Properties

Label 105.3.k.d.62.14
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 62.14
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.28094 - 2.28094i) q^{2} +(2.80094 - 1.07458i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 - 8.83986i) q^{6} +(-6.22100 - 3.20922i) q^{7} +(-5.48661 - 5.48661i) q^{8} +(6.69054 - 6.01969i) q^{9} +O(q^{10})\) \(q+(2.28094 - 2.28094i) q^{2} +(2.80094 - 1.07458i) 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} +(-6.88316 - 17.9412i) q^{12} +(5.82807 + 5.82807i) q^{13} +(-21.5098 + 6.86971i) q^{14} +(-0.0592799 + 14.9999i) q^{15} +0.592330 q^{16} +(-6.84147 - 6.84147i) q^{17} +(1.53016 - 28.9913i) q^{18} -25.0261 q^{19} +(29.8564 + 11.5900i) q^{20} +(-20.8732 - 2.30385i) 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} +(12.2711 - 24.0503i) q^{27} +(-20.5564 + 39.8481i) q^{28} -10.6354 q^{29} +(34.0787 + 34.3491i) q^{30} -26.9470i q^{31} +(23.2975 - 23.2975i) q^{32} +(12.0036 + 31.2877i) 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} +(-52.8657 + 42.3558i) q^{42} +(1.25060 - 1.25060i) q^{43} +71.5513 q^{44} +(15.9526 + 42.0775i) q^{45} +106.562 q^{46} +(59.1134 + 59.1134i) q^{47} +(1.65908 - 0.636508i) 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} +(-70.0965 + 26.8926i) q^{57} +(-24.2588 + 24.2588i) q^{58} -70.2066i q^{59} +(96.0805 + 0.379712i) q^{60} -14.1716i q^{61} +(-61.4646 - 61.4646i) q^{62} +(-60.9404 + 15.9771i) 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} +(-69.7361 - 3.68068i) q^{72} +(-51.1141 - 51.1141i) q^{73} -95.2731 q^{74} +(-69.8090 - 27.4172i) q^{75} +160.302i q^{76} +(35.8484 - 69.4914i) q^{77} +(74.4687 - 28.5700i) 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} +(-14.7571 + 133.702i) q^{84} +(44.2679 - 19.5099i) q^{85} -5.70508i q^{86} +(-29.7891 + 11.4286i) q^{87} +(61.2879 - 61.2879i) q^{88} -70.8895i q^{89} +(132.363 + 59.5894i) q^{90} +(-17.5529 - 54.9600i) q^{91} +(149.626 - 149.626i) q^{92} +(-28.9568 - 75.4769i) 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 \(-0.451394\pi\)
0.988364 0.152108i \(-0.0486063\pi\)
\(3\) 2.80094 1.07458i 0.933647 0.358195i
\(4\) 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 \(0.830478\pi\)
\(12\) −6.88316 17.9412i −0.573596 1.49510i
\(13\) 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
\(15\) −0.0592799 + 14.9999i −0.00395199 + 0.999992i
\(16\) 0.592330 0.0370206
\(17\) −6.84147 6.84147i −0.402440 0.402440i 0.476652 0.879092i \(-0.341850\pi\)
−0.879092 + 0.476652i \(0.841850\pi\)
\(18\) 1.53016 28.9913i 0.0850091 1.61063i
\(19\) −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
\(21\) −20.8732 2.30385i −0.993964 0.109707i
\(22\) 25.4792 + 25.4792i 1.15814 + 1.15814i
\(23\) 23.3593 + 23.3593i 1.01562 + 1.01562i 0.999876 + 0.0157445i \(0.00501183\pi\)
0.0157445 + 0.999876i \(0.494988\pi\)
\(24\) −21.2635 9.47185i −0.885980 0.394661i
\(25\) −18.4521 16.8677i −0.738083 0.674710i
\(26\) 26.5870 1.02258
\(27\) 12.2711 24.0503i 0.454487 0.890754i
\(28\) −20.5564 + 39.8481i −0.734157 + 1.42315i
\(29\) −10.6354 −0.366738 −0.183369 0.983044i \(-0.558700\pi\)
−0.183369 + 0.983044i \(0.558700\pi\)
\(30\) 34.0787 + 34.3491i 1.13596 + 1.14497i
\(31\) 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
\(33\) 12.0036 + 31.2877i 0.363745 + 0.948113i
\(34\) −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 \(-0.631687\pi\)
−0.402005 + 0.915637i \(0.631687\pi\)
\(42\) −52.8657 + 42.3558i −1.25871 + 1.00847i
