Properties

Label 570.2.i.j.391.1
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.29654208.1
Defining polynomial: \(x^{6} + 14 x^{4} + 49 x^{2} + 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(2.35084i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.j.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +0.473560 q^{11} +1.00000 q^{12} +(0.263220 + 0.455910i) q^{13} +(2.29911 - 3.98217i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.27267 - 3.93637i) q^{17} +1.00000 q^{18} +(2.56233 - 3.52626i) q^{19} +1.00000 q^{20} +(2.29911 - 3.98217i) q^{21} +(-0.236780 + 0.410115i) q^{22} +(0.236780 + 0.410115i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.526440 q^{26} +1.00000 q^{27} +(2.29911 + 3.98217i) q^{28} +(-4.32555 - 7.49206i) q^{29} +1.00000 q^{30} -0.526440 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.236780 + 0.410115i) q^{33} +(2.27267 + 3.93637i) q^{34} +(2.29911 - 3.98217i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(1.77267 + 3.98217i) q^{38} -0.526440 q^{39} +(-0.500000 + 0.866025i) q^{40} +(5.63410 - 9.75854i) q^{41} +(2.29911 + 3.98217i) q^{42} +(-6.33499 + 10.9725i) q^{43} +(-0.236780 - 0.410115i) q^{44} +1.00000 q^{45} -0.473560 q^{46} +(-4.07177 - 7.05251i) q^{47} +(-0.500000 - 0.866025i) q^{48} +14.1435 q^{49} +1.00000 q^{50} +(2.27267 + 3.93637i) q^{51} +(0.263220 - 0.455910i) q^{52} +(-0.964114 - 1.66990i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.236780 + 0.410115i) q^{55} -4.59821 q^{56} +(1.77267 + 3.98217i) q^{57} +8.65109 q^{58} +(-3.00000 + 5.19615i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.53589 - 2.66023i) q^{61} +(0.263220 - 0.455910i) q^{62} +(2.29911 + 3.98217i) q^{63} +1.00000 q^{64} -0.526440 q^{65} +(-0.236780 - 0.410115i) q^{66} +(-4.53589 - 7.85638i) q^{67} -4.54533 q^{68} -0.473560 q^{69} +(2.29911 + 3.98217i) q^{70} +(2.27267 - 3.93637i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.46411 - 2.53592i) q^{73} +(0.500000 - 0.866025i) q^{74} +1.00000 q^{75} +(-4.33499 - 0.455910i) q^{76} -2.17753 q^{77} +(0.263220 - 0.455910i) q^{78} +(0.736780 - 1.27614i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.63410 + 9.75854i) q^{82} +4.10576 q^{83} -4.59821 q^{84} +(2.27267 + 3.93637i) q^{85} +(-6.33499 - 10.9725i) q^{86} +8.65109 q^{87} +0.473560 q^{88} +(0.964114 + 1.66990i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-1.21034 - 2.09637i) q^{91} +(0.236780 - 0.410115i) q^{92} +(0.263220 - 0.455910i) q^{93} +8.14354 q^{94} +(1.77267 + 3.98217i) q^{95} +1.00000 q^{96} +(-8.79911 + 15.2405i) q^{97} +(-7.07177 + 12.2487i) q^{98} +(-0.236780 - 0.410115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 3q^{6} + 2q^{7} + 6q^{8} - 3q^{9} - 3q^{10} + 8q^{11} + 6q^{12} - q^{13} - q^{14} - 3q^{15} - 3q^{16} + 4q^{17} + 6q^{18} - 2q^{19} + 6q^{20} - q^{21} - 4q^{22} + 4q^{23} - 3q^{24} - 3q^{25} + 2q^{26} + 6q^{27} - q^{28} - 6q^{29} + 6q^{30} + 2q^{31} - 3q^{32} - 4q^{33} + 4q^{34} - q^{35} - 3q^{36} - 6q^{37} + q^{38} + 2q^{39} - 3q^{40} - 8q^{41} - q^{42} - 11q^{43} - 4q^{44} + 6q^{45} - 8q^{46} - 3q^{48} + 36q^{49} + 6q^{50} + 4q^{51} - q^{52} - 18q^{53} - 3q^{54} - 4q^{55} + 2q^{56} + q^{57} + 12q^{58} - 18q^{59} - 3q^{60} + 3q^{61} - q^{62} - q^{63} + 6q^{64} + 2q^{65} - 4q^{66} - 15q^{67} - 8q^{68} - 8q^{69} - q^{70} + 4q^{71} - 3q^{72} + 21q^{73} + 3q^{74} + 6q^{75} + q^{76} + 32q^{77} - q^{78} + 7q^{79} - 3q^{80} - 3q^{81} - 8q^{82} + 4q^{83} + 2q^{84} + 4q^{85} - 11q^{86} + 12q^{87} + 8q^{88} + 18q^{89} - 3q^{90} - 15q^{91} + 4q^{92} - q^{93} + q^{95} + 6q^{96} - 38q^{97} - 18q^{98} - 4q^{99} + O(q^{100}) \)

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
\(7\) −4.59821 −1.73796 −0.868980 0.494847i \(-0.835224\pi\)
−0.868980 + 0.494847i \(0.835224\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 0.473560 0.142784 0.0713919 0.997448i \(-0.477256\pi\)
0.0713919 + 0.997448i \(0.477256\pi\)
\(12\) 1.00000 0.288675
\(13\) 0.263220 + 0.455910i 0.0730041 + 0.126447i 0.900217 0.435442i \(-0.143408\pi\)
−0.827213 + 0.561889i \(0.810075\pi\)
\(14\) 2.29911 3.98217i 0.614462 1.06428i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.27267 3.93637i 0.551202 0.954711i −0.446986 0.894541i \(-0.647503\pi\)
0.998188 0.0601695i \(-0.0191641\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.56233 3.52626i 0.587838 0.808979i
\(20\) 1.00000 0.223607
\(21\) 2.29911 3.98217i 0.501706 0.868980i
\(22\) −0.236780 + 0.410115i −0.0504817 + 0.0874369i
\(23\) 0.236780 + 0.410115i 0.0493721 + 0.0855149i 0.889655 0.456633i \(-0.150945\pi\)
−0.840283 + 0.542148i \(0.817611\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −0.526440 −0.103243
\(27\) 1.00000 0.192450
\(28\) 2.29911 + 3.98217i 0.434490 + 0.752559i
\(29\) −4.32555 7.49206i −0.803234 1.39124i −0.917477 0.397789i \(-0.869778\pi\)
0.114244 0.993453i \(-0.463556\pi\)
\(30\) 1.00000 0.182574
\(31\) −0.526440 −0.0945514 −0.0472757 0.998882i \(-0.515054\pi\)
−0.0472757 + 0.998882i \(0.515054\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.236780 + 0.410115i −0.0412181 + 0.0713919i
\(34\) 2.27267 + 3.93637i 0.389759 + 0.675082i
\(35\) 2.29911 3.98217i 0.388620 0.673109i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 1.77267 + 3.98217i 0.287564 + 0.645993i
\(39\) −0.526440 −0.0842978
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 5.63410 9.75854i 0.879898 1.52403i 0.0284461 0.999595i \(-0.490944\pi\)
0.851452 0.524433i \(-0.175723\pi\)
\(42\) 2.29911 + 3.98217i 0.354760 + 0.614462i
\(43\) −6.33499 + 10.9725i −0.966077 + 1.67329i −0.259384 + 0.965774i \(0.583520\pi\)
