Properties

Label 144.2.k.c.109.2
Level $144$
Weight $2$
Character 144.109
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.629407744.1
Defining polynomial: \(x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.2
Root \(-0.767178 - 1.18804i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.2.k.c.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +O(q^{10})\) \(q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +(4.64575 + 1.00000i) q^{10} +(-0.841723 + 0.841723i) q^{11} +(-2.64575 - 2.64575i) q^{13} +(4.33130 - 2.79694i) q^{14} +(-2.64575 - 3.00000i) q^{16} +3.06871 q^{17} +(1.64575 + 1.64575i) q^{19} +(-2.37608 - 6.28651i) q^{20} +(1.64575 + 0.354249i) q^{22} +7.82087i q^{23} -6.29150i q^{25} +(-1.11349 + 5.17302i) q^{26} +(-6.64575 - 3.00000i) q^{28} +(-0.692633 - 0.692633i) q^{29} -0.354249 q^{31} +(-1.53436 + 5.44479i) q^{32} +(-2.35425 - 3.64575i) q^{34} +(-8.66259 - 8.66259i) q^{35} +(4.64575 - 4.64575i) q^{37} +(0.692633 - 3.21780i) q^{38} +(-5.64575 + 7.64575i) q^{40} -6.43560i q^{41} +(-5.64575 + 5.64575i) q^{43} +(-0.841723 - 2.22699i) q^{44} +(9.29150 - 6.00000i) q^{46} +11.1878 q^{47} -6.29150 q^{49} +(-7.47455 + 4.82670i) q^{50} +(7.00000 - 2.64575i) q^{52} +(-5.44479 + 5.44479i) q^{53} -4.00000i q^{55} +(1.53436 + 10.1969i) q^{56} +(-0.291503 + 1.35425i) q^{58} +(7.82087 - 7.82087i) q^{59} +(4.64575 + 4.64575i) q^{61} +(0.271772 + 0.420861i) q^{62} +(7.64575 - 2.35425i) q^{64} +12.5730 q^{65} +(4.00000 + 4.00000i) q^{67} +(-2.52517 + 5.59388i) q^{68} +(-3.64575 + 16.9373i) q^{70} -3.36689i q^{71} +7.29150i q^{73} +(-9.08345 - 1.95522i) q^{74} +(-4.35425 + 1.64575i) q^{76} +(-3.06871 - 3.06871i) q^{77} +4.35425 q^{79} +(13.4148 + 0.841723i) q^{80} +(-7.64575 + 4.93725i) q^{82} +(0.841723 + 0.841723i) q^{83} +(-7.29150 + 7.29150i) q^{85} +(11.0387 + 2.37608i) q^{86} +(-2.00000 + 2.70850i) q^{88} -9.50432i q^{89} +(9.64575 - 9.64575i) q^{91} +(-14.2565 - 6.43560i) q^{92} +(-8.58301 - 13.2915i) q^{94} -7.82087 q^{95} +10.5830 q^{97} +(4.82670 + 7.47455i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} + 16q^{10} - 8q^{19} - 8q^{22} - 32q^{28} - 24q^{31} - 40q^{34} + 16q^{37} - 24q^{40} - 24q^{43} + 32q^{46} - 8q^{49} + 56q^{52} + 40q^{58} + 16q^{61} + 40q^{64} + 32q^{67} - 8q^{70} - 56q^{76} + 56q^{79} - 40q^{82} - 16q^{85} - 16q^{88} + 56q^{91} + 16q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.767178 1.18804i −0.542477 0.840071i
\(3\) 0 0
\(4\) −0.822876 + 1.82288i −0.411438 + 0.911438i
\(5\) −2.37608 + 2.37608i −1.06261 + 1.06261i −0.0647108 + 0.997904i \(0.520612\pi\)
−0.997904 + 0.0647108i \(0.979388\pi\)
\(6\) 0 0
\(7\) 3.64575i 1.37796i 0.724778 + 0.688982i \(0.241942\pi\)
−0.724778 + 0.688982i \(0.758058\pi\)
\(8\) 2.79694 0.420861i 0.988868 0.148797i
\(9\) 0 0
\(10\) 4.64575 + 1.00000i 1.46912 + 0.316228i
\(11\) −0.841723 + 0.841723i −0.253789 + 0.253789i −0.822522 0.568733i \(-0.807434\pi\)
0.568733 + 0.822522i \(0.307434\pi\)
\(12\) 0 0
\(13\) −2.64575 2.64575i −0.733799 0.733799i 0.237571 0.971370i \(-0.423649\pi\)
−0.971370 + 0.237571i \(0.923649\pi\)
\(14\) 4.33130 2.79694i 1.15759 0.747514i
\(15\) 0 0
\(16\) −2.64575 3.00000i −0.661438 0.750000i
\(17\) 3.06871 0.744272 0.372136 0.928178i \(-0.378625\pi\)
0.372136 + 0.928178i \(0.378625\pi\)
\(18\) 0 0
\(19\) 1.64575 + 1.64575i 0.377561 + 0.377561i 0.870222 0.492660i \(-0.163976\pi\)
−0.492660 + 0.870222i \(0.663976\pi\)
\(20\) −2.37608 6.28651i −0.531307 1.40571i
\(21\) 0 0
\(22\) 1.64575 + 0.354249i 0.350875 + 0.0755261i
\(23\) 7.82087i 1.63076i 0.578923 + 0.815382i \(0.303473\pi\)
−0.578923 + 0.815382i \(0.696527\pi\)
\(24\) 0 0
\(25\) 6.29150i 1.25830i
\(26\) −1.11349 + 5.17302i −0.218374 + 1.01451i
\(27\) 0 0
\(28\) −6.64575 3.00000i −1.25593 0.566947i
\(29\) −0.692633 0.692633i −0.128619 0.128619i 0.639867 0.768486i \(-0.278989\pi\)
−0.768486 + 0.639867i \(0.778989\pi\)
\(30\) 0 0
\(31\) −0.354249 −0.0636249 −0.0318125 0.999494i \(-0.510128\pi\)
−0.0318125 + 0.999494i \(0.510128\pi\)
\(32\) −1.53436 + 5.44479i −0.271238 + 0.962512i
\(33\) 0 0
\(34\) −2.35425 3.64575i −0.403750 0.625241i
\(35\) −8.66259 8.66259i −1.46425 1.46425i
\(36\) 0 0
\(37\) 4.64575 4.64575i 0.763757 0.763757i −0.213242 0.976999i \(-0.568402\pi\)
0.976999 + 0.213242i \(0.0684024\pi\)
\(38\) 0.692633 3.21780i 0.112360 0.521996i
\(39\) 0 0
\(40\) −5.64575 + 7.64575i −0.892672 + 1.20890i
\(41\) 6.43560i 1.00507i −0.864556 0.502536i \(-0.832400\pi\)
0.864556 0.502536i \(-0.167600\pi\)
\(42\) 0 0
\(43\) −5.64575 + 5.64575i −0.860969 + 0.860969i −0.991451 0.130482i \(-0.958348\pi\)
0.130482 + 0.991451i \(0.458348\pi\)
\(44\) −0.841723 2.22699i −0.126894 0.335731i
\(45\) 0 0
