Properties

Label 1680.2.cz.d.97.1
Level 1680
Weight 2
Character 1680.97
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 97.1
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 \(\chi\) \(=\) 1680.97
Dual form 1680.2.cz.d.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.28999 - 1.82645i) q^{5} +(1.97552 + 1.75993i) q^{7} +1.00000i q^{9} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(-0.379340 + 2.20366i) q^{15} +(-4.74624 + 4.74624i) q^{17} -6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} +(0.707107 - 0.707107i) q^{27} -0.304889i q^{29} +7.25379i q^{31} +(-1.88930 - 1.88930i) q^{33} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} -1.73544i q^{39} -7.05736i q^{41} +(-0.304889 + 0.304889i) q^{43} +(1.82645 - 1.28999i) q^{45} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 + 4.99031i) q^{53} +(-3.44668 - 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} +7.98837 q^{59} +5.53409i q^{61} +(-1.75993 + 1.97552i) q^{63} +(0.658323 - 3.82432i) q^{65} +(3.43055 + 3.43055i) q^{67} -0.248455 q^{69} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +(4.51422 - 2.14984i) q^{75} +(5.27832 + 4.70230i) q^{77} +11.2973i q^{79} -1.00000 q^{81} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(-0.215589 + 0.215589i) q^{87} +6.91251 q^{89} +(0.264559 + 4.58392i) q^{91} +(5.12921 - 5.12921i) q^{93} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

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

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

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
\(7\) 1.97552 + 1.75993i 0.746675 + 0.665189i
\(8\) 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 \(-0.172635\pi\)
−0.516150 + 0.856498i \(0.672635\pi\)
\(14\) 0 0
\(15\) −0.379340 + 2.20366i −0.0979452 + 0.568982i
\(16\) 0 0
\(17\) −4.74624 + 4.74624i −1.15113 + 1.15113i −0.164807 + 0.986326i \(0.552700\pi\)
−0.986326 + 0.164807i \(0.947300\pi\)
\(18\) 0 0
\(19\) −6.01729 −1.38046 −0.690231 0.723589i \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(20\) 0 0
\(21\) −0.152445 2.64136i −0.0332662 0.576391i
\(22\) 0 0
\(23\) 0.175684 0.175684i 0.0366327 0.0366327i −0.688553 0.725186i \(-0.741754\pi\)
0.725186 + 0.688553i \(0.241754\pi\)
\(24\) 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 \(-0.990988\pi\)
0.999599 0.0283083i \(-0.00901200\pi\)
\(30\) 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
\(35\) 0.666037 5.87847i 0.112581 0.993643i
\(36\) 0 0
\(37\) −0.735441 0.735441i −0.120906 0.120906i 0.644065 0.764971i \(-0.277247\pi\)
−0.764971 + 0.644065i \(0.777247\pi\)
\(38\) 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 −0.729972 0.683477i \(-0.760467\pi\)
0.683477 + 0.729972i \(0.260467\pi\)
\(44\) 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 \(-0.768293\pi\)
0.665326 + 0.746553i \(0.268293\pi\)
\(48\) 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 −0.961228 0.275756i \(-0.911072\pi\)
0.275756 + 0.961228i \(0.411072\pi\)
\(54\) 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 \(-0.325932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(60\) 0 0
\(61\) 5.53409i 0.708567i 0.935138 + 0.354284i \(0.115275\pi\)
