Properties

Label 2646.2.h.o.667.3
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.3
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.o.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.58836 q^{5} +1.00000 q^{8} +(-0.794182 - 1.37556i) q^{10} +1.58836 q^{11} +(-2.40545 - 4.16635i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.69963 - 4.67589i) q^{17} +(3.54944 - 6.14781i) q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} -0.300372 q^{23} -2.47710 q^{25} +(-2.40545 + 4.16635i) q^{26} +(-4.13781 + 7.16689i) q^{29} +(-1.35600 + 2.34867i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69963 + 4.67589i) q^{34} +(0.500000 - 0.866025i) q^{37} -7.09888 q^{38} +1.58836 q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(-0.794182 + 1.37556i) q^{44} +(0.150186 + 0.260130i) q^{46} +(-1.33310 - 2.30900i) q^{47} +(1.23855 + 2.14523i) q^{50} +4.81089 q^{52} +(-2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +8.27561 q^{58} +(-3.23855 + 5.60933i) q^{59} +(-2.23855 - 3.87728i) q^{61} +2.71201 q^{62} +1.00000 q^{64} +(-3.82072 - 6.61769i) q^{65} +(5.02654 - 8.70623i) q^{67} +5.39926 q^{68} -12.7207 q^{71} +(-8.02654 - 13.9024i) q^{73} -1.00000 q^{74} +(3.54944 + 6.14781i) q^{76} +(-4.19344 - 7.26325i) q^{79} +(-0.794182 - 1.37556i) q^{80} +(2.93818 - 5.08907i) q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +1.66621 q^{86} +1.58836 q^{88} +(1.60507 - 2.78007i) q^{89} +(0.150186 - 0.260130i) q^{92} +(-1.33310 + 2.30900i) q^{94} +(5.63781 - 9.76497i) q^{95} +(-0.712008 + 1.23323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + O(q^{10}) \) \( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.58836 0.710338 0.355169 0.934802i \(-0.384423\pi\)
0.355169 + 0.934802i \(0.384423\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.794182 1.37556i −0.251142 0.434991i
\(11\) 1.58836 0.478910 0.239455 0.970907i \(-0.423031\pi\)
0.239455 + 0.970907i \(0.423031\pi\)
\(12\) 0 0
\(13\) −2.40545 4.16635i −0.667151 1.15554i −0.978697 0.205308i \(-0.934180\pi\)
0.311547 0.950231i \(-0.399153\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.69963 4.67589i −0.654756 1.13407i −0.981955 0.189115i \(-0.939438\pi\)
0.327199 0.944955i \(-0.393895\pi\)
\(18\) 0 0
\(19\) 3.54944 6.14781i 0.814298 1.41041i −0.0955331 0.995426i \(-0.530456\pi\)
0.909831 0.414979i \(-0.136211\pi\)
\(20\) −0.794182 + 1.37556i −0.177584 + 0.307585i
\(21\) 0 0
\(22\) −0.794182 1.37556i −0.169320 0.293271i
\(23\) −0.300372 −0.0626319 −0.0313159 0.999510i \(-0.509970\pi\)
−0.0313159 + 0.999510i \(0.509970\pi\)
\(24\) 0 0
\(25\) −2.47710 −0.495420
\(26\) −2.40545 + 4.16635i −0.471747 + 0.817089i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.13781 + 7.16689i −0.768371 + 1.33086i 0.170074 + 0.985431i \(0.445599\pi\)
−0.938446 + 0.345427i \(0.887734\pi\)
\(30\) 0 0
\(31\) −1.35600 + 2.34867i −0.243545 + 0.421833i −0.961722 0.274028i \(-0.911644\pi\)
0.718176 + 0.695861i \(0.244977\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.69963 + 4.67589i −0.462982 + 0.801909i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) −7.09888 −1.15159
\(39\) 0 0
\(40\) 1.58836 0.251142
\(41\) 2.93818 + 5.08907i 0.458866 + 0.794780i 0.998901 0.0468628i \(-0.0149223\pi\)
−0.540035 + 0.841643i \(0.681589\pi\)
\(42\) 0 0
\(43\) −0.833104 + 1.44298i −0.127047 + 0.220052i −0.922531 0.385922i \(-0.873883\pi\)
0.795484 + 0.605974i \(0.207217\pi\)
\(44\) −0.794182 + 1.37556i −0.119727 + 0.207374i
\(45\) 0 0
\(46\) 0.150186 + 0.260130i 0.0221437 + 0.0383540i
\(47\) −1.33310 2.30900i −0.194453 0.336803i 0.752268 0.658857i \(-0.228960\pi\)
−0.946721 + 0.322055i \(0.895627\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.23855 + 2.14523i 0.175157 + 0.303382i
\(51\) 0 0
\(52\) 4.81089 0.667151
\(53\) −2.44437 4.23377i −0.335760 0.581553i 0.647871 0.761750i \(-0.275660\pi\)
−0.983630 + 0.180197i \(0.942326\pi\)
\(54\) 0 0
\(55\) 2.52290 0.340188
\(56\) 0 0
\(57\) 0 0
\(58\) 8.27561 1.08664
\(59\) −3.23855 + 5.60933i −0.421623 + 0.730273i −0.996098 0.0882491i \(-0.971873\pi\)
0.574475 + 0.818522i \(0.305206\pi\)
\(60\) 0 0
\(61\) −2.23855 3.87728i −0.286617 0.496435i 0.686383 0.727240i \(-0.259197\pi\)
−0.973000 + 0.230805i \(0.925864\pi\)
\(62\) 2.71201 0.344425
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.82072 6.61769i −0.473902 0.820823i
