Properties

Label 128.5.f.a.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 \(0.153862 + 2.82424i\) of defining polynomial
Character \(\chi\) \(=\) 128.95
Dual form 128.5.f.a.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.42589 + 9.42589i) q^{3} +(2.84710 - 2.84710i) q^{5} +76.7794 q^{7} -96.6949i q^{9} +O(q^{10})\) \(q+(-9.42589 + 9.42589i) q^{3} +(2.84710 - 2.84710i) q^{5} +76.7794 q^{7} -96.6949i q^{9} +(121.488 + 121.488i) q^{11} +(-27.1604 - 27.1604i) q^{13} +53.6729i q^{15} -88.0613 q^{17} +(-261.112 + 261.112i) q^{19} +(-723.714 + 723.714i) q^{21} -93.4210 q^{23} +608.788i q^{25} +(147.938 + 147.938i) q^{27} +(-272.522 - 272.522i) q^{29} +1232.20i q^{31} -2290.26 q^{33} +(218.599 - 218.599i) q^{35} +(1046.16 - 1046.16i) q^{37} +512.021 q^{39} +915.267i q^{41} +(1116.82 + 1116.82i) q^{43} +(-275.300 - 275.300i) q^{45} +1720.70i q^{47} +3494.07 q^{49} +(830.056 - 830.056i) q^{51} +(-734.019 + 734.019i) q^{53} +691.775 q^{55} -4922.43i q^{57} +(-1202.73 - 1202.73i) q^{59} +(-580.221 - 580.221i) q^{61} -7424.17i q^{63} -154.657 q^{65} +(-1483.97 + 1483.97i) q^{67} +(880.576 - 880.576i) q^{69} -5571.73 q^{71} +6615.21i q^{73} +(-5738.37 - 5738.37i) q^{75} +(9327.75 + 9327.75i) q^{77} -5391.66i q^{79} +5043.39 q^{81} +(-2554.07 + 2554.07i) q^{83} +(-250.719 + 250.719i) q^{85} +5137.52 q^{87} -10962.7i q^{89} +(-2085.35 - 2085.35i) q^{91} +(-11614.6 - 11614.6i) q^{93} +1486.83i q^{95} +4713.20 q^{97} +(11747.2 - 11747.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + 94q^{11} + 2q^{13} - 4q^{17} - 706q^{19} + 164q^{21} - 1148q^{23} - 1664q^{27} - 862q^{29} - 4q^{33} + 1340q^{35} + 1826q^{37} - 2684q^{39} + 1694q^{43} - 1410q^{45} + 682q^{49} - 3012q^{51} + 482q^{53} + 11780q^{55} - 2786q^{59} + 3778q^{61} - 2020q^{65} + 7998q^{67} - 9628q^{69} - 19964q^{71} + 17570q^{75} + 9508q^{77} + 1454q^{81} - 17282q^{83} - 9948q^{85} + 49284q^{87} - 28036q^{91} - 8896q^{93} - 4q^{97} + 49214q^{99} + O(q^{100}) \)

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
\(3\) −9.42589 + 9.42589i −1.04732 + 1.04732i −0.0484980 + 0.998823i \(0.515443\pi\)
−0.998823 + 0.0484980i \(0.984557\pi\)
\(4\) 0 0
\(5\) 2.84710 2.84710i 0.113884 0.113884i −0.647868 0.761752i \(-0.724339\pi\)
0.761752 + 0.647868i \(0.224339\pi\)
\(6\) 0 0
\(7\) 76.7794 1.56693 0.783463 0.621439i \(-0.213451\pi\)
0.783463 + 0.621439i \(0.213451\pi\)
\(8\) 0 0
\(9\) 96.6949i 1.19376i
\(10\) 0 0
\(11\) 121.488 + 121.488i 1.00403 + 1.00403i 0.999992 + 0.00403849i \(0.00128549\pi\)
0.00403849 + 0.999992i \(0.498715\pi\)
\(12\) 0 0
\(13\) −27.1604 27.1604i −0.160712 0.160712i 0.622170 0.782882i \(-0.286251\pi\)
−0.782882 + 0.622170i \(0.786251\pi\)
\(14\) 0 0
\(15\) 53.6729i 0.238546i
\(16\) 0 0
\(17\) −88.0613 −0.304710 −0.152355 0.988326i \(-0.548686\pi\)
−0.152355 + 0.988326i \(0.548686\pi\)
\(18\) 0 0
\(19\) −261.112 + 261.112i −0.723302 + 0.723302i −0.969276 0.245974i \(-0.920892\pi\)
0.245974 + 0.969276i \(0.420892\pi\)
\(20\) 0 0
\(21\) −723.714 + 723.714i −1.64107 + 1.64107i
\(22\) 0 0
\(23\) −93.4210 −0.176599 −0.0882996 0.996094i \(-0.528143\pi\)
−0.0882996 + 0.996094i \(0.528143\pi\)
\(24\) 0 0
\(25\) 608.788i 0.974061i
\(26\) 0 0
\(27\) 147.938 + 147.938i 0.202933 + 0.202933i
\(28\) 0 0
\(29\) −272.522 272.522i −0.324045 0.324045i 0.526272 0.850316i \(-0.323590\pi\)
−0.850316 + 0.526272i \(0.823590\pi\)
\(30\) 0 0
\(31\) 1232.20i 1.28220i 0.767455 + 0.641102i \(0.221523\pi\)
−0.767455 + 0.641102i \(0.778477\pi\)
\(32\) 0 0
\(33\) −2290.26 −2.10308
\(34\) 0 0
\(35\) 218.599 218.599i 0.178448 0.178448i
\(36\) 0 0
\(37\) 1046.16 1046.16i 0.764177 0.764177i −0.212898 0.977075i \(-0.568290\pi\)
0.977075 + 0.212898i \(0.0682901\pi\)
\(38\) 0 0
\(39\) 512.021 0.336635
\(40\) 0 0
\(41\) 915.267i 0.544478i 0.962230 + 0.272239i \(0.0877641\pi\)
−0.962230 + 0.272239i \(0.912236\pi\)
\(42\) 0 0
\(43\) 1116.82 + 1116.82i 0.604013 + 0.604013i 0.941375 0.337362i \(-0.109535\pi\)
