Properties

Label 3150.2.m.a.1457.2
Level 3150
Weight 2
Character 3150.1457
Analytic conductor 25.153
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1457.2
Root \(-0.707107 - 0.707107i\)
Character \(\chi\) = 3150.1457
Dual form 3150.2.m.a.2843.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.41421i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(3.41421 - 3.41421i) q^{17} -2.82843i q^{19} +(2.41421 + 2.41421i) q^{22} +(-0.828427 - 0.828427i) q^{23} +5.65685i q^{26} +(-0.707107 + 0.707107i) q^{28} +4.82843 q^{29} +10.2426 q^{31} +(-0.707107 + 0.707107i) q^{32} -4.82843i q^{34} +(2.24264 + 2.24264i) q^{37} +(-2.00000 - 2.00000i) q^{38} -8.82843i q^{41} +(8.07107 - 8.07107i) q^{43} +3.41421 q^{44} -1.17157 q^{46} +(0.757359 - 0.757359i) q^{47} +1.00000i q^{49} +(4.00000 + 4.00000i) q^{52} +(-5.41421 - 5.41421i) q^{53} +1.00000i q^{56} +(3.41421 - 3.41421i) q^{58} +2.82843 q^{59} +9.89949 q^{61} +(7.24264 - 7.24264i) q^{62} +1.00000i q^{64} +(-5.58579 - 5.58579i) q^{67} +(-3.41421 - 3.41421i) q^{68} +6.82843i q^{71} +(7.07107 - 7.07107i) q^{73} +3.17157 q^{74} -2.82843 q^{76} +(2.41421 - 2.41421i) q^{77} -5.65685i q^{79} +(-6.24264 - 6.24264i) q^{82} +(4.82843 + 4.82843i) q^{83} -11.4142i q^{86} +(2.41421 - 2.41421i) q^{88} -8.82843 q^{89} +5.65685 q^{91} +(-0.828427 + 0.828427i) q^{92} -1.07107i q^{94} +(7.41421 + 7.41421i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q - 16q^{13} - 4q^{14} - 4q^{16} + 8q^{17} + 4q^{22} + 8q^{23} + 8q^{29} + 24q^{31} - 8q^{37} - 8q^{38} + 4q^{43} + 8q^{44} - 16q^{46} + 20q^{47} + 16q^{52} - 16q^{53} + 8q^{58} + 12q^{62} - 28q^{67} - 8q^{68} + 24q^{74} + 4q^{77} - 8q^{82} + 8q^{83} + 4q^{88} - 24q^{89} + 8q^{92} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 3.41421i 1.02942i 0.857363 + 0.514712i \(0.172101\pi\)
−0.857363 + 0.514712i \(0.827899\pi\)
\(12\) 0 0
\(13\) −4.00000 + 4.00000i −1.10940 + 1.10940i −0.116171 + 0.993229i \(0.537062\pi\)
−0.993229 + 0.116171i \(0.962938\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.41421 3.41421i 0.828068 0.828068i −0.159181 0.987249i \(-0.550885\pi\)
0.987249 + 0.159181i \(0.0508853\pi\)
\(18\) 0 0
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.41421 + 2.41421i 0.514712 + 0.514712i
\(23\) −0.828427 0.828427i −0.172739 0.172739i 0.615443 0.788182i \(-0.288977\pi\)
−0.788182 + 0.615443i \(0.788977\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 5.65685i 1.10940i
\(27\) 0 0
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) 4.82843 0.896616 0.448308 0.893879i \(-0.352027\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(30\) 0 0
\(31\) 10.2426 1.83963 0.919816 0.392349i \(-0.128338\pi\)
0.919816 + 0.392349i \(0.128338\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) 4.82843i 0.828068i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.24264 + 2.24264i 0.368688 + 0.368688i 0.866999 0.498311i \(-0.166046\pi\)
−0.498311 + 0.866999i \(0.666046\pi\)
\(38\) −2.00000 2.00000i −0.324443 0.324443i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.82843i 1.37877i −0.724396 0.689384i \(-0.757881\pi\)
0.724396 0.689384i \(-0.242119\pi\)
\(42\) 0 0
\(43\) 8.07107 8.07107i 1.23083 1.23083i 0.267180 0.963647i \(-0.413908\pi\)
0.963647 0.267180i \(-0.0860917\pi\)
\(44\) 3.41421 0.514712
\(45\) 0 0
\(46\) −1.17157 −0.172739
\(47\) 0.757359 0.757359i 0.110472 0.110472i −0.649710 0.760182i \(-0.725110\pi\)
