Properties

Label 900.3.f.e.199.3
Level $900$
Weight $3$
Character 900.199
Analytic conductor $24.523$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.3
Root \(0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 900.199
Dual form 900.3.f.e.199.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17557 - 1.61803i) q^{2} +(-1.23607 + 3.80423i) q^{4} -8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} +O(q^{10})\) \(q+(-1.17557 - 1.61803i) q^{2} +(-1.23607 + 3.80423i) q^{4} -8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} -1.79611i q^{11} +0.472136i q^{13} +(10.0000 + 13.7638i) q^{14} +(-12.9443 - 9.40456i) q^{16} -23.8885i q^{17} +9.40456i q^{19} +(-2.90617 + 2.11146i) q^{22} -16.1150 q^{23} +(0.763932 - 0.555029i) q^{26} +(10.5146 - 32.3607i) q^{28} +6.94427 q^{29} +47.4468i q^{31} +32.0000i q^{32} +(-38.6525 + 28.0827i) q^{34} -26.3607i q^{37} +(15.2169 - 11.0557i) q^{38} +41.4164 q^{41} +2.00811 q^{43} +(6.83282 + 2.22012i) q^{44} +(18.9443 + 26.0746i) q^{46} +35.3481 q^{47} +23.3607 q^{49} +(-1.79611 - 0.583592i) q^{52} +21.6393i q^{53} +(-64.7214 + 21.0292i) q^{56} +(-8.16348 - 11.2361i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(76.7706 - 55.7771i) q^{62} +(51.7771 - 37.6183i) q^{64} +88.8693 q^{67} +(90.8774 + 29.5279i) q^{68} +39.4144i q^{71} +137.554i q^{73} +(-42.6525 + 30.9888i) q^{74} +(-35.7771 - 11.6247i) q^{76} +15.2786i q^{77} +113.703i q^{79} +(-48.6879 - 67.0132i) q^{82} +21.2412 q^{83} +(-2.36068 - 3.24920i) q^{86} +(-4.44023 - 13.6656i) q^{88} +67.4427 q^{89} -4.01623i q^{91} +(19.9192 - 61.3050i) q^{92} +(-41.5542 - 57.1944i) q^{94} +39.1672i q^{97} +(-27.4621 - 37.7984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{4} + O(q^{10}) \) \( 8q + 8q^{4} + 80q^{14} - 32q^{16} + 24q^{26} - 16q^{29} - 184q^{34} + 224q^{41} - 160q^{44} + 80q^{46} + 8q^{49} - 160q^{56} + 256q^{61} + 128q^{64} - 216q^{74} + 160q^{86} - 176q^{89} + 240q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17557 1.61803i −0.587785 0.809017i
\(3\) 0 0
\(4\) −1.23607 + 3.80423i −0.309017 + 0.951057i
\(5\) 0 0
\(6\) 0 0
\(7\) −8.50651 −1.21522 −0.607608 0.794237i \(-0.707871\pi\)
−0.607608 + 0.794237i \(0.707871\pi\)
\(8\) 7.60845 2.47214i 0.951057 0.309017i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.79611i 0.163283i −0.996662 0.0816415i \(-0.973984\pi\)
0.996662 0.0816415i \(-0.0260162\pi\)
\(12\) 0 0
\(13\) 0.472136i 0.0363182i 0.999835 + 0.0181591i \(0.00578053\pi\)
−0.999835 + 0.0181591i \(0.994219\pi\)
\(14\) 10.0000 + 13.7638i 0.714286 + 0.983130i
\(15\) 0 0
\(16\) −12.9443 9.40456i −0.809017 0.587785i
\(17\) 23.8885i 1.40521i −0.711581 0.702604i \(-0.752020\pi\)
0.711581 0.702604i \(-0.247980\pi\)
\(18\) 0 0
\(19\) 9.40456i 0.494977i 0.968891 + 0.247489i \(0.0796053\pi\)
−0.968891 + 0.247489i \(0.920395\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.90617 + 2.11146i −0.132099 + 0.0959753i
\(23\) −16.1150 −0.700650 −0.350325 0.936628i \(-0.613929\pi\)
−0.350325 + 0.936628i \(0.613929\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.763932 0.555029i 0.0293820 0.0213473i
\(27\) 0 0
\(28\) 10.5146 32.3607i 0.375522 1.15574i
\(29\) 6.94427 0.239458 0.119729 0.992807i \(-0.461797\pi\)
0.119729 + 0.992807i \(0.461797\pi\)
\(30\) 0 0
\(31\) 47.4468i 1.53054i 0.643708 + 0.765271i \(0.277395\pi\)
−0.643708 + 0.765271i \(0.722605\pi\)
\(32\) 32.0000i 1.00000i
\(33\) 0 0
\(34\) −38.6525 + 28.0827i −1.13684 + 0.825961i
\(35\) 0 0
\(36\) 0 0
\(37\) 26.3607i 0.712451i −0.934400 0.356225i \(-0.884064\pi\)
0.934400 0.356225i \(-0.115936\pi\)
\(38\) 15.2169 11.0557i 0.400445 0.290940i
\(39\) 0 0
\(40\) 0 0
\(41\) 41.4164 1.01016 0.505078 0.863074i \(-0.331464\pi\)
0.505078 + 0.863074i \(0.331464\pi\)
\(42\) 0 0
\(43\) 2.00811 0.0467003 0.0233502 0.999727i \(-0.492567\pi\)
0.0233502 + 0.999727i \(0.492567\pi\)
\(44\) 6.83282 + 2.22012i 0.155291 + 0.0504572i
\(45\) 0 0
\(46\) 18.9443 + 26.0746i 0.411832 + 0.566838i
\(47\) 35.3481 0.752087 0.376044 0.926602i \(-0.377284\pi\)
0.376044 + 0.926602i \(0.377284\pi\)
\(48\) 0 0
\(49\) 23.3607 0.476749
