	3896.97i	−0.160658	+	0.278268i
$582$	−7236.06	−	12533.2i	−0.515369	−	0.892645i
$583$	1463.85	+	2535.47i	0.103991	+	0.180117i
$584$	9485.71			0.672126
$585$		0			0
$586$	8536.93			0.601804
$587$	−7469.69	−	12937.9i	−0.525225	−	0.909717i	−0.999568	−	0.0293768i	$-0.990648\pi$
$587$	−7469.69	−	12937.9i	−0.525225	−	0.909717i	0.474343	−	0.880340i	$-0.342686\pi$
$588$	−15504.4	−	26854.5i	−1.08740	−	1.88344i
$589$	2812.93	−	4872.14i	0.196782	−	0.340837i
$590$	59346.7			4.14113
$591$	4591.28	−	7952.33i	0.319560	−	0.553495i
$592$	−2927.67	+	5070.88i	−0.203254	+	0.352047i
$593$	−6296.13			−0.436006			−0.218003	−	0.975948i	$-0.569954\pi$
$593$	−6296.13			−0.436006			−0.218003	+	0.975948i	$0.569954\pi$
$594$	5748.50	−	9956.69i	0.397077	−	0.687757i
$595$	4182.20	+	7243.78i	0.288157	+	0.499103i
$596$	−20083.3	−	34785.3i	−1.38027	−	2.39071i
$597$	22304.4			1.52908
$598$		0			0
$599$	−3518.96			−0.240035			−0.120017	−	0.992772i	$-0.538295\pi$
$599$	−3518.96			−0.240035			−0.120017	+	0.992772i	$0.538295\pi$
$600$	11946.1	+	20691.3i	0.812831	+	1.40786i
$601$	−2690.33	−	4659.78i	−0.182597	−	0.316267i	0.760167	−	0.649727i	$-0.225117\pi$
$601$	−2690.33	−	4659.78i	−0.182597	−	0.316267i	−0.942764	+	0.333460i	$0.891784\pi$
$602$	−1287.95	+	2230.80i	−0.0871976	+	0.151031i
$603$	−997.110			−0.0673391
$604$	−1595.00	+	2762.62i	−0.107450	+	0.186108i
$605$	−5542.41	+	9599.73i	−0.372448	+	0.645098i
$606$	−25187.3			−1.68839
$607$	−10354.3	+	17934.2i	−0.692369	+	1.19922i	0.278690	+	0.960381i	$0.410100\pi$
$607$	−10354.3	+	17934.2i	−0.692369	+	1.19922i	−0.971059	+	0.238838i	$0.923234\pi$
$608$	−1106.42	−	1916.38i	−0.0738016	−	0.127828i
$609$	−3018.61	−	5228.39i	−0.200855	−	0.347890i
$610$	−50077.1			−3.32387
$611$		0			0
$612$	−22360.1			−1.47688
$613$	4281.83	+	7416.35i	0.282123	+	0.488652i	0.971907	−	0.235363i	$-0.0756280\pi$
$613$	4281.83	+	7416.35i	0.282123	+	0.488652i	−0.689784	+	0.724015i	$0.742295\pi$
$614$	−11463.0	−	19854.4i	−0.753433	−	1.30498i
$615$	9060.38	−	15693.0i	0.594064	−	1.02895i
$616$	3812.28			0.249352
$617$	15224.8	−	26370.1i	0.993400	−	1.72062i	0.397365	−	0.917661i	$-0.369925\pi$
$617$	15224.8	−	26370.1i	0.993400	−	1.72062i	0.596035	−	0.802958i	$-0.296742\pi$
$618$	2396.77	−	4151.32i	0.156007	−	0.270211i
$619$	−26233.1			−1.70339			−0.851693	−	0.524041i	$-0.824424\pi$
$619$	−26233.1			−1.70339			−0.851693	+	0.524041i	$0.824424\pi$
$620$	12780.6	−	22136.7i	0.827874	−	1.43392i
$621$	−4223.35	−	7315.06i	−0.272910	−	0.472694i
$622$	11487.9	+	19897.7i	0.740553	+	1.28267i
$623$	1487.99			0.0956905
$624$		0			0
$625$	−17528.4			−1.12182
$626$	−24481.4	−	42403.0i	−1.56305	−	2.70729i
$627$	3939.06	+	6822.66i	0.250895	+	0.434563i
$628$	−5393.45	+	9341.73i	−0.342710	+	0.593592i
$629$	−14719.6			−0.933084
$630$	−1814.45	+	3142.72i	−0.114745	+	0.198744i
$631$	−10319.7	+	17874.3i	−0.651066	+	1.12768i	0.331799	+	0.943350i	$0.392344\pi$
$631$	−10319.7	+	17874.3i	−0.651066	+	1.12768i	−0.982865	+	0.184329i	$0.940989\pi$
$632$	11541.6			0.726425
$633$	9453.61	−	16374.1i	0.593597	−	1.02814i
$634$	−14293.3	−	24756.8i	−0.895365	−	1.55082i
$635$	2209.19	+	3826.43i	0.138062	+	0.239130i
$636$	−11391.5			−0.710226
$637$		0			0
$638$	−26843.1			−1.66572
$639$	5591.03	+	9683.95i	0.346131	+	0.599517i
$640$	−19951.9	−	34557.7i	−1.23229	−	2.13439i
$641$	2215.89	−	3838.03i	0.136540	−	0.236494i	−0.789645	−	0.613565i	$-0.789735\pi$
