Properties

Label 504.2.c.f.253.2
Level 504
Weight 2
Character 504.253
Analytic conductor 4.024
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.2
Root \(-1.19503 - 0.756243i\)
Character \(\chi\) = 504.253
Dual form 504.2.c.f.253.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19503 + 0.756243i) q^{2} +(0.856193 - 1.80747i) q^{4} -4.10245i q^{5} +1.00000 q^{7} +(0.343707 + 2.80747i) q^{8} +O(q^{10})\) \(q+(-1.19503 + 0.756243i) q^{2} +(0.856193 - 1.80747i) q^{4} -4.10245i q^{5} +1.00000 q^{7} +(0.343707 + 2.80747i) q^{8} +(3.10245 + 4.90255i) q^{10} +2.67767i q^{11} -3.02497i q^{13} +(-1.19503 + 0.756243i) q^{14} +(-2.53387 - 3.09508i) q^{16} +5.12742 q^{17} -2.78012i q^{19} +(-7.41503 - 3.51249i) q^{20} +(-2.02497 - 3.19990i) q^{22} -7.12742 q^{23} -11.8301 q^{25} +(2.28761 + 3.61493i) q^{26} +(0.856193 - 1.80747i) q^{28} -8.83006i q^{29} -1.42477 q^{31} +(5.36868 + 1.78249i) q^{32} +(-6.12742 + 3.87757i) q^{34} -4.10245i q^{35} -1.42477i q^{37} +(2.10245 + 3.32233i) q^{38} +(11.5175 - 1.41004i) q^{40} -5.12742 q^{41} -2.39980i q^{43} +(4.83980 + 2.29261i) q^{44} +(8.51748 - 5.39006i) q^{46} +9.56024 q^{47} +1.00000 q^{49} +(14.1373 - 8.94640i) q^{50} +(-5.46753 - 2.58996i) q^{52} -2.78012i q^{53} +10.9850 q^{55} +(0.343707 + 2.80747i) q^{56} +(6.67767 + 10.5522i) q^{58} +4.00000i q^{59} +5.17992i q^{61} +(1.70265 - 1.07747i) q^{62} +(-7.76373 + 1.92989i) q^{64} -12.4098 q^{65} +0.244852i q^{67} +(4.39006 - 9.26763i) q^{68} +(3.10245 + 4.90255i) q^{70} +4.27787 q^{71} -4.15495 q^{73} +(1.07747 + 1.70265i) q^{74} +(-5.02497 - 2.38032i) q^{76} +2.67767i q^{77} +6.25484 q^{79} +(-12.6974 + 10.3951i) q^{80} +(6.12742 - 3.87757i) q^{82} -9.35535i q^{83} -21.0350i q^{85} +(1.81483 + 2.86783i) q^{86} +(-7.51748 + 0.920336i) q^{88} -11.2824 q^{89} -3.02497i q^{91} +(-6.10245 + 12.8826i) q^{92} +(-11.4248 + 7.22986i) q^{94} -11.4053 q^{95} +6.69460 q^{97} +(-1.19503 + 0.756243i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} + O(q^{10}) \) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} - 4q^{10} - 6q^{16} - 4q^{17} - 24q^{20} - 12q^{23} - 24q^{25} + 28q^{26} + 2q^{28} + 8q^{31} + 30q^{32} - 4q^{34} - 12q^{38} + 28q^{40} + 4q^{41} - 16q^{44} + 4q^{46} + 8q^{49} + 20q^{50} - 12q^{52} - 8q^{55} + 6q^{56} + 44q^{58} - 12q^{62} + 26q^{64} + 16q^{65} + 16q^{68} - 4q^{70} + 28q^{71} - 8q^{73} - 4q^{74} - 24q^{76} - 40q^{79} + 4q^{80} + 4q^{82} - 24q^{86} + 4q^{88} - 20q^{89} - 20q^{92} - 72q^{94} - 40q^{95} + 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19503 + 0.756243i −0.845014 + 0.534745i
\(3\) 0 0
\(4\) 0.856193 1.80747i 0.428097 0.903733i
\(5\) 4.10245i 1.83467i −0.398117 0.917335i \(-0.630336\pi\)
0.398117 0.917335i \(-0.369664\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0.343707 + 2.80747i 0.121519 + 0.992589i
\(9\) 0 0
\(10\) 3.10245 + 4.90255i 0.981080 + 1.55032i
\(11\) 2.67767i 0.807349i 0.914903 + 0.403674i \(0.132267\pi\)
−0.914903 + 0.403674i \(0.867733\pi\)
\(12\) 0 0
\(13\) 3.02497i 0.838976i −0.907761 0.419488i \(-0.862210\pi\)
0.907761 0.419488i \(-0.137790\pi\)
\(14\) −1.19503 + 0.756243i −0.319385 + 0.202114i
\(15\) 0 0
\(16\) −2.53387 3.09508i −0.633467 0.773770i
\(17\) 5.12742 1.24358 0.621791 0.783183i \(-0.286405\pi\)
0.621791 + 0.783183i \(0.286405\pi\)
\(18\) 0 0
\(19\) 2.78012i 0.637803i −0.947788 0.318902i \(-0.896686\pi\)
0.947788 0.318902i \(-0.103314\pi\)
\(20\) −7.41503 3.51249i −1.65805 0.785416i
\(21\) 0 0
\(22\) −2.02497 3.19990i −0.431725 0.682221i
\(23\) −7.12742 −1.48617 −0.743085 0.669197i \(-0.766638\pi\)
−0.743085 + 0.669197i \(0.766638\pi\)
\(24\) 0 0
\(25\) −11.8301 −2.36601
\(26\) 2.28761 + 3.61493i 0.448638 + 0.708946i
\(27\) 0 0
\(28\) 0.856193 1.80747i 0.161805 0.341579i
\(29\) 8.83006i 1.63970i −0.572577 0.819851i \(-0.694056\pi\)
0.572577 0.819851i \(-0.305944\pi\)
\(30\) 0 0
\(31\) −1.42477 −0.255897 −0.127948 0.991781i \(-0.540839\pi\)
−0.127948 + 0.991781i \(0.540839\pi\)
\(32\) 5.36868 + 1.78249i 0.949057 + 0.315103i
\(33\) 0 0
\(34\) −6.12742 + 3.87757i −1.05084 + 0.664998i
\(35\) 4.10245i 0.693440i
\(36\) 0 0
\(37\) 1.42477i 0.234231i −0.993118 0.117116i \(-0.962635\pi\)
0.993118 0.117116i \(-0.0373648\pi\)
\(38\) 2.10245 + 3.32233i 0.341062 + 0.538952i
\(39\) 0 0
\(40\) 11.5175 1.41004i 1.82107 0.222947i
\(41\) −5.12742 −0.800768 −0.400384 0.916347i \(-0.631123\pi\)
−0.400384 + 0.916347i \(0.631123\pi\)