\(43\) 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
\(45\) 15.9526 + 42.0775i 0.354502 + 0.935055i
\(46\) 106.562 2.31657
\(47\) 59.1134 + 59.1134i 1.25773 + 1.25773i 0.952173 + 0.305558i \(0.0988431\pi\)
0.305558 + 0.952173i \(0.401157\pi\)
\(48\) 1.65908 0.636508i 0.0345642 0.0132606i
\(49\) 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 \(-0.362979\pi\)
−0.908772 + 0.417293i \(0.862979\pi\)
\(54\) −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
\(57\) −70.0965 + 26.8926i −1.22976 + 0.471800i
\(58\) −24.2588 + 24.2588i −0.418254 + 0.418254i
\(59\) 70.2066i 1.18994i −0.803747 0.594971i \(-0.797163\pi\)
0.803747 0.594971i \(-0.202837\pi\)
\(60\) 96.0805 + 0.379712i 1.60134 + 0.00632854i
\(61\) 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
\(63\) −60.9404 + 15.9771i −0.967308 + 0.253605i
\(64\) 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 \(0.0886774\pi\)
−0.961445 + 0.274999i \(0.911323\pi\)
\(72\) −69.7361 3.68068i −0.968557 0.0511205i
\(73\) −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
\(75\) −69.8090 27.4172i −0.930787 0.365563i
\(76\) 160.302i 2.10924i
\(77\) 35.8484 69.4914i 0.465564 0.902485i
\(78\) 74.4687 28.5700i 0.954726 0.366282i
\(79\) 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 −0.492667 0.870218i \(-0.663978\pi\)
0.870218 + 0.492667i \(0.163978\pi\)
\(84\) −14.7571 + 133.702i −0.175680 + 1.59169i
\(85\) 44.2679 19.5099i 0.520799 0.229528i
\(86\) 5.70508i 0.0663381i
\(87\) −29.7891 + 11.4286i −0.342404 + 0.131364i
\(88\) 61.2879 61.2879i 0.696453 0.696453i
\(89\) 70.8895i 0.796511i −0.917274 0.398256i \(-0.869616\pi\)
0.917274 0.398256i \(-0.130384\pi\)
\(90\) 132.363 + 59.5894i 1.47070 + 0.662105i
\(91\) −17.5529 54.9600i −0.192889 0.603957i
\(92\) 149.626 149.626i 1.62637 1.62637i
\(93\) −28.9568 75.4769i −0.311363 0.811579i
\(94\) 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 \(-0.412311\pi\)
0.272012 + 0.962294i \(0.412311\pi\)
\(102\) −87.4175 + 33.5378i −0.857034 + 0.328802i
\(103\) 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
\(105\) 48.5067 93.1241i 0.461969 0.886896i
\(106\) −118.830 −1.12103
\(107\) −89.1318 + 89.1318i −0.833007 + 0.833007i −0.987927 0.154920i \(-0.950488\pi\)
0.154920 + 0.987927i \(0.450488\pi\)
\(108\) −154.052 78.6017i −1.42641 0.727794i
\(109\) 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 0.992552 0.121825i \(-0.0388747\pi\)
−0.121825 + 0.992552i \(0.538875\pi\)
\(114\) −98.5457 + 221.227i −0.864436 + 1.94059i
\(115\) −151.147 + 66.6139i −1.31432 + 0.579251i
\(116\) 68.1242i 0.587277i
\(117\) 74.0762 + 3.90974i 0.633129 + 0.0334166i
\(118\) −160.137 160.137i −1.35710 1.35710i
\(119\) 20.6050 + 64.5166i 0.173152 + 0.542157i
\(120\) 82.6238 81.9733i 0.688532 0.683111i
\(121\) −3.77875 −0.0312293
\(122\) −32.3246 32.3246i −0.264956 0.264956i
\(123\) −92.3314 + 35.4230i −0.750661 + 0.287992i
\(124\) −172.607 −1.39199
\(125\) 112.010 55.4868i 0.896079 0.443894i
\(126\) −102.559 + 175.445i −0.813958 + 1.39242i
\(127\) 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 \(-0.588178\pi\)
−0.273489 + 0.961875i \(0.588178\pi\)
\(132\) 200.411 76.8879i 1.51826 0.582484i
\(133\) 155.687 + 80.3142i 1.17058 + 0.603866i
\(134\) −28.0309 −0.209186
\(135\) 89.8981 + 100.714i 0.665912 + 0.746031i
\(136\) 75.0730i 0.552008i
\(137\) −57.1182 + 57.1182i −0.416921 + 0.416921i −0.884141 0.467220i \(-0.845256\pi\)
0.467220 + 0.884141i \(0.345256\pi\)
