Properties

Label 128.5.f.a.31.6
Level 128
Weight 5
Character 128.31
Analytic conductor 13.231
Analytic rank 0
Dimension 14
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.6
Root \(2.24452 - 1.72109i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.a.95.6

$q$-expansion

\(f(q)\) \(=\) \(q+(5.54016 + 5.54016i) q^{3} +(-21.7374 - 21.7374i) q^{5} +6.62054 q^{7} -19.6133i q^{9} +O(q^{10})\) \(q+(5.54016 + 5.54016i) q^{3} +(-21.7374 - 21.7374i) q^{5} +6.62054 q^{7} -19.6133i q^{9} +(-90.9986 + 90.9986i) q^{11} +(-221.402 + 221.402i) q^{13} -240.857i q^{15} -132.575 q^{17} +(-402.520 - 402.520i) q^{19} +(36.6788 + 36.6788i) q^{21} -27.5037 q^{23} +320.028i q^{25} +(557.414 - 557.414i) q^{27} +(-174.909 + 174.909i) q^{29} -1083.96i q^{31} -1008.29 q^{33} +(-143.913 - 143.913i) q^{35} +(-553.474 - 553.474i) q^{37} -2453.20 q^{39} +1803.47i q^{41} +(17.8633 - 17.8633i) q^{43} +(-426.342 + 426.342i) q^{45} +2268.26i q^{47} -2357.17 q^{49} +(-734.489 - 734.489i) q^{51} +(822.415 + 822.415i) q^{53} +3956.14 q^{55} -4460.05i q^{57} +(-972.483 + 972.483i) q^{59} +(2056.32 - 2056.32i) q^{61} -129.851i q^{63} +9625.38 q^{65} +(4611.22 + 4611.22i) q^{67} +(-152.375 - 152.375i) q^{69} +3105.84 q^{71} -723.400i q^{73} +(-1773.00 + 1773.00i) q^{75} +(-602.460 + 602.460i) q^{77} -3418.44i q^{79} +4587.64 q^{81} +(-161.591 - 161.591i) q^{83} +(2881.84 + 2881.84i) q^{85} -1938.05 q^{87} +1464.04i q^{89} +(-1465.80 + 1465.80i) q^{91} +(6005.32 - 6005.32i) q^{93} +17499.5i q^{95} -8264.99 q^{97} +(1784.78 + 1784.78i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + 94q^{11} + 2q^{13} - 4q^{17} - 706q^{19} + 164q^{21} - 1148q^{23} - 1664q^{27} - 862q^{29} - 4q^{33} + 1340q^{35} + 1826q^{37} - 2684q^{39} + 1694q^{43} - 1410q^{45} + 682q^{49} - 3012q^{51} + 482q^{53} + 11780q^{55} - 2786q^{59} + 3778q^{61} - 2020q^{65} + 7998q^{67} - 9628q^{69} - 19964q^{71} + 17570q^{75} + 9508q^{77} + 1454q^{81} - 17282q^{83} - 9948q^{85} + 49284q^{87} - 28036q^{91} - 8896q^{93} - 4q^{97} + 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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 0
\(3\) 5.54016 + 5.54016i 0.615573 + 0.615573i 0.944393 0.328820i \(-0.106651\pi\)
−0.328820 + 0.944393i \(0.606651\pi\)
\(4\) 0 0
\(5\) −21.7374 21.7374i −0.869495 0.869495i 0.122921 0.992416i \(-0.460774\pi\)
−0.992416 + 0.122921i \(0.960774\pi\)
\(6\) 0 0
\(7\) 6.62054 0.135113 0.0675565 0.997715i \(-0.478480\pi\)
0.0675565 + 0.997715i \(0.478480\pi\)
\(8\) 0 0
\(9\) 19.6133i 0.242140i
\(10\) 0 0
\(11\) −90.9986 + 90.9986i −0.752054 + 0.752054i −0.974862 0.222808i \(-0.928478\pi\)
0.222808 + 0.974862i \(0.428478\pi\)
\(12\) 0 0
\(13\) −221.402 + 221.402i −1.31007 + 1.31007i −0.388707 + 0.921362i \(0.627078\pi\)
−0.921362 + 0.388707i \(0.872922\pi\)
\(14\) 0 0
\(15\) 240.857i 1.07048i
\(16\) 0 0
\(17\) −132.575 −0.458738 −0.229369 0.973339i \(-0.573666\pi\)
−0.229369 + 0.973339i \(0.573666\pi\)
\(18\) 0 0
\(19\) −402.520 402.520i −1.11501 1.11501i −0.992462 0.122552i \(-0.960892\pi\)
−0.122552 0.992462i \(-0.539108\pi\)
\(20\) 0 0
\(21\) 36.6788 + 36.6788i 0.0831720 + 0.0831720i
\(22\) 0 0
\(23\) −27.5037 −0.0519918 −0.0259959 0.999662i \(-0.508276\pi\)
−0.0259959 + 0.999662i \(0.508276\pi\)
\(24\) 0 0
\(25\) 320.028i 0.512044i
\(26\) 0 0
\(27\) 557.414 557.414i 0.764628 0.764628i
\(28\) 0 0
\(29\) −174.909 + 174.909i −0.207978 + 0.207978i −0.803407 0.595430i \(-0.796982\pi\)
0.595430 + 0.803407i \(0.296982\pi\)
\(30\) 0 0
\(31\) 1083.96i 1.12795i −0.825791 0.563976i \(-0.809271\pi\)
0.825791 0.563976i \(-0.190729\pi\)
\(32\) 0 0
\(33\) −1008.29 −0.925888
\(34\) 0 0
\(35\) −143.913 143.913i −0.117480 0.117480i
\(36\) 0 0
\(37\) −553.474 553.474i −0.404291 0.404291i 0.475451 0.879742i \(-0.342285\pi\)
−0.879742 + 0.475451i \(0.842285\pi\)
\(38\) 0 0
\(39\) −2453.20 −1.61289
\(40\) 0 0
\(41\) 1803.47i 1.07285i 0.843947 + 0.536427i \(0.180226\pi\)
−0.843947 + 0.536427i \(0.819774\pi\)
\(42\) 0 0
