Properties

Label 720.2.u.a.179.3
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.3
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.41522 - 1.73123i) q^{5} -3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +O(q^{10})\) \(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.41522 - 1.73123i) q^{5} -3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +(-1.61739 + 2.71736i) q^{10} +(0.761375 - 0.761375i) q^{11} +(4.33164 - 4.33164i) q^{13} +(0.795824 + 5.32284i) q^{14} +(3.31562 - 2.23755i) q^{16} -6.44408 q^{17} +(-2.98007 + 2.98007i) q^{19} +(1.69394 - 4.13891i) q^{20} +(-0.905695 + 1.22413i) q^{22} -1.73120 q^{23} +(-0.994326 - 4.90013i) q^{25} +(-5.15271 + 6.96434i) q^{26} +(-2.22619 - 7.27847i) q^{28} +(-0.289500 + 0.289500i) q^{29} +3.89823i q^{31} +(-4.16955 + 3.82294i) q^{32} +(9.01313 - 1.34756i) q^{34} +(-6.58847 - 5.38582i) q^{35} +(1.64445 + 1.64445i) q^{37} +(3.54494 - 4.79130i) q^{38} +(-1.50375 + 6.14319i) q^{40} +2.59735 q^{41} +(-7.61730 + 7.61730i) q^{43} +(1.01078 - 1.90154i) q^{44} +(2.42137 - 0.362022i) q^{46} +5.14100i q^{47} -7.48300 q^{49} +(2.41543 + 6.64573i) q^{50} +(5.75057 - 10.8183i) q^{52} +(5.10351 - 5.10351i) q^{53} +(-0.240606 - 2.39563i) q^{55} +(4.63574 + 9.71462i) q^{56} +(0.344376 - 0.465454i) q^{58} +(5.68382 - 5.68382i) q^{59} +(-0.647296 - 0.647296i) q^{61} +(-0.815183 - 5.45232i) q^{62} +(5.03237 - 6.21894i) q^{64} +(-1.36887 - 13.6293i) q^{65} +(-9.09323 - 9.09323i) q^{67} +(-12.3246 + 3.76959i) q^{68} +(10.3413 + 6.15522i) q^{70} -8.79742i q^{71} +12.1321 q^{73} +(-2.64392 - 1.95616i) q^{74} +(-3.95625 + 7.44275i) q^{76} +(-2.89753 - 2.89753i) q^{77} -12.0907i q^{79} +(0.818604 - 8.90673i) q^{80} +(-3.63283 + 0.543148i) q^{82} +(0.925156 - 0.925156i) q^{83} +(-9.11977 + 11.1562i) q^{85} +(9.06116 - 12.2470i) q^{86} +(-1.01610 + 2.87100i) q^{88} +13.2896 q^{89} +(-16.4847 - 16.4847i) q^{91} +(-3.31099 + 1.01270i) q^{92} +(-1.07507 - 7.19055i) q^{94} +(0.941748 + 9.37663i) q^{95} -9.56150i q^{97} +(10.4662 - 1.56482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39867 + 0.209116i −0.989007 + 0.147868i
\(3\) 0 0
\(4\) 1.91254 0.584968i 0.956270 0.292484i
\(5\) 1.41522 1.73123i 0.632904 0.774230i
\(6\) 0 0
\(7\) 3.80565i 1.43840i −0.694802 0.719201i \(-0.744508\pi\)
0.694802 0.719201i \(-0.255492\pi\)
\(8\) −2.55268 + 1.21812i −0.902509 + 0.430670i
\(9\) 0 0
\(10\) −1.61739 + 2.71736i −0.511463 + 0.859305i
\(11\) 0.761375 0.761375i 0.229563 0.229563i −0.582947 0.812510i \(-0.698100\pi\)
0.812510 + 0.582947i \(0.198100\pi\)
\(12\) 0 0
\(13\) 4.33164 4.33164i 1.20138 1.20138i 0.227634 0.973747i \(-0.426901\pi\)
0.973747 0.227634i \(-0.0730991\pi\)
\(14\) 0.795824 + 5.32284i 0.212693 + 1.42259i
\(15\) 0 0
\(16\) 3.31562 2.23755i 0.828906 0.559388i
\(17\) −6.44408 −1.56292 −0.781460 0.623955i \(-0.785525\pi\)
−0.781460 + 0.623955i \(0.785525\pi\)
\(18\) 0 0
\(19\) −2.98007 + 2.98007i −0.683674 + 0.683674i −0.960826 0.277152i \(-0.910610\pi\)
0.277152 + 0.960826i \(0.410610\pi\)
\(20\) 1.69394 4.13891i 0.378777 0.925488i
\(21\) 0 0
\(22\) −0.905695 + 1.22413i −0.193095 + 0.260985i
\(23\) −1.73120 −0.360980 −0.180490 0.983577i \(-0.557768\pi\)
−0.180490 + 0.983577i \(0.557768\pi\)
\(24\) 0 0
\(25\) −0.994326 4.90013i −0.198865 0.980027i
\(26\) −5.15271 + 6.96434i −1.01053 + 1.36582i
\(27\) 0 0
\(28\) −2.22619 7.27847i −0.420710 1.37550i
\(29\) −0.289500 + 0.289500i −0.0537589 + 0.0537589i −0.733475 0.679716i \(-0.762103\pi\)
0.679716 + 0.733475i \(0.262103\pi\)
\(30\) 0 0
\(31\) 3.89823i 0.700142i 0.936723 + 0.350071i \(0.113843\pi\)
−0.936723 + 0.350071i \(0.886157\pi\)
\(32\) −4.16955 + 3.82294i −0.737079 + 0.675807i
\(33\) 0 0
\(34\) 9.01313 1.34756i 1.54574 0.231105i
\(35\) −6.58847 5.38582i −1.11365 0.910370i
\(36\) 0 0
\(37\) 1.64445 + 1.64445i 0.270346 + 0.270346i 0.829239 0.558893i \(-0.188774\pi\)
−0.558893 + 0.829239i \(0.688774\pi\)
\(38\) 3.54494 4.79130i 0.575066 0.777252i
\(39\) 0 0
\(40\) −1.50375 + 6.14319i −0.237764 + 0.971323i
\(41\) 2.59735 0.405638 0.202819 0.979216i \(-0.434990\pi\)
0.202819 + 0.979216i \(0.434990\pi\)
\(42\) 0 0
\(43\) −7.61730 + 7.61730i −1.16163 + 1.16163i −0.177507 + 0.984119i \(0.556803\pi\)
−0.984119 + 0.177507i \(0.943197\pi\)
\(44\) 1.01078 1.90154i 0.152381 0.286668i
\(45\) 0 0
\(46\) 2.42137 0.362022i 0.357012 0.0533773i
\(47\) 5.14100i 0.749892i 0.927047 + 0.374946i \(0.122339\pi\)
−0.927047 + 0.374946i \(0.877661\pi\)
\(48\) 0 0
\(49\) −7.48300 −1.06900
\(50\) 2.41543 + 6.64573i 0.341593 + 0.939848i
\(51\) 0 0
\(52\) 5.75057 10.8183i 0.797460 1.50023i
\(53\) 5.10351 5.10351i 0.701021 0.701021i −0.263609 0.964630i \(-0.584913\pi\)
0.964630 + 0.263609i \(0.0849128\pi\)
\(54\) 0 0
\(55\) −0.240606 2.39563i −0.0324434 0.323026i