0.760182 + 0.649710i \(0.225110\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.00000 + 4.00000i 0.554700 + 0.554700i
\(53\) −5.41421 5.41421i −0.743699 0.743699i 0.229588 0.973288i \(-0.426262\pi\)
−0.973288 + 0.229588i \(0.926262\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 3.41421 3.41421i 0.448308 0.448308i
\(59\) 2.82843 0.368230 0.184115 0.982905i \(-0.441058\pi\)
0.184115 + 0.982905i \(0.441058\pi\)
\(60\) 0 0
\(61\) 9.89949 1.26750 0.633750 0.773538i \(-0.281515\pi\)
0.633750 + 0.773538i \(0.281515\pi\)
\(62\) 7.24264 7.24264i 0.919816 0.919816i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −5.58579 5.58579i −0.682412 0.682412i 0.278131 0.960543i \(-0.410285\pi\)
−0.960543 + 0.278131i \(0.910285\pi\)
\(68\) −3.41421 3.41421i −0.414034 0.414034i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.82843i 0.810385i 0.914231 + 0.405193i \(0.132796\pi\)
−0.914231 + 0.405193i \(0.867204\pi\)
\(72\) 0 0
\(73\) 7.07107 7.07107i 0.827606 0.827606i −0.159579 0.987185i \(-0.551014\pi\)
0.987185 + 0.159579i \(0.0510137\pi\)
\(74\) 3.17157 0.368688
\(75\) 0 0
\(76\) −2.82843 −0.324443
\(77\) 2.41421 2.41421i 0.275125 0.275125i
\(78\) 0 0
\(79\) 5.65685i 0.636446i −0.948016 0.318223i \(-0.896914\pi\)
0.948016 0.318223i \(-0.103086\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.24264 6.24264i −0.689384 0.689384i
\(83\) 4.82843 + 4.82843i 0.529989 + 0.529989i 0.920569 0.390580i \(-0.127726\pi\)
−0.390580 + 0.920569i \(0.627726\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 11.4142i 1.23083i
\(87\) 0 0
\(88\) 2.41421 2.41421i 0.257356 0.257356i
\(89\) −8.82843 −0.935811 −0.467906 0.883778i \(-0.654991\pi\)
−0.467906 + 0.883778i \(0.654991\pi\)
\(90\) 0 0
\(91\) 5.65685 0.592999
\(92\) −0.828427 + 0.828427i −0.0863695 + 0.0863695i
\(93\) 0 0
\(94\) 1.07107i 0.110472i
\(95\) 0 0
\(96\) 0 0
\(97\) 7.41421 + 7.41421i 0.752799 + 0.752799i 0.975001 0.222201i \(-0.0713243\pi\)
−0.222201 + 0.975001i \(0.571324\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 6.34315i 0.631167i 0.948898 + 0.315583i \(0.102200\pi\)
−0.948898 + 0.315583i \(0.897800\pi\)
\(102\) 0 0
\(103\) 4.58579 4.58579i 0.451851 0.451851i −0.444118 0.895969i \(-0.646483\pi\)
0.895969 + 0.444118i \(0.146483\pi\)
\(104\) 5.65685 0.554700
\(105\) 0 0
\(106\) −7.65685 −0.743699
\(107\) −10.8284 + 10.8284i −1.04682 + 1.04682i −0.0479750 + 0.998849i \(0.515277\pi\)
−0.998849 + 0.0479750i \(0.984723\pi\)
\(108\) 0 0
\(109\) 13.3137i 1.27522i −0.770358 0.637611i \(-0.779923\pi\)
0.770358 0.637611i \(-0.220077\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) 11.3137 + 11.3137i 1.06430 + 1.06430i 0.997785 + 0.0665190i \(0.0211893\pi\)
0.0665190 + 0.997785i \(0.478811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.82843i 0.448308i
\(117\) 0 0
\(118\) 2.00000 2.00000i 0.184115 0.184115i
\(119\) −4.82843 −0.442621
\(120\) 0 0
\(121\) −0.656854 −0.0597140
\(122\) 7.00000 7.00000i 0.633750 0.633750i
\(123\) 0 0
\(124\) 10.2426i 0.919816i
\(125\) 0 0
\(126\) 0 0
\(127\) 3.65685 + 3.65685i 0.324493 + 0.324493i 0.850488 0.525995i \(-0.176307\pi\)
−0.525995 + 0.850488i \(0.676307\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.485281i 0.0423992i −0.999775 0.0211996i \(-0.993251\pi\)
0.999775 0.0211996i \(-0.00674855\pi\)
\(132\) 0 0
\(133\) −2.00000 + 2.00000i −0.173422 + 0.173422i
\(134\) −7.89949 −0.682412
\(135\) 0 0
\(136\) −4.82843 −0.414034
