Properties

Label 1680.2.cz.d.433.8
Level 1680
Weight 2
Character 1680.433
Analytic conductor 13.415
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.cz (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 433.8
Root \(-0.944649 - 1.05244i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 1680.433
Dual form 1680.2.cz.d.97.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{3} +(1.28999 - 1.82645i) q^{5} +(1.75993 - 1.97552i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{3} +(1.28999 - 1.82645i) q^{5} +(1.75993 - 1.97552i) q^{7} -1.00000i q^{9} +2.67187 q^{11} +(-1.22714 + 1.22714i) q^{13} +(-0.379340 - 2.20366i) q^{15} +(4.74624 + 4.74624i) q^{17} +6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(0.175684 + 0.175684i) q^{23} +(-1.67187 - 4.71220i) q^{25} +(-0.707107 - 0.707107i) q^{27} +0.304889i q^{29} +7.25379i q^{31} +(1.88930 - 1.88930i) q^{33} +(-1.33791 - 5.76281i) q^{35} +(-0.735441 + 0.735441i) q^{37} +1.73544i q^{39} -7.05736i q^{41} +(-0.304889 - 0.304889i) q^{43} +(-1.82645 - 1.28999i) q^{45} +(0.556866 + 0.556866i) q^{47} +(-0.805321 - 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 - 4.99031i) q^{53} +(3.44668 - 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} -7.98837 q^{59} +5.53409i q^{61} +(-1.97552 - 1.75993i) q^{63} +(0.658323 + 3.82432i) q^{65} +(3.43055 - 3.43055i) q^{67} +0.248455 q^{69} -15.3087 q^{71} +(-10.0208 + 10.0208i) q^{73} +(-4.51422 - 2.14984i) q^{75} +(4.70230 - 5.27832i) q^{77} -11.2973i q^{79} -1.00000 q^{81} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(0.215589 + 0.215589i) q^{87} -6.91251 q^{89} +(0.264559 + 4.58392i) q^{91} +(5.12921 + 5.12921i) q^{93} +(7.76222 - 10.9903i) q^{95} +(8.84137 + 8.84137i) q^{97} -2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(1\)

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
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 0 0
\(5\) 1.28999 1.82645i 0.576899 0.816815i
\(6\) 0 0
\(7\) 1.75993 1.97552i 0.665189 0.746675i
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.67187 0.805600 0.402800 0.915288i \(-0.368037\pi\)
0.402800 + 0.915288i \(0.368037\pi\)
\(12\) 0 0
\(13\) −1.22714 + 1.22714i −0.340348 + 0.340348i −0.856498 0.516150i \(-0.827365\pi\)
0.516150 + 0.856498i \(0.327365\pi\)
\(14\) 0 0
\(15\) −0.379340 2.20366i −0.0979452 0.568982i
\(16\) 0 0
\(17\) 4.74624 + 4.74624i 1.15113 + 1.15113i 0.986326 + 0.164807i \(0.0527002\pi\)
0.164807 + 0.986326i \(0.447300\pi\)
\(18\) 0 0
\(19\) 6.01729 1.38046 0.690231 0.723589i \(-0.257509\pi\)
0.690231 + 0.723589i \(0.257509\pi\)
\(20\) 0 0
\(21\) −0.152445 2.64136i −0.0332662 0.576391i
\(22\) 0 0
\(23\) 0.175684 + 0.175684i 0.0366327 + 0.0366327i 0.725186 0.688553i \(-0.241754\pi\)
−0.688553 + 0.725186i \(0.741754\pi\)
\(24\) 0 0
\(25\) −1.67187 4.71220i −0.334374 0.942440i
\(26\) 0 0
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0 0
\(29\) 0.304889i 0.0566165i 0.999599 + 0.0283083i \(0.00901200\pi\)
−0.999599 + 0.0283083i \(0.990988\pi\)
\(30\) 0 0
\(31\) 7.25379i 1.30282i 0.758726 + 0.651410i \(0.225822\pi\)
−0.758726 + 0.651410i \(0.774178\pi\)
\(32\) 0 0
\(33\) 1.88930 1.88930i 0.328885 0.328885i
\(34\) 0 0
\(35\) −1.33791 5.76281i −0.226148 0.974093i
\(36\) 0 0
\(37\) −0.735441 + 0.735441i −0.120906 + 0.120906i −0.764971 0.644065i \(-0.777247\pi\)
0.644065 + 0.764971i \(0.277247\pi\)
\(38\) 0 0
\(39\) 1.73544i 0.277893i
\(40\) 0 0
\(41\) 7.05736i 1.10217i −0.834447 0.551087i \(-0.814213\pi\)
0.834447 0.551087i \(-0.185787\pi\)
\(42\) 0 0
\(43\) −0.304889 0.304889i −0.0464952 0.0464952i 0.683477 0.729972i \(-0.260467\pi\)
−0.729972 + 0.683477i \(0.760467\pi\)
\(44\) 0 0
\(45\) −1.82645 1.28999i −0.272272 0.192300i
\(46\) 0 0
\(47\) 0.556866 + 0.556866i 0.0812273 + 0.0812273i 0.746553 0.665326i \(-0.231707\pi\)
−0.665326 + 0.746553i \(0.731707\pi\)
\(48\) 0 0
\(49\) −0.805321 6.95352i −0.115046 0.993360i
\(50\) 0 0
\(51\) 6.71220 0.939896
\(52\) 0 0
\(53\) −4.99031 4.99031i −0.685472 0.685472i 0.275756 0.961228i \(-0.411072\pi\)
−0.961228 + 0.275756i \(0.911072\pi\)
\(54\) 0 0
