Properties

Label 128.5.f.a.31.7
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 31.7
Root \(1.03712 + 2.63142i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.a.95.7

$q$-expansion

\(f(q)\) \(=\) \(q+(11.5209 + 11.5209i) q^{3} +(14.6016 + 14.6016i) q^{5} +24.0210 q^{7} +184.461i q^{9} +O(q^{10})\) \(q+(11.5209 + 11.5209i) q^{3} +(14.6016 + 14.6016i) q^{5} +24.0210 q^{7} +184.461i q^{9} +(61.7287 - 61.7287i) q^{11} +(37.5611 - 37.5611i) q^{13} +336.446i q^{15} +96.8718 q^{17} +(-156.751 - 156.751i) q^{19} +(276.742 + 276.742i) q^{21} -959.783 q^{23} -198.587i q^{25} +(-1191.96 + 1191.96i) q^{27} +(350.180 - 350.180i) q^{29} +237.885i q^{31} +1422.34 q^{33} +(350.744 + 350.744i) q^{35} +(560.815 + 560.815i) q^{37} +865.473 q^{39} +1802.95i q^{41} +(206.090 - 206.090i) q^{43} +(-2693.42 + 2693.42i) q^{45} -1599.92i q^{47} -1823.99 q^{49} +(1116.05 + 1116.05i) q^{51} +(2234.17 + 2234.17i) q^{53} +1802.67 q^{55} -3611.82i q^{57} +(2353.11 - 2353.11i) q^{59} +(4443.45 - 4443.45i) q^{61} +4430.92i q^{63} +1096.90 q^{65} +(-3995.40 - 3995.40i) q^{67} +(-11057.5 - 11057.5i) q^{69} -4929.25 q^{71} +2651.57i q^{73} +(2287.90 - 2287.90i) q^{75} +(1482.78 - 1482.78i) q^{77} -8792.34i q^{79} -12523.4 q^{81} +(-228.231 - 228.231i) q^{83} +(1414.48 + 1414.48i) q^{85} +8068.75 q^{87} -10596.7i q^{89} +(902.254 - 902.254i) q^{91} +(-2740.64 + 2740.64i) q^{93} -4577.63i q^{95} +11048.3 q^{97} +(11386.5 + 11386.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + 94q^{11} + 2q^{13} - 4q^{17} - 706q^{19} + 164q^{21} - 1148q^{23} - 1664q^{27} - 862q^{29} - 4q^{33} + 1340q^{35} + 1826q^{37} - 2684q^{39} + 1694q^{43} - 1410q^{45} + 682q^{49} - 3012q^{51} + 482q^{53} + 11780q^{55} - 2786q^{59} + 3778q^{61} - 2020q^{65} + 7998q^{67} - 9628q^{69} - 19964q^{71} + 17570q^{75} + 9508q^{77} + 1454q^{81} - 17282q^{83} - 9948q^{85} + 49284q^{87} - 28036q^{91} - 8896q^{93} - 4q^{97} + 49214q^{99} + O(q^{100}) \)

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
\(3\) 11.5209 + 11.5209i 1.28010 + 1.28010i 0.940612 + 0.339485i \(0.110253\pi\)
0.339485 + 0.940612i \(0.389747\pi\)
\(4\) 0 0
\(5\) 14.6016 + 14.6016i 0.584063 + 0.584063i 0.936017 0.351954i \(-0.114483\pi\)
−0.351954 + 0.936017i \(0.614483\pi\)
\(6\) 0 0
\(7\) 24.0210 0.490224 0.245112 0.969495i \(-0.421175\pi\)
0.245112 + 0.969495i \(0.421175\pi\)
\(8\) 0 0
\(9\) 184.461i 2.27729i
\(10\) 0 0
\(11\) 61.7287 61.7287i 0.510154 0.510154i −0.404419 0.914574i \(-0.632526\pi\)
0.914574 + 0.404419i \(0.132526\pi\)
\(12\) 0 0
\(13\) 37.5611 37.5611i 0.222255 0.222255i −0.587192 0.809447i \(-0.699767\pi\)
0.809447 + 0.587192i \(0.199767\pi\)
\(14\) 0 0
\(15\) 336.446i 1.49531i
\(16\) 0 0
\(17\) 96.8718 0.335197 0.167598 0.985855i \(-0.446399\pi\)
0.167598 + 0.985855i \(0.446399\pi\)
\(18\) 0 0
\(19\) −156.751 156.751i −0.434214 0.434214i 0.455845 0.890059i \(-0.349337\pi\)
−0.890059 + 0.455845i \(0.849337\pi\)
\(20\) 0 0
\(21\) 276.742 + 276.742i 0.627534 + 0.627534i
\(22\) 0 0
\(23\) −959.783 −1.81433 −0.907167 0.420770i \(-0.861760\pi\)
−0.907167 + 0.420770i \(0.861760\pi\)
\(24\) 0 0
\(25\) 198.587i 0.317740i
\(26\) 0 0
\(27\) −1191.96 + 1191.96i −1.63506 + 1.63506i
\(28\) 0 0
\(29\) 350.180 350.180i 0.416385 0.416385i −0.467571 0.883956i \(-0.654871\pi\)
0.883956 + 0.467571i \(0.154871\pi\)
\(30\) 0 0
\(31\) 237.885i 0.247539i 0.992311 + 0.123769i \(0.0394983\pi\)
−0.992311 + 0.123769i \(0.960502\pi\)
\(32\) 0 0
\(33\) 1422.34 1.30609
\(34\) 0 0
\(35\) 350.744 + 350.744i 0.286322 + 0.286322i
\(36\) 0 0
\(37\) 560.815 + 560.815i 0.409653 + 0.409653i 0.881617 0.471965i \(-0.156455\pi\)
−0.471965 + 0.881617i \(0.656455\pi\)
\(38\) 0 0
\(39\) 865.473 0.569016
\(40\) 0 0
\(41\) 1802.95i 1.07255i 0.844044 + 0.536274i \(0.180169\pi\)
−0.844044 + 0.536274i \(0.819831\pi\)
\(42\) 0 0
\(43\) 206.090 206.090i 0.111460 0.111460i −0.649177 0.760637i \(-0.724887\pi\)
0.760637 + 0.649177i \(0.224887\pi\)
\(44\) 0 0
