Properties

Label 429.2.b.b.298.3
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 298.3
Root \(-2.15754i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.12

$q$-expansion

\(f(q)\) \(=\) \(q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.15754i q^{2} +1.00000 q^{3} -2.65498 q^{4} +0.710210i q^{5} -2.15754i q^{6} -2.30964i q^{7} +1.41315i q^{8} +1.00000 q^{9} +1.53231 q^{10} -1.00000i q^{11} -2.65498 q^{12} +(-1.40848 - 3.31906i) q^{13} -4.98315 q^{14} +0.710210i q^{15} -2.26104 q^{16} +6.68027 q^{17} -2.15754i q^{18} -0.242517i q^{19} -1.88559i q^{20} -2.30964i q^{21} -2.15754 q^{22} -9.53531 q^{23} +1.41315i q^{24} +4.49560 q^{25} +(-7.16101 + 3.03885i) q^{26} +1.00000 q^{27} +6.13206i q^{28} -2.95273 q^{29} +1.53231 q^{30} -4.02017i q^{31} +7.70458i q^{32} -1.00000i q^{33} -14.4130i q^{34} +1.64033 q^{35} -2.65498 q^{36} -3.42304i q^{37} -0.523240 q^{38} +(-1.40848 - 3.31906i) q^{39} -1.00363 q^{40} +9.46022i q^{41} -4.98315 q^{42} +11.8791 q^{43} +2.65498i q^{44} +0.710210i q^{45} +20.5728i q^{46} +12.9178i q^{47} -2.26104 q^{48} +1.66555 q^{49} -9.69944i q^{50} +6.68027 q^{51} +(3.73948 + 8.81205i) q^{52} +6.78954 q^{53} -2.15754i q^{54} +0.710210 q^{55} +3.26386 q^{56} -0.242517i q^{57} +6.37063i q^{58} -7.81320i q^{59} -1.88559i q^{60} +0.910585 q^{61} -8.67368 q^{62} -2.30964i q^{63} +12.1009 q^{64} +(2.35723 - 1.00032i) q^{65} -2.15754 q^{66} +9.32216i q^{67} -17.7360 q^{68} -9.53531 q^{69} -3.53908i q^{70} +12.9704i q^{71} +1.41315i q^{72} -8.51665i q^{73} -7.38534 q^{74} +4.49560 q^{75} +0.643877i q^{76} -2.30964 q^{77} +(-7.16101 + 3.03885i) q^{78} +1.82360 q^{79} -1.60581i q^{80} +1.00000 q^{81} +20.4108 q^{82} +4.64671i q^{83} +6.13206i q^{84} +4.74440i q^{85} -25.6297i q^{86} -2.95273 q^{87} +1.41315 q^{88} -14.7714i q^{89} +1.53231 q^{90} +(-7.66585 + 3.25308i) q^{91} +25.3161 q^{92} -4.02017i q^{93} +27.8707 q^{94} +0.172238 q^{95} +7.70458i q^{96} +1.86542i q^{97} -3.59349i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.15754i 1.52561i −0.646628 0.762806i \(-0.723821\pi\)
0.646628 0.762806i \(-0.276179\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.65498 −1.32749
\(5\) 0.710210i 0.317616i 0.987310 + 0.158808i \(0.0507650\pi\)
−0.987310 + 0.158808i \(0.949235\pi\)
\(6\) 2.15754i 0.880812i
\(7\) 2.30964i 0.872963i −0.899713 0.436482i \(-0.856224\pi\)
0.899713 0.436482i \(-0.143776\pi\)
\(8\) 1.41315i 0.499622i
\(9\) 1.00000 0.333333
\(10\) 1.53231 0.484558
\(11\) 1.00000i 0.301511i
\(12\) −2.65498 −0.766427
\(13\) −1.40848 3.31906i −0.390642 0.920543i
\(14\) −4.98315 −1.33180
\(15\) 0.710210i 0.183375i
\(16\) −2.26104 −0.565261
\(17\) 6.68027 1.62020 0.810102 0.586289i \(-0.199412\pi\)
0.810102 + 0.586289i \(0.199412\pi\)
\(18\) 2.15754i 0.508537i
\(19\) 0.242517i 0.0556372i −0.999613 0.0278186i \(-0.991144\pi\)
0.999613 0.0278186i \(-0.00885607\pi\)
\(20\) 1.88559i 0.421631i
\(21\) 2.30964i 0.504005i
\(22\) −2.15754 −0.459989
\(23\) −9.53531 −1.98825 −0.994125 0.108242i \(-0.965478\pi\)
−0.994125 + 0.108242i \(0.965478\pi\)
\(24\) 1.41315i 0.288457i
\(25\) 4.49560 0.899120
\(26\) −7.16101 + 3.03885i −1.40439 + 0.595968i
\(27\) 1.00000 0.192450
\(28\) 6.13206i 1.15885i
\(29\) −2.95273 −0.548308 −0.274154 0.961686i \(-0.588398\pi\)
−0.274154 + 0.961686i \(0.588398\pi\)
\(30\) 1.53231 0.279760
\(31\) 4.02017i 0.722044i −0.932557 0.361022i \(-0.882428\pi\)
0.932557 0.361022i \(-0.117572\pi\)
\(32\) 7.70458i 1.36199i
\(33\) 1.00000i 0.174078i
\(34\) 14.4130i 2.47180i
\(35\) 1.64033 0.277267
\(36\) −2.65498 −0.442497
\(37\) 3.42304i 0.562744i −0.959599 0.281372i \(-0.909211\pi\)
0.959599 0.281372i \(-0.0907895\pi\)
\(38\) −0.523240 −0.0848807
\(39\) −1.40848 3.31906i −0.225537 0.531476i
\(40\) −1.00363 −0.158688
\(41\) 9.46022i 1.47744i 0.674013 + 0.738719i \(0.264569\pi\)
−0.674013 + 0.738719i \(0.735431\pi\)
\(42\) −4.98315 −0.768916
\(43\) 11.8791 1.81155 0.905776 0.423757i \(-0.139289\pi\)
0.905776 + 0.423757i \(0.139289\pi\)
\(44\) 2.65498i 0.400253i
\(45\) 0.710210i 0.105872i
\(46\) 20.5728i 3.03330i
\(47\) 12.9178i 1.88426i 0.335249 + 0.942130i \(0.391180\pi\)
−0.335249 + 0.942130i \(0.608820\pi\)
\(48\) −2.26104 −0.326353
\(49\) 1.66555 0.237935
\(50\) 9.69944i 1.37171i
\(51\) 6.68027 0.935425
\(52\) 3.73948 + 8.81205i 0.518573 + 1.22201i
