Properties

Label 429.2.b.b.298.8
Level $429$
Weight $2$
Character 429.298
Analytic conductor $3.426$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.8
Root \(0.409068i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.7

$q$-expansion

\(f(q)\) \(=\) \(q+0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} +4.13953i q^{5} +0.409068i q^{6} -5.18273i q^{7} +1.56782i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} +4.13953i q^{5} +0.409068i q^{6} -5.18273i q^{7} +1.56782i q^{8} +1.00000 q^{9} -1.69335 q^{10} -1.00000i q^{11} +1.83266 q^{12} +(2.62060 + 2.47638i) q^{13} +2.12009 q^{14} +4.13953i q^{15} +3.02398 q^{16} +0.488730 q^{17} +0.409068i q^{18} -0.446180i q^{19} +7.58636i q^{20} -5.18273i q^{21} +0.409068 q^{22} -5.50882 q^{23} +1.56782i q^{24} -12.1357 q^{25} +(-1.01301 + 1.07200i) q^{26} +1.00000 q^{27} -9.49821i q^{28} -6.58571 q^{29} -1.69335 q^{30} +1.52580i q^{31} +4.37265i q^{32} -1.00000i q^{33} +0.199924i q^{34} +21.4541 q^{35} +1.83266 q^{36} +7.87139i q^{37} +0.182518 q^{38} +(2.62060 + 2.47638i) q^{39} -6.49004 q^{40} -8.78563i q^{41} +2.12009 q^{42} +4.57514 q^{43} -1.83266i q^{44} +4.13953i q^{45} -2.25348i q^{46} -5.42082i q^{47} +3.02398 q^{48} -19.8607 q^{49} -4.96433i q^{50} +0.488730 q^{51} +(4.80268 + 4.53837i) q^{52} +8.66677 q^{53} +0.409068i q^{54} +4.13953 q^{55} +8.12559 q^{56} -0.446180i q^{57} -2.69400i q^{58} -5.60493i q^{59} +7.58636i q^{60} -0.855775 q^{61} -0.624155 q^{62} -5.18273i q^{63} +4.25925 q^{64} +(-10.2510 + 10.8481i) q^{65} +0.409068 q^{66} -3.87464i q^{67} +0.895677 q^{68} -5.50882 q^{69} +8.77618i q^{70} -8.49886i q^{71} +1.56782i q^{72} -5.95291i q^{73} -3.21993 q^{74} -12.1357 q^{75} -0.817698i q^{76} -5.18273 q^{77} +(-1.01301 + 1.07200i) q^{78} -8.91459 q^{79} +12.5179i q^{80} +1.00000 q^{81} +3.59392 q^{82} +0.457495i q^{83} -9.49821i q^{84} +2.02311i q^{85} +1.87154i q^{86} -6.58571 q^{87} +1.56782 q^{88} +4.68461i q^{89} -1.69335 q^{90} +(12.8344 - 13.5819i) q^{91} -10.0958 q^{92} +1.52580i q^{93} +2.21748 q^{94} +1.84697 q^{95} +4.37265i q^{96} -2.06057i q^{97} -8.12439i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.409068i 0.289255i 0.989486 + 0.144627i \(0.0461984\pi\)
−0.989486 + 0.144627i \(0.953802\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.83266 0.916332
\(5\) 4.13953i 1.85125i 0.378437 + 0.925627i \(0.376462\pi\)
−0.378437 + 0.925627i \(0.623538\pi\)
\(6\) 0.409068i 0.167001i
\(7\) 5.18273i 1.95889i −0.201714 0.979445i \(-0.564651\pi\)
0.201714 0.979445i \(-0.435349\pi\)
\(8\) 1.56782i 0.554308i
\(9\) 1.00000 0.333333
\(10\) −1.69335 −0.535484
\(11\) 1.00000i 0.301511i
\(12\) 1.83266 0.529044
\(13\) 2.62060 + 2.47638i 0.726824 + 0.686823i
\(14\) 2.12009 0.566618
\(15\) 4.13953i 1.06882i
\(16\) 3.02398 0.755995
\(17\) 0.488730 0.118534 0.0592672 0.998242i \(-0.481124\pi\)
0.0592672 + 0.998242i \(0.481124\pi\)
\(18\) 0.409068i 0.0964183i
\(19\) 0.446180i 0.102361i −0.998689 0.0511803i \(-0.983702\pi\)
0.998689 0.0511803i \(-0.0162983\pi\)
\(20\) 7.58636i 1.69636i
\(21\) 5.18273i 1.13097i
\(22\) 0.409068 0.0872136
\(23\) −5.50882 −1.14867 −0.574334 0.818621i \(-0.694739\pi\)
−0.574334 + 0.818621i \(0.694739\pi\)
\(24\) 1.56782i 0.320030i
\(25\) −12.1357 −2.42714
\(26\) −1.01301 + 1.07200i −0.198667 + 0.210237i
\(27\) 1.00000 0.192450
\(28\) 9.49821i 1.79499i
\(29\) −6.58571 −1.22294 −0.611468 0.791269i \(-0.709421\pi\)
−0.611468 + 0.791269i \(0.709421\pi\)
\(30\) −1.69335 −0.309162
\(31\) 1.52580i 0.274041i 0.990568 + 0.137021i \(0.0437527\pi\)
−0.990568 + 0.137021i \(0.956247\pi\)
\(32\) 4.37265i 0.772983i
\(33\) 1.00000i 0.174078i
\(34\) 0.199924i 0.0342866i
\(35\) 21.4541 3.62640
\(36\) 1.83266 0.305444
\(37\) 7.87139i 1.29405i 0.762470 + 0.647024i \(0.223987\pi\)
−0.762470 + 0.647024i \(0.776013\pi\)
\(38\) 0.182518 0.0296083
\(39\) 2.62060 + 2.47638i 0.419632 + 0.396538i
\(40\) −6.49004 −1.02617
\(41\) 8.78563i 1.37209i −0.727561 0.686043i \(-0.759346\pi\)
0.727561 0.686043i \(-0.240654\pi\)
\(42\) 2.12009 0.327137
\(43\) 4.57514 0.697702 0.348851 0.937178i \(-0.386572\pi\)
0.348851 + 0.937178i \(0.386572\pi\)
\(44\) 1.83266i 0.276284i
\(45\) 4.13953i 0.617085i
\(46\) 2.25348i 0.332258i
\(47\) 5.42082i 0.790708i −0.918529 0.395354i \(-0.870622\pi\)
0.918529 0.395354i \(-0.129378\pi\)
\(48\) 3.02398 0.436474
\(49\) −19.8607 −2.83725
