Properties

Label 600.2.d.g.349.3
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.214798336.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.3
Root \(1.41216 - 0.0762223i\) of \(x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16\)
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.g.349.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +1.43055i q^{11} +(1.33594 - 1.48838i) q^{12} -0.241319 q^{13} +(-2.55298 + 1.13905i) q^{14} +(-0.430552 - 3.97676i) q^{16} -7.38407i q^{17} +(-0.576222 - 1.29150i) q^{18} +3.04033i q^{19} +1.97676i q^{21} +(1.84756 - 0.824316i) q^{22} -0.874337i q^{23} +(-2.69204 - 0.867721i) q^{24} +(0.139054 + 0.311664i) q^{26} -1.00000 q^{27} +(2.94217 + 2.64082i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(-4.88789 + 2.84756i) q^{32} -1.43055i q^{33} +(-9.53652 + 4.25487i) q^{34} +(-1.33594 + 1.48838i) q^{36} -8.81463 q^{37} +(3.92658 - 1.75191i) q^{38} +0.241319 q^{39} -1.91319 q^{41} +(2.55298 - 1.13905i) q^{42} -11.2452 q^{43} +(-2.12921 - 1.91113i) q^{44} +(-1.12921 + 0.503813i) q^{46} -3.34374i q^{47} +(0.430552 + 3.97676i) q^{48} +3.09242 q^{49} +7.38407i q^{51} +(0.322387 - 0.359175i) q^{52} +9.20632 q^{53} +(0.576222 + 1.29150i) q^{54} +(1.71528 - 5.32151i) q^{56} -3.04033i q^{57} +(-11.7258 + 5.23163i) q^{58} -6.43616i q^{59} -4.57331i q^{61} +(4.29150 + 9.61862i) q^{62} -1.97676i q^{63} +(6.49412 + 4.67187i) q^{64} +(-1.84756 + 0.824316i) q^{66} -4.86671 q^{67} +(10.9903 + 9.86465i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(2.69204 + 0.867721i) q^{72} +4.12714i q^{73} +(5.07918 + 11.3841i) q^{74} +(-4.52517 - 4.06169i) q^{76} +2.82786 q^{77} +(-0.139054 - 0.311664i) q^{78} +13.6757 q^{79} +1.00000 q^{81} +(1.10242 + 2.47088i) q^{82} -12.3320 q^{83} +(-2.94217 - 2.64082i) q^{84} +(6.47972 + 14.5231i) q^{86} +9.07918i q^{87} +(-1.24132 + 3.85110i) q^{88} +8.08066 q^{89} +0.477031i q^{91} +(1.30135 + 1.16806i) q^{92} +7.44764 q^{93} +(-4.31844 + 1.92674i) q^{94} +(4.88789 - 2.84756i) q^{96} +10.6757i q^{97} +(-1.78192 - 3.99385i) q^{98} +1.43055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + 4q^{12} + 6q^{14} + 8q^{16} - 2q^{18} + 20q^{22} + 8q^{24} - 2q^{26} - 8q^{27} + 24q^{28} + 8q^{31} - 12q^{32} - 12q^{34} - 4q^{36} + 14q^{38} - 6q^{42} - 8q^{43} + 12q^{44} + 20q^{46} - 8q^{48} + 24q^{52} + 8q^{53} + 2q^{54} + 8q^{56} - 20q^{58} + 26q^{62} + 32q^{64} - 20q^{66} + 24q^{67} + 36q^{68} - 40q^{71} - 8q^{72} - 8q^{74} - 20q^{76} - 24q^{77} + 2q^{78} + 16q^{79} + 8q^{81} - 16q^{82} - 32q^{83} - 24q^{84} - 18q^{86} - 8q^{88} + 28q^{92} - 8q^{93} + 4q^{94} + 12q^{96} - 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.576222 1.29150i −0.407451 0.913227i
\(3\) −1.00000 −0.577350
\(4\) −1.33594 + 1.48838i −0.667968 + 0.744190i
\(5\) 0 0
\(6\) 0.576222 + 1.29150i 0.235242 + 0.527252i
\(7\) 1.97676i 0.747145i −0.927601 0.373573i \(-0.878133\pi\)
0.927601 0.373573i \(-0.121867\pi\)
\(8\) 2.69204 + 0.867721i 0.951779 + 0.306786i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.43055i 0.431328i 0.976468 + 0.215664i \(0.0691915\pi\)
−0.976468 + 0.215664i \(0.930808\pi\)
\(12\) 1.33594 1.48838i 0.385651 0.429658i
\(13\) −0.241319 −0.0669300 −0.0334650 0.999440i \(-0.510654\pi\)
−0.0334650 + 0.999440i \(0.510654\pi\)
\(14\) −2.55298 + 1.13905i −0.682313 + 0.304425i
\(15\) 0 0
\(16\) −0.430552 3.97676i −0.107638 0.994190i
\(17\) 7.38407i 1.79090i −0.445161 0.895450i \(-0.646854\pi\)
0.445161 0.895450i \(-0.353146\pi\)
\(18\) −0.576222 1.29150i −0.135817 0.304409i
\(19\) 3.04033i 0.697500i 0.937216 + 0.348750i \(0.113394\pi\)
−0.937216 + 0.348750i \(0.886606\pi\)
\(20\) 0 0
\(21\) 1.97676i 0.431365i
\(22\) 1.84756 0.824316i 0.393900 0.175745i
\(23\) 0.874337i 0.182312i −0.995837 0.0911560i \(-0.970944\pi\)
0.995837 0.0911560i \(-0.0290562\pi\)
\(24\) −2.69204 0.867721i −0.549510 0.177123i
\(25\) 0 0
\(26\) 0.139054 + 0.311664i 0.0272707 + 0.0611223i
\(27\) −1.00000 −0.192450
\(28\) 2.94217 + 2.64082i 0.556018 + 0.499069i
\(29\) 9.07918i 1.68596i −0.537943 0.842981i \(-0.680799\pi\)
0.537943 0.842981i \(-0.319201\pi\)
\(30\) 0 0
\(31\) −7.44764 −1.33764 −0.668818 0.743426i \(-0.733200\pi\)
−0.668818 + 0.743426i \(0.733200\pi\)
\(32\) −4.88789 + 2.84756i −0.864064 + 0.503381i
\(33\) 1.43055i 0.249027i
\(34\) −9.53652 + 4.25487i −1.63550 + 0.729704i
\(35\) 0 0
\(36\) −1.33594 + 1.48838i −0.222656 + 0.248063i
\(37\) −8.81463 −1.44912 −0.724558 0.689214i \(-0.757956\pi\)
−0.724558 + 0.689214i \(0.757956\pi\)
\(38\) 3.92658 1.75191i 0.636976 0.284197i
\(39\) 0.241319 0.0386420
\(40\) 0 0
\(41\) −1.91319 −0.298790 −0.149395 0.988778i \(-0.547733\pi\)
−0.149395 + 0.988778i \(0.547733\pi\)
\(42\) 2.55298 1.13905i 0.393934 0.175760i
\(43\) −11.2452 −1.71487 −0.857437 0.514589i \(-0.827944\pi\)
