Properties

Label 688.2.i.e.49.1
Level 688
Weight 2
Character 688.49
Analytic conductor 5.494
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 688.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.49370765906\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.1
Root \(0.809017 - 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 688.49
Dual form 688.2.i.e.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30902 + 2.26728i) q^{3} +(-0.618034 + 1.07047i) q^{5} +(-2.11803 - 3.66854i) q^{7} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\) \(q+(-1.30902 + 2.26728i) q^{3} +(-0.618034 + 1.07047i) q^{5} +(-2.11803 - 3.66854i) q^{7} +(-1.92705 - 3.33775i) q^{9} +3.61803 q^{11} +(-0.690983 - 1.19682i) q^{13} +(-1.61803 - 2.80252i) q^{15} +(-3.04508 - 5.27424i) q^{17} +(-0.618034 + 1.07047i) q^{19} +11.0902 q^{21} +(2.19098 - 3.79489i) q^{23} +(1.73607 + 3.00696i) q^{25} +2.23607 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-4.73607 + 8.20311i) q^{33} +5.23607 q^{35} +(2.42705 - 4.20378i) q^{37} +3.61803 q^{39} +9.47214 q^{41} +(6.50000 - 0.866025i) q^{43} +4.76393 q^{45} -1.14590 q^{47} +(-5.47214 + 9.47802i) q^{49} +15.9443 q^{51} +(0.690983 - 1.19682i) q^{53} +(-2.23607 + 3.87298i) q^{55} +(-1.61803 - 2.80252i) q^{57} -5.09017 q^{59} +(-1.42705 - 2.47172i) q^{61} +(-8.16312 + 14.1389i) q^{63} +1.70820 q^{65} +(-1.92705 + 3.33775i) q^{67} +(5.73607 + 9.93516i) q^{69} +(-5.39919 - 9.35167i) q^{71} +(-0.927051 - 1.60570i) q^{73} -9.09017 q^{75} +(-7.66312 - 13.2729i) q^{77} +(-0.690983 - 1.19682i) q^{79} +(2.85410 - 4.94345i) q^{81} +(8.01722 - 13.8862i) q^{83} +7.52786 q^{85} +7.85410 q^{87} +(0.927051 - 1.60570i) q^{89} +(-2.92705 + 5.06980i) q^{91} +(-0.763932 - 1.32317i) q^{95} -9.23607 q^{97} +(-6.97214 - 12.0761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + 10q^{11} - 5q^{13} - 2q^{15} - q^{17} + 2q^{19} + 22q^{21} + 11q^{23} - 2q^{25} - 6q^{29} - 10q^{33} + 12q^{35} + 3q^{37} + 10q^{39} + 20q^{41} + 26q^{43} + 28q^{45} - 18q^{47} - 4q^{49} + 28q^{51} + 5q^{53} - 2q^{57} + 2q^{59} + q^{61} - 17q^{63} - 20q^{65} - q^{67} + 14q^{69} + 3q^{71} + 3q^{73} - 14q^{75} - 15q^{77} - 5q^{79} - 2q^{81} + 3q^{83} + 48q^{85} + 18q^{87} - 3q^{89} - 5q^{91} - 12q^{95} - 28q^{97} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).

\(n\) \(431\) \(433\) \(517\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.30902 + 2.26728i −0.755761 + 1.30902i 0.189234 + 0.981932i \(0.439400\pi\)
−0.944995 + 0.327085i \(0.893934\pi\)
\(4\) 0 0
\(5\) −0.618034 + 1.07047i −0.276393 + 0.478727i −0.970486 0.241159i \(-0.922473\pi\)
0.694092 + 0.719886i \(0.255806\pi\)
\(6\) 0 0
\(7\) −2.11803 3.66854i −0.800542 1.38658i −0.919260 0.393651i \(-0.871212\pi\)
0.118718 0.992928i \(-0.462121\pi\)
\(8\) 0 0
\(9\) −1.92705 3.33775i −0.642350 1.11258i
\(10\) 0 0
\(11\) 3.61803 1.09088 0.545439 0.838150i \(-0.316363\pi\)
0.545439 + 0.838150i \(0.316363\pi\)
\(12\) 0 0
\(13\) −0.690983 1.19682i −0.191644 0.331937i 0.754151 0.656701i \(-0.228049\pi\)
−0.945795 + 0.324763i \(0.894715\pi\)
\(14\) 0 0
\(15\) −1.61803 2.80252i −0.417775 0.723607i
\(16\) 0 0
\(17\) −3.04508 5.27424i −0.738542 1.27919i −0.953152 0.302492i \(-0.902182\pi\)
0.214610 0.976700i \(-0.431152\pi\)
\(18\) 0 0
\(19\) −0.618034 + 1.07047i −0.141787 + 0.245582i −0.928170 0.372158i \(-0.878618\pi\)
0.786383 + 0.617740i \(0.211951\pi\)
\(20\) 0 0
\(21\) 11.0902 2.42007
\(22\) 0 0
\(23\) 2.19098 3.79489i 0.456852 0.791290i −0.541941 0.840417i \(-0.682310\pi\)
0.998793 + 0.0491264i \(0.0156437\pi\)
\(24\) 0 0
\(25\) 1.73607 + 3.00696i 0.347214 + 0.601392i
\(26\) 0 0
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0 0
\(33\) −4.73607 + 8.20311i −0.824444 + 1.42798i
\(34\) 0 0
\(35\) 5.23607 0.885057
\(36\) 0 0
\(37\) 2.42705 4.20378i 0.399005 0.691096i −0.594599 0.804023i \(-0.702689\pi\)
0.993603 + 0.112926i \(0.0360224\pi\)
\(38\) 0 0
\(39\) 3.61803 0.579349
\(40\) 0 0
\(41\) 9.47214 1.47930 0.739650 0.672992i \(-0.234991\pi\)
0.739650 + 0.672992i \(0.234991\pi\)
\(42\) 0 0
\(43\) 6.50000 0.866025i 0.991241 0.132068i
\(44\) 0 0
\(45\) 4.76393 0.710165
