Properties

Label 210.2.i.a.121.1
Level $210$
Weight $2$
Character 210.121
Analytic conductor $1.677$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 210.121
Dual form 210.2.i.a.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +7.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +1.00000 q^{20} +(0.500000 - 2.59808i) q^{21} -1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.50000 + 6.06218i) q^{26} +1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -8.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} -4.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +1.00000 q^{36} +(1.50000 - 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-3.50000 - 6.06218i) q^{39} +(-0.500000 + 0.866025i) q^{40} +9.00000 q^{41} +(2.00000 + 1.73205i) q^{42} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(-3.50000 - 6.06218i) q^{52} +(0.500000 + 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -1.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(2.00000 - 3.46410i) q^{61} +6.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{65} +(0.500000 + 0.866025i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(2.00000 - 3.46410i) q^{68} +1.00000 q^{69} +(0.500000 - 2.59808i) q^{70} -14.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 + 12.1244i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-0.500000 + 0.866025i) q^{75} +1.00000 q^{76} +(-0.500000 + 2.59808i) q^{77} +7.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +12.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} -4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(4.00000 + 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(14.0000 + 12.1244i) q^{91} +1.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-0.500000 + 0.866025i) q^{96} -16.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} - q^{5} + 2q^{6} + 4q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} - q^{5} + 2q^{6} + 4q^{7} + 2q^{8} - q^{9} - q^{10} + q^{11} - q^{12} + 14q^{13} - 5q^{14} + 2q^{15} - q^{16} + 4q^{17} - q^{18} - q^{19} + 2q^{20} + q^{21} - 2q^{22} - q^{23} - q^{24} - q^{25} - 7q^{26} + 2q^{27} + q^{28} - 16q^{29} - q^{30} - 6q^{31} - q^{32} + q^{33} - 8q^{34} - 5q^{35} + 2q^{36} + 3q^{37} - q^{38} - 7q^{39} - q^{40} + 18q^{41} + 4q^{42} - 8q^{43} + q^{44} - q^{45} - q^{46} + 3q^{47} + 2q^{48} + 2q^{49} + 2q^{50} + 4q^{51} - 7q^{52} + q^{53} - q^{54} - 2q^{55} + 4q^{56} + 2q^{57} + 8q^{58} - 12q^{59} - q^{60} + 4q^{61} + 12q^{62} - 5q^{63} + 2q^{64} - 7q^{65} + q^{66} - 12q^{67} + 4q^{68} + 2q^{69} + q^{70} - 28q^{71} - q^{72} + 14q^{73} + 3q^{74} - q^{75} + 2q^{76} - q^{77} + 14q^{78} - 4q^{79} - q^{80} - q^{81} - 9q^{82} + 24q^{83} - 5q^{84} - 8q^{85} + 4q^{86} + 8q^{87} + q^{88} + 2q^{89} + 2q^{90} + 28q^{91} + 2q^{92} - 6q^{93} + 3q^{94} - q^{95} - q^{96} - 32q^{97} - 13q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 1.00000 0.408248
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 1.00000 0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) −1.00000 −0.213201
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.50000 + 6.06218i −0.686406 + 1.18889i
\(27\) 1.00000 0.192450
\(28\) 0.500000 2.59808i 0.0944911 0.490990i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.500000 0.866025i 0.0870388 0.150756i
\(34\) −4.00000 −0.685994
\(35\) −2.50000 + 0.866025i −0.422577 + 0.146385i
\(36\) 1.00000 0.166667
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) −0.500000 0.866025i −0.0811107 0.140488i
\(39\) −3.50000 6.06218i −0.560449 0.970725i
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 2.00000 + 1.73205i 0.308607 + 0.267261i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 1.00000 0.141421
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) −3.50000 6.06218i −0.485363 0.840673i
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −1.00000 −0.134840
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 1.00000 0.132453
\(58\) 4.00000 6.92820i 0.525226 0.909718i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 6.00000 0.762001
