Properties

Label 105.2.j.a.92.8
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 92.8
Character \(\chi\) = 105.92
Dual form 105.2.j.a.8.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.347054 - 0.347054i) q^{2} +(0.176396 - 1.72305i) q^{3} +1.75911i q^{4} +(1.16790 - 1.90683i) q^{5} +(-0.536770 - 0.659208i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.30461 + 1.30461i) q^{8} +(-2.93777 - 0.607876i) q^{9} +O(q^{10})\) \(q+(0.347054 - 0.347054i) q^{2} +(0.176396 - 1.72305i) 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} +(3.03102 + 0.310299i) q^{12} +(2.14945 - 2.14945i) q^{13} -0.490808 q^{14} +(-3.07954 - 2.34871i) q^{15} -2.61267 q^{16} +(-3.26719 + 3.26719i) q^{17} +(-1.23053 + 0.808598i) 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} +(-1.56561 + 4.95468i) q^{27} +(1.24388 - 1.24388i) q^{28} +2.86924 q^{29} +(-1.88389 + 0.253638i) q^{30} -5.28599 q^{31} +(-3.51596 + 3.51596i) q^{32} +(4.60289 + 0.471218i) 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} +(-0.0865765 + 0.845684i) q^{42} +(0.759108 - 0.759108i) q^{43} -4.69922 q^{44} +(-4.59015 + 4.89189i) q^{45} +1.76869 q^{46} +(7.66034 - 7.66034i) q^{47} +(-0.460865 + 4.50176i) 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} +(9.03442 + 0.924894i) q^{57} +(0.995779 - 0.995779i) q^{58} -0.159437 q^{59} +(4.13163 - 5.41724i) q^{60} +4.72534 q^{61} +(-1.83452 + 1.83452i) q^{62} +(1.64748 + 2.50715i) 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} +(-3.03961 - 4.62569i) q^{72} +(4.16486 - 4.16486i) q^{73} -1.48737 q^{74} +(-8.07519 + 3.12910i) q^{75} -9.22351 q^{76} +(1.88894 - 1.88894i) q^{77} +(-2.57069 - 0.263173i) 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} +(0.506122 - 4.94383i) q^{87} +(-3.48510 + 3.48510i) q^{88} -3.95125 q^{89} +(0.104719 + 3.29077i) q^{90} -3.03977 q^{91} +(-4.48247 + 4.48247i) q^{92} +(-0.932426 + 9.10800i) 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 −0.573677 0.819081i \(-0.694484\pi\)
0.819081 + 0.573677i \(0.194484\pi\)
\(3\) 0.176396 1.72305i 0.101842 0.994801i
\(4\) 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 \(0.131936\pi\)
−0.915322 + 0.402724i \(0.868064\pi\)
\(12\) 3.03102 + 0.310299i 0.874981 + 0.0895757i
\(13\) 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
\(15\) −3.07954 2.34871i −0.795134 0.606434i
\(16\) −2.61267 −0.653169
\(17\) −3.26719 + 3.26719i −0.792410 + 0.792410i −0.981886 0.189475i \(-0.939321\pi\)
0.189475 + 0.981886i \(0.439321\pi\)
\(18\) −1.23053 + 0.808598i −0.290038 + 0.190588i
\(19\) 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 0.920967 0.389641i \(-0.127401\pi\)
−0.389641 + 0.920967i \(0.627401\pi\)
\(24\) 2.47803 2.01778i 0.505826 0.411877i
\(25\) −2.27200 4.45399i −0.454400 0.890798i
\(26\) 1.49195i 0.292595i
\(27\) −1.56561 + 4.95468i −0.301301 + 0.953529i
\(28\) 1.24388 1.24388i 0.235071 0.235071i
\(29\) 2.86924 0.532804 0.266402 0.963862i \(-0.414165\pi\)
0.266402 + 0.963862i \(0.414165\pi\)
\(30\) −1.88389 + 0.253638i −0.343950 + 0.0463078i
\(31\) −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
\(33\) 4.60289 + 0.471218i 0.801260 + 0.0820286i
\(34\) 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 \(-0.640619\pi\)
0.427537 0.903998i \(-0.359381\pi\)
\(42\) −0.0865765 + 0.845684i −0.0133590 + 0.130492i
