Properties

Label 105.3.k.d.62.4
Level 105
Weight 3
Character 105.62
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 62.4
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28094 + 2.28094i) q^{2} +(1.07458 - 2.80094i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +O(q^{10})\) \(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} +(-3.20922 - 6.22100i) 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} +(-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} +(-24.0503 + 12.2711i) q^{27} +(-39.8481 + 20.5564i) 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} +(34.8036 - 3.70223i) 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} +(42.3558 - 52.8657i) 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} +(-15.9771 + 60.9404i) 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} +(-70.9406 + 87.8297i) 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} +(-69.4914 + 35.8484i) 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} +(14.7571 + 133.702i) 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} +(-26.2933 - 155.859i) q^{98} +(-67.2426 + 74.7363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28094 + 2.28094i −1.14047 + 1.14047i −0.152108 + 0.988364i \(0.548606\pi\)
−0.988364 + 0.152108i \(0.951394\pi\)
\(3\) 1.07458 2.80094i 0.358195 0.933647i
\(4\) 6.40541i 1.60135i
\(5\) −1.80941 + 4.66112i −0.361882 + 0.932224i
\(6\) 3.93772 + 8.83986i 0.656287 + 1.47331i
\(7\) −3.20922 6.22100i −0.458460 0.888715i
\(8\) 5.48661 + 5.48661i 0.685827 + 0.685827i
\(9\) −6.69054 6.01969i −0.743393 0.668855i
\(10\) −6.50460 14.7589i −0.650460 1.47589i
\(11\) 11.1704i 1.01549i −0.861506 0.507747i \(-0.830478\pi\)
0.861506 0.507747i \(-0.169522\pi\)
\(12\) −17.9412 6.88316i −1.49510 0.573596i
\(13\) −5.82807 5.82807i −0.448313 0.448313i 0.446480 0.894794i \(-0.352677\pi\)
−0.894794 + 0.446480i \(0.852677\pi\)
\(14\) 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 \(-0.341850\pi\)
−0.879092 + 0.476652i \(0.841850\pi\)
\(18\) 28.9913 1.53016i 1.61063 0.0850091i
\(19\) 25.0261 1.31716 0.658581 0.752510i \(-0.271157\pi\)
0.658581 + 0.752510i \(0.271157\pi\)
\(20\) 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 \(-0.994988\pi\)
−0.0157445 0.999876i \(-0.505012\pi\)
\(24\) 21.2635 9.47185i 0.885980 0.394661i
\(25\) −18.4521 16.8677i −0.738083 0.674710i
\(26\) 26.5870 1.02258
\(27\) −24.0503 + 12.2711i −0.890754 + 0.454487i
\(28\) −39.8481 + 20.5564i −1.42315 + 0.734157i
\(29\) 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
\(35\) 34.8036 3.70223i 0.994390 0.105778i
\(36\) −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 \(0.631687\pi\)
\(42\) 42.3558 52.8657i 1.00847 1.25871i
\(43\) 1.25060 1.25060i 0.0290836 0.0290836i −0.692415 0.721499i \(-0.743453\pi\)
0.721499 + 0.692415i \(0.243453\pi\)
\(44\) −71.5513 −1.62617
\(45\) 40.1644 20.2933i 0.892543 0.450963i
\(46\) 106.562 2.31657
\(47\) 59.1134 + 59.1134i 1.25773 + 1.25773i 0.952173 + 0.305558i \(0.0988431\pi\)
0.305558 + 0.952173i \(0.401157\pi\)
\(48\) 0.636508 1.65908i 0.0132606 0.0345642i
\(49\) −28.4018 + 39.9292i −0.579629 + 0.814881i
\(50\) 80.5625 3.61381i 1.61125 0.0722761i
\(51\) −26.5143 + 11.8108i −0.519888 + 0.231585i
\(52\) −37.3312 + 37.3312i −0.717908 + 0.717908i
