LMFDB - Embedded newform 690.3.g.a.461.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(461,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.461");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.g (of order $2$, degree $1$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.16
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +3.16228 q^{10} -14.6872i q^{11} +(-1.76041 - 5.73594i) q^{12} +18.4837 q^{13} -4.53789i q^{14} +(6.41297 - 1.96819i) q^{15} +4.00000 q^{16} -27.0341i q^{17} +(-7.14007 - 10.5366i) q^{18} -5.52980 q^{19} +4.47214i q^{20} +(-2.82437 - 9.20266i) q^{21} +20.7708 q^{22} +4.79583i q^{23} +(8.11184 - 2.48959i) q^{24} -5.00000 q^{25} +26.1399i q^{26} +(-21.0377 - 16.9238i) q^{27} +6.41754 q^{28} +8.45614i q^{29} +(2.78345 + 9.06931i) q^{30} +49.6101 q^{31} +5.65685i q^{32} +(42.1224 - 12.9277i) q^{33} +38.2320 q^{34} +7.17503i q^{35} +(14.9010 - 10.0976i) q^{36} +42.6353 q^{37} -7.82032i q^{38} +(16.2694 + 53.0108i) q^{39} -6.32456 q^{40} -20.1288i q^{41} +(13.0145 - 3.99426i) q^{42} -17.0418 q^{43} +29.3744i q^{44} +(11.2894 + 16.6598i) q^{45} -6.78233 q^{46} -52.7239i q^{47} +(3.52081 + 11.4719i) q^{48} -38.7038 q^{49} -7.07107i q^{50} +(77.5330 - 23.7955i) q^{51} -36.9675 q^{52} -3.72931i q^{53} +(23.9339 - 29.7518i) q^{54} -32.8416 q^{55} +9.07578i q^{56} +(-4.86735 - 15.8593i) q^{57} -11.9588 q^{58} -29.1113i q^{59} +(-12.8259 + 3.93639i) q^{60} +8.31060 q^{61} +70.1592i q^{62} +(23.9069 - 16.2004i) q^{63} -8.00000 q^{64} -41.3309i q^{65} +(18.2825 + 59.5701i) q^{66} +0.327172 q^{67} +54.0683i q^{68} +(-13.7543 + 4.22131i) q^{69} -10.1470 q^{70} +69.2777i q^{71} +(14.2801 + 21.0732i) q^{72} +22.6543 q^{73} +60.2955i q^{74} +(-4.40102 - 14.3398i) q^{75} +11.0596 q^{76} +47.1278i q^{77} +(-74.9685 + 23.0085i) q^{78} +68.6785 q^{79} -8.94427i q^{80} +(30.0195 - 75.2319i) q^{81} +28.4664 q^{82} -73.2079i q^{83} +(5.64874 + 18.4053i) q^{84} -60.4501 q^{85} -24.1008i q^{86} +(-24.2519 + 7.44312i) q^{87} -41.5416 q^{88} +72.4059i q^{89} +(-23.5605 + 15.9657i) q^{90} -59.3101 q^{91} -9.59166i q^{92} +(43.6669 + 142.280i) q^{93} +74.5628 q^{94} +12.3650i q^{95} +(-16.2237 + 4.97918i) q^{96} +89.0797 q^{97} -54.7354i q^{98} +(74.1525 + 109.427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	0.880203	+	2.86797i	0.293401	+	0.955989i
$3$	0.880203	+	2.86797i	0.293401	+	0.955989i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−4.05592	+	1.24480i	−0.675987	+	0.207466i
$7$	−3.20877			−0.458396			−0.229198	−	0.973380i	$-0.573610\pi$
$7$	−3.20877			−0.458396			−0.229198	+	0.973380i	$0.573610\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−7.45049	+	5.04879i	−0.827832	+	0.560977i
$10$	3.16228			0.316228
$11$		−	14.6872i		−	1.33520i	−0.744521	−	0.667599i	$-0.767322\pi$
$11$		−	14.6872i		−	1.33520i	0.744521	−	0.667599i	$-0.232678\pi$
$12$	−1.76041	−	5.73594i	−0.146701	−	0.477995i
$13$	18.4837			1.42183			0.710913	−	0.703280i	$-0.248282\pi$
$13$	18.4837			1.42183			0.710913	+	0.703280i	$0.248282\pi$
$14$		−	4.53789i		−	0.324135i
$15$	6.41297	−	1.96819i	0.427531	−	0.131213i
$16$	4.00000			0.250000
$17$		−	27.0341i		−	1.59024i	−0.606450	−	0.795121i	$-0.707407\pi$
$17$		−	27.0341i		−	1.59024i	0.606450	−	0.795121i	$-0.292593\pi$
$18$	−7.14007	−	10.5366i	−0.396670	−	0.585365i
$19$	−5.52980			−0.291042			−0.145521	−	0.989355i	$-0.546486\pi$
$19$	−5.52980			−0.291042			−0.145521	+	0.989355i	$0.546486\pi$
$20$			4.47214i			0.223607i
$21$	−2.82437	−	9.20266i	−0.134494	−	0.438222i
$22$	20.7708			0.944128
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	8.11184	−	2.48959i	0.337993	−	0.103733i
$25$	−5.00000			−0.200000
$26$			26.1399i			1.00538i
$27$	−21.0377	−	16.9238i	−0.779174	−	0.626807i
$28$	6.41754			0.229198
$29$			8.45614i			0.291591i	0.989315	+	0.145796i	$0.0465742\pi$
$29$			8.45614i			0.291591i	−0.989315	+	0.145796i	$0.953426\pi$
$30$	2.78345	+	9.06931i	0.0927816	+	0.302310i
$31$	49.6101			1.60032			0.800162	−	0.599783i	$-0.204747\pi$
$31$	49.6101			1.60032			0.800162	+	0.599783i	$0.204747\pi$
$32$			5.65685i			0.176777i
$33$	42.1224	−	12.9277i	1.27644	−	0.391749i
$34$	38.2320			1.12447
$35$			7.17503i			0.205001i
$36$	14.9010	−	10.0976i	0.413916	−	0.280488i
$37$	42.6353			1.15231			0.576153	−	0.817342i	$-0.304553\pi$
$37$	42.6353			1.15231			0.576153	+	0.817342i	$0.304553\pi$
$38$		−	7.82032i		−	0.205798i
$39$	16.2694	+	53.0108i	0.417165	+	1.35925i
$40$	−6.32456			−0.158114
$41$		−	20.1288i		−	0.490946i	−0.969403	−	0.245473i	$-0.921057\pi$
$41$		−	20.1288i		−	0.490946i	0.969403	−	0.245473i	$-0.0789432\pi$
$42$	13.0145	−	3.99426i	0.309870	−	0.0951015i
$43$	−17.0418			−0.396321			−0.198161	−	0.980170i	$-0.563497\pi$
$43$	−17.0418			−0.396321			−0.198161	+	0.980170i	$0.563497\pi$
$44$			29.3744i			0.667599i
$45$	11.2894	+	16.6598i	0.250876	+	0.370218i
$46$	−6.78233			−0.147442
$47$		−	52.7239i		−	1.12178i	−0.827889	−	0.560892i	$-0.810458\pi$
$47$		−	52.7239i		−	1.12178i	0.827889	−	0.560892i	$-0.189542\pi$
$48$	3.52081	+	11.4719i	0.0733503	+	0.238997i
$49$	−38.7038			−0.789873
$50$		−	7.07107i		−	0.141421i
$51$	77.5330	−	23.7955i	1.52026	−	0.466579i
$52$	−36.9675			−0.710913
$53$		−	3.72931i		−	0.0703643i	−0.999381	−	0.0351821i	$-0.988799\pi$
$53$		−	3.72931i		−	0.0703643i	0.999381	−	0.0351821i	$-0.0112011\pi$
$54$	23.9339	−	29.7518i	0.443220	−	0.550959i
$55$	−32.8416			−0.597119
$56$			9.07578i			0.162067i
$57$	−4.86735	−	15.8593i	−0.0853921	−	0.278233i
$58$	−11.9588			−0.206186
$59$		−	29.1113i		−	0.493412i	−0.969090	−	0.246706i	$-0.920652\pi$
$59$		−	29.1113i		−	0.493412i	0.969090	−	0.246706i	$-0.0793481\pi$
$60$	−12.8259	+	3.93639i	−0.213766	+	0.0656065i
$61$	8.31060			0.136239			0.0681196	−	0.997677i	$-0.478300\pi$
$61$	8.31060			0.136239			0.0681196	+	0.997677i	$0.478300\pi$
$62$			70.1592i			1.13160i
$63$	23.9069	−	16.2004i	0.379475	−	0.257149i
$64$	−8.00000			−0.125000
$65$		−	41.3309i		−	0.635860i
$66$	18.2825	+	59.5701i	0.277008	+	0.902577i
$67$	0.327172			0.00488317			0.00244158	−	0.999997i	$-0.499223\pi$
$67$	0.327172			0.00488317			0.00244158	+	0.999997i	$0.499223\pi$
$68$			54.0683i			0.795121i
$69$	−13.7543	+	4.22131i	−0.199338	+	0.0611783i
$70$	−10.1470			−0.144958
$71$			69.2777i			0.975742i	0.872916	+	0.487871i	$0.162226\pi$
$71$			69.2777i			0.975742i	−0.872916	+	0.487871i	$0.837774\pi$
$72$	14.2801	+	21.0732i	0.198335	+	0.292683i
$73$	22.6543			0.310333			0.155166	−	0.987888i	$-0.450409\pi$
$73$	22.6543			0.310333			0.155166	+	0.987888i	$0.450409\pi$
$74$			60.2955i			0.814804i
$75$	−4.40102	−	14.3398i	−0.0586802	−	0.191198i
$76$	11.0596			0.145521
$77$			47.1278i			0.612050i
$78$	−74.9685	+	23.0085i	−0.961135	+	0.294980i
$79$	68.6785			0.869348			0.434674	−	0.900588i	$-0.356864\pi$
$79$	68.6785			0.869348			0.434674	+	0.900588i	$0.356864\pi$
$80$		−	8.94427i		−	0.111803i
$81$	30.0195	−	75.2319i	0.370611	−	0.928788i
$82$	28.4664			0.347151
$83$		−	73.2079i		−	0.882022i	−0.897502	−	0.441011i	$-0.854620\pi$
$83$		−	73.2079i		−	0.882022i	0.897502	−	0.441011i	$-0.145380\pi$