\(138\) 298.475 114.510i 2.16286 0.829784i
\(139\) 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
\(147\) 122.459 + 81.3191i 0.833054 + 0.553191i
\(148\) −133.774 + 133.774i −0.903880 + 0.903880i
\(149\) −62.9077 −0.422199 −0.211100 0.977465i \(-0.567704\pi\)
−0.211100 + 0.977465i \(0.567704\pi\)
\(150\) −221.768 + 96.6933i −1.47845 + 0.644622i
\(151\) −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
\(153\) −86.9567 4.58958i −0.568344 0.0299972i
\(154\) −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
\(162\) −164.281 203.179i −1.01408 1.25419i
\(163\) −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
\(165\) −167.555 0.662183i −1.01549 0.00401323i
\(166\) 142.955i 0.861173i
\(167\) 151.924 + 151.924i 0.909725 + 0.909725i 0.996250 0.0865247i \(-0.0275761\pi\)
−0.0865247 + 0.996250i \(0.527576\pi\)
\(168\) 101.883 + 127.164i 0.606447 + 0.756927i
\(169\) 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 \(-0.724134\pi\)
0.762169 + 0.647378i \(0.224134\pi\)
\(174\) −41.8793 + 94.0154i −0.240685 + 0.540319i
\(175\) 60.6582 + 164.151i 0.346618 + 0.938006i
\(176\) 6.61658i 0.0375942i
\(177\) −75.4429 196.645i −0.426231 1.11099i
\(178\) −161.695 161.695i −0.908399 0.908399i
\(179\) 157.790 0.881508 0.440754 0.897628i \(-0.354711\pi\)
0.440754 + 0.897628i \(0.354711\pi\)
\(180\) 269.524 102.183i 1.49735 0.567683i
\(181\) 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
\(183\) −15.2286 39.6938i −0.0832162 0.216906i
\(184\) 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
\(189\) −153.522 + 110.237i −0.812284 + 0.583262i
\(190\) −162.784 369.358i −0.856760 1.94399i
\(191\) 8.99622i 0.0471007i −0.999723 0.0235503i \(-0.992503\pi\)
0.999723 0.0235503i \(-0.00749699\pi\)
\(192\) −111.662 291.050i −0.581571 1.51588i
\(193\) 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
\(195\) −87.7659 + 87.0749i −0.450082 + 0.446538i
\(196\) 255.763 181.925i 1.30491 0.928190i
\(197\) −113.154 + 113.154i −0.574386 + 0.574386i −0.933351 0.358965i \(-0.883130\pi\)
0.358965 + 0.933351i \(0.383130\pi\)
\(198\) 323.846 + 17.0926i 1.63559 + 0.0863262i
\(199\) 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
\(207\) 296.902 + 15.6705i 1.43431 + 0.0757028i
\(208\) 3.45214 + 3.45214i 0.0165968 + 0.0165968i
\(209\) 279.552i 1.33757i
\(210\) −101.770 323.052i −0.484618 1.53834i
\(211\) −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
\(213\) 41.9623 + 109.376i 0.197006 + 0.513503i
\(214\) 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
\(222\) −266.854 + 102.379i −1.20205 + 0.461166i
\(223\) −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
\(225\) −224.993 1.77838i −0.999969 0.00790392i
\(226\) 448.854 1.98608
\(227\) −23.2602 23.2602i −0.102468 0.102468i 0.654014 0.756482i \(-0.273084\pi\)
−0.756482 + 0.654014i \(0.773084\pi\)
\(228\) 172.258 + 448.997i 0.755519 + 1.96929i
\(229\) −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
\(231\) 25.7350 233.163i 0.111407 1.00937i
\(232\) 58.3524 + 58.3524i 0.251519 + 0.251519i
\(233\) 90.6015 + 90.6015i 0.388847 + 0.388847i 0.874276 0.485429i \(-0.161336\pi\)
−0.485429 + 0.874276i \(0.661336\pi\)
\(234\) 177.881 160.046i 0.760177 0.683956i
\(235\) −382.495 + 168.574i −1.62764 + 0.717338i
\(236\) −449.702 −1.90552
\(237\) 18.0958 + 47.1673i 0.0763535 + 0.199018i
\(238\) 194.158 + 100.160i 0.815789 + 0.420840i
\(239\) −406.988 −1.70288 −0.851439 0.524454i \(-0.824269\pi\)
−0.851439 + 0.524454i \(0.824269\pi\)