\(50\) 0 0
\(51\) 0 0
\(52\) −1.79611 0.583592i −0.0345406 0.0112229i
\(53\) 21.6393i 0.408289i 0.978941 + 0.204145i \(0.0654413\pi\)
−0.978941 + 0.204145i \(0.934559\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −64.7214 + 21.0292i −1.15574 + 0.375522i
\(57\) 0 0
\(58\) −8.16348 11.2361i −0.140750 0.193725i
\(59\) 73.8644i 1.25194i 0.779848 + 0.625970i \(0.215297\pi\)
−0.779848 + 0.625970i \(0.784703\pi\)
\(60\) 0 0
\(61\) −26.1378 −0.428488 −0.214244 0.976780i \(-0.568729\pi\)
−0.214244 + 0.976780i \(0.568729\pi\)
\(62\) 76.7706 55.7771i 1.23824 0.899630i
\(63\) 0 0
\(64\) 51.7771 37.6183i 0.809017 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) 88.8693 1.32641 0.663204 0.748439i \(-0.269196\pi\)
0.663204 + 0.748439i \(0.269196\pi\)
\(68\) 90.8774 + 29.5279i 1.33643 + 0.434233i
\(69\) 0 0
\(70\) 0 0
\(71\) 39.4144i 0.555132i 0.960707 + 0.277566i \(0.0895277\pi\)
−0.960707 + 0.277566i \(0.910472\pi\)
\(72\) 0 0
\(73\) 137.554i 1.88430i 0.335186 + 0.942152i \(0.391201\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(74\) −42.6525 + 30.9888i −0.576385 + 0.418768i
\(75\) 0 0
\(76\) −35.7771 11.6247i −0.470751 0.152956i
\(77\) 15.2786i 0.198424i
\(78\) 0 0
\(79\) 113.703i 1.43928i 0.694350 + 0.719638i \(0.255692\pi\)
−0.694350 + 0.719638i \(0.744308\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −48.6879 67.0132i −0.593755 0.817234i
\(83\) 21.2412 0.255919 0.127959 0.991779i \(-0.459157\pi\)
0.127959 + 0.991779i \(0.459157\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.36068 3.24920i −0.0274498 0.0377814i
\(87\) 0 0
\(88\) −4.44023 13.6656i −0.0504572 0.155291i
\(89\) 67.4427 0.757783 0.378892 0.925441i \(-0.376305\pi\)
0.378892 + 0.925441i \(0.376305\pi\)
\(90\) 0 0
\(91\) 4.01623i 0.0441344i
\(92\) 19.9192 61.3050i 0.216513 0.666358i
\(93\) 0 0
\(94\) −41.5542 57.1944i −0.442066 0.608451i
\(95\) 0 0
\(96\) 0 0
\(97\) 39.1672i 0.403785i 0.979408 + 0.201893i \(0.0647092\pi\)
−0.979408 + 0.201893i \(0.935291\pi\)
\(98\) −27.4621 37.7984i −0.280226 0.385698i
\(99\) 0 0
\(100\) 0 0
\(101\) −99.8885 −0.988995 −0.494498 0.869179i \(-0.664648\pi\)
−0.494498 + 0.869179i \(0.664648\pi\)
\(102\) 0 0
\(103\) 35.7721 0.347302 0.173651 0.984807i \(-0.444444\pi\)
0.173651 + 0.984807i \(0.444444\pi\)
\(104\) 1.16718 + 3.59222i 0.0112229 + 0.0345406i
\(105\) 0 0
\(106\) 35.0132 25.4385i 0.330313 0.239986i
\(107\) 121.099 1.13177 0.565884 0.824485i \(-0.308535\pi\)
0.565884 + 0.824485i \(0.308535\pi\)
\(108\) 0 0
\(109\) 197.469 1.81164 0.905821 0.423660i \(-0.139255\pi\)
0.905821 + 0.423660i \(0.139255\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 110.111 + 80.0000i 0.983130 + 0.714286i
\(113\) 81.2786i 0.719280i −0.933091 0.359640i \(-0.882900\pi\)
0.933091 0.359640i \(-0.117100\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −8.58359 + 26.4176i −0.0739965 + 0.227738i
\(117\) 0 0
\(118\) 119.515 86.8328i 1.01284 0.735871i
\(119\) 203.208i 1.70763i
\(120\) 0 0
\(121\) 117.774 0.973339
\(122\) 30.7268 + 42.2918i 0.251859 + 0.346654i
\(123\) 0 0
\(124\) −180.498 58.6475i −1.45563 0.472964i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.84616 −0.0145367 −0.00726834 0.999974i \(-0.502314\pi\)
−0.00726834 + 0.999974i \(0.502314\pi\)
\(128\) −121.735 39.5542i −0.951057 0.309017i
\(129\) 0 0
\(130\) 0 0
\(131\) 225.609i 1.72221i −0.508428 0.861105i \(-0.669773\pi\)
0.508428 0.861105i \(-0.330227\pi\)
\(132\) 0 0
\(133\) 80.0000i 0.601504i
\(134\) −104.472 143.794i −0.779643 1.07309i
\(135\) 0 0
\(136\) −59.0557 181.755i −0.434233 1.33643i
\(137\) 52.8328i 0.385641i −0.981234 0.192820i \(-0.938236\pi\)
0.981234 0.192820i \(-0.0617635\pi\)
\(138\) 0 0
\(139\) 125.852i 0.905407i 0.891661 + 0.452703i \(0.149540\pi\)
−0.891661 + 0.452703i \(0.850460\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 63.7738 46.3344i 0.449111 0.326298i
\(143\) 0.848009 0.00593013
\(144\) 0 0
\(145\) 0 0
\(146\) 222.567 161.705i 1.52443 1.10757i
\(147\) 0 0
\(148\) 100.282 + 32.5836i 0.677581 + 0.220159i
\(149\) 132.971 0.892420 0.446210 0.894928i \(-0.352773\pi\)