\(53\) 6.78954 0.932615 0.466307 0.884623i \(-0.345584\pi\)
0.466307 + 0.884623i \(0.345584\pi\)
\(54\) 2.15754i 0.293604i
\(55\) 0.710210 0.0957647
\(56\) 3.26386 0.436152
\(57\) 0.242517i 0.0321221i
\(58\) 6.37063i 0.836504i
\(59\) 7.81320i 1.01719i −0.861005 0.508596i \(-0.830165\pi\)
0.861005 0.508596i \(-0.169835\pi\)
\(60\) 1.88559i 0.243429i
\(61\) 0.910585 0.116588 0.0582942 0.998299i \(-0.481434\pi\)
0.0582942 + 0.998299i \(0.481434\pi\)
\(62\) −8.67368 −1.10156
\(63\) 2.30964i 0.290988i
\(64\) 12.1009 1.51261
\(65\) 2.35723 1.00032i 0.292379 0.124074i
\(66\) −2.15754 −0.265575
\(67\) 9.32216i 1.13888i 0.822032 + 0.569442i \(0.192841\pi\)
−0.822032 + 0.569442i \(0.807159\pi\)
\(68\) −17.7360 −2.15080
\(69\) −9.53531 −1.14792
\(70\) 3.53908i 0.423001i
\(71\) 12.9704i 1.53930i 0.638466 + 0.769650i \(0.279569\pi\)
−0.638466 + 0.769650i \(0.720431\pi\)
\(72\) 1.41315i 0.166541i
\(73\) 8.51665i 0.996798i −0.866948 0.498399i \(-0.833921\pi\)
0.866948 0.498399i \(-0.166079\pi\)
\(74\) −7.38534 −0.858529
\(75\) 4.49560 0.519107
\(76\) 0.643877i 0.0738578i
\(77\) −2.30964 −0.263208
\(78\) −7.16101 + 3.03885i −0.810825 + 0.344082i
\(79\) 1.82360 0.205172 0.102586 0.994724i \(-0.467288\pi\)
0.102586 + 0.994724i \(0.467288\pi\)
\(80\) 1.60581i 0.179536i
\(81\) 1.00000 0.111111
\(82\) 20.4108 2.25400
\(83\) 4.64671i 0.510042i 0.966935 + 0.255021i \(0.0820824\pi\)
−0.966935 + 0.255021i \(0.917918\pi\)
\(84\) 6.13206i 0.669062i
\(85\) 4.74440i 0.514602i
\(86\) 25.6297i 2.76372i
\(87\) −2.95273 −0.316566
\(88\) 1.41315 0.150642
\(89\) 14.7714i 1.56576i −0.622171 0.782881i \(-0.713749\pi\)
0.622171 0.782881i \(-0.286251\pi\)
\(90\) 1.53231 0.161519
\(91\) −7.66585 + 3.25308i −0.803600 + 0.341016i
\(92\) 25.3161 2.63938
\(93\) 4.02017i 0.416872i
\(94\) 27.8707 2.87465
\(95\) 0.172238 0.0176712
\(96\) 7.70458i 0.786345i
\(97\) 1.86542i 0.189405i 0.995506 + 0.0947025i \(0.0301900\pi\)
−0.995506 + 0.0947025i \(0.969810\pi\)
\(98\) 3.59349i 0.362997i
\(99\) 1.00000i 0.100504i
\(100\) −11.9357 −1.19357
\(101\) 2.45086 0.243870 0.121935 0.992538i \(-0.461090\pi\)
0.121935 + 0.992538i \(0.461090\pi\)
\(102\) 14.4130i 1.42709i
\(103\) −10.2811 −1.01302 −0.506512 0.862233i \(-0.669066\pi\)
−0.506512 + 0.862233i \(0.669066\pi\)
\(104\) 4.69032 1.99039i 0.459924 0.195173i
\(105\) 1.64033 0.160080
\(106\) 14.6487i 1.42281i
\(107\) 19.6690 1.90148 0.950739 0.309993i \(-0.100327\pi\)
0.950739 + 0.309993i \(0.100327\pi\)
\(108\) −2.65498 −0.255476
\(109\) 1.27506i 0.122128i 0.998134 + 0.0610642i \(0.0194494\pi\)
−0.998134 + 0.0610642i \(0.980551\pi\)
\(110\) 1.53231i 0.146100i
\(111\) 3.42304i 0.324900i
\(112\) 5.22220i 0.493452i
\(113\) −0.638739 −0.0600875 −0.0300438 0.999549i \(-0.509565\pi\)
−0.0300438 + 0.999549i \(0.509565\pi\)
\(114\) −0.523240 −0.0490059
\(115\) 6.77207i 0.631499i
\(116\) 7.83943 0.727873
\(117\) −1.40848 3.31906i −0.130214 0.306848i
\(118\) −16.8573 −1.55184
\(119\) 15.4290i 1.41438i
\(120\) −1.00363 −0.0916185
\(121\) −1.00000 −0.0909091
\(122\) 1.96462i 0.177869i
\(123\) 9.46022i 0.853000i
\(124\) 10.6735i 0.958506i
\(125\) 6.74387i 0.603190i
\(126\) −4.98315 −0.443934
\(127\) −10.3681 −0.920021 −0.460010 0.887914i \(-0.652154\pi\)
−0.460010 + 0.887914i \(0.652154\pi\)
\(128\) 10.6989i 0.945660i
\(129\) 11.8791 1.04590
\(130\) −2.15822 5.08582i −0.189289 0.446056i
\(131\) −5.68692 −0.496868 −0.248434 0.968649i \(-0.579916\pi\)
−0.248434 + 0.968649i \(0.579916\pi\)
\(132\) 2.65498i 0.231086i
\(133\) −0.560127 −0.0485692
\(134\) 20.1129 1.73749
\(135\) 0.710210i 0.0611251i
\(136\) 9.44019i 0.809490i
\(137\) 4.86363i 0.415528i −0.978179 0.207764i \(-0.933381\pi\)
0.978179 0.207764i \(-0.0666186\pi\)
\(138\) 20.5728i 1.75127i
\(139\) −4.41515 −0.374488 −0.187244 0.982313i \(-0.559956\pi\)
−0.187244 + 0.982313i \(0.559956\pi\)
\(140\) −4.35505 −0.368069
\(141\) 12.9178i 1.08788i
\(142\) 27.9841 2.34837
\(143\) −3.31906 + 1.40848i −0.277554 + 0.117783i
\(144\) −2.26104 −0.188420
\(145\) 2.09706i 0.174151i
\(146\) −18.3750 −1.52073
\(147\) 1.66555 0.137372
\(148\) 9.08810i 0.747037i
\(149\) 9.50356i 0.778562i 0.921119 + 0.389281i \(0.127276\pi\)
−0.921119 + 0.389281i \(0.872724\pi\)
\(150\) 9.69944i 0.791956i
\(151\) 15.2126i 1.23798i −0.785398 0.618991i \(-0.787542\pi\)
0.785398 0.618991i \(-0.212458\pi\)
