Properties

Label 576.2.bb.a.337.1
Level $576$
Weight $2$
Character 576.337
Analytic conductor $4.599$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 337.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.337
Dual form 576.2.bb.a.241.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205 q^{3} +(-0.133975 - 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +3.00000 q^{9} +O(q^{10})\) \(q+1.73205 q^{3} +(-0.133975 - 0.500000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +3.00000 q^{9} +(0.500000 + 0.133975i) q^{11} +(4.59808 - 1.23205i) q^{13} +(-0.232051 - 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-3.69615 + 2.13397i) q^{21} +(0.401924 + 0.232051i) q^{23} +(4.09808 - 2.36603i) q^{25} +5.19615 q^{27} +(0.866025 - 3.23205i) q^{29} +(-0.598076 + 1.03590i) q^{31} +(0.866025 + 0.232051i) q^{33} +(0.901924 + 0.901924i) q^{35} +(-7.73205 + 7.73205i) q^{37} +(7.96410 - 2.13397i) q^{39} +(-9.69615 - 5.59808i) q^{41} +(-8.69615 - 2.33013i) q^{43} +(-0.401924 - 1.50000i) q^{45} +(-4.59808 - 7.96410i) q^{47} +(-0.464102 + 0.803848i) q^{49} +6.92820 q^{51} +(2.26795 - 2.26795i) q^{53} -0.267949i q^{55} +(5.19615 + 5.19615i) q^{57} +(1.50000 + 5.59808i) q^{59} +(-3.86603 + 14.4282i) q^{61} +(-6.40192 + 3.69615i) q^{63} +(-1.23205 - 2.13397i) q^{65} +(-1.23205 + 0.330127i) q^{67} +(0.696152 + 0.401924i) q^{69} -10.9282i q^{71} +0.535898i q^{73} +(7.09808 - 4.09808i) q^{75} +(-1.23205 + 0.330127i) q^{77} +(-0.866025 - 1.50000i) q^{79} +9.00000 q^{81} +(-3.16025 + 11.7942i) q^{83} +(-0.535898 - 2.00000i) q^{85} +(1.50000 - 5.59808i) q^{87} -11.8564i q^{89} +(-8.29423 + 8.29423i) q^{91} +(-1.03590 + 1.79423i) q^{93} +(1.09808 - 1.90192i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(1.50000 + 0.401924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} - 12q^{7} + 12q^{9} + O(q^{10}) \) \( 4q - 4q^{5} - 12q^{7} + 12q^{9} + 2q^{11} + 8q^{13} + 6q^{15} + 16q^{17} + 12q^{19} + 6q^{21} + 12q^{23} + 6q^{25} + 8q^{31} + 14q^{35} - 24q^{37} + 18q^{39} - 18q^{41} - 14q^{43} - 12q^{45} - 8q^{47} + 12q^{49} + 16q^{53} + 6q^{59} - 12q^{61} - 36q^{63} + 2q^{65} + 2q^{67} - 18q^{69} + 18q^{75} + 2q^{77} + 36q^{81} + 22q^{83} - 16q^{85} + 6q^{87} - 2q^{91} - 18q^{93} - 6q^{95} - 2q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.73205 1.00000
\(4\) 0 0
\(5\) −0.133975 0.500000i −0.0599153 0.223607i 0.929476 0.368883i \(-0.120260\pi\)
−0.989391 + 0.145276i \(0.953593\pi\)
\(6\) 0 0
\(7\) −2.13397 + 1.23205i −0.806567 + 0.465671i −0.845762 0.533560i \(-0.820854\pi\)
0.0391956 + 0.999232i \(0.487520\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 0.500000 + 0.133975i 0.150756 + 0.0403949i 0.333408 0.942783i \(-0.391801\pi\)
−0.182652 + 0.983178i \(0.558468\pi\)
\(12\) 0 0
\(13\) 4.59808 1.23205i 1.27528 0.341709i 0.443227 0.896410i \(-0.353834\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) −0.232051 0.866025i −0.0599153 0.223607i
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 0 0
\(21\) −3.69615 + 2.13397i −0.806567 + 0.465671i
\(22\) 0 0
\(23\) 0.401924 + 0.232051i 0.0838069 + 0.0483859i 0.541318 0.840818i \(-0.317926\pi\)
−0.457511 + 0.889204i \(0.651259\pi\)
\(24\) 0 0
\(25\) 4.09808 2.36603i 0.819615 0.473205i
\(26\) 0 0
\(27\) 5.19615 1.00000
\(28\) 0 0
\(29\) 0.866025 3.23205i 0.160817 0.600177i −0.837720 0.546100i \(-0.816112\pi\)
0.998537 0.0540766i \(-0.0172215\pi\)
\(30\) 0 0
\(31\) −0.598076 + 1.03590i −0.107418 + 0.186053i −0.914723 0.404081i \(-0.867592\pi\)
0.807306 + 0.590133i \(0.200925\pi\)
\(32\) 0 0
\(33\) 0.866025 + 0.232051i 0.150756 + 0.0403949i
\(34\) 0 0
\(35\) 0.901924 + 0.901924i 0.152453 + 0.152453i
\(36\) 0 0
\(37\) −7.73205 + 7.73205i −1.27114 + 1.27114i −0.325651 + 0.945490i \(0.605584\pi\)
−0.945490 + 0.325651i \(0.894416\pi\)
\(38\) 0 0
\(39\) 7.96410 2.13397i 1.27528 0.341709i
\(40\) 0 0
\(41\) −9.69615 5.59808i −1.51428 0.874273i −0.999860 0.0167371i \(-0.994672\pi\)
−0.514425 0.857536i \(-0.671994\pi\)
\(42\) 0 0
\(43\) −8.69615 2.33013i −1.32615 0.355341i −0.474872 0.880055i \(-0.657506\pi\)
−0.851279 + 0.524714i \(0.824172\pi\)
\(44\) 0 0
\(45\) −0.401924 1.50000i −0.0599153 0.223607i
\(46\) 0 0
\(47\) −4.59808 7.96410i −0.670698 1.16168i −0.977706 0.209977i \(-0.932661\pi\)
