Properties

Label 882.2.f.p.295.1
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 295.1
Root \(1.01575 + 1.40294i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.p.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.01575 + 1.75934i) q^{5} +(1.72286 + 0.178197i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 1.58114i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.01575 + 1.75934i) q^{5} +(1.72286 + 0.178197i) q^{6} +1.00000 q^{8} +(-2.00000 + 2.23607i) q^{9} -2.03151 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-1.01575 + 1.40294i) q^{12} +(-2.12132 - 3.67423i) q^{13} +(2.06351 - 2.85008i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.41421 q^{17} +(-0.936492 - 2.85008i) q^{18} +0.796921 q^{19} +(1.01575 - 1.75934i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-3.37298 - 5.84218i) q^{23} +(-0.707107 - 1.58114i) q^{24} +(0.436492 - 0.756026i) q^{25} +4.24264 q^{26} +(4.94975 + 1.58114i) q^{27} +(-4.43649 + 7.68423i) q^{29} +(1.43649 + 3.21209i) q^{30} +(-2.73861 - 4.74342i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.89144 + 0.712788i) q^{33} +(0.707107 - 1.22474i) q^{34} +(2.93649 + 0.614017i) q^{36} -9.74597 q^{37} +(-0.398461 + 0.690154i) q^{38} +(-4.30948 + 5.95218i) q^{39} +(1.01575 + 1.75934i) q^{40} +(2.82843 + 4.89898i) q^{41} +(-4.43649 + 7.68423i) q^{43} +4.00000 q^{44} +(-5.96550 - 1.24738i) q^{45} +6.74597 q^{46} +(3.44572 - 5.96816i) q^{47} +(1.72286 + 0.178197i) q^{48} +(0.436492 + 0.756026i) q^{50} +(1.00000 + 2.23607i) q^{51} +(-2.12132 + 3.67423i) q^{52} -10.6190 q^{53} +(-3.84418 + 3.49604i) q^{54} -8.12602 q^{55} +(-0.563508 - 1.26004i) q^{57} +(-4.43649 - 7.68423i) q^{58} +(1.32440 + 2.29393i) q^{59} +(-3.50000 - 0.362008i) q^{60} +(0.398461 - 0.690154i) q^{61} +5.47723 q^{62} +1.00000 q^{64} +(4.30948 - 7.46423i) q^{65} +(-4.06301 + 5.61177i) q^{66} +(-0.436492 - 0.756026i) q^{67} +(0.707107 + 1.22474i) q^{68} +(-6.85224 + 9.46420i) q^{69} -2.12702 q^{71} +(-2.00000 + 2.23607i) q^{72} -15.3767 q^{73} +(4.87298 - 8.44025i) q^{74} +(-1.50403 - 0.155563i) q^{75} +(-0.398461 - 0.690154i) q^{76} +(-3.00000 - 6.70820i) q^{78} +(-2.93649 + 5.08615i) q^{79} -2.03151 q^{80} +(-1.00000 - 8.94427i) q^{81} -5.65685 q^{82} +(4.15283 - 7.19291i) q^{83} +(-1.43649 - 2.48808i) q^{85} +(-4.43649 - 7.68423i) q^{86} +(15.2869 + 1.58114i) q^{87} +(-2.00000 + 3.46410i) q^{88} -7.07107 q^{89} +(4.06301 - 4.54259i) q^{90} +(-3.37298 + 5.84218i) q^{92} +(-5.56351 + 7.68423i) q^{93} +(3.44572 + 5.96816i) q^{94} +(0.809475 + 1.40205i) q^{95} +(-1.01575 + 1.40294i) q^{96} +(-8.92295 + 15.4550i) q^{97} +(-3.74597 - 11.4003i) 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
\(5\) 1.01575 + 1.75934i 0.454259 + 0.786799i 0.998645 0.0520355i \(-0.0165709\pi\)
−0.544387 + 0.838834i \(0.683238\pi\)
\(6\) 1.72286 + 0.178197i 0.703355 + 0.0727486i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.00000 + 2.23607i −0.666667 + 0.745356i
\(10\) −2.03151 −0.642419
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) −1.01575 + 1.40294i −0.293223 + 0.404994i
\(13\) −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
\(15\) 2.06351 2.85008i 0.532796 0.735889i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.41421 −0.342997 −0.171499 0.985184i \(-0.554861\pi\)
−0.171499 + 0.985184i \(0.554861\pi\)
\(18\) −0.936492 2.85008i −0.220733 0.671771i
\(19\) 0.796921 0.182826 0.0914131 0.995813i \(-0.470862\pi\)
0.0914131 + 0.995813i \(0.470862\pi\)
\(20\) 1.01575 1.75934i 0.227129 0.393399i
\(21\) 0 0
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) −3.37298 5.84218i −0.703316 1.21818i −0.967296 0.253650i \(-0.918369\pi\)
0.263980 0.964528i \(-0.414965\pi\)
\(24\) −0.707107 1.58114i −0.144338 0.322749i
\(25\) 0.436492 0.756026i 0.0872983 0.151205i
\(26\) 4.24264 0.832050
\(27\) 4.94975 + 1.58114i 0.952579 + 0.304290i
\(28\) 0 0
\(29\) −4.43649 + 7.68423i −0.823836 + 1.42693i 0.0789700 + 0.996877i \(0.474837\pi\)
−0.902806 + 0.430049i \(0.858496\pi\)
\(30\) 1.43649 + 3.21209i 0.262266 + 0.586445i
\(31\) −2.73861 4.74342i −0.491869 0.851943i 0.508087 0.861306i \(-0.330353\pi\)
−0.999956 + 0.00936313i \(0.997020\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 6.89144 + 0.712788i 1.19965 + 0.124080i
\(34\) 0.707107 1.22474i 0.121268 0.210042i
\(35\) 0 0
\(36\) 2.93649 + 0.614017i 0.489415 + 0.102336i
\(37\) −9.74597 −1.60223 −0.801114 0.598512i \(-0.795759\pi\)
−0.801114 + 0.598512i \(0.795759\pi\)
\(38\) −0.398461 + 0.690154i −0.0646388 + 0.111958i
\(39\) −4.30948 + 5.95218i −0.690068 + 0.953111i
\(40\) 1.01575 + 1.75934i 0.160605 + 0.278175i
\(41\) 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
\(43\) −4.43649 + 7.68423i −0.676559 + 1.17183i 0.299452 + 0.954111i \(0.403196\pi\)
−0.976011 + 0.217723i \(0.930137\pi\)
\(44\) 4.00000 0.603023
\(45\) −5.96550 1.24738i −0.889284 0.185948i
\(46\) 6.74597 0.994639
\(47\) 3.44572 5.96816i 0.502610 0.870546i −0.497386 0.867530i \(-0.665707\pi\)
0.999995 0.00301623i \(-0.000960097\pi\)
\(48\) 1.72286 + 0.178197i 0.248673 + 0.0257205i
\(49\) 0 0
\(50\) 0.436492 + 0.756026i 0.0617292 + 0.106918i
\(51\) 1.00000 + 2.23607i 0.140028 + 0.313112i
