Properties

Label 576.2.bb.a.241.1
Level $576$
Weight $2$
Character 576.241
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 241.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.241
Dual form 576.2.bb.a.337.1

$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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 −0.989391 0.145276i \(-0.953593\pi\)
0.929476 + 0.368883i \(0.120260\pi\)
\(6\) 0 0
\(7\) −2.13397 1.23205i −0.806567 0.465671i 0.0391956 0.999232i \(-0.487520\pi\)
−0.845762 + 0.533560i \(0.820854\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 0.500000 0.133975i 0.150756 0.0403949i −0.182652 0.983178i \(-0.558468\pi\)
0.333408 + 0.942783i \(0.391801\pi\)
\(12\) 0 0
\(13\) 4.59808 + 1.23205i 1.27528 + 0.341709i 0.832050 0.554700i \(-0.187167\pi\)
0.443227 + 0.896410i \(0.353834\pi\)
\(14\) 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 −0.273597 0.961844i \(-0.588214\pi\)
0.961844 + 0.273597i \(0.0882135\pi\)
\(20\) 0 0
\(21\) −3.69615 2.13397i −0.806567 0.465671i
\(22\) 0 0
\(23\) 0.401924 0.232051i 0.0838069 0.0483859i −0.457511 0.889204i \(-0.651259\pi\)
0.541318 + 0.840818i \(0.317926\pi\)
\(24\) 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 0.998537 + 0.0540766i \(0.0172215\pi\)
−0.837720 + 0.546100i \(0.816112\pi\)
\(30\) 0 0
\(31\) −0.598076 1.03590i −0.107418 0.186053i 0.807306 0.590133i \(-0.200925\pi\)
−0.914723 + 0.404081i \(0.867592\pi\)
\(32\) 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 −0.945490 0.325651i \(-0.894416\pi\)
−0.325651 0.945490i \(-0.605584\pi\)
\(38\) 0 0
\(39\) 7.96410 + 2.13397i 1.27528 + 0.341709i
\(40\) 0 0
\(41\) −9.69615 + 5.59808i −1.51428 + 0.874273i −0.514425 + 0.857536i \(0.671994\pi\)
−0.999860 + 0.0167371i \(0.994672\pi\)
\(42\) 0 0
\(43\) −8.69615 + 2.33013i −1.32615 + 0.355341i −0.851279 0.524714i \(-0.824172\pi\)
−0.474872 + 0.880055i \(0.657506\pi\)
\(44\) 0 0
\(45\) −0.401924 + 1.50000i −0.0599153 + 0.223607i
\(46\) 0 0
\(47\) −4.59808 + 7.96410i −0.670698 + 1.16168i 0.307008 + 0.951707i \(0.400672\pi\)
−0.977706 + 0.209977i \(0.932661\pi\)
\(48\) 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 0.845501 0.533974i \(-0.179302\pi\)
−0.533974 + 0.845501i \(0.679302\pi\)
\(54\) 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 −0.796910 0.604098i \(-0.793533\pi\)
0.992193 0.124709i \(-0.0397998\pi\)
\(60\) 0 0
\(61\) −3.86603 14.4282i −0.494994 1.84734i −0.530065 0.847957i \(-0.677832\pi\)
0.0350707 0.999385i \(-0.488834\pi\)
\(62\) 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 0.182773 0.983155i \(-0.441493\pi\)
−0.333292 + 0.942824i \(0.608159\pi\)
\(68\) 0 0
\(69\) 0.696152 0.401924i 0.0838069 0.0483859i
\(70\) 0 0
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 0 0
\(73\) 0.535898i 0.0627222i −0.999508 0.0313611i \(-0.990016\pi\)
0.999508 0.0313611i \(-0.00998418\pi\)
\(74\) 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 −0.910622 0.413239i \(-0.864397\pi\)
0.813187 + 0.582003i \(0.197731\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −3.16025 11.7942i −0.346883 1.29458i −0.890397 0.455185i \(-0.849573\pi\)
0.543514 0.839400i \(-0.317093\pi\)
