Properties

Label 105.3.k.d.62.3
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 32
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.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 62.3
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28094 + 2.28094i) q^{2} +(-1.07458 + 2.80094i) q^{3} -6.40541i q^{4} +(1.80941 - 4.66112i) q^{5} +(-3.93772 - 8.83986i) q^{6} +(-6.22100 - 3.20922i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +O(q^{10})\) \(q+(-2.28094 + 2.28094i) q^{2} +(-1.07458 + 2.80094i) q^{3} -6.40541i q^{4} +(1.80941 - 4.66112i) q^{5} +(-3.93772 - 8.83986i) q^{6} +(-6.22100 - 3.20922i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +(6.50460 + 14.7589i) q^{10} -11.1704i q^{11} +(17.9412 + 6.88316i) q^{12} +(5.82807 + 5.82807i) q^{13} +(21.5098 - 6.86971i) q^{14} +(11.1112 + 10.0768i) q^{15} +0.592330 q^{16} +(6.84147 + 6.84147i) q^{17} +(28.9913 - 1.53016i) q^{18} -25.0261 q^{19} +(-29.8564 - 11.5900i) q^{20} +(15.6738 - 13.9761i) q^{21} +(25.4792 + 25.4792i) q^{22} +(-23.3593 - 23.3593i) q^{23} +(-21.2635 + 9.47185i) q^{24} +(-18.4521 - 16.8677i) q^{25} -26.5870 q^{26} +(24.0503 - 12.2711i) q^{27} +(-20.5564 + 39.8481i) q^{28} +10.6354 q^{29} +(-48.3286 + 2.35930i) q^{30} -26.9470i q^{31} +(-23.2975 + 23.2975i) q^{32} +(31.2877 + 12.0036i) q^{33} -31.2100 q^{34} +(-26.2149 + 23.1901i) q^{35} +(-38.5586 + 42.8557i) q^{36} +(-20.8846 - 20.8846i) q^{37} +(57.0831 - 57.0831i) q^{38} +(-22.5868 + 10.0613i) q^{39} +(35.5013 - 15.6462i) q^{40} +32.9644 q^{41} +(-3.87246 + 67.6298i) q^{42} +(1.25060 - 1.25060i) q^{43} -71.5513 q^{44} +(-40.1644 + 20.2933i) q^{45} +106.562 q^{46} +(-59.1134 - 59.1134i) q^{47} +(-0.636508 + 1.65908i) q^{48} +(28.4018 + 39.9292i) q^{49} +(80.5625 - 3.61381i) q^{50} +(-26.5143 + 11.8108i) q^{51} +(37.3312 - 37.3312i) q^{52} +(26.0484 + 26.0484i) q^{53} +(-26.8677 + 82.8473i) q^{54} +(-52.0668 - 20.2119i) q^{55} +(-16.5245 - 51.7400i) q^{56} +(26.8926 - 70.0965i) q^{57} +(-24.2588 + 24.2588i) q^{58} +70.2066i q^{59} +(64.5461 - 71.1716i) q^{60} -14.1716i q^{61} +(61.4646 + 61.4646i) q^{62} +(22.3033 + 58.9200i) q^{63} -103.911i q^{64} +(37.7107 - 16.6200i) q^{65} +(-98.7451 + 43.9861i) q^{66} +(-6.14458 - 6.14458i) q^{67} +(43.8225 - 43.8225i) q^{68} +(90.5294 - 40.3264i) q^{69} +(6.89950 - 112.690i) q^{70} -39.0498i q^{71} +(-3.68068 - 69.7361i) q^{72} +(-51.1141 - 51.1141i) q^{73} +95.2731 q^{74} +(67.0738 - 33.5574i) q^{75} +160.302i q^{76} +(-35.8484 + 69.4914i) q^{77} +(28.5700 - 74.4687i) q^{78} +16.8398i q^{79} +(1.07177 - 2.76092i) q^{80} +(8.52661 + 80.5500i) q^{81} +(-75.1900 + 75.1900i) q^{82} +(-31.3367 + 31.3367i) q^{83} +(-89.5226 - 100.397i) q^{84} +(44.2679 - 19.5099i) q^{85} +5.70508i q^{86} +(-11.4286 + 29.7891i) q^{87} +(61.2879 - 61.2879i) q^{88} +70.8895i q^{89} +(45.3249 - 137.901i) q^{90} +(-17.5529 - 54.9600i) q^{91} +(-149.626 + 149.626i) q^{92} +(75.4769 + 28.9568i) q^{93} +269.669 q^{94} +(-45.2824 + 116.650i) q^{95} +(-40.2198 - 90.2902i) q^{96} +(-114.216 + 114.216i) q^{97} +(-155.859 - 26.2933i) q^{98} +(-67.2426 + 74.7363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28094 + 2.28094i −1.14047 + 1.14047i −0.152108 + 0.988364i \(0.548606\pi\)
−0.988364 + 0.152108i \(0.951394\pi\)
\(3\) −1.07458 + 2.80094i −0.358195 + 0.933647i
\(4\) 6.40541i 1.60135i
\(5\) 1.80941 4.66112i 0.361882 0.932224i
\(6\) −3.93772 8.83986i −0.656287 1.47331i
\(7\) −6.22100 3.20922i −0.888715 0.458460i
\(8\) 5.48661 + 5.48661i 0.685827 + 0.685827i
\(9\) −6.69054 6.01969i −0.743393 0.668855i
\(10\) 6.50460 + 14.7589i 0.650460 + 1.47589i
\(11\) 11.1704i 1.01549i −0.861506 0.507747i \(-0.830478\pi\)
0.861506 0.507747i \(-0.169522\pi\)
\(12\) 17.9412 + 6.88316i 1.49510 + 0.573596i
\(13\) 5.82807 + 5.82807i 0.448313 + 0.448313i 0.894794 0.446480i \(-0.147323\pi\)
−0.446480 + 0.894794i \(0.647323\pi\)
\(14\) 21.5098 6.86971i 1.53642 0.490694i
\(15\) 11.1112 + 10.0768i 0.740744 + 0.671787i
\(16\) 0.592330 0.0370206
\(17\) 6.84147 + 6.84147i 0.402440 + 0.402440i 0.879092 0.476652i \(-0.158150\pi\)
−0.476652 + 0.879092i \(0.658150\pi\)
\(18\) 28.9913 1.53016i 1.61063 0.0850091i
\(19\) −25.0261 −1.31716 −0.658581 0.752510i \(-0.728843\pi\)
−0.658581 + 0.752510i \(0.728843\pi\)
\(20\) −29.8564 11.5900i −1.49282 0.579500i
\(21\) 15.6738 13.9761i 0.746373 0.665528i
\(22\) 25.4792 + 25.4792i 1.15814 + 1.15814i
\(23\) −23.3593 23.3593i −1.01562 1.01562i −0.999876 0.0157445i \(-0.994988\pi\)
−0.0157445 0.999876i \(-0.505012\pi\)
\(24\) −21.2635 + 9.47185i −0.885980 + 0.394661i
\(25\) −18.4521 16.8677i −0.738083 0.674710i
\(26\) −26.5870 −1.02258
\(27\) 24.0503 12.2711i 0.890754 0.454487i
\(28\) −20.5564 + 39.8481i −0.734157 + 1.42315i
\(29\) 10.6354 0.366738 0.183369 0.983044i \(-0.441300\pi\)
0.183369 + 0.983044i \(0.441300\pi\)
\(30\) −48.3286 + 2.35930i −1.61095 + 0.0786432i
\(31\) 26.9470i 0.869257i −0.900610 0.434629i \(-0.856880\pi\)
0.900610 0.434629i \(-0.143120\pi\)
\(32\) −23.2975 + 23.2975i −0.728048 + 0.728048i
\(33\) 31.2877 + 12.0036i 0.948113 + 0.363745i
\(34\) −31.2100 −0.917942
\(35\) −26.2149 + 23.1901i −0.748997 + 0.662573i
\(36\) −38.5586 + 42.8557i −1.07107 + 1.19044i
\(37\) −20.8846 20.8846i −0.564448 0.564448i 0.366120 0.930568i \(-0.380686\pi\)
−0.930568 + 0.366120i \(0.880686\pi\)
\(38\) 57.0831 57.0831i 1.50219 1.50219i
\(39\) −22.5868 + 10.0613i −0.579150 + 0.257983i
\(40\) 35.5013 15.6462i 0.887532 0.391156i
\(41\) 32.9644 0.804010 0.402005 0.915637i \(-0.368313\pi\)
0.402005 + 0.915637i \(0.368313\pi\)
\(42\) −3.87246 + 67.6298i −0.0922014 + 1.61023i
\(43\) 1.25060 1.25060i 0.0290836 0.0290836i −0.692415 0.721499i \(-0.743453\pi\)
0.721499 + 0.692415i \(0.243453\pi\)
