Properties

Label 108.5.d.b.55.8
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{24} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.8
Root \(-2.23772 + 3.87585i\) of \(x^{16} + 38 x^{14} + 1016 x^{12} + 13512 x^{10} + 130640 x^{8} + 569472 x^{6} + 1783808 x^{4} + 352256 x^{2} + 65536\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.b.55.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.988828 + 3.87585i) q^{2} +(-14.0444 - 7.66510i) q^{4} +20.7568 q^{5} +5.38785i q^{7} +(43.5963 - 46.8547i) q^{8} +O(q^{10})\) \(q+(-0.988828 + 3.87585i) q^{2} +(-14.0444 - 7.66510i) q^{4} +20.7568 q^{5} +5.38785i q^{7} +(43.5963 - 46.8547i) q^{8} +(-20.5250 + 80.4504i) q^{10} -115.619i q^{11} +207.234 q^{13} +(-20.8825 - 5.32765i) q^{14} +(138.493 + 215.304i) q^{16} +383.437 q^{17} +618.390i q^{19} +(-291.518 - 159.103i) q^{20} +(448.121 + 114.327i) q^{22} +82.9899i q^{23} -194.153 q^{25} +(-204.919 + 803.209i) q^{26} +(41.2984 - 75.6693i) q^{28} +201.949 q^{29} +196.140i q^{31} +(-971.432 + 323.878i) q^{32} +(-379.153 + 1486.14i) q^{34} +111.835i q^{35} +340.480 q^{37} +(-2396.79 - 611.481i) q^{38} +(904.922 - 972.556i) q^{40} +2797.22 q^{41} +254.774i q^{43} +(-886.230 + 1623.80i) q^{44} +(-321.656 - 82.0627i) q^{46} -2257.41i q^{47} +2371.97 q^{49} +(191.984 - 752.509i) q^{50} +(-2910.49 - 1588.47i) q^{52} +4111.23 q^{53} -2399.88i q^{55} +(252.446 + 234.890i) q^{56} +(-199.693 + 782.726i) q^{58} +1598.57i q^{59} -6081.09 q^{61} +(-760.210 - 193.949i) q^{62} +(-294.723 - 4085.38i) q^{64} +4301.53 q^{65} -7383.67i q^{67} +(-5385.15 - 2939.08i) q^{68} +(-433.455 - 110.585i) q^{70} -9347.39i q^{71} -5320.95 q^{73} +(-336.676 + 1319.65i) q^{74} +(4740.02 - 8684.94i) q^{76} +622.936 q^{77} +5971.42i q^{79} +(2874.67 + 4469.03i) q^{80} +(-2765.97 + 10841.6i) q^{82} +10091.0i q^{83} +7958.94 q^{85} +(-987.466 - 251.928i) q^{86} +(-5417.28 - 5040.55i) q^{88} -13611.5 q^{89} +1116.55i q^{91} +(636.126 - 1165.55i) q^{92} +(8749.37 + 2232.19i) q^{94} +12835.8i q^{95} +2179.54 q^{97} +(-2345.47 + 9193.41i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 28q^{4} + O(q^{10}) \) \( 16q + 28q^{4} + 176q^{10} + 176q^{13} + 88q^{16} + 384q^{22} + 2736q^{25} + 1812q^{28} + 1520q^{34} + 80q^{37} - 688q^{40} - 1824q^{46} - 7904q^{49} - 5236q^{52} - 11584q^{58} - 1648q^{61} + 5056q^{64} + 26688q^{70} + 80q^{73} - 8388q^{76} - 38464q^{82} - 16832q^{85} - 29520q^{88} - 4512q^{94} + 14864q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.988828 + 3.87585i −0.247207 + 0.968963i
\(3\) 0 0
\(4\) −14.0444 7.66510i −0.877777 0.479069i
\(5\) 20.7568 0.830274 0.415137 0.909759i \(-0.363734\pi\)
0.415137 + 0.909759i \(0.363734\pi\)
\(6\) 0 0
\(7\) 5.38785i 0.109956i 0.998488 + 0.0549780i \(0.0175089\pi\)
−0.998488 + 0.0549780i \(0.982491\pi\)
\(8\) 43.5963 46.8547i 0.681192 0.732104i
\(9\) 0 0
\(10\) −20.5250 + 80.4504i −0.205250 + 0.804504i
\(11\) 115.619i 0.955527i −0.878488 0.477764i \(-0.841448\pi\)
0.878488 0.477764i \(-0.158552\pi\)
\(12\) 0 0
\(13\) 207.234 1.22624 0.613119 0.789991i \(-0.289915\pi\)
0.613119 + 0.789991i \(0.289915\pi\)
\(14\) −20.8825 5.32765i −0.106543 0.0271819i
\(15\) 0 0
\(16\) 138.493 + 215.304i 0.540986 + 0.841031i
\(17\) 383.437 1.32677 0.663385 0.748278i \(-0.269119\pi\)
0.663385 + 0.748278i \(0.269119\pi\)
\(18\) 0 0
\(19\) 618.390i 1.71299i 0.516155 + 0.856495i \(0.327363\pi\)
−0.516155 + 0.856495i \(0.672637\pi\)
\(20\) −291.518 159.103i −0.728796 0.397758i
\(21\) 0 0
\(22\) 448.121 + 114.327i 0.925870 + 0.236213i
\(23\) 82.9899i 0.156881i 0.996919 + 0.0784403i \(0.0249940\pi\)
−0.996919 + 0.0784403i \(0.975006\pi\)
\(24\) 0 0
\(25\) −194.153 −0.310645
\(26\) −204.919 + 803.209i −0.303135 + 1.18818i
\(27\) 0 0
\(28\) 41.2984 75.6693i 0.0526765 0.0965170i
\(29\) 201.949 0.240130 0.120065 0.992766i \(-0.461690\pi\)
0.120065 + 0.992766i \(0.461690\pi\)
\(30\) 0 0
\(31\) 196.140i 0.204100i 0.994779 + 0.102050i \(0.0325402\pi\)
−0.994779 + 0.102050i \(0.967460\pi\)
\(32\) −971.432 + 323.878i −0.948664 + 0.316287i
\(33\) 0 0
\(34\) −379.153 + 1486.14i −0.327987 + 1.28559i
\(35\) 111.835i 0.0912937i
\(36\) 0 0
\(37\) 340.480 0.248707 0.124354 0.992238i \(-0.460314\pi\)
0.124354 + 0.992238i \(0.460314\pi\)
\(38\) −2396.79 611.481i −1.65982 0.423463i
\(39\) 0 0
\(40\) 904.922 972.556i 0.565576 0.607847i
\(41\) 2797.22 1.66402 0.832011 0.554758i \(-0.187189\pi\)