\(137\) 12.0000 12.0000i 1.02523 1.02523i 0.0255558 0.999673i \(-0.491864\pi\)
0.999673 0.0255558i \(-0.00813555\pi\)
\(138\) 0 0
\(139\) 6.34315i 0.538019i 0.963138 + 0.269009i \(0.0866962\pi\)
−0.963138 + 0.269009i \(0.913304\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.82843 + 4.82843i 0.405193 + 0.405193i
\(143\) −13.6569 13.6569i −1.14204 1.14204i
\(144\) 0 0
\(145\) 0 0
\(146\) 10.0000i 0.827606i
\(147\) 0 0
\(148\) 2.24264 2.24264i 0.184344 0.184344i
\(149\) −20.1421 −1.65011 −0.825054 0.565054i \(-0.808855\pi\)
−0.825054 + 0.565054i \(0.808855\pi\)
\(150\) 0 0
\(151\) −13.1716 −1.07189 −0.535944 0.844254i \(-0.680044\pi\)
−0.535944 + 0.844254i \(0.680044\pi\)
\(152\) −2.00000 + 2.00000i −0.162221 + 0.162221i
\(153\) 0 0
\(154\) 3.41421i 0.275125i
\(155\) 0 0
\(156\) 0 0
\(157\) −1.65685 1.65685i −0.132231 0.132231i 0.637893 0.770125i \(-0.279806\pi\)
−0.770125 + 0.637893i \(0.779806\pi\)
\(158\) −4.00000 4.00000i −0.318223 0.318223i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.17157i 0.0923329i
\(162\) 0 0
\(163\) 13.7279 13.7279i 1.07525 1.07525i 0.0783260 0.996928i \(-0.475042\pi\)
0.996928 0.0783260i \(-0.0249575\pi\)
\(164\) −8.82843 −0.689384
\(165\) 0 0
\(166\) 6.82843 0.529989
\(167\) −10.4142 + 10.4142i −0.805876 + 0.805876i −0.984007 0.178131i \(-0.942995\pi\)
0.178131 + 0.984007i \(0.442995\pi\)
\(168\) 0 0
\(169\) 19.0000i 1.46154i
\(170\) 0 0
\(171\) 0 0
\(172\) −8.07107 8.07107i −0.615413 0.615413i
\(173\) 5.48528 + 5.48528i 0.417038 + 0.417038i 0.884182 0.467143i \(-0.154717\pi\)
−0.467143 + 0.884182i \(0.654717\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.41421i 0.257356i
\(177\) 0 0
\(178\) −6.24264 + 6.24264i −0.467906 + 0.467906i
\(179\) −19.4142 −1.45109 −0.725543 0.688177i \(-0.758411\pi\)
−0.725543 + 0.688177i \(0.758411\pi\)
\(180\) 0 0
\(181\) −4.92893 −0.366365 −0.183182 0.983079i \(-0.558640\pi\)
−0.183182 + 0.983079i \(0.558640\pi\)
\(182\) 4.00000 4.00000i 0.296500 0.296500i
\(183\) 0 0
\(184\) 1.17157i 0.0863695i
\(185\) 0 0
\(186\) 0 0
\(187\) 11.6569 + 11.6569i 0.852434 + 0.852434i
\(188\) −0.757359 0.757359i −0.0552361 0.0552361i
\(189\) 0 0
\(190\) 0 0
\(191\) 25.6569i 1.85646i −0.372001 0.928232i \(-0.621328\pi\)
0.372001 0.928232i \(-0.378672\pi\)
\(192\) 0 0
\(193\) 3.48528 3.48528i 0.250876 0.250876i −0.570454 0.821330i \(-0.693233\pi\)
0.821330 + 0.570454i \(0.193233\pi\)
\(194\) 10.4853 0.752799
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −1.75736 + 1.75736i −0.125207 + 0.125207i −0.766933 0.641727i \(-0.778218\pi\)
0.641727 + 0.766933i \(0.278218\pi\)
\(198\) 0 0
\(199\) 23.8995i 1.69419i 0.531441 + 0.847095i \(0.321651\pi\)
−0.531441 + 0.847095i \(0.678349\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.48528 + 4.48528i 0.315583 + 0.315583i
\(203\) −3.41421 3.41421i −0.239631 0.239631i
\(204\) 0 0
\(205\) 0 0
\(206\) 6.48528i 0.451851i
\(207\) 0 0
\(208\) 4.00000 4.00000i 0.277350 0.277350i
\(209\) 9.65685 0.667979
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −5.41421 + 5.41421i −0.371850 + 0.371850i
\(213\) 0 0
\(214\) 15.3137i 1.04682i
\(215\) 0 0
\(216\) 0 0
\(217\) −7.24264 7.24264i −0.491662 0.491662i
\(218\) −9.41421 9.41421i −0.637611 0.637611i
\(219\) 0 0
\(220\) 0 0
\(221\) 27.3137i 1.83732i
\(222\) 0 0
\(223\) 15.3137 15.3137i 1.02548 1.02548i 0.0258150 0.999667i \(-0.491782\pi\)
