Properties

Label 105.3.o.b.44.13
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 44.13
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.897800 - 1.55504i) q^{2} +(-2.91099 + 0.725349i) q^{3} +(0.387909 + 0.671879i) q^{4} +(3.31295 + 3.74491i) q^{5} +(-1.48554 + 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} +8.57546 q^{8} +(7.94774 - 4.22297i) q^{9} +O(q^{10})\) \(q+(0.897800 - 1.55504i) q^{2} +(-2.91099 + 0.725349i) q^{3} +(0.387909 + 0.671879i) q^{4} +(3.31295 + 3.74491i) q^{5} +(-1.48554 + 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} +8.57546 q^{8} +(7.94774 - 4.22297i) q^{9} +(8.79784 - 1.78957i) q^{10} +(-1.00783 + 0.581870i) q^{11} +(-1.61655 - 1.67446i) q^{12} -12.4799i q^{13} +(9.41362 + 8.32879i) q^{14} +(-12.3603 - 8.49836i) q^{15} +(6.14742 - 10.6476i) q^{16} +(9.31485 + 16.1338i) q^{17} +(0.568609 - 16.1504i) q^{18} +(-15.2033 + 26.3329i) q^{19} +(-1.23100 + 3.67859i) q^{20} +(-0.912610 - 20.9802i) q^{21} +2.08961i q^{22} +(13.7201 - 23.7640i) q^{23} +(-24.9631 + 6.22021i) q^{24} +(-3.04875 + 24.8134i) q^{25} +(-19.4067 - 11.2045i) q^{26} +(-20.0727 + 18.0579i) q^{27} +(-5.15012 + 1.72310i) q^{28} -52.6691i q^{29} +(-24.3124 + 11.5909i) q^{30} +(-17.2838 - 29.9364i) q^{31} +(6.11262 + 10.5874i) q^{32} +(2.51172 - 2.42485i) q^{33} +33.4515 q^{34} +(-30.3119 + 17.4982i) q^{35} +(5.92032 + 3.70178i) q^{36} +(0.357210 + 0.206235i) q^{37} +(27.2991 + 47.2834i) q^{38} +(9.05229 + 36.3289i) q^{39} +(28.4101 + 32.1144i) q^{40} -17.2132i q^{41} +(-33.4442 - 17.4169i) q^{42} +7.86972i q^{43} +(-0.781892 - 0.451426i) q^{44} +(42.1451 + 15.7731i) q^{45} +(-24.6359 - 42.6706i) q^{46} +(17.4089 - 30.1530i) q^{47} +(-10.1718 + 35.4542i) q^{48} +(-45.1040 - 19.1475i) q^{49} +(35.8486 + 27.0184i) q^{50} +(-38.8181 - 40.2088i) q^{51} +(8.38498 - 4.84107i) q^{52} +(-17.8667 - 30.9460i) q^{53} +(10.0595 + 47.4261i) q^{54} +(-5.51794 - 1.84653i) q^{55} +(-11.9688 + 58.8229i) q^{56} +(25.1561 - 87.6825i) q^{57} +(-81.9023 - 47.2863i) q^{58} +(32.3428 - 18.6731i) q^{59} +(0.915180 - 11.6012i) q^{60} +(25.4414 - 44.0659i) q^{61} -62.0697 q^{62} +(17.8745 + 60.4111i) q^{63} +71.1310 q^{64} +(46.7362 - 41.3453i) q^{65} +(-1.51570 - 6.08285i) q^{66} +(24.9784 - 14.4213i) q^{67} +(-7.22664 + 12.5169i) q^{68} +(-22.7020 + 79.1285i) q^{69} +(-0.00374100 + 62.8460i) q^{70} +66.8477i q^{71} +(68.1555 - 36.2139i) q^{72} +(46.7701 - 27.0027i) q^{73} +(0.641406 - 0.370316i) q^{74} +(-9.12351 - 74.4430i) q^{75} -23.5900 q^{76} +(-2.58468 - 7.72527i) q^{77} +(64.6199 + 18.5395i) q^{78} +(-16.6402 + 28.8216i) q^{79} +(60.2405 - 12.2535i) q^{80} +(45.3330 - 67.1261i) q^{81} +(-26.7672 - 15.4540i) q^{82} -72.0714 q^{83} +(13.7421 - 8.75156i) q^{84} +(-29.5601 + 88.3338i) q^{85} +(12.2377 + 7.06544i) q^{86} +(38.2035 + 153.319i) q^{87} +(-8.64260 + 4.98981i) q^{88} +(41.4850 + 23.9513i) q^{89} +(62.3656 - 51.3760i) q^{90} +(85.6053 + 17.4183i) q^{91} +21.2887 q^{92} +(72.0274 + 74.6079i) q^{93} +(-31.2594 - 54.1428i) q^{94} +(-148.982 + 30.3045i) q^{95} +(-25.4733 - 26.3860i) q^{96} +66.7480i q^{97} +(-70.2695 + 52.9477i) q^{98} +(-5.55274 + 8.88059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.897800 1.55504i 0.448900 0.777518i −0.549415 0.835550i \(-0.685149\pi\)
0.998315 + 0.0580320i \(0.0184826\pi\)
\(3\) −2.91099 + 0.725349i −0.970330 + 0.241783i
\(4\) 0.387909 + 0.671879i 0.0969773 + 0.167970i
\(5\) 3.31295 + 3.74491i 0.662590 + 0.748983i
\(6\) −1.48554 + 5.17791i −0.247591 + 0.862986i
\(7\) −1.39571 + 6.85945i −0.199386 + 0.979921i
\(8\) 8.57546 1.07193
\(9\) 7.94774 4.22297i 0.883082 0.469219i
\(10\) 8.79784 1.78957i 0.879784 0.178957i
\(11\) −1.00783 + 0.581870i −0.0916208 + 0.0528973i −0.545110 0.838364i \(-0.683512\pi\)
0.453490 + 0.891262i \(0.350179\pi\)
\(12\) −1.61655 1.67446i −0.134712 0.139539i
\(13\) 12.4799i 0.959993i −0.877270 0.479996i \(-0.840638\pi\)
0.877270 0.479996i \(-0.159362\pi\)
\(14\) 9.41362 + 8.32879i 0.672401 + 0.594913i
\(15\) −12.3603 8.49836i −0.824022 0.566558i
\(16\) 6.14742 10.6476i 0.384213 0.665477i
\(17\) 9.31485 + 16.1338i 0.547933 + 0.949047i 0.998416 + 0.0562623i \(0.0179183\pi\)
−0.450483 + 0.892785i \(0.648748\pi\)
\(18\) 0.568609 16.1504i 0.0315894 0.897244i
\(19\) −15.2033 + 26.3329i −0.800174 + 1.38594i 0.119327 + 0.992855i \(0.461926\pi\)
−0.919501 + 0.393087i \(0.871407\pi\)
\(20\) −1.23100 + 3.67859i −0.0615502 + 0.183929i
\(21\) −0.912610 20.9802i −0.0434576 0.999055i
\(22\) 2.08961i 0.0949824i
\(23\) 13.7201 23.7640i 0.596527 1.03322i −0.396802 0.917904i \(-0.629880\pi\)
0.993329 0.115311i \(-0.0367865\pi\)
\(24\) −24.9631 + 6.22021i −1.04013 + 0.259175i
\(25\) −3.04875 + 24.8134i −0.121950 + 0.992536i
\(26\) −19.4067 11.2045i −0.746412 0.430941i
\(27\) −20.0727 + 18.0579i −0.743432 + 0.668812i
\(28\) −5.15012 + 1.72310i −0.183933 + 0.0615392i
\(29\) 52.6691i 1.81617i −0.418781 0.908087i \(-0.637543\pi\)
0.418781 0.908087i \(-0.362457\pi\)
\(30\) −24.3124 + 11.5909i −0.810412 + 0.386364i
\(31\) −17.2838 29.9364i −0.557542 0.965692i −0.997701 0.0677718i \(-0.978411\pi\)
0.440158 0.897920i \(-0.354922\pi\)
\(32\) 6.11262 + 10.5874i 0.191019 + 0.330855i
\(33\) 2.51172 2.42485i 0.0761128 0.0734802i
\(34\) 33.4515 0.983868
\(35\) −30.3119 + 17.4982i −0.866055 + 0.499948i
\(36\) 5.92032 + 3.70178i 0.164453 + 0.102827i
\(37\) 0.357210 + 0.206235i 0.00965431 + 0.00557392i 0.504819 0.863225i \(-0.331559\pi\)
−0.495165 + 0.868799i \(0.664892\pi\)
\(38\) 27.2991 + 47.2834i 0.718396 + 1.24430i
\(39\) 9.05229 + 36.3289i 0.232110 + 0.931510i
\(40\) 28.4101 + 32.1144i 0.710252 + 0.802859i
\(41\) 17.2132i 0.419835i −0.977719 0.209918i \(-0.932680\pi\)
0.977719 0.209918i \(-0.0673195\pi\)
\(42\) −33.4442 17.4169i −0.796291 0.414687i
\(43\) 7.86972i 0.183017i 0.995804 + 0.0915084i \(0.0291688\pi\)
−0.995804 + 0.0915084i \(0.970831\pi\)
\(44\) −0.781892 0.451426i −0.0177703 0.0102597i