\(50\) 4.96433i 0.702062i
\(51\) 0.488730 0.0684359
\(52\) 4.80268 + 4.53837i 0.666012 + 0.629358i
\(53\) 8.66677 1.19047 0.595236 0.803551i \(-0.297059\pi\)
0.595236 + 0.803551i \(0.297059\pi\)
\(54\) 0.409068i 0.0556671i
\(55\) 4.13953 0.558174
\(56\) 8.12559 1.08583
\(57\) 0.446180i 0.0590980i
\(58\) 2.69400i 0.353740i
\(59\) 5.60493i 0.729700i −0.931066 0.364850i \(-0.881120\pi\)
0.931066 0.364850i \(-0.118880\pi\)
\(60\) 7.58636i 0.979395i
\(61\) −0.855775 −0.109571 −0.0547854 0.998498i \(-0.517447\pi\)
−0.0547854 + 0.998498i \(0.517447\pi\)
\(62\) −0.624155 −0.0792678
\(63\) 5.18273i 0.652963i
\(64\) 4.25925 0.532406
\(65\) −10.2510 + 10.8481i −1.27148 + 1.34554i
\(66\) 0.409068 0.0503528
\(67\) 3.87464i 0.473363i −0.971587 0.236681i \(-0.923940\pi\)
0.971587 0.236681i \(-0.0760598\pi\)
\(68\) 0.895677 0.108617
\(69\) −5.50882 −0.663184
\(70\) 8.77618i 1.04895i
\(71\) 8.49886i 1.00863i −0.863520 0.504315i \(-0.831745\pi\)
0.863520 0.504315i \(-0.168255\pi\)
\(72\) 1.56782i 0.184769i
\(73\) 5.95291i 0.696735i −0.937358 0.348368i \(-0.886736\pi\)
0.937358 0.348368i \(-0.113264\pi\)
\(74\) −3.21993 −0.374310
\(75\) −12.1357 −1.40131
\(76\) 0.817698i 0.0937963i
\(77\) −5.18273 −0.590627
\(78\) −1.01301 + 1.07200i −0.114700 + 0.121381i
\(79\) −8.91459 −1.00297 −0.501485 0.865166i \(-0.667213\pi\)
−0.501485 + 0.865166i \(0.667213\pi\)
\(80\) 12.5179i 1.39954i
\(81\) 1.00000 0.111111
\(82\) 3.59392 0.396882
\(83\) 0.457495i 0.0502166i 0.999685 + 0.0251083i \(0.00799306\pi\)
−0.999685 + 0.0251083i \(0.992007\pi\)
\(84\) 9.49821i 1.03634i
\(85\) 2.02311i 0.219437i
\(86\) 1.87154i 0.201814i
\(87\) −6.58571 −0.706062
\(88\) 1.56782 0.167130
\(89\) 4.68461i 0.496568i 0.968687 + 0.248284i \(0.0798666\pi\)
−0.968687 + 0.248284i \(0.920133\pi\)
\(90\) −1.69335 −0.178495
\(91\) 12.8344 13.5819i 1.34541 1.42377i
\(92\) −10.0958 −1.05256
\(93\) 1.52580i 0.158218i
\(94\) 2.21748 0.228716
\(95\) 1.84697 0.189496
\(96\) 4.37265i 0.446282i
\(97\) 2.06057i 0.209219i −0.994513 0.104609i \(-0.966641\pi\)
0.994513 0.104609i \(-0.0333592\pi\)
\(98\) 8.12439i 0.820687i
\(99\) 1.00000i 0.100504i
\(100\) −22.2407 −2.22407
\(101\) −3.86561 −0.384642 −0.192321 0.981332i \(-0.561602\pi\)
−0.192321 + 0.981332i \(0.561602\pi\)
\(102\) 0.199924i 0.0197954i
\(103\) −0.350877 −0.0345730 −0.0172865 0.999851i \(-0.505503\pi\)
−0.0172865 + 0.999851i \(0.505503\pi\)
\(104\) −3.88251 + 4.10863i −0.380712 + 0.402885i
\(105\) 21.4541 2.09370
\(106\) 3.54530i 0.344350i
\(107\) −12.5796 −1.21612 −0.608060 0.793891i \(-0.708052\pi\)
−0.608060 + 0.793891i \(0.708052\pi\)
\(108\) 1.83266 0.176348
\(109\) 4.61460i 0.441999i −0.975274 0.220999i \(-0.929068\pi\)
0.975274 0.220999i \(-0.0709319\pi\)
\(110\) 1.69335i 0.161455i
\(111\) 7.87139i 0.747119i
\(112\) 15.6725i 1.48091i
\(113\) 2.22602 0.209407 0.104703 0.994504i \(-0.466611\pi\)
0.104703 + 0.994504i \(0.466611\pi\)
\(114\) 0.182518 0.0170944
\(115\) 22.8039i 2.12648i
\(116\) −12.0694 −1.12061
\(117\) 2.62060 + 2.47638i 0.242275 + 0.228941i
\(118\) 2.29280 0.211069
\(119\) 2.53296i 0.232196i
\(120\) −6.49004 −0.592457
\(121\) −1.00000 −0.0909091
\(122\) 0.350070i 0.0316939i
\(123\) 8.78563i 0.792174i
\(124\) 2.79627i 0.251113i
\(125\) 29.5385i 2.64200i
\(126\) 2.12009 0.188873
\(127\) 18.2528 1.61967 0.809836 0.586656i \(-0.199556\pi\)
0.809836 + 0.586656i \(0.199556\pi\)
\(128\) 10.4876i 0.926985i
\(129\) 4.57514 0.402818
\(130\) −4.43760 4.19337i −0.389203 0.367783i
\(131\) 3.18466 0.278245 0.139122 0.990275i \(-0.455572\pi\)
0.139122 + 0.990275i \(0.455572\pi\)
\(132\) 1.83266i 0.159513i
\(133\) −2.31243 −0.200513
\(134\) 1.58499 0.136922
\(135\) 4.13953i 0.356274i
\(136\) 0.766241i 0.0657046i
\(137\) 5.11813i 0.437271i 0.975807 + 0.218635i \(0.0701606\pi\)
−0.975807 + 0.218635i \(0.929839\pi\)
\(138\) 2.25348i 0.191829i
\(139\) −10.7714 −0.913617 −0.456809 0.889565i \(-0.651008\pi\)
−0.456809 + 0.889565i \(0.651008\pi\)
\(140\) 39.3181 3.32299
\(141\) 5.42082i 0.456515i
\(142\) 3.47661 0.291751
\(143\) 2.47638 2.62060i 0.207085 0.219146i
\(144\) 3.02398 0.251998
\(145\) 27.2617i 2.26396i
\(146\) 2.43514 0.201534
\(147\) −19.8607 −1.63809
\(148\) 14.4256i 1.18578i
\(149\) 4.42220i 0.362281i 0.983457 + 0.181140i \(0.0579788\pi\)
−0.983457 + 0.181140i \(0.942021\pi\)
\(150\) 4.96433i 0.405336i
