Properties

Label 384.3.l.a.31.2
Level $384$
Weight $3$
Character 384.31
Analytic conductor $10.463$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.2
Root \(1.78012 - 0.911682i\) of defining polynomial
Character \(\chi\) \(=\) 384.31
Dual form 384.3.l.a.223.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(-1.00772 - 1.00772i) q^{5} +10.0236 q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(-1.00772 - 1.00772i) q^{5} +10.0236 q^{7} +3.00000i q^{9} +(-2.26517 + 2.26517i) q^{11} +(6.88229 - 6.88229i) q^{13} +2.46840i q^{15} -22.3801 q^{17} +(16.8918 + 16.8918i) q^{19} +(-12.2763 - 12.2763i) q^{21} +33.2007 q^{23} -22.9690i q^{25} +(3.67423 - 3.67423i) q^{27} +(24.6412 - 24.6412i) q^{29} -41.3761i q^{31} +5.54852 q^{33} +(-10.1010 - 10.1010i) q^{35} +(6.60031 + 6.60031i) q^{37} -16.8581 q^{39} -47.1477i q^{41} +(48.8218 - 48.8218i) q^{43} +(3.02316 - 3.02316i) q^{45} +45.6048i q^{47} +51.4717 q^{49} +(27.4100 + 27.4100i) q^{51} +(-25.1401 - 25.1401i) q^{53} +4.56532 q^{55} -41.3762i q^{57} +(-6.23974 + 6.23974i) q^{59} +(-35.9513 + 35.9513i) q^{61} +30.0707i q^{63} -13.8709 q^{65} +(-10.2045 - 10.2045i) q^{67} +(-40.6624 - 40.6624i) q^{69} +11.9529 q^{71} +111.332i q^{73} +(-28.1312 + 28.1312i) q^{75} +(-22.7051 + 22.7051i) q^{77} +4.46031i q^{79} -9.00000 q^{81} +(-10.1751 - 10.1751i) q^{83} +(22.5530 + 22.5530i) q^{85} -60.3583 q^{87} -21.9364i q^{89} +(68.9850 - 68.9850i) q^{91} +(-50.6752 + 50.6752i) q^{93} -34.0444i q^{95} +107.309 q^{97} +(-6.79552 - 6.79552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} - 128q^{23} - 32q^{29} - 96q^{35} + 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} + 160q^{53} - 256q^{55} + 128q^{59} + 32q^{61} - 32q^{65} - 320q^{67} - 96q^{69} + 512q^{71} - 192q^{75} - 224q^{77} - 144q^{81} + 160q^{83} - 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) −1.00772 1.00772i −0.201544 0.201544i 0.599117 0.800661i \(-0.295518\pi\)
−0.800661 + 0.599117i \(0.795518\pi\)
\(6\) 0 0
\(7\) 10.0236 1.43194 0.715969 0.698133i \(-0.245985\pi\)
0.715969 + 0.698133i \(0.245985\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −2.26517 + 2.26517i −0.205925 + 0.205925i −0.802533 0.596608i \(-0.796515\pi\)
0.596608 + 0.802533i \(0.296515\pi\)
\(12\) 0 0
\(13\) 6.88229 6.88229i 0.529407 0.529407i −0.390989 0.920395i \(-0.627867\pi\)
0.920395 + 0.390989i \(0.127867\pi\)
\(14\) 0 0
\(15\) 2.46840i 0.164560i
\(16\) 0 0
\(17\) −22.3801 −1.31648 −0.658240 0.752809i \(-0.728699\pi\)
−0.658240 + 0.752809i \(0.728699\pi\)
\(18\) 0 0
\(19\) 16.8918 + 16.8918i 0.889041 + 0.889041i 0.994431 0.105390i \(-0.0336092\pi\)
−0.105390 + 0.994431i \(0.533609\pi\)
\(20\) 0 0
\(21\) −12.2763 12.2763i −0.584586 0.584586i
\(22\) 0 0
\(23\) 33.2007 1.44351 0.721755 0.692149i \(-0.243336\pi\)
0.721755 + 0.692149i \(0.243336\pi\)
\(24\) 0 0
\(25\) 22.9690i 0.918760i
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) 24.6412 24.6412i 0.849696 0.849696i −0.140399 0.990095i \(-0.544839\pi\)
0.990095 + 0.140399i \(0.0448385\pi\)
\(30\) 0 0
\(31\) 41.3761i 1.33471i −0.744738 0.667357i \(-0.767426\pi\)
0.744738 0.667357i \(-0.232574\pi\)
\(32\) 0 0
\(33\) 5.54852 0.168137
\(34\) 0 0
\(35\) −10.1010 10.1010i −0.288599 0.288599i
\(36\) 0 0
\(37\) 6.60031 + 6.60031i 0.178387 + 0.178387i 0.790652 0.612266i \(-0.209742\pi\)
−0.612266 + 0.790652i \(0.709742\pi\)
\(38\) 0 0
\(39\) −16.8581 −0.432259
\(40\) 0 0
\(41\) 47.1477i 1.14994i −0.818173 0.574972i \(-0.805013\pi\)
0.818173 0.574972i \(-0.194987\pi\)
\(42\) 0 0
\(43\) 48.8218 48.8218i 1.13539 1.13539i 0.146124 0.989266i \(-0.453320\pi\)
0.989266 0.146124i \(-0.0466799\pi\)
\(44\) 0 0
\(45\) 3.02316 3.02316i 0.0671814 0.0671814i
\(46\) 0 0
\(47\) 45.6048i 0.970315i 0.874427 + 0.485157i \(0.161238\pi\)
−0.874427 + 0.485157i \(0.838762\pi\)
\(48\) 0 0
\(49\) 51.4717 1.05044
\(50\) 0 0
\(51\) 27.4100 + 27.4100i 0.537450 + 0.537450i
\(52\) 0 0
