Properties

Label 144.3.o.a.31.3
Level $144$
Weight $3$
Character 144.31
Analytic conductor $3.924$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(-2.06288i\) of defining polynomial
Character \(\chi\) \(=\) 144.31
Dual form 144.3.o.a.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +O(q^{10})\) \(q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +(-3.70016 + 2.13629i) q^{11} +(0.869235 - 1.50556i) q^{13} +(-25.8164 - 10.0390i) q^{15} +12.3476 q^{17} -33.9338i q^{19} +(11.5590 + 14.4019i) q^{21} +(-3.35035 - 1.93433i) q^{23} +(-30.1260 - 52.1798i) q^{25} +(11.9428 + 24.2151i) q^{27} +(17.8409 + 30.9014i) q^{29} +(38.8262 + 22.4163i) q^{31} +(8.02306 + 9.99624i) q^{33} +56.8361i q^{35} -32.7130 q^{37} +(-4.86083 - 1.89019i) q^{39} +(21.8565 - 37.8565i) q^{41} +(33.9339 - 19.5918i) q^{43} +(-17.9836 + 81.1296i) q^{45} +(39.8784 - 23.0238i) q^{47} +(-5.55415 + 9.62007i) q^{49} +(-5.63558 - 36.6116i) q^{51} +46.3143 q^{53} +39.4496i q^{55} +(-100.617 + 15.4878i) q^{57} +(23.2710 + 13.4355i) q^{59} +(23.4545 + 40.6243i) q^{61} +(37.4270 - 40.8467i) q^{63} +(-8.02582 - 13.9011i) q^{65} +(-56.9984 - 32.9080i) q^{67} +(-4.20629 + 10.8169i) q^{69} +96.7955i q^{71} -14.0622 q^{73} +(-140.967 + 113.142i) q^{75} +(13.1502 - 22.7768i) q^{77} +(34.3954 - 19.8582i) q^{79} +(66.3487 - 46.4634i) q^{81} +(81.7202 - 47.1812i) q^{83} +(57.0039 - 98.7336i) q^{85} +(83.4822 - 67.0034i) q^{87} -81.8478 q^{89} +10.7014i q^{91} +(48.7454 - 125.354i) q^{93} +(-271.341 - 156.659i) q^{95} +(-7.99028 - 13.8396i) q^{97} +(25.9778 - 28.3514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + 18q^{11} + 5q^{13} - 21q^{15} + 6q^{17} - 33q^{21} - 81q^{23} - 23q^{25} + 108q^{27} + 69q^{29} + 45q^{31} + 72q^{33} - 20q^{37} - 141q^{39} + 54q^{41} - 117q^{45} + 207q^{47} + 41q^{49} - 141q^{51} - 252q^{53} - 273q^{57} - 306q^{59} + 7q^{61} + 441q^{63} + 93q^{65} + 12q^{67} + 189q^{69} + 74q^{73} - 387q^{75} + 207q^{77} + 33q^{79} + 117q^{81} + 549q^{83} - 30q^{85} - 87q^{87} - 168q^{89} - 27q^{93} - 684q^{95} - 10q^{97} + 585q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

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

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
\(3\) −0.456412 2.96508i −0.152137 0.988359i
\(4\) 0 0
\(5\) 4.61660 7.99619i 0.923321 1.59924i 0.129080 0.991634i \(-0.458797\pi\)
0.794240 0.607604i \(-0.207869\pi\)
\(6\) 0 0
\(7\) −5.33093 + 3.07781i −0.761561 + 0.439687i −0.829856 0.557978i \(-0.811577\pi\)
0.0682950 + 0.997665i \(0.478244\pi\)
\(8\) 0 0
\(9\) −8.58338 + 2.70659i −0.953709 + 0.300732i
\(10\) 0 0
\(11\) −3.70016 + 2.13629i −0.336378 + 0.194208i −0.658669 0.752433i \(-0.728880\pi\)
0.322291 + 0.946641i \(0.395547\pi\)
\(12\) 0 0
\(13\) 0.869235 1.50556i 0.0668642 0.115812i −0.830655 0.556787i \(-0.812034\pi\)
0.897519 + 0.440975i \(0.145367\pi\)
\(14\) 0 0
\(15\) −25.8164 10.0390i −1.72109 0.669269i
\(16\) 0 0
\(17\) 12.3476 0.726329 0.363164 0.931725i \(-0.381696\pi\)
0.363164 + 0.931725i \(0.381696\pi\)
\(18\) 0 0
\(19\) 33.9338i 1.78599i −0.450065 0.892996i \(-0.648599\pi\)
0.450065 0.892996i \(-0.351401\pi\)
\(20\) 0 0
\(21\) 11.5590 + 14.4019i 0.550431 + 0.685803i
\(22\) 0 0
\(23\) −3.35035 1.93433i −0.145668 0.0841012i 0.425395 0.905008i \(-0.360135\pi\)
−0.571062 + 0.820907i \(0.693469\pi\)
\(24\) 0 0
\(25\) −30.1260 52.1798i −1.20504 2.08719i
\(26\) 0 0
\(27\) 11.9428 + 24.2151i 0.442326 + 0.896854i
\(28\) 0 0
\(29\) 17.8409 + 30.9014i 0.615204 + 1.06556i 0.990349 + 0.138598i \(0.0442596\pi\)
−0.375145 + 0.926966i \(0.622407\pi\)
\(30\) 0 0
\(31\) 38.8262 + 22.4163i 1.25246 + 0.723107i 0.971597 0.236641i \(-0.0760466\pi\)
0.280861 + 0.959748i \(0.409380\pi\)
\(32\) 0 0
\(33\) 8.02306 + 9.99624i 0.243123 + 0.302916i
\(34\) 0 0
\(35\) 56.8361i 1.62389i
\(36\) 0 0
\(37\) −32.7130 −0.884134 −0.442067 0.896982i \(-0.645755\pi\)
−0.442067 + 0.896982i \(0.645755\pi\)
\(38\) 0 0
\(39\) −4.86083 1.89019i −0.124637 0.0484665i
\(40\) 0 0
\(41\) 21.8565 37.8565i 0.533085 0.923330i −0.466168 0.884696i \(-0.654366\pi\)
0.999253 0.0386343i \(-0.0123007\pi\)
\(42\) 0 0
\(43\) 33.9339 19.5918i 0.789161 0.455622i −0.0505063 0.998724i \(-0.516084\pi\)
0.839667 + 0.543102i \(0.182750\pi\)
\(44\) 0 0
