LMFDB - Embedded newform 169.4.c.f.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.f.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.219224 + 0.379706i) q^{2} +(1.84233 - 3.19101i) q^{3} +(3.90388 + 6.76172i) q^{4} +17.8078 q^{5} +(0.807764 + 1.39909i) q^{6} +(2.71922 + 4.70983i) q^{7} -6.93087 q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})$	\(q+(-0.219224 + 0.379706i) q^{2} +(1.84233 - 3.19101i) q^{3} +(3.90388 + 6.76172i) q^{4} +17.8078 q^{5} +(0.807764 + 1.39909i) q^{6} +(2.71922 + 4.70983i) q^{7} -6.93087 q^{8} +(6.71165 + 11.6249i) q^{9} +(-3.90388 + 6.76172i) q^{10} +(-11.2116 + 19.4191i) q^{11} +28.7689 q^{12} -2.38447 q^{14} +(32.8078 - 56.8247i) q^{15} +(-29.7116 + 51.4621i) q^{16} +(-33.9924 - 58.8766i) q^{17} -5.88540 q^{18} +(-40.4039 - 69.9816i) q^{19} +(69.5194 + 120.411i) q^{20} +20.0388 q^{21} +(-4.91571 - 8.51427i) q^{22} +(-70.2656 + 121.704i) q^{23} +(-12.7689 + 22.1165i) q^{24} +192.116 q^{25} +148.946 q^{27} +(-21.2311 + 36.7733i) q^{28} +(53.3466 - 92.3990i) q^{29} +(14.3845 + 24.9146i) q^{30} +276.155 q^{31} +(-40.7505 - 70.5819i) q^{32} +(41.3111 + 71.5529i) q^{33} +29.8078 q^{34} +(48.4233 + 83.8716i) q^{35} +(-52.4029 + 90.7646i) q^{36} +(-2.14584 + 3.71670i) q^{37} +35.4299 q^{38} -123.423 q^{40} +(113.884 - 197.254i) q^{41} +(-4.39298 + 7.60887i) q^{42} +(-13.7647 - 23.8411i) q^{43} -175.076 q^{44} +(119.519 + 207.014i) q^{45} +(-30.8078 - 53.3606i) q^{46} -318.617 q^{47} +(109.477 + 189.620i) q^{48} +(156.712 - 271.433i) q^{49} +(-42.1165 + 72.9479i) q^{50} -250.501 q^{51} -67.6562 q^{53} +(-32.6525 + 56.5558i) q^{54} +(-199.654 + 345.811i) q^{55} +(-18.8466 - 32.6432i) q^{56} -297.749 q^{57} +(23.3897 + 40.5121i) q^{58} +(-145.557 - 252.113i) q^{59} +512.311 q^{60} +(-331.655 - 574.444i) q^{61} +(-60.5398 + 104.858i) q^{62} +(-36.5009 + 63.2215i) q^{63} -439.652 q^{64} -36.2255 q^{66} +(-212.551 + 368.149i) q^{67} +(265.405 - 459.695i) q^{68} +(258.905 + 448.436i) q^{69} -42.4621 q^{70} +(-76.4815 - 132.470i) q^{71} +(-46.5175 - 80.5708i) q^{72} -117.268 q^{73} +(-0.940837 - 1.62958i) q^{74} +(353.942 - 613.045i) q^{75} +(315.464 - 546.400i) q^{76} -121.948 q^{77} +202.462 q^{79} +(-529.098 + 916.425i) q^{80} +(93.1932 - 161.415i) q^{81} +(49.9323 + 86.4853i) q^{82} -336.155 q^{83} +(78.2292 + 135.497i) q^{84} +(-605.329 - 1048.46i) q^{85} +12.0702 q^{86} +(-196.564 - 340.459i) q^{87} +(77.7065 - 134.592i) q^{88} +(359.097 - 621.974i) q^{89} -104.806 q^{90} -1097.23 q^{92} +(508.769 - 881.214i) q^{93} +(69.8485 - 120.981i) q^{94} +(-719.503 - 1246.22i) q^{95} -300.303 q^{96} +(379.684 + 657.632i) q^{97} +(68.7098 + 119.009i) q^{98} -300.994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9} + 5 q^{10} + 17 q^{11} + 280 q^{12} - 92 q^{14} + 90 q^{15} - 57 q^{16} - 70 q^{17} + 430 q^{18} - 141 q^{19} + 175 q^{20} - 126 q^{21} + 170 q^{22} - 145 q^{23} - 216 q^{24} + 150 q^{25} + 670 q^{27} + 80 q^{28} - 34 q^{29} + 140 q^{30} + 280 q^{31} + 105 q^{32} + 425 q^{33} + 78 q^{34} + 70 q^{35} - 725 q^{36} - 190 q^{37} + 620 q^{38} - 370 q^{40} + 538 q^{41} + 370 q^{42} - 455 q^{43} - 1360 q^{44} + 375 q^{45} - 82 q^{46} - 120 q^{47} + 240 q^{48} + 565 q^{49} + 450 q^{50} - 466 q^{51} + 1090 q^{53} - 914 q^{54} - 510 q^{55} + 172 q^{56} + 450 q^{57} - 595 q^{58} - 809 q^{59} + 400 q^{60} - 502 q^{61} + 500 q^{62} + 390 q^{63} - 2542 q^{64} - 3196 q^{66} - 475 q^{67} + 505 q^{68} + 479 q^{69} + 160 q^{70} + 127 q^{71} - 1155 q^{72} - 1170 q^{73} - 849 q^{74} + 1725 q^{75} - 140 q^{76} + 510 q^{77} + 480 q^{79} - 1065 q^{80} - 122 q^{81} + 1515 q^{82} - 520 q^{83} + 1220 q^{84} - 1205 q^{85} + 3924 q^{86} - 1615 q^{87} + 1020 q^{88} + 921 q^{89} - 1450 q^{90} - 2080 q^{92} + 2200 q^{93} - 1040 q^{94} - 1270 q^{95} - 3840 q^{96} - 415 q^{97} + 1285 q^{98} - 4420 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9 + 5 * q^10 + 17 * q^11 + 280 * q^12 - 92 * q^14 + 90 * q^15 - 57 * q^16 - 70 * q^17 + 430 * q^18 - 141 * q^19 + 175 * q^20 - 126 * q^21 + 170 * q^22 - 145 * q^23 - 216 * q^24 + 150 * q^25 + 670 * q^27 + 80 * q^28 - 34 * q^29 + 140 * q^30 + 280 * q^31 + 105 * q^32 + 425 * q^33 + 78 * q^34 + 70 * q^35 - 725 * q^36 - 190 * q^37 + 620 * q^38 - 370 * q^40 + 538 * q^41 + 370 * q^42 - 455 * q^43 - 1360 * q^44 + 375 * q^45 - 82 * q^46 - 120 * q^47 + 240 * q^48 + 565 * q^49 + 450 * q^50 - 466 * q^51 + 1090 * q^53 - 914 * q^54 - 510 * q^55 + 172 * q^56 + 450 * q^57 - 595 * q^58 - 809 * q^59 + 400 * q^60 - 502 * q^61 + 500 * q^62 + 390 * q^63 - 2542 * q^64 - 3196 * q^66 - 475 * q^67 + 505 * q^68 + 479 * q^69 + 160 * q^70 + 127 * q^71 - 1155 * q^72 - 1170 * q^73 - 849 * q^74 + 1725 * q^75 - 140 * q^76 + 510 * q^77 + 480 * q^79 - 1065 * q^80 - 122 * q^81 + 1515 * q^82 - 520 * q^83 + 1220 * q^84 - 1205 * q^85 + 3924 * q^86 - 1615 * q^87 + 1020 * q^88 + 921 * q^89 - 1450 * q^90 - 2080 * q^92 + 2200 * q^93 - 1040 * q^94 - 1270 * q^95 - 3840 * q^96 - 415 * q^97 + 1285 * q^98 - 4420 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.219224	+	0.379706i	−0.0775072	+	0.134246i	−0.902174	−	0.431373i	$-0.858029\pi$
$2$	−0.219224	+	0.379706i	−0.0775072	+	0.134246i	0.824667	+	0.565619i	$0.191363\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	−0.632486	−	0.774572i	$-0.717965\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	0.987042	+	0.160462i	$0.0512985\pi$
$4$	3.90388	+	6.76172i	0.487985	+	0.845215i
$5$	17.8078			1.59277			0.796387	−	0.604787i	$-0.206742\pi$
$5$	17.8078			1.59277			0.796387	+	0.604787i	$0.206742\pi$
$6$	0.807764	+	1.39909i	0.0549614	+	0.0951959i
$7$	2.71922	+	4.70983i	0.146824	+	0.254307i	0.930052	−	0.367428i	$-0.119761\pi$
$7$	2.71922	+	4.70983i	0.146824	+	0.254307i	−0.783228	+	0.621735i	$0.786428\pi$
$8$	−6.93087			−0.306304
$9$	6.71165	+	11.6249i	0.248579	+	0.430552i
$10$	−3.90388	+	6.76172i	−0.123452	+	0.213824i
$11$	−11.2116	+	19.4191i	−0.307313	+	0.532281i	−0.977774	−	0.209664i	$-0.932763\pi$
$11$	−11.2116	+	19.4191i	−0.307313	+	0.532281i	0.670461	+	0.741945i	$0.266096\pi$
$12$	28.7689			0.692073
$13$		0			0
$13$		0			0
$14$	−2.38447			−0.0455198
$15$	32.8078	−	56.8247i	0.564729	−	0.978139i
$16$	−29.7116	+	51.4621i	−0.464244	+	0.804095i
$17$	−33.9924	−	58.8766i	−0.484963	−	0.839981i	0.514888	−	0.857258i	$-0.327834\pi$
$17$	−33.9924	−	58.8766i	−0.484963	−	0.839981i	−0.999851	+	0.0172769i	$0.994500\pi$
$18$	−5.88540			−0.0770668
$19$	−40.4039	−	69.9816i	−0.487857	−	0.844993i	0.512045	−	0.858958i	$-0.328888\pi$
$19$	−40.4039	−	69.9816i	−0.487857	−	0.844993i	−0.999902	+	0.0139650i	$0.995555\pi$
$20$	69.5194	+	120.411i	0.777251	+	1.34624i
$21$	20.0388			0.208230
$22$	−4.91571	−	8.51427i	−0.0476379	−	0.0825113i
$23$	−70.2656	+	121.704i	−0.637017	+	1.10335i	0.349067	+	0.937098i	$0.386499\pi$
$23$	−70.2656	+	121.704i	−0.637017	+	1.10335i	−0.986084	+	0.166248i	$0.946835\pi$
$24$	−12.7689	+	22.1165i	−0.108602	+	0.188104i
$25$	192.116			1.53693
$26$		0			0
