Properties

Label 570.2.d.d.229.3
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.3
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.d.229.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.17009 + 0.539189i) q^{5} +1.00000 q^{6} -1.07838i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.17009 + 0.539189i) q^{5} +1.00000 q^{6} -1.07838i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.539189 - 2.17009i) q^{10} +3.41855 q^{11} -1.00000i q^{12} +0.921622i q^{13} -1.07838 q^{14} +(-0.539189 + 2.17009i) q^{15} +1.00000 q^{16} +0.340173i q^{17} +1.00000i q^{18} +1.00000 q^{19} +(-2.17009 - 0.539189i) q^{20} +1.07838 q^{21} -3.41855i q^{22} +0.921622i q^{23} -1.00000 q^{24} +(4.41855 + 2.34017i) q^{25} +0.921622 q^{26} -1.00000i q^{27} +1.07838i q^{28} +1.41855 q^{29} +(2.17009 + 0.539189i) q^{30} +7.26180 q^{31} -1.00000i q^{32} +3.41855i q^{33} +0.340173 q^{34} +(0.581449 - 2.34017i) q^{35} +1.00000 q^{36} +5.60197i q^{37} -1.00000i q^{38} -0.921622 q^{39} +(-0.539189 + 2.17009i) q^{40} -1.07838 q^{41} -1.07838i q^{42} -0.738205i q^{43} -3.41855 q^{44} +(-2.17009 - 0.539189i) q^{45} +0.921622 q^{46} -7.75872i q^{47} +1.00000i q^{48} +5.83710 q^{49} +(2.34017 - 4.41855i) q^{50} -0.340173 q^{51} -0.921622i q^{52} -2.68035i q^{53} -1.00000 q^{54} +(7.41855 + 1.84324i) q^{55} +1.07838 q^{56} +1.00000i q^{57} -1.41855i q^{58} -8.34017 q^{59} +(0.539189 - 2.17009i) q^{60} +2.00000 q^{61} -7.26180i q^{62} +1.07838i q^{63} -1.00000 q^{64} +(-0.496928 + 2.00000i) q^{65} +3.41855 q^{66} -4.68035i q^{67} -0.340173i q^{68} -0.921622 q^{69} +(-2.34017 - 0.581449i) q^{70} -10.8371 q^{71} -1.00000i q^{72} +6.83710i q^{73} +5.60197 q^{74} +(-2.34017 + 4.41855i) q^{75} -1.00000 q^{76} -3.68649i q^{77} +0.921622i q^{78} -4.73820 q^{79} +(2.17009 + 0.539189i) q^{80} +1.00000 q^{81} +1.07838i q^{82} -11.0205i q^{83} -1.07838 q^{84} +(-0.183417 + 0.738205i) q^{85} -0.738205 q^{86} +1.41855i q^{87} +3.41855i q^{88} -9.75872 q^{89} +(-0.539189 + 2.17009i) q^{90} +0.993857 q^{91} -0.921622i q^{92} +7.26180i q^{93} -7.75872 q^{94} +(2.17009 + 0.539189i) q^{95} +1.00000 q^{96} +16.2557i q^{97} -5.83710i q^{98} -3.41855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} - 8q^{11} + 6q^{16} + 6q^{19} - 2q^{20} - 6q^{24} - 2q^{25} + 12q^{26} - 20q^{29} + 2q^{30} + 28q^{31} - 20q^{34} + 32q^{35} + 6q^{36} - 12q^{39} + 8q^{44} - 2q^{45} + 12q^{46} - 22q^{49} - 8q^{50} + 20q^{51} - 6q^{54} + 16q^{55} - 28q^{59} + 12q^{61} - 6q^{64} + 32q^{65} - 8q^{66} - 12q^{69} + 8q^{70} - 8q^{71} - 4q^{74} + 8q^{75} - 6q^{76} - 44q^{79} + 2q^{80} + 6q^{81} + 8q^{85} - 20q^{86} - 8q^{89} - 64q^{91} + 4q^{94} + 2q^{95} + 6q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) 1.00000 0.408248
\(7\) 1.07838i 0.407588i −0.979014 0.203794i \(-0.934673\pi\)
0.979014 0.203794i \(-0.0653274\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 0.539189 2.17009i 0.170506 0.686242i
\(11\) 3.41855 1.03073 0.515366 0.856970i \(-0.327656\pi\)
0.515366 + 0.856970i \(0.327656\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.921622i 0.255612i 0.991799 + 0.127806i \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(14\) −1.07838 −0.288209
\(15\) −0.539189 + 2.17009i −0.139218 + 0.560314i
\(16\) 1.00000 0.250000
\(17\) 0.340173i 0.0825041i 0.999149 + 0.0412520i \(0.0131347\pi\)
−0.999149 + 0.0412520i \(0.986865\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 0.229416
\(20\) −2.17009 0.539189i −0.485246 0.120566i
\(21\) 1.07838 0.235321
\(22\) 3.41855i 0.728837i
\(23\) 0.921622i 0.192172i 0.995373 + 0.0960858i \(0.0306323\pi\)
−0.995373 + 0.0960858i \(0.969368\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) 0.921622 0.180745
\(27\) 1.00000i 0.192450i
\(28\) 1.07838i 0.203794i
\(29\) 1.41855 0.263418 0.131709 0.991288i \(-0.457954\pi\)
0.131709 + 0.991288i \(0.457954\pi\)
\(30\) 2.17009 + 0.539189i 0.396202 + 0.0984420i
\(31\) 7.26180 1.30426 0.652128 0.758108i \(-0.273876\pi\)
0.652128 + 0.758108i \(0.273876\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.41855i 0.595093i
\(34\) 0.340173 0.0583392
\(35\) 0.581449 2.34017i 0.0982829 0.395561i
\(36\) 1.00000 0.166667
\(37\) 5.60197i 0.920958i 0.887671 + 0.460479i \(0.152322\pi\)
−0.887671 + 0.460479i \(0.847678\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −0.921622 −0.147578
\(40\) −0.539189 + 2.17009i −0.0852532 + 0.343121i
\(41\) −1.07838 −0.168414 −0.0842072 0.996448i \(-0.526836\pi\)
−0.0842072 + 0.996448i \(0.526836\pi\)
\(42\) 1.07838i 0.166397i
\(43\) 0.738205i 0.112575i −0.998415 0.0562876i \(-0.982074\pi\)
0.998415 0.0562876i \(-0.0179264\pi\)
\(44\) −3.41855 −0.515366