\(240\) −0.0351132 + 8.88488i −0.000146305 + 0.0370203i
\(241\) 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
\(243\) −62.6752 234.778i −0.257923 0.966166i
\(244\) −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 \(-0.418057\pi\)
0.254597 + 0.967047i \(0.418057\pi\)
\(252\) 102.340 + 390.348i 0.406111 + 1.54900i
\(253\) −260.933 + 260.933i −1.03136 + 1.03136i
\(254\) 786.070 3.09477
\(255\) 103.027 102.216i 0.404027 0.400846i
\(256\) −240.473 −0.939346
\(257\) −100.099 100.099i −0.389491 0.389491i 0.485015 0.874506i \(-0.338814\pi\)
−0.874506 + 0.485015i \(0.838814\pi\)
\(258\) −6.13059 15.9796i −0.0237620 0.0619364i
\(259\) 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 \(-0.333588\pi\)
−0.866426 + 0.499306i \(0.833588\pi\)
\(264\) 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
\(267\) −76.1767 198.557i −0.285306 0.743660i
\(268\) −39.3586 + 39.3586i −0.146860 + 0.146860i
\(269\) 213.738i 0.794565i 0.917696 + 0.397282i \(0.130047\pi\)
−0.917696 + 0.397282i \(0.869953\pi\)
\(270\) 434.776 + 24.6709i 1.61028 + 0.0913736i
\(271\) 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
\(273\) −108.224 135.078i −0.396424 0.494790i
\(274\) 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 \(-0.845190\pi\)
0.884045 0.467401i \(-0.154810\pi\)
\(282\) 755.326 289.782i 2.67846 1.02759i
\(283\) −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
\(285\) 1.48354 375.388i 0.00520541 1.31715i
\(286\) 296.989i 1.03842i
\(287\) 205.072 + 105.790i 0.714536 + 0.368607i
\(288\) 15.6291 296.117i 0.0542676 1.02818i
\(289\) 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 \(-0.991028\pi\)
0.0281818 + 0.999603i \(0.491028\pi\)
\(294\) 464.806 93.8378i 1.58097 0.319176i
\(295\) 327.241 + 127.032i 1.10929 + 0.430618i
\(296\) 229.171i 0.774227i
\(297\) 268.653 + 137.074i 0.904555 + 0.461529i
\(298\) −143.489 + 143.489i −0.481507 + 0.481507i
\(299\) 272.279i 0.910632i
\(300\) −175.619 + 447.156i −0.585395 + 1.49052i
\(301\) −11.7934 + 3.76652i −0.0391807 + 0.0125134i
\(302\) −47.0815 + 47.0815i −0.155899 + 0.155899i
\(303\) 153.902 59.0445i 0.507926 0.194867i
\(304\) −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 \(-0.658057\pi\)
−0.476397 + 0.879230i \(0.658057\pi\)
\(312\) −68.7226 179.128i −0.220265 0.574128i
\(313\) 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
\(315\) 35.7948 312.960i 0.113634 0.993523i
\(316\) 107.866 0.341348
\(317\) −43.8360 + 43.8360i −0.138284 + 0.138284i −0.772860 0.634576i \(-0.781175\pi\)
0.634576 + 0.772860i \(0.281175\pi\)
\(318\) −332.835 + 127.692i −1.04665 + 0.401549i
\(319\) 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
\(327\) −98.0263 255.509i −0.299775 0.781373i
\(328\) 180.863 + 180.863i 0.551412 + 0.551412i
\(329\) −178.037 557.453i −0.541145 1.69438i
\(330\) −383.695 + 380.674i −1.16271 + 1.15356i
\(331\) −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
\(333\) −265.448 14.0103i −0.797140 0.0420731i
\(334\) 693.061 2.07503
\(335\) 39.7587 17.5226i 0.118683 0.0523062i
\(336\) −12.3638 1.36464i −0.0367972 0.00406142i
\(337\) 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
\(342\) −38.2940 + 725.539i −0.111971 + 2.12146i
\(343\) −48.5462 339.547i −0.141534 0.989933i
\(344\) −13.7231 −0.0398927
\(345\) −351.771 + 349.002i −1.01963 + 1.01160i
\(346\) 90.5940i 0.261832i
\(347\) −358.869 + 358.869i −1.03421 + 1.03421i −0.0348116 + 0.999394i \(0.511083\pi\)
−0.999394 + 0.0348116i \(0.988917\pi\)