\(43\) 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
\(45\) −4.59015 + 4.89189i −0.684259 + 0.729239i
\(46\) 1.76869 0.260779
\(47\) 7.66034 7.66034i 1.11738 1.11738i 0.125250 0.992125i \(-0.460027\pi\)
0.992125 0.125250i \(-0.0399734\pi\)
\(48\) −0.460865 + 4.50176i −0.0665201 + 0.649773i
\(49\) 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 0.333463 0.942763i \(-0.391783\pi\)
−0.942763 + 0.333463i \(0.891783\pi\)
\(54\) 1.17619 + 2.26289i 0.160059 + 0.307940i
\(55\) 5.09384 + 3.11990i 0.686854 + 0.420687i
\(56\) 1.84500i 0.246548i
\(57\) 9.03442 + 0.924894i 1.19664 + 0.122505i
\(58\) 0.995779 0.995779i 0.130752 0.130752i
\(59\) −0.159437 −0.0207569 −0.0103785 0.999946i \(-0.503304\pi\)
−0.0103785 + 0.999946i \(0.503304\pi\)
\(60\) 4.13163 5.41724i 0.533391 0.699363i
\(61\) 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
\(63\) 1.64748 + 2.50715i 0.207563 + 0.315871i
\(64\) 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 \(0.298533\pi\)
−0.591508 + 0.806299i \(0.701467\pi\)
\(72\) −3.03961 4.62569i −0.358221 0.545143i
\(73\) 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
\(75\) −8.07519 + 3.12910i −0.932443 + 0.361317i
\(76\) −9.22351 −1.05801
\(77\) 1.88894 1.88894i 0.215265 0.215265i
\(78\) −2.57069 0.263173i −0.291073 0.0297985i
\(79\) 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 0.449883 0.893087i \(-0.351466\pi\)
−0.893087 + 0.449883i \(0.851466\pi\)
\(84\) −1.92384 2.36267i −0.209908 0.257789i
\(85\) 2.41421 + 10.0457i 0.261858 + 1.08961i
\(86\) 0.526902i 0.0568173i
\(87\) 0.506122 4.94383i 0.0542619 0.530034i
\(88\) −3.48510 + 3.48510i −0.371513 + 0.371513i
\(89\) −3.95125 −0.418832 −0.209416 0.977827i \(-0.567156\pi\)
−0.209416 + 0.977827i \(0.567156\pi\)
\(90\) 0.104719 + 3.29077i 0.0110384 + 0.346878i
\(91\) −3.03977 −0.318655
\(92\) −4.48247 + 4.48247i −0.467330 + 0.467330i
\(93\) −0.932426 + 9.10800i −0.0966881 + 0.944455i
\(94\) 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 \(-0.940083\pi\)
0.982336 0.187124i \(-0.0599167\pi\)
\(102\) 3.90749 + 0.400027i 0.386899 + 0.0396086i
\(103\) −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
\(105\) 0.516777 + 3.83835i 0.0504323 + 0.374585i
\(106\) −3.07890 −0.299049
\(107\) 0.710397 0.710397i 0.0686766 0.0686766i −0.671934 0.740611i \(-0.734536\pi\)
0.740611 + 0.671934i \(0.234536\pi\)
\(108\) −8.71582 2.75407i −0.838680 0.265011i
\(109\) 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 0.922173 0.386779i \(-0.126412\pi\)
−0.386779 + 0.922173i \(0.626412\pi\)
\(114\) 3.45642 2.81444i 0.323723 0.263597i
\(115\) 7.83488 1.88289i 0.730607 0.175581i
\(116\) 5.04730i 0.468630i
\(117\) −7.62117 + 5.00798i −0.704577 + 0.462988i
\(118\) −0.0553332 + 0.0553332i −0.00509383 + 0.00509383i
\(119\) 4.62051 0.423561
\(120\) −0.953453 7.08176i −0.0870380 0.646473i
\(121\) 3.86380 0.351254
\(122\) 1.63995 1.63995i 0.148474 0.148474i
\(123\) −19.9474 2.04210i −1.79859 0.184130i
\(124\) 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 \(0.143023\pi\)
−0.900743 + 0.434353i \(0.856977\pi\)
\(132\) −0.828923 + 8.09697i −0.0721485 + 0.704751i
\(133\) 3.70756 3.70756i 0.321487 0.321487i
\(134\) −3.75620 −0.324486
\(135\) 7.61926 + 8.77194i 0.655761 + 0.754968i
\(136\) −8.52483 −0.730998
\(137\) 13.6645 13.6645i 1.16744 1.16744i 0.184630 0.982808i \(-0.440891\pi\)