0.307008 0.951707i \(-0.400672\pi\)
\(48\) 0 0
\(49\) −0.464102 + 0.803848i −0.0663002 + 0.114835i
\(50\) 0 0
\(51\) 6.92820 0.970143
\(52\) 0 0
\(53\) 2.26795 2.26795i 0.311527 0.311527i −0.533974 0.845501i \(-0.679302\pi\)
0.845501 + 0.533974i \(0.179302\pi\)
\(54\) 0 0
\(55\) 0.267949i 0.0361303i
\(56\) 0 0
\(57\) 5.19615 + 5.19615i 0.688247 + 0.688247i
\(58\) 0 0
\(59\) 1.50000 + 5.59808i 0.195283 + 0.728807i 0.992193 + 0.124709i \(0.0397998\pi\)
−0.796910 + 0.604098i \(0.793533\pi\)
\(60\) 0 0
\(61\) −3.86603 + 14.4282i −0.494994 + 1.84734i 0.0350707 + 0.999385i \(0.488834\pi\)
−0.530065 + 0.847957i \(0.677832\pi\)
\(62\) 0 0
\(63\) −6.40192 + 3.69615i −0.806567 + 0.465671i
\(64\) 0 0
\(65\) −1.23205 2.13397i −0.152817 0.264687i
\(66\) 0 0
\(67\) −1.23205 + 0.330127i −0.150519 + 0.0403314i −0.333292 0.942824i \(-0.608159\pi\)
0.182773 + 0.983155i \(0.441493\pi\)
\(68\) 0 0
\(69\) 0.696152 + 0.401924i 0.0838069 + 0.0483859i
\(70\) 0 0
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) 0 0
\(73\) 0.535898i 0.0627222i 0.999508 + 0.0313611i \(0.00998418\pi\)
−0.999508 + 0.0313611i \(0.990016\pi\)
\(74\) 0 0
\(75\) 7.09808 4.09808i 0.819615 0.473205i
\(76\) 0 0
\(77\) −1.23205 + 0.330127i −0.140405 + 0.0376215i
\(78\) 0 0
\(79\) −0.866025 1.50000i −0.0974355 0.168763i 0.813187 0.582003i \(-0.197731\pi\)
−0.910622 + 0.413239i \(0.864397\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −3.16025 + 11.7942i −0.346883 + 1.29458i 0.543514 + 0.839400i \(0.317093\pi\)
−0.890397 + 0.455185i \(0.849573\pi\)
\(84\) 0 0
\(85\) −0.535898 2.00000i −0.0581263 0.216930i
\(86\) 0 0
\(87\) 1.50000 5.59808i 0.160817 0.600177i
\(88\) 0 0
\(89\) 11.8564i 1.25678i −0.777900 0.628388i \(-0.783715\pi\)
0.777900 0.628388i \(-0.216285\pi\)
\(90\) 0 0
\(91\) −8.29423 + 8.29423i −0.869471 + 0.869471i
\(92\) 0 0
\(93\) −1.03590 + 1.79423i −0.107418 + 0.186053i
\(94\) 0 0
\(95\) 1.09808 1.90192i 0.112660 0.195133i
\(96\) 0 0
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 0 0
\(99\) 1.50000 + 0.401924i 0.150756 + 0.0403949i
\(100\) 0 0
\(101\) −1.86603 0.500000i −0.185676 0.0497519i 0.164783 0.986330i \(-0.447308\pi\)
−0.350459 + 0.936578i \(0.613974\pi\)
\(102\) 0 0
\(103\) 1.79423 + 1.03590i 0.176791 + 0.102070i 0.585784 0.810467i \(-0.300787\pi\)
−0.408993 + 0.912537i \(0.634120\pi\)
\(104\) 0 0
\(105\) 1.56218 + 1.56218i 0.152453 + 0.152453i
\(106\) 0 0
\(107\) 11.3923 11.3923i 1.10134 1.10134i 0.107086 0.994250i \(-0.465848\pi\)
0.994250 0.107086i \(-0.0341520\pi\)
\(108\) 0 0
\(109\) 1.73205 + 1.73205i 0.165900 + 0.165900i 0.785175 0.619274i \(-0.212573\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(110\) 0 0
\(111\) −13.3923 + 13.3923i −1.27114 + 1.27114i
\(112\) 0 0
\(113\) −2.76795 + 4.79423i −0.260387 + 0.451003i −0.966345 0.257251i \(-0.917183\pi\)
0.705958 + 0.708254i \(0.250517\pi\)
\(114\) 0 0
\(115\) 0.0621778 0.232051i 0.00579811 0.0216388i
\(116\) 0 0
\(117\) 13.7942 3.69615i 1.27528 0.341709i
\(118\) 0 0
\(119\) −8.53590 + 4.92820i −0.782485 + 0.451768i
\(120\) 0 0
\(121\) −9.29423 5.36603i −0.844930 0.487820i
\(122\) 0 0
\(123\) −16.7942 9.69615i −1.51428 0.874273i
\(124\) 0 0
\(125\) −3.56218 3.56218i −0.318611 0.318611i
\(126\) 0 0
\(127\) 20.3923 1.80952 0.904762 0.425917i \(-0.140048\pi\)
0.904762 + 0.425917i \(0.140048\pi\)
\(128\) 0 0
\(129\) −15.0622 4.03590i −1.32615 0.355341i
\(130\) 0 0
\(131\) −11.6962 + 3.13397i −1.02190 + 0.273817i −0.730593 0.682814i \(-0.760756\pi\)
−0.291305 + 0.956630i \(0.594089\pi\)
\(132\) 0 0
\(133\) −10.0981 2.70577i −0.875614 0.234620i
\(134\) 0 0
\(135\) −0.696152 2.59808i −0.0599153 0.223607i
\(136\) 0 0
\(137\) −14.4282 + 8.33013i −1.23268 + 0.711691i −0.967589 0.252531i \(-0.918737\pi\)
−0.265096 + 0.964222i \(0.585404\pi\)
\(138\) 0 0
\(139\) 1.16025 + 4.33013i 0.0984115 + 0.367277i 0.997515 0.0704603i \(-0.0224468\pi\)
−0.899103 + 0.437737i \(0.855780\pi\)
\(140\) 0 0
\(141\) −7.96410 13.7942i −0.670698 1.16168i
\(142\) 0 0
\(143\) 2.46410 0.206059
\(144\) 0 0
\(145\) −1.73205 −0.143839
\(146\) 0 0
\(147\) −0.803848 + 1.39230i −0.0663002 + 0.114835i
\(148\) 0 0
\(149\) 3.93782 + 14.6962i 0.322599 + 1.20396i 0.916704 + 0.399568i \(0.130840\pi\)
−0.594105 + 0.804388i \(0.702493\pi\)
\(150\) 0 0