−0.706693 + 0.707520i \(0.749814\pi\)
\(44\) −0.236780 0.410115i −0.0356959 0.0618272i
\(45\) 1.00000 0.149071
\(46\) −0.473560 −0.0698227
\(47\) −4.07177 7.05251i −0.593929 1.02871i −0.993697 0.112099i \(-0.964243\pi\)
0.399768 0.916616i \(-0.369091\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 14.1435 2.02051
\(50\) 1.00000 0.141421
\(51\) 2.27267 + 3.93637i 0.318237 + 0.551202i
\(52\) 0.263220 0.455910i 0.0365020 0.0632234i
\(53\) −0.964114 1.66990i −0.132431 0.229378i 0.792182 0.610285i \(-0.208945\pi\)
−0.924613 + 0.380907i \(0.875612\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −0.236780 + 0.410115i −0.0319274 + 0.0552999i
\(56\) −4.59821 −0.614462
\(57\) 1.77267 + 3.98217i 0.234795 + 0.527451i
\(58\) 8.65109 1.13594
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) −1.53589 2.66023i −0.196650 0.340608i 0.750790 0.660541i \(-0.229673\pi\)
−0.947440 + 0.319933i \(0.896340\pi\)
\(62\) 0.263220 0.455910i 0.0334290 0.0579007i
\(63\) 2.29911 + 3.98217i 0.289660 + 0.501706i
\(64\) 1.00000 0.125000
\(65\) −0.526440 −0.0652968
\(66\) −0.236780 0.410115i −0.0291456 0.0504817i
\(67\) −4.53589 7.85638i −0.554147 0.959810i −0.997969 0.0636955i \(-0.979711\pi\)
0.443823 0.896115i \(-0.353622\pi\)
\(68\) −4.54533 −0.551202
\(69\) −0.473560 −0.0570100
\(70\) 2.29911 + 3.98217i 0.274796 + 0.475960i
\(71\) 2.27267 3.93637i 0.269716 0.467161i −0.699073 0.715051i \(-0.746404\pi\)
0.968788 + 0.247889i \(0.0797369\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 1.46411 2.53592i 0.171362 0.296807i −0.767535 0.641008i \(-0.778517\pi\)
0.938896 + 0.344201i \(0.111850\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 1.00000 0.115470
\(76\) −4.33499 0.455910i −0.497258 0.0522965i
\(77\) −2.17753 −0.248153
\(78\) 0.263220 0.455910i 0.0298038 0.0516217i
\(79\) 0.736780 1.27614i 0.0828942 0.143577i −0.821598 0.570068i \(-0.806917\pi\)
0.904492 + 0.426491i \(0.140250\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.63410 + 9.75854i 0.622182 + 1.07765i
\(83\) 4.10576 0.450666 0.225333 0.974282i \(-0.427653\pi\)
0.225333 + 0.974282i \(0.427653\pi\)
\(84\) −4.59821 −0.501706
\(85\) 2.27267 + 3.93637i 0.246505 + 0.426960i
\(86\) −6.33499 10.9725i −0.683120 1.18320i
\(87\) 8.65109 0.927494
\(88\) 0.473560 0.0504817
\(89\) 0.964114 + 1.66990i 0.102196 + 0.177009i 0.912589 0.408878i \(-0.134080\pi\)
−0.810393 + 0.585886i \(0.800746\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) −1.21034 2.09637i −0.126878 0.219759i
\(92\) 0.236780 0.410115i 0.0246860 0.0427575i
\(93\) 0.263220 0.455910i 0.0272946 0.0472757i
\(94\) 8.14354 0.839942
\(95\) 1.77267 + 3.98217i 0.181872 + 0.408562i
\(96\) 1.00000 0.102062
\(97\) −8.79911 + 15.2405i −0.893414 + 1.54744i −0.0576582 + 0.998336i \(0.518363\pi\)
−0.835756 + 0.549102i \(0.814970\pi\)
\(98\) −7.07177 + 12.2487i −0.714357 + 1.23730i
\(99\) −0.236780 0.410115i −0.0237973 0.0412181i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −6.59821 11.4284i −0.656547 1.13717i −0.981504 0.191443i \(-0.938683\pi\)
0.324957 0.945729i \(-0.394650\pi\)
\(102\) −4.54533 −0.450055
\(103\) −12.7418 −1.25548 −0.627741 0.778422i \(-0.716020\pi\)
−0.627741 + 0.778422i \(0.716020\pi\)
\(104\) 0.263220 + 0.455910i 0.0258108 + 0.0447057i
\(105\) 2.29911 + 3.98217i 0.224370 + 0.388620i
\(106\) 1.92823 0.187286
\(107\) −10.7946 −1.04356 −0.521778 0.853081i \(-0.674731\pi\)
−0.521778 + 0.853081i \(0.674731\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −3.27267 + 5.66842i −0.313465 + 0.542936i −0.979110 0.203332i \(-0.934823\pi\)
0.665645 + 0.746268i \(0.268156\pi\)
\(110\) −0.236780 0.410115i −0.0225761 0.0391030i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) 2.29911 3.98217i 0.217245 0.376279i
\(113\) 16.7946 1.57991 0.789953 0.613167i \(-0.210105\pi\)
0.789953 + 0.613167i \(0.210105\pi\)
\(114\) −4.33499 0.455910i −0.406009 0.0426999i
\(115\) −0.473560 −0.0441597
\(116\) −4.32555 + 7.49206i −0.401617 + 0.695621i
\(117\) 0.263220 0.455910i 0.0243347 0.0421489i
\(118\) −3.00000 5.19615i −0.276172 0.478345i
\(119\) −10.4502 + 18.1003i −0.957968 + 1.65925i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −10.7757 −0.979613
\(122\) 3.07177 0.278105
\(123\) 5.63410 + 9.75854i 0.508009 + 0.879898i
\(124\) 0.263220 + 0.455910i 0.0236378 + 0.0409419i
\(125\) 1.00000 0.0894427
\(126\) −4.59821 −0.409641
\(127\) −7.10766 12.3108i −0.630703 1.09241i −0.987408 0.158192i \(-0.949433\pi\)
0.356706 0.934217i \(-0.383900\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −6.33499 10.9725i −0.557765 0.966077i
\(130\) 0.263220 0.455910i 0.0230859 0.0399860i
\(131\) −7.43320 + 12.8747i −0.649442 + 1.12487i 0.333815 + 0.942639i \(0.391664\pi\)
−0.983256 + 0.182227i \(0.941669\pi\)
\(132\) 0.473560 0.0412181
\(133\) −11.7821 + 16.2145i −1.02164 + 1.40597i
\(134\) 9.07177 0.783682
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 2.27267 3.93637i 0.194879 0.337541i
\(137\) −4.66998 8.08865i −0.398983 0.691060i 0.594617 0.804009i \(-0.297304\pi\)
−0.993601 + 0.112949i \(0.963970\pi\)
\(138\) 0.236780 0.410115i 0.0201561 0.0349113i
\(139\) −2.26322 3.92001i −0.191964 0.332491i 0.753937 0.656947i \(-0.228152\pi\)
−0.945901 + 0.324455i \(0.894819\pi\)
\(140\) −4.59821 −0.388620
\(141\) 8.14354 0.685810
\(142\) 2.27267 + 3.93637i 0.190718 + 0.330333i
\(143\) 0.124650 + 0.215901i 0.0104238 + 0.0180545i
\(144\) 1.00000 0.0833333
\(145\) 8.65109 0.718434
\(146\) 1.46411 + 2.53592i 0.121171 + 0.209874i
\(147\) −7.07177 + 12.2487i −0.583270 + 1.01025i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 1.20089 2.08001i 0.0983811 0.170401i −0.812634 0.582775i \(-0.801967\pi\)