$641$	2215.89	−	3838.03i	0.136540	−	0.236494i	0.926185	+	0.377070i	$0.123068\pi$
$642$	−32260.9			−1.98323
$643$	7088.03	−	12276.8i	0.434719	−	0.752956i	−0.562553	−	0.826761i	$-0.690181\pi$
$643$	7088.03	−	12276.8i	0.434719	−	0.752956i	0.997273	+	0.0738050i	$0.0235142\pi$
$644$	2908.82	−	5038.22i	0.177987	−	0.308282i
$645$	−11644.0			−0.710824
$646$	−15924.3	+	27581.8i	−0.969868	+	1.67986i
$647$	−2825.40	−	4893.73i	−0.171681	−	0.297361i	0.767327	−	0.641257i	$-0.221587\pi$
$647$	−2825.40	−	4893.73i	−0.171681	−	0.297361i	−0.939008	+	0.343896i	$0.888253\pi$
$648$	16300.1	+	28232.5i	0.988159	+	1.71154i
$649$	19767.2			1.19558
$650$		0			0
$651$	2907.82			0.175064
$652$	22710.1	+	39335.0i	1.36410	+	2.36270i
$653$	9218.14	+	15966.3i	0.552425	+	0.956829i	0.998099	+	0.0616333i	$0.0196309\pi$
$653$	9218.14	+	15966.3i	0.552425	+	0.956829i	−0.445673	+	0.895196i	$0.647036\pi$
$654$	−17420.8	+	30173.7i	−1.04160	+	1.80410i
$655$	18317.8			1.09273
$656$	4853.09	−	8405.80i	0.288844	−	0.500292i
$657$	−1503.76	+	2604.59i	−0.0892957	+	0.154665i
$658$	767.415			0.0454665
$659$	7665.97	−	13277.8i	0.453147	−	0.784873i	−0.545433	−	0.838155i	$-0.683635\pi$
$659$	7665.97	−	13277.8i	0.453147	−	0.784873i	0.998580	+	0.0532813i	$0.0169680\pi$
$660$	17897.2	+	30998.9i	1.05553	+	1.82823i
$661$	−11147.6	−	19308.2i	−0.655961	−	1.13616i	−0.981652	−	0.190681i	$-0.938930\pi$
$661$	−11147.6	−	19308.2i	−0.655961	−	1.13616i	0.325691	−	0.945476i	$-0.394403\pi$
$662$	13566.2			0.796471
$663$		0			0
$664$	−37478.9			−2.19046
$665$	1701.89	+	2947.76i	0.0992427	+	0.171893i
$666$	−3193.06	−	5530.54i	−0.185779	−	0.321778i
$667$	−9860.64	+	17079.1i	−0.572422	+	0.991464i
$668$	−42283.4			−2.44909
$669$	8055.19	−	13952.0i	0.465518	−	0.806301i
$670$	−3226.44	+	5588.36i	−0.186042	+	0.322235i
$671$	−16679.7			−0.959629
$672$	571.873	−	990.513i	0.0328281	−	0.0568599i
$673$	8085.84	+	14005.1i	0.463129	+	0.802164i	0.999115	−	0.0420635i	$-0.0133932\pi$
$673$	8085.84	+	14005.1i	0.463129	+	0.802164i	−0.535985	+	0.844227i	$0.680060\pi$
$674$	592.725	+	1026.63i	0.0338738	+	0.0586711i
$675$	10369.1			0.591272
$676$		0			0
$677$	33614.4			1.90828			0.954141	−	0.299358i	$-0.0967725\pi$
$677$	33614.4			1.90828			0.954141	+	0.299358i	$0.0967725\pi$
$678$	−21946.9	−	38013.2i	−1.24317	−	2.15323i
$679$	−1041.33	−	1803.64i	−0.0588551	−	0.101940i
$680$	−34833.4	+	60333.2i	−1.96441	+	3.40246i
$681$	−6154.53			−0.346318
$682$	6464.46	−	11196.8i	0.362957	−	0.628661i
$683$	−11238.7	+	19466.1i	−0.629632	+	1.09055i	0.357993	+	0.933724i	$0.383461\pi$
$683$	−11238.7	+	19466.1i	−0.629632	+	1.09055i	−0.987625	+	0.156831i	$0.949872\pi$
$684$	−9099.12			−0.508646
$685$	5940.65	−	10289.5i	0.331358	−	0.573929i
$686$	−6971.08	−	12074.3i	−0.387984	−	0.672008i
$687$	−1356.35	−	2349.27i	−0.0753247	−	0.130466i
$688$	−6236.97			−0.345614
$689$		0			0
$690$	39934.7			2.20332
$691$	−3809.47	−	6598.19i	−0.209723	−	0.363252i	0.741904	−	0.670506i	$-0.233923\pi$
$691$	−3809.47	−	6598.19i	−0.209723	−	0.363252i	−0.951627	+	0.307255i	$0.900590\pi$
$692$	−2613.48	−	4526.67i	−0.143569	−	0.248668i
$693$	−604.357	+	1046.78i	−0.0331279	+	0.0573792i
$694$	50128.9			2.74188
$695$	15479.8	−	26811.7i	0.844864	−	1.46335i
$696$	25141.9	−	43547.1i	1.36926	−	2.37162i
$697$	24400.2			1.32600
$698$	−20410.0	+	35351.2i	−1.10678	+	1.91699i