\(45\) −2693.42 + 2693.42i −1.33008 + 1.33008i
\(46\) 0 0
\(47\) 1599.92i 0.724274i −0.932125 0.362137i \(-0.882047\pi\)
0.932125 0.362137i \(-0.117953\pi\)
\(48\) 0 0
\(49\) −1823.99 −0.759681
\(50\) 0 0
\(51\) 1116.05 + 1116.05i 0.429084 + 0.429084i
\(52\) 0 0
\(53\) 2234.17 + 2234.17i 0.795360 + 0.795360i 0.982360 0.187000i \(-0.0598765\pi\)
−0.187000 + 0.982360i \(0.559876\pi\)
\(54\) 0 0
\(55\) 1802.67 0.595925
\(56\) 0 0
\(57\) 3611.82i 1.11167i
\(58\) 0 0
\(59\) 2353.11 2353.11i 0.675988 0.675988i −0.283102 0.959090i \(-0.591364\pi\)
0.959090 + 0.283102i \(0.0913636\pi\)
\(60\) 0 0
\(61\) 4443.45 4443.45i 1.19415 1.19415i 0.218264 0.975890i \(-0.429961\pi\)
0.975890 0.218264i \(-0.0700395\pi\)
\(62\) 0 0
\(63\) 4430.92i 1.11638i
\(64\) 0 0
\(65\) 1096.90 0.259622
\(66\) 0 0
\(67\) −3995.40 3995.40i −0.890042 0.890042i 0.104485 0.994527i \(-0.466681\pi\)
−0.994527 + 0.104485i \(0.966681\pi\)
\(68\) 0 0
\(69\) −11057.5 11057.5i −2.32252 2.32252i
\(70\) 0 0
\(71\) −4929.25 −0.977832 −0.488916 0.872331i \(-0.662608\pi\)
−0.488916 + 0.872331i \(0.662608\pi\)
\(72\) 0 0
\(73\) 2651.57i 0.497574i 0.968558 + 0.248787i \(0.0800319\pi\)
−0.968558 + 0.248787i \(0.919968\pi\)
\(74\) 0 0
\(75\) 2287.90 2287.90i 0.406737 0.406737i
\(76\) 0 0
\(77\) 1482.78 1482.78i 0.250090 0.250090i
\(78\) 0 0
\(79\) 8792.34i 1.40880i −0.709801 0.704402i \(-0.751215\pi\)
0.709801 0.704402i \(-0.248785\pi\)
\(80\) 0 0
\(81\) −12523.4 −1.90877
\(82\) 0 0
\(83\) −228.231 228.231i −0.0331298 0.0331298i 0.690348 0.723478i \(-0.257458\pi\)
−0.723478 + 0.690348i \(0.757458\pi\)
\(84\) 0 0
\(85\) 1414.48 + 1414.48i 0.195776 + 0.195776i
\(86\) 0 0
\(87\) 8068.75 1.06603
\(88\) 0 0
\(89\) 10596.7i 1.33780i −0.743353 0.668899i \(-0.766766\pi\)
0.743353 0.668899i \(-0.233234\pi\)
\(90\) 0 0
\(91\) 902.254 902.254i 0.108955 0.108955i
\(92\) 0 0
\(93\) −2740.64 + 2740.64i −0.316873 + 0.316873i
\(94\) 0 0
\(95\) 4577.63i 0.507217i
\(96\) 0 0
\(97\) 11048.3 1.17422 0.587111 0.809506i \(-0.300265\pi\)
0.587111 + 0.809506i \(0.300265\pi\)
\(98\) 0 0
\(99\) 11386.5 + 11386.5i 1.16177 + 1.16177i
\(100\) 0 0
\(101\) 7543.12 + 7543.12i 0.739449 + 0.739449i 0.972471 0.233022i \(-0.0748615\pi\)
−0.233022 + 0.972471i \(0.574861\pi\)
\(102\) 0 0
\(103\) 6124.81 0.577322 0.288661 0.957431i \(-0.406790\pi\)
0.288661 + 0.957431i \(0.406790\pi\)
\(104\) 0 0
\(105\) 8081.75i 0.733039i
\(106\) 0 0
\(107\) 4636.79 4636.79i 0.404995 0.404995i −0.474994 0.879989i \(-0.657550\pi\)
0.879989 + 0.474994i \(0.157550\pi\)
\(108\) 0 0
\(109\) −15235.6 + 15235.6i −1.28235 + 1.28235i −0.343022 + 0.939327i \(0.611451\pi\)
−0.939327 + 0.343022i \(0.888549\pi\)
\(110\) 0 0
\(111\) 12922.1i 1.04879i
\(112\) 0 0
\(113\) 2902.13 0.227279 0.113639 0.993522i \(-0.463749\pi\)
0.113639 + 0.993522i \(0.463749\pi\)
\(114\) 0 0
\(115\) −14014.4 14014.4i −1.05969 1.05969i
\(116\) 0 0
\(117\) 6928.55 + 6928.55i 0.506140 + 0.506140i
\(118\) 0 0
\(119\) 2326.95 0.164321
\(120\) 0 0
\(121\) 7020.14i 0.479485i
\(122\) 0 0
\(123\) −20771.6 + 20771.6i −1.37296 + 1.37296i
\(124\) 0 0
\(125\) 12025.7 12025.7i 0.769644 0.769644i
\(126\) 0 0
\(127\) 3992.46i 0.247533i −0.992311 0.123766i \(-0.960503\pi\)
0.992311 0.123766i \(-0.0394974\pi\)
\(128\) 0 0
\(129\) 4748.66 0.285359
\(130\) 0 0
\(131\) 16640.1 + 16640.1i 0.969645 + 0.969645i 0.999553 0.0299081i \(-0.00952147\pi\)
−0.0299081 + 0.999553i \(0.509521\pi\)
\(132\) 0 0
\(133\) −3765.31 3765.31i −0.212862 0.212862i
\(134\) 0 0
\(135\) −34808.9 −1.90995
\(136\) 0 0
\(137\) 10746.6i 0.572573i −0.958144 0.286286i \(-0.907579\pi\)
0.958144 0.286286i \(-0.0924209\pi\)
\(138\) 0 0
\(139\) −7583.76 + 7583.76i −0.392514 + 0.392514i −0.875582 0.483069i \(-0.839522\pi\)
0.483069 + 0.875582i \(0.339522\pi\)
\(140\) 0 0
\(141\) 18432.5 18432.5i 0.927140 0.927140i
\(142\) 0 0
\(143\) 4637.20i 0.226769i
\(144\) 0 0
\(145\) 10226.4 0.486390
\(146\) 0 0
\(147\) −21014.0 21014.0i −0.972464 0.972464i
