Properties

Label 684.3.m.a.353.19
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.19
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.19

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.358884 - 2.97846i) q^{3} +0.408400i q^{5} +(-0.674294 + 1.16791i) q^{7} +(-8.74240 + 2.13784i) q^{9} +O(q^{10})\) \(q+(-0.358884 - 2.97846i) q^{3} +0.408400i q^{5} +(-0.674294 + 1.16791i) q^{7} +(-8.74240 + 2.13784i) q^{9} +(16.2588 + 9.38701i) q^{11} +(3.16100 - 5.47501i) q^{13} +(1.21640 - 0.146568i) q^{15} +(1.03860 + 0.599639i) q^{17} +(-4.34979 - 18.4954i) q^{19} +(3.72057 + 1.58921i) q^{21} +(15.2278 + 8.79180i) q^{23} +24.8332 q^{25} +(9.50497 + 25.2716i) q^{27} -18.6058i q^{29} +(16.2202 + 28.0943i) q^{31} +(22.1238 - 51.7949i) q^{33} +(-0.476974 - 0.275381i) q^{35} +18.2245 q^{37} +(-17.4415 - 7.45001i) q^{39} -38.8063i q^{41} +(-33.5545 - 58.1180i) q^{43} +(-0.873093 - 3.57039i) q^{45} -72.1364i q^{47} +(23.5907 + 40.8602i) q^{49} +(1.41326 - 3.30864i) q^{51} +(5.40004 - 3.11771i) q^{53} +(-3.83365 + 6.64008i) q^{55} +(-53.5266 + 19.5934i) q^{57} -46.7552i q^{59} +16.6456 q^{61} +(3.39814 - 11.6519i) q^{63} +(2.23599 + 1.29095i) q^{65} +(-27.5634 + 47.7412i) q^{67} +(20.7210 - 48.5107i) q^{69} +(48.7622 + 28.1528i) q^{71} +(-27.9801 + 48.4629i) q^{73} +(-8.91224 - 73.9646i) q^{75} +(-21.9264 + 12.6592i) q^{77} +(-39.1200 - 67.7578i) q^{79} +(71.8593 - 37.3797i) q^{81} +(-57.7054 - 33.3162i) q^{83} +(-0.244892 + 0.424166i) q^{85} +(-55.4167 + 6.67734i) q^{87} +(130.049 - 75.0837i) q^{89} +(4.26289 + 7.38353i) q^{91} +(77.8564 - 58.3939i) q^{93} +(7.55351 - 1.77645i) q^{95} +(37.2866 + 64.5822i) q^{97} +(-162.209 - 47.3064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(3\) −0.358884 2.97846i −0.119628 0.992819i
\(4\) 0 0
\(5\) 0.408400i 0.0816799i 0.999166 + 0.0408400i \(0.0130034\pi\)
−0.999166 + 0.0408400i \(0.986997\pi\)
\(6\) 0 0
\(7\) −0.674294 + 1.16791i −0.0963277 + 0.166844i −0.910162 0.414253i \(-0.864043\pi\)
0.813834 + 0.581097i \(0.197376\pi\)
\(8\) 0 0
\(9\) −8.74240 + 2.13784i −0.971378 + 0.237538i
\(10\) 0 0
\(11\) 16.2588 + 9.38701i 1.47807 + 0.853365i 0.999693 0.0247891i \(-0.00789141\pi\)
0.478378 + 0.878154i \(0.341225\pi\)
\(12\) 0 0
\(13\) 3.16100 5.47501i 0.243154 0.421155i −0.718457 0.695571i \(-0.755151\pi\)
0.961611 + 0.274416i \(0.0884847\pi\)
\(14\) 0 0
\(15\) 1.21640 0.146568i 0.0810934 0.00977120i
\(16\) 0 0
\(17\) 1.03860 + 0.599639i 0.0610944 + 0.0352729i 0.530236 0.847850i \(-0.322103\pi\)
−0.469142 + 0.883123i \(0.655437\pi\)
\(18\) 0 0
\(19\) −4.34979 18.4954i −0.228936 0.973441i
\(20\) 0 0
\(21\) 3.72057 + 1.58921i 0.177170 + 0.0756767i
\(22\) 0 0
\(23\) 15.2278 + 8.79180i 0.662080 + 0.382252i 0.793069 0.609132i \(-0.208482\pi\)
−0.130989 + 0.991384i \(0.541815\pi\)
\(24\) 0 0
\(25\) 24.8332 0.993328
\(26\) 0 0
\(27\) 9.50497 + 25.2716i 0.352036 + 0.935986i
\(28\) 0 0
\(29\) 18.6058i 0.641581i −0.947150 0.320790i \(-0.896052\pi\)
0.947150 0.320790i \(-0.103948\pi\)
\(30\) 0 0
\(31\) 16.2202 + 28.0943i 0.523234 + 0.906267i 0.999634 + 0.0270391i \(0.00860787\pi\)
−0.476401 + 0.879228i \(0.658059\pi\)
\(32\) 0 0
\(33\) 22.1238 51.7949i 0.670418 1.56954i
\(34\) 0 0
\(35\) −0.476974 0.275381i −0.0136278 0.00786804i
\(36\) 0 0
\(37\) 18.2245 0.492555 0.246278 0.969199i \(-0.420793\pi\)
0.246278 + 0.969199i \(0.420793\pi\)
\(38\) 0 0
\(39\) −17.4415 7.45001i −0.447218 0.191026i
\(40\) 0 0
\(41\) 38.8063i 0.946495i −0.880929 0.473248i \(-0.843082\pi\)
0.880929 0.473248i \(-0.156918\pi\)
\(42\) 0 0
\(43\) −33.5545 58.1180i −0.780337 1.35158i −0.931746 0.363111i \(-0.881714\pi\)
0.151409 0.988471i \(-0.451619\pi\)
\(44\) 0 0
\(45\) −0.873093 3.57039i −0.0194021 0.0793421i
\(46\) 0 0
\(47\) 72.1364i 1.53482i −0.641158 0.767409i \(-0.721546\pi\)
0.641158 0.767409i \(-0.278454\pi\)
\(48\) 0 0
\(49\) 23.5907 + 40.8602i 0.481442 + 0.833882i
\(50\) 0 0
\(51\) 1.41326 3.30864i 0.0277110 0.0648753i
\(52\) 0 0
\(53\) 5.40004 3.11771i 0.101887 0.0588248i −0.448190 0.893938i \(-0.647931\pi\)
0.550078 + 0.835113i \(0.314598\pi\)
\(54\) 0 0
\(55\) −3.83365 + 6.64008i −0.0697028 + 0.120729i
\(56\) 0 0
\(57\) −53.5266 + 19.5934i −0.939064 + 0.343743i
\(58\) 0 0
\(59\) 46.7552i 0.792461i −0.918151 0.396230i \(-0.870318\pi\)
