Properties

Label 882.2.f.p.295.2
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3317760000.3
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.2
Root \(-1.72286 - 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.p.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 + 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72286 - 2.98408i) q^{5} +(-1.01575 - 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 + 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.72286 - 2.98408i) q^{5} +(-1.01575 - 1.40294i) q^{6} +1.00000 q^{8} +(-2.00000 - 2.23607i) q^{9} +3.44572 q^{10} +(-2.00000 + 3.46410i) q^{11} +(1.72286 - 0.178197i) q^{12} +(-2.12132 - 3.67423i) q^{13} +(5.93649 - 0.614017i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.41421 q^{17} +(2.93649 - 0.614017i) q^{18} +6.27415 q^{19} +(-1.72286 + 2.98408i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(4.37298 + 7.57423i) q^{23} +(-0.707107 + 1.58114i) q^{24} +(-3.43649 + 5.95218i) q^{25} +4.24264 q^{26} +(4.94975 - 1.58114i) q^{27} +(-0.563508 + 0.976025i) q^{29} +(-2.43649 + 5.44816i) q^{30} +(2.73861 + 4.74342i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.06301 - 5.61177i) q^{33} +(0.707107 - 1.22474i) q^{34} +(-0.936492 + 2.85008i) q^{36} +5.74597 q^{37} +(-3.13707 + 5.43357i) q^{38} +(7.30948 - 0.756026i) q^{39} +(-1.72286 - 2.98408i) q^{40} +(2.82843 + 4.89898i) q^{41} +(-0.563508 + 0.976025i) q^{43} +4.00000 q^{44} +(-3.22689 + 9.82059i) q^{45} -8.74597 q^{46} +(-2.03151 + 3.51867i) q^{47} +(-1.01575 - 1.40294i) q^{48} +(-3.43649 - 5.95218i) q^{50} +(1.00000 - 2.23607i) q^{51} +(-2.12132 + 3.67423i) q^{52} +12.6190 q^{53} +(-1.10557 + 5.07718i) q^{54} +13.7829 q^{55} +(-4.43649 + 9.92030i) q^{57} +(-0.563508 - 0.976025i) q^{58} +(-4.15283 - 7.19291i) q^{59} +(-3.50000 - 4.83414i) q^{60} +(3.13707 - 5.43357i) q^{61} -5.47723 q^{62} +1.00000 q^{64} +(-7.30948 + 12.6604i) q^{65} +(6.89144 - 0.712788i) q^{66} +(3.43649 + 5.95218i) q^{67} +(0.707107 + 1.22474i) q^{68} +(-15.0681 + 1.55850i) q^{69} -9.87298 q^{71} +(-2.00000 - 2.23607i) q^{72} -4.42227 q^{73} +(-2.87298 + 4.97615i) q^{74} +(-6.98125 - 9.64240i) q^{75} +(-3.13707 - 5.43357i) q^{76} +(-3.00000 + 6.70820i) q^{78} +(0.936492 - 1.62205i) q^{79} +3.44572 q^{80} +(-1.00000 + 8.94427i) q^{81} -5.65685 q^{82} +(-1.32440 + 2.29393i) q^{83} +(2.43649 + 4.22013i) q^{85} +(-0.563508 - 0.976025i) q^{86} +(-1.14477 - 1.58114i) q^{87} +(-2.00000 + 3.46410i) q^{88} -7.07107 q^{89} +(-6.89144 - 7.70486i) q^{90} +(4.37298 - 7.57423i) q^{92} +(-9.43649 + 0.976025i) q^{93} +(-2.03151 - 3.51867i) q^{94} +(-10.8095 - 18.7226i) q^{95} +(1.72286 - 0.178197i) q^{96} +(7.50873 - 13.0055i) q^{97} +(11.7460 - 2.45607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{9} - 16 q^{11} + 32 q^{15} - 4 q^{16} + 8 q^{18} - 16 q^{22} + 4 q^{23} - 12 q^{25} - 20 q^{29} - 4 q^{30} - 4 q^{32} + 8 q^{36} - 16 q^{37} + 12 q^{39} - 20 q^{43} + 32 q^{44} - 8 q^{46} - 12 q^{50} + 8 q^{51} + 8 q^{53} - 20 q^{57} - 20 q^{58} - 28 q^{60} + 8 q^{64} - 12 q^{65} + 12 q^{67} - 48 q^{71} - 16 q^{72} + 8 q^{74} - 24 q^{78} - 8 q^{79} - 8 q^{81} + 4 q^{85} - 20 q^{86} - 16 q^{88} + 4 q^{92} - 60 q^{93} - 40 q^{95} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.707107 + 1.58114i −0.408248 + 0.912871i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.72286 2.98408i −0.770486 1.33452i −0.937297 0.348532i \(-0.886680\pi\)
0.166810 0.985989i \(-0.446653\pi\)
\(6\) −1.01575 1.40294i −0.414679 0.572749i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 2.23607i −0.666667 0.745356i
\(10\) 3.44572 1.08963
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 1.72286 0.178197i 0.497347 0.0514410i
\(13\) −2.12132 3.67423i −0.588348 1.01905i −0.994449 0.105221i \(-0.966445\pi\)
0.406100 0.913828i \(-0.366888\pi\)
\(14\) 0 0
\(15\) 5.93649 0.614017i 1.53280 0.158538i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.41421 −0.342997 −0.171499 0.985184i \(-0.554861\pi\)
−0.171499 + 0.985184i \(0.554861\pi\)
\(18\) 2.93649 0.614017i 0.692138 0.144725i
\(19\) 6.27415 1.43939 0.719694 0.694291i \(-0.244282\pi\)
0.719694 + 0.694291i \(0.244282\pi\)
\(20\) −1.72286 + 2.98408i −0.385243 + 0.667261i
\(21\) 0 0
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) 4.37298 + 7.57423i 0.911830 + 1.57934i 0.811477 + 0.584384i \(0.198664\pi\)
0.100353 + 0.994952i \(0.468003\pi\)
\(24\) −0.707107 + 1.58114i −0.144338 + 0.322749i
\(25\) −3.43649 + 5.95218i −0.687298 + 1.19044i
\(26\) 4.24264 0.832050
\(27\) 4.94975 1.58114i 0.952579 0.304290i
\(28\) 0 0
\(29\) −0.563508 + 0.976025i −0.104641 + 0.181243i −0.913591 0.406633i \(-0.866703\pi\)
0.808951 + 0.587877i \(0.200036\pi\)
\(30\) −2.43649 + 5.44816i −0.444840 + 0.994694i
\(31\) 2.73861 + 4.74342i 0.491869 + 0.851943i 0.999956 0.00936313i \(-0.00298042\pi\)
−0.508087 + 0.861306i \(0.669647\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.06301 5.61177i −0.707280 0.976883i
\(34\) 0.707107 1.22474i 0.121268 0.210042i
\(35\) 0 0
\(36\) −0.936492 + 2.85008i −0.156082 + 0.475014i
\(37\) 5.74597 0.944631 0.472316 0.881430i \(-0.343418\pi\)
0.472316 + 0.881430i \(0.343418\pi\)
\(38\) −3.13707 + 5.43357i −0.508900 + 0.881442i
\(39\) 7.30948 0.756026i 1.17045 0.121061i
\(40\) −1.72286 2.98408i −0.272408 0.471825i
