LMFDB - Embedded newform 169.4.c.l.146.7

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			146.7
Root			$-1.08068 + 1.87179i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.l.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58068 + 2.73781i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(-0.997073 + 1.72698i) q^{4} -13.6039 q^{5} +(11.2051 - 19.4079i) q^{6} +(-7.16574 + 12.4114i) q^{7} +18.9866 q^{8} +(-11.6258 + 20.1364i) q^{9} +O(q^{10})$	\(q+(1.58068 + 2.73781i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(-0.997073 + 1.72698i) q^{4} -13.6039 q^{5} +(11.2051 - 19.4079i) q^{6} +(-7.16574 + 12.4114i) q^{7} +18.9866 q^{8} +(-11.6258 + 20.1364i) q^{9} +(-21.5034 - 37.2450i) q^{10} +(33.8611 + 58.6492i) q^{11} +14.1362 q^{12} -45.3068 q^{14} +(48.2180 + 83.5160i) q^{15} +(37.9883 + 65.7976i) q^{16} +(-0.168897 + 0.292539i) q^{17} -73.5064 q^{18} +(-20.2615 + 35.0939i) q^{19} +(13.5641 - 23.4937i) q^{20} +101.593 q^{21} +(-107.047 + 185.411i) q^{22} +(77.8158 + 134.781i) q^{23} +(-67.2965 - 116.561i) q^{24} +60.0670 q^{25} -26.5720 q^{27} +(-14.2895 - 24.7502i) q^{28} +(16.8963 + 29.2652i) q^{29} +(-152.434 + 264.024i) q^{30} -157.397 q^{31} +(-44.1478 + 76.4663i) q^{32} +(240.036 - 415.754i) q^{33} -1.06789 q^{34} +(97.4822 - 168.844i) q^{35} +(-23.1835 - 40.1550i) q^{36} +(29.3102 + 50.7667i) q^{37} -128.107 q^{38} -258.293 q^{40} +(-29.6744 - 51.3976i) q^{41} +(160.586 + 278.144i) q^{42} +(104.155 - 180.402i) q^{43} -135.048 q^{44} +(158.156 - 273.935i) q^{45} +(-246.003 + 426.090i) q^{46} -221.212 q^{47} +(269.293 - 466.428i) q^{48} +(68.8044 + 119.173i) q^{49} +(94.9464 + 164.452i) q^{50} +2.39457 q^{51} -409.639 q^{53} +(-42.0017 - 72.7491i) q^{54} +(-460.645 - 797.860i) q^{55} +(-136.053 + 235.651i) q^{56} +287.260 q^{57} +(-53.4150 + 92.5175i) q^{58} +(-86.7937 + 150.331i) q^{59} -192.308 q^{60} +(-280.398 + 485.664i) q^{61} +(-248.793 - 430.922i) q^{62} +(-166.615 - 288.585i) q^{63} +328.679 q^{64} +1517.68 q^{66} +(134.537 + 233.025i) q^{67} +(-0.336806 - 0.583366i) q^{68} +(551.623 - 955.440i) q^{69} +616.351 q^{70} +(-30.4877 + 52.8062i) q^{71} +(-220.734 + 382.323i) q^{72} +282.066 q^{73} +(-92.6598 + 160.491i) q^{74} +(-212.902 - 368.758i) q^{75} +(-40.4043 - 69.9823i) q^{76} -970.560 q^{77} +984.026 q^{79} +(-516.790 - 895.106i) q^{80} +(408.078 + 706.813i) q^{81} +(93.8112 - 162.486i) q^{82} +1201.86 q^{83} +(-101.296 + 175.450i) q^{84} +(2.29767 - 3.97968i) q^{85} +658.543 q^{86} +(119.775 - 207.456i) q^{87} +(642.908 + 1113.55i) q^{88} +(269.949 + 467.566i) q^{89} +999.976 q^{90} -310.352 q^{92} +(557.879 + 966.275i) q^{93} +(-349.664 - 605.636i) q^{94} +(275.636 - 477.415i) q^{95} +625.913 q^{96} +(-793.627 + 1374.60i) q^{97} +(-217.515 + 376.747i) q^{98} -1574.65 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 $

$2$	1.58068	+	2.73781i	0.558853	+	0.967962i	0.997593	+	0.0693479i	$0.0220919\pi$
$2$	1.58068	+	2.73781i	0.558853	+	0.967962i	−0.438739	+	0.898614i	$0.644575\pi$
$3$	−3.54442	−	6.13911i	−0.682123	−	1.18147i	−0.974332	−	0.225118i	$-0.927723\pi$
$3$	−3.54442	−	6.13911i	−0.682123	−	1.18147i	0.292208	−	0.956355i	$-0.405610\pi$
$4$	−0.997073	+	1.72698i	−0.124634	+	0.215873i
$5$	−13.6039			−1.21677			−0.608386	−	0.793641i	$-0.708183\pi$
$5$	−13.6039			−1.21677			−0.608386	+	0.793641i	$0.708183\pi$
$6$	11.2051	−	19.4079i	0.762414	−	1.32054i
$7$	−7.16574	+	12.4114i	−0.386913	+	0.670154i	−0.992033	−	0.125981i	$-0.959792\pi$
$7$	−7.16574	+	12.4114i	−0.386913	+	0.670154i	0.605119	+	0.796135i	$0.293125\pi$
$8$	18.9866			0.839098
$9$	−11.6258	+	20.1364i	−0.430585	+	0.745794i
$10$	−21.5034	−	37.2450i	−0.679998	−	1.17779i
$11$	33.8611	+	58.6492i	0.928138	+	1.60758i	0.786436	+	0.617672i	$0.211924\pi$
$11$	33.8611	+	58.6492i	0.928138	+	1.60758i	0.141702	+	0.989909i	$0.454743\pi$
$12$	14.1362			0.340063
$13$		0			0
$13$		0			0
$14$	−45.3068			−0.864911
$15$	48.2180	+	83.5160i	0.829989	+	1.43758i
$16$	37.9883	+	65.7976i	0.593567	+	1.02809i
$17$	−0.168897	+	0.292539i	−0.00240963	+	0.00417360i	−0.867228	−	0.497912i	$-0.834100\pi$
$17$	−0.168897	+	0.292539i	−0.00240963	+	0.00417360i	0.864818	+	0.502085i	$0.167434\pi$
$18$	−73.5064			−0.962535
$19$	−20.2615	+	35.0939i	−0.244647	+	0.423741i	−0.962032	−	0.272935i	$-0.912005\pi$
$19$	−20.2615	+	35.0939i	−0.244647	+	0.423741i	0.717385	+	0.696677i	$0.245339\pi$
$20$	13.5641	−	23.4937i	0.151651	−	0.262668i
$21$	101.593			1.05569
$22$	−107.047	+	185.411i	−1.03739	+	1.79680i
$23$	77.8158	+	134.781i	0.705466	+	1.22190i	0.966523	+	0.256580i	$0.0825956\pi$
$23$	77.8158	+	134.781i	0.705466	+	1.22190i	−0.261057	+	0.965323i	$0.584071\pi$
$24$	−67.2965	−	116.561i	−0.572368	−	0.991371i
$25$	60.0670			0.480536
$26$		0			0
$27$	−26.5720			−0.189399
$28$	−14.2895	−	24.7502i	−0.0964452	−	0.167048i
$29$	16.8963	+	29.2652i	0.108192	+	0.187393i	0.915038	−	0.403368i	$-0.132161\pi$
$29$	16.8963	+	29.2652i	0.108192	+	0.187393i	−0.806846	+	0.590762i	$0.798827\pi$
$30$	−152.434	+	264.024i	−0.927684	+	1.60680i
$31$	−157.397			−0.911911			−0.455956	−	0.890003i	$-0.650702\pi$
$31$	−157.397			−0.911911			−0.455956	+	0.890003i	$0.650702\pi$
$32$	−44.1478	+	76.4663i	−0.243885	+	0.422421i
$33$	240.036	−	415.754i	1.26621	−	2.19314i
$34$	−1.06789			−0.00538651
$35$	97.4822	−	168.844i	0.470786	−	0.815425i
$36$	−23.1835	−	40.1550i	−0.107331	−	0.185903i
$37$	29.3102	+	50.7667i	0.130231	+	0.225567i	0.923766	−	0.382958i	$-0.125095\pi$
$37$	29.3102	+	50.7667i	0.130231	+	0.225567i	−0.793534	+	0.608526i	$0.791761\pi$
$38$	−128.107			−0.546888
$39$		0			0
$40$	−258.293			−1.02099
$41$	−29.6744	−	51.3976i	−0.113033	−	0.195779i	0.803959	−	0.594685i	$-0.202723\pi$
$41$	−29.6744	−	51.3976i	−0.113033	−	0.195779i	−0.916992	+	0.398906i	$0.869390\pi$
$42$	160.586	+	278.144i	0.589976	+	1.02187i
$43$	104.155	−	180.402i	0.369385	−	0.639793i	−0.620085	−	0.784535i	$-0.712902\pi$
$43$	104.155	−	180.402i	0.369385	−	0.639793i	0.989469	+	0.144742i	$0.0462352\pi$
$44$	−135.048			−0.462711
$45$	158.156	−	273.935i	0.523924	−	0.907462i
$46$	−246.003	+	426.090i	−0.788504	+	1.36573i
$47$	−221.212			−0.686533			−0.343266	−	0.939238i	$-0.611533\pi$
$47$	−221.212			−0.686533			−0.343266	+	0.939238i	$0.611533\pi$
$48$	269.293	−	466.428i	0.809772	−	1.40257i
$49$	68.8044	+	119.173i	0.200596	+	0.347442i
$50$	94.9464	+	164.452i	0.268549	+	0.465141i
$51$	2.39457			0.00657465
$52$		0			0
$53$	−409.639			−1.06167			−0.530833	−	0.847477i	$-0.678121\pi$
$53$	−409.639			−1.06167			−0.530833	+	0.847477i	$0.678121\pi$
$54$	−42.0017	−	72.7491i	−0.105847	−	0.183332i
$55$	−460.645	−	797.860i	−1.12933	−	1.95606i
$56$	−136.053	+	235.651i	−0.324658	+	0.562325i
$57$	287.260			0.667518
$58$	−53.4150	+	92.5175i	−0.120927	+	0.209451i
$59$	−86.7937	+	150.331i	−0.191518	+	0.331719i	−0.945754	−	0.324885i	$-0.894674\pi$
$59$	−86.7937	+	150.331i	−0.191518	+	0.331719i	0.754235	+	0.656604i	$0.228008\pi$
$60$	−192.308			−0.413780
$61$	−280.398	+	485.664i	−0.588546	+	1.01939i	0.405877	+	0.913928i	$0.366966\pi$
$61$	−280.398	+	485.664i	−0.588546	+	1.01939i	−0.994423	+	0.105464i	$0.966367\pi$
$62$	−248.793	−	430.922i	−0.509625	−	0.882696i
$63$	−166.615	−	288.585i	−0.333198	−	0.577116i
$64$	328.679			0.641951
$65$		0			0
$66$	1517.68			2.83050
$67$	134.537	+	233.025i	0.245318	+	0.424903i	0.962221	−	0.272270i	$-0.0877744\pi$
$67$	134.537	+	233.025i	0.245318	+	0.424903i	−0.716903	+	0.697173i	$0.754441\pi$
$68$	−0.336806	−	0.583366i	−0.000600644	−	0.00104035i
$69$	551.623	−	955.440i	0.962430	−	1.66698i
$70$	616.351			1.05240
$71$	−30.4877	+	52.8062i	−0.0509609	+	0.0882669i	−0.890381	−	0.455217i	$-0.849562\pi$
$71$	−30.4877	+	52.8062i	−0.0509609	+	0.0882669i	0.839420	+	0.543484i	$0.182895\pi$
$72$	−220.734	+	382.323i	−0.361303	+	0.625794i
$73$	282.066			0.452238			0.226119	−	0.974100i	$-0.427396\pi$
$73$	282.066			0.452238			0.226119	+	0.974100i	$0.427396\pi$
$74$	−92.6598	+	160.491i	−0.145561	+	0.252118i
$75$	−212.902	−	368.758i	−0.327785	−	0.567740i
$76$	−40.4043	−	69.9823i	−0.0609828	−	0.105625i
