Properties

Label 1680.2.cz.d.97.2
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: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
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 97.2
Root \(1.36166 - 0.381939i\) of defining polynomial
Character \(\chi\) \(=\) 1680.97
Dual form 1680.2.cz.d.433.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.03649 + 1.98133i) q^{5} +(-2.57351 - 0.614060i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{3} +(-1.03649 + 1.98133i) q^{5} +(-2.57351 - 0.614060i) q^{7} +1.00000i q^{9} +3.85136 q^{11} +(-3.66816 - 3.66816i) q^{13} +(2.13393 - 0.668102i) q^{15} +(1.49007 - 1.49007i) q^{17} -0.0697674 q^{19} +(1.38554 + 2.25395i) q^{21} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +(0.707107 - 0.707107i) q^{27} +2.77107i q^{29} +2.39674i q^{31} +(-2.72332 - 2.72332i) q^{33} +(3.88408 - 4.46250i) q^{35} +(6.18757 + 6.18757i) q^{37} +5.18757i q^{39} +8.68077i q^{41} +(2.77107 - 2.77107i) q^{43} +(-1.98133 - 1.03649i) q^{45} +(-5.49042 + 5.49042i) q^{47} +(6.24586 + 3.16057i) q^{49} -2.10728 q^{51} +(6.13823 - 6.13823i) q^{53} +(-3.99191 + 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} +6.97440 q^{59} +14.3107i q^{61} +(0.614060 - 2.57351i) q^{63} +(11.0699 - 3.46582i) q^{65} +(-0.416491 - 0.416491i) q^{67} -0.755439 q^{69} +8.12783 q^{71} +(9.55210 + 9.55210i) q^{73} +(-0.888068 + 4.92050i) q^{75} +(-9.91150 - 2.36497i) q^{77} +9.86329i q^{79} -1.00000 q^{81} +(-1.63570 - 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(1.95945 - 1.95945i) q^{87} -5.05313 q^{89} +(7.18757 + 11.6925i) q^{91} +(1.69475 - 1.69475i) q^{93} +(0.0723134 - 0.138232i) q^{95} +(6.85851 - 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

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
\(7\) −2.57351 0.614060i −0.972694 0.232093i
\(8\) 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 \(-0.994423\pi\)
−0.0175187 0.999847i \(-0.505577\pi\)
\(14\) 0 0
\(15\) 2.13393 0.668102i 0.550977 0.172503i
\(16\) 0 0
\(17\) 1.49007 1.49007i 0.361395 0.361395i −0.502931 0.864326i \(-0.667745\pi\)
0.864326 + 0.502931i \(0.167745\pi\)
\(18\) 0 0
\(19\) −0.0697674 −0.0160057 −0.00800286 0.999968i \(-0.502547\pi\)
−0.00800286 + 0.999968i \(0.502547\pi\)
\(20\) 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 \(0.0690512\pi\)
−0.976563 + 0.215233i \(0.930949\pi\)
\(32\) 0 0
\(33\) −2.72332 2.72332i −0.474070 0.474070i
\(34\) 0 0
\(35\) 3.88408 4.46250i 0.656529 0.754301i
\(36\) 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 \(0.237090\pi\)
−0.735196 + 0.677854i \(0.762910\pi\)
\(42\) 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 −0.983230 0.182370i \(-0.941623\pi\)
0.182370 + 0.983230i \(0.441623\pi\)
\(48\) 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 \(-0.349998\pi\)
0.453995 + 0.891004i \(0.349998\pi\)
\(60\) 0 0
\(61\) 14.3107i 1.83230i 0.400835 + 0.916150i \(0.368720\pi\)
−0.400835 + 0.916150i \(0.631280\pi\)
\(62\) 0 0
\(63\) 0.614060 2.57351i 0.0773643 0.324231i
\(64\) 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 \(0.0401987\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(74\) 0 0
\(75\) −0.888068 + 4.92050i −0.102545 + 0.568171i
\(76\) 0 0
\(77\) −9.91150 2.36497i −1.12952 0.269513i
\(78\) 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 0.611615 0.791156i \(-0.290520\pi\)
−0.791156 + 0.611615i \(0.790520\pi\)
\(84\) 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 \(-0.586302\pi\)
−0.267815 + 0.963470i \(0.586302\pi\)
