Properties

Label 105.2.j.a.92.5
Level 105
Weight 2
Character 105.92
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 92.5
Character \(\chi\) = 105.92
Dual form 105.2.j.a.8.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +O(q^{10})\) \(q+(-0.347054 + 0.347054i) q^{2} +(1.72305 - 0.176396i) q^{3} +1.75911i q^{4} +(-1.16790 + 1.90683i) q^{5} +(-0.536770 + 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.30461 - 1.30461i) q^{8} +(2.93777 - 0.607876i) q^{9} +(-0.256447 - 1.06710i) q^{10} -2.67137i q^{11} +(0.310299 + 3.03102i) q^{12} +(2.14945 - 2.14945i) q^{13} +0.490808 q^{14} +(-1.67599 + 3.49157i) q^{15} -2.61267 q^{16} +(3.26719 - 3.26719i) q^{17} +(-0.808598 + 1.23053i) q^{18} +5.24329i q^{19} +(-3.35432 - 2.05447i) q^{20} +(-1.34311 - 1.09365i) q^{21} +(0.927108 + 0.927108i) q^{22} +(-2.54815 - 2.54815i) q^{23} +(-2.47803 - 2.01778i) q^{24} +(-2.27200 - 4.45399i) q^{25} +1.49195i q^{26} +(4.95468 - 1.56561i) q^{27} +(1.24388 - 1.24388i) q^{28} -2.86924 q^{29} +(-0.630101 - 1.79342i) q^{30} -5.28599 q^{31} +(3.51596 - 3.51596i) q^{32} +(-0.471218 - 4.60289i) q^{33} +2.26778i q^{34} +(2.17417 - 0.522500i) q^{35} +(1.06932 + 5.16785i) q^{36} +(-2.14286 - 2.14286i) q^{37} +(-1.81970 - 1.81970i) q^{38} +(3.32444 - 4.08274i) q^{39} +(4.01133 - 0.964012i) q^{40} +11.5768i q^{41} +(0.845684 - 0.0865765i) q^{42} +(0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +(-2.27192 + 6.31177i) q^{45} +1.76869 q^{46} +(-7.66034 + 7.66034i) q^{47} +(-4.50176 + 0.460865i) q^{48} +1.00000i q^{49} +(2.33428 + 0.757266i) q^{50} +(5.05320 - 6.20584i) q^{51} +(3.78111 + 3.78111i) q^{52} +(4.43577 + 4.43577i) q^{53} +(-1.17619 + 2.26289i) q^{54} +(5.09384 + 3.11990i) q^{55} +1.84500i q^{56} +(0.924894 + 9.03442i) q^{57} +(0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +(-6.14204 - 2.94825i) q^{60} +4.72534 q^{61} +(1.83452 - 1.83452i) q^{62} +(-2.50715 - 1.64748i) q^{63} -2.78490i q^{64} +(1.58828 + 6.60897i) q^{65} +(1.76099 + 1.43391i) q^{66} +(-5.41156 - 5.41156i) q^{67} +(5.74734 + 5.74734i) q^{68} +(-4.84006 - 3.94109i) q^{69} +(-0.573216 + 0.935887i) q^{70} -13.5880i q^{71} +(-4.62569 - 3.03961i) q^{72} +(4.16486 - 4.16486i) q^{73} +1.48737 q^{74} +(-4.70043 - 7.27365i) q^{75} -9.22351 q^{76} +(-1.88894 + 1.88894i) q^{77} +(0.263173 + 2.57069i) q^{78} +3.89710i q^{79} +(3.05135 - 4.98193i) q^{80} +(8.26097 - 3.57160i) q^{81} +(-4.01778 - 4.01778i) q^{82} +(4.03778 + 4.03778i) q^{83} +(1.92384 - 2.36267i) q^{84} +(2.41421 + 10.0457i) q^{85} +0.526902i q^{86} +(-4.94383 + 0.506122i) q^{87} +(-3.48510 + 3.48510i) q^{88} +3.95125 q^{89} +(-1.40205 - 2.97900i) q^{90} -3.03977 q^{91} +(4.48247 - 4.48247i) q^{92} +(-9.10800 + 0.932426i) q^{93} -5.31710i q^{94} +(-9.99806 - 6.12366i) q^{95} +(5.43796 - 6.67836i) q^{96} +(-1.86878 - 1.86878i) q^{97} +(-0.347054 - 0.347054i) q^{98} +(-1.62386 - 7.84786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.347054 + 0.347054i −0.245404 + 0.245404i −0.819081 0.573677i \(-0.805516\pi\)
0.573677 + 0.819081i \(0.305516\pi\)
\(3\) 1.72305 0.176396i 0.994801 0.101842i
\(4\) 1.75911i 0.879554i
\(5\) −1.16790 + 1.90683i −0.522302 + 0.852760i
\(6\) −0.536770 + 0.659208i −0.219135 + 0.269120i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −1.30461 1.30461i −0.461250 0.461250i
\(9\) 2.93777 0.607876i 0.979256 0.202625i
\(10\) −0.256447 1.06710i −0.0810957 0.337446i
\(11\) 2.67137i 0.805448i −0.915322 0.402724i \(-0.868064\pi\)
0.915322 0.402724i \(-0.131936\pi\)
\(12\) 0.310299 + 3.03102i 0.0895757 + 0.874981i
\(13\) 2.14945 2.14945i 0.596149 0.596149i −0.343137 0.939285i \(-0.611489\pi\)
0.939285 + 0.343137i \(0.111489\pi\)
\(14\) 0.490808 0.131174
\(15\) −1.67599 + 3.49157i −0.432740 + 0.901519i
\(16\) −2.61267 −0.653169
\(17\) 3.26719 3.26719i 0.792410 0.792410i −0.189475 0.981886i \(-0.560679\pi\)
0.981886 + 0.189475i \(0.0606787\pi\)
\(18\) −0.808598 + 1.23053i −0.190588 + 0.290038i
\(19\) 5.24329i 1.20289i 0.798913 + 0.601446i \(0.205409\pi\)
−0.798913 + 0.601446i \(0.794591\pi\)
\(20\) −3.35432 2.05447i −0.750049 0.459393i
\(21\) −1.34311 1.09365i −0.293090 0.238653i
\(22\) 0.927108 + 0.927108i 0.197660 + 0.197660i
\(23\) −2.54815 2.54815i −0.531326 0.531326i 0.389641 0.920967i \(-0.372599\pi\)
−0.920967 + 0.389641i \(0.872599\pi\)
\(24\) −2.47803 2.01778i −0.505826 0.411877i
\(25\) −2.27200 4.45399i −0.454400 0.890798i
\(26\) 1.49195i 0.292595i
\(27\) 4.95468 1.56561i 0.953529 0.301301i
\(28\) 1.24388 1.24388i 0.235071 0.235071i
\(29\) −2.86924 −0.532804 −0.266402 0.963862i \(-0.585835\pi\)
−0.266402 + 0.963862i \(0.585835\pi\)
\(30\) −0.630101 1.79342i −0.115040 0.327432i
\(31\) −5.28599 −0.949391 −0.474696 0.880150i \(-0.657442\pi\)
−0.474696 + 0.880150i \(0.657442\pi\)
\(32\) 3.51596 3.51596i 0.621540 0.621540i
\(33\) −0.471218 4.60289i −0.0820286 0.801260i
\(34\) 2.26778i 0.388921i
\(35\) 2.17417 0.522500i 0.367501 0.0883186i
\(36\) 1.06932 + 5.16785i 0.178220 + 0.861309i
\(37\) −2.14286 2.14286i −0.352284 0.352284i 0.508675 0.860959i \(-0.330136\pi\)
−0.860959 + 0.508675i \(0.830136\pi\)
\(38\) −1.81970 1.81970i −0.295195 0.295195i
\(39\) 3.32444 4.08274i 0.532336 0.653762i
\(40\) 4.01133 0.964012i 0.634248 0.152424i
\(41\) 11.5768i 1.80800i 0.427537 + 0.903998i \(0.359381\pi\)
−0.427537 + 0.903998i \(0.640619\pi\)
\(42\) 0.845684 0.0865765i 0.130492 0.0133590i
\(43\) 0.759108 0.759108i 0.115763 0.115763i −0.646852 0.762615i \(-0.723915\pi\)
0.762615 + 0.646852i \(0.223915\pi\)
\(44\) 4.69922 0.708434
\(45\) −2.27192 + 6.31177i −0.338677 + 0.940903i
\(46\) 1.76869 0.260779
\(47\) −7.66034 + 7.66034i −1.11738 + 1.11738i −0.125250 + 0.992125i \(0.539973\pi\)
