Properties

Label 570.2.i.f.121.2
Level $570$
Weight $2$
Character 570.121
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: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.f.391.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +3.44949 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.72474 - 2.98735i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.22474 + 5.58542i) q^{17} +1.00000 q^{18} +(3.17423 - 2.98735i) q^{19} +1.00000 q^{20} +(1.72474 + 2.98735i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-1.94949 + 3.37662i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.89898 q^{26} -1.00000 q^{27} +(-1.72474 + 2.98735i) q^{28} +(2.67423 - 4.63191i) q^{29} -1.00000 q^{30} +8.89898 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(3.22474 - 5.58542i) q^{34} +(-1.72474 - 2.98735i) q^{35} +(-0.500000 - 0.866025i) q^{36} -0.101021 q^{37} +(-4.17423 - 1.25529i) q^{38} +4.89898 q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.17423 + 8.96204i) q^{41} +(1.72474 - 2.98735i) q^{42} +(-3.89898 - 6.75323i) q^{43} +(1.50000 - 2.59808i) q^{44} +1.00000 q^{45} +3.89898 q^{46} +(5.44949 - 9.43879i) q^{47} +(0.500000 - 0.866025i) q^{48} +4.89898 q^{49} +1.00000 q^{50} +(-3.22474 + 5.58542i) q^{51} +(2.44949 + 4.24264i) q^{52} +(1.27526 - 2.20881i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{55} +3.44949 q^{56} +(4.17423 + 1.25529i) q^{57} -5.34847 q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-3.77526 + 6.53893i) q^{61} +(-4.44949 - 7.70674i) q^{62} +(-1.72474 + 2.98735i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-1.50000 + 2.59808i) q^{66} +(-3.67423 + 6.36396i) q^{67} -6.44949 q^{68} -3.89898 q^{69} +(-1.72474 + 2.98735i) q^{70} +(-5.67423 - 9.82806i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.77526 - 4.80688i) q^{73} +(0.0505103 + 0.0874863i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} -10.3485 q^{77} +(-2.44949 - 4.24264i) q^{78} +(1.44949 + 2.51059i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.17423 - 8.96204i) q^{82} -7.79796 q^{83} -3.44949 q^{84} +(3.22474 - 5.58542i) q^{85} +(-3.89898 + 6.75323i) q^{86} +5.34847 q^{87} -3.00000 q^{88} +(0.275255 - 0.476756i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(8.44949 - 14.6349i) q^{91} +(-1.94949 - 3.37662i) q^{92} +(4.44949 + 7.70674i) q^{93} -10.8990 q^{94} +(-4.17423 - 1.25529i) q^{95} -1.00000 q^{96} +(6.77526 + 11.7351i) q^{97} +(-2.44949 - 4.24264i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} - 4q^{12} - 2q^{14} + 2q^{15} - 2q^{16} + 8q^{17} + 4q^{18} - 2q^{19} + 4q^{20} + 2q^{21} + 6q^{22} + 2q^{23} + 2q^{24} - 2q^{25} - 4q^{27} - 2q^{28} - 4q^{29} - 4q^{30} + 16q^{31} - 2q^{32} - 6q^{33} + 8q^{34} - 2q^{35} - 2q^{36} - 20q^{37} - 2q^{38} - 2q^{40} + 6q^{41} + 2q^{42} + 4q^{43} + 6q^{44} + 4q^{45} - 4q^{46} + 12q^{47} + 2q^{48} + 4q^{50} - 8q^{51} + 10q^{53} + 2q^{54} + 6q^{55} + 4q^{56} + 2q^{57} + 8q^{58} + 12q^{59} + 2q^{60} - 20q^{61} - 8q^{62} - 2q^{63} + 4q^{64} - 6q^{66} - 16q^{68} + 4q^{69} - 2q^{70} - 8q^{71} - 2q^{72} - 16q^{73} + 10q^{74} - 4q^{75} + 4q^{76} - 12q^{77} - 4q^{79} - 2q^{80} - 2q^{81} + 6q^{82} + 8q^{83} - 4q^{84} + 8q^{85} + 4q^{86} - 8q^{87} - 12q^{88} + 6q^{89} - 2q^{90} + 24q^{91} + 2q^{92} + 8q^{93} - 24q^{94} - 2q^{95} - 4q^{96} + 32q^{97} + 6q^{99} + O(q^{100}) \)

Character values

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

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

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
\(7\) 3.44949 1.30378 0.651892 0.758312i \(-0.273975\pi\)
0.651892 + 0.758312i \(0.273975\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) −1.72474 2.98735i −0.460957 0.798402i
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.22474 + 5.58542i 0.782116 + 1.35466i 0.930707 + 0.365765i \(0.119193\pi\)
−0.148592 + 0.988899i \(0.547474\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.17423 2.98735i 0.728219 0.685344i
\(20\) 1.00000 0.223607
\(21\) 1.72474 + 2.98735i 0.376370 + 0.651892i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −1.94949 + 3.37662i −0.406497 + 0.704073i −0.994494 0.104790i \(-0.966583\pi\)
0.587998 + 0.808863i \(0.299916\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −4.89898 −0.960769
\(27\) −1.00000 −0.192450
\(28\) −1.72474 + 2.98735i −0.325946 + 0.564555i
\(29\) 2.67423 4.63191i 0.496593 0.860124i −0.503399 0.864054i \(-0.667918\pi\)
0.999992 + 0.00392972i \(0.00125087\pi\)
\(30\) −1.00000 −0.182574
\(31\) 8.89898 1.59830 0.799152 0.601129i \(-0.205282\pi\)
0.799152 + 0.601129i \(0.205282\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 3.22474 5.58542i 0.553039 0.957892i
\(35\) −1.72474 2.98735i −0.291535 0.504954i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.101021 −0.0166077 −0.00830384 0.999966i \(-0.502643\pi\)
−0.00830384 + 0.999966i \(0.502643\pi\)
\(38\) −4.17423 1.25529i −0.677150 0.203636i
\(39\) 4.89898 0.784465
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 5.17423 + 8.96204i 0.808080 + 1.39964i 0.914192 + 0.405281i \(0.132826\pi\)
−0.106113 + 0.994354i \(0.533840\pi\)
\(42\) 1.72474 2.98735i 0.266134 0.460957i
\(43\) −3.89898 6.75323i −0.594589 1.02986i −0.993605 0.112914i \(-0.963982\pi\)
0.399016 0.916944i \(-0.369352\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 1.00000 0.149071
\(46\) 3.89898 0.574873
\(47\) 5.44949 9.43879i 0.794890 1.37679i −0.128019 0.991772i \(-0.540862\pi\)