\(66\) 0 0
\(67\) 5.02654 8.70623i 0.614090 1.06363i −0.376454 0.926435i \(-0.622857\pi\)
0.990543 0.137199i \(-0.0438101\pi\)
\(68\) 5.39926 0.654756
\(69\) 0 0
\(70\) 0 0
\(71\) −12.7207 −1.50967 −0.754833 0.655917i \(-0.772282\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(72\) 0 0
\(73\) −8.02654 13.9024i −0.939436 1.62715i −0.766527 0.642213i \(-0.778017\pi\)
−0.172909 0.984938i \(-0.555317\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 3.54944 + 6.14781i 0.407149 + 0.705203i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.19344 7.26325i −0.471799 0.817179i 0.527681 0.849443i \(-0.323062\pi\)
−0.999479 + 0.0322635i \(0.989728\pi\)
\(80\) −0.794182 1.37556i −0.0887922 0.153793i
\(81\) 0 0
\(82\) 2.93818 5.08907i 0.324467 0.561994i
\(83\) 1.18292 2.04887i 0.129842 0.224893i −0.793773 0.608214i \(-0.791886\pi\)
0.923615 + 0.383321i \(0.125220\pi\)
\(84\) 0 0
\(85\) −4.28799 7.42702i −0.465098 0.805573i
\(86\) 1.66621 0.179672
\(87\) 0 0
\(88\) 1.58836 0.169320
\(89\) 1.60507 2.78007i 0.170138 0.294687i −0.768330 0.640054i \(-0.778912\pi\)
0.938468 + 0.345367i \(0.112245\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.150186 0.260130i 0.0156580 0.0271204i
\(93\) 0 0
\(94\) −1.33310 + 2.30900i −0.137499 + 0.238156i
\(95\) 5.63781 9.76497i 0.578427 1.00186i
\(96\) 0 0
\(97\) −0.712008 + 1.23323i −0.0722934 + 0.125216i −0.899906 0.436084i \(-0.856365\pi\)
0.827613 + 0.561300i \(0.189698\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.23855 2.14523i 0.123855 0.214523i
\(101\) 12.0334 1.19737 0.598685 0.800985i \(-0.295690\pi\)
0.598685 + 0.800985i \(0.295690\pi\)
\(102\) 0 0
\(103\) 6.09888 0.600941 0.300470 0.953791i \(-0.402856\pi\)
0.300470 + 0.953791i \(0.402856\pi\)
\(104\) −2.40545 4.16635i −0.235873 0.408545i
\(105\) 0 0
\(106\) −2.44437 + 4.23377i −0.237418 + 0.411220i
\(107\) 1.54325 2.67299i 0.149192 0.258408i −0.781737 0.623608i \(-0.785666\pi\)
0.930929 + 0.365200i \(0.118999\pi\)
\(108\) 0 0
\(109\) 1.14400 + 1.98146i 0.109575 + 0.189789i 0.915598 0.402095i \(-0.131718\pi\)
−0.806023 + 0.591884i \(0.798384\pi\)
\(110\) −1.26145 2.18490i −0.120275 0.208322i
\(111\) 0 0
\(112\) 0 0
\(113\) 9.73236 + 16.8569i 0.915543 + 1.58577i 0.806104 + 0.591774i \(0.201572\pi\)
0.109440 + 0.993993i \(0.465094\pi\)
\(114\) 0 0
\(115\) −0.477100 −0.0444898
\(116\) −4.13781 7.16689i −0.384186 0.665429i
\(117\) 0 0
\(118\) 6.47710 0.596265
\(119\) 0 0
\(120\) 0 0
\(121\) −8.47710 −0.770645
\(122\) −2.23855 + 3.87728i −0.202669 + 0.351033i
\(123\) 0 0
\(124\) −1.35600 2.34867i −0.121773 0.210917i
\(125\) −11.8764 −1.06225
\(126\) 0 0
\(127\) −13.4400 −1.19260 −0.596302 0.802760i \(-0.703364\pi\)
−0.596302 + 0.802760i \(0.703364\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −3.82072 + 6.61769i −0.335100 + 0.580410i
\(131\) −3.17673 −0.277552 −0.138776 0.990324i \(-0.544317\pi\)
−0.138776 + 0.990324i \(0.544317\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −10.0531 −0.868454
\(135\) 0 0
\(136\) −2.69963 4.67589i −0.231491 0.400955i
\(137\) 21.2632 1.81664 0.908320 0.418275i \(-0.137365\pi\)
0.908320 + 0.418275i \(0.137365\pi\)
\(138\) 0 0
\(139\) −6.52654 11.3043i −0.553574 0.958818i −0.998013 0.0630092i \(-0.979930\pi\)
0.444439 0.895809i \(-0.353403\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.36033 + 11.0164i 0.533747 + 0.924478i
\(143\) −3.82072 6.61769i −0.319505 0.553399i
\(144\) 0 0
\(145\) −6.57234 + 11.3836i −0.545803 + 0.945359i
\(146\) −8.02654 + 13.9024i −0.664281 + 1.15057i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) −5.20877 −0.426719 −0.213360 0.976974i \(-0.568441\pi\)
−0.213360 + 0.976974i \(0.568441\pi\)
\(150\) 0 0
\(151\) −0.522900 −0.0425530 −0.0212765 0.999774i \(-0.506773\pi\)
−0.0212765 + 0.999774i \(0.506773\pi\)
\(152\) 3.54944 6.14781i 0.287898 0.498654i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.15383 + 3.73054i −0.173000 + 0.299644i
\(156\) 0 0
\(157\) 4.43199 7.67643i 0.353711 0.612646i −0.633185 0.774000i \(-0.718253\pi\)
0.986897 + 0.161354i \(0.0515862\pi\)
\(158\) −4.19344 + 7.26325i −0.333612 + 0.577833i
\(159\) 0 0
\(160\) −0.794182 + 1.37556i −0.0627856 + 0.108748i
\(161\) 0 0
\(162\) 0 0
\(163\) 10.9814 19.0204i 0.860132 1.48979i −0.0116689 0.999932i \(-0.503714\pi\)