\(45\) 42.1451 + 15.7731i 0.936558 + 0.350513i
\(46\) −24.6359 42.6706i −0.535562 0.927621i
\(47\) 17.4089 30.1530i 0.370401 0.641554i −0.619226 0.785213i \(-0.712553\pi\)
0.989627 + 0.143659i \(0.0458868\pi\)
\(48\) −10.1718 + 35.4542i −0.211913 + 0.738629i
\(49\) −45.1040 19.1475i −0.920490 0.390766i
\(50\) 35.8486 + 27.0184i 0.716971 + 0.540368i
\(51\) −38.8181 40.2088i −0.761139 0.788408i
\(52\) 8.38498 4.84107i 0.161250 0.0930975i
\(53\) −17.8667 30.9460i −0.337107 0.583886i 0.646780 0.762676i \(-0.276115\pi\)
−0.983887 + 0.178790i \(0.942782\pi\)
\(54\) 10.0595 + 47.4261i 0.186286 + 0.878261i
\(55\) −5.51794 1.84653i −0.100326 0.0335732i
\(56\) −11.9688 + 58.8229i −0.213729 + 1.05041i
\(57\) 25.1561 87.6825i 0.441336 1.53829i
\(58\) −81.9023 47.2863i −1.41211 0.815281i
\(59\) 32.3428 18.6731i 0.548184 0.316494i −0.200205 0.979754i \(-0.564161\pi\)
0.748389 + 0.663260i \(0.230828\pi\)
\(60\) 0.915180 11.6012i 0.0152530 0.193354i
\(61\) 25.4414 44.0659i 0.417073 0.722391i −0.578571 0.815632i \(-0.696389\pi\)
0.995644 + 0.0932408i \(0.0297226\pi\)
\(62\) −62.0697 −1.00112
\(63\) 17.8745 + 60.4111i 0.283723 + 0.958906i
\(64\) 71.1310 1.11142
\(65\) 46.7362 41.3453i 0.719018 0.636081i
\(66\) −1.51570 6.08285i −0.0229652 0.0921643i
\(67\) 24.9784 14.4213i 0.372812 0.215243i −0.301874 0.953348i \(-0.597612\pi\)
0.674686 + 0.738105i \(0.264279\pi\)
\(68\) −7.22664 + 12.5169i −0.106274 + 0.184072i
\(69\) −22.7020 + 79.1285i −0.329014 + 1.14679i
\(70\) −0.00374100 + 62.8460i −5.34428e−5 + 0.897800i
\(71\) 66.8477i 0.941518i 0.882262 + 0.470759i \(0.156020\pi\)
−0.882262 + 0.470759i \(0.843980\pi\)
\(72\) 68.1555 36.2139i 0.946604 0.502971i
\(73\) 46.7701 27.0027i 0.640686 0.369900i −0.144192 0.989550i \(-0.546058\pi\)
0.784879 + 0.619649i \(0.212725\pi\)
\(74\) 0.641406 0.370316i 0.00866765 0.00500427i
\(75\) −9.12351 74.4430i −0.121647 0.992573i
\(76\) −23.5900 −0.310395
\(77\) −2.58468 7.72527i −0.0335672 0.100328i
\(78\) 64.6199 + 18.5395i 0.828460 + 0.237685i
\(79\) −16.6402 + 28.8216i −0.210635 + 0.364831i −0.951914 0.306367i \(-0.900887\pi\)
0.741278 + 0.671198i \(0.234220\pi\)
\(80\) 60.2405 12.2535i 0.753007 0.153169i
\(81\) 45.3330 67.1261i 0.559667 0.828718i
\(82\) −26.7672 15.4540i −0.326429 0.188464i
\(83\) −72.0714 −0.868330 −0.434165 0.900833i \(-0.642957\pi\)
−0.434165 + 0.900833i \(0.642957\pi\)
\(84\) 13.7421 8.75156i 0.163597 0.104185i
\(85\) −29.5601 + 88.3338i −0.347765 + 1.03922i
\(86\) 12.2377 + 7.06544i 0.142299 + 0.0821562i
\(87\) 38.2035 + 153.319i 0.439120 + 1.76229i
\(88\) −8.64260 + 4.98981i −0.0982114 + 0.0567024i
\(89\) 41.4850 + 23.9513i 0.466123 + 0.269116i 0.714615 0.699518i \(-0.246602\pi\)
−0.248492 + 0.968634i \(0.579935\pi\)
\(90\) 62.3656 51.3760i 0.692951 0.570845i
\(91\) 85.6053 + 17.4183i 0.940717 + 0.191410i
\(92\) 21.2887 0.231398
\(93\) 72.0274 + 74.6079i 0.774488 + 0.802236i
\(94\) −31.2594 54.1428i −0.332546 0.575987i
\(95\) −148.982 + 30.3045i −1.56823 + 0.318994i
\(96\) −25.4733 26.3860i −0.265347 0.274854i
\(97\) 66.7480i 0.688124i 0.938947 + 0.344062i \(0.111803\pi\)
−0.938947 + 0.344062i \(0.888197\pi\)
\(98\) −70.2695 + 52.9477i −0.717036 + 0.540283i
\(99\) −5.55274 + 8.88059i −0.0560883 + 0.0897029i
\(100\) −17.8542 + 7.57696i −0.178542 + 0.0757696i
\(101\) 19.3539 11.1740i 0.191623 0.110633i −0.401119 0.916026i \(-0.631379\pi\)
0.592742 + 0.805392i \(0.298045\pi\)
\(102\) −97.3771 + 24.2640i −0.954677 + 0.237883i
\(103\) −12.8487 7.41823i −0.124745 0.0720216i 0.436329 0.899787i \(-0.356278\pi\)
−0.561074 + 0.827766i \(0.689612\pi\)
\(104\) 107.021i 1.02905i
\(105\) 75.5454 72.9238i 0.719480 0.694513i
\(106\) −64.1628 −0.605309
\(107\) 16.9958 29.4376i 0.158840 0.275118i −0.775611 0.631211i \(-0.782558\pi\)
0.934450 + 0.356093i \(0.115891\pi\)
\(108\) −19.9191 6.48156i −0.184436 0.0600144i
\(109\) 45.3155 + 78.4888i 0.415739 + 0.720081i 0.995506 0.0947015i \(-0.0301897\pi\)
−0.579767 + 0.814782i \(0.696856\pi\)
\(110\) −7.82542 + 6.92278i −0.0711402 + 0.0629344i
\(111\) −1.18943 0.341247i −0.0107156 0.00307429i
\(112\) 64.4569 + 57.0288i 0.575508 + 0.509186i
\(113\) −76.2557 −0.674830 −0.337415 0.941356i \(-0.609552\pi\)
−0.337415 + 0.941356i \(0.609552\pi\)
\(114\) −113.764 117.840i −0.997932 1.03368i
\(115\) 134.448 27.3481i 1.16911 0.237809i
\(116\) 35.3872 20.4308i 0.305062 0.176128i
\(117\) −52.7023 99.1870i −0.450447 0.847752i
\(118\) 67.0590i 0.568297i
\(119\) −123.670 + 41.3767i −1.03924 + 0.347703i
\(120\) −105.996 72.8774i −0.883296 0.607312i
\(121\) −59.8229 + 103.616i −0.494404 + 0.856332i
\(122\) −45.6827 79.1247i −0.374448 0.648563i
\(123\) 12.4856 + 50.1076i 0.101509 + 0.407379i
\(124\) 13.4091 23.2253i 0.108138 0.187300i
\(125\) −103.024 + 70.7882i −0.824195 + 0.566306i
\(126\) 109.989 + 26.4415i 0.872930 + 0.209854i
\(127\) 0.573646i 0.00451690i −0.999997 0.00225845i \(-0.999281\pi\)
0.999997 0.00225845i \(-0.000718888\pi\)
\(128\) 39.4109 68.2617i 0.307898 0.533295i
\(129\) −5.70830 22.9087i −0.0442504 0.177587i
\(130\) −22.3337 109.796i −0.171797 0.844586i
\(131\) −199.680 115.285i −1.52427 0.880039i −0.999587 0.0287429i \(-0.990850\pi\)
−0.524686 0.851296i \(-0.675817\pi\)
\(132\) 2.60352 + 0.746951i 0.0197237 + 0.00565872i
\(133\) −159.410 141.039i −1.19857 1.06045i
\(134\) 51.7898i 0.386491i
\(135\) −134.125 15.3454i −0.993519 0.113670i
\(136\) 79.8792 + 138.355i 0.587347 + 1.01731i
\(137\) 13.9490 + 24.1603i 0.101817 + 0.176353i 0.912433 0.409225i \(-0.134201\pi\)
−0.810616 + 0.585578i \(0.800868\pi\)
\(138\) 102.666 + 106.344i 0.743955 + 0.770609i
\(139\) −130.478 −0.938693 −0.469346 0.883014i \(-0.655510\pi\)
−0.469346 + 0.883014i \(0.655510\pi\)
\(140\) −23.5149 13.5782i −0.167964 0.0969873i
\(141\) −28.8056 + 100.403i −0.204295 + 0.712076i
\(142\) 103.951 + 60.0159i 0.732047 + 0.422647i
\(143\) 7.26169 + 12.5776i 0.0507810 + 0.0879553i