\(42\) 0 0
\(43\) 2.39980i 0.365966i −0.983116 0.182983i \(-0.941425\pi\)
0.983116 0.182983i \(-0.0585754\pi\)
\(44\) 4.83980 + 2.29261i 0.729628 + 0.345623i
\(45\) 0 0
\(46\) 8.51748 5.39006i 1.25583 0.794721i
\(47\) 9.56024 1.39450 0.697252 0.716826i \(-0.254406\pi\)
0.697252 + 0.716826i \(0.254406\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 14.1373 8.94640i 1.99931 1.26521i
\(51\) 0 0
\(52\) −5.46753 2.58996i −0.758211 0.359163i
\(53\) 2.78012i 0.381879i −0.981602 0.190939i \(-0.938847\pi\)
0.981602 0.190939i \(-0.0611534\pi\)
\(54\) 0 0
\(55\) 10.9850 1.48122
\(56\) 0.343707 + 2.80747i 0.0459298 + 0.375163i
\(57\) 0 0
\(58\) 6.67767 + 10.5522i 0.876822 + 1.38557i
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) 5.17992i 0.663221i 0.943416 + 0.331610i \(0.107592\pi\)
−0.943416 + 0.331610i \(0.892408\pi\)
\(62\) 1.70265 1.07747i 0.216236 0.136839i
\(63\) 0 0
\(64\) −7.76373 + 1.92989i −0.970466 + 0.241237i
\(65\) −12.4098 −1.53924
\(66\) 0 0
\(67\) 0.244852i 0.0299135i 0.999888 + 0.0149567i \(0.00476105\pi\)
−0.999888 + 0.0149567i \(0.995239\pi\)
\(68\) 4.39006 9.26763i 0.532373 1.12387i
\(69\) 0 0
\(70\) 3.10245 + 4.90255i 0.370813 + 0.585966i
\(71\) 4.27787 0.507690 0.253845 0.967245i \(-0.418305\pi\)
0.253845 + 0.967245i \(0.418305\pi\)
\(72\) 0 0
\(73\) −4.15495 −0.486300 −0.243150 0.969989i \(-0.578181\pi\)
−0.243150 + 0.969989i \(0.578181\pi\)
\(74\) 1.07747 + 1.70265i 0.125254 + 0.197929i
\(75\) 0 0
\(76\) −5.02497 2.38032i −0.576404 0.273041i
\(77\) 2.67767i 0.305149i
\(78\) 0 0
\(79\) 6.25484 0.703724 0.351862 0.936052i \(-0.385549\pi\)
0.351862 + 0.936052i \(0.385549\pi\)
\(80\) −12.6974 + 10.3951i −1.41961 + 1.16220i
\(81\) 0 0
\(82\) 6.12742 3.87757i 0.676660 0.428206i
\(83\) 9.35535i 1.02688i −0.858125 0.513441i \(-0.828370\pi\)
0.858125 0.513441i \(-0.171630\pi\)
\(84\) 0 0
\(85\) 21.0350i 2.28156i
\(86\) 1.81483 + 2.86783i 0.195698 + 0.309246i
\(87\) 0 0
\(88\) −7.51748 + 0.920336i −0.801366 + 0.0981081i
\(89\) −11.2824 −1.19593 −0.597964 0.801523i \(-0.704024\pi\)
−0.597964 + 0.801523i \(0.704024\pi\)
\(90\) 0 0
\(91\) 3.02497i 0.317103i
\(92\) −6.10245 + 12.8826i −0.636224 + 1.34310i
\(93\) 0 0
\(94\) −11.4248 + 7.22986i −1.17838 + 0.745704i
\(95\) −11.4053 −1.17016
\(96\) 0 0
\(97\) 6.69460 0.679733 0.339867 0.940474i \(-0.389618\pi\)
0.339867 + 0.940474i \(0.389618\pi\)
\(98\) −1.19503 + 0.756243i −0.120716 + 0.0763921i
\(99\) 0 0
\(100\) −10.1288 + 21.3824i −1.01288 + 2.13824i
\(101\) 1.45779i 0.145056i 0.997366 + 0.0725279i \(0.0231066\pi\)
−0.997366 + 0.0725279i \(0.976893\pi\)
\(102\) 0 0
\(103\) 8.13547 0.801611 0.400806 0.916163i \(-0.368730\pi\)
0.400806 + 0.916163i \(0.368730\pi\)
\(104\) 8.49251 1.03970i 0.832759 0.101951i
\(105\) 0 0
\(106\) 2.10245 + 3.32233i 0.204208 + 0.322693i
\(107\) 5.32233i 0.514529i 0.966341 + 0.257264i \(0.0828211\pi\)
−0.966341 + 0.257264i \(0.917179\pi\)
\(108\) 0 0
\(109\) 13.5602i 1.29884i 0.760432 + 0.649418i \(0.224987\pi\)
−0.760432 + 0.649418i \(0.775013\pi\)
\(110\) −13.1274 + 8.30734i −1.25165 + 0.792074i
\(111\) 0 0
\(112\) −2.53387 3.09508i −0.239428 0.292458i
\(113\) 4.15495 0.390865 0.195432 0.980717i \(-0.437389\pi\)
0.195432 + 0.980717i \(0.437389\pi\)
\(114\) 0 0
\(115\) 29.2398i 2.72663i
\(116\) −15.9600 7.56024i −1.48185 0.701951i
\(117\) 0 0
\(118\) −3.02497 4.78012i −0.278471 0.440046i
\(119\) 5.12742 0.470030
\(120\) 0 0
\(121\) 3.83006 0.348188
\(122\) −3.91728 6.19016i −0.354654 0.560431i
\(123\) 0 0
\(124\) −1.21988 + 2.57523i −0.109548 + 0.231262i
\(125\) 28.0200i 2.50618i
\(126\) 0 0
\(127\) −0.694597 −0.0616355 −0.0308177 0.999525i \(-0.509811\pi\)
−0.0308177 + 0.999525i \(0.509811\pi\)
\(128\) 7.81842 8.17755i 0.691058 0.722800i
\(129\) 0 0
\(130\) 14.8301 9.38481i 1.30068 0.823102i
\(131\) 12.2049i 1.06635i −0.846006 0.533173i \(-0.820999\pi\)
0.846006 0.533173i \(-0.179001\pi\)
\(132\) 0 0
\(133\) 2.78012i 0.241067i
\(134\) −0.185168 0.292606i −0.0159961 0.0252773i
\(135\) 0 0
\(136\) 1.76233 + 14.3951i 0.151119 + 1.23437i
\(137\) 15.1044 1.29045 0.645227 0.763991i \(-0.276763\pi\)
0.645227 + 0.763991i \(0.276763\pi\)
\(138\) 0 0
\(139\) 7.61018i 0.645487i 0.946486 + 0.322744i \(0.104605\pi\)
−0.946486 + 0.322744i \(0.895395\pi\)
\(140\) −7.41503 3.51249i −0.626685 0.296859i
\(141\) 0 0
\(142\) −5.11219 + 3.23511i −0.429005 + 0.271485i
\(143\) 8.09989 0.677347
\(144\) 0 0