$77$	−970.560			−1.43644
$78$		0			0
$79$	984.026			1.40141			0.700706	−	0.713450i	$-0.252868\pi$
$79$	984.026			1.40141			0.700706	+	0.713450i	$0.252868\pi$
$80$	−516.790	−	895.106i	−0.722236	−	1.25095i
$81$	408.078	+	706.813i	0.559778	+	0.969565i
$82$	93.8112	−	162.486i	0.126338	−	0.218824i
$83$	1201.86			1.58942			0.794709	−	0.606991i	$-0.207624\pi$
$83$	1201.86			1.58942			0.794709	+	0.606991i	$0.207624\pi$
$84$	−101.296	+	175.450i	−0.131575	+	0.227895i
$85$	2.29767	−	3.97968i	0.00293197	−	0.00507832i
$86$	658.543			0.825727
$87$	119.775	−	207.456i	0.147600	−	0.255651i
$88$	642.908	+	1113.55i	0.778798	+	1.34892i
$89$	269.949	+	467.566i	0.321512	+	0.556875i	0.980800	−	0.195015i	$-0.0624756\pi$
$89$	269.949	+	467.566i	0.321512	+	0.556875i	−0.659288	+	0.751890i	$0.729142\pi$
$90$	999.976			1.17119
$91$		0			0
$92$	−310.352			−0.351701
$93$	557.879	+	966.275i	0.622036	+	1.07740i
$94$	−349.664	−	605.636i	−0.383671	−	0.664538i
$95$	275.636	−	477.415i	0.297680	−	0.515597i
$96$	625.913			0.665438
$97$	−793.627	+	1374.60i	−0.830728	+	1.43886i	0.0667329	+	0.997771i	$0.478742\pi$
$97$	−793.627	+	1374.60i	−0.830728	+	1.43886i	−0.897461	+	0.441093i	$0.854591\pi$
$98$	−217.515	+	376.747i	−0.224207	+	0.388339i
$99$	−1574.65			−1.59857
$100$	−59.8912	+	103.735i	−0.0598912	+	0.103735i
$101$	−580.363	−	1005.22i	−0.571765	−	0.990326i	−0.996385	−	0.0849545i	$-0.972926\pi$
$101$	−580.363	−	1005.22i	−0.571765	−	0.990326i	0.424620	−	0.905372i	$-0.360408\pi$
$102$	3.78504	+	6.55589i	0.00367427	+	0.00636402i
$103$	−82.2962			−0.0787270			−0.0393635	−	0.999225i	$-0.512533\pi$
$103$	−82.2962			−0.0787270			−0.0393635	+	0.999225i	$0.512533\pi$
$104$		0			0
$105$	−1382.07			−1.28454
$106$	−647.507	−	1121.51i	−0.593315	−	1.02765i
$107$	−661.022	−	1144.92i	−0.597229	−	1.03443i	−0.993228	−	0.116180i	$-0.962935\pi$
$107$	−661.022	−	1144.92i	−0.597229	−	1.03443i	0.396000	−	0.918251i	$-0.370398\pi$
$108$	26.4942	−	45.8894i	0.0236056	−	0.0408862i
$109$	−2073.41			−1.82199			−0.910994	−	0.412420i	$-0.864684\pi$
$109$	−2073.41			−1.82199			−0.910994	+	0.412420i	$0.864684\pi$
$110$	1456.26	−	2522.32i	1.26226	−	2.18630i
$111$	207.775	−	359.877i	0.177668	−	0.307730i
$112$	−1088.86			−0.918636
$113$	801.411	−	1388.09i	0.667172	−	1.15558i	−0.311519	−	0.950240i	$-0.600838\pi$
$113$	801.411	−	1388.09i	0.667172	−	1.15558i	0.978691	−	0.205336i	$-0.0658288\pi$
$114$	454.065	+	786.464i	0.373045	+	0.646133i
$115$	−1058.60	−	1833.55i	−0.858392	−	1.48678i
$116$	−67.3872			−0.0539375
$117$		0			0
$118$	−548.771			−0.428122
$119$	−2.42055	−	4.19252i	−0.00186463	−	0.00322964i
$120$	915.497	+	1585.69i	0.696442	+	1.20627i
$121$	−1627.65	+	2819.18i	−1.22288	+	2.11809i
$122$	−1772.87			−1.31564
$123$	−210.357	+	364.349i	−0.154205	+	0.267091i
$124$	156.936	−	271.821i	0.113655	−	0.196857i
$125$	883.344			0.632070
$126$	526.727	−	912.319i	0.372418	−	0.645046i
$127$	−307.248	−	532.169i	−0.214676	−	0.371829i	0.738496	−	0.674257i	$-0.235536\pi$
$127$	−307.248	−	532.169i	−0.214676	−	0.371829i	−0.953172	+	0.302428i	$0.902203\pi$
$128$	872.717	+	1511.59i	0.602641	+	1.04380i
$129$	−1476.68			−1.00786
$130$		0			0
$131$	−330.171			−0.220208			−0.110104	−	0.993920i	$-0.535118\pi$
$131$	−330.171			−0.220208			−0.110104	+	0.993920i	$0.535118\pi$
$132$	478.667	+	829.075i	0.315626	+	0.546680i
$133$	−290.377	−	502.947i	−0.189315	−	0.327902i
$134$	−425.318	+	736.673i	−0.274193	+	0.474917i
$135$	361.484			0.230456
$136$	−3.20679	+	5.55433i	−0.00202191	+	0.00350206i
$137$	1151.27	−	1994.06i	0.717953	−	1.24353i	−0.243856	−	0.969811i	$-0.578413\pi$
$137$	1151.27	−	1994.06i	0.717953	−	1.24353i	0.961809	−	0.273720i	$-0.0882541\pi$
$138$	3487.75			2.15143
$139$	−603.611	+	1045.48i	−0.368328	+	0.637963i	−0.989304	−	0.145866i	$-0.953403\pi$
$139$	−603.611	+	1045.48i	−0.368328	+	0.637963i	0.620976	+	0.783829i	$0.286736\pi$
$140$	194.394	+	336.700i	0.117352	+	0.203260i
$141$	784.066	+	1358.04i	0.468300	+	0.811119i
$142$	−192.765			−0.113919
$143$		0			0
$144$	−1766.57			−1.02232
$145$	−229.856	−	398.122i	−0.131645	−	0.228015i
$146$	445.856	+	772.245i	0.252735	+	0.437750i
$147$	487.743	−	844.796i	0.273662	−	0.473997i
$148$	−116.898			−0.0649251
$149$	169.469	−	293.529i	0.0931774	−	0.161388i	−0.815669	−	0.578519i	$-0.803631\pi$
$149$	169.469	−	293.529i	0.0931774	−	0.161388i	0.908846	+	0.417131i	$0.136964\pi$
$150$	673.060	−	1165.77i	0.366367	−	0.634567i
$151$	−1694.81			−0.913386			−0.456693	−	0.889624i	$-0.650966\pi$
$151$	−1694.81			−0.913386			−0.456693	+	0.889624i	$0.650966\pi$
$152$	−384.697	+	666.314i	−0.205283	+	0.355561i
$153$	−3.92713	−	6.80199i	−0.00207510	−	0.00359417i
$154$	−1534.14	−	2657.21i	−0.802757	−	1.39042i
$155$	2141.21			1.10959
$156$		0			0
$157$	9.59250			0.00487621			0.00243811	−	0.999997i	$-0.499224\pi$
$157$	9.59250			0.00487621			0.00243811	+	0.999997i	$0.499224\pi$
$158$	1555.43	+	2694.08i	0.783184	+	1.35651i
$159$	1451.93	+	2514.82i	0.724187	+	1.25433i
$160$	600.584	−	1040.24i	0.296752	−	0.513990i
$161$	−2230.43			−1.09182
$162$	−1290.08	+	2234.48i	−0.625668	+	1.08369i
$163$	61.0501	−	105.742i	0.0293363	−	0.0508119i	−0.850985	−	0.525191i	$-0.823994\pi$
$163$	61.0501	−	105.742i	0.0293363	−	0.0508119i	0.880321	+	0.474379i	$0.157327\pi$
$164$	118.350			0.0563512
$165$	−3265.43	+	5655.90i	−1.54069	+	2.66855i
$166$	1899.76	+	3290.48i	0.888251	+	1.53850i
$167$	1105.62	+	1914.99i	0.512309	+	0.887346i	0.999898	+	0.0142723i	$0.00454318\pi$
$167$	1105.62	+	1914.99i	0.512309	+	0.887346i	−0.487589	+	0.873073i	$0.662123\pi$
$168$	1928.92			0.885828
$169$		0			0
$170$	14.5275			0.00655416
$171$	−471.111	−	815.988i	−0.210683	−	0.364913i
$172$	207.701	+	359.749i	0.0920758	+	0.159480i
$173$	106.937	−	185.220i	0.0469957	−	0.0813989i	−0.841571	−	0.540147i	$-0.818369\pi$
$173$	106.937	−	185.220i	0.0469957	−	0.0813989i	0.888566	+	0.458748i	$0.151702\pi$
$174$	757.301			0.329947
$175$	−430.424	+	745.517i	−0.185926	+	0.322033i
$176$	−2572.65	+	4455.96i	−1.10182	+	1.90841i
$177$	1230.53			0.522556
$178$	−853.405	+	1478.14i	−0.359356	+	0.622423i
$179$	−1483.70	−	2569.85i	−0.619537	−	1.07307i	−0.989570	−	0.144051i	$-0.953987\pi$
$179$	−1483.70	−	2569.85i	−0.619537	−	1.07307i	0.370033	−	0.929019i	$-0.379346\pi$
$180$	315.387	+	546.266i	0.130598	+	0.226202i
$181$	2329.44			0.956609			0.478304	−	0.878194i	$-0.341252\pi$
$181$	2329.44			0.956609			0.478304	+	0.878194i	$0.341252\pi$
$182$		0			0
$183$	3975.39			1.60584
$184$	1477.46	+	2559.03i	0.591955	+	1.02530i
$185$	−398.734	−	690.627i	−0.158462	−	0.274464i
$186$	−1763.65	+	3054.73i	−0.695254	+	1.20421i
$187$	−22.8762			−0.00894586
$188$	220.564	−	382.028i	0.0855654	−	0.148204i
$189$	190.408	−	329.796i	0.0732812	−	0.126927i
$190$	1742.76			0.665438
$191$	2239.88	−	3879.58i	0.848544	−	1.46972i	−0.0339639	−	0.999423i	$-0.510813\pi$
$191$	2239.88	−	3879.58i	0.848544	−	1.46972i	0.882508	−	0.470298i	$-0.155854\pi$
$192$	−1164.97	−	2017.79i	−0.437890	−	0.758447i
$193$	651.313	+	1128.11i	0.242915	+	0.420741i	0.961543	−	0.274653i	$-0.0885631\pi$
$193$	651.313	+	1128.11i	0.242915	+	0.420741i	−0.718629	+	0.695394i	$0.755230\pi$
$194$	−5017.87			−1.85702
$195$		0			0
$196$	−274.412			−0.100004
$197$	−370.477	−	641.685i	−0.133987	−	0.232072i	0.791223	−	0.611528i	$-0.209445\pi$
$197$	−370.477	−	641.685i	−0.133987	−	0.232072i	−0.925210	+	0.379456i	$0.876111\pi$
$198$	−2489.01	−	4311.09i	−0.893365	−	1.54735i
$199$	2344.37	−	4060.57i	0.835115	−	1.44646i	−0.0588210	−	0.998269i	$-0.518734\pi$
$199$	2344.37	−	4060.57i	0.835115	−	1.44646i	0.893936	−	0.448194i	$-0.147933\pi$
$200$	1140.47			0.403217
$201$	953.709	−	1651.87i	0.334674	−	0.579672i
$202$	1834.73	−	3177.85i	0.639066	−	1.10689i
$203$	−484.297			−0.167443
$204$	−2.38756	+	4.13538i	−0.000819426	+	0.00141929i
$205$	403.688	+	699.209i	0.137536	+	0.238219i
$206$	−130.084	−	225.311i	−0.0439969	−	0.0762048i
$207$	−3618.68			−1.21505
$208$		0			0
$209$	−2744.30			−0.908265
$210$	−2184.61	−	3783.85i	−0.717867	−	1.24338i