\(53\) −25.1401 25.1401i −0.474341 0.474341i 0.428975 0.903316i \(-0.358875\pi\)
−0.903316 + 0.428975i \(0.858875\pi\)
\(54\) 0 0
\(55\) 4.56532 0.0830059
\(56\) 0 0
\(57\) 41.3762i 0.725899i
\(58\) 0 0
\(59\) −6.23974 + 6.23974i −0.105758 + 0.105758i −0.758006 0.652248i \(-0.773826\pi\)
0.652248 + 0.758006i \(0.273826\pi\)
\(60\) 0 0
\(61\) −35.9513 + 35.9513i −0.589366 + 0.589366i −0.937460 0.348093i \(-0.886829\pi\)
0.348093 + 0.937460i \(0.386829\pi\)
\(62\) 0 0
\(63\) 30.0707i 0.477312i
\(64\) 0 0
\(65\) −13.8709 −0.213398
\(66\) 0 0
\(67\) −10.2045 10.2045i −0.152307 0.152307i 0.626841 0.779147i \(-0.284348\pi\)
−0.779147 + 0.626841i \(0.784348\pi\)
\(68\) 0 0
\(69\) −40.6624 40.6624i −0.589310 0.589310i
\(70\) 0 0
\(71\) 11.9529 0.168350 0.0841752 0.996451i \(-0.473174\pi\)
0.0841752 + 0.996451i \(0.473174\pi\)
\(72\) 0 0
\(73\) 111.332i 1.52510i 0.646929 + 0.762550i \(0.276053\pi\)
−0.646929 + 0.762550i \(0.723947\pi\)
\(74\) 0 0
\(75\) −28.1312 + 28.1312i −0.375082 + 0.375082i
\(76\) 0 0
\(77\) −22.7051 + 22.7051i −0.294871 + 0.294871i
\(78\) 0 0
\(79\) 4.46031i 0.0564596i 0.999601 + 0.0282298i \(0.00898702\pi\)
−0.999601 + 0.0282298i \(0.991013\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −10.1751 10.1751i −0.122592 0.122592i 0.643149 0.765741i \(-0.277627\pi\)
−0.765741 + 0.643149i \(0.777627\pi\)
\(84\) 0 0
\(85\) 22.5530 + 22.5530i 0.265329 + 0.265329i
\(86\) 0 0
\(87\) −60.3583 −0.693774
\(88\) 0 0
\(89\) 21.9364i 0.246476i −0.992377 0.123238i \(-0.960672\pi\)
0.992377 0.123238i \(-0.0393279\pi\)
\(90\) 0 0
\(91\) 68.9850 68.9850i 0.758077 0.758077i
\(92\) 0 0
\(93\) −50.6752 + 50.6752i −0.544895 + 0.544895i
\(94\) 0 0
\(95\) 34.0444i 0.358362i
\(96\) 0 0
\(97\) 107.309 1.10628 0.553140 0.833088i \(-0.313429\pi\)
0.553140 + 0.833088i \(0.313429\pi\)
\(98\) 0 0
\(99\) −6.79552 6.79552i −0.0686416 0.0686416i
\(100\) 0 0
\(101\) 100.780 + 100.780i 0.997824 + 0.997824i 0.999998 0.00217389i \(-0.000691973\pi\)
−0.00217389 + 0.999998i \(0.500692\pi\)
\(102\) 0 0
\(103\) 58.0562 0.563653 0.281826 0.959465i \(-0.409060\pi\)
0.281826 + 0.959465i \(0.409060\pi\)
\(104\) 0 0
\(105\) 24.7422i 0.235640i
\(106\) 0 0
\(107\) −112.747 + 112.747i −1.05371 + 1.05371i −0.0552381 + 0.998473i \(0.517592\pi\)
−0.998473 + 0.0552381i \(0.982408\pi\)
\(108\) 0 0
\(109\) 81.1384 81.1384i 0.744389 0.744389i −0.229030 0.973419i \(-0.573555\pi\)
0.973419 + 0.229030i \(0.0735554\pi\)
\(110\) 0 0
\(111\) 16.1674i 0.145652i
\(112\) 0 0
\(113\) −171.844 −1.52074 −0.760371 0.649489i \(-0.774983\pi\)
−0.760371 + 0.649489i \(0.774983\pi\)
\(114\) 0 0
\(115\) −33.4571 33.4571i −0.290931 0.290931i
\(116\) 0 0
\(117\) 20.6469 + 20.6469i 0.176469 + 0.176469i
\(118\) 0 0
\(119\) −224.329 −1.88512
\(120\) 0 0
\(121\) 110.738i 0.915190i
\(122\) 0 0
\(123\) −57.7439 + 57.7439i −0.469463 + 0.469463i
\(124\) 0 0
\(125\) −48.3394 + 48.3394i −0.386715 + 0.386715i
\(126\) 0 0
\(127\) 36.8333i 0.290026i −0.989430 0.145013i \(-0.953678\pi\)
0.989430 0.145013i \(-0.0463224\pi\)
\(128\) 0 0
\(129\) −119.588 −0.927042
\(130\) 0 0
\(131\) 12.3686 + 12.3686i 0.0944170 + 0.0944170i 0.752738 0.658321i \(-0.228733\pi\)
−0.658321 + 0.752738i \(0.728733\pi\)
\(132\) 0 0
\(133\) 169.316 + 169.316i 1.27305 + 1.27305i
\(134\) 0 0
\(135\) −7.40521 −0.0548534
\(136\) 0 0
\(137\) 145.679i 1.06335i 0.846949 + 0.531674i \(0.178437\pi\)
−0.846949 + 0.531674i \(0.821563\pi\)
\(138\) 0 0
\(139\) −82.5709 + 82.5709i −0.594035 + 0.594035i −0.938719 0.344684i \(-0.887986\pi\)
0.344684 + 0.938719i \(0.387986\pi\)
\(140\) 0 0
\(141\) 55.8542 55.8542i 0.396129 0.396129i
\(142\) 0 0
\(143\) 31.1791i 0.218036i
\(144\) 0 0
\(145\) −49.6629 −0.342503
\(146\) 0 0
\(147\) −63.0398 63.0398i −0.428842 0.428842i
\(148\) 0 0
\(149\) −196.248 196.248i −1.31710 1.31710i −0.916059 0.401043i \(-0.868648\pi\)
−0.401043 0.916059i \(-0.631352\pi\)
\(150\) 0 0