0.832011 + 0.554758i \(0.187189\pi\)
\(42\) 0 0
\(43\) 254.774i 0.137790i 0.997624 + 0.0688951i \(0.0219474\pi\)
−0.997624 + 0.0688951i \(0.978053\pi\)
\(44\) −886.230 + 1623.80i −0.457763 + 0.838740i
\(45\) 0 0
\(46\) −321.656 82.0627i −0.152011 0.0387820i
\(47\) 2257.41i 1.02191i −0.859607 0.510956i \(-0.829291\pi\)
0.859607 0.510956i \(-0.170709\pi\)
\(48\) 0 0
\(49\) 2371.97 0.987910
\(50\) 191.984 752.509i 0.0767937 0.301004i
\(51\) 0 0
\(52\) −2910.49 1588.47i −1.07636 0.587452i
\(53\) 4111.23 1.46359 0.731796 0.681524i \(-0.238683\pi\)
0.731796 + 0.681524i \(0.238683\pi\)
\(54\) 0 0
\(55\) 2399.88i 0.793349i
\(56\) 252.446 + 234.890i 0.0804993 + 0.0749012i
\(57\) 0 0
\(58\) −199.693 + 782.726i −0.0593618 + 0.232677i
\(59\) 1598.57i 0.459226i 0.973282 + 0.229613i \(0.0737461\pi\)
−0.973282 + 0.229613i \(0.926254\pi\)
\(60\) 0 0
\(61\) −6081.09 −1.63426 −0.817131 0.576452i \(-0.804437\pi\)
−0.817131 + 0.576452i \(0.804437\pi\)
\(62\) −760.210 193.949i −0.197765 0.0504549i
\(63\) 0 0
\(64\) −294.723 4085.38i −0.0719539 0.997408i
\(65\) 4301.53 1.01811
\(66\) 0 0
\(67\) 7383.67i 1.64484i −0.568884 0.822418i \(-0.692625\pi\)
0.568884 0.822418i \(-0.307375\pi\)
\(68\) −5385.15 2939.08i −1.16461 0.635614i
\(69\) 0 0
\(70\) −433.455 110.585i −0.0884602 0.0225684i
\(71\) 9347.39i 1.85427i −0.374723 0.927137i \(-0.622262\pi\)
0.374723 0.927137i \(-0.377738\pi\)
\(72\) 0 0
\(73\) −5320.95 −0.998490 −0.499245 0.866461i \(-0.666389\pi\)
−0.499245 + 0.866461i \(0.666389\pi\)
\(74\) −336.676 + 1319.65i −0.0614822 + 0.240988i
\(75\) 0 0
\(76\) 4740.02 8684.94i 0.820640 1.50362i
\(77\) 622.936 0.105066
\(78\) 0 0
\(79\) 5971.42i 0.956806i 0.878141 + 0.478403i \(0.158784\pi\)
−0.878141 + 0.478403i \(0.841216\pi\)
\(80\) 2874.67 + 4469.03i 0.449167 + 0.698286i
\(81\) 0 0
\(82\) −2765.97 + 10841.6i −0.411358 + 1.61238i
\(83\) 10091.0i 1.46480i 0.680876 + 0.732399i \(0.261599\pi\)
−0.680876 + 0.732399i \(0.738401\pi\)
\(84\) 0 0
\(85\) 7958.94 1.10158
\(86\) −987.466 251.928i −0.133514 0.0340627i
\(87\) 0 0
\(88\) −5417.28 5040.55i −0.699546 0.650898i
\(89\) −13611.5 −1.71841 −0.859206 0.511631i \(-0.829042\pi\)
−0.859206 + 0.511631i \(0.829042\pi\)
\(90\) 0 0
\(91\) 1116.55i 0.134832i
\(92\) 636.126 1165.55i 0.0751566 0.137706i
\(93\) 0 0
\(94\) 8749.37 + 2232.19i 0.990195 + 0.252624i
\(95\) 12835.8i 1.42225i
\(96\) 0 0
\(97\) 2179.54 0.231645 0.115822 0.993270i \(-0.463050\pi\)
0.115822 + 0.993270i \(0.463050\pi\)
\(98\) −2345.47 + 9193.41i −0.244218 + 0.957248i
\(99\) 0 0
\(100\) 2726.77 + 1488.20i 0.272677 + 0.148820i
\(101\) −3242.55 −0.317866 −0.158933 0.987289i \(-0.550805\pi\)
−0.158933 + 0.987289i \(0.550805\pi\)
\(102\) 0 0
\(103\) 3261.34i 0.307412i 0.988117 + 0.153706i \(0.0491209\pi\)
−0.988117 + 0.153706i \(0.950879\pi\)
\(104\) 9034.65 9709.89i 0.835304 0.897734i
\(105\) 0 0
\(106\) −4065.30 + 15934.5i −0.361810 + 1.41817i
\(107\) 15927.7i 1.39119i −0.718434 0.695595i \(-0.755141\pi\)
0.718434 0.695595i \(-0.244859\pi\)
\(108\) 0 0
\(109\) 7377.06 0.620913 0.310456 0.950588i \(-0.399518\pi\)
0.310456 + 0.950588i \(0.399518\pi\)
\(110\) 9301.58 + 2373.07i 0.768726 + 0.196122i
\(111\) 0 0
\(112\) −1160.03 + 746.177i −0.0924765 + 0.0594847i
\(113\) −7121.69 −0.557733 −0.278867 0.960330i \(-0.589959\pi\)
−0.278867 + 0.960330i \(0.589959\pi\)
\(114\) 0 0
\(115\) 1722.61i 0.130254i
\(116\) −2836.27 1547.96i −0.210781 0.115039i
\(117\) 0 0
\(118\) −6195.80 1580.71i −0.444973 0.113524i
\(119\) 2065.90i 0.145886i
\(120\) 0 0
\(121\) 1273.29 0.0869676
\(122\) 6013.15 23569.4i 0.404001 1.58354i
\(123\) 0 0
\(124\) 1503.43 2754.68i 0.0977779 0.179154i
\(125\) −17003.0 −1.08819
\(126\) 0 0
\(127\) 16366.5i 1.01472i 0.861733 + 0.507362i \(0.169379\pi\)
−0.861733 + 0.507362i \(0.830621\pi\)
\(128\) 16125.8 + 2897.44i 0.984239 + 0.176846i
\(129\) 0 0
\(130\) −4253.47 + 16672.1i −0.251685 + 0.986514i
\(131\) 17497.0i 1.01958i 0.860299 + 0.509790i \(0.170277\pi\)
−0.860299 + 0.509790i \(0.829723\pi\)
\(132\) 0 0
\(133\) −3331.79 −0.188354
\(134\) 28618.0 + 7301.18i 1.59378 + 0.406615i
\(135\) 0 0
\(136\) 16716.4 17965.8i 0.903786 0.971334i
\(137\) −8028.61 −0.427759 −0.213880 0.976860i \(-0.568610\pi\)
−0.213880 + 0.976860i \(0.568610\pi\)
\(138\) 0 0
\(139\) 15001.1i 0.776417i 0.921572 + 0.388208i \(0.126906\pi\)
−0.921572 + 0.388208i \(0.873094\pi\)
\(140\) 857.224 1570.66i 0.0437359 0.0801355i
