Properties

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

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{73})\)
Defining polynomial: \(x^{4} - x^{3} + 19 x^{2} + 18 x + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(2.38600 + 4.13267i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.g.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} -4.77200 q^{11} +1.00000 q^{12} +(-1.88600 - 3.26665i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +(-1.38600 - 4.13267i) q^{19} +1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(-2.38600 + 4.13267i) q^{22} +(-2.38600 - 4.13267i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.77200 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.00000 q^{30} -5.77200 q^{31} +(0.500000 + 0.866025i) q^{32} +(2.38600 - 4.13267i) q^{33} +(0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.00000 q^{37} +(-4.27200 - 0.866025i) q^{38} +3.77200 q^{39} +(0.500000 - 0.866025i) q^{40} +(-2.38600 + 4.13267i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.113999 + 0.197452i) q^{43} +(2.38600 + 4.13267i) q^{44} +1.00000 q^{45} -4.77200 q^{46} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(-1.88600 + 3.26665i) q^{52} +(-0.613999 - 1.06348i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.38600 - 4.13267i) q^{55} +1.00000 q^{56} +(4.27200 + 0.866025i) q^{57} +6.00000 q^{58} +(-1.77200 + 3.06920i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(2.88600 + 4.99870i) q^{61} +(-2.88600 + 4.99870i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +3.77200 q^{65} +(-2.38600 - 4.13267i) q^{66} +(1.11400 + 1.92950i) q^{67} +4.77200 q^{69} +(-0.500000 - 0.866025i) q^{70} +(-4.77200 + 8.26535i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.88600 - 10.1949i) q^{73} +(-0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(-2.88600 + 3.26665i) q^{76} +4.77200 q^{77} +(1.88600 - 3.26665i) q^{78} +(7.65800 - 13.2640i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.38600 + 4.13267i) q^{82} +6.00000 q^{83} -1.00000 q^{84} +(0.113999 + 0.197452i) q^{86} -6.00000 q^{87} +4.77200 q^{88} +(4.15800 + 7.20187i) q^{89} +(0.500000 - 0.866025i) q^{90} +(1.88600 + 3.26665i) q^{91} +(-2.38600 + 4.13267i) q^{92} +(2.88600 - 4.99870i) q^{93} +(4.27200 + 0.866025i) q^{95} -1.00000 q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(2.38600 + 4.13267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 4q^{8} - 2q^{9} + 2q^{10} - 2q^{11} + 4q^{12} + q^{13} - 2q^{14} - 2q^{15} - 2q^{16} - 4q^{18} + 3q^{19} + 4q^{20} + 2q^{21} - q^{22} - q^{23} + 2q^{24} - 2q^{25} + 2q^{26} + 4q^{27} + 2q^{28} + 12q^{29} - 4q^{30} - 6q^{31} + 2q^{32} + q^{33} + 2q^{35} - 2q^{36} - 4q^{37} - 2q^{39} + 2q^{40} - q^{41} - 2q^{42} - 9q^{43} + q^{44} + 4q^{45} - 2q^{46} - 2q^{48} - 24q^{49} - 4q^{50} + q^{52} - 11q^{53} + 2q^{54} + q^{55} + 4q^{56} + 24q^{58} + 10q^{59} - 2q^{60} + 3q^{61} - 3q^{62} + 2q^{63} + 4q^{64} - 2q^{65} - q^{66} + 13q^{67} + 2q^{69} - 2q^{70} - 2q^{71} + 2q^{72} + 15q^{73} - 2q^{74} + 4q^{75} - 3q^{76} + 2q^{77} - q^{78} + 5q^{79} - 2q^{80} - 2q^{81} + q^{82} + 24q^{83} - 4q^{84} + 9q^{86} - 24q^{87} + 2q^{88} - 9q^{89} + 2q^{90} - q^{91} - q^{92} + 3q^{93} - 4q^{96} + 20q^{97} - 12q^{98} + q^{99} + O(q^{100}) \)

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
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −4.77200 −1.43881 −0.719406 0.694589i \(-0.755586\pi\)
−0.719406 + 0.694589i \(0.755586\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.88600 3.26665i −0.523083 0.906006i −0.999639 0.0268618i \(-0.991449\pi\)
0.476557 0.879144i \(-0.341885\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.38600 4.13267i −0.317970 0.948101i
\(20\) 1.00000 0.223607
\(21\) 0.500000 0.866025i 0.109109 0.188982i
\(22\) −2.38600 + 4.13267i −0.508697 + 0.881089i
\(23\) −2.38600 4.13267i −0.497516 0.861722i 0.502480 0.864589i \(-0.332421\pi\)
−0.999996 + 0.00286638i \(0.999088\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.77200 −0.739750
\(27\) 1.00000 0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) −1.00000 −0.182574
\(31\) −5.77200 −1.03668 −0.518341 0.855174i \(-0.673450\pi\)
−0.518341 + 0.855174i \(0.673450\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.38600 4.13267i 0.415349 0.719406i
\(34\) 0 0
\(35\) 0.500000 0.866025i 0.0845154 0.146385i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −4.27200 0.866025i −0.693010 0.140488i
\(39\) 3.77200 0.604004
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −2.38600 + 4.13267i −0.372631 + 0.645415i −0.989969 0.141282i \(-0.954878\pi\)
0.617339 + 0.786698i \(0.288211\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −0.113999 + 0.197452i −0.0173847 + 0.0301112i −0.874587 0.484869i \(-0.838867\pi\)
0.857202 + 0.514980i \(0.172201\pi\)
\(44\) 2.38600 + 4.13267i 0.359703 + 0.623024i
\(45\) 1.00000 0.149071
\(46\) −4.77200 −0.703593
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −1.88600 + 3.26665i −0.261541 + 0.453003i
\(53\) −0.613999 1.06348i −0.0843393 0.146080i 0.820770 0.571258i \(-0.193545\pi\)
