Properties

Label 1680.2.cz.d.97.7
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 97.7
Root \(-1.36166 + 0.381939i\) 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.433.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +3.85136 q^{11} +(3.66816 + 3.66816i) q^{13} +(2.13393 - 0.668102i) q^{15} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.77107i q^{29} -2.39674i q^{31} +(2.72332 + 2.72332i) q^{33} +(-5.73544 - 1.45077i) q^{35} +(6.18757 + 6.18757i) q^{37} +5.18757i q^{39} -8.68077i q^{41} +(2.77107 - 2.77107i) q^{43} +(1.98133 + 1.03649i) q^{45} +(5.49042 - 5.49042i) q^{47} +(-6.24586 + 3.16057i) q^{49} -2.10728 q^{51} +(6.13823 - 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} -6.97440 q^{59} -14.3107i q^{61} +(2.57351 - 0.614060i) q^{63} +(11.0699 - 3.46582i) q^{65} +(-0.416491 - 0.416491i) q^{67} +0.755439 q^{69} +8.12783 q^{71} +(-9.55210 - 9.55210i) q^{73} +(0.888068 - 4.92050i) q^{75} +(-2.36497 - 9.91150i) q^{77} +9.86329i q^{79} -1.00000 q^{81} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(-1.95945 + 1.95945i) q^{87} +5.05313 q^{89} +(7.18757 - 11.6925i) q^{91} +(1.69475 - 1.69475i) q^{93} +(0.0723134 - 0.138232i) q^{95} +(-6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

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
\(5\) 1.03649 1.98133i 0.463534 0.886079i
\(6\) 0 0
\(7\) −0.614060 2.57351i −0.232093 0.972694i
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 3.85136 1.16123 0.580615 0.814179i \(-0.302812\pi\)
0.580615 + 0.814179i \(0.302812\pi\)
\(12\) 0 0
\(13\) 3.66816 + 3.66816i 1.01737 + 1.01737i 0.999847 + 0.0175187i \(0.00557667\pi\)
0.0175187 + 0.999847i \(0.494423\pi\)
\(14\) 0 0
\(15\) 2.13393 0.668102i 0.550977 0.172503i
\(16\) 0 0
\(17\) −1.49007 + 1.49007i −0.361395 + 0.361395i −0.864326 0.502931i \(-0.832255\pi\)
0.502931 + 0.864326i \(0.332255\pi\)
\(18\) 0 0
\(19\) 0.0697674 0.0160057 0.00800286 0.999968i \(-0.497453\pi\)
0.00800286 + 0.999968i \(0.497453\pi\)
\(20\) 0 0
\(21\) 1.38554 2.25395i 0.302349 0.491852i
\(22\) 0 0
\(23\) 0.534176 0.534176i 0.111383 0.111383i −0.649218 0.760602i \(-0.724904\pi\)
0.760602 + 0.649218i \(0.224904\pi\)
\(24\) 0 0
\(25\) −2.85136 4.10728i −0.570272 0.821456i
\(26\) 0 0
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) 2.77107i 0.514576i 0.966335 + 0.257288i \(0.0828288\pi\)
−0.966335 + 0.257288i \(0.917171\pi\)
\(30\) 0 0
\(31\) 2.39674i 0.430467i −0.976563 0.215233i \(-0.930949\pi\)
0.976563 0.215233i \(-0.0690512\pi\)
\(32\) 0 0
\(33\) 2.72332 + 2.72332i 0.474070 + 0.474070i
\(34\) 0 0
\(35\) −5.73544 1.45077i −0.969466 0.245224i
\(36\) 0 0
\(37\) 6.18757 + 6.18757i 1.01723 + 1.01723i 0.999849 + 0.0173805i \(0.00553267\pi\)
0.0173805 + 0.999849i \(0.494467\pi\)
\(38\) 0 0
\(39\) 5.18757i 0.830675i
\(40\) 0 0
\(41\) 8.68077i 1.35571i −0.735196 0.677854i \(-0.762910\pi\)
0.735196 0.677854i \(-0.237090\pi\)
\(42\) 0 0
\(43\) 2.77107 2.77107i 0.422585 0.422585i −0.463508 0.886093i \(-0.653409\pi\)
0.886093 + 0.463508i \(0.153409\pi\)
\(44\) 0 0
\(45\) 1.98133 + 1.03649i 0.295360 + 0.154511i
\(46\) 0 0
\(47\) 5.49042 5.49042i 0.800860 0.800860i −0.182370 0.983230i \(-0.558377\pi\)
0.983230 + 0.182370i \(0.0583768\pi\)
\(48\) 0 0
\(49\) −6.24586 + 3.16057i −0.892266 + 0.451510i
\(50\) 0 0
\(51\) −2.10728 −0.295078
\(52\) 0 0
\(53\) 6.13823 6.13823i 0.843151 0.843151i −0.146116 0.989267i \(-0.546677\pi\)
0.989267 + 0.146116i \(0.0466774\pi\)
\(54\) 0 0
\(55\) 3.99191 7.63083i 0.538269 1.02894i
\(56\) 0 0
\(57\) 0.0493330 + 0.0493330i 0.00653431 + 0.00653431i
\(58\) 0 0
\(59\) −6.97440 −0.907990 −0.453995 0.891004i \(-0.650002\pi\)
−0.453995 + 0.891004i \(0.650002\pi\)
\(60\) 0 0
\(61\) 14.3107i 1.83230i −0.400835 0.916150i \(-0.631280\pi\)
0.400835 0.916150i \(-0.368720\pi\)
\(62\) 0 0
\(63\) 2.57351 0.614060i 0.324231 0.0773643i
\(64\) 0 0
\(65\) 11.0699 3.46582i 1.37305 0.429883i
\(66\) 0 0
\(67\) −0.416491 0.416491i −0.0508824 0.0508824i 0.681208 0.732090i \(-0.261455\pi\)