\(45\) −17.9836 + 81.1296i −0.399636 + 1.80288i
\(46\) 0 0
\(47\) 39.8784 23.0238i 0.848477 0.489868i −0.0116600 0.999932i \(-0.503712\pi\)
0.860137 + 0.510064i \(0.170378\pi\)
\(48\) 0 0
\(49\) −5.55415 + 9.62007i −0.113350 + 0.196328i
\(50\) 0 0
\(51\) −5.63558 36.6116i −0.110502 0.717874i
\(52\) 0 0
\(53\) 46.3143 0.873854 0.436927 0.899497i \(-0.356067\pi\)
0.436927 + 0.899497i \(0.356067\pi\)
\(54\) 0 0
\(55\) 39.4496i 0.717265i
\(56\) 0 0
\(57\) −100.617 + 15.4878i −1.76520 + 0.271716i
\(58\) 0 0
\(59\) 23.2710 + 13.4355i 0.394423 + 0.227720i 0.684075 0.729412i \(-0.260206\pi\)
−0.289652 + 0.957132i \(0.593539\pi\)
\(60\) 0 0
\(61\) 23.4545 + 40.6243i 0.384500 + 0.665973i 0.991700 0.128576i \(-0.0410407\pi\)
−0.607200 + 0.794549i \(0.707707\pi\)
\(62\) 0 0
\(63\) 37.4270 40.8467i 0.594079 0.648360i
\(64\) 0 0
\(65\) −8.02582 13.9011i −0.123474 0.213864i
\(66\) 0 0
\(67\) −56.9984 32.9080i −0.850722 0.491164i 0.0101725 0.999948i \(-0.496762\pi\)
−0.860894 + 0.508784i \(0.830095\pi\)
\(68\) 0 0
\(69\) −4.20629 + 10.8169i −0.0609607 + 0.156767i
\(70\) 0 0
\(71\) 96.7955i 1.36332i 0.731671 + 0.681658i \(0.238741\pi\)
−0.731671 + 0.681658i \(0.761259\pi\)
\(72\) 0 0
\(73\) −14.0622 −0.192633 −0.0963163 0.995351i \(-0.530706\pi\)
−0.0963163 + 0.995351i \(0.530706\pi\)
\(74\) 0 0
\(75\) −140.967 + 113.142i −1.87957 + 1.50855i
\(76\) 0 0
\(77\) 13.1502 22.7768i 0.170782 0.295803i
\(78\) 0 0
\(79\) 34.3954 19.8582i 0.435385 0.251369i −0.266253 0.963903i \(-0.585786\pi\)
0.701638 + 0.712534i \(0.252452\pi\)
\(80\) 0 0
\(81\) 66.3487 46.4634i 0.819120 0.573622i
\(82\) 0 0
\(83\) 81.7202 47.1812i 0.984581 0.568448i 0.0809306 0.996720i \(-0.474211\pi\)
0.903650 + 0.428272i \(0.140877\pi\)
\(84\) 0 0
\(85\) 57.0039 98.7336i 0.670634 1.16157i
\(86\) 0 0
\(87\) 83.4822 67.0034i 0.959565 0.770154i
\(88\) 0 0
\(89\) −81.8478 −0.919639 −0.459819 0.888012i \(-0.652086\pi\)
−0.459819 + 0.888012i \(0.652086\pi\)
\(90\) 0 0
\(91\) 10.7014i 0.117597i
\(92\) 0 0
\(93\) 48.7454 125.354i 0.524144 1.34789i
\(94\) 0 0
\(95\) −271.341 156.659i −2.85623 1.64904i
\(96\) 0 0
\(97\) −7.99028 13.8396i −0.0823741 0.142676i 0.821895 0.569639i \(-0.192917\pi\)
−0.904269 + 0.426963i \(0.859584\pi\)
\(98\) 0 0
\(99\) 25.9778 28.3514i 0.262402 0.286378i
\(100\) 0 0
\(101\) 50.6344 + 87.7014i 0.501331 + 0.868330i 0.999999 + 0.00153723i \(0.000489314\pi\)
−0.498668 + 0.866793i \(0.666177\pi\)
\(102\) 0 0
\(103\) −88.4092 51.0431i −0.858341 0.495564i 0.00511517 0.999987i \(-0.498372\pi\)
−0.863456 + 0.504423i \(0.831705\pi\)
\(104\) 0 0
\(105\) 168.524 25.9407i 1.60499 0.247054i
\(106\) 0 0
\(107\) 73.1463i 0.683610i −0.939771 0.341805i \(-0.888962\pi\)
0.939771 0.341805i \(-0.111038\pi\)
\(108\) 0 0
\(109\) −33.9344 −0.311325 −0.155663 0.987810i \(-0.549751\pi\)
−0.155663 + 0.987810i \(0.549751\pi\)
\(110\) 0 0
\(111\) 14.9306 + 96.9965i 0.134510 + 0.873842i
\(112\) 0 0
\(113\) −13.9292 + 24.1262i −0.123268 + 0.213506i −0.921054 0.389434i \(-0.872671\pi\)
0.797787 + 0.602940i \(0.206004\pi\)
\(114\) 0 0
\(115\) −30.9345 + 17.8600i −0.268996 + 0.155305i
\(116\) 0 0
\(117\) −3.38604 + 15.2754i −0.0289405 + 0.130559i
\(118\) 0 0
\(119\) −65.8241 + 38.0035i −0.553143 + 0.319358i
\(120\) 0 0
\(121\) −51.3725 + 88.9798i −0.424566 + 0.735371i
\(122\) 0 0
\(123\) −122.223 47.5280i −0.993684 0.386407i
\(124\) 0 0
\(125\) −325.490 −2.60392
\(126\) 0 0
\(127\) 117.905i 0.928387i 0.885734 + 0.464193i \(0.153656\pi\)
−0.885734 + 0.464193i \(0.846344\pi\)
\(128\) 0 0
\(129\) −73.5789 91.6748i −0.570379 0.710657i
\(130\) 0 0
\(131\) 73.5214 + 42.4476i 0.561232 + 0.324027i 0.753640 0.657288i \(-0.228296\pi\)
−0.192408 + 0.981315i \(0.561630\pi\)
\(132\) 0 0
\(133\) 104.442 + 180.899i 0.785278 + 1.36014i
\(134\) 0 0
\(135\) 248.763 + 16.2943i 1.84269 + 0.120699i
\(136\) 0 0
\(137\) 3.97975 + 6.89314i 0.0290493 + 0.0503149i 0.880185 0.474632i \(-0.157419\pi\)
−0.851135 + 0.524946i \(0.824085\pi\)
\(138\) 0 0
\(139\) 17.9239 + 10.3484i 0.128949 + 0.0744488i 0.563087 0.826398i \(-0.309614\pi\)
−0.434138 + 0.900846i \(0.642947\pi\)
\(140\) 0 0
\(141\) −86.4683 107.734i −0.613251 0.764073i
\(142\) 0 0
\(143\) 7.42775i 0.0519423i
\(144\) 0 0
\(145\) 329.458 2.27212
\(146\) 0 0
\(147\) 31.0592 + 12.0778i 0.211287 + 0.0821617i