$27$	148.946			1.06165
$28$	−21.2311	+	36.7733i	−0.143296	+	0.248196i
$29$	53.3466	−	92.3990i	0.341594	−	0.591657i	−0.643135	−	0.765753i	$-0.722367\pi$
$29$	53.3466	−	92.3990i	0.341594	−	0.591657i	0.984729	+	0.174095i	$0.0557001\pi$
$30$	14.3845	+	24.9146i	0.0875411	+	0.151626i
$31$	276.155			1.59997			0.799983	−	0.600023i	$-0.204842\pi$
$31$	276.155			1.59997			0.799983	+	0.600023i	$0.204842\pi$
$32$	−40.7505	−	70.5819i	−0.225117	−	0.389913i
$33$	41.3111	+	71.5529i	0.217919	+	0.377447i
$34$	29.8078			0.150353
$35$	48.4233	+	83.8716i	0.233858	+	0.405054i
$36$	−52.4029	+	90.7646i	−0.242606	+	0.420206i
$37$	−2.14584	+	3.71670i	−0.00953442	+	0.0165141i	−0.870753	−	0.491720i	$-0.836368\pi$
$37$	−2.14584	+	3.71670i	−0.00953442	+	0.0165141i	0.861219	+	0.508234i	$0.169702\pi$
$38$	35.4299			0.151250
$39$		0			0
$40$	−123.423			−0.487873
$41$	113.884	−	197.254i	0.433799	−	0.751362i	−0.563398	−	0.826186i	$-0.690506\pi$
$41$	113.884	−	197.254i	0.433799	−	0.751362i	0.997197	+	0.0748237i	$0.0238394\pi$
$42$	−4.39298	+	7.60887i	−0.0161393	+	0.0279541i
$43$	−13.7647	−	23.8411i	−0.0488162	−	0.0845521i	0.840585	−	0.541680i	$-0.182212\pi$
$43$	−13.7647	−	23.8411i	−0.0488162	−	0.0845521i	−0.889401	+	0.457128i	$0.848878\pi$
$44$	−175.076			−0.599856
$45$	119.519	+	207.014i	0.395931	+	0.685773i
$46$	−30.8078	−	53.3606i	−0.0987469	−	0.171035i
$47$	−318.617			−0.988832			−0.494416	−	0.869225i	$-0.664618\pi$
$47$	−318.617			−0.988832			−0.494416	+	0.869225i	$0.664618\pi$
$48$	109.477	+	189.620i	0.329202	+	0.570194i
$49$	156.712	−	271.433i	0.456885	−	0.791348i
$50$	−42.1165	+	72.9479i	−0.119123	+	0.206328i
$51$	−250.501			−0.687787
$52$		0			0
$53$	−67.6562			−0.175345			−0.0876726	−	0.996149i	$-0.527943\pi$
$53$	−67.6562			−0.175345			−0.0876726	+	0.996149i	$0.527943\pi$
$54$	−32.6525	+	56.5558i	−0.0822859	+	0.142523i
$55$	−199.654	+	345.811i	−0.489480	+	0.847804i
$56$	−18.8466	−	32.6432i	−0.0449729	−	0.0778953i
$57$	−297.749			−0.691892
$58$	23.3897	+	40.5121i	0.0529519	+	0.0917155i
$59$	−145.557	−	252.113i	−0.321186	−	0.556310i	0.659547	−	0.751663i	$-0.270748\pi$
$59$	−145.557	−	252.113i	−0.321186	−	0.556310i	−0.980733	+	0.195353i	$0.937415\pi$
$60$	512.311			1.10232
$61$	−331.655	−	574.444i	−0.696133	−	1.20574i	−0.969797	−	0.243912i	$-0.921569\pi$
$61$	−331.655	−	574.444i	−0.696133	−	1.20574i	0.273664	−	0.961825i	$-0.411764\pi$
$62$	−60.5398	+	104.858i	−0.124009	+	0.214790i
$63$	−36.5009	+	63.2215i	−0.0729950	+	0.126431i
$64$	−439.652			−0.858696
$65$		0			0
$66$	−36.2255			−0.0675613
$67$	−212.551	+	368.149i	−0.387570	+	0.671291i	−0.992122	−	0.125275i	$-0.960019\pi$
$67$	−212.551	+	368.149i	−0.387570	+	0.671291i	0.604552	+	0.796566i	$0.293352\pi$
$68$	265.405	−	459.695i	0.473310	−	0.819796i
$69$	258.905	+	448.436i	0.451717	+	0.782397i
$70$	−42.4621			−0.0725028
$71$	−76.4815	−	132.470i	−0.127841	−	0.221427i	0.794999	−	0.606611i	$-0.207471\pi$
$71$	−76.4815	−	132.470i	−0.127841	−	0.221427i	−0.922840	+	0.385184i	$0.874138\pi$
$72$	−46.5175	−	80.5708i	−0.0761409	−	0.131880i
$73$	−117.268			−0.188016			−0.0940081	−	0.995571i	$-0.529968\pi$
$73$	−117.268			−0.188016			−0.0940081	+	0.995571i	$0.529968\pi$
$74$	−0.940837	−	1.62958i	−0.00147797	−	0.00255993i
$75$	353.942	−	613.045i	0.544929	−	0.943845i
$76$	315.464	−	546.400i	0.476134	−	0.824689i
$77$	−121.948			−0.180484
$78$		0			0
$79$	202.462			0.288339			0.144169	−	0.989553i	$-0.453949\pi$
$79$	202.462			0.288339			0.144169	+	0.989553i	$0.453949\pi$
$80$	−529.098	+	916.425i	−0.739437	+	1.28074i
$81$	93.1932	−	161.415i	0.127837	−	0.221420i
$82$	49.9323	+	86.4853i	0.0672452	+	0.116472i
$83$	−336.155			−0.444552			−0.222276	−	0.974984i	$-0.571349\pi$
$83$	−336.155			−0.444552			−0.222276	+	0.974984i	$0.571349\pi$
$84$	78.2292	+	135.497i	0.101613	+	0.175999i
$85$	−605.329	−	1048.46i	−0.772437	−	1.33790i
$86$	12.0702			0.0151344
$87$	−196.564	−	340.459i	−0.242228	−	0.419552i
$88$	77.7065	−	134.592i	0.0941311	−	0.163040i
$89$	359.097	−	621.974i	0.427688	−	0.740777i	−0.568979	−	0.822352i	$-0.692662\pi$
$89$	359.097	−	621.974i	0.427688	−	0.740777i	0.996667	+	0.0815748i	$0.0259949\pi$
$90$	−104.806			−0.122750
$91$		0			0
$92$	−1097.23			−1.24342
$93$	508.769	−	881.214i	0.567278	−	0.982555i
$94$	69.8485	−	120.981i	0.0766417	−	0.132747i
$95$	−719.503	−	1246.22i	−0.777047	−	1.34588i
$96$	−300.303			−0.319266
$97$	379.684	+	657.632i	0.397434	+	0.688376i	0.993409	−	0.114628i	$-0.0365675\pi$
$97$	379.684	+	657.632i	0.397434	+	0.688376i	−0.595975	+	0.803003i	$0.703234\pi$
$98$	68.7098	+	119.009i	0.0708238	+	0.122670i
$99$	−300.994			−0.305566
$100$	750.000	+	1299.04i	0.750000	+	1.29904i
$101$	174.348	−	301.980i	0.171766	−	0.297507i	−0.767272	−	0.641322i	$-0.778386\pi$
$101$	174.348	−	301.980i	0.171766	−	0.297507i	0.939037	+	0.343816i	$0.111720\pi$
$102$	54.9157	−	95.1168i	0.0533085	−	0.0923330i
$103$	−580.303			−0.555136			−0.277568	−	0.960706i	$-0.589528\pi$
$103$	−580.303			−0.555136			−0.277568	+	0.960706i	$0.589528\pi$
$104$		0			0
$105$	356.847			0.331663
$106$	14.8318	−	25.6895i	0.0135905	−	0.0235395i
$107$	−285.747	+	494.928i	−0.258170	+	0.447163i	−0.965752	−	0.259468i	$-0.916453\pi$
$107$	−285.747	+	494.928i	−0.258170	+	0.447163i	0.707582	+	0.706631i	$0.249786\pi$
$108$	581.468	+	1007.13i	0.518072	+	0.897327i
$109$	−176.004			−0.154661			−0.0773307	−	0.997005i	$-0.524640\pi$
$109$	−176.004			−0.154661			−0.0773307	+	0.997005i	$0.524640\pi$
$110$	−87.5379	−	151.620i	−0.0758765	−	0.131422i
$111$	7.90668	+	13.6948i	0.00676098	+	0.0117104i
$112$	−323.170			−0.272649
$113$	−632.441	−	1095.42i	−0.526505	−	0.911933i	−0.999523	−	0.0308807i	$-0.990169\pi$
$113$	−632.441	−	1095.42i	−0.526505	−	0.911933i	0.473018	−	0.881053i	$-0.343165\pi$
$114$	65.2736	−	113.057i	0.0536266	−	0.0928840i
$115$	−1251.27	+	2167.27i	−1.01462	+	1.75738i
$116$	833.035			0.666770
$117$		0			0
$118$	127.638			0.0995768
$119$	184.866	−	320.197i	0.142409	−	0.246659i
$120$	−227.386	+	393.845i	−0.172979	+	0.299608i
$121$	414.098	+	717.239i	0.311118	+	0.538872i
$122$	290.827			0.215821
$123$	−419.625	−	726.812i	−0.307613	−	0.532801i
$124$	1078.08	+	1867.29i	0.780760	+	1.35232i
$125$	1195.19			0.855211
$126$	−16.0037	−	27.7193i	−0.0113153	−	0.0195986i
$127$	−1302.05	+	2255.22i	−0.909752	+	1.57574i	−0.0953448	+	0.995444i	$0.530395\pi$
$127$	−1302.05	+	2255.22i	−0.909752	+	1.57574i	−0.814408	+	0.580293i	$0.802938\pi$
$128$	422.386	−	731.594i	0.291672	−	0.505190i
$129$	−101.436			−0.0692323
$130$		0			0
$131$	2131.70			1.42174			0.710870	−	0.703324i	$-0.248302\pi$
$131$	2131.70			1.42174			0.710870	+	0.703324i	$0.248302\pi$
$132$	−322.547	+	558.668i	−0.212683	+	0.368377i
$133$	219.734	−	380.591i	0.143259	−	0.248131i
$134$	−93.1922	−	161.414i	−0.0600790	−	0.104060i
$135$	2652.40			1.69098
$136$	235.597	+	408.066i	0.148546	+	0.257290i
$137$	343.992	+	595.812i	0.214520	+	0.371560i	0.953124	−	0.302580i	$-0.0978479\pi$