\(46\) 9.29150 6.00000i 1.36996 0.884652i
\(47\) 11.1878 1.63190 0.815951 0.578121i \(-0.196214\pi\)
0.815951 + 0.578121i \(0.196214\pi\)
\(48\) 0 0
\(49\) −6.29150 −0.898786
\(50\) −7.47455 + 4.82670i −1.05706 + 0.682599i
\(51\) 0 0
\(52\) 7.00000 2.64575i 0.970725 0.366900i
\(53\) −5.44479 + 5.44479i −0.747900 + 0.747900i −0.974084 0.226185i \(-0.927375\pi\)
0.226185 + 0.974084i \(0.427375\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) 1.53436 + 10.1969i 0.205037 + 1.36262i
\(57\) 0 0
\(58\) −0.291503 + 1.35425i −0.0382762 + 0.177822i
\(59\) 7.82087 7.82087i 1.01819 1.01819i 0.0183591 0.999831i \(-0.494156\pi\)
0.999831 0.0183591i \(-0.00584422\pi\)
\(60\) 0 0
\(61\) 4.64575 + 4.64575i 0.594828 + 0.594828i 0.938932 0.344104i \(-0.111817\pi\)
−0.344104 + 0.938932i \(0.611817\pi\)
\(62\) 0.271772 + 0.420861i 0.0345151 + 0.0534495i
\(63\) 0 0
\(64\) 7.64575 2.35425i 0.955719 0.294281i
\(65\) 12.5730 1.55949
\(66\) 0 0
\(67\) 4.00000 + 4.00000i 0.488678 + 0.488678i 0.907889 0.419211i \(-0.137693\pi\)
−0.419211 + 0.907889i \(0.637693\pi\)
\(68\) −2.52517 + 5.59388i −0.306222 + 0.678358i
\(69\) 0 0
\(70\) −3.64575 + 16.9373i −0.435751 + 2.02439i
\(71\) 3.36689i 0.399577i −0.979839 0.199788i \(-0.935975\pi\)
0.979839 0.199788i \(-0.0640254\pi\)
\(72\) 0 0
\(73\) 7.29150i 0.853406i 0.904392 + 0.426703i \(0.140325\pi\)
−0.904392 + 0.426703i \(0.859675\pi\)
\(74\) −9.08345 1.95522i −1.05593 0.227289i
\(75\) 0 0
\(76\) −4.35425 + 1.64575i −0.499467 + 0.188781i
\(77\) −3.06871 3.06871i −0.349712 0.349712i
\(78\) 0 0
\(79\) 4.35425 0.489891 0.244946 0.969537i \(-0.421230\pi\)
0.244946 + 0.969537i \(0.421230\pi\)
\(80\) 13.4148 + 0.841723i 1.49981 + 0.0941075i
\(81\) 0 0
\(82\) −7.64575 + 4.93725i −0.844332 + 0.545228i
\(83\) 0.841723 + 0.841723i 0.0923911 + 0.0923911i 0.751792 0.659401i \(-0.229190\pi\)
−0.659401 + 0.751792i \(0.729190\pi\)
\(84\) 0 0
\(85\) −7.29150 + 7.29150i −0.790875 + 0.790875i
\(86\) 11.0387 + 2.37608i 1.19033 + 0.256219i
\(87\) 0 0
\(88\) −2.00000 + 2.70850i −0.213201 + 0.288727i
\(89\) 9.50432i 1.00746i −0.863862 0.503728i \(-0.831961\pi\)
0.863862 0.503728i \(-0.168039\pi\)
\(90\) 0 0
\(91\) 9.64575 9.64575i 1.01115 1.01115i
\(92\) −14.2565 6.43560i −1.48634 0.670958i
\(93\) 0 0
\(94\) −8.58301 13.2915i −0.885269 1.37091i
\(95\) −7.82087 −0.802404
\(96\) 0 0
\(97\) 10.5830 1.07454 0.537271 0.843410i \(-0.319455\pi\)
0.537271 + 0.843410i \(0.319455\pi\)
\(98\) 4.82670 + 7.47455i 0.487571 + 0.755044i
\(99\) 0 0
\(100\) 11.4686 + 5.17712i 1.14686 + 0.517712i
\(101\) −2.37608 + 2.37608i −0.236429 + 0.236429i −0.815370 0.578941i \(-0.803466\pi\)
0.578941 + 0.815370i \(0.303466\pi\)
\(102\) 0 0
\(103\) 1.06275i 0.104715i 0.998628 + 0.0523577i \(0.0166736\pi\)
−0.998628 + 0.0523577i \(0.983326\pi\)
\(104\) −8.51350 6.28651i −0.834818 0.616443i
\(105\) 0 0
\(106\) 10.6458 + 2.29150i 1.03401 + 0.222570i
\(107\) −9.50432 + 9.50432i −0.918817 + 0.918817i −0.996943 0.0781266i \(-0.975106\pi\)
0.0781266 + 0.996943i \(0.475106\pi\)
\(108\) 0 0
\(109\) −1.35425 1.35425i −0.129713 0.129713i 0.639269 0.768983i \(-0.279237\pi\)
−0.768983 + 0.639269i \(0.779237\pi\)
\(110\) −4.75216 + 3.06871i −0.453100 + 0.292590i
\(111\) 0 0
\(112\) 10.9373 9.64575i 1.03347 0.911438i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −18.5830 18.5830i −1.73287 1.73287i
\(116\) 1.83254 0.692633i 0.170147 0.0643094i
\(117\) 0 0
\(118\) −15.2915 3.29150i −1.40770 0.303007i
\(119\) 11.1878i 1.02558i
\(120\) 0 0
\(121\) 9.58301i 0.871182i
\(122\) 1.95522 9.08345i 0.177017 0.822377i
\(123\) 0 0
\(124\) 0.291503 0.645751i 0.0261777 0.0579902i
\(125\) 3.06871 + 3.06871i 0.274474 + 0.274474i
\(126\) 0 0
\(127\) −14.9373 −1.32547 −0.662733 0.748855i \(-0.730604\pi\)
−0.662733 + 0.748855i \(0.730604\pi\)
\(128\) −8.66259 7.27733i −0.765672 0.643231i
\(129\) 0 0
\(130\) −9.64575 14.9373i −0.845988 1.31008i
\(131\) −1.68345 1.68345i −0.147083 0.147083i 0.629730 0.776814i \(-0.283165\pi\)
−0.776814 + 0.629730i \(0.783165\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.00000i −0.520266 + 0.520266i
\(134\) 1.68345 7.82087i 0.145428 0.675620i
\(135\) 0 0
\(136\) 8.58301 1.29150i 0.735987 0.110745i
\(137\) 15.9399i 1.36184i 0.732358 + 0.680920i \(0.238420\pi\)
−0.732358 + 0.680920i \(0.761580\pi\)
\(138\) 0 0
\(139\) 6.58301 6.58301i 0.558363 0.558363i −0.370478 0.928841i \(-0.620806\pi\)
0.928841 + 0.370478i \(0.120806\pi\)
\(140\) 22.9191 8.66259i 1.93701 0.732123i
\(141\) 0 0
\(142\) −4.00000 + 2.58301i −0.335673 + 0.216761i
\(143\) 4.45398 0.372460
\(144\) 0 0
\(145\) 3.29150 0.273344
\(146\) 8.66259 5.59388i 0.716921 0.462953i
\(147\) 0 0
\(148\) 4.64575 + 12.2915i 0.381878 + 1.01036i