\(148\) 0 0
\(149\) 65.6122 113.644i 0.440350 0.762709i −0.557365 0.830267i \(-0.688188\pi\)
0.997715 + 0.0675588i \(0.0215210\pi\)
\(150\) 0 0
\(151\) −204.949 + 118.328i −1.35728 + 0.783627i −0.989257 0.146189i \(-0.953299\pi\)
−0.368025 + 0.929816i \(0.619966\pi\)
\(152\) 0 0
\(153\) −105.984 + 33.4199i −0.692706 + 0.218431i
\(154\) 0 0
\(155\) 358.490 206.974i 2.31284 1.33532i
\(156\) 0 0
\(157\) −74.8892 + 129.712i −0.477001 + 0.826190i −0.999653 0.0263562i \(-0.991610\pi\)
0.522651 + 0.852546i \(0.324943\pi\)
\(158\) 0 0
\(159\) −21.1384 137.325i −0.132946 0.863682i
\(160\) 0 0
\(161\) 23.8140 0.147913
\(162\) 0 0
\(163\) 152.365i 0.934756i −0.884057 0.467378i \(-0.845199\pi\)
0.884057 0.467378i \(-0.154801\pi\)
\(164\) 0 0
\(165\) 116.971 18.0053i 0.708916 0.109123i
\(166\) 0 0
\(167\) −21.5631 12.4494i −0.129120 0.0745476i 0.434049 0.900889i \(-0.357085\pi\)
−0.563169 + 0.826342i \(0.690418\pi\)
\(168\) 0 0
\(169\) 82.9889 + 143.741i 0.491058 + 0.850538i
\(170\) 0 0
\(171\) 91.8451 + 291.267i 0.537106 + 1.70332i
\(172\) 0 0
\(173\) −54.0452 93.6091i −0.312400 0.541093i 0.666481 0.745522i \(-0.267800\pi\)
−0.978881 + 0.204429i \(0.934466\pi\)
\(174\) 0 0
\(175\) 321.199 + 185.445i 1.83543 + 1.05968i
\(176\) 0 0
\(177\) 29.2162 75.1323i 0.165063 0.424477i
\(178\) 0 0
\(179\) 313.318i 1.75038i 0.483779 + 0.875190i \(0.339264\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(180\) 0 0
\(181\) 20.5886 0.113749 0.0568746 0.998381i \(-0.481886\pi\)
0.0568746 + 0.998381i \(0.481886\pi\)
\(182\) 0 0
\(183\) 109.749 88.0858i 0.599724 0.481343i
\(184\) 0 0
\(185\) −151.023 + 261.579i −0.816339 + 1.41394i
\(186\) 0 0
\(187\) −45.6881 + 26.3780i −0.244321 + 0.141059i
\(188\) 0 0
\(189\) −138.196 92.3310i −0.731194 0.488524i
\(190\) 0 0
\(191\) −23.6619 + 13.6612i −0.123884 + 0.0715247i −0.560662 0.828045i \(-0.689453\pi\)
0.436777 + 0.899570i \(0.356120\pi\)
\(192\) 0 0
\(193\) −65.7227 + 113.835i −0.340532 + 0.589819i −0.984532 0.175207i \(-0.943941\pi\)
0.644000 + 0.765026i \(0.277274\pi\)
\(194\) 0 0
\(195\) −37.5549 + 30.1418i −0.192589 + 0.154574i
\(196\) 0 0
\(197\) −126.466 −0.641961 −0.320981 0.947086i \(-0.604012\pi\)
−0.320981 + 0.947086i \(0.604012\pi\)
\(198\) 0 0
\(199\) 76.0070i 0.381945i 0.981595 + 0.190972i \(0.0611641\pi\)
−0.981595 + 0.190972i \(0.938836\pi\)
\(200\) 0 0
\(201\) −71.5601 + 184.024i −0.356021 + 0.915543i
\(202\) 0 0
\(203\) −190.217 109.822i −0.937030 0.540995i
\(204\) 0 0
\(205\) −201.805 349.537i −0.984417 1.70506i
\(206\) 0 0
\(207\) 33.9928 + 7.53502i 0.164216 + 0.0364011i
\(208\) 0 0
\(209\) 72.4925 + 125.561i 0.346854 + 0.600769i
\(210\) 0 0
\(211\) −91.8563 53.0332i −0.435338 0.251342i 0.266280 0.963896i \(-0.414205\pi\)
−0.701618 + 0.712553i \(0.747539\pi\)
\(212\) 0 0
\(213\) 287.006 44.1786i 1.34745 0.207411i
\(214\) 0 0
\(215\) 361.789i 1.68274i
\(216\) 0 0
\(217\) −275.973 −1.27176
\(218\) 0 0
\(219\) 6.41814 + 41.6954i 0.0293066 + 0.190390i
\(220\) 0 0
\(221\) 10.7330 18.5900i 0.0485654 0.0841177i
\(222\) 0 0
\(223\) 55.1700 31.8524i 0.247399 0.142836i −0.371174 0.928563i \(-0.621045\pi\)
0.618573 + 0.785728i \(0.287711\pi\)
\(224\) 0 0
\(225\) 399.813 + 366.340i 1.77695 + 1.62818i
\(226\) 0 0
\(227\) −304.643 + 175.886i −1.34204 + 0.774827i −0.987106 0.160065i \(-0.948830\pi\)
−0.354933 + 0.934892i \(0.615496\pi\)
\(228\) 0 0
\(229\) 102.232 177.072i 0.446429 0.773238i −0.551721 0.834029i \(-0.686029\pi\)
0.998151 + 0.0607903i \(0.0193621\pi\)
\(230\) 0 0
\(231\) −73.5369 28.5958i −0.318342 0.123791i
\(232\) 0 0
\(233\) 236.626 1.01556 0.507782 0.861486i \(-0.330466\pi\)
0.507782 + 0.861486i \(0.330466\pi\)
\(234\) 0 0
\(235\) 425.167i 1.80922i
\(236\) 0 0
\(237\) −74.5795 92.9215i −0.314682 0.392074i
\(238\) 0 0
\(239\) 16.1578 + 9.32873i 0.0676060 + 0.0390324i 0.533422 0.845849i \(-0.320906\pi\)
−0.465816 + 0.884882i \(0.654239\pi\)
\(240\) 0 0
\(241\) −37.2290 64.4826i −0.154477 0.267562i 0.778391 0.627779i \(-0.216036\pi\)
−0.932869 + 0.360217i \(0.882703\pi\)
\(242\) 0 0
\(243\) −168.050 175.523i −0.691564 0.722316i
\(244\) 0 0
\(245\) 51.2826 + 88.8241i 0.209317 + 0.362547i
\(246\) 0 0
\(247\) −51.0894 29.4965i −0.206840 0.119419i
\(248\) 0 0
\(249\) −177.194 220.773i −0.711622 0.886637i