−0.935138 + 0.354284i \(0.884725\pi\)
\(62\) 0 0
\(63\) −1.75993 + 1.97552i −0.221730 + 0.248892i
\(64\) 0 0
\(65\) 0.658323 3.82432i 0.0816549 0.474348i
\(66\) 0 0
\(67\) 3.43055 + 3.43055i 0.419109 + 0.419109i 0.884896 0.465788i \(-0.154229\pi\)
−0.465788 + 0.884896i \(0.654229\pi\)
\(68\) 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 0.981527 + 0.191323i \(0.0612778\pi\)
0.191323 + 0.981527i \(0.438722\pi\)
\(74\) 0 0
\(75\) 4.51422 2.14984i 0.521257 0.248242i
\(76\) 0 0
\(77\) 5.27832 + 4.70230i 0.601521 + 0.535876i
\(78\) 0 0
\(79\) 11.2973i 1.27104i 0.772084 + 0.635521i \(0.219215\pi\)
−0.772084 + 0.635521i \(0.780785\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 4.88941 + 4.88941i 0.536682 + 0.536682i 0.922553 0.385871i \(-0.126099\pi\)
−0.385871 + 0.922553i \(0.626099\pi\)
\(84\) 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 \(-0.380603\pi\)
0.366363 + 0.930472i \(0.380603\pi\)
\(90\) 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 \(-0.968907\pi\)
0.0975276 + 0.995233i \(0.468907\pi\)
\(98\) 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 \(-0.0892171\pi\)
−0.276628 + 0.960977i \(0.589217\pi\)
\(104\) 0 0
\(105\) −4.62766 + 3.68575i −0.451614 + 0.359692i
\(106\) 0 0
\(107\) 7.47295 + 7.47295i 0.722437 + 0.722437i 0.969101 0.246664i \(-0.0793344\pi\)
−0.246664 + 0.969101i \(0.579334\pi\)
\(108\) 0 0
\(109\) 5.95352i 0.570244i −0.958491 0.285122i \(-0.907966\pi\)
0.958491 0.285122i \(-0.0920341\pi\)
\(110\) 0 0
\(111\) 1.04007i 0.0987192i
\(112\) 0 0
\(113\) 6.99031 6.99031i 0.657593 0.657593i −0.297217 0.954810i \(-0.596058\pi\)
0.954810 + 0.297217i \(0.0960585\pi\)
\(114\) 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 0.568678 0.822560i \(-0.307455\pi\)
−0.822560 + 0.568678i \(0.807455\pi\)
\(128\) 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
\(133\) −11.8873 10.5900i −1.03076 0.918268i
\(134\) 0 0
\(135\) −2.20366 0.379340i −0.189661 0.0326484i
\(136\) 0 0
\(137\) 7.51943 + 7.51943i 0.642428 + 0.642428i 0.951152 0.308724i \(-0.0999019\pi\)
−0.308724 + 0.951152i \(0.599902\pi\)
\(138\) 0 0
\(139\) −7.78902 −0.660656 −0.330328 0.943866i \(-0.607159\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(140\) 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
\(147\) 4.34743 5.48633i 0.358570 0.452505i
\(148\) 0 0
\(149\) 14.2855i 1.17031i 0.810920 + 0.585157i \(0.198967\pi\)
−0.810920 + 0.585157i \(0.801033\pi\)
\(150\) 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 \(-0.710789\pi\)
0.788633 + 0.614864i \(0.210789\pi\)
\(158\) 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 0.0739001 0.997266i \(-0.476455\pi\)
0.997266 0.0739001i \(-0.0235446\pi\)
\(164\) 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 \(-0.639218\pi\)
0.905870 + 0.423555i \(0.139218\pi\)
\(168\) 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 \(-0.131437\pi\)
−0.401288 + 0.915952i \(0.631437\pi\)
\(174\) 0 0
\(175\) −11.5959 + 6.36666i −0.876570 + 0.481274i
\(176\) 0 0
\(177\) −5.64863 5.64863i −0.424577 0.424577i
\(178\) 0 0
\(179\) 1.30103i 0.0972437i −0.998817 0.0486218i \(-0.984517\pi\)
0.998817 0.0486218i \(-0.0154829\pi\)