0.446210 + 0.894928i \(0.352773\pi\)
\(150\) 0 0
\(151\) 151.221i 1.00146i −0.865603 0.500732i \(-0.833064\pi\)
0.865603 0.500732i \(-0.166936\pi\)
\(152\) 23.2494 + 71.5542i 0.152956 + 0.470751i
\(153\) 0 0
\(154\) 24.7214 17.9611i 0.160528 0.116631i
\(155\) 0 0
\(156\) 0 0
\(157\) 36.7477i 0.234062i 0.993128 + 0.117031i \(0.0373376\pi\)
−0.993128 + 0.117031i \(0.962662\pi\)
\(158\) 183.975 133.666i 1.16440 0.845985i
\(159\) 0 0
\(160\) 0 0
\(161\) 137.082 0.851441
\(162\) 0 0
\(163\) −302.854 −1.85800 −0.929000 0.370079i \(-0.879331\pi\)
−0.929000 + 0.370079i \(0.879331\pi\)
\(164\) −51.1935 + 157.557i −0.312155 + 0.960716i
\(165\) 0 0
\(166\) −24.9706 34.3691i −0.150425 0.207043i
\(167\) −99.3839 −0.595113 −0.297557 0.954704i \(-0.596172\pi\)
−0.297557 + 0.954704i \(0.596172\pi\)
\(168\) 0 0
\(169\) 168.777 0.998681
\(170\) 0 0
\(171\) 0 0
\(172\) −2.48217 + 7.63932i −0.0144312 + 0.0444147i
\(173\) 181.639i 1.04994i 0.851121 + 0.524969i \(0.175923\pi\)
−0.851121 + 0.524969i \(0.824077\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −16.8916 + 23.2494i −0.0959753 + 0.132099i
\(177\) 0 0
\(178\) −79.2837 109.125i −0.445414 0.613060i
\(179\) 260.907i 1.45758i −0.684735 0.728792i \(-0.740082\pi\)
0.684735 0.728792i \(-0.259918\pi\)
\(180\) 0 0
\(181\) 157.777 0.871697 0.435848 0.900020i \(-0.356448\pi\)
0.435848 + 0.900020i \(0.356448\pi\)
\(182\) −6.49839 + 4.72136i −0.0357055 + 0.0259415i
\(183\) 0 0
\(184\) −122.610 + 39.8384i −0.666358 + 0.216513i
\(185\) 0 0
\(186\) 0 0
\(187\) −42.9065 −0.229447
\(188\) −43.6926 + 134.472i −0.232408 + 0.715277i
\(189\) 0 0
\(190\) 0 0
\(191\) 324.095i 1.69683i 0.529328 + 0.848417i \(0.322444\pi\)
−0.529328 + 0.848417i \(0.677556\pi\)
\(192\) 0 0
\(193\) 181.777i 0.941850i 0.882173 + 0.470925i \(0.156080\pi\)
−0.882173 + 0.470925i \(0.843920\pi\)
\(194\) 63.3738 46.0438i 0.326669 0.237339i
\(195\) 0 0
\(196\) −28.8754 + 88.8693i −0.147323 + 0.453415i
\(197\) 140.525i 0.713324i 0.934234 + 0.356662i \(0.116085\pi\)
−0.934234 + 0.356662i \(0.883915\pi\)
\(198\) 0 0
\(199\) 168.234i 0.845397i −0.906270 0.422698i \(-0.861083\pi\)
0.906270 0.422698i \(-0.138917\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 117.426 + 161.623i 0.581317 + 0.800114i
\(203\) −59.0715 −0.290993
\(204\) 0 0
\(205\) 0 0
\(206\) −42.0526 57.8805i −0.204139 0.280973i
\(207\) 0 0
\(208\) 4.44023 6.11146i 0.0213473 0.0293820i
\(209\) 16.8916 0.0808213
\(210\) 0 0
\(211\) 93.9455i 0.445240i 0.974905 + 0.222620i \(0.0714608\pi\)
−0.974905 + 0.222620i \(0.928539\pi\)
\(212\) −82.3209 26.7477i −0.388306 0.126168i
\(213\) 0 0
\(214\) −142.361 195.943i −0.665237 0.915620i
\(215\) 0 0
\(216\) 0 0
\(217\) 403.607i 1.85994i
\(218\) −232.139 319.512i −1.06486 1.46565i
\(219\) 0 0
\(220\) 0 0
\(221\) 11.2786 0.0510346
\(222\) 0 0
\(223\) −214.035 −0.959797 −0.479899 0.877324i \(-0.659327\pi\)
−0.479899 + 0.877324i \(0.659327\pi\)
\(224\) 272.208i 1.21522i
\(225\) 0 0
\(226\) −131.512 + 95.5488i −0.581910 + 0.422782i
\(227\) 41.4225 0.182478 0.0912389 0.995829i \(-0.470917\pi\)
0.0912389 + 0.995829i \(0.470917\pi\)
\(228\) 0 0
\(229\) −73.2786 −0.319994 −0.159997 0.987117i \(-0.551148\pi\)
−0.159997 + 0.987117i \(0.551148\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 52.8352 17.1672i 0.227738 0.0739965i
\(233\) 307.050i 1.31781i 0.752227 + 0.658905i \(0.228980\pi\)
−0.752227 + 0.658905i \(0.771020\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −280.997 91.3014i −1.19066 0.386870i
\(237\) 0 0
\(238\) 328.798 238.885i 1.38150 1.00372i
\(239\) 42.9065i 0.179525i −0.995963 0.0897625i \(-0.971389\pi\)
0.995963 0.0897625i \(-0.0286108\pi\)
\(240\) 0 0
\(241\) −135.082 −0.560506 −0.280253 0.959926i \(-0.590418\pi\)
−0.280253 + 0.959926i \(0.590418\pi\)
\(242\) −138.452 190.562i −0.572114 0.787448i
\(243\) 0 0
\(244\) 32.3081 99.4340i 0.132410 0.407516i
\(245\) 0 0
\(246\) 0 0
\(247\) −4.44023 −0.0179767
\(248\) 117.295 + 360.997i 0.472964 + 1.45563i
\(249\) 0 0
\(250\) 0 0
\(251\) 221.169i 0.881152i 0.897715 + 0.440576i \(0.145226\pi\)
−0.897715 + 0.440576i \(0.854774\pi\)
\(252\) 0 0