0.918151 0.396230i \(-0.129682\pi\)
\(60\) 0 0
\(61\) 16.6456 0.272878 0.136439 0.990648i \(-0.456434\pi\)
0.136439 + 0.990648i \(0.456434\pi\)
\(62\) 0 0
\(63\) 3.39814 11.6519i 0.0539388 0.184951i
\(64\) 0 0
\(65\) 2.23599 + 1.29095i 0.0343999 + 0.0198608i
\(66\) 0 0
\(67\) −27.5634 + 47.7412i −0.411394 + 0.712556i −0.995042 0.0994509i \(-0.968291\pi\)
0.583648 + 0.812007i \(0.301625\pi\)
\(68\) 0 0
\(69\) 20.7210 48.5107i 0.300304 0.703054i
\(70\) 0 0
\(71\) 48.7622 + 28.1528i 0.686791 + 0.396519i 0.802409 0.596775i \(-0.203551\pi\)
−0.115618 + 0.993294i \(0.536885\pi\)
\(72\) 0 0
\(73\) −27.9801 + 48.4629i −0.383289 + 0.663875i −0.991530 0.129877i \(-0.958542\pi\)
0.608242 + 0.793752i \(0.291875\pi\)
\(74\) 0 0
\(75\) −8.91224 73.9646i −0.118830 0.986195i
\(76\) 0 0
\(77\) −21.9264 + 12.6592i −0.284758 + 0.164405i
\(78\) 0 0
\(79\) −39.1200 67.7578i −0.495189 0.857693i 0.504795 0.863239i \(-0.331568\pi\)
−0.999985 + 0.00554598i \(0.998235\pi\)
\(80\) 0 0
\(81\) 71.8593 37.3797i 0.887152 0.461478i
\(82\) 0 0
\(83\) −57.7054 33.3162i −0.695246 0.401400i 0.110329 0.993895i \(-0.464810\pi\)
−0.805574 + 0.592495i \(0.798143\pi\)
\(84\) 0 0
\(85\) −0.244892 + 0.424166i −0.00288108 + 0.00499018i
\(86\) 0 0
\(87\) −55.4167 + 6.67734i −0.636973 + 0.0767510i
\(88\) 0 0
\(89\) 130.049 75.0837i 1.46122 0.843637i 0.462154 0.886800i \(-0.347077\pi\)
0.999068 + 0.0431625i \(0.0137433\pi\)
\(90\) 0 0
\(91\) 4.26289 + 7.38353i 0.0468449 + 0.0811377i
\(92\) 0 0
\(93\) 77.8564 58.3939i 0.837166 0.627891i
\(94\) 0 0
\(95\) 7.55351 1.77645i 0.0795106 0.0186995i
\(96\) 0 0
\(97\) 37.2866 + 64.5822i 0.384398 + 0.665796i 0.991685 0.128686i \(-0.0410758\pi\)
−0.607288 + 0.794482i \(0.707742\pi\)
\(98\) 0 0
\(99\) −162.209 47.3064i −1.63847 0.477842i
\(100\) 0 0
\(101\) 9.68089i 0.0958504i −0.998851 0.0479252i \(-0.984739\pi\)
0.998851 0.0479252i \(-0.0152609\pi\)
\(102\) 0 0
\(103\) −61.7097 106.884i −0.599123 1.03771i −0.992951 0.118527i \(-0.962183\pi\)
0.393828 0.919184i \(-0.371151\pi\)
\(104\) 0 0
\(105\) −0.649033 + 1.51948i −0.00618126 + 0.0144712i
\(106\) 0 0
\(107\) 4.24390i 0.0396626i −0.999803 0.0198313i \(-0.993687\pi\)
0.999803 0.0198313i \(-0.00631292\pi\)
\(108\) 0 0
\(109\) 55.1273 95.4833i 0.505755 0.875993i −0.494223 0.869335i \(-0.664547\pi\)
0.999978 0.00665808i \(-0.00211935\pi\)
\(110\) 0 0
\(111\) −6.54050 54.2810i −0.0589234 0.489018i
\(112\) 0 0
\(113\) 182.752 105.512i 1.61727 0.933732i 0.629649 0.776880i \(-0.283199\pi\)
0.987622 0.156852i \(-0.0501346\pi\)
\(114\) 0 0
\(115\) −3.59057 + 6.21905i −0.0312223 + 0.0540787i
\(116\) 0 0
\(117\) −15.9300 + 54.6225i −0.136154 + 0.466859i
\(118\) 0 0
\(119\) −1.40065 + 0.808665i −0.0117702 + 0.00679551i
\(120\) 0 0
\(121\) 115.732 + 200.454i 0.956463 + 1.65664i
\(122\) 0 0
\(123\) −115.583 + 13.9270i −0.939698 + 0.113227i
\(124\) 0 0
\(125\) 20.3519i 0.162815i
\(126\) 0 0
\(127\) 101.232 + 175.338i 0.797099 + 1.38062i 0.921498 + 0.388383i \(0.126966\pi\)
−0.124399 + 0.992232i \(0.539700\pi\)
\(128\) 0 0
\(129\) −161.060 + 120.798i −1.24853 + 0.936420i
\(130\) 0 0
\(131\) 11.2194i 0.0856439i −0.999083 0.0428220i \(-0.986365\pi\)
0.999083 0.0428220i \(-0.0136348\pi\)
\(132\) 0 0
\(133\) 24.5340 + 7.39116i 0.184466 + 0.0555726i
\(134\) 0 0
\(135\) −10.3209 + 3.88183i −0.0764513 + 0.0287543i
\(136\) 0 0
\(137\) 28.5762i 0.208585i 0.994547 + 0.104293i \(0.0332579\pi\)
−0.994547 + 0.104293i \(0.966742\pi\)
\(138\) 0 0
\(139\) −5.42714 + 9.40008i −0.0390442 + 0.0676265i −0.884887 0.465806i \(-0.845765\pi\)
0.845843 + 0.533432i \(0.179098\pi\)
\(140\) 0 0
\(141\) −214.855 + 25.8886i −1.52380 + 0.183607i
\(142\) 0 0
\(143\) 102.788 59.3447i 0.718797 0.414998i
\(144\) 0 0
\(145\) 7.59862 0.0524043
\(146\) 0 0
\(147\) 113.234 84.9278i 0.770300 0.577740i
\(148\) 0 0
\(149\) 213.661i 1.43397i 0.697090 + 0.716984i \(0.254478\pi\)
−0.697090 + 0.716984i \(0.745522\pi\)
\(150\) 0 0
\(151\) −39.8969 + 69.1035i −0.264218 + 0.457639i −0.967358 0.253412i \(-0.918447\pi\)
0.703140 + 0.711051i \(0.251781\pi\)
\(152\) 0 0
\(153\) −10.3618 3.02191i −0.0677244 0.0197511i
\(154\) 0 0
\(155\) −11.4737 + 6.62434i −0.0740239 + 0.0427377i
\(156\) 0 0
\(157\) −161.183 −1.02665 −0.513323 0.858196i \(-0.671586\pi\)