\(141\) 0 0
\(142\) 36229.1 + 9242.96i 1.79672 + 0.458389i
\(143\) 23960.2i 1.17170i
\(144\) 0 0
\(145\) 4191.83 0.199374
\(146\) 5261.50 20623.2i 0.246834 0.967499i
\(147\) 0 0
\(148\) −4781.85 2609.81i −0.218310 0.119148i
\(149\) −1457.01 −0.0656279 −0.0328140 0.999461i \(-0.510447\pi\)
−0.0328140 + 0.999461i \(0.510447\pi\)
\(150\) 0 0
\(151\) 15413.9i 0.676019i −0.941143 0.338009i \(-0.890246\pi\)
0.941143 0.338009i \(-0.109754\pi\)
\(152\) 28974.5 + 26959.5i 1.25409 + 1.16688i
\(153\) 0 0
\(154\) −615.977 + 2414.41i −0.0259731 + 0.101805i
\(155\) 4071.25i 0.169459i
\(156\) 0 0
\(157\) −23328.9 −0.946443 −0.473222 0.880943i \(-0.656909\pi\)
−0.473222 + 0.880943i \(0.656909\pi\)
\(158\) −23144.3 5904.71i −0.927109 0.236529i
\(159\) 0 0
\(160\) −20163.9 + 6722.68i −0.787651 + 0.262605i
\(161\) −447.137 −0.0172500
\(162\) 0 0
\(163\) 31514.9i 1.18615i −0.805146 0.593077i \(-0.797913\pi\)
0.805146 0.593077i \(-0.202087\pi\)
\(164\) −39285.4 21441.0i −1.46064 0.797181i
\(165\) 0 0
\(166\) −39111.2 9978.26i −1.41933 0.362108i
\(167\) 45156.1i 1.61914i 0.587025 + 0.809569i \(0.300299\pi\)
−0.587025 + 0.809569i \(0.699701\pi\)
\(168\) 0 0
\(169\) 14385.0 0.503659
\(170\) −7870.02 + 30847.6i −0.272319 + 1.06739i
\(171\) 0 0
\(172\) 1952.87 3578.16i 0.0660109 0.120949i
\(173\) −39788.6 −1.32943 −0.664716 0.747096i \(-0.731447\pi\)
−0.664716 + 0.747096i \(0.731447\pi\)
\(174\) 0 0
\(175\) 1046.07i 0.0341573i
\(176\) 24893.2 16012.3i 0.803628 0.516927i
\(177\) 0 0
\(178\) 13459.5 52756.3i 0.424803 1.66508i
\(179\) 22082.3i 0.689188i −0.938752 0.344594i \(-0.888017\pi\)
0.938752 0.344594i \(-0.111983\pi\)
\(180\) 0 0
\(181\) −9867.01 −0.301181 −0.150591 0.988596i \(-0.548118\pi\)
−0.150591 + 0.988596i \(0.548118\pi\)
\(182\) −4327.57 1104.07i −0.130647 0.0333315i
\(183\) 0 0
\(184\) 3888.46 + 3618.05i 0.114853 + 0.106866i
\(185\) 7067.30 0.206495
\(186\) 0 0
\(187\) 44332.5i 1.26777i
\(188\) −17303.2 + 31704.0i −0.489566 + 0.897012i
\(189\) 0 0
\(190\) −49749.7 12692.4i −1.37811 0.351590i
\(191\) 6985.96i 0.191496i −0.995406 0.0957479i \(-0.969476\pi\)
0.995406 0.0957479i \(-0.0305243\pi\)
\(192\) 0 0
\(193\) −39647.8 −1.06440 −0.532199 0.846619i \(-0.678634\pi\)
−0.532199 + 0.846619i \(0.678634\pi\)
\(194\) −2155.19 + 8447.59i −0.0572642 + 0.224455i
\(195\) 0 0
\(196\) −33313.0 18181.4i −0.867165 0.473277i
\(197\) 25520.9 0.657602 0.328801 0.944399i \(-0.393355\pi\)
0.328801 + 0.944399i \(0.393355\pi\)
\(198\) 0 0
\(199\) 20635.7i 0.521091i 0.965462 + 0.260546i \(0.0839024\pi\)
−0.965462 + 0.260546i \(0.916098\pi\)
\(200\) −8464.36 + 9096.99i −0.211609 + 0.227425i
\(201\) 0 0
\(202\) 3206.32 12567.6i 0.0785786 0.308000i
\(203\) 1088.07i 0.0264038i
\(204\) 0 0
\(205\) 58061.5 1.38159
\(206\) −12640.5 3224.90i −0.297871 0.0759944i
\(207\) 0 0
\(208\) 28700.4 + 44618.4i 0.663378 + 1.03130i
\(209\) 71497.5 1.63681
\(210\) 0 0
\(211\) 37403.1i 0.840123i −0.907496 0.420062i \(-0.862008\pi\)
0.907496 0.420062i \(-0.137992\pi\)
\(212\) −57739.9 31513.0i −1.28471 0.701161i
\(213\) 0 0
\(214\) 61733.5 + 15749.8i 1.34801 + 0.343912i
\(215\) 5288.31i 0.114404i
\(216\) 0 0
\(217\) −1056.77 −0.0224420
\(218\) −7294.65 + 28592.4i −0.153494 + 0.601641i
\(219\) 0 0
\(220\) −18395.3 + 33705.0i −0.380069 + 0.696384i
\(221\) 79461.2 1.62694
\(222\) 0 0
\(223\) 63893.4i 1.28483i 0.766356 + 0.642416i \(0.222068\pi\)
−0.766356 + 0.642416i \(0.777932\pi\)
\(224\) −1745.00 5233.92i −0.0347777 0.104311i
\(225\) 0 0
\(226\) 7042.13 27602.6i 0.137876 0.540423i
\(227\) 52128.0i 1.01162i −0.862644 0.505812i \(-0.831193\pi\)
0.862644 0.505812i \(-0.168807\pi\)
\(228\) 0 0
\(229\) −30234.6 −0.576545 −0.288272 0.957548i \(-0.593081\pi\)
−0.288272 + 0.957548i \(0.593081\pi\)
\(230\) −6676.57 1703.36i −0.126211 0.0321997i
\(231\) 0 0
\(232\) 8804.25 9462.28i 0.163575 0.175800i
\(233\) 5080.01 0.0935735 0.0467868 0.998905i \(-0.485102\pi\)
0.0467868 + 0.998905i \(0.485102\pi\)
\(234\) 0 0
\(235\) 46856.6i 0.848468i
\(236\) 12253.2 22451.0i 0.220001 0.403098i
\(237\) 0 0
\(238\) −8007.11 2042.82i −0.141359 0.0360641i
\(239\) 40740.6i 0.713234i −0.934251 0.356617i \(-0.883930\pi\)
0.934251 0.356617i \(-0.116070\pi\)
\(240\) 0 0
\(241\) −34834.0 −0.599749 −0.299875 0.953979i \(-0.596945\pi\)
−0.299875 + 0.953979i \(0.596945\pi\)
\(242\) −1259.07 + 4935.09i −0.0214990 + 0.0842684i
\(243\) 0 0
\(244\) 85405.5 + 46612.2i 1.43452 + 0.782924i