\(53\) 26.0484 + 26.0484i 0.491478 + 0.491478i 0.908772 0.417293i \(-0.137021\pi\)
−0.417293 + 0.908772i \(0.637021\pi\)
\(54\) 26.8677 82.8473i 0.497550 1.53421i
\(55\) 52.0668 + 20.2119i 0.946669 + 0.367489i
\(56\) 16.5245 51.7400i 0.295080 0.923929i
\(57\) 26.8926 70.0965i 0.471800 1.22976i
\(58\) −24.2588 + 24.2588i −0.418254 + 0.418254i
\(59\) 70.2066i 1.18994i −0.803747 0.594971i \(-0.797163\pi\)
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
\(63\) −15.9771 + 60.9404i −0.253605 + 0.967308i
\(64\) 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
\(70\) −70.9406 + 87.8297i −1.01344 + 1.25471i
\(71\) 39.0498i 0.549997i −0.961445 0.274999i \(-0.911323\pi\)
0.961445 0.274999i \(-0.0886774\pi\)
\(72\) −3.68068 69.7361i −0.0511205 0.968557i
\(73\) 51.1141 + 51.1141i 0.700193 + 0.700193i 0.964452 0.264259i \(-0.0851274\pi\)
−0.264259 + 0.964452i \(0.585127\pi\)
\(74\) 95.2731 1.28747
\(75\) −67.0738 + 33.5574i −0.894318 + 0.447432i
\(76\) 160.302i 2.10924i
\(77\) −69.4914 + 35.8484i −0.902485 + 0.465564i
\(78\) 28.5700 74.4687i 0.366282 0.954726i
\(79\) 16.8398i 0.213162i 0.994304 + 0.106581i \(0.0339903\pi\)
−0.994304 + 0.106581i \(0.966010\pi\)
\(80\) −1.07177 + 2.76092i −0.0133971 + 0.0345115i
\(81\) 8.52661 + 80.5500i 0.105267 + 0.994444i
\(82\) 75.1900 75.1900i 0.916951 0.916951i
\(83\) 31.3367 31.3367i 0.377551 0.377551i −0.492667 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
\(87\) 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 0.197101 0.980383i \(-0.436847\pi\)
0.980383 0.197101i \(-0.0631528\pi\)
\(98\) −26.2933 155.859i −0.268299 1.59040i
\(99\) −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 \(0.412311\pi\)
\(102\) 33.5378 87.4175i 0.328802 0.857034i
\(103\) −109.306 109.306i −1.06123 1.06123i −0.997999 0.0632258i \(-0.979861\pi\)
−0.0632258 0.997999i \(-0.520139\pi\)
\(104\) 63.9528i 0.614931i
\(105\) 27.0297 101.461i 0.257426 0.966298i
\(106\) −118.830 −1.12103
\(107\) 89.1318 89.1318i 0.833007 0.833007i −0.154920 0.987927i \(-0.549512\pi\)
0.987927 + 0.154920i \(0.0495120\pi\)
\(108\) 78.6017 + 154.052i 0.727794 + 1.42641i
\(109\) 91.2226i 0.836904i −0.908239 0.418452i \(-0.862573\pi\)
0.908239 0.418452i \(-0.137427\pi\)
\(110\) −164.864 + 72.6592i −1.49876 + 0.660538i
\(111\) −80.9387 + 36.0542i −0.729177 + 0.324813i
\(112\) −1.90092 3.68489i −0.0169725 0.0329008i
\(113\) −98.3921 98.3921i −0.870726 0.870726i 0.121825 0.992552i \(-0.461125\pi\)
−0.992552 + 0.121825i \(0.961125\pi\)
\(114\) 98.5457 + 221.227i 0.864436 + 1.94059i
\(115\) 151.147 66.6139i 1.31432 0.579251i
\(116\) 68.1242i 0.587277i
\(117\) 3.90974 + 74.0762i 0.0334166 + 0.633129i
\(118\) 160.137 + 160.137i 1.35710 + 1.35710i
\(119\) −20.6050 + 64.5166i −0.173152 + 0.542157i
\(120\) 5.67508 + 116.250i 0.0472924 + 0.968752i
\(121\) −3.77875 −0.0312293
\(122\) −32.3246 32.3246i −0.264956 0.264956i
\(123\) −35.4230 + 92.3314i −0.287992 + 0.750661i
\(124\) 172.607 1.39199
\(125\) 112.010 55.4868i 0.896079 0.443894i
\(126\) −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 \(0.588178\pi\)
\(132\) −76.8879 + 200.411i −0.582484 + 1.51826i
\(133\) −80.3142 155.687i −0.603866 1.17058i
\(134\) 28.0309 0.209186