\(41\) 2.82843 + 4.89898i 0.441726 + 0.765092i 0.997818 0.0660290i \(-0.0210330\pi\)
−0.556092 + 0.831121i \(0.687700\pi\)
\(42\) 0 0
\(43\) −0.563508 + 0.976025i −0.0859342 + 0.148842i −0.905789 0.423729i \(-0.860721\pi\)
0.819855 + 0.572572i \(0.194054\pi\)
\(44\) 4.00000 0.603023
\(45\) −3.22689 + 9.82059i −0.481036 + 1.46397i
\(46\) −8.74597 −1.28952
\(47\) −2.03151 + 3.51867i −0.296326 + 0.513251i −0.975292 0.220918i \(-0.929095\pi\)
0.678967 + 0.734169i \(0.262428\pi\)
\(48\) −1.01575 1.40294i −0.146611 0.202497i
\(49\) 0 0
\(50\) −3.43649 5.95218i −0.485993 0.841765i
\(51\) 1.00000 2.23607i 0.140028 0.313112i
\(52\) −2.12132 + 3.67423i −0.294174 + 0.509525i
\(53\) 12.6190 1.73335 0.866673 0.498877i \(-0.166254\pi\)
0.866673 + 0.498877i \(0.166254\pi\)
\(54\) −1.10557 + 5.07718i −0.150449 + 0.690916i
\(55\) 13.7829 1.85848
\(56\) 0 0
\(57\) −4.43649 + 9.92030i −0.587628 + 1.31398i
\(58\) −0.563508 0.976025i −0.0739923 0.128158i
\(59\) −4.15283 7.19291i −0.540652 0.936437i −0.998867 0.0475951i \(-0.984844\pi\)
0.458215 0.888842i \(-0.348489\pi\)
\(60\) −3.50000 4.83414i −0.451848 0.624085i
\(61\) 3.13707 5.43357i 0.401661 0.695697i −0.592265 0.805743i \(-0.701766\pi\)
0.993927 + 0.110045i \(0.0350997\pi\)
\(62\) −5.47723 −0.695608
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.30948 + 12.6604i −0.906629 + 1.57033i
\(66\) 6.89144 0.712788i 0.848278 0.0877381i
\(67\) 3.43649 + 5.95218i 0.419834 + 0.727174i 0.995922 0.0902132i \(-0.0287549\pi\)
−0.576088 + 0.817388i \(0.695422\pi\)
\(68\) 0.707107 + 1.22474i 0.0857493 + 0.148522i
\(69\) −15.0681 + 1.55850i −1.81398 + 0.187622i
\(70\) 0 0
\(71\) −9.87298 −1.17171 −0.585854 0.810417i \(-0.699241\pi\)
−0.585854 + 0.810417i \(0.699241\pi\)
\(72\) −2.00000 2.23607i −0.235702 0.263523i
\(73\) −4.42227 −0.517587 −0.258794 0.965933i \(-0.583325\pi\)
−0.258794 + 0.965933i \(0.583325\pi\)
\(74\) −2.87298 + 4.97615i −0.333978 + 0.578466i
\(75\) −6.98125 9.64240i −0.806126 1.11341i
\(76\) −3.13707 5.43357i −0.359847 0.623273i
\(77\) 0 0
\(78\) −3.00000 + 6.70820i −0.339683 + 0.759555i
\(79\) 0.936492 1.62205i 0.105364 0.182495i −0.808523 0.588464i \(-0.799733\pi\)
0.913887 + 0.405969i \(0.133066\pi\)
\(80\) 3.44572 0.385243
\(81\) −1.00000 + 8.94427i −0.111111 + 0.993808i
\(82\) −5.65685 −0.624695
\(83\) −1.32440 + 2.29393i −0.145372 + 0.251791i −0.929512 0.368793i \(-0.879771\pi\)
0.784140 + 0.620584i \(0.213104\pi\)
\(84\) 0 0
\(85\) 2.43649 + 4.22013i 0.264275 + 0.457737i
\(86\) −0.563508 0.976025i −0.0607647 0.105247i
\(87\) −1.14477 1.58114i −0.122732 0.169516i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) −7.07107 −0.749532 −0.374766 0.927119i \(-0.622277\pi\)
−0.374766 + 0.927119i \(0.622277\pi\)
\(90\) −6.89144 7.70486i −0.726421 0.812164i
\(91\) 0 0
\(92\) 4.37298 7.57423i 0.455915 0.789668i
\(93\) −9.43649 + 0.976025i −0.978519 + 0.101209i
\(94\) −2.03151 3.51867i −0.209534 0.362923i
\(95\) −10.8095 18.7226i −1.10903 1.92089i
\(96\) 1.72286 0.178197i 0.175839 0.0181872i
\(97\) 7.50873 13.0055i 0.762396 1.32051i −0.179216 0.983810i \(-0.557356\pi\)
0.941612 0.336699i \(-0.109311\pi\)
\(98\) 0 0
\(99\) 11.7460 2.45607i 1.18051 0.246844i
\(100\) 6.87298 0.687298
\(101\) −6.67261 + 11.5573i −0.663949 + 1.14999i 0.315620 + 0.948886i \(0.397788\pi\)
−0.979569 + 0.201108i \(0.935546\pi\)
\(102\) 1.43649 + 1.98406i 0.142234 + 0.196451i
\(103\) 1.94169 + 3.36311i 0.191321 + 0.331377i 0.945688 0.325075i \(-0.105390\pi\)
−0.754368 + 0.656452i \(0.772056\pi\)
\(104\) −2.12132 3.67423i −0.208013 0.360288i
\(105\) 0 0
\(106\) −6.30948 + 10.9283i −0.612830 + 1.06145i
\(107\) 0.254033 0.0245583 0.0122792 0.999925i \(-0.496091\pi\)
0.0122792 + 0.999925i \(0.496091\pi\)
\(108\) −3.84418 3.49604i −0.369906 0.336406i
\(109\) 16.8730 1.61614 0.808069 0.589087i \(-0.200513\pi\)
0.808069 + 0.589087i \(0.200513\pi\)
\(110\) −6.89144 + 11.9363i −0.657073 + 1.13808i
\(111\) −4.06301 + 9.08517i −0.385644 + 0.862326i
\(112\) 0 0
\(113\) −1.93649 3.35410i −0.182170 0.315527i 0.760449 0.649397i \(-0.224979\pi\)
−0.942619 + 0.333870i \(0.891645\pi\)
\(114\) −6.37298 8.80226i −0.596885 0.824407i
\(115\) 15.0681 26.0987i 1.40511 2.43371i
\(116\) 1.12702 0.104641
\(117\) −3.97320 + 12.0919i −0.367322 + 1.11790i
\(118\) 8.30565 0.764597
\(119\) 0 0
\(120\) 5.93649 0.614017i 0.541925 0.0560518i
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 3.13707 + 5.43357i 0.284017 + 0.491932i
\(123\) −9.74597 + 1.00803i −0.878764 + 0.0908914i
\(124\) 2.73861 4.74342i 0.245935 0.425971i
\(125\) 6.45378 0.577243
\(126\) 0 0
\(127\) −0.745967 −0.0661938 −0.0330969 0.999452i \(-0.510537\pi\)
−0.0330969 + 0.999452i \(0.510537\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.14477 1.58114i −0.100791 0.139212i
\(130\) −7.30948 12.6604i −0.641083 1.11039i
\(131\) 6.67261 + 11.5573i 0.582988 + 1.00977i 0.995123 + 0.0986425i \(0.0314500\pi\)
−0.412135 + 0.911123i \(0.635217\pi\)
\(132\) −2.82843 + 6.32456i −0.246183 + 0.550482i
\(133\) 0 0
\(134\) −6.87298 −0.593735
\(135\) −13.2460 12.0464i −1.14003 1.03679i
\(136\) −1.41421 −0.121268
\(137\) 7.74597 13.4164i 0.661783 1.14624i −0.318364 0.947968i \(-0.603134\pi\)
0.980147 0.198273i \(-0.0635331\pi\)
\(138\) 6.18433 13.8286i 0.526445 1.17717i
\(139\) 9.93870 + 17.2143i 0.842989 + 1.46010i 0.887356 + 0.461085i \(0.152540\pi\)