0.922909 0.385018i \(-0.125805\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 4.89898 0.699854
\(50\) 1.00000 0.141421
\(51\) −3.22474 + 5.58542i −0.451555 + 0.782116i
\(52\) 2.44949 + 4.24264i 0.339683 + 0.588348i
\(53\) 1.27526 2.20881i 0.175170 0.303403i −0.765050 0.643971i \(-0.777286\pi\)
0.940220 + 0.340568i \(0.110619\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 1.50000 + 2.59808i 0.202260 + 0.350325i
\(56\) 3.44949 0.460957
\(57\) 4.17423 + 1.25529i 0.552891 + 0.166268i
\(58\) −5.34847 −0.702288
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) −3.77526 + 6.53893i −0.483372 + 0.837225i −0.999818 0.0190952i \(-0.993921\pi\)
0.516446 + 0.856320i \(0.327255\pi\)
\(62\) −4.44949 7.70674i −0.565086 0.978757i
\(63\) −1.72474 + 2.98735i −0.217297 + 0.376370i
\(64\) 1.00000 0.125000
\(65\) −4.89898 −0.607644
\(66\) −1.50000 + 2.59808i −0.184637 + 0.319801i
\(67\) −3.67423 + 6.36396i −0.448879 + 0.777482i −0.998313 0.0580554i \(-0.981510\pi\)
0.549434 + 0.835537i \(0.314843\pi\)
\(68\) −6.44949 −0.782116
\(69\) −3.89898 −0.469382
\(70\) −1.72474 + 2.98735i −0.206146 + 0.357056i
\(71\) −5.67423 9.82806i −0.673408 1.16638i −0.976932 0.213553i \(-0.931497\pi\)
0.303524 0.952824i \(-0.401837\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −2.77526 4.80688i −0.324819 0.562603i 0.656657 0.754190i \(-0.271970\pi\)
−0.981476 + 0.191587i \(0.938637\pi\)
\(74\) 0.0505103 + 0.0874863i 0.00587170 + 0.0101701i
\(75\) −1.00000 −0.115470
\(76\) 1.00000 + 4.24264i 0.114708 + 0.486664i
\(77\) −10.3485 −1.17932
\(78\) −2.44949 4.24264i −0.277350 0.480384i
\(79\) 1.44949 + 2.51059i 0.163080 + 0.282463i 0.935972 0.352075i \(-0.114524\pi\)
−0.772892 + 0.634538i \(0.781190\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.17423 8.96204i 0.571399 0.989691i
\(83\) −7.79796 −0.855937 −0.427969 0.903794i \(-0.640771\pi\)
−0.427969 + 0.903794i \(0.640771\pi\)
\(84\) −3.44949 −0.376370
\(85\) 3.22474 5.58542i 0.349773 0.605824i
\(86\) −3.89898 + 6.75323i −0.420438 + 0.728220i
\(87\) 5.34847 0.573416
\(88\) −3.00000 −0.319801
\(89\) 0.275255 0.476756i 0.0291770 0.0505360i −0.851068 0.525055i \(-0.824045\pi\)
0.880245 + 0.474519i \(0.157378\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 8.44949 14.6349i 0.885747 1.53416i
\(92\) −1.94949 3.37662i −0.203248 0.352036i
\(93\) 4.44949 + 7.70674i 0.461391 + 0.799152i
\(94\) −10.8990 −1.12414
\(95\) −4.17423 1.25529i −0.428267 0.128791i
\(96\) −1.00000 −0.102062
\(97\) 6.77526 + 11.7351i 0.687923 + 1.19152i 0.972509 + 0.232867i \(0.0748106\pi\)
−0.284586 + 0.958651i \(0.591856\pi\)
\(98\) −2.44949 4.24264i −0.247436 0.428571i
\(99\) 1.50000 2.59808i 0.150756 0.261116i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 5.44949 9.43879i 0.542244 0.939195i −0.456530 0.889708i \(-0.650908\pi\)
0.998775 0.0494871i \(-0.0157587\pi\)
\(102\) 6.44949 0.638595
\(103\) −13.2474 −1.30531 −0.652655 0.757655i \(-0.726345\pi\)
−0.652655 + 0.757655i \(0.726345\pi\)
\(104\) 2.44949 4.24264i 0.240192 0.416025i
\(105\) 1.72474 2.98735i 0.168318 0.291535i
\(106\) −2.55051 −0.247727
\(107\) −17.3485 −1.67714 −0.838570 0.544794i \(-0.816608\pi\)
−0.838570 + 0.544794i \(0.816608\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 6.67423 + 11.5601i 0.639276 + 1.10726i 0.985592 + 0.169140i \(0.0540991\pi\)
−0.346316 + 0.938118i \(0.612568\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) −0.0505103 0.0874863i −0.00479422 0.00830384i
\(112\) −1.72474 2.98735i −0.162973 0.282278i
\(113\) −14.4495 −1.35929 −0.679647 0.733539i \(-0.737867\pi\)
−0.679647 + 0.733539i \(0.737867\pi\)
\(114\) −1.00000 4.24264i −0.0936586 0.397360i
\(115\) 3.89898 0.363582
\(116\) 2.67423 + 4.63191i 0.248296 + 0.430062i
\(117\) 2.44949 + 4.24264i 0.226455 + 0.392232i
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) 11.1237 + 19.2669i 1.01971 + 1.76619i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) 7.55051 0.683591
\(123\) −5.17423 + 8.96204i −0.466545 + 0.808080i
\(124\) −4.44949 + 7.70674i −0.399576 + 0.692086i
\(125\) 1.00000 0.0894427
\(126\) 3.44949 0.307305
\(127\) −7.17423 + 12.4261i −0.636610 + 1.10264i 0.349561 + 0.936914i \(0.386331\pi\)
−0.986172 + 0.165728i \(0.947003\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 3.89898 6.75323i 0.343286 0.594589i
\(130\) 2.44949 + 4.24264i 0.214834 + 0.372104i
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 3.00000 0.261116
\(133\) 10.9495 10.3048i 0.949441 0.893541i
\(134\) 7.34847 0.634811
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 3.22474 + 5.58542i 0.276520 + 0.478946i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 1.94949 + 3.37662i 0.165952 + 0.287437i
\(139\) −7.34847 + 12.7279i −0.623289 + 1.07957i 0.365580 + 0.930780i \(0.380871\pi\)
−0.988869 + 0.148788i \(0.952463\pi\)
\(140\) 3.44949 0.291535
\(141\) 10.8990 0.917860
\(142\) −5.67423 + 9.82806i −0.476171 + 0.824753i
\(143\) −7.34847 + 12.7279i −0.614510 + 1.06436i
\(144\) 1.00000 0.0833333
\(145\) −5.34847 −0.444166
\(146\) −2.77526 + 4.80688i −0.229682 + 0.397820i
\(147\) 2.44949 + 4.24264i 0.202031 + 0.349927i
\(148\) 0.0505103 0.0874863i 0.00415192 0.00719133i
\(149\) −9.22474 15.9777i −0.755721 1.30895i −0.945015 0.327026i \(-0.893954\pi\)
0.189295 0.981920i \(-0.439380\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −19.3485 −1.57456 −0.787278 0.616598i \(-0.788510\pi\)
−0.787278 + 0.616598i \(0.788510\pi\)
\(152\) 3.17423 2.98735i 0.257464 0.242306i
\(153\) −6.44949 −0.521410