\(135\) −13.6804 134.305i −0.101336 0.994852i
\(136\) 75.0730i 0.552008i
\(137\) 57.1182 57.1182i 0.416921 0.416921i −0.467220 0.884141i \(-0.654744\pi\)
0.884141 + 0.467220i \(0.154744\pi\)
\(138\) 114.510 298.475i 0.829784 2.16286i
\(139\) −41.4536 −0.298227 −0.149113 0.988820i \(-0.547642\pi\)
−0.149113 + 0.988820i \(0.547642\pi\)
\(140\) −23.7143 222.932i −0.169388 1.59237i
\(141\) 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
\(147\) 81.3191 + 122.459i 0.553191 + 0.833054i
\(148\) −133.774 + 133.774i −0.903880 + 0.903880i
\(149\) 62.9077 0.422199 0.211100 0.977465i \(-0.432296\pi\)
0.211100 + 0.977465i \(0.432296\pi\)
\(150\) 76.4492 229.534i 0.509661 1.53023i
\(151\) −20.6412 −0.136697 −0.0683484 0.997662i \(-0.521773\pi\)
−0.0683484 + 0.997662i \(0.521773\pi\)
\(152\) 137.308 + 137.308i 0.903345 + 0.903345i
\(153\) 4.58958 + 86.9567i 0.0299972 + 0.568344i
\(154\) 76.7377 240.274i 0.498297 1.56022i
\(155\) −125.603 48.7581i −0.810343 0.314568i
\(156\) 64.4470 + 144.678i 0.413122 + 0.927423i
\(157\) −213.253 + 213.253i −1.35830 + 1.35830i −0.482284 + 0.876015i \(0.660193\pi\)
−0.876015 + 0.482284i \(0.839807\pi\)
\(158\) −38.4106 38.4106i −0.243105 0.243105i
\(159\) 100.951 44.9687i 0.634912 0.282822i
\(160\) −66.4378 150.747i −0.415237 0.942171i
\(161\) −70.3531 + 220.283i −0.436976 + 1.36822i
\(162\) −203.179 164.281i −1.25419 1.01408i
\(163\) −19.5250 + 19.5250i −0.119785 + 0.119785i −0.764458 0.644673i \(-0.776993\pi\)
0.644673 + 0.764458i \(0.276993\pi\)
\(164\) 211.151i 1.28750i
\(165\) 112.562 124.117i 0.682196 0.752222i
\(166\) 142.955i 0.861173i
\(167\) 151.924 + 151.924i 0.909725 + 0.909725i 0.996250 0.0865247i \(-0.0275761\pi\)
−0.0865247 + 0.996250i \(0.527576\pi\)
\(168\) −127.164 101.883i −0.756927 0.606447i
\(169\) 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
\(175\) −45.7175 + 168.923i −0.261243 + 0.965273i
\(176\) 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 \(0.948065\pi\)
\(182\) −85.3236 165.398i −0.468811 0.908780i
\(183\) 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
\(189\) 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 \(0.00749699\pi\)
−0.999723 + 0.0235503i \(0.992503\pi\)
\(192\) −291.050 111.662i −1.51588 0.581571i
\(193\) 96.1055 96.1055i 0.497956 0.497956i −0.412845 0.910801i \(-0.635465\pi\)
0.910801 + 0.412845i \(0.135465\pi\)
\(194\) 521.041i 2.68578i
\(195\) −6.02827 123.485i −0.0309142 0.633257i
\(196\) 255.763 + 181.925i 1.30491 + 0.928190i
\(197\) 113.154 113.154i 0.574386 0.574386i −0.358965 0.933351i \(-0.616870\pi\)
0.933351 + 0.358965i \(0.116870\pi\)
\(198\) −17.0926 323.846i −0.0863262 1.63559i
\(199\) −122.026 −0.613196 −0.306598 0.951839i \(-0.599191\pi\)
−0.306598 + 0.951839i \(0.599191\pi\)
\(200\) −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
\(203\) −34.1314 66.1629i −0.168135 0.325926i
\(204\) 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
\(210\) 169.774 + 293.081i 0.808449 + 1.39562i
\(211\) −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
\(217\) 167.637 86.4788i 0.772522 0.398520i
\(218\) 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 \(-0.214618\pi\)
−0.624306 + 0.781180i \(0.714618\pi\)
\(224\) 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 \(-0.273084\pi\)
