Properties

Label 128.4.g.a.17.1
Level $128$
Weight $4$
Character 128.17
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 17.1
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.54796 + 8.56554i) q^{3} +(-7.55322 + 3.12865i) q^{5} +(-7.16166 + 7.16166i) q^{7} +(-41.6886 - 41.6886i) q^{9} +O(q^{10})\) \(q+(-3.54796 + 8.56554i) q^{3} +(-7.55322 + 3.12865i) q^{5} +(-7.16166 + 7.16166i) q^{7} +(-41.6886 - 41.6886i) q^{9} +(-0.758120 - 1.83026i) q^{11} +(71.0832 + 29.4436i) q^{13} -75.7978i q^{15} -98.5470i q^{17} +(-89.5748 - 37.1031i) q^{19} +(-35.9342 - 86.7528i) q^{21} +(-24.9355 - 24.9355i) q^{23} +(-41.1256 + 41.1256i) q^{25} +(273.726 - 113.381i) q^{27} +(-57.8528 + 139.669i) q^{29} -58.0545 q^{31} +18.3670 q^{33} +(31.6873 - 76.4999i) q^{35} +(-202.968 + 84.0720i) q^{37} +(-504.401 + 504.401i) q^{39} +(-45.3618 - 45.3618i) q^{41} +(-89.7175 - 216.597i) q^{43} +(445.312 + 184.454i) q^{45} +4.38416i q^{47} +240.421i q^{49} +(844.109 + 349.641i) q^{51} +(8.98141 + 21.6830i) q^{53} +(11.4525 + 11.4525i) q^{55} +(635.616 - 635.616i) q^{57} +(-287.366 + 119.031i) q^{59} +(-28.2072 + 68.0983i) q^{61} +597.119 q^{63} -629.026 q^{65} +(-293.521 + 708.622i) q^{67} +(302.057 - 125.116i) q^{69} +(579.730 - 579.730i) q^{71} +(-258.894 - 258.894i) q^{73} +(-206.351 - 498.176i) q^{75} +(18.5371 + 7.67833i) q^{77} +834.510i q^{79} +1155.05i q^{81} +(-234.905 - 97.3009i) q^{83} +(308.319 + 744.347i) q^{85} +(-991.082 - 991.082i) q^{87} +(179.539 - 179.539i) q^{89} +(-719.939 + 298.208i) q^{91} +(205.975 - 497.268i) q^{93} +792.661 q^{95} -624.033 q^{97} +(-44.6962 + 107.906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) −3.54796 + 8.56554i −0.682806 + 1.64844i 0.0759878 + 0.997109i \(0.475789\pi\)
−0.758794 + 0.651331i \(0.774211\pi\)
\(4\) 0 0
\(5\) −7.55322 + 3.12865i −0.675581 + 0.279835i −0.693978 0.719996i \(-0.744144\pi\)
0.0183975 + 0.999831i \(0.494144\pi\)
\(6\) 0 0
\(7\) −7.16166 + 7.16166i −0.386693 + 0.386693i −0.873506 0.486813i \(-0.838159\pi\)
0.486813 + 0.873506i \(0.338159\pi\)
\(8\) 0 0
\(9\) −41.6886 41.6886i −1.54402 1.54402i
\(10\) 0 0
\(11\) −0.758120 1.83026i −0.0207802 0.0501678i 0.913149 0.407626i \(-0.133643\pi\)
−0.933929 + 0.357458i \(0.883643\pi\)
\(12\) 0 0
\(13\) 71.0832 + 29.4436i 1.51653 + 0.628168i 0.976893 0.213728i \(-0.0685606\pi\)
0.539639 + 0.841896i \(0.318561\pi\)
\(14\) 0 0
\(15\) 75.7978i 1.30473i
\(16\) 0 0
\(17\) 98.5470i 1.40595i −0.711214 0.702975i \(-0.751854\pi\)
0.711214 0.702975i \(-0.248146\pi\)
\(18\) 0 0
\(19\) −89.5748 37.1031i −1.08157 0.448002i −0.230512 0.973070i \(-0.574040\pi\)
−0.851060 + 0.525068i \(0.824040\pi\)
\(20\) 0 0
\(21\) −35.9342 86.7528i −0.373404 0.901477i
\(22\) 0 0
\(23\) −24.9355 24.9355i −0.226062 0.226062i 0.584984 0.811045i \(-0.301101\pi\)
−0.811045 + 0.584984i \(0.801101\pi\)
\(24\) 0 0
\(25\) −41.1256 + 41.1256i −0.329005 + 0.329005i
\(26\) 0 0
\(27\) 273.726 113.381i 1.95106 0.808154i
\(28\) 0 0
\(29\) −57.8528 + 139.669i −0.370448 + 0.894341i 0.623226 + 0.782042i \(0.285822\pi\)
−0.993674 + 0.112299i \(0.964178\pi\)
\(30\) 0 0
\(31\) −58.0545 −0.336351 −0.168176 0.985757i \(-0.553788\pi\)
−0.168176 + 0.985757i \(0.553788\pi\)
\(32\) 0 0
\(33\) 18.3670 0.0968874
\(34\) 0 0
\(35\) 31.6873 76.4999i 0.153032 0.369453i
\(36\) 0 0
\(37\) −202.968 + 84.0720i −0.901829 + 0.373550i −0.784923 0.619593i \(-0.787298\pi\)
−0.116906 + 0.993143i \(0.537298\pi\)
\(38\) 0 0
\(39\) −504.401 + 504.401i −2.07100 + 2.07100i
\(40\) 0 0
\(41\) −45.3618 45.3618i −0.172788 0.172788i 0.615415 0.788203i \(-0.288988\pi\)
−0.788203 + 0.615415i \(0.788988\pi\)
\(42\) 0 0
\(43\) −89.7175 216.597i −0.318181 0.768157i −0.999351 0.0360314i \(-0.988528\pi\)
0.681170 0.732126i \(-0.261472\pi\)
\(44\) 0 0
\(45\) 445.312 + 184.454i 1.47518 + 0.611041i
\(46\) 0 0
\(47\) 4.38416i 0.0136063i 0.999977 + 0.00680315i \(0.00216553\pi\)
−0.999977 + 0.00680315i \(0.997834\pi\)
\(48\) 0 0
\(49\) 240.421i 0.700937i
\(50\) 0 0
\(51\) 844.109 + 349.641i 2.31762 + 0.959992i
\(52\) 0 0
\(53\) 8.98141 + 21.6830i 0.0232772 + 0.0561961i 0.935091 0.354408i \(-0.115318\pi\)
−0.911814 + 0.410604i \(0.865318\pi\)
\(54\) 0 0