$699$	9087.59	+	15740.2i	0.491737	+	0.851714i
$700$	3570.85	+	6184.90i	0.192808	+	0.333953i
$701$	−18164.3			−0.978684			−0.489342	−	0.872092i	$-0.662763\pi$
$701$	−18164.3			−0.978684			−0.489342	+	0.872092i	$0.662763\pi$
$702$		0			0
$703$	−5989.95			−0.321359
$704$	−7513.85	−	13014.4i	−0.402257	−	0.696730i
$705$	1734.49	+	3004.23i	0.0926593	+	0.160491i
$706$	11456.0	−	19842.4i	0.610698	−	1.05776i
$707$	−3624.66			−0.192814
$708$	−38456.5	+	66608.6i	−2.04136	+	3.53574i
$709$	8353.25	−	14468.3i	0.442472	−	0.766385i	−0.555400	−	0.831583i	$-0.687435\pi$
$709$	8353.25	−	14468.3i	0.442472	−	0.766385i	0.997872	+	0.0651986i	$0.0207681\pi$
$710$	72365.7			3.82512
$711$	−1829.68	+	3169.10i	−0.0965096	+	0.167159i
$712$	6196.71	+	10733.0i	0.326168	+	0.564940i
$713$	−4749.36	−	8226.13i	−0.249460	−	0.432077i
$714$	−16461.5			−0.862825
$715$		0			0
$716$	−16883.6			−0.881244
$717$	−18012.0	−	31197.6i	−0.938171	−	1.62496i
$718$	18299.1	+	31695.0i	0.951137	+	1.64742i
$719$	−2274.70	+	3939.89i	−0.117986	+	0.204358i	−0.918969	−	0.394329i	$-0.870977\pi$
$719$	−2274.70	+	3939.89i	−0.117986	+	0.204358i	0.800983	+	0.598686i	$0.204310\pi$
$720$	−8786.58			−0.454800
$721$	344.915	−	597.410i	0.0178159	−	0.0308581i
$722$	10119.2	−	17527.0i	0.521603	−	0.903443i
$723$	7115.26			0.366002
$724$	10955.4	−	18975.3i	0.562367	−	0.974048i
$725$	−12104.9	−	20966.3i	−0.620088	−	1.07402i
$726$	−10907.7	−	18892.7i	−0.557607	−	0.965804i
$727$	−6246.70			−0.318676			−0.159338	−	0.987224i	$-0.550936\pi$
$727$	−6246.70			−0.318676			−0.159338	+	0.987224i	$0.550936\pi$
$728$		0			0
$729$	5839.14			0.296659
$730$	9731.71	+	16855.8i	0.493407	+	0.854605i
$731$	−7839.50	−	13578.4i	−0.396654	−	0.687026i
$732$	32449.8	−	56204.7i	1.63850	−	2.83796i
$733$	3447.16			0.173702			0.0868511	−	0.996221i	$-0.472320\pi$
$733$	3447.16			0.173702			0.0868511	+	0.996221i	$0.472320\pi$
$734$	28895.8	−	50049.0i	1.45308	−	2.51681i
$735$	15316.0	−	26528.2i	0.768627	−	1.33130i
$736$	−3736.17			−0.187116
$737$	−1074.66	+	1861.37i	−0.0537119	+	0.0930318i
$738$	5293.02	+	9167.77i	0.264009	+	0.457277i
$739$	18516.5	+	32071.4i	0.921703	+	1.59644i	0.796779	+	0.604271i	$0.206536\pi$
$739$	18516.5	+	32071.4i	0.921703	+	1.59644i	0.124925	+	0.992166i	$0.460131\pi$
$740$	−27215.4			−1.35197
$741$		0			0
$742$	−2489.43			−0.123167
$743$	7649.01	+	13248.5i	0.377678	+	0.654158i	0.990724	−	0.135890i	$-0.0433892\pi$
$743$	7649.01	+	13248.5i	0.377678	+	0.654158i	−0.613046	+	0.790047i	$0.710056\pi$
$744$	12109.6	+	20974.4i	0.596717	+	1.03354i
$745$	19839.3	−	34362.6i	0.975643	−	1.68986i
$746$	−28059.1			−1.37710
$747$	5941.49	−	10291.0i	0.291015	−	0.504052i
$748$	−24099.2	+	41741.0i	−1.17801	+	2.04038i
$749$	−4642.62			−0.226485
$750$	4055.93	−	7025.08i	0.197469	−	0.342026i
$751$	4922.27	+	8525.62i	0.239169	+	0.414253i	0.960476	−	0.278362i	$-0.0897916\pi$
$751$	4922.27	+	8525.62i	0.239169	+	0.414253i	−0.721307	+	0.692616i	$0.756458\pi$
$752$	929.062	+	1609.18i	0.0450524	+	0.0780331i
$753$	20174.9			0.976382
$754$		0			0
$755$	−3151.24			−0.151901
$756$	3218.81	+	5575.14i	0.154850	+	0.268209i
$757$	−2960.65	−	5128.00i	−0.142149	−	0.246209i	0.786157	−	0.618027i	$-0.212068\pi$
$757$	−2960.65	−	5128.00i	−0.142149	−	0.246209i	−0.928306	+	0.371818i	$0.878735\pi$
$758$	21408.8	−	37081.2i	1.02586	−	1.77685i
$759$	13301.4			0.636116
