Properties

Label 429.2.b.b.298.6
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 298.6
Root \(-0.584778i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.9

$q$-expansion

\(f(q)\) \(=\) \(q-0.584778i q^{2} +1.00000 q^{3} +1.65803 q^{4} -1.95350i q^{5} -0.584778i q^{6} -1.51078i q^{7} -2.13914i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.584778i q^{2} +1.00000 q^{3} +1.65803 q^{4} -1.95350i q^{5} -0.584778i q^{6} -1.51078i q^{7} -2.13914i q^{8} +1.00000 q^{9} -1.14237 q^{10} -1.00000i q^{11} +1.65803 q^{12} +(-3.49467 + 0.887280i) q^{13} -0.883474 q^{14} -1.95350i q^{15} +2.06515 q^{16} -3.44198 q^{17} -0.584778i q^{18} +5.09587i q^{19} -3.23897i q^{20} -1.51078i q^{21} -0.584778 q^{22} +0.701611 q^{23} -2.13914i q^{24} +1.18383 q^{25} +(0.518862 + 2.04361i) q^{26} +1.00000 q^{27} -2.50493i q^{28} +5.04937 q^{29} -1.14237 q^{30} +7.26957i q^{31} -5.48593i q^{32} -1.00000i q^{33} +2.01280i q^{34} -2.95132 q^{35} +1.65803 q^{36} +2.08160i q^{37} +2.97995 q^{38} +(-3.49467 + 0.887280i) q^{39} -4.17882 q^{40} +1.03658i q^{41} -0.883474 q^{42} +5.48659 q^{43} -1.65803i q^{44} -1.95350i q^{45} -0.410287i q^{46} -3.75225i q^{47} +2.06515 q^{48} +4.71753 q^{49} -0.692276i q^{50} -3.44198 q^{51} +(-5.79429 + 1.47114i) q^{52} -0.502747 q^{53} -0.584778i q^{54} -1.95350 q^{55} -3.23178 q^{56} +5.09587i q^{57} -2.95276i q^{58} +2.65023i q^{59} -3.23897i q^{60} -5.38195 q^{61} +4.25109 q^{62} -1.51078i q^{63} +0.922236 q^{64} +(1.73330 + 6.82685i) q^{65} -0.584778 q^{66} -8.47197i q^{67} -5.70692 q^{68} +0.701611 q^{69} +1.72587i q^{70} -2.31533i q^{71} -2.13914i q^{72} -2.21094i q^{73} +1.21727 q^{74} +1.18383 q^{75} +8.44913i q^{76} -1.51078 q^{77} +(0.518862 + 2.04361i) q^{78} -5.54589 q^{79} -4.03427i q^{80} +1.00000 q^{81} +0.606168 q^{82} +14.5137i q^{83} -2.50493i q^{84} +6.72392i q^{85} -3.20844i q^{86} +5.04937 q^{87} -2.13914 q^{88} +1.80966i q^{89} -1.14237 q^{90} +(1.34049 + 5.27970i) q^{91} +1.16330 q^{92} +7.26957i q^{93} -2.19424 q^{94} +9.95480 q^{95} -5.48593i q^{96} +14.5085i q^{97} -2.75871i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.584778i 0.413501i −0.978394 0.206750i \(-0.933711\pi\)
0.978394 0.206750i \(-0.0662888\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.65803 0.829017
\(5\) 1.95350i 0.873633i −0.899551 0.436817i \(-0.856106\pi\)
0.899551 0.436817i \(-0.143894\pi\)
\(6\) 0.584778i 0.238735i
\(7\) 1.51078i 0.571023i −0.958375 0.285511i \(-0.907837\pi\)
0.958375 0.285511i \(-0.0921634\pi\)
\(8\) 2.13914i 0.756300i
\(9\) 1.00000 0.333333
\(10\) −1.14237 −0.361248
\(11\) 1.00000i 0.301511i
\(12\) 1.65803 0.478633
\(13\) −3.49467 + 0.887280i −0.969248 + 0.246087i
\(14\) −0.883474 −0.236118
\(15\) 1.95350i 0.504392i
\(16\) 2.06515 0.516286
\(17\) −3.44198 −0.834803 −0.417401 0.908722i \(-0.637059\pi\)
−0.417401 + 0.908722i \(0.637059\pi\)
\(18\) 0.584778i 0.137834i
\(19\) 5.09587i 1.16907i 0.811368 + 0.584536i \(0.198724\pi\)
−0.811368 + 0.584536i \(0.801276\pi\)
\(20\) 3.23897i 0.724257i
\(21\) 1.51078i 0.329680i
\(22\) −0.584778 −0.124675
\(23\) 0.701611 0.146296 0.0731480 0.997321i \(-0.476695\pi\)
0.0731480 + 0.997321i \(0.476695\pi\)
\(24\) 2.13914i 0.436650i
\(25\) 1.18383 0.236765
\(26\) 0.518862 + 2.04361i 0.101757 + 0.400785i
\(27\) 1.00000 0.192450
\(28\) 2.50493i 0.473388i
\(29\) 5.04937 0.937645 0.468822 0.883292i \(-0.344678\pi\)
0.468822 + 0.883292i \(0.344678\pi\)
\(30\) −1.14237 −0.208567
\(31\) 7.26957i 1.30565i 0.757507 + 0.652827i \(0.226417\pi\)
−0.757507 + 0.652827i \(0.773583\pi\)
\(32\) 5.48593i 0.969785i
\(33\) 1.00000i 0.174078i
\(34\) 2.01280i 0.345192i
\(35\) −2.95132 −0.498864
\(36\) 1.65803 0.276339
\(37\) 2.08160i 0.342213i 0.985253 + 0.171106i \(0.0547342\pi\)
−0.985253 + 0.171106i \(0.945266\pi\)
\(38\) 2.97995 0.483413
\(39\) −3.49467 + 0.887280i −0.559595 + 0.142079i
\(40\) −4.17882 −0.660729
\(41\) 1.03658i 0.161886i 0.996719 + 0.0809430i \(0.0257932\pi\)
−0.996719 + 0.0809430i \(0.974207\pi\)
\(42\) −0.883474 −0.136323
\(43\) 5.48659 0.836698 0.418349 0.908286i \(-0.362609\pi\)
0.418349 + 0.908286i \(0.362609\pi\)
\(44\) 1.65803i 0.249958i
\(45\) 1.95350i 0.291211i
\(46\) 0.410287i 0.0604935i
\(47\) 3.75225i 0.547322i −0.961826 0.273661i \(-0.911765\pi\)
0.961826 0.273661i \(-0.0882347\pi\)
\(48\) 2.06515 0.298078
\(49\) 4.71753 0.673933