−0.337362 + 0.941375i \(0.609535\pi\)
\(44\) 0 0
\(45\) −275.300 275.300i −0.135951 0.135951i
\(46\) 0 0
\(47\) 1720.70i 0.778949i 0.921037 + 0.389475i \(0.127343\pi\)
−0.921037 + 0.389475i \(0.872657\pi\)
\(48\) 0 0
\(49\) 3494.07 1.45526
\(50\) 0 0
\(51\) 830.056 830.056i 0.319130 0.319130i
\(52\) 0 0
\(53\) −734.019 + 734.019i −0.261310 + 0.261310i −0.825586 0.564276i \(-0.809155\pi\)
0.564276 + 0.825586i \(0.309155\pi\)
\(54\) 0 0
\(55\) 691.775 0.228686
\(56\) 0 0
\(57\) 4922.43i 1.51506i
\(58\) 0 0
\(59\) −1202.73 1202.73i −0.345512 0.345512i 0.512923 0.858435i \(-0.328563\pi\)
−0.858435 + 0.512923i \(0.828563\pi\)
\(60\) 0 0
\(61\) −580.221 580.221i −0.155932 0.155932i 0.624830 0.780761i \(-0.285168\pi\)
−0.780761 + 0.624830i \(0.785168\pi\)
\(62\) 0 0
\(63\) 7424.17i 1.87054i
\(64\) 0 0
\(65\) −154.657 −0.0366051
\(66\) 0 0
\(67\) −1483.97 + 1483.97i −0.330580 + 0.330580i −0.852807 0.522227i \(-0.825101\pi\)
0.522227 + 0.852807i \(0.325101\pi\)
\(68\) 0 0
\(69\) 880.576 880.576i 0.184956 0.184956i
\(70\) 0 0
\(71\) −5571.73 −1.10528 −0.552641 0.833419i \(-0.686380\pi\)
−0.552641 + 0.833419i \(0.686380\pi\)
\(72\) 0 0
\(73\) 6615.21i 1.24136i 0.784064 + 0.620681i \(0.213144\pi\)
−0.784064 + 0.620681i \(0.786856\pi\)
\(74\) 0 0
\(75\) −5738.37 5738.37i −1.02015 1.02015i
\(76\) 0 0
\(77\) 9327.75 + 9327.75i 1.57324 + 1.57324i
\(78\) 0 0
\(79\) 5391.66i 0.863910i −0.901895 0.431955i \(-0.857824\pi\)
0.901895 0.431955i \(-0.142176\pi\)
\(80\) 0 0
\(81\) 5043.39 0.768692
\(82\) 0 0
\(83\) −2554.07 + 2554.07i −0.370747 + 0.370747i −0.867749 0.497002i \(-0.834434\pi\)
0.497002 + 0.867749i \(0.334434\pi\)
\(84\) 0 0
\(85\) −250.719 + 250.719i −0.0347017 + 0.0347017i
\(86\) 0 0
\(87\) 5137.52 0.678758
\(88\) 0 0
\(89\) 10962.7i 1.38400i −0.721898 0.691999i \(-0.756730\pi\)
0.721898 0.691999i \(-0.243270\pi\)
\(90\) 0 0
\(91\) −2085.35 2085.35i −0.251824 0.251824i
\(92\) 0 0
\(93\) −11614.6 11614.6i −1.34288 1.34288i
\(94\) 0 0
\(95\) 1486.83i 0.164745i
\(96\) 0 0
\(97\) 4713.20 0.500925 0.250462 0.968126i \(-0.419417\pi\)
0.250462 + 0.968126i \(0.419417\pi\)
\(98\) 0 0
\(99\) 11747.2 11747.2i 1.19858 1.19858i
\(100\) 0 0
\(101\) 11381.0 11381.0i 1.11568 1.11568i 0.123307 0.992369i \(-0.460650\pi\)
0.992369 0.123307i \(-0.0393499\pi\)
\(102\) 0 0
\(103\) −175.758 −0.0165668 −0.00828342 0.999966i \(-0.502637\pi\)
−0.00828342 + 0.999966i \(0.502637\pi\)
\(104\) 0 0
\(105\) 4120.97i 0.373784i
\(106\) 0 0
\(107\) 15151.8 + 15151.8i 1.32342 + 1.32342i 0.910988 + 0.412432i \(0.135321\pi\)
0.412432 + 0.910988i \(0.364679\pi\)
\(108\) 0 0
\(109\) 2349.51 + 2349.51i 0.197754 + 0.197754i 0.799036 0.601283i \(-0.205343\pi\)
−0.601283 + 0.799036i \(0.705343\pi\)
\(110\) 0 0
\(111\) 19721.9i 1.60068i
\(112\) 0 0
\(113\) −8526.30 −0.667734 −0.333867 0.942620i \(-0.608354\pi\)
−0.333867 + 0.942620i \(0.608354\pi\)
\(114\) 0 0
\(115\) −265.979 + 265.979i −0.0201118 + 0.0201118i
\(116\) 0 0
\(117\) −2626.27 + 2626.27i −0.191852 + 0.191852i
\(118\) 0 0
\(119\) −6761.29 −0.477459
\(120\) 0 0
\(121\) 14877.5i 1.01615i
\(122\) 0 0
\(123\) −8627.21 8627.21i −0.570243 0.570243i
\(124\) 0 0
\(125\) 3512.72 + 3512.72i 0.224814 + 0.224814i
\(126\) 0 0
\(127\) 2844.31i 0.176347i 0.996105 + 0.0881737i \(0.0281031\pi\)
−0.996105 + 0.0881737i \(0.971897\pi\)
\(128\) 0 0
\(129\) −21054.1 −1.26519
\(130\) 0 0
\(131\) −6989.87 + 6989.87i −0.407311 + 0.407311i −0.880800 0.473489i \(-0.842994\pi\)
0.473489 + 0.880800i \(0.342994\pi\)
\(132\) 0 0
\(133\) −20048.0 + 20048.0i −1.13336 + 1.13336i
\(134\) 0 0
\(135\) 842.390 0.0462217
\(136\) 0 0
\(137\) 3669.69i 0.195519i −0.995210 0.0977594i \(-0.968832\pi\)
0.995210 0.0977594i \(-0.0311676\pi\)
\(138\) 0 0
\(139\) 4401.33 + 4401.33i 0.227800 + 0.227800i 0.811773 0.583973i \(-0.198503\pi\)
−0.583973 + 0.811773i \(0.698503\pi\)
\(140\) 0 0
\(141\) −16219.1 16219.1i −0.815810 0.815810i
\(142\) 0 0
\(143\) 6599.30i 0.322720i
\(144\) 0 0
\(145\) −1551.79 −0.0738071