−0.0443665 + 0.999015i \(0.514127\pi\)
\(140\) 0 0
\(141\) −4.12702 5.70017i −0.347558 0.480041i
\(142\) 4.93649 8.55025i 0.414261 0.717521i
\(143\) 16.9706 1.41915
\(144\) 2.93649 0.614017i 0.244708 0.0511681i
\(145\) 3.88338 0.322497
\(146\) 2.21113 3.82980i 0.182995 0.316956i
\(147\) 0 0
\(148\) −2.87298 4.97615i −0.236158 0.409037i
\(149\) 7.87298 + 13.6364i 0.644980 + 1.11714i 0.984306 + 0.176469i \(0.0564676\pi\)
−0.339326 + 0.940669i \(0.610199\pi\)
\(150\) 11.8412 1.22474i 0.966829 0.100000i
\(151\) −5.50000 + 9.52628i −0.447584 + 0.775238i −0.998228 0.0595022i \(-0.981049\pi\)
0.550645 + 0.834740i \(0.314382\pi\)
\(152\) 6.27415 0.508900
\(153\) 2.82843 + 3.16228i 0.228665 + 0.255655i
\(154\) 0 0
\(155\) 9.43649 16.3445i 0.757957 1.31282i
\(156\) −4.30948 5.95218i −0.345034 0.476556i
\(157\) 5.96550 + 10.3325i 0.476099 + 0.824627i 0.999625 0.0273823i \(-0.00871714\pi\)
−0.523526 + 0.852010i \(0.675384\pi\)
\(158\) 0.936492 + 1.62205i 0.0745033 + 0.129043i
\(159\) −8.92295 + 19.9523i −0.707636 + 1.58232i
\(160\) −1.72286 + 2.98408i −0.136204 + 0.235912i
\(161\) 0 0
\(162\) −7.24597 5.33816i −0.569297 0.419406i
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 2.82843 4.89898i 0.220863 0.382546i
\(165\) −9.74597 + 21.7926i −0.758722 + 1.69656i
\(166\) −1.32440 2.29393i −0.102793 0.178043i
\(167\) 4.77012 + 8.26209i 0.369123 + 0.639340i 0.989429 0.145021i \(-0.0463248\pi\)
−0.620306 + 0.784360i \(0.712991\pi\)
\(168\) 0 0
\(169\) −2.50000 + 4.33013i −0.192308 + 0.333087i
\(170\) −4.87298 −0.373741
\(171\) −12.5483 14.0294i −0.959592 1.07286i
\(172\) 1.12702 0.0859342
\(173\) 6.36396 11.0227i 0.483843 0.838041i −0.515985 0.856598i \(-0.672574\pi\)
0.999828 + 0.0185571i \(0.00590724\pi\)
\(174\) 1.94169 0.200831i 0.147199 0.0152250i
\(175\) 0 0
\(176\) −2.00000 3.46410i −0.150756 0.261116i
\(177\) 14.3095 1.48004i 1.07557 0.111247i
\(178\) 3.53553 6.12372i 0.264999 0.458993i
\(179\) −6.87298 −0.513711 −0.256855 0.966450i \(-0.582686\pi\)
−0.256855 + 0.966450i \(0.582686\pi\)
\(180\) 10.1183 2.11573i 0.754176 0.157697i
\(181\) 13.3452 0.991942 0.495971 0.868339i \(-0.334812\pi\)
0.495971 + 0.868339i \(0.334812\pi\)
\(182\) 0 0
\(183\) 6.37298 + 8.80226i 0.471104 + 0.650682i
\(184\) 4.37298 + 7.57423i 0.322381 + 0.558380i
\(185\) −9.89949 17.1464i −0.727825 1.26063i
\(186\) 3.87298 8.66025i 0.283981 0.635001i
\(187\) 2.82843 4.89898i 0.206835 0.358249i
\(188\) 4.06301 0.296326
\(189\) 0 0
\(190\) 21.6190 1.56840
\(191\) 3.06351 5.30615i 0.221668 0.383940i −0.733647 0.679531i \(-0.762183\pi\)
0.955314 + 0.295591i \(0.0955167\pi\)
\(192\) −0.707107 + 1.58114i −0.0510310 + 0.114109i
\(193\) −11.9365 20.6746i −0.859207 1.48819i −0.872686 0.488282i \(-0.837624\pi\)
0.0134785 0.999909i \(-0.495710\pi\)
\(194\) 7.50873 + 13.0055i 0.539096 + 0.933741i
\(195\) −14.8492 20.5095i −1.06338 1.46872i
\(196\) 0 0
\(197\) 16.6190 1.18405 0.592026 0.805919i \(-0.298328\pi\)
0.592026 + 0.805919i \(0.298328\pi\)
\(198\) −3.74597 + 11.4003i −0.266214 + 0.810187i
\(199\) −12.1890 −0.864058 −0.432029 0.901860i \(-0.642202\pi\)
−0.432029 + 0.901860i \(0.642202\pi\)
\(200\) −3.43649 + 5.95218i −0.242997 + 0.420883i
\(201\) −11.8412 + 1.22474i −0.835213 + 0.0863868i
\(202\) −6.67261 11.5573i −0.469483 0.813168i
\(203\) 0 0
\(204\) −2.43649 + 0.252009i −0.170589 + 0.0176441i
\(205\) 9.74597 16.8805i 0.680688 1.17899i
\(206\) −3.88338 −0.270568
\(207\) 8.19052 24.9267i 0.569281 1.73253i
\(208\) 4.24264 0.294174
\(209\) −12.5483 + 21.7343i −0.867984 + 1.50339i
\(210\) 0 0
\(211\) −10.3095 17.8565i −0.709734 1.22929i −0.964956 0.262412i \(-0.915482\pi\)
0.255222 0.966882i \(-0.417851\pi\)
\(212\) −6.30948 10.9283i −0.433337 0.750561i
\(213\) 6.98125 15.6106i 0.478348 1.06962i
\(214\) −0.127017 + 0.219999i −0.00868268 + 0.0150388i
\(215\) 3.88338 0.264845
\(216\) 4.94975 1.58114i 0.336788 0.107583i
\(217\) 0 0
\(218\) −8.43649 + 14.6124i −0.571391 + 0.989679i
\(219\) 3.12702 6.99222i 0.211304 0.472491i
\(220\) −6.89144 11.9363i −0.464621 0.804747i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) −5.83648 8.06126i −0.391719 0.541036i
\(223\) −11.2239 + 19.4404i −0.751608 + 1.30182i 0.195436 + 0.980717i \(0.437388\pi\)
−0.947043 + 0.321106i \(0.895945\pi\)
\(224\) 0 0
\(225\) 20.1825 4.22013i 1.34550 0.281342i
\(226\) 3.87298 0.257627
\(227\) 5.16858 8.95224i 0.343051 0.594181i −0.641947 0.766749i \(-0.721873\pi\)
0.984998 + 0.172568i \(0.0552064\pi\)
\(228\) 10.8095 1.11803i 0.715875 0.0740436i
\(229\) 6.67261 + 11.5573i 0.440938 + 0.763728i 0.997759 0.0669049i \(-0.0213124\pi\)
−0.556821 + 0.830632i \(0.687979\pi\)
\(230\) 15.0681 + 26.0987i 0.993559 + 1.72090i
\(231\) 0 0
\(232\) −0.563508 + 0.976025i −0.0369961 + 0.0640792i
\(233\) 7.25403 0.475228 0.237614 0.971360i \(-0.423635\pi\)
0.237614 + 0.971360i \(0.423635\pi\)
\(234\) −8.48528 9.48683i −0.554700 0.620174i
\(235\) 14.0000 0.913259
\(236\) −4.15283 + 7.19291i −0.270326 + 0.468218i
\(237\) 1.90249 + 2.62769i 0.123580 + 0.170687i
\(238\) 0 0
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) −2.43649 + 5.44816i −0.157275 + 0.351677i
\(241\) −11.8412 + 20.5095i −0.762758 + 1.32114i 0.178666 + 0.983910i \(0.442822\pi\)
−0.941424 + 0.337226i \(0.890511\pi\)
\(242\) 5.00000 0.321412
\(243\) −13.4350 7.90569i −0.861858 0.507151i
\(244\) −6.27415 −0.401661