$760$	−14175.0	+	24551.7i	−0.676552	+	1.17182i
$761$	−8936.23	+	15478.0i	−0.425674	+	0.737289i	−0.996483	−	0.0837936i	$-0.973296\pi$
$761$	−8936.23	+	15478.0i	−0.425674	+	0.737289i	0.570809	+	0.821083i	$0.306630\pi$
$762$	−8695.58			−0.413396
$763$	−2507.00	+	4342.24i	−0.118951	+	0.206029i
$764$	6917.44	+	11981.4i	0.327571	+	0.567370i
$765$	−11044.2	−	19129.1i	−0.521966	−	0.904071i
$766$	−5070.61			−0.239176
$767$		0			0
$768$	48211.2			2.26520
$769$	−5632.60	−	9755.95i	−0.264131	−	0.457488i	0.703205	−	0.710988i	$-0.251752\pi$
$769$	−5632.60	−	9755.95i	−0.264131	−	0.457488i	−0.967336	+	0.253499i	$0.918418\pi$
$770$	3911.15	+	6774.30i	0.183049	+	0.317051i
$771$	19584.1	−	33920.6i	0.914791	−	1.58446i
$772$	39956.3			1.86277
$773$	−13801.8	+	23905.5i	−0.642196	+	1.11232i	0.342745	+	0.939428i	$0.388643\pi$
$773$	−13801.8	+	23905.5i	−0.642196	+	1.11232i	−0.984941	+	0.172888i	$0.944690\pi$
$774$	3401.17	−	5891.00i	0.157949	−	0.273576i
$775$	11660.6			0.540465
$776$	8673.20	−	15022.4i	0.401224	−	0.694940i
$777$	−1548.00	−	2681.22i	−0.0714726	−	0.123794i
$778$	28698.4	+	49707.0i	1.32248	+	2.29059i
$779$	9929.31			0.456681
$780$		0			0
$781$	24103.5			1.10434
$782$	26886.7	+	46569.1i	1.22950	+	2.12955i
$783$	−10911.5	−	18899.3i	−0.498014	−	0.862585i
$784$	8203.87	−	14209.5i	0.373719	−	0.647300i
$785$	−10655.8			−0.484488
$786$	−18025.2	+	31220.5i	−0.817985	+	1.41679i
$787$	−12081.5	+	20925.8i	−0.547218	+	0.947809i	0.451246	+	0.892400i	$0.350980\pi$
$787$	−12081.5	+	20925.8i	−0.547218	+	0.947809i	−0.998464	+	0.0554093i	$0.982354\pi$
$788$	22861.2			1.03350
$789$	−19113.4	+	33105.4i	−0.862429	+	1.49377i
$790$	11840.9	+	20509.1i	0.533267	+	0.923646i
$791$	−3158.35	−	5470.42i	−0.141970	−	0.245899i
$792$	−10067.3			−0.451675
$793$		0			0
$794$	−50726.7			−2.26728
$795$	−5626.56	−	9745.48i	−0.251011	−	0.434763i
$796$	27764.9	+	48090.3i	1.23631	+	2.14135i
$797$	−15192.8	+	26314.7i	−0.675228	+	1.16953i	0.301174	+	0.953569i	$0.402622\pi$
$797$	−15192.8	+	26314.7i	−0.675228	+	1.16953i	−0.976402	+	0.215961i	$0.930712\pi$
$798$	−6698.79			−0.297161
$799$	−2335.55	+	4045.29i	−0.103412	+	0.179114i
$800$	2293.25	−	3972.03i	0.101348	−	0.175541i
$801$	−3929.43			−0.173333
$802$	19206.8	−	33267.1i	0.845655	−	1.46472i
$803$	3241.44	+	5614.33i	0.142451	+	0.246732i
$804$	−4181.45	−	7242.48i	−0.183418	−	0.317690i
$805$	5746.94			0.251619
$806$		0			0
$807$	−5227.46			−0.228024
$808$	−15094.8	−	26145.0i	−0.657220	−	1.13834i
$809$	20988.4	+	36353.0i	0.912131	+	1.57986i	0.811048	+	0.584979i	$0.198897\pi$
$809$	20988.4	+	36353.0i	0.912131	+	1.57986i	0.101083	+	0.994878i	$0.467769\pi$
$810$	−33445.6	+	57929.4i	−1.45081	+	2.51288i
$811$	9674.05			0.418868			0.209434	−	0.977823i	$-0.432838\pi$
$811$	9674.05			0.418868			0.209434	+	0.977823i	$0.432838\pi$
$812$	7515.24	−	13016.8i	0.324795	−	0.562561i
$813$	6391.98	−	11071.2i	0.275740	−	0.477596i
$814$	−13765.6			−0.592733
$815$	−22434.1	+	38857.1i	−0.964213	+	1.67007i
$816$	−19929.0	−	34518.0i	−0.854967	−	1.48085i
$817$	−3190.17	−	5525.54i	−0.136610	−	0.236615i
$818$	28245.7			1.20732
$819$		0			0
$820$	45114.0			1.92128
$821$	12713.0	+	22019.6i	0.540423	+	0.936040i	0.998880	+	0.0473231i	$0.0150690\pi$
$821$	12713.0	+	22019.6i	0.540423	+	0.936040i	−0.458457	+	0.888717i	$0.651598\pi$
$822$	11691.5	+	20250.2i	0.496091	+	0.859254i
