Properties

Label 1792.2.m.h.449.5
Level $1792$
Weight $2$
Character 1792.449
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 449.5
Root \(-0.424637 + 3.22544i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.171192 - 0.171192i) q^{3} +(-0.268425 - 0.268425i) q^{5} +1.00000i q^{7} +2.94139i q^{9} +O(q^{10})\) \(q+(0.171192 - 0.171192i) q^{3} +(-0.268425 - 0.268425i) q^{5} +1.00000i q^{7} +2.94139i q^{9} +(-1.84927 - 1.84927i) q^{11} +(1.63574 - 1.63574i) q^{13} -0.0919045 q^{15} -7.37134 q^{17} +(3.84975 - 3.84975i) q^{19} +(0.171192 + 0.171192i) q^{21} -6.44892i q^{23} -4.85590i q^{25} +(1.01712 + 1.01712i) q^{27} +(3.58700 - 3.58700i) q^{29} +6.10161 q^{31} -0.633164 q^{33} +(0.268425 - 0.268425i) q^{35} +(7.41852 + 7.41852i) q^{37} -0.560052i q^{39} +0.836588i q^{41} +(3.88949 + 3.88949i) q^{43} +(0.789540 - 0.789540i) q^{45} +6.02070 q^{47} -1.00000 q^{49} +(-1.26192 + 1.26192i) q^{51} +(0.575460 + 0.575460i) q^{53} +0.992782i q^{55} -1.31810i q^{57} +(-5.33013 - 5.33013i) q^{59} +(0.929862 - 0.929862i) q^{61} -2.94139 q^{63} -0.878144 q^{65} +(6.21819 - 6.21819i) q^{67} +(-1.10401 - 1.10401i) q^{69} -11.4285i q^{71} +3.68616i q^{73} +(-0.831293 - 0.831293i) q^{75} +(1.84927 - 1.84927i) q^{77} +4.21672 q^{79} -8.47591 q^{81} +(12.0147 - 12.0147i) q^{83} +(1.97865 + 1.97865i) q^{85} -1.22813i q^{87} +9.32780i q^{89} +(1.63574 + 1.63574i) q^{91} +(1.04455 - 1.04455i) q^{93} -2.06673 q^{95} -13.9032 q^{97} +(5.43943 - 5.43943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.171192 0.171192i 0.0988380 0.0988380i −0.655959 0.754797i \(-0.727735\pi\)
0.754797 + 0.655959i \(0.227735\pi\)
\(4\) 0 0
\(5\) −0.268425 0.268425i −0.120043 0.120043i 0.644533 0.764576i \(-0.277052\pi\)
−0.764576 + 0.644533i \(0.777052\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.94139i 0.980462i
\(10\) 0 0
\(11\) −1.84927 1.84927i −0.557577 0.557577i 0.371040 0.928617i \(-0.379001\pi\)
−0.928617 + 0.371040i \(0.879001\pi\)
\(12\) 0 0
\(13\) 1.63574 1.63574i 0.453672 0.453672i −0.442899 0.896571i \(-0.646050\pi\)
0.896571 + 0.442899i \(0.146050\pi\)
\(14\) 0 0
\(15\) −0.0919045 −0.0237296
\(16\) 0 0
\(17\) −7.37134 −1.78781 −0.893906 0.448255i \(-0.852046\pi\)
−0.893906 + 0.448255i \(0.852046\pi\)
\(18\) 0 0
\(19\) 3.84975 3.84975i 0.883193 0.883193i −0.110665 0.993858i \(-0.535298\pi\)
0.993858 + 0.110665i \(0.0352979\pi\)
\(20\) 0 0
\(21\) 0.171192 + 0.171192i 0.0373573 + 0.0373573i
\(22\) 0 0
\(23\) 6.44892i 1.34469i −0.740236 0.672347i \(-0.765286\pi\)
0.740236 0.672347i \(-0.234714\pi\)
\(24\) 0 0
\(25\) 4.85590i 0.971179i
\(26\) 0 0
\(27\) 1.01712 + 1.01712i 0.195745 + 0.195745i
\(28\) 0 0
\(29\) 3.58700 3.58700i 0.666089 0.666089i −0.290720 0.956808i \(-0.593895\pi\)
0.956808 + 0.290720i \(0.0938947\pi\)
\(30\) 0 0
\(31\) 6.10161 1.09588 0.547941 0.836517i \(-0.315412\pi\)
0.547941 + 0.836517i \(0.315412\pi\)
\(32\) 0 0
\(33\) −0.633164 −0.110220
\(34\) 0 0
\(35\) 0.268425 0.268425i 0.0453720 0.0453720i
\(36\) 0 0
\(37\) 7.41852 + 7.41852i 1.21960 + 1.21960i 0.967773 + 0.251825i \(0.0810307\pi\)
0.251825 + 0.967773i \(0.418969\pi\)
\(38\) 0 0
\(39\) 0.560052i 0.0896801i
\(40\) 0 0
\(41\) 0.836588i 0.130653i 0.997864 + 0.0653265i \(0.0208089\pi\)
−0.997864 + 0.0653265i \(0.979191\pi\)
\(42\) 0 0
\(43\) 3.88949 + 3.88949i 0.593141 + 0.593141i 0.938479 0.345337i \(-0.112236\pi\)
−0.345337 + 0.938479i \(0.612236\pi\)
\(44\) 0 0
\(45\) 0.789540 0.789540i 0.117698 0.117698i
\(46\) 0 0
\(47\) 6.02070 0.878209 0.439104 0.898436i \(-0.355296\pi\)
0.439104 + 0.898436i \(0.355296\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −1.26192 + 1.26192i −0.176704 + 0.176704i
\(52\) 0 0
\(53\) 0.575460 + 0.575460i 0.0790455 + 0.0790455i 0.745524 0.666479i \(-0.232199\pi\)
−0.666479 + 0.745524i \(0.732199\pi\)
\(54\) 0 0
\(55\) 0.992782i 0.133867i
\(56\) 0 0
\(57\) 1.31810i 0.174586i
\(58\) 0 0
\(59\) −5.33013 5.33013i −0.693924 0.693924i 0.269169 0.963093i \(-0.413251\pi\)