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) 0.921622 0.135886
\(47\) 7.75872i 1.13173i −0.824499 0.565863i \(-0.808543\pi\)
0.824499 0.565863i \(-0.191457\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.83710 0.833872
\(50\) 2.34017 4.41855i 0.330950 0.624877i
\(51\) −0.340173 −0.0476337
\(52\) 0.921622i 0.127806i
\(53\) 2.68035i 0.368174i −0.982910 0.184087i \(-0.941067\pi\)
0.982910 0.184087i \(-0.0589328\pi\)
\(54\) −1.00000 −0.136083
\(55\) 7.41855 + 1.84324i 1.00032 + 0.248543i
\(56\) 1.07838 0.144104
\(57\) 1.00000i 0.132453i
\(58\) 1.41855i 0.186265i
\(59\) −8.34017 −1.08580 −0.542899 0.839798i \(-0.682673\pi\)
−0.542899 + 0.839798i \(0.682673\pi\)
\(60\) 0.539189 2.17009i 0.0696090 0.280157i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 7.26180i 0.922249i
\(63\) 1.07838i 0.135863i
\(64\) −1.00000 −0.125000
\(65\) −0.496928 + 2.00000i −0.0616364 + 0.248069i
\(66\) 3.41855 0.420795
\(67\) 4.68035i 0.571795i −0.958260 0.285898i \(-0.907708\pi\)
0.958260 0.285898i \(-0.0922917\pi\)
\(68\) 0.340173i 0.0412520i
\(69\) −0.921622 −0.110950
\(70\) −2.34017 0.581449i −0.279704 0.0694965i
\(71\) −10.8371 −1.28613 −0.643064 0.765813i \(-0.722337\pi\)
−0.643064 + 0.765813i \(0.722337\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 6.83710i 0.800222i 0.916467 + 0.400111i \(0.131028\pi\)
−0.916467 + 0.400111i \(0.868972\pi\)
\(74\) 5.60197 0.651216
\(75\) −2.34017 + 4.41855i −0.270220 + 0.510210i
\(76\) −1.00000 −0.114708
\(77\) 3.68649i 0.420114i
\(78\) 0.921622i 0.104353i
\(79\) −4.73820 −0.533090 −0.266545 0.963823i \(-0.585882\pi\)
−0.266545 + 0.963823i \(0.585882\pi\)
\(80\) 2.17009 + 0.539189i 0.242623 + 0.0602831i
\(81\) 1.00000 0.111111
\(82\) 1.07838i 0.119087i
\(83\) 11.0205i 1.20966i −0.796355 0.604830i \(-0.793241\pi\)
0.796355 0.604830i \(-0.206759\pi\)
\(84\) −1.07838 −0.117661
\(85\) −0.183417 + 0.738205i −0.0198944 + 0.0800695i
\(86\) −0.738205 −0.0796027
\(87\) 1.41855i 0.152085i
\(88\) 3.41855i 0.364419i
\(89\) −9.75872 −1.03442 −0.517211 0.855858i \(-0.673030\pi\)
−0.517211 + 0.855858i \(0.673030\pi\)
\(90\) −0.539189 + 2.17009i −0.0568355 + 0.228747i
\(91\) 0.993857 0.104185
\(92\) 0.921622i 0.0960858i
\(93\) 7.26180i 0.753013i
\(94\) −7.75872 −0.800251
\(95\) 2.17009 + 0.539189i 0.222646 + 0.0553196i
\(96\) 1.00000 0.102062
\(97\) 16.2557i 1.65051i 0.564759 + 0.825256i \(0.308969\pi\)
−0.564759 + 0.825256i \(0.691031\pi\)
\(98\) 5.83710i 0.589636i
\(99\) −3.41855 −0.343577
\(100\) −4.41855 2.34017i −0.441855 0.234017i
\(101\) −13.0205 −1.29559 −0.647795 0.761815i \(-0.724309\pi\)
−0.647795 + 0.761815i \(0.724309\pi\)
\(102\) 0.340173i 0.0336821i
\(103\) 14.3402i 1.41298i −0.707723 0.706490i \(-0.750278\pi\)
0.707723 0.706490i \(-0.249722\pi\)
\(104\) −0.921622 −0.0903725
\(105\) 2.34017 + 0.581449i 0.228377 + 0.0567436i
\(106\) −2.68035 −0.260338
\(107\) 10.8371i 1.04766i −0.851822 0.523831i \(-0.824502\pi\)
0.851822 0.523831i \(-0.175498\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −18.6225 −1.78371 −0.891855 0.452321i \(-0.850596\pi\)
−0.891855 + 0.452321i \(0.850596\pi\)
\(110\) 1.84324 7.41855i 0.175746 0.707331i
\(111\) −5.60197 −0.531715
\(112\) 1.07838i 0.101897i
\(113\) 13.5174i 1.27161i 0.771848 + 0.635807i \(0.219333\pi\)
−0.771848 + 0.635807i \(0.780667\pi\)
\(114\) 1.00000 0.0936586
\(115\) −0.496928 + 2.00000i −0.0463388 + 0.186501i
\(116\) −1.41855 −0.131709
\(117\) 0.921622i 0.0852040i
\(118\) 8.34017i 0.767775i
\(119\) 0.366835 0.0336277
\(120\) −2.17009 0.539189i −0.198101 0.0492210i
\(121\) 0.686489 0.0624081
\(122\) 2.00000i 0.181071i
\(123\) 1.07838i 0.0972340i
\(124\) −7.26180 −0.652128
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) 1.07838 0.0960695
\(127\) 16.4969i 1.46387i 0.681377 + 0.731933i \(0.261382\pi\)
−0.681377 + 0.731933i \(0.738618\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.738205 0.0649953
\(130\) 2.00000 + 0.496928i 0.175412 + 0.0435835i
\(131\) 0.581449 0.0508015 0.0254007 0.999677i \(-0.491914\pi\)
0.0254007 + 0.999677i \(0.491914\pi\)
\(132\) 3.41855i 0.297547i
\(133\) 1.07838i 0.0935072i
\(134\) −4.68035 −0.404320
\(135\) 0.539189 2.17009i 0.0464060 0.186771i
\(136\) −0.340173 −0.0291696
\(137\) 5.81658i 0.496944i −0.968639 0.248472i \(-0.920072\pi\)
0.968639 0.248472i \(-0.0799284\pi\)
\(138\) 0.921622i 0.0784537i
\(139\) −6.15676 −0.522209 −0.261105 0.965311i \(-0.584087\pi\)
−0.261105 + 0.965311i \(0.584087\pi\)
\(140\) −0.581449 + 2.34017i −0.0491414 + 0.197781i
\(141\) 7.75872 0.653402
\(142\) 10.8371i 0.909429i
\(143\) 3.15061i 0.263467i
\(144\) −1.00000 −0.0833333
\(145\) 3.07838 + 0.764867i 0.255645 + 0.0635187i
\(146\) 6.83710 0.565843