0.911015 + 0.412374i \(0.135300\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −15.7418 −1.28105 −0.640523 0.767939i \(-0.721282\pi\)
−0.640523 + 0.767939i \(0.721282\pi\)
\(152\) 2.56233 3.52626i 0.207832 0.286017i
\(153\) −4.54533 −0.367468
\(154\) 1.08876 1.88580i 0.0877352 0.151962i
\(155\) 0.263220 0.455910i 0.0211423 0.0366196i
\(156\) 0.263220 + 0.455910i 0.0210745 + 0.0365020i
\(157\) 4.09821 7.09831i 0.327073 0.566507i −0.654857 0.755753i \(-0.727271\pi\)
0.981930 + 0.189246i \(0.0606044\pi\)
\(158\) 0.736780 + 1.27614i 0.0586151 + 0.101524i
\(159\) 1.92823 0.152919
\(160\) 1.00000 0.0790569
\(161\) −1.08876 1.88580i −0.0858067 0.148622i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 15.5793 1.22027 0.610133 0.792299i \(-0.291116\pi\)
0.610133 + 0.792299i \(0.291116\pi\)
\(164\) −11.2682 −0.879898
\(165\) −0.236780 0.410115i −0.0184333 0.0319274i
\(166\) −2.05288 + 3.55569i −0.159334 + 0.275975i
\(167\) −6.23678 10.8024i −0.482617 0.835916i 0.517184 0.855874i \(-0.326980\pi\)
−0.999801 + 0.0199577i \(0.993647\pi\)
\(168\) 2.29911 3.98217i 0.177380 0.307231i
\(169\) 6.36143 11.0183i 0.489341 0.847563i
\(170\) −4.54533 −0.348611
\(171\) −4.33499 0.455910i −0.331505 0.0348643i
\(172\) 12.6700 0.966077
\(173\) −7.56233 + 13.0983i −0.574953 + 0.995848i 0.421094 + 0.907017i \(0.361646\pi\)
−0.996047 + 0.0888306i \(0.971687\pi\)
\(174\) −4.32555 + 7.49206i −0.327919 + 0.567972i
\(175\) 2.29911 + 3.98217i 0.173796 + 0.301024i
\(176\) −0.236780 + 0.410115i −0.0178480 + 0.0309136i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −1.92823 −0.144527
\(179\) −1.42068 −0.106187 −0.0530933 0.998590i \(-0.516908\pi\)
−0.0530933 + 0.998590i \(0.516908\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 4.39732 + 7.61637i 0.326850 + 0.566121i 0.981885 0.189478i \(-0.0606795\pi\)
−0.655035 + 0.755598i \(0.727346\pi\)
\(182\) 2.42068 0.179433
\(183\) 3.07177 0.227072
\(184\) 0.236780 + 0.410115i 0.0174557 + 0.0302341i
\(185\) 0.500000 0.866025i 0.0367607 0.0636715i
\(186\) 0.263220 + 0.455910i 0.0193002 + 0.0334290i
\(187\) 1.07624 1.86411i 0.0787028 0.136317i
\(188\) −4.07177 + 7.05251i −0.296964 + 0.514357i
\(189\) −4.59821 −0.334471
\(190\) −4.33499 0.455910i −0.314493 0.0330752i
\(191\) 9.15864 0.662696 0.331348 0.943509i \(-0.392497\pi\)
0.331348 + 0.943509i \(0.392497\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −0.588765 + 1.01977i −0.0423802 + 0.0734047i −0.886437 0.462848i \(-0.846827\pi\)
0.844057 + 0.536253i \(0.180161\pi\)
\(194\) −8.79911 15.2405i −0.631739 1.09420i
\(195\) 0.263220 0.455910i 0.0188496 0.0326484i
\(196\) −7.07177 12.2487i −0.505127 0.874905i
\(197\) 12.2153 0.870305 0.435153 0.900357i \(-0.356694\pi\)
0.435153 + 0.900357i \(0.356694\pi\)
\(198\) 0.473560 0.0336545
\(199\) −1.06233 1.84000i −0.0753062 0.130434i 0.825913 0.563797i \(-0.190660\pi\)
−0.901219 + 0.433363i \(0.857327\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 9.07177 0.639873
\(202\) 13.1964 0.928497
\(203\) 19.8898 + 34.4501i 1.39599 + 2.41792i
\(204\) 2.27267 3.93637i 0.159118 0.275601i
\(205\) 5.63410 + 9.75854i 0.393502 + 0.681566i
\(206\) 6.37088 11.0347i 0.443880 0.768823i
\(207\) 0.236780 0.410115i 0.0164574 0.0285050i
\(208\) −0.526440 −0.0365020
\(209\) 1.21342 1.66990i 0.0839337 0.115509i
\(210\) −4.59821 −0.317307
\(211\) 9.49553 16.4467i 0.653699 1.13224i −0.328519 0.944497i \(-0.606550\pi\)
0.982218 0.187743i \(-0.0601171\pi\)
\(212\) −0.964114 + 1.66990i −0.0662157 + 0.114689i
\(213\) 2.27267 + 3.93637i 0.155720 + 0.269716i
\(214\) 5.39732 9.34843i 0.368953 0.639045i
\(215\) −6.33499 10.9725i −0.432043 0.748320i
\(216\) 1.00000 0.0680414
\(217\) 2.42068 0.164327
\(218\) −3.27267 5.66842i −0.221653 0.383914i
\(219\) 1.46411 + 2.53592i 0.0989357 + 0.171362i
\(220\) 0.473560 0.0319274
\(221\) 2.39284 0.160960
\(222\) 0.500000 + 0.866025i 0.0335578 + 0.0581238i
\(223\) −10.4238 + 18.0545i −0.698026 + 1.20902i 0.271123 + 0.962545i \(0.412605\pi\)
−0.969150 + 0.246472i \(0.920729\pi\)
\(224\) 2.29911 + 3.98217i 0.153615 + 0.266070i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −8.39732 + 14.5446i −0.558581 + 0.967491i
\(227\) 4.79463 0.318231 0.159115 0.987260i \(-0.449136\pi\)
0.159115 + 0.987260i \(0.449136\pi\)
\(228\) 2.56233 3.52626i 0.169694 0.233532i
\(229\) −18.5264 −1.22426 −0.612131 0.790757i \(-0.709687\pi\)
−0.612131 + 0.790757i \(0.709687\pi\)
\(230\) 0.236780 0.410115i 0.0156128 0.0270422i
\(231\) 1.08876 1.88580i 0.0716355 0.124076i
\(232\) −4.32555 7.49206i −0.283986 0.491878i
\(233\) 12.7229 22.0366i 0.833502 1.44367i −0.0617416 0.998092i \(-0.519665\pi\)
0.895244 0.445576i \(-0.147001\pi\)
\(234\) 0.263220 + 0.455910i 0.0172072 + 0.0298038i
\(235\) 8.14354 0.531226
\(236\) 6.00000 0.390567
\(237\) 0.736780 + 1.27614i 0.0478590 + 0.0828942i
\(238\) −10.4502 18.1003i −0.677386 1.17327i
\(239\) −9.33996 −0.604152 −0.302076 0.953284i \(-0.597680\pi\)
−0.302076 + 0.953284i \(0.597680\pi\)
\(240\) 1.00000 0.0645497
\(241\) 7.21034 + 12.4887i 0.464459 + 0.804466i 0.999177 0.0405642i \(-0.0129155\pi\)
−0.534718 + 0.845031i \(0.679582\pi\)
\(242\) 5.38787 9.33207i 0.346345 0.599888i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −1.53589 + 2.66023i −0.0983250 + 0.170304i
\(245\) −7.07177 + 12.2487i −0.451799 + 0.782539i
\(246\) −11.2682 −0.718434
\(247\) 2.28211 + 0.240009i 0.145207 + 0.0152714i
\(248\) −0.526440 −0.0334290
\(249\) −2.05288 + 3.55569i −0.130096 + 0.225333i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 11.6171 + 20.1214i 0.733265 + 1.27005i 0.955480 + 0.295055i \(0.0953379\pi\)
