Properties

Label 144.3.o.a.79.3
Level $144$
Weight $3$
Character 144.79
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 79.3
Root \(2.06288i\) of defining polynomial
Character \(\chi\) \(=\) 144.79
Dual form 144.3.o.a.31.3

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.456412 + 2.96508i −0.152137 + 0.988359i
\(4\) 0 0
\(5\) 4.61660 + 7.99619i 0.923321 + 1.59924i 0.794240 + 0.607604i \(0.207869\pi\)
0.129080 + 0.991634i \(0.458797\pi\)
\(6\) 0 0
\(7\) −5.33093 3.07781i −0.761561 0.439687i 0.0682950 0.997665i \(-0.478244\pi\)
−0.829856 + 0.557978i \(0.811577\pi\)
\(8\) 0 0
\(9\) −8.58338 2.70659i −0.953709 0.300732i
\(10\) 0 0
\(11\) −3.70016 2.13629i −0.336378 0.194208i 0.322291 0.946641i \(-0.395547\pi\)
−0.658669 + 0.752433i \(0.728880\pi\)
\(12\) 0 0
\(13\) 0.869235 + 1.50556i 0.0668642 + 0.115812i 0.897519 0.440975i \(-0.145367\pi\)
−0.830655 + 0.556787i \(0.812034\pi\)
\(14\) 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 \(0.351401\pi\)
−0.450065 + 0.892996i \(0.648599\pi\)
\(20\) 0 0
\(21\) 11.5590 14.4019i 0.550431 0.685803i
\(22\) 0 0
\(23\) −3.35035 + 1.93433i −0.145668 + 0.0841012i −0.571062 0.820907i \(-0.693469\pi\)
0.425395 + 0.905008i \(0.360135\pi\)
\(24\) 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 −0.375145 0.926966i \(-0.622407\pi\)
0.990349 0.138598i \(-0.0442596\pi\)
\(30\) 0 0
\(31\) 38.8262 22.4163i 1.25246 0.723107i 0.280861 0.959748i \(-0.409380\pi\)
0.971597 + 0.236641i \(0.0760466\pi\)
\(32\) 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 0.999253 + 0.0386343i \(0.0123007\pi\)
−0.466168 + 0.884696i \(0.654366\pi\)
\(42\) 0 0
\(43\) 33.9339 + 19.5918i 0.789161 + 0.455622i 0.839667 0.543102i \(-0.182750\pi\)
−0.0505063 + 0.998724i \(0.516084\pi\)
\(44\) 0 0
\(45\) −17.9836 81.1296i −0.399636 1.80288i
\(46\) 0 0
\(47\) 39.8784 + 23.0238i 0.848477 + 0.489868i 0.860137 0.510064i \(-0.170378\pi\)
−0.0116600 + 0.999932i \(0.503712\pi\)
\(48\) 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 −0.289652 0.957132i \(-0.593539\pi\)
0.684075 + 0.729412i \(0.260206\pi\)
\(60\) 0 0
\(61\) 23.4545 40.6243i 0.384500 0.665973i −0.607200 0.794549i \(-0.707707\pi\)
0.991700 + 0.128576i \(0.0410407\pi\)
\(62\) 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 −0.860894 0.508784i \(-0.830095\pi\)
0.0101725 + 0.999948i \(0.496762\pi\)
\(68\) 0 0
\(69\) −4.20629 10.8169i −0.0609607 0.156767i
\(70\) 0 0
\(71\) 96.7955i 1.36332i −0.731671 0.681658i \(-0.761259\pi\)
0.731671 0.681658i \(-0.238741\pi\)
\(72\) 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 0.701638 0.712534i \(-0.252452\pi\)
−0.266253 + 0.963903i \(0.585786\pi\)
\(80\) 0 0
\(81\) 66.3487 + 46.4634i 0.819120 + 0.573622i
\(82\) 0 0
\(83\) 81.7202 + 47.1812i 0.984581 + 0.568448i 0.903650 0.428272i \(-0.140877\pi\)
0.0809306 + 0.996720i \(0.474211\pi\)
\(84\) 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 −0.904269 0.426963i \(-0.859584\pi\)
0.821895 + 0.569639i \(0.192917\pi\)
\(98\) 0 0
\(99\) 25.9778 + 28.3514i 0.262402 + 0.286378i
\(100\) 0 0
\(101\) 50.6344 87.7014i 0.501331 0.868330i −0.498668 0.866793i \(-0.666177\pi\)
0.999999 0.00153723i \(-0.000489314\pi\)
\(102\) 0 0
\(103\) −88.4092 + 51.0431i −0.858341 + 0.495564i −0.863456 0.504423i \(-0.831705\pi\)
0.00511517 + 0.999987i \(0.498372\pi\)
\(104\) 0 0
\(105\) 168.524 + 25.9407i 1.60499 + 0.247054i