\(253\) 28.9443i 0.114404i
\(254\) 2.17029 + 2.98715i 0.00854445 + 0.0117604i
\(255\) 0 0
\(256\) 79.1084 + 243.470i 0.309017 + 0.951057i
\(257\) 257.056i 1.00022i −0.865963 0.500108i \(-0.833293\pi\)
0.865963 0.500108i \(-0.166707\pi\)
\(258\) 0 0
\(259\) 224.237i 0.865781i
\(260\) 0 0
\(261\) 0 0
\(262\) −365.044 + 265.220i −1.39330 + 1.01229i
\(263\) −164.168 −0.624212 −0.312106 0.950047i \(-0.601034\pi\)
−0.312106 + 0.950047i \(0.601034\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −129.443 + 94.0456i −0.486627 + 0.353555i
\(267\) 0 0
\(268\) −109.849 + 338.079i −0.409882 + 1.26149i
\(269\) −35.4752 −0.131878 −0.0659391 0.997824i \(-0.521004\pi\)
−0.0659391 + 0.997824i \(0.521004\pi\)
\(270\) 0 0
\(271\) 298.950i 1.10314i 0.834130 + 0.551568i \(0.185970\pi\)
−0.834130 + 0.551568i \(0.814030\pi\)
\(272\) −224.661 + 309.220i −0.825961 + 1.13684i
\(273\) 0 0
\(274\) −85.4853 + 62.1087i −0.311990 + 0.226674i
\(275\) 0 0
\(276\) 0 0
\(277\) 457.246i 1.65071i 0.564616 + 0.825354i \(0.309024\pi\)
−0.564616 + 0.825354i \(0.690976\pi\)
\(278\) 203.632 147.947i 0.732490 0.532185i
\(279\) 0 0
\(280\) 0 0
\(281\) 5.63932 0.0200688 0.0100344 0.999950i \(-0.496806\pi\)
0.0100344 + 0.999950i \(0.496806\pi\)
\(282\) 0 0
\(283\) 169.918 0.600418 0.300209 0.953874i \(-0.402944\pi\)
0.300209 + 0.953874i \(0.402944\pi\)
\(284\) −149.941 48.7188i −0.527962 0.171545i
\(285\) 0 0
\(286\) −0.996894 1.37211i −0.00348564 0.00479758i
\(287\) −352.309 −1.22756
\(288\) 0 0
\(289\) −281.663 −0.974611
\(290\) 0 0
\(291\) 0 0
\(292\) −523.287 170.026i −1.79208 0.582282i
\(293\) 26.8591i 0.0916694i 0.998949 + 0.0458347i \(0.0145947\pi\)
−0.998949 + 0.0458347i \(0.985405\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −65.1672 200.564i −0.220159 0.677581i
\(297\) 0 0
\(298\) −156.316 215.151i −0.524551 0.721983i
\(299\) 7.60845i 0.0254463i
\(300\) 0 0
\(301\) −17.0820 −0.0567510
\(302\) −244.681 + 177.771i −0.810201 + 0.588645i
\(303\) 0 0
\(304\) 88.4458 121.735i 0.290940 0.400445i
\(305\) 0 0
\(306\) 0 0
\(307\) −118.031 −0.384466 −0.192233 0.981349i \(-0.561573\pi\)
−0.192233 + 0.981349i \(0.561573\pi\)
\(308\) −58.1234 18.8854i −0.188712 0.0613164i
\(309\) 0 0
\(310\) 0 0
\(311\) 121.835i 0.391753i −0.980629 0.195877i \(-0.937245\pi\)
0.980629 0.195877i \(-0.0627552\pi\)
\(312\) 0 0
\(313\) 219.548i 0.701431i 0.936482 + 0.350716i \(0.114062\pi\)
−0.936482 + 0.350716i \(0.885938\pi\)
\(314\) 59.4590 43.1995i 0.189360 0.137578i
\(315\) 0 0
\(316\) −432.551 140.544i −1.36883 0.444761i
\(317\) 366.859i 1.15728i 0.815582 + 0.578642i \(0.196417\pi\)
−0.815582 + 0.578642i \(0.803583\pi\)
\(318\) 0 0
\(319\) 12.4727i 0.0390993i
\(320\) 0 0
\(321\) 0 0
\(322\) −161.150 221.803i −0.500465 0.688830i
\(323\) 224.661 0.695546
\(324\) 0 0
\(325\) 0 0
\(326\) 356.026 + 490.028i 1.09211 + 1.50315i
\(327\) 0 0
\(328\) 315.115 102.387i 0.960716 0.312155i
\(329\) −300.689 −0.913948
\(330\) 0 0
\(331\) 162.846i 0.491981i −0.969272 0.245990i \(-0.920887\pi\)
0.969272 0.245990i \(-0.0791132\pi\)
\(332\) −26.2556 + 80.8065i −0.0790832 + 0.243393i
\(333\) 0 0
\(334\) 116.833 + 160.807i 0.349799 + 0.481457i
\(335\) 0 0
\(336\) 0 0
\(337\) 17.1084i 0.0507666i −0.999678 0.0253833i \(-0.991919\pi\)
0.999678 0.0253833i \(-0.00808063\pi\)
\(338\) −198.409 273.087i −0.587010 0.807950i
\(339\) 0 0
\(340\) 0 0
\(341\) 85.2198 0.249911
\(342\) 0 0
\(343\) 218.101 0.635863
\(344\) 15.2786 4.96433i 0.0444147 0.0144312i
\(345\) 0 0
\(346\) 293.899 213.530i 0.849418 0.617138i
\(347\) −167.498 −0.482703 −0.241351 0.970438i \(-0.577591\pi\)
−0.241351 + 0.970438i \(0.577591\pi\)
\(348\) 0 0
\(349\) 483.495 1.38537 0.692687 0.721239i \(-0.256427\pi\)
0.692687 + 0.721239i \(0.256427\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 57.4756 0.163283
\(353\) 307.994i 0.872504i −0.899825 0.436252i \(-0.856306\pi\)
0.899825 0.436252i \(-0.143694\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −83.3638 + 256.567i −0.234168 + 0.720695i
\(357\) 0 0
\(358\) −422.157 + 306.715i −1.17921 + 0.856746i
\(359\) 23.2494i 0.0647615i −0.999476 0.0323807i \(-0.989691\pi\)
