Properties

Label 570.2.i.i.391.1
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \(x^{4} + 7 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.i.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} -2.64575 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 - 0.866025i) q^{6} -2.64575 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -6.29150 q^{11} -1.00000 q^{12} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.82288 - 4.88936i) q^{17} -1.00000 q^{18} +(-1.67712 - 4.02334i) q^{19} -1.00000 q^{20} +(-1.32288 + 2.29129i) q^{21} +(-3.14575 + 5.44860i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +(1.32288 + 2.29129i) q^{28} +(1.82288 + 3.15731i) q^{29} -1.00000 q^{30} +7.29150 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.14575 + 5.44860i) q^{33} +(-2.82288 - 4.88936i) q^{34} +(-1.32288 + 2.29129i) q^{35} +(-0.500000 + 0.866025i) q^{36} +8.29150 q^{37} +(-4.32288 - 0.559237i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(4.32288 - 7.48744i) q^{41} +(1.32288 + 2.29129i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(3.14575 + 5.44860i) q^{44} -1.00000 q^{45} -1.00000 q^{46} +(-6.29150 - 10.8972i) q^{47} +(0.500000 + 0.866025i) q^{48} -1.00000 q^{50} +(-2.82288 - 4.88936i) q^{51} +(2.32288 + 4.02334i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.14575 + 5.44860i) q^{55} +2.64575 q^{56} +(-4.32288 - 0.559237i) q^{57} +3.64575 q^{58} +(-2.64575 + 4.58258i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-3.46863 - 6.00784i) q^{61} +(3.64575 - 6.31463i) q^{62} +(1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(3.14575 + 5.44860i) q^{66} +(4.82288 + 8.35347i) q^{67} -5.64575 q^{68} -1.00000 q^{69} +(1.32288 + 2.29129i) q^{70} +(6.82288 - 11.8176i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-6.82288 + 11.8176i) q^{73} +(4.14575 - 7.18065i) q^{74} -1.00000 q^{75} +(-2.64575 + 3.46410i) q^{76} +16.6458 q^{77} +(-2.64575 + 4.58258i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.32288 - 7.48744i) q^{82} +16.5830 q^{83} +2.64575 q^{84} +(-2.82288 - 4.88936i) q^{85} +(3.00000 + 5.19615i) q^{86} +3.64575 q^{87} +6.29150 q^{88} +(-6.61438 - 11.4564i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-0.500000 + 0.866025i) q^{92} +(3.64575 - 6.31463i) q^{93} -12.5830 q^{94} +(-4.32288 - 0.559237i) q^{95} +1.00000 q^{96} +(0.822876 - 1.42526i) q^{97} +(3.14575 + 5.44860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 4q^{8} - 2q^{9} - 2q^{10} - 4q^{11} - 4q^{12} - 2q^{15} - 2q^{16} + 6q^{17} - 4q^{18} - 12q^{19} - 4q^{20} - 2q^{22} - 2q^{23} - 2q^{24} - 2q^{25} - 4q^{27} + 2q^{29} - 4q^{30} + 8q^{31} + 2q^{32} - 2q^{33} - 6q^{34} - 2q^{36} + 12q^{37} - 12q^{38} - 2q^{40} + 12q^{41} - 12q^{43} + 2q^{44} - 4q^{45} - 4q^{46} - 4q^{47} + 2q^{48} - 4q^{50} - 6q^{51} + 4q^{53} - 2q^{54} - 2q^{55} - 12q^{57} + 4q^{58} - 2q^{60} + 2q^{61} + 4q^{62} + 4q^{64} + 2q^{66} + 14q^{67} - 12q^{68} - 4q^{69} + 22q^{71} + 2q^{72} - 22q^{73} + 6q^{74} - 4q^{75} + 56q^{77} + 2q^{80} - 2q^{81} - 12q^{82} + 24q^{83} - 6q^{85} + 12q^{86} + 4q^{87} + 4q^{88} - 2q^{90} - 2q^{92} + 4q^{93} - 8q^{94} - 12q^{95} + 4q^{96} - 2q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −2.64575 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −6.29150 −1.89696 −0.948480 0.316838i \(-0.897379\pi\)
−0.948480 + 0.316838i \(0.897379\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) −1.32288 + 2.29129i −0.353553 + 0.612372i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.82288 4.88936i 0.684648 1.18584i −0.288899 0.957359i \(-0.593289\pi\)
0.973547 0.228486i \(-0.0733774\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.67712 4.02334i −0.384759 0.923017i
\(20\) −1.00000 −0.223607
\(21\) −1.32288 + 2.29129i −0.288675 + 0.500000i
\(22\) −3.14575 + 5.44860i −0.670676 + 1.16165i
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.32288 + 2.29129i 0.250000 + 0.433013i
\(29\) 1.82288 + 3.15731i 0.338500 + 0.586298i 0.984151 0.177334i \(-0.0567473\pi\)
−0.645651 + 0.763632i \(0.723414\pi\)
\(30\) −1.00000 −0.182574
\(31\) 7.29150 1.30959 0.654796 0.755805i \(-0.272754\pi\)
0.654796 + 0.755805i \(0.272754\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −3.14575 + 5.44860i −0.547605 + 0.948480i
\(34\) −2.82288 4.88936i −0.484119 0.838519i
\(35\) −1.32288 + 2.29129i −0.223607 + 0.387298i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 8.29150 1.36311 0.681557 0.731765i \(-0.261303\pi\)
0.681557 + 0.731765i \(0.261303\pi\)
\(38\) −4.32288 0.559237i −0.701263 0.0907202i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 4.32288 7.48744i 0.675120 1.16934i −0.301314 0.953525i \(-0.597425\pi\)
0.976434 0.215817i \(-0.0692414\pi\)
\(42\) 1.32288 + 2.29129i 0.204124 + 0.353553i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) 3.14575 + 5.44860i 0.474240 + 0.821408i
\(45\) −1.00000 −0.149071
\(46\) −1.00000 −0.147442
\(47\) −6.29150 10.8972i −0.917710 1.58952i −0.802884 0.596135i \(-0.796702\pi\)
−0.114825 0.993386i \(-0.536631\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −2.82288 4.88936i −0.395282 0.684648i
\(52\) 0 0
\(53\) 2.32288 + 4.02334i 0.319072 + 0.552648i 0.980295 0.197541i \(-0.0632956\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −3.14575 + 5.44860i −0.424173 + 0.734689i