\(250\) 0 0
\(251\) 206.637i 0.823257i 0.911352 + 0.411628i \(0.135040\pi\)
−0.911352 + 0.411628i \(0.864960\pi\)
\(252\) 0 0
\(253\) 16.5291 0.0653325
\(254\) 0 0
\(255\) −318.770 123.958i −1.25008 0.486109i
\(256\) 0 0
\(257\) 148.678 257.517i 0.578513 1.00201i −0.417138 0.908843i \(-0.636967\pi\)
0.995650 0.0931698i \(-0.0296999\pi\)
\(258\) 0 0
\(259\) 174.390 100.684i 0.673322 0.388743i
\(260\) 0 0
\(261\) −236.773 216.950i −0.907175 0.831226i
\(262\) 0 0
\(263\) 123.730 71.4357i 0.470457 0.271619i −0.245974 0.969276i \(-0.579108\pi\)
0.716431 + 0.697658i \(0.245774\pi\)
\(264\) 0 0
\(265\) 213.815 370.338i 0.806847 1.39750i
\(266\) 0 0
\(267\) 37.3563 + 242.685i 0.139911 + 0.908934i
\(268\) 0 0
\(269\) 370.517 1.37738 0.688692 0.725054i \(-0.258185\pi\)
0.688692 + 0.725054i \(0.258185\pi\)
\(270\) 0 0
\(271\) 368.022i 1.35801i 0.734132 + 0.679007i \(0.237589\pi\)
−0.734132 + 0.679007i \(0.762411\pi\)
\(272\) 0 0
\(273\) 31.7304 4.88423i 0.116229 0.0178909i
\(274\) 0 0
\(275\) 222.942 + 128.716i 0.810700 + 0.468058i
\(276\) 0 0
\(277\) −15.3234 26.5409i −0.0553191 0.0958154i 0.837040 0.547142i \(-0.184284\pi\)
−0.892359 + 0.451327i \(0.850951\pi\)
\(278\) 0 0
\(279\) −393.932 87.3210i −1.41194 0.312979i
\(280\) 0 0
\(281\) −231.041 400.176i −0.822212 1.42411i −0.904032 0.427465i \(-0.859407\pi\)
0.0818203 0.996647i \(-0.473927\pi\)
\(282\) 0 0
\(283\) −422.693 244.042i −1.49361 0.862339i −0.493642 0.869665i \(-0.664335\pi\)
−0.999973 + 0.00732653i \(0.997668\pi\)
\(284\) 0 0
\(285\) −340.663 + 876.050i −1.19531 + 3.07386i
\(286\) 0 0
\(287\) 269.081i 0.937563i
\(288\) 0 0
\(289\) −136.537 −0.472447
\(290\) 0 0
\(291\) −37.3886 + 30.0084i −0.128483 + 0.103122i
\(292\) 0 0
\(293\) 215.030 372.442i 0.733890 1.27113i −0.221319 0.975201i \(-0.571036\pi\)
0.955209 0.295933i \(-0.0956305\pi\)
\(294\) 0 0
\(295\) 214.866 124.053i 0.728358 0.420518i
\(296\) 0 0
\(297\) −95.9207 64.0863i −0.322965 0.215779i
\(298\) 0 0
\(299\) −5.82449 + 3.36277i −0.0194799 + 0.0112467i
\(300\) 0 0
\(301\) −120.599 + 208.884i −0.400663 + 0.693968i
\(302\) 0 0
\(303\) 236.931 190.163i 0.781951 0.627600i
\(304\) 0 0
\(305\) 433.120 1.42007
\(306\) 0 0
\(307\) 276.184i 0.899621i 0.893124 + 0.449810i \(0.148508\pi\)
−0.893124 + 0.449810i \(0.851492\pi\)
\(308\) 0 0
\(309\) −110.996 + 285.437i −0.359209 + 0.923743i
\(310\) 0 0
\(311\) 172.998 + 99.8806i 0.556264 + 0.321159i 0.751645 0.659568i \(-0.229261\pi\)
−0.195380 + 0.980728i \(0.562594\pi\)
\(312\) 0 0
\(313\) 59.3385 + 102.777i 0.189580 + 0.328362i 0.945110 0.326752i \(-0.105954\pi\)
−0.755530 + 0.655114i \(0.772621\pi\)
\(314\) 0 0
\(315\) −153.832 487.846i −0.488356 1.54872i
\(316\) 0 0
\(317\) 193.261 + 334.738i 0.609657 + 1.05596i 0.991297 + 0.131645i \(0.0420260\pi\)
−0.381640 + 0.924311i \(0.624641\pi\)
\(318\) 0 0
\(319\) −132.028 76.2267i −0.413882 0.238955i
\(320\) 0 0
\(321\) −216.884 + 33.3848i −0.675652 + 0.104003i
\(322\) 0 0
\(323\) 419.001i 1.29722i
\(324\) 0 0
\(325\) −104.746 −0.322297
\(326\) 0 0
\(327\) 15.4881 + 100.618i 0.0473641 + 0.307701i
\(328\) 0 0
\(329\) −141.726 + 245.476i −0.430778 + 0.746129i
\(330\) 0 0
\(331\) 282.733 163.236i 0.854179 0.493161i −0.00787942 0.999969i \(-0.502508\pi\)
0.862059 + 0.506808i \(0.169175\pi\)
\(332\) 0 0
\(333\) 280.788 88.5407i 0.843206 0.265888i
\(334\) 0 0
\(335\) −526.278 + 303.847i −1.57098 + 0.907005i
\(336\) 0 0
\(337\) 57.4906 99.5766i 0.170595 0.295479i −0.768033 0.640410i \(-0.778764\pi\)
0.938628 + 0.344931i \(0.112098\pi\)
\(338\) 0 0
\(339\) 77.8934 + 30.2898i 0.229774 + 0.0893506i
\(340\) 0 0
\(341\) −191.551 −0.561733
\(342\) 0 0
\(343\) 370.004i 1.07873i
\(344\) 0 0
\(345\) 67.0753 + 83.5717i 0.194421 + 0.242237i
\(346\) 0 0
\(347\) 502.945 + 290.375i 1.44941 + 0.836817i 0.998446 0.0557260i \(-0.0177473\pi\)
0.450963 + 0.892543i \(0.351081\pi\)
\(348\) 0 0
\(349\) −175.463 303.912i −0.502761 0.870807i −0.999995 0.00319067i \(-0.998984\pi\)
0.497234 0.867616i \(-0.334349\pi\)
\(350\) 0 0
\(351\) 46.8383 + 3.06797i 0.133442 + 0.00874066i
\(352\) 0 0
\(353\) −67.7870 117.411i −0.192031 0.332608i 0.753892 0.656998i \(-0.228174\pi\)
−0.945923 + 0.324390i \(0.894841\pi\)
\(354\) 0 0
\(355\) 773.995 + 446.866i 2.18027 + 1.25878i
\(356\) 0 0