\(348\) 73.2051 + 190.812i 0.210360 + 0.548310i
\(349\) 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 \(-0.889645\pi\)
0.339788 + 0.940502i \(0.389645\pi\)
\(354\) −620.616 276.454i −1.75315 0.780944i
\(355\) −182.016 70.6570i −0.512721 0.199034i
\(356\) −454.077 −1.27550
\(357\) 127.042 + 158.565i 0.355860 + 0.444161i
\(358\) 359.910 359.910i 1.00534 1.00534i
\(359\) −194.091 −0.540643 −0.270321 0.962770i \(-0.587130\pi\)
−0.270321 + 0.962770i \(0.587130\pi\)
\(360\) 143.337 318.389i 0.398159 0.884413i
\(361\) 265.304 0.734915
\(362\) −134.124 134.124i −0.370508 0.370508i
\(363\) −10.5840 + 4.06058i −0.0291571 + 0.0111862i
\(364\) −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
\(372\) −483.461 + 185.480i −1.29963 + 0.498603i
\(373\) 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
\(375\) 254.108 275.779i 0.677621 0.735411i
\(376\) 648.665i 1.72517i
\(377\) −61.9839 61.9839i −0.164414 0.164414i
\(378\) −98.7311 + 601.618i −0.261193 + 1.59158i
\(379\) 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 −0.698810 0.715307i \(-0.746287\pi\)
0.715307 + 0.698810i \(0.246287\pi\)
\(384\) −557.401 248.295i −1.45157 0.646602i
\(385\) 259.043 + 292.832i 0.672839 + 0.760603i
\(386\) 438.422i 1.13581i
\(387\) 0.838958 15.8954i 0.00216785 0.0410733i
\(388\) 731.601 + 731.601i 1.88557 + 1.88557i
\(389\) 234.607 0.603103 0.301551 0.953450i \(-0.402496\pi\)
0.301551 + 0.953450i \(0.402496\pi\)
\(390\) −1.57608 + 398.802i −0.00404122 + 1.02257i
\(391\) 319.624i 0.817452i
\(392\) 63.2462 374.906i 0.161342 0.956392i
\(393\) −200.699 + 76.9985i −0.510685 + 0.195925i
\(394\) 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
\(399\) 522.375 + 57.6562i 1.30921 + 0.144502i
\(400\) −10.9297 9.99126i −0.0273243 0.0249782i
\(401\) 255.719i 0.637703i 0.947805 + 0.318851i \(0.103297\pi\)
−0.947805 + 0.318851i \(0.896703\pi\)
\(402\) −78.5128 + 30.1215i −0.195306 + 0.0749292i
\(403\) 157.049 157.049i 0.389700 0.389700i
\(404\) 351.955i 0.871175i
\(405\) 360.025 + 185.491i 0.888951 + 0.458003i
\(406\) 228.766 73.0621i 0.563462 0.179956i
\(407\) 233.290 233.290i 0.573194 0.573194i
\(408\) 80.6723 + 210.275i 0.197726 + 0.515380i
\(409\) −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
\(417\) 116.109 44.5453i 0.278439 0.106823i
\(418\) −637.643 637.643i −1.52546 1.52546i
\(419\) 476.333i 1.13683i 0.822741 + 0.568417i \(0.192444\pi\)
−0.822741 + 0.568417i \(0.807556\pi\)
\(420\) −596.498 310.706i −1.42023 0.739775i
\(421\) −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
\(423\) 751.345 + 39.6560i 1.77623 + 0.0937494i
\(424\) 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 \(0.964499\pi\)
\(432\) 7.26856 14.2457i 0.0168254 0.0329762i
\(433\) −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
\(435\) 0.630465 159.530i 0.00144935 0.366735i
\(436\) −584.318 −1.34018
\(437\) −584.591 584.591i −1.33774 1.33774i
\(438\) −653.114 + 250.568i −1.49113 + 0.572073i
\(439\) −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
\(441\) 430.385 + 96.1775i 0.975929 + 0.218090i
\(442\) −181.894 181.894i −0.411526 0.411526i
\(443\) −214.203 214.203i −0.483528 0.483528i 0.422728 0.906256i \(-0.361072\pi\)
−0.906256 + 0.422728i \(0.861072\pi\)
\(444\) −230.942 + 518.446i −0.520140 + 1.16767i
\(445\) 330.425 + 128.268i 0.742527 + 0.288243i
\(446\) −159.588 −0.357821
\(447\) −176.201 + 67.5996i −0.394185 + 0.151230i
\(448\) −333.475 + 646.433i −0.744363 + 1.44293i