\(152\) 0.342711 0.0277976
\(153\) 6.68027 0.540068
\(154\) 4.98315i 0.401554i
\(155\) 2.85516 0.229332
\(156\) 3.73948 + 8.81205i 0.299398 + 0.705528i
\(157\) 20.1949 1.61173 0.805866 0.592098i \(-0.201700\pi\)
0.805866 + 0.592098i \(0.201700\pi\)
\(158\) 3.93450i 0.313012i
\(159\) 6.78954 0.538445
\(160\) −5.47187 −0.432589
\(161\) 22.0232i 1.73567i
\(162\) 2.15754i 0.169512i
\(163\) 16.4974i 1.29217i 0.763264 + 0.646087i \(0.223596\pi\)
−0.763264 + 0.646087i \(0.776404\pi\)
\(164\) 25.1167i 1.96129i
\(165\) 0.710210 0.0552898
\(166\) 10.0255 0.778126
\(167\) 5.50507i 0.425995i 0.977053 + 0.212998i \(0.0683226\pi\)
−0.977053 + 0.212998i \(0.931677\pi\)
\(168\) 3.26386 0.251812
\(169\) −9.03237 + 9.34967i −0.694798 + 0.719205i
\(170\) 10.2362 0.785082
\(171\) 0.242517i 0.0185457i
\(172\) −31.5389 −2.40482
\(173\) 12.7126 0.966524 0.483262 0.875476i \(-0.339452\pi\)
0.483262 + 0.875476i \(0.339452\pi\)
\(174\) 6.37063i 0.482956i
\(175\) 10.3832i 0.784899i
\(176\) 2.26104i 0.170432i
\(177\) 7.81320i 0.587276i
\(178\) −31.8698 −2.38875
\(179\) −24.4279 −1.82583 −0.912913 0.408154i \(-0.866172\pi\)
−0.912913 + 0.408154i \(0.866172\pi\)
\(180\) 1.88559i 0.140544i
\(181\) −0.931324 −0.0692248 −0.0346124 0.999401i \(-0.511020\pi\)
−0.0346124 + 0.999401i \(0.511020\pi\)
\(182\) 7.01866 + 16.5394i 0.520258 + 1.22598i
\(183\) 0.910585 0.0673124
\(184\) 13.4748i 0.993374i
\(185\) 2.43108 0.178736
\(186\) −8.67368 −0.635985
\(187\) 6.68027i 0.488510i
\(188\) 34.2966i 2.50134i
\(189\) 2.30964i 0.168002i
\(190\) 0.371610i 0.0269594i
\(191\) 4.68209 0.338784 0.169392 0.985549i \(-0.445820\pi\)
0.169392 + 0.985549i \(0.445820\pi\)
\(192\) 12.1009 0.873304
\(193\) 10.2671i 0.739039i 0.929223 + 0.369520i \(0.120478\pi\)
−0.929223 + 0.369520i \(0.879522\pi\)
\(194\) 4.02473 0.288959
\(195\) 2.35723 1.00032i 0.168805 0.0716341i
\(196\) −4.42200 −0.315857
\(197\) 11.5842i 0.825341i 0.910880 + 0.412671i \(0.135404\pi\)
−0.910880 + 0.412671i \(0.864596\pi\)
\(198\) −2.15754 −0.153330
\(199\) −17.2330 −1.22162 −0.610808 0.791779i \(-0.709155\pi\)
−0.610808 + 0.791779i \(0.709155\pi\)
\(200\) 6.35294i 0.449221i
\(201\) 9.32216i 0.657535i
\(202\) 5.28783i 0.372050i
\(203\) 6.81975i 0.478652i
\(204\) −17.7360 −1.24177
\(205\) −6.71875 −0.469258
\(206\) 22.1818i 1.54548i
\(207\) −9.53531 −0.662750
\(208\) 3.18463 + 7.50454i 0.220814 + 0.520346i
\(209\) −0.242517 −0.0167752
\(210\) 3.53908i 0.244220i
\(211\) −10.6905 −0.735967 −0.367983 0.929832i \(-0.619952\pi\)
−0.367983 + 0.929832i \(0.619952\pi\)
\(212\) −18.0261 −1.23804
\(213\) 12.9704i 0.888716i
\(214\) 42.4367i 2.90092i
\(215\) 8.43668i 0.575377i
\(216\) 1.41315i 0.0961523i
\(217\) −9.28516 −0.630318
\(218\) 2.75099 0.186320
\(219\) 8.51665i 0.575502i
\(220\) −1.88559 −0.127127
\(221\) −9.40902 22.1722i −0.632919 1.49147i
\(222\) −7.38534 −0.495672
\(223\) 5.33992i 0.357587i −0.983887 0.178794i \(-0.942781\pi\)
0.983887 0.178794i \(-0.0572194\pi\)
\(224\) 17.7948 1.18897
\(225\) 4.49560 0.299707
\(226\) 1.37811i 0.0916702i
\(227\) 7.82431i 0.519318i −0.965700 0.259659i \(-0.916390\pi\)
0.965700 0.259659i \(-0.0836101\pi\)
\(228\) 0.643877i 0.0426418i
\(229\) 10.6805i 0.705784i 0.935664 + 0.352892i \(0.114802\pi\)
−0.935664 + 0.352892i \(0.885198\pi\)
\(230\) −14.6110 −0.963422
\(231\) −2.30964 −0.151963
\(232\) 4.17263i 0.273947i
\(233\) −15.4509 −1.01222 −0.506112 0.862468i \(-0.668918\pi\)
−0.506112 + 0.862468i \(0.668918\pi\)
\(234\) −7.16101 + 3.03885i −0.468130 + 0.198656i
\(235\) −9.17437 −0.598470
\(236\) 20.7439i 1.35031i
\(237\) 1.82360 0.118456
\(238\) −33.2888 −2.15779
\(239\) 16.9365i 1.09553i −0.836632 0.547765i \(-0.815479\pi\)
0.836632 0.547765i \(-0.184521\pi\)
\(240\) 1.60581i 0.103655i
\(241\) 0.0799646i 0.00515098i 0.999997 + 0.00257549i \(0.000819804\pi\)
−0.999997 + 0.00257549i \(0.999180\pi\)
\(242\) 2.15754i 0.138692i
\(243\) 1.00000 0.0641500
\(244\) −2.41758 −0.154770
\(245\) 1.18289i 0.0755720i
\(246\) 20.4108 1.30135
\(247\) −0.804929 + 0.341580i −0.0512164 + 0.0217342i
\(248\) 5.68108 0.360749
\(249\) 4.64671i 0.294473i
\(250\) 14.5502 0.920234
\(251\) 7.57174 0.477924 0.238962 0.971029i \(-0.423193\pi\)
0.238962 + 0.971029i \(0.423193\pi\)
\(252\) 6.13206i 0.386283i
\(253\) 9.53531i 0.599480i
\(254\) 22.3696i 1.40359i