−0.513323 + 0.858196i \(0.671586\pi\)
\(158\) 0 0
\(159\) −11.2240 14.9649i −0.0705909 0.0941187i
\(160\) 0 0
\(161\) −20.5361 + 11.8565i −0.127553 + 0.0736429i
\(162\) 0 0
\(163\) 92.2041 0.565670 0.282835 0.959169i \(-0.408725\pi\)
0.282835 + 0.959169i \(0.408725\pi\)
\(164\) 0 0
\(165\) 21.1530 + 9.03535i 0.128200 + 0.0547597i
\(166\) 0 0
\(167\) 215.048 + 124.158i 1.28771 + 0.743462i 0.978246 0.207448i \(-0.0665156\pi\)
0.309468 + 0.950910i \(0.399849\pi\)
\(168\) 0 0
\(169\) 64.5162 + 111.745i 0.381752 + 0.661215i
\(170\) 0 0
\(171\) 77.5678 + 152.395i 0.453613 + 0.891199i
\(172\) 0 0
\(173\) 91.7749 52.9863i 0.530491 0.306279i −0.210725 0.977545i \(-0.567583\pi\)
0.741216 + 0.671266i \(0.234249\pi\)
\(174\) 0 0
\(175\) −16.7449 + 29.0030i −0.0956850 + 0.165731i
\(176\) 0 0
\(177\) −139.258 + 16.7797i −0.786770 + 0.0948005i
\(178\) 0 0
\(179\) 15.0274i 0.0839519i −0.999119 0.0419759i \(-0.986635\pi\)
0.999119 0.0419759i \(-0.0133653\pi\)
\(180\) 0 0
\(181\) 122.841 + 212.766i 0.678678 + 1.17551i 0.975379 + 0.220535i \(0.0707802\pi\)
−0.296701 + 0.954970i \(0.595886\pi\)
\(182\) 0 0
\(183\) −5.97383 49.5781i −0.0326439 0.270919i
\(184\) 0 0
\(185\) 7.44290i 0.0402319i
\(186\) 0 0
\(187\) 11.2576 + 19.4988i 0.0602012 + 0.104272i
\(188\) 0 0
\(189\) −35.9242 5.93954i −0.190075 0.0314261i
\(190\) 0 0
\(191\) −170.032 98.1680i −0.890220 0.513969i −0.0162053 0.999869i \(-0.505159\pi\)
−0.874014 + 0.485900i \(0.838492\pi\)
\(192\) 0 0
\(193\) −244.586 −1.26729 −0.633643 0.773625i \(-0.718441\pi\)
−0.633643 + 0.773625i \(0.718441\pi\)
\(194\) 0 0
\(195\) 3.04258 7.12311i 0.0156030 0.0365288i
\(196\) 0 0
\(197\) 63.2665i 0.321150i 0.987024 + 0.160575i \(0.0513348\pi\)
−0.987024 + 0.160575i \(0.948665\pi\)
\(198\) 0 0
\(199\) 78.9137 + 136.683i 0.396551 + 0.686847i 0.993298 0.115583i \(-0.0368736\pi\)
−0.596747 + 0.802430i \(0.703540\pi\)
\(200\) 0 0
\(201\) 152.087 + 64.9629i 0.756653 + 0.323198i
\(202\) 0 0
\(203\) 21.7300 + 12.5458i 0.107044 + 0.0618020i
\(204\) 0 0
\(205\) 15.8485 0.0773097
\(206\) 0 0
\(207\) −151.923 44.3068i −0.733930 0.214042i
\(208\) 0 0
\(209\) 102.894 341.544i 0.492317 1.63418i
\(210\) 0 0
\(211\) −255.404 −1.21045 −0.605223 0.796056i \(-0.706916\pi\)
−0.605223 + 0.796056i \(0.706916\pi\)
\(212\) 0 0
\(213\) 66.3521 155.340i 0.311512 0.729294i
\(214\) 0 0
\(215\) 23.7354 13.7036i 0.110397 0.0637378i
\(216\) 0 0
\(217\) −43.7488 −0.201608
\(218\) 0 0
\(219\) 154.386 + 65.9449i 0.704960 + 0.301118i
\(220\) 0 0
\(221\) 6.56606 3.79091i 0.0297107 0.0171535i
\(222\) 0 0
\(223\) 45.1583 + 78.2165i 0.202504 + 0.350746i 0.949334 0.314268i \(-0.101759\pi\)
−0.746831 + 0.665014i \(0.768426\pi\)
\(224\) 0 0
\(225\) −217.102 + 53.0894i −0.964898 + 0.235953i
\(226\) 0 0
\(227\) −380.442 219.649i −1.67596 0.967615i −0.964195 0.265195i \(-0.914564\pi\)
−0.711763 0.702420i \(-0.752103\pi\)
\(228\) 0 0
\(229\) 187.314 + 324.438i 0.817967 + 1.41676i 0.907178 + 0.420747i \(0.138232\pi\)
−0.0892114 + 0.996013i \(0.528435\pi\)
\(230\) 0 0
\(231\) 45.5739 + 60.7636i 0.197290 + 0.263046i
\(232\) 0 0
\(233\) 20.3281 + 11.7364i 0.0872451 + 0.0503710i 0.542988 0.839741i \(-0.317293\pi\)
−0.455743 + 0.890112i \(0.650626\pi\)
\(234\) 0 0
\(235\) 29.4605 0.125364
\(236\) 0 0
\(237\) −187.774 + 140.834i −0.792295 + 0.594237i
\(238\) 0 0
\(239\) −98.5086 + 56.8740i −0.412170 + 0.237966i −0.691722 0.722164i \(-0.743148\pi\)
0.279552 + 0.960131i \(0.409814\pi\)
\(240\) 0 0
\(241\) −150.618 −0.624973 −0.312486 0.949922i \(-0.601162\pi\)
−0.312486 + 0.949922i \(0.601162\pi\)
\(242\) 0 0
\(243\) −137.123 200.615i −0.564292 0.825575i
\(244\) 0 0
\(245\) −16.6873 + 9.63441i −0.0681114 + 0.0393241i
\(246\) 0 0
\(247\) −115.012 34.6488i −0.465636 0.140278i
\(248\) 0 0
\(249\) −78.5214 + 183.830i −0.315347 + 0.738272i
\(250\) 0 0
\(251\) 291.490 168.292i 1.16131 0.670485i 0.209695 0.977767i \(-0.432753\pi\)
0.951619 + 0.307282i \(0.0994195\pi\)
\(252\) 0 0
\(253\) 165.057 + 285.888i 0.652401 + 1.12999i
\(254\) 0 0
\(255\) 1.35125 + 0.577174i 0.00529901 + 0.00226343i
\(256\) 0 0
\(257\) −285.715 164.958i −1.11173 0.641859i −0.172455 0.985017i \(-0.555170\pi\)
−0.939278 + 0.343158i \(0.888503\pi\)
\(258\) 0 0