−0.857437 + 0.514589i \(0.827944\pi\)
\(44\) −2.12921 1.91113i −0.320990 0.288113i
\(45\) 0 0
\(46\) −1.12921 + 0.503813i −0.166492 + 0.0742831i
\(47\) 3.34374i 0.487735i −0.969809 0.243867i \(-0.921584\pi\)
0.969809 0.243867i \(-0.0784162\pi\)
\(48\) 0.430552 + 3.97676i 0.0621448 + 0.573996i
\(49\) 3.09242 0.441774
\(50\) 0 0
\(51\) 7.38407i 1.03398i
\(52\) 0.322387 0.359175i 0.0447071 0.0498086i
\(53\) 9.20632 1.26459 0.632293 0.774729i \(-0.282114\pi\)
0.632293 + 0.774729i \(0.282114\pi\)
\(54\) 0.576222 + 1.29150i 0.0784139 + 0.175751i
\(55\) 0 0
\(56\) 1.71528 5.32151i 0.229213 0.711117i
\(57\) 3.04033i 0.402702i
\(58\) −11.7258 + 5.23163i −1.53967 + 0.686946i
\(59\) 6.43616i 0.837917i −0.908005 0.418958i \(-0.862395\pi\)
0.908005 0.418958i \(-0.137605\pi\)
\(60\) 0 0
\(61\) 4.57331i 0.585552i −0.956181 0.292776i \(-0.905421\pi\)
0.956181 0.292776i \(-0.0945790\pi\)
\(62\) 4.29150 + 9.61862i 0.545021 + 1.22157i
\(63\) 1.97676i 0.249048i
\(64\) 6.49412 + 4.67187i 0.811765 + 0.583984i
\(65\) 0 0
\(66\) −1.84756 + 0.824316i −0.227418 + 0.101466i
\(67\) −4.86671 −0.594563 −0.297282 0.954790i \(-0.596080\pi\)
−0.297282 + 0.954790i \(0.596080\pi\)
\(68\) 10.9903 + 9.86465i 1.33277 + 1.19626i
\(69\) 0.874337i 0.105258i
\(70\) 0 0
\(71\) −8.21808 −0.975307 −0.487653 0.873037i \(-0.662147\pi\)
−0.487653 + 0.873037i \(0.662147\pi\)
\(72\) 2.69204 + 0.867721i 0.317260 + 0.102262i
\(73\) 4.12714i 0.483045i 0.970395 + 0.241523i \(0.0776468\pi\)
−0.970395 + 0.241523i \(0.922353\pi\)
\(74\) 5.07918 + 11.3841i 0.590443 + 1.32337i
\(75\) 0 0
\(76\) −4.52517 4.06169i −0.519072 0.465907i
\(77\) 2.82786 0.322264
\(78\) −0.139054 0.311664i −0.0157447 0.0352890i
\(79\) 13.6757 1.53864 0.769320 0.638864i \(-0.220595\pi\)
0.769320 + 0.638864i \(0.220595\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 1.10242 + 2.47088i 0.121742 + 0.272863i
\(83\) −12.3320 −1.35361 −0.676806 0.736162i \(-0.736636\pi\)
−0.676806 + 0.736162i \(0.736636\pi\)
\(84\) −2.94217 2.64082i −0.321017 0.288138i
\(85\) 0 0
\(86\) 6.47972 + 14.5231i 0.698726 + 1.56607i
\(87\) 9.07918i 0.973391i
\(88\) −1.24132 + 3.85110i −0.132325 + 0.410528i
\(89\) 8.08066 0.856548 0.428274 0.903649i \(-0.359122\pi\)
0.428274 + 0.903649i \(0.359122\pi\)
\(90\) 0 0
\(91\) 0.477031i 0.0500064i
\(92\) 1.30135 + 1.16806i 0.135675 + 0.121779i
\(93\) 7.44764 0.772285
\(94\) −4.31844 + 1.92674i −0.445413 + 0.198728i
\(95\) 0 0
\(96\) 4.88789 2.84756i 0.498868 0.290627i
\(97\) 10.6757i 1.08396i 0.840393 + 0.541978i \(0.182324\pi\)
−0.840393 + 0.541978i \(0.817676\pi\)
\(98\) −1.78192 3.99385i −0.180001 0.403440i
\(99\) 1.43055i 0.143776i
\(100\) 0 0
\(101\) 13.2063i 1.31408i −0.753856 0.657039i \(-0.771809\pi\)
0.753856 0.657039i \(-0.228191\pi\)
\(102\) 9.53652 4.25487i 0.944256 0.421295i
\(103\) 19.4244i 1.91394i −0.290181 0.956972i \(-0.593716\pi\)
0.290181 0.956972i \(-0.406284\pi\)
\(104\) −0.649641 0.209398i −0.0637025 0.0205331i
\(105\) 0 0
\(106\) −5.30489 11.8900i −0.515256 1.15485i
\(107\) 14.8085 1.43159 0.715795 0.698311i \(-0.246065\pi\)
0.715795 + 0.698311i \(0.246065\pi\)
\(108\) 1.33594 1.48838i 0.128550 0.143219i
\(109\) 15.2296i 1.45873i −0.684126 0.729364i \(-0.739816\pi\)
0.684126 0.729364i \(-0.260184\pi\)
\(110\) 0 0
\(111\) 8.81463 0.836647
\(112\) −7.86110 + 0.851098i −0.742804 + 0.0804212i
\(113\) 1.13890i 0.107138i 0.998564 + 0.0535692i \(0.0170598\pi\)
−0.998564 + 0.0535692i \(0.982940\pi\)
\(114\) −3.92658 + 1.75191i −0.367758 + 0.164081i
\(115\) 0 0
\(116\) 13.5133 + 12.1292i 1.25468 + 1.12617i
\(117\) −0.241319 −0.0223100
\(118\) −8.31229 + 3.70866i −0.765208 + 0.341410i
\(119\) −14.5965 −1.33806
\(120\) 0 0
\(121\) 8.95352 0.813956
\(122\) −5.90642 + 2.63524i −0.534742 + 0.238583i
\(123\) 1.91319 0.172507
\(124\) 9.94957 11.0849i 0.893498 0.995456i
\(125\) 0 0
\(126\) −2.55298 + 1.13905i −0.227438 + 0.101475i
\(127\) 2.43616i 0.216174i 0.994141 + 0.108087i \(0.0344725\pi\)
−0.994141 + 0.108087i \(0.965527\pi\)
\(128\) 2.29166 11.0792i 0.202556 0.979271i
\(129\) 11.2452 0.990083
\(130\) 0 0
\(131\) 6.90143i 0.602981i 0.953469 + 0.301491i \(0.0974842\pi\)
−0.953469 + 0.301491i \(0.902516\pi\)
\(132\) 2.12921 + 1.91113i 0.185324 + 0.166342i
\(133\) 6.01001 0.521134
\(134\) 2.80431 + 6.28535i 0.242255 + 0.542972i
\(135\) 0 0
\(136\) 6.40731 19.8782i 0.549423 1.70454i
\(137\) 5.39022i 0.460518i −0.973129 0.230259i \(-0.926043\pi\)
0.973129 0.230259i \(-0.0739573\pi\)
\(138\) 1.12921 0.503813i 0.0961243 0.0428874i
\(139\) 17.4244i 1.47792i 0.673750 + 0.738959i \(0.264682\pi\)
−0.673750 + 0.738959i \(0.735318\pi\)
\(140\) 0 0
\(141\) 3.34374i 0.281594i
\(142\) 4.73544 + 10.6136i 0.397389 + 0.890677i
\(143\) 0.345220i 0.0288687i