−0.732090 + 0.681208i \(0.761455\pi\)
\(68\) 0 0
\(69\) 0.755439 0.0909442
\(70\) 0 0
\(71\) 8.12783 0.964595 0.482298 0.876007i \(-0.339802\pi\)
0.482298 + 0.876007i \(0.339802\pi\)
\(72\) 0 0
\(73\) −9.55210 9.55210i −1.11799 1.11799i −0.992036 0.125953i \(-0.959801\pi\)
−0.125953 0.992036i \(-0.540199\pi\)
\(74\) 0 0
\(75\) 0.888068 4.92050i 0.102545 0.568171i
\(76\) 0 0
\(77\) −2.36497 9.91150i −0.269513 1.12952i
\(78\) 0 0
\(79\) 9.86329i 1.10971i 0.831948 + 0.554854i \(0.187226\pi\)
−0.831948 + 0.554854i \(0.812774\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 1.63570 + 1.63570i 0.179541 + 0.179541i 0.791156 0.611615i \(-0.209480\pi\)
−0.611615 + 0.791156i \(0.709480\pi\)
\(84\) 0 0
\(85\) 1.40788 + 4.49678i 0.152706 + 0.487744i
\(86\) 0 0
\(87\) −1.95945 + 1.95945i −0.210075 + 0.210075i
\(88\) 0 0
\(89\) 5.05313 0.535631 0.267815 0.963470i \(-0.413698\pi\)
0.267815 + 0.963470i \(0.413698\pi\)
\(90\) 0 0
\(91\) 7.18757 11.6925i 0.753462 1.22571i
\(92\) 0 0
\(93\) 1.69475 1.69475i 0.175737 0.175737i
\(94\) 0 0
\(95\) 0.0723134 0.138232i 0.00741920 0.0141823i
\(96\) 0 0
\(97\) −6.85851 + 6.85851i −0.696376 + 0.696376i −0.963627 0.267251i \(-0.913885\pi\)
0.267251 + 0.963627i \(0.413885\pi\)
\(98\) 0 0
\(99\) 3.85136i 0.387076i
\(100\) 0 0
\(101\) 19.1953i 1.91000i 0.296605 + 0.955000i \(0.404145\pi\)
−0.296605 + 0.955000i \(0.595855\pi\)
\(102\) 0 0
\(103\) 2.33825 + 2.33825i 0.230394 + 0.230394i 0.812857 0.582463i \(-0.197911\pi\)
−0.582463 + 0.812857i \(0.697911\pi\)
\(104\) 0 0
\(105\) −3.02972 5.08142i −0.295671 0.495895i
\(106\) 0 0
\(107\) 6.39747 + 6.39747i 0.618467 + 0.618467i 0.945138 0.326671i \(-0.105927\pi\)
−0.326671 + 0.945138i \(0.605927\pi\)
\(108\) 0 0
\(109\) 2.16057i 0.206945i −0.994632 0.103473i \(-0.967005\pi\)
0.994632 0.103473i \(-0.0329954\pi\)
\(110\) 0 0
\(111\) 8.75054i 0.830564i
\(112\) 0 0
\(113\) −4.13823 + 4.13823i −0.389292 + 0.389292i −0.874435 0.485143i \(-0.838768\pi\)
0.485143 + 0.874435i \(0.338768\pi\)
\(114\) 0 0
\(115\) −0.504711 1.61205i −0.0470645 0.150325i
\(116\) 0 0
\(117\) −3.66816 + 3.66816i −0.339122 + 0.339122i
\(118\) 0 0
\(119\) 4.74970 + 2.91971i 0.435404 + 0.267650i
\(120\) 0 0
\(121\) 3.83298 0.348453
\(122\) 0 0
\(123\) 6.13823 6.13823i 0.553466 0.553466i
\(124\) 0 0
\(125\) −11.0933 + 1.39233i −0.992215 + 0.124533i
\(126\) 0 0
\(127\) 4.83298 + 4.83298i 0.428858 + 0.428858i 0.888239 0.459381i \(-0.151929\pi\)
−0.459381 + 0.888239i \(0.651929\pi\)
\(128\) 0 0
\(129\) 3.91889 0.345039
\(130\) 0 0
\(131\) 0.647499i 0.0565722i 0.999600 + 0.0282861i \(0.00900495\pi\)
−0.999600 + 0.0282861i \(0.990995\pi\)
\(132\) 0 0
\(133\) −0.0428413 0.179547i −0.00371481 0.0155687i
\(134\) 0 0
\(135\) 0.668102 + 2.13393i 0.0575011 + 0.183659i
\(136\) 0 0
\(137\) 10.2369 + 10.2369i 0.874597 + 0.874597i 0.992969 0.118372i \(-0.0377676\pi\)
−0.118372 + 0.992969i \(0.537768\pi\)
\(138\) 0 0
\(139\) −22.1663 −1.88012 −0.940060 0.341009i \(-0.889231\pi\)
−0.940060 + 0.341009i \(0.889231\pi\)
\(140\) 0 0
\(141\) 7.76463 0.653900
\(142\) 0 0
\(143\) 14.1274 + 14.1274i 1.18139 + 1.18139i
\(144\) 0 0
\(145\) 5.49042 + 2.87220i 0.455955 + 0.238523i
\(146\) 0 0
\(147\) −6.65135 2.18163i −0.548594 0.179938i
\(148\) 0 0
\(149\) 11.0475i 0.905050i −0.891752 0.452525i \(-0.850523\pi\)
0.891752 0.452525i \(-0.149477\pi\)
\(150\) 0 0
\(151\) −18.3990 −1.49729 −0.748645 0.662972i \(-0.769295\pi\)
−0.748645 + 0.662972i \(0.769295\pi\)
\(152\) 0 0
\(153\) −1.49007 1.49007i −0.120465 0.120465i
\(154\) 0 0
\(155\) −4.74873 2.48420i −0.381428 0.199536i
\(156\) 0 0
\(157\) 1.04994 1.04994i 0.0837946 0.0837946i −0.663967 0.747762i \(-0.731129\pi\)
0.747762 + 0.663967i \(0.231129\pi\)
\(158\) 0 0
\(159\) 8.68077 0.688430
\(160\) 0 0
\(161\) −1.70272 1.04669i −0.134193 0.0824907i
\(162\) 0 0
\(163\) −5.50539 + 5.50539i −0.431215 + 0.431215i −0.889042 0.457826i \(-0.848628\pi\)
0.457826 + 0.889042i \(0.348628\pi\)
\(164\) 0 0
\(165\) 8.21852 2.57310i 0.639811 0.200316i