\(44\) −71.5513 −1.62617
\(45\) −40.1644 + 20.2933i −0.892543 + 0.450963i
\(46\) 106.562 2.31657
\(47\) −59.1134 59.1134i −1.25773 1.25773i −0.952173 0.305558i \(-0.901157\pi\)
−0.305558 0.952173i \(-0.598843\pi\)
\(48\) −0.636508 + 1.65908i −0.0132606 + 0.0345642i
\(49\) 28.4018 + 39.9292i 0.579629 + 0.814881i
\(50\) 80.5625 3.61381i 1.61125 0.0722761i
\(51\) −26.5143 + 11.8108i −0.519888 + 0.231585i
\(52\) 37.3312 37.3312i 0.717908 0.717908i
\(53\) 26.0484 + 26.0484i 0.491478 + 0.491478i 0.908772 0.417293i \(-0.137021\pi\)
−0.417293 + 0.908772i \(0.637021\pi\)
\(54\) −26.8677 + 82.8473i −0.497550 + 1.53421i
\(55\) −52.0668 20.2119i −0.946669 0.367489i
\(56\) −16.5245 51.7400i −0.295080 0.923929i
\(57\) 26.8926 70.0965i 0.471800 1.22976i
\(58\) −24.2588 + 24.2588i −0.418254 + 0.418254i
\(59\) 70.2066i 1.18994i 0.803747 + 0.594971i \(0.202837\pi\)
−0.803747 + 0.594971i \(0.797163\pi\)
\(60\) 64.5461 71.1716i 1.07577 1.18619i
\(61\) 14.1716i 0.232321i −0.993230 0.116161i \(-0.962941\pi\)
0.993230 0.116161i \(-0.0370587\pi\)
\(62\) 61.4646 + 61.4646i 0.991364 + 0.991364i
\(63\) 22.3033 + 58.9200i 0.354021 + 0.935237i
\(64\) 103.911i 1.62362i
\(65\) 37.7107 16.6200i 0.580165 0.255692i
\(66\) −98.7451 + 43.9861i −1.49614 + 0.666456i
\(67\) −6.14458 6.14458i −0.0917101 0.0917101i 0.659763 0.751473i \(-0.270657\pi\)
−0.751473 + 0.659763i \(0.770657\pi\)
\(68\) 43.8225 43.8225i 0.644448 0.644448i
\(69\) 90.5294 40.3264i 1.31202 0.584441i
\(70\) 6.89950 112.690i 0.0985643 1.60986i
\(71\) 39.0498i 0.549997i −0.961445 0.274999i \(-0.911323\pi\)
0.961445 0.274999i \(-0.0886774\pi\)
\(72\) −3.68068 69.7361i −0.0511205 0.968557i
\(73\) −51.1141 51.1141i −0.700193 0.700193i 0.264259 0.964452i \(-0.414873\pi\)
−0.964452 + 0.264259i \(0.914873\pi\)
\(74\) 95.2731 1.28747
\(75\) 67.0738 33.5574i 0.894318 0.447432i
\(76\) 160.302i 2.10924i
\(77\) −35.8484 + 69.4914i −0.465564 + 0.902485i
\(78\) 28.5700 74.4687i 0.366282 0.954726i
\(79\) 16.8398i 0.213162i 0.994304 + 0.106581i \(0.0339903\pi\)
−0.994304 + 0.106581i \(0.966010\pi\)
\(80\) 1.07177 2.76092i 0.0133971 0.0345115i
\(81\) 8.52661 + 80.5500i 0.105267 + 0.994444i
\(82\) −75.1900 + 75.1900i −0.916951 + 0.916951i
\(83\) −31.3367 + 31.3367i −0.377551 + 0.377551i −0.870218 0.492667i \(-0.836022\pi\)
0.492667 + 0.870218i \(0.336022\pi\)
\(84\) −89.5226 100.397i −1.06575 1.19521i
\(85\) 44.2679 19.5099i 0.520799 0.229528i
\(86\) 5.70508i 0.0663381i
\(87\) −11.4286 + 29.7891i −0.131364 + 0.342404i
\(88\) 61.2879 61.2879i 0.696453 0.696453i
\(89\) 70.8895i 0.796511i 0.917274 + 0.398256i \(0.130384\pi\)
−0.917274 + 0.398256i \(0.869616\pi\)
\(90\) 45.3249 137.901i 0.503610 1.53223i
\(91\) −17.5529 54.9600i −0.192889 0.603957i
\(92\) −149.626 + 149.626i −1.62637 + 1.62637i
\(93\) 75.4769 + 28.9568i 0.811579 + 0.311363i
\(94\) 269.669 2.86882
\(95\) −45.2824 + 116.650i −0.476657 + 1.22789i
\(96\) −40.2198 90.2902i −0.418957 0.940522i
\(97\) −114.216 + 114.216i −1.17748 + 1.17748i −0.197101 + 0.980383i \(0.563153\pi\)
−0.980383 + 0.197101i \(0.936847\pi\)
\(98\) −155.859 26.2933i −1.59040 0.268299i
\(99\) −67.2426 + 74.7363i −0.679218 + 0.754912i
\(100\) −108.045 + 118.193i −1.08045 + 1.18193i
\(101\) −54.9464 −0.544024 −0.272012 0.962294i \(-0.587689\pi\)
−0.272012 + 0.962294i \(0.587689\pi\)
\(102\) 33.5378 87.4175i 0.328802 0.857034i
\(103\) 109.306 + 109.306i 1.06123 + 1.06123i 0.997999 + 0.0632258i \(0.0201388\pi\)
0.0632258 + 0.997999i \(0.479861\pi\)
\(104\) 63.9528i 0.614931i
\(105\) −36.7839 98.3461i −0.350323 0.936629i
\(106\) −118.830 −1.12103
\(107\) 89.1318 89.1318i 0.833007 0.833007i −0.154920 0.987927i \(-0.549512\pi\)
0.987927 + 0.154920i \(0.0495120\pi\)
\(108\) −78.6017 154.052i −0.727794 1.42641i
\(109\) 91.2226i 0.836904i −0.908239 0.418452i \(-0.862573\pi\)
0.908239 0.418452i \(-0.137427\pi\)
\(110\) 164.864 72.6592i 1.49876 0.660538i
\(111\) 80.9387 36.0542i 0.729177 0.324813i
\(112\) −3.68489 1.90092i −0.0329008 0.0169725i
\(113\) −98.3921 98.3921i −0.870726 0.870726i 0.121825 0.992552i \(-0.461125\pi\)
−0.992552 + 0.121825i \(0.961125\pi\)
\(114\) 98.5457 + 221.227i 0.864436 + 1.94059i
\(115\) −151.147 + 66.6139i −1.31432 + 0.579251i
\(116\) 68.1242i 0.587277i
\(117\) −3.90974 74.0762i −0.0334166 0.633129i
\(118\) −160.137 160.137i −1.35710 1.35710i
\(119\) −20.6050 64.5166i −0.173152 0.542157i
\(120\) 5.67508 + 116.250i 0.0472924 + 0.968752i
\(121\) −3.77875 −0.0312293
\(122\) 32.3246 + 32.3246i 0.264956 + 0.264956i
\(123\) −35.4230 + 92.3314i −0.287992 + 0.750661i
\(124\) −172.607 −1.39199
\(125\) −112.010 + 55.4868i −0.896079 + 0.443894i
\(126\) −185.266 83.5204i −1.47036 0.662861i
\(127\) 172.312 + 172.312i 1.35679 + 1.35679i 0.877843 + 0.478948i \(0.158982\pi\)
0.478948 + 0.877843i \(0.341018\pi\)
\(128\) 143.826 + 143.826i 1.12364 + 1.12364i
\(129\) 2.15897 + 4.84672i 0.0167362 + 0.0375714i
\(130\) −48.1068 + 123.925i −0.370052 + 0.953271i
\(131\) 71.6542 0.546979 0.273489 0.961875i \(-0.411822\pi\)
0.273489 + 0.961875i \(0.411822\pi\)
\(132\) 76.8879 200.411i 0.582484 1.51826i
\(133\) 155.687 + 80.3142i 1.17058 + 0.603866i
\(134\) 28.0309 0.209186
\(135\) −13.6804 134.305i −0.101336 0.994852i
\(136\) 75.0730i 0.552008i
\(137\) 57.1182 57.1182i 0.416921 0.416921i −0.467220 0.884141i \(-0.654744\pi\)
0.884141 + 0.467220i \(0.154744\pi\)
\(138\) −114.510 + 298.475i −0.829784 + 2.16286i
\(139\) 41.4536 0.298227 0.149113 0.988820i \(-0.452358\pi\)
0.149113 + 0.988820i \(0.452358\pi\)
\(140\) 148.542 + 167.917i 1.06101 + 1.19941i
\(141\) 229.095 102.051i 1.62479 0.723765i
\(142\) 89.0704 + 89.0704i 0.627256 + 0.627256i
\(143\) 65.1021 65.1021i 0.455260 0.455260i