\(149\) 3.76135 3.76135i 0.308141 0.308141i −0.536047 0.844188i \(-0.680083\pi\)
0.844188 + 0.536047i \(0.180083\pi\)
\(150\) 0 0
\(151\) 15.6458i 1.27323i −0.771180 0.636617i \(-0.780333\pi\)
0.771180 0.636617i \(-0.219667\pi\)
\(152\) 5.29570 + 3.91044i 0.429538 + 0.317178i
\(153\) 0 0
\(154\) −1.29150 + 6.00000i −0.104072 + 0.483494i
\(155\) 0.841723 0.841723i 0.0676088 0.0676088i
\(156\) 0 0
\(157\) −1.35425 1.35425i −0.108081 0.108081i 0.650998 0.759079i \(-0.274350\pi\)
−0.759079 + 0.650998i \(0.774350\pi\)
\(158\) −3.34048 5.17302i −0.265755 0.411543i
\(159\) 0 0
\(160\) −9.29150 16.5830i −0.734558 1.31100i
\(161\) −28.5129 −2.24714
\(162\) 0 0
\(163\) 6.35425 + 6.35425i 0.497703 + 0.497703i 0.910722 0.413019i \(-0.135526\pi\)
−0.413019 + 0.910722i \(0.635526\pi\)
\(164\) 11.7313 + 5.29570i 0.916061 + 0.413525i
\(165\) 0 0
\(166\) 0.354249 1.64575i 0.0274950 0.127735i
\(167\) 4.45398i 0.344659i −0.985039 0.172330i \(-0.944871\pi\)
0.985039 0.172330i \(-0.0551294\pi\)
\(168\) 0 0
\(169\) 1.00000i 0.0769231i
\(170\) 14.2565 + 3.06871i 1.09342 + 0.235359i
\(171\) 0 0
\(172\) −5.64575 14.9373i −0.430485 1.13895i
\(173\) 5.44479 + 5.44479i 0.413960 + 0.413960i 0.883115 0.469156i \(-0.155442\pi\)
−0.469156 + 0.883115i \(0.655442\pi\)
\(174\) 0 0
\(175\) 22.9373 1.73389
\(176\) 4.75216 + 0.298179i 0.358207 + 0.0224761i
\(177\) 0 0
\(178\) −11.2915 + 7.29150i −0.846334 + 0.546521i
\(179\) 9.50432 + 9.50432i 0.710386 + 0.710386i 0.966616 0.256230i \(-0.0824804\pi\)
−0.256230 + 0.966616i \(0.582480\pi\)
\(180\) 0 0
\(181\) 4.64575 4.64575i 0.345316 0.345316i −0.513045 0.858361i \(-0.671483\pi\)
0.858361 + 0.513045i \(0.171483\pi\)
\(182\) −18.8595 4.05952i −1.39796 0.300912i
\(183\) 0 0
\(184\) 3.29150 + 21.8745i 0.242653 + 1.61261i
\(185\) 22.0773i 1.62316i
\(186\) 0 0
\(187\) −2.58301 + 2.58301i −0.188888 + 0.188888i
\(188\) −9.20614 + 20.3939i −0.671427 + 1.48738i
\(189\) 0 0
\(190\) 6.00000 + 9.29150i 0.435286 + 0.674076i
\(191\) −11.1878 −0.809518 −0.404759 0.914423i \(-0.632645\pi\)
−0.404759 + 0.914423i \(0.632645\pi\)
\(192\) 0 0
\(193\) −19.8745 −1.43060 −0.715299 0.698818i \(-0.753710\pi\)
−0.715299 + 0.698818i \(0.753710\pi\)
\(194\) −8.11905 12.5730i −0.582914 0.902691i
\(195\) 0 0
\(196\) 5.17712 11.4686i 0.369795 0.819188i
\(197\) 8.81168 8.81168i 0.627806 0.627806i −0.319709 0.947516i \(-0.603585\pi\)
0.947516 + 0.319709i \(0.103585\pi\)
\(198\) 0 0
\(199\) 8.35425i 0.592217i 0.955154 + 0.296108i \(0.0956890\pi\)
−0.955154 + 0.296108i \(0.904311\pi\)
\(200\) −2.64785 17.5970i −0.187231 1.24429i
\(201\) 0 0
\(202\) 4.64575 + 1.00000i 0.326874 + 0.0703598i
\(203\) 2.52517 2.52517i 0.177232 0.177232i
\(204\) 0 0
\(205\) 15.2915 + 15.2915i 1.06800 + 1.06800i
\(206\) 1.26258 0.815315i 0.0879684 0.0568057i
\(207\) 0 0
\(208\) −0.937254 + 14.9373i −0.0649869 + 1.03571i
\(209\) −2.77053 −0.191642
\(210\) 0 0
\(211\) 6.58301 + 6.58301i 0.453193 + 0.453193i 0.896413 0.443220i \(-0.146164\pi\)
−0.443220 + 0.896413i \(0.646164\pi\)
\(212\) −5.44479 14.4056i −0.373950 0.989378i
\(213\) 0 0
\(214\) 18.5830 + 4.00000i 1.27031 + 0.273434i
\(215\) 26.8295i 1.82976i
\(216\) 0 0
\(217\) 1.29150i 0.0876729i
\(218\) −0.569951 + 2.64785i −0.0386020 + 0.179335i
\(219\) 0 0
\(220\) 7.29150 + 3.29150i 0.491593 + 0.221913i
\(221\) −8.11905 8.11905i −0.546146 0.546146i
\(222\) 0 0
\(223\) −19.6458 −1.31558 −0.657788 0.753203i \(-0.728508\pi\)
−0.657788 + 0.753203i \(0.728508\pi\)
\(224\) −19.8504 5.59388i −1.32631 0.373757i
\(225\) 0 0
\(226\) 0 0
\(227\) 18.1669 + 18.1669i 1.20578 + 1.20578i 0.972381 + 0.233399i \(0.0749848\pi\)
0.233399 + 0.972381i \(0.425015\pi\)
\(228\) 0 0
\(229\) 2.06275 2.06275i 0.136310 0.136310i −0.635659 0.771970i \(-0.719272\pi\)
0.771970 + 0.635659i \(0.219272\pi\)
\(230\) −7.82087 + 36.3338i −0.515693 + 2.39578i
\(231\) 0 0
\(232\) −2.22876 1.64575i −0.146325 0.108049i
\(233\) 21.7792i 1.42680i −0.700757 0.713400i \(-0.747154\pi\)
0.700757 0.713400i \(-0.252846\pi\)
\(234\) 0 0
\(235\) −26.5830 + 26.5830i −1.73408 + 1.73408i
\(236\) 7.82087 + 20.6921i 0.509095 + 1.34694i
\(237\) 0 0
\(238\) 13.2915 8.58301i 0.861560 0.556354i
\(239\) −23.4626 −1.51767 −0.758835 0.651283i \(-0.774231\pi\)
−0.758835 + 0.651283i \(0.774231\pi\)
\(240\) 0 0
\(241\) 9.29150 0.598518 0.299259 0.954172i \(-0.403260\pi\)
0.299259 + 0.954172i \(0.403260\pi\)
\(242\) 11.3850 7.35187i 0.731855 0.472596i
\(243\) 0 0
\(244\) −12.2915 + 4.64575i −0.786883 + 0.297414i
\(245\) 14.9491 14.9491i 0.955063 0.955063i
\(246\) 0 0
\(247\) 8.70850i 0.554108i
\(248\) −0.990812 + 0.149090i −0.0629167 + 0.00946720i
\(249\) 0 0
\(250\) 1.29150 6.00000i 0.0816818 0.379473i