\(106\) 0 0
\(107\) 73.1463i 0.683610i 0.939771 + 0.341805i \(0.111038\pi\)
−0.939771 + 0.341805i \(0.888962\pi\)
\(108\) 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 0.797787 0.602940i \(-0.206004\pi\)
−0.921054 + 0.389434i \(0.872671\pi\)
\(114\) 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 \(-0.846344\pi\)
0.885734 0.464193i \(-0.153656\pi\)
\(128\) 0 0
\(129\) −73.5789 + 91.6748i −0.570379 + 0.710657i
\(130\) 0 0
\(131\) 73.5214 42.4476i 0.561232 0.324027i −0.192408 0.981315i \(-0.561630\pi\)
0.753640 + 0.657288i \(0.228296\pi\)
\(132\) 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 −0.851135 0.524946i \(-0.824085\pi\)
0.880185 + 0.474632i \(0.157419\pi\)
\(138\) 0 0
\(139\) 17.9239 10.3484i 0.128949 0.0744488i −0.434138 0.900846i \(-0.642947\pi\)
0.563087 + 0.826398i \(0.309614\pi\)
\(140\) 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 0.997715 0.0675588i \(-0.0215210\pi\)
−0.557365 + 0.830267i \(0.688188\pi\)
\(150\) 0 0
\(151\) −204.949 118.328i −1.35728 0.783627i −0.368025 0.929816i \(-0.619966\pi\)
−0.989257 + 0.146189i \(0.953299\pi\)
\(152\) 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 0.522651 0.852546i \(-0.324943\pi\)
−0.999653 + 0.0263562i \(0.991610\pi\)
\(158\) 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 \(0.154801\pi\)
−0.884057 + 0.467378i \(0.845199\pi\)
\(164\) 0 0
\(165\) 116.971 + 18.0053i 0.708916 + 0.109123i
\(166\) 0 0
\(167\) −21.5631 + 12.4494i −0.129120 + 0.0745476i −0.563169 0.826342i \(-0.690418\pi\)
0.434049 + 0.900889i \(0.357085\pi\)
\(168\) 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 −0.978881 0.204429i \(-0.934466\pi\)
0.666481 + 0.745522i \(0.267800\pi\)
\(174\) 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 \(-0.660736\pi\)
0.483779 0.875190i \(-0.339264\pi\)
\(180\) 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 0.436777 0.899570i \(-0.356120\pi\)
−0.560662 + 0.828045i \(0.689453\pi\)
\(192\) 0 0
\(193\) −65.7227 113.835i −0.340532 0.589819i 0.644000 0.765026i \(-0.277274\pi\)
−0.984532 + 0.175207i \(0.943941\pi\)
\(194\) 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 \(-0.938836\pi\)
0.981595 0.190972i \(-0.0611641\pi\)
\(200\) 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 −0.701618 0.712553i \(-0.747539\pi\)
0.266280 + 0.963896i \(0.414205\pi\)
\(212\) 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 0.618573 0.785728i \(-0.287711\pi\)
−0.371174 + 0.928563i \(0.621045\pi\)
\(224\) 0 0
\(225\) 399.813 366.340i 1.77695 1.62818i
\(226\) 0 0
\(227\) −304.643 175.886i −1.34204 0.774827i −0.354933 0.934892i \(-0.615496\pi\)
−0.987106 + 0.160065i \(0.948830\pi\)
\(228\) 0 0
\(229\) 102.232 + 177.072i 0.446429 + 0.773238i 0.998151 0.0607903i \(-0.0193621\pi\)
−0.551721 + 0.834029i \(0.686029\pi\)
\(230\) 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 −0.465816 0.884882i \(-0.654239\pi\)
0.533422 + 0.845849i \(0.320906\pi\)
\(240\) 0 0
\(241\) −37.2290 + 64.4826i −0.154477 + 0.267562i −0.932869 0.360217i \(-0.882703\pi\)
0.778391 + 0.627779i \(0.216036\pi\)
\(242\) 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 \(-0.864960\pi\)
0.911352 0.411628i \(-0.135040\pi\)
\(252\) 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 0.995650 + 0.0931698i \(0.0296999\pi\)
−0.417138 + 0.908843i \(0.636967\pi\)