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) −3.50000 + 6.06218i −0.434122 + 0.751921i
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 1.00000 0.120386
\(70\) 0.500000 2.59808i 0.0597614 0.310530i
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 1.00000 0.114708
\(77\) −0.500000 + 2.59808i −0.0569803 + 0.296078i
\(78\) 7.00000 0.792594
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.50000 + 7.79423i −0.496942 + 0.860729i
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −2.50000 + 0.866025i −0.272772 + 0.0944911i
\(85\) −4.00000 −0.433861
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 4.00000 + 6.92820i 0.428845 + 0.742781i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i \(-0.799529\pi\)
0.914146 + 0.405385i \(0.132862\pi\)
\(90\) 1.00000 0.105409
\(91\) 14.0000 + 12.1244i 1.46760 + 1.27098i
\(92\) 1.00000 0.104257
\(93\) −3.00000 + 5.19615i −0.311086 + 0.538816i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) −0.500000 0.866025i −0.0512989 0.0888523i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) −1.00000 −0.100504
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 2.00000 + 3.46410i 0.198030 + 0.342997i
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) 7.00000 0.686406
\(105\) 2.00000 + 1.73205i 0.195180 + 0.169031i
\(106\) −1.00000 −0.0971286
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 0.500000 0.866025i 0.0476731 0.0825723i
\(111\) −3.00000 −0.284747
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) −0.500000 0.866025i −0.0466252 0.0807573i
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) −3.50000 + 6.06218i −0.323575 + 0.560449i
\(118\) 12.0000 1.10469
\(119\) −2.00000 + 10.3923i −0.183340 + 0.952661i
\(120\) 1.00000 0.0912871
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 2.00000 + 3.46410i 0.181071 + 0.313625i
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 1.00000 0.0894427
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) −3.50000 6.06218i −0.306970 0.531688i
\(131\) 6.50000 11.2583i 0.567908 0.983645i −0.428865 0.903369i \(-0.641086\pi\)
0.996773 0.0802763i \(-0.0255803\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 12.0000 1.03664
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 + 1.73205i 0.169031 + 0.146385i
\(141\) −3.00000 −0.252646
\(142\) 7.00000 12.1244i 0.587427 1.01745i
\(143\) 3.50000 + 6.06218i 0.292685 + 0.506945i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) −14.0000 −1.15865
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) −3.00000 −0.246598
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) −0.500000 + 0.866025i −0.0405554 + 0.0702439i
\(153\) −4.00000 −0.323381
\(154\) −2.00000 1.73205i −0.161165 0.139573i
\(155\) 6.00000 0.481932
\(156\) −3.50000 + 6.06218i −0.280224 + 0.485363i
\(157\) −7.50000 12.9904i −0.598565 1.03675i −0.993033 0.117836i \(-0.962404\pi\)
0.394468 0.918910i \(-0.370929\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 1.00000 0.0790569
\(161\) −2.50000 + 0.866025i −0.197028 + 0.0682524i
\(162\) 1.00000 0.0785674
\(163\) −4.00000 + 6.92820i −0.313304 + 0.542659i −0.979076 0.203497i \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) −5.00000 −0.386912 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(168\) 0.500000 2.59808i 0.0385758 0.200446i
\(169\) 36.0000 2.76923
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0.500000 2.59808i 0.0377964 0.196396i
\(176\) −1.00000 −0.0753778
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 1.00000 + 1.73205i 0.0749532 + 0.129823i
\(179\) −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) −17.5000 + 6.06218i −1.29719 + 0.449359i
\(183\) −4.00000 −0.295689
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) −3.00000 −0.218797
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 1.00000 0.0725476
\(191\) 5.00000 8.66025i 0.361787 0.626634i −0.626468 0.779447i \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −13.0000 22.5167i −0.935760 1.62078i −0.773272 0.634074i \(-0.781381\pi\)
