Properties

Label 105.3.k.d.83.3
Level 105
Weight 3
Character 105.83
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

Related objects

Downloads

Learn more about

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 83.3
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.d.62.3

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28094 2.28094i −1.14047 1.14047i −0.988364 0.152108i \(-0.951394\pi\)
−0.152108 0.988364i \(-0.548606\pi\)
\(3\) −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 \(0.169522\pi\)
−0.861506 + 0.507747i \(0.830478\pi\)
\(12\) 17.9412 6.88316i 1.49510 0.573596i
\(13\) 5.82807 5.82807i 0.448313 0.448313i −0.446480 0.894794i \(-0.647323\pi\)
0.894794 + 0.446480i \(0.147323\pi\)
\(14\) 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 −0.476652 0.879092i \(-0.658150\pi\)
0.879092 + 0.476652i \(0.158150\pi\)
\(18\) 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 −0.0157445 + 0.999876i \(0.505012\pi\)
−0.999876 + 0.0157445i \(0.994988\pi\)
\(24\) −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 \(0.143120\pi\)
−0.900610 + 0.434629i \(0.856880\pi\)
\(32\) −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 −0.930568 0.366120i \(-0.880686\pi\)
0.366120 + 0.930568i \(0.380686\pi\)
\(38\) 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 0.721499 0.692415i \(-0.243453\pi\)
−0.692415 + 0.721499i \(0.743453\pi\)
\(44\) −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 −0.305558 + 0.952173i \(0.598843\pi\)
−0.952173 + 0.305558i \(0.901157\pi\)
\(48\) −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 −0.417293 0.908772i \(-0.637021\pi\)
0.908772 + 0.417293i \(0.137021\pi\)
\(54\) −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 \(-0.797163\pi\)
0.803747 0.594971i \(-0.202837\pi\)
\(60\) 64.5461 + 71.1716i 1.07577 + 1.18619i
\(61\) 14.1716i 0.232321i 0.993230 + 0.116161i \(0.0370587\pi\)
−0.993230 + 0.116161i \(0.962941\pi\)
\(62\) 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 −0.751473 0.659763i \(-0.770657\pi\)
0.659763 + 0.751473i \(0.270657\pi\)
\(68\) 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 \(0.0886774\pi\)
−0.961445 + 0.274999i \(0.911323\pi\)
\(72\) −3.68068 + 69.7361i −0.0511205 + 0.968557i
\(73\) −51.1141 + 51.1141i −0.700193 + 0.700193i −0.964452 0.264259i \(-0.914873\pi\)
0.264259 + 0.964452i \(0.414873\pi\)
\(74\) 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 \(-0.966010\pi\)
0.994304 0.106581i \(-0.0339903\pi\)
\(80\) 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 0.492667 0.870218i \(-0.336022\pi\)
−0.870218 + 0.492667i \(0.836022\pi\)
\(84\) −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 \(-0.869616\pi\)
0.917274 0.398256i \(-0.130384\pi\)
\(90\) 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 −0.980383 0.197101i \(-0.936847\pi\)
−0.197101 0.980383i \(-0.563153\pi\)
\(98\) −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 0.0632258 0.997999i \(-0.479861\pi\)
0.997999 0.0632258i \(-0.0201388\pi\)
\(104\) 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 0.987927 0.154920i \(-0.0495120\pi\)
−0.154920 + 0.987927i \(0.549512\pi\)
\(108\) −78.6017 + 154.052i −0.727794 + 1.42641i
\(109\) 91.2226i 0.836904i 0.908239 + 0.418452i \(0.137427\pi\)
−0.908239 + 0.418452i \(0.862573\pi\)
\(110\) 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 −0.992552 0.121825i \(-0.961125\pi\)
0.121825 + 0.992552i \(0.461125\pi\)
\(114\) 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 0.478948 0.877843i \(-0.341018\pi\)
0.877843 0.478948i \(-0.158982\pi\)
\(128\) 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 0.884141 0.467220i \(-0.154744\pi\)
−0.467220 + 0.884141i \(0.654744\pi\)
\(138\) −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 0.876015 + 0.482284i \(0.160193\pi\)
0.482284 + 0.876015i \(0.339807\pi\)
\(158\) −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 0.644673 0.764458i \(-0.276993\pi\)
−0.764458 + 0.644673i \(0.776993\pi\)
\(164\) 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 −0.996250 0.0865247i \(-0.972424\pi\)
0.0865247 + 0.996250i \(0.472424\pi\)
\(168\) 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 0.647378 0.762169i \(-0.275866\pi\)
−0.762169 + 0.647378i \(0.775866\pi\)
\(174\) −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 \(0.0519351\pi\)
−0.986719 + 0.162436i \(0.948065\pi\)
\(182\) 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 \(-0.992503\pi\)
0.999723 0.0235503i \(-0.00749699\pi\)
\(192\) 291.050 111.662i 1.51588 0.581571i