\(52\) −2.12132 + 3.67423i −0.294174 + 0.509525i
\(53\) −10.6190 −1.45862 −0.729312 0.684181i \(-0.760160\pi\)
−0.729312 + 0.684181i \(0.760160\pi\)
\(54\) −3.84418 + 3.49604i −0.523127 + 0.475750i
\(55\) −8.12602 −1.09571
\(56\) 0 0
\(57\) −0.563508 1.26004i −0.0746385 0.166897i
\(58\) −4.43649 7.68423i −0.582540 1.00899i
\(59\) 1.32440 + 2.29393i 0.172422 + 0.298644i 0.939266 0.343190i \(-0.111507\pi\)
−0.766844 + 0.641833i \(0.778174\pi\)
\(60\) −3.50000 0.362008i −0.451848 0.0467351i
\(61\) 0.398461 0.690154i 0.0510176 0.0883652i −0.839389 0.543531i \(-0.817087\pi\)
0.890406 + 0.455166i \(0.150420\pi\)
\(62\) 5.47723 0.695608
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.30948 7.46423i 0.534525 0.925824i
\(66\) −4.06301 + 5.61177i −0.500122 + 0.690761i
\(67\) −0.436492 0.756026i −0.0533259 0.0923632i 0.838130 0.545470i \(-0.183649\pi\)
−0.891456 + 0.453107i \(0.850316\pi\)
\(68\) 0.707107 + 1.22474i 0.0857493 + 0.148522i
\(69\) −6.85224 + 9.46420i −0.824912 + 1.13936i
\(70\) 0 0
\(71\) −2.12702 −0.252430 −0.126215 0.992003i \(-0.540283\pi\)
−0.126215 + 0.992003i \(0.540283\pi\)
\(72\) −2.00000 + 2.23607i −0.235702 + 0.263523i
\(73\) −15.3767 −1.79971 −0.899855 0.436190i \(-0.856327\pi\)
−0.899855 + 0.436190i \(0.856327\pi\)
\(74\) 4.87298 8.44025i 0.566473 0.981160i
\(75\) −1.50403 0.155563i −0.173670 0.0179629i
\(76\) −0.398461 0.690154i −0.0457066 0.0791661i
\(77\) 0 0
\(78\) −3.00000 6.70820i −0.339683 0.759555i
\(79\) −2.93649 + 5.08615i −0.330381 + 0.572237i −0.982587 0.185805i \(-0.940511\pi\)
0.652205 + 0.758042i \(0.273844\pi\)
\(80\) −2.03151 −0.227129
\(81\) −1.00000 8.94427i −0.111111 0.993808i
\(82\) −5.65685 −0.624695
\(83\) 4.15283 7.19291i 0.455832 0.789524i −0.542904 0.839795i \(-0.682675\pi\)
0.998736 + 0.0502709i \(0.0160085\pi\)
\(84\) 0 0
\(85\) −1.43649 2.48808i −0.155809 0.269870i
\(86\) −4.43649 7.68423i −0.478399 0.828612i
\(87\) 15.2869 + 1.58114i 1.63893 + 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 \(0.622277\pi\)
\(90\) 4.06301 4.54259i 0.428279 0.478831i
\(91\) 0 0
\(92\) −3.37298 + 5.84218i −0.351658 + 0.609089i
\(93\) −5.56351 + 7.68423i −0.576909 + 0.796817i
\(94\) 3.44572 + 5.96816i 0.355399 + 0.615569i
\(95\) 0.809475 + 1.40205i 0.0830504 + 0.143847i
\(96\) −1.01575 + 1.40294i −0.103670 + 0.143187i
\(97\) −8.92295 + 15.4550i −0.905988 + 1.56922i −0.0864021 + 0.996260i \(0.527537\pi\)
−0.819586 + 0.572957i \(0.805796\pi\)
\(98\) 0 0
\(99\) −3.74597 11.4003i −0.376484 1.14578i
\(100\) −0.872983 −0.0872983
\(101\) −3.93399 + 6.81388i −0.391447 + 0.678006i −0.992641 0.121097i \(-0.961359\pi\)
0.601194 + 0.799103i \(0.294692\pi\)
\(102\) −2.43649 0.252009i −0.241249 0.0249526i
\(103\) −9.01276 15.6106i −0.888054 1.53815i −0.842173 0.539207i \(-0.818724\pi\)
−0.0458803 0.998947i \(-0.514609\pi\)
\(104\) −2.12132 3.67423i −0.208013 0.360288i
\(105\) 0 0
\(106\) 5.30948 9.19628i 0.515702 0.893222i
\(107\) 15.7460 1.52222 0.761110 0.648623i \(-0.224655\pi\)
0.761110 + 0.648623i \(0.224655\pi\)
\(108\) −1.10557 5.07718i −0.106383 0.488552i
\(109\) 9.12702 0.874210 0.437105 0.899411i \(-0.356004\pi\)
0.437105 + 0.899411i \(0.356004\pi\)
\(110\) 4.06301 7.03734i 0.387393 0.670984i
\(111\) 6.89144 + 15.4097i 0.654106 + 1.46263i
\(112\) 0 0
\(113\) 1.93649 + 3.35410i 0.182170 + 0.315527i 0.942619 0.333870i \(-0.108355\pi\)
−0.760449 + 0.649397i \(0.775021\pi\)
\(114\) 1.37298 + 0.142009i 0.128592 + 0.0133004i
\(115\) 6.85224 11.8684i 0.638974 1.10674i
\(116\) 8.87298 0.823836
\(117\) 12.4585 + 2.60505i 1.15179 + 0.240837i
\(118\) −2.64880 −0.243842
\(119\) 0 0
\(120\) 2.06351 2.85008i 0.188372 0.260176i
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0.398461 + 0.690154i 0.0360749 + 0.0624836i
\(123\) 5.74597 7.93624i 0.518096 0.715586i
\(124\) −2.73861 + 4.74342i −0.245935 + 0.425971i
\(125\) 11.9310 1.06714
\(126\) 0 0
\(127\) 14.7460 1.30849 0.654246 0.756281i \(-0.272986\pi\)
0.654246 + 0.756281i \(0.272986\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 15.2869 + 1.58114i 1.34594 + 0.139212i
\(130\) 4.30948 + 7.46423i 0.377966 + 0.654656i
\(131\) 3.93399 + 6.81388i 0.343715 + 0.595331i 0.985119 0.171871i \(-0.0549814\pi\)
−0.641405 + 0.767203i \(0.721648\pi\)
\(132\) −2.82843 6.32456i −0.246183 0.550482i
\(133\) 0 0
\(134\) 0.872983 0.0754143
\(135\) 2.24597 + 10.3143i 0.193302 + 0.887715i
\(136\) −1.41421 −0.121268
\(137\) −7.74597 + 13.4164i −0.661783 + 1.14624i 0.318364 + 0.947968i \(0.396866\pi\)
−0.980147 + 0.198273i \(0.936467\pi\)
\(138\) −4.77012 10.6663i −0.406059 0.907977i
\(139\) −9.23159 15.9896i −0.783013 1.35622i −0.930179 0.367107i \(-0.880348\pi\)
0.147165 0.989112i \(-0.452985\pi\)
\(140\) 0 0
\(141\) −11.8730 1.22803i −0.999886 0.103419i
\(142\) 1.06351 1.84205i 0.0892476 0.154581i
\(143\) 16.9706 1.41915
\(144\) −0.936492 2.85008i −0.0780410 0.237507i
\(145\) −18.0255 −1.49694
\(146\) 7.68836 13.3166i 0.636293 1.10209i
\(147\) 0 0
\(148\) 4.87298 + 8.44025i 0.400557 + 0.693785i
\(149\) 0.127017 + 0.219999i 0.0104056 + 0.0180230i 0.871181 0.490961i \(-0.163354\pi\)
−0.860776 + 0.508984i \(0.830021\pi\)
\(150\) 0.886735 1.22474i 0.0724016 0.100000i