0.871801 0.489860i \(-0.162952\pi\)
\(164\) −5.87636 −0.458866
\(165\) 0 0
\(166\) −2.36584 −0.183624
\(167\) 1.65019 + 2.85821i 0.127695 + 0.221175i 0.922783 0.385319i \(-0.125909\pi\)
−0.795088 + 0.606494i \(0.792575\pi\)
\(168\) 0 0
\(169\) −5.07234 + 8.78555i −0.390180 + 0.675812i
\(170\) −4.28799 + 7.42702i −0.328874 + 0.569626i
\(171\) 0 0
\(172\) −0.833104 1.44298i −0.0635236 0.110026i
\(173\) −9.55377 16.5476i −0.726360 1.25809i −0.958412 0.285389i \(-0.907877\pi\)
0.232052 0.972703i \(-0.425456\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.794182 1.37556i −0.0598637 0.103687i
\(177\) 0 0
\(178\) −3.21015 −0.240611
\(179\) 8.03706 + 13.9206i 0.600718 + 1.04047i 0.992712 + 0.120507i \(0.0384520\pi\)
−0.391994 + 0.919968i \(0.628215\pi\)
\(180\) 0 0
\(181\) −8.05308 −0.598581 −0.299291 0.954162i \(-0.596750\pi\)
−0.299291 + 0.954162i \(0.596750\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.300372 −0.0221437
\(185\) 0.794182 1.37556i 0.0583894 0.101133i
\(186\) 0 0
\(187\) −4.28799 7.42702i −0.313569 0.543118i
\(188\) 2.66621 0.194453
\(189\) 0 0
\(190\) −11.2756 −0.818019
\(191\) −11.9814 20.7524i −0.866946 1.50159i −0.865102 0.501596i \(-0.832746\pi\)
−0.00184390 0.999998i \(-0.500587\pi\)
\(192\) 0 0
\(193\) −4.88255 + 8.45682i −0.351453 + 0.608735i −0.986504 0.163735i \(-0.947646\pi\)
0.635051 + 0.772470i \(0.280979\pi\)
\(194\) 1.42402 0.102238
\(195\) 0 0
\(196\) 0 0
\(197\) 18.2436 1.29980 0.649900 0.760020i \(-0.274811\pi\)
0.649900 + 0.760020i \(0.274811\pi\)
\(198\) 0 0
\(199\) −9.04944 15.6741i −0.641498 1.11111i −0.985098 0.171991i \(-0.944980\pi\)
0.343601 0.939116i \(-0.388353\pi\)
\(200\) −2.47710 −0.175157
\(201\) 0 0
\(202\) −6.01671 10.4212i −0.423334 0.733236i
\(203\) 0 0
\(204\) 0 0
\(205\) 4.66690 + 8.08330i 0.325950 + 0.564562i
\(206\) −3.04944 5.28179i −0.212465 0.368000i
\(207\) 0 0
\(208\) −2.40545 + 4.16635i −0.166788 + 0.288885i
\(209\) 5.63781 9.76497i 0.389975 0.675457i
\(210\) 0 0
\(211\) 0.166208 + 0.287880i 0.0114422 + 0.0198185i 0.871690 0.490058i \(-0.163024\pi\)
−0.860248 + 0.509877i \(0.829691\pi\)
\(212\) 4.88874 0.335760
\(213\) 0 0
\(214\) −3.08650 −0.210989
\(215\) −1.32327 + 2.29197i −0.0902464 + 0.156311i
\(216\) 0 0
\(217\) 0 0
\(218\) 1.14400 1.98146i 0.0774812 0.134201i
\(219\) 0 0
\(220\) −1.26145 + 2.18490i −0.0850469 + 0.147306i
\(221\) −12.9876 + 22.4952i −0.873642 + 1.51319i
\(222\) 0 0
\(223\) −3.16621 + 5.48403i −0.212025 + 0.367238i −0.952348 0.305013i \(-0.901339\pi\)
0.740323 + 0.672251i \(0.234672\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 9.73236 16.8569i 0.647387 1.12131i
\(227\) −23.3090 −1.54707 −0.773537 0.633751i \(-0.781515\pi\)
−0.773537 + 0.633751i \(0.781515\pi\)
\(228\) 0 0
\(229\) 4.95420 0.327383 0.163691 0.986512i \(-0.447660\pi\)
0.163691 + 0.986512i \(0.447660\pi\)
\(230\) 0.238550 + 0.413181i 0.0157295 + 0.0272443i
\(231\) 0 0
\(232\) −4.13781 + 7.16689i −0.271660 + 0.470529i
\(233\) 7.13781 12.3630i 0.467613 0.809930i −0.531702 0.846932i \(-0.678447\pi\)
0.999315 + 0.0370017i \(0.0117807\pi\)
\(234\) 0 0
\(235\) −2.11745 3.66754i −0.138127 0.239244i
\(236\) −3.23855 5.60933i −0.210812 0.365136i
\(237\) 0 0
\(238\) 0 0
\(239\) −2.48762 4.30868i −0.160911 0.278706i 0.774285 0.632837i \(-0.218110\pi\)
−0.935196 + 0.354132i \(0.884776\pi\)
\(240\) 0 0
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) 4.23855 + 7.34138i 0.272464 + 0.471922i
\(243\) 0 0
\(244\) 4.47710 0.286617
\(245\) 0 0
\(246\) 0 0
\(247\) −34.1520 −2.17304
\(248\) −1.35600 + 2.34867i −0.0861063 + 0.149141i
\(249\) 0 0
\(250\) 5.93818 + 10.2852i 0.375563 + 0.650495i
\(251\) 2.43268 0.153549 0.0767746 0.997048i \(-0.475538\pi\)
0.0767746 + 0.997048i \(0.475538\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) 6.71998 + 11.6393i 0.421649 + 0.730318i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.987620 −0.0616061 −0.0308030 0.999525i \(-0.509806\pi\)
−0.0308030 + 0.999525i \(0.509806\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.64145 0.473902
\(261\) 0 0
\(262\) 1.58836 + 2.75113i 0.0981295 + 0.169965i
\(263\) −17.1854 −1.05970 −0.529848 0.848092i \(-0.677751\pi\)
−0.529848 + 0.848092i \(0.677751\pi\)
\(264\) 0 0
\(265\) −3.88255 6.72477i −0.238503 0.413099i
\(266\) 0 0