\(55\) 11.4525 + 11.4525i 0.0280774 + 0.0280774i
\(56\) 0 0
\(57\) 635.616 635.616i 1.47701 1.47701i
\(58\) 0 0
\(59\) −287.366 + 119.031i −0.634099 + 0.262652i −0.676494 0.736448i \(-0.736501\pi\)
0.0423945 + 0.999101i \(0.486501\pi\)
\(60\) 0 0
\(61\) −28.2072 + 68.0983i −0.0592060 + 0.142936i −0.950714 0.310069i \(-0.899648\pi\)
0.891508 + 0.453005i \(0.149648\pi\)
\(62\) 0 0
\(63\) 597.119 1.19413
\(64\) 0 0
\(65\) −629.026 −1.20032
\(66\) 0 0
\(67\) −293.521 + 708.622i −0.535213 + 1.29212i 0.392818 + 0.919616i \(0.371500\pi\)
−0.928031 + 0.372502i \(0.878500\pi\)
\(68\) 0 0
\(69\) 302.057 125.116i 0.527005 0.218293i
\(70\) 0 0
\(71\) 579.730 579.730i 0.969032 0.969032i −0.0305030 0.999535i \(-0.509711\pi\)
0.999535 + 0.0305030i \(0.00971091\pi\)
\(72\) 0 0
\(73\) −258.894 258.894i −0.415085 0.415085i 0.468420 0.883506i \(-0.344823\pi\)
−0.883506 + 0.468420i \(0.844823\pi\)
\(74\) 0 0
\(75\) −206.351 498.176i −0.317698 0.766991i
\(76\) 0 0
\(77\) 18.5371 + 7.67833i 0.0274351 + 0.0113640i
\(78\) 0 0
\(79\) 834.510i 1.18848i 0.804289 + 0.594239i \(0.202547\pi\)
−0.804289 + 0.594239i \(0.797453\pi\)
\(80\) 0 0
\(81\) 1155.05i 1.58443i
\(82\) 0 0
\(83\) −234.905 97.3009i −0.310653 0.128677i 0.221910 0.975067i \(-0.428771\pi\)
−0.532563 + 0.846391i \(0.678771\pi\)
\(84\) 0 0
\(85\) 308.319 + 744.347i 0.393434 + 0.949833i
\(86\) 0 0
\(87\) −991.082 991.082i −1.22132 1.22132i
\(88\) 0 0
\(89\) 179.539 179.539i 0.213833 0.213833i −0.592061 0.805893i \(-0.701685\pi\)
0.805893 + 0.592061i \(0.201685\pi\)
\(90\) 0 0
\(91\) −719.939 + 298.208i −0.829342 + 0.343525i
\(92\) 0 0
\(93\) 205.975 497.268i 0.229663 0.554455i
\(94\) 0 0
\(95\) 792.661 0.856056
\(96\) 0 0
\(97\) −624.033 −0.653205 −0.326603 0.945162i \(-0.605904\pi\)
−0.326603 + 0.945162i \(0.605904\pi\)
\(98\) 0 0
\(99\) −44.6962 + 107.906i −0.0453751 + 0.109545i
\(100\) 0 0
\(101\) −1513.83 + 627.049i −1.49140 + 0.617760i −0.971622 0.236540i \(-0.923987\pi\)
−0.519782 + 0.854299i \(0.673987\pi\)
\(102\) 0 0
\(103\) −146.406 + 146.406i −0.140056 + 0.140056i −0.773659 0.633603i \(-0.781575\pi\)
0.633603 + 0.773659i \(0.281575\pi\)
\(104\) 0 0
\(105\) 542.838 + 542.838i 0.504529 + 0.504529i
\(106\) 0 0
\(107\) −375.001 905.331i −0.338810 0.817960i −0.997831 0.0658347i \(-0.979029\pi\)
0.659021 0.752125i \(-0.270971\pi\)
\(108\) 0 0
\(109\) −330.443 136.874i −0.290373 0.120277i 0.232742 0.972539i \(-0.425230\pi\)
−0.523115 + 0.852262i \(0.675230\pi\)
\(110\) 0 0
\(111\) 2036.81i 1.74167i
\(112\) 0 0
\(113\) 743.066i 0.618600i 0.950965 + 0.309300i \(0.100095\pi\)
−0.950965 + 0.309300i \(0.899905\pi\)
\(114\) 0 0
\(115\) 266.358 + 110.329i 0.215983 + 0.0894630i
\(116\) 0 0
\(117\) −1735.89 4190.82i −1.37165 3.31147i
\(118\) 0 0
\(119\) 705.760 + 705.760i 0.543672 + 0.543672i
\(120\) 0 0
\(121\) 938.384 938.384i 0.705022 0.705022i
\(122\) 0 0
\(123\) 549.491 227.606i 0.402812 0.166850i
\(124\) 0 0
\(125\) 573.044 1383.45i 0.410037 0.989917i
\(126\) 0 0
\(127\) 316.036 0.220816 0.110408 0.993886i \(-0.464784\pi\)
0.110408 + 0.993886i \(0.464784\pi\)
\(128\) 0 0
\(129\) 2173.59 1.48352
\(130\) 0 0
\(131\) 126.926 306.426i 0.0846532 0.204371i −0.875884 0.482521i \(-0.839721\pi\)
0.960538 + 0.278150i \(0.0897212\pi\)
\(132\) 0 0
\(133\) 907.224 375.785i 0.591476 0.244997i
\(134\) 0 0
\(135\) −1712.78 + 1712.78i −1.09195 + 1.09195i
\(136\) 0 0
\(137\) −465.127 465.127i −0.290062 0.290062i 0.547043 0.837105i \(-0.315754\pi\)
−0.837105 + 0.547043i \(0.815754\pi\)
\(138\) 0 0
\(139\) −158.069 381.612i −0.0964548 0.232863i 0.868286 0.496064i \(-0.165222\pi\)
−0.964741 + 0.263201i \(0.915222\pi\)
\(140\) 0 0
\(141\) −37.5528 15.5549i −0.0224292 0.00929046i
\(142\) 0 0
\(143\) 152.423i 0.0891345i
\(144\) 0 0
\(145\) 1235.95i 0.707864i
\(146\) 0 0
\(147\) −2059.34 853.006i −1.15545 0.478604i
\(148\) 0 0
\(149\) 316.900 + 765.063i 0.174238 + 0.420647i 0.986740 0.162312i \(-0.0518949\pi\)
−0.812502 + 0.582959i \(0.801895\pi\)
\(150\) 0 0
\(151\) 1447.99 + 1447.99i 0.780369 + 0.780369i 0.979893 0.199524i \(-0.0639397\pi\)
−0.199524 + 0.979893i \(0.563940\pi\)
\(152\) 0 0
\(153\) −4108.29 + 4108.29i −2.17082 + 2.17082i
\(154\) 0 0