\(43\) 17.8633 17.8633i 0.00966108 0.00966108i −0.702260 0.711921i \(-0.747825\pi\)
0.711921 + 0.702260i \(0.247825\pi\)
\(44\) 0 0
\(45\) −426.342 + 426.342i −0.210539 + 0.210539i
\(46\) 0 0
\(47\) 2268.26i 1.02683i 0.858141 + 0.513414i \(0.171620\pi\)
−0.858141 + 0.513414i \(0.828380\pi\)
\(48\) 0 0
\(49\) −2357.17 −0.981744
\(50\) 0 0
\(51\) −734.489 734.489i −0.282387 0.282387i
\(52\) 0 0
\(53\) 822.415 + 822.415i 0.292779 + 0.292779i 0.838177 0.545398i \(-0.183622\pi\)
−0.545398 + 0.838177i \(0.683622\pi\)
\(54\) 0 0
\(55\) 3956.14 1.30782
\(56\) 0 0
\(57\) 4460.05i 1.37275i
\(58\) 0 0
\(59\) −972.483 + 972.483i −0.279369 + 0.279369i −0.832857 0.553488i \(-0.813296\pi\)
0.553488 + 0.832857i \(0.313296\pi\)
\(60\) 0 0
\(61\) 2056.32 2056.32i 0.552626 0.552626i −0.374572 0.927198i \(-0.622210\pi\)
0.927198 + 0.374572i \(0.122210\pi\)
\(62\) 0 0
\(63\) 129.851i 0.0327163i
\(64\) 0 0
\(65\) 9625.38 2.27820
\(66\) 0 0
\(67\) 4611.22 + 4611.22i 1.02723 + 1.02723i 0.999619 + 0.0276077i \(0.00878893\pi\)
0.0276077 + 0.999619i \(0.491211\pi\)
\(68\) 0 0
\(69\) −152.375 152.375i −0.0320048 0.0320048i
\(70\) 0 0
\(71\) 3105.84 0.616115 0.308058 0.951368i \(-0.400321\pi\)
0.308058 + 0.951368i \(0.400321\pi\)
\(72\) 0 0
\(73\) 723.400i 0.135748i −0.997694 0.0678739i \(-0.978378\pi\)
0.997694 0.0678739i \(-0.0216216\pi\)
\(74\) 0 0
\(75\) −1773.00 + 1773.00i −0.315200 + 0.315200i
\(76\) 0 0
\(77\) −602.460 + 602.460i −0.101612 + 0.101612i
\(78\) 0 0
\(79\) 3418.44i 0.547739i −0.961767 0.273869i \(-0.911696\pi\)
0.961767 0.273869i \(-0.0883036\pi\)
\(80\) 0 0
\(81\) 4587.64 0.699228
\(82\) 0 0
\(83\) −161.591 161.591i −0.0234563 0.0234563i 0.695281 0.718738i \(-0.255280\pi\)
−0.718738 + 0.695281i \(0.755280\pi\)
\(84\) 0 0
\(85\) 2881.84 + 2881.84i 0.398871 + 0.398871i
\(86\) 0 0
\(87\) −1938.05 −0.256051
\(88\) 0 0
\(89\) 1464.04i 0.184830i 0.995721 + 0.0924150i \(0.0294586\pi\)
−0.995721 + 0.0924150i \(0.970541\pi\)
\(90\) 0 0
\(91\) −1465.80 + 1465.80i −0.177007 + 0.177007i
\(92\) 0 0
\(93\) 6005.32 6005.32i 0.694337 0.694337i
\(94\) 0 0
\(95\) 17499.5i 1.93900i
\(96\) 0 0
\(97\) −8264.99 −0.878413 −0.439207 0.898386i \(-0.644740\pi\)
−0.439207 + 0.898386i \(0.644740\pi\)
\(98\) 0 0
\(99\) 1784.78 + 1784.78i 0.182102 + 0.182102i
\(100\) 0 0
\(101\) −5035.04 5035.04i −0.493583 0.493583i 0.415850 0.909433i \(-0.363484\pi\)
−0.909433 + 0.415850i \(0.863484\pi\)
\(102\) 0 0
\(103\) −1427.24 −0.134531 −0.0672653 0.997735i \(-0.521427\pi\)
−0.0672653 + 0.997735i \(0.521427\pi\)
\(104\) 0 0
\(105\) 1594.60i 0.144635i
\(106\) 0 0
\(107\) 9978.53 9978.53i 0.871564 0.871564i −0.121079 0.992643i \(-0.538635\pi\)
0.992643 + 0.121079i \(0.0386355\pi\)
\(108\) 0 0
\(109\) −9.47842 + 9.47842i −0.000797780 + 0.000797780i −0.707506 0.706708i \(-0.750180\pi\)
0.706708 + 0.707506i \(0.250180\pi\)
\(110\) 0 0
\(111\) 6132.67i 0.497741i
\(112\) 0 0
\(113\) −13634.7 −1.06780 −0.533900 0.845548i \(-0.679274\pi\)
−0.533900 + 0.845548i \(0.679274\pi\)
\(114\) 0 0
\(115\) 597.858 + 597.858i 0.0452067 + 0.0452067i
\(116\) 0 0
\(117\) 4342.42 + 4342.42i 0.317220 + 0.317220i
\(118\) 0 0
\(119\) −877.721 −0.0619816
\(120\) 0 0
\(121\) 1920.47i 0.131171i
\(122\) 0 0
\(123\) −9991.49 + 9991.49i −0.660419 + 0.660419i
\(124\) 0 0
\(125\) −6629.30 + 6629.30i −0.424275 + 0.424275i
\(126\) 0 0
\(127\) 8047.14i 0.498923i −0.968385 0.249462i \(-0.919746\pi\)
0.968385 0.249462i \(-0.0802537\pi\)
\(128\) 0 0
\(129\) 197.931 0.0118942
\(130\) 0 0
\(131\) −15904.8 15904.8i −0.926799 0.926799i 0.0706991 0.997498i \(-0.477477\pi\)
−0.997498 + 0.0706991i \(0.977477\pi\)
\(132\) 0 0
\(133\) −2664.90 2664.90i −0.150653 0.150653i
\(134\) 0 0
\(135\) −24233.4 −1.32968
\(136\) 0 0
\(137\) 31169.3i 1.66068i 0.557257 + 0.830340i \(0.311854\pi\)
−0.557257 + 0.830340i \(0.688146\pi\)
\(138\) 0 0
\(139\) 21432.1 21432.1i 1.10926 1.10926i 0.116017 0.993247i \(-0.462987\pi\)
0.993247 0.116017i \(-0.0370126\pi\)
\(140\) 0 0
