Properties

Label 128.4.g.a.113.1
Level $128$
Weight $4$
Character 128.113
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 113.1
Character \(\chi\) \(=\) 128.113
Dual form 128.4.g.a.17.1

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

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

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 −0.758794 0.651331i \(-0.774211\pi\)
0.0759878 0.997109i \(-0.475789\pi\)
\(4\) 0 0
\(5\) −7.55322 3.12865i −0.675581 0.279835i 0.0183975 0.999831i \(-0.494144\pi\)
−0.693978 + 0.719996i \(0.744144\pi\)
\(6\) 0 0
\(7\) −7.16166 7.16166i −0.386693 0.386693i 0.486813 0.873506i \(-0.338159\pi\)
−0.873506 + 0.486813i \(0.838159\pi\)
\(8\) 0 0
\(9\) −41.6886 + 41.6886i −1.54402 + 1.54402i
\(10\) 0 0
\(11\) −0.758120 + 1.83026i −0.0207802 + 0.0501678i −0.933929 0.357458i \(-0.883643\pi\)
0.913149 + 0.407626i \(0.133643\pi\)
\(12\) 0 0
\(13\) 71.0832 29.4436i 1.51653 0.628168i 0.539639 0.841896i \(-0.318561\pi\)
0.976893 + 0.213728i \(0.0685606\pi\)
\(14\) 0 0
\(15\) 75.7978i 1.30473i
\(16\) 0 0
\(17\) 98.5470i 1.40595i 0.711214 + 0.702975i \(0.248146\pi\)
−0.711214 + 0.702975i \(0.751854\pi\)
\(18\) 0 0
\(19\) −89.5748 + 37.1031i −1.08157 + 0.448002i −0.851060 0.525068i \(-0.824040\pi\)
−0.230512 + 0.973070i \(0.574040\pi\)
\(20\) 0 0
\(21\) −35.9342 + 86.7528i −0.373404 + 0.901477i
\(22\) 0 0
\(23\) −24.9355 + 24.9355i −0.226062 + 0.226062i −0.811045 0.584984i \(-0.801101\pi\)
0.584984 + 0.811045i \(0.301101\pi\)
\(24\) 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 −0.993674 0.112299i \(-0.964178\pi\)
0.623226 0.782042i \(-0.285822\pi\)
\(30\) 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 −0.116906 0.993143i \(-0.537298\pi\)
−0.784923 + 0.619593i \(0.787298\pi\)
\(38\) 0 0
\(39\) −504.401 504.401i −2.07100 2.07100i
\(40\) 0 0
\(41\) −45.3618 + 45.3618i −0.172788 + 0.172788i −0.788203 0.615415i \(-0.788988\pi\)
0.615415 + 0.788203i \(0.288988\pi\)
\(42\) 0 0
\(43\) −89.7175 + 216.597i −0.318181 + 0.768157i 0.681170 + 0.732126i \(0.261472\pi\)
−0.999351 + 0.0360314i \(0.988528\pi\)
\(44\) 0 0
\(45\) 445.312 184.454i 1.47518 0.611041i
\(46\) 0 0
\(47\) 4.38416i 0.0136063i −0.999977 0.00680315i \(-0.997834\pi\)
0.999977 0.00680315i \(-0.00216553\pi\)
\(48\) 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 −0.911814 0.410604i \(-0.865318\pi\)
0.935091 + 0.354408i \(0.115318\pi\)
\(54\) 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 0.0423945 0.999101i \(-0.486501\pi\)
−0.676494 + 0.736448i \(0.736501\pi\)
\(60\) 0 0
\(61\) −28.2072 68.0983i −0.0592060 0.142936i 0.891508 0.453005i \(-0.149648\pi\)
−0.950714 + 0.310069i \(0.899648\pi\)
\(62\) 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 −0.928031 0.372502i \(-0.878500\pi\)
0.392818 0.919616i \(-0.371500\pi\)
\(68\) 0 0
\(69\) 302.057 + 125.116i 0.527005 + 0.218293i
\(70\) 0 0
\(71\) 579.730 + 579.730i 0.969032 + 0.969032i 0.999535 0.0305030i \(-0.00971091\pi\)