\(155\) 438.498 181.632i 0.227233 0.0941228i
\(156\) 0 0
\(157\) −1154.08 + 2786.21i −0.586662 + 1.41633i 0.300013 + 0.953935i \(0.403009\pi\)
−0.886675 + 0.462393i \(0.846991\pi\)
\(158\) 0 0
\(159\) −217.593 −0.108530
\(160\) 0 0
\(161\) 357.160 0.174833
\(162\) 0 0
\(163\) −1315.01 + 3174.72i −0.631899 + 1.52554i 0.205333 + 0.978692i \(0.434172\pi\)
−0.837232 + 0.546848i \(0.815828\pi\)
\(164\) 0 0
\(165\) −138.730 + 57.4638i −0.0654552 + 0.0271125i
\(166\) 0 0
\(167\) 2616.84 2616.84i 1.21256 1.21256i 0.242376 0.970182i \(-0.422073\pi\)
0.970182 0.242376i \(-0.0779268\pi\)
\(168\) 0 0
\(169\) 2632.38 + 2632.38i 1.19817 + 1.19817i
\(170\) 0 0
\(171\) 2187.47 + 5281.03i 0.978247 + 2.36170i
\(172\) 0 0
\(173\) 1699.43 + 703.925i 0.746849 + 0.309355i 0.723455 0.690371i \(-0.242553\pi\)
0.0233941 + 0.999726i \(0.492553\pi\)
\(174\) 0 0
\(175\) 589.055i 0.254448i
\(176\) 0 0
\(177\) 2883.76i 1.22461i
\(178\) 0 0
\(179\) −1726.10 714.972i −0.720751 0.298545i −0.00800596 0.999968i \(-0.502548\pi\)
−0.712745 + 0.701423i \(0.752548\pi\)
\(180\) 0 0
\(181\) 1087.42 + 2625.26i 0.446559 + 1.07809i 0.973602 + 0.228251i \(0.0733006\pi\)
−0.527043 + 0.849839i \(0.676699\pi\)
\(182\) 0 0
\(183\) −483.221 483.221i −0.195195 0.195195i
\(184\) 0 0
\(185\) 1270.03 1270.03i 0.504726 0.504726i
\(186\) 0 0
\(187\) −180.367 + 74.7105i −0.0705334 + 0.0292159i
\(188\) 0 0
\(189\) −1148.33 + 2772.32i −0.441953 + 1.06697i
\(190\) 0 0
\(191\) −1649.64 −0.624940 −0.312470 0.949928i \(-0.601156\pi\)
−0.312470 + 0.949928i \(0.601156\pi\)
\(192\) 0 0
\(193\) −1928.59 −0.719291 −0.359645 0.933089i \(-0.617102\pi\)
−0.359645 + 0.933089i \(0.617102\pi\)
\(194\) 0 0
\(195\) 2231.76 5387.95i 0.819588 1.97866i
\(196\) 0 0
\(197\) 3725.06 1542.97i 1.34720 0.558030i 0.411692 0.911323i \(-0.364938\pi\)
0.935513 + 0.353293i \(0.114938\pi\)
\(198\) 0 0
\(199\) −361.648 + 361.648i −0.128827 + 0.128827i −0.768580 0.639753i \(-0.779036\pi\)
0.639753 + 0.768580i \(0.279036\pi\)
\(200\) 0 0
\(201\) −5028.33 5028.33i −1.76453 1.76453i
\(202\) 0 0
\(203\) −585.940 1414.58i −0.202586 0.489086i
\(204\) 0 0
\(205\) 484.549 + 200.707i 0.165085 + 0.0683803i
\(206\) 0 0
\(207\) 2079.06i 0.698089i
\(208\) 0 0
\(209\) 192.074i 0.0635696i
\(210\) 0 0
\(211\) 5549.04 + 2298.49i 1.81048 + 0.749927i 0.981721 + 0.190325i \(0.0609543\pi\)
0.828762 + 0.559601i \(0.189046\pi\)
\(212\) 0 0
\(213\) 2908.84 + 7022.56i 0.935730 + 2.25905i
\(214\) 0 0
\(215\) 1355.31 + 1355.31i 0.429914 + 0.429914i
\(216\) 0 0
\(217\) 415.767 415.767i 0.130065 0.130065i
\(218\) 0 0
\(219\) 3136.11 1299.02i 0.967666 0.400820i
\(220\) 0 0
\(221\) 2901.58 7005.03i 0.883174 2.13217i
\(222\) 0 0
\(223\) −2968.26 −0.891344 −0.445672 0.895196i \(-0.647035\pi\)
−0.445672 + 0.895196i \(0.647035\pi\)
\(224\) 0 0
\(225\) 3428.94 1.01598
\(226\) 0 0
\(227\) 947.980 2288.63i 0.277179 0.669169i −0.722576 0.691291i \(-0.757042\pi\)
0.999755 + 0.0221219i \(0.00704218\pi\)
\(228\) 0 0
\(229\) −5763.17 + 2387.18i −1.66306 + 0.688862i −0.998305 0.0581984i \(-0.981464\pi\)
−0.664756 + 0.747061i \(0.731464\pi\)
\(230\) 0 0
\(231\) −131.538 + 131.538i −0.0374657 + 0.0374657i
\(232\) 0 0
\(233\) 3036.23 + 3036.23i 0.853691 + 0.853691i 0.990586 0.136895i \(-0.0437122\pi\)
−0.136895 + 0.990586i \(0.543712\pi\)
\(234\) 0 0
\(235\) −13.7165 33.1146i −0.00380751 0.00919215i
\(236\) 0 0
\(237\) −7148.03 2960.81i −1.95913 0.811500i
\(238\) 0 0
\(239\) 6291.50i 1.70278i 0.524537 + 0.851388i \(0.324239\pi\)
−0.524537 + 0.851388i \(0.675761\pi\)
\(240\) 0 0
\(241\) 795.320i 0.212577i 0.994335 + 0.106289i \(0.0338967\pi\)
−0.994335 + 0.106289i \(0.966103\pi\)
\(242\) 0 0
\(243\) −2503.05 1036.80i −0.660786 0.273706i
\(244\) 0 0
\(245\) −752.193 1815.95i −0.196146 0.473539i
\(246\) 0 0
\(247\) −5274.81 5274.81i −1.35882 1.35882i
\(248\) 0 0
\(249\) 1666.87 1666.87i 0.424231 0.424231i
\(250\) 0 0
\(251\) −6040.73 + 2502.15i −1.51907 + 0.629221i −0.977406 0.211372i \(-0.932207\pi\)
−0.541668 + 0.840593i \(0.682207\pi\)
\(252\) 0 0
\(253\) −26.7345 + 64.5428i −0.00664341 + 0.0160386i
\(254\) 0 0
\(255\) −7469.64 −1.83438
\(256\) 0 0
\(257\) −3591.20 −0.871645 −0.435823 0.900033i \(-0.643543\pi\)