$137$	343.992	+	595.812i	0.214520	+	0.371560i	−0.738604	+	0.674140i	$0.764515\pi$
$138$	−227.032			−0.140045
$139$	339.790	+	588.534i	0.207343	+	0.359128i	0.950877	−	0.309570i	$-0.100185\pi$
$139$	339.790	+	588.534i	0.207343	+	0.359128i	−0.743534	+	0.668698i	$0.766852\pi$
$140$	−378.078	+	654.850i	−0.228239	+	0.395321i
$141$	−586.998	+	1016.71i	−0.350597	+	0.607252i
$142$	67.0662			0.0396343
$143$		0			0
$144$	−797.656			−0.461607
$145$	949.983	−	1645.42i	0.544082	−	0.942377i
$146$	25.7079	−	44.5274i	0.0145726	−	0.0252405i
$147$	−577.429	−	1000.14i	−0.323983	−	0.561155i
$148$	−33.5084			−0.0186106
$149$	−987.731	−	1710.80i	−0.543074	−	0.940632i	−0.998725	−	0.0504739i	$-0.983927\pi$
$149$	−987.731	−	1710.80i	−0.543074	−	0.940632i	0.455651	−	0.890159i	$-0.349407\pi$
$150$	155.185	+	268.788i	0.0844719	+	0.146310i
$151$	−1803.24			−0.971824			−0.485912	−	0.874008i	$-0.661513\pi$
$151$	−1803.24			−0.971824			−0.485912	+	0.874008i	$0.661513\pi$
$152$	280.034	+	485.033i	0.149433	+	0.258825i
$153$	456.290	−	790.318i	0.241104	−	0.417604i
$154$	26.7339	−	46.3044i	0.0139888	−	0.0242293i
$155$	4917.71			2.54839
$156$		0			0
$157$	−397.168			−0.201894			−0.100947	−	0.994892i	$-0.532187\pi$
$157$	−397.168			−0.201894			−0.100947	+	0.994892i	$0.532187\pi$
$158$	−44.3845	+	76.8762i	−0.0223483	+	0.0387085i
$159$	−124.645	+	215.892i	−0.0621698	+	0.107681i
$160$	−725.675	−	1256.91i	−0.358560	−	0.621044i
$161$	−764.272			−0.374118
$162$	40.8603	+	70.7721i	0.0198166	+	0.0343233i
$163$	470.696	+	815.270i	0.226183	+	0.391760i	0.956674	−	0.291162i	$-0.0940420\pi$
$163$	470.696	+	815.270i	0.226183	+	0.391760i	−0.730491	+	0.682922i	$0.760709\pi$
$164$	1778.37			0.846750
$165$	735.658	+	1274.20i	0.347096	+	0.601189i
$166$	73.6932	−	127.640i	0.0344560	−	0.0596796i
$167$	1840.22	−	3187.35i	0.852696	−	1.47691i	−0.0260704	−	0.999660i	$-0.508299\pi$
$167$	1840.22	−	3187.35i	0.852696	−	1.47691i	0.878766	−	0.477252i	$-0.158367\pi$
$168$	−138.886			−0.0637817
$169$		0			0
$170$	530.810			0.239478
$171$	542.353	−	939.383i	0.242543	−	0.420096i
$172$	107.471	−	186.146i	0.0476431	−	0.0825203i
$173$	−711.387	−	1232.16i	−0.312634	−	0.541499i	0.666297	−	0.745686i	$-0.267878\pi$
$173$	−711.387	−	1232.16i	−0.312634	−	0.541499i	−0.978932	+	0.204187i	$0.934545\pi$
$174$	172.366			0.0750978
$175$	522.408	+	904.837i	0.225659	+	0.390853i
$176$	−666.233	−	1153.95i	−0.285336	−	0.494217i
$177$	−1072.66			−0.455514
$178$	157.445	+	272.703i	0.0662978	+	0.114831i
$179$	−583.946	+	1011.42i	−0.243833	+	0.422331i	−0.961803	−	0.273743i	$-0.911738\pi$
$179$	−583.946	+	1011.42i	−0.243833	+	0.422331i	0.717970	+	0.696074i	$0.245072\pi$
$180$	−933.179	+	1616.31i	−0.386417	+	0.669294i
$181$	−1133.96			−0.465673			−0.232836	−	0.972516i	$-0.574801\pi$
$181$	−1133.96			−0.465673			−0.232836	+	0.972516i	$0.574801\pi$
$182$		0			0
$183$	−2444.07			−0.987274
$184$	487.002	−	843.512i	0.195121	−	0.337959i
$185$	−38.2126	+	66.1861i	−0.0151862	+	0.0263032i
$186$	223.068	+	386.366i	0.0879364	+	0.152310i
$187$	1524.44			0.596141
$188$	−1243.84	−	2154.40i	−0.482536	−	0.835776i
$189$	405.018	+	701.511i	0.155877	+	0.269986i
$190$	630.928			0.240907
$191$	−1341.06	−	2322.78i	−0.508040	−	0.879952i	−0.999957	−	0.00930919i	$-0.997037\pi$
$191$	−1341.06	−	2322.78i	−0.508040	−	0.879952i	0.491916	−	0.870642i	$-0.336297\pi$
$192$	−809.985	+	1402.93i	−0.304456	+	0.527334i
$193$	−985.333	+	1706.65i	−0.367491	+	0.636514i	−0.989173	−	0.146757i	$-0.953117\pi$
$193$	−985.333	+	1706.65i	−0.367491	+	0.636514i	0.621681	+	0.783270i	$0.286450\pi$
$194$	−332.943			−0.123216
$195$		0			0
$196$	2447.14			0.891813
$197$	−2008.02	+	3478.00i	−0.726222	+	1.25785i	0.232247	+	0.972657i	$0.425392\pi$
$197$	−2008.02	+	3478.00i	−0.726222	+	1.25785i	−0.958469	+	0.285197i	$0.907941\pi$
$198$	65.9851	−	114.290i	0.0236836	−	0.0410212i
$199$	2113.03	+	3659.87i	0.752707	+	1.30373i	0.946506	+	0.322685i	$0.104585\pi$
$199$	2113.03	+	3659.87i	0.752707	+	1.30373i	−0.193800	+	0.981041i	$0.562081\pi$
$200$	−1331.53			−0.470768
$201$	783.177	+	1356.50i	0.274831	+	0.476021i
$202$	76.4426	+	132.402i	0.0266261	+	0.0461178i
$203$	580.245			0.200617
$204$	−977.926	−	1693.82i	−0.335630	−	0.581328i
$205$	2028.03	−	3512.65i	0.690944	−	1.19675i
$206$	127.216	−	220.345i	0.0430270	−	0.0745250i
$207$	−1886.39			−0.633398
$208$		0			0
$209$	1811.98			0.599699
$210$	−78.2292	+	135.497i	−0.0257063	+	0.0445247i
$211$	−682.334	+	1181.84i	−0.222625	+	0.385597i	−0.955604	−	0.294654i	$-0.904796\pi$
$211$	−682.334	+	1181.84i	−0.222625	+	0.385597i	0.732980	+	0.680251i	$0.238129\pi$
$212$	−264.122	−	457.473i	−0.0855659	−	0.148204i
$213$	−563.617			−0.181307
$214$	−125.285	−	217.000i	−0.0400201	−	0.0693168i
$215$	−245.118	−	424.557i	−0.0777532	−	0.134672i
$216$	−1032.33			−0.325189
$217$	750.928	+	1300.65i	0.234914	+	0.406883i
$218$	38.5842	−	66.8297i	0.0119874	−	0.0207628i
$219$	−216.046	+	374.203i	−0.0666624	+	0.115463i
$220$	−3117.71			−0.955436
$221$		0			0
$222$	−6.93332			−0.00209610
$223$	−529.734	+	917.527i	−0.159075	+	0.275525i	−0.934535	−	0.355871i	$-0.884184\pi$
$223$	−529.734	+	917.527i	−0.159075	+	0.275525i	0.775461	+	0.631396i	$0.217518\pi$
$224$	221.619	−	383.856i	0.0661052	−	0.114498i
$225$	1289.42	+	2233.34i	0.382050	+	0.661729i
$226$	554.584			0.163232
$227$	1732.10	+	3000.08i	0.506446	+	0.877190i	0.999972	+	0.00745930i	$0.00237439\pi$
$227$	1732.10	+	3000.08i	0.506446	+	0.877190i	−0.493526	+	0.869731i	$0.664292\pi$
$228$	−1162.38	−	2013.30i	−0.337633	−	0.584797i
$229$	2324.64			0.670815			0.335407	−	0.942073i	$-0.391126\pi$
$229$	2324.64			0.670815			0.335407	+	0.942073i	$0.391126\pi$
$230$	−548.617	−	950.233i	−0.157282	−	0.272420i
$231$	−224.668	+	389.137i	−0.0639917	+	0.110837i
$232$	−369.738	+	640.405i	−0.104631	+	0.181227i
$233$	−3731.01			−1.04904			−0.524521	−	0.851398i	$-0.675755\pi$
$233$	−3731.01			−1.04904			−0.524521	+	0.851398i	$0.675755\pi$
$234$		0			0
$235$	−5673.86			−1.57499
$236$	1136.48	−	1968.44i	0.313468	−	0.542942i
$237$	373.002	−	646.058i	0.102232	−	0.177072i
$238$	81.0540	+	140.390i	0.0220754	+	0.0382357i
$239$	−6044.47			−1.63592			−0.817958	−	0.575278i	$-0.804894\pi$
$239$	−6044.47			−1.63592			−0.817958	+	0.575278i	$0.804894\pi$
$240$	1949.55	+	3376.71i	0.524344	+	0.908191i
$241$	−2586.98	−	4480.78i	−0.691461	−	1.19765i	−0.971359	−	0.237616i	$-0.923634\pi$
$241$	−2586.98	−	4480.78i	−0.691461	−	1.19765i	0.279898	−	0.960030i	$-0.409699\pi$
$242$	−363.120			−0.0964556
$243$	1667.39	+	2888.00i	0.440176	+	0.762408i
$244$	2589.49	−	4485.12i	0.679405	−	1.17676i
$245$	2790.68	−	4833.61i	0.727715	−	1.26044i
$246$	367.967			0.0953688
$247$		0			0
$248$	−1914.00			−0.490076
$249$	−619.309	+	1072.67i	−0.157619	+	0.273004i
$250$	−262.015	+	453.823i	−0.0662851	+	0.114809i
$251$	−2810.37	−	4867.70i	−0.706728	−	1.22409i	−0.966064	−	0.258301i	$-0.916837\pi$
$251$	−2810.37	−	4867.70i	−0.706728	−	1.22409i	0.259337	−	0.965787i	$-0.416496\pi$
$252$	−569.981			−0.142482