\(46\) 0 0
\(47\) −1.14590 −0.167146 −0.0835732 0.996502i \(-0.526633\pi\)
−0.0835732 + 0.996502i \(0.526633\pi\)
\(48\) 0 0
\(49\) −5.47214 + 9.47802i −0.781734 + 1.35400i
\(50\) 0 0
\(51\) 15.9443 2.23264
\(52\) 0 0
\(53\) 0.690983 1.19682i 0.0949138 0.164396i −0.814659 0.579941i \(-0.803076\pi\)
0.909573 + 0.415545i \(0.136409\pi\)
\(54\) 0 0
\(55\) −2.23607 + 3.87298i −0.301511 + 0.522233i
\(56\) 0 0
\(57\) −1.61803 2.80252i −0.214314 0.371202i
\(58\) 0 0
\(59\) −5.09017 −0.662684 −0.331342 0.943511i \(-0.607501\pi\)
−0.331342 + 0.943511i \(0.607501\pi\)
\(60\) 0 0
\(61\) −1.42705 2.47172i −0.182715 0.316472i 0.760089 0.649819i \(-0.225155\pi\)
−0.942804 + 0.333347i \(0.891822\pi\)
\(62\) 0 0
\(63\) −8.16312 + 14.1389i −1.02846 + 1.78134i
\(64\) 0 0
\(65\) 1.70820 0.211877
\(66\) 0 0
\(67\) −1.92705 + 3.33775i −0.235427 + 0.407771i −0.959397 0.282061i \(-0.908982\pi\)
0.723970 + 0.689832i \(0.242315\pi\)
\(68\) 0 0
\(69\) 5.73607 + 9.93516i 0.690541 + 1.19605i
\(70\) 0 0
\(71\) −5.39919 9.35167i −0.640766 1.10984i −0.985262 0.171051i \(-0.945284\pi\)
0.344497 0.938788i \(-0.388050\pi\)
\(72\) 0 0
\(73\) −0.927051 1.60570i −0.108503 0.187933i 0.806661 0.591015i \(-0.201272\pi\)
−0.915164 + 0.403082i \(0.867939\pi\)
\(74\) 0 0
\(75\) −9.09017 −1.04964
\(76\) 0 0
\(77\) −7.66312 13.2729i −0.873293 1.51259i
\(78\) 0 0
\(79\) −0.690983 1.19682i −0.0777417 0.134653i 0.824534 0.565813i \(-0.191438\pi\)
−0.902275 + 0.431161i \(0.858104\pi\)
\(80\) 0 0
\(81\) 2.85410 4.94345i 0.317122 0.549272i
\(82\) 0 0
\(83\) 8.01722 13.8862i 0.880004 1.52421i 0.0286698 0.999589i \(-0.490873\pi\)
0.851335 0.524623i \(-0.175794\pi\)
\(84\) 0 0
\(85\) 7.52786 0.816511
\(86\) 0 0
\(87\) 7.85410 0.842048
\(88\) 0 0
\(89\) 0.927051 1.60570i 0.0982672 0.170204i −0.812700 0.582682i \(-0.802003\pi\)
0.910968 + 0.412478i \(0.135337\pi\)
\(90\) 0 0
\(91\) −2.92705 + 5.06980i −0.306838 + 0.531460i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.763932 1.32317i −0.0783778 0.135754i
\(96\) 0 0
\(97\) −9.23607 −0.937781 −0.468890 0.883256i \(-0.655346\pi\)
−0.468890 + 0.883256i \(0.655346\pi\)
\(98\) 0 0
\(99\) −6.97214 12.0761i −0.700726 1.21369i
\(100\) 0 0
\(101\) −1.88197 3.25966i −0.187263 0.324348i 0.757074 0.653329i \(-0.226628\pi\)
−0.944337 + 0.328981i \(0.893295\pi\)
\(102\) 0 0
\(103\) −8.20820 14.2170i −0.808778 1.40085i −0.913710 0.406366i \(-0.866796\pi\)
0.104932 0.994479i \(-0.466537\pi\)
\(104\) 0 0
\(105\) −6.85410 + 11.8717i −0.668892 + 1.15855i
\(106\) 0 0
\(107\) −7.52786 −0.727746 −0.363873 0.931449i \(-0.618546\pi\)
−0.363873 + 0.931449i \(0.618546\pi\)
\(108\) 0 0
\(109\) 6.92705 11.9980i 0.663491 1.14920i −0.316201 0.948692i \(-0.602407\pi\)
0.979692 0.200508i \(-0.0642593\pi\)
\(110\) 0 0
\(111\) 6.35410 + 11.0056i 0.603105 + 1.04461i
\(112\) 0 0
\(113\) −15.6180 −1.46922 −0.734611 0.678489i \(-0.762635\pi\)
−0.734611 + 0.678489i \(0.762635\pi\)
\(114\) 0 0
\(115\) 2.70820 + 4.69075i 0.252541 + 0.437414i
\(116\) 0 0
\(117\) −2.66312 + 4.61266i −0.246205 + 0.426440i
\(118\) 0 0
\(119\) −12.8992 + 22.3420i −1.18247 + 2.04809i
\(120\) 0 0
\(121\) 2.09017 0.190015
\(122\) 0 0
\(123\) −12.3992 + 21.4760i −1.11800 + 1.93643i
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) 14.6525 1.30020 0.650098 0.759850i \(-0.274728\pi\)
0.650098 + 0.759850i \(0.274728\pi\)
\(128\) 0 0
\(129\) −6.54508 + 15.8710i −0.576263 + 1.39736i
\(130\) 0 0
\(131\) −9.94427 −0.868835 −0.434418 0.900712i \(-0.643046\pi\)
−0.434418 + 0.900712i \(0.643046\pi\)
\(132\) 0 0
\(133\) 5.23607 0.454025
\(134\) 0 0
\(135\) −1.38197 + 2.39364i −0.118941 + 0.206011i
\(136\) 0 0
\(137\) 3.70820 0.316813 0.158407 0.987374i \(-0.449364\pi\)
0.158407 + 0.987374i \(0.449364\pi\)
\(138\) 0 0
\(139\) −2.64590 + 4.58283i −0.224422 + 0.388711i −0.956146 0.292891i \(-0.905383\pi\)
0.731724 + 0.681601i \(0.238716\pi\)
\(140\) 0 0
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) 0 0
\(143\) −2.50000 4.33013i −0.209061 0.362103i
\(144\) 0 0
\(145\) 3.70820 0.307950
\(146\) 0 0
\(147\) −14.3262 24.8138i −1.18161 2.04661i
\(148\) 0 0