\(56\) 4.63574 + 9.71462i 0.619477 + 1.29817i
\(57\) 0 0
\(58\) 0.344376 0.465454i 0.0452187 0.0611171i
\(59\) 5.68382 5.68382i 0.739971 0.739971i −0.232601 0.972572i \(-0.574724\pi\)
0.972572 + 0.232601i \(0.0747237\pi\)
\(60\) 0 0
\(61\) −0.647296 0.647296i −0.0828778 0.0828778i 0.664453 0.747330i \(-0.268665\pi\)
−0.747330 + 0.664453i \(0.768665\pi\)
\(62\) −0.815183 5.45232i −0.103528 0.692446i
\(63\) 0 0
\(64\) 5.03237 6.21894i 0.629046 0.777368i
\(65\) −1.36887 13.6293i −0.169787 1.69050i
\(66\) 0 0
\(67\) −9.09323 9.09323i −1.11091 1.11091i −0.993027 0.117887i \(-0.962388\pi\)
−0.117887 0.993027i \(-0.537612\pi\)
\(68\) −12.3246 + 3.76959i −1.49457 + 0.457129i
\(69\) 0 0
\(70\) 10.3413 + 6.15522i 1.23603 + 0.735689i
\(71\) 8.79742i 1.04406i −0.852927 0.522031i \(-0.825175\pi\)
0.852927 0.522031i \(-0.174825\pi\)
\(72\) 0 0
\(73\) 12.1321 1.41995 0.709976 0.704225i \(-0.248706\pi\)
0.709976 + 0.704225i \(0.248706\pi\)
\(74\) −2.64392 1.95616i −0.307350 0.227399i
\(75\) 0 0
\(76\) −3.95625 + 7.44275i −0.453814 + 0.853741i
\(77\) −2.89753 2.89753i −0.330204 0.330204i
\(78\) 0 0
\(79\) 12.0907i 1.36031i −0.733068 0.680155i \(-0.761912\pi\)
0.733068 0.680155i \(-0.238088\pi\)
\(80\) 0.818604 8.90673i 0.0915227 0.995803i
\(81\) 0 0
\(82\) −3.63283 + 0.543148i −0.401179 + 0.0599807i
\(83\) 0.925156 0.925156i 0.101549 0.101549i −0.654507 0.756056i \(-0.727124\pi\)
0.756056 + 0.654507i \(0.227124\pi\)
\(84\) 0 0
\(85\) −9.11977 + 11.1562i −0.989178 + 1.21006i
\(86\) 9.06116 12.2470i 0.977090 1.32062i
\(87\) 0 0
\(88\) −1.01610 + 2.87100i −0.108317 + 0.306049i
\(89\) 13.2896 1.40870 0.704349 0.709854i \(-0.251239\pi\)
0.704349 + 0.709854i \(0.251239\pi\)
\(90\) 0 0
\(91\) −16.4847 16.4847i −1.72807 1.72807i
\(92\) −3.31099 + 1.01270i −0.345195 + 0.105581i
\(93\) 0 0
\(94\) −1.07507 7.19055i −0.110885 0.741649i
\(95\) 0.941748 + 9.37663i 0.0966213 + 0.962022i
\(96\) 0 0
\(97\) 9.56150i 0.970823i −0.874286 0.485411i \(-0.838670\pi\)
0.874286 0.485411i \(-0.161330\pi\)
\(98\) 10.4662 1.56482i 1.05725 0.158070i
\(99\) 0 0
\(100\) −4.76811 8.79006i −0.476811 0.879006i
\(101\) −11.7354 11.7354i −1.16771 1.16771i −0.982744 0.184969i \(-0.940782\pi\)
−0.184969 0.982744i \(-0.559218\pi\)
\(102\) 0 0
\(103\) 9.72480i 0.958213i 0.877757 + 0.479107i \(0.159039\pi\)
−0.877757 + 0.479107i \(0.840961\pi\)
\(104\) −5.78084 + 16.3338i −0.566858 + 1.60166i
\(105\) 0 0
\(106\) −6.07088 + 8.20534i −0.589656 + 0.796973i
\(107\) 8.15735 + 8.15735i 0.788601 + 0.788601i 0.981265 0.192664i \(-0.0617127\pi\)
−0.192664 + 0.981265i \(0.561713\pi\)
\(108\) 0 0
\(109\) 8.72633 + 8.72633i 0.835831 + 0.835831i 0.988307 0.152477i \(-0.0487249\pi\)
−0.152477 + 0.988307i \(0.548725\pi\)
\(110\) 0.837493 + 3.30037i 0.0798519 + 0.314678i
\(111\) 0 0
\(112\) −8.51535 12.6181i −0.804625 1.19230i
\(113\) 16.2773 1.53124 0.765619 0.643295i \(-0.222433\pi\)
0.765619 + 0.643295i \(0.222433\pi\)
\(114\) 0 0
\(115\) −2.45002 + 2.99711i −0.228466 + 0.279482i
\(116\) −0.384333 + 0.723030i −0.0356844 + 0.0671316i
\(117\) 0 0
\(118\) −6.76120 + 9.13836i −0.622419 + 0.841254i
\(119\) 24.5240i 2.24811i
\(120\) 0 0
\(121\) 9.84061i 0.894601i
\(122\) 1.04071 + 0.769992i 0.0942217 + 0.0697118i
\(123\) 0 0
\(124\) 2.28034 + 7.45552i 0.204781 + 0.669525i
\(125\) −9.89045 5.21334i −0.884629 0.466295i
\(126\) 0 0
\(127\) −8.61277 −0.764260 −0.382130 0.924109i \(-0.624809\pi\)
−0.382130 + 0.924109i \(0.624809\pi\)
\(128\) −5.73813 + 9.75058i −0.507184 + 0.861838i
\(129\) 0 0
\(130\) 4.76469 + 18.7766i 0.417891 + 1.64682i
\(131\) −7.09695 7.09695i −0.620064 0.620064i 0.325484 0.945548i \(-0.394473\pi\)
−0.945548 + 0.325484i \(0.894473\pi\)
\(132\) 0 0
\(133\) 11.3411 + 11.3411i 0.983398 + 0.983398i
\(134\) 14.6199 + 10.8169i 1.26297 + 0.934434i
\(135\) 0 0
\(136\) 16.4497 7.84967i 1.41055 0.673103i
\(137\) 9.30582i 0.795050i −0.917591 0.397525i \(-0.869869\pi\)
0.917591 0.397525i \(-0.130131\pi\)
\(138\) 0 0
\(139\) 9.16328 + 9.16328i 0.777219 + 0.777219i 0.979357 0.202138i \(-0.0647889\pi\)
−0.202138 + 0.979357i \(0.564789\pi\)
\(140\) −15.7512 6.44656i −1.33122 0.544834i
\(141\) 0 0
\(142\) 1.83968 + 12.3047i 0.154383 + 1.03258i
\(143\) 6.59601i 0.551586i
\(144\) 0 0
\(145\) 0.0914866 + 0.910898i 0.00759755 + 0.0756460i
\(146\) −16.9687 + 2.53702i −1.40434 + 0.209965i
\(147\) 0 0
\(148\) 4.10703 + 2.18313i 0.337596 + 0.179452i
\(149\) −0.389077 0.389077i −0.0318744 0.0318744i 0.690990 0.722864i \(-0.257175\pi\)
−0.722864 + 0.690990i \(0.757175\pi\)
\(150\) 0 0
\(151\) 12.5843 1.02409 0.512047 0.858958i \(-0.328887\pi\)
0.512047 + 0.858958i \(0.328887\pi\)
\(152\) 3.97709 11.2372i 0.322584 0.911461i
\(153\) 0 0
\(154\) 4.65860 + 3.44676i 0.375401 + 0.277748i
\(155\) 6.74873 + 5.51683i 0.542071 + 0.443123i
\(156\) 0 0