\(245\) 49234.6 0.820236
\(246\) 0 0
\(247\) 128151.i 2.10053i
\(248\) 9190.08 + 8550.98i 0.149422 + 0.139031i
\(249\) 0 0
\(250\) 16813.1 65901.2i 0.269009 1.05442i
\(251\) 71105.6i 1.12864i −0.825555 0.564321i \(-0.809138\pi\)
0.825555 0.564321i \(-0.190862\pi\)
\(252\) 0 0
\(253\) 9595.19 0.149904
\(254\) −63434.1 16183.6i −0.983230 0.250847i
\(255\) 0 0
\(256\) −27175.6 + 59636.0i −0.414667 + 0.909973i
\(257\) −4341.02 −0.0657242 −0.0328621 0.999460i \(-0.510462\pi\)
−0.0328621 + 0.999460i \(0.510462\pi\)
\(258\) 0 0
\(259\) 1834.46i 0.0273469i
\(260\) −60412.6 32971.6i −0.893677 0.487746i
\(261\) 0 0
\(262\) −67815.8 17301.5i −0.987934 0.252047i
\(263\) 112382.i 1.62475i 0.583135 + 0.812375i \(0.301826\pi\)
−0.583135 + 0.812375i \(0.698174\pi\)
\(264\) 0 0
\(265\) 85336.1 1.21518
\(266\) 3294.57 12913.5i 0.0465624 0.182508i
\(267\) 0 0
\(268\) −56596.5 + 103699.i −0.787989 + 1.44380i
\(269\) 67178.9 0.928385 0.464193 0.885734i \(-0.346345\pi\)
0.464193 + 0.885734i \(0.346345\pi\)
\(270\) 0 0
\(271\) 30451.7i 0.414641i 0.978273 + 0.207321i \(0.0664744\pi\)
−0.978273 + 0.207321i \(0.933526\pi\)
\(272\) 53103.1 + 82555.4i 0.717765 + 1.11586i
\(273\) 0 0
\(274\) 7938.92 31117.7i 0.105745 0.414483i
\(275\) 22447.8i 0.296830i
\(276\) 0 0
\(277\) 16480.0 0.214782 0.107391 0.994217i \(-0.465750\pi\)
0.107391 + 0.994217i \(0.465750\pi\)
\(278\) −58142.2 14833.6i −0.752319 0.191936i
\(279\) 0 0
\(280\) 5239.98 + 4875.58i 0.0668365 + 0.0621885i
\(281\) 22525.2 0.285270 0.142635 0.989775i \(-0.454442\pi\)
0.142635 + 0.989775i \(0.454442\pi\)
\(282\) 0 0
\(283\) 69282.8i 0.865073i −0.901616 0.432537i \(-0.857619\pi\)
0.901616 0.432537i \(-0.142381\pi\)
\(284\) −71648.7 + 131279.i −0.888324 + 1.62764i
\(285\) 0 0
\(286\) 92866.0 + 23692.5i 1.13534 + 0.289653i
\(287\) 15071.0i 0.182969i
\(288\) 0 0
\(289\) 63502.6 0.760319
\(290\) −4145.00 + 16246.9i −0.0492866 + 0.193186i
\(291\) 0 0
\(292\) 74729.8 + 40785.6i 0.876452 + 0.478345i
\(293\) −92504.8 −1.07753 −0.538764 0.842456i \(-0.681109\pi\)
−0.538764 + 0.842456i \(0.681109\pi\)
\(294\) 0 0
\(295\) 33181.2i 0.381283i
\(296\) 14843.7 15953.1i 0.169417 0.182080i
\(297\) 0 0
\(298\) 1440.73 5647.13i 0.0162237 0.0635910i
\(299\) 17198.3i 0.192373i
\(300\) 0 0
\(301\) −1372.68 −0.0151509
\(302\) 59742.0 + 15241.7i 0.655037 + 0.167117i
\(303\) 0 0
\(304\) −133142. + 85642.3i −1.44068 + 0.926705i
\(305\) −126224. −1.35689
\(306\) 0 0
\(307\) 79741.9i 0.846077i 0.906112 + 0.423038i \(0.139036\pi\)
−0.906112 + 0.423038i \(0.860964\pi\)
\(308\) −8748.79 4774.87i −0.0922246 0.0503338i
\(309\) 0 0
\(310\) −15779.6 4025.76i −0.164199 0.0418914i
\(311\) 115631.i 1.19551i −0.801679 0.597755i \(-0.796060\pi\)
0.801679 0.597755i \(-0.203940\pi\)
\(312\) 0 0
\(313\) −25857.6 −0.263936 −0.131968 0.991254i \(-0.542130\pi\)
−0.131968 + 0.991254i \(0.542130\pi\)
\(314\) 23068.2 90419.2i 0.233967 0.917068i
\(315\) 0 0
\(316\) 45771.6 83865.3i 0.458376 0.839862i
\(317\) −78300.9 −0.779198 −0.389599 0.920985i \(-0.627386\pi\)
−0.389599 + 0.920985i \(0.627386\pi\)
\(318\) 0 0
\(319\) 23349.1i 0.229451i
\(320\) −6117.53 84799.7i −0.0597415 0.828122i
\(321\) 0 0
\(322\) 442.141 1733.04i 0.00426432 0.0167146i
\(323\) 237113.i 2.27274i
\(324\) 0 0
\(325\) −40235.2 −0.380925
\(326\) 122147. + 31162.8i 1.14934 + 0.293226i
\(327\) 0 0
\(328\) 121949. 131063.i 1.13352 1.21824i
\(329\) 12162.6 0.112366
\(330\) 0 0
\(331\) 159345.i 1.45439i −0.686429 0.727197i \(-0.740823\pi\)
0.686429 0.727197i \(-0.259177\pi\)
\(332\) 77348.5 141722.i 0.701739 1.28577i
\(333\) 0 0
\(334\) −175018. 44651.6i −1.56888 0.400262i
\(335\) 153262.i 1.36566i
\(336\) 0 0
\(337\) 32887.8 0.289584 0.144792 0.989462i \(-0.453749\pi\)
0.144792 + 0.989462i \(0.453749\pi\)
\(338\) −14224.3 + 55754.2i −0.124508 + 0.488027i
\(339\) 0 0
\(340\) −111779. 61006.0i −0.966944 0.527734i
\(341\) 22677.5 0.195023
\(342\) 0 0
\(343\) 25716.0i 0.218583i
\(344\) 11937.4 + 11107.2i 0.100877 + 0.0938616i
\(345\) 0 0
\(346\) 39344.0 154215.i 0.328645 1.28817i
\(347\) 68679.4i 0.570385i −0.958470 0.285192i \(-0.907943\pi\)
0.958470 0.285192i \(-0.0920575\pi\)
\(348\) 0 0
\(349\) −228554. −1.87645 −0.938226 0.346024i \(-0.887532\pi\)
−0.938226 + 0.346024i \(0.887532\pi\)
\(350\) 4054.40 + 1034.38i 0.0330972 + 0.00844393i
\(351\) 0 0
\(352\) 37446.4 + 112316.i 0.302221 + 0.906474i
