Properties

Label 105.2.d.b.64.3
Level 105
Weight 2
Character 105.64
Analytic conductor 0.838
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.3
Root \(0.403032 - 0.403032i\)
Character \(\chi\) = 105.64
Dual form 105.2.d.b.64.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(-1.48119 - 1.67513i) q^{5} -0.193937 q^{6} +1.00000i q^{7} -0.768452i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(-1.48119 - 1.67513i) q^{5} -0.193937 q^{6} +1.00000i q^{7} -0.768452i q^{8} -1.00000 q^{9} +(-0.324869 + 0.287258i) q^{10} +2.00000 q^{11} -1.96239i q^{12} +1.35026i q^{13} +0.193937 q^{14} +(-1.67513 + 1.48119i) q^{15} +3.77575 q^{16} +3.35026i q^{17} +0.193937i q^{18} -5.35026 q^{19} +(-2.90668 - 3.28726i) q^{20} +1.00000 q^{21} -0.387873i q^{22} +4.96239i q^{23} -0.768452 q^{24} +(-0.612127 + 4.96239i) q^{25} +0.261865 q^{26} +1.00000i q^{27} +1.96239i q^{28} -7.92478 q^{29} +(0.287258 + 0.324869i) q^{30} +4.57452 q^{31} -2.26916i q^{32} -2.00000i q^{33} +0.649738 q^{34} +(1.67513 - 1.48119i) q^{35} -1.96239 q^{36} +0.775746i q^{37} +1.03761i q^{38} +1.35026 q^{39} +(-1.28726 + 1.13823i) q^{40} +3.73813 q^{41} -0.193937i q^{42} -12.6253i q^{43} +3.92478 q^{44} +(1.48119 + 1.67513i) q^{45} +0.962389 q^{46} -9.92478i q^{47} -3.77575i q^{48} -1.00000 q^{49} +(0.962389 + 0.118714i) q^{50} +3.35026 q^{51} +2.64974i q^{52} +8.57452i q^{53} +0.193937 q^{54} +(-2.96239 - 3.35026i) q^{55} +0.768452 q^{56} +5.35026i q^{57} +1.53690i q^{58} +8.62530 q^{59} +(-3.28726 + 2.90668i) q^{60} -8.70052 q^{61} -0.887166i q^{62} -1.00000i q^{63} +7.11142 q^{64} +(2.26187 - 2.00000i) q^{65} -0.387873 q^{66} -9.92478i q^{67} +6.57452i q^{68} +4.96239 q^{69} +(-0.287258 - 0.324869i) q^{70} +2.00000 q^{71} +0.768452i q^{72} -9.35026i q^{73} +0.150446 q^{74} +(4.96239 + 0.612127i) q^{75} -10.4993 q^{76} +2.00000i q^{77} -0.261865i q^{78} -10.7005 q^{79} +(-5.59261 - 6.32487i) q^{80} +1.00000 q^{81} -0.724961i q^{82} +3.22425i q^{83} +1.96239 q^{84} +(5.61213 - 4.96239i) q^{85} -2.44851 q^{86} +7.92478i q^{87} -1.53690i q^{88} -1.03761 q^{89} +(0.324869 - 0.287258i) q^{90} -1.35026 q^{91} +9.73813i q^{92} -4.57452i q^{93} -1.92478 q^{94} +(7.92478 + 8.96239i) q^{95} -2.26916 q^{96} +18.4993i q^{97} +0.193937i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 10q^{4} + 2q^{5} - 2q^{6} - 6q^{9} - 12q^{10} + 12q^{11} + 2q^{14} + 26q^{16} - 12q^{19} - 30q^{20} + 6q^{21} + 18q^{24} - 2q^{25} + 20q^{26} - 4q^{29} - 10q^{30} + 4q^{31} + 24q^{34} + 10q^{36} - 12q^{39} + 4q^{40} + 4q^{41} - 20q^{44} - 2q^{45} - 16q^{46} - 6q^{49} - 16q^{50} + 2q^{54} + 4q^{55} - 18q^{56} - 32q^{59} - 8q^{60} - 12q^{61} - 26q^{64} + 32q^{65} - 4q^{66} + 8q^{69} + 10q^{70} + 12q^{71} + 88q^{74} + 8q^{75} + 4q^{76} - 24q^{79} + 46q^{80} + 6q^{81} - 10q^{84} + 32q^{85} - 8q^{86} - 28q^{89} + 12q^{90} + 12q^{91} + 32q^{94} + 4q^{95} - 58q^{96} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.193937i 0.137134i −0.997647 0.0685669i \(-0.978157\pi\)
0.997647 0.0685669i \(-0.0218427\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.96239 0.981194
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) −0.193937 −0.0791743
\(7\) 1.00000i 0.377964i
\(8\) 0.768452i 0.271689i
\(9\) −1.00000 −0.333333
\(10\) −0.324869 + 0.287258i −0.102733 + 0.0908389i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.96239i 0.566493i
\(13\) 1.35026i 0.374495i 0.982313 + 0.187248i \(0.0599567\pi\)
−0.982313 + 0.187248i \(0.940043\pi\)
\(14\) 0.193937 0.0518317
\(15\) −1.67513 + 1.48119i −0.432517 + 0.382443i
\(16\) 3.77575 0.943937
\(17\) 3.35026i 0.812558i 0.913749 + 0.406279i \(0.133174\pi\)
−0.913749 + 0.406279i \(0.866826\pi\)
\(18\) 0.193937i 0.0457113i
\(19\) −5.35026 −1.22743 −0.613717 0.789526i \(-0.710326\pi\)
−0.613717 + 0.789526i \(0.710326\pi\)
\(20\) −2.90668 3.28726i −0.649953 0.735053i
\(21\) 1.00000 0.218218
\(22\) 0.387873i 0.0826948i
\(23\) 4.96239i 1.03473i 0.855765 + 0.517365i \(0.173087\pi\)
−0.855765 + 0.517365i \(0.826913\pi\)
\(24\) −0.768452 −0.156860
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) 0.261865 0.0513560
\(27\) 1.00000i 0.192450i
\(28\) 1.96239i 0.370857i
\(29\) −7.92478 −1.47159 −0.735797 0.677202i \(-0.763192\pi\)
−0.735797 + 0.677202i \(0.763192\pi\)
\(30\) 0.287258 + 0.324869i 0.0524458 + 0.0593127i
\(31\) 4.57452 0.821607 0.410804 0.911724i \(-0.365248\pi\)
0.410804 + 0.911724i \(0.365248\pi\)
\(32\) 2.26916i 0.401134i
\(33\) 2.00000i 0.348155i
\(34\) 0.649738 0.111429
\(35\) 1.67513 1.48119i 0.283149 0.250368i
\(36\) −1.96239 −0.327065
\(37\) 0.775746i 0.127532i 0.997965 + 0.0637660i \(0.0203111\pi\)
−0.997965 + 0.0637660i \(0.979689\pi\)
\(38\) 1.03761i 0.168323i