\(144\) 3.89338 110.585i 0.0270373 0.767951i
\(145\) 197.241 174.490i 1.36028 1.20338i
\(146\) 96.9723i 0.664194i
\(147\) 145.186 + 23.0221i 0.987660 + 0.156613i
\(148\) 0.320002i 0.00216218i
\(149\) 137.529 + 79.4024i 0.923013 + 0.532902i 0.884595 0.466360i \(-0.154435\pi\)
0.0384179 + 0.999262i \(0.487768\pi\)
\(150\) −123.953 52.6476i −0.826351 0.350984i
\(151\) 24.0390 + 41.6367i 0.159198 + 0.275740i 0.934580 0.355753i \(-0.115776\pi\)
−0.775381 + 0.631493i \(0.782442\pi\)
\(152\) −130.375 + 225.817i −0.857733 + 1.48564i
\(153\) 142.165 + 88.8908i 0.929180 + 0.580986i
\(154\) −14.3336 2.91649i −0.0930753 0.0189382i
\(155\) 54.8490 163.904i 0.353865 1.05745i
\(156\) −20.8971 + 20.1744i −0.133956 + 0.129323i
\(157\) −112.848 + 65.1528i −0.718777 + 0.414986i −0.814302 0.580441i \(-0.802880\pi\)
0.0955254 + 0.995427i \(0.469547\pi\)
\(158\) 29.8791 + 51.7522i 0.189108 + 0.327545i
\(159\) 74.4564 + 77.1239i 0.468279 + 0.485056i
\(160\) −19.3980 + 57.9666i −0.121237 + 0.362292i
\(161\) 143.858 + 127.280i 0.893530 + 0.790559i
\(162\) −63.6835 130.760i −0.393108 0.807163i
\(163\) −121.121 69.9292i −0.743073 0.429013i 0.0801127 0.996786i \(-0.474472\pi\)
−0.823185 + 0.567773i \(0.807805\pi\)
\(164\) 11.5652 6.67717i 0.0705195 0.0407145i
\(165\) 17.4020 + 1.37279i 0.105467 + 0.00831991i
\(166\) −64.7057 + 112.074i −0.389794 + 0.675142i
\(167\) 224.419 1.34383 0.671915 0.740629i \(-0.265472\pi\)
0.671915 + 0.740629i \(0.265472\pi\)
\(168\) −7.82605 179.915i −0.0465836 1.07092i
\(169\) 13.2519 0.0784136
\(170\) 110.823 + 125.273i 0.651901 + 0.736900i
\(171\) −9.62879 + 273.490i −0.0563087 + 1.59936i
\(172\) −5.28750 + 3.05274i −0.0307413 + 0.0177485i
\(173\) 146.827 254.312i 0.848711 1.47001i −0.0336474 0.999434i \(-0.510712\pi\)
0.882359 0.470577i \(-0.155954\pi\)
\(174\) 272.716 + 78.2422i 1.56733 + 0.449668i
\(175\) −165.951 55.5449i −0.948292 0.317400i
\(176\) 14.3080i 0.0812954i
\(177\) −80.6051 + 77.8172i −0.455396 + 0.439645i
\(178\) 74.4904 43.0071i 0.418485 0.241613i
\(179\) −211.424 + 122.066i −1.18114 + 0.681933i −0.956278 0.292458i \(-0.905527\pi\)
−0.224863 + 0.974390i \(0.572194\pi\)
\(180\) 5.75087 + 34.4349i 0.0319493 + 0.191305i
\(181\) 81.3669 0.449541 0.224771 0.974412i \(-0.427837\pi\)
0.224771 + 0.974412i \(0.427837\pi\)
\(182\) 103.942 117.481i 0.571112 0.645501i
\(183\) −42.0967 + 146.729i −0.230036 + 0.801799i
\(184\) 117.656 203.787i 0.639437 1.10754i
\(185\) 0.411085 + 2.02096i 0.00222208 + 0.0109241i
\(186\) 180.684 45.0222i 0.971421 0.242055i
\(187\) −18.7756 10.8401i −0.100404 0.0579683i
\(188\) 27.0122 0.143682
\(189\) −95.8518 162.891i −0.507152 0.861856i
\(190\) −86.6317 + 258.880i −0.455956 + 1.36253i
\(191\) 207.381 + 119.732i 1.08577 + 0.626867i 0.932446 0.361310i \(-0.117670\pi\)
0.153319 + 0.988177i \(0.451004\pi\)
\(192\) −207.062 + 51.5948i −1.07845 + 0.268723i
\(193\) −1.39114 + 0.803175i −0.00720798 + 0.00416153i −0.503600 0.863937i \(-0.667991\pi\)
0.496392 + 0.868099i \(0.334658\pi\)
\(194\) 103.796 + 59.9264i 0.535029 + 0.308899i
\(195\) −106.059 + 154.256i −0.543891 + 0.791055i
\(196\) −4.63145 37.7319i −0.0236298 0.192510i
\(197\) −286.325 −1.45343 −0.726713 0.686941i \(-0.758953\pi\)
−0.726713 + 0.686941i \(0.758953\pi\)
\(198\) 8.82438 + 16.6077i 0.0445676 + 0.0838773i
\(199\) −44.6292 77.3000i −0.224267 0.388442i 0.731832 0.681485i \(-0.238665\pi\)
−0.956099 + 0.293043i \(0.905332\pi\)
\(200\) −26.1444 + 212.786i −0.130722 + 1.06393i
\(201\) −62.2515 + 60.0983i −0.309709 + 0.298997i
\(202\) 40.1280i 0.198653i
\(203\) 361.281 + 73.5105i 1.77971 + 0.362121i
\(204\) 11.9575 41.6784i 0.0586154 0.204306i
\(205\) 64.4621 57.0266i 0.314449 0.278178i
\(206\) −23.0712 + 13.3202i −0.111996 + 0.0646610i
\(207\) 8.68944 246.809i 0.0419780 1.19232i
\(208\) −132.882 76.7192i −0.638853 0.368842i
\(209\) 35.3854i 0.169308i
\(210\) −45.5744 182.947i −0.217021 0.871176i
\(211\) 174.205 0.825617 0.412808 0.910818i \(-0.364548\pi\)
0.412808 + 0.910818i \(0.364548\pi\)
\(212\) 13.8613 24.0085i 0.0653835 0.113247i
\(213\) −48.4880 194.593i −0.227643 0.913583i
\(214\) −30.5177 52.8582i −0.142606 0.247001i
\(215\) −29.4714 + 26.0720i −0.137076 + 0.121265i
\(216\) −172.132 + 154.855i −0.796909 + 0.716921i
\(217\) 229.471 76.7750i 1.05747 0.353802i
\(218\) 162.737 0.746501
\(219\) −116.561 + 112.529i −0.532242 + 0.513833i
\(220\) −0.899819 4.42367i −0.00409009 0.0201076i
\(221\) 201.348 116.249i 0.911078 0.526011i
\(222\) −1.59852 + 1.54323i −0.00720053 + 0.00695148i
\(223\) 149.196i 0.669041i −0.942388 0.334521i \(-0.891426\pi\)
0.942388 0.334521i \(-0.108574\pi\)
\(224\) −81.1549 + 27.1523i −0.362299 + 0.121216i
\(225\) 80.5557 + 210.085i 0.358025 + 0.933712i
\(226\) −68.4624 + 118.580i −0.302931 + 0.524692i
\(227\) −46.1279 79.8959i −0.203207 0.351964i 0.746353 0.665550i \(-0.231803\pi\)
−0.949560 + 0.313586i \(0.898470\pi\)
\(228\) 68.6703 17.1110i 0.301186 0.0750482i
\(229\) −74.0138 + 128.196i −0.323205 + 0.559807i −0.981147 0.193261i \(-0.938094\pi\)
0.657943 + 0.753068i \(0.271427\pi\)
\(230\) 78.1802 233.625i 0.339914 1.01576i
\(231\) 13.1275 + 20.6134i 0.0568290 + 0.0892355i
\(232\) 451.661i 1.94682i
\(233\) −201.616 + 349.210i −0.865306 + 1.49875i 0.00143686 + 0.999999i \(0.499543\pi\)
−0.866743 + 0.498755i \(0.833791\pi\)
\(234\) −201.555 7.09619i −0.861348 0.0303256i
\(235\) 170.595 34.7008i 0.725937 0.147663i
\(236\) 25.0922 + 14.4870i 0.106323 + 0.0613855i
\(237\) 27.5337 95.9695i 0.116176 0.404935i
\(238\) −46.6885 + 229.459i −0.196170 + 0.964113i
\(239\) 42.1167i 0.176220i 0.996111 + 0.0881102i \(0.0280828\pi\)
−0.996111 + 0.0881102i \(0.971917\pi\)
\(240\) −166.472 + 79.3654i −0.693632 + 0.330689i
\(241\) −133.166 230.650i −0.552554 0.957052i −0.998089 0.0617877i \(-0.980320\pi\)
0.445535 0.895265i \(-0.353014\pi\)
\(242\) 107.418 + 186.053i 0.443876 + 0.768815i
\(243\) −83.2741 + 228.286i −0.342692 + 0.939448i