\(245\) 0 0
\(246\) 4.00000 8.94427i 0.255031 0.570266i
\(247\) −13.3095 23.0527i −0.846862 1.46681i
\(248\) 2.73861 + 4.74342i 0.173902 + 0.301207i
\(249\) −2.69052 3.71611i −0.170505 0.235499i
\(250\) −3.22689 + 5.58913i −0.204086 + 0.353488i
\(251\) −9.46183 −0.597225 −0.298613 0.954374i \(-0.596524\pi\)
−0.298613 + 0.954374i \(0.596524\pi\)
\(252\) 0 0
\(253\) −34.9839 −2.19942
\(254\) 0.372983 0.646026i 0.0234031 0.0405353i
\(255\) −8.39547 + 0.868351i −0.525745 + 0.0543782i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50403 + 2.60505i 0.0938187 + 0.162499i 0.909115 0.416545i \(-0.136759\pi\)
−0.815296 + 0.579044i \(0.803426\pi\)
\(258\) 1.94169 0.200831i 0.120884 0.0125032i
\(259\) 0 0
\(260\) 14.6190 0.906629
\(261\) 3.30948 0.692007i 0.204851 0.0428342i
\(262\) −13.3452 −0.824470
\(263\) 8.80948 15.2585i 0.543216 0.940877i −0.455501 0.890235i \(-0.650540\pi\)
0.998717 0.0506418i \(-0.0161267\pi\)
\(264\) −4.06301 5.61177i −0.250061 0.345380i
\(265\) −21.7407 37.6560i −1.33552 2.31319i
\(266\) 0 0
\(267\) 5.00000 11.1803i 0.305995 0.684226i
\(268\) 3.43649 5.95218i 0.209917 0.363587i
\(269\) 2.03151 0.123863 0.0619316 0.998080i \(-0.480274\pi\)
0.0619316 + 0.998080i \(0.480274\pi\)
\(270\) 17.0554 5.44816i 1.03796 0.331565i
\(271\) −7.07107 −0.429537 −0.214768 0.976665i \(-0.568900\pi\)
−0.214768 + 0.976665i \(0.568900\pi\)
\(272\) 0.707107 1.22474i 0.0428746 0.0742611i
\(273\) 0 0
\(274\) 7.74597 + 13.4164i 0.467951 + 0.810515i
\(275\) −13.7460 23.8087i −0.828913 1.43572i
\(276\) 8.88374 + 12.2701i 0.534738 + 0.738572i
\(277\) −7.18246 + 12.4404i −0.431552 + 0.747470i −0.997007 0.0773089i \(-0.975367\pi\)
0.565455 + 0.824779i \(0.308701\pi\)
\(278\) −19.8774 −1.19217
\(279\) 5.12938 15.6106i 0.307088 0.934580i
\(280\) 0 0
\(281\) −4.37298 + 7.57423i −0.260870 + 0.451841i −0.966473 0.256767i \(-0.917343\pi\)
0.705603 + 0.708607i \(0.250676\pi\)
\(282\) 7.00000 0.724016i 0.416844 0.0431146i
\(283\) 2.51978 + 4.36439i 0.149785 + 0.259436i 0.931148 0.364641i \(-0.118808\pi\)
−0.781363 + 0.624077i \(0.785475\pi\)
\(284\) 4.93649 + 8.55025i 0.292927 + 0.507364i
\(285\) 37.2464 3.85243i 2.20629 0.228198i
\(286\) −8.48528 + 14.6969i −0.501745 + 0.869048i
\(287\) 0 0
\(288\) −0.936492 + 2.85008i −0.0551833 + 0.167943i
\(289\) −15.0000 −0.882353
\(290\) −1.94169 + 3.36311i −0.114020 + 0.197489i
\(291\) 15.2540 + 21.0686i 0.894207 + 1.23506i
\(292\) 2.21113 + 3.82980i 0.129397 + 0.224122i
\(293\) −0.398461 0.690154i −0.0232783 0.0403192i 0.854152 0.520024i \(-0.174077\pi\)
−0.877430 + 0.479705i \(0.840744\pi\)
\(294\) 0 0
\(295\) −14.3095 + 24.7847i −0.833130 + 1.44302i
\(296\) 5.74597 0.333978
\(297\) −4.42227 + 20.3087i −0.256606 + 1.17843i
\(298\) −15.7460 −0.912139
\(299\) 18.5530 32.1347i 1.07295 1.85840i
\(300\) −4.85993 + 10.8671i −0.280588 + 0.627415i
\(301\) 0 0
\(302\) −5.50000 9.52628i −0.316489 0.548176i
\(303\) −13.5554 18.7226i −0.778740 1.07558i
\(304\) −3.13707 + 5.43357i −0.179923 + 0.311637i
\(305\) −21.6190 −1.23790
\(306\) −4.15283 + 0.868351i −0.237401 + 0.0496403i
\(307\) −14.2205 −0.811609 −0.405805 0.913960i \(-0.633009\pi\)
−0.405805 + 0.913960i \(0.633009\pi\)
\(308\) 0 0
\(309\) −6.69052 + 0.692007i −0.380611 + 0.0393669i
\(310\) 9.43649 + 16.3445i 0.535957 + 0.928304i
\(311\) −0.707107 1.22474i −0.0400963 0.0694489i 0.845281 0.534322i \(-0.179433\pi\)
−0.885377 + 0.464873i \(0.846100\pi\)
\(312\) 7.30948 0.756026i 0.413818 0.0428015i
\(313\) 7.86799 13.6278i 0.444725 0.770286i −0.553308 0.832977i \(-0.686635\pi\)
0.998033 + 0.0626904i \(0.0199681\pi\)
\(314\) −11.9310 −0.673305
\(315\) 0 0
\(316\) −1.87298 −0.105364
\(317\) −12.3095 + 21.3206i −0.691369 + 1.19749i 0.280020 + 0.959994i \(0.409659\pi\)
−0.971389 + 0.237492i \(0.923675\pi\)
\(318\) −12.8177 17.7037i −0.718783 0.992772i
\(319\) −2.25403 3.90410i −0.126202 0.218588i
\(320\) −1.72286 2.98408i −0.0963108 0.166815i
\(321\) −0.179629 + 0.401662i −0.0100259 + 0.0224186i
\(322\) 0 0
\(323\) −8.87298 −0.493706
\(324\) 8.24597 3.60611i 0.458109 0.200339i
\(325\) 29.1596 1.61748
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) −11.9310 + 26.6785i −0.659786 + 1.47533i
\(328\) 2.82843 + 4.89898i 0.156174 + 0.270501i
\(329\) 0 0
\(330\) −14.0000 19.3366i −0.770675 1.06444i
\(331\) −10.1825 + 17.6365i −0.559679 + 0.969392i 0.437844 + 0.899051i \(0.355742\pi\)
−0.997523 + 0.0703409i \(0.977591\pi\)
\(332\) 2.64880 0.145372
\(333\) −11.4919 12.8484i −0.629754 0.704086i
\(334\) −9.54024 −0.522019
\(335\) 11.8412 20.5095i 0.646953 1.12056i
\(336\) 0 0
\(337\) −7.87298 13.6364i −0.428869 0.742822i 0.567904 0.823095i \(-0.307754\pi\)
−0.996773 + 0.0802722i \(0.974421\pi\)
\(338\) −2.50000 4.33013i −0.135982 0.235528i
\(339\) 6.67261 0.690154i 0.362406 0.0374840i
\(340\) 2.43649 4.22013i 0.132137 0.228869i
\(341\) −21.9089 −1.18643
\(342\) 18.4240 3.85243i 0.996255 0.208316i
\(343\) 0 0
\(344\) −0.563508 + 0.976025i −0.0303823 + 0.0526237i
\(345\) 30.6109 + 42.2793i 1.64803 + 2.27624i
\(346\) 6.36396 + 11.0227i 0.342129 + 0.592584i
\(347\) −3.87298 6.70820i −0.207913 0.360115i 0.743144 0.669131i \(-0.233334\pi\)
−0.951057 + 0.309016i \(0.900000\pi\)
\(348\) −0.796921 + 1.78197i −0.0427195 + 0.0955236i
\(349\) −8.21584 + 14.2302i −0.439784 + 0.761728i −0.997672 0.0681880i \(-0.978278\pi\)