\(147\) 5.83710i 0.481436i
\(148\) 5.60197i 0.460479i
\(149\) −8.34017 −0.683254 −0.341627 0.939836i \(-0.610978\pi\)
−0.341627 + 0.939836i \(0.610978\pi\)
\(150\) 4.41855 + 2.34017i 0.360773 + 0.191074i
\(151\) 16.2557 1.32287 0.661433 0.750004i \(-0.269949\pi\)
0.661433 + 0.750004i \(0.269949\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 0.340173i 0.0275014i
\(154\) −3.68649 −0.297066
\(155\) 15.7587 + 3.91548i 1.26577 + 0.314499i
\(156\) 0.921622 0.0737888
\(157\) 3.65983i 0.292086i 0.989278 + 0.146043i \(0.0466538\pi\)
−0.989278 + 0.146043i \(0.953346\pi\)
\(158\) 4.73820i 0.376951i
\(159\) 2.68035 0.212565
\(160\) 0.539189 2.17009i 0.0426266 0.171560i
\(161\) 0.993857 0.0783269
\(162\) 1.00000i 0.0785674i
\(163\) 6.89496i 0.540055i −0.962853 0.270027i \(-0.912967\pi\)
0.962853 0.270027i \(-0.0870328\pi\)
\(164\) 1.07838 0.0842072
\(165\) −1.84324 + 7.41855i −0.143496 + 0.577533i
\(166\) −11.0205 −0.855358
\(167\) 4.68035i 0.362176i −0.983467 0.181088i \(-0.942038\pi\)
0.983467 0.181088i \(-0.0579619\pi\)
\(168\) 1.07838i 0.0831986i
\(169\) 12.1506 0.934662
\(170\) 0.738205 + 0.183417i 0.0566177 + 0.0140675i
\(171\) −1.00000 −0.0764719
\(172\) 0.738205i 0.0562876i
\(173\) 4.52359i 0.343922i 0.985104 + 0.171961i \(0.0550103\pi\)
−0.985104 + 0.171961i \(0.944990\pi\)
\(174\) 1.41855 0.107540
\(175\) 2.52359 4.76487i 0.190766 0.360190i
\(176\) 3.41855 0.257683
\(177\) 8.34017i 0.626886i
\(178\) 9.75872i 0.731447i
\(179\) −14.4969 −1.08355 −0.541776 0.840523i \(-0.682248\pi\)
−0.541776 + 0.840523i \(0.682248\pi\)
\(180\) 2.17009 + 0.539189i 0.161749 + 0.0401888i
\(181\) −12.7792 −0.949874 −0.474937 0.880020i \(-0.657529\pi\)
−0.474937 + 0.880020i \(0.657529\pi\)
\(182\) 0.993857i 0.0736696i
\(183\) 2.00000i 0.147844i
\(184\) −0.921622 −0.0679429
\(185\) −3.02052 + 12.1568i −0.222073 + 0.893782i
\(186\) 7.26180 0.532461
\(187\) 1.16290i 0.0850396i
\(188\) 7.75872i 0.565863i
\(189\) −1.07838 −0.0784404
\(190\) 0.539189 2.17009i 0.0391169 0.157435i
\(191\) −4.39803 −0.318230 −0.159115 0.987260i \(-0.550864\pi\)
−0.159115 + 0.987260i \(0.550864\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 24.6225i 1.77237i −0.463336 0.886183i \(-0.653348\pi\)
0.463336 0.886183i \(-0.346652\pi\)
\(194\) 16.2557 1.16709
\(195\) −2.00000 0.496928i −0.143223 0.0355858i
\(196\) −5.83710 −0.416936
\(197\) 3.91548i 0.278966i −0.990224 0.139483i \(-0.955456\pi\)
0.990224 0.139483i \(-0.0445441\pi\)
\(198\) 3.41855i 0.242946i
\(199\) −8.99386 −0.637558 −0.318779 0.947829i \(-0.603273\pi\)
−0.318779 + 0.947829i \(0.603273\pi\)
\(200\) −2.34017 + 4.41855i −0.165475 + 0.312439i
\(201\) 4.68035 0.330126
\(202\) 13.0205i 0.916121i
\(203\) 1.52973i 0.107366i
\(204\) 0.340173 0.0238169
\(205\) −2.34017 0.581449i −0.163445 0.0406102i
\(206\) −14.3402 −0.999127
\(207\) 0.921622i 0.0640572i
\(208\) 0.921622i 0.0639030i
\(209\) 3.41855 0.236466
\(210\) 0.581449 2.34017i 0.0401238 0.161487i
\(211\) −4.68035 −0.322208 −0.161104 0.986937i \(-0.551506\pi\)
−0.161104 + 0.986937i \(0.551506\pi\)
\(212\) 2.68035i 0.184087i
\(213\) 10.8371i 0.742546i
\(214\) −10.8371 −0.740809
\(215\) 0.398032 1.60197i 0.0271455 0.109253i
\(216\) 1.00000 0.0680414
\(217\) 7.83096i 0.531600i
\(218\) 18.6225i 1.26127i
\(219\) −6.83710 −0.462009
\(220\) −7.41855 1.84324i −0.500159 0.124272i
\(221\) −0.313511 −0.0210890
\(222\) 5.60197i 0.375979i
\(223\) 14.3402i 0.960289i −0.877189 0.480145i \(-0.840584\pi\)
0.877189 0.480145i \(-0.159416\pi\)
\(224\) −1.07838 −0.0720521
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 13.5174 0.899167
\(227\) 19.2039i 1.27461i 0.770612 + 0.637305i \(0.219951\pi\)
−0.770612 + 0.637305i \(0.780049\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) −2.31351 −0.152881 −0.0764406 0.997074i \(-0.524356\pi\)
−0.0764406 + 0.997074i \(0.524356\pi\)
\(230\) 2.00000 + 0.496928i 0.131876 + 0.0327665i
\(231\) 3.68649 0.242553
\(232\) 1.41855i 0.0931324i
\(233\) 25.6475i 1.68023i −0.542411 0.840113i \(-0.682489\pi\)
0.542411 0.840113i \(-0.317511\pi\)
\(234\) −0.921622 −0.0602483
\(235\) 4.18342 16.8371i 0.272896 1.09833i
\(236\) 8.34017 0.542899
\(237\) 4.73820i 0.307779i
\(238\) 0.366835i 0.0237784i
\(239\) −3.60197 −0.232992 −0.116496 0.993191i \(-0.537166\pi\)
−0.116496 + 0.993191i \(0.537166\pi\)
\(240\) −0.539189 + 2.17009i −0.0348045 + 0.140078i
\(241\) −2.36683 −0.152461 −0.0762306 0.997090i \(-0.524289\pi\)
−0.0762306 + 0.997090i \(0.524289\pi\)
\(242\) 0.686489i 0.0441292i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) 12.6670 + 3.14730i 0.809266 + 0.201074i
\(246\) −1.07838 −0.0687549
\(247\) 0.921622i 0.0586414i