\(90\) 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 −0.267251 0.963627i \(-0.586115\pi\)
0.963627 + 0.267251i \(0.0861152\pi\)
\(98\) 0 0
\(99\) 3.85136i 0.387076i
\(100\) 0 0
\(101\) 19.1953i 1.91000i −0.296605 0.955000i \(-0.595855\pi\)
0.296605 0.955000i \(-0.404145\pi\)
\(102\) 0 0
\(103\) −2.33825 2.33825i −0.230394 0.230394i 0.582463 0.812857i \(-0.302089\pi\)
−0.812857 + 0.582463i \(0.802089\pi\)
\(104\) 0 0
\(105\) −5.90192 + 0.409006i −0.575969 + 0.0399149i
\(106\) 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 \(-0.990995\pi\)
0.999600 0.0282861i \(-0.00900495\pi\)
\(132\) 0 0
\(133\) 0.179547 + 0.0428413i 0.0155687 + 0.00371481i
\(134\) 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 \(-0.110769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(140\) 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
\(147\) −2.18163 6.65135i −0.179938 0.548594i
\(148\) 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 −0.747762 0.663967i \(-0.768871\pi\)
0.663967 + 0.747762i \(0.268871\pi\)
\(158\) 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 −0.776431 0.630203i \(-0.782972\pi\)
0.630203 + 0.776431i \(0.282972\pi\)
\(168\) 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 0.495498 0.868609i \(-0.334986\pi\)
−0.868609 + 0.495498i \(0.834986\pi\)
\(174\) 0 0
\(175\) 4.81588 + 12.3210i 0.364046 + 0.931381i
\(176\) 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 \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 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 \(-0.469819\pi\)
0.0946750 + 0.995508i \(0.469819\pi\)
\(200\) 0 0
\(201\) 0.589007i 0.0415453i
\(202\) 0 0
\(203\) 1.70161 7.13138i 0.119429 0.500524i
\(204\) 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
\(217\) 1.47174 6.16802i 0.0999082 0.418712i
\(218\) 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 0.980334 0.197346i \(-0.0632321\pi\)
−0.197346 + 0.980334i \(0.563232\pi\)
\(224\) 0 0
\(225\) 4.10728 2.85136i 0.273819 0.190091i
\(226\) 0 0
\(227\) −1.10518 + 1.10518i −0.0733535 + 0.0733535i −0.742832 0.669478i \(-0.766518\pi\)
0.669478 + 0.742832i \(0.266518\pi\)
\(228\) 0 0
\(229\) 7.83309 0.517625 0.258812 0.965928i \(-0.416669\pi\)
0.258812 + 0.965928i \(0.416669\pi\)
\(230\) 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 \(0.0284354\pi\)
−0.996013 + 0.0892136i \(0.971565\pi\)
\(242\) 0 0
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) −12.7359 + 9.09922i −0.813670 + 0.581328i
\(246\) 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 \(0.0616623\pi\)
−0.981295 + 0.192509i \(0.938338\pi\)
\(252\) 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 −0.767252 0.641346i \(-0.778376\pi\)
0.641346 + 0.767252i \(0.278376\pi\)
\(258\) 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 \(-0.228091\pi\)
0.754064 + 0.656801i \(0.228091\pi\)
\(270\) 0 0
\(271\) 4.13470i 0.251165i −0.992083 0.125583i \(-0.959920\pi\)
0.992083 0.125583i \(-0.0400800\pi\)
\(272\) 0 0
\(273\) 3.18548 13.3502i 0.192794 0.807993i
\(274\) 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 0.754923 0.655813i \(-0.227674\pi\)
−0.655813 + 0.754923i \(0.727674\pi\)
\(284\) 0 0
\(285\) −0.148878 + 0.0466117i −0.00881879 + 0.00276104i
\(286\) 0 0
\(287\) 5.33051 22.3400i 0.314650 1.31869i
\(288\) 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 0.103400 0.994640i \(-0.467028\pi\)
−0.994640 + 0.103400i \(0.967028\pi\)
\(294\) 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 −0.153721 0.988114i \(-0.549126\pi\)