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 0 0
\(151\) 8.85410 0.720537 0.360268 0.932849i \(-0.382685\pi\)
0.360268 + 0.932849i \(0.382685\pi\)
\(152\) 0 0
\(153\) −11.7361 + 20.3275i −0.948805 + 1.64338i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.57295 + 4.45648i 0.205344 + 0.355666i 0.950242 0.311512i \(-0.100835\pi\)
−0.744898 + 0.667178i \(0.767502\pi\)
\(158\) 0 0
\(159\) 1.80902 + 3.13331i 0.143464 + 0.248488i
\(160\) 0 0
\(161\) −18.5623 −1.46291
\(162\) 0 0
\(163\) 7.00000 + 12.1244i 0.548282 + 0.949653i 0.998392 + 0.0566798i \(0.0180514\pi\)
−0.450110 + 0.892973i \(0.648615\pi\)
\(164\) 0 0
\(165\) −5.85410 10.1396i −0.455741 0.789367i
\(166\) 0 0
\(167\) 7.11803 12.3288i 0.550810 0.954031i −0.447406 0.894331i \(-0.647652\pi\)
0.998216 0.0597001i \(-0.0190144\pi\)
\(168\) 0 0
\(169\) 5.54508 9.60437i 0.426545 0.738798i
\(170\) 0 0
\(171\) 4.76393 0.364307
\(172\) 0 0
\(173\) −3.76393 −0.286166 −0.143083 0.989711i \(-0.545702\pi\)
−0.143083 + 0.989711i \(0.545702\pi\)
\(174\) 0 0
\(175\) 7.35410 12.7377i 0.555918 0.962878i
\(176\) 0 0
\(177\) 6.66312 11.5409i 0.500831 0.867464i
\(178\) 0 0
\(179\) 4.82624 + 8.35929i 0.360730 + 0.624803i 0.988081 0.153934i \(-0.0491943\pi\)
−0.627351 + 0.778736i \(0.715861\pi\)
\(180\) 0 0
\(181\) 9.69098 + 16.7853i 0.720325 + 1.24764i 0.960869 + 0.277002i \(0.0893407\pi\)
−0.240544 + 0.970638i \(0.577326\pi\)
\(182\) 0 0
\(183\) 7.47214 0.552356
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) −11.0172 19.0824i −0.805659 1.39544i
\(188\) 0 0
\(189\) −4.73607 8.20311i −0.344498 0.596688i
\(190\) 0 0
\(191\) −7.26393 + 12.5815i −0.525600 + 0.910365i 0.473956 + 0.880549i \(0.342826\pi\)
−0.999555 + 0.0298167i \(0.990508\pi\)
\(192\) 0 0
\(193\) 2.70820 0.194941 0.0974704 0.995238i \(-0.468925\pi\)
0.0974704 + 0.995238i \(0.468925\pi\)
\(194\) 0 0
\(195\) −2.23607 + 3.87298i −0.160128 + 0.277350i
\(196\) 0 0
\(197\) 1.47214 + 2.54981i 0.104885 + 0.181667i 0.913691 0.406409i \(-0.133219\pi\)
−0.808806 + 0.588076i \(0.799886\pi\)
\(198\) 0 0
\(199\) −1.94427 −0.137826 −0.0689129 0.997623i \(-0.521953\pi\)
−0.0689129 + 0.997623i \(0.521953\pi\)
\(200\) 0 0
\(201\) −5.04508 8.73834i −0.355853 0.616355i
\(202\) 0 0
\(203\) −6.35410 + 11.0056i −0.445971 + 0.772444i
\(204\) 0 0
\(205\) −5.85410 + 10.1396i −0.408868 + 0.708181i
\(206\) 0 0
\(207\) −16.8885 −1.17383
\(208\) 0 0
\(209\) −2.23607 + 3.87298i −0.154672 + 0.267900i
\(210\) 0 0
\(211\) 9.23607 0.635837 0.317919 0.948118i \(-0.397016\pi\)
0.317919 + 0.948118i \(0.397016\pi\)
\(212\) 0 0
\(213\) 28.2705 1.93706
\(214\) 0 0
\(215\) −3.09017 + 7.49326i −0.210748 + 0.511036i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.85410 0.328010
\(220\) 0 0
\(221\) −4.20820 + 7.28882i −0.283074 + 0.490299i
\(222\) 0 0
\(223\) −2.76393 −0.185087 −0.0925433 0.995709i \(-0.529500\pi\)
−0.0925433 + 0.995709i \(0.529500\pi\)
\(224\) 0 0
\(225\) 6.69098 11.5891i 0.446066 0.772608i
\(226\) 0 0
\(227\) −0.736068 + 1.27491i −0.0488545 + 0.0846186i −0.889419 0.457094i \(-0.848890\pi\)
0.840564 + 0.541712i \(0.182224\pi\)
\(228\) 0 0
\(229\) 1.14590 + 1.98475i 0.0757231 + 0.131156i 0.901400 0.432986i \(-0.142540\pi\)
−0.825677 + 0.564143i \(0.809207\pi\)
\(230\) 0 0
\(231\) 40.1246 2.64001
\(232\) 0 0
\(233\) −9.01722 15.6183i −0.590738 1.02319i −0.994133 0.108162i \(-0.965503\pi\)
0.403395 0.915026i \(-0.367830\pi\)
\(234\) 0 0
\(235\) 0.708204 1.22665i 0.0461981 0.0800175i
\(236\) 0 0
\(237\) 3.61803 0.235017
\(238\) 0 0
\(239\) −4.14590 + 7.18091i −0.268176 + 0.464494i −0.968391 0.249438i \(-0.919754\pi\)
0.700215 + 0.713932i \(0.253087\pi\)
\(240\) 0 0
\(241\) −2.13525 3.69837i −0.137544 0.238233i 0.789022 0.614364i \(-0.210587\pi\)
−0.926566 + 0.376131i \(0.877254\pi\)
\(242\) 0 0
\(243\) 10.8262 + 18.7516i 0.694503 + 1.20292i
\(244\) 0 0
\(245\) −6.76393 11.7155i −0.432132 0.748474i
\(246\) 0 0
\(247\) 1.70820 0.108690
\(248\) 0 0
\(249\) 20.9894 + 36.3546i 1.33015 + 2.30388i
\(250\) 0 0
\(251\) −14.5902 25.2709i −0.920923 1.59509i −0.797990 0.602671i \(-0.794103\pi\)
−0.122934 0.992415i \(-0.539230\pi\)
\(252\) 0 0
\(253\) 7.92705 13.7301i 0.498369 0.863201i