\(259\) −12.2887 + 21.2846i −0.0474467 + 0.0821801i
\(260\) 0 0
\(261\) 39.7763 + 162.660i 0.152400 + 0.623217i
\(262\) 0 0
\(263\) −415.338 + 239.796i −1.57923 + 0.911770i −0.584265 + 0.811563i \(0.698617\pi\)
−0.994967 + 0.100207i \(0.968049\pi\)
\(264\) 0 0
\(265\) 1.27327 + 2.20537i 0.00480480 + 0.00832216i
\(266\) 0 0
\(267\) −270.306 360.398i −1.01238 1.34981i
\(268\) 0 0
\(269\) 76.7941 + 44.3371i 0.285480 + 0.164822i 0.635902 0.771770i \(-0.280628\pi\)
−0.350422 + 0.936592i \(0.613962\pi\)
\(270\) 0 0
\(271\) −245.103 + 424.531i −0.904439 + 1.56654i −0.0827714 + 0.996569i \(0.526377\pi\)
−0.821668 + 0.569966i \(0.806956\pi\)
\(272\) 0 0
\(273\) 20.4617 15.3467i 0.0749511 0.0562148i
\(274\) 0 0
\(275\) 403.758 + 233.110i 1.46821 + 0.847671i
\(276\) 0 0
\(277\) −48.2162 + 83.5130i −0.174066 + 0.301491i −0.939838 0.341622i \(-0.889024\pi\)
0.765772 + 0.643112i \(0.222357\pi\)
\(278\) 0 0
\(279\) −201.865 210.935i −0.723531 0.756041i
\(280\) 0 0
\(281\) 489.608i 1.74238i 0.490947 + 0.871189i \(0.336651\pi\)
−0.490947 + 0.871189i \(0.663349\pi\)
\(282\) 0 0
\(283\) −154.090 −0.544486 −0.272243 0.962229i \(-0.587765\pi\)
−0.272243 + 0.962229i \(0.587765\pi\)
\(284\) 0 0
\(285\) −8.00192 21.8603i −0.0280769 0.0767027i
\(286\) 0 0
\(287\) 45.3223 + 26.1669i 0.157918 + 0.0911737i
\(288\) 0 0
\(289\) −143.781 249.036i −0.497512 0.861715i
\(290\) 0 0
\(291\) 178.974 134.234i 0.615030 0.461285i
\(292\) 0 0
\(293\) 407.976 235.545i 1.39241 0.803907i 0.398827 0.917026i \(-0.369417\pi\)
0.993581 + 0.113119i \(0.0360840\pi\)
\(294\) 0 0
\(295\) 19.0948 0.0647281
\(296\) 0 0
\(297\) −82.6858 + 500.109i −0.278404 + 1.68387i
\(298\) 0 0
\(299\) 96.2705 55.5818i 0.321975 0.185892i
\(300\) 0 0
\(301\) 90.5023 0.300672
\(302\) 0 0
\(303\) −28.8341 + 3.47432i −0.0951621 + 0.0114664i
\(304\) 0 0
\(305\) 6.79804i 0.0222887i
\(306\) 0 0
\(307\) 22.2167 38.4804i 0.0723670 0.125343i −0.827571 0.561361i \(-0.810278\pi\)
0.899938 + 0.436017i \(0.143611\pi\)
\(308\) 0 0
\(309\) −296.204 + 222.159i −0.958587 + 0.718960i
\(310\) 0 0
\(311\) 198.767 114.758i 0.639122 0.368997i −0.145155 0.989409i \(-0.546368\pi\)
0.784276 + 0.620412i \(0.213035\pi\)
\(312\) 0 0
\(313\) 27.3554 0.0873975 0.0436988 0.999045i \(-0.486086\pi\)
0.0436988 + 0.999045i \(0.486086\pi\)
\(314\) 0 0
\(315\) 4.75863 + 1.38780i 0.0151067 + 0.00440571i
\(316\) 0 0
\(317\) 476.138i 1.50201i −0.660294 0.751007i \(-0.729568\pi\)
0.660294 0.751007i \(-0.270432\pi\)
\(318\) 0 0
\(319\) 174.653 302.508i 0.547502 0.948302i
\(320\) 0 0
\(321\) −12.6403 + 1.52307i −0.0393778 + 0.00474476i
\(322\) 0 0
\(323\) 6.57284 21.8177i 0.0203493 0.0675470i
\(324\) 0 0
\(325\) 78.4978 135.962i 0.241532 0.418345i
\(326\) 0 0
\(327\) −304.177 129.927i −0.930205 0.397330i
\(328\) 0 0
\(329\) 84.2490 + 48.6412i 0.256076 + 0.147845i
\(330\) 0 0
\(331\) 243.510 421.772i 0.735680 1.27424i −0.218744 0.975782i \(-0.570196\pi\)
0.954424 0.298453i \(-0.0964706\pi\)
\(332\) 0 0
\(333\) −159.326 + 38.9612i −0.478457 + 0.117000i
\(334\) 0 0
\(335\) −19.4975 11.2569i −0.0582015 0.0336026i
\(336\) 0 0
\(337\) 228.628 0.678420 0.339210 0.940711i \(-0.389840\pi\)
0.339210 + 0.940711i \(0.389840\pi\)
\(338\) 0 0
\(339\) −379.849 506.451i −1.12050 1.49396i
\(340\) 0 0
\(341\) 609.039i 1.78604i
\(342\) 0 0
\(343\) −129.709 −0.378160
\(344\) 0 0
\(345\) 19.8118 + 8.46244i 0.0574254 + 0.0245288i
\(346\) 0 0
\(347\) 146.453i 0.422056i −0.977480 0.211028i \(-0.932319\pi\)
0.977480 0.211028i \(-0.0676811\pi\)
\(348\) 0 0
\(349\) 204.639 354.445i 0.586358 1.01560i −0.408347 0.912827i \(-0.633895\pi\)
0.994705 0.102775i \(-0.0327720\pi\)
\(350\) 0 0
\(351\) 168.408 + 27.8438i 0.479794 + 0.0793270i
\(352\) 0 0
\(353\) −297.654 171.851i −0.843213 0.486829i 0.0151420 0.999885i \(-0.495180\pi\)
−0.858355 + 0.513056i \(0.828513\pi\)
\(354\) 0 0
\(355\) −11.4976 + 19.9144i −0.0323876 + 0.0560970i
\(356\) 0 0
\(357\) 2.91124 + 3.88156i 0.00815475 + 0.0108727i
\(358\) 0 0
\(359\) 221.301 + 127.768i 0.616438 + 0.355900i 0.775481 0.631371i \(-0.217508\pi\)
−0.159043 + 0.987272i \(0.550841\pi\)
\(360\) 0 0
\(361\) −323.159 + 160.902i −0.895176 + 0.445712i
\(362\) 0 0
\(363\) 555.508 416.642i 1.53033 1.14777i
\(364\) 0 0
\(365\) −19.7922 11.4270i −0.0542253 0.0313070i