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 0.598076 + 0.160254i 0.0480386 + 0.0128719i
\(156\) 0 0
\(157\) 0.866025 0.232051i 0.0691164 0.0185197i −0.224095 0.974567i \(-0.571943\pi\)
0.293212 + 0.956048i \(0.405276\pi\)
\(158\) 0 0
\(159\) 3.92820 3.92820i 0.311527 0.311527i
\(160\) 0 0
\(161\) −1.14359 −0.0901278
\(162\) 0 0
\(163\) −11.9282 11.9282i −0.934289 0.934289i 0.0636813 0.997970i \(-0.479716\pi\)
−0.997970 + 0.0636813i \(0.979716\pi\)
\(164\) 0 0
\(165\) 0.464102i 0.0361303i
\(166\) 0 0
\(167\) −8.25833 4.76795i −0.639049 0.368955i 0.145199 0.989402i \(-0.453618\pi\)
−0.784248 + 0.620447i \(0.786951\pi\)
\(168\) 0 0
\(169\) 8.36603 4.83013i 0.643540 0.371548i
\(170\) 0 0
\(171\) 9.00000 + 9.00000i 0.688247 + 0.688247i
\(172\) 0 0
\(173\) 2.40192 8.96410i 0.182615 0.681528i −0.812514 0.582942i \(-0.801901\pi\)
0.995129 0.0985859i \(-0.0314319\pi\)
\(174\) 0 0
\(175\) −5.83013 + 10.0981i −0.440716 + 0.763343i
\(176\) 0 0
\(177\) 2.59808 + 9.69615i 0.195283 + 0.728807i
\(178\) 0 0
\(179\) −7.92820 7.92820i −0.592582 0.592582i 0.345746 0.938328i \(-0.387626\pi\)
−0.938328 + 0.345746i \(0.887626\pi\)
\(180\) 0 0
\(181\) −4.26795 + 4.26795i −0.317234 + 0.317234i −0.847704 0.530470i \(-0.822016\pi\)
0.530470 + 0.847704i \(0.322016\pi\)
\(182\) 0 0
\(183\) −6.69615 + 24.9904i −0.494994 + 1.84734i
\(184\) 0 0
\(185\) 4.90192 + 2.83013i 0.360397 + 0.208075i
\(186\) 0 0
\(187\) 2.00000 + 0.535898i 0.146254 + 0.0391888i
\(188\) 0 0
\(189\) −11.0885 + 6.40192i −0.806567 + 0.465671i
\(190\) 0 0
\(191\) −6.59808 11.4282i −0.477420 0.826916i 0.522245 0.852795i \(-0.325095\pi\)
−0.999665 + 0.0258797i \(0.991761\pi\)
\(192\) 0 0
\(193\) −1.23205 + 2.13397i −0.0886850 + 0.153607i −0.906956 0.421226i \(-0.861600\pi\)
0.818271 + 0.574833i \(0.194933\pi\)
\(194\) 0 0
\(195\) −2.13397 3.69615i −0.152817 0.264687i
\(196\) 0 0
\(197\) 10.4641 10.4641i 0.745536 0.745536i −0.228101 0.973637i \(-0.573252\pi\)
0.973637 + 0.228101i \(0.0732517\pi\)
\(198\) 0 0
\(199\) 5.85641i 0.415150i −0.978219 0.207575i \(-0.933443\pi\)
0.978219 0.207575i \(-0.0665570\pi\)
\(200\) 0 0
\(201\) −2.13397 + 0.571797i −0.150519 + 0.0403314i
\(202\) 0 0
\(203\) 2.13397 + 7.96410i 0.149776 + 0.558970i
\(204\) 0 0
\(205\) −1.50000 + 5.59808i −0.104765 + 0.390987i
\(206\) 0 0
\(207\) 1.20577 + 0.696152i 0.0838069 + 0.0483859i
\(208\) 0 0
\(209\) 1.09808 + 1.90192i 0.0759555 + 0.131559i
\(210\) 0 0
\(211\) −1.96410 + 0.526279i −0.135214 + 0.0362306i −0.325791 0.945442i \(-0.605631\pi\)
0.190577 + 0.981672i \(0.438964\pi\)
\(212\) 0 0
\(213\) 18.9282i 1.29694i
\(214\) 0 0
\(215\) 4.66025i 0.317827i
\(216\) 0 0
\(217\) 2.94744i 0.200085i
\(218\) 0 0
\(219\) 0.928203i 0.0627222i
\(220\) 0 0
\(221\) 18.3923 4.92820i 1.23720 0.331507i
\(222\) 0 0
\(223\) 7.79423 + 13.5000i 0.521940 + 0.904027i 0.999674 + 0.0255224i \(0.00812491\pi\)
−0.477734 + 0.878504i \(0.658542\pi\)
\(224\) 0 0
\(225\) 12.2942 7.09808i 0.819615 0.473205i
\(226\) 0 0
\(227\) 4.62436 17.2583i 0.306929 1.14548i −0.624343 0.781151i \(-0.714633\pi\)
0.931272 0.364325i \(-0.118700\pi\)
\(228\) 0 0
\(229\) −2.52628 9.42820i −0.166941 0.623033i −0.997785 0.0665269i \(-0.978808\pi\)
0.830843 0.556506i \(-0.187858\pi\)
\(230\) 0 0
\(231\) −2.13397 + 0.571797i −0.140405 + 0.0376215i
\(232\) 0 0
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) 0 0
\(235\) −3.36603 + 3.36603i −0.219575 + 0.219575i
\(236\) 0 0
\(237\) −1.50000 2.59808i −0.0974355 0.168763i
\(238\) 0 0
\(239\) 5.59808 9.69615i 0.362109 0.627192i −0.626198 0.779664i \(-0.715390\pi\)
0.988308 + 0.152472i \(0.0487233\pi\)
\(240\) 0 0
\(241\) −6.23205 10.7942i −0.401442 0.695317i 0.592458 0.805601i \(-0.298157\pi\)
−0.993900 + 0.110284i \(0.964824\pi\)
\(242\) 0 0
\(243\) 15.5885 1.00000
\(244\) 0 0
\(245\) 0.464102 + 0.124356i 0.0296504 + 0.00794479i
\(246\) 0 0
\(247\) 17.4904 + 10.0981i 1.11289 + 0.642525i
\(248\) 0 0
\(249\) −5.47372 + 20.4282i −0.346883 + 1.29458i
\(250\) 0 0
\(251\) −7.39230 + 7.39230i −0.466598 + 0.466598i −0.900811 0.434212i \(-0.857027\pi\)
0.434212 + 0.900811i \(0.357027\pi\)
\(252\) 0 0
\(253\) 0.169873 + 0.169873i 0.0106798 + 0.0106798i
\(254\) 0 0
\(255\) −0.928203 3.46410i −0.0581263 0.216930i
\(256\) 0 0
