Properties

Label 288.2.i.f.193.2
Level $288$
Weight $2$
Character 288.193
Analytic conductor $2.300$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.170772624.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 12 x^{3} + 20 x^{2} - 24 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.2
Root \(1.41203 - 0.0786378i\) of defining polynomial
Character \(\chi\) \(=\) 288.193
Dual form 288.2.i.f.97.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.637910 + 1.61030i) q^{3} +(1.68614 - 2.92048i) q^{5} +(-2.35143 - 4.07279i) q^{7} +(-2.18614 - 2.05446i) q^{9} +O(q^{10})\) \(q+(-0.637910 + 1.61030i) q^{3} +(1.68614 - 2.92048i) q^{5} +(-2.35143 - 4.07279i) q^{7} +(-2.18614 - 2.05446i) q^{9} +(-0.437696 - 0.758112i) q^{11} +(0.686141 - 1.18843i) q^{13} +(3.62725 + 4.57820i) q^{15} -2.37228 q^{17} +5.57825 q^{19} +(8.05842 - 1.18843i) q^{21} +(-2.35143 + 4.07279i) q^{23} +(-3.18614 - 5.51856i) q^{25} +(4.70285 - 2.20979i) q^{27} +(2.68614 + 4.65253i) q^{29} +(3.22682 - 5.58902i) q^{31} +(1.50000 - 0.221215i) q^{33} -15.8593 q^{35} +4.00000 q^{37} +(1.47603 + 1.86301i) q^{39} +(-0.500000 + 0.866025i) q^{41} +(0.437696 + 0.758112i) q^{43} +(-9.68614 + 2.92048i) q^{45} +(-2.35143 - 4.07279i) q^{47} +(-7.55842 + 13.0916i) q^{49} +(1.51330 - 3.82009i) q^{51} -4.00000 q^{53} -2.95207 q^{55} +(-3.55842 + 8.98266i) q^{57} +(-4.26516 + 7.38747i) q^{59} +(1.05842 + 1.83324i) q^{61} +(-3.22682 + 13.7346i) q^{63} +(-2.31386 - 4.00772i) q^{65} +(4.26516 - 7.38747i) q^{67} +(-5.05842 - 6.38458i) q^{69} +9.40571 q^{71} +10.3723 q^{73} +(10.9190 - 1.61030i) q^{75} +(-2.05842 + 3.56529i) q^{77} +(-3.22682 - 5.58902i) q^{79} +(0.558422 + 8.98266i) q^{81} +(1.47603 + 2.55657i) q^{83} +(-4.00000 + 6.92820i) q^{85} +(-9.20550 + 1.35760i) q^{87} +12.7446 q^{89} -6.45364 q^{91} +(6.94158 + 8.76144i) q^{93} +(9.40571 - 16.2912i) q^{95} +(-4.50000 - 7.79423i) q^{97} +(-0.600642 + 2.55657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{5} - 6q^{9} + O(q^{10}) \) \( 8q + 2q^{5} - 6q^{9} - 6q^{13} + 4q^{17} + 30q^{21} - 14q^{25} + 10q^{29} + 12q^{33} + 32q^{37} - 4q^{41} - 66q^{45} - 26q^{49} - 32q^{53} + 6q^{57} - 26q^{61} - 30q^{65} - 6q^{69} + 60q^{73} + 18q^{77} - 30q^{81} - 32q^{85} + 56q^{89} + 90q^{93} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) −0.637910 + 1.61030i −0.368298 + 0.929708i
\(4\) 0 0
\(5\) 1.68614 2.92048i 0.754065 1.30608i −0.191773 0.981439i \(-0.561424\pi\)
0.945838 0.324640i \(-0.105243\pi\)
\(6\) 0 0
\(7\) −2.35143 4.07279i −0.888756 1.53937i −0.841347 0.540495i \(-0.818237\pi\)
−0.0474088 0.998876i \(-0.515096\pi\)
\(8\) 0 0
\(9\) −2.18614 2.05446i −0.728714 0.684819i
\(10\) 0 0
\(11\) −0.437696 0.758112i −0.131970 0.228579i 0.792466 0.609917i \(-0.208797\pi\)
−0.924436 + 0.381337i \(0.875464\pi\)
\(12\) 0 0
\(13\) 0.686141 1.18843i 0.190301 0.329611i −0.755049 0.655669i \(-0.772387\pi\)
0.945350 + 0.326057i \(0.105720\pi\)
\(14\) 0 0
\(15\) 3.62725 + 4.57820i 0.936551 + 1.18209i
\(16\) 0 0
\(17\) −2.37228 −0.575363 −0.287681 0.957726i \(-0.592884\pi\)
−0.287681 + 0.957726i \(0.592884\pi\)
\(18\) 0 0
\(19\) 5.57825 1.27974 0.639869 0.768484i \(-0.278989\pi\)
0.639869 + 0.768484i \(0.278989\pi\)
\(20\) 0 0
\(21\) 8.05842 1.18843i 1.75849 0.259337i
\(22\) 0 0
\(23\) −2.35143 + 4.07279i −0.490307 + 0.849236i −0.999938 0.0111571i \(-0.996448\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(24\) 0 0
\(25\) −3.18614 5.51856i −0.637228 1.10371i
\(26\) 0 0
\(27\) 4.70285 2.20979i 0.905065 0.425274i
\(28\) 0 0
\(29\) 2.68614 + 4.65253i 0.498804 + 0.863954i 0.999999 0.00138070i \(-0.000439492\pi\)
−0.501195 + 0.865334i \(0.667106\pi\)
\(30\) 0 0
\(31\) 3.22682 5.58902i 0.579554 1.00382i −0.415976 0.909375i \(-0.636560\pi\)
0.995530 0.0944415i \(-0.0301065\pi\)
\(32\) 0 0
\(33\) 1.50000 0.221215i 0.261116 0.0385086i
\(34\) 0 0
\(35\) −15.8593 −2.68072
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 1.47603 + 1.86301i 0.236355 + 0.298320i
\(40\) 0 0
\(41\) −0.500000 + 0.866025i −0.0780869 + 0.135250i −0.902424 0.430848i \(-0.858214\pi\)
0.824338 + 0.566099i \(0.191548\pi\)
\(42\) 0 0
\(43\) 0.437696 + 0.758112i 0.0667481 + 0.115611i 0.897468 0.441079i \(-0.145404\pi\)
−0.830720 + 0.556690i \(0.812071\pi\)