\(148\) 0 0
\(149\) −3385.37 3385.37i −0.152487 0.152487i 0.626741 0.779228i \(-0.284389\pi\)
−0.779228 + 0.626741i \(0.784389\pi\)
\(150\) 0 0
\(151\) −21697.8 −0.951617 −0.475809 0.879549i \(-0.657845\pi\)
−0.475809 + 0.879549i \(0.657845\pi\)
\(152\) 0 0
\(153\) 17869.0i 0.763341i
\(154\) 0 0
\(155\) −3473.49 + 3473.49i −0.144578 + 0.144578i
\(156\) 0 0
\(157\) −14212.7 + 14212.7i −0.576603 + 0.576603i −0.933966 0.357363i \(-0.883676\pi\)
0.357363 + 0.933966i \(0.383676\pi\)
\(158\) 0 0
\(159\) 51479.0i 2.03627i
\(160\) 0 0
\(161\) −23054.9 −0.889430
\(162\) 0 0
\(163\) −7450.28 7450.28i −0.280412 0.280412i 0.552861 0.833273i \(-0.313536\pi\)
−0.833273 + 0.552861i \(0.813536\pi\)
\(164\) 0 0
\(165\) 20768.4 + 20768.4i 0.762841 + 0.762841i
\(166\) 0 0
\(167\) 3997.25 0.143327 0.0716635 0.997429i \(-0.477169\pi\)
0.0716635 + 0.997429i \(0.477169\pi\)
\(168\) 0 0
\(169\) 25739.3i 0.901205i
\(170\) 0 0
\(171\) 28914.4 28914.4i 0.988832 0.988832i
\(172\) 0 0
\(173\) 16996.8 16996.8i 0.567903 0.567903i −0.363638 0.931540i \(-0.618465\pi\)
0.931540 + 0.363638i \(0.118465\pi\)
\(174\) 0 0
\(175\) 4770.26i 0.155764i
\(176\) 0 0
\(177\) 54219.8 1.73066
\(178\) 0 0
\(179\) 24121.3 + 24121.3i 0.752826 + 0.752826i 0.975006 0.222180i \(-0.0713173\pi\)
−0.222180 + 0.975006i \(0.571317\pi\)
\(180\) 0 0
\(181\) −13837.8 13837.8i −0.422386 0.422386i 0.463638 0.886025i \(-0.346544\pi\)
−0.886025 + 0.463638i \(0.846544\pi\)
\(182\) 0 0
\(183\) 102385. 3.05726
\(184\) 0 0
\(185\) 16377.6i 0.478526i
\(186\) 0 0
\(187\) 5979.77 5979.77i 0.171002 0.171002i
\(188\) 0 0
\(189\) −28632.0 + 28632.0i −0.801544 + 0.801544i
\(190\) 0 0
\(191\) 11717.4i 0.321193i 0.987020 + 0.160596i \(0.0513417\pi\)
−0.987020 + 0.160596i \(0.948658\pi\)
\(192\) 0 0
\(193\) −68633.2 −1.84255 −0.921276 0.388910i \(-0.872852\pi\)
−0.921276 + 0.388910i \(0.872852\pi\)
\(194\) 0 0
\(195\) 12637.3 + 12637.3i 0.332341 + 0.332341i
\(196\) 0 0
\(197\) 22885.3 + 22885.3i 0.589689 + 0.589689i 0.937547 0.347858i \(-0.113091\pi\)
−0.347858 + 0.937547i \(0.613091\pi\)
\(198\) 0 0
\(199\) −59936.9 −1.51352 −0.756761 0.653692i \(-0.773219\pi\)
−0.756761 + 0.653692i \(0.773219\pi\)
\(200\) 0 0
\(201\) 92060.9i 2.27868i
\(202\) 0 0
\(203\) 8411.65 8411.65i 0.204122 0.204122i
\(204\) 0 0
\(205\) −26326.0 + 26326.0i −0.626436 + 0.626436i
\(206\) 0 0
\(207\) 177042.i 4.13177i
\(208\) 0 0
\(209\) −19352.1 −0.443032
\(210\) 0 0
\(211\) −12558.8 12558.8i −0.282086 0.282086i 0.551854 0.833941i \(-0.313920\pi\)
−0.833941 + 0.551854i \(0.813920\pi\)
\(212\) 0 0
\(213\) −56789.2 56789.2i −1.25172 1.25172i
\(214\) 0 0
\(215\) 6018.47 0.130199
\(216\) 0 0
\(217\) 5714.22i 0.121349i
\(218\) 0 0
\(219\) −30548.4 + 30548.4i −0.636943 + 0.636943i
\(220\) 0 0
\(221\) 3638.61 3638.61i 0.0744992 0.0744992i
\(222\) 0 0
\(223\) 22761.5i 0.457711i 0.973460 + 0.228856i \(0.0734983\pi\)
−0.973460 + 0.228856i \(0.926502\pi\)
\(224\) 0 0
\(225\) 36631.6 0.723586
\(226\) 0 0
\(227\) 6480.30 + 6480.30i 0.125760 + 0.125760i 0.767186 0.641425i \(-0.221657\pi\)
−0.641425 + 0.767186i \(0.721657\pi\)
\(228\) 0 0
\(229\) −36068.6 36068.6i −0.687795 0.687795i 0.273949 0.961744i \(-0.411670\pi\)
−0.961744 + 0.273949i \(0.911670\pi\)
\(230\) 0 0
\(231\) 34165.9 0.640278
\(232\) 0 0
\(233\) 68226.4i 1.25673i −0.777920 0.628363i \(-0.783725\pi\)
0.777920 0.628363i \(-0.216275\pi\)
\(234\) 0 0
\(235\) 23361.4 23361.4i 0.423022 0.423022i
\(236\) 0 0
\(237\) 101295. 101295.i 1.80340 1.80340i
\(238\) 0 0
\(239\) 100556.i 1.76040i 0.474599 + 0.880202i \(0.342593\pi\)
−0.474599 + 0.880202i \(0.657407\pi\)
\(240\) 0 0
\(241\) −35563.1 −0.612302 −0.306151 0.951983i \(-0.599041\pi\)
−0.306151 + 0.951983i \(0.599041\pi\)
\(242\) 0 0
\(243\) −47732.3 47732.3i −0.808351 0.808351i
\(244\) 0 0
\(245\) −26633.2 26633.2i −0.443702 0.443702i
\(246\) 0 0
\(247\) −11775.5 −0.193013
\(248\) 0 0
\(249\) 5258.84i 0.0848186i
\(250\) 0 0