\(55\) 3.44668 4.88005i 0.464750 0.658026i
\(56\) 0 0
\(57\) 4.25487 4.25487i 0.563571 0.563571i
\(58\) 0 0
\(59\) −7.98837 −1.04000 −0.519999 0.854167i \(-0.674068\pi\)
−0.519999 + 0.854167i \(0.674068\pi\)
\(60\) 0 0
\(61\) 5.53409i 0.708567i 0.935138 + 0.354284i \(0.115275\pi\)
−0.935138 + 0.354284i \(0.884725\pi\)
\(62\) 0 0
\(63\) −1.97552 1.75993i −0.248892 0.221730i
\(64\) 0 0
\(65\) 0.658323 + 3.82432i 0.0816549 + 0.474348i
\(66\) 0 0
\(67\) 3.43055 3.43055i 0.419109 0.419109i −0.465788 0.884896i \(-0.654229\pi\)
0.884896 + 0.465788i \(0.154229\pi\)
\(68\) 0 0
\(69\) 0.248455 0.0299104
\(70\) 0 0
\(71\) −15.3087 −1.81681 −0.908407 0.418087i \(-0.862701\pi\)
−0.908407 + 0.418087i \(0.862701\pi\)
\(72\) 0 0
\(73\) −10.0208 + 10.0208i −1.17285 + 1.17285i −0.191323 + 0.981527i \(0.561278\pi\)
−0.981527 + 0.191323i \(0.938722\pi\)
\(74\) 0 0
\(75\) −4.51422 2.14984i −0.521257 0.248242i
\(76\) 0 0
\(77\) 4.70230 5.27832i 0.535876 0.601521i
\(78\) 0 0
\(79\) 11.2973i 1.27104i −0.772084 0.635521i \(-0.780785\pi\)
0.772084 0.635521i \(-0.219215\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −4.88941 + 4.88941i −0.536682 + 0.536682i −0.922553 0.385871i \(-0.873901\pi\)
0.385871 + 0.922553i \(0.373901\pi\)
\(84\) 0 0
\(85\) 14.7914 2.54621i 1.60435 0.276175i
\(86\) 0 0
\(87\) 0.215589 + 0.215589i 0.0231136 + 0.0231136i
\(88\) 0 0
\(89\) −6.91251 −0.732725 −0.366363 0.930472i \(-0.619397\pi\)
−0.366363 + 0.930472i \(0.619397\pi\)
\(90\) 0 0
\(91\) 0.264559 + 4.58392i 0.0277333 + 0.480525i
\(92\) 0 0
\(93\) 5.12921 + 5.12921i 0.531874 + 0.531874i
\(94\) 0 0
\(95\) 7.76222 10.9903i 0.796387 1.12758i
\(96\) 0 0
\(97\) 8.84137 + 8.84137i 0.897705 + 0.897705i 0.995233 0.0975276i \(-0.0310934\pi\)
−0.0975276 + 0.995233i \(0.531093\pi\)
\(98\) 0 0
\(99\) 2.67187i 0.268533i
\(100\) 0 0
\(101\) 7.22962i 0.719374i −0.933073 0.359687i \(-0.882883\pi\)
0.933073 0.359687i \(-0.117117\pi\)
\(102\) 0 0
\(103\) −6.94538 + 6.94538i −0.684349 + 0.684349i −0.960977 0.276628i \(-0.910783\pi\)
0.276628 + 0.960977i \(0.410783\pi\)
\(104\) 0 0
\(105\) −5.02097 3.12888i −0.489996 0.305347i
\(106\) 0 0
\(107\) 7.47295 7.47295i 0.722437 0.722437i −0.246664 0.969101i \(-0.579334\pi\)
0.969101 + 0.246664i \(0.0793344\pi\)
\(108\) 0 0
\(109\) 5.95352i 0.570244i 0.958491 + 0.285122i \(0.0920341\pi\)
−0.958491 + 0.285122i \(0.907966\pi\)
\(110\) 0 0
\(111\) 1.04007i 0.0987192i
\(112\) 0 0
\(113\) 6.99031 + 6.99031i 0.657593 + 0.657593i 0.954810 0.297217i \(-0.0960585\pi\)
−0.297217 + 0.954810i \(0.596058\pi\)
\(114\) 0 0
\(115\) 0.547509 0.0942489i 0.0510555 0.00878876i
\(116\) 0 0
\(117\) 1.22714 + 1.22714i 0.113449 + 0.113449i
\(118\) 0 0
\(119\) 17.7293 1.02324i 1.62524 0.0938002i
\(120\) 0 0
\(121\) −3.86110 −0.351009
\(122\) 0 0
\(123\) −4.99031 4.99031i −0.449961 0.449961i
\(124\) 0 0
\(125\) −10.7633 3.02508i −0.962700 0.270571i
\(126\) 0 0
\(127\) −2.86110 + 2.86110i −0.253882 + 0.253882i −0.822560 0.568678i \(-0.807455\pi\)
0.568678 + 0.822560i \(0.307455\pi\)
\(128\) 0 0
\(129\) −0.431179 −0.0379632
\(130\) 0 0
\(131\) 9.34764i 0.816707i −0.912824 0.408353i \(-0.866103\pi\)
0.912824 0.408353i \(-0.133897\pi\)
\(132\) 0 0
\(133\) 10.5900 11.8873i 0.918268 1.03076i
\(134\) 0 0
\(135\) −2.20366 + 0.379340i −0.189661 + 0.0326484i
\(136\) 0 0
\(137\) 7.51943 7.51943i 0.642428 0.642428i −0.308724 0.951152i \(-0.599902\pi\)
0.951152 + 0.308724i \(0.0999019\pi\)
\(138\) 0 0
\(139\) 7.78902 0.660656 0.330328 0.943866i \(-0.392841\pi\)
0.330328 + 0.943866i \(0.392841\pi\)
\(140\) 0 0
\(141\) 0.787528 0.0663218
\(142\) 0 0
\(143\) −3.27877 + 3.27877i −0.274184 + 0.274184i
\(144\) 0 0
\(145\) 0.556866 + 0.393303i 0.0462452 + 0.0326620i
\(146\) 0 0
\(147\) −5.48633 4.34743i −0.452505 0.358570i
\(148\) 0 0
\(149\) 14.2855i 1.17031i −0.810920 0.585157i \(-0.801033\pi\)
0.810920 0.585157i \(-0.198967\pi\)
\(150\) 0 0
\(151\) −9.77990 −0.795877 −0.397939 0.917412i \(-0.630274\pi\)
−0.397939 + 0.917412i \(0.630274\pi\)
\(152\) 0 0
\(153\) 4.74624 4.74624i 0.383711 0.383711i
\(154\) 0 0