0.999476 0.0323807i \(-0.0103089\pi\)
\(360\) 0 0
\(361\) 272.554 0.754998
\(362\) −185.478 255.289i −0.512370 0.705217i
\(363\) 0 0
\(364\) 15.2786 + 4.96433i 0.0419743 + 0.0136383i
\(365\) 0 0
\(366\) 0 0
\(367\) −517.325 −1.40960 −0.704802 0.709404i \(-0.748964\pi\)
−0.704802 + 0.709404i \(0.748964\pi\)
\(368\) 208.596 + 151.554i 0.566838 + 0.411832i
\(369\) 0 0
\(370\) 0 0
\(371\) 184.075i 0.496159i
\(372\) 0 0
\(373\) 88.3545i 0.236875i −0.992961 0.118438i \(-0.962211\pi\)
0.992961 0.118438i \(-0.0377886\pi\)
\(374\) 50.4396 + 69.4242i 0.134865 + 0.185626i
\(375\) 0 0
\(376\) 268.944 87.3853i 0.715277 0.232408i
\(377\) 3.27864i 0.00869666i
\(378\) 0 0
\(379\) 19.3332i 0.0510112i −0.999675 0.0255056i \(-0.991880\pi\)
0.999675 0.0255056i \(-0.00811956\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 524.397 380.997i 1.37277 0.997374i
\(383\) −431.612 −1.12692 −0.563462 0.826142i \(-0.690531\pi\)
−0.563462 + 0.826142i \(0.690531\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 294.122 213.692i 0.761973 0.553606i
\(387\) 0 0
\(388\) −149.001 48.4133i −0.384023 0.124777i
\(389\) −296.354 −0.761837 −0.380918 0.924609i \(-0.624392\pi\)
−0.380918 + 0.924609i \(0.624392\pi\)
\(390\) 0 0
\(391\) 384.963i 0.984560i
\(392\) 177.739 57.7508i 0.453415 0.147323i
\(393\) 0 0
\(394\) 227.374 165.197i 0.577091 0.419281i
\(395\) 0 0
\(396\) 0 0
\(397\) 86.1904i 0.217104i 0.994091 + 0.108552i \(0.0346214\pi\)
−0.994091 + 0.108552i \(0.965379\pi\)
\(398\) −272.208 + 197.771i −0.683940 + 0.496912i
\(399\) 0 0
\(400\) 0 0
\(401\) −442.997 −1.10473 −0.552365 0.833602i \(-0.686275\pi\)
−0.552365 + 0.833602i \(0.686275\pi\)
\(402\) 0 0
\(403\) −22.4014 −0.0555865
\(404\) 123.469 379.999i 0.305616 0.940591i
\(405\) 0 0
\(406\) 69.4427 + 95.5797i 0.171041 + 0.235418i
\(407\) −47.3467 −0.116331
\(408\) 0 0
\(409\) −63.4102 −0.155037 −0.0775186 0.996991i \(-0.524700\pi\)
−0.0775186 + 0.996991i \(0.524700\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −44.2167 + 136.085i −0.107322 + 0.330304i
\(413\) 628.328i 1.52138i
\(414\) 0 0
\(415\) 0 0
\(416\) −15.1084 −0.0363182
\(417\) 0 0
\(418\) −19.8573 27.3313i −0.0475056 0.0653858i
\(419\) 435.678i 1.03980i −0.854226 0.519902i \(-0.825968\pi\)
0.854226 0.519902i \(-0.174032\pi\)
\(420\) 0 0
\(421\) −582.912 −1.38459 −0.692294 0.721615i \(-0.743400\pi\)
−0.692294 + 0.721615i \(0.743400\pi\)
\(422\) 152.007 110.440i 0.360206 0.261705i
\(423\) 0 0
\(424\) 53.4953 + 164.642i 0.126168 + 0.388306i
\(425\) 0 0
\(426\) 0 0
\(427\) 222.341 0.520705
\(428\) −149.687 + 460.689i −0.349736 + 1.07638i
\(429\) 0 0
\(430\) 0 0
\(431\) 375.882i 0.872117i −0.899918 0.436058i \(-0.856374\pi\)
0.899918 0.436058i \(-0.143626\pi\)
\(432\) 0 0
\(433\) 368.164i 0.850263i −0.905131 0.425132i \(-0.860228\pi\)
0.905131 0.425132i \(-0.139772\pi\)
\(434\) −653.050 + 474.468i −1.50472 + 1.09324i
\(435\) 0 0
\(436\) −244.085 + 751.217i −0.559828 + 1.72297i
\(437\) 151.554i 0.346806i
\(438\) 0 0
\(439\) 483.549i 1.10148i −0.834677 0.550739i \(-0.814346\pi\)
0.834677 0.550739i \(-0.185654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −13.2588 18.2492i −0.0299974 0.0412878i
\(443\) −279.181 −0.630205 −0.315102 0.949058i \(-0.602039\pi\)
−0.315102 + 0.949058i \(0.602039\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 251.613 + 346.316i 0.564155 + 0.776492i
\(447\) 0 0
\(448\) −440.442 + 320.000i −0.983130 + 0.714286i
\(449\) 756.079 1.68392 0.841959 0.539542i \(-0.181403\pi\)
0.841959 + 0.539542i \(0.181403\pi\)
\(450\) 0 0
\(451\) 74.3885i 0.164941i
\(452\) 309.202 + 100.466i 0.684076 + 0.222270i
\(453\) 0 0
\(454\) −48.6950 67.0230i −0.107258 0.147628i
\(455\) 0 0
\(456\) 0 0
\(457\) 285.672i 0.625103i −0.949901 0.312551i \(-0.898816\pi\)
0.949901 0.312551i \(-0.101184\pi\)
\(458\) 86.1442 + 118.567i 0.188088 + 0.258881i
\(459\) 0 0
\(460\) 0 0
\(461\) 99.1146 0.214999 0.107500 0.994205i \(-0.465716\pi\)
0.107500 + 0.994205i \(0.465716\pi\)
\(462\) 0 0
\(463\) 630.603 1.36199 0.680997 0.732286i \(-0.261547\pi\)
0.680997 + 0.732286i \(0.261547\pi\)