\(56\) 2.64575 0.353553
\(57\) −4.32288 0.559237i −0.572579 0.0740728i
\(58\) 3.64575 0.478711
\(59\) −2.64575 + 4.58258i −0.344447 + 0.596601i −0.985253 0.171103i \(-0.945267\pi\)
0.640806 + 0.767703i \(0.278600\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) −3.46863 6.00784i −0.444112 0.769225i 0.553878 0.832598i \(-0.313147\pi\)
−0.997990 + 0.0633732i \(0.979814\pi\)
\(62\) 3.64575 6.31463i 0.463011 0.801958i
\(63\) 1.32288 + 2.29129i 0.166667 + 0.288675i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.14575 + 5.44860i 0.387215 + 0.670676i
\(67\) 4.82288 + 8.35347i 0.589208 + 1.02054i 0.994336 + 0.106278i \(0.0338935\pi\)
−0.405128 + 0.914260i \(0.632773\pi\)
\(68\) −5.64575 −0.684648
\(69\) −1.00000 −0.120386
\(70\) 1.32288 + 2.29129i 0.158114 + 0.273861i
\(71\) 6.82288 11.8176i 0.809726 1.40249i −0.103327 0.994647i \(-0.532949\pi\)
0.913054 0.407840i \(-0.133718\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −6.82288 + 11.8176i −0.798557 + 1.38314i 0.121998 + 0.992530i \(0.461070\pi\)
−0.920556 + 0.390611i \(0.872264\pi\)
\(74\) 4.14575 7.18065i 0.481934 0.834734i
\(75\) −1.00000 −0.115470
\(76\) −2.64575 + 3.46410i −0.303488 + 0.397360i
\(77\) 16.6458 1.89696
\(78\) 0 0
\(79\) −2.64575 + 4.58258i −0.297670 + 0.515580i −0.975603 0.219544i \(-0.929543\pi\)
0.677932 + 0.735124i \(0.262876\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.32288 7.48744i −0.477382 0.826849i
\(83\) 16.5830 1.82022 0.910111 0.414365i \(-0.135996\pi\)
0.910111 + 0.414365i \(0.135996\pi\)
\(84\) 2.64575 0.288675
\(85\) −2.82288 4.88936i −0.306184 0.530326i
\(86\) 3.00000 + 5.19615i 0.323498 + 0.560316i
\(87\) 3.64575 0.390866
\(88\) 6.29150 0.670676
\(89\) −6.61438 11.4564i −0.701123 1.21438i −0.968073 0.250670i \(-0.919349\pi\)
0.266950 0.963710i \(-0.413984\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 0 0
\(92\) −0.500000 + 0.866025i −0.0521286 + 0.0902894i
\(93\) 3.64575 6.31463i 0.378047 0.654796i
\(94\) −12.5830 −1.29784
\(95\) −4.32288 0.559237i −0.443518 0.0573765i
\(96\) 1.00000 0.102062
\(97\) 0.822876 1.42526i 0.0835504 0.144713i −0.821222 0.570609i \(-0.806707\pi\)
0.904773 + 0.425895i \(0.140041\pi\)
\(98\) 0 0
\(99\) 3.14575 + 5.44860i 0.316160 + 0.547605i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −5.93725 10.2836i −0.590779 1.02326i −0.994128 0.108213i \(-0.965487\pi\)
0.403349 0.915046i \(-0.367846\pi\)
\(102\) −5.64575 −0.559013
\(103\) 1.93725 0.190883 0.0954417 0.995435i \(-0.469574\pi\)
0.0954417 + 0.995435i \(0.469574\pi\)
\(104\) 0 0
\(105\) 1.32288 + 2.29129i 0.129099 + 0.223607i
\(106\) 4.64575 0.451235
\(107\) 4.35425 0.420941 0.210471 0.977600i \(-0.432500\pi\)
0.210471 + 0.977600i \(0.432500\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 0.177124 0.306788i 0.0169654 0.0293850i −0.857418 0.514621i \(-0.827933\pi\)
0.874383 + 0.485236i \(0.161266\pi\)
\(110\) 3.14575 + 5.44860i 0.299936 + 0.519504i
\(111\) 4.14575 7.18065i 0.393497 0.681557i
\(112\) 1.32288 2.29129i 0.125000 0.216506i
\(113\) −5.64575 −0.531108 −0.265554 0.964096i \(-0.585555\pi\)
−0.265554 + 0.964096i \(0.585555\pi\)
\(114\) −2.64575 + 3.46410i −0.247797 + 0.324443i
\(115\) −1.00000 −0.0932505
\(116\) 1.82288 3.15731i 0.169250 0.293149i
\(117\) 0 0
\(118\) 2.64575 + 4.58258i 0.243561 + 0.421860i
\(119\) −7.46863 + 12.9360i −0.684648 + 1.18584i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 28.5830 2.59846
\(122\) −6.93725 −0.628069
\(123\) −4.32288 7.48744i −0.389781 0.675120i
\(124\) −3.64575 6.31463i −0.327398 0.567070i
\(125\) −1.00000 −0.0894427
\(126\) 2.64575 0.235702
\(127\) 5.61438 + 9.72439i 0.498196 + 0.862900i 0.999998 0.00208239i \(-0.000662847\pi\)
−0.501802 + 0.864982i \(0.667330\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 3.00000 + 5.19615i 0.264135 + 0.457496i
\(130\) 0 0
\(131\) 3.85425 6.67575i 0.336747 0.583263i −0.647072 0.762429i \(-0.724007\pi\)
0.983819 + 0.179166i \(0.0573399\pi\)
\(132\) 6.29150 0.547605
\(133\) 4.43725 + 10.6448i 0.384759 + 0.923017i
\(134\) 9.64575 0.833266
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −2.82288 + 4.88936i −0.242060 + 0.419260i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −1.64575 2.85052i −0.139591 0.241778i 0.787751 0.615994i \(-0.211245\pi\)
−0.927342 + 0.374215i \(0.877912\pi\)
\(140\) 2.64575 0.223607
\(141\) −12.5830 −1.05968
\(142\) −6.82288 11.8176i −0.572563 0.991708i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 3.64575 0.302763
\(146\) 6.82288 + 11.8176i 0.564665 + 0.978029i
\(147\) 0 0
\(148\) −4.14575 7.18065i −0.340779 0.590246i
\(149\) 8.11438 14.0545i 0.664756 1.15139i −0.314596 0.949226i \(-0.601869\pi\)
0.979351 0.202165i \(-0.0647977\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −20.2288 −1.64619 −0.823096 0.567902i \(-0.807755\pi\)
−0.823096 + 0.567902i \(0.807755\pi\)
\(152\) 1.67712 + 4.02334i 0.136033 + 0.326336i
\(153\) −5.64575 −0.456432
\(154\) 8.32288 14.4156i 0.670676 1.16165i
\(155\) 3.64575 6.31463i 0.292834 0.507203i
\(156\) 0 0
\(157\) 6.43725 11.1497i 0.513749 0.889839i −0.486124 0.873890i \(-0.661590\pi\)
0.999873 0.0159492i \(-0.00507700\pi\)