−0.992125 + 0.125250i \(0.960027\pi\)
\(48\) −4.50176 + 0.460865i −0.649773 + 0.0665201i
\(49\) 1.00000i 0.142857i
\(50\) 2.33428 + 0.757266i 0.330117 + 0.107094i
\(51\) 5.05320 6.20584i 0.707589 0.868991i
\(52\) 3.78111 + 3.78111i 0.524345 + 0.524345i
\(53\) 4.43577 + 4.43577i 0.609300 + 0.609300i 0.942763 0.333463i \(-0.108217\pi\)
−0.333463 + 0.942763i \(0.608217\pi\)
\(54\) −1.17619 + 2.26289i −0.160059 + 0.307940i
\(55\) 5.09384 + 3.11990i 0.686854 + 0.420687i
\(56\) 1.84500i 0.246548i
\(57\) 0.924894 + 9.03442i 0.122505 + 1.19664i
\(58\) 0.995779 0.995779i 0.130752 0.130752i
\(59\) 0.159437 0.0207569 0.0103785 0.999946i \(-0.496696\pi\)
0.0103785 + 0.999946i \(0.496696\pi\)
\(60\) −6.14204 2.94825i −0.792934 0.380618i
\(61\) 4.72534 0.605018 0.302509 0.953147i \(-0.402176\pi\)
0.302509 + 0.953147i \(0.402176\pi\)
\(62\) 1.83452 1.83452i 0.232984 0.232984i
\(63\) −2.50715 1.64748i −0.315871 0.207563i
\(64\) 2.78490i 0.348112i
\(65\) 1.58828 + 6.60897i 0.197002 + 0.819742i
\(66\) 1.76099 + 1.43391i 0.216762 + 0.176502i
\(67\) −5.41156 5.41156i −0.661127 0.661127i 0.294519 0.955646i \(-0.404841\pi\)
−0.955646 + 0.294519i \(0.904841\pi\)
\(68\) 5.74734 + 5.74734i 0.696967 + 0.696967i
\(69\) −4.84006 3.94109i −0.582675 0.474452i
\(70\) −0.573216 + 0.935887i −0.0685125 + 0.111860i
\(71\) 13.5880i 1.61260i −0.591508 0.806299i \(-0.701467\pi\)
0.591508 0.806299i \(-0.298533\pi\)
\(72\) −4.62569 3.03961i −0.545143 0.358221i
\(73\) 4.16486 4.16486i 0.487460 0.487460i −0.420044 0.907504i \(-0.637985\pi\)
0.907504 + 0.420044i \(0.137985\pi\)
\(74\) 1.48737 0.172904
\(75\) −4.70043 7.27365i −0.542758 0.839889i
\(76\) −9.22351 −1.05801
\(77\) −1.88894 + 1.88894i −0.215265 + 0.215265i
\(78\) 0.263173 + 2.57069i 0.0297985 + 0.291073i
\(79\) 3.89710i 0.438458i 0.975673 + 0.219229i \(0.0703542\pi\)
−0.975673 + 0.219229i \(0.929646\pi\)
\(80\) 3.05135 4.98193i 0.341152 0.556996i
\(81\) 8.26097 3.57160i 0.917886 0.396844i
\(82\) −4.01778 4.01778i −0.443689 0.443689i
\(83\) 4.03778 + 4.03778i 0.443204 + 0.443204i 0.893087 0.449883i \(-0.148534\pi\)
−0.449883 + 0.893087i \(0.648534\pi\)
\(84\) 1.92384 2.36267i 0.209908 0.257789i
\(85\) 2.41421 + 10.0457i 0.261858 + 1.08961i
\(86\) 0.526902i 0.0568173i
\(87\) −4.94383 + 0.506122i −0.530034 + 0.0542619i
\(88\) −3.48510 + 3.48510i −0.371513 + 0.371513i
\(89\) 3.95125 0.418832 0.209416 0.977827i \(-0.432844\pi\)
0.209416 + 0.977827i \(0.432844\pi\)
\(90\) −1.40205 2.97900i −0.147789 0.314014i
\(91\) −3.03977 −0.318655
\(92\) 4.48247 4.48247i 0.467330 0.467330i
\(93\) −9.10800 + 0.932426i −0.944455 + 0.0966881i
\(94\) 5.31710i 0.548417i
\(95\) −9.99806 6.12366i −1.02578 0.628274i
\(96\) 5.43796 6.67836i 0.555009 0.681607i
\(97\) −1.86878 1.86878i −0.189746 0.189746i 0.605840 0.795586i \(-0.292837\pi\)
−0.795586 + 0.605840i \(0.792837\pi\)
\(98\) −0.347054 0.347054i −0.0350577 0.0350577i
\(99\) −1.62386 7.84786i −0.163204 0.788740i
\(100\) 7.83504 3.99670i 0.783504 0.399670i
\(101\) 3.76115i 0.374249i 0.982336 + 0.187124i \(0.0599167\pi\)
−0.982336 + 0.187124i \(0.940083\pi\)
\(102\) 0.400027 + 3.90749i 0.0396086 + 0.386899i
\(103\) −8.85701 + 8.85701i −0.872707 + 0.872707i −0.992767 0.120060i \(-0.961691\pi\)
0.120060 + 0.992767i \(0.461691\pi\)
\(104\) −5.60838 −0.549947
\(105\) 3.65402 1.28380i 0.356596 0.125286i
\(106\) −3.07890 −0.299049
\(107\) −0.710397 + 0.710397i −0.0686766 + 0.0686766i −0.740611 0.671934i \(-0.765464\pi\)
0.671934 + 0.740611i \(0.265464\pi\)
\(108\) 2.75407 + 8.71582i 0.265011 + 0.838680i
\(109\) 19.0144i 1.82125i 0.413237 + 0.910623i \(0.364398\pi\)
−0.413237 + 0.910623i \(0.635602\pi\)
\(110\) −2.85061 + 0.685064i −0.271795 + 0.0653183i
\(111\) −4.07024 3.31425i −0.386330 0.314575i
\(112\) 1.84744 + 1.84744i 0.174567 + 0.174567i
\(113\) −5.69132 5.69132i −0.535394 0.535394i 0.386779 0.922173i \(-0.373588\pi\)
−0.922173 + 0.386779i \(0.873588\pi\)
\(114\) −3.45642 2.81444i −0.323723 0.263597i
\(115\) 7.83488 1.88289i 0.730607 0.175581i
\(116\) 5.04730i 0.468630i
\(117\) 5.00798 7.62117i 0.462988 0.704577i
\(118\) −0.0553332 + 0.0553332i −0.00509383 + 0.00509383i
\(119\) −4.62051 −0.423561
\(120\) 6.74166 2.36862i 0.615427 0.216224i
\(121\) 3.86380 0.351254
\(122\) −1.63995 + 1.63995i −0.148474 + 0.148474i
\(123\) 2.04210 + 19.9474i 0.184130 + 1.79859i
\(124\) 9.29862i 0.835041i
\(125\) 11.1465 + 0.869508i 0.996971 + 0.0777712i
\(126\) 1.44188 0.298350i 0.128453 0.0265792i
\(127\) −12.1366 12.1366i −1.07695 1.07695i −0.996781 0.0801668i \(-0.974455\pi\)
−0.0801668 0.996781i \(-0.525545\pi\)
\(128\) 7.99843 + 7.99843i 0.706968 + 0.706968i
\(129\) 1.17407 1.44188i 0.103371 0.126950i
\(130\) −2.84489 1.74245i −0.249513 0.152823i
\(131\) 9.94280i 0.868706i −0.900743 0.434353i \(-0.856977\pi\)
0.900743 0.434353i \(-0.143023\pi\)
\(132\) 8.09697 0.828923i 0.704751 0.0721485i
\(133\) 3.70756 3.70756i 0.321487 0.321487i
\(134\) 3.75620 0.324486
\(135\) −2.80124 + 11.2762i −0.241093 + 0.970502i
\(136\) −8.52483 −0.730998
\(137\) −13.6645 + 13.6645i −1.16744 + 1.16744i −0.184630 + 0.982808i \(0.559109\pi\)
−0.982808 + 0.184630i \(0.940891\pi\)
\(138\) 3.04753 0.311989i 0.259423 0.0265583i
\(139\) 16.7933i 1.42439i −0.701982 0.712195i \(-0.747701\pi\)
0.701982 0.712195i \(-0.252299\pi\)
\(140\) 0.919133 + 3.82459i 0.0776809 + 0.323237i
\(141\) −11.8479 + 14.5504i −0.997770 + 1.22536i
\(142\) 4.71576 + 4.71576i 0.395738 + 0.395738i
\(143\) −5.74196 5.74196i −0.480167 0.480167i
\(144\) −7.67544 + 1.58818i −0.639620 + 0.132349i
\(145\) 3.35099 5.47115i 0.278285 0.454354i
\(146\) 2.89086i 0.239249i
\(147\) 0.176396 + 1.72305i 0.0145489 + 0.142114i