$253$	−1575.59	−	2729.00i	−0.391527	−	0.678144i
$254$	−570.882	−	988.796i	−0.141025	−	0.244262i
$255$	−4460.86			−1.09549
$256$	−1573.42	−	2725.24i	−0.384135	−	0.665341i
$257$	837.070	−	1449.85i	0.203171	−	0.351903i	−0.746377	−	0.665523i	$-0.768209\pi$
$257$	837.070	−	1449.85i	0.203171	−	0.351903i	0.949549	+	0.313620i	$0.101542\pi$
$258$	22.2372	−	38.5160i	0.00536601	−	0.00929420i
$259$	−23.3401			−0.00559954
$260$		0			0
$261$	1432.17			0.339653
$262$	−467.320	+	809.422i	−0.110195	+	0.190864i
$263$	3154.59	−	5463.91i	0.739622	−	1.28106i	−0.213044	−	0.977043i	$-0.568338\pi$
$263$	3154.59	−	5463.91i	0.739622	−	1.28106i	0.952666	−	0.304020i	$-0.0983289\pi$
$264$	−286.322	−	495.924i	−0.0667496	−	0.115614i
$265$	−1204.81			−0.279285
$266$	96.3419	+	166.869i	0.0222072	+	0.0384639i
$267$	−1323.15	−	2291.76i	−0.303279	−	0.525294i
$268$	−3319.09			−0.756514
$269$	1241.37	+	2150.11i	0.281366	+	0.487340i	0.971721	−	0.236131i	$-0.0758793\pi$
$269$	1241.37	+	2150.11i	0.281366	+	0.487340i	−0.690356	+	0.723470i	$0.742546\pi$
$270$	−581.468	+	1007.13i	−0.131063	+	0.227008i
$271$	1417.86	−	2455.81i	0.317819	−	0.550478i	−0.662214	−	0.749315i	$-0.730383\pi$
$271$	1417.86	−	2455.81i	0.317819	−	0.550478i	0.980033	+	0.198837i	$0.0637163\pi$
$272$	4039.88			0.900566
$273$		0			0
$274$	−301.645			−0.0665075
$275$	−2153.94	+	3730.74i	−0.472318	+	0.818080i
$276$	−2021.47	+	3501.28i	−0.440863	+	0.763596i
$277$	1918.76	+	3323.38i	0.416198	+	0.720876i	0.995553	−	0.0941989i	$-0.0300290\pi$
$277$	1918.76	+	3323.38i	0.416198	+	0.720876i	−0.579355	+	0.815075i	$0.696696\pi$
$278$	−297.960			−0.0642822
$279$	1853.46	+	3210.28i	0.397719	+	0.688869i
$280$	−335.616	−	581.303i	−0.0716317	−	0.124070i
$281$	9122.13			1.93659			0.968293	−	0.249819i	$-0.0803712\pi$
$281$	9122.13			1.93659			0.968293	+	0.249819i	$0.0803712\pi$
$282$	−257.368	−	445.774i	−0.0543476	−	0.0941328i
$283$	−1063.92	+	1842.77i	−0.223476	+	0.387072i	−0.955861	−	0.293819i	$-0.905074\pi$
$283$	−1063.92	+	1842.77i	−0.223476	+	0.387072i	0.732385	+	0.680891i	$0.238407\pi$
$284$	597.150	−	1034.29i	0.124769	−	0.216106i
$285$	−5302.24			−1.10203
$286$		0			0
$287$	1238.71			0.254769
$288$	547.005	−	947.441i	0.111919	−	0.193849i
$289$	145.530	−	252.066i	0.0296215	−	0.0513059i
$290$	416.518	+	721.430i	0.0843405	+	0.146082i
$291$	2798.01			0.563651
$292$	−457.800	−	792.934i	−0.0917491	−	0.158914i
$293$	4137.38	+	7166.16i	0.824944	+	1.42884i	0.901962	+	0.431815i	$0.142127\pi$
$293$	4137.38	+	7166.16i	0.824944	+	1.42884i	−0.0770183	+	0.997030i	$0.524540\pi$
$294$	506.344			0.100444
$295$	−2592.05	−	4489.56i	−0.511576	−	0.886076i
$296$	14.8725	−	25.7600i	0.00292043	−	0.00505834i
$297$	−1669.93	+	2892.40i	−0.326260	+	0.565099i
$298$	866.136			0.168369
$299$		0			0
$300$	5526.99			1.06367
$301$	74.8585	−	129.659i	0.0143348	−	0.0248286i
$302$	395.312	−	684.701i	0.0753234	−	0.130464i
$303$	−642.414	−	1112.69i	−0.121801	−	0.210966i
$304$	4801.86			0.905940
$305$	−5906.04	−	10229.6i	−1.10878	−	1.92047i
$306$	200.059	+	346.513i	0.0373746	+	0.0647347i
$307$	3610.49			0.671211			0.335605	−	0.942003i	$-0.391059\pi$
$307$	3610.49			0.671211			0.335605	+	0.942003i	$0.391059\pi$
$308$	−476.070	−	824.578i	−0.0880734	−	0.152548i
$309$	−1069.11	+	1851.75i	−0.196827	+	0.340914i
$310$	−1078.08	+	1867.29i	−0.197518	+	0.342112i
$311$	3331.06			0.607354			0.303677	−	0.952775i	$-0.401786\pi$
$311$	3331.06			0.607354			0.303677	+	0.952775i	$0.401786\pi$
$312$		0			0
$313$	−358.125			−0.0646724			−0.0323362	−	0.999477i	$-0.510295\pi$
$313$	−358.125			−0.0646724			−0.0323362	+	0.999477i	$0.510295\pi$
$314$	87.0685	−	150.807i	0.0156483	−	0.0271036i
$315$	−650.000	+	1125.83i	−0.116265	+	0.201376i
$316$	790.388	+	1368.99i	0.140705	+	0.243708i
$317$	−3047.46			−0.539944			−0.269972	−	0.962868i	$-0.587014\pi$
$317$	−3047.46			−0.539944			−0.269972	+	0.962868i	$0.587014\pi$
$318$	−54.6503	−	94.6570i	−0.00963721	−	0.0166921i
$319$	1196.21	+	2071.89i	0.209952	+	0.363647i
$320$	−7829.23			−1.36771
$321$	1052.88	+	1823.64i	0.183072	+	0.317089i
$322$	167.546	−	290.199i	0.0289969	−	0.0502241i
$323$	−2746.85	+	4757.69i	−0.473185	+	0.819581i
$324$	1455.26			0.249530
$325$		0			0
$326$	−412.751			−0.0701232
$327$	−324.257	+	561.629i	−0.0548362	+	0.0949791i
$328$	−789.318	+	1367.14i	−0.132874	+	0.230145i
$329$	−866.392	−	1500.63i	−0.145185	−	0.251467i
$330$	−645.094			−0.107610
$331$	3847.39	+	6663.87i	0.638887	+	1.10658i	0.985677	+	0.168641i	$0.0539380\pi$
$331$	3847.39	+	6663.87i	0.638887	+	1.10658i	−0.346791	+	0.937942i	$0.612729\pi$
$332$	−1312.31	−	2272.99i	−0.216935	−	0.375742i
$333$	−57.6084			−0.00948025
$334$	806.838	+	1397.48i	0.132180	+	0.228943i
$335$	−3785.05	+	6555.90i	−0.617312	+	1.06922i
$336$	−595.386	+	1031.24i	−0.0966696	+	0.167437i
$337$	4712.21			0.761693			0.380846	−	0.924638i	$-0.375633\pi$
$337$	4712.21			0.761693			0.380846	+	0.924638i	$0.375633\pi$
$338$		0			0
$339$	−4660.66			−0.746703
$340$	4726.27	−	8186.13i	0.753876	−	1.30575i
$341$	−3096.16	+	5362.70i	−0.491690	+	0.851632i
$342$	237.793	+	411.870i	0.0375976	+	0.0651210i
$343$	3569.92			0.561976
$344$	95.4013	+	165.240i	0.0149526	+	0.0258986i
$345$	4610.52	+	7985.65i	0.719484	+	1.24618i
$346$	623.811			0.0969257
$347$	2630.99	+	4557.01i	0.407029	+	0.704995i	0.994555	−	0.104210i	$-0.0332315\pi$
$347$	2630.99	+	4557.01i	0.407029	+	0.704995i	−0.587526	+	0.809205i	$0.699898\pi$
$348$	1534.72	−	2658.22i	0.236408	−	0.409470i
$349$	25.1672	−	43.5909i	0.00386009	−	0.00668587i	−0.864089	−	0.503339i	$-0.832105\pi$
$349$	25.1672	−	43.5909i	0.00386009	−	0.00668587i	0.867949	+	0.496653i	$0.165438\pi$
$350$	−458.096			−0.0699608
$351$		0			0
$352$	1827.52			0.276725
$353$	4528.82	−	7844.14i	0.682846	−	1.18272i	−0.291263	−	0.956643i	$-0.594075\pi$
$353$	4528.82	−	7844.14i	0.682846	−	1.18272i	0.974109	−	0.226081i	$-0.0725914\pi$
$354$	235.152	−	407.295i	0.0353056	−	0.0611511i
$355$	−1361.96	−	2358.99i	−0.203621	−	0.352683i
$356$	5607.49			0.834821
$357$	−681.168	−	1179.82i	−0.100984	−	0.174909i
$358$	−256.029	−	443.456i	−0.0377977	−	0.0654675i
$359$	−7177.86			−1.05525			−0.527623	−	0.849479i	$-0.676917\pi$
$359$	−7177.86			−1.05525			−0.527623	+	0.849479i	$0.676917\pi$
$360$	−828.373	−	1434.78i	−0.121275	−	0.210055i
$361$	164.553	−	285.014i	0.0239908	−	0.0415532i
$362$	248.591	−	430.573i	0.0360930	−	0.0625150i
$363$	3051.62			0.441235
$364$		0			0
$365$	−2088.28			−0.299467
$366$	535.798	−	928.030i	0.0765209	−	0.132538i
$367$	−2002.07	+	3467.69i	−0.284761	+	0.493221i	−0.972551	−	0.232689i	$-0.925248\pi$
$367$	−2002.07	+	3467.69i	−0.284761	+	0.493221i	0.687790	+	0.725910i	$0.258581\pi$
$368$	−4175.41	−	7232.03i	−0.591463	−	1.02444i
$369$	3057.41			0.431334
$370$	−16.7542	−	29.0191i	−0.00235408	−	0.00407738i
$371$	−183.972	−	318.649i	−0.0257449	−	0.0445915i
$372$	7944.70			1.10729
$373$	5007.09	+	8672.53i	0.695060	+	1.20388i	0.970161	+	0.242464i	$0.0779555\pi$