0.982808 0.184630i \(-0.0591086\pi\)
\(138\) 0.311989 3.04753i 0.0265583 0.259423i
\(139\) 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
\(147\) 1.72305 + 0.176396i 0.142114 + 0.0145489i
\(148\) 3.76952 3.76952i 0.309853 0.309853i
\(149\) 9.31256 0.762915 0.381458 0.924386i \(-0.375422\pi\)
0.381458 + 0.924386i \(0.375422\pi\)
\(150\) −1.71656 + 3.88849i −0.140157 + 0.317494i
\(151\) 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
\(153\) 11.5843 7.61221i 0.936535 0.615410i
\(154\) 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
\(162\) 4.10654 1.62746i 0.322640 0.127866i
\(163\) −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
\(165\) 6.27426 8.22658i 0.488451 0.640439i
\(166\) −2.80266 −0.217528
\(167\) 1.58004 1.58004i 0.122268 0.122268i −0.643325 0.765593i \(-0.722446\pi\)
0.765593 + 0.643325i \(0.222446\pi\)
\(168\) −3.17902 0.325450i −0.245267 0.0251090i
\(169\) 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 0.639536 0.768761i \(-0.279127\pi\)
−0.768761 + 0.639536i \(0.779127\pi\)
\(174\) −1.54012 1.89142i −0.116756 0.143388i
\(175\) −1.54290 + 4.75599i −0.116632 + 0.359519i
\(176\) 6.97941i 0.526093i
\(177\) −0.0281240 + 0.274717i −0.00211393 + 0.0206490i
\(178\) −1.37130 + 1.37130i −0.102783 + 0.102783i
\(179\) −8.44380 −0.631119 −0.315560 0.948906i \(-0.602192\pi\)
−0.315560 + 0.948906i \(0.602192\pi\)
\(180\) −8.60535 8.07456i −0.641405 0.601842i
\(181\) 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
\(183\) 0.833531 8.14198i 0.0616164 0.601872i
\(184\) 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 \(0.00644395\pi\)
−0.999795 + 0.0202429i \(0.993556\pi\)
\(192\) −4.79850 0.491244i −0.346302 0.0354525i
\(193\) 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
\(195\) −11.6677 + 1.57089i −0.835543 + 0.112493i
\(196\) −1.75911 −0.125651
\(197\) −10.1505 + 10.1505i −0.723190 + 0.723190i −0.969254 0.246064i \(-0.920863\pi\)
0.246064 + 0.969254i \(0.420863\pi\)
\(198\) −2.16006 3.28719i −0.153509 0.233611i
\(199\) 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
\(207\) −5.93692 9.03483i −0.412644 0.627964i
\(208\) −5.61580 + 5.61580i −0.389386 + 0.389386i
\(209\) −14.0067 −0.968867
\(210\) 1.51146 + 1.15276i 0.104301 + 0.0795483i
\(211\) −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
\(213\) 23.4127 + 2.39687i 1.60421 + 0.164231i
\(214\) 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
\(222\) −0.262367 + 2.56281i −0.0176089 + 0.172005i
\(223\) −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
\(225\) 3.96714 + 14.4659i 0.264476 + 0.964392i
\(226\) 3.95038 0.262776
\(227\) 0.242326 0.242326i 0.0160838 0.0160838i −0.699019 0.715103i \(-0.746380\pi\)
0.715103 + 0.699019i \(0.246380\pi\)
\(228\) −1.62699 + 15.8925i −0.107750 + 1.05251i
\(229\) 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 0.745092 0.666962i \(-0.232406\pi\)
−0.666962 + 0.745092i \(0.732406\pi\)
\(234\) −0.906918 + 4.38299i −0.0592871 + 0.286525i
\(235\) −5.66043 23.5535i −0.369246 1.53646i
\(236\) 0.280467i 0.0182568i
\(237\) 6.71488 + 0.687432i 0.436178 + 0.0446535i
\(238\) 1.60356 1.60356i 0.103944 0.103944i
\(239\) 5.15325 0.333336 0.166668 0.986013i \(-0.446699\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(240\) 8.04584 + 6.13641i 0.519357 + 0.396104i