\(244\) 39.4759 0.161786
\(245\) −77.7214 232.345i −0.317230 0.948349i
\(246\) 89.1286 + 25.5710i 0.362312 + 0.103947i
\(247\) 328.632 + 189.736i 1.33049 + 0.768161i
\(248\) −148.217 256.719i −0.597648 1.03516i
\(249\) 209.799 52.2770i 0.842567 0.209948i
\(250\) 17.5829 + 223.760i 0.0703316 + 0.895041i
\(251\) 426.902i 1.70081i −0.526133 0.850403i \(-0.676358\pi\)
0.526133 0.850403i \(-0.323642\pi\)
\(252\) −33.6552 + 35.4435i −0.133552 + 0.140649i
\(253\) 31.9333i 0.126219i
\(254\) −0.892041 0.515020i −0.00351197 0.00202764i
\(255\) 21.9762 278.580i 0.0861811 1.09247i
\(256\) 71.4957 + 123.834i 0.279280 + 0.483727i
\(257\) −8.35527 + 14.4718i −0.0325108 + 0.0563103i −0.881823 0.471581i \(-0.843684\pi\)
0.849312 + 0.527891i \(0.177017\pi\)
\(258\) −40.7487 11.6908i −0.157941 0.0453132i
\(259\) −1.91322 + 2.16242i −0.00738694 + 0.00834910i
\(260\) 45.9084 + 15.3628i 0.176571 + 0.0590877i
\(261\) −222.420 418.600i −0.852183 1.60383i
\(262\) −358.545 + 207.006i −1.36849 + 0.790099i
\(263\) 0.756335 + 1.31001i 0.00287580 + 0.00498103i 0.867460 0.497507i \(-0.165751\pi\)
−0.864584 + 0.502488i \(0.832418\pi\)
\(264\) 21.5392 20.7942i 0.0815878 0.0787659i
\(265\) 56.6986 169.432i 0.213957 0.639364i
\(266\) −362.439 + 121.263i −1.36255 + 0.455875i
\(267\) −138.135 39.6311i −0.517361 0.148431i
\(268\) 19.3787 + 11.1883i 0.0723087 + 0.0417474i
\(269\) −10.5890 + 6.11353i −0.0393641 + 0.0227269i −0.519553 0.854438i \(-0.673901\pi\)
0.480189 + 0.877165i \(0.340568\pi\)
\(270\) −144.280 + 194.792i −0.534371 + 0.721452i
\(271\) −117.307 + 203.182i −0.432868 + 0.749749i −0.997119 0.0758540i \(-0.975832\pi\)
0.564251 + 0.825603i \(0.309165\pi\)
\(272\) 229.049 0.842092
\(273\) −261.830 + 11.3893i −0.959086 + 0.0417190i
\(274\) 50.0935 0.182823
\(275\) −11.3656 26.7816i −0.0413293 0.0973878i
\(276\) −61.9711 + 15.4417i −0.224533 + 0.0559482i
\(277\) −427.929 + 247.065i −1.54487 + 0.891930i −0.546348 + 0.837558i \(0.683982\pi\)
−0.998521 + 0.0543719i \(0.982684\pi\)
\(278\) −117.143 + 202.898i −0.421379 + 0.729850i
\(279\) −263.788 164.938i −0.945477 0.591175i
\(280\) −259.939 + 150.055i −0.928353 + 0.535911i
\(281\) 67.0586i 0.238643i 0.992856 + 0.119321i \(0.0380719\pi\)
−0.992856 + 0.119321i \(0.961928\pi\)
\(282\) 130.268 + 134.935i 0.461944 + 0.478494i
\(283\) −118.530 + 68.4334i −0.418834 + 0.241814i −0.694579 0.719417i \(-0.744409\pi\)
0.275744 + 0.961231i \(0.411076\pi\)
\(284\) −44.9136 + 25.9309i −0.158146 + 0.0913058i
\(285\) 411.704 196.280i 1.44458 0.688702i
\(286\) 26.0782 0.0911825
\(287\) 118.073 + 24.0246i 0.411405 + 0.0837094i
\(288\) 93.2917 + 58.3322i 0.323929 + 0.202542i
\(289\) −29.0330 + 50.2867i −0.100460 + 0.174002i
\(290\) −94.2549 463.374i −0.325017 1.59784i
\(291\) −48.4156 194.303i −0.166377 0.667707i
\(292\) 36.2851 + 20.9492i 0.124264 + 0.0717439i
\(293\) −98.9599 −0.337747 −0.168874 0.985638i \(-0.554013\pi\)
−0.168874 + 0.985638i \(0.554013\pi\)
\(294\) 166.148 205.100i 0.565130 0.697620i
\(295\) 177.079 + 59.2579i 0.600269 + 0.200874i
\(296\) 3.06324 + 1.76856i 0.0103488 + 0.00597487i
\(297\) 9.72244 29.8790i 0.0327355 0.100603i
\(298\) 246.947 142.575i 0.828681 0.478439i
\(299\) −296.572 171.226i −0.991879 0.572662i
\(300\) 46.4776 35.0070i 0.154925 0.116690i
\(301\) −53.9819 10.9838i −0.179342 0.0364911i
\(302\) 86.3287 0.285857
\(303\) −48.2339 + 46.5657i −0.159188 + 0.153682i
\(304\) 186.922 + 323.759i 0.614875 + 1.06500i
\(305\) 249.309 50.7120i 0.817407 0.166269i
\(306\) 265.864 141.265i 0.868836 0.461650i
\(307\) 441.330i 1.43756i 0.695239 + 0.718778i \(0.255298\pi\)
−0.695239 + 0.718778i \(0.744702\pi\)
\(308\) 4.18782 4.73329i 0.0135968 0.0153678i
\(309\) 42.7834 + 12.2746i 0.138458 + 0.0397235i
\(310\) −205.634 232.445i −0.663334 0.749824i
\(311\) −19.4380 + 11.2225i −0.0625015 + 0.0360853i −0.530925 0.847419i \(-0.678155\pi\)
0.468424 + 0.883504i \(0.344822\pi\)
\(312\) 77.6276 + 311.537i 0.248806 + 0.998516i
\(313\) 217.506 + 125.577i 0.694908 + 0.401206i 0.805448 0.592666i \(-0.201925\pi\)
−0.110540 + 0.993872i \(0.535258\pi\)
\(314\) 233.977i 0.745149i
\(315\) −167.017 + 267.077i −0.530212 + 0.847865i
\(316\) −25.8195 −0.0817074
\(317\) 17.4496 30.2237i 0.0550462 0.0953428i −0.837189 0.546913i \(-0.815803\pi\)
0.892235 + 0.451570i \(0.149136\pi\)
\(318\) 186.777 46.5405i 0.587350 0.146354i
\(319\) 30.6466 + 53.0814i 0.0960707 + 0.166399i
\(320\) 235.653 + 266.379i 0.736416 + 0.832435i
\(321\) −28.1221 + 98.0206i −0.0876079 + 0.305360i
\(322\) 327.081 109.433i 1.01578 0.339854i
\(323\) −566.466 −1.75377
\(324\) 62.6857 + 4.41944i 0.193474 + 0.0136403i
\(325\) 309.669 + 38.0481i 0.952828 + 0.117071i
\(326\) −217.485 + 125.565i −0.667131 + 0.385168i
\(327\) −188.845 195.611i −0.577508 0.598198i
\(328\) 147.611i 0.450035i
\(329\) 182.535 + 161.500i 0.554819 + 0.490881i
\(330\) 17.7583 25.8283i 0.0538130 0.0782676i
\(331\) 136.010 235.577i 0.410908 0.711713i −0.584082 0.811695i \(-0.698545\pi\)
0.994989 + 0.0999821i \(0.0318786\pi\)
\(332\) −27.9572 48.4232i −0.0842083 0.145853i
\(333\) 3.70993 + 0.130616i 0.0111409 + 0.000392240i
\(334\) 201.484 348.980i 0.603245 1.04485i
\(335\) 136.759 + 45.7650i 0.408235 + 0.136612i
\(336\) −228.999 119.257i −0.681546 0.354930i
\(337\) 600.523i 1.78197i −0.454036 0.890983i \(-0.650016\pi\)
0.454036 0.890983i \(-0.349984\pi\)
\(338\) 11.8976 20.6072i 0.0351999 0.0609680i
\(339\) 221.980 55.3121i 0.654808 0.163162i
\(340\) −70.8162 + 14.4047i −0.208283 + 0.0423668i
\(341\) 34.8383 + 20.1139i 0.102165 + 0.0589850i
\(342\) 416.642 + 260.513i 1.21825 + 0.761733i
\(343\) 194.293 282.664i 0.566453 0.824094i
\(344\) 67.4865i 0.196182i
\(345\) −371.540 + 177.132i −1.07693 + 0.513425i
\(346\) −263.643 456.643i −0.761973 1.31978i
\(347\) −77.0212 133.405i −0.221963 0.384451i 0.733441 0.679753i \(-0.237913\pi\)
−0.955404 + 0.295302i \(0.904580\pi\)
\(348\) −88.1924 + 85.1420i −0.253426 + 0.244661i