\(154\) 5.17423 + 8.96204i 0.416952 + 0.722182i
\(155\) −4.44949 7.70674i −0.357392 0.619020i
\(156\) −2.44949 + 4.24264i −0.196116 + 0.339683i
\(157\) −0.601021 1.04100i −0.0479667 0.0830807i 0.841045 0.540965i \(-0.181941\pi\)
−0.889012 + 0.457884i \(0.848607\pi\)
\(158\) 1.44949 2.51059i 0.115315 0.199732i
\(159\) 2.55051 0.202269
\(160\) 1.00000 0.0790569
\(161\) −6.72474 + 11.6476i −0.529984 + 0.917959i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −12.6969 −0.994501 −0.497250 0.867607i \(-0.665657\pi\)
−0.497250 + 0.867607i \(0.665657\pi\)
\(164\) −10.3485 −0.808080
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 3.89898 + 6.75323i 0.302619 + 0.524152i
\(167\) −9.84847 + 17.0580i −0.762097 + 1.31999i 0.179670 + 0.983727i \(0.442497\pi\)
−0.941768 + 0.336265i \(0.890836\pi\)
\(168\) 1.72474 + 2.98735i 0.133067 + 0.230479i
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) −6.44949 −0.494653
\(171\) 1.00000 + 4.24264i 0.0764719 + 0.324443i
\(172\) 7.79796 0.594589
\(173\) 4.72474 + 8.18350i 0.359216 + 0.622180i 0.987830 0.155537i \(-0.0497109\pi\)
−0.628614 + 0.777717i \(0.716378\pi\)
\(174\) −2.67423 4.63191i −0.202733 0.351144i
\(175\) −1.72474 + 2.98735i −0.130378 + 0.225822i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) −3.00000 + 5.19615i −0.225494 + 0.390567i
\(178\) −0.550510 −0.0412625
\(179\) −1.20204 −0.0898448 −0.0449224 0.998990i \(-0.514304\pi\)
−0.0449224 + 0.998990i \(0.514304\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 8.57321 14.8492i 0.637242 1.10374i −0.348793 0.937200i \(-0.613409\pi\)
0.986035 0.166536i \(-0.0532582\pi\)
\(182\) −16.8990 −1.25264
\(183\) −7.55051 −0.558150
\(184\) −1.94949 + 3.37662i −0.143718 + 0.248927i
\(185\) 0.0505103 + 0.0874863i 0.00371359 + 0.00643212i
\(186\) 4.44949 7.70674i 0.326252 0.565086i
\(187\) −9.67423 16.7563i −0.707450 1.22534i
\(188\) 5.44949 + 9.43879i 0.397445 + 0.688395i
\(189\) −3.44949 −0.250913
\(190\) 1.00000 + 4.24264i 0.0725476 + 0.307794i
\(191\) 15.7980 1.14310 0.571550 0.820567i \(-0.306342\pi\)
0.571550 + 0.820567i \(0.306342\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 3.32577 + 5.76039i 0.239394 + 0.414642i 0.960541 0.278140i \(-0.0897180\pi\)
−0.721147 + 0.692782i \(0.756385\pi\)
\(194\) 6.77526 11.7351i 0.486435 0.842530i
\(195\) −2.44949 4.24264i −0.175412 0.303822i
\(196\) −2.44949 + 4.24264i −0.174964 + 0.303046i
\(197\) 11.4495 0.815742 0.407871 0.913039i \(-0.366271\pi\)
0.407871 + 0.913039i \(0.366271\pi\)
\(198\) −3.00000 −0.213201
\(199\) −0.775255 + 1.34278i −0.0549564 + 0.0951872i −0.892195 0.451651i \(-0.850835\pi\)
0.837238 + 0.546838i \(0.184169\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −7.34847 −0.518321
\(202\) −10.8990 −0.766850
\(203\) 9.22474 15.9777i 0.647450 1.12142i
\(204\) −3.22474 5.58542i −0.225777 0.391058i
\(205\) 5.17423 8.96204i 0.361384 0.625936i
\(206\) 6.62372 + 11.4726i 0.461497 + 0.799336i
\(207\) −1.94949 3.37662i −0.135499 0.234691i
\(208\) −4.89898 −0.339683
\(209\) −9.52270 + 8.96204i −0.658699 + 0.619917i
\(210\) −3.44949 −0.238037
\(211\) 5.82577 + 10.0905i 0.401062 + 0.694660i 0.993854 0.110695i \(-0.0353078\pi\)
−0.592792 + 0.805355i \(0.701974\pi\)
\(212\) 1.27526 + 2.20881i 0.0875849 + 0.151701i
\(213\) 5.67423 9.82806i 0.388792 0.673408i
\(214\) 8.67423 + 15.0242i 0.592958 + 1.02703i
\(215\) −3.89898 + 6.75323i −0.265908 + 0.460567i
\(216\) −1.00000 −0.0680414
\(217\) 30.6969 2.08384
\(218\) 6.67423 11.5601i 0.452036 0.782950i
\(219\) 2.77526 4.80688i 0.187534 0.324819i
\(220\) −3.00000 −0.202260
\(221\) 31.5959 2.12537
\(222\) −0.0505103 + 0.0874863i −0.00339003 + 0.00587170i
\(223\) −0.724745 1.25529i −0.0485325 0.0840608i 0.840739 0.541441i \(-0.182121\pi\)
−0.889271 + 0.457380i \(0.848788\pi\)
\(224\) −1.72474 + 2.98735i −0.115239 + 0.199600i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 7.22474 + 12.5136i 0.480583 + 0.832394i
\(227\) 3.34847 0.222246 0.111123 0.993807i \(-0.464555\pi\)
0.111123 + 0.993807i \(0.464555\pi\)
\(228\) −3.17423 + 2.98735i −0.210219 + 0.197842i
\(229\) −20.6969 −1.36769 −0.683846 0.729626i \(-0.739694\pi\)
−0.683846 + 0.729626i \(0.739694\pi\)
\(230\) −1.94949 3.37662i −0.128546 0.222647i
\(231\) −5.17423 8.96204i −0.340440 0.589659i
\(232\) 2.67423 4.63191i 0.175572 0.304100i
\(233\) 4.10102 + 7.10318i 0.268667 + 0.465345i 0.968518 0.248944i \(-0.0800836\pi\)
−0.699851 + 0.714289i \(0.746750\pi\)
\(234\) 2.44949 4.24264i 0.160128 0.277350i
\(235\) −10.8990 −0.710971
\(236\) −6.00000 −0.390567
\(237\) −1.44949 + 2.51059i −0.0941545 + 0.163080i
\(238\) 11.1237 19.2669i 0.721044 1.24888i
\(239\) −10.2020 −0.659915 −0.329958 0.943996i \(-0.607034\pi\)
−0.329958 + 0.943996i \(0.607034\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 11.3485 19.6561i 0.731019 1.26616i −0.225429 0.974260i \(-0.572378\pi\)
0.956448 0.291903i \(-0.0942883\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −3.77526 6.53893i −0.241686 0.418612i
\(245\) −2.44949 4.24264i −0.156492 0.271052i
\(246\) 10.3485 0.659794
\(247\) −4.89898 20.7846i −0.311715 1.32249i
\(248\) 8.89898 0.565086
\(249\) −3.89898 6.75323i −0.247088 0.427969i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 10.8990 18.8776i 0.687937 1.19154i −0.284566 0.958656i \(-0.591850\pi\)
0.972504 0.232886i \(-0.0748170\pi\)
\(252\) −1.72474 2.98735i −0.108649 0.188185i
\(253\) 5.84847 10.1298i 0.367690 0.636858i
\(254\) 14.3485 0.900303
\(255\) 6.44949 0.403883