\(255\) 4.74440i 0.297106i
\(256\) 1.11835 0.0698970
\(257\) −23.0242 −1.43621 −0.718105 0.695935i \(-0.754990\pi\)
−0.718105 + 0.695935i \(0.754990\pi\)
\(258\) 25.6297i 1.59564i
\(259\) −7.90600 −0.491255
\(260\) −6.25840 + 2.65582i −0.388130 + 0.164707i
\(261\) −2.95273 −0.182769
\(262\) 12.2698i 0.758028i
\(263\) −5.95047 −0.366922 −0.183461 0.983027i \(-0.558730\pi\)
−0.183461 + 0.983027i \(0.558730\pi\)
\(264\) 1.41315 0.0869731
\(265\) 4.82200i 0.296213i
\(266\) 1.20850i 0.0740977i
\(267\) 14.7714i 0.903994i
\(268\) 24.7502i 1.51186i
\(269\) −1.17571 −0.0716841 −0.0358420 0.999357i \(-0.511411\pi\)
−0.0358420 + 0.999357i \(0.511411\pi\)
\(270\) 1.53231 0.0932532
\(271\) 7.12706i 0.432938i 0.976290 + 0.216469i \(0.0694540\pi\)
−0.976290 + 0.216469i \(0.930546\pi\)
\(272\) −15.1044 −0.915837
\(273\) −7.66585 + 3.25308i −0.463959 + 0.196886i
\(274\) −10.4935 −0.633934
\(275\) 4.49560i 0.271095i
\(276\) 25.3161 1.52385
\(277\) 11.9736 0.719426 0.359713 0.933063i \(-0.382875\pi\)
0.359713 + 0.933063i \(0.382875\pi\)
\(278\) 9.52586i 0.571323i
\(279\) 4.02017i 0.240681i
\(280\) 2.31803i 0.138529i
\(281\) 18.7901i 1.12092i −0.828181 0.560461i \(-0.810624\pi\)
0.828181 0.560461i \(-0.189376\pi\)
\(282\) 27.8707 1.65968
\(283\) −10.5237 −0.625568 −0.312784 0.949824i \(-0.601262\pi\)
−0.312784 + 0.949824i \(0.601262\pi\)
\(284\) 34.4361i 2.04341i
\(285\) 0.172238 0.0102025
\(286\) 3.03885 + 7.16101i 0.179691 + 0.423440i
\(287\) 21.8497 1.28975
\(288\) 7.70458i 0.453997i
\(289\) 27.6260 1.62506
\(290\) −4.52448 −0.265687
\(291\) 1.86542i 0.109353i
\(292\) 22.6115i 1.32324i
\(293\) 14.0111i 0.818540i 0.912413 + 0.409270i \(0.134217\pi\)
−0.912413 + 0.409270i \(0.865783\pi\)
\(294\) 3.59349i 0.209576i
\(295\) 5.54901 0.323076
\(296\) 4.83725 0.281159
\(297\) 1.00000i 0.0580259i
\(298\) 20.5043 1.18778
\(299\) 13.4303 + 31.6483i 0.776693 + 1.83027i
\(300\) −11.9357 −0.689110
\(301\) 27.4366i 1.58142i
\(302\) −32.8217 −1.88868
\(303\) 2.45086 0.140798
\(304\) 0.548341i 0.0314495i
\(305\) 0.646706i 0.0370303i
\(306\) 14.4130i 0.823934i
\(307\) 2.52126i 0.143896i −0.997408 0.0719481i \(-0.977078\pi\)
0.997408 0.0719481i \(-0.0229216\pi\)
\(308\) 6.13206 0.349406
\(309\) −10.2811 −0.584870
\(310\) 6.16013i 0.349872i
\(311\) 22.9380 1.30069 0.650347 0.759638i \(-0.274624\pi\)
0.650347 + 0.759638i \(0.274624\pi\)
\(312\) 4.69032 1.99039i 0.265537 0.112683i
\(313\) −21.6566 −1.22410 −0.612051 0.790818i \(-0.709655\pi\)
−0.612051 + 0.790818i \(0.709655\pi\)
\(314\) 43.5714i 2.45888i
\(315\) 1.64033 0.0924222
\(316\) −4.84163 −0.272363
\(317\) 26.6050i 1.49429i 0.664664 + 0.747143i \(0.268575\pi\)
−0.664664 + 0.747143i \(0.731425\pi\)
\(318\) 14.6487i 0.821458i
\(319\) 2.95273i 0.165321i
\(320\) 8.59415i 0.480428i
\(321\) 19.6690 1.09782
\(322\) 47.5159 2.64796
\(323\) 1.62008i 0.0901435i
\(324\) −2.65498 −0.147499
\(325\) −6.33196 14.9212i −0.351234 0.827679i
\(326\) 35.5937 1.97135
\(327\) 1.27506i 0.0705108i
\(328\) −13.3687 −0.738161
\(329\) 29.8356 1.64489
\(330\) 1.53231i 0.0843507i
\(331\) 24.7670i 1.36132i −0.732600 0.680659i \(-0.761693\pi\)
0.732600 0.680659i \(-0.238307\pi\)
\(332\) 12.3369i 0.677076i
\(333\) 3.42304i 0.187581i
\(334\) 11.8774 0.649903
\(335\) −6.62069 −0.361727
\(336\) 5.22220i 0.284894i
\(337\) 28.2890 1.54100 0.770499 0.637441i \(-0.220007\pi\)
0.770499 + 0.637441i \(0.220007\pi\)
\(338\) 20.1723 + 19.4877i 1.09723 + 1.05999i
\(339\) −0.638739 −0.0346916
\(340\) 12.5963i 0.683129i
\(341\) −4.02017 −0.217704
\(342\) −0.523240 −0.0282936
\(343\) 20.0143i 1.08067i
\(344\) 16.7869i 0.905091i
\(345\) 6.77207i 0.364596i
\(346\) 27.4280i 1.47454i
\(347\) −18.0814 −0.970661 −0.485331 0.874331i \(-0.661301\pi\)
−0.485331 + 0.874331i \(0.661301\pi\)
\(348\) 7.83943 0.420238
\(349\) 21.0326i 1.12585i −0.826508 0.562924i \(-0.809676\pi\)
0.826508 0.562924i \(-0.190324\pi\)
\(350\) −22.4022 −1.19745
\(351\) −1.40848 3.31906i −0.0751791 0.177159i
\(352\) 7.70458 0.410655
\(353\) 2.20127i 0.117162i 0.998283 + 0.0585810i \(0.0186576\pi\)
−0.998283 + 0.0585810i \(0.981342\pi\)
\(354\) −16.8573 −0.895955
\(355\) −9.21169 −0.488906
\(356\) 39.2177i 2.07853i
\(357\) 15.4290i 0.816591i
\(358\) 52.7041i 2.78550i
\(359\) 7.76540i 0.409842i 0.978778 + 0.204921i \(0.0656938\pi\)