\(155\) 13.2487 + 9.35729i 1.06416 + 0.751596i
\(156\) 0 0
\(157\) −2.17731 2.17731i −0.173768 0.173768i 0.614864 0.788633i \(-0.289211\pi\)
−0.788633 + 0.614864i \(0.789211\pi\)
\(158\) 0 0
\(159\) −7.05736 −0.559685
\(160\) 0 0
\(161\) 0.656257 0.0378756i 0.0517203 0.00298502i
\(162\) 0 0
\(163\) 13.6757 + 13.6757i 1.07117 + 1.07117i 0.997266 + 0.0739001i \(0.0235446\pi\)
0.0739001 + 0.997266i \(0.476455\pi\)
\(164\) 0 0
\(165\) −1.01355 5.88789i −0.0789046 0.458371i
\(166\) 0 0
\(167\) −6.23288 6.23288i −0.482315 0.482315i 0.423555 0.905870i \(-0.360782\pi\)
−0.905870 + 0.423555i \(0.860782\pi\)
\(168\) 0 0
\(169\) 9.98824i 0.768326i
\(170\) 0 0
\(171\) 6.01729i 0.460154i
\(172\) 0 0
\(173\) −6.76935 + 6.76935i −0.514664 + 0.514664i −0.915952 0.401288i \(-0.868563\pi\)
0.401288 + 0.915952i \(0.368563\pi\)
\(174\) 0 0
\(175\) −12.2514 4.99032i −0.926119 0.377233i
\(176\) 0 0
\(177\) −5.64863 + 5.64863i −0.424577 + 0.424577i
\(178\) 0 0
\(179\) 1.30103i 0.0972437i 0.998817 + 0.0486218i \(0.0154829\pi\)
−0.998817 + 0.0486218i \(0.984517\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 0 0
\(183\) 3.91319 + 3.91319i 0.289271 + 0.289271i
\(184\) 0 0
\(185\) 0.394541 + 2.29196i 0.0290072 + 0.168508i
\(186\) 0 0
\(187\) 12.6814 + 12.6814i 0.927352 + 0.927352i
\(188\) 0 0
\(189\) −2.64136 + 0.152445i −0.192130 + 0.0110887i
\(190\) 0 0
\(191\) −1.93791 −0.140222 −0.0701110 0.997539i \(-0.522335\pi\)
−0.0701110 + 0.997539i \(0.522335\pi\)
\(192\) 0 0
\(193\) −7.82786 7.82786i −0.563462 0.563462i 0.366827 0.930289i \(-0.380444\pi\)
−0.930289 + 0.366827i \(0.880444\pi\)
\(194\) 0 0
\(195\) 3.16970 + 2.23870i 0.226987 + 0.160316i
\(196\) 0 0
\(197\) −8.50767 + 8.50767i −0.606146 + 0.606146i −0.941937 0.335790i \(-0.890997\pi\)
0.335790 + 0.941937i \(0.390997\pi\)
\(198\) 0 0
\(199\) −3.25460 −0.230712 −0.115356 0.993324i \(-0.536801\pi\)
−0.115356 + 0.993324i \(0.536801\pi\)
\(200\) 0 0
\(201\) 4.85153i 0.342201i
\(202\) 0 0
\(203\) 0.602314 + 0.536583i 0.0422741 + 0.0376607i
\(204\) 0 0
\(205\) −12.8900 9.10390i −0.900273 0.635844i
\(206\) 0 0
\(207\) 0.175684 0.175684i 0.0122109 0.0122109i
\(208\) 0 0
\(209\) 16.0774 1.11210
\(210\) 0 0
\(211\) 17.2508 1.18759 0.593797 0.804615i \(-0.297628\pi\)
0.593797 + 0.804615i \(0.297628\pi\)
\(212\) 0 0
\(213\) −10.8249 + 10.8249i −0.741711 + 0.741711i
\(214\) 0 0
\(215\) −0.950169 + 0.163563i −0.0648010 + 0.0111549i
\(216\) 0 0
\(217\) 14.3300 + 12.7661i 0.972782 + 0.866622i
\(218\) 0 0
\(219\) 14.1716i 0.957628i
\(220\) 0 0
\(221\) −11.6486 −0.783572
\(222\) 0 0
\(223\) −4.58392 + 4.58392i −0.306962 + 0.306962i −0.843730 0.536768i \(-0.819645\pi\)
0.536768 + 0.843730i \(0.319645\pi\)
\(224\) 0 0
\(225\) −4.71220 + 1.67187i −0.314147 + 0.111458i
\(226\) 0 0
\(227\) 14.1613 + 14.1613i 0.939918 + 0.939918i 0.998295 0.0583764i \(-0.0185924\pi\)
−0.0583764 + 0.998295i \(0.518592\pi\)
\(228\) 0 0
\(229\) 28.9307 1.91180 0.955898 0.293699i \(-0.0948864\pi\)
0.955898 + 0.293699i \(0.0948864\pi\)
\(230\) 0 0
\(231\) −0.407313 7.05736i −0.0267992 0.464340i
\(232\) 0 0
\(233\) −4.78546 4.78546i −0.313506 0.313506i 0.532760 0.846266i \(-0.321155\pi\)
−0.846266 + 0.532760i \(0.821155\pi\)
\(234\) 0 0
\(235\) 1.73544 0.298741i 0.113208 0.0194877i
\(236\) 0 0
\(237\) −7.98837 7.98837i −0.518901 0.518901i
\(238\) 0 0
\(239\) 16.1769i 1.04640i 0.852210 + 0.523200i \(0.175262\pi\)
−0.852210 + 0.523200i \(0.824738\pi\)
\(240\) 0 0
\(241\) 11.3707i 0.732454i −0.930526 0.366227i \(-0.880649\pi\)
0.930526 0.366227i \(-0.119351\pi\)
\(242\) 0 0
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) −13.7391 7.49906i −0.877762 0.479098i
\(246\) 0 0
\(247\) −7.38407 + 7.38407i −0.469837 + 0.469837i
\(248\) 0 0
\(249\) 6.91467i 0.438199i
\(250\) 0 0
\(251\) 6.95039i 0.438705i −0.975646 0.219352i \(-0.929606\pi\)
0.975646 0.219352i \(-0.0703944\pi\)
\(252\) 0 0
\(253\) 0.469405 + 0.469405i 0.0295112 + 0.0295112i
\(254\) 0 0
\(255\) 8.65865 12.2595i 0.542226 0.767722i
\(256\) 0 0
\(257\) −10.0889 10.0889i −0.629329 0.629329i 0.318570 0.947899i \(-0.396797\pi\)