\(248\) 7.26180i 0.461124i
\(249\) 11.0205 0.698397
\(250\) 7.46081 8.32684i 0.471863 0.526636i
\(251\) 6.73820 0.425312 0.212656 0.977127i \(-0.431789\pi\)
0.212656 + 0.977127i \(0.431789\pi\)
\(252\) 1.07838i 0.0679314i
\(253\) 3.15061i 0.198077i
\(254\) 16.4969 1.03511
\(255\) −0.738205 0.183417i −0.0462282 0.0114860i
\(256\) 1.00000 0.0625000
\(257\) 9.20394i 0.574126i 0.957912 + 0.287063i \(0.0926789\pi\)
−0.957912 + 0.287063i \(0.907321\pi\)
\(258\) 0.738205i 0.0459586i
\(259\) 6.04104 0.375372
\(260\) 0.496928 2.00000i 0.0308182 0.124035i
\(261\) −1.41855 −0.0878061
\(262\) 0.581449i 0.0359221i
\(263\) 25.7998i 1.59088i −0.606031 0.795441i \(-0.707239\pi\)
0.606031 0.795441i \(-0.292761\pi\)
\(264\) −3.41855 −0.210397
\(265\) 1.44521 5.81658i 0.0887787 0.357310i
\(266\) −1.07838 −0.0661196
\(267\) 9.75872i 0.597224i
\(268\) 4.68035i 0.285898i
\(269\) −4.73820 −0.288893 −0.144447 0.989513i \(-0.546140\pi\)
−0.144447 + 0.989513i \(0.546140\pi\)
\(270\) −2.17009 0.539189i −0.132067 0.0328140i
\(271\) 16.3668 0.994214 0.497107 0.867689i \(-0.334396\pi\)
0.497107 + 0.867689i \(0.334396\pi\)
\(272\) 0.340173i 0.0206260i
\(273\) 0.993857i 0.0601510i
\(274\) −5.81658 −0.351393
\(275\) 15.1050 + 8.00000i 0.910868 + 0.482418i
\(276\) 0.921622 0.0554751
\(277\) 12.6537i 0.760286i 0.924928 + 0.380143i \(0.124125\pi\)
−0.924928 + 0.380143i \(0.875875\pi\)
\(278\) 6.15676i 0.369258i
\(279\) −7.26180 −0.434752
\(280\) 2.34017 + 0.581449i 0.139852 + 0.0347482i
\(281\) 9.44521 0.563454 0.281727 0.959495i \(-0.409093\pi\)
0.281727 + 0.959495i \(0.409093\pi\)
\(282\) 7.75872i 0.462025i
\(283\) 15.8888i 0.944492i −0.881467 0.472246i \(-0.843443\pi\)
0.881467 0.472246i \(-0.156557\pi\)
\(284\) 10.8371 0.643064
\(285\) −0.539189 + 2.17009i −0.0319388 + 0.128545i
\(286\) 3.15061 0.186300
\(287\) 1.16290i 0.0686437i
\(288\) 1.00000i 0.0589256i
\(289\) 16.8843 0.993193
\(290\) 0.764867 3.07838i 0.0449145 0.180769i
\(291\) −16.2557 −0.952923
\(292\) 6.83710i 0.400111i
\(293\) 4.47027i 0.261156i −0.991438 0.130578i \(-0.958317\pi\)
0.991438 0.130578i \(-0.0416833\pi\)
\(294\) 5.83710 0.340427
\(295\) −18.0989 4.49693i −1.05376 0.261821i
\(296\) −5.60197 −0.325608
\(297\) 3.41855i 0.198364i
\(298\) 8.34017i 0.483133i
\(299\) −0.849388 −0.0491214
\(300\) 2.34017 4.41855i 0.135110 0.255105i
\(301\) −0.796064 −0.0458843
\(302\) 16.2557i 0.935408i
\(303\) 13.0205i 0.748009i
\(304\) 1.00000 0.0573539
\(305\) 4.34017 + 1.07838i 0.248518 + 0.0617477i
\(306\) −0.340173 −0.0194464
\(307\) 15.3197i 0.874339i 0.899379 + 0.437169i \(0.144019\pi\)
−0.899379 + 0.437169i \(0.855981\pi\)
\(308\) 3.68649i 0.210057i
\(309\) 14.3402 0.815784
\(310\) 3.91548 15.7587i 0.222384 0.895035i
\(311\) −4.39803 −0.249390 −0.124695 0.992195i \(-0.539795\pi\)
−0.124695 + 0.992195i \(0.539795\pi\)
\(312\) 0.921622i 0.0521766i
\(313\) 8.31351i 0.469907i −0.972007 0.234954i \(-0.924506\pi\)
0.972007 0.234954i \(-0.0754939\pi\)
\(314\) 3.65983 0.206536
\(315\) −0.581449 + 2.34017i −0.0327610 + 0.131854i
\(316\) 4.73820 0.266545
\(317\) 0.470266i 0.0264128i 0.999913 + 0.0132064i \(0.00420385\pi\)
−0.999913 + 0.0132064i \(0.995796\pi\)
\(318\) 2.68035i 0.150306i
\(319\) 4.84939 0.271514
\(320\) −2.17009 0.539189i −0.121312 0.0301416i
\(321\) 10.8371 0.604868
\(322\) 0.993857i 0.0553855i
\(323\) 0.340173i 0.0189277i
\(324\) −1.00000 −0.0555556
\(325\) −2.15676 + 4.07223i −0.119635 + 0.225887i
\(326\) −6.89496 −0.381877
\(327\) 18.6225i 1.02983i
\(328\) 1.07838i 0.0595435i
\(329\) −8.36683 −0.461279
\(330\) 7.41855 + 1.84324i 0.408378 + 0.101467i
\(331\) 31.5174 1.73236 0.866178 0.499736i \(-0.166570\pi\)
0.866178 + 0.499736i \(0.166570\pi\)
\(332\) 11.0205i 0.604830i
\(333\) 5.60197i 0.306986i
\(334\) −4.68035 −0.256097
\(335\) 2.52359 10.1568i 0.137878 0.554923i
\(336\) 1.07838 0.0588303
\(337\) 0.0578588i 0.00315177i 0.999999 + 0.00157589i \(0.000501620\pi\)
−0.999999 + 0.00157589i \(0.999498\pi\)
\(338\) 12.1506i 0.660906i
\(339\) −13.5174 −0.734167
\(340\) 0.183417 0.738205i 0.00994721 0.0400348i
\(341\) 24.8248 1.34434
\(342\) 1.00000i 0.0540738i
\(343\) 13.8432i 0.747465i
\(344\) 0.738205 0.0398013
\(345\) −2.00000 0.496928i −0.107676 0.0267537i
\(346\) 4.52359 0.243190
\(347\) 6.34017i 0.340358i −0.985413 0.170179i \(-0.945565\pi\)
0.985413 0.170179i \(-0.0544346\pi\)
\(348\) 1.41855i 0.0760423i
\(349\) 20.5236 1.09860 0.549301 0.835624i \(-0.314894\pi\)
0.549301 + 0.835624i \(0.314894\pi\)
\(350\) −4.76487 2.52359i −0.254693 0.134892i
\(351\) 0.921622 0.0491926
\(352\) 3.41855i 0.182209i
\(353\) 22.3812i 1.19123i 0.803269 + 0.595616i \(0.203092\pi\)
−0.803269 + 0.595616i \(0.796908\pi\)