\(141\) −12566.5 + 12566.5i −0.632088 + 0.632088i
\(142\) 0 0
\(143\) 40294.4i 1.97048i
\(144\) 0 0
\(145\) 7604.14 0.361671
\(146\) 0 0
\(147\) −13059.1 13059.1i −0.604335 0.604335i
\(148\) 0 0
\(149\) −11772.7 11772.7i −0.530276 0.530276i 0.390378 0.920654i \(-0.372344\pi\)
−0.920654 + 0.390378i \(0.872344\pi\)
\(150\) 0 0
\(151\) 19454.9 0.853246 0.426623 0.904429i \(-0.359703\pi\)
0.426623 + 0.904429i \(0.359703\pi\)
\(152\) 0 0
\(153\) 2600.25i 0.111079i
\(154\) 0 0
\(155\) −23562.5 + 23562.5i −0.980749 + 0.980749i
\(156\) 0 0
\(157\) −18097.5 + 18097.5i −0.734208 + 0.734208i −0.971450 0.237242i \(-0.923756\pi\)
0.237242 + 0.971450i \(0.423756\pi\)
\(158\) 0 0
\(159\) 9112.62i 0.360453i
\(160\) 0 0
\(161\) −182.089 −0.00702478
\(162\) 0 0
\(163\) 17673.1 + 17673.1i 0.665178 + 0.665178i 0.956596 0.291418i \(-0.0941270\pi\)
−0.291418 + 0.956596i \(0.594127\pi\)
\(164\) 0 0
\(165\) 21917.6 + 21917.6i 0.805056 + 0.805056i
\(166\) 0 0
\(167\) 11374.1 0.407834 0.203917 0.978988i \(-0.434633\pi\)
0.203917 + 0.978988i \(0.434633\pi\)
\(168\) 0 0
\(169\) 69476.3i 2.43256i
\(170\) 0 0
\(171\) −7894.76 + 7894.76i −0.269989 + 0.269989i
\(172\) 0 0
\(173\) 11289.3 11289.3i 0.377204 0.377204i −0.492888 0.870092i \(-0.664059\pi\)
0.870092 + 0.492888i \(0.164059\pi\)
\(174\) 0 0
\(175\) 2118.76i 0.0691838i
\(176\) 0 0
\(177\) −10775.4 −0.343944
\(178\) 0 0
\(179\) −25338.8 25338.8i −0.790825 0.790825i 0.190803 0.981628i \(-0.438891\pi\)
−0.981628 + 0.190803i \(0.938891\pi\)
\(180\) 0 0
\(181\) −22579.8 22579.8i −0.689228 0.689228i 0.272833 0.962061i \(-0.412039\pi\)
−0.962061 + 0.272833i \(0.912039\pi\)
\(182\) 0 0
\(183\) 22784.7 0.680363
\(184\) 0 0
\(185\) 24062.2i 0.703058i
\(186\) 0 0
\(187\) 12064.2 12064.2i 0.344996 0.344996i
\(188\) 0 0
\(189\) 3690.38 3690.38i 0.103311 0.103311i
\(190\) 0 0
\(191\) 62994.4i 1.72677i 0.504543 + 0.863386i \(0.331661\pi\)
−0.504543 + 0.863386i \(0.668339\pi\)
\(192\) 0 0
\(193\) −25039.7 −0.672225 −0.336112 0.941822i \(-0.609112\pi\)
−0.336112 + 0.941822i \(0.609112\pi\)
\(194\) 0 0
\(195\) 53326.1 + 53326.1i 1.40240 + 1.40240i
\(196\) 0 0
\(197\) 6468.96 + 6468.96i 0.166687 + 0.166687i 0.785521 0.618834i \(-0.212395\pi\)
−0.618834 + 0.785521i \(0.712395\pi\)
\(198\) 0 0
\(199\) −55793.6 −1.40889 −0.704446 0.709757i \(-0.748805\pi\)
−0.704446 + 0.709757i \(0.748805\pi\)
\(200\) 0 0
\(201\) 51093.8i 1.26467i
\(202\) 0 0
\(203\) −1157.99 + 1157.99i −0.0281005 + 0.0281005i
\(204\) 0 0
\(205\) 39202.6 39202.6i 0.932841 0.932841i
\(206\) 0 0
\(207\) 539.439i 0.0125893i
\(208\) 0 0
\(209\) 73257.5 1.67710
\(210\) 0 0
\(211\) −11403.6 11403.6i −0.256139 0.256139i 0.567343 0.823482i \(-0.307971\pi\)
−0.823482 + 0.567343i \(0.807971\pi\)
\(212\) 0 0
\(213\) 17206.8 + 17206.8i 0.379264 + 0.379264i
\(214\) 0 0
\(215\) −776.604 −0.0168005
\(216\) 0 0
\(217\) 7176.41i 0.152401i
\(218\) 0 0
\(219\) 4007.75 4007.75i 0.0835627 0.0835627i
\(220\) 0 0
\(221\) 29352.4 29352.4i 0.600979 0.600979i
\(222\) 0 0
\(223\) 15194.4i 0.305545i −0.988261 0.152772i \(-0.951180\pi\)
0.988261 0.152772i \(-0.0488201\pi\)
\(224\) 0 0
\(225\) 6276.81 0.123986
\(226\) 0 0
\(227\) 47509.0 + 47509.0i 0.921986 + 0.921986i 0.997170 0.0751841i \(-0.0239544\pi\)
−0.0751841 + 0.997170i \(0.523954\pi\)
\(228\) 0 0
\(229\) −15628.9 15628.9i −0.298028 0.298028i 0.542213 0.840241i \(-0.317587\pi\)
−0.840241 + 0.542213i \(0.817587\pi\)
\(230\) 0 0
\(231\) −6675.44 −0.125100
\(232\) 0 0
\(233\) 63151.2i 1.16324i −0.813460 0.581621i \(-0.802419\pi\)
0.813460 0.581621i \(-0.197581\pi\)
\(234\) 0 0
\(235\) 49306.1 49306.1i 0.892823 0.892823i
\(236\) 0 0
\(237\) 18938.7 18938.7i 0.337173 0.337173i
\(238\) 0 0
\(239\) 33331.4i 0.583522i 0.956491 + 0.291761i \(0.0942412\pi\)
−0.956491 + 0.291761i \(0.905759\pi\)
\(240\) 0 0
\(241\) 5625.72 0.0968599 0.0484299 0.998827i \(-0.484578\pi\)
0.0484299 + 0.998827i \(0.484578\pi\)
\(242\) 0 0
\(243\) −19734.3 19734.3i −0.334202 0.334202i
\(244\) 0 0