−0.978778 + 0.204921i \(0.934306\pi\)
\(360\) −1.00363 −0.0528959
\(361\) 18.9412 0.996905
\(362\) 2.00937i 0.105610i
\(363\) −1.00000 −0.0524864
\(364\) 20.3527 8.63687i 1.06677 0.452695i
\(365\) 6.04861 0.316599
\(366\) 1.96462i 0.102692i
\(367\) −11.9604 −0.624326 −0.312163 0.950028i \(-0.601054\pi\)
−0.312163 + 0.950028i \(0.601054\pi\)
\(368\) 21.5597 1.12388
\(369\) 9.46022i 0.492480i
\(370\) 5.24514i 0.272682i
\(371\) 15.6814i 0.814138i
\(372\) 10.6735i 0.553394i
\(373\) 14.1243 0.731330 0.365665 0.930747i \(-0.380842\pi\)
0.365665 + 0.930747i \(0.380842\pi\)
\(374\) −14.4130 −0.745276
\(375\) 6.74387i 0.348252i
\(376\) −18.2548 −0.941418
\(377\) 4.15885 + 9.80029i 0.214192 + 0.504741i
\(378\) −4.98315 −0.256305
\(379\) 3.34432i 0.171786i −0.996304 0.0858931i \(-0.972626\pi\)
0.996304 0.0858931i \(-0.0273744\pi\)
\(380\) −0.457288 −0.0234584
\(381\) −10.3681 −0.531174
\(382\) 10.1018i 0.516853i
\(383\) 5.63621i 0.287997i −0.989578 0.143998i \(-0.954004\pi\)
0.989578 0.143998i \(-0.0459960\pi\)
\(384\) 10.6989i 0.545977i
\(385\) 1.64033i 0.0835991i
\(386\) 22.1516 1.12749
\(387\) 11.8791 0.603850
\(388\) 4.95266i 0.251433i
\(389\) −14.3490 −0.727523 −0.363761 0.931492i \(-0.618508\pi\)
−0.363761 + 0.931492i \(0.618508\pi\)
\(390\) −2.15822 5.08582i −0.109286 0.257531i
\(391\) −63.6984 −3.22137
\(392\) 2.35366i 0.118878i
\(393\) −5.68692 −0.286867
\(394\) 24.9934 1.25915
\(395\) 1.29514i 0.0651657i
\(396\) 2.65498i 0.133418i
\(397\) 14.8769i 0.746648i 0.927701 + 0.373324i \(0.121782\pi\)
−0.927701 + 0.373324i \(0.878218\pi\)
\(398\) 37.1809i 1.86371i
\(399\) −0.560127 −0.0280414
\(400\) −10.1647 −0.508237
\(401\) 19.6380i 0.980675i −0.871533 0.490337i \(-0.836874\pi\)
0.871533 0.490337i \(-0.163126\pi\)
\(402\) 20.1129 1.00314
\(403\) −13.3432 + 5.66233i −0.664672 + 0.282061i
\(404\) −6.50698 −0.323734
\(405\) 0.710210i 0.0352906i
\(406\) 14.7139 0.730237
\(407\) −3.42304 −0.169674
\(408\) 9.44019i 0.467359i
\(409\) 23.1731i 1.14584i 0.819613 + 0.572918i \(0.194189\pi\)
−0.819613 + 0.572918i \(0.805811\pi\)
\(410\) 14.4960i 0.715905i
\(411\) 4.86363i 0.239905i
\(412\) 27.2961 1.34478
\(413\) −18.0457 −0.887971
\(414\) 20.5728i 1.01110i
\(415\) −3.30014 −0.161997
\(416\) 25.5720 10.8517i 1.25377 0.532050i
\(417\) −4.41515 −0.216211
\(418\) 0.523240i 0.0255925i
\(419\) −3.70294 −0.180900 −0.0904502 0.995901i \(-0.528831\pi\)
−0.0904502 + 0.995901i \(0.528831\pi\)
\(420\) −4.35505 −0.212505
\(421\) 23.7239i 1.15623i 0.815955 + 0.578116i \(0.196212\pi\)
−0.815955 + 0.578116i \(0.803788\pi\)
\(422\) 23.0653i 1.12280i
\(423\) 12.9178i 0.628086i
\(424\) 9.59460i 0.465955i
\(425\) 30.0318 1.45676
\(426\) 27.9841 1.35583
\(427\) 2.10313i 0.101777i
\(428\) −52.2209 −2.52419
\(429\) −3.31906 + 1.40848i −0.160246 + 0.0680020i
\(430\) 18.2025 0.877802
\(431\) 31.0695i 1.49656i −0.663381 0.748282i \(-0.730879\pi\)
0.663381 0.748282i \(-0.269121\pi\)
\(432\) −2.26104 −0.108784
\(433\) −23.0541 −1.10791 −0.553954 0.832547i \(-0.686882\pi\)
−0.553954 + 0.832547i \(0.686882\pi\)
\(434\) 20.0331i 0.961620i
\(435\) 2.09706i 0.100546i
\(436\) 3.38525i 0.162124i
\(437\) 2.31247i 0.110621i
\(438\) −18.3750 −0.877992
\(439\) −2.39273 −0.114199 −0.0570994 0.998368i \(-0.518185\pi\)
−0.0570994 + 0.998368i \(0.518185\pi\)
\(440\) 1.00363i 0.0478462i
\(441\) 1.66555 0.0793118
\(442\) −47.8375 + 20.3003i −2.27540 + 0.965589i
\(443\) −17.1624 −0.815411 −0.407705 0.913113i \(-0.633671\pi\)
−0.407705 + 0.913113i \(0.633671\pi\)
\(444\) 9.08810i 0.431302i
\(445\) 10.4908 0.497311
\(446\) −11.5211 −0.545539
\(447\) 9.50356i 0.449503i
\(448\) 27.9487i 1.32045i
\(449\) 29.0646i 1.37164i −0.727769 0.685822i \(-0.759443\pi\)
0.727769 0.685822i \(-0.240557\pi\)
\(450\) 9.69944i 0.457236i
\(451\) 9.46022 0.445465
\(452\) 1.69584 0.0797656
\(453\) 15.2126i 0.714749i
\(454\) −16.8813 −0.792277
\(455\) −2.31037 5.44437i −0.108312 0.255236i
\(456\) 0.342711 0.0160489
\(457\) 31.9111i 1.49274i −0.665532 0.746369i \(-0.731795\pi\)
0.665532 0.746369i \(-0.268205\pi\)
\(458\) 23.0435 1.07675
\(459\) 6.68027 0.311808
\(460\) 17.9797i 0.838308i
\(461\) 0.706685i 0.0329136i −0.999865 0.0164568i \(-0.994761\pi\)
0.999865 0.0164568i \(-0.00523860\pi\)
\(462\) 4.98315i 0.231837i
\(463\) 25.7813i 1.19816i −0.800690 0.599079i \(-0.795533\pi\)