\(39\) 1.35026 0.216215
\(40\) −1.28726 + 1.13823i −0.203533 + 0.179969i
\(41\) 3.73813 0.583799 0.291899 0.956449i \(-0.405713\pi\)
0.291899 + 0.956449i \(0.405713\pi\)
\(42\) 0.193937i 0.0299251i
\(43\) 12.6253i 1.92534i −0.270677 0.962670i \(-0.587248\pi\)
0.270677 0.962670i \(-0.412752\pi\)
\(44\) 3.92478 0.591682
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) 0.962389 0.141896
\(47\) 9.92478i 1.44768i −0.689969 0.723839i \(-0.742376\pi\)
0.689969 0.723839i \(-0.257624\pi\)
\(48\) 3.77575i 0.544982i
\(49\) −1.00000 −0.142857
\(50\) 0.962389 + 0.118714i 0.136102 + 0.0167887i
\(51\) 3.35026 0.469130
\(52\) 2.64974i 0.367453i
\(53\) 8.57452i 1.17780i 0.808206 + 0.588900i \(0.200439\pi\)
−0.808206 + 0.588900i \(0.799561\pi\)
\(54\) 0.193937 0.0263914
\(55\) −2.96239 3.35026i −0.399448 0.451749i
\(56\) 0.768452 0.102689
\(57\) 5.35026i 0.708659i
\(58\) 1.53690i 0.201805i
\(59\) 8.62530 1.12292 0.561459 0.827504i \(-0.310240\pi\)
0.561459 + 0.827504i \(0.310240\pi\)
\(60\) −3.28726 + 2.90668i −0.424383 + 0.375251i
\(61\) −8.70052 −1.11399 −0.556994 0.830517i \(-0.688045\pi\)
−0.556994 + 0.830517i \(0.688045\pi\)
\(62\) 0.887166i 0.112670i
\(63\) 1.00000i 0.125988i
\(64\) 7.11142 0.888927
\(65\) 2.26187 2.00000i 0.280550 0.248069i
\(66\) −0.387873 −0.0477439
\(67\) 9.92478i 1.21250i −0.795272 0.606252i \(-0.792672\pi\)
0.795272 0.606252i \(-0.207328\pi\)
\(68\) 6.57452i 0.797277i
\(69\) 4.96239 0.597401
\(70\) −0.287258 0.324869i −0.0343339 0.0388293i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0.768452i 0.0905629i
\(73\) 9.35026i 1.09437i −0.837013 0.547183i \(-0.815700\pi\)
0.837013 0.547183i \(-0.184300\pi\)
\(74\) 0.150446 0.0174889
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) −10.4993 −1.20435
\(77\) 2.00000i 0.227921i
\(78\) 0.261865i 0.0296504i
\(79\) −10.7005 −1.20390 −0.601951 0.798533i \(-0.705610\pi\)
−0.601951 + 0.798533i \(0.705610\pi\)
\(80\) −5.59261 6.32487i −0.625273 0.707142i
\(81\) 1.00000 0.111111
\(82\) 0.724961i 0.0800586i
\(83\) 3.22425i 0.353908i 0.984219 + 0.176954i \(0.0566244\pi\)
−0.984219 + 0.176954i \(0.943376\pi\)
\(84\) 1.96239 0.214114
\(85\) 5.61213 4.96239i 0.608721 0.538247i
\(86\) −2.44851 −0.264029
\(87\) 7.92478i 0.849625i
\(88\) 1.53690i 0.163835i
\(89\) −1.03761 −0.109987 −0.0549933 0.998487i \(-0.517514\pi\)
−0.0549933 + 0.998487i \(0.517514\pi\)
\(90\) 0.324869 0.287258i 0.0342442 0.0302796i
\(91\) −1.35026 −0.141546
\(92\) 9.73813i 1.01527i
\(93\) 4.57452i 0.474355i
\(94\) −1.92478 −0.198526
\(95\) 7.92478 + 8.96239i 0.813065 + 0.919522i
\(96\) −2.26916 −0.231595
\(97\) 18.4993i 1.87832i 0.343482 + 0.939159i \(0.388394\pi\)
−0.343482 + 0.939159i \(0.611606\pi\)
\(98\) 0.193937i 0.0195906i
\(99\) −2.00000 −0.201008
\(100\) −1.20123 + 9.73813i −0.120123 + 0.973813i
\(101\) −17.6629 −1.75753 −0.878763 0.477259i \(-0.841630\pi\)
−0.878763 + 0.477259i \(0.841630\pi\)
\(102\) 0.649738i 0.0643337i
\(103\) 6.70052i 0.660222i 0.943942 + 0.330111i \(0.107086\pi\)
−0.943942 + 0.330111i \(0.892914\pi\)
\(104\) 1.03761 0.101746
\(105\) −1.48119 1.67513i −0.144550 0.163476i
\(106\) 1.66291 0.161516
\(107\) 13.7381i 1.32812i −0.747681 0.664058i \(-0.768833\pi\)
0.747681 0.664058i \(-0.231167\pi\)
\(108\) 1.96239i 0.188831i
\(109\) 2.77575 0.265868 0.132934 0.991125i \(-0.457560\pi\)
0.132934 + 0.991125i \(0.457560\pi\)
\(110\) −0.649738 + 0.574515i −0.0619501 + 0.0547779i
\(111\) 0.775746 0.0736306
\(112\) 3.77575i 0.356774i
\(113\) 12.0508i 1.13364i 0.823841 + 0.566821i \(0.191827\pi\)
−0.823841 + 0.566821i \(0.808173\pi\)
\(114\) 1.03761 0.0971812
\(115\) 8.31265 7.35026i 0.775159 0.685415i
\(116\) −15.5515 −1.44392
\(117\) 1.35026i 0.124832i
\(118\) 1.67276i 0.153990i
\(119\) −3.35026 −0.307118
\(120\) 1.13823 + 1.28726i 0.103905 + 0.117510i
\(121\) −7.00000 −0.636364
\(122\) 1.68735i 0.152765i
\(123\) 3.73813i 0.337056i
\(124\) 8.97698 0.806156
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) −0.193937 −0.0172772
\(127\) 2.70052i 0.239633i −0.992796 0.119816i \(-0.961769\pi\)
0.992796 0.119816i \(-0.0382306\pi\)
\(128\) 5.91748i 0.523037i
\(129\) −12.6253 −1.11160
\(130\) −0.387873 0.438658i −0.0340187 0.0384729i
\(131\) 20.6253 1.80204 0.901020 0.433777i \(-0.142819\pi\)
0.901020 + 0.433777i \(0.142819\pi\)
\(132\) 3.92478i 0.341608i
\(133\) 5.35026i 0.463927i
\(134\) −1.92478 −0.166275
\(135\) 1.67513 1.48119i 0.144172 0.127481i
\(136\) 2.57452 0.220763
\(137\) 22.4993i 1.92224i −0.276124 0.961122i \(-0.589050\pi\)
0.276124 0.961122i \(-0.410950\pi\)
\(138\) 0.962389i 0.0819240i
\(139\) 3.27504 0.277785 0.138893 0.990307i \(-0.455646\pi\)
0.138893 + 0.990307i \(0.455646\pi\)