$84$	5.64874	+	18.4053i	0.0672469	+	0.219111i
$85$	−60.4501			−0.711178
$86$		−	24.1008i		−	0.280242i
$87$	−24.2519	+	7.44312i	−0.278758	+	0.0855531i
$88$	−41.5416			−0.472064
$89$			72.4059i			0.813550i	0.913528	+	0.406775i	$0.133347\pi$
$89$			72.4059i			0.813550i	−0.913528	+	0.406775i	$0.866653\pi$
$90$	−23.5605	+	15.9657i	−0.261783	+	0.177396i
$91$	−59.3101			−0.651759
$92$		−	9.59166i		−	0.104257i
$93$	43.6669	+	142.280i	0.469537	+	1.52989i
$94$	74.5628			0.793222
$95$			12.3650i			0.130158i
$96$	−16.2237	+	4.97918i	−0.168997	+	0.0518665i
$97$	89.0797			0.918348			0.459174	−	0.888346i	$-0.348145\pi$
$97$	89.0797			0.918348			0.459174	+	0.888346i	$0.348145\pi$
$98$		−	54.7354i		−	0.558525i
$99$	74.1525	+	109.427i	0.749015	+	1.10532i
$100$	10.0000			0.100000
$101$		−	84.9463i		−	0.841052i	−0.907280	−	0.420526i	$-0.861845\pi$
$101$		−	84.9463i		−	0.841052i	0.907280	−	0.420526i	$-0.138155\pi$
$102$	33.6520	+	109.648i	0.329921	+	1.07498i
$103$	−161.088			−1.56396			−0.781981	−	0.623303i	$-0.785791\pi$
$103$	−161.088			−1.56396			−0.781981	+	0.623303i	$0.785791\pi$
$104$		−	52.2799i		−	0.502691i
$105$	−20.5778	+	6.31548i	−0.195979	+	0.0601475i
$106$	5.27404			0.0497551
$107$			27.8404i			0.260191i	0.991501	+	0.130095i	$0.0415284\pi$
$107$			27.8404i			0.260191i	−0.991501	+	0.130095i	$0.958472\pi$
$108$	42.0754	+	33.8476i	0.389587	+	0.313404i
$109$	213.350			1.95734			0.978672	−	0.205431i	$-0.0658596\pi$
$109$	213.350			1.95734			0.978672	+	0.205431i	$0.0658596\pi$
$110$		−	46.4450i		−	0.422227i
$111$	37.5278	+	122.277i	0.338088	+	1.10159i
$112$	−12.8351			−0.114599
$113$		−	33.6988i		−	0.298219i	−0.988821	−	0.149110i	$-0.952359\pi$
$113$		−	33.6988i		−	0.298219i	0.988821	−	0.149110i	$-0.0476408\pi$
$114$	22.4284	−	6.88347i	0.196741	−	0.0603813i
$115$	10.7238			0.0932505
$116$		−	16.9123i		−	0.145796i
$117$	−137.713	+	93.3205i	−1.17703	+	0.797611i
$118$	41.1696			0.348895
$119$			86.7463i			0.728961i
$120$	−5.56689	−	18.1386i	−0.0463908	−	0.151155i
$121$	−94.7135			−0.782756
$122$			11.7530i			0.0963357i
$123$	57.7287	−	17.7174i	0.469339	−	0.144044i
$124$	−99.2201			−0.800162
$125$			11.1803i			0.0894427i
$126$	22.9108	+	33.8095i	0.181832	+	0.268329i
$127$	−150.876			−1.18800			−0.593999	−	0.804466i	$-0.702452\pi$
$127$	−150.876			−1.18800			−0.593999	+	0.804466i	$0.702452\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−15.0003	−	48.8754i	−0.116281	−	0.378879i
$130$	58.4507			0.449621
$131$		−	132.703i		−	1.01300i	−0.862239	−	0.506501i	$-0.830939\pi$
$131$		−	132.703i		−	1.01300i	0.862239	−	0.506501i	$-0.169061\pi$
$132$	−84.2448	+	25.8554i	−0.638218	+	0.195874i
$133$	17.7439			0.133413
$134$			0.462692i			0.00345292i
$135$	−37.8428	+	47.0417i	−0.280317	+	0.348457i
$136$	−76.4641			−0.562236
$137$		−	41.0423i		−	0.299579i	−0.988718	−	0.149789i	$-0.952140\pi$
$137$		−	41.0423i		−	0.299579i	0.988718	−	0.149789i	$-0.0478596\pi$
$138$	−5.96983	−	19.4515i	−0.0432596	−	0.140953i
$139$	−100.667			−0.724219			−0.362110	−	0.932135i	$-0.617943\pi$
$139$	−100.667			−0.724219			−0.362110	+	0.932135i	$0.617943\pi$
$140$		−	14.3501i		−	0.102500i
$141$	151.210	−	46.4077i	1.07241	−	0.329133i
$142$	−97.9734			−0.689954
$143$		−	271.474i		−	1.89842i
$144$	−29.8019	+	20.1952i	−0.206958	+	0.140244i
$145$	18.9085			0.130403
$146$			32.0380i			0.219438i
$147$	−34.0672	−	111.001i	−0.231750	−	0.755110i
$148$	−85.2707			−0.576153
$149$		−	54.7479i		−	0.367435i	−0.982979	−	0.183718i	$-0.941187\pi$
$149$		−	54.7479i		−	0.367435i	0.982979	−	0.183718i	$-0.0588132\pi$
$150$	20.2796	−	6.22398i	0.135197	−	0.0414932i
$151$	91.6265			0.606798			0.303399	−	0.952864i	$-0.401879\pi$
$151$	91.6265			0.606798			0.303399	+	0.952864i	$0.401879\pi$
$152$			15.6406i			0.102899i
$153$	136.490	+	201.417i	0.892089	+	1.31645i
$154$	−66.6488			−0.432785
$155$		−	110.931i		−	0.715687i
$156$	−32.5389	−	106.022i	−0.208583	−	0.679625i
$157$	76.9201			0.489937			0.244968	−	0.969531i	$-0.421222\pi$
$157$	76.9201			0.489937			0.244968	+	0.969531i	$0.421222\pi$
$158$			97.1261i			0.614722i
$159$	10.6955	−	3.28255i	0.0672675	−	0.0206450i
$160$	12.6491			0.0790569
$161$		−	15.3887i		−	0.0955822i
$162$	106.394	+	42.4539i	0.656753	+	0.262061i
$163$	−28.7684			−0.176493			−0.0882465	−	0.996099i	$-0.528126\pi$
$163$	−28.7684			−0.176493			−0.0882465	+	0.996099i	$0.528126\pi$
$164$			40.2575i			0.245473i
$165$	−28.9072	−	94.1885i	−0.175195	−	0.570840i
$166$	103.532			0.623684
$167$			61.3209i			0.367191i	0.983002	+	0.183595i	$0.0587737\pi$
$167$			61.3209i			0.367191i	−0.983002	+	0.183595i	$0.941226\pi$
$168$	−26.0290	+	7.98853i	−0.154935	+	0.0475508i
$169$	172.648			1.02159
$170$		−	85.4894i		−	0.502879i
$171$	41.1997	−	27.9188i	0.240934	−	0.163268i
$172$	34.0836			0.198161
$173$		−	267.085i		−	1.54385i	−0.635716	−	0.771923i	$-0.719295\pi$
$173$		−	267.085i		−	1.54385i	0.635716	−	0.771923i	$-0.280705\pi$
$174$	−10.5262	−	34.2974i	−0.0604952	−	0.197112i
$175$	16.0439			0.0916792
$176$		−	58.7488i		−	0.333800i
$177$	83.4903	−	25.6238i	0.471696	−	0.144767i
$178$	−102.397			−0.575266
$179$			49.4363i			0.276180i	0.990420	+	0.138090i	$0.0440964\pi$
$179$			49.4363i			0.276180i	−0.990420	+	0.138090i	$0.955904\pi$
$180$	−22.5789	−	33.3196i	−0.125438	−	0.185109i
$181$	285.987			1.58004			0.790019	−	0.613082i	$-0.210070\pi$
$181$	285.987			1.58004			0.790019	+	0.613082i	$0.210070\pi$
$182$		−	83.8771i		−	0.460863i
$183$	7.31501	+	23.8345i	0.0399727	+	0.130243i
$184$	13.5647			0.0737210
$185$		−	95.3355i		−	0.515327i
$186$	−201.214	+	61.7544i	−1.08180	+	0.332013i
$187$	−397.055			−2.12329
$188$			105.448i			0.560892i
$189$	67.5052	+	54.3046i	0.357170	+	0.287326i
$190$	−17.4868			−0.0920356
$191$		−	265.836i		−	1.39181i	−0.718133	−	0.695906i	$-0.755003\pi$
$191$		−	265.836i		−	1.39181i	0.718133	−	0.695906i	$-0.244997\pi$
$192$	−7.04162	−	22.9437i	−0.0366751	−	0.119499i
$193$	−229.353			−1.18836			−0.594178	−	0.804333i	$-0.702523\pi$
$193$	−229.353			−1.18836			−0.594178	+	0.804333i	$0.702523\pi$
$194$			125.978i			0.649370i
$195$	118.536	−	36.3796i	0.607875	−	0.186562i
$196$	77.4076			0.394937
$197$			79.4445i			0.403272i	0.979461	+	0.201636i	$0.0646258\pi$
$197$			79.4445i			0.403272i	−0.979461	+	0.201636i	$0.935374\pi$
$198$	−154.753	+	104.867i	−0.781579	+	0.529634i
$199$	−216.050			−1.08568			−0.542840	−	0.839836i	$-0.682651\pi$
$199$	−216.050			−1.08568			−0.542840	+	0.839836i	$0.682651\pi$
$200$			14.1421i			0.0707107i
$201$	0.287978	+	0.938320i	0.00143273	+	0.00466826i
$202$	120.132			0.594714
$203$		−	27.1338i		−	0.133664i
$204$	−155.066	+	47.5910i	−0.760128	+	0.233289i
$205$	−45.0093			−0.219558
$206$		−	227.813i		−	1.10589i
$207$	−24.2131	−	35.7313i	−0.116972	−	0.172615i
$208$	73.9349			0.355456
$209$			81.2172i			0.388599i
$210$	−8.93144	−	29.1014i	−0.0425307	−	0.138578i
$211$	111.332			0.527640			0.263820	−	0.964572i	$-0.415017\pi$
$211$	111.332			0.527640			0.263820	+	0.964572i	$0.415017\pi$
$212$			7.45861i			0.0351821i
$213$	−198.686	+	60.9784i	−0.932799	+	0.286284i