−0.222215 + 0.974998i \(0.571329\pi\)
\(252\) 2.29911 3.98217i 0.144830 0.250853i
\(253\) 0.112130 + 0.194214i 0.00704953 + 0.0122101i
\(254\) 14.2153 0.891948
\(255\) −4.54533 −0.284640
\(256\) −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 \(0.893253\pi\)
\(258\) 12.6700 0.788799
\(259\) 4.59821 0.285719
\(260\) 0.263220 + 0.455910i 0.0163242 + 0.0282743i
\(261\) −4.32555 + 7.49206i −0.267745 + 0.463747i
\(262\) −7.43320 12.8747i −0.459225 0.795401i
\(263\) 11.2897 19.5543i 0.696150 1.20577i −0.273641 0.961832i \(-0.588228\pi\)
0.969791 0.243936i \(-0.0784386\pi\)
\(264\) −0.236780 + 0.410115i −0.0145728 + 0.0252408i
\(265\) 1.92823 0.118450
\(266\) −8.15109 18.3108i −0.499775 1.12271i
\(267\) −1.92823 −0.118006
\(268\) −4.53589 + 7.85638i −0.277073 + 0.479905i
\(269\) 0.253774 0.439550i 0.0154729 0.0267998i −0.858185 0.513340i \(-0.828408\pi\)
0.873658 + 0.486540i \(0.161741\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −13.1247 + 22.7326i −0.797266 + 1.38090i 0.124125 + 0.992267i \(0.460388\pi\)
−0.921390 + 0.388638i \(0.872946\pi\)
\(272\) 2.27267 + 3.93637i 0.137801 + 0.238678i
\(273\) 2.42068 0.146506
\(274\) 9.33996 0.564248
\(275\) −0.236780 0.410115i −0.0142784 0.0247309i
\(276\) 0.236780 + 0.410115i 0.0142525 + 0.0246860i
\(277\) 32.2493 1.93767 0.968836 0.247702i \(-0.0796753\pi\)
0.968836 + 0.247702i \(0.0796753\pi\)
\(278\) 4.52644 0.271478
\(279\) 0.263220 + 0.455910i 0.0157586 + 0.0272946i
\(280\) 2.29911 3.98217i 0.137398 0.237980i
\(281\) 0.107657 + 0.186467i 0.00642225 + 0.0111237i 0.869219 0.494428i \(-0.164622\pi\)
−0.862796 + 0.505552i \(0.831289\pi\)
\(282\) −4.07177 + 7.05251i −0.242470 + 0.419971i
\(283\) 14.2153 24.6216i 0.845013 1.46360i −0.0405976 0.999176i \(-0.512926\pi\)
0.885610 0.464429i \(-0.153741\pi\)
\(284\) −4.54533 −0.269716
\(285\) −4.33499 0.455910i −0.256783 0.0270058i
\(286\) −0.249301 −0.0147415
\(287\) −25.9068 + 44.8718i −1.52923 + 2.64870i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −1.83002 3.16968i −0.107648 0.186452i
\(290\) −4.32555 + 7.49206i −0.254005 + 0.439949i
\(291\) −8.79911 15.2405i −0.515813 0.893414i
\(292\) −2.92823 −0.171362
\(293\) 23.2682 1.35934 0.679671 0.733517i \(-0.262122\pi\)
0.679671 + 0.733517i \(0.262122\pi\)
\(294\) −7.07177 12.2487i −0.412434 0.714357i
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) −1.00000 −0.0581238
\(297\) 0.473560 0.0274788
\(298\) 1.20089 + 2.08001i 0.0695660 + 0.120492i
\(299\) −0.124650 + 0.215901i −0.00720872 + 0.0124859i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 29.1296 50.4540i 1.67900 2.90812i
\(302\) 7.87088 13.6328i 0.452918 0.784477i
\(303\) 13.1964 0.758115
\(304\) 1.77267 + 3.98217i 0.101669 + 0.228393i
\(305\) 3.07177 0.175889
\(306\) 2.27267 3.93637i 0.129920 0.225027i
\(307\) −6.99553 + 12.1166i −0.399256 + 0.691531i −0.993634 0.112654i \(-0.964065\pi\)
0.594378 + 0.804185i \(0.297398\pi\)
\(308\) 1.08876 + 1.88580i 0.0620381 + 0.107453i
\(309\) 6.37088 11.0347i 0.362426 0.627741i
\(310\) 0.263220 + 0.455910i 0.0149499 + 0.0258940i
\(311\) 31.4457 1.78312 0.891562 0.452899i \(-0.149610\pi\)
0.891562 + 0.452899i \(0.149610\pi\)
\(312\) −0.526440 −0.0298038
\(313\) −15.6171 27.0496i −0.882731 1.52893i −0.848293 0.529528i \(-0.822369\pi\)
−0.0344382 0.999407i \(-0.510964\pi\)
\(314\) 4.09821 + 7.09831i 0.231275 + 0.400581i
\(315\) −4.59821 −0.259080
\(316\) −1.47356 −0.0828942
\(317\) −10.1794 17.6313i −0.571734 0.990272i −0.996388 0.0849162i \(-0.972938\pi\)
0.424654 0.905355i \(-0.360396\pi\)
\(318\) −0.964114 + 1.66990i −0.0540649 + 0.0936431i
\(319\) −2.04841 3.54794i −0.114689 0.198647i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 5.39732 9.34843i 0.301249 0.521778i
\(322\) 2.17753 0.121349
\(323\) −8.05735 18.1003i −0.448323 1.00713i
\(324\) 1.00000 0.0555556
\(325\) 0.263220 0.455910i 0.0146008 0.0252893i
\(326\) −7.78966 + 13.4921i −0.431429 + 0.747258i
\(327\) −3.27267 5.66842i −0.180979 0.313465i
\(328\) 5.63410 9.75854i 0.311091 0.538825i
\(329\) 18.7229 + 32.4289i 1.03222 + 1.78787i
\(330\) 0.473560 0.0260686
\(331\) −3.40179 −0.186979 −0.0934896 0.995620i \(-0.529802\pi\)
−0.0934896 + 0.995620i \(0.529802\pi\)
\(332\) −2.05288 3.55569i −0.112666 0.195144i
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 12.4736 0.682523
\(335\) 9.07177 0.495644
\(336\) 2.29911 + 3.98217i 0.125426 + 0.217245i
\(337\) 5.40676 9.36479i 0.294525 0.510132i −0.680349 0.732888i \(-0.738172\pi\)
0.974874 + 0.222756i \(0.0715052\pi\)
\(338\) 6.36143 + 11.0183i 0.346016 + 0.599318i
\(339\) −8.39732 + 14.5446i −0.456080 + 0.789953i
\(340\) 2.27267 3.93637i 0.123253 0.213480i
\(341\) −0.249301 −0.0135004
\(342\) 2.56233 3.52626i 0.138555 0.190678i
\(343\) −32.8475 −1.77360
\(344\) −6.33499 + 10.9725i −0.341560 + 0.591599i
\(345\) 0.236780 0.410115i 0.0127478 0.0220799i
\(346\) −7.56233 13.0983i −0.406553 0.704171i
\(347\) 4.57932 7.93161i 0.245831 0.425791i −0.716534 0.697552i \(-0.754273\pi\)
0.962365 + 0.271761i \(0.0876059\pi\)
\(348\) −4.32555 7.49206i −0.231874 0.401617i
\(349\) 4.08687 0.218765 0.109382 0.994000i \(-0.465113\pi\)
0.109382 + 0.994000i \(0.465113\pi\)
\(350\) −4.59821 −0.245785
\(351\) 0.263220 + 0.455910i 0.0140496 + 0.0243347i
\(352\) −0.236780 0.410115i −0.0126204 0.0218592i
\(353\) −17.8097 −0.947916 −0.473958 0.880547i \(-0.657175\pi\)
−0.473958 + 0.880547i \(0.657175\pi\)
\(354\) 6.00000 0.318896
\(355\) 2.27267 + 3.93637i 0.120621 + 0.208921i
\(356\) 0.964114 1.66990i 0.0510980 0.0885043i