0.800690 0.599079i \(-0.204467\pi\)
\(464\) 6.67624 0.309937
\(465\) 2.85516 0.132405
\(466\) 33.3360i 1.54426i
\(467\) −37.3541 −1.72854 −0.864270 0.503028i \(-0.832219\pi\)
−0.864270 + 0.503028i \(0.832219\pi\)
\(468\) 3.73948 + 8.81205i 0.172858 + 0.407337i
\(469\) 21.5309 0.994203
\(470\) 19.7941i 0.913033i
\(471\) 20.1949 0.930533
\(472\) 11.0412 0.508212
\(473\) 11.8791i 0.546203i
\(474\) 3.93450i 0.180718i
\(475\) 1.09026i 0.0500245i
\(476\) 40.9638i 1.87757i
\(477\) 6.78954 0.310872
\(478\) −36.5411 −1.67135
\(479\) 1.74064i 0.0795318i −0.999209 0.0397659i \(-0.987339\pi\)
0.999209 0.0397659i \(-0.0126612\pi\)
\(480\) −5.47187 −0.249756
\(481\) −11.3613 + 4.82128i −0.518030 + 0.219831i
\(482\) 0.172527 0.00785839
\(483\) 22.0232i 1.00209i
\(484\) 2.65498 0.120681
\(485\) −1.32484 −0.0601580
\(486\) 2.15754i 0.0978680i
\(487\) 5.69783i 0.258193i 0.991632 + 0.129097i \(0.0412078\pi\)
−0.991632 + 0.129097i \(0.958792\pi\)
\(488\) 1.28679i 0.0582502i
\(489\) 16.4974i 0.746037i
\(490\) 2.55213 0.115293
\(491\) 27.7388 1.25183 0.625917 0.779890i \(-0.284725\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(492\) 25.1167i 1.13235i
\(493\) −19.7250 −0.888370
\(494\) 0.736972 + 1.73667i 0.0331580 + 0.0781363i
\(495\) 0.710210 0.0319216
\(496\) 9.08977i 0.408143i
\(497\) 29.9569 1.34375
\(498\) 10.0255 0.449251
\(499\) 8.27073i 0.370249i 0.982715 + 0.185124i \(0.0592688\pi\)
−0.982715 + 0.185124i \(0.940731\pi\)
\(500\) 17.9048i 0.800729i
\(501\) 5.50507i 0.245948i
\(502\) 16.3363i 0.729126i
\(503\) −12.7099 −0.566706 −0.283353 0.959016i \(-0.591447\pi\)
−0.283353 + 0.959016i \(0.591447\pi\)
\(504\) 3.26386 0.145384
\(505\) 1.74062i 0.0774568i
\(506\) 20.5728 0.914573
\(507\) −9.03237 + 9.34967i −0.401142 + 0.415233i
\(508\) 27.5271 1.22132
\(509\) 5.55978i 0.246433i 0.992380 + 0.123216i \(0.0393210\pi\)
−0.992380 + 0.123216i \(0.960679\pi\)
\(510\) 10.2362 0.453268
\(511\) −19.6704 −0.870168
\(512\) 23.8107i 1.05230i
\(513\) 0.242517i 0.0107074i
\(514\) 49.6756i 2.19110i
\(515\) 7.30172i 0.321752i
\(516\) −31.5389 −1.38842
\(517\) 12.9178 0.568126
\(518\) 17.0575i 0.749464i
\(519\) 12.7126 0.558023
\(520\) 1.41359 + 3.33111i 0.0619901 + 0.146079i
\(521\) −4.41425 −0.193392 −0.0966958 0.995314i \(-0.530827\pi\)
−0.0966958 + 0.995314i \(0.530827\pi\)
\(522\) 6.37063i 0.278835i
\(523\) 15.5162 0.678474 0.339237 0.940701i \(-0.389831\pi\)
0.339237 + 0.940701i \(0.389831\pi\)
\(524\) 15.0986 0.659587
\(525\) 10.3832i 0.453162i
\(526\) 12.8384i 0.559780i
\(527\) 26.8558i 1.16986i
\(528\) 2.26104i 0.0983992i
\(529\) 67.9221 2.95314
\(530\) 10.4037 0.451906
\(531\) 7.81320i 0.339064i
\(532\) 1.48713 0.0644751
\(533\) 31.3991 13.3245i 1.36005 0.577150i
\(534\) −31.8698 −1.37914
\(535\) 13.9691i 0.603939i
\(536\) −13.1736 −0.569011
\(537\) −24.4279 −1.05414
\(538\) 2.53663i 0.109362i
\(539\) 1.66555i 0.0717402i
\(540\) 1.88559i 0.0811430i
\(541\) 27.9827i 1.20307i 0.798846 + 0.601536i \(0.205444\pi\)
−0.798846 + 0.601536i \(0.794556\pi\)
\(542\) 15.3769 0.660495
\(543\) −0.931324 −0.0399669
\(544\) 51.4687i 2.20670i
\(545\) −0.905559 −0.0387899
\(546\) 7.01866 + 16.5394i 0.300371 + 0.707820i
\(547\) −24.1470 −1.03245 −0.516226 0.856453i \(-0.672663\pi\)
−0.516226 + 0.856453i \(0.672663\pi\)
\(548\) 12.9128i 0.551609i
\(549\) 0.910585 0.0388628
\(550\) −9.69944 −0.413586
\(551\) 0.716086i 0.0305063i
\(552\) 13.4748i 0.573524i
\(553\) 4.21188i 0.179107i
\(554\) 25.8336i 1.09756i
\(555\) 2.43108 0.103193
\(556\) 11.7221 0.497129
\(557\) 19.1326i 0.810675i −0.914167 0.405337i \(-0.867154\pi\)
0.914167 0.405337i \(-0.132846\pi\)
\(558\) −8.67368 −0.367186
\(559\) −16.7315 39.4276i −0.707668 1.66761i
\(560\) −3.70886 −0.156728
\(561\) 6.68027i 0.282041i
\(562\) −40.5404 −1.71009
\(563\) 3.91199 0.164871 0.0824353 0.996596i \(-0.473730\pi\)
0.0824353 + 0.996596i \(0.473730\pi\)
\(564\) 34.2966i 1.44415i
\(565\) 0.453639i 0.0190847i
\(566\) 22.7053i 0.954373i
\(567\) 2.30964i 0.0969959i
\(568\) −18.3290 −0.769069
\(569\) 15.8002 0.662377 0.331189 0.943565i \(-0.392550\pi\)
0.331189 + 0.943565i \(0.392550\pi\)
\(570\) 0.371610i 0.0155650i
\(571\) −20.2458 −0.847262 −0.423631 0.905835i \(-0.639245\pi\)
−0.423631 + 0.905835i \(0.639245\pi\)
\(572\) 8.81205 3.73948i 0.368450 0.156356i
\(573\) 4.68209 0.195597