\(151\) 4.64014i 0.377609i 0.982015 + 0.188805i \(0.0604613\pi\)
−0.982015 + 0.188805i \(0.939539\pi\)
\(152\) 0.699530 0.0567394
\(153\) 0.488730 0.0395115
\(154\) 2.12009i 0.170842i
\(155\) −6.31608 −0.507320
\(156\) 4.80268 + 4.53837i 0.384522 + 0.363360i
\(157\) 10.8227 0.863745 0.431873 0.901935i \(-0.357853\pi\)
0.431873 + 0.901935i \(0.357853\pi\)
\(158\) 3.64667i 0.290114i
\(159\) 8.66677 0.687319
\(160\) −18.1007 −1.43099
\(161\) 28.5508i 2.25011i
\(162\) 0.409068i 0.0321394i
\(163\) 24.4714i 1.91675i 0.285519 + 0.958373i \(0.407834\pi\)
−0.285519 + 0.958373i \(0.592166\pi\)
\(164\) 16.1011i 1.25729i
\(165\) 4.13953 0.322262
\(166\) −0.187147 −0.0145254
\(167\) 1.26722i 0.0980603i 0.998797 + 0.0490302i \(0.0156130\pi\)
−0.998797 + 0.0490302i \(0.984387\pi\)
\(168\) 8.12559 0.626903
\(169\) 0.735113 + 12.9792i 0.0565471 + 0.998400i
\(170\) −0.827590 −0.0634733
\(171\) 0.446180i 0.0341202i
\(172\) 8.38469 0.639326
\(173\) −3.24638 −0.246818 −0.123409 0.992356i \(-0.539383\pi\)
−0.123409 + 0.992356i \(0.539383\pi\)
\(174\) 2.69400i 0.204232i
\(175\) 62.8961i 4.75450i
\(176\) 3.02398i 0.227941i
\(177\) 5.60493i 0.421292i
\(178\) −1.91633 −0.143635
\(179\) 16.5303 1.23553 0.617765 0.786363i \(-0.288038\pi\)
0.617765 + 0.786363i \(0.288038\pi\)
\(180\) 7.58636i 0.565454i
\(181\) −12.2065 −0.907303 −0.453651 0.891179i \(-0.649879\pi\)
−0.453651 + 0.891179i \(0.649879\pi\)
\(182\) 5.55592 + 5.25014i 0.411832 + 0.389167i
\(183\) −0.855775 −0.0632607
\(184\) 8.63684i 0.636717i
\(185\) −32.5838 −2.39561
\(186\) −0.624155 −0.0457653
\(187\) 0.488730i 0.0357395i
\(188\) 9.93454i 0.724551i
\(189\) 5.18273i 0.376988i
\(190\) 0.755539i 0.0548125i
\(191\) −17.4410 −1.26199 −0.630995 0.775787i \(-0.717353\pi\)
−0.630995 + 0.775787i \(0.717353\pi\)
\(192\) 4.25925 0.307385
\(193\) 0.941498i 0.0677705i 0.999426 + 0.0338852i \(0.0107881\pi\)
−0.999426 + 0.0338852i \(0.989212\pi\)
\(194\) 0.842912 0.0605175
\(195\) −10.2510 + 10.8481i −0.734092 + 0.776846i
\(196\) −36.3980 −2.59986
\(197\) 16.7419i 1.19281i 0.802684 + 0.596404i \(0.203404\pi\)
−0.802684 + 0.596404i \(0.796596\pi\)
\(198\) 0.409068 0.0290712
\(199\) −13.1573 −0.932693 −0.466347 0.884602i \(-0.654430\pi\)
−0.466347 + 0.884602i \(0.654430\pi\)
\(200\) 19.0266i 1.34538i
\(201\) 3.87464i 0.273296i
\(202\) 1.58130i 0.111260i
\(203\) 34.1320i 2.39560i
\(204\) 0.895677 0.0627100
\(205\) 36.3684 2.54008
\(206\) 0.143533i 0.0100004i
\(207\) −5.50882 −0.382890
\(208\) 7.92465 + 7.48852i 0.549476 + 0.519235i
\(209\) −0.446180 −0.0308629
\(210\) 8.77618i 0.605614i
\(211\) 13.5657 0.933898 0.466949 0.884284i \(-0.345353\pi\)
0.466949 + 0.884284i \(0.345353\pi\)
\(212\) 15.8833 1.09087
\(213\) 8.49886i 0.582332i
\(214\) 5.14593i 0.351768i
\(215\) 18.9389i 1.29162i
\(216\) 1.56782i 0.106677i
\(217\) 7.90780 0.536816
\(218\) 1.88769 0.127850
\(219\) 5.95291i 0.402260i
\(220\) 7.58636 0.511473
\(221\) 1.28077 + 1.21028i 0.0861537 + 0.0814122i
\(222\) −3.21993 −0.216108
\(223\) 11.8725i 0.795044i 0.917593 + 0.397522i \(0.130130\pi\)
−0.917593 + 0.397522i \(0.869870\pi\)
\(224\) 22.6623 1.51419
\(225\) −12.1357 −0.809047
\(226\) 0.910595i 0.0605719i
\(227\) 13.0255i 0.864532i −0.901746 0.432266i \(-0.857714\pi\)
0.901746 0.432266i \(-0.142286\pi\)
\(228\) 0.817698i 0.0541533i
\(229\) 6.45867i 0.426801i −0.976965 0.213401i \(-0.931546\pi\)
0.976965 0.213401i \(-0.0684540\pi\)
\(230\) 9.32836 0.615094
\(231\) −5.18273 −0.340999
\(232\) 10.3252i 0.677883i
\(233\) 13.2616 0.868795 0.434397 0.900721i \(-0.356961\pi\)
0.434397 + 0.900721i \(0.356961\pi\)
\(234\) −1.01301 + 1.07200i −0.0662223 + 0.0700791i
\(235\) 22.4396 1.46380
\(236\) 10.2720i 0.668647i
\(237\) −8.91459 −0.579065
\(238\) 1.03615 0.0671637
\(239\) 0.426040i 0.0275583i 0.999905 + 0.0137791i \(0.00438617\pi\)
−0.999905 + 0.0137791i \(0.995614\pi\)
\(240\) 12.5179i 0.808024i
\(241\) 12.9860i 0.836503i −0.908331 0.418251i \(-0.862643\pi\)
0.908331 0.418251i \(-0.137357\pi\)
\(242\) 0.409068i 0.0262959i
\(243\) 1.00000 0.0641500
\(244\) −1.56835 −0.100403
\(245\) 82.2141i 5.25246i
\(246\) 3.59392 0.229140
\(247\) 1.10491 1.16926i 0.0703037 0.0743982i
\(248\) −2.39218 −0.151903
\(249\) 0.457495i 0.0289926i
\(250\) 12.0832 0.764211
\(251\) −4.37202 −0.275959 −0.137980 0.990435i \(-0.544061\pi\)
−0.137980 + 0.990435i \(0.544061\pi\)