−0.0305030 + 0.999535i \(0.509711\pi\)
\(72\) 0 0
\(73\) −258.894 + 258.894i −0.415085 + 0.415085i −0.883506 0.468420i \(-0.844823\pi\)
0.468420 + 0.883506i \(0.344823\pi\)
\(74\) 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 \(-0.797453\pi\)
0.804289 0.594239i \(-0.202547\pi\)
\(80\) 0 0
\(81\) 1155.05i 1.58443i
\(82\) 0 0
\(83\) −234.905 + 97.3009i −0.310653 + 0.128677i −0.532563 0.846391i \(-0.678771\pi\)
0.221910 + 0.975067i \(0.428771\pi\)
\(84\) 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 0.805893 0.592061i \(-0.201685\pi\)
−0.592061 + 0.805893i \(0.701685\pi\)
\(90\) 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 −0.519782 0.854299i \(-0.673987\pi\)
−0.971622 + 0.236540i \(0.923987\pi\)
\(102\) 0 0
\(103\) −146.406 146.406i −0.140056 0.140056i 0.633603 0.773659i \(-0.281575\pi\)
−0.773659 + 0.633603i \(0.781575\pi\)
\(104\) 0 0
\(105\) 542.838 542.838i 0.504529 0.504529i
\(106\) 0 0
\(107\) −375.001 + 905.331i −0.338810 + 0.817960i 0.659021 + 0.752125i \(0.270971\pi\)
−0.997831 + 0.0658347i \(0.979029\pi\)
\(108\) 0 0
\(109\) −330.443 + 136.874i −0.290373 + 0.120277i −0.523115 0.852262i \(-0.675230\pi\)
0.232742 + 0.972539i \(0.425230\pi\)
\(110\) 0 0
\(111\) 2036.81i 1.74167i
\(112\) 0 0
\(113\) 743.066i 0.618600i −0.950965 0.309300i \(-0.899905\pi\)
0.950965 0.309300i \(-0.100095\pi\)
\(114\) 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 0.960538 0.278150i \(-0.0897212\pi\)
−0.875884 + 0.482521i \(0.839721\pi\)
\(132\) 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 −0.837105 0.547043i \(-0.815754\pi\)
0.547043 + 0.837105i \(0.315754\pi\)
\(138\) 0 0
\(139\) −158.069 + 381.612i −0.0964548 + 0.232863i −0.964741 0.263201i \(-0.915222\pi\)
0.868286 + 0.496064i \(0.165222\pi\)
\(140\) 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 −0.812502 0.582959i \(-0.801895\pi\)
0.986740 + 0.162312i \(0.0518949\pi\)
\(150\) 0 0
\(151\) 1447.99 1447.99i 0.780369 0.780369i −0.199524 0.979893i \(-0.563940\pi\)
0.979893 + 0.199524i \(0.0639397\pi\)
\(152\) 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 −0.886675 0.462393i \(-0.846991\pi\)
0.300013 0.953935i \(-0.403009\pi\)
\(158\) 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 −0.837232 0.546848i \(-0.815828\pi\)
0.205333 0.978692i \(-0.434172\pi\)
\(164\) 0 0
\(165\) −138.730 57.4638i −0.0654552 0.0271125i
\(166\) 0 0
\(167\) 2616.84 + 2616.84i 1.21256 + 1.21256i 0.970182 + 0.242376i \(0.0779268\pi\)
0.242376 + 0.970182i \(0.422073\pi\)
\(168\) 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 0.0233941 0.999726i \(-0.492553\pi\)
0.723455 + 0.690371i \(0.242553\pi\)
\(174\) 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 −0.712745 0.701423i \(-0.752548\pi\)
−0.00800596 + 0.999968i \(0.502548\pi\)
\(180\) 0 0
\(181\) 1087.42 2625.26i 0.446559 1.07809i −0.527043 0.849839i \(-0.676699\pi\)
0.973602 0.228251i \(-0.0733006\pi\)
\(182\) 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 0.935513 0.353293i \(-0.114938\pi\)