\(241\) −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
\(243\) 7.61123 13.6040i 0.488261 0.872698i
\(244\) 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 \(0.0433613\pi\)
−0.990736 + 0.135802i \(0.956639\pi\)
\(252\) −4.41035 + 2.89810i −0.277826 + 0.182563i
\(253\) −6.80704 + 6.80704i −0.427955 + 0.427955i
\(254\) −8.42409 −0.528575
\(255\) 17.7351 2.38777i 1.11062 0.149528i
\(256\) 0.0180230 0.00112644
\(257\) −5.82885 + 5.82885i −0.363594 + 0.363594i −0.865134 0.501540i \(-0.832767\pi\)
0.501540 + 0.865134i \(0.332767\pi\)
\(258\) −0.907876 0.0929433i −0.0565219 0.00578640i
\(259\) 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 0.705177 0.709031i \(-0.250867\pi\)
−0.709031 + 0.705177i \(0.750867\pi\)
\(264\) 5.39022 + 6.61974i 0.331745 + 0.407417i
\(265\) −13.6388 + 3.27771i −0.837826 + 0.201348i
\(266\) 2.57345i 0.157788i
\(267\) −0.696985 + 6.80819i −0.0426548 + 0.416654i
\(268\) 9.51951 9.51951i 0.581497 0.581497i
\(269\) −29.6699 −1.80901 −0.904504 0.426465i \(-0.859759\pi\)
−0.904504 + 0.426465i \(0.859759\pi\)
\(270\) 5.68862 + 0.400043i 0.346199 + 0.0243459i
\(271\) 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
\(273\) −0.536204 + 5.23767i −0.0324525 + 0.316998i
\(274\) 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 \(-0.772043\pi\)
0.754341 0.656483i \(-0.227957\pi\)
\(282\) −9.16160 0.937914i −0.545565 0.0558520i
\(283\) 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
\(285\) 12.3150 16.1469i 0.729475 0.956461i
\(286\) 3.98553 0.235670
\(287\) −8.18605 + 8.18605i −0.483207 + 0.483207i
\(288\) 12.4664 8.19181i 0.734587 0.482707i
\(289\) 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 0.803497 0.595309i \(-0.202970\pi\)
−0.595309 + 0.803497i \(0.702970\pi\)
\(294\) 0.659208 0.536770i 0.0384458 0.0313051i
\(295\) −0.186207 + 0.304019i −0.0108414 + 0.0177007i
\(296\) 5.59120i 0.324982i
\(297\) −13.2358 4.18231i −0.768018 0.242683i
\(298\) 3.23196 3.23196i 0.187222 0.187222i
\(299\) 10.9542 0.633499
\(300\) −5.50442 14.2051i −0.317798 0.820134i
\(301\) −1.07354 −0.0618778
\(302\) 7.07531 7.07531i 0.407139 0.407139i
\(303\) −6.48063 0.663452i −0.372303 0.0381143i
\(304\) 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 \(-0.803301\pi\)
0.815068 0.579365i \(-0.196699\pi\)
\(312\) 0.989296 9.66350i 0.0560078 0.547088i
\(313\) −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
\(315\) 6.70481 0.213361i 0.377773 0.0120215i
\(316\) −6.85542 −0.385647
\(317\) −22.9540 + 22.9540i −1.28922 + 1.28922i −0.353965 + 0.935259i \(0.615167\pi\)
−0.935259 + 0.353965i \(0.884833\pi\)
\(318\) −0.543105 + 5.30509i −0.0304558 + 0.297494i
\(319\) 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
\(327\) 32.7626 + 3.35406i 1.81178 + 0.185480i
\(328\) 15.1033 15.1033i 0.833938 0.833938i
\(329\) −10.8334 −0.597262
\(330\) −0.677561 5.03257i −0.0372985 0.277034i
\(331\) −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
\(333\) 4.99263 + 7.59782i 0.273595 + 0.416358i
\(334\) 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
\(342\) −4.23971 6.45202i −0.229257 0.348885i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 1.98068 0.106791
\(345\) −1.86227 13.8320i −0.100261 0.744689i
\(346\) −1.17977 −0.0634251
\(347\) −5.06341 + 5.06341i −0.271818 + 0.271818i −0.829832 0.558014i \(-0.811564\pi\)