\(252\) 9.49821i 0.598331i
\(253\) 5.50882i 0.346337i
\(254\) 7.46663i 0.468498i
\(255\) 2.02311i 0.126692i
\(256\) 4.22834 0.264271
\(257\) 11.2798 0.703614 0.351807 0.936073i \(-0.385567\pi\)
0.351807 + 0.936073i \(0.385567\pi\)
\(258\) 1.87154i 0.116517i
\(259\) 40.7953 2.53490
\(260\) −18.7867 + 19.8808i −1.16510 + 1.23296i
\(261\) −6.58571 −0.407645
\(262\) 1.30274i 0.0804836i
\(263\) −0.914614 −0.0563975 −0.0281988 0.999602i \(-0.508977\pi\)
−0.0281988 + 0.999602i \(0.508977\pi\)
\(264\) 1.56782 0.0964927
\(265\) 35.8763i 2.20387i
\(266\) 0.945942i 0.0579994i
\(267\) 4.68461i 0.286694i
\(268\) 7.10091i 0.433757i
\(269\) 13.1384 0.801064 0.400532 0.916283i \(-0.368825\pi\)
0.400532 + 0.916283i \(0.368825\pi\)
\(270\) −1.69335 −0.103054
\(271\) 12.3173i 0.748224i 0.927384 + 0.374112i \(0.122052\pi\)
−0.927384 + 0.374112i \(0.877948\pi\)
\(272\) 1.47791 0.0896115
\(273\) 12.8344 13.5819i 0.776773 0.822013i
\(274\) −2.09366 −0.126483
\(275\) 12.1357i 0.731810i
\(276\) −10.0958 −0.607697
\(277\) 20.1395 1.21006 0.605031 0.796202i \(-0.293161\pi\)
0.605031 + 0.796202i \(0.293161\pi\)
\(278\) 4.40623i 0.264268i
\(279\) 1.52580i 0.0913471i
\(280\) 33.6361i 2.01014i
\(281\) 6.66666i 0.397699i 0.980030 + 0.198850i \(0.0637206\pi\)
−0.980030 + 0.198850i \(0.936279\pi\)
\(282\) 2.21748 0.132049
\(283\) −27.5589 −1.63820 −0.819102 0.573647i \(-0.805528\pi\)
−0.819102 + 0.573647i \(0.805528\pi\)
\(284\) 15.5755i 0.924239i
\(285\) 1.84697 0.109405
\(286\) 1.07200 + 1.01301i 0.0633890 + 0.0599004i
\(287\) −45.5336 −2.68776
\(288\) 4.37265i 0.257661i
\(289\) −16.7611 −0.985950
\(290\) 11.1519 0.654863
\(291\) 2.06057i 0.120793i
\(292\) 10.9097i 0.638440i
\(293\) 13.8127i 0.806945i 0.914992 + 0.403472i \(0.132197\pi\)
−0.914992 + 0.403472i \(0.867803\pi\)
\(294\) 8.12439i 0.473824i
\(295\) 23.2018 1.35086
\(296\) −12.3409 −0.717301
\(297\) 1.00000i 0.0580259i
\(298\) −1.80898 −0.104791
\(299\) −14.4364 13.6419i −0.834880 0.788933i
\(300\) −22.2407 −1.28406
\(301\) 23.7117i 1.36672i
\(302\) −1.89813 −0.109225
\(303\) −3.86561 −0.222073
\(304\) 1.34924i 0.0773842i
\(305\) 3.54251i 0.202843i
\(306\) 0.199924i 0.0114289i
\(307\) 21.0868i 1.20349i −0.798690 0.601743i \(-0.794473\pi\)
0.798690 0.601743i \(-0.205527\pi\)
\(308\) −9.49821 −0.541210
\(309\) −0.350877 −0.0199607
\(310\) 2.58371i 0.146745i
\(311\) 29.7858 1.68900 0.844498 0.535558i \(-0.179899\pi\)
0.844498 + 0.535558i \(0.179899\pi\)
\(312\) −3.88251 + 4.10863i −0.219804 + 0.232606i
\(313\) 26.3709 1.49057 0.745287 0.666744i \(-0.232312\pi\)
0.745287 + 0.666744i \(0.232312\pi\)
\(314\) 4.42722i 0.249842i
\(315\) 21.4541 1.20880
\(316\) −16.3374 −0.919053
\(317\) 24.5073i 1.37647i 0.725490 + 0.688233i \(0.241613\pi\)
−0.725490 + 0.688233i \(0.758387\pi\)
\(318\) 3.54530i 0.198810i
\(319\) 6.58571i 0.368729i
\(320\) 17.6313i 0.985619i
\(321\) −12.5796 −0.702127
\(322\) −11.6792 −0.650857
\(323\) 0.218061i 0.0121333i
\(324\) 1.83266 0.101815
\(325\) −31.8029 30.0526i −1.76410 1.66702i
\(326\) −10.0105 −0.554428
\(327\) 4.61460i 0.255188i
\(328\) 13.7743 0.760558
\(329\) −28.0947 −1.54891
\(330\) 1.69335i 0.0932158i
\(331\) 10.4965i 0.576939i 0.957489 + 0.288469i \(0.0931464\pi\)
−0.957489 + 0.288469i \(0.906854\pi\)
\(332\) 0.838434i 0.0460150i
\(333\) 7.87139i 0.431349i
\(334\) −0.518379 −0.0283644
\(335\) 16.0392 0.876315
\(336\) 15.6725i 0.855004i
\(337\) −21.9103 −1.19353 −0.596765 0.802416i \(-0.703547\pi\)
−0.596765 + 0.802416i \(0.703547\pi\)
\(338\) −5.30938 + 0.300711i −0.288792 + 0.0163565i
\(339\) 2.22602 0.120901
\(340\) 3.70768i 0.201077i
\(341\) 1.52580 0.0826266
\(342\) 0.182518 0.00986944
\(343\) 66.6537i 3.59896i
\(344\) 7.17299i 0.386742i
\(345\) 22.8039i 1.22772i
\(346\) 1.32799i 0.0713933i
\(347\) −16.4119 −0.881036 −0.440518 0.897744i \(-0.645205\pi\)
−0.440518 + 0.897744i \(0.645205\pi\)
\(348\) −12.0694 −0.646987
\(349\) 25.0915i 1.34312i 0.740951 + 0.671559i \(0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(350\) −25.7288 −1.37526
\(351\) 2.62060 + 2.47638i 0.139877 + 0.132179i
\(352\) 4.37265 0.233063
\(353\) 9.19662i 0.489486i 0.969588 + 0.244743i \(0.0787037\pi\)
−0.969588 + 0.244743i \(0.921296\pi\)
\(354\) 2.29280 0.121861
\(355\) 35.1813 1.86723
\(356\) 8.58532i 0.455021i
\(357\) 2.53296i 0.134058i
\(358\) 6.76200i 0.357383i