\(148\) 3.76952 3.76952i 0.309853 0.309853i
\(149\) −9.31256 −0.762915 −0.381458 0.924386i \(-0.624578\pi\)
−0.381458 + 0.924386i \(0.624578\pi\)
\(150\) 4.15565 + 0.893047i 0.339307 + 0.0729169i
\(151\) 20.3868 1.65905 0.829527 0.558466i \(-0.188610\pi\)
0.829527 + 0.558466i \(0.188610\pi\)
\(152\) 6.84046 6.84046i 0.554834 0.554834i
\(153\) 7.61221 11.5843i 0.615410 0.936535i
\(154\) 1.31113i 0.105654i
\(155\) 6.17353 10.0795i 0.495869 0.809603i
\(156\) 7.18199 + 5.84804i 0.575019 + 0.468218i
\(157\) 6.32887 + 6.32887i 0.505098 + 0.505098i 0.913018 0.407919i \(-0.133746\pi\)
−0.407919 + 0.913018i \(0.633746\pi\)
\(158\) −1.35250 1.35250i −0.107599 0.107599i
\(159\) 8.42549 + 6.86058i 0.668185 + 0.544080i
\(160\) 2.59804 + 10.8106i 0.205393 + 0.854657i
\(161\) 3.60363i 0.284006i
\(162\) −1.62746 + 4.10654i −0.127866 + 0.322640i
\(163\) −6.45638 + 6.45638i −0.505703 + 0.505703i −0.913205 0.407502i \(-0.866400\pi\)
0.407502 + 0.913205i \(0.366400\pi\)
\(164\) −20.3649 −1.59023
\(165\) 9.32726 + 4.47720i 0.726126 + 0.348549i
\(166\) −2.80266 −0.217528
\(167\) −1.58004 + 1.58004i −0.122268 + 0.122268i −0.765593 0.643325i \(-0.777554\pi\)
0.643325 + 0.765593i \(0.277554\pi\)
\(168\) 0.325450 + 3.17902i 0.0251090 + 0.245267i
\(169\) 3.75977i 0.289213i
\(170\) −4.32427 2.64855i −0.331657 0.203134i
\(171\) 3.18727 + 15.4036i 0.243737 + 1.17794i
\(172\) 1.33535 + 1.33535i 0.101820 + 0.101820i
\(173\) 1.69970 + 1.69970i 0.129226 + 0.129226i 0.768761 0.639536i \(-0.220873\pi\)
−0.639536 + 0.768761i \(0.720873\pi\)
\(174\) 1.54012 1.89142i 0.116756 0.143388i
\(175\) −1.54290 + 4.75599i −0.116632 + 0.359519i
\(176\) 6.97941i 0.526093i
\(177\) 0.274717 0.0281240i 0.0206490 0.00211393i
\(178\) −1.37130 + 1.37130i −0.102783 + 0.102783i
\(179\) 8.44380 0.631119 0.315560 0.948906i \(-0.397808\pi\)
0.315560 + 0.948906i \(0.397808\pi\)
\(180\) −11.1031 3.99654i −0.827575 0.297885i
\(181\) 5.51483 0.409914 0.204957 0.978771i \(-0.434295\pi\)
0.204957 + 0.978771i \(0.434295\pi\)
\(182\) 1.05496 1.05496i 0.0781992 0.0781992i
\(183\) 8.14198 0.833531i 0.601872 0.0616164i
\(184\) 6.64869i 0.490148i
\(185\) 6.58872 1.58342i 0.484413 0.116415i
\(186\) 2.83736 3.48456i 0.208045 0.255501i
\(187\) −8.72787 8.72787i −0.638245 0.638245i
\(188\) −13.4754 13.4754i −0.982792 0.982792i
\(189\) −4.61054 2.39644i −0.335368 0.174315i
\(190\) 5.59510 1.34463i 0.405911 0.0975494i
\(191\) 0.559524i 0.0404858i −0.999795 0.0202429i \(-0.993556\pi\)
0.999795 0.0202429i \(-0.00644395\pi\)
\(192\) −0.491244 4.79850i −0.0354525 0.346302i
\(193\) 7.05199 7.05199i 0.507613 0.507613i −0.406180 0.913793i \(-0.633139\pi\)
0.913793 + 0.406180i \(0.133139\pi\)
\(194\) 1.29713 0.0931287
\(195\) 3.90248 + 11.1074i 0.279462 + 0.795417i
\(196\) −1.75911 −0.125651
\(197\) 10.1505 10.1505i 0.723190 0.723190i −0.246064 0.969254i \(-0.579137\pi\)
0.969254 + 0.246064i \(0.0791372\pi\)
\(198\) 3.28719 + 2.16006i 0.233611 + 0.153509i
\(199\) 11.6748i 0.827604i 0.910367 + 0.413802i \(0.135799\pi\)
−0.910367 + 0.413802i \(0.864201\pi\)
\(200\) −2.84664 + 8.77481i −0.201288 + 0.620472i
\(201\) −10.2789 8.36978i −0.725020 0.590359i
\(202\) −1.30532 1.30532i −0.0918421 0.0918421i
\(203\) 2.02886 + 2.02886i 0.142398 + 0.142398i
\(204\) 10.9167 + 8.88912i 0.764324 + 0.622363i
\(205\) −22.0750 13.5206i −1.54179 0.944320i
\(206\) 6.14771i 0.428332i
\(207\) −9.03483 5.93692i −0.627964 0.412644i
\(208\) −5.61580 + 5.61580i −0.389386 + 0.389386i
\(209\) 14.0067 0.968867
\(210\) −0.822591 + 1.71369i −0.0567642 + 0.118256i
\(211\) −0.777102 −0.0534979 −0.0267490 0.999642i \(-0.508515\pi\)
−0.0267490 + 0.999642i \(0.508515\pi\)
\(212\) −7.80300 + 7.80300i −0.535912 + 0.535912i
\(213\) −2.39687 23.4127i −0.164231 1.60421i
\(214\) 0.493091i 0.0337070i
\(215\) 0.560925 + 2.33405i 0.0382547 + 0.159181i
\(216\) −8.50645 4.42142i −0.578790 0.300840i
\(217\) 3.73776 + 3.73776i 0.253736 + 0.253736i
\(218\) −6.59901 6.59901i −0.446941 0.446941i
\(219\) 6.44157 7.91090i 0.435281 0.534569i
\(220\) −5.48824 + 8.96062i −0.370017 + 0.604125i
\(221\) 14.0453i 0.944789i
\(222\) 2.56281 0.262367i 0.172005 0.0176089i
\(223\) −3.33811 + 3.33811i −0.223536 + 0.223536i −0.809986 0.586450i \(-0.800525\pi\)
0.586450 + 0.809986i \(0.300525\pi\)
\(224\) −4.97232 −0.332227
\(225\) −9.38209 11.7037i −0.625473 0.780246i
\(226\) 3.95038 0.262776
\(227\) −0.242326 + 0.242326i −0.0160838 + 0.0160838i −0.715103 0.699019i \(-0.753620\pi\)
0.699019 + 0.715103i \(0.253620\pi\)
\(228\) −15.8925 + 1.62699i −1.05251 + 0.107750i
\(229\) 13.4793i 0.890735i −0.895348 0.445368i \(-0.853073\pi\)
0.895348 0.445368i \(-0.146927\pi\)
\(230\) −2.06566 + 3.37259i −0.136205 + 0.222382i
\(231\) −2.92153 + 3.58793i −0.192223 + 0.236069i
\(232\) 3.74324 + 3.74324i 0.245756 + 0.245756i
\(233\) −1.19260 1.19260i −0.0781301 0.0781301i 0.666962 0.745092i \(-0.267594\pi\)
−0.745092 + 0.666962i \(0.767594\pi\)
\(234\) 0.906918 + 4.38299i 0.0592871 + 0.286525i
\(235\) −5.66043 23.5535i −0.369246 1.53646i
\(236\) 0.280467i 0.0182568i
\(237\) 0.687432 + 6.71488i 0.0446535 + 0.436178i
\(238\) 1.60356 1.60356i 0.103944 0.103944i
\(239\) −5.15325 −0.333336 −0.166668 0.986013i \(-0.553301\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(240\) 4.37883 9.12233i 0.282652 0.588844i
\(241\) −14.9174 −0.960914 −0.480457 0.877018i \(-0.659529\pi\)
−0.480457 + 0.877018i \(0.659529\pi\)
\(242\) −1.34094 + 1.34094i −0.0861992 + 0.0861992i
\(243\) 13.6040 7.61123i 0.872698 0.488261i
\(244\) 8.31238i 0.532146i
\(245\) −1.90683 1.16790i −0.121823 0.0746146i
\(246\) −7.63153 6.21409i −0.486569 0.396196i
\(247\) 11.2702 + 11.2702i 0.717103 + 0.717103i