\(151\) −5.50000 + 9.52628i −0.447584 + 0.775238i −0.998228 0.0595022i \(-0.981049\pi\)
0.550645 + 0.834740i \(0.314382\pi\)
\(152\) 0.796921 0.0646388
\(153\) 2.82843 3.16228i 0.228665 0.255655i
\(154\) 0 0
\(155\) 5.56351 9.63628i 0.446872 0.774005i
\(156\) 7.30948 + 0.756026i 0.585226 + 0.0605305i
\(157\) 3.22689 + 5.58913i 0.257534 + 0.446061i 0.965581 0.260104i \(-0.0837568\pi\)
−0.708047 + 0.706165i \(0.750424\pi\)
\(158\) −2.93649 5.08615i −0.233615 0.404633i
\(159\) 7.50873 + 16.7900i 0.595481 + 1.33154i
\(160\) 1.01575 1.75934i 0.0803023 0.139088i
\(161\) 0 0
\(162\) 8.24597 + 3.60611i 0.647864 + 0.283323i
\(163\) 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
\(165\) 5.74597 + 12.8484i 0.447323 + 1.00024i
\(166\) 4.15283 + 7.19291i 0.322322 + 0.558278i
\(167\) −6.18433 10.7116i −0.478558 0.828887i 0.521140 0.853471i \(-0.325507\pi\)
−0.999698 + 0.0245846i \(0.992174\pi\)
\(168\) 0 0
\(169\) −2.50000 + 4.33013i −0.192308 + 0.333087i
\(170\) 2.87298 0.220348
\(171\) −1.59384 + 1.78197i −0.121884 + 0.136271i
\(172\) 8.87298 0.676559
\(173\) 6.36396 11.0227i 0.483843 0.838041i −0.515985 0.856598i \(-0.672574\pi\)
0.999828 + 0.0185571i \(0.00590724\pi\)
\(174\) −9.01276 + 12.4483i −0.683256 + 0.943702i
\(175\) 0 0
\(176\) −2.00000 3.46410i −0.150756 0.261116i
\(177\) 2.69052 3.71611i 0.202232 0.279320i
\(178\) 3.53553 6.12372i 0.264999 0.458993i
\(179\) 0.872983 0.0652498 0.0326249 0.999468i \(-0.489613\pi\)
0.0326249 + 0.999468i \(0.489613\pi\)
\(180\) 1.90249 + 5.78996i 0.141803 + 0.431558i
\(181\) 7.86799 0.584823 0.292412 0.956293i \(-0.405542\pi\)
0.292412 + 0.956293i \(0.405542\pi\)
\(182\) 0 0
\(183\) −1.37298 0.142009i −0.101494 0.0104976i
\(184\) −3.37298 5.84218i −0.248660 0.430691i
\(185\) −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
\(188\) −6.89144 −0.502610
\(189\) 0 0
\(190\) −1.61895 −0.117451
\(191\) 6.93649 12.0144i 0.501907 0.869328i −0.498091 0.867125i \(-0.665965\pi\)
0.999998 0.00220333i \(-0.000701341\pi\)
\(192\) −0.707107 1.58114i −0.0510310 0.114109i
\(193\) −8.06351 13.9664i −0.580424 1.00532i −0.995429 0.0955048i \(-0.969553\pi\)
0.415005 0.909819i \(-0.363780\pi\)
\(194\) −8.92295 15.4550i −0.640630 1.10960i
\(195\) −14.8492 1.53587i −1.06338 0.109986i
\(196\) 0 0
\(197\) −6.61895 −0.471581 −0.235790 0.971804i \(-0.575768\pi\)
−0.235790 + 0.971804i \(0.575768\pi\)
\(198\) 11.7460 + 2.45607i 0.834750 + 0.174545i
\(199\) 20.6743 1.46556 0.732782 0.680464i \(-0.238222\pi\)
0.732782 + 0.680464i \(0.238222\pi\)
\(200\) 0.436492 0.756026i 0.0308646 0.0534591i
\(201\) −0.886735 + 1.22474i −0.0625455 + 0.0863868i
\(202\) −3.93399 6.81388i −0.276795 0.479423i
\(203\) 0 0
\(204\) 1.43649 1.98406i 0.100575 0.138912i
\(205\) −5.74597 + 9.95231i −0.401316 + 0.695099i
\(206\) 18.0255 1.25590
\(207\) 19.8095 + 4.14214i 1.37685 + 0.287898i
\(208\) 4.24264 0.294174
\(209\) −1.59384 + 2.76062i −0.110248 + 0.190956i
\(210\) 0 0
\(211\) 1.30948 + 2.26808i 0.0901480 + 0.156141i 0.907573 0.419894i \(-0.137933\pi\)
−0.817425 + 0.576035i \(0.804599\pi\)
\(212\) 5.30948 + 9.19628i 0.364656 + 0.631603i
\(213\) 1.50403 + 3.36311i 0.103054 + 0.230436i
\(214\) −7.87298 + 13.6364i −0.538186 + 0.932166i
\(215\) −18.0255 −1.22933
\(216\) 4.94975 + 1.58114i 0.336788 + 0.107583i
\(217\) 0 0
\(218\) −4.56351 + 7.90423i −0.309080 + 0.535342i
\(219\) 10.8730 + 24.3127i 0.734728 + 1.64290i
\(220\) 4.06301 + 7.03734i 0.273928 + 0.474458i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) −16.7909 1.73670i −1.12693 0.116560i
\(223\) −5.74667 + 9.95352i −0.384825 + 0.666537i −0.991745 0.128226i \(-0.959072\pi\)
0.606920 + 0.794763i \(0.292405\pi\)
\(224\) 0 0
\(225\) 0.817542 + 2.48808i 0.0545028 + 0.165872i
\(226\) −3.87298 −0.257627
\(227\) −3.04726 + 5.27801i −0.202254 + 0.350314i −0.949254 0.314510i \(-0.898160\pi\)
0.747001 + 0.664823i \(0.231493\pi\)
\(228\) −0.809475 + 1.11803i −0.0536088 + 0.0740436i
\(229\) 3.93399 + 6.81388i 0.259966 + 0.450274i 0.966232 0.257672i \(-0.0829554\pi\)
−0.706267 + 0.707946i \(0.749622\pi\)
\(230\) 6.85224 + 11.8684i 0.451823 + 0.782580i
\(231\) 0 0
\(232\) −4.43649 + 7.68423i −0.291270 + 0.504494i
\(233\) 22.7460 1.49014 0.745069 0.666987i \(-0.232417\pi\)
0.745069 + 0.666987i \(0.232417\pi\)
\(234\) −8.48528 + 9.48683i −0.554700 + 0.620174i
\(235\) 14.0000 0.913259
\(236\) 1.32440 2.29393i 0.0862110 0.149322i
\(237\) 10.1183 + 1.04655i 0.657256 + 0.0679806i
\(238\) 0 0
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 1.43649 + 3.21209i 0.0927251 + 0.207340i
\(241\) −0.886735 + 1.53587i −0.0571197 + 0.0989341i −0.893171 0.449717i \(-0.851525\pi\)
0.836052 + 0.548651i \(0.184858\pi\)
\(242\) 5.00000 0.321412
\(243\) −13.4350 + 7.90569i −0.861858 + 0.507151i
\(244\) −0.796921 −0.0510176
\(245\) 0 0
\(246\) 4.00000 + 8.94427i 0.255031 + 0.570266i
\(247\) −1.69052 2.92808i −0.107566 0.186309i
\(248\) −2.73861 4.74342i −0.173902 0.301207i
\(249\) −14.3095 1.48004i −0.906826 0.0937939i
\(250\) −5.96550 + 10.3325i −0.377291 + 0.653488i
\(251\) −25.8935 −1.63438 −0.817192 0.576366i \(-0.804470\pi\)
−0.817192 + 0.576366i \(0.804470\pi\)
\(252\) 0 0
\(253\) 26.9839 1.69646
\(254\) −7.37298 + 12.7704i −0.462622 + 0.801285i