−0.963093 + 0.269169i \(0.913251\pi\)
\(60\) 0 0
\(61\) 0.929862 0.929862i 0.119057 0.119057i −0.645068 0.764125i \(-0.723171\pi\)
0.764125 + 0.645068i \(0.223171\pi\)
\(62\) 0 0
\(63\) −2.94139 −0.370580
\(64\) 0 0
\(65\) −0.878144 −0.108920
\(66\) 0 0
\(67\) 6.21819 6.21819i 0.759672 0.759672i −0.216590 0.976263i \(-0.569494\pi\)
0.976263 + 0.216590i \(0.0694935\pi\)
\(68\) 0 0
\(69\) −1.10401 1.10401i −0.132907 0.132907i
\(70\) 0 0
\(71\) 11.4285i 1.35631i −0.734919 0.678155i \(-0.762780\pi\)
0.734919 0.678155i \(-0.237220\pi\)
\(72\) 0 0
\(73\) 3.68616i 0.431433i 0.976456 + 0.215716i \(0.0692087\pi\)
−0.976456 + 0.215716i \(0.930791\pi\)
\(74\) 0 0
\(75\) −0.831293 0.831293i −0.0959895 0.0959895i
\(76\) 0 0
\(77\) 1.84927 1.84927i 0.210744 0.210744i
\(78\) 0 0
\(79\) 4.21672 0.474418 0.237209 0.971459i \(-0.423767\pi\)
0.237209 + 0.971459i \(0.423767\pi\)
\(80\) 0 0
\(81\) −8.47591 −0.941768
\(82\) 0 0
\(83\) 12.0147 12.0147i 1.31878 1.31878i 0.404038 0.914742i \(-0.367607\pi\)
0.914742 0.404038i \(-0.132393\pi\)
\(84\) 0 0
\(85\) 1.97865 + 1.97865i 0.214614 + 0.214614i
\(86\) 0 0
\(87\) 1.22813i 0.131670i
\(88\) 0 0
\(89\) 9.32780i 0.988745i 0.869250 + 0.494373i \(0.164602\pi\)
−0.869250 + 0.494373i \(0.835398\pi\)
\(90\) 0 0
\(91\) 1.63574 + 1.63574i 0.171472 + 0.171472i
\(92\) 0 0
\(93\) 1.04455 1.04455i 0.108315 0.108315i
\(94\) 0 0
\(95\) −2.06673 −0.212043
\(96\) 0 0
\(97\) −13.9032 −1.41166 −0.705828 0.708384i \(-0.749425\pi\)
−0.705828 + 0.708384i \(0.749425\pi\)
\(98\) 0 0
\(99\) 5.43943 5.43943i 0.546683 0.546683i
\(100\) 0 0
\(101\) 0.813911 + 0.813911i 0.0809872 + 0.0809872i 0.746440 0.665453i \(-0.231762\pi\)
−0.665453 + 0.746440i \(0.731762\pi\)
\(102\) 0 0
\(103\) 8.39975i 0.827652i −0.910356 0.413826i \(-0.864192\pi\)
0.910356 0.413826i \(-0.135808\pi\)
\(104\) 0 0
\(105\) 0.0919045i 0.00896896i
\(106\) 0 0
\(107\) 0.705176 + 0.705176i 0.0681719 + 0.0681719i 0.740371 0.672199i \(-0.234650\pi\)
−0.672199 + 0.740371i \(0.734650\pi\)
\(108\) 0 0
\(109\) 12.1263 12.1263i 1.16149 1.16149i 0.177337 0.984150i \(-0.443252\pi\)
0.984150 0.177337i \(-0.0567481\pi\)
\(110\) 0 0
\(111\) 2.53999 0.241085
\(112\) 0 0
\(113\) −3.51705 −0.330856 −0.165428 0.986222i \(-0.552901\pi\)
−0.165428 + 0.986222i \(0.552901\pi\)
\(114\) 0 0
\(115\) −1.73105 + 1.73105i −0.161421 + 0.161421i
\(116\) 0 0
\(117\) 4.81133 + 4.81133i 0.444808 + 0.444808i
\(118\) 0 0
\(119\) 7.37134i 0.675729i
\(120\) 0 0
\(121\) 4.16036i 0.378215i
\(122\) 0 0
\(123\) 0.143218 + 0.143218i 0.0129135 + 0.0129135i
\(124\) 0 0
\(125\) −2.64556 + 2.64556i −0.236626 + 0.236626i
\(126\) 0 0
\(127\) 5.86352 0.520303 0.260152 0.965568i \(-0.416227\pi\)
0.260152 + 0.965568i \(0.416227\pi\)
\(128\) 0 0
\(129\) 1.33170 0.117250
\(130\) 0 0
\(131\) −7.79029 + 7.79029i −0.680641 + 0.680641i −0.960145 0.279504i \(-0.909830\pi\)
0.279504 + 0.960145i \(0.409830\pi\)
\(132\) 0 0
\(133\) 3.84975 + 3.84975i 0.333816 + 0.333816i
\(134\) 0 0
\(135\) 0.546040i 0.0469957i
\(136\) 0 0
\(137\) 6.34879i 0.542414i 0.962521 + 0.271207i \(0.0874228\pi\)
−0.962521 + 0.271207i \(0.912577\pi\)
\(138\) 0 0
\(139\) −14.1119 14.1119i −1.19696 1.19696i −0.975073 0.221885i \(-0.928779\pi\)
−0.221885 0.975073i \(-0.571221\pi\)
\(140\) 0 0
\(141\) 1.03070 1.03070i 0.0868004 0.0868004i
\(142\) 0 0
\(143\) −6.04986 −0.505914
\(144\) 0 0
\(145\) −1.92568 −0.159919
\(146\) 0 0
\(147\) −0.171192 + 0.171192i −0.0141197 + 0.0141197i
\(148\) 0 0
\(149\) −7.08686 7.08686i −0.580578 0.580578i 0.354484 0.935062i \(-0.384657\pi\)
−0.935062 + 0.354484i \(0.884657\pi\)
\(150\) 0 0
\(151\) 8.28521i 0.674241i 0.941462 + 0.337120i \(0.109453\pi\)
−0.941462 + 0.337120i \(0.890547\pi\)
\(152\) 0 0
\(153\) 21.6819i 1.75288i
\(154\) 0 0
\(155\) −1.63782 1.63782i −0.131553 0.131553i
\(156\) 0 0
\(157\) −7.68999 + 7.68999i −0.613728 + 0.613728i −0.943915 0.330188i \(-0.892888\pi\)
0.330188 + 0.943915i \(0.392888\pi\)