0.999667 0.0258150i \(-0.00821809\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) 6.82843 6.82843i 0.453219 0.453219i −0.443203 0.896421i \(-0.646158\pi\)
0.896421 + 0.443203i \(0.146158\pi\)
\(228\) 0 0
\(229\) 0.242641i 0.0160341i 0.999968 + 0.00801707i \(0.00255194\pi\)
−0.999968 + 0.00801707i \(0.997448\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.41421 3.41421i −0.224154 0.224154i
\(233\) 9.17157 + 9.17157i 0.600850 + 0.600850i 0.940538 0.339688i \(-0.110322\pi\)
−0.339688 + 0.940538i \(0.610322\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.82843i 0.184115i
\(237\) 0 0
\(238\) −3.41421 + 3.41421i −0.221311 + 0.221311i
\(239\) −2.34315 −0.151565 −0.0757827 0.997124i \(-0.524146\pi\)
−0.0757827 + 0.997124i \(0.524146\pi\)
\(240\) 0 0
\(241\) 24.1421 1.55513 0.777566 0.628802i \(-0.216454\pi\)
0.777566 + 0.628802i \(0.216454\pi\)
\(242\) −0.464466 + 0.464466i −0.0298570 + 0.0298570i
\(243\) 0 0
\(244\) 9.89949i 0.633750i
\(245\) 0 0
\(246\) 0 0
\(247\) 11.3137 + 11.3137i 0.719874 + 0.719874i
\(248\) −7.24264 7.24264i −0.459908 0.459908i
\(249\) 0 0
\(250\) 0 0
\(251\) 18.6274i 1.17575i 0.808951 + 0.587876i \(0.200036\pi\)
−0.808951 + 0.587876i \(0.799964\pi\)
\(252\) 0 0
\(253\) 2.82843 2.82843i 0.177822 0.177822i
\(254\) 5.17157 0.324493
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.4142 11.4142i 0.711999 0.711999i −0.254954 0.966953i \(-0.582060\pi\)
0.966953 + 0.254954i \(0.0820604\pi\)
\(258\) 0 0
\(259\) 3.17157i 0.197072i
\(260\) 0 0
\(261\) 0 0
\(262\) −0.343146 0.343146i −0.0211996 0.0211996i
\(263\) −3.65685 3.65685i −0.225491 0.225491i 0.585315 0.810806i \(-0.300971\pi\)
−0.810806 + 0.585315i \(0.800971\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.82843i 0.173422i
\(267\) 0 0
\(268\) −5.58579 + 5.58579i −0.341206 + 0.341206i
\(269\) 5.65685 0.344904 0.172452 0.985018i \(-0.444831\pi\)
0.172452 + 0.985018i \(0.444831\pi\)
\(270\) 0 0
\(271\) 23.8995 1.45179 0.725895 0.687805i \(-0.241426\pi\)
0.725895 + 0.687805i \(0.241426\pi\)
\(272\) −3.41421 + 3.41421i −0.207017 + 0.207017i
\(273\) 0 0
\(274\) 16.9706i 1.02523i
\(275\) 0 0
\(276\) 0 0
\(277\) 21.8995 + 21.8995i 1.31581 + 1.31581i 0.917057 + 0.398756i \(0.130558\pi\)
0.398756 + 0.917057i \(0.369442\pi\)
\(278\) 4.48528 + 4.48528i 0.269009 + 0.269009i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.92893i 0.294035i −0.989134 0.147018i \(-0.953033\pi\)
0.989134 0.147018i \(-0.0469674\pi\)
\(282\) 0 0
\(283\) −1.31371 + 1.31371i −0.0780919 + 0.0780919i −0.745074 0.666982i \(-0.767586\pi\)
0.666982 + 0.745074i \(0.267586\pi\)
\(284\) 6.82843 0.405193
\(285\) 0 0
\(286\) −19.3137 −1.14204
\(287\) −6.24264 + 6.24264i −0.368491 + 0.368491i
\(288\) 0 0
\(289\) 6.31371i 0.371395i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.07107 7.07107i −0.413803 0.413803i
\(293\) −2.65685 2.65685i −0.155215 0.155215i 0.625227 0.780443i \(-0.285006\pi\)
−0.780443 + 0.625227i \(0.785006\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.17157i 0.184344i
\(297\) 0 0
\(298\) −14.2426 + 14.2426i −0.825054 + 0.825054i
\(299\) 6.62742 0.383273
\(300\) 0 0
\(301\) −11.4142 −0.657904
\(302\) −9.31371 + 9.31371i −0.535944 + 0.535944i
\(303\) 0 0
\(304\) 2.82843i 0.162221i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) −2.41421 2.41421i −0.137563 0.137563i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.828427i 0.0469758i 0.999724 + 0.0234879i \(0.00747712\pi\)
−0.999724 + 0.0234879i \(0.992523\pi\)