\(357\) 142.726 + 177.828i 0.399794 + 0.498118i
\(358\) 0 0
\(359\) 108.852i 0.303210i −0.988441 0.151605i \(-0.951556\pi\)
0.988441 0.151605i \(-0.0484441\pi\)
\(360\) 0 0
\(361\) −790.506 −2.18977
\(362\) 0 0
\(363\) 287.279 + 111.712i 0.791403 + 0.307747i
\(364\) 0 0
\(365\) −64.9195 + 112.444i −0.177862 + 0.308065i
\(366\) 0 0
\(367\) 14.6619 8.46503i 0.0399506 0.0230655i −0.479892 0.877328i \(-0.659324\pi\)
0.519842 + 0.854262i \(0.325991\pi\)
\(368\) 0 0
\(369\) −85.1402 + 384.094i −0.230732 + 1.04090i
\(370\) 0 0
\(371\) −246.898 + 142.547i −0.665493 + 0.384223i
\(372\) 0 0
\(373\) −18.5300 + 32.0949i −0.0496783 + 0.0860454i −0.889795 0.456360i \(-0.849153\pi\)
0.840117 + 0.542405i \(0.182486\pi\)
\(374\) 0 0
\(375\) 148.557 + 965.102i 0.396153 + 2.57361i
\(376\) 0 0
\(377\) 62.0318 0.164540
\(378\) 0 0
\(379\) 531.193i 1.40156i 0.713375 + 0.700782i \(0.247166\pi\)
−0.713375 + 0.700782i \(0.752834\pi\)
\(380\) 0 0
\(381\) 349.598 53.8133i 0.917580 0.141242i
\(382\) 0 0
\(383\) 324.004 + 187.064i 0.845963 + 0.488417i 0.859287 0.511494i \(-0.170908\pi\)
−0.0133235 + 0.999911i \(0.504241\pi\)
\(384\) 0 0
\(385\) −121.418 210.303i −0.315373 0.546241i
\(386\) 0 0
\(387\) −238.241 + 260.009i −0.615609 + 0.671857i
\(388\) 0 0
\(389\) 271.593 + 470.412i 0.698182 + 1.20929i 0.969096 + 0.246683i \(0.0793406\pi\)
−0.270915 + 0.962603i \(0.587326\pi\)
\(390\) 0 0
\(391\) −41.3688 23.8843i −0.105802 0.0610851i
\(392\) 0 0
\(393\) 92.3044 237.370i 0.234871 0.603995i
\(394\) 0 0
\(395\) 366.709i 0.928378i
\(396\) 0 0
\(397\) 606.097 1.52669 0.763346 0.645990i \(-0.223555\pi\)
0.763346 + 0.645990i \(0.223555\pi\)
\(398\) 0 0
\(399\) 488.711 392.243i 1.22484 0.983065i
\(400\) 0 0
\(401\) −293.529 + 508.408i −0.731994 + 1.26785i 0.224036 + 0.974581i \(0.428077\pi\)
−0.956030 + 0.293269i \(0.905257\pi\)
\(402\) 0 0
\(403\) 67.4982 38.9701i 0.167489 0.0967000i
\(404\) 0 0
\(405\) −65.2245 745.040i −0.161048 1.83961i
\(406\) 0 0
\(407\) 121.043 69.8844i 0.297404 0.171706i
\(408\) 0 0
\(409\) 129.882 224.961i 0.317559 0.550028i −0.662419 0.749133i \(-0.730470\pi\)
0.979978 + 0.199105i \(0.0638036\pi\)
\(410\) 0 0
\(411\) 18.6223 14.9464i 0.0453097 0.0363659i
\(412\) 0 0
\(413\) −165.408 −0.400503
\(414\) 0 0
\(415\) 871.267i 2.09944i
\(416\) 0 0
\(417\) 22.5031 57.8689i 0.0539642 0.138774i
\(418\) 0 0
\(419\) −297.997 172.049i −0.711210 0.410617i 0.100299 0.994957i \(-0.468020\pi\)
−0.811509 + 0.584340i \(0.801353\pi\)
\(420\) 0 0
\(421\) 153.263 + 265.460i 0.364046 + 0.630546i 0.988623 0.150417i \(-0.0480617\pi\)
−0.624576 + 0.780964i \(0.714728\pi\)
\(422\) 0 0
\(423\) −279.975 + 305.557i −0.661880 + 0.722356i
\(424\) 0 0
\(425\) −371.984 644.295i −0.875256 1.51599i
\(426\) 0 0
\(427\) −250.068 144.377i −0.585640 0.338119i
\(428\) 0 0
\(429\) 22.0239 3.39011i 0.0513376 0.00790235i
\(430\) 0 0
\(431\) 208.029i 0.482667i 0.970442 + 0.241333i \(0.0775847\pi\)
−0.970442 + 0.241333i \(0.922415\pi\)
\(432\) 0 0
\(433\) 353.874 0.817260 0.408630 0.912700i \(-0.366007\pi\)
0.408630 + 0.912700i \(0.366007\pi\)
\(434\) 0 0
\(435\) −150.368 976.867i −0.345674 2.24567i
\(436\) 0 0
\(437\) −65.6392 + 113.690i −0.150204 + 0.260161i
\(438\) 0 0
\(439\) −200.356 + 115.675i −0.456391 + 0.263497i −0.710525 0.703672i \(-0.751543\pi\)
0.254135 + 0.967169i \(0.418209\pi\)
\(440\) 0 0
\(441\) 21.6358 97.6055i 0.0490607 0.221328i
\(442\) 0 0
\(443\) 221.434 127.845i 0.499851 0.288589i −0.228801 0.973473i \(-0.573480\pi\)
0.728652 + 0.684884i \(0.240147\pi\)
\(444\) 0 0
\(445\) −377.859 + 654.471i −0.849121 + 1.47072i
\(446\) 0 0
\(447\) −366.908 142.677i −0.820824 0.319188i
\(448\) 0 0
\(449\) 323.060 0.719509 0.359755 0.933047i \(-0.382860\pi\)
0.359755 + 0.933047i \(0.382860\pi\)
\(450\) 0 0
\(451\) 186.767i 0.414118i
\(452\) 0 0
\(453\) 444.392 + 553.685i 0.980998 + 1.22226i
\(454\) 0 0
\(455\) 85.5702 + 49.4039i 0.188066 + 0.108580i
\(456\) 0 0
\(457\) 277.264 + 480.235i 0.606704 + 1.05084i 0.991780 + 0.127957i \(0.0408418\pi\)
−0.385076 + 0.922885i \(0.625825\pi\)
\(458\) 0 0
\(459\) 147.465 + 298.998i 0.321274 + 0.651411i
\(460\) 0 0
\(461\) −368.753 638.699i −0.799898 1.38546i −0.919682 0.392664i \(-0.871553\pi\)
0.119784 0.992800i \(-0.461780\pi\)
\(462\) 0 0