\(258\) 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 0.716431 0.697658i \(-0.245774\pi\)
−0.245974 + 0.969276i \(0.579108\pi\)
\(264\) 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 \(-0.762411\pi\)
0.734132 0.679007i \(-0.237589\pi\)
\(272\) 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 −0.892359 0.451327i \(-0.850951\pi\)
0.837040 + 0.547142i \(0.184284\pi\)
\(278\) 0 0
\(279\) −393.932 + 87.3210i −1.41194 + 0.312979i
\(280\) 0 0
\(281\) −231.041 + 400.176i −0.822212 + 1.42411i 0.0818203 + 0.996647i \(0.473927\pi\)
−0.904032 + 0.427465i \(0.859407\pi\)
\(282\) 0 0
\(283\) −422.693 + 244.042i −1.49361 + 0.862339i −0.999973 0.00732653i \(-0.997668\pi\)
−0.493642 + 0.869665i \(0.664335\pi\)
\(284\) 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 0.955209 + 0.295933i \(0.0956305\pi\)
−0.221319 + 0.975201i \(0.571036\pi\)
\(294\) 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 \(-0.851492\pi\)
0.893124 0.449810i \(-0.148508\pi\)
\(308\) 0 0
\(309\) −110.996 285.437i −0.359209 0.923743i
\(310\) 0 0
\(311\) 172.998 99.8806i 0.556264 0.321159i −0.195380 0.980728i \(-0.562594\pi\)
0.751645 + 0.659568i \(0.229261\pi\)
\(312\) 0 0
\(313\) 59.3385 102.777i 0.189580 0.328362i −0.755530 0.655114i \(-0.772621\pi\)
0.945110 + 0.326752i \(0.105954\pi\)
\(314\) 0 0
\(315\) −153.832 + 487.846i −0.488356 + 1.54872i
\(316\) 0 0
\(317\) 193.261 334.738i 0.609657 1.05596i −0.381640 0.924311i \(-0.624641\pi\)
0.991297 0.131645i \(-0.0420260\pi\)
\(318\) 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 0.862059 0.506808i \(-0.169175\pi\)
−0.00787942 + 0.999969i \(0.502508\pi\)
\(332\) 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 0.938628 0.344931i \(-0.112098\pi\)
−0.768033 + 0.640410i \(0.778764\pi\)
\(338\) 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 0.450963 0.892543i \(-0.351081\pi\)
0.998446 + 0.0557260i \(0.0177473\pi\)
\(348\) 0 0
\(349\) −175.463 + 303.912i −0.502761 + 0.870807i 0.497234 + 0.867616i \(0.334349\pi\)
−0.999995 + 0.00319067i \(0.998984\pi\)
\(350\) 0 0
\(351\) 46.8383 3.06797i 0.133442 0.00874066i
\(352\) 0 0
\(353\) −67.7870 + 117.411i −0.192031 + 0.332608i −0.945923 0.324390i \(-0.894841\pi\)
0.753892 + 0.656998i \(0.228174\pi\)
\(354\) 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 \(0.0484441\pi\)
−0.988441 + 0.151605i \(0.951556\pi\)
\(360\) 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 0.519842 0.854262i \(-0.325991\pi\)
−0.479892 + 0.877328i \(0.659324\pi\)
\(368\) 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 0.840117 0.542405i \(-0.182486\pi\)
−0.889795 + 0.456360i \(0.849153\pi\)
\(374\) 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 \(-0.752834\pi\)
0.713375 0.700782i \(-0.247166\pi\)
\(380\) 0 0
\(381\) 349.598 + 53.8133i 0.917580 + 0.141242i
\(382\) 0 0
\(383\) 324.004 187.064i 0.845963 0.488417i −0.0133235 0.999911i \(-0.504241\pi\)
0.859287 + 0.511494i \(0.170908\pi\)
\(384\) 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 −0.270915 0.962603i \(-0.587326\pi\)
0.969096 0.246683i \(-0.0793406\pi\)
\(390\) 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 −0.956030 0.293269i \(-0.905257\pi\)
0.224036 0.974581i \(-0.428077\pi\)
\(402\) 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 0.979978 0.199105i \(-0.0638036\pi\)
−0.662419 + 0.749133i \(0.730470\pi\)