−0.435823 + 0.900033i \(0.643543\pi\)
\(258\) 0 0
\(259\) 851.491 2055.68i 0.204282 0.493181i
\(260\) 0 0
\(261\) 8234.41 3410.80i 1.95286 0.808902i
\(262\) 0 0
\(263\) 2616.63 2616.63i 0.613491 0.613491i −0.330363 0.943854i \(-0.607171\pi\)
0.943854 + 0.330363i \(0.107171\pi\)
\(264\) 0 0
\(265\) −135.677 135.677i −0.0314513 0.0314513i
\(266\) 0 0
\(267\) 900.853 + 2174.85i 0.206484 + 0.498497i
\(268\) 0 0
\(269\) −6877.53 2848.77i −1.55885 0.645697i −0.573961 0.818883i \(-0.694594\pi\)
−0.984889 + 0.173186i \(0.944594\pi\)
\(270\) 0 0
\(271\) 6338.06i 1.42070i 0.703848 + 0.710350i \(0.251463\pi\)
−0.703848 + 0.710350i \(0.748537\pi\)
\(272\) 0 0
\(273\) 7224.70i 1.60168i
\(274\) 0 0
\(275\) 106.449 + 44.0926i 0.0233422 + 0.00966867i
\(276\) 0 0
\(277\) 655.560 + 1582.66i 0.142198 + 0.343296i 0.978893 0.204373i \(-0.0655155\pi\)
−0.836695 + 0.547669i \(0.815515\pi\)
\(278\) 0 0
\(279\) 2420.21 + 2420.21i 0.519334 + 0.519334i
\(280\) 0 0
\(281\) −3436.47 + 3436.47i −0.729547 + 0.729547i −0.970529 0.240983i \(-0.922530\pi\)
0.240983 + 0.970529i \(0.422530\pi\)
\(282\) 0 0
\(283\) 5101.55 2113.13i 1.07158 0.443861i 0.224029 0.974582i \(-0.428079\pi\)
0.847546 + 0.530722i \(0.178079\pi\)
\(284\) 0 0
\(285\) −2812.33 + 6789.57i −0.584520 + 1.41116i
\(286\) 0 0
\(287\) 649.732 0.133632
\(288\) 0 0
\(289\) −4798.52 −0.976698
\(290\) 0 0
\(291\) 2214.05 5345.18i 0.446013 1.07677i
\(292\) 0 0
\(293\) 2820.64 1168.35i 0.562402 0.232954i −0.0833258 0.996522i \(-0.526554\pi\)
0.645727 + 0.763568i \(0.276554\pi\)
\(294\) 0 0
\(295\) 1798.13 1798.13i 0.354886 0.354886i
\(296\) 0 0
\(297\) −415.034 415.034i −0.0810866 0.0810866i
\(298\) 0 0
\(299\) −1038.30 2506.69i −0.200825 0.484835i
\(300\) 0 0
\(301\) 2193.72 + 908.669i 0.420080 + 0.174003i
\(302\) 0 0
\(303\) 15191.5i 2.88030i
\(304\) 0 0
\(305\) 602.612i 0.113133i
\(306\) 0 0
\(307\) −424.120 175.676i −0.0788463 0.0326592i 0.342912 0.939368i \(-0.388587\pi\)
−0.421758 + 0.906708i \(0.638587\pi\)
\(308\) 0 0
\(309\) −734.603 1773.49i −0.135243 0.326506i
\(310\) 0 0
\(311\) 3761.67 + 3761.67i 0.685868 + 0.685868i 0.961316 0.275448i \(-0.0888262\pi\)
−0.275448 + 0.961316i \(0.588826\pi\)
\(312\) 0 0
\(313\) 718.221 718.221i 0.129700 0.129700i −0.639277 0.768977i \(-0.720766\pi\)
0.768977 + 0.639277i \(0.220766\pi\)
\(314\) 0 0
\(315\) −4510.17 + 1868.18i −0.806729 + 0.334158i
\(316\) 0 0
\(317\) 1315.47 3175.83i 0.233073 0.562689i −0.763463 0.645852i \(-0.776502\pi\)
0.996536 + 0.0831634i \(0.0265023\pi\)
\(318\) 0 0
\(319\) 299.491 0.0525651
\(320\) 0 0
\(321\) 9085.14 1.57970
\(322\) 0 0
\(323\) −3656.40 + 8827.33i −0.629869 + 1.52064i
\(324\) 0 0
\(325\) −4134.23 + 1712.45i −0.705617 + 0.292276i
\(326\) 0 0
\(327\) 2344.80 2344.80i 0.396537 0.396537i
\(328\) 0 0
\(329\) −31.3979 31.3979i −0.00526147 0.00526147i
\(330\) 0 0
\(331\) −515.566 1244.69i −0.0856136 0.206689i 0.875274 0.483626i \(-0.160681\pi\)
−0.960888 + 0.276937i \(0.910681\pi\)
\(332\) 0 0
\(333\) 11966.3 + 4956.60i 1.96921 + 0.815675i
\(334\) 0 0
\(335\) 6270.70i 1.02270i
\(336\) 0 0
\(337\) 4770.86i 0.771173i 0.922672 + 0.385587i \(0.126001\pi\)
−0.922672 + 0.385587i \(0.873999\pi\)
\(338\) 0 0
\(339\) −6364.77 2636.37i −1.01972 0.422384i
\(340\) 0 0
\(341\) 44.0123 + 106.255i 0.00698944 + 0.0168740i
\(342\) 0 0
\(343\) −4178.26 4178.26i −0.657741 0.657741i
\(344\) 0 0
\(345\) −1890.06 + 1890.06i −0.294949 + 0.294949i
\(346\) 0 0
\(347\) −2534.53 + 1049.84i −0.392105 + 0.162415i −0.570021 0.821630i \(-0.693065\pi\)
0.177915 + 0.984046i \(0.443065\pi\)
\(348\) 0 0
\(349\) 1115.54 2693.15i 0.171099 0.413069i −0.814949 0.579533i \(-0.803235\pi\)
0.986048 + 0.166464i \(0.0532349\pi\)
\(350\) 0 0
\(351\) 22795.6 3.46650
\(352\) 0 0
\(353\) 2416.71 0.364387 0.182193 0.983263i \(-0.441680\pi\)
0.182193 + 0.983263i \(0.441680\pi\)
\(354\) 0 0
\(355\) −2565.06 + 6192.60i −0.383490 + 0.925828i
\(356\) 0 0
\(357\) −8549.23 + 3541.21i −1.26743 + 0.524988i
\(358\) 0 0
\(359\) −8445.07 + 8445.07i −1.24154 + 1.24154i −0.282182 + 0.959361i \(0.591058\pi\)
−0.959361 + 0.282182i \(0.908942\pi\)
\(360\) 0 0
\(361\) 1796.96 + 1796.96i 0.261986 + 0.261986i
\(362\) 0 0