\(353\) −46025.5 −0.369359 −0.184680 0.982799i \(-0.559125\pi\)
−0.184680 + 0.982799i \(0.559125\pi\)
\(354\) 0 0
\(355\) 194022.i 1.53956i
\(356\) 191166. + 104334.i 1.50838 + 0.823237i
\(357\) 0 0
\(358\) 85587.6 + 21835.6i 0.667797 + 0.170372i
\(359\) 131445.i 1.01990i 0.860205 + 0.509948i \(0.170335\pi\)
−0.860205 + 0.509948i \(0.829665\pi\)
\(360\) 0 0
\(361\) −252085. −1.93434
\(362\) 9756.77 38243.0i 0.0744542 0.291834i
\(363\) 0 0
\(364\) 8558.44 15681.3i 0.0645939 0.118353i
\(365\) −110446. −0.829020
\(366\) 0 0
\(367\) 120649.i 0.895756i 0.894095 + 0.447878i \(0.147820\pi\)
−0.894095 + 0.447878i \(0.852180\pi\)
\(368\) −17868.1 + 11493.5i −0.131942 + 0.0848703i
\(369\) 0 0
\(370\) −6988.34 + 27391.8i −0.0510470 + 0.200086i
\(371\) 22150.7i 0.160931i
\(372\) 0 0
\(373\) 183241. 1.31706 0.658530 0.752555i \(-0.271179\pi\)
0.658530 + 0.752555i \(0.271179\pi\)
\(374\) 171826. + 43837.2i 1.22842 + 0.313400i
\(375\) 0 0
\(376\) −105770. 98414.6i −0.748147 0.696119i
\(377\) 41850.8 0.294457
\(378\) 0 0
\(379\) 210539.i 1.46573i −0.680374 0.732865i \(-0.738183\pi\)
0.680374 0.732865i \(-0.261817\pi\)
\(380\) 98387.8 180272.i 0.681356 1.24842i
\(381\) 0 0
\(382\) 27076.5 + 6907.91i 0.185552 + 0.0473391i
\(383\) 115027.i 0.784153i −0.919933 0.392076i \(-0.871757\pi\)
0.919933 0.392076i \(-0.128243\pi\)
\(384\) 0 0
\(385\) 12930.2 0.0872336
\(386\) 39204.8 153669.i 0.263127 1.03136i
\(387\) 0 0
\(388\) −30610.5 16706.4i −0.203332 0.110974i
\(389\) −227952. −1.50641 −0.753206 0.657785i \(-0.771493\pi\)
−0.753206 + 0.657785i \(0.771493\pi\)
\(390\) 0 0
\(391\) 31821.4i 0.208145i
\(392\) 103409. 111138.i 0.672957 0.723253i
\(393\) 0 0
\(394\) −25235.8 + 98915.2i −0.162564 + 0.637192i
\(395\) 123948.i 0.794411i
\(396\) 0 0
\(397\) 253211. 1.60657 0.803287 0.595592i \(-0.203082\pi\)
0.803287 + 0.595592i \(0.203082\pi\)
\(398\) −79981.0 20405.2i −0.504918 0.128817i
\(399\) 0 0
\(400\) −26888.8 41802.0i −0.168055 0.261262i
\(401\) −113054. −0.703071 −0.351535 0.936175i \(-0.614340\pi\)
−0.351535 + 0.936175i \(0.614340\pi\)
\(402\) 0 0
\(403\) 40646.9i 0.250275i
\(404\) 45539.7 + 24854.4i 0.279015 + 0.152279i
\(405\) 0 0
\(406\) −4217.21 1075.92i −0.0255843 0.00652719i
\(407\) 39365.9i 0.237647i
\(408\) 0 0
\(409\) 77602.4 0.463905 0.231952 0.972727i \(-0.425489\pi\)
0.231952 + 0.972727i \(0.425489\pi\)
\(410\) −57412.9 + 225038.i −0.341540 + 1.33871i
\(411\) 0 0
\(412\) 24998.5 45803.6i 0.147272 0.269839i
\(413\) −8612.83 −0.0504947
\(414\) 0 0
\(415\) 209457.i 1.21618i
\(416\) −201314. + 67118.5i −1.16329 + 0.387843i
\(417\) 0 0
\(418\) −70698.7 + 277114.i −0.404631 + 1.58601i
\(419\) 46895.2i 0.267116i −0.991041 0.133558i \(-0.957360\pi\)
0.991041 0.133558i \(-0.0426403\pi\)
\(420\) 0 0
\(421\) 40148.2 0.226518 0.113259 0.993566i \(-0.463871\pi\)
0.113259 + 0.993566i \(0.463871\pi\)
\(422\) 144969. + 36985.3i 0.814048 + 0.207684i
\(423\) 0 0
\(424\) 179234. 192630.i 0.996987 1.07150i
\(425\) −74445.5 −0.412155
\(426\) 0 0
\(427\) 32764.0i 0.179697i
\(428\) −122088. + 223696.i −0.666475 + 1.22115i
\(429\) 0 0
\(430\) −20496.7 5229.22i −0.110853 0.0282814i
\(431\) 257425.i 1.38579i 0.721040 + 0.692893i \(0.243664\pi\)
−0.721040 + 0.692893i \(0.756336\pi\)
\(432\) 0 0
\(433\) −29760.6 −0.158732 −0.0793661 0.996846i \(-0.525290\pi\)
−0.0793661 + 0.996846i \(0.525290\pi\)
\(434\) 1044.97 4095.89i 0.00554783 0.0217455i
\(435\) 0 0
\(436\) −103607. 56545.9i −0.545023 0.297460i
\(437\) −51320.1 −0.268735
\(438\) 0 0
\(439\) 249198.i 1.29305i 0.762892 + 0.646526i \(0.223779\pi\)
−0.762892 + 0.646526i \(0.776221\pi\)
\(440\) −112446. 104626.i −0.580815 0.540424i
\(441\) 0 0
\(442\) −78573.4 + 307980.i −0.402190 + 1.57644i
\(443\) 53833.8i 0.274314i −0.990549 0.137157i \(-0.956204\pi\)
0.990549 0.137157i \(-0.0437964\pi\)
\(444\) 0 0
\(445\) −282533. −1.42675
\(446\) −247641. 63179.6i −1.24495 0.317619i
\(447\) 0 0
\(448\) 22011.4 1587.92i 0.109671 0.00791177i
\(449\) 127961. 0.634726 0.317363 0.948304i \(-0.397203\pi\)
0.317363 + 0.948304i \(0.397203\pi\)
\(450\) 0 0
\(451\) 323412.i 1.59002i
\(452\) 100020. + 54588.5i 0.489566 + 0.267192i
\(453\) 0 0
\(454\) 202040. + 51545.6i 0.980227 + 0.250081i
\(455\) 23176.0i 0.111948i
\(456\) 0 0
\(457\) 138874. 0.664951 0.332475 0.943112i \(-0.392116\pi\)
0.332475 + 0.943112i \(0.392116\pi\)
\(458\) 29896.8 117185.i 0.142526 0.558650i
\(459\) 0 0
\(460\) 13204.0 24193.1i 0.0624006 0.114334i