\(349\) −20.2324 −0.0579726 −0.0289863 0.999580i \(-0.509228\pi\)
−0.0289863 + 0.999580i \(0.509228\pi\)
\(350\) −235.365 + 208.192i −0.672472 + 0.594833i
\(351\) 225.361 + 250.505i 0.642055 + 0.713689i
\(352\) −12.3210 7.11351i −0.0350027 0.0202088i
\(353\) 162.715 + 281.830i 0.460948 + 0.798386i 0.999008 0.0445203i \(-0.0141760\pi\)
−0.538060 + 0.842907i \(0.680843\pi\)
\(354\) 48.6412 + 195.208i 0.137405 + 0.551436i
\(355\) −250.339 + 221.463i −0.705180 + 0.623840i
\(356\) 37.1638i 0.104393i
\(357\) 329.989 210.151i 0.924339 0.588658i
\(358\) 438.363i 1.22448i
\(359\) 499.939 + 288.640i 1.39259 + 0.804011i 0.993601 0.112945i \(-0.0360285\pi\)
0.398987 + 0.916957i \(0.369362\pi\)
\(360\) 361.414 + 135.262i 1.00393 + 0.375727i
\(361\) −281.781 488.059i −0.780556 1.35196i
\(362\) 73.0513 126.528i 0.201799 0.349526i
\(363\) 98.9858 345.018i 0.272688 0.950464i
\(364\) 21.5041 + 64.2730i 0.0590772 + 0.176574i
\(365\) 256.070 + 85.6913i 0.701561 + 0.234771i
\(366\) 190.375 + 197.195i 0.520150 + 0.538785i
\(367\) −435.739 + 251.574i −1.18730 + 0.685487i −0.957692 0.287796i \(-0.907077\pi\)
−0.229607 + 0.973283i \(0.573744\pi\)
\(368\) −168.687 292.174i −0.458388 0.793950i
\(369\) −72.6910 136.806i −0.196995 0.370749i
\(370\) 3.51174 + 1.17517i 0.00949120 + 0.00317614i
\(371\) 237.209 79.3640i 0.639377 0.213919i
\(372\) −22.1874 + 77.3348i −0.0596434 + 0.207889i
\(373\) 185.731 + 107.232i 0.497938 + 0.287484i 0.727861 0.685724i \(-0.240514\pi\)
−0.229924 + 0.973209i \(0.573848\pi\)
\(374\) −33.7134 + 19.4644i −0.0901428 + 0.0520440i
\(375\) 248.557 280.793i 0.662818 0.748780i
\(376\) 149.289 258.576i 0.397045 0.687703i
\(377\) −657.305 −1.74351
\(378\) −339.357 + 2.80951i −0.897770 + 0.00743255i
\(379\) −505.361 −1.33341 −0.666704 0.745323i \(-0.732295\pi\)
−0.666704 + 0.745323i \(0.732295\pi\)
\(380\) −78.1525 88.3425i −0.205664 0.232480i
\(381\) 0.416094 + 1.66988i 0.00109211 + 0.00438289i
\(382\) 372.374 214.990i 0.974800 0.562801i
\(383\) 202.429 350.617i 0.528535 0.915449i −0.470912 0.882180i \(-0.656075\pi\)
0.999446 0.0332689i \(-0.0105918\pi\)
\(384\) −65.2112 + 227.296i −0.169821 + 0.591917i
\(385\) 20.3676 35.2728i 0.0529028 0.0916177i
\(386\) 2.88436i 0.00747244i
\(387\) 33.2336 + 62.5465i 0.0858749 + 0.161619i
\(388\) −44.8466 + 25.8922i −0.115584 + 0.0667324i
\(389\) −168.810 + 97.4627i −0.433960 + 0.250547i −0.701032 0.713130i \(-0.747277\pi\)
0.267072 + 0.963676i \(0.413944\pi\)
\(390\) 144.654 + 303.416i 0.370907 + 0.777990i
\(391\) 511.204 1.30743
\(392\) −386.788 164.199i −0.986703 0.418875i
\(393\) 664.888 + 190.756i 1.69183 + 0.485385i
\(394\) −257.063 + 445.245i −0.652443 + 1.13006i
\(395\) −163.063 + 33.1686i −0.412817 + 0.0839711i
\(396\) −8.12063 0.285904i −0.0205067 0.000721980i
\(397\) −500.171 288.774i −1.25988 0.727390i −0.286826 0.957983i \(-0.592600\pi\)
−0.973050 + 0.230593i \(0.925933\pi\)
\(398\) −160.272 −0.402694
\(399\) 566.343 + 294.936i 1.41941 + 0.739188i
\(400\) 245.462 + 185.000i 0.613656 + 0.462501i
\(401\) −199.268 115.047i −0.496927 0.286901i 0.230517 0.973068i \(-0.425958\pi\)
−0.727443 + 0.686168i \(0.759292\pi\)
\(402\) 37.5657 + 150.760i 0.0934470 + 0.375024i
\(403\) −373.604 + 215.700i −0.927057 + 0.535237i
\(404\) 15.0151 + 8.66897i 0.0371661 + 0.0214579i
\(405\) 401.567 52.6171i 0.991525 0.129919i
\(406\) 438.669 495.806i 1.08047 1.22120i
\(407\) −0.480008 −0.00117938
\(408\) −332.883 344.809i −0.815890 0.845121i
\(409\) 290.480 + 503.125i 0.710219 + 1.23014i 0.964775 + 0.263077i \(0.0847375\pi\)
−0.254556 + 0.967058i \(0.581929\pi\)
\(410\) −30.8043 151.439i −0.0751324 0.369364i
\(411\) −58.1300 60.2126i −0.141435 0.146503i
\(412\) 11.5104i 0.0279378i
\(413\) 82.9464 + 247.916i 0.200839 + 0.600281i
\(414\) −375.996 235.098i −0.908203 0.567869i
\(415\) −238.769 269.901i −0.575347 0.650364i
\(416\) 132.129 76.2850i 0.317619 0.183377i
\(417\) 379.821 94.6424i 0.910842 0.226960i
\(418\) −55.0256 31.7690i −0.131640 0.0760025i
\(419\) 220.813i 0.527000i −0.964659 0.263500i \(-0.915123\pi\)
0.964659 0.263500i \(-0.0848769\pi\)
\(420\) 78.3007 + 22.4695i 0.186430 + 0.0534989i
\(421\) −747.852 −1.77637 −0.888185 0.459486i \(-0.848033\pi\)
−0.888185 + 0.459486i \(0.848033\pi\)
\(422\) 156.401 270.895i 0.370620 0.641932i
\(423\) 11.0257 313.166i 0.0260654 0.740344i
\(424\) −153.215 265.376i −0.361356 0.625887i
\(425\) −428.733 + 181.945i −1.00878 + 0.428107i
\(426\) −346.132 99.3053i −0.812516 0.233111i
\(427\) 266.759 + 236.017i 0.624728 + 0.552734i
\(428\) 26.3714 0.0616153
\(429\) −30.2619 31.3461i −0.0705405 0.0730677i
\(430\) 14.0834 + 69.2365i 0.0327521 + 0.161015i
\(431\) −310.115 + 179.045i −0.719523 + 0.415417i −0.814577 0.580055i \(-0.803031\pi\)
0.0950539 + 0.995472i \(0.469698\pi\)
\(432\) 68.8792 + 324.736i 0.159443 + 0.751703i
\(433\) 622.750i 1.43822i 0.694896 + 0.719110i \(0.255450\pi\)
−0.694896 + 0.719110i \(0.744550\pi\)
\(434\) 86.6310 425.764i 0.199611 0.981022i
\(435\) −447.601 + 651.007i −1.02897 + 1.49657i
\(436\) −35.1566 + 60.8931i −0.0806345 + 0.139663i
\(437\) 417.182 + 722.581i 0.954651 + 1.65350i
\(438\) 70.3388 + 282.285i 0.160591 + 0.644487i
\(439\) 194.411 336.729i 0.442849 0.767036i −0.555051 0.831816i \(-0.687301\pi\)
0.997900 + 0.0647799i \(0.0206345\pi\)
\(440\) −47.3189 15.8348i −0.107543 0.0359882i
\(441\) −439.334 + 38.2934i −0.996223 + 0.0868331i
\(442\) 417.472i 0.944506i
\(443\) 192.113 332.750i 0.433664 0.751128i −0.563522 0.826101i \(-0.690554\pi\)
0.997186 + 0.0749733i \(0.0238872\pi\)
\(444\) −0.232113 0.931523i −0.000522778 0.00209802i
\(445\) 47.7418 + 234.707i 0.107285 + 0.527432i
\(446\) −232.005 133.948i −0.520191 0.300333i
\(447\) −457.940 131.383i −1.02447 0.293922i
\(448\) −99.2779 + 487.919i −0.221602 + 1.08911i
\(449\) 33.9684i 0.0756535i −0.999284 0.0378267i \(-0.987957\pi\)
0.999284 0.0378267i \(-0.0120435\pi\)