0.988114 + 0.153721i \(0.0491256\pi\)
\(308\) 0 0
\(309\) 3.30678i 0.188116i
\(310\) 0 0
\(311\) 2.86218i 0.162299i −0.996702 0.0811497i \(-0.974141\pi\)
0.996702 0.0811497i \(-0.0258592\pi\)
\(312\) 0 0
\(313\) −9.41824 9.41824i −0.532350 0.532350i 0.388921 0.921271i \(-0.372848\pi\)
−0.921271 + 0.388921i \(0.872848\pi\)
\(314\) 0 0
\(315\) 4.46250 + 3.88408i 0.251434 + 0.218843i
\(316\) 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
\(343\) −14.1330 11.9691i −0.763109 0.646270i
\(344\) 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 \(-0.649518\pi\)
−0.452641 + 0.891693i \(0.649518\pi\)
\(350\) 0 0
\(351\) −5.18757 −0.276892
\(352\) 0 0
\(353\) −11.1265 11.1265i −0.592202 0.592202i 0.346024 0.938226i \(-0.387532\pi\)
−0.938226 + 0.346024i \(0.887532\pi\)
\(354\) 0 0
\(355\) −8.42444 + 16.1039i −0.447123 + 0.854708i
\(356\) 0 0
\(357\) 5.42309 + 1.29400i 0.287021 + 0.0684855i
\(358\) 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 −0.978078 0.208238i \(-0.933227\pi\)
0.208238 + 0.978078i \(0.433227\pi\)
\(368\) 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 \(-0.976944\pi\)
−0.0723706 0.997378i \(-0.523056\pi\)
\(384\) 0 0
\(385\) 14.9590 17.1867i 0.762381 0.875916i
\(386\) 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 −0.517575 0.855638i \(-0.673165\pi\)
0.855638 + 0.517575i \(0.173165\pi\)
\(398\) 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 \(-0.415918\pi\)
0.261090 + 0.965315i \(0.415918\pi\)
\(410\) 0 0
\(411\) 14.4772i 0.714106i
\(412\) 0 0
\(413\) −17.9487 4.28270i −0.883196 0.210738i
\(414\) 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 \(-0.623996\pi\)
−0.379766 + 0.925083i \(0.623996\pi\)
\(420\) 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
\(427\) 8.78764 36.8287i 0.425264 1.78227i
\(428\) 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 0.664404 0.747374i \(-0.268686\pi\)
−0.747374 + 0.664404i \(0.768686\pi\)
\(434\) 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 \(-0.275975\pi\)
0.647116 + 0.762392i \(0.275975\pi\)
\(440\) 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
\(455\) −30.6166 + 2.12175i −1.43533 + 0.0994691i
\(456\) 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 \(0.00616607\pi\)
−0.999812 + 0.0193701i \(0.993834\pi\)
\(462\) 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 \(-0.474299\pi\)
0.996742 0.0806551i \(-0.0257012\pi\)
\(468\) 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 \(-0.125157\pi\)
0.923691 + 0.383138i \(0.125157\pi\)
\(480\) 0 0
\(481\) 45.3940i 2.06979i
\(482\) 0 0
\(483\) 1.94413 + 0.463885i 0.0884609 + 0.0211075i
\(484\) 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
\(497\) −20.9170 4.99097i −0.938256 0.223876i
\(498\) 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 \(-0.944145\pi\)
−0.174573 0.984644i \(-0.555855\pi\)
\(504\) 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 \(-0.192402\pi\)
0.822816 + 0.568309i \(0.192402\pi\)
\(510\) 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 \(-0.981922\pi\)
0.998388 0.0567639i \(-0.0180782\pi\)
\(522\) 0 0
\(523\) 6.08854 + 6.08854i 0.266233 + 0.266233i 0.827581 0.561347i \(-0.189717\pi\)
−0.561347 + 0.827581i \(0.689717\pi\)
\(524\) 0 0
\(525\) 5.30693 12.1176i 0.231613 0.528856i
\(526\) 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
\(553\) 6.05665 25.3832i 0.257555 1.07941i
\(554\) 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 \(0.00325926\pi\)
0.0102391 + 0.999948i \(0.496741\pi\)