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.89898 3.28913i 0.118455 0.205170i −0.800701 0.599065i \(-0.795539\pi\)
0.919156 + 0.393895i \(0.128873\pi\)
\(258\) −7.79796 −0.485480
\(259\) −0.348469 −0.0216528
\(260\) 2.44949 4.24264i 0.151911 0.263117i
\(261\) 2.67423 + 4.63191i 0.165531 + 0.286708i
\(262\) 1.50000 2.59808i 0.0926703 0.160510i
\(263\) −9.94949 17.2330i −0.613512 1.06263i −0.990644 0.136474i \(-0.956423\pi\)
0.377132 0.926160i \(-0.376910\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) −2.55051 −0.156677
\(266\) −14.3990 4.33013i −0.882858 0.265497i
\(267\) 0.550510 0.0336907
\(268\) −3.67423 6.36396i −0.224440 0.388741i
\(269\) −0.123724 0.214297i −0.00754361 0.0130659i 0.862229 0.506519i \(-0.169068\pi\)
−0.869773 + 0.493453i \(0.835735\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 2.55051 + 4.41761i 0.154932 + 0.268351i 0.933034 0.359787i \(-0.117151\pi\)
−0.778102 + 0.628138i \(0.783817\pi\)
\(272\) 3.22474 5.58542i 0.195529 0.338666i
\(273\) 16.8990 1.02277
\(274\) −12.0000 −0.724947
\(275\) 1.50000 2.59808i 0.0904534 0.156670i
\(276\) 1.94949 3.37662i 0.117345 0.203248i
\(277\) −3.10102 −0.186322 −0.0931611 0.995651i \(-0.529697\pi\)
−0.0931611 + 0.995651i \(0.529697\pi\)
\(278\) 14.6969 0.881464
\(279\) −4.44949 + 7.70674i −0.266384 + 0.461391i
\(280\) −1.72474 2.98735i −0.103073 0.178528i
\(281\) 0.174235 0.301783i 0.0103940 0.0180029i −0.860782 0.508974i \(-0.830025\pi\)
0.871176 + 0.490972i \(0.163358\pi\)
\(282\) −5.44949 9.43879i −0.324512 0.562072i
\(283\) −8.34847 14.4600i −0.496265 0.859556i 0.503726 0.863864i \(-0.331962\pi\)
−0.999991 + 0.00430747i \(0.998629\pi\)
\(284\) 11.3485 0.673408
\(285\) −1.00000 4.24264i −0.0592349 0.251312i
\(286\) 14.6969 0.869048
\(287\) 17.8485 + 30.9145i 1.05356 + 1.82482i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −12.2980 + 21.3007i −0.723409 + 1.25298i
\(290\) 2.67423 + 4.63191i 0.157036 + 0.271995i
\(291\) −6.77526 + 11.7351i −0.397172 + 0.687923i
\(292\) 5.55051 0.324819
\(293\) −6.55051 −0.382685 −0.191342 0.981523i \(-0.561284\pi\)
−0.191342 + 0.981523i \(0.561284\pi\)
\(294\) 2.44949 4.24264i 0.142857 0.247436i
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) −0.101021 −0.00587170
\(297\) 3.00000 0.174078
\(298\) −9.22474 + 15.9777i −0.534375 + 0.925565i
\(299\) 9.55051 + 16.5420i 0.552320 + 0.956647i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) −13.4495 23.2952i −0.775216 1.34271i
\(302\) 9.67423 + 16.7563i 0.556690 + 0.964215i
\(303\) 10.8990 0.626130
\(304\) −4.17423 1.25529i −0.239409 0.0719961i
\(305\) 7.55051 0.432341
\(306\) 3.22474 + 5.58542i 0.184346 + 0.319297i
\(307\) −7.12372 12.3387i −0.406572 0.704204i 0.587931 0.808911i \(-0.299943\pi\)
−0.994503 + 0.104707i \(0.966609\pi\)
\(308\) 5.17423 8.96204i 0.294829 0.510659i
\(309\) −6.62372 11.4726i −0.376811 0.652655i
\(310\) −4.44949 + 7.70674i −0.252714 + 0.437714i
\(311\) 9.79796 0.555591 0.277796 0.960640i \(-0.410396\pi\)
0.277796 + 0.960640i \(0.410396\pi\)
\(312\) 4.89898 0.277350
\(313\) 3.79796 6.57826i 0.214673 0.371825i −0.738498 0.674256i \(-0.764465\pi\)
0.953171 + 0.302430i \(0.0977980\pi\)
\(314\) −0.601021 + 1.04100i −0.0339175 + 0.0587469i
\(315\) 3.44949 0.194357
\(316\) −2.89898 −0.163080
\(317\) −2.27526 + 3.94086i −0.127791 + 0.221341i −0.922820 0.385230i \(-0.874122\pi\)
0.795029 + 0.606571i \(0.207455\pi\)
\(318\) −1.27526 2.20881i −0.0715128 0.123864i
\(319\) −8.02270 + 13.8957i −0.449185 + 0.778012i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −8.67423 15.0242i −0.484149 0.838570i
\(322\) 13.4495 0.749511
\(323\) 26.9217 + 8.09601i 1.49796 + 0.450474i
\(324\) 1.00000 0.0555556
\(325\) 2.44949 + 4.24264i 0.135873 + 0.235339i
\(326\) 6.34847 + 10.9959i 0.351609 + 0.609005i
\(327\) −6.67423 + 11.5601i −0.369086 + 0.639276i
\(328\) 5.17423 + 8.96204i 0.285699 + 0.494846i
\(329\) 18.7980 32.5590i 1.03637 1.79504i
\(330\) 3.00000 0.165145
\(331\) 3.65153 0.200706 0.100353 0.994952i \(-0.468003\pi\)
0.100353 + 0.994952i \(0.468003\pi\)
\(332\) 3.89898 6.75323i 0.213984 0.370632i
\(333\) 0.0505103 0.0874863i 0.00276795 0.00479422i
\(334\) 19.6969 1.07777
\(335\) 7.34847 0.401490
\(336\) 1.72474 2.98735i 0.0940925 0.162973i
\(337\) −11.2474 19.4812i −0.612688 1.06121i −0.990785 0.135440i \(-0.956755\pi\)
0.378098 0.925766i \(-0.376578\pi\)
\(338\) −5.50000 + 9.52628i −0.299161 + 0.518161i
\(339\) −7.22474 12.5136i −0.392394 0.679647i
\(340\) 3.22474 + 5.58542i 0.174886 + 0.302912i
\(341\) −26.6969 −1.44572
\(342\) 3.17423 2.98735i 0.171643 0.161537i
\(343\) −7.24745 −0.391325
\(344\) −3.89898 6.75323i −0.210219 0.364110i
\(345\) 1.94949 + 3.37662i 0.104957 + 0.181791i
\(346\) 4.72474 8.18350i 0.254004 0.439948i
\(347\) 3.89898 + 6.75323i 0.209308 + 0.362532i 0.951497 0.307659i \(-0.0995455\pi\)
−0.742189 + 0.670191i \(0.766212\pi\)
\(348\) −2.67423 + 4.63191i −0.143354 + 0.248296i
\(349\) 24.0454 1.28712 0.643561 0.765395i \(-0.277456\pi\)
0.643561 + 0.765395i \(0.277456\pi\)
\(350\) 3.44949 0.184383
\(351\) −2.44949 + 4.24264i −0.130744 + 0.226455i
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −20.6515 −1.09917 −0.549585 0.835438i \(-0.685214\pi\)
−0.549585 + 0.835438i \(0.685214\pi\)
\(354\) 6.00000 0.318896
\(355\) −5.67423 + 9.82806i −0.301157 + 0.521619i
\(356\) 0.275255 + 0.476756i 0.0145885 + 0.0252680i
\(357\) −11.1237 + 19.2669i −0.588730 + 1.01971i
\(358\) 0.601021 + 1.04100i 0.0317649 + 0.0550185i
\(359\) −10.7753 18.6633i −0.568696 0.985011i −0.996695 0.0812316i \(-0.974115\pi\)
