Properties

Label 144.2.k.c.109.3
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 109.3
Root \(0.767178 + 1.18804i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.2.k.c.37.3

$q$-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 \(-0.479388\pi\)
0.997904 0.0647108i \(-0.0206125\pi\)
\(6\) 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 −0.568733 0.822522i \(-0.692566\pi\)
0.822522 + 0.568733i \(0.192566\pi\)
\(12\) 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 \(-0.621375\pi\)
−0.372136 + 0.928178i \(0.621375\pi\)
\(18\) 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 \(-0.696527\pi\)
0.578923 0.815382i \(-0.303473\pi\)
\(24\) 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 0.768486 0.639867i \(-0.221011\pi\)
−0.639867 + 0.768486i \(0.721011\pi\)
\(30\) 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 \(0.167600\pi\)
−0.864556 + 0.502536i \(0.832400\pi\)
\(42\) 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 \(-0.803786\pi\)
−0.815951 + 0.578121i \(0.803786\pi\)
\(48\) 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 −0.226185 0.974084i \(-0.572625\pi\)
0.974084 + 0.226185i \(0.0726253\pi\)
\(54\) 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 \(0.505844\pi\)
−0.999831 + 0.0183591i \(0.994156\pi\)
\(60\) 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 \(0.0640254\pi\)
−0.979839 + 0.199788i \(0.935975\pi\)
\(72\) 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 0.659401 0.751792i \(-0.270810\pi\)
−0.751792 + 0.659401i \(0.770810\pi\)
\(84\) 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 \(0.168039\pi\)
−0.863862 + 0.503728i \(0.831961\pi\)
\(90\) 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 −0.578941 0.815370i \(-0.696534\pi\)
0.815370 + 0.578941i \(0.196534\pi\)
\(102\) 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 −0.0781266 0.996943i \(-0.524894\pi\)
0.996943 + 0.0781266i \(0.0248938\pi\)
\(108\) 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 0.776814 0.629730i \(-0.216835\pi\)
−0.629730 + 0.776814i \(0.716835\pi\)
\(132\) 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 \(-0.761580\pi\)
0.732358 0.680920i \(-0.238420\pi\)
\(138\) 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 −0.844188 0.536047i \(-0.819917\pi\)
0.536047 + 0.844188i \(0.319917\pi\)
\(150\) 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 \(0.0551294\pi\)
−0.985039 + 0.172330i \(0.944871\pi\)
\(168\) 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 0.469156 0.883115i \(-0.344558\pi\)
−0.883115 + 0.469156i \(0.844558\pi\)
\(174\) 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 0.256230 0.966616i \(-0.417520\pi\)
−0.966616 + 0.256230i \(0.917520\pi\)
\(180\) 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 \(-0.367355\pi\)
0.404759 + 0.914423i \(0.367355\pi\)
\(192\) 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 −0.947516 0.319709i \(-0.896415\pi\)
0.319709 + 0.947516i \(0.396415\pi\)
\(198\) 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 \(-0.925015\pi\)
−0.233399 0.972381i \(-0.574985\pi\)
\(228\) 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 \(0.252846\pi\)
−0.700757 + 0.713400i \(0.747154\pi\)
\(234\) 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 \(-0.225769\pi\)
0.758835 + 0.651283i \(0.225769\pi\)
\(240\) 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 −0.159317 0.987228i \(-0.550929\pi\)
0.987228 + 0.159317i \(0.0509291\pi\)
\(252\) 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 \(-0.669043\pi\)
−0.506452 + 0.862268i \(0.669043\pi\)
\(258\) 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 \(0.160182\pi\)
−0.876031 + 0.482256i \(0.839818\pi\)
\(264\) 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 0.398215 0.917292i \(-0.369630\pi\)
−0.917292 + 0.398215i \(0.869630\pi\)
\(270\) 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 \(0.0914923\pi\)
−0.958975 + 0.283490i \(0.908508\pi\)
\(282\) 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 −0.992834 0.119498i \(-0.961871\pi\)
0.119498 + 0.992834i \(0.461871\pi\)
\(294\) 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 \(0.146257\pi\)
−0.896284 + 0.443481i \(0.853743\pi\)
\(312\) 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 0.637224 0.770678i \(-0.280082\pi\)
−0.770678 + 0.637224i \(0.780082\pi\)