\(359\) 22.6236i 1.19403i −0.802231 0.597013i \(-0.796354\pi\)
0.802231 0.597013i \(-0.203646\pi\)
\(360\) −6.49004 −0.342055
\(361\) 18.8009 0.989522
\(362\) 4.99329i 0.262442i
\(363\) −1.00000 −0.0524864
\(364\) 23.5211 24.8910i 1.23284 1.30464i
\(365\) 24.6422 1.28983
\(366\) 0.350070i 0.0182985i
\(367\) −13.9344 −0.727371 −0.363685 0.931522i \(-0.618482\pi\)
−0.363685 + 0.931522i \(0.618482\pi\)
\(368\) −16.6586 −0.868388
\(369\) 8.78563i 0.457362i
\(370\) 13.3290i 0.692942i
\(371\) 44.9175i 2.33200i
\(372\) 2.79627i 0.144980i
\(373\) 20.5104 1.06199 0.530995 0.847375i \(-0.321818\pi\)
0.530995 + 0.847375i \(0.321818\pi\)
\(374\) 0.199924 0.0103378
\(375\) 29.5385i 1.52536i
\(376\) 8.49887 0.438296
\(377\) −17.2585 16.3087i −0.888859 0.839941i
\(378\) 2.12009 0.109046
\(379\) 2.32811i 0.119587i −0.998211 0.0597934i \(-0.980956\pi\)
0.998211 0.0597934i \(-0.0190442\pi\)
\(380\) 3.38488 0.173641
\(381\) 18.2528 0.935118
\(382\) 7.13457i 0.365037i
\(383\) 27.2203i 1.39089i 0.718578 + 0.695447i \(0.244793\pi\)
−0.718578 + 0.695447i \(0.755207\pi\)
\(384\) 10.4876i 0.535195i
\(385\) 21.4541i 1.09340i
\(386\) −0.385137 −0.0196029
\(387\) 4.57514 0.232567
\(388\) 3.77632i 0.191714i
\(389\) 24.9318 1.26409 0.632047 0.774930i \(-0.282215\pi\)
0.632047 + 0.774930i \(0.282215\pi\)
\(390\) −4.43760 4.19337i −0.224706 0.212340i
\(391\) −2.69233 −0.136157
\(392\) 31.1381i 1.57271i
\(393\) 3.18466 0.160645
\(394\) −6.84856 −0.345026
\(395\) 36.9022i 1.85675i
\(396\) 1.83266i 0.0920948i
\(397\) 31.3269i 1.57225i 0.618066 + 0.786126i \(0.287916\pi\)
−0.618066 + 0.786126i \(0.712084\pi\)
\(398\) 5.38222i 0.269786i
\(399\) −2.31243 −0.115766
\(400\) −36.6981 −1.83491
\(401\) 8.94790i 0.446837i −0.974723 0.223418i \(-0.928278\pi\)
0.974723 0.223418i \(-0.0717216\pi\)
\(402\) 1.58499 0.0790522
\(403\) −3.77845 + 3.99851i −0.188218 + 0.199180i
\(404\) −7.08435 −0.352460
\(405\) 4.13953i 0.205695i
\(406\) −13.9623 −0.692937
\(407\) 7.87139 0.390170
\(408\) 0.766241i 0.0379346i
\(409\) 30.0934i 1.48802i −0.668166 0.744012i \(-0.732921\pi\)
0.668166 0.744012i \(-0.267079\pi\)
\(410\) 14.8771i 0.734730i
\(411\) 5.11813i 0.252459i
\(412\) −0.643040 −0.0316803
\(413\) −29.0489 −1.42940
\(414\) 2.25348i 0.110753i
\(415\) −1.89381 −0.0929636
\(416\) −10.8283 + 11.4590i −0.530903 + 0.561823i
\(417\) −10.7714 −0.527477
\(418\) 0.182518i 0.00892725i
\(419\) 32.6525 1.59518 0.797588 0.603202i \(-0.206109\pi\)
0.797588 + 0.603202i \(0.206109\pi\)
\(420\) 39.3181 1.91853
\(421\) 28.3956i 1.38392i −0.721938 0.691958i \(-0.756748\pi\)
0.721938 0.691958i \(-0.243252\pi\)
\(422\) 5.54928i 0.270135i
\(423\) 5.42082i 0.263569i
\(424\) 13.5879i 0.659888i
\(425\) −5.93108 −0.287700
\(426\) 3.47661 0.168442
\(427\) 4.43525i 0.214637i
\(428\) −23.0542 −1.11437
\(429\) 2.47638 2.62060i 0.119561 0.126524i
\(430\) −7.74731 −0.373608
\(431\) 14.1585i 0.681992i 0.940065 + 0.340996i \(0.110764\pi\)
−0.940065 + 0.340996i \(0.889236\pi\)
\(432\) 3.02398 0.145491
\(433\) −15.5980 −0.749590 −0.374795 0.927108i \(-0.622287\pi\)
−0.374795 + 0.927108i \(0.622287\pi\)
\(434\) 3.23483i 0.155277i
\(435\) 27.2617i 1.30710i
\(436\) 8.45701i 0.405017i
\(437\) 2.45793i 0.117579i
\(438\) 2.43514 0.116356
\(439\) −16.0616 −0.766579 −0.383289 0.923628i \(-0.625209\pi\)
−0.383289 + 0.923628i \(0.625209\pi\)
\(440\) 6.49004i 0.309400i
\(441\) −19.8607 −0.945749
\(442\) −0.495087 + 0.523921i −0.0235489 + 0.0249204i
\(443\) −8.20834 −0.389990 −0.194995 0.980804i \(-0.562469\pi\)
−0.194995 + 0.980804i \(0.562469\pi\)
\(444\) 14.4256i 0.684609i
\(445\) −19.3921 −0.919273
\(446\) −4.85668 −0.229970
\(447\) 4.42220i 0.209163i
\(448\) 22.0746i 1.04292i
\(449\) 10.4304i 0.492242i −0.969239 0.246121i \(-0.920844\pi\)
0.969239 0.246121i \(-0.0791561\pi\)
\(450\) 4.96433i 0.234021i
\(451\) −8.78563 −0.413699
\(452\) 4.07955 0.191886
\(453\) 4.64014i 0.218013i
\(454\) 5.32831 0.250070
\(455\) 56.2226 + 53.1284i 2.63576 + 2.49070i
\(456\) 0.699530 0.0327585
\(457\) 18.1240i 0.847807i −0.905707 0.423904i \(-0.860660\pi\)
0.905707 0.423904i \(-0.139340\pi\)
\(458\) 2.64204 0.123454
\(459\) 0.488730 0.0228120
\(460\) 41.7919i 1.94856i
\(461\) 28.6242i 1.33316i 0.745432 + 0.666581i \(0.232243\pi\)
−0.745432 + 0.666581i \(0.767757\pi\)
\(462\) 2.12009i 0.0986356i
\(463\) 9.44955i 0.439158i 0.975595 + 0.219579i \(0.0704683\pi\)