0.411692 + 0.911323i \(0.364938\pi\)
\(198\) 0 0
\(199\) −361.648 361.648i −0.128827 0.128827i 0.639753 0.768580i \(-0.279036\pi\)
−0.768580 + 0.639753i \(0.779036\pi\)
\(200\) 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 0.828762 0.559601i \(-0.189046\pi\)
0.981721 0.190325i \(-0.0609543\pi\)
\(212\) 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 0.999755 0.0221219i \(-0.00704218\pi\)
−0.722576 + 0.691291i \(0.757042\pi\)
\(228\) 0 0
\(229\) −5763.17 2387.18i −1.66306 0.688862i −0.664756 0.747061i \(-0.731464\pi\)
−0.998305 + 0.0581984i \(0.981464\pi\)
\(230\) 0 0
\(231\) −131.538 131.538i −0.0374657 0.0374657i
\(232\) 0 0
\(233\) 3036.23 3036.23i 0.853691 0.853691i −0.136895 0.990586i \(-0.543712\pi\)
0.990586 + 0.136895i \(0.0437122\pi\)
\(234\) 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 \(-0.675761\pi\)
0.524537 0.851388i \(-0.324239\pi\)
\(240\) 0 0
\(241\) 795.320i 0.212577i −0.994335 0.106289i \(-0.966103\pi\)
0.994335 0.106289i \(-0.0338967\pi\)
\(242\) 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 −0.541668 0.840593i \(-0.682207\pi\)
−0.977406 + 0.211372i \(0.932207\pi\)
\(252\) 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 0.943854 0.330363i \(-0.107171\pi\)
−0.330363 + 0.943854i \(0.607171\pi\)
\(264\) 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 −0.984889 0.173186i \(-0.944594\pi\)
−0.573961 + 0.818883i \(0.694594\pi\)
\(270\) 0 0
\(271\) 6338.06i 1.42070i −0.703848 0.710350i \(-0.748537\pi\)
0.703848 0.710350i \(-0.251463\pi\)
\(272\) 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 −0.836695 0.547669i \(-0.815515\pi\)
0.978893 + 0.204373i \(0.0655155\pi\)
\(278\) 0 0
\(279\) 2420.21 2420.21i 0.519334 0.519334i
\(280\) 0 0
\(281\) −3436.47 3436.47i −0.729547 0.729547i 0.240983 0.970529i \(-0.422530\pi\)
−0.970529 + 0.240983i \(0.922530\pi\)
\(282\) 0 0
\(283\) 5101.55 + 2113.13i 1.07158 + 0.443861i 0.847546 0.530722i \(-0.178079\pi\)
0.224029 + 0.974582i \(0.428079\pi\)
\(284\) 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 0.645727 0.763568i \(-0.276554\pi\)
−0.0833258 + 0.996522i \(0.526554\pi\)
\(294\) 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 −0.421758 0.906708i \(-0.638587\pi\)
0.342912 + 0.939368i \(0.388587\pi\)
\(308\) 0 0
\(309\) −734.603 + 1773.49i −0.135243 + 0.326506i
\(310\) 0 0
\(311\) 3761.67 3761.67i 0.685868 0.685868i −0.275448 0.961316i \(-0.588826\pi\)
0.961316 + 0.275448i \(0.0888262\pi\)
\(312\) 0 0
\(313\) 718.221 + 718.221i 0.129700 + 0.129700i 0.768977 0.639277i \(-0.220766\pi\)
−0.639277 + 0.768977i \(0.720766\pi\)
\(314\) 0 0
\(315\) −4510.17 1868.18i −0.806729 0.334158i
\(316\) 0 0
\(317\) 1315.47 + 3175.83i 0.233073 + 0.562689i 0.996536 0.0831634i \(-0.0265023\pi\)
−0.763463 + 0.645852i \(0.776502\pi\)
\(318\) 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 −0.960888 0.276937i \(-0.910681\pi\)
0.875274 + 0.483626i \(0.160681\pi\)