\(354\) −8.34017 −0.443275
\(355\) −23.5174 5.84324i −1.24818 0.310127i
\(356\) 9.75872 0.517211
\(357\) 0.366835i 0.0194150i
\(358\) 14.4969i 0.766186i
\(359\) 0.282314 0.0149000 0.00744999 0.999972i \(-0.497629\pi\)
0.00744999 + 0.999972i \(0.497629\pi\)
\(360\) 0.539189 2.17009i 0.0284177 0.114374i
\(361\) 1.00000 0.0526316
\(362\) 12.7792i 0.671662i
\(363\) 0.686489i 0.0360313i
\(364\) −0.993857 −0.0520923
\(365\) −3.68649 + 14.8371i −0.192960 + 0.776609i
\(366\) 2.00000 0.104542
\(367\) 27.9155i 1.45718i 0.684952 + 0.728588i \(0.259823\pi\)
−0.684952 + 0.728588i \(0.740177\pi\)
\(368\) 0.921622i 0.0480429i
\(369\) 1.07838 0.0561381
\(370\) 12.1568 + 3.02052i 0.632000 + 0.157029i
\(371\) −2.89043 −0.150063
\(372\) 7.26180i 0.376507i
\(373\) 3.44521i 0.178386i −0.996014 0.0891932i \(-0.971571\pi\)
0.996014 0.0891932i \(-0.0284288\pi\)
\(374\) 1.16290 0.0601321
\(375\) −7.46081 + 8.32684i −0.385275 + 0.429996i
\(376\) 7.75872 0.400126
\(377\) 1.30737i 0.0673329i
\(378\) 1.07838i 0.0554658i
\(379\) 28.5113 1.46453 0.732264 0.681021i \(-0.238464\pi\)
0.732264 + 0.681021i \(0.238464\pi\)
\(380\) −2.17009 0.539189i −0.111323 0.0276598i
\(381\) −16.4969 −0.845163
\(382\) 4.39803i 0.225023i
\(383\) 2.63931i 0.134862i −0.997724 0.0674312i \(-0.978520\pi\)
0.997724 0.0674312i \(-0.0214803\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 1.98771 8.00000i 0.101303 0.407718i
\(386\) −24.6225 −1.25325
\(387\) 0.738205i 0.0375251i
\(388\) 16.2557i 0.825256i
\(389\) 22.1834 1.12474 0.562372 0.826884i \(-0.309889\pi\)
0.562372 + 0.826884i \(0.309889\pi\)
\(390\) −0.496928 + 2.00000i −0.0251630 + 0.101274i
\(391\) −0.313511 −0.0158549
\(392\) 5.83710i 0.294818i
\(393\) 0.581449i 0.0293302i
\(394\) −3.91548 −0.197259
\(395\) −10.2823 2.55479i −0.517359 0.128545i
\(396\) 3.41855 0.171789
\(397\) 24.2245i 1.21579i 0.794017 + 0.607895i \(0.207986\pi\)
−0.794017 + 0.607895i \(0.792014\pi\)
\(398\) 8.99386i 0.450821i
\(399\) 1.07838 0.0539864
\(400\) 4.41855 + 2.34017i 0.220928 + 0.117009i
\(401\) 12.7649 0.637447 0.318724 0.947848i \(-0.396746\pi\)
0.318724 + 0.947848i \(0.396746\pi\)
\(402\) 4.68035i 0.233434i
\(403\) 6.69263i 0.333384i
\(404\) 13.0205 0.647795
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) −1.52973 −0.0759194
\(407\) 19.1506i 0.949261i
\(408\) 0.340173i 0.0168411i
\(409\) −22.8781 −1.13125 −0.565626 0.824662i \(-0.691365\pi\)
−0.565626 + 0.824662i \(0.691365\pi\)
\(410\) −0.581449 + 2.34017i −0.0287157 + 0.115573i
\(411\) 5.81658 0.286911
\(412\) 14.3402i 0.706490i
\(413\) 8.99386i 0.442559i
\(414\) −0.921622 −0.0452953
\(415\) 5.94214 23.9155i 0.291688 1.17396i
\(416\) 0.921622 0.0451862
\(417\) 6.15676i 0.301498i
\(418\) 3.41855i 0.167207i
\(419\) −3.47187 −0.169612 −0.0848061 0.996397i \(-0.527027\pi\)
−0.0848061 + 0.996397i \(0.527027\pi\)
\(420\) −2.34017 0.581449i −0.114189 0.0283718i
\(421\) −20.4657 −0.997439 −0.498719 0.866764i \(-0.666196\pi\)
−0.498719 + 0.866764i \(0.666196\pi\)
\(422\) 4.68035i 0.227836i
\(423\) 7.75872i 0.377242i
\(424\) 2.68035 0.130169
\(425\) −0.796064 + 1.50307i −0.0386148 + 0.0729097i
\(426\) −10.8371 −0.525059
\(427\) 2.15676i 0.104373i
\(428\) 10.8371i 0.523831i
\(429\) −3.15061 −0.152113
\(430\) −1.60197 0.398032i −0.0772538 0.0191948i
\(431\) −33.1917 −1.59879 −0.799393 0.600809i \(-0.794845\pi\)
−0.799393 + 0.600809i \(0.794845\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 41.1338i 1.97676i 0.151991 + 0.988382i \(0.451432\pi\)
−0.151991 + 0.988382i \(0.548568\pi\)
\(434\) −7.83096 −0.375898
\(435\) −0.764867 + 3.07838i −0.0366726 + 0.147597i
\(436\) 18.6225 0.891855
\(437\) 0.921622i 0.0440872i
\(438\) 6.83710i 0.326689i
\(439\) −19.1461 −0.913792 −0.456896 0.889520i \(-0.651039\pi\)
−0.456896 + 0.889520i \(0.651039\pi\)
\(440\) −1.84324 + 7.41855i −0.0878732 + 0.353666i
\(441\) −5.83710 −0.277957
\(442\) 0.313511i 0.0149122i
\(443\) 37.4908i 1.78124i 0.454747 + 0.890620i \(0.349730\pi\)
−0.454747 + 0.890620i \(0.650270\pi\)
\(444\) 5.60197 0.265858
\(445\) −21.1773 5.26180i −1.00390 0.249433i
\(446\) −14.3402 −0.679027
\(447\) 8.34017i 0.394477i
\(448\) 1.07838i 0.0509486i
\(449\) −6.43907 −0.303878 −0.151939 0.988390i \(-0.548552\pi\)
−0.151939 + 0.988390i \(0.548552\pi\)
\(450\) −2.34017 + 4.41855i −0.110317 + 0.208292i
\(451\) −3.68649 −0.173590
\(452\) 13.5174i 0.635807i
\(453\) 16.2557i 0.763757i
\(454\) 19.2039 0.901285
\(455\) 2.15676 + 0.535877i 0.101110 + 0.0251223i
\(456\) −1.00000 −0.0468293
\(457\) 13.6742i 0.639652i −0.947476 0.319826i \(-0.896376\pi\)
0.947476 0.319826i \(-0.103624\pi\)
\(458\) 2.31351i 0.108103i
\(459\) 0.340173 0.0158779