−0.162488 0.986710i \(-0.551952\pi\)
\(194\) 8.00000 13.8564i 0.574367 0.994832i
\(195\) 7.00000 0.501280
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0.500000 0.866025i 0.0355335 0.0615457i
\(199\) 6.00000 + 10.3923i 0.425329 + 0.736691i 0.996451 0.0841740i \(-0.0268252\pi\)
−0.571122 + 0.820865i \(0.693492\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 0 0
\(203\) −16.0000 13.8564i −1.12298 0.972529i
\(204\) −4.00000 −0.280056
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) −3.50000 + 6.06218i −0.242681 + 0.420336i
\(209\) −1.00000 −0.0691714
\(210\) −2.50000 + 0.866025i −0.172516 + 0.0597614i
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) 0.500000 0.866025i 0.0343401 0.0594789i
\(213\) 7.00000 + 12.1244i 0.479632 + 0.830747i
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 1.00000 0.0680414
\(217\) 3.00000 15.5885i 0.203653 1.05821i
\(218\) −10.0000 −0.677285
\(219\) 7.00000 12.1244i 0.473016 0.819288i
\(220\) 0.500000 + 0.866025i 0.0337100 + 0.0583874i
\(221\) 14.0000 + 24.2487i 0.941742 + 1.63114i
\(222\) 1.50000 2.59808i 0.100673 0.174371i
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 1.00000 0.0666667
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) −0.500000 0.866025i −0.0331133 0.0573539i
\(229\) 11.0000 19.0526i 0.726900 1.25903i −0.231287 0.972886i \(-0.574293\pi\)
0.958187 0.286143i \(-0.0923732\pi\)
\(230\) 1.00000 0.0659380
\(231\) 2.50000 0.866025i 0.164488 0.0569803i
\(232\) −8.00000 −0.525226
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) −3.50000 6.06218i −0.228802 0.396297i
\(235\) 1.50000 + 2.59808i 0.0978492 + 0.169480i
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) 4.00000 0.259828
\(238\) −8.00000 6.92820i −0.518563 0.449089i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −4.00000 −0.256074
\(245\) −6.50000 2.59808i −0.415270 0.165985i
\(246\) 9.00000 0.573819
\(247\) −3.50000 + 6.06218i −0.222700 + 0.385727i
\(248\) −3.00000 5.19615i −0.190500 0.329956i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 2.00000 + 1.73205i 0.125988 + 0.109109i
\(253\) −1.00000 −0.0628695
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 2.00000 + 3.46410i 0.125245 + 0.216930i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.00000 6.92820i 0.249513 0.432169i −0.713878 0.700270i \(-0.753063\pi\)
0.963391 + 0.268101i \(0.0863961\pi\)
\(258\) −4.00000 −0.249029
\(259\) 7.50000 2.59808i 0.466027 0.161437i
\(260\) 7.00000 0.434122
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 6.50000 + 11.2583i 0.401571 + 0.695542i
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) −1.00000 −0.0614295
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) −2.00000 −0.122398
\(268\) −6.00000 + 10.3923i −0.366508 + 0.634811i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) −4.00000 −0.242536
\(273\) 3.50000 18.1865i 0.211830 1.10070i
\(274\) −2.00000 −0.120824
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 6.00000 0.359211
\(280\) −2.50000 + 0.866025i −0.149404 + 0.0517549i
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) 1.00000 + 1.73205i 0.0594438 + 0.102960i 0.894216 0.447636i \(-0.147734\pi\)
−0.834772 + 0.550596i \(0.814401\pi\)
\(284\) 7.00000 + 12.1244i 0.415374 + 0.719448i
\(285\) −0.500000 + 0.866025i −0.0296174 + 0.0512989i
\(286\) −7.00000 −0.413919
\(287\) 18.0000 + 15.5885i 1.06251 + 0.920158i
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 4.00000 + 6.92820i 0.234888 + 0.406838i
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) 7.00000 12.1244i 0.409644 0.709524i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 12.0000 0.698667
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) 0.500000 + 0.866025i 0.0290129 + 0.0502519i
\(298\) 2.00000 + 3.46410i 0.115857 + 0.200670i
\(299\) −3.50000 + 6.06218i −0.202410 + 0.350585i
\(300\) 1.00000 0.0577350
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) −2.00000 −0.115087