\(312\) 0 0
\(313\) 6.24264 6.24264i 0.352855 0.352855i −0.508316 0.861171i \(-0.669732\pi\)
0.861171 + 0.508316i \(0.169732\pi\)
\(314\) −2.34315 −0.132231
\(315\) 0 0
\(316\) −5.65685 −0.318223
\(317\) 0.727922 0.727922i 0.0408842 0.0408842i −0.686369 0.727253i \(-0.740797\pi\)
0.727253 + 0.686369i \(0.240797\pi\)
\(318\) 0 0
\(319\) 16.4853i 0.922999i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.828427 + 0.828427i 0.0461664 + 0.0461664i
\(323\) −9.65685 9.65685i −0.537322 0.537322i
\(324\) 0 0
\(325\) 0 0
\(326\) 19.4142i 1.07525i
\(327\) 0 0
\(328\) −6.24264 + 6.24264i −0.344692 + 0.344692i
\(329\) −1.07107 −0.0590499
\(330\) 0 0
\(331\) −26.6274 −1.46358 −0.731788 0.681533i \(-0.761314\pi\)
−0.731788 + 0.681533i \(0.761314\pi\)
\(332\) 4.82843 4.82843i 0.264994 0.264994i
\(333\) 0 0
\(334\) 14.7279i 0.805876i
\(335\) 0 0
\(336\) 0 0
\(337\) −15.8284 15.8284i −0.862229 0.862229i 0.129367 0.991597i \(-0.458705\pi\)
−0.991597 + 0.129367i \(0.958705\pi\)
\(338\) −13.4350 13.4350i −0.730769 0.730769i
\(339\) 0 0
\(340\) 0 0
\(341\) 34.9706i 1.89376i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −11.4142 −0.615413
\(345\) 0 0
\(346\) 7.75736 0.417038
\(347\) 8.48528 8.48528i 0.455514 0.455514i −0.441666 0.897180i \(-0.645612\pi\)
0.897180 + 0.441666i \(0.145612\pi\)
\(348\) 0 0
\(349\) 7.27208i 0.389265i −0.980876 0.194633i \(-0.937649\pi\)
0.980876 0.194633i \(-0.0623515\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.41421 2.41421i −0.128678 0.128678i
\(353\) −18.3848 18.3848i −0.978523 0.978523i 0.0212513 0.999774i \(-0.493235\pi\)
−0.999774 + 0.0212513i \(0.993235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.82843i 0.467906i
\(357\) 0 0
\(358\) −13.7279 + 13.7279i −0.725543 + 0.725543i
\(359\) 15.7990 0.833839 0.416919 0.908943i \(-0.363110\pi\)
0.416919 + 0.908943i \(0.363110\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) −3.48528 + 3.48528i −0.183182 + 0.183182i
\(363\) 0 0
\(364\) 5.65685i 0.296500i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.75736 + 1.75736i 0.0917334 + 0.0917334i 0.751484 0.659751i \(-0.229338\pi\)
−0.659751 + 0.751484i \(0.729338\pi\)
\(368\) 0.828427 + 0.828427i 0.0431847 + 0.0431847i
\(369\) 0 0
\(370\) 0 0
\(371\) 7.65685i 0.397524i
\(372\) 0 0
\(373\) −3.07107 + 3.07107i −0.159014 + 0.159014i −0.782130 0.623116i \(-0.785867\pi\)
0.623116 + 0.782130i \(0.285867\pi\)
\(374\) 16.4853 0.852434
\(375\) 0 0
\(376\) −1.07107 −0.0552361
\(377\) −19.3137 + 19.3137i −0.994707 + 0.994707i
\(378\) 0 0
\(379\) 13.7990i 0.708806i 0.935093 + 0.354403i \(0.115316\pi\)
−0.935093 + 0.354403i \(0.884684\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −18.1421 18.1421i −0.928232 0.928232i
\(383\) 1.58579 + 1.58579i 0.0810299 + 0.0810299i 0.746460 0.665430i \(-0.231752\pi\)
−0.665430 + 0.746460i \(0.731752\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.92893i 0.250876i
\(387\) 0 0
\(388\) 7.41421 7.41421i 0.376400 0.376400i
\(389\) −29.7990 −1.51087 −0.755434 0.655224i \(-0.772574\pi\)
−0.755434 + 0.655224i \(0.772574\pi\)
\(390\) 0 0
\(391\) −5.65685 −0.286079
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 0 0
\(394\) 2.48528i 0.125207i
\(395\) 0 0
\(396\) 0 0
\(397\) 15.0711 + 15.0711i 0.756395 + 0.756395i 0.975664 0.219269i \(-0.0703673\pi\)
−0.219269 + 0.975664i \(0.570367\pi\)
\(398\) 16.8995 + 16.8995i 0.847095 + 0.847095i
\(399\) 0 0