\(166\) 0 0
\(167\) 1.88968 1.88968i 0.146228 0.146228i −0.630203 0.776431i \(-0.717028\pi\)
0.776431 + 0.630203i \(0.217028\pi\)
\(168\) 0 0
\(169\) 13.9108i 1.07006i
\(170\) 0 0
\(171\) 0.0697674i 0.00533524i
\(172\) 0 0
\(173\) 4.90751 + 4.90751i 0.373111 + 0.373111i 0.868609 0.495498i \(-0.165014\pi\)
−0.495498 + 0.868609i \(0.665014\pi\)
\(174\) 0 0
\(175\) −8.81920 + 9.86011i −0.666669 + 0.745354i
\(176\) 0 0
\(177\) −4.93165 4.93165i −0.370685 0.370685i
\(178\) 0 0
\(179\) 18.5857i 1.38916i −0.719416 0.694579i \(-0.755591\pi\)
0.719416 0.694579i \(-0.244409\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 0 0
\(183\) 10.1192 10.1192i 0.748034 0.748034i
\(184\) 0 0
\(185\) 18.6730 5.84625i 1.37287 0.429825i
\(186\) 0 0
\(187\) −5.73880 + 5.73880i −0.419663 + 0.419663i
\(188\) 0 0
\(189\) 2.25395 + 1.38554i 0.163951 + 0.100783i
\(190\) 0 0
\(191\) 5.39351 0.390261 0.195130 0.980777i \(-0.437487\pi\)
0.195130 + 0.980777i \(0.437487\pi\)
\(192\) 0 0
\(193\) −4.80599 + 4.80599i −0.345943 + 0.345943i −0.858596 0.512653i \(-0.828663\pi\)
0.512653 + 0.858596i \(0.328663\pi\)
\(194\) 0 0
\(195\) 10.2783 + 5.37688i 0.736044 + 0.385046i
\(196\) 0 0
\(197\) 12.6739 + 12.6739i 0.902981 + 0.902981i 0.995693 0.0927124i \(-0.0295537\pi\)
−0.0927124 + 0.995693i \(0.529554\pi\)
\(198\) 0 0
\(199\) −2.67111 −0.189350 −0.0946750 0.995508i \(-0.530181\pi\)
−0.0946750 + 0.995508i \(0.530181\pi\)
\(200\) 0 0
\(201\) 0.589007i 0.0415453i
\(202\) 0 0
\(203\) 7.13138 1.70161i 0.500524 0.119429i
\(204\) 0 0
\(205\) −17.1995 8.99757i −1.20127 0.628417i
\(206\) 0 0
\(207\) 0.534176 + 0.534176i 0.0371278 + 0.0371278i
\(208\) 0 0
\(209\) 0.268699 0.0185863
\(210\) 0 0
\(211\) 12.0239 0.827757 0.413879 0.910332i \(-0.364174\pi\)
0.413879 + 0.910332i \(0.364174\pi\)
\(212\) 0 0
\(213\) 5.74724 + 5.74724i 0.393794 + 0.393794i
\(214\) 0 0
\(215\) −2.61822 8.36262i −0.178561 0.570326i
\(216\) 0 0
\(217\) −6.16802 + 1.47174i −0.418712 + 0.0999082i
\(218\) 0 0
\(219\) 13.5087i 0.912834i
\(220\) 0 0
\(221\) −10.9316 −0.735342
\(222\) 0 0
\(223\) −11.6925 11.6925i −0.782988 0.782988i 0.197346 0.980334i \(-0.436768\pi\)
−0.980334 + 0.197346i \(0.936768\pi\)
\(224\) 0 0
\(225\) 4.10728 2.85136i 0.273819 0.190091i
\(226\) 0 0
\(227\) 1.10518 1.10518i 0.0733535 0.0733535i −0.669478 0.742832i \(-0.733482\pi\)
0.742832 + 0.669478i \(0.233482\pi\)
\(228\) 0 0
\(229\) −7.83309 −0.517625 −0.258812 0.965928i \(-0.583331\pi\)
−0.258812 + 0.965928i \(0.583331\pi\)
\(230\) 0 0
\(231\) 5.33620 8.68077i 0.351096 0.571153i
\(232\) 0 0
\(233\) 1.00797 1.00797i 0.0660345 0.0660345i −0.673318 0.739353i \(-0.735132\pi\)
0.739353 + 0.673318i \(0.235132\pi\)
\(234\) 0 0
\(235\) −5.18757 16.5691i −0.338399 1.08085i
\(236\) 0 0
\(237\) −6.97440 + 6.97440i −0.453036 + 0.453036i
\(238\) 0 0
\(239\) 20.2805i 1.31183i 0.754833 + 0.655917i \(0.227718\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(240\) 0 0
\(241\) 2.76994i 0.178427i −0.996013 0.0892136i \(-0.971565\pi\)
0.996013 0.0892136i \(-0.0284354\pi\)
\(242\) 0 0
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) −0.211650 + 15.6510i −0.0135218 + 0.999909i
\(246\) 0 0
\(247\) 0.255918 + 0.255918i 0.0162837 + 0.0162837i
\(248\) 0 0
\(249\) 2.31322i 0.146595i
\(250\) 0 0
\(251\) 6.09982i 0.385017i −0.981295 0.192509i \(-0.938338\pi\)
0.981295 0.192509i \(-0.0616623\pi\)
\(252\) 0 0
\(253\) 2.05731 2.05731i 0.129342 0.129342i
\(254\) 0 0
\(255\) −2.18418 + 4.17522i −0.136779 + 0.261463i
\(256\) 0 0
\(257\) 2.01843 2.01843i 0.125906 0.125906i −0.641346 0.767252i \(-0.721624\pi\)
0.767252 + 0.641346i \(0.221624\pi\)
\(258\) 0 0
\(259\) 12.1242 19.7233i 0.753361 1.22554i
\(260\) 0 0
\(261\) −2.77107 −0.171525
\(262\) 0 0
\(263\) −16.7686 + 16.7686i −1.03400 + 1.03400i −0.0345941 + 0.999401i \(0.511014\pi\)
−0.999401 + 0.0345941i \(0.988986\pi\)
\(264\) 0 0
\(265\) −5.79964 18.5241i −0.356269 1.13793i
\(266\) 0 0
\(267\) 3.57310 + 3.57310i 0.218670 + 0.218670i