\(193\) 96.1055 + 96.1055i 0.497956 + 0.497956i 0.910801 0.412845i \(-0.135465\pi\)
−0.412845 + 0.910801i \(0.635465\pi\)
\(194\) 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 0.933351 0.358965i \(-0.116870\pi\)
−0.358965 + 0.933351i \(0.616870\pi\)
\(198\) −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 −0.781180 0.624306i \(-0.785382\pi\)
0.624306 + 0.781180i \(0.285382\pi\)
\(224\) 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 −0.654014 0.756482i \(-0.726916\pi\)
0.756482 + 0.654014i \(0.226916\pi\)
\(228\) −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 −0.874276 0.485429i \(-0.838664\pi\)
0.485429 + 0.874276i \(0.338664\pi\)
\(234\) 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 \(-0.921881\pi\)
0.970036 0.242962i \(-0.0781191\pi\)
\(242\) 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 −0.485015 0.874506i \(-0.661186\pi\)
0.874506 + 0.485015i \(0.161186\pi\)
\(258\) −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 −0.499306 0.866426i \(-0.666412\pi\)
0.866426 + 0.499306i \(0.166412\pi\)
\(264\) 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 \(0.130047\pi\)
−0.917696 + 0.397282i \(0.869953\pi\)
\(270\) 337.546 275.138i 1.25017 1.01903i
\(271\) 525.042i 1.93743i −0.248184 0.968713i \(-0.579834\pi\)
0.248184 0.968713i \(-0.420166\pi\)
\(272\) 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 −0.892451 0.451144i \(-0.851016\pi\)
0.451144 + 0.892451i \(0.351016\pi\)
\(278\) −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 \(-0.845190\pi\)
0.884045 0.467401i \(-0.154810\pi\)
\(282\) −289.782 755.326i −1.02759 2.67846i
\(283\) −266.792 + 266.792i −0.942728 + 0.942728i −0.998446 0.0557189i \(-0.982255\pi\)
0.0557189 + 0.998446i \(0.482255\pi\)
\(284\) −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 0.999603 0.0281818i \(-0.00897172\pi\)
−0.0281818 + 0.999603i \(0.508972\pi\)
\(294\) 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 0.985622 0.168965i \(-0.0540424\pi\)
−0.168965 + 0.985622i \(0.554042\pi\)
\(308\) 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 −0.322124 0.946697i \(-0.604397\pi\)
0.946697 + 0.322124i \(0.104397\pi\)
\(314\) 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 0.772860 0.634576i \(-0.218825\pi\)
−0.634576 + 0.772860i \(0.718825\pi\)
\(318\) 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 −0.337211 0.941429i \(-0.609484\pi\)
0.941429 + 0.337211i \(0.109484\pi\)
\(338\) 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 0.999394 + 0.0348116i \(0.0110831\pi\)
0.0348116 + 0.999394i \(0.488917\pi\)
\(348\) 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 0.940502 0.339788i \(-0.110355\pi\)
−0.339788 + 0.940502i \(0.610355\pi\)
\(354\) 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 0.188526 0.982068i \(-0.439629\pi\)
−0.982068 + 0.188526i \(0.939629\pi\)
\(368\) −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 0.758219 0.652000i \(-0.226070\pi\)
−0.652000 + 0.758219i \(0.726070\pi\)
\(374\) 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 \(0.172609\pi\)
−0.856541 + 0.516078i \(0.827391\pi\)
\(380\) 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 0.698810 0.715307i \(-0.253713\pi\)
−0.715307 + 0.698810i \(0.753713\pi\)
\(384\) −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 0.944236 0.329269i \(-0.106802\pi\)
−0.329269 + 0.944236i \(0.606802\pi\)
\(398\) −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 \(0.103297\pi\)
−0.947805 + 0.318851i \(0.896703\pi\)
\(402\) −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 \(0.192444\pi\)
−0.822741 + 0.568417i \(0.807556\pi\)
\(420\) −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 \(0.0355010\pi\)
−0.993787 + 0.111299i \(0.964499\pi\)
\(432\) 14.2457 + 7.26856i 0.0329762 + 0.0168254i
\(433\) −273.161 + 273.161i −0.630857 + 0.630857i −0.948283 0.317426i \(-0.897182\pi\)
0.317426 + 0.948283i \(0.397182\pi\)
\(434\) −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 −0.422728 0.906256i \(-0.638928\pi\)
0.906256 + 0.422728i \(0.138928\pi\)
\(444\) −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 −0.686154 0.727457i \(-0.740702\pi\)
0.727457 + 0.686154i \(0.240702\pi\)
\(458\) 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 0.980388 0.197079i \(-0.0631454\pi\)
−0.197079 + 0.980388i \(0.563145\pi\)
\(464\) 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 −0.769931 0.638128i \(-0.779709\pi\)
0.638128 + 0.769931i \(0.279709\pi\)
\(468\) −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 \(0.203928\pi\)