\(303\) 0 0
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 2.50000 0.866025i 0.142451 0.0493464i
\(309\) 16.0000 0.910208
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) −8.00000 13.8564i −0.453638 0.785725i 0.544970 0.838455i \(-0.316541\pi\)
−0.998609 + 0.0527306i \(0.983208\pi\)
\(312\) −3.50000 6.06218i −0.198148 0.343203i
\(313\) 12.0000 20.7846i 0.678280 1.17482i −0.297218 0.954810i \(-0.596059\pi\)
0.975499 0.220006i \(-0.0706077\pi\)
\(314\) 15.0000 0.846499
\(315\) 0.500000 2.59808i 0.0281718 0.146385i
\(316\) 4.00000 0.225018
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 0.500000 + 0.866025i 0.0280386 + 0.0485643i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −18.0000 −1.00466
\(322\) 0.500000 2.59808i 0.0278639 0.144785i
\(323\) −4.00000 −0.222566
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −3.50000 6.06218i −0.194145 0.336269i
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) 5.00000 8.66025i 0.276501 0.478913i
\(328\) 9.00000 0.496942
\(329\) 7.50000 2.59808i 0.413488 0.143237i
\(330\) −1.00000 −0.0550482
\(331\) 4.50000 7.79423i 0.247342 0.428410i −0.715445 0.698669i \(-0.753776\pi\)
0.962788 + 0.270259i \(0.0871094\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) 1.50000 + 2.59808i 0.0821995 + 0.142374i
\(334\) 2.50000 4.33013i 0.136794 0.236934i
\(335\) 12.0000 0.655630
\(336\) 2.00000 + 1.73205i 0.109109 + 0.0944911i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −18.0000 + 31.1769i −0.979071 + 1.69580i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 1.00000 0.0540738
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −4.00000 −0.215666
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 17.0000 + 29.4449i 0.912608 + 1.58068i 0.810366 + 0.585923i \(0.199268\pi\)
0.102241 + 0.994760i \(0.467399\pi\)
\(348\) 4.00000 6.92820i 0.214423 0.371391i
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 2.00000 + 1.73205i 0.106904 + 0.0925820i
\(351\) 7.00000 0.373632
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 4.00000 + 6.92820i 0.212899 + 0.368751i 0.952620 0.304162i \(-0.0983763\pi\)
−0.739722 + 0.672913i \(0.765043\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) 7.00000 12.1244i 0.371521 0.643494i
\(356\) −2.00000 −0.106000
\(357\) 10.0000 3.46410i 0.529256 0.183340i
\(358\) 13.0000 0.687071
\(359\) −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i \(0.565588\pi\)
−0.745409 + 0.666608i \(0.767746\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 6.00000 10.3923i 0.315353 0.546207i
\(363\) −10.0000 −0.524864
\(364\) 3.50000 18.1865i 0.183450 0.953233i
\(365\) −14.0000 −0.732793
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) −9.50000 16.4545i −0.495896 0.858917i 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) −3.00000 −0.155963
\(371\) −0.500000 + 2.59808i −0.0259587 + 0.134885i
\(372\) 6.00000 0.311086
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) −2.00000 3.46410i −0.103418 0.179124i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) −56.0000 −2.88415
\(378\) −2.50000 + 0.866025i −0.128586 + 0.0445435i
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) −0.500000 + 0.866025i −0.0256495 + 0.0444262i
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) 5.00000 + 8.66025i 0.255822 + 0.443097i
\(383\) −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i \(-0.941102\pi\)
0.650796 + 0.759253i \(0.274435\pi\)
\(384\) 1.00000 0.0510310
\(385\) −2.00000 1.73205i −0.101929 0.0882735i
\(386\) 26.0000 1.32337
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) 7.00000 + 12.1244i 0.354914 + 0.614729i 0.987103 0.160085i \(-0.0511768\pi\)
−0.632189 + 0.774814i \(0.717843\pi\)
\(390\) −3.50000 + 6.06218i −0.177229 + 0.306970i
\(391\) −4.00000 −0.202289
\(392\) 1.00000 + 6.92820i 0.0505076 + 0.349927i
\(393\) −13.0000 −0.655763
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) −2.00000 3.46410i −0.100631 0.174298i