\(251\) −13.1166 + 13.1166i −0.827911 + 0.827911i −0.987228 0.159317i \(-0.949071\pi\)
0.159317 + 0.987228i \(0.449071\pi\)
\(252\) 0 0
\(253\) −6.58301 6.58301i −0.413870 0.413870i
\(254\) 11.4595 + 17.7460i 0.719035 + 1.11349i
\(255\) 0 0
\(256\) −2.00000 + 15.8745i −0.125000 + 0.992157i
\(257\) 16.2381 1.01290 0.506452 0.862268i \(-0.330957\pi\)
0.506452 + 0.862268i \(0.330957\pi\)
\(258\) 0 0
\(259\) 16.9373 + 16.9373i 1.05243 + 1.05243i
\(260\) −10.3460 + 22.9191i −0.641634 + 1.42138i
\(261\) 0 0
\(262\) −0.708497 + 3.29150i −0.0437711 + 0.203350i
\(263\) 15.6417i 0.964511i −0.876031 0.482256i \(-0.839818\pi\)
0.876031 0.482256i \(-0.160182\pi\)
\(264\) 0 0
\(265\) 25.8745i 1.58946i
\(266\) 11.7313 + 2.52517i 0.719292 + 0.154828i
\(267\) 0 0
\(268\) −10.5830 + 4.00000i −0.646460 + 0.244339i
\(269\) 8.51350 + 8.51350i 0.519077 + 0.519077i 0.917292 0.398215i \(-0.130370\pi\)
−0.398215 + 0.917292i \(0.630370\pi\)
\(270\) 0 0
\(271\) 11.6458 0.707429 0.353715 0.935353i \(-0.384918\pi\)
0.353715 + 0.935353i \(0.384918\pi\)
\(272\) −8.11905 9.20614i −0.492290 0.558204i
\(273\) 0 0
\(274\) 18.9373 12.2288i 1.14404 0.738766i
\(275\) 5.29570 + 5.29570i 0.319343 + 0.319343i
\(276\) 0 0
\(277\) 20.5203 20.5203i 1.23294 1.23294i 0.270115 0.962828i \(-0.412938\pi\)
0.962828 0.270115i \(-0.0870616\pi\)
\(278\) −12.8712 2.77053i −0.771964 0.166166i
\(279\) 0 0
\(280\) −27.8745 20.5830i −1.66582 1.23007i
\(281\) 9.50432i 0.566980i −0.958975 0.283490i \(-0.908508\pi\)
0.958975 0.283490i \(-0.0914923\pi\)
\(282\) 0 0
\(283\) 18.5830 18.5830i 1.10465 1.10465i 0.110803 0.993842i \(-0.464658\pi\)
0.993842 0.110803i \(-0.0353421\pi\)
\(284\) 6.13742 + 2.77053i 0.364189 + 0.164401i
\(285\) 0 0
\(286\) −3.41699 5.29150i −0.202051 0.312893i
\(287\) 23.4626 1.38495
\(288\) 0 0
\(289\) −7.58301 −0.446059
\(290\) −2.52517 3.91044i −0.148283 0.229629i
\(291\) 0 0
\(292\) −13.2915 6.00000i −0.777826 0.351123i
\(293\) 14.9491 14.9491i 0.873336 0.873336i −0.119498 0.992834i \(-0.538129\pi\)
0.992834 + 0.119498i \(0.0381286\pi\)
\(294\) 0 0
\(295\) 37.1660i 2.16389i
\(296\) 11.0387 14.9491i 0.641610 0.868899i
\(297\) 0 0
\(298\) −7.35425 1.58301i −0.426020 0.0917010i
\(299\) 20.6921 20.6921i 1.19665 1.19665i
\(300\) 0 0
\(301\) −20.5830 20.5830i −1.18638 1.18638i
\(302\) −18.5878 + 12.0031i −1.06961 + 0.690699i
\(303\) 0 0
\(304\) 0.583005 9.29150i 0.0334376 0.532904i
\(305\) −22.0773 −1.26415
\(306\) 0 0
\(307\) −20.0000 20.0000i −1.14146 1.14146i −0.988183 0.153277i \(-0.951017\pi\)
−0.153277 0.988183i \(-0.548983\pi\)
\(308\) 8.11905 3.06871i 0.462626 0.174856i
\(309\) 0 0
\(310\) −1.64575 0.354249i −0.0934724 0.0201200i
\(311\) 15.6417i 0.886962i −0.896284 0.443481i \(-0.853743\pi\)
0.896284 0.443481i \(-0.146257\pi\)
\(312\) 0 0
\(313\) 1.29150i 0.0730000i −0.999334 0.0365000i \(-0.988379\pi\)
0.999334 0.0365000i \(-0.0116209\pi\)
\(314\) −0.569951 + 2.64785i −0.0321642 + 0.149427i
\(315\) 0 0
\(316\) −3.58301 + 7.93725i −0.201560 + 0.446505i
\(317\) 2.37608 + 2.37608i 0.133454 + 0.133454i 0.770678 0.637224i \(-0.219918\pi\)
−0.637224 + 0.770678i \(0.719918\pi\)
\(318\) 0 0
\(319\) 1.16601 0.0652841
\(320\) −12.5730 + 23.7608i −0.702854 + 1.32827i
\(321\) 0 0
\(322\) 21.8745 + 33.8745i 1.21902 + 1.88775i
\(323\) 5.05034 + 5.05034i 0.281008 + 0.281008i
\(324\) 0 0
\(325\) −16.6458 + 16.6458i −0.923340 + 0.923340i
\(326\) 2.67426 12.4239i 0.148113 0.688098i
\(327\) 0 0
\(328\) −2.70850 18.0000i −0.149552 0.993884i
\(329\) 40.7878i 2.24870i
\(330\) 0 0
\(331\) −8.00000 + 8.00000i −0.439720 + 0.439720i −0.891918 0.452198i \(-0.850640\pi\)
0.452198 + 0.891918i \(0.350640\pi\)
\(332\) −2.22699 + 0.841723i −0.122222 + 0.0461955i
\(333\) 0 0
\(334\) −5.29150 + 3.41699i −0.289538 + 0.186970i
\(335\) −19.0086 −1.03855
\(336\) 0 0
\(337\) 15.2915 0.832981 0.416491 0.909140i \(-0.363260\pi\)
0.416491 + 0.909140i \(0.363260\pi\)
\(338\) 1.18804 0.767178i 0.0646208 0.0417290i
\(339\) 0 0
\(340\) −7.29150 19.2915i −0.395437 1.04623i
\(341\) 0.298179 0.298179i 0.0161473 0.0161473i
\(342\) 0 0
\(343\) 2.58301i 0.139469i
\(344\) −13.4148 + 18.1669i −0.723275 + 0.979494i
\(345\) 0 0
\(346\) 2.29150 10.6458i 0.123192 0.572319i
\(347\) −0.841723 + 0.841723i −0.0451861 + 0.0451861i −0.729339 0.684153i \(-0.760172\pi\)
0.684153 + 0.729339i \(0.260172\pi\)
\(348\) 0 0
\(349\) −23.2288 23.2288i −1.24341 1.24341i −0.958579 0.284828i \(-0.908063\pi\)
−0.284828 0.958579i \(-0.591937\pi\)
\(350\) −17.5970 27.2504i −0.940597 1.45659i
\(351\) 0 0
\(352\) −3.29150 5.87451i −0.175438 0.313112i
\(353\) −28.5129 −1.51759 −0.758796 0.651329i \(-0.774212\pi\)
−0.758796 + 0.651329i \(0.774212\pi\)
\(354\) 0 0
\(355\) 8.00000 + 8.00000i 0.424596 + 0.424596i