\(318\) 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 −0.684153 0.729339i \(-0.739828\pi\)
0.729339 + 0.684153i \(0.239828\pi\)
\(348\) 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 \(-0.225788\pi\)
0.758796 + 0.651329i \(0.225788\pi\)
\(354\) 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 \(-0.832738\pi\)
0.865089 0.501619i \(-0.167262\pi\)
\(360\) 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 \(-0.592271\pi\)
−0.285834 + 0.958279i \(0.592271\pi\)
\(384\) 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 −0.493316 0.869850i \(-0.664215\pi\)
0.869850 + 0.493316i \(0.164215\pi\)
\(390\) 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 \(-0.573829\pi\)
−0.229866 + 0.973222i \(0.573829\pi\)
\(402\) 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 0.309962 0.950749i \(-0.399684\pi\)
−0.950749 + 0.309962i \(0.899684\pi\)
\(420\) 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 \(-0.508335\pi\)
−0.0261816 + 0.999657i \(0.508335\pi\)
\(432\) 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 \(-0.465220\pi\)
0.994036 0.109048i \(-0.0347803\pi\)
\(444\) 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 \(-0.849322\pi\)
−0.890037 + 0.455889i \(0.849322\pi\)
\(450\) 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 0.881878 0.471477i \(-0.156279\pi\)
−0.471477 + 0.881878i \(0.656279\pi\)
\(462\) 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 0.920293 0.391231i \(-0.127951\pi\)
−0.391231 + 0.920293i \(0.627951\pi\)
\(468\) 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 \(-0.409524\pi\)
0.280426 + 0.959876i \(0.409524\pi\)
\(480\) 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 −0.948050 0.318121i \(-0.896948\pi\)
0.318121 + 0.948050i \(0.396948\pi\)
\(492\) 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 \(0.194570\pi\)
−0.818926 + 0.573899i \(0.805430\pi\)
\(504\) 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 \(0.0753731\pi\)
0.234585 + 0.972096i \(0.424627\pi\)
\(510\) 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 \(0.134422\pi\)
−0.912148 + 0.409860i \(0.865578\pi\)
\(522\) 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 \(-0.984075\pi\)
−0.0500103 0.998749i \(-0.515925\pi\)
\(558\) 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 0.963261 0.268566i \(-0.0865498\pi\)
−0.268566 + 0.963261i \(0.586550\pi\)
\(564\) 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 \(-0.919226\pi\)
0.967976 0.251044i \(-0.0807739\pi\)
\(570\) 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 −0.980598 0.196028i \(-0.937196\pi\)
0.196028 + 0.980598i \(0.437196\pi\)
\(588\) 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 \(-0.581099\pi\)
−0.252034 + 0.967718i \(0.581099\pi\)
\(594\) 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 \(-0.788390\pi\)
0.787045 0.616896i \(-0.211610\pi\)
\(600\) 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 \(0.173389\pi\)
−0.855274 + 0.518175i \(0.826611\pi\)
\(618\) 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 \(-0.558196\pi\)
−0.181810 + 0.983334i \(0.558196\pi\)
\(642\) 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 \(-0.950870\pi\)
0.988112 0.153735i \(-0.0491302\pi\)
\(648\) 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 0.546706 0.837324i \(-0.315881\pi\)
−0.837324 + 0.546706i \(0.815881\pi\)
\(654\) 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 0.998142 0.0609372i \(-0.0194089\pi\)
−0.0609372 + 0.998142i \(0.519409\pi\)
\(660\) 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 −0.808802 0.588081i \(-0.799883\pi\)
0.588081 + 0.808802i \(0.299883\pi\)
\(678\) 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 \(-0.339994\pi\)
0.876298 0.481769i \(-0.160006\pi\)
\(684\) 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 0.319413 0.947616i \(-0.396514\pi\)
−0.947616 + 0.319413i \(0.896514\pi\)
\(702\) 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 \(-0.560313\pi\)
−0.188346 + 0.982103i \(0.560313\pi\)
\(720\) 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 \(0.0860255\pi\)
−0.963702 + 0.266979i \(0.913974\pi\)
\(744\) 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 \(0.0372140\pi\)
−0.993174 + 0.116645i \(0.962786\pi\)
\(762\) 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 −0.392707 0.919664i \(-0.628461\pi\)
0.919664 + 0.392707i \(0.128461\pi\)
\(774\) 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
\(789\)