\(461\) 242960. 1.14323 0.571613 0.820523i \(-0.306318\pi\)
0.571613 + 0.820523i \(0.306318\pi\)
\(462\) 0 0
\(463\) 277264.i 1.29340i 0.762746 + 0.646699i \(0.223851\pi\)
−0.762746 + 0.646699i \(0.776149\pi\)
\(464\) 27968.5 + 43480.5i 0.129907 + 0.201957i
\(465\) 0 0
\(466\) −5023.26 + 19689.4i −0.0231320 + 0.0906692i
\(467\) 123580.i 0.566649i 0.959024 + 0.283325i \(0.0914374\pi\)
−0.959024 + 0.283325i \(0.908563\pi\)
\(468\) 0 0
\(469\) 39782.1 0.180860
\(470\) 181609. + 46333.1i 0.822133 + 0.209747i
\(471\) 0 0
\(472\) 74900.3 + 69691.6i 0.336202 + 0.312821i
\(473\) 29456.7 0.131662
\(474\) 0 0
\(475\) 120062.i 0.532132i
\(476\) 15835.3 29014.4i 0.0698896 0.128056i
\(477\) 0 0
\(478\) 157905. + 40285.5i 0.691097 + 0.176316i
\(479\) 56214.6i 0.245007i −0.992468 0.122503i \(-0.960908\pi\)
0.992468 0.122503i \(-0.0390922\pi\)
\(480\) 0 0
\(481\) 70559.1 0.304974
\(482\) 34444.9 135011.i 0.148262 0.581134i
\(483\) 0 0
\(484\) −17882.7 9759.92i −0.0763382 0.0416635i
\(485\) 45240.5 0.192328
\(486\) 0 0
\(487\) 271980.i 1.14678i 0.819283 + 0.573389i \(0.194372\pi\)
−0.819283 + 0.573389i \(0.805628\pi\)
\(488\) −265113. + 284928.i −1.11325 + 1.19645i
\(489\) 0 0
\(490\) −48684.6 + 190826.i −0.202768 + 0.794778i
\(491\) 335208.i 1.39044i −0.718798 0.695219i \(-0.755307\pi\)
0.718798 0.695219i \(-0.244693\pi\)
\(492\) 0 0
\(493\) 77434.8 0.318597
\(494\) −496696. 126720.i −2.03534 0.519267i
\(495\) 0 0
\(496\) −42229.7 + 27163.9i −0.171654 + 0.110415i
\(497\) 50362.3 0.203889
\(498\) 0 0
\(499\) 287692.i 1.15538i 0.816255 + 0.577692i \(0.196047\pi\)
−0.816255 + 0.577692i \(0.803953\pi\)
\(500\) 238798. + 130330.i 0.955193 + 0.521320i
\(501\) 0 0
\(502\) 275595. + 70311.2i 1.09361 + 0.279008i
\(503\) 338788.i 1.33903i −0.742797 0.669517i \(-0.766501\pi\)
0.742797 0.669517i \(-0.233499\pi\)
\(504\) 0 0
\(505\) −67305.0 −0.263915
\(506\) −9487.99 + 37189.5i −0.0370572 + 0.145251i
\(507\) 0 0
\(508\) 125451. 229858.i 0.486123 0.890702i
\(509\) 444920. 1.71730 0.858651 0.512561i \(-0.171303\pi\)
0.858651 + 0.512561i \(0.171303\pi\)
\(510\) 0 0
\(511\) 28668.5i 0.109790i
\(512\) −204268. 164298.i −0.779221 0.626749i
\(513\) 0 0
\(514\) 4292.52 16825.1i 0.0162475 0.0636843i
\(515\) 67695.1i 0.255236i
\(516\) 0 0
\(517\) −260999. −0.976466
\(518\) −7110.08 1813.96i −0.0264981 0.00676034i
\(519\) 0 0
\(520\) 187531. 201547.i 0.693531 0.745365i
\(521\) 275911. 1.01647 0.508233 0.861220i \(-0.330299\pi\)
0.508233 + 0.861220i \(0.330299\pi\)
\(522\) 0 0
\(523\) 85712.3i 0.313357i 0.987650 + 0.156679i \(0.0500787\pi\)
−0.987650 + 0.156679i \(0.949921\pi\)
\(524\) 134116. 245736.i 0.488448 0.894964i
\(525\) 0 0
\(526\) −435577. 111127.i −1.57432 0.401650i
\(527\) 75207.3i 0.270794i
\(528\) 0 0
\(529\) 272954. 0.975388
\(530\) −84382.7 + 330750.i −0.300401 + 1.17747i
\(531\) 0 0
\(532\) 46793.1 + 25538.5i 0.165333 + 0.0902344i
\(533\) 579680. 2.04049
\(534\) 0 0
\(535\) 330610.i 1.15507i
\(536\) −345959. 321901.i −1.20419 1.12045i
\(537\) 0 0
\(538\) −66428.4 + 260375.i −0.229503 + 0.899571i
\(539\) 274244.i 0.943975i
\(540\) 0 0
\(541\) 250046. 0.854331 0.427165 0.904174i \(-0.359512\pi\)
0.427165 + 0.904174i \(0.359512\pi\)
\(542\) −118026. 30111.5i −0.401772 0.102502i
\(543\) 0 0
\(544\) −372482. + 124187.i −1.25866 + 0.419640i
\(545\) 153125. 0.515528
\(546\) 0 0
\(547\) 435437.i 1.45529i −0.685951 0.727647i \(-0.740614\pi\)
0.685951 0.727647i \(-0.259386\pi\)
\(548\) 112757. + 61540.1i 0.375477 + 0.204926i
\(549\) 0 0
\(550\) −87004.2 22197.0i −0.287617 0.0733784i
\(551\) 124883.i 0.411341i
\(552\) 0 0
\(553\) −32173.1 −0.105207
\(554\) −16295.9 + 63874.2i −0.0530957 + 0.208116i
\(555\) 0 0
\(556\) 114985. 210683.i 0.371957 0.681521i
\(557\) −466836. −1.50471 −0.752356 0.658756i \(-0.771083\pi\)
−0.752356 + 0.658756i \(0.771083\pi\)
\(558\) 0 0
\(559\) 52797.9i 0.168964i
\(560\) −24078.5 + 15488.3i −0.0767808 + 0.0493886i
\(561\) 0 0
\(562\) −22273.6 + 87304.4i −0.0705208 + 0.276416i
\(563\) 75191.2i 0.237219i 0.992941 + 0.118610i \(0.0378437\pi\)
−0.992941 + 0.118610i \(0.962156\pi\)
\(564\) 0 0
\(565\) −147824. −0.463071
\(566\) 268530. + 68508.8i 0.838224 + 0.213852i
\(567\) 0 0
\(568\) −437969. 407512.i −1.35752 1.26312i
\(569\) −66289.8 −0.204749 −0.102375 0.994746i \(-0.532644\pi\)
−0.102375 + 0.994746i \(0.532644\pi\)
\(570\) 0 0
\(571\) 377844.i 1.15888i −0.815014 0.579442i \(-0.803271\pi\)
