Properties

Label 128.5.f.b.95.1
Level $128$
Weight $5$
Character 128.95
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 95.1
Root \(1.03712 + 2.63142i\) of defining polynomial
Character \(\chi\) \(=\) 128.95
Dual form 128.5.f.b.31.1

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 −0.339485 + 0.940612i \(0.610253\pi\)
−0.940612 + 0.339485i \(0.889747\pi\)
\(4\) 0 0
\(5\) 14.6016 14.6016i 0.584063 0.584063i −0.351954 0.936017i \(-0.614483\pi\)
0.936017 + 0.351954i \(0.114483\pi\)
\(6\) 0 0
\(7\) −24.0210 −0.490224 −0.245112 0.969495i \(-0.578825\pi\)
−0.245112 + 0.969495i \(0.578825\pi\)
\(8\) 0 0
\(9\) 184.461i 2.27729i
\(10\) 0 0
\(11\) −61.7287 61.7287i −0.510154 0.510154i 0.404419 0.914574i \(-0.367474\pi\)
−0.914574 + 0.404419i \(0.867474\pi\)
\(12\) 0 0
\(13\) 37.5611 + 37.5611i 0.222255 + 0.222255i 0.809447 0.587192i \(-0.199767\pi\)
−0.587192 + 0.809447i \(0.699767\pi\)
\(14\) 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 \(-0.650663\pi\)
0.890059 + 0.455845i \(0.150663\pi\)
\(20\) 0 0
\(21\) 276.742 276.742i 0.627534 0.627534i
\(22\) 0 0
\(23\) 959.783 1.81433 0.907167 0.420770i \(-0.138240\pi\)
0.907167 + 0.420770i \(0.138240\pi\)
\(24\) 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 0.883956 0.467571i \(-0.154871\pi\)
−0.467571 + 0.883956i \(0.654871\pi\)
\(30\) 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 −0.471965 0.881617i \(-0.656455\pi\)
0.881617 + 0.471965i \(0.156455\pi\)
\(38\) 0 0
\(39\) −865.473 −0.569016
\(40\) 0 0
\(41\) 1802.95i 1.07255i −0.844044 0.536274i \(-0.819831\pi\)
0.844044 0.536274i \(-0.180169\pi\)
\(42\) 0 0
\(43\) −206.090 206.090i −0.111460 0.111460i 0.649177 0.760637i \(-0.275113\pi\)
−0.760637 + 0.649177i \(0.775113\pi\)
\(44\) 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 −0.187000 0.982360i \(-0.559876\pi\)
0.982360 + 0.187000i \(0.0598765\pi\)
\(54\) 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 \(-0.408636\pi\)
−0.959090 + 0.283102i \(0.908636\pi\)
\(60\) 0 0
\(61\) 4443.45 + 4443.45i 1.19415 + 1.19415i 0.975890 + 0.218264i \(0.0700395\pi\)
0.218264 + 0.975890i \(0.429961\pi\)
\(62\) 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 \(-0.533319\pi\)
0.994527 + 0.104485i \(0.0333193\pi\)
\(68\) 0 0
\(69\) −11057.5 + 11057.5i −2.32252 + 2.32252i
\(70\) 0 0
\(71\) 4929.25 0.977832 0.488916 0.872331i \(-0.337392\pi\)
0.488916 + 0.872331i \(0.337392\pi\)
\(72\) 0 0
\(73\) 2651.57i 0.497574i −0.968558 0.248787i \(-0.919968\pi\)
0.968558 0.248787i \(-0.0800319\pi\)
\(74\) 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 \(-0.742542\pi\)
0.723478 + 0.690348i \(0.242542\pi\)
\(84\) 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 \(0.233234\pi\)
−0.743353 + 0.668899i \(0.766766\pi\)
\(90\) 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 −0.233022 0.972471i \(-0.574861\pi\)
0.972471 + 0.233022i \(0.0748615\pi\)
\(102\) 0 0
\(103\) −6124.81 −0.577322 −0.288661 0.957431i \(-0.593210\pi\)
−0.288661 + 0.957431i \(0.593210\pi\)
\(104\) 0 0
\(105\) 8081.75i 0.733039i
\(106\) 0 0
\(107\) −4636.79 4636.79i −0.404995 0.404995i 0.474994 0.879989i \(-0.342450\pi\)
−0.879989 + 0.474994i \(0.842450\pi\)
\(108\) 0 0
\(109\) −15235.6 15235.6i −1.28235 1.28235i −0.939327 0.343022i \(-0.888549\pi\)
−0.343022 0.939327i \(-0.611451\pi\)
\(110\) 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 \(-0.990479\pi\)
0.0299081 + 0.999553i \(0.490479\pi\)
\(132\) 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 \(0.0924209\pi\)
−0.958144 + 0.286286i \(0.907579\pi\)
\(138\) 0 0