\(356\) 17.3252 + 7.82087i 0.918233 + 0.414505i
\(357\) 0 0
\(358\) 4.00000 18.5830i 0.211407 0.982142i
\(359\) 19.0086i 1.00324i 0.865089 + 0.501619i \(0.167262\pi\)
−0.865089 + 0.501619i \(0.832738\pi\)
\(360\) 0 0
\(361\) 13.5830i 0.714895i
\(362\) −9.08345 1.95522i −0.477416 0.102764i
\(363\) 0 0
\(364\) 9.64575 + 25.5203i 0.505575 + 1.33763i
\(365\) −17.3252 17.3252i −0.906842 0.906842i
\(366\) 0 0
\(367\) −12.8118 −0.668769 −0.334384 0.942437i \(-0.608528\pi\)
−0.334384 + 0.942437i \(0.608528\pi\)
\(368\) 23.4626 20.6921i 1.22307 1.07865i
\(369\) 0 0
\(370\) 26.2288 16.9373i 1.36357 0.880526i
\(371\) −19.8504 19.8504i −1.03058 1.03058i
\(372\) 0 0
\(373\) −3.93725 + 3.93725i −0.203863 + 0.203863i −0.801653 0.597790i \(-0.796046\pi\)
0.597790 + 0.801653i \(0.296046\pi\)
\(374\) 5.05034 + 1.08709i 0.261147 + 0.0562119i
\(375\) 0 0
\(376\) 31.2915 4.70850i 1.61374 0.242822i
\(377\) 3.66507i 0.188761i
\(378\) 0 0
\(379\) 13.6458 13.6458i 0.700935 0.700935i −0.263676 0.964611i \(-0.584935\pi\)
0.964611 + 0.263676i \(0.0849350\pi\)
\(380\) 6.43560 14.2565i 0.330140 0.731342i
\(381\) 0 0
\(382\) 8.58301 + 13.2915i 0.439145 + 0.680052i
\(383\) 11.1878 0.571668 0.285834 0.958279i \(-0.407729\pi\)
0.285834 + 0.958279i \(0.407729\pi\)
\(384\) 0 0
\(385\) 14.5830 0.743219
\(386\) 15.2473 + 23.6117i 0.776066 + 1.20180i
\(387\) 0 0
\(388\) −8.70850 + 19.2915i −0.442107 + 0.979378i
\(389\) −7.42642 + 7.42642i −0.376534 + 0.376534i −0.869850 0.493316i \(-0.835785\pi\)
0.493316 + 0.869850i \(0.335785\pi\)
\(390\) 0 0
\(391\) 24.0000i 1.21373i
\(392\) −17.5970 + 2.64785i −0.888781 + 0.133737i
\(393\) 0 0
\(394\) −17.2288 3.70850i −0.867972 0.186831i
\(395\) −10.3460 + 10.3460i −0.520566 + 0.520566i
\(396\) 0 0
\(397\) 23.9373 + 23.9373i 1.20138 + 1.20138i 0.973748 + 0.227628i \(0.0730971\pi\)
0.227628 + 0.973748i \(0.426903\pi\)
\(398\) 9.92518 6.40920i 0.497504 0.321264i
\(399\) 0 0
\(400\) −18.8745 + 16.6458i −0.943725 + 0.832288i
\(401\) 9.20614 0.459733 0.229866 0.973222i \(-0.426171\pi\)
0.229866 + 0.973222i \(0.426171\pi\)
\(402\) 0 0
\(403\) 0.937254 + 0.937254i 0.0466879 + 0.0466879i
\(404\) −2.37608 6.28651i −0.118214 0.312766i
\(405\) 0 0
\(406\) −4.93725 1.06275i −0.245032 0.0527432i
\(407\) 7.82087i 0.387666i
\(408\) 0 0
\(409\) 17.1660i 0.848805i 0.905474 + 0.424402i \(0.139516\pi\)
−0.905474 + 0.424402i \(0.860484\pi\)
\(410\) 6.43560 29.8982i 0.317832 1.47657i
\(411\) 0 0
\(412\) −1.93725 0.874508i −0.0954417 0.0430839i
\(413\) 28.5129 + 28.5129i 1.40303 + 1.40303i
\(414\) 0 0
\(415\) −4.00000 −0.196352
\(416\) 18.4651 10.3460i 0.905325 0.507256i
\(417\) 0 0
\(418\) 2.12549 + 3.29150i 0.103961 + 0.160993i
\(419\) 13.1166 + 13.1166i 0.640786 + 0.640786i 0.950749 0.309962i \(-0.100316\pi\)
−0.309962 + 0.950749i \(0.600316\pi\)
\(420\) 0 0
\(421\) 16.6458 16.6458i 0.811264 0.811264i −0.173559 0.984823i \(-0.555527\pi\)
0.984823 + 0.173559i \(0.0555268\pi\)
\(422\) 2.77053 12.8712i 0.134867 0.626561i
\(423\) 0 0
\(424\) −12.9373 + 17.5203i −0.628289 + 0.850859i
\(425\) 19.3068i 0.936518i
\(426\) 0 0
\(427\) −16.9373 + 16.9373i −0.819651 + 0.819651i
\(428\) −9.50432 25.1461i −0.459408 1.21548i
\(429\) 0 0
\(430\) −31.8745 + 20.5830i −1.53713 + 0.992601i
\(431\) 1.08709 0.0523632 0.0261816 0.999657i \(-0.491665\pi\)
0.0261816 + 0.999657i \(0.491665\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) −1.53436 + 0.990812i −0.0736515 + 0.0475605i
\(435\) 0 0
\(436\) 3.58301 1.35425i 0.171595 0.0648567i
\(437\) −12.8712 + 12.8712i −0.615713 + 0.615713i
\(438\) 0 0
\(439\) 37.5203i 1.79074i −0.445319 0.895372i \(-0.646910\pi\)
0.445319 0.895372i \(-0.353090\pi\)
\(440\) −1.68345 11.1878i −0.0802551 0.533356i
\(441\) 0 0
\(442\) −3.41699 + 15.8745i −0.162530 + 0.755073i
\(443\) −23.2172 + 23.2172i −1.10308 + 1.10308i −0.109048 + 0.994036i \(0.534780\pi\)
−0.994036 + 0.109048i \(0.965220\pi\)
\(444\) 0 0
\(445\) 22.5830 + 22.5830i 1.07054 + 1.07054i
\(446\) 15.0718 + 23.3399i 0.713670 + 1.10518i
\(447\) 0 0
\(448\) 8.58301 + 27.8745i 0.405509 + 1.31695i
\(449\) 37.7191 1.78007 0.890037 0.455889i \(-0.150678\pi\)
0.890037 + 0.455889i \(0.150678\pi\)
\(450\) 0 0
\(451\) 5.41699 + 5.41699i 0.255076 + 0.255076i
\(452\) 0 0
\(453\) 0 0
\(454\) 7.64575 35.5203i 0.358833 1.66705i
\(455\) 45.8381i 2.14892i
\(456\) 0 0
\(457\) 26.5830i 1.24350i 0.783216 + 0.621750i \(0.213578\pi\)
−0.783216 + 0.621750i \(0.786422\pi\)
\(458\) −4.03312 0.868130i −0.188455 0.0405651i
\(459\) 0 0
\(460\) 49.1660 18.5830i 2.29238 0.866437i
\(461\) −8.81168 8.81168i −0.410401 0.410401i 0.471477 0.881878i \(-0.343721\pi\)
−0.881878 + 0.471477i \(0.843721\pi\)
\(462\) 0 0