−0.756482 + 0.654014i \(0.773084\pi\)
\(228\) −448.997 172.258i −1.96929 0.755519i
\(229\) 91.1105 0.397862 0.198931 0.980013i \(-0.436253\pi\)
0.198931 + 0.980013i \(0.436253\pi\)
\(230\) −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 0.485429 0.874276i \(-0.338664\pi\)
−0.874276 + 0.485429i \(0.838664\pi\)
\(234\) −177.881 160.046i −0.760177 0.683956i
\(235\) −382.495 + 168.574i −1.62764 + 0.717338i
\(236\) −449.702 −1.90552
\(237\) 47.1673 + 18.0958i 0.199018 + 0.0763535i
\(238\) −100.160 194.158i −0.420840 0.815789i
\(239\) 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
\(245\) −134.724 204.632i −0.549895 0.835234i
\(246\) −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 \(0.418057\pi\)
\(252\) 390.348 + 102.340i 1.54900 + 0.406111i
\(253\) −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 \(-0.338814\pi\)
−0.874506 + 0.485015i \(0.838814\pi\)
\(258\) 15.9796 + 6.13059i 0.0619364 + 0.0237620i
\(259\) −62.8998 + 196.946i −0.242856 + 0.760410i
\(260\) −106.458 241.553i −0.409453 0.929049i
\(261\) −71.1566 64.0218i −0.272631 0.245294i
\(262\) 163.439 163.439i 0.623814 0.623814i
\(263\) 96.5525 + 96.5525i 0.367120 + 0.367120i 0.866426 0.499306i \(-0.166412\pi\)
−0.499306 + 0.866426i \(0.666412\pi\)
\(264\) −105.805 237.523i −0.400776 0.899708i
\(265\) −168.547 + 74.2824i −0.636025 + 0.280311i
\(266\) 538.306 + 171.922i 2.02371 + 0.646323i
\(267\) −198.557 76.1767i −0.743660 0.285306i
\(268\) −39.3586 + 39.3586i −0.146860 + 0.146860i
\(269\) 213.738i 0.794565i 0.917696 + 0.397282i \(0.130047\pi\)
−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
\(273\) 135.078 + 108.224i 0.494790 + 0.396424i
\(274\) 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
\(280\) 211.267 + 170.641i 0.754525 + 0.609434i
\(281\) 262.680i 0.934803i 0.884045 + 0.467401i \(0.154810\pi\)
−0.884045 + 0.467401i \(0.845190\pi\)
\(282\) −289.782 + 755.326i −1.02759 + 2.67846i
\(283\) 266.792 + 266.792i 0.942728 + 0.942728i 0.998446 0.0557189i \(-0.0177451\pi\)
−0.0557189 + 0.998446i \(0.517745\pi\)
\(284\) −250.130 −0.880740
\(285\) 278.069 + 252.183i 0.975680 + 0.884852i
\(286\) 296.989i 1.03842i
\(287\) 105.790 + 205.072i 0.368607 + 0.714536i
\(288\) 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 \(-0.991028\pi\)
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
\(297\) 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 \(-0.945958\pi\)
0.168965 + 0.985622i \(0.445958\pi\)
\(308\) 229.624 + 445.121i 0.745532 + 1.44520i
\(309\) −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 \(0.658057\pi\)
\(312\) −179.128 68.7226i −0.574128 0.220265i
\(313\) −195.491 195.491i −0.624573 0.624573i 0.322124 0.946697i \(-0.395603\pi\)
−0.946697 + 0.322124i \(0.895603\pi\)
\(314\) 972.836i 3.09820i
\(315\) −255.141 184.737i −0.809973 0.586468i
\(316\) 107.866 0.341348
\(317\) 43.8360 43.8360i 0.138284 0.138284i −0.634576 0.772860i \(-0.718825\pi\)
0.772860 + 0.634576i \(0.218825\pi\)
\(318\) −127.692 + 332.835i −0.401549 + 1.04665i
\(319\) 118.802i 0.372420i
\(320\) 484.344 + 188.018i 1.51357 + 0.587557i
\(321\) −153.873 345.432i −0.479356 1.07611i
\(322\) −341.982 662.925i −1.06206 2.05877i
\(323\) −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