−0.905109 + 0.425179i \(0.860211\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 2.38600 4.13267i 0.321728 0.557250i
\(56\) 1.00000 0.133631
\(57\) 4.27200 + 0.866025i 0.565840 + 0.114708i
\(58\) 6.00000 0.787839
\(59\) −1.77200 + 3.06920i −0.230695 + 0.399575i −0.958013 0.286725i \(-0.907433\pi\)
0.727318 + 0.686301i \(0.240767\pi\)
\(60\) −0.500000 + 0.866025i −0.0645497 + 0.111803i
\(61\) 2.88600 + 4.99870i 0.369515 + 0.640018i 0.989490 0.144603i \(-0.0461907\pi\)
−0.619975 + 0.784621i \(0.712857\pi\)
\(62\) −2.88600 + 4.99870i −0.366522 + 0.634836i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 3.77200 0.467859
\(66\) −2.38600 4.13267i −0.293696 0.508697i
\(67\) 1.11400 + 1.92950i 0.136097 + 0.235726i 0.926016 0.377485i \(-0.123211\pi\)
−0.789919 + 0.613211i \(0.789878\pi\)
\(68\) 0 0
\(69\) 4.77200 0.574482
\(70\) −0.500000 0.866025i −0.0597614 0.103510i
\(71\) −4.77200 + 8.26535i −0.566332 + 0.980917i 0.430592 + 0.902547i \(0.358305\pi\)
−0.996924 + 0.0783698i \(0.975029\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 5.88600 10.1949i 0.688904 1.19322i −0.283288 0.959035i \(-0.591425\pi\)
0.972193 0.234182i \(-0.0752413\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 1.00000 0.115470
\(76\) −2.88600 + 3.26665i −0.331047 + 0.374710i
\(77\) 4.77200 0.543820
\(78\) 1.88600 3.26665i 0.213548 0.369875i
\(79\) 7.65800 13.2640i 0.861593 1.49232i −0.00879850 0.999961i \(-0.502801\pi\)
0.870391 0.492361i \(-0.163866\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.38600 + 4.13267i 0.263490 + 0.456378i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 0.113999 + 0.197452i 0.0122928 + 0.0212918i
\(87\) −6.00000 −0.643268
\(88\) 4.77200 0.508697
\(89\) 4.15800 + 7.20187i 0.440747 + 0.763397i 0.997745 0.0671171i \(-0.0213801\pi\)
−0.556998 + 0.830514i \(0.688047\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) 1.88600 + 3.26665i 0.197707 + 0.342438i
\(92\) −2.38600 + 4.13267i −0.248758 + 0.430861i
\(93\) 2.88600 4.99870i 0.299264 0.518341i
\(94\) 0 0
\(95\) 4.27200 + 0.866025i 0.438298 + 0.0888523i
\(96\) −1.00000 −0.102062
\(97\) 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i \(-0.663839\pi\)
0.999961 0.00888289i \(-0.00282755\pi\)
\(98\) −3.00000 + 5.19615i −0.303046 + 0.524891i
\(99\) 2.38600 + 4.13267i 0.239802 + 0.415349i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 1.88600 + 3.26665i 0.184938 + 0.320321i
\(105\) 0.500000 + 0.866025i 0.0487950 + 0.0845154i
\(106\) −1.22800 −0.119274
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 3.77200 6.53330i 0.361292 0.625777i −0.626882 0.779115i \(-0.715669\pi\)
0.988174 + 0.153338i \(0.0490023\pi\)
\(110\) −2.38600 4.13267i −0.227496 0.394035i
\(111\) 0.500000 0.866025i 0.0474579 0.0821995i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 3.54400 0.333392 0.166696 0.986008i \(-0.446690\pi\)
0.166696 + 0.986008i \(0.446690\pi\)
\(114\) 2.88600 3.26665i 0.270299 0.305950i
\(115\) 4.77200 0.444991
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) −1.88600 + 3.26665i −0.174361 + 0.302002i
\(118\) 1.77200 + 3.06920i 0.163126 + 0.282543i
\(119\) 0 0
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 11.7720 1.07018
\(122\) 5.77200 0.522572
\(123\) −2.38600 4.13267i −0.215138 0.372631i
\(124\) 2.88600 + 4.99870i 0.259171 + 0.448897i
\(125\) 1.00000 0.0894427
\(126\) 1.00000 0.0890871
\(127\) −8.15800 14.1301i −0.723906 1.25384i −0.959423 0.281971i \(-0.909012\pi\)
0.235517 0.971870i \(-0.424322\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −0.113999 0.197452i −0.0100371 0.0173847i
\(130\) 1.88600 3.26665i 0.165413 0.286504i
\(131\) −7.15800 + 12.3980i −0.625398 + 1.08322i 0.363066 + 0.931763i \(0.381730\pi\)
−0.988464 + 0.151457i \(0.951603\pi\)
\(132\) −4.77200 −0.415349
\(133\) 1.38600 + 4.13267i 0.120182 + 0.358348i
\(134\) 2.22800 0.192470
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) −7.77200 13.4615i −0.664007 1.15009i −0.979554 0.201184i \(-0.935521\pi\)
0.315547 0.948910i \(-0.397812\pi\)
\(138\) 2.38600 4.13267i 0.203110 0.351797i
\(139\) 1.11400 + 1.92950i 0.0944882 + 0.163658i 0.909395 0.415934i \(-0.136545\pi\)
−0.814907 + 0.579592i \(0.803212\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) 4.77200 + 8.26535i 0.400458 + 0.693613i
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −5.88600 10.1949i −0.487129 0.843732i
\(147\) 3.00000 5.19615i 0.247436 0.428571i
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) −1.77200 + 3.06920i −0.145168 + 0.251438i −0.929436 0.368984i \(-0.879706\pi\)
0.784268 + 0.620423i \(0.213039\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.38600 + 4.13267i 0.112420 + 0.335204i
\(153\) 0 0
\(154\) 2.38600 4.13267i 0.192269 0.333020i
\(155\) 2.88600 4.99870i 0.231809 0.401505i
\(156\) −1.88600 3.26665i −0.151001 0.261541i
\(157\) −10.2720 + 17.7916i −0.819795 + 1.41993i 0.0860381 + 0.996292i \(0.472579\pi\)
−0.905833 + 0.423635i \(0.860754\pi\)
\(158\) −7.65800 13.2640i −0.609238 1.05523i
\(159\) 1.22800 0.0973866