\(146\) 0 0
\(147\) −32934.7 + 32934.7i −1.52412 + 1.52412i
\(148\) 0 0
\(149\) −15737.5 + 15737.5i −0.708863 + 0.708863i −0.966296 0.257433i \(-0.917123\pi\)
0.257433 + 0.966296i \(0.417123\pi\)
\(150\) 0 0
\(151\) 41972.2 1.84080 0.920402 0.390974i \(-0.127862\pi\)
0.920402 + 0.390974i \(0.127862\pi\)
\(152\) 0 0
\(153\) 8515.08i 0.363752i
\(154\) 0 0
\(155\) 3508.19 + 3508.19i 0.146023 + 0.146023i
\(156\) 0 0
\(157\) 24735.4 + 24735.4i 1.00351 + 1.00351i 0.999994 + 0.00351271i \(0.00111813\pi\)
0.00351271 + 0.999994i \(0.498882\pi\)
\(158\) 0 0
\(159\) 13837.6i 0.547350i
\(160\) 0 0
\(161\) −7172.80 −0.276718
\(162\) 0 0
\(163\) 24429.8 24429.8i 0.919483 0.919483i −0.0775084 0.996992i \(-0.524696\pi\)
0.996992 + 0.0775084i \(0.0246965\pi\)
\(164\) 0 0
\(165\) −6520.60 + 6520.60i −0.239508 + 0.239508i
\(166\) 0 0
\(167\) −52178.2 −1.87093 −0.935463 0.353425i \(-0.885017\pi\)
−0.935463 + 0.353425i \(0.885017\pi\)
\(168\) 0 0
\(169\) 27085.6i 0.948343i
\(170\) 0 0
\(171\) 25248.2 + 25248.2i 0.863452 + 0.863452i
\(172\) 0 0
\(173\) −26316.2 26316.2i −0.879289 0.879289i 0.114172 0.993461i \(-0.463578\pi\)
−0.993461 + 0.114172i \(0.963578\pi\)
\(174\) 0 0
\(175\) 46742.4i 1.52628i
\(176\) 0 0
\(177\) 22673.5 0.723723
\(178\) 0 0
\(179\) 4815.78 4815.78i 0.150301 0.150301i −0.627952 0.778252i \(-0.716106\pi\)
0.778252 + 0.627952i \(0.216106\pi\)
\(180\) 0 0
\(181\) 23924.9 23924.9i 0.730286 0.730286i −0.240391 0.970676i \(-0.577276\pi\)
0.970676 + 0.240391i \(0.0772755\pi\)
\(182\) 0 0
\(183\) 10938.2 0.326621
\(184\) 0 0
\(185\) 5957.04i 0.174055i
\(186\) 0 0
\(187\) −10698.4 10698.4i −0.305939 0.305939i
\(188\) 0 0
\(189\) 11358.6 + 11358.6i 0.317981 + 0.317981i
\(190\) 0 0
\(191\) 45079.4i 1.23569i −0.786298 0.617847i \(-0.788005\pi\)
0.786298 0.617847i \(-0.211995\pi\)
\(192\) 0 0
\(193\) 50286.0 1.34999 0.674997 0.737820i \(-0.264145\pi\)
0.674997 + 0.737820i \(0.264145\pi\)
\(194\) 0 0
\(195\) 1457.78 1457.78i 0.0383373 0.0383373i
\(196\) 0 0
\(197\) 25662.2 25662.2i 0.661243 0.661243i −0.294430 0.955673i \(-0.595130\pi\)
0.955673 + 0.294430i \(0.0951297\pi\)
\(198\) 0 0
\(199\) 44599.1 1.12621 0.563106 0.826385i \(-0.309606\pi\)
0.563106 + 0.826385i \(0.309606\pi\)
\(200\) 0 0
\(201\) 27975.5i 0.692447i
\(202\) 0 0
\(203\) −20924.0 20924.0i −0.507754 0.507754i
\(204\) 0 0
\(205\) 2605.86 + 2605.86i 0.0620073 + 0.0620073i
\(206\) 0 0
\(207\) 9033.33i 0.210818i
\(208\) 0 0
\(209\) −63443.8 −1.45244
\(210\) 0 0
\(211\) 25828.5 25828.5i 0.580143 0.580143i −0.354800 0.934942i \(-0.615451\pi\)
0.934942 + 0.354800i \(0.115451\pi\)
\(212\) 0 0
\(213\) 52518.5 52518.5i 1.15759 1.15759i
\(214\) 0 0
\(215\) 6359.40 0.137575
\(216\) 0 0
\(217\) 94607.4i 2.00912i
\(218\) 0 0
\(219\) −62354.3 62354.3i −1.30010 1.30010i
\(220\) 0 0
\(221\) 2391.78 + 2391.78i 0.0489707 + 0.0489707i
\(222\) 0 0
\(223\) 72650.0i 1.46092i −0.682957 0.730459i \(-0.739306\pi\)
0.682957 0.730459i \(-0.260694\pi\)
\(224\) 0 0
\(225\) 58866.7 1.16280
\(226\) 0 0
\(227\) 18858.2 18858.2i 0.365972 0.365972i −0.500034 0.866006i \(-0.666679\pi\)
0.866006 + 0.500034i \(0.166679\pi\)
\(228\) 0 0
\(229\) −41675.9 + 41675.9i −0.794721 + 0.794721i −0.982258 0.187537i \(-0.939950\pi\)
0.187537 + 0.982258i \(0.439950\pi\)
\(230\) 0 0
\(231\) −175845. −3.29538
\(232\) 0 0
\(233\) 2767.61i 0.0509792i −0.999675 0.0254896i \(-0.991886\pi\)
0.999675 0.0254896i \(-0.00811447\pi\)
\(234\) 0 0
\(235\) 4899.00 + 4899.00i 0.0887099 + 0.0887099i
\(236\) 0 0
\(237\) 50821.2 + 50821.2i 0.904791 + 0.904791i
\(238\) 0 0
\(239\) 49981.8i 0.875016i 0.899215 + 0.437508i \(0.144139\pi\)
−0.899215 + 0.437508i \(0.855861\pi\)
\(240\) 0 0
\(241\) −44076.0 −0.758872 −0.379436 0.925218i \(-0.623882\pi\)
−0.379436 + 0.925218i \(0.623882\pi\)
\(242\) 0 0
\(243\) −59521.4 + 59521.4i −1.00800 + 1.00800i
\(244\) 0 0
\(245\) 9947.97 9947.97i 0.165730 0.165730i
\(246\) 0 0
\(247\) 14183.8 0.232487
\(248\) 0 0
\(249\) 48148.8i 0.776582i