0.815014 0.579442i \(-0.196729\pi\)
\(572\) −183657. + 336507.i −0.561327 + 1.02850i
\(573\) 0 0
\(574\) −58413.0 14902.6i −0.177291 0.0452313i
\(575\) 16112.8i 0.0487342i
\(576\) 0 0
\(577\) −415556. −1.24818 −0.624091 0.781352i \(-0.714530\pi\)
−0.624091 + 0.781352i \(0.714530\pi\)
\(578\) −62793.2 + 246127.i −0.187956 + 0.736721i
\(579\) 0 0
\(580\) −58872.0 32130.8i −0.175006 0.0955137i
\(581\) −54368.7 −0.161063
\(582\) 0 0
\(583\) 475335.i 1.39850i
\(584\) −231974. + 249311.i −0.680163 + 0.730999i
\(585\) 0 0
\(586\) 91471.3 358535.i 0.266373 1.04409i
\(587\) 342605.i 0.994301i 0.867664 + 0.497151i \(0.165620\pi\)
−0.867664 + 0.497151i \(0.834380\pi\)
\(588\) 0 0
\(589\) −121291. −0.349621
\(590\) −128605. 32810.5i −0.369449 0.0942559i
\(591\) 0 0
\(592\) 47154.0 + 73306.8i 0.134547 + 0.209171i
\(593\) 125568. 0.357082 0.178541 0.983932i \(-0.442862\pi\)
0.178541 + 0.983932i \(0.442862\pi\)
\(594\) 0 0
\(595\) 42881.5i 0.121126i
\(596\) 20462.8 + 11168.1i 0.0576067 + 0.0314403i
\(597\) 0 0
\(598\) −66658.2 17006.2i −0.186402 0.0475559i
\(599\) 317723.i 0.885512i 0.896642 + 0.442756i \(0.145999\pi\)
−0.896642 + 0.442756i \(0.854001\pi\)
\(600\) 0 0
\(601\) −168972. −0.467806 −0.233903 0.972260i \(-0.575150\pi\)
−0.233903 + 0.972260i \(0.575150\pi\)
\(602\) 1357.35 5320.32i 0.00374540 0.0146806i
\(603\) 0 0
\(604\) −118149. + 216480.i −0.323859 + 0.593394i
\(605\) 26429.5 0.0722070
\(606\) 0 0
\(607\) 644373.i 1.74888i 0.485135 + 0.874440i \(0.338771\pi\)
−0.485135 + 0.874440i \(0.661229\pi\)
\(608\) −200283. 600723.i −0.541796 1.62505i
\(609\) 0 0
\(610\) 124814. 489227.i 0.335432 1.31477i
\(611\) 467812.i 1.25311i
\(612\) 0 0
\(613\) 228892. 0.609129 0.304564 0.952492i \(-0.401489\pi\)
0.304564 + 0.952492i \(0.401489\pi\)
\(614\) −309068. 78851.0i −0.819817 0.209156i
\(615\) 0 0
\(616\) 27157.7 29187.5i 0.0715702 0.0769193i
\(617\) −329605. −0.865813 −0.432906 0.901439i \(-0.642512\pi\)
−0.432906 + 0.901439i \(0.642512\pi\)
\(618\) 0 0
\(619\) 223932.i 0.584434i 0.956352 + 0.292217i \(0.0943930\pi\)
−0.956352 + 0.292217i \(0.905607\pi\)
\(620\) 31206.5 57178.4i 0.0811824 0.148747i
\(621\) 0 0
\(622\) 448168. + 114339.i 1.15840 + 0.295538i
\(623\) 73336.9i 0.188950i
\(624\) 0 0
\(625\) −231584. −0.592854
\(626\) 25568.7 100220.i 0.0652468 0.255744i
\(627\) 0 0
\(628\) 327641. + 178818.i 0.830766 + 0.453411i
\(629\) 130553. 0.329977
\(630\) 0 0
\(631\) 681430.i 1.71144i −0.517437 0.855721i \(-0.673114\pi\)
0.517437 0.855721i \(-0.326886\pi\)
\(632\) 279789. + 260332.i 0.700482 + 0.651769i
\(633\) 0 0
\(634\) 77426.1 303482.i 0.192623 0.755014i
\(635\) 339717.i 0.842499i
\(636\) 0 0
\(637\) 491554. 1.21141
\(638\) 90497.8 + 23088.3i 0.222329 + 0.0567219i
\(639\) 0 0
\(640\) 334720. + 60141.7i 0.817188 + 0.146830i
\(641\) −346761. −0.843945 −0.421973 0.906609i \(-0.638662\pi\)
−0.421973 + 0.906609i \(0.638662\pi\)
\(642\) 0 0
\(643\) 124932.i 0.302169i 0.988521 + 0.151085i \(0.0482766\pi\)
−0.988521 + 0.151085i \(0.951723\pi\)
\(644\) 6279.78 + 3427.35i 0.0151416 + 0.00826392i
\(645\) 0 0
\(646\) −919015. 234464.i −2.20221 0.561838i
\(647\) 43450.9i 0.103798i −0.998652 0.0518992i \(-0.983473\pi\)
0.998652 0.0518992i \(-0.0165274\pi\)
\(648\) 0 0
\(649\) 184824. 0.438803
\(650\) 39785.7 155946.i 0.0941673 0.369102i
\(651\) 0 0
\(652\) −241565. + 442609.i −0.568249 + 1.04118i
\(653\) −344790. −0.808589 −0.404294 0.914629i \(-0.632483\pi\)
−0.404294 + 0.914629i \(0.632483\pi\)
\(654\) 0 0
\(655\) 363183.i 0.846530i
\(656\) 387394. + 602253.i 0.900214 + 1.39950i
\(657\) 0 0
\(658\) −12026.7 + 47140.3i −0.0277775 + 0.108878i
\(659\) 670185.i 1.54321i −0.636105 0.771603i \(-0.719455\pi\)
0.636105 0.771603i \(-0.280545\pi\)
\(660\) 0 0
\(661\) −619584. −1.41807 −0.709034 0.705174i \(-0.750869\pi\)
−0.709034 + 0.705174i \(0.750869\pi\)
\(662\) 617597. + 157565.i 1.40925 + 0.359536i
\(663\) 0 0
\(664\) 472810. + 439930.i 1.07239 + 0.997809i
\(665\) −69157.4 −0.156385
\(666\) 0 0
\(667\) 16759.8i 0.0376718i
\(668\) 346126. 634193.i 0.775678 1.42124i
\(669\) 0 0
\(670\) 594019. + 151549.i 1.32328 + 0.337602i
\(671\) 703088.i 1.56158i
\(672\) 0 0
\(673\) −233848. −0.516302 −0.258151 0.966105i \(-0.583113\pi\)
−0.258151 + 0.966105i \(0.583113\pi\)
\(674\) −32520.3 + 127468.i −0.0715872 + 0.280596i
\(675\) 0 0
\(676\) −202029. 110263.i −0.442101 0.241287i