−0.975595 + 0.219579i \(0.929532\pi\)
\(464\) −19.9151 −0.924534
\(465\) −6.31608 −0.292901
\(466\) 5.42489i 0.251303i
\(467\) −19.1423 −0.885800 −0.442900 0.896571i \(-0.646050\pi\)
−0.442900 + 0.896571i \(0.646050\pi\)
\(468\) 4.80268 + 4.53837i 0.222004 + 0.209786i
\(469\) −20.0812 −0.927265
\(470\) 9.17934i 0.423412i
\(471\) 10.8227 0.498683
\(472\) 8.78753 0.404479
\(473\) 4.57514i 0.210365i
\(474\) 3.64667i 0.167497i
\(475\) 5.41471i 0.248444i
\(476\) 4.64206i 0.212768i
\(477\) 8.66677 0.396824
\(478\) −0.174280 −0.00797136
\(479\) 11.5433i 0.527428i −0.964601 0.263714i \(-0.915052\pi\)
0.964601 0.263714i \(-0.0849476\pi\)
\(480\) −18.1007 −0.826182
\(481\) −19.4925 + 20.6278i −0.888783 + 0.940546i
\(482\) 5.31216 0.241962
\(483\) 28.5508i 1.29910i
\(484\) −1.83266 −0.0833029
\(485\) 8.52977 0.387317
\(486\) 0.409068i 0.0185557i
\(487\) 34.7318i 1.57385i 0.617051 + 0.786923i \(0.288327\pi\)
−0.617051 + 0.786923i \(0.711673\pi\)
\(488\) 1.34170i 0.0607360i
\(489\) 24.4714i 1.10663i
\(490\) 33.6311 1.51930
\(491\) −19.9935 −0.902295 −0.451148 0.892449i \(-0.648985\pi\)
−0.451148 + 0.892449i \(0.648985\pi\)
\(492\) 16.1011i 0.725894i
\(493\) −3.21863 −0.144960
\(494\) 0.478307 + 0.451983i 0.0215200 + 0.0203357i
\(495\) 4.13953 0.186058
\(496\) 4.61398i 0.207174i
\(497\) −44.0473 −1.97579
\(498\) −0.187147 −0.00838624
\(499\) 10.3565i 0.463623i −0.972761 0.231811i \(-0.925535\pi\)
0.972761 0.231811i \(-0.0744652\pi\)
\(500\) 54.1340i 2.42095i
\(501\) 1.26722i 0.0566151i
\(502\) 1.78845i 0.0798226i
\(503\) 41.2438 1.83897 0.919486 0.393124i \(-0.128606\pi\)
0.919486 + 0.393124i \(0.128606\pi\)
\(504\) 8.12559 0.361943
\(505\) 16.0018i 0.712070i
\(506\) −2.25348 −0.100180
\(507\) 0.735113 + 12.9792i 0.0326475 + 0.576426i
\(508\) 33.4512 1.48416
\(509\) 9.47338i 0.419900i 0.977712 + 0.209950i \(0.0673301\pi\)
−0.977712 + 0.209950i \(0.932670\pi\)
\(510\) −0.827590 −0.0366463
\(511\) −30.8523 −1.36483
\(512\) 22.7049i 1.00343i
\(513\) 0.446180i 0.0196993i
\(514\) 4.61420i 0.203524i
\(515\) 1.45247i 0.0640033i
\(516\) 8.38469 0.369115
\(517\) −5.42082 −0.238407
\(518\) 16.6881i 0.733231i
\(519\) −3.24638 −0.142500
\(520\) −17.0078 16.0718i −0.745842 0.704794i
\(521\) −6.47023 −0.283466 −0.141733 0.989905i \(-0.545267\pi\)
−0.141733 + 0.989905i \(0.545267\pi\)
\(522\) 2.69400i 0.117913i
\(523\) 16.1999 0.708372 0.354186 0.935175i \(-0.384758\pi\)
0.354186 + 0.935175i \(0.384758\pi\)
\(524\) 5.83640 0.254964
\(525\) 62.8961i 2.74501i
\(526\) 0.374140i 0.0163133i
\(527\) 0.745703i 0.0324833i
\(528\) 3.02398i 0.131602i
\(529\) 7.34712 0.319440
\(530\) −14.6759 −0.637479
\(531\) 5.60493i 0.243233i
\(532\) −4.23791 −0.183737
\(533\) 21.7565 23.0237i 0.942380 0.997265i
\(534\) −1.91633 −0.0829275
\(535\) 52.0738i 2.25135i
\(536\) 6.07474 0.262389
\(537\) 16.5303 0.713334
\(538\) 5.37451i 0.231712i
\(539\) 19.8607i 0.855462i
\(540\) 7.58636i 0.326465i
\(541\) 6.65767i 0.286236i 0.989706 + 0.143118i \(0.0457128\pi\)
−0.989706 + 0.143118i \(0.954287\pi\)
\(542\) −5.03862 −0.216427
\(543\) −12.2065 −0.523832
\(544\) 2.13705i 0.0916251i
\(545\) 19.1023 0.818252
\(546\) 5.55592 + 5.25014i 0.237771 + 0.224685i
\(547\) 2.06963 0.0884912 0.0442456 0.999021i \(-0.485912\pi\)
0.0442456 + 0.999021i \(0.485912\pi\)
\(548\) 9.37980i 0.400685i
\(549\) −0.855775 −0.0365236
\(550\) −4.96433 −0.211680
\(551\) 2.93841i 0.125181i
\(552\) 8.63684i 0.367608i
\(553\) 46.2020i 1.96471i
\(554\) 8.23841i 0.350016i
\(555\) −32.5838 −1.38311
\(556\) −19.7403 −0.837176
\(557\) 12.3459i 0.523111i −0.965188 0.261556i \(-0.915764\pi\)
0.965188 0.261556i \(-0.0842355\pi\)
\(558\) −0.624155 −0.0264226
\(559\) 11.9896 + 11.3298i 0.507107 + 0.479198i
\(560\) 64.8767 2.74154
\(561\) 0.488730i 0.0206342i
\(562\) −2.72712 −0.115037
\(563\) 3.72355 0.156929 0.0784645 0.996917i \(-0.474998\pi\)
0.0784645 + 0.996917i \(0.474998\pi\)
\(564\) 9.93454i 0.418320i
\(565\) 9.21469i 0.387665i
\(566\) 11.2735i 0.473859i
\(567\) 5.18273i 0.217654i
\(568\) 13.3247 0.559091
\(569\) −27.2092 −1.14067 −0.570334 0.821413i \(-0.693186\pi\)
−0.570334 + 0.821413i \(0.693186\pi\)
\(570\) 0.755539i 0.0316460i
\(571\) −31.1102 −1.30192 −0.650961 0.759112i \(-0.725634\pi\)
−0.650961 + 0.759112i \(0.725634\pi\)
\(572\) 4.53837 4.80268i 0.189759 0.200810i
\(573\) −17.4410 −0.728610