\(139\) 7583.76 + 7583.76i 0.392514 + 0.392514i 0.875582 0.483069i \(-0.160478\pi\)
−0.483069 + 0.875582i \(0.660478\pi\)
\(140\) 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 −0.779228 0.626741i \(-0.784389\pi\)
0.626741 + 0.779228i \(0.284389\pi\)
\(150\) 0 0
\(151\) 21697.8 0.951617 0.475809 0.879549i \(-0.342155\pi\)
0.475809 + 0.879549i \(0.342155\pi\)
\(152\) 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 0.357363 0.933966i \(-0.383676\pi\)
−0.933966 + 0.357363i \(0.883676\pi\)
\(158\) 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 \(-0.686464\pi\)
0.833273 + 0.552861i \(0.186464\pi\)
\(164\) 0 0
\(165\) 20768.4 20768.4i 0.762841 0.762841i
\(166\) 0 0
\(167\) −3997.25 −0.143327 −0.0716635 0.997429i \(-0.522831\pi\)
−0.0716635 + 0.997429i \(0.522831\pi\)
\(168\) 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 0.931540 0.363638i \(-0.118465\pi\)
−0.363638 + 0.931540i \(0.618465\pi\)
\(174\) 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 \(-0.928683\pi\)
0.222180 + 0.975006i \(0.428683\pi\)
\(180\) 0 0
\(181\) −13837.8 + 13837.8i −0.422386 + 0.422386i −0.886025 0.463638i \(-0.846544\pi\)
0.463638 + 0.886025i \(0.346544\pi\)
\(182\) 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 −0.347858 0.937547i \(-0.613091\pi\)
0.937547 + 0.347858i \(0.113091\pi\)
\(198\) 0 0
\(199\) 59936.9 1.51352 0.756761 0.653692i \(-0.226781\pi\)
0.756761 + 0.653692i \(0.226781\pi\)
\(200\) 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 \(-0.686080\pi\)
0.833941 + 0.551854i \(0.186080\pi\)
\(212\) 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 \(-0.778343\pi\)
0.641425 + 0.767186i \(0.278343\pi\)
\(228\) 0 0
\(229\) −36068.6 + 36068.6i −0.687795 + 0.687795i −0.961744 0.273949i \(-0.911670\pi\)
0.273949 + 0.961744i \(0.411670\pi\)
\(230\) 0 0
\(231\) −34165.9 −0.640278
\(232\) 0 0
\(233\) 68226.4i 1.25673i 0.777920 + 0.628363i \(0.216275\pi\)
−0.777920 + 0.628363i \(0.783725\pi\)
\(234\) 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 \(-0.143691\pi\)
−0.436244 + 0.899829i \(0.643691\pi\)
\(252\) 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 \(-0.446239\pi\)
0.168092 + 0.985771i \(0.446239\pi\)
\(264\) 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 0.195290 0.980745i \(-0.437435\pi\)
−0.980745 + 0.195290i \(0.937435\pi\)
\(270\) 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 −0.0116353 0.999932i \(-0.503704\pi\)
0.999932 + 0.0116353i \(0.00370370\pi\)
\(278\) 0 0
\(279\) 43880.4 0.563718
\(280\) 0 0
\(281\) 77682.2i 0.983805i −0.870650 0.491903i \(-0.836302\pi\)
0.870650 0.491903i \(-0.163698\pi\)
\(282\) 0 0
\(283\) 43834.7 + 43834.7i 0.547325 + 0.547325i 0.925666 0.378341i \(-0.123505\pi\)
−0.378341 + 0.925666i \(0.623505\pi\)
\(284\) 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 −0.968856 0.247625i \(-0.920350\pi\)
0.247625 + 0.968856i \(0.420350\pi\)
\(294\) 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 0.0595972 0.998223i \(-0.481018\pi\)
0.998223 0.0595972i \(-0.0189816\pi\)
\(308\) 0 0
\(309\) 70563.1 70563.1i 0.739028 0.739028i
\(310\) 0 0
\(311\) −127678. −1.32006 −0.660031 0.751238i \(-0.729457\pi\)
−0.660031 + 0.751238i \(0.729457\pi\)
\(312\) 0 0
\(313\) 24132.5i 0.246328i −0.992386 0.123164i \(-0.960696\pi\)
0.992386 0.123164i \(-0.0393042\pi\)
\(314\) 0 0
\(315\) 64698.5 + 64698.5i 0.652039 + 0.652039i
\(316\) 0 0
\(317\) 63739.0 + 63739.0i 0.634289 + 0.634289i 0.949141 0.314852i \(-0.101955\pi\)
−0.314852 + 0.949141i \(0.601955\pi\)
\(318\) 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 0.999877 + 0.0156868i \(0.00499346\pi\)