$823$	−7194.13	+	12460.6i	−0.304704	+	0.527763i	−0.977195	−	0.212342i	$-0.931891\pi$
$823$	−7194.13	+	12460.6i	−0.304704	+	0.527763i	0.672491	+	0.740105i	$0.265224\pi$
$824$	5745.56			0.242908
$825$	−8164.40	+	14141.2i	−0.344543	+	0.596766i
$826$	−8404.03	+	14556.2i	−0.354012	+	0.613166i
$827$	−3850.25			−0.161894			−0.0809469	−	0.996718i	$-0.525794\pi$
$827$	−3850.25			−0.161894			−0.0809469	+	0.996718i	$0.525794\pi$
$828$	−7681.49	+	13304.7i	−0.322404	+	0.558420i
$829$	959.292	+	1661.54i	0.0401901	+	0.0696113i	0.885421	−	0.464790i	$-0.153870\pi$
$829$	959.292	+	1661.54i	0.0401901	+	0.0696113i	−0.845231	+	0.534402i	$0.820537\pi$
$830$	−38450.9	−	66598.9i	−1.60801	−	2.78516i
$831$	−40789.2			−1.70272
$832$		0			0
$833$	41247.1			1.71564
$834$	30464.9	+	52766.7i	1.26488	+	2.19084i
$835$	−20884.8	−	36173.6i	−0.865567	−	1.49921i
$836$	−9806.83	+	16985.9i	−0.405713	+	0.702716i
$837$	10511.0			0.434066
$838$	20677.9	−	35815.2i	0.852395	−	1.47639i
$839$	15706.1	−	27203.7i	0.646285	−	1.11940i	−0.337718	−	0.941247i	$-0.609655\pi$
$839$	15706.1	−	27203.7i	0.646285	−	1.11940i	0.984003	−	0.178152i	$-0.0570117\pi$
$840$	−14653.1			−0.601882
$841$	−13281.5	+	23004.3i	−0.544571	+	0.943224i
$842$	−39991.0	−	69266.4i	−1.63679	−	2.83501i
$843$	2897.00	+	5017.75i	0.118360	+	0.205006i
$844$	47072.0			1.91977
$845$		0			0
$846$	−2026.56			−0.0823577
$847$	−1569.71	−	2718.82i	−0.0636787	−	0.110295i
$848$	−3013.80	−	5220.06i	−0.122045	−	0.211389i
$849$	−16541.2	+	28650.1i	−0.668658	+	1.15815i
$850$	−66012.0			−2.66376
$851$	−5056.72	+	8758.49i	−0.203692	+	0.352805i
$852$	−46892.7	+	81220.6i	−1.88559	+	3.26593i
$853$	−18315.5			−0.735184			−0.367592	−	0.929987i	$-0.619818\pi$
$853$	−18315.5			−0.735184			−0.367592	+	0.929987i	$0.619818\pi$
$854$	7091.37	−	12282.6i	0.284147	−	0.492157i
$855$	−4494.28	−	7784.32i	−0.179767	−	0.311366i
$856$	−19334.1	−	33487.6i	−0.771992	−	1.33713i
$857$	9579.31			0.381824			0.190912	−	0.981607i	$-0.438856\pi$
$857$	9579.31			0.381824			0.190912	+	0.981607i	$0.438856\pi$
$858$		0			0
$859$	−7136.55			−0.283465			−0.141732	−	0.989905i	$-0.545267\pi$
$859$	−7136.55			−0.283465			−0.141732	+	0.989905i	$0.545267\pi$
$860$	−14494.6	−	25105.4i	−0.574724	−	0.995451i
$861$	2566.06	+	4444.55i	0.101569	+	0.175923i
$862$	−16545.1	+	28657.0i	−0.653746	+	1.13232i
$863$	−17239.2			−0.679986			−0.339993	−	0.940428i	$-0.610425\pi$
$863$	−17239.2			−0.679986			−0.339993	+	0.940428i	$0.610425\pi$
$864$	2067.17	−	3580.44i	0.0813964	−	0.140983i
$865$	2581.72	−	4471.67i	0.101481	−	0.175770i
$866$	−30447.8			−1.19476
$867$	34877.0	−	60408.7i	1.36619	−	2.36631i
$868$	3619.70	+	6269.51i	0.141545	+	0.245163i
$869$	3943.97	+	6831.16i	0.153959	+	0.266664i
$870$	103176.			4.02067
$871$		0			0
$872$	−41761.3			−1.62181
$873$	2749.91	+	4762.98i	0.106610	+	0.184653i
$874$	10941.2	+	18950.7i	0.423444	+	0.733427i
$875$	583.682	−	1010.97i	0.0225509	−	0.0390594i
$876$	−25224.5			−0.972895
$877$	−16524.4	+	28621.1i	−0.636247	+	1.10201i	0.350003	+	0.936749i	$0.386181\pi$
$877$	−16524.4	+	28621.1i	−0.636247	+	1.10201i	−0.986250	+	0.165263i	$0.947153\pi$
$878$	−21462.8	+	37174.6i	−0.824981	+	1.42891i
$879$	−10929.4			−0.419384
$880$	−9469.97	+	16402.5i	−0.362764	+	0.628326i
$881$	−9763.90	−	16911.6i	−0.373387	−	0.646726i	0.616697	−	0.787201i	$-0.288470\pi$