\(268\) 0 0
\(269\) −24.7351 −1.50813 −0.754064 0.656801i \(-0.771909\pi\)
−0.754064 + 0.656801i \(0.771909\pi\)
\(270\) 0 0
\(271\) 4.13470i 0.251165i 0.992083 + 0.125583i \(0.0400800\pi\)
−0.992083 + 0.125583i \(0.959920\pi\)
\(272\) 0 0
\(273\) 13.3502 3.18548i 0.807993 0.192794i
\(274\) 0 0
\(275\) −10.9816 15.8186i −0.662217 0.953898i
\(276\) 0 0
\(277\) −12.1128 12.1128i −0.727786 0.727786i 0.242393 0.970178i \(-0.422068\pi\)
−0.970178 + 0.242393i \(0.922068\pi\)
\(278\) 0 0
\(279\) 2.39674 0.143489
\(280\) 0 0
\(281\) 5.25279 0.313355 0.156678 0.987650i \(-0.449922\pi\)
0.156678 + 0.987650i \(0.449922\pi\)
\(282\) 0 0
\(283\) −1.66729 1.66729i −0.0991101 0.0991101i 0.655813 0.754923i \(-0.272326\pi\)
−0.754923 + 0.655813i \(0.772326\pi\)
\(284\) 0 0
\(285\) 0.148878 0.0466117i 0.00881879 0.00276104i
\(286\) 0 0
\(287\) −22.3400 + 5.33051i −1.31869 + 0.314650i
\(288\) 0 0
\(289\) 12.5594i 0.738787i
\(290\) 0 0
\(291\) −9.69940 −0.568589
\(292\) 0 0
\(293\) 15.2556 + 15.2556i 0.891240 + 0.891240i 0.994640 0.103400i \(-0.0329722\pi\)
−0.103400 + 0.994640i \(0.532972\pi\)
\(294\) 0 0
\(295\) −7.22893 + 13.8186i −0.420884 + 0.804551i
\(296\) 0 0
\(297\) −2.72332 + 2.72332i −0.158023 + 0.158023i
\(298\) 0 0
\(299\) 3.91889 0.226635
\(300\) 0 0
\(301\) −8.83298 5.42977i −0.509125 0.312967i
\(302\) 0 0
\(303\) −13.5731 + 13.5731i −0.779754 + 0.779754i
\(304\) 0 0
\(305\) −28.3543 14.8330i −1.62356 0.849334i
\(306\) 0 0
\(307\) −14.6198 + 14.6198i −0.834394 + 0.834394i −0.988114 0.153721i \(-0.950874\pi\)
0.153721 + 0.988114i \(0.450874\pi\)
\(308\) 0 0
\(309\) 3.30678i 0.188116i
\(310\) 0 0
\(311\) 2.86218i 0.162299i 0.996702 + 0.0811497i \(0.0258592\pi\)
−0.996702 + 0.0811497i \(0.974141\pi\)
\(312\) 0 0
\(313\) 9.41824 + 9.41824i 0.532350 + 0.532350i 0.921271 0.388921i \(-0.127152\pi\)
−0.388921 + 0.921271i \(0.627152\pi\)
\(314\) 0 0
\(315\) 1.45077 5.73544i 0.0817414 0.323155i
\(316\) 0 0
\(317\) 7.38310 + 7.38310i 0.414676 + 0.414676i 0.883364 0.468688i \(-0.155273\pi\)
−0.468688 + 0.883364i \(0.655273\pi\)
\(318\) 0 0
\(319\) 10.6724i 0.597540i
\(320\) 0 0
\(321\) 9.04739i 0.504976i
\(322\) 0 0
\(323\) −0.103958 + 0.103958i −0.00578440 + 0.00578440i
\(324\) 0 0
\(325\) 4.60691 25.5254i 0.255545 1.41590i
\(326\) 0 0
\(327\) 1.52776 1.52776i 0.0844851 0.0844851i
\(328\) 0 0
\(329\) −17.5011 10.7582i −0.964866 0.593118i
\(330\) 0 0
\(331\) −23.6200 −1.29827 −0.649136 0.760672i \(-0.724870\pi\)
−0.649136 + 0.760672i \(0.724870\pi\)
\(332\) 0 0
\(333\) −6.18757 + 6.18757i −0.339076 + 0.339076i
\(334\) 0 0
\(335\) −1.25690 + 0.393517i −0.0686716 + 0.0215001i
\(336\) 0 0
\(337\) −4.93809 4.93809i −0.268995 0.268995i 0.559700 0.828695i \(-0.310916\pi\)
−0.828695 + 0.559700i \(0.810916\pi\)
\(338\) 0 0
\(339\) −5.85234 −0.317856
\(340\) 0 0
\(341\) 9.23070i 0.499870i
\(342\) 0 0
\(343\) 11.9691 + 14.1330i 0.646270 + 0.763109i
\(344\) 0 0
\(345\) 0.783008 1.49678i 0.0421558 0.0805838i
\(346\) 0 0
\(347\) −5.83694 5.83694i −0.313343 0.313343i 0.532860 0.846203i \(-0.321117\pi\)
−0.846203 + 0.532860i \(0.821117\pi\)
\(348\) 0 0
\(349\) 16.9121 0.905282 0.452641 0.891693i \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(350\) 0 0
\(351\) −5.18757 −0.276892
\(352\) 0 0
\(353\) 11.1265 + 11.1265i 0.592202 + 0.592202i 0.938226 0.346024i \(-0.112468\pi\)
−0.346024 + 0.938226i \(0.612468\pi\)
\(354\) 0 0
\(355\) 8.42444 16.1039i 0.447123 0.854708i
\(356\) 0 0
\(357\) 1.29400 + 5.42309i 0.0684855 + 0.287021i
\(358\) 0 0
\(359\) 8.14864i 0.430069i 0.976606 + 0.215034i \(0.0689864\pi\)
−0.976606 + 0.215034i \(0.931014\pi\)
\(360\) 0 0
\(361\) −18.9951 −0.999744
\(362\) 0 0
\(363\) 2.71033 + 2.71033i 0.142255 + 0.142255i
\(364\) 0 0
\(365\) −28.8266 + 9.02520i −1.50885 + 0.472401i
\(366\) 0 0
\(367\) 14.7480 14.7480i 0.769840 0.769840i −0.208238 0.978078i \(-0.566773\pi\)
0.978078 + 0.208238i \(0.0667728\pi\)
\(368\) 0 0
\(369\) 8.68077 0.451903
\(370\) 0 0
\(371\) −19.5660 12.0275i −1.01582 0.624438i