\(50\) 0.692276i 0.0979026i
\(51\) −3.44198 −0.481974
\(52\) −5.79429 + 1.47114i −0.803523 + 0.204010i
\(53\) −0.502747 −0.0690575 −0.0345288 0.999404i \(-0.510993\pi\)
−0.0345288 + 0.999404i \(0.510993\pi\)
\(54\) 0.584778i 0.0795783i
\(55\) −1.95350 −0.263410
\(56\) −3.23178 −0.431865
\(57\) 5.09587i 0.674964i
\(58\) 2.95276i 0.387717i
\(59\) 2.65023i 0.345031i 0.985007 + 0.172515i \(0.0551894\pi\)
−0.985007 + 0.172515i \(0.944811\pi\)
\(60\) 3.23897i 0.418150i
\(61\) −5.38195 −0.689088 −0.344544 0.938770i \(-0.611967\pi\)
−0.344544 + 0.938770i \(0.611967\pi\)
\(62\) 4.25109 0.539889
\(63\) 1.51078i 0.190341i
\(64\) 0.922236 0.115279
\(65\) 1.73330 + 6.82685i 0.214990 + 0.846767i
\(66\) −0.584778 −0.0719813
\(67\) 8.47197i 1.03502i −0.855679 0.517508i \(-0.826860\pi\)
0.855679 0.517508i \(-0.173140\pi\)
\(68\) −5.70692 −0.692066
\(69\) 0.701611 0.0844640
\(70\) 1.72587i 0.206281i
\(71\) 2.31533i 0.274779i −0.990517 0.137390i \(-0.956129\pi\)
0.990517 0.137390i \(-0.0438712\pi\)
\(72\) 2.13914i 0.252100i
\(73\) 2.21094i 0.258771i −0.991594 0.129385i \(-0.958700\pi\)
0.991594 0.129385i \(-0.0413004\pi\)
\(74\) 1.21727 0.141505
\(75\) 1.18383 0.136696
\(76\) 8.44913i 0.969181i
\(77\) −1.51078 −0.172170
\(78\) 0.518862 + 2.04361i 0.0587496 + 0.231393i
\(79\) −5.54589 −0.623961 −0.311981 0.950088i \(-0.600992\pi\)
−0.311981 + 0.950088i \(0.600992\pi\)
\(80\) 4.03427i 0.451045i
\(81\) 1.00000 0.111111
\(82\) 0.606168 0.0669400
\(83\) 14.5137i 1.59308i 0.604585 + 0.796541i \(0.293339\pi\)
−0.604585 + 0.796541i \(0.706661\pi\)
\(84\) 2.50493i 0.273310i
\(85\) 6.72392i 0.729311i
\(86\) 3.20844i 0.345975i
\(87\) 5.04937 0.541350
\(88\) −2.13914 −0.228033
\(89\) 1.80966i 0.191824i 0.995390 + 0.0959119i \(0.0305767\pi\)
−0.995390 + 0.0959119i \(0.969423\pi\)
\(90\) −1.14237 −0.120416
\(91\) 1.34049 + 5.27970i 0.140521 + 0.553462i
\(92\) 1.16330 0.121282
\(93\) 7.26957i 0.753819i
\(94\) −2.19424 −0.226318
\(95\) 9.95480 1.02134
\(96\) 5.48593i 0.559906i
\(97\) 14.5085i 1.47312i 0.676372 + 0.736560i \(0.263551\pi\)
−0.676372 + 0.736560i \(0.736449\pi\)
\(98\) 2.75871i 0.278672i
\(99\) 1.00000i 0.100504i
\(100\) 1.96282 0.196282
\(101\) −8.63799 −0.859512 −0.429756 0.902945i \(-0.641400\pi\)
−0.429756 + 0.902945i \(0.641400\pi\)
\(102\) 2.01280i 0.199296i
\(103\) 2.90048 0.285792 0.142896 0.989738i \(-0.454358\pi\)
0.142896 + 0.989738i \(0.454358\pi\)
\(104\) 1.89802 + 7.47559i 0.186116 + 0.733042i
\(105\) −2.95132 −0.288019
\(106\) 0.293995i 0.0285554i
\(107\) −2.29234 −0.221609 −0.110805 0.993842i \(-0.535343\pi\)
−0.110805 + 0.993842i \(0.535343\pi\)
\(108\) 1.65803 0.159544
\(109\) 12.8818i 1.23386i 0.787019 + 0.616929i \(0.211623\pi\)
−0.787019 + 0.616929i \(0.788377\pi\)
\(110\) 1.14237i 0.108920i
\(111\) 2.08160i 0.197577i
\(112\) 3.11999i 0.294811i
\(113\) −12.6273 −1.18788 −0.593940 0.804509i \(-0.702428\pi\)
−0.593940 + 0.804509i \(0.702428\pi\)
\(114\) 2.97995 0.279098
\(115\) 1.37060i 0.127809i
\(116\) 8.37203 0.777324
\(117\) −3.49467 + 0.887280i −0.323083 + 0.0820291i
\(118\) 1.54980 0.142670
\(119\) 5.20009i 0.476691i
\(120\) −4.17882 −0.381472
\(121\) −1.00000 −0.0909091
\(122\) 3.14725i 0.284939i
\(123\) 1.03658i 0.0934649i
\(124\) 12.0532i 1.08241i
\(125\) 12.0801i 1.08048i
\(126\) −0.883474 −0.0787061
\(127\) −5.05085 −0.448190 −0.224095 0.974567i \(-0.571943\pi\)
−0.224095 + 0.974567i \(0.571943\pi\)
\(128\) 11.5112i 1.01745i
\(129\) 5.48659 0.483068
\(130\) 3.99220 1.01360i 0.350139 0.0888985i
\(131\) 15.9772 1.39594 0.697968 0.716129i \(-0.254088\pi\)
0.697968 + 0.716129i \(0.254088\pi\)
\(132\) 1.65803i 0.144313i
\(133\) 7.69876 0.667567
\(134\) −4.95422 −0.427980
\(135\) 1.95350i 0.168131i
\(136\) 7.36288i 0.631361i
\(137\) 17.2582i 1.47447i 0.675639 + 0.737233i \(0.263868\pi\)
−0.675639 + 0.737233i \(0.736132\pi\)
\(138\) 0.410287i 0.0349260i
\(139\) −5.70544 −0.483929 −0.241965 0.970285i \(-0.577792\pi\)
−0.241965 + 0.970285i \(0.577792\pi\)
\(140\) −4.89339 −0.413567
\(141\) 3.75225i 0.315997i
\(142\) −1.35395 −0.113621
\(143\) 0.887280 + 3.49467i 0.0741981 + 0.292239i
\(144\) 2.06515 0.172095
\(145\) 9.86396i 0.819158i
\(146\) −1.29291 −0.107002
\(147\) 4.71753 0.389095
\(148\) 3.45136i 0.283700i
\(149\) 0.161015i 0.0131908i −0.999978 0.00659542i \(-0.997901\pi\)
0.999978 0.00659542i \(-0.00209940\pi\)