\(145\) −36.2249 −3.00831
\(146\) 4.96529 3.14215i 0.410930 0.260046i
\(147\) 0 0
\(148\) −2.57523 1.21988i −0.211682 0.100274i
\(149\) 5.21988i 0.427629i 0.976874 + 0.213815i \(0.0685889\pi\)
−0.976874 + 0.213815i \(0.931411\pi\)
\(150\) 0 0
\(151\) −5.56024 −0.452486 −0.226243 0.974071i \(-0.572644\pi\)
−0.226243 + 0.974071i \(0.572644\pi\)
\(152\) 7.80509 0.955547i 0.633077 0.0775051i
\(153\) 0 0
\(154\) −2.02497 3.19990i −0.163177 0.257855i
\(155\) 5.84505i 0.469486i
\(156\) 0 0
\(157\) 0.519169i 0.0414342i 0.999785 + 0.0207171i \(0.00659493\pi\)
−0.999785 + 0.0207171i \(0.993405\pi\)
\(158\) −7.47472 + 4.73018i −0.594656 + 0.376313i
\(159\) 0 0
\(160\) 7.31259 22.0247i 0.578111 1.74121i
\(161\) −7.12742 −0.561719
\(162\) 0 0
\(163\) 8.65464i 0.677883i −0.940807 0.338942i \(-0.889931\pi\)
0.940807 0.338942i \(-0.110069\pi\)
\(164\) −4.39006 + 9.26763i −0.342806 + 0.723681i
\(165\) 0 0
\(166\) 7.07492 + 11.1799i 0.549120 + 0.867730i
\(167\) 25.1044 1.94264 0.971318 0.237786i \(-0.0764216\pi\)
0.971318 + 0.237786i \(0.0764216\pi\)
\(168\) 0 0
\(169\) 3.84954 0.296119
\(170\) 15.9075 + 25.1374i 1.22005 + 1.92795i
\(171\) 0 0
\(172\) −4.33756 2.05469i −0.330736 0.156669i
\(173\) 1.94750i 0.148066i −0.997256 0.0740328i \(-0.976413\pi\)
0.997256 0.0740328i \(-0.0235869\pi\)
\(174\) 0 0
\(175\) −11.8301 −0.894269
\(176\) 8.28761 6.78487i 0.624702 0.511429i
\(177\) 0 0
\(178\) 13.4828 8.53221i 1.01058 0.639516i
\(179\) 22.6976i 1.69650i 0.529595 + 0.848251i \(0.322344\pi\)
−0.529595 + 0.848251i \(0.677656\pi\)
\(180\) 0 0
\(181\) 10.5353i 0.783080i −0.920161 0.391540i \(-0.871942\pi\)
0.920161 0.391540i \(-0.128058\pi\)
\(182\) 2.28761 + 3.61493i 0.169569 + 0.267957i
\(183\) 0 0
\(184\) −2.44974 20.0100i −0.180598 1.47516i
\(185\) −5.84505 −0.429737
\(186\) 0 0
\(187\) 13.7296i 1.00400i
\(188\) 8.18541 17.2798i 0.596982 1.26026i
\(189\) 0 0
\(190\) 13.6297 8.62517i 0.988800 0.625736i
\(191\) 4.27787 0.309536 0.154768 0.987951i \(-0.450537\pi\)
0.154768 + 0.987951i \(0.450537\pi\)
\(192\) 0 0
\(193\) 23.1400 1.66565 0.832825 0.553536i \(-0.186722\pi\)
0.832825 + 0.553536i \(0.186722\pi\)
\(194\) −8.00024 + 5.06274i −0.574384 + 0.363484i
\(195\) 0 0
\(196\) 0.856193 1.80747i 0.0611566 0.129105i
\(197\) 19.4747i 1.38752i −0.720208 0.693758i \(-0.755954\pi\)
0.720208 0.693758i \(-0.244046\pi\)
\(198\) 0 0
\(199\) −17.5602 −1.24481 −0.622406 0.782694i \(-0.713845\pi\)
−0.622406 + 0.782694i \(0.713845\pi\)
\(200\) −4.06608 33.2125i −0.287515 2.34848i
\(201\) 0 0
\(202\) −1.10245 1.74211i −0.0775678 0.122574i
\(203\) 8.83006i 0.619749i
\(204\) 0 0
\(205\) 21.0350i 1.46915i
\(206\) −9.72213 + 6.15239i −0.677373 + 0.428657i
\(207\) 0 0
\(208\) −9.36253 + 7.66488i −0.649175 + 0.531464i
\(209\) 7.44425 0.514930
\(210\) 0 0
\(211\) 23.9600i 1.64948i 0.565514 + 0.824739i \(0.308678\pi\)
−0.565514 + 0.824739i \(0.691322\pi\)
\(212\) −5.02497 2.38032i −0.345116 0.163481i
\(213\) 0 0
\(214\) −4.02497 6.36034i −0.275141 0.434784i
\(215\) −9.84505 −0.671427
\(216\) 0 0
\(217\) −1.42477 −0.0967199
\(218\) −10.2548 16.2049i −0.694545 1.09753i
\(219\) 0 0
\(220\) 9.40529 19.8550i 0.634105 1.33863i
\(221\) 15.5103i 1.04334i
\(222\) 0 0
\(223\) 2.74966 0.184131 0.0920653 0.995753i \(-0.470653\pi\)
0.0920653 + 0.995753i \(0.470653\pi\)
\(224\) 5.36868 + 1.78249i 0.358710 + 0.119098i
\(225\) 0 0
\(226\) −4.96529 + 3.14215i −0.330286 + 0.209013i
\(227\) 8.30478i 0.551208i 0.961271 + 0.275604i \(0.0888778\pi\)
−0.961271 + 0.275604i \(0.911122\pi\)
\(228\) 0 0
\(229\) 11.9245i 0.787991i −0.919112 0.393995i \(-0.871093\pi\)
0.919112 0.393995i \(-0.128907\pi\)
\(230\) −22.1124 34.9425i −1.45805 2.30404i
\(231\) 0 0
\(232\) 24.7901 3.03496i 1.62755 0.199255i
\(233\) 3.56024 0.233239 0.116620 0.993177i \(-0.462794\pi\)
0.116620 + 0.993177i \(0.462794\pi\)
\(234\) 0 0
\(235\) 39.2204i 2.55845i
\(236\) 7.22986 + 3.42477i 0.470624 + 0.222934i
\(237\) 0 0
\(238\) −6.12742 + 3.87757i −0.397182 + 0.251346i
\(239\) −26.9425 −1.74277 −0.871383 0.490604i \(-0.836776\pi\)
−0.871383 + 0.490604i \(0.836776\pi\)
\(240\) 0 0
\(241\) 25.8151 1.66290 0.831448 0.555603i \(-0.187513\pi\)
0.831448 + 0.555603i \(0.187513\pi\)
\(242\) −4.57704 + 2.89646i −0.294223 + 0.186191i
\(243\) 0 0
\(244\) 9.36253 + 4.43501i 0.599375 + 0.283923i
\(245\) 4.10245i 0.262096i
\(246\) 0 0
\(247\) −8.40978 −0.535102
\(248\) −0.489704 4.00000i −0.0310963 0.254000i