\(410\) 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 −0.811509 0.584340i \(-0.801353\pi\)
0.100299 + 0.994957i \(0.468020\pi\)
\(420\) 0 0
\(421\) 153.263 265.460i 0.364046 0.630546i −0.624576 0.780964i \(-0.714728\pi\)
0.988623 + 0.150417i \(0.0480617\pi\)
\(422\) 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 \(-0.922415\pi\)
0.970442 0.241333i \(-0.0775847\pi\)
\(432\) 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 0.254135 0.967169i \(-0.418209\pi\)
−0.710525 + 0.703672i \(0.751543\pi\)
\(440\) 0 0
\(441\) 21.6358 + 97.6055i 0.0490607 + 0.221328i
\(442\) 0 0
\(443\) 221.434 + 127.845i 0.499851 + 0.288589i 0.728652 0.684884i \(-0.240147\pi\)
−0.228801 + 0.973473i \(0.573480\pi\)
\(444\) 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 −0.385076 0.922885i \(-0.625825\pi\)
0.991780 0.127957i \(-0.0408418\pi\)
\(458\) 0 0
\(459\) 147.465 298.998i 0.321274 0.651411i
\(460\) 0 0
\(461\) −368.753 + 638.699i −0.799898 + 1.38546i 0.119784 + 0.992800i \(0.461780\pi\)
−0.919682 + 0.392664i \(0.871553\pi\)
\(462\) 0 0
\(463\) −116.461 + 67.2386i −0.251535 + 0.145224i −0.620467 0.784233i \(-0.713057\pi\)
0.368932 + 0.929456i \(0.379724\pi\)
\(464\) 0 0
\(465\) −777.315 + 968.486i −1.67164 + 2.08277i
\(466\) 0 0
\(467\) 595.000i 1.27409i 0.770827 + 0.637045i \(0.219844\pi\)
−0.770827 + 0.637045i \(0.780156\pi\)
\(468\) 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 0.0356829 0.999363i \(-0.488639\pi\)
−0.847632 + 0.530584i \(0.821973\pi\)
\(480\) 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 \(-0.960669\pi\)
0.992376 0.123249i \(-0.0393312\pi\)
\(488\) 0 0
\(489\) −451.775 69.5413i −0.923875 0.142211i
\(490\) 0 0
\(491\) −372.302 + 214.949i −0.758252 + 0.437777i −0.828668 0.559741i \(-0.810901\pi\)
0.0704158 + 0.997518i \(0.477567\pi\)
\(492\) 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 0.303802 0.952735i \(-0.401744\pi\)
0.976994 + 0.213268i \(0.0684107\pi\)
\(500\) 0 0
\(501\) −27.0719 69.6182i −0.0540358 0.138959i
\(502\) 0 0
\(503\) 951.782i 1.89221i 0.323859 + 0.946105i \(0.395020\pi\)
−0.323859 + 0.946105i \(0.604980\pi\)
\(504\) 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 0.900843 0.434146i \(-0.142950\pi\)
−0.826403 + 0.563079i \(0.809616\pi\)
\(510\) 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 \(0.0506678\pi\)
−0.987358 + 0.158506i \(0.949332\pi\)
\(524\) 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 0.999383 0.0351259i \(-0.0111832\pi\)
0.469272 + 0.883054i \(0.344517\pi\)
\(548\) 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 −0.939529 0.342470i \(-0.888736\pi\)
−0.173177 + 0.984891i \(0.555403\pi\)
\(564\) 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 −0.173819 0.984778i \(-0.555611\pi\)
0.939752 0.341857i \(-0.111056\pi\)
\(570\) 0 0
\(571\) −210.649 + 121.618i −0.368912 + 0.212991i −0.672983 0.739658i \(-0.734987\pi\)
0.304071 + 0.952649i \(0.401654\pi\)
\(572\) 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 −0.219178 0.975685i \(-0.570338\pi\)
−0.954557 + 0.298029i \(0.903671\pi\)
\(588\) 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 −0.314639 0.949211i \(-0.601883\pi\)
0.664722 + 0.747091i \(0.268550\pi\)
\(600\) 0 0
\(601\) 135.406 234.529i 0.225300 0.390232i −0.731109 0.682261i \(-0.760997\pi\)
0.956410 + 0.292029i \(0.0943303\pi\)
\(602\) 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 −0.197345 0.980334i \(-0.563232\pi\)