\(363\) 4708.42 + 11367.1i 0.680793 + 1.64358i
\(364\) 0 0
\(365\) 2765.47 + 1145.49i 0.396579 + 0.164268i
\(366\) 0 0
\(367\) 1632.32i 0.232170i 0.993239 + 0.116085i \(0.0370345\pi\)
−0.993239 + 0.116085i \(0.962966\pi\)
\(368\) 0 0
\(369\) 3782.14i 0.533578i
\(370\) 0 0
\(371\) −219.608 90.9648i −0.0307318 0.0127295i
\(372\) 0 0
\(373\) −5198.39 12550.0i −0.721615 1.74213i −0.668700 0.743533i \(-0.733149\pi\)
−0.0529149 0.998599i \(-0.516851\pi\)
\(374\) 0 0
\(375\) 9816.87 + 9816.87i 1.35184 + 1.35184i
\(376\) 0 0
\(377\) −8224.72 + 8224.72i −1.12359 + 1.12359i
\(378\) 0 0
\(379\) 4404.78 1824.52i 0.596987 0.247280i −0.0636663 0.997971i \(-0.520279\pi\)
0.660653 + 0.750691i \(0.270279\pi\)
\(380\) 0 0
\(381\) −1121.28 + 2707.02i −0.150775 + 0.364002i
\(382\) 0 0
\(383\) −7295.56 −0.973331 −0.486665 0.873589i \(-0.661787\pi\)
−0.486665 + 0.873589i \(0.661787\pi\)
\(384\) 0 0
\(385\) −164.038 −0.0217147
\(386\) 0 0
\(387\) −5289.44 + 12769.8i −0.694773 + 1.67733i
\(388\) 0 0
\(389\) −2614.79 + 1083.08i −0.340810 + 0.141168i −0.546523 0.837444i \(-0.684049\pi\)
0.205712 + 0.978612i \(0.434049\pi\)
\(390\) 0 0
\(391\) −2457.32 + 2457.32i −0.317832 + 0.317832i
\(392\) 0 0
\(393\) 2174.38 + 2174.38i 0.279091 + 0.279091i
\(394\) 0 0
\(395\) −2610.89 6303.24i −0.332577 0.802913i
\(396\) 0 0
\(397\) −1867.07 773.367i −0.236034 0.0977687i 0.261531 0.965195i \(-0.415773\pi\)
−0.497566 + 0.867426i \(0.665773\pi\)
\(398\) 0 0
\(399\) 9104.14i 1.14230i
\(400\) 0 0
\(401\) 12147.1i 1.51271i 0.654162 + 0.756354i \(0.273021\pi\)
−0.654162 + 0.756354i \(0.726979\pi\)
\(402\) 0 0
\(403\) −4126.70 1709.33i −0.510088 0.211285i
\(404\) 0 0
\(405\) −3613.75 8724.36i −0.443379 1.07041i
\(406\) 0 0
\(407\) 307.748 + 307.748i 0.0374803 + 0.0374803i
\(408\) 0 0
\(409\) 9049.93 9049.93i 1.09411 1.09411i 0.0990235 0.995085i \(-0.468428\pi\)
0.995085 0.0990235i \(-0.0315719\pi\)
\(410\) 0 0
\(411\) 5634.32 2333.81i 0.676206 0.280094i
\(412\) 0 0
\(413\) 1205.56 2910.48i 0.143636 0.346768i
\(414\) 0 0
\(415\) 2078.71 0.245879
\(416\) 0 0
\(417\) 3829.54 0.449720
\(418\) 0 0
\(419\) 5216.15 12592.9i 0.608176 1.46827i −0.256806 0.966463i \(-0.582670\pi\)
0.864982 0.501803i \(-0.167330\pi\)
\(420\) 0 0
\(421\) 12044.9 4989.15i 1.39437 0.577568i 0.446088 0.894989i \(-0.352817\pi\)
0.948285 + 0.317421i \(0.102817\pi\)
\(422\) 0 0
\(423\) 182.770 182.770i 0.0210084 0.0210084i
\(424\) 0 0
\(425\) 4052.81 + 4052.81i 0.462565 + 0.462565i
\(426\) 0 0
\(427\) −285.686 689.708i −0.0323778 0.0781670i
\(428\) 0 0
\(429\) 1305.58 + 540.791i 0.146933 + 0.0608616i
\(430\) 0 0
\(431\) 3074.64i 0.343620i −0.985130 0.171810i \(-0.945039\pi\)
0.985130 0.171810i \(-0.0549615\pi\)
\(432\) 0 0
\(433\) 3478.83i 0.386101i −0.981189 0.193051i \(-0.938162\pi\)
0.981189 0.193051i \(-0.0618381\pi\)
\(434\) 0 0
\(435\) 10586.6 + 4385.12i 1.16687 + 0.483334i
\(436\) 0 0
\(437\) 1308.41 + 3158.78i 0.143226 + 0.345778i
\(438\) 0 0
\(439\) −6595.03 6595.03i −0.717001 0.717001i 0.250989 0.967990i \(-0.419244\pi\)
−0.967990 + 0.250989i \(0.919244\pi\)
\(440\) 0 0
\(441\) 10022.8 10022.8i 1.08226 1.08226i
\(442\) 0 0
\(443\) −1177.46 + 487.720i −0.126282 + 0.0523076i −0.444930 0.895566i \(-0.646771\pi\)
0.318648 + 0.947873i \(0.396771\pi\)
\(444\) 0 0
\(445\) −794.385 + 1917.82i −0.0846235 + 0.204299i
\(446\) 0 0
\(447\) −7677.53 −0.812382
\(448\) 0 0
\(449\) −517.491 −0.0543918 −0.0271959 0.999630i \(-0.508658\pi\)
−0.0271959 + 0.999630i \(0.508658\pi\)
\(450\) 0 0
\(451\) −48.6344 + 117.414i −0.00507784 + 0.0122590i
\(452\) 0 0
\(453\) −17540.2 + 7265.40i −1.81923 + 0.753550i
\(454\) 0 0
\(455\) 4504.87 4504.87i 0.464157 0.464157i
\(456\) 0 0
\(457\) 1142.85 + 1142.85i 0.116981 + 0.116981i 0.763174 0.646193i \(-0.223640\pi\)
−0.646193 + 0.763174i \(0.723640\pi\)
\(458\) 0 0
\(459\) −11173.3 26974.8i −1.13622 2.74309i
\(460\) 0 0
\(461\) −7860.73 3256.02i −0.794166 0.328954i −0.0515489 0.998670i \(-0.516416\pi\)
−0.742617 + 0.669716i \(0.766416\pi\)
\(462\) 0 0
\(463\) 2545.63i 0.255519i −0.991805 0.127760i \(-0.959221\pi\)
0.991805 0.127760i \(-0.0407786\pi\)
\(464\) 0 0
\(465\) 4400.40i 0.438847i
\(466\) 0 0