\(249\) 0 0
\(250\) −21.1899 33.4847i −1.34017 2.11776i
\(251\) 27.1543i 1.71397i 0.515345 + 0.856983i \(0.327664\pi\)
−0.515345 + 0.856983i \(0.672336\pi\)
\(252\) 0 0
\(253\) 19.0849i 1.19986i
\(254\) 0.830064 0.525284i 0.0520828 0.0329592i
\(255\) 0 0
\(256\) −3.15904 + 15.6850i −0.197440 + 0.980315i
\(257\) 31.3823 1.95757 0.978786 0.204887i \(-0.0656827\pi\)
0.978786 + 0.204887i \(0.0656827\pi\)
\(258\) 0 0
\(259\) 1.42477i 0.0885310i
\(260\) −10.6252 + 22.4303i −0.658945 + 1.39107i
\(261\) 0 0
\(262\) 9.22986 + 14.5852i 0.570223 + 0.901077i
\(263\) 11.0275 0.679987 0.339993 0.940428i \(-0.389575\pi\)
0.339993 + 0.940428i \(0.389575\pi\)
\(264\) 0 0
\(265\) −11.4053 −0.700621
\(266\) 2.10245 + 3.32233i 0.128909 + 0.203705i
\(267\) 0 0
\(268\) 0.442562 + 0.209641i 0.0270338 + 0.0128058i
\(269\) 21.0019i 1.28051i 0.768162 + 0.640255i \(0.221171\pi\)
−0.768162 + 0.640255i \(0.778829\pi\)
\(270\) 0 0
\(271\) 28.6451 1.74007 0.870034 0.492991i \(-0.164097\pi\)
0.870034 + 0.492991i \(0.164097\pi\)
\(272\) −12.9922 15.8698i −0.787767 0.962246i
\(273\) 0 0
\(274\) −18.0502 + 11.4226i −1.09045 + 0.690063i
\(275\) 31.6771i 1.91020i
\(276\) 0 0
\(277\) 2.96504i 0.178152i −0.996025 0.0890761i \(-0.971609\pi\)
0.996025 0.0890761i \(-0.0283914\pi\)
\(278\) −5.75515 9.09440i −0.345171 0.545446i
\(279\) 0 0
\(280\) 11.5175 1.41004i 0.688301 0.0842660i
\(281\) −26.4098 −1.57548 −0.787738 0.616011i \(-0.788748\pi\)
−0.787738 + 0.616011i \(0.788748\pi\)
\(282\) 0 0
\(283\) 11.2698i 0.669922i −0.942232 0.334961i \(-0.891277\pi\)
0.942232 0.334961i \(-0.108723\pi\)
\(284\) 3.66269 7.73211i 0.217340 0.458816i
\(285\) 0 0
\(286\) −9.67961 + 6.12548i −0.572367 + 0.362207i
\(287\) −5.12742 −0.302662
\(288\) 0 0
\(289\) 9.29042 0.546495
\(290\) 43.2898 27.3948i 2.54206 1.60868i
\(291\) 0 0
\(292\) −3.55744 + 7.50993i −0.208183 + 0.439485i
\(293\) 10.5622i 0.617049i 0.951216 + 0.308524i \(0.0998351\pi\)
−0.951216 + 0.308524i \(0.900165\pi\)
\(294\) 0 0
\(295\) 16.4098 0.955415
\(296\) 4.00000 0.489704i 0.232495 0.0284635i
\(297\) 0 0
\(298\) −3.94750 6.23791i −0.228672 0.361353i
\(299\) 21.5602i 1.24686i
\(300\) 0 0
\(301\) 2.39980i 0.138322i
\(302\) 6.64465 4.20489i 0.382357 0.241964i
\(303\) 0 0
\(304\) −8.60469 + 7.04445i −0.493513 + 0.404027i
\(305\) 21.2503 1.21679
\(306\) 0 0
\(307\) 10.7801i 0.615254i 0.951507 + 0.307627i \(0.0995349\pi\)
−0.951507 + 0.307627i \(0.900465\pi\)
\(308\) 4.83980 + 2.29261i 0.275773 + 0.130633i
\(309\) 0 0
\(310\) −4.42028 6.98501i −0.251055 0.396722i
\(311\) −9.56024 −0.542111 −0.271056 0.962564i \(-0.587373\pi\)
−0.271056 + 0.962564i \(0.587373\pi\)
\(312\) 0 0
\(313\) 7.69909 0.435178 0.217589 0.976040i \(-0.430181\pi\)
0.217589 + 0.976040i \(0.430181\pi\)
\(314\) −0.392618 0.620423i −0.0221567 0.0350125i
\(315\) 0 0
\(316\) 5.35535 11.3054i 0.301262 0.635979i
\(317\) 10.7801i 0.605472i −0.953074 0.302736i \(-0.902100\pi\)
0.953074 0.302736i \(-0.0979000\pi\)
\(318\) 0 0
\(319\) 23.6440 1.32381
\(320\) 7.91728 + 31.8503i 0.442589 + 1.78049i
\(321\) 0 0
\(322\) 8.51748 5.39006i 0.474660 0.300376i
\(323\) 14.2548i 0.793160i
\(324\) 0 0
\(325\) 35.7856i 1.98503i
\(326\) 6.54501 + 10.3425i 0.362494 + 0.572821i
\(327\) 0 0
\(328\) −1.76233 14.3951i −0.0973084 0.794834i
\(329\) 9.56024 0.527073
\(330\) 0 0
\(331\) 25.2104i 1.38569i −0.721088 0.692844i \(-0.756357\pi\)
0.721088 0.692844i \(-0.243643\pi\)
\(332\) −16.9095 8.00998i −0.928028 0.439605i
\(333\) 0 0
\(334\) −30.0005 + 18.9850i −1.64155 + 1.03881i
\(335\) 1.00449 0.0548813
\(336\) 0 0
\(337\) −23.9700 −1.30573 −0.652865 0.757474i \(-0.726433\pi\)
−0.652865 + 0.757474i \(0.726433\pi\)
\(338\) −4.60032 + 2.91119i −0.250224 + 0.158348i
\(339\) 0 0
\(340\) −38.0200 18.0100i −2.06192 0.976729i
\(341\) 3.81508i 0.206598i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.73736 0.824828i 0.363254 0.0444718i
\(345\) 0 0
\(346\) 1.47278 + 2.32732i 0.0791772 + 0.125117i
\(347\) 6.98757i 0.375112i 0.982254 + 0.187556i \(0.0600567\pi\)
−0.982254 + 0.187556i \(0.939943\pi\)
\(348\) 0 0
\(349\) 20.8900i 1.11822i 0.829095 + 0.559108i \(0.188856\pi\)
−0.829095 + 0.559108i \(0.811144\pi\)
\(350\) 14.1373 8.94640i 0.755669 0.478205i
\(351\) 0 0
\(352\) −4.77294 + 14.3756i −0.254398 + 0.766220i
\(353\) −3.38225 −0.180019 −0.0900096 0.995941i \(-0.528690\pi\)
−0.0900096 + 0.995941i \(0.528690\pi\)
\(354\) 0 0
\(355\) 17.5497i 0.931444i