\(251\) −29206.3 + 29206.3i −0.463585 + 0.463585i −0.899829 0.436244i \(-0.856309\pi\)
0.436244 + 0.899829i \(0.356309\pi\)
\(252\) 0 0
\(253\) −59246.1 + 59246.1i −0.925591 + 0.925591i
\(254\) 0 0
\(255\) 32592.1i 0.501224i
\(256\) 0 0
\(257\) 2932.77 0.0444029 0.0222015 0.999754i \(-0.492932\pi\)
0.0222015 + 0.999754i \(0.492932\pi\)
\(258\) 0 0
\(259\) 13471.3 + 13471.3i 0.200821 + 0.200821i
\(260\) 0 0
\(261\) 64594.4 + 64594.4i 0.948230 + 0.948230i
\(262\) 0 0
\(263\) −23253.5 −0.336184 −0.168092 0.985771i \(-0.553761\pi\)
−0.168092 + 0.985771i \(0.553761\pi\)
\(264\) 0 0
\(265\) 65244.7i 0.929081i
\(266\) 0 0
\(267\) 122083. 122083.i 1.71251 1.71251i
\(268\) 0 0
\(269\) −56836.3 + 56836.3i −0.785455 + 0.785455i −0.980745 0.195290i \(-0.937435\pi\)
0.195290 + 0.980745i \(0.437435\pi\)
\(270\) 0 0
\(271\) 91679.6i 1.24834i −0.781287 0.624172i \(-0.785436\pi\)
0.781287 0.624172i \(-0.214564\pi\)
\(272\) 0 0
\(273\) 20789.5 0.278945
\(274\) 0 0
\(275\) −12258.5 12258.5i −0.162096 0.162096i
\(276\) 0 0
\(277\) 75831.0 + 75831.0i 0.988297 + 0.988297i 0.999932 0.0116353i \(-0.00370370\pi\)
−0.0116353 + 0.999932i \(0.503704\pi\)
\(278\) 0 0
\(279\) −43880.4 −0.563718
\(280\) 0 0
\(281\) 77682.2i 0.983805i 0.870650 + 0.491903i \(0.163698\pi\)
−0.870650 + 0.491903i \(0.836302\pi\)
\(282\) 0 0
\(283\) −43834.7 + 43834.7i −0.547325 + 0.547325i −0.925666 0.378341i \(-0.876495\pi\)
0.378341 + 0.925666i \(0.376495\pi\)
\(284\) 0 0
\(285\) 52738.3 52738.3i 0.649286 0.649286i
\(286\) 0 0
\(287\) 43308.7i 0.525788i
\(288\) 0 0
\(289\) −74136.9 −0.887643
\(290\) 0 0
\(291\) 127286. + 127286.i 1.50312 + 1.50312i
\(292\) 0 0
\(293\) −61916.9 61916.9i −0.721231 0.721231i 0.247625 0.968856i \(-0.420350\pi\)
−0.968856 + 0.247625i \(0.920350\pi\)
\(294\) 0 0
\(295\) 68718.4 0.789639
\(296\) 0 0
\(297\) 147156.i 1.66826i
\(298\) 0 0
\(299\) −36050.5 + 36050.5i −0.403245 + 0.403245i
\(300\) 0 0
\(301\) 4950.47 4950.47i 0.0546404 0.0546404i
\(302\) 0 0
\(303\) 173807.i 1.89313i
\(304\) 0 0
\(305\) 129763. 1.39492
\(306\) 0 0
\(307\) −99698.5 99698.5i −1.05782 1.05782i −0.998223 0.0595972i \(-0.981018\pi\)
−0.0595972 0.998223i \(-0.518982\pi\)
\(308\) 0 0
\(309\) 70563.1 + 70563.1i 0.739028 + 0.739028i
\(310\) 0 0
\(311\) 127678. 1.32006 0.660031 0.751238i \(-0.270543\pi\)
0.660031 + 0.751238i \(0.270543\pi\)
\(312\) 0 0
\(313\) 24132.5i 0.246328i 0.992386 + 0.123164i \(0.0393042\pi\)
−0.992386 + 0.123164i \(0.960696\pi\)
\(314\) 0 0
\(315\) −64698.5 + 64698.5i −0.652039 + 0.652039i
\(316\) 0 0
\(317\) 63739.0 63739.0i 0.634289 0.634289i −0.314852 0.949141i \(-0.601955\pi\)
0.949141 + 0.314852i \(0.101955\pi\)
\(318\) 0 0
\(319\) 43232.3i 0.424841i
\(320\) 0 0
\(321\) 106840. 1.03687
\(322\) 0 0
\(323\) −15184.8 15184.8i −0.145547 0.145547i
\(324\) 0 0
\(325\) −7459.16 7459.16i −0.0706193 0.0706193i
\(326\) 0 0
\(327\) −351055. −3.28306
\(328\) 0 0
\(329\) 38431.6i 0.355056i
\(330\) 0 0
\(331\) −111266. + 111266.i −1.01556 + 1.01556i −0.0156868 + 0.999877i \(0.504993\pi\)
−0.999877 + 0.0156868i \(0.995007\pi\)
\(332\) 0 0
\(333\) −103448. + 103448.i −0.932899 + 0.932899i
\(334\) 0 0
\(335\) 116678.i 1.03968i
\(336\) 0 0
\(337\) −89183.5 −0.785280 −0.392640 0.919692i \(-0.628438\pi\)
−0.392640 + 0.919692i \(0.628438\pi\)
\(338\) 0 0
\(339\) 33435.0 + 33435.0i 0.290939 + 0.290939i
\(340\) 0 0
\(341\) 14684.3 + 14684.3i 0.126283 + 0.126283i
\(342\) 0 0
\(343\) −101488. −0.862637
\(344\) 0 0
\(345\) 322915.i 2.71300i
\(346\) 0 0
\(347\) −17075.7 + 17075.7i −0.141814 + 0.141814i −0.774450 0.632635i \(-0.781973\pi\)
0.632635 + 0.774450i \(0.281973\pi\)
\(348\) 0 0
\(349\) 25961.7 25961.7i 0.213149 0.213149i −0.592455 0.805604i \(-0.701841\pi\)
0.805604 + 0.592455i \(0.201841\pi\)
\(350\) 0 0
\(351\) 89542.5i 0.726800i
\(352\) 0 0
\(353\) 221897. 1.78075 0.890374 0.455230i \(-0.150443\pi\)
0.890374 + 0.455230i \(0.150443\pi\)
\(354\) 0 0
\(355\) −71974.9 71974.9i −0.571116 0.571116i