\(366\) 0 0
\(367\) −435.247 −1.18596 −0.592980 0.805217i \(-0.702049\pi\)
−0.592980 + 0.805217i \(0.702049\pi\)
\(368\) 0 0
\(369\) 82.9617 + 339.260i 0.224828 + 0.919405i
\(370\) 0 0
\(371\) 8.40902i 0.0226658i
\(372\) 0 0
\(373\) 240.282 + 416.180i 0.644187 + 1.11577i 0.984489 + 0.175449i \(0.0561376\pi\)
−0.340301 + 0.940316i \(0.610529\pi\)
\(374\) 0 0
\(375\) 60.6171 7.30396i 0.161646 0.0194772i
\(376\) 0 0
\(377\) −101.867 58.8131i −0.270205 0.156003i
\(378\) 0 0
\(379\) −48.0148 −0.126688 −0.0633440 0.997992i \(-0.520177\pi\)
−0.0633440 + 0.997992i \(0.520177\pi\)
\(380\) 0 0
\(381\) 485.907 364.440i 1.27535 0.956535i
\(382\) 0 0
\(383\) 3.54731i 0.00926191i 0.999989 + 0.00463096i \(0.00147408\pi\)
−0.999989 + 0.00463096i \(0.998526\pi\)
\(384\) 0 0
\(385\) −5.17002 8.95473i −0.0134286 0.0232590i
\(386\) 0 0
\(387\) 417.594 + 436.357i 1.07905 + 1.12754i
\(388\) 0 0
\(389\) 380.289i 0.977608i 0.872394 + 0.488804i \(0.162567\pi\)
−0.872394 + 0.488804i \(0.837433\pi\)
\(390\) 0 0
\(391\) 10.5438 + 18.2624i 0.0269663 + 0.0467069i
\(392\) 0 0
\(393\) −33.4164 + 4.02645i −0.0850289 + 0.0102454i
\(394\) 0 0
\(395\) 27.6722 15.9766i 0.0700563 0.0404470i
\(396\) 0 0
\(397\) 269.312 466.462i 0.678368 1.17497i −0.297105 0.954845i \(-0.596021\pi\)
0.975472 0.220122i \(-0.0706456\pi\)
\(398\) 0 0
\(399\) 13.2094 75.7260i 0.0331062 0.189790i
\(400\) 0 0
\(401\) 182.689i 0.455583i −0.973710 0.227791i \(-0.926850\pi\)
0.973710 0.227791i \(-0.0731505\pi\)
\(402\) 0 0
\(403\) 205.089 0.508905
\(404\) 0 0
\(405\) 15.2659 + 29.3473i 0.0376935 + 0.0724625i
\(406\) 0 0
\(407\) 296.309 + 171.074i 0.728032 + 0.420329i
\(408\) 0 0
\(409\) −72.2717 + 125.178i −0.176703 + 0.306059i −0.940749 0.339103i \(-0.889877\pi\)
0.764046 + 0.645162i \(0.223210\pi\)
\(410\) 0 0
\(411\) 85.1130 10.2555i 0.207088 0.0249527i
\(412\) 0 0
\(413\) 54.6059 + 31.5267i 0.132218 + 0.0763359i
\(414\) 0 0
\(415\) 13.6063 23.5669i 0.0327863 0.0567876i
\(416\) 0 0
\(417\) 29.9454 + 12.7910i 0.0718116 + 0.0306738i
\(418\) 0 0
\(419\) −177.986 + 102.760i −0.424787 + 0.245251i −0.697123 0.716951i \(-0.745537\pi\)
0.272336 + 0.962202i \(0.412204\pi\)
\(420\) 0 0
\(421\) 365.466 + 633.006i 0.868091 + 1.50358i 0.863945 + 0.503587i \(0.167987\pi\)
0.00414664 + 0.999991i \(0.498680\pi\)
\(422\) 0 0
\(423\) 154.216 + 630.646i 0.364577 + 1.49089i
\(424\) 0 0
\(425\) 25.7919 + 14.8909i 0.0606868 + 0.0350375i
\(426\) 0 0
\(427\) −11.2240 + 19.4405i −0.0262857 + 0.0455282i
\(428\) 0 0
\(429\) −213.645 284.852i −0.498006 0.663990i
\(430\) 0 0
\(431\) −283.508 + 163.683i −0.657791 + 0.379776i −0.791435 0.611253i \(-0.790666\pi\)
0.133644 + 0.991029i \(0.457332\pi\)
\(432\) 0 0
\(433\) −19.1647 33.1942i −0.0442603 0.0766610i 0.843047 0.537841i \(-0.180760\pi\)
−0.887307 + 0.461179i \(0.847426\pi\)
\(434\) 0 0
\(435\) −2.72702 22.6321i −0.00626902 0.0520279i
\(436\) 0 0
\(437\) 96.3699 319.887i 0.220526 0.732008i
\(438\) 0 0
\(439\) −259.325 449.164i −0.590717 1.02315i −0.994136 0.108137i \(-0.965511\pi\)
0.403419 0.915016i \(-0.367822\pi\)
\(440\) 0 0
\(441\) −293.592 306.783i −0.665741 0.695654i
\(442\) 0 0
\(443\) 351.874i 0.794298i −0.917754 0.397149i \(-0.870000\pi\)
0.917754 0.397149i \(-0.130000\pi\)
\(444\) 0 0
\(445\) 30.6642 + 53.1119i 0.0689082 + 0.119353i
\(446\) 0 0
\(447\) 636.381 76.6796i 1.42367 0.171543i
\(448\) 0 0
\(449\) 135.369i 0.301490i 0.988573 + 0.150745i \(0.0481673\pi\)
−0.988573 + 0.150745i \(0.951833\pi\)
\(450\) 0 0
\(451\) 364.275 630.943i 0.807706 1.39899i
\(452\) 0 0
\(453\) 220.140 + 94.0311i 0.485961 + 0.207574i
\(454\) 0 0
\(455\) −3.01543 + 1.74096i −0.00662732 + 0.00382629i
\(456\) 0 0
\(457\) −211.591 + 366.486i −0.463000 + 0.801940i −0.999109 0.0422092i \(-0.986560\pi\)
0.536109 + 0.844149i \(0.319894\pi\)
\(458\) 0 0
\(459\) −5.28194 + 31.9468i −0.0115075 + 0.0696008i
\(460\) 0 0
\(461\) 11.8711 6.85378i 0.0257507 0.0148672i −0.487069 0.873363i \(-0.661934\pi\)
0.512820 + 0.858496i \(0.328601\pi\)
\(462\) 0 0
\(463\) 284.747 + 493.196i 0.615004 + 1.06522i 0.990384 + 0.138348i \(0.0441791\pi\)
−0.375379 + 0.926871i \(0.622488\pi\)
\(464\) 0 0
\(465\) 23.8480 + 31.7965i 0.0512861 + 0.0683797i
\(466\) 0 0