\(357\) −10.4502 18.1003i −0.553083 0.957968i
\(358\) 0.710340 1.23035i 0.0375427 0.0650258i
\(359\) 4.79911 8.31229i 0.253287 0.438706i −0.711142 0.703049i \(-0.751822\pi\)
0.964429 + 0.264343i \(0.0851549\pi\)
\(360\) 1.00000 0.0527046
\(361\) −5.86898 18.0708i −0.308894 0.951097i
\(362\) −8.79463 −0.462236
\(363\) 5.38787 9.33207i 0.282790 0.489806i
\(364\) −1.21034 + 2.09637i −0.0634391 + 0.109880i
\(365\) 1.46411 + 2.53592i 0.0766353 + 0.132736i
\(366\) −1.53589 + 2.66023i −0.0802820 + 0.139053i
\(367\) −0.683901 1.18455i −0.0356993 0.0618330i 0.847624 0.530598i \(-0.178033\pi\)
−0.883323 + 0.468765i \(0.844699\pi\)
\(368\) −0.473560 −0.0246860
\(369\) −11.2682 −0.586599
\(370\) 0.500000 + 0.866025i 0.0259938 + 0.0450225i
\(371\) 4.43320 + 7.67853i 0.230160 + 0.398649i
\(372\) −0.526440 −0.0272946
\(373\) −24.6171 −1.27463 −0.637313 0.770605i \(-0.719954\pi\)
−0.637313 + 0.770605i \(0.719954\pi\)
\(374\) 1.07624 + 1.86411i 0.0556513 + 0.0963908i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) −4.07177 7.05251i −0.209986 0.363706i
\(377\) 2.27714 3.94412i 0.117279 0.203133i
\(378\) 2.29911 3.98217i 0.118253 0.204821i
\(379\) 15.7606 0.809570 0.404785 0.914412i \(-0.367346\pi\)
0.404785 + 0.914412i \(0.367346\pi\)
\(380\) 2.56233 3.52626i 0.131445 0.180893i
\(381\) 14.2153 0.728273
\(382\) −4.57932 + 7.93161i −0.234298 + 0.405817i
\(383\) −10.0718 + 17.4448i −0.514643 + 0.891389i 0.485212 + 0.874396i \(0.338742\pi\)
−0.999856 + 0.0169922i \(0.994591\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 1.08876 1.88580i 0.0554886 0.0961091i
\(386\) −0.588765 1.01977i −0.0299673 0.0519050i
\(387\) 12.6700 0.644051
\(388\) 17.5982 0.893414
\(389\) 10.3255 + 17.8844i 0.523526 + 0.906773i 0.999625 + 0.0273819i \(0.00871701\pi\)
−0.476099 + 0.879392i \(0.657950\pi\)
\(390\) 0.263220 + 0.455910i 0.0133287 + 0.0230859i
\(391\) 2.15249 0.108856
\(392\) 14.1435 0.714357
\(393\) −7.43320 12.8747i −0.374955 0.649442i
\(394\) −6.10766 + 10.5788i −0.307699 + 0.532951i
\(395\) 0.736780 + 1.27614i 0.0370714 + 0.0642096i
\(396\) −0.236780 + 0.410115i −0.0118986 + 0.0206091i
\(397\) −13.6435 + 23.6313i −0.684750 + 1.18602i 0.288766 + 0.957400i \(0.406755\pi\)
−0.973515 + 0.228622i \(0.926578\pi\)
\(398\) 2.12465 0.106499
\(399\) −8.15109 18.3108i −0.408065 0.916689i
\(400\) 1.00000 0.0500000
\(401\) −17.1435 + 29.6935i −0.856108 + 1.48282i 0.0195060 + 0.999810i \(0.493791\pi\)
−0.875614 + 0.483012i \(0.839543\pi\)
\(402\) −4.53589 + 7.85638i −0.226229 + 0.391841i
\(403\) −0.138569 0.240009i −0.00690263 0.0119557i
\(404\) −6.59821 + 11.4284i −0.328273 + 0.568586i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −39.7795 −1.97423
\(407\) −0.473560 −0.0234735
\(408\) 2.27267 + 3.93637i 0.112514 + 0.194879i
\(409\) 10.3803 + 17.9792i 0.513274 + 0.889016i 0.999881 + 0.0153958i \(0.00490083\pi\)
−0.486608 + 0.873621i \(0.661766\pi\)
\(410\) −11.2682 −0.556496
\(411\) 9.33996 0.460706
\(412\) 6.37088 + 11.0347i 0.313871 + 0.543640i
\(413\) 13.7946 23.8930i 0.678789 1.17570i
\(414\) 0.236780 + 0.410115i 0.0116371 + 0.0201561i
\(415\) −2.05288 + 3.55569i −0.100772 + 0.174542i
\(416\) 0.263220 0.455910i 0.0129054 0.0223528i
\(417\) 4.52644 0.221661
\(418\) 0.839464 + 1.88580i 0.0410595 + 0.0922373i
\(419\) −27.5642 −1.34660 −0.673300 0.739369i \(-0.735124\pi\)
−0.673300 + 0.739369i \(0.735124\pi\)
\(420\) 2.29911 3.98217i 0.112185 0.194310i
\(421\) 2.72733 4.72388i 0.132922 0.230228i −0.791880 0.610677i \(-0.790897\pi\)
0.924802 + 0.380449i \(0.124231\pi\)
\(422\) 9.49553 + 16.4467i 0.462235 + 0.800615i
\(423\) −4.07177 + 7.05251i −0.197976 + 0.342905i
\(424\) −0.964114 1.66990i −0.0468215 0.0810973i
\(425\) −4.54533 −0.220481
\(426\) −4.54533 −0.220222
\(427\) 7.06233 + 12.2323i 0.341770 + 0.591963i
\(428\) 5.39732 + 9.34843i 0.260889 + 0.451873i
\(429\) −0.249301 −0.0120364
\(430\) 12.6700 0.611001
\(431\) 20.0484 + 34.7249i 0.965698 + 1.67264i 0.707729 + 0.706484i \(0.249720\pi\)
0.257969 + 0.966153i \(0.416947\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −5.60766 9.71275i −0.269487 0.466765i 0.699243 0.714884i \(-0.253521\pi\)
−0.968729 + 0.248120i \(0.920187\pi\)
\(434\) −1.21034 + 2.09637i −0.0580982 + 0.100629i
\(435\) −4.32555 + 7.49206i −0.207394 + 0.359217i
\(436\) 6.54533 0.313465
\(437\) 2.05288 + 0.215901i 0.0982025 + 0.0103279i
\(438\) −2.92823 −0.139916
\(439\) −7.18698 + 12.4482i −0.343016 + 0.594121i −0.984991 0.172605i \(-0.944782\pi\)
0.641976 + 0.766725i \(0.278115\pi\)
\(440\) −0.236780 + 0.410115i −0.0112881 + 0.0195515i
\(441\) −7.07177 12.2487i −0.336751 0.583270i
\(442\) −1.19642 + 2.07226i −0.0569080 + 0.0985675i
\(443\) 3.25377 + 5.63570i 0.154591 + 0.267760i 0.932910 0.360109i \(-0.117261\pi\)
−0.778319 + 0.627869i \(0.783927\pi\)
\(444\) −1.00000 −0.0474579
\(445\) −1.92823 −0.0914068
\(446\) −10.4238 18.0545i −0.493579 0.854904i
\(447\) 1.20089 + 2.08001i 0.0568004 + 0.0983811i
\(448\) −4.59821 −0.217245
\(449\) −1.92823 −0.0909988 −0.0454994 0.998964i \(-0.514488\pi\)
−0.0454994 + 0.998964i \(0.514488\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) 2.66808 4.62126i 0.125635 0.217607i
\(452\) −8.39732 14.5446i −0.394977 0.684119i
\(453\) 7.87088 13.6328i 0.369806 0.640523i
\(454\) −2.39732 + 4.15227i −0.112512 + 0.194876i
\(455\) 2.42068 0.113483
\(456\) 1.77267 + 3.98217i 0.0830127 + 0.186482i
\(457\) −29.2531 −1.36840 −0.684201 0.729293i \(-0.739849\pi\)
−0.684201 + 0.729293i \(0.739849\pi\)
\(458\) 9.26322 16.0444i 0.432842 0.749704i
\(459\) 2.27267 3.93637i 0.106079 0.183734i
\(460\) 0.236780 + 0.410115i 0.0110399 + 0.0191217i