0.557889 + 0.829916i \(0.311612\pi\)
\(350\) 0 0
\(351\) −16.3095 14.8324i −0.870535 0.791697i
\(352\) 4.00000 0.213201
\(353\) 1.94169 3.36311i 0.103346 0.179000i −0.809715 0.586823i \(-0.800378\pi\)
0.913061 + 0.407823i \(0.133712\pi\)
\(354\) −5.87298 + 13.1324i −0.312146 + 0.697979i
\(355\) 17.0098 + 29.4618i 0.902785 + 1.56367i
\(356\) 3.53553 + 6.12372i 0.187383 + 0.324557i
\(357\) 0 0
\(358\) 3.43649 5.95218i 0.181624 0.314582i
\(359\) 18.2379 0.962560 0.481280 0.876567i \(-0.340172\pi\)
0.481280 + 0.876567i \(0.340172\pi\)
\(360\) −3.22689 + 9.82059i −0.170072 + 0.517591i
\(361\) 20.3649 1.07184
\(362\) −6.67261 + 11.5573i −0.350704 + 0.607438i
\(363\) 8.61430 0.890985i 0.452133 0.0467646i
\(364\) 0 0
\(365\) 7.61895 + 13.1964i 0.398794 + 0.690732i
\(366\) −10.8095 + 1.11803i −0.565020 + 0.0584406i
\(367\) 3.44572 5.96816i 0.179865 0.311535i −0.761969 0.647613i \(-0.775767\pi\)
0.941834 + 0.336078i \(0.109101\pi\)
\(368\) −8.74597 −0.455915
\(369\) 5.29760 16.1225i 0.275782 0.839305i
\(370\) 19.7990 1.02930
\(371\) 0 0
\(372\) 5.56351 + 7.68423i 0.288454 + 0.398409i
\(373\) 0.563508 + 0.976025i 0.0291774 + 0.0505367i 0.880245 0.474519i \(-0.157378\pi\)
−0.851068 + 0.525055i \(0.824045\pi\)
\(374\) 2.82843 + 4.89898i 0.146254 + 0.253320i
\(375\) −4.56351 + 10.2043i −0.235659 + 0.526949i
\(376\) −2.03151 + 3.51867i −0.104767 + 0.181462i
\(377\) 4.78153 0.246261
\(378\) 0 0
\(379\) 26.3649 1.35427 0.677137 0.735857i \(-0.263220\pi\)
0.677137 + 0.735857i \(0.263220\pi\)
\(380\) −10.8095 + 18.7226i −0.554514 + 0.960447i
\(381\) 0.527478 1.17948i 0.0270235 0.0604264i
\(382\) 3.06351 + 5.30615i 0.156743 + 0.271486i
\(383\) −6.45378 11.1783i −0.329773 0.571183i 0.652694 0.757622i \(-0.273639\pi\)
−0.982467 + 0.186439i \(0.940305\pi\)
\(384\) −1.01575 1.40294i −0.0518349 0.0715936i
\(385\) 0 0
\(386\) 23.8730 1.21510
\(387\) 3.30948 0.692007i 0.168230 0.0351767i
\(388\) −15.0175 −0.762396
\(389\) −6.56351 + 11.3683i −0.332783 + 0.576397i −0.983056 0.183303i \(-0.941321\pi\)
0.650273 + 0.759700i \(0.274654\pi\)
\(390\) 25.1864 2.60505i 1.27536 0.131912i
\(391\) −6.18433 10.7116i −0.312755 0.541708i
\(392\) 0 0
\(393\) −22.9919 + 2.37808i −1.15979 + 0.119958i
\(394\) −8.30948 + 14.3924i −0.418625 + 0.725080i
\(395\) −6.45378 −0.324725
\(396\) −8.00000 8.94427i −0.402015 0.449467i
\(397\) −7.07107 −0.354887 −0.177443 0.984131i \(-0.556783\pi\)
−0.177443 + 0.984131i \(0.556783\pi\)
\(398\) 6.09452 10.5560i 0.305491 0.529125i
\(399\) 0 0
\(400\) −3.43649 5.95218i −0.171825 0.297609i
\(401\) 1.93649 + 3.35410i 0.0967038 + 0.167496i 0.910318 0.413909i \(-0.135837\pi\)
−0.813615 + 0.581405i \(0.802503\pi\)
\(402\) 4.85993 10.8671i 0.242391 0.542004i
\(403\) 11.6190 20.1246i 0.578781 1.00248i
\(404\) 13.3452 0.663949
\(405\) 28.4133 12.4256i 1.41187 0.617435i
\(406\) 0 0
\(407\) −11.4919 + 19.9046i −0.569634 + 0.986635i
\(408\) 1.00000 2.23607i 0.0495074 0.110702i
\(409\) 11.5717 + 20.0428i 0.572186 + 0.991055i 0.996341 + 0.0854655i \(0.0272378\pi\)
−0.424155 + 0.905589i \(0.639429\pi\)
\(410\) 9.74597 + 16.8805i 0.481319 + 0.833669i
\(411\) 15.7360 + 21.7343i 0.776199 + 1.07207i
\(412\) 1.94169 3.36311i 0.0956603 0.165688i
\(413\) 0 0
\(414\) 17.4919 + 19.5566i 0.859682 + 0.961153i
\(415\) 9.12702 0.448028
\(416\) −2.12132 + 3.67423i −0.104006 + 0.180144i
\(417\) −34.2460 + 3.54209i −1.67703 + 0.173457i
\(418\) −12.5483 21.7343i −0.613757 1.06306i
\(419\) −15.6854 27.1679i −0.766280 1.32724i −0.939567 0.342365i \(-0.888772\pi\)
0.173287 0.984871i \(-0.444561\pi\)
\(420\) 0 0
\(421\) 6.43649 11.1483i 0.313695 0.543336i −0.665464 0.746430i \(-0.731766\pi\)
0.979159 + 0.203094i \(0.0650996\pi\)
\(422\) 20.6190 1.00371
\(423\) 11.9310 2.49476i 0.580105 0.121299i
\(424\) 12.6190 0.612830
\(425\) 4.85993 8.41765i 0.235741 0.408316i
\(426\) 10.0285 + 13.8512i 0.485883 + 0.671094i
\(427\) 0 0
\(428\) −0.127017 0.219999i −0.00613958 0.0106341i
\(429\) −12.0000 + 26.8328i −0.579365 + 1.29550i
\(430\) −1.94169 + 3.36311i −0.0936367 + 0.162183i
\(431\) −21.4919 −1.03523 −0.517615 0.855614i \(-0.673180\pi\)
−0.517615 + 0.855614i \(0.673180\pi\)
\(432\) −1.10557 + 5.07718i −0.0531916 + 0.244276i
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) −2.74597 + 6.14017i −0.131659 + 0.294399i
\(436\) −8.43649 14.6124i −0.404035 0.699809i
\(437\) 27.4367 + 47.5218i 1.31248 + 2.27328i
\(438\) 4.49193 + 6.20419i 0.214633 + 0.296448i
\(439\) −5.47723 + 9.48683i −0.261414 + 0.452782i −0.966618 0.256223i \(-0.917522\pi\)
0.705204 + 0.709004i \(0.250855\pi\)
\(440\) 13.7829 0.657073
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 7.18246 12.4404i 0.341249 0.591060i −0.643416 0.765517i \(-0.722483\pi\)
0.984665 + 0.174456i \(0.0558168\pi\)
\(444\) 9.89949 1.02391i 0.469809 0.0485928i
\(445\) 12.1825 + 21.1006i 0.577504 + 1.00027i
\(446\) −11.2239 19.4404i −0.531467 0.920527i
\(447\) −27.1281 + 2.80588i −1.28311 + 0.132714i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −6.43649 + 19.5886i −0.303419 + 0.923415i
\(451\) −22.6274 −1.06548
\(452\) −1.93649 + 3.35410i −0.0910849 + 0.157764i
\(453\) −11.1733 15.4324i −0.524967 0.725076i
\(454\) 5.16858 + 8.95224i 0.242573 + 0.420150i
\(455\) 0 0
\(456\) −4.43649 + 9.92030i −0.207758 + 0.464560i
\(457\) −13.0635 + 22.6267i −0.611085 + 1.05843i 0.379973 + 0.924998i \(0.375933\pi\)