\(467\) 7269.46 + 3011.11i 0.720322 + 0.298367i 0.712568 0.701603i \(-0.247532\pi\)
0.00775364 + 0.999970i \(0.497532\pi\)
\(468\) 0 0
\(469\) −2972.81 7177.01i −0.292690 0.706617i
\(470\) 0 0
\(471\) −19770.7 19770.7i −1.93415 1.93415i
\(472\) 0 0
\(473\) −328.413 + 328.413i −0.0319249 + 0.0319249i
\(474\) 0 0
\(475\) 5209.71 2157.93i 0.503237 0.208448i
\(476\) 0 0
\(477\) 529.513 1278.36i 0.0508276 0.122709i
\(478\) 0 0
\(479\) 19071.7 1.81922 0.909612 0.415459i \(-0.136379\pi\)
0.909612 + 0.415459i \(0.136379\pi\)
\(480\) 0 0
\(481\) −16903.0 −1.60231
\(482\) 0 0
\(483\) −1267.19 + 3059.27i −0.119377 + 0.288202i
\(484\) 0 0
\(485\) 4713.46 1952.38i 0.441293 0.182790i
\(486\) 0 0
\(487\) −4422.93 + 4422.93i −0.411544 + 0.411544i −0.882276 0.470732i \(-0.843990\pi\)
0.470732 + 0.882276i \(0.343990\pi\)
\(488\) 0 0
\(489\) −22527.6 22527.6i −2.08330 2.08330i
\(490\) 0 0
\(491\) 1908.12 + 4606.60i 0.175381 + 0.423408i 0.986987 0.160797i \(-0.0514065\pi\)
−0.811606 + 0.584205i \(0.801407\pi\)
\(492\) 0 0
\(493\) 13764.0 + 5701.22i 1.25740 + 0.520832i
\(494\) 0 0
\(495\) 954.878i 0.0867042i
\(496\) 0 0
\(497\) 8303.65i 0.749436i
\(498\) 0 0
\(499\) 9996.34 + 4140.62i 0.896789 + 0.371462i 0.782985 0.622041i \(-0.213696\pi\)
0.113804 + 0.993503i \(0.463696\pi\)
\(500\) 0 0
\(501\) 13130.2 + 31699.1i 1.17089 + 2.82677i
\(502\) 0 0
\(503\) 6186.59 + 6186.59i 0.548402 + 0.548402i 0.925978 0.377576i \(-0.123242\pi\)
−0.377576 + 0.925978i \(0.623242\pi\)
\(504\) 0 0
\(505\) 9472.48 9472.48i 0.834693 0.834693i
\(506\) 0 0
\(507\) −31887.3 + 13208.2i −2.79323 + 1.15699i
\(508\) 0 0
\(509\) 1472.42 3554.75i 0.128220 0.309551i −0.846713 0.532051i \(-0.821422\pi\)
0.974933 + 0.222500i \(0.0714216\pi\)
\(510\) 0 0
\(511\) 3708.22 0.321021
\(512\) 0 0
\(513\) −28725.7 −2.47226
\(514\) 0 0
\(515\) 647.783 1563.89i 0.0554267 0.133812i
\(516\) 0 0
\(517\) 8.02418 3.32372i 0.000682598 0.000282741i
\(518\) 0 0
\(519\) −12059.0 + 12059.0i −1.01991 + 1.01991i
\(520\) 0 0
\(521\) −41.6914 41.6914i −0.00350582 0.00350582i 0.705352 0.708858i \(-0.250789\pi\)
−0.708858 + 0.705352i \(0.750789\pi\)
\(522\) 0 0
\(523\) −6675.06 16115.0i −0.558088 1.34734i −0.911278 0.411791i \(-0.864903\pi\)
0.353191 0.935551i \(-0.385097\pi\)
\(524\) 0 0
\(525\) 5045.58 + 2089.95i 0.419442 + 0.173739i
\(526\) 0 0
\(527\) 5721.10i 0.472894i
\(528\) 0 0
\(529\) 10923.4i 0.897792i
\(530\) 0 0
\(531\) 16942.1 + 7017.65i 1.38460 + 0.573522i
\(532\) 0 0
\(533\) −1888.85 4560.08i −0.153499 0.370579i
\(534\) 0 0
\(535\) 5664.92 + 5664.92i 0.457787 + 0.457787i
\(536\) 0 0
\(537\) 12248.3 12248.3i 0.984266 0.984266i
\(538\) 0 0
\(539\) 440.035 182.268i 0.0351644 0.0145656i
\(540\) 0 0
\(541\) −5953.02 + 14371.9i −0.473087 + 1.14213i 0.489704 + 0.871889i \(0.337105\pi\)
−0.962792 + 0.270245i \(0.912895\pi\)
\(542\) 0 0
\(543\) −26344.9 −2.08208
\(544\) 0 0
\(545\) 2924.14 0.229828
\(546\) 0 0
\(547\) −2956.49 + 7137.60i −0.231098 + 0.557919i −0.996307 0.0858625i \(-0.972635\pi\)
0.765209 + 0.643782i \(0.222635\pi\)
\(548\) 0 0
\(549\) 4014.84 1663.00i 0.312112 0.129281i
\(550\) 0 0
\(551\) 10364.3 10364.3i 0.801333 0.801333i
\(552\) 0 0
\(553\) −5976.48 5976.48i −0.459576 0.459576i
\(554\) 0 0
\(555\) 6372.47 + 15384.5i 0.487381 + 1.17664i
\(556\) 0 0
\(557\) −6601.43 2734.40i −0.502176 0.208008i 0.117192 0.993109i \(-0.462611\pi\)
−0.619367 + 0.785101i \(0.712611\pi\)
\(558\) 0 0
\(559\) 18038.0i 1.36481i
\(560\) 0 0
\(561\) 1810.01i 0.136219i
\(562\) 0 0
\(563\) −17608.4 7293.65i −1.31813 0.545987i −0.390883 0.920440i \(-0.627830\pi\)
−0.927246 + 0.374453i \(0.877830\pi\)
\(564\) 0 0
\(565\) −2324.79 5612.54i −0.173106 0.417914i
\(566\) 0 0
\(567\) −8272.09 8272.09i −0.612690 0.612690i
\(568\) 0 0
\(569\) −13651.2 + 13651.2i −1.00578 + 1.00578i −0.00579351 + 0.999983i \(0.501844\pi\)
−0.999983 + 0.00579351i \(0.998156\pi\)
\(570\) 0 0
\(571\) 15023.6 6222.97i 1.10108 0.456083i 0.243224 0.969970i \(-0.421795\pi\)
0.857858 + 0.513887i \(0.171795\pi\)
\(572\) 0 0
\(573\) 5852.85 14130.0i 0.426713 1.03018i
\(574\) 0 0
\(575\) 2050.98 0.148751
\(576\) 0 0
\(577\) 17031.0 1.22879 0.614394 0.788999i \(-0.289400\pi\)
0.614394 + 0.788999i \(0.289400\pi\)
\(578\) 0 0