\(44\) 0 0
\(45\) −9.68614 + 2.92048i −1.44392 + 0.435360i
\(46\) 0 0
\(47\) −2.35143 4.07279i −0.342991 0.594078i 0.641996 0.766708i \(-0.278107\pi\)
−0.984987 + 0.172630i \(0.944773\pi\)
\(48\) 0 0
\(49\) −7.55842 + 13.0916i −1.07977 + 1.87022i
\(50\) 0 0
\(51\) 1.51330 3.82009i 0.211905 0.534919i
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) −2.95207 −0.398057
\(56\) 0 0
\(57\) −3.55842 + 8.98266i −0.471325 + 1.18978i
\(58\) 0 0
\(59\) −4.26516 + 7.38747i −0.555276 + 0.961767i 0.442606 + 0.896716i \(0.354054\pi\)
−0.997882 + 0.0650505i \(0.979279\pi\)
\(60\) 0 0
\(61\) 1.05842 + 1.83324i 0.135517 + 0.234722i 0.925795 0.378026i \(-0.123397\pi\)
−0.790278 + 0.612749i \(0.790064\pi\)
\(62\) 0 0
\(63\) −3.22682 + 13.7346i −0.406541 + 1.73040i
\(64\) 0 0
\(65\) −2.31386 4.00772i −0.286999 0.497097i
\(66\) 0 0
\(67\) 4.26516 7.38747i 0.521072 0.902523i −0.478628 0.878018i \(-0.658866\pi\)
0.999700 0.0245053i \(-0.00780106\pi\)
\(68\) 0 0
\(69\) −5.05842 6.38458i −0.608962 0.768613i
\(70\) 0 0
\(71\) 9.40571 1.11625 0.558126 0.829756i \(-0.311520\pi\)
0.558126 + 0.829756i \(0.311520\pi\)
\(72\) 0 0
\(73\) 10.3723 1.21398 0.606992 0.794708i \(-0.292376\pi\)
0.606992 + 0.794708i \(0.292376\pi\)
\(74\) 0 0
\(75\) 10.9190 1.61030i 1.26082 0.185942i
\(76\) 0 0
\(77\) −2.05842 + 3.56529i −0.234579 + 0.406303i
\(78\) 0 0
\(79\) −3.22682 5.58902i −0.363046 0.628813i 0.625415 0.780292i \(-0.284930\pi\)
−0.988460 + 0.151479i \(0.951596\pi\)
\(80\) 0 0
\(81\) 0.558422 + 8.98266i 0.0620469 + 0.998073i
\(82\) 0 0
\(83\) 1.47603 + 2.55657i 0.162016 + 0.280620i 0.935592 0.353084i \(-0.114867\pi\)
−0.773576 + 0.633704i \(0.781534\pi\)
\(84\) 0 0
\(85\) −4.00000 + 6.92820i −0.433861 + 0.751469i
\(86\) 0 0
\(87\) −9.20550 + 1.35760i −0.986933 + 0.145550i
\(88\) 0 0
\(89\) 12.7446 1.35092 0.675460 0.737396i \(-0.263945\pi\)
0.675460 + 0.737396i \(0.263945\pi\)
\(90\) 0 0
\(91\) −6.45364 −0.676525
\(92\) 0 0
\(93\) 6.94158 + 8.76144i 0.719808 + 0.908519i
\(94\) 0 0
\(95\) 9.40571 16.2912i 0.965005 1.67144i
\(96\) 0 0
\(97\) −4.50000 7.79423i −0.456906 0.791384i 0.541890 0.840450i \(-0.317709\pi\)
−0.998796 + 0.0490655i \(0.984376\pi\)
\(98\) 0 0
\(99\) −0.600642 + 2.55657i −0.0603668 + 0.256945i
\(100\) 0 0
\(101\) −1.05842 1.83324i −0.105317 0.182414i 0.808551 0.588426i \(-0.200252\pi\)
−0.913868 + 0.406012i \(0.866919\pi\)
\(102\) 0 0
\(103\) 2.35143 4.07279i 0.231693 0.401304i −0.726613 0.687047i \(-0.758907\pi\)
0.958306 + 0.285742i \(0.0922402\pi\)
\(104\) 0 0
\(105\) 10.1168 25.5383i 0.987303 2.49229i
\(106\) 0 0
\(107\) 5.57825 0.539270 0.269635 0.962963i \(-0.413097\pi\)
0.269635 + 0.962963i \(0.413097\pi\)
\(108\) 0 0
\(109\) −5.48913 −0.525763 −0.262881 0.964828i \(-0.584673\pi\)
−0.262881 + 0.964828i \(0.584673\pi\)
\(110\) 0 0
\(111\) −2.55164 + 6.44121i −0.242191 + 0.611372i
\(112\) 0 0
\(113\) −8.68614 + 15.0448i −0.817123 + 1.41530i 0.0906698 + 0.995881i \(0.471099\pi\)
−0.907793 + 0.419418i \(0.862234\pi\)
\(114\) 0 0
\(115\) 7.92967 + 13.7346i 0.739446 + 1.28076i
\(116\) 0 0
\(117\) −3.94158 + 1.18843i −0.364399 + 0.109870i
\(118\) 0 0
\(119\) 5.57825 + 9.66181i 0.511357 + 0.885696i
\(120\) 0 0
\(121\) 5.11684 8.86263i 0.465168 0.805694i
\(122\) 0 0
\(123\) −1.07561 1.35760i −0.0969842 0.122410i
\(124\) 0 0
\(125\) −4.62772 −0.413916
\(126\) 0 0
\(127\) −11.1565 −0.989979 −0.494989 0.868899i \(-0.664828\pi\)
−0.494989 + 0.868899i \(0.664828\pi\)
\(128\) 0 0
\(129\) −1.50000 + 0.221215i −0.132068 + 0.0194769i
\(130\) 0 0
\(131\) −3.22682 + 5.58902i −0.281929 + 0.488315i −0.971860 0.235560i \(-0.924307\pi\)
0.689931 + 0.723875i \(0.257641\pi\)
\(132\) 0 0
\(133\) −13.1168 22.7190i −1.13737 1.96999i
\(134\) 0 0
\(135\) 1.47603 17.4606i 0.127037 1.50277i
\(136\) 0 0
\(137\) −5.24456 9.08385i −0.448073 0.776086i 0.550187 0.835041i \(-0.314556\pi\)
−0.998261 + 0.0589556i \(0.981223\pi\)
\(138\) 0 0
\(139\) −9.84341 + 17.0493i −0.834907 + 1.44610i 0.0591995 + 0.998246i \(0.481145\pi\)
−0.894106 + 0.447855i \(0.852188\pi\)
\(140\) 0 0
\(141\) 8.05842 1.18843i 0.678642 0.100084i
\(142\) 0 0
\(143\) −1.20128 −0.100456
\(144\) 0 0
\(145\) 18.1168 1.50452
\(146\) 0 0
\(147\) −16.2598 20.5226i −1.34108 1.69267i