\(372\) 0 0
\(373\) 1.49461 1.49461i 0.0773880 0.0773880i −0.667353 0.744741i \(-0.732573\pi\)
0.744741 + 0.667353i \(0.232573\pi\)
\(374\) 0 0
\(375\) −8.82867 6.85963i −0.455911 0.354230i
\(376\) 0 0
\(377\) −10.1648 + 10.1648i −0.523511 + 0.523511i
\(378\) 0 0
\(379\) 18.7135i 0.961248i 0.876927 + 0.480624i \(0.159590\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(380\) 0 0
\(381\) 6.83487i 0.350161i
\(382\) 0 0
\(383\) 20.9354 + 20.9354i 1.06975 + 1.06975i 0.997378 + 0.0723706i \(0.0230564\pi\)
0.0723706 + 0.997378i \(0.476944\pi\)
\(384\) 0 0
\(385\) −22.0893 5.58742i −1.12577 0.284761i
\(386\) 0 0
\(387\) 2.77107 + 2.77107i 0.140862 + 0.140862i
\(388\) 0 0
\(389\) 25.6611i 1.30107i −0.759477 0.650535i \(-0.774545\pi\)
0.759477 0.650535i \(-0.225455\pi\)
\(390\) 0 0
\(391\) 1.59192i 0.0805069i
\(392\) 0 0
\(393\) −0.457851 + 0.457851i −0.0230955 + 0.0230955i
\(394\) 0 0
\(395\) 19.5425 + 10.2232i 0.983288 + 0.514387i
\(396\) 0 0
\(397\) −6.73585 + 6.73585i −0.338063 + 0.338063i −0.855638 0.517575i \(-0.826835\pi\)
0.517575 + 0.855638i \(0.326835\pi\)
\(398\) 0 0
\(399\) 0.0966653 0.157252i 0.00483932 0.00787245i
\(400\) 0 0
\(401\) 14.7503 0.736593 0.368296 0.929708i \(-0.379941\pi\)
0.368296 + 0.929708i \(0.379941\pi\)
\(402\) 0 0
\(403\) 8.79162 8.79162i 0.437942 0.437942i
\(404\) 0 0
\(405\) −1.03649 + 1.98133i −0.0515038 + 0.0984532i
\(406\) 0 0
\(407\) 23.8305 + 23.8305i 1.18124 + 1.18124i
\(408\) 0 0
\(409\) −10.5604 −0.522180 −0.261090 0.965315i \(-0.584082\pi\)
−0.261090 + 0.965315i \(0.584082\pi\)
\(410\) 0 0
\(411\) 14.4772i 0.714106i
\(412\) 0 0
\(413\) 4.28270 + 17.9487i 0.210738 + 0.883196i
\(414\) 0 0
\(415\) 4.93625 1.54547i 0.242311 0.0758641i
\(416\) 0 0
\(417\) −15.6739 15.6739i −0.767556 0.767556i
\(418\) 0 0
\(419\) 15.5472 0.759532 0.379766 0.925083i \(-0.376004\pi\)
0.379766 + 0.925083i \(0.376004\pi\)
\(420\) 0 0
\(421\) 3.29886 0.160776 0.0803882 0.996764i \(-0.474384\pi\)
0.0803882 + 0.996764i \(0.474384\pi\)
\(422\) 0 0
\(423\) 5.49042 + 5.49042i 0.266953 + 0.266953i
\(424\) 0 0
\(425\) 10.3689 + 1.87141i 0.502964 + 0.0907766i
\(426\) 0 0
\(427\) −36.8287 + 8.78764i −1.78227 + 0.425264i
\(428\) 0 0
\(429\) 19.9792i 0.964604i
\(430\) 0 0
\(431\) 14.0911 0.678743 0.339371 0.940652i \(-0.389786\pi\)
0.339371 + 0.940652i \(0.389786\pi\)
\(432\) 0 0
\(433\) 1.72650 + 1.72650i 0.0829702 + 0.0829702i 0.747374 0.664404i \(-0.231314\pi\)
−0.664404 + 0.747374i \(0.731314\pi\)
\(434\) 0 0
\(435\) 1.85136 + 5.91327i 0.0887660 + 0.283519i
\(436\) 0 0
\(437\) 0.0372681 0.0372681i 0.00178277 0.00178277i
\(438\) 0 0
\(439\) −27.1172 −1.29423 −0.647116 0.762392i \(-0.724025\pi\)
−0.647116 + 0.762392i \(0.724025\pi\)
\(440\) 0 0
\(441\) −3.16057 6.24586i −0.150503 0.297422i
\(442\) 0 0
\(443\) 24.1502 24.1502i 1.14741 1.14741i 0.160349 0.987060i \(-0.448738\pi\)
0.987060 0.160349i \(-0.0512618\pi\)
\(444\) 0 0
\(445\) 5.23754 10.0119i 0.248283 0.474611i
\(446\) 0 0
\(447\) 7.81179 7.81179i 0.369485 0.369485i
\(448\) 0 0
\(449\) 9.80267i 0.462617i 0.972881 + 0.231308i \(0.0743006\pi\)
−0.972881 + 0.231308i \(0.925699\pi\)
\(450\) 0 0
\(451\) 33.4328i 1.57429i
\(452\) 0 0
\(453\) −13.0101 13.0101i −0.611266 0.611266i
\(454\) 0 0
\(455\) −15.7169 26.3602i −0.736819 1.23578i
\(456\) 0 0
\(457\) 0.550071 + 0.550071i 0.0257312 + 0.0257312i 0.719855 0.694124i \(-0.244208\pi\)
−0.694124 + 0.719855i \(0.744208\pi\)
\(458\) 0 0
\(459\) 2.10728i 0.0983594i
\(460\) 0 0
\(461\) 0.831786i 0.0387401i −0.999812 0.0193701i \(-0.993834\pi\)
0.999812 0.0193701i \(-0.00616607\pi\)
\(462\) 0 0
\(463\) −5.45140 + 5.45140i −0.253348 + 0.253348i −0.822342 0.568994i \(-0.807333\pi\)
0.568994 + 0.822342i \(0.307333\pi\)
\(464\) 0 0
\(465\) −1.60127 5.11446i −0.0742569 0.237177i
\(466\) 0 0
\(467\) −23.2827 + 23.2827i −1.07740 + 1.07740i −0.0806551 + 0.996742i \(0.525701\pi\)
−0.996742 + 0.0806551i \(0.974299\pi\)
\(468\) 0 0
\(469\) −0.816091 + 1.32759i −0.0376836 + 0.0613025i
\(470\) 0 0