\(464\) −89.8885 65.3078i −0.193725 0.140750i
\(465\) 0 0
\(466\) 496.817 360.958i 1.06613 0.774589i
\(467\) −496.010 −1.06212 −0.531060 0.847334i \(-0.678206\pi\)
−0.531060 + 0.847334i \(0.678206\pi\)
\(468\) 0 0
\(469\) −755.967 −1.61187
\(470\) 0 0
\(471\) 0 0
\(472\) 182.603 + 561.994i 0.386870 + 1.19066i
\(473\) 3.60680i 0.00762537i
\(474\) 0 0
\(475\) 0 0
\(476\) −773.050 251.179i −1.62405 0.527687i
\(477\) 0 0
\(478\) −69.4242 + 50.4396i −0.145239 + 0.105522i
\(479\) 579.090i 1.20896i 0.796621 + 0.604478i \(0.206618\pi\)
−0.796621 + 0.604478i \(0.793382\pi\)
\(480\) 0 0
\(481\) 12.4458 0.0258749
\(482\) 158.798 + 218.567i 0.329457 + 0.453459i
\(483\) 0 0
\(484\) −145.577 + 448.039i −0.300778 + 0.925700i
\(485\) 0 0
\(486\) 0 0
\(487\) 626.363 1.28617 0.643084 0.765796i \(-0.277655\pi\)
0.643084 + 0.765796i \(0.277655\pi\)
\(488\) −198.868 + 64.6161i −0.407516 + 0.132410i
\(489\) 0 0
\(490\) 0 0
\(491\) 22.3013i 0.0454201i −0.999742 0.0227100i \(-0.992771\pi\)
0.999742 0.0227100i \(-0.00722945\pi\)
\(492\) 0 0
\(493\) 165.889i 0.336488i
\(494\) 5.21981 + 7.18445i 0.0105664 + 0.0145434i
\(495\) 0 0
\(496\) 446.217 614.165i 0.899630 1.23824i
\(497\) 335.279i 0.674605i
\(498\) 0 0
\(499\) 627.362i 1.25724i −0.777714 0.628619i \(-0.783621\pi\)
0.777714 0.628619i \(-0.216379\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 357.859 260.000i 0.712867 0.517928i
\(503\) 780.853 1.55239 0.776196 0.630492i \(-0.217147\pi\)
0.776196 + 0.630492i \(0.217147\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 46.8328 34.0260i 0.0925550 0.0672451i
\(507\) 0 0
\(508\) 2.28198 7.02321i 0.00449208 0.0138252i
\(509\) −288.950 −0.567683 −0.283841 0.958871i \(-0.591609\pi\)
−0.283841 + 0.958871i \(0.591609\pi\)
\(510\) 0 0
\(511\) 1170.11i 2.28984i
\(512\) 300.946 414.217i 0.587785 0.809017i
\(513\) 0 0
\(514\) −415.925 + 302.187i −0.809192 + 0.587913i
\(515\) 0 0
\(516\) 0 0
\(517\) 63.4891i 0.122803i
\(518\) 362.824 263.607i 0.700432 0.508893i
\(519\) 0 0
\(520\) 0 0
\(521\) 602.984 1.15736 0.578680 0.815555i \(-0.303568\pi\)
0.578680 + 0.815555i \(0.303568\pi\)
\(522\) 0 0
\(523\) −367.962 −0.703560 −0.351780 0.936083i \(-0.614423\pi\)
−0.351780 + 0.936083i \(0.614423\pi\)
\(524\) 858.269 + 278.869i 1.63792 + 0.532192i
\(525\) 0 0
\(526\) 192.991 + 265.629i 0.366902 + 0.504998i
\(527\) 1133.44 2.15073
\(528\) 0 0
\(529\) −269.308 −0.509089
\(530\) 0 0
\(531\) 0 0
\(532\) 304.338 + 98.8854i 0.572064 + 0.185875i
\(533\) 19.5542i 0.0366870i
\(534\) 0 0
\(535\) 0 0
\(536\) 676.158 219.697i 1.26149 0.409882i
\(537\) 0 0
\(538\) 41.7036 + 57.4001i 0.0775161 + 0.106692i
\(539\) 41.9584i 0.0778449i
\(540\) 0 0
\(541\) −616.885 −1.14027 −0.570134 0.821551i \(-0.693109\pi\)
−0.570134 + 0.821551i \(0.693109\pi\)
\(542\) 483.711 351.437i 0.892455 0.648407i
\(543\) 0 0
\(544\) 764.433 1.40521
\(545\) 0 0
\(546\) 0 0
\(547\) −97.8499 −0.178885 −0.0894423 0.995992i \(-0.528508\pi\)
−0.0894423 + 0.995992i \(0.528508\pi\)
\(548\) 200.988 + 65.3050i 0.366766 + 0.119170i
\(549\) 0 0
\(550\) 0 0
\(551\) 65.3078i 0.118526i
\(552\) 0 0
\(553\) 967.214i 1.74903i
\(554\) 739.840 537.525i 1.33545 0.970262i
\(555\) 0 0
\(556\) −478.768 155.561i −0.861093 0.279786i
\(557\) 896.302i 1.60916i 0.593845 + 0.804580i \(0.297609\pi\)
−0.593845 + 0.804580i \(0.702391\pi\)
\(558\) 0 0
\(559\) 0.948103i 0.00169607i
\(560\) 0 0
\(561\) 0 0
\(562\) −6.62942 9.12461i −0.0117961 0.0162360i
\(563\) 771.186 1.36978 0.684890 0.728647i \(-0.259850\pi\)
0.684890 + 0.728647i \(0.259850\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −199.751 274.933i −0.352917 0.485748i
\(567\) 0 0
\(568\) 97.4377 + 299.882i 0.171545 + 0.527962i
\(569\) 8.74767 0.0153738 0.00768688 0.999970i \(-0.497553\pi\)
0.00768688 + 0.999970i \(0.497553\pi\)
\(570\) 0 0
\(571\) 511.138i 0.895164i 0.894243 + 0.447582i \(0.147715\pi\)
−0.894243 + 0.447582i \(0.852285\pi\)
\(572\) −1.04820 + 3.22602i −0.00183251 + 0.00563989i
\(573\) 0 0
\(574\) 414.164 + 570.048i 0.721540 + 0.993115i
\(575\) 0 0
\(576\) 0 0
\(577\) 713.712i 1.23694i 0.785810 + 0.618468i \(0.212246\pi\)