−0.991058 + 0.133433i \(0.957400\pi\)
\(458\) −13.3452 −0.623581
\(459\) −7.00000 + 2.23607i −0.326732 + 0.104371i
\(460\) −30.1361 −1.40511
\(461\) 14.1813 24.5628i 0.660491 1.14400i −0.319996 0.947419i \(-0.603682\pi\)
0.980487 0.196585i \(-0.0629851\pi\)
\(462\) 0 0
\(463\) 0.809475 + 1.40205i 0.0376195 + 0.0651589i 0.884222 0.467067i \(-0.154689\pi\)
−0.846603 + 0.532226i \(0.821356\pi\)
\(464\) −0.563508 0.976025i −0.0261602 0.0453108i
\(465\) 19.1703 + 26.4777i 0.889001 + 1.22787i
\(466\) −3.62702 + 6.28218i −0.168018 + 0.291016i
\(467\) −6.19574 −0.286705 −0.143352 0.989672i \(-0.545788\pi\)
−0.143352 + 0.989672i \(0.545788\pi\)
\(468\) 12.4585 2.60505i 0.575893 0.120419i
\(469\) 0 0
\(470\) −7.00000 + 12.1244i −0.322886 + 0.559255i
\(471\) −20.5554 + 2.12607i −0.947145 + 0.0979641i
\(472\) −4.15283 7.19291i −0.191149 0.331080i
\(473\) −2.25403 3.90410i −0.103641 0.179511i
\(474\) −3.22689 + 0.333760i −0.148216 + 0.0153301i
\(475\) −21.5611 + 37.3448i −0.989289 + 1.71350i
\(476\) 0 0
\(477\) −25.2379 28.2168i −1.15556 1.29196i
\(478\) −15.0000 −0.686084
\(479\) 1.94169 3.36311i 0.0887182 0.153664i −0.818251 0.574861i \(-0.805056\pi\)
0.906970 + 0.421196i \(0.138390\pi\)
\(480\) −3.50000 4.83414i −0.159752 0.220647i
\(481\) −12.1890 21.1120i −0.555772 0.962626i
\(482\) −11.8412 20.5095i −0.539351 0.934184i
\(483\) 0 0
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −51.7460 −2.34966
\(486\) 13.5640 7.68223i 0.615278 0.348473i
\(487\) −0.491933 −0.0222916 −0.0111458 0.999938i \(-0.503548\pi\)
−0.0111458 + 0.999938i \(0.503548\pi\)
\(488\) 3.13707 5.43357i 0.142009 0.245966i
\(489\) −7.07107 + 15.8114i −0.319765 + 0.715016i
\(490\) 0 0
\(491\) −0.872983 1.51205i −0.0393972 0.0682379i 0.845654 0.533731i \(-0.179210\pi\)
−0.885052 + 0.465493i \(0.845877\pi\)
\(492\) 5.74597 + 7.93624i 0.259048 + 0.357793i
\(493\) 0.796921 1.38031i 0.0358915 0.0621659i
\(494\) 26.6190 1.19764
\(495\) −27.5658 30.8195i −1.23899 1.38523i
\(496\) −5.47723 −0.245935
\(497\) 0 0
\(498\) 4.56351 0.472008i 0.204496 0.0211512i
\(499\) 14.8730 + 25.7608i 0.665806 + 1.15321i 0.979066 + 0.203543i \(0.0652456\pi\)
−0.313260 + 0.949667i \(0.601421\pi\)
\(500\) −3.22689 5.58913i −0.144311 0.249954i
\(501\) −16.4365 + 1.70004i −0.734328 + 0.0759523i
\(502\) 4.73092 8.19419i 0.211151 0.365724i
\(503\) 3.88338 0.173152 0.0865758 0.996245i \(-0.472408\pi\)
0.0865758 + 0.996245i \(0.472408\pi\)
\(504\) 0 0
\(505\) 45.9839 2.04626
\(506\) 17.4919 30.2969i 0.777611 1.34686i
\(507\) −5.07877 7.01471i −0.225556 0.311534i
\(508\) 0.372983 + 0.646026i 0.0165485 + 0.0286628i
\(509\) 11.4035 + 19.7515i 0.505452 + 0.875469i 0.999980 + 0.00630722i \(0.00200766\pi\)
−0.494528 + 0.869162i \(0.664659\pi\)
\(510\) 3.44572 7.70486i 0.152579 0.341177i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 31.0554 9.92030i 1.37113 0.437992i
\(514\) −3.00806 −0.132680
\(515\) 6.69052 11.5883i 0.294820 0.510643i
\(516\) −0.796921 + 1.78197i −0.0350825 + 0.0784468i
\(517\) −8.12602 14.0747i −0.357382 0.619004i
\(518\) 0 0
\(519\) 12.9284 + 17.8565i 0.567495 + 0.783815i
\(520\) −7.30948 + 12.6604i −0.320542 + 0.555194i
\(521\) −1.41421 −0.0619578 −0.0309789 0.999520i \(-0.509862\pi\)
−0.0309789 + 0.999520i \(0.509862\pi\)
\(522\) −1.05544 + 3.21209i −0.0461954 + 0.140589i
\(523\) −18.2836 −0.799484 −0.399742 0.916628i \(-0.630900\pi\)
−0.399742 + 0.916628i \(0.630900\pi\)
\(524\) 6.67261 11.5573i 0.291494 0.504883i
\(525\) 0 0
\(526\) 8.80948 + 15.2585i 0.384111 + 0.665300i
\(527\) −3.87298 6.70820i −0.168710 0.292214i
\(528\) 6.89144 0.712788i 0.299911 0.0310201i
\(529\) −26.7460 + 46.3254i −1.16287 + 2.01415i
\(530\) 43.4814 1.88871
\(531\) −7.77817 + 23.6718i −0.337544 + 1.02727i
\(532\) 0 0
\(533\) 12.0000 20.7846i 0.519778 0.900281i
\(534\) 7.18246 + 9.92030i 0.310815 + 0.429293i
\(535\) −0.437664 0.758056i −0.0189219 0.0327736i
\(536\) 3.43649 + 5.95218i 0.148434 + 0.257095i
\(537\) 4.85993 10.8671i 0.209722 0.468952i
\(538\) −1.01575 + 1.75934i −0.0437922 + 0.0758504i
\(539\) 0 0
\(540\) −3.80948 + 17.4945i −0.163934 + 0.752845i
\(541\) −38.1109 −1.63851 −0.819257 0.573426i \(-0.805614\pi\)
−0.819257 + 0.573426i \(0.805614\pi\)
\(542\) 3.53553 6.12372i 0.151864 0.263036i
\(543\) −9.43649 + 21.1006i −0.404959 + 0.905515i
\(544\) 0.707107 + 1.22474i 0.0303170 + 0.0525105i
\(545\) −29.0698 50.3503i −1.24521 2.15677i
\(546\) 0 0
\(547\) 16.4919 28.5649i 0.705144 1.22135i −0.261495 0.965205i \(-0.584216\pi\)
0.966639 0.256141i \(-0.0824511\pi\)
\(548\) −15.4919 −0.661783
\(549\) −18.4240 + 3.85243i −0.786316 + 0.164418i
\(550\) 27.4919 1.17226
\(551\) −3.53553 + 6.12372i −0.150619 + 0.260879i
\(552\) −15.0681 + 1.55850i −0.641340 + 0.0663344i
\(553\) 0 0
\(554\) −7.18246 12.4404i −0.305153 0.528541i
\(555\) 34.1109 3.52812i 1.44793 0.149760i
\(556\) 9.93870 17.2143i 0.421495 0.730050i
\(557\) 26.6190 1.12788 0.563941 0.825815i \(-0.309285\pi\)
0.563941 + 0.825815i \(0.309285\pi\)
\(558\) 10.9545 + 12.2474i 0.463739 + 0.518476i
\(559\) 4.78153 0.202237
\(560\) 0 0
\(561\) 5.74597 + 7.93624i 0.242595 + 0.335068i
\(562\) −4.37298 7.57423i −0.184463 0.319500i
\(563\) −10.8254 18.7502i −0.456238 0.790227i 0.542521 0.840042i \(-0.317470\pi\)
−0.998758 + 0.0498156i \(0.984137\pi\)
\(564\) −2.87298 + 6.42419i −0.120974 + 0.270507i