0.558014 + 0.829832i \(0.311564\pi\)
\(348\) 8.69672 + 0.890323i 0.466193 + 0.0477263i
\(349\) 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 0.906352 0.422523i \(-0.138856\pi\)
−0.422523 + 0.906352i \(0.638856\pi\)
\(354\) 0.0855810 + 0.105102i 0.00454858 + 0.00558611i
\(355\) 25.9100 + 15.8695i 1.37516 + 0.842264i
\(356\) 6.95068i 0.368385i
\(357\) 0.815038 7.96134i 0.0431364 0.421359i
\(358\) −2.93045 + 2.93045i −0.154879 + 0.154879i
\(359\) 25.2640 1.33338 0.666692 0.745333i \(-0.267710\pi\)
0.666692 + 0.745333i \(0.267710\pi\)
\(360\) −12.3704 + 0.393650i −0.651976 + 0.0207472i
\(361\) −8.49208 −0.446951
\(362\) 1.91394 1.91394i 0.100594 0.100594i
\(363\) 0.681558 6.65750i 0.0357725 0.349428i
\(364\) 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
\(372\) −16.0219 1.64024i −0.830699 0.0850424i
\(373\) 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
\(375\) −3.46439 + 19.0525i −0.178901 + 0.983867i
\(376\) 19.9875 1.03078
\(377\) 6.16727 6.16727i 0.317630 0.317630i
\(378\) 0.768413 2.43180i 0.0395229 0.125078i
\(379\) 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 0.995919 0.0902463i \(-0.0287654\pi\)
−0.0902463 + 0.995919i \(0.528765\pi\)
\(384\) −15.1925 + 12.3708i −0.775291 + 0.631293i
\(385\) −1.39579 5.80799i −0.0711360 0.296003i
\(386\) 4.89484i 0.249141i
\(387\) −2.69153 + 1.76864i −0.136818 + 0.0899050i
\(388\) 3.28738 3.28738i 0.166892 0.166892i
\(389\) 18.3513 0.930446 0.465223 0.885193i \(-0.345974\pi\)
0.465223 + 0.885193i \(0.345974\pi\)
\(390\) −3.50414 + 4.59451i −0.177439 + 0.232652i
\(391\) −16.6506 −0.842056
\(392\) −1.30461 + 1.30461i −0.0658928 + 0.0658928i
\(393\) 17.1319 + 1.75387i 0.864189 + 0.0884710i
\(394\) 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 \(0.329246\pi\)
−0.511079 + 0.859534i \(0.670754\pi\)
\(402\) −0.662578 + 6.47210i −0.0330464 + 0.322799i
\(403\) −11.3619 + 11.3619i −0.565979 + 0.565979i
\(404\) 6.61627 0.329172
\(405\) 16.4585 11.5810i 0.817827 0.575464i
\(406\) −1.40824 −0.0698900
\(407\) 5.72437 5.72437i 0.283746 0.283746i
\(408\) −1.50375 + 14.6887i −0.0744465 + 0.727198i
\(409\) 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
\(417\) −28.9356 2.96227i −1.41698 0.145063i
\(418\) −4.86109 + 4.86109i −0.237764 + 0.237764i
\(419\) 6.20644 0.303204 0.151602 0.988442i \(-0.451557\pi\)
0.151602 + 0.988442i \(0.451557\pi\)
\(420\) −6.75207 + 0.909066i −0.329467 + 0.0443579i
\(421\) 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
\(423\) −27.1608 + 17.8478i −1.32061 + 0.867788i
\(424\) 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 \(-0.934904\pi\)
0.979161 0.203084i \(-0.0650963\pi\)
\(432\) 4.09043 12.9450i 0.196801 0.622815i
\(433\) −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
\(435\) −8.83593 6.73900i −0.423651 0.323110i
\(436\) −33.4483 −1.60188
\(437\) −13.3607 + 13.3607i −0.639128 + 0.639128i
\(438\) −4.98108 0.509935i −0.238005 0.0243657i
\(439\) 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 \(-0.953341\pi\)
−0.146059 0.989276i \(-0.546659\pi\)
\(444\) −5.83013 7.15998i −0.276686 0.339798i
\(445\) −4.61468 + 7.53437i −0.218757 + 0.357163i
\(446\) 2.31700i 0.109713i
\(447\) 1.64270 16.0460i 0.0776970 0.758948i
\(448\) −1.96922 + 1.96922i −0.0930368 + 0.0930368i
\(449\) 23.6736 1.11723 0.558613 0.829428i \(-0.311334\pi\)