−0.947899 + 0.318570i \(0.896797\pi\)
\(258\) 0 0
\(259\) 0.158553 + 2.74720i 0.00985202 + 0.170703i
\(260\) 0 0
\(261\) 0.304889 0.0188722
\(262\) 0 0
\(263\) −18.1984 18.1984i −1.12216 1.12216i −0.991416 0.130744i \(-0.958263\pi\)
−0.130744 0.991416i \(-0.541737\pi\)
\(264\) 0 0
\(265\) −15.5520 + 2.67714i −0.955352 + 0.164456i
\(266\) 0 0
\(267\) −4.88789 + 4.88789i −0.299134 + 0.299134i
\(268\) 0 0
\(269\) 15.5119 0.945775 0.472888 0.881123i \(-0.343212\pi\)
0.472888 + 0.881123i \(0.343212\pi\)
\(270\) 0 0
\(271\) 13.3418i 0.810458i −0.914215 0.405229i \(-0.867192\pi\)
0.914215 0.405229i \(-0.132808\pi\)
\(272\) 0 0
\(273\) 3.42839 + 3.05425i 0.207496 + 0.184852i
\(274\) 0 0
\(275\) −4.46702 12.5904i −0.269372 0.759229i
\(276\) 0 0
\(277\) −2.00561 + 2.00561i −0.120505 + 0.120505i −0.764788 0.644282i \(-0.777156\pi\)
0.644282 + 0.764788i \(0.277156\pi\)
\(278\) 0 0
\(279\) 7.25379 0.434273
\(280\) 0 0
\(281\) 13.5557 0.808664 0.404332 0.914612i \(-0.367504\pi\)
0.404332 + 0.914612i \(0.367504\pi\)
\(282\) 0 0
\(283\) −16.2444 + 16.2444i −0.965627 + 0.965627i −0.999429 0.0338017i \(-0.989239\pi\)
0.0338017 + 0.999429i \(0.489239\pi\)
\(284\) 0 0
\(285\) −2.28260 13.2600i −0.135210 0.785457i
\(286\) 0 0
\(287\) −13.9419 12.4204i −0.822966 0.733155i
\(288\) 0 0
\(289\) 28.0537i 1.65021i
\(290\) 0 0
\(291\) 12.5036 0.732973
\(292\) 0 0
\(293\) 2.41765 2.41765i 0.141240 0.141240i −0.632951 0.774192i \(-0.718157\pi\)
0.774192 + 0.632951i \(0.218157\pi\)
\(294\) 0 0
\(295\) −10.3049 + 14.5904i −0.599974 + 0.849486i
\(296\) 0 0
\(297\) −1.88930 1.88930i −0.109628 0.109628i
\(298\) 0 0
\(299\) −0.431179 −0.0249357
\(300\) 0 0
\(301\) −1.13890 + 0.0657309i −0.0656449 + 0.00378867i
\(302\) 0 0
\(303\) −5.11211 5.11211i −0.293683 0.293683i
\(304\) 0 0
\(305\) 10.1078 + 7.13890i 0.578769 + 0.408772i
\(306\) 0 0
\(307\) 7.21300 + 7.21300i 0.411667 + 0.411667i 0.882319 0.470652i \(-0.155981\pi\)
−0.470652 + 0.882319i \(0.655981\pi\)
\(308\) 0 0
\(309\) 9.82225i 0.558768i
\(310\) 0 0
\(311\) 10.2542i 0.581460i −0.956805 0.290730i \(-0.906102\pi\)
0.956805 0.290730i \(-0.0938981\pi\)
\(312\) 0 0
\(313\) −22.0904 + 22.0904i −1.24862 + 1.24862i −0.292293 + 0.956329i \(0.594418\pi\)
−0.956329 + 0.292293i \(0.905582\pi\)
\(314\) 0 0
\(315\) −5.76281 + 1.33791i −0.324698 + 0.0753826i
\(316\) 0 0
\(317\) −12.2563 + 12.2563i −0.688385 + 0.688385i −0.961875 0.273490i \(-0.911822\pi\)
0.273490 + 0.961875i \(0.411822\pi\)
\(318\) 0 0
\(319\) 0.814625i 0.0456102i
\(320\) 0 0
\(321\) 10.5683i 0.589867i
\(322\) 0 0
\(323\) 28.5595 + 28.5595i 1.58909 + 1.58909i
\(324\) 0 0
\(325\) 7.83417 + 3.73092i 0.434561 + 0.206954i
\(326\) 0 0
\(327\) 4.20978 + 4.20978i 0.232801 + 0.232801i
\(328\) 0 0
\(329\) 2.08014 0.120054i 0.114682 0.00661882i
\(330\) 0 0
\(331\) −1.26308 −0.0694252 −0.0347126 0.999397i \(-0.511052\pi\)
−0.0347126 + 0.999397i \(0.511052\pi\)
\(332\) 0 0
\(333\) 0.735441 + 0.735441i 0.0403019 + 0.0403019i
\(334\) 0 0
\(335\) −1.84038 10.6911i −0.100551 0.584118i
\(336\) 0 0
\(337\) −9.55621 + 9.55621i −0.520560 + 0.520560i −0.917741 0.397180i \(-0.869989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(338\) 0 0
\(339\) 9.88579 0.536922
\(340\) 0 0
\(341\) 19.3812i 1.04955i
\(342\) 0 0
\(343\) −15.1541 10.6468i −0.818244 0.574871i
\(344\) 0 0
\(345\) 0.320503 0.453791i 0.0172553 0.0244313i
\(346\) 0 0
\(347\) −6.54975 + 6.54975i −0.351609 + 0.351609i −0.860708 0.509099i \(-0.829979\pi\)
0.509099 + 0.860708i \(0.329979\pi\)
\(348\) 0 0
\(349\) 2.77139 0.148349 0.0741746 0.997245i \(-0.476368\pi\)
0.0741746 + 0.997245i \(0.476368\pi\)
\(350\) 0 0
\(351\) 1.73544 0.0926310
\(352\) 0 0
\(353\) 0.970568 0.970568i 0.0516581 0.0516581i −0.680806 0.732464i \(-0.738370\pi\)
0.732464 + 0.680806i \(0.238370\pi\)
\(354\) 0 0
\(355\) −19.7481 + 27.9607i −1.04812 + 1.48400i
\(356\) 0 0
\(357\) 11.8130 13.2601i 0.625209 0.701797i
\(358\) 0 0
\(359\) 9.32813i 0.492320i −0.969229 0.246160i \(-0.920831\pi\)
0.969229 0.246160i \(-0.0791688\pi\)
\(360\) 0 0
\(361\) 17.2078 0.905674
\(362\) 0 0