\(565\) −6.67261 + 11.5573i −0.280719 + 0.486219i
\(566\) −5.03956 −0.211829
\(567\) 0 0
\(568\) −9.87298 −0.414261
\(569\) 11.7460 20.3446i 0.492417 0.852890i −0.507545 0.861625i \(-0.669447\pi\)
0.999962 + 0.00873460i \(0.00278035\pi\)
\(570\) −15.2869 + 34.1826i −0.640298 + 1.43175i
\(571\) −15.7460 27.2728i −0.658948 1.14133i −0.980888 0.194572i \(-0.937668\pi\)
0.321940 0.946760i \(-0.395665\pi\)
\(572\) −8.48528 14.6969i −0.354787 0.614510i
\(573\) 6.22354 + 8.59585i 0.259992 + 0.359097i
\(574\) 0 0
\(575\) −60.1109 −2.50680
\(576\) −2.00000 2.23607i −0.0833333 0.0931695i
\(577\) −24.2213 −1.00834 −0.504172 0.863603i \(-0.668202\pi\)
−0.504172 + 0.863603i \(0.668202\pi\)
\(578\) 7.50000 12.9904i 0.311959 0.540329i
\(579\) 41.1298 4.25409i 1.70930 0.176794i
\(580\) −1.94169 3.36311i −0.0806244 0.139645i
\(581\) 0 0
\(582\) −25.8730 + 2.67607i −1.07247 + 0.110927i
\(583\) −25.2379 + 43.7133i −1.04525 + 1.81042i
\(584\) −4.42227 −0.182995
\(585\) 42.9284 8.97628i 1.77487 0.371124i
\(586\) 0.796921 0.0329205
\(587\) 4.28184 7.41637i 0.176731 0.306106i −0.764028 0.645183i \(-0.776781\pi\)
0.940759 + 0.339076i \(0.110115\pi\)
\(588\) 0 0
\(589\) 17.1825 + 29.7609i 0.707991 + 1.22628i
\(590\) −14.3095 24.7847i −0.589112 1.02037i
\(591\) −11.7514 + 26.2769i −0.483387 + 1.08089i
\(592\) −2.87298 + 4.97615i −0.118079 + 0.204519i
\(593\) −33.7615 −1.38642 −0.693209 0.720736i \(-0.743804\pi\)
−0.693209 + 0.720736i \(0.743804\pi\)
\(594\) −15.3767 13.9842i −0.630914 0.573777i
\(595\) 0 0
\(596\) 7.87298 13.6364i 0.322490 0.558569i
\(597\) 8.61895 19.2726i 0.352750 0.788773i
\(598\) 18.5530 + 32.1347i 0.758688 + 1.31409i
\(599\) 22.6190 + 39.1772i 0.924185 + 1.60074i 0.792866 + 0.609396i \(0.208588\pi\)
0.131319 + 0.991340i \(0.458079\pi\)
\(600\) −6.98125 9.64240i −0.285008 0.393649i
\(601\) −2.39076 + 4.14092i −0.0975213 + 0.168912i −0.910658 0.413161i \(-0.864425\pi\)
0.813137 + 0.582073i \(0.197758\pi\)
\(602\) 0 0
\(603\) 6.43649 19.5886i 0.262114 0.797709i
\(604\) 11.0000 0.447584
\(605\) −8.61430 + 14.9204i −0.350221 + 0.606601i
\(606\) 22.9919 2.37808i 0.933983 0.0966028i
\(607\) 13.3452 + 23.1146i 0.541666 + 0.938192i 0.998809 + 0.0487991i \(0.0155394\pi\)
−0.457143 + 0.889393i \(0.651127\pi\)
\(608\) −3.13707 5.43357i −0.127225 0.220360i
\(609\) 0 0
\(610\) 10.8095 18.7226i 0.437663 0.758054i
\(611\) 17.2379 0.697371
\(612\) 1.32440 4.03063i 0.0535357 0.162929i
\(613\) 26.6190 1.07513 0.537565 0.843223i \(-0.319344\pi\)
0.537565 + 0.843223i \(0.319344\pi\)
\(614\) 7.11027 12.3154i 0.286947 0.497007i
\(615\) 19.7990 + 27.3460i 0.798372 + 1.10270i
\(616\) 0 0
\(617\) 6.12702 + 10.6123i 0.246664 + 0.427235i 0.962598 0.270933i \(-0.0873321\pi\)
−0.715934 + 0.698168i \(0.753999\pi\)
\(618\) 2.74597 6.14017i 0.110459 0.246994i
\(619\) −18.9515 + 32.8249i −0.761723 + 1.31934i 0.180238 + 0.983623i \(0.442313\pi\)
−0.941962 + 0.335721i \(0.891020\pi\)
\(620\) −18.8730 −0.757957
\(621\) 33.6211 + 30.5762i 1.34917 + 1.22698i
\(622\) 1.41421 0.0567048
\(623\) 0 0
\(624\) −3.00000 + 6.70820i −0.120096 + 0.268543i
\(625\) 6.06351 + 10.5023i 0.242540 + 0.420092i
\(626\) 7.86799 + 13.6278i 0.314468 + 0.544675i
\(627\) −25.4919 35.2091i −1.01805 1.40611i
\(628\) 5.96550 10.3325i 0.238049 0.412314i
\(629\) −8.12602 −0.324006
\(630\) 0 0
\(631\) −4.38105 −0.174407 −0.0872034 0.996191i \(-0.527793\pi\)
−0.0872034 + 0.996191i \(0.527793\pi\)
\(632\) 0.936492 1.62205i 0.0372516 0.0645217i
\(633\) 35.5236 3.67423i 1.41193 0.146038i
\(634\) −12.3095 21.3206i −0.488872 0.846751i
\(635\) 1.28520 + 2.22602i 0.0510014 + 0.0883371i
\(636\) 21.7407 2.24866i 0.862074 0.0891651i
\(637\) 0 0
\(638\) 4.50807 0.178476
\(639\) 19.7460 + 22.0767i 0.781138 + 0.873339i
\(640\) 3.44572 0.136204
\(641\) −8.55544 + 14.8185i −0.337920 + 0.585294i −0.984041 0.177941i \(-0.943057\pi\)
0.646122 + 0.763234i \(0.276390\pi\)
\(642\) −0.258035 0.356394i −0.0101838 0.0140657i
\(643\) 1.76206 + 3.05198i 0.0694890 + 0.120358i 0.898676 0.438612i \(-0.144530\pi\)
−0.829187 + 0.558971i \(0.811196\pi\)
\(644\) 0 0
\(645\) −2.74597 + 6.14017i −0.108122 + 0.241769i
\(646\) 4.43649 7.68423i 0.174551 0.302332i
\(647\) 5.47723 0.215332 0.107666 0.994187i \(-0.465662\pi\)
0.107666 + 0.994187i \(0.465662\pi\)
\(648\) −1.00000 + 8.94427i −0.0392837 + 0.351364i
\(649\) 33.2226 1.30410
\(650\) −14.5798 + 25.2530i −0.571867 + 0.990502i
\(651\) 0 0
\(652\) −5.00000 8.66025i −0.195815 0.339162i
\(653\) 7.25403 + 12.5644i 0.283872 + 0.491681i 0.972335 0.233590i \(-0.0750475\pi\)
−0.688463 + 0.725272i \(0.741714\pi\)
\(654\) −17.1388 23.6718i −0.670179 0.925641i
\(655\) 22.9919 39.8232i 0.898369 1.55602i
\(656\) −5.65685 −0.220863
\(657\) 8.84454 + 9.88849i 0.345058 + 0.385787i
\(658\) 0 0
\(659\) −14.5635 + 25.2247i −0.567314 + 0.982616i 0.429517 + 0.903059i \(0.358684\pi\)
−0.996830 + 0.0795572i \(0.974649\pi\)
\(660\) 23.7460 2.45607i 0.924310 0.0956023i
\(661\) −23.1043 40.0178i −0.898652 1.55651i −0.829218 0.558925i \(-0.811214\pi\)
−0.0694345 0.997587i \(-0.522119\pi\)
\(662\) −10.1825 17.6365i −0.395752 0.685463i
\(663\) −10.3372 + 1.06918i −0.401462 + 0.0415236i
\(664\) −1.32440 + 2.29393i −0.0513967 + 0.0890216i
\(665\) 0 0
\(666\) 16.8730 3.52812i 0.653815 0.136712i
\(667\) −9.85685 −0.381659
\(668\) 4.77012 8.26209i 0.184561 0.319670i