0.0156868 + 0.999877i \(0.495007\pi\)
\(332\) 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 \(-0.218027\pi\)
−0.632635 + 0.774450i \(0.718027\pi\)
\(348\) 0 0
\(349\) 25961.7 + 25961.7i 0.213149 + 0.213149i 0.805604 0.592455i \(-0.201841\pi\)
−0.592455 + 0.805604i \(0.701841\pi\)
\(350\) 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 \(-0.636027\pi\)
−0.414454 + 0.910070i \(0.636027\pi\)
\(360\) 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 −0.325096 0.945681i \(-0.605397\pi\)
0.945681 + 0.325096i \(0.105397\pi\)
\(374\) 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 −0.981939 0.189199i \(-0.939411\pi\)
−0.189199 0.981939i \(-0.560589\pi\)
\(380\) 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 −0.0812004 + 0.996698i \(0.525875\pi\)
−0.996698 + 0.0812004i \(0.974125\pi\)
\(390\) 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 0.263729 0.964597i \(-0.415047\pi\)
−0.964597 + 0.263729i \(0.915047\pi\)
\(398\) 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 \(-0.809293\pi\)
0.825830 0.563919i \(-0.190707\pi\)
\(410\) 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 \(-0.633909\pi\)
0.912808 + 0.408389i \(0.133909\pi\)
\(420\) 0 0
\(421\) 42983.4 42983.4i 0.242514 0.242514i −0.575375 0.817889i \(-0.695144\pi\)
0.817889 + 0.575375i \(0.195144\pi\)
\(422\) 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 \(-0.343310\pi\)
0.472617 + 0.881268i \(0.343310\pi\)
\(440\) 0 0
\(441\) 336455.i 1.73002i
\(442\) 0 0
\(443\) 3141.28 + 3141.28i 0.0160066 + 0.0160066i 0.715065 0.699058i \(-0.246397\pi\)
−0.699058 + 0.715065i \(0.746397\pi\)
\(444\) 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 \(0.177384\pi\)
−0.848703 + 0.528870i \(0.822616\pi\)
\(458\) 0 0
\(459\) 115467. + 115467.i 0.548066 + 0.548066i
\(460\) 0 0
\(461\) 137539. + 137539.i 0.647176 + 0.647176i 0.952310 0.305133i \(-0.0987010\pi\)
−0.305133 + 0.952310i \(0.598701\pi\)
\(462\) 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 \(-0.515570\pi\)
0.998804 + 0.0488961i \(0.0155703\pi\)
\(468\) 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 \(-0.577875\pi\)
−0.242218 + 0.970222i \(0.577875\pi\)
\(488\) 0 0
\(489\) 171667.i 0.717910i
\(490\) 0 0
\(491\) −83485.8 83485.8i −0.346298 0.346298i 0.512431 0.858728i \(-0.328745\pi\)
−0.858728 + 0.512431i \(0.828745\pi\)
\(492\) 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 \(-0.742505\pi\)
0.723559 + 0.690262i \(0.242505\pi\)
\(500\) 0 0
\(501\) 46051.8 46051.8i 0.183472 0.183472i
\(502\) 0 0
\(503\) 302384. 1.19515 0.597575 0.801813i \(-0.296131\pi\)
0.597575 + 0.801813i \(0.296131\pi\)
\(504\) 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 0.783424 0.621488i \(-0.213471\pi\)
−0.621488 + 0.783424i \(0.713471\pi\)
\(510\) 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 \(0.00988289\pi\)
−0.999518 + 0.0310430i \(0.990117\pi\)
\(522\) 0 0
\(523\) 92911.9 + 92911.9i 0.339678 + 0.339678i 0.856246 0.516568i \(-0.172791\pi\)
−0.516568 + 0.856246i \(0.672791\pi\)
\(524\) 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 0.773196 0.634168i \(-0.218657\pi\)
−0.634168 + 0.773196i \(0.718657\pi\)
\(542\) 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 \(-0.926034\pi\)
0.230284 + 0.973123i \(0.426034\pi\)
\(548\) 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 0.247537 0.968878i \(-0.420379\pi\)
−0.968878 + 0.247537i \(0.920379\pi\)
\(558\) 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 \(-0.898382\pi\)
0.313847 + 0.949474i \(0.398382\pi\)
\(564\) 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 \(-0.738580\pi\)