\(151\) 64.5007 0.427157 0.213578 0.976926i \(-0.431488\pi\)
0.213578 + 0.976926i \(0.431488\pi\)
\(152\) 0 0
\(153\) 67.1404i 0.438826i
\(154\) 0 0
\(155\) −41.6956 + 41.6956i −0.269004 + 0.269004i
\(156\) 0 0
\(157\) −54.4202 + 54.4202i −0.346625 + 0.346625i −0.858851 0.512226i \(-0.828821\pi\)
0.512226 + 0.858851i \(0.328821\pi\)
\(158\) 0 0
\(159\) 61.5803i 0.387298i
\(160\) 0 0
\(161\) 332.789 2.06701
\(162\) 0 0
\(163\) −104.803 104.803i −0.642961 0.642961i 0.308321 0.951282i \(-0.400233\pi\)
−0.951282 + 0.308321i \(0.900233\pi\)
\(164\) 0 0
\(165\) −5.59136 5.59136i −0.0338870 0.0338870i
\(166\) 0 0
\(167\) 53.3110 0.319228 0.159614 0.987180i \(-0.448975\pi\)
0.159614 + 0.987180i \(0.448975\pi\)
\(168\) 0 0
\(169\) 74.2683i 0.439457i
\(170\) 0 0
\(171\) −50.6753 + 50.6753i −0.296347 + 0.296347i
\(172\) 0 0
\(173\) 41.5780 41.5780i 0.240335 0.240335i −0.576654 0.816989i \(-0.695642\pi\)
0.816989 + 0.576654i \(0.195642\pi\)
\(174\) 0 0
\(175\) 230.231i 1.31561i
\(176\) 0 0
\(177\) 15.2842 0.0863513
\(178\) 0 0
\(179\) −53.0709 53.0709i −0.296486 0.296486i 0.543150 0.839636i \(-0.317231\pi\)
−0.839636 + 0.543150i \(0.817231\pi\)
\(180\) 0 0
\(181\) 66.6042 + 66.6042i 0.367979 + 0.367979i 0.866740 0.498761i \(-0.166211\pi\)
−0.498761 + 0.866740i \(0.666211\pi\)
\(182\) 0 0
\(183\) 88.0625 0.481216
\(184\) 0 0
\(185\) 13.3025i 0.0719056i
\(186\) 0 0
\(187\) 50.6949 50.6949i 0.271096 0.271096i
\(188\) 0 0
\(189\) 36.8289 36.8289i 0.194862 0.194862i
\(190\) 0 0
\(191\) 113.753i 0.595567i 0.954633 + 0.297784i \(0.0962474\pi\)
−0.954633 + 0.297784i \(0.903753\pi\)
\(192\) 0 0
\(193\) −26.5596 −0.137615 −0.0688073 0.997630i \(-0.521919\pi\)
−0.0688073 + 0.997630i \(0.521919\pi\)
\(194\) 0 0
\(195\) 16.9883 + 16.9883i 0.0871193 + 0.0871193i
\(196\) 0 0
\(197\) −51.8935 51.8935i −0.263419 0.263419i 0.563023 0.826442i \(-0.309638\pi\)
−0.826442 + 0.563023i \(0.809638\pi\)
\(198\) 0 0
\(199\) −136.741 −0.687140 −0.343570 0.939127i \(-0.611636\pi\)
−0.343570 + 0.939127i \(0.611636\pi\)
\(200\) 0 0
\(201\) 24.9959i 0.124358i
\(202\) 0 0
\(203\) 246.992 246.992i 1.21671 1.21671i
\(204\) 0 0
\(205\) −47.5118 + 47.5118i −0.231765 + 0.231765i
\(206\) 0 0
\(207\) 99.6022i 0.481170i
\(208\) 0 0
\(209\) −76.5255 −0.366151
\(210\) 0 0
\(211\) 141.171 + 141.171i 0.669057 + 0.669057i 0.957498 0.288441i \(-0.0931368\pi\)
−0.288441 + 0.957498i \(0.593137\pi\)
\(212\) 0 0
\(213\) −14.6392 14.6392i −0.0687288 0.0687288i
\(214\) 0 0
\(215\) −98.3975 −0.457663
\(216\) 0 0
\(217\) 414.736i 1.91123i
\(218\) 0 0
\(219\) 136.354 136.354i 0.622620 0.622620i
\(220\) 0 0
\(221\) −154.027 + 154.027i −0.696953 + 0.696953i
\(222\) 0 0
\(223\) 122.607i 0.549806i 0.961472 + 0.274903i \(0.0886457\pi\)
−0.961472 + 0.274903i \(0.911354\pi\)
\(224\) 0 0
\(225\) 68.9070 0.306253
\(226\) 0 0
\(227\) 295.844 + 295.844i 1.30328 + 1.30328i 0.926168 + 0.377112i \(0.123083\pi\)
0.377112 + 0.926168i \(0.376917\pi\)
\(228\) 0 0
\(229\) −73.3817 73.3817i −0.320444 0.320444i 0.528493 0.848937i \(-0.322757\pi\)
−0.848937 + 0.528493i \(0.822757\pi\)
\(230\) 0 0
\(231\) 55.6159 0.240761
\(232\) 0 0
\(233\) 156.229i 0.670509i −0.942128 0.335255i \(-0.891178\pi\)
0.942128 0.335255i \(-0.108822\pi\)
\(234\) 0 0
\(235\) 45.9569 45.9569i 0.195561 0.195561i
\(236\) 0 0
\(237\) 5.46274 5.46274i 0.0230495 0.0230495i
\(238\) 0 0
\(239\) 13.1716i 0.0551113i 0.999620 + 0.0275557i \(0.00877235\pi\)
−0.999620 + 0.0275557i \(0.991228\pi\)
\(240\) 0 0
\(241\) −189.519 −0.786386 −0.393193 0.919456i \(-0.628630\pi\)
−0.393193 + 0.919456i \(0.628630\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) −51.8692 51.8692i −0.211711 0.211711i
\(246\) 0 0
\(247\) 232.508 0.941328
\(248\) 0 0
\(249\) 24.9238i 0.100096i
\(250\) 0 0
\(251\) 27.4434 27.4434i 0.109336 0.109336i −0.650322 0.759658i \(-0.725366\pi\)
0.759658 + 0.650322i \(0.225366\pi\)
\(252\) 0 0
\(253\) −75.2053 + 75.2053i −0.297254 + 0.297254i