\(84\) 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 \(0.216285\pi\)
−0.777900 + 0.628388i \(0.783715\pi\)
\(90\) 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 −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 1.50000 0.401924i 0.150756 0.0403949i
\(100\) 0 0
\(101\) −1.86603 + 0.500000i −0.185676 + 0.0497519i −0.350459 0.936578i \(-0.613974\pi\)
0.164783 + 0.986330i \(0.447308\pi\)
\(102\) 0 0
\(103\) 1.79423 1.03590i 0.176791 0.102070i −0.408993 0.912537i \(-0.634120\pi\)
0.585784 + 0.810467i \(0.300787\pi\)
\(104\) 0 0
\(105\) 1.56218 1.56218i 0.152453 0.152453i
\(106\) 0 0
\(107\) 11.3923 + 11.3923i 1.10134 + 1.10134i 0.994250 + 0.107086i \(0.0341520\pi\)
0.107086 + 0.994250i \(0.465848\pi\)
\(108\) 0 0
\(109\) 1.73205 1.73205i 0.165900 0.165900i −0.619274 0.785175i \(-0.712573\pi\)
0.785175 + 0.619274i \(0.212573\pi\)
\(110\) 0 0
\(111\) −13.3923 13.3923i −1.27114 1.27114i
\(112\) 0 0
\(113\) −2.76795 4.79423i −0.260387 0.451003i 0.705958 0.708254i \(-0.250517\pi\)
−0.966345 + 0.257251i \(0.917183\pi\)
\(114\) 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 −0.291305 0.956630i \(-0.594089\pi\)
−0.730593 + 0.682814i \(0.760756\pi\)
\(132\) 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 −0.265096 0.964222i \(-0.585404\pi\)
−0.967589 + 0.252531i \(0.918737\pi\)
\(138\) 0 0
\(139\) 1.16025 4.33013i 0.0984115 0.367277i −0.899103 0.437737i \(-0.855780\pi\)
0.997515 + 0.0704603i \(0.0224468\pi\)
\(140\) 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 −0.594105 0.804388i \(-0.702493\pi\)
0.916704 0.399568i \(-0.130840\pi\)
\(150\) 0 0
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) 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 0.293212 0.956048i \(-0.405276\pi\)
−0.224095 + 0.974567i \(0.571943\pi\)
\(158\) 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 −0.997970 0.0636813i \(-0.979716\pi\)
0.0636813 + 0.997970i \(0.479716\pi\)
\(164\) 0 0
\(165\) 0.464102i 0.0361303i
\(166\) 0 0
\(167\) −8.25833 + 4.76795i −0.639049 + 0.368955i −0.784248 0.620447i \(-0.786951\pi\)
0.145199 + 0.989402i \(0.453618\pi\)
\(168\) 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 0.995129 + 0.0985859i \(0.0314319\pi\)
−0.812514 + 0.582942i \(0.801901\pi\)
\(174\) 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 −0.938328 0.345746i \(-0.887626\pi\)
0.345746 + 0.938328i \(0.387626\pi\)
\(180\) 0 0
\(181\) −4.26795 4.26795i −0.317234 0.317234i 0.530470 0.847704i \(-0.322016\pi\)
−0.847704 + 0.530470i \(0.822016\pi\)
\(182\) 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 −0.999665 0.0258797i \(-0.991761\pi\)
0.522245 + 0.852795i \(0.325095\pi\)
\(192\) 0 0
\(193\) −1.23205 2.13397i −0.0886850 0.153607i 0.818271 0.574833i \(-0.194933\pi\)
−0.906956 + 0.421226i \(0.861600\pi\)
\(194\) 0 0
\(195\) −2.13397 + 3.69615i −0.152817 + 0.264687i
\(196\) 0 0
\(197\) 10.4641 + 10.4641i 0.745536 + 0.745536i 0.973637 0.228101i \(-0.0732517\pi\)
−0.228101 + 0.973637i \(0.573252\pi\)
\(198\) 0 0
\(199\) 5.85641i 0.415150i 0.978219 + 0.207575i \(0.0665570\pi\)
−0.978219 + 0.207575i \(0.933443\pi\)