\(267\) 0 0
\(268\) 5.02654 + 8.70623i 0.307045 + 0.531817i
\(269\) 11.4523 + 19.8360i 0.698262 + 1.20942i 0.969069 + 0.246791i \(0.0793761\pi\)
−0.270807 + 0.962634i \(0.587291\pi\)
\(270\) 0 0
\(271\) −7.00364 + 12.1307i −0.425441 + 0.736885i −0.996462 0.0840504i \(-0.973214\pi\)
0.571021 + 0.820936i \(0.306548\pi\)
\(272\) −2.69963 + 4.67589i −0.163689 + 0.283518i
\(273\) 0 0
\(274\) −10.6316 18.4145i −0.642279 1.11246i
\(275\) −3.93454 −0.237261
\(276\) 0 0
\(277\) 28.2953 1.70010 0.850049 0.526703i \(-0.176572\pi\)
0.850049 + 0.526703i \(0.176572\pi\)
\(278\) −6.52654 + 11.3043i −0.391436 + 0.677987i
\(279\) 0 0
\(280\) 0 0
\(281\) 8.79782 15.2383i 0.524834 0.909039i −0.474748 0.880122i \(-0.657461\pi\)
0.999582 0.0289175i \(-0.00920600\pi\)
\(282\) 0 0
\(283\) −9.26145 + 16.0413i −0.550536 + 0.953556i 0.447700 + 0.894184i \(0.352243\pi\)
−0.998236 + 0.0593725i \(0.981090\pi\)
\(284\) 6.36033 11.0164i 0.377416 0.653704i
\(285\) 0 0
\(286\) −3.82072 + 6.61769i −0.225924 + 0.391312i
\(287\) 0 0
\(288\) 0 0
\(289\) −6.07598 + 10.5239i −0.357411 + 0.619054i
\(290\) 13.1447 0.771882
\(291\) 0 0
\(292\) 16.0531 0.939436
\(293\) −7.04256 12.1981i −0.411431 0.712619i 0.583616 0.812030i \(-0.301638\pi\)
−0.995046 + 0.0994108i \(0.968304\pi\)
\(294\) 0 0
\(295\) −5.14400 + 8.90966i −0.299495 + 0.518741i
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) 2.60439 + 4.51093i 0.150868 + 0.261311i
\(299\) 0.722528 + 1.25146i 0.0417849 + 0.0723736i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.261450 + 0.452845i 0.0150448 + 0.0260583i
\(303\) 0 0
\(304\) −7.09888 −0.407149
\(305\) −3.55563 6.15854i −0.203595 0.352637i
\(306\) 0 0
\(307\) 5.85532 0.334180 0.167090 0.985942i \(-0.446563\pi\)
0.167090 + 0.985942i \(0.446563\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.30766 0.244658
\(311\) −0.405446 + 0.702253i −0.0229907 + 0.0398211i −0.877292 0.479957i \(-0.840652\pi\)
0.854301 + 0.519778i \(0.173985\pi\)
\(312\) 0 0
\(313\) 5.28799 + 9.15907i 0.298895 + 0.517701i 0.975883 0.218292i \(-0.0700486\pi\)
−0.676988 + 0.735994i \(0.736715\pi\)
\(314\) −8.86398 −0.500223
\(315\) 0 0
\(316\) 8.38688 0.471799
\(317\) 6.09820 + 10.5624i 0.342509 + 0.593243i 0.984898 0.173136i \(-0.0553900\pi\)
−0.642389 + 0.766379i \(0.722057\pi\)
\(318\) 0 0
\(319\) −6.57234 + 11.3836i −0.367981 + 0.637361i
\(320\) 1.58836 0.0887922
\(321\) 0 0
\(322\) 0 0
\(323\) −38.3287 −2.13267
\(324\) 0 0
\(325\) 5.95853 + 10.3205i 0.330520 + 0.572477i
\(326\) −21.9629 −1.21641
\(327\) 0 0
\(328\) 2.93818 + 5.08907i 0.162234 + 0.280997i
\(329\) 0 0
\(330\) 0 0
\(331\) 7.83310 + 13.5673i 0.430546 + 0.745728i 0.996920 0.0784202i \(-0.0249876\pi\)
−0.566374 + 0.824148i \(0.691654\pi\)
\(332\) 1.18292 + 2.04887i 0.0649211 + 0.112447i
\(333\) 0 0
\(334\) 1.65019 2.85821i 0.0902942 0.156394i
\(335\) 7.98398 13.8287i 0.436211 0.755540i
\(336\) 0 0
\(337\) −4.21201 7.29541i −0.229443 0.397406i 0.728200 0.685364i \(-0.240357\pi\)
−0.957643 + 0.287958i \(0.907024\pi\)
\(338\) 10.1447 0.551798
\(339\) 0 0
\(340\) 8.57598 0.465098
\(341\) −2.15383 + 3.73054i −0.116636 + 0.202020i
\(342\) 0 0
\(343\) 0 0
\(344\) −0.833104 + 1.44298i −0.0449179 + 0.0778002i
\(345\) 0 0
\(346\) −9.55377 + 16.5476i −0.513614 + 0.889606i
\(347\) 0.283662 0.491316i 0.0152277 0.0263752i −0.858311 0.513130i \(-0.828486\pi\)
0.873539 + 0.486754i \(0.161819\pi\)
\(348\) 0 0
\(349\) 0.00364189 0.00630794i 0.000194946 0.000337656i −0.865928 0.500169i \(-0.833271\pi\)
0.866123 + 0.499831i \(0.166605\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.794182 + 1.37556i −0.0423300 + 0.0733178i
\(353\) 6.65383 0.354148 0.177074 0.984198i \(-0.443337\pi\)
0.177074 + 0.984198i \(0.443337\pi\)
\(354\) 0 0
\(355\) −20.2051 −1.07237
\(356\) 1.60507 + 2.78007i 0.0850688 + 0.147343i
\(357\) 0 0
\(358\) 8.03706 13.9206i 0.424772 0.735727i
\(359\) 0.398568 0.690339i 0.0210356 0.0364347i −0.855316 0.518107i \(-0.826637\pi\)
0.876352 + 0.481672i \(0.159970\pi\)
\(360\) 0 0
\(361\) −15.6971 27.1881i −0.826162 1.43095i
\(362\) 4.02654 + 6.97418i 0.211630 + 0.366555i
\(363\) 0 0
\(364\) 0 0
\(365\) −12.7491 22.0820i −0.667317 1.15583i
\(366\) 0 0
\(367\) 15.4327 0.805579 0.402790 0.915293i \(-0.368041\pi\)
0.402790 + 0.915293i \(0.368041\pi\)