\(245\) 51238.7 + 51238.7i 0.853622 + 0.853622i
\(246\) 0 0
\(247\) 178237. 2.92149
\(248\) 0 0
\(249\) 1790.47i 0.0288782i
\(250\) 0 0
\(251\) −62195.0 + 62195.0i −0.987206 + 0.987206i −0.999919 0.0127130i \(-0.995953\pi\)
0.0127130 + 0.999919i \(0.495953\pi\)
\(252\) 0 0
\(253\) 2502.80 2502.80i 0.0391007 0.0391007i
\(254\) 0 0
\(255\) 31931.7i 0.491068i
\(256\) 0 0
\(257\) 22791.9 0.345075 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(258\) 0 0
\(259\) −3664.30 3664.30i −0.0546250 0.0546250i
\(260\) 0 0
\(261\) 3430.55 + 3430.55i 0.0503597 + 0.0503597i
\(262\) 0 0
\(263\) −126611. −1.83047 −0.915233 0.402926i \(-0.867993\pi\)
−0.915233 + 0.402926i \(0.867993\pi\)
\(264\) 0 0
\(265\) 35754.3i 0.509139i
\(266\) 0 0
\(267\) −8111.00 + 8111.00i −0.113776 + 0.113776i
\(268\) 0 0
\(269\) −65428.7 + 65428.7i −0.904198 + 0.904198i −0.995796 0.0915982i \(-0.970802\pi\)
0.0915982 + 0.995796i \(0.470802\pi\)
\(270\) 0 0
\(271\) 93429.2i 1.27217i −0.771621 0.636083i \(-0.780554\pi\)
0.771621 0.636083i \(-0.219446\pi\)
\(272\) 0 0
\(273\) −16241.5 −0.217922
\(274\) 0 0
\(275\) −29122.0 29122.0i −0.385085 0.385085i
\(276\) 0 0
\(277\) −105271. 105271.i −1.37198 1.37198i −0.857504 0.514477i \(-0.827986\pi\)
−0.514477 0.857504i \(-0.672014\pi\)
\(278\) 0 0
\(279\) −21260.1 −0.273122
\(280\) 0 0
\(281\) 42955.1i 0.544004i 0.962297 + 0.272002i \(0.0876857\pi\)
−0.962297 + 0.272002i \(0.912314\pi\)
\(282\) 0 0
\(283\) −36538.7 + 36538.7i −0.456226 + 0.456226i −0.897414 0.441189i \(-0.854557\pi\)
0.441189 + 0.897414i \(0.354557\pi\)
\(284\) 0 0
\(285\) −96949.8 + 96949.8i −1.19360 + 1.19360i
\(286\) 0 0
\(287\) 11939.9i 0.144957i
\(288\) 0 0
\(289\) −65944.8 −0.789559
\(290\) 0 0
\(291\) −45789.3 45789.3i −0.540727 0.540727i
\(292\) 0 0
\(293\) 45359.7 + 45359.7i 0.528367 + 0.528367i 0.920085 0.391719i \(-0.128119\pi\)
−0.391719 + 0.920085i \(0.628119\pi\)
\(294\) 0 0
\(295\) 42278.5 0.485820
\(296\) 0 0
\(297\) 101448.i 1.15008i
\(298\) 0 0
\(299\) 6089.36 6089.36i 0.0681129 0.0681129i
\(300\) 0 0
\(301\) 118.265 118.265i 0.00130534 0.00130534i
\(302\) 0 0
\(303\) 55789.9i 0.607673i
\(304\) 0 0
\(305\) −89398.0 −0.961011
\(306\) 0 0
\(307\) −10035.4 10035.4i −0.106478 0.106478i 0.651861 0.758339i \(-0.273989\pi\)
−0.758339 + 0.651861i \(0.773989\pi\)
\(308\) 0 0
\(309\) −7907.11 7907.11i −0.0828134 0.0828134i
\(310\) 0 0
\(311\) −102401. −1.05873 −0.529365 0.848394i \(-0.677570\pi\)
−0.529365 + 0.848394i \(0.677570\pi\)
\(312\) 0 0
\(313\) 60933.1i 0.621963i −0.950416 0.310981i \(-0.899342\pi\)
0.950416 0.310981i \(-0.100658\pi\)
\(314\) 0 0
\(315\) −2822.62 + 2822.62i −0.0284466 + 0.0284466i
\(316\) 0 0
\(317\) 10217.2 10217.2i 0.101675 0.101675i −0.654439 0.756115i \(-0.727095\pi\)
0.756115 + 0.654439i \(0.227095\pi\)
\(318\) 0 0
\(319\) 31833.0i 0.312821i
\(320\) 0 0
\(321\) 110565. 1.07302
\(322\) 0 0
\(323\) 53364.3 + 53364.3i 0.511500 + 0.511500i
\(324\) 0 0
\(325\) −70854.6 70854.6i −0.670813 0.670813i
\(326\) 0 0
\(327\) −105.024 −0.000982183
\(328\) 0 0
\(329\) 15017.1i 0.138738i
\(330\) 0 0
\(331\) 123603. 123603.i 1.12817 1.12817i 0.137692 0.990475i \(-0.456032\pi\)
0.990475 0.137692i \(-0.0439684\pi\)
\(332\) 0 0
\(333\) −10855.5 + 10855.5i −0.0978949 + 0.0978949i
\(334\) 0 0
\(335\) 200472.i 1.78634i
\(336\) 0 0
\(337\) −102441. −0.902018 −0.451009 0.892519i \(-0.648936\pi\)
−0.451009 + 0.892519i \(0.648936\pi\)
\(338\) 0 0
\(339\) −75538.6 75538.6i −0.657309 0.657309i
\(340\) 0 0
\(341\) 98639.0 + 98639.0i 0.848281 + 0.848281i
\(342\) 0 0
\(343\) −31501.6 −0.267760
\(344\) 0 0
\(345\) 6624.45i 0.0556560i
\(346\) 0 0
\(347\) 63342.4 63342.4i 0.526061 0.526061i −0.393335 0.919395i \(-0.628679\pi\)
0.919395 + 0.393335i \(0.128679\pi\)
\(348\) 0 0
\(349\) 114645. 114645.i 0.941247 0.941247i −0.0571205 0.998367i \(-0.518192\pi\)
0.998367 + 0.0571205i \(0.0181919\pi\)
\(350\) 0 0
\(351\) 246824.i 2.00343i
\(352\) 0 0
\(353\) −94430.7 −0.757816 −0.378908 0.925434i \(-0.623700\pi\)