−0.801702 + 0.597724i \(0.796072\pi\)
\(480\) −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 −0.236262 0.971689i \(-0.575922\pi\)
0.971689 + 0.236262i \(0.0759224\pi\)
\(488\) 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 \(-0.772310\pi\)
0.754891 0.655850i \(-0.227690\pi\)
\(492\) 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 \(0.178328\pi\)
−0.847130 + 0.531386i \(0.821672\pi\)
\(500\) 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 −0.999694 0.0247567i \(-0.992119\pi\)
−0.0247567 0.999694i \(-0.507881\pi\)
\(504\) −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 \(-0.780211\pi\)
0.770935 0.636914i \(-0.219789\pi\)
\(510\) −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 −0.0122109 0.999925i \(-0.503887\pi\)
0.999925 + 0.0122109i \(0.00388694\pi\)
\(524\) 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 −0.903489 0.428611i \(-0.859003\pi\)
0.428611 + 0.903489i \(0.359003\pi\)
\(548\) −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 0.592984 0.805214i \(-0.297950\pi\)
−0.805214 + 0.592984i \(0.797950\pi\)
\(558\) −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 −0.999937 0.0112552i \(-0.996417\pi\)
−0.0112552 0.999937i \(-0.503583\pi\)
\(564\) −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 0.649170 0.760643i \(-0.275116\pi\)
−0.760643 + 0.649170i \(0.775116\pi\)
\(578\) 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 −0.992777 0.119971i \(-0.961720\pi\)
0.119971 + 0.992777i \(0.461720\pi\)
\(588\) 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 0.852250 0.523135i \(-0.175238\pi\)
−0.523135 + 0.852250i \(0.675238\pi\)
\(594\) 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 \(0.0125377\pi\)
−0.999224 + 0.0393782i \(0.987462\pi\)
\(602\) 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 0.934954 + 0.354769i \(0.115440\pi\)
0.354769 + 0.934954i \(0.384560\pi\)
\(608\) 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 0.999141 0.0414311i \(-0.0131917\pi\)
−0.0414311 + 0.999141i \(0.513192\pi\)
\(614\) 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 0.303150 0.952943i \(-0.401962\pi\)
−0.952943 + 0.303150i \(0.901962\pi\)
\(618\) 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 \(-0.965713\pi\)
0.994204 0.107509i \(-0.0342873\pi\)
\(642\) −1138.89 + 436.936i −1.77397 + 0.680585i
\(643\) −340.846 + 340.846i −0.530087 + 0.530087i −0.920598 0.390511i \(-0.872298\pi\)
0.390511 + 0.920598i \(0.372298\pi\)
\(644\) 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 −0.840043 0.542520i \(-0.817470\pi\)
0.542520 + 0.840043i \(0.317470\pi\)
\(648\) −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 −0.830482 0.557046i \(-0.811935\pi\)
0.557046 + 0.830482i \(0.311935\pi\)
\(654\) −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 \(0.186479\pi\)
−0.833247 + 0.552901i \(0.813521\pi\)
\(662\) 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 −0.987570 0.157179i \(-0.949760\pi\)
−0.157179 0.987570i \(-0.550240\pi\)
\(674\) −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 −0.313162 0.949700i \(-0.601388\pi\)
0.949700 + 0.313162i \(0.101388\pi\)
\(678\) −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 −0.581818 + 0.813319i \(0.697658\pi\)
−0.813319 + 0.581818i \(0.802342\pi\)
\(684\) 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 \(-0.899723\pi\)
0.950787 0.309844i \(-0.100277\pi\)
\(692\) 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 \(0.282073\pi\)
−0.632393 + 0.774647i \(0.717927\pi\)
\(702\) −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 \(-0.912572\pi\)
0.962516 0.271223i \(-0.0874281\pi\)
\(710\) 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 \(-0.964460\pi\)
0.993773 0.111419i \(-0.0355396\pi\)
\(720\) −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 0.0944960 0.995525i \(-0.469876\pi\)
−0.995525 + 0.0944960i \(0.969876\pi\)
\(728\) 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 −0.538838 0.842410i \(-0.681136\pi\)
0.842410 + 0.538838i \(0.181136\pi\)
\(734\) 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 \(-0.925410\pi\)
0.972670 0.232192i \(-0.0745899\pi\)
\(740\) 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 −0.742856 0.669451i \(-0.766529\pi\)
0.669451 + 0.742856i \(0.266529\pi\)
\(744\) 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 −0.181690 + 0.983356i \(0.558157\pi\)
−0.983356 + 0.181690i \(0.941843\pi\)
\(758\) 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 0.533467i
\(768\) 258.408 + 673.550i 0.336469 + 0.877018i