\(368\) 0.150186 + 0.260130i 0.00782898 + 0.0135602i
\(369\) 0 0
\(370\) −1.58836 −0.0825751
\(371\) 0 0
\(372\) 0 0
\(373\) 10.2422 0.530321 0.265160 0.964204i \(-0.414575\pi\)
0.265160 + 0.964204i \(0.414575\pi\)
\(374\) −4.28799 + 7.42702i −0.221727 + 0.384042i
\(375\) 0 0
\(376\) −1.33310 2.30900i −0.0687496 0.119078i
\(377\) 39.8131 2.05048
\(378\) 0 0
\(379\) 25.0087 1.28461 0.642304 0.766450i \(-0.277979\pi\)
0.642304 + 0.766450i \(0.277979\pi\)
\(380\) 5.63781 + 9.76497i 0.289213 + 0.500932i
\(381\) 0 0
\(382\) −11.9814 + 20.7524i −0.613023 + 1.06179i
\(383\) −6.26695 −0.320226 −0.160113 0.987099i \(-0.551186\pi\)
−0.160113 + 0.987099i \(0.551186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.76509 0.497030
\(387\) 0 0
\(388\) −0.712008 1.23323i −0.0361467 0.0626080i
\(389\) 21.6342 1.09690 0.548448 0.836185i \(-0.315219\pi\)
0.548448 + 0.836185i \(0.315219\pi\)
\(390\) 0 0
\(391\) 0.810892 + 1.40451i 0.0410086 + 0.0710290i
\(392\) 0 0
\(393\) 0 0
\(394\) −9.12178 15.7994i −0.459549 0.795962i
\(395\) −6.66071 11.5367i −0.335137 0.580473i
\(396\) 0 0
\(397\) −2.05308 + 3.55605i −0.103041 + 0.178473i −0.912936 0.408102i \(-0.866191\pi\)
0.809895 + 0.586575i \(0.199524\pi\)
\(398\) −9.04944 + 15.6741i −0.453608 + 0.785671i
\(399\) 0 0
\(400\) 1.23855 + 2.14523i 0.0619275 + 0.107262i
\(401\) −16.7417 −0.836041 −0.418021 0.908438i \(-0.637276\pi\)
−0.418021 + 0.908438i \(0.637276\pi\)
\(402\) 0 0
\(403\) 13.0472 0.649926
\(404\) −6.01671 + 10.4212i −0.299343 + 0.518476i
\(405\) 0 0
\(406\) 0 0
\(407\) 0.794182 1.37556i 0.0393661 0.0681842i
\(408\) 0 0
\(409\) −4.38255 + 7.59079i −0.216703 + 0.375341i −0.953798 0.300449i \(-0.902864\pi\)
0.737095 + 0.675789i \(0.236197\pi\)
\(410\) 4.66690 8.08330i 0.230482 0.399206i
\(411\) 0 0
\(412\) −3.04944 + 5.28179i −0.150235 + 0.260215i
\(413\) 0 0
\(414\) 0 0
\(415\) 1.87890 3.25436i 0.0922318 0.159750i
\(416\) 4.81089 0.235873
\(417\) 0 0
\(418\) −11.2756 −0.551508
\(419\) −0.210149 0.363988i −0.0102664 0.0177820i 0.860847 0.508865i \(-0.169935\pi\)
−0.871113 + 0.491083i \(0.836601\pi\)
\(420\) 0 0
\(421\) 3.28799 5.69497i 0.160247 0.277556i −0.774710 0.632316i \(-0.782104\pi\)
0.934957 + 0.354761i \(0.115438\pi\)
\(422\) 0.166208 0.287880i 0.00809086 0.0140138i
\(423\) 0 0
\(424\) −2.44437 4.23377i −0.118709 0.205610i
\(425\) 6.68725 + 11.5827i 0.324379 + 0.561841i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.54325 + 2.67299i 0.0745959 + 0.129204i
\(429\) 0 0
\(430\) 2.64654 0.127628
\(431\) −11.0439 19.1287i −0.531968 0.921395i −0.999304 0.0373155i \(-0.988119\pi\)
0.467336 0.884080i \(-0.345214\pi\)
\(432\) 0 0
\(433\) 9.43268 0.453306 0.226653 0.973976i \(-0.427222\pi\)
0.226653 + 0.973976i \(0.427222\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.28799 −0.109575
\(437\) −1.06615 + 1.84663i −0.0510010 + 0.0883363i
\(438\) 0 0
\(439\) −15.6032 27.0256i −0.744701 1.28986i −0.950334 0.311231i \(-0.899259\pi\)
0.205634 0.978629i \(-0.434074\pi\)
\(440\) 2.52290 0.120275
\(441\) 0 0
\(442\) 25.9752 1.23552
\(443\) 6.52723 + 11.3055i 0.310118 + 0.537140i 0.978388 0.206779i \(-0.0662981\pi\)
−0.668270 + 0.743919i \(0.732965\pi\)
\(444\) 0 0
\(445\) 2.54944 4.41576i 0.120855 0.209327i
\(446\) 6.33242 0.299849
\(447\) 0 0
\(448\) 0 0
\(449\) 9.91706 0.468015 0.234008 0.972235i \(-0.424816\pi\)
0.234008 + 0.972235i \(0.424816\pi\)
\(450\) 0 0
\(451\) 4.66690 + 8.08330i 0.219756 + 0.380628i
\(452\) −19.4647 −0.915543
\(453\) 0 0
\(454\) 11.6545 + 20.1862i 0.546974 + 0.947386i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.2615 + 21.2375i 0.573566 + 0.993446i 0.996196 + 0.0871436i \(0.0277739\pi\)
−0.422629 + 0.906303i \(0.638893\pi\)
\(458\) −2.47710 4.29046i −0.115747 0.200480i
\(459\) 0 0
\(460\) 0.238550 0.413181i 0.0111224 0.0192646i
\(461\) 1.75526 3.04020i 0.0817506 0.141596i −0.822251 0.569125i \(-0.807282\pi\)
0.904002 + 0.427528i \(0.140616\pi\)
\(462\) 0 0
\(463\) 8.69413 + 15.0587i 0.404050 + 0.699836i 0.994210 0.107451i \(-0.0342687\pi\)
−0.590160 + 0.807286i \(0.700935\pi\)
\(464\) 8.27561 0.384186
\(465\) 0 0
\(466\) −14.2756 −0.661305
\(467\) 6.69894 11.6029i 0.309990 0.536918i −0.668370 0.743829i \(-0.733008\pi\)
0.978360 + 0.206911i \(0.0663410\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.11745 + 3.66754i −0.0976709 + 0.169171i