\(160\) −1.00000 −0.0790569
\(161\) 2.38600 + 4.13267i 0.188043 + 0.325700i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) 7.31601 0.573034 0.286517 0.958075i \(-0.407503\pi\)
0.286517 + 0.958075i \(0.407503\pi\)
\(164\) 4.77200 0.372631
\(165\) 2.38600 + 4.13267i 0.185750 + 0.321728i
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −7.15800 12.3980i −0.553903 0.959388i −0.997988 0.0634033i \(-0.979805\pi\)
0.444085 0.895985i \(-0.353529\pi\)
\(168\) −0.500000 + 0.866025i −0.0385758 + 0.0668153i
\(169\) −0.613999 + 1.06348i −0.0472307 + 0.0818060i
\(170\) 0 0
\(171\) −2.88600 + 3.26665i −0.220698 + 0.249807i
\(172\) 0.227998 0.0173847
\(173\) 7.15800 12.3980i 0.544213 0.942604i −0.454443 0.890776i \(-0.650162\pi\)
0.998656 0.0518286i \(-0.0165049\pi\)
\(174\) −3.00000 + 5.19615i −0.227429 + 0.393919i
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) 2.38600 4.13267i 0.179852 0.311512i
\(177\) −1.77200 3.06920i −0.133192 0.230695i
\(178\) 8.31601 0.623311
\(179\) −26.3160 −1.96695 −0.983475 0.181042i \(-0.942053\pi\)
−0.983475 + 0.181042i \(0.942053\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 8.54400 + 14.7986i 0.635071 + 1.09997i 0.986500 + 0.163760i \(0.0523624\pi\)
−0.351429 + 0.936214i \(0.614304\pi\)
\(182\) 3.77200 0.279599
\(183\) −5.77200 −0.426679
\(184\) 2.38600 + 4.13267i 0.175898 + 0.304665i
\(185\) 0.500000 0.866025i 0.0367607 0.0636715i
\(186\) −2.88600 4.99870i −0.211612 0.366522i
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 2.88600 3.26665i 0.209373 0.236988i
\(191\) −9.54400 −0.690580 −0.345290 0.938496i \(-0.612219\pi\)
−0.345290 + 0.938496i \(0.612219\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 2.88600 4.99870i 0.207739 0.359814i −0.743263 0.668999i \(-0.766723\pi\)
0.951002 + 0.309185i \(0.100056\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) −1.88600 + 3.26665i −0.135059 + 0.233930i
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) 14.3160 1.01997 0.509987 0.860182i \(-0.329650\pi\)
0.509987 + 0.860182i \(0.329650\pi\)
\(198\) 4.77200 0.339131
\(199\) −12.6580 21.9243i −0.897302 1.55417i −0.830929 0.556378i \(-0.812191\pi\)
−0.0663726 0.997795i \(-0.521143\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) −2.22800 −0.157151
\(202\) 6.00000 0.422159
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) −2.38600 4.13267i −0.166646 0.288639i
\(206\) −6.50000 + 11.2583i −0.452876 + 0.784405i
\(207\) −2.38600 + 4.13267i −0.165839 + 0.287241i
\(208\) 3.77200 0.261541
\(209\) 6.61400 + 19.7211i 0.457500 + 1.36414i
\(210\) 1.00000 0.0690066
\(211\) 1.72800 2.99298i 0.118960 0.206045i −0.800396 0.599472i \(-0.795377\pi\)
0.919356 + 0.393427i \(0.128711\pi\)
\(212\) −0.613999 + 1.06348i −0.0421696 + 0.0730399i
\(213\) −4.77200 8.26535i −0.326972 0.566332i
\(214\) 0 0
\(215\) −0.113999 0.197452i −0.00777467 0.0134661i
\(216\) −1.00000 −0.0680414
\(217\) 5.77200 0.391829
\(218\) −3.77200 6.53330i −0.255472 0.442491i
\(219\) 5.88600 + 10.1949i 0.397739 + 0.688904i
\(220\) −4.77200 −0.321728
\(221\) 0 0
\(222\) −0.500000 0.866025i −0.0335578 0.0581238i
\(223\) 12.5000 21.6506i 0.837062 1.44983i −0.0552786 0.998471i \(-0.517605\pi\)
0.892341 0.451363i \(-0.149062\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 1.77200 3.06920i 0.117872 0.204160i
\(227\) −25.0880 −1.66515 −0.832575 0.553913i \(-0.813134\pi\)
−0.832575 + 0.553913i \(0.813134\pi\)
\(228\) −1.38600 4.13267i −0.0917902 0.273693i
\(229\) −18.8600 −1.24630 −0.623152 0.782101i \(-0.714148\pi\)
−0.623152 + 0.782101i \(0.714148\pi\)
\(230\) 2.38600 4.13267i 0.157328 0.272501i
\(231\) −2.38600 + 4.13267i −0.156987 + 0.271910i
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 10.7720 18.6577i 0.705697 1.22230i −0.260742 0.965409i \(-0.583967\pi\)
0.966439 0.256895i \(-0.0826995\pi\)
\(234\) 1.88600 + 3.26665i 0.123292 + 0.213548i
\(235\) 0 0
\(236\) 3.54400 0.230695
\(237\) 7.65800 + 13.2640i 0.497441 + 0.861593i
\(238\) 0 0
\(239\) −3.54400 −0.229243 −0.114621 0.993409i \(-0.536565\pi\)
−0.114621 + 0.993409i \(0.536565\pi\)
\(240\) 1.00000 0.0645497
\(241\) 1.65800 + 2.87175i 0.106801 + 0.184985i 0.914473 0.404648i \(-0.132606\pi\)
−0.807671 + 0.589633i \(0.799272\pi\)
\(242\) 5.88600 10.1949i 0.378366 0.655350i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 2.88600 4.99870i 0.184757 0.320009i
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) −4.77200 −0.304252
\(247\) −10.8860 + 12.3218i −0.692660 + 0.784018i
\(248\) 5.77200 0.366522
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 7.77200 + 13.4615i 0.490564 + 0.849682i 0.999941 0.0108612i \(-0.00345730\pi\)
−0.509377 + 0.860544i \(0.670124\pi\)
\(252\) 0.500000 0.866025i 0.0314970 0.0545545i
\(253\) 11.3860 + 19.7211i 0.715832 + 1.23986i
\(254\) −16.3160 −1.02376
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) −0.227998 −0.0141945
\(259\) 1.00000 0.0621370
\(260\) −1.88600 3.26665i −0.116965 0.202589i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 7.15800 + 12.3980i 0.442223 + 0.765953i