\(148\) 0 0
\(149\) 8.68614 15.0448i 0.711596 1.23252i −0.252661 0.967555i \(-0.581306\pi\)
0.964258 0.264966i \(-0.0853608\pi\)
\(150\) 0 0
\(151\) 2.35143 + 4.07279i 0.191356 + 0.331439i 0.945700 0.325041i \(-0.105378\pi\)
−0.754344 + 0.656480i \(0.772045\pi\)
\(152\) 0 0
\(153\) 5.18614 + 4.87375i 0.419275 + 0.394019i
\(154\) 0 0
\(155\) −10.8817 18.8477i −0.874043 1.51389i
\(156\) 0 0
\(157\) −7.05842 + 12.2255i −0.563323 + 0.975705i 0.433880 + 0.900971i \(0.357144\pi\)
−0.997203 + 0.0747341i \(0.976189\pi\)
\(158\) 0 0
\(159\) 2.55164 6.44121i 0.202358 0.510821i
\(160\) 0 0
\(161\) 22.1168 1.74305
\(162\) 0 0
\(163\) 18.8114 1.47342 0.736712 0.676207i \(-0.236377\pi\)
0.736712 + 0.676207i \(0.236377\pi\)
\(164\) 0 0
\(165\) 1.88316 4.75372i 0.146603 0.370077i
\(166\) 0 0
\(167\) −3.22682 + 5.58902i −0.249699 + 0.432491i −0.963442 0.267916i \(-0.913665\pi\)
0.713743 + 0.700407i \(0.246998\pi\)
\(168\) 0 0
\(169\) 5.55842 + 9.62747i 0.427571 + 0.740575i
\(170\) 0 0
\(171\) −12.1948 11.4603i −0.932562 0.876388i
\(172\) 0 0
\(173\) −2.68614 4.65253i −0.204223 0.353725i 0.745662 0.666325i \(-0.232134\pi\)
−0.949885 + 0.312599i \(0.898800\pi\)
\(174\) 0 0
\(175\) −14.9840 + 25.9530i −1.13268 + 1.96186i
\(176\) 0 0
\(177\) −9.17527 11.5807i −0.689655 0.870461i
\(178\) 0 0
\(179\) 18.8114 1.40603 0.703016 0.711174i \(-0.251836\pi\)
0.703016 + 0.711174i \(0.251836\pi\)
\(180\) 0 0
\(181\) 26.2337 1.94993 0.974967 0.222348i \(-0.0713722\pi\)
0.974967 + 0.222348i \(0.0713722\pi\)
\(182\) 0 0
\(183\) −3.62725 + 0.534935i −0.268134 + 0.0395435i
\(184\) 0 0
\(185\) 6.74456 11.6819i 0.495870 0.858872i
\(186\) 0 0
\(187\) 1.03834 + 1.79846i 0.0759308 + 0.131516i
\(188\) 0 0
\(189\) −20.0584 13.9576i −1.45904 1.01527i
\(190\) 0 0
\(191\) 8.80507 + 15.2508i 0.637112 + 1.10351i 0.986063 + 0.166370i \(0.0532046\pi\)
−0.348951 + 0.937141i \(0.613462\pi\)
\(192\) 0 0
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) 0 0
\(195\) 7.92967 1.16944i 0.567856 0.0837456i
\(196\) 0 0
\(197\) −10.7446 −0.765518 −0.382759 0.923848i \(-0.625026\pi\)
−0.382759 + 0.923848i \(0.625026\pi\)
\(198\) 0 0
\(199\) 17.0606 1.20940 0.604698 0.796455i \(-0.293294\pi\)
0.604698 + 0.796455i \(0.293294\pi\)
\(200\) 0 0
\(201\) 9.17527 + 11.5807i 0.647173 + 0.816842i
\(202\) 0 0
\(203\) 12.6325 21.8802i 0.886630 1.53569i
\(204\) 0 0
\(205\) 1.68614 + 2.92048i 0.117765 + 0.203975i
\(206\) 0 0
\(207\) 13.5079 4.07279i 0.938865 0.283079i
\(208\) 0 0
\(209\) −2.44158 4.22894i −0.168887 0.292522i
\(210\) 0 0
\(211\) −7.92967 + 13.7346i −0.545901 + 0.945529i 0.452648 + 0.891689i \(0.350479\pi\)
−0.998550 + 0.0538397i \(0.982854\pi\)
\(212\) 0 0
\(213\) −6.00000 + 15.1460i −0.411113 + 1.03779i
\(214\) 0 0
\(215\) 2.95207 0.201329
\(216\) 0 0
\(217\) −30.3505 −2.06033
\(218\) 0 0
\(219\) −6.61659 + 16.7025i −0.447107 + 1.12865i
\(220\) 0 0
\(221\) −1.62772 + 2.81929i −0.109492 + 0.189646i
\(222\) 0 0
\(223\) −2.35143 4.07279i −0.157463 0.272734i 0.776490 0.630130i \(-0.216998\pi\)
−0.933953 + 0.357395i \(0.883665\pi\)
\(224\) 0 0
\(225\) −4.37228 + 18.6101i −0.291485 + 1.24068i
\(226\) 0 0
\(227\) 10.7188 + 18.5655i 0.711432 + 1.23224i 0.964320 + 0.264740i \(0.0852862\pi\)
−0.252888 + 0.967496i \(0.581380\pi\)
\(228\) 0 0
\(229\) −0.686141 + 1.18843i −0.0453415 + 0.0785337i −0.887805 0.460219i \(-0.847771\pi\)
0.842464 + 0.538753i \(0.181104\pi\)
\(230\) 0 0
\(231\) −4.42810 5.58902i −0.291348 0.367730i
\(232\) 0 0
\(233\) −25.8614 −1.69424 −0.847119 0.531404i \(-0.821665\pi\)
−0.847119 + 0.531404i \(0.821665\pi\)
\(234\) 0 0
\(235\) −15.8593 −1.03455
\(236\) 0 0
\(237\) 11.0584 1.63086i 0.718322 0.105936i
\(238\) 0 0
\(239\) 8.80507 15.2508i 0.569552 0.986494i −0.427058 0.904224i \(-0.640450\pi\)
0.996610 0.0822694i \(-0.0262168\pi\)
\(240\) 0 0
\(241\) −5.87228 10.1711i −0.378267 0.655177i 0.612543 0.790437i \(-0.290147\pi\)
−0.990810 + 0.135260i \(0.956813\pi\)
\(242\) 0 0
\(243\) −14.8210 4.83090i −0.950768 0.309903i
\(244\) 0 0
\(245\) 25.4891 + 44.1485i 1.62844 + 2.82054i
\(246\) 0 0
\(247\) 3.82746 6.62936i 0.243536 0.421816i
\(248\) 0 0
\(249\) −5.05842 + 0.746000i −0.320564 + 0.0472758i
\(250\) 0 0
\(251\) 16.7347 1.05629 0.528144 0.849155i \(-0.322888\pi\)