\(574\) 18.6263i 0.777448i
\(575\) 66.8534 2.78798
\(576\) 4.25925 0.177469
\(577\) 5.53948i 0.230611i −0.993330 0.115306i \(-0.963215\pi\)
0.993330 0.115306i \(-0.0367848\pi\)
\(578\) 6.85645i 0.285191i
\(579\) 0.941498i 0.0391273i
\(580\) 49.9616i 2.07454i
\(581\) 2.37107 0.0983687
\(582\) 0.842912 0.0349398
\(583\) 8.66677i 0.358941i
\(584\) 9.33309 0.386206
\(585\) −10.2510 + 10.8481i −0.423828 + 0.448512i
\(586\) −5.65032 −0.233413
\(587\) 27.8516i 1.14956i −0.818308 0.574780i \(-0.805088\pi\)
0.818308 0.574780i \(-0.194912\pi\)
\(588\) −36.3980 −1.50103
\(589\) 0.680780 0.0280511
\(590\) 9.49111i 0.390743i
\(591\) 16.7419i 0.688668i
\(592\) 23.8029i 0.978294i
\(593\) 0.298235i 0.0122470i 0.999981 + 0.00612351i \(0.00194919\pi\)
−0.999981 + 0.00612351i \(0.998051\pi\)
\(594\) 0.409068 0.0167843
\(595\) 10.4852 0.429853
\(596\) 8.10440i 0.331969i
\(597\) −13.1573 −0.538491
\(598\) 5.58048 5.90548i 0.228203 0.241493i
\(599\) 22.8194 0.932375 0.466188 0.884686i \(-0.345627\pi\)
0.466188 + 0.884686i \(0.345627\pi\)
\(600\) 19.0266i 0.776758i
\(601\) −2.27297 −0.0927164 −0.0463582 0.998925i \(-0.514762\pi\)
−0.0463582 + 0.998925i \(0.514762\pi\)
\(602\) 9.69971 0.395331
\(603\) 3.87464i 0.157788i
\(604\) 8.50381i 0.346015i
\(605\) 4.13953i 0.168296i
\(606\) 1.58130i 0.0642358i
\(607\) −4.31576 −0.175171 −0.0875857 0.996157i \(-0.527915\pi\)
−0.0875857 + 0.996157i \(0.527915\pi\)
\(608\) 1.95099 0.0791231
\(609\) 34.1320i 1.38310i
\(610\) 1.44913 0.0586734
\(611\) 13.4240 14.2058i 0.543077 0.574706i
\(612\) 0.895677 0.0362056
\(613\) 11.3555i 0.458646i 0.973350 + 0.229323i \(0.0736512\pi\)
−0.973350 + 0.229323i \(0.926349\pi\)
\(614\) 8.62593 0.348114
\(615\) 36.3684 1.46651
\(616\) 8.12559i 0.327390i
\(617\) 23.6846i 0.953507i −0.879037 0.476753i \(-0.841814\pi\)
0.879037 0.476753i \(-0.158186\pi\)
\(618\) 0.143533i 0.00577373i
\(619\) 27.4080i 1.10162i 0.834631 + 0.550810i \(0.185681\pi\)
−0.834631 + 0.550810i \(0.814319\pi\)
\(620\) −11.5753 −0.464873
\(621\) −5.50882 −0.221061
\(622\) 12.1844i 0.488550i
\(623\) 24.2791 0.972721
\(624\) 7.92465 + 7.48852i 0.317240 + 0.299781i
\(625\) 61.5968 2.46387
\(626\) 10.7875i 0.431156i
\(627\) −0.446180 −0.0178187
\(628\) 19.8344 0.791477
\(629\) 3.84698i 0.153389i
\(630\) 8.77618i 0.349651i
\(631\) 42.3930i 1.68764i −0.536627 0.843819i \(-0.680302\pi\)
0.536627 0.843819i \(-0.319698\pi\)
\(632\) 13.9765i 0.555954i
\(633\) 13.5657 0.539186
\(634\) −10.0251 −0.398149
\(635\) 75.5579i 2.99842i
\(636\) 15.8833 0.629812
\(637\) −52.0471 49.1826i −2.06218 1.94869i
\(638\) −2.69400 −0.106657
\(639\) 8.49886i 0.336210i
\(640\) −43.4139 −1.71608
\(641\) −18.4040 −0.726916 −0.363458 0.931611i \(-0.618404\pi\)
−0.363458 + 0.931611i \(0.618404\pi\)
\(642\) 5.14593i 0.203094i
\(643\) 0.572048i 0.0225594i 0.999936 + 0.0112797i \(0.00359051\pi\)
−0.999936 + 0.0112797i \(0.996409\pi\)
\(644\) 52.3239i 2.06185i
\(645\) 18.9389i 0.745719i
\(646\) 0.0892020 0.00350961
\(647\) −16.2324 −0.638163 −0.319082 0.947727i \(-0.603374\pi\)
−0.319082 + 0.947727i \(0.603374\pi\)
\(648\) 1.56782i 0.0615898i
\(649\) −5.60493 −0.220013
\(650\) 12.2936 13.0095i 0.482193 0.510276i
\(651\) 7.90780 0.309931
\(652\) 44.8478i 1.75638i
\(653\) −2.56096 −0.100218 −0.0501090 0.998744i \(-0.515957\pi\)
−0.0501090 + 0.998744i \(0.515957\pi\)
\(654\) 1.88769 0.0738144
\(655\) 13.1830i 0.515102i
\(656\) 26.5676i 1.03729i
\(657\) 5.95291i 0.232245i
\(658\) 11.4926i 0.448029i
\(659\) −37.8432 −1.47416 −0.737082 0.675804i \(-0.763797\pi\)
−0.737082 + 0.675804i \(0.763797\pi\)
\(660\) 7.58636 0.295299
\(661\) 33.9955i 1.32227i −0.750267 0.661135i \(-0.770075\pi\)
0.750267 0.661135i \(-0.229925\pi\)
\(662\) −4.29378 −0.166882
\(663\) 1.28077 + 1.21028i 0.0497409 + 0.0470034i
\(664\) −0.717270 −0.0278355
\(665\) 9.57238i 0.371201i
\(666\) −3.21993 −0.124770
\(667\) 36.2795 1.40475
\(668\) 2.32238i 0.0898558i
\(669\) 11.8725i 0.459019i
\(670\) 6.56112i 0.253478i
\(671\) 0.855775i 0.0330368i
\(672\) 22.6623 0.874217
\(673\) 34.7689 1.34024 0.670122 0.742251i \(-0.266242\pi\)
0.670122 + 0.742251i \(0.266242\pi\)
\(674\) 8.96280i 0.345234i
\(675\) −12.1357 −0.467103
\(676\) 1.34721 + 23.7865i 0.0518159 + 0.914865i
\(677\) −31.6215 −1.21531 −0.607656 0.794201i \(-0.707890\pi\)
−0.607656 + 0.794201i \(0.707890\pi\)
\(678\) 0.910595i 0.0349712i