−0.785810 + 0.618468i \(0.787754\pi\)
\(578\) 331.114 + 455.740i 0.572862 + 0.788477i
\(579\) 0 0
\(580\) 0 0
\(581\) −180.689 −0.310996
\(582\) 0 0
\(583\) 38.8666 0.0666666
\(584\) 340.053 + 1046.57i 0.582282 + 1.79208i
\(585\) 0 0
\(586\) 43.4590 31.5748i 0.0741621 0.0538819i
\(587\) 422.169 0.719198 0.359599 0.933107i \(-0.382914\pi\)
0.359599 + 0.933107i \(0.382914\pi\)
\(588\) 0 0
\(589\) −446.217 −0.757584
\(590\) 0 0
\(591\) 0 0
\(592\) −247.911 + 341.220i −0.418768 + 0.576385i
\(593\) 308.663i 0.520510i 0.965540 + 0.260255i \(0.0838067\pi\)
−0.965540 + 0.260255i \(0.916193\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −164.361 + 505.850i −0.275773 + 0.848742i
\(597\) 0 0
\(598\) −12.3107 + 8.94427i −0.0205865 + 0.0149570i
\(599\) 462.196i 0.771612i −0.922580 0.385806i \(-0.873923\pi\)
0.922580 0.385806i \(-0.126077\pi\)
\(600\) 0 0
\(601\) 355.358 0.591277 0.295639 0.955300i \(-0.404468\pi\)
0.295639 + 0.955300i \(0.404468\pi\)
\(602\) 20.0811 + 27.6393i 0.0333574 + 0.0459125i
\(603\) 0 0
\(604\) 575.279 + 186.919i 0.952448 + 0.309469i
\(605\) 0 0
\(606\) 0 0
\(607\) 630.403 1.03856 0.519278 0.854605i \(-0.326201\pi\)
0.519278 + 0.854605i \(0.326201\pi\)
\(608\) −300.946 −0.494977
\(609\) 0 0
\(610\) 0 0
\(611\) 16.6891i 0.0273144i
\(612\) 0 0
\(613\) 812.525i 1.32549i 0.748846 + 0.662745i \(0.230608\pi\)
−0.748846 + 0.662745i \(0.769392\pi\)
\(614\) 138.754 + 190.978i 0.225984 + 0.311040i
\(615\) 0 0
\(616\) 37.7709 + 116.247i 0.0613164 + 0.188712i
\(617\) 437.935i 0.709781i −0.934908 0.354891i \(-0.884518\pi\)
0.934908 0.354891i \(-0.115482\pi\)
\(618\) 0 0
\(619\) 770.250i 1.24435i 0.782880 + 0.622173i \(0.213750\pi\)
−0.782880 + 0.622173i \(0.786250\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −197.134 + 143.226i −0.316935 + 0.230267i
\(623\) −573.702 −0.920870
\(624\) 0 0
\(625\) 0 0
\(626\) 355.236 258.094i 0.567470 0.412291i
\(627\) 0 0
\(628\) −139.796 45.4226i −0.222606 0.0723290i
\(629\) −629.718 −1.00114
\(630\) 0 0
\(631\) 875.496i 1.38747i −0.720228 0.693737i \(-0.755963\pi\)
0.720228 0.693737i \(-0.244037\pi\)
\(632\) 281.089 + 865.102i 0.444761 + 1.36883i
\(633\) 0 0
\(634\) 593.591 431.269i 0.936263 0.680235i
\(635\) 0 0
\(636\) 0 0
\(637\) 11.0294i 0.0173146i
\(638\) −20.1812 + 14.6625i −0.0316320 + 0.0229820i
\(639\) 0 0
\(640\) 0 0
\(641\) −842.571 −1.31446 −0.657232 0.753689i \(-0.728273\pi\)
−0.657232 + 0.753689i \(0.728273\pi\)
\(642\) 0 0
\(643\) 1153.20 1.79348 0.896738 0.442563i \(-0.145931\pi\)
0.896738 + 0.442563i \(0.145931\pi\)
\(644\) −169.443 + 521.491i −0.263110 + 0.809769i
\(645\) 0 0
\(646\) −264.105 363.510i −0.408832 0.562708i
\(647\) 355.751 0.549847 0.274924 0.961466i \(-0.411347\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(648\) 0 0
\(649\) 132.669 0.204420
\(650\) 0 0
\(651\) 0 0
\(652\) 374.348 1152.13i 0.574154 1.76706i
\(653\) 557.915i 0.854387i 0.904160 + 0.427194i \(0.140498\pi\)
−0.904160 + 0.427194i \(0.859502\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −536.105 389.503i −0.817234 0.593755i
\(657\) 0 0
\(658\) 353.481 + 486.525i 0.537205 + 0.739399i
\(659\) 284.157i 0.431194i 0.976482 + 0.215597i \(0.0691697\pi\)
−0.976482 + 0.215597i \(0.930830\pi\)
\(660\) 0 0
\(661\) 716.735 1.08432 0.542160 0.840275i \(-0.317607\pi\)
0.542160 + 0.840275i \(0.317607\pi\)
\(662\) −263.490 + 191.437i −0.398021 + 0.289179i
\(663\) 0 0
\(664\) 161.613 52.5112i 0.243393 0.0790832i
\(665\) 0 0
\(666\) 0 0
\(667\) −111.907 −0.167776
\(668\) 122.845 378.079i 0.183900 0.565986i
\(669\) 0 0
\(670\) 0 0
\(671\) 46.9464i 0.0699648i
\(672\) 0 0
\(673\) 695.378i 1.03325i −0.856212 0.516625i \(-0.827188\pi\)
0.856212 0.516625i \(-0.172812\pi\)
\(674\) −27.6819 + 20.1121i −0.0410711 + 0.0298399i
\(675\) 0 0
\(676\) −208.620 + 642.066i −0.308609 + 0.949802i
\(677\) 820.237i 1.21158i −0.795626 0.605788i \(-0.792858\pi\)
0.795626 0.605788i \(-0.207142\pi\)
\(678\) 0 0
\(679\) 333.176i 0.490686i
\(680\) 0 0
\(681\) 0 0
\(682\) −100.182 137.889i −0.146894 0.202183i
\(683\) 335.508 0.491227 0.245613 0.969368i \(-0.421011\pi\)