\(180\) 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 −0.930289 0.366827i \(-0.880444\pi\)
0.366827 + 0.930289i \(0.380444\pi\)
\(194\) 0 0
\(195\) −3.16970 + 2.23870i −0.226987 + 0.160316i
\(196\) 0 0
\(197\) −8.50767 8.50767i −0.606146 0.606146i 0.335790 0.941937i \(-0.390997\pi\)
−0.941937 + 0.335790i \(0.890997\pi\)
\(198\) 0 0
\(199\) 3.25460 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(200\) 0 0
\(201\) 4.85153i 0.342201i
\(202\) 0 0
\(203\) 0.536583 0.602314i 0.0376607 0.0422741i
\(204\) 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
\(217\) −12.7661 + 14.3300i −0.866622 + 0.972782i
\(218\) 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 \(-0.180355\pi\)
−0.536768 + 0.843730i \(0.680355\pi\)
\(224\) 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 \(-0.981408\pi\)
0.0583764 + 0.998295i \(0.481408\pi\)
\(228\) 0 0
\(229\) −28.9307 −1.91180 −0.955898 0.293699i \(-0.905114\pi\)
−0.955898 + 0.293699i \(0.905114\pi\)
\(230\) 0 0
\(231\) −0.407313 7.05736i −0.0267992 0.464340i
\(232\) 0 0
\(233\) −4.78546 + 4.78546i −0.313506 + 0.313506i −0.846266 0.532760i \(-0.821155\pi\)
0.532760 + 0.846266i \(0.321155\pi\)
\(234\) 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 \(-0.824738\pi\)
0.852210 0.523200i \(-0.175262\pi\)
\(240\) 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
\(245\) 11.6614 10.4408i 0.745022 0.667040i
\(246\) 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 \(-0.603203\pi\)
0.947899 + 0.318570i \(0.103203\pi\)
\(258\) 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 −0.130744 + 0.991416i \(0.541737\pi\)
−0.991416 + 0.130744i \(0.958263\pi\)
\(264\) 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 \(-0.656788\pi\)
−0.472888 + 0.881123i \(0.656788\pi\)
\(270\) 0 0
\(271\) 13.3418i 0.810458i −0.914215 0.405229i \(-0.867192\pi\)
0.914215 0.405229i \(-0.132808\pi\)
\(272\) 0 0
\(273\) 3.05425 3.42839i 0.184852 0.207496i
\(274\) 0 0
\(275\) −4.46702 + 12.5904i −0.269372 + 0.759229i
\(276\) 0 0
\(277\) −2.00561 2.00561i −0.120505 0.120505i 0.644282 0.764788i \(-0.277156\pi\)
−0.764788 + 0.644282i \(0.777156\pi\)
\(278\) 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 \(-0.0107615\pi\)
−0.0338017 + 0.999429i \(0.510761\pi\)
\(284\) 0 0
\(285\) 2.28260 13.2600i 0.135210 0.785457i
\(286\) 0 0
\(287\) 12.4204 13.9419i 0.733155 0.822966i
\(288\) 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 \(-0.281843\pi\)
−0.774192 + 0.632951i \(0.781843\pi\)
\(294\) 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 \(-0.844019\pi\)
0.470652 + 0.882319i \(0.344019\pi\)
\(308\) 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 0.956329 + 0.292293i \(0.0944182\pi\)
0.292293 + 0.956329i \(0.405582\pi\)
\(314\) 0 0
\(315\) 5.87847 + 0.666037i 0.331214 + 0.0375269i
\(316\) 0 0
\(317\) −12.2563 12.2563i −0.688385 0.688385i 0.273490 0.961875i \(-0.411822\pi\)
−0.961875 + 0.273490i \(0.911822\pi\)
\(318\) 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 0.397180 0.917741i \(-0.369989\pi\)
−0.917741 + 0.397180i \(0.869989\pi\)
\(338\) 0 0
\(339\) −9.88579 −0.536922
\(340\) 0 0
\(341\) 19.3812i 1.04955i
\(342\) 0 0
\(343\) −10.6468 + 15.1541i −0.574871 + 0.818244i