\(257\) −5.16025 + 8.93782i −0.321888 + 0.557526i −0.980878 0.194626i \(-0.937651\pi\)
0.658990 + 0.752152i \(0.270984\pi\)
\(258\) 0 0
\(259\) 6.97372 26.0263i 0.433326 1.61719i
\(260\) 0 0
\(261\) 2.59808 9.69615i 0.160817 0.600177i
\(262\) 0 0
\(263\) 3.40192 1.96410i 0.209772 0.121112i −0.391434 0.920206i \(-0.628021\pi\)
0.601205 + 0.799095i \(0.294687\pi\)
\(264\) 0 0
\(265\) −1.43782 0.830127i −0.0883247 0.0509943i
\(266\) 0 0
\(267\) 20.5359i 1.25678i
\(268\) 0 0
\(269\) 7.73205 + 7.73205i 0.471431 + 0.471431i 0.902378 0.430946i \(-0.141820\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(270\) 0 0
\(271\) 14.9282 0.906824 0.453412 0.891301i \(-0.350207\pi\)
0.453412 + 0.891301i \(0.350207\pi\)
\(272\) 0 0
\(273\) −14.3660 + 14.3660i −0.869471 + 0.869471i
\(274\) 0 0
\(275\) 2.36603 0.633975i 0.142677 0.0382301i
\(276\) 0 0
\(277\) 13.7942 + 3.69615i 0.828815 + 0.222080i 0.648197 0.761473i \(-0.275523\pi\)
0.180618 + 0.983553i \(0.442190\pi\)
\(278\) 0 0
\(279\) −1.79423 + 3.10770i −0.107418 + 0.186053i
\(280\) 0 0
\(281\) −16.9641 + 9.79423i −1.01199 + 0.584275i −0.911775 0.410691i \(-0.865288\pi\)
−0.100219 + 0.994965i \(0.531954\pi\)
\(282\) 0 0
\(283\) −4.16025 15.5263i −0.247301 0.922942i −0.972213 0.234099i \(-0.924786\pi\)
0.724911 0.688842i \(-0.241881\pi\)
\(284\) 0 0
\(285\) 1.90192 3.29423i 0.112660 0.195133i
\(286\) 0 0
\(287\) 27.5885 1.62850
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −0.866025 1.50000i −0.0507673 0.0879316i
\(292\) 0 0
\(293\) 3.86603 + 14.4282i 0.225856 + 0.842905i 0.982060 + 0.188569i \(0.0603849\pi\)
−0.756204 + 0.654336i \(0.772948\pi\)
\(294\) 0 0
\(295\) 2.59808 1.50000i 0.151266 0.0873334i
\(296\) 0 0
\(297\) 2.59808 + 0.696152i 0.150756 + 0.0403949i
\(298\) 0 0
\(299\) 2.13397 + 0.571797i 0.123411 + 0.0330679i
\(300\) 0 0
\(301\) 21.4282 5.74167i 1.23510 0.330944i
\(302\) 0 0
\(303\) −3.23205 0.866025i −0.185676 0.0497519i
\(304\) 0 0
\(305\) 7.73205 0.442736
\(306\) 0 0
\(307\) 5.92820 + 5.92820i 0.338340 + 0.338340i 0.855742 0.517402i \(-0.173101\pi\)
−0.517402 + 0.855742i \(0.673101\pi\)
\(308\) 0 0
\(309\) 3.10770 + 1.79423i 0.176791 + 0.102070i
\(310\) 0 0
\(311\) 27.1865 + 15.6962i 1.54161 + 0.890047i 0.998738 + 0.0502299i \(0.0159954\pi\)
0.542869 + 0.839817i \(0.317338\pi\)
\(312\) 0 0
\(313\) 7.83975 4.52628i 0.443129 0.255840i −0.261795 0.965123i \(-0.584314\pi\)
0.704924 + 0.709283i \(0.250981\pi\)
\(314\) 0 0
\(315\) 2.70577 + 2.70577i 0.152453 + 0.152453i
\(316\) 0 0
\(317\) −0.545517 + 2.03590i −0.0306393 + 0.114347i −0.979552 0.201192i \(-0.935519\pi\)
0.948913 + 0.315539i \(0.102185\pi\)
\(318\) 0 0
\(319\) 0.866025 1.50000i 0.0484881 0.0839839i
\(320\) 0 0
\(321\) 19.7321 19.7321i 1.10134 1.10134i
\(322\) 0 0
\(323\) 12.0000 + 12.0000i 0.667698 + 0.667698i
\(324\) 0 0
\(325\) 15.9282 15.9282i 0.883538 0.883538i
\(326\) 0 0
\(327\) 3.00000 + 3.00000i 0.165900 + 0.165900i
\(328\) 0 0
\(329\) 19.6244 + 11.3301i 1.08193 + 0.624650i
\(330\) 0 0
\(331\) 26.3564 + 7.06218i 1.44868 + 0.388172i 0.895564 0.444933i \(-0.146772\pi\)
0.553115 + 0.833105i \(0.313439\pi\)
\(332\) 0 0
\(333\) −23.1962 + 23.1962i −1.27114 + 1.27114i
\(334\) 0 0
\(335\) 0.330127 + 0.571797i 0.0180368 + 0.0312406i
\(336\) 0 0
\(337\) 0.696152 1.20577i 0.0379218 0.0656826i −0.846442 0.532482i \(-0.821260\pi\)
0.884363 + 0.466799i \(0.154593\pi\)
\(338\) 0 0
\(339\) −4.79423 + 8.30385i −0.260387 + 0.451003i
\(340\) 0 0
\(341\) −0.437822 + 0.437822i −0.0237094 + 0.0237094i
\(342\) 0 0
\(343\) 19.5359i 1.05484i
\(344\) 0 0
\(345\) 0.107695 0.401924i 0.00579811 0.0216388i
\(346\) 0 0
\(347\) 5.23205 + 19.5263i 0.280871 + 1.04823i 0.951804 + 0.306707i \(0.0992273\pi\)
−0.670933 + 0.741518i \(0.734106\pi\)
\(348\) 0 0
\(349\) −2.13397 + 7.96410i −0.114229 + 0.426309i −0.999228 0.0392843i \(-0.987492\pi\)
0.884999 + 0.465593i \(0.154159\pi\)
\(350\) 0 0
\(351\) 23.8923 6.40192i 1.27528 0.341709i
\(352\) 0 0
\(353\) −15.2321 26.3827i −0.810720 1.40421i −0.912361 0.409387i \(-0.865742\pi\)
0.101640 0.994821i \(-0.467591\pi\)
\(354\) 0 0
\(355\) −5.46410 + 1.46410i −0.290004 + 0.0777064i
\(356\) 0 0
\(357\) −14.7846 + 8.53590i −0.782485 + 0.451768i
\(358\) 0 0
\(359\) 15.0718i 0.795459i 0.917503 + 0.397730i \(0.130202\pi\)