\(471\) 1.48484 0.0684180
\(472\) 0 0
\(473\) 10.6724 10.6724i 0.490718 0.490718i
\(474\) 0 0
\(475\) −0.198932 0.286554i −0.00912762 0.0131480i
\(476\) 0 0
\(477\) 6.13823 + 6.13823i 0.281050 + 0.281050i
\(478\) 0 0
\(479\) −40.4319 −1.84738 −0.923691 0.383138i \(-0.874843\pi\)
−0.923691 + 0.383138i \(0.874843\pi\)
\(480\) 0 0
\(481\) 45.3940i 2.06979i
\(482\) 0 0
\(483\) −0.463885 1.94413i −0.0211075 0.0884609i
\(484\) 0 0
\(485\) 6.48019 + 20.6978i 0.294250 + 0.939839i
\(486\) 0 0
\(487\) 7.22893 + 7.22893i 0.327574 + 0.327574i 0.851663 0.524089i \(-0.175594\pi\)
−0.524089 + 0.851663i \(0.675594\pi\)
\(488\) 0 0
\(489\) −7.78580 −0.352086
\(490\) 0 0
\(491\) −20.1040 −0.907279 −0.453639 0.891185i \(-0.649875\pi\)
−0.453639 + 0.891185i \(0.649875\pi\)
\(492\) 0 0
\(493\) −4.12910 4.12910i −0.185965 0.185965i
\(494\) 0 0
\(495\) 7.63083 + 3.99191i 0.342980 + 0.179423i
\(496\) 0 0
\(497\) −4.99097 20.9170i −0.223876 0.938256i
\(498\) 0 0
\(499\) 15.4227i 0.690414i 0.938527 + 0.345207i \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(500\) 0 0
\(501\) 2.67241 0.119394
\(502\) 0 0
\(503\) 25.9985 + 25.9985i 1.15922 + 1.15922i 0.984644 + 0.174573i \(0.0558546\pi\)
0.174573 + 0.984644i \(0.444145\pi\)
\(504\) 0 0
\(505\) 38.0322 + 19.8958i 1.69241 + 0.885350i
\(506\) 0 0
\(507\) −9.83645 + 9.83645i −0.436852 + 0.436852i
\(508\) 0 0
\(509\) −37.1271 −1.64563 −0.822816 0.568309i \(-0.807598\pi\)
−0.822816 + 0.568309i \(0.807598\pi\)
\(510\) 0 0
\(511\) −18.7168 + 30.4479i −0.827983 + 1.34694i
\(512\) 0 0
\(513\) −0.0493330 + 0.0493330i −0.00217810 + 0.00217810i
\(514\) 0 0
\(515\) 7.05642 2.20927i 0.310943 0.0973519i
\(516\) 0 0
\(517\) 21.1456 21.1456i 0.929982 0.929982i
\(518\) 0 0
\(519\) 6.94026i 0.304644i
\(520\) 0 0
\(521\) 2.59132i 0.113528i 0.998388 + 0.0567639i \(0.0180782\pi\)
−0.998388 + 0.0567639i \(0.981922\pi\)
\(522\) 0 0
\(523\) −6.08854 6.08854i −0.266233 0.266233i 0.561347 0.827581i \(-0.310283\pi\)
−0.827581 + 0.561347i \(0.810283\pi\)
\(524\) 0 0
\(525\) −13.2083 + 0.736034i −0.576456 + 0.0321232i
\(526\) 0 0
\(527\) 3.57131 + 3.57131i 0.155569 + 0.155569i
\(528\) 0 0
\(529\) 22.4293i 0.975187i
\(530\) 0 0
\(531\) 6.97440i 0.302663i
\(532\) 0 0
\(533\) 31.8425 31.8425i 1.37925 1.37925i
\(534\) 0 0
\(535\) 19.3065 6.04458i 0.834691 0.261330i
\(536\) 0 0
\(537\) 13.1421 13.1421i 0.567122 0.567122i
\(538\) 0 0
\(539\) −24.0551 + 12.1725i −1.03613 + 0.524307i
\(540\) 0 0
\(541\) −33.4638 −1.43872 −0.719360 0.694638i \(-0.755565\pi\)
−0.719360 + 0.694638i \(0.755565\pi\)
\(542\) 0 0
\(543\) 6.00000 6.00000i 0.257485 0.257485i
\(544\) 0 0
\(545\) −4.28081 2.23942i −0.183370 0.0959262i
\(546\) 0 0
\(547\) 0.828381 + 0.828381i 0.0354190 + 0.0354190i 0.724594 0.689175i \(-0.242027\pi\)
−0.689175 + 0.724594i \(0.742027\pi\)
\(548\) 0 0
\(549\) 14.3107 0.610767
\(550\) 0 0
\(551\) 0.193331i 0.00823616i
\(552\) 0 0
\(553\) 25.3832 6.05665i 1.07941 0.257555i
\(554\) 0 0
\(555\) 17.3377 + 9.06988i 0.735946 + 0.384995i
\(556\) 0 0
\(557\) 14.7120 + 14.7120i 0.623366 + 0.623366i 0.946391 0.323024i \(-0.104700\pi\)
−0.323024 + 0.946391i \(0.604700\pi\)
\(558\) 0 0
\(559\) 20.3295 0.859846
\(560\) 0 0
\(561\) −8.11589 −0.342653
\(562\) 0 0
\(563\) −23.9693 23.9693i −1.01019 1.01019i −0.999948 0.0102391i \(-0.996741\pi\)
−0.0102391 0.999948i \(-0.503259\pi\)
\(564\) 0 0
\(565\) 3.90996 + 12.4885i 0.164493 + 0.525394i
\(566\) 0 0
\(567\) 0.614060 + 2.57351i 0.0257881 + 0.108077i
\(568\) 0 0
\(569\) 15.6660i 0.656751i −0.944547 0.328376i \(-0.893499\pi\)
0.944547 0.328376i \(-0.106501\pi\)
\(570\) 0 0
\(571\) −36.9887 −1.54793 −0.773964 0.633229i \(-0.781729\pi\)
−0.773964 + 0.633229i \(0.781729\pi\)
\(572\) 0 0
\(573\) 3.81379 + 3.81379i 0.159323 + 0.159323i
\(574\) 0 0
\(575\) −3.71714 0.670882i −0.155015 0.0279777i
\(576\) 0 0
\(577\) −15.5587 + 15.5587i −0.647717 + 0.647717i −0.952441 0.304724i \(-0.901436\pi\)
0.304724 + 0.952441i \(0.401436\pi\)
\(578\) 0 0
\(579\) −6.79669 −0.282461
