Properties

Label 1792.2.m.e.449.4
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 449.4
Root \(-0.424637 + 3.22544i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.e.1345.4

$q$-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 −0.754797 0.655959i \(-0.772265\pi\)
0.655959 + 0.754797i \(0.272265\pi\)
\(4\) 0 0
\(5\) 0.268425 + 0.268425i 0.120043 + 0.120043i 0.764576 0.644533i \(-0.222948\pi\)
−0.644533 + 0.764576i \(0.722948\pi\)
\(6\) 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 0.928617 0.371040i \(-0.120999\pi\)
−0.371040 + 0.928617i \(0.620999\pi\)
\(12\) 0 0
\(13\) −1.63574 + 1.63574i −0.453672 + 0.453672i −0.896571 0.442899i \(-0.853950\pi\)
0.442899 + 0.896571i \(0.353950\pi\)
\(14\) 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 −0.993858 0.110665i \(-0.964702\pi\)
0.110665 + 0.993858i \(0.464702\pi\)
\(20\) 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 −0.956808 0.290720i \(-0.906105\pi\)
0.290720 + 0.956808i \(0.406105\pi\)
\(30\) 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 \(-0.918969\pi\)
−0.251825 0.967773i \(-0.581031\pi\)
\(38\) 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 0.345337 0.938479i \(-0.387764\pi\)
−0.938479 + 0.345337i \(0.887764\pi\)
\(44\) 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 0.666479 0.745524i \(-0.267801\pi\)
−0.745524 + 0.666479i \(0.767801\pi\)
\(54\) 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 0.963093 0.269169i \(-0.0867489\pi\)
−0.269169 + 0.963093i \(0.586749\pi\)
\(60\) 0 0
\(61\) −0.929862 + 0.929862i −0.119057 + 0.119057i −0.764125 0.645068i \(-0.776829\pi\)
0.645068 + 0.764125i \(0.276829\pi\)
\(62\) 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 −0.976263 0.216590i \(-0.930506\pi\)
0.216590 + 0.976263i \(0.430506\pi\)
\(68\) 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 \(0.632393\pi\)
−0.914742 + 0.404038i \(0.867607\pi\)
\(84\) 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 0.665453 0.746440i \(-0.268238\pi\)
−0.746440 + 0.665453i \(0.768238\pi\)
\(102\) 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 0.672199 0.740371i \(-0.265350\pi\)
−0.740371 + 0.672199i \(0.765350\pi\)
\(108\) 0 0
\(109\) −12.1263 + 12.1263i −1.16149 + 1.16149i −0.177337 + 0.984150i \(0.556748\pi\)
−0.984150 + 0.177337i \(0.943252\pi\)
\(110\) 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 −0.279504 0.960145i \(-0.590170\pi\)
0.960145 + 0.279504i \(0.0901699\pi\)
\(132\) 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 \(0.0712210\pi\)
0.221885 + 0.975073i \(0.428779\pi\)
\(140\) 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 0.935062 0.354484i \(-0.115343\pi\)
−0.354484 + 0.935062i \(0.615343\pi\)
\(150\) 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 −0.330188 0.943915i \(-0.607112\pi\)
0.943915 + 0.330188i \(0.107112\pi\)
\(158\) 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 −0.860140 0.510059i \(-0.829624\pi\)
0.510059 + 0.860140i \(0.329624\pi\)
\(164\) 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 −0.902669 0.430336i \(-0.858395\pi\)
0.430336 + 0.902669i \(0.358395\pi\)
\(174\) 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 −0.626890 0.779108i \(-0.715672\pi\)
0.779108 + 0.626890i \(0.215672\pi\)
\(180\) 0 0
\(181\) 16.7116 + 16.7116i 1.24217 + 1.24217i 0.959101 + 0.283064i \(0.0913509\pi\)
0.283064 + 0.959101i \(0.408649\pi\)
\(182\) 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 \(-0.992908\pi\)
−0.0222782 0.999752i \(-0.507092\pi\)
\(198\) 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 −0.527501 0.849555i \(-0.676871\pi\)
0.849555 + 0.527501i \(0.176871\pi\)
\(212\) 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 −0.983602 0.180353i \(-0.942276\pi\)
0.180353 + 0.983602i \(0.442276\pi\)
\(228\) 0 0
\(229\) −13.5287 13.5287i −0.893999 0.893999i 0.100898 0.994897i \(-0.467829\pi\)
−0.994897 + 0.100898i \(0.967829\pi\)
\(230\) 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 0.936041 0.351891i \(-0.114461\pi\)
−0.351891 + 0.936041i \(0.614461\pi\)
\(252\) 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 \(0.563537\pi\)
−0.980145 + 0.198284i \(0.936463\pi\)
\(270\) 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 \(0.0270822\pi\)
0.0849786 + 0.996383i \(0.472918\pi\)
\(278\) 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 0.939372 0.342900i \(-0.111409\pi\)
−0.342900 + 0.939372i \(0.611409\pi\)
\(284\) 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 \(0.0534566\pi\)
0.167151 + 0.985931i \(0.446543\pi\)
\(294\) 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 −0.611543 0.791211i \(-0.709451\pi\)
0.791211 + 0.611543i \(0.209451\pi\)
\(308\) 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 −0.711260 0.702929i \(-0.751875\pi\)
0.702929 + 0.711260i \(0.251875\pi\)
\(318\) 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 \(-0.963756\pi\)
−0.113618 0.993525i \(-0.536244\pi\)