\(144\) −0.430552 3.97676i −0.0358793 0.331397i
\(145\) 0 0
\(146\) 5.33019 2.37815i 0.441130 0.196817i
\(147\) −3.09242 −0.255058
\(148\) 11.7758 13.1195i 0.967962 1.07842i
\(149\) 2.28551i 0.187236i −0.995608 0.0936180i \(-0.970157\pi\)
0.995608 0.0936180i \(-0.0298432\pi\)
\(150\) 0 0
\(151\) 6.66425 0.542329 0.271164 0.962533i \(-0.412591\pi\)
0.271164 + 0.962533i \(0.412591\pi\)
\(152\) −2.63816 + 8.18468i −0.213983 + 0.663865i
\(153\) 7.38407i 0.596967i
\(154\) −1.62948 3.65217i −0.131307 0.294301i
\(155\) 0 0
\(156\) −0.322387 + 0.359175i −0.0258116 + 0.0287570i
\(157\) −17.4144 −1.38982 −0.694910 0.719097i \(-0.744556\pi\)
−0.694910 + 0.719097i \(0.744556\pi\)
\(158\) −7.88026 17.6622i −0.626920 1.40513i
\(159\) −9.20632 −0.730109
\(160\) 0 0
\(161\) −1.72836 −0.136214
\(162\) −0.576222 1.29150i −0.0452723 0.101470i
\(163\) 4.66187 0.365145 0.182573 0.983192i \(-0.441557\pi\)
0.182573 + 0.983192i \(0.441557\pi\)
\(164\) 2.55590 2.84756i 0.199582 0.222357i
\(165\) 0 0
\(166\) 7.10597 + 15.9267i 0.551530 + 1.23615i
\(167\) 0.137419i 0.0106338i −0.999986 0.00531690i \(-0.998308\pi\)
0.999986 0.00531690i \(-0.00169243\pi\)
\(168\) −1.71528 + 5.32151i −0.132336 + 0.410564i
\(169\) −12.9418 −0.995520
\(170\) 0 0
\(171\) 3.04033i 0.232500i
\(172\) 15.0228 16.7371i 1.14548 1.27619i
\(173\) −3.96675 −0.301587 −0.150793 0.988565i \(-0.548183\pi\)
−0.150793 + 0.988565i \(0.548183\pi\)
\(174\) 11.7258 5.23163i 0.888927 0.396609i
\(175\) 0 0
\(176\) 5.68896 0.615927i 0.428822 0.0464272i
\(177\) 6.43616i 0.483771i
\(178\) −4.65626 10.4362i −0.349001 0.782223i
\(179\) 4.68749i 0.350359i 0.984537 + 0.175180i \(0.0560506\pi\)
−0.984537 + 0.175180i \(0.943949\pi\)
\(180\) 0 0
\(181\) 9.10242i 0.676578i −0.941042 0.338289i \(-0.890152\pi\)
0.941042 0.338289i \(-0.109848\pi\)
\(182\) 0.616084 0.274876i 0.0456672 0.0203751i
\(183\) 4.57331i 0.338068i
\(184\) 0.758681 2.35375i 0.0559307 0.173521i
\(185\) 0 0
\(186\) −4.29150 9.61862i −0.314668 0.705271i
\(187\) 10.5633 0.772465
\(188\) 4.97676 + 4.46702i 0.362968 + 0.325791i
\(189\) 1.97676i 0.143788i
\(190\) 0 0
\(191\) 15.2063 1.10029 0.550145 0.835069i \(-0.314572\pi\)
0.550145 + 0.835069i \(0.314572\pi\)
\(192\) −6.49412 4.67187i −0.468673 0.337163i
\(193\) 20.7564i 1.49408i 0.664780 + 0.747039i \(0.268525\pi\)
−0.664780 + 0.747039i \(0.731475\pi\)
\(194\) 13.7877 6.15159i 0.989898 0.441659i
\(195\) 0 0
\(196\) −4.13127 + 4.60269i −0.295091 + 0.328764i
\(197\) 23.2508 1.65655 0.828275 0.560322i \(-0.189323\pi\)
0.828275 + 0.560322i \(0.189323\pi\)
\(198\) 1.84756 0.824316i 0.131300 0.0585816i
\(199\) 7.21633 0.511552 0.255776 0.966736i \(-0.417669\pi\)
0.255776 + 0.966736i \(0.417669\pi\)
\(200\) 0 0
\(201\) 4.86671 0.343271
\(202\) −17.0559 + 7.60978i −1.20005 + 0.535422i
\(203\) −17.9474 −1.25966
\(204\) −10.9903 9.86465i −0.769476 0.690663i
\(205\) 0 0
\(206\) −25.0866 + 11.1928i −1.74787 + 0.779838i
\(207\) 0.874337i 0.0607707i
\(208\) 0.103901 + 0.959669i 0.00720420 + 0.0665411i
\(209\) −4.34935 −0.300851
\(210\) 0 0
\(211\) 4.38407i 0.301812i 0.988548 + 0.150906i \(0.0482191\pi\)
−0.988548 + 0.150906i \(0.951781\pi\)
\(212\) −12.2991 + 13.7025i −0.844703 + 0.941092i
\(213\) 8.21808 0.563094
\(214\) −8.53298 19.1251i −0.583302 1.30737i
\(215\) 0 0
\(216\) −2.69204 0.867721i −0.183170 0.0590409i
\(217\) 14.7222i 0.999409i
\(218\) −19.6690 + 8.77561i −1.33215 + 0.594360i
\(219\) 4.12714i 0.278886i
\(220\) 0 0
\(221\) 1.78192i 0.119865i
\(222\) −5.07918 11.3841i −0.340892 0.764049i
\(223\) 4.98852i 0.334056i 0.985952 + 0.167028i \(0.0534170\pi\)
−0.985952 + 0.167028i \(0.946583\pi\)
\(224\) 5.62894 + 9.66218i 0.376099 + 0.645582i
\(225\) 0 0
\(226\) 1.47088 0.656257i 0.0978416 0.0436536i
\(227\) 11.2569 0.747149 0.373574 0.927600i \(-0.378132\pi\)
0.373574 + 0.927600i \(0.378132\pi\)
\(228\) 4.52517 + 4.06169i 0.299687 + 0.268992i
\(229\) 15.8364i 1.04650i 0.852180 + 0.523249i \(0.175280\pi\)
−0.852180 + 0.523249i \(0.824720\pi\)
\(230\) 0 0
\(231\) −2.82786 −0.186059
\(232\) 7.87820 24.4415i 0.517229 1.60466i
\(233\) 10.9591i 0.717956i 0.933346 + 0.358978i \(0.116875\pi\)
−0.933346 + 0.358978i \(0.883125\pi\)
\(234\) 0.139054 + 0.311664i 0.00909022 + 0.0203741i
\(235\) 0 0
\(236\) 9.57945 + 8.59830i 0.623569 + 0.559701i
\(237\) −13.6757 −0.888334
\(238\) 8.41086 + 18.8514i 0.545195 + 1.22196i
\(239\) −17.3182 −1.12022 −0.560111 0.828418i \(-0.689242\pi\)
−0.560111 + 0.828418i \(0.689242\pi\)
\(240\) 0 0
\(241\) 4.76869 0.307178 0.153589 0.988135i \(-0.450917\pi\)
0.153589 + 0.988135i \(0.450917\pi\)
\(242\) −5.15922 11.5635i −0.331647 0.743327i
\(243\) −1.00000 −0.0641500
\(244\) 6.80682 + 6.10964i 0.435762 + 0.391130i
\(245\) 0 0
\(246\) −1.10242 2.47088i −0.0702879 0.157538i
\(247\) 0.733691i 0.0466836i