\(150\) 0.692276i 0.0565241i
\(151\) 16.3107i 1.32734i −0.748025 0.663671i \(-0.768997\pi\)
0.748025 0.663671i \(-0.231003\pi\)
\(152\) 10.9008 0.884170
\(153\) −3.44198 −0.278268
\(154\) 0.883474i 0.0711924i
\(155\) 14.2011 1.14066
\(156\) −5.79429 + 1.47114i −0.463914 + 0.117786i
\(157\) −14.2192 −1.13481 −0.567407 0.823437i \(-0.692053\pi\)
−0.567407 + 0.823437i \(0.692053\pi\)
\(158\) 3.24312i 0.258008i
\(159\) −0.502747 −0.0398704
\(160\) −10.7168 −0.847236
\(161\) 1.05998i 0.0835384i
\(162\) 0.584778i 0.0459445i
\(163\) 13.0186i 1.01970i −0.860264 0.509848i \(-0.829702\pi\)
0.860264 0.509848i \(-0.170298\pi\)
\(164\) 1.71868i 0.134206i
\(165\) −1.95350 −0.152080
\(166\) 8.48728 0.658740
\(167\) 14.0271i 1.08545i −0.839911 0.542724i \(-0.817393\pi\)
0.839911 0.542724i \(-0.182607\pi\)
\(168\) −3.23178 −0.249337
\(169\) 11.4255 6.20151i 0.878882 0.477039i
\(170\) 3.93200 0.301571
\(171\) 5.09587i 0.389691i
\(172\) 9.09696 0.693637
\(173\) −17.8674 −1.35844 −0.679218 0.733936i \(-0.737681\pi\)
−0.679218 + 0.733936i \(0.737681\pi\)
\(174\) 2.95276i 0.223848i
\(175\) 1.78851i 0.135198i
\(176\) 2.06515i 0.155666i
\(177\) 2.65023i 0.199204i
\(178\) 1.05825 0.0793193
\(179\) −17.2723 −1.29099 −0.645495 0.763764i \(-0.723349\pi\)
−0.645495 + 0.763764i \(0.723349\pi\)
\(180\) 3.23897i 0.241419i
\(181\) −3.70318 −0.275255 −0.137628 0.990484i \(-0.543948\pi\)
−0.137628 + 0.990484i \(0.543948\pi\)
\(182\) 3.08745 0.783889i 0.228857 0.0581057i
\(183\) −5.38195 −0.397845
\(184\) 1.50084i 0.110644i
\(185\) 4.06641 0.298969
\(186\) 4.25109 0.311705
\(187\) 3.44198i 0.251703i
\(188\) 6.22136i 0.453740i
\(189\) 1.51078i 0.109893i
\(190\) 5.82135i 0.422325i
\(191\) −20.6259 −1.49243 −0.746217 0.665702i \(-0.768132\pi\)
−0.746217 + 0.665702i \(0.768132\pi\)
\(192\) 0.922236 0.0665566
\(193\) 18.8475i 1.35667i −0.734753 0.678335i \(-0.762702\pi\)
0.734753 0.678335i \(-0.237298\pi\)
\(194\) 8.48429 0.609136
\(195\) 1.73330 + 6.82685i 0.124124 + 0.488881i
\(196\) 7.82183 0.558702
\(197\) 7.18370i 0.511818i −0.966701 0.255909i \(-0.917625\pi\)
0.966701 0.255909i \(-0.0823747\pi\)
\(198\) −0.584778 −0.0415584
\(199\) 18.9591 1.34398 0.671989 0.740562i \(-0.265440\pi\)
0.671989 + 0.740562i \(0.265440\pi\)
\(200\) 2.53237i 0.179066i
\(201\) 8.47197i 0.597566i
\(202\) 5.05131i 0.355409i
\(203\) 7.62851i 0.535417i
\(204\) −5.70692 −0.399564
\(205\) 2.02496 0.141429
\(206\) 1.69614i 0.118175i
\(207\) 0.701611 0.0487653
\(208\) −7.21701 + 1.83236i −0.500409 + 0.127051i
\(209\) 5.09587 0.352489
\(210\) 1.72587i 0.119096i
\(211\) −19.9916 −1.37628 −0.688139 0.725578i \(-0.741572\pi\)
−0.688139 + 0.725578i \(0.741572\pi\)
\(212\) −0.833571 −0.0572499
\(213\) 2.31533i 0.158644i
\(214\) 1.34051i 0.0916356i
\(215\) 10.7181i 0.730967i
\(216\) 2.13914i 0.145550i
\(217\) 10.9828 0.745558
\(218\) 7.53303 0.510201
\(219\) 2.21094i 0.149401i
\(220\) −3.23897 −0.218372
\(221\) 12.0286 3.05400i 0.809131 0.205434i
\(222\) 1.21727 0.0816981
\(223\) 27.7784i 1.86018i −0.367330 0.930091i \(-0.619728\pi\)
0.367330 0.930091i \(-0.380272\pi\)
\(224\) −8.28806 −0.553769
\(225\) 1.18383 0.0789218
\(226\) 7.38419i 0.491189i
\(227\) 28.6524i 1.90173i 0.309612 + 0.950863i \(0.399801\pi\)
−0.309612 + 0.950863i \(0.600199\pi\)
\(228\) 8.44913i 0.559557i
\(229\) 4.83459i 0.319479i −0.987159 0.159739i \(-0.948935\pi\)
0.987159 0.159739i \(-0.0510654\pi\)
\(230\) −0.801497 −0.0528491
\(231\) −1.51078 −0.0994023
\(232\) 10.8013i 0.709141i
\(233\) −13.6237 −0.892518 −0.446259 0.894904i \(-0.647244\pi\)
−0.446259 + 0.894904i \(0.647244\pi\)
\(234\) 0.518862 + 2.04361i 0.0339191 + 0.133595i
\(235\) −7.33004 −0.478159
\(236\) 4.39417i 0.286036i
\(237\) −5.54589 −0.360244
\(238\) 3.04090 0.197112
\(239\) 5.99903i 0.388045i −0.980997 0.194023i \(-0.937846\pi\)
0.980997 0.194023i \(-0.0621535\pi\)
\(240\) 4.03427i 0.260411i
\(241\) 12.9290i 0.832831i 0.909174 + 0.416416i \(0.136714\pi\)
−0.909174 + 0.416416i \(0.863286\pi\)
\(242\) 0.584778i 0.0375910i
\(243\) 1.00000 0.0641500
\(244\) −8.92346 −0.571266
\(245\) 9.21571i 0.588770i
\(246\) 0.606168 0.0386478
\(247\) −4.52146 17.8084i −0.287694 1.13312i
\(248\) 15.5506 0.987466
\(249\) 14.5137i 0.919766i
\(250\) −7.06420 −0.446779
\(251\) 23.9724 1.51313 0.756563 0.653921i \(-0.226877\pi\)
0.756563 + 0.653921i \(0.226877\pi\)