0.558613 + 0.829428i \(0.311334\pi\)
\(450\) 6.39725 + 3.64363i 0.301569 + 0.171762i
\(451\) 30.9259 1.45625
\(452\) −10.0116 + 10.0116i −0.470908 + 0.470908i
\(453\) 3.59615 35.1274i 0.168962 1.65043i
\(454\) 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 \(0.182693\pi\)
−0.839764 + 0.542951i \(0.817307\pi\)
\(462\) −2.25913 0.231278i −0.105104 0.0107600i
\(463\) −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
\(465\) 16.2784 + 12.4152i 0.754893 + 0.575743i
\(466\) 0.827796 0.0383469
\(467\) 8.00621 8.00621i 0.370483 0.370483i −0.497170 0.867653i \(-0.665627\pi\)
0.867653 + 0.497170i \(0.165627\pi\)
\(468\) −8.80957 13.4065i −0.407223 0.619714i
\(469\) 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
\(477\) 10.3349 + 15.7277i 0.473201 + 0.720121i
\(478\) 1.78845 1.78845i 0.0818019 0.0818019i
\(479\) 20.1199 0.919304 0.459652 0.888099i \(-0.347974\pi\)
0.459652 + 0.888099i \(0.347974\pi\)
\(480\) 19.0855 2.56958i 0.871131 0.117285i
\(481\) −9.21192 −0.420027
\(482\) −5.17713 + 5.17713i −0.235812 + 0.235812i
\(483\) −6.20921 0.635665i −0.282529 0.0289238i
\(484\) 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 \(-0.983505\pi\)
0.998658 0.0517963i \(-0.0164947\pi\)
\(492\) 3.59228 35.0896i 0.161952 1.58196i
\(493\) −9.37435 + 9.37435i −0.422199 + 0.422199i
\(494\) 7.82270 0.351960
\(495\) −13.0680 12.2620i −0.587364 0.551135i
\(496\) 13.8106 0.620113
\(497\) 9.60816 9.60816i 0.430985 0.430985i
\(498\) −0.494377 + 4.82910i −0.0221536 + 0.216397i
\(499\) 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 0.596434 0.802662i \(-0.296584\pi\)
−0.802662 + 0.596434i \(0.796584\pi\)
\(504\) −1.12153 + 5.42018i −0.0499570 + 0.241434i
\(505\) −7.17188 4.39266i −0.319144 0.195471i
\(506\) 4.72482i 0.210044i
\(507\) 6.47826 + 0.663208i 0.287709 + 0.0294541i
\(508\) 21.3496 21.3496i 0.947234 0.947234i
\(509\) −13.6161 −0.603525 −0.301762 0.953383i \(-0.597575\pi\)
−0.301762 + 0.953383i \(0.597575\pi\)
\(510\) 5.32635 6.98372i 0.235855 0.309244i
\(511\) −5.89000 −0.260558
\(512\) 16.0031 16.0031i 0.707245 0.707245i
\(513\) −25.9788 8.20894i −1.14699 0.362433i
\(514\) 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 \(-0.868046\pi\)
0.915299 0.402775i \(-0.131954\pi\)
\(522\) −3.53068 + 2.32006i −0.154534 + 0.101546i
\(523\) −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
\(525\) 7.92263 + 3.49742i 0.345772 + 0.152640i
\(526\) −0.0433754 −0.00189126
\(527\) 17.2703 17.2703i 0.752308 0.752308i
\(528\) −12.0258 1.23114i −0.523358 0.0535785i
\(529\) 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
\(537\) −1.48945 + 14.5491i −0.0642746 + 0.627838i
\(538\) −10.2971 + 10.2971i −0.443938 + 0.443938i
\(539\) −2.67137 −0.115064
\(540\) −15.4308 + 13.4031i −0.664035 + 0.576777i
\(541\) 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
\(543\) 0.972793 9.50229i 0.0417465 0.407783i
\(544\) 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
\(552\) 11.4560 + 1.17280i 0.487600 + 0.0499178i
\(553\) 2.75566 2.75566i 0.117183 0.117183i
\(554\) 2.92314 0.124192
\(555\) 1.56607 + 11.6320i 0.0664761 + 0.493750i
\(556\) 29.5412 1.25283
\(557\) 10.4002 10.4002i 0.440672 0.440672i −0.451566 0.892238i \(-0.649134\pi\)
0.892238 + 0.451566i \(0.149134\pi\)
\(558\) 6.50456 4.27424i 0.275360 0.180943i