\(356\) 0 0
\(357\) 26808.5 + 26808.5i 0.210347 + 0.210347i
\(358\) 0 0
\(359\) 106831. 0.828908 0.414454 0.910070i \(-0.363973\pi\)
0.414454 + 0.910070i \(0.363973\pi\)
\(360\) 0 0
\(361\) 81179.1i 0.622917i
\(362\) 0 0
\(363\) −80878.1 + 80878.1i −0.613787 + 0.613787i
\(364\) 0 0
\(365\) −38717.2 + 38717.2i −0.290615 + 0.290615i
\(366\) 0 0
\(367\) 79074.9i 0.587093i −0.955945 0.293546i \(-0.905164\pi\)
0.955945 0.293546i \(-0.0948355\pi\)
\(368\) 0 0
\(369\) −332574. −2.44250
\(370\) 0 0
\(371\) 53666.8 + 53666.8i 0.389904 + 0.389904i
\(372\) 0 0
\(373\) 86341.4 + 86341.4i 0.620585 + 0.620585i 0.945681 0.325096i \(-0.105397\pi\)
−0.325096 + 0.945681i \(0.605397\pi\)
\(374\) 0 0
\(375\) 277093. 1.97044
\(376\) 0 0
\(377\) 26306.3i 0.185087i
\(378\) 0 0
\(379\) 168223. 168223.i 1.17114 1.17114i 0.189199 0.981939i \(-0.439411\pi\)
0.981939 0.189199i \(-0.0605890\pi\)
\(380\) 0 0
\(381\) 45996.6 45996.6i 0.316866 0.316866i
\(382\) 0 0
\(383\) 22177.8i 0.151189i −0.997139 0.0755946i \(-0.975915\pi\)
0.997139 0.0755946i \(-0.0240855\pi\)
\(384\) 0 0
\(385\) 43301.9 0.292137
\(386\) 0 0
\(387\) 38015.4 + 38015.4i 0.253827 + 0.253827i
\(388\) 0 0
\(389\) −163109. 163109.i −1.07790 1.07790i −0.996698 0.0812004i \(-0.974125\pi\)
−0.0812004 0.996698i \(-0.525875\pi\)
\(390\) 0 0
\(391\) −92975.9 −0.608159
\(392\) 0 0
\(393\) 383416.i 2.48248i
\(394\) 0 0
\(395\) 128382. 128382.i 0.822831 0.822831i
\(396\) 0 0
\(397\) −110463. + 110463.i −0.700868 + 0.700868i −0.964597 0.263729i \(-0.915047\pi\)
0.263729 + 0.964597i \(0.415047\pi\)
\(398\) 0 0
\(399\) 86759.4i 0.544968i
\(400\) 0 0
\(401\) 43913.8 0.273094 0.136547 0.990634i \(-0.456399\pi\)
0.136547 + 0.990634i \(0.456399\pi\)
\(402\) 0 0
\(403\) 8935.22 + 8935.22i 0.0550168 + 0.0550168i
\(404\) 0 0
\(405\) −182862. 182862.i −1.11484 1.11484i
\(406\) 0 0
\(407\) 69236.7 0.417972
\(408\) 0 0
\(409\) 188666.i 1.12784i 0.825830 + 0.563919i \(0.190707\pi\)
−0.825830 + 0.563919i \(0.809293\pi\)
\(410\) 0 0
\(411\) 123810. 123810.i 0.732948 0.732948i
\(412\) 0 0
\(413\) 56524.0 56524.0i 0.331385 0.331385i
\(414\) 0 0
\(415\) 6665.07i 0.0386998i
\(416\) 0 0
\(417\) −174743. −1.00491
\(418\) 0 0
\(419\) −88556.3 88556.3i −0.504419 0.504419i 0.408389 0.912808i \(-0.366091\pi\)
−0.912808 + 0.408389i \(0.866091\pi\)
\(420\) 0 0
\(421\) 42983.4 + 42983.4i 0.242514 + 0.242514i 0.817889 0.575375i \(-0.195144\pi\)
−0.575375 + 0.817889i \(0.695144\pi\)
\(422\) 0 0
\(423\) 295123. 1.64938
\(424\) 0 0
\(425\) 19237.5i 0.106505i
\(426\) 0 0
\(427\) 106736. 106736.i 0.585403 0.585403i
\(428\) 0 0
\(429\) 53424.5 53424.5i 0.290286 0.290286i
\(430\) 0 0
\(431\) 163696.i 0.881219i 0.897699 + 0.440609i \(0.145238\pi\)
−0.897699 + 0.440609i \(0.854762\pi\)
\(432\) 0 0
\(433\) 49710.2 0.265137 0.132568 0.991174i \(-0.457678\pi\)
0.132568 + 0.991174i \(0.457678\pi\)
\(434\) 0 0
\(435\) 117816. + 117816.i 0.622626 + 0.622626i
\(436\) 0 0
\(437\) 150447. + 150447.i 0.787809 + 0.787809i
\(438\) 0 0
\(439\) −182166. −0.945233 −0.472617 0.881268i \(-0.656690\pi\)
−0.472617 + 0.881268i \(0.656690\pi\)
\(440\) 0 0
\(441\) 336455.i 1.73002i
\(442\) 0 0
\(443\) −3141.28 + 3141.28i −0.0160066 + 0.0160066i −0.715065 0.699058i \(-0.753603\pi\)
0.699058 + 0.715065i \(0.253603\pi\)
\(444\) 0 0
\(445\) 154729. 154729.i 0.781359 0.781359i
\(446\) 0 0
\(447\) 78004.9i 0.390397i
\(448\) 0 0
\(449\) −108328. −0.537341 −0.268670 0.963232i \(-0.586584\pi\)
−0.268670 + 0.963232i \(0.586584\pi\)
\(450\) 0 0
\(451\) 111294. + 111294.i 0.547165 + 0.547165i
\(452\) 0 0
\(453\) −249978. 249978.i −1.21816 1.21816i
\(454\) 0 0
\(455\) 26348.7 0.127273
\(456\) 0 0
\(457\) 220908.i 1.05774i −0.848703 0.528870i \(-0.822616\pi\)
0.848703 0.528870i \(-0.177384\pi\)
\(458\) 0 0
\(459\) −115467. + 115467.i −0.548066 + 0.548066i
\(460\) 0 0
\(461\) 137539. 137539.i 0.647176 0.647176i −0.305133 0.952310i \(-0.598701\pi\)
0.952310 + 0.305133i \(0.0987010\pi\)
\(462\) 0 0