\(679\) −10.6794 −0.409836
\(680\) −3.17188 −0.121636
\(681\) 13.0255i 0.499138i
\(682\) 0.624155i 0.0239001i
\(683\) 29.1127i 1.11397i −0.830523 0.556984i \(-0.811959\pi\)
0.830523 0.556984i \(-0.188041\pi\)
\(684\) 0.817698i 0.0312654i
\(685\) −21.1866 −0.809500
\(686\) −27.2659 −1.04102
\(687\) 6.45867i 0.246414i
\(688\) 13.8351 0.527459
\(689\) 22.7122 + 21.4622i 0.865264 + 0.817644i
\(690\) 9.32836 0.355125
\(691\) 6.72289i 0.255751i −0.991790 0.127875i \(-0.959184\pi\)
0.991790 0.127875i \(-0.0408158\pi\)
\(692\) −5.94953 −0.226167
\(693\) −5.18273 −0.196876
\(694\) 6.71357i 0.254844i
\(695\) 44.5885i 1.69134i
\(696\) 10.3252i 0.391376i
\(697\) 4.29380i 0.162639i
\(698\) −10.2641 −0.388503
\(699\) 13.2616 0.501599
\(700\) 115.267i 4.35670i
\(701\) 33.5332 1.26653 0.633265 0.773935i \(-0.281714\pi\)
0.633265 + 0.773935i \(0.281714\pi\)
\(702\) −1.01301 + 1.07200i −0.0382335 + 0.0404602i
\(703\) 3.51205 0.132460
\(704\) 4.25925i 0.160526i
\(705\) 22.4396 0.845126
\(706\) −3.76204 −0.141586
\(707\) 20.0344i 0.753471i
\(708\) 10.2720i 0.386044i
\(709\) 40.1123i 1.50645i 0.657764 + 0.753224i \(0.271502\pi\)
−0.657764 + 0.753224i \(0.728498\pi\)
\(710\) 14.3915i 0.540105i
\(711\) −8.91459 −0.334323
\(712\) −7.34463 −0.275252
\(713\) 8.40535i 0.314783i
\(714\) 1.03615 0.0387770
\(715\) 10.8481 + 10.2510i 0.405694 + 0.383367i
\(716\) 30.2944 1.13216
\(717\) 0.426040i 0.0159108i
\(718\) 9.25458 0.345378
\(719\) −7.15141 −0.266703 −0.133351 0.991069i \(-0.542574\pi\)
−0.133351 + 0.991069i \(0.542574\pi\)
\(720\) 12.5179i 0.466513i
\(721\) 1.81850i 0.0677246i
\(722\) 7.69086i 0.286224i
\(723\) 12.9860i 0.482955i
\(724\) −22.3704 −0.831390
\(725\) 79.9222 2.96824
\(726\) 0.409068i 0.0151819i
\(727\) 38.2917 1.42016 0.710081 0.704120i \(-0.248658\pi\)
0.710081 + 0.704120i \(0.248658\pi\)
\(728\) 21.2940 + 20.1220i 0.789206 + 0.745772i
\(729\) 1.00000 0.0370370
\(730\) 10.0804i 0.373091i
\(731\) 2.23601 0.0827017
\(732\) −1.56835 −0.0579678
\(733\) 35.4025i 1.30762i −0.756658 0.653811i \(-0.773169\pi\)
0.756658 0.653811i \(-0.226831\pi\)
\(734\) 5.70013i 0.210395i
\(735\) 82.2141i 3.03251i
\(736\) 24.0882i 0.887902i
\(737\) −3.87464 −0.142724
\(738\) 3.59392 0.132294
\(739\) 2.87016i 0.105580i −0.998606 0.0527902i \(-0.983189\pi\)
0.998606 0.0527902i \(-0.0168115\pi\)
\(740\) −59.7152 −2.19517
\(741\) 1.10491 1.16926i 0.0405899 0.0429538i
\(742\) 18.3743 0.674543
\(743\) 23.1129i 0.847930i 0.905679 + 0.423965i \(0.139362\pi\)
−0.905679 + 0.423965i \(0.860638\pi\)
\(744\) −2.39218 −0.0877014
\(745\) −18.3058 −0.670673
\(746\) 8.39016i 0.307185i
\(747\) 0.457495i 0.0167389i
\(748\) 0.895677i 0.0327492i
\(749\) 65.1969i 2.38224i
\(750\) 12.0832 0.441218
\(751\) 37.5587 1.37054 0.685268 0.728291i \(-0.259685\pi\)
0.685268 + 0.728291i \(0.259685\pi\)
\(752\) 16.3925i 0.597771i
\(753\) −4.37202 −0.159325
\(754\) 6.67137 7.05991i 0.242957 0.257107i
\(755\) −19.2080 −0.699050
\(756\) 9.49821i 0.345446i
\(757\) −47.4259 −1.72372 −0.861862 0.507143i \(-0.830702\pi\)
−0.861862 + 0.507143i \(0.830702\pi\)
\(758\) 0.952354 0.0345910
\(759\) 5.50882i 0.199958i
\(760\) 2.89572i 0.105039i
\(761\) 23.0592i 0.835895i −0.908471 0.417947i \(-0.862750\pi\)
0.908471 0.417947i \(-0.137250\pi\)
\(762\) 7.46663i 0.270487i
\(763\) −23.9163 −0.865826
\(764\) −31.9636 −1.15640
\(765\) 2.02311i 0.0731458i
\(766\) −11.1350 −0.402323
\(767\) 13.8799 14.6883i 0.501175 0.530364i
\(768\) 4.22834 0.152577
\(769\) 40.2536i 1.45158i −0.687915 0.725792i \(-0.741474\pi\)
0.687915 0.725792i \(-0.258526\pi\)
\(770\) 8.77618 0.316272
\(771\) 11.2798 0.406232
\(772\) 1.72545i 0.0621003i
\(773\) 25.6183i 0.921426i 0.887549 + 0.460713i \(0.152406\pi\)
−0.887549 + 0.460713i \(0.847594\pi\)
\(774\) 1.87154i 0.0672712i
\(775\) 18.5166i 0.665137i
\(776\) 3.23060 0.115972
\(777\) 40.7953 1.46352
\(778\) 10.1988i 0.365645i
\(779\) −3.91997 −0.140448
\(780\) −18.7867 + 19.8808i −0.672672 + 0.711848i
\(781\) −8.49886 −0.304113
\(782\) 1.10134i 0.0393840i
\(783\) −6.58571 −0.235354
\(784\) −60.0585 −2.14495
\(785\) 44.8009i 1.59901i
\(786\) 1.30274i 0.0464673i
\(787\) 23.3425i 0.832070i −0.909349 0.416035i \(-0.863419\pi\)
0.909349 0.416035i \(-0.136581\pi\)
\(788\) 30.6822i 1.09301i
\(789\) −0.914614 −0.0325611
\(790\) 15.0955 0.537074
\(791\) 11.5369i 0.410204i
\(792\) 1.56782 <