−0.917503 + 0.397730i \(0.869798\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) −16.0981 9.29423i −0.844930 0.487820i
\(364\) 0 0
\(365\) 0.267949 0.0717968i 0.0140251 0.00375801i
\(366\) 0 0
\(367\) −15.4545 26.7679i −0.806717 1.39728i −0.915125 0.403169i \(-0.867909\pi\)
0.108408 0.994106i \(-0.465425\pi\)
\(368\) 0 0
\(369\) −29.0885 16.7942i −1.51428 0.874273i
\(370\) 0 0
\(371\) −2.04552 + 7.63397i −0.106198 + 0.396336i
\(372\) 0 0
\(373\) 3.59808 + 13.4282i 0.186301 + 0.695286i 0.994348 + 0.106168i \(0.0338581\pi\)
−0.808047 + 0.589118i \(0.799475\pi\)
\(374\) 0 0
\(375\) −6.16987 6.16987i −0.318611 0.318611i
\(376\) 0 0
\(377\) 15.9282i 0.820344i
\(378\) 0 0
\(379\) −15.5885 + 15.5885i −0.800725 + 0.800725i −0.983209 0.182484i \(-0.941586\pi\)
0.182484 + 0.983209i \(0.441586\pi\)
\(380\) 0 0
\(381\) 35.3205 1.80952
\(382\) 0 0
\(383\) −12.3301 + 21.3564i −0.630040 + 1.09126i 0.357503 + 0.933912i \(0.383628\pi\)
−0.987543 + 0.157349i \(0.949705\pi\)
\(384\) 0 0
\(385\) 0.330127 + 0.571797i 0.0168248 + 0.0291415i
\(386\) 0 0
\(387\) −26.0885 6.99038i −1.32615 0.355341i
\(388\) 0 0
\(389\) 7.59808 + 2.03590i 0.385238 + 0.103224i 0.446240 0.894914i \(-0.352763\pi\)
−0.0610019 + 0.998138i \(0.519430\pi\)
\(390\) 0 0
\(391\) 1.60770 + 0.928203i 0.0813046 + 0.0469413i
\(392\) 0 0
\(393\) −20.2583 + 5.42820i −1.02190 + 0.273817i
\(394\) 0 0
\(395\) −0.633975 + 0.633975i −0.0318987 + 0.0318987i
\(396\) 0 0
\(397\) −21.0526 21.0526i −1.05660 1.05660i −0.998299 0.0582984i \(-0.981433\pi\)
−0.0582984 0.998299i \(-0.518567\pi\)
\(398\) 0 0
\(399\) −17.4904 4.68653i −0.875614 0.234620i
\(400\) 0 0
\(401\) 1.16025 2.00962i 0.0579403 0.100356i −0.835600 0.549338i \(-0.814880\pi\)
0.893541 + 0.448982i \(0.148213\pi\)
\(402\) 0 0
\(403\) −1.47372 + 5.50000i −0.0734112 + 0.273975i
\(404\) 0 0
\(405\) −1.20577 4.50000i −0.0599153 0.223607i
\(406\) 0 0
\(407\) −4.90192 + 2.83013i −0.242979 + 0.140284i
\(408\) 0 0
\(409\) 4.62436 + 2.66987i 0.228660 + 0.132017i 0.609954 0.792437i \(-0.291188\pi\)
−0.381294 + 0.924454i \(0.624521\pi\)
\(410\) 0 0
\(411\) −24.9904 + 14.4282i −1.23268 + 0.711691i
\(412\) 0 0
\(413\) −10.0981 10.0981i −0.496894 0.496894i
\(414\) 0 0
\(415\) 6.32051 0.310262
\(416\) 0 0
\(417\) 2.00962 + 7.50000i 0.0984115 + 0.367277i
\(418\) 0 0
\(419\) −1.96410 + 0.526279i −0.0959526 + 0.0257104i −0.306476 0.951878i \(-0.599150\pi\)
0.210523 + 0.977589i \(0.432483\pi\)
\(420\) 0 0
\(421\) 10.7942 + 2.89230i 0.526079 + 0.140962i 0.512077 0.858940i \(-0.328876\pi\)
0.0140017 + 0.999902i \(0.495543\pi\)
\(422\) 0 0
\(423\) −13.7942 23.8923i −0.670698 1.16168i
\(424\) 0 0
\(425\) 16.3923 9.46410i 0.795144 0.459076i
\(426\) 0 0
\(427\) −9.52628 35.5526i −0.461009 1.72051i
\(428\) 0 0
\(429\) 4.26795 0.206059
\(430\) 0 0
\(431\) −31.3205 −1.50866 −0.754328 0.656498i \(-0.772037\pi\)
−0.754328 + 0.656498i \(0.772037\pi\)
\(432\) 0 0
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) 0 0
\(435\) −3.00000 −0.143839
\(436\) 0 0
\(437\) 0.509619 + 1.90192i 0.0243784 + 0.0909814i
\(438\) 0 0
\(439\) −18.0622 + 10.4282i −0.862061 + 0.497711i −0.864702 0.502286i \(-0.832493\pi\)
0.00264111 + 0.999997i \(0.499159\pi\)
\(440\) 0 0
\(441\) −1.39230 + 2.41154i −0.0663002 + 0.114835i
\(442\) 0 0
\(443\) −16.1603 4.33013i −0.767797 0.205731i −0.146399 0.989226i \(-0.546768\pi\)
−0.621398 + 0.783495i \(0.713435\pi\)
\(444\) 0 0
\(445\) −5.92820 + 1.58846i −0.281024 + 0.0753001i
\(446\) 0 0
\(447\) 6.82051 + 25.4545i 0.322599 + 1.20396i
\(448\) 0 0
\(449\) 0.679492 0.0320672 0.0160336 0.999871i \(-0.494896\pi\)
0.0160336 + 0.999871i \(0.494896\pi\)
\(450\) 0 0
\(451\) −4.09808 4.09808i −0.192971 0.192971i
\(452\) 0 0
\(453\) −10.5000 + 6.06218i −0.493333 + 0.284826i
\(454\) 0 0
\(455\) 5.25833 + 3.03590i 0.246514 + 0.142325i
\(456\) 0 0
\(457\) 19.0359 10.9904i 0.890462 0.514108i 0.0163683 0.999866i \(-0.494790\pi\)
0.874094 + 0.485758i \(0.161456\pi\)
\(458\) 0 0
\(459\) 20.7846 0.970143
\(460\) 0 0
\(461\) −0.598076 + 2.23205i −0.0278552 + 0.103957i −0.978454 0.206466i \(-0.933804\pi\)
0.950599 + 0.310423i \(0.100471\pi\)
\(462\) 0 0
\(463\) −3.33013 + 5.76795i −0.154764 + 0.268059i −0.932973 0.359946i \(-0.882795\pi\)
0.778209 + 0.628005i \(0.216128\pi\)
\(464\) 0 0