\(157\) 0.397418 0.397418i 0.0317174 0.0317174i −0.691070 0.722788i \(-0.742860\pi\)
0.722788 + 0.691070i \(0.242860\pi\)
\(158\) 2.52836 + 16.9109i 0.201146 + 1.34536i
\(159\) 0 0
\(160\) 0.717588 + 12.6287i 0.0567303 + 0.998390i
\(161\) 6.58835i 0.519235i
\(162\) 0 0
\(163\) 7.61573 + 7.61573i 0.596510 + 0.596510i 0.939382 0.342872i \(-0.111400\pi\)
−0.342872 + 0.939382i \(0.611400\pi\)
\(164\) 4.96754 1.51937i 0.387899 0.118643i
\(165\) 0 0
\(166\) −1.10052 + 1.48745i −0.0854169 + 0.115449i
\(167\) −2.33425 −0.180629 −0.0903147 0.995913i \(-0.528787\pi\)
−0.0903147 + 0.995913i \(0.528787\pi\)
\(168\) 0 0
\(169\) 24.5262i 1.88663i
\(170\) 10.4226 17.5109i 0.799376 1.34303i
\(171\) 0 0
\(172\) −10.1125 + 19.0243i −0.771072 + 1.45059i
\(173\) −0.625160 0.625160i −0.0475300 0.0475300i 0.682942 0.730472i \(-0.260700\pi\)
−0.730472 + 0.682942i \(0.760700\pi\)
\(174\) 0 0
\(175\) −18.6482 + 3.78406i −1.40967 + 0.286048i
\(176\) 0.820818 4.22805i 0.0618715 0.318701i
\(177\) 0 0
\(178\) −18.5878 + 2.77908i −1.39321 + 0.208301i
\(179\) −4.33232 4.33232i −0.323813 0.323813i 0.526415 0.850228i \(-0.323536\pi\)
−0.850228 + 0.526415i \(0.823536\pi\)
\(180\) 0 0
\(181\) 0.834317 0.834317i 0.0620143 0.0620143i −0.675419 0.737434i \(-0.736037\pi\)
0.737434 + 0.675419i \(0.236037\pi\)
\(182\) 26.5039 + 19.6094i 1.96460 + 1.45355i
\(183\) 0 0
\(184\) 4.41920 2.10881i 0.325788 0.155464i
\(185\) 5.17418 0.519672i 0.380413 0.0382071i
\(186\) 0 0
\(187\) −4.90637 + 4.90637i −0.358789 + 0.358789i
\(188\) 3.00732 + 9.83238i 0.219332 + 0.717100i
\(189\) 0 0
\(190\) −3.27800 12.9178i −0.237811 0.937159i
\(191\) 18.1527 1.31349 0.656743 0.754114i \(-0.271934\pi\)
0.656743 + 0.754114i \(0.271934\pi\)
\(192\) 0 0
\(193\) 15.2659i 1.09886i 0.835538 + 0.549432i \(0.185156\pi\)
−0.835538 + 0.549432i \(0.814844\pi\)
\(194\) 1.99947 + 13.3734i 0.143553 + 0.960151i
\(195\) 0 0
\(196\) −14.3115 + 4.37732i −1.02225 + 0.312665i
\(197\) −0.287217 + 0.287217i −0.0204633 + 0.0204633i −0.717264 0.696801i \(-0.754606\pi\)
0.696801 + 0.717264i \(0.254606\pi\)
\(198\) 0 0
\(199\) 15.9569 1.13115 0.565576 0.824696i \(-0.308654\pi\)
0.565576 + 0.824696i \(0.308654\pi\)
\(200\) 8.50715 + 11.2973i 0.601546 + 0.798838i
\(201\) 0 0
\(202\) 18.8679 + 13.9598i 1.32754 + 0.982210i
\(203\) 1.10174 + 1.10174i 0.0773269 + 0.0773269i
\(204\) 0 0
\(205\) 3.67581 4.49661i 0.256730 0.314057i
\(206\) −2.03361 13.6018i −0.141689 0.947680i
\(207\) 0 0
\(208\) 4.66982 24.0544i 0.323794 1.66787i
\(209\) 4.53790i 0.313893i
\(210\) 0 0
\(211\) −15.7303 + 15.7303i −1.08292 + 1.08292i −0.0866837 + 0.996236i \(0.527627\pi\)
−0.996236 + 0.0866837i \(0.972373\pi\)
\(212\) 6.77528 12.7461i 0.465328 0.875403i
\(213\) 0 0
\(214\) −13.1153 9.70358i −0.896540 0.663323i
\(215\) 2.40718 + 23.9674i 0.164169 + 1.63457i
\(216\) 0 0
\(217\) 14.8353 1.00709
\(218\) −14.0300 10.3804i −0.950235 0.703050i
\(219\) 0 0
\(220\) −1.86154 4.44099i −0.125505 0.299411i
\(221\) −27.9135 + 27.9135i −1.87766 + 1.87766i
\(222\) 0 0
\(223\) −12.4886 −0.836301 −0.418150 0.908378i \(-0.637322\pi\)
−0.418150 + 0.908378i \(0.637322\pi\)
\(224\) 14.5488 + 15.8678i 0.972082 + 1.06022i
\(225\) 0 0
\(226\) −22.7665 + 3.40384i −1.51440 + 0.226420i
\(227\) −20.1265 + 20.1265i −1.33584 + 1.33584i −0.435800 + 0.900043i \(0.643535\pi\)
−0.900043 + 0.435800i \(0.856465\pi\)
\(228\) 0 0
\(229\) 5.05312 5.05312i 0.333920 0.333920i −0.520153 0.854073i \(-0.674125\pi\)
0.854073 + 0.520153i \(0.174125\pi\)
\(230\) 2.80002 4.70430i 0.184628 0.310192i
\(231\) 0 0
\(232\) 0.386356 1.09165i 0.0253655 0.0716702i
\(233\) 12.6841i 0.830960i −0.909602 0.415480i \(-0.863614\pi\)
0.909602 0.415480i \(-0.136386\pi\)
\(234\) 0 0
\(235\) 8.90027 + 7.27563i 0.580589 + 0.474610i
\(236\) 7.54569 14.1954i 0.491182 0.924042i
\(237\) 0 0
\(238\) −5.12836 34.3009i −0.332422 2.22339i
\(239\) −5.00305 −0.323621 −0.161810 0.986822i \(-0.551733\pi\)
−0.161810 + 0.986822i \(0.551733\pi\)
\(240\) 0 0
\(241\) −9.34398 −0.601898 −0.300949 0.953640i \(-0.597303\pi\)
−0.300949 + 0.953640i \(0.597303\pi\)
\(242\) −2.05783 13.7637i −0.132283 0.884767i
\(243\) 0 0
\(244\) −1.61663 0.859333i −0.103494 0.0550132i
\(245\) −10.5901 + 12.9548i −0.676574 + 0.827652i
\(246\) 0 0
\(247\) 25.8172i 1.64271i
\(248\) −4.74851 9.95093i −0.301531 0.631885i
\(249\) 0 0
\(250\) 14.9237 + 5.22347i 0.943855 + 0.330361i
\(251\) 11.8770 11.8770i 0.749672 0.749672i −0.224745 0.974418i \(-0.572155\pi\)
0.974418 + 0.224745i \(0.0721550\pi\)
\(252\) 0 0
\(253\) −1.31809 + 1.31809i −0.0828678 + 0.0828678i
\(254\) 12.0464 1.80107i 0.755859 0.113009i
\(255\) 0 0
\(256\) 5.98673 14.8378i 0.374170 0.927360i
\(257\) 4.63622 0.289199 0.144600 0.989490i \(-0.453811\pi\)
0.144600 + 0.989490i \(0.453811\pi\)
\(258\) 0 0