\(574\) 47.1417i 1.96766i
\(575\) −42.8669 −1.78768
\(576\) 12.1009 0.504202
\(577\) 7.07073i 0.294358i −0.989110 0.147179i \(-0.952981\pi\)
0.989110 0.147179i \(-0.0470194\pi\)
\(578\) 59.6042i 2.47921i
\(579\) 10.2671i 0.426685i
\(580\) 5.56764i 0.231184i
\(581\) 10.7322 0.445248
\(582\) 4.02473 0.166830
\(583\) 6.78954i 0.281194i
\(584\) 12.0353 0.498023
\(585\) 2.35723 1.00032i 0.0974596 0.0413580i
\(586\) 30.2296 1.24877
\(587\) 27.1767i 1.12170i 0.827917 + 0.560851i \(0.189526\pi\)
−0.827917 + 0.560851i \(0.810474\pi\)
\(588\) −4.42200 −0.182360
\(589\) −0.974959 −0.0401725
\(590\) 11.9722i 0.492889i
\(591\) 11.5842i 0.476511i
\(592\) 7.73963i 0.318097i
\(593\) 20.0431i 0.823070i −0.911394 0.411535i \(-0.864993\pi\)
0.911394 0.411535i \(-0.135007\pi\)
\(594\) −2.15754 −0.0885249
\(595\) 10.9579 0.449228
\(596\) 25.2318i 1.03353i
\(597\) −17.2330 −0.705300
\(598\) 68.2825 28.9764i 2.79228 1.18493i
\(599\) −24.5855 −1.00454 −0.502268 0.864712i \(-0.667501\pi\)
−0.502268 + 0.864712i \(0.667501\pi\)
\(600\) 6.35294i 0.259358i
\(601\) −34.1098 −1.39137 −0.695683 0.718349i \(-0.744898\pi\)
−0.695683 + 0.718349i \(0.744898\pi\)
\(602\) −59.1955 −2.41263
\(603\) 9.32216i 0.379628i
\(604\) 40.3891i 1.64341i
\(605\) 0.710210i 0.0288741i
\(606\) 5.28783i 0.214803i
\(607\) 20.9453 0.850143 0.425071 0.905160i \(-0.360249\pi\)
0.425071 + 0.905160i \(0.360249\pi\)
\(608\) 1.86849 0.0757773
\(609\) 6.81975i 0.276350i
\(610\) 1.39530 0.0564938
\(611\) 42.8751 18.1945i 1.73454 0.736071i
\(612\) −17.7360 −0.716935
\(613\) 22.2792i 0.899848i −0.893067 0.449924i \(-0.851451\pi\)
0.893067 0.449924i \(-0.148549\pi\)
\(614\) −5.43973 −0.219530
\(615\) −6.71875 −0.270926
\(616\) 3.26386i 0.131505i
\(617\) 27.4366i 1.10456i 0.833660 + 0.552279i \(0.186242\pi\)
−0.833660 + 0.552279i \(0.813758\pi\)
\(618\) 22.1818i 0.892284i
\(619\) 47.9288i 1.92642i 0.268747 + 0.963211i \(0.413390\pi\)
−0.268747 + 0.963211i \(0.586610\pi\)
\(620\) −7.58040 −0.304436
\(621\) −9.53531 −0.382639
\(622\) 49.4896i 1.98435i
\(623\) −34.1166 −1.36685
\(624\) 3.18463 + 7.50454i 0.127487 + 0.300422i
\(625\) 17.6884 0.707538
\(626\) 46.7250i 1.86751i
\(627\) −0.242517 −0.00968519
\(628\) −53.6171 −2.13956
\(629\) 22.8668i 0.911760i
\(630\) 3.53908i 0.141000i
\(631\) 23.8277i 0.948567i −0.880372 0.474284i \(-0.842707\pi\)
0.880372 0.474284i \(-0.157293\pi\)
\(632\) 2.57702i 0.102508i
\(633\) −10.6905 −0.424911
\(634\) 57.4013 2.27970
\(635\) 7.36353i 0.292213i
\(636\) −18.0261 −0.714781
\(637\) −2.34589 5.52806i −0.0929475 0.219030i
\(638\) 6.37063 0.252216
\(639\) 12.9704i 0.513100i
\(640\) 7.59848 0.300356
\(641\) 8.30355 0.327970 0.163985 0.986463i \(-0.447565\pi\)
0.163985 + 0.986463i \(0.447565\pi\)
\(642\) 42.4367i 1.67484i
\(643\) 29.9185i 1.17987i 0.807451 + 0.589934i \(0.200846\pi\)
−0.807451 + 0.589934i \(0.799154\pi\)
\(644\) 58.4710i 2.30408i
\(645\) 8.43668i 0.332194i
\(646\) −3.49538 −0.137524
\(647\) −5.87308 −0.230895 −0.115447 0.993314i \(-0.536830\pi\)
−0.115447 + 0.993314i \(0.536830\pi\)
\(648\) 1.41315i 0.0555136i
\(649\) −7.81320 −0.306695
\(650\) −32.1931 + 13.6615i −1.26272 + 0.535847i
\(651\) −9.28516 −0.363914
\(652\) 43.8002i 1.71535i
\(653\) −5.43262 −0.212595 −0.106297 0.994334i \(-0.533900\pi\)
−0.106297 + 0.994334i \(0.533900\pi\)
\(654\) 2.75099 0.107572
\(655\) 4.03891i 0.157813i
\(656\) 21.3900i 0.835138i
\(657\) 8.51665i 0.332266i
\(658\) 64.3715i 2.50946i
\(659\) 26.5954 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(660\) −1.88559 −0.0733966
\(661\) 27.7763i 1.08037i 0.841545 + 0.540187i \(0.181646\pi\)
−0.841545 + 0.540187i \(0.818354\pi\)
\(662\) −53.4359 −2.07684
\(663\) −9.40902 22.1722i −0.365416 0.861099i
\(664\) −6.56647 −0.254828
\(665\) 0.397808i 0.0154263i
\(666\) −7.38534 −0.286176
\(667\) 28.1552 1.09017
\(668\) 14.6158i 0.565504i
\(669\) 5.33992i 0.206453i
\(670\) 14.2844i 0.551855i
\(671\) 0.910585i 0.0351527i
\(672\) 17.7948 0.686450
\(673\) −3.00054 −0.115663 −0.0578313 0.998326i \(-0.518419\pi\)
−0.0578313 + 0.998326i \(0.518419\pi\)
\(674\) 61.0346i 2.35096i
\(675\) 4.49560 0.173036
\(676\) 23.9808 24.8232i 0.922337 0.954737i
\(677\) −25.1724 −0.967452 −0.483726 0.875219i \(-0.660717\pi\)
−0.483726 + 0.875219i \(0.660717\pi\)
\(678\) 1.37811i 0.0529258i
\(679\) 4.30846 0.165344