\(579\) 6842.58 16519.4i 0.491136 1.18571i
\(580\) 0 0
\(581\) 2379.15 985.475i 0.169886 0.0703690i
\(582\) 0 0
\(583\) 32.8767 32.8767i 0.00233553 0.00233553i
\(584\) 0 0
\(585\) 26223.2 + 26223.2i 1.85333 + 1.85333i
\(586\) 0 0
\(587\) 6926.72 + 16722.6i 0.487046 + 1.17583i 0.956199 + 0.292717i \(0.0945594\pi\)
−0.469153 + 0.883117i \(0.655441\pi\)
\(588\) 0 0
\(589\) 5200.22 + 2154.00i 0.363788 + 0.150686i
\(590\) 0 0
\(591\) 37381.5i 2.60181i
\(592\) 0 0
\(593\) 23359.0i 1.61760i −0.588082 0.808801i \(-0.700117\pi\)
0.588082 0.808801i \(-0.299883\pi\)
\(594\) 0 0
\(595\) −7538.84 3122.69i −0.519432 0.215156i
\(596\) 0 0
\(597\) −1814.60 4380.82i −0.124399 0.300327i
\(598\) 0 0
\(599\) 8027.34 + 8027.34i 0.547559 + 0.547559i 0.925734 0.378175i \(-0.123448\pi\)
−0.378175 + 0.925734i \(0.623448\pi\)
\(600\) 0 0
\(601\) 11725.6 11725.6i 0.795837 0.795837i −0.186599 0.982436i \(-0.559747\pi\)
0.982436 + 0.186599i \(0.0597466\pi\)
\(602\) 0 0
\(603\) 41777.9 17305.0i 2.82144 1.16868i
\(604\) 0 0
\(605\) −4151.95 + 10023.7i −0.279010 + 0.673589i
\(606\) 0 0
\(607\) 25799.6 1.72516 0.862580 0.505920i \(-0.168847\pi\)
0.862580 + 0.505920i \(0.168847\pi\)
\(608\) 0 0
\(609\) 14195.6 0.944555
\(610\) 0 0
\(611\) −129.086 + 311.640i −0.00854705 + 0.0206344i
\(612\) 0 0
\(613\) 8320.05 3446.28i 0.548195 0.227070i −0.0913562 0.995818i \(-0.529120\pi\)
0.639551 + 0.768748i \(0.279120\pi\)
\(614\) 0 0
\(615\) −3438.32 + 3438.32i −0.225442 + 0.225442i
\(616\) 0 0
\(617\) −14643.0 14643.0i −0.955437 0.955437i 0.0436114 0.999049i \(-0.486114\pi\)
−0.999049 + 0.0436114i \(0.986114\pi\)
\(618\) 0 0
\(619\) 842.686 + 2034.42i 0.0547180 + 0.132101i 0.948874 0.315654i \(-0.102224\pi\)
−0.894156 + 0.447755i \(0.852224\pi\)
\(620\) 0 0
\(621\) −9652.70 3998.28i −0.623751 0.258366i
\(622\) 0 0
\(623\) 2571.60i 0.165376i
\(624\) 0 0
\(625\) 4972.32i 0.318228i
\(626\) 0 0
\(627\) −1645.22 681.473i −0.104791 0.0434057i
\(628\) 0 0
\(629\) 8285.04 + 20001.9i 0.525193 + 1.26793i
\(630\) 0 0
\(631\) −16113.6 16113.6i −1.01660 1.01660i −0.999860 0.0167358i \(-0.994673\pi\)
−0.0167358 0.999860i \(-0.505327\pi\)
\(632\) 0 0
\(633\) −39375.6 + 39375.6i −2.47242 + 2.47242i
\(634\) 0 0
\(635\) −2387.09 + 988.765i −0.149179 + 0.0617921i
\(636\) 0 0
\(637\) −7078.87 + 17089.9i −0.440306 + 1.06299i
\(638\) 0 0
\(639\) −48336.2 −2.99241
\(640\) 0 0
\(641\) 21358.0 1.31605 0.658026 0.752995i \(-0.271392\pi\)
0.658026 + 0.752995i \(0.271392\pi\)
\(642\) 0 0
\(643\) 1217.22 2938.63i 0.0746540 0.180231i −0.882147 0.470974i \(-0.843903\pi\)
0.956801 + 0.290743i \(0.0939026\pi\)
\(644\) 0 0
\(645\) −16417.6 + 6800.39i −1.00224 + 0.415139i
\(646\) 0 0
\(647\) −16654.8 + 16654.8i −1.01200 + 1.01200i −0.0120763 + 0.999927i \(0.503844\pi\)
−0.999927 + 0.0120763i \(0.996156\pi\)
\(648\) 0 0
\(649\) 435.716 + 435.716i 0.0263534 + 0.0263534i
\(650\) 0 0
\(651\) 2086.14 + 5036.39i 0.125595 + 0.303213i
\(652\) 0 0
\(653\) 20645.8 + 8551.79i 1.23727 + 0.512492i 0.902859 0.429937i \(-0.141464\pi\)
0.334406 + 0.942429i \(0.391464\pi\)
\(654\) 0 0
\(655\) 2711.61i 0.161758i
\(656\) 0 0
\(657\) 21585.8i 1.28180i
\(658\) 0 0
\(659\) −3783.98 1567.37i −0.223676 0.0926498i 0.268031 0.963410i \(-0.413627\pi\)
−0.491707 + 0.870760i \(0.663627\pi\)
\(660\) 0 0
\(661\) −9874.75 23839.8i −0.581064 1.40281i −0.891849 0.452333i \(-0.850592\pi\)
0.310785 0.950480i \(-0.399408\pi\)
\(662\) 0 0
\(663\) 49707.2 + 49707.2i 2.91172 + 2.91172i
\(664\) 0 0
\(665\) −5676.77 + 5676.77i −0.331031 + 0.331031i
\(666\) 0 0
\(667\) 4925.31 2040.13i 0.285920 0.118432i
\(668\) 0 0
\(669\) 10531.3 25424.8i 0.608615 1.46933i
\(670\) 0 0
\(671\) 146.022 0.00840109
\(672\) 0 0
\(673\) 8888.42 0.509099 0.254549 0.967060i \(-0.418073\pi\)
0.254549 + 0.967060i \(0.418073\pi\)
\(674\) 0 0
\(675\) −6594.28 + 15920.0i −0.376020 + 0.907794i
\(676\) 0 0
\(677\) −12382.5 + 5128.98i −0.702949 + 0.291171i −0.705383 0.708826i \(-0.749225\pi\)
0.00243434 + 0.999997i \(0.499225\pi\)
\(678\) 0 0
\(679\) 4469.11 4469.11i 0.252590 0.252590i
\(680\) 0 0
\(681\) 16239.9 + 16239.9i 0.913826 + 0.913826i
\(682\) 0 0
\(683\) 3359.39 + 8110.29i 0.188204 + 0.454365i 0.989614 0.143751i \(-0.0459163\pi\)