\(255\) −2.91824 + 4.03063i −0.182747 + 0.252408i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.98125 + 12.0919i 0.435479 + 0.754271i 0.997335 0.0729640i \(-0.0232458\pi\)
−0.561856 + 0.827235i \(0.689912\pi\)
\(258\) −9.01276 + 12.4483i −0.561110 + 0.774996i
\(259\) 0 0
\(260\) −8.61895 −0.534525
\(261\) −8.30948 25.2888i −0.514344 1.56533i
\(262\) −7.86799 −0.486086
\(263\) −2.80948 + 4.86615i −0.173240 + 0.300060i −0.939551 0.342410i \(-0.888757\pi\)
0.766311 + 0.642470i \(0.222090\pi\)
\(264\) 6.89144 + 0.712788i 0.424139 + 0.0438691i
\(265\) −10.7862 18.6823i −0.662593 1.14764i
\(266\) 0 0
\(267\) 5.00000 + 11.1803i 0.305995 + 0.684226i
\(268\) −0.436492 + 0.756026i −0.0266630 + 0.0461816i
\(269\) −3.44572 −0.210089 −0.105045 0.994468i \(-0.533499\pi\)
−0.105045 + 0.994468i \(0.533499\pi\)
\(270\) −10.0554 3.21209i −0.611955 0.195482i
\(271\) −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
\(275\) 1.74597 + 3.02410i 0.105286 + 0.182360i
\(276\) 11.6224 + 1.20211i 0.699584 + 0.0723586i
\(277\) 12.1825 21.1006i 0.731973 1.26781i −0.224066 0.974574i \(-0.571933\pi\)
0.956039 0.293240i \(-0.0947336\pi\)
\(278\) 18.4632 1.10735
\(279\) 16.0838 + 3.36311i 0.962914 + 0.201344i
\(280\) 0 0
\(281\) 3.37298 5.84218i 0.201215 0.348515i −0.747705 0.664031i \(-0.768844\pi\)
0.948920 + 0.315516i \(0.102178\pi\)
\(282\) 7.00000 9.66829i 0.416844 0.575738i
\(283\) 5.25839 + 9.10781i 0.312579 + 0.541403i 0.978920 0.204244i \(-0.0654737\pi\)
−0.666341 + 0.745647i \(0.732140\pi\)
\(284\) 1.06351 + 1.84205i 0.0631076 + 0.109306i
\(285\) 1.64445 2.27129i 0.0974090 0.134540i
\(286\) −8.48528 + 14.6969i −0.501745 + 0.869048i
\(287\) 0 0
\(288\) 2.93649 + 0.614017i 0.173034 + 0.0361813i
\(289\) −15.0000 −0.882353
\(290\) 9.01276 15.6106i 0.529247 0.916683i
\(291\) 30.7460 + 3.18008i 1.80236 + 0.186420i
\(292\) 7.68836 + 13.3166i 0.449927 + 0.779297i
\(293\) −3.13707 5.43357i −0.183270 0.317433i 0.759722 0.650248i \(-0.225335\pi\)
−0.942992 + 0.332815i \(0.892002\pi\)
\(294\) 0 0
\(295\) −2.69052 + 4.66013i −0.156648 + 0.271323i
\(296\) −9.74597 −0.566473
\(297\) −15.3767 + 13.9842i −0.892248 + 0.811443i
\(298\) −0.254033 −0.0147158
\(299\) −14.3104 + 24.7863i −0.827589 + 1.43343i
\(300\) 0.617292 + 1.38031i 0.0356394 + 0.0796921i
\(301\) 0 0
\(302\) −5.50000 9.52628i −0.316489 0.548176i
\(303\) 13.5554 + 1.40205i 0.778740 + 0.0805458i
\(304\) −0.398461 + 0.690154i −0.0228533 + 0.0395830i
\(305\) 1.61895 0.0927008
\(306\) 1.32440 + 4.03063i 0.0757109 + 0.230416i
\(307\) 24.1200 1.37660 0.688302 0.725425i \(-0.258357\pi\)
0.688302 + 0.725425i \(0.258357\pi\)
\(308\) 0 0
\(309\) −18.3095 + 25.2888i −1.04159 + 1.43863i
\(310\) 5.56351 + 9.63628i 0.315986 + 0.547304i
\(311\) −0.707107 1.22474i −0.0400963 0.0694489i 0.845281 0.534322i \(-0.179433\pi\)
−0.885377 + 0.464873i \(0.846100\pi\)
\(312\) −4.30948 + 5.95218i −0.243976 + 0.336976i
\(313\) 13.3452 23.1146i 0.754316 1.30651i −0.191397 0.981513i \(-0.561302\pi\)
0.945714 0.325001i \(-0.105365\pi\)
\(314\) −6.45378 −0.364208
\(315\) 0 0
\(316\) 5.87298 0.330381
\(317\) −0.690525 + 1.19602i −0.0387837 + 0.0671754i −0.884766 0.466036i \(-0.845682\pi\)
0.845982 + 0.533212i \(0.179015\pi\)
\(318\) −18.2950 1.89226i −1.02593 0.106113i
\(319\) −17.7460 30.7369i −0.993583 1.72094i
\(320\) 1.01575 + 1.75934i 0.0567823 + 0.0983499i
\(321\) −11.1341 24.8966i −0.621444 1.38959i
\(322\) 0 0
\(323\) −1.12702 −0.0627089
\(324\) −7.24597 + 5.33816i −0.402554 + 0.296565i
\(325\) −3.70375 −0.205447
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) −6.45378 14.4311i −0.356895 0.798041i
\(328\) 2.82843 + 4.89898i 0.156174 + 0.270501i
\(329\) 0 0
\(330\) −14.0000 1.44803i −0.770675 0.0797116i
\(331\) 9.18246 15.9045i 0.504714 0.874190i −0.495272 0.868738i \(-0.664931\pi\)
0.999985 0.00545133i \(-0.00173522\pi\)
\(332\) −8.30565 −0.455832
\(333\) 19.4919 21.7926i 1.06815 1.19423i
\(334\) 12.3687 0.676783
\(335\) 0.886735 1.53587i 0.0484475 0.0839136i
\(336\) 0 0
\(337\) −0.127017 0.219999i −0.00691904 0.0119841i 0.862545 0.505980i \(-0.168869\pi\)
−0.869464 + 0.493996i \(0.835536\pi\)
\(338\) −2.50000 4.33013i −0.135982 0.235528i
\(339\) 3.93399 5.43357i 0.213665 0.295111i
\(340\) −1.43649 + 2.48808i −0.0779047 + 0.134935i
\(341\) 21.9089 1.18643
\(342\) −0.746310 2.27129i −0.0403558 0.122817i
\(343\) 0 0
\(344\) −4.43649 + 7.68423i −0.239200 + 0.414306i
\(345\) −23.6109 2.44210i −1.27117 0.131478i
\(346\) 6.36396 + 11.0227i 0.342129 + 0.592584i
\(347\) 3.87298 + 6.70820i 0.207913 + 0.360115i 0.951057 0.309016i \(-0.0999997\pi\)
−0.743144 + 0.669131i \(0.766666\pi\)
\(348\) −6.27415 14.0294i −0.336330 0.752056i
\(349\) 8.21584 14.2302i 0.439784 0.761728i −0.557889 0.829916i \(-0.688388\pi\)
0.997672 + 0.0681880i \(0.0217218\pi\)
\(350\) 0 0
\(351\) −4.69052 21.5406i −0.250362 1.14975i
\(352\) 4.00000 0.213201
\(353\) −9.01276 + 15.6106i −0.479701 + 0.830866i −0.999729 0.0232830i \(-0.992588\pi\)
0.520028 + 0.854149i \(0.325921\pi\)
\(354\) 1.87298 + 4.18812i 0.0995479 + 0.222596i
\(355\) −2.16052 3.74214i −0.114669 0.198612i
\(356\) 3.53553 + 6.12372i 0.187383 + 0.324557i
\(357\) 0 0