\(158\) 2.64575 + 4.58258i 0.210485 + 0.364570i
\(159\) 4.64575 0.368432
\(160\) 1.00000 0.0790569
\(161\) 1.32288 + 2.29129i 0.104257 + 0.180579i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −2.70850 −0.212146 −0.106073 0.994358i \(-0.533828\pi\)
−0.106073 + 0.994358i \(0.533828\pi\)
\(164\) −8.64575 −0.675120
\(165\) 3.14575 + 5.44860i 0.244896 + 0.424173i
\(166\) 8.29150 14.3613i 0.643545 1.11465i
\(167\) −8.79150 15.2273i −0.680307 1.17833i −0.974887 0.222699i \(-0.928513\pi\)
0.294580 0.955627i \(-0.404820\pi\)
\(168\) 1.32288 2.29129i 0.102062 0.176777i
\(169\) 6.50000 11.2583i 0.500000 0.866025i
\(170\) −5.64575 −0.433009
\(171\) −2.64575 + 3.46410i −0.202326 + 0.264906i
\(172\) 6.00000 0.457496
\(173\) −3.96863 + 6.87386i −0.301729 + 0.522610i −0.976528 0.215392i \(-0.930897\pi\)
0.674799 + 0.738002i \(0.264230\pi\)
\(174\) 1.82288 3.15731i 0.138192 0.239355i
\(175\) 1.32288 + 2.29129i 0.100000 + 0.173205i
\(176\) 3.14575 5.44860i 0.237120 0.410704i
\(177\) 2.64575 + 4.58258i 0.198867 + 0.344447i
\(178\) −13.2288 −0.991537
\(179\) 3.58301 0.267806 0.133903 0.990994i \(-0.457249\pi\)
0.133903 + 0.990994i \(0.457249\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) 7.17712 + 12.4311i 0.533471 + 0.924000i 0.999236 + 0.0390908i \(0.0124462\pi\)
−0.465764 + 0.884909i \(0.654221\pi\)
\(182\) 0 0
\(183\) −6.93725 −0.512817
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 4.14575 7.18065i 0.304802 0.527932i
\(186\) −3.64575 6.31463i −0.267319 0.463011i
\(187\) −17.7601 + 30.7614i −1.29875 + 2.24950i
\(188\) −6.29150 + 10.8972i −0.458855 + 0.794760i
\(189\) 2.64575 0.192450
\(190\) −2.64575 + 3.46410i −0.191943 + 0.251312i
\(191\) −4.58301 −0.331615 −0.165807 0.986158i \(-0.553023\pi\)
−0.165807 + 0.986158i \(0.553023\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −5.82288 + 10.0855i −0.419140 + 0.725971i −0.995853 0.0909752i \(-0.971002\pi\)
0.576713 + 0.816947i \(0.304335\pi\)
\(194\) −0.822876 1.42526i −0.0590790 0.102328i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.64575 −0.188502 −0.0942510 0.995548i \(-0.530046\pi\)
−0.0942510 + 0.995548i \(0.530046\pi\)
\(198\) 6.29150 0.447118
\(199\) −1.53137 2.65242i −0.108556 0.188025i 0.806629 0.591058i \(-0.201289\pi\)
−0.915186 + 0.403033i \(0.867956\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 9.64575 0.680359
\(202\) −11.8745 −0.835487
\(203\) −4.82288 8.35347i −0.338500 0.586298i
\(204\) −2.82288 + 4.88936i −0.197641 + 0.342324i
\(205\) −4.32288 7.48744i −0.301923 0.522946i
\(206\) 0.968627 1.67771i 0.0674874 0.116892i
\(207\) −0.500000 + 0.866025i −0.0347524 + 0.0601929i
\(208\) 0 0
\(209\) 10.5516 + 25.3128i 0.729872 + 1.75093i
\(210\) 2.64575 0.182574
\(211\) 9.26013 16.0390i 0.637494 1.10417i −0.348487 0.937313i \(-0.613305\pi\)
0.985981 0.166858i \(-0.0533621\pi\)
\(212\) 2.32288 4.02334i 0.159536 0.276324i
\(213\) −6.82288 11.8176i −0.467496 0.809726i
\(214\) 2.17712 3.77089i 0.148825 0.257773i
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) 1.00000 0.0680414
\(217\) −19.2915 −1.30959
\(218\) −0.177124 0.306788i −0.0119964 0.0207783i
\(219\) 6.82288 + 11.8176i 0.461047 + 0.798557i
\(220\) 6.29150 0.424173
\(221\) 0 0
\(222\) −4.14575 7.18065i −0.278245 0.481934i
\(223\) −3.32288 + 5.75539i −0.222516 + 0.385409i −0.955571 0.294760i \(-0.904760\pi\)
0.733055 + 0.680169i \(0.238094\pi\)
\(224\) −1.32288 2.29129i −0.0883883 0.153093i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −2.82288 + 4.88936i −0.187775 + 0.325236i
\(227\) 22.8118 1.51407 0.757035 0.653374i \(-0.226647\pi\)
0.757035 + 0.653374i \(0.226647\pi\)
\(228\) 1.67712 + 4.02334i 0.111070 + 0.266452i
\(229\) 14.7085 0.971965 0.485982 0.873969i \(-0.338462\pi\)
0.485982 + 0.873969i \(0.338462\pi\)
\(230\) −0.500000 + 0.866025i −0.0329690 + 0.0571040i
\(231\) 8.32288 14.4156i 0.547605 0.948480i
\(232\) −1.82288 3.15731i −0.119678 0.207288i
\(233\) −10.2915 + 17.8254i −0.674219 + 1.16778i 0.302478 + 0.953156i \(0.402186\pi\)
−0.976697 + 0.214625i \(0.931147\pi\)
\(234\) 0 0
\(235\) −12.5830 −0.820825
\(236\) 5.29150 0.344447
\(237\) 2.64575 + 4.58258i 0.171860 + 0.297670i
\(238\) 7.46863 + 12.9360i 0.484119 + 0.838519i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 1.00000 0.0645497
\(241\) −0.708497 1.22715i −0.0456383 0.0790479i 0.842304 0.539003i \(-0.181199\pi\)
−0.887942 + 0.459955i \(0.847866\pi\)
\(242\) 14.2915 24.7536i 0.918693 1.59122i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −3.46863 + 6.00784i −0.222056 + 0.384612i
\(245\) 0 0
\(246\) −8.64575 −0.551233
\(247\) 0 0
\(248\) −7.29150 −0.463011
\(249\) 8.29150 14.3613i 0.525453 0.910111i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 1.29150 + 2.23695i 0.0815189 + 0.141195i 0.903903 0.427738i \(-0.140690\pi\)
−0.822384 + 0.568933i \(0.807356\pi\)
\(252\) 1.32288 2.29129i 0.0833333 0.144338i
\(253\) 3.14575 + 5.44860i 0.197772 + 0.342551i
\(254\) 11.2288 0.704555
\(255\) −5.64575 −0.353551
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 6.00000 0.373544
\(259\) −21.9373 −1.36311
\(260\) 0 0
\(261\) 1.82288 3.15731i 0.112833 0.195433i
\(262\) −3.85425 6.67575i −0.238116 0.412429i