\(254\) 0 0
\(255\) 55.2432i 0.216640i
\(256\) 0 0
\(257\) 135.375 0.526752 0.263376 0.964693i \(-0.415164\pi\)
0.263376 + 0.964693i \(0.415164\pi\)
\(258\) 0 0
\(259\) 66.1586 + 66.1586i 0.255438 + 0.255438i
\(260\) 0 0
\(261\) 73.9236 + 73.9236i 0.283232 + 0.283232i
\(262\) 0 0
\(263\) 31.6123 0.120199 0.0600994 0.998192i \(-0.480858\pi\)
0.0600994 + 0.998192i \(0.480858\pi\)
\(264\) 0 0
\(265\) 50.6684i 0.191201i
\(266\) 0 0
\(267\) −26.8665 + 26.8665i −0.100624 + 0.100624i
\(268\) 0 0
\(269\) 194.213 194.213i 0.721981 0.721981i −0.247028 0.969008i \(-0.579454\pi\)
0.969008 + 0.247028i \(0.0794538\pi\)
\(270\) 0 0
\(271\) 291.647i 1.07619i 0.842884 + 0.538095i \(0.180856\pi\)
−0.842884 + 0.538095i \(0.819144\pi\)
\(272\) 0 0
\(273\) −168.978 −0.618967
\(274\) 0 0
\(275\) 52.0287 + 52.0287i 0.189195 + 0.189195i
\(276\) 0 0
\(277\) −305.166 305.166i −1.10168 1.10168i −0.994208 0.107475i \(-0.965723\pi\)
−0.107475 0.994208i \(-0.534277\pi\)
\(278\) 0 0
\(279\) 124.128 0.444905
\(280\) 0 0
\(281\) 211.861i 0.753955i −0.926222 0.376978i \(-0.876963\pi\)
0.926222 0.376978i \(-0.123037\pi\)
\(282\) 0 0
\(283\) −105.325 + 105.325i −0.372175 + 0.372175i −0.868269 0.496094i \(-0.834767\pi\)
0.496094 + 0.868269i \(0.334767\pi\)
\(284\) 0 0
\(285\) −41.6957 + 41.6957i −0.146301 + 0.146301i
\(286\) 0 0
\(287\) 472.588i 1.64665i
\(288\) 0 0
\(289\) 211.871 0.733117
\(290\) 0 0
\(291\) −131.426 131.426i −0.451637 0.451637i
\(292\) 0 0
\(293\) 171.289 + 171.289i 0.584603 + 0.584603i 0.936165 0.351562i \(-0.114349\pi\)
−0.351562 + 0.936165i \(0.614349\pi\)
\(294\) 0 0
\(295\) 12.5758 0.0426300
\(296\) 0 0
\(297\) 16.6455i 0.0560456i
\(298\) 0 0
\(299\) 228.497 228.497i 0.764204 0.764204i
\(300\) 0 0
\(301\) 489.368 489.368i 1.62581 1.62581i
\(302\) 0 0
\(303\) 246.860i 0.814720i
\(304\) 0 0
\(305\) 72.4579 0.237567
\(306\) 0 0
\(307\) 27.1124 + 27.1124i 0.0883140 + 0.0883140i 0.749884 0.661570i \(-0.230109\pi\)
−0.661570 + 0.749884i \(0.730109\pi\)
\(308\) 0 0
\(309\) −71.1041 71.1041i −0.230110 0.230110i
\(310\) 0 0
\(311\) 371.124 1.19333 0.596663 0.802492i \(-0.296493\pi\)
0.596663 + 0.802492i \(0.296493\pi\)
\(312\) 0 0
\(313\) 374.501i 1.19649i −0.801313 0.598245i \(-0.795865\pi\)
0.801313 0.598245i \(-0.204135\pi\)
\(314\) 0 0
\(315\) 30.3029 30.3029i 0.0961996 0.0961996i
\(316\) 0 0
\(317\) 48.5840 48.5840i 0.153262 0.153262i −0.626311 0.779573i \(-0.715436\pi\)
0.779573 + 0.626311i \(0.215436\pi\)
\(318\) 0 0
\(319\) 111.633i 0.349947i
\(320\) 0 0
\(321\) 276.173 0.860352
\(322\) 0 0
\(323\) −378.040 378.040i −1.17040 1.17040i
\(324\) 0 0
\(325\) −158.079 158.079i −0.486398 0.486398i
\(326\) 0 0
\(327\) −198.748 −0.607791
\(328\) 0 0
\(329\) 457.122i 1.38943i
\(330\) 0 0
\(331\) 1.88883 1.88883i 0.00570644 0.00570644i −0.704248 0.709954i \(-0.748716\pi\)
0.709954 + 0.704248i \(0.248716\pi\)
\(332\) 0 0
\(333\) −19.8009 + 19.8009i −0.0594622 + 0.0594622i
\(334\) 0 0
\(335\) 20.5667i 0.0613931i
\(336\) 0 0
\(337\) −386.980 −1.14831 −0.574154 0.818747i \(-0.694669\pi\)
−0.574154 + 0.818747i \(0.694669\pi\)
\(338\) 0 0
\(339\) 210.465 + 210.465i 0.620840 + 0.620840i
\(340\) 0 0
\(341\) 93.7240 + 93.7240i 0.274851 + 0.274851i
\(342\) 0 0
\(343\) 24.7757 0.0722325
\(344\) 0 0
\(345\) 81.9528i 0.237544i
\(346\) 0 0
\(347\) −441.887 + 441.887i −1.27345 + 1.27345i −0.329183 + 0.944266i \(0.606773\pi\)
−0.944266 + 0.329183i \(0.893227\pi\)
\(348\) 0 0
\(349\) −119.382 + 119.382i −0.342068 + 0.342068i −0.857144 0.515076i \(-0.827764\pi\)
0.515076 + 0.857144i \(0.327764\pi\)
\(350\) 0 0
\(351\) 50.5743i 0.144086i
\(352\) 0 0
\(353\) −515.642 −1.46074 −0.730371 0.683050i \(-0.760653\pi\)
−0.730371 + 0.683050i \(0.760653\pi\)
\(354\) 0 0
\(355\) −12.0452 12.0452i −0.0339301 0.0339301i
\(356\) 0 0
\(357\) 274.745 + 274.745i 0.769595 + 0.769595i
\(358\) 0 0
\(359\) 428.264 1.19294 0.596468 0.802637i \(-0.296570\pi\)