\(450\) 399.013 + 63.3476i 0.886695 + 0.140772i
\(451\) 10.0159 + 17.3480i 0.0222081 + 0.0384656i
\(452\) −29.5803 51.2346i −0.0654432 0.113351i
\(453\) −100.178 103.767i −0.221144 0.229067i
\(454\) −165.655 −0.364878
\(455\) 218.376 + 378.290i 0.479947 + 0.831407i
\(456\) 215.725 751.918i 0.473082 1.64894i
\(457\) 432.197 + 249.529i 0.945726 + 0.546015i 0.891751 0.452527i \(-0.149477\pi\)
0.0539752 + 0.998542i \(0.482811\pi\)
\(458\) 132.899 + 230.188i 0.290173 + 0.502595i
\(459\) −478.317 155.641i −1.04208 0.339088i
\(460\) 70.5282 + 79.7241i 0.153322 + 0.173313i
\(461\) 816.492i 1.77113i 0.464513 + 0.885566i \(0.346229\pi\)
−0.464513 + 0.885566i \(0.653771\pi\)
\(462\) 43.8404 1.90700i 0.0948927 0.00412771i
\(463\) 353.851i 0.764258i −0.924109 0.382129i \(-0.875191\pi\)
0.924109 0.382129i \(-0.124809\pi\)
\(464\) −560.801 323.779i −1.20862 0.697799i
\(465\) −40.7771 + 516.909i −0.0876926 + 1.11163i
\(466\) 362.022 + 627.041i 0.776872 + 1.34558i
\(467\) −127.057 + 220.068i −0.272070 + 0.471238i −0.969392 0.245520i \(-0.921041\pi\)
0.697322 + 0.716758i \(0.254375\pi\)
\(468\) 46.1979 73.8851i 0.0987135 0.157874i
\(469\) 64.0596 + 191.466i 0.136588 + 0.408243i
\(470\) 99.1994 296.436i 0.211063 0.630715i
\(471\) 281.241 271.513i 0.597114 0.576462i
\(472\) 277.355 160.131i 0.587616 0.339260i
\(473\) −4.57916 7.93133i −0.00968109 0.0167681i
\(474\) −124.516 128.977i −0.262693 0.272104i
\(475\) −607.058 457.528i −1.27802 0.963217i
\(476\) −75.7728 67.0406i −0.159186 0.140842i
\(477\) −272.684 170.500i −0.571664 0.357442i
\(478\) 65.4930 + 37.8124i 0.137015 + 0.0791054i
\(479\) 220.662 127.400i 0.460673 0.265970i −0.251654 0.967817i \(-0.580975\pi\)
0.712327 + 0.701847i \(0.247641\pi\)
\(480\) 14.4213 182.811i 0.0300443 0.380856i
\(481\) 2.57379 4.45794i 0.00535092 0.00926807i
\(482\) −478.224 −0.992167
\(483\) −511.093 266.163i −1.05816 0.551062i
\(484\) −92.8234 −0.191784
\(485\) −249.966 + 221.133i −0.515393 + 0.455944i
\(486\) 280.229 + 334.449i 0.576603 + 0.688167i
\(487\) −144.819 + 83.6115i −0.297370 + 0.171687i −0.641261 0.767323i \(-0.721588\pi\)
0.343891 + 0.939010i \(0.388255\pi\)
\(488\) 218.172 377.885i 0.447074 0.774355i
\(489\) 403.305 + 115.708i 0.824754 + 0.236622i
\(490\) −431.084 87.7402i −0.879763 0.179062i
\(491\) 663.001i 1.35031i −0.737677 0.675154i \(-0.764077\pi\)
0.737677 0.675154i \(-0.235923\pi\)
\(492\) −28.8229 + 27.8260i −0.0585832 + 0.0565569i
\(493\) 849.752 490.605i 1.72363 0.995141i
\(494\) 590.092 340.690i 1.19452 0.689655i
\(495\) −51.6530 + 8.62640i −0.104349 + 0.0174271i
\(496\) −425.003 −0.856861
\(497\) −458.539 93.2998i −0.922613 0.187726i
\(498\) 107.065 373.180i 0.214991 0.749357i
\(499\) 213.627 370.012i 0.428109 0.741507i −0.568596 0.822617i \(-0.692513\pi\)
0.996705 + 0.0811099i \(0.0258465\pi\)
\(500\) −87.5252 41.7605i −0.175050 0.0835209i
\(501\) −653.283 + 162.783i −1.30396 + 0.324915i
\(502\) −663.848 383.273i −1.32241 0.763492i
\(503\) 503.059 1.00012 0.500059 0.865991i \(-0.333312\pi\)
0.500059 + 0.865991i \(0.333312\pi\)
\(504\) 153.283 + 518.053i 0.304132 + 1.02788i
\(505\) 105.964 + 35.4598i 0.209830 + 0.0702175i
\(506\) 49.6575 + 28.6698i 0.0981373 + 0.0566596i
\(507\) −38.5762 + 9.61226i −0.0760871 + 0.0189591i
\(508\) 0.385421 0.222523i 0.000758702 0.000438037i
\(509\) −481.244 277.846i −0.945469 0.545867i −0.0537984 0.998552i \(-0.517133\pi\)
−0.891670 + 0.452685i \(0.850466\pi\)
\(510\) −413.472 284.283i −0.810729 0.557418i
\(511\) 119.947 + 358.505i 0.234729 + 0.701575i
\(512\) 572.043 1.11727
\(513\) −170.347 803.111i −0.332059 1.56552i
\(514\) 15.0027 + 25.9855i 0.0291882 + 0.0505554i
\(515\) −14.7866 72.6936i −0.0287119 0.141153i
\(516\) 13.1776 12.7218i 0.0255379 0.0246546i
\(517\) 40.5188i 0.0783729i
\(518\) 1.64495 + 4.91654i 0.00317557 + 0.00949139i
\(519\) −242.947 + 846.801i −0.468106 + 1.63160i
\(520\) 400.784 354.555i 0.770739 0.681836i
\(521\) −209.107 + 120.728i −0.401358 + 0.231724i −0.687070 0.726591i \(-0.741103\pi\)
0.285712 + 0.958316i \(0.407770\pi\)
\(522\) −850.626 29.9481i −1.62955 0.0573718i
\(523\) 683.792 + 394.788i 1.30744 + 0.754852i 0.981669 0.190596i \(-0.0610421\pi\)
0.325773 + 0.945448i \(0.394375\pi\)
\(524\) 178.881i 0.341375i
\(525\) 523.372 + 41.3183i 0.996898 + 0.0787014i
\(526\) 2.71615 0.00516379
\(527\) 321.992 557.707i 0.610991 1.05827i
\(528\) −10.3783 41.6505i −0.0196559 0.0788834i
\(529\) −111.984 193.961i −0.211689 0.366656i
\(530\) −212.568 240.284i −0.401072 0.453366i
\(531\) 178.196 284.992i 0.335586 0.536708i
\(532\) 32.9247 161.814i 0.0618885 0.304162i
\(533\) −214.820 −0.403039
\(534\) −185.646 + 179.225i −0.347651 + 0.335627i
\(535\) 166.548 33.8775i 0.311304 0.0633224i
\(536\) 214.202 123.669i 0.399630 0.230726i
\(537\) 526.914 508.689i 0.981218 0.947280i
\(538\) 21.9549i 0.0408084i
\(539\) 56.5985 6.94725i 0.105007 0.0128891i
\(540\) −41.7181 96.0683i −0.0772557 0.177904i
\(541\) −394.171 + 682.723i −0.728596 + 1.26197i 0.228880 + 0.973455i \(0.426494\pi\)
−0.957477 + 0.288511i \(0.906840\pi\)
\(542\) 210.637 + 364.834i 0.388629 + 0.673125i
\(543\) −236.858 + 59.0195i −0.436203 + 0.108691i
\(544\) −113.876 + 197.240i −0.209332 + 0.362573i
\(545\) −143.806 + 429.732i −0.263864 + 0.788499i
\(546\) −217.361 + 417.381i −0.398097 + 0.764434i
\(547\) 2.30392i 0.00421191i −0.999998 0.00210596i \(-0.999330\pi\)
0.999998 0.00210596i \(-0.000670347\pi\)
\(548\) −10.8219 + 18.7440i −0.0197479 + 0.0342044i
\(549\) 16.1130 457.662i 0.0293497 0.833629i
\(550\) −51.8504 6.37070i −0.0942735 0.0115831i
\(551\) 1386.93 + 800.744i 2.51711 + 1.45326i
\(552\) −194.680 + 678.564i −0.352681 + 1.22928i
\(553\) −174.476 154.369i −0.315508 0.279148i
\(554\) 887.259i 1.60155i
\(555\) −2.66257 5.58483i −0.00479742 0.0100628i
\(556\) −50.6137 87.6656i −0.0910319 0.157672i
\(557\) 178.710 + 309.535i 0.320844 + 0.555718i 0.980662 0.195707i \(-0.0627003\pi\)