\(263\) −2.14575 + 3.71655i −0.132313 + 0.229172i −0.924568 0.381018i \(-0.875574\pi\)
0.792255 + 0.610190i \(0.208907\pi\)
\(264\) 3.14575 5.44860i 0.193608 0.335338i
\(265\) 4.64575 0.285386
\(266\) 11.4373 + 1.47960i 0.701263 + 0.0907202i
\(267\) −13.2288 −0.809587
\(268\) 4.82288 8.35347i 0.294604 0.510269i
\(269\) −6.46863 + 11.2040i −0.394399 + 0.683119i −0.993024 0.117910i \(-0.962381\pi\)
0.598625 + 0.801029i \(0.295714\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −5.93725 + 10.2836i −0.360662 + 0.624686i −0.988070 0.154005i \(-0.950783\pi\)
0.627408 + 0.778691i \(0.284116\pi\)
\(272\) 2.82288 + 4.88936i 0.171162 + 0.296461i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 3.14575 + 5.44860i 0.189696 + 0.328563i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) −3.29150 −0.197411
\(279\) −3.64575 6.31463i −0.218265 0.378047i
\(280\) 1.32288 2.29129i 0.0790569 0.136931i
\(281\) 9.90588 + 17.1575i 0.590935 + 1.02353i 0.994107 + 0.108406i \(0.0345745\pi\)
−0.403171 + 0.915124i \(0.632092\pi\)
\(282\) −6.29150 + 10.8972i −0.374654 + 0.648919i
\(283\) −9.93725 + 17.2118i −0.590708 + 1.02314i 0.403429 + 0.915011i \(0.367818\pi\)
−0.994137 + 0.108126i \(0.965515\pi\)
\(284\) −13.6458 −0.809726
\(285\) −2.64575 + 3.46410i −0.156721 + 0.205196i
\(286\) 0 0
\(287\) −11.4373 + 19.8099i −0.675120 + 1.16934i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −7.43725 12.8817i −0.437486 0.757747i
\(290\) 1.82288 3.15731i 0.107043 0.185404i
\(291\) −0.822876 1.42526i −0.0482378 0.0835504i
\(292\) 13.6458 0.798557
\(293\) −9.35425 −0.546481 −0.273241 0.961946i \(-0.588095\pi\)
−0.273241 + 0.961946i \(0.588095\pi\)
\(294\) 0 0
\(295\) 2.64575 + 4.58258i 0.154042 + 0.266808i
\(296\) −8.29150 −0.481934
\(297\) 6.29150 0.365070
\(298\) −8.11438 14.0545i −0.470053 0.814156i
\(299\) 0 0
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) 7.93725 13.7477i 0.457496 0.792406i
\(302\) −10.1144 + 17.5186i −0.582017 + 1.00808i
\(303\) −11.8745 −0.682173
\(304\) 4.32288 + 0.559237i 0.247934 + 0.0320744i
\(305\) −6.93725 −0.397226
\(306\) −2.82288 + 4.88936i −0.161373 + 0.279506i
\(307\) 12.7601 22.1012i 0.728259 1.26138i −0.229359 0.973342i \(-0.573663\pi\)
0.957618 0.288040i \(-0.0930036\pi\)
\(308\) −8.32288 14.4156i −0.474240 0.821408i
\(309\) 0.968627 1.67771i 0.0551033 0.0954417i
\(310\) −3.64575 6.31463i −0.207065 0.358647i
\(311\) −25.1660 −1.42703 −0.713517 0.700638i \(-0.752899\pi\)
−0.713517 + 0.700638i \(0.752899\pi\)
\(312\) 0 0
\(313\) 1.29150 + 2.23695i 0.0730000 + 0.126440i 0.900215 0.435446i \(-0.143409\pi\)
−0.827215 + 0.561886i \(0.810076\pi\)
\(314\) −6.43725 11.1497i −0.363275 0.629211i
\(315\) 2.64575 0.149071
\(316\) 5.29150 0.297670
\(317\) −2.03137 3.51844i −0.114093 0.197615i 0.803324 0.595543i \(-0.203063\pi\)
−0.917417 + 0.397927i \(0.869730\pi\)
\(318\) 2.32288 4.02334i 0.130260 0.225618i
\(319\) −11.4686 19.8642i −0.642120 1.11218i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 2.17712 3.77089i 0.121515 0.210471i
\(322\) 2.64575 0.147442
\(323\) −24.4059 3.15731i −1.35798 0.175678i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −1.35425 + 2.34563i −0.0750049 + 0.129912i
\(327\) −0.177124 0.306788i −0.00979500 0.0169654i
\(328\) −4.32288 + 7.48744i −0.238691 + 0.413425i
\(329\) 16.6458 + 28.8313i 0.917710 + 1.58952i
\(330\) 6.29150 0.346336
\(331\) −18.6458 −1.02486 −0.512432 0.858728i \(-0.671255\pi\)
−0.512432 + 0.858728i \(0.671255\pi\)
\(332\) −8.29150 14.3613i −0.455055 0.788179i
\(333\) −4.14575 7.18065i −0.227186 0.393497i
\(334\) −17.5830 −0.962099
\(335\) 9.64575 0.527004
\(336\) −1.32288 2.29129i −0.0721688 0.125000i
\(337\) −3.35425 + 5.80973i −0.182718 + 0.316476i −0.942805 0.333345i \(-0.891823\pi\)
0.760087 + 0.649821i \(0.225156\pi\)
\(338\) −6.50000 11.2583i −0.353553 0.612372i
\(339\) −2.82288 + 4.88936i −0.153318 + 0.265554i
\(340\) −2.82288 + 4.88936i −0.153092 + 0.265163i
\(341\) −45.8745 −2.48424
\(342\) 1.67712 + 4.02334i 0.0906885 + 0.217557i
\(343\) 18.5203 1.00000
\(344\) 3.00000 5.19615i 0.161749 0.280158i
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) 3.96863 + 6.87386i 0.213355 + 0.369541i
\(347\) −6.29150 + 10.8972i −0.337746 + 0.584992i −0.984008 0.178122i \(-0.942998\pi\)
0.646263 + 0.763115i \(0.276331\pi\)
\(348\) −1.82288 3.15731i −0.0977164 0.169250i
\(349\) 17.0627 0.913348 0.456674 0.889634i \(-0.349041\pi\)
0.456674 + 0.889634i \(0.349041\pi\)
\(350\) 2.64575 0.141421
\(351\) 0 0
\(352\) −3.14575 5.44860i −0.167669 0.290411i
\(353\) −7.06275 −0.375912 −0.187956 0.982177i \(-0.560186\pi\)
−0.187956 + 0.982177i \(0.560186\pi\)
\(354\) 5.29150 0.281240
\(355\) −6.82288 11.8176i −0.362121 0.627211i
\(356\) −6.61438 + 11.4564i −0.350561 + 0.607190i
\(357\) 7.46863 + 12.9360i 0.395282 + 0.684648i
\(358\) 1.79150 3.10297i 0.0946839 0.163997i
\(359\) −2.46863 + 4.27579i −0.130289 + 0.225667i −0.923788 0.382904i \(-0.874924\pi\)
0.793499 + 0.608572i \(0.208257\pi\)
\(360\) 1.00000 0.0527046
\(361\) −13.3745 + 13.4953i −0.703921 + 0.710278i
\(362\) 14.3542 0.754443
\(363\) 14.2915 24.7536i 0.750109 1.29923i
\(364\) 0 0
\(365\) 6.82288 + 11.8176i 0.357126 + 0.618560i
\(366\) −3.46863 + 6.00784i −0.181308 + 0.314035i