$881$	−9763.90	−	16911.6i	−0.373387	−	0.646726i	−0.990084	+	0.140475i	$0.955137\pi$
$882$	8947.54	+	15497.6i	0.341587	+	0.591645i
$883$	−26361.3			−1.00467			−0.502337	−	0.864672i	$-0.667526\pi$
$883$	−26361.3			−1.00467			−0.502337	+	0.864672i	$0.667526\pi$
$884$		0			0
$885$	−75978.4			−2.88586
$886$	10432.2	+	18069.1i	0.395572	+	0.685151i
$887$	−10702.9	−	18538.0i	−0.405151	−	0.701742i	0.589188	−	0.807996i	$-0.299448\pi$
$887$	−10702.9	−	18538.0i	−0.405151	−	0.701742i	−0.994339	+	0.106254i	$0.966114\pi$
$888$	12893.2	−	22331.7i	0.487240	−	0.843924i
$889$	−1251.37			−0.0472098
$890$	−12714.8	+	22022.7i	−0.478879	+	0.829442i
$891$	−11140.0	+	19295.1i	−0.418861	+	0.725489i
$892$	40109.0			1.50555
$893$	−950.419	+	1646.17i	−0.0356154	+	0.0616877i
$894$	39044.6	+	67627.2i	1.46068	+	2.52997i
$895$	−8339.23	−	14444.0i	−0.311452	−	0.539451i
$896$	11301.5			0.421379
$897$		0			0
$898$	22286.5			0.828184
$899$	−12270.5	−	21253.1i	−0.455221	−	0.788466i
$900$	−9429.77	−	16332.8i	−0.349251	−	0.604920i
$901$	7576.34	−	13122.6i	0.280138	−	0.485213i
$902$	22818.8			0.842330
$903$	1648.89	−	2855.97i	0.0607661	−	0.105250i
$904$	26305.7	−	45562.9i	0.967827	−	1.67633i
$905$	21644.5			0.795015
$906$	3100.89	−	5370.90i	0.113709	−	0.196949i
$907$	−14443.7	−	25017.3i	−0.528772	−	0.915860i	−0.999437	−	0.0335483i	$-0.989319\pi$
$907$	−14443.7	−	25017.3i	−0.528772	−	0.915860i	0.470665	−	0.882312i	$-0.344014\pi$
$908$	−7661.27	−	13269.7i	−0.280009	−	0.484990i
$909$	9571.86			0.349261
$910$		0			0
$911$	−31360.9			−1.14054			−0.570271	−	0.821456i	$-0.693162\pi$
$911$	−31360.9			−1.14054			−0.570271	+	0.821456i	$0.693162\pi$
$912$	−8109.81	−	14046.6i	−0.294455	−	0.510010i
$913$	−12807.2	−	22182.7i	−0.464246	−	0.804098i
$914$	39639.2	−	68657.1i	1.43452	−	2.48466i
$915$	64111.0			2.31633
$916$	3376.82	−	5848.82i	0.121805	−	0.210972i
$917$	−2593.97	+	4492.89i	−0.0934139	+	0.161798i
$918$	−59504.0			−2.13935
$919$	552.304	−	956.619i	0.0198246	−	0.0343373i	−0.855943	−	0.517070i	$-0.827023\pi$
$919$	552.304	−	956.619i	0.0198246	−	0.0343373i	0.875768	+	0.482733i	$0.160356\pi$
$920$	23933.0	+	41453.2i	0.857661	+	1.48551i
$921$	14675.4	+	25418.6i	0.525050	+	0.909414i
$922$	−46618.2			−1.66517
$923$		0			0
$924$	−10137.6			−0.360935
$925$	−6207.61	−	10751.9i	−0.220654	−	0.382184i
$926$	−43210.6	−	74842.9i	−1.53346	−	2.65604i
$927$	−910.838	+	1577.62i	−0.0322717	+	0.0558962i
$928$	−9652.81			−0.341454
$929$	−19217.9	+	33286.4i	−0.678708	+	1.17556i	0.296663	+	0.954982i	$0.404126\pi$
$929$	−19217.9	+	33286.4i	−0.678708	+	1.17556i	−0.975370	+	0.220574i	$0.929207\pi$
$930$	−24847.2	+	43036.6i	−0.876099	+	1.51745i
$931$	16784.9			0.590874
$932$	−22624.8	+	39187.3i	−0.795171	+	1.37728i
$933$	−14707.4	−	25473.9i	−0.516075	−	0.893867i
$934$	−19893.8	−	34457.1i	−0.696944	−	1.20714i
$935$	−47612.7			−1.66535
$936$		0			0
$937$	21008.7			0.732469			0.366235	−	0.930522i	$-0.380647\pi$
$937$	21008.7			0.732469			0.366235	+	0.930522i	$0.380647\pi$
$938$	−913.787	−	1582.73i	−0.0318083	−	0.0550936i
$939$	31342.2	+	54286.2i	1.08926	+	1.88665i
$940$	−4318.25	+	7479.43i	−0.149836	+	0.259524i
$941$	12695.6			0.439814			0.219907	−	0.975521i	$-0.429425\pi$
$941$	12695.6			0.439814			0.219907	+	0.975521i	$0.429425\pi$
$942$	10485.6	−	18161.6i	0.362674	−	0.628169i
$943$	8382.34	−	14518.6i	0.289466	−	0.501370i
$944$	−40697.0			−1.40315