\(140\) 3.28726 2.90668i 0.277824 0.245659i
\(141\) −9.92478 −0.835817
\(142\) 0.387873i 0.0325496i
\(143\) 2.70052i 0.225829i
\(144\) −3.77575 −0.314646
\(145\) 11.7381 + 13.2750i 0.974799 + 1.10243i
\(146\) −1.81336 −0.150075
\(147\) 1.00000i 0.0824786i
\(148\) 1.52232i 0.125134i
\(149\) 4.44851 0.364436 0.182218 0.983258i \(-0.441672\pi\)
0.182218 + 0.983258i \(0.441672\pi\)
\(150\) 0.118714 0.962389i 0.00969294 0.0785787i
\(151\) 1.29948 0.105750 0.0528749 0.998601i \(-0.483162\pi\)
0.0528749 + 0.998601i \(0.483162\pi\)
\(152\) 4.11142i 0.333480i
\(153\) 3.35026i 0.270853i
\(154\) 0.387873 0.0312557
\(155\) −6.77575 7.66291i −0.544241 0.615500i
\(156\) 2.64974 0.212149
\(157\) 2.64974i 0.211472i 0.994394 + 0.105736i \(0.0337199\pi\)
−0.994394 + 0.105736i \(0.966280\pi\)
\(158\) 2.07522i 0.165096i
\(159\) 8.57452 0.680003
\(160\) −3.80114 + 3.36107i −0.300506 + 0.265716i
\(161\) −4.96239 −0.391091
\(162\) 0.193937i 0.0152371i
\(163\) 5.29948i 0.415087i 0.978226 + 0.207544i \(0.0665469\pi\)
−0.978226 + 0.207544i \(0.933453\pi\)
\(164\) 7.33567 0.572820
\(165\) −3.35026 + 2.96239i −0.260818 + 0.230622i
\(166\) 0.625301 0.0485327
\(167\) 14.5501i 1.12592i 0.826485 + 0.562959i \(0.190337\pi\)
−0.826485 + 0.562959i \(0.809663\pi\)
\(168\) 0.768452i 0.0592874i
\(169\) 11.1768 0.859753
\(170\) −0.962389 1.08840i −0.0738118 0.0834762i
\(171\) 5.35026 0.409145
\(172\) 24.7757i 1.88913i
\(173\) 4.49929i 0.342075i −0.985265 0.171037i \(-0.945288\pi\)
0.985265 0.171037i \(-0.0547119\pi\)
\(174\) 1.53690 0.116512
\(175\) −4.96239 0.612127i −0.375121 0.0462724i
\(176\) 7.55149 0.569215
\(177\) 8.62530i 0.648317i
\(178\) 0.201231i 0.0150829i
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 2.90668 + 3.28726i 0.216651 + 0.245018i
\(181\) 10.6253 0.789772 0.394886 0.918730i \(-0.370784\pi\)
0.394886 + 0.918730i \(0.370784\pi\)
\(182\) 0.261865i 0.0194107i
\(183\) 8.70052i 0.643161i
\(184\) 3.81336 0.281124
\(185\) 1.29948 1.14903i 0.0955394 0.0844784i
\(186\) −0.887166 −0.0650502
\(187\) 6.70052i 0.489991i
\(188\) 19.4763i 1.42045i
\(189\) −1.00000 −0.0727393
\(190\) 1.73813 1.53690i 0.126098 0.111499i
\(191\) −13.8496 −1.00212 −0.501059 0.865413i \(-0.667056\pi\)
−0.501059 + 0.865413i \(0.667056\pi\)
\(192\) 7.11142i 0.513222i
\(193\) 15.3258i 1.10318i 0.834116 + 0.551588i \(0.185978\pi\)
−0.834116 + 0.551588i \(0.814022\pi\)
\(194\) 3.58769 0.257581
\(195\) −2.00000 2.26187i −0.143223 0.161976i
\(196\) −1.96239 −0.140171
\(197\) 0.574515i 0.0409325i 0.999791 + 0.0204663i \(0.00651507\pi\)
−0.999791 + 0.0204663i \(0.993485\pi\)
\(198\) 0.387873i 0.0275649i
\(199\) 0.201231 0.0142649 0.00713244 0.999975i \(-0.497730\pi\)
0.00713244 + 0.999975i \(0.497730\pi\)
\(200\) 3.81336 + 0.470390i 0.269645 + 0.0332616i
\(201\) −9.92478 −0.700040
\(202\) 3.42548i 0.241016i
\(203\) 7.92478i 0.556210i
\(204\) 6.57452 0.460308
\(205\) −5.53690 6.26187i −0.386714 0.437348i
\(206\) 1.29948 0.0905388
\(207\) 4.96239i 0.344910i
\(208\) 5.09825i 0.353500i
\(209\) −10.7005 −0.740171
\(210\) −0.324869 + 0.287258i −0.0224181 + 0.0198227i
\(211\) 6.44851 0.443934 0.221967 0.975054i \(-0.428752\pi\)
0.221967 + 0.975054i \(0.428752\pi\)
\(212\) 16.8265i 1.15565i
\(213\) 2.00000i 0.137038i
\(214\) −2.66433 −0.182130
\(215\) −21.1490 + 18.7005i −1.44235 + 1.27537i
\(216\) 0.768452 0.0522865
\(217\) 4.57452i 0.310538i
\(218\) 0.538319i 0.0364595i
\(219\) −9.35026 −0.631832
\(220\) −5.81336 6.57452i −0.391936 0.443254i
\(221\) −4.52373 −0.304299
\(222\) 0.150446i 0.0100972i
\(223\) 1.55149i 0.103896i 0.998650 + 0.0519478i \(0.0165429\pi\)
−0.998650 + 0.0519478i \(0.983457\pi\)
\(224\) 2.26916 0.151615
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) 2.33709 0.155461
\(227\) 13.1490i 0.872732i 0.899769 + 0.436366i \(0.143735\pi\)
−0.899769 + 0.436366i \(0.856265\pi\)
\(228\) 10.4993i 0.695333i
\(229\) −2.77575 −0.183426 −0.0917132 0.995785i \(-0.529234\pi\)
−0.0917132 + 0.995785i \(0.529234\pi\)
\(230\) −1.42548 1.61213i −0.0939937 0.106300i
\(231\) 2.00000 0.131590
\(232\) 6.08981i 0.399816i
\(233\) 0.0507852i 0.00332705i −0.999999 0.00166353i \(-0.999470\pi\)
0.999999 0.00166353i \(-0.000529517\pi\)
\(234\) −0.261865 −0.0171187
\(235\) −16.6253 + 14.7005i −1.08452 + 0.958956i
\(236\) 16.9262 1.10180
\(237\) 10.7005i 0.695074i
\(238\) 0.649738i 0.0421163i
\(239\) −5.84955 −0.378376 −0.189188 0.981941i \(-0.560586\pi\)
−0.189188 + 0.981941i \(0.560586\pi\)
\(240\) −6.32487 + 5.59261i −0.408269 + 0.361002i
\(241\) −0.0752228 −0.00484553 −0.00242276 0.999997i \(-0.500771\pi\)
−0.00242276 + 0.999997i \(0.500771\pi\)
\(242\) 1.35756i 0.0872670i
\(243\) 1.00000i 0.0641500i
\(244\) −17.0738 −1.09304