\(367\) 0.937254 + 1.62337i 0.0489243 + 0.0847393i 0.889450 0.457032i \(-0.151087\pi\)
−0.840526 + 0.541771i \(0.817754\pi\)
\(368\) 1.00000 0.0521286
\(369\) −8.64575 −0.450080
\(370\) −4.14575 7.18065i −0.215527 0.373304i
\(371\) −6.14575 10.6448i −0.319072 0.552648i
\(372\) −7.29150 −0.378047
\(373\) 18.2915 0.947098 0.473549 0.880767i \(-0.342973\pi\)
0.473549 + 0.880767i \(0.342973\pi\)
\(374\) 17.7601 + 30.7614i 0.918354 + 1.59064i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 6.29150 + 10.8972i 0.324459 + 0.561980i
\(377\) 0 0
\(378\) 1.32288 2.29129i 0.0680414 0.117851i
\(379\) 17.8745 0.918152 0.459076 0.888397i \(-0.348181\pi\)
0.459076 + 0.888397i \(0.348181\pi\)
\(380\) 1.67712 + 4.02334i 0.0860347 + 0.206393i
\(381\) 11.2288 0.575267
\(382\) −2.29150 + 3.96900i −0.117243 + 0.203072i
\(383\) 18.2915 31.6818i 0.934652 1.61886i 0.159399 0.987214i \(-0.449044\pi\)
0.775253 0.631651i \(-0.217622\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 8.32288 14.4156i 0.424173 0.734689i
\(386\) 5.82288 + 10.0855i 0.296377 + 0.513339i
\(387\) 6.00000 0.304997
\(388\) −1.64575 −0.0835504
\(389\) 8.76013 + 15.1730i 0.444156 + 0.769301i 0.997993 0.0633241i \(-0.0201702\pi\)
−0.553837 + 0.832625i \(0.686837\pi\)
\(390\) 0 0
\(391\) −5.64575 −0.285518
\(392\) 0 0
\(393\) −3.85425 6.67575i −0.194421 0.336747i
\(394\) −1.32288 + 2.29129i −0.0666455 + 0.115433i
\(395\) 2.64575 + 4.58258i 0.133122 + 0.230574i
\(396\) 3.14575 5.44860i 0.158080 0.273803i
\(397\) 13.7288 23.7789i 0.689027 1.19343i −0.283127 0.959083i \(-0.591372\pi\)
0.972153 0.234346i \(-0.0752950\pi\)
\(398\) −3.06275 −0.153522
\(399\) 11.4373 + 1.47960i 0.572579 + 0.0740728i
\(400\) 1.00000 0.0500000
\(401\) −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i \(-0.881200\pi\)
0.781345 + 0.624099i \(0.214534\pi\)
\(402\) 4.82288 8.35347i 0.240543 0.416633i
\(403\) 0 0
\(404\) −5.93725 + 10.2836i −0.295389 + 0.511629i
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) −9.64575 −0.478711
\(407\) −52.1660 −2.58577
\(408\) 2.82288 + 4.88936i 0.139753 + 0.242060i
\(409\) 9.20850 + 15.9496i 0.455331 + 0.788656i 0.998707 0.0508330i \(-0.0161876\pi\)
−0.543376 + 0.839489i \(0.682854\pi\)
\(410\) −8.64575 −0.426983
\(411\) 12.0000 0.591916
\(412\) −0.968627 1.67771i −0.0477208 0.0826549i
\(413\) 7.00000 12.1244i 0.344447 0.596601i
\(414\) 0.500000 + 0.866025i 0.0245737 + 0.0425628i
\(415\) 8.29150 14.3613i 0.407014 0.704969i
\(416\) 0 0
\(417\) −3.29150 −0.161186
\(418\) 27.1974 + 3.51844i 1.33027 + 0.172093i
\(419\) 38.1660 1.86453 0.932266 0.361774i \(-0.117829\pi\)
0.932266 + 0.361774i \(0.117829\pi\)
\(420\) 1.32288 2.29129i 0.0645497 0.111803i
\(421\) 9.46863 16.4001i 0.461473 0.799294i −0.537562 0.843224i \(-0.680655\pi\)
0.999035 + 0.0439302i \(0.0139879\pi\)
\(422\) −9.26013 16.0390i −0.450776 0.780767i
\(423\) −6.29150 + 10.8972i −0.305903 + 0.529840i
\(424\) −2.32288 4.02334i −0.112809 0.195391i
\(425\) −5.64575 −0.273859
\(426\) −13.6458 −0.661139
\(427\) 9.17712 + 15.8952i 0.444112 + 0.769225i
\(428\) −2.17712 3.77089i −0.105235 0.182273i
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) −14.1771 24.5555i −0.682888 1.18280i −0.974096 0.226137i \(-0.927390\pi\)
0.291207 0.956660i \(-0.405943\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −2.46863 4.27579i −0.118635 0.205481i 0.800592 0.599210i \(-0.204518\pi\)
−0.919227 + 0.393728i \(0.871185\pi\)
\(434\) −9.64575 + 16.7069i −0.463011 + 0.801958i
\(435\) 1.82288 3.15731i 0.0874002 0.151382i
\(436\) −0.354249 −0.0169654
\(437\) −2.64575 + 3.46410i −0.126563 + 0.165710i
\(438\) 13.6458 0.652019
\(439\) 1.53137 2.65242i 0.0730884 0.126593i −0.827165 0.561959i \(-0.810048\pi\)
0.900253 + 0.435366i \(0.143381\pi\)
\(440\) 3.14575 5.44860i 0.149968 0.259752i
\(441\) 0 0
\(442\) 0 0
\(443\) 12.5314 + 21.7050i 0.595384 + 1.03123i 0.993493 + 0.113896i \(0.0363332\pi\)
−0.398109 + 0.917338i \(0.630333\pi\)
\(444\) −8.29150 −0.393497
\(445\) −13.2288 −0.627103
\(446\) 3.32288 + 5.75539i 0.157343 + 0.272526i
\(447\) −8.11438 14.0545i −0.383797 0.664756i
\(448\) −2.64575 −0.125000
\(449\) −17.3542 −0.818998 −0.409499 0.912311i \(-0.634296\pi\)
−0.409499 + 0.912311i \(0.634296\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −27.1974 + 47.1073i −1.28067 + 2.21819i
\(452\) 2.82288 + 4.88936i 0.132777 + 0.229976i
\(453\) −10.1144 + 17.5186i −0.475215 + 0.823096i
\(454\) 11.4059 19.7556i 0.535305 0.927175i
\(455\) 0 0
\(456\) 4.32288 + 0.559237i 0.202437 + 0.0261887i
\(457\) 1.77124 0.0828553 0.0414276 0.999142i \(-0.486809\pi\)
0.0414276 + 0.999142i \(0.486809\pi\)
\(458\) 7.35425 12.7379i 0.343641 0.595204i
\(459\) −2.82288 + 4.88936i −0.131761 + 0.228216i
\(460\) 0.500000 + 0.866025i 0.0233126 + 0.0403786i
\(461\) 17.5830 30.4547i 0.818922 1.41841i −0.0875548 0.996160i \(-0.527905\pi\)
0.906477 0.422255i \(-0.138761\pi\)
\(462\) −8.32288 14.4156i −0.387215 0.670676i
\(463\) 29.3542 1.36421 0.682104 0.731255i \(-0.261065\pi\)
0.682104 + 0.731255i \(0.261065\pi\)
\(464\) −3.64575 −0.169250
\(465\) −3.64575 6.31463i −0.169068 0.292834i
\(466\) 10.2915 + 17.8254i 0.476745 + 0.825746i
\(467\) 15.5203 0.718192 0.359096 0.933301i \(-0.383085\pi\)