\(259\) 6.25821 6.25821i 0.388866 0.388866i
\(260\) −10.5907 25.2658i −0.656808 1.56692i
\(261\) 0 0
\(262\) 11.4104 + 8.44219i 0.704935 + 0.521560i
\(263\) 11.6055 0.715624 0.357812 0.933794i \(-0.383523\pi\)
0.357812 + 0.933794i \(0.383523\pi\)
\(264\) 0 0
\(265\) −1.61279 16.0579i −0.0990728 0.986430i
\(266\) −18.2340 13.4908i −1.11800 0.827175i
\(267\) 0 0
\(268\) −22.7104 12.0719i −1.38726 0.737410i
\(269\) −9.90154 + 9.90154i −0.603708 + 0.603708i −0.941294 0.337587i \(-0.890389\pi\)
0.337587 + 0.941294i \(0.390389\pi\)
\(270\) 0 0
\(271\) 3.50755i 0.213068i −0.994309 0.106534i \(-0.966025\pi\)
0.994309 0.106534i \(-0.0339753\pi\)
\(272\) −21.3662 + 14.4190i −1.29551 + 0.874279i
\(273\) 0 0
\(274\) 1.94600 + 13.0158i 0.117562 + 0.786310i
\(275\) −4.48790 2.97379i −0.270630 0.179326i
\(276\) 0 0
\(277\) −5.62344 5.62344i −0.337880 0.337880i 0.517689 0.855569i \(-0.326792\pi\)
−0.855569 + 0.517689i \(0.826792\pi\)
\(278\) −14.7326 10.9002i −0.883601 0.653750i
\(279\) 0 0
\(280\) 23.3788 + 5.72275i 1.39715 + 0.342000i
\(281\) 24.9686 1.48950 0.744752 0.667341i \(-0.232568\pi\)
0.744752 + 0.667341i \(0.232568\pi\)
\(282\) 0 0
\(283\) 18.5071 18.5071i 1.10014 1.10014i 0.105742 0.994394i \(-0.466278\pi\)
0.994394 0.105742i \(-0.0337217\pi\)
\(284\) −5.14621 16.8254i −0.305371 0.998405i
\(285\) 0 0
\(286\) 1.37933 + 9.22562i 0.0815617 + 0.545523i
\(287\) 9.88461i 0.583470i
\(288\) 0 0
\(289\) 24.5262 1.44272
\(290\) −0.318443 1.25491i −0.0186996 0.0736910i
\(291\) 0 0
\(292\) 23.2031 7.09688i 1.35786 0.415314i
\(293\) 3.44258 3.44258i 0.201118 0.201118i −0.599361 0.800479i \(-0.704579\pi\)
0.800479 + 0.599361i \(0.204579\pi\)
\(294\) 0 0
\(295\) −1.79618 17.8839i −0.104577 1.04124i
\(296\) −6.20090 2.19462i −0.360420 0.127560i
\(297\) 0 0
\(298\) 0.625552 + 0.462827i 0.0362372 + 0.0268108i
\(299\) −7.49894 + 7.49894i −0.433675 + 0.433675i
\(300\) 0 0
\(301\) 28.9888 + 28.9888i 1.67089 + 1.67089i
\(302\) −17.6012 + 2.63158i −1.01284 + 0.151430i
\(303\) 0 0
\(304\) −3.21273 + 16.5488i −0.184263 + 0.949141i
\(305\) −2.03668 + 0.204556i −0.116620 + 0.0117128i
\(306\) 0 0
\(307\) −13.4561 13.4561i −0.767977 0.767977i 0.209773 0.977750i \(-0.432728\pi\)
−0.977750 + 0.209773i \(0.932728\pi\)
\(308\) −7.23661 3.84668i −0.412344 0.219185i
\(309\) 0 0
\(310\) −10.5929 6.30495i −0.601636 0.358097i
\(311\) 10.6693i 0.604999i 0.953150 + 0.302500i \(0.0978211\pi\)
−0.953150 + 0.302500i \(0.902179\pi\)
\(312\) 0 0
\(313\) 10.3187 0.583250 0.291625 0.956533i \(-0.405804\pi\)
0.291625 + 0.956533i \(0.405804\pi\)
\(314\) −0.472749 + 0.638963i −0.0266788 + 0.0360587i
\(315\) 0 0
\(316\) −7.07268 23.1240i −0.397869 1.30082i
\(317\) 15.8698 + 15.8698i 0.891336 + 0.891336i 0.994649 0.103313i \(-0.0329444\pi\)
−0.103313 + 0.994649i \(0.532944\pi\)
\(318\) 0 0
\(319\) 0.440837i 0.0246821i
\(320\) −3.64454 17.5133i −0.203736 0.979026i
\(321\) 0 0
\(322\) −1.37773 9.21491i −0.0767780 0.513527i
\(323\) 19.2038 19.2038i 1.06853 1.06853i
\(324\) 0 0
\(325\) −25.5327 16.9186i −1.41630 0.938473i
\(326\) −12.2444 9.05929i −0.678157 0.501748i
\(327\) 0 0
\(328\) −6.63021 + 3.16388i −0.366092 + 0.174696i
\(329\) 19.5649 1.07865
\(330\) 0 0
\(331\) −9.80202 9.80202i −0.538768 0.538768i 0.384399 0.923167i \(-0.374409\pi\)
−0.923167 + 0.384399i \(0.874409\pi\)
\(332\) 1.22821 2.31058i 0.0674068 0.126810i
\(333\) 0 0
\(334\) 3.26484 0.488129i 0.178644 0.0267092i
\(335\) −28.6114 + 2.87360i −1.56321 + 0.157002i
\(336\) 0 0
\(337\) 13.6823i 0.745323i −0.927967 0.372662i \(-0.878445\pi\)
0.927967 0.372662i \(-0.121555\pi\)
\(338\) 5.12884 + 34.3040i 0.278972 + 1.86589i
\(339\) 0 0
\(340\) −10.9159 + 26.6715i −0.591998 + 1.44646i
\(341\) 2.96801 + 2.96801i 0.160727 + 0.160727i
\(342\) 0 0
\(343\) 1.83811i 0.0992487i
\(344\) 10.1658 28.7233i 0.548101 1.54866i
\(345\) 0 0
\(346\) 1.00512 + 0.743660i 0.0540357 + 0.0399794i
\(347\) −15.5812 15.5812i −0.836445 0.836445i 0.151944 0.988389i \(-0.451447\pi\)
−0.988389 + 0.151944i \(0.951447\pi\)
\(348\) 0 0
\(349\) −4.64370 4.64370i −0.248572 0.248572i 0.571813 0.820384i \(-0.306240\pi\)
−0.820384 + 0.571813i \(0.806240\pi\)
\(350\) 25.2913 9.19229i 1.35188 0.491349i
\(351\) 0 0
\(352\) −0.263896 + 6.08528i −0.0140657 + 0.324347i
\(353\) −19.8254 −1.05520 −0.527601 0.849492i \(-0.676908\pi\)
−0.527601 + 0.849492i \(0.676908\pi\)
\(354\) 0 0
\(355\) −15.2304 12.4502i −0.808344 0.660790i
\(356\) 25.4169 7.77401i 1.34710 0.412022i
\(357\) 0 0
\(358\) 6.96543 + 5.15352i 0.368135 + 0.272372i
\(359\) 20.1443i 1.06318i 0.847003 + 0.531589i \(0.178405\pi\)
−0.847003 + 0.531589i \(0.821595\pi\)
\(360\) 0 0
\(361\) 1.23840i 0.0651788i
\(362\) −0.992463 + 1.34140i −0.0521627 + 0.0705025i
\(363\) 0 0
\(364\) −41.1707 21.8847i −2.15793 1.14707i