\(332\) 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 \(-0.873999\pi\)
0.922672 0.385587i \(-0.126001\pi\)
\(338\) 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 0.177915 0.984046i \(-0.443065\pi\)
−0.570021 + 0.821630i \(0.693065\pi\)
\(348\) 0 0
\(349\) 1115.54 + 2693.15i 0.171099 + 0.413069i 0.986048 0.166464i \(-0.0532349\pi\)
−0.814949 + 0.579533i \(0.803235\pi\)
\(350\) 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 −0.959361 0.282182i \(-0.908942\pi\)
−0.282182 0.959361i \(-0.591058\pi\)
\(360\) 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 \(-0.962966\pi\)
0.993239 0.116085i \(-0.0370345\pi\)
\(368\) 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 −0.0529149 + 0.998599i \(0.516851\pi\)
−0.668700 + 0.743533i \(0.733149\pi\)
\(374\) 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 0.660653 0.750691i \(-0.270279\pi\)
−0.0636663 + 0.997971i \(0.520279\pi\)
\(380\) 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 0.205712 0.978612i \(-0.434049\pi\)
−0.546523 + 0.837444i \(0.684049\pi\)
\(390\) 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 −0.497566 0.867426i \(-0.665773\pi\)
0.261531 + 0.965195i \(0.415773\pi\)
\(398\) 0 0
\(399\) 9104.14i 1.14230i
\(400\) 0 0
\(401\) 12147.1i 1.51271i −0.654162 0.756354i \(-0.726979\pi\)
0.654162 0.756354i \(-0.273021\pi\)
\(402\) 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 0.995085 + 0.0990235i \(0.0315719\pi\)
0.0990235 + 0.995085i \(0.468428\pi\)
\(410\) 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 0.864982 + 0.501803i \(0.167330\pi\)
−0.256806 + 0.966463i \(0.582670\pi\)
\(420\) 0 0
\(421\) 12044.9 + 4989.15i 1.39437 + 0.577568i 0.948285 0.317421i \(-0.102817\pi\)
0.446088 + 0.894989i \(0.352817\pi\)
\(422\) 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 \(0.0549615\pi\)
−0.985130 + 0.171810i \(0.945039\pi\)
\(432\) 0 0
\(433\) 3478.83i 0.386101i 0.981189 + 0.193051i \(0.0618381\pi\)
−0.981189 + 0.193051i \(0.938162\pi\)
\(434\) 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 −0.967990 0.250989i \(-0.919244\pi\)
0.250989 + 0.967990i \(0.419244\pi\)
\(440\) 0 0
\(441\) 10022.8 + 10022.8i 1.08226 + 1.08226i
\(442\) 0 0
\(443\) −1177.46 487.720i −0.126282 0.0523076i 0.318648 0.947873i \(-0.396771\pi\)
−0.444930 + 0.895566i \(0.646771\pi\)
\(444\) 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 −0.646193 0.763174i \(-0.723640\pi\)
0.763174 + 0.646193i \(0.223640\pi\)
\(458\) 0 0
\(459\) −11173.3 + 26974.8i −1.13622 + 2.74309i
\(460\) 0 0
\(461\) −7860.73 + 3256.02i −0.794166 + 0.328954i −0.742617 0.669716i \(-0.766416\pi\)
−0.0515489 + 0.998670i \(0.516416\pi\)
\(462\) 0 0
\(463\) 2545.63i 0.255519i 0.991805 + 0.127760i \(0.0407786\pi\)
−0.991805 + 0.127760i \(0.959221\pi\)
\(464\) 0 0
\(465\) 4400.40i 0.438847i
\(466\) 0 0
\(467\) 7269.46 3011.11i 0.720322 0.298367i 0.00775364 0.999970i \(-0.497532\pi\)
0.712568 + 0.701603i \(0.247532\pi\)