\(263\) −3.61400 + 6.25963i −0.222849 + 0.385985i −0.955672 0.294434i \(-0.904869\pi\)
0.732823 + 0.680419i \(0.238202\pi\)
\(264\) −2.38600 + 4.13267i −0.146848 + 0.254349i
\(265\) 1.22800 0.0754353
\(266\) 4.27200 + 0.866025i 0.261933 + 0.0530994i
\(267\) −8.31601 −0.508931
\(268\) 1.11400 1.92950i 0.0680483 0.117863i
\(269\) 4.22800 7.32311i 0.257786 0.446498i −0.707863 0.706350i \(-0.750341\pi\)
0.965648 + 0.259852i \(0.0836738\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −14.7720 + 25.5859i −0.897335 + 1.55423i −0.0664476 + 0.997790i \(0.521167\pi\)
−0.830888 + 0.556440i \(0.812167\pi\)
\(272\) 0 0
\(273\) −3.77200 −0.228292
\(274\) −15.5440 −0.939048
\(275\) 2.38600 + 4.13267i 0.143881 + 0.249210i
\(276\) −2.38600 4.13267i −0.143620 0.248758i
\(277\) −29.0880 −1.74773 −0.873864 0.486170i \(-0.838394\pi\)
−0.873864 + 0.486170i \(0.838394\pi\)
\(278\) 2.22800 0.133626
\(279\) 2.88600 + 4.99870i 0.172780 + 0.299264i
\(280\) −0.500000 + 0.866025i −0.0298807 + 0.0517549i
\(281\) −9.61400 16.6519i −0.573523 0.993371i −0.996200 0.0870909i \(-0.972243\pi\)
0.422677 0.906280i \(-0.361090\pi\)
\(282\) 0 0
\(283\) −12.3160 + 21.3319i −0.732111 + 1.26805i 0.223869 + 0.974619i \(0.428131\pi\)
−0.955980 + 0.293433i \(0.905202\pi\)
\(284\) 9.54400 0.566332
\(285\) −2.88600 + 3.26665i −0.170952 + 0.193500i
\(286\) 18.0000 1.06436
\(287\) 2.38600 4.13267i 0.140841 0.243944i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −3.00000 + 5.19615i −0.176166 + 0.305129i
\(291\) 5.00000 + 8.66025i 0.293105 + 0.507673i
\(292\) −11.7720 −0.688904
\(293\) −28.7720 −1.68088 −0.840439 0.541906i \(-0.817703\pi\)
−0.840439 + 0.541906i \(0.817703\pi\)
\(294\) −3.00000 5.19615i −0.174964 0.303046i
\(295\) −1.77200 3.06920i −0.103170 0.178696i
\(296\) 1.00000 0.0581238
\(297\) −4.77200 −0.276900
\(298\) 1.77200 + 3.06920i 0.102649 + 0.177794i
\(299\) −9.00000 + 15.5885i −0.520483 + 0.901504i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) 0.113999 0.197452i 0.00657080 0.0113810i
\(302\) 4.00000 6.92820i 0.230174 0.398673i
\(303\) −6.00000 −0.344691
\(304\) 4.27200 + 0.866025i 0.245016 + 0.0496700i
\(305\) −5.77200 −0.330504
\(306\) 0 0
\(307\) 3.22800 5.59106i 0.184232 0.319098i −0.759086 0.650991i \(-0.774354\pi\)
0.943317 + 0.331892i \(0.107687\pi\)
\(308\) −2.38600 4.13267i −0.135955 0.235481i
\(309\) 6.50000 11.2583i 0.369772 0.640464i
\(310\) −2.88600 4.99870i −0.163914 0.283907i
\(311\) 8.45600 0.479496 0.239748 0.970835i \(-0.422935\pi\)
0.239748 + 0.970835i \(0.422935\pi\)
\(312\) −3.77200 −0.213548
\(313\) 9.77200 + 16.9256i 0.552346 + 0.956692i 0.998105 + 0.0615384i \(0.0196007\pi\)
−0.445759 + 0.895153i \(0.647066\pi\)
\(314\) 10.2720 + 17.7916i 0.579683 + 1.00404i
\(315\) −1.00000 −0.0563436
\(316\) −15.3160 −0.861593
\(317\) −14.3860 24.9173i −0.807998 1.39949i −0.914248 0.405155i \(-0.867218\pi\)
0.106250 0.994339i \(-0.466116\pi\)
\(318\) 0.613999 1.06348i 0.0344314 0.0596369i
\(319\) −14.3160 24.7960i −0.801542 1.38831i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 4.77200 0.265933
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −1.88600 + 3.26665i −0.104617 + 0.181201i
\(326\) 3.65800 6.33585i 0.202598 0.350910i
\(327\) 3.77200 + 6.53330i 0.208592 + 0.361292i
\(328\) 2.38600 4.13267i 0.131745 0.228189i
\(329\) 0 0
\(330\) 4.77200 0.262690
\(331\) −9.45600 −0.519749 −0.259874 0.965642i \(-0.583681\pi\)
−0.259874 + 0.965642i \(0.583681\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) −14.3160 −0.783337
\(335\) −2.22800 −0.121729
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 2.34200 4.05646i 0.127577 0.220969i −0.795160 0.606399i \(-0.792613\pi\)
0.922737 + 0.385430i \(0.125947\pi\)
\(338\) 0.613999 + 1.06348i 0.0333971 + 0.0578456i
\(339\) −1.77200 + 3.06920i −0.0962419 + 0.166696i
\(340\) 0 0
\(341\) 27.5440 1.49159
\(342\) 1.38600 + 4.13267i 0.0749463 + 0.223469i
\(343\) 13.0000 0.701934
\(344\) 0.113999 0.197452i 0.00614642 0.0106459i
\(345\) −2.38600 + 4.13267i −0.128458 + 0.222496i
\(346\) −7.15800 12.3980i −0.384817 0.666522i
\(347\) −4.77200 + 8.26535i −0.256174 + 0.443707i −0.965214 0.261462i \(-0.915795\pi\)
0.709039 + 0.705169i \(0.249129\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −17.7720 −0.951313 −0.475657 0.879631i \(-0.657790\pi\)
−0.475657 + 0.879631i \(0.657790\pi\)
\(350\) 1.00000 0.0534522
\(351\) −1.88600 3.26665i −0.100667 0.174361i
\(352\) −2.38600 4.13267i −0.127174 0.220272i
\(353\) 3.54400 0.188628 0.0943141 0.995542i \(-0.469934\pi\)
0.0943141 + 0.995542i \(0.469934\pi\)
\(354\) −3.54400 −0.188362
\(355\) −4.77200 8.26535i −0.253272 0.438679i
\(356\) 4.15800 7.20187i 0.220374 0.381698i
\(357\) 0 0
\(358\) −13.1580 + 22.7903i −0.695422 + 1.20451i
\(359\) 6.54400 11.3345i 0.345379 0.598215i −0.640043 0.768339i \(-0.721084\pi\)
0.985423 + 0.170124i \(0.0544169\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −15.1580 + 11.4558i −0.797790 + 0.602936i
\(362\) 17.0880 0.898126
\(363\) −5.88600 + 10.1949i −0.308935 + 0.535091i
\(364\) 1.88600 3.26665i 0.0988533 0.171219i