\(250\) 0 0
\(251\) −31786.2 31786.2i −0.504534 0.504534i 0.408309 0.912844i \(-0.366119\pi\)
−0.912844 + 0.408309i \(0.866119\pi\)
\(252\) 0 0
\(253\) −11349.5 11349.5i −0.177311 0.177311i
\(254\) 0 0
\(255\) 4726.51i 0.0726876i
\(256\) 0 0
\(257\) 70865.6 1.07292 0.536462 0.843924i \(-0.319760\pi\)
0.536462 + 0.843924i \(0.319760\pi\)
\(258\) 0 0
\(259\) 80323.4 80323.4i 1.19741 1.19741i
\(260\) 0 0
\(261\) −26351.5 + 26351.5i −0.386833 + 0.386833i
\(262\) 0 0
\(263\) 113289. 1.63786 0.818929 0.573894i \(-0.194568\pi\)
0.818929 + 0.573894i \(0.194568\pi\)
\(264\) 0 0
\(265\) 4179.65i 0.0595180i
\(266\) 0 0
\(267\) 103333. + 103333.i 1.44949 + 1.44949i
\(268\) 0 0
\(269\) −70652.7 70652.7i −0.976393 0.976393i 0.0233352 0.999728i \(-0.492572\pi\)
−0.999728 + 0.0233352i \(0.992572\pi\)
\(270\) 0 0
\(271\) 110180.i 1.50025i −0.661294 0.750126i \(-0.729993\pi\)
0.661294 0.750126i \(-0.270007\pi\)
\(272\) 0 0
\(273\) 39312.7 0.527481
\(274\) 0 0
\(275\) −73960.2 + 73960.2i −0.977987 + 0.977987i
\(276\) 0 0
\(277\) −34611.0 + 34611.0i −0.451081 + 0.451081i −0.895713 0.444632i \(-0.853334\pi\)
0.444632 + 0.895713i \(0.353334\pi\)
\(278\) 0 0
\(279\) 119147. 1.53065
\(280\) 0 0
\(281\) 147980.i 1.87408i −0.349216 0.937042i \(-0.613552\pi\)
0.349216 0.937042i \(-0.386448\pi\)
\(282\) 0 0
\(283\) 39761.2 + 39761.2i 0.496463 + 0.496463i 0.910335 0.413872i \(-0.135824\pi\)
−0.413872 + 0.910335i \(0.635824\pi\)
\(284\) 0 0
\(285\) −14014.7 14014.7i −0.172541 0.172541i
\(286\) 0 0
\(287\) 70273.6i 0.853156i
\(288\) 0 0
\(289\) −75766.2 −0.907152
\(290\) 0 0
\(291\) −44426.1 + 44426.1i −0.524629 + 0.524629i
\(292\) 0 0
\(293\) 708.909 708.909i 0.00825763 0.00825763i −0.702966 0.711224i \(-0.748141\pi\)
0.711224 + 0.702966i \(0.248141\pi\)
\(294\) 0 0
\(295\) −6848.56 −0.0786965
\(296\) 0 0
\(297\) 35945.3i 0.407502i
\(298\) 0 0
\(299\) 2537.35 + 2537.35i 0.0283816 + 0.0283816i
\(300\) 0 0
\(301\) 85748.8 + 85748.8i 0.946444 + 0.946444i
\(302\) 0 0
\(303\) 214552.i 2.33694i
\(304\) 0 0
\(305\) −3303.90 −0.0355162
\(306\) 0 0
\(307\) −20597.1 + 20597.1i −0.218539 + 0.218539i −0.807883 0.589344i \(-0.799386\pi\)
0.589344 + 0.807883i \(0.299386\pi\)
\(308\) 0 0
\(309\) 1656.67 1656.67i 0.0173508 0.0173508i
\(310\) 0 0
\(311\) −82310.6 −0.851011 −0.425505 0.904956i \(-0.639904\pi\)
−0.425505 + 0.904956i \(0.639904\pi\)
\(312\) 0 0
\(313\) 120415.i 1.22911i 0.788872 + 0.614557i \(0.210665\pi\)
−0.788872 + 0.614557i \(0.789335\pi\)
\(314\) 0 0
\(315\) −21137.4 21137.4i −0.213025 0.213025i
\(316\) 0 0
\(317\) −14795.3 14795.3i −0.147233 0.147233i 0.629648 0.776881i \(-0.283199\pi\)
−0.776881 + 0.629648i \(0.783199\pi\)
\(318\) 0 0
\(319\) 66216.1i 0.650702i
\(320\) 0 0
\(321\) −285639. −2.77209
\(322\) 0 0
\(323\) 22993.9 22993.9i 0.220398 0.220398i
\(324\) 0 0
\(325\) 16534.9 16534.9i 0.156543 0.156543i
\(326\) 0 0
\(327\) −44292.5 −0.414224
\(328\) 0 0
\(329\) 132114.i 1.22056i
\(330\) 0 0
\(331\) 82868.2 + 82868.2i 0.756366 + 0.756366i 0.975659 0.219293i \(-0.0703752\pi\)
−0.219293 + 0.975659i \(0.570375\pi\)
\(332\) 0 0
\(333\) −101158. 101158.i −0.912247 0.912247i
\(334\) 0 0
\(335\) 8450.04i 0.0752955i
\(336\) 0 0
\(337\) 78854.4 0.694331 0.347165 0.937804i \(-0.387144\pi\)
0.347165 + 0.937804i \(0.387144\pi\)
\(338\) 0 0
\(339\) 80368.0 80368.0i 0.699332 0.699332i
\(340\) 0 0
\(341\) −149697. + 149697.i −1.28737 + 1.28737i
\(342\) 0 0
\(343\) 83925.2 0.713352
\(344\) 0 0
\(345\) 5014.18i 0.0421271i
\(346\) 0 0
\(347\) −59543.0 59543.0i −0.494506 0.494506i 0.415216 0.909723i \(-0.363706\pi\)
−0.909723 + 0.415216i \(0.863706\pi\)
\(348\) 0 0
\(349\) 756.172 + 756.172i 0.00620826 + 0.00620826i 0.710204 0.703996i \(-0.248603\pi\)
−0.703996 + 0.710204i \(0.748603\pi\)
\(350\) 0 0
\(351\) 8036.11i 0.0652276i
\(352\) 0 0
\(353\) 23723.5 0.190384 0.0951918 0.995459i \(-0.469654\pi\)
0.0951918 + 0.995459i \(0.469654\pi\)
\(354\) 0 0
\(355\) −15863.3 + 15863.3i −0.125874 + 0.125874i