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) −12.0000 −0.601506
\(399\) 2.00000 + 1.73205i 0.100125 + 0.0867110i
\(400\) 1.00000 0.0500000
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) −6.00000 10.3923i −0.299253 0.518321i
\(403\) −21.0000 36.3731i −1.04608 1.81187i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 20.0000 6.92820i 0.992583 0.343841i
\(407\) 3.00000 0.148704
\(408\) 2.00000 3.46410i 0.0990148 0.171499i
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) −4.50000 7.79423i −0.222239 0.384930i
\(411\) 1.00000 1.73205i 0.0493264 0.0854358i
\(412\) 16.0000 0.788263
\(413\) 6.00000 31.1769i 0.295241 1.53412i
\(414\) 1.00000 0.0491473
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) −3.50000 6.06218i −0.171602 0.297223i
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 0.500000 0.866025i 0.0244558 0.0423587i
\(419\) 11.0000 0.537385 0.268693 0.963226i \(-0.413408\pi\)
0.268693 + 0.963226i \(0.413408\pi\)
\(420\) 0.500000 2.59808i 0.0243975 0.126773i
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 7.50000 12.9904i 0.365094 0.632362i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) −14.0000 −0.678302
\(427\) 10.0000 3.46410i 0.483934 0.167640i
\(428\) −18.0000 −0.870063
\(429\) 3.50000 6.06218i 0.168982 0.292685i
\(430\) 2.00000 + 3.46410i 0.0964486 + 0.167054i
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 40.0000 1.92228 0.961139 0.276066i \(-0.0890309\pi\)
0.961139 + 0.276066i \(0.0890309\pi\)
\(434\) 12.0000 + 10.3923i 0.576018 + 0.498847i
\(435\) −8.00000 −0.383571
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) −0.500000 0.866025i −0.0239182 0.0414276i
\(438\) 7.00000 + 12.1244i 0.334473 + 0.579324i
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) −28.0000 −1.33182
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 1.50000 + 2.59808i 0.0711868 + 0.123299i
\(445\) 1.00000 + 1.73205i 0.0474045 + 0.0821071i
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) −4.00000 −0.189194
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) −25.0000 −1.17982 −0.589911 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) 4.50000 + 7.79423i 0.211897 + 0.367016i
\(452\) 3.00000 + 5.19615i 0.141108 + 0.244406i
\(453\) 1.00000 1.73205i 0.0469841 0.0813788i
\(454\) −20.0000 −0.938647
\(455\) −17.5000 + 6.06218i −0.820413 + 0.284199i
\(456\) 1.00000 0.0468293
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 11.0000 + 19.0526i 0.513996 + 0.890268i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) −0.500000 + 0.866025i −0.0233126 + 0.0403786i
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) −0.500000 + 2.59808i −0.0232621 + 0.120873i
\(463\) 33.0000 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) −3.00000 5.19615i −0.139122 0.240966i
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) 7.00000 0.323575
\(469\) 6.00000 31.1769i 0.277054 1.43962i
\(470\) −3.00000 −0.138380
\(471\) −7.50000 + 12.9904i −0.345582 + 0.598565i
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) 1.00000 0.0458831
\(476\) 10.0000 3.46410i 0.458349 0.158777i
\(477\) −1.00000 −0.0457869
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) −13.0000 22.5167i −0.593985 1.02881i −0.993689 0.112168i \(-0.964220\pi\)
0.399704 0.916644i \(-0.369113\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) 7.00000 0.318841
\(483\) 2.00000 + 1.73205i 0.0910032 + 0.0788110i
\(484\) −10.0000 −0.454545
\(485\) 8.00000 13.8564i 0.363261 0.629187i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i \(-0.108650\pi\)
−0.761052 + 0.648691i \(0.775317\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 8.00000 0.361773
\(490\) 5.50000 4.33013i 0.248465 0.195615i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −4.50000 + 7.79423i −0.202876 + 0.351391i
\(493\) −16.0000 27.7128i −0.720604 1.24812i
\(494\) −3.50000 6.06218i −0.157472 0.272750i
\(495\) 0.500000 0.866025i 0.0224733 0.0389249i
\(496\) 6.00000 0.269408
\(497\) −28.0000 24.2487i −1.25597 1.08770i