\(365\) 5.88600 + 10.1949i 0.308087 + 0.533623i
\(366\) −2.88600 + 4.99870i −0.150854 + 0.261286i
\(367\) 8.88600 + 15.3910i 0.463845 + 0.803404i 0.999149 0.0412561i \(-0.0131360\pi\)
−0.535303 + 0.844660i \(0.679803\pi\)
\(368\) 4.77200 0.248758
\(369\) 4.77200 0.248420
\(370\) −0.500000 0.866025i −0.0259938 0.0450225i
\(371\) 0.613999 + 1.06348i 0.0318772 + 0.0552130i
\(372\) −5.77200 −0.299264
\(373\) −8.77200 −0.454197 −0.227099 0.973872i \(-0.572924\pi\)
−0.227099 + 0.973872i \(0.572924\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 11.3160 19.5999i 0.582804 1.00945i
\(378\) −0.500000 + 0.866025i −0.0257172 + 0.0445435i
\(379\) −17.7720 −0.912886 −0.456443 0.889753i \(-0.650877\pi\)
−0.456443 + 0.889753i \(0.650877\pi\)
\(380\) −1.38600 4.13267i −0.0711003 0.212002i
\(381\) 16.3160 0.835894
\(382\) −4.77200 + 8.26535i −0.244157 + 0.422892i
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −2.38600 + 4.13267i −0.121602 + 0.210621i
\(386\) −2.88600 4.99870i −0.146894 0.254427i
\(387\) 0.227998 0.0115898
\(388\) −10.0000 −0.507673
\(389\) −12.5440 21.7269i −0.636006 1.10160i −0.986301 0.164956i \(-0.947252\pi\)
0.350295 0.936640i \(-0.386081\pi\)
\(390\) 1.88600 + 3.26665i 0.0955014 + 0.165413i
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) −7.15800 12.3980i −0.361073 0.625398i
\(394\) 7.15800 12.3980i 0.360615 0.624603i
\(395\) 7.65800 + 13.2640i 0.385316 + 0.667387i
\(396\) 2.38600 4.13267i 0.119901 0.207675i
\(397\) 16.0440 27.7890i 0.805225 1.39469i −0.110913 0.993830i \(-0.535378\pi\)
0.916139 0.400861i \(-0.131289\pi\)
\(398\) −25.3160 −1.26898
\(399\) −4.27200 0.866025i −0.213868 0.0433555i
\(400\) 1.00000 0.0500000
\(401\) 12.5440 21.7269i 0.626418 1.08499i −0.361847 0.932237i \(-0.617854\pi\)
0.988265 0.152750i \(-0.0488129\pi\)
\(402\) −1.11400 + 1.92950i −0.0555612 + 0.0962349i
\(403\) 10.8860 + 18.8551i 0.542270 + 0.939240i
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −6.00000 −0.297775
\(407\) 4.77200 0.236539
\(408\) 0 0
\(409\) −14.7020 25.4646i −0.726967 1.25914i −0.958159 0.286236i \(-0.907596\pi\)
0.231192 0.972908i \(-0.425738\pi\)
\(410\) −4.77200 −0.235672
\(411\) 15.5440 0.766729
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) 1.77200 3.06920i 0.0871945 0.151025i
\(414\) 2.38600 + 4.13267i 0.117266 + 0.203110i
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) 1.88600 3.26665i 0.0924688 0.160161i
\(417\) −2.22800 −0.109106
\(418\) 20.3860 + 4.13267i 0.997112 + 0.202136i
\(419\) 17.8600 0.872519 0.436259 0.899821i \(-0.356303\pi\)
0.436259 + 0.899821i \(0.356303\pi\)
\(420\) 0.500000 0.866025i 0.0243975 0.0422577i
\(421\) 0.227998 0.394904i 0.0111119 0.0192465i −0.860416 0.509592i \(-0.829796\pi\)
0.871528 + 0.490346i \(0.163130\pi\)
\(422\) −1.72800 2.99298i −0.0841176 0.145696i
\(423\) 0 0
\(424\) 0.613999 + 1.06348i 0.0298184 + 0.0516470i
\(425\) 0 0
\(426\) −9.54400 −0.462408
\(427\) −2.88600 4.99870i −0.139663 0.241904i
\(428\) 0 0
\(429\) −18.0000 −0.869048
\(430\) −0.227998 −0.0109950
\(431\) −15.5440 26.9230i −0.748728 1.29684i −0.948432 0.316979i \(-0.897331\pi\)
0.199704 0.979856i \(-0.436002\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 7.65800 + 13.2640i 0.368020 + 0.637430i 0.989256 0.146194i \(-0.0467024\pi\)
−0.621236 + 0.783624i \(0.713369\pi\)
\(434\) 2.88600 4.99870i 0.138532 0.239945i
\(435\) 3.00000 5.19615i 0.143839 0.249136i
\(436\) −7.54400 −0.361292
\(437\) −13.7720 + 15.5885i −0.658804 + 0.745697i
\(438\) 11.7720 0.562488
\(439\) 10.6580 18.4602i 0.508679 0.881057i −0.491271 0.871007i \(-0.663467\pi\)
0.999949 0.0100505i \(-0.00319922\pi\)
\(440\) −2.38600 + 4.13267i −0.113748 + 0.197018i
\(441\) 3.00000 + 5.19615i 0.142857 + 0.247436i
\(442\) 0 0
\(443\) −2.45600 4.25391i −0.116688 0.202109i 0.801765 0.597639i \(-0.203894\pi\)
−0.918453 + 0.395530i \(0.870561\pi\)
\(444\) −1.00000 −0.0474579
\(445\) −8.31601 −0.394216
\(446\) −12.5000 21.6506i −0.591892 1.02519i
\(447\) −1.77200 3.06920i −0.0838128 0.145168i
\(448\) −1.00000 −0.0472456
\(449\) 10.7720 0.508362 0.254181 0.967157i \(-0.418194\pi\)
0.254181 + 0.967157i \(0.418194\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 11.3860 19.7211i 0.536146 0.928632i
\(452\) −1.77200 3.06920i −0.0833480 0.144363i
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) −12.5440 + 21.7269i −0.588719 + 1.01969i
\(455\) −3.77200 −0.176834
\(456\) −4.27200 0.866025i −0.200055 0.0405554i
\(457\) 16.8600 0.788678 0.394339 0.918965i \(-0.370974\pi\)
0.394339 + 0.918965i \(0.370974\pi\)
\(458\) −9.43000 + 16.3332i −0.440635 + 0.763203i
\(459\) 0 0
\(460\) −2.38600 4.13267i −0.111248 0.192687i
\(461\) 8.31601 14.4037i 0.387315 0.670849i −0.604772 0.796398i \(-0.706736\pi\)
0.992087 + 0.125549i \(0.0400693\pi\)
\(462\) 2.38600 + 4.13267i 0.111007 + 0.192269i
\(463\) −23.6320 −1.09827 −0.549136 0.835733i \(-0.685043\pi\)
−0.549136 + 0.835733i \(0.685043\pi\)
\(464\) −6.00000 −0.278543
\(465\) 2.88600 + 4.99870i 0.133835 + 0.231809i
\(466\) −10.7720 18.6577i −0.499003 0.864299i