\(344\) 0 0
\(345\) 0.320503 + 0.453791i 0.0172553 + 0.0244313i
\(346\) 0 0
\(347\) −6.54975 6.54975i −0.351609 0.351609i 0.509099 0.860708i \(-0.329979\pi\)
−0.860708 + 0.509099i \(0.829979\pi\)
\(348\) 0 0
\(349\) −2.77139 −0.148349 −0.0741746 0.997245i \(-0.523632\pi\)
−0.0741746 + 0.997245i \(0.523632\pi\)
\(350\) 0 0
\(351\) 1.73544 0.0926310
\(352\) 0 0
\(353\) −0.970568 0.970568i −0.0516581 0.0516581i 0.680806 0.732464i \(-0.261630\pi\)
−0.732464 + 0.680806i \(0.761630\pi\)
\(354\) 0 0
\(355\) 19.7481 + 27.9607i 1.04812 + 1.48400i
\(356\) 0 0
\(357\) 13.2601 + 11.8130i 0.701797 + 0.625209i
\(358\) 0 0
\(359\) 9.32813i 0.492320i 0.969229 + 0.246160i \(0.0791688\pi\)
−0.969229 + 0.246160i \(0.920831\pi\)
\(360\) 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 \(-0.909351\pi\)
0.280948 + 0.959723i \(0.409351\pi\)
\(368\) 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 0.0732339 0.997315i \(-0.476668\pi\)
0.997315 0.0732339i \(-0.0233320\pi\)
\(374\) 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 \(-0.808787\pi\)
0.824933 0.565230i \(-0.191213\pi\)
\(380\) 0 0
\(381\) 4.04621i 0.207294i
\(382\) 0 0
\(383\) 0.390382 + 0.390382i 0.0199476 + 0.0199476i 0.717010 0.697063i \(-0.245510\pi\)
−0.697063 + 0.717010i \(0.745510\pi\)
\(384\) 0 0
\(385\) 1.77957 15.7065i 0.0906950 0.800478i
\(386\) 0 0
\(387\) −0.304889 0.304889i −0.0154984 0.0154984i
\(388\) 0 0
\(389\) 25.9300i 1.31470i 0.753584 + 0.657352i \(0.228323\pi\)
−0.753584 + 0.657352i \(0.771677\pi\)
\(390\) 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 \(-0.958467\pi\)
0.130109 + 0.991500i \(0.458467\pi\)
\(398\) 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 \(-0.520813\pi\)
−0.0653386 + 0.997863i \(0.520813\pi\)
\(410\) 0 0
\(411\) 10.6341i 0.524540i
\(412\) 0 0
\(413\) 15.7812 + 14.0589i 0.776540 + 0.691795i
\(414\) 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 \(-0.578789\pi\)
−0.245003 + 0.969522i \(0.578789\pi\)
\(420\) 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
\(427\) −9.73958 + 10.9327i −0.471332 + 0.529069i
\(428\) 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 \(-0.0986349\pi\)
−0.304935 + 0.952373i \(0.598635\pi\)
\(434\) 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 \(-0.709955\pi\)
−0.612795 + 0.790242i \(0.709955\pi\)
\(440\) 0 0
\(441\) −6.95352 + 0.805321i −0.331120 + 0.0383486i
\(442\) 0 0
\(443\) 15.6351 15.6351i 0.742845 0.742845i −0.230279 0.973125i \(-0.573964\pi\)
0.973125 + 0.230279i \(0.0739640\pi\)
\(444\) 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 \(-0.947033\pi\)
0.986187 0.165635i \(-0.0529673\pi\)
\(450\) 0 0
\(451\) 18.8564i 0.887912i
\(452\) 0 0
\(453\) 6.91544 + 6.91544i 0.324916 + 0.324916i
\(454\) 0 0
\(455\) 8.03104 6.39640i 0.376501 0.299868i
\(456\) 0 0
\(457\) 11.2119 + 11.2119i 0.524472 + 0.524472i 0.918919 0.394447i \(-0.129064\pi\)
−0.394447 + 0.918919i \(0.629064\pi\)
\(458\) 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 −0.863057 0.505106i \(-0.831453\pi\)
0.505106 + 0.863057i \(0.331453\pi\)
\(464\) 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 \(-0.768859\pi\)
0.663997 + 0.747735i \(0.268859\pi\)