0.596468 + 0.802637i \(0.296570\pi\)
\(360\) 0 0
\(361\) 209.664i 0.580786i
\(362\) 0 0
\(363\) 135.626 135.626i 0.373625 0.373625i
\(364\) 0 0
\(365\) 112.192 112.192i 0.307375 0.307375i
\(366\) 0 0
\(367\) 219.482i 0.598043i 0.954246 + 0.299021i \(0.0966602\pi\)
−0.954246 + 0.299021i \(0.903340\pi\)
\(368\) 0 0
\(369\) 141.443 0.383315
\(370\) 0 0
\(371\) −251.993 251.993i −0.679226 0.679226i
\(372\) 0 0
\(373\) −425.005 425.005i −1.13942 1.13942i −0.988554 0.150870i \(-0.951793\pi\)
−0.150870 0.988554i \(-0.548207\pi\)
\(374\) 0 0
\(375\) 118.407 0.315752
\(376\) 0 0
\(377\) 339.175i 0.899669i
\(378\) 0 0
\(379\) −365.916 + 365.916i −0.965476 + 0.965476i −0.999424 0.0339473i \(-0.989192\pi\)
0.0339473 + 0.999424i \(0.489192\pi\)
\(380\) 0 0
\(381\) −45.1114 + 45.1114i −0.118403 + 0.118403i
\(382\) 0 0
\(383\) 213.276i 0.556857i 0.960457 + 0.278428i \(0.0898135\pi\)
−0.960457 + 0.278428i \(0.910187\pi\)
\(384\) 0 0
\(385\) 45.7608 0.118859
\(386\) 0 0
\(387\) 146.465 + 146.465i 0.378464 + 0.378464i
\(388\) 0 0
\(389\) 210.798 + 210.798i 0.541898 + 0.541898i 0.924085 0.382187i \(-0.124829\pi\)
−0.382187 + 0.924085i \(0.624829\pi\)
\(390\) 0 0
\(391\) −743.037 −1.90035
\(392\) 0 0
\(393\) 30.2968i 0.0770912i
\(394\) 0 0
\(395\) 4.49475 4.49475i 0.0113791 0.0113791i
\(396\) 0 0
\(397\) −392.907 + 392.907i −0.989690 + 0.989690i −0.999947 0.0102579i \(-0.996735\pi\)
0.0102579 + 0.999947i \(0.496735\pi\)
\(398\) 0 0
\(399\) 414.737i 1.03944i
\(400\) 0 0
\(401\) 29.3290 0.0731396 0.0365698 0.999331i \(-0.488357\pi\)
0.0365698 + 0.999331i \(0.488357\pi\)
\(402\) 0 0
\(403\) −284.762 284.762i −0.706606 0.706606i
\(404\) 0 0
\(405\) 9.06949 + 9.06949i 0.0223938 + 0.0223938i
\(406\) 0 0
\(407\) −29.9017 −0.0734684
\(408\) 0 0
\(409\) 601.115i 1.46972i 0.678219 + 0.734860i \(0.262752\pi\)
−0.678219 + 0.734860i \(0.737248\pi\)
\(410\) 0 0
\(411\) 178.419 178.419i 0.434110 0.434110i
\(412\) 0 0
\(413\) −62.5444 + 62.5444i −0.151439 + 0.151439i
\(414\) 0 0
\(415\) 20.5073i 0.0494153i
\(416\) 0 0
\(417\) 202.257 0.485028
\(418\) 0 0
\(419\) 518.885 + 518.885i 1.23839 + 1.23839i 0.960659 + 0.277729i \(0.0895819\pi\)
0.277729 + 0.960659i \(0.410418\pi\)
\(420\) 0 0
\(421\) 411.213 + 411.213i 0.976754 + 0.976754i 0.999736 0.0229817i \(-0.00731596\pi\)
−0.0229817 + 0.999736i \(0.507316\pi\)
\(422\) 0 0
\(423\) −136.814 −0.323438
\(424\) 0 0
\(425\) 514.049i 1.20953i
\(426\) 0 0
\(427\) −360.360 + 360.360i −0.843936 + 0.843936i
\(428\) 0 0
\(429\) 38.1865 38.1865i 0.0890128 0.0890128i
\(430\) 0 0
\(431\) 41.1083i 0.0953789i 0.998862 + 0.0476895i \(0.0151858\pi\)
−0.998862 + 0.0476895i \(0.984814\pi\)
\(432\) 0 0
\(433\) −351.682 −0.812199 −0.406100 0.913829i \(-0.633111\pi\)
−0.406100 + 0.913829i \(0.633111\pi\)
\(434\) 0 0
\(435\) 60.8244 + 60.8244i 0.139826 + 0.139826i
\(436\) 0 0
\(437\) 560.819 + 560.819i 1.28334 + 1.28334i
\(438\) 0 0
\(439\) −775.613 −1.76677 −0.883386 0.468646i \(-0.844742\pi\)
−0.883386 + 0.468646i \(0.844742\pi\)
\(440\) 0 0
\(441\) 154.415i 0.350148i
\(442\) 0 0
\(443\) 241.372 241.372i 0.544858 0.544858i −0.380091 0.924949i \(-0.624107\pi\)
0.924949 + 0.380091i \(0.124107\pi\)
\(444\) 0 0
\(445\) −22.1058 + 22.1058i −0.0496759 + 0.0496759i
\(446\) 0 0
\(447\) 480.708i 1.07541i
\(448\) 0 0
\(449\) 266.360 0.593228 0.296614 0.954997i \(-0.404142\pi\)
0.296614 + 0.954997i \(0.404142\pi\)
\(450\) 0 0
\(451\) 106.798 + 106.798i 0.236802 + 0.236802i
\(452\) 0 0
\(453\) −78.9969 78.9969i −0.174386 0.174386i
\(454\) 0 0
\(455\) −139.035 −0.305572
\(456\) 0 0
\(457\) 515.244i 1.12745i −0.825963 0.563725i \(-0.809368\pi\)
0.825963 0.563725i \(-0.190632\pi\)
\(458\) 0 0
\(459\) −82.2299 + 82.2299i −0.179150 + 0.179150i
\(460\) 0 0
\(461\) −5.67717 + 5.67717i −0.0123149 + 0.0123149i −0.713237 0.700923i \(-0.752772\pi\)
0.700923 + 0.713237i \(0.252772\pi\)
\(462\) 0 0
\(463\) 464.510i 1.00326i −0.865082 0.501631i \(-0.832733\pi\)