\(144\) −3.96301 3.56564i −0.0275209 0.0247614i
\(145\) 19.2438 49.5729i 0.132716 0.341882i
\(146\) 233.177 1.59710
\(147\) −142.359 + 36.6445i −0.968431 + 0.249282i
\(148\) −133.774 + 133.774i −0.903880 + 0.903880i
\(149\) 62.9077 0.422199 0.211100 0.977465i \(-0.432296\pi\)
0.211100 + 0.977465i \(0.432296\pi\)
\(150\) −76.4492 + 229.534i −0.509661 + 1.53023i
\(151\) −20.6412 −0.136697 −0.0683484 0.997662i \(-0.521773\pi\)
−0.0683484 + 0.997662i \(0.521773\pi\)
\(152\) −137.308 137.308i −0.903345 0.903345i
\(153\) −4.58958 86.9567i −0.0299972 0.568344i
\(154\) −76.7377 240.274i −0.498297 1.56022i
\(155\) −125.603 48.7581i −0.810343 0.314568i
\(156\) 64.4470 + 144.678i 0.413122 + 0.927423i
\(157\) 213.253 213.253i 1.35830 1.35830i 0.482284 0.876015i \(-0.339807\pi\)
0.876015 0.482284i \(-0.160193\pi\)
\(158\) −38.4106 38.4106i −0.243105 0.243105i
\(159\) −100.951 + 44.9687i −0.634912 + 0.282822i
\(160\) 66.4378 + 150.747i 0.415237 + 0.942171i
\(161\) 70.3531 + 220.283i 0.436976 + 1.36822i
\(162\) −203.179 164.281i −1.25419 1.01408i
\(163\) −19.5250 + 19.5250i −0.119785 + 0.119785i −0.764458 0.644673i \(-0.776993\pi\)
0.644673 + 0.764458i \(0.276993\pi\)
\(164\) 211.151i 1.28750i
\(165\) 112.562 124.117i 0.682196 0.752222i
\(166\) 142.955i 0.861173i
\(167\) −151.924 151.924i −0.909725 0.909725i 0.0865247 0.996250i \(-0.472424\pi\)
−0.996250 + 0.0865247i \(0.972424\pi\)
\(168\) 162.678 + 9.31486i 0.968320 + 0.0554456i
\(169\) 101.067i 0.598030i
\(170\) −56.4717 + 145.474i −0.332186 + 0.855728i
\(171\) 167.438 + 150.649i 0.979169 + 0.880990i
\(172\) −8.01059 8.01059i −0.0465732 0.0465732i
\(173\) −19.8589 + 19.8589i −0.114791 + 0.114791i −0.762169 0.647378i \(-0.775866\pi\)
0.647378 + 0.762169i \(0.275866\pi\)
\(174\) −41.8793 94.0154i −0.240685 0.540319i
\(175\) 60.6582 + 164.151i 0.346618 + 0.938006i
\(176\) 6.61658i 0.0375942i
\(177\) −196.645 75.4429i −1.11099 0.426231i
\(178\) −161.695 161.695i −0.908399 0.908399i
\(179\) −157.790 −0.881508 −0.440754 0.897628i \(-0.645289\pi\)
−0.440754 + 0.897628i \(0.645289\pi\)
\(180\) 129.987 + 257.270i 0.722151 + 1.42928i
\(181\) 58.8019i 0.324872i −0.986719 0.162436i \(-0.948065\pi\)
0.986719 0.162436i \(-0.0519351\pi\)
\(182\) 165.398 + 85.3236i 0.908780 + 0.468811i
\(183\) 39.6938 + 15.2286i 0.216906 + 0.0832162i
\(184\) 256.327i 1.39308i
\(185\) −135.134 + 59.5568i −0.730455 + 0.321928i
\(186\) −238.207 + 106.110i −1.28068 + 0.570483i
\(187\) 76.4223 76.4223i 0.408675 0.408675i
\(188\) −378.646 + 378.646i −2.01407 + 2.01407i
\(189\) −188.998 0.844085i −0.999990 0.00446606i
\(190\) −162.784 369.358i −0.856760 1.94399i
\(191\) 8.99622i 0.0471007i 0.999723 + 0.0235503i \(0.00749699\pi\)
−0.999723 + 0.0235503i \(0.992503\pi\)
\(192\) 291.050 + 111.662i 1.51588 + 0.581571i
\(193\) 96.1055 96.1055i 0.497956 0.497956i −0.412845 0.910801i \(-0.635465\pi\)
0.910801 + 0.412845i \(0.135465\pi\)
\(194\) 521.041i 2.68578i
\(195\) 6.02827 + 123.485i 0.0309142 + 0.633257i
\(196\) 255.763 181.925i 1.30491 0.928190i
\(197\) 113.154 113.154i 0.574386 0.574386i −0.358965 0.933351i \(-0.616870\pi\)
0.933351 + 0.358965i \(0.116870\pi\)
\(198\) −17.0926 323.846i −0.0863262 1.63559i
\(199\) 122.026 0.613196 0.306598 0.951839i \(-0.400809\pi\)
0.306598 + 0.951839i \(0.400809\pi\)
\(200\) −8.69270 193.786i −0.0434635 0.968931i
\(201\) 23.8135 10.6077i 0.118475 0.0527748i
\(202\) 125.330 125.330i 0.620444 0.620444i
\(203\) −66.1629 34.1314i −0.325926 0.168135i
\(204\) 75.6532 + 169.835i 0.370849 + 0.832525i
\(205\) 59.6461 153.651i 0.290956 0.749517i
\(206\) −498.643 −2.42060
\(207\) 15.6705 + 296.902i 0.0757028 + 1.43431i
\(208\) 3.45214 + 3.45214i 0.0165968 + 0.0165968i
\(209\) 279.552i 1.33757i
\(210\) 308.224 + 140.420i 1.46773 + 0.668666i
\(211\) −4.27938 −0.0202814 −0.0101407 0.999949i \(-0.503228\pi\)
−0.0101407 + 0.999949i \(0.503228\pi\)
\(212\) 166.850 166.850i 0.787031 0.787031i
\(213\) 109.376 + 41.9623i 0.513503 + 0.197006i
\(214\) 406.609i 1.90004i
\(215\) −3.56634 8.09202i −0.0165876 0.0376373i
\(216\) 199.282 + 64.6280i 0.922602 + 0.299204i
\(217\) −86.4788 + 167.637i −0.398520 + 0.772522i
\(218\) 208.074 + 208.074i 0.954466 + 0.954466i
\(219\) 198.094 88.2411i 0.904538 0.402928i
\(220\) −129.465 + 333.509i −0.588480 + 1.51595i
\(221\) 79.7452i 0.360838i
\(222\) −102.379 + 266.854i −0.461166 + 1.20205i
\(223\) −34.9829 34.9829i −0.156874 0.156874i 0.624306 0.781180i \(-0.285382\pi\)
−0.781180 + 0.624306i \(0.785382\pi\)
\(224\) 219.701 70.1671i 0.980808 0.313246i
\(225\) 21.9158 + 223.930i 0.0974035 + 0.995245i
\(226\) 448.854 1.98608
\(227\) 23.2602 + 23.2602i 0.102468 + 0.102468i 0.756482 0.654014i \(-0.226916\pi\)
−0.654014 + 0.756482i \(0.726916\pi\)
\(228\) −448.997 172.258i −1.96929 0.755519i
\(229\) −91.1105 −0.397862 −0.198931 0.980013i \(-0.563747\pi\)
−0.198931 + 0.980013i \(0.563747\pi\)
\(230\) 192.815 496.700i 0.838326 2.15957i
\(231\) −156.119 175.084i −0.675840 0.757938i
\(232\) 58.3524 + 58.3524i 0.251519 + 0.251519i
\(233\) −90.6015 90.6015i −0.388847 0.388847i 0.485429 0.874276i \(-0.338664\pi\)
−0.874276 + 0.485429i \(0.838664\pi\)
\(234\) 177.881 + 160.046i 0.760177 + 0.683956i
\(235\) −382.495 + 168.574i −1.62764 + 0.717338i
\(236\) 449.702 1.90552
\(237\) −47.1673 18.0958i −0.199018 0.0763535i
\(238\) 194.158 + 100.160i 0.815789 + 0.420840i
\(239\) 406.988 1.70288 0.851439 0.524454i \(-0.175731\pi\)
0.851439 + 0.524454i \(0.175731\pi\)
\(240\) 6.58147 + 5.96879i 0.0274228 + 0.0248700i
\(241\) 117.108i 0.485924i 0.970036 + 0.242962i \(0.0781191\pi\)
−0.970036 + 0.242962i \(0.921881\pi\)
\(242\) 8.61911 8.61911i 0.0356161 0.0356161i
\(243\) −234.778 62.6752i −0.966166 0.257923i