\(461\) 0.473560 0.820230i 0.0220559 0.0382019i −0.854787 0.518979i \(-0.826312\pi\)
0.876843 + 0.480777i \(0.159645\pi\)
\(462\) 1.08876 + 1.88580i 0.0506539 + 0.0877352i
\(463\) 16.7418 0.778055 0.389028 0.921226i \(-0.372811\pi\)
0.389028 + 0.921226i \(0.372811\pi\)
\(464\) 8.65109 0.401617
\(465\) 0.263220 + 0.455910i 0.0122065 + 0.0211423i
\(466\) 12.7229 + 22.0366i 0.589375 + 1.02083i
\(467\) 19.7040 0.911791 0.455895 0.890033i \(-0.349319\pi\)
0.455895 + 0.890033i \(0.349319\pi\)
\(468\) −0.526440 −0.0243347
\(469\) 20.8570 + 36.1253i 0.963085 + 1.66811i
\(470\) −4.07177 + 7.05251i −0.187817 + 0.325308i
\(471\) 4.09821 + 7.09831i 0.188836 + 0.327073i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) −1.47356 −0.0676829
\(475\) −4.33499 0.455910i −0.198903 0.0209186i
\(476\) 20.9004 0.957968
\(477\) −0.964114 + 1.66990i −0.0441438 + 0.0764593i
\(478\) 4.66998 8.08865i 0.213600 0.369966i
\(479\) −15.3444 26.5773i −0.701105 1.21435i −0.968079 0.250646i \(-0.919357\pi\)
0.266974 0.963704i \(-0.413976\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) −0.263220 0.455910i −0.0120018 0.0207877i
\(482\) −14.4207 −0.656844
\(483\) 2.17753 0.0990810
\(484\) 5.38787 + 9.33207i 0.244903 + 0.424185i
\(485\) −8.79911 15.2405i −0.399547 0.692035i
\(486\) 1.00000 0.0453609
\(487\) −41.9103 −1.89914 −0.949569 0.313557i \(-0.898479\pi\)
−0.949569 + 0.313557i \(0.898479\pi\)
\(488\) −1.53589 2.66023i −0.0695263 0.120423i
\(489\) −7.78966 + 13.4921i −0.352261 + 0.610133i
\(490\) −7.07177 12.2487i −0.319470 0.553338i
\(491\) 7.81610 13.5379i 0.352736 0.610956i −0.633992 0.773340i \(-0.718585\pi\)
0.986728 + 0.162384i \(0.0519182\pi\)
\(492\) 5.63410 9.75854i 0.254005 0.439949i
\(493\) −39.3221 −1.77098
\(494\) −1.34891 + 1.85636i −0.0606903 + 0.0835217i
\(495\) 0.473560 0.0212850
\(496\) 0.263220 0.455910i 0.0118189 0.0204710i
\(497\) −10.4502 + 18.1003i −0.468755 + 0.811908i
\(498\) −2.05288 3.55569i −0.0919917 0.159334i
\(499\) −0.102684 + 0.177854i −0.00459676 + 0.00796183i −0.868315 0.496014i \(-0.834797\pi\)
0.863718 + 0.503976i \(0.168130\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 12.4736 0.557278
\(502\) −23.2342 −1.03699
\(503\) −1.81610 3.14558i −0.0809759 0.140254i 0.822693 0.568485i \(-0.192470\pi\)
−0.903669 + 0.428231i \(0.859137\pi\)
\(504\) 2.29911 + 3.98217i 0.102410 + 0.177380i
\(505\) 13.1964 0.587233
\(506\) −0.224259 −0.00996954
\(507\) 6.36143 + 11.0183i 0.282521 + 0.489341i
\(508\) −7.10766 + 12.3108i −0.315351 + 0.546204i
\(509\) −5.01889 8.69298i −0.222458 0.385309i 0.733095 0.680126i \(-0.238075\pi\)
−0.955554 + 0.294816i \(0.904742\pi\)
\(510\) 2.27267 3.93637i 0.100635 0.174305i
\(511\) −6.73231 + 11.6607i −0.297820 + 0.515839i
\(512\) 1.00000 0.0441942
\(513\) 2.56233 3.52626i 0.113129 0.155688i
\(514\) 6.00000 0.264649
\(515\) 6.37088 11.0347i 0.280734 0.486246i
\(516\) −6.33499 + 10.9725i −0.278882 + 0.483039i
\(517\) −1.92823 3.33979i −0.0848034 0.146884i
\(518\) −2.29911 + 3.98217i −0.101017 + 0.174966i
\(519\) −7.56233 13.0983i −0.331949 0.574953i
\(520\) −0.526440 −0.0230859
\(521\) −6.24930 −0.273787 −0.136893 0.990586i \(-0.543712\pi\)
−0.136893 + 0.990586i \(0.543712\pi\)
\(522\) −4.32555 7.49206i −0.189324 0.327919i
\(523\) −13.2776 22.9975i −0.580591 1.00561i −0.995409 0.0957084i \(-0.969488\pi\)
0.414819 0.909904i \(-0.363845\pi\)
\(524\) 14.8664 0.649442
\(525\) −4.59821 −0.200682
\(526\) 11.2897 + 19.5543i 0.492253 + 0.852606i
\(527\) −1.19642 + 2.07226i −0.0521169 + 0.0902692i
\(528\) −0.236780 0.410115i −0.0103045 0.0178480i
\(529\) 11.3879 19.7244i 0.495125 0.857581i
\(530\) −0.964114 + 1.66990i −0.0418785 + 0.0725356i
\(531\) 6.00000 0.260378
\(532\) 19.9332 + 2.09637i 0.864214 + 0.0908892i
\(533\) 5.93202 0.256944
\(534\) 0.964114 1.66990i 0.0417213 0.0722634i
\(535\) 5.39732 9.34843i 0.233346 0.404168i
\(536\) −4.53589 7.85638i −0.195920 0.339344i
\(537\) 0.710340 1.23035i 0.0306535 0.0530933i
\(538\) 0.253774 + 0.439550i 0.0109410 + 0.0189503i
\(539\) 6.69782 0.288496
\(540\) 1.00000 0.0430331
\(541\) 15.0390 + 26.0482i 0.646575 + 1.11990i 0.983935 + 0.178526i \(0.0571328\pi\)
−0.337360 + 0.941376i \(0.609534\pi\)
\(542\) −13.1247 22.7326i −0.563752 0.976447i
\(543\) −8.79463 −0.377414
\(544\) −4.54533 −0.194879
\(545\) −3.27267 5.66842i −0.140186 0.242809i
\(546\) −1.21034 + 2.09637i −0.0517978 + 0.0897164i
\(547\) 3.26322 + 5.65206i 0.139525 + 0.241665i 0.927317 0.374277i \(-0.122109\pi\)
−0.787792 + 0.615942i \(0.788776\pi\)
\(548\) −4.66998 + 8.08865i −0.199492 + 0.345530i
\(549\) −1.53589 + 2.66023i −0.0655500 + 0.113536i
\(550\) 0.473560 0.0201927
\(551\) −37.5024 3.94412i −1.59766 0.168025i
\(552\) −0.473560 −0.0201561
\(553\) −3.38787 + 5.86796i −0.144067 + 0.249531i
\(554\) −16.1247 + 27.9287i −0.685071 + 1.18658i
\(555\) 0.500000 + 0.866025i 0.0212238 + 0.0367607i
\(556\) −2.26322 + 3.92001i −0.0959819 + 0.166246i
\(557\) 15.1077 + 26.1672i 0.640132 + 1.10874i 0.985403 + 0.170238i \(0.0544537\pi\)
−0.345271 + 0.938503i \(0.612213\pi\)
\(558\) −0.526440 −0.0222860
\(559\) −6.66998 −0.282110
\(560\) 2.29911 + 3.98217i 0.0971549 + 0.168277i
\(561\) 1.07624 + 1.86411i 0.0454391 + 0.0787028i
\(562\) −0.215313 −0.00908243
\(563\) 11.2342 0.473465 0.236733 0.971575i \(-0.423923\pi\)
0.236733 + 0.971575i \(0.423923\pi\)
\(564\) −4.07177 7.05251i −0.171452 0.296964i
\(565\) −8.39732 + 14.5446i −0.353278 + 0.611895i
\(566\) 14.2153 + 24.6216i 0.597514 + 1.03492i
\(567\) 2.29911 3.98217i 0.0965533 0.167235i
\(568\) 2.27267 3.93637i 0.0953589 0.165167i