0.865082 0.501631i \(-0.167267\pi\)
\(464\) 0 0
\(465\) 102.133 0.219641
\(466\) 0 0
\(467\) −495.985 495.985i −1.06207 1.06207i −0.997942 0.0641248i \(-0.979574\pi\)
−0.0641248 0.997942i \(-0.520426\pi\)
\(468\) 0 0
\(469\) −102.286 102.286i −0.218094 0.218094i
\(470\) 0 0
\(471\) 133.302 0.283018
\(472\) 0 0
\(473\) 221.180i 0.467610i
\(474\) 0 0
\(475\) 387.987 387.987i 0.816815 0.816815i
\(476\) 0 0
\(477\) 75.4202 75.4202i 0.158114 0.158114i
\(478\) 0 0
\(479\) 378.802i 0.790818i −0.918505 0.395409i \(-0.870603\pi\)
0.918505 0.395409i \(-0.129397\pi\)
\(480\) 0 0
\(481\) 90.8504 0.188878
\(482\) 0 0
\(483\) −407.582 407.582i −0.843855 0.843855i
\(484\) 0 0
\(485\) −108.138 108.138i −0.222964 0.222964i
\(486\) 0 0
\(487\) 147.446 0.302764 0.151382 0.988475i \(-0.451628\pi\)
0.151382 + 0.988475i \(0.451628\pi\)
\(488\) 0 0
\(489\) 256.713i 0.524976i
\(490\) 0 0
\(491\) −109.547 + 109.547i −0.223110 + 0.223110i −0.809807 0.586697i \(-0.800428\pi\)
0.586697 + 0.809807i \(0.300428\pi\)
\(492\) 0 0
\(493\) −551.473 + 551.473i −1.11861 + 1.11861i
\(494\) 0 0
\(495\) 13.6960i 0.0276686i
\(496\) 0 0
\(497\) 119.810 0.241067
\(498\) 0 0
\(499\) 360.523 + 360.523i 0.722491 + 0.722491i 0.969112 0.246621i \(-0.0793202\pi\)
−0.246621 + 0.969112i \(0.579320\pi\)
\(500\) 0 0
\(501\) −65.2924 65.2924i −0.130324 0.130324i
\(502\) 0 0
\(503\) −927.420 −1.84378 −0.921889 0.387454i \(-0.873355\pi\)
−0.921889 + 0.387454i \(0.873355\pi\)
\(504\) 0 0
\(505\) 203.117i 0.402211i
\(506\) 0 0
\(507\) 90.9597 90.9597i 0.179408 0.179408i
\(508\) 0 0
\(509\) −677.931 + 677.931i −1.33189 + 1.33189i −0.428208 + 0.903680i \(0.640855\pi\)
−0.903680 + 0.428208i \(0.859145\pi\)
\(510\) 0 0
\(511\) 1115.95i 2.18385i
\(512\) 0 0
\(513\) 124.129 0.241966
\(514\) 0 0
\(515\) −58.5045 58.5045i −0.113601 0.113601i
\(516\) 0 0
\(517\) −103.303 103.303i −0.199812 0.199812i
\(518\) 0 0
\(519\) −101.845 −0.196233
\(520\) 0 0
\(521\) 143.173i 0.274804i −0.990515 0.137402i \(-0.956125\pi\)
0.990515 0.137402i \(-0.0438753\pi\)
\(522\) 0 0
\(523\) −226.187 + 226.187i −0.432481 + 0.432481i −0.889471 0.456991i \(-0.848927\pi\)
0.456991 + 0.889471i \(0.348927\pi\)
\(524\) 0 0
\(525\) −281.974 + 281.974i −0.537094 + 0.537094i
\(526\) 0 0
\(527\) 926.004i 1.75712i
\(528\) 0 0
\(529\) 573.288 1.08372
\(530\) 0 0
\(531\) −18.7192 18.7192i −0.0352528 0.0352528i
\(532\) 0 0
\(533\) −324.484 324.484i −0.608788 0.608788i
\(534\) 0 0
\(535\) 227.235 0.424739
\(536\) 0 0
\(537\) 129.997i 0.242080i
\(538\) 0 0
\(539\) −116.592 + 116.592i −0.216312 + 0.216312i
\(540\) 0 0
\(541\) 156.708 156.708i 0.289663 0.289663i −0.547284 0.836947i \(-0.684338\pi\)
0.836947 + 0.547284i \(0.184338\pi\)
\(542\) 0 0
\(543\) 163.146i 0.300454i
\(544\) 0 0
\(545\) −163.530 −0.300055
\(546\) 0 0
\(547\) −247.357 247.357i −0.452207 0.452207i 0.443880 0.896086i \(-0.353602\pi\)
−0.896086 + 0.443880i \(0.853602\pi\)
\(548\) 0 0
\(549\) −107.854 107.854i −0.196455 0.196455i
\(550\) 0 0
\(551\) 832.466 1.51083
\(552\) 0 0
\(553\) 44.7082i 0.0808466i
\(554\) 0 0
\(555\) −16.2922 + 16.2922i −0.0293553 + 0.0293553i
\(556\) 0 0
\(557\) 661.193 661.193i 1.18706 1.18706i 0.209184 0.977876i \(-0.432919\pi\)
0.977876 0.209184i \(-0.0670808\pi\)
\(558\) 0 0
\(559\) 672.011i 1.20217i
\(560\) 0 0
\(561\) −124.177 −0.221349
\(562\) 0 0
\(563\) −246.685 246.685i −0.438162 0.438162i 0.453231 0.891393i \(-0.350271\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(564\) 0 0
\(565\) 173.171 + 173.171i 0.306497 + 0.306497i
\(566\) 0 0
\(567\) −90.2120 −0.159104
\(568\) 0 0
\(569\) 243.567i 0.428061i −0.976827 0.214030i \(-0.931341\pi\)
0.976827 0.214030i \(-0.0686592\pi\)
\(570\) 0 0
\(571\) −59.9229 + 59.9229i −0.104944 + 0.104944i −0.757629 0.652685i \(-0.773642\pi\)
0.652685 + 0.757629i \(0.273642\pi\)
\(572\) 0 0
\(573\) 139.319 139.319i 0.243139 0.243139i
\(574\) 0 0