−0.659819 + 0.751425i \(0.729367\pi\)
\(558\) −493.313 + 262.118i −0.884074 + 0.469746i
\(559\) 98.2134 0.175695
\(560\) −0.0256154 + 430.319i −4.57417e−5 + 0.768427i
\(561\) 62.5183 + 17.9365i 0.111441 + 0.0319724i
\(562\) 104.279 + 60.2052i 0.185549 + 0.107127i
\(563\) 331.223 + 573.695i 0.588318 + 1.01900i 0.994453 + 0.105183i \(0.0335430\pi\)
−0.406135 + 0.913813i \(0.633124\pi\)
\(564\) −78.6324 + 19.5933i −0.139419 + 0.0347399i
\(565\) −252.631 285.571i −0.447135 0.505436i
\(566\) 245.758i 0.434202i
\(567\) 397.177 + 404.648i 0.700488 + 0.713665i
\(568\) 573.250i 1.00924i
\(569\) −286.622 165.481i −0.503729 0.290828i 0.226523 0.974006i \(-0.427264\pi\)
−0.730252 + 0.683178i \(0.760597\pi\)
\(570\) 64.4057 816.435i 0.112992 1.43234i
\(571\) 420.825 + 728.890i 0.736996 + 1.27651i 0.953842 + 0.300309i \(0.0970897\pi\)
−0.216846 + 0.976206i \(0.569577\pi\)
\(572\) −5.63375 + 9.75795i −0.00984922 + 0.0170593i
\(573\) −690.532 198.114i −1.20512 0.345748i
\(574\) 143.365 162.039i 0.249765 0.282298i
\(575\) 547.835 + 412.893i 0.952757 + 0.718075i
\(576\) 565.330 300.384i 0.981476 0.521500i
\(577\) −446.025 + 257.513i −0.773007 + 0.446296i −0.833946 0.551845i \(-0.813924\pi\)
0.0609390 + 0.998141i \(0.480590\pi\)
\(578\) 52.1317 + 90.2948i 0.0901933 + 0.156219i
\(579\) 3.46701 3.34710i 0.00598793 0.00578082i
\(580\) 193.748 + 64.8358i 0.334048 + 0.111786i
\(581\) 100.590 494.370i 0.173133 0.850895i
\(582\) −345.615 99.1571i −0.593841 0.170373i
\(583\) 36.0131 + 20.7922i 0.0617720 + 0.0356641i
\(584\) 401.075 231.561i 0.686773 0.396508i
\(585\) 196.847 525.967i 0.336490 0.899089i
\(586\) −88.8462 + 153.886i −0.151615 + 0.262604i
\(587\) 935.242 1.59326 0.796629 0.604469i \(-0.206615\pi\)
0.796629 + 0.604469i \(0.206615\pi\)
\(588\) 40.8509 + 106.478i 0.0694744 + 0.181085i
\(589\) 1051.08 1.78452
\(590\) 251.130 222.163i 0.425644 0.376548i
\(591\) 833.489 207.686i 1.41030 0.351414i
\(592\) 4.39183 2.53563i 0.00741863 0.00428315i
\(593\) 244.872 424.131i 0.412938 0.715229i −0.582272 0.812994i \(-0.697836\pi\)
0.995210 + 0.0977651i \(0.0311694\pi\)
\(594\) −37.7341 41.9441i −0.0635254 0.0706130i
\(595\) −564.664 326.054i −0.949015 0.547989i
\(596\) 123.204i 0.206718i
\(597\) 185.985 + 192.648i 0.311532 + 0.322693i
\(598\) −532.525 + 307.453i −0.890510 + 0.514136i
\(599\) 406.061 234.439i 0.677898 0.391384i −0.121165 0.992632i \(-0.538663\pi\)
0.799063 + 0.601248i \(0.205330\pi\)
\(600\) −78.2384 638.383i −0.130397 1.06397i
\(601\) 679.264 1.13022 0.565112 0.825014i \(-0.308833\pi\)
0.565112 + 0.825014i \(0.308833\pi\)
\(602\) −65.5452 + 74.0825i −0.108879 + 0.123061i
\(603\) 137.621 220.100i 0.228227 0.365008i
\(604\) −18.6499 + 32.3025i −0.0308773 + 0.0534810i
\(605\) −586.224 + 119.244i −0.968965 + 0.197097i
\(606\) 29.1068 + 116.812i 0.0480310 + 0.192759i
\(607\) 530.707 + 306.404i 0.874312 + 0.504784i 0.868779 0.495201i \(-0.164905\pi\)
0.00553303 + 0.999985i \(0.498239\pi\)
\(608\) −371.728 −0.611395
\(609\) −1105.01 + 48.0663i −1.81446 + 0.0789266i
\(610\) 144.971 433.214i 0.237657 0.710186i
\(611\) −376.307 217.261i −0.615887 0.355583i
\(612\) −4.57689 + 129.999i −0.00747857 + 0.212417i
\(613\) 173.001 99.8821i 0.282220 0.162940i −0.352208 0.935922i \(-0.614569\pi\)
0.634428 + 0.772982i \(0.281236\pi\)
\(614\) 686.284 + 396.226i 1.11773 + 0.645319i
\(615\) −146.284 + 212.761i −0.237861 + 0.345953i
\(616\) −22.1648 66.2478i −0.0359818 0.107545i
\(617\) 530.227 0.859363 0.429682 0.902980i \(-0.358626\pi\)
0.429682 + 0.902980i \(0.358626\pi\)
\(618\) 57.4983 55.5096i 0.0930393 0.0898213i
\(619\) −410.628 711.228i −0.663373 1.14900i −0.979724 0.200353i \(-0.935791\pi\)
0.316351 0.948642i \(-0.397542\pi\)
\(620\) 131.400 26.7281i 0.211936 0.0431099i
\(621\) 153.728 + 724.763i 0.247549 + 1.16709i
\(622\) 40.3023i 0.0647947i
\(623\) −222.194 + 251.135i −0.356651 + 0.403106i
\(624\) 442.465 + 126.943i 0.709079 + 0.203435i
\(625\) −606.410 151.300i −0.970256 0.242079i
\(626\) 390.555 225.487i 0.623889 0.360202i
\(627\) 25.6668 + 103.007i 0.0409359 + 0.164285i
\(628\) −87.5496 50.5468i −0.139410 0.0804885i
\(629\) 7.68420i 0.0122165i
\(630\) 265.367 + 499.499i 0.421218 + 0.792856i
\(631\) 314.044 0.497692 0.248846 0.968543i \(-0.419949\pi\)
0.248846 + 0.968543i \(0.419949\pi\)
\(632\) −142.697 + 247.159i −0.225787 + 0.391074i
\(633\) −507.110 + 126.360i −0.801121 + 0.199620i
\(634\) −31.3326 54.2697i −0.0494205 0.0855988i
\(635\) 2.14826 1.90046i 0.00338308 0.00299285i
\(636\) −22.9356 + 79.9427i −0.0360622 + 0.125696i
\(637\) −238.959 + 562.894i −0.375133 + 0.883664i
\(638\) 110.058 0.172505
\(639\) 282.296 + 531.288i 0.441778 + 0.831437i
\(640\) 386.201 78.5571i 0.603438 0.122745i
\(641\) −633.511 + 365.758i −0.988317 + 0.570605i −0.904771 0.425899i \(-0.859958\pi\)
−0.0835460 + 0.996504i \(0.526625\pi\)
\(642\) 127.177 + 131.734i 0.198096 + 0.205193i
\(643\) 326.029i 0.507044i 0.967330 + 0.253522i \(0.0815890\pi\)
−0.967330 + 0.253522i \(0.918411\pi\)
\(644\) −29.7127 + 146.028i −0.0461377 + 0.226752i
\(645\) 66.8797 97.2724i 0.103690 0.150810i
\(646\) −508.574 + 880.875i −0.787266 + 1.36358i
\(647\) −286.539 496.301i −0.442874 0.767080i 0.555028 0.831832i \(-0.312708\pi\)
−0.997901 + 0.0647521i \(0.979374\pi\)
\(648\) 388.752 575.638i 0.599925 0.888330i
\(649\) −21.7307 + 37.6387i −0.0334834 + 0.0579949i
\(650\) 337.187 447.387i 0.518749 0.688287i
\(651\) −612.298 + 389.938i −0.940550 + 0.598982i
\(652\) 108.505i 0.166418i
\(653\) −451.271 + 781.625i −0.691074 + 1.19698i 0.280412 + 0.959880i \(0.409529\pi\)
−0.971486 + 0.237096i \(0.923804\pi\)
\(654\) −473.727 + 118.041i −0.724353 + 0.180491i
\(655\) −229.796 1129.72i −0.350833 1.72476i
\(656\) −183.280 105.817i −0.279391 0.161306i
\(657\) 257.685 412.119i 0.392214 0.627275i
\(658\) 415.019 138.855i 0.630727 0.211025i
\(659\) 1144.56i 1.73681i −0.495855 0.868405i \(-0.665145\pi\)