\(200\) 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 0.190577 0.981672i \(-0.438964\pi\)
−0.325791 + 0.945442i \(0.605631\pi\)
\(212\) 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 −0.477734 0.878504i \(-0.658542\pi\)
0.999674 0.0255224i \(-0.00812491\pi\)
\(224\) 0 0
\(225\) 12.2942 + 7.09808i 0.819615 + 0.473205i
\(226\) 0 0
\(227\) 4.62436 + 17.2583i 0.306929 + 1.14548i 0.931272 + 0.364325i \(0.118700\pi\)
−0.624343 + 0.781151i \(0.714633\pi\)
\(228\) 0 0
\(229\) −2.52628 + 9.42820i −0.166941 + 0.623033i 0.830843 + 0.556506i \(0.187858\pi\)
−0.997785 + 0.0665269i \(0.978808\pi\)
\(230\) 0 0
\(231\) −2.13397 0.571797i −0.140405 0.0376215i
\(232\) 0 0
\(233\) 22.9282i 1.50208i −0.660259 0.751038i \(-0.729553\pi\)
0.660259 0.751038i \(-0.270447\pi\)
\(234\) 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 0.988308 0.152472i \(-0.0487233\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(240\) 0 0
\(241\) −6.23205 + 10.7942i −0.401442 + 0.695317i −0.993900 0.110284i \(-0.964824\pi\)
0.592458 + 0.805601i \(0.298157\pi\)
\(242\) 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 0.434212 0.900811i \(-0.357027\pi\)
−0.900811 + 0.434212i \(0.857027\pi\)
\(252\) 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 0.658990 0.752152i \(-0.270984\pi\)
−0.980878 + 0.194626i \(0.937651\pi\)
\(258\) 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 0.601205 0.799095i \(-0.294687\pi\)
−0.391434 + 0.920206i \(0.628021\pi\)
\(264\) 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 −0.430946 0.902378i \(-0.641820\pi\)
0.902378 + 0.430946i \(0.141820\pi\)
\(270\) 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 0.180618 0.983553i \(-0.442190\pi\)
0.648197 + 0.761473i \(0.275523\pi\)
\(278\) 0 0
\(279\) −1.79423 3.10770i −0.107418 0.186053i
\(280\) 0 0
\(281\) −16.9641 9.79423i −1.01199 0.584275i −0.100219 0.994965i \(-0.531954\pi\)
−0.911775 + 0.410691i \(0.865288\pi\)
\(282\) 0 0
\(283\) −4.16025 + 15.5263i −0.247301 + 0.922942i 0.724911 + 0.688842i \(0.241881\pi\)
−0.972213 + 0.234099i \(0.924786\pi\)
\(284\) 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 −0.756204 0.654336i \(-0.772948\pi\)
0.982060 0.188569i \(-0.0603849\pi\)
\(294\) 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 −0.517402 0.855742i \(-0.673101\pi\)
0.855742 + 0.517402i \(0.173101\pi\)
\(308\) 0 0
\(309\) 3.10770 1.79423i 0.176791 0.102070i
\(310\) 0 0
\(311\) 27.1865 15.6962i 1.54161 0.890047i 0.542869 0.839817i \(-0.317338\pi\)
0.998738 0.0502299i \(-0.0159954\pi\)
\(312\) 0 0
\(313\) 7.83975 + 4.52628i 0.443129 + 0.255840i 0.704924 0.709283i \(-0.250981\pi\)
−0.261795 + 0.965123i \(0.584314\pi\)
\(314\) 0 0
\(315\) 2.70577 2.70577i 0.152453 0.152453i
\(316\) 0 0
\(317\) −0.545517 2.03590i −0.0306393 0.114347i 0.948913 0.315539i \(-0.102185\pi\)
−0.979552 + 0.201192i \(0.935519\pi\)
\(318\) 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 0.553115 0.833105i \(-0.313439\pi\)
0.895564 + 0.444933i \(0.146772\pi\)
\(332\) 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 0.884363 0.466799i \(-0.154593\pi\)
−0.846442 + 0.532482i \(0.821260\pi\)