\(463\) −116.461 67.2386i −0.251535 0.145224i 0.368932 0.929456i \(-0.379724\pi\)
−0.620467 + 0.784233i \(0.713057\pi\)
\(464\) 0 0
\(465\) −777.315 968.486i −1.67164 2.08277i
\(466\) 0 0
\(467\) 595.000i 1.27409i −0.770827 0.637045i \(-0.780156\pi\)
0.770827 0.637045i \(-0.219844\pi\)
\(468\) 0 0
\(469\) 405.139 0.863835
\(470\) 0 0
\(471\) 418.786 + 162.850i 0.889143 + 0.345754i
\(472\) 0 0
\(473\) −83.7073 + 144.985i −0.176971 + 0.306523i
\(474\) 0 0
\(475\) −1770.66 + 1022.29i −3.72771 + 2.15219i
\(476\) 0 0
\(477\) −397.533 + 125.354i −0.833402 + 0.262796i
\(478\) 0 0
\(479\) −388.924 + 224.545i −0.811950 + 0.468779i −0.847632 0.530584i \(-0.821973\pi\)
0.0356829 + 0.999363i \(0.488639\pi\)
\(480\) 0 0
\(481\) −28.4352 + 49.2513i −0.0591169 + 0.102394i
\(482\) 0 0
\(483\) −10.8690 70.6103i −0.0225031 0.146191i
\(484\) 0 0
\(485\) −147.552 −0.304231
\(486\) 0 0
\(487\) 120.044i 0.246497i 0.992376 + 0.123249i \(0.0393312\pi\)
−0.992376 + 0.123249i \(0.960669\pi\)
\(488\) 0 0
\(489\) −451.775 + 69.5413i −0.923875 + 0.142211i
\(490\) 0 0
\(491\) −372.302 214.949i −0.758252 0.437777i 0.0704158 0.997518i \(-0.477567\pi\)
−0.828668 + 0.559741i \(0.810901\pi\)
\(492\) 0 0
\(493\) 220.292 + 381.557i 0.446840 + 0.773950i
\(494\) 0 0
\(495\) −106.774 338.611i −0.215705 0.684062i
\(496\) 0 0
\(497\) −297.918 516.010i −0.599433 1.03825i
\(498\) 0 0
\(499\) 639.117 + 368.994i 1.28080 + 0.739467i 0.976994 0.213268i \(-0.0684107\pi\)
0.303802 + 0.952735i \(0.401744\pi\)
\(500\) 0 0
\(501\) −27.0719 + 69.6182i −0.0540358 + 0.138959i
\(502\) 0 0
\(503\) 951.782i 1.89221i −0.323859 0.946105i \(-0.604980\pi\)
0.323859 0.946105i \(-0.395020\pi\)
\(504\) 0 0
\(505\) 935.036 1.85156
\(506\) 0 0
\(507\) 388.326 311.673i 0.765929 0.614741i
\(508\) 0 0
\(509\) 37.8898 65.6271i 0.0744398 0.128933i −0.826403 0.563079i \(-0.809616\pi\)
0.900843 + 0.434146i \(0.142950\pi\)
\(510\) 0 0
\(511\) 74.9644 43.2807i 0.146701 0.0846981i
\(512\) 0 0
\(513\) 821.710 405.265i 1.60177 0.789991i
\(514\) 0 0
\(515\) −816.300 + 471.291i −1.58505 + 0.915128i
\(516\) 0 0
\(517\) −98.3710 + 170.384i −0.190273 + 0.329562i
\(518\) 0 0
\(519\) −252.891 + 202.973i −0.487267 + 0.391084i
\(520\) 0 0
\(521\) 24.6152 0.0472461 0.0236230 0.999721i \(-0.492480\pi\)
0.0236230 + 0.999721i \(0.492480\pi\)
\(522\) 0 0
\(523\) 165.798i 0.317013i −0.987358 0.158506i \(-0.949332\pi\)
0.987358 0.158506i \(-0.0506678\pi\)
\(524\) 0 0
\(525\) 403.259 1037.02i 0.768111 1.97528i
\(526\) 0 0
\(527\) 479.410 + 276.787i 0.909696 + 0.525213i
\(528\) 0 0
\(529\) −257.017 445.166i −0.485854 0.841524i
\(530\) 0 0
\(531\) −236.108 52.3369i −0.444648 0.0985630i
\(532\) 0 0
\(533\) −37.9968 65.8124i −0.0712886 0.123476i
\(534\) 0 0
\(535\) −584.892 337.687i −1.09326 0.631191i
\(536\) 0 0
\(537\) 929.013 143.002i 1.73001 0.266298i
\(538\) 0 0
\(539\) 47.4611i 0.0880539i
\(540\) 0 0
\(541\) −184.323 −0.340708 −0.170354 0.985383i \(-0.554491\pi\)
−0.170354 + 0.985383i \(0.554491\pi\)
\(542\) 0 0
\(543\) −9.39688 61.0469i −0.0173055 0.112425i
\(544\) 0 0
\(545\) −156.662 + 271.346i −0.287453 + 0.497883i
\(546\) 0 0
\(547\) 803.354 463.817i 1.46865 0.847928i 0.469272 0.883054i \(-0.344517\pi\)
0.999383 + 0.0351259i \(0.0111832\pi\)
\(548\) 0 0
\(549\) −311.272 285.212i −0.566980 0.519512i
\(550\) 0 0
\(551\) 1048.60 605.411i 1.90309 1.09875i
\(552\) 0 0
\(553\) −122.240 + 211.725i −0.221048 + 0.382866i
\(554\) 0 0
\(555\) 844.531 + 328.407i 1.52168 + 0.591724i
\(556\) 0 0
\(557\) −492.087 −0.883459 −0.441730 0.897148i \(-0.645635\pi\)
−0.441730 + 0.897148i \(0.645635\pi\)
\(558\) 0 0
\(559\) 68.1193i 0.121859i
\(560\) 0 0
\(561\) 99.0654 + 123.429i 0.176587 + 0.220017i
\(562\) 0 0
\(563\) −626.453 361.683i −1.11271 0.642421i −0.173177 0.984891i \(-0.555403\pi\)
−0.939529 + 0.342470i \(0.888736\pi\)
\(564\) 0 0
\(565\) 128.612 + 222.762i 0.227631 + 0.394269i
\(566\) 0 0
\(567\) −210.695 + 451.902i −0.371595 + 0.797005i
\(568\) 0 0
\(569\) 435.816 + 754.855i 0.765933 + 1.32664i 0.939752 + 0.341857i \(0.111056\pi\)
−0.173819 + 0.984778i \(0.555611\pi\)
\(570\) 0 0
\(571\) −210.649 121.618i −0.368912 0.212991i 0.304071 0.952649i \(-0.401654\pi\)
−0.672983 + 0.739658i \(0.734987\pi\)
\(572\) 0 0
\(573\) 51.3061 + 63.9243i 0.0895395 + 0.111561i