0.427999 0.903779i \(-0.359219\pi\)
\(360\) 1.00000 0.0527046
\(361\) 1.15153 18.9651i 0.0606069 0.998162i
\(362\) −17.1464 −0.901196
\(363\) −1.00000 1.73205i −0.0524864 0.0909091i
\(364\) 8.44949 + 14.6349i 0.442874 + 0.767080i
\(365\) −2.77526 + 4.80688i −0.145263 + 0.251604i
\(366\) 3.77526 + 6.53893i 0.197336 + 0.341796i
\(367\) −5.55051 + 9.61377i −0.289734 + 0.501834i −0.973746 0.227636i \(-0.926900\pi\)
0.684012 + 0.729471i \(0.260234\pi\)
\(368\) 3.89898 0.203248
\(369\) −10.3485 −0.538720
\(370\) 0.0505103 0.0874863i 0.00262590 0.00454820i
\(371\) 4.39898 7.61926i 0.228384 0.395572i
\(372\) −8.89898 −0.461391
\(373\) 5.89898 0.305438 0.152719 0.988270i \(-0.451197\pi\)
0.152719 + 0.988270i \(0.451197\pi\)
\(374\) −9.67423 + 16.7563i −0.500243 + 0.866446i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 5.44949 9.43879i 0.281036 0.486769i
\(377\) −13.1010 22.6916i −0.674737 1.16868i
\(378\) 1.72474 + 2.98735i 0.0887113 + 0.153652i
\(379\) 22.6969 1.16586 0.582932 0.812521i \(-0.301906\pi\)
0.582932 + 0.812521i \(0.301906\pi\)
\(380\) 3.17423 2.98735i 0.162835 0.153248i
\(381\) −14.3485 −0.735094
\(382\) −7.89898 13.6814i −0.404147 0.700003i
\(383\) 9.24745 + 16.0171i 0.472523 + 0.818433i 0.999506 0.0314428i \(-0.0100102\pi\)
−0.526983 + 0.849876i \(0.676677\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 5.17423 + 8.96204i 0.263703 + 0.456748i
\(386\) 3.32577 5.76039i 0.169277 0.293196i
\(387\) 7.79796 0.396393
\(388\) −13.5505 −0.687923
\(389\) −5.57321 + 9.65309i −0.282573 + 0.489431i −0.972018 0.234907i \(-0.924521\pi\)
0.689445 + 0.724338i \(0.257855\pi\)
\(390\) −2.44949 + 4.24264i −0.124035 + 0.214834i
\(391\) −25.1464 −1.27171
\(392\) 4.89898 0.247436
\(393\) −1.50000 + 2.59808i −0.0756650 + 0.131056i
\(394\) −5.72474 9.91555i −0.288408 0.499538i
\(395\) 1.44949 2.51059i 0.0729317 0.126321i
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 18.7474 + 32.4715i 0.940907 + 1.62970i 0.763745 + 0.645518i \(0.223358\pi\)
0.177162 + 0.984182i \(0.443308\pi\)
\(398\) 1.55051 0.0777201
\(399\) 14.3990 + 4.33013i 0.720851 + 0.216777i
\(400\) 1.00000 0.0500000
\(401\) −7.89898 13.6814i −0.394456 0.683218i 0.598575 0.801066i \(-0.295734\pi\)
−0.993032 + 0.117848i \(0.962400\pi\)
\(402\) 3.67423 + 6.36396i 0.183254 + 0.317406i
\(403\) 21.7980 37.7552i 1.08583 1.88072i
\(404\) 5.44949 + 9.43879i 0.271122 + 0.469598i
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) −18.4495 −0.915633
\(407\) 0.303062 0.0150222
\(408\) −3.22474 + 5.58542i −0.159649 + 0.276520i
\(409\) −19.7474 + 34.2036i −0.976448 + 1.69126i −0.301379 + 0.953505i \(0.597447\pi\)
−0.675070 + 0.737754i \(0.735886\pi\)
\(410\) −10.3485 −0.511074
\(411\) 12.0000 0.591916
\(412\) 6.62372 11.4726i 0.326327 0.565216i
\(413\) 10.3485 + 17.9241i 0.509215 + 0.881986i
\(414\) −1.94949 + 3.37662i −0.0958122 + 0.165952i
\(415\) 3.89898 + 6.75323i 0.191393 + 0.331503i
\(416\) 2.44949 + 4.24264i 0.120096 + 0.208013i
\(417\) −14.6969 −0.719712
\(418\) 12.5227 + 3.76588i 0.612505 + 0.184195i
\(419\) 12.1010 0.591174 0.295587 0.955316i \(-0.404485\pi\)
0.295587 + 0.955316i \(0.404485\pi\)
\(420\) 1.72474 + 2.98735i 0.0841589 + 0.145768i
\(421\) 16.6742 + 28.8806i 0.812652 + 1.40756i 0.911001 + 0.412403i \(0.135311\pi\)
−0.0983489 + 0.995152i \(0.531356\pi\)
\(422\) 5.82577 10.0905i 0.283594 0.491199i
\(423\) 5.44949 + 9.43879i 0.264963 + 0.458930i
\(424\) 1.27526 2.20881i 0.0619319 0.107269i
\(425\) −6.44949 −0.312846
\(426\) −11.3485 −0.549835
\(427\) −13.0227 + 22.5560i −0.630213 + 1.09156i
\(428\) 8.67423 15.0242i 0.419285 0.726223i
\(429\) −14.6969 −0.709575
\(430\) 7.79796 0.376051
\(431\) −12.6742 + 21.9524i −0.610496 + 1.05741i 0.380660 + 0.924715i \(0.375697\pi\)
−0.991157 + 0.132696i \(0.957637\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 5.67423 9.82806i 0.272686 0.472307i −0.696862 0.717205i \(-0.745421\pi\)
0.969549 + 0.244898i \(0.0787546\pi\)
\(434\) −15.3485 26.5843i −0.736750 1.27609i
\(435\) −2.67423 4.63191i −0.128220 0.222083i
\(436\) −13.3485 −0.639276
\(437\) 3.89898 + 16.5420i 0.186513 + 0.791310i
\(438\) −5.55051 −0.265214
\(439\) 5.67423 + 9.82806i 0.270816 + 0.469068i 0.969071 0.246782i \(-0.0793730\pi\)
−0.698255 + 0.715849i \(0.746040\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) −2.44949 + 4.24264i −0.116642 + 0.202031i
\(442\) −15.7980 27.3629i −0.751432 1.30152i
\(443\) −13.1237 + 22.7310i −0.623527 + 1.07998i 0.365297 + 0.930891i \(0.380968\pi\)
−0.988824 + 0.149089i \(0.952366\pi\)
\(444\) 0.101021 0.00479422
\(445\) −0.550510 −0.0260967
\(446\) −0.724745 + 1.25529i −0.0343177 + 0.0594399i
\(447\) 9.22474 15.9777i 0.436315 0.755721i
\(448\) 3.44949 0.162973
\(449\) 33.2474 1.56904 0.784522 0.620101i \(-0.212908\pi\)
0.784522 + 0.620101i \(0.212908\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −15.5227 26.8861i −0.730936 1.26602i
\(452\) 7.22474 12.5136i 0.339823 0.588591i
\(453\) −9.67423 16.7563i −0.454535 0.787278i
\(454\) −1.67423 2.89986i −0.0785757 0.136097i
\(455\) −16.8990 −0.792236
\(456\) 4.17423 + 1.25529i 0.195476 + 0.0587846i
\(457\) 32.0454 1.49902 0.749510 0.661992i \(-0.230289\pi\)
0.749510 + 0.661992i \(0.230289\pi\)
\(458\) 10.3485 + 17.9241i 0.483552 + 0.837537i
\(459\) −3.22474 5.58542i −0.150518 0.260705i
\(460\) −1.94949 + 3.37662i −0.0908954 + 0.157435i
\(461\) 4.10102 + 7.10318i 0.191004 + 0.330828i 0.945583 0.325381i \(-0.105492\pi\)