\(400\) 0 0
\(401\) 26.8701i 1.34183i −0.741536 0.670913i \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) 0 0
\(403\) −40.9706 + 40.9706i −2.04089 + 2.04089i
\(404\) 6.34315 0.315583
\(405\) 0 0
\(406\) −4.82843 −0.239631
\(407\) −7.65685 + 7.65685i −0.379536 + 0.379536i
\(408\) 0 0
\(409\) 10.0000i 0.494468i 0.968956 + 0.247234i \(0.0795217\pi\)
−0.968956 + 0.247234i \(0.920478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.58579 4.58579i −0.225925 0.225925i
\(413\) −2.00000 2.00000i −0.0984136 0.0984136i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.65685i 0.277350i
\(417\) 0 0
\(418\) 6.82843 6.82843i 0.333989 0.333989i
\(419\) −26.6274 −1.30083 −0.650417 0.759577i \(-0.725406\pi\)
−0.650417 + 0.759577i \(0.725406\pi\)
\(420\) 0 0
\(421\) 4.62742 0.225527 0.112763 0.993622i \(-0.464030\pi\)
0.112763 + 0.993622i \(0.464030\pi\)
\(422\) −2.82843 + 2.82843i −0.137686 + 0.137686i
\(423\) 0 0
\(424\) 7.65685i 0.371850i
\(425\) 0 0
\(426\) 0 0
\(427\) −7.00000 7.00000i −0.338754 0.338754i
\(428\) 10.8284 + 10.8284i 0.523412 + 0.523412i
\(429\) 0 0
\(430\) 0 0
\(431\) 2.14214i 0.103183i −0.998668 0.0515915i \(-0.983571\pi\)
0.998668 0.0515915i \(-0.0164294\pi\)
\(432\) 0 0
\(433\) −9.75736 + 9.75736i −0.468909 + 0.468909i −0.901561 0.432652i \(-0.857578\pi\)
0.432652 + 0.901561i \(0.357578\pi\)
\(434\) −10.2426 −0.491662
\(435\) 0 0
\(436\) −13.3137 −0.637611
\(437\) −2.34315 + 2.34315i −0.112088 + 0.112088i
\(438\) 0 0
\(439\) 15.8995i 0.758841i −0.925224 0.379421i \(-0.876123\pi\)
0.925224 0.379421i \(-0.123877\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 19.3137 + 19.3137i 0.918659 + 0.918659i
\(443\) −20.4853 20.4853i −0.973285 0.973285i 0.0263672 0.999652i \(-0.491606\pi\)
−0.999652 + 0.0263672i \(0.991606\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 21.6569i 1.02548i
\(447\) 0 0
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) −8.72792 −0.411896 −0.205948 0.978563i \(-0.566028\pi\)
−0.205948 + 0.978563i \(0.566028\pi\)
\(450\) 0 0
\(451\) 30.1421 1.41934
\(452\) 11.3137 11.3137i 0.532152 0.532152i
\(453\) 0 0
\(454\) 9.65685i 0.453219i
\(455\) 0 0
\(456\) 0 0
\(457\) −7.82843 7.82843i −0.366198 0.366198i 0.499890 0.866089i \(-0.333374\pi\)
−0.866089 + 0.499890i \(0.833374\pi\)
\(458\) 0.171573 + 0.171573i 0.00801707 + 0.00801707i
\(459\) 0 0
\(460\) 0 0
\(461\) 17.3137i 0.806380i 0.915116 + 0.403190i \(0.132099\pi\)
−0.915116 + 0.403190i \(0.867901\pi\)
\(462\) 0 0
\(463\) −19.7990 + 19.7990i −0.920137 + 0.920137i −0.997039 0.0769016i \(-0.975497\pi\)
0.0769016 + 0.997039i \(0.475497\pi\)
\(464\) −4.82843 −0.224154
\(465\) 0 0
\(466\) 12.9706 0.600850
\(467\) −14.0000 + 14.0000i −0.647843 + 0.647843i −0.952471 0.304629i \(-0.901468\pi\)
0.304629 + 0.952471i \(0.401468\pi\)
\(468\) 0 0
\(469\) 7.89949i 0.364765i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.00000 2.00000i −0.0920575 0.0920575i
\(473\) 27.5563 + 27.5563i 1.26704 + 1.26704i
\(474\) 0 0
\(475\) 0 0
\(476\) 4.82843i 0.221311i
\(477\) 0 0
\(478\) −1.65685 + 1.65685i −0.0757827 + 0.0757827i
\(479\) −24.8284 −1.13444 −0.567220 0.823566i \(-0.691981\pi\)
−0.567220 + 0.823566i \(0.691981\pi\)
\(480\) 0 0
\(481\) −17.9411 −0.818045
\(482\) 17.0711 17.0711i 0.777566 0.777566i
\(483\) 0 0
\(484\) 0.656854i 0.0298570i
\(485\) 0 0
\(486\) 0 0
\(487\) 14.9706 + 14.9706i 0.678381 + 0.678381i 0.959634 0.281253i \(-0.0907499\pi\)