\(471\) 0 0
\(472\) −3.23855 + 5.60933i −0.149066 + 0.258190i
\(473\) −1.32327 + 2.29197i −0.0608441 + 0.105385i
\(474\) 0 0
\(475\) −8.79232 + 15.2287i −0.403419 + 0.698743i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.48762 + 4.30868i −0.113781 + 0.197075i
\(479\) 20.8058 0.950641 0.475321 0.879813i \(-0.342332\pi\)
0.475321 + 0.879813i \(0.342332\pi\)
\(480\) 0 0
\(481\) −4.81089 −0.219358
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 4.23855 7.34138i 0.192661 0.333699i
\(485\) −1.13093 + 1.95882i −0.0513528 + 0.0889456i
\(486\) 0 0
\(487\) 16.2472 + 28.1410i 0.736231 + 1.27519i 0.954181 + 0.299230i \(0.0967298\pi\)
−0.217950 + 0.975960i \(0.569937\pi\)
\(488\) −2.23855 3.87728i −0.101334 0.175516i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.66071 + 16.7328i 0.435982 + 0.755142i 0.997375 0.0724067i \(-0.0230679\pi\)
−0.561394 + 0.827549i \(0.689735\pi\)
\(492\) 0 0
\(493\) 44.6822 2.01238
\(494\) 17.0760 + 29.5765i 0.768285 + 1.33071i
\(495\) 0 0
\(496\) 2.71201 0.121773
\(497\) 0 0
\(498\) 0 0
\(499\) −11.1506 −0.499169 −0.249585 0.968353i \(-0.580294\pi\)
−0.249585 + 0.968353i \(0.580294\pi\)
\(500\) 5.93818 10.2852i 0.265563 0.459969i
\(501\) 0 0
\(502\) −1.21634 2.10676i −0.0542878 0.0940293i
\(503\) −40.7651 −1.81763 −0.908813 0.417204i \(-0.863010\pi\)
−0.908813 + 0.417204i \(0.863010\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) 0.238550 + 0.413181i 0.0106048 + 0.0183681i
\(507\) 0 0
\(508\) 6.71998 11.6393i 0.298151 0.516413i
\(509\) 1.44506 0.0640510 0.0320255 0.999487i \(-0.489804\pi\)
0.0320255 + 0.999487i \(0.489804\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0.493810 + 0.855304i 0.0217810 + 0.0377259i
\(515\) 9.68725 0.426871
\(516\) 0 0
\(517\) −2.11745 3.66754i −0.0931255 0.161298i
\(518\) 0 0
\(519\) 0 0
\(520\) −3.82072 6.61769i −0.167550 0.290205i
\(521\) 9.64214 + 16.7007i 0.422430 + 0.731670i 0.996177 0.0873630i \(-0.0278440\pi\)
−0.573747 + 0.819033i \(0.694511\pi\)
\(522\) 0 0
\(523\) 18.3454 31.7752i 0.802189 1.38943i −0.115984 0.993251i \(-0.537002\pi\)
0.918173 0.396180i \(-0.129665\pi\)
\(524\) 1.58836 2.75113i 0.0693880 0.120184i
\(525\) 0 0
\(526\) 8.59269 + 14.8830i 0.374659 + 0.648929i
\(527\) 14.6428 0.637851
\(528\) 0 0
\(529\) −22.9098 −0.996077
\(530\) −3.88255 + 6.72477i −0.168647 + 0.292105i
\(531\) 0 0
\(532\) 0 0
\(533\) 14.1353 24.4830i 0.612266 1.06048i
\(534\) 0 0
\(535\) 2.45125 4.24568i 0.105977 0.183557i
\(536\) 5.02654 8.70623i 0.217114 0.376052i
\(537\) 0 0
\(538\) 11.4523 19.8360i 0.493745 0.855192i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.62543 + 2.81532i −0.0698825 + 0.121040i −0.898849 0.438258i \(-0.855596\pi\)
0.828967 + 0.559298i \(0.188929\pi\)
\(542\) 14.0073 0.601664
\(543\) 0 0
\(544\) 5.39926 0.231491
\(545\) 1.81708 + 3.14728i 0.0778352 + 0.134815i
\(546\) 0 0
\(547\) −2.95853 + 5.12432i −0.126498 + 0.219100i −0.922317 0.386433i \(-0.873707\pi\)
0.795820 + 0.605534i \(0.207040\pi\)
\(548\) −10.6316 + 18.4145i −0.454160 + 0.786628i
\(549\) 0 0
\(550\) 1.96727 + 3.40741i 0.0838846 + 0.145292i
\(551\) 29.3738 + 50.8769i 1.25137 + 2.16743i
\(552\) 0 0
\(553\) 0 0
\(554\) −14.1476 24.5044i −0.601076 1.04109i
\(555\) 0 0
\(556\) 13.0531 0.553574
\(557\) −12.8040 22.1772i −0.542523 0.939678i −0.998758 0.0498188i \(-0.984136\pi\)
0.456235 0.889859i \(-0.349198\pi\)
\(558\) 0 0
\(559\) 8.01594 0.339038
\(560\) 0 0
\(561\) 0 0
\(562\) −17.5956 −0.742228
\(563\) 23.3189 40.3895i 0.982773 1.70221i 0.331330 0.943515i \(-0.392503\pi\)
0.651443 0.758698i \(-0.274164\pi\)
\(564\) 0 0
\(565\) 15.4585 + 26.7750i 0.650345 + 1.12643i
\(566\) 18.5229 0.778576
\(567\) 0 0
\(568\) −12.7207 −0.533747
\(569\) 15.5989 + 27.0181i 0.653939 + 1.13266i 0.982159 + 0.188054i \(0.0602182\pi\)
−0.328219 + 0.944602i \(0.606449\pi\)
\(570\) 0 0
\(571\) 7.83812 13.5760i 0.328015 0.568139i −0.654103 0.756406i \(-0.726954\pi\)
0.982118 + 0.188267i \(0.0602869\pi\)
\(572\) 7.64145 0.319505
\(573\) 0 0
\(574\) 0 0
\(575\) 0.744051 0.0310291
\(576\) 0 0
\(577\) −6.99567 12.1169i −0.291234 0.504431i 0.682868 0.730542i \(-0.260732\pi\)
−0.974102 + 0.226110i \(0.927399\pi\)
\(578\) 12.1520 0.505455
\(579\) 0 0
\(580\) −6.57234 11.3836i −0.272902 0.472680i
\(581\) 0 0
\(582\) 0 0
\(583\) −3.88255 6.72477i −0.160799 0.278511i