\(254\) 0 0
\(255\) −9.85410 + 17.0678i −0.617088 + 1.06883i
\(256\) 0 0
\(257\) 3.43769 0.214437 0.107219 0.994235i \(-0.465805\pi\)
0.107219 + 0.994235i \(0.465805\pi\)
\(258\) 0 0
\(259\) −20.5623 −1.27768
\(260\) 0 0
\(261\) −5.78115 + 10.0133i −0.357844 + 0.619805i
\(262\) 0 0
\(263\) 13.7533 23.8214i 0.848064 1.46889i −0.0348693 0.999392i \(-0.511101\pi\)
0.882933 0.469498i \(-0.155565\pi\)
\(264\) 0 0
\(265\) 0.854102 + 1.47935i 0.0524671 + 0.0908756i
\(266\) 0 0
\(267\) 2.42705 + 4.20378i 0.148533 + 0.257267i
\(268\) 0 0
\(269\) 11.5623 0.704966 0.352483 0.935818i \(-0.385337\pi\)
0.352483 + 0.935818i \(0.385337\pi\)
\(270\) 0 0
\(271\) 6.92705 + 11.9980i 0.420788 + 0.728827i 0.996017 0.0891660i \(-0.0284202\pi\)
−0.575228 + 0.817993i \(0.695087\pi\)
\(272\) 0 0
\(273\) −7.66312 13.2729i −0.463793 0.803313i
\(274\) 0 0
\(275\) 6.28115 + 10.8793i 0.378768 + 0.656045i
\(276\) 0 0
\(277\) 6.23607 10.8012i 0.374689 0.648980i −0.615591 0.788065i \(-0.711083\pi\)
0.990280 + 0.139085i \(0.0444161\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.73607 + 6.47106i −0.222875 + 0.386031i −0.955680 0.294408i \(-0.904878\pi\)
0.732805 + 0.680439i \(0.238211\pi\)
\(282\) 0 0
\(283\) 5.38197 + 9.32184i 0.319925 + 0.554126i 0.980472 0.196659i \(-0.0630091\pi\)
−0.660547 + 0.750784i \(0.729676\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) −20.0623 34.7489i −1.18424 2.05116i
\(288\) 0 0
\(289\) −10.0451 + 17.3986i −0.590887 + 1.02345i
\(290\) 0 0
\(291\) 12.0902 20.9408i 0.708738 1.22757i
\(292\) 0 0
\(293\) −12.0902 −0.706315 −0.353158 0.935564i \(-0.614892\pi\)
−0.353158 + 0.935564i \(0.614892\pi\)
\(294\) 0 0
\(295\) 3.14590 5.44886i 0.183161 0.317245i
\(296\) 0 0
\(297\) 8.09017 0.469439
\(298\) 0 0
\(299\) −6.05573 −0.350212
\(300\) 0 0
\(301\) −16.9443 22.0113i −0.976652 1.26871i
\(302\) 0 0
\(303\) 9.85410 0.566103
\(304\) 0 0
\(305\) 3.52786 0.202005
\(306\) 0 0
\(307\) −11.6074 + 20.1046i −0.662469 + 1.14743i 0.317496 + 0.948260i \(0.397158\pi\)
−0.979965 + 0.199170i \(0.936175\pi\)
\(308\) 0 0
\(309\) 42.9787 2.44497
\(310\) 0 0
\(311\) −14.9164 + 25.8360i −0.845832 + 1.46502i 0.0390649 + 0.999237i \(0.487562\pi\)
−0.884897 + 0.465787i \(0.845771\pi\)
\(312\) 0 0
\(313\) −6.56231 + 11.3662i −0.370923 + 0.642458i −0.989708 0.143103i \(-0.954292\pi\)
0.618784 + 0.785561i \(0.287625\pi\)
\(314\) 0 0
\(315\) −10.0902 17.4767i −0.568517 0.984700i
\(316\) 0 0
\(317\) 33.3050 1.87059 0.935296 0.353866i \(-0.115133\pi\)
0.935296 + 0.353866i \(0.115133\pi\)
\(318\) 0 0
\(319\) −5.42705 9.39993i −0.303857 0.526295i
\(320\) 0 0
\(321\) 9.85410 17.0678i 0.550002 0.952632i
\(322\) 0 0
\(323\) 7.52786 0.418862
\(324\) 0 0
\(325\) 2.39919 4.15551i 0.133083 0.230506i
\(326\) 0 0
\(327\) 18.1353 + 31.4112i 1.00288 + 1.73704i
\(328\) 0 0
\(329\) 2.42705 + 4.20378i 0.133808 + 0.231762i
\(330\) 0 0
\(331\) −2.73607 4.73901i −0.150388 0.260479i 0.780982 0.624553i \(-0.214719\pi\)
−0.931370 + 0.364074i \(0.881386\pi\)
\(332\) 0 0
\(333\) −18.7082 −1.02520
\(334\) 0 0
\(335\) −2.38197 4.12569i −0.130141 0.225410i
\(336\) 0 0
\(337\) −14.0000 24.2487i −0.762629 1.32091i −0.941491 0.337037i \(-0.890575\pi\)
0.178863 0.983874i \(-0.442758\pi\)
\(338\) 0 0
\(339\) 20.4443 35.4105i 1.11038 1.92324i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 16.7082 0.902158
\(344\) 0 0
\(345\) −14.1803 −0.763444
\(346\) 0 0
\(347\) 5.04508 8.73834i 0.270834 0.469099i −0.698241 0.715862i \(-0.746034\pi\)
0.969076 + 0.246764i \(0.0793671\pi\)
\(348\) 0 0
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) 0 0
\(351\) −1.54508 2.67617i −0.0824705 0.142843i
\(352\) 0 0
\(353\) 8.61803 + 14.9269i 0.458692 + 0.794477i 0.998892 0.0470591i \(-0.0149849\pi\)
−0.540200 + 0.841536i \(0.681652\pi\)
\(354\) 0 0
\(355\) 13.3475 0.708413
\(356\) 0 0
\(357\) −33.7705 58.4922i −1.78732 3.09574i
\(358\) 0 0
\(359\) −2.67376 4.63109i −0.141116 0.244420i 0.786801 0.617206i \(-0.211736\pi\)
−0.927917 + 0.372787i \(0.878402\pi\)
\(360\) 0 0
\(361\) 8.73607 + 15.1313i 0.459793 + 0.796385i
\(362\) 0 0
\(363\) −2.73607 + 4.73901i −0.143606 + 0.248733i