\(248\) −20.0493 6.46247i −1.27313 0.410367i
\(249\) 12.3320 0.781508
\(250\) 0 0
\(251\) 6.15837i 0.388713i −0.980931 0.194356i \(-0.937738\pi\)
0.980931 0.194356i \(-0.0622618\pi\)
\(252\) 2.94217 + 2.64082i 0.185339 + 0.166356i
\(253\) 1.25079 0.0786362
\(254\) 3.14630 1.40377i 0.197416 0.0880804i
\(255\) 0 0
\(256\) −15.6293 + 3.42440i −0.976828 + 0.214025i
\(257\) 14.1584i 0.883175i −0.897218 0.441587i \(-0.854416\pi\)
0.897218 0.441587i \(-0.145584\pi\)
\(258\) −6.47972 14.5231i −0.403410 0.904170i
\(259\) 17.4244i 1.08270i
\(260\) 0 0
\(261\) 9.07918i 0.561987i
\(262\) 8.91319 3.97676i 0.550659 0.245685i
\(263\) 15.5960i 0.961691i 0.876805 + 0.480845i \(0.159670\pi\)
−0.876805 + 0.480845i \(0.840330\pi\)
\(264\) 1.24132 3.85110i 0.0763979 0.237019i
\(265\) 0 0
\(266\) −3.46310 7.76191i −0.212336 0.475913i
\(267\) −8.08066 −0.494528
\(268\) 6.50161 7.24352i 0.397149 0.442468i
\(269\) 11.3182i 0.690084i 0.938587 + 0.345042i \(0.112135\pi\)
−0.938587 + 0.345042i \(0.887865\pi\)
\(270\) 0 0
\(271\) −6.20485 −0.376918 −0.188459 0.982081i \(-0.560349\pi\)
−0.188459 + 0.982081i \(0.560349\pi\)
\(272\) −29.3647 + 3.17923i −1.78050 + 0.192769i
\(273\) 0.477031i 0.0288712i
\(274\) −6.96146 + 3.10597i −0.420557 + 0.187638i
\(275\) 0 0
\(276\) −1.30135 1.16806i −0.0783319 0.0703089i
\(277\) 18.9288 1.13732 0.568661 0.822572i \(-0.307462\pi\)
0.568661 + 0.822572i \(0.307462\pi\)
\(278\) 22.5036 10.0403i 1.34968 0.602179i
\(279\) −7.44764 −0.445879
\(280\) 0 0
\(281\) −21.6231 −1.28993 −0.644963 0.764214i \(-0.723127\pi\)
−0.644963 + 0.764214i \(0.723127\pi\)
\(282\) 4.31844 1.92674i 0.257159 0.114736i
\(283\) 29.1522 1.73292 0.866460 0.499247i \(-0.166390\pi\)
0.866460 + 0.499247i \(0.166390\pi\)
\(284\) 10.9788 12.2316i 0.651473 0.725814i
\(285\) 0 0
\(286\) −0.445851 + 0.198923i −0.0263637 + 0.0117626i
\(287\) 3.78192i 0.223240i
\(288\) −4.88789 + 2.84756i −0.288021 + 0.167794i
\(289\) −37.5245 −2.20733
\(290\) 0 0
\(291\) 10.6757i 0.625822i
\(292\) −6.14275 5.51359i −0.359477 0.322659i
\(293\) 2.32427 0.135785 0.0678927 0.997693i \(-0.478372\pi\)
0.0678927 + 0.997693i \(0.478372\pi\)
\(294\) 1.78192 + 3.99385i 0.103924 + 0.232926i
\(295\) 0 0
\(296\) −23.7293 7.64863i −1.37924 0.444568i
\(297\) 1.43055i 0.0830090i
\(298\) −2.95173 + 1.31696i −0.170989 + 0.0762895i
\(299\) 0.210995i 0.0122021i
\(300\) 0 0
\(301\) 22.2290i 1.28126i
\(302\) −3.84009 8.60686i −0.220972 0.495269i
\(303\) 13.2063i 0.758683i
\(304\) 12.0907 1.30902i 0.693447 0.0750775i
\(305\) 0 0
\(306\) −9.53652 + 4.25487i −0.545166 + 0.243235i
\(307\) 3.52297 0.201066 0.100533 0.994934i \(-0.467945\pi\)
0.100533 + 0.994934i \(0.467945\pi\)
\(308\) −3.77784 + 4.20893i −0.215262 + 0.239826i
\(309\) 19.4244i 1.10502i
\(310\) 0 0
\(311\) −21.6757 −1.22912 −0.614559 0.788871i \(-0.710666\pi\)
−0.614559 + 0.788871i \(0.710666\pi\)
\(312\) 0.649641 + 0.209398i 0.0367787 + 0.0118548i
\(313\) 12.5486i 0.709288i 0.935001 + 0.354644i \(0.115398\pi\)
−0.935001 + 0.354644i \(0.884602\pi\)
\(314\) 10.0346 + 22.4907i 0.566283 + 1.26922i
\(315\) 0 0
\(316\) −18.2699 + 20.3547i −1.02776 + 1.14504i
\(317\) −10.8611 −0.610020 −0.305010 0.952349i \(-0.598660\pi\)
−0.305010 + 0.952349i \(0.598660\pi\)
\(318\) 5.30489 + 11.8900i 0.297483 + 0.666755i
\(319\) 12.9882 0.727202
\(320\) 0 0
\(321\) −14.8085 −0.826529
\(322\) 0.995917 + 2.23217i 0.0555003 + 0.124394i
\(323\) 22.4500 1.24915
\(324\) −1.33594 + 1.48838i −0.0742186 + 0.0826878i
\(325\) 0 0
\(326\) −2.68627 6.02079i −0.148779 0.333461i
\(327\) 15.2296i 0.842197i
\(328\) −5.15038 1.66011i −0.284382 0.0916645i
\(329\) −6.60978 −0.364409
\(330\) 0 0
\(331\) 1.23185i 0.0677088i −0.999427 0.0338544i \(-0.989222\pi\)
0.999427 0.0338544i \(-0.0107783\pi\)
\(332\) 16.4747 18.3547i 0.904169 1.00734i
\(333\) −8.81463 −0.483038
\(334\) −0.177476 + 0.0791838i −0.00971107 + 0.00433275i
\(335\) 0 0
\(336\) 7.86110 0.851098i 0.428858 0.0464312i
\(337\) 4.13890i 0.225460i 0.993626 + 0.112730i \(0.0359595\pi\)
−0.993626 + 0.112730i \(0.964040\pi\)
\(338\) 7.45733 + 16.7143i 0.405625 + 0.909136i
\(339\) 1.13890i 0.0618564i
\(340\) 0 0
\(341\) 10.6542i 0.576959i
\(342\) 3.92658 1.75191i 0.212325 0.0947322i
\(343\) 19.9503i 1.07721i
\(344\) −30.2724 9.75767i −1.63218 0.526098i
\(345\) 0 0
\(346\) 2.28573 + 5.12306i 0.122882 + 0.275417i
\(347\) −17.4586 −0.937226 −0.468613 0.883404i \(-0.655246\pi\)
−0.468613 + 0.883404i \(0.655246\pi\)
\(348\) −13.5133 12.1292i −0.724388 0.650194i
\(349\) 21.2196i 1.13586i −0.823078 0.567928i \(-0.807745\pi\)
0.823078 0.567928i \(-0.192255\pi\)
\(350\) 0 0
\(351\) 0.241319 0.0128807
\(352\) −4.07358 6.99237i −0.217122 0.372695i
\(353\) 21.0398i 1.11984i −0.828548 0.559918i \(-0.810833\pi\)
0.828548 0.559918i \(-0.189167\pi\)