\(460\) 0.496928 2.00000i 0.0231694 0.0932505i
\(461\) 27.5441 1.28286 0.641429 0.767183i \(-0.278342\pi\)
0.641429 + 0.767183i \(0.278342\pi\)
\(462\) 3.68649i 0.171511i
\(463\) 28.5958i 1.32896i −0.747306 0.664480i \(-0.768653\pi\)
0.747306 0.664480i \(-0.231347\pi\)
\(464\) 1.41855 0.0658546
\(465\) −3.91548 + 15.7587i −0.181576 + 0.730793i
\(466\) −25.6475 −1.18810
\(467\) 35.5318i 1.64422i 0.569331 + 0.822108i \(0.307202\pi\)
−0.569331 + 0.822108i \(0.692798\pi\)
\(468\) 0.921622i 0.0426020i
\(469\) −5.04718 −0.233057
\(470\) −16.8371 4.18342i −0.776638 0.192967i
\(471\) −3.65983 −0.168636
\(472\) 8.34017i 0.383888i
\(473\) 2.52359i 0.116035i
\(474\) −4.73820 −0.217633
\(475\) 4.41855 + 2.34017i 0.202737 + 0.107375i
\(476\) −0.366835 −0.0168139
\(477\) 2.68035i 0.122725i
\(478\) 3.60197i 0.164750i
\(479\) −24.6491 −1.12625 −0.563124 0.826372i \(-0.690401\pi\)
−0.563124 + 0.826372i \(0.690401\pi\)
\(480\) 2.17009 + 0.539189i 0.0990504 + 0.0246105i
\(481\) −5.16290 −0.235408
\(482\) 2.36683i 0.107806i
\(483\) 0.993857i 0.0452221i
\(484\) −0.686489 −0.0312040
\(485\) −8.76487 + 35.2762i −0.397992 + 1.60181i
\(486\) 1.00000 0.0453609
\(487\) 15.3340i 0.694851i −0.937708 0.347426i \(-0.887056\pi\)
0.937708 0.347426i \(-0.112944\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 6.89496 0.311801
\(490\) 3.14730 12.6670i 0.142181 0.572237i
\(491\) −32.7792 −1.47931 −0.739653 0.672988i \(-0.765010\pi\)
−0.739653 + 0.672988i \(0.765010\pi\)
\(492\) 1.07838i 0.0486170i
\(493\) 0.482553i 0.0217331i
\(494\) 0.921622 0.0414657
\(495\) −7.41855 1.84324i −0.333439 0.0828477i
\(496\) 7.26180 0.326064
\(497\) 11.6865i 0.524211i
\(498\) 11.0205i 0.493841i
\(499\) 25.6742 1.14934 0.574668 0.818387i \(-0.305131\pi\)
0.574668 + 0.818387i \(0.305131\pi\)
\(500\) −8.32684 7.46081i −0.372388 0.333658i
\(501\) 4.68035 0.209102
\(502\) 6.73820i 0.300741i
\(503\) 24.7526i 1.10366i −0.833956 0.551832i \(-0.813929\pi\)
0.833956 0.551832i \(-0.186071\pi\)
\(504\) −1.07838 −0.0480348
\(505\) −28.2557 7.02052i −1.25736 0.312409i
\(506\) 3.15061 0.140062
\(507\) 12.1506i 0.539628i
\(508\) 16.4969i 0.731933i
\(509\) 20.9360 0.927972 0.463986 0.885843i \(-0.346419\pi\)
0.463986 + 0.885843i \(0.346419\pi\)
\(510\) −0.183417 + 0.738205i −0.00812186 + 0.0326883i
\(511\) 7.37298 0.326161
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 9.20394 0.405968
\(515\) 7.73206 31.1194i 0.340715 1.37129i
\(516\) −0.738205 −0.0324977
\(517\) 26.5236i 1.16651i
\(518\) 6.04104i 0.265428i
\(519\) −4.52359 −0.198564
\(520\) −2.00000 0.496928i −0.0877058 0.0217918i
\(521\) 23.5486 1.03168 0.515842 0.856683i \(-0.327479\pi\)
0.515842 + 0.856683i \(0.327479\pi\)
\(522\) 1.41855i 0.0620883i
\(523\) 14.7838i 0.646449i 0.946322 + 0.323225i \(0.104767\pi\)
−0.946322 + 0.323225i \(0.895233\pi\)
\(524\) −0.581449 −0.0254007
\(525\) 4.76487 + 2.52359i 0.207956 + 0.110139i
\(526\) −25.7998 −1.12492
\(527\) 2.47027i 0.107606i
\(528\) 3.41855i 0.148773i
\(529\) 22.1506 0.963070
\(530\) −5.81658 1.44521i −0.252656 0.0627760i
\(531\) 8.34017 0.361933
\(532\) 1.07838i 0.0467536i
\(533\) 0.993857i 0.0430487i
\(534\) −9.75872 −0.422301
\(535\) 5.84324 23.5174i 0.252625 1.01675i
\(536\) 4.68035 0.202160
\(537\) 14.4969i 0.625589i
\(538\) 4.73820i 0.204279i
\(539\) 19.9544 0.859498
\(540\) −0.539189 + 2.17009i −0.0232030 + 0.0933857i
\(541\) −40.8371 −1.75572 −0.877862 0.478914i \(-0.841031\pi\)
−0.877862 + 0.478914i \(0.841031\pi\)
\(542\) 16.3668i 0.703016i
\(543\) 12.7792i 0.548410i
\(544\) 0.340173 0.0145848
\(545\) −40.4124 10.0410i −1.73108 0.430111i
\(546\) 0.993857 0.0425332
\(547\) 42.0410i 1.79754i 0.438415 + 0.898772i \(0.355540\pi\)
−0.438415 + 0.898772i \(0.644460\pi\)
\(548\) 5.81658i 0.248472i
\(549\) −2.00000 −0.0853579
\(550\) 8.00000 15.1050i 0.341121 0.644081i
\(551\) 1.41855 0.0604323
\(552\) 0.921622i 0.0392268i
\(553\) 5.10957i 0.217281i
\(554\) 12.6537 0.537604
\(555\) −12.1568 3.02052i −0.516026 0.128214i
\(556\) 6.15676 0.261105
\(557\) 26.7526i 1.13354i −0.823875 0.566772i \(-0.808192\pi\)
0.823875 0.566772i \(-0.191808\pi\)
\(558\) 7.26180i 0.307416i
\(559\) 0.680346 0.0287756
\(560\) 0.581449 2.34017i 0.0245707 0.0988904i
\(561\) −1.16290 −0.0490976
\(562\) 9.44521i 0.398422i
\(563\) 21.9877i 0.926672i 0.886183 + 0.463336i \(0.153348\pi\)
−0.886183 + 0.463336i \(0.846652\pi\)
\(564\) −7.75872 −0.326701
\(565\) −7.28846 + 29.3340i −0.306628 + 1.23409i
\(566\) −15.8888 −0.667857
\(567\) 1.07838i 0.0452876i
\(568\) 10.8371i 0.454715i
\(569\) 32.5958 1.36649 0.683244 0.730190i \(-0.260569\pi\)
0.683244 + 0.730190i \(0.260569\pi\)
\(570\) 2.17009 + 0.539189i 0.0908949 + 0.0225841i