\(580\) 0 0
\(581\) 3.20506 5.21389i 0.132968 0.216309i
\(582\) 0 0
\(583\) 23.6405 23.6405i 0.979091 0.979091i
\(584\) 0 0
\(585\) 3.46582 + 11.0699i 0.143294 + 0.457683i
\(586\) 0 0
\(587\) −15.7111 + 15.7111i −0.648468 + 0.648468i −0.952623 0.304155i \(-0.901626\pi\)
0.304155 + 0.952623i \(0.401626\pi\)
\(588\) 0 0
\(589\) 0.167214i 0.00688993i
\(590\) 0 0
\(591\) 17.9237i 0.737281i
\(592\) 0 0
\(593\) 1.85199 + 1.85199i 0.0760523 + 0.0760523i 0.744110 0.668057i \(-0.232874\pi\)
−0.668057 + 0.744110i \(0.732874\pi\)
\(594\) 0 0
\(595\) 10.7080 6.38447i 0.438984 0.261738i
\(596\) 0 0
\(597\) −1.88876 1.88876i −0.0773018 0.0773018i
\(598\) 0 0
\(599\) 47.3151i 1.93324i −0.256208 0.966622i \(-0.582473\pi\)
0.256208 0.966622i \(-0.417527\pi\)
\(600\) 0 0
\(601\) 11.0819i 0.452041i 0.974123 + 0.226021i \(0.0725717\pi\)
−0.974123 + 0.226021i \(0.927428\pi\)
\(602\) 0 0
\(603\) 0.416491 0.416491i 0.0169608 0.0169608i
\(604\) 0 0
\(605\) 3.97286 7.59441i 0.161520 0.308757i
\(606\) 0 0
\(607\) 7.54653 7.54653i 0.306304 0.306304i −0.537170 0.843474i \(-0.680507\pi\)
0.843474 + 0.537170i \(0.180507\pi\)
\(608\) 0 0
\(609\) 6.24586 + 3.83943i 0.253095 + 0.155581i
\(610\) 0 0
\(611\) 40.2795 1.62953
\(612\) 0 0
\(613\) −2.62487 + 2.62487i −0.106017 + 0.106017i −0.758126 0.652108i \(-0.773885\pi\)
0.652108 + 0.758126i \(0.273885\pi\)
\(614\) 0 0
\(615\) −5.79964 18.5241i −0.233864 0.746965i
\(616\) 0 0
\(617\) 11.3212 + 11.3212i 0.455774 + 0.455774i 0.897266 0.441491i \(-0.145550\pi\)
−0.441491 + 0.897266i \(0.645550\pi\)
\(618\) 0 0
\(619\) −9.06771 −0.364462 −0.182231 0.983256i \(-0.558332\pi\)
−0.182231 + 0.983256i \(0.558332\pi\)
\(620\) 0 0
\(621\) 0.755439i 0.0303147i
\(622\) 0 0
\(623\) −3.10292 13.0043i −0.124316 0.521005i
\(624\) 0 0
\(625\) −8.73948 + 23.4227i −0.349579 + 0.936907i
\(626\) 0 0
\(627\) 0.189999 + 0.189999i 0.00758783 + 0.00758783i
\(628\) 0 0
\(629\) −18.4398 −0.735244
\(630\) 0 0
\(631\) 9.67260 0.385060 0.192530 0.981291i \(-0.438331\pi\)
0.192530 + 0.981291i \(0.438331\pi\)
\(632\) 0 0
\(633\) 8.50216 + 8.50216i 0.337930 + 0.337930i
\(634\) 0 0
\(635\) 14.5851 4.56639i 0.578792 0.181212i
\(636\) 0 0
\(637\) −34.5043 11.3173i −1.36711 0.448409i
\(638\) 0 0
\(639\) 8.12783i 0.321532i
\(640\) 0 0
\(641\) −40.5847 −1.60300 −0.801500 0.597995i \(-0.795964\pi\)
−0.801500 + 0.597995i \(0.795964\pi\)
\(642\) 0 0
\(643\) 3.89544 + 3.89544i 0.153621 + 0.153621i 0.779733 0.626112i \(-0.215355\pi\)
−0.626112 + 0.779733i \(0.715355\pi\)
\(644\) 0 0
\(645\) 4.06191 7.76463i 0.159937 0.305732i
\(646\) 0 0
\(647\) 16.8414 16.8414i 0.662104 0.662104i −0.293772 0.955876i \(-0.594911\pi\)
0.955876 + 0.293772i \(0.0949106\pi\)
\(648\) 0 0
\(649\) −26.8609 −1.05438
\(650\) 0 0
\(651\) −5.40212 3.32077i −0.211726 0.130151i
\(652\) 0 0
\(653\) −22.9951 + 22.9951i −0.899867 + 0.899867i −0.995424 0.0955569i \(-0.969537\pi\)
0.0955569 + 0.995424i \(0.469537\pi\)
\(654\) 0 0
\(655\) 1.28291 + 0.671128i 0.0501275 + 0.0262232i
\(656\) 0 0
\(657\) 9.55210 9.55210i 0.372663 0.372663i
\(658\) 0 0
\(659\) 32.7543i 1.27593i −0.770067 0.637963i \(-0.779777\pi\)
0.770067 0.637963i \(-0.220223\pi\)
\(660\) 0 0
\(661\) 32.5174i 1.26478i −0.774650 0.632391i \(-0.782074\pi\)
0.774650 0.632391i \(-0.217926\pi\)
\(662\) 0 0
\(663\) −7.72984 7.72984i −0.300202 0.300202i
\(664\) 0 0
\(665\) −0.400147 0.101216i −0.0155170 0.00392499i
\(666\) 0 0
\(667\) 1.48024 + 1.48024i 0.0573152 + 0.0573152i
\(668\) 0 0
\(669\) 16.5357i 0.639307i
\(670\) 0 0
\(671\) 55.1158i 2.12772i
\(672\) 0 0
\(673\) −16.7534 + 16.7534i −0.645796 + 0.645796i −0.951974 0.306179i \(-0.900950\pi\)
0.306179 + 0.951974i \(0.400950\pi\)
\(674\) 0 0
\(675\) 4.92050 + 0.888068i 0.189390 + 0.0341818i
\(676\) 0 0
\(677\) 6.85568 6.85568i 0.263485 0.263485i −0.562983 0.826468i \(-0.690346\pi\)
0.826468 + 0.562983i \(0.190346\pi\)
\(678\) 0 0
\(679\) 21.8620 + 13.4389i 0.838985 + 0.515737i
\(680\) 0 0
\(681\) 1.56296 0.0598929
\(682\) 0 0