\(245\) 1.48119 + 1.67513i 0.0946300 + 0.107020i
\(246\) −0.724961 −0.0462218
\(247\) 7.22425i 0.459668i
\(248\) 3.51530i 0.223222i
\(249\) 3.22425 0.204329
\(250\) −1.22662 1.78797i −0.0775785 0.113081i
\(251\) 19.2243 1.21342 0.606712 0.794922i \(-0.292488\pi\)
0.606712 + 0.794922i \(0.292488\pi\)
\(252\) 1.96239i 0.123619i
\(253\) 9.92478i 0.623965i
\(254\) −0.523730 −0.0328618
\(255\) −4.96239 5.61213i −0.310757 0.351445i
\(256\) 13.0752 0.817201
\(257\) 7.35026i 0.458497i −0.973368 0.229248i \(-0.926373\pi\)
0.973368 0.229248i \(-0.0736268\pi\)
\(258\) 2.44851i 0.152437i
\(259\) −0.775746 −0.0482025
\(260\) 4.43866 3.92478i 0.275274 0.243404i
\(261\) 7.92478 0.490531
\(262\) 4.00000i 0.247121i
\(263\) 12.9624i 0.799295i −0.916669 0.399648i \(-0.869133\pi\)
0.916669 0.399648i \(-0.130867\pi\)
\(264\) −1.53690 −0.0945899
\(265\) 14.3634 12.7005i 0.882339 0.780187i
\(266\) −1.03761 −0.0636200
\(267\) 1.03761i 0.0635008i
\(268\) 19.4763i 1.18970i
\(269\) −4.11142 −0.250678 −0.125339 0.992114i \(-0.540002\pi\)
−0.125339 + 0.992114i \(0.540002\pi\)
\(270\) −0.287258 0.324869i −0.0174819 0.0197709i
\(271\) −16.4241 −0.997691 −0.498846 0.866691i \(-0.666243\pi\)
−0.498846 + 0.866691i \(0.666243\pi\)
\(272\) 12.6497i 0.767003i
\(273\) 1.35026i 0.0817216i
\(274\) −4.36344 −0.263605
\(275\) −1.22425 + 9.92478i −0.0738253 + 0.598487i
\(276\) 9.73813 0.586167
\(277\) 11.0738i 0.665361i 0.943040 + 0.332680i \(0.107953\pi\)
−0.943040 + 0.332680i \(0.892047\pi\)
\(278\) 0.635150i 0.0380938i
\(279\) −4.57452 −0.273869
\(280\) −1.13823 1.28726i −0.0680221 0.0769284i
\(281\) 14.3733 0.857438 0.428719 0.903438i \(-0.358965\pi\)
0.428719 + 0.903438i \(0.358965\pi\)
\(282\) 1.92478i 0.114619i
\(283\) 1.14903i 0.0683028i 0.999417 + 0.0341514i \(0.0108728\pi\)
−0.999417 + 0.0341514i \(0.989127\pi\)
\(284\) 3.92478 0.232893
\(285\) 8.96239 7.92478i 0.530886 0.469423i
\(286\) 0.523730 0.0309688
\(287\) 3.73813i 0.220655i
\(288\) 2.26916i 0.133711i
\(289\) 5.77575 0.339750
\(290\) 2.57452 2.27645i 0.151181 0.133678i
\(291\) 18.4993 1.08445
\(292\) 18.3488i 1.07379i
\(293\) 0.649738i 0.0379581i 0.999820 + 0.0189791i \(0.00604158\pi\)
−0.999820 + 0.0189791i \(0.993958\pi\)
\(294\) 0.193937 0.0113106
\(295\) −12.7757 14.4485i −0.743833 0.841225i
\(296\) 0.596124 0.0346490
\(297\) 2.00000i 0.116052i
\(298\) 0.862728i 0.0499765i
\(299\) −6.70052 −0.387501
\(300\) 9.73813 + 1.20123i 0.562231 + 0.0693531i
\(301\) 12.6253 0.727710
\(302\) 0.252016i 0.0145019i
\(303\) 17.6629i 1.01471i
\(304\) −20.2012 −1.15862
\(305\) 12.8872 + 14.5745i 0.737917 + 0.834534i
\(306\) −0.649738 −0.0371431
\(307\) 24.1016i 1.37555i −0.725924 0.687775i \(-0.758588\pi\)
0.725924 0.687775i \(-0.241412\pi\)
\(308\) 3.92478i 0.223635i
\(309\) 6.70052 0.381179
\(310\) −1.48612 + 1.31406i −0.0844059 + 0.0746339i
\(311\) 8.25202 0.467929 0.233964 0.972245i \(-0.424830\pi\)
0.233964 + 0.972245i \(0.424830\pi\)
\(312\) 1.03761i 0.0587432i
\(313\) 14.9018i 0.842297i −0.906992 0.421148i \(-0.861627\pi\)
0.906992 0.421148i \(-0.138373\pi\)
\(314\) 0.513881 0.0290000
\(315\) −1.67513 + 1.48119i −0.0943829 + 0.0834558i
\(316\) −20.9986 −1.18126
\(317\) 10.1260i 0.568733i −0.958716 0.284367i \(-0.908217\pi\)
0.958716 0.284367i \(-0.0917833\pi\)
\(318\) 1.66291i 0.0932515i
\(319\) −15.8496 −0.887405
\(320\) −10.5334 11.9126i −0.588835 0.665932i
\(321\) −13.7381 −0.766788
\(322\) 0.962389i 0.0536318i
\(323\) 17.9248i 0.997361i
\(324\) 1.96239 0.109022
\(325\) −6.70052 0.826531i −0.371678 0.0458477i
\(326\) 1.02776 0.0569225
\(327\) 2.77575i 0.153499i
\(328\) 2.87258i 0.158612i
\(329\) 9.92478 0.547171
\(330\) 0.574515 + 0.649738i 0.0316260 + 0.0357669i
\(331\) 27.8496 1.53075 0.765375 0.643585i \(-0.222554\pi\)
0.765375 + 0.643585i \(0.222554\pi\)
\(332\) 6.32724i 0.347252i
\(333\) 0.775746i 0.0425106i
\(334\) 2.82179 0.154402
\(335\) −16.6253 + 14.7005i −0.908337 + 0.803175i
\(336\) 3.77575 0.205984
\(337\) 3.84955i 0.209699i 0.994488 + 0.104849i \(0.0334360\pi\)
−0.994488 + 0.104849i \(0.966564\pi\)
\(338\) 2.16759i 0.117901i
\(339\) 12.0508 0.654509
\(340\) 11.0132 9.73813i 0.597273 0.528125i
\(341\) 9.14903 0.495448
\(342\) 1.03761i 0.0561076i
\(343\) 1.00000i 0.0539949i
\(344\) −9.70194 −0.523093
\(345\) −7.35026 8.31265i −0.395725 0.447538i
\(346\) −0.872577 −0.0469101
\(347\) 9.58769i 0.514694i −0.966319 0.257347i \(-0.917152\pi\)
0.966319 0.257347i \(-0.0828484\pi\)
\(348\) 15.5515i 0.833648i
\(349\) 15.1490 0.810909 0.405455 0.914115i \(-0.367113\pi\)
0.405455 + 0.914115i \(0.367113\pi\)
\(350\) −0.118714 + 0.962389i −0.00634552 + 0.0514418i
\(351\) −1.35026 −0.0720716
\(352\) 4.53832i 0.241893i