−0.801410 + 0.598116i \(0.795916\pi\)
\(684\) 0 0
\(685\) 4968.43 + 2057.99i 0.277130 + 0.114791i
\(686\) 0 0
\(687\) 57834.3i 3.21181i
\(688\) 0 0
\(689\) 1805.74i 0.0998453i
\(690\) 0 0
\(691\) −19614.8 8124.74i −1.07986 0.447293i −0.229401 0.973332i \(-0.573677\pi\)
−0.850460 + 0.526039i \(0.823677\pi\)
\(692\) 0 0
\(693\) −452.688 1092.89i −0.0248142 0.0599067i
\(694\) 0 0
\(695\) 2387.86 + 2387.86i 0.130326 + 0.130326i
\(696\) 0 0
\(697\) −4470.27 + 4470.27i −0.242932 + 0.242932i
\(698\) 0 0
\(699\) −36779.4 + 15234.5i −1.99016 + 0.824353i
\(700\) 0 0
\(701\) −7415.56 + 17902.8i −0.399546 + 0.964590i 0.588227 + 0.808696i \(0.299826\pi\)
−0.987774 + 0.155895i \(0.950174\pi\)
\(702\) 0 0
\(703\) 21300.1 1.14274
\(704\) 0 0
\(705\) 332.310 0.0177525
\(706\) 0 0
\(707\) 6350.83 15332.3i 0.337832 0.815599i
\(708\) 0 0
\(709\) −4168.86 + 1726.80i −0.220825 + 0.0914686i −0.490353 0.871524i \(-0.663132\pi\)
0.269528 + 0.962992i \(0.413132\pi\)
\(710\) 0 0
\(711\) 34789.6 34789.6i 1.83504 1.83504i
\(712\) 0 0
\(713\) 1447.62 + 1447.62i 0.0760362 + 0.0760362i
\(714\) 0 0
\(715\) 476.877 + 1151.28i 0.0249429 + 0.0602176i
\(716\) 0 0
\(717\) −53890.1 22322.0i −2.80692 1.16267i
\(718\) 0 0
\(719\) 13109.2i 0.679961i −0.940432 0.339981i \(-0.889580\pi\)
0.940432 0.339981i \(-0.110420\pi\)
\(720\) 0 0
\(721\) 2097.02i 0.108318i
\(722\) 0 0
\(723\) −6812.35 2821.77i −0.350420 0.145149i
\(724\) 0 0
\(725\) −3364.74 8123.21i −0.172363 0.416122i
\(726\) 0 0
\(727\) −19846.0 19846.0i −1.01245 1.01245i −0.999922 0.0125242i \(-0.996013\pi\)
−0.0125242 0.999922i \(-0.503987\pi\)
\(728\) 0 0
\(729\) −4290.62 + 4290.62i −0.217986 + 0.217986i
\(730\) 0 0
\(731\) −21345.0 + 8841.39i −1.07999 + 0.447347i
\(732\) 0 0
\(733\) −1724.21 + 4162.60i −0.0868827 + 0.209753i −0.961349 0.275333i \(-0.911212\pi\)
0.874466 + 0.485086i \(0.161212\pi\)
\(734\) 0 0
\(735\) 18223.4 0.914531
\(736\) 0 0
\(737\) 1519.49 0.0759445
\(738\) 0 0
\(739\) −6958.79 + 16800.0i −0.346391 + 0.836263i 0.650649 + 0.759379i \(0.274497\pi\)
−0.997040 + 0.0768839i \(0.975503\pi\)
\(740\) 0 0
\(741\) 63896.5 26466.8i 3.16774 1.31212i
\(742\) 0 0
\(743\) 1100.04 1100.04i 0.0543157 0.0543157i −0.679427 0.733743i \(-0.737772\pi\)
0.733743 + 0.679427i \(0.237772\pi\)
\(744\) 0 0
\(745\) −4787.23 4787.23i −0.235423 0.235423i
\(746\) 0 0
\(747\) 5736.53 + 13849.2i 0.280975 + 0.678335i
\(748\) 0 0
\(749\) 9169.30 + 3798.05i 0.447315 + 0.185284i
\(750\) 0 0
\(751\) 22547.4i 1.09556i 0.836623 + 0.547780i \(0.184527\pi\)
−0.836623 + 0.547780i \(0.815473\pi\)
\(752\) 0 0
\(753\) 60619.7i 2.93374i
\(754\) 0 0
\(755\) −15467.2 6406.73i −0.745576 0.308828i
\(756\) 0 0
\(757\) 1904.46 + 4597.78i 0.0914383 + 0.220752i 0.962982 0.269567i \(-0.0868805\pi\)
−0.871543 + 0.490318i \(0.836880\pi\)
\(758\) 0 0
\(759\) −457.991 457.991i −0.0219025 0.0219025i
\(760\) 0 0
\(761\) 7703.17 7703.17i 0.366938 0.366938i −0.499421 0.866359i \(-0.666454\pi\)
0.866359 + 0.499421i \(0.166454\pi\)
\(762\) 0 0
\(763\) 3346.76 1386.28i 0.158796 0.0657753i
\(764\) 0 0
\(765\) 18177.4 43884.2i 0.859093 2.07403i
\(766\) 0 0
\(767\) −23931.6 −1.12662
\(768\) 0 0
\(769\) −29833.1 −1.39897 −0.699485 0.714648i \(-0.746587\pi\)
−0.699485 + 0.714648i \(0.746587\pi\)
\(770\) 0 0
\(771\) 12741.4 30760.6i 0.595165 1.43685i
\(772\) 0 0
\(773\) 736.895 305.232i 0.0342876 0.0142024i −0.365474 0.930822i \(-0.619093\pi\)
0.399761 + 0.916619i \(0.369093\pi\)
\(774\) 0 0
\(775\) 2387.53 2387.53i 0.110661 0.110661i
\(776\) 0 0
\(777\) 14587.0 + 14587.0i 0.673493 + 0.673493i
\(778\) 0 0
\(779\) 2380.21 + 5746.34i 0.109474 + 0.264293i
\(780\) 0 0
\(781\) −1500.56 621.554i −0.0687508 0.0284775i
\(782\) 0 0
\(783\) 44790.4i 2.04429i
\(784\) 0 0
\(785\) 24655.6i 1.12101i
\(786\) 0 0
\(787\) −23884.7 9893.38i −1.08183 0.448108i −0.230678 0.973030i \(-0.574094\pi\)
−0.851150 + 0.524922i \(0.824094\pi\)
\(788\) 0 0
\(789\) 13129.1 + 31696.5i 0.592408 + 1.43020i
\(790\) 0 0
\(791\) −5321.59 5321.59i −0.239208 0.239208i
\(792\) 0 0
\(793\) −4010.12 + 4010.12i −0.179576 + 0.179576i
\(794\) 0 0
\(795\) 1643.53 680.771i 0.0733206 0.0303704i
\(796\) 0 0
\(797\) 5927.29