\(364\) 0 0
\(365\) 2.29180 0.119958
\(366\) 0 0
\(367\) 9.59017 16.6107i 0.500603 0.867069i −0.499397 0.866373i \(-0.666445\pi\)
1.00000 0.000696189i \(-0.000221604\pi\)
\(368\) 0 0
\(369\) −18.2533 31.6156i −0.950228 1.64584i
\(370\) 0 0
\(371\) −5.85410 −0.303930
\(372\) 0 0
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 0 0
\(375\) 13.7082 23.7433i 0.707889 1.22610i
\(376\) 0 0
\(377\) −2.07295 + 3.59045i −0.106762 + 0.184918i
\(378\) 0 0
\(379\) 27.3607 1.40542 0.702712 0.711475i \(-0.251972\pi\)
0.702712 + 0.711475i \(0.251972\pi\)
\(380\) 0 0
\(381\) −19.1803 + 33.2213i −0.982639 + 1.70198i
\(382\) 0 0
\(383\) −38.1246 −1.94808 −0.974038 0.226383i \(-0.927310\pi\)
−0.974038 + 0.226383i \(0.927310\pi\)
\(384\) 0 0
\(385\) 18.9443 0.965489
\(386\) 0 0
\(387\) −15.4164 20.0265i −0.783660 1.01800i
\(388\) 0 0
\(389\) −35.0689 −1.77806 −0.889031 0.457846i \(-0.848621\pi\)
−0.889031 + 0.457846i \(0.848621\pi\)
\(390\) 0 0
\(391\) −26.6869 −1.34962
\(392\) 0 0
\(393\) 13.0172 22.5465i 0.656632 1.13732i
\(394\) 0 0
\(395\) 1.70820 0.0859491
\(396\) 0 0
\(397\) −16.2082 + 28.0734i −0.813466 + 1.40897i 0.0969574 + 0.995289i \(0.469089\pi\)
−0.910424 + 0.413677i \(0.864244\pi\)
\(398\) 0 0
\(399\) −6.85410 + 11.8717i −0.343134 + 0.594326i
\(400\) 0 0
\(401\) 12.7082 + 22.0113i 0.634617 + 1.09919i 0.986596 + 0.163182i \(0.0521756\pi\)
−0.351979 + 0.936008i \(0.614491\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 3.52786 + 6.11044i 0.175301 + 0.303630i
\(406\) 0 0
\(407\) 8.78115 15.2094i 0.435266 0.753902i
\(408\) 0 0
\(409\) 8.90983 0.440563 0.220281 0.975436i \(-0.429302\pi\)
0.220281 + 0.975436i \(0.429302\pi\)
\(410\) 0 0
\(411\) −4.85410 + 8.40755i −0.239435 + 0.414714i
\(412\) 0 0
\(413\) 10.7812 + 18.6735i 0.530506 + 0.918863i
\(414\) 0 0
\(415\) 9.90983 + 17.1643i 0.486454 + 0.842564i
\(416\) 0 0
\(417\) −6.92705 11.9980i −0.339219 0.587545i
\(418\) 0 0
\(419\) 10.2361 0.500065 0.250032 0.968237i \(-0.419559\pi\)
0.250032 + 0.968237i \(0.419559\pi\)
\(420\) 0 0
\(421\) 3.82624 + 6.62724i 0.186479 + 0.322992i 0.944074 0.329734i \(-0.106959\pi\)
−0.757595 + 0.652725i \(0.773626\pi\)
\(422\) 0 0
\(423\) 2.20820 + 3.82472i 0.107367 + 0.185964i
\(424\) 0 0
\(425\) 10.5729 18.3129i 0.512863 0.888305i
\(426\) 0 0
\(427\) −6.04508 + 10.4704i −0.292542 + 0.506698i
\(428\) 0 0
\(429\) 13.0902 0.631999
\(430\) 0 0
\(431\) 24.7984 1.19450 0.597248 0.802057i \(-0.296261\pi\)
0.597248 + 0.802057i \(0.296261\pi\)
\(432\) 0 0
\(433\) 17.3541 30.0582i 0.833985 1.44450i −0.0608693 0.998146i \(-0.519387\pi\)
0.894854 0.446359i \(-0.147279\pi\)
\(434\) 0 0
\(435\) −4.85410 + 8.40755i −0.232736 + 0.403111i
\(436\) 0 0
\(437\) 2.70820 + 4.69075i 0.129551 + 0.224389i
\(438\) 0 0
\(439\) 0.572949 + 0.992377i 0.0273454 + 0.0473636i 0.879374 0.476131i \(-0.157961\pi\)
−0.852029 + 0.523495i \(0.824628\pi\)
\(440\) 0 0
\(441\) 42.1803 2.00859
\(442\) 0 0
\(443\) 1.23607 + 2.14093i 0.0587274 + 0.101719i 0.893894 0.448278i \(-0.147962\pi\)
−0.835167 + 0.549996i \(0.814629\pi\)
\(444\) 0 0
\(445\) 1.14590 + 1.98475i 0.0543208 + 0.0940863i
\(446\) 0 0
\(447\) −11.7812 20.4056i −0.557229 0.965150i
\(448\) 0 0
\(449\) 16.4164 28.4341i 0.774738 1.34189i −0.160203 0.987084i \(-0.551215\pi\)
0.934942 0.354802i \(-0.115452\pi\)
\(450\) 0 0
\(451\) 34.2705 1.61374
\(452\) 0 0
\(453\) −11.5902 + 20.0748i −0.544554 + 0.943195i
\(454\) 0 0
\(455\) −3.61803 6.26662i −0.169616 0.293784i
\(456\) 0 0
\(457\) −15.7082 −0.734799 −0.367399 0.930063i \(-0.619752\pi\)
−0.367399 + 0.930063i \(0.619752\pi\)
\(458\) 0 0
\(459\) −6.80902 11.7936i −0.317818 0.550476i
\(460\) 0 0
\(461\) 15.7984 27.3636i 0.735804 1.27445i −0.218566 0.975822i \(-0.570138\pi\)
0.954370 0.298627i \(-0.0965287\pi\)
\(462\) 0 0
\(463\) −14.9164 + 25.8360i −0.693224 + 1.20070i 0.277551 + 0.960711i \(0.410477\pi\)
−0.970776 + 0.239989i \(0.922856\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.52786 + 13.0386i −0.348348 + 0.603356i −0.985956 0.167004i \(-0.946591\pi\)
0.637608 + 0.770361i \(0.279924\pi\)
\(468\) 0 0
\(469\) 16.3262 0.753876
\(470\) 0 0