\(248\) 6.89616 + 6.89616i 0.437907 + 0.437907i
\(249\) 7.66953 + 6.24504i 0.486037 + 0.395763i
\(250\) −4.17019 + 3.56666i −0.263746 + 0.225575i
\(251\) 4.30303i 0.271605i −0.990736 0.135802i \(-0.956639\pi\)
0.990736 0.135802i \(-0.0433613\pi\)
\(252\) 2.89810 4.41035i 0.182563 0.277826i
\(253\) −6.80704 + 6.80704i −0.427955 + 0.427955i
\(254\) 8.42409 0.528575
\(255\) 5.93183 + 16.8834i 0.371465 + 1.05728i
\(256\) 0.0180230 0.00112644
\(257\) 5.82885 5.82885i 0.363594 0.363594i −0.501540 0.865134i \(-0.667233\pi\)
0.865134 + 0.501540i \(0.167233\pi\)
\(258\) 0.0929433 + 0.907876i 0.00578640 + 0.0565219i
\(259\) 3.03046i 0.188304i
\(260\) −11.6259 + 2.79396i −0.721007 + 0.173274i
\(261\) −8.42916 + 1.74414i −0.521752 + 0.107960i
\(262\) 3.45068 + 3.45068i 0.213184 + 0.213184i
\(263\) 0.0624909 + 0.0624909i 0.00385335 + 0.00385335i 0.709031 0.705177i \(-0.249133\pi\)
−0.705177 + 0.709031i \(0.749133\pi\)
\(264\) −5.39022 + 6.61974i −0.331745 + 0.407417i
\(265\) −13.6388 + 3.27771i −0.837826 + 0.201348i
\(266\) 2.57345i 0.157788i
\(267\) 6.80819 0.696985i 0.416654 0.0426548i
\(268\) 9.51951 9.51951i 0.581497 0.581497i
\(269\) 29.6699 1.80901 0.904504 0.426465i \(-0.140241\pi\)
0.904504 + 0.426465i \(0.140241\pi\)
\(270\) −2.94127 4.88563i −0.179000 0.297330i
\(271\) 22.6377 1.37514 0.687571 0.726117i \(-0.258677\pi\)
0.687571 + 0.726117i \(0.258677\pi\)
\(272\) −8.53611 + 8.53611i −0.517578 + 0.517578i
\(273\) −5.23767 + 0.536204i −0.316998 + 0.0324525i
\(274\) 9.48463i 0.572988i
\(275\) −11.8982 + 6.06935i −0.717491 + 0.365996i
\(276\) 6.93281 8.51419i 0.417306 0.512494i
\(277\) 4.21136 + 4.21136i 0.253036 + 0.253036i 0.822214 0.569178i \(-0.192738\pi\)
−0.569178 + 0.822214i \(0.692738\pi\)
\(278\) 5.82817 + 5.82817i 0.349551 + 0.349551i
\(279\) −15.5290 + 3.21323i −0.929698 + 0.192371i
\(280\) −3.51810 2.15478i −0.210247 0.128773i
\(281\) 22.0093i 1.31297i 0.754341 + 0.656483i \(0.227957\pi\)
−0.754341 + 0.656483i \(0.772043\pi\)
\(282\) −0.937914 9.16160i −0.0558520 0.545565i
\(283\) 9.59899 9.59899i 0.570601 0.570601i −0.361695 0.932296i \(-0.617802\pi\)
0.932296 + 0.361695i \(0.117802\pi\)
\(284\) 23.9027 1.41837
\(285\) −18.3073 8.78772i −1.08443 0.520540i
\(286\) 3.98553 0.235670
\(287\) 8.18605 8.18605i 0.483207 0.483207i
\(288\) 8.19181 12.4664i 0.482707 0.734587i
\(289\) 4.34908i 0.255828i
\(290\) 0.735807 + 3.06176i 0.0432081 + 0.179792i
\(291\) −3.54963 2.89034i −0.208083 0.169435i
\(292\) 7.32643 + 7.32643i 0.428747 + 0.428747i
\(293\) −3.56359 3.56359i −0.208187 0.208187i 0.595309 0.803497i \(-0.297030\pi\)
−0.803497 + 0.595309i \(0.797030\pi\)
\(294\) −0.659208 0.536770i −0.0384458 0.0313051i
\(295\) −0.186207 + 0.304019i −0.0108414 + 0.0177007i
\(296\) 5.59120i 0.324982i
\(297\) −4.18231 13.2358i −0.242683 0.768018i
\(298\) 3.23196 3.23196i 0.187222 0.187222i
\(299\) −10.9542 −0.633499
\(300\) 12.7951 8.26856i 0.738727 0.477385i
\(301\) −1.07354 −0.0618778
\(302\) −7.07531 + 7.07531i −0.407139 + 0.407139i
\(303\) 0.663452 + 6.48063i 0.0381143 + 0.372303i
\(304\) 13.6990i 0.785692i
\(305\) −5.51874 + 9.01042i −0.316002 + 0.515935i
\(306\) 1.37853 + 6.66222i 0.0788053 + 0.380854i
\(307\) 10.4746 + 10.4746i 0.597814 + 0.597814i 0.939730 0.341916i \(-0.111076\pi\)
−0.341916 + 0.939730i \(0.611076\pi\)
\(308\) −3.32285 3.32285i −0.189337 0.189337i
\(309\) −13.6987 + 16.8234i −0.779291 + 0.957048i
\(310\) 1.35558 + 5.64066i 0.0769915 + 0.320368i
\(311\) 20.4344i 1.15873i 0.815068 + 0.579365i \(0.196699\pi\)
−0.815068 + 0.579365i \(0.803301\pi\)
\(312\) −9.66350 + 0.989296i −0.547088 + 0.0560078i
\(313\) −16.4829 + 16.4829i −0.931670 + 0.931670i −0.997810 0.0661408i \(-0.978931\pi\)
0.0661408 + 0.997810i \(0.478931\pi\)
\(314\) −4.39291 −0.247906
\(315\) 6.06958 2.85661i 0.341982 0.160952i
\(316\) −6.85542 −0.385647
\(317\) 22.9540 22.9540i 1.28922 1.28922i 0.353965 0.935259i \(-0.384833\pi\)
0.935259 0.353965i \(-0.115167\pi\)
\(318\) −5.30509 + 0.543105i −0.297494 + 0.0304558i
\(319\) 7.66479i 0.429146i
\(320\) 5.31032 + 3.25249i 0.296856 + 0.181820i
\(321\) −1.09873 + 1.34936i −0.0613254 + 0.0753137i
\(322\) −1.25065 1.25065i −0.0696961 0.0696961i
\(323\) 17.1308 + 17.1308i 0.953185 + 0.953185i
\(324\) 6.28283 + 14.5319i 0.349046 + 0.807330i
\(325\) −14.4571 4.69006i −0.801938 0.260158i
\(326\) 4.48142i 0.248203i
\(327\) 3.35406 + 32.7626i 0.185480 + 1.81178i
\(328\) 15.1033 15.1033i 0.833938 0.833938i
\(329\) 10.8334 0.597262
\(330\) −4.79089 + 1.68323i −0.263730 + 0.0926589i
\(331\) −2.21461 −0.121726 −0.0608631 0.998146i \(-0.519385\pi\)
−0.0608631 + 0.998146i \(0.519385\pi\)
\(332\) −7.10290 + 7.10290i −0.389822 + 0.389822i
\(333\) −7.59782 4.99263i −0.416358 0.273595i
\(334\) 1.09672i 0.0600099i
\(335\) 16.6391 3.99874i 0.909091 0.218475i
\(336\) 3.50910 + 2.85734i 0.191437 + 0.155881i
\(337\) 10.8541 + 10.8541i 0.591263 + 0.591263i 0.937972 0.346710i \(-0.112701\pi\)
−0.346710 + 0.937972i \(0.612701\pi\)
\(338\) −1.30484 1.30484i −0.0709741 0.0709741i
\(339\) −10.8103 8.80247i −0.587136 0.478085i
\(340\) −17.6715 + 4.24686i −0.958374 + 0.230318i
\(341\) 14.1208i 0.764685i
\(342\) −6.45202 4.23971i −0.348885 0.229257i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −1.98068 −0.106791
\(345\) 13.1677 4.62635i 0.708926 0.249075i
\(346\) −1.17977 −0.0634251
\(347\) 5.06341 5.06341i 0.271818 0.271818i −0.558014 0.829832i \(-0.688436\pi\)
0.829832 + 0.558014i \(0.188436\pi\)
\(348\) −0.890323 8.69672i −0.0477263 0.466193i
\(349\) 7.42733i 0.397576i −0.980043 0.198788i \(-0.936300\pi\)
0.980043 0.198788i \(-0.0637005\pi\)
\(350\) −1.11512 2.18605i −0.0596055 0.116849i