\(336\) −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
\(342\) 725.539 38.2940i 2.12146 0.111971i
\(343\) 339.547 + 48.5462i 0.989933 + 0.141534i
\(344\) 13.7231 0.0398927
\(345\) −24.1617 494.936i −0.0700338 1.43460i
\(346\) 90.5940i 0.261832i
\(347\) 358.869 358.869i 1.03421 1.03421i 0.0348116 0.999394i \(-0.488917\pi\)
0.999394 0.0348116i \(-0.0110831\pi\)
\(348\) −190.812 73.2051i −0.548310 0.210360i
\(349\) −51.4939 −0.147547 −0.0737735 0.997275i \(-0.523504\pi\)
−0.0737735 + 0.997275i \(0.523504\pi\)
\(350\) −281.025 489.582i −0.802927 1.39881i
\(351\) 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
\(357\) 158.565 + 127.042i 0.444161 + 0.355860i
\(358\) 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 \(-0.560371\pi\)
0.982068 + 0.188526i \(0.0603710\pi\)
\(368\) −13.8364 13.8364i −0.0375989 0.0375989i
\(369\) 220.550 + 198.436i 0.597696 + 0.537766i
\(370\) −172.388 + 444.079i −0.465913 + 1.20021i
\(371\) 78.4520 245.642i 0.211461 0.662107i
\(372\) 185.480 483.461i 0.498603 1.29963i
\(373\) 39.6194 39.6194i 0.106218 0.106218i −0.652000 0.758219i \(-0.726070\pi\)
0.758219 + 0.652000i \(0.226070\pi\)
\(374\) 348.630i 0.932165i
\(375\) −35.0511 373.358i −0.0934695 0.995622i
\(376\) 648.665i 1.72517i
\(377\) −61.9839 61.9839i −0.164414 0.164414i
\(378\) −601.618 + 98.7311i −1.59158 + 0.261193i
\(379\) 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
\(385\) −41.3555 388.772i −0.107417 1.00980i
\(386\) 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
\(392\) −374.906 + 63.2462i −0.956392 + 0.161342i
\(393\) −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 \(-0.893198\pi\)
0.329269 + 0.944236i \(0.393198\pi\)
\(398\) 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 \(-0.896703\pi\)
0.947805 0.318851i \(-0.103297\pi\)
\(402\) 30.1215 78.5128i 0.0749292 0.195306i
\(403\) 157.049 157.049i 0.389700 0.389700i
\(404\) 351.955i 0.871175i
\(405\) −390.881 106.004i −0.965139 0.261739i
\(406\) 228.766 + 73.0621i 0.563462 + 0.179956i
\(407\) −233.290 + 233.290i −0.573194 + 0.573194i
\(408\) −210.275 80.6723i −0.515380 0.197726i
\(409\) 549.262 1.34294 0.671469 0.741033i \(-0.265664\pi\)
0.671469 + 0.741033i \(0.265664\pi\)
\(410\) 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
\(413\) −436.756 + 225.309i −1.05752 + 0.545541i
\(414\) −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 \(0.807556\pi\)
\(420\) −649.902 173.136i −1.54738 0.412230i
\(421\) −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
\(427\) 88.1615 45.4798i 0.206467 0.106510i
\(428\) −570.926 570.926i −1.33394 1.33394i
\(429\) 112.390 + 252.305i 0.261980 + 0.588123i
\(430\) −26.5921 10.3228i −0.0618420 0.0240066i
\(431\) 95.9393i 0.222597i −0.993787 0.111299i \(-0.964499\pi\)
0.993787 0.111299i \(-0.0355010\pi\)
\(432\) −14.2457 + 7.26856i −0.0329762 + 0.0168254i
\(433\) 273.161 + 273.161i 0.630857 + 0.630857i 0.948283 0.317426i \(-0.102818\pi\)
−0.317426 + 0.948283i \(0.602818\pi\)
\(434\) −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 \(-0.350859\pi\)
0.451585 + 0.892228i \(0.350859\pi\)
\(440\) 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 0.906256 0.422728i \(-0.138928\pi\)
−0.422728 + 0.906256i \(0.638928\pi\)