\(356\) −9.65988 + 20.3925i −0.511973 + 1.08080i
\(357\) 0 0
\(358\) −17.1649 27.1244i −0.907195 1.43357i
\(359\) −20.6877 −1.09185 −0.545926 0.837833i \(-0.683822\pi\)
−0.545926 + 0.837833i \(0.683822\pi\)
\(360\) 0 0
\(361\) 11.2709 0.593207
\(362\) 7.96722 + 12.5900i 0.418748 + 0.661714i
\(363\) 0 0
\(364\) −5.46753 2.58996i −0.286577 0.135751i
\(365\) 17.0455i 0.892200i
\(366\) 0 0
\(367\) −9.56024 −0.499040 −0.249520 0.968370i \(-0.580273\pi\)
−0.249520 + 0.968370i \(0.580273\pi\)
\(368\) 18.0599 + 22.0599i 0.941439 + 1.14995i
\(369\) 0 0
\(370\) 6.98501 4.42028i 0.363133 0.229799i
\(371\) 2.78012i 0.144337i
\(372\) 0 0
\(373\) 1.95006i 0.100970i −0.998725 0.0504850i \(-0.983923\pi\)
0.998725 0.0504850i \(-0.0160767\pi\)
\(374\) −10.3829 16.4072i −0.536886 0.848397i
\(375\) 0 0
\(376\) 3.28592 + 26.8400i 0.169459 + 1.38417i
\(377\) −26.7107 −1.37567
\(378\) 0 0
\(379\) 32.3698i 1.66273i −0.555730 0.831363i \(-0.687561\pi\)
0.555730 0.831363i \(-0.312439\pi\)
\(380\) −9.76513 + 20.6147i −0.500941 + 1.05751i
\(381\) 0 0
\(382\) −5.11219 + 3.23511i −0.261562 + 0.165523i
\(383\) 17.8451 0.911840 0.455920 0.890021i \(-0.349310\pi\)
0.455920 + 0.890021i \(0.349310\pi\)
\(384\) 0 0
\(385\) 10.9850 0.559848
\(386\) −27.6529 + 17.4994i −1.40750 + 0.890698i
\(387\) 0 0
\(388\) 5.73187 12.1003i 0.290991 0.614297i
\(389\) 6.11937i 0.310264i 0.987894 + 0.155132i \(0.0495803\pi\)
−0.987894 + 0.155132i \(0.950420\pi\)
\(390\) 0 0
\(391\) −36.5453 −1.84817
\(392\) 0.343707 + 2.80747i 0.0173598 + 0.141798i
\(393\) 0 0
\(394\) 14.7276 + 23.2729i 0.741967 + 1.17247i
\(395\) 25.6601i 1.29110i
\(396\) 0 0
\(397\) 3.71957i 0.186680i −0.995634 0.0933399i \(-0.970246\pi\)
0.995634 0.0933399i \(-0.0297543\pi\)
\(398\) 20.9850 13.2798i 1.05188 0.665657i
\(399\) 0 0
\(400\) 29.9758 + 36.6150i 1.49879 + 1.83075i
\(401\) 32.5258 1.62426 0.812130 0.583477i \(-0.198308\pi\)
0.812130 + 0.583477i \(0.198308\pi\)
\(402\) 0 0
\(403\) 4.30990i 0.214691i
\(404\) 2.63491 + 1.24815i 0.131092 + 0.0620979i
\(405\) 0 0
\(406\) 6.67767 + 10.5522i 0.331407 + 0.523696i
\(407\) 3.81508 0.189106
\(408\) 0 0
\(409\) −1.13436 −0.0560903 −0.0280452 0.999607i \(-0.508928\pi\)
−0.0280452 + 0.999607i \(0.508928\pi\)
\(410\) −15.9075 25.1374i −0.785617 1.24145i
\(411\) 0 0
\(412\) 6.96553 14.7046i 0.343167 0.724443i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) −38.3798 −1.88399
\(416\) 5.39199 16.2401i 0.264364 0.796237i
\(417\) 0 0
\(418\) −8.89611 + 5.62966i −0.435123 + 0.275356i
\(419\) 1.56024i 0.0762227i 0.999273 + 0.0381113i \(0.0121342\pi\)
−0.999273 + 0.0381113i \(0.987866\pi\)
\(420\) 0 0
\(421\) 31.8845i 1.55396i 0.629528 + 0.776978i \(0.283248\pi\)
−0.629528 + 0.776978i \(0.716752\pi\)
\(422\) −18.1196 28.6330i −0.882049 1.39383i
\(423\) 0 0
\(424\) 7.80509 0.955547i 0.379049 0.0464055i
\(425\) −60.6577 −2.94233
\(426\) 0 0
\(427\) 5.17992i 0.250674i
\(428\) 9.61992 + 4.55694i 0.464997 + 0.220268i
\(429\) 0 0
\(430\) 11.7651 7.44525i 0.567365 0.359042i
\(431\) −8.87258 −0.427377 −0.213689 0.976902i \(-0.568548\pi\)
−0.213689 + 0.976902i \(0.568548\pi\)
\(432\) 0 0
\(433\) 11.5602 0.555550 0.277775 0.960646i \(-0.410403\pi\)
0.277775 + 0.960646i \(0.410403\pi\)
\(434\) 1.70265 1.07747i 0.0817296 0.0517204i
\(435\) 0 0
\(436\) 24.5097 + 11.6102i 1.17380 + 0.556027i
\(437\) 19.8151i 0.947884i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 3.77563 + 30.8400i 0.179996 + 1.47024i
\(441\) 0 0
\(442\) 11.7296 + 18.5353i 0.557918 + 0.881633i
\(443\) 5.87807i 0.279276i 0.990203 + 0.139638i \(0.0445938\pi\)
−0.990203 + 0.139638i \(0.955406\pi\)
\(444\) 0 0
\(445\) 46.2853i 2.19413i
\(446\) −3.28592 + 2.07941i −0.155593 + 0.0984629i
\(447\) 0 0
\(448\) −7.76373 + 1.92989i −0.366802 + 0.0911788i
\(449\) 11.8451 0.559003 0.279501 0.960145i \(-0.409831\pi\)
0.279501 + 0.960145i \(0.409831\pi\)
\(450\) 0 0
\(451\) 13.7296i 0.646499i
\(452\) 3.55744 7.50993i 0.167328 0.353237i
\(453\) 0 0
\(454\) −6.28043 9.92446i −0.294755 0.465778i
\(455\) −12.4098 −0.581780
\(456\) 0 0
\(457\) −28.2088 −1.31955 −0.659775 0.751463i \(-0.729348\pi\)
−0.659775 + 0.751463i \(0.729348\pi\)
\(458\) 9.01779 + 14.2501i 0.421374 + 0.665863i
\(459\) 0 0
\(460\) 52.8500 + 25.0350i 2.46415 + 1.16726i
\(461\) 11.0519i 0.514737i −0.966313 0.257369i \(-0.917145\pi\)
0.966313 0.257369i \(-0.0828555\pi\)
\(462\) 0 0