\(463\) 30.9373 1.43778 0.718888 0.695126i \(-0.244651\pi\)
0.718888 + 0.695126i \(0.244651\pi\)
\(464\) −0.245364 + 3.91044i −0.0113908 + 0.181537i
\(465\) 0 0
\(466\) −25.8745 + 16.7085i −1.19861 + 0.774006i
\(467\) −11.4331 11.4331i −0.529062 0.529062i 0.391231 0.920293i \(-0.372049\pi\)
−0.920293 + 0.391231i \(0.872049\pi\)
\(468\) 0 0
\(469\) −14.5830 + 14.5830i −0.673381 + 0.673381i
\(470\) 51.9756 + 11.1878i 2.39745 + 0.516053i
\(471\) 0 0
\(472\) 18.5830 25.1660i 0.855352 1.15836i
\(473\) 9.50432i 0.437009i
\(474\) 0 0
\(475\) 10.3542 10.3542i 0.475086 0.475086i
\(476\) −20.3939 9.20614i −0.934753 0.421963i
\(477\) 0 0
\(478\) 18.0000 + 27.8745i 0.823301 + 1.27495i
\(479\) −12.2748 −0.560852 −0.280426 0.959876i \(-0.590476\pi\)
−0.280426 + 0.959876i \(0.590476\pi\)
\(480\) 0 0
\(481\) −24.5830 −1.12089
\(482\) −7.12824 11.0387i −0.324682 0.502798i
\(483\) 0 0
\(484\) −17.4686 7.88562i −0.794028 0.358437i
\(485\) −25.1461 + 25.1461i −1.14182 + 1.14182i
\(486\) 0 0
\(487\) 18.2288i 0.826024i −0.910726 0.413012i \(-0.864477\pi\)
0.910726 0.413012i \(-0.135523\pi\)
\(488\) 14.9491 + 11.0387i 0.676714 + 0.499697i
\(489\) 0 0
\(490\) −29.2288 6.29150i −1.32042 0.284221i
\(491\) 13.9583 13.9583i 0.629929 0.629929i −0.318121 0.948050i \(-0.603052\pi\)
0.948050 + 0.318121i \(0.103052\pi\)
\(492\) 0 0
\(493\) −2.12549 2.12549i −0.0957274 0.0957274i
\(494\) −10.3460 + 6.68097i −0.465490 + 0.300591i
\(495\) 0 0
\(496\) 0.937254 + 1.06275i 0.0420839 + 0.0477187i
\(497\) 12.2748 0.550602
\(498\) 0 0
\(499\) −10.5830 10.5830i −0.473760 0.473760i 0.429369 0.903129i \(-0.358736\pi\)
−0.903129 + 0.429369i \(0.858736\pi\)
\(500\) −8.11905 + 3.06871i −0.363095 + 0.137237i
\(501\) 0 0
\(502\) 25.6458 + 5.52026i 1.14463 + 0.246381i
\(503\) 25.7424i 1.14780i −0.818926 0.573899i \(-0.805430\pi\)
0.818926 0.573899i \(-0.194570\pi\)
\(504\) 0 0
\(505\) 11.2915i 0.502465i
\(506\) −2.77053 + 12.8712i −0.123165 + 0.572195i
\(507\) 0 0
\(508\) 12.2915 27.2288i 0.545347 1.20808i
\(509\) −27.2240 27.2240i −1.20668 1.20668i −0.972096 0.234585i \(-0.924627\pi\)
−0.234585 0.972096i \(-0.575373\pi\)
\(510\) 0 0
\(511\) −26.5830 −1.17596
\(512\) 20.3939 9.80250i 0.901291 0.433213i
\(513\) 0 0
\(514\) −12.4575 19.2915i −0.549477 0.850912i
\(515\) −2.52517 2.52517i −0.111272 0.111272i
\(516\) 0 0
\(517\) −9.41699 + 9.41699i −0.414159 + 0.414159i
\(518\) 7.12824 33.1160i 0.313197 1.45503i
\(519\) 0 0
\(520\) 35.1660 5.29150i 1.54213 0.232048i
\(521\) 18.7105i 0.819720i −0.912148 0.409860i \(-0.865578\pi\)
0.912148 0.409860i \(-0.134422\pi\)
\(522\) 0 0
\(523\) −3.06275 + 3.06275i −0.133925 + 0.133925i −0.770891 0.636967i \(-0.780189\pi\)
0.636967 + 0.770891i \(0.280189\pi\)
\(524\) 4.45398 1.68345i 0.194573 0.0735417i
\(525\) 0 0
\(526\) −18.5830 + 12.0000i −0.810258 + 0.523225i
\(527\) −1.08709 −0.0473543
\(528\) 0 0
\(529\) −38.1660 −1.65939
\(530\) −30.7399 + 19.8504i −1.33526 + 0.862244i
\(531\) 0 0
\(532\) −6.00000 15.8745i −0.260133 0.688247i
\(533\) −17.0270 + 17.0270i −0.737522 + 0.737522i
\(534\) 0 0
\(535\) 45.1660i 1.95270i
\(536\) 12.8712 + 9.50432i 0.555951 + 0.410524i
\(537\) 0 0
\(538\) 3.58301 16.6458i 0.154474 0.717649i
\(539\) 5.29570 5.29570i 0.228102 0.228102i
\(540\) 0 0
\(541\) 8.52026 + 8.52026i 0.366315 + 0.366315i 0.866131 0.499817i \(-0.166599\pi\)
−0.499817 + 0.866131i \(0.666599\pi\)
\(542\) −8.93436 13.8356i −0.383764 0.594290i
\(543\) 0 0
\(544\) −4.70850 + 16.7085i −0.201875 + 0.716371i
\(545\) 6.43560 0.275671
\(546\) 0 0
\(547\) −0.937254 0.937254i −0.0400741 0.0400741i 0.686786 0.726860i \(-0.259021\pi\)
−0.726860 + 0.686786i \(0.759021\pi\)
\(548\) −29.0565 13.1166i −1.24123 0.560312i
\(549\) 0 0
\(550\) 2.22876 10.3542i 0.0950345 0.441507i
\(551\) 2.27980i 0.0971229i
\(552\) 0 0
\(553\) 15.8745i 0.675053i
\(554\) −40.1216 8.63619i −1.70460 0.366916i
\(555\) 0 0
\(556\) 6.58301 + 17.4170i 0.279182 + 0.738645i
\(557\) 24.7516 + 24.7516i 1.04876 + 1.04876i 0.998749 + 0.0500103i \(0.0159254\pi\)
0.0500103 + 0.998749i \(0.484075\pi\)
\(558\) 0 0
\(559\) 29.8745 1.26356
\(560\) −3.06871 + 48.9068i −0.129677 + 2.06669i
\(561\) 0 0
\(562\) −11.2915 + 7.29150i −0.476303 + 0.307573i
\(563\) −16.4835 16.4835i −0.694695 0.694695i 0.268566 0.963261i \(-0.413450\pi\)
−0.963261 + 0.268566i \(0.913450\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −36.3338 7.82087i −1.52722 0.328736i
\(567\) 0 0
\(568\) −1.41699 9.41699i −0.0594558 0.395128i
\(569\) 11.9767i 0.502088i 0.967976 + 0.251044i \(0.0807739\pi\)
−0.967976 + 0.251044i \(0.919226\pi\)
\(570\) 0 0
\(571\) 4.00000 4.00000i 0.167395 0.167395i −0.618438 0.785833i \(-0.712234\pi\)
0.785833 + 0.618438i \(0.212234\pi\)