0.528144 + 0.849155i \(0.322888\pi\)
\(252\) 0 0
\(253\) 4.11684 0.258824
\(254\) 0 0
\(255\) −8.60485 10.8608i −0.538857 0.680128i
\(256\) 0 0
\(257\) −8.24456 + 14.2800i −0.514282 + 0.890762i 0.485581 + 0.874192i \(0.338608\pi\)
−0.999863 + 0.0165703i \(0.994725\pi\)
\(258\) 0 0
\(259\) −9.40571 16.2912i −0.584442 1.01228i
\(260\) 0 0
\(261\) 3.68614 15.6896i 0.228166 0.971165i
\(262\) 0 0
\(263\) −8.80507 15.2508i −0.542944 0.940406i −0.998733 0.0503185i \(-0.983976\pi\)
0.455790 0.890088i \(-0.349357\pi\)
\(264\) 0 0
\(265\) −6.74456 + 11.6819i −0.414315 + 0.717615i
\(266\) 0 0
\(267\) −8.12989 + 20.5226i −0.497541 + 1.25596i
\(268\) 0 0
\(269\) −13.4891 −0.822446 −0.411223 0.911535i \(-0.634898\pi\)
−0.411223 + 0.911535i \(0.634898\pi\)
\(270\) 0 0
\(271\) −22.3130 −1.35542 −0.677709 0.735330i \(-0.737027\pi\)
−0.677709 + 0.735330i \(0.737027\pi\)
\(272\) 0 0
\(273\) 4.11684 10.3923i 0.249163 0.628971i
\(274\) 0 0
\(275\) −2.78912 + 4.83090i −0.168190 + 0.291314i
\(276\) 0 0
\(277\) 2.05842 + 3.56529i 0.123679 + 0.214218i 0.921216 0.389052i \(-0.127197\pi\)
−0.797537 + 0.603270i \(0.793864\pi\)
\(278\) 0 0
\(279\) −18.5367 + 5.58902i −1.10976 + 0.334606i
\(280\) 0 0
\(281\) 1.43070 + 2.47805i 0.0853486 + 0.147828i 0.905540 0.424262i \(-0.139466\pi\)
−0.820191 + 0.572090i \(0.806133\pi\)
\(282\) 0 0
\(283\) 7.92967 13.7346i 0.471370 0.816437i −0.528093 0.849186i \(-0.677093\pi\)
0.999464 + 0.0327491i \(0.0104262\pi\)
\(284\) 0 0
\(285\) 20.2337 + 25.5383i 1.19854 + 1.51276i
\(286\) 0 0
\(287\) 4.70285 0.277601
\(288\) 0 0
\(289\) −11.3723 −0.668958
\(290\) 0 0
\(291\) 15.4217 2.27434i 0.904033 0.133324i
\(292\) 0 0
\(293\) 7.31386 12.6680i 0.427280 0.740071i −0.569350 0.822095i \(-0.692805\pi\)
0.996630 + 0.0820241i \(0.0261384\pi\)
\(294\) 0 0
\(295\) 14.3833 + 24.9126i 0.837429 + 1.45047i
\(296\) 0 0
\(297\) −3.73369 2.59808i −0.216651 0.150756i
\(298\) 0 0
\(299\) 3.22682 + 5.58902i 0.186612 + 0.323221i
\(300\) 0 0
\(301\) 2.05842 3.56529i 0.118645 0.205500i
\(302\) 0 0
\(303\) 3.62725 0.534935i 0.208380 0.0307312i
\(304\) 0 0
\(305\) 7.13859 0.408755
\(306\) 0 0
\(307\) −20.8881 −1.19215 −0.596073 0.802930i \(-0.703273\pi\)
−0.596073 + 0.802930i \(0.703273\pi\)
\(308\) 0 0
\(309\) 5.05842 + 6.38458i 0.287764 + 0.363206i
\(310\) 0 0
\(311\) −13.5079 + 23.3964i −0.765964 + 1.32669i 0.173771 + 0.984786i \(0.444405\pi\)
−0.939735 + 0.341903i \(0.888929\pi\)
\(312\) 0 0
\(313\) 7.61684 + 13.1928i 0.430529 + 0.745699i 0.996919 0.0784388i \(-0.0249935\pi\)
−0.566389 + 0.824138i \(0.691660\pi\)
\(314\) 0 0
\(315\) 34.6708 + 32.5823i 1.95348 + 1.83581i
\(316\) 0 0
\(317\) −1.31386 2.27567i −0.0737937 0.127814i 0.826767 0.562544i \(-0.190177\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(318\) 0 0
\(319\) 2.35143 4.07279i 0.131655 0.228033i
\(320\) 0 0
\(321\) −3.55842 + 8.98266i −0.198612 + 0.501363i
\(322\) 0 0
\(323\) −13.2332 −0.736313
\(324\) 0 0
\(325\) −8.74456 −0.485061
\(326\) 0 0
\(327\) 3.50157 8.83915i 0.193637 0.488806i
\(328\) 0 0
\(329\) −11.0584 + 19.1537i −0.609671 + 1.05598i
\(330\) 0 0
\(331\) −4.97760 8.62146i −0.273594 0.473879i 0.696186 0.717862i \(-0.254879\pi\)
−0.969779 + 0.243983i \(0.921546\pi\)
\(332\) 0 0
\(333\) −8.74456 8.21782i −0.479199 0.450334i
\(334\) 0 0
\(335\) −14.3833 24.9126i −0.785844 1.36112i
\(336\) 0 0
\(337\) 4.50000 7.79423i 0.245131 0.424579i −0.717038 0.697034i \(-0.754502\pi\)
0.962168 + 0.272456i \(0.0878358\pi\)
\(338\) 0 0
\(339\) −18.6857 23.5846i −1.01487 1.28094i
\(340\) 0 0
\(341\) −5.64947 −0.305936
\(342\) 0 0
\(343\) 38.1723 2.06111
\(344\) 0 0
\(345\) −27.1753 + 4.00772i −1.46307 + 0.215768i
\(346\) 0 0
\(347\) 4.26516 7.38747i 0.228966 0.396580i −0.728536 0.685007i \(-0.759799\pi\)
0.957502 + 0.288427i \(0.0931323\pi\)
\(348\) 0 0
\(349\) 2.94158 + 5.09496i 0.157459 + 0.272727i 0.933952 0.357399i \(-0.116336\pi\)
−0.776493 + 0.630126i \(0.783003\pi\)
\(350\) 0 0
\(351\) 0.600642 7.10524i 0.0320599 0.379250i
\(352\) 0 0
\(353\) −7.61684 13.1928i −0.405404 0.702180i 0.588965 0.808159i \(-0.299536\pi\)
−0.994368 + 0.105979i \(0.966202\pi\)
\(354\) 0 0
\(355\) 15.8593 27.4692i 0.841727 1.45791i
\(356\) 0 0