\(365\) 17.1695 21.0034i 0.898694 1.09937i
\(366\) 0 0
\(367\) 36.1117 1.88502 0.942508 0.334183i \(-0.108460\pi\)
0.942508 + 0.334183i \(0.108460\pi\)
\(368\) −5.74001 + 3.87365i −0.299219 + 0.201928i
\(369\) 0 0
\(370\) −7.12828 + 1.80885i −0.370582 + 0.0940378i
\(371\) −19.4222 19.4222i −1.00835 1.00835i
\(372\) 0 0
\(373\) 1.62188 + 1.62188i 0.0839777 + 0.0839777i 0.747848 0.663870i \(-0.231087\pi\)
−0.663870 + 0.747848i \(0.731087\pi\)
\(374\) 5.83637 7.88838i 0.301792 0.407898i
\(375\) 0 0
\(376\) −6.26236 13.1233i −0.322956 0.676785i
\(377\) 2.50802i 0.129170i
\(378\) 0 0
\(379\) −10.9432 10.9432i −0.562115 0.562115i 0.367793 0.929908i \(-0.380114\pi\)
−0.929908 + 0.367793i \(0.880114\pi\)
\(380\) 7.28616 + 17.3823i 0.373772 + 0.891693i
\(381\) 0 0
\(382\) −25.3896 + 3.79603i −1.29905 + 0.194222i
\(383\) 31.2822i 1.59845i 0.601035 + 0.799223i \(0.294755\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(384\) 0 0
\(385\) −9.11693 + 0.915665i −0.464642 + 0.0466666i
\(386\) −3.19235 21.3519i −0.162486 1.08678i
\(387\) 0 0
\(388\) −5.59317 18.2868i −0.283950 0.928369i
\(389\) 4.10132 + 4.10132i 0.207945 + 0.207945i 0.803394 0.595448i \(-0.203026\pi\)
−0.595448 + 0.803394i \(0.703026\pi\)
\(390\) 0 0
\(391\) 11.1560 0.564183
\(392\) 19.1017 9.11518i 0.964782 0.460386i
\(393\) 0 0
\(394\) 0.341659 0.461782i 0.0172125 0.0232643i
\(395\) −20.9318 17.1110i −1.05319 0.860946i
\(396\) 0 0
\(397\) −22.7531 + 22.7531i −1.14194 + 1.14194i −0.153849 + 0.988094i \(0.549167\pi\)
−0.988094 + 0.153849i \(0.950833\pi\)
\(398\) −22.3183 + 3.33684i −1.11872 + 0.167261i
\(399\) 0 0
\(400\) −14.2611 14.0221i −0.713056 0.701107i
\(401\) 21.2428i 1.06082i 0.847743 + 0.530408i \(0.177961\pi\)
−0.847743 + 0.530408i \(0.822039\pi\)
\(402\) 0 0
\(403\) 16.8857 + 16.8857i 0.841138 + 0.841138i
\(404\) −29.3092 15.5796i −1.45819 0.775112i
\(405\) 0 0
\(406\) −1.77136 1.31057i −0.0879110 0.0650427i
\(407\) 2.50409 0.124123
\(408\) 0 0
\(409\) 3.41459i 0.168841i 0.996430 + 0.0844204i \(0.0269039\pi\)
−0.996430 + 0.0844204i \(0.973096\pi\)
\(410\) −4.20092 + 7.05794i −0.207469 + 0.348567i
\(411\) 0 0
\(412\) 5.68870 + 18.5991i 0.280262 + 0.916311i
\(413\) −21.6307 21.6307i −1.06438 1.06438i
\(414\) 0 0
\(415\) −0.292364 2.91095i −0.0143516 0.142893i
\(416\) −1.50137 + 34.6206i −0.0736106 + 1.69741i
\(417\) 0 0
\(418\) −0.948949 6.34701i −0.0464146 0.310443i
\(419\) 2.45392 + 2.45392i 0.119882 + 0.119882i 0.764503 0.644621i \(-0.222985\pi\)
−0.644621 + 0.764503i \(0.722985\pi\)
\(420\) 0 0
\(421\) 16.7130 16.7130i 0.814540 0.814540i −0.170770 0.985311i \(-0.554626\pi\)
0.985311 + 0.170770i \(0.0546257\pi\)
\(422\) 18.7120 25.2909i 0.910887 1.23114i
\(423\) 0 0
\(424\) −6.81095 + 19.2443i −0.330769 + 0.934587i
\(425\) 6.40752 + 31.5769i 0.310811 + 1.53170i
\(426\) 0 0
\(427\) −2.46339 + 2.46339i −0.119212 + 0.119212i
\(428\) 20.3731 + 10.8295i 0.984769 + 0.523462i
\(429\) 0 0
\(430\) −8.37883 33.0191i −0.404063 1.59232i
\(431\) 20.7930 1.00156 0.500782 0.865573i \(-0.333046\pi\)
0.500782 + 0.865573i \(0.333046\pi\)
\(432\) 0 0
\(433\) 8.98760i 0.431916i 0.976403 + 0.215958i \(0.0692875\pi\)
−0.976403 + 0.215958i \(0.930712\pi\)
\(434\) −20.7497 + 3.10230i −0.996015 + 0.148915i
\(435\) 0 0
\(436\) 21.7941 + 11.5848i 1.04375 + 0.554813i
\(437\) 5.15910 5.15910i 0.246793 0.246793i
\(438\) 0 0
\(439\) 18.6849 0.891780 0.445890 0.895088i \(-0.352887\pi\)
0.445890 + 0.895088i \(0.352887\pi\)
\(440\) 3.53235 + 5.82219i 0.168398 + 0.277562i
\(441\) 0 0
\(442\) 33.2045 44.8788i 1.57938 2.13467i
\(443\) −1.69635 1.69635i −0.0805958 0.0805958i 0.665660 0.746255i \(-0.268150\pi\)
−0.746255 + 0.665660i \(0.768150\pi\)
\(444\) 0 0
\(445\) 18.8077 23.0074i 0.891570 1.09066i
\(446\) 17.4674 2.61158i 0.827108 0.123662i
\(447\) 0 0
\(448\) −23.6671 19.1515i −1.11817 0.904821i
\(449\) 20.9833i 0.990264i −0.868818 0.495132i \(-0.835120\pi\)
0.868818 0.495132i \(-0.164880\pi\)
\(450\) 0 0
\(451\) 1.97756 1.97756i 0.0931196 0.0931196i
\(452\) 31.1309 9.52169i 1.46428 0.447863i
\(453\) 0 0
\(454\) 23.9415 32.3591i 1.12363 1.51869i
\(455\) −51.8683 + 5.20943i −2.43162 + 0.244222i
\(456\) 0 0
\(457\) 0.679238 0.0317734 0.0158867 0.999874i \(-0.494943\pi\)
0.0158867 + 0.999874i \(0.494943\pi\)
\(458\) −6.01094 + 8.12432i −0.280873 + 0.379625i
\(459\) 0 0
\(460\) −2.93256 + 7.16528i −0.136731 + 0.334083i
\(461\) −30.3013 + 30.3013i −1.41127 + 1.41127i −0.660048 + 0.751223i \(0.729464\pi\)
−0.751223 + 0.660048i \(0.770536\pi\)
\(462\) 0 0
\(463\) 40.6442 1.88889 0.944447 0.328664i \(-0.106598\pi\)
0.944447 + 0.328664i \(0.106598\pi\)
\(464\) −0.312102 + 1.60765i −0.0144890 + 0.0746331i
\(465\) 0 0
\(466\) 2.65244 + 17.7408i 0.122872 + 0.821825i
\(467\) 20.4572 20.4572i 0.946646 0.946646i −0.0520011 0.998647i \(-0.516560\pi\)