\(569\) −15.3740 −0.644510 −0.322255 0.946653i \(-0.604441\pi\)
−0.322255 + 0.946653i \(0.604441\pi\)
\(570\) 2.56233 3.52626i 0.107324 0.147699i
\(571\) 18.8513 0.788903 0.394451 0.918917i \(-0.370935\pi\)
0.394451 + 0.918917i \(0.370935\pi\)
\(572\) 0.124650 0.215901i 0.00521190 0.00902727i
\(573\) −4.57932 + 7.93161i −0.191304 + 0.331348i
\(574\) −25.9068 44.8718i −1.08133 1.87291i
\(575\) 0.236780 0.410115i 0.00987441 0.0171030i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −19.3489 −0.805506 −0.402753 0.915309i \(-0.631947\pi\)
−0.402753 + 0.915309i \(0.631947\pi\)
\(578\) 3.66004 0.152237
\(579\) −0.588765 1.01977i −0.0244682 0.0423802i
\(580\) −4.32555 7.49206i −0.179608 0.311091i
\(581\) −18.8791 −0.783239
\(582\) 17.5982 0.729469
\(583\) −0.456566 0.790796i −0.0189090 0.0327514i
\(584\) 1.46411 2.53592i 0.0605855 0.104937i
\(585\) 0.263220 + 0.455910i 0.0108828 + 0.0188496i
\(586\) −11.6341 + 20.1508i −0.480600 + 0.832424i
\(587\) −8.01889 + 13.8891i −0.330975 + 0.573266i −0.982703 0.185187i \(-0.940711\pi\)
0.651728 + 0.758453i \(0.274044\pi\)
\(588\) 14.1435 0.583270
\(589\) −1.34891 + 1.85636i −0.0555809 + 0.0764901i
\(590\) 6.00000 0.247016
\(591\) −6.10766 + 10.5788i −0.251235 + 0.435153i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) −14.4880 25.0939i −0.594950 1.03048i −0.993554 0.113360i \(-0.963839\pi\)
0.398604 0.917123i \(-0.369495\pi\)
\(594\) −0.236780 + 0.410115i −0.00971521 + 0.0168272i
\(595\) −10.4502 18.1003i −0.428416 0.742039i
\(596\) −2.40179 −0.0983811
\(597\) 2.12465 0.0869562
\(598\) −0.124650 0.215901i −0.00509734 0.00882885i
\(599\) −23.1391 40.0780i −0.945437 1.63754i −0.754874 0.655869i \(-0.772302\pi\)
−0.190562 0.981675i \(-0.561031\pi\)
\(600\) 1.00000 0.0408248
\(601\) −10.6072 −0.432675 −0.216337 0.976319i \(-0.569411\pi\)
−0.216337 + 0.976319i \(0.569411\pi\)
\(602\) 29.1296 + 50.4540i 1.18723 + 2.05635i
\(603\) −4.53589 + 7.85638i −0.184716 + 0.319937i
\(604\) 7.87088 + 13.6328i 0.320261 + 0.554709i
\(605\) 5.38787 9.33207i 0.219048 0.379402i
\(606\) −6.59821 + 11.4284i −0.268034 + 0.464248i
\(607\) 28.0439 1.13827 0.569134 0.822245i \(-0.307279\pi\)
0.569134 + 0.822245i \(0.307279\pi\)
\(608\) −4.33499 0.455910i −0.175807 0.0184896i
\(609\) −39.7795 −1.61195
\(610\) −1.53589 + 2.66023i −0.0621862 + 0.107710i
\(611\) 2.14354 3.71272i 0.0867184 0.150201i
\(612\) 2.27267 + 3.93637i 0.0918671 + 0.159118i
\(613\) −12.4143 + 21.5022i −0.501409 + 0.868466i 0.498589 + 0.866838i \(0.333852\pi\)
−0.999999 + 0.00162804i \(0.999482\pi\)
\(614\) −6.99553 12.1166i −0.282316 0.488987i
\(615\) −11.2682 −0.454377
\(616\) −2.17753 −0.0877352
\(617\) 6.00000 + 10.3923i 0.241551 + 0.418378i 0.961156 0.276005i \(-0.0890106\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(618\) 6.37088 + 11.0347i 0.256274 + 0.443880i
\(619\) 33.7946 1.35832 0.679160 0.733990i \(-0.262344\pi\)
0.679160 + 0.733990i \(0.262344\pi\)
\(620\) −0.526440 −0.0211423
\(621\) 0.236780 + 0.410115i 0.00950166 + 0.0164574i
\(622\) −15.7229 + 27.2328i −0.630429 + 1.09194i
\(623\) −4.43320 7.67853i −0.177612 0.307634i
\(624\) 0.263220 0.455910i 0.0105372 0.0182510i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 31.2342 1.24837
\(627\) 0.839464 + 1.88580i 0.0335250 + 0.0753114i
\(628\) −8.19642 −0.327073
\(629\) −2.27267 + 3.93637i −0.0906171 + 0.156953i
\(630\) 2.29911 3.98217i 0.0915986 0.158653i
\(631\) 7.11520 + 12.3239i 0.283252 + 0.490607i 0.972184 0.234220i \(-0.0752534\pi\)
−0.688932 + 0.724826i \(0.741920\pi\)
\(632\) 0.736780 1.27614i 0.0293075 0.0507621i
\(633\) 9.49553 + 16.4467i 0.377413 + 0.653699i
\(634\) 20.3589 0.808553
\(635\) 14.2153 0.564117
\(636\) −0.964114 1.66990i −0.0382296 0.0662157i
\(637\) 3.72286 + 6.44818i 0.147505 + 0.255486i
\(638\) 4.09681 0.162194
\(639\) −4.54533 −0.179811
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −13.1624 + 22.7980i −0.519885 + 0.900467i 0.479848 + 0.877352i \(0.340692\pi\)
−0.999733 + 0.0231153i \(0.992642\pi\)
\(642\) 5.39732 + 9.34843i 0.213015 + 0.368953i
\(643\) −8.25875 + 14.3046i −0.325693 + 0.564117i −0.981652 0.190679i \(-0.938931\pi\)
0.655959 + 0.754796i \(0.272264\pi\)
\(644\) −1.08876 + 1.88580i −0.0429033 + 0.0743108i
\(645\) 12.6700 0.498880
\(646\) 19.7040 + 2.07226i 0.775242 + 0.0815321i
\(647\) 29.2592 1.15030 0.575150 0.818048i \(-0.304944\pi\)
0.575150 + 0.818048i \(0.304944\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −1.42068 + 2.46069i −0.0557666 + 0.0965906i
\(650\) 0.263220 + 0.455910i 0.0103243 + 0.0178823i
\(651\) −1.21034 + 2.09637i −0.0474370 + 0.0821633i
\(652\) −7.78966 13.4921i −0.305067 0.528391i
\(653\) −41.7668 −1.63446 −0.817230 0.576311i \(-0.804492\pi\)
−0.817230 + 0.576311i \(0.804492\pi\)
\(654\) 6.54533 0.255943
\(655\) −7.43320 12.8747i −0.290439 0.503055i
\(656\) 5.63410 + 9.75854i 0.219975 + 0.381007i
\(657\) −2.92823 −0.114241
\(658\) −37.4457 −1.45979
\(659\) −12.9596 22.4468i −0.504836 0.874402i −0.999984 0.00559311i \(-0.998220\pi\)
0.495148 0.868808i \(-0.335114\pi\)
\(660\) −0.236780 + 0.410115i −0.00921665 + 0.0159637i
\(661\) 14.8135 + 25.6578i 0.576179 + 0.997972i 0.995912 + 0.0903242i \(0.0287903\pi\)
−0.419733 + 0.907648i \(0.637876\pi\)
\(662\) 1.70089 2.94604i 0.0661071 0.114501i
\(663\) −1.19642 + 2.07226i −0.0464652 + 0.0804800i
\(664\) 4.10576 0.159334
\(665\) −8.15109 18.3108i −0.316086 0.710064i
\(666\) −1.00000 −0.0387492
\(667\) 2.04841 3.54794i 0.0793146 0.137377i
\(668\) −6.23678 + 10.8024i −0.241308 + 0.417958i
\(669\) −10.4238 18.0545i −0.403006 0.698026i
\(670\) −4.53589 + 7.85638i −0.175237 + 0.303519i