\(252\) 2.50493i 0.157796i
\(253\) 0.701611i 0.0441099i
\(254\) 2.95363i 0.185327i
\(255\) 6.72392i 0.421068i
\(256\) −4.88701 −0.305438
\(257\) −16.3441 −1.01952 −0.509758 0.860318i \(-0.670265\pi\)
−0.509758 + 0.860318i \(0.670265\pi\)
\(258\) 3.20844i 0.199749i
\(259\) 3.14485 0.195411
\(260\) 2.87388 + 11.3192i 0.178230 + 0.701984i
\(261\) 5.04937 0.312548
\(262\) 9.34313i 0.577220i
\(263\) 10.1510 0.625936 0.312968 0.949764i \(-0.398677\pi\)
0.312968 + 0.949764i \(0.398677\pi\)
\(264\) −2.13914 −0.131655
\(265\) 0.982117i 0.0603310i
\(266\) 4.50207i 0.276040i
\(267\) 1.80966i 0.110750i
\(268\) 14.0468i 0.858045i
\(269\) 16.5294 1.00781 0.503907 0.863758i \(-0.331895\pi\)
0.503907 + 0.863758i \(0.331895\pi\)
\(270\) −1.14237 −0.0695222
\(271\) 20.8927i 1.26914i −0.772865 0.634570i \(-0.781177\pi\)
0.772865 0.634570i \(-0.218823\pi\)
\(272\) −7.10819 −0.430997
\(273\) 1.34049 + 5.27970i 0.0811301 + 0.319542i
\(274\) 10.0922 0.609693
\(275\) 1.18383i 0.0713874i
\(276\) 1.16330 0.0700221
\(277\) 17.3070 1.03988 0.519938 0.854204i \(-0.325955\pi\)
0.519938 + 0.854204i \(0.325955\pi\)
\(278\) 3.33642i 0.200105i
\(279\) 7.26957i 0.435218i
\(280\) 6.31329i 0.377291i
\(281\) 16.0666i 0.958450i 0.877692 + 0.479225i \(0.159082\pi\)
−0.877692 + 0.479225i \(0.840918\pi\)
\(282\) −2.19424 −0.130665
\(283\) 17.2180 1.02350 0.511751 0.859134i \(-0.328997\pi\)
0.511751 + 0.859134i \(0.328997\pi\)
\(284\) 3.83890i 0.227797i
\(285\) 9.95480 0.589671
\(286\) 2.04361 0.518862i 0.120841 0.0306810i
\(287\) 1.56604 0.0924406
\(288\) 5.48593i 0.323262i
\(289\) −5.15277 −0.303104
\(290\) −5.76823 −0.338722
\(291\) 14.5085i 0.850506i
\(292\) 3.66581i 0.214525i
\(293\) 5.29670i 0.309436i −0.987959 0.154718i \(-0.950553\pi\)
0.987959 0.154718i \(-0.0494470\pi\)
\(294\) 2.75871i 0.160891i
\(295\) 5.17723 0.301430
\(296\) 4.45283 0.258816
\(297\) 1.00000i 0.0580259i
\(298\) −0.0941580 −0.00545443
\(299\) −2.45190 + 0.622525i −0.141797 + 0.0360016i
\(300\) 1.96282 0.113324
\(301\) 8.28906i 0.477773i
\(302\) −9.53812 −0.548857
\(303\) −8.63799 −0.496240
\(304\) 10.5237i 0.603576i
\(305\) 10.5137i 0.602010i
\(306\) 2.01280i 0.115064i
\(307\) 26.3020i 1.50113i −0.660794 0.750567i \(-0.729780\pi\)
0.660794 0.750567i \(-0.270220\pi\)
\(308\) −2.50493 −0.142732
\(309\) 2.90048 0.165002
\(310\) 8.30451i 0.471665i
\(311\) −32.8590 −1.86326 −0.931632 0.363403i \(-0.881615\pi\)
−0.931632 + 0.363403i \(0.881615\pi\)
\(312\) 1.89802 + 7.47559i 0.107454 + 0.423222i
\(313\) 33.2130 1.87731 0.938655 0.344858i \(-0.112073\pi\)
0.938655 + 0.344858i \(0.112073\pi\)
\(314\) 8.31507i 0.469247i
\(315\) −2.95132 −0.166288
\(316\) −9.19527 −0.517274
\(317\) 30.8436i 1.73235i 0.499740 + 0.866175i \(0.333429\pi\)
−0.499740 + 0.866175i \(0.666571\pi\)
\(318\) 0.293995i 0.0164864i
\(319\) 5.04937i 0.282711i
\(320\) 1.80159i 0.100712i
\(321\) −2.29234 −0.127946
\(322\) −0.619855 −0.0345432
\(323\) 17.5399i 0.975945i
\(324\) 1.65803 0.0921130
\(325\) −4.13709 + 1.05039i −0.229484 + 0.0582649i
\(326\) −7.61300 −0.421645
\(327\) 12.8818i 0.712368i
\(328\) 2.21738 0.122434
\(329\) −5.66884 −0.312534
\(330\) 1.14237i 0.0628852i
\(331\) 5.75414i 0.316276i 0.987417 + 0.158138i \(0.0505491\pi\)
−0.987417 + 0.158138i \(0.949451\pi\)
\(332\) 24.0641i 1.32069i
\(333\) 2.08160i 0.114071i
\(334\) −8.20273 −0.448833
\(335\) −16.5500 −0.904224
\(336\) 3.11999i 0.170209i
\(337\) −10.9245 −0.595094 −0.297547 0.954707i \(-0.596169\pi\)
−0.297547 + 0.954707i \(0.596169\pi\)
\(338\) −3.62651 6.68137i −0.197256 0.363419i
\(339\) −12.6273 −0.685823
\(340\) 11.1485i 0.604612i
\(341\) 7.26957 0.393669
\(342\) 2.97995 0.161138
\(343\) 17.7027i 0.955854i
\(344\) 11.7366i 0.632795i
\(345\) 1.37060i 0.0737906i
\(346\) 10.4485i 0.561715i
\(347\) 16.3474 0.877572 0.438786 0.898591i \(-0.355409\pi\)
0.438786 + 0.898591i \(0.355409\pi\)
\(348\) 8.37203 0.448788
\(349\) 8.62758i 0.461824i −0.972975 0.230912i \(-0.925829\pi\)
0.972975 0.230912i \(-0.0741709\pi\)
\(350\) −1.04588 −0.0559046
\(351\) −3.49467 + 0.887280i −0.186532 + 0.0473595i
\(352\) −5.48593 −0.292401
\(353\) 16.5793i 0.882425i 0.897403 + 0.441212i \(0.145451\pi\)
−0.897403 + 0.441212i \(0.854549\pi\)
\(354\) 1.54980 0.0823708
\(355\) −4.52300 −0.240056
\(356\) 3.00048i 0.159025i
\(357\) 5.20009i 0.275218i
\(358\) 10.1005i 0.533826i