\(449\) 147.297 0.328055 0.164027 0.986456i \(-0.447551\pi\)
0.164027 + 0.986456i \(0.447551\pi\)
\(450\) −517.253 + 509.140i −1.14945 + 1.13142i
\(451\) 368.227i 0.816468i
\(452\) 630.242 630.242i 1.39434 1.39434i
\(453\) −57.8148 + 22.1807i −0.127627 + 0.0489641i
\(454\) −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 \(-0.566574\pi\)
−0.207628 + 0.978208i \(0.566574\pi\)
\(462\) −473.132 590.533i −1.02410 1.27821i
\(463\) 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
\(465\) 404.201 + 1.59741i 0.869251 + 0.00343530i
\(466\) 413.314 0.886939
\(467\) 61.5519 + 61.5519i 0.131803 + 0.131803i 0.769931 0.638128i \(-0.220291\pi\)
−0.638128 + 0.769931i \(0.720291\pi\)
\(468\) 25.0435 474.488i 0.0535118 1.01386i
\(469\) 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
\(477\) −331.081 17.4744i −0.694089 0.0366340i
\(478\) −928.316 + 928.316i −1.94208 + 1.94208i
\(479\) 572.620i 1.19545i 0.801702 + 0.597724i \(0.203928\pi\)
−0.801702 + 0.597724i \(0.796072\pi\)
\(480\) 348.079 + 350.841i 0.725165 + 0.730919i
\(481\) 243.434i 0.506099i
\(482\) 267.116 + 267.116i 0.554183 + 0.554183i
\(483\) −433.768 541.400i −0.898070 1.12091i
\(484\) 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 \(-0.772310\pi\)
0.754891 0.655850i \(-0.227690\pi\)
\(492\) 226.899 + 591.421i 0.461177 + 1.20207i
\(493\) 72.7618 + 72.7618i 0.147590 + 0.147590i
\(494\) −665.369 −1.34690
\(495\) −470.024 + 178.198i −0.949544 + 0.359995i
\(496\) 15.9615i 0.0321804i
\(497\) 125.319 242.929i 0.252152 0.488791i
\(498\) −153.617 400.408i −0.308468 0.804032i
\(499\) 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 \(-0.492119\pi\)
0.999694 0.0247567i \(-0.00788111\pi\)
\(504\) 422.017 + 246.696i 0.837335 + 0.489477i
\(505\) −99.4205 + 256.112i −0.196872 + 0.507152i
\(506\) 1190.35i 2.35247i
\(507\) −108.605 283.083i −0.214211 0.558349i
\(508\) 1103.73 1103.73i 2.17270 2.17270i
\(509\) 648.378i 1.27383i −0.770935 0.636914i \(-0.780211\pi\)
0.770935 0.636914i \(-0.219789\pi\)
\(510\) 1.85013 468.147i 0.00362770 0.917935i
\(511\) 153.945 + 482.017i 0.301261 + 0.943282i
\(512\) 26.7994 26.7994i 0.0523425 0.0523425i
\(513\) −307.098 + 601.886i −0.598632 + 1.17327i
\(514\) −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 \(-0.560058\pi\)
−0.187561 + 0.982253i \(0.560058\pi\)
\(522\) −16.2739 + 308.334i −0.0311761 + 0.590679i
\(523\) 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
\(525\) 346.294 + 394.595i 0.659608 + 0.751610i
\(526\) −440.462 −0.837380
\(527\) −184.357 + 184.357i −0.349824 + 0.349824i
\(528\) 7.11008 + 18.5327i 0.0134661 + 0.0350997i
\(529\) 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
\(537\) 441.960 169.559i 0.823018 0.315752i
\(538\) 487.524 + 487.524i 0.906179 + 0.906179i
\(539\) −446.026 + 317.261i −0.827507 + 0.588610i
\(540\) 645.116 575.834i 1.19466 1.06636i
\(541\) −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
\(543\) −63.1875 164.701i −0.116367 0.303316i
\(544\) −318.779 −0.585990
\(545\) 425.199 + 165.059i 0.780182 + 0.302860i
\(546\) −554.957 61.2524i −1.01641 0.112184i
\(547\) −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
\(552\) −275.445 717.956i −0.498994 1.30064i
\(553\) 54.0426 104.760i 0.0977263 0.189440i
\(554\) −557.655 −1.00660
\(555\) 314.504 312.028i 0.566674 0.562213i
\(556\) 265.527i 0.477567i
\(557\) 118.212 118.212i 0.212230 0.212230i −0.592984 0.805214i \(-0.702050\pi\)
0.805214 + 0.592984i \(0.202050\pi\)