\(356\) 0 0
\(357\) 63731.2 63731.2i 0.500053 0.500053i
\(358\) 0 0
\(359\) −146064. −1.13333 −0.566663 0.823950i \(-0.691766\pi\)
−0.566663 + 0.823950i \(0.691766\pi\)
\(360\) 0 0
\(361\) 6038.12i 0.0463327i
\(362\) 0 0
\(363\) −140234. 140234.i −1.06424 1.06424i
\(364\) 0 0
\(365\) 18834.2 + 18834.2i 0.141371 + 0.141371i
\(366\) 0 0
\(367\) 151129.i 1.12206i 0.827797 + 0.561028i \(0.189594\pi\)
−0.827797 + 0.561028i \(0.810406\pi\)
\(368\) 0 0
\(369\) 88501.7 0.649978
\(370\) 0 0
\(371\) −56357.5 + 56357.5i −0.409453 + 0.409453i
\(372\) 0 0
\(373\) −26207.7 + 26207.7i −0.188370 + 0.188370i −0.794991 0.606621i \(-0.792524\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(374\) 0 0
\(375\) −66221.0 −0.470905
\(376\) 0 0
\(377\) 14803.6i 0.104156i
\(378\) 0 0
\(379\) 110424. + 110424.i 0.768752 + 0.768752i 0.977887 0.209135i \(-0.0670647\pi\)
−0.209135 + 0.977887i \(0.567065\pi\)
\(380\) 0 0
\(381\) −26810.1 26810.1i −0.184692 0.184692i
\(382\) 0 0
\(383\) 10514.9i 0.0716819i −0.999358 0.0358409i \(-0.988589\pi\)
0.999358 0.0358409i \(-0.0114110\pi\)
\(384\) 0 0
\(385\) 53114.1 0.358334
\(386\) 0 0
\(387\) 107991. 107991.i 0.721049 0.721049i
\(388\) 0 0
\(389\) 166762. 166762.i 1.10204 1.10204i 0.107877 0.994164i \(-0.465595\pi\)
0.994164 0.107877i \(-0.0344054\pi\)
\(390\) 0 0
\(391\) 8226.78 0.0538116
\(392\) 0 0
\(393\) 131772.i 0.853172i
\(394\) 0 0
\(395\) −15350.6 15350.6i −0.0983855 0.0983855i
\(396\) 0 0
\(397\) 192542. + 192542.i 1.22164 + 1.22164i 0.967048 + 0.254594i \(0.0819419\pi\)
0.254594 + 0.967048i \(0.418058\pi\)
\(398\) 0 0
\(399\) 377941.i 2.37399i
\(400\) 0 0
\(401\) 91157.6 0.566897 0.283448 0.958987i \(-0.408522\pi\)
0.283448 + 0.958987i \(0.408522\pi\)
\(402\) 0 0
\(403\) 33467.0 33467.0i 0.206066 0.206066i
\(404\) 0 0
\(405\) 14359.0 14359.0i 0.0875417 0.0875417i
\(406\) 0 0
\(407\) 254191. 1.53451
\(408\) 0 0
\(409\) 107774.i 0.644272i −0.946693 0.322136i \(-0.895599\pi\)
0.946693 0.322136i \(-0.104401\pi\)
\(410\) 0 0
\(411\) 34590.1 + 34590.1i 0.204771 + 0.204771i
\(412\) 0 0
\(413\) −92344.5 92344.5i −0.541391 0.541391i
\(414\) 0 0
\(415\) 14543.4i 0.0844442i
\(416\) 0 0
\(417\) −82972.9 −0.477160
\(418\) 0 0
\(419\) −118524. + 118524.i −0.675115 + 0.675115i −0.958891 0.283776i \(-0.908413\pi\)
0.283776 + 0.958891i \(0.408413\pi\)
\(420\) 0 0
\(421\) 226616. 226616.i 1.27858 1.27858i 0.337113 0.941464i \(-0.390549\pi\)
0.941464 0.337113i \(-0.109451\pi\)
\(422\) 0 0
\(423\) 166383. 0.929882
\(424\) 0 0
\(425\) 53610.7i 0.296807i
\(426\) 0 0
\(427\) −44549.0 44549.0i −0.244333 0.244333i
\(428\) 0 0
\(429\) 62204.3 + 62204.3i 0.337991 + 0.337991i
\(430\) 0 0
\(431\) 5397.51i 0.0290562i 0.999894 + 0.0145281i \(0.00462460\pi\)
−0.999894 + 0.0145281i \(0.995375\pi\)
\(432\) 0 0
\(433\) 163835. 0.873840 0.436920 0.899500i \(-0.356069\pi\)
0.436920 + 0.899500i \(0.356069\pi\)
\(434\) 0 0
\(435\) 14627.0 14627.0i 0.0772997 0.0772997i
\(436\) 0 0
\(437\) 24393.4 24393.4i 0.127735 0.127735i
\(438\) 0 0
\(439\) −158472. −0.822289 −0.411144 0.911570i \(-0.634871\pi\)
−0.411144 + 0.911570i \(0.634871\pi\)
\(440\) 0 0
\(441\) 337859.i 1.73723i
\(442\) 0 0
\(443\) −137929. 137929.i −0.702826 0.702826i 0.262190 0.965016i \(-0.415555\pi\)
−0.965016 + 0.262190i \(0.915555\pi\)
\(444\) 0 0
\(445\) −31211.8 31211.8i −0.157615 0.157615i
\(446\) 0 0
\(447\) 296680.i 1.48482i
\(448\) 0 0
\(449\) 327336. 1.62368 0.811841 0.583879i \(-0.198466\pi\)
0.811841 + 0.583879i \(0.198466\pi\)
\(450\) 0 0
\(451\) −111194. + 111194.i −0.546672 + 0.546672i
\(452\) 0 0
\(453\) −395625. + 395625.i −1.92791 + 1.92791i
\(454\) 0 0
\(455\) −11874.4 −0.0573575
\(456\) 0 0
\(457\) 154510.i 0.739817i 0.929068 + 0.369909i \(0.120611\pi\)
−0.929068 + 0.369909i \(0.879389\pi\)
\(458\) 0 0
\(459\) −13027.6 13027.6i −0.0618358 0.0618358i
\(460\) 0 0
\(461\) −19296.3 19296.3i −0.0907971 0.0907971i 0.660249 0.751046i \(-0.270451\pi\)
−0.751046 + 0.660249i \(0.770451\pi\)