\(158\) 0 0
\(159\) 0.197029 0.0156254
\(160\) 0 0
\(161\) 6.44892 0.508246
\(162\) 0 0
\(163\) 4.46953 4.46953i 0.350081 0.350081i −0.510059 0.860140i \(-0.670376\pi\)
0.860140 + 0.510059i \(0.170376\pi\)
\(164\) 0 0
\(165\) 0.169957 + 0.169957i 0.0132311 + 0.0132311i
\(166\) 0 0
\(167\) 12.8905i 0.997493i 0.866748 + 0.498747i \(0.166206\pi\)
−0.866748 + 0.498747i \(0.833794\pi\)
\(168\) 0 0
\(169\) 7.64873i 0.588364i
\(170\) 0 0
\(171\) 11.3236 + 11.3236i 0.865938 + 0.865938i
\(172\) 0 0
\(173\) 6.21257 6.21257i 0.472333 0.472333i −0.430336 0.902669i \(-0.641605\pi\)
0.902669 + 0.430336i \(0.141605\pi\)
\(174\) 0 0
\(175\) 4.85590 0.367071
\(176\) 0 0
\(177\) −1.82496 −0.137172
\(178\) 0 0
\(179\) −2.03654 + 2.03654i −0.152218 + 0.152218i −0.779108 0.626890i \(-0.784328\pi\)
0.626890 + 0.779108i \(0.284328\pi\)
\(180\) 0 0
\(181\) −16.7116 16.7116i −1.24217 1.24217i −0.959101 0.283064i \(-0.908649\pi\)
−0.283064 0.959101i \(-0.591351\pi\)
\(182\) 0 0
\(183\) 0.318371i 0.0235346i
\(184\) 0 0
\(185\) 3.98263i 0.292809i
\(186\) 0 0
\(187\) 13.6316 + 13.6316i 0.996843 + 0.996843i
\(188\) 0 0
\(189\) −1.01712 + 1.01712i −0.0739846 + 0.0739846i
\(190\) 0 0
\(191\) −5.11015 −0.369758 −0.184879 0.982761i \(-0.559189\pi\)
−0.184879 + 0.982761i \(0.559189\pi\)
\(192\) 0 0
\(193\) 0.676235 0.0486765 0.0243382 0.999704i \(-0.492252\pi\)
0.0243382 + 0.999704i \(0.492252\pi\)
\(194\) 0 0
\(195\) −0.150332 + 0.150332i −0.0107655 + 0.0107655i
\(196\) 0 0
\(197\) 14.3449 + 14.3449i 1.02203 + 1.02203i 0.999752 + 0.0222782i \(0.00709197\pi\)
0.0222782 + 0.999752i \(0.492908\pi\)
\(198\) 0 0
\(199\) 4.94660i 0.350655i −0.984510 0.175328i \(-0.943902\pi\)
0.984510 0.175328i \(-0.0560984\pi\)
\(200\) 0 0
\(201\) 2.12901i 0.150169i
\(202\) 0 0
\(203\) 3.58700 + 3.58700i 0.251758 + 0.251758i
\(204\) 0 0
\(205\) 0.224561 0.224561i 0.0156840 0.0156840i
\(206\) 0 0
\(207\) 18.9688 1.31842
\(208\) 0 0
\(209\) −14.2385 −0.984897
\(210\) 0 0
\(211\) −4.67810 + 4.67810i −0.322054 + 0.322054i −0.849555 0.527501i \(-0.823129\pi\)
0.527501 + 0.849555i \(0.323129\pi\)
\(212\) 0 0
\(213\) −1.95647 1.95647i −0.134055 0.134055i
\(214\) 0 0
\(215\) 2.08807i 0.142405i
\(216\) 0 0
\(217\) 6.10161i 0.414204i
\(218\) 0 0
\(219\) 0.631044 + 0.631044i 0.0426420 + 0.0426420i
\(220\) 0 0
\(221\) −12.0576 + 12.0576i −0.811080 + 0.811080i
\(222\) 0 0
\(223\) 4.16691 0.279037 0.139518 0.990219i \(-0.455445\pi\)
0.139518 + 0.990219i \(0.455445\pi\)
\(224\) 0 0
\(225\) 14.2831 0.952204
\(226\) 0 0
\(227\) 12.1022 12.1022i 0.803248 0.803248i −0.180353 0.983602i \(-0.557724\pi\)
0.983602 + 0.180353i \(0.0577241\pi\)
\(228\) 0 0
\(229\) 13.5287 + 13.5287i 0.893999 + 0.893999i 0.994897 0.100898i \(-0.0321714\pi\)
−0.100898 + 0.994897i \(0.532171\pi\)
\(230\) 0 0
\(231\) 0.633164i 0.0416591i
\(232\) 0 0
\(233\) 13.3857i 0.876924i 0.898750 + 0.438462i \(0.144477\pi\)
−0.898750 + 0.438462i \(0.855523\pi\)
\(234\) 0 0
\(235\) −1.61610 1.61610i −0.105423 0.105423i
\(236\) 0 0
\(237\) 0.721871 0.721871i 0.0468905 0.0468905i
\(238\) 0 0
\(239\) −20.6475 −1.33558 −0.667788 0.744352i \(-0.732759\pi\)
−0.667788 + 0.744352i \(0.732759\pi\)
\(240\) 0 0
\(241\) −0.401861 −0.0258861 −0.0129431 0.999916i \(-0.504120\pi\)
−0.0129431 + 0.999916i \(0.504120\pi\)
\(242\) 0 0
\(243\) −4.50237 + 4.50237i −0.288827 + 0.288827i
\(244\) 0 0
\(245\) 0.268425 + 0.268425i 0.0171490 + 0.0171490i
\(246\) 0 0
\(247\) 12.5944i 0.801360i
\(248\) 0 0
\(249\) 4.11364i 0.260691i
\(250\) 0 0
\(251\) −9.25468 9.25468i −0.584150 0.584150i 0.351891 0.936041i \(-0.385539\pi\)
−0.936041 + 0.351891i \(0.885539\pi\)
\(252\) 0 0
\(253\) −11.9258 + 11.9258i −0.749771 + 0.749771i
\(254\) 0 0
\(255\) 0.677459 0.0424241
\(256\) 0 0
\(257\) 16.3273 1.01847 0.509234 0.860628i \(-0.329929\pi\)
0.509234 + 0.860628i \(0.329929\pi\)
\(258\) 0 0
\(259\) −7.41852 + 7.41852i −0.460965 + 0.460965i
\(260\) 0 0