$373$	5007.09	+	8672.53i	0.695060	+	1.20388i	−0.275101	+	0.961415i	$0.588711\pi$
$374$	−334.194	+	578.841i	−0.0462053	+	0.0800299i
$375$	2201.94	−	3813.87i	0.303221	−	0.525194i
$376$	2208.30			0.302883
$377$		0			0
$378$	−355.158			−0.0483263
$379$	−4084.56	+	7074.66i	−0.553587	+	0.958842i	0.444425	+	0.895816i	$0.353408\pi$
$379$	−4084.56	+	7074.66i	−0.553587	+	0.958842i	−0.998012	+	0.0630252i	$0.979925\pi$
$380$	5617.71	−	9730.16i	0.758375	−	1.31354i
$381$	4797.62	+	8309.73i	0.645117	+	1.11738i
$382$	1175.97			0.157507
$383$	−3655.12	−	6330.86i	−0.487645	−	0.844626i	0.512254	−	0.858834i	$-0.328811\pi$
$383$	−3655.12	−	6330.86i	−0.487645	−	0.844626i	−0.999899	+	0.0142079i	$0.995477\pi$
$384$	−1556.35	−	2695.67i	−0.206828	−	0.358237i
$385$	−2171.62			−0.287470
$386$	−432.017	−	748.275i	−0.0569665	−	0.0986689i
$387$	184.767	−	320.027i	0.0242694	−	0.0420358i
$388$	−2964.48	+	5134.64i	−0.387884	+	0.671834i
$389$	8785.47			1.14509			0.572546	−	0.819872i	$-0.305956\pi$
$389$	8785.47			1.14509			0.572546	+	0.819872i	$0.305956\pi$
$390$		0			0
$391$	9553.99			1.23572
$392$	−1086.15	+	1881.26i	−0.139946	+	0.242393i
$393$	3927.30	−	6802.29i	0.504087	−	0.873104i
$394$	−880.412	−	1524.92i	−0.112575	−	0.194986i
$395$	3605.40			0.459259
$396$	−1175.05	−	2035.24i	−0.149112	−	0.258269i
$397$	5633.40	+	9757.33i	0.712171	+	1.23352i	0.964040	+	0.265756i	$0.0856214\pi$
$397$	5633.40	+	9757.33i	0.712171	+	1.23352i	−0.251869	+	0.967761i	$0.581045\pi$
$398$	−1852.90			−0.233361
$399$	−809.646	−	1402.35i	−0.101586	−	0.175953i
$400$	−5708.10	+	9886.71i	−0.713512	+	1.23584i
$401$	788.117	−	1365.06i	0.0981464	−	0.169995i	−0.812771	−	0.582583i	$-0.802042\pi$
$401$	788.117	−	1365.06i	0.0981464	−	0.169995i	0.910917	+	0.412589i	$0.135375\pi$
$402$	−686.763			−0.0852055
$403$		0			0
$404$	2722.54			0.335276
$405$	1659.56	−	2874.45i	0.203616	−	0.352672i
$406$	−127.203	+	220.323i	−0.0155493	+	0.0269321i
$407$	−48.1168	−	83.3407i	−0.00586010	−	0.0101500i
$408$	1736.19			0.210672
$409$	3377.89	+	5850.68i	0.408377	+	0.707329i	0.994708	−	0.102742i	$-0.0327617\pi$
$409$	3377.89	+	5850.68i	0.408377	+	0.707329i	−0.586331	+	0.810071i	$0.699428\pi$
$410$	889.183	+	1540.11i	0.107106	+	0.185514i
$411$	2534.99			0.304238
$412$	−2265.43	−	3923.85i	−0.270898	−	0.469209i
$413$	791.606	−	1371.10i	0.0943157	−	0.163360i
$414$	413.542	−	716.275i	0.0490929	−	0.0850314i
$415$	−5986.17			−0.708072
$416$		0			0
$417$	2504.02			0.294059
$418$	−397.228	+	688.019i	−0.0464810	+	0.0805074i
$419$	−5378.09	+	9315.13i	−0.627057	+	1.08610i	0.361082	+	0.932534i	$0.382408\pi$
$419$	−5378.09	+	9315.13i	−0.627057	+	1.08610i	−0.988139	+	0.153561i	$0.950926\pi$
$420$	1393.09	+	2412.90i	0.161847	+	0.280327i
$421$	−7886.03			−0.912925			−0.456463	−	0.889743i	$-0.650884\pi$
$421$	−7886.03			−0.912925			−0.456463	+	0.889743i	$0.650884\pi$
$422$	−299.167	−	518.173i	−0.0345100	−	0.0597731i
$423$	−2138.45	−	3703.90i	−0.245803	−	0.425744i
$424$	468.916			0.0537089
$425$	−6530.50	−	11311.2i	−0.745355	−	1.29099i
$426$	123.558	−	214.009i	0.0140526	−	0.0243398i
$427$	1803.69	−	3124.08i	0.204418	−	0.354063i
$428$	−4462.08			−0.503932
$429$		0			0
$430$	214.943			0.0241057
$431$	−7042.31	+	12197.6i	−0.787044	+	1.36320i	0.140726	+	0.990049i	$0.455056\pi$
$431$	−7042.31	+	12197.6i	−0.787044	+	1.36320i	−0.927770	+	0.373152i	$0.878277\pi$
$432$	−4425.43	+	7665.07i	−0.492867	+	0.853671i
$433$	−932.072	−	1614.40i	−0.103447	−	0.179175i	0.809656	−	0.586905i	$-0.199654\pi$
$433$	−932.072	−	1614.40i	−0.103447	−	0.179175i	−0.913103	+	0.407730i	$0.866321\pi$
$434$	−658.485			−0.0728301
$435$	−3500.36	−	6062.81i	−0.385815	−	0.668252i
$436$	−687.098	−	1190.09i	−0.0754725	−	0.130722i
$437$	11356.0			1.24309
$438$	−94.7249	−	164.068i	−0.0103336	−	0.0178984i
$439$	−3077.24	+	5329.94i	−0.334553	+	0.579463i	−0.983399	−	0.181457i	$-0.941919\pi$
$439$	−3077.24	+	5329.94i	−0.334553	+	0.579463i	0.648846	+	0.760920i	$0.275252\pi$
$440$	1383.78	−	2396.77i	0.149930	−	0.259686i
$441$	4207.17			0.454289
$442$		0			0
$443$	−14539.3			−1.55933			−0.779663	−	0.626200i	$-0.784609\pi$
$443$	−14539.3			−1.55933			−0.779663	+	0.626200i	$0.784609\pi$
$444$	−61.7335	+	106.926i	−0.00659852	+	0.0114290i
$445$	6394.72	−	11076.0i	0.681210	−	1.17989i
$446$	−232.261	−	402.287i	−0.0246589	−	0.0427104i
$447$	−7278.90			−0.770202
$448$	−1195.51	−	2070.69i	−0.126077	−	0.218373i
$449$	−3521.93	−	6100.17i	−0.370179	−	0.641169i	0.619414	−	0.785065i	$-0.287370\pi$
$449$	−3521.93	−	6100.17i	−0.370179	−	0.641169i	−0.989593	+	0.143896i	$0.954037\pi$
$450$	−1130.68			−0.118446
$451$	2553.66	+	4423.08i	0.266624	+	0.461806i
$452$	4937.95	−	8552.78i	0.513853	−	0.890020i
$453$	−3322.16	+	5754.15i	−0.344567	+	0.596807i
$454$	−1518.87			−0.157013
$455$		0			0
$456$	2063.66			0.211929
$457$	7049.43	−	12210.0i	0.721572	−	1.24980i	−0.238798	−	0.971069i	$-0.576753\pi$
$457$	7049.43	−	12210.0i	0.721572	−	1.24980i	0.960370	−	0.278730i	$-0.0899133\pi$
$458$	−509.616	+	882.681i	−0.0519930	+	0.0900545i
$459$	−5063.04	−	8769.44i	−0.514863	−	0.891770i
$460$	−19539.3			−1.98049
$461$	7224.85	+	12513.8i	0.729924	+	1.26426i	0.956915	+	0.290368i	$0.0937777\pi$
$461$	7224.85	+	12513.8i	0.729924	+	1.26426i	−0.226991	+	0.973897i	$0.572889\pi$
$462$	−98.5051	−	170.616i	−0.00991964	−	0.0171813i
$463$	−15806.5			−1.58659			−0.793293	−	0.608840i	$-0.791635\pi$
$463$	−15806.5			−1.58659			−0.793293	+	0.608840i	$0.791635\pi$
$464$	3170.03	+	5490.65i	0.317166	+	0.549347i
$465$	9060.04	−	15692.4i	0.903547	−	1.56499i
$466$	817.926	−	1416.69i	0.0813083	−	0.140830i
$467$	−15071.3			−1.49340			−0.746699	−	0.665162i	$-0.768362\pi$
$467$	−15071.3			−1.49340			−0.746699	+	0.665162i	$0.768362\pi$
$468$		0			0
$469$	−2311.89			−0.227619
$470$	1243.84	−	2154.40i	0.122073	−	0.211437i
$471$	−731.713	+	1267.36i	−0.0715830	+	0.123985i
$472$	1008.84	+	1747.36i	0.0983804	+	0.170400i
$473$	617.299			0.0600073
$474$	163.542	+	283.262i	0.0158475	+	0.0274487i
$475$	−7762.25	−	13444.6i	−0.749803	−	1.29870i
$476$	2886.78			0.277973
$477$	−454.085	−	786.498i	−0.0435872	−	0.0754953i
$478$	1325.09	−	2295.12i	0.126795	−	0.219616i
$479$	−196.272	+	339.954i	−0.0187222	+	0.0324277i	−0.875235	−	0.483698i	$-0.839293\pi$
$479$	−196.272	+	339.954i	−0.0187222	+	0.0324277i	0.856513	+	0.516126i	$0.172626\pi$
$480$	−5347.73			−0.508519
$481$		0			0
$482$	2268.51			0.214373
$483$	−1408.04	+	2438.80i	−0.132646	+	0.229750i
$484$	−3233.18	+	5600.03i	−0.303642	+	0.525923i
$485$	6761.33	+	11711.0i	0.633023	+	1.09643i
$486$	−1462.12			−0.136467
$487$	4748.94	+	8225.41i	0.441879	+	0.765357i	0.997829	−	0.0658588i	$-0.0209787\pi$
$487$	4748.94	+	8225.41i	0.441879	+	0.765357i	−0.555950	+	0.831216i	$0.687645\pi$
$488$	2298.66	+	3981.40i	0.213228	+	0.369322i
$489$	3468.71			0.320778
$490$	1223.57	+	2119.28i	0.112806	+	0.195386i
$491$	946.912	−	1640.10i	0.0870337	−	0.150747i	−0.819222	−	0.573476i	$-0.805595\pi$