\(244\) −90.7749 −0.372028
\(245\) 237.505 60.1360i 0.969408 0.245453i
\(246\) −129.805 291.401i −0.527662 1.18456i
\(247\) −145.854 145.854i −0.590501 0.590501i
\(248\) 147.848 147.848i 0.596160 0.596160i
\(249\) −54.0984 121.446i −0.217263 0.487736i
\(250\) 128.926 382.051i 0.515705 1.52820i
\(251\) −127.808 −0.509195 −0.254597 0.967047i \(-0.581943\pi\)
−0.254597 + 0.967047i \(0.581943\pi\)
\(252\) 377.407 142.862i 1.49765 0.566913i
\(253\) −260.933 + 260.933i −1.03136 + 1.03136i
\(254\) −786.070 −3.09477
\(255\) 7.07648 + 144.957i 0.0277509 + 0.568459i
\(256\) −240.473 −0.939346
\(257\) 100.099 + 100.099i 0.389491 + 0.389491i 0.874506 0.485015i \(-0.161186\pi\)
−0.485015 + 0.874506i \(0.661186\pi\)
\(258\) −15.9796 6.13059i −0.0619364 0.0237620i
\(259\) 62.8998 + 196.946i 0.242856 + 0.760410i
\(260\) −106.458 241.553i −0.409453 0.929049i
\(261\) −71.1566 64.0218i −0.272631 0.245294i
\(262\) −163.439 + 163.439i −0.623814 + 0.623814i
\(263\) 96.5525 + 96.5525i 0.367120 + 0.367120i 0.866426 0.499306i \(-0.166412\pi\)
−0.499306 + 0.866426i \(0.666412\pi\)
\(264\) 105.805 + 237.523i 0.400776 + 0.899708i
\(265\) 168.547 74.2824i 0.636025 0.280311i
\(266\) −538.306 + 171.922i −2.02371 + 0.646323i
\(267\) −198.557 76.1767i −0.743660 0.285306i
\(268\) −39.3586 + 39.3586i −0.146860 + 0.146860i
\(269\) 213.738i 0.794565i −0.917696 0.397282i \(-0.869953\pi\)
0.917696 0.397282i \(-0.130047\pi\)
\(270\) 337.546 + 275.138i 1.25017 + 1.01903i
\(271\) 525.042i 1.93743i 0.248184 + 0.968713i \(0.420166\pi\)
−0.248184 + 0.968713i \(0.579834\pi\)
\(272\) 4.05241 + 4.05241i 0.0148986 + 0.0148986i
\(273\) 172.802 + 9.89457i 0.632974 + 0.0362439i
\(274\) 260.567i 0.950974i
\(275\) −188.420 + 206.118i −0.685164 + 0.749520i
\(276\) −258.308 579.879i −0.935897 2.10101i
\(277\) −122.242 122.242i −0.441307 0.441307i 0.451144 0.892451i \(-0.351016\pi\)
−0.892451 + 0.451144i \(0.851016\pi\)
\(278\) −94.5532 + 94.5532i −0.340120 + 0.340120i
\(279\) −162.213 + 180.290i −0.581407 + 0.646200i
\(280\) −271.066 16.5962i −0.968093 0.0592720i
\(281\) 262.680i 0.934803i 0.884045 + 0.467401i \(0.154810\pi\)
−0.884045 + 0.467401i \(0.845190\pi\)
\(282\) −289.782 + 755.326i −1.02759 + 2.67846i
\(283\) −266.792 266.792i −0.942728 0.942728i 0.0557189 0.998446i \(-0.482255\pi\)
−0.998446 + 0.0557189i \(0.982255\pi\)
\(284\) −250.130 −0.880740
\(285\) −278.069 252.183i −0.975680 0.884852i
\(286\) 296.989i 1.03842i
\(287\) −205.072 105.790i −0.714536 0.368607i
\(288\) 296.117 15.6291i 1.02818 0.0542676i
\(289\) 195.389i 0.676085i
\(290\) 69.1790 + 156.967i 0.238548 + 0.541266i
\(291\) −197.178 442.647i −0.677586 1.52112i
\(292\) −327.407 + 327.407i −1.12126 + 1.12126i
\(293\) 284.626 284.626i 0.971421 0.971421i −0.0281818 0.999603i \(-0.508972\pi\)
0.999603 + 0.0281818i \(0.00897172\pi\)
\(294\) 241.130 408.298i 0.820169 1.38877i
\(295\) 327.241 + 127.032i 1.10929 + 0.430618i
\(296\) 229.171i 0.774227i
\(297\) −137.074 268.653i −0.461529 0.904555i
\(298\) −143.489 + 143.489i −0.481507 + 0.481507i
\(299\) 272.279i 0.910632i
\(300\) −214.949 429.636i −0.716497 1.43212i
\(301\) −11.7934 + 3.76652i −0.0391807 + 0.0125134i
\(302\) 47.0815 47.0815i 0.155899 0.155899i
\(303\) 59.0445 153.902i 0.194867 0.507926i
\(304\) −14.8237 −0.0487621
\(305\) −66.0555 25.6422i −0.216575 0.0840727i
\(306\) 208.812 + 187.875i 0.682392 + 0.613970i
\(307\) 250.714 250.714i 0.816657 0.816657i −0.168965 0.985622i \(-0.554042\pi\)
0.985622 + 0.168965i \(0.0540424\pi\)
\(308\) 445.121 + 229.624i 1.44520 + 0.745532i
\(309\) −423.619 + 188.701i −1.37093 + 0.610684i
\(310\) 397.708 175.279i 1.28293 0.565417i
\(311\) 296.319 0.952794 0.476397 0.879230i \(-0.341943\pi\)
0.476397 + 0.879230i \(0.341943\pi\)
\(312\) −179.128 68.7226i −0.574128 0.220265i
\(313\) 195.491 + 195.491i 0.624573 + 0.624573i 0.946697 0.322124i \(-0.104397\pi\)
−0.322124 + 0.946697i \(0.604397\pi\)
\(314\) 972.836i 3.09820i
\(315\) 314.989 + 2.65166i 0.999965 + 0.00841798i
\(316\) 107.866 0.341348
\(317\) 43.8360 43.8360i 0.138284 0.138284i −0.634576 0.772860i \(-0.718825\pi\)
0.772860 + 0.634576i \(0.218825\pi\)
\(318\) 127.692 332.835i 0.401549 1.04665i
\(319\) 118.802i 0.372420i
\(320\) −484.344 188.018i −1.51357 0.587557i
\(321\) 153.873 + 345.432i 0.479356 + 1.07611i
\(322\) −662.925 341.982i −2.05877 1.06206i
\(323\) −171.215 171.215i −0.530078 0.530078i
\(324\) 515.956 54.6165i 1.59246 0.168569i
\(325\) −9.23369 205.846i −0.0284113 0.633374i
\(326\) 89.0709i 0.273224i
\(327\) 255.509 + 98.0263i 0.781373 + 0.299775i
\(328\) 180.863 + 180.863i 0.551412 + 0.551412i
\(329\) 178.037 + 557.453i 0.541145 + 1.69438i
\(330\) 26.3544 + 539.852i 0.0798617 + 1.63591i
\(331\) −452.094 −1.36584 −0.682922 0.730492i \(-0.739291\pi\)
−0.682922 + 0.730492i \(0.739291\pi\)
\(332\) 200.725 + 200.725i 0.604593 + 0.604593i
\(333\) 14.0103 + 265.448i 0.0420731 + 0.797140i
\(334\) 693.061 2.07503
\(335\) −39.7587 + 17.5226i −0.118683 + 0.0523062i
\(336\) 9.28408 8.27845i 0.0276312 0.0246383i
\(337\) 203.621 + 203.621i 0.604218 + 0.604218i 0.941429 0.337211i \(-0.109484\pi\)
−0.337211 + 0.941429i \(0.609484\pi\)
\(338\) 230.529 + 230.529i 0.682037 + 0.682037i
\(339\) 381.321 169.860i 1.12484 0.501061i
\(340\) −124.969 283.554i −0.367556 0.833984i
\(341\) −301.010 −0.882726
\(342\) −725.539 + 38.2940i −2.12146 + 0.111971i
\(343\) −48.5462 339.547i −0.141534 0.989933i
\(344\) 13.7231 0.0398927
\(345\) −24.1617 494.936i −0.0700338 1.43460i
\(346\) 90.5940i 0.261832i
\(347\) 358.869 358.869i 1.03421 1.03421i 0.0348116 0.999394i \(-0.488917\pi\)
0.999394 0.0348116i \(-0.0110831\pi\)
\(348\) 190.812 + 73.2051i 0.548310 + 0.210360i