\(261\) 10.5507 + 10.5507i 0.653075 + 0.653075i
\(262\) 0 0
\(263\) 13.3352i 0.822284i 0.911571 + 0.411142i \(0.134870\pi\)
−0.911571 + 0.411142i \(0.865130\pi\)
\(264\) 0 0
\(265\) 0.308935i 0.0189777i
\(266\) 0 0
\(267\) 1.59685 + 1.59685i 0.0977256 + 0.0977256i
\(268\) 0 0
\(269\) 19.3277 19.3277i 1.17843 1.17843i 0.198284 0.980145i \(-0.436463\pi\)
0.980145 0.198284i \(-0.0635367\pi\)
\(270\) 0 0
\(271\) −24.5968 −1.49415 −0.747074 0.664741i \(-0.768542\pi\)
−0.747074 + 0.664741i \(0.768542\pi\)
\(272\) 0 0
\(273\) 0.560052 0.0338959
\(274\) 0 0
\(275\) −8.97989 + 8.97989i −0.541508 + 0.541508i
\(276\) 0 0
\(277\) −17.9974 17.9974i −1.08136 1.08136i −0.996383 0.0849786i \(-0.972918\pi\)
−0.0849786 0.996383i \(-0.527082\pi\)
\(278\) 0 0
\(279\) 17.9472i 1.07447i
\(280\) 0 0
\(281\) 13.7357i 0.819404i 0.912219 + 0.409702i \(0.134367\pi\)
−0.912219 + 0.409702i \(0.865633\pi\)
\(282\) 0 0
\(283\) −10.0342 10.0342i −0.596473 0.596473i 0.342900 0.939372i \(-0.388591\pi\)
−0.939372 + 0.342900i \(0.888591\pi\)
\(284\) 0 0
\(285\) −0.353810 + 0.353810i −0.0209579 + 0.0209579i
\(286\) 0 0
\(287\) −0.836588 −0.0493822
\(288\) 0 0
\(289\) 37.3366 2.19627
\(290\) 0 0
\(291\) −2.38012 + 2.38012i −0.139525 + 0.139525i
\(292\) 0 0
\(293\) −19.7376 19.7376i −1.15308 1.15308i −0.985931 0.167151i \(-0.946543\pi\)
−0.167151 0.985931i \(-0.553457\pi\)
\(294\) 0 0
\(295\) 2.86148i 0.166602i
\(296\) 0 0
\(297\) 3.76187i 0.218286i
\(298\) 0 0
\(299\) −10.5487 10.5487i −0.610050 0.610050i
\(300\) 0 0
\(301\) −3.88949 + 3.88949i −0.224186 + 0.224186i
\(302\) 0 0
\(303\) 0.278671 0.0160092
\(304\) 0 0
\(305\) −0.499195 −0.0285838
\(306\) 0 0
\(307\) −3.14804 + 3.14804i −0.179668 + 0.179668i −0.791211 0.611543i \(-0.790549\pi\)
0.611543 + 0.791211i \(0.290549\pi\)
\(308\) 0 0
\(309\) −1.43797 1.43797i −0.0818035 0.0818035i
\(310\) 0 0
\(311\) 32.2711i 1.82993i 0.403535 + 0.914964i \(0.367781\pi\)
−0.403535 + 0.914964i \(0.632219\pi\)
\(312\) 0 0
\(313\) 22.3372i 1.26257i −0.775550 0.631286i \(-0.782527\pi\)
0.775550 0.631286i \(-0.217473\pi\)
\(314\) 0 0
\(315\) 0.789540 + 0.789540i 0.0444856 + 0.0444856i
\(316\) 0 0
\(317\) 0.148346 0.148346i 0.00833196 0.00833196i −0.702929 0.711260i \(-0.748125\pi\)
0.711260 + 0.702929i \(0.248125\pi\)
\(318\) 0 0
\(319\) −13.2667 −0.742792
\(320\) 0 0
\(321\) 0.241442 0.0134760
\(322\) 0 0
\(323\) −28.3778 + 28.3778i −1.57898 + 1.57898i
\(324\) 0 0
\(325\) −7.94297 7.94297i −0.440597 0.440597i
\(326\) 0 0
\(327\) 4.15186i 0.229598i
\(328\) 0 0
\(329\) 6.02070i 0.331932i
\(330\) 0 0
\(331\) 20.1427 + 20.1427i 1.10714 + 1.10714i 0.993525 + 0.113618i \(0.0362440\pi\)
0.113618 + 0.993525i \(0.463756\pi\)
\(332\) 0 0
\(333\) −21.8207 + 21.8207i −1.19577 + 1.19577i
\(334\) 0 0
\(335\) −3.33823 −0.182387
\(336\) 0 0
\(337\) 6.83335 0.372236 0.186118 0.982527i \(-0.440409\pi\)
0.186118 + 0.982527i \(0.440409\pi\)
\(338\) 0 0
\(339\) −0.602092 + 0.602092i −0.0327012 + 0.0327012i
\(340\) 0 0
\(341\) −11.2836 11.2836i −0.611039 0.611039i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0.592685i 0.0319091i
\(346\) 0 0
\(347\) −19.8489 19.8489i −1.06554 1.06554i −0.997696 0.0678488i \(-0.978386\pi\)
−0.0678488 0.997696i \(-0.521614\pi\)
\(348\) 0 0
\(349\) −16.6099 + 16.6099i −0.889105 + 0.889105i −0.994437 0.105332i \(-0.966409\pi\)
0.105332 + 0.994437i \(0.466409\pi\)
\(350\) 0 0
\(351\) 3.32748 0.177608
\(352\) 0 0
\(353\) 5.41293 0.288101 0.144051 0.989570i \(-0.453987\pi\)
0.144051 + 0.989570i \(0.453987\pi\)
\(354\) 0 0
\(355\) −3.06768 + 3.06768i −0.162816 + 0.162816i
\(356\) 0 0
\(357\) −1.26192 1.26192i −0.0667878 0.0667878i
\(358\) 0 0
\(359\) 29.1561i 1.53880i −0.638768 0.769399i \(-0.720556\pi\)
0.638768 0.769399i \(-0.279444\pi\)
\(360\) 0 0
\(361\) 10.6412i 0.560061i
\(362\) 0 0
\(363\) −0.712223 0.712223i −0.0373820 0.0373820i
\(364\) 0 0
\(365\) 0.989457 0.989457i 0.0517906 0.0517906i
\(366\) 0 0
\(367\) −6.14461 −0.320746 −0.160373 0.987056i \(-0.551270\pi\)