0.245613 + 0.969368i \(0.421011\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −256.393 352.895i −0.373751 0.514424i
\(687\) 0 0
\(688\) −25.9936 18.8854i −0.0377814 0.0274498i
\(689\) −10.2167 −0.0148283
\(690\) 0 0
\(691\) 336.568i 0.487074i 0.969892 + 0.243537i \(0.0783077\pi\)
−0.969892 + 0.243537i \(0.921692\pi\)
\(692\) −690.997 224.519i −0.998551 0.324449i
\(693\) 0 0
\(694\) 196.906 + 271.017i 0.283726 + 0.390515i
\(695\) 0 0
\(696\) 0 0
\(697\) 989.378i 1.41948i
\(698\) −568.383 782.312i −0.814302 1.12079i
\(699\) 0 0
\(700\) 0 0
\(701\) 429.364 0.612502 0.306251 0.951951i \(-0.400925\pi\)
0.306251 + 0.951951i \(0.400925\pi\)
\(702\) 0 0
\(703\) 247.911 0.352647
\(704\) −67.5666 92.9974i −0.0959753 0.132099i
\(705\) 0 0
\(706\) −498.344 + 362.068i −0.705870 + 0.512845i
\(707\) 849.703 1.20184
\(708\) 0 0
\(709\) −1224.60 −1.72722 −0.863609 0.504162i \(-0.831801\pi\)
−0.863609 + 0.504162i \(0.831801\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 513.135 166.728i 0.720695 0.234168i
\(713\) 764.604i 1.07238i
\(714\) 0 0
\(715\) 0 0
\(716\) 992.551 + 322.499i 1.38624 + 0.450418i
\(717\) 0 0
\(718\) −37.6183 + 27.3313i −0.0523931 + 0.0380658i
\(719\) 496.022i 0.689877i 0.938625 + 0.344939i \(0.112100\pi\)
−0.938625 + 0.344939i \(0.887900\pi\)
\(720\) 0 0
\(721\) −304.296 −0.422047
\(722\) −320.407 441.002i −0.443777 0.610806i
\(723\) 0 0
\(724\) −195.023 + 600.220i −0.269369 + 0.829033i
\(725\) 0 0
\(726\) 0 0
\(727\) −152.843 −0.210238 −0.105119 0.994460i \(-0.533522\pi\)
−0.105119 + 0.994460i \(0.533522\pi\)
\(728\) −9.92866 30.5573i −0.0136383 0.0419743i
\(729\) 0 0
\(730\) 0 0
\(731\) 47.9709i 0.0656237i
\(732\) 0 0
\(733\) 761.286i 1.03859i −0.854595 0.519295i \(-0.826195\pi\)
0.854595 0.519295i \(-0.173805\pi\)
\(734\) 608.152 + 837.049i 0.828544 + 1.14039i
\(735\) 0 0
\(736\) 515.679i 0.700650i
\(737\) 159.619i 0.216580i
\(738\) 0 0
\(739\) 183.975i 0.248951i 0.992223 + 0.124476i \(0.0397249\pi\)
−0.992223 + 0.124476i \(0.960275\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −297.840 + 216.393i −0.401401 + 0.291635i
\(743\) 495.247 0.666551 0.333275 0.942830i \(-0.391846\pi\)
0.333275 + 0.942830i \(0.391846\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −142.961 + 103.867i −0.191636 + 0.139232i
\(747\) 0 0
\(748\) 53.0353 163.226i 0.0709029 0.218217i
\(749\) −1030.13 −1.37534
\(750\) 0 0
\(751\) 800.059i 1.06533i 0.846328 + 0.532663i \(0.178809\pi\)
−0.846328 + 0.532663i \(0.821191\pi\)
\(752\) −457.555 332.433i −0.608451 0.442066i
\(753\) 0 0
\(754\) 5.30495 3.85427i 0.00703574 0.00511177i
\(755\) 0 0
\(756\) 0 0
\(757\) 276.367i 0.365082i 0.983198 + 0.182541i \(0.0584322\pi\)
−0.983198 + 0.182541i \(0.941568\pi\)
\(758\) −31.2818 + 22.7276i −0.0412689 + 0.0299836i
\(759\) 0 0
\(760\) 0 0
\(761\) −891.207 −1.17110 −0.585550 0.810636i \(-0.699121\pi\)
−0.585550 + 0.810636i \(0.699121\pi\)
\(762\) 0 0
\(763\) −1679.77 −2.20154
\(764\) −1232.93 400.604i −1.61379 0.524351i
\(765\) 0 0
\(766\) 507.390 + 698.363i 0.662389 + 0.911700i
\(767\) −34.8740 −0.0454681
\(768\) 0 0
\(769\) 835.430 1.08639 0.543193 0.839608i \(-0.317215\pi\)
0.543193 + 0.839608i \(0.317215\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −691.521 224.689i −0.895753 0.291048i
\(773\) 213.522i 0.276225i −0.990417 0.138112i \(-0.955897\pi\)
0.990417 0.138112i \(-0.0441035\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 96.8266 + 298.002i 0.124777 + 0.384023i
\(777\) 0 0
\(778\) 348.386 + 479.512i 0.447796 + 0.616339i
\(779\) 389.503i 0.500004i
\(780\) 0 0
\(781\) 70.7926 0.0906436
\(782\) 622.883 452.551i 0.796526 0.578710i
\(783\) 0 0
\(784\) −302.387 219.697i −0.385698 0.280226i
\(785\) 0 0
\(786\) 0 0
\(787\) −370.182 −0.470371 −0.235185 0.971951i \(-0.575570\pi\)
−0.235185 + 0.971951i \(0.575570\pi\)
\(788\) −534.588 173.698i −0.678411 0.220429i
\(789\) 0 0
\(790\) 0 0
\(791\) 691.397i 0.874080i
\(792\) 0 0
\(793\) 12.3406i 0.0155619i
\(794\) 139.459 101.323i 0.175641 0.127611i
\(795\) 0 0
\(796\) 640.000 + 207.949i 0.804020 + 0.261242i