\(558\) −781.229 41.2333i −1.40005 0.0738947i
\(559\) 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 \(-0.496417\pi\)
0.999937 0.0112552i \(-0.00358273\pi\)
\(564\) 653.678 1467.45i 1.15900 2.60186i
\(565\) −636.649 + 280.586i −1.12681 + 0.496612i
\(566\) −1217.08 −2.15031
\(567\) −311.547 + 473.738i −0.549465 + 0.835517i
\(568\) 214.251 214.251i 0.377203 0.377203i
\(569\) 602.118 1.05820 0.529102 0.848558i \(-0.322529\pi\)
0.529102 + 0.848558i \(0.322529\pi\)
\(570\) −852.855 859.623i −1.49624 1.50811i
\(571\) −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
\(573\) −9.66720 25.1979i −0.0168712 0.0439754i
\(574\) 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
\(582\) 559.902 + 1459.40i 0.962031 + 2.50757i
\(583\) 290.972 290.972i 0.499094 0.499094i
\(584\) 560.886i 0.960422i
\(585\) −152.258 + 338.204i −0.260270 + 0.578126i
\(586\) 1298.43i 2.21576i
\(587\) 512.337 + 512.337i 0.872806 + 0.872806i 0.992777 0.119971i \(-0.0382803\pi\)
−0.119971 + 0.992777i \(0.538280\pi\)
\(588\) 520.882 784.400i 0.885855 1.33401i
\(589\) 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 \(-0.824762\pi\)
0.523135 + 0.852250i \(0.324762\pi\)
\(594\) 925.441 300.124i 1.55798 0.505260i
\(595\) −338.003 20.6944i −0.568072 0.0347805i
\(596\) 402.950i 0.676090i
\(597\) 341.788 131.127i 0.572509 0.219644i
\(598\) 621.053 + 621.053i 1.03855 + 1.03855i
\(599\) 93.4354 0.155986 0.0779928 0.996954i \(-0.475149\pi\)
0.0779928 + 0.996954i \(0.475149\pi\)
\(600\) 232.587 + 533.443i 0.387646 + 0.889071i
\(601\) 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
\(603\) −78.0990 4.12207i −0.129517 0.00683593i
\(604\) 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
\(609\) 221.995 + 24.5023i 0.364524 + 0.0402337i
\(610\) 209.157 92.1804i 0.342881 0.151115i
\(611\) 689.034i 1.12772i
\(612\) −29.3981 + 556.994i −0.0480362 + 0.910120i
\(613\) 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
\(615\) 1.95413 494.462i 0.00317744 0.804004i
\(616\) −577.959 + 184.586i −0.938245 + 0.299652i
\(617\) 400.922 400.922i 0.649793 0.649793i −0.303150 0.952943i \(-0.598038\pi\)
0.952943 + 0.303150i \(0.0980383\pi\)
\(618\) 1396.67 535.833i 2.25998 0.867044i
\(619\) 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
\(627\) −300.402 783.009i −0.479111 1.24882i
\(628\) −1365.97 1365.97i −2.17512 2.17512i
\(629\) 285.762i 0.454312i
\(630\) −632.198 795.489i −1.00349 1.26268i
\(631\) 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
\(633\) −11.9863 + 4.59856i −0.0189357 + 0.00726470i
\(634\) 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 \(-0.0342873\pi\)
\(642\) 436.936 + 1138.89i 0.680585 + 1.77397i
\(643\) −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
\(645\) 18.6847 + 18.8329i 0.0289685 + 0.0291983i
\(646\) 781.065 1.20908
\(647\) 192.497 + 192.497i 0.297523 + 0.297523i 0.840043 0.542520i \(-0.182530\pi\)
−0.542520 + 0.840043i \(0.682530\pi\)
\(648\) −488.729 + 395.164i −0.754211 + 0.609822i
\(649\) 784.239 1.20838
\(650\) −490.586 448.463i −0.754748 0.689943i
\(651\) −62.0817 + 562.471i −0.0953636 + 0.864010i
\(652\) 125.066 + 125.066i 0.191819 + 0.191819i
\(653\) 178.554 + 178.554i 0.273436 + 0.273436i 0.830482 0.557046i \(-0.188065\pi\)
−0.557046 + 0.830482i \(0.688065\pi\)
\(654\) −806.394 359.209i −1.23302 0.549250i
\(655\) 129.652 333.989i 0.197942 0.509907i
\(656\) −19.5258 −0.0297649
\(657\) −649.672 34.2897i −0.988846 0.0521913i
\(658\) −1677.61 865.427i −2.54956 1.31524i