\(462\) 0 0
\(463\) 26503.6i 0.123635i −0.998087 0.0618176i \(-0.980310\pi\)
0.998087 0.0618176i \(-0.0196897\pi\)
\(464\) 0 0
\(465\) −66135.7 −0.305865
\(466\) 0 0
\(467\) 111797. 111797.i 0.512622 0.512622i −0.402707 0.915329i \(-0.631931\pi\)
0.915329 + 0.402707i \(0.131931\pi\)
\(468\) 0 0
\(469\) −113939. + 113939.i −0.517994 + 0.517994i
\(470\) 0 0
\(471\) −466307. −2.10199
\(472\) 0 0
\(473\) 271360.i 1.21290i
\(474\) 0 0
\(475\) −158962. 158962.i −0.704541 0.704541i
\(476\) 0 0
\(477\) 70975.8 + 70975.8i 0.311942 + 0.311942i
\(478\) 0 0
\(479\) 225380.i 0.982301i 0.871075 + 0.491150i \(0.163423\pi\)
−0.871075 + 0.491150i \(0.836577\pi\)
\(480\) 0 0
\(481\) −56828.1 −0.245625
\(482\) 0 0
\(483\) 67610.1 67610.1i 0.289813 0.289813i
\(484\) 0 0
\(485\) 13419.0 13419.0i 0.0570473 0.0570473i
\(486\) 0 0
\(487\) −8483.58 −0.0357702 −0.0178851 0.999840i \(-0.505693\pi\)
−0.0178851 + 0.999840i \(0.505693\pi\)
\(488\) 0 0
\(489\) 460544.i 1.92599i
\(490\) 0 0
\(491\) 69265.0 + 69265.0i 0.287310 + 0.287310i 0.836016 0.548706i \(-0.184879\pi\)
−0.548706 + 0.836016i \(0.684879\pi\)
\(492\) 0 0
\(493\) 23998.6 + 23998.6i 0.0987399 + 0.0987399i
\(494\) 0 0
\(495\) 66891.1i 0.272997i
\(496\) 0 0
\(497\) −427794. −1.73190
\(498\) 0 0
\(499\) 86869.4 86869.4i 0.348872 0.348872i −0.510817 0.859689i \(-0.670657\pi\)
0.859689 + 0.510817i \(0.170657\pi\)
\(500\) 0 0
\(501\) 491827. 491827.i 1.95946 1.95946i
\(502\) 0 0
\(503\) −112271. −0.443745 −0.221872 0.975076i \(-0.571217\pi\)
−0.221872 + 0.975076i \(0.571217\pi\)
\(504\) 0 0
\(505\) 64805.7i 0.254115i
\(506\) 0 0
\(507\) 255306. + 255306.i 0.993220 + 0.993220i
\(508\) 0 0
\(509\) 167589. + 167589.i 0.646861 + 0.646861i 0.952233 0.305372i \(-0.0987808\pi\)
−0.305372 + 0.952233i \(0.598781\pi\)
\(510\) 0 0
\(511\) 507912.i 1.94512i
\(512\) 0 0
\(513\) −77256.9 −0.293564
\(514\) 0 0
\(515\) −500.399 + 500.399i −0.00188670 + 0.00188670i
\(516\) 0 0
\(517\) −209044. + 209044.i −0.782089 + 0.782089i
\(518\) 0 0
\(519\) 496108. 1.84180
\(520\) 0 0
\(521\) 287463.i 1.05903i −0.848302 0.529513i \(-0.822375\pi\)
0.848302 0.529513i \(-0.177625\pi\)
\(522\) 0 0
\(523\) −203069. 203069.i −0.742404 0.742404i 0.230636 0.973040i \(-0.425919\pi\)
−0.973040 + 0.230636i \(0.925919\pi\)
\(524\) 0 0
\(525\) −440588. 440588.i −1.59851 1.59851i
\(526\) 0 0
\(527\) 108509.i 0.390701i
\(528\) 0 0
\(529\) −271114. −0.968813
\(530\) 0 0
\(531\) −116297. + 116297.i −0.412459 + 0.412459i
\(532\) 0 0
\(533\) 24859.0 24859.0i 0.0875042 0.0875042i
\(534\) 0 0
\(535\) 86277.6 0.301433
\(536\) 0 0
\(537\) 90786.1i 0.314826i
\(538\) 0 0
\(539\) 424486. + 424486.i 1.46112 + 1.46112i
\(540\) 0 0
\(541\) −308972. 308972.i −1.05566 1.05566i −0.998357 0.0573036i \(-0.981750\pi\)
−0.0573036 0.998357i \(-0.518250\pi\)
\(542\) 0 0
\(543\) 451027.i 1.52969i
\(544\) 0 0
\(545\) 13378.6 0.0450420
\(546\) 0 0
\(547\) −8623.13 + 8623.13i −0.0288198 + 0.0288198i −0.721370 0.692550i \(-0.756487\pi\)
0.692550 + 0.721370i \(0.256487\pi\)
\(548\) 0 0
\(549\) −56104.4 + 56104.4i −0.186145 + 0.186145i
\(550\) 0 0
\(551\) 142317. 0.468765
\(552\) 0 0
\(553\) 413968.i 1.35368i
\(554\) 0 0
\(555\) 56150.4 + 56150.4i 0.182292 + 0.182292i
\(556\) 0 0
\(557\) 208785. + 208785.i 0.672961 + 0.672961i 0.958398 0.285437i \(-0.0921387\pi\)
−0.285437 + 0.958398i \(0.592139\pi\)
\(558\) 0 0
\(559\) 60666.5i 0.194145i
\(560\) 0 0
\(561\) 201683. 0.640832
\(562\) 0 0
\(563\) 127891. 127891.i 0.403480 0.403480i −0.475977 0.879458i \(-0.657906\pi\)
0.879458 + 0.475977i \(0.157906\pi\)
\(564\) 0 0
\(565\) −24275.2 + 24275.2i −0.0760443 + 0.0760443i
\(566\) 0 0
\(567\) 387228. 1.20448
\(568\) 0 0
\(569\) 488561.i 1.50902i 0.656290 + 0.754509i \(0.272125\pi\)
−0.656290 + 0.754509i \(0.727875\pi\)
\(570\) 0 0
\(571\) −17324.2 17324.2i −0.0531352 0.0531352i 0.680040 0.733175i \(-0.261962\pi\)
−0.733175 + 0.680040i \(0.761962\pi\)
\(572\) 0 0
\(573\) 424913. + 424913.i 1.29417 + 1.29417i