\(357\) −19.1168 + 2.81929i −1.01177 + 0.149213i
\(358\) 0 0
\(359\) −33.4695 −1.76645 −0.883226 0.468948i \(-0.844633\pi\)
−0.883226 + 0.468948i \(0.844633\pi\)
\(360\) 0 0
\(361\) 12.1168 0.637729
\(362\) 0 0
\(363\) 11.0074 + 13.8932i 0.577740 + 0.729205i
\(364\) 0 0
\(365\) 17.4891 30.2921i 0.915423 1.58556i
\(366\) 0 0
\(367\) 15.5846 + 26.9933i 0.813509 + 1.40904i 0.910393 + 0.413744i \(0.135779\pi\)
−0.0968838 + 0.995296i \(0.530888\pi\)
\(368\) 0 0
\(369\) 2.87228 0.866025i 0.149525 0.0450835i
\(370\) 0 0
\(371\) 9.40571 + 16.2912i 0.488320 + 0.845795i
\(372\) 0 0
\(373\) −0.0584220 + 0.101190i −0.00302498 + 0.00523941i −0.867534 0.497378i \(-0.834296\pi\)
0.864509 + 0.502617i \(0.167630\pi\)
\(374\) 0 0
\(375\) 2.95207 7.45202i 0.152444 0.384821i
\(376\) 0 0
\(377\) 7.37228 0.379692
\(378\) 0 0
\(379\) −3.82746 −0.196604 −0.0983018 0.995157i \(-0.531341\pi\)
−0.0983018 + 0.995157i \(0.531341\pi\)
\(380\) 0 0
\(381\) 7.11684 17.9653i 0.364607 0.920391i
\(382\) 0 0
\(383\) −10.8817 + 18.8477i −0.556031 + 0.963074i 0.441791 + 0.897118i \(0.354343\pi\)
−0.997823 + 0.0659564i \(0.978990\pi\)
\(384\) 0 0
\(385\) 6.94158 + 12.0232i 0.353776 + 0.612757i
\(386\) 0 0
\(387\) 0.600642 2.55657i 0.0305324 0.129958i
\(388\) 0 0
\(389\) −16.1753 28.0164i −0.820119 1.42049i −0.905594 0.424147i \(-0.860574\pi\)
0.0854750 0.996340i \(-0.472759\pi\)
\(390\) 0 0
\(391\) 5.57825 9.66181i 0.282104 0.488619i
\(392\) 0 0
\(393\) −6.94158 8.76144i −0.350156 0.441956i
\(394\) 0 0
\(395\) −21.7635 −1.09504
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 44.9519 6.62936i 2.25041 0.331883i
\(400\) 0 0
\(401\) 8.98913 15.5696i 0.448895 0.777510i −0.549419 0.835547i \(-0.685151\pi\)
0.998314 + 0.0580372i \(0.0184842\pi\)
\(402\) 0 0
\(403\) −4.42810 7.66970i −0.220580 0.382055i
\(404\) 0 0
\(405\) 27.1753 + 13.5152i 1.35035 + 0.671574i
\(406\) 0 0
\(407\) −1.75079 3.03245i −0.0867832 0.150313i
\(408\) 0 0
\(409\) 14.8723 25.7595i 0.735387 1.27373i −0.219166 0.975688i \(-0.570334\pi\)
0.954553 0.298040i \(-0.0963329\pi\)
\(410\) 0 0
\(411\) 17.9733 2.65064i 0.886557 0.130747i
\(412\) 0 0
\(413\) 40.1168 1.97402
\(414\) 0 0
\(415\) 9.95521 0.488682
\(416\) 0 0
\(417\) −21.1753 26.7268i −1.03696 1.30882i
\(418\) 0 0
\(419\) −7.92967 + 13.7346i −0.387390 + 0.670979i −0.992098 0.125468i \(-0.959957\pi\)
0.604708 + 0.796448i \(0.293290\pi\)
\(420\) 0 0
\(421\) 8.31386 + 14.4000i 0.405193 + 0.701814i 0.994344 0.106208i \(-0.0338711\pi\)
−0.589151 + 0.808023i \(0.700538\pi\)
\(422\) 0 0
\(423\) −3.22682 + 13.7346i −0.156893 + 0.667799i
\(424\) 0 0
\(425\) 7.55842 + 13.0916i 0.366637 + 0.635034i
\(426\) 0 0
\(427\) 4.97760 8.62146i 0.240883 0.417222i
\(428\) 0 0
\(429\) 0.766312 1.93443i 0.0369979 0.0933952i
\(430\) 0 0
\(431\) −11.1565 −0.537389 −0.268695 0.963225i \(-0.586592\pi\)
−0.268695 + 0.963225i \(0.586592\pi\)
\(432\) 0 0
\(433\) −0.883156 −0.0424418 −0.0212209 0.999775i \(-0.506755\pi\)
−0.0212209 + 0.999775i \(0.506755\pi\)
\(434\) 0 0
\(435\) −11.5569 + 29.1736i −0.554112 + 1.39877i
\(436\) 0 0
\(437\) −13.1168 + 22.7190i −0.627464 + 1.08680i
\(438\) 0 0
\(439\) −10.8817 18.8477i −0.519357 0.899553i −0.999747 0.0224981i \(-0.992838\pi\)
0.480390 0.877055i \(-0.340495\pi\)
\(440\) 0 0
\(441\) 43.4198 13.0916i 2.06761 0.623408i
\(442\) 0 0
\(443\) −10.7188 18.5655i −0.509265 0.882074i −0.999942 0.0107321i \(-0.996584\pi\)
0.490677 0.871342i \(-0.336750\pi\)
\(444\) 0 0
\(445\) 21.4891 37.2203i 1.01868 1.76441i
\(446\) 0 0
\(447\) 18.6857 + 23.5846i 0.883805 + 1.11551i
\(448\) 0 0
\(449\) −0.883156 −0.0416787 −0.0208394 0.999783i \(-0.506634\pi\)
−0.0208394 + 0.999783i \(0.506634\pi\)
\(450\) 0 0
\(451\) 0.875393 0.0412206
\(452\) 0 0
\(453\) −8.05842 + 1.18843i −0.378618 + 0.0558373i
\(454\) 0 0
\(455\) −10.8817 + 18.8477i −0.510144 + 0.883595i
\(456\) 0 0
\(457\) −9.98913 17.3017i −0.467272 0.809338i 0.532029 0.846726i \(-0.321430\pi\)
−0.999301 + 0.0373879i \(0.988096\pi\)
\(458\) 0 0
\(459\) −11.1565 + 5.24224i −0.520741 + 0.244687i
\(460\) 0 0
\(461\) 5.94158 + 10.2911i 0.276727 + 0.479305i 0.970569 0.240822i \(-0.0774169\pi\)
−0.693842 + 0.720127i \(0.744084\pi\)
\(462\) 0 0
\(463\) −0.274750 + 0.475881i −0.0127687 + 0.0221161i −0.872339 0.488901i \(-0.837398\pi\)