$214$	−39.3723			−0.183983
$215$			38.1067i			0.177240i
$216$	−47.8677	+	59.5036i	−0.221610	+	0.275480i
$217$	−159.187			−0.733582
$218$			301.723i			1.38405i
$219$	19.9404	+	64.9717i	0.0910519	+	0.296675i
$220$	65.6831			0.298560
$221$		−	499.692i		−	2.26105i
$222$	−172.926	+	53.0723i	−0.778944	+	0.239064i
$223$	−257.455			−1.15451			−0.577254	−	0.816565i	$-0.695876\pi$
$223$	−257.455			−1.15451			−0.577254	+	0.816565i	$0.695876\pi$
$224$		−	18.1516i		−	0.0810337i
$225$	37.2524	−	25.2439i	0.165566	−	0.112195i
$226$	47.6573			0.210873
$227$		−	2.14581i		−	0.00945290i	−0.999989	−	0.00472645i	$-0.998496\pi$
$227$		−	2.14581i		−	0.00945290i	0.999989	−	0.00472645i	$-0.00150448\pi$
$228$	9.73470	+	31.7186i	0.0426960	+	0.139117i
$229$	−107.929			−0.471305			−0.235653	−	0.971837i	$-0.575723\pi$
$229$	−107.929			−0.471305			−0.235653	+	0.971837i	$0.575723\pi$
$230$			15.1658i			0.0659380i
$231$	−135.161	+	41.4821i	−0.585113	+	0.179576i
$232$	23.9176			0.103093
$233$		−	155.714i		−	0.668300i	−0.942520	−	0.334150i	$-0.891551\pi$
$233$		−	155.714i		−	0.668300i	0.942520	−	0.334150i	$-0.108449\pi$
$234$	−131.975	−	194.755i	−0.563996	−	0.832287i
$235$	−117.894			−0.501677
$236$			58.2226i			0.246706i
$237$	60.4510	+	196.968i	0.255068	+	0.831088i
$238$	−122.678			−0.515453
$239$			435.813i			1.82349i	0.410761	+	0.911743i	$0.365263\pi$
$239$			435.813i			1.82349i	−0.410761	+	0.911743i	$0.634737\pi$
$240$	25.6519	−	7.87278i	0.106883	−	0.0328032i
$241$	449.437			1.86488			0.932442	−	0.361320i	$-0.117674\pi$
$241$	449.437			1.86488			0.932442	+	0.361320i	$0.117674\pi$
$242$		−	133.945i		−	0.553492i
$243$	242.186	+	19.8755i	0.996649	+	0.0817923i
$244$	−16.6212			−0.0681196
$245$			86.5443i			0.353242i
$246$	25.0562	+	81.6407i	0.101854	+	0.331873i
$247$	−102.211			−0.413811
$248$		−	140.318i		−	0.565800i
$249$	209.958	−	64.4378i	0.843204	−	0.258786i
$250$	−15.8114			−0.0632456
$251$		−	273.849i		−	1.09103i	−0.838100	−	0.545517i	$-0.816333\pi$
$251$		−	273.849i		−	1.09103i	0.838100	−	0.545517i	$-0.183667\pi$
$252$	−47.8138	+	32.4008i	−0.189737	+	0.128575i
$253$	70.4373			0.278408
$254$		−	213.370i		−	0.840041i
$255$	−53.2084	−	173.369i	−0.208660	−	0.679879i
$256$	16.0000			0.0625000
$257$			381.933i			1.48612i	0.669225	+	0.743059i	$0.266626\pi$
$257$			381.933i			1.48612i	−0.669225	+	0.743059i	$0.733374\pi$
$258$	69.1203	−	21.2136i	0.267908	−	0.0822232i
$259$	−136.807			−0.528213
$260$			82.6618i			0.317930i
$261$	−42.6933	−	63.0024i	−0.163576	−	0.241388i
$262$	187.671			0.716301
$263$		−	80.3574i		−	0.305541i	−0.988262	−	0.152771i	$-0.951180\pi$
$263$		−	80.3574i		−	0.305541i	0.988262	−	0.152771i	$-0.0488196\pi$
$264$	−36.5651	−	119.140i	−0.138504	−	0.451288i
$265$	−8.33898			−0.0314679
$266$			25.0936i			0.0943369i
$267$	−207.658	+	63.7319i	−0.777745	+	0.238696i
$268$	−0.654345			−0.00244158
$269$		−	387.384i		−	1.44009i	−0.693928	−	0.720045i	$-0.744121\pi$
$269$		−	387.384i		−	1.44009i	0.693928	−	0.720045i	$-0.255879\pi$
$270$	−66.5271	−	53.5177i	−0.246397	−	0.198214i
$271$	−456.085			−1.68297			−0.841485	−	0.540280i	$-0.818318\pi$
$271$	−456.085			−1.68297			−0.841485	+	0.540280i	$0.818318\pi$
$272$		−	108.137i		−	0.397561i
$273$	−52.2049	−	170.099i	−0.191227	−	0.623075i
$274$	58.0426			0.211834
$275$			73.4359i			0.267040i
$276$	27.5086	−	8.44261i	0.0996688	−	0.0305892i
$277$	250.843			0.905570			0.452785	−	0.891620i	$-0.350430\pi$
$277$	250.843			0.905570			0.452785	+	0.891620i	$0.350430\pi$
$278$		−	142.364i		−	0.512101i
$279$	−369.619	+	250.471i	−1.32480	+	0.897745i
$280$	20.2941			0.0724788
$281$		−	0.440087i		−	0.00156615i	−1.00000		0.000783073i	$-0.999751\pi$
$281$		−	0.440087i		−	0.00156615i	1.00000		0.000783073i	$-0.000249260\pi$
$282$	65.6304	+	213.844i	0.232732	+	0.758311i
$283$	−131.628			−0.465118			−0.232559	−	0.972582i	$-0.574710\pi$
$283$	−131.628			−0.465118			−0.232559	+	0.972582i	$0.574710\pi$
$284$		−	138.555i		−	0.487871i
$285$	−35.4625	+	10.8837i	−0.124430	+	0.0381885i
$286$	383.922			1.34239
$287$			64.5886i			0.225048i
$288$	−28.5603	−	42.1463i	−0.0991676	−	0.146341i
$289$	−441.844			−1.52887
$290$			26.7407i			0.0922092i
$291$	78.4083	+	255.478i	0.269444	+	0.877931i
$292$	−45.3085			−0.155166
$293$		−	94.8962i		−	0.323878i	−0.986801	−	0.161939i	$-0.948225\pi$
$293$		−	94.8962i		−	0.323878i	0.986801	−	0.161939i	$-0.0517748\pi$
$294$	156.979	−	48.1783i	0.533944	−	0.163872i
$295$	−65.0948			−0.220660
$296$		−	120.591i		−	0.407402i
$297$	−248.563	+	308.985i	−0.836912	+	1.04035i
$298$	77.4252			0.259816
$299$			88.6449i			0.296471i
$300$	8.80203	+	28.6797i	0.0293401	+	0.0955989i
$301$	54.6833			0.181672
$302$			129.579i			0.429071i
$303$	243.623	−	74.7700i	0.804037	−	0.246766i
$304$	−22.1192			−0.0727605
$305$		−	18.5831i		−	0.0609281i
$306$	−284.847	+	193.025i	−0.930873	+	0.630802i
$307$	21.3796			0.0696403			0.0348202	−	0.999394i	$-0.488914\pi$
$307$	21.3796			0.0696403			0.0348202	+	0.999394i	$0.488914\pi$
$308$		−	94.2557i		−	0.306025i
$309$	−141.790	−	461.995i	−0.458868	−	1.49513i
$310$	156.881			0.506067
$311$			401.801i			1.29196i	0.763353	+	0.645982i	$0.223552\pi$
$311$			401.801i			1.29196i	−0.763353	+	0.645982i	$0.776448\pi$
$312$	149.937	−	46.0169i	0.480567	−	0.147490i
$313$	−430.198			−1.37443			−0.687217	−	0.726452i	$-0.741168\pi$
$313$	−430.198			−1.37443			−0.687217	+	0.726452i	$0.741168\pi$
$314$			108.781i			0.346438i
$315$	−36.2252	−	53.4575i	−0.115001	−	0.169706i
$316$	−137.357			−0.434674
$317$		−	268.540i		−	0.847129i	−0.905866	−	0.423564i	$-0.860779\pi$
$317$		−	268.540i		−	0.847129i	0.905866	−	0.423564i	$-0.139221\pi$
$318$	4.64222	+	15.1258i	0.0145982	+	0.0475653i
$319$	124.197			0.389332
$320$			17.8885i			0.0559017i
$321$	−79.8454	+	24.5052i	−0.248740	+	0.0763403i
$322$	21.7629			0.0675868
$323$			149.493i			0.462828i
$324$	−60.0389	+	150.464i	−0.185305	+	0.464394i
$325$	−92.4187			−0.284365
$326$		−	40.6846i		−	0.124799i
$327$	187.792	+	611.882i	0.574287	+	1.87120i
$328$	−56.9328			−0.173576
$329$			169.179i			0.514222i
$330$	133.203	−	40.8810i	0.403645	−	0.123882i
$331$	284.638			0.859935			0.429967	−	0.902844i	$-0.358525\pi$
$331$	284.638			0.859935			0.429967	+	0.902844i	$0.358525\pi$
$332$			146.416i			0.441011i
$333$	−317.654	+	215.257i	−0.953916	+	0.646417i
$334$	−86.7208			−0.259643
$335$		−	0.731580i		−	0.00218382i
$336$	−11.2975	−	36.8106i	−0.0336235	−	0.109555i
$337$	210.916			0.625864			0.312932	−	0.949776i	$-0.398689\pi$
$337$	210.916			0.625864			0.312932	+	0.949776i	$0.398689\pi$
$338$			244.162i			0.722371i
$339$	96.6471	−	29.6618i	0.285095	−	0.0874979i
$340$	120.900			0.355589
$341$		−	728.632i		−	2.13675i
$342$	39.4831	+	58.2652i	0.115448	+	0.170366i
$343$	281.421			0.820471
$344$			48.2016i			0.140121i
$345$	9.43913	+	30.7555i	0.0273598	+	0.0891465i
$346$	377.716			1.09166
$347$			469.776i			1.35382i	0.736065	+	0.676911i	$0.236682\pi$
$347$			469.776i			1.35382i	−0.736065	+	0.676911i	$0.763318\pi$
$348$	48.5039	−	14.8862i	0.139379	−	0.0427766i