\(349\) 51.4939 0.147547 0.0737735 0.997275i \(-0.476496\pi\)
0.0737735 + 0.997275i \(0.476496\pi\)
\(350\) −512.777 236.062i −1.46508 0.674462i
\(351\) 211.684 + 68.6501i 0.603089 + 0.195584i
\(352\) 260.244 + 260.244i 0.739329 + 0.739329i
\(353\) 212.052 212.052i 0.600714 0.600714i −0.339788 0.940502i \(-0.610355\pi\)
0.940502 + 0.339788i \(0.110355\pi\)
\(354\) 620.616 276.454i 1.75315 0.780944i
\(355\) −182.016 70.6570i −0.512721 0.199034i
\(356\) 454.077 1.27550
\(357\) 202.849 + 11.6151i 0.568205 + 0.0325352i
\(358\) 359.910 359.910i 1.00534 1.00534i
\(359\) 194.091 0.540643 0.270321 0.962770i \(-0.412870\pi\)
0.270321 + 0.962770i \(0.412870\pi\)
\(360\) −331.708 109.025i −0.921412 0.302847i
\(361\) 265.304 0.734915
\(362\) 134.124 + 134.124i 0.370508 + 0.370508i
\(363\) 4.06058 10.5840i 0.0111862 0.0291571i
\(364\) −352.042 + 112.434i −0.967148 + 0.308883i
\(365\) −330.735 + 145.763i −0.906123 + 0.399350i
\(366\) −125.275 + 55.8038i −0.342281 + 0.152469i
\(367\) −291.230 + 291.230i −0.793542 + 0.793542i −0.982068 0.188526i \(-0.939629\pi\)
0.188526 + 0.982068i \(0.439629\pi\)
\(368\) −13.8364 13.8364i −0.0375989 0.0375989i
\(369\) −220.550 198.436i −0.597696 0.537766i
\(370\) 172.388 444.079i 0.465913 1.20021i
\(371\) −78.4520 245.642i −0.211461 0.662107i
\(372\) 185.480 483.461i 0.498603 1.29963i
\(373\) 39.6194 39.6194i 0.106218 0.106218i −0.652000 0.758219i \(-0.726070\pi\)
0.758219 + 0.652000i \(0.226070\pi\)
\(374\) 348.630i 0.932165i
\(375\) −35.0511 373.358i −0.0934695 0.995622i
\(376\) 648.665i 1.72517i
\(377\) 61.9839 + 61.9839i 0.164414 + 0.164414i
\(378\) 433.019 429.169i 1.14555 1.13537i
\(379\) 391.187i 1.03216i −0.856541 0.516078i \(-0.827391\pi\)
0.856541 0.516078i \(-0.172609\pi\)
\(380\) 747.188 + 290.052i 1.96629 + 0.763296i
\(381\) −667.801 + 297.473i −1.75276 + 0.780769i
\(382\) −20.5199 20.5199i −0.0537170 0.0537170i
\(383\) −6.31835 + 6.31835i −0.0164970 + 0.0164970i −0.715307 0.698810i \(-0.753713\pi\)
0.698810 + 0.715307i \(0.253713\pi\)
\(384\) −557.401 + 248.295i −1.45157 + 0.646602i
\(385\) 259.043 + 292.832i 0.672839 + 0.760603i
\(386\) 438.422i 1.13581i
\(387\) −15.8954 + 0.838958i −0.0410733 + 0.00216785i
\(388\) 731.601 + 731.601i 1.88557 + 1.88557i
\(389\) −234.607 −0.603103 −0.301551 0.953450i \(-0.597504\pi\)
−0.301551 + 0.953450i \(0.597504\pi\)
\(390\) −295.413 267.912i −0.757468 0.686955i
\(391\) 319.624i 0.817452i
\(392\) −63.2462 + 374.906i −0.161342 + 0.956392i
\(393\) −76.9985 + 200.699i −0.195925 + 0.510685i
\(394\) 516.196i 1.31014i
\(395\) 78.4923 + 30.4701i 0.198715 + 0.0771394i
\(396\) 478.717 + 430.717i 1.20888 + 1.08767i
\(397\) 244.142 244.142i 0.614967 0.614967i −0.329269 0.944236i \(-0.606802\pi\)
0.944236 + 0.329269i \(0.106802\pi\)
\(398\) −278.335 + 278.335i −0.699333 + 0.699333i
\(399\) −392.254 + 349.767i −0.983094 + 0.876608i
\(400\) −10.9297 9.99126i −0.0273243 0.0249782i
\(401\) 255.719i 0.637703i −0.947805 0.318851i \(-0.896703\pi\)
0.947805 0.318851i \(-0.103297\pi\)
\(402\) −30.1215 + 78.5128i −0.0749292 + 0.195306i
\(403\) 157.049 157.049i 0.389700 0.389700i
\(404\) 351.955i 0.871175i
\(405\) 390.881 + 106.004i 0.965139 + 0.261739i
\(406\) 228.766 73.0621i 0.563462 0.179956i
\(407\) −233.290 + 233.290i −0.573194 + 0.573194i
\(408\) −210.275 80.6723i −0.515380 0.197726i
\(409\) −549.262 −1.34294 −0.671469 0.741033i \(-0.734336\pi\)
−0.671469 + 0.741033i \(0.734336\pi\)
\(410\) 214.420 + 486.519i 0.522976 + 1.18663i
\(411\) 98.6064 + 221.363i 0.239918 + 0.538596i
\(412\) 700.151 700.151i 1.69940 1.69940i
\(413\) 225.309 436.756i 0.545541 1.05752i
\(414\) −712.960 641.473i −1.72213 1.54945i
\(415\) 89.3634 + 202.765i 0.215333 + 0.488591i
\(416\) −271.559 −0.652787
\(417\) −44.5453 + 116.109i −0.106823 + 0.278439i
\(418\) −637.643 637.643i −1.52546 1.52546i
\(419\) 476.333i 1.13683i −0.822741 0.568417i \(-0.807556\pi\)
0.822741 0.568417i \(-0.192444\pi\)
\(420\) −629.947 + 235.616i −1.49987 + 0.560990i
\(421\) −736.969 −1.75052 −0.875261 0.483652i \(-0.839310\pi\)
−0.875261 + 0.483652i \(0.839310\pi\)
\(422\) 9.76103 9.76103i 0.0231304 0.0231304i
\(423\) 39.6560 + 751.345i 0.0937494 + 1.77623i
\(424\) 285.835i 0.674138i
\(425\) −10.8393 241.640i −0.0255041 0.568564i
\(426\) −345.195 + 153.767i −0.810316 + 0.360956i
\(427\) −45.4798 + 88.1615i −0.106510 + 0.206467i
\(428\) −570.926 570.926i −1.33394 1.33394i
\(429\) 112.390 + 252.305i 0.261980 + 0.588123i
\(430\) 26.5921 + 10.3228i 0.0618420 + 0.0240066i
\(431\) 95.9393i 0.222597i −0.993787 0.111299i \(-0.964499\pi\)
0.993787 0.111299i \(-0.0355010\pi\)
\(432\) 14.2457 7.26856i 0.0329762 0.0168254i
\(433\) −273.161 273.161i −0.630857 0.630857i 0.317426 0.948283i \(-0.397182\pi\)
−0.948283 + 0.317426i \(0.897182\pi\)
\(434\) −185.118 579.625i −0.426539 1.33554i
\(435\) 118.172 + 107.171i 0.271659 + 0.246370i
\(436\) −584.318 −1.34018
\(437\) 584.591 + 584.591i 1.33774 + 1.33774i
\(438\) −250.568 + 653.114i −0.572073 + 1.49113i
\(439\) −396.491 −0.903169 −0.451585 0.892228i \(-0.649141\pi\)
−0.451585 + 0.892228i \(0.649141\pi\)
\(440\) −174.775 396.565i −0.397217 0.901284i
\(441\) 50.3379 438.118i 0.114145 0.993464i
\(442\) −181.894 181.894i −0.411526 0.411526i
\(443\) 214.203 + 214.203i 0.483528 + 0.483528i 0.906256 0.422728i \(-0.138928\pi\)
−0.422728 + 0.906256i \(0.638928\pi\)
\(444\) −230.942 518.446i −0.520140 1.16767i
\(445\) 330.425 + 128.268i 0.742527 + 0.288243i
\(446\) 159.588 0.357821
\(447\) −67.5996 + 176.201i −0.151230 + 0.394185i
\(448\) −333.475 + 646.433i −0.744363 + 1.44293i
\(449\) −147.297 −0.328055 −0.164027 0.986456i \(-0.552449\pi\)
−0.164027 + 0.986456i \(0.552449\pi\)
\(450\) −560.761 460.783i −1.24614 1.02396i