\(463\) 53332.6i 0.248789i −0.992233 0.124394i \(-0.960301\pi\)
0.992233 0.124394i \(-0.0396988\pi\)
\(464\) 0 0
\(465\) −80035.3 −0.370148
\(466\) 0 0
\(467\) −207164. 207164.i −0.949908 0.949908i 0.0488961 0.998804i \(-0.484430\pi\)
−0.998804 + 0.0488961i \(0.984430\pi\)
\(468\) 0 0
\(469\) −95973.3 95973.3i −0.436320 0.436320i
\(470\) 0 0
\(471\) −327485. −1.47622
\(472\) 0 0
\(473\) 25443.3i 0.113724i
\(474\) 0 0
\(475\) −31128.8 + 31128.8i −0.137967 + 0.137967i
\(476\) 0 0
\(477\) −412116. + 412116.i −1.81127 + 1.81127i
\(478\) 0 0
\(479\) 269434.i 1.17430i −0.809477 0.587152i \(-0.800249\pi\)
0.809477 0.587152i \(-0.199751\pi\)
\(480\) 0 0
\(481\) 42129.6 0.182095
\(482\) 0 0
\(483\) −265613. 265613.i −1.13856 1.13856i
\(484\) 0 0
\(485\) 161322. + 161322.i 0.685821 + 0.685821i
\(486\) 0 0
\(487\) 114893. 0.484436 0.242218 0.970222i \(-0.422125\pi\)
0.242218 + 0.970222i \(0.422125\pi\)
\(488\) 0 0
\(489\) 171667.i 0.717910i
\(490\) 0 0
\(491\) 83485.8 83485.8i 0.346298 0.346298i −0.512431 0.858728i \(-0.671255\pi\)
0.858728 + 0.512431i \(0.171255\pi\)
\(492\) 0 0
\(493\) 33922.5 33922.5i 0.139571 0.139571i
\(494\) 0 0
\(495\) 332522.i 1.35710i
\(496\) 0 0
\(497\) −118405. −0.479356
\(498\) 0 0
\(499\) −8291.04 8291.04i −0.0332972 0.0332972i 0.690262 0.723559i \(-0.257495\pi\)
−0.723559 + 0.690262i \(0.757495\pi\)
\(500\) 0 0
\(501\) 46051.8 + 46051.8i 0.183472 + 0.183472i
\(502\) 0 0
\(503\) −302384. −1.19515 −0.597575 0.801813i \(-0.703869\pi\)
−0.597575 + 0.801813i \(0.703869\pi\)
\(504\) 0 0
\(505\) 220283.i 0.863770i
\(506\) 0 0
\(507\) −296539. + 296539.i −1.15363 + 1.15363i
\(508\) 0 0
\(509\) 41954.6 41954.6i 0.161936 0.161936i −0.621488 0.783424i \(-0.713471\pi\)
0.783424 + 0.621488i \(0.213471\pi\)
\(510\) 0 0
\(511\) 63693.3i 0.243923i
\(512\) 0 0
\(513\) 373681. 1.41993
\(514\) 0 0
\(515\) 89431.9 + 89431.9i 0.337193 + 0.337193i
\(516\) 0 0
\(517\) −98761.0 98761.0i −0.369492 0.369492i
\(518\) 0 0
\(519\) 391635. 1.45394
\(520\) 0 0
\(521\) 16852.7i 0.0620860i −0.999518 0.0310430i \(-0.990117\pi\)
0.999518 0.0310430i \(-0.00988289\pi\)
\(522\) 0 0
\(523\) −92911.9 + 92911.9i −0.339678 + 0.339678i −0.856246 0.516568i \(-0.827209\pi\)
0.516568 + 0.856246i \(0.327209\pi\)
\(524\) 0 0
\(525\) 54957.5 54957.5i 0.199392 0.199392i
\(526\) 0 0
\(527\) 23044.3i 0.0829741i
\(528\) 0 0
\(529\) 641343. 2.29181
\(530\) 0 0
\(531\) 434057. + 434057.i 1.53942 + 1.53942i
\(532\) 0 0
\(533\) 67720.9 + 67720.9i 0.238379 + 0.238379i
\(534\) 0 0
\(535\) 135409. 0.473086
\(536\) 0 0
\(537\) 555796.i 1.92738i
\(538\) 0 0
\(539\) −112593. + 112593.i −0.387554 + 0.387554i
\(540\) 0 0
\(541\) 40690.8 40690.8i 0.139028 0.139028i −0.634168 0.773196i \(-0.718657\pi\)
0.773196 + 0.634168i \(0.218657\pi\)
\(542\) 0 0
\(543\) 318847.i 1.08139i
\(544\) 0 0
\(545\) −444928. −1.49795
\(546\) 0 0
\(547\) 222264. + 222264.i 0.742839 + 0.742839i 0.973123 0.230284i \(-0.0739656\pi\)
−0.230284 + 0.973123i \(0.573966\pi\)
\(548\) 0 0
\(549\) 819641. + 819641.i 2.71944 + 2.71944i
\(550\) 0 0
\(551\) −109782. −0.361600
\(552\) 0 0
\(553\) 211201.i 0.690629i
\(554\) 0 0
\(555\) −188684. + 188684.i −0.612560 + 0.612560i
\(556\) 0 0
\(557\) −223795. + 223795.i −0.721341 + 0.721341i −0.968878 0.247537i \(-0.920379\pi\)
0.247537 + 0.968878i \(0.420379\pi\)
\(558\) 0 0
\(559\) 15481.9i 0.0495451i
\(560\) 0 0
\(561\) 137784. 0.437798
\(562\) 0 0
\(563\) 201474. + 201474.i 0.635626 + 0.635626i 0.949474 0.313847i \(-0.101618\pi\)
−0.313847 + 0.949474i \(0.601618\pi\)
\(564\) 0 0
\(565\) 42375.6 + 42375.6i 0.132745 + 0.132745i
\(566\) 0 0
\(567\) −300825. −0.935724
\(568\) 0 0
\(569\) 473995.i 1.46403i 0.681289 + 0.732014i \(0.261420\pi\)
−0.681289 + 0.732014i \(0.738580\pi\)
\(570\) 0 0
\(571\) 303262. 303262.i 0.930133 0.930133i −0.0675806 0.997714i \(-0.521528\pi\)
0.997714 + 0.0675806i \(0.0215280\pi\)
\(572\) 0 0
\(573\) −134995. + 134995.i −0.411158 + 0.411158i