\(559\) 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 0.459755 0.888046i \(-0.347937\pi\)
−0.888046 + 0.459755i \(0.847937\pi\)
\(564\) 25.5957 20.8417i 1.07777 0.877592i
\(565\) 17.4993 4.20546i 0.736200 0.176925i
\(566\) 6.66273i 0.280055i
\(567\) −3.31589 8.36689i −0.139254 0.351376i
\(568\) −17.7271 + 17.7271i −0.743811 + 0.743811i
\(569\) −39.8275 −1.66965 −0.834827 0.550512i \(-0.814433\pi\)
−0.834827 + 0.550512i \(0.814433\pi\)
\(570\) −1.32990 9.87780i −0.0557033 0.413735i
\(571\) −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
\(573\) 0.964086 + 0.0986978i 0.0402753 + 0.00412316i
\(574\) 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
\(582\) −0.228809 + 2.23502i −0.00948443 + 0.0926445i
\(583\) 11.8496 11.8496i 0.490759 0.490759i
\(584\) 10.8670 0.449681
\(585\) 0.648568 + 20.3811i 0.0268150 + 0.842655i
\(586\) 2.47352 0.102180
\(587\) −27.2778 + 27.2778i −1.12588 + 1.12588i −0.135034 + 0.990841i \(0.543114\pi\)
−0.990841 + 0.135034i \(0.956886\pi\)
\(588\) −0.310299 + 3.03102i −0.0127965 + 0.124997i
\(589\) 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 0.731515 0.681826i \(-0.238814\pi\)
−0.681826 + 0.731515i \(0.738814\pi\)
\(594\) −6.04501 + 3.14204i −0.248030 + 0.128919i
\(595\) 5.39631 8.81052i 0.221227 0.361196i
\(596\) 16.3818i 0.671025i
\(597\) 20.1162 + 2.05939i 0.823301 + 0.0842850i
\(598\) 3.80170 3.80170i 0.155463 0.155463i
\(599\) 15.6005 0.637421 0.318710 0.947852i \(-0.396750\pi\)
0.318710 + 0.947852i \(0.396750\pi\)
\(600\) −14.6172 6.45274i −0.596747 0.263432i
\(601\) 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
\(603\) 12.6083 + 19.1875i 0.513452 + 0.781374i
\(604\) 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
\(612\) 13.3907 + 20.3780i 0.541287 + 0.823733i
\(613\) 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
\(615\) −27.1906 + 35.6513i −1.09643 + 1.43760i
\(616\) 4.92867 0.198582
\(617\) 3.21465 3.21465i 0.129417 0.129417i −0.639431 0.768848i \(-0.720830\pi\)
0.768848 + 0.639431i \(0.220830\pi\)
\(618\) 10.5928 + 1.08443i 0.426104 + 0.0436222i
\(619\) 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
\(627\) −2.47073 + 24.1343i −0.0986716 + 0.963830i
\(628\) −11.1332 + 11.1332i −0.444261 + 0.444261i
\(629\) 14.0023 0.558307
\(630\) 2.25288 2.40098i 0.0897569 0.0956572i
\(631\) 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
\(633\) −0.137078 + 1.33898i −0.00544834 + 0.0532197i
\(634\) 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 \(-0.637691\pi\)
0.419204 0.907892i \(-0.362309\pi\)
\(642\) −0.849619 0.0869793i −0.0335318 0.00343280i
\(643\) −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
\(645\) −4.12062 + 0.554781i −0.162249 + 0.0218445i
\(646\) −11.8906 −0.467831
\(647\) 11.1176 11.1176i 0.437079 0.437079i −0.453949 0.891028i \(-0.649985\pi\)
0.891028 + 0.453949i \(0.149985\pi\)
\(648\) 6.11781 + 15.4369i 0.240330 + 0.606419i
\(649\) 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 \(0.0722669\pi\)
0.225088 + 0.974339i \(0.427733\pi\)
\(654\) 12.5344 10.2063i 0.490135 0.399100i
\(655\) 18.9592 + 11.6122i 0.740798 + 0.453727i
\(656\) 30.2465i 1.18093i
\(657\) −14.7671 + 9.70367i −0.576120 + 0.378576i
\(658\) −3.75976 + 3.75976i −0.146571 + 0.146571i
\(659\) −50.9397 −1.98433 −0.992165 0.124933i \(-0.960129\pi\)