\(467\) 253.177i 0.542135i 0.962560 + 0.271067i \(0.0873766\pi\)
−0.962560 + 0.271067i \(0.912623\pi\)
\(468\) 0 0
\(469\) −37.1717 64.3832i −0.0792573 0.137278i
\(470\) 0 0
\(471\) 57.8461 + 480.078i 0.122816 + 1.01927i
\(472\) 0 0
\(473\) 1259.90i 2.66365i
\(474\) 0 0
\(475\) −108.019 459.300i −0.227409 0.966947i
\(476\) 0 0
\(477\) −40.5441 + 38.8007i −0.0849982 + 0.0813432i
\(478\) 0 0
\(479\) 804.989i 1.68056i −0.542151 0.840281i \(-0.682390\pi\)
0.542151 0.840281i \(-0.317610\pi\)
\(480\) 0 0
\(481\) 57.6078 99.7796i 0.119767 0.207442i
\(482\) 0 0
\(483\) 42.6842 + 56.9107i 0.0883731 + 0.117828i
\(484\) 0 0
\(485\) −26.3754 + 15.2278i −0.0543822 + 0.0313976i
\(486\) 0 0
\(487\) 61.4828 0.126248 0.0631240 0.998006i \(-0.479894\pi\)
0.0631240 + 0.998006i \(0.479894\pi\)
\(488\) 0 0
\(489\) −33.0906 274.626i −0.0676699 0.561607i
\(490\) 0 0
\(491\) 30.9649i 0.0630650i 0.999503 + 0.0315325i \(0.0100388\pi\)
−0.999503 + 0.0315325i \(0.989961\pi\)
\(492\) 0 0
\(493\) 11.1568 19.3241i 0.0226304 0.0391970i
\(494\) 0 0
\(495\) 19.3199 66.2460i 0.0390301 0.133830i
\(496\) 0 0
\(497\) −65.7600 + 37.9666i −0.132314 + 0.0763915i
\(498\) 0 0
\(499\) −399.854 −0.801311 −0.400656 0.916229i \(-0.631218\pi\)
−0.400656 + 0.916229i \(0.631218\pi\)
\(500\) 0 0
\(501\) 292.622 685.070i 0.584077 1.36741i
\(502\) 0 0
\(503\) −687.500 + 396.928i −1.36680 + 0.789122i −0.990518 0.137384i \(-0.956131\pi\)
−0.376281 + 0.926506i \(0.622797\pi\)
\(504\) 0 0
\(505\) 3.95367 0.00782905
\(506\) 0 0
\(507\) 309.675 232.262i 0.610798 0.458111i
\(508\) 0 0
\(509\) 50.5625 + 29.1923i 0.0993370 + 0.0573523i 0.548846 0.835924i \(-0.315068\pi\)
−0.449508 + 0.893276i \(0.648401\pi\)
\(510\) 0 0
\(511\) −37.7336 65.3565i −0.0738426 0.127899i
\(512\) 0 0
\(513\) 426.064 285.724i 0.830534 0.556968i
\(514\) 0 0
\(515\) 43.6515 25.2022i 0.0847602 0.0489363i
\(516\) 0 0
\(517\) 677.146 1172.85i 1.30976 2.26857i
\(518\) 0 0
\(519\) −190.754 254.332i −0.367541 0.490042i
\(520\) 0 0
\(521\) 288.228i 0.553221i −0.960982 0.276611i \(-0.910789\pi\)
0.960982 0.276611i \(-0.0892112\pi\)
\(522\) 0 0
\(523\) −250.728 434.274i −0.479404 0.830352i 0.520317 0.853973i \(-0.325814\pi\)
−0.999721 + 0.0236209i \(0.992481\pi\)
\(524\) 0 0
\(525\) 92.3936 + 39.4652i 0.175988 + 0.0751718i
\(526\) 0 0
\(527\) 38.9051i 0.0738238i
\(528\) 0 0
\(529\) −109.908 190.367i −0.207766 0.359862i
\(530\) 0 0
\(531\) 99.9551 + 408.753i 0.188239 + 0.769779i
\(532\) 0 0
\(533\) −212.465 122.667i −0.398621 0.230144i
\(534\) 0 0
\(535\) 1.73321 0.00323964
\(536\) 0 0
\(537\) −44.7584 + 5.39309i −0.0833490 + 0.0100430i
\(538\) 0 0
\(539\) 885.783i 1.64338i
\(540\) 0 0
\(541\) 43.5607 + 75.4493i 0.0805188 + 0.139463i 0.903473 0.428645i \(-0.141009\pi\)
−0.822954 + 0.568108i \(0.807676\pi\)
\(542\) 0 0
\(543\) 589.630 442.234i 1.08587 0.814428i
\(544\) 0 0
\(545\) 38.9953 + 22.5140i 0.0715511 + 0.0413100i
\(546\) 0 0
\(547\) −99.5526 −0.181997 −0.0909987 0.995851i \(-0.529006\pi\)
−0.0909987 + 0.995851i \(0.529006\pi\)
\(548\) 0 0
\(549\) −145.522 + 35.5856i −0.265068 + 0.0648189i
\(550\) 0 0
\(551\) −344.122 + 80.9315i −0.624541 + 0.146881i
\(552\) 0 0
\(553\) 105.513 0.190802
\(554\) 0 0
\(555\) 22.1683 2.67114i 0.0399430 0.00481286i
\(556\) 0 0
\(557\) −371.103 + 214.256i −0.666252 + 0.384661i −0.794655 0.607061i \(-0.792348\pi\)
0.128403 + 0.991722i \(0.459015\pi\)
\(558\) 0 0
\(559\) −424.263 −0.758967
\(560\) 0 0
\(561\) 54.0361 40.5282i 0.0963210 0.0722427i
\(562\) 0 0
\(563\) 34.3925 19.8565i 0.0610880 0.0352692i −0.469145 0.883121i \(-0.655438\pi\)
0.530233 + 0.847852i \(0.322104\pi\)
\(564\) 0 0
\(565\) 43.0909 + 74.6357i 0.0762672 + 0.132099i
\(566\) 0 0
\(567\) −4.79806 + 109.130i −0.00846219 + 0.192469i
\(568\) 0 0
\(569\) −174.227 100.590i −0.306199 0.176784i 0.339025 0.940777i \(-0.389903\pi\)
−0.645224 + 0.763993i \(0.723236\pi\)
\(570\) 0 0
\(571\) −409.604 709.455i −0.717345 1.24248i −0.962048 0.272880i \(-0.912024\pi\)
0.244703 0.969598i \(-0.421310\pi\)
\(572\) 0 0
\(573\) −231.367 + 541.664i −0.403782 + 0.945312i
\(574\) 0 0
\(575\) 378.156 + 218.329i 0.657663 + 0.379702i
\(576\) 0 0
\(577\) −193.192 −0.334821 −0.167411 0.985887i \(-0.553541\pi\)
−0.167411 + 0.985887i \(0.553541\pi\)
\(578\) 0 0