\(358\) −0.436492 + 0.756026i −0.0230693 + 0.0399572i
\(359\) −28.2379 −1.49034 −0.745170 0.666875i \(-0.767632\pi\)
−0.745170 + 0.666875i \(0.767632\pi\)
\(360\) −5.96550 1.24738i −0.314409 0.0657426i
\(361\) −18.3649 −0.966575
\(362\) −3.93399 + 6.81388i −0.206766 + 0.358129i
\(363\) −5.07877 + 7.01471i −0.266566 + 0.368177i
\(364\) 0 0
\(365\) −15.6190 27.0528i −0.817533 1.41601i
\(366\) 0.809475 1.11803i 0.0423119 0.0584406i
\(367\) −2.03151 + 3.51867i −0.106044 + 0.183673i −0.914164 0.405344i \(-0.867152\pi\)
0.808120 + 0.589017i \(0.200485\pi\)
\(368\) 6.74597 0.351658
\(369\) −16.6113 3.47340i −0.864750 0.180818i
\(370\) 19.7990 1.02930
\(371\) 0 0
\(372\) 9.43649 + 0.976025i 0.489259 + 0.0506045i
\(373\) 4.43649 + 7.68423i 0.229713 + 0.397874i 0.957723 0.287692i \(-0.0928880\pi\)
−0.728010 + 0.685566i \(0.759555\pi\)
\(374\) 2.82843 + 4.89898i 0.146254 + 0.253320i
\(375\) −8.43649 18.8646i −0.435659 0.974162i
\(376\) 3.44572 5.96816i 0.177699 0.307784i
\(377\) 37.6449 1.93881
\(378\) 0 0
\(379\) −12.3649 −0.635143 −0.317572 0.948234i \(-0.602867\pi\)
−0.317572 + 0.948234i \(0.602867\pi\)
\(380\) 0.809475 1.40205i 0.0415252 0.0719237i
\(381\) −10.4270 23.3154i −0.534190 1.19449i
\(382\) 6.93649 + 12.0144i 0.354902 + 0.614708i
\(383\) −11.9310 20.6651i −0.609646 1.05594i −0.991299 0.131632i \(-0.957978\pi\)
0.381653 0.924306i \(-0.375355\pi\)
\(384\) 1.72286 + 0.178197i 0.0879193 + 0.00909358i
\(385\) 0 0
\(386\) 16.1270 0.820844
\(387\) −8.30948 25.2888i −0.422394 1.28550i
\(388\) 17.8459 0.905988
\(389\) −10.4365 + 18.0765i −0.529151 + 0.916517i 0.470271 + 0.882522i \(0.344156\pi\)
−0.999422 + 0.0339945i \(0.989177\pi\)
\(390\) 8.75472 12.0919i 0.443313 0.612296i
\(391\) 4.77012 + 8.26209i 0.241235 + 0.417832i
\(392\) 0 0
\(393\) 7.99193 11.0383i 0.403140 0.556810i
\(394\) 3.30948 5.73218i 0.166729 0.288783i
\(395\) −11.9310 −0.600314
\(396\) −8.00000 + 8.94427i −0.402015 + 0.449467i
\(397\) −7.07107 −0.354887 −0.177443 0.984131i \(-0.556783\pi\)
−0.177443 + 0.984131i \(0.556783\pi\)
\(398\) −10.3372 + 17.9045i −0.518155 + 0.897471i
\(399\) 0 0
\(400\) 0.436492 + 0.756026i 0.0218246 + 0.0378013i
\(401\) −1.93649 3.35410i −0.0967038 0.167496i 0.813615 0.581405i \(-0.197497\pi\)
−0.910318 + 0.413909i \(0.864163\pi\)
\(402\) −0.617292 1.38031i −0.0307877 0.0688435i
\(403\) −11.6190 + 20.1246i −0.578781 + 1.00248i
\(404\) 7.86799 0.391447
\(405\) 14.7202 10.8445i 0.731454 0.538868i
\(406\) 0 0
\(407\) 19.4919 33.7610i 0.966179 1.67347i
\(408\) 1.00000 + 2.23607i 0.0495074 + 0.110702i
\(409\) −15.8144 27.3913i −0.781971 1.35441i −0.930792 0.365549i \(-0.880881\pi\)
0.148821 0.988864i \(-0.452452\pi\)
\(410\) −5.74597 9.95231i −0.283773 0.491509i
\(411\) 26.6904 + 2.76062i 1.31654 + 0.136171i
\(412\) −9.01276 + 15.6106i −0.444027 + 0.769077i
\(413\) 0 0
\(414\) −13.4919 + 15.0844i −0.663092 + 0.741360i
\(415\) 16.8730 0.828262
\(416\) −2.12132 + 3.67423i −0.104006 + 0.180144i
\(417\) −18.7540 + 25.9028i −0.918389 + 1.26846i
\(418\) −1.59384 2.76062i −0.0779574 0.135026i
\(419\) −1.99230 3.45077i −0.0973304 0.168581i 0.813248 0.581917i \(-0.197697\pi\)
−0.910579 + 0.413335i \(0.864364\pi\)
\(420\) 0 0
\(421\) 2.56351 4.44013i 0.124938 0.216399i −0.796771 0.604282i \(-0.793460\pi\)
0.921709 + 0.387883i \(0.126794\pi\)
\(422\) −2.61895 −0.127488
\(423\) 6.45378 + 19.6412i 0.313793 + 0.954987i
\(424\) −10.6190 −0.515702
\(425\) −0.617292 + 1.06918i −0.0299431 + 0.0518629i
\(426\) −3.66455 0.379028i −0.177548 0.0183640i
\(427\) 0 0
\(428\) −7.87298 13.6364i −0.380555 0.659141i
\(429\) −12.0000 26.8328i −0.579365 1.29550i
\(430\) 9.01276 15.6106i 0.434634 0.752808i
\(431\) 9.49193 0.457210 0.228605 0.973519i \(-0.426584\pi\)
0.228605 + 0.973519i \(0.426584\pi\)
\(432\) −3.84418 + 3.49604i −0.184953 + 0.168203i
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) 12.7460 + 28.5008i 0.611122 + 1.36651i
\(436\) −4.56351 7.90423i −0.218552 0.378544i
\(437\) −2.68800 4.65576i −0.128585 0.222715i
\(438\) −26.4919 2.74009i −1.26583 0.130926i
\(439\) 5.47723 9.48683i 0.261414 0.452782i −0.705204 0.709004i \(-0.749145\pi\)
0.966618 + 0.256223i \(0.0824780\pi\)
\(440\) −8.12602 −0.387393
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −12.1825 + 21.1006i −0.578806 + 1.00252i 0.416811 + 0.908993i \(0.363148\pi\)
−0.995617 + 0.0935281i \(0.970185\pi\)
\(444\) 9.89949 13.6730i 0.469809 0.648893i
\(445\) −7.18246 12.4404i −0.340481 0.589731i
\(446\) −5.74667 9.95352i −0.272113 0.471313i
\(447\) 0.258035 0.356394i 0.0122046 0.0168569i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −2.56351 0.536026i −0.120845 0.0252685i
\(451\) −22.6274 −1.06548
\(452\) 1.93649 3.35410i 0.0910849 0.157764i
\(453\) 18.9515 + 1.96017i 0.890417 + 0.0920967i
\(454\) −3.04726 5.27801i −0.143015 0.247709i
\(455\) 0 0
\(456\) −0.563508 1.26004i −0.0263887 0.0590069i
\(457\) −16.9365 + 29.3349i −0.792256 + 1.37223i 0.132312 + 0.991208i \(0.457760\pi\)
−0.924567 + 0.381019i \(0.875573\pi\)
\(458\) −7.86799 −0.367647
\(459\) −7.00000 2.23607i −0.326732 0.104371i
\(460\) −13.7045 −0.638974
\(461\) −4.98895 + 8.64112i −0.232359 + 0.402457i −0.958502 0.285087i \(-0.907978\pi\)