−0.160373 + 0.987056i \(0.551270\pi\)
\(368\) 0 0
\(369\) −2.46073 −0.128100
\(370\) 0 0
\(371\) −0.575460 + 0.575460i −0.0298764 + 0.0298764i
\(372\) 0 0
\(373\) 20.9348 + 20.9348i 1.08396 + 1.08396i 0.996136 + 0.0878283i \(0.0279927\pi\)
0.0878283 + 0.996136i \(0.472007\pi\)
\(374\) 0 0
\(375\) 0.905802i 0.0467754i
\(376\) 0 0
\(377\) 11.7348i 0.604371i
\(378\) 0 0
\(379\) 23.6398 + 23.6398i 1.21429 + 1.21429i 0.969601 + 0.244693i \(0.0786872\pi\)
0.244693 + 0.969601i \(0.421313\pi\)
\(380\) 0 0
\(381\) 1.00379 1.00379i 0.0514257 0.0514257i
\(382\) 0 0
\(383\) 6.99982 0.357674 0.178837 0.983879i \(-0.442767\pi\)
0.178837 + 0.983879i \(0.442767\pi\)
\(384\) 0 0
\(385\) −0.992782 −0.0505968
\(386\) 0 0
\(387\) −11.4405 + 11.4405i −0.581552 + 0.581552i
\(388\) 0 0
\(389\) −15.4838 15.4838i −0.785060 0.785060i 0.195620 0.980680i \(-0.437328\pi\)
−0.980680 + 0.195620i \(0.937328\pi\)
\(390\) 0 0
\(391\) 47.5372i 2.40406i
\(392\) 0 0
\(393\) 2.66728i 0.134546i
\(394\) 0 0
\(395\) −1.13187 1.13187i −0.0569506 0.0569506i
\(396\) 0 0
\(397\) −5.65923 + 5.65923i −0.284029 + 0.284029i −0.834713 0.550685i \(-0.814367\pi\)
0.550685 + 0.834713i \(0.314367\pi\)
\(398\) 0 0
\(399\) 1.31810 0.0659874
\(400\) 0 0
\(401\) 26.7191 1.33429 0.667144 0.744929i \(-0.267517\pi\)
0.667144 + 0.744929i \(0.267517\pi\)
\(402\) 0 0
\(403\) 9.98063 9.98063i 0.497171 0.497171i
\(404\) 0 0
\(405\) 2.27514 + 2.27514i 0.113053 + 0.113053i
\(406\) 0 0
\(407\) 27.4378i 1.36004i
\(408\) 0 0
\(409\) 20.7456i 1.02581i −0.858447 0.512903i \(-0.828570\pi\)
0.858447 0.512903i \(-0.171430\pi\)
\(410\) 0 0
\(411\) 1.08687 + 1.08687i 0.0536111 + 0.0536111i
\(412\) 0 0
\(413\) 5.33013 5.33013i 0.262279 0.262279i
\(414\) 0 0
\(415\) −6.45006 −0.316621
\(416\) 0 0
\(417\) −4.83171 −0.236610
\(418\) 0 0
\(419\) 6.11779 6.11779i 0.298874 0.298874i −0.541699 0.840573i \(-0.682219\pi\)
0.840573 + 0.541699i \(0.182219\pi\)
\(420\) 0 0
\(421\) 9.03252 + 9.03252i 0.440218 + 0.440218i 0.892085 0.451867i \(-0.149242\pi\)
−0.451867 + 0.892085i \(0.649242\pi\)
\(422\) 0 0
\(423\) 17.7092i 0.861050i
\(424\) 0 0
\(425\) 35.7945i 1.73629i
\(426\) 0 0
\(427\) 0.929862 + 0.929862i 0.0449992 + 0.0449992i
\(428\) 0 0
\(429\) −1.03569 + 1.03569i −0.0500036 + 0.0500036i
\(430\) 0 0
\(431\) −2.81338 −0.135516 −0.0677579 0.997702i \(-0.521585\pi\)
−0.0677579 + 0.997702i \(0.521585\pi\)
\(432\) 0 0
\(433\) −20.6954 −0.994558 −0.497279 0.867591i \(-0.665667\pi\)
−0.497279 + 0.867591i \(0.665667\pi\)
\(434\) 0 0
\(435\) −0.329661 + 0.329661i −0.0158060 + 0.0158060i
\(436\) 0 0
\(437\) −24.8267 24.8267i −1.18762 1.18762i
\(438\) 0 0
\(439\) 15.6336i 0.746151i 0.927801 + 0.373075i \(0.121697\pi\)
−0.927801 + 0.373075i \(0.878303\pi\)
\(440\) 0 0
\(441\) 2.94139i 0.140066i
\(442\) 0 0
\(443\) 18.6608 + 18.6608i 0.886603 + 0.886603i 0.994195 0.107592i \(-0.0343141\pi\)
−0.107592 + 0.994195i \(0.534314\pi\)
\(444\) 0 0
\(445\) 2.50381 2.50381i 0.118692 0.118692i
\(446\) 0 0
\(447\) −2.42643 −0.114766
\(448\) 0 0
\(449\) 26.8536 1.26730 0.633650 0.773620i \(-0.281556\pi\)
0.633650 + 0.773620i \(0.281556\pi\)
\(450\) 0 0
\(451\) 1.54708 1.54708i 0.0728492 0.0728492i
\(452\) 0 0
\(453\) 1.41837 + 1.41837i 0.0666406 + 0.0666406i
\(454\) 0 0
\(455\) 0.878144i 0.0411680i
\(456\) 0 0
\(457\) 0.385896i 0.0180514i −0.999959 0.00902572i \(-0.997127\pi\)
0.999959 0.00902572i \(-0.00287302\pi\)
\(458\) 0 0
\(459\) −7.49754 7.49754i −0.349955 0.349955i
\(460\) 0 0
\(461\) 2.13650 2.13650i 0.0995065 0.0995065i −0.655601 0.755108i \(-0.727585\pi\)
0.755108 + 0.655601i \(0.227585\pi\)
\(462\) 0 0
\(463\) 32.5560 1.51301 0.756503 0.653991i \(-0.226906\pi\)
0.756503 + 0.653991i \(0.226906\pi\)
\(464\) 0 0
\(465\) −0.560766 −0.0260049
\(466\) 0 0
\(467\) −8.00295 + 8.00295i −0.370332 + 0.370332i −0.867598 0.497266i \(-0.834337\pi\)
0.497266 + 0.867598i \(0.334337\pi\)
\(468\) 0 0
\(469\) 6.21819 + 6.21819i 0.287129 + 0.287129i