\(468\) 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 \(-0.529819\pi\)
−0.0935425 + 0.995615i \(0.529819\pi\)
\(480\) 0 0
\(481\) 1.80498i 0.0823001i
\(482\) 0 0
\(483\) −0.490826 0.437262i −0.0223334 0.0198961i
\(484\) 0 0
\(485\) 27.5536 + 4.74311i 1.25114 + 0.215374i
\(486\) 0 0
\(487\) 10.3049 + 10.3049i 0.466959 + 0.466959i 0.900928 0.433969i \(-0.142887\pi\)
−0.433969 + 0.900928i \(0.642887\pi\)
\(488\) 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
\(497\) −30.2427 26.9423i −1.35657 1.20853i
\(498\) 0 0
\(499\) 23.7564i 1.06348i −0.846907 0.531741i \(-0.821538\pi\)
0.846907 0.531741i \(-0.178462\pi\)
\(500\) 0 0
\(501\) −8.81463 −0.393808
\(502\) 0 0
\(503\) 17.9504 + 17.9504i 0.800367 + 0.800367i 0.983153 0.182786i \(-0.0585115\pi\)
−0.182786 + 0.983153i \(0.558511\pi\)
\(504\) 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 \(-0.377818\pi\)
0.374489 + 0.927231i \(0.377818\pi\)
\(510\) 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 \(-0.237877\pi\)
−0.679669 + 0.733519i \(0.737877\pi\)
\(524\) 0 0
\(525\) 12.7015 + 3.69766i 0.554338 + 0.161379i
\(526\) 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 0.620340 0.784333i \(-0.286995\pi\)
−0.784333 + 0.620340i \(0.786995\pi\)
\(548\) 0 0
\(549\) −5.53409 −0.236189
\(550\) 0 0
\(551\) 1.83461i 0.0781569i
\(552\) 0 0
\(553\) −19.8823 + 22.3179i −0.845483 + 0.949054i
\(554\) 0 0
\(555\) 1.89964 1.34168i 0.0806353 0.0569510i
\(556\) 0 0
\(557\) −16.3147 16.3147i −0.691275 0.691275i 0.271238 0.962512i \(-0.412567\pi\)
−0.962512 + 0.271238i \(0.912567\pi\)
\(558\) 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 −0.999999 0.00103054i \(-0.999672\pi\)
−0.00103054 0.999999i \(-0.500328\pi\)
\(564\) 0 0
\(565\) −21.7849 3.75008i −0.916497 0.157767i
\(566\) 0 0
\(567\) −1.97552 1.75993i −0.0829638 0.0739099i
\(568\) 0 0
\(569\) 0.277792i 0.0116457i −0.999983 0.00582283i \(-0.998147\pi\)
0.999983 0.00582283i \(-0.00185348\pi\)
\(570\) 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 0.268625 0.963245i \(-0.413431\pi\)
0.963245 0.268625i \(-0.0865693\pi\)
\(578\) 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 −0.105375 + 0.994433i \(0.533604\pi\)
−0.994433 + 0.105375i \(0.966396\pi\)
\(588\) 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 \(-0.104608\pi\)
−0.322751 + 0.946484i \(0.604608\pi\)
\(594\) 0 0
\(595\) 24.7395 + 31.0618i 1.01422 + 1.27341i
\(596\) 0 0
\(597\) −2.30135 2.30135i −0.0941878 0.0941878i
\(598\) 0 0
\(599\) 22.2776i 0.910238i 0.890431 + 0.455119i \(0.150403\pi\)
−0.890431 + 0.455119i \(0.849597\pi\)
\(600\) 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 \(-0.744737\pi\)
0.718700 + 0.695320i \(0.244737\pi\)
\(608\) 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 −0.956613 0.291361i \(-0.905892\pi\)
0.291361 + 0.956613i \(0.405892\pi\)
\(614\) 0 0
\(615\) 15.5520 + 2.67714i 0.627117 + 0.107953i
\(616\) 0 0
\(617\) −3.70013 3.70013i −0.148962 0.148962i 0.628692 0.777654i \(-0.283590\pi\)
−0.777654 + 0.628692i \(0.783590\pi\)
\(618\) 0 0
\(619\) 39.8840 1.60307 0.801536 0.597946i \(-0.204016\pi\)
0.801536 + 0.597946i \(0.204016\pi\)
\(620\) 0 0
\(621\) 0.248455i 0.00997015i