\(451\) 368.227i 0.816468i
\(452\) −630.242 + 630.242i −1.39434 + 1.39434i
\(453\) 22.1807 57.8148i 0.0489641 0.127627i
\(454\) −106.110 −0.233723
\(455\) −287.936 17.6290i −0.632826 0.0387451i
\(456\) 532.142 237.043i 1.16698 0.519832i
\(457\) 18.8754 + 18.8754i 0.0413028 + 0.0413028i 0.727457 0.686154i \(-0.240702\pi\)
−0.686154 + 0.727457i \(0.740702\pi\)
\(458\) 207.818 207.818i 0.453751 0.453751i
\(459\) 248.492 + 80.5871i 0.541378 + 0.175571i
\(460\) 426.690 + 968.158i 0.927586 + 2.10469i
\(461\) 191.433 0.415256 0.207628 0.978208i \(-0.433426\pi\)
0.207628 + 0.978208i \(0.433426\pi\)
\(462\) 755.455 + 43.2571i 1.63518 + 0.0936300i
\(463\) 362.672 362.672i 0.783309 0.783309i −0.197079 0.980388i \(-0.563145\pi\)
0.980388 + 0.197079i \(0.0631454\pi\)
\(464\) 6.29967 0.0135769
\(465\) 271.540 299.412i 0.583956 0.643897i
\(466\) 413.314 0.886939
\(467\) −61.5519 61.5519i −0.131803 0.131803i 0.638128 0.769931i \(-0.279709\pi\)
−0.769931 + 0.638128i \(0.779709\pi\)
\(468\) −474.488 + 25.0435i −1.01386 + 0.0535118i
\(469\) 18.5061 + 57.9448i 0.0394587 + 0.123550i
\(470\) 487.941 1256.96i 1.03817 2.67438i
\(471\) 368.151 + 826.467i 0.781636 + 1.75471i
\(472\) −385.197 + 385.197i −0.816094 + 0.816094i
\(473\) −13.9697 13.9697i −0.0295343 0.0295343i
\(474\) 148.861 66.3104i 0.314053 0.139895i
\(475\) 461.783 + 422.133i 0.972175 + 0.888701i
\(476\) −413.256 + 131.984i −0.868184 + 0.277277i
\(477\) −17.4744 331.081i −0.0366340 0.694089i
\(478\) −928.316 + 928.316i −1.94208 + 1.94208i
\(479\) 572.620i 1.19545i −0.801702 0.597724i \(-0.796072\pi\)
0.801702 0.597724i \(-0.203928\pi\)
\(480\) −493.627 + 24.0978i −1.02839 + 0.0502038i
\(481\) 243.434i 0.506099i
\(482\) −267.116 267.116i −0.554183 0.554183i
\(483\) −692.601 39.6580i −1.43396 0.0821078i
\(484\) 24.2044i 0.0500092i
\(485\) 325.711 + 739.038i 0.671569 + 1.52379i
\(486\) 678.475 392.558i 1.39604 0.807732i
\(487\) 358.153 + 358.153i 0.735427 + 0.735427i 0.971689 0.236262i \(-0.0759224\pi\)
−0.236262 + 0.971689i \(0.575922\pi\)
\(488\) 77.7540 77.7540i 0.159332 0.159332i
\(489\) −33.7071 75.6696i −0.0689307 0.154744i
\(490\) −404.569 + 678.903i −0.825651 + 1.38552i
\(491\) 644.045i 1.31170i 0.754891 + 0.655850i \(0.227690\pi\)
−0.754891 + 0.655850i \(0.772310\pi\)
\(492\) 591.421 + 226.899i 1.20207 + 0.461177i
\(493\) 72.7618 + 72.7618i 0.147590 + 0.147590i
\(494\) 665.369 1.34690
\(495\) 226.685 + 448.654i 0.457950 + 0.906372i
\(496\) 15.9615i 0.0321804i
\(497\) −125.319 + 242.929i −0.252152 + 0.488791i
\(498\) 400.408 + 153.617i 0.804032 + 0.308468i
\(499\) 530.323i 1.06277i −0.847130 0.531386i \(-0.821672\pi\)
0.847130 0.531386i \(-0.178328\pi\)
\(500\) 355.416 + 717.470i 0.710831 + 1.43494i
\(501\) 588.786 262.275i 1.17522 0.523503i
\(502\) 291.523 291.523i 0.580723 0.580723i
\(503\) −515.298 + 515.298i −1.02445 + 1.02445i −0.0247567 + 0.999694i \(0.507881\pi\)
−0.999694 + 0.0247567i \(0.992119\pi\)
\(504\) −200.901 + 445.641i −0.398614 + 0.884208i
\(505\) −99.4205 + 256.112i −0.196872 + 0.507152i
\(506\) 1190.35i 2.35247i
\(507\) 283.083 + 108.605i 0.558349 + 0.214211i
\(508\) 1103.73 1103.73i 2.17270 2.17270i
\(509\) 648.378i 1.27383i 0.770935 + 0.636914i \(0.219789\pi\)
−0.770935 + 0.636914i \(0.780211\pi\)
\(510\) −346.780 314.498i −0.679960 0.616662i
\(511\) 153.945 + 482.017i 0.301261 + 0.943282i
\(512\) −26.7994 + 26.7994i −0.0523425 + 0.0523425i
\(513\) −601.886 + 307.098i −1.17327 + 0.598632i
\(514\) −456.642 −0.888408
\(515\) 707.269 311.710i 1.37334 0.605262i
\(516\) 31.0452 13.8291i 0.0601652 0.0268006i
\(517\) −660.323 + 660.323i −1.27722 + 1.27722i
\(518\) −592.694 305.752i −1.14420 0.590256i
\(519\) −34.2835 76.9636i −0.0660568 0.148292i
\(520\) 298.092 + 115.717i 0.573253 + 0.222532i
\(521\) 195.439 0.375123 0.187561 0.982253i \(-0.439942\pi\)
0.187561 + 0.982253i \(0.439942\pi\)
\(522\) 308.334 16.2739i 0.590679 0.0311761i
\(523\) 516.575 + 516.575i 0.987715 + 0.987715i 0.999925 0.0122109i \(-0.00388694\pi\)
−0.0122109 + 0.999925i \(0.503887\pi\)
\(524\) 458.975i 0.875906i
\(525\) −524.960 6.49413i −0.999923 0.0123698i
\(526\) −440.462 −0.837380
\(527\) 184.357 184.357i 0.349824 0.349824i
\(528\) 18.5327 + 7.11008i 0.0350997 + 0.0134661i
\(529\) 562.311i 1.06297i
\(530\) −215.011 + 553.879i −0.405682 + 1.04506i
\(531\) 422.622 469.720i 0.795899 0.884595i
\(532\) 514.446 997.242i 0.967003 1.87451i
\(533\) 192.119 + 192.119i 0.360448 + 0.360448i
\(534\) 626.653 279.143i 1.17351 0.522740i
\(535\) −254.178 576.730i −0.475099 1.07800i
\(536\) 67.4259i 0.125795i
\(537\) 169.559 441.960i 0.315752 0.823018i
\(538\) 487.524 + 487.524i 0.906179 + 0.906179i
\(539\) 446.026 317.261i 0.827507 0.588610i
\(540\) −860.279 + 87.6283i −1.59311 + 0.162275i
\(541\) −165.071 −0.305123 −0.152561 0.988294i \(-0.548752\pi\)
−0.152561 + 0.988294i \(0.548752\pi\)
\(542\) −1197.59 1197.59i −2.20958 2.20958i
\(543\) 164.701 + 63.1875i 0.303316 + 0.116367i
\(544\) −318.779 −0.585990
\(545\) −425.199 165.059i −0.780182 0.302860i
\(546\) −416.720 + 371.583i −0.763224 + 0.680554i
\(547\) −259.758 259.758i −0.474878 0.474878i 0.428611 0.903489i \(-0.359003\pi\)
−0.903489 + 0.428611i \(0.859003\pi\)
\(548\) −365.866 365.866i −0.667638 0.667638i
\(549\) −85.3086 + 94.8155i −0.155389 + 0.172706i
\(550\) −40.3678 899.919i −0.0733960 1.63622i
\(551\) −266.162 −0.483053
\(552\) 717.956 + 275.445i 1.30064 + 0.498994i
\(553\) 54.0426 104.760i 0.0977263 0.189440i
\(554\) 557.655 1.00660
\(555\) −21.6020 442.502i −0.0389225 0.797300i
\(556\) 265.527i 0.477567i
\(557\) −118.212 + 118.212i −0.212230 + 0.212230i −0.805214 0.592984i \(-0.797950\pi\)
0.592984 + 0.805214i \(0.297950\pi\)