0.750322 + 0.661073i \(0.229899\pi\)
\(608\) 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 0.565423 0.824801i \(-0.308713\pi\)
−0.997010 + 0.0772706i \(0.975379\pi\)
\(618\) 0 0
\(619\) 761.814 + 439.833i 1.23072 + 0.710555i 0.967179 0.254095i \(-0.0817774\pi\)
0.263537 + 0.964649i \(0.415111\pi\)
\(620\) 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 \(-0.920871\pi\)
0.969260 0.246037i \(-0.0791286\pi\)
\(632\) 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 −0.996870 0.0790578i \(-0.974809\pi\)
0.566901 + 0.823786i \(0.308142\pi\)
\(642\) 0 0
\(643\) −352.044 + 203.253i −0.547503 + 0.316101i −0.748114 0.663570i \(-0.769041\pi\)
0.200611 + 0.979671i \(0.435707\pi\)
\(644\) 0 0
\(645\) −1072.73 165.125i −1.66315 0.256008i
\(646\) 0 0
\(647\) 652.891i 1.00910i −0.863381 0.504552i \(-0.831658\pi\)
0.863381 0.504552i \(-0.168342\pi\)
\(648\) 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 0.927930 + 0.372754i \(0.121586\pi\)
−0.141151 + 0.989988i \(0.545080\pi\)
\(654\) 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 0.515532 0.856870i \(-0.327594\pi\)
−0.484306 + 0.874899i \(0.660928\pi\)
\(660\) 0 0
\(661\) 328.164 + 568.396i 0.496465 + 0.859903i 0.999992 0.00407665i \(-0.00129764\pi\)
−0.503526 + 0.863980i \(0.667964\pi\)
\(662\) 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 −0.390479 0.920612i \(-0.627691\pi\)
0.992513 0.122141i \(-0.0389760\pi\)
\(674\) 0 0
\(675\) 903.748 + 1352.68i 1.33889 + 2.00397i
\(676\) 0 0
\(677\) −199.580 + 345.683i −0.294801 + 0.510610i −0.974939 0.222474i \(-0.928587\pi\)
0.680138 + 0.733084i \(0.261920\pi\)
\(678\) 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 \(0.0476238\pi\)
−0.988829 + 0.149057i \(0.952376\pi\)
\(684\) 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 0.303478 0.952838i \(-0.401852\pi\)
−0.673443 + 0.739239i \(0.735185\pi\)
\(692\) 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 −0.975065 0.221920i \(-0.928768\pi\)
0.679721 + 0.733471i \(0.262101\pi\)
\(710\) 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 \(-0.897550\pi\)
0.948650 0.316328i \(-0.102450\pi\)
\(720\) 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 0.350549 0.936544i \(-0.385995\pi\)
−0.635797 + 0.771857i \(0.719328\pi\)
\(728\) 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 0.685468 0.728103i \(-0.259598\pi\)
−0.973289 + 0.229581i \(0.926264\pi\)
\(734\) 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 \(-0.967596\pi\)
0.994823 0.101626i \(-0.0324044\pi\)
\(740\) 0 0
\(741\) −64.1416 164.947i −0.0865608 0.222600i
\(742\) 0 0
\(743\) 726.756 419.593i 0.978137 0.564728i 0.0764298 0.997075i \(-0.475648\pi\)
0.901707 + 0.432347i \(0.142315\pi\)
\(744\) 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 −0.858912 0.512122i \(-0.828859\pi\)
0.0140549 + 0.999901i \(0.495526\pi\)
\(752\) 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 0.999735 0.0230176i \(-0.00732737\pi\)
−0.519801 + 0.854287i \(0.673994\pi\)
\(762\) 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 0.997484 + 0.0708938i \(0.0225851\pi\)
−0.437346 + 0.899293i \(0.644082\pi\)
\(770\) 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 −0.0560758 0.998427i \(-0.517859\pi\)
0.836625 + 0.547776i \(0.184526\pi\)
\(788\) 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