−0.992165 + 0.124933i \(0.960129\pi\)
\(660\) 14.4714 + 11.0371i 0.563300 + 0.429619i
\(661\) −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
\(663\) 24.2007 + 2.47753i 0.939877 + 0.0962194i
\(664\) 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
\(672\) 0.877097 8.56753i 0.0338347 0.330500i
\(673\) 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
\(675\) 25.6252 4.28384i 0.986313 0.164885i
\(676\) −6.61384 −0.254379
\(677\) −8.67613 + 8.67613i −0.333451 + 0.333451i −0.853895 0.520445i \(-0.825766\pi\)
0.520445 + 0.853895i \(0.325766\pi\)
\(678\) 0.696831 6.80669i 0.0267616 0.261409i
\(679\) 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 0.996911 0.0785378i \(-0.0250251\pi\)
−0.0785378 + 0.996911i \(0.525025\pi\)
\(684\) 27.0965 + 5.60675i 1.03606 + 0.214379i
\(685\) −10.0971 42.0147i −0.385789 1.60530i
\(686\) 0.490808i 0.0187391i
\(687\) −23.2254 2.37769i −0.886104 0.0907145i
\(688\) −1.98330 + 1.98330i −0.0756127 + 0.0756127i
\(689\) −19.0689 −0.726467
\(690\) −5.44675 4.15413i −0.207354 0.158145i
\(691\) −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
\(693\) −6.69752 + 4.40103i −0.254418 + 0.167181i
\(694\) 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 \(0.0146340\pi\)
−0.998943 + 0.0459577i \(0.985366\pi\)
\(702\) 7.39211 + 2.33580i 0.278997 + 0.0881592i
\(703\) 11.2356 11.2356i 0.423760 0.423760i
\(704\) 7.43948 0.280386
\(705\) −41.5822 + 5.59843i −1.56608 + 0.210849i
\(706\) 6.30965 0.237467
\(707\) −2.65954 + 2.65954i −0.100022 + 0.100022i
\(708\) −0.483257 0.0494732i −0.0181619 0.00185932i
\(709\) 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
\(717\) 0.909011 8.87927i 0.0339476 0.331603i
\(718\) 8.76797 8.76797i 0.327218 0.327218i
\(719\) −24.2165 −0.903125 −0.451562 0.892240i \(-0.649133\pi\)
−0.451562 + 0.892240i \(0.649133\pi\)
\(720\) 11.9926 12.7809i 0.446936 0.476316i
\(721\) 12.5257 0.466482
\(722\) −2.94721 + 2.94721i −0.109684 + 0.109684i
\(723\) −2.63137 + 25.7033i −0.0978616 + 0.955917i
\(724\) 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
\(732\) 14.3226 + 1.46627i 0.529379 + 0.0541949i
\(733\) 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
\(735\) 2.34871 3.07954i 0.0866334 0.113591i
\(736\) −17.9184 −0.660481
\(737\) 14.4563 14.4563i 0.532503 0.532503i
\(738\) 9.36099 + 14.2456i 0.344583 + 0.524388i
\(739\) 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 0.785574 0.618768i \(-0.212368\pi\)
−0.618768 + 0.785574i \(0.712368\pi\)
\(744\) −13.0989 + 10.6659i −0.480227 + 0.391032i
\(745\) 10.8762 17.7575i 0.398472 0.650584i
\(746\) 9.05496i 0.331526i
\(747\) 9.40761 + 14.3166i 0.344206 + 0.523815i
\(748\) 15.3533 15.3533i 0.561371 0.561371i
\(749\) −1.00465 −0.0367092
\(750\) 5.40991 + 7.81457i 0.197542 + 0.285348i
\(751\) −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
\(753\) 7.41432 + 0.759037i 0.270193 + 0.0276609i
\(754\) 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 \(-0.837741\pi\)
0.872865 0.487961i \(-0.162259\pi\)
\(762\) −1.48598 + 14.5151i −0.0538312 + 0.525826i
\(763\) 13.4452 13.4452i 0.486749 0.486749i
\(764\) −0.984264 −0.0356094
\(765\) −0.985834 30.9796i −0.0356429 1.12007i
\(766\) 12.3026 0.444512
\(767\) −0.342701 + 0.342701i −0.0123742 + 0.0123742i
\(768\) 0.00317918 0.0310544i 0.000114719 0.00112058i
\(769\) 31.3935i