\(468\) 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 0.470732 0.882276i \(-0.343990\pi\)
−0.882276 + 0.470732i \(0.843990\pi\)
\(488\) 0 0
\(489\) −22527.6 + 22527.6i −2.08330 + 2.08330i
\(490\) 0 0
\(491\) 1908.12 4606.60i 0.175381 0.423408i −0.811606 0.584205i \(-0.801407\pi\)
0.986987 + 0.160797i \(0.0514065\pi\)
\(492\) 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 0.113804 0.993503i \(-0.463696\pi\)
0.782985 + 0.622041i \(0.213696\pi\)
\(500\) 0 0
\(501\) 13130.2 31699.1i 1.17089 2.82677i
\(502\) 0 0
\(503\) 6186.59 6186.59i 0.548402 0.548402i −0.377576 0.925978i \(-0.623242\pi\)
0.925978 + 0.377576i \(0.123242\pi\)
\(504\) 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 0.974933 0.222500i \(-0.0714216\pi\)
−0.846713 + 0.532051i \(0.821422\pi\)
\(510\) 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 −0.708858 0.705352i \(-0.750789\pi\)
0.705352 + 0.708858i \(0.250789\pi\)
\(522\) 0 0
\(523\) −6675.06 + 16115.0i −0.558088 + 1.34734i 0.353191 + 0.935551i \(0.385097\pi\)
−0.911278 + 0.411791i \(0.864903\pi\)
\(524\) 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 −0.962792 0.270245i \(-0.912895\pi\)
0.489704 0.871889i \(-0.337105\pi\)
\(542\) 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 0.765209 0.643782i \(-0.222635\pi\)
−0.996307 + 0.0858625i \(0.972635\pi\)
\(548\) 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 −0.619367 0.785101i \(-0.712611\pi\)
0.117192 + 0.993109i \(0.462611\pi\)
\(558\) 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 −0.927246 0.374453i \(-0.877830\pi\)
−0.390883 + 0.920440i \(0.627830\pi\)
\(564\) 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 −0.999983 0.00579351i \(-0.998156\pi\)
−0.00579351 0.999983i \(-0.501844\pi\)
\(570\) 0 0
\(571\) 15023.6 + 6222.97i 1.10108 + 0.456083i 0.857858 0.513887i \(-0.171795\pi\)
0.243224 + 0.969970i \(0.421795\pi\)
\(572\) 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 −0.469153 0.883117i \(-0.655441\pi\)
0.956199 0.292717i \(-0.0945594\pi\)
\(588\) 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 \(0.299883\pi\)
−0.588082 + 0.808801i \(0.700117\pi\)
\(594\) 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 −0.378175 0.925734i \(-0.623448\pi\)
0.925734 + 0.378175i \(0.123448\pi\)
\(600\) 0 0
\(601\) 11725.6 + 11725.6i 0.795837 + 0.795837i 0.982436 0.186599i \(-0.0597466\pi\)
−0.186599 + 0.982436i \(0.559747\pi\)
\(602\) 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 0.639551 0.768748i \(-0.279120\pi\)
−0.0913562 + 0.995818i \(0.529120\pi\)
\(614\) 0 0
\(615\) −3438.32 3438.32i −0.225442 0.225442i
\(616\) 0 0
\(617\) −14643.0 + 14643.0i −0.955437 + 0.955437i −0.999049 0.0436114i \(-0.986114\pi\)
0.0436114 + 0.999049i \(0.486114\pi\)
\(618\) 0 0
\(619\) 842.686 2034.42i 0.0547180 0.132101i −0.894156 0.447755i \(-0.852224\pi\)
0.948874 + 0.315654i \(0.102224\pi\)
\(620\) 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 −0.0167358 + 0.999860i \(0.505327\pi\)