\(572\) −3.66507 + 8.11905i −0.153244 + 0.339475i
\(573\) 0 0
\(574\) −18.0000 27.8745i −0.751305 1.16346i
\(575\) 49.2050 2.05199
\(576\) 0 0
\(577\) 35.0405 1.45876 0.729378 0.684111i \(-0.239810\pi\)
0.729378 + 0.684111i \(0.239810\pi\)
\(578\) 5.81752 + 9.00891i 0.241977 + 0.374721i
\(579\) 0 0
\(580\) −2.70850 + 6.00000i −0.112464 + 0.249136i
\(581\) −3.06871 + 3.06871i −0.127312 + 0.127312i
\(582\) 0 0
\(583\) 9.16601i 0.379617i
\(584\) 3.06871 + 20.3939i 0.126984 + 0.843906i
\(585\) 0 0
\(586\) −29.2288 6.29150i −1.20743 0.259900i
\(587\) 19.0086 19.0086i 0.784570 0.784570i −0.196028 0.980598i \(-0.562804\pi\)
0.980598 + 0.196028i \(0.0628044\pi\)
\(588\) 0 0
\(589\) −0.583005 0.583005i −0.0240223 0.0240223i
\(590\) 44.1547 28.5129i 1.81782 1.17386i
\(591\) 0 0
\(592\) −26.2288 1.64575i −1.07800 0.0676400i
\(593\) 12.2748 0.504068 0.252034 0.967718i \(-0.418901\pi\)
0.252034 + 0.967718i \(0.418901\pi\)
\(594\) 0 0
\(595\) −26.5830 26.5830i −1.08980 1.08980i
\(596\) 3.76135 + 9.95158i 0.154071 + 0.407633i
\(597\) 0 0
\(598\) −40.4575 8.70850i −1.65443 0.356117i
\(599\) 30.1964i 1.23379i 0.787045 + 0.616896i \(0.211610\pi\)
−0.787045 + 0.616896i \(0.788390\pi\)
\(600\) 0 0
\(601\) 7.29150i 0.297427i 0.988880 + 0.148713i \(0.0475132\pi\)
−0.988880 + 0.148713i \(0.952487\pi\)
\(602\) −8.66259 + 40.2443i −0.353061 + 1.64023i
\(603\) 0 0
\(604\) 28.5203 + 12.8745i 1.16047 + 0.523856i
\(605\) −22.7700 22.7700i −0.925731 0.925731i
\(606\) 0 0
\(607\) −44.1033 −1.79010 −0.895048 0.445970i \(-0.852859\pi\)
−0.895048 + 0.445970i \(0.852859\pi\)
\(608\) −11.4859 + 6.43560i −0.465816 + 0.260998i
\(609\) 0 0
\(610\) 16.9373 + 26.2288i 0.685769 + 1.06197i
\(611\) −29.6000 29.6000i −1.19749 1.19749i
\(612\) 0 0
\(613\) 21.3542 21.3542i 0.862490 0.862490i −0.129137 0.991627i \(-0.541221\pi\)
0.991627 + 0.129137i \(0.0412206\pi\)
\(614\) −8.41723 + 39.1044i −0.339692 + 1.57812i
\(615\) 0 0
\(616\) −9.87451 7.29150i −0.397855 0.293783i
\(617\) 25.7424i 1.03635i −0.855274 0.518175i \(-0.826611\pi\)
0.855274 0.518175i \(-0.173389\pi\)
\(618\) 0 0
\(619\) 21.1660 21.1660i 0.850734 0.850734i −0.139490 0.990224i \(-0.544546\pi\)
0.990224 + 0.139490i \(0.0445462\pi\)
\(620\) 0.841723 + 2.22699i 0.0338044 + 0.0894380i
\(621\) 0 0
\(622\) −18.5830 + 12.0000i −0.745111 + 0.481156i
\(623\) 34.6504 1.38824
\(624\) 0 0
\(625\) 16.8745 0.674980
\(626\) −1.53436 + 0.990812i −0.0613252 + 0.0396008i
\(627\) 0 0
\(628\) 3.58301 1.35425i 0.142977 0.0540404i
\(629\) 14.2565 14.2565i 0.568443 0.568443i
\(630\) 0 0
\(631\) 18.2288i 0.725675i 0.931852 + 0.362838i \(0.118192\pi\)
−0.931852 + 0.362838i \(0.881808\pi\)
\(632\) 12.1786 1.83254i 0.484438 0.0728943i
\(633\) 0 0
\(634\) 1.00000 4.64575i 0.0397151 0.184506i
\(635\) 35.4921 35.4921i 1.40846 1.40846i
\(636\) 0 0
\(637\) 16.6458 + 16.6458i 0.659529 + 0.659529i
\(638\) −0.894538 1.38527i −0.0354151 0.0548432i
\(639\) 0 0
\(640\) 37.8745 3.29150i 1.49712 0.130108i
\(641\) 9.20614 0.363621 0.181810 0.983334i \(-0.441804\pi\)
0.181810 + 0.983334i \(0.441804\pi\)
\(642\) 0 0
\(643\) 1.64575 + 1.64575i 0.0649021 + 0.0649021i 0.738813 0.673911i \(-0.235387\pi\)
−0.673911 + 0.738813i \(0.735387\pi\)
\(644\) 23.4626 51.9756i 0.924556 2.04812i
\(645\) 0 0
\(646\) 2.12549 9.87451i 0.0836264 0.388507i
\(647\) 7.82087i 0.307470i 0.988112 + 0.153735i \(0.0491302\pi\)
−0.988112 + 0.153735i \(0.950870\pi\)
\(648\) 0 0
\(649\) 13.1660i 0.516811i
\(650\) 32.5461 + 7.00555i 1.27656 + 0.274780i
\(651\) 0 0
\(652\) −16.8118 + 6.35425i −0.658399 + 0.248852i
\(653\) 7.42642 + 7.42642i 0.290618 + 0.290618i 0.837324 0.546706i \(-0.184119\pi\)
−0.546706 + 0.837324i \(0.684119\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) −19.3068 + 17.0270i −0.753804 + 0.664793i
\(657\) 0 0
\(658\) 48.4575 31.2915i 1.88907 1.21987i
\(659\) −24.0590 24.0590i −0.937204 0.937204i 0.0609372 0.998142i \(-0.480591\pi\)
−0.998142 + 0.0609372i \(0.980591\pi\)
\(660\) 0 0
\(661\) −29.2288 + 29.2288i −1.13687 + 1.13687i −0.147858 + 0.989009i \(0.547238\pi\)
−0.989009 + 0.147858i \(0.952762\pi\)
\(662\) 15.6417 + 3.36689i 0.607934 + 0.130858i
\(663\) 0 0
\(664\) 2.70850 + 2.00000i 0.105110 + 0.0776151i
\(665\) 28.5129i 1.10568i
\(666\) 0 0
\(667\) 5.41699 5.41699i 0.209747 0.209747i
\(668\) 8.11905 + 3.66507i 0.314135 + 0.141806i
\(669\) 0 0
\(670\) 14.5830 + 22.5830i 0.563391 + 0.872458i
\(671\) −7.82087 −0.301921
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) −11.7313 18.1669i −0.451873 0.699763i
\(675\) 0 0
\(676\) −1.82288 0.822876i −0.0701106 0.0316491i
\(677\) 5.74297 5.74297i 0.220720 0.220720i −0.588081 0.808802i \(-0.700117\pi\)
0.808802 + 0.588081i \(0.200117\pi\)
\(678\) 0 0