0.495855 0.868405i \(-0.334855\pi\)
\(660\) 5.82807 + 12.2246i 0.00883041 + 0.0185221i
\(661\) −374.330 648.358i −0.566308 0.980875i −0.996927 0.0783407i \(-0.975038\pi\)
0.430618 0.902534i \(-0.358296\pi\)
\(662\) −244.220 423.002i −0.368913 0.638976i
\(663\) −501.802 + 484.446i −0.756866 + 0.730688i
\(664\) −618.046 −0.930792
\(665\) 0.0633499 1064.23i 9.52630e−5 1.60035i
\(666\) 3.53389 5.65181i 0.00530614 0.00848620i
\(667\) −1251.62 722.626i −1.87650 1.08340i
\(668\) 87.0544 + 150.783i 0.130321 + 0.225723i
\(669\) 108.219 + 434.309i 0.161763 + 0.649191i
\(670\) 193.948 171.577i 0.289475 0.256085i
\(671\) 59.2145i 0.0882481i
\(672\) 216.546 137.906i 0.322242 0.205217i
\(673\) 351.912i 0.522900i 0.965217 + 0.261450i \(0.0842007\pi\)
−0.965217 + 0.261450i \(0.915799\pi\)
\(674\) −933.834 539.149i −1.38551 0.799925i
\(675\) −386.882 553.125i −0.573158 0.819445i
\(676\) 5.14054 + 8.90367i 0.00760434 + 0.0131711i
\(677\) −284.770 + 493.237i −0.420636 + 0.728562i −0.996002 0.0893336i \(-0.971526\pi\)
0.575366 + 0.817896i \(0.304860\pi\)
\(678\) 113.281 394.846i 0.167082 0.582368i
\(679\) −457.854 93.1606i −0.674307 0.137203i
\(680\) −253.491 + 757.503i −0.372781 + 1.11397i
\(681\) 192.230 + 199.117i 0.282277 + 0.292390i
\(682\) 62.5556 36.1165i 0.0917238 0.0529567i
\(683\) −390.284 675.992i −0.571426 0.989740i −0.996420 0.0845432i \(-0.973057\pi\)
0.424993 0.905196i \(-0.360276\pi\)
\(684\) −187.487 + 99.6199i −0.274104 + 0.145643i
\(685\) −44.2661 + 132.280i −0.0646220 + 0.193109i
\(686\) −265.116 555.909i −0.386467 0.810363i
\(687\) 122.467 426.863i 0.178263 0.621343i
\(688\) 83.7939 + 48.3784i 0.121793 + 0.0703175i
\(689\) −386.203 + 222.974i −0.560527 + 0.323620i
\(690\) −58.1225 + 736.787i −0.0842355 + 1.06781i
\(691\) −237.246 + 410.922i −0.343337 + 0.594678i −0.985050 0.172267i \(-0.944891\pi\)
0.641713 + 0.766945i \(0.278224\pi\)
\(692\) 227.822 0.329223
\(693\) −53.1659 50.4834i −0.0767185 0.0728476i
\(694\) −276.599 −0.398557
\(695\) −432.268 488.630i −0.621968 0.703065i
\(696\) 327.612 + 1314.78i 0.470707 + 1.88906i
\(697\) 277.715 160.339i 0.398443 0.230041i
\(698\) −18.1647 + 31.4621i −0.0260239 + 0.0450747i
\(699\) 333.604 1162.79i 0.477259 1.66350i
\(700\) −27.0545 133.045i −0.0386493 0.190065i
\(701\) 319.674i 0.456025i −0.973658 0.228013i \(-0.926777\pi\)
0.973658 0.228013i \(-0.0732227\pi\)
\(702\) 591.873 125.541i 0.843125 0.178834i
\(703\) −10.8615 + 6.27091i −0.0154503 + 0.00892021i
\(704\) −71.6879 + 41.3890i −0.101829 + 0.0587912i
\(705\) −471.431 + 224.755i −0.668696 + 0.318801i
\(706\) 584.342 0.827679
\(707\) 49.6349 + 148.353i 0.0702050 + 0.209834i
\(708\) −83.5512 23.9709i −0.118010 0.0338571i
\(709\) 679.847 1177.53i 0.958882 1.66083i 0.233657 0.972319i \(-0.424931\pi\)
0.725225 0.688512i \(-0.241736\pi\)
\(710\) 119.629 + 588.116i 0.168491 + 0.828332i
\(711\) −10.5388 + 299.338i −0.0148225 + 0.421010i
\(712\) 355.753 + 205.394i 0.499653 + 0.288475i
\(713\) −948.544 −1.33036
\(714\) −30.5282 701.818i −0.0427566 0.982939i
\(715\) −23.0445 + 68.8634i −0.0322300 + 0.0963124i
\(716\) −164.027 94.7010i −0.229088 0.132264i
\(717\) −30.5493 122.601i −0.0426071 0.170992i
\(718\) 897.691 518.282i 1.25027 0.721842i
\(719\) −10.4725 6.04630i −0.0145654 0.00840932i 0.492700 0.870199i \(-0.336010\pi\)
−0.507265 + 0.861790i \(0.669343\pi\)
\(720\) 427.030 351.782i 0.593097 0.488586i
\(721\) 68.8180 77.7816i 0.0954480 0.107880i
\(722\) −1011.93 −1.40157
\(723\) 554.945 + 574.827i 0.767559 + 0.795059i
\(724\) 31.5630 + 54.6687i 0.0435953 + 0.0755092i
\(725\) 1306.90 + 160.575i 1.80262 + 0.221482i
\(726\) −447.646 463.684i −0.616593 0.638683i
\(727\) 806.023i 1.10870i −0.832284 0.554349i \(-0.812967\pi\)
0.832284 0.554349i \(-0.187033\pi\)
\(728\) 734.105 + 149.370i 1.00839 + 0.205178i
\(729\) 76.8232 724.941i 0.105382 0.994432i
\(730\) 363.153 321.264i 0.497469 0.440088i
\(731\) −126.968 + 73.3053i −0.173692 + 0.100281i
\(732\) −114.914 + 28.6338i −0.156986 + 0.0391172i
\(733\) 229.808 + 132.680i 0.313517 + 0.181009i 0.648499 0.761215i \(-0.275397\pi\)
−0.334982 + 0.942224i \(0.608730\pi\)
\(734\) 903.452i 1.23086i
\(735\) 394.778 + 619.980i 0.537113 + 0.843510i
\(736\) 335.464 0.455793
\(737\) −16.7827 + 29.0684i −0.0227716 + 0.0394415i
\(738\) −278.001 9.78760i −0.376695 0.0132623i
\(739\) 288.214 + 499.201i 0.390005 + 0.675509i 0.992450 0.122652i \(-0.0391398\pi\)
−0.602444 + 0.798161i \(0.705807\pi\)
\(740\) −1.19838 + 1.06015i −0.00161943 + 0.00143263i
\(741\) −1094.27 313.946i −1.47675 0.423679i
\(742\) 89.5524 440.121i 0.120691 0.593155i
\(743\) −142.356 −0.191596 −0.0957979 0.995401i \(-0.530540\pi\)
−0.0957979 + 0.995401i \(0.530540\pi\)
\(744\) 617.668 + 639.797i 0.830200 + 0.859943i
\(745\) 158.271 + 778.090i 0.212445 + 1.04442i
\(746\) 333.498 192.545i 0.447049 0.258104i
\(747\) −572.805 + 304.356i −0.766807 + 0.407437i
\(748\) 16.8199i 0.0224864i
\(749\) 178.205 + 157.668i 0.237924 + 0.210505i
\(750\) −213.488 638.610i −0.284651 0.851481i
\(751\) −39.6817 + 68.7308i −0.0528385 + 0.0915190i −0.891235 0.453542i \(-0.850160\pi\)
0.838396 + 0.545061i \(0.183494\pi\)
\(752\) −214.039 370.726i −0.284626 0.492987i
\(753\) 309.653 + 1242.71i 0.411226 + 1.65034i
\(754\) −590.129 + 1022.13i −0.782664 + 1.35561i
\(755\) −76.2860 + 227.964i −0.101041 + 0.301939i
\(756\) 72.2611 127.588i 0.0955834 0.168767i
\(757\) 1310.05i 1.73058i 0.501268 + 0.865292i \(0.332867\pi\)
−0.501268 + 0.865292i \(0.667133\pi\)
\(758\) −453.714 + 785.855i −0.598567 + 1.03675i
\(759\) −23.1628 92.9576i −0.0305176 0.122474i
\(760\) −1277.59 + 259.875i −1.68104 + 0.341941i
\(761\) −363.973 210.140i −0.478283 0.276137i 0.241418 0.970421i \(-0.422388\pi\)
−0.719701 + 0.694284i \(0.755721\pi\)
\(762\) 2.97029 + 0.852177i 0.00389802 + 0.00111834i
\(763\) −601.637 + 201.292i −0.788515 + 0.263817i
\(764\) 185.780i 0.243167i
\(765\) 138.095 +