\(669\) −22.8014 31.4929i −0.881553 1.21759i
\(670\) 11.8412 + 20.5095i 0.457465 + 0.792353i
\(671\) 12.5483 + 21.7343i 0.484421 + 0.839043i
\(672\) 0 0
\(673\) −7.11895 + 12.3304i −0.274415 + 0.475301i −0.969987 0.243155i \(-0.921818\pi\)
0.695572 + 0.718456i \(0.255151\pi\)
\(674\) 15.7460 0.606512
\(675\) −7.59855 + 34.8953i −0.292468 + 1.34312i
\(676\) 5.00000 0.192308
\(677\) 6.36396 11.0227i 0.244587 0.423637i −0.717428 0.696632i \(-0.754681\pi\)
0.962015 + 0.272995i \(0.0880143\pi\)
\(678\) −2.73861 + 6.12372i −0.105176 + 0.235180i
\(679\) 0 0
\(680\) 2.43649 + 4.22013i 0.0934352 + 0.161834i
\(681\) 10.5000 + 14.5024i 0.402361 + 0.555734i
\(682\) 10.9545 18.9737i 0.419468 0.726539i
\(683\) 7.74597 0.296391 0.148196 0.988958i \(-0.452653\pi\)
0.148196 + 0.988958i \(0.452653\pi\)
\(684\) −5.87569 + 17.8819i −0.224662 + 0.683730i
\(685\) −53.3809 −2.03958
\(686\) 0 0
\(687\) −22.9919 + 2.37808i −0.877197 + 0.0907293i
\(688\) −0.563508 0.976025i −0.0214836 0.0372106i
\(689\) −26.7688 46.3650i −1.01981 1.76637i
\(690\) −51.9204 + 5.37017i −1.97657 + 0.204439i
\(691\) 8.52448 14.7648i 0.324287 0.561681i −0.657081 0.753820i \(-0.728209\pi\)
0.981368 + 0.192139i \(0.0615424\pi\)
\(692\) −12.7279 −0.483843
\(693\) 0 0
\(694\) 7.74597 0.294033
\(695\) 34.2460 59.3158i 1.29902 2.24997i
\(696\) −1.14477 1.58114i −0.0433924 0.0599329i
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) −8.21584 14.2302i −0.310974 0.538623i
\(699\) −5.12938 + 11.4696i −0.194011 + 0.433821i
\(700\) 0 0
\(701\) −16.2540 −0.613906 −0.306953 0.951725i \(-0.599310\pi\)
−0.306953 + 0.951725i \(0.599310\pi\)
\(702\) 21.0000 6.70820i 0.792594 0.253185i
\(703\) 36.0510 1.35969
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) −9.89949 + 22.1359i −0.372837 + 0.833688i
\(706\) 1.94169 + 3.36311i 0.0730765 + 0.126572i
\(707\) 0 0
\(708\) −8.43649 11.6523i −0.317063 0.437922i
\(709\) 26.3649 45.6654i 0.990155 1.71500i 0.373857 0.927486i \(-0.378035\pi\)
0.616298 0.787513i \(-0.288632\pi\)
\(710\) −34.0195 −1.27673
\(711\) −5.50000 + 1.15004i −0.206266 + 0.0431300i
\(712\) −7.07107 −0.264999
\(713\) −23.9518 + 41.4858i −0.897003 + 1.55365i
\(714\) 0 0
\(715\) −29.2379 50.6415i −1.09344 1.89389i
\(716\) 3.43649 + 5.95218i 0.128428 + 0.222443i
\(717\) −25.8429 + 2.67295i −0.965121 + 0.0998233i
\(718\) −9.11895 + 15.7945i −0.340316 + 0.589445i
\(719\) 23.5027 0.876504 0.438252 0.898852i \(-0.355598\pi\)
0.438252 + 0.898852i \(0.355598\pi\)
\(720\) −6.89144 7.70486i −0.256829 0.287143i
\(721\) 0 0
\(722\) −10.1825 + 17.6365i −0.378952 + 0.656364i
\(723\) −24.0554 33.2250i −0.894632 1.23565i
\(724\) −6.67261 11.5573i −0.247985 0.429523i
\(725\) −3.87298 6.70820i −0.143839 0.249136i
\(726\) −3.53553 + 7.90569i −0.131216 + 0.293408i
\(727\) 1.68366 2.91618i 0.0624434 0.108155i −0.833114 0.553102i \(-0.813444\pi\)
0.895557 + 0.444947i \(0.146777\pi\)
\(728\) 0 0
\(729\) 22.0000 15.6525i 0.814815 0.579721i
\(730\) −15.2379 −0.563980
\(731\) 0.796921 1.38031i 0.0294752 0.0510525i
\(732\) 4.43649 9.92030i 0.163977 0.366665i
\(733\) −18.5138 32.0668i −0.683823 1.18442i −0.973805 0.227384i \(-0.926983\pi\)
0.289983 0.957032i \(-0.406350\pi\)
\(734\) 3.44572 + 5.96816i 0.127184 + 0.220289i
\(735\) 0 0
\(736\) 4.37298 7.57423i 0.161190 0.279190i
\(737\) −27.4919 −1.01268
\(738\) 11.3137 + 12.6491i 0.416463 + 0.465620i
\(739\) −30.0000 −1.10357 −0.551784 0.833987i \(-0.686053\pi\)
−0.551784 + 0.833987i \(0.686053\pi\)
\(740\) −9.89949 + 17.1464i −0.363913 + 0.630315i
\(741\) 45.8607 4.74342i 1.68474 0.174254i
\(742\) 0 0
\(743\) 6.12702 + 10.6123i 0.224778 + 0.389328i 0.956253 0.292541i \(-0.0945008\pi\)
−0.731475 + 0.681869i \(0.761167\pi\)
\(744\) −9.43649 + 0.976025i −0.345959 + 0.0357828i
\(745\) 27.1281 46.9872i 0.993896 1.72148i
\(746\) −1.12702 −0.0412630
\(747\) 7.77817 1.62641i 0.284589 0.0595071i
\(748\) −5.65685 −0.206835
\(749\) 0 0
\(750\) −6.55544 9.05427i −0.239371 0.330615i
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) −2.03151 3.51867i −0.0740814 0.128313i
\(753\) 6.69052 14.9605i 0.243816 0.545190i
\(754\) −2.39076 + 4.14092i −0.0870665 + 0.150804i
\(755\) 37.9029 1.37943
\(756\) 0 0
\(757\) 31.2379 1.13536 0.567680 0.823249i \(-0.307841\pi\)
0.567680 + 0.823249i \(0.307841\pi\)
\(758\) −13.1825 + 22.8327i −0.478808 + 0.829321i
\(759\) 24.7373 55.3144i 0.897908 2.00778i
\(760\) −10.8095 18.7226i −0.392101 0.679139i
\(761\) −15.2869 26.4777i −0.554150 0.959816i −0.997969 0.0636995i \(-0.979710\pi\)
0.443819 0.896116i \(-0.353623\pi\)
\(762\) 0.757718 + 1.04655i 0.0274492 + 0.0379124i
\(763\) 0 0
\(764\) −6.12702 −0.221668
\(765\) 4.56351 13.8884i 0.164994 0.502137i
\(766\) 12.9076 0.466369
\(767\) −17.6190 + 30.5169i −0.636183 + 1.10190i
\(768\) 1.72286 0.178197i 0.0621683 0.00643013i
\(769\) −0.617292 1.06918i −0.0222601 0.0385557i 0.854681 0.519154i \(-0.173753\pi\)
−0.876941 + 0.480598i \(0.840420\pi\)
\(770\) 0 0
\(771\) −5.18246 + 0.536026i −0.186642 + 0.0193045i
\(772\) −11.9365 + 20.6746i −0.429604 + 0.744095i
\(773\) 2.03151 0.0730682 0.0365341 0.999332i \(-0.488368\pi\)
0.0365341 + 0.999332i \(0.488368\pi\)
\(774\) −1.05544 + 3.21209i −0.0379371 + 0.115456i
\(775\) −37.6449 −1.35224
\(776\) 7.50873 13.0055i 0.269548 0.466870i
\(777\) 0 0
\(778\) −6.56351 11.3683i −0.235313 0.407574i
\(779\) 17.7460 +