\(498\) 12.0000 0.537733
\(499\) −12.0000 + 20.7846i −0.537194 + 0.930447i 0.461860 + 0.886953i \(0.347182\pi\)
−0.999054 + 0.0434940i \(0.986151\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 2.50000 + 4.33013i 0.111692 + 0.193456i
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) 28.0000 1.24846 0.624229 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) −2.50000 + 0.866025i −0.111359 + 0.0385758i
\(505\) 0 0
\(506\) 0.500000 0.866025i 0.0222277 0.0384995i
\(507\) −18.0000 31.1769i −0.799408 1.38462i
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) −4.00000 −0.177123
\(511\) −7.00000 + 36.3731i −0.309662 + 1.60905i
\(512\) 1.00000 0.0441942
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) 4.00000 + 6.92820i 0.176432 + 0.305590i
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 3.00000 0.131940
\(518\) −1.50000 + 7.79423i −0.0659062 + 0.342459i
\(519\) −21.0000 −0.921798
\(520\) −3.50000 + 6.06218i −0.153485 + 0.265844i
\(521\) 10.5000 + 18.1865i 0.460013 + 0.796766i 0.998961 0.0455727i \(-0.0145113\pi\)
−0.538948 + 0.842339i \(0.681178\pi\)
\(522\) 4.00000 + 6.92820i 0.175075 + 0.303239i
\(523\) 7.00000 12.1244i 0.306089 0.530161i −0.671414 0.741082i \(-0.734313\pi\)
0.977503 + 0.210921i \(0.0676463\pi\)
\(524\) −13.0000 −0.567908
\(525\) −2.50000 + 0.866025i −0.109109 + 0.0377964i
\(526\) −16.0000 −0.697633
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0.500000 + 0.866025i 0.0217597 + 0.0376889i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0.500000 0.866025i 0.0217186 0.0376177i
\(531\) 12.0000 0.520756
\(532\) 2.00000 + 1.73205i 0.0867110 + 0.0750939i
\(533\) 63.0000 2.72883
\(534\) 1.00000 1.73205i 0.0432742 0.0749532i
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) −6.50000 + 11.2583i −0.280496 + 0.485833i
\(538\) 0 0
\(539\) −5.50000 + 4.33013i −0.236902 + 0.186512i
\(540\) 1.00000 0.0430331
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) 6.00000 + 10.3923i 0.257485 + 0.445976i
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) −10.0000 −0.428353
\(546\) 14.0000 + 12.1244i 0.599145 + 0.518875i
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) 0.500000 + 0.866025i 0.0213201 + 0.0369274i
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 1.00000 0.0425628
\(553\) −10.0000 + 3.46410i −0.425243 + 0.147309i
\(554\) −2.00000 −0.0849719
\(555\) 1.50000 2.59808i 0.0636715 0.110282i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −22.5000 38.9711i −0.953356 1.65126i −0.738087 0.674705i \(-0.764271\pi\)
−0.215268 0.976555i \(-0.569063\pi\)
\(558\) −3.00000 + 5.19615i −0.127000 + 0.219971i
\(559\) −28.0000 −1.18427
\(560\) 0.500000 2.59808i 0.0211289 0.109789i
\(561\) 4.00000 0.168880
\(562\) −1.50000 + 2.59808i −0.0632737 + 0.109593i
\(563\) −7.00000 12.1244i −0.295015 0.510981i 0.679974 0.733237i \(-0.261991\pi\)
−0.974988 + 0.222256i \(0.928658\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) −2.00000 −0.0840663
\(567\) 0.500000 2.59808i 0.0209980 0.109109i
\(568\) −14.0000 −0.587427
\(569\) 18.5000 32.0429i 0.775560 1.34331i −0.158919 0.987292i \(-0.550801\pi\)
0.934479 0.356018i \(-0.115866\pi\)
\(570\) −0.500000 0.866025i −0.0209427 0.0362738i
\(571\) 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i \(-0.113131\pi\)
−0.770108 + 0.637913i \(0.779798\pi\)
\(572\) 3.50000 6.06218i 0.146342 0.253472i
\(573\) −10.0000 −0.417756
\(574\) −22.5000 + 7.79423i −0.939132 + 0.325325i
\(575\) 1.00000 0.0417029
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −13.0000 + 22.5167i −0.540262 + 0.935760i
\(580\) −8.00000 −0.332182
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) −16.0000 −0.663221
\(583\) −0.500000 + 0.866025i −0.0207079 + 0.0358671i
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) −3.50000 6.06218i −0.144707 0.250640i
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) −6.50000 2.59808i −0.268055 0.107143i
\(589\) 6.00000 0.247226
\(590\) −6.00000 + 10.3923i −0.247016 + 0.427844i