\(363\) −2.73021 + 2.73021i −0.143299 + 0.143299i
\(364\) 0 0
\(365\) 5.37586 + 31.2293i 0.281385 + 1.63462i
\(366\) 0 0
\(367\) 13.0035 + 13.0035i 0.678776 + 0.678776i 0.959723 0.280948i \(-0.0906487\pi\)
−0.280948 + 0.959723i \(0.590649\pi\)
\(368\) 0 0
\(369\) −7.05736 −0.367392
\(370\) 0 0
\(371\) −18.6410 + 1.07586i −0.967793 + 0.0558557i
\(372\) 0 0
\(373\) 20.6757 + 20.6757i 1.07055 + 1.07055i 0.997315 + 0.0732339i \(0.0233320\pi\)
0.0732339 + 0.997315i \(0.476668\pi\)
\(374\) 0 0
\(375\) −9.74986 + 5.47176i −0.503481 + 0.282560i
\(376\) 0 0
\(377\) −0.374143 0.374143i −0.0192693 0.0192693i
\(378\) 0 0
\(379\) 22.0077i 1.13046i 0.824933 + 0.565230i \(0.191213\pi\)
−0.824933 + 0.565230i \(0.808787\pi\)
\(380\) 0 0
\(381\) 4.04621i 0.207294i
\(382\) 0 0
\(383\) −0.390382 + 0.390382i −0.0199476 + 0.0199476i −0.717010 0.697063i \(-0.754490\pi\)
0.697063 + 0.717010i \(0.254490\pi\)
\(384\) 0 0
\(385\) −3.57472 15.3975i −0.182185 0.784729i
\(386\) 0 0
\(387\) −0.304889 + 0.304889i −0.0154984 + 0.0154984i
\(388\) 0 0
\(389\) 25.9300i 1.31470i −0.753584 0.657352i \(-0.771677\pi\)
0.753584 0.657352i \(-0.228323\pi\)
\(390\) 0 0
\(391\) 1.66768i 0.0843381i
\(392\) 0 0
\(393\) −6.60978 6.60978i −0.333419 0.333419i
\(394\) 0 0
\(395\) −20.6339 14.5733i −1.03821 0.733263i
\(396\) 0 0
\(397\) 17.1631 + 17.1631i 0.861391 + 0.861391i 0.991500 0.130109i \(-0.0415327\pi\)
−0.130109 + 0.991500i \(0.541533\pi\)
\(398\) 0 0
\(399\) −0.917304 15.8938i −0.0459226 0.795686i
\(400\) 0 0
\(401\) −12.9418 −0.646281 −0.323140 0.946351i \(-0.604739\pi\)
−0.323140 + 0.946351i \(0.604739\pi\)
\(402\) 0 0
\(403\) −8.90143 8.90143i −0.443412 0.443412i
\(404\) 0 0
\(405\) −1.28999 + 1.82645i −0.0640999 + 0.0907572i
\(406\) 0 0
\(407\) −1.96500 + 1.96500i −0.0974016 + 0.0974016i
\(408\) 0 0
\(409\) 2.64278 0.130677 0.0653386 0.997863i \(-0.479187\pi\)
0.0653386 + 0.997863i \(0.479187\pi\)
\(410\) 0 0
\(411\) 10.6341i 0.524540i
\(412\) 0 0
\(413\) −14.0589 + 15.7812i −0.691795 + 0.776540i
\(414\) 0 0
\(415\) 2.62301 + 15.2376i 0.128759 + 0.747982i
\(416\) 0 0
\(417\) 5.50767 5.50767i 0.269712 0.269712i
\(418\) 0 0
\(419\) 10.0302 0.490007 0.245003 0.969522i \(-0.421211\pi\)
0.245003 + 0.969522i \(0.421211\pi\)
\(420\) 0 0
\(421\) −26.6440 −1.29855 −0.649274 0.760555i \(-0.724927\pi\)
−0.649274 + 0.760555i \(0.724927\pi\)
\(422\) 0 0
\(423\) 0.556866 0.556866i 0.0270758 0.0270758i
\(424\) 0 0
\(425\) 14.4301 30.3004i 0.699965 1.46978i
\(426\) 0 0
\(427\) 10.9327 + 9.73958i 0.529069 + 0.471332i
\(428\) 0 0
\(429\) 4.63688i 0.223870i
\(430\) 0 0
\(431\) −22.3747 −1.07775 −0.538876 0.842385i \(-0.681151\pi\)
−0.538876 + 0.842385i \(0.681151\pi\)
\(432\) 0 0
\(433\) −13.4723 + 13.4723i −0.647438 + 0.647438i −0.952373 0.304935i \(-0.901365\pi\)
0.304935 + 0.952373i \(0.401365\pi\)
\(434\) 0 0
\(435\) 0.671871 0.115657i 0.0322138 0.00554532i
\(436\) 0 0
\(437\) 1.05714 + 1.05714i 0.0505700 + 0.0505700i
\(438\) 0 0
\(439\) 25.6790 1.22559 0.612795 0.790242i \(-0.290045\pi\)
0.612795 + 0.790242i \(0.290045\pi\)
\(440\) 0 0
\(441\) −6.95352 + 0.805321i −0.331120 + 0.0383486i
\(442\) 0 0
\(443\) 15.6351 + 15.6351i 0.742845 + 0.742845i 0.973125 0.230279i \(-0.0739640\pi\)
−0.230279 + 0.973125i \(0.573964\pi\)
\(444\) 0 0
\(445\) −8.91705 + 12.6254i −0.422709 + 0.598501i
\(446\) 0 0
\(447\) −10.1014 10.1014i −0.477779 0.477779i
\(448\) 0 0
\(449\) 7.01947i 0.331269i 0.986187 + 0.165635i \(0.0529673\pi\)
−0.986187 + 0.165635i \(0.947033\pi\)
\(450\) 0 0
\(451\) 18.8564i 0.887912i
\(452\) 0 0
\(453\) −6.91544 + 6.91544i −0.324916 + 0.324916i
\(454\) 0 0
\(455\) 8.71359 + 5.42999i 0.408500 + 0.254562i
\(456\) 0 0
\(457\) 11.2119 11.2119i 0.524472 0.524472i −0.394447 0.918919i \(-0.629064\pi\)
0.918919 + 0.394447i \(0.129064\pi\)
\(458\) 0 0
\(459\) 6.71220i 0.313299i
\(460\) 0 0
\(461\) 29.9845i 1.39652i −0.715846 0.698259i \(-0.753959\pi\)
0.715846 0.698259i \(-0.246041\pi\)
\(462\) 0 0
\(463\) −7.70220 7.70220i −0.357951 0.357951i 0.505106 0.863057i \(-0.331453\pi\)
−0.863057 + 0.505106i \(0.831453\pi\)
\(464\) 0 0