\(470\) 0 0
\(471\) 2.63294i 0.121319i
\(472\) 0 0
\(473\) 14.3855i 0.661444i
\(474\) 0 0
\(475\) −18.6940 18.6940i −0.857739 0.857739i
\(476\) 0 0
\(477\) −1.69265 + 1.69265i −0.0775012 + 0.0775012i
\(478\) 0 0
\(479\) −20.2388 −0.924735 −0.462368 0.886688i \(-0.653000\pi\)
−0.462368 + 0.886688i \(0.653000\pi\)
\(480\) 0 0
\(481\) 24.2695 1.10659
\(482\) 0 0
\(483\) 1.10401 1.10401i 0.0502341 0.0502341i
\(484\) 0 0
\(485\) 3.73196 + 3.73196i 0.169459 + 0.169459i
\(486\) 0 0
\(487\) 36.6988i 1.66298i 0.555537 + 0.831492i \(0.312513\pi\)
−0.555537 + 0.831492i \(0.687487\pi\)
\(488\) 0 0
\(489\) 1.53030i 0.0692026i
\(490\) 0 0
\(491\) −13.6015 13.6015i −0.613829 0.613829i 0.330113 0.943942i \(-0.392913\pi\)
−0.943942 + 0.330113i \(0.892913\pi\)
\(492\) 0 0
\(493\) −26.4410 + 26.4410i −1.19084 + 1.19084i
\(494\) 0 0
\(495\) −2.92015 −0.131251
\(496\) 0 0
\(497\) 11.4285 0.512637
\(498\) 0 0
\(499\) −24.1970 + 24.1970i −1.08321 + 1.08321i −0.0869972 + 0.996209i \(0.527727\pi\)
−0.996209 + 0.0869972i \(0.972273\pi\)
\(500\) 0 0
\(501\) 2.20675 + 2.20675i 0.0985903 + 0.0985903i
\(502\) 0 0
\(503\) 13.4123i 0.598026i 0.954249 + 0.299013i \(0.0966574\pi\)
−0.954249 + 0.299013i \(0.903343\pi\)
\(504\) 0 0
\(505\) 0.436947i 0.0194439i
\(506\) 0 0
\(507\) 1.30940 + 1.30940i 0.0581527 + 0.0581527i
\(508\) 0 0
\(509\) −18.9792 + 18.9792i −0.841240 + 0.841240i −0.989020 0.147781i \(-0.952787\pi\)
0.147781 + 0.989020i \(0.452787\pi\)
\(510\) 0 0
\(511\) −3.68616 −0.163066
\(512\) 0 0
\(513\) 7.83132 0.345761
\(514\) 0 0
\(515\) −2.25470 + 2.25470i −0.0993540 + 0.0993540i
\(516\) 0 0
\(517\) −11.1339 11.1339i −0.489669 0.489669i
\(518\) 0 0
\(519\) 2.12709i 0.0933689i
\(520\) 0 0
\(521\) 0.00960703i 0.000420892i 1.00000 0.000210446i \(6.69870e-5\pi\)
−1.00000 0.000210446i \(0.999933\pi\)
\(522\) 0 0
\(523\) 23.5829 + 23.5829i 1.03121 + 1.03121i 0.999497 + 0.0317098i \(0.0100952\pi\)
0.0317098 + 0.999497i \(0.489905\pi\)
\(524\) 0 0
\(525\) 0.831293 0.831293i 0.0362806 0.0362806i
\(526\) 0 0
\(527\) −44.9770 −1.95923
\(528\) 0 0
\(529\) −18.5886 −0.808201
\(530\) 0 0
\(531\) 15.6780 15.6780i 0.680366 0.680366i
\(532\) 0 0
\(533\) 1.36844 + 1.36844i 0.0592736 + 0.0592736i
\(534\) 0 0
\(535\) 0.378573i 0.0163671i
\(536\) 0 0
\(537\) 0.697281i 0.0300899i
\(538\) 0 0
\(539\) 1.84927 + 1.84927i 0.0796539 + 0.0796539i
\(540\) 0 0
\(541\) −11.6478 + 11.6478i −0.500776 + 0.500776i −0.911679 0.410903i \(-0.865214\pi\)
0.410903 + 0.911679i \(0.365214\pi\)
\(542\) 0 0
\(543\) −5.72181 −0.245546
\(544\) 0 0
\(545\) −6.50998 −0.278857
\(546\) 0 0
\(547\) −14.0041 + 14.0041i −0.598773 + 0.598773i −0.939986 0.341213i \(-0.889162\pi\)
0.341213 + 0.939986i \(0.389162\pi\)
\(548\) 0 0
\(549\) 2.73508 + 2.73508i 0.116730 + 0.116730i
\(550\) 0 0
\(551\) 27.6181i 1.17657i
\(552\) 0 0
\(553\) 4.21672i 0.179313i
\(554\) 0 0
\(555\) −0.681796 0.681796i −0.0289406 0.0289406i
\(556\) 0 0
\(557\) 24.3807 24.3807i 1.03305 1.03305i 0.0336103 0.999435i \(-0.489299\pi\)
0.999435 0.0336103i \(-0.0107005\pi\)
\(558\) 0 0
\(559\) 12.7244 0.538183
\(560\) 0 0
\(561\) 4.66727 0.197052
\(562\) 0 0
\(563\) −26.2789 + 26.2789i −1.10752 + 1.10752i −0.114046 + 0.993475i \(0.536381\pi\)
−0.993475 + 0.114046i \(0.963619\pi\)
\(564\) 0 0
\(565\) 0.944062 + 0.944062i 0.0397170 + 0.0397170i
\(566\) 0 0
\(567\) 8.47591i 0.355955i
\(568\) 0 0
\(569\) 36.8053i 1.54296i 0.636255 + 0.771479i \(0.280483\pi\)
−0.636255 + 0.771479i \(0.719517\pi\)
\(570\) 0 0
\(571\) 23.0536 + 23.0536i 0.964762 + 0.964762i 0.999400 0.0346376i \(-0.0110277\pi\)
−0.0346376 + 0.999400i \(0.511028\pi\)
\(572\) 0 0
\(573\) −0.874820 + 0.874820i −0.0365461 + 0.0365461i
\(574\) 0 0
\(575\) −31.3153 −1.30594
\(576\) 0 0
\(577\) −3.51057 −0.146147 −0.0730735 0.997327i \(-0.523281\pi\)
−0.0730735 + 0.997327i \(0.523281\pi\)
\(578\) 0 0
\(579\) 0.115766 0.115766i 0.00481109 0.00481109i
\(580\) 0 0