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −6.00000 + 10.3923i −0.246390 + 0.426761i −0.962522 0.271205i \(-0.912578\pi\)
0.716131 + 0.697966i \(0.245911\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −8.00000 6.92820i −0.327968 0.284029i
\(596\) −4.00000 −0.163846
\(597\) 6.00000 10.3923i 0.245564 0.425329i
\(598\) −3.50000 6.06218i −0.143126 0.247901i
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 10.0000 3.46410i 0.407570 0.141186i
\(603\) 12.0000 0.488678
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) −12.5000 + 21.6506i −0.507359 + 0.878772i 0.492604 + 0.870253i \(0.336045\pi\)
−0.999964 + 0.00851879i \(0.997288\pi\)
\(608\) 1.00000 0.0405554
\(609\) −4.00000 + 20.7846i −0.162088 + 0.842235i
\(610\) −4.00000 −0.161955
\(611\) 10.5000 18.1865i 0.424785 0.735748i
\(612\) 2.00000 + 3.46410i 0.0808452 + 0.140028i
\(613\) 7.50000 + 12.9904i 0.302922 + 0.524677i 0.976797 0.214169i \(-0.0687045\pi\)
−0.673874 + 0.738846i \(0.735371\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 9.00000 0.362915
\(616\) −0.500000 + 2.59808i −0.0201456 + 0.104679i
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) −8.00000 + 13.8564i −0.321807 + 0.557386i
\(619\) 3.50000 + 6.06218i 0.140677 + 0.243659i 0.927752 0.373198i \(-0.121739\pi\)
−0.787075 + 0.616858i \(0.788405\pi\)
\(620\) −3.00000 5.19615i −0.120483 0.208683i
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 16.0000 0.641542
\(623\) 5.00000 1.73205i 0.200321 0.0693932i
\(624\) 7.00000 0.280224
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 12.0000 + 20.7846i 0.479616 + 0.830720i
\(627\) 0.500000 + 0.866025i 0.0199681 + 0.0345857i
\(628\) −7.50000 + 12.9904i −0.299283 + 0.518373i
\(629\) 12.0000 0.478471
\(630\) 2.00000 + 1.73205i 0.0796819 + 0.0690066i
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) −2.00000 + 3.46410i −0.0795557 + 0.137795i
\(633\) 7.50000 + 12.9904i 0.298098 + 0.516321i
\(634\) −5.00000 8.66025i −0.198575 0.343943i
\(635\) −2.50000 + 4.33013i −0.0992095 + 0.171836i
\(636\) −1.00000 −0.0396526
\(637\) 7.00000 + 48.4974i 0.277350 + 1.92154i
\(638\) 8.00000 0.316723
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 11.5000 + 19.9186i 0.454223 + 0.786737i 0.998643 0.0520757i \(-0.0165837\pi\)
−0.544420 + 0.838812i \(0.683250\pi\)
\(642\) 9.00000 15.5885i 0.355202 0.615227i
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) 2.00000 + 1.73205i 0.0788110 + 0.0682524i
\(645\) −4.00000 −0.157500
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) 7.50000 + 12.9904i 0.294855 + 0.510705i 0.974951 0.222419i \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 7.00000 0.274563
\(651\) −15.0000 + 5.19615i −0.587896 + 0.203653i
\(652\) 8.00000 0.313304
\(653\) −14.5000 + 25.1147i −0.567429 + 0.982816i 0.429390 + 0.903119i \(0.358728\pi\)
−0.996819 + 0.0796966i \(0.974605\pi\)
\(654\) 5.00000 + 8.66025i 0.195515 + 0.338643i
\(655\) 6.50000 + 11.2583i 0.253976 + 0.439899i
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) −14.0000 −0.546192
\(658\) −1.50000 + 7.79423i −0.0584761 + 0.303851i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) −4.00000 6.92820i −0.155582 0.269476i 0.777689 0.628649i \(-0.216392\pi\)
−0.933271 + 0.359174i \(0.883059\pi\)
\(662\) 4.50000 + 7.79423i 0.174897 + 0.302931i
\(663\) 14.0000 24.2487i 0.543715 0.941742i
\(664\) 12.0000 0.465690
\(665\) 0.500000 2.59808i 0.0193892 0.100749i
\(666\) −3.00000 −0.116248
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) 2.50000 + 4.33013i 0.0967279 + 0.167538i
\(669\) 2.00000 + 3.46410i 0.0773245 + 0.133930i
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) 4.00000 0.154418
\(672\) −2.50000 + 0.866025i −0.0964396 + 0.0334077i
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) −18.0000 31.1769i −0.692308 1.19911i
\(677\) −0.500000 + 0.866025i −0.0192166 + 0.0332841i −0.875474 0.483266i \(-0.839451\pi\)
0.856257 + 0.516550i \(0.172784\pi\)
\(678\) −6.00000 −0.230429
\(679\) −32.0000 27.7128i −1.22805 1.06352i