$349$	−533.718			−1.52928			−0.764639	−	0.644459i	$-0.777083\pi$
$349$	−533.718			−1.52928			−0.764639	+	0.644459i	$0.777083\pi$
$350$			22.6894i			0.0648270i
$351$	−388.855	−	312.815i	−1.10785	−	0.891210i
$352$	83.0833			0.236032
$353$			213.137i			0.603788i	0.953341	+	0.301894i	$0.0976189\pi$
$353$			213.137i			0.603788i	−0.953341	+	0.301894i	$0.902381\pi$
$354$	36.2376	+	118.073i	0.102366	+	0.333540i
$355$	154.910			0.436365
$356$		−	144.812i		−	0.406775i
$357$	−248.786	+	76.3544i	−0.696879	+	0.213878i
$358$	−69.9135			−0.195289
$359$		−	606.042i		−	1.68814i	−0.536233	−	0.844070i	$-0.680153\pi$
$359$		−	606.042i		−	1.68814i	0.536233	−	0.844070i	$-0.319847\pi$
$360$	47.1210	−	31.9313i	0.130892	−	0.0886982i
$361$	−330.421			−0.915294
$362$			404.447i			1.11726i
$363$	−83.3671	−	271.635i	−0.229661	−	0.748307i
$364$	118.620			0.325880
$365$		−	50.6565i		−	0.138785i
$366$	−33.7071	+	10.3450i	−0.0920959	+	0.0282650i
$367$	379.037			1.03280			0.516399	−	0.856348i	$-0.327272\pi$
$367$	379.037			1.03280			0.516399	+	0.856348i	$0.327272\pi$
$368$			19.1833i			0.0521286i
$369$	101.626	+	149.969i	0.275409	+	0.406420i
$370$	134.825			0.364391
$371$			11.9665i			0.0322547i
$372$	−87.3339	−	284.560i	−0.234768	−	0.764947i
$373$	−88.5064			−0.237283			−0.118641	−	0.992937i	$-0.537854\pi$
$373$	−88.5064			−0.237283			−0.118641	+	0.992937i	$0.537854\pi$
$374$		−	561.521i		−	1.50139i
$375$	−32.0649	+	9.84097i	−0.0855063	+	0.0262426i
$376$	−149.126			−0.396611
$377$			156.301i			0.414592i
$378$	−76.7983	+	95.4668i	−0.203170	+	0.252558i
$379$	565.323			1.49162			0.745809	−	0.666160i	$-0.232063\pi$
$379$	565.323			1.49162			0.745809	+	0.666160i	$0.232063\pi$
$380$		−	24.7300i		−	0.0650790i
$381$	−132.801	−	432.707i	−0.348560	−	1.13571i
$382$	375.949			0.984160
$383$			592.968i			1.54822i	0.633051	+	0.774110i	$0.281802\pi$
$383$			592.968i			1.54822i	−0.633051	+	0.774110i	$0.718198\pi$
$384$	32.4474	−	9.95836i	0.0844983	−	0.0259332i
$385$	105.381			0.273717
$386$		−	324.354i		−	0.840295i
$387$	126.970	−	86.0406i	0.328087	−	0.222327i
$388$	−178.159			−0.459174
$389$			626.639i			1.61090i	0.592666	+	0.805448i	$0.298075\pi$
$389$			626.639i			1.61090i	−0.592666	+	0.805448i	$0.701925\pi$
$390$	51.4485	+	167.635i	0.131919	+	0.429833i
$391$	129.651			0.331589
$392$			109.471i			0.279262i
$393$	380.589	−	116.806i	0.968419	−	0.297216i
$394$	−112.352			−0.285156
$395$		−	153.570i		−	0.388784i
$396$	−148.305	−	218.853i	−0.374508	−	0.552660i
$397$	−29.5114			−0.0743361			−0.0371681	−	0.999309i	$-0.511834\pi$
$397$	−29.5114			−0.0743361			−0.0371681	+	0.999309i	$0.511834\pi$
$398$		−	305.541i		−	0.767691i
$399$	15.6182	+	50.8889i	0.0391434	+	0.127541i
$400$	−20.0000			−0.0500000
$401$		−	467.472i		−	1.16576i	−0.812557	−	0.582882i	$-0.801925\pi$
$401$		−	467.472i		−	1.16576i	0.812557	−	0.582882i	$-0.198075\pi$
$402$	−1.32698	+	0.407263i	−0.00330096	+	0.00101309i
$403$	916.979			2.27538
$404$			169.893i			0.420526i
$405$	−168.224	−	67.1255i	−0.415367	−	0.165742i
$406$	38.3730			0.0945148
$407$		−	626.193i		−	1.53856i
$408$	−67.3039	−	219.297i	−0.164961	−	0.537491i
$409$	−397.499			−0.971880			−0.485940	−	0.873992i	$-0.661523\pi$
$409$	−397.499			−0.971880			−0.485940	+	0.873992i	$0.661523\pi$
$410$		−	63.6528i		−	0.155251i
$411$	117.708	−	36.1256i	0.286394	−	0.0878968i
$412$	322.176			0.781981
$413$			93.4115i			0.226178i
$414$	50.5316	−	34.2426i	0.122057	−	0.0827115i
$415$	−163.698			−0.394452
$416$			104.560i			0.251346i
$417$	−88.6070	−	288.708i	−0.212487	−	0.692346i
$418$	−114.859			−0.274781
$419$			456.925i			1.09051i	0.838269	+	0.545257i	$0.183568\pi$
$419$			456.925i			1.09051i	−0.838269	+	0.545257i	$0.816432\pi$
$420$	41.1555	−	12.6310i	0.0979893	−	0.0300737i
$421$	−312.034			−0.741174			−0.370587	−	0.928798i	$-0.620843\pi$
$421$	−312.034			−0.741174			−0.370587	+	0.928798i	$0.620843\pi$
$422$			157.447i			0.373098i
$423$	266.192	+	392.818i	0.629295	+	0.928649i
$424$	−10.5481			−0.0248775
$425$			135.171i			0.318049i
$426$	−86.2365	−	280.985i	−0.202433	−	0.659588i
$427$	−26.6668			−0.0624515
$428$		−	55.6808i		−	0.130095i
$429$	778.579	−	238.952i	1.81487	−	0.556998i
$430$	−53.8910			−0.125328
$431$			572.063i			1.32729i	0.748046	+	0.663647i	$0.230992\pi$
$431$			572.063i			1.32729i	−0.748046	+	0.663647i	$0.769008\pi$
$432$	−84.1508	−	67.6952i	−0.194794	−	0.156702i
$433$	565.137			1.30517			0.652583	−	0.757717i	$-0.273685\pi$
$433$	565.137			1.30517			0.652583	+	0.757717i	$0.273685\pi$
$434$		−	225.125i		−	0.518721i
$435$	16.6433	+	54.2290i	0.0382605	+	0.124664i
$436$	−426.701			−0.978672
$437$		−	26.5200i		−	0.0606865i
$438$	−91.8839	+	28.1999i	−0.209781	+	0.0643834i
$439$	752.081			1.71317			0.856584	−	0.516008i	$-0.172582\pi$
$439$	752.081			1.71317			0.856584	+	0.516008i	$0.172582\pi$
$440$			92.8899i			0.211113i
$441$	288.362	−	195.407i	0.653882	−	0.443100i
$442$	706.671			1.59880
$443$			761.734i			1.71949i	0.510724	+	0.859745i	$0.329378\pi$
$443$			761.734i			1.71949i	−0.510724	+	0.859745i	$0.670622\pi$
$444$	−75.0555	−	244.554i	−0.169044	−	0.550797i
$445$	161.905			0.363830
$446$		−	364.097i		−	0.816360i
$447$	157.015	−	48.1892i	0.351264	−	0.107806i
$448$	25.6702			0.0572995
$449$			149.930i			0.333920i	0.985964	+	0.166960i	$0.0533951\pi$
$449$			149.930i			0.333920i	−0.985964	+	0.166960i	$0.946605\pi$
$450$	35.7003	+	52.6829i	0.0793341	+	0.117073i
$451$	−295.635			−0.655510
$452$			67.3976i			0.149110i
$453$	80.6499	+	262.782i	0.178035	+	0.580092i
$454$	3.03463			0.00668421
$455$			132.621i			0.291475i
$456$	−44.8569	+	13.7669i	−0.0983703	+	0.0301907i
$457$	415.935			0.910143			0.455071	−	0.890455i	$-0.349614\pi$
$457$	415.935			0.910143			0.455071	+	0.890455i	$0.349614\pi$
$458$		−	152.635i		−	0.333263i
$459$	−457.520	+	568.736i	−0.996776	+	1.23908i
$460$	−21.4476			−0.0466252
$461$			798.234i			1.73153i	0.500454	+	0.865763i	$0.333167\pi$
$461$			798.234i			1.73153i	−0.500454	+	0.865763i	$0.666833\pi$
$462$	−58.6645	−	191.147i	−0.126979	−	0.413737i
$463$	−566.084			−1.22264			−0.611322	−	0.791382i	$-0.709362\pi$
$463$	−566.084			−1.22264			−0.611322	+	0.791382i	$0.709362\pi$
$464$			33.8246i			0.0728978i
$465$	318.148	−	97.6422i	0.684189	−	0.209983i
$466$	220.213			0.472560
$467$			704.756i			1.50911i	0.656234	+	0.754557i	$0.272148\pi$
$467$			704.756i			1.50911i	−0.656234	+	0.754557i	$0.727852\pi$
$468$	275.426	−	186.641i	0.588516	−	0.398805i
$469$	−1.04982			−0.00223843
$470$		−	166.728i		−	0.354739i
$471$	67.7053	+	220.604i	0.143748	+	0.468374i
$472$	−82.3392			−0.174447
$473$			250.296i			0.529168i
$474$	−278.555	+	85.4907i	−0.587668	+	0.180360i
$475$	27.6490			0.0582084
$476$		−	173.493i		−	0.364480i
$477$	18.8285	+	27.7851i	0.0394727	+	0.0582498i
$478$	−616.333			−1.28940
$479$		−	464.409i		−	0.969539i	−0.874642	−	0.484770i	$-0.838903\pi$
$479$		−	464.409i		−	0.969539i	0.874642	−	0.484770i	$-0.161097\pi$
$480$	11.1338	+	36.2772i	0.0231954	+	0.0755776i
$481$	788.060			1.63838
$482$			635.600i			1.31867i
$483$	44.1344	−	13.5452i	0.0913755	−	0.0280439i