0.998647 + 0.0520011i \(0.0165599\pi\)
\(468\) 0 0
\(469\) −34.6057 + 34.6057i −1.59794 + 1.59794i
\(470\) −13.9700 8.31500i −0.644387 0.383542i
\(471\) 0 0
\(472\) −7.58542 + 21.4326i −0.349147 + 0.986514i
\(473\) 11.5992i 0.533334i
\(474\) 0 0
\(475\) 17.5659 + 11.6396i 0.805978 + 0.534060i
\(476\) 14.3457 + 46.9031i 0.657536 + 2.14980i
\(477\) 0 0
\(478\) 6.99760 1.04622i 0.320063 0.0478530i
\(479\) 20.9399 0.956768 0.478384 0.878151i \(-0.341223\pi\)
0.478384 + 0.878151i \(0.341223\pi\)
\(480\) 0 0
\(481\) 14.2463 0.649577
\(482\) 13.0691 1.95398i 0.595282 0.0890013i
\(483\) 0 0
\(484\) 5.75645 + 18.8206i 0.261657 + 0.855481i
\(485\) −16.5532 13.5316i −0.751641 0.614438i
\(486\) 0 0
\(487\) 27.6996i 1.25519i −0.778540 0.627595i \(-0.784039\pi\)
0.778540 0.627595i \(-0.215961\pi\)
\(488\) 2.44083 + 0.863857i 0.110491 + 0.0391050i
\(489\) 0 0
\(490\) 12.1029 20.3340i 0.546754 0.918597i
\(491\) 12.9711 12.9711i 0.585377 0.585377i −0.350999 0.936376i \(-0.614158\pi\)
0.936376 + 0.350999i \(0.114158\pi\)
\(492\) 0 0
\(493\) 1.86557 1.86557i 0.0840208 0.0840208i
\(494\) −5.39879 36.1096i −0.242903 1.62465i
\(495\) 0 0
\(496\) 8.72248 + 12.9251i 0.391651 + 0.580352i
\(497\) −33.4799 −1.50178
\(498\) 0 0
\(499\) −8.96696 + 8.96696i −0.401416 + 0.401416i −0.878732 0.477316i \(-0.841610\pi\)
0.477316 + 0.878732i \(0.341610\pi\)
\(500\) −21.9655 4.18512i −0.982329 0.187164i
\(501\) 0 0
\(502\) −14.1283 + 19.0957i −0.630579 + 0.852283i
\(503\) 9.23509 0.411772 0.205886 0.978576i \(-0.433992\pi\)
0.205886 + 0.978576i \(0.433992\pi\)
\(504\) 0 0
\(505\) −36.9247 + 3.70856i −1.64313 + 0.165029i
\(506\) 1.56794 2.11921i 0.0697034 0.0942104i
\(507\) 0 0
\(508\) −16.4723 + 5.03820i −0.730839 + 0.223534i
\(509\) 0.418802 0.418802i 0.0185631 0.0185631i −0.697764 0.716327i \(-0.745822\pi\)
0.716327 + 0.697764i \(0.245822\pi\)
\(510\) 0 0
\(511\) 46.1705i 2.04246i
\(512\) −5.27062 + 22.0050i −0.232931 + 0.972493i
\(513\) 0 0
\(514\) −6.48452 + 0.969508i −0.286020 + 0.0427632i
\(515\) 16.8359 + 13.7627i 0.741878 + 0.606457i
\(516\) 0 0
\(517\) 3.91423 + 3.91423i 0.172148 + 0.172148i
\(518\) −7.44446 + 10.0618i −0.327091 + 0.442092i
\(519\) 0 0
\(520\) 20.0964 + 33.1238i 0.881284 + 1.45257i
\(521\) −31.0344 −1.35964 −0.679821 0.733378i \(-0.737943\pi\)
−0.679821 + 0.733378i \(0.737943\pi\)
\(522\) 0 0
\(523\) −12.5701 + 12.5701i −0.549653 + 0.549653i −0.926340 0.376687i \(-0.877063\pi\)
0.376687 + 0.926340i \(0.377063\pi\)
\(524\) −17.7247 9.42172i −0.774307 0.411590i
\(525\) 0 0
\(526\) −16.2322 + 2.42689i −0.707757 + 0.105818i
\(527\) 25.1205i 1.09427i
\(528\) 0 0
\(529\) −20.0029 −0.869693
\(530\) 5.61373 + 22.1224i 0.243845 + 0.960937i
\(531\) 0 0
\(532\) 28.3245 + 15.0561i 1.22802 + 0.652766i
\(533\) 11.2508 11.2508i 0.487326 0.487326i
\(534\) 0 0
\(535\) 25.6667 2.57785i 1.10967 0.111450i
\(536\) 34.2887 + 12.1355i 1.48105 + 0.524173i
\(537\) 0 0
\(538\) 11.7784 15.9195i 0.507802 0.686340i
\(539\) −5.69737 + 5.69737i −0.245403 + 0.245403i
\(540\) 0 0
\(541\) 7.64792 + 7.64792i 0.328810 + 0.328810i 0.852134 0.523324i \(-0.175308\pi\)
−0.523324 + 0.852134i \(0.675308\pi\)
\(542\) 0.733485 + 4.90589i 0.0315059 + 0.210726i
\(543\) 0 0
\(544\) 26.8689 24.6354i 1.15200 1.05623i
\(545\) 27.4569 2.75766i 1.17613 0.118125i
\(546\) 0 0
\(547\) −5.50694 5.50694i −0.235460 0.235460i 0.579507 0.814967i \(-0.303245\pi\)
−0.814967 + 0.579507i \(0.803245\pi\)
\(548\) −5.44361 17.7978i −0.232540 0.760283i
\(549\) 0 0
\(550\) 6.89894 + 3.22084i 0.294172 + 0.137337i
\(551\) 1.72546i 0.0735071i
\(552\) 0 0
\(553\) −46.0130 −1.95667
\(554\) 9.04128 + 6.68937i 0.384127 + 0.284204i
\(555\) 0 0
\(556\) 22.8854 + 12.1649i 0.970556 + 0.515907i
\(557\) 13.9022 + 13.9022i 0.589056 + 0.589056i 0.937376 0.348320i \(-0.113248\pi\)
−0.348320 + 0.937376i \(0.613248\pi\)
\(558\) 0 0
\(559\) 65.9908i 2.79111i
\(560\) −33.8959 3.11532i −1.43236 0.131646i
\(561\) 0 0
\(562\) −34.9228 + 5.22135i −1.47313 + 0.220249i
\(563\) 4.81937 4.81937i 0.203112 0.203112i −0.598220 0.801332i \(-0.704125\pi\)
0.801332 + 0.598220i \(0.204125\pi\)
\(564\) 0 0
\(565\) 23.0359 28.1797i 0.969126 1.18553i
\(566\) −22.0152 + 29.7555i −0.925367 + 1.25072i
\(567\) 0 0
\(568\) 10.7163 + 22.4570i 0.449646 + 0.942275i
\(569\) −17.9682 −0.753268 −0.376634 0.926362i \(-0.622919\pi\)
−0.376634 + 0.926362i \(0.622919\pi\)
\(570\) 0 0
\(571\) 3.94277 + 3.94277i 0.165000 + 0.165000i 0.784777 0.619778i \(-0.212777\pi\)
−0.619778 + 0.784777i \(0.712777\pi\)
\(572\) −3.85846 12.6151i −0.161330 0.527465i
\(573\) 0 0
\(574\) 2.06703 + 13.8253i 0.0862763 + 0.577056i
\(575\) 1.72138 + 8.48312i 0.0717865 + 0.353770i
\(576\) 0 0
\(577\) 16.1502i 0.672343i −0.941801 0.336172i \(-0.890868\pi\)