−0.378908 + 0.925434i \(0.623700\pi\)
\(354\) 0 0
\(355\) −67512.8 67512.8i −0.535709 0.535709i
\(356\) 0 0
\(357\) −4862.71 4862.71i −0.0381542 0.0381542i
\(358\) 0 0
\(359\) 59001.0 0.457794 0.228897 0.973451i \(-0.426488\pi\)
0.228897 + 0.973451i \(0.426488\pi\)
\(360\) 0 0
\(361\) 193724.i 1.48651i
\(362\) 0 0
\(363\) 10639.7 10639.7i 0.0807453 0.0807453i
\(364\) 0 0
\(365\) −15724.8 + 15724.8i −0.118032 + 0.118032i
\(366\) 0 0
\(367\) 120112.i 0.891775i 0.895089 + 0.445888i \(0.147112\pi\)
−0.895089 + 0.445888i \(0.852888\pi\)
\(368\) 0 0
\(369\) 35372.0 0.259781
\(370\) 0 0
\(371\) 5444.83 + 5444.83i 0.0395582 + 0.0395582i
\(372\) 0 0
\(373\) 113849. + 113849.i 0.818300 + 0.818300i 0.985862 0.167562i \(-0.0535894\pi\)
−0.167562 + 0.985862i \(0.553589\pi\)
\(374\) 0 0
\(375\) −73454.7 −0.522345
\(376\) 0 0
\(377\) 77450.4i 0.544930i
\(378\) 0 0
\(379\) −75841.4 + 75841.4i −0.527993 + 0.527993i −0.919973 0.391981i \(-0.871790\pi\)
0.391981 + 0.919973i \(0.371790\pi\)
\(380\) 0 0
\(381\) 44582.4 44582.4i 0.307124 0.307124i
\(382\) 0 0
\(383\) 80282.4i 0.547297i −0.961830 0.273648i \(-0.911770\pi\)
0.961830 0.273648i \(-0.0882304\pi\)
\(384\) 0 0
\(385\) 26191.8 0.176703
\(386\) 0 0
\(387\) −350.360 350.360i −0.00233933 0.00233933i
\(388\) 0 0
\(389\) −89476.2 89476.2i −0.591301 0.591301i 0.346682 0.937983i \(-0.387308\pi\)
−0.937983 + 0.346682i \(0.887308\pi\)
\(390\) 0 0
\(391\) 3646.31 0.0238507
\(392\) 0 0
\(393\) 176230.i 1.14102i
\(394\) 0 0
\(395\) −74307.8 + 74307.8i −0.476256 + 0.476256i
\(396\) 0 0
\(397\) −128824. + 128824.i −0.817363 + 0.817363i −0.985725 0.168362i \(-0.946152\pi\)
0.168362 + 0.985725i \(0.446152\pi\)
\(398\) 0 0
\(399\) 29527.9i 0.185476i
\(400\) 0 0
\(401\) 71110.1 0.442224 0.221112 0.975248i \(-0.429031\pi\)
0.221112 + 0.975248i \(0.429031\pi\)
\(402\) 0 0
\(403\) 239991. + 239991.i 1.47769 + 1.47769i
\(404\) 0 0
\(405\) −99723.2 99723.2i −0.607976 0.607976i
\(406\) 0 0
\(407\) 100731. 0.608097
\(408\) 0 0
\(409\) 87416.4i 0.522572i −0.965261 0.261286i \(-0.915853\pi\)
0.965261 0.261286i \(-0.0841466\pi\)
\(410\) 0 0
\(411\) −172683. + 172683.i −1.02227 + 1.02227i
\(412\) 0 0
\(413\) −6438.36 + 6438.36i −0.0377464 + 0.0377464i
\(414\) 0 0
\(415\) 7025.11i 0.0407903i
\(416\) 0 0
\(417\) 237474. 1.36567
\(418\) 0 0
\(419\) 156666. + 156666.i 0.892373 + 0.892373i 0.994746 0.102373i \(-0.0326436\pi\)
−0.102373 + 0.994746i \(0.532644\pi\)
\(420\) 0 0
\(421\) −20636.7 20636.7i −0.116433 0.116433i 0.646490 0.762923i \(-0.276236\pi\)
−0.762923 + 0.646490i \(0.776236\pi\)
\(422\) 0 0
\(423\) 44488.2 0.248636
\(424\) 0 0
\(425\) 42427.8i 0.234894i
\(426\) 0 0
\(427\) 13614.0 13614.0i 0.0746670 0.0746670i
\(428\) 0 0
\(429\) 223238. 223238.i 1.21298 1.21298i
\(430\) 0 0
\(431\) 294349.i 1.58456i 0.610160 + 0.792279i \(0.291105\pi\)
−0.610160 + 0.792279i \(0.708895\pi\)
\(432\) 0 0
\(433\) 240460. 1.28253 0.641264 0.767321i \(-0.278411\pi\)
0.641264 + 0.767321i \(0.278411\pi\)
\(434\) 0 0
\(435\) 42128.1 + 42128.1i 0.222635 + 0.222635i
\(436\) 0 0
\(437\) 11070.8 + 11070.8i 0.0579716 + 0.0579716i
\(438\) 0 0
\(439\) 294699. 1.52915 0.764574 0.644536i \(-0.222949\pi\)
0.764574 + 0.644536i \(0.222949\pi\)
\(440\) 0 0
\(441\) 46231.9i 0.237719i
\(442\) 0 0
\(443\) 118964. 118964.i 0.606187 0.606187i −0.335760 0.941948i \(-0.608993\pi\)
0.941948 + 0.335760i \(0.108993\pi\)
\(444\) 0 0
\(445\) 31824.4 31824.4i 0.160709 0.160709i
\(446\) 0 0
\(447\) 130445.i 0.652847i
\(448\) 0 0
\(449\) −82129.5 −0.407386 −0.203693 0.979035i \(-0.565294\pi\)
−0.203693 + 0.979035i \(0.565294\pi\)
\(450\) 0 0
\(451\) −164113. 164113.i −0.806844 0.806844i
\(452\) 0 0
\(453\) 107783. + 107783.i 0.525235 + 0.525235i
\(454\) 0 0
\(455\) 63725.2 0.307814
\(456\) 0 0
\(457\) 172358.i 0.825277i −0.910895 0.412638i \(-0.864607\pi\)
0.910895 0.412638i \(-0.135393\pi\)
\(458\) 0 0
\(459\) −73899.3 + 73899.3i −0.350764 + 0.350764i
\(460\) 0 0
\(461\) −96898.8 + 96898.8i −0.455950 + 0.455950i −0.897323 0.441374i \(-0.854491\pi\)