\(581\) 12.0147 + 12.0147i 0.498452 + 0.498452i
\(582\) 0 0
\(583\) 2.12837i 0.0881480i
\(584\) 0 0
\(585\) 2.58296i 0.106792i
\(586\) 0 0
\(587\) −28.0315 28.0315i −1.15699 1.15699i −0.985120 0.171865i \(-0.945021\pi\)
−0.171865 0.985120i \(-0.554979\pi\)
\(588\) 0 0
\(589\) 23.4897 23.4897i 0.967876 0.967876i
\(590\) 0 0
\(591\) 4.91147 0.202031
\(592\) 0 0
\(593\) 6.27767 0.257793 0.128896 0.991658i \(-0.458857\pi\)
0.128896 + 0.991658i \(0.458857\pi\)
\(594\) 0 0
\(595\) −1.97865 + 1.97865i −0.0811167 + 0.0811167i
\(596\) 0 0
\(597\) −0.846821 0.846821i −0.0346581 0.0346581i
\(598\) 0 0
\(599\) 10.3600i 0.423300i −0.977346 0.211650i \(-0.932116\pi\)
0.977346 0.211650i \(-0.0678836\pi\)
\(600\) 0 0
\(601\) 23.9656i 0.977576i −0.872403 0.488788i \(-0.837439\pi\)
0.872403 0.488788i \(-0.162561\pi\)
\(602\) 0 0
\(603\) 18.2901 + 18.2901i 0.744830 + 0.744830i
\(604\) 0 0
\(605\) −1.11674 + 1.11674i −0.0454021 + 0.0454021i
\(606\) 0 0
\(607\) 14.4285 0.585633 0.292817 0.956169i \(-0.405407\pi\)
0.292817 + 0.956169i \(0.405407\pi\)
\(608\) 0 0
\(609\) 1.22813 0.0497665
\(610\) 0 0
\(611\) 9.84828 9.84828i 0.398419 0.398419i
\(612\) 0 0
\(613\) 3.13825 + 3.13825i 0.126753 + 0.126753i 0.767637 0.640885i \(-0.221432\pi\)
−0.640885 + 0.767637i \(0.721432\pi\)
\(614\) 0 0
\(615\) 0.0768862i 0.00310035i
\(616\) 0 0
\(617\) 15.7644i 0.634651i 0.948317 + 0.317325i \(0.102785\pi\)
−0.948317 + 0.317325i \(0.897215\pi\)
\(618\) 0 0
\(619\) −6.16647 6.16647i −0.247851 0.247851i 0.572237 0.820088i \(-0.306076\pi\)
−0.820088 + 0.572237i \(0.806076\pi\)
\(620\) 0 0
\(621\) 6.55934 6.55934i 0.263217 0.263217i
\(622\) 0 0
\(623\) −9.32780 −0.373711
\(624\) 0 0
\(625\) −22.8592 −0.914369
\(626\) 0 0
\(627\) −2.43752 + 2.43752i −0.0973453 + 0.0973453i
\(628\) 0 0
\(629\) −54.6844 54.6844i −2.18041 2.18041i
\(630\) 0 0
\(631\) 30.5796i 1.21736i −0.793417 0.608678i \(-0.791700\pi\)
0.793417 0.608678i \(-0.208300\pi\)
\(632\) 0 0
\(633\) 1.60171i 0.0636623i
\(634\) 0 0
\(635\) −1.57391 1.57391i −0.0624588 0.0624588i
\(636\) 0 0
\(637\) −1.63574 + 1.63574i −0.0648103 + 0.0648103i
\(638\) 0 0
\(639\) 33.6155 1.32981
\(640\) 0 0
\(641\) −18.6228 −0.735556 −0.367778 0.929914i \(-0.619881\pi\)
−0.367778 + 0.929914i \(0.619881\pi\)
\(642\) 0 0
\(643\) 27.8340 27.8340i 1.09766 1.09766i 0.102981 0.994683i \(-0.467162\pi\)
0.994683 0.102981i \(-0.0328381\pi\)
\(644\) 0 0
\(645\) −0.357461 0.357461i −0.0140750 0.0140750i
\(646\) 0 0
\(647\) 29.2607i 1.15036i −0.818029 0.575178i \(-0.804933\pi\)
0.818029 0.575178i \(-0.195067\pi\)
\(648\) 0 0
\(649\) 19.7138i 0.773833i
\(650\) 0 0
\(651\) 1.04455 + 1.04455i 0.0409392 + 0.0409392i
\(652\) 0 0
\(653\) 17.3825 17.3825i 0.680229 0.680229i −0.279822 0.960052i \(-0.590276\pi\)
0.960052 + 0.279822i \(0.0902756\pi\)
\(654\) 0 0
\(655\) 4.18221 0.163413
\(656\) 0 0
\(657\) −10.8424 −0.423004
\(658\) 0 0
\(659\) 27.7030 27.7030i 1.07916 1.07916i 0.0825717 0.996585i \(-0.473687\pi\)
0.996585 0.0825717i \(-0.0263134\pi\)
\(660\) 0 0
\(661\) 18.7539 + 18.7539i 0.729443 + 0.729443i 0.970509 0.241066i \(-0.0774970\pi\)
−0.241066 + 0.970509i \(0.577497\pi\)
\(662\) 0 0
\(663\) 4.12833i 0.160331i
\(664\) 0 0
\(665\) 2.06673i 0.0801445i
\(666\) 0 0
\(667\) −23.1323 23.1323i −0.895685 0.895685i
\(668\) 0 0
\(669\) 0.713343 0.713343i 0.0275794 0.0275794i
\(670\) 0 0
\(671\) −3.43914 −0.132767
\(672\) 0 0
\(673\) 8.89179 0.342753 0.171377 0.985206i \(-0.445179\pi\)
0.171377 + 0.985206i \(0.445179\pi\)
\(674\) 0 0
\(675\) 4.93903 4.93903i 0.190103 0.190103i
\(676\) 0 0
\(677\) 23.0023 + 23.0023i 0.884049 + 0.884049i 0.993943 0.109895i \(-0.0350514\pi\)
−0.109895 + 0.993943i \(0.535051\pi\)
\(678\) 0 0
\(679\) 13.9032i 0.533556i
\(680\) 0 0
\(681\) 4.14360i 0.158783i
\(682\) 0 0
\(683\) −8.13050 8.13050i −0.311105 0.311105i 0.534233 0.845337i \(-0.320601\pi\)
−0.845337 + 0.534233i \(0.820601\pi\)
\(684\) 0 0
\(685\) 1.70417 1.70417i 0.0651131 0.0651131i
\(686\) 0 0