$484$	189.427			0.391378
$485$		−	199.188i		−	0.410698i
$486$	−28.1083	+	342.502i	−0.0578359	+	0.704738i
$487$	−764.898			−1.57063			−0.785316	−	0.619095i	$-0.787500\pi$
$487$	−764.898			−1.57063			−0.785316	+	0.619095i	$0.787500\pi$
$488$		−	23.5059i		−	0.0481679i
$489$	−25.3220	−	82.5067i	−0.0517832	−	0.168725i
$490$	−122.392			−0.249780
$491$			739.524i			1.50616i	0.657930	+	0.753079i	$0.271432\pi$
$491$			739.524i			1.50616i	−0.657930	+	0.753079i	$0.728568\pi$
$492$	−115.457	+	35.4348i	−0.234669	+	0.0720220i
$493$	228.604			0.463701
$494$		−	144.549i		−	0.292609i
$495$	244.685	−	165.810i	0.494314	−	0.334970i
$496$	198.440			0.400081
$497$		−	222.296i		−	0.447276i
$498$	91.1288	+	296.925i	0.182990	+	0.596235i
$499$	622.508			1.24751			0.623756	−	0.781619i	$-0.285606\pi$
$499$	622.508			1.24751			0.623756	+	0.781619i	$0.285606\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	−175.866	+	53.9748i	−0.351031	+	0.107734i
$502$	387.281			0.771477
$503$		−	736.196i		−	1.46361i	−0.681514	−	0.731805i	$-0.738678\pi$
$503$		−	736.196i		−	1.46361i	0.681514	−	0.731805i	$-0.261322\pi$
$504$	−45.8217	−	67.6189i	−0.0909160	−	0.134165i
$505$	−189.946			−0.376130
$506$			99.6134i			0.196864i
$507$	151.966	+	495.150i	0.299735	+	0.976627i
$508$	301.751			0.593999
$509$			618.281i			1.21470i	0.794435	+	0.607349i	$0.207767\pi$
$509$			618.281i			1.21470i	−0.794435	+	0.607349i	$0.792233\pi$
$510$	245.181	−	75.2481i	0.480747	−	0.147545i
$511$	−72.6924			−0.142255
$512$			22.6274i			0.0441942i
$513$	116.334	+	93.5852i	0.226773	+	0.182427i
$514$	−540.134			−1.05084
$515$			360.204i			0.699425i
$516$	30.0005	+	97.7508i	0.0581406	+	0.189440i
$517$	−774.366			−1.49781
$518$		−	193.474i		−	0.373503i
$519$	765.992	−	235.089i	1.47590	−	0.452966i
$520$	−116.901			−0.224810
$521$			141.633i			0.271848i	0.990719	+	0.135924i	$0.0434003\pi$
$521$			141.633i			0.271848i	−0.990719	+	0.135924i	$0.956600\pi$
$522$	89.0988	−	60.3774i	0.170687	−	0.115666i
$523$	−582.032			−1.11287			−0.556435	−	0.830891i	$-0.687831\pi$
$523$	−582.032			−1.11287			−0.556435	+	0.830891i	$0.687831\pi$
$524$			265.407i			0.506501i
$525$	14.1219	+	46.0133i	0.0268988	+	0.0876443i
$526$	113.642			0.216050
$527$		−	1341.16i		−	2.54490i
$528$	168.490	−	51.7108i	0.319109	−	0.0979372i
$529$	−23.0000			−0.0434783
$530$		−	11.7931i		−	0.0222511i
$531$	146.977	+	216.893i	0.276792	+	0.408462i
$532$	−35.4877			−0.0667063
$533$		−	372.055i		−	0.698039i
$534$	−90.1305	−	293.673i	−0.168784	−	0.549949i
$535$	62.2531			0.116361
$536$		−	0.925383i		−	0.00172646i
$537$	−141.782	+	43.5140i	−0.264026	+	0.0810316i
$538$	547.844			1.01830
$539$			568.450i			1.05464i
$540$	75.6855	−	94.0835i	0.140158	−	0.174229i
$541$	687.177			1.27020			0.635099	−	0.772431i	$-0.280959\pi$
$541$	687.177			1.27020			0.635099	+	0.772431i	$0.280959\pi$
$542$		−	645.002i		−	1.19004i
$543$	251.727	+	820.202i	0.463585	+	1.51050i
$544$	152.928			0.281118
$545$		−	477.066i		−	0.875351i
$546$	240.557	−	73.8289i	0.440580	−	0.135218i
$547$	−751.639			−1.37411			−0.687055	−	0.726605i	$-0.741097\pi$
$547$	−751.639			−1.37411			−0.687055	+	0.726605i	$0.741097\pi$
$548$			82.0846i			0.149789i
$549$	−61.9180	+	41.9584i	−0.112783	+	0.0764270i
$550$	−103.854			−0.188826
$551$		−	46.7608i		−	0.0848653i
$552$	11.9397	+	38.9030i	0.0216298	+	0.0704765i
$553$	−220.374			−0.398506
$554$			354.745i			0.640335i
$555$	273.419	−	83.9146i	0.492647	−	0.151198i
$556$	201.333			0.362110
$557$			486.059i			0.872638i	0.899792	+	0.436319i	$0.143718\pi$
$557$			486.059i			0.872638i	−0.899792	+	0.436319i	$0.856282\pi$
$558$	−354.219	−	522.720i	−0.634801	−	0.936775i
$559$	−314.996			−0.563500
$560$			28.7001i			0.0512502i
$561$	−349.489	−	1138.74i	−0.622976	−	2.02984i
$562$	0.622377			0.00110743
$563$			677.685i			1.20370i	0.798608	+	0.601852i	$0.205570\pi$
$563$			677.685i			1.20370i	−0.798608	+	0.601852i	$0.794430\pi$
$564$	−302.421	+	92.8154i	−0.536207	+	0.164566i
$565$	−75.3528			−0.133368
$566$		−	186.151i		−	0.328888i
$567$	−96.3256	+	241.402i	−0.169886	+	0.425753i
$568$	195.947			0.344977
$569$			1092.44i			1.91992i	0.280130	+	0.959962i	$0.409623\pi$
$569$			1092.44i			1.91992i	−0.280130	+	0.959962i	$0.590377\pi$
$570$	−15.3919	−	50.1515i	−0.0270033	−	0.0879851i
$571$	−985.455			−1.72584			−0.862920	−	0.505340i	$-0.831367\pi$
$571$	−985.455			−1.72584			−0.862920	+	0.505340i	$0.831367\pi$
$572$			542.948i			0.949210i
$573$	762.410	−	233.990i	1.33056	−	0.408359i
$574$	−91.3421			−0.159133
$575$		−	23.9792i		−	0.0417029i
$576$	59.6039	−	40.3903i	0.103479	−	0.0701221i
$577$	756.257			1.31067			0.655335	−	0.755338i	$-0.272527\pi$
$577$	756.257			1.31067			0.655335	+	0.755338i	$0.272527\pi$
$578$		−	624.862i		−	1.08108i
$579$	−201.877	−	657.777i	−0.348665	−	1.13606i
$580$	−37.8170			−0.0652017
$581$			234.907i			0.404315i
$582$	−361.300	+	110.886i	−0.620791	+	0.190526i
$583$	−54.7730			−0.0939503
$584$		−	64.0760i		−	0.109719i
$585$	208.671	+	307.935i	0.356702	+	0.526385i
$586$	134.204			0.229016
$587$			41.9003i			0.0713804i	0.999363	+	0.0356902i	$0.0113630\pi$
$587$			41.9003i			0.0713804i	−0.999363	+	0.0356902i	$0.988637\pi$
$588$	68.1344	+	222.002i	0.115875	+	0.377555i
$589$	−274.334			−0.465762
$590$		−	92.0580i		−	0.156030i
$591$	−227.844	+	69.9273i	−0.385524	+	0.118320i
$592$	170.541			0.288077
$593$		−	959.818i		−	1.61858i	−0.587410	−	0.809290i	$-0.699852\pi$
$593$		−	959.818i		−	1.61858i	0.587410	−	0.809290i	$-0.300148\pi$
$594$	−436.970	−	351.521i	−0.735640	−	0.591786i
$595$	193.971			0.326001
$596$			109.496i			0.183718i
$597$	−190.168	−	619.625i	−0.318539	−	1.03790i
$598$	−125.363			−0.209637
$599$			705.255i			1.17739i	0.808356	+	0.588694i	$0.200358\pi$
$599$			705.255i			1.17739i	−0.808356	+	0.588694i	$0.799642\pi$
$600$	−40.5592	+	12.4480i	−0.0675987	+	0.0207466i
$601$	598.282			0.995478			0.497739	−	0.867327i	$-0.334164\pi$
$601$	598.282			0.995478			0.497739	+	0.867327i	$0.334164\pi$
$602$			77.3339i			0.128462i
$603$	−2.43759	+	1.65182i	−0.00404244	+	0.00273934i
$604$	−183.253			−0.303399
$605$			211.786i			0.350059i
$606$	105.741	+	344.535i	0.174490	+	0.568540i
$607$	−394.189			−0.649405			−0.324702	−	0.945816i	$-0.605264\pi$
$607$	−394.189			−0.649405			−0.324702	+	0.945816i	$0.605264\pi$
$608$		−	31.2813i		−	0.0514495i
$609$	77.8190	−	23.8833i	0.127782	−	0.0392172i
$610$	26.2804			0.0430826
$611$		−	974.534i		−	1.59498i
$612$	−272.979	−	402.835i	−0.446044	−	0.658227i
$613$	−369.754			−0.603187			−0.301594	−	0.953437i	$-0.597519\pi$
$613$	−369.754			−0.603187			−0.301594	+	0.953437i	$0.597519\pi$
$614$			30.2353i			0.0492431i
$615$	−39.6173	−	129.085i	−0.0644184	−	0.209895i
$616$	133.298			0.216392
$617$			171.624i			0.278158i	0.990281	+	0.139079i	$0.0444143\pi$
$617$			171.624i			0.278158i	−0.990281	+	0.139079i	$0.955586\pi$
$618$	653.360	−	200.522i	1.05722	−	0.324469i
$619$	690.409			1.11536			0.557681	−	0.830055i	$-0.311691\pi$
$619$	690.409			1.11536			0.557681	+	0.830055i	$0.311691\pi$
$620$			221.863i			0.357843i