0.441374 + 0.897323i \(0.354491\pi\)
\(462\) 0 0
\(463\) 142244.i 0.663549i 0.943359 + 0.331775i \(0.107647\pi\)
−0.943359 + 0.331775i \(0.892353\pi\)
\(464\) 0 0
\(465\) −261080. −1.20745
\(466\) 0 0
\(467\) −139194. 139194.i −0.638246 0.638246i 0.311877 0.950123i \(-0.399042\pi\)
−0.950123 + 0.311877i \(0.899042\pi\)
\(468\) 0 0
\(469\) 30528.8 + 30528.8i 0.138792 + 0.138792i
\(470\) 0 0
\(471\) −200526. −0.903917
\(472\) 0 0
\(473\) 3251.08i 0.0145313i
\(474\) 0 0
\(475\) 128818. 128818.i 0.570936 0.570936i
\(476\) 0 0
\(477\) 16130.3 16130.3i 0.0708934 0.0708934i
\(478\) 0 0
\(479\) 216764.i 0.944749i −0.881398 0.472374i \(-0.843397\pi\)
0.881398 0.472374i \(-0.156603\pi\)
\(480\) 0 0
\(481\) 245080. 1.05930
\(482\) 0 0
\(483\) −1008.80 1008.80i −0.00432426 0.00432426i
\(484\) 0 0
\(485\) 179659. + 179659.i 0.763776 + 0.763776i
\(486\) 0 0
\(487\) −146986. −0.619752 −0.309876 0.950777i \(-0.600287\pi\)
−0.309876 + 0.950777i \(0.600287\pi\)
\(488\) 0 0
\(489\) 195824.i 0.818931i
\(490\) 0 0
\(491\) −207292. + 207292.i −0.859843 + 0.859843i −0.991319 0.131476i \(-0.958028\pi\)
0.131476 + 0.991319i \(0.458028\pi\)
\(492\) 0 0
\(493\) 23188.7 23188.7i 0.0954074 0.0954074i
\(494\) 0 0
\(495\) 77593.1i 0.316674i
\(496\) 0 0
\(497\) 20562.3 0.0832452
\(498\) 0 0
\(499\) 5591.76 + 5591.76i 0.0224568 + 0.0224568i 0.718246 0.695789i \(-0.244945\pi\)
−0.695789 + 0.718246i \(0.744945\pi\)
\(500\) 0 0
\(501\) 63014.2 + 63014.2i 0.251051 + 0.251051i
\(502\) 0 0
\(503\) −154345. −0.610037 −0.305018 0.952346i \(-0.598663\pi\)
−0.305018 + 0.952346i \(0.598663\pi\)
\(504\) 0 0
\(505\) 218897.i 0.858337i
\(506\) 0 0
\(507\) 384909. 384909.i 1.49742 1.49742i
\(508\) 0 0
\(509\) 7996.84 7996.84i 0.0308662 0.0308662i −0.691505 0.722371i \(-0.743052\pi\)
0.722371 + 0.691505i \(0.243052\pi\)
\(510\) 0 0
\(511\) 4789.30i 0.0183413i
\(512\) 0 0
\(513\) −448740. −1.70514
\(514\) 0 0
\(515\) 31024.4 + 31024.4i 0.116974 + 0.116974i
\(516\) 0 0
\(517\) −206409. 206409.i −0.772231 0.772231i
\(518\) 0 0
\(519\) 125089. 0.464393
\(520\) 0 0
\(521\) 215831.i 0.795130i 0.917574 + 0.397565i \(0.130145\pi\)
−0.917574 + 0.397565i \(0.869855\pi\)
\(522\) 0 0
\(523\) −73690.2 + 73690.2i −0.269405 + 0.269405i −0.828861 0.559455i \(-0.811010\pi\)
0.559455 + 0.828861i \(0.311010\pi\)
\(524\) 0 0
\(525\) −11738.2 + 11738.2i −0.0425877 + 0.0425877i
\(526\) 0 0
\(527\) 143707.i 0.517435i
\(528\) 0 0
\(529\) −279085. −0.997297
\(530\) 0 0
\(531\) 19073.6 + 19073.6i 0.0676464 + 0.0676464i
\(532\) 0 0
\(533\) −399290. 399290.i −1.40551 1.40551i
\(534\) 0 0
\(535\) −433814. −1.51564
\(536\) 0 0
\(537\) 280762.i 0.973622i
\(538\) 0 0
\(539\) 214499. 214499.i 0.738325 0.738325i
\(540\) 0 0
\(541\) −260589. + 260589.i −0.890352 + 0.890352i −0.994556 0.104204i \(-0.966771\pi\)
0.104204 + 0.994556i \(0.466771\pi\)
\(542\) 0 0
\(543\) 250191.i 0.848540i
\(544\) 0 0
\(545\) 412.072 0.00138733
\(546\) 0 0
\(547\) −87290.1 87290.1i −0.291736 0.291736i 0.546030 0.837766i \(-0.316139\pi\)
−0.837766 + 0.546030i \(0.816139\pi\)
\(548\) 0 0
\(549\) −40331.3 40331.3i −0.133813 0.133813i
\(550\) 0 0
\(551\) 140809. 0.463796
\(552\) 0 0
\(553\) 22631.9i 0.0740066i
\(554\) 0 0
\(555\) −133308. + 133308.i −0.432783 + 0.432783i
\(556\) 0 0
\(557\) 342322. 342322.i 1.10338 1.10338i 0.109377 0.994000i \(-0.465114\pi\)
0.994000 0.109377i \(-0.0348855\pi\)
\(558\) 0 0
\(559\) 7909.94i 0.0253134i
\(560\) 0 0
\(561\) 133675. 0.424741
\(562\) 0 0
\(563\) −77521.3 77521.3i −0.244571 0.244571i 0.574167 0.818738i \(-0.305326\pi\)
−0.818738 + 0.574167i \(0.805326\pi\)
\(564\) 0 0
\(565\) 296383. + 296383.i 0.928447 + 0.928447i
\(566\) 0 0
\(567\) 30372.6 0.0944749
\(568\) 0 0
\(569\) 304409.i 0.940229i 0.882605 + 0.470115i \(0.155787\pi\)
−0.882605 + 0.470115i \(0.844213\pi\)
\(570\) 0 0
\(571\) −254051. + 254051.i −0.779201 + 0.779201i −0.979695 0.200494i \(-0.935745\pi\)
0.200494 + 0.979695i \(0.435745\pi\)