\(444\) 230.942 + 518.446i 0.520140 + 1.16767i
\(445\) 330.425 + 128.268i 0.742527 + 0.288243i
\(446\) −159.588 −0.357821
\(447\) 67.5996 176.201i 0.151230 0.394185i
\(448\) −646.433 + 333.475i −1.44293 + 0.744363i
\(449\) −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
\(455\) −224.415 181.261i −0.493220 0.398376i
\(456\) 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 \(0.566574\pi\)
\(462\) −590.533 473.132i −1.27821 1.02410i
\(463\) 362.672 362.672i 0.783309 0.783309i −0.197079 0.980388i \(-0.563145\pi\)
0.980388 + 0.197079i \(0.0631454\pi\)
\(464\) 6.29967 0.0135769
\(465\) −271.540 + 299.412i −0.583956 + 0.643897i
\(466\) 413.314 0.886939
\(467\) 61.5519 + 61.5519i 0.131803 + 0.131803i 0.769931 0.638128i \(-0.220291\pi\)
−0.638128 + 0.769931i \(0.720291\pi\)
\(468\) 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
\(483\) 541.400 + 433.768i 1.12091 + 0.898070i
\(484\) 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
\(490\) 774.053 + 159.457i 1.57970 + 0.325422i
\(491\) 644.045i 1.31170i 0.754891 + 0.655850i \(0.227690\pi\)
−0.754891 + 0.655850i \(0.772310\pi\)
\(492\) 591.421 + 226.899i 1.20207 + 0.461177i
\(493\) −72.7618 72.7618i −0.147590 0.147590i
\(494\) 665.369 1.34690
\(495\) −226.685 448.654i −0.457950 0.906372i
\(496\) 15.9615i 0.0321804i
\(497\) −242.929 + 125.319i −0.488791 + 0.252152i
\(498\) 400.408 + 153.617i 0.804032 + 0.308468i
\(499\) 530.323i 1.06277i −0.847130 0.531386i \(-0.821672\pi\)
0.847130 0.531386i \(-0.178328\pi\)
\(500\) −355.416 717.470i −0.710831 1.43494i
\(501\) 588.786 262.275i 1.17522 0.523503i
\(502\) −291.523 + 291.523i −0.580723 + 0.580723i
\(503\) 515.298 515.298i 1.02445 1.02445i 0.0247567 0.999694i \(-0.492119\pi\)
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
\(507\) −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
\(518\) −305.752 592.694i −0.590256 1.14420i
\(519\) −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 \(0.560058\pi\)
\(522\) 308.334 16.2739i 0.590679 0.0311761i
\(523\) −516.575 516.575i −0.987715 0.987715i 0.0122109 0.999925i \(-0.496113\pi\)
−0.999925 + 0.0122109i \(0.996113\pi\)
\(524\) 458.975i 0.875906i
\(525\) 424.016 + 309.574i 0.807649 + 0.589664i
\(526\) −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
\(532\) −997.242 + 514.446i −1.87451 + 0.967003i
\(533\) 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
\(546\) −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
\(552\) −717.956 275.445i −1.30064 0.498994i
\(553\) 104.760 54.0426i 0.189440 0.0977263i
\(554\) 557.655 1.00660
\(555\) −21.6020 442.502i −0.0389225 0.797300i
\(556\) 265.527i 0.477567i
\(557\) −118.212 + 118.212i −0.212230 + 0.212230i −0.805214 0.592984i \(-0.797950\pi\)
0.592984 + 0.805214i \(0.297950\pi\)
\(558\) 41.2333 + 781.229i 0.0738947 + 1.40005i
\(559\) −14.5771 −0.0260772
\(560\) 20.6152 2.19294i 0.0368129 0.00391597i
\(561\) 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
\(567\) 473.738 311.547i 0.835517 0.549465i
\(568\) 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 \(-0.724884\pi\)
0.760643 + 0.649170i \(0.224884\pi\)
\(578\) 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 \(-0.0382803\pi\)
−0.119971 + 0.992777i \(0.538280\pi\)