\(687\) 4.63201 0.176722
\(688\) 0 0
\(689\) 1.88260 0.0717215
\(690\) 0 0
\(691\) 1.09420 1.09420i 0.0416253 0.0416253i −0.685988 0.727613i \(-0.740630\pi\)
0.727613 + 0.685988i \(0.240630\pi\)
\(692\) 0 0
\(693\) 5.43943 + 5.43943i 0.206627 + 0.206627i
\(694\) 0 0
\(695\) 7.57597i 0.287373i
\(696\) 0 0
\(697\) 6.16677i 0.233583i
\(698\) 0 0
\(699\) 2.29152 + 2.29152i 0.0866734 + 0.0866734i
\(700\) 0 0
\(701\) −11.5656 + 11.5656i −0.436825 + 0.436825i −0.890942 0.454117i \(-0.849955\pi\)
0.454117 + 0.890942i \(0.349955\pi\)
\(702\) 0 0
\(703\) 57.1189 2.15428
\(704\) 0 0
\(705\) −0.553329 −0.0208396
\(706\) 0 0
\(707\) −0.813911 + 0.813911i −0.0306103 + 0.0306103i
\(708\) 0 0
\(709\) 2.69651 + 2.69651i 0.101270 + 0.101270i 0.755926 0.654657i \(-0.227187\pi\)
−0.654657 + 0.755926i \(0.727187\pi\)
\(710\) 0 0
\(711\) 12.4030i 0.465149i
\(712\) 0 0
\(713\) 39.3488i 1.47363i
\(714\) 0 0
\(715\) 1.62393 + 1.62393i 0.0607315 + 0.0607315i
\(716\) 0 0
\(717\) −3.53470 + 3.53470i −0.132006 + 0.132006i
\(718\) 0 0
\(719\) 6.08527 0.226942 0.113471 0.993541i \(-0.463803\pi\)
0.113471 + 0.993541i \(0.463803\pi\)
\(720\) 0 0
\(721\) 8.39975 0.312823
\(722\) 0 0
\(723\) −0.0687956 + 0.0687956i −0.00255854 + 0.00255854i
\(724\) 0 0
\(725\) −17.4181 17.4181i −0.646891 0.646891i
\(726\) 0 0
\(727\) 41.6162i 1.54346i 0.635951 + 0.771729i \(0.280608\pi\)
−0.635951 + 0.771729i \(0.719392\pi\)
\(728\) 0 0
\(729\) 23.8862i 0.884674i
\(730\) 0 0
\(731\) −28.6707 28.6707i −1.06042 1.06042i
\(732\) 0 0
\(733\) 23.5929 23.5929i 0.871422 0.871422i −0.121206 0.992627i \(-0.538676\pi\)
0.992627 + 0.121206i \(0.0386760\pi\)
\(734\) 0 0
\(735\) 0.0919045 0.00338995
\(736\) 0 0
\(737\) −22.9983 −0.847152
\(738\) 0 0
\(739\) −7.53135 + 7.53135i −0.277045 + 0.277045i −0.831928 0.554883i \(-0.812763\pi\)
0.554883 + 0.831928i \(0.312763\pi\)
\(740\) 0 0
\(741\) −2.15606 2.15606i −0.0792048 0.0792048i
\(742\) 0 0
\(743\) 14.4179i 0.528943i 0.964393 + 0.264472i \(0.0851975\pi\)
−0.964393 + 0.264472i \(0.914802\pi\)
\(744\) 0 0
\(745\) 3.80457i 0.139389i
\(746\) 0 0
\(747\) 35.3397 + 35.3397i 1.29301 + 1.29301i
\(748\) 0 0
\(749\) −0.705176 + 0.705176i −0.0257666 + 0.0257666i
\(750\) 0 0
\(751\) 17.6760 0.645008 0.322504 0.946568i \(-0.395475\pi\)
0.322504 + 0.946568i \(0.395475\pi\)
\(752\) 0 0
\(753\) −3.16866 −0.115472
\(754\) 0 0
\(755\) 2.22395 2.22395i 0.0809379 0.0809379i
\(756\) 0 0
\(757\) 21.3351 + 21.3351i 0.775437 + 0.775437i 0.979051 0.203614i \(-0.0652687\pi\)
−0.203614 + 0.979051i \(0.565269\pi\)
\(758\) 0 0
\(759\) 4.08323i 0.148212i
\(760\) 0 0
\(761\) 22.2510i 0.806597i 0.915068 + 0.403299i \(0.132136\pi\)
−0.915068 + 0.403299i \(0.867864\pi\)
\(762\) 0 0
\(763\) 12.1263 + 12.1263i 0.439001 + 0.439001i
\(764\) 0 0
\(765\) −5.81997 + 5.81997i −0.210421 + 0.210421i
\(766\) 0 0
\(767\) −17.4374 −0.629628
\(768\) 0 0
\(769\) −30.5537 −1.10179 −0.550897 0.834573i \(-0.685714\pi\)
−0.550897 + 0.834573i \(0.685714\pi\)
\(770\) 0 0
\(771\) 2.79511 2.79511i 0.100663 0.100663i
\(772\) 0 0
\(773\) 19.1590 + 19.1590i 0.689100 + 0.689100i 0.962033 0.272933i \(-0.0879938\pi\)
−0.272933 + 0.962033i \(0.587994\pi\)
\(774\) 0 0
\(775\) 29.6288i 1.06430i
\(776\) 0 0
\(777\) 2.53999i 0.0911217i
\(778\) 0 0
\(779\) 3.22065 + 3.22065i 0.115392 + 0.115392i
\(780\) 0 0
\(781\) −21.1344 + 21.1344i −0.756247 + 0.756247i
\(782\) 0 0
\(783\) 7.29682 0.260767
\(784\) 0 0
\(785\) 4.12836 0.147348
\(786\) 0 0
\(787\) 13.8172 13.8172i 0.492528 0.492528i −0.416574 0.909102i \(-0.636769\pi\)
0.909102 + 0.416574i \(0.136769\pi\)
\(788\) 0 0
\(789\) 2.28289 + 2.28289i 0.0812729 + 0.0812729i
\(790\) 0 0
\(791\) 3.51705i 0.125052i
\(792\) 0 0
\(793\) 3.04202i 0.108025i
\(794\) 0 0
\(795\) −0.0528874 0.0528874i −0.00187572 0.00187572i
\(796\) 0 0
\(797\) 8.78511 8.78511i 0.311185 0.311185i −0.534184 0.845368i \(-0.679381\pi\)
0.845368 + 0.534184i \(0.179381\pi\)
\(798\) 0 0
\(799\) −44.3806