\(572\) 0 0
\(573\) −348999. + 348999.i −1.06295 + 1.06295i
\(574\) 0 0
\(575\) 8801.94i 0.0266221i
\(576\) 0 0
\(577\) −486229. −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(578\) 0 0
\(579\) −138724. 138724.i −0.413803 0.413803i
\(580\) 0 0
\(581\) −1069.82 1069.82i −0.00316926 0.00316926i
\(582\) 0 0
\(583\) −149677. −0.440371
\(584\) 0 0
\(585\) 188786.i 0.551642i
\(586\) 0 0
\(587\) −26612.4 + 26612.4i −0.0772339 + 0.0772339i −0.744668 0.667435i \(-0.767392\pi\)
0.667435 + 0.744668i \(0.267392\pi\)
\(588\) 0 0
\(589\) −436317. + 436317.i −1.25768 + 1.25768i
\(590\) 0 0
\(591\) 71678.1i 0.205216i
\(592\) 0 0
\(593\) 301795. 0.858228 0.429114 0.903250i \(-0.358826\pi\)
0.429114 + 0.903250i \(0.358826\pi\)
\(594\) 0 0
\(595\) 19079.4 + 19079.4i 0.0538927 + 0.0538927i
\(596\) 0 0
\(597\) −309105. 309105.i −0.867276 0.867276i
\(598\) 0 0
\(599\) 208748. 0.581795 0.290897 0.956754i \(-0.406046\pi\)
0.290897 + 0.956754i \(0.406046\pi\)
\(600\) 0 0
\(601\) 355946.i 0.985451i 0.870185 + 0.492725i \(0.163999\pi\)
−0.870185 + 0.492725i \(0.836001\pi\)
\(602\) 0 0
\(603\) 90441.4 90441.4i 0.248733 0.248733i
\(604\) 0 0
\(605\) −41746.1 + 41746.1i −0.114053 + 0.114053i
\(606\) 0 0
\(607\) 680696.i 1.84746i −0.383040 0.923732i \(-0.625123\pi\)
0.383040 0.923732i \(-0.374877\pi\)
\(608\) 0 0
\(609\) −12830.9 −0.0345958
\(610\) 0 0
\(611\) −502197. 502197.i −1.34522 1.34522i
\(612\) 0 0
\(613\) 504818. + 504818.i 1.34343 + 1.34343i 0.892625 + 0.450800i \(0.148861\pi\)
0.450800 + 0.892625i \(0.351139\pi\)
\(614\) 0 0
\(615\) 434378. 1.14846
\(616\) 0 0
\(617\) 601668.i 1.58047i −0.612803 0.790236i \(-0.709958\pi\)
0.612803 0.790236i \(-0.290042\pi\)
\(618\) 0 0
\(619\) −34687.6 + 34687.6i −0.0905300 + 0.0905300i −0.750922 0.660391i \(-0.770390\pi\)
0.660391 + 0.750922i \(0.270390\pi\)
\(620\) 0 0
\(621\) −15330.9 + 15330.9i −0.0397544 + 0.0397544i
\(622\) 0 0
\(623\) 9692.72i 0.0249729i
\(624\) 0 0
\(625\) 488225. 1.24985
\(626\) 0 0
\(627\) 405858. + 405858.i 1.03238 + 1.03238i
\(628\) 0 0
\(629\) 73377.0 + 73377.0i 0.185464 + 0.185464i
\(630\) 0 0
\(631\) −557209. −1.39946 −0.699728 0.714409i \(-0.746696\pi\)
−0.699728 + 0.714409i \(0.746696\pi\)
\(632\) 0 0
\(633\) 126355.i 0.315345i
\(634\) 0 0
\(635\) −174924. + 174924.i −0.433812 + 0.433812i
\(636\) 0 0
\(637\) 521881. 521881.i 1.28615 1.28615i
\(638\) 0 0
\(639\) 60915.8i 0.149186i
\(640\) 0 0
\(641\) 354670. 0.863193 0.431597 0.902067i \(-0.357950\pi\)
0.431597 + 0.902067i \(0.357950\pi\)
\(642\) 0 0
\(643\) −89105.3 89105.3i −0.215517 0.215517i 0.591089 0.806606i \(-0.298698\pi\)
−0.806606 + 0.591089i \(0.798698\pi\)
\(644\) 0 0
\(645\) −4302.51 4302.51i −0.0103420 0.0103420i
\(646\) 0 0
\(647\) 669197. 1.59862 0.799311 0.600918i \(-0.205198\pi\)
0.799311 + 0.600918i \(0.205198\pi\)
\(648\) 0 0
\(649\) 176989.i 0.420201i
\(650\) 0 0
\(651\) 39758.5 39758.5i 0.0938140 0.0938140i
\(652\) 0 0
\(653\) −6136.50 + 6136.50i −0.0143911 + 0.0143911i −0.714266 0.699875i \(-0.753239\pi\)
0.699875 + 0.714266i \(0.253239\pi\)
\(654\) 0 0
\(655\) 691457.i 1.61169i
\(656\) 0 0
\(657\) −14188.3 −0.0328700
\(658\) 0 0
\(659\) 484888. + 484888.i 1.11653 + 1.11653i 0.992247 + 0.124283i \(0.0396632\pi\)
0.124283 + 0.992247i \(0.460337\pi\)
\(660\) 0 0
\(661\) 71185.1 + 71185.1i 0.162924 + 0.162924i 0.783861 0.620937i \(-0.213248\pi\)
−0.620937 + 0.783861i \(0.713248\pi\)
\(662\) 0 0
\(663\) 325234. 0.739892
\(664\) 0 0
\(665\) 115856.i 0.261984i
\(666\) 0 0
\(667\) 4810.65 4810.65i 0.0108131 0.0108131i
\(668\) 0 0
\(669\) 84179.5 84179.5i 0.188085 0.188085i
\(670\) 0 0
\(671\) 374244.i 0.831209i
\(672\) 0 0
\(673\) 116807. 0.257893 0.128947 0.991652i \(-0.458840\pi\)
0.128947 + 0.991652i \(0.458840\pi\)
\(674\) 0 0
\(675\) 178388. + 178388.i 0.391523 + 0.391523i
\(676\) 0 0
\(677\) −562443. 562443.i −1.22716 1.22716i −0.965033 0.262127i \(-0.915576\pi\)
−0.262127 0.965033i \(-0.584424\pi\)
\(678\) 0 0
\(679\) −54718.7 −0.118685