$621$	81.1637	−	100.893i	0.130698	−	0.162469i
$622$	−568.232			−0.913556
$623$		−	232.334i		−	0.372928i
$624$	65.0777	+	212.043i	0.104291	+	0.339813i
$625$	25.0000			0.0400000
$626$		−	608.392i		−	0.971872i
$627$	−232.928	+	71.4877i	−0.371497	+	0.114015i
$628$	−153.840			−0.244968
$629$		−	1152.61i		−	1.83245i
$630$	75.6003	−	51.2302i	0.120000	−	0.0813178i
$631$	912.234			1.44570			0.722848	−	0.691007i	$-0.242833\pi$
$631$	912.234			1.44570			0.722848	+	0.691007i	$0.242833\pi$
$632$		−	194.252i		−	0.307361i
$633$	97.9948	+	319.297i	0.154810	+	0.504418i
$634$	379.773			0.599011
$635$			337.368i			0.531289i
$636$	−21.3911	+	6.56510i	−0.0336338	+	0.0103225i
$637$	−715.390			−1.12306
$638$			175.641i			0.275299i
$639$	−349.768	−	516.152i	−0.547368	−	0.807750i
$640$	−25.2982			−0.0395285
$641$			249.344i			0.388993i	0.980903	+	0.194496i	$0.0623072\pi$
$641$			249.344i			0.388993i	−0.980903	+	0.194496i	$0.937693\pi$
$642$	−34.6556	−	112.919i	−0.0539807	−	0.175886i
$643$	46.5166			0.0723431			0.0361715	−	0.999346i	$-0.488484\pi$
$643$	46.5166			0.0723431			0.0361715	+	0.999346i	$0.488484\pi$
$644$			30.7775i			0.0477911i
$645$	−109.289	+	33.5416i	−0.169440	+	0.0520025i
$646$	−211.416			−0.327269
$647$			334.980i			0.517744i	0.965912	+	0.258872i	$0.0833507\pi$
$647$			334.980i			0.517744i	−0.965912	+	0.258872i	$0.916649\pi$
$648$	−212.788	−	84.9078i	−0.328376	−	0.131031i
$649$	−427.563			−0.658803
$650$		−	130.700i		−	0.201076i
$651$	−140.117	−	456.544i	−0.215234	−	0.701297i
$652$	57.5367			0.0882465
$653$		−	767.471i		−	1.17530i	−0.809115	−	0.587650i	$-0.800053\pi$
$653$		−	767.471i		−	1.17530i	0.809115	−	0.587650i	$-0.199947\pi$
$654$	−865.332	+	265.578i	−1.32314	+	0.406082i
$655$	−296.734			−0.453028
$656$		−	80.5151i		−	0.122736i
$657$	−168.785	+	114.377i	−0.256903	+	0.174089i
$658$	−239.255			−0.363610
$659$			515.713i			0.782569i	0.920270	+	0.391285i	$0.127969\pi$
$659$			515.713i			0.782569i	−0.920270	+	0.391285i	$0.872031\pi$
$660$	57.8145	+	188.377i	0.0875977	+	0.285420i
$661$	−392.863			−0.594346			−0.297173	−	0.954824i	$-0.596044\pi$
$661$	−392.863			−0.594346			−0.297173	+	0.954824i	$0.596044\pi$
$662$			402.540i			0.608066i
$663$	1433.10	−	439.830i	2.16154	−	0.663394i
$664$	−207.063			−0.311842
$665$		−	39.6765i		−	0.0596639i
$666$	−304.419	−	449.231i	−0.457086	−	0.674520i
$667$	−40.5542			−0.0608009
$668$		−	122.642i		−	0.183595i
$669$	−226.613	−	738.374i	−0.338734	−	1.10370i
$670$	1.03461			0.00154419
$671$		−	122.059i		−	0.181907i
$672$	52.0581	−	15.9771i	0.0774674	−	0.0237754i
$673$	817.428			1.21460			0.607302	−	0.794471i	$-0.292252\pi$
$673$	817.428			1.21460			0.607302	+	0.794471i	$0.292252\pi$
$674$			298.280i			0.442553i
$675$	105.189	+	84.6190i	0.155835	+	0.125361i
$676$	−345.297			−0.510794
$677$		−	78.0109i		−	0.115230i	−0.998339	−	0.0576151i	$-0.981650\pi$
$677$		−	78.0109i		−	0.115230i	0.998339	−	0.0576151i	$-0.0183496\pi$
$678$	41.9481	+	136.680i	0.0618703	+	0.201592i
$679$	−285.837			−0.420967
$680$			170.979i			0.251439i
$681$	6.15411	−	1.88875i	0.00903687	−	0.00277349i
$682$	1030.44			1.51091
$683$			1048.62i			1.53532i	0.640857	+	0.767661i	$0.278579\pi$
$683$			1048.62i			1.53532i	−0.640857	+	0.767661i	$0.721421\pi$
$684$	−82.3994	+	55.8376i	−0.120467	+	0.0816339i
$685$	−91.7734			−0.133976
$686$			397.990i			0.580160i
$687$	−94.9993	−	309.537i	−0.138281	−	0.450563i
$688$	−68.1673			−0.0990804
$689$		−	68.9315i		−	0.100046i
$690$	−43.4949	+	13.3489i	−0.0630361	+	0.0193463i
$691$	−1164.83			−1.68571			−0.842855	−	0.538141i	$-0.819127\pi$
$691$	−1164.83			−1.68571			−0.842855	+	0.538141i	$0.819127\pi$
$692$			534.171i			0.771923i
$693$	−237.938	−	351.125i	−0.343346	−	0.506674i
$694$	−664.364			−0.957297
$695$			225.097i			0.323881i
$696$	21.0523	+	68.5949i	0.0302476	+	0.0985558i
$697$	−544.164			−0.780723
$698$		−	754.791i		−	1.08136i
$699$	446.583	−	137.060i	0.638888	−	0.196080i
$700$	−32.0877			−0.0458396
$701$		−	522.136i		−	0.744845i	−0.928063	−	0.372423i	$-0.878527\pi$
$701$		−	522.136i		−	0.744845i	0.928063	−	0.372423i	$-0.121473\pi$
$702$	442.387	−	549.924i	0.630181	−	0.783368i
$703$	−235.765			−0.335370
$704$			117.498i			0.166900i
$705$	−103.771	−	338.117i	−0.147193	−	0.479598i
$706$	−301.422			−0.426943
$707$			272.573i			0.385535i
$708$	−166.981	+	51.2477i	−0.235848	+	0.0723837i
$709$	1140.17			1.60813			0.804066	−	0.594540i	$-0.202666\pi$
$709$	1140.17			1.60813			0.804066	+	0.594540i	$0.202666\pi$
$710$			219.075i			0.308557i
$711$	−511.688	+	346.743i	−0.719674	+	0.487684i
$712$	204.795			0.287633
$713$			237.922i			0.333691i
$714$	−107.981	−	351.836i	−0.151234	−	0.492768i
$715$	−607.034			−0.848999
$716$		−	98.8726i		−	0.138090i
$717$	−1249.90	+	383.604i	−1.74323	+	0.535013i
$718$	857.073			1.19370
$719$		−	398.568i		−	0.554336i	−0.960821	−	0.277168i	$-0.910604\pi$
$719$		−	398.568i		−	0.554336i	0.960821	−	0.277168i	$-0.0893959\pi$
$720$	45.1577	+	66.6392i	0.0627191	+	0.0925544i
$721$	516.895			0.716914
$722$		−	467.286i		−	0.647211i
$723$	395.596	+	1288.97i	0.547159	+	1.78281i
$724$	−571.974			−0.790019
$725$		−	42.2807i		−	0.0583182i
$726$	384.150	−	117.899i	0.529133	−	0.162395i
$727$	541.732			0.745161			0.372581	−	0.928000i	$-0.378473\pi$
$727$	541.732			0.745161			0.372581	+	0.928000i	$0.378473\pi$
$728$			167.754i			0.230432i
$729$	156.170	+	712.076i	0.214225	+	0.976784i
$730$	71.6391			0.0981358
$731$			460.711i			0.630247i
$732$	−14.6300	−	47.6690i	−0.0199864	−	0.0651216i
$733$	−93.0260			−0.126911			−0.0634556	−	0.997985i	$-0.520212\pi$
$733$	−93.0260			−0.126911			−0.0634556	+	0.997985i	$0.520212\pi$
$734$			536.039i			0.730298i
$735$	−248.206	+	76.1766i	−0.337696	+	0.103642i
$736$	−27.1293			−0.0368605
$737$		−	4.80524i		−	0.00652000i
$738$	−212.088	+	143.721i	−0.287383	+	0.194744i
$739$	1323.24			1.79058			0.895290	−	0.445483i	$-0.146968\pi$
$739$	1323.24			1.79058			0.895290	+	0.445483i	$0.146968\pi$
$740$			190.671i			0.257664i
$741$	−89.9667	−	293.139i	−0.121413	−	0.395599i
$742$	−16.9232			−0.0228075
$743$			219.461i			0.295371i	0.989034	+	0.147686i	$0.0471824\pi$
$743$			219.461i			0.295371i	−0.989034	+	0.147686i	$0.952818\pi$
$744$	402.429	−	123.509i	0.540899	−	0.166006i
$745$	−122.420			−0.164322
$746$		−	125.167i		−	0.167784i
$747$	369.611	+	545.434i	0.494794	+	0.730166i
$748$	794.111			1.06165
$749$		−	89.3336i		−	0.119270i
$750$	−13.9172	−	45.3466i	−0.0185563	−	0.0604621i
$751$	−249.205			−0.331830			−0.165915	−	0.986140i	$-0.553058\pi$
$751$	−249.205			−0.331830			−0.165915	+	0.986140i	$0.553058\pi$
$752$		−	210.896i		−	0.280446i
$753$	785.391	−	241.043i	1.04302	−	0.320110i
$754$	−221.043			−0.293161
$755$		−	204.883i		−	0.271368i
$756$	−135.010	−	108.609i	−0.178585	−	0.143663i
$757$	−1195.89			−1.57978			−0.789889	−	0.613249i	$-0.789862\pi$
$757$	−1195.89			−1.57978			−0.789889	+	0.613249i	$0.789862\pi$
$758$			799.488i			1.05473i
$759$	61.9991	+	202.012i	0.0816853	+	0.266155i
$760$	34.9735			0.0460178
$761$		−	267.295i		−	0.351241i	−0.984458	−	0.175621i	$-0.943807\pi$