$945$	−3179.70	+	5507.40i	−0.109456	+	0.189583i
$946$	−7331.41	−	12698.4i	−0.251971	−	0.436427i
$947$	−24359.7	−	42192.3i	−0.835886	−	1.44780i	−0.893307	−	0.449448i	$-0.851621\pi$
$947$	−24359.7	−	42192.3i	−0.835886	−	1.44780i	0.0574201	−	0.998350i	$-0.481713\pi$
$948$	−30691.5			−1.05149
$949$		0			0
$950$	−26862.7			−0.917410
$951$	18299.0	+	31694.8i	0.623960	+	1.08073i
$952$	−9865.45	−	17087.5i	−0.335862	−	0.581731i
$953$	5673.66	−	9827.06i	0.192852	−	0.334029i	−0.753342	−	0.657628i	$-0.771560\pi$
$953$	5673.66	−	9827.06i	0.192852	−	0.334029i	0.946194	+	0.323599i	$0.104893\pi$
$954$	6574.00			0.223104
$955$	−6833.39	+	11835.8i	−0.231543	+	0.401044i
$956$	44843.2	−	77670.7i	1.51708	−	2.62767i
$957$	34365.7			1.16080
$958$	−7657.39	+	13263.0i	−0.258245	+	0.447294i
$959$	1682.50	+	2914.18i	0.0566535	+	0.0981268i
$960$	28880.7	+	50022.9i	0.970960	+	1.68175i
$961$	−17970.9			−0.603232
$962$		0			0
$963$	12260.0			0.410254
$964$	8857.20	+	15341.1i	0.295925	+	0.512556i
$965$	19735.4	+	34182.7i	0.658346	+	1.14029i
$966$	−5655.12	+	9794.96i	−0.188355	+	0.326240i
$967$	−10585.2			−0.352014			−0.176007	−	0.984389i	$-0.556318\pi$
$967$	−10585.2			−0.352014			−0.176007	+	0.984389i	$0.556318\pi$
$968$	13074.1	−	22644.9i	0.434107	−	0.751896i
$969$	20387.1	−	35311.5i	0.675880	−	1.17066i
$970$	35592.5			1.17815
$971$	26865.4	−	46532.2i	0.887900	−	1.53789i	0.0455470	−	0.998962i	$-0.485497\pi$
$971$	26865.4	−	46532.2i	0.887900	−	1.53789i	0.842353	−	0.538926i	$-0.181170\pi$
$972$	−23210.0	−	40200.9i	−0.765907	−	1.32659i
$973$	4384.15	+	7593.57i	0.144450	+	0.250194i
$974$	36243.2			1.19231
$975$		0			0
$976$	34340.4			1.12624
$977$	−4767.16	−	8256.96i	−0.156105	−	0.270382i	0.777356	−	0.629061i	$-0.216561\pi$
$977$	−4767.16	−	8256.96i	−0.156105	−	0.270382i	−0.933461	+	0.358679i	$0.883227\pi$
$978$	−44151.4	−	76472.5i	−1.44357	−	2.50033i
$979$	−4235.05	+	7335.33i	−0.138256	+	0.239467i
$980$	76262.7			2.48584
$981$	6620.38	−	11466.8i	0.215466	−	0.373199i
$982$	38754.5	−	67124.7i	1.25937	−	2.18130i
$983$	8972.94			0.291142			0.145571	−	0.989348i	$-0.453498\pi$
$983$	8972.94			0.291142			0.145571	+	0.989348i	$0.453498\pi$
$984$	−21372.6	+	37018.5i	−0.692413	+	1.19930i
$985$	11291.7	+	19557.8i	0.365263	+	0.632654i
$986$	69464.7	+	120316.i	2.24362	+	3.88606i
$987$	−982.480			−0.0316846
$988$		0			0
$989$	−10772.6			−0.346359
$990$	−10328.4	−	17889.3i	−0.331574	−	0.574303i
$991$	17450.3	+	30224.8i	0.559362	+	0.968843i	0.997550	+	0.0699598i	$0.0222871\pi$
$991$	17450.3	+	30224.8i	0.559362	+	0.968843i	−0.438188	+	0.898883i	$0.644380\pi$
$992$	2324.63	−	4026.37i	0.0744022	−	0.128868i
$993$	−17368.0			−0.555043
$994$	−10247.6	+	17749.4i	−0.326998	+	0.566376i
$995$	−27427.6	+	47505.9i	−0.873881	+	1.51361i
$996$	99664.2			3.17066
$997$	24077.5	−	41703.4i	0.764836	−	1.32473i	−0.175498	−	0.984480i	$-0.556153\pi$
$997$	24077.5	−	41703.4i	0.764836	−	1.32473i	0.940333	−	0.340254i	$-0.110513\pi$
$998$	25031.4	+	43355.6i	0.793942	+	1.37515i
$999$	−5595.61	−	9691.89i	−0.177215	−	0.306945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.l.146.1		18
13.2	odd	12		169.4.b.g.168.2		18
13.3	even	3		169.4.a.k.1.9	✓	9
13.4	even	6		169.4.c.k.22.9		18
13.5	odd	4		169.4.e.h.23.2		36
13.6	odd	12		169.4.e.h.147.17		36
13.7	odd	12		169.4.e.h.147.2		36
13.8	odd	4		169.4.e.h.23.17		36
13.9	even	3	inner	169.4.c.l.22.1		18