−0.281253 + 0.959634i \(0.590750\pi\)
\(488\) −7.00000 7.00000i −0.316875 0.316875i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.27208i 0.0574081i −0.999588 0.0287040i \(-0.990862\pi\)
0.999588 0.0287040i \(-0.00913803\pi\)
\(492\) 0 0
\(493\) 16.4853 16.4853i 0.742460 0.742460i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) −10.2426 −0.459908
\(497\) 4.82843 4.82843i 0.216585 0.216585i
\(498\) 0 0
\(499\) 27.4558i 1.22909i 0.788881 + 0.614546i \(0.210661\pi\)
−0.788881 + 0.614546i \(0.789339\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 13.1716 + 13.1716i 0.587876 + 0.587876i
\(503\) 14.5563 + 14.5563i 0.649036 + 0.649036i 0.952760 0.303724i \(-0.0982302\pi\)
−0.303724 + 0.952760i \(0.598230\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.00000i 0.177822i
\(507\) 0 0
\(508\) 3.65685 3.65685i 0.162247 0.162247i
\(509\) 29.6569 1.31452 0.657258 0.753665i \(-0.271716\pi\)
0.657258 + 0.753665i \(0.271716\pi\)
\(510\) 0 0
\(511\) −10.0000 −0.442374
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 16.1421i 0.711999i
\(515\) 0 0
\(516\) 0 0
\(517\) 2.58579 + 2.58579i 0.113723 + 0.113723i
\(518\) −2.24264 2.24264i −0.0985360 0.0985360i
\(519\) 0 0
\(520\) 0 0
\(521\) 30.7696i 1.34804i −0.738714 0.674019i \(-0.764566\pi\)
0.738714 0.674019i \(-0.235434\pi\)
\(522\) 0 0
\(523\) 2.68629 2.68629i 0.117463 0.117463i −0.645932 0.763395i \(-0.723531\pi\)
0.763395 + 0.645932i \(0.223531\pi\)
\(524\) −0.485281 −0.0211996
\(525\) 0 0
\(526\) −5.17157 −0.225491
\(527\) 34.9706 34.9706i 1.52334 1.52334i
\(528\) 0 0
\(529\) 21.6274i 0.940322i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000 + 2.00000i 0.0867110 + 0.0867110i
\(533\) 35.3137 + 35.3137i 1.52961 + 1.52961i
\(534\) 0 0
\(535\) 0 0
\(536\) 7.89949i 0.341206i
\(537\) 0 0
\(538\) 4.00000 4.00000i 0.172452 0.172452i
\(539\) −3.41421 −0.147061
\(540\) 0 0
\(541\) 33.1127 1.42363 0.711813 0.702369i \(-0.247874\pi\)
0.711813 + 0.702369i \(0.247874\pi\)
\(542\) 16.8995 16.8995i 0.725895 0.725895i
\(543\) 0 0
\(544\) 4.82843i 0.207017i
\(545\) 0 0
\(546\) 0 0
\(547\) −18.5563 18.5563i −0.793412 0.793412i 0.188635 0.982047i \(-0.439594\pi\)
−0.982047 + 0.188635i \(0.939594\pi\)
\(548\) −12.0000 12.0000i −0.512615 0.512615i
\(549\) 0 0
\(550\) 0 0
\(551\) 13.6569i 0.581802i
\(552\) 0 0
\(553\) −4.00000 + 4.00000i −0.170097 + 0.170097i
\(554\) 30.9706 1.31581
\(555\) 0 0
\(556\) 6.34315 0.269009
\(557\) −23.5563 + 23.5563i −0.998115 + 0.998115i −0.999998 0.00188368i \(-0.999400\pi\)
0.00188368 + 0.999998i \(0.499400\pi\)
\(558\) 0 0
\(559\) 64.5685i 2.73096i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.48528 3.48528i −0.147018 0.147018i
\(563\) 29.3137 + 29.3137i 1.23543 + 1.23543i 0.961851 + 0.273575i \(0.0882061\pi\)
0.273575 + 0.961851i \(0.411794\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.85786i 0.0780919i
\(567\) 0 0
\(568\) 4.82843 4.82843i 0.202596 0.202596i
\(569\) 33.8995 1.42114 0.710570 0.703626i \(-0.248437\pi\)
0.710570 + 0.703626i \(0.248437\pi\)
\(570\) 0 0
\(571\) −44.9706 −1.88196 −0.940980 0.338463i \(-0.890093\pi\)
−0.940980 + 0.338463i \(0.890093\pi\)
\(572\) −13.6569 + 13.6569i −0.571022 + 0.571022i
\(573\) 0 0
\(574\) 8.82843i 0.368491i
\(575\) 0 0
\(576\) 0 0
\(577\) −14.7279 14.7279i −0.613131 0.613131i 0.330629 0.943761i \(-0.392739\pi\)
−0.943761 + 0.330629i \(0.892739\pi\)
\(578\) −4.46447 4.46447i −0.185697 0.185697i