\(351\) 7.28463 14.0150i 0.388825 0.748066i
\(352\) −9.39243 9.39243i −0.500618 0.500618i
\(353\) −9.09032 9.09032i −0.483829 0.483829i 0.422523 0.906352i \(-0.361144\pi\)
−0.906352 + 0.422523i \(0.861144\pi\)
\(354\) −0.0855810 + 0.105102i −0.00454858 + 0.00558611i
\(355\) 25.9100 + 15.8695i 1.37516 + 0.842264i
\(356\) 6.95068i 0.368385i
\(357\) −7.96134 + 0.815038i −0.421359 + 0.0431364i
\(358\) −2.93045 + 2.93045i −0.154879 + 0.154879i
\(359\) −25.2640 −1.33338 −0.666692 0.745333i \(-0.732290\pi\)
−0.666692 + 0.745333i \(0.732290\pi\)
\(360\) 11.1984 5.27044i 0.590206 0.277776i
\(361\) −8.49208 −0.446951
\(362\) −1.91394 + 1.91394i −0.100594 + 0.100594i
\(363\) 6.65750 0.681558i 0.349428 0.0357725i
\(364\) 5.34729i 0.280274i
\(365\) 3.07752 + 12.8058i 0.161085 + 0.670288i
\(366\) −2.53642 + 3.11498i −0.132581 + 0.162823i
\(367\) 1.61189 + 1.61189i 0.0841399 + 0.0841399i 0.747924 0.663784i \(-0.231051\pi\)
−0.663784 + 0.747924i \(0.731051\pi\)
\(368\) 6.65749 + 6.65749i 0.347045 + 0.347045i
\(369\) 7.03727 + 34.0100i 0.366346 + 1.77049i
\(370\) −1.73711 + 2.83617i −0.0903081 + 0.147445i
\(371\) 6.27313i 0.325685i
\(372\) −1.64024 16.0219i −0.0850424 0.830699i
\(373\) 13.0455 13.0455i 0.675469 0.675469i −0.283502 0.958972i \(-0.591496\pi\)
0.958972 + 0.283502i \(0.0914964\pi\)
\(374\) 6.05808 0.313256
\(375\) 19.3593 0.467991i 0.999708 0.0241669i
\(376\) 19.9875 1.03078
\(377\) −6.16727 + 6.16727i −0.317630 + 0.317630i
\(378\) 2.43180 0.768413i 0.125078 0.0395229i
\(379\) 19.0635i 0.979228i −0.871939 0.489614i \(-0.837138\pi\)
0.871939 0.489614i \(-0.162862\pi\)
\(380\) 10.7722 17.5877i 0.552601 0.902228i
\(381\) −23.0527 18.7710i −1.18103 0.961670i
\(382\) 0.194185 + 0.194185i 0.00993537 + 0.00993537i
\(383\) −17.7244 17.7244i −0.905673 0.905673i 0.0902463 0.995919i \(-0.471235\pi\)
−0.995919 + 0.0902463i \(0.971235\pi\)
\(384\) 15.1925 + 12.3708i 0.775291 + 0.631293i
\(385\) −1.39579 5.80799i −0.0711360 0.296003i
\(386\) 4.89484i 0.249141i
\(387\) 1.76864 2.69153i 0.0899050 0.136818i
\(388\) 3.28738 3.28738i 0.166892 0.166892i
\(389\) −18.3513 −0.930446 −0.465223 0.885193i \(-0.654026\pi\)
−0.465223 + 0.885193i \(0.654026\pi\)
\(390\) −5.20923 2.50049i −0.263779 0.126617i
\(391\) −16.6506 −0.842056
\(392\) 1.30461 1.30461i 0.0658928 0.0658928i
\(393\) −1.75387 17.1319i −0.0884710 0.864189i
\(394\) 7.04550i 0.354947i
\(395\) −7.43110 4.55144i −0.373899 0.229008i
\(396\) 13.8052 2.85655i 0.693739 0.143547i
\(397\) −10.9124 10.9124i −0.547679 0.547679i 0.378090 0.925769i \(-0.376581\pi\)
−0.925769 + 0.378090i \(0.876581\pi\)
\(398\) −4.05178 4.05178i −0.203097 0.203097i
\(399\) 5.73430 7.04230i 0.287074 0.352556i
\(400\) 5.93600 + 11.6368i 0.296800 + 0.581841i
\(401\) 34.4243i 1.71907i −0.511079 0.859534i \(-0.670754\pi\)
0.511079 0.859534i \(-0.329246\pi\)
\(402\) 6.47210 0.662578i 0.322799 0.0330464i
\(403\) −11.3619 + 11.3619i −0.565979 + 0.565979i
\(404\) −6.61627 −0.329172
\(405\) −2.83759 + 19.9236i −0.141001 + 0.990009i
\(406\) −1.40824 −0.0698900
\(407\) −5.72437 + 5.72437i −0.283746 + 0.283746i
\(408\) −14.6887 + 1.50375i −0.727198 + 0.0744465i
\(409\) 7.59254i 0.375427i −0.982224 0.187714i \(-0.939892\pi\)
0.982224 0.187714i \(-0.0601077\pi\)
\(410\) 12.3536 2.96884i 0.610101 0.146621i
\(411\) −21.1342 + 25.9549i −1.04247 + 1.28026i
\(412\) −15.5804 15.5804i −0.767593 0.767593i
\(413\) −0.112739 0.112739i −0.00554752 0.00554752i
\(414\) 5.19600 1.07514i 0.255369 0.0528404i
\(415\) −12.4151 + 2.98363i −0.609434 + 0.146460i
\(416\) 15.1147i 0.741061i
\(417\) −2.96227 28.9356i −0.145063 1.41698i
\(418\) −4.86109 + 4.86109i −0.237764 + 0.237764i
\(419\) −6.20644 −0.303204 −0.151602 0.988442i \(-0.548443\pi\)
−0.151602 + 0.988442i \(0.548443\pi\)
\(420\) 2.25835 + 6.42781i 0.110196 + 0.313645i
\(421\) 25.1339 1.22495 0.612474 0.790490i \(-0.290174\pi\)
0.612474 + 0.790490i \(0.290174\pi\)
\(422\) 0.269696 0.269696i 0.0131286 0.0131286i
\(423\) −17.8478 + 27.1608i −0.867788 + 1.32061i
\(424\) 11.5739i 0.562079i
\(425\) −21.9751 7.12897i −1.06595 0.345806i
\(426\) 8.95731 + 7.29363i 0.433983 + 0.353377i
\(427\) −3.34132 3.34132i −0.161698 0.161698i
\(428\) −1.24966 1.24966i −0.0604048 0.0604048i
\(429\) −10.9065 8.88079i −0.526571 0.428769i
\(430\) −1.00471 0.615371i −0.0484515 0.0296758i
\(431\) 8.43225i 0.406167i 0.979161 + 0.203084i \(0.0650963\pi\)
−0.979161 + 0.203084i \(0.934904\pi\)
\(432\) −12.9450 + 4.09043i −0.622815 + 0.196801i
\(433\) −18.8277 + 18.8277i −0.904802 + 0.904802i −0.995847 0.0910444i \(-0.970979\pi\)
0.0910444 + 0.995847i \(0.470979\pi\)
\(434\) −2.59440 −0.124535
\(435\) 4.80882 10.0181i 0.230566 0.480333i
\(436\) −33.4483 −1.60188
\(437\) 13.3607 13.3607i 0.639128 0.639128i
\(438\) 0.509935 + 4.98108i 0.0243657 + 0.238005i
\(439\) 4.88270i 0.233039i −0.993188 0.116519i \(-0.962826\pi\)
0.993188 0.116519i \(-0.0371737\pi\)
\(440\) −2.57523 10.7157i −0.122769 0.510853i
\(441\) 0.607876 + 2.93777i 0.0289465 + 0.139894i
\(442\) 4.87447 + 4.87447i 0.231855 + 0.231855i
\(443\) 23.8960 + 23.8960i 1.13534 + 1.13534i 0.989276 + 0.146059i \(0.0466590\pi\)
0.146059 + 0.989276i \(0.453341\pi\)
\(444\) 5.83013 7.15998i 0.276686 0.339798i
\(445\) −4.61468 + 7.53437i −0.218757 + 0.357163i
\(446\) 2.31700i 0.109713i
\(447\) −16.0460 + 1.64270i −0.758948 + 0.0776970i
\(448\) −1.96922 + 1.96922i −0.0930368 + 0.0930368i
\(449\) −23.6736 −1.11723 −0.558613 0.829428i \(-0.688666\pi\)
−0.558613 + 0.829428i \(0.688666\pi\)
\(450\) 7.31790 + 0.805721i 0.344969 + 0.0379820i
\(451\) 30.9259 1.45625
\(452\) 10.0116 10.0116i 0.470908 0.470908i
\(453\) 35.1274 3.59615i 1.65043 0.168962i