−0.999860 + 0.0167358i \(0.994673\pi\)
\(632\) 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 0.956801 0.290743i \(-0.0939026\pi\)
−0.882147 + 0.470974i \(0.843903\pi\)
\(644\) 0 0
\(645\) −16417.6 6800.39i −1.00224 0.415139i
\(646\) 0 0
\(647\) −16654.8 16654.8i −1.01200 1.01200i −0.999927 0.0120763i \(-0.996156\pi\)
−0.0120763 0.999927i \(-0.503844\pi\)
\(648\) 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 0.334406 0.942429i \(-0.391464\pi\)
0.902859 + 0.429937i \(0.141464\pi\)
\(654\) 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 −0.491707 0.870760i \(-0.663627\pi\)
0.268031 + 0.963410i \(0.413627\pi\)
\(660\) 0 0
\(661\) −9874.75 + 23839.8i −0.581064 + 1.40281i 0.310785 + 0.950480i \(0.399408\pi\)
−0.891849 + 0.452333i \(0.850592\pi\)
\(662\) 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 0.00243434 0.999997i \(-0.499225\pi\)
−0.705383 + 0.708826i \(0.749225\pi\)
\(678\) 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 −0.801410 0.598116i \(-0.795916\pi\)
0.989614 + 0.143751i \(0.0459163\pi\)
\(684\) 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 −0.850460 0.526039i \(-0.823677\pi\)
−0.229401 + 0.973332i \(0.573677\pi\)
\(692\) 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 −0.987774 0.155895i \(-0.950174\pi\)
0.588227 0.808696i \(-0.299826\pi\)
\(702\) 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 0.269528 0.962992i \(-0.413132\pi\)
−0.490353 + 0.871524i \(0.663132\pi\)
\(710\) 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 \(0.110420\pi\)
−0.940432 + 0.339981i \(0.889580\pi\)
\(720\) 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 −0.0125242 + 0.999922i \(0.503987\pi\)
−0.999922 + 0.0125242i \(0.996013\pi\)
\(728\) 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 0.874466 0.485086i \(-0.161212\pi\)
−0.961349 + 0.275333i \(0.911212\pi\)
\(734\) 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 −0.997040 0.0768839i \(-0.975503\pi\)
0.650649 0.759379i \(-0.274497\pi\)
\(740\) 0 0
\(741\) 63896.5 + 26466.8i 3.16774 + 1.31212i
\(742\) 0 0
\(743\) 1100.04 + 1100.04i 0.0543157 + 0.0543157i 0.733743 0.679427i \(-0.237772\pi\)
−0.679427 + 0.733743i \(0.737772\pi\)
\(744\) 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 \(-0.815473\pi\)
0.836623 0.547780i \(-0.184527\pi\)
\(752\) 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 −0.871543 0.490318i \(-0.836880\pi\)
0.962982 + 0.269567i \(0.0868805\pi\)
\(758\) 0 0
\(759\) −457.991 + 457.991i −0.0219025 + 0.0219025i
\(760\) 0 0
\(761\) 7703.17 + 7703.17i 0.366938 + 0.366938i 0.866359 0.499421i \(-0.166454\pi\)
−0.499421 + 0.866359i \(0.666454\pi\)
\(762\) 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 0.399761 0.916619i \(-0.369093\pi\)
−0.365474 + 0.930822i \(0.619093\pi\)
\(774\) 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 −0.851150 0.524922i \(-0.824094\pi\)
−0.230678 + 0.973030i \(0.574094\pi\)
\(788\) 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