$491$	946.912	−	1640.10i	0.0870337	−	0.150747i	0.906256	+	0.422729i	$0.138928\pi$
$492$	3276.34	−	5674.78i	0.300221	−	0.519998i
$493$	−7253.52			−0.662641
$494$		0			0
$495$	−5360.04			−0.486699
$496$	−8205.03	+	14211.5i	−0.742775	+	1.28652i
$497$	415.941	−	720.430i	0.0375402	−	0.0650216i
$498$	−271.534	−	470.311i	−0.0244332	−	0.0423196i
$499$	13370.1			1.19945			0.599727	−	0.800205i	$-0.295276\pi$
$499$	13370.1			1.19945			0.599727	+	0.800205i	$0.295276\pi$
$500$	4665.90	+	8081.57i	0.417330	+	0.722838i
$501$	−6780.57	−	11744.3i	−0.604658	−	1.04730i
$502$	2464.39			0.219106
$503$	−2777.36	−	4810.52i	−0.246195	−	0.426423i	0.716272	−	0.697822i	$-0.245847\pi$
$503$	−2777.36	−	4810.52i	−0.246195	−	0.426423i	−0.962467	+	0.271399i	$0.912514\pi$
$504$	252.983	−	438.180i	0.0223587	−	0.0387263i
$505$	3104.76	−	5377.60i	0.273584	−	0.473861i
$506$	1381.62			0.121385
$507$		0			0
$508$	−20332.3			−1.77578
$509$	1098.78	−	1903.13i	0.0956824	−	0.165727i	−0.814211	−	0.580569i	$-0.802830\pi$
$509$	1098.78	−	1903.13i	0.0956824	−	0.165727i	0.909893	+	0.414843i	$0.136163\pi$
$510$	977.926	−	1693.82i	0.0849084	−	0.147066i
$511$	−318.878	−	552.313i	−0.0276053	−	0.0478139i
$512$	8137.89			0.702437
$513$	−6018.00	−	10423.5i	−0.517936	−	0.897091i
$514$	367.011	+	635.682i	0.0314945	+	0.0545500i
$515$	−10333.9			−0.884206
$516$	−395.996	−	685.884i	−0.0337844	−	0.0585162i
$517$	3572.23	−	6187.28i	0.303881	−	0.526337i
$518$	5.11669	−	8.86237i	0.000434005	−	0.000751718i
$519$	−5242.44			−0.443386
$520$		0			0
$521$	17005.2			1.42997			0.714983	−	0.699142i	$-0.246435\pi$
$521$	17005.2			1.42997			0.714983	+	0.699142i	$0.246435\pi$
$522$	−313.966	+	543.805i	−0.0263255	+	0.0455972i
$523$	7243.11	−	12545.4i	0.605581	−	1.04890i	−0.386378	−	0.922341i	$-0.626274\pi$
$523$	7243.11	−	12545.4i	0.605581	−	1.04890i	0.991959	−	0.126557i	$-0.0403928\pi$
$524$	8321.92	+	14414.0i	0.693788	+	1.20168i
$525$	3849.79			0.320035
$526$	1383.12	+	2395.64i	0.114652	+	0.198583i
$527$	−9387.19	−	16259.1i	−0.775925	−	1.34394i
$528$	−4909.68			−0.404671
$529$	−3791.02	−	6566.23i	−0.311582	−	0.539675i
$530$	264.122	−	457.473i	0.0216466	−	0.0374931i
$531$	1953.86	−	3384.18i	0.159680	−	0.276574i
$532$	3431.27			0.279632
$533$		0			0
$534$	1160.26			0.0940252
$535$	−5088.51	+	8813.56i	−0.411206	+	0.712230i
$536$	1473.16	−	2551.59i	0.118714	−	0.205619i
$537$	2151.64	+	3726.75i	0.172905	+	0.299481i
$538$	−1088.55			−0.0872315
$539$	3513.99	+	6086.41i	0.280813	+	0.486383i
$540$	10354.6	+	17934.8i	0.825172	+	1.42924i
$541$	15266.7			1.21325			0.606623	−	0.794990i	$-0.292524\pi$
$541$	15266.7			1.21325			0.606623	+	0.794990i	$0.292524\pi$
$542$	621.657	+	1076.74i	0.0492665	+	0.0853321i
$543$	−2089.13	+	3618.48i	−0.165107	+	0.285974i
$544$	−2770.41	+	4798.50i	−0.218347	+	0.378187i
$545$	−3134.23			−0.246341
$546$		0			0
$547$	15260.5			1.19286			0.596430	−	0.802665i	$-0.296586\pi$
$547$	15260.5			1.19286			0.596430	+	0.802665i	$0.296586\pi$
$548$	−2685.81	+	4651.96i	−0.209365	+	0.362631i
$549$	4451.91	−	7710.93i	0.346089	−	0.599443i
$550$	−944.390	−	1635.73i	−0.0732162	−	0.126814i
$551$	−8621.64			−0.666595
$552$	−1794.44	−	3108.05i	−0.138363	−	0.239651i
$553$	550.540	+	953.563i	0.0423351	+	0.0733266i
$554$	−1682.55			−0.129033
$555$	140.800	+	243.873i	0.0107687	+	0.0186520i
$556$	−2653.00	+	4595.13i	−0.202360	+	0.350498i
$557$	−5221.05	+	9043.12i	−0.397169	+	0.687916i	−0.993375	−	0.114915i	$-0.963341\pi$
$557$	−5221.05	+	9043.12i	−0.397169	+	0.687916i	0.596207	+	0.802831i	$0.296674\pi$
$558$	−1625.29			−0.123304
$559$		0			0
$560$	−5754.94			−0.434269
$561$	2808.53	−	4864.51i	0.211366	−	0.366096i
$562$	−1999.79	+	3463.73i	−0.150099	+	0.259980i
$563$	−3572.63	−	6187.98i	−0.267440	−	0.463219i	0.700760	−	0.713397i	$-0.252844\pi$
$563$	−3572.63	−	6187.98i	−0.267440	−	0.463219i	−0.968200	+	0.250178i	$0.919511\pi$
$564$	−9166.29			−0.684344
$565$	−11262.4	−	19507.0i	−0.838604	−	1.45250i
$566$	−466.475	−	807.958i	−0.0346420	−	0.0600018i
$567$	1013.65			0.0750783
$568$	530.083	+	918.131i	0.0391581	+	0.0678238i
$569$	−2219.43	+	3844.17i	−0.163521	+	0.283226i	−0.936129	−	0.351657i	$-0.885618\pi$
$569$	−2219.43	+	3844.17i	−0.163521	+	0.283226i	0.772608	+	0.634883i	$0.218952\pi$
$570$	1162.38	−	2013.30i	0.0854151	−	0.147943i
$571$	10117.3			0.741497			0.370748	−	0.928733i	$-0.379101\pi$
$571$	10117.3			0.741497			0.370748	+	0.928733i	$0.379101\pi$
$572$		0			0
$573$	−9882.70			−0.720516
$574$	−271.554	+	470.346i	−0.0197464	+	0.0342018i
$575$	−13499.2	+	23381.3i	−0.979052	+	1.69577i
$576$	−2950.79	−	5110.92i	−0.213454	−	0.369714i
$577$	−3105.60			−0.224069			−0.112035	−	0.993704i	$-0.535737\pi$
$577$	−3105.60			−0.224069			−0.112035	+	0.993704i	$0.535737\pi$
$578$	63.8074	+	110.518i	0.00459176	+	0.00795316i
$579$	3630.62	+	6288.41i	0.260593	+	0.451360i
$580$	14834.5			1.06202
$581$	−914.081	−	1583.24i	−0.0652711	−	0.113053i
$582$	−613.390	+	1062.42i	−0.0436870	+	0.0756682i
$583$	758.538	−	1313.83i	0.0538858	−	0.0933329i
$584$	812.769			0.0575901
$585$		0			0
$586$	−3628.05			−0.255757
$587$	9831.16	−	17028.1i	0.691270	−	1.19731i	−0.280152	−	0.959956i	$-0.590385\pi$
$587$	9831.16	−	17028.1i	0.691270	−	1.19731i	0.971422	−	0.237359i	$-0.0762818\pi$
$588$	4508.43	−	7808.83i	0.316198	−	0.547671i
$589$	−11157.7	−	19325.8i	−0.780555	−	1.35196i
$590$	2272.95			0.158603
$591$	7398.88	+	12815.2i	0.514974	+	0.891960i
$592$	−127.513	−	220.859i	−0.00885261	−	0.0153332i
$593$	−6395.51			−0.442888			−0.221444	−	0.975173i	$-0.571077\pi$
$593$	−6395.51			−0.442888			−0.221444	+	0.975173i	$0.571077\pi$
$594$	−732.176	−	1268.17i	−0.0505750	−	0.0875985i
$595$	3292.05	−	5702.00i	0.226825	−	0.392872i
$596$	7711.97	−	13357.5i	0.530025	−	0.918029i
$597$	15571.6			1.06751
$598$		0			0
$599$	8878.48			0.605618			0.302809	−	0.953051i	$-0.402076\pi$
$599$	8878.48			0.605618			0.302809	+	0.953051i	$0.402076\pi$
$600$	−2453.12	+	4248.94i	−0.166914	+	0.289103i
$601$	−9550.29	+	16541.6i	−0.648194	+	1.12270i	0.335360	+	0.942090i	$0.391142\pi$
$601$	−9550.29	+	16541.6i	−0.648194	+	1.12270i	−0.983554	+	0.180615i	$0.942191\pi$
$602$	32.8215	+	56.8485i	0.00222210	+	0.00384879i
$603$	−5706.26			−0.385368
$604$	−7039.63	−	12193.0i	−0.474236	−	0.821401i
$605$	7374.16	+	12772.4i	0.495541	+	0.858302i
$606$	563.330			0.0377619
$607$	−8297.88	−	14372.4i	−0.554861	−	0.961047i	−0.997914	−	0.0645522i	$-0.979438\pi$
$607$	−8297.88	−	14372.4i	−0.554861	−	0.961047i	0.443053	−	0.896495i	$-0.353895\pi$
$608$	−3292.95	+	5703.56i	−0.219650	+	0.380444i
$609$	1069.00	−	1851.57i	0.0711300	−	0.123201i
$610$	5178.97			0.343755
$611$		0			0
$612$	7125.21			0.470620
$613$	8234.58	−	14262.7i	0.542564	−	0.939748i	−0.456192	−	0.889881i	$-0.650787\pi$
$613$	8234.58	−	14262.7i	0.542564	−	0.939748i	0.998756	−	0.0498668i	$-0.0158797\pi$
$614$	−791.505	+	1370.93i	−0.0520237	+	0.0901077i
$615$	−7472.59	−	12942.9i	−0.489958	−	0.848631i
$616$	845.205			0.0552829