\(467\) 25.0880 1.16093 0.580467 0.814284i \(-0.302870\pi\)
0.580467 + 0.814284i \(0.302870\pi\)
\(468\) 3.77200 0.174361
\(469\) −1.11400 1.92950i −0.0514397 0.0890962i
\(470\) 0 0
\(471\) −10.2720 17.7916i −0.473309 0.819795i
\(472\) 1.77200 3.06920i 0.0815630 0.141271i
\(473\) 0.544004 0.942242i 0.0250133 0.0433243i
\(474\) 15.3160 0.703487
\(475\) −2.88600 + 3.26665i −0.132419 + 0.149884i
\(476\) 0 0
\(477\) −0.613999 + 1.06348i −0.0281131 + 0.0486933i
\(478\) −1.77200 + 3.06920i −0.0810495 + 0.140382i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 1.88600 + 3.26665i 0.0859942 + 0.148946i
\(482\) 3.31601 0.151040
\(483\) −4.77200 −0.217134
\(484\) −5.88600 10.1949i −0.267545 0.463402i
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) −1.00000 −0.0453609
\(487\) 16.3160 0.739349 0.369674 0.929161i \(-0.379469\pi\)
0.369674 + 0.929161i \(0.379469\pi\)
\(488\) −2.88600 4.99870i −0.130643 0.226281i
\(489\) −3.65800 + 6.33585i −0.165421 + 0.286517i
\(490\) −3.00000 5.19615i −0.135526 0.234738i
\(491\) −16.1580 + 27.9865i −0.729200 + 1.26301i 0.228021 + 0.973656i \(0.426774\pi\)
−0.957222 + 0.289356i \(0.906559\pi\)
\(492\) −2.38600 + 4.13267i −0.107569 + 0.186315i
\(493\) 0 0
\(494\) 5.22800 + 15.5885i 0.235219 + 0.701358i
\(495\) −4.77200 −0.214486
\(496\) 2.88600 4.99870i 0.129585 0.224448i
\(497\) 4.77200 8.26535i 0.214054 0.370752i
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) 14.8160 25.6621i 0.663256 1.14879i −0.316500 0.948593i \(-0.602508\pi\)
0.979755 0.200200i \(-0.0641591\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 14.3160 0.639592
\(502\) 15.5440 0.693763
\(503\) 4.15800 + 7.20187i 0.185396 + 0.321116i 0.943710 0.330774i \(-0.107310\pi\)
−0.758314 + 0.651890i \(0.773976\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) −6.00000 −0.266996
\(506\) 22.7720 1.01234
\(507\) −0.613999 1.06348i −0.0272687 0.0472307i
\(508\) −8.15800 + 14.1301i −0.361953 + 0.626921i
\(509\) 8.31601 + 14.4037i 0.368600 + 0.638435i 0.989347 0.145577i \(-0.0465037\pi\)
−0.620747 + 0.784011i \(0.713170\pi\)
\(510\) 0 0
\(511\) −5.88600 + 10.1949i −0.260381 + 0.450994i
\(512\) −1.00000 −0.0441942
\(513\) −1.38600 4.13267i −0.0611934 0.182462i
\(514\) 30.0000 1.32324
\(515\) 6.50000 11.2583i 0.286424 0.496101i
\(516\) −0.113999 + 0.197452i −0.00501853 + 0.00869235i
\(517\) 0 0
\(518\) 0.500000 0.866025i 0.0219687 0.0380510i
\(519\) 7.15800 + 12.3980i 0.314201 + 0.544213i
\(520\) −3.77200 −0.165413
\(521\) −33.5440 −1.46959 −0.734795 0.678290i \(-0.762722\pi\)
−0.734795 + 0.678290i \(0.762722\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) 1.65800 + 2.87175i 0.0724994 + 0.125573i 0.899996 0.435898i \(-0.143569\pi\)
−0.827497 + 0.561471i \(0.810236\pi\)
\(524\) 14.3160 0.625398
\(525\) −1.00000 −0.0436436
\(526\) 3.61400 + 6.25963i 0.157578 + 0.272933i
\(527\) 0 0
\(528\) 2.38600 + 4.13267i 0.103837 + 0.179852i
\(529\) 0.113999 0.197452i 0.00495648 0.00858488i
\(530\) 0.613999 1.06348i 0.0266704 0.0461945i
\(531\) 3.54400 0.153797
\(532\) 2.88600 3.26665i 0.125124 0.141627i
\(533\) 18.0000 0.779667
\(534\) −4.15800 + 7.20187i −0.179934 + 0.311655i
\(535\) 0 0
\(536\) −1.11400 1.92950i −0.0481174 0.0833418i
\(537\) 13.1580 22.7903i 0.567810 0.983475i
\(538\) −4.22800 7.32311i −0.182282 0.315722i
\(539\) 28.6320 1.23327
\(540\) 1.00000 0.0430331
\(541\) 4.65800 + 8.06790i 0.200263 + 0.346866i 0.948613 0.316438i \(-0.102487\pi\)
−0.748350 + 0.663304i \(0.769154\pi\)
\(542\) 14.7720 + 25.5859i 0.634512 + 1.09901i
\(543\) −17.0880 −0.733317
\(544\) 0 0
\(545\) 3.77200 + 6.53330i 0.161575 + 0.279856i
\(546\) −1.88600 + 3.26665i −0.0807134 + 0.139800i
\(547\) 15.4300 + 26.7256i 0.659739 + 1.14270i 0.980683 + 0.195604i \(0.0626667\pi\)
−0.320944 + 0.947098i \(0.604000\pi\)
\(548\) −7.77200 + 13.4615i −0.332003 + 0.575047i
\(549\) 2.88600 4.99870i 0.123172 0.213339i
\(550\) 4.77200 0.203479
\(551\) 17.3160 19.5999i 0.737687 0.834984i
\(552\) −4.77200 −0.203110
\(553\) −7.65800 + 13.2640i −0.325651 + 0.564045i
\(554\) −14.5440 + 25.1910i −0.617916 + 1.07026i
\(555\) 0.500000 + 0.866025i 0.0212238 + 0.0367607i
\(556\) 1.11400 1.92950i 0.0472441 0.0818292i
\(557\) −5.38600 9.32883i −0.228212 0.395275i 0.729066 0.684443i \(-0.239955\pi\)
−0.957278 + 0.289168i \(0.906621\pi\)
\(558\) 5.77200 0.244348
\(559\) 0.860009 0.0363745
\(560\) 0.500000 + 0.866025i 0.0211289 + 0.0365963i
\(561\) 0 0
\(562\) −19.2280 −0.811084
\(563\) 20.4560 0.862117 0.431059 0.902324i \(-0.358140\pi\)
0.431059 + 0.902324i \(0.358140\pi\)
\(564\) 0 0
\(565\) −1.77200 + 3.06920i −0.0745487 + 0.129122i
\(566\) 12.3160 + 21.3319i 0.517680 + 0.896649i
\(567\) 0.500000 0.866025i 0.0209980 0.0363696i
\(568\) 4.77200 8.26535i 0.200229 0.346806i
\(569\) 10.7720 0.451586 0.225793 0.974175i \(-0.427503\pi\)
0.225793 + 0.974175i \(0.427503\pi\)
\(570\) 1.38600 + 4.13267i 0.0580532 + 0.173099i
\(571\) 40.8600 1.70994 0.854969 0.518679i \(-0.173576\pi\)
0.854969 + 0.518679i \(0.173576\pi\)
\(572\) 9.00000 15.5885i 0.376309 0.651786i
\(573\) 4.77200 8.26535i 0.199353 0.345290i