\(465\) 15.9849 2.75166i 0.741280 0.127605i
\(466\) 0 0
\(467\) 1.80961 + 1.80961i 0.0837386 + 0.0837386i 0.747735 0.663997i \(-0.231141\pi\)
−0.663997 + 0.747735i \(0.731141\pi\)
\(468\) 0 0
\(469\) −0.739590 12.8146i −0.0341511 0.591724i
\(470\) 0 0
\(471\) −3.07918 −0.141881
\(472\) 0 0
\(473\) −0.814625 0.814625i −0.0374565 0.0374565i
\(474\) 0 0
\(475\) −10.0601 28.3547i −0.461591 1.30100i
\(476\) 0 0
\(477\) −4.99031 + 4.99031i −0.228491 + 0.228491i
\(478\) 0 0
\(479\) 4.09455 0.187085 0.0935425 0.995615i \(-0.470181\pi\)
0.0935425 + 0.995615i \(0.470181\pi\)
\(480\) 0 0
\(481\) 1.80498i 0.0823001i
\(482\) 0 0
\(483\) 0.437262 0.490826i 0.0198961 0.0223334i
\(484\) 0 0
\(485\) 27.5536 4.74311i 1.25114 0.215374i
\(486\) 0 0
\(487\) 10.3049 10.3049i 0.466959 0.466959i −0.433969 0.900928i \(-0.642887\pi\)
0.900928 + 0.433969i \(0.142887\pi\)
\(488\) 0 0
\(489\) 19.3404 0.874603
\(490\) 0 0
\(491\) 8.55953 0.386286 0.193143 0.981171i \(-0.438132\pi\)
0.193143 + 0.981171i \(0.438132\pi\)
\(492\) 0 0
\(493\) −1.44708 + 1.44708i −0.0651732 + 0.0651732i
\(494\) 0 0
\(495\) −4.88005 3.44668i −0.219342 0.154917i
\(496\) 0 0
\(497\) −26.9423 + 30.2427i −1.20853 + 1.35657i
\(498\) 0 0
\(499\) 23.7564i 1.06348i 0.846907 + 0.531741i \(0.178462\pi\)
−0.846907 + 0.531741i \(0.821538\pi\)
\(500\) 0 0
\(501\) −8.81463 −0.393808
\(502\) 0 0
\(503\) −17.9504 + 17.9504i −0.800367 + 0.800367i −0.983153 0.182786i \(-0.941489\pi\)
0.182786 + 0.983153i \(0.441489\pi\)
\(504\) 0 0
\(505\) −13.2046 9.32611i −0.587596 0.415007i
\(506\) 0 0
\(507\) 7.06275 + 7.06275i 0.313668 + 0.313668i
\(508\) 0 0
\(509\) −16.8977 −0.748979 −0.374489 0.927231i \(-0.622182\pi\)
−0.374489 + 0.927231i \(0.622182\pi\)
\(510\) 0 0
\(511\) 2.16039 + 37.4322i 0.0955698 + 1.65590i
\(512\) 0 0
\(513\) −4.25487 4.25487i −0.187857 0.187857i
\(514\) 0 0
\(515\) 3.72598 + 21.6449i 0.164186 + 0.953787i
\(516\) 0 0
\(517\) 1.48788 + 1.48788i 0.0654367 + 0.0654367i
\(518\) 0 0
\(519\) 9.57331i 0.420221i
\(520\) 0 0
\(521\) 7.88477i 0.345438i −0.984971 0.172719i \(-0.944745\pi\)
0.984971 0.172719i \(-0.0552552\pi\)
\(522\) 0 0
\(523\) −1.23149 + 1.23149i −0.0538493 + 0.0538493i −0.733519 0.679669i \(-0.762123\pi\)
0.679669 + 0.733519i \(0.262123\pi\)
\(524\) 0 0
\(525\) −12.1917 + 5.13436i −0.532091 + 0.224082i
\(526\) 0 0
\(527\) −34.4283 + 34.4283i −1.49972 + 1.49972i
\(528\) 0 0
\(529\) 22.9383i 0.997316i
\(530\) 0 0
\(531\) 7.98837i 0.346666i
\(532\) 0 0
\(533\) 8.66039 + 8.66039i 0.375123 + 0.375123i
\(534\) 0 0
\(535\) −4.00900 23.2890i −0.173324 1.00687i
\(536\) 0 0
\(537\) 0.919968 + 0.919968i 0.0396996 + 0.0396996i
\(538\) 0 0
\(539\) −2.15171 18.5789i −0.0926809 0.800250i
\(540\) 0 0
\(541\) 34.9495 1.50260 0.751298 0.659963i \(-0.229428\pi\)
0.751298 + 0.659963i \(0.229428\pi\)
\(542\) 0 0
\(543\) 6.00000 + 6.00000i 0.257485 + 0.257485i
\(544\) 0 0
\(545\) 10.8738 + 7.67996i 0.465784 + 0.328973i
\(546\) 0 0
\(547\) −3.83548 + 3.83548i −0.163993 + 0.163993i −0.784333 0.620340i \(-0.786995\pi\)
0.620340 + 0.784333i \(0.286995\pi\)
\(548\) 0 0
\(549\) 5.53409 0.236189
\(550\) 0 0
\(551\) 1.83461i 0.0781569i
\(552\) 0 0
\(553\) −22.3179 19.8823i −0.949054 0.845483i
\(554\) 0 0
\(555\) 1.89964 + 1.34168i 0.0806353 + 0.0569510i
\(556\) 0 0
\(557\) −16.3147 + 16.3147i −0.691275 + 0.691275i −0.962512 0.271238i \(-0.912567\pi\)
0.271238 + 0.962512i \(0.412567\pi\)
\(558\) 0 0
\(559\) 0.748285 0.0316491
\(560\) 0 0
\(561\) 17.9341 0.757180
\(562\) 0 0
\(563\) 23.7521 23.7521i 1.00103 1.00103i 0.00103054 0.999999i \(-0.499672\pi\)
0.999999 0.00103054i \(-0.000328032\pi\)
\(564\) 0 0
\(565\) 21.7849 3.75008i 0.916497 0.157767i
\(566\) 0 0
\(567\) −1.75993 + 1.97552i −0.0739099 + 0.0829638i
\(568\) 0 0
\(569\) 0.277792i 0.0116457i 0.999983 + 0.00582283i \(0.00185348\pi\)
−0.999983 + 0.00582283i \(0.998147\pi\)
\(570\) 0 0
\(571\) 3.11538 0.130375 0.0651874 0.997873i \(-0.479235\pi\)
0.0651874 + 0.997873i \(0.479235\pi\)
\(572\) 0 0
\(573\) −1.37031 + 1.37031i −0.0572454 + 0.0572454i
\(574\) 0 0
\(575\) 0.534138 1.12158i 0.0222751 0.0467731i