\(465\) 1.03590 + 0.277568i 0.0480386 + 0.0128719i
\(466\) 0 0
\(467\) 19.7846 + 19.7846i 0.915523 + 0.915523i 0.996700 0.0811771i \(-0.0258679\pi\)
−0.0811771 + 0.996700i \(0.525868\pi\)
\(468\) 0 0
\(469\) 2.22243 2.22243i 0.102622 0.102622i
\(470\) 0 0
\(471\) 1.50000 0.401924i 0.0691164 0.0185197i
\(472\) 0 0
\(473\) −4.03590 2.33013i −0.185571 0.107139i
\(474\) 0 0
\(475\) 19.3923 + 5.19615i 0.889780 + 0.238416i
\(476\) 0 0
\(477\) 6.80385 6.80385i 0.311527 0.311527i
\(478\) 0 0
\(479\) −0.669873 1.16025i −0.0306073 0.0530134i 0.850316 0.526272i \(-0.176411\pi\)
−0.880923 + 0.473259i \(0.843077\pi\)
\(480\) 0 0
\(481\) −26.0263 + 45.0788i −1.18670 + 2.05542i
\(482\) 0 0
\(483\) −1.98076 −0.0901278
\(484\) 0 0
\(485\) −0.366025 + 0.366025i −0.0166204 + 0.0166204i
\(486\) 0 0
\(487\) 34.7846i 1.57624i −0.615521 0.788121i \(-0.711054\pi\)
0.615521 0.788121i \(-0.288946\pi\)
\(488\) 0 0
\(489\) −20.6603 20.6603i −0.934289 0.934289i
\(490\) 0 0
\(491\) −0.500000 1.86603i −0.0225647 0.0842125i 0.953725 0.300679i \(-0.0972134\pi\)
−0.976290 + 0.216467i \(0.930547\pi\)
\(492\) 0 0
\(493\) 3.46410 12.9282i 0.156015 0.582257i
\(494\) 0 0
\(495\) 0.803848i 0.0361303i
\(496\) 0 0
\(497\) 13.4641 + 23.3205i 0.603947 + 1.04607i
\(498\) 0 0
\(499\) 2.50000 0.669873i 0.111915 0.0299876i −0.202427 0.979297i \(-0.564883\pi\)
0.314342 + 0.949310i \(0.398216\pi\)
\(500\) 0 0
\(501\) −14.3038 8.25833i −0.639049 0.368955i
\(502\) 0 0
\(503\) 13.8564i 0.617827i 0.951090 + 0.308913i \(0.0999653\pi\)
−0.951090 + 0.308913i \(0.900035\pi\)
\(504\) 0 0
\(505\) 1.00000i 0.0444994i
\(506\) 0 0
\(507\) 14.4904 8.36603i 0.643540 0.371548i
\(508\) 0 0
\(509\) −21.2583 + 5.69615i −0.942259 + 0.252478i −0.697074 0.716999i \(-0.745515\pi\)
−0.245185 + 0.969476i \(0.578849\pi\)
\(510\) 0 0
\(511\) −0.660254 1.14359i −0.0292079 0.0505896i
\(512\) 0 0
\(513\) 15.5885 + 15.5885i 0.688247 + 0.688247i
\(514\) 0 0
\(515\) 0.277568 1.03590i 0.0122311 0.0456471i
\(516\) 0 0
\(517\) −1.23205 4.59808i −0.0541855 0.202223i
\(518\) 0 0
\(519\) 4.16025 15.5263i 0.182615 0.681528i
\(520\) 0 0
\(521\) 14.1436i 0.619642i −0.950795 0.309821i \(-0.899731\pi\)
0.950795 0.309821i \(-0.100269\pi\)
\(522\) 0 0
\(523\) 2.12436 2.12436i 0.0928916 0.0928916i −0.659134 0.752026i \(-0.729077\pi\)
0.752026 + 0.659134i \(0.229077\pi\)
\(524\) 0 0
\(525\) −10.0981 + 17.4904i −0.440716 + 0.763343i
\(526\) 0 0
\(527\) −2.39230 + 4.14359i −0.104210 + 0.180498i
\(528\) 0 0
\(529\) −11.3923 19.7321i −0.495318 0.857915i
\(530\) 0 0
\(531\) 4.50000 + 16.7942i 0.195283 + 0.728807i
\(532\) 0 0
\(533\) −51.4808 13.7942i −2.22988 0.597494i
\(534\) 0 0
\(535\) −7.22243 4.16987i −0.312253 0.180279i
\(536\) 0 0
\(537\) −13.7321 13.7321i −0.592582 0.592582i
\(538\) 0 0
\(539\) −0.339746 + 0.339746i −0.0146339 + 0.0146339i
\(540\) 0 0
\(541\) −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) 0 0
\(543\) −7.39230 + 7.39230i −0.317234 + 0.317234i
\(544\) 0 0
\(545\) 0.633975 1.09808i 0.0271565 0.0470364i
\(546\) 0 0
\(547\) −7.57180 + 28.2583i −0.323747 + 1.20824i 0.591819 + 0.806071i \(0.298410\pi\)
−0.915566 + 0.402168i \(0.868257\pi\)
\(548\) 0 0
\(549\) −11.5981 + 43.2846i −0.494994 + 1.84734i
\(550\) 0 0
\(551\) 12.2942 7.09808i 0.523752 0.302388i
\(552\) 0 0
\(553\) 3.69615 + 2.13397i 0.157176 + 0.0907458i
\(554\) 0 0
\(555\) 8.49038 + 4.90192i 0.360397 + 0.208075i
\(556\) 0 0
\(557\) 27.9808 + 27.9808i 1.18558 + 1.18558i 0.978276 + 0.207307i \(0.0664699\pi\)
0.207307 + 0.978276i \(0.433530\pi\)
\(558\) 0 0
\(559\) −42.8564 −1.81263
\(560\) 0 0
\(561\) 3.46410 + 0.928203i 0.146254 + 0.0391888i
\(562\) 0 0
\(563\) 29.3564 7.86603i 1.23723 0.331513i 0.419836 0.907600i \(-0.362088\pi\)
0.817389 + 0.576086i \(0.195421\pi\)
\(564\) 0 0
\(565\) 2.76795 + 0.741670i 0.116448 + 0.0312023i
\(566\) 0 0
\(567\) −19.2058 + 11.0885i −0.806567 + 0.465671i
\(568\) 0 0
\(569\) 24.4808 14.1340i 1.02629 0.592527i 0.110368 0.993891i \(-0.464797\pi\)
0.915919 + 0.401364i \(0.131464\pi\)
\(570\) 0 0
\(571\) −1.44744 5.40192i −0.0605735 0.226063i 0.929003 0.370073i \(-0.120667\pi\)
−0.989576 + 0.144009i \(0.954001\pi\)
\(572\) 0 0
\(573\) −11.4282 19.7942i −0.477420 0.826916i
\(574\) 0 0
\(575\) 2.19615 0.0915859
\(576\) 0 0