\(359\) 15.5233i 0.819289i 0.912245 + 0.409645i \(0.134347\pi\)
−0.912245 + 0.409645i \(0.865653\pi\)
\(360\) −4.17882 −0.220243
\(361\) −6.96788 −0.366731
\(362\) 2.16554i 0.113818i
\(363\) −1.00000 −0.0524864
\(364\) 2.22258 + 8.75392i 0.116495 + 0.458830i
\(365\) −4.31907 −0.226071
\(366\) 3.14725i 0.164509i
\(367\) 23.4682 1.22503 0.612514 0.790460i \(-0.290158\pi\)
0.612514 + 0.790460i \(0.290158\pi\)
\(368\) 1.44893 0.0755306
\(369\) 1.03658i 0.0539620i
\(370\) 2.37795i 0.123624i
\(371\) 0.759541i 0.0394334i
\(372\) 12.0532i 0.624929i
\(373\) 12.3222 0.638018 0.319009 0.947752i \(-0.396650\pi\)
0.319009 + 0.947752i \(0.396650\pi\)
\(374\) 2.01280 0.104079
\(375\) 12.0801i 0.623815i
\(376\) −8.02659 −0.413940
\(377\) −17.6459 + 4.48021i −0.908810 + 0.230742i
\(378\) −0.883474 −0.0454410
\(379\) 22.8695i 1.17473i −0.809322 0.587365i \(-0.800165\pi\)
0.809322 0.587365i \(-0.199835\pi\)
\(380\) 16.5054 0.846709
\(381\) −5.05085 −0.258763
\(382\) 12.0616i 0.617123i
\(383\) 35.5259i 1.81529i −0.419737 0.907646i \(-0.637878\pi\)
0.419737 0.907646i \(-0.362122\pi\)
\(384\) 11.5112i 0.587427i
\(385\) 2.95132i 0.150413i
\(386\) −11.0216 −0.560984
\(387\) 5.48659 0.278899
\(388\) 24.0557i 1.22124i
\(389\) 2.67074 0.135412 0.0677060 0.997705i \(-0.478432\pi\)
0.0677060 + 0.997705i \(0.478432\pi\)
\(390\) 3.99220 1.01360i 0.202153 0.0513256i
\(391\) −2.41493 −0.122128
\(392\) 10.0915i 0.509696i
\(393\) 15.9772 0.805944
\(394\) −4.20087 −0.211637
\(395\) 10.8339i 0.545113i
\(396\) 1.65803i 0.0833193i
\(397\) 36.4406i 1.82890i 0.404698 + 0.914451i \(0.367377\pi\)
−0.404698 + 0.914451i \(0.632623\pi\)
\(398\) 11.0869i 0.555736i
\(399\) 7.69876 0.385420
\(400\) 2.44477 0.122239
\(401\) 13.6597i 0.682132i −0.940039 0.341066i \(-0.889212\pi\)
0.940039 0.341066i \(-0.110788\pi\)
\(402\) −4.95422 −0.247094
\(403\) −6.45015 25.4048i −0.321305 1.26550i
\(404\) −14.3221 −0.712550
\(405\) 1.95350i 0.0970703i
\(406\) −4.46099 −0.221395
\(407\) 2.08160 0.103181
\(408\) 7.36288i 0.364517i
\(409\) 25.8507i 1.27823i 0.769110 + 0.639117i \(0.220700\pi\)
−0.769110 + 0.639117i \(0.779300\pi\)
\(410\) 1.18415i 0.0584810i
\(411\) 17.2582i 0.851283i
\(412\) 4.80909 0.236927
\(413\) 4.00393 0.197020
\(414\) 0.410287i 0.0201645i
\(415\) 28.3525 1.39177
\(416\) 4.86756 + 19.1715i 0.238652 + 0.939962i
\(417\) −5.70544 −0.279397
\(418\) 2.97995i 0.145754i
\(419\) 22.6067 1.10441 0.552205 0.833708i \(-0.313787\pi\)
0.552205 + 0.833708i \(0.313787\pi\)
\(420\) −4.89339 −0.238773
\(421\) 24.6918i 1.20341i 0.798720 + 0.601703i \(0.205511\pi\)
−0.798720 + 0.601703i \(0.794489\pi\)
\(422\) 11.6907i 0.569092i
\(423\) 3.75225i 0.182441i
\(424\) 1.07544i 0.0522282i
\(425\) −4.07471 −0.197652
\(426\) −1.35395 −0.0655993
\(427\) 8.13097i 0.393485i
\(428\) −3.80079 −0.183718
\(429\) 0.887280 + 3.49467i 0.0428383 + 0.168724i
\(430\) −6.26770 −0.302255
\(431\) 30.1126i 1.45047i 0.688499 + 0.725237i \(0.258270\pi\)
−0.688499 + 0.725237i \(0.741730\pi\)
\(432\) 2.06515 0.0993594
\(433\) −30.9402 −1.48689 −0.743445 0.668797i \(-0.766809\pi\)
−0.743445 + 0.668797i \(0.766809\pi\)
\(434\) 6.42248i 0.308289i
\(435\) 9.86396i 0.472941i
\(436\) 21.3585i 1.02289i
\(437\) 3.57532i 0.171031i
\(438\) −1.29291 −0.0617775
\(439\) 7.02158 0.335122 0.167561 0.985862i \(-0.446411\pi\)
0.167561 + 0.985862i \(0.446411\pi\)
\(440\) 4.17882i 0.199217i
\(441\) 4.71753 0.224644
\(442\) −1.78591 7.03406i −0.0849472 0.334576i
\(443\) −22.5411 −1.07096 −0.535480 0.844548i \(-0.679869\pi\)
−0.535480 + 0.844548i \(0.679869\pi\)
\(444\) 3.45136i 0.163794i
\(445\) 3.53518 0.167584
\(446\) −16.2442 −0.769187
\(447\) 0.161015i 0.00761574i
\(448\) 1.39330i 0.0658272i
\(449\) 9.41670i 0.444401i 0.975001 + 0.222201i \(0.0713240\pi\)
−0.975001 + 0.222201i \(0.928676\pi\)
\(450\) 0.692276i 0.0326342i
\(451\) 1.03658 0.0488105
\(452\) −20.9365 −0.984772
\(453\) 16.3107i 0.766341i
\(454\) 16.7553 0.786365
\(455\) 10.3139 2.61865i 0.483523 0.122764i
\(456\) 10.9008 0.510476
\(457\) 3.48691i 0.163111i −0.996669 0.0815554i \(-0.974011\pi\)
0.996669 0.0815554i \(-0.0259887\pi\)
\(458\) −2.82717 −0.132105
\(459\) −3.44198 −0.160658
\(460\) 2.27250i 0.105956i
\(461\) 15.1983i 0.707855i 0.935273 + 0.353928i \(0.115154\pi\)
−0.935273 + 0.353928i \(0.884846\pi\)
\(462\) 0.883474i 0.0411029i