\(354\) 8.31229 3.70866i 0.441793 0.197113i
\(355\) 0 0
\(356\) −10.7952 + 12.0271i −0.572147 + 0.637435i
\(357\) 14.5965 0.772531
\(358\) 6.05388 2.70103i 0.319957 0.142754i
\(359\) −23.5153 −1.24109 −0.620546 0.784170i \(-0.713089\pi\)
−0.620546 + 0.784170i \(0.713089\pi\)
\(360\) 0 0
\(361\) 9.75639 0.513494
\(362\) −11.7558 + 5.24502i −0.617869 + 0.275672i
\(363\) −8.95352 −0.469938
\(364\) −0.710003 0.637282i −0.0372143 0.0334027i
\(365\) 0 0
\(366\) 5.90642 2.63524i 0.308733 0.137746i
\(367\) 25.4012i 1.32593i −0.748650 0.662965i \(-0.769298\pi\)
0.748650 0.662965i \(-0.230702\pi\)
\(368\) −3.47703 + 0.376448i −0.181253 + 0.0196237i
\(369\) −1.91319 −0.0995967
\(370\) 0 0
\(371\) 18.1987i 0.944829i
\(372\) −9.94957 + 11.0849i −0.515861 + 0.574727i
\(373\) 10.0677 0.521286 0.260643 0.965435i \(-0.416065\pi\)
0.260643 + 0.965435i \(0.416065\pi\)
\(374\) −6.08681 13.6425i −0.314741 0.705436i
\(375\) 0 0
\(376\) 2.90143 9.00148i 0.149630 0.464216i
\(377\) 2.19098i 0.112841i
\(378\) 2.55298 1.13905i 0.131311 0.0585866i
\(379\) 18.9674i 0.974289i −0.873321 0.487145i \(-0.838038\pi\)
0.873321 0.487145i \(-0.161962\pi\)
\(380\) 0 0
\(381\) 2.43616i 0.124808i
\(382\) −8.76222 19.6389i −0.448314 1.00482i
\(383\) 28.7446i 1.46878i 0.678727 + 0.734391i \(0.262532\pi\)
−0.678727 + 0.734391i \(0.737468\pi\)
\(384\) −2.29166 + 11.0792i −0.116946 + 0.565382i
\(385\) 0 0
\(386\) 26.8068 11.9603i 1.36443 0.608763i
\(387\) −11.2452 −0.571624
\(388\) −15.8895 14.2621i −0.806669 0.724048i
\(389\) 29.8161i 1.51174i 0.654724 + 0.755868i \(0.272785\pi\)
−0.654724 + 0.755868i \(0.727215\pi\)
\(390\) 0 0
\(391\) −6.45617 −0.326503
\(392\) 8.32490 + 2.68335i 0.420471 + 0.135530i
\(393\) 6.90143i 0.348131i
\(394\) −13.3976 30.0283i −0.674962 1.51281i
\(395\) 0 0
\(396\) −2.12921 1.91113i −0.106997 0.0960377i
\(397\) 2.73167 0.137099 0.0685494 0.997648i \(-0.478163\pi\)
0.0685494 + 0.997648i \(0.478163\pi\)
\(398\) −4.15821 9.31988i −0.208432 0.467163i
\(399\) −6.01001 −0.300877
\(400\) 0 0
\(401\) 25.8744 1.29211 0.646054 0.763292i \(-0.276418\pi\)
0.646054 + 0.763292i \(0.276418\pi\)
\(402\) −2.80431 6.28535i −0.139866 0.313485i
\(403\) 1.79726 0.0895279
\(404\) 19.6560 + 17.6428i 0.977924 + 0.877762i
\(405\) 0 0
\(406\) 10.3417 + 23.1790i 0.513249 + 1.15035i
\(407\) 12.6098i 0.625044i
\(408\) −6.40731 + 19.8782i −0.317209 + 0.984117i
\(409\) −22.4786 −1.11150 −0.555748 0.831351i \(-0.687568\pi\)
−0.555748 + 0.831351i \(0.687568\pi\)
\(410\) 0 0
\(411\) 5.39022i 0.265880i
\(412\) 28.9109 + 25.9498i 1.42434 + 1.27845i
\(413\) −12.7227 −0.626045
\(414\) −1.12921 + 0.503813i −0.0554974 + 0.0247610i
\(415\) 0 0
\(416\) 1.17954 0.687170i 0.0578318 0.0336913i
\(417\) 17.4244i 0.853277i
\(418\) 2.50619 + 5.61718i 0.122582 + 0.274745i
\(419\) 24.5307i 1.19840i −0.800598 0.599201i \(-0.795485\pi\)
0.800598 0.599201i \(-0.204515\pi\)
\(420\) 0 0
\(421\) 33.3856i 1.62712i 0.581483 + 0.813558i \(0.302473\pi\)
−0.581483 + 0.813558i \(0.697527\pi\)
\(422\) 5.66202 2.52620i 0.275623 0.122974i
\(423\) 3.34374i 0.162578i
\(424\) 24.7838 + 7.98852i 1.20361 + 0.387957i
\(425\) 0 0
\(426\) −4.73544 10.6136i −0.229433 0.514232i
\(427\) −9.04033 −0.437492
\(428\) −19.7832 + 22.0406i −0.956256 + 1.06537i
\(429\) 0.345220i 0.0166674i
\(430\) 0 0
\(431\) 11.6548 0.561391 0.280696 0.959797i \(-0.409435\pi\)
0.280696 + 0.959797i \(0.409435\pi\)
\(432\) 0.430552 + 3.97676i 0.0207149 + 0.191332i
\(433\) 19.7681i 0.949996i −0.879987 0.474998i \(-0.842449\pi\)
0.879987 0.474998i \(-0.157551\pi\)
\(434\) 19.0137 8.48326i 0.912687 0.407210i
\(435\) 0 0
\(436\) 22.6674 + 20.3457i 1.08557 + 0.974383i
\(437\) 2.65827 0.127163
\(438\) −5.33019 + 2.37815i −0.254687 + 0.113632i
\(439\) 25.1699 1.20129 0.600646 0.799515i \(-0.294910\pi\)
0.600646 + 0.799515i \(0.294910\pi\)
\(440\) 0 0
\(441\) 3.09242 0.147258
\(442\) 2.30135 1.02678i 0.109464 0.0488390i
\(443\) 19.5515 0.928922 0.464461 0.885594i \(-0.346248\pi\)
0.464461 + 0.885594i \(0.346248\pi\)
\(444\) −11.7758 + 13.1195i −0.558853 + 0.622625i
\(445\) 0 0
\(446\) 6.44266 2.87449i 0.305069 0.136111i
\(447\) 2.28551i 0.108101i
\(448\) 9.23517 12.8373i 0.436321 0.606507i
\(449\) 19.9612 0.942029 0.471014 0.882125i \(-0.343888\pi\)
0.471014 + 0.882125i \(0.343888\pi\)
\(450\) 0 0
\(451\) 2.73692i 0.128876i
\(452\) −1.69511 1.52149i −0.0797313 0.0715650i
\(453\) −6.66425 −0.313114
\(454\) −6.48650 14.5383i −0.304426 0.682317i
\(455\) 0 0
\(456\) 2.63816 8.18468i 0.123543 0.383283i
\(457\) 5.01176i 0.234440i −0.993106 0.117220i \(-0.962602\pi\)
0.993106 0.117220i \(-0.0373983\pi\)
\(458\) 20.4527 9.12528i 0.955690 0.426396i
\(459\) 7.38407i 0.344659i
\(460\) 0 0
\(461\) 5.12566i 0.238726i 0.992851 + 0.119363i \(0.0380852\pi\)