\(588\) 784.400 520.882i 1.33401 0.885855i
\(589\) 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
\(595\) −263.437 212.779i −0.442751 0.357613i
\(596\) 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 \(0.987462\pi\)
\(602\) 35.4913 18.3089i 0.0589557 0.0304134i
\(603\) 4.12207 + 78.0990i 0.00683593 + 0.129517i
\(604\) 132.216i 0.218900i
\(605\) 6.83729 17.6132i 0.0113013 0.0291127i
\(606\) 216.364 + 485.719i 0.357036 + 0.801516i
\(607\) −782.862 + 782.862i −1.28972 + 1.28972i −0.354769 + 0.934954i \(0.615440\pi\)
−0.934954 + 0.354769i \(0.884560\pi\)
\(608\) −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
\(612\) 556.994 29.3981i 0.910120 0.0480362i
\(613\) 587.076 587.076i 0.957710 0.957710i −0.0414311 0.999141i \(-0.513192\pi\)
0.999141 + 0.0414311i \(0.0131917\pi\)
\(614\) 1143.73i 1.86275i
\(615\) −366.273 332.176i −0.595566 0.540124i
\(616\) −577.959 184.586i −0.938245 0.299652i
\(617\) −400.922 + 400.922i −0.649793 + 0.649793i −0.952943 0.303150i \(-0.901962\pi\)
0.303150 + 0.952943i \(0.401962\pi\)
\(618\) 535.833 1396.67i 0.867044 2.25998i
\(619\) −382.132 −0.617338 −0.308669 0.951170i \(-0.599883\pi\)
−0.308669 + 0.951170i \(0.599883\pi\)
\(620\) −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
\(623\) −441.004 + 227.500i −0.707872 + 0.365169i
\(624\) −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
\(630\) 1003.34 160.588i 1.59260 0.254901i
\(631\) 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
\(637\) 398.238 67.1823i 0.625177 0.105467i
\(638\) 270.981 + 270.981i 0.424735 + 0.424735i
\(639\) −235.068 + 261.264i −0.367868 + 0.408864i
\(640\) −930.630 + 410.150i −1.45411 + 0.640860i
\(641\) 137.826i 0.215017i 0.994204 + 0.107509i \(0.0342873\pi\)
−0.994204 + 0.107509i \(0.965713\pi\)
\(642\) 1138.89 + 436.936i 1.77397 + 0.680585i
\(643\) 340.846 + 340.846i 0.530087 + 0.530087i 0.920598 0.390511i \(-0.127702\pi\)
−0.390511 + 0.920598i \(0.627702\pi\)
\(644\) 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 \(-0.182530\pi\)
−0.542520 + 0.840043i \(0.682530\pi\)
\(648\) −395.164 + 488.729i −0.609822 + 0.754211i
\(649\) −784.239 −1.20838
\(650\) −490.586 448.463i −0.754748 0.689943i
\(651\) −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 0.557046 0.830482i \(-0.311935\pi\)
−0.830482 + 0.557046i \(0.811935\pi\)
\(654\) 806.394 359.209i 1.23302 0.549250i
\(655\) 129.652 333.989i 0.197942 0.509907i
\(656\) −19.5258 −0.0297649
\(657\) −34.2897 649.672i −0.0521913 0.988846i
\(658\) 865.427 + 1677.61i 1.31524 + 2.54956i
\(659\) 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
\(665\) 870.998 92.6523i 1.30977 0.139327i
\(666\) −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
\(672\) 432.621 539.969i 0.643781 0.803525i
\(673\) −770.416 + 770.416i −1.14475 + 1.14475i −0.157179 + 0.987570i \(0.550240\pi\)
−0.987570 + 0.157179i \(0.949760\pi\)
\(674\) −928.898 −1.37819
\(675\) 650.765 + 179.247i 0.964097 + 0.265551i
\(676\) −647.377 −0.957658
\(677\) −430.936 430.936i −0.636538 0.636538i 0.313162 0.949700i \(-0.398612\pi\)
−0.949700 + 0.313162i \(0.898612\pi\)
\(678\) 482.331 1257.21i 0.711403 1.85430i
\(679\) −1077.08 343.994i −1.58628 0.506618i
\(680\) 349.924 + 135.838i 0.514595 + 0.199761i