\(576\) 0 0
\(577\) −29.5905 29.5905i −1.23187 1.23187i −0.963245 0.268625i \(-0.913431\pi\)
−0.268625 0.963245i \(-0.586569\pi\)
\(578\) 0 0
\(579\) −11.0703 −0.460064
\(580\) 0 0
\(581\) 1.05410 + 18.2641i 0.0437316 + 0.757722i
\(582\) 0 0
\(583\) −13.3335 13.3335i −0.552216 0.552216i
\(584\) 0 0
\(585\) 3.82432 0.658323i 0.158116 0.0272183i
\(586\) 0 0
\(587\) 26.6462 + 26.6462i 1.09981 + 1.09981i 0.994433 + 0.105375i \(0.0336041\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(588\) 0 0
\(589\) 43.6482i 1.79849i
\(590\) 0 0
\(591\) 12.0317i 0.494916i
\(592\) 0 0
\(593\) −15.1889 + 15.1889i −0.623733 + 0.623733i −0.946484 0.322751i \(-0.895392\pi\)
0.322751 + 0.946484i \(0.395392\pi\)
\(594\) 0 0
\(595\) 21.0017 33.7017i 0.860985 1.38164i
\(596\) 0 0
\(597\) −2.30135 + 2.30135i −0.0941878 + 0.0941878i
\(598\) 0 0
\(599\) 22.2776i 0.910238i −0.890431 0.455119i \(-0.849597\pi\)
0.890431 0.455119i \(-0.150403\pi\)
\(600\) 0 0
\(601\) 22.3458i 0.911503i 0.890107 + 0.455752i \(0.150629\pi\)
−0.890107 + 0.455752i \(0.849371\pi\)
\(602\) 0 0
\(603\) −3.43055 3.43055i −0.139703 0.139703i
\(604\) 0 0
\(605\) −4.98077 + 7.05213i −0.202497 + 0.286710i
\(606\) 0 0
\(607\) −0.576027 0.576027i −0.0233802 0.0233802i 0.695320 0.718700i \(-0.255263\pi\)
−0.718700 + 0.695320i \(0.755263\pi\)
\(608\) 0 0
\(609\) 0.805321 0.0464788i 0.0326333 0.00188341i
\(610\) 0 0
\(611\) −1.36671 −0.0552911
\(612\) 0 0
\(613\) −16.4709 16.4709i −0.665253 0.665253i 0.291361 0.956613i \(-0.405892\pi\)
−0.956613 + 0.291361i \(0.905892\pi\)
\(614\) 0 0
\(615\) −15.5520 + 2.67714i −0.627117 + 0.107953i
\(616\) 0 0
\(617\) −3.70013 + 3.70013i −0.148962 + 0.148962i −0.777654 0.628692i \(-0.783590\pi\)
0.628692 + 0.777654i \(0.283590\pi\)
\(618\) 0 0
\(619\) −39.8840 −1.60307 −0.801536 0.597946i \(-0.795984\pi\)
−0.801536 + 0.597946i \(0.795984\pi\)
\(620\) 0 0
\(621\) 0.248455i 0.00997015i
\(622\) 0 0
\(623\) −12.1655 + 13.6558i −0.487401 + 0.547107i
\(624\) 0 0
\(625\) −19.4097 + 15.7564i −0.776388 + 0.630256i
\(626\) 0 0
\(627\) 11.3685 11.3685i 0.454013 0.454013i
\(628\) 0 0
\(629\) −6.98117 −0.278357
\(630\) 0 0
\(631\) 33.9725 1.35242 0.676211 0.736708i \(-0.263621\pi\)
0.676211 + 0.736708i \(0.263621\pi\)
\(632\) 0 0
\(633\) 12.1981 12.1981i 0.484833 0.484833i
\(634\) 0 0
\(635\) 1.53489 + 8.91646i 0.0609103 + 0.353839i
\(636\) 0 0
\(637\) 9.52120 + 7.54472i 0.377244 + 0.298933i
\(638\) 0 0
\(639\) 15.3087i 0.605605i
\(640\) 0 0
\(641\) −18.1113 −0.715352 −0.357676 0.933846i \(-0.616431\pi\)
−0.357676 + 0.933846i \(0.616431\pi\)
\(642\) 0 0
\(643\) 32.1062 32.1062i 1.26614 1.26614i 0.318082 0.948063i \(-0.396961\pi\)
0.948063 0.318082i \(-0.103039\pi\)
\(644\) 0 0
\(645\) −0.556214 + 0.787528i −0.0219009 + 0.0310089i
\(646\) 0 0
\(647\) 12.9277 + 12.9277i 0.508241 + 0.508241i 0.913986 0.405745i \(-0.132988\pi\)
−0.405745 + 0.913986i \(0.632988\pi\)
\(648\) 0 0
\(649\) −21.3439 −0.837821
\(650\) 0 0
\(651\) 19.1598 1.10580i 0.750934 0.0433398i
\(652\) 0 0
\(653\) −9.39937 9.39937i −0.367826 0.367826i 0.498858 0.866684i \(-0.333753\pi\)
−0.866684 + 0.498858i \(0.833753\pi\)
\(654\) 0 0
\(655\) −17.0730 12.0583i −0.667099 0.471158i
\(656\) 0 0
\(657\) 10.0208 + 10.0208i 0.390950 + 0.390950i
\(658\) 0 0
\(659\) 9.13808i 0.355969i −0.984033 0.177985i \(-0.943042\pi\)
0.984033 0.177985i \(-0.0569577\pi\)
\(660\) 0 0
\(661\) 28.4837i 1.10789i −0.832554 0.553943i \(-0.813122\pi\)
0.832554 0.553943i \(-0.186878\pi\)
\(662\) 0 0
\(663\) −8.23683 + 8.23683i −0.319892 + 0.319892i
\(664\) 0 0
\(665\) −8.05059 34.6765i −0.312188 1.34470i
\(666\) 0 0
\(667\) −0.0535642 + 0.0535642i −0.00207401 + 0.00207401i
\(668\) 0 0
\(669\) 6.48264i 0.250633i
\(670\) 0 0
\(671\) 14.7864i 0.570821i
\(672\) 0 0
\(673\) 26.8815 + 26.8815i 1.03621 + 1.03621i 0.999319 + 0.0368867i \(0.0117441\pi\)
0.0368867 + 0.999319i \(0.488256\pi\)
\(674\) 0 0
\(675\) −2.14984 + 4.51422i −0.0827473 + 0.173752i
\(676\) 0 0
\(677\) 1.19694 + 1.19694i 0.0460022 + 0.0460022i 0.729734 0.683731i \(-0.239644\pi\)
−0.683731 + 0.729734i \(0.739644\pi\)