−0.992851 + 0.119363i \(0.961915\pi\)
\(462\) 1.62948 + 3.65217i 0.0758101 + 0.169915i
\(463\) 5.79515i 0.269324i 0.990892 + 0.134662i \(0.0429948\pi\)
−0.990892 + 0.134662i \(0.957005\pi\)
\(464\) −36.1057 + 3.90906i −1.67617 + 0.181474i
\(465\) 0 0
\(466\) 14.1537 6.31490i 0.655657 0.292532i
\(467\) −16.8208 −0.778373 −0.389186 0.921159i \(-0.627244\pi\)
−0.389186 + 0.921159i \(0.627244\pi\)
\(468\) 0.322387 0.359175i 0.0149024 0.0166029i
\(469\) 9.62032i 0.444225i
\(470\) 0 0
\(471\) 17.4144 0.802413
\(472\) 5.58479 17.3264i 0.257061 0.797511i
\(473\) 16.0868i 0.739672i
\(474\) 7.88026 + 17.6622i 0.361952 + 0.811251i
\(475\) 0 0
\(476\) 19.5000 21.7252i 0.893783 0.995773i
\(477\) 9.20632 0.421529
\(478\) 9.97914 + 22.3664i 0.456435 + 1.02302i
\(479\) 36.9065 1.68630 0.843151 0.537678i \(-0.180698\pi\)
0.843151 + 0.537678i \(0.180698\pi\)
\(480\) 0 0
\(481\) 2.12714 0.0969892
\(482\) −2.74782 6.15875i −0.125160 0.280523i
\(483\) 1.72836 0.0786429
\(484\) −11.9613 + 13.3262i −0.543697 + 0.605738i
\(485\) 0 0
\(486\) 0.576222 + 1.29150i 0.0261380 + 0.0585836i
\(487\) 5.14984i 0.233361i −0.993169 0.116681i \(-0.962775\pi\)
0.993169 0.116681i \(-0.0372254\pi\)
\(488\) 3.96835 12.3115i 0.179639 0.557316i
\(489\) −4.66187 −0.210817
\(490\) 0 0
\(491\) 23.1154i 1.04318i −0.853195 0.521591i \(-0.825339\pi\)
0.853195 0.521591i \(-0.174661\pi\)
\(492\) −2.55590 + 2.84756i −0.115229 + 0.128378i
\(493\) −67.0414 −3.01939
\(494\) −0.947560 + 0.422769i −0.0426328 + 0.0190213i
\(495\) 0 0
\(496\) 3.20660 + 29.6175i 0.143980 + 1.32986i
\(497\) 16.2452i 0.728696i
\(498\) −7.10597 15.9267i −0.318426 0.713694i
\(499\) 14.3111i 0.640654i −0.947307 0.320327i \(-0.896207\pi\)
0.947307 0.320327i \(-0.103793\pi\)
\(500\) 0 0
\(501\) 0.137419i 0.00613942i
\(502\) −7.95352 + 3.54859i −0.354983 + 0.158381i
\(503\) 15.4224i 0.687650i −0.939034 0.343825i \(-0.888277\pi\)
0.939034 0.343825i \(-0.111723\pi\)
\(504\) 1.71528 5.32151i 0.0764045 0.237039i
\(505\) 0 0
\(506\) −0.720730 1.61539i −0.0320404 0.0718127i
\(507\) 12.9418 0.574764
\(508\) −3.62593 3.25455i −0.160875 0.144397i
\(509\) 43.1578i 1.91294i −0.291835 0.956469i \(-0.594266\pi\)
0.291835 0.956469i \(-0.405734\pi\)
\(510\) 0 0
\(511\) 8.15837 0.360905
\(512\) 13.4285 + 18.2119i 0.593463 + 0.804861i
\(513\) 3.04033i 0.134234i
\(514\) −18.2855 + 8.15837i −0.806539 + 0.359850i
\(515\) 0 0
\(516\) −15.0228 + 16.7371i −0.661343 + 0.736810i
\(517\) 4.78340 0.210374
\(518\) 22.5036 10.0403i 0.988751 0.441147i
\(519\) 3.96675 0.174121
\(520\) 0 0
\(521\) −17.8232 −0.780848 −0.390424 0.920635i \(-0.627672\pi\)
−0.390424 + 0.920635i \(0.627672\pi\)
\(522\) −11.7258 + 5.23163i −0.513222 + 0.228982i
\(523\) 24.7502 1.08225 0.541126 0.840941i \(-0.317998\pi\)
0.541126 + 0.840941i \(0.317998\pi\)
\(524\) −10.2720 9.21987i −0.448733 0.402772i
\(525\) 0 0
\(526\) 20.1422 8.98677i 0.878242 0.391842i
\(527\) 54.9939i 2.39557i
\(528\) −5.68896 + 0.615927i −0.247580 + 0.0268048i
\(529\) 22.2355 0.966762
\(530\) 0 0
\(531\) 6.43616i 0.279306i
\(532\) −8.02898 + 8.94517i −0.348100 + 0.387822i
\(533\) 0.461690 0.0199980
\(534\) 4.65626 + 10.4362i 0.201496 + 0.451617i
\(535\) 0 0
\(536\) −13.1014 4.22295i −0.565893 0.182403i
\(537\) 4.68749i 0.202280i
\(538\) 14.6175 6.52181i 0.630203 0.281175i
\(539\) 4.42386i 0.190549i
\(540\) 0 0
\(541\) 16.9982i 0.730812i 0.930848 + 0.365406i \(0.119070\pi\)
−0.930848 + 0.365406i \(0.880930\pi\)
\(542\) 3.57537 + 8.01355i 0.153575 + 0.344211i
\(543\) 9.10242i 0.390622i
\(544\) 21.0266 + 36.0925i 0.901506 + 1.54745i
\(545\) 0 0
\(546\) −0.616084 + 0.274876i −0.0263660 + 0.0117636i
\(547\) 37.2385 1.59220 0.796101 0.605163i \(-0.206892\pi\)
0.796101 + 0.605163i \(0.206892\pi\)
\(548\) 8.02270 + 7.20099i 0.342713 + 0.307611i
\(549\) 4.57331i 0.195184i
\(550\) 0 0
\(551\) 27.6037 1.17596
\(552\) −0.758681 + 2.35375i −0.0322916 + 0.100182i
\(553\) 27.0336i 1.14959i
\(554\) −10.9072 24.4465i −0.463403 1.03863i
\(555\) 0 0
\(556\) −25.9341 23.2779i −1.09985 0.987202i
\(557\) −14.7604 −0.625420 −0.312710 0.949849i \(-0.601237\pi\)
−0.312710 + 0.949849i \(0.601237\pi\)
\(558\) 4.29150 + 9.61862i 0.181674 + 0.407189i
\(559\) 2.71368 0.114776
\(560\) 0 0
\(561\) −10.5633 −0.445983
\(562\) 12.4597 + 27.9262i 0.525581 + 1.17800i
\(563\) −3.00561 −0.126671 −0.0633356 0.997992i \(-0.520174\pi\)
−0.0633356 + 0.997992i \(0.520174\pi\)
\(564\) −4.97676 4.46702i −0.209559 0.188096i
\(565\) 0 0
\(566\) −16.7982 37.6500i −0.706079 1.58255i
\(567\) 1.97676i 0.0830161i
\(568\) −22.1234 7.13100i −0.928276 0.299210i
\(569\) 23.1840 0.971923 0.485962 0.873980i \(-0.338469\pi\)
0.485962 + 0.873980i \(0.338469\pi\)
\(570\) 0 0
\(571\) 0.202739i 0.00848438i 0.999991 + 0.00424219i \(0.00135033\pi\)