\(622\) 0 0
\(623\) 13.6558 + 12.1655i 0.547107 + 0.487401i
\(624\) 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
\(637\) −7.54472 + 9.52120i −0.298933 + 0.377244i
\(638\) 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 −0.948063 0.318082i \(-0.896961\pi\)
−0.318082 0.948063i \(-0.603039\pi\)
\(644\) 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 \(-0.867012\pi\)
0.405745 + 0.913986i \(0.367012\pi\)
\(648\) 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 −0.866684 0.498858i \(-0.833753\pi\)
0.498858 + 0.866684i \(0.333753\pi\)
\(654\) 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 \(0.0569577\pi\)
−0.984033 + 0.177985i \(0.943042\pi\)
\(660\) 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
\(665\) −4.00774 + 35.3725i −0.155413 + 1.37169i
\(666\) 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 0.0368867 0.999319i \(-0.488256\pi\)
0.999319 0.0368867i \(-0.0117441\pi\)
\(674\) 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 \(-0.760356\pi\)
0.683731 + 0.729734i \(0.260356\pi\)
\(678\) 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 −0.751809 0.659381i \(-0.770818\pi\)
0.659381 + 0.751809i \(0.270818\pi\)
\(684\) 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
\(693\) −4.70230 + 5.27832i −0.178625 + 0.200507i
\(694\) 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
\(707\) 12.7236 14.2822i 0.478520 0.537138i
\(708\) 0 0
\(709\) 24.6722i 0.926585i 0.886205 + 0.463293i \(0.153332\pi\)
−0.886205 + 0.463293i \(0.846668\pi\)
\(710\) 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 \(-0.311662\pi\)
0.557758 + 0.830003i \(0.311662\pi\)
\(720\) 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 0.113491 0.993539i \(-0.463797\pi\)
0.993539 0.113491i \(-0.0362034\pi\)
\(728\) 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 \(-0.282204\pi\)
−0.774908 + 0.632074i \(0.782204\pi\)
\(734\) 0 0
\(735\) −15.6287 0.863100i −0.576472 0.0318359i
\(736\) 0 0
\(737\) 9.16599 + 9.16599i 0.337634 + 0.337634i
\(738\) 0 0
\(739\) 11.9735i 0.440454i 0.975449 + 0.220227i \(0.0706797\pi\)
−0.975449 + 0.220227i \(0.929320\pi\)
\(740\) 0 0
\(741\) 10.4427i 0.383621i
\(742\) 0 0
\(743\) 12.0406 12.0406i 0.441728 0.441728i −0.450864 0.892593i \(-0.648884\pi\)
0.892593 + 0.450864i \(0.148884\pi\)
\(744\) 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 0.997768 + 0.0667825i \(0.0212733\pi\)
0.0667825 + 0.997768i \(0.478727\pi\)
\(758\) 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
\(763\) 10.4778 11.7613i 0.379320 0.425787i
\(764\) 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 \(-0.392169\pi\)
0.332320 + 0.943167i \(0.392169\pi\)
\(770\) 0 0
\(771\) −14.2679 −0.513845
\(772\) 0 0
\(773\) 17.7963 + 17.7963i 0.640088 + 0.640088i 0.950577 0.310489i \(-0.100493\pi\)
−0.310489 + 0.950577i \(0.600493\pi\)
\(774\) 0 0
\(775\) −34.1813 12.1274i −1.22783 0.435629i
\(776\) 0 0
\(777\) −1.83045 + 2.05468i −0.0656670 + 0.0737111i
\(778\) 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 \(-0.617278\pi\)
0.932890 + 0.360160i \(0.117278\pi\)
\(788\) 0 0
\(789\) 25.7364 0.916240
\(790\) 0 0
\(791\) 26.1119 1.50704i 0.928432 0.0535840i