\(471\) −13.4721 −0.620763
\(472\) 0 0
\(473\) 23.5172 3.13331i 1.08132 0.144070i
\(474\) 0 0
\(475\) −4.29180 −0.196921
\(476\) 0 0
\(477\) −5.32624 −0.243872
\(478\) 0 0
\(479\) −6.90983 + 11.9682i −0.315718 + 0.546840i −0.979590 0.201007i \(-0.935579\pi\)
0.663872 + 0.747846i \(0.268912\pi\)
\(480\) 0 0
\(481\) −6.70820 −0.305868
\(482\) 0 0
\(483\) 24.2984 42.0860i 1.10561 1.91498i
\(484\) 0 0
\(485\) 5.70820 9.88690i 0.259196 0.448941i
\(486\) 0 0
\(487\) 0.663119 + 1.14856i 0.0300488 + 0.0520460i 0.880659 0.473751i \(-0.157100\pi\)
−0.850610 + 0.525797i \(0.823767\pi\)
\(488\) 0 0
\(489\) −36.6525 −1.65748
\(490\) 0 0
\(491\) 10.8262 + 18.7516i 0.488581 + 0.846248i 0.999914 0.0131354i \(-0.00418125\pi\)
−0.511332 + 0.859383i \(0.670848\pi\)
\(492\) 0 0
\(493\) −9.13525 + 15.8227i −0.411431 + 0.712620i
\(494\) 0 0
\(495\) 17.2361 0.774704
\(496\) 0 0
\(497\) −22.8713 + 39.6143i −1.02592 + 1.77694i
\(498\) 0 0
\(499\) 6.92705 + 11.9980i 0.310097 + 0.537104i 0.978383 0.206800i \(-0.0663050\pi\)
−0.668286 + 0.743905i \(0.732972\pi\)
\(500\) 0 0
\(501\) 18.6353 + 32.2772i 0.832562 + 1.44204i
\(502\) 0 0
\(503\) −6.73607 11.6672i −0.300346 0.520215i 0.675868 0.737023i \(-0.263769\pi\)
−0.976214 + 0.216807i \(0.930436\pi\)
\(504\) 0 0
\(505\) 4.65248 0.207032
\(506\) 0 0
\(507\) 14.5172 + 25.1446i 0.644732 + 1.11671i
\(508\) 0 0
\(509\) −9.35410 16.2018i −0.414613 0.718131i 0.580774 0.814064i \(-0.302750\pi\)
−0.995388 + 0.0959332i \(0.969416\pi\)
\(510\) 0 0
\(511\) −3.92705 + 6.80185i −0.173723 + 0.300896i
\(512\) 0 0
\(513\) −1.38197 + 2.39364i −0.0610153 + 0.105682i
\(514\) 0 0
\(515\) 20.2918 0.894163
\(516\) 0 0
\(517\) −4.14590 −0.182336
\(518\) 0 0
\(519\) 4.92705 8.53390i 0.216274 0.374597i
\(520\) 0 0
\(521\) 11.0172 19.0824i 0.482673 0.836015i −0.517129 0.855908i \(-0.672999\pi\)
0.999802 + 0.0198930i \(0.00633256\pi\)
\(522\) 0 0
\(523\) 17.9164 + 31.0321i 0.783430 + 1.35694i 0.929933 + 0.367730i \(0.119865\pi\)
−0.146503 + 0.989210i \(0.546802\pi\)
\(524\) 0 0
\(525\) 19.2533 + 33.3477i 0.840282 + 1.45541i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.89919 + 3.28949i 0.0825733 + 0.143021i
\(530\) 0 0
\(531\) 9.80902 + 16.9897i 0.425675 + 0.737291i
\(532\) 0 0
\(533\) −6.54508 11.3364i −0.283499 0.491035i
\(534\) 0 0
\(535\) 4.65248 8.05832i 0.201144 0.348392i
\(536\) 0 0
\(537\) −25.2705 −1.09050
\(538\) 0 0
\(539\) −19.7984 + 34.2918i −0.852776 + 1.47705i
\(540\) 0 0
\(541\) 18.9721 + 32.8607i 0.815676 + 1.41279i 0.908842 + 0.417141i \(0.136968\pi\)
−0.0931658 + 0.995651i \(0.529699\pi\)
\(542\) 0 0
\(543\) −50.7426 −2.17758
\(544\) 0 0
\(545\) 8.56231 + 14.8303i 0.366769 + 0.635262i
\(546\) 0 0
\(547\) 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i \(-0.685132\pi\)
0.998318 + 0.0579790i \(0.0184657\pi\)
\(548\) 0 0
\(549\) −5.50000 + 9.52628i −0.234734 + 0.406572i
\(550\) 0 0
\(551\) 3.70820 0.157975
\(552\) 0 0
\(553\) −2.92705 + 5.06980i −0.124471 + 0.215590i
\(554\) 0 0
\(555\) −15.7082 −0.666776
\(556\) 0 0
\(557\) −38.5623 −1.63394 −0.816969 0.576682i \(-0.804347\pi\)
−0.816969 + 0.576682i \(0.804347\pi\)
\(558\) 0 0
\(559\) −5.52786 7.18091i −0.233804 0.303720i
\(560\) 0 0
\(561\) 57.6869 2.43554
\(562\) 0 0
\(563\) 1.32624 0.0558943 0.0279471 0.999609i \(-0.491103\pi\)
0.0279471 + 0.999609i \(0.491103\pi\)
\(564\) 0 0
\(565\) 9.65248 16.7186i 0.406083 0.703356i
\(566\) 0 0
\(567\) −24.1803 −1.01548
\(568\) 0 0
\(569\) 12.9721 22.4684i 0.543820 0.941924i −0.454860 0.890563i \(-0.650311\pi\)
0.998680 0.0513613i \(-0.0163560\pi\)
\(570\) 0 0
\(571\) −21.5902 + 37.3953i −0.903520 + 1.56494i −0.0806295 + 0.996744i \(0.525693\pi\)
−0.822891 + 0.568199i \(0.807640\pi\)
\(572\) 0 0
\(573\) −19.0172 32.9388i −0.794456 1.37604i
\(574\) 0 0
\(575\) 15.2148 0.634500
\(576\) 0 0
\(577\) 14.1074 + 24.4347i 0.587298 + 1.01723i 0.994585 + 0.103930i \(0.0331418\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(578\) 0 0
\(579\) −3.54508 + 6.14027i −0.147329 + 0.255181i
\(580\) 0 0
\(581\) −67.9230 −2.81792
\(582\) 0 0
\(583\) 2.50000 4.33013i 0.103539 0.179336i
\(584\) 0 0