\(454\) 0.168200i 0.00789404i
\(455\) 3.55016 5.79633i 0.166434 0.271736i
\(456\) 10.5798 12.9930i 0.495444 0.608455i
\(457\) 10.2580 + 10.2580i 0.479849 + 0.479849i 0.905083 0.425234i \(-0.139808\pi\)
−0.425234 + 0.905083i \(0.639808\pi\)
\(458\) 4.67803 + 4.67803i 0.218590 + 0.218590i
\(459\) 11.0728 21.3030i 0.516832 0.994341i
\(460\) 3.31221 + 13.7824i 0.154433 + 0.642608i
\(461\) 23.3153i 1.08590i −0.839764 0.542951i \(-0.817307\pi\)
0.839764 0.542951i \(-0.182693\pi\)
\(462\) −0.231278 2.25913i −0.0107600 0.105104i
\(463\) −17.0563 + 17.0563i −0.792672 + 0.792672i −0.981928 0.189256i \(-0.939392\pi\)
0.189256 + 0.981928i \(0.439392\pi\)
\(464\) 7.49639 0.348011
\(465\) 8.85928 18.4564i 0.410839 0.855894i
\(466\) 0.827796 0.0383469
\(467\) −8.00621 + 8.00621i −0.370483 + 0.370483i −0.867653 0.497170i \(-0.834373\pi\)
0.497170 + 0.867653i \(0.334373\pi\)
\(468\) 13.4065 + 8.80957i 0.619714 + 0.407223i
\(469\) 7.65310i 0.353387i
\(470\) 10.1388 + 6.20986i 0.467668 + 0.286439i
\(471\) 12.0213 + 9.78854i 0.553913 + 0.451032i
\(472\) −0.208003 0.208003i −0.00957413 0.00957413i
\(473\) −2.02786 2.02786i −0.0932409 0.0932409i
\(474\) −2.56900 2.09185i −0.117998 0.0960817i
\(475\) 23.3535 11.9128i 1.07153 0.546595i
\(476\) 8.12797i 0.372545i
\(477\) 15.7277 + 10.3349i 0.720121 + 0.473201i
\(478\) 1.78845 1.78845i 0.0818019 0.0818019i
\(479\) −20.1199 −0.919304 −0.459652 0.888099i \(-0.652026\pi\)
−0.459652 + 0.888099i \(0.652026\pi\)
\(480\) 6.38349 + 18.1689i 0.291365 + 0.829295i
\(481\) −9.21192 −0.420027
\(482\) 5.17713 5.17713i 0.235812 0.235812i
\(483\) 0.635665 + 6.20921i 0.0289238 + 0.282529i
\(484\) 6.79683i 0.308947i
\(485\) 5.74600 1.38089i 0.260912 0.0627030i
\(486\) −2.07982 + 7.36283i −0.0943425 + 0.333985i
\(487\) 7.77959 + 7.77959i 0.352527 + 0.352527i 0.861049 0.508522i \(-0.169808\pi\)
−0.508522 + 0.861049i \(0.669808\pi\)
\(488\) −6.16474 6.16474i −0.279064 0.279064i
\(489\) −9.98576 + 12.2635i −0.451572 + 0.554576i
\(490\) 1.06710 0.256447i 0.0482065 0.0115851i
\(491\) 2.29546i 0.103593i 0.998658 + 0.0517963i \(0.0164947\pi\)
−0.998658 + 0.0517963i \(0.983505\pi\)
\(492\) −35.0896 + 3.59228i −1.58196 + 0.161952i
\(493\) −9.37435 + 9.37435i −0.422199 + 0.422199i
\(494\) −7.82270 −0.351960
\(495\) 16.8610 + 6.06912i 0.757848 + 0.272787i
\(496\) 13.8106 0.620113
\(497\) −9.60816 + 9.60816i −0.430985 + 0.430985i
\(498\) −4.82910 + 0.494377i −0.216397 + 0.0221536i
\(499\) 12.3264i 0.551806i −0.961185 0.275903i \(-0.911023\pi\)
0.961185 0.275903i \(-0.0889769\pi\)
\(500\) −1.52956 + 19.6079i −0.0684039 + 0.876890i
\(501\) −2.44378 + 3.00120i −0.109180 + 0.134084i
\(502\) 1.49338 + 1.49338i 0.0666529 + 0.0666529i
\(503\) 4.62523 + 4.62523i 0.206229 + 0.206229i 0.802662 0.596434i \(-0.203416\pi\)
−0.596434 + 0.802662i \(0.703416\pi\)
\(504\) 1.12153 + 5.42018i 0.0499570 + 0.241434i
\(505\) −7.17188 4.39266i −0.319144 0.195471i
\(506\) 4.72482i 0.210044i
\(507\) 0.663208 + 6.47826i 0.0294541 + 0.287709i
\(508\) 21.3496 21.3496i 0.947234 0.947234i
\(509\) 13.6161 0.603525 0.301762 0.953383i \(-0.402425\pi\)
0.301762 + 0.953383i \(0.402425\pi\)
\(510\) −7.91811 3.80079i −0.350620 0.168302i
\(511\) −5.89000 −0.260558
\(512\) −16.0031 + 16.0031i −0.707245 + 0.707245i
\(513\) 8.20894 + 25.9788i 0.362433 + 1.14699i
\(514\) 4.04585i 0.178455i
\(515\) −6.54468 27.2329i −0.288393 1.20003i
\(516\) 2.53642 + 2.06532i 0.111660 + 0.0909207i
\(517\) 20.4636 + 20.4636i 0.899987 + 0.899987i
\(518\) −1.05173 1.05173i −0.0462105 0.0462105i
\(519\) 3.22848 + 2.62884i 0.141715 + 0.115393i
\(520\) 6.55005 10.6942i 0.287239 0.468973i
\(521\) 18.3870i 0.805550i 0.915299 + 0.402775i \(0.131954\pi\)
−0.915299 + 0.402775i \(0.868046\pi\)
\(522\) 2.32006 3.53068i 0.101546 0.154534i
\(523\) −8.91043 + 8.91043i −0.389626 + 0.389626i −0.874554 0.484928i \(-0.838846\pi\)
0.484928 + 0.874554i \(0.338846\pi\)
\(524\) 17.4905 0.764074
\(525\) −1.81954 + 8.46695i −0.0794114 + 0.369528i
\(526\) −0.0433754 −0.00189126
\(527\) −17.2703 + 17.2703i −0.752308 + 0.752308i
\(528\) 1.23114 + 12.0258i 0.0535785 + 0.523358i
\(529\) 10.0139i 0.435385i
\(530\) 3.59586 5.87094i 0.156194 0.255017i
\(531\) 0.468389 0.0969179i 0.0203264 0.00420588i
\(532\) 6.52201 + 6.52201i 0.282765 + 0.282765i
\(533\) 24.8837 + 24.8837i 1.07783 + 1.07783i
\(534\) −2.12091 + 2.60470i −0.0917810 + 0.112716i
\(535\) −0.524931 2.18428i −0.0226947 0.0944347i
\(536\) 14.1200i 0.609889i
\(537\) 14.5491 1.48945i 0.627838 0.0642746i
\(538\) −10.2971 + 10.2971i −0.443938 + 0.443938i
\(539\) 2.67137 0.115064
\(540\) −19.8361 4.92769i −0.853609 0.212054i
\(541\) 27.8258 1.19632 0.598162 0.801375i \(-0.295898\pi\)
0.598162 + 0.801375i \(0.295898\pi\)
\(542\) −7.85649 + 7.85649i −0.337465 + 0.337465i
\(543\) 9.50229 0.972793i 0.407783 0.0417465i
\(544\) 22.9746i 0.985030i
\(545\) −36.2572 22.2070i −1.55309 0.951242i
\(546\) 1.63166 2.00384i 0.0698286 0.0857566i
\(547\) −13.2773 13.2773i −0.567695 0.567695i 0.363787 0.931482i \(-0.381483\pi\)
−0.931482 + 0.363787i \(0.881483\pi\)
\(548\) −24.0373 24.0373i −1.02682 1.02682i
\(549\) 13.8820 2.87242i 0.592468 0.122592i
\(550\) 2.02294 6.23572i 0.0862583 0.265892i
\(551\) 15.0442i 0.640906i
\(552\) 1.17280 + 11.4560i 0.0499178 + 0.487600i
\(553\) 2.75566 2.75566i 0.117183 0.117183i
\(554\) −2.92314 −0.124192
\(555\) 11.0734 3.89052i 0.470038 0.165143i
\(556\) 29.5412 1.25283
\(557\) −10.4002 + 10.4002i −0.440672 + 0.440672i −0.892238 0.451566i \(-0.850866\pi\)
0.451566 + 0.892238i \(0.350866\pi\)
\(558\) 4.27424 6.50456i 0.180943 0.275360i
\(559\) 3.26332i 0.138024i
\(560\) −5.68039 + 1.36512i −0.240040 + 0.0576869i