\(558\) −41.2333 781.229i −0.0738947 1.40005i
\(559\) 14.5771 0.0260772
\(560\) −15.5279 + 13.7362i −0.0277283 + 0.0245289i
\(561\) 131.932 + 296.176i 0.235173 + 0.527944i
\(562\) −599.158 599.158i −1.06612 1.06612i
\(563\) −569.301 + 569.301i −1.01119 + 1.01119i −0.0112552 + 0.999937i \(0.503583\pi\)
−0.999937 + 0.0112552i \(0.996417\pi\)
\(564\) −653.678 1467.45i −1.15900 2.60186i
\(565\) −636.649 + 280.586i −1.12681 + 0.496612i
\(566\) 1217.08 2.15031
\(567\) 205.459 528.465i 0.362361 0.932038i
\(568\) 214.251 214.251i 0.377203 0.377203i
\(569\) −602.118 −1.05820 −0.529102 0.848558i \(-0.677471\pi\)
−0.529102 + 0.848558i \(0.677471\pi\)
\(570\) 1209.47 59.0439i 2.12189 0.103586i
\(571\) −883.761 −1.54774 −0.773871 0.633343i \(-0.781682\pi\)
−0.773871 + 0.633343i \(0.781682\pi\)
\(572\) −417.006 417.006i −0.729032 0.729032i
\(573\) −25.1979 9.66720i −0.0439754 0.0168712i
\(574\) 709.058 226.456i 1.23529 0.394523i
\(575\) 37.0092 + 825.045i 0.0643638 + 1.43486i
\(576\) −625.515 + 695.223i −1.08596 + 1.20698i
\(577\) −64.3197 + 64.3197i −0.111473 + 0.111473i −0.760643 0.649170i \(-0.775116\pi\)
0.649170 + 0.760643i \(0.275116\pi\)
\(578\) 445.670 + 445.670i 0.771056 + 0.771056i
\(579\) 165.912 + 372.459i 0.286550 + 0.643280i
\(580\) −317.535 123.264i −0.547474 0.212525i
\(581\) 295.513 94.3795i 0.508627 0.162443i
\(582\) 1459.40 + 559.902i 2.50757 + 0.962031i
\(583\) 290.972 290.972i 0.499094 0.499094i
\(584\) 560.886i 0.960422i
\(585\) −352.352 115.810i −0.602311 0.197966i
\(586\) 1298.43i 2.21576i
\(587\) −512.337 512.337i −0.872806 0.872806i 0.119971 0.992777i \(-0.461720\pi\)
−0.992777 + 0.119971i \(0.961720\pi\)
\(588\) 234.723 + 911.870i 0.399189 + 1.55080i
\(589\) 674.377i 1.14495i
\(590\) −1036.17 + 456.666i −1.75623 + 0.774010i
\(591\) 195.344 + 438.531i 0.330532 + 0.742016i
\(592\) −12.3706 12.3706i −0.0208962 0.0208962i
\(593\) 195.165 195.165i 0.329114 0.329114i −0.523135 0.852250i \(-0.675238\pi\)
0.852250 + 0.523135i \(0.175238\pi\)
\(594\) 925.441 + 300.124i 1.55798 + 0.505260i
\(595\) −338.003 20.6944i −0.568072 0.0347805i
\(596\) 402.950i 0.676090i
\(597\) −131.127 + 341.788i −0.219644 + 0.572509i
\(598\) 621.053 + 621.053i 1.03855 + 1.03855i
\(599\) −93.4354 −0.155986 −0.0779928 0.996954i \(-0.524851\pi\)
−0.0779928 + 0.996954i \(0.524851\pi\)
\(600\) 552.125 + 183.892i 0.920208 + 0.306486i
\(601\) 47.3325i 0.0787563i −0.999224 0.0393782i \(-0.987462\pi\)
0.999224 0.0393782i \(-0.0125377\pi\)
\(602\) 18.3089 35.4913i 0.0304134 0.0589557i
\(603\) 4.12207 + 78.0990i 0.00683593 + 0.129517i
\(604\) 132.216i 0.218900i
\(605\) −6.83729 + 17.6132i −0.0113013 + 0.0291127i
\(606\) 216.364 + 485.719i 0.357036 + 0.801516i
\(607\) 782.862 782.862i 1.28972 1.28972i 0.354769 0.934954i \(-0.384560\pi\)
0.934954 0.354769i \(-0.115440\pi\)
\(608\) 583.046 583.046i 0.958957 0.958957i
\(609\) 166.697 148.641i 0.273723 0.244074i
\(610\) 209.157 92.1804i 0.342881 0.151115i
\(611\) 689.034i 1.12772i
\(612\) −556.994 + 29.3981i −0.910120 + 0.0480362i
\(613\) 587.076 587.076i 0.957710 0.957710i −0.0414311 0.999141i \(-0.513192\pi\)
0.999141 + 0.0414311i \(0.0131917\pi\)
\(614\) 1143.73i 1.86275i
\(615\) 366.273 + 332.176i 0.595566 + 0.540124i
\(616\) −577.959 + 184.586i −0.938245 + 0.299652i
\(617\) −400.922 + 400.922i −0.649793 + 0.649793i −0.952943 0.303150i \(-0.901962\pi\)
0.303150 + 0.952943i \(0.401962\pi\)
\(618\) 535.833 1396.67i 0.867044 2.25998i
\(619\) 382.132 0.617338 0.308669 0.951170i \(-0.400117\pi\)
0.308669 + 0.951170i \(0.400117\pi\)
\(620\) −312.316 + 804.540i −0.503735 + 1.29764i
\(621\) −848.443 275.154i −1.36625 0.443082i
\(622\) −675.887 + 675.887i −1.08663 + 1.08663i
\(623\) 227.500 441.004i 0.365169 0.707872i
\(624\) −13.3789 + 5.95963i −0.0214405 + 0.00955068i
\(625\) 55.9588 + 622.490i 0.0895341 + 0.995984i
\(626\) −891.810 −1.42462
\(627\) −783.009 300.402i −1.24882 0.479111i
\(628\) −1365.97 1365.97i −2.17512 2.17512i
\(629\) 285.762i 0.454312i
\(630\) −724.520 + 712.424i −1.15003 + 1.13083i
\(631\) 1097.98 1.74006 0.870031 0.492997i \(-0.164099\pi\)
0.870031 + 0.492997i \(0.164099\pi\)
\(632\) −92.3934 + 92.3934i −0.146192 + 0.146192i
\(633\) 4.59856 11.9863i 0.00726470 0.0189357i
\(634\) 199.975i 0.315418i
\(635\) 1114.95 491.386i 1.75583 0.773836i
\(636\) 288.043 + 646.633i 0.452898 + 1.01672i
\(637\) −67.1823 + 398.238i −0.105467 + 0.625177i
\(638\) 270.981 + 270.981i 0.424735 + 0.424735i
\(639\) −235.068 + 261.264i −0.367868 + 0.408864i
\(640\) 930.630 410.150i 1.45411 0.640860i
\(641\) 137.826i 0.215017i 0.994204 + 0.107509i \(0.0342873\pi\)
−0.994204 + 0.107509i \(0.965713\pi\)
\(642\) −1138.89 436.936i −1.77397 0.680585i
\(643\) −340.846 340.846i −0.530087 0.530087i 0.390511 0.920598i \(-0.372298\pi\)
−0.920598 + 0.390511i \(0.872298\pi\)
\(644\) 1411.01 450.640i 2.19100 0.699752i
\(645\) 26.4976 1.29355i 0.0410815 0.00200551i
\(646\) 781.065 1.20908
\(647\) −192.497 192.497i −0.297523 0.297523i 0.542520 0.840043i \(-0.317470\pi\)
−0.840043 + 0.542520i \(0.817470\pi\)
\(648\) −395.164 + 488.729i −0.609822 + 0.754211i
\(649\) 784.239 1.20838
\(650\) 490.586 + 448.463i 0.754748 + 0.689943i
\(651\) −376.613 422.362i −0.578515 0.648790i
\(652\) 125.066 + 125.066i 0.191819 + 0.191819i
\(653\) −178.554 178.554i −0.273436 0.273436i 0.557046 0.830482i \(-0.311935\pi\)
−0.830482 + 0.557046i \(0.811935\pi\)
\(654\) −806.394 + 359.209i −1.23302 + 0.549250i
\(655\) 129.652 333.989i 0.197942 0.509907i
\(656\) 19.5258 0.0297649
\(657\) 34.2897 + 649.672i 0.0521913 + 0.988846i
\(658\) −1677.61 865.427i −2.54956 1.31524i
\(659\) 984.529 1.49397 0.746987 0.664838i \(-0.231500\pi\)
0.746987 + 0.664838i \(0.231500\pi\)