\(463\) 15.9882i 0.743035i −0.928426 0.371518i \(-0.878838\pi\)
0.928426 0.371518i \(-0.121162\pi\)
\(464\) 10.4277 0.484093
\(465\) 14.2011 0.658562
\(466\) 7.96684i 0.369057i
\(467\) −32.9225 −1.52347 −0.761736 0.647888i \(-0.775652\pi\)
−0.761736 + 0.647888i \(0.775652\pi\)
\(468\) −5.79429 + 1.47114i −0.267841 + 0.0680035i
\(469\) −12.7993 −0.591017
\(470\) 4.28645i 0.197719i
\(471\) −14.2192 −0.655185
\(472\) 5.66921 0.260947
\(473\) 5.48659i 0.252274i
\(474\) 3.24312i 0.148961i
\(475\) 6.03262i 0.276796i
\(476\) 8.62193i 0.395185i
\(477\) −0.502747 −0.0230192
\(478\) −3.50811 −0.160457
\(479\) 33.6023i 1.53533i −0.640853 0.767664i \(-0.721419\pi\)
0.640853 0.767664i \(-0.278581\pi\)
\(480\) −10.7168 −0.489152
\(481\) −1.84696 7.27451i −0.0842142 0.331689i
\(482\) 7.56061 0.344376
\(483\) 1.05998i 0.0482309i
\(484\) −1.65803 −0.0753652
\(485\) 28.3425 1.28697
\(486\) 0.584778i 0.0265261i
\(487\) 3.70001i 0.167663i 0.996480 + 0.0838316i \(0.0267158\pi\)
−0.996480 + 0.0838316i \(0.973284\pi\)
\(488\) 11.5127i 0.521158i
\(489\) 13.0186i 0.588722i
\(490\) −5.38915 −0.243457
\(491\) 10.1397 0.457599 0.228799 0.973474i \(-0.426520\pi\)
0.228799 + 0.973474i \(0.426520\pi\)
\(492\) 1.71868i 0.0774840i
\(493\) −17.3798 −0.782749
\(494\) −10.4140 + 2.64405i −0.468546 + 0.118962i
\(495\) −1.95350 −0.0878034
\(496\) 15.0127i 0.674091i
\(497\) −3.49796 −0.156905
\(498\) 8.48728 0.380324
\(499\) 15.1124i 0.676525i −0.941052 0.338263i \(-0.890161\pi\)
0.941052 0.338263i \(-0.109839\pi\)
\(500\) 20.0293i 0.895736i
\(501\) 14.0271i 0.626683i
\(502\) 14.0185i 0.625678i
\(503\) 11.9190 0.531441 0.265721 0.964050i \(-0.414390\pi\)
0.265721 + 0.964050i \(0.414390\pi\)
\(504\) −3.23178 −0.143955
\(505\) 16.8743i 0.750898i
\(506\) −0.410287 −0.0182395
\(507\) 11.4255 6.20151i 0.507423 0.275419i
\(508\) −8.37448 −0.371558
\(509\) 35.2059i 1.56047i −0.625485 0.780236i \(-0.715099\pi\)
0.625485 0.780236i \(-0.284901\pi\)
\(510\) 3.93200 0.174112
\(511\) −3.34025 −0.147764
\(512\) 20.1645i 0.891154i
\(513\) 5.09587i 0.224988i
\(514\) 9.55767i 0.421571i
\(515\) 5.66609i 0.249678i
\(516\) 9.09696 0.400471
\(517\) −3.75225 −0.165024
\(518\) 1.83904i 0.0808028i
\(519\) −17.8674 −0.784294
\(520\) 14.6036 3.70778i 0.640410 0.162597i
\(521\) −2.84143 −0.124485 −0.0622426 0.998061i \(-0.519825\pi\)
−0.0622426 + 0.998061i \(0.519825\pi\)
\(522\) 2.95276i 0.129239i
\(523\) −17.8564 −0.780804 −0.390402 0.920644i \(-0.627664\pi\)
−0.390402 + 0.920644i \(0.627664\pi\)
\(524\) 26.4908 1.15725
\(525\) 1.78851i 0.0780568i
\(526\) 5.93607i 0.258825i
\(527\) 25.0217i 1.08996i
\(528\) 2.06515i 0.0898739i
\(529\) −22.5077 −0.978597
\(530\) 0.574321 0.0249469
\(531\) 2.65023i 0.115010i
\(532\) 12.7648 0.553424
\(533\) −0.919734 3.62249i −0.0398381 0.156908i
\(534\) 1.05825 0.0457950
\(535\) 4.47810i 0.193605i
\(536\) −18.1227 −0.782782
\(537\) −17.2723 −0.745354
\(538\) 9.66602i 0.416732i
\(539\) 4.71753i 0.203198i
\(540\) 3.23897i 0.139383i
\(541\) 3.56883i 0.153436i 0.997053 + 0.0767179i \(0.0244441\pi\)
−0.997053 + 0.0767179i \(0.975556\pi\)
\(542\) −12.2176 −0.524791
\(543\) −3.70318 −0.158919
\(544\) 18.8825i 0.809579i
\(545\) 25.1647 1.07794
\(546\) 3.08745 0.783889i 0.132131 0.0335473i
\(547\) 3.50639 0.149923 0.0749613 0.997186i \(-0.476117\pi\)
0.0749613 + 0.997186i \(0.476117\pi\)
\(548\) 28.6146i 1.22236i
\(549\) −5.38195 −0.229696
\(550\) −0.692276 −0.0295188
\(551\) 25.7309i 1.09617i
\(552\) 1.50084i 0.0638802i
\(553\) 8.37864i 0.356296i
\(554\) 10.1207i 0.429989i
\(555\) 4.06641 0.172610
\(556\) −9.45982 −0.401186
\(557\) 7.38164i 0.312770i −0.987696 0.156385i \(-0.950016\pi\)
0.987696 0.156385i \(-0.0499841\pi\)
\(558\) 4.25109 0.179963
\(559\) −19.1738 + 4.86815i −0.810967 + 0.205901i
\(560\) −6.09491 −0.257557
\(561\) 3.44198i 0.145321i
\(562\) 9.39537 0.396320
\(563\) 35.5383 1.49776 0.748879 0.662706i \(-0.230592\pi\)
0.748879 + 0.662706i \(0.230592\pi\)
\(564\) 6.22136i 0.261967i
\(565\) 24.6675i 1.03777i
\(566\) 10.0687i 0.423219i
\(567\) 1.51078i 0.0634470i
\(568\) −4.95281 −0.207815
\(569\) 19.6546 0.823966 0.411983 0.911192i \(-0.364836\pi\)
0.411983 + 0.911192i \(0.364836\pi\)
\(570\) 5.82135i 0.243830i
\(571\) 18.6081 0.778726 0.389363 0.921084i \(-0.372695\pi\)
0.389363 + 0.921084i \(0.372695\pi\)
\(572\) 1.47114 + 5.79429i 0.0615115 + 0.242271i
\(573\) −20.6259 −0.861658