\(463\) −22.2548 −1.03427 −0.517135 0.855904i \(-0.673001\pi\)
−0.517135 + 0.855904i \(0.673001\pi\)
\(464\) −27.3298 + 22.3742i −1.26875 + 1.03870i
\(465\) 0 0
\(466\) −4.25459 + 2.69241i −0.197090 + 0.124723i
\(467\) 21.4552i 0.992830i 0.868085 + 0.496415i \(0.165351\pi\)
−0.868085 + 0.496415i \(0.834649\pi\)
\(468\) 0 0
\(469\) 0.244852i 0.0113062i
\(470\) 29.6601 + 46.8695i 1.36812 + 2.16193i
\(471\) 0 0
\(472\) −11.2299 + 1.37483i −0.516896 + 0.0632816i
\(473\) 6.42588 0.295462
\(474\) 0 0
\(475\) 32.8890i 1.50905i
\(476\) 4.39006 9.26763i 0.201218 0.424781i
\(477\) 0 0
\(478\) 32.1971 20.3751i 1.47266 0.931934i
\(479\) −8.09989 −0.370093 −0.185047 0.982730i \(-0.559244\pi\)
−0.185047 + 0.982730i \(0.559244\pi\)
\(480\) 0 0
\(481\) −4.30990 −0.196514
\(482\) −30.8498 + 19.5225i −1.40517 + 0.889224i
\(483\) 0 0
\(484\) 3.27927 6.92271i 0.149058 0.314669i
\(485\) 27.4642i 1.24709i
\(486\) 0 0
\(487\) −16.4098 −0.743598 −0.371799 0.928313i \(-0.621259\pi\)
−0.371799 + 0.928313i \(0.621259\pi\)
\(488\) −14.5424 + 1.78038i −0.658306 + 0.0805938i
\(489\) 0 0
\(490\) 3.10245 + 4.90255i 0.140154 + 0.221474i
\(491\) 39.5971i 1.78699i −0.449070 0.893497i \(-0.648245\pi\)
0.449070 0.893497i \(-0.351755\pi\)
\(492\) 0 0
\(493\) 45.2754i 2.03910i
\(494\) 10.0499 6.35984i 0.452168 0.286143i
\(495\) 0 0
\(496\) 3.61018 + 4.40978i 0.162102 + 0.198005i
\(497\) 4.27787 0.191889
\(498\) 0 0
\(499\) 1.14946i 0.0514568i 0.999669 + 0.0257284i \(0.00819050\pi\)
−0.999669 + 0.0257284i \(0.991809\pi\)
\(500\) 50.6451 + 23.9905i 2.26492 + 1.07289i
\(501\) 0 0
\(502\) −20.5353 32.4502i −0.916534 1.44832i
\(503\) −9.00449 −0.401490 −0.200745 0.979643i \(-0.564336\pi\)
−0.200745 + 0.979643i \(0.564336\pi\)
\(504\) 0 0
\(505\) 5.98052 0.266130
\(506\) 14.4328 + 22.8070i 0.641617 + 1.01390i
\(507\) 0 0
\(508\) −0.594709 + 1.25546i −0.0263859 + 0.0557020i
\(509\) 36.5122i 1.61838i −0.587550 0.809188i \(-0.699907\pi\)
0.587550 0.809188i \(-0.300093\pi\)
\(510\) 0 0
\(511\) −4.15495 −0.183804
\(512\) −8.08656 21.1331i −0.357379 0.933960i
\(513\) 0 0
\(514\) −37.5027 + 23.7326i −1.65417 + 1.04680i
\(515\) 33.3753i 1.47069i
\(516\) 0 0
\(517\) 25.5992i 1.12585i
\(518\) 1.07747 + 1.70265i 0.0473415 + 0.0748100i
\(519\) 0 0
\(520\) −4.26533 34.8400i −0.187047 1.52784i
\(521\) 18.0929 0.792666 0.396333 0.918107i \(-0.370282\pi\)
0.396333 + 0.918107i \(0.370282\pi\)
\(522\) 0 0
\(523\) 14.7107i 0.643254i 0.946866 + 0.321627i \(0.104230\pi\)
−0.946866 + 0.321627i \(0.895770\pi\)
\(524\) −22.0599 10.4497i −0.963692 0.456499i
\(525\) 0 0
\(526\) −13.1782 + 8.33949i −0.574598 + 0.363619i
\(527\) −7.30540 −0.318228
\(528\) 0 0
\(529\) 27.8001 1.20870
\(530\) 13.6297 8.62517i 0.592035 0.374654i
\(531\) 0 0
\(532\) −5.02497 2.38032i −0.217860 0.103200i
\(533\) 15.5103i 0.671825i
\(534\) 0 0
\(535\) 21.8346 0.943990
\(536\) −0.687414 + 0.0841574i −0.0296918 + 0.00363505i
\(537\) 0 0
\(538\) −15.8826 25.0979i −0.684746 1.08205i
\(539\) 2.67767i 0.115336i
\(540\) 0 0
\(541\) 37.7157i 1.62152i −0.585376 0.810762i \(-0.699053\pi\)
0.585376 0.810762i \(-0.300947\pi\)
\(542\) −34.2318 + 21.6627i −1.47038 + 0.930492i
\(543\) 0 0
\(544\) 27.5275 + 9.13959i 1.18023 + 0.391857i
\(545\) 55.6302 2.38293
\(546\) 0 0
\(547\) 23.1144i 0.988299i 0.869377 + 0.494149i \(0.164520\pi\)
−0.869377 + 0.494149i \(0.835480\pi\)
\(548\) 12.9323 27.3007i 0.552439 1.16623i
\(549\) 0 0
\(550\) 23.9555 + 37.8550i 1.02147 + 1.61414i
\(551\) −24.5486 −1.04581
\(552\) 0 0
\(553\) 6.25484 0.265983
\(554\) 2.24229 + 3.54332i 0.0952659 + 0.150541i
\(555\) 0 0
\(556\) 13.7551 + 6.51579i 0.583348 + 0.276331i
\(557\) 11.1899i 0.474131i 0.971494 + 0.237066i \(0.0761857\pi\)
−0.971494 + 0.237066i \(0.923814\pi\)
\(558\) 0 0
\(559\) −7.25933 −0.307037
\(560\) −12.6974 + 10.3951i −0.536563 + 0.439271i
\(561\) 0 0
\(562\) 31.5605 19.9722i 1.33130 0.842477i
\(563\) 2.81058i 0.118452i −0.998245 0.0592260i \(-0.981137\pi\)
0.998245 0.0592260i \(-0.0188632\pi\)
\(564\) 0 0
\(565\) 17.0455i 0.717108i
\(566\) 8.52273 + 13.4678i 0.358237 + 0.566093i
\(567\) 0 0
\(568\) 1.47034 + 12.0100i 0.0616939 + 0.503928i
\(569\) 20.0699 0.841374 0.420687 0.907206i \(-0.361789\pi\)
0.420687 + 0.907206i \(0.361789\pi\)
\(570\) 0 0
\(571\) 2.46584i 0.103192i 0.998668 + 0.0515961i \(0.0164309\pi\)
−0.998668 + 0.0515961i \(0.983569\pi\)
\(572\) 6.93507 14.6403i 0.289970 0.612141i
\(573\) 0 0
\(574\) 6.12742 3.87757i 0.255753 0.161847i