\(564\) 0 0
\(565\) −3.90996 12.4885i −0.164493 0.525394i
\(566\) 0 0
\(567\) 2.57351 + 0.614060i 0.108077 + 0.0257881i
\(568\) 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 −0.304724 0.952441i \(-0.598564\pi\)
0.952441 + 0.304724i \(0.0985641\pi\)
\(578\) 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 −0.304155 0.952623i \(-0.598374\pi\)
0.952623 + 0.304155i \(0.0983740\pi\)
\(588\) 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 0.668057 0.744110i \(-0.267126\pi\)
−0.744110 + 0.668057i \(0.767126\pi\)
\(594\) 0 0
\(595\) −0.861891 12.4370i −0.0353341 0.509867i
\(596\) 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 \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) 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 −0.843474 0.537170i \(-0.819493\pi\)
0.537170 + 0.843474i \(0.319493\pi\)
\(608\) 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 \(-0.441668\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(620\) 0 0
\(621\) 0.755439i 0.0303147i
\(622\) 0 0
\(623\) 13.0043 + 3.10292i 0.521005 + 0.124316i
\(624\) 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
\(637\) −11.3173 34.5043i −0.448409 1.36711i
\(638\) 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 0.626112 0.779733i \(-0.284645\pi\)
−0.779733 + 0.626112i \(0.784645\pi\)
\(644\) 0 0
\(645\) 4.06191 7.76463i 0.159937 0.305732i
\(646\) 0 0
\(647\) −16.8414 + 16.8414i −0.662104 + 0.662104i −0.955876 0.293772i \(-0.905089\pi\)
0.293772 + 0.955876i \(0.405089\pi\)
\(648\) 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 \(0.217926\pi\)
−0.774650 + 0.632391i \(0.782074\pi\)
\(662\) 0 0
\(663\) 7.72984 + 7.72984i 0.300202 + 0.300202i
\(664\) 0 0
\(665\) −0.270982 + 0.311337i −0.0105082 + 0.0120731i
\(666\) 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 −0.826468 0.562983i \(-0.809654\pi\)
0.562983 + 0.826468i \(0.309654\pi\)
\(678\) 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 \(-0.700634\pi\)
0.589395 0.807845i \(-0.299366\pi\)
\(692\) 0 0
\(693\) 2.36497 9.91150i 0.0898376 0.376507i
\(694\) 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
\(707\) −11.7870 + 49.3991i −0.443297 + 1.85785i
\(708\) 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 \(-0.382659\pi\)
0.360346 + 0.932819i \(0.382659\pi\)
\(720\) 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 −0.755710 0.654907i \(-0.772708\pi\)
0.654907 + 0.755710i \(0.272708\pi\)
\(728\) 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 0.661700 0.749769i \(-0.269835\pi\)
−0.749769 + 0.661700i \(0.769835\pi\)
\(734\) 0 0
\(735\) 15.4398 + 2.57155i 0.569505 + 0.0948532i
\(736\) 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 \(0.170217\pi\)
−0.860395 + 0.509629i \(0.829783\pi\)
\(762\) 0 0
\(763\) −1.32672 + 5.56025i −0.0480305 + 0.201294i
\(764\) 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 \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)
\(770\) 0 0
\(771\) 2.85449 0.102802
\(772\) 0 0
\(773\) 31.7247 + 31.7247i 1.14106 + 1.14106i 0.988257 + 0.152800i \(0.0488290\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(774\) 0 0
\(775\) 9.84407 6.83396i 0.353609 0.245483i
\(776\) 0 0
\(777\) −5.37335 + 22.5196i −0.192768 + 0.807885i
\(778\) 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 −0.983120 0.182964i \(-0.941431\pi\)
0.182964 + 0.983120i \(0.441431\pi\)
\(788\) 0 0
\(789\) 23.7144 0.844254
\(790\) 0 0
\(791\) 13.1909 8.10864i 0.469014 0.288310i
\(792\) 0 0
\(793\) 52.4941