\(574\) −2.38600 4.13267i −0.0995898 0.172495i
\(575\) −2.38600 + 4.13267i −0.0995031 + 0.172344i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −7.54400 −0.314061 −0.157030 0.987594i \(-0.550192\pi\)
−0.157030 + 0.987594i \(0.550192\pi\)
\(578\) 17.0000 0.707107
\(579\) 2.88600 + 4.99870i 0.119938 + 0.207739i
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) −6.00000 −0.248922
\(582\) 10.0000 0.414513
\(583\) 2.93000 + 5.07492i 0.121348 + 0.210182i
\(584\) −5.88600 + 10.1949i −0.243564 + 0.421866i
\(585\) −1.88600 3.26665i −0.0779765 0.135059i
\(586\) −14.3860 + 24.9173i −0.594280 + 1.02932i
\(587\) 4.22800 7.32311i 0.174508 0.302257i −0.765483 0.643456i \(-0.777500\pi\)
0.939991 + 0.341199i \(0.110833\pi\)
\(588\) −6.00000 −0.247436
\(589\) 8.00000 + 23.8538i 0.329634 + 0.982879i
\(590\) −3.54400 −0.145904
\(591\) −7.15800 + 12.3980i −0.294441 + 0.509987i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) 4.77200 + 8.26535i 0.195963 + 0.339417i 0.947216 0.320597i \(-0.103884\pi\)
−0.751253 + 0.660014i \(0.770550\pi\)
\(594\) −2.38600 + 4.13267i −0.0978988 + 0.169566i
\(595\) 0 0
\(596\) 3.54400 0.145168
\(597\) 25.3160 1.03612
\(598\) 9.00000 + 15.5885i 0.368037 + 0.637459i
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 15.6320 0.637643 0.318822 0.947815i \(-0.396713\pi\)
0.318822 + 0.947815i \(0.396713\pi\)
\(602\) −0.113999 0.197452i −0.00464625 0.00804755i
\(603\) 1.11400 1.92950i 0.0453655 0.0785754i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) −5.88600 + 10.1949i −0.239300 + 0.414480i
\(606\) −3.00000 + 5.19615i −0.121867 + 0.211079i
\(607\) −5.91199 −0.239960 −0.119980 0.992776i \(-0.538283\pi\)
−0.119980 + 0.992776i \(0.538283\pi\)
\(608\) 2.88600 3.26665i 0.117043 0.132480i
\(609\) 6.00000 0.243132
\(610\) −2.88600 + 4.99870i −0.116851 + 0.202391i
\(611\) 0 0
\(612\) 0 0
\(613\) −3.93000 + 6.80697i −0.158731 + 0.274931i −0.934411 0.356195i \(-0.884074\pi\)
0.775680 + 0.631126i \(0.217407\pi\)
\(614\) −3.22800 5.59106i −0.130271 0.225637i
\(615\) 4.77200 0.192426
\(616\) −4.77200 −0.192269
\(617\) −15.5440 26.9230i −0.625778 1.08388i −0.988390 0.151939i \(-0.951448\pi\)
0.362612 0.931940i \(-0.381885\pi\)
\(618\) −6.50000 11.2583i −0.261468 0.452876i
\(619\) 37.1760 1.49423 0.747115 0.664695i \(-0.231438\pi\)
0.747115 + 0.664695i \(0.231438\pi\)
\(620\) −5.77200 −0.231809
\(621\) −2.38600 4.13267i −0.0957469 0.165839i
\(622\) 4.22800 7.32311i 0.169527 0.293630i
\(623\) −4.15800 7.20187i −0.166587 0.288537i
\(624\) −1.88600 + 3.26665i −0.0755005 + 0.130771i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 19.5440 0.781135
\(627\) −20.3860 4.13267i −0.814138 0.165043i
\(628\) 20.5440 0.819795
\(629\) 0 0
\(630\) −0.500000 + 0.866025i −0.0199205 + 0.0345033i
\(631\) 0.569995 + 0.987261i 0.0226912 + 0.0393022i 0.877148 0.480220i \(-0.159443\pi\)
−0.854457 + 0.519522i \(0.826110\pi\)
\(632\) −7.65800 + 13.2640i −0.304619 + 0.527616i
\(633\) 1.72800 + 2.99298i 0.0686818 + 0.118960i
\(634\) −28.7720 −1.14268
\(635\) 16.3160 0.647481
\(636\) −0.613999 1.06348i −0.0243466 0.0421696i
\(637\) 11.3160 + 19.5999i 0.448356 + 0.776576i
\(638\) −28.6320 −1.13355
\(639\) 9.54400 0.377555
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −1.22800 + 2.12696i −0.0485030 + 0.0840097i −0.889258 0.457407i \(-0.848778\pi\)
0.840755 + 0.541416i \(0.182112\pi\)
\(642\) 0 0
\(643\) −12.6580 + 21.9243i −0.499183 + 0.864610i −1.00000 0.000943247i \(-0.999700\pi\)
0.500817 + 0.865553i \(0.333033\pi\)
\(644\) 2.38600 4.13267i 0.0940216 0.162850i
\(645\) 0.227998 0.00897742
\(646\) 0 0
\(647\) −38.3160 −1.50636 −0.753179 0.657816i \(-0.771481\pi\)
−0.753179 + 0.657816i \(0.771481\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 8.45600 14.6462i 0.331927 0.574914i
\(650\) 1.88600 + 3.26665i 0.0739750 + 0.128129i
\(651\) −2.88600 + 4.99870i −0.113111 + 0.195915i
\(652\) −3.65800 6.33585i −0.143258 0.248131i
\(653\) 3.68399 0.144166 0.0720829 0.997399i \(-0.477035\pi\)
0.0720829 + 0.997399i \(0.477035\pi\)
\(654\) 7.54400 0.294994
\(655\) −7.15800 12.3980i −0.279686 0.484431i
\(656\) −2.38600 4.13267i −0.0931577 0.161354i
\(657\) −11.7720 −0.459270
\(658\) 0 0
\(659\) −19.1580 33.1826i −0.746290 1.29261i −0.949590 0.313495i \(-0.898500\pi\)
0.203300 0.979117i \(-0.434833\pi\)
\(660\) 2.38600 4.13267i 0.0928750 0.160864i
\(661\) −3.31601 5.74349i −0.128978 0.223396i 0.794303 0.607522i \(-0.207836\pi\)
−0.923281 + 0.384126i \(0.874503\pi\)
\(662\) −4.72800 + 8.18913i −0.183759 + 0.318280i
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −4.27200 0.866025i −0.165661 0.0335830i
\(666\) 1.00000 0.0387492
\(667\) 14.3160 24.7960i 0.554318 0.960107i
\(668\) −7.15800 + 12.3980i −0.276951 + 0.479694i
\(669\) 12.5000 + 21.6506i 0.483278 + 0.837062i
\(670\) −1.11400 + 1.92950i −0.0430375 + 0.0745432i
\(671\) −13.7720 23.8538i −0.531662 0.920866i
\(672\) 1.00000 0.0385758
\(673\) −29.7720 −1.14763 −0.573813 0.818986i \(-0.694536\pi\)
−0.573813 + 0.818986i \(0.694536\pi\)
\(674\) −2.34200 4.05646i −0.0902104 0.156249i