0.726143 + 0.687544i \(0.241311\pi\)
\(462\) 0 0
\(463\) −10.8095 18.7226i −0.502359 0.870111i −0.999996 0.00272598i \(-0.999132\pi\)
0.497637 0.867385i \(-0.334201\pi\)
\(464\) −4.43649 7.68423i −0.205959 0.356731i
\(465\) −19.1703 1.98280i −0.889001 0.0919502i
\(466\) −11.3730 + 19.6986i −0.526843 + 0.912519i
\(467\) −39.0591 −1.80744 −0.903720 0.428125i \(-0.859174\pi\)
−0.903720 + 0.428125i \(0.859174\pi\)
\(468\) −3.97320 12.0919i −0.183661 0.558948i
\(469\) 0 0
\(470\) −7.00000 + 12.1244i −0.322886 + 0.559255i
\(471\) 6.55544 9.05427i 0.302059 0.417199i
\(472\) 1.32440 + 2.29393i 0.0609604 + 0.105587i
\(473\) −17.7460 30.7369i −0.815960 1.41328i
\(474\) −5.96550 + 8.23945i −0.274005 + 0.378451i
\(475\) 0.347849 0.602493i 0.0159604 0.0276443i
\(476\) 0 0
\(477\) 21.2379 23.7447i 0.972417 1.08719i
\(478\) −15.0000 −0.686084
\(479\) −9.01276 + 15.6106i −0.411803 + 0.713265i −0.995087 0.0990041i \(-0.968434\pi\)
0.583284 + 0.812269i \(0.301768\pi\)
\(480\) −3.50000 0.362008i −0.159752 0.0165233i
\(481\) 20.6743 + 35.8090i 0.942668 + 1.63275i
\(482\) −0.886735 1.53587i −0.0403897 0.0699570i
\(483\) 0 0
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −36.2540 −1.64621
\(486\) −0.129018 15.5879i −0.00585235 0.707083i
\(487\) 30.4919 1.38172 0.690861 0.722988i \(-0.257232\pi\)
0.690861 + 0.722988i \(0.257232\pi\)
\(488\) 0.398461 0.690154i 0.0180375 0.0312418i
\(489\) −7.07107 15.8114i −0.319765 0.715016i
\(490\) 0 0
\(491\) 6.87298 + 11.9044i 0.310173 + 0.537236i 0.978400 0.206722i \(-0.0662796\pi\)
−0.668226 + 0.743958i \(0.732946\pi\)
\(492\) −9.74597 1.00803i −0.439382 0.0454457i
\(493\) 6.27415 10.8671i 0.282573 0.489431i
\(494\) 3.38105 0.152121
\(495\) 16.2520 18.1703i 0.730475 0.816696i
\(496\) 5.47723 0.245935
\(497\) 0 0
\(498\) 8.43649 11.6523i 0.378048 0.522154i
\(499\) 7.12702 + 12.3444i 0.319049 + 0.552609i 0.980290 0.197564i \(-0.0633032\pi\)
−0.661241 + 0.750174i \(0.729970\pi\)
\(500\) −5.96550 10.3325i −0.266785 0.462086i
\(501\) −12.5635 + 17.3525i −0.561296 + 0.775253i
\(502\) 12.9468 22.4244i 0.577842 1.00085i
\(503\) −18.0255 −0.803718 −0.401859 0.915702i \(-0.631636\pi\)
−0.401859 + 0.915702i \(0.631636\pi\)
\(504\) 0 0
\(505\) −15.9839 −0.711273
\(506\) −13.4919 + 23.3687i −0.599790 + 1.03887i
\(507\) 8.61430 + 0.890985i 0.382574 + 0.0395700i
\(508\) −7.37298 12.7704i −0.327123 0.566594i
\(509\) 16.8807 + 29.2383i 0.748226 + 1.29597i 0.948672 + 0.316261i \(0.102427\pi\)
−0.200446 + 0.979705i \(0.564239\pi\)
\(510\) −2.03151 4.54259i −0.0899566 0.201149i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 3.94456 + 1.26004i 0.174157 + 0.0556323i
\(514\) −13.9625 −0.615860
\(515\) 18.3095 31.7129i 0.806812 1.39744i
\(516\) −6.27415 14.0294i −0.276204 0.617611i
\(517\) 13.7829 + 23.8726i 0.606170 + 1.04992i
\(518\) 0 0
\(519\) −21.9284 2.26808i −0.962551 0.0995575i
\(520\) 4.30948 7.46423i 0.188983 0.327328i
\(521\) −1.41421 −0.0619578 −0.0309789 0.999520i \(-0.509862\pi\)
−0.0309789 + 0.999520i \(0.509862\pi\)
\(522\) 26.0554 + 5.44816i 1.14042 + 0.238460i
\(523\) 31.0115 1.35604 0.678019 0.735045i \(-0.262839\pi\)
0.678019 + 0.735045i \(0.262839\pi\)
\(524\) 3.93399 6.81388i 0.171857 0.297666i
\(525\) 0 0
\(526\) −2.80948 4.86615i −0.122499 0.212174i
\(527\) 3.87298 + 6.70820i 0.168710 + 0.292214i
\(528\) −4.06301 + 5.61177i −0.176820 + 0.244221i
\(529\) −11.2540 + 19.4926i −0.489306 + 0.847502i
\(530\) 21.5725 0.937048
\(531\) −7.77817 1.62641i −0.337544 0.0705800i
\(532\) 0 0
\(533\) 12.0000 20.7846i 0.519778 0.900281i
\(534\) −12.1825 1.26004i −0.527187 0.0545274i
\(535\) 15.9940 + 27.7024i 0.691481 + 1.19768i
\(536\) −0.436492 0.756026i −0.0188536 0.0326553i
\(537\) −0.617292 1.38031i −0.0266381 0.0595647i
\(538\) 1.72286 2.98408i 0.0742778 0.128653i
\(539\) 0 0
\(540\) 7.80948 7.10222i 0.336066 0.305631i
\(541\) 16.1109 0.692661 0.346330 0.938113i \(-0.387428\pi\)
0.346330 + 0.938113i \(0.387428\pi\)
\(542\) 3.53553 6.12372i 0.151864 0.263036i
\(543\) −5.56351 12.4404i −0.238753 0.533868i
\(544\) 0.707107 + 1.22474i 0.0303170 + 0.0525105i
\(545\) 9.27079 + 16.0575i 0.397117 + 0.687827i
\(546\) 0 0
\(547\) −14.4919 + 25.1008i −0.619630 + 1.07323i 0.369923 + 0.929062i \(0.379384\pi\)
−0.989553 + 0.144169i \(0.953949\pi\)
\(548\) 15.4919 0.661783
\(549\) 0.746310 + 2.27129i 0.0318517 + 0.0969364i
\(550\) −3.49193 −0.148897
\(551\) −3.53553 + 6.12372i −0.150619 + 0.260879i
\(552\) −6.85224 + 9.46420i −0.291651 + 0.402823i
\(553\) 0 0
\(554\) 12.1825 + 21.1006i 0.517583 + 0.896480i
\(555\) −20.1109 + 27.7768i −0.853659 + 1.17906i
\(556\) −9.23159 + 15.9896i −0.391507 + 0.678109i
\(557\) 3.38105 0.143260 0.0716298 0.997431i \(-0.477180\pi\)
0.0716298 + 0.997431i \(0.477180\pi\)
\(558\) −10.9545 + 12.2474i −0.463739 + 0.518476i
\(559\) 37.6449 1.59221
\(560\) 0 0
\(561\) −9.74597 1.00803i −0.411475 0.0425592i
\(562\) 3.37298 + 5.84218i 0.142281 + 0.246437i
\(563\) −2.60960 4.51995i −0.109981 0.190493i 0.805781 0.592213i \(-0.201746\pi\)
−0.915762 + 0.401720i \(0.868412\pi\)
\(564\) 4.87298 + 10.8963i 0.205190 + 0.458818i
\(565\) −3.93399 + 6.81388i −0.165504 + 0.286662i
\(566\) −10.5168 −0.442054
\(567\) 0 0