$617$	5057.99	+	8760.69i	0.330027	+	0.571624i	0.982517	−	0.186174i	$-0.0596087\pi$
$617$	5057.99	+	8760.69i	0.330027	+	0.571624i	−0.652489	+	0.757798i	$0.726275\pi$
$618$	−468.748	−	811.895i	−0.0305110	−	0.0528466i
$619$	−18854.8			−1.22430			−0.612148	−	0.790743i	$-0.709694\pi$
$619$	−18854.8			−1.22430			−0.612148	+	0.790743i	$0.709694\pi$
$620$	19198.2	+	33252.2i	1.24357	+	2.15393i
$621$	−10465.8	+	18127.3i	−0.676292	+	1.17137i
$622$	−730.247	+	1264.83i	−0.0470743	+	0.0815352i
$623$	3905.86			0.251180
$624$		0			0
$625$	−2730.82			−0.174773
$626$	78.5095	−	135.983i	0.00501258	−	0.00868204i
$627$	3338.26	−	5782.03i	0.212627	−	0.368281i
$628$	−1550.50	−	2685.54i	−0.0985215	−	0.170644i
$629$	291.769			0.0184954
$630$	−284.991	−	493.618i	−0.0180227	−	0.0312162i
$631$	9473.12	+	16407.9i	0.597653	+	1.03517i	0.993167	+	0.116705i	$0.0372333\pi$
$631$	9473.12	+	16407.9i	0.597653	+	1.03517i	−0.395514	+	0.918460i	$0.629433\pi$
$632$	−1403.24			−0.0883194
$633$	2514.17	+	4354.66i	0.157866	+	0.273432i
$634$	668.074	−	1157.14i	0.0418496	−	0.0724856i
$635$	−23186.7	+	40160.5i	−1.44903	+	2.50979i
$636$	−1946.40			−0.121352
$637$		0			0
$638$	−1048.95			−0.0650912
$639$	1026.63	−	1778.18i	0.0635571	−	0.110084i
$640$	7521.75	−	13028.1i	0.464568	−	0.804655i
$641$	11793.5	+	20426.9i	0.726698	+	1.25868i	0.958271	+	0.285861i	$0.0922795\pi$
$641$	11793.5	+	20426.9i	0.726698	+	1.25868i	−0.231573	+	0.972818i	$0.574387\pi$
$642$	−923.263			−0.0567575
$643$	−13576.5	−	23515.2i	−0.832669	−	1.44222i	−0.895915	−	0.444226i	$-0.853479\pi$
$643$	−13576.5	−	23515.2i	−0.832669	−	1.44222i	0.0632461	−	0.997998i	$-0.479855\pi$
$644$	−2983.63	−	5167.79i	−0.182564	−	0.316211i
$645$	−1806.35			−0.110272
$646$	−1204.35	−	2085.99i	−0.0733506	−	0.127047i
$647$	−3428.36	+	5938.09i	−0.208319	+	0.360820i	−0.951185	−	0.308620i	$-0.900133\pi$
$647$	−3428.36	+	5938.09i	−0.208319	+	0.360820i	0.742866	+	0.669440i	$0.233466\pi$
$648$	−645.910	+	1118.75i	−0.0391570	+	0.0678219i
$649$	6527.75			0.394817
$650$		0			0
$651$	5533.83			0.333161
$652$	−3675.09	+	6365.44i	−0.220748	+	0.382346i
$653$	4036.95	−	6992.20i	0.241926	−	0.419029i	−0.719337	−	0.694662i	$-0.755554\pi$
$653$	4036.95	−	6992.20i	0.241926	−	0.419029i	0.961263	+	0.275633i	$0.0888874\pi$
$654$	−142.169	−	246.245i	−0.00850041	−	0.0147231i
$655$	37960.9			2.26451
$656$	6767.39	+	11721.5i	0.402778	+	0.697632i
$657$	−787.061	−	1363.23i	−0.0467370	−	0.0809508i
$658$	759.734			0.0450114
$659$	−2652.86	−	4594.89i	−0.156815	−	0.271611i	0.776904	−	0.629620i	$-0.216789\pi$
$659$	−2652.86	−	4594.89i	−0.156815	−	0.271611i	−0.933718	+	0.358008i	$0.883456\pi$
$660$	−5743.84	+	9948.63i	−0.338756	+	0.586742i
$661$	12924.2	−	22385.3i	0.760502	−	1.31723i	−0.182091	−	0.983282i	$-0.558286\pi$
$661$	12924.2	−	22385.3i	0.760502	−	1.31723i	0.942592	−	0.333946i	$-0.108380\pi$
$662$	−3373.75			−0.198073
$663$		0			0
$664$	2329.85			0.136168
$665$	3912.98	−	6777.48i	0.228179	−	0.395217i
$666$	12.6291	−	21.8743i	0.000734788	−	0.00127269i
$667$	7496.86	+	12984.9i	0.435202	+	0.753792i
$668$	28735.9			1.66441
$669$	1951.89	+	3380.77i	0.112802	+	0.195379i
$670$	−1659.55	−	2874.42i	−0.0956923	−	0.165744i
$671$	14873.6			0.855722
$672$	−816.591	−	1414.38i	−0.0468760	−	0.0811917i
$673$	7264.55	−	12582.6i	0.416089	−	0.720687i	−0.579453	−	0.815005i	$-0.696734\pi$
$673$	7264.55	−	12582.6i	0.416089	−	0.720687i	0.995542	+	0.0943186i	$0.0300673\pi$
$674$	−1033.03	+	1789.26i	−0.0590367	+	0.102255i
$675$	28615.0			1.63169
$676$		0			0
$677$	12058.1			0.684535			0.342267	−	0.939603i	$-0.388805\pi$
$677$	12058.1			0.684535			0.342267	+	0.939603i	$0.388805\pi$
$678$	1021.73	−	1769.68i	0.0578749	−	0.100242i
$679$	−2064.89	+	3576.50i	−0.116706	+	0.202140i
$680$	4195.46	+	7266.74i	0.236601	+	0.409804i
$681$	12764.4			0.718255
$682$	−1357.50	−	2351.26i	−0.0762190	−	0.132015i
$683$	15014.4	+	26005.7i	0.841156	+	1.45693i	0.888918	+	0.458067i	$0.151458\pi$
$683$	15014.4	+	26005.7i	0.841156	+	1.45693i	−0.0477615	+	0.998859i	$0.515209\pi$
$684$	8469.13			0.473429
$685$	6125.74	+	10610.1i	0.341682	+	0.591811i
$686$	−782.611	+	1355.52i	−0.0435572	+	0.0754433i
$687$	4282.75	−	7417.94i	0.237842	−	0.411954i
$688$	1635.89			0.0906505
$689$		0			0
$690$	−4042.94			−0.223061
$691$	224.848	−	389.448i	0.0123786	−	0.0214404i	−0.859770	−	0.510682i	$-0.829393\pi$
$691$	224.848	−	389.448i	0.0123786	−	0.0214404i	0.872148	+	0.489241i	$0.162726\pi$
$692$	5554.34	−	9620.40i	0.305122	−	0.528487i
$693$	−818.471	−	1417.63i	−0.0448646	−	0.0777077i
$694$	−2307.10			−0.126191
$695$	6050.90	+	10480.5i	0.330250	+	0.572010i
$696$	1362.36	+	2359.68i	0.0741955	+	0.128510i
$697$	−15484.8			−0.841506
$698$	11.0345	+	19.1123i	0.000598370	+	0.00103641i
$699$	−6873.75	+	11905.7i	−0.371944	+	0.644227i
$700$	−4078.84	+	7064.75i	−0.220236	+	0.381461i
$701$	−26986.0			−1.45399			−0.726994	−	0.686644i	$-0.759083\pi$
$701$	−26986.0			−1.45399			−0.726994	+	0.686644i	$0.759083\pi$
$702$		0			0
$703$	346.801			0.0186057
$704$	4929.23	−	8537.67i	0.263888	−	0.457068i
$705$	−10453.1	+	18105.3i	−0.558422	+	0.967215i
$706$	1985.65	+	3439.24i	0.105851	+	0.183339i
$707$	1896.37			0.100877
$708$	−4187.53	−	7253.01i	−0.222284	−	0.385007i
$709$	−4549.44	−	7879.85i	−0.240984	−	0.417396i	0.720011	−	0.693963i	$-0.244137\pi$
$709$	−4549.44	−	7879.85i	−0.240984	−	0.417396i	−0.960995	+	0.276566i	$0.910803\pi$
$710$	1194.30			0.0631285
$711$	1358.85	+	2353.60i	0.0716751	+	0.124145i
$712$	−2488.85	+	4310.82i	−0.131002	+	0.226903i
$713$	−19404.2	+	33609.1i	−1.01921	+	1.76532i
$714$	597.312			0.0313079
$715$		0			0
$716$	−9118.62			−0.475948
$717$	−11135.9	+	19287.9i	−0.580025	+	1.00463i
$718$	1573.56	−	2725.48i	0.0817892	−	0.141663i
$719$	3146.78	+	5450.38i	0.163220	+	0.282705i	0.936022	−	0.351942i	$-0.114479\pi$
$719$	3146.78	+	5450.38i	0.163220	+	0.282705i	−0.772802	+	0.634647i	$0.781145\pi$
$720$	−14204.5			−0.735235
$721$	−1577.97	−	2733.13i	−0.0815074	−	0.141175i
$722$	72.1476	+	124.963i	0.00371892	+	0.00644135i
$723$	−19064.3			−0.980648
$724$	−4426.86	−	7667.54i	−0.227242	−	0.393594i
$725$	10248.8	−	17751.4i	0.525006	−	0.909337i
$726$	−668.987	+	1158.72i	−0.0341989	+	0.0592343i
$727$	18070.7			0.921878			0.460939	−	0.887432i	$-0.347513\pi$
$727$	18070.7			0.921878			0.460939	+	0.887432i	$0.347513\pi$
$728$		0			0
$729$	17319.9			0.879944
$730$	457.800	−	792.934i	0.0232109	−	0.0402025i
$731$	−935.790	+	1620.84i	−0.0473481	+	0.0820093i
$732$	−9541.37	−	16526.1i	−0.481775	−	0.834459i
$733$	−34771.5			−1.75214			−0.876068	−	0.482188i	$-0.839842\pi$
$733$	−34771.5			−1.75214			−0.876068	+	0.482188i	$0.839842\pi$
$734$	−877.803	−	1520.40i	−0.0441421	−	0.0764563i
$735$	−10282.7	−	17810.2i	−0.516032	−	0.893794i
$736$	11453.4			0.573613
$737$	−4766.09	−	8255.10i	−0.238210	−	0.412592i
$738$	−670.256	+	1160.92i	−0.0334315	+	0.0579051i
$739$	11815.7	−	20465.4i	0.588158	−	1.01872i	−0.406316	−	0.913733i	$-0.633187\pi$