\(332\) 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 \(0.0216136\pi\)
0.0678488 + 0.997696i \(0.478386\pi\)
\(348\) 0 0
\(349\) 16.6099 16.6099i 0.889105 0.889105i −0.105332 0.994437i \(-0.533591\pi\)
0.994437 + 0.105332i \(0.0335906\pi\)
\(350\) 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 \(-0.972007\pi\)
−0.0878283 0.996136i \(-0.527993\pi\)
\(374\) 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 \(-0.921313\pi\)
−0.244693 0.969601i \(-0.578687\pi\)
\(380\) 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 0.980680 0.195620i \(-0.0626720\pi\)
−0.195620 + 0.980680i \(0.562672\pi\)
\(390\) 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 −0.550685 0.834713i \(-0.685633\pi\)
0.834713 + 0.550685i \(0.185633\pi\)
\(398\) 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 −0.840573 0.541699i \(-0.817781\pi\)
0.541699 + 0.840573i \(0.317781\pi\)
\(420\) 0 0
\(421\) −9.03252 9.03252i −0.440218 0.440218i 0.451867 0.892085i \(-0.350758\pi\)
−0.892085 + 0.451867i \(0.850758\pi\)
\(422\) 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 0.107592 0.994195i \(-0.465686\pi\)
−0.994195 + 0.107592i \(0.965686\pi\)
\(444\) 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 −0.755108 0.655601i \(-0.772415\pi\)
0.655601 + 0.755108i \(0.272415\pi\)
\(462\) 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 −0.497266 0.867598i \(-0.665663\pi\)
0.867598 + 0.497266i \(0.165663\pi\)
\(468\) 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 0.943942 0.330113i \(-0.107087\pi\)
−0.330113 + 0.943942i \(0.607087\pi\)
\(492\) 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 \(-0.472273\pi\)
0.996209 0.0869972i \(-0.0277271\pi\)
\(500\) 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 −0.147781 0.989020i \(-0.547213\pi\)
0.989020 + 0.147781i \(0.0472129\pi\)
\(510\) 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 \(-0.989905\pi\)
−0.0317098 0.999497i \(-0.510095\pi\)
\(524\) 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 −0.410903 0.911679i \(-0.634786\pi\)
0.911679 + 0.410903i \(0.134786\pi\)
\(542\) 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 −0.341213 0.939986i \(-0.610838\pi\)
0.939986 + 0.341213i \(0.110838\pi\)
\(548\) 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 \(0.510701\pi\)
−0.999435 + 0.0336103i \(0.989299\pi\)
\(558\) 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 \(-0.463619\pi\)
0.993475 0.114046i \(-0.0363812\pi\)
\(564\) 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 0.0346376 0.999400i \(-0.488972\pi\)
−0.999400 + 0.0346376i \(0.988972\pi\)
\(572\) 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 \(0.0549793\pi\)
0.171865 + 0.985120i \(0.445021\pi\)
\(588\) 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 0.640885 0.767637i \(-0.278568\pi\)
−0.767637 + 0.640885i \(0.778568\pi\)
\(614\) 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 0.820088 0.572237i \(-0.193924\pi\)
−0.572237 + 0.820088i \(0.693924\pi\)
\(620\) 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 \(0.532838\pi\)
−0.994683 + 0.102981i \(0.967162\pi\)
\(644\) 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 −0.960052 0.279822i \(-0.909724\pi\)
0.279822 + 0.960052i \(0.409724\pi\)
\(654\) 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 \(0.526313\pi\)
−0.996585 + 0.0825717i \(0.973687\pi\)
\(660\) 0 0
\(661\) −18.7539 18.7539i −0.729443 0.729443i 0.241066 0.970509i \(-0.422503\pi\)
−0.970509 + 0.241066i \(0.922503\pi\)
\(662\) 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 0.109895 0.993943i \(-0.464949\pi\)
−0.993943 + 0.109895i \(0.964949\pi\)
\(678\) 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 0.845337 0.534233i \(-0.179399\pi\)
−0.534233 + 0.845337i \(0.679399\pi\)
\(684\) 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 −0.727613 0.685988i \(-0.759370\pi\)
0.685988 + 0.727613i \(0.259370\pi\)
\(692\) 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 −0.454117 0.890942i \(-0.650045\pi\)
0.890942 + 0.454117i \(0.150045\pi\)
\(702\) 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 0.654657 0.755926i \(-0.272813\pi\)
−0.755926 + 0.654657i \(0.772813\pi\)
\(710\) 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 −0.992627 0.121206i \(-0.961324\pi\)
0.121206 + 0.992627i \(0.461324\pi\)
\(734\) 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 −0.554883 0.831928i \(-0.687237\pi\)
0.831928 + 0.554883i \(0.187237\pi\)
\(740\) 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 0.203614 0.979051i \(-0.434731\pi\)
−0.979051 + 0.203614i \(0.934731\pi\)
\(758\) 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 0.272933 0.962033i \(-0.412006\pi\)
−0.962033 + 0.272933i \(0.912006\pi\)
\(774\) 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 −0.909102 0.416574i \(-0.863231\pi\)
0.416574 + 0.909102i \(0.363231\pi\)
\(788\) 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 −0.845368 0.534184i \(-0.820619\pi\)
0.534184 + 0.845368i \(0.320619\pi\)
\(798\) 0