\(574\) 0 0
\(575\) 233.094i 0.405382i
\(576\) 0 0
\(577\) −201.625 −0.349436 −0.174718 0.984619i \(-0.555901\pi\)
−0.174718 + 0.984619i \(0.555901\pi\)
\(578\) 0 0
\(579\) 367.526 + 142.917i 0.634761 + 0.246835i
\(580\) 0 0
\(581\) −290.430 + 503.039i −0.499879 + 0.865815i
\(582\) 0 0
\(583\) −171.370 + 98.9406i −0.293945 + 0.169710i
\(584\) 0 0
\(585\) 106.513 + 97.5960i 0.182074 + 0.166831i
\(586\) 0 0
\(587\) −688.983 + 397.784i −1.17374 + 0.677656i −0.954557 0.298029i \(-0.903671\pi\)
−0.219178 + 0.975685i \(0.570338\pi\)
\(588\) 0 0
\(589\) 760.672 1317.52i 1.29146 2.23688i
\(590\) 0 0
\(591\) 57.7207 + 374.983i 0.0976662 + 0.634489i
\(592\) 0 0
\(593\) −1078.05 −1.81796 −0.908980 0.416839i \(-0.863138\pi\)
−0.908980 + 0.416839i \(0.863138\pi\)
\(594\) 0 0
\(595\) 701.789i 1.17948i
\(596\) 0 0
\(597\) 225.367 34.6905i 0.377499 0.0581080i
\(598\) 0 0
\(599\) 209.699 + 121.070i 0.350082 + 0.202120i 0.664722 0.747091i \(-0.268550\pi\)
−0.314639 + 0.949211i \(0.601883\pi\)
\(600\) 0 0
\(601\) 135.406 + 234.529i 0.225300 + 0.390232i 0.956410 0.292029i \(-0.0943303\pi\)
−0.731109 + 0.682261i \(0.760997\pi\)
\(602\) 0 0
\(603\) 578.307 + 128.191i 0.959050 + 0.212588i
\(604\) 0 0
\(605\) 474.333 + 821.569i 0.784022 + 1.35797i
\(606\) 0 0
\(607\) 335.657 + 193.792i 0.552977 + 0.319261i 0.750322 0.661073i \(-0.229899\pi\)
−0.197345 + 0.980334i \(0.563232\pi\)
\(608\) 0 0
\(609\) −238.813 + 614.133i −0.392140 + 1.00843i
\(610\) 0 0
\(611\) 80.0524i 0.131019i
\(612\) 0 0
\(613\) −1120.09 −1.82722 −0.913610 0.406591i \(-0.866718\pi\)
−0.913610 + 0.406591i \(0.866718\pi\)
\(614\) 0 0
\(615\) −944.299 + 757.902i −1.53545 + 1.23236i
\(616\) 0 0
\(617\) −266.289 + 461.226i −0.431587 + 0.747530i −0.997010 0.0772706i \(-0.975379\pi\)
0.565423 + 0.824801i \(0.308713\pi\)
\(618\) 0 0
\(619\) 761.814 439.833i 1.23072 0.710555i 0.263537 0.964649i \(-0.415111\pi\)
0.967179 + 0.254095i \(0.0817774\pi\)
\(620\) 0 0
\(621\) 6.82723 104.230i 0.0109939 0.167843i
\(622\) 0 0
\(623\) 436.325 251.912i 0.700361 0.404354i
\(624\) 0 0
\(625\) −749.506 + 1298.18i −1.19921 + 2.07709i
\(626\) 0 0
\(627\) 339.211 272.253i 0.541006 0.434216i
\(628\) 0 0
\(629\) −403.926 −0.642172
\(630\) 0 0
\(631\) 310.499i 0.492075i 0.969260 + 0.246037i \(0.0791286\pi\)
−0.969260 + 0.246037i \(0.920871\pi\)
\(632\) 0 0
\(633\) −115.323 + 296.566i −0.182186 + 0.468509i
\(634\) 0 0
\(635\) 942.792 + 544.321i 1.48471 + 0.857199i
\(636\) 0 0
\(637\) 9.65572 + 16.7242i 0.0151581 + 0.0262546i
\(638\) 0 0
\(639\) −261.986 830.832i −0.409994 1.30021i
\(640\) 0 0
\(641\) −275.610 477.371i −0.429969 0.744728i 0.566901 0.823786i \(-0.308142\pi\)
−0.996870 + 0.0790578i \(0.974809\pi\)
\(642\) 0 0
\(643\) −352.044 203.253i −0.547503 0.316101i 0.200611 0.979671i \(-0.435707\pi\)
−0.748114 + 0.663570i \(0.769041\pi\)
\(644\) 0 0
\(645\) −1072.73 + 165.125i −1.66315 + 0.256008i
\(646\) 0 0
\(647\) 652.891i 1.00910i 0.863381 + 0.504552i \(0.168342\pi\)
−0.863381 + 0.504552i \(0.831658\pi\)
\(648\) 0 0
\(649\) −114.808 −0.176900
\(650\) 0 0
\(651\) 125.957 + 818.281i 0.193483 + 1.25696i
\(652\) 0 0
\(653\) 513.767 889.870i 0.786779 1.36274i −0.141151 0.989988i \(-0.545080\pi\)
0.927930 0.372754i \(-0.121586\pi\)
\(654\) 0 0
\(655\) 678.838 391.927i 1.03639 0.598362i
\(656\) 0 0
\(657\) 120.701 38.0606i 0.183715 0.0579309i
\(658\) 0 0
\(659\) 20.5780 11.8807i 0.0312261 0.0180284i −0.484306 0.874899i \(-0.660928\pi\)
0.515532 + 0.856870i \(0.327594\pi\)
\(660\) 0 0
\(661\) 328.164 568.396i 0.496465 0.859903i −0.503526 0.863980i \(-0.667964\pi\)
0.999992 + 0.00407665i \(0.00129764\pi\)
\(662\) 0 0
\(663\) −60.0195 23.3393i −0.0905271 0.0352026i
\(664\) 0 0
\(665\) 1928.67 2.90025
\(666\) 0 0
\(667\) 138.041i 0.206957i
\(668\) 0 0
\(669\) −119.625 149.046i −0.178812 0.222789i
\(670\) 0 0
\(671\) −173.571 100.211i −0.258675 0.149346i
\(672\) 0 0
\(673\) 405.169 + 701.773i 0.602034 + 1.04275i 0.992513 + 0.122141i \(0.0389760\pi\)
−0.390479 + 0.920612i \(0.627691\pi\)
\(674\) 0 0
\(675\) 903.748 1352.68i 1.33889 2.00397i
\(676\) 0 0
\(677\) −199.580 345.683i −0.294801 0.510610i 0.680138 0.733084i \(-0.261920\pi\)
−0.974939 + 0.222474i \(0.928587\pi\)
\(678\) 0 0
\(679\) 85.1912 + 49.1852i 0.125466 + 0.0724377i