$739$	11815.7	−	20465.4i	0.588158	−	1.01872i	0.994474	−	0.104986i	$-0.0334799\pi$
$740$	−596.710			−0.0296425
$741$		0			0
$742$	161.324			0.00798167
$743$	16251.4	−	28148.3i	0.802431	−	1.38985i	−0.115581	−	0.993298i	$-0.536873\pi$
$743$	16251.4	−	28148.3i	0.802431	−	1.38985i	0.918012	−	0.396553i	$-0.129794\pi$
$744$	−3526.21	+	6107.58i	−0.173760	+	0.300961i
$745$	−17589.3	−	30465.5i	−0.864995	−	1.49822i
$746$	−4390.69			−0.215489
$747$	−2256.16	−	3907.78i	−0.110507	−	0.191403i
$748$	5951.25	+	10307.9i	0.290908	+	0.503868i
$749$	−3108.04			−0.151622
$750$	965.435	+	1672.18i	0.0470036	+	0.0814126i
$751$	−1010.43	+	1750.12i	−0.0490960	+	0.0850368i	−0.889529	−	0.456879i	$-0.848967\pi$
$751$	−1010.43	+	1750.12i	−0.0490960	+	0.0850368i	0.840433	+	0.541915i	$0.182301\pi$
$752$	9466.65	−	16396.7i	0.459060	−	0.795115i
$753$	−20710.5			−1.00230
$754$		0			0
$755$	−32111.6			−1.54790
$756$	−3162.28	+	5477.23i	−0.152131	+	0.263499i
$757$	−6284.11	+	10884.4i	−0.301717	+	0.522589i	−0.976525	−	0.215404i	$-0.930893\pi$
$757$	−6284.11	+	10884.4i	−0.301717	+	0.522589i	0.674808	+	0.737993i	$0.264226\pi$
$758$	−1790.86	−	3101.87i	−0.0858141	−	0.148634i
$759$	−11611.0			−0.555273
$760$	4986.78	+	8637.36i	0.238013	+	0.412250i
$761$	−4352.40	−	7538.59i	−0.207325	−	0.359098i	0.743546	−	0.668685i	$-0.233143\pi$
$761$	−4352.40	−	7538.59i	−0.207325	−	0.359098i	−0.950871	+	0.309587i	$0.899809\pi$
$762$	−4207.01			−0.200005
$763$	−478.593	−	828.948i	−0.0227081	−	0.0393315i
$764$	10470.7	−	18135.8i	0.495832	−	0.858807i
$765$	8125.51	−	14073.8i	0.384024	−	0.665149i
$766$	3205.16			0.151184
$767$		0			0
$768$	−11595.0			−0.544790
$769$	−10957.9	+	18979.7i	−0.513853	+	0.890020i	0.486018	+	0.873949i	$0.338449\pi$
$769$	−10957.9	+	18979.7i	−0.513853	+	0.890020i	−0.999871	+	0.0160706i	$0.994884\pi$
$770$	476.070	−	824.578i

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)

\(f(q)\)	\(=\)	\(q+(-0.219224 + 0.379706i) q^{2} +(1.84233 - 3.19101i) q^{3} +(3.90388 + 6.76172i) q^{4} +17.8078 q^{5} +(0.807764 + 1.39909i) q^{6} +(2.71922 + 4.70983i) q^{7} -6.93087 q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})\)	\(q+(-0.219224 + 0.379706i) q^{2} +(1.84233 - 3.19101i) q^{3} +(3.90388 + 6.76172i) q^{4} +17.8078 q^{5} +(0.807764 + 1.39909i) q^{6} +(2.71922 + 4.70983i) q^{7} -6.93087 q^{8} +(6.71165 + 11.6249i) q^{9} +(-3.90388 + 6.76172i) q^{10} +(-11.2116 + 19.4191i) q^{11} +28.7689 q^{12} -2.38447 q^{14} +(32.8078 - 56.8247i) q^{15} +(-29.7116 + 51.4621i) q^{16} +(-33.9924 - 58.8766i) q^{17} -5.88540 q^{18} +(-40.4039 - 69.9816i) q^{19} +(69.5194 + 120.411i) q^{20} +20.0388 q^{21} +(-4.91571 - 8.51427i) q^{22} +(-70.2656 + 121.704i) q^{23} +(-12.7689 + 22.1165i) q^{24} +192.116 q^{25} +148.946 q^{27} +(-21.2311 + 36.7733i) q^{28} +(53.3466 - 92.3990i) q^{29} +(14.3845 + 24.9146i) q^{30} +276.155 q^{31} +(-40.7505 - 70.5819i) q^{32} +(41.3111 + 71.5529i) q^{33} +29.8078 q^{34} +(48.4233 + 83.8716i) q^{35} +(-52.4029 + 90.7646i) q^{36} +(-2.14584 + 3.71670i) q^{37} +35.4299 q^{38} -123.423 q^{40} +(113.884 - 197.254i) q^{41} +(-4.39298 + 7.60887i) q^{42} +(-13.7647 - 23.8411i) q^{43} -175.076 q^{44} +(119.519 + 207.014i) q^{45} +(-30.8078 - 53.3606i) q^{46} -318.617 q^{47} +(109.477 + 189.620i) q^{48} +(156.712 - 271.433i) q^{49} +(-42.1165 + 72.9479i) q^{50} -250.501 q^{51} -67.6562 q^{53} +(-32.6525 + 56.5558i) q^{54} +(-199.654 + 345.811i) q^{55} +(-18.8466 - 32.6432i) q^{56} -297.749 q^{57} +(23.3897 + 40.5121i) q^{58} +(-145.557 - 252.113i) q^{59} +512.311 q^{60} +(-331.655 - 574.444i) q^{61} +(-60.5398 + 104.858i) q^{62} +(-36.5009 + 63.2215i) q^{63} -439.652 q^{64} -36.2255 q^{66} +(-212.551 + 368.149i) q^{67} +(265.405 - 459.695i) q^{68} +(258.905 + 448.436i) q^{69} -42.4621 q^{70} +(-76.4815 - 132.470i) q^{71} +(-46.5175 - 80.5708i) q^{72} -117.268 q^{73} +(-0.940837 - 1.62958i) q^{74} +(353.942 - 613.045i) q^{75} +(315.464 - 546.400i) q^{76} -121.948 q^{77} +202.462 q^{79} +(-529.098 + 916.425i) q^{80} +(93.1932 - 161.415i) q^{81} +(49.9323 + 86.4853i) q^{82} -336.155 q^{83} +(78.2292 + 135.497i) q^{84} +(-605.329 - 1048.46i) q^{85} +12.0702 q^{86} +(-196.564 - 340.459i) q^{87} +(77.7065 - 134.592i) q^{88} +(359.097 - 621.974i) q^{89} -104.806 q^{90} -1097.23 q^{92} +(508.769 - 881.214i) q^{93} +(69.8485 - 120.981i) q^{94} +(-719.503 - 1246.22i) q^{95} -300.303 q^{96} +(379.684 + 657.632i) q^{97} +(68.7098 + 119.009i) q^{98} -300.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9	\( 4 q - 5 q^{2} - 5 q^{3} - 5 q^{4} + 30 q^{5} - 38 q^{6} + 15 q^{7} + 30 q^{8} - 35 q^{9} + 5 q^{10} + 17 q^{11} + 280 q^{12} - 92 q^{14} + 90 q^{15} - 57 q^{16} - 70 q^{17} + 430 q^{18} - 141 q^{19} + 175 q^{20} - 126 q^{21} + 170 q^{22} - 145 q^{23} - 216 q^{24} + 150 q^{25} + 670 q^{27} + 80 q^{28} - 34 q^{29} + 140 q^{30} + 280 q^{31} + 105 q^{32} + 425 q^{33} + 78 q^{34} + 70 q^{35} - 725 q^{36} - 190 q^{37} + 620 q^{38} - 370 q^{40} + 538 q^{41} + 370 q^{42} - 455 q^{43} - 1360 q^{44} + 375 q^{45} - 82 q^{46} - 120 q^{47} + 240 q^{48} + 565 q^{49} + 450 q^{50} - 466 q^{51} + 1090 q^{53} - 914 q^{54} - 510 q^{55} + 172 q^{56} + 450 q^{57} - 595 q^{58} - 809 q^{59} + 400 q^{60} - 502 q^{61} + 500 q^{62} + 390 q^{63} - 2542 q^{64} - 3196 q^{66} - 475 q^{67} + 505 q^{68} + 479 q^{69} + 160 q^{70} + 127 q^{71} - 1155 q^{72} - 1170 q^{73} - 849 q^{74} + 1725 q^{75} - 140 q^{76} + 510 q^{77} + 480 q^{79} - 1065 q^{80} - 122 q^{81} + 1515 q^{82} - 520 q^{83} + 1220 q^{84} - 1205 q^{85} + 3924 q^{86} - 1615 q^{87} + 1020 q^{88} + 921 q^{89} - 1450 q^{90} - 2080 q^{92} + 2200 q^{93} - 1040 q^{94} - 1270 q^{95} - 3840 q^{96} - 415 q^{97} + 1285 q^{98} - 4420 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 + 30 * q^5 - 38 * q^6 + 15 * q^7 + 30 * q^8 - 35 * q^9 + 5 * q^10 + 17 * q^11 + 280 * q^12 - 92 * q^14 + 90 * q^15 - 57 * q^16 - 70 * q^17 + 430 * q^18 - 141 * q^19 + 175 * q^20 - 126 * q^21 + 170 * q^22 - 145 * q^23 - 216 * q^24 + 150 * q^25 + 670 * q^27 + 80 * q^28 - 34 * q^29 + 140 * q^30 + 280 * q^31 + 105 * q^32 + 425 * q^33 + 78 * q^34 + 70 * q^35 - 725 * q^36 - 190 * q^37 + 620 * q^38 - 370 * q^40 + 538 * q^41 + 370 * q^42 - 455 * q^43 - 1360 * q^44 + 375 * q^45 - 82 * q^46 - 120 * q^47 + 240 * q^48 + 565 * q^49 + 450 * q^50 - 466 * q^51 + 1090 * q^53 - 914 * q^54 - 510 * q^55 + 172 * q^56 + 450 * q^57 - 595 * q^58 - 809 * q^59 + 400 * q^60 - 502 * q^61 + 500 * q^62 + 390 * q^63 - 2542 * q^64 - 3196 * q^66 - 475 * q^67 + 505 * q^68 + 479 * q^69 + 160 * q^70 + 127 * q^71 - 1155 * q^72 - 1170 * q^73 - 849 * q^74 + 1725 * q^75 - 140 * q^76 + 510 * q^77 + 480 * q^79 - 1065 * q^80 - 122 * q^81 + 1515 * q^82 - 520 * q^83 + 1220 * q^84 - 1205 * q^85 + 3924 * q^86 - 1615 * q^87 + 1020 * q^88 + 921 * q^89 - 1450 * q^90 - 2080 * q^92 + 2200 * q^93 - 1040 * q^94 - 1270 * q^95 - 3840 * q^96 - 415 * q^97 + 1285 * q^98 - 4420 * q^99

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