$211$	1602.56	+	2775.71i	0.522865	+	0.905628i	0.999646	+	0.0266064i	$0.00847009\pi$
$211$	1602.56	+	2775.71i	0.522865	+	0.905628i	−0.476781	+	0.879022i	$0.658197\pi$
$212$	408.440	−	707.439i	0.132320	−	0.229185i
$213$	432.244			0.139046
$214$	2089.72	−	3619.51i	0.667526	−	1.15619i
$215$	−1416.92	+	2454.18i	−0.449457	+	0.778482i
$216$	−504.513			−0.158925
$217$	1127.86	−	1953.51i	0.352831	−	0.611121i
$218$	−3277.39	−	5676.60i	−1.01822	−	1.76362i
$219$	−999.761	−	1731.64i	−0.308482	−	0.534307i
$220$	1837.18			0.563014
$221$		0			0
$222$	1313.70			0.397161
$223$	528.695	+	915.726i	0.158762	+	0.274984i	0.934423	−	0.356166i	$-0.115916\pi$
$223$	528.695	+	915.726i	0.158762	+	0.274984i	−0.775660	+	0.631151i	$0.782583\pi$
$224$	−632.704	−	1095.87i	−0.188724	−	0.326880i
$225$	−698.326	+	1209.54i	−0.206911	+	0.358381i
$226$	5067.09			1.49141
$227$	2579.84	−	4468.42i	0.754317	−	1.30652i	−0.191396	−	0.981513i	$-0.561301\pi$
$227$	2579.84	−	4468.42i	0.754317	−	1.30652i	0.945713	−	0.325003i	$-0.105365\pi$
$228$	−286.419	+	496.093i	−0.0831956	+	0.144099i
$229$	−1698.25			−0.490059			−0.245030	−	0.969516i	$-0.578798\pi$
$229$	−1698.25			−0.490059			−0.245030	+	0.969516i	$0.578798\pi$
$230$	3346.61	−	5796.50i	0.959430	−	1.66178i
$231$	3440.07	+	5958.37i	0.979826	+	1.69711i
$232$	320.803	+	555.647i	0.0907834	+	0.157241i
$233$	3162.23			0.889119			0.444559	−	0.895749i	$-0.353360\pi$
$233$	3162.23			0.889119			0.444559	+	0.895749i	$0.353360\pi$
$234$		0			0
$235$	3009.35			0.835354
$236$	−173.079	−	299.782i	−0.0477394	−	0.0826871i
$237$	−3487.80	−	6041.04i	−0.955936	−	1.65573i
$238$	7.65221	−	13.2540i	0.00208411	−	0.00360979i
$239$	−2350.04			−0.636030			−0.318015	−	0.948086i	$-0.603016\pi$
$239$	−2350.04			−0.636030			−0.318015	+	0.948086i	$0.603016\pi$
$240$	−3663.44	+	6345.26i	−0.985308	+	1.70660i
$241$	−2583.59	+	4474.91i	−0.690555	+	1.19608i	0.281102	+	0.959678i	$0.409300\pi$
$241$	−2583.59	+	4474.91i	−0.690555	+	1.19608i	−0.971656	+	0.236398i	$0.924033\pi$
$242$	−10291.2			−2.73364
$243$	2534.08	−	4389.15i	0.668976	−	1.15870i
$244$	−559.155	−	968.485i	−0.146706	−	0.254102i
$245$	−936.011	−	1621.22i	−0.244080	−	0.422759i
$246$	−1330.02			−0.344712
$247$		0			0
$248$	−2988.43			−0.765183
$249$	−4259.91	−	7378.37i	−1.08418	−	1.87785i
$250$	1396.28	+	2418.43i	0.353234	+	0.611820i
$251$	−1447.00	+	2506.28i	−0.363880	+	0.630259i	−0.988596	−	0.150593i	$-0.951882\pi$
$251$	−1447.00	+	2506.28i	−0.363880	+	0.630259i	0.624715	+	0.780853i	$0.285215\pi$
$252$	664.508			0.166111
$253$	−5269.86	+	9127.67i	−1.30954	+	2.26819i
$254$	971.318	−	1682.37i	0.239945	−	0.415596i
$255$	−32.5756			−0.00799986
$256$	−1444.25	+	2501.52i	−0.352600	+	0.610722i
$257$	3081.31	+	5336.99i	0.747887	+	1.29538i	0.948834	+	0.315776i	$0.102265\pi$
$257$	3081.31	+	5336.99i	0.747887	+	1.29538i	−0.200946	+	0.979602i	$0.564402\pi$
$258$	−2334.15	−	4042.87i	−0.563248	−	0.975574i
$259$	−840.116			−0.201553
$260$		0			0
$261$	−785.729			−0.186343
$262$	−521.894	−	903.946i	−0.123064	−	0.213153i
$263$	99.7136	+	172.709i	0.0233787	+	0.0404931i	0.877478	−	0.479617i	$-0.159224\pi$
$263$	99.7136	+	172.709i	0.0233787	+	0.0404931i	−0.854099	+	0.520110i	$0.825891\pi$
$264$	4557.47	−	7893.77i	1.06247	−	1.84026i
$265$	5572.70			1.29181
$266$	917.982	−	1589.99i	0.211598	−	0.366499i
$267$	1913.63	−	3314.50i	0.438622	−	0.759715i
$268$	−536.572			−0.122300
$269$	−554.001	+	959.559i	−0.125569	+	0.217492i	−0.921955	−	0.387296i	$-0.873409\pi$
$269$	−554.001	+	959.559i	−0.125569	+	0.217492i	0.796386	+	0.604788i	$0.206742\pi$
$270$	571.389	+	989.675i	0.128791	+	0.223073i
$271$	203.027	+	351.653i	0.0455093	+	0.0788244i	0.887883	−	0.460070i	$-0.152176\pi$
$271$	203.027	+	351.653i	0.0455093	+	0.0788244i	−0.842373	+	0.538894i	$0.818842\pi$
$272$	−25.6645			−0.00572110
$273$		0			0
$274$	7279.13			1.60492
$275$	2033.94	+	3522.88i	0.446003	+	0.772501i
$276$	1100.02	+	1905.29i	0.239903	+	0.415525i
$277$	−144.405	+	250.117i	−0.0313230	+	0.0542530i	−0.881262	−	0.472628i	$-0.843305\pi$
$277$	−144.405	+	250.117i	−0.0313230	+	0.0542530i	0.849939	+	0.526881i	$0.176639\pi$
$278$	−3816.45			−0.823366
$279$	1829.86	−	3169.41i	0.392655	−	0.680098i
$280$	1850.86	−	3205.78i	0.395035	−	0.684221i
$281$	5134.93			1.09012			0.545061	−	0.838396i	$-0.316506\pi$
$281$	5134.93			1.09012			0.545061	+	0.838396i	$0.316506\pi$
$282$	−2478.71	+	4293.25i	−0.523422	+	0.906593i
$283$	−2637.20	−	4567.76i	−0.553940	−	0.959453i	−0.997985	−	0.0634483i	$-0.979790\pi$
$283$	−2637.20	−	4567.76i	−0.553940	−	0.959453i	0.444045	−	0.896005i	$-0.353543\pi$
$284$	−60.7969	−	105.303i	−0.0127029	−	0.0220021i
$285$	−3907.87			−0.812218
$286$		0			0
$287$	850.556			0.174936
$288$	−1026.51	−	1777.96i	−0.210026	−	0.363776i
$289$	2456.44	+	4254.68i	0.499988	+	0.866005i
$290$	726.655	−	1258.60i	0.147140	−	0.254854i
$291$	11251.8			2.26664
$292$	−281.241	+	487.124i	−0.0563643	+	0.0976258i
$293$	−722.845	+	1252.00i	−0.144127	+	0.249634i	−0.929047	−	0.369962i	$-0.879371\pi$
$293$	−722.845	+	1252.00i	−0.144127	+	0.249634i	0.784920	+	0.619597i	$0.212704\pi$
$294$	3083.86			0.611749
$295$	1180.74	−	2045.09i	0.233034	−	0.403627i
$296$	556.501	+	963.888i	0.109277	+	0.189273i
$297$	−899.758	−	1558.43i	−0.175789	−	0.304475i
$298$	1071.50			0.208290
$299$		0			0
$300$	849.117			0.163413
$301$	1492.70	+	2585.43i	0.285840	+	0.495089i
$302$	−2678.94	−	4640.06i	−0.510449	−	0.884124i
$303$	−4114.10	+	7125.83i	−0.780029	+	1.35105i
$304$	−3078.79			−0.580858
$305$	3814.52	−	6606.94i	0.716127	−	1.24037i
$306$	12.4150	−	21.5035i	0.00231935	−	0.00401723i
$307$	9421.42			1.75149			0.875747	−	0.482770i	$-0.160369\pi$
$307$	9421.42			1.75149			0.875747	+	0.482770i	$0.160369\pi$
$308$	967.719	−	1676.14i	0.179029	−	0.310087i
$309$	291.692	+	505.225i	0.0537015	+	0.0930138i
$310$	3384.56	+	5862.23i	0.620097	+	1.07404i
$311$	7885.87			1.43784			0.718918	−	0.695095i	$-0.244638\pi$
$311$	7885.87			1.43784			0.718918	+	0.695095i	$0.244638\pi$
$312$		0			0
$313$	−550.423			−0.0993986			−0.0496993	−	0.998764i	$-0.515826\pi$
$313$	−550.423			−0.0993986			−0.0496993	+	0.998764i	$0.515826\pi$
$314$	15.1626	+	26.2625i	0.00272509	+	0.00471999i
$315$	2266.61	+	3925.89i	0.405426	+	0.702219i
$316$	−981.146	+	1699.39i	−0.174664	+	0.302527i
$317$	−150.974			−0.0267494			−0.0133747	−	0.999911i	$-0.504257\pi$
$317$	−150.974			−0.0267494			−0.0133747	+	0.999911i	$0.504257\pi$
$318$	−4590.07	+	7950.23i	−0.809428	+	1.40197i
$319$	−1144.25	+	1981.90i	−0.200833	+	0.347854i
$320$	−4471.32			−0.781108
$321$	−4685.88	+	8116.18i	−0.814767	+	1.41122i
$322$	−3525.59	−	6106.50i	−0.610166	−	1.05684i
$323$	−6.84422	−	11.8545i	−0.00117902	−	0.00204212i
$324$	−1627.54			−0.279070
$325$		0			0
$326$	386.002			0.0655787
$327$	7349.03	+	12728.9i	1.24282	+	2.15263i
$328$	−563.416	−	975.866i	−0.0948459	−	0.164278i
$329$	1585.14	−	2745.55i	0.265629	−	0.460082i
$330$	−20646.4			−3.44408
$331$	3539.64	−	6130.84i	0.587784	−	1.01807i	−0.406738	−	0.913545i	$-0.633334\pi$
$331$	3539.64	−	6130.84i	0.587784	−	1.01807i	0.994522	−	0.104527i	$-0.0333327\pi$
$332$	−1198.35	+	2075.60i	−0.198096	+	0.343112i
$333$	−1363.02			−0.224303
$334$	−3495.26	+	6053.97i	−0.572612	+	0.991792i
$335$	−1830.23	−	3170.05i	−0.298496	−	0.517010i
$336$	3859.36	+	6684.61i	0.626623	+	1.08534i
$337$	−6633.34			−1.07223			−0.536114	−	0.844145i	$-0.680108\pi$
$337$	−6633.34			−1.07223			−0.536114	+	0.844145i	$0.680108\pi$
$338$		0			0
$339$	−11362.1			−1.82037
$340$	4.58189	+	7.93607i	0.000730847	+	0.00126586i
$341$	−5329.62	−	9231.18i	−0.846379	−	1.46597i
$342$	1489.35	−	2579.62i	0.235481	−	0.407866i
$343$	−6887.83			−1.08428
$344$	1977.56	−	3425.23i	0.309950	−	0.536849i
$345$	−7504.25	+	12997.7i	−1.17106	+	2.02833i
$346$	676.130			0.105055
$347$	−3202.08	+	5546.17i	−0.495380	+	0.858023i	−0.999986	−	0.00532645i	$-0.998305\pi$
$347$	−3202.08	+	5546.17i	−0.495380	+	0.858023i	0.504606	+	0.863350i	$0.331638\pi$
$348$	238.848	+	413.698i	0.0367920	+	0.0637256i
$349$	84.0492	+	145.577i	0.0128913	+	0.0223283i	0.872399	−	0.488794i	$-0.162563\pi$