13.10	even	6		169.4.a.l.1.1	yes	9
13.11	odd	12		169.4.b.g.168.17		18
13.12	even	2		169.4.c.k.146.9		18
39.23	odd	6		1521.4.a.bg.1.9		9
39.29	odd	6		1521.4.a.bh.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.9	✓	9	13.3	even	3
169.4.a.l.1.1	yes	9	13.10	even	6
169.4.b.g.168.2		18	13.2	odd	12
169.4.b.g.168.17		18	13.11	odd	12
169.4.c.k.22.9		18	13.4	even	6
169.4.c.k.146.9		18	13.12	even	2
169.4.c.l.22.1		18	13.9	even	3	inner
169.4.c.l.146.1		18	1.1	even	1	trivial
169.4.e.h.23.2		36	13.5	odd	4
169.4.e.h.23.17		36	13.8	odd	4
169.4.e.h.147.2		36	13.7	odd	12
169.4.e.h.147.17		36	13.6	odd	12
1521.4.a.bg.1.9		9	39.23	odd	6
1521.4.a.bh.1.1		9	39.29	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)

\(f(q)\)	\(=\)	\(q+(-2.42009 - 4.19172i) q^{2} +(3.09831 + 5.36643i) q^{3} +(-7.71365 + 13.3604i) q^{4} -15.2399 q^{5} +(14.9964 - 25.9745i) q^{6} +(2.15810 - 3.73794i) q^{7} +35.9495 q^{8} +(-5.69903 + 9.87102i) q^{9} +O(q^{10})\)	\(q+(-2.42009 - 4.19172i) q^{2} +(3.09831 + 5.36643i) q^{3} +(-7.71365 + 13.3604i) q^{4} -15.2399 q^{5} +(14.9964 - 25.9745i) q^{6} +(2.15810 - 3.73794i) q^{7} +35.9495 q^{8} +(-5.69903 + 9.87102i) q^{9} +(36.8818 + 63.8811i) q^{10} +(12.2846 + 21.2775i) q^{11} -95.5971 q^{12} -20.8912 q^{14} +(-47.2178 - 81.7836i) q^{15} +(-25.2917 - 43.8065i) q^{16} +(63.5802 - 110.124i) q^{17} +55.1687 q^{18} +(25.8731 - 44.8135i) q^{19} +(117.555 - 203.611i) q^{20} +26.7459 q^{21} +(59.4595 - 102.987i) q^{22} +(-43.6842 - 75.6632i) q^{23} +(111.383 + 192.920i) q^{24} +107.253 q^{25} +96.6792 q^{27} +(33.2937 + 57.6664i) q^{28} +(-112.863 - 195.484i) q^{29} +(-228.542 + 395.847i) q^{30} +108.720 q^{31} +(21.3817 - 37.0342i) q^{32} +(-76.1228 + 131.849i) q^{33} -615.479 q^{34} +(-32.8892 + 56.9657i) q^{35} +(-87.9208 - 152.283i) q^{36} +(-57.8782 - 100.248i) q^{37} -250.461 q^{38} -547.865 q^{40} +(95.9425 + 166.177i) q^{41} +(-64.7274 - 112.111i) q^{42} +(61.6504 - 106.782i) q^{43} -379.036 q^{44} +(86.8524 - 150.433i) q^{45} +(-211.439 + 366.223i) q^{46} -36.7339 q^{47} +(156.723 - 271.452i) q^{48} +(162.185 + 280.913i) q^{49} +(-259.562 - 449.574i) q^{50} +787.965 q^{51} +119.162 q^{53} +(-233.972 - 405.252i) q^{54} +(-187.215 - 324.266i) q^{55} +(77.5827 - 134.377i) q^{56} +320.651 q^{57} +(-546.276 + 946.178i) q^{58} +(402.276 - 696.763i) q^{59} +1456.89 q^{60} +(-339.443 + 587.933i) q^{61} +(-263.113 - 455.725i) q^{62} +(24.5982 + 42.6053i) q^{63} -611.650 q^{64} +736.896 q^{66} +(43.7403 + 75.7604i) q^{67} +(980.872 + 1698.92i) q^{68} +(270.694 - 468.856i) q^{69} +318.379 q^{70} +(490.525 - 849.614i) q^{71} +(-204.877 + 354.858i) q^{72} +263.862 q^{73} +(-280.140 + 485.218i) q^{74} +(332.303 + 575.566i) q^{75} +(399.152 + 691.352i) q^{76} +106.045 q^{77} +321.051 q^{79} +(385.441 + 667.604i) q^{80} +(453.416 + 785.339i) q^{81} +(464.378 - 804.327i) q^{82} -1042.54 q^{83} +(-206.308 + 357.337i) q^{84} +(-968.953 + 1678.28i) q^{85} -596.798 q^{86} +(699.368 - 1211.34i) q^{87} +(441.624 + 764.915i) q^{88} +(172.373 + 298.558i) q^{89} -840.762 q^{90} +1347.86 q^{92} +(336.849 + 583.440i) q^{93} +(88.8993 + 153.978i) q^{94} +(-394.302 + 682.951i) q^{95} +264.989 q^{96} +(241.261 - 417.876i) q^{97} +(785.005 - 1359.67i) q^{98} -280.041 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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