\(338\) 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 −0.670933 0.741518i \(-0.734106\pi\)
0.951804 0.306707i \(-0.0992273\pi\)
\(348\) 0 0
\(349\) −2.13397 7.96410i −0.114229 0.426309i 0.884999 0.465593i \(-0.154159\pi\)
−0.999228 + 0.0392843i \(0.987492\pi\)
\(350\) 0 0
\(351\) 23.8923 + 6.40192i 1.27528 + 0.341709i
\(352\) 0 0
\(353\) −15.2321 + 26.3827i −0.810720 + 1.40421i 0.101640 + 0.994821i \(0.467591\pi\)
−0.912361 + 0.409387i \(0.865742\pi\)
\(354\) 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 \(-0.869798\pi\)
0.917503 0.397730i \(-0.130202\pi\)
\(360\) 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 0.108408 + 0.994106i \(0.465425\pi\)
−0.915125 + 0.403169i \(0.867909\pi\)
\(368\) 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 −0.808047 0.589118i \(-0.799475\pi\)
0.994348 0.106168i \(-0.0338581\pi\)
\(374\) 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 0.182484 0.983209i \(-0.441586\pi\)
−0.983209 + 0.182484i \(0.941586\pi\)
\(380\) 0 0
\(381\) 35.3205 1.80952
\(382\) 0 0
\(383\) −12.3301 21.3564i −0.630040 1.09126i −0.987543 0.157349i \(-0.949705\pi\)
0.357503 0.933912i \(-0.383628\pi\)
\(384\) 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 −0.0610019 0.998138i \(-0.519430\pi\)
0.446240 + 0.894914i \(0.352763\pi\)
\(390\) 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 −0.0582984 + 0.998299i \(0.518567\pi\)
−0.998299 + 0.0582984i \(0.981433\pi\)
\(398\) 0 0
\(399\) −17.4904 + 4.68653i −0.875614 + 0.234620i
\(400\) 0 0
\(401\) 1.16025 + 2.00962i 0.0579403 + 0.100356i 0.893541 0.448982i \(-0.148213\pi\)
−0.835600 + 0.549338i \(0.814880\pi\)
\(402\) 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 −0.381294 0.924454i \(-0.624521\pi\)
0.609954 + 0.792437i \(0.291188\pi\)
\(410\) 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 0.210523 0.977589i \(-0.432483\pi\)
−0.306476 + 0.951878i \(0.599150\pi\)
\(420\) 0 0
\(421\) 10.7942 2.89230i 0.526079 0.140962i 0.0140017 0.999902i \(-0.495543\pi\)
0.512077 + 0.858940i \(0.328876\pi\)
\(422\) 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 0.00264111 0.999997i \(-0.499159\pi\)
−0.864702 + 0.502286i \(0.832493\pi\)
\(440\) 0 0
\(441\) −1.39230 2.41154i −0.0663002 0.114835i
\(442\) 0 0
\(443\) −16.1603 + 4.33013i −0.767797 + 0.205731i −0.621398 0.783495i \(-0.713435\pi\)
−0.146399 + 0.989226i \(0.546768\pi\)
\(444\) 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 0.874094 0.485758i \(-0.161456\pi\)
0.0163683 + 0.999866i \(0.494790\pi\)
\(458\) 0 0
\(459\) 20.7846 0.970143
\(460\) 0 0
\(461\) −0.598076 2.23205i −0.0278552 0.103957i 0.950599 0.310423i \(-0.100471\pi\)
−0.978454 + 0.206466i \(0.933804\pi\)
\(462\) 0 0
\(463\) −3.33013 5.76795i −0.154764 0.268059i 0.778209 0.628005i \(-0.216128\pi\)
−0.932973 + 0.359946i \(0.882795\pi\)
\(464\) 0 0
\(465\) 1.03590 0.277568i 0.0480386 0.0128719i
\(466\) 0 0
\(467\) 19.7846 19.7846i 0.915523 0.915523i −0.0811771 0.996700i \(-0.525868\pi\)
0.996700 + 0.0811771i \(0.0258679\pi\)
\(468\) 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 −0.880923 0.473259i \(-0.843077\pi\)
0.850316 + 0.526272i \(0.176411\pi\)