\(574\) 0.915788i 0.0382243i
\(575\) 0.830586 0.0346378
\(576\) 0.922236 0.0384265
\(577\) 25.5485i 1.06360i 0.846871 + 0.531799i \(0.178484\pi\)
−0.846871 + 0.531799i \(0.821516\pi\)
\(578\) 3.01323i 0.125334i
\(579\) 18.8475i 0.783274i
\(580\) 16.3548i 0.679096i
\(581\) 21.9270 0.909686
\(582\) 8.48429 0.351685
\(583\) 0.502747i 0.0208216i
\(584\) −4.72950 −0.195708
\(585\) 1.73330 + 6.82685i 0.0716633 + 0.282256i
\(586\) −3.09739 −0.127952
\(587\) 2.35936i 0.0973813i 0.998814 + 0.0486907i \(0.0155049\pi\)
−0.998814 + 0.0486907i \(0.984495\pi\)
\(588\) 7.82183 0.322567
\(589\) −37.0448 −1.52640
\(590\) 3.02753i 0.124642i
\(591\) 7.18370i 0.295498i
\(592\) 4.29881i 0.176680i
\(593\) 11.6707i 0.479257i −0.970865 0.239628i \(-0.922974\pi\)
0.970865 0.239628i \(-0.0770256\pi\)
\(594\) −0.584778 −0.0239938
\(595\) 10.1584 0.416453
\(596\) 0.266968i 0.0109354i
\(597\) 18.9591 0.775946
\(598\) 0.364040 + 1.43382i 0.0148867 + 0.0586332i
\(599\) 9.12181 0.372707 0.186354 0.982483i \(-0.440333\pi\)
0.186354 + 0.982483i \(0.440333\pi\)
\(600\) 2.53237i 0.103384i
\(601\) 6.90316 0.281586 0.140793 0.990039i \(-0.455035\pi\)
0.140793 + 0.990039i \(0.455035\pi\)
\(602\) −4.84726 −0.197560
\(603\) 8.47197i 0.345005i
\(604\) 27.0436i 1.10039i
\(605\) 1.95350i 0.0794212i
\(606\) 5.05131i 0.205196i
\(607\) 11.5559 0.469038 0.234519 0.972112i \(-0.424648\pi\)
0.234519 + 0.972112i \(0.424648\pi\)
\(608\) 27.9556 1.13375
\(609\) 7.62851i 0.309123i
\(610\) 6.14816 0.248932
\(611\) 3.32930 + 13.1129i 0.134689 + 0.530491i
\(612\) −5.70692 −0.230689
\(613\) 37.7362i 1.52415i −0.647488 0.762075i \(-0.724181\pi\)
0.647488 0.762075i \(-0.275819\pi\)
\(614\) −15.3808 −0.620720
\(615\) 2.02496 0.0816541
\(616\) 3.23178i 0.130212i
\(617\) 28.2159i 1.13593i −0.823053 0.567964i \(-0.807731\pi\)
0.823053 0.567964i \(-0.192269\pi\)
\(618\) 1.69614i 0.0682286i
\(619\) 38.4407i 1.54506i 0.634978 + 0.772530i \(0.281009\pi\)
−0.634978 + 0.772530i \(0.718991\pi\)
\(620\) 23.5460 0.945628
\(621\) 0.701611 0.0281547
\(622\) 19.2152i 0.770461i
\(623\) 2.73401 0.109536
\(624\) −7.21701 + 1.83236i −0.288911 + 0.0733532i
\(625\) −17.6794 −0.707177
\(626\) 19.4222i 0.776269i
\(627\) 5.09587 0.203509
\(628\) −23.5759 −0.940781
\(629\) 7.16483i 0.285680i
\(630\) 1.72587i 0.0687603i
\(631\) 16.9688i 0.675519i −0.941232 0.337759i \(-0.890331\pi\)
0.941232 0.337759i \(-0.109669\pi\)
\(632\) 11.8634i 0.471902i
\(633\) −19.9916 −0.794595
\(634\) 18.0367 0.716328
\(635\) 9.86685i 0.391554i
\(636\) −0.833571 −0.0330532
\(637\) −16.4862 + 4.18577i −0.653208 + 0.165846i
\(638\) −2.95276 −0.116901
\(639\) 2.31533i 0.0915930i
\(640\) −22.4871 −0.888881
\(641\) −6.00876 −0.237332 −0.118666 0.992934i \(-0.537862\pi\)
−0.118666 + 0.992934i \(0.537862\pi\)
\(642\) 1.34051i 0.0529059i
\(643\) 9.64269i 0.380270i −0.981758 0.190135i \(-0.939107\pi\)
0.981758 0.190135i \(-0.0608927\pi\)
\(644\) 1.75749i 0.0692547i
\(645\) 10.7181i 0.422024i
\(646\) −10.2569 −0.403554
\(647\) 34.1912 1.34420 0.672098 0.740463i \(-0.265394\pi\)
0.672098 + 0.740463i \(0.265394\pi\)
\(648\) 2.13914i 0.0840333i
\(649\) 2.65023 0.104031
\(650\) 0.614243 + 2.41928i 0.0240926 + 0.0948919i
\(651\) 10.9828 0.430448
\(652\) 21.5853i 0.845345i
\(653\) −2.32307 −0.0909086 −0.0454543 0.998966i \(-0.514474\pi\)
−0.0454543 + 0.998966i \(0.514474\pi\)
\(654\) 7.53303 0.294565
\(655\) 31.2115i 1.21954i
\(656\) 2.14068i 0.0835796i
\(657\) 2.21094i 0.0862568i
\(658\) 3.31502i 0.129233i
\(659\) 4.07928 0.158906 0.0794532 0.996839i \(-0.474683\pi\)
0.0794532 + 0.996839i \(0.474683\pi\)
\(660\) −3.23897 −0.126077
\(661\) 42.2740i 1.64427i 0.569293 + 0.822135i \(0.307217\pi\)
−0.569293 + 0.822135i \(0.692783\pi\)
\(662\) 3.36489 0.130780
\(663\) 12.0286 3.05400i 0.467152 0.118608i
\(664\) 31.0467 1.20485
\(665\) 15.0395i 0.583209i
\(666\) 1.21727 0.0471684
\(667\) 3.54270 0.137174
\(668\) 23.2574i 0.899854i
\(669\) 27.7784i 1.07398i
\(670\) 9.67809i 0.373897i
\(671\) 5.38195i 0.207768i
\(672\) −8.28806 −0.319719
\(673\) 10.6688 0.411252 0.205626 0.978631i \(-0.434077\pi\)
0.205626 + 0.978631i \(0.434077\pi\)
\(674\) 6.38840i 0.246072i
\(675\) 1.18383 0.0455655
\(676\) 18.9438 10.2823i 0.728608 0.395473i
\(677\) 24.2174 0.930752 0.465376 0.885113i \(-0.345919\pi\)
0.465376 + 0.885113i \(0.345919\pi\)