\(577\) 37.1769 1.54770 0.773848 0.633372i \(-0.218330\pi\)
0.773848 + 0.633372i \(0.218330\pi\)
\(578\) 0 0
\(579\) −2.13397 + 3.69615i −0.0886850 + 0.153607i
\(580\) 0 0
\(581\) −7.78719 29.0622i −0.323067 1.20570i
\(582\) 0 0
\(583\) 1.43782 0.830127i 0.0595485 0.0343803i
\(584\) 0 0
\(585\) −3.69615 6.40192i −0.152817 0.264687i
\(586\) 0 0
\(587\) 2.96410 + 0.794229i 0.122342 + 0.0327813i 0.319470 0.947596i \(-0.396495\pi\)
−0.197129 + 0.980378i \(0.563162\pi\)
\(588\) 0 0
\(589\) −4.90192 + 1.31347i −0.201980 + 0.0541204i
\(590\) 0 0
\(591\) 18.1244 18.1244i 0.745536 0.745536i
\(592\) 0 0
\(593\) 1.46410 0.0601234 0.0300617 0.999548i \(-0.490430\pi\)
0.0300617 + 0.999548i \(0.490430\pi\)
\(594\) 0 0
\(595\) 3.60770 + 3.60770i 0.147901 + 0.147901i
\(596\) 0 0
\(597\) 10.1436i 0.415150i
\(598\) 0 0
\(599\) −30.3109 17.5000i −1.23847 0.715031i −0.269688 0.962948i \(-0.586921\pi\)
−0.968781 + 0.247917i \(0.920254\pi\)
\(600\) 0 0
\(601\) −30.2321 + 17.4545i −1.23319 + 0.711983i −0.967694 0.252128i \(-0.918869\pi\)
−0.265497 + 0.964112i \(0.585536\pi\)
\(602\) 0 0
\(603\) −3.69615 + 0.990381i −0.150519 + 0.0403314i
\(604\) 0 0
\(605\) −1.43782 + 5.36603i −0.0584558 + 0.218160i
\(606\) 0 0
\(607\) 4.59808 7.96410i 0.186630 0.323253i −0.757494 0.652842i \(-0.773577\pi\)
0.944125 + 0.329589i \(0.106910\pi\)
\(608\) 0 0
\(609\) 3.69615 + 13.7942i 0.149776 + 0.558970i
\(610\) 0 0
\(611\) −30.9545 30.9545i −1.25228 1.25228i
\(612\) 0 0
\(613\) −7.58846 + 7.58846i −0.306495 + 0.306495i −0.843548 0.537053i \(-0.819537\pi\)
0.537053 + 0.843548i \(0.319537\pi\)
\(614\) 0 0
\(615\) −2.59808 + 9.69615i −0.104765 + 0.390987i
\(616\) 0 0
\(617\) −8.08846 4.66987i −0.325629 0.188002i 0.328270 0.944584i \(-0.393534\pi\)
−0.653899 + 0.756582i \(0.726868\pi\)
\(618\) 0 0
\(619\) 33.0885 + 8.86603i 1.32994 + 0.356356i 0.852692 0.522414i \(-0.174969\pi\)
0.477246 + 0.878770i \(0.341635\pi\)
\(620\) 0 0
\(621\) 2.08846 + 1.20577i 0.0838069 + 0.0483859i
\(622\) 0 0
\(623\) 14.6077 + 25.3013i 0.585245 + 1.01367i
\(624\) 0 0
\(625\) 10.5263 18.2321i 0.421051 0.729282i
\(626\) 0 0
\(627\) 1.90192 + 3.29423i 0.0759555 + 0.131559i
\(628\) 0 0
\(629\) −30.9282 + 30.9282i −1.23319 + 1.23319i
\(630\) 0 0
\(631\) 32.2487i 1.28380i 0.766788 + 0.641900i \(0.221854\pi\)
−0.766788 + 0.641900i \(0.778146\pi\)
\(632\) 0 0
\(633\) −3.40192 + 0.911543i −0.135214 + 0.0362306i
\(634\) 0 0
\(635\) −2.73205 10.1962i −0.108418 0.404622i
\(636\) 0 0
\(637\) −1.14359 + 4.26795i −0.0453108 + 0.169102i
\(638\) 0 0
\(639\) 32.7846i 1.29694i
\(640\) 0 0
\(641\) 5.76795 + 9.99038i 0.227820 + 0.394596i 0.957162 0.289553i \(-0.0935068\pi\)
−0.729342 + 0.684150i \(0.760173\pi\)
\(642\) 0 0
\(643\) −1.03590 + 0.277568i −0.0408518 + 0.0109462i −0.279187 0.960237i \(-0.590065\pi\)
0.238335 + 0.971183i \(0.423398\pi\)
\(644\) 0 0
\(645\) 8.07180i 0.317827i
\(646\) 0 0
\(647\) 46.3923i 1.82387i −0.410335 0.911935i \(-0.634588\pi\)
0.410335 0.911935i \(-0.365412\pi\)
\(648\) 0 0
\(649\) 3.00000i 0.117760i
\(650\) 0 0
\(651\) 5.10512i 0.200085i
\(652\) 0 0
\(653\) −21.3301 + 5.71539i −0.834712 + 0.223661i −0.650768 0.759276i \(-0.725553\pi\)
−0.183944 + 0.982937i \(0.558886\pi\)
\(654\) 0 0
\(655\) 3.13397 + 5.42820i 0.122455 + 0.212097i
\(656\) 0 0
\(657\) 1.60770i 0.0627222i
\(658\) 0 0
\(659\) 2.23205 8.33013i 0.0869484 0.324496i −0.908728 0.417390i \(-0.862945\pi\)
0.995676 + 0.0928939i \(0.0296117\pi\)
\(660\) 0 0
\(661\) 4.20577 + 15.6962i 0.163586 + 0.610510i 0.998216 + 0.0596998i \(0.0190143\pi\)
−0.834631 + 0.550810i \(0.814319\pi\)
\(662\) 0 0
\(663\) 31.8564 8.53590i 1.23720 0.331507i
\(664\) 0 0
\(665\) 5.41154i 0.209851i
\(666\) 0 0
\(667\) 1.09808 1.09808i 0.0425177 0.0425177i
\(668\) 0 0
\(669\) 13.5000 + 23.3827i 0.521940 + 0.904027i
\(670\) 0 0
\(671\) −3.86603 + 6.69615i −0.149246 + 0.258502i
\(672\) 0 0
\(673\) 3.83975 + 6.65064i 0.148011 + 0.256363i 0.930492 0.366311i \(-0.119379\pi\)
−0.782481 + 0.622674i \(0.786046\pi\)
\(674\) 0 0
\(675\) 21.2942 12.2942i 0.819615 0.473205i
\(676\) 0 0
\(677\) 45.6506 + 12.2321i 1.75450 + 0.470116i 0.985577 0.169229i \(-0.0541279\pi\)
0.768920 + 0.639345i \(0.220795\pi\)
\(678\) 0 0
\(679\) 2.13397 + 1.23205i 0.0818944 + 0.0472818i
\(680\) 0 0
\(681\) 8.00962 29.8923i 0.306929 1.14548i