\(575\) 762.587i 1.32624i
\(576\) 0 0
\(577\) 136.609 0.236757 0.118378 0.992969i \(-0.462230\pi\)
0.118378 + 0.992969i \(0.462230\pi\)
\(578\) 0 0
\(579\) 32.5287 + 32.5287i 0.0561809 + 0.0561809i
\(580\) 0 0
\(581\) −101.991 101.991i −0.175543 0.175543i
\(582\) 0 0
\(583\) 113.893 0.195357
\(584\) 0 0
\(585\) 41.6126i 0.0711326i
\(586\) 0 0
\(587\) 331.817 331.817i 0.565276 0.565276i −0.365525 0.930801i \(-0.619111\pi\)
0.930801 + 0.365525i \(0.119111\pi\)
\(588\) 0 0
\(589\) 698.916 698.916i 1.18661 1.18661i
\(590\) 0 0
\(591\) 127.113i 0.215081i
\(592\) 0 0
\(593\) 131.285 0.221391 0.110695 0.993854i \(-0.464692\pi\)
0.110695 + 0.993854i \(0.464692\pi\)
\(594\) 0 0
\(595\) 226.061 + 226.061i 0.379934 + 0.379934i
\(596\) 0 0
\(597\) 167.473 + 167.473i 0.280524 + 0.280524i
\(598\) 0 0
\(599\) −136.119 −0.227243 −0.113621 0.993524i \(-0.536245\pi\)
−0.113621 + 0.993524i \(0.536245\pi\)
\(600\) 0 0
\(601\) 498.566i 0.829561i −0.909922 0.414780i \(-0.863858\pi\)
0.909922 0.414780i \(-0.136142\pi\)
\(602\) 0 0
\(603\) 30.6136 30.6136i 0.0507689 0.0507689i
\(604\) 0 0
\(605\) 111.593 111.593i 0.184451 0.184451i
\(606\) 0 0
\(607\) 568.740i 0.936969i −0.883472 0.468484i \(-0.844800\pi\)
0.883472 0.468484i \(-0.155200\pi\)
\(608\) 0 0
\(609\) −605.005 −0.993441
\(610\) 0 0
\(611\) 313.865 + 313.865i 0.513691 + 0.513691i
\(612\) 0 0
\(613\) 168.441 + 168.441i 0.274782 + 0.274782i 0.831022 0.556240i \(-0.187756\pi\)
−0.556240 + 0.831022i \(0.687756\pi\)
\(614\) 0 0
\(615\) 116.380 0.189235
\(616\) 0 0
\(617\) 599.157i 0.971081i 0.874214 + 0.485541i \(0.161377\pi\)
−0.874214 + 0.485541i \(0.838623\pi\)
\(618\) 0 0
\(619\) −126.719 + 126.719i −0.204715 + 0.204715i −0.802017 0.597301i \(-0.796240\pi\)
0.597301 + 0.802017i \(0.296240\pi\)
\(620\) 0 0
\(621\) 121.987 121.987i 0.196437 0.196437i
\(622\) 0 0
\(623\) 219.881i 0.352939i
\(624\) 0 0
\(625\) −476.800 −0.762879
\(626\) 0 0
\(627\) 93.7242 + 93.7242i 0.149480 + 0.149480i
\(628\) 0 0
\(629\) −147.716 147.716i −0.234842 0.234842i
\(630\) 0 0
\(631\) 668.283 1.05909 0.529543 0.848283i \(-0.322363\pi\)
0.529543 + 0.848283i \(0.322363\pi\)
\(632\) 0 0
\(633\) 345.797i 0.546283i
\(634\) 0 0
\(635\) −37.1177 + 37.1177i −0.0584531 + 0.0584531i
\(636\) 0 0
\(637\) 354.243 354.243i 0.556112 0.556112i
\(638\) 0 0
\(639\) 35.8586i 0.0561168i
\(640\) 0 0
\(641\) 484.574 0.755966 0.377983 0.925813i \(-0.376618\pi\)
0.377983 + 0.925813i \(0.376618\pi\)
\(642\) 0 0
\(643\) −75.2980 75.2980i −0.117104 0.117104i 0.646126 0.763230i \(-0.276388\pi\)
−0.763230 + 0.646126i \(0.776388\pi\)
\(644\) 0 0
\(645\) 120.512 + 120.512i 0.186840 + 0.186840i
\(646\) 0 0
\(647\) −582.307 −0.900011 −0.450006 0.893026i \(-0.648578\pi\)
−0.450006 + 0.893026i \(0.648578\pi\)
\(648\) 0 0
\(649\) 28.2682i 0.0435565i
\(650\) 0 0
\(651\) −507.946 + 507.946i −0.780255 + 0.780255i
\(652\) 0 0
\(653\) −457.453 + 457.453i −0.700541 + 0.700541i −0.964527 0.263986i \(-0.914963\pi\)
0.263986 + 0.964527i \(0.414963\pi\)
\(654\) 0 0
\(655\) 24.9283i 0.0380584i
\(656\) 0 0
\(657\) −333.997 −0.508367
\(658\) 0 0
\(659\) 430.079 + 430.079i 0.652623 + 0.652623i 0.953624 0.301001i \(-0.0973207\pi\)
−0.301001 + 0.953624i \(0.597321\pi\)
\(660\) 0 0
\(661\) 513.622 + 513.622i 0.777038 + 0.777038i 0.979326 0.202288i \(-0.0648376\pi\)
−0.202288 + 0.979326i \(0.564838\pi\)
\(662\) 0 0
\(663\) 377.287 0.569060
\(664\) 0 0
\(665\) 341.246i 0.513152i
\(666\) 0 0
\(667\) 818.105 818.105i 1.22654 1.22654i
\(668\) 0 0
\(669\) 150.162 150.162i 0.224457 0.224457i
\(670\) 0 0
\(671\) 162.872i 0.242730i
\(672\) 0 0
\(673\) −1112.68 −1.65332 −0.826659 0.562703i \(-0.809761\pi\)
−0.826659 + 0.562703i \(0.809761\pi\)
\(674\) 0 0
\(675\) −84.3935 84.3935i −0.125027 0.125027i
\(676\) 0 0
\(677\) −633.271 633.271i −0.935408 0.935408i 0.0626291 0.998037i \(-0.480051\pi\)
−0.998037 + 0.0626291i \(0.980051\pi\)
\(678\) 0 0
\(679\) 1075.62 1.58412