−0.754580 + 0.656209i \(0.772159\pi\)
\(462\) −5.17423 + 8.96204i −0.240727 + 0.416952i
\(463\) −30.3485 −1.41041 −0.705206 0.709002i \(-0.749146\pi\)
−0.705206 + 0.709002i \(0.749146\pi\)
\(464\) −5.34847 −0.248296
\(465\) 4.44949 7.70674i 0.206340 0.357392i
\(466\) 4.10102 7.10318i 0.189976 0.329048i
\(467\) −15.7526 −0.728941 −0.364471 0.931215i \(-0.618750\pi\)
−0.364471 + 0.931215i \(0.618750\pi\)
\(468\) −4.89898 −0.226455
\(469\) −12.6742 + 21.9524i −0.585242 + 1.01367i
\(470\) 5.44949 + 9.43879i 0.251366 + 0.435379i
\(471\) 0.601021 1.04100i 0.0276936 0.0479667i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 11.6969 + 20.2597i 0.537826 + 0.931542i
\(474\) 2.89898 0.133155
\(475\) 1.00000 + 4.24264i 0.0458831 + 0.194666i
\(476\) −22.2474 −1.01971
\(477\) 1.27526 + 2.20881i 0.0583899 + 0.101134i
\(478\) 5.10102 + 8.83523i 0.233315 + 0.404114i
\(479\) 17.0227 29.4842i 0.777787 1.34717i −0.155427 0.987847i \(-0.549675\pi\)
0.933215 0.359320i \(-0.116991\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) −0.247449 + 0.428594i −0.0112827 + 0.0195422i
\(482\) −22.6969 −1.03382
\(483\) −13.4495 −0.611973
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 6.77526 11.7351i 0.307648 0.532863i
\(486\) −1.00000 −0.0453609
\(487\) 6.14643 0.278521 0.139261 0.990256i \(-0.455527\pi\)
0.139261 + 0.990256i \(0.455527\pi\)
\(488\) −3.77526 + 6.53893i −0.170898 + 0.296004i
\(489\) −6.34847 10.9959i −0.287088 0.497250i
\(490\) −2.44949 + 4.24264i −0.110657 + 0.191663i
\(491\) 17.3990 + 30.1359i 0.785205 + 1.36001i 0.928877 + 0.370389i \(0.120776\pi\)
−0.143672 + 0.989625i \(0.545891\pi\)
\(492\) −5.17423 8.96204i −0.233273 0.404040i
\(493\) 34.4949 1.55357
\(494\) −15.5505 + 14.6349i −0.699651 + 0.658457i
\(495\) −3.00000 −0.134840
\(496\) −4.44949 7.70674i −0.199788 0.346043i
\(497\) −19.5732 33.9018i −0.877979 1.52070i
\(498\) −3.89898 + 6.75323i −0.174717 + 0.302619i
\(499\) −7.72474 13.3797i −0.345807 0.598955i 0.639693 0.768631i \(-0.279062\pi\)
−0.985500 + 0.169675i \(0.945728\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −19.6969 −0.879994
\(502\) −21.7980 −0.972891
\(503\) −15.8485 + 27.4504i −0.706648 + 1.22395i 0.259445 + 0.965758i \(0.416460\pi\)
−0.966093 + 0.258193i \(0.916873\pi\)
\(504\) −1.72474 + 2.98735i −0.0768262 + 0.133067i
\(505\) −10.8990 −0.484998
\(506\) −11.6969 −0.519992
\(507\) 5.50000 9.52628i 0.244264 0.423077i
\(508\) −7.17423 12.4261i −0.318305 0.551321i
\(509\) −3.44949 + 5.97469i −0.152896 + 0.264824i −0.932291 0.361709i \(-0.882193\pi\)
0.779395 + 0.626533i \(0.215527\pi\)
\(510\) −3.22474 5.58542i −0.142794 0.247327i
\(511\) −9.57321 16.5813i −0.423494 0.733513i
\(512\) 1.00000 0.0441942
\(513\) −3.17423 + 2.98735i −0.140146 + 0.131895i
\(514\) −3.79796 −0.167521
\(515\) 6.62372 + 11.4726i 0.291876 + 0.505544i
\(516\) 3.89898 + 6.75323i 0.171643 + 0.297294i
\(517\) −16.3485 + 28.3164i −0.719005 + 1.24535i
\(518\) 0.174235 + 0.301783i 0.00765543 + 0.0132596i
\(519\) −4.72474 + 8.18350i −0.207393 + 0.359216i
\(520\) −4.89898 −0.214834
\(521\) 10.8990 0.477493 0.238746 0.971082i \(-0.423264\pi\)
0.238746 + 0.971082i \(0.423264\pi\)
\(522\) 2.67423 4.63191i 0.117048 0.202733i
\(523\) 15.5732 26.9736i 0.680969 1.17947i −0.293716 0.955893i \(-0.594892\pi\)
0.974685 0.223580i \(-0.0717745\pi\)
\(524\) −3.00000 −0.131056
\(525\) −3.44949 −0.150548
\(526\) −9.94949 + 17.2330i −0.433818 + 0.751395i
\(527\) 28.6969 + 49.7046i 1.25006 + 2.16516i
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) 3.89898 + 6.75323i 0.169521 + 0.293619i
\(530\) 1.27526 + 2.20881i 0.0553935 + 0.0959444i
\(531\) −6.00000 −0.260378
\(532\) 3.44949 + 14.6349i 0.149554 + 0.634505i
\(533\) 50.6969 2.19593
\(534\) −0.275255 0.476756i −0.0119115 0.0206312i
\(535\) 8.67423 + 15.0242i 0.375020 + 0.649553i
\(536\) −3.67423 + 6.36396i −0.158703 + 0.274881i
\(537\) −0.601021 1.04100i −0.0259359 0.0449224i
\(538\) −0.123724 + 0.214297i −0.00533414 + 0.00923899i
\(539\) −14.6969 −0.633042
\(540\) −1.00000 −0.0430331
\(541\) −14.4495 + 25.0273i −0.621232 + 1.07601i 0.368025 + 0.929816i \(0.380034\pi\)
−0.989257 + 0.146189i \(0.953299\pi\)
\(542\) 2.55051 4.41761i 0.109554 0.189753i
\(543\) 17.1464 0.735824
\(544\) −6.44949 −0.276520
\(545\) 6.67423 11.5601i 0.285893 0.495181i
\(546\) −8.44949 14.6349i −0.361605 0.626318i
\(547\) 16.3485 28.3164i 0.699010 1.21072i −0.269800 0.962916i \(-0.586958\pi\)
0.968810 0.247805i \(-0.0797091\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) −3.77526 6.53893i −0.161124 0.279075i
\(550\) −3.00000 −0.127920
\(551\) −5.34847 22.6916i −0.227852 0.966696i
\(552\) −3.89898 −0.165952
\(553\) 5.00000 + 8.66025i 0.212622 + 0.368271i
\(554\) 1.55051 + 2.68556i 0.0658749 + 0.114099i
\(555\) −0.0505103 + 0.0874863i −0.00214404 + 0.00371359i
\(556\) −7.34847 12.7279i −0.311645 0.539784i
\(557\) 1.82577 3.16232i 0.0773602 0.133992i −0.824750 0.565497i \(-0.808684\pi\)
0.902110 + 0.431506i \(0.142018\pi\)
\(558\) 8.89898 0.376724
\(559\) −38.2020 −1.61577
\(560\) −1.72474 + 2.98735i −0.0728838 + 0.126238i
\(561\) 9.67423 16.7563i 0.408447 0.707450i
\(562\) −0.348469 −0.0146993
\(563\) −29.3939 −1.23880 −0.619402 0.785074i \(-0.712625\pi\)
−0.619402 + 0.785074i \(0.712625\pi\)
\(564\) −5.44949 + 9.43879i −0.229465 + 0.397445i
\(565\) 7.22474 + 12.5136i 0.303947 + 0.526452i
\(566\) −8.34847 + 14.4600i −0.350912 + 0.607798i
\(567\) −1.72474 2.98735i −0.0724325 0.125457i
\(568\) −5.67423 9.82806i −0.238086 0.412376i