0.359096 + 0.933301i \(0.383085\pi\)
\(468\) 0 0
\(469\) −12.7601 22.1012i −0.589208 1.02054i
\(470\) −6.29150 + 10.8972i −0.290205 + 0.502650i
\(471\) −6.43725 11.1497i −0.296613 0.513749i
\(472\) 2.64575 4.58258i 0.121781 0.210930i
\(473\) 18.8745 32.6916i 0.867851 1.50316i
\(474\) 5.29150 0.243047
\(475\) −2.64575 + 3.46410i −0.121395 + 0.158944i
\(476\) 14.9373 0.684648
\(477\) 2.32288 4.02334i 0.106357 0.184216i
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −2.46863 4.27579i −0.112794 0.195366i 0.804102 0.594492i \(-0.202647\pi\)
−0.916896 + 0.399126i \(0.869313\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 0 0
\(482\) −1.41699 −0.0645423
\(483\) 2.64575 0.120386
\(484\) −14.2915 24.7536i −0.649614 1.12516i
\(485\) −0.822876 1.42526i −0.0373649 0.0647178i
\(486\) 1.00000 0.0453609
\(487\) 20.6458 0.935548 0.467774 0.883848i \(-0.345056\pi\)
0.467774 + 0.883848i \(0.345056\pi\)
\(488\) 3.46863 + 6.00784i 0.157017 + 0.271962i
\(489\) −1.35425 + 2.34563i −0.0612412 + 0.106073i
\(490\) 0 0
\(491\) −19.7288 + 34.1712i −0.890346 + 1.54213i −0.0508857 + 0.998704i \(0.516204\pi\)
−0.839461 + 0.543421i \(0.817129\pi\)
\(492\) −4.32288 + 7.48744i −0.194890 + 0.337560i
\(493\) 20.5830 0.927012
\(494\) 0 0
\(495\) 6.29150 0.282782
\(496\) −3.64575 + 6.31463i −0.163699 + 0.283535i
\(497\) −18.0516 + 31.2663i −0.809726 + 1.40249i
\(498\) −8.29150 14.3613i −0.371551 0.643545i
\(499\) −3.67712 + 6.36897i −0.164611 + 0.285114i −0.936517 0.350622i \(-0.885970\pi\)
0.771906 + 0.635736i \(0.219303\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) −17.5830 −0.785551
\(502\) 2.58301 0.115285
\(503\) −13.3745 23.1653i −0.596340 1.03289i −0.993356 0.115079i \(-0.963288\pi\)
0.397016 0.917811i \(-0.370046\pi\)
\(504\) −1.32288 2.29129i −0.0589256 0.102062i
\(505\) −11.8745 −0.528409
\(506\) 6.29150 0.279691
\(507\) −6.50000 11.2583i −0.288675 0.500000i
\(508\) 5.61438 9.72439i 0.249098 0.431450i
\(509\) 1.35425 + 2.34563i 0.0600260 + 0.103968i 0.894477 0.447114i \(-0.147548\pi\)
−0.834451 + 0.551082i \(0.814215\pi\)
\(510\) −2.82288 + 4.88936i −0.124999 + 0.216505i
\(511\) 18.0516 31.2663i 0.798557 1.38314i
\(512\) −1.00000 −0.0441942
\(513\) 1.67712 + 4.02334i 0.0740468 + 0.177635i
\(514\) −6.00000 −0.264649
\(515\) 0.968627 1.67771i 0.0426828 0.0739288i
\(516\) 3.00000 5.19615i 0.132068 0.228748i
\(517\) 39.5830 + 68.5598i 1.74086 + 3.01526i
\(518\) −10.9686 + 18.9982i −0.481934 + 0.834734i
\(519\) 3.96863 + 6.87386i 0.174203 + 0.301729i
\(520\) 0 0
\(521\) 22.4575 0.983882 0.491941 0.870629i \(-0.336288\pi\)
0.491941 + 0.870629i \(0.336288\pi\)
\(522\) −1.82288 3.15731i −0.0797851 0.138192i
\(523\) 6.88562 + 11.9262i 0.301087 + 0.521498i 0.976382 0.216049i \(-0.0693171\pi\)
−0.675295 + 0.737547i \(0.735984\pi\)
\(524\) −7.70850 −0.336747
\(525\) 2.64575 0.115470
\(526\) 2.14575 + 3.71655i 0.0935592 + 0.162049i
\(527\) 20.5830 35.6508i 0.896610 1.55297i
\(528\) −3.14575 5.44860i −0.136901 0.237120i
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 2.32288 4.02334i 0.100899 0.174763i
\(531\) 5.29150 0.229632
\(532\) 7.00000 9.16515i 0.303488 0.397360i
\(533\) 0 0
\(534\) −6.61438 + 11.4564i −0.286232 + 0.495769i
\(535\) 2.17712 3.77089i 0.0941253 0.163030i
\(536\) −4.82288 8.35347i −0.208316 0.360815i
\(537\) 1.79150 3.10297i 0.0773090 0.133903i
\(538\) 6.46863 + 11.2040i 0.278882 + 0.483038i
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −8.93725 15.4798i −0.384243 0.665528i 0.607421 0.794380i \(-0.292204\pi\)
−0.991664 + 0.128852i \(0.958871\pi\)
\(542\) 5.93725 + 10.2836i 0.255027 + 0.441720i
\(543\) 14.3542 0.616000
\(544\) 5.64575 0.242060
\(545\) −0.177124 0.306788i −0.00758717 0.0131414i
\(546\) 0 0
\(547\) −9.35425 16.2020i −0.399959 0.692749i 0.593762 0.804641i \(-0.297642\pi\)
−0.993720 + 0.111892i \(0.964309\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −3.46863 + 6.00784i −0.148037 + 0.256408i
\(550\) 6.29150 0.268271
\(551\) 9.64575 12.6293i 0.410923 0.538024i
\(552\) 1.00000 0.0425628
\(553\) 7.00000 12.1244i 0.297670 0.515580i
\(554\) −4.00000 + 6.92820i −0.169944 + 0.294351i
\(555\) −4.14575 7.18065i −0.175977 0.304802i
\(556\) −1.64575 + 2.85052i −0.0697954 + 0.120889i
\(557\) 12.2601 + 21.2352i 0.519478 + 0.899763i 0.999744 + 0.0226397i \(0.00720704\pi\)
−0.480265 + 0.877123i \(0.659460\pi\)
\(558\) −7.29150 −0.308674
\(559\) 0 0
\(560\) −1.32288 2.29129i −0.0559017 0.0968246i
\(561\) 17.7601 + 30.7614i 0.749833 + 1.29875i
\(562\) 19.8118 0.835709
\(563\) 21.4170 0.902619 0.451309 0.892368i \(-0.350957\pi\)
0.451309 + 0.892368i \(0.350957\pi\)
\(564\) 6.29150 + 10.8972i 0.264920 + 0.458855i
\(565\) −2.82288 + 4.88936i −0.118759 + 0.205697i
\(566\) 9.93725 + 17.2118i 0.417694 + 0.723467i
\(567\) 1.32288 2.29129i 0.0555556 0.0962250i
\(568\) −6.82288 + 11.8176i −0.286282 + 0.495854i
\(569\) 5.35425 0.224462 0.112231 0.993682i \(-0.464200\pi\)
0.112231 + 0.993682i \(0.464200\pi\)
\(570\) 1.67712 + 4.02334i 0.0702470 + 0.168519i
\(571\) 26.4575 1.10721 0.553606 0.832779i \(-0.313251\pi\)
0.553606 + 0.832779i \(0.313251\pi\)
\(572\) 0 0
\(573\) −2.29150 + 3.96900i −0.0957289 + 0.165807i
\(574\) 11.4373 + 19.8099i 0.477382 + 0.826849i