\(561\) −16.5781 13.4990i −0.699927 0.569926i
\(562\) −7.63842 7.63842i −0.322207 0.322207i
\(563\) 10.1623 + 10.1623i 0.428291 + 0.428291i 0.888046 0.459755i \(-0.152063\pi\)
−0.459755 + 0.888046i \(0.652063\pi\)
\(564\) −25.5957 20.8417i −1.07777 0.877592i
\(565\) 17.4993 4.20546i 0.736200 0.176925i
\(566\) 6.66273i 0.280055i
\(567\) −8.36689 3.31589i −0.351376 0.139254i
\(568\) −17.7271 + 17.7271i −0.743811 + 0.743811i
\(569\) 39.8275 1.66965 0.834827 0.550512i \(-0.185567\pi\)
0.834827 + 0.550512i \(0.185567\pi\)
\(570\) 9.40342 3.30380i 0.393866 0.138381i
\(571\) −43.8314 −1.83429 −0.917143 0.398558i \(-0.869511\pi\)
−0.917143 + 0.398558i \(0.869511\pi\)
\(572\) 10.1007 10.1007i 0.422332 0.422332i
\(573\) −0.0986978 0.964086i −0.00412316 0.0402753i
\(574\) 5.68199i 0.237162i
\(575\) −5.56003 + 17.1388i −0.231869 + 0.714739i
\(576\) −1.69287 8.18138i −0.0705363 0.340891i
\(577\) −27.8182 27.8182i −1.15809 1.15809i −0.984886 0.173202i \(-0.944589\pi\)
−0.173202 0.984886i \(-0.555411\pi\)
\(578\) 1.50936 + 1.50936i 0.0627812 + 0.0627812i
\(579\) 10.9070 13.3948i 0.453278 0.556670i
\(580\) 9.62434 + 5.89476i 0.399629 + 0.244767i
\(581\) 5.71029i 0.236903i
\(582\) 2.23502 0.228809i 0.0926445 0.00948443i
\(583\) 11.8496 11.8496i 0.490759 0.490759i
\(584\) −10.8670 −0.449681
\(585\) 8.68344 + 18.4502i 0.359016 + 0.762820i
\(586\) 2.47352 0.102180
\(587\) 27.2778 27.2778i 1.12588 1.12588i 0.135034 0.990841i \(-0.456886\pi\)
0.990841 0.135034i \(-0.0431144\pi\)
\(588\) −3.03102 + 0.310299i −0.124997 + 0.0127965i
\(589\) 27.7160i 1.14202i
\(590\) −0.0408871 0.170135i −0.00168330 0.00700434i
\(591\) 15.6992 19.2802i 0.645779 0.793081i
\(592\) 5.59860 + 5.59860i 0.230101 + 0.230101i
\(593\) −1.21000 1.21000i −0.0496886 0.0496886i 0.681826 0.731515i \(-0.261186\pi\)
−0.731515 + 0.681826i \(0.761186\pi\)
\(594\) 6.04501 + 3.14204i 0.248030 + 0.128919i
\(595\) 5.39631 8.81052i 0.221227 0.361196i
\(596\) 16.3818i 0.671025i
\(597\) 2.05939 + 20.1162i 0.0842850 + 0.823301i
\(598\) 3.80170 3.80170i 0.155463 0.155463i
\(599\) −15.6005 −0.637421 −0.318710 0.947852i \(-0.603250\pi\)
−0.318710 + 0.947852i \(0.603250\pi\)
\(600\) −3.35706 + 15.6215i −0.137051 + 0.637746i
\(601\) 14.2954 0.583122 0.291561 0.956552i \(-0.405825\pi\)
0.291561 + 0.956552i \(0.405825\pi\)
\(602\) 0.372576 0.372576i 0.0151851 0.0151851i
\(603\) −19.1875 12.6083i −0.781374 0.513452i
\(604\) 35.8626i 1.45923i
\(605\) −4.51254 + 7.36760i −0.183461 + 0.299536i
\(606\) −2.47938 2.01887i −0.100718 0.0820111i
\(607\) −26.8784 26.8784i −1.09096 1.09096i −0.995426 0.0955365i \(-0.969543\pi\)
−0.0955365 0.995426i \(-0.530457\pi\)
\(608\) 18.4352 + 18.4352i 0.747646 + 0.747646i
\(609\) 3.85369 + 3.13793i 0.156160 + 0.127155i
\(610\) −1.21180 5.04240i −0.0490643 0.204161i
\(611\) 32.9310i 1.33224i
\(612\) 20.3780 + 13.3907i 0.823733 + 0.541287i
\(613\) 2.77744 2.77744i 0.112180 0.112180i −0.648789 0.760969i \(-0.724724\pi\)
0.760969 + 0.648789i \(0.224724\pi\)
\(614\) −7.27046 −0.293412
\(615\) −40.4212 19.4027i −1.62994 0.782392i
\(616\) 4.92867 0.198582
\(617\) −3.21465 + 3.21465i −0.129417 + 0.129417i −0.768848 0.639431i \(-0.779170\pi\)
0.639431 + 0.768848i \(0.279170\pi\)
\(618\) −1.08443 10.5928i −0.0436222 0.426104i
\(619\) 48.7011i 1.95746i 0.205146 + 0.978731i \(0.434233\pi\)
−0.205146 + 0.978731i \(0.565767\pi\)
\(620\) 17.7309 + 10.8599i 0.712090 + 0.436144i
\(621\) −16.6147 8.63587i −0.666724 0.346545i
\(622\) −7.09184 7.09184i −0.284357 0.284357i
\(623\) −2.79396 2.79396i −0.111938 0.111938i
\(624\) −8.68567 + 10.6669i −0.347705 + 0.427017i
\(625\) −14.6760 + 20.2389i −0.587041 + 0.809557i
\(626\) 11.4409i 0.457271i
\(627\) 24.1343 2.47073i 0.963830 0.0986716i
\(628\) −11.1332 + 11.1332i −0.444261 + 0.444261i
\(629\) −14.0023 −0.558307
\(630\) −1.11507 + 3.09786i −0.0444256 + 0.123422i
\(631\) 15.0588 0.599480 0.299740 0.954021i \(-0.403100\pi\)
0.299740 + 0.954021i \(0.403100\pi\)
\(632\) 5.08420 5.08420i 0.202239 0.202239i
\(633\) −1.33898 + 0.137078i −0.0532197 + 0.00544834i
\(634\) 15.9325i 0.632761i
\(635\) 37.3168 8.96805i 1.48087 0.355886i
\(636\) −12.0685 + 14.8213i −0.478547 + 0.587704i
\(637\) 2.14945 + 2.14945i 0.0851641 + 0.0851641i
\(638\) −2.66009 2.66009i −0.105314 0.105314i
\(639\) −8.25981 39.9184i −0.326753 1.57915i
\(640\) −24.5930 + 5.91025i −0.972126 + 0.233623i
\(641\) 45.9720i 1.81578i 0.419204 + 0.907892i \(0.362309\pi\)
−0.419204 + 0.907892i \(0.637691\pi\)
\(642\) −0.0869793 0.849619i −0.00343280 0.0335318i
\(643\) −5.91991 + 5.91991i −0.233458 + 0.233458i −0.814135 0.580676i \(-0.802788\pi\)
0.580676 + 0.814135i \(0.302788\pi\)
\(644\) −6.33917 −0.249798
\(645\) 1.37822 + 3.92274i 0.0542672 + 0.154458i
\(646\) −11.8906 −0.467831
\(647\) −11.1176 + 11.1176i −0.437079 + 0.437079i −0.891028 0.453949i \(-0.850015\pi\)
0.453949 + 0.891028i \(0.350015\pi\)
\(648\) −15.4369 6.11781i −0.606419 0.240330i
\(649\) 0.425915i 0.0167186i
\(650\) 6.64511 3.38970i 0.260642 0.132955i
\(651\) 7.09965 + 5.78100i 0.278257 + 0.226575i
\(652\) −11.3575 11.3575i −0.444793 0.444793i
\(653\) −30.6500 30.6500i −1.19943 1.19943i −0.974339 0.225088i \(-0.927733\pi\)
−0.225088 0.974339i \(-0.572267\pi\)
\(654\) −12.5344 10.2063i −0.490135 0.399100i
\(655\) 18.9592 + 11.6122i 0.740798 + 0.453727i
\(656\) 30.2465i 1.18093i
\(657\) 9.70367 14.7671i 0.378576 0.576120i
\(658\) −3.75976 + 3.75976i −0.146571 + 0.146571i
\(659\) 50.9397 1.98433 0.992165 0.124933i \(-0.0398714\pi\)
0.992165 + 0.124933i \(0.0398714\pi\)
\(660\) −7.87587 + 16.4077i −0.306568 + 0.638667i
\(661\) −20.5394 −0.798889 −0.399445 0.916757i \(-0.630797\pi\)