\(660\) −795.018 721.009i −1.20457 1.09244i
\(661\) 730.936i 1.10580i −0.833247 0.552901i \(-0.813521\pi\)
0.833247 0.552901i \(-0.186479\pi\)
\(662\) 1031.20 1031.20i 1.55771 1.55771i
\(663\) −223.362 85.6929i −0.336895 0.129250i
\(664\) −343.865 −0.517869
\(665\) 656.056 580.356i 0.986550 0.872716i
\(666\) −637.428 573.515i −0.957099 0.861133i
\(667\) −248.435 248.435i −0.372467 0.372467i
\(668\) −973.137 + 973.137i −1.45679 + 1.45679i
\(669\) 135.577 60.3930i 0.202656 0.0902735i
\(670\) 50.7193 130.655i 0.0757004 0.195008i
\(671\) −158.303 −0.235921
\(672\) −39.5532 + 690.770i −0.0588590 + 1.02793i
\(673\) −770.416 + 770.416i −1.14475 + 1.14475i −0.157179 + 0.987570i \(0.550240\pi\)
−0.987570 + 0.157179i \(0.949760\pi\)
\(674\) −928.898 −1.37819
\(675\) −650.765 179.247i −0.964097 0.265551i
\(676\) −647.377 −0.957658
\(677\) 430.936 + 430.936i 0.636538 + 0.636538i 0.949700 0.313162i \(-0.101388\pi\)
−0.313162 + 0.949700i \(0.601388\pi\)
\(678\) −482.331 + 1257.21i −0.711403 + 1.85430i
\(679\) 1077.08 343.994i 1.58628 0.506618i
\(680\) 349.924 + 135.838i 0.514595 + 0.199761i
\(681\) −90.1453 + 40.1553i −0.132372 + 0.0589652i
\(682\) 686.586 686.586i 1.00672 1.00672i
\(683\) −952.879 952.879i −1.39514 1.39514i −0.813319 0.581818i \(-0.802342\pi\)
−0.581818 0.813319i \(-0.697658\pi\)
\(684\) 964.971 1072.51i 1.41078 1.56800i
\(685\) −162.885 369.585i −0.237788 0.539540i
\(686\) 885.219 + 663.757i 1.29041 + 0.967576i
\(687\) 97.9059 255.195i 0.142512 0.371463i
\(688\) 0.740765 0.740765i 0.00107669 0.00107669i
\(689\) 303.623i 0.440673i
\(690\) 1184.03 + 1073.81i 1.71599 + 1.55625i
\(691\) 428.205i 0.619689i 0.950787 + 0.309844i \(0.100277\pi\)
−0.950787 + 0.309844i \(0.899723\pi\)
\(692\) 127.204 + 127.204i 0.183821 + 0.183821i
\(693\) 658.162 249.138i 0.949728 0.359507i
\(694\) 1637.12i 2.35897i
\(695\) 75.0064 193.220i 0.107923 0.278014i
\(696\) −226.146 + 100.737i −0.324922 + 0.144737i
\(697\) 225.525 + 225.525i 0.323565 + 0.323565i
\(698\) −117.455 + 117.455i −0.168273 + 0.168273i
\(699\) 351.128 156.410i 0.502329 0.223763i
\(700\) 1051.46 388.541i 1.50208 0.555058i
\(701\) 1086.06i 1.54929i −0.632393 0.774647i \(-0.717927\pi\)
0.632393 0.774647i \(-0.282073\pi\)
\(702\) −639.427 + 326.253i −0.910865 + 0.464748i
\(703\) 522.659 + 522.659i 0.743469 + 0.743469i
\(704\) −1160.74 −1.64877
\(705\) −61.1440 1252.49i −0.0867290 1.77659i
\(706\) 967.358i 1.37020i
\(707\) 341.822 + 176.335i 0.483482 + 0.249413i
\(708\) −483.243 + 1259.59i −0.682547 + 1.77908i
\(709\) 384.594i 0.542446i 0.962516 + 0.271223i \(0.0874281\pi\)
−0.962516 + 0.271223i \(0.912572\pi\)
\(710\) 576.333 254.003i 0.811736 0.357751i
\(711\) 101.370 112.667i 0.142574 0.158463i
\(712\) −388.943 + 388.943i −0.546269 + 0.546269i
\(713\) −629.462 + 629.462i −0.882836 + 0.882836i
\(714\) −489.181 + 436.194i −0.685127 + 0.610916i
\(715\) −185.653 421.245i −0.259654 0.589154i
\(716\) 1010.71i 1.41161i
\(717\) −437.342 + 1139.95i −0.609961 + 1.58989i
\(718\) −442.710 + 442.710i −0.616588 + 0.616588i
\(719\) 160.221i 0.222838i 0.993773 + 0.111419i \(0.0355396\pi\)
−0.993773 + 0.111419i \(0.964460\pi\)
\(720\) −23.7906 + 12.0203i −0.0330425 + 0.0166949i
\(721\) −329.207 1030.78i −0.456597 1.42966i
\(722\) −605.144 + 605.144i −0.838150 + 0.838150i
\(723\) −328.012 125.842i −0.453682 0.174056i
\(724\) −376.650 −0.520235
\(725\) −196.245 179.395i −0.270683 0.247442i
\(726\) 14.8797 + 33.4036i 0.0204954 + 0.0460104i
\(727\) −655.048 + 655.048i −0.901029 + 0.901029i −0.995525 0.0944960i \(-0.969876\pi\)
0.0944960 + 0.995525i \(0.469876\pi\)
\(728\) 205.239 397.851i 0.281921 0.546498i
\(729\) 427.838 590.250i 0.586884 0.809671i
\(730\) 421.912 1086.86i 0.577961 1.48886i
\(731\) 17.1118 0.0234088
\(732\) 97.5452 254.255i 0.133258 0.347343i
\(733\) 222.518 + 222.518i 0.303572 + 0.303572i 0.842410 0.538838i \(-0.181136\pi\)
−0.538838 + 0.842410i \(0.681136\pi\)
\(734\) 1328.56i 1.81003i
\(735\) −86.7817 + 729.859i −0.118070 + 0.993005i
\(736\) 1088.43 1.47884
\(737\) −68.6376 + 68.6376i −0.0931311 + 0.0931311i
\(738\) 955.682 50.4409i 1.29496 0.0683481i
\(739\) 343.180i 0.464385i 0.972670 + 0.232192i \(0.0745899\pi\)
−0.972670 + 0.232192i \(0.925410\pi\)
\(740\) 381.486 + 865.590i 0.515521 + 1.16972i
\(741\) 565.260 251.796i 0.762834 0.339805i
\(742\) 739.240 + 381.351i 0.996280 + 0.513950i
\(743\) −54.5399 54.5399i −0.0734050 0.0734050i 0.669451 0.742856i \(-0.266529\pi\)
−0.742856 + 0.669451i \(0.766529\pi\)
\(744\) 255.238 + 572.987i 0.343062 + 0.770144i
\(745\) 113.826 293.220i 0.152786 0.393584i
\(746\) 180.739i 0.242278i
\(747\) 398.297 21.0221i 0.533196 0.0281421i
\(748\) −489.516 489.516i −0.654433 0.654433i
\(749\) −840.533 + 268.446i −1.12221 + 0.358405i
\(750\) 931.559 + 771.660i 1.24208 + 1.02888i
\(751\) 969.222 1.29057 0.645287 0.763940i \(-0.276738\pi\)
0.645287 + 0.763940i \(0.276738\pi\)
\(752\) −35.0146 35.0146i −0.0465620 0.0465620i
\(753\) 137.340 357.982i 0.182391 0.475408i
\(754\) −282.764 −0.375018
\(755\) −37.3484 + 96.2112i −0.0494681 + 0.127432i
\(756\) −5.40671 + 1210.61i −0.00715174 + 1.60134i
\(757\) −881.940 881.940i −1.16505 1.16505i −0.983356 0.181690i \(-0.941843\pi\)
−0.181690 0.983356i \(-0.558157\pi\)
\(758\) 892.277 + 892.277i 1.17715 + 1.17715i
\(759\) −450.464 1011.25i −0.593497 1.33235i
\(760\) −888.458 + 391.564i −1.16902 + 0.515216i
\(761\) −1174.77 −1.54372 −0.771859 0.635794i \(-0.780673\pi\)
−0.771859 + 0.635794i \(0.780673\pi\)
\(762\) 844.699 2201.74i 1.10853 2.88942i
\(763\) −292.753 + 567.496i −0.383687 + 0.743769i
\(764\) 57.6245 0.0754248
\(765\) −413.620 135.948i −0.540680 0.177709i
\(766\) 28.8236i 0.0376288i
\(767\) −409.169 + 409.169i −0.533467 +