\(569\) −2.55051 −0.106923 −0.0534615 0.998570i \(-0.517025\pi\)
−0.0534615 + 0.998570i \(0.517025\pi\)
\(570\) −3.17423 + 2.98735i −0.132954 + 0.125126i
\(571\) −27.7980 −1.16331 −0.581654 0.813436i \(-0.697594\pi\)
−0.581654 + 0.813436i \(0.697594\pi\)
\(572\) −7.34847 12.7279i −0.307255 0.532181i
\(573\) 7.89898 + 13.6814i 0.329985 + 0.571550i
\(574\) 17.8485 30.9145i 0.744981 1.29034i
\(575\) −1.94949 3.37662i −0.0812993 0.140815i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −23.1464 −0.963598 −0.481799 0.876282i \(-0.660017\pi\)
−0.481799 + 0.876282i \(0.660017\pi\)
\(578\) 24.5959 1.02306
\(579\) −3.32577 + 5.76039i −0.138214 + 0.239394i
\(580\) 2.67423 4.63191i 0.111042 0.192330i
\(581\) −26.8990 −1.11596
\(582\) 13.5505 0.561687
\(583\) −3.82577 + 6.62642i −0.158447 + 0.274438i
\(584\) −2.77526 4.80688i −0.114841 0.198910i
\(585\) 2.44949 4.24264i 0.101274 0.175412i
\(586\) 3.27526 + 5.67291i 0.135300 + 0.234346i
\(587\) −8.24745 14.2850i −0.340409 0.589605i 0.644100 0.764941i \(-0.277232\pi\)
−0.984509 + 0.175336i \(0.943899\pi\)
\(588\) −4.89898 −0.202031
\(589\) 28.2474 26.5843i 1.16392 1.09539i
\(590\) −6.00000 −0.247016
\(591\) 5.72474 + 9.91555i 0.235485 + 0.407871i
\(592\) 0.0505103 + 0.0874863i 0.00207596 + 0.00359567i
\(593\) 0.426786 0.739215i 0.0175260 0.0303559i −0.857129 0.515101i \(-0.827754\pi\)
0.874655 + 0.484745i \(0.161088\pi\)
\(594\) −1.50000 2.59808i −0.0615457 0.106600i
\(595\) 11.1237 19.2669i 0.456028 0.789864i
\(596\) 18.4495 0.755721
\(597\) −1.55051 −0.0634582
\(598\) 9.55051 16.5420i 0.390549 0.676451i
\(599\) −5.32577 + 9.22450i −0.217605 + 0.376903i −0.954075 0.299567i \(-0.903158\pi\)
0.736470 + 0.676470i \(0.236491\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) −13.4495 + 23.2952i −0.548160 + 0.949441i
\(603\) −3.67423 6.36396i −0.149626 0.259161i
\(604\) 9.67423 16.7563i 0.393639 0.681803i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) −5.44949 9.43879i −0.221370 0.383425i
\(607\) 24.5505 0.996474 0.498237 0.867041i \(-0.333981\pi\)
0.498237 + 0.867041i \(0.333981\pi\)
\(608\) 1.00000 + 4.24264i 0.0405554 + 0.172062i
\(609\) 18.4495 0.747611
\(610\) −3.77526 6.53893i −0.152856 0.264754i
\(611\) −26.6969 46.2405i −1.08004 1.87069i
\(612\) 3.22474 5.58542i 0.130353 0.225777i
\(613\) 18.7474 + 32.4715i 0.757202 + 1.31151i 0.944272 + 0.329166i \(0.106768\pi\)
−0.187070 + 0.982347i \(0.559899\pi\)
\(614\) −7.12372 + 12.3387i −0.287490 + 0.497947i
\(615\) 10.3485 0.417291
\(616\) −10.3485 −0.416952
\(617\) 11.7980 20.4347i 0.474968 0.822669i −0.524621 0.851336i \(-0.675793\pi\)
0.999589 + 0.0286672i \(0.00912632\pi\)
\(618\) −6.62372 + 11.4726i −0.266445 + 0.461497i
\(619\) −21.0454 −0.845886 −0.422943 0.906156i \(-0.639003\pi\)
−0.422943 + 0.906156i \(0.639003\pi\)
\(620\) 8.89898 0.357392
\(621\) 1.94949 3.37662i 0.0782303 0.135499i
\(622\) −4.89898 8.48528i −0.196431 0.340229i
\(623\) 0.949490 1.64456i 0.0380405 0.0658881i
\(624\) −2.44949 4.24264i −0.0980581 0.169842i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −7.59592 −0.303594
\(627\) −12.5227 3.76588i −0.500109 0.150395i
\(628\) 1.20204 0.0479667
\(629\) −0.325765 0.564242i −0.0129891 0.0224978i
\(630\) −1.72474 2.98735i −0.0687155 0.119019i
\(631\) 0.876276 1.51775i 0.0348840 0.0604208i −0.848056 0.529906i \(-0.822227\pi\)
0.882940 + 0.469485i \(0.155560\pi\)
\(632\) 1.44949 + 2.51059i 0.0576576 + 0.0998659i
\(633\) −5.82577 + 10.0905i −0.231553 + 0.401062i
\(634\) 4.55051 0.180724
\(635\) 14.3485 0.569402
\(636\) −1.27526 + 2.20881i −0.0505672 + 0.0875849i
\(637\) 12.0000 20.7846i 0.475457 0.823516i
\(638\) 16.0454 0.635244
\(639\) 11.3485 0.448939
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 20.3485 + 35.2446i 0.803716 + 1.39208i 0.917154 + 0.398532i \(0.130480\pi\)
−0.113438 + 0.993545i \(0.536186\pi\)
\(642\) −8.67423 + 15.0242i −0.342345 + 0.592958i
\(643\) 2.12372 + 3.67840i 0.0837515 + 0.145062i 0.904859 0.425712i \(-0.139976\pi\)
−0.821107 + 0.570774i \(0.806643\pi\)
\(644\) −6.72474 11.6476i −0.264992 0.458980i
\(645\) −7.79796 −0.307044
\(646\) −6.44949 27.3629i −0.253752 1.07658i
\(647\) 9.89898 0.389169 0.194585 0.980886i \(-0.437664\pi\)
0.194585 + 0.980886i \(0.437664\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −9.00000 15.5885i −0.353281 0.611900i
\(650\) 2.44949 4.24264i 0.0960769 0.166410i
\(651\) 15.3485 + 26.5843i 0.601554 + 1.04192i
\(652\) 6.34847 10.9959i 0.248625 0.430632i
\(653\) −25.6515 −1.00382 −0.501911 0.864919i \(-0.667370\pi\)
−0.501911 + 0.864919i \(0.667370\pi\)
\(654\) 13.3485 0.521966
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 5.17423 8.96204i 0.202020 0.349909i
\(657\) 5.55051 0.216546
\(658\) −37.5959 −1.46564
\(659\) 8.29796 14.3725i 0.323243 0.559873i −0.657913 0.753094i \(-0.728560\pi\)
0.981155 + 0.193222i \(0.0618937\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) −2.89898 + 5.02118i −0.112757 + 0.195301i −0.916881 0.399161i \(-0.869302\pi\)
0.804124 + 0.594462i \(0.202635\pi\)
\(662\) −1.82577 3.16232i −0.0709604 0.122907i
\(663\) 15.7980 + 27.3629i 0.613542 + 1.06269i
\(664\) −7.79796 −0.302619
\(665\) −14.3990 4.33013i −0.558368 0.167915i
\(666\) −0.101021 −0.00391447
\(667\) 10.4268 + 18.0597i 0.403727 + 0.699275i
\(668\) −9.84847 17.0580i −0.381049 0.659996i
\(669\) 0.724745 1.25529i 0.0280203 0.0485325i
\(670\) −3.67423 6.36396i −0.141948 0.245861i
\(671\) 11.3258 19.6168i 0.437226 0.757298i
\(672\) −3.44949 −0.133067