\(480\) 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 \(0.288946\pi\)
−0.615521 + 0.788121i \(0.711054\pi\)
\(488\) 0 0
\(489\) −20.6603 + 20.6603i −0.934289 + 0.934289i
\(490\) 0 0
\(491\) −0.500000 + 1.86603i −0.0225647 + 0.0842125i −0.976290 0.216467i \(-0.930547\pi\)
0.953725 + 0.300679i \(0.0972134\pi\)
\(492\) 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 0.314342 0.949310i \(-0.398216\pi\)
−0.202427 + 0.979297i \(0.564883\pi\)
\(500\) 0 0
\(501\) −14.3038 + 8.25833i −0.639049 + 0.368955i
\(502\) 0 0
\(503\) 13.8564i 0.617827i −0.951090 0.308913i \(-0.900035\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(504\) 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 −0.245185 0.969476i \(-0.578849\pi\)
−0.697074 + 0.716999i \(0.745515\pi\)
\(510\) 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 \(0.100269\pi\)
−0.950795 + 0.309821i \(0.899731\pi\)
\(522\) 0 0
\(523\) 2.12436 + 2.12436i 0.0928916 + 0.0928916i 0.752026 0.659134i \(-0.229077\pi\)
−0.659134 + 0.752026i \(0.729077\pi\)
\(524\) 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 −0.951756 0.306856i \(-0.900723\pi\)
0.306856 + 0.951756i \(0.400723\pi\)
\(542\) 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 −0.915566 0.402168i \(-0.868257\pi\)
0.591819 0.806071i \(-0.298410\pi\)
\(548\) 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 0.207307 0.978276i \(-0.433530\pi\)
0.978276 0.207307i \(-0.0664699\pi\)
\(558\) 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 0.817389 0.576086i \(-0.195421\pi\)
0.419836 + 0.907600i \(0.362088\pi\)
\(564\) 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 0.915919 0.401364i \(-0.131464\pi\)
0.110368 + 0.993891i \(0.464797\pi\)
\(570\) 0 0
\(571\) −1.44744 + 5.40192i −0.0605735 + 0.226063i −0.989576 0.144009i \(-0.954001\pi\)
0.929003 + 0.370073i \(0.120667\pi\)
\(572\) 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 −0.197129 0.980378i \(-0.563162\pi\)
0.319470 + 0.947596i \(0.396495\pi\)
\(588\) 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 −0.968781 0.247917i \(-0.920254\pi\)
−0.269688 + 0.962948i \(0.586921\pi\)
\(600\) 0 0
\(601\) −30.2321 17.4545i −1.23319 0.711983i −0.265497 0.964112i \(-0.585536\pi\)
−0.967694 + 0.252128i \(0.918869\pi\)
\(602\) 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 0.944125 0.329589i \(-0.106910\pi\)
−0.757494 + 0.652842i \(0.773577\pi\)
\(608\) 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 0.537053 0.843548i \(-0.319537\pi\)
−0.843548 + 0.537053i \(0.819537\pi\)
\(614\) 0 0
\(615\) −2.59808 9.69615i −0.104765 0.390987i
\(616\) 0 0
\(617\) −8.08846 + 4.66987i −0.325629 + 0.188002i −0.653899 0.756582i \(-0.726868\pi\)
0.328270 + 0.944584i \(0.393534\pi\)
\(618\) 0 0
\(619\) 33.0885 8.86603i 1.32994 0.356356i 0.477246 0.878770i \(-0.341635\pi\)
0.852692 + 0.522414i \(0.174969\pi\)
\(620\) 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 \(-0.778146\pi\)
0.766788 0.641900i \(-0.221854\pi\)
\(632\) 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 −0.729342 0.684150i \(-0.760173\pi\)
0.957162 + 0.289553i \(0.0935068\pi\)
\(642\) 0 0