\(683\) −23.2345 + 23.2345i −0.889042 + 0.889042i −0.994431 0.105389i \(-0.966391\pi\)
0.105389 + 0.994431i \(0.466391\pi\)
\(684\) 0 0
\(685\) 30.8932 9.67222i 1.18037 0.369557i
\(686\) 0 0
\(687\) −5.53883 5.53883i −0.211319 0.211319i
\(688\) 0 0
\(689\) 45.0321 1.71559
\(690\) 0 0
\(691\) 42.4714i 1.61569i 0.589395 + 0.807845i \(0.299366\pi\)
−0.589395 + 0.807845i \(0.700634\pi\)
\(692\) 0 0
\(693\) 9.91150 2.36497i 0.376507 0.0898376i
\(694\) 0 0
\(695\) −22.9752 + 43.9188i −0.871500 + 1.66594i
\(696\) 0 0
\(697\) 12.9350 + 12.9350i 0.489947 + 0.489947i
\(698\) 0 0
\(699\) 1.42549 0.0539169
\(700\) 0 0
\(701\) 17.0793 0.645077 0.322539 0.946556i \(-0.395464\pi\)
0.322539 + 0.946556i \(0.395464\pi\)
\(702\) 0 0
\(703\) 0.431690 + 0.431690i 0.0162815 + 0.0162815i
\(704\) 0 0
\(705\) 8.04799 15.3843i 0.303105 0.579407i
\(706\) 0 0
\(707\) 49.3991 11.7870i 1.85785 0.443297i
\(708\) 0 0
\(709\) 32.6742i 1.22710i 0.789654 + 0.613552i \(0.210260\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(710\) 0 0
\(711\) −9.86329 −0.369902
\(712\) 0 0
\(713\) −1.28028 1.28028i −0.0479469 0.0479469i
\(714\) 0 0
\(715\) 42.6341 13.3481i 1.59443 0.499192i
\(716\) 0 0
\(717\) −14.3405 + 14.3405i −0.535554 + 0.535554i
\(718\) 0 0
\(719\) −19.3248 −0.720693 −0.360346 0.932819i \(-0.617341\pi\)
−0.360346 + 0.932819i \(0.617341\pi\)
\(720\) 0 0
\(721\) 4.58166 7.45331i 0.170630 0.277576i
\(722\) 0 0
\(723\) 1.95864 1.95864i 0.0728426 0.0728426i
\(724\) 0 0
\(725\) 11.3816 7.90133i 0.422701 0.293448i
\(726\) 0 0
\(727\) 2.71795 2.71795i 0.100803 0.100803i −0.654907 0.755710i \(-0.727292\pi\)
0.755710 + 0.654907i \(0.227292\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 8.25820i 0.305440i
\(732\) 0 0
\(733\) 2.38437 + 2.38437i 0.0880686 + 0.0880686i 0.749769 0.661700i \(-0.230165\pi\)
−0.661700 + 0.749769i \(0.730165\pi\)
\(734\) 0 0
\(735\) −11.2166 + 10.9173i −0.413731 + 0.402691i
\(736\) 0 0
\(737\) −1.60406 1.60406i −0.0590862 0.0590862i
\(738\) 0 0
\(739\) 4.95679i 0.182339i −0.995835 0.0911693i \(-0.970940\pi\)
0.995835 0.0911693i \(-0.0290605\pi\)
\(740\) 0 0
\(741\) 0.361923i 0.0132956i
\(742\) 0 0
\(743\) −15.6556 + 15.6556i −0.574347 + 0.574347i −0.933340 0.358993i \(-0.883120\pi\)
0.358993 + 0.933340i \(0.383120\pi\)
\(744\) 0 0
\(745\) −21.8889 11.4507i −0.801946 0.419521i
\(746\) 0 0
\(747\) −1.63570 + 1.63570i −0.0598470 + 0.0598470i
\(748\) 0 0
\(749\) 12.5355 20.3924i 0.458037 0.745120i
\(750\) 0 0
\(751\) 11.1909 0.408361 0.204181 0.978933i \(-0.434547\pi\)
0.204181 + 0.978933i \(0.434547\pi\)
\(752\) 0 0
\(753\) 4.31322 4.31322i 0.157183 0.157183i
\(754\) 0 0
\(755\) −19.0704 + 36.4545i −0.694045 + 1.32672i
\(756\) 0 0
\(757\) 29.4977 + 29.4977i 1.07211 + 1.07211i 0.997189 + 0.0749214i \(0.0238706\pi\)
0.0749214 + 0.997189i \(0.476129\pi\)
\(758\) 0 0
\(759\) 2.90947 0.105607
\(760\) 0 0
\(761\) 28.1175i 1.01926i −0.860395 0.509629i \(-0.829783\pi\)
0.860395 0.509629i \(-0.170217\pi\)
\(762\) 0 0
\(763\) −5.56025 + 1.32672i −0.201294 + 0.0480305i
\(764\) 0 0
\(765\) −4.49678 + 1.40788i −0.162581 + 0.0509019i
\(766\) 0 0
\(767\) −25.5832 25.5832i −0.923757 0.923757i
\(768\) 0 0
\(769\) −6.61248 −0.238452 −0.119226 0.992867i \(-0.538041\pi\)
−0.119226 + 0.992867i \(0.538041\pi\)
\(770\) 0 0
\(771\) 2.85449 0.102802
\(772\) 0 0
\(773\) −31.7247 31.7247i −1.14106 1.14106i −0.988257 0.152800i \(-0.951171\pi\)
−0.152800 0.988257i \(-0.548829\pi\)
\(774\) 0 0
\(775\) −9.84407 + 6.83396i −0.353609 + 0.245483i
\(776\) 0 0
\(777\) 22.5196 5.37335i 0.807885 0.192768i
\(778\) 0 0
\(779\) 0.605634i 0.0216991i
\(780\) 0 0
\(781\) 31.3032 1.12012
\(782\) 0 0
\(783\) −1.95945 1.95945i −0.0700249 0.0700249i
\(784\) 0 0
\(785\) −0.992027 3.16855i −0.0354070 0.113090i
\(786\) 0 0
\(787\) 22.4472 22.4472i 0.800155 0.800155i −0.182964 0.983120i \(-0.558569\pi\)
0.983120 + 0.182964i \(0.0585693\pi\)
\(788\) 0 0
\(789\) −23.7144 −0.844254
\(790\) 0 0
\(791\) 13.1909 + 8.10864i 0.469014 + 0.288310i