\(575\) 84.3178 3.51630
\(576\) 0 0
\(577\) 4.84954 0.201889 0.100945 0.994892i \(-0.467814\pi\)
0.100945 + 0.994892i \(0.467814\pi\)
\(578\) −11.1023 + 7.02581i −0.461796 + 0.292235i
\(579\) 0 0
\(580\) −31.0155 + 65.4752i −1.28785 + 2.71871i
\(581\) 9.35535i 0.388125i
\(582\) 0 0
\(583\) 7.44425 0.308309
\(584\) −1.42809 11.6649i −0.0590946 0.482696i
\(585\) 0 0
\(586\) −7.98757 12.6221i −0.329963 0.521415i
\(587\) 19.0155i 0.784853i 0.919783 + 0.392426i \(0.128364\pi\)
−0.919783 + 0.392426i \(0.871636\pi\)
\(588\) 0 0
\(589\) 3.96104i 0.163212i
\(590\) −19.6102 + 12.4098i −0.807338 + 0.510903i
\(591\) 0 0
\(592\) −4.40978 + 3.61018i −0.181241 + 0.148378i
\(593\) −24.0379 −0.987118 −0.493559 0.869712i \(-0.664304\pi\)
−0.493559 + 0.869712i \(0.664304\pi\)
\(594\) 0 0
\(595\) 21.0350i 0.862349i
\(596\) 9.43476 + 4.46923i 0.386463 + 0.183067i
\(597\) 0 0
\(598\) −16.3048 25.7651i −0.666752 1.05361i
\(599\) −33.9631 −1.38769 −0.693847 0.720122i \(-0.744086\pi\)
−0.693847 + 0.720122i \(0.744086\pi\)
\(600\) 0 0
\(601\) 10.0999 0.411983 0.205992 0.978554i \(-0.433958\pi\)
0.205992 + 0.978554i \(0.433958\pi\)
\(602\) 1.81483 + 2.86783i 0.0739670 + 0.116884i
\(603\) 0 0
\(604\) −4.76064 + 10.0499i −0.193708 + 0.408926i
\(605\) 15.7126i 0.638809i
\(606\) 0 0
\(607\) 8.17105 0.331653 0.165826 0.986155i \(-0.446971\pi\)
0.165826 + 0.986155i \(0.446971\pi\)
\(608\) 4.95555 14.9256i 0.200974 0.605312i
\(609\) 0 0
\(610\) −25.3948 + 16.0704i −1.02821 + 0.650672i
\(611\) 28.9195i 1.16996i
\(612\) 0 0
\(613\) 23.0206i 0.929793i −0.885365 0.464896i \(-0.846092\pi\)
0.885365 0.464896i \(-0.153908\pi\)
\(614\) −8.15239 12.8826i −0.329004 0.519898i
\(615\) 0 0
\(616\) −7.51748 + 0.920336i −0.302888 + 0.0370814i
\(617\) −31.1044 −1.25222 −0.626108 0.779737i \(-0.715353\pi\)
−0.626108 + 0.779737i \(0.715353\pi\)
\(618\) 0 0
\(619\) 40.9195i 1.64469i −0.568988 0.822346i \(-0.692665\pi\)
0.568988 0.822346i \(-0.307335\pi\)
\(620\) 10.5647 + 5.00449i 0.424290 + 0.200985i
\(621\) 0 0
\(622\) 11.4248 7.22986i 0.458092 0.289891i
\(623\) −11.2824 −0.452018
\(624\) 0 0
\(625\) 55.8001 2.23200
\(626\) −9.20064 + 5.82238i −0.367732 + 0.232709i
\(627\) 0 0
\(628\) 0.938381 + 0.444509i 0.0374455 + 0.0177378i
\(629\) 7.30540i 0.291286i
\(630\) 0 0
\(631\) −2.29380 −0.0913147 −0.0456573 0.998957i \(-0.514538\pi\)
−0.0456573 + 0.998957i \(0.514538\pi\)
\(632\) 2.14983 + 17.5602i 0.0855157 + 0.698509i
\(633\) 0 0
\(634\) 8.15239 + 12.8826i 0.323773 + 0.511632i
\(635\) 2.84954i 0.113081i
\(636\) 0 0
\(637\) 3.02497i 0.119854i
\(638\) −28.2553 + 17.8806i −1.11864 + 0.707901i
\(639\) 0 0
\(640\) −33.5479 32.0747i −1.32610 1.26786i
\(641\) −27.0654 −1.06902 −0.534510 0.845162i \(-0.679504\pi\)
−0.534510 + 0.845162i \(0.679504\pi\)
\(642\) 0 0
\(643\) 31.9895i 1.26154i −0.775969 0.630771i \(-0.782739\pi\)
0.775969 0.630771i \(-0.217261\pi\)
\(644\) −6.10245 + 12.8826i −0.240470 + 0.507644i
\(645\) 0 0
\(646\) 10.7801 + 17.0350i 0.424138 + 0.670231i
\(647\) 12.5947 0.495149 0.247575 0.968869i \(-0.420366\pi\)
0.247575 + 0.968869i \(0.420366\pi\)
\(648\) 0 0
\(649\) −10.7107 −0.420432
\(650\) −27.0626 42.7649i −1.06148 1.67738i
\(651\) 0 0
\(652\) −15.6430 7.41004i −0.612626 0.290200i
\(653\) 21.8346i 0.854452i −0.904145 0.427226i \(-0.859491\pi\)
0.904145 0.427226i \(-0.140509\pi\)
\(654\) 0 0
\(655\) −50.0699 −1.95639
\(656\) 12.9922 + 15.8698i 0.507260 + 0.619610i
\(657\) 0 0
\(658\) −11.4248 + 7.22986i −0.445384 + 0.281849i
\(659\) 24.7865i 0.965547i 0.875745 + 0.482773i \(0.160371\pi\)
−0.875745 + 0.482773i \(0.839629\pi\)
\(660\) 0 0
\(661\) 3.09101i 0.120227i 0.998192 + 0.0601133i \(0.0191462\pi\)
−0.998192 + 0.0601133i \(0.980854\pi\)
\(662\) 19.0652 + 30.1272i 0.740989 + 1.17093i
\(663\) 0 0
\(664\) 26.2648 3.21550i 1.01927 0.124786i
\(665\) −11.4053 −0.442278
\(666\) 0 0
\(667\) 62.9356i 2.43687i
\(668\) 21.4942 45.3753i 0.831635 1.75562i
\(669\) 0 0
\(670\) −1.20040 + 0.759641i −0.0463755 + 0.0293475i
\(671\) −13.8701 −0.535451
\(672\) 0 0
\(673\) −27.6496 −1.06581 −0.532907 0.846174i \(-0.678901\pi\)
−0.532907 + 0.846174i \(0.678901\pi\)
\(674\) 28.6449 18.1272i 1.10336 0.698232i
\(675\) 0 0
\(676\) 3.29595 6.95792i 0.126767 0.267612i
\(677\) 5.84249i 0.224545i −0.993677 0.112273i \(-0.964187\pi\)
0.993677 0.112273i \(-0.0358130\pi\)
\(678\) 0 0
\(679\) 6.69460 0.256915