\(673\) 8.49490 0.327454 0.163727 0.986506i \(-0.447648\pi\)
0.163727 + 0.986506i \(0.447648\pi\)
\(674\) −11.2474 + 19.4812i −0.433236 + 0.750386i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 11.0000 0.423077
\(677\) −23.9444 −0.920258 −0.460129 0.887852i \(-0.652197\pi\)
−0.460129 + 0.887852i \(0.652197\pi\)
\(678\) −7.22474 + 12.5136i −0.277465 + 0.480583i
\(679\) 23.3712 + 40.4801i 0.896903 + 1.55348i
\(680\) 3.22474 5.58542i 0.123663 0.214191i
\(681\) 1.67423 + 2.89986i 0.0641568 + 0.111123i
\(682\) 13.3485 + 23.1202i 0.511139 + 0.885319i
\(683\) −42.2474 −1.61655 −0.808277 0.588803i \(-0.799600\pi\)
−0.808277 + 0.588803i \(0.799600\pi\)
\(684\) −4.17423 1.25529i −0.159606 0.0479974i
\(685\) −12.0000 −0.458496
\(686\) 3.62372 + 6.27647i 0.138354 + 0.239637i
\(687\) −10.3485 17.9241i −0.394819 0.683846i
\(688\) −3.89898 + 6.75323i −0.148647 + 0.257465i
\(689\) −6.24745 10.8209i −0.238009 0.412243i
\(690\) 1.94949 3.37662i 0.0742158 0.128546i
\(691\) −26.5505 −1.01003 −0.505015 0.863111i \(-0.668513\pi\)
−0.505015 + 0.863111i \(0.668513\pi\)
\(692\) −9.44949 −0.359216
\(693\) 5.17423 8.96204i 0.196553 0.340440i
\(694\) 3.89898 6.75323i 0.148003 0.256349i
\(695\) 14.6969 0.557487
\(696\) 5.34847 0.202733
\(697\) −33.3712 + 57.8006i −1.26402 + 2.18935i
\(698\) −12.0227 20.8239i −0.455066 0.788198i
\(699\) −4.10102 + 7.10318i −0.155115 + 0.268667i
\(700\) −1.72474 2.98735i −0.0651892 0.112911i
\(701\) −11.8990 20.6096i −0.449418 0.778415i 0.548930 0.835868i \(-0.315035\pi\)
−0.998348 + 0.0574531i \(0.981702\pi\)
\(702\) 4.89898 0.184900
\(703\) −0.320663 + 0.301783i −0.0120940 + 0.0113820i
\(704\) −3.00000 −0.113067
\(705\) −5.44949 9.43879i −0.205240 0.355486i
\(706\) 10.3258 + 17.8848i 0.388615 + 0.673101i
\(707\) 18.7980 32.5590i 0.706970 1.22451i
\(708\) −3.00000 5.19615i −0.112747 0.195283i
\(709\) 4.47219 7.74607i 0.167957 0.290910i −0.769745 0.638352i \(-0.779616\pi\)
0.937701 + 0.347442i \(0.112950\pi\)
\(710\) 11.3485 0.425900
\(711\) −2.89898 −0.108720
\(712\) 0.275255 0.476756i 0.0103156 0.0178672i
\(713\) −17.3485 + 30.0484i −0.649705 + 1.12532i
\(714\) 22.2474 0.832590
\(715\) 14.6969 0.549634
\(716\) 0.601021 1.04100i 0.0224612 0.0389039i
\(717\) −5.10102 8.83523i −0.190501 0.329958i
\(718\) −10.7753 + 18.6633i −0.402129 + 0.696508i
\(719\) 2.65153 + 4.59259i 0.0988854 + 0.171275i 0.911224 0.411912i \(-0.135139\pi\)
−0.812338 + 0.583187i \(0.801806\pi\)
\(720\) −0.500000 0.866025i −0.0186339 0.0322749i
\(721\) −45.6969 −1.70184
\(722\) −17.0000 + 8.48528i −0.632674 + 0.315789i
\(723\) 22.6969 0.844108
\(724\) 8.57321 + 14.8492i 0.318621 + 0.551868i
\(725\) 2.67423 + 4.63191i 0.0993186 + 0.172025i
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −13.8990 24.0737i −0.515485 0.892846i −0.999838 0.0179734i \(-0.994279\pi\)
0.484354 0.874872i \(-0.339055\pi\)
\(728\) 8.44949 14.6349i 0.313159 0.542407i
\(729\) 1.00000 0.0370370
\(730\) 5.55051 0.205434
\(731\) 25.1464 43.5549i 0.930074 1.61094i
\(732\) 3.77526 6.53893i 0.139537 0.241686i
\(733\) 36.5959 1.35170 0.675851 0.737039i \(-0.263776\pi\)
0.675851 + 0.737039i \(0.263776\pi\)
\(734\) 11.1010 0.409746
\(735\) 2.44949 4.24264i 0.0903508 0.156492i
\(736\) −1.94949 3.37662i −0.0718591 0.124464i
\(737\) 11.0227 19.0919i 0.406027 0.703259i
\(738\) 5.17423 + 8.96204i 0.190466 + 0.329897i
\(739\) 7.97219 + 13.8082i 0.293262 + 0.507944i 0.974579 0.224044i \(-0.0719259\pi\)
−0.681317 + 0.731988i \(0.738593\pi\)
\(740\) −0.101021 −0.00371359
\(741\) 15.5505 14.6349i 0.571262 0.537628i
\(742\) −8.79796 −0.322983
\(743\) −4.84847 8.39780i −0.177873 0.308085i 0.763279 0.646069i \(-0.223588\pi\)
−0.941152 + 0.337984i \(0.890255\pi\)
\(744\) 4.44949 + 7.70674i 0.163126 + 0.282543i
\(745\) −9.22474 + 15.9777i −0.337969 + 0.585379i
\(746\) −2.94949 5.10867i −0.107988 0.187042i
\(747\) 3.89898 6.75323i 0.142656 0.247088i
\(748\) 19.3485 0.707450
\(749\) −59.8434 −2.18663
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) −26.4949 + 45.8905i −0.966813 + 1.67457i −0.262148 + 0.965028i \(0.584431\pi\)
−0.704664 + 0.709541i \(0.748902\pi\)
\(752\) −10.8990 −0.397445
\(753\) 21.7980 0.794362
\(754\) −13.1010 + 22.6916i −0.477111 + 0.826381i
\(755\) 9.67423 + 16.7563i 0.352081 + 0.609823i
\(756\) 1.72474 2.98735i 0.0627284 0.108649i
\(757\) −27.1969 47.1065i −0.988490 1.71211i −0.625265 0.780412i \(-0.715009\pi\)
−0.363224 0.931702i \(-0.618324\pi\)
\(758\) −11.3485 19.6561i −0.412195 0.713943i
\(759\) 11.6969 0.424572
\(760\) −4.17423 1.25529i −0.151415 0.0455343i
\(761\) 16.5505 0.599956 0.299978 0.953946i \(-0.403021\pi\)
0.299978 + 0.953946i \(0.403021\pi\)
\(762\) 7.17423 + 12.4261i 0.259895 + 0.450152i
\(763\) 23.0227 + 39.8765i 0.833478 + 1.44363i
\(764\) −7.89898 + 13.6814i −0.285775 + 0.494977i
\(765\) 3.22474 + 5.58542i 0.116591 + 0.201941i
\(766\) 9.24745 16.0171i 0.334124 0.578720i
\(767\) 29.3939 1.06135
\(768\) −1.00000 −0.0360844
\(769\) 7.10102 12.2993i 0.256069 0.443525i −0.709116 0.705092i \(-0.750906\pi\)
0.965185 + 0.261567i \(0.0842391\pi\)
\(770\) 5.17423 8.96204i 0.186466 0.322969i
\(771\) 3.79796 0.136780
\(772\) −6.65153 −0.239394
\(773\) 0.477296 0.826701i 0.0171671 0.0297344i −0.857314 0.514794i \(-0.827869\pi\)
0.874481 + 0.485059i \(0.161202\pi\)
\(774\) −3.89898 6.75323i −0.140146 0.242740i
\(775\) −4.44949 + 7.70674i −0.159830 + 0.276834i
\(776\) 6.77526 + 11.7351i 0.243217 + 0.421265i
\(777\) −0.174235 0.301783i −0.00625063 0.0108264i
\(778\) 11.1464