0.681289 0.732014i \(-0.261420\pi\)
\(570\) 0 0
\(571\) −303262. 303262.i −0.930133 0.930133i 0.0675806 0.997714i \(-0.478472\pi\)
−0.997714 + 0.0675806i \(0.978472\pi\)
\(572\) 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 \(-0.0759014\pi\)
−0.236198 + 0.971705i \(0.575901\pi\)
\(588\) 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 \(-0.373812\pi\)
0.386129 + 0.922445i \(0.373812\pi\)
\(600\) 0 0
\(601\) 323876.i 0.896665i 0.893867 + 0.448333i \(0.147982\pi\)
−0.893867 + 0.448333i \(0.852018\pi\)
\(602\) 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 −0.865693 0.500576i \(-0.833122\pi\)
0.500576 + 0.865693i \(0.333122\pi\)
\(614\) 0 0
\(615\) 606596. 1.60380
\(616\) 0 0
\(617\) 106650.i 0.280149i 0.990141 + 0.140074i \(0.0447342\pi\)
−0.990141 + 0.140074i \(0.955266\pi\)
\(618\) 0 0
\(619\) 373667. + 373667.i 0.975221 + 0.975221i 0.999700 0.0244790i \(-0.00779267\pi\)
−0.0244790 + 0.999700i \(0.507793\pi\)
\(620\) 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 \(-0.689113\pi\)
−0.559777 + 0.828644i \(0.689113\pi\)
\(632\) 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 \(-0.711093\pi\)
0.788045 + 0.615617i \(0.211093\pi\)
\(644\) 0 0
\(645\) 69338.0 69338.0i 0.166668 0.166668i
\(646\) 0 0
\(647\) 138722. 0.331388 0.165694 0.986177i \(-0.447014\pi\)
0.165694 + 0.986177i \(0.447014\pi\)
\(648\) 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 −0.994847 0.101387i \(-0.967672\pi\)
−0.101387 0.994847i \(-0.532328\pi\)
\(654\) 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 \(-0.844991\pi\)
0.467955 + 0.883752i \(0.344991\pi\)
\(660\) 0 0
\(661\) −142726. + 142726.i −0.326664 + 0.326664i −0.851317 0.524652i \(-0.824195\pi\)
0.524652 + 0.851317i \(0.324195\pi\)
\(662\) 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 −0.946222 0.323517i \(-0.895135\pi\)
0.323517 + 0.946222i \(0.395135\pi\)
\(678\) 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 \(-0.341255\pi\)
−0.878199 + 0.478295i \(0.841255\pi\)
\(684\) 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 −0.151383 + 0.988475i \(0.548373\pi\)
−0.988475 + 0.151383i \(0.951627\pi\)
\(692\) 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 0.774015 0.633167i \(-0.218245\pi\)
−0.633167 + 0.774015i \(0.718245\pi\)
\(702\) 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 −0.827512 0.561448i \(-0.810244\pi\)
0.561448 + 0.827512i \(0.310244\pi\)
\(710\) 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 \(-0.716535\pi\)
−0.628999 + 0.777406i \(0.716535\pi\)
\(728\) 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 0.986897 + 0.161352i \(0.0515856\pi\)
0.161352 + 0.986897i \(0.448414\pi\)
\(734\) 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 \(-0.664531\pi\)
0.869360 + 0.494179i \(0.164531\pi\)
\(740\) 0 0
\(741\) −135664. + 135664.i −0.247075 + 0.247075i
\(742\) 0 0
\(743\) 183598. 0.332576 0.166288 0.986077i \(-0.446822\pi\)
0.166288 + 0.986077i \(0.446822\pi\)
\(744\) 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 −0.246507 0.969141i \(-0.579283\pi\)
0.969141 + 0.246507i \(0.0792828\pi\)
\(758\) 0 0
\(759\) 1.36513e6 2.36969
\(760\) 0 0
\(761\) 315375.i 0.544575i 0.962216 + 0.272287i \(0.0877801\pi\)
−0.962216 + 0.272287i \(0.912220\pi\)
\(762\) 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 −0.569347 0.822098i \(-0.692804\pi\)
0.822098 + 0.569347i \(0.192804\pi\)
\(774\) 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 \(-0.784801\pi\)
0.625730 + 0.780040i \(0.284801\pi\)
\(788\) 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
\(796\) 0 0