\(574\) 0 0
\(575\) 56873.6i 0.172018i
\(576\) 0 0
\(577\) −9362.93 −0.0281229 −0.0140615 0.999901i \(-0.504476\pi\)
−0.0140615 + 0.999901i \(0.504476\pi\)
\(578\) 0 0
\(579\) −473990. + 473990.i −1.41388 + 1.41388i
\(580\) 0 0
\(581\) −196100. + 196100.i −0.580932 + 0.580932i
\(582\) 0 0
\(583\) −178348. −0.524725
\(584\) 0 0
\(585\) 14954.5i 0.0436978i
\(586\) 0 0
\(587\) 46301.5 + 46301.5i 0.134375 + 0.134375i 0.771095 0.636720i \(-0.219709\pi\)
−0.636720 + 0.771095i \(0.719709\pi\)
\(588\) 0 0
\(589\) −321742. 321742.i −0.927422 0.927422i
\(590\) 0 0
\(591\) 483778.i 1.38507i
\(592\) 0 0
\(593\) −194145. −0.552099 −0.276049 0.961143i \(-0.589025\pi\)
−0.276049 + 0.961143i \(0.589025\pi\)
\(594\) 0 0
\(595\) −19250.1 + 19250.1i −0.0543749 + 0.0543749i
\(596\) 0 0
\(597\) −420387. + 420387.i −1.17951 + 1.17951i
\(598\) 0 0
\(599\) −474516. −1.32250 −0.661252 0.750164i \(-0.729975\pi\)
−0.661252 + 0.750164i \(0.729975\pi\)
\(600\) 0 0
\(601\) 87515.3i 0.242290i −0.992635 0.121145i \(-0.961343\pi\)
0.992635 0.121145i \(-0.0386566\pi\)
\(602\) 0 0
\(603\) 143493. + 143493.i 0.394634 + 0.394634i
\(604\) 0 0
\(605\) 42357.8 + 42357.8i 0.115724 + 0.115724i
\(606\) 0 0
\(607\) 687260.i 1.86528i −0.360808 0.932640i \(-0.617499\pi\)
0.360808 0.932640i \(-0.382501\pi\)
\(608\) 0 0
\(609\) 394456. 1.06356
\(610\) 0 0
\(611\) 46734.8 46734.8i 0.125187 0.125187i
\(612\) 0 0
\(613\) 220862. 220862.i 0.587761 0.587761i −0.349263 0.937025i \(-0.613568\pi\)
0.937025 + 0.349263i \(0.113568\pi\)
\(614\) 0 0
\(615\) −49125.1 −0.129883
\(616\) 0 0
\(617\) 518967.i 1.36323i −0.731711 0.681615i \(-0.761278\pi\)
0.731711 0.681615i \(-0.238722\pi\)
\(618\) 0 0
\(619\) −77555.3 77555.3i −0.202409 0.202409i 0.598622 0.801031i \(-0.295715\pi\)
−0.801031 + 0.598622i \(0.795715\pi\)
\(620\) 0 0
\(621\) −13820.5 13820.5i −0.0358378 0.0358378i
\(622\) 0 0
\(623\) 841705.i 2.16862i
\(624\) 0 0
\(625\) −360490. −0.922855
\(626\) 0 0
\(627\) 598015. 598015.i 1.52117 1.52117i
\(628\) 0 0
\(629\) −92126.1 + 92126.1i −0.232853 + 0.232853i
\(630\) 0 0
\(631\) −344653. −0.865612 −0.432806 0.901487i \(-0.642477\pi\)
−0.432806 + 0.901487i \(0.642477\pi\)
\(632\) 0 0
\(633\) 486914.i 1.21519i
\(634\) 0 0
\(635\) 8098.03 + 8098.03i 0.0200832 + 0.0200832i
\(636\) 0 0
\(637\) −94900.2 94900.2i −0.233877 0.233877i
\(638\) 0 0
\(639\) 538758.i 1.31945i
\(640\) 0 0
\(641\) −183353. −0.446243 −0.223122 0.974791i \(-0.571625\pi\)
−0.223122 + 0.974791i \(0.571625\pi\)
\(642\) 0 0
\(643\) −541900. + 541900.i −1.31068 + 1.31068i −0.389768 + 0.920913i \(0.627445\pi\)
−0.920913 + 0.389768i \(0.872555\pi\)
\(644\) 0 0
\(645\) −59943.0 + 59943.0i −0.144085 + 0.144085i
\(646\) 0 0
\(647\) 358562. 0.856555 0.428278 0.903647i \(-0.359121\pi\)
0.428278 + 0.903647i \(0.359121\pi\)
\(648\) 0 0
\(649\) 292233.i 0.693808i
\(650\) 0 0
\(651\) −891760. 891760.i −2.10419 2.10419i
\(652\) 0 0
\(653\) 73642.4 + 73642.4i 0.172704 + 0.172704i 0.788166 0.615463i \(-0.211031\pi\)
−0.615463 + 0.788166i \(0.711031\pi\)
\(654\) 0 0
\(655\) 39801.7i 0.0927725i
\(656\) 0 0
\(657\) 639657. 1.48189
\(658\) 0 0
\(659\) 22081.7 22081.7i 0.0508467 0.0508467i −0.681226 0.732073i \(-0.738553\pi\)
0.732073 + 0.681226i \(0.238553\pi\)
\(660\) 0 0
\(661\) −20869.3 + 20869.3i −0.0477644 + 0.0477644i −0.730586 0.682821i \(-0.760753\pi\)
0.682821 + 0.730586i \(0.260753\pi\)
\(662\) 0 0
\(663\) −45089.3 −0.102576
\(664\) 0 0
\(665\) 114157.i 0.258143i
\(666\) 0 0
\(667\) 25459.3 + 25459.3i 0.0572261 + 0.0572261i
\(668\) 0 0
\(669\) 684791. + 684791.i 1.53005 + 1.53005i
\(670\) 0 0
\(671\) 140979.i 0.313120i
\(672\) 0 0
\(673\) 379771. 0.838479 0.419239 0.907876i \(-0.362297\pi\)
0.419239 + 0.907876i \(0.362297\pi\)
\(674\) 0 0
\(675\) −90063.0 + 90063.0i −0.197669 + 0.197669i
\(676\) 0 0
\(677\) 156167. 156167.i 0.340731 0.340731i −0.515911 0.856642i \(-0.672546\pi\)
0.856642 + 0.515911i \(0.172546\pi\)
\(678\) 0 0
\(679\) 361877. 0.784912
\(680\) 0 0