\(680\) −4.00000 −0.153393
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) −2.00000 −0.0764161
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) −22.0000 −0.839352
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 3.50000 + 6.06218i 0.133339 + 0.230951i
\(690\) −0.500000 0.866025i −0.0190347 0.0329690i
\(691\) −6.00000 + 10.3923i −0.228251 + 0.395342i −0.957290 0.289130i \(-0.906634\pi\)
0.729039 + 0.684472i \(0.239967\pi\)
\(692\) −21.0000 −0.798300
\(693\) −2.00000 1.73205i −0.0759737 0.0657952i
\(694\) −34.0000 −1.29062
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 14.0000 24.2487i 0.529908 0.917827i
\(699\) 26.0000 0.983410
\(700\) −2.50000 + 0.866025i −0.0944911 + 0.0327327i
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) −3.50000 + 6.06218i −0.132099 + 0.228802i
\(703\) 1.50000 + 2.59808i 0.0565736 + 0.0979883i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 1.50000 2.59808i 0.0564933 0.0978492i
\(706\) −8.00000 −0.301084
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i \(-0.857265\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(710\) 7.00000 + 12.1244i 0.262705 + 0.455019i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) 1.00000 1.73205i 0.0374766 0.0649113i
\(713\) 6.00000 0.224702
\(714\) −2.00000 + 10.3923i −0.0748481 + 0.388922i
\(715\) −7.00000 −0.261785
\(716\) −6.50000 + 11.2583i −0.242916 + 0.420744i
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) −18.0000 31.1769i −0.671754 1.16351i
\(719\) −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i \(-0.994448\pi\)
0.515030 + 0.857172i \(0.327781\pi\)
\(720\) 1.00000 0.0372678
\(721\) −40.0000 + 13.8564i −1.48968 + 0.516040i
\(722\) −18.0000 −0.669891
\(723\) −3.50000 + 6.06218i −0.130166 + 0.225455i
\(724\) 6.00000 + 10.3923i 0.222988 + 0.386227i
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 14.0000 + 12.1244i 0.518875 + 0.449359i
\(729\) 1.00000 0.0370370
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) −18.5000 + 32.0429i −0.683313 + 1.18353i 0.290651 + 0.956829i \(0.406128\pi\)
−0.973964 + 0.226704i \(0.927205\pi\)
\(734\) 19.0000 0.701303
\(735\) 1.00000 + 6.92820i 0.0368856 + 0.255551i
\(736\) 1.00000 0.0368605
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) −4.50000 7.79423i −0.165647 0.286910i
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 1.50000 2.59808i 0.0551411 0.0955072i
\(741\) 7.00000 0.257151
\(742\) −2.00000 1.73205i −0.0734223 0.0635856i
\(743\) −9.00000 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) 2.00000 + 3.46410i 0.0732743 + 0.126915i
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) −6.00000 + 10.3923i −0.219529 + 0.380235i
\(748\) 4.00000 0.146254
\(749\) 45.0000 15.5885i 1.64426 0.569590i
\(750\) 1.00000 0.0365148
\(751\) 13.0000 22.5167i 0.474377 0.821645i −0.525193 0.850983i \(-0.676007\pi\)
0.999570 + 0.0293387i \(0.00934013\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) 28.0000 48.4974i 1.01970 1.76617i
\(755\) −2.00000 −0.0727875
\(756\) 0.500000 2.59808i 0.0181848 0.0944911i
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) 0.500000 + 0.866025i 0.0181489 + 0.0314347i
\(760\) −0.500000 0.866025i −0.0181369 0.0314140i
\(761\) 8.50000 14.7224i 0.308125 0.533688i −0.669827 0.742517i \(-0.733632\pi\)
0.977952 + 0.208829i \(0.0669652\pi\)
\(762\) 5.00000 0.181131
\(763\) −5.00000 + 25.9808i −0.181012 + 0.940567i
\(764\) −10.0000 −0.361787
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) −6.50000 11.2583i −0.234855 0.406780i
\(767\) −42.0000 72.7461i −1.51653 2.62671i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) 2.50000 0.866025i 0.0900937 0.0312094i
\(771\) −8.00000 −0.288113
\(772\) −13.0000 + 22.5167i −0.467880 + 0.810392i
\(773\) −21.5000 37.2391i −0.773301 1.33940i −0.935744 0.352679i \(-0.885271\pi\)
0.162443 0.986718i \(-0.448063\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) −3.00000 + 5.19615i −0.107763 + 0.186651i
\(776\) −16.0000 −0.574367
\(777\)