$349$	84.0492	+	145.577i	0.0128913	+	0.0223283i	−0.859508	+	0.511123i	$0.829230\pi$
$350$	−2721.45			−0.415621
$351$		0			0
$352$	−5979.58			−0.905434
$353$	−4225.96	−	7319.58i	−0.637182	−	1.10363i	−0.986048	−	0.166459i	$-0.946767\pi$
$353$	−4225.96	−	7319.58i	−0.637182	−	1.10363i	0.348866	−	0.937172i	$-0.386567\pi$
$354$	1945.07	+	3368.96i	0.292032	+	0.505815i
$355$	414.753	−	718.373i	0.0620078	−	0.107401i
$356$	−1076.64			−0.160285
$357$	−17.1589	+	29.7200i	−0.00254382	+	0.00440603i
$358$	4690.51	−	8124.20i	0.692461	−	1.19938i
$359$	−2631.92			−0.386929			−0.193464	−	0.981107i	$-0.561972\pi$
$359$	−2631.92			−0.386929			−0.193464	+	0.981107i	$0.561972\pi$
$360$	3002.85	−	5201.10i	0.439623	−	0.761450i
$361$	2608.45	+	4517.96i	0.380295	+	0.658691i
$362$	3682.09	+	6377.58i	0.534604	+	0.925961i
$363$	23076.3			3.33662
$364$		0			0
$365$	−3837.21			−0.550271
$366$	6283.81	+	10883.9i	0.897431	+	1.55440i
$367$	6634.93	+	11492.0i	0.943708	+	1.63455i	0.758318	+	0.651885i	$0.226021\pi$
$367$	6634.93	+	11492.0i	0.943708	+	1.63455i	0.185390	+	0.982665i	$0.440645\pi$
$368$	−5912.18	+	10240.2i	−0.837482	+	1.45056i
$369$	1379.95			0.194681
$370$	1260.54	−	2183.31i	0.177114	−	0.306771i
$371$	2935.37	−	5084.20i	0.410773	−	0.711479i
$372$	−2224.98			−0.310108
$373$	5840.03	−	10115.2i	0.810684	−	1.40415i	−0.101701	−	0.994815i	$-0.532429\pi$
$373$	5840.03	−	10115.2i	0.810684	−	1.40415i	0.912386	−	0.409332i	$-0.134238\pi$
$374$	−36.1599	−	62.6308i	−0.00499943	−	0.00865926i
$375$	−3130.94	−	5422.95i	−0.431150	−	0.746773i
$376$	−4200.06			−0.576068
$377$		0			0
$378$	1203.89			0.163814
$379$	−1689.11	−	2925.63i	−0.228928	−	0.396516i	0.728562	−	0.684979i	$-0.240189\pi$
$379$	−1689.11	−	2925.63i	−0.228928	−	0.396516i	−0.957491	+	0.288464i	$0.906856\pi$
$380$	549.657	+	952.035i	0.0742022	+	0.128522i
$381$	−2178.03	+	3772.46i	−0.292871	+	0.507267i
$382$	14162.1			1.89685
$383$	−2190.46	+	3793.98i	−0.292238	+	0.506171i	−0.974339	−	0.225087i	$-0.927733\pi$
$383$	−2190.46	+	3793.98i	−0.292238	+	0.506171i	0.682101	+	0.731258i	$0.261067\pi$
$384$	6186.55	−	10715.4i	0.822151	−	1.42401i
$385$	13203.4			1.74782
$386$	−2059.03	+	3566.35i	−0.271507	+	0.470265i
$387$	2421.77	+	4194.64i	0.318103	+	0.550970i
$388$	−1582.61	−	2741.16i	−0.207074	−	0.358663i
$389$	−12484.0			−1.62716			−0.813578	−	0.581456i	$-0.802483\pi$
$389$	−12484.0			−1.62716			−0.813578	+	0.581456i	$0.802483\pi$
$390$		0			0
$391$	−52.5716			−0.00679964
$392$	1306.36	+	2262.69i	0.168320	+	0.291538i
$393$	1170.26	+	2026.96i	0.150209	+	0.260169i
$394$	1171.21	−	2028.59i	0.149758	−	0.259388i
$395$	−13386.6			−1.70520
$396$	1570.04	−	2719.39i	0.199236	−	0.345087i
$397$	4725.24	−	8184.36i	0.597363	−	1.03466i	−0.395846	−	0.918317i	$-0.629549\pi$
$397$	4725.24	−	8184.36i	0.597363	−	1.03466i	0.993209	−	0.116346i	$-0.0371181\pi$
$398$	14822.8			1.86683
$399$	−2058.43	+	3565.31i	−0.258272	+	0.447340i
$400$	2281.84	+	3952.27i	0.285230	+	0.494033i
$401$	1453.01	+	2516.69i	0.180948	+	0.313411i	0.942204	−	0.335041i	$-0.108750\pi$
$401$	1453.01	+	2516.69i	0.180948	+	0.313411i	−0.761256	+	0.648452i	$0.775417\pi$
$402$	6030.02			0.748134
$403$		0			0
$404$	2314.66			0.285046
$405$	−5551.47	−	9615.43i	−0.681123	−	1.17974i
$406$	−765.516	−	1325.91i	−0.0935762	−	0.162079i
$407$	−1984.95	+	3438.04i	−0.241745	+	0.418715i
$408$	45.4648			0.00551678
$409$	−2897.96	+	5019.42i	−0.350355	+	0.606832i	−0.986312	−	0.164892i	$-0.947272\pi$
$409$	−2897.96	+	5019.42i	−0.350355	+	0.606832i	0.635957	+	0.771725i	$0.280606\pi$
$410$	−1276.20	+	2210.45i	−0.153725	+	0.266259i
$411$	−16322.3			−1.95893
$412$	82.0553	−	142.124i	0.00981208	−	0.0169950i
$413$	−1243.88	−	2154.47i	−0.148202	−	0.256693i
$414$	−5719.96	−	9907.26i	−0.679036	−	1.17612i
$415$	−16350.1			−1.93396
$416$		0			0
$417$	8557.79			1.00498
$418$	−4337.85	−	7513.38i	−0.507587	−	0.879167i
$419$	2071.23	+	3587.48i	0.241495	+	0.418281i	0.961140	−	0.276060i	$-0.0890290\pi$
$419$	2071.23	+	3587.48i	0.241495	+	0.418281i	−0.719645	+	0.694342i	$0.755696\pi$
$420$	1378.03	−	2386.81i	0.160097	−	0.277296i
$421$	1426.92			0.165187			0.0825935	−	0.996583i	$-0.473680\pi$
$421$	1426.92			0.165187			0.0825935	+	0.996583i	$0.473680\pi$
$422$	−5066.24	+	8774.99i	−0.584410	+	1.01223i
$423$	2571.76	−	4454.42i	0.295610	−	0.512012i
$424$	−7777.66			−0.890841
$425$	−10.1452	+	17.5719i	−0.00115791	+	0.00200556i
$426$	683.238	+	1183.40i	0.0777066	+	0.134592i
$427$	−4018.52	−	6960.28i	−0.455433	−	0.788833i
$428$	2636.35			0.297740
$429$		0			0
$430$	−8958.78			−1.00472
$431$	1271.54	+	2202.37i	0.142106	+	0.246136i	0.928290	−	0.371858i	$-0.121279\pi$
$431$	1271.54	+	2202.37i	0.142106	+	0.246136i	−0.786183	+	0.617994i	$0.787946\pi$
$432$	−1009.42	−	1748.38i	−0.112421	−	0.194719i
$433$	1724.22	−	2986.43i	0.191364	−	0.331452i	−0.754338	−	0.656486i	$-0.772042\pi$
$433$	1724.22	−	2986.43i	0.191364	−	0.331452i	0.945703	+	0.325033i	$0.105376\pi$
$434$	7131.14			0.788723
$435$	−1629.41	+	2822.22i	−0.179596	+	0.311069i
$436$	2067.34	−	3580.74i	0.227082	−	0.393317i
$437$	−6306.65			−0.690361
$438$	3160.60	−	5474.31i	0.344793	−	0.597198i
$439$	6321.28	+	10948.8i	0.687240	+	1.19033i	0.972727	+	0.231952i	$0.0745112\pi$
$439$	6321.28	+	10948.8i	0.687240	+	1.19033i	−0.285487	+	0.958382i	$0.592155\pi$
$440$	−8746.08	−	15148.7i	−0.947621	−	1.64133i
$441$	−3199.62			−0.345494
$442$		0			0
$443$	8486.59			0.910181			0.455091	−	0.890445i	$-0.349607\pi$
$443$	8486.59			0.910181			0.455091	+	0.890445i	$0.349607\pi$
$444$	414.334	+	717.647i	0.0442870	+	0.0767072i
$445$	−3672.37	−	6360.73i	−0.391207	−	0.677590i
$446$	−1671.39	+	2894.93i	−0.177450	+	0.307352i
$447$	−2402.67			−0.254234
$448$	−2355.23	+	4079.37i	−0.248379	+	0.430206i
$449$	−5684.77	+	9846.32i	−0.597508	+	1.03491i	0.395680	+	0.918389i	$0.370509\pi$
$449$	−5684.77	+	9846.32i	−0.597508	+	1.03491i	−0.993188	+	0.116526i	$0.962824\pi$
$450$	−4415.31			−0.462532
$451$	2009.62	−	3480.76i	0.209821	−	0.363420i
$452$	1598.13	+	2768.05i	0.166305	+	0.288048i
$453$	6007.10	+	10404.6i	0.623042	+	1.07914i
$454$	16311.6			1.68621
$455$		0			0
$456$	5454.10			0.560113
$457$	−5644.51	−	9776.58i	−0.577766	−	1.00072i	−0.995735	−	0.0922591i	$-0.970591\pi$
$457$	−5644.51	−	9776.58i	−0.577766	−	1.00072i	0.417969	−	0.908461i	$-0.362742\pi$
$458$	−2684.38	−	4649.49i	−0.273871	−	0.474359i
$459$	4.48795	−	7.77335i	0.000456382	−	0.000790477i
$460$	4222.01			0.427940
$461$	−1917.06	+	3320.44i	−0.193680	+	0.335463i	−0.946467	−	0.322801i	$-0.895376\pi$
$461$	−1917.06	+	3320.44i	−0.193680	+	0.335463i	0.752787	+	0.658264i	$0.228709\pi$
$462$	−10875.3	+	18836.5i	−1.09516	+	1.89687i
$463$	1294.44			0.129930			0.0649651	−	0.997888i	$-0.479306\pi$
$463$	1294.44			0.129930			0.0649651	+	0.997888i	$0.479306\pi$
$464$	−1283.72	+	2223.47i	−0.128438	+	0.222461i
$465$	−7589.35	−	13145.1i	−0.756876	−	1.31095i
$466$	4998.46	+	8657.59i	0.496887	+	0.860634i
$467$	13861.5			1.37352			0.686760	−	0.726884i	$-0.259032\pi$
$467$	13861.5			1.37352			0.686760	+	0.726884i	$0.259032\pi$
$468$		0			0
$469$	−3856.22			−0.379667
$470$	4756.80	+	8239.03i	0.466840	+	0.808591i
$471$	−33.9998	−	58.8894i	−0.00332618	−	0.00576111i
$472$	−1647.92	+	2854.28i	−0.160703	+	0.278345i
$473$	14107.3			1.37136
$474$	11026.2	−	19097.9i	1.06846	−	1.85062i
$475$	−1217.04	+	2107.98i	−0.117562	+	0.203623i
$476$	9.65386			0.000929588
$477$	4762.38	−	8248.68i	0.457137	−	0.791784i
$478$	−3714.65	−	6433.96i	−0.355448	−	0.615653i
$479$	4813.83	+	8337.79i	0.459185	+	0.795331i	0.998918	−	0.0465049i	$-0.0148083\pi$
$479$	4813.83	+	8337.79i	0.459185	+	0.795331i	−0.539733	+	0.841836i	$0.681475\pi$
$480$	−8514.88			−0.809686
$481$		0			0
$482$	−16335.3			−1.54368
$483$	7905.58	+	13692.9i	0.744754	+	1.28995i
$484$	−3245.78	−	5621.85i	−0.304825	−	0.527972i
$485$	10796.5	−	18700.0i	1.01081	−	1.75077i
$486$	16022.2			1.49544
$487$	5976.42	−	10351.5i	0.556094	−	0.963183i	−0.441724	−	0.897151i	$-0.645633\pi$
$487$	5976.42	−	10351.5i	0.556094	−	0.963183i	0.997818	−	0.0660314i	$-0.0210338\pi$