\(575\) −0.500000 + 0.866025i −0.0208514 + 0.0361158i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 2.93725 0.122279 0.0611397 0.998129i \(-0.480526\pi\)
0.0611397 + 0.998129i \(0.480526\pi\)
\(578\) −14.8745 −0.618698
\(579\) 5.82288 + 10.0855i 0.241990 + 0.419140i
\(580\) −1.82288 3.15731i −0.0756908 0.131100i
\(581\) −43.8745 −1.82022
\(582\) −1.64575 −0.0682186
\(583\) −14.6144 25.3128i −0.605266 1.04835i
\(584\) 6.82288 11.8176i 0.282333 0.489014i
\(585\) 0 0
\(586\) −4.67712 + 8.10102i −0.193210 + 0.334650i
\(587\) −16.3542 + 28.3264i −0.675012 + 1.16916i 0.301453 + 0.953481i \(0.402528\pi\)
−0.976465 + 0.215674i \(0.930805\pi\)
\(588\) 0 0
\(589\) −12.2288 29.3362i −0.503877 1.20878i
\(590\) 5.29150 0.217848
\(591\) −1.32288 + 2.29129i −0.0544158 + 0.0942510i
\(592\) −4.14575 + 7.18065i −0.170389 + 0.295123i
\(593\) 17.8229 + 30.8701i 0.731898 + 1.26768i 0.956071 + 0.293135i \(0.0946985\pi\)
−0.224173 + 0.974549i \(0.571968\pi\)
\(594\) 3.14575 5.44860i 0.129072 0.223559i
\(595\) 7.46863 + 12.9360i 0.306184 + 0.530326i
\(596\) −16.2288 −0.664756
\(597\) −3.06275 −0.125350
\(598\) 0 0
\(599\) 8.76013 + 15.1730i 0.357929 + 0.619952i 0.987615 0.156899i \(-0.0501496\pi\)
−0.629686 + 0.776850i \(0.716816\pi\)
\(600\) 1.00000 0.0408248
\(601\) −16.2915 −0.664544 −0.332272 0.943184i \(-0.607815\pi\)
−0.332272 + 0.943184i \(0.607815\pi\)
\(602\) −7.93725 13.7477i −0.323498 0.560316i
\(603\) 4.82288 8.35347i 0.196403 0.340179i
\(604\) 10.1144 + 17.5186i 0.411548 + 0.712822i
\(605\) 14.2915 24.7536i 0.581032 1.00638i
\(606\) −5.93725 + 10.2836i −0.241184 + 0.417744i
\(607\) −7.22876 −0.293406 −0.146703 0.989181i \(-0.546866\pi\)
−0.146703 + 0.989181i \(0.546866\pi\)
\(608\) 2.64575 3.46410i 0.107299 0.140488i
\(609\) −9.64575 −0.390866
\(610\) −3.46863 + 6.00784i −0.140441 + 0.243250i
\(611\) 0 0
\(612\) 2.82288 + 4.88936i 0.114108 + 0.197641i
\(613\) 14.4373 25.0061i 0.583115 1.00999i −0.411992 0.911187i \(-0.635167\pi\)
0.995108 0.0987978i \(-0.0314997\pi\)
\(614\) −12.7601 22.1012i −0.514957 0.891932i
\(615\) −8.64575 −0.348630
\(616\) −16.6458 −0.670676
\(617\) 1.29150 + 2.23695i 0.0519939 + 0.0900561i 0.890851 0.454296i \(-0.150109\pi\)
−0.838857 + 0.544352i \(0.816776\pi\)
\(618\) −0.968627 1.67771i −0.0389639 0.0674874i
\(619\) −18.0627 −0.726003 −0.363002 0.931789i \(-0.618248\pi\)
−0.363002 + 0.931789i \(0.618248\pi\)
\(620\) −7.29150 −0.292834
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) −12.5830 + 21.7944i −0.504533 + 0.873876i
\(623\) 17.5000 + 30.3109i 0.701123 + 1.21438i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 2.58301 0.103238
\(627\) 27.1974 + 3.51844i 1.08616 + 0.140513i
\(628\) −12.8745 −0.513749
\(629\) 23.4059 40.5402i 0.933254 1.61644i
\(630\) 1.32288 2.29129i 0.0527046 0.0912871i
\(631\) −8.17712 14.1632i −0.325526 0.563828i 0.656093 0.754680i \(-0.272208\pi\)
−0.981619 + 0.190853i \(0.938875\pi\)
\(632\) 2.64575 4.58258i 0.105242 0.182285i
\(633\) −9.26013 16.0390i −0.368057 0.637494i
\(634\) −4.06275 −0.161352
\(635\) 11.2288 0.445600
\(636\) −2.32288 4.02334i −0.0921080 0.159536i
\(637\) 0 0
\(638\) −22.9373 −0.908095
\(639\) −13.6458 −0.539818
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 10.6458 18.4390i 0.420482 0.728296i −0.575505 0.817798i \(-0.695194\pi\)
0.995987 + 0.0895025i \(0.0285277\pi\)
\(642\) −2.17712 3.77089i −0.0859242 0.148825i
\(643\) −0.594119 + 1.02904i −0.0234298 + 0.0405816i −0.877503 0.479572i \(-0.840792\pi\)
0.854073 + 0.520154i \(0.174125\pi\)
\(644\) 1.32288 2.29129i 0.0521286 0.0902894i
\(645\) 6.00000 0.236250
\(646\) −14.9373 + 19.5575i −0.587698 + 0.769478i
\(647\) 36.8745 1.44969 0.724843 0.688914i \(-0.241912\pi\)
0.724843 + 0.688914i \(0.241912\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 16.6458 28.8313i 0.653403 1.13173i
\(650\) 0 0
\(651\) −9.64575 + 16.7069i −0.378047 + 0.654796i
\(652\) 1.35425 + 2.34563i 0.0530365 + 0.0918619i
\(653\) 25.9373 1.01500 0.507502 0.861651i \(-0.330569\pi\)
0.507502 + 0.861651i \(0.330569\pi\)
\(654\) −0.354249 −0.0138522
\(655\) −3.85425 6.67575i −0.150598 0.260843i
\(656\) 4.32288 + 7.48744i 0.168780 + 0.292335i
\(657\) 13.6458 0.532371
\(658\) 33.2915 1.29784
\(659\) −4.79150 8.29913i −0.186650 0.323288i 0.757481 0.652857i \(-0.226430\pi\)
−0.944131 + 0.329569i \(0.893097\pi\)
\(660\) 3.14575 5.44860i 0.122448 0.212087i
\(661\) 17.2915 + 29.9498i 0.672562 + 1.16491i 0.977175 + 0.212435i \(0.0681393\pi\)
−0.304614 + 0.952476i \(0.598527\pi\)
\(662\) −9.32288 + 16.1477i −0.362344 + 0.627598i
\(663\) 0 0
\(664\) −16.5830 −0.643545
\(665\) 11.4373 + 1.47960i 0.443518 + 0.0573765i
\(666\) −8.29150 −0.321289
\(667\) 1.82288 3.15731i 0.0705820 0.122252i
\(668\) −8.79150 + 15.2273i −0.340153 + 0.589163i
\(669\) 3.32288 + 5.75539i 0.128470 + 0.222516i
\(670\) 4.82288 8.35347i 0.186324 0.322723i
\(671\) 21.8229 + 37.7983i 0.842463 + 1.45919i
\(672\) −2.64575 −0.102062
\(673\) −37.8745 −1.45995 −0.729977 0.683471i \(-0.760469\pi\)
−0.729977 + 0.683471i \(0.760469\pi\)
\(674\) 3.35425 + 5.80973i 0.129201 + 0.223782i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −13.0000 −0.500000
\(677\) −14.7712 −0.567705 −0.283853 0.958868i \(-0.591613\pi\)