\(574\) 0 0
\(575\) 190601.i 0.576486i
\(576\) 0 0
\(577\) −340809. −1.02367 −0.511834 0.859084i \(-0.671034\pi\)
−0.511834 + 0.859084i \(0.671034\pi\)
\(578\) 0 0
\(579\) −790714. 790714.i −2.35864 2.35864i
\(580\) 0 0
\(581\) −5482.33 5482.33i −0.0162410 0.0162410i
\(582\) 0 0
\(583\) 275824. 0.811512
\(584\) 0 0
\(585\) 202336.i 0.591236i
\(586\) 0 0
\(587\) −253433. + 253433.i −0.735507 + 0.735507i −0.971705 0.236198i \(-0.924099\pi\)
0.236198 + 0.971705i \(0.424099\pi\)
\(588\) 0 0
\(589\) 37288.7 37288.7i 0.107485 0.107485i
\(590\) 0 0
\(591\) 527316.i 1.50972i
\(592\) 0 0
\(593\) 117236. 0.333390 0.166695 0.986009i \(-0.446691\pi\)
0.166695 + 0.986009i \(0.446691\pi\)
\(594\) 0 0
\(595\) 33977.2 + 33977.2i 0.0959741 + 0.0959741i
\(596\) 0 0
\(597\) −690526. 690526.i −1.93745 1.93745i
\(598\) 0 0
\(599\) −277087. −0.772257 −0.386129 0.922445i \(-0.626188\pi\)
−0.386129 + 0.922445i \(0.626188\pi\)
\(600\) 0 0
\(601\) 323876.i 0.896665i −0.893867 0.448333i \(-0.852018\pi\)
0.893867 0.448333i \(-0.147982\pi\)
\(602\) 0 0
\(603\) 736994. 736994.i 2.02689 2.02689i
\(604\) 0 0
\(605\) −102505. + 102505.i −0.280050 + 0.280050i
\(606\) 0 0
\(607\) 715467.i 1.94184i 0.239414 + 0.970918i \(0.423045\pi\)
−0.239414 + 0.970918i \(0.576955\pi\)
\(608\) 0 0
\(609\) 193819. 0.522591
\(610\) 0 0
\(611\) −60094.8 60094.8i −0.160974 0.160974i
\(612\) 0 0
\(613\) −137200. 137200.i −0.365117 0.365117i 0.500576 0.865693i \(-0.333122\pi\)
−0.865693 + 0.500576i \(0.833122\pi\)
\(614\) 0 0
\(615\) −606596. −1.60380
\(616\) 0 0
\(617\) 106650.i 0.280149i −0.990141 0.140074i \(-0.955266\pi\)
0.990141 0.140074i \(-0.0447342\pi\)
\(618\) 0 0
\(619\) −373667. + 373667.i −0.975221 + 0.975221i −0.999700 0.0244790i \(-0.992207\pi\)
0.0244790 + 0.999700i \(0.492207\pi\)
\(620\) 0 0
\(621\) 1.14402e6 1.14402e6i 2.96654 2.96654i
\(622\) 0 0
\(623\) 254543.i 0.655820i
\(624\) 0 0
\(625\) 227071. 0.581302
\(626\) 0 0
\(627\) −222953. 222953.i −0.567124 0.567124i
\(628\) 0 0
\(629\) 54327.1 + 54327.1i 0.137314 + 0.137314i
\(630\) 0 0
\(631\) 445762. 1.11955 0.559777 0.828644i \(-0.310887\pi\)
0.559777 + 0.828644i \(0.310887\pi\)
\(632\) 0 0
\(633\) 289376.i 0.722195i
\(634\) 0 0
\(635\) 58296.2 58296.2i 0.144575 0.144575i
\(636\) 0 0
\(637\) −68511.2 + 68511.2i −0.168843 + 0.168843i
\(638\) 0 0
\(639\) 909253.i 2.22681i
\(640\) 0 0
\(641\) −412550. −1.00406 −0.502031 0.864850i \(-0.667414\pi\)
−0.502031 + 0.864850i \(0.667414\pi\)
\(642\) 0 0
\(643\) −71290.0 71290.0i −0.172428 0.172428i 0.615617 0.788045i \(-0.288907\pi\)
−0.788045 + 0.615617i \(0.788907\pi\)
\(644\) 0 0
\(645\) 69338.0 + 69338.0i 0.166668 + 0.166668i
\(646\) 0 0
\(647\) −138722. −0.331388 −0.165694 0.986177i \(-0.552986\pi\)
−0.165694 + 0.986177i \(0.552986\pi\)
\(648\) 0 0
\(649\) 290509.i 0.689716i
\(650\) 0 0
\(651\) −65832.7 + 65832.7i −0.155339 + 0.155339i
\(652\) 0 0
\(653\) −467444. + 467444.i −1.09623 + 1.09623i −0.101387 + 0.994847i \(0.532328\pi\)
−0.994847 + 0.101387i \(0.967672\pi\)
\(654\) 0 0
\(655\) 485943.i 1.13267i
\(656\) 0 0
\(657\) −489111. −1.13312
\(658\) 0 0
\(659\) 180573. + 180573.i 0.415797 + 0.415797i 0.883752 0.467955i \(-0.155009\pi\)
−0.467955 + 0.883752i \(0.655009\pi\)
\(660\) 0 0
\(661\) −142726. 142726.i −0.326664 0.326664i 0.524652 0.851317i \(-0.324195\pi\)
−0.851317 + 0.524652i \(0.824195\pi\)
\(662\) 0 0
\(663\) 83840.0 0.190732
\(664\) 0 0
\(665\) 109959.i 0.248650i
\(666\) 0 0
\(667\) −336097. + 336097.i −0.755462 + 0.755462i
\(668\) 0 0
\(669\) −262232. + 262232.i −0.585914 + 0.585914i
\(670\) 0 0
\(671\) 548576.i 1.21841i
\(672\) 0 0
\(673\) −272445. −0.601517 −0.300759 0.953700i \(-0.597240\pi\)
−0.300759 + 0.953700i \(0.597240\pi\)
\(674\) 0 0
\(675\) 236708. + 236708.i 0.519523 + 0.519523i
\(676\) 0 0
\(677\) −285404. 285404.i −0.622706 0.622706i 0.323517 0.946222i \(-0.395135\pi\)
−0.946222 + 0.323517i \(0.895135\pi\)
\(678\) 0 0
\(679\) 265390. 0.575632
\(680\) 0 0