$488$	−5323.81	+	9221.11i	−0.493848	+	0.855369i
$489$	−865.548			−0.0800438
$490$	2959.06	−	5125.24i	0.272810	−	0.472520i
$491$	−2705.06	−	4685.30i	−0.248631	−	0.430641i	0.714516	−	0.699620i	$-0.246647\pi$
$491$	−2705.06	−	4685.30i	−0.248631	−	0.430641i	−0.963146	+	0.268979i	$0.913314\pi$
$492$	−419.482	−	726.565i	−0.0384385	−	0.0665774i
$493$	−11.4149			−0.00104281
$494$		0			0
$495$	21421.4			1.94509
$496$	−5979.22	−	10356.3i	−0.541280	−	0.937525i
$497$	−436.934	−	756.791i	−0.0394349	−	0.0683033i
$498$	13467.1	−	23325.6i	1.21179	−	2.09889i
$499$	−14472.9			−1.29838			−0.649192	−	0.760624i	$-0.724893\pi$
$499$	−14472.9			−1.29838			−0.649192	+	0.760624i	$0.724893\pi$
$500$	−880.759	+	1525.52i	−0.0787775	+	0.136447i
$501$	7837.58	−	13575.1i	0.698916	−	1.21056i
$502$	−9148.97			−0.813423
$503$	300.970	−	521.296i	0.0266791	−	0.0462096i	−0.852378	−	0.522927i	$-0.824840\pi$
$503$	300.970	−	521.296i	0.0266791	−	0.0462096i	0.879057	+	0.476717i	$0.158173\pi$
$504$	−3163.45	−	5479.25i	−0.279586	−	0.484257i
$505$	7895.22	+	13674.9i	0.695708	+	1.20500i
$506$	−33319.8			−2.92736
$507$		0			0
$508$	1225.39			0.107024
$509$	−8710.42	−	15086.9i	−0.758512	−	1.31378i	−0.943609	−	0.331061i	$-0.892593\pi$
$509$	−8710.42	−	15086.9i	−0.758512	−	1.31378i	0.185097	−	0.982720i	$-0.440740\pi$
$510$	−51.4915	−	89.1859i	−0.00447075	−	0.00774356i
$511$	−2021.21	+	3500.85i	−0.174977	+	0.303069i
$512$	4831.90			0.417074
$513$	538.388	−	932.515i	0.0463361	−	0.0802564i
$514$	−9741.11	+	16872.1i	−0.835919	+	1.44785i
$515$	1119.55			0.0957929
$516$	1472.36	−	2550.20i	0.125614	−	0.217570i
$517$	−7490.48	−	12973.9i	−0.637197	−	1.10366i
$518$	−1327.95	−	2300.08i	−0.112639	−	0.195096i
$519$	−1516.11			−0.128227
$520$		0			0
$521$	12881.5			1.08320			0.541601	−	0.840636i	$-0.317818\pi$
$521$	12881.5			1.08320			0.541601	+	0.840636i	$0.317818\pi$
$522$	−1241.98	−	2151.18i	−0.104138	−	0.180373i
$523$	−8267.01	−	14318.9i	−0.691188	−	1.19717i	−0.971449	−	0.237249i	$-0.923754\pi$
$523$	−8267.01	−	14318.9i	−0.691188	−	1.19717i	0.280261	−	0.959924i	$-0.409579\pi$
$524$	329.205	−	570.199i	0.0274454	−	0.0475368i
$525$	6102.41			0.507297
$526$	−315.230	+	545.994i	−0.0261305	+	0.0452594i
$527$	26.5839	−	46.0446i	0.00219737	−	0.00380595i
$528$	36474.2			3.00632
$529$	−6027.10	+	10439.2i	−0.495365	+	0.857997i
$530$	8808.64	+	15257.0i	0.721930	+	1.25042i
$531$	−2018.09	−	3495.43i	−0.164930	−	0.285666i
$532$	1158.11			0.0943802
$533$		0			0
$534$	12099.3			0.980501
$535$	8992.50	+	15575.5i	0.726691	+	1.25867i
$536$	2554.40	+	4424.35i	0.205846	+	0.356535i
$537$	−10517.7	+	18217.2i	−0.845202	+	1.46393i
$538$	−3502.79			−0.280699
$539$	−4659.59	+	8070.65i	−0.372361	+	0.644949i
$540$	−360.426	+	624.276i	−0.0287227	+	0.0497492i
$541$	−19026.9			−1.51207			−0.756035	−	0.654531i	$-0.772866\pi$
$541$	−19026.9			−1.51207			−0.756035	+	0.654531i	$0.772866\pi$
$542$	−641.840	+	1111.70i	−0.0508660	+	0.0881025i
$543$	−8256.52	−	14300.7i	−0.652525	−	1.13021i
$544$	−14.9129	−	25.8299i	−0.00117534	−	0.00203575i
$545$	28206.5			2.21694
$546$		0			0
$547$	8153.61			0.637336			0.318668	−	0.947866i	$-0.396764\pi$
$547$	8153.61			0.637336			0.318668	+	0.947866i	$0.396764\pi$
$548$	2295.80	+	3976.44i	0.178963	+	0.309973i
$549$	−6519.70	−	11292.4i	−0.506838	−	0.877869i
$550$	−6429.99	+	11137.1i	−0.498501	+	0.863429i
$551$	−1369.37			−0.105875
$552$	10473.5	−	18140.6i	0.807573	−	1.39876i
$553$	−7051.27	+	12213.2i	−0.542225	+	0.939162i
$554$	−913.031			−0.0700198
$555$	−2826.56	+	4895.74i	−0.216181	+	0.374437i
$556$	−1203.69	−	2084.85i	−0.0918125	−	0.159024i
$557$	−654.031	−	1132.81i	−0.0497525	−	0.0861739i	0.840077	−	0.542468i	$-0.182510\pi$
$557$	−654.031	−	1132.81i	−0.0497525	−	0.0861739i	−0.889829	+	0.456294i	$0.849177\pi$
$558$	11569.7			0.877746
$559$		0			0
$560$	14812.7			1.11777
$561$	81.0829	+	140.440i	0.00610218	+	0.0105693i
$562$	8116.66	+	14058.5i	0.609218	+	1.05520i
$563$	10368.0	−	17958.0i	0.776129	−	1.34429i	−0.158029	−	0.987434i	$-0.550514\pi$
$563$	10368.0	−	17958.0i	0.776129	−	1.34429i	0.934158	−	0.356860i	$-0.116153\pi$
$564$	−3127.09			−0.233465
$565$	−10902.3	+	18883.4i	−0.811797	+	1.40607i
$566$	8337.11	−	14440.3i	0.619143	−	1.07239i
$567$	−11696.7			−0.866343
$568$	−578.858	+	1002.61i	−0.0427612	+	0.0740645i
$569$	7490.98	+	12974.8i	0.551913	+	0.955941i	0.998137	+	0.0610196i	$0.0194352\pi$
$569$	7490.98	+	12974.8i	0.551913	+	0.955941i	−0.446224	+	0.894921i	$0.647231\pi$
$570$	−6177.07	−	10699.0i	−0.453911	−	0.786197i
$571$	−5668.79			−0.415467			−0.207734	−	0.978185i	$-0.566609\pi$
$571$	−5668.79			−0.415467			−0.207734	+	0.978185i	$0.566609\pi$
$572$		0			0
$573$	−31756.2			−2.31525
$574$	1344.45	+	2328.66i	0.0977637	+	0.169332i
$575$	4674.16	+	8095.89i	0.339002	+	0.587168i
$576$	−3821.15	+	6618.42i	−0.276414	+	0.478763i
$577$	6872.94			0.495882			0.247941	−	0.968775i	$-0.420246\pi$
$577$	6872.94			0.495882			0.247941	+	0.968775i	$0.420246\pi$
$578$	−7765.68	+	13450.6i	−0.558840	+	0.967940i
$579$	4617.05	−	7996.97i	0.331396	−	0.573994i
$580$	916.731			0.0656297
$581$	−8612.24	+	14916.8i	−0.614967	+	1.06515i
$582$	17785.4	+	30805.3i	1.26672	+	2.19402i
$583$	−13870.8	−	24025.0i	−0.985372	−	1.70671i
$584$	5355.49			0.379472
$585$		0			0
$586$	−4570.34			−0.322182
$587$	−9296.71	−	16102.4i	−0.653691	−	1.13223i	−0.982220	−	0.187732i	$-0.939886\pi$
$587$	−9296.71	−	16102.4i	−0.653691	−	1.13223i	0.328530	−	0.944494i	$-0.393447\pi$
$588$	972.631	+	1684.65i	0.0682154	+	0.118152i
$589$	3189.08	−	5523.65i	0.223097	−	0.386415i
$590$	7465.44			0.520928
$591$	−2626.25	+	4548.80i	−0.182791	+	0.316603i
$592$	−2226.89	+	3857.08i	−0.154602	+	0.267779i
$593$	15612.6			1.08117			0.540583	−	0.841291i	$-0.318204\pi$
$593$	15612.6			1.08117			0.540583	+	0.841291i	$0.318204\pi$
$594$	2844.45	−	4926.74i	0.196480	−	0.340314i
$595$	32.9290	+	57.0347i	0.00226884	+	0.00392974i
$596$	337.946	+	585.339i	0.0232262	+	0.0402289i
$597$	−33237.7			−2.27861
$598$		0			0
$599$	−22979.8			−1.56749			−0.783747	−	0.621081i	$-0.786694\pi$
$599$	−22979.8			−1.56749			−0.783747	+	0.621081i	$0.786694\pi$
$600$	−4042.30	−	7001.46i	−0.275044	−	0.476389i
$601$	−1390.88	−	2409.08i	−0.0944015	−	0.163508i	0.814957	−	0.579521i	$-0.196760\pi$
$601$	−1390.88	−	2409.08i	−0.0944015	−	0.163508i	−0.909359	+	0.416013i	$0.863427\pi$
$602$	−4718.95	+	8173.46i	−0.319485	+	0.553364i
$603$	−6256.38			−0.422520
$604$	1689.85	−	2926.90i	0.113839	−	0.197175i
$605$	22142.5	−	38351.9i	1.48797	−	2.57723i
$606$	−26012.2			−1.74369
$607$	2039.29	−	3532.15i	0.136363	−	0.236187i	−0.789755	−	0.613423i	$-0.789792\pi$
$607$	2039.29	−	3532.15i	0.136363	−	0.236187i	0.926117	+	0.377236i	$0.123125\pi$
$608$	−1789.00	−	3098.64i	−0.119331	−	0.206688i
$609$	1716.55	+	2973.15i	0.114217	+	0.197829i
$610$	24118.1			1.60084
$611$		0			0
$612$	15.6625			0.00103451
$613$	13145.1	+	22767.9i	0.866107	+	1.50014i	0.865944	+	0.500142i	$0.166719\pi$
$613$	13145.1	+	22767.9i	0.866107	+	1.50014i	0.000163453		1.00000i	$0.499948\pi$
$614$	14892.2	+	25794.1i	0.978828	+	1.69538i
$615$	2861.68	−	4956.58i	0.187633	−	0.324989i
$616$	−18427.6			−1.20531
$617$	−2425.85	+	4201.69i	−0.158283	+	0.274155i	−0.934250	−	0.356619i	$-0.883929\pi$
$617$	−2425.85	+	4201.69i	−0.158283	+	0.274155i	0.775966	+	0.630774i	$0.217263\pi$
$618$	−922.141	+	1597.20i	−0.0600226	+	0.103962i
$619$	4957.05			0.321875			0.160937	−	0.986965i	$-0.448548\pi$
$619$	4957.05			0.321875			0.160937	+	0.986965i	$0.448548\pi$
$620$	−2134.94	+	3697.83i	−0.138293	+	0.239530i
$621$	−2067.72	−	3581.40i	−0.133615	−	0.231428i
$622$	12465.0	+	21590.0i	0.803539	+	1.39177i
$623$	−7737.54			−0.497589
$624$		0			0
$625$	−19525.3			−1.24962
$626$	−870.041	−	1506.95i	−0.0555492	−	0.0962141i
$627$	9726.96	+	16847.6i	0.619549	+	1.07309i
$628$	−9.56443	+	16.5661i	−0.000607742	+	0.00105264i
$629$	−19.8017			−0.00125524
$630$	−7165.56	+	12411.1i	−0.453148	+	0.784875i
$631$	−1362.55	+	2360.01i	−0.0859627	+	0.148892i	−0.905801	−	0.423703i	$-0.860730\pi$