\(677\) −703621. −1.53519 −0.767594 0.640936i \(-0.778546\pi\)
−0.767594 + 0.640936i \(0.778546\pi\)
\(678\) 0 0
\(679\) 11743.0i 0.0254707i
\(680\) 346980. 372913.i 0.750390 0.806474i
\(681\) 0 0
\(682\) −22424.1 + 87894.5i −0.0482111 + 0.188970i
\(683\) 8903.15i 0.0190855i 0.999954 + 0.00954273i \(0.00303759\pi\)
−0.999954 + 0.00954273i \(0.996962\pi\)
\(684\) 0 0
\(685\) −166649. −0.355157
\(686\) −99671.5 25428.7i −0.211799 0.0540352i
\(687\) 0 0
\(688\) −54853.9 + 35284.3i −0.115886 + 0.0745426i
\(689\) 851987. 1.79471
\(690\) 0 0
\(691\) 186507.i 0.390606i 0.980743 + 0.195303i \(0.0625690\pi\)
−0.980743 + 0.195303i \(0.937431\pi\)
\(692\) 558808. + 304983.i 1.16694 + 0.636889i
\(693\) 0 0
\(694\) 266191. + 67912.1i 0.552681 + 0.141003i
\(695\) 311376.i 0.644638i
\(696\) 0 0
\(697\) 1.07256e6 2.20778
\(698\) 226000. 885840.i 0.463872 1.81821i
\(699\) 0 0
\(700\) −8018.21 + 14691.4i −0.0163637 + 0.0299825i
\(701\) −498328. −1.01410 −0.507048 0.861918i \(-0.669264\pi\)
−0.507048 + 0.861918i \(0.669264\pi\)
\(702\) 0 0
\(703\) 210549.i 0.426033i
\(704\) −472347. + 34075.5i −0.953051 + 0.0687539i
\(705\) 0 0
\(706\) 45511.3 178388.i 0.0913082 0.357895i
\(707\) 17470.3i 0.0349512i
\(708\) 0 0
\(709\) 84448.4 0.167996 0.0839980 0.996466i \(-0.473231\pi\)
0.0839980 + 0.996466i \(0.473231\pi\)
\(710\) 752002. + 191855.i 1.49177 + 0.380589i
\(711\) 0 0
\(712\) −593413. + 637764.i −1.17057 + 1.25806i
\(713\) −16277.6 −0.0320193
\(714\) 0 0
\(715\) 497338.i 0.972835i
\(716\) −169263. + 310133.i −0.330168 + 0.604954i
\(717\) 0 0
\(718\) −509462. 129977.i −0.988241 0.252125i
\(719\) 563153.i 1.08935i −0.838646 0.544677i \(-0.816652\pi\)
0.838646 0.544677i \(-0.183348\pi\)
\(720\) 0 0
\(721\) −17571.6 −0.0338018
\(722\) 249268. 977043.i 0.478182 1.87430i
\(723\) 0 0
\(724\) 138577. + 75631.6i 0.264370 + 0.144287i
\(725\) −39209.1 −0.0745953
\(726\) 0 0
\(727\) 829063.i 1.56862i 0.620367 + 0.784312i \(0.286984\pi\)
−0.620367 + 0.784312i \(0.713016\pi\)
\(728\) 52315.4 + 48677.3i 0.0987113 + 0.0918467i
\(729\) 0 0
\(730\) 109212. 428073.i 0.204939 0.803289i
\(731\) 97689.7i 0.182816i
\(732\) 0 0
\(733\) 345658. 0.643338 0.321669 0.946852i \(-0.395756\pi\)
0.321669 + 0.946852i \(0.395756\pi\)
\(734\) −467616. 119301.i −0.867954 0.221437i
\(735\) 0 0
\(736\) −26878.6 80619.0i −0.0496193 0.148827i
\(737\) −853691. −1.57169
\(738\) 0 0
\(739\) 662859.i 1.21376i 0.794794 + 0.606879i \(0.207579\pi\)
−0.794794 + 0.606879i \(0.792421\pi\)
\(740\) −99256.2 54171.5i −0.181257 0.0989253i
\(741\) 0 0
\(742\) −85852.7 21903.2i −0.155936 0.0397832i
\(743\) 346708.i 0.628039i −0.949417 0.314019i \(-0.898324\pi\)
0.949417 0.314019i \(-0.101676\pi\)
\(744\) 0 0
\(745\) −30242.8 −0.0544891
\(746\) −181194. + 710216.i −0.325586 + 1.27618i
\(747\) 0 0
\(748\) −339813. + 622625.i −0.607347 + 1.11282i
\(749\) 85816.2 0.152970
\(750\) 0 0
\(751\) 218129.i 0.386752i −0.981125 0.193376i \(-0.938056\pi\)
0.981125 0.193376i \(-0.0619438\pi\)
\(752\) 486028. 312634.i 0.859461 0.552841i
\(753\) 0 0
\(754\) −41383.3 + 162208.i −0.0727917 + 0.285318i
\(755\) 319944.i 0.561281i
\(756\) 0 0
\(757\) 454177. 0.792563 0.396281 0.918129i \(-0.370300\pi\)
0.396281 + 0.918129i \(0.370300\pi\)
\(758\) 816017. + 208187.i 1.42024 + 0.362339i
\(759\) 0 0
\(760\) 601418. + 559594.i 1.04124 + 0.968827i
\(761\) −779754. −1.34644 −0.673222 0.739441i \(-0.735090\pi\)
−0.673222 + 0.739441i \(0.735090\pi\)
\(762\) 0 0
\(763\) 39746.5i 0.0682731i
\(764\) −53548.1 + 98113.9i −0.0917396 + 0.168091i
\(765\) 0 0
\(766\) 445826. + 113742.i 0.759815 + 0.193848i
\(767\) 331278.i 0.563120i
\(768\) 0 0
\(769\) 1.04561e6 1.76814 0.884072 0.467350i \(-0.154791\pi\)
0.884072 + 0.467350i \(0.154791\pi\)
\(770\) −12785.7 + 50115.5i −0.0215647 + 0.0845261i
\(771\) 0 0
\(772\) 556831. + 303904.i 0.934305 + 0.509920i
\(773\) 240697. 0.402820 0.201410 0.979507i \(-0.435448\pi\)
0.201410 + 0.979507i \(0.435448\pi\)
\(774\) 0 0
\(775\) 38081.2i 0.0634027i
\(776\) 95020.1 102122.i 0.157795 0.169588i
\(777\) 0 0
\(778\) 225405. 883506.i 0.372395 1.45966i
\(779\) 1.72977e6i 2.85046i
\(780\) 0 0
\(781\) −1.08073e6 −1.77181
\(782\) −123335. 31465.8i −0.201684 0.0514548i
\(783\) 0 0
\(784\) 328500. + 510695.i 0.534446 + 0.830863i
\(785\) −484234. −0.785807
\(786\) 0 0
\(787\) 453844.i 0.732753i 0.930467 + 0.366376i \(0.119402\pi\)
−0.930467 + 0.366376i \(0.880598\pi\)