\(659\) −984.529 −1.49397 −0.746987 0.664838i \(-0.768500\pi\)
−0.746987 + 0.664838i \(0.768500\pi\)
\(660\) −4.24155 + 1073.26i −0.00642660 + 1.62615i
\(661\) 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
\(663\) −85.6929 223.362i −0.129250 0.336895i
\(664\) −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
\(672\) −539.969 + 432.621i −0.803525 + 0.643781i
\(673\) −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
\(675\) −632.103 + 236.793i −0.936449 + 0.350804i
\(676\) −647.377 −0.957658
\(677\) −430.936 430.936i −0.636538 0.636538i 0.313162 0.949700i \(-0.398612\pi\)
−0.949700 + 0.313162i \(0.898612\pi\)
\(678\) 1257.21 482.331i 1.85430 0.711403i
\(679\) 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 \(0.197658\pi\)
0.581818 + 0.813319i \(0.302342\pi\)
\(684\) 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
\(687\) −255.195 + 97.9059i −0.371463 + 0.142512i
\(688\) 0.740765 0.740765i 0.00107669 0.00107669i
\(689\) 303.623i 0.440673i
\(690\) −6.31701 + 1598.42i −0.00915508 + 2.31656i
\(691\) 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
\(693\) −178.471 680.731i −0.257534 0.982296i
\(694\) 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 \(0.717927\pi\)
\(702\) 326.253 639.427i 0.464748 0.910865i
\(703\) 522.659 + 522.659i 0.743469 + 0.743469i
\(704\) 1160.74 1.64877
\(705\) −890.198 + 883.190i −1.26269 + 1.25275i
\(706\) 967.358i 1.37020i
\(707\) −341.822 176.335i −0.483482 0.249413i
\(708\) −1259.59 + 483.243i −1.77908 + 0.682547i
\(709\) 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
\(714\) 651.455 + 71.9031i 0.912401 + 0.100705i
\(715\) −185.653 421.245i −0.259654 0.589154i
\(716\) 1010.71i 1.41161i
\(717\) −1139.95 + 437.342i −1.58989 + 0.609961i
\(718\) −442.710 + 442.710i −0.616588 + 0.616588i
\(719\) 160.221i 0.222838i −0.993773 0.111419i \(-0.964460\pi\)
0.993773 0.111419i \(-0.0355396\pi\)
\(720\) 9.44920 + 24.9237i 0.0131239 + 0.0346163i
\(721\) −329.207 1030.78i −0.456597 1.42966i
\(722\) 605.144 605.144i 0.838150 0.838150i
\(723\) 125.842 + 328.012i 0.174056 + 0.453682i
\(724\) −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
\(732\) −254.255 + 97.5452i −0.347343 + 0.133258i
\(733\) 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
\(735\) −600.616 + 423.657i −0.817165 + 0.576404i
\(736\) 1088.43 1.47884
\(737\) 68.6376 68.6376i 0.0931311 0.0931311i
\(738\) −50.4409 + 955.682i −0.0683481 + 1.29496i
\(739\) 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 0.742856 0.669451i \(-0.233471\pi\)
−0.669451 + 0.742856i \(0.733471\pi\)
\(744\) −255.238 + 572.987i −0.343062 + 0.770144i
\(745\) 113.826 293.220i 0.152786 0.393584i
\(746\) 180.739i 0.242278i
\(747\) 21.0221 398.297i 0.0281421 0.533196i
\(748\) −489.516 489.516i −0.654433 0.654433i
\(749\) 840.533 268.446i 1.12221 0.358405i
\(750\) −49.4309 1208.64i −0.0659079 1.61152i
\(751\) 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
\(753\) 357.982 137.340i 0.475408 0.182391i
\(754\) −282.764 −0.375018
\(755\) 37.3484 96.2112i 0.0494681 0.127432i
\(756\) 706.111 + 983.370i 0.934009 + 1.30075i
\(757\) −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 \(-0.219327\pi\)
0.771859 + 0.635794i \(0.219327\pi\)
\(762\) 2201.74 844.699i 2.88942 1.10853i
\(763\) −292.753 + 567.496i −0.383687 + 0.743769i
\(764\) −57.6245 −0.0754248
\(765\) 178.733 397.011i 0.233638 0.518969i
\(766\) 28.8236i 0.0376288i
\(767\) 409.169 409.169i