\(680\) 0 0
\(681\) 724.668i 1.06412i
\(682\) 0 0
\(683\) 429.651 429.651i 0.629065 0.629065i −0.318768 0.947833i \(-0.603269\pi\)
0.947833 + 0.318768i \(0.103269\pi\)
\(684\) 0 0
\(685\) 146.803 146.803i 0.214312 0.214312i
\(686\) 0 0
\(687\) 179.748i 0.261642i
\(688\) 0 0
\(689\) −346.042 −0.502239
\(690\) 0 0
\(691\) 151.617 + 151.617i 0.219417 + 0.219417i 0.808253 0.588836i \(-0.200414\pi\)
−0.588836 + 0.808253i \(0.700414\pi\)
\(692\) 0 0
\(693\) −68.1153 68.1153i −0.0982904 0.0982904i
\(694\) 0 0
\(695\) 166.417 0.239449
\(696\) 0 0
\(697\) 1055.17i 1.51388i
\(698\) 0 0
\(699\) −191.340 + 191.340i −0.273734 + 0.273734i
\(700\) 0 0
\(701\) 920.704 920.704i 1.31341 1.31341i 0.394533 0.918882i \(-0.370906\pi\)
0.918882 0.394533i \(-0.129094\pi\)
\(702\) 0 0
\(703\) 222.982i 0.317186i
\(704\) 0 0
\(705\) −112.571 −0.159675
\(706\) 0 0
\(707\) 1010.18 + 1010.18i 1.42882 + 1.42882i
\(708\) 0 0
\(709\) −405.348 405.348i −0.571718 0.571718i 0.360890 0.932608i \(-0.382473\pi\)
−0.932608 + 0.360890i \(0.882473\pi\)
\(710\) 0 0
\(711\) −13.3809 −0.0188199
\(712\) 0 0
\(713\) 1373.72i 1.92667i
\(714\) 0 0
\(715\) 31.4199 31.4199i 0.0439439 0.0439439i
\(716\) 0 0
\(717\) 16.1319 16.1319i 0.0224991 0.0224991i
\(718\) 0 0
\(719\) 880.704i 1.22490i 0.790509 + 0.612450i \(0.209816\pi\)
−0.790509 + 0.612450i \(0.790184\pi\)
\(720\) 0 0
\(721\) 581.930 0.807115
\(722\) 0 0
\(723\) 232.112 + 232.112i 0.321041 + 0.321041i
\(724\) 0 0
\(725\) −565.983 565.983i −0.780667 0.780667i
\(726\) 0 0
\(727\) 1000.46 1.37615 0.688077 0.725637i \(-0.258455\pi\)
0.688077 + 0.725637i \(0.258455\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −1092.64 + 1092.64i −1.49472 + 1.49472i
\(732\) 0 0
\(733\) −540.306 + 540.306i −0.737116 + 0.737116i −0.972019 0.234903i \(-0.924523\pi\)
0.234903 + 0.972019i \(0.424523\pi\)
\(734\) 0 0
\(735\) 127.053i 0.172861i
\(736\) 0 0
\(737\) 46.2301 0.0627274
\(738\) 0 0
\(739\) −893.726 893.726i −1.20937 1.20937i −0.971230 0.238142i \(-0.923462\pi\)
−0.238142 0.971230i \(-0.576538\pi\)
\(740\) 0 0
\(741\) −284.763 284.763i −0.384296 0.384296i
\(742\) 0 0
\(743\) 1295.75 1.74394 0.871969 0.489561i \(-0.162843\pi\)
0.871969 + 0.489561i \(0.162843\pi\)
\(744\) 0 0
\(745\) 395.527i 0.530909i
\(746\) 0 0
\(747\) 30.5253 30.5253i 0.0408639 0.0408639i
\(748\) 0 0
\(749\) −1130.13 + 1130.13i −1.50885 + 1.50885i
\(750\) 0 0
\(751\) 229.818i 0.306016i −0.988225 0.153008i \(-0.951104\pi\)
0.988225 0.153008i \(-0.0488961\pi\)
\(752\) 0 0
\(753\) −67.2223 −0.0892726
\(754\) 0 0
\(755\) −64.9987 64.9987i −0.0860910 0.0860910i
\(756\) 0 0
\(757\) 373.678 + 373.678i 0.493630 + 0.493630i 0.909448 0.415818i \(-0.136505\pi\)
−0.415818 + 0.909448i \(0.636505\pi\)
\(758\) 0 0
\(759\) 184.215 0.242707
\(760\) 0 0
\(761\) 384.012i 0.504615i 0.967647 + 0.252307i \(0.0811894\pi\)
−0.967647 + 0.252307i \(0.918811\pi\)
\(762\) 0 0
\(763\) 813.296 813.296i 1.06592 1.06592i
\(764\) 0 0
\(765\) −67.6589 + 67.6589i −0.0884429 + 0.0884429i
\(766\) 0 0
\(767\) 85.8874i 0.111978i
\(768\) 0 0
\(769\) 865.026 1.12487 0.562436 0.826841i \(-0.309864\pi\)
0.562436 + 0.826841i \(0.309864\pi\)
\(770\) 0 0
\(771\) −165.800 165.800i −0.215045 0.215045i
\(772\) 0 0
\(773\) 1.78859 + 1.78859i 0.00231383 + 0.00231383i 0.708263 0.705949i \(-0.249479\pi\)
−0.705949 + 0.708263i \(0.749479\pi\)
\(774\) 0 0
\(775\) −950.368 −1.22628
\(776\) 0 0
\(777\) 162.055i 0.208565i
\(778\) 0 0
\(779\) 796.409 796.409i 1.02235 1.02235i
\(780\) 0 0
\(781\) −27.0753 + 27.0753i −0.0346675 + 0.0346675i
\(782\) 0 0
\(783\) 181.075i 0.231258i
\(784\) 0 0
\(785\) 109.681 0.139721
\(786\) 0 0
\(787\) −143.702 143.702i −0.182595 0.182595i 0.609891 0.792485i \(-0.291213\pi\)
−0.792485 + 0.609891i \(0.791213\pi\)
\(788\) 0 0
\(789\) −38.7170 38.7170i −0.0490710 0.0490710i
\(790\) 0 0
\(791\) −1722.49 −2.17761
\(792\) 0 0
\(793\) 494.855i 0.624029i
\(794\) 0 0
\(795\)