\(585\) −3.29180 5.70156i −0.136099 0.235730i
\(586\) 0 0
\(587\) 7.87132 + 13.6335i 0.324884 + 0.562716i 0.981489 0.191519i \(-0.0613413\pi\)
−0.656605 + 0.754235i \(0.728008\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −7.70820 −0.317073
\(592\) 0 0
\(593\) 15.2361 + 26.3896i 0.625670 + 1.08369i 0.988411 + 0.151803i \(0.0485078\pi\)
−0.362741 + 0.931890i \(0.618159\pi\)
\(594\) 0 0
\(595\) −15.9443 27.6163i −0.653651 1.13216i
\(596\) 0 0
\(597\) 2.54508 4.40822i 0.104163 0.180416i
\(598\) 0 0
\(599\) 18.1180 31.3814i 0.740283 1.28221i −0.212084 0.977252i \(-0.568025\pi\)
0.952366 0.304956i \(-0.0986417\pi\)
\(600\) 0 0
\(601\) 29.4164 1.19992 0.599960 0.800030i \(-0.295183\pi\)
0.599960 + 0.800030i \(0.295183\pi\)
\(602\) 0 0
\(603\) 14.8541 0.604906
\(604\) 0 0
\(605\) −1.29180 + 2.23746i −0.0525190 + 0.0909655i
\(606\) 0 0
\(607\) −11.9271 + 20.6583i −0.484104 + 0.838493i −0.999833 0.0182588i \(-0.994188\pi\)
0.515729 + 0.856752i \(0.327521\pi\)
\(608\) 0 0
\(609\) −16.6353 28.8131i −0.674095 1.16757i
\(610\) 0 0
\(611\) 0.791796 + 1.37143i 0.0320326 + 0.0554822i
\(612\) 0 0
\(613\) 5.20163 0.210092 0.105046 0.994467i \(-0.466501\pi\)
0.105046 + 0.994467i \(0.466501\pi\)
\(614\) 0 0
\(615\) −15.3262 26.5458i −0.618014 1.07043i
\(616\) 0 0
\(617\) −4.85410 8.40755i −0.195419 0.338475i 0.751619 0.659598i \(-0.229273\pi\)
−0.947038 + 0.321122i \(0.895940\pi\)
\(618\) 0 0
\(619\) −15.1353 26.2150i −0.608337 1.05367i −0.991514 0.129996i \(-0.958503\pi\)
0.383177 0.923675i \(-0.374830\pi\)
\(620\) 0 0
\(621\) 4.89919 8.48564i 0.196598 0.340517i
\(622\) 0 0
\(623\) −7.85410 −0.314668
\(624\) 0 0
\(625\) −2.20820 + 3.82472i −0.0883282 + 0.152989i
\(626\) 0 0
\(627\) −5.85410 10.1396i −0.233790 0.404937i
\(628\) 0 0
\(629\) −29.5623 −1.17873
\(630\) 0 0
\(631\) −13.5451 23.4608i −0.539221 0.933959i −0.998946 0.0458973i \(-0.985385\pi\)
0.459725 0.888061i \(-0.347948\pi\)
\(632\) 0 0
\(633\) −12.0902 + 20.9408i −0.480541 + 0.832322i
\(634\) 0 0
\(635\) −9.05573 + 15.6850i −0.359366 + 0.622439i
\(636\) 0 0
\(637\) 15.1246 0.599259
\(638\) 0 0
\(639\) −20.8090 + 36.0423i −0.823192 + 1.42581i
\(640\) 0 0
\(641\) 10.8197 0.427351 0.213675 0.976905i \(-0.431457\pi\)
0.213675 + 0.976905i \(0.431457\pi\)
\(642\) 0 0
\(643\) −9.43769 −0.372186 −0.186093 0.982532i \(-0.559583\pi\)
−0.186093 + 0.982532i \(0.559583\pi\)
\(644\) 0 0
\(645\) −12.9443 16.8151i −0.509680 0.662094i
\(646\) 0 0
\(647\) 21.6738 0.852084 0.426042 0.904703i \(-0.359908\pi\)
0.426042 + 0.904703i \(0.359908\pi\)
\(648\) 0 0
\(649\) −18.4164 −0.722907
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −32.8885 −1.28703 −0.643514 0.765434i \(-0.722524\pi\)
−0.643514 + 0.765434i \(0.722524\pi\)
\(654\) 0 0
\(655\) 6.14590 10.6450i 0.240140 0.415935i
\(656\) 0 0
\(657\) −3.57295 + 6.18853i −0.139394 + 0.241438i
\(658\) 0 0
\(659\) −14.6803 25.4271i −0.571865 0.990499i −0.996375 0.0850756i \(-0.972887\pi\)
0.424510 0.905423i \(-0.360447\pi\)
\(660\) 0 0
\(661\) −43.3951 −1.68787 −0.843937 0.536442i \(-0.819768\pi\)
−0.843937 + 0.536442i \(0.819768\pi\)
\(662\) 0 0
\(663\) −11.0172 19.0824i −0.427873 0.741098i
\(664\) 0 0
\(665\) −3.23607 + 5.60503i −0.125489 + 0.217354i
\(666\) 0 0
\(667\) −13.1459 −0.509011
\(668\) 0 0
\(669\) 3.61803 6.26662i 0.139881 0.242281i
\(670\) 0 0
\(671\) −5.16312 8.94278i −0.199320 0.345232i
\(672\) 0 0
\(673\) −6.91641 11.9796i −0.266608 0.461778i 0.701376 0.712792i \(-0.252570\pi\)
−0.967984 + 0.251013i \(0.919236\pi\)
\(674\) 0 0
\(675\) 3.88197 + 6.72376i 0.149417 + 0.258798i
\(676\) 0 0
\(677\) −31.7639 −1.22079 −0.610394 0.792098i \(-0.708989\pi\)
−0.610394 + 0.792098i \(0.708989\pi\)
\(678\) 0 0
\(679\) 19.5623 + 33.8829i 0.750732 + 1.30031i
\(680\) 0 0
\(681\) −1.92705 3.33775i −0.0738448 0.127903i
\(682\) 0 0
\(683\) −5.56231 + 9.63420i −0.212836 + 0.368642i −0.952601 0.304223i \(-0.901603\pi\)
0.739765 + 0.672865i \(0.234937\pi\)
\(684\) 0 0
\(685\) −2.29180 + 3.96951i −0.0875650 + 0.151667i
\(686\) 0 0
\(687\) −6.00000 −0.228914
\(688\) 0 0
\(689\) −1.90983 −0.0727587
\(690\) 0 0
\(691\) 7.86475 13.6221i 0.299189 0.518211i −0.676762 0.736202i \(-0.736617\pi\)