0.941801 0.336172i \(-0.109132\pi\)
\(578\) −34.3040 + 5.12884i −1.42686 + 0.213331i
\(579\) 0 0
\(580\) 0.707818 + 1.68861i 0.0293906 + 0.0701158i
\(581\) −3.52082 3.52082i −0.146068 0.146068i
\(582\) 0 0
\(583\) 7.77137i 0.321857i
\(584\) −30.9693 + 14.7783i −1.28152 + 0.611532i
\(585\) 0 0
\(586\) −4.09512 + 5.53492i −0.169168 + 0.228645i
\(587\) 17.3882 + 17.3882i 0.717687 + 0.717687i 0.968131 0.250444i \(-0.0805767\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(588\) 0 0
\(589\) −11.6170 11.6170i −0.478669 0.478669i
\(590\) 6.25206 + 24.6380i 0.257393 + 1.01433i
\(591\) 0 0
\(592\) 9.13193 + 1.77284i 0.375320 + 0.0728632i
\(593\) 18.7727 0.770904 0.385452 0.922728i \(-0.374045\pi\)
0.385452 + 0.922728i \(0.374045\pi\)
\(594\) 0 0
\(595\) 42.4566 + 34.7067i 1.74055 + 1.42284i
\(596\) −0.971723 0.516528i −0.0398033 0.0211578i
\(597\) 0 0
\(598\) 8.92037 12.0567i 0.364781 0.493034i
\(599\) 15.7898i 0.645154i −0.946543 0.322577i \(-0.895451\pi\)
0.946543 0.322577i \(-0.104549\pi\)
\(600\) 0 0
\(601\) 19.1187i 0.779868i −0.920843 0.389934i \(-0.872498\pi\)
0.920843 0.389934i \(-0.127502\pi\)
\(602\) −46.6077 34.4836i −1.89959 1.40545i
\(603\) 0 0
\(604\) 24.0679 7.36140i 0.979310 0.299531i
\(605\) 17.0364 + 13.9266i 0.692628 + 0.566197i
\(606\) 0 0
\(607\) 20.4524 0.830139 0.415069 0.909790i \(-0.363757\pi\)
0.415069 + 0.909790i \(0.363757\pi\)
\(608\) 1.03291 23.8182i 0.0418899 0.965954i
\(609\) 0 0
\(610\) 2.80587 0.712009i 0.113606 0.0288284i
\(611\) 22.2690 + 22.2690i 0.900907 + 0.900907i
\(612\) 0 0
\(613\) 0.158629 + 0.158629i 0.00640697 + 0.00640697i 0.710303 0.703896i \(-0.248558\pi\)
−0.703896 + 0.710303i \(0.748558\pi\)
\(614\) 21.6344 + 16.0067i 0.873094 + 0.645976i
\(615\) 0 0
\(616\) 10.9260 + 3.86693i 0.440222 + 0.155803i
\(617\) 28.8981i 1.16340i 0.813405 + 0.581698i \(0.197611\pi\)
−0.813405 + 0.581698i \(0.802389\pi\)
\(618\) 0 0
\(619\) −13.3003 13.3003i −0.534582 0.534582i 0.387350 0.921933i \(-0.373390\pi\)
−0.921933 + 0.387350i \(0.873390\pi\)
\(620\) 16.1344 + 6.60337i 0.647973 + 0.265198i
\(621\) 0 0
\(622\) −2.23112 14.9228i −0.0894597 0.598348i
\(623\) 50.5757i 2.02627i
\(624\) 0 0
\(625\) −23.0226 + 9.74467i −0.920905 + 0.389787i
\(626\) −14.4325 + 2.15782i −0.576838 + 0.0862437i
\(627\) 0 0
\(628\) 0.527602 0.992556i 0.0210536 0.0396073i
\(629\) −10.5970 10.5970i −0.422529 0.422529i
\(630\) 0 0
\(631\) −40.6293 −1.61743 −0.808713 0.588203i \(-0.799836\pi\)
−0.808713 + 0.588203i \(0.799836\pi\)
\(632\) 14.7279 + 30.8637i 0.585845 + 1.22769i
\(633\) 0 0
\(634\) −25.5152 18.8779i −1.01334 0.749738i
\(635\) −12.1889 + 14.9107i −0.483703 + 0.591713i
\(636\) 0 0
\(637\) −32.4136 + 32.4136i −1.28428 + 1.28428i
\(638\) −0.0921862 0.616584i −0.00364969 0.0244108i
\(639\) 0 0
\(640\) 8.75983 + 23.7332i 0.346263 + 0.938138i
\(641\) 2.75673i 0.108884i 0.998517 + 0.0544422i \(0.0173380\pi\)
−0.998517 + 0.0544422i \(0.982662\pi\)
\(642\) 0 0
\(643\) 14.9757 + 14.9757i 0.590582 + 0.590582i 0.937789 0.347206i \(-0.112870\pi\)
−0.347206 + 0.937789i \(0.612870\pi\)
\(644\) 3.85398 + 12.6005i 0.151868 + 0.496529i
\(645\) 0 0
\(646\) −22.8439 + 30.8756i −0.898782 + 1.21478i
\(647\) 35.4556 1.39390 0.696952 0.717117i \(-0.254539\pi\)
0.696952 + 0.717117i \(0.254539\pi\)
\(648\) 0 0
\(649\) 8.65505i 0.339740i
\(650\) 39.2497 + 18.3241i 1.53950 + 0.718732i
\(651\) 0 0
\(652\) 19.0203 + 10.1104i 0.744894 + 0.395955i
\(653\) 24.6436 + 24.6436i 0.964380 + 0.964380i 0.999387 0.0350074i \(-0.0111455\pi\)
−0.0350074 + 0.999387i \(0.511145\pi\)
\(654\) 0 0
\(655\) −22.3302 + 2.24275i −0.872513 + 0.0876314i
\(656\) 8.61184 5.81170i 0.336236 0.226909i
\(657\) 0 0
\(658\) −27.3648 + 4.09133i −1.06679 + 0.159497i
\(659\) −27.1141 27.1141i −1.05621 1.05621i −0.998323 0.0578905i \(-0.981563\pi\)
−0.0578905 0.998323i \(-0.518437\pi\)
\(660\) 0 0
\(661\) −20.5120 + 20.5120i −0.797822 + 0.797822i −0.982752 0.184929i \(-0.940794\pi\)
0.184929 + 0.982752i \(0.440794\pi\)
\(662\) 15.7595 + 11.6600i 0.612512 + 0.453179i
\(663\) 0 0
\(664\) −1.23468 + 3.48858i −0.0479148 + 0.135383i
\(665\) 35.6842 3.58396i 1.38377 0.138980i
\(666\) 0 0
\(667\) 0.501183 0.501183i 0.0194059 0.0194059i
\(668\) −4.46434 + 1.36546i −0.172731 + 0.0528313i
\(669\) 0 0
\(670\) 39.4169 10.0023i 1.52281 0.386423i
\(671\) −0.985671 −0.0380514
\(672\) 0 0
\(673\) 27.8896i 1.07506i 0.843243 + 0.537532i \(0.180643\pi\)
−0.843243 + 0.537532i \(0.819357\pi\)
\(674\) 2.86120 + 19.1370i 0.110209 + 0.737130i
\(675\) 0 0
\(676\) −14.3471 46.9074i −0.551810 1.80413i
\(677\) −1.09939 + 1.09939i −0.0422530 + 0.0422530i −0.727918 0.685665i \(-0.759512\pi\)
0.685665 + 0.727918i \(0.259512\pi\)
\(678\) 0 0
\(679\) −36.3877 −1.39643
\(680\) 9.69029 39.5872i 0.371606 1.51810i
\(681\) 0 0