\(643\) −1.03590 0.277568i −0.0408518 0.0109462i 0.238335 0.971183i \(-0.423398\pi\)
−0.279187 + 0.960237i \(0.590065\pi\)
\(644\) 0 0
\(645\) 8.07180i 0.317827i
\(646\) 0 0
\(647\) 46.3923i 1.82387i 0.410335 + 0.911935i \(0.365412\pi\)
−0.410335 + 0.911935i \(0.634588\pi\)
\(648\) 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 −0.183944 0.982937i \(-0.558886\pi\)
−0.650768 + 0.759276i \(0.725553\pi\)
\(654\) 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 0.995676 0.0928939i \(-0.0296117\pi\)
−0.908728 + 0.417390i \(0.862945\pi\)
\(660\) 0 0
\(661\) 4.20577 15.6962i 0.163586 0.610510i −0.834631 0.550810i \(-0.814319\pi\)
0.998216 0.0596998i \(-0.0190143\pi\)
\(662\) 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 −0.782481 0.622674i \(-0.786046\pi\)
0.930492 + 0.366311i \(0.119379\pi\)
\(674\) 0 0
\(675\) 21.2942 + 12.2942i 0.819615 + 0.473205i
\(676\) 0 0
\(677\) 45.6506 12.2321i 1.75450 0.470116i 0.768920 0.639345i \(-0.220795\pi\)
0.985577 + 0.169229i \(0.0541279\pi\)
\(678\) 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 0.802706 0.596375i \(-0.203393\pi\)
−0.596375 + 0.802706i \(0.703393\pi\)
\(684\) 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 −0.993775 0.111405i \(-0.964465\pi\)
0.804932 0.593367i \(-0.202202\pi\)
\(692\) 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 −0.982325 0.187181i \(-0.940065\pi\)
0.187181 + 0.982325i \(0.440065\pi\)
\(702\) 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 −0.915285 0.402808i \(-0.868034\pi\)
−0.591256 + 0.806484i \(0.701368\pi\)
\(710\) 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 0.658545 0.752541i \(-0.271172\pi\)
−0.322447 + 0.946587i \(0.604506\pi\)
\(728\) 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 0.728429 0.685121i \(-0.240251\pi\)
0.288277 + 0.957547i \(0.406917\pi\)
\(734\) 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 0.0985823 0.995129i \(-0.468569\pi\)
0.995129 0.0985823i \(-0.0314308\pi\)
\(740\) 0 0
\(741\) 30.2942 17.4904i 1.11289 0.642525i
\(742\) 0 0
\(743\) 25.1147 14.5000i 0.921370 0.531953i 0.0372984 0.999304i \(-0.488125\pi\)
0.884072 + 0.467351i \(0.154791\pi\)
\(744\) 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 0.766908 0.641757i \(-0.221794\pi\)
−0.939232 + 0.343283i \(0.888461\pi\)
\(752\) 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 0.843991 0.536358i \(-0.180200\pi\)
−0.536358 + 0.843991i \(0.680200\pi\)
\(758\) 0 0
\(759\) 0.294229 0.294229i 0.0106798 0.0106798i
\(760\) 0 0
\(761\) 25.2846 14.5981i 0.916566 0.529180i 0.0340283 0.999421i \(-0.489166\pi\)
0.882538 + 0.470241i \(0.155833\pi\)
\(762\) 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 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) 0 0
\(771\) −8.93782 15.4808i −0.321888 0.557526i
\(772\) 0 0
\(773\) 7.58846 + 7.58846i 0.272938 + 0.272938i 0.830282 0.557344i \(-0.188179\pi\)
−0.557344 + 0.830282i \(0.688179\pi\)
\(774\) 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 0.805023 0.593244i \(-0.202153\pi\)
0.400548 + 0.916276i \(0.368820\pi\)
\(788\) 0 0
\(789\) 5.89230 + 3.40192i 0.209772 + 0.121112i
\(790\) 0 0
\(791\) 13.6410i 0.485019i
\(792\) 0 0