\(679\) 38.5830i 1.48068i
\(680\) −17.3252 + 23.4626i −0.664391 + 0.899750i
\(681\) 0 0
\(682\) −0.583005 0.125492i −0.0223244 0.00480534i
\(683\) −35.4921 + 35.4921i −1.35807 + 1.35807i −0.481769 + 0.876298i \(0.660006\pi\)
−0.876298 + 0.481769i \(0.839994\pi\)
\(684\) 0 0
\(685\) −37.8745 37.8745i −1.44711 1.44711i
\(686\) 3.06871 1.98162i 0.117164 0.0756588i
\(687\) 0 0
\(688\) 31.8745 + 2.00000i 1.21520 + 0.0762493i
\(689\) 28.8111 1.09762
\(690\) 0 0
\(691\) 1.64575 + 1.64575i 0.0626073 + 0.0626073i 0.737717 0.675110i \(-0.235904\pi\)
−0.675110 + 0.737717i \(0.735904\pi\)
\(692\) −14.4056 + 5.44479i −0.547617 + 0.206980i
\(693\) 0 0
\(694\) 1.64575 + 0.354249i 0.0624719 + 0.0134471i
\(695\) 31.2835i 1.18665i
\(696\) 0 0
\(697\) 19.7490i 0.748047i
\(698\) −9.77609 + 45.4173i −0.370030 + 1.71907i
\(699\) 0 0
\(700\) −18.8745 + 41.8118i −0.713389 + 1.58034i
\(701\) 16.6326 + 16.6326i 0.628203 + 0.628203i 0.947616 0.319413i \(-0.103486\pi\)
−0.319413 + 0.947616i \(0.603486\pi\)
\(702\) 0 0
\(703\) 15.2915 0.576730
\(704\) −4.45398 + 8.41723i −0.167866 + 0.317236i
\(705\) 0 0
\(706\) 21.8745 + 33.8745i 0.823258 + 1.27488i
\(707\) −8.66259 8.66259i −0.325790 0.325790i
\(708\) 0 0
\(709\) −35.2288 + 35.2288i −1.32304 + 1.32304i −0.411744 + 0.911299i \(0.635080\pi\)
−0.911299 + 0.411744i \(0.864920\pi\)
\(710\) 3.36689 15.6417i 0.126357 0.587024i
\(711\) 0 0
\(712\) −4.00000 26.5830i −0.149906 0.996240i
\(713\) 2.77053i 0.103757i
\(714\) 0 0
\(715\) −10.5830 + 10.5830i −0.395782 + 0.395782i
\(716\) −25.1461 + 9.50432i −0.939752 + 0.355193i
\(717\) 0 0
\(718\) 22.5830 14.5830i 0.842790 0.544233i
\(719\) 10.1007 0.376692 0.188346 0.982103i \(-0.439687\pi\)
0.188346 + 0.982103i \(0.439687\pi\)
\(720\) 0 0
\(721\) −3.87451 −0.144294
\(722\) −16.1371 + 10.4206i −0.600562 + 0.387814i
\(723\) 0 0
\(724\) 4.64575 + 12.2915i 0.172658 + 0.456810i
\(725\) −4.35770 + 4.35770i −0.161841 + 0.161841i
\(726\) 0 0
\(727\) 35.3948i 1.31272i 0.754448 + 0.656360i \(0.227905\pi\)
−0.754448 + 0.656360i \(0.772095\pi\)
\(728\) 22.9191 31.0381i 0.849437 1.15035i
\(729\) 0 0
\(730\) −7.29150 + 33.8745i −0.269871 + 1.25375i
\(731\) −17.3252 + 17.3252i −0.640795 + 0.640795i
\(732\) 0 0
\(733\) −7.35425 7.35425i −0.271635 0.271635i 0.558123 0.829758i \(-0.311522\pi\)
−0.829758 + 0.558123i \(0.811522\pi\)
\(734\) 9.82890 + 15.2209i 0.362791 + 0.561813i
\(735\) 0 0
\(736\) −42.5830 12.0000i −1.56963 0.442326i
\(737\) −6.73378 −0.248042
\(738\) 0 0
\(739\) 33.1660 + 33.1660i 1.22003 + 1.22003i 0.967620 + 0.252411i \(0.0812236\pi\)
0.252411 + 0.967620i \(0.418776\pi\)
\(740\) −40.2443 18.1669i −1.47941 0.667829i
\(741\) 0 0
\(742\) −8.35425 + 38.8118i −0.306694 + 1.42482i
\(743\) 14.5547i 0.533958i −0.963702 0.266979i \(-0.913974\pi\)
0.963702 0.266979i \(-0.0860255\pi\)
\(744\) 0 0
\(745\) 17.8745i 0.654871i
\(746\) 7.69819 + 1.65704i 0.281851 + 0.0606685i
\(747\) 0 0
\(748\) −2.58301 6.83399i −0.0944440 0.249875i
\(749\) −34.6504 34.6504i −1.26610 1.26610i
\(750\) 0 0
\(751\) −2.93725 −0.107182 −0.0535910 0.998563i \(-0.517067\pi\)
−0.0535910 + 0.998563i \(0.517067\pi\)
\(752\) −29.6000 33.5633i −1.07940 1.22393i
\(753\) 0 0
\(754\) 4.35425 2.81176i 0.158572 0.102398i
\(755\) 37.1755 + 37.1755i 1.35296 + 1.35296i
\(756\) 0 0
\(757\) 19.2288 19.2288i 0.698881 0.698881i −0.265288 0.964169i \(-0.585467\pi\)
0.964169 + 0.265288i \(0.0854671\pi\)
\(758\) −26.6804 5.74297i −0.969076 0.208594i
\(759\) 0 0
\(760\) −21.8745 + 3.29150i −0.793472 + 0.119395i
\(761\) 6.43560i 0.233290i −0.993174 0.116645i \(-0.962786\pi\)
0.993174 0.116645i \(-0.0372140\pi\)
\(762\) 0 0
\(763\) 4.93725 4.93725i 0.178741 0.178741i
\(764\) 9.20614 20.3939i 0.333066 0.737825i
\(765\) 0 0
\(766\) −8.58301 13.2915i −0.310117 0.480242i
\(767\) −41.3842 −1.49430
\(768\) 0 0
\(769\) 6.70850 0.241915 0.120957 0.992658i \(-0.461404\pi\)
0.120957 + 0.992658i \(0.461404\pi\)
\(770\) −11.1878 17.3252i −0.403179 0.624356i
\(771\) 0 0
\(772\) 16.3542 36.2288i 0.588602 1.30390i
\(773\) −14.6509 + 14.6509i −0.526957 + 0.526957i −0.919664 0.392707i \(-0.871539\pi\)
0.392707 + 0.919664i \(0.371539\pi\)
\(774\) 0 0
\(775\) 2.22876i 0.0800593i
\(776\) 29.6000 4.45398i 1.06258 0.159889i
\(777\) 0 0
\(778\) 14.5203 + 3.12549i 0.520577 + 0.112054i
\(779\) 10.5914 10.5914i 0.379476 0.379476i
\(780\) 0 0
\(781\) 2.83399 + 2.83399i 0.101408 + 0.101408i
\(782\) 28.5129 18.4123i 1.01962 0.658422i
\(783\) 0 0
\(784\) 16.6458 + 18.8745i 0.594491 + 0.674090i
\(785\) 6.43560 0.229697
\(786\) 0 0
\(787\) −20.2288 20.2288i −0.721077 0.721077i 0.247747 0.968825i \(-0.420310\pi\)
−0.968825 + 0.247747i \(0.920310\pi\)
\(788\) 8.81168 + 23.3135i 0.313903 + 0.830510i