\(353\) 20.3488i 1.08306i −0.840681 0.541530i \(-0.817845\pi\)
0.840681 0.541530i \(-0.182155\pi\)
\(354\) −1.67276 −0.0889063
\(355\) −2.96239 3.35026i −0.157227 0.177813i
\(356\) −2.03620 −0.107918
\(357\) 3.35026i 0.177315i
\(358\) 1.93937i 0.102499i
\(359\) 31.4010 1.65728 0.828642 0.559779i \(-0.189114\pi\)
0.828642 + 0.559779i \(0.189114\pi\)
\(360\) 1.28726 1.13823i 0.0678444 0.0599898i
\(361\) 9.62530 0.506595
\(362\) 2.06063i 0.108305i
\(363\) 7.00000i 0.367405i
\(364\) −2.64974 −0.138884
\(365\) −15.6629 + 13.8496i −0.819834 + 0.724919i
\(366\) 1.68735 0.0881992
\(367\) 29.4010i 1.53472i 0.641215 + 0.767361i \(0.278431\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(368\) 18.7367i 0.976719i
\(369\) −3.73813 −0.194600
\(370\) −0.222839 0.252016i −0.0115849 0.0131017i
\(371\) −8.57452 −0.445167
\(372\) 8.97698i 0.465435i
\(373\) 16.0000i 0.828449i 0.910175 + 0.414224i \(0.135947\pi\)
−0.910175 + 0.414224i \(0.864053\pi\)
\(374\) 1.29948 0.0671943
\(375\) −6.32487 9.21933i −0.326615 0.476084i
\(376\) −7.62672 −0.393318
\(377\) 10.7005i 0.551105i
\(378\) 0.193937i 0.00997502i
\(379\) −10.7005 −0.549649 −0.274824 0.961494i \(-0.588620\pi\)
−0.274824 + 0.961494i \(0.588620\pi\)
\(380\) 15.5515 + 17.5877i 0.797775 + 0.902229i
\(381\) −2.70052 −0.138352
\(382\) 2.68594i 0.137424i
\(383\) 16.7757i 0.857201i −0.903494 0.428600i \(-0.859007\pi\)
0.903494 0.428600i \(-0.140993\pi\)
\(384\) −5.91748 −0.301975
\(385\) 3.35026 2.96239i 0.170745 0.150977i
\(386\) 2.97224 0.151283
\(387\) 12.6253i 0.641780i
\(388\) 36.3028i 1.84300i
\(389\) 29.3258 1.48688 0.743439 0.668804i \(-0.233193\pi\)
0.743439 + 0.668804i \(0.233193\pi\)
\(390\) −0.438658 + 0.387873i −0.0222123 + 0.0196407i
\(391\) −16.6253 −0.840778
\(392\) 0.768452i 0.0388127i
\(393\) 20.6253i 1.04041i
\(394\) 0.111420 0.00561324
\(395\) 15.8496 + 17.9248i 0.797478 + 0.901893i
\(396\) −3.92478 −0.197227
\(397\) 18.3488i 0.920902i −0.887685 0.460451i \(-0.847688\pi\)
0.887685 0.460451i \(-0.152312\pi\)
\(398\) 0.0390260i 0.00195620i
\(399\) −5.35026 −0.267848
\(400\) −2.31124 + 18.7367i −0.115562 + 0.936836i
\(401\) −37.3258 −1.86396 −0.931981 0.362506i \(-0.881921\pi\)
−0.931981 + 0.362506i \(0.881921\pi\)
\(402\) 1.92478i 0.0959992i
\(403\) 6.17679i 0.307688i
\(404\) −34.6615 −1.72447
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) −1.53690 −0.0762753
\(407\) 1.55149i 0.0769046i
\(408\) 2.57452i 0.127458i
\(409\) 22.3733 1.10629 0.553144 0.833086i \(-0.313428\pi\)
0.553144 + 0.833086i \(0.313428\pi\)
\(410\) −1.21440 + 1.07381i −0.0599752 + 0.0530316i
\(411\) −22.4993 −1.10981
\(412\) 13.1490i 0.647806i
\(413\) 8.62530i 0.424423i
\(414\) −0.962389 −0.0472988
\(415\) 5.40105 4.77575i 0.265127 0.234432i
\(416\) 3.06396 0.150223
\(417\) 3.27504i 0.160379i
\(418\) 2.07522i 0.101502i
\(419\) −23.4763 −1.14689 −0.573445 0.819244i \(-0.694394\pi\)
−0.573445 + 0.819244i \(0.694394\pi\)
\(420\) −2.90668 3.28726i −0.141831 0.160402i
\(421\) −25.2243 −1.22935 −0.614677 0.788779i \(-0.710714\pi\)
−0.614677 + 0.788779i \(0.710714\pi\)
\(422\) 1.25060i 0.0608783i
\(423\) 9.92478i 0.482559i
\(424\) 6.58910 0.319995
\(425\) −16.6253 2.05079i −0.806446 0.0994777i
\(426\) −0.387873 −0.0187925
\(427\) 8.70052i 0.421048i
\(428\) 26.9596i 1.30314i
\(429\) 2.70052 0.130383
\(430\) 3.62672 + 4.10157i 0.174896 + 0.197795i
\(431\) −19.4010 −0.934516 −0.467258 0.884121i \(-0.654758\pi\)
−0.467258 + 0.884121i \(0.654758\pi\)
\(432\) 3.77575i 0.181661i
\(433\) 6.49929i 0.312336i 0.987731 + 0.156168i \(0.0499141\pi\)
−0.987731 + 0.156168i \(0.950086\pi\)
\(434\) 0.887166 0.0425853
\(435\) 13.2750 11.7381i 0.636489 0.562800i
\(436\) 5.44709 0.260868
\(437\) 26.5501i 1.27006i
\(438\) 1.81336i 0.0866456i
\(439\) 14.6497 0.699194 0.349597 0.936900i \(-0.386319\pi\)
0.349597 + 0.936900i \(0.386319\pi\)
\(440\) −2.57452 + 2.27645i −0.122735 + 0.108526i
\(441\) 1.00000 0.0476190
\(442\) 0.877317i 0.0417297i
\(443\) 19.1392i 0.909330i 0.890663 + 0.454665i \(0.150241\pi\)
−0.890663 + 0.454665i \(0.849759\pi\)
\(444\) 1.52232 0.0722459
\(445\) 1.53690 + 1.73813i 0.0728562 + 0.0823955i
\(446\) 0.300891 0.0142476
\(447\) 4.44851i 0.210407i
\(448\) 7.11142i 0.335983i
\(449\) 32.8021 1.54803 0.774013 0.633169i \(-0.218246\pi\)
0.774013 + 0.633169i \(0.218246\pi\)
\(450\) −0.962389 0.118714i −0.0453674 0.00559622i
\(451\) 7.47627 0.352044
\(452\) 23.6483i 1.11232i
\(453\) 1.29948i 0.0610547i
\(454\) 2.55008 0.119681
\(455\) 2.00000 + 2.26187i 0.0937614 + 0.106038i
\(456\) 4.11142 0.192535
\(457\) 18.7005i 0.874774i 0.899273 + 0.437387i \(0.144096\pi\)
−0.899273 + 0.437387i \(0.855904\pi\)
\(458\) 0.538319i 0.0251540i
\(459\) −3.35026 −0.156377