\(680\) 59.0549 7.22986i 2.26465 0.277253i
\(681\) 0 0
\(682\) 2.88512 + 4.55913i 0.110477 + 0.174578i
\(683\) 15.5433i 0.594748i −0.954761 0.297374i \(-0.903889\pi\)
0.954761 0.297374i \(-0.0961109\pi\)
\(684\) 0 0
\(685\) 61.9649i 2.36756i
\(686\) −1.19503 + 0.756243i −0.0456265 + 0.0288735i
\(687\) 0 0
\(688\) −7.42757 + 6.08077i −0.283174 + 0.231827i
\(689\) −8.40978 −0.320387
\(690\) 0 0
\(691\) 42.9304i 1.63315i 0.577239 + 0.816575i \(0.304130\pi\)
−0.577239 + 0.816575i \(0.695870\pi\)
\(692\) −3.52004 1.66743i −0.133812 0.0633863i
\(693\) 0 0
\(694\) −5.28430 8.35036i −0.200589 0.316975i
\(695\) 31.2204 1.18426
\(696\) 0 0
\(697\) −26.2904 −0.995820
\(698\) −15.7979 24.9642i −0.597960 0.944908i
\(699\) 0 0
\(700\) −10.1288 + 21.3824i −0.382833 + 0.808180i
\(701\) 5.21476i 0.196959i −0.995139 0.0984795i \(-0.968602\pi\)
0.995139 0.0984795i \(-0.0313979\pi\)
\(702\) 0 0
\(703\) −3.96104 −0.149393
\(704\) −5.16762 20.7887i −0.194762 0.783505i
\(705\) 0 0
\(706\) 4.04189 2.55781i 0.152119 0.0962643i
\(707\) 1.45779i 0.0548260i
\(708\) 0 0
\(709\) 41.6601i 1.56458i 0.622915 + 0.782289i \(0.285948\pi\)
−0.622915 + 0.782289i \(0.714052\pi\)
\(710\) 13.2719 + 20.9725i 0.498084 + 0.787083i
\(711\) 0 0
\(712\) −3.87783 31.6749i −0.145328 1.18707i
\(713\) 10.1549 0.380306
\(714\) 0 0
\(715\) 33.2294i 1.24271i
\(716\) 41.0252 + 19.4336i 1.53318 + 0.726266i
\(717\) 0 0
\(718\) 24.7224 15.6449i 0.922631 0.583862i
\(719\) −14.3547 −0.535341 −0.267670 0.963511i \(-0.586254\pi\)
−0.267670 + 0.963511i \(0.586254\pi\)
\(720\) 0 0
\(721\) 8.13547 0.302981
\(722\) −13.4691 + 8.52356i −0.501268 + 0.317214i
\(723\) 0 0
\(724\) −19.0421 9.02022i −0.707695 0.335234i
\(725\) 104.460i 3.87955i
\(726\) 0 0
\(727\) 53.4647 1.98290 0.991448 0.130501i \(-0.0416587\pi\)
0.991448 + 0.130501i \(0.0416587\pi\)
\(728\) 8.49251 1.03970i 0.314753 0.0385340i
\(729\) 0 0
\(730\) −12.8905 20.3698i −0.477099 0.753921i
\(731\) 12.3048i 0.455109i
\(732\) 0 0
\(733\) 49.1149i 1.81410i −0.421025 0.907049i \(-0.638329\pi\)
0.421025 0.907049i \(-0.361671\pi\)
\(734\) 11.4248 7.22986i 0.421696 0.266859i
\(735\) 0 0
\(736\) −38.2648 12.7046i −1.41046 0.468297i
\(737\) −0.655634 −0.0241506
\(738\) 0 0
\(739\) 7.75515i 0.285278i 0.989775 + 0.142639i \(0.0455587\pi\)
−0.989775 + 0.142639i \(0.954441\pi\)
\(740\) −5.00449 + 10.5647i −0.183969 + 0.388367i
\(741\) 0 0
\(742\) 2.10245 + 3.32233i 0.0771832 + 0.121966i
\(743\) −30.9886 −1.13686 −0.568430 0.822732i \(-0.692449\pi\)
−0.568430 + 0.822732i \(0.692449\pi\)
\(744\) 0 0
\(745\) 21.4143 0.784558
\(746\) 1.47472 + 2.33038i 0.0539932 + 0.0853211i
\(747\) 0 0
\(748\) 24.8157 + 11.7551i 0.907352 + 0.429811i
\(749\) 5.32233i 0.194474i
\(750\) 0 0
\(751\) −34.9105 −1.27390 −0.636951 0.770905i \(-0.719804\pi\)
−0.636951 + 0.770905i \(0.719804\pi\)
\(752\) −24.2244 29.5897i −0.883372 1.07903i
\(753\) 0 0
\(754\) 31.9201 20.1998i 1.16246 0.735632i
\(755\) 22.8106i 0.830162i
\(756\) 0 0
\(757\) 9.25034i 0.336209i −0.985769 0.168105i \(-0.946235\pi\)
0.985769 0.168105i \(-0.0537647\pi\)
\(758\) 24.4795 + 38.6829i 0.889134 + 1.40503i
\(759\) 0 0
\(760\) −3.92008 32.0200i −0.142196 1.16149i
\(761\) 11.8381 0.429131 0.214566 0.976710i \(-0.431166\pi\)
0.214566 + 0.976710i \(0.431166\pi\)
\(762\) 0 0
\(763\) 13.5602i 0.490914i
\(764\) 3.66269 7.73211i 0.132511 0.279738i
\(765\) 0 0
\(766\) −21.3254 + 13.4952i −0.770517 + 0.487601i
\(767\) 12.0999 0.436902
\(768\) 0 0
\(769\) −20.0699 −0.723740 −0.361870 0.932229i \(-0.617861\pi\)
−0.361870 + 0.932229i \(0.617861\pi\)
\(770\) −13.1274 + 8.30734i −0.473079 + 0.299376i
\(771\) 0 0
\(772\) 19.8123 41.8247i 0.713059 1.50530i
\(773\) 18.8521i 0.678063i −0.940775 0.339032i \(-0.889901\pi\)
0.940775 0.339032i \(-0.110099\pi\)
\(774\) 0 0
\(775\) 16.8551 0.605455
\(776\) 2.30098 + 18.7949i 0.0826004 + 0.674696i
\(777\) 0 0
\(778\) −4.62773 7.31283i −0.165912 0.262178i
\(779\) 14.2548i 0.510733i
\(780\) 0 0
\(781\) 11.4547i 0.409883i
\(782\) 43.6727 27.6371i 1.56173 0.988300i
\(783\) 0 0
\(784\) −2.53387 3.09508i −0.0904952 0.110539i
\(785\) 2.12986 0.0760181
\(786\) 0 0
\(787\) 25.9111i 0.923631i −0.886976 0.461815i \(-0.847198\pi\)
0.886976 0.461815i \(-0.152802\pi\)
\(788\) −35.1999 16.6741i −1.25394 0.593991i
\(789\) 0 0
\(790\) 19.4053 + 30.6646i 0.690409 + 1.09100i
\(791\) 4.15495 0.147733
\(792\) 0 0
\(793\) 15.6691 0.556427
\(794\) 2.81290 + 4.44500i 0.0998260