\(682\) −4.77193 3.53060i −0.182726 0.135194i
\(683\) 16.3630 + 16.3630i 0.626115 + 0.626115i 0.947088 0.320974i \(-0.104010\pi\)
−0.320974 + 0.947088i \(0.604010\pi\)
\(684\) 0 0
\(685\) −16.1105 13.1698i −0.615552 0.503190i
\(686\) −0.384379 2.57091i −0.0146757 0.0981577i
\(687\) 0 0
\(688\) −8.21200 + 42.3002i −0.313079 + 1.61268i
\(689\) 44.2131i 1.68439i
\(690\) 0 0
\(691\) −1.38110 + 1.38110i −0.0525396 + 0.0525396i −0.732888 0.680349i \(-0.761828\pi\)
0.680349 + 0.732888i \(0.261828\pi\)
\(692\) −1.56134 0.829945i −0.0593534 0.0315498i
\(693\) 0 0
\(694\) 25.0513 + 18.5347i 0.950934 + 0.703567i
\(695\) 28.8318 2.89574i 1.09365 0.109842i
\(696\) 0 0
\(697\) −16.7375 −0.633980
\(698\) 7.46607 + 5.52392i 0.282595 + 0.209084i
\(699\) 0 0
\(700\) −33.4519 + 18.1458i −1.26436 + 0.685846i
\(701\) 21.1577 21.1577i 0.799115 0.799115i −0.183841 0.982956i \(-0.558853\pi\)
0.982956 + 0.183841i \(0.0588531\pi\)
\(702\) 0 0
\(703\) −9.80115 −0.369657
\(704\) −0.903429 8.56647i −0.0340493 0.322861i
\(705\) 0 0
\(706\) 27.7292 4.14582i 1.04360 0.156030i
\(707\) −44.6608 + 44.6608i −1.67964 + 1.67964i
\(708\) 0 0
\(709\) 3.59943 3.59943i 0.135180 0.135180i −0.636279 0.771459i \(-0.719527\pi\)
0.771459 + 0.636279i \(0.219527\pi\)
\(710\) 23.9058 + 14.2288i 0.897167 + 0.533999i
\(711\) 0 0
\(712\) −33.9242 + 16.1884i −1.27136 + 0.606684i
\(713\) 6.74861i 0.252738i
\(714\) 0 0
\(715\) −11.4192 9.33478i −0.427055 0.349101i
\(716\) −10.8200 5.75147i −0.404363 0.214942i
\(717\) 0 0
\(718\) −4.21251 28.1752i −0.157209 1.05149i
\(719\) −24.6502 −0.919298 −0.459649 0.888101i \(-0.652025\pi\)
−0.459649 + 0.888101i \(0.652025\pi\)
\(720\) 0 0
\(721\) 37.0092 1.37830
\(722\) −0.258969 1.73211i −0.00963784 0.0644623i
\(723\) 0 0
\(724\) 1.10762 2.08371i 0.0411642 0.0774406i
\(725\) 1.70645 + 1.13073i 0.0633759 + 0.0419944i
\(726\) 0 0
\(727\) 47.1505i 1.74872i 0.485281 + 0.874358i \(0.338717\pi\)
−0.485281 + 0.874358i \(0.661283\pi\)
\(728\) 62.1606 + 21.9999i 2.30383 + 0.815370i
\(729\) 0 0
\(730\) −19.6223 + 32.9673i −0.726253 + 1.22017i
\(731\) 49.0865 49.0865i 1.81553 1.81553i
\(732\) 0 0
\(733\) −12.4236 + 12.4236i −0.458875 + 0.458875i −0.898286 0.439411i \(-0.855187\pi\)
0.439411 + 0.898286i \(0.355187\pi\)
\(734\) −50.5083 + 7.55155i −1.86429 + 0.278733i
\(735\) 0 0
\(736\) 7.21832 6.61828i 0.266071 0.243953i
\(737\) −13.8467 −0.510050
\(738\) 0 0
\(739\) −10.3865 + 10.3865i −0.382075 + 0.382075i −0.871849 0.489774i \(-0.837079\pi\)
0.489774 + 0.871849i \(0.337079\pi\)
\(740\) 9.59184 4.02063i 0.352603 0.147801i
\(741\) 0 0
\(742\) 31.2267 + 23.1037i 1.14637 + 0.848163i
\(743\) −34.4041 −1.26216 −0.631082 0.775716i \(-0.717389\pi\)
−0.631082 + 0.775716i \(0.717389\pi\)
\(744\) 0 0
\(745\) −1.22421 + 0.122954i −0.0448516 + 0.00450470i
\(746\) −2.60763 1.92931i −0.0954721 0.0706370i
\(747\) 0 0
\(748\) −6.51356 + 12.2537i −0.238159 + 0.448040i
\(749\) 31.0440 31.0440i 1.13432 1.13432i
\(750\) 0 0
\(751\) 6.29639i 0.229759i 0.993379 + 0.114879i \(0.0366481\pi\)
−0.993379 + 0.114879i \(0.963352\pi\)
\(752\) 11.5033 + 17.0456i 0.419481 + 0.621590i
\(753\) 0 0
\(754\) −0.524469 3.50789i −0.0191000 0.127750i
\(755\) 17.8095 21.7863i 0.648153 0.792884i
\(756\) 0 0
\(757\) 13.9886 + 13.9886i 0.508425 + 0.508425i 0.914043 0.405618i \(-0.132944\pi\)
−0.405618 + 0.914043i \(0.632944\pi\)
\(758\) 17.5943 + 13.0175i 0.639054 + 0.472817i
\(759\) 0 0
\(760\) −13.8258 22.7884i −0.501516 0.826622i
\(761\) −45.7177 −1.65726 −0.828632 0.559793i \(-0.810881\pi\)
−0.828632 + 0.559793i \(0.810881\pi\)
\(762\) 0 0
\(763\) 33.2094 33.2094i 1.20226 1.20226i
\(764\) 34.7179 10.6188i 1.25605 0.384174i
\(765\) 0 0
\(766\) −6.54162 43.7534i −0.236358 1.58087i
\(767\) 49.2406i 1.77797i
\(768\) 0 0
\(769\) −34.9628 −1.26079 −0.630395 0.776274i \(-0.717107\pi\)
−0.630395 + 0.776274i \(0.717107\pi\)
\(770\) 12.5601 3.18721i 0.452634 0.114859i
\(771\) 0 0
\(772\) 8.93007 + 29.1967i 0.321400 + 1.05081i
\(773\) −30.9289 + 30.9289i −1.11243 + 1.11243i −0.119614 + 0.992820i \(0.538166\pi\)
−0.992820 + 0.119614i \(0.961834\pi\)
\(774\) 0 0
\(775\) 19.1018 3.87611i 0.686158 0.139234i
\(776\) 11.6470 + 24.4075i 0.418105 + 0.876177i
\(777\) 0 0
\(778\) −6.59404 4.87873i −0.236408 0.174911i
\(779\) −7.74028 + 7.74028i −0.277324 + 0.277324i
\(780\) 0 0
\(781\) −6.69814 6.69814i −0.239678 0.239678i
\(782\) −15.6035 + 2.33290i −0.557981 + 0.0834244i
\(783\) 0 0
\(784\) −24.8108 + 16.7436i −0.886100 + 0.597985i
\(785\) −0.125590 1.25046i −0.00448251 0.0446307i
\(786\) 0 0
\(787\) −12.2948 12.2948i −0.438261 0.438261i 0.453165 0.891427i \(-0.350295\pi\)
−0.891427 + 0.453165i \(0.850295\pi\)
\(788\) −0.381301 + 0.717326i −0.0135833 + 0.0255537i
\(789\) 0 0
\(790\) 32.8548 + 19.5554i 1.16892 + 0.695748i
\(791\) 61.9457i 2.20253i