−0.999991 + 0.00424219i \(0.998650\pi\)
\(572\) 0.513819 + 0.461192i 0.0214838 + 0.0192834i
\(573\) −15.2063 −0.635253
\(574\) 4.88434 2.17923i 0.203869 0.0909592i
\(575\) 0 0
\(576\) 6.49412 + 4.67187i 0.270588 + 0.194661i
\(577\) 21.8023i 0.907643i 0.891093 + 0.453821i \(0.149940\pi\)
−0.891093 + 0.453821i \(0.850060\pi\)
\(578\) 21.6225 + 48.4629i 0.899376 + 2.01579i
\(579\) 20.7564i 0.862606i
\(580\) 0 0
\(581\) 24.3774i 1.01134i
\(582\) −13.7877 + 6.15159i −0.571518 + 0.254992i
\(583\) 13.1701i 0.545451i
\(584\) −3.58120 + 11.1104i −0.148191 + 0.459752i
\(585\) 0 0
\(586\) −1.33930 3.00179i −0.0553258 0.124003i
\(587\) −36.7126 −1.51529 −0.757645 0.652667i \(-0.773650\pi\)
−0.757645 + 0.652667i \(0.773650\pi\)
\(588\) 4.13127 4.60269i 0.170371 0.189812i
\(589\) 22.6433i 0.933001i
\(590\) 0 0
\(591\) −23.2508 −0.956409
\(592\) 3.79515 + 35.0537i 0.155980 + 1.44070i
\(593\) 10.6036i 0.435439i −0.976011 0.217719i \(-0.930138\pi\)
0.976011 0.217719i \(-0.0698618\pi\)
\(594\) −1.84756 + 0.824316i −0.0758061 + 0.0338221i
\(595\) 0 0
\(596\) 3.40170 + 3.05329i 0.139339 + 0.125068i
\(597\) −7.21633 −0.295345
\(598\) 0.272499 0.121580i 0.0111433 0.00497177i
\(599\) 25.7988 1.05411 0.527056 0.849831i \(-0.323296\pi\)
0.527056 + 0.849831i \(0.323296\pi\)
\(600\) 0 0
\(601\) 18.5021 0.754717 0.377358 0.926067i \(-0.376832\pi\)
0.377358 + 0.926067i \(0.376832\pi\)
\(602\) 28.7087 12.8089i 1.17008 0.522050i
\(603\) −4.86671 −0.198188
\(604\) −8.90300 + 9.91893i −0.362258 + 0.403596i
\(605\) 0 0
\(606\) 17.0559 7.60978i 0.692850 0.309126i
\(607\) 37.5828i 1.52544i −0.646730 0.762719i \(-0.723864\pi\)
0.646730 0.762719i \(-0.276136\pi\)
\(608\) −8.65751 14.8608i −0.351108 0.602685i
\(609\) 17.9474 0.727264
\(610\) 0 0
\(611\) 0.806910i 0.0326441i
\(612\) 10.9903 + 9.86465i 0.444257 + 0.398755i
\(613\) 4.93405 0.199284 0.0996422 0.995023i \(-0.468230\pi\)
0.0996422 + 0.995023i \(0.468230\pi\)
\(614\) −2.03001 4.54991i −0.0819247 0.183619i
\(615\) 0 0
\(616\) 7.61270 + 2.45379i 0.306724 + 0.0988661i
\(617\) 6.26043i 0.252035i −0.992028 0.126018i \(-0.959780\pi\)
0.992028 0.126018i \(-0.0402196\pi\)
\(618\) 25.0866 11.1928i 1.00913 0.450239i
\(619\) 8.02562i 0.322577i −0.986907 0.161288i \(-0.948435\pi\)
0.986907 0.161288i \(-0.0515649\pi\)
\(620\) 0 0
\(621\) 0.874337i 0.0350860i
\(622\) 12.4900 + 27.9942i 0.500805 + 1.12246i
\(623\) 15.9735i 0.639966i
\(624\) −0.103901 0.959669i −0.00415935 0.0384175i
\(625\) 0 0
\(626\) 16.2065 7.23078i 0.647741 0.289000i
\(627\) 4.34935 0.173696
\(628\) 23.2645 25.9192i 0.928355 1.03429i
\(629\) 65.0878i 2.59522i
\(630\) 0 0
\(631\) −26.5248 −1.05594 −0.527968 0.849264i \(-0.677046\pi\)
−0.527968 + 0.849264i \(0.677046\pi\)
\(632\) 36.8156 + 11.8667i 1.46444 + 0.472032i
\(633\) 4.38407i 0.174251i
\(634\) 6.25841 + 14.0271i 0.248553 + 0.557087i
\(635\) 0 0
\(636\) 12.2991 13.7025i 0.487689 0.543340i
\(637\) −0.746260 −0.0295679
\(638\) −7.48412 16.7743i −0.296299 0.664101i
\(639\) −8.21808 −0.325102
\(640\) 0 0
\(641\) −26.5863 −1.05009 −0.525047 0.851073i \(-0.675952\pi\)
−0.525047 + 0.851073i \(0.675952\pi\)
\(642\) 8.53298 + 19.1251i 0.336770 + 0.754808i
\(643\) −2.89233 −0.114062 −0.0570312 0.998372i \(-0.518163\pi\)
−0.0570312 + 0.998372i \(0.518163\pi\)
\(644\) 2.30897 2.57245i 0.0909862 0.101369i
\(645\) 0 0
\(646\) −12.9362 28.9942i −0.508968 1.14076i
\(647\) 12.3472i 0.485420i −0.970099 0.242710i \(-0.921964\pi\)
0.970099 0.242710i \(-0.0780363\pi\)
\(648\) 2.69204 + 0.867721i 0.105753 + 0.0340873i
\(649\) 9.20726 0.361417
\(650\) 0 0
\(651\) 14.7222i 0.577009i
\(652\) −6.22795 + 6.93863i −0.243905 + 0.271738i
\(653\) −39.0507 −1.52817 −0.764086 0.645114i \(-0.776810\pi\)
−0.764086 + 0.645114i \(0.776810\pi\)
\(654\) 19.6690 8.77561i 0.769117 0.343154i
\(655\) 0 0
\(656\) 0.823728 + 7.60830i 0.0321612 + 0.297054i
\(657\) 4.12714i 0.161015i
\(658\) 3.80870 + 8.53652i 0.148479 + 0.332788i
\(659\) 23.7738i 0.926094i −0.886334 0.463047i \(-0.846756\pi\)
0.886334 0.463047i \(-0.153244\pi\)
\(660\) 0 0
\(661\) 21.5051i 0.836450i −0.908343 0.418225i \(-0.862652\pi\)
0.908343 0.418225i \(-0.137348\pi\)
\(662\) −1.59094 + 0.709822i −0.0618335 + 0.0275880i
\(663\) 1.78192i 0.0692040i
\(664\) −33.1982 10.7007i −1.28834 0.415268i
\(665\) 0 0
\(666\) 5.07918 + 11.3841i 0.196814 + 0.441124i
\(667\) −7.93827 −0.307371
\(668\) 0.204532 + 0.183583i 0.00791356 + 0.00710303i
\(669\) 4.98852i 0.192867i
\(670\) 0 0
\(671\) 6.54235 0.252565
\(672\) −5.62894 9.66218i −0.217141 0.372727i
\(673\) 36.1896i 1.39501i 0.716582 + 0.697503i \(0.245706\pi\)
−0.716582 + 0.697503i \(0.754294\pi\)
\(674\) 5.34538 2.38492i 0.205896 0.0918639i
\(675\) 0 0
\(676\) 17.2894 19.2623i 0.664976 0.740856i
\(677\) 9.17214 0.352514 0.176257 0.984344i \(-0.443601\pi\)