\(678\) 0 0
\(679\) 33.0264 1.90611i 1.26744 0.0731496i
\(680\) 0 0
\(681\) 20.0271 0.767440
\(682\) 0 0
\(683\) −2.41553 2.41553i −0.0924275 0.0924275i 0.659381 0.751809i \(-0.270818\pi\)
−0.751809 + 0.659381i \(0.770818\pi\)
\(684\) 0 0
\(685\) −4.03393 23.4338i −0.154129 0.895361i
\(686\) 0 0
\(687\) 20.4571 20.4571i 0.780487 0.780487i
\(688\) 0 0
\(689\) 12.2476 0.466598
\(690\) 0 0
\(691\) 41.6703i 1.58521i −0.609735 0.792606i \(-0.708724\pi\)
0.609735 0.792606i \(-0.291276\pi\)
\(692\) 0 0
\(693\) −5.27832 4.70230i −0.200507 0.178625i
\(694\) 0 0
\(695\) 10.0477 14.2263i 0.381132 0.539634i
\(696\) 0 0
\(697\) 33.4960 33.4960i 1.26875 1.26875i
\(698\) 0 0
\(699\) −6.76767 −0.255977
\(700\) 0 0
\(701\) 13.7870 0.520727 0.260364 0.965511i \(-0.416158\pi\)
0.260364 + 0.965511i \(0.416158\pi\)
\(702\) 0 0
\(703\) −4.42536 + 4.42536i −0.166906 + 0.166906i
\(704\) 0 0
\(705\) 1.01590 1.43838i 0.0382610 0.0541727i
\(706\) 0 0
\(707\) −14.2822 12.7236i −0.537138 0.478520i
\(708\) 0 0
\(709\) 24.6722i 0.926585i −0.886205 0.463293i \(-0.846668\pi\)
0.886205 0.463293i \(-0.153332\pi\)
\(710\) 0 0
\(711\) −11.2973 −0.423680
\(712\) 0 0
\(713\) −1.27438 + 1.27438i −0.0477257 + 0.0477257i
\(714\) 0 0
\(715\) 1.75895 + 10.2181i 0.0657811 + 0.382135i
\(716\) 0 0
\(717\) 11.4388 + 11.4388i 0.427191 + 0.427191i
\(718\) 0 0
\(719\) −29.9117 −1.11552 −0.557758 0.830003i \(-0.688338\pi\)
−0.557758 + 0.830003i \(0.688338\pi\)
\(720\) 0 0
\(721\) 1.49735 + 25.9441i 0.0557642 + 0.966207i
\(722\) 0 0
\(723\) −8.04033 8.04033i −0.299023 0.299023i
\(724\) 0 0
\(725\) 1.43670 0.509736i 0.0533577 0.0189311i
\(726\) 0 0
\(727\) −29.8488 29.8488i −1.10703 1.10703i −0.993539 0.113491i \(-0.963797\pi\)
−0.113491 0.993539i \(-0.536203\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 2.89416i 0.107044i
\(732\) 0 0
\(733\) 3.86707 3.86707i 0.142834 0.142834i −0.632074 0.774908i \(-0.717796\pi\)
0.774908 + 0.632074i \(0.217796\pi\)
\(734\) 0 0
\(735\) −15.0177 + 4.41240i −0.553935 + 0.162754i
\(736\) 0 0
\(737\) 9.16599 9.16599i 0.337634 0.337634i
\(738\) 0 0
\(739\) 11.9735i 0.440454i −0.975449 0.220227i \(-0.929320\pi\)
0.975449 0.220227i \(-0.0706797\pi\)
\(740\) 0 0
\(741\) 10.4427i 0.383621i
\(742\) 0 0
\(743\) 12.0406 + 12.0406i 0.441728 + 0.441728i 0.892593 0.450864i \(-0.148884\pi\)
−0.450864 + 0.892593i \(0.648884\pi\)
\(744\) 0 0
\(745\) −26.0918 18.4281i −0.955931 0.675154i
\(746\) 0 0
\(747\) 4.88941 + 4.88941i 0.178894 + 0.178894i
\(748\) 0 0
\(749\) −1.61109 27.9148i −0.0588679 1.01998i
\(750\) 0 0
\(751\) 24.1119 0.879855 0.439928 0.898033i \(-0.355004\pi\)
0.439928 + 0.898033i \(0.355004\pi\)
\(752\) 0 0
\(753\) −4.91467 4.91467i −0.179100 0.179100i
\(754\) 0 0
\(755\) −12.6159 + 17.8625i −0.459141 + 0.650085i
\(756\) 0 0
\(757\) 29.2896 29.2896i 1.06455 1.06455i 0.0667825 0.997768i \(-0.478727\pi\)
0.997768 0.0667825i \(-0.0212733\pi\)
\(758\) 0 0
\(759\) 0.663839 0.0240958
\(760\) 0 0
\(761\) 32.3002i 1.17088i −0.810716 0.585440i \(-0.800922\pi\)
0.810716 0.585440i \(-0.199078\pi\)
\(762\) 0 0
\(763\) 11.7613 + 10.4778i 0.425787 + 0.379320i
\(764\) 0 0
\(765\) −2.54621 14.7914i −0.0920584 0.534784i
\(766\) 0 0
\(767\) 9.80287 9.80287i 0.353961 0.353961i
\(768\) 0 0
\(769\) −18.4310 −0.664640 −0.332320 0.943167i \(-0.607831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(770\) 0 0
\(771\) −14.2679 −0.513845
\(772\) 0 0
\(773\) −17.7963 + 17.7963i −0.640088 + 0.640088i −0.950577 0.310489i \(-0.899507\pi\)
0.310489 + 0.950577i \(0.399507\pi\)
\(774\) 0 0
\(775\) 34.1813 12.1274i 1.22783 0.435629i
\(776\) 0 0
\(777\) 2.05468 + 1.83045i 0.0737111 + 0.0656670i
\(778\) 0 0
\(779\) 42.4662i 1.52151i
\(780\) 0 0
\(781\) −40.9030 −1.46362
\(782\) 0 0
\(783\) 0.215589 0.215589i 0.00770453 0.00770453i
\(784\) 0 0
\(785\) −6.78546 + 1.16806i −0.242184 + 0.0416898i
\(786\) 0 0
\(787\) −16.0671 16.0671i −0.572730 0.572730i 0.360160 0.932890i \(-0.382722\pi\)
−0.932890 + 0.360160i \(0.882722\pi\)
\(788\) 0 0
\(789\) −25.7364 −0.916240
\(790\) 0 0
\(791\) 26.1119 1.50704i 0.928432