\(680\) 0 0
\(681\) 660.557 + 823.014i 0.969981 + 1.20854i
\(682\) 0 0
\(683\) 203.612i 0.298114i −0.988829 0.149057i \(-0.952376\pi\)
0.988829 0.149057i \(-0.0476238\pi\)
\(684\) 0 0
\(685\) 73.4918 0.107287
\(686\) 0 0
\(687\) −571.691 222.309i −0.832156 0.323594i
\(688\) 0 0
\(689\) 40.2580 69.7288i 0.0584296 0.101203i
\(690\) 0 0
\(691\) −255.646 + 147.597i −0.369965 + 0.213599i −0.673443 0.739239i \(-0.735185\pi\)
0.303478 + 0.952838i \(0.401852\pi\)
\(692\) 0 0
\(693\) −51.2255 + 231.094i −0.0739185 + 0.333469i
\(694\) 0 0
\(695\) 165.495 95.5487i 0.238123 0.137480i
\(696\) 0 0
\(697\) 269.875 467.437i 0.387195 0.670641i
\(698\) 0 0
\(699\) −107.999 701.615i −0.154505 1.00374i
\(700\) 0 0
\(701\) 283.069 0.403808 0.201904 0.979405i \(-0.435287\pi\)
0.201904 + 0.979405i \(0.435287\pi\)
\(702\) 0 0
\(703\) 1110.08i 1.57906i
\(704\) 0 0
\(705\) −1260.65 + 194.051i −1.78816 + 0.275250i
\(706\) 0 0
\(707\) −539.857 311.686i −0.763588 0.440858i
\(708\) 0 0
\(709\) −209.399 362.690i −0.295344 0.511551i 0.679721 0.733471i \(-0.262101\pi\)
−0.975065 + 0.221920i \(0.928768\pi\)
\(710\) 0 0
\(711\) −241.481 + 263.545i −0.339635 + 0.370667i
\(712\) 0 0
\(713\) −86.7210 150.205i −0.121628 0.210666i
\(714\) 0 0
\(715\) 59.3937 + 34.2910i 0.0830681 + 0.0479594i
\(716\) 0 0
\(717\) 20.2858 52.1670i 0.0282926 0.0727573i
\(718\) 0 0
\(719\) 454.879i 0.632655i 0.948650 + 0.316328i \(0.102450\pi\)
−0.948650 + 0.316328i \(0.897550\pi\)
\(720\) 0 0
\(721\) 628.404 0.871572
\(722\) 0 0
\(723\) −174.204 + 139.818i −0.240946 + 0.193385i
\(724\) 0 0
\(725\) 1074.95 1861.87i 1.48269 2.56810i
\(726\) 0 0
\(727\) −207.375 + 119.728i −0.285247 + 0.164688i −0.635797 0.771857i \(-0.719328\pi\)
0.350549 + 0.936544i \(0.385995\pi\)
\(728\) 0 0
\(729\) −443.739 + 578.392i −0.608695 + 0.793404i
\(730\) 0 0
\(731\) 419.002 241.911i 0.573190 0.330931i
\(732\) 0 0
\(733\) −210.973 + 365.416i −0.287822 + 0.498522i −0.973289 0.229581i \(-0.926264\pi\)
0.685468 + 0.728103i \(0.259598\pi\)
\(734\) 0 0
\(735\) 239.964 192.597i 0.326482 0.262037i
\(736\) 0 0
\(737\) 281.204 0.381552
\(738\) 0 0
\(739\) 150.203i 0.203251i 0.994823 + 0.101626i \(0.0324044\pi\)
−0.994823 + 0.101626i \(0.967596\pi\)
\(740\) 0 0
\(741\) −64.1416 + 164.947i −0.0865608 + 0.222600i
\(742\) 0 0
\(743\) 726.756 + 419.593i 0.978137 + 0.564728i 0.901707 0.432347i \(-0.142315\pi\)
0.0764298 + 0.997075i \(0.475648\pi\)
\(744\) 0 0
\(745\) −605.810 1049.29i −0.813168 1.40845i
\(746\) 0 0
\(747\) −573.735 + 626.157i −0.768052 + 0.838229i
\(748\) 0 0
\(749\) 225.130 + 389.937i 0.300575 + 0.520611i
\(750\) 0 0
\(751\) −634.488 366.322i −0.844858 0.487779i 0.0140549 0.999901i \(-0.495526\pi\)
−0.858912 + 0.512122i \(0.828859\pi\)
\(752\) 0 0
\(753\) 612.696 94.3117i 0.813673 0.125248i
\(754\) 0 0
\(755\) 2185.09i 2.89415i
\(756\) 0 0
\(757\) −1455.19 −1.92231 −0.961153 0.276015i \(-0.910986\pi\)
−0.961153 + 0.276015i \(0.910986\pi\)
\(758\) 0 0
\(759\) −7.54409 49.0102i −0.00993951 0.0645720i
\(760\) 0 0
\(761\) 365.230 632.596i 0.479934 0.831270i −0.519801 0.854287i \(-0.673994\pi\)
0.999735 + 0.0230176i \(0.00732737\pi\)
\(762\) 0 0
\(763\) 180.902 104.444i 0.237093 0.136886i
\(764\) 0 0
\(765\) −222.054 + 1001.75i −0.290267 + 1.30948i
\(766\) 0 0
\(767\) 40.4559 23.3572i 0.0527456 0.0304527i
\(768\) 0 0
\(769\) 430.746 746.074i 0.560138 0.970187i −0.437346 0.899293i \(-0.644082\pi\)
0.997484 0.0708938i \(-0.0225851\pi\)
\(770\) 0 0
\(771\) −831.417 323.307i −1.07836 0.419335i
\(772\) 0 0
\(773\) −981.517 −1.26975 −0.634875 0.772615i \(-0.718948\pi\)
−0.634875 + 0.772615i \(0.718948\pi\)
\(774\) 0 0
\(775\) 2701.26i 3.48550i
\(776\) 0 0
\(777\) −378.131 471.128i −0.486655 0.606342i
\(778\) 0 0
\(779\) −1284.62 741.675i −1.64906 0.952085i
\(780\) 0 0
\(781\) −206.783 358.159i −0.264767 0.458590i
\(782\) 0 0
\(783\) −535.208 + 801.068i −0.683535 + 1.02308i
\(784\) 0 0
\(785\) 691.467 + 1197.66i 0.880850 + 1.52568i
\(786\) 0 0
\(787\) 614.292 + 354.662i 0.780549 + 0.450650i 0.836625 0.547776i \(-0.184526\pi\)
−0.0560758 + 0.998427i \(0.517859\pi\)
\(788\) 0 0
\(789\) −268.284 334.266i −0.340031 0.423658i
\(790\) 0 0
\(791\) 171.486i 0.216797i
\(792\) 0 0
\(793\) 81.5498 0.102837
\(794\) 0 0
\(795\)