\(681\) −90.1453 + 40.1553i −0.132372 + 0.0589652i
\(682\) −686.586 + 686.586i −1.00672 + 1.00672i
\(683\) −952.879 952.879i −1.39514 1.39514i −0.813319 0.581818i \(-0.802342\pi\)
−0.581818 0.813319i \(-0.697658\pi\)
\(684\) −964.971 + 1072.51i −1.41078 + 1.56800i
\(685\) 162.885 + 369.585i 0.237788 + 0.539540i
\(686\) −885.219 + 663.757i −1.29041 + 0.967576i
\(687\) 97.9059 255.195i 0.142512 0.371463i
\(688\) 0.740765 0.740765i 0.00107669 0.00107669i
\(689\) 303.623i 0.440673i
\(690\) 1184.03 + 1073.81i 1.71599 + 1.55625i
\(691\) 428.205i 0.619689i −0.950787 0.309844i \(-0.899723\pi\)
0.950787 0.309844i \(-0.100277\pi\)
\(692\) −127.204 127.204i −0.183821 0.183821i
\(693\) 680.731 + 178.471i 0.982296 + 0.257534i
\(694\) 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
\(700\) 1082.02 + 292.839i 1.54574 + 0.418342i
\(701\) 1086.06i 1.54929i −0.632393 0.774647i \(-0.717927\pi\)
0.632393 0.774647i \(-0.282073\pi\)
\(702\) −639.427 + 326.253i −0.910865 + 0.464748i
\(703\) −522.659 522.659i −0.743469 0.743469i
\(704\) −1160.74 −1.64877
\(705\) 61.1440 + 1252.49i 0.0867290 + 1.77659i
\(706\) 967.358i 1.37020i
\(707\) −176.335 341.822i −0.249413 0.483482i
\(708\) −483.243 + 1259.59i −0.682547 + 1.77908i
\(709\) 384.594i 0.542446i 0.962516 + 0.271223i \(0.0874281\pi\)
−0.962516 + 0.271223i \(0.912572\pi\)
\(710\) −576.333 + 254.003i −0.811736 + 0.357751i
\(711\) 101.370 112.667i 0.142574 0.158463i
\(712\) 388.943 388.943i 0.546269 0.546269i
\(713\) 629.462 629.462i 0.882836 0.882836i
\(714\) −651.455 + 71.9031i −0.912401 + 0.100705i
\(715\) −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 \(-0.530124\pi\)
0.995525 + 0.0944960i \(0.0301240\pi\)
\(728\) −397.851 + 205.239i −0.546498 + 0.281921i
\(729\) 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 \(-0.318864\pi\)
−0.842410 + 0.538838i \(0.818864\pi\)
\(734\) 1328.56i 1.81003i
\(735\) −717.936 + 157.460i −0.976783 + 0.214231i
\(736\) 1088.43 1.47884
\(737\) −68.6376 + 68.6376i −0.0931311 + 0.0931311i
\(738\) −955.682 + 50.4409i −1.29496 + 0.0683481i
\(739\) 343.180i 0.464385i 0.972670 + 0.232192i \(0.0745899\pi\)
−0.972670 + 0.232192i \(0.925410\pi\)
\(740\) −381.486 865.590i −0.515521 1.16972i
\(741\) −565.260 + 251.796i −0.762834 + 0.339805i
\(742\) 381.351 + 739.240i 0.513950 + 0.996280i
\(743\) −54.5399 54.5399i −0.0734050 0.0734050i 0.669451 0.742856i \(-0.266529\pi\)
−0.742856 + 0.669451i \(0.766529\pi\)
\(744\) 255.238 + 572.987i 0.343062 + 0.770144i
\(745\) −113.826 + 293.220i −0.152786 + 0.393584i
\(746\) 180.739i 0.242278i
\(747\) −398.297 + 21.0221i −0.533196 + 0.0281421i
\(748\) 489.516 + 489.516i 0.654433 + 0.654433i
\(749\) −840.533 268.446i −1.12221 0.358405i
\(750\) 931.559 + 771.660i 1.24208 + 1.02888i
\(751\) 969.222 1.29057 0.645287 0.763940i \(-0.276738\pi\)
0.645287 + 0.763940i \(0.276738\pi\)
\(752\) 35.0146 + 35.0146i 0.0465620 + 0.0465620i
\(753\) 137.340 357.982i 0.182391 0.475408i
\(754\) 282.764 0.375018
\(755\) 37.3484 96.2112i 0.0494681 0.127432i
\(756\) 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 \(0.219327\pi\)
\(762\) −844.699 + 2201.74i −1.10853 + 2.88942i
\(763\) −567.496 + 292.753i −0.743769 + 0.383687i
\(764\) 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