\(682\) 0 0
\(683\) 5.39230 5.39230i 0.206331 0.206331i −0.596375 0.802706i \(-0.703393\pi\)
0.802706 + 0.596375i \(0.203393\pi\)
\(684\) 0 0
\(685\) 6.09808 + 6.09808i 0.232996 + 0.232996i
\(686\) 0 0
\(687\) −4.37564 16.3301i −0.166941 0.623033i
\(688\) 0 0
\(689\) 7.63397 13.2224i 0.290831 0.503735i
\(690\) 0 0
\(691\) −4.96410 + 18.5263i −0.188843 + 0.704773i 0.804932 + 0.593367i \(0.202202\pi\)
−0.993775 + 0.111405i \(0.964465\pi\)
\(692\) 0 0
\(693\) −3.69615 + 0.990381i −0.140405 + 0.0376215i
\(694\) 0 0
\(695\) 2.00962 1.16025i 0.0762292 0.0440109i
\(696\) 0 0
\(697\) −38.7846 22.3923i −1.46907 0.848169i
\(698\) 0 0
\(699\) 39.7128i 1.50208i
\(700\) 0 0
\(701\) −21.0526 21.0526i −0.795144 0.795144i 0.187181 0.982325i \(-0.440065\pi\)
−0.982325 + 0.187181i \(0.940065\pi\)
\(702\) 0 0
\(703\) −46.3923 −1.74972
\(704\) 0 0
\(705\) −5.83013 + 5.83013i −0.219575 + 0.219575i
\(706\) 0 0
\(707\) 4.59808 1.23205i 0.172928 0.0463360i
\(708\) 0 0
\(709\) −40.1147 10.7487i −1.50654 0.403676i −0.591256 0.806484i \(-0.701368\pi\)
−0.915285 + 0.402808i \(0.868034\pi\)
\(710\) 0 0
\(711\) −2.59808 4.50000i −0.0974355 0.168763i
\(712\) 0 0
\(713\) −0.480762 + 0.277568i −0.0180047 + 0.0103950i
\(714\) 0 0
\(715\) −0.330127 1.23205i −0.0123461 0.0460761i
\(716\) 0 0
\(717\) 9.69615 16.7942i 0.362109 0.627192i
\(718\) 0 0
\(719\) −23.3205 −0.869708 −0.434854 0.900501i \(-0.643200\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(720\) 0 0
\(721\) −5.10512 −0.190125
\(722\) 0 0
\(723\) −10.7942 18.6962i −0.401442 0.695317i
\(724\) 0 0
\(725\) −4.09808 15.2942i −0.152199 0.568013i
\(726\) 0 0
\(727\) 9.06218 5.23205i 0.336098 0.194046i −0.322447 0.946587i \(-0.604506\pi\)
0.658545 + 0.752541i \(0.271172\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) −34.7846 9.32051i −1.28656 0.344731i
\(732\) 0 0
\(733\) 27.5263 7.37564i 1.01671 0.272426i 0.288277 0.957547i \(-0.406917\pi\)
0.728429 + 0.685121i \(0.240251\pi\)
\(734\) 0 0
\(735\) 0.803848 + 0.215390i 0.0296504 + 0.00794479i
\(736\) 0 0
\(737\) −0.660254 −0.0243208
\(738\) 0 0
\(739\) 29.7321 + 29.7321i 1.09371 + 1.09371i 0.995129 + 0.0985823i \(0.0314308\pi\)
0.0985823 + 0.995129i \(0.468569\pi\)
\(740\) 0 0
\(741\) 30.2942 + 17.4904i 1.11289 + 0.642525i
\(742\) 0 0
\(743\) 25.1147 + 14.5000i 0.921370 + 0.531953i 0.884072 0.467351i \(-0.154791\pi\)
0.0372984 + 0.999304i \(0.488125\pi\)
\(744\) 0 0
\(745\) 6.82051 3.93782i 0.249884 0.144271i
\(746\) 0 0
\(747\) −9.48076 + 35.3827i −0.346883 + 1.29458i
\(748\) 0 0
\(749\) −10.2750 + 38.3468i −0.375440 + 1.40116i
\(750\) 0 0
\(751\) −4.72243 + 8.17949i −0.172324 + 0.298474i −0.939232 0.343283i \(-0.888461\pi\)
0.766908 + 0.641757i \(0.221794\pi\)
\(752\) 0 0
\(753\) −12.8038 + 12.8038i −0.466598 + 0.466598i
\(754\) 0 0
\(755\) 2.56218 + 2.56218i 0.0932472 + 0.0932472i
\(756\) 0 0
\(757\) 8.46410 8.46410i 0.307633 0.307633i −0.536358 0.843991i \(-0.680200\pi\)
0.843991 + 0.536358i \(0.180200\pi\)
\(758\) 0 0
\(759\) 0.294229 + 0.294229i 0.0106798 + 0.0106798i
\(760\) 0 0
\(761\) 25.2846 + 14.5981i 0.916566 + 0.529180i 0.882538 0.470241i \(-0.155833\pi\)
0.0340283 + 0.999421i \(0.489166\pi\)
\(762\) 0 0
\(763\) −5.83013 1.56218i −0.211065 0.0565546i
\(764\) 0 0
\(765\) −1.60770 6.00000i −0.0581263 0.216930i
\(766\) 0 0
\(767\) 13.7942 + 23.8923i 0.498081 + 0.862701i
\(768\) 0 0
\(769\) −3.50000 + 6.06218i −0.126213 + 0.218608i −0.922207 0.386698i \(-0.873616\pi\)
0.795993 + 0.605305i \(0.206949\pi\)
\(770\) 0 0
\(771\) −8.93782 + 15.4808i −0.321888 + 0.557526i
\(772\) 0 0
\(773\) 7.58846 7.58846i 0.272938 0.272938i −0.557344 0.830282i \(-0.688179\pi\)
0.830282 + 0.557344i \(0.188179\pi\)
\(774\) 0 0
\(775\) 5.66025i 0.203322i
\(776\) 0 0
\(777\) 12.0788 45.0788i 0.433326 1.61719i
\(778\) 0 0
\(779\) −12.2942 45.8827i −0.440486 1.64392i
\(780\) 0 0
\(781\) 1.46410 5.46410i 0.0523897 0.195521i
\(782\) 0 0
\(783\) 4.50000 16.7942i 0.160817 0.600177i
\(784\) 0 0
\(785\) −0.232051 0.401924i −0.00828225 0.0143453i
\(786\) 0 0
\(787\) 33.8205 9.06218i 1.20557 0.323032i 0.400548 0.916276i \(-0.368820\pi\)
0.805023 + 0.593244i \(0.202153\pi\)
\(788\) 0 0
\(789\) 5.89230 3.40192i 0.209772 0.121112i
\(790\) 0 0
\(791\) 13.6410i 0.485019i
\(792\) 0 0
\(793\)