\(579\) 87.7781 + 728.490i 0.151603 + 1.25819i
\(580\) 0 0
\(581\) 77.8208 44.9298i 0.133943 0.0773319i
\(582\) 0 0
\(583\) 117.064 0.200796
\(584\) 0 0
\(585\) −22.3078 6.50582i −0.0381330 0.0111211i
\(586\) 0 0
\(587\) −246.428 + 142.275i −0.419809 + 0.242377i −0.694996 0.719014i \(-0.744594\pi\)
0.275186 + 0.961391i \(0.411260\pi\)
\(588\) 0 0
\(589\) 449.060 422.204i 0.762411 0.716815i
\(590\) 0 0
\(591\) 188.436 22.7053i 0.318843 0.0384185i
\(592\) 0 0
\(593\) −639.315 + 369.109i −1.07810 + 0.622443i −0.930384 0.366587i \(-0.880526\pi\)
−0.147719 + 0.989029i \(0.547193\pi\)
\(594\) 0 0
\(595\) −0.330259 0.572025i −0.000555056 0.000961386i
\(596\) 0 0
\(597\) 378.782 284.094i 0.634476 0.475870i
\(598\) 0 0
\(599\) 740.966 + 427.797i 1.23700 + 0.714185i 0.968481 0.249088i \(-0.0801310\pi\)
0.268523 + 0.963273i \(0.413464\pi\)
\(600\) 0 0
\(601\) −78.0380 + 135.166i −0.129847 + 0.224901i −0.923617 0.383316i \(-0.874782\pi\)
0.793770 + 0.608218i \(0.208115\pi\)
\(602\) 0 0
\(603\) 138.907 476.299i 0.230360 0.789883i
\(604\) 0 0
\(605\) −81.8652 + 47.2649i −0.135314 + 0.0781238i
\(606\) 0 0
\(607\) −382.625 662.726i −0.630354 1.09181i −0.987479 0.157749i \(-0.949576\pi\)
0.357125 0.934057i \(-0.383757\pi\)
\(608\) 0 0
\(609\) 29.5686 69.2242i 0.0485527 0.113669i
\(610\) 0 0
\(611\) −394.948 228.023i −0.646396 0.373197i
\(612\) 0 0
\(613\) −280.740 + 486.256i −0.457978 + 0.793241i −0.998854 0.0478616i \(-0.984759\pi\)
0.540876 + 0.841102i \(0.318093\pi\)
\(614\) 0 0
\(615\) −5.68777 47.2040i −0.00924840 0.0767545i
\(616\) 0 0
\(617\) −422.747 244.073i −0.685165 0.395580i 0.116633 0.993175i \(-0.462790\pi\)
−0.801798 + 0.597595i \(0.796123\pi\)
\(618\) 0 0
\(619\) −469.611 + 813.389i −0.758660 + 1.31404i 0.184874 + 0.982762i \(0.440812\pi\)
−0.943534 + 0.331276i \(0.892521\pi\)
\(620\) 0 0
\(621\) −77.4429 + 468.398i −0.124707 + 0.754265i
\(622\) 0 0
\(623\) 202.514i 0.325062i
\(624\) 0 0
\(625\) 612.519 0.980030
\(626\) 0 0
\(627\) −1054.20 183.891i −1.68134 0.293287i
\(628\) 0 0
\(629\) 18.9281 + 10.9281i 0.0300924 + 0.0173738i
\(630\) 0 0
\(631\) −390.095 675.665i −0.618217 1.07078i −0.989811 0.142388i \(-0.954522\pi\)
0.371594 0.928395i \(-0.378811\pi\)
\(632\) 0 0
\(633\) 91.6604 + 760.710i 0.144803 + 1.20175i
\(634\) 0 0
\(635\) −71.6081 + 41.3429i −0.112769 + 0.0651070i
\(636\) 0 0
\(637\) 298.280 0.468258
\(638\) 0 0
\(639\) −486.485 141.878i −0.761322 0.222031i
\(640\) 0 0
\(641\) −123.462 + 71.2809i −0.192609 + 0.111203i −0.593203 0.805053i \(-0.702137\pi\)
0.400594 + 0.916255i \(0.368804\pi\)
\(642\) 0 0
\(643\) −316.855 −0.492776 −0.246388 0.969171i \(-0.579244\pi\)
−0.246388 + 0.969171i \(0.579244\pi\)
\(644\) 0 0
\(645\) −49.3339 65.7768i −0.0764867 0.101980i
\(646\) 0 0
\(647\) 713.825i 1.10328i 0.834081 + 0.551642i \(0.185998\pi\)
−0.834081 + 0.551642i \(0.814002\pi\)
\(648\) 0 0
\(649\) 438.891 760.182i 0.676258 1.17131i
\(650\) 0 0
\(651\) 15.7008 + 130.304i 0.0241179 + 0.200160i
\(652\) 0 0
\(653\) 473.652 273.463i 0.725348 0.418780i −0.0913700 0.995817i \(-0.529125\pi\)
0.816718 + 0.577037i \(0.195791\pi\)
\(654\) 0 0
\(655\) 4.58198 0.00699539
\(656\) 0 0
\(657\) 141.007 483.499i 0.214623 0.735920i
\(658\) 0 0
\(659\) 954.820i 1.44889i 0.689331 + 0.724446i \(0.257904\pi\)
−0.689331 + 0.724446i \(0.742096\pi\)
\(660\) 0 0
\(661\) 133.808 231.761i 0.202432 0.350623i −0.746879 0.664959i \(-0.768449\pi\)
0.949311 + 0.314337i \(0.101782\pi\)
\(662\) 0 0
\(663\) −13.6475 18.1962i −0.0205845 0.0274453i
\(664\) 0 0
\(665\) −3.01855 + 10.0197i −0.00453917 + 0.0150672i
\(666\) 0 0
\(667\) 163.579 283.327i 0.245246 0.424778i
\(668\) 0 0
\(669\) 216.758 162.573i 0.324003 0.243008i
\(670\) 0 0
\(671\) 270.637 + 156.252i 0.403333 + 0.232865i
\(672\) 0 0
\(673\) 96.0817 166.418i 0.142766 0.247278i −0.785771 0.618517i \(-0.787734\pi\)
0.928537 + 0.371239i \(0.121067\pi\)
\(674\) 0 0
\(675\) 236.039 + 627.576i 0.349687 + 0.929742i
\(676\) 0 0
\(677\) −302.982 174.926i −0.447536 0.258385i 0.259253 0.965809i \(-0.416524\pi\)
−0.706789 + 0.707425i \(0.749857\pi\)
\(678\) 0 0
\(679\) −100.568 −0.148113
\(680\) 0 0
\(681\) −517.679 + 1211.96i −0.760175 + 1.77968i
\(682\) 0 0
\(683\) 221.137i 0.323773i 0.986809 + 0.161886i \(0.0517578\pi\)