−0.399445 + 0.916757i \(0.630797\pi\)
\(662\) 0.768589 0.768589i 0.0298721 0.0298721i
\(663\) −2.47753 24.2007i −0.0962194 0.939877i
\(664\) 10.5355i 0.408856i
\(665\) 2.73962 + 11.3998i 0.106238 + 0.442064i
\(666\) 4.36956 0.904139i 0.169317 0.0350347i
\(667\) 7.31125 + 7.31125i 0.283093 + 0.283093i
\(668\) −2.77947 2.77947i −0.107541 0.107541i
\(669\) −5.16288 + 6.34054i −0.199609 + 0.245139i
\(670\) −4.38688 + 7.16244i −0.169480 + 0.276709i
\(671\) 12.6231i 0.487310i
\(672\) −8.56753 + 0.877097i −0.330500 + 0.0338347i
\(673\) 25.4635 25.4635i 0.981544 0.981544i −0.0182887 0.999833i \(-0.505822\pi\)
0.999833 + 0.0182887i \(0.00582181\pi\)
\(674\) −7.53394 −0.290196
\(675\) −18.2302 18.5110i −0.701682 0.712490i
\(676\) −6.61384 −0.254379
\(677\) 8.67613 8.67613i 0.333451 0.333451i −0.520445 0.853895i \(-0.674234\pi\)
0.853895 + 0.520445i \(0.174234\pi\)
\(678\) 6.80669 0.696831i 0.261409 0.0267616i
\(679\) 2.64285i 0.101423i
\(680\) 9.95618 16.2554i 0.381802 0.623366i
\(681\) −0.374794 + 0.460284i −0.0143621 + 0.0176381i
\(682\) −4.90068 4.90068i −0.187657 0.187657i
\(683\) −24.0010 24.0010i −0.918373 0.918373i 0.0785378 0.996911i \(-0.474975\pi\)
−0.996911 + 0.0785378i \(0.974975\pi\)
\(684\) −27.0965 + 5.60675i −1.03606 + 0.214379i
\(685\) −10.0971 42.0147i −0.385789 1.60530i
\(686\) 0.490808i 0.0187391i
\(687\) −2.37769 23.2254i −0.0907145 0.886104i
\(688\) −1.98330 + 1.98330i −0.0756127 + 0.0756127i
\(689\) 19.0689 0.726467
\(690\) −2.96431 + 6.17550i −0.112849 + 0.235097i
\(691\) −32.5680 −1.23894 −0.619472 0.785019i \(-0.712653\pi\)
−0.619472 + 0.785019i \(0.712653\pi\)
\(692\) −2.98996 + 2.98996i −0.113661 + 0.113661i
\(693\) −4.40103 + 6.69752i −0.167181 + 0.254418i
\(694\) 3.51455i 0.133410i
\(695\) 32.0220 + 19.6130i 1.21466 + 0.743962i
\(696\) 7.11007 + 5.78948i 0.269506 + 0.219450i
\(697\) 37.8237 + 37.8237i 1.43267 + 1.43267i
\(698\) 2.57768 + 2.57768i 0.0975667 + 0.0975667i
\(699\) −2.26528 1.84454i −0.0856808 0.0697670i
\(700\) −8.36630 2.71412i −0.316217 0.102584i
\(701\) 2.43359i 0.0919155i −0.998943 0.0459577i \(-0.985366\pi\)
0.998943 0.0459577i \(-0.0146340\pi\)
\(702\) 2.33580 + 7.39211i 0.0881592 + 0.278997i
\(703\) 11.2356 11.2356i 0.423760 0.423760i
\(704\) −7.43948 −0.280386
\(705\) −13.9079 39.5853i −0.523802 1.49087i
\(706\) 6.30965 0.237467
\(707\) 2.65954 2.65954i 0.100022 0.100022i
\(708\) 0.0494732 + 0.483257i 0.00185932 + 0.0181619i
\(709\) 12.3477i 0.463728i 0.972748 + 0.231864i \(0.0744825\pi\)
−0.972748 + 0.231864i \(0.925518\pi\)
\(710\) −14.4997 + 3.48460i −0.544164 + 0.130775i
\(711\) 2.36895 + 11.4488i 0.0888427 + 0.429363i
\(712\) −5.15485 5.15485i −0.193186 0.193186i
\(713\) 13.4695 + 13.4695i 0.504436 + 0.504436i
\(714\) 2.48015 3.04587i 0.0928173 0.113989i
\(715\) 17.6550 4.24288i 0.660259 0.158675i
\(716\) 14.8536i 0.555103i
\(717\) −8.87927 + 0.909011i −0.331603 + 0.0339476i
\(718\) 8.76797 8.76797i 0.327218 0.327218i
\(719\) 24.2165 0.903125 0.451562 0.892240i \(-0.350867\pi\)
0.451562 + 0.892240i \(0.350867\pi\)
\(720\) 5.93578 16.4906i 0.221213 0.614568i
\(721\) 12.5257 0.466482
\(722\) 2.94721 2.94721i 0.109684 0.109684i
\(723\) −25.7033 + 2.63137i −0.955917 + 0.0978616i
\(724\) 9.70117i 0.360541i
\(725\) 6.51891 + 12.7795i 0.242106 + 0.474621i
\(726\) −2.07397 + 2.54704i −0.0769723 + 0.0945297i
\(727\) −25.8923 25.8923i −0.960293 0.960293i 0.0389483 0.999241i \(-0.487599\pi\)
−0.999241 + 0.0389483i \(0.987599\pi\)
\(728\) 3.96573 + 3.96573i 0.146980 + 0.146980i
\(729\) 22.0977 15.5142i 0.818435 0.574599i
\(730\) −5.51237 3.37624i −0.204022 0.124960i
\(731\) 4.96030i 0.183463i
\(732\) 1.46627 + 14.3226i 0.0541949 + 0.529379i
\(733\) 13.4535 13.4535i 0.496918 0.496918i −0.413559 0.910477i \(-0.635715\pi\)
0.910477 + 0.413559i \(0.135715\pi\)
\(734\) −1.11882 −0.0412965
\(735\) −3.49157 1.67599i −0.128788 0.0618200i
\(736\) −17.9184 −0.660481
\(737\) −14.4563 + 14.4563i −0.532503 + 0.532503i
\(738\) −14.2456 9.36099i −0.524388 0.344583i
\(739\) 1.96813i 0.0723987i 0.999345 + 0.0361994i \(0.0115251\pi\)
−0.999345 + 0.0361994i \(0.988475\pi\)
\(740\) 2.78540 + 11.5903i 0.102393 + 0.426067i
\(741\) 21.4070 + 17.4310i 0.786406 + 0.640343i
\(742\) 2.17711 + 2.17711i 0.0799243 + 0.0799243i
\(743\) −4.54680 4.54680i −0.166806 0.166806i 0.618768 0.785574i \(-0.287632\pi\)
−0.785574 + 0.618768i \(0.787632\pi\)
\(744\) 13.0989 + 10.6659i 0.480227 + 0.391032i
\(745\) 10.8762 17.7575i 0.398472 0.650584i
\(746\) 9.05496i 0.331526i
\(747\) 14.3166 + 9.40761i 0.523815 + 0.344206i
\(748\) 15.3533 15.3533i 0.561371 0.561371i
\(749\) 1.00465 0.0367092
\(750\) −6.55628 + 6.88112i −0.239402 + 0.251263i
\(751\) −0.491718 −0.0179430 −0.00897152 0.999960i \(-0.502856\pi\)
−0.00897152 + 0.999960i \(0.502856\pi\)
\(752\) 20.0140 20.0140i 0.729835 0.729835i
\(753\) −0.759037 7.41432i −0.0276609 0.270193i
\(754\) 4.28075i 0.155896i
\(755\) −23.8098 + 38.8742i −0.866528 + 1.41478i
\(756\) 4.21559 8.11044i 0.153320 0.294974i
\(757\) 3.50957 + 3.50957i 0.127558 + 0.127558i 0.768003 0.640446i \(-0.221250\pi\)
−0.640446 + 0.768003i \(0.721250\pi\)
\(758\) 6.61607 + 6.61607i 0.240306 + 0.240306i
\(759\) −10.5281 + 12.9296i −0.382146 + 0.469314i
\(760\) 5.05459 + 21.0326i 0.183349 + 0.762932i
\(761\) 26.9220i 0.975922i 0.872865 + 0.487961i \(0.162259\pi\)
−0.872865 + 0.487961i \(0.837741\pi\)
\(762\) 14.5151 1.48598i 0.525826 0.0538312i
\(763\) 13.4452 13.4452i 0.486749 0.486749i
\(764\) 0.984264 0.0356094
\(765\) 13.1990 + 28.0445i 0.477210 + 1.01395i
\(766\) 12.3026 0.444512
\(767\) 0.342701 0.342701i 0.0123742 0.0123742i
\(768\) 0.0310544 0.00317918i 0.00112058 0.000114719i
\(769\) 31.3935i