0.859570 + 0.511017i \(0.170731\pi\)
\(464\) 0 0
\(465\) 37.2921 5.49972i 1.72938 0.255043i
\(466\) 0 0
\(467\) 9.73160 0.450325 0.225162 0.974321i \(-0.427709\pi\)
0.225162 + 0.974321i \(0.427709\pi\)
\(468\) 0 0
\(469\) −40.1168 −1.85242
\(470\) 0 0
\(471\) −15.1842 19.1650i −0.699650 0.883076i
\(472\) 0 0
\(473\) 0.383156 0.663646i 0.0176175 0.0305145i
\(474\) 0 0
\(475\) −17.7731 30.7839i −0.815485 1.41246i
\(476\) 0 0
\(477\) 8.74456 + 8.21782i 0.400386 + 0.376268i
\(478\) 0 0
\(479\) 2.35143 + 4.07279i 0.107439 + 0.186091i 0.914732 0.404061i \(-0.132401\pi\)
−0.807293 + 0.590151i \(0.799068\pi\)
\(480\) 0 0
\(481\) 2.74456 4.75372i 0.125141 0.216751i
\(482\) 0 0
\(483\) −14.1086 + 35.6148i −0.641962 + 1.62053i
\(484\) 0 0
\(485\) −30.3505 −1.37815
\(486\) 0 0
\(487\) −11.1565 −0.505549 −0.252775 0.967525i \(-0.581343\pi\)
−0.252775 + 0.967525i \(0.581343\pi\)
\(488\) 0 0
\(489\) −12.0000 + 30.2921i −0.542659 + 1.36985i
\(490\) 0 0
\(491\) 20.1245 34.8567i 0.908206 1.57306i 0.0916519 0.995791i \(-0.470785\pi\)
0.816554 0.577268i \(-0.195881\pi\)
\(492\) 0 0
\(493\) −6.37228 11.0371i −0.286993 0.497087i
\(494\) 0 0
\(495\) 6.45364 + 6.06490i 0.290070 + 0.272597i
\(496\) 0 0
\(497\) −22.1168 38.3075i −0.992076 1.71833i
\(498\) 0 0
\(499\) 6.89134 11.9361i 0.308499 0.534335i −0.669536 0.742780i \(-0.733507\pi\)
0.978034 + 0.208445i \(0.0668402\pi\)
\(500\) 0 0
\(501\) −6.94158 8.76144i −0.310127 0.391432i
\(502\) 0 0
\(503\) −31.7187 −1.41427 −0.707133 0.707080i \(-0.750012\pi\)
−0.707133 + 0.707080i \(0.750012\pi\)
\(504\) 0 0
\(505\) −7.13859 −0.317663
\(506\) 0 0
\(507\) −19.0489 + 2.80927i −0.845991 + 0.124764i
\(508\) 0 0
\(509\) −19.1753 + 33.2125i −0.849929 + 1.47212i 0.0313424 + 0.999509i \(0.490022\pi\)
−0.881271 + 0.472611i \(0.843312\pi\)
\(510\) 0 0
\(511\) −24.3897 42.2441i −1.07894 1.86877i
\(512\) 0 0
\(513\) 26.2337 12.3267i 1.15825 0.544239i
\(514\) 0 0
\(515\) −7.92967 13.7346i −0.349423 0.605219i
\(516\) 0 0
\(517\) −2.05842 + 3.56529i −0.0905293 + 0.156801i
\(518\) 0 0
\(519\) 9.20550 1.35760i 0.404076 0.0595919i
\(520\) 0 0
\(521\) 35.3505 1.54873 0.774367 0.632736i \(-0.218068\pi\)
0.774367 + 0.632736i \(0.218068\pi\)
\(522\) 0 0
\(523\) 12.9073 0.564396 0.282198 0.959356i \(-0.408936\pi\)
0.282198 + 0.959356i \(0.408936\pi\)
\(524\) 0 0
\(525\) −32.2337 40.6844i −1.40679 1.77561i
\(526\) 0 0
\(527\) −7.65492 + 13.2587i −0.333454 + 0.577559i
\(528\) 0 0
\(529\) 0.441578 + 0.764836i 0.0191990 + 0.0332537i
\(530\) 0 0
\(531\) 24.5015 7.38747i 1.06327 0.320589i
\(532\) 0 0
\(533\) 0.686141 + 1.18843i 0.0297201 + 0.0514766i
\(534\) 0 0
\(535\) 9.40571 16.2912i 0.406644 0.704329i
\(536\) 0 0
\(537\) −12.0000 + 30.2921i −0.517838 + 1.30720i
\(538\) 0 0
\(539\) 13.2332 0.569993
\(540\) 0 0
\(541\) −2.74456 −0.117998 −0.0589990 0.998258i \(-0.518791\pi\)
−0.0589990 + 0.998258i \(0.518791\pi\)
\(542\) 0 0
\(543\) −16.7347 + 42.2441i −0.718157 + 1.81287i
\(544\) 0 0
\(545\) −9.25544 + 16.0309i −0.396459 + 0.686688i
\(546\) 0 0
\(547\) 5.14055 + 8.90370i 0.219794 + 0.380695i 0.954745 0.297426i \(-0.0961281\pi\)
−0.734951 + 0.678120i \(0.762795\pi\)
\(548\) 0 0
\(549\) 1.45245 6.18220i 0.0619892 0.263850i
\(550\) 0 0
\(551\) 14.9840 + 25.9530i 0.638338 + 1.10563i
\(552\) 0 0
\(553\) −15.1753 + 26.2843i −0.645318 + 1.11772i
\(554\) 0 0
\(555\) 14.5090 + 18.3128i 0.615872 + 0.777335i
\(556\) 0 0
\(557\) −7.25544 −0.307423 −0.153711 0.988116i \(-0.549123\pi\)
−0.153711 + 0.988116i \(0.549123\pi\)
\(558\) 0 0
\(559\) 1.20128 0.0508089
\(560\) 0 0
\(561\) −3.55842 + 0.524785i −0.150237 + 0.0221564i
\(562\) 0 0
\(563\) −3.38977 + 5.87125i −0.142862 + 0.247444i −0.928573 0.371150i \(-0.878964\pi\)
0.785711 + 0.618593i \(0.212297\pi\)
\(564\) 0 0
\(565\) 29.2921 + 50.7354i 1.23233 + 2.13446i
\(566\) 0 0
\(567\) 35.2714 23.3964i 1.48126 0.982557i
\(568\) 0 0
\(569\) 14.1277 + 24.4699i 0.592265 + 1.02583i 0.993927 + 0.110045i \(0.0350994\pi\)
−0.401662 + 0.915788i \(0.631567\pi\)
\(570\) 0 0
\(571\) −20.1245 + 34.8567i −0.842184 + 1.45871i 0.0458596 + 0.998948i \(0.485397\pi\)
−0.888044 + 0.459758i \(0.847936\pi\)
\(572\) 0 0
\(573\) −30.1753 + 4.45015i −1.26059 + 0.185908i
\(574\) 0 0