\(584\) −8.02654 13.9024i −0.332141 0.575285i
\(585\) 0 0
\(586\) −7.04256 + 12.1981i −0.290926 + 0.503898i
\(587\) 1.44801 2.50803i 0.0597658 0.103517i −0.834594 0.550865i \(-0.814298\pi\)
0.894360 + 0.447348i \(0.147631\pi\)
\(588\) 0 0
\(589\) 9.62612 + 16.6729i 0.396637 + 0.686996i
\(590\) 10.2880 0.423550
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) −2.04394 + 3.54021i −0.0839346 + 0.145379i −0.904937 0.425546i \(-0.860082\pi\)
0.821002 + 0.570925i \(0.193415\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.60439 4.51093i 0.106680 0.184775i
\(597\) 0 0
\(598\) 0.722528 1.25146i 0.0295464 0.0511758i
\(599\) −9.88255 + 17.1171i −0.403790 + 0.699385i −0.994180 0.107734i \(-0.965641\pi\)
0.590390 + 0.807118i \(0.298974\pi\)
\(600\) 0 0
\(601\) 13.4320 23.2649i 0.547902 0.948994i −0.450516 0.892768i \(-0.648760\pi\)
0.998418 0.0562261i \(-0.0179068\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.261450 0.452845i 0.0106383 0.0184260i
\(605\) −13.4647 −0.547419
\(606\) 0 0
\(607\) 15.2422 0.618661 0.309331 0.950955i \(-0.399895\pi\)
0.309331 + 0.950955i \(0.399895\pi\)
\(608\) 3.54944 + 6.14781i 0.143949 + 0.249327i
\(609\) 0 0
\(610\) −3.55563 + 6.15854i −0.143963 + 0.249352i
\(611\) −6.41342 + 11.1084i −0.259459 + 0.449396i
\(612\) 0 0
\(613\) −1.36033 2.35617i −0.0549434 0.0951648i 0.837246 0.546827i \(-0.184165\pi\)
−0.892189 + 0.451662i \(0.850831\pi\)
\(614\) −2.92766 5.07085i −0.118151 0.204643i
\(615\) 0 0
\(616\) 0 0
\(617\) 9.21812 + 15.9663i 0.371108 + 0.642777i 0.989736 0.142906i \(-0.0456448\pi\)
−0.618629 + 0.785684i \(0.712311\pi\)
\(618\) 0 0
\(619\) −0.107546 −0.00432262 −0.00216131 0.999998i \(-0.500688\pi\)
−0.00216131 + 0.999998i \(0.500688\pi\)
\(620\) −2.15383 3.73054i −0.0864998 0.149822i
\(621\) 0 0
\(622\) 0.810892 0.0325138
\(623\) 0 0
\(624\) 0 0
\(625\) −6.47848 −0.259139
\(626\) 5.28799 9.15907i 0.211351 0.366070i
\(627\) 0 0
\(628\) 4.43199 + 7.67643i 0.176856 + 0.306323i
\(629\) −5.39926 −0.215282
\(630\) 0 0
\(631\) 35.7266 1.42225 0.711126 0.703064i \(-0.248185\pi\)
0.711126 + 0.703064i \(0.248185\pi\)
\(632\) −4.19344 7.26325i −0.166806 0.288916i
\(633\) 0 0
\(634\) 6.09820 10.5624i 0.242190 0.419486i
\(635\) −21.3475 −0.847152
\(636\) 0 0
\(637\) 0 0
\(638\) 13.1447 0.520403
\(639\) 0 0
\(640\) −0.794182 1.37556i −0.0313928 0.0543739i
\(641\) −17.3128 −0.683813 −0.341906 0.939734i \(-0.611073\pi\)
−0.341906 + 0.939734i \(0.611073\pi\)
\(642\) 0 0
\(643\) −14.4821 25.0838i −0.571119 0.989207i −0.996451 0.0841700i \(-0.973176\pi\)
0.425332 0.905037i \(-0.360157\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 19.1643 + 33.1936i 0.754011 + 1.30599i
\(647\) 1.27816 + 2.21384i 0.0502497 + 0.0870350i 0.890056 0.455851i \(-0.150665\pi\)
−0.839807 + 0.542886i \(0.817332\pi\)
\(648\) 0 0
\(649\) −5.14400 + 8.90966i −0.201920 + 0.349735i
\(650\) 5.95853 10.3205i 0.233713 0.404802i
\(651\) 0 0
\(652\) 10.9814 + 19.0204i 0.430066 + 0.744896i
\(653\) −29.9766 −1.17308 −0.586538 0.809922i \(-0.699509\pi\)
−0.586538 + 0.809922i \(0.699509\pi\)
\(654\) 0 0
\(655\) −5.04580 −0.197156
\(656\) 2.93818 5.08907i 0.114717 0.198695i
\(657\) 0 0
\(658\) 0 0
\(659\) 7.63162 13.2183i 0.297286 0.514914i −0.678228 0.734851i \(-0.737252\pi\)
0.975514 + 0.219937i \(0.0705853\pi\)
\(660\) 0 0
\(661\) −13.6261 + 23.6011i −0.529994 + 0.917977i 0.469393 + 0.882989i \(0.344473\pi\)
−0.999388 + 0.0349881i \(0.988861\pi\)
\(662\) 7.83310 13.5673i 0.304442 0.527309i
\(663\) 0 0
\(664\) 1.18292 2.04887i 0.0459061 0.0795117i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.24288 2.15273i 0.0481245 0.0833541i
\(668\) −3.30037 −0.127695
\(669\) 0 0
\(670\) −15.9680 −0.616896
\(671\) −3.55563 6.15854i −0.137264 0.237748i
\(672\) 0 0
\(673\) 23.2280 40.2320i 0.895372 1.55083i 0.0620280 0.998074i \(-0.480243\pi\)
0.833344 0.552755i \(-0.186423\pi\)
\(674\) −4.21201 + 7.29541i −0.162240 + 0.281009i
\(675\) 0 0
\(676\) −5.07234 8.78555i −0.195090 0.337906i
\(677\) −2.54944 4.41576i −0.0979830 0.169712i 0.812867 0.582450i \(-0.197906\pi\)
−0.910850 + 0.412738i \(0.864572\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.28799 7.42702i −0.164437 0.284813i
\(681\) 0 0
\(682\) 4.30766 0.164949
\(683\) 7.77197 + 13.4614i 0.297386 + 0.515088i 0.975537 0.219835i \(-0.0705518\pi\)