$761$		−	267.295i		−	0.351241i	0.984458	−	0.175621i	$-0.0561932\pi$
$762$	611.940	−	187.809i	0.803071	−	0.246469i
$763$	−684.593			−0.897238
$764$			531.672i			0.695906i
$765$	450.383	−	305.200i	0.588736	−	0.398954i
$766$	−838.584			−1.09476
$767$		−	538.085i		−	0.701545i
$768$	14.0832	+	45.8875i	0.0183376	+	0.0597493i
$769$	758.937			0.986914			0.493457	−	0.869770i	$-0.335733\pi$
$769$	758.937			0.986914			0.493457	+	0.869770i	$0.335733\pi$
$770$			149.031i			0.193547i
$771$	−1095.37	+	336.178i	−1.42071	+	0.436029i
$772$	458.706			0.594178
$773$		−	669.855i		−	0.866565i	−0.901258	−	0.433282i	$-0.857355\pi$
$773$		−	669.855i		−	0.866565i	0.901258	−	0.433282i	$-0.142645\pi$
$774$	121.680	+	179.562i	0.157209	+	0.231993i
$775$	−248.050			−0.320065
$776$		−	251.956i		−	0.324685i
$777$	−120.418	−	392.358i	−0.154978	−	0.504966i
$778$	−886.201			−1.13908
$779$			111.308i			0.142886i
$780$	−237.071	+	72.7591i	−0.303938	+	0.0932809i
$781$	1017.49			1.30281
$782$			183.354i			0.234469i
$783$	143.110	−	177.898i	0.182771	−	0.227200i
$784$	−154.815			−0.197468
$785$		−	171.999i		−	0.219106i
$786$	165.188	+	538.234i	0.210163	+	0.684776i
$787$	−943.544			−1.19891			−0.599456	−	0.800408i	$-0.704616\pi$
$787$	−943.544			−1.19891			−0.599456	+	0.800408i	$0.704616\pi$
$788$		−	158.889i		−	0.201636i
$789$	230.462	−	70.7308i	0.292094	−	0.0896461i
$790$	217.181			0.274912
$791$			108.132i			0.136703i
$792$	309.505	−	209.735i	0.390790	−	0.264817i
$793$	153.611			0.193708
$794$		−	41.7355i		−	0.0525636i
$795$	−7.34000	−	23.9159i	−0.00923270	−	0.0300829i
$796$	432.100			0.542840
$797$			103.307i			0.129620i	0.997898	+	0.0648099i	$0.0206441\pi$
$797$			103.307i			0.129620i	−0.997898	+	0.0648099i	$0.979356\pi$
$798$	−71.9677	+	22.0875i	−0.0901851	+	0.0276785i
$799$	−1425.34			−1.78391
$800$		−	28.2843i		−	0.0353553i
$801$	−365.562	−	539.459i	−0.456382	−	0.673482i
$802$	661.105			0.824320
$803$		−	332.728i		−	0.414356i
$804$	−0.575956	−	1.87664i	−0.000716363	−	0.00233413i
$805$	−34.4102			−0.0427456
$806$			1296.80i			1.60894i
$807$	1111.01	−	340.977i	1.37671	−	0.422524i
$808$	−240.264			−0.297357
$809$		−	226.335i		−	0.279771i	−0.990168	−	0.139886i	$-0.955327\pi$
$809$		−	226.335i		−	0.279771i	0.990168	−	0.139886i	$-0.0446735\pi$
$810$	94.9299	−	237.904i	0.117197	−	0.293709i
$811$	−315.381			−0.388879			−0.194440	−	0.980915i	$-0.562289\pi$
$811$	−315.381			−0.388879			−0.194440	+	0.980915i	$0.562289\pi$
$812$			54.2677i			0.0668321i
$813$	−401.448	−	1308.04i	−0.493785	−	1.60890i
$814$	885.571			1.08793
$815$			64.3280i			0.0789301i
$816$	310.132	−	95.1821i	0.380064	−	0.116645i
$817$	94.2379			0.115346
$818$		−	562.149i		−	0.687223i
$819$	441.889	−	299.444i	0.539547	−	0.365622i
$820$	90.0186			0.109779
$821$		−	584.660i		−	0.712131i	−0.934461	−	0.356066i	$-0.884118\pi$
$821$		−	584.660i		−	0.712131i	0.934461	−	0.356066i	$-0.115882\pi$
$822$	51.0893	+	166.464i	0.0621524	+	0.202511i
$823$	−779.130			−0.946695			−0.473348	−	0.880876i	$-0.656955\pi$
$823$	−779.130			−0.946695			−0.473348	+	0.880876i	$0.656955\pi$
$824$			455.626i			0.552944i
$825$	−210.612	+	64.6385i	−0.255287	+	0.0783497i
$826$	−132.104			−0.159932
$827$		−	492.498i		−	0.595523i	−0.954640	−	0.297762i	$-0.903760\pi$
$827$		−	492.498i		−	0.595523i	0.954640	−	0.297762i	$-0.0962401\pi$
$828$	48.4263	+	71.4625i	0.0584859	+	0.0863074i
$829$	−49.2776			−0.0594422			−0.0297211	−	0.999558i	$-0.509462\pi$
$829$	−49.2776			−0.0594422			−0.0297211	+	0.999558i	$0.509462\pi$
$830$		−	231.504i		−	0.278920i
$831$	220.793	+	719.410i	0.265695	+	0.865716i
$832$	−147.870			−0.177728
$833$			1046.32i			1.25609i
$834$	408.295	−	125.309i	0.489563	−	0.150251i
$835$	137.118			0.164213
$836$		−	162.434i		−	0.194300i
$837$	−1043.68	−	839.591i	−1.24693	−	1.00310i
$838$	−646.190			−0.771109
$839$		−	541.096i		−	0.644930i	−0.946581	−	0.322465i	$-0.895489\pi$
$839$		−	541.096i		−	0.644930i	0.946581	−	0.322465i	$-0.104511\pi$
$840$	17.8629	+	58.2027i	0.0212653	+	0.0692889i
$841$	769.494			0.914975
$842$		−	441.283i		−	0.524089i
$843$	1.26216	−	0.387366i	0.00149722	−	0.000459509i
$844$	−222.664			−0.263820
$845$		−	386.053i		−	0.456868i
$846$	−555.529	+	376.452i	−0.656654	+	0.444979i
$847$	303.914			0.358812
$848$		−	14.9172i		−	0.0175911i
$849$	−115.860	−	377.506i	−0.136466	−	0.444648i
$850$	−191.160			−0.224894
$851$			204.472i			0.240273i
$852$	397.372	−	121.957i	0.466399	−	0.143142i
$853$	−1323.07			−1.55108			−0.775542	−	0.631296i	$-0.782523\pi$
$853$	−1323.07			−1.55108			−0.775542	+	0.631296i	$0.782523\pi$
$854$		−	37.7126i		−	0.0441599i
$855$	−62.4283	−	92.1253i	−0.0730156	−	0.107749i
$856$	78.7446			0.0919914
$857$		−	918.224i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$857$		−	918.224i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$858$	337.930	+	1101.08i	0.393857	+	1.28331i
$859$	−325.789			−0.379266			−0.189633	−	0.981855i	$-0.560730\pi$
$859$	−325.789			−0.379266			−0.189633	+	0.981855i	$0.560730\pi$
$860$		−	76.2134i		−	0.0886202i
$861$	−185.238	+	56.8511i	−0.215143	+	0.0660292i
$862$	−809.020			−0.938538
$863$		−	1332.56i		−	1.54410i	−0.635564	−	0.772048i	$-0.719232\pi$
$863$		−	1332.56i		−	1.54410i	0.635564	−	0.772048i	$-0.280768\pi$
$864$	95.7354	−	119.007i	0.110805	−	0.137740i
$865$	−597.221			−0.690429
$866$			799.224i			0.922892i
$867$	−388.913	−	1267.19i	−0.448573	−	1.46159i
$868$	318.375			0.366791
$869$		−	1008.69i		−	1.16075i
$870$	−76.6914	+	23.5372i	−0.0881510	+	0.0270543i
$871$	6.04737			0.00694301
$872$		−	603.446i		−	0.692025i
$873$	−663.687	+	449.745i	−0.760237	+	0.515172i
$874$	37.5049			0.0429118
$875$		−	35.8752i		−	0.0410002i
$876$	−39.8807	−	129.943i	−0.0455259	−	0.148337i
$877$	−1208.83			−1.37836			−0.689182	−	0.724588i	$-0.742030\pi$
$877$	−1208.83			−1.37836			−0.689182	+	0.724588i	$0.742030\pi$
$878$			1063.60i			1.21139i
$879$	272.159	−	83.5279i	0.309624	−	0.0950261i
$880$	−131.366			−0.149280
$881$			1411.07i			1.60167i	0.598886	+	0.800834i	$0.295610\pi$
$881$			1411.07i			1.60167i	−0.598886	+	0.800834i	$0.704390\pi$
$882$	276.348	+	407.805i	0.313319	+	0.462364i
$883$	−226.026			−0.255975			−0.127987	−	0.991776i	$-0.540852\pi$
$883$	−226.026			−0.255975			−0.127987	+	0.991776i	$0.540852\pi$
$884$			999.383i			1.13052i
$885$	−57.2967	−	186.690i	−0.0647420	−	0.210949i
$886$	−1077.25			−1.21586
$887$		−	719.925i		−	0.811641i	−0.913953	−	0.405820i	$-0.866986\pi$
$887$		−	719.925i		−	0.811641i	0.913953	−	0.405820i	$-0.133014\pi$
$888$	345.851	−	106.145i	0.389472	−	0.119532i
$889$	484.126			0.544573
$890$			228.968i			0.257267i
$891$	−1104.94	−	440.901i	−1.24012	−	0.494839i
$892$	514.911			0.577254
$893$			291.553i			0.326487i
$894$	68.1499	+	222.053i	0.0762303	+	0.248381i
$895$	110.543			0.123512
$896$			36.3031i			0.0405169i
$897$	−254.231	+	78.0255i	−0.283423	+	0.0869849i
$898$	−212.033			−0.236117
$899$			419.510i			0.466640i
$900$	−74.5049	+	50.4879i	−0.0827832	+	0.0560977i
$901$	−100.819			−0.111896
$902$		−	418.091i		−	0.463516i
$903$	48.1324	+	156.830i	0.0533028	+	0.173677i