\(575\) 29.9679 1.24975
\(576\) 0 0
\(577\) 0.883156 0.0367663 0.0183831 0.999831i \(-0.494148\pi\)
0.0183831 + 0.999831i \(0.494148\pi\)
\(578\) 0 0
\(579\) −1.07561 1.35760i −0.0447007 0.0564198i
\(580\) 0 0
\(581\) 6.94158 12.0232i 0.287985 0.498805i
\(582\) 0 0
\(583\) 1.75079 + 3.03245i 0.0725101 + 0.125591i
\(584\) 0 0
\(585\) −3.17527 + 13.5152i −0.131281 + 0.558783i
\(586\) 0 0
\(587\) 19.2491 + 33.3404i 0.794496 + 1.37611i 0.923159 + 0.384419i \(0.125598\pi\)
−0.128663 + 0.991688i \(0.541068\pi\)
\(588\) 0 0
\(589\) 18.0000 31.1769i 0.741677 1.28462i
\(590\) 0 0
\(591\) 6.85407 17.3020i 0.281939 0.711708i
\(592\) 0 0
\(593\) 39.7228 1.63122 0.815610 0.578602i \(-0.196401\pi\)
0.815610 + 0.578602i \(0.196401\pi\)
\(594\) 0 0
\(595\) 37.6228 1.54239
\(596\) 0 0
\(597\) −10.8832 + 27.4728i −0.445418 + 1.12439i
\(598\) 0 0
\(599\) 15.5846 26.9933i 0.636769 1.10292i −0.349368 0.936986i \(-0.613604\pi\)
0.986137 0.165931i \(-0.0530630\pi\)
\(600\) 0 0
\(601\) 18.6168 + 32.2453i 0.759397 + 1.31531i 0.943159 + 0.332343i \(0.107839\pi\)
−0.183762 + 0.982971i \(0.558827\pi\)
\(602\) 0 0
\(603\) −24.5015 + 7.38747i −0.997777 + 0.300841i
\(604\) 0 0
\(605\) −17.2554 29.8873i −0.701533 1.21509i
\(606\) 0 0
\(607\) 0.274750 0.475881i 0.0111518 0.0193154i −0.860396 0.509627i \(-0.829784\pi\)
0.871547 + 0.490311i \(0.163117\pi\)
\(608\) 0 0
\(609\) 27.1753 + 34.2998i 1.10120 + 1.38990i
\(610\) 0 0
\(611\) −6.45364 −0.261086
\(612\) 0 0
\(613\) −32.4674 −1.31134 −0.655672 0.755045i \(-0.727615\pi\)
−0.655672 + 0.755045i \(0.727615\pi\)
\(614\) 0 0
\(615\) −5.77846 + 0.852189i −0.233010 + 0.0343636i
\(616\) 0 0
\(617\) 13.1277 22.7379i 0.528502 0.915392i −0.470946 0.882162i \(-0.656087\pi\)
0.999448 0.0332302i \(-0.0105794\pi\)
\(618\) 0 0
\(619\) 5.14055 + 8.90370i 0.206616 + 0.357870i 0.950646 0.310276i \(-0.100422\pi\)
−0.744030 + 0.668146i \(0.767088\pi\)
\(620\) 0 0
\(621\) −2.05842 + 24.3499i −0.0826016 + 0.977128i
\(622\) 0 0
\(623\) −29.9679 51.9060i −1.20064 2.07957i
\(624\) 0 0
\(625\) 8.12772 14.0776i 0.325109 0.563105i
\(626\) 0 0
\(627\) 8.36737 1.23399i 0.334161 0.0492809i
\(628\) 0 0
\(629\) −9.48913 −0.378356
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −17.0584 21.5306i −0.678011 0.855765i
\(634\) 0 0
\(635\) −18.8114 + 32.5823i −0.746508 + 1.29299i
\(636\) 0 0
\(637\) 10.3723 + 17.9653i 0.410965 + 0.711812i
\(638\) 0 0
\(639\) −20.5622 19.3236i −0.813428 0.764430i
\(640\) 0 0
\(641\) −1.12772 1.95327i −0.0445422 0.0771494i 0.842895 0.538078i \(-0.180850\pi\)
−0.887437 + 0.460929i \(0.847516\pi\)
\(642\) 0 0
\(643\) −1.31309 + 2.27434i −0.0517832 + 0.0896911i −0.890755 0.454484i \(-0.849824\pi\)
0.838972 + 0.544175i \(0.183157\pi\)
\(644\) 0 0
\(645\) −1.88316 + 4.75372i −0.0741492 + 0.187178i
\(646\) 0 0
\(647\) −4.15335 −0.163285 −0.0816426 0.996662i \(-0.526017\pi\)
−0.0816426 + 0.996662i \(0.526017\pi\)
\(648\) 0 0
\(649\) 7.46738 0.293120
\(650\) 0 0
\(651\) 19.3609 48.8735i 0.758814 1.91550i
\(652\) 0 0
\(653\) −11.9416 + 20.6834i −0.467310 + 0.809405i −0.999302 0.0373444i \(-0.988110\pi\)
0.531992 + 0.846749i \(0.321443\pi\)
\(654\) 0 0
\(655\) 10.8817 + 18.8477i 0.425185 + 0.736442i
\(656\) 0 0
\(657\) −22.6753 21.3094i −0.884646 0.831359i
\(658\) 0 0
\(659\) −20.2875 35.1389i −0.790287 1.36882i −0.925789 0.378040i \(-0.876598\pi\)
0.135502 0.990777i \(-0.456735\pi\)
\(660\) 0 0
\(661\) −7.05842 + 12.2255i −0.274541 + 0.475519i −0.970019 0.243028i \(-0.921859\pi\)
0.695478 + 0.718547i \(0.255193\pi\)
\(662\) 0 0
\(663\) −3.50157 4.41957i −0.135990 0.171642i
\(664\) 0 0
\(665\) −88.4674 −3.43062
\(666\) 0 0
\(667\) −25.2651 −0.978267
\(668\) 0 0
\(669\) 8.05842 1.18843i 0.311557 0.0459474i
\(670\) 0 0
\(671\) 0.926535 1.60481i 0.0357685 0.0619528i
\(672\) 0 0
\(673\) 14.1753 + 24.5523i 0.546416 + 0.946421i 0.998516 + 0.0544536i \(0.0173417\pi\)
−0.452100 + 0.891967i \(0.649325\pi\)
\(674\) 0 0
\(675\) −27.1788 18.9123i −1.04611 0.727934i
\(676\) 0 0
\(677\) 25.1753 + 43.6048i 0.967564 + 1.67587i 0.702562 + 0.711622i \(0.252039\pi\)
0.265002 + 0.964248i \(0.414627\pi\)
\(678\) 0 0
\(679\) −21.1628 + 36.6551i −0.812156 + 1.40669i
\(680\) 0 0
\(681\) −36.7337 + 5.41737i −1.40764 + 0.207594i