\(568\) −2.12702 −0.0892476
\(569\) −3.74597 + 6.48820i −0.157039 + 0.272000i −0.933800 0.357796i \(-0.883528\pi\)
0.776761 + 0.629796i \(0.216862\pi\)
\(570\) 1.14477 + 2.55978i 0.0479492 + 0.107218i
\(571\) −0.254033 0.439999i −0.0106310 0.0184134i 0.860661 0.509178i \(-0.170051\pi\)
−0.871292 + 0.490765i \(0.836717\pi\)
\(572\) −8.48528 14.6969i −0.354787 0.614510i
\(573\) −23.9012 2.47212i −0.998487 0.103274i
\(574\) 0 0
\(575\) −5.88912 −0.245593
\(576\) −2.00000 + 2.23607i −0.0833333 + 0.0931695i
\(577\) −35.1757 −1.46438 −0.732192 0.681098i \(-0.761503\pi\)
−0.732192 + 0.681098i \(0.761503\pi\)
\(578\) 7.50000 12.9904i 0.311959 0.540329i
\(579\) −16.3811 + 22.6253i −0.680774 + 0.940274i
\(580\) 9.01276 + 15.6106i 0.374234 + 0.648193i
\(581\) 0 0
\(582\) −18.1270 + 25.0367i −0.751389 + 1.03781i
\(583\) 21.2379 36.7851i 0.879584 1.52348i
\(584\) −15.3767 −0.636293
\(585\) 8.07157 + 24.5647i 0.333719 + 1.01563i
\(586\) 6.27415 0.259183
\(587\) −14.8884 + 25.7875i −0.614512 + 1.06437i 0.375958 + 0.926637i \(0.377314\pi\)
−0.990470 + 0.137729i \(0.956020\pi\)
\(588\) 0 0
\(589\) −2.18246 3.78013i −0.0899266 0.155757i
\(590\) −2.69052 4.66013i −0.110767 0.191854i
\(591\) 4.68030 + 10.4655i 0.192522 + 0.430492i
\(592\) 4.87298 8.44025i 0.200278 0.346892i
\(593\) −22.8070 −0.936573 −0.468287 0.883577i \(-0.655129\pi\)
−0.468287 + 0.883577i \(0.655129\pi\)
\(594\) −4.42227 20.3087i −0.181448 0.833276i
\(595\) 0 0
\(596\) 0.127017 0.219999i 0.00520280 0.00901152i
\(597\) −14.6190 32.6890i −0.598314 1.33787i
\(598\) −14.3104 24.7863i −0.585194 1.01359i
\(599\) −0.618950 1.07205i −0.0252896 0.0438029i 0.853104 0.521742i \(-0.174717\pi\)
−0.878393 + 0.477939i \(0.841384\pi\)
\(600\) −1.50403 0.155563i −0.0614017 0.00635083i
\(601\) −18.8224 + 32.6014i −0.767783 + 1.32984i 0.170979 + 0.985275i \(0.445307\pi\)
−0.938762 + 0.344565i \(0.888026\pi\)
\(602\) 0 0
\(603\) 2.56351 + 0.536026i 0.104394 + 0.0218287i
\(604\) 11.0000 0.447584
\(605\) 5.07877 8.79668i 0.206481 0.357636i
\(606\) −7.99193 + 11.0383i −0.324650 + 0.448402i
\(607\) 7.86799 + 13.6278i 0.319352 + 0.553134i 0.980353 0.197251i \(-0.0632015\pi\)
−0.661001 + 0.750385i \(0.729868\pi\)
\(608\) −0.398461 0.690154i −0.0161597 0.0279894i
\(609\) 0 0
\(610\) −0.809475 + 1.40205i −0.0327747 + 0.0567674i
\(611\) −29.2379 −1.18284
\(612\) −4.15283 0.868351i −0.167868 0.0351010i
\(613\) 3.38105 0.136559 0.0682797 0.997666i \(-0.478249\pi\)
0.0682797 + 0.997666i \(0.478249\pi\)
\(614\) −12.0600 + 20.8886i −0.486703 + 0.842994i
\(615\) 19.7990 + 2.04783i 0.798372 + 0.0825764i
\(616\) 0 0
\(617\) 13.8730 + 24.0287i 0.558505 + 0.967360i 0.997622 + 0.0689293i \(0.0219583\pi\)
−0.439116 + 0.898430i \(0.644708\pi\)
\(618\) −12.7460 28.5008i −0.512718 1.14647i
\(619\) 11.1733 19.3527i 0.449092 0.777850i −0.549235 0.835668i \(-0.685081\pi\)
0.998327 + 0.0578175i \(0.0184142\pi\)
\(620\) −11.1270 −0.446872
\(621\) −7.45812 34.2505i −0.299284 1.37442i
\(622\) 1.41421 0.0567048
\(623\) 0 0
\(624\) −3.00000 6.70820i −0.120096 0.268543i
\(625\) 9.93649 + 17.2105i 0.397460 + 0.688420i
\(626\) 13.3452 + 23.1146i 0.533382 + 0.923845i
\(627\) 5.49193 + 0.568036i 0.219327 + 0.0226852i
\(628\) 3.22689 5.58913i 0.128767 0.223031i
\(629\) 13.7829 0.549559
\(630\) 0 0
\(631\) −27.6190 −1.09949 −0.549747 0.835332i \(-0.685276\pi\)
−0.549747 + 0.835332i \(0.685276\pi\)
\(632\) −2.93649 + 5.08615i −0.116807 + 0.202316i
\(633\) 2.66021 3.67423i 0.105734 0.146038i
\(634\) −0.690525 1.19602i −0.0274243 0.0475002i
\(635\) 14.9783 + 25.9431i 0.594394 + 1.02952i
\(636\) 10.7862 14.8978i 0.427702 0.590735i
\(637\) 0 0
\(638\) 35.4919 1.40514
\(639\) 4.25403 4.75615i 0.168287 0.188151i
\(640\) −2.03151 −0.0803023
\(641\) 18.5554 32.1390i 0.732896 1.26941i −0.222744 0.974877i \(-0.571502\pi\)
0.955640 0.294536i \(-0.0951651\pi\)
\(642\) 27.1281 + 2.80588i 1.07066 + 0.110739i
\(643\) −20.1468 34.8953i −0.794514 1.37614i −0.923147 0.384446i \(-0.874392\pi\)
0.128634 0.991692i \(-0.458941\pi\)
\(644\) 0 0
\(645\) 12.7460 + 28.5008i 0.501872 + 1.12222i
\(646\) 0.563508 0.976025i 0.0221709 0.0384012i
\(647\) −5.47723 −0.215332 −0.107666 0.994187i \(-0.534338\pi\)
−0.107666 + 0.994187i \(0.534338\pi\)
\(648\) −1.00000 8.94427i −0.0392837 0.351364i
\(649\) −10.5952 −0.415898
\(650\) 1.85188 3.20755i 0.0726366 0.125810i
\(651\) 0 0
\(652\) −5.00000 8.66025i −0.195815 0.339162i
\(653\) 22.7460 + 39.3972i 0.890118 + 1.54173i 0.839732 + 0.543001i \(0.182712\pi\)
0.0503861 + 0.998730i \(0.483955\pi\)
\(654\) 15.7246 + 1.62641i 0.614879 + 0.0635975i
\(655\) −7.99193 + 13.8424i −0.312271 + 0.540869i
\(656\) −5.65685 −0.220863
\(657\) 30.7534 34.3834i 1.19981 1.34142i
\(658\) 0 0
\(659\) −18.4365 + 31.9329i −0.718184 + 1.24393i 0.243535 + 0.969892i \(0.421693\pi\)
−0.961719 + 0.274039i \(0.911640\pi\)
\(660\) 8.25403 11.4003i 0.321288 0.443758i
\(661\) 12.4977 + 21.6466i 0.486104 + 0.841956i 0.999872 0.0159726i \(-0.00508447\pi\)
−0.513769 + 0.857929i \(0.671751\pi\)
\(662\) 9.18246 + 15.9045i 0.356886 + 0.618145i
\(663\) 6.09452 8.41765i 0.236691 0.326914i
\(664\) 4.15283 7.19291i 0.161161 0.279139i
\(665\) 0 0
\(666\) 9.12702 + 27.7768i 0.353665 + 1.07633i