$631$	−1362.55	+	2360.01i	−0.0859627	+	0.148892i	0.819838	+	0.572595i	$0.194063\pi$
$632$	18683.3			1.17592
$633$	11360.3	−	19676.5i	0.713317	−	1.23550i
$634$	−238.641	−	413.339i	−0.0149490	−	0.0258924i
$635$	4179.78	+	7239.59i	0.261212	+	0.452432i
$636$	−5790.73			−0.361034
$637$		0			0
$638$	−7234.77			−0.448946
$639$	−708.887	−	1227.83i	−0.0438860	−	0.0760127i
$640$	−11872.4	−	20563.6i	−0.733277	−	1.27007i
$641$	−10698.2	+	18529.7i	−0.659207	+	1.14178i	0.321614	+	0.946871i	$0.395775\pi$
$641$	−10698.2	+	18529.7i	−0.659207	+	1.14178i	−0.980821	+	0.194909i	$0.937559\pi$
$642$	−29627.4			−1.82134
$643$	10916.9	−	18908.6i	0.669549	−	1.15969i	−0.308481	−	0.951230i	$-0.599821\pi$
$643$	10916.9	−	18908.6i	0.669549	−	1.15969i	0.978030	−	0.208462i	$-0.0668459\pi$
$644$	2223.90	−	3851.91i	0.136078	−	0.235693i
$645$	20088.6			1.22634
$646$	21.6370	−	37.4764i	0.00131780	−	0.00228249i
$647$	2434.53	+	4216.73i	0.147931	+	0.256224i	0.930463	−	0.366387i	$-0.119405\pi$
$647$	2434.53	+	4216.73i	0.147931	+	0.256224i	−0.782532	+	0.622611i	$0.786072\pi$
$648$	7748.03	+	13420.0i	0.469709	+	0.813560i
$649$	−11755.7			−0.711021
$650$		0			0
$651$	−15990.5			−0.962696
$652$	121.743	+	210.865i	0.00731260	+	0.0126658i
$653$	8423.48	+	14589.9i	0.504803	+	0.874344i	0.999985	+	0.00555458i	$0.00176809\pi$
$653$	8423.48	+	14589.9i	0.504803	+	0.874344i	−0.495182	+	0.868789i	$0.664899\pi$
$654$	−23232.9	+	40240.5i	−1.38911	+	2.40601i
$655$	4491.63			0.267943
$656$	2254.56	−	3905.01i	0.134186	−	0.232416i
$657$	−3279.24	+	5679.82i	−0.194727	+	0.337277i
$658$	10022.4			0.593790
$659$	12370.5	−	21426.4i	0.731240	−	1.26654i	−0.225114	−	0.974332i	$-0.572275\pi$
$659$	12370.5	−	21426.4i	0.731240	−	1.26654i	0.956354	−	0.292212i	$-0.0943912\pi$
$660$	−6511.75	−	11278.7i	−0.384045	−	0.665185i
$661$	−8261.00	−	14308.5i	−0.486105	−	0.841959i	0.513767	−	0.857930i	$-0.328249\pi$
$661$	−8261.00	−	14308.5i	−0.486105	−	0.841959i	−0.999872	+	0.0159708i	$0.994916\pi$
$662$	22380.1			1.31394
$663$		0			0
$664$	22819.3			1.33368
$665$	3950.26	+	6842.06i	0.230353	+	0.398983i
$666$	−2154.49	−	3731.68i	−0.125352	−	0.217116i
$667$	−2629.59	+	4554.59i	−0.152651	+	0.264399i
$668$	−4409.55			−0.255405
$669$	3747.83	−	6491.43i	0.216591	−	0.375147i
$670$	5786.00	−	10021.6i	0.333631	−	0.577866i
$671$	−37978.4			−2.18501
$672$	−4485.13	+	7768.47i	−0.257467	+	0.445946i
$673$	10360.8	+	17945.4i	0.593429	+	1.02785i	0.993766	+	0.111482i	$0.0355597\pi$
$673$	10360.8	+	17945.4i	0.593429	+	1.02785i	−0.400337	+	0.916368i	$0.631107\pi$
$674$	−10485.2	−	18160.8i	−0.599219	−	1.03788i
$675$	−1596.10			−0.0910133
$676$		0			0
$677$	32407.3			1.83975			0.919877	−	0.392207i	$-0.128288\pi$
$677$	32407.3			1.83975			0.919877	+	0.392207i	$0.128288\pi$
$678$	−17959.9	−	31107.4i	−1.01732	−	1.76205i
$679$	−11373.9	−	19700.1i	−0.642840	−	1.11343i
$680$	43.6250	−	75.5607i	0.00246021	−	0.00426121i
$681$	−36576.1			−2.05815
$682$	16848.8	−	29183.0i	0.946004	−	1.63853i
$683$	5061.89	−	8767.45i	0.283584	−	0.491182i	−0.688681	−	0.725065i	$-0.741810\pi$
$683$	5061.89	−	8767.45i	0.283584	−	0.491182i	0.972265	+	0.233883i	$0.0751432\pi$
$684$	1878.93			0.105033
$685$	−15661.8	+	27127.0i	−0.873586	+	1.51309i
$686$	−10887.4	−	18857.6i	−0.605954	−	1.04954i
$687$	6019.31	+	10425.7i	0.334281	+	0.578991i
$688$	15826.7			0.877018
$689$		0			0
$690$	−47447.1			−2.61780
$691$	14852.2	+	25724.9i	0.817665	+	1.41624i	0.907399	+	0.420271i	$0.138065\pi$
$691$	14852.2	+	25724.9i	0.817665	+	1.41624i	−0.0897342	+	0.995966i	$0.528602\pi$
$692$	213.248	+	369.356i	0.0117145	+	0.0202902i
$693$	11283.5	−	19543.6i	0.618507	−	1.07129i
$694$	−20245.8			−1.10738
$695$	8211.48	−	14222.7i	0.448172	−	0.776256i
$696$	2274.12	−	3938.89i	0.123851	−	0.214516i
$697$	20.0477			0.00108947
$698$	−265.709	+	460.221i	−0.0144086	+	0.0249565i
$699$	−11208.3	−	19413.3i	−0.606489	−	1.05047i
$700$	−858.329	−	1486.67i	−0.0463454	−	0.0802726i
$701$	−20585.2			−1.10912			−0.554558	−	0.832145i	$-0.687113\pi$
$701$	−20585.2			−1.10912			−0.554558	+	0.832145i	$0.687113\pi$
$702$		0			0
$703$	−2375.47			−0.127443
$704$	11129.4	+	19276.7i	0.595819	+	1.03199i
$705$	−10666.4	−	18474.7i	−0.569815	−	0.986948i
$706$	13359.8	−	23139.8i	0.712183	−	1.23354i
$707$	16634.9			0.884894
$708$	−1226.93	+	2125.11i	−0.0651283	+	0.112806i
$709$	−14830.1	+	25686.5i	−0.785552	+	1.36062i	0.143117	+	0.989706i	$0.454287\pi$
$709$	−14830.1	+	25686.5i	−0.785552	+	1.36062i	−0.928669	+	0.370910i	$0.879046\pi$
$710$	2622.36			0.138613
$711$	−11440.1	+	19814.8i	−0.603427	+	1.04517i
$712$	5125.42	+	8877.49i	0.269780	+	0.467273i
$713$	−12247.9	−	21214.1i	−0.643322	−	1.11427i
$714$	−108.491			−0.00568649
$715$		0			0
$716$	5917.44			0.308862
$717$	8329.51	+	14427.1i	0.433851	+	0.751452i
$718$	−4160.21	−	7205.70i	−0.216236	−	0.374532i
$719$	−639.842	+	1108.24i	−0.0331879	+	0.0574831i	−0.882142	−	0.470983i	$-0.843899\pi$
$719$	−639.842	+	1108.24i	−0.0331879	+	0.0574831i	0.848954	+	0.528466i	$0.177233\pi$
$720$	24032.4			1.24393
$721$	589.713	−	1021.41i	0.0304605	−	0.0527592i
$722$	−8246.22	+	14282.9i	−0.425059	+	0.736223i
$723$	36629.3			1.88417
$724$	−2322.62	+	4022.90i	−0.119226	+	0.206506i
$725$	1014.91	+	1757.87i	0.0519900	+	0.0900493i
$726$	36476.2	+	63178.6i	1.86468	+	3.22972i
$727$	6202.77			0.316435			0.158217	−	0.987404i	$-0.449425\pi$
$727$	6202.77			0.316435			0.158217	+	0.987404i	$0.449425\pi$
$728$		0			0
$729$	−13891.1			−0.705740
$730$	−6065.39	−	10505.6i	−0.307521	−	0.532642i
$731$	35.1831	+	60.9390i	0.00178016	+	0.00308332i
$732$	−3963.76	+	6865.43i	−0.200143	+	0.346658i
$733$	−35501.2			−1.78891			−0.894453	−	0.447162i	$-0.852435\pi$
$733$	−35501.2			−1.78891			−0.894453	+	0.447162i	$0.852435\pi$
$734$	−20975.4	+	36330.4i	−1.05479	+	1.82695i
$735$	−6635.23	+	11492.5i	−0.332985	+	0.576747i
$736$	−13741.6			−0.688209
$737$	−9111.13	+	15780.9i	−0.455377	+	0.788736i
$738$	2181.26	+	3778.05i	0.108798	+	0.188444i
$739$	1946.76	+	3371.89i	0.0969050	+	0.167844i	0.910402	−	0.413725i	$-0.135772\pi$
$739$	1946.76	+	3371.89i	0.0969050	+	0.167844i	−0.813497	+	0.581569i	$0.802439\pi$
$740$	1590.27			0.0789991
$741$		0			0
$742$	18559.5			0.918247
$743$	1107.50	+	1918.24i	0.0546839	+	0.0947152i	0.892072	−	0.451894i	$-0.149252\pi$
$743$	1107.50	+	1918.24i	0.0546839	+	0.0947152i	−0.837388	+	0.546609i	$0.815918\pi$
$744$	10592.2	+	18346.3i	0.521949	+	0.904042i
$745$	−2305.44	+	3993.15i	−0.113376	+	0.196373i
$746$	36924.8			1.81221
$747$	−13972.6	+	24201.3i	−0.684379	+	1.18538i
$748$	22.8093	−	39.5068i	0.00111496	−	0.00193117i
$749$	18946.9			0.924303
$750$	9898.01	−	17143.8i	0.481899	−	0.834673i
$751$	−1302.17	−	2255.42i	−0.0632714	−	0.109589i	0.832655	−	0.553793i	$-0.186820\pi$
$751$	−1302.17	−	2255.42i	−0.0632714	−	0.109589i	−0.895926	+	0.444204i	$0.853487\pi$
$752$	−8403.45	−	14555.2i	−0.407503	−	0.705816i
$753$	20515.1			0.992845
$754$		0			0
$755$	23056.0			1.11138
$756$	379.701	+	657.662i	0.0182667	+	0.0316388i
$757$	4842.86	+	8388.08i	0.232519	+	0.402734i	0.958549	−	0.284929i	$-0.0919700\pi$
$757$	4842.86	+	8388.08i	0.232519	+	0.402734i	−0.726030	+	0.687663i	$0.758637\pi$
$758$	5339.88	−	9248.94i	0.255875	−	0.443188i
$759$	74714.4			3.57307
$760$	5233.39	−	9064.49i	0.249783	−	0.432636i
$761$	5052.81	−	8751.73i	0.240689	−	0.416885i	−0.720222	−	0.693744i	$-0.755960\pi$
$761$	5052.81	−	8751.73i	0.240689	−	0.416885i	0.960911	+	0.276858i	$0.0892933\pi$
$762$	−13771.0			−0.654687
$763$	14857.5	−	25734.0i	0.704951	−	1.22101i
$764$	4466.64	+	7736.45i	0.211515	+	0.366355i
$765$	53.4244	+	92.5338i	0.00252492	+	0.00437329i
$766$	−13849.6			−0.653273
$767$		0			0
$768$	20476.1			0.962068
$769$	2286.60	+	3960.50i	0.107226	+	0.185721i	0.914646	−	0.404257i	$-0.132470\pi$
$769$	2286.60	+	3960.50i	0.107226	+	0.185721i	−0.807419	+	0.589978i	$0.799136\pi$
$770$	20870.3	+	36148.5i	0.976773	+	1.69182i
$771$	21842.9	−	37833.0i	1.02030	−	1.76722i
$772$	−2597.63			−0.121102
$773$	−3723.07	+	6448.54i	−0.173233	+	0.300049i	−0.939548	−	0.342416i	$-0.888755\pi$