0.975951 + 0.217992i \(0.0699506\pi\)
\(692\) 0 0
\(693\) −29.5344 + 51.1552i −1.12192 + 1.94322i
\(694\) 0 0
\(695\) −3.27051 5.66469i −0.124058 0.214874i
\(696\) 0 0
\(697\) −28.8435 49.9583i −1.09252 1.89231i
\(698\) 0 0
\(699\) 47.2148 1.78583
\(700\) 0 0
\(701\) 7.25329 + 12.5631i 0.273953 + 0.474500i 0.969870 0.243621i \(-0.0783354\pi\)
−0.695917 + 0.718122i \(0.745002\pi\)
\(702\) 0 0
\(703\) 3.00000 + 5.19615i 0.113147 + 0.195977i
\(704\) 0 0
\(705\) 1.85410 + 3.21140i 0.0698295 + 0.120948i
\(706\) 0 0
\(707\) −7.97214 + 13.8081i −0.299823 + 0.519309i
\(708\) 0 0
\(709\) 28.8885 1.08493 0.542466 0.840078i \(-0.317491\pi\)
0.542466 + 0.840078i \(0.317491\pi\)
\(710\) 0 0
\(711\) −2.66312 + 4.61266i −0.0998748 + 0.172988i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 6.18034 0.231132
\(716\) 0 0
\(717\) −10.8541 18.7999i −0.405354 0.702093i
\(718\) 0 0
\(719\) −5.39919 + 9.35167i −0.201356 + 0.348758i −0.948965 0.315380i \(-0.897868\pi\)
0.747610 + 0.664138i \(0.231201\pi\)
\(720\) 0 0
\(721\) −34.7705 + 60.2243i −1.29492 + 2.24287i
\(722\) 0 0
\(723\) 11.1803 0.415801
\(724\) 0 0
\(725\) 5.20820 9.02087i 0.193428 0.335027i
\(726\) 0 0
\(727\) 17.9787 0.666794 0.333397 0.942787i \(-0.391805\pi\)
0.333397 + 0.942787i \(0.391805\pi\)
\(728\) 0 0
\(729\) −39.5623 −1.46527
\(730\) 0 0
\(731\) −24.3607 31.6455i −0.901012 1.17045i
\(732\) 0 0
\(733\) 24.5410 0.906443 0.453222 0.891398i \(-0.350275\pi\)
0.453222 + 0.891398i \(0.350275\pi\)
\(734\) 0 0
\(735\) 35.4164 1.30635
\(736\) 0 0
\(737\) −6.97214 + 12.0761i −0.256822 + 0.444829i
\(738\) 0 0
\(739\) −49.5410 −1.82240 −0.911198 0.411969i \(-0.864841\pi\)
−0.911198 + 0.411969i \(0.864841\pi\)
\(740\) 0 0
\(741\) −2.23607 + 3.87298i −0.0821440 + 0.142278i
\(742\) 0 0
\(743\) 16.6803 28.8912i 0.611942 1.05992i −0.378970 0.925409i \(-0.623722\pi\)
0.990913 0.134506i \(-0.0429449\pi\)
\(744\) 0 0
\(745\) −5.56231 9.63420i −0.203787 0.352970i
\(746\) 0 0
\(747\) −61.7984 −2.26108
\(748\) 0 0
\(749\) 15.9443 + 27.6163i 0.582591 + 1.00908i
\(750\) 0 0
\(751\) −18.9894 + 32.8905i −0.692931 + 1.20019i 0.277942 + 0.960598i \(0.410348\pi\)
−0.970873 + 0.239595i \(0.922985\pi\)
\(752\) 0 0
\(753\) 76.3951 2.78399
\(754\) 0 0
\(755\) −5.47214 + 9.47802i −0.199151 + 0.344940i
\(756\) 0 0
\(757\) 15.4894 + 26.8284i 0.562970 + 0.975093i 0.997235 + 0.0743080i \(0.0236748\pi\)
−0.434265 + 0.900785i \(0.642992\pi\)
\(758\) 0 0
\(759\) 20.7533 + 35.9458i 0.753297 + 1.30475i
\(760\) 0 0
\(761\) −0.545085 0.944115i −0.0197593 0.0342241i 0.855977 0.517014i \(-0.172957\pi\)
−0.875736 + 0.482790i \(0.839623\pi\)
\(762\) 0 0
\(763\) −58.6869 −2.12461
\(764\) 0 0
\(765\) −14.5066 25.1261i −0.524486 0.908437i
\(766\) 0 0
\(767\) 3.51722 + 6.09201i 0.126999 + 0.219970i
\(768\) 0 0
\(769\) −9.94427 + 17.2240i −0.358600 + 0.621113i −0.987727 0.156189i \(-0.950079\pi\)
0.629128 + 0.777302i \(0.283412\pi\)
\(770\) 0 0
\(771\) −4.50000 + 7.79423i −0.162064 + 0.280702i
\(772\) 0 0
\(773\) 15.5967 0.560976 0.280488 0.959858i \(-0.409504\pi\)
0.280488 + 0.959858i \(0.409504\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 26.9164 46.6206i 0.965621 1.67250i
\(778\) 0 0
\(779\) −5.85410 + 10.1396i −0.209745 + 0.363289i
\(780\) 0 0
\(781\) −19.5344 33.8346i −0.698997 1.21070i
\(782\) 0 0
\(783\) −3.35410 5.80948i −0.119866 0.207614i
\(784\) 0 0
\(785\) −6.36068 −0.227022
\(786\) 0 0
\(787\) 5.22542 + 9.05070i 0.186266 + 0.322623i 0.944002 0.329938i \(-0.107028\pi\)
−0.757736 + 0.652561i \(0.773695\pi\)
\(788\) 0 0
\(789\) 36.0066 + 62.3652i 1.28187 + 2.22026i
\(790\) 0 0
\(791\) 33.0795 + 57.2954i 1.17617 + 2.03719i
\(792\) 0 0
\(793\) −1.97214 + 3.41584i −0.0700326 + 0.121300i
\(794\) 0 0
\(795\) −4.47214 −0.158610
\(796\) 0 0
\(797\) 4.11803 7.13264i 0.145868 0.252651i −0.783828 0.620978i \(-0.786736\pi\)
0.929697 + 0.368326i \(0.120069\pi\)
\(798\) 0 0
\(799\) 3.48936 + 6.04374i 0.123445 + 0.213812i
\(800\) 0 0
\(801\) −7.14590 −0.252488
\(802\) 0 0
\(803\) −3.35410 5.80948i −0.118364 0.205012i
\(804\) 0 0
\(805\) 11.4721 19.8703i 0.404340 0.700337i
\(806\) 0 0