\(678\) 7.38419i 0.283588i
\(679\) 21.9193 0.841185
\(680\) 14.3834 0.551578
\(681\) 28.6524i 1.09796i
\(682\) 4.25109i 0.162783i
\(683\) 37.1698i 1.42226i −0.703059 0.711132i \(-0.748183\pi\)
0.703059 0.711132i \(-0.251817\pi\)
\(684\) 8.44913i 0.323060i
\(685\) 33.7139 1.28814
\(686\) −10.3521 −0.395246
\(687\) 4.83459i 0.184451i
\(688\) 11.3306 0.431976
\(689\) 1.75693 0.446077i 0.0669339 0.0169942i
\(690\) −0.801497 −0.0305125
\(691\) 15.9632i 0.607268i −0.952789 0.303634i \(-0.901800\pi\)
0.952789 0.303634i \(-0.0981999\pi\)
\(692\) −29.6248 −1.12617
\(693\) −1.51078 −0.0573899
\(694\) 9.55959i 0.362877i
\(695\) 11.1456i 0.422777i
\(696\) 10.8013i 0.409423i
\(697\) 3.56788i 0.135143i
\(698\) −5.04522 −0.190965
\(699\) −13.6237 −0.515295
\(700\) 2.96540i 0.112082i
\(701\) 2.01736 0.0761947 0.0380974 0.999274i \(-0.487870\pi\)
0.0380974 + 0.999274i \(0.487870\pi\)
\(702\) 0.518862 + 2.04361i 0.0195832 + 0.0771311i
\(703\) −10.6076 −0.400072
\(704\) 0.922236i 0.0347581i
\(705\) −7.33004 −0.276065
\(706\) 9.69519 0.364883
\(707\) 13.0501i 0.490801i
\(708\) 4.39417i 0.165143i
\(709\) 29.6428i 1.11326i 0.830761 + 0.556629i \(0.187905\pi\)
−0.830761 + 0.556629i \(0.812095\pi\)
\(710\) 2.64495i 0.0992634i
\(711\) −5.54589 −0.207987
\(712\) 3.87112 0.145076
\(713\) 5.10041i 0.191012i
\(714\) 3.04090 0.113803
\(715\) 6.82685 1.73330i 0.255310 0.0648219i
\(716\) −28.6380 −1.07025
\(717\) 5.99903i 0.224038i
\(718\) 9.07770 0.338777
\(719\) −32.3389 −1.20604 −0.603018 0.797728i \(-0.706035\pi\)
−0.603018 + 0.797728i \(0.706035\pi\)
\(720\) 4.03427i 0.150348i
\(721\) 4.38199i 0.163194i
\(722\) 4.07467i 0.151643i
\(723\) 12.9290i 0.480835i
\(724\) −6.13999 −0.228191
\(725\) 5.97758 0.222002
\(726\) 0.584778i 0.0217032i
\(727\) −37.9325 −1.40684 −0.703419 0.710775i \(-0.748344\pi\)
−0.703419 + 0.710775i \(0.748344\pi\)
\(728\) 11.2940 2.86749i 0.418584 0.106276i
\(729\) 1.00000 0.0370370
\(730\) 2.52570i 0.0934803i
\(731\) −18.8847 −0.698478
\(732\) −8.92346 −0.329821
\(733\) 16.7917i 0.620217i −0.950701 0.310109i \(-0.899635\pi\)
0.950701 0.310109i \(-0.100365\pi\)
\(734\) 13.7237i 0.506550i
\(735\) 9.21571i 0.339927i
\(736\) 3.84899i 0.141876i
\(737\) −8.47197 −0.312069
\(738\) 0.606168 0.0223133
\(739\) 25.4629i 0.936668i 0.883551 + 0.468334i \(0.155146\pi\)
−0.883551 + 0.468334i \(0.844854\pi\)
\(740\) 6.74225 0.247850
\(741\) −4.52146 17.8084i −0.166100 0.654208i
\(742\) 0.444164 0.0163058
\(743\) 4.81269i 0.176560i −0.996096 0.0882802i \(-0.971863\pi\)
0.996096 0.0882802i \(-0.0281371\pi\)
\(744\) 15.5506 0.570114
\(745\) −0.314543 −0.0115240
\(746\) 7.20574i 0.263821i
\(747\) 14.5137i 0.531027i
\(748\) 5.70692i 0.208666i
\(749\) 3.46324i 0.126544i
\(750\) −7.06420 −0.257948
\(751\) 24.9537 0.910574 0.455287 0.890345i \(-0.349537\pi\)
0.455287 + 0.890345i \(0.349537\pi\)
\(752\) 7.74895i 0.282575i
\(753\) 23.9724 0.873603
\(754\) 2.61993 + 10.3189i 0.0954122 + 0.375794i
\(755\) −31.8629 −1.15961
\(756\) 2.50493i 0.0911035i
\(757\) −33.8373 −1.22984 −0.614919 0.788591i \(-0.710811\pi\)
−0.614919 + 0.788591i \(0.710811\pi\)
\(758\) −13.3736 −0.485752
\(759\) 0.701611i 0.0254669i
\(760\) 21.2947i 0.772440i
\(761\) 50.5981i 1.83418i −0.398679 0.917091i \(-0.630531\pi\)
0.398679 0.917091i \(-0.369469\pi\)
\(762\) 2.95363i 0.106999i
\(763\) 19.4617 0.704561
\(764\) −34.1984 −1.23725
\(765\) 6.72392i 0.243104i
\(766\) −20.7748 −0.750624
\(767\) −2.35150 9.26169i −0.0849076 0.334420i
\(768\) −4.88701 −0.176345
\(769\) 26.1333i 0.942389i −0.882029 0.471195i \(-0.843823\pi\)
0.882029 0.471195i \(-0.156177\pi\)
\(770\) 1.72587 0.0621960
\(771\) −16.3441 −0.588618
\(772\) 31.2497i 1.12470i
\(773\) 0.778578i 0.0280035i 0.999902 + 0.0140018i \(0.00445704\pi\)
−0.999902 + 0.0140018i \(0.995543\pi\)
\(774\) 3.20844i 0.115325i
\(775\) 8.60591i 0.309133i
\(776\) 31.0358 1.11412
\(777\) 3.14485 0.112821
\(778\) 1.56179i 0.0559930i
\(779\) −5.28226 −0.189257
\(780\) 2.87388 + 11.3192i 0.102901 + 0.405291i
\(781\) −2.31533 −0.0828490
\(782\) 1.41220i 0.0505002i
\(783\) 5.04937 0.180450
\(784\) 9.74239 0.347942
\(785\) 27.7772i 0.991411i
\(786\) 9.34313i 0.333258i
\(787\) 33.9128i 1.20886i 0.796658 + 0.604431i \(0.206599\pi\)
−0.796658 + 0.604431i \(0.793401\pi\)
\(788\) 11.9108i 0.424305i
\(789\) 10.1510 0.361384
\(790\) 6.33544 0.225405
\(791\) 19.0772i