$904$	−95.3146			−0.105436
$905$		−	639.486i		−	0.706615i
$906$	−371.630	+	114.056i	−0.410187	+	0.125890i
$907$	−533.280			−0.587961			−0.293980	−	0.955811i	$-0.594980\pi$
$907$	−533.280			−0.587961			−0.293980	+	0.955811i	$0.594980\pi$
$908$			4.29162i			0.00472645i
$909$	428.876	+	632.891i	0.471811	+	0.696250i
$910$	−187.555			−0.206104
$911$			1612.75i			1.77030i	0.465303	+	0.885152i	$0.345946\pi$
$911$			1612.75i			1.77030i	−0.465303	+	0.885152i	$0.654054\pi$
$912$	−19.4694	−	63.4372i	−0.0213480	−	0.0695583i
$913$	−1075.22			−1.17768
$914$			588.221i			0.643568i
$915$	53.2956	−	16.3569i	0.0582466	−	0.0178764i
$916$	215.858			0.235653
$917$			425.814i			0.464356i
$918$	−804.314	−	647.031i	−0.876159	−	0.704827i
$919$	−114.368			−0.124448			−0.0622242	−	0.998062i	$-0.519819\pi$
$919$	−114.368			−0.124448			−0.0622242	+	0.998062i	$0.519819\pi$
$920$		−	30.3315i		−	0.0329690i
$921$	18.8184	+	61.3160i	0.0204325	+	0.0665754i
$922$	−1128.87			−1.22437
$923$			1280.51i			1.38733i
$924$	270.322	−	82.9641i	0.292557	−	0.0897880i
$925$	−213.177			−0.230461
$926$		−	800.564i		−	0.864540i
$927$	1200.18	−	813.300i	1.29470	−	0.877346i
$928$	−47.8352			−0.0515465
$929$			96.6423i			0.104028i	0.998646	+	0.0520142i	$0.0165641\pi$
$929$			96.6423i			0.104028i	−0.998646	+	0.0520142i	$0.983436\pi$
$930$	138.087	+	449.929i	0.148481	+	0.483795i
$931$	214.024			0.229886
$932$			311.428i			0.334150i
$933$	−1152.35	+	353.666i	−1.23510	+	0.379063i
$934$	−996.676			−1.06711
$935$			887.843i			0.949564i
$936$	263.950	+	389.510i	0.281998	+	0.416144i
$937$	129.844			0.138574			0.0692869	−	0.997597i	$-0.477928\pi$
$937$	129.844			0.138574			0.0692869	+	0.997597i	$0.477928\pi$
$938$		−	1.48467i		−	0.00158281i
$939$	−378.662	−	1233.79i	−0.403261	−	1.31395i
$940$	235.788			0.250839
$941$			1705.82i			1.81278i	0.422445	+	0.906389i	$0.361172\pi$
$941$			1705.82i			1.81278i	−0.422445	+	0.906389i	$0.638828\pi$
$942$	−311.982	+	95.7497i	−0.331191	+	0.101645i
$943$	96.5342			0.102369
$944$		−	116.445i		−	0.123353i
$945$	121.429	−	150.946i	0.128496	−	0.159731i
$946$	−353.973			−0.374178
$947$			103.955i			0.109773i	0.998493	+	0.0548866i	$0.0174797\pi$
$947$			103.955i			0.109773i	−0.998493	+	0.0548866i	$0.982520\pi$
$948$	−120.902	−	393.936i	−0.127534	−	0.415544i
$949$	418.735			0.441239
$950$			39.1016i			0.0411596i
$951$	770.164	−	236.370i	0.809846	−	0.248548i
$952$	245.356			0.257727
$953$		−	567.724i		−	0.595722i	−0.954609	−	0.297861i	$-0.903727\pi$
$953$		−	567.724i		−	0.595722i	0.954609	−	0.297861i	$-0.0962733\pi$
$954$	−39.2941	+	26.6275i	−0.0411888	+	0.0279114i
$955$	−594.428			−0.622438
$956$		−	871.626i		−	0.911743i
$957$	109.319	+	356.193i	0.114230	+	0.372197i
$958$	656.774			0.685568
$959$			131.695i			0.137326i
$960$	−51.3038	+	15.7456i	−0.0534414	+	0.0164016i
$961$	1500.16			1.56104
$962$			1114.49i			1.15851i
$963$	−140.560	−	207.425i	−0.145961	−	0.215394i
$964$	−898.874			−0.932442
$965$			512.848i			0.531449i
$966$	19.1558	+	62.4154i	0.0198300	+	0.0646123i
$967$	803.246			0.830658			0.415329	−	0.909671i	$-0.363666\pi$
$967$	803.246			0.830658			0.415329	+	0.909671i	$0.363666\pi$
$968$			267.890i			0.276746i
$969$	−428.742	+	131.585i	−0.442458	+	0.135794i
$970$	281.695			0.290407
$971$		−	571.568i		−	0.588639i	−0.955707	−	0.294319i	$-0.904907\pi$
$971$		−	571.568i		−	0.588639i	0.955707	−	0.294319i	$-0.0950929\pi$
$972$	−484.372	−	39.7511i	−0.498325	−	0.0408962i
$973$	323.016			0.331979
$974$		−	1081.73i		−	1.11060i
$975$	−81.3472	−	265.054i	−0.0834330	−	0.271850i
$976$	33.2424			0.0340598
$977$		−	1763.11i		−	1.80462i	−0.431090	−	0.902309i	$-0.641871\pi$
$977$		−	1763.11i		−	1.80462i	0.431090	−	0.902309i	$-0.358129\pi$
$978$	116.682	−	35.8107i	0.119307	−	0.0366163i
$979$	1063.44			1.08625
$980$		−	173.089i		−	0.176621i
$981$	−1589.56	+	1077.16i	−1.62035	+	1.09802i
$982$	−1045.84			−1.06501
$983$			963.314i			0.979974i	0.871730	+	0.489987i	$0.162998\pi$
$983$			963.314i			0.979974i	−0.871730	+	0.489987i	$0.837002\pi$
$984$	−50.1124	−	163.281i	−0.0509272	−	0.165936i
$985$	177.643			0.180349
$986$			323.295i			0.327886i
$987$	−485.200	+	148.912i	−0.491590	+	0.150873i
$988$	204.423			0.206906
$989$		−	81.7297i		−	0.0826387i
$990$	234.491	+	346.038i	0.236859	+	0.349533i
$991$	831.222			0.838771			0.419385	−	0.907808i	$-0.362246\pi$
$991$	831.222			0.838771			0.419385	+	0.907808i	$0.362246\pi$
$992$			280.637i			0.282900i
$993$	250.540	+	816.334i	0.252306	+	0.822089i
$994$	314.374			0.316272
$995$			483.103i			0.485530i
$996$	−419.916	+	128.876i	−0.421602	+	0.129393i
$997$	1680.64			1.68570			0.842851	−	0.538147i	$-0.180875\pi$
$997$	1680.64			1.68570			0.842851	+	0.538147i	$0.180875\pi$
$998$			880.360i			0.882124i
$999$	−896.950	−	721.552i	−0.897848	−	0.722274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.16	yes	56
3.2	odd	2	inner	690.3.g.a.461.15	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.15	✓	56	3.2	odd	2	inner
690.3.g.a.461.16	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +3.16228 q^{10} -14.6872i q^{11} +(-1.76041 - 5.73594i) q^{12} +18.4837 q^{13} -4.53789i q^{14} +(6.41297 - 1.96819i) q^{15} +4.00000 q^{16} -27.0341i q^{17} +(-7.14007 - 10.5366i) q^{18} -5.52980 q^{19} +4.47214i q^{20} +(-2.82437 - 9.20266i) q^{21} +20.7708 q^{22} +4.79583i q^{23} +(8.11184 - 2.48959i) q^{24} -5.00000 q^{25} +26.1399i q^{26} +(-21.0377 - 16.9238i) q^{27} +6.41754 q^{28} +8.45614i q^{29} +(2.78345 + 9.06931i) q^{30} +49.6101 q^{31} +5.65685i q^{32} +(42.1224 - 12.9277i) q^{33} +38.2320 q^{34} +7.17503i q^{35} +(14.9010 - 10.0976i) q^{36} +42.6353 q^{37} -7.82032i q^{38} +(16.2694 + 53.0108i) q^{39} -6.32456 q^{40} -20.1288i q^{41} +(13.0145 - 3.99426i) q^{42} -17.0418 q^{43} +29.3744i q^{44} +(11.2894 + 16.6598i) q^{45} -6.78233 q^{46} -52.7239i q^{47} +(3.52081 + 11.4719i) q^{48} -38.7038 q^{49} -7.07107i q^{50} +(77.5330 - 23.7955i) q^{51} -36.9675 q^{52} -3.72931i q^{53} +(23.9339 - 29.7518i) q^{54} -32.8416 q^{55} +9.07578i q^{56} +(-4.86735 - 15.8593i) q^{57} -11.9588 q^{58} -29.1113i q^{59} +(-12.8259 + 3.93639i) q^{60} +8.31060 q^{61} +70.1592i q^{62} +(23.9069 - 16.2004i) q^{63} -8.00000 q^{64} -41.3309i q^{65} +(18.2825 + 59.5701i) q^{66} +0.327172 q^{67} +54.0683i q^{68} +(-13.7543 + 4.22131i) q^{69} -10.1470 q^{70} +69.2777i q^{71} +(14.2801 + 21.0732i) q^{72} +22.6543 q^{73} +60.2955i q^{74} +(-4.40102 - 14.3398i) q^{75} +11.0596 q^{76} +47.1278i q^{77} +(-74.9685 + 23.0085i) q^{78} +68.6785 q^{79} -8.94427i q^{80} +(30.0195 - 75.2319i) q^{81} +28.4664 q^{82} -73.2079i q^{83} +(5.64874 + 18.4053i) q^{84} -60.4501 q^{85} -24.1008i q^{86} +(-24.2519 + 7.44312i) q^{87} -41.5416 q^{88} +72.4059i q^{89} +(-23.5605 + 15.9657i) q^{90} -59.3101 q^{91} -9.59166i q^{92} +(43.6669 + 142.280i) q^{93} +74.5628 q^{94} +12.3650i q^{95} +(-16.2237 + 4.97918i) q^{96} +89.0797 q^{97} -54.7354i q^{98} +(74.1525 + 109.427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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