\(680\) −6.70452 −0.257107
\(681\) 7.82431i 0.299828i
\(682\) 8.67368i 0.332132i
\(683\) 39.1652i 1.49861i −0.662223 0.749307i \(-0.730387\pi\)
0.662223 0.749307i \(-0.269613\pi\)
\(684\) 0.643877i 0.0246193i
\(685\) 3.45420 0.131978
\(686\) −43.1817 −1.64869
\(687\) 10.6805i 0.407485i
\(688\) −26.8592 −1.02400
\(689\) −9.56293 22.5349i −0.364318 0.858512i
\(690\) −14.6110 −0.556232
\(691\) 33.3472i 1.26859i 0.773092 + 0.634294i \(0.218709\pi\)
−0.773092 + 0.634294i \(0.781291\pi\)
\(692\) −33.7518 −1.28305
\(693\) −2.30964 −0.0877361
\(694\) 39.0114i 1.48085i
\(695\) 3.13568i 0.118943i
\(696\) 4.17263i 0.158163i
\(697\) 63.1969i 2.39375i
\(698\) −45.3787 −1.71761
\(699\) −15.4509 −0.584408
\(700\) 27.5673i 1.04195i
\(701\) −8.45704 −0.319418 −0.159709 0.987164i \(-0.551056\pi\)
−0.159709 + 0.987164i \(0.551056\pi\)
\(702\) −7.16101 + 3.03885i −0.270275 + 0.114694i
\(703\) −0.830144 −0.0313095
\(704\) 12.1009i 0.456068i
\(705\) −9.17437 −0.345527
\(706\) 4.74934 0.178744
\(707\) 5.66061i 0.212889i
\(708\) 20.7439i 0.779603i
\(709\) 7.03783i 0.264311i 0.991229 + 0.132156i \(0.0421899\pi\)
−0.991229 + 0.132156i \(0.957810\pi\)
\(710\) 19.8746i 0.745880i
\(711\) 1.82360 0.0683905
\(712\) 20.8741 0.782290
\(713\) 38.3336i 1.43560i
\(714\) −33.2888 −1.24580
\(715\) −1.00032 2.35723i −0.0374097 0.0881555i
\(716\) 64.8555 2.42377
\(717\) 16.9365i 0.632504i
\(718\) 16.7542 0.625260
\(719\) 5.52947 0.206215 0.103107 0.994670i \(-0.467121\pi\)
0.103107 + 0.994670i \(0.467121\pi\)
\(720\) 1.60581i 0.0598452i
\(721\) 23.7456i 0.884333i
\(722\) 40.8664i 1.52089i
\(723\) 0.0799646i 0.00297392i
\(724\) 2.47265 0.0918952
\(725\) −13.2743 −0.492995
\(726\) 2.15754i 0.0800738i
\(727\) 38.7533 1.43728 0.718640 0.695383i \(-0.244765\pi\)
0.718640 + 0.695383i \(0.244765\pi\)
\(728\) −4.59708 10.8330i −0.170379 0.401496i
\(729\) 1.00000 0.0370370
\(730\) 13.0501i 0.483006i
\(731\) 79.3558 2.93508
\(732\) −2.41758 −0.0893565
\(733\) 9.60595i 0.354804i 0.984138 + 0.177402i \(0.0567693\pi\)
−0.984138 + 0.177402i \(0.943231\pi\)
\(734\) 25.8050i 0.952480i
\(735\) 1.18289i 0.0436315i
\(736\) 73.4655i 2.70798i
\(737\) 9.32216 0.343386
\(738\) 20.4108 0.751332
\(739\) 21.6659i 0.796995i −0.917169 0.398497i \(-0.869532\pi\)
0.917169 0.398497i \(-0.130468\pi\)
\(740\) −6.45446 −0.237271
\(741\) −0.804929 + 0.341580i −0.0295698 + 0.0125483i
\(742\) −33.8333 −1.24206
\(743\) 12.3149i 0.451790i 0.974152 + 0.225895i \(0.0725305\pi\)
−0.974152 + 0.225895i \(0.927469\pi\)
\(744\) 5.68108 0.208279
\(745\) −6.74952 −0.247283
\(746\) 30.4738i 1.11572i
\(747\) 4.64671i 0.170014i
\(748\) 17.7360i 0.648492i
\(749\) 45.4285i 1.65992i
\(750\) 14.5502 0.531297
\(751\) −2.50813 −0.0915231 −0.0457616 0.998952i \(-0.514571\pi\)
−0.0457616 + 0.998952i \(0.514571\pi\)
\(752\) 29.2078i 1.06510i
\(753\) 7.57174 0.275930
\(754\) 21.1445 8.97290i 0.770038 0.326774i
\(755\) 10.8041 0.393202
\(756\) 6.13206i 0.223021i
\(757\) 2.89889 0.105362 0.0526809 0.998611i \(-0.483223\pi\)
0.0526809 + 0.998611i \(0.483223\pi\)
\(758\) −7.21551 −0.262079
\(759\) 9.53531i 0.346110i
\(760\) 0.243397i 0.00882894i
\(761\) 33.6764i 1.22077i 0.792105 + 0.610384i \(0.208985\pi\)
−0.792105 + 0.610384i \(0.791015\pi\)
\(762\) 22.3696i 0.810365i
\(763\) 2.94493 0.106614
\(764\) −12.4309 −0.449733
\(765\) 4.74440i 0.171534i
\(766\) −12.1604 −0.439371
\(767\) −25.9325 + 11.0047i −0.936369 + 0.397358i
\(768\) 1.11835 0.0403551
\(769\) 25.1224i 0.905935i 0.891527 + 0.452968i \(0.149635\pi\)
−0.891527 + 0.452968i \(0.850365\pi\)
\(770\) −3.53908 −0.127540
\(771\) −23.0242 −0.829196
\(772\) 27.2588i 0.981067i
\(773\) 31.6336i 1.13778i 0.822413 + 0.568891i \(0.192627\pi\)
−0.822413 + 0.568891i \(0.807373\pi\)
\(774\) 25.6297i 0.921241i
\(775\) 18.0731i 0.649204i
\(776\) −2.63611 −0.0946310
\(777\) −7.90600 −0.283626
\(778\) 30.9585i 1.10992i
\(779\) 2.29426 0.0822005
\(780\) −6.25840 + 2.65582i −0.224087 + 0.0950936i
\(781\) 12.9704 0.464117
\(782\) 137.432i 4.91456i
\(783\) −2.95273 −0.105522
\(784\) −3.76587 −0.134495
\(785\) 14.3426i 0.511911i
\(786\) 12.2698i 0.437648i
\(787\) 23.2041i 0.827137i −0.910473 0.413569i \(-0.864282\pi\)
0.910473 0.413569i \(-0.135718\pi\)
\(788\) 30.7559i 1.09563i
\(789\) −5.95047 −0.211842
\(790\) 2.79432 0.0994175
\(791\) 1.47526i 0.0524542i