\(571\) −32.1445 −1.34520 −0.672602 0.740004i \(-0.734823\pi\)
−0.672602 + 0.740004i \(0.734823\pi\)
\(572\) 3.15061i 0.131734i
\(573\) 4.39803i 0.183730i
\(574\) 1.16290 0.0485384
\(575\) −2.15676 + 4.07223i −0.0899429 + 0.169824i
\(576\) 1.00000 0.0416667
\(577\) 13.6742i 0.569265i −0.958637 0.284632i \(-0.908129\pi\)
0.958637 0.284632i \(-0.0918715\pi\)
\(578\) 16.8843i 0.702294i
\(579\) 24.6225 1.02328
\(580\) −3.07838 0.764867i −0.127823 0.0317594i
\(581\) −11.8843 −0.493043
\(582\) 16.2557i 0.673818i
\(583\) 9.16290i 0.379488i
\(584\) −6.83710 −0.282921
\(585\) 0.496928 2.00000i 0.0205455 0.0826898i
\(586\) −4.47027 −0.184665
\(587\) 30.9672i 1.27815i −0.769143 0.639076i \(-0.779317\pi\)
0.769143 0.639076i \(-0.220683\pi\)
\(588\) 5.83710i 0.240718i
\(589\) 7.26180 0.299217
\(590\) −4.49693 + 18.0989i −0.185136 + 0.745120i
\(591\) 3.91548 0.161061
\(592\) 5.60197i 0.230239i
\(593\) 42.3812i 1.74039i 0.492709 + 0.870194i \(0.336007\pi\)
−0.492709 + 0.870194i \(0.663993\pi\)
\(594\) −3.41855 −0.140265
\(595\) 0.796064 + 0.197793i 0.0326354 + 0.00810874i
\(596\) 8.34017 0.341627
\(597\) 8.99386i 0.368094i
\(598\) 0.849388i 0.0347340i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −4.41855 2.34017i −0.180387 0.0955372i
\(601\) 11.4764 0.468133 0.234066 0.972221i \(-0.424797\pi\)
0.234066 + 0.972221i \(0.424797\pi\)
\(602\) 0.796064i 0.0324451i
\(603\) 4.68035i 0.190598i
\(604\) −16.2557 −0.661433
\(605\) 1.48974 + 0.370147i 0.0605666 + 0.0150486i
\(606\) −13.0205 −0.528922
\(607\) 15.3340i 0.622389i −0.950346 0.311195i \(-0.899271\pi\)
0.950346 0.311195i \(-0.100729\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 1.52973 0.0619879
\(610\) 1.07838 4.34017i 0.0436622 0.175728i
\(611\) 7.15061 0.289283
\(612\) 0.340173i 0.0137507i
\(613\) 4.34017i 0.175298i −0.996151 0.0876490i \(-0.972065\pi\)
0.996151 0.0876490i \(-0.0279354\pi\)
\(614\) 15.3197 0.618251
\(615\) 0.581449 2.34017i 0.0234463 0.0943649i
\(616\) 3.68649 0.148533
\(617\) 30.1834i 1.21514i −0.794267 0.607569i \(-0.792145\pi\)
0.794267 0.607569i \(-0.207855\pi\)
\(618\) 14.3402i 0.576846i
\(619\) 7.94668 0.319404 0.159702 0.987165i \(-0.448947\pi\)
0.159702 + 0.987165i \(0.448947\pi\)
\(620\) −15.7587 3.91548i −0.632886 0.157249i
\(621\) 0.921622 0.0369834
\(622\) 4.39803i 0.176345i
\(623\) 10.5236i 0.421619i
\(624\) −0.921622 −0.0368944
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) −8.31351 −0.332275
\(627\) 3.41855i 0.136524i
\(628\) 3.65983i 0.146043i
\(629\) −1.90564 −0.0759828
\(630\) 2.34017 + 0.581449i 0.0932347 + 0.0231655i
\(631\) 8.68035 0.345559 0.172780 0.984961i \(-0.444725\pi\)
0.172780 + 0.984961i \(0.444725\pi\)
\(632\) 4.73820i 0.188476i
\(633\) 4.68035i 0.186027i
\(634\) 0.470266 0.0186767
\(635\) −8.89496 + 35.7998i −0.352986 + 1.42067i
\(636\) −2.68035 −0.106283
\(637\) 5.37960i 0.213148i
\(638\) 4.84939i 0.191989i
\(639\) 10.8371 0.428709
\(640\) −0.539189 + 2.17009i −0.0213133 + 0.0857802i
\(641\) −41.6430 −1.64480 −0.822400 0.568910i \(-0.807365\pi\)
−0.822400 + 0.568910i \(0.807365\pi\)
\(642\) 10.8371i 0.427706i
\(643\) 29.7854i 1.17462i 0.809362 + 0.587310i \(0.199813\pi\)
−0.809362 + 0.587310i \(0.800187\pi\)
\(644\) −0.993857 −0.0391634
\(645\) 1.60197 + 0.398032i 0.0630774 + 0.0156725i
\(646\) 0.340173 0.0133839
\(647\) 28.9216i 1.13703i 0.822674 + 0.568513i \(0.192481\pi\)
−0.822674 + 0.568513i \(0.807519\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −28.5113 −1.11917
\(650\) 4.07223 + 2.15676i 0.159726 + 0.0845949i
\(651\) 7.83096 0.306919
\(652\) 6.89496i 0.270027i
\(653\) 41.9565i 1.64189i −0.571011 0.820943i \(-0.693448\pi\)
0.571011 0.820943i \(-0.306552\pi\)
\(654\) −18.6225 −0.728197
\(655\) 1.26180 + 0.313511i 0.0493024 + 0.0122499i
\(656\) −1.07838 −0.0421036
\(657\) 6.83710i 0.266741i
\(658\) 8.36683i 0.326173i
\(659\) −43.0082 −1.67536 −0.837681 0.546159i \(-0.816089\pi\)
−0.837681 + 0.546159i \(0.816089\pi\)
\(660\) 1.84324 7.41855i 0.0717482 0.288767i
\(661\) −34.3090 −1.33446 −0.667232 0.744850i \(-0.732521\pi\)
−0.667232 + 0.744850i \(0.732521\pi\)
\(662\) 31.5174i 1.22496i
\(663\) 0.313511i 0.0121758i
\(664\) 11.0205 0.427679
\(665\) 0.581449 2.34017i 0.0225476 0.0907480i
\(666\) −5.60197 −0.217072
\(667\) 1.30737i 0.0506215i
\(668\) 4.68035i 0.181088i
\(669\) 14.3402 0.554423
\(670\) −10.1568 2.52359i −0.392390 0.0974948i
\(671\) 6.83710 0.263943
\(672\) 1.07838i 0.0415993i
\(673\) 31.0928i 1.19854i 0.800548 + 0.599269i \(0.204542\pi\)
−0.800548 + 0.599269i \(0.795458\pi\)
\(674\) 0.0578588 0.00222864
\(675\) 2.34017 4.41855i 0.0900733 0.170070i
\(676\) −12.1506 −0.467331
\(677\) 35.9877i 1.38312i −0.722319 0.691560i \(-0.756924\pi\)