\(680\) 0 0
\(681\) 526415.i 1.13510i
\(682\) 0 0
\(683\) 392290. 392290.i 0.840941 0.840941i −0.148040 0.988981i \(-0.547297\pi\)
0.988981 + 0.148040i \(0.0472965\pi\)
\(684\) 0 0
\(685\) 677539. 677539.i 1.44395 1.44395i
\(686\) 0 0
\(687\) 173173.i 0.366916i
\(688\) 0 0
\(689\) −364168. −0.767120
\(690\) 0 0
\(691\) 424716. + 424716.i 0.889493 + 0.889493i 0.994474 0.104981i \(-0.0334781\pi\)
−0.104981 + 0.994474i \(0.533478\pi\)
\(692\) 0 0
\(693\) 11816.2 + 11816.2i 0.0246044 + 0.0246044i
\(694\) 0 0
\(695\) −931755. −1.92900
\(696\) 0 0
\(697\) 239095.i 0.492159i
\(698\) 0 0
\(699\) 349868. 349868.i 0.716060 0.716060i
\(700\) 0 0
\(701\) 92393.5 92393.5i 0.188021 0.188021i −0.606819 0.794840i \(-0.707555\pi\)
0.794840 + 0.606819i \(0.207555\pi\)
\(702\) 0 0
\(703\) 445569.i 0.901580i
\(704\) 0 0
\(705\) 546327. 1.09920
\(706\) 0 0
\(707\) −33334.7 33334.7i −0.0666896 0.0666896i
\(708\) 0 0
\(709\) −29997.3 29997.3i −0.0596746 0.0596746i 0.676640 0.736314i \(-0.263435\pi\)
−0.736314 + 0.676640i \(0.763435\pi\)
\(710\) 0 0
\(711\) −67046.9 −0.132629
\(712\) 0 0
\(713\) 29812.9i 0.0586443i
\(714\) 0 0
\(715\) −875896. + 875896.i −1.71333 + 1.71333i
\(716\) 0 0
\(717\) −184661. + 184661.i −0.359200 + 0.359200i
\(718\) 0 0
\(719\) 284133.i 0.549622i 0.961498 + 0.274811i \(0.0886152\pi\)
−0.961498 + 0.274811i \(0.911385\pi\)
\(720\) 0 0
\(721\) −9449.07 −0.0181769
\(722\) 0 0
\(723\) 31167.4 + 31167.4i 0.0596243 + 0.0596243i
\(724\) 0 0
\(725\) −55975.8 55975.8i −0.106494 0.106494i
\(726\) 0 0
\(727\) −39096.3 −0.0739719 −0.0369860 0.999316i \(-0.511776\pi\)
−0.0369860 + 0.999316i \(0.511776\pi\)
\(728\) 0 0
\(729\) 590261.i 1.11068i
\(730\) 0 0
\(731\) −2368.24 + 2368.24i −0.00443191 + 0.00443191i
\(732\) 0 0
\(733\) −82927.3 + 82927.3i −0.154344 + 0.154344i −0.780055 0.625711i \(-0.784809\pi\)
0.625711 + 0.780055i \(0.284809\pi\)
\(734\) 0 0
\(735\) 567741.i 1.05093i
\(736\) 0 0
\(737\) −839229. −1.54506
\(738\) 0 0
\(739\) −97643.8 97643.8i −0.178795 0.178795i 0.612035 0.790830i \(-0.290351\pi\)
−0.790830 + 0.612035i \(0.790351\pi\)
\(740\) 0 0
\(741\) 987462. + 987462.i 1.79839 + 1.79839i
\(742\) 0 0
\(743\) 552181. 1.00024 0.500120 0.865956i \(-0.333289\pi\)
0.500120 + 0.865956i \(0.333289\pi\)
\(744\) 0 0
\(745\) 511813.i 0.922145i
\(746\) 0 0
\(747\) −3169.33 + 3169.33i −0.00567971 + 0.00567971i
\(748\) 0 0
\(749\) 66063.3 66063.3i 0.117760 0.117760i
\(750\) 0 0
\(751\) 318447.i 0.564621i −0.959323 0.282310i \(-0.908899\pi\)
0.959323 0.282310i \(-0.0911008\pi\)
\(752\) 0 0
\(753\) −689140. −1.21539
\(754\) 0 0
\(755\) −422898. 422898.i −0.741894 0.741894i
\(756\) 0 0
\(757\) 478701. + 478701.i 0.835357 + 0.835357i 0.988244 0.152886i \(-0.0488569\pi\)
−0.152886 + 0.988244i \(0.548857\pi\)
\(758\) 0 0
\(759\) 27731.8 0.0481386
\(760\) 0 0
\(761\) 398315.i 0.687793i −0.939008 0.343896i \(-0.888253\pi\)
0.939008 0.343896i \(-0.111747\pi\)
\(762\) 0 0
\(763\) −62.7523 + 62.7523i −0.000107790 + 0.000107790i
\(764\) 0 0
\(765\) 56522.5 56522.5i 0.0965826 0.0965826i
\(766\) 0 0
\(767\) 430619.i 0.731985i
\(768\) 0 0
\(769\) 658868. 1.11416 0.557078 0.830460i \(-0.311922\pi\)
0.557078 + 0.830460i \(0.311922\pi\)
\(770\) 0 0
\(771\) 126271. + 126271.i 0.212419 + 0.212419i
\(772\) 0 0
\(773\) −833367. 833367.i −1.39469 1.39469i −0.814439 0.580250i \(-0.802955\pi\)
−0.580250 0.814439i \(-0.697045\pi\)
\(774\) 0 0
\(775\) 346898. 0.577561
\(776\) 0 0
\(777\) 40601.6i 0.0672513i
\(778\) 0 0
\(779\) 725932. 725932.i 1.19625 1.19625i
\(780\) 0 0
\(781\) −282627. + 282627.i −0.463352 + 0.463352i
\(782\) 0 0
\(783\) 194994.i 0.318051i
\(784\) 0 0
\(785\) 786784. 1.27678
\(786\) 0 0
\(787\) −265518. 265518.i −0.428691 0.428691i 0.459491 0.888182i \(-0.348032\pi\)
−0.888182 + 0.459491i \(0.848032\pi\)
\(788\) 0 0
\(789\) −701447. 701447.i −1.12679 1.12679i
\(790\) 0 0
\(791\) −90269.3 −0.144274
\(792\) 0 0
\(793\) 910545.i 1.44795i
\(794\) 0 0
\(795\) 198084. 198084.i 0.313412