\(460\) 16.3127 14.4241i 0.760581 0.672526i
\(461\) −6.96239 −0.324271 −0.162135 0.986769i \(-0.551838\pi\)
−0.162135 + 0.986769i \(0.551838\pi\)
\(462\) 0.387873i 0.0180455i
\(463\) 5.29948i 0.246288i 0.992389 + 0.123144i \(0.0392976\pi\)
−0.992389 + 0.123144i \(0.960702\pi\)
\(464\) −29.9219 −1.38909
\(465\) −7.66291 + 6.77575i −0.355359 + 0.314218i
\(466\) −0.00984911 −0.000456251
\(467\) 13.1490i 0.608465i 0.952598 + 0.304232i \(0.0983999\pi\)
−0.952598 + 0.304232i \(0.901600\pi\)
\(468\) 2.64974i 0.122484i
\(469\) 9.92478 0.458284
\(470\) 2.85097 + 3.22425i 0.131505 + 0.148724i
\(471\) 2.64974 0.122093
\(472\) 6.62813i 0.305084i
\(473\) 25.2506i 1.16102i
\(474\) 2.07522 0.0953181
\(475\) 3.27504 26.5501i 0.150269 1.21820i
\(476\) −6.57452 −0.301342
\(477\) 8.57452i 0.392600i
\(478\) 1.13444i 0.0518882i
\(479\) −5.14903 −0.235265 −0.117633 0.993057i \(-0.537531\pi\)
−0.117633 + 0.993057i \(0.537531\pi\)
\(480\) 3.36107 + 3.80114i 0.153411 + 0.173497i
\(481\) −1.04746 −0.0477601
\(482\) 0.0145884i 0.000664486i
\(483\) 4.96239i 0.225797i
\(484\) −13.7367 −0.624396
\(485\) 30.9887 27.4010i 1.40713 1.24422i
\(486\) −0.193937 −0.00879714
\(487\) 22.1768i 1.00493i 0.864599 + 0.502463i \(0.167573\pi\)
−0.864599 + 0.502463i \(0.832427\pi\)
\(488\) 6.68594i 0.302658i
\(489\) 5.29948 0.239651
\(490\) 0.324869 0.287258i 0.0146761 0.0129770i
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 7.33567i 0.330718i
\(493\) 26.5501i 1.19576i
\(494\) −1.40105 −0.0630361
\(495\) 2.96239 + 3.35026i 0.133149 + 0.150583i
\(496\) 17.2722 0.775545
\(497\) 2.00000i 0.0897123i
\(498\) 0.625301i 0.0280204i
\(499\) 6.55008 0.293222 0.146611 0.989194i \(-0.453163\pi\)
0.146611 + 0.989194i \(0.453163\pi\)
\(500\) 18.0919 12.4119i 0.809095 0.555075i
\(501\) 14.5501 0.650050
\(502\) 3.72829i 0.166402i
\(503\) 8.77575i 0.391291i 0.980675 + 0.195646i \(0.0626802\pi\)
−0.980675 + 0.195646i \(0.937320\pi\)
\(504\) −0.768452 −0.0342296
\(505\) 26.1622 + 29.5877i 1.16420 + 1.31663i
\(506\) 1.92478 0.0855668
\(507\) 11.1768i 0.496379i
\(508\) 5.29948i 0.235126i
\(509\) −13.1392 −0.582384 −0.291192 0.956665i \(-0.594052\pi\)
−0.291192 + 0.956665i \(0.594052\pi\)
\(510\) −1.08840 + 0.962389i −0.0481950 + 0.0426153i
\(511\) 9.35026 0.413631
\(512\) 14.3707i 0.635103i
\(513\) 5.35026i 0.236220i
\(514\) −1.42548 −0.0628754
\(515\) 11.2243 9.92478i 0.494600 0.437338i
\(516\) −24.7757 −1.09069
\(517\) 19.8496i 0.872982i
\(518\) 0.150446i 0.00661020i
\(519\) −4.49929 −0.197497
\(520\) −1.53690 1.73813i −0.0673977 0.0762223i
\(521\) −37.6629 −1.65004 −0.825021 0.565102i \(-0.808837\pi\)
−0.825021 + 0.565102i \(0.808837\pi\)
\(522\) 1.53690i 0.0672685i
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) 40.4749 1.76815
\(525\) −0.612127 + 4.96239i −0.0267154 + 0.216576i
\(526\) −2.51388 −0.109610
\(527\) 15.3258i 0.667603i
\(528\) 7.55149i 0.328637i
\(529\) −1.62530 −0.0706652
\(530\) −2.46310 2.78560i −0.106990 0.120999i
\(531\) −8.62530 −0.374306
\(532\) 10.4993i 0.455202i
\(533\) 5.04746i 0.218630i
\(534\) 0.201231 0.00870811
\(535\) −23.0132 + 20.3488i −0.994946 + 0.879757i
\(536\) −7.62672 −0.329424
\(537\) 10.0000i 0.431532i
\(538\) 0.797355i 0.0343764i
\(539\) −2.00000 −0.0861461
\(540\) 3.28726 2.90668i 0.141461 0.125084i
\(541\) −22.4749 −0.966269 −0.483135 0.875546i \(-0.660502\pi\)
−0.483135 + 0.875546i \(0.660502\pi\)
\(542\) 3.18523i 0.136817i
\(543\) 10.6253i 0.455975i
\(544\) 7.60228 0.325945
\(545\) −4.11142 4.64974i −0.176114 0.199173i
\(546\) 0.261865 0.0112068
\(547\) 25.9248i 1.10846i 0.832362 + 0.554232i \(0.186988\pi\)
−0.832362 + 0.554232i \(0.813012\pi\)
\(548\) 44.1524i 1.88610i
\(549\) 8.70052 0.371329
\(550\) 1.92478 + 0.237428i 0.0820728 + 0.0101239i
\(551\) 42.3996 1.80629
\(552\) 3.81336i 0.162307i
\(553\) 10.7005i 0.455033i
\(554\) 2.14762 0.0912435
\(555\) −1.14903 1.29948i −0.0487736 0.0551597i
\(556\) 6.42690 0.272561
\(557\) 28.5256i 1.20867i 0.796730 + 0.604335i \(0.206561\pi\)
−0.796730 + 0.604335i \(0.793439\pi\)
\(558\) 0.887166i 0.0375567i
\(559\) 17.0475 0.721031
\(560\) 6.32487 5.59261i 0.267275 0.236331i
\(561\) 6.70052 0.282896
\(562\) 2.78751i 0.117584i
\(563\) 11.6267i 0.490008i −0.969522 0.245004i \(-0.921211\pi\)
0.969522 0.245004i \(-0.0787892\pi\)
\(564\) −19.4763 −0.820099
\(565\) 20.1866 17.8496i 0.849258 0.750936i
\(566\) 0.222839 0.00936663
\(567\) 1.00000i 0.0419961i
\(568\) 1.53690i 0.0644871i
\(569\) −9.32582 −0.390959 −0.195479 0.980708i \(-0.562626\pi\)
−0.195479 + 0.980708i \(0.562626\pi\)
\(570\) −1.53690 1.73813i −0.0643738 0.0728025i
\(571\) −19.6991 −0.824382 −0.412191 0.911097i \(-0.635236\pi\)
−0.412191 + 0.911097i \(0.635236\pi\)