$773$	−3723.07	+	6448.54i	−0.173233	+	0.300049i	0.766315	+	0.642465i	$0.222088\pi$
$774$	−7656.08	+	13260.7i	−0.355545	+	0.615823i
$775$	−9454.34			−0.438206
$776$	−15068.3	+	26099.1i	−0.697062	+	1.20735i
$777$	2977.72	+	5157.57i	0.137484	+	0.238129i
$778$	−19733.1	−	34178.8i	−0.909341	−	1.57503i
$779$	2404.99			0.110613
$780$		0			0
$781$	−4129.39			−0.189195
$782$	−83.0986	−	143.931i	−0.00380000	−	0.00658180i
$783$	−448.968	−	777.635i	−0.0204914	−	0.0354922i
$784$	−5227.52	+	9054.34i	−0.238134	+	0.412461i
$785$	−130.496			−0.00593324
$786$	−3699.62	+	6407.92i	−0.167889	+	0.290793i
$787$	−1633.56	+	2829.40i	−0.0739898	+	0.128154i	−0.900647	−	0.434552i	$-0.856907\pi$
$787$	−1633.56	+	2829.40i	−0.0739898	+	0.128154i	0.826657	+	0.562707i	$0.190240\pi$
$788$	1477.57			0.0667973
$789$	706.853	−	1224.31i	0.0318943	−	0.0552426i
$790$	−21159.9	−	36650.0i	−0.952957	−	1.65057i
$791$	11485.4	+	19893.3i	0.516276	+	0.894216i
$792$	−29897.3			−1.34135
$793$		0			0
$794$	29876.3			1.33535
$795$	−19752.0	−	34211.4i	−0.881171	−	1.52623i
$796$	4675.02	+	8097.37i	0.208168	+	0.360557i
$797$	1582.88	−	2741.62i	0.0703492	−	0.121848i	−0.828705	−	0.559685i	$-0.810922\pi$
$797$	1582.88	−	2741.62i	0.0703492	−	0.121848i	0.899054	+	0.437837i	$0.144255\pi$
$798$	−13014.9			−0.577344
$799$	37.3621	−	64.7130i	0.00165429	−	0.00286531i
$800$	−2651.83	+	4593.10i	−0.117195	+	0.202988i
$801$	−12553.5			−0.553752
$802$	−4593.49	+	7956.15i	−0.202246	+	0.350301i
$803$	9551.09	+	16543.0i	0.419739	+	0.727010i
$804$	1901.84	+	3294.07i	0.0834236	+	0.144494i
$805$	30342.6			1.32849
$806$		0			0
$807$	7854.45			0.342614
$808$	−11019.1	−	19085.7i	−0.479767	−	0.830981i
$809$	−6794.86	−	11769.0i	−0.295296	−	0.511468i	0.679758	−	0.733437i	$-0.262085\pi$
$809$	−6794.86	−	11769.0i	−0.295296	−	0.511468i	−0.975054	+	0.221969i	$0.928752\pi$
$810$	17550.2	−	30397.8i	0.761296	−	1.31860i
$811$	24977.7			1.08149			0.540744	−	0.841188i	$-0.318143\pi$
$811$	24977.7			1.08149			0.540744	+	0.841188i	$0.318143\pi$
$812$	482.879	−	836.371i	0.0208691	−	0.0361464i
$813$	1439.22	−	2492.81i	0.0620859	−	0.107536i
$814$	−12550.3			−0.540401
$815$	−830.521	+	1438.50i	−0.0356956	+	0.0618265i
$816$	90.9657	+	157.557i	0.00390249	+	0.00675932i
$817$	4220.68	+	7310.43i	0.180738	+	0.313047i
$818$	−18323.0			−0.783188
$819$		0			0
$820$	−1610.03			−0.0685666
$821$	4158.69	+	7203.06i	0.176784	+	0.306198i	0.940777	−	0.339026i	$-0.110097\pi$
$821$	4158.69	+	7203.06i	0.176784	+	0.306198i	−0.763993	+	0.645224i	$0.776764\pi$
$822$	−25800.3	−	44687.4i	−1.09475	−	1.89617i
$823$	−7231.47	+	12525.3i	−0.306286	+	0.530502i	−0.977547	−	0.210719i	$-0.932420\pi$
$823$	−7231.47	+	12525.3i	−0.306286	+	0.530502i	0.671261	+	0.741221i	$0.265753\pi$
$824$	−1562.53			−0.0660597
$825$	14418.2	−	24973.1i	0.608459	−	1.05388i
$826$	3932.35	−	6811.02i	0.165646	−	0.286908i
$827$	17881.0			0.751854			0.375927	−	0.926649i	$-0.377324\pi$
$827$	17881.0			0.751854			0.375927	+	0.926649i	$0.377324\pi$
$828$	3608.09	−	6249.39i	0.151437	−	0.262296i
$829$	−175.584	−	304.121i	−0.00735620	−	0.0127413i	0.862324	−	0.506357i	$-0.169008\pi$
$829$	−175.584	−	304.121i	−0.00735620	−	0.0127413i	−0.869680	+	0.493616i	$0.835675\pi$
$830$	−25844.2	−	44763.4i	−1.08080	−	1.87200i
$831$	2047.33			0.0854646
$832$		0			0
$833$	−46.4836			−0.00193345
$834$	13527.1	+	23429.6i	0.561637	+	0.972784i
$835$	−15040.8	−	26051.5i	−0.623364	−	1.07970i
$836$	2736.27	−	4739.36i	0.113201	−	0.196070i
$837$	4182.34			0.172716
$838$	−6547.90	+	11341.3i	−0.269920	+	0.467516i
$839$	16712.9	−	28947.7i	0.687717	−	1.19116i	−0.284857	−	0.958570i	$-0.591946\pi$
$839$	16712.9	−	28947.7i	0.687717	−	1.19116i	0.972575	−	0.232592i	$-0.0747205\pi$
$840$	−26240.8			−1.07785
$841$	11623.5	−	20132.5i	0.476589	−	0.825477i
$842$	2255.50	+	3906.63i	0.0923153	+	0.159895i
$843$	−18200.3	−	31523.9i	−0.743598	−	1.28795i
$844$	−6391.46			−0.260667
$845$		0			0
$846$	16260.5			0.660811
$847$	−23326.7	−	40402.9i	−0.946297	−	1.63903i
$848$	−15561.5	−	26953.3i	−0.630169	−	1.09149i
$849$	−18694.7	+	32380.1i	−0.755711	+	1.30893i
$850$	−64.1449			−0.00258841
$851$	−4561.59	+	7900.91i	−0.183748	+	0.318260i
$852$	−430.979	+	746.478i	−0.0173299	+	0.0300163i
$853$	−35097.5			−1.40881			−0.704406	−	0.709797i	$-0.748787\pi$
$853$	−35097.5			−1.40881			−0.704406	+	0.709797i	$0.748787\pi$
$854$	12704.0	−	22003.9i	0.509040	−	0.881684i
$855$	6408.96	+	11100.6i	0.256353	+	0.444016i
$856$	−12550.6	−	21738.2i	−0.501133	−	0.867988i
$857$	15015.8			0.598519			0.299259	−	0.954172i	$-0.403260\pi$
$857$	15015.8			0.598519			0.299259	+	0.954172i	$0.403260\pi$
$858$		0			0
$859$	19647.1			0.780383			0.390192	−	0.920734i	$-0.372409\pi$
$859$	19647.1			0.780383			0.390192	+	0.920734i	$0.372409\pi$
$860$	−2825.55	−	4893.99i	−0.112035	−	0.194051i
$861$	−3014.72	−	5221.65i	−0.119328	−	0.206682i
$862$	−4019.78	+	6962.47i	−0.158833	+	0.275107i
$863$	−9035.14			−0.356385			−0.178192	−	0.983996i	$-0.557025\pi$
$863$	−9035.14			−0.356385			−0.178192	+	0.983996i	$0.557025\pi$
$864$	1173.10	−	2031.86i	0.0461916	−	0.0800062i
$865$	−1454.76	+	2519.72i	−0.0571831	+	0.0990440i
$866$	10901.7			0.427778
$867$	17413.3	−	30160.7i	0.682108	−	1.18144i
$868$	2249.12	+	3895.59i	0.0879495	+	0.152333i
$869$	33320.2	+	57712.3i	1.30070	+	2.25288i
$870$	−10302.3			−0.401471
$871$		0			0
$872$	−39367.0			−1.52883
$873$	−18453.1	−	31961.7i	−0.715398	−	1.23911i
$874$	−9968.77	−	17266.4i	−0.385811	−	0.668244i
$875$	−6329.81	+	10963.6i	−0.244556	+	0.423584i
$876$	3987.34			0.153790
$877$	4127.08	−	7148.31i	0.158907	−	0.275235i	−0.775568	−	0.631264i	$-0.782536\pi$
$877$	4127.08	−	7148.31i	0.158907	−	0.275235i	0.934475	+	0.356029i	$0.115870\pi$
$878$	−19983.8	+	34612.9i	−0.768133	+	1.33044i
$879$	10248.3			0.393248
$880$	34998.2	−	60618.6i	1.34067	−	2.32211i
$881$	21053.7	+	36466.1i	0.805128	+	1.39452i	0.916205	+	0.400710i	$0.131237\pi$
$881$	21053.7	+	36466.1i	0.805128	+	1.39452i	−0.111077	+	0.993812i	$0.535430\pi$
$882$	−5057.57	−	8759.96i	−0.193081	−	0.334425i
$883$	−17584.7			−0.670183			−0.335091	−	0.942186i	$-0.608767\pi$
$883$	−17584.7			−0.670183			−0.335091	+	0.942186i	$0.608767\pi$
$884$		0			0
$885$	−16740.1			−0.635832
$886$	13414.6	+	23234.7i	0.508658	+	0.881021i
$887$	11922.9	+	20651.1i	0.451333	+	0.781731i	0.998469	−	0.0553122i	$-0.0176154\pi$
$887$	11922.9	+	20651.1i	0.451333	+	0.781731i	−0.547136	+	0.837043i	$0.684282\pi$
$888$	3944.94	−	6832.84i	0.149081	−	0.258215i
$889$	8806.63			0.332244
$890$	11609.7	−	20108.5i	0.437255	−	0.757347i
$891$	−27636.0	+	47866.9i	−1.03910	+	1.79978i
$892$	−2108.59			−0.0791488
$893$	4482.07	−	7763.17i	0.167958	−	0.290912i
$894$	−3797.85	−	6578.07i	−0.142079	−	0.246089i
$895$	20184.2	+	34960.0i	0.753836	+	1.30568i
$896$	−25014.6			−0.932679
$897$		0			0
$898$	−35943.1			−1.33568
$899$	−2659.41	−	4606.24i	−0.0986612	−	0.170886i
$900$	−1392.56	−	2411.99i	−0.0515764	−	0.0893330i
$901$	69.1870	−	119.835i	0.00255822	−	0.00443096i
$902$	12706.2			0.469036
$903$	10581.5	−	18327.7i	0.389956	−	0.675423i
$904$	15216.1	−	26355.0i	0.559823	−	0.969641i
$905$	−31689.6			−1.16398
$906$	−18990.5	+	32892.6i	−0.696378	+	1.20616i
$907$	−15282.9	−	26470.7i	−0.559492	−	0.969069i	−0.997539	−	0.0701164i	$-0.977663\pi$
$907$	−15282.9	−	26470.7i	−0.559492	−	0.969069i	0.438047	−	0.898952i	$-0.355670\pi$
$908$	5144.58	+	8910.67i	0.188027	+	0.325673i
$909$	26988.7			0.984773
$910$		0			0
$911$	18556.9			0.674882			0.337441	−	0.941347i	$-0.390439\pi$
$911$	18556.9			0.674882			0.337441	+	0.941347i	$0.390439\pi$
$912$	10912.5	+	18901.0i	0.396217	+	0.686268i
$913$	40696.5	+	70488.3i	1.47520	+	2.55512i
$914$	17844.3	−	30907.2i	0.645773	−	1.11851i
$915$	−54081.0			−1.95395
$916$	1693.28	−	2932.85i	0.0610781	−	0.105790i
$917$	2365.92	−	4097.89i	0.0852012	−	0.147573i
$918$	28.3760			0.00102020
$919$	4969.41	−	8607.27i	0.178374	−	0.308953i	−0.762950	−	0.646458i	$-0.776250\pi$
$919$	4969.41	−	8607.27i	0.178374	−	0.308953i	0.941324	+	0.337505i	$0.109583\pi$
$920$	−20099.3	−	34812.9i	−0.720275	−	1.24755i