−0.986809 + 0.161886i \(0.948242\pi\)
\(684\) 0 0
\(685\) −11.6705 −0.0170372
\(686\) 0 0
\(687\) 899.100 674.343i 1.30873 0.981577i
\(688\) 0 0
\(689\) 39.4204i 0.0572139i
\(690\) 0 0
\(691\) −64.4573 + 111.643i −0.0932811 + 0.161568i −0.908890 0.417036i \(-0.863069\pi\)
0.815609 + 0.578604i \(0.196402\pi\)
\(692\) 0 0
\(693\) 164.626 157.547i 0.237556 0.227341i
\(694\) 0 0
\(695\) −3.83899 2.21644i −0.00552372 0.00318912i
\(696\) 0 0
\(697\) 23.2698 40.3044i 0.0333856 0.0578255i
\(698\) 0 0
\(699\) 27.6611 64.7584i 0.0395723 0.0926444i
\(700\) 0 0
\(701\) −286.317 165.305i −0.408441 0.235813i 0.281679 0.959509i \(-0.409109\pi\)
−0.690120 + 0.723695i \(0.742442\pi\)
\(702\) 0 0
\(703\) −79.2729 337.070i −0.112764 0.479474i
\(704\) 0 0
\(705\) −10.5729 87.7468i −0.0149970 0.124464i
\(706\) 0 0
\(707\) 11.3064 + 6.52777i 0.0159921 + 0.00923305i
\(708\) 0 0
\(709\) 454.924 0.641642 0.320821 0.947140i \(-0.396041\pi\)
0.320821 + 0.947140i \(0.396041\pi\)
\(710\) 0 0
\(711\) 486.858 + 508.733i 0.684751 + 0.715518i
\(712\) 0 0
\(713\) 570.421i 0.800029i
\(714\) 0 0
\(715\) 24.2363 + 41.9786i 0.0338970 + 0.0587113i
\(716\) 0 0
\(717\) 204.750 + 272.993i 0.285565 + 0.380743i
\(718\) 0 0
\(719\) 104.799 + 60.5055i 0.145756 + 0.0841523i 0.571104 0.820877i \(-0.306515\pi\)
−0.425348 + 0.905030i \(0.639848\pi\)
\(720\) 0 0
\(721\) 166.442 0.230849
\(722\) 0 0
\(723\) 54.0546 + 448.611i 0.0747643 + 0.620485i
\(724\) 0 0
\(725\) 462.043i 0.637300i
\(726\) 0 0
\(727\) −234.018 405.331i −0.321895 0.557539i 0.658984 0.752157i \(-0.270987\pi\)
−0.980879 + 0.194618i \(0.937653\pi\)
\(728\) 0 0
\(729\) −548.311 + 480.412i −0.752141 + 0.659002i
\(730\) 0 0
\(731\) 80.4822i 0.110099i
\(732\) 0 0
\(733\) −618.776 1071.75i −0.844170 1.46215i −0.886340 0.463035i \(-0.846761\pi\)
0.0421703 0.999110i \(-0.486573\pi\)
\(734\) 0 0
\(735\) 34.6845 + 46.2447i 0.0471898 + 0.0629180i
\(736\) 0 0
\(737\) −896.295 + 517.476i −1.21614 + 0.702139i
\(738\) 0 0
\(739\) 202.246 350.300i 0.273675 0.474020i −0.696125 0.717921i \(-0.745094\pi\)
0.969800 + 0.243901i \(0.0784273\pi\)
\(740\) 0 0
\(741\) −61.9238 + 354.994i −0.0835679 + 0.479074i
\(742\) 0 0
\(743\) 43.4991i 0.0585452i −0.999571 0.0292726i \(-0.990681\pi\)
0.999571 0.0292726i \(-0.00931908\pi\)
\(744\) 0 0
\(745\) −87.2591 −0.117126
\(746\) 0 0
\(747\) 575.709 + 167.899i 0.770694 + 0.224764i
\(748\) 0 0
\(749\) 4.95650 + 2.86164i 0.00661749 + 0.00382061i
\(750\) 0 0
\(751\) −422.721 + 732.175i −0.562878 + 0.974933i 0.434366 + 0.900737i \(0.356973\pi\)
−0.997244 + 0.0741967i \(0.976361\pi\)
\(752\) 0 0
\(753\) −605.860 807.792i −0.804596 1.07277i
\(754\) 0 0
\(755\) −28.2218 16.2939i −0.0373799 0.0215813i
\(756\) 0 0
\(757\) −301.336 + 521.930i −0.398067 + 0.689472i −0.993487 0.113942i \(-0.963652\pi\)
0.595421 + 0.803414i \(0.296985\pi\)
\(758\) 0 0
\(759\) 792.268 594.217i 1.04383 0.782895i
\(760\) 0 0
\(761\) −737.213 + 425.630i −0.968743 + 0.559304i −0.898853 0.438251i \(-0.855598\pi\)
−0.0698901 + 0.997555i \(0.522265\pi\)
\(762\) 0 0
\(763\) 74.3440 + 128.768i 0.0974364 + 0.168765i
\(764\) 0 0
\(765\) 1.23415 4.23177i 0.00161327 0.00553172i
\(766\) 0 0
\(767\) −255.985 147.793i −0.333749 0.192690i
\(768\) 0 0
\(769\) 257.280 445.622i 0.334564 0.579483i −0.648837 0.760928i \(-0.724744\pi\)
0.983401 + 0.181445i \(0.0580775\pi\)
\(770\) 0 0
\(771\) −388.781 + 910.191i −0.504255 + 1.18053i
\(772\) 0 0
\(773\) 1074.64 620.446i 1.39023 0.802647i 0.396886 0.917868i \(-0.370091\pi\)
0.993340 + 0.115221i \(0.0367576\pi\)
\(774\) 0 0
\(775\) 402.801 + 697.671i 0.519743 + 0.900221i
\(776\) 0 0
\(777\) 67.8056 + 28.9626i 0.0872659 + 0.0372749i
\(778\) 0 0
\(779\) −717.738 + 168.799i −0.921358 + 0.216687i
\(780\) 0 0
\(781\) 528.542 + 915.462i 0.676751 + 1.17217i
\(782\) 0 0
\(783\) 470.200 176.848i 0.600511 0.225860i
\(784\) 0 0
\(785\) 65.8272i 0.0838563i
\(786\) 0 0
\(787\) 440.525 + 763.012i 0.559752 + 0.969519i 0.997517 + 0.0704296i \(0.0224370\pi\)
−0.437765 + 0.899090i \(0.644230\pi\)
\(788\) 0 0
\(789\) 863.279 + 1151.01i 1.09414 + 1.45882i
\(790\) 0 0
\(791\) 284.584i 0.359777i
\(792\) 0 0
\(793\) 52.6167 91.1347i 0.0663514 0.114924i
\(794\) 0 0
\(795\) 6.11165 4.58386i 0.00768761 0.00576586i
\(796\) 0 0
\(797\)