\(572\) 5.29948i 0.221582i
\(573\) 13.8496i 0.578573i
\(574\) 0.724961 0.0302593
\(575\) −24.6253 3.03761i −1.02695 0.126677i
\(576\) −7.11142 −0.296309
\(577\) 32.7974i 1.36537i −0.730712 0.682686i \(-0.760812\pi\)
0.730712 0.682686i \(-0.239188\pi\)
\(578\) 1.12013i 0.0465912i
\(579\) 15.3258 0.636920
\(580\) 23.0348 + 26.0508i 0.956467 + 1.08170i
\(581\) −3.22425 −0.133765
\(582\) 3.58769i 0.148715i
\(583\) 17.1490i 0.710240i
\(584\) −7.18523 −0.297327
\(585\) −2.26187 + 2.00000i −0.0935166 + 0.0826898i
\(586\) 0.126008 0.00520534
\(587\) 18.8218i 0.776859i −0.921479 0.388429i \(-0.873018\pi\)
0.921479 0.388429i \(-0.126982\pi\)
\(588\) 1.96239i 0.0809275i
\(589\) −24.4749 −1.00847
\(590\) −2.80209 + 2.47768i −0.115360 + 0.102005i
\(591\) 0.574515 0.0236324
\(592\) 2.92902i 0.120382i
\(593\) 33.7499i 1.38594i 0.720965 + 0.692971i \(0.243699\pi\)
−0.720965 + 0.692971i \(0.756301\pi\)
\(594\) 0.387873 0.0159146
\(595\) 4.96239 + 5.61213i 0.203438 + 0.230075i
\(596\) 8.72970 0.357582
\(597\) 0.201231i 0.00823583i
\(598\) 1.29948i 0.0531395i
\(599\) 20.2981 0.829356 0.414678 0.909968i \(-0.363894\pi\)
0.414678 + 0.909968i \(0.363894\pi\)
\(600\) 0.470390 3.81336i 0.0192036 0.155680i
\(601\) −13.8496 −0.564935 −0.282468 0.959277i \(-0.591153\pi\)
−0.282468 + 0.959277i \(0.591153\pi\)
\(602\) 2.44851i 0.0997937i
\(603\) 9.92478i 0.404168i
\(604\) 2.55008 0.103761
\(605\) 10.3684 + 11.7259i 0.421534 + 0.476726i
\(606\) 3.42548 0.139151
\(607\) 25.2506i 1.02489i 0.858720 + 0.512445i \(0.171260\pi\)
−0.858720 + 0.512445i \(0.828740\pi\)
\(608\) 12.1406i 0.492366i
\(609\) −7.92478 −0.321128
\(610\) 2.82653 2.49929i 0.114443 0.101193i
\(611\) 13.4010 0.542148
\(612\) 6.57452i 0.265759i
\(613\) 9.14903i 0.369526i −0.982783 0.184763i \(-0.940848\pi\)
0.982783 0.184763i \(-0.0591517\pi\)
\(614\) −4.67418 −0.188634
\(615\) −6.26187 + 5.53690i −0.252503 + 0.223270i
\(616\) 1.53690 0.0619236
\(617\) 15.9492i 0.642091i −0.947064 0.321046i \(-0.895966\pi\)
0.947064 0.321046i \(-0.104034\pi\)
\(618\) 1.29948i 0.0522726i
\(619\) −11.1735 −0.449100 −0.224550 0.974463i \(-0.572091\pi\)
−0.224550 + 0.974463i \(0.572091\pi\)
\(620\) −13.2966 15.0376i −0.534006 0.603925i
\(621\) −4.96239 −0.199134
\(622\) 1.60037i 0.0641689i
\(623\) 1.03761i 0.0415710i
\(624\) 5.09825 0.204093
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) −2.89000 −0.115507
\(627\) 10.7005i 0.427338i
\(628\) 5.19982i 0.207495i
\(629\) −2.59895 −0.103627
\(630\) 0.287258 + 0.324869i 0.0114446 + 0.0129431i
\(631\) −14.5501 −0.579229 −0.289615 0.957143i \(-0.593527\pi\)
−0.289615 + 0.957143i \(0.593527\pi\)
\(632\) 8.22284i 0.327087i
\(633\) 6.44851i 0.256305i
\(634\) −1.96380 −0.0779926
\(635\) −4.52373 + 4.00000i −0.179519 + 0.158735i
\(636\) 16.8265 0.667215
\(637\) 1.35026i 0.0534993i
\(638\) 3.07381i 0.121693i
\(639\) −2.00000 −0.0791188
\(640\) −9.91256 + 8.76494i −0.391828 + 0.346465i
\(641\) −38.7269 −1.52962 −0.764810 0.644256i \(-0.777167\pi\)
−0.764810 + 0.644256i \(0.777167\pi\)
\(642\) 2.66433i 0.105153i
\(643\) 11.9511i 0.471306i −0.971837 0.235653i \(-0.924277\pi\)
0.971837 0.235653i \(-0.0757229\pi\)
\(644\) −9.73813 −0.383736
\(645\) 18.7005 + 21.1490i 0.736332 + 0.832742i
\(646\) −3.47627 −0.136772
\(647\) 14.5501i 0.572023i 0.958226 + 0.286011i \(0.0923295\pi\)
−0.958226 + 0.286011i \(0.907671\pi\)
\(648\) 0.768452i 0.0301876i
\(649\) 17.2506 0.677145
\(650\) −0.160295 + 1.29948i −0.00628727 + 0.0509697i
\(651\) 4.57452 0.179289
\(652\) 10.3996i 0.407281i
\(653\) 49.9756i 1.95569i 0.209319 + 0.977847i \(0.432875\pi\)
−0.209319 + 0.977847i \(0.567125\pi\)
\(654\) −0.538319 −0.0210499
\(655\) −30.5501 34.5501i −1.19369 1.34998i
\(656\) 14.1142 0.551069
\(657\) 9.35026i 0.364788i
\(658\) 1.92478i 0.0750356i
\(659\) 16.9525 0.660377 0.330189 0.943915i \(-0.392888\pi\)
0.330189 + 0.943915i \(0.392888\pi\)
\(660\) −6.57452 + 5.81336i −0.255913 + 0.226285i
\(661\) −15.6531 −0.608834 −0.304417 0.952539i \(-0.598462\pi\)
−0.304417 + 0.952539i \(0.598462\pi\)
\(662\) 5.40105i 0.209918i
\(663\) 4.52373i 0.175687i
\(664\) 2.47768 0.0961528
\(665\) −8.96239 + 7.92478i −0.347547 + 0.307310i
\(666\) −0.150446 −0.00582965
\(667\) 39.3258i 1.52270i
\(668\) 28.5529i 1.10475i
\(669\) 1.55149 0.0599842
\(670\) 2.85097 + 3.22425i 0.110143 + 0.124564i
\(671\) −17.4010 −0.671760
\(672\) 2.26916i 0.0875347i
\(673\) 26.0263i 1.00324i 0.865088 + 0.501621i \(0.167263\pi\)
−0.865088 + 0.501621i \(0.832737\pi\)
\(674\) 0.746569 0.0287568
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) 21.9332 0.843585
\(677\) 35.4518i 1.36252i 0.732039 + 0.681262i \(0.238569\pi\)
−0.732039 + 0.681262i \(0.761431\pi\)