−0.283853 + 0.958868i \(0.591613\pi\)
\(678\) 2.82288 + 4.88936i 0.108412 + 0.187775i
\(679\) −2.17712 + 3.77089i −0.0835504 + 0.144713i
\(680\) 2.82288 + 4.88936i 0.108252 + 0.187499i
\(681\) 11.4059 19.7556i 0.437074 0.757035i
\(682\) −22.9373 + 39.7285i −0.878313 + 1.52128i
\(683\) 13.0627 0.499832 0.249916 0.968268i \(-0.419597\pi\)
0.249916 + 0.968268i \(0.419597\pi\)
\(684\) 4.32288 + 0.559237i 0.165289 + 0.0213830i
\(685\) 12.0000 0.458496
\(686\) 9.26013 16.0390i 0.353553 0.612372i
\(687\) 7.35425 12.7379i 0.280582 0.485982i
\(688\) −3.00000 5.19615i −0.114374 0.198101i
\(689\) 0 0
\(690\) 0.500000 + 0.866025i 0.0190347 + 0.0329690i
\(691\) 33.8118 1.28626 0.643130 0.765757i \(-0.277635\pi\)
0.643130 + 0.765757i \(0.277635\pi\)
\(692\) 7.93725 0.301729
\(693\) −8.32288 14.4156i −0.316160 0.547605i
\(694\) 6.29150 + 10.8972i 0.238822 + 0.413652i
\(695\) −3.29150 −0.124854
\(696\) −3.64575 −0.138192
\(697\) −24.4059 42.2722i −0.924439 1.60117i
\(698\) 8.53137 14.7768i 0.322917 0.559309i
\(699\) 10.2915 + 17.8254i 0.389260 + 0.674219i
\(700\) 1.32288 2.29129i 0.0500000 0.0866025i
\(701\) −22.1660 + 38.3927i −0.837199 + 1.45007i 0.0550290 + 0.998485i \(0.482475\pi\)
−0.892228 + 0.451586i \(0.850858\pi\)
\(702\) 0 0
\(703\) −13.9059 33.3595i −0.524470 1.25818i
\(704\) −6.29150 −0.237120
\(705\) −6.29150 + 10.8972i −0.236952 + 0.410412i
\(706\) −3.53137 + 6.11652i −0.132905 + 0.230198i
\(707\) 15.7085 + 27.2079i 0.590779 + 1.02326i
\(708\) 2.64575 4.58258i 0.0994334 0.172224i
\(709\) −4.53137 7.84857i −0.170179 0.294759i 0.768303 0.640086i \(-0.221101\pi\)
−0.938482 + 0.345327i \(0.887768\pi\)
\(710\) −13.6458 −0.512116
\(711\) 5.29150 0.198447
\(712\) 6.61438 + 11.4564i 0.247884 + 0.429348i
\(713\) −3.64575 6.31463i −0.136534 0.236485i
\(714\) 14.9373 0.559013
\(715\) 0 0
\(716\) −1.79150 3.10297i −0.0669516 0.115964i
\(717\) −12.0000 + 20.7846i −0.448148 + 0.776215i
\(718\) 2.46863 + 4.27579i 0.0921283 + 0.159571i
\(719\) 6.35425 11.0059i 0.236973 0.410450i −0.722871 0.690983i \(-0.757178\pi\)
0.959844 + 0.280533i \(0.0905112\pi\)
\(720\) 0.500000 0.866025i 0.0186339 0.0322749i
\(721\) −5.12549 −0.190883
\(722\) 5.00000 + 18.3303i 0.186081 + 0.682183i
\(723\) −1.41699 −0.0526986
\(724\) 7.17712 12.4311i 0.266736 0.462000i
\(725\) 1.82288 3.15731i 0.0676999 0.117260i
\(726\) −14.2915 24.7536i −0.530407 0.918693i
\(727\) −5.93725 + 10.2836i −0.220201 + 0.381399i −0.954869 0.297028i \(-0.904005\pi\)
0.734668 + 0.678427i \(0.237338\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 13.6458 0.505052
\(731\) 16.9373 + 29.3362i 0.626447 + 1.08504i
\(732\) 3.46863 + 6.00784i 0.128204 + 0.222056i
\(733\) −12.2915 −0.453997 −0.226999 0.973895i \(-0.572891\pi\)
−0.226999 + 0.973895i \(0.572891\pi\)
\(734\) 1.87451 0.0691893
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) −30.3431 52.5559i −1.11770 1.93592i
\(738\) −4.32288 + 7.48744i −0.159127 + 0.275616i
\(739\) −19.4889 + 33.7557i −0.716910 + 1.24173i 0.245308 + 0.969445i \(0.421111\pi\)
−0.962218 + 0.272280i \(0.912222\pi\)
\(740\) −8.29150 −0.304802
\(741\) 0 0
\(742\) −12.2915 −0.451235
\(743\) 20.7915 36.0119i 0.762766 1.32115i −0.178653 0.983912i \(-0.557174\pi\)
0.941419 0.337238i \(-0.109493\pi\)
\(744\) −3.64575 + 6.31463i −0.133660 + 0.231505i
\(745\) −8.11438 14.0545i −0.297288 0.514918i
\(746\) 9.14575 15.8409i 0.334850 0.579977i
\(747\) −8.29150 14.3613i −0.303370 0.525453i
\(748\) 35.5203 1.29875
\(749\) −11.5203 −0.420941
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) 22.0000 + 38.1051i 0.802791 + 1.39048i 0.917772 + 0.397108i \(0.129986\pi\)
−0.114981 + 0.993368i \(0.536681\pi\)
\(752\) 12.5830 0.458855
\(753\) 2.58301 0.0941299
\(754\) 0 0
\(755\) −10.1144 + 17.5186i −0.368100 + 0.637568i
\(756\) −1.32288 2.29129i −0.0481125 0.0833333i
\(757\) −11.7288 + 20.3148i −0.426289 + 0.738354i −0.996540 0.0831165i \(-0.973513\pi\)
0.570251 + 0.821471i \(0.306846\pi\)
\(758\) 8.93725 15.4798i 0.324616 0.562251i
\(759\) 6.29150 0.228367
\(760\) 4.32288 + 0.559237i 0.156807 + 0.0202857i
\(761\) −20.5203 −0.743859 −0.371929 0.928261i \(-0.621304\pi\)
−0.371929 + 0.928261i \(0.621304\pi\)
\(762\) 5.61438 9.72439i 0.203387 0.352277i
\(763\) −0.468627 + 0.811686i −0.0169654 + 0.0293850i
\(764\) 2.29150 + 3.96900i 0.0829037 + 0.143593i
\(765\) −2.82288 + 4.88936i −0.102061 + 0.176775i
\(766\) −18.2915 31.6818i −0.660899 1.14471i
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −9.64575 16.7069i −0.347835 0.602467i 0.638030 0.770012i \(-0.279750\pi\)
−0.985865 + 0.167544i \(0.946416\pi\)
\(770\) −8.32288 14.4156i −0.299936 0.519504i
\(771\) −6.00000 −0.216085
\(772\) 11.6458 0.419140
\(773\) 0.968627 + 1.67771i 0.0348391 + 0.0603431i 0.882919 0.469525i \(-0.155575\pi\)
−0.848080 + 0.529868i \(0.822241\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) −3.64575 6.31463i −0.130959 0.226828i
\(776\) −0.822876 + 1.42526i −0.0295395 + 0.0511639i
\(777\) −10.9686 + 18.9982i −0.393497 + 0.681557i
\(778\) 17.5203 0.628132
\(779\) −37.3745 4.83502i −1.33908 0.173233i
\(780\) 0 0
\(781\) −42.9261 + 74.3503i −1.53602 + 2.66046i
\(782\) −2.82288 + 4.88936i −0.100946 + 0.174843i