\(681\) 149317.i 0.321970i
\(682\) 0 0
\(683\) 186551. 186551.i 0.399904 0.399904i −0.478295 0.878199i \(-0.658745\pi\)
0.878199 + 0.478295i \(0.158745\pi\)
\(684\) 0 0
\(685\) 156918. 156918.i 0.334419 0.334419i
\(686\) 0 0
\(687\) 831084.i 1.76089i
\(688\) 0 0
\(689\) 167836. 0.353546
\(690\) 0 0
\(691\) 544261. + 544261.i 1.13986 + 1.13986i 0.988475 + 0.151383i \(0.0483727\pi\)
0.151383 + 0.988475i \(0.451627\pi\)
\(692\) 0 0
\(693\) 273515. + 273515.i 0.569528 + 0.569528i
\(694\) 0 0
\(695\) −221470. −0.458506
\(696\) 0 0
\(697\) 174655.i 0.359514i
\(698\) 0 0
\(699\) 786027. 786027.i 1.60873 1.60873i
\(700\) 0 0
\(701\) 69213.2 69213.2i 0.140849 0.140849i −0.633167 0.774015i \(-0.718245\pi\)
0.774015 + 0.633167i \(0.218245\pi\)
\(702\) 0 0
\(703\) 175817.i 0.355754i
\(704\) 0 0
\(705\) 538287. 1.08302
\(706\) 0 0
\(707\) 181193. + 181193.i 0.362496 + 0.362496i
\(708\) 0 0
\(709\) −133745. 133745.i −0.266063 0.266063i 0.561448 0.827512i \(-0.310244\pi\)
−0.827512 + 0.561448i \(0.810244\pi\)
\(710\) 0 0
\(711\) 1.62184e6 3.20826
\(712\) 0 0
\(713\) 228318.i 0.449118i
\(714\) 0 0
\(715\) 67710.4 67710.4i 0.132447 0.132447i
\(716\) 0 0
\(717\) −1.15849e6 + 1.15849e6i −2.25349 + 2.25349i
\(718\) 0 0
\(719\) 762270.i 1.47452i 0.675609 + 0.737261i \(0.263881\pi\)
−0.675609 + 0.737261i \(0.736119\pi\)
\(720\) 0 0
\(721\) 147124. 0.283017
\(722\) 0 0
\(723\) −409718. 409718.i −0.783805 0.783805i
\(724\) 0 0
\(725\) −69541.2 69541.2i −0.132302 0.132302i
\(726\) 0 0
\(727\) 664888. 1.25800 0.628999 0.777406i \(-0.283465\pi\)
0.628999 + 0.777406i \(0.283465\pi\)
\(728\) 0 0
\(729\) 85436.8i 0.160764i
\(730\) 0 0
\(731\) 19964.3 19964.3i 0.0373610 0.0373610i
\(732\) 0 0
\(733\) 616942. 616942.i 1.14825 1.14825i 0.161352 0.986897i \(-0.448414\pi\)
0.986897 0.161352i \(-0.0515856\pi\)
\(734\) 0 0
\(735\) 613675.i 1.13596i
\(736\) 0 0
\(737\) −493261. −0.908117
\(738\) 0 0
\(739\) −204895. 204895.i −0.375182 0.375182i 0.494179 0.869360i \(-0.335469\pi\)
−0.869360 + 0.494179i \(0.835469\pi\)
\(740\) 0 0
\(741\) −135664. 135664.i −0.247075 0.247075i
\(742\) 0 0
\(743\) −183598. −0.332576 −0.166288 0.986077i \(-0.553178\pi\)
−0.166288 + 0.986077i \(0.553178\pi\)
\(744\) 0 0
\(745\) 98863.7i 0.178125i
\(746\) 0 0
\(747\) 42099.7 42099.7i 0.0754462 0.0754462i
\(748\) 0 0
\(749\) 111380. 111380.i 0.198538 0.198538i
\(750\) 0 0
\(751\) 167996.i 0.297864i 0.988847 + 0.148932i \(0.0475836\pi\)
−0.988847 + 0.148932i \(0.952416\pi\)
\(752\) 0 0
\(753\) −672964. −1.18687
\(754\) 0 0
\(755\) −316823. 316823.i −0.555805 0.555805i
\(756\) 0 0
\(757\) 414105. + 414105.i 0.722634 + 0.722634i 0.969141 0.246507i \(-0.0792828\pi\)
−0.246507 + 0.969141i \(0.579283\pi\)
\(758\) 0 0
\(759\) −1.36513e6 −2.36969
\(760\) 0 0
\(761\) 315375.i 0.544575i −0.962216 0.272287i \(-0.912220\pi\)
0.962216 0.272287i \(-0.0877801\pi\)
\(762\) 0 0
\(763\) −365974. + 365974.i −0.628638 + 0.628638i
\(764\) 0 0
\(765\) −260916. + 260916.i −0.445839 + 0.445839i
\(766\) 0 0
\(767\) 176771.i 0.300483i
\(768\) 0 0
\(769\) 156016. 0.263825 0.131913 0.991261i \(-0.457888\pi\)
0.131913 + 0.991261i \(0.457888\pi\)
\(770\) 0 0
\(771\) 33788.0 + 33788.0i 0.0568400 + 0.0568400i
\(772\) 0 0
\(773\) 151026. + 151026.i 0.252751 + 0.252751i 0.822098 0.569347i \(-0.192804\pi\)
−0.569347 + 0.822098i \(0.692804\pi\)
\(774\) 0 0
\(775\) 47240.9 0.0786529
\(776\) 0 0
\(777\) 310402.i 0.514142i
\(778\) 0 0
\(779\) 282615. 282615.i 0.465715 0.465715i
\(780\) 0 0
\(781\) −304276. + 304276.i −0.498845 + 0.498845i
\(782\) 0 0
\(783\) 834798.i 1.36163i
\(784\) 0 0
\(785\) −415056. −0.673546
\(786\) 0 0
\(787\) 95574.5 + 95574.5i 0.154310 + 0.154310i 0.780040 0.625730i \(-0.215199\pi\)
−0.625730 + 0.780040i \(0.715199\pi\)
\(788\) 0 0
\(789\) −267901. 267901.i −0.430348 0.430348i
\(790\) 0 0
\(791\) 69711.8 0.111418
\(792\) 0 0
\(793\) 333802.i 0.530814i
\(794\) 0 0
\(795\) −751676. + 751676.i −1.18931 + 1.18931i