\(678\) 2.33709i 0.0897553i
\(679\) −18.4993 −0.709938
\(680\) −3.81336 4.31265i −0.146236 0.165383i
\(681\) 13.1490 0.503872
\(682\) 1.77433i 0.0679427i
\(683\) 23.6629i 0.905436i −0.891654 0.452718i \(-0.850454\pi\)
0.891654 0.452718i \(-0.149546\pi\)
\(684\) 10.4993 0.401450
\(685\) −37.6893 + 33.3258i −1.44003 + 1.27331i
\(686\) −0.193937 −0.00740453
\(687\) 2.77575i 0.105901i
\(688\) 47.6699i 1.81740i
\(689\) −11.5778 −0.441081
\(690\) −1.61213 + 1.42548i −0.0613726 + 0.0542673i
\(691\) −0.574515 −0.0218556 −0.0109278 0.999940i \(-0.503478\pi\)
−0.0109278 + 0.999940i \(0.503478\pi\)
\(692\) 8.82936i 0.335642i
\(693\) 2.00000i 0.0759737i
\(694\) −1.85940 −0.0705820
\(695\) −4.85097 5.48612i −0.184008 0.208100i
\(696\) 6.08981 0.230834
\(697\) 12.5237i 0.474370i
\(698\) 2.93795i 0.111203i
\(699\) −0.0507852 −0.00192087
\(700\) −9.73813 1.20123i −0.368067 0.0454023i
\(701\) 42.7269 1.61377 0.806886 0.590707i \(-0.201151\pi\)
0.806886 + 0.590707i \(0.201151\pi\)
\(702\) 0.261865i 0.00988346i
\(703\) 4.15045i 0.156537i
\(704\) 14.2228 0.536043
\(705\) 14.7005 + 16.6253i 0.553654 + 0.626145i
\(706\) −3.94639 −0.148524
\(707\) 17.6629i 0.664282i
\(708\) 16.9262i 0.636125i
\(709\) −27.2506 −1.02342 −0.511709 0.859159i \(-0.670987\pi\)
−0.511709 + 0.859159i \(0.670987\pi\)
\(710\) −0.649738 + 0.574515i −0.0243842 + 0.0215612i
\(711\) 10.7005 0.401301
\(712\) 0.797355i 0.0298821i
\(713\) 22.7005i 0.850141i
\(714\) 0.649738 0.0243158
\(715\) 4.52373 4.00000i 0.169178 0.149592i
\(716\) −19.6239 −0.733379
\(717\) 5.84955i 0.218456i
\(718\) 6.08981i 0.227270i
\(719\) 10.7005 0.399062 0.199531 0.979891i \(-0.436058\pi\)
0.199531 + 0.979891i \(0.436058\pi\)
\(720\) 5.59261 + 6.32487i 0.208424 + 0.235714i
\(721\) −6.70052 −0.249541
\(722\) 1.86670i 0.0694713i
\(723\) 0.0752228i 0.00279757i
\(724\) 20.8510 0.774920
\(725\) 4.85097 39.3258i 0.180160 1.46052i
\(726\) 1.35756 0.0503836
\(727\) 39.9511i 1.48171i −0.671668 0.740853i \(-0.734422\pi\)
0.671668 0.740853i \(-0.265578\pi\)
\(728\) 1.03761i 0.0384564i
\(729\) −1.00000 −0.0370370
\(730\) 2.68594 + 3.03761i 0.0994109 + 0.112427i
\(731\) 42.2981 1.56445
\(732\) 17.0738i 0.631066i
\(733\) 30.3488i 1.12096i −0.828168 0.560480i \(-0.810617\pi\)
0.828168 0.560480i \(-0.189383\pi\)
\(734\) 5.70194 0.210462
\(735\) 1.67513 1.48119i 0.0617881 0.0546347i
\(736\) 11.2605 0.415066
\(737\) 19.8496i 0.731168i
\(738\) 0.724961i 0.0266862i
\(739\) −37.2506 −1.37029 −0.685143 0.728409i \(-0.740260\pi\)
−0.685143 + 0.728409i \(0.740260\pi\)
\(740\) 2.55008 2.25485i 0.0937427 0.0828898i
\(741\) −7.22425 −0.265390
\(742\) 1.66291i 0.0610474i
\(743\) 26.3634i 0.967181i 0.875294 + 0.483590i \(0.160668\pi\)
−0.875294 + 0.483590i \(0.839332\pi\)
\(744\) −3.51530 −0.128877
\(745\) −6.58910 7.45183i −0.241406 0.273014i
\(746\) 3.10299 0.113608
\(747\) 3.22425i 0.117969i
\(748\) 13.1490i 0.480776i
\(749\) 13.7381 0.501981
\(750\) −1.78797 + 1.22662i −0.0652873 + 0.0447900i
\(751\) 50.6516 1.84830 0.924152 0.382024i \(-0.124773\pi\)
0.924152 + 0.382024i \(0.124773\pi\)
\(752\) 37.4734i 1.36652i
\(753\) 19.2243i 0.700571i
\(754\) −2.07522 −0.0755752
\(755\) −1.92478 2.17679i −0.0700498 0.0792216i
\(756\) −1.96239 −0.0713714
\(757\) 38.9525i 1.41575i −0.706336 0.707877i \(-0.749653\pi\)
0.706336 0.707877i \(-0.250347\pi\)
\(758\) 2.07522i 0.0753755i
\(759\) 9.92478 0.360247
\(760\) 6.88717 6.08981i 0.249824 0.220901i
\(761\) 48.2130 1.74772 0.873860 0.486178i \(-0.161609\pi\)
0.873860 + 0.486178i \(0.161609\pi\)
\(762\) 0.523730i 0.0189727i
\(763\) 2.77575i 0.100489i
\(764\) −27.1782 −0.983273
\(765\) −5.61213 + 4.96239i −0.202907 + 0.179416i
\(766\) −3.25343 −0.117551
\(767\) 11.6464i 0.420528i
\(768\) 13.0752i 0.471811i
\(769\) −4.44851 −0.160417 −0.0802086 0.996778i \(-0.525559\pi\)
−0.0802086 + 0.996778i \(0.525559\pi\)
\(770\) −0.574515 0.649738i −0.0207041 0.0234149i
\(771\) −7.35026 −0.264713
\(772\) 30.0752i 1.08243i
\(773\) 39.3014i 1.41357i 0.707427 + 0.706786i \(0.249856\pi\)
−0.707427 + 0.706786i \(0.750144\pi\)
\(774\) 2.44851 0.0880098
\(775\) −2.80018 + 22.7005i −0.100586 + 0.815427i
\(776\) 14.2158 0.510318
\(777\) 0.775746i 0.0278297i
\(778\) 5.68735i 0.203901i
\(779\) −20.0000 −0.716574
\(780\) −3.92478 4.43866i −0.140530 0.158929i
\(781\) 4.00000 0.143131
\(782\) 3.22425i 0.115299i
\(783\) 7.92478i 0.283208i
\(784\) −3.77575 −0.134848
\(785\) 4.43866 3.92478i 0.158423 0.140081i
\(786\) −4.00000 −0.142675
\(787\) 0.897015i 0.0319751i −0.999872 0.0159876i \(-0.994911\pi\)
0.999872 0.0159876i \(-0.00508922\pi\)
\(788\) 1.12742i 0.0401628i
\(789\) −12.9624 −0.461473
\(790\) 3.47627 3.07381i 0.123680 0.109361i
\(791\) −12.0508