0.176257 + 0.984344i \(0.443601\pi\)
\(678\) −1.47088 + 0.656257i −0.0564889 + 0.0252034i
\(679\) 21.1034 0.809873
\(680\) 0 0
\(681\) −11.2569 −0.431367
\(682\) −13.7599 + 6.13921i −0.526895 + 0.235083i
\(683\) 16.3974 0.627429 0.313714 0.949517i \(-0.398427\pi\)
0.313714 + 0.949517i \(0.398427\pi\)
\(684\) −4.52517 4.06169i −0.173024 0.155302i
\(685\) 0 0
\(686\) −25.7658 + 11.4958i −0.983742 + 0.438912i
\(687\) 15.8364i 0.604196i
\(688\) 4.84163 + 44.7194i 0.184586 + 1.70491i
\(689\) −2.22166 −0.0846387
\(690\) 0 0
\(691\) 24.4904i 0.931657i −0.884875 0.465828i \(-0.845756\pi\)
0.884875 0.465828i \(-0.154244\pi\)
\(692\) 5.29933 5.90404i 0.201450 0.224438i
\(693\) 2.82786 0.107421
\(694\) 10.0600 + 22.5477i 0.381873 + 0.855900i
\(695\) 0 0
\(696\) −7.87820 + 24.4415i −0.298622 + 0.926452i
\(697\) 14.1271i 0.535104i
\(698\) −27.4050 + 12.2272i −1.03730 + 0.462806i
\(699\) 10.9591i 0.414512i
\(700\) 0 0
\(701\) 12.3887i 0.467916i 0.972247 + 0.233958i \(0.0751679\pi\)
−0.972247 + 0.233958i \(0.924832\pi\)
\(702\) −0.139054 0.311664i −0.00524824 0.0117630i
\(703\) 26.7994i 1.01076i
\(704\) −6.68335 + 9.29018i −0.251888 + 0.350137i
\(705\) 0 0
\(706\) −27.1729 + 12.1236i −1.02266 + 0.456278i
\(707\) −26.1057 −0.981807
\(708\) −9.57945 8.59830i −0.360018 0.323144i
\(709\) 33.4144i 1.25490i 0.778655 + 0.627452i \(0.215902\pi\)
−0.778655 + 0.627452i \(0.784098\pi\)
\(710\) 0 0
\(711\) 13.6757 0.512880
\(712\) 21.7534 + 7.01176i 0.815244 + 0.262777i
\(713\) 6.51175i 0.243867i
\(714\) −8.41086 18.8514i −0.314768 0.705496i
\(715\) 0 0
\(716\) −6.97676 6.26218i −0.260734 0.234029i
\(717\) 17.3182 0.646761
\(718\) 13.5501 + 30.3700i 0.505684 + 1.13340i
\(719\) 33.8938 1.26403 0.632013 0.774958i \(-0.282229\pi\)
0.632013 + 0.774958i \(0.282229\pi\)
\(720\) 0 0
\(721\) −38.3974 −1.42999
\(722\) −5.62185 12.6004i −0.209224 0.468937i
\(723\) −4.76869 −0.177349
\(724\) 13.5479 + 12.1603i 0.503503 + 0.451932i
\(725\) 0 0
\(726\) 5.15922 + 11.5635i 0.191477 + 0.429160i
\(727\) 14.1846i 0.526076i 0.964785 + 0.263038i \(0.0847245\pi\)
−0.964785 + 0.263038i \(0.915275\pi\)
\(728\) −0.413929 + 1.28418i −0.0153412 + 0.0475950i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 83.0352i 3.07117i
\(732\) −6.80682 6.10964i −0.251587 0.225819i
\(733\) −8.09296 −0.298920 −0.149460 0.988768i \(-0.547754\pi\)
−0.149460 + 0.988768i \(0.547754\pi\)
\(734\) −32.8056 + 14.6367i −1.21088 + 0.540251i
\(735\) 0 0
\(736\) 2.48972 + 4.27366i 0.0917725 + 0.157529i
\(737\) 6.96208i 0.256452i
\(738\) 1.10242 + 2.47088i 0.0405808 + 0.0909544i
\(739\) 22.0919i 0.812663i −0.913726 0.406331i \(-0.866808\pi\)
0.913726 0.406331i \(-0.133192\pi\)
\(740\) 0 0
\(741\) 0.733691i 0.0269528i
\(742\) −23.5036 + 10.4865i −0.862844 + 0.384971i
\(743\) 8.78340i 0.322232i 0.986936 + 0.161116i \(0.0515093\pi\)
−0.986936 + 0.161116i \(0.948491\pi\)
\(744\) 20.0493 + 6.46247i 0.735044 + 0.236926i
\(745\) 0 0
\(746\) −5.80123 13.0024i −0.212398 0.476052i
\(747\) −12.3320 −0.451204
\(748\) −14.1119 + 15.7222i −0.515982 + 0.574861i
\(749\) 29.2728i 1.06961i
\(750\) 0 0
\(751\) 13.3779 0.488167 0.244084 0.969754i \(-0.421513\pi\)
0.244084 + 0.969754i \(0.421513\pi\)
\(752\) −13.2973 + 1.43965i −0.484901 + 0.0524988i
\(753\) 6.15837i 0.224423i
\(754\) 2.82965 1.26249i 0.103050 0.0459773i
\(755\) 0 0
\(756\) −2.94217 2.64082i −0.107006 0.0960459i
\(757\) 9.72450 0.353443 0.176721 0.984261i \(-0.443451\pi\)
0.176721 + 0.984261i \(0.443451\pi\)
\(758\) −24.4963 + 10.9294i −0.889747 + 0.396975i
\(759\) −1.25079 −0.0454006
\(760\) 0 0
\(761\) 33.8835 1.22828 0.614138 0.789198i \(-0.289504\pi\)
0.614138 + 0.789198i \(0.289504\pi\)
\(762\) −3.14630 + 1.40377i −0.113978 + 0.0508532i
\(763\) −30.1052 −1.08988
\(764\) −20.3147 + 22.6328i −0.734959 + 0.818826i
\(765\) 0 0
\(766\) 37.1236 16.5633i 1.34133 0.598456i
\(767\) 1.55317i 0.0560817i
\(768\) 15.6293 3.42440i 0.563972 0.123568i
\(769\) −18.7334 −0.675545 −0.337772 0.941228i \(-0.609673\pi\)
−0.337772 + 0.941228i \(0.609673\pi\)
\(770\) 0 0
\(771\) 14.1584i 0.509901i
\(772\) −30.8934 27.7292i −1.11188 0.997996i
\(773\) 22.5006 0.809292 0.404646 0.914474i \(-0.367395\pi\)
0.404646 + 0.914474i \(0.367395\pi\)
\(774\) 6.47972 + 14.5231i 0.232909 + 0.522023i
\(775\) 0 0
\(776\) −9.26355 + 28.7395i −0.332542 + 1.03169i
\(777\) 17.4244i 0.625097i
\(778\) 38.5074 17.1807i 1.38056 0.615958i
\(779\) 5.81673i 0.208406i
\(780\) 0 0
\(781\) 11.7564i 0.420677i
\(782\) 3.72019 + 8.33813i 0.133034 + 0.298171i
\(783\) 9.07918i 0.324464i
\(784\) −1.33145 12.2978i −0.0475517 0.439207i
\(785\) 0 0
\(786\) −8.91319 + 3.97676i −0.317923 + 0.141846i
\(787\) −28.1063 −1.00188 −0.500940 0.865482i \(-0.667012\pi\)
−0.500940 + 0.865482i \(0.667012\pi\)