$921$	−33393.4	−	57839.1i	−1.19474	−	2.06934i
$922$	−12121.0			−0.432954
$923$		0			0
$924$	−13720.0			−0.488479
$925$	1760.57	+	3049.40i	0.0625809	+	0.108393i
$926$	2046.09	+	3543.93i	0.0726119	+	0.125768i
$927$	956.758	−	1657.15i	0.0338986	−	0.0587142i
$928$	−2983.73			−0.105545
$929$	2976.80	−	5155.97i	0.105130	−	0.182090i	−0.808661	−	0.588274i	$-0.799807\pi$
$929$	2976.80	−	5155.97i	0.105130	−	0.182090i	0.913791	+	0.406184i	$0.133141\pi$
$930$	23992.6	−	41556.4i	0.845966	−	1.46526i
$931$	−5576.31			−0.196301
$932$	−3152.98	+	5461.11i	−0.110815	+	0.191936i
$933$	−27950.8	−	48412.2i	−0.980781	−	1.69876i
$934$	21910.6	+	37950.2i	0.767597	+	1.32952i
$935$	311.207			0.0108851
$936$		0			0
$937$	−24568.0			−0.856564			−0.428282	−	0.903645i	$-0.640881\pi$
$937$	−24568.0			−0.856564			−0.428282	+	0.903645i	$0.640881\pi$
$938$	−6095.44	−	10557.6i	−0.212178	−	0.367503i
$939$	1950.93	+	3379.11i	0.0678021	+	0.117437i
$940$	−3000.54	+	5197.09i	−0.104114	+	0.180330i
$941$	−11024.8			−0.381931			−0.190965	−	0.981597i	$-0.561162\pi$
$941$	−11024.8			−0.381931			−0.190965	+	0.981597i	$0.561162\pi$
$942$	107.485	−	186.170i	0.00371769	−	0.00643923i
$943$	4618.27	−	7999.09i	0.159482	−	0.276231i
$944$	−13188.6			−0.454715
$945$	−2590.30	+	4486.53i	−0.0891666	+	0.154441i
$946$	22299.0	+	38623.0i	0.766388	+	1.32742i
$947$	−3085.73	−	5344.64i	−0.105885	−	0.183398i	0.808215	−	0.588888i	$-0.200434\pi$
$947$	−3085.73	−	5344.64i	−0.105885	−	0.183398i	−0.914099	+	0.405490i	$0.867101\pi$
$948$	13910.4			0.476569
$949$		0			0
$950$	−7695.01			−0.262799
$951$	535.116	+	926.847i	0.0182464	+	0.0316037i
$952$	−45.9581	−	79.6017i	−0.00156461	−	0.00270998i
$953$	9419.22	−	16314.6i	0.320166	−	0.554544i	−0.660356	−	0.750953i	$-0.729595\pi$
$953$	9419.22	−	16314.6i	0.320166	−	0.554544i	0.980522	+	0.196408i	$0.0629279\pi$
$954$	30111.1			1.02189
$955$	−30471.1	+	52777.6i	−1.03248	+	1.78832i
$956$	2343.16	−	4058.47i	0.0792711	−	0.137302i
$957$	16222.8			0.547973
$958$	−15218.2	+	26358.7i	−0.513234	+	0.888947i
$959$	16499.4	+	28577.8i	0.555571	+	0.962278i
$960$	15848.2	+	27449.9i	0.532812	+	0.922857i
$961$	−5017.33			−0.168418
$962$		0			0
$963$	30739.6			1.02863
$964$	−5152.06	−	8923.62i	−0.172133	−	0.298144i
$965$	−8860.42	−	15346.7i	−0.295572	−	0.511946i
$966$	−24992.3	+	43288.0i	−0.832417	+	1.44179i
$967$	24934.5			0.829203			0.414602	−	0.910003i	$-0.363921\pi$
$967$	24934.5			0.829203			0.414602	+	0.910003i	$0.363921\pi$
$968$	−30903.6	+	53526.6i	−1.02612	+	1.77728i
$969$	−48.5175	+	84.0348i	−0.00160847	+	0.00278595i
$970$	68262.8			2.25957
$971$	−16080.6	+	27852.4i	−0.531463	+	0.920520i	0.467863	+	0.883801i	$0.345024\pi$
$971$	−16080.6	+	27852.4i	−0.531463	+	0.920520i	−0.999326	+	0.0367194i	$0.988309\pi$
$972$	5053.32	+	8752.61i	0.166755	+	0.288827i
$973$	−8650.63	−	14983.3i	−0.285022	−	0.493673i
$974$	37787.2			1.24310
$975$		0			0
$976$	−42607.4			−1.39737
$977$	9432.00	+	16336.7i	0.308860	+	0.534961i	0.978113	−	0.208073i	$-0.0667192\pi$
$977$	9432.00	+	16336.7i	0.308860	+	0.534961i	−0.669253	+	0.743034i	$0.733386\pi$
$978$	−1368.15	−	2369.71i	−0.0447327	−	0.0774794i
$979$	−18281.6	+	31664.6i	−0.596815	+	1.03371i
$980$	3733.08			0.121683
$981$	24105.0	−	41751.1i	0.784520	−	1.35883i
$982$	8551.64	−	14811.9i	0.277896	−	0.481330i
$983$	−7883.83			−0.255804			−0.127902	−	0.991787i	$-0.540824\pi$
$983$	−7883.83			−0.255804			−0.127902	+	0.991787i	$0.540824\pi$
$984$	−3993.97	+	6917.75i	−0.129393	+	0.224116i
$985$	5039.94	+	8729.44i	0.163031	+	0.282379i
$986$	−18.0433	−	31.2520i	−0.000582776	−	0.00100940i
$987$	−22473.6			−0.724766
$988$		0			0
$989$	32419.7			1.04235
$990$	33860.3	+	58647.8i	1.08702	+	1.88278i
$991$	−7086.14	−	12273.6i	−0.227143	−	0.393423i	0.729817	−	0.683642i	$-0.239605\pi$
$991$	−7086.14	−	12273.6i	−0.227143	−	0.393423i	−0.956960	+	0.290219i	$0.906272\pi$
$992$	6948.72	−	12035.5i	0.222401	−	0.385210i
$993$	−50183.9			−1.60376
$994$	1381.30	−	2392.48i	0.0440767	−	0.0763430i
$995$	−31892.6	+	55239.7i	−1.01615	+	1.76002i
$996$	16989.7			0.540503
$997$	−26231.4	+	45434.1i	−0.833256	+	1.44324i	0.0621870	+	0.998065i	$0.480192\pi$
$997$	−26231.4	+	45434.1i	−0.833256	+	1.44324i	−0.895443	+	0.445177i	$0.853141\pi$
$998$	−22876.9	−	39623.9i	−0.725607	−	1.25679i
$999$	−778.830	−	1348.97i	−0.0246658	−	0.0427224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.l.146.7		18
13.2	odd	12		169.4.b.g.168.14		18
13.3	even	3		169.4.a.k.1.3	✓	9
13.4	even	6		169.4.c.k.22.3		18
13.5	odd	4		169.4.e.h.23.14		36
13.6	odd	12		169.4.e.h.147.5		36
13.7	odd	12		169.4.e.h.147.14		36
13.8	odd	4		169.4.e.h.23.5		36
13.9	even	3	inner	169.4.c.l.22.7		18
13.10	even	6		169.4.a.l.1.7	yes	9
13.11	odd	12		169.4.b.g.168.5		18
13.12	even	2		169.4.c.k.146.3		18
39.23	odd	6		1521.4.a.bg.1.3		9
39.29	odd	6		1521.4.a.bh.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.3	✓	9	13.3	even	3
169.4.a.l.1.7	yes	9	13.10	even	6
169.4.b.g.168.5		18	13.11	odd	12
169.4.b.g.168.14		18	13.2	odd	12
169.4.c.k.22.3		18	13.4	even	6
169.4.c.k.146.3		18	13.12	even	2
169.4.c.l.22.7		18	13.9	even	3	inner
169.4.c.l.146.7		18	1.1	even	1	trivial
169.4.e.h.23.5		36	13.8	odd	4
169.4.e.h.23.14		36	13.5	odd	4
169.4.e.h.147.5		36	13.6	odd	12
169.4.e.h.147.14		36	13.7	odd	12
1521.4.a.bg.1.3		9	39.23	odd	6
1521.4.a.bh.1.7		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)

\(f(q)\)	\(=\)	\(q+(1.58068 + 2.73781i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(-0.997073 + 1.72698i) q^{4} -13.6039 q^{5} +(11.2051 - 19.4079i) q^{6} +(-7.16574 + 12.4114i) q^{7} +18.9866 q^{8} +(-11.6258 + 20.1364i) q^{9} +O(q^{10})\)	\(q+(1.58068 + 2.73781i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(-0.997073 + 1.72698i) q^{4} -13.6039 q^{5} +(11.2051 - 19.4079i) q^{6} +(-7.16574 + 12.4114i) q^{7} +18.9866 q^{8} +(-11.6258 + 20.1364i) q^{9} +(-21.5034 - 37.2450i) q^{10} +(33.8611 + 58.6492i) q^{11} +14.1362 q^{12} -45.3068 q^{14} +(48.2180 + 83.5160i) q^{15} +(37.9883 + 65.7976i) q^{16} +(-0.168897 + 0.292539i) q^{17} -73.5064 q^{18} +(-20.2615 + 35.0939i) q^{19} +(13.5641 - 23.4937i) q^{20} +101.593 q^{21} +(-107.047 + 185.411i) q^{22} +(77.8158 + 134.781i) q^{23} +(-67.2965 - 116.561i) q^{24} +60.0670 q^{25} -26.5720 q^{27} +(-14.2895 - 24.7502i) q^{28} +(16.8963 + 29.2652i) q^{29} +(-152.434 + 264.024i) q^{30} -157.397 q^{31} +(-44.1478 + 76.4663i) q^{32} +(240.036 - 415.754i) q^{33} -1.06789 q^{34} +(97.4822 - 168.844i) q^{35} +(-23.1835 - 40.1550i) q^{36} +(29.3102 + 50.7667i) q^{37} -128.107 q^{38} -258.293 q^{40} +(-29.6744 - 51.3976i) q^{41} +(160.586 + 278.144i) q^{42} +(104.155 - 180.402i) q^{43} -135.048 q^{44} +(158.156 - 273.935i) q^{45} +(-246.003 + 426.090i) q^{46} -221.212 q^{47} +(269.293 - 466.428i) q^{48} +(68.8044 + 119.173i) q^{49} +(94.9464 + 164.452i) q^{50} +2.39457 q^{51} -409.639 q^{53} +(-42.0017 - 72.7491i) q^{54} +(-460.645 - 797.860i) q^{55} +(-136.053 + 235.651i) q^{56} +287.260 q^{57} +(-53.4150 + 92.5175i) q^{58} +(-86.7937 + 150.331i) q^{59} -192.308 q^{60} +(-280.398 + 485.664i) q^{61} +(-248.793 - 430.922i) q^{62} +(-166.615 - 288.585i) q^{63} +328.679 q^{64} +1517.68 q^{66} +(134.537 + 233.025i) q^{67} +(-0.336806 - 0.583366i) q^{68} +(551.623 - 955.440i) q^{69} +616.351 q^{70} +(-30.4877 + 52.8062i) q^{71} +(-220.734 + 382.323i) q^{72} +282.066 q^{73} +(-92.6598 + 160.491i) q^{74} +(-212.902 - 368.758i) q^{75} +(-40.4043 - 69.9823i) q^{76} -970.560 q^{77} +984.026 q^{79} +(-516.790 - 895.106i) q^{80} +(408.078 + 706.813i) q^{81} +(93.8112 - 162.486i) q^{82} +1201.86 q^{83} +(-101.296 + 175.450i) q^{84} +(2.29767 - 3.97968i) q^{85} +658.543 q^{86} +(119.775 - 207.456i) q^{87} +(642.908 + 1113.55i) q^{88} +(269.949 + 467.566i) q^{89} +999.976 q^{90} -310.352 q^{92} +(557.879 + 966.275i) q^{93} +(-349.664 - 605.636i) q^{94} +(275.636 - 477.415i) q^{95} +625.913 q^{96} +(-793.627 + 1374.60i) q^{97} +(-217.515 + 376.747i) q^{98} -1574.65 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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