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 1.22800 0.0472307
\(677\) −8.31601 −0.319610 −0.159805 0.987149i \(-0.551087\pi\)
−0.159805 + 0.987149i \(0.551087\pi\)
\(678\) 1.77200 + 3.06920i 0.0680533 + 0.117872i
\(679\) −5.00000 + 8.66025i −0.191882 + 0.332350i
\(680\) 0 0
\(681\) 12.5440 21.7269i 0.480687 0.832575i
\(682\) 13.7720 23.8538i 0.527357 0.913409i
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 4.27200 + 0.866025i 0.163344 + 0.0331133i
\(685\) 15.5440 0.593906
\(686\) 6.50000 11.2583i 0.248171 0.429845i
\(687\) 9.43000 16.3332i 0.359777 0.623152i
\(688\) −0.113999 0.197452i −0.00434617 0.00752779i
\(689\) −2.31601 + 4.01144i −0.0882328 + 0.152824i
\(690\) 2.38600 + 4.13267i 0.0908335 + 0.157328i
\(691\) 49.8600 1.89676 0.948382 0.317130i \(-0.102719\pi\)
0.948382 + 0.317130i \(0.102719\pi\)
\(692\) −14.3160 −0.544213
\(693\) −2.38600 4.13267i −0.0906367 0.156987i
\(694\) 4.77200 + 8.26535i 0.181143 + 0.313748i
\(695\) −2.22800 −0.0845128
\(696\) 6.00000 0.227429
\(697\) 0 0
\(698\) −8.88600 + 15.3910i −0.336340 + 0.582558i
\(699\) 10.7720 + 18.6577i 0.407435 + 0.705697i
\(700\) 0.500000 0.866025i 0.0188982 0.0327327i
\(701\) 8.31601 14.4037i 0.314091 0.544022i −0.665153 0.746707i \(-0.731634\pi\)
0.979244 + 0.202685i \(0.0649669\pi\)
\(702\) −3.77200 −0.142365
\(703\) 1.38600 + 4.13267i 0.0522740 + 0.155867i
\(704\) −4.77200 −0.179852
\(705\) 0 0
\(706\) 1.77200 3.06920i 0.0666902 0.115511i
\(707\) −3.00000 5.19615i −0.112827 0.195421i
\(708\) −1.77200 + 3.06920i −0.0665959 + 0.115347i
\(709\) 13.1140 + 22.7141i 0.492507 + 0.853046i 0.999963 0.00863116i \(-0.00274742\pi\)
−0.507456 + 0.861678i \(0.669414\pi\)
\(710\) −9.54400 −0.358180
\(711\) −15.3160 −0.574395
\(712\) −4.15800 7.20187i −0.155828 0.269902i
\(713\) 13.7720 + 23.8538i 0.515766 + 0.893332i
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 13.1580 + 22.7903i 0.491738 + 0.851715i
\(717\) 1.77200 3.06920i 0.0661766 0.114621i
\(718\) −6.54400 11.3345i −0.244220 0.423002i
\(719\) 11.3160 19.5999i 0.422016 0.730953i −0.574121 0.818771i \(-0.694656\pi\)
0.996137 + 0.0878178i \(0.0279893\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 13.0000 0.484145
\(722\) 2.34200 + 18.8551i 0.0871601 + 0.701714i
\(723\) −3.31601 −0.123324
\(724\) 8.54400 14.7986i 0.317535 0.549987i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 5.88600 + 10.1949i 0.218450 + 0.378366i
\(727\) 8.20201 14.2063i 0.304196 0.526882i −0.672886 0.739746i \(-0.734946\pi\)
0.977082 + 0.212864i \(0.0682790\pi\)
\(728\) −1.88600 3.26665i −0.0698998 0.121070i
\(729\) 1.00000 0.0370370
\(730\) 11.7720 0.435701
\(731\) 0 0
\(732\) 2.88600 + 4.99870i 0.106670 + 0.184757i
\(733\) −37.4040 −1.38155 −0.690774 0.723070i \(-0.742730\pi\)
−0.690774 + 0.723070i \(0.742730\pi\)
\(734\) 17.7720 0.655977
\(735\) 3.00000 + 5.19615i 0.110657 + 0.191663i
\(736\) 2.38600 4.13267i 0.0879492 0.152332i
\(737\) −5.31601 9.20759i −0.195818 0.339166i
\(738\) 2.38600 4.13267i 0.0878299 0.152126i
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) −1.00000 −0.0367607
\(741\) −5.22800 15.5885i −0.192055 0.572656i
\(742\) 1.22800 0.0450812
\(743\) −14.3860 + 24.9173i −0.527771 + 0.914127i 0.471705 + 0.881757i \(0.343639\pi\)
−0.999476 + 0.0323700i \(0.989695\pi\)
\(744\) −2.88600 + 4.99870i −0.105806 + 0.183261i
\(745\) −1.77200 3.06920i −0.0649211 0.112447i
\(746\) −4.38600 + 7.59678i −0.160583 + 0.278138i
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −21.1140 36.5705i −0.770461 1.33448i −0.937311 0.348495i \(-0.886693\pi\)
0.166850 0.985982i \(-0.446640\pi\)
\(752\) 0 0
\(753\) −15.5440 −0.566455
\(754\) −11.3160 19.5999i −0.412105 0.713786i
\(755\) −4.00000 + 6.92820i −0.145575 + 0.252143i
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −10.8160 + 18.7339i −0.393114 + 0.680894i −0.992859 0.119298i \(-0.961936\pi\)
0.599744 + 0.800192i \(0.295269\pi\)
\(758\) −8.88600 + 15.3910i −0.322754 + 0.559026i
\(759\) −22.7720 −0.826571
\(760\) −4.27200 0.866025i −0.154962 0.0314140i
\(761\) −54.9480 −1.99186 −0.995932 0.0901077i \(-0.971279\pi\)
−0.995932 + 0.0901077i \(0.971279\pi\)
\(762\) 8.15800 14.1301i 0.295533 0.511879i
\(763\) −3.77200 + 6.53330i −0.136556 + 0.236521i
\(764\) 4.77200 + 8.26535i 0.172645 + 0.299030i
\(765\) 0 0
\(766\) −12.0000 20.7846i −0.433578 0.750978i
\(767\) 13.3680 0.482690
\(768\) 1.00000 0.0360844
\(769\) 3.43000 + 5.94094i 0.123689 + 0.214236i 0.921220 0.389043i \(-0.127194\pi\)
−0.797531 + 0.603278i \(0.793861\pi\)
\(770\) 2.38600 + 4.13267i 0.0859855 + 0.148931i
\(771\) −30.0000 −1.08042
\(772\) −5.77200 −0.207739
\(773\) −2.38600 4.13267i −0.0858185 0.148642i 0.819921 0.572476i \(-0.194017\pi\)
−0.905740 + 0.423834i \(0.860684\pi\)
\(774\) 0.113999 0.197452i 0.00409761 0.00709727i
\(775\) 2.88600 + 4.99870i 0.103668 + 0.179559i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) −0.500000 + 0.866025i −0.0179374 + 0.0310685i
\(778\) −25.0880 −0.899449
\(779\) 20.3860 + 4.13267i 0.730404 + 0.148068i
\(780\) 3.77200 0.135059