\(667\) 59.8569 2.31767
\(668\) −6.18433 + 10.7116i −0.239279 + 0.414443i
\(669\) 19.8014 + 2.04808i 0.765567 + 0.0791833i
\(670\) 0.886735 + 1.53587i 0.0342576 + 0.0593359i
\(671\) 1.59384 + 2.76062i 0.0615296 + 0.106572i
\(672\) 0 0
\(673\) 16.1190 27.9188i 0.621340 1.07619i −0.367897 0.929867i \(-0.619922\pi\)
0.989236 0.146326i \(-0.0467447\pi\)
\(674\) 0.254033 0.00978500
\(675\) 3.35591 3.05198i 0.129169 0.117471i
\(676\) 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
\(680\) −1.43649 2.48808i −0.0550869 0.0954134i
\(681\) 10.5000 + 1.08602i 0.402361 + 0.0416166i
\(682\) −10.9545 + 18.9737i −0.419468 + 0.726539i
\(683\) −7.74597 −0.296391 −0.148196 0.988958i \(-0.547347\pi\)
−0.148196 + 0.988958i \(0.547347\pi\)
\(684\) 2.34015 + 0.489323i 0.0894780 + 0.0187097i
\(685\) −31.4720 −1.20248
\(686\) 0 0
\(687\) 7.99193 11.0383i 0.304911 0.421139i
\(688\) −4.43649 7.68423i −0.169140 0.292958i
\(689\) 22.5262 + 39.0165i 0.858180 + 1.48641i
\(690\) 13.9204 19.2266i 0.529939 0.731943i
\(691\) −10.6458 + 18.4391i −0.404986 + 0.701455i −0.994320 0.106434i \(-0.966057\pi\)
0.589334 + 0.807889i \(0.299390\pi\)
\(692\) −12.7279 −0.483843
\(693\) 0 0
\(694\) −7.74597 −0.294033
\(695\) 18.7540 32.4829i 0.711381 1.23215i
\(696\) 15.2869 + 1.58114i 0.579449 + 0.0599329i
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 8.21584 + 14.2302i 0.310974 + 0.538623i
\(699\) −16.0838 35.9645i −0.608346 1.36030i
\(700\) 0 0
\(701\) −31.7460 −1.19903 −0.599514 0.800364i \(-0.704640\pi\)
−0.599514 + 0.800364i \(0.704640\pi\)
\(702\) 21.0000 + 6.70820i 0.792594 + 0.253185i
\(703\) −7.76677 −0.292929
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) −9.89949 22.1359i −0.372837 0.833688i
\(706\) −9.01276 15.6106i −0.339200 0.587511i
\(707\) 0 0
\(708\) −4.56351 0.472008i −0.171507 0.0177391i
\(709\) −12.3649 + 21.4167i −0.464374 + 0.804320i −0.999173 0.0406597i \(-0.987054\pi\)
0.534799 + 0.844979i \(0.320387\pi\)
\(710\) 4.32105 0.162166
\(711\) −5.50000 16.7385i −0.206266 0.627743i
\(712\) −7.07107 −0.264999
\(713\) −18.4746 + 31.9989i −0.691879 + 1.19837i
\(714\) 0 0
\(715\) 17.2379 + 29.8569i 0.644661 + 1.11659i
\(716\) −0.436492 0.756026i −0.0163125 0.0282540i
\(717\) 15.2363 21.0441i 0.569010 0.785907i
\(718\) 14.1190 24.4547i 0.526915 0.912643i
\(719\) −9.36061 −0.349092 −0.174546 0.984649i \(-0.555846\pi\)
−0.174546 + 0.984649i \(0.555846\pi\)
\(720\) 4.06301 4.54259i 0.151420 0.169292i
\(721\) 0 0
\(722\) 9.18246 15.9045i 0.341736 0.591904i
\(723\) 3.05544 + 0.316027i 0.113633 + 0.0117532i
\(724\) −3.93399 6.81388i −0.146206 0.253236i
\(725\) 3.87298 + 6.70820i 0.143839 + 0.249136i
\(726\) −3.53553 7.90569i −0.131216 0.293408i
\(727\) 18.1153 31.3767i 0.671861 1.16370i −0.305515 0.952187i \(-0.598829\pi\)
0.977376 0.211509i \(-0.0678379\pi\)
\(728\) 0 0
\(729\) 22.0000 + 15.6525i 0.814815 + 0.579721i
\(730\) 31.2379 1.15617
\(731\) 6.27415 10.8671i 0.232058 0.401936i
\(732\) 0.563508 + 1.26004i 0.0208279 + 0.0465725i
\(733\) −4.82073 8.34975i −0.178058 0.308405i 0.763157 0.646213i \(-0.223648\pi\)
−0.941215 + 0.337808i \(0.890315\pi\)
\(734\) −2.03151 3.51867i −0.0749843 0.129877i
\(735\) 0 0
\(736\) −3.37298 + 5.84218i −0.124330 + 0.215346i
\(737\) 3.49193 0.128627
\(738\) 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
\(741\) −3.43431 + 4.74342i −0.126163 + 0.174254i
\(742\) 0 0
\(743\) 13.8730 + 24.0287i 0.508950 + 0.881528i 0.999946 + 0.0103660i \(0.00329968\pi\)
−0.490996 + 0.871162i \(0.663367\pi\)
\(744\) −5.56351 + 7.68423i −0.203968 + 0.281718i
\(745\) −0.258035 + 0.446930i −0.00945367 + 0.0163742i
\(746\) −8.87298 −0.324863
\(747\) 7.77817 + 23.6718i 0.284589 + 0.866106i
\(748\) −5.65685 −0.206835
\(749\) 0 0
\(750\) 20.5554 + 2.12607i 0.750579 + 0.0776330i
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 3.44572 + 5.96816i 0.125652 + 0.217636i
\(753\) 18.3095 + 40.9412i 0.667234 + 1.49198i
\(754\) −18.8224 + 32.6014i −0.685473 + 1.18727i
\(755\) −22.3466 −0.813275
\(756\) 0 0
\(757\) −15.2379 −0.553831 −0.276915 0.960894i \(-0.589312\pi\)
−0.276915 + 0.960894i \(0.589312\pi\)
\(758\) 6.18246 10.7083i 0.224557 0.388944i
\(759\) −19.0805 42.6652i −0.692577 1.54865i
\(760\) 0.809475 + 1.40205i 0.0293627 + 0.0508578i
\(761\) 1.14477 + 1.98280i 0.0414979 + 0.0718765i 0.886028 0.463631i \(-0.153454\pi\)
−0.844530 + 0.535508i \(0.820120\pi\)
\(762\) 25.4052 + 2.62769i 0.920334 + 0.0951910i
\(763\) 0 0
\(764\) −13.8730 −0.501907
\(765\) 8.43649 + 1.76406i 0.305022 + 0.0637797i
\(766\) 23.8620 0.862169
\(767\) 5.61895 9.73231i 0.202889 0.351413i
\(768\) −1.01575 + 1.40294i −0.0366528 + 0.0506243i
\(769\) 4.85993 + 8.41765i 0.175254 + 0.303548i 0.940249 0.340488i \(-0.110592\pi\)
−0.764995 + 0.644036i \(0.777259\pi\)
\(770\) 0 0
\(771\) 14.1825 19.5886i 0.510769 0.705466i
\(772\) −8.06351 + 13.9664i −0.290212 + 0.502662i
\(773\) −3.44572 −0.123934 −0.0619670 0.998078i \(-0.519737\pi\)
−0.0619670 + 0.998078i \(0.519737\pi\)
\(774\) 26.0554 + 5.44816i 0.936544 + 0.195830i
\(775\) −4.78153 −0.171758
\(776\) −8.92295 + 15.4550i −0.320315 + 0.554802i
\(777\) 0 0
\(778\) −10.4365 18.0765i −0.374166 0.648075i
\(779\) 2.25403 +