\(671\) −0.727334 1.25978i −0.0280784 0.0486333i
\(672\) −4.59821 −0.177380
\(673\) 39.7606 1.53266 0.766330 0.642447i \(-0.222081\pi\)
0.766330 + 0.642447i \(0.222081\pi\)
\(674\) 5.40676 + 9.36479i 0.208261 + 0.360718i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) −12.7229 −0.489341
\(677\) −14.3589 −0.551856 −0.275928 0.961178i \(-0.588985\pi\)
−0.275928 + 0.961178i \(0.588985\pi\)
\(678\) −8.39732 14.5446i −0.322497 0.558581i
\(679\) 40.4601 70.0790i 1.55272 2.68939i
\(680\) 2.27267 + 3.93637i 0.0871527 + 0.150953i
\(681\) −2.39732 + 4.15227i −0.0918654 + 0.159115i
\(682\) 0.124650 0.215901i 0.00477311 0.00826727i
\(683\) 10.7946 0.413045 0.206523 0.978442i \(-0.433785\pi\)
0.206523 + 0.978442i \(0.433785\pi\)
\(684\) 1.77267 + 3.98217i 0.0677796 + 0.152262i
\(685\) 9.33996 0.356862
\(686\) 16.4238 28.4468i 0.627062 1.08610i
\(687\) 9.26322 16.0444i 0.353414 0.612131i
\(688\) −6.33499 10.9725i −0.241519 0.418324i
\(689\) 0.507548 0.879099i 0.0193360 0.0334910i
\(690\) 0.236780 + 0.410115i 0.00901407 + 0.0156128i
\(691\) −28.4646 −1.08284 −0.541422 0.840751i \(-0.682114\pi\)
−0.541422 + 0.840751i \(0.682114\pi\)
\(692\) 15.1247 0.574953
\(693\) 1.08876 + 1.88580i 0.0413588 + 0.0716355i
\(694\) 4.57932 + 7.93161i 0.173829 + 0.301080i
\(695\) 4.52644 0.171698
\(696\) 8.65109 0.327919
\(697\) −25.6088 44.3558i −0.970004 1.68010i
\(698\) −2.04343 + 3.53933i −0.0773451 + 0.133966i
\(699\) 12.7229 + 22.0366i 0.481223 + 0.833502i
\(700\) 2.29911 3.98217i 0.0868980 0.150512i
\(701\) 16.7606 29.0303i 0.633041 1.09646i −0.353886 0.935289i \(-0.615140\pi\)
0.986927 0.161170i \(-0.0515268\pi\)
\(702\) −0.526440 −0.0198692
\(703\) −2.56233 + 3.52626i −0.0966399 + 0.132995i
\(704\) 0.473560 0.0178480
\(705\) −4.07177 + 7.05251i −0.153352 + 0.265613i
\(706\) 8.90486 15.4237i 0.335139 0.580478i
\(707\) 30.3400 + 52.5504i 1.14105 + 1.97636i
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) 20.8758 + 36.1580i 0.784009 + 1.35794i 0.929589 + 0.368597i \(0.120162\pi\)
−0.145580 + 0.989346i \(0.546505\pi\)
\(710\) −4.54533 −0.170583
\(711\) −1.47356 −0.0552628
\(712\) 0.964114 + 1.66990i 0.0361317 + 0.0625820i
\(713\) −0.124650 0.215901i −0.00466820 0.00808555i
\(714\) 20.9004 0.782177
\(715\) −0.249301 −0.00932333
\(716\) 0.710340 + 1.23035i 0.0265467 + 0.0459802i
\(717\) 4.66998 8.08865i 0.174404 0.302076i
\(718\) 4.79911 + 8.31229i 0.179101 + 0.310212i
\(719\) −3.03399 + 5.25502i −0.113149 + 0.195979i −0.917038 0.398799i \(-0.869427\pi\)
0.803890 + 0.594779i \(0.202760\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 58.5893 2.18198
\(722\) 18.5843 + 3.95273i 0.691636 + 0.147105i
\(723\) −14.4207 −0.536311
\(724\) 4.39732 7.61637i 0.163425 0.283060i
\(725\) −4.32555 + 7.49206i −0.160647 + 0.278248i
\(726\) 5.38787 + 9.33207i 0.199963 + 0.346345i
\(727\) 7.80855 13.5248i 0.289603 0.501607i −0.684112 0.729377i \(-0.739810\pi\)
0.973715 + 0.227770i \(0.0731433\pi\)
\(728\) −1.21034 2.09637i −0.0448582 0.0776967i
\(729\) 1.00000 0.0370370
\(730\) −2.92823 −0.108379
\(731\) 28.7946 + 49.8738i 1.06501 + 1.84465i
\(732\) −1.53589 2.66023i −0.0567680 0.0983250i
\(733\) 20.4736 0.756208 0.378104 0.925763i \(-0.376576\pi\)
0.378104 + 0.925763i \(0.376576\pi\)
\(734\) 1.36780 0.0504865
\(735\) −7.07177 12.2487i −0.260846 0.451799i
\(736\) 0.236780 0.410115i 0.00872783 0.0151170i
\(737\) −2.14802 3.72047i −0.0791232 0.137045i
\(738\) 5.63410 9.75854i 0.207394 0.359217i
\(739\) 14.8973 25.8029i 0.548007 0.949175i −0.450404 0.892825i \(-0.648720\pi\)
0.998411 0.0563507i \(-0.0179465\pi\)
\(740\) −1.00000 −0.0367607
\(741\) −1.34891 + 1.85636i −0.0495534 + 0.0681952i
\(742\) −8.86640 −0.325496
\(743\) 15.5767 26.9797i 0.571455 0.989790i −0.424962 0.905211i \(-0.639712\pi\)
0.996417 0.0845782i \(-0.0269543\pi\)
\(744\) 0.263220 0.455910i 0.00965011 0.0167145i
\(745\) 1.20089 + 2.08001i 0.0439974 + 0.0762057i
\(746\) 12.3086 21.3190i 0.450648 0.780545i
\(747\) −2.05288 3.55569i −0.0751109 0.130096i
\(748\) −2.15249 −0.0787028
\(749\) 49.6360 1.81366
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) −14.3879 24.9205i −0.525021 0.909363i −0.999575 0.0291367i \(-0.990724\pi\)
0.474555 0.880226i \(-0.342609\pi\)
\(752\) 8.14354 0.296964
\(753\) −23.2342 −0.846701
\(754\) 2.27714 + 3.94412i 0.0829285 + 0.143636i
\(755\) 7.87088 13.6328i 0.286451 0.496147i
\(756\) 2.29911 + 3.98217i 0.0836177 + 0.144830i
\(757\) 11.2040 19.4058i 0.407215 0.705317i −0.587361 0.809325i \(-0.699833\pi\)
0.994577 + 0.104007i \(0.0331666\pi\)
\(758\) −7.88032 + 13.6491i −0.286226 + 0.495758i
\(759\) −0.224259 −0.00814010
\(760\) 1.77267 + 3.98217i 0.0643013 + 0.144448i
\(761\) −17.5175 −0.635009 −0.317504 0.948257i \(-0.602845\pi\)
−0.317504 + 0.948257i \(0.602845\pi\)
\(762\) −7.10766 + 12.3108i −0.257483 + 0.445974i
\(763\) 15.0484 26.0646i 0.544789 0.943602i
\(764\) −4.57932 7.93161i −0.165674 0.286956i
\(765\) 2.27267 3.93637i 0.0821684 0.142320i
\(766\) −10.0718 17.4448i −0.363908 0.630307i
\(767\) −3.15864 −0.114052
\(768\) 1.00000 0.0360844
\(769\) 20.2821 + 35.1296i 0.731392 + 1.26681i 0.956288 + 0.292425i \(0.0944622\pi\)
−0.224897 + 0.974383i \(0.572205\pi\)
\(770\) 1.08876 + 1.88580i 0.0392364 + 0.0679594i
\(771\) 6.00000 0.216085
\(772\) 1.17753 0.0423802
\(773\) −7.30408 12.6510i −0.262709 0.455026i 0.704252 0.709951i \(-0.251283\pi\)
−0.966961 + 0.254924i \(0.917949\pi\)
\(774\) −6.33499 + 10.9725i −0.227707 + 0.394399i
\(775\) 0.263220 + 0.455910i 0.00945514 + 0.0163768i
\(776\) −8.79911 + 15.2405i −0.315869 + 0.547102i
\(777\) −2.29911 + 3.98217i −0.0824799 + 0.142859i