\(682\) 0 0
\(683\) −9.73160 −0.372369 −0.186185 0.982515i \(-0.559612\pi\)
−0.186185 + 0.982515i \(0.559612\pi\)
\(684\) 0 0
\(685\) −35.3723 −1.35151
\(686\) 0 0
\(687\) −1.47603 1.86301i −0.0563142 0.0710781i
\(688\) 0 0
\(689\) −2.74456 + 4.75372i −0.104560 + 0.181102i
\(690\) 0 0
\(691\) 9.13096 + 15.8153i 0.347358 + 0.601642i 0.985779 0.168045i \(-0.0537455\pi\)
−0.638421 + 0.769687i \(0.720412\pi\)
\(692\) 0 0
\(693\) 11.8247 3.56529i 0.449185 0.135434i
\(694\) 0 0
\(695\) 33.1947 + 57.4950i 1.25915 + 2.18091i
\(696\) 0 0
\(697\) 1.18614 2.05446i 0.0449283 0.0778181i
\(698\) 0 0
\(699\) 16.4973 41.6447i 0.623984 1.57515i
\(700\) 0 0
\(701\) 23.2554 0.878346 0.439173 0.898403i \(-0.355272\pi\)
0.439173 + 0.898403i \(0.355272\pi\)
\(702\) 0 0
\(703\) 22.3130 0.841550
\(704\) 0 0
\(705\) 10.1168 25.5383i 0.381022 0.961829i
\(706\) 0 0
\(707\) −4.97760 + 8.62146i −0.187202 + 0.324244i
\(708\) 0 0
\(709\) −13.8030 23.9075i −0.518382 0.897864i −0.999772 0.0213574i \(-0.993201\pi\)
0.481390 0.876507i \(-0.340132\pi\)
\(710\) 0 0
\(711\) −4.42810 + 18.8477i −0.166067 + 0.706845i
\(712\) 0 0
\(713\) 15.1753 + 26.2843i 0.568318 + 0.984356i
\(714\) 0 0
\(715\) −2.02554 + 3.50833i −0.0757507 + 0.131204i
\(716\) 0 0
\(717\) 18.9416 + 23.9075i 0.707386 + 0.892841i
\(718\) 0 0
\(719\) −15.3098 −0.570961 −0.285481 0.958385i \(-0.592153\pi\)
−0.285481 + 0.958385i \(0.592153\pi\)
\(720\) 0 0
\(721\) −22.1168 −0.823674
\(722\) 0 0
\(723\) 20.1245 2.96790i 0.748439 0.110377i
\(724\) 0 0
\(725\) 17.1168 29.6472i 0.635704 1.10107i
\(726\) 0 0
\(727\) 10.0064 + 17.3315i 0.371115 + 0.642790i 0.989737 0.142898i \(-0.0456422\pi\)
−0.618622 + 0.785689i \(0.712309\pi\)
\(728\) 0 0
\(729\) 17.2337 20.7846i 0.638285 0.769800i
\(730\) 0 0
\(731\) −1.03834 1.79846i −0.0384043 0.0665183i
\(732\) 0 0
\(733\) −20.0584 + 34.7422i −0.740875 + 1.28323i 0.211223 + 0.977438i \(0.432255\pi\)
−0.952097 + 0.305795i \(0.901078\pi\)
\(734\) 0 0
\(735\) −87.3521 + 12.8824i −3.22203 + 0.475175i
\(736\) 0 0
\(737\) −7.46738 −0.275064
\(738\) 0 0
\(739\) −7.32903 −0.269603 −0.134801 0.990873i \(-0.543040\pi\)
−0.134801 + 0.990873i \(0.543040\pi\)
\(740\) 0 0
\(741\) 8.23369 + 10.3923i 0.302472 + 0.381771i
\(742\) 0 0
\(743\) 24.6644 42.7200i 0.904850 1.56725i 0.0837309 0.996488i \(-0.473316\pi\)
0.821119 0.570757i \(-0.193350\pi\)
\(744\) 0 0
\(745\) −29.2921 50.7354i −1.07318 1.85880i
\(746\) 0 0
\(747\) 2.02554 8.62146i 0.0741105 0.315443i
\(748\) 0 0
\(749\) −13.1168 22.7190i −0.479279 0.830136i
\(750\) 0 0
\(751\) −10.8817 + 18.8477i −0.397081 + 0.687764i −0.993364 0.115010i \(-0.963310\pi\)
0.596284 + 0.802774i \(0.296643\pi\)
\(752\) 0 0
\(753\) −10.6753 + 26.9480i −0.389028 + 0.982039i
\(754\) 0 0
\(755\) 15.8593 0.577181
\(756\) 0 0
\(757\) 34.4674 1.25274 0.626369 0.779527i \(-0.284540\pi\)
0.626369 + 0.779527i \(0.284540\pi\)
\(758\) 0 0
\(759\) −2.62618 + 6.62936i −0.0953242 + 0.240630i
\(760\) 0 0
\(761\) −7.31386 + 12.6680i −0.265127 + 0.459214i −0.967597 0.252500i \(-0.918747\pi\)
0.702470 + 0.711714i \(0.252081\pi\)
\(762\) 0 0
\(763\) 12.9073 + 22.3561i 0.467275 + 0.809344i
\(764\) 0 0
\(765\) 22.9783 6.92820i 0.830780 0.250490i
\(766\) 0 0
\(767\) 5.85300 + 10.1377i 0.211339 + 0.366051i
\(768\) 0 0
\(769\) 16.0584 27.8140i 0.579082 1.00300i −0.416503 0.909134i \(-0.636745\pi\)
0.995585 0.0938645i \(-0.0299220\pi\)
\(770\) 0 0
\(771\) −17.7358 22.3856i −0.638740 0.806197i
\(772\) 0 0
\(773\) −7.25544 −0.260960 −0.130480 0.991451i \(-0.541652\pi\)
−0.130480 + 0.991451i \(0.541652\pi\)
\(774\) 0 0
\(775\) −41.1244 −1.47723
\(776\) 0 0
\(777\) 32.2337 4.75372i 1.15638 0.170539i
\(778\) 0 0
\(779\) −2.78912 + 4.83090i −0.0999307 + 0.173085i
\(780\) 0 0
\(781\) −4.11684 7.13058i −0.147312 0.255152i
\(782\) 0 0
\(783\) 22.9136 + 15.9444i 0.818866 + 0.569806i
\(784\) 0 0
\(785\) 23.8030 + 41.2280i 0.849565 + 1.47149i
\(786\) 0 0
\(787\) 4.42810 7.66970i 0.157845 0.273395i −0.776246 0.630430i \(-0.782879\pi\)
0.934091 + 0.357034i \(0.116212\pi\)
\(788\) 0 0
\(789\) 30.1753 4.45015i 1.07427 0.158430i
\(790\) 0 0
\(791\) 81.6993 2.90489
\(792\) 0 0
\(793\) 2.90491 0.103156
\(794\) 0 0
\(795\) −14.5090 18.3128i −0.514581 0.649488i
\(796\) 0 0