−0.678151 + 0.734923i \(0.737218\pi\)
\(684\) 0 0
\(685\) 33.7738 1.29043
\(686\) 0 0
\(687\) 0 0
\(688\) 1.66621 0.0635236
\(689\) −11.7596 + 20.3682i −0.448005 + 0.775967i
\(690\) 0 0
\(691\) 11.6483 + 20.1755i 0.443123 + 0.767512i 0.997919 0.0644744i \(-0.0205371\pi\)
−0.554796 + 0.831986i \(0.687204\pi\)
\(692\) 19.1075 0.726360
\(693\) 0 0
\(694\) −0.567323 −0.0215353
\(695\) −10.3665 17.9553i −0.393225 0.681085i
\(696\) 0 0
\(697\) 15.8640 27.4772i 0.600891 1.04077i
\(698\) −0.00728378 −0.000275695
\(699\) 0 0
\(700\) 0 0
\(701\) 45.6464 1.72404 0.862020 0.506874i \(-0.169199\pi\)
0.862020 + 0.506874i \(0.169199\pi\)
\(702\) 0 0
\(703\) −3.54944 6.14781i −0.133870 0.231869i
\(704\) 1.58836 0.0598637
\(705\) 0 0
\(706\) −3.32691 5.76238i −0.125210 0.216870i
\(707\) 0 0
\(708\) 0 0
\(709\) −9.00069 15.5897i −0.338028 0.585482i 0.646034 0.763309i \(-0.276427\pi\)
−0.984062 + 0.177827i \(0.943093\pi\)
\(710\) 10.1025 + 17.4981i 0.379141 + 0.656692i
\(711\) 0 0
\(712\) 1.60507 2.78007i 0.0601527 0.104188i
\(713\) 0.407305 0.705474i 0.0152537 0.0264202i
\(714\) 0 0
\(715\) −6.06870 10.5113i −0.226957 0.393100i
\(716\) −16.0741 −0.600718
\(717\) 0 0
\(718\) −0.797135 −0.0297488
\(719\) 18.4389 31.9371i 0.687654 1.19105i −0.284941 0.958545i \(-0.591974\pi\)
0.972595 0.232506i \(-0.0746926\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.6971 + 27.1881i −0.584185 + 1.01184i
\(723\) 0 0
\(724\) 4.02654 6.97418i 0.149645 0.259193i
\(725\) 10.2498 17.7531i 0.380666 0.659334i
\(726\) 0 0
\(727\) −15.2429 + 26.4014i −0.565327 + 0.979175i 0.431692 + 0.902021i \(0.357917\pi\)
−0.997019 + 0.0771543i \(0.975417\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −12.7491 + 22.0820i −0.471864 + 0.817293i
\(731\) 8.99628 0.332739
\(732\) 0 0
\(733\) −6.15059 −0.227177 −0.113589 0.993528i \(-0.536235\pi\)
−0.113589 + 0.993528i \(0.536235\pi\)
\(734\) −7.71634 13.3651i −0.284815 0.493314i
\(735\) 0 0
\(736\) 0.150186 0.260130i 0.00553593 0.00958851i
\(737\) 7.98398 13.8287i 0.294094 0.509385i
\(738\) 0 0
\(739\) −20.3912 35.3186i −0.750103 1.29922i −0.947772 0.318947i \(-0.896671\pi\)
0.197670 0.980269i \(-0.436663\pi\)
\(740\) 0.794182 + 1.37556i 0.0291947 + 0.0505667i
\(741\) 0 0
\(742\) 0 0
\(743\) −7.25271 12.5621i −0.266076 0.460858i 0.701769 0.712405i \(-0.252394\pi\)
−0.967845 + 0.251547i \(0.919061\pi\)
\(744\) 0 0
\(745\) −8.27342 −0.303115
\(746\) −5.12110 8.87000i −0.187497 0.324754i
\(747\) 0 0
\(748\) 8.57598 0.313569
\(749\) 0 0
\(750\) 0 0
\(751\) 4.18911 0.152863 0.0764314 0.997075i \(-0.475647\pi\)
0.0764314 + 0.997075i \(0.475647\pi\)
\(752\) −1.33310 + 2.30900i −0.0486133 + 0.0842007i
\(753\) 0 0
\(754\) −19.9065 34.4791i −0.724953 1.25566i
\(755\) −0.830556 −0.0302270
\(756\) 0 0
\(757\) 2.38688 0.0867525 0.0433763 0.999059i \(-0.486189\pi\)
0.0433763 + 0.999059i \(0.486189\pi\)
\(758\) −12.5043 21.6581i −0.454178 0.786659i
\(759\) 0 0
\(760\) 5.63781 9.76497i 0.204505 0.354213i
\(761\) 3.63416 0.131738 0.0658692 0.997828i \(-0.479018\pi\)
0.0658692 + 0.997828i \(0.479018\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 23.9629 0.866946
\(765\) 0 0
\(766\) 3.13348 + 5.42734i 0.113217 + 0.196098i
\(767\) 31.1606 1.12515
\(768\) 0 0
\(769\) 19.9672 + 34.5842i 0.720035 + 1.24714i 0.960985 + 0.276600i \(0.0892078\pi\)
−0.240950 + 0.970538i \(0.577459\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.88255 8.45682i −0.175727 0.304368i
\(773\) 18.0698 + 31.2978i 0.649925 + 1.12570i 0.983140 + 0.182853i \(0.0585332\pi\)
−0.333215 + 0.942851i \(0.608133\pi\)
\(774\) 0 0
\(775\) 3.35896 5.81788i 0.120657 0.208985i
\(776\) −0.712008 + 1.23323i −0.0255596 + 0.0442705i
\(777\) 0 0
\(778\) −10.8171 18.7357i −0.387811 0.671709i
\(779\) 41.7156 1.49462
\(780\) 0 0
\(781\) −20.2051 −0.722994
\(782\) 0.810892 1.40451i 0.0289974 0.0502251i
\(783\) 0 0
\(784\) 0 0
\(785\) 7.03961 12.1930i 0.251254 0.435186i
\(786\) 0 0
\(787\) −22.3189 + 38.6574i −0.795582 + 1.37799i 0.126888 + 0.991917i \(0.459501\pi\)
−0.922469 + 0.386071i \(0.873832\pi\)
\(788\) −9.12178 + 15.7994i −0.324950 + 0.562830i
\(789\) 0 0
\(790\) −6.66071 + 11.5367i −0.236977 + 0.410457i
\(791\) 0 0
\(792\) 0 0
\(793\) −10.7694 + 18.6532i −0.382433 + 0.662394i
\(794\) 4.10617 0.145722
\(795\)