\(681\) 355511.i 0.766581i
\(682\) 0 0
\(683\) 164044. + 164044.i 0.351656 + 0.351656i 0.860725 0.509070i \(-0.170010\pi\)
−0.509070 + 0.860725i \(0.670010\pi\)
\(684\) 0 0
\(685\) −10448.0 10448.0i −0.0222665 0.0222665i
\(686\) 0 0
\(687\) 785666.i 1.66466i
\(688\) 0 0
\(689\) 39872.4 0.0839912
\(690\) 0 0
\(691\) −288207. + 288207.i −0.603599 + 0.603599i −0.941266 0.337667i \(-0.890362\pi\)
0.337667 + 0.941266i \(0.390362\pi\)
\(692\) 0 0
\(693\) 901945. 901945.i 1.87808 1.87808i
\(694\) 0 0
\(695\) 25062.1 0.0518856
\(696\) 0 0
\(697\) 80599.7i 0.165908i
\(698\) 0 0
\(699\) 26087.2 + 26087.2i 0.0533916 + 0.0533916i
\(700\) 0 0
\(701\) −323248. 323248.i −0.657808 0.657808i 0.297053 0.954861i \(-0.403996\pi\)
−0.954861 + 0.297053i \(0.903996\pi\)
\(702\) 0 0
\(703\) 546329.i 1.10546i
\(704\) 0 0
\(705\) −92355.0 −0.185816
\(706\) 0 0
\(707\) 873826. 873826.i 1.74818 1.74818i
\(708\) 0 0
\(709\) 580085. 580085.i 1.15398 1.15398i 0.168235 0.985747i \(-0.446193\pi\)
0.985747 0.168235i \(-0.0538067\pi\)
\(710\) 0 0
\(711\) −521346. −1.03130
\(712\) 0 0
\(713\) 115113.i 0.226436i
\(714\) 0 0
\(715\) −18788.9 18788.9i −0.0367526 0.0367526i
\(716\) 0 0
\(717\) −471123. 471123.i −0.916423 0.916423i
\(718\) 0 0
\(719\) 332243.i 0.642684i 0.946963 + 0.321342i \(0.104134\pi\)
−0.946963 + 0.321342i \(0.895866\pi\)
\(720\) 0 0
\(721\) −13494.5 −0.0259590
\(722\) 0 0
\(723\) 415456. 415456.i 0.794783 0.794783i
\(724\) 0 0
\(725\) 165908. 165908.i 0.315639 0.315639i
\(726\) 0 0
\(727\) −362311. −0.685508 −0.342754 0.939425i \(-0.611360\pi\)
−0.342754 + 0.939425i \(0.611360\pi\)
\(728\) 0 0
\(729\) 713570.i 1.34271i
\(730\) 0 0
\(731\) −98348.7 98348.7i −0.184049 0.184049i
\(732\) 0 0
\(733\) −377844. 377844.i −0.703242 0.703242i 0.261863 0.965105i \(-0.415663\pi\)
−0.965105 + 0.261863i \(0.915663\pi\)
\(734\) 0 0
\(735\) 187537.i 0.347146i
\(736\) 0 0
\(737\) −360569. −0.663825
\(738\) 0 0
\(739\) 467502. 467502.i 0.856042 0.856042i −0.134828 0.990869i \(-0.543048\pi\)
0.990869 + 0.134828i \(0.0430480\pi\)
\(740\) 0 0
\(741\) −133695. + 133695.i −0.243489 + 0.243489i
\(742\) 0 0
\(743\) 555820. 1.00683 0.503415 0.864045i \(-0.332077\pi\)
0.503415 + 0.864045i \(0.332077\pi\)
\(744\) 0 0
\(745\) 89612.4i 0.161456i
\(746\) 0 0
\(747\) 246966. + 246966.i 0.442584 + 0.442584i
\(748\) 0 0
\(749\) 1.16335e6 + 1.16335e6i 2.07370 + 2.07370i
\(750\) 0 0
\(751\) 308308.i 0.546644i −0.961923 0.273322i \(-0.911878\pi\)
0.961923 0.273322i \(-0.0881224\pi\)
\(752\) 0 0
\(753\) 599226. 1.05682
\(754\) 0 0
\(755\) 119499. 119499.i 0.209638 0.209638i
\(756\) 0 0
\(757\) −34980.2 + 34980.2i −0.0610423 + 0.0610423i −0.736969 0.675927i \(-0.763744\pi\)
0.675927 + 0.736969i \(0.263744\pi\)
\(758\) 0 0
\(759\) 213958. 0.371403
\(760\) 0 0
\(761\) 545745.i 0.942368i −0.882035 0.471184i \(-0.843827\pi\)
0.882035 0.471184i \(-0.156173\pi\)
\(762\) 0 0
\(763\) 180394. + 180394.i 0.309866 + 0.309866i
\(764\) 0 0
\(765\) 24243.3 + 24243.3i 0.0414256 + 0.0414256i
\(766\) 0 0
\(767\) 65332.9i 0.111056i
\(768\) 0 0
\(769\) 510362. 0.863030 0.431515 0.902106i \(-0.357979\pi\)
0.431515 + 0.902106i \(0.357979\pi\)
\(770\) 0 0
\(771\) −667972. + 667972.i −1.12370 + 1.12370i
\(772\) 0 0
\(773\) −596763. + 596763.i −0.998718 + 0.998718i −0.999999 0.00128103i \(-0.999592\pi\)
0.00128103 + 0.999999i \(0.499592\pi\)
\(774\) 0 0
\(775\) −750148. −1.24895
\(776\) 0 0
\(777\) 1.51424e6i 2.50814i
\(778\) 0 0
\(779\) −238987. 238987.i −0.393822 0.393822i
\(780\) 0 0
\(781\) −676897. 676897.i −1.10974 1.10974i
\(782\) 0 0
\(783\) 80632.7i 0.131519i
\(784\) 0 0
\(785\) 140849. 0.228567
\(786\) 0 0
\(787\) −463254. + 463254.i −0.747945 + 0.747945i −0.974093 0.226148i \(-0.927387\pi\)
0.226148 + 0.974093i \(0.427387\pi\)
\(788\) 0 0
\(789\) −1.06785e6 + 1.06785e6i −1.71536 + 1.71536i
\(790\) 0 0
\(791\) −654644. −1.04629
\(792\) 0 0
\(793\) 31518.0i 0.0501202i
\(794\) 0 0
\(795\) −39396.9 39396.9i −0.0623344 0.0623344i