0.722319 0.691560i \(-0.243076\pi\)
\(678\) 13.5174i 0.519134i
\(679\) 17.5297 0.672729
\(680\) −0.738205 0.183417i −0.0283089 0.00703374i
\(681\) −19.2039 −0.735896
\(682\) 24.8248i 0.950591i
\(683\) 27.4017i 1.04850i 0.851565 + 0.524249i \(0.175654\pi\)
−0.851565 + 0.524249i \(0.824346\pi\)
\(684\) 1.00000 0.0382360
\(685\) 3.13624 12.6225i 0.119829 0.482280i
\(686\) −13.8432 −0.528538
\(687\) 2.31351i 0.0882659i
\(688\) 0.738205i 0.0281438i
\(689\) 2.47027 0.0941097
\(690\) −0.496928 + 2.00000i −0.0189177 + 0.0761387i
\(691\) 3.83096 0.145737 0.0728683 0.997342i \(-0.476785\pi\)
0.0728683 + 0.997342i \(0.476785\pi\)
\(692\) 4.52359i 0.171961i
\(693\) 3.68649i 0.140038i
\(694\) −6.34017 −0.240670
\(695\) −13.3607 3.31965i −0.506800 0.125922i
\(696\) −1.41855 −0.0537700
\(697\) 0.366835i 0.0138949i
\(698\) 20.5236i 0.776829i
\(699\) 25.6475 0.970079
\(700\) −2.52359 + 4.76487i −0.0953828 + 0.180095i
\(701\) 46.5790 1.75926 0.879632 0.475654i \(-0.157789\pi\)
0.879632 + 0.475654i \(0.157789\pi\)
\(702\) 0.921622i 0.0347844i
\(703\) 5.60197i 0.211282i
\(704\) −3.41855 −0.128841
\(705\) 16.8371 + 4.18342i 0.634122 + 0.157557i
\(706\) 22.3812 0.842328
\(707\) 14.0410i 0.528068i
\(708\) 8.34017i 0.313443i
\(709\) −15.1917 −0.570534 −0.285267 0.958448i \(-0.592082\pi\)
−0.285267 + 0.958448i \(0.592082\pi\)
\(710\) −5.84324 + 23.5174i −0.219293 + 0.882594i
\(711\) 4.73820 0.177697
\(712\) 9.75872i 0.365724i
\(713\) 6.69263i 0.250641i
\(714\) 0.366835 0.0137285
\(715\) −1.69878 + 6.83710i −0.0635306 + 0.255693i
\(716\) 14.4969 0.541776
\(717\) 3.60197i 0.134518i
\(718\) 0.282314i 0.0105359i
\(719\) 8.45136 0.315182 0.157591 0.987504i \(-0.449627\pi\)
0.157591 + 0.987504i \(0.449627\pi\)
\(720\) −2.17009 0.539189i −0.0808743 0.0200944i
\(721\) −15.4641 −0.575914
\(722\) 1.00000i 0.0372161i
\(723\) 2.36683i 0.0880235i
\(724\) 12.7792 0.474937
\(725\) 6.26794 + 3.31965i 0.232785 + 0.123289i
\(726\) 0.686489 0.0254780
\(727\) 39.9688i 1.48236i 0.671306 + 0.741180i \(0.265734\pi\)
−0.671306 + 0.741180i \(0.734266\pi\)
\(728\) 0.993857i 0.0368348i
\(729\) −1.00000 −0.0370370
\(730\) 14.8371 + 3.68649i 0.549146 + 0.136443i
\(731\) 0.251117 0.00928791
\(732\) 2.00000i 0.0739221i
\(733\) 38.7480i 1.43119i −0.698515 0.715596i \(-0.746155\pi\)
0.698515 0.715596i \(-0.253845\pi\)
\(734\) 27.9155 1.03038
\(735\) −3.14730 + 12.6670i −0.116090 + 0.467230i
\(736\) 0.921622 0.0339714
\(737\) 16.0000i 0.589368i
\(738\) 1.07838i 0.0396956i
\(739\) 15.1506 0.557324 0.278662 0.960389i \(-0.410109\pi\)
0.278662 + 0.960389i \(0.410109\pi\)
\(740\) 3.02052 12.1568i 0.111036 0.446891i
\(741\) −0.921622 −0.0338566
\(742\) 2.89043i 0.106111i
\(743\) 28.8781i 1.05944i −0.848174 0.529718i \(-0.822298\pi\)
0.848174 0.529718i \(-0.177702\pi\)
\(744\) −7.26180 −0.266230
\(745\) −18.0989 4.49693i −0.663092 0.164755i
\(746\) −3.44521 −0.126138
\(747\) 11.0205i 0.403220i
\(748\) 1.16290i 0.0425198i
\(749\) −11.6865 −0.427015
\(750\) 8.32684 + 7.46081i 0.304053 + 0.272430i
\(751\) −14.2679 −0.520644 −0.260322 0.965522i \(-0.583829\pi\)
−0.260322 + 0.965522i \(0.583829\pi\)
\(752\) 7.75872i 0.282932i
\(753\) 6.73820i 0.245554i
\(754\) 1.30737 0.0476115
\(755\) 35.2762 + 8.76487i 1.28383 + 0.318986i
\(756\) 1.07838 0.0392202
\(757\) 22.2122i 0.807315i 0.914910 + 0.403658i \(0.132261\pi\)
−0.914910 + 0.403658i \(0.867739\pi\)
\(758\) 28.5113i 1.03558i
\(759\) −3.15061 −0.114360
\(760\) −0.539189 + 2.17009i −0.0195584 + 0.0787173i
\(761\) 2.48255 0.0899925 0.0449962 0.998987i \(-0.485672\pi\)
0.0449962 + 0.998987i \(0.485672\pi\)
\(762\) 16.4969i 0.597621i
\(763\) 20.0821i 0.727020i
\(764\) 4.39803 0.159115
\(765\) 0.183417 0.738205i 0.00663147 0.0266898i
\(766\) −2.63931 −0.0953621
\(767\) 7.68649i 0.277543i
\(768\) 1.00000i 0.0360844i
\(769\) 22.3135 0.804646 0.402323 0.915498i \(-0.368203\pi\)
0.402323 + 0.915498i \(0.368203\pi\)
\(770\) −8.00000 1.98771i −0.288300 0.0716322i
\(771\) −9.20394 −0.331472
\(772\) 24.6225i 0.886183i
\(773\) 24.2101i 0.870776i −0.900243 0.435388i \(-0.856611\pi\)
0.900243 0.435388i \(-0.143389\pi\)
\(774\) 0.738205 0.0265342
\(775\) 32.0866 + 16.9939i 1.15259 + 0.610437i
\(776\) −16.2557 −0.583544
\(777\) 6.04104i 0.216721i
\(778\) 22.1834i 0.795314i
\(779\) −1.07838 −0.0386369
\(780\) 2.00000 + 0.496928i 0.0716115 + 0.0177929i
\(781\) −37.0472 −1.32565
\(782\) 0.313511i 0.0112111i
\(783\) 1.41855i 0.0506949i
\(784\) 5.83710 0.208468
\(785\) −1.97334 + 7.94214i −0.0704315 + 0.283467i
\(786\) 0.581449 0.0207396
\(787\) 31.0349i 1.10627i 0.833090 + 0.553137i \(0.186569\pi\)
−0.833090 + 0.553137i \(0.813431\pi\)
\(788\)