\(579\) 0 0
\(580\) 0 0
\(581\) 6.82843i 0.283291i
\(582\) 0 0
\(583\) 18.4853 18.4853i 0.765582 0.765582i
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) −3.75736 −0.155215
\(587\) −21.7990 + 21.7990i −0.899741 + 0.899741i −0.995413 0.0956723i \(-0.969500\pi\)
0.0956723 + 0.995413i \(0.469500\pi\)
\(588\) 0 0
\(589\) 28.9706i 1.19371i
\(590\) 0 0
\(591\) 0 0
\(592\) −2.24264 2.24264i −0.0921720 0.0921720i
\(593\) 20.3848 + 20.3848i 0.837102 + 0.837102i 0.988477 0.151374i \(-0.0483698\pi\)
−0.151374 + 0.988477i \(0.548370\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.1421i 0.825054i
\(597\) 0 0
\(598\) 4.68629 4.68629i 0.191637 0.191637i
\(599\) −7.31371 −0.298830 −0.149415 0.988775i \(-0.547739\pi\)
−0.149415 + 0.988775i \(0.547739\pi\)
\(600\) 0 0
\(601\) 24.1421 0.984778 0.492389 0.870375i \(-0.336124\pi\)
0.492389 + 0.870375i \(0.336124\pi\)
\(602\) −8.07107 + 8.07107i −0.328952 + 0.328952i
\(603\) 0 0
\(604\) 13.1716i 0.535944i
\(605\) 0 0
\(606\) 0 0
\(607\) −15.3137 15.3137i −0.621564 0.621564i 0.324367 0.945931i \(-0.394849\pi\)
−0.945931 + 0.324367i \(0.894849\pi\)
\(608\) 2.00000 + 2.00000i 0.0811107 + 0.0811107i
\(609\) 0 0
\(610\) 0 0
\(611\) 6.05887i 0.245116i
\(612\) 0 0
\(613\) −5.07107 + 5.07107i −0.204818 + 0.204818i −0.802061 0.597242i \(-0.796263\pi\)
0.597242 + 0.802061i \(0.296263\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −3.41421 −0.137563
\(617\) −24.0416 + 24.0416i −0.967880 + 0.967880i −0.999500 0.0316203i \(-0.989933\pi\)
0.0316203 + 0.999500i \(0.489933\pi\)
\(618\) 0 0
\(619\) 46.1421i 1.85461i 0.374308 + 0.927305i \(0.377880\pi\)
−0.374308 + 0.927305i \(0.622120\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0.585786 + 0.585786i 0.0234879 + 0.0234879i
\(623\) 6.24264 + 6.24264i 0.250106 + 0.250106i
\(624\) 0 0
\(625\) 0 0
\(626\) 8.82843i 0.352855i
\(627\) 0 0
\(628\) −1.65685 + 1.65685i −0.0661157 + 0.0661157i
\(629\) 15.3137 0.610598
\(630\) 0 0
\(631\) −39.7990 −1.58437 −0.792186 0.610279i \(-0.791057\pi\)
−0.792186 + 0.610279i \(0.791057\pi\)
\(632\) −4.00000 + 4.00000i −0.159111 + 0.159111i
\(633\) 0 0
\(634\) 1.02944i 0.0408842i
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 4.00000i −0.158486 0.158486i
\(638\) 11.6569 + 11.6569i 0.461499 + 0.461499i
\(639\) 0 0
\(640\) 0 0
\(641\) 21.2132i 0.837871i 0.908016 + 0.418936i \(0.137597\pi\)
−0.908016 + 0.418936i \(0.862403\pi\)
\(642\) 0 0
\(643\) −22.9706 + 22.9706i −0.905871 + 0.905871i −0.995936 0.0900653i \(-0.971292\pi\)
0.0900653 + 0.995936i \(0.471292\pi\)
\(644\) 1.17157 0.0461664
\(645\) 0 0
\(646\) −13.6569 −0.537322
\(647\) −24.7574 + 24.7574i −0.973312 + 0.973312i −0.999653 0.0263408i \(-0.991614\pi\)
0.0263408 + 0.999653i \(0.491614\pi\)
\(648\) 0 0
\(649\) 9.65685i 0.379065i
\(650\) 0 0
\(651\) 0 0
\(652\) −13.7279 13.7279i −0.537627 0.537627i
\(653\) 5.75736 + 5.75736i 0.225303 + 0.225303i 0.810727 0.585424i \(-0.199072\pi\)
−0.585424 + 0.810727i \(0.699072\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 8.82843i 0.344692i
\(657\) 0 0
\(658\) −0.757359 + 0.757359i −0.0295249 + 0.0295249i
\(659\) 1.27208 0.0495531 0.0247766 0.999693i \(-0.492113\pi\)
0.0247766 + 0.999693i \(0.492113\pi\)
\(660\) 0 0
\(661\) −8.04163 −0.312783 −0.156392 0.987695i \(-0.549986\pi\)
−0.156392 + 0.987695i \(0.549986\pi\)
\(662\) −18.8284 + 18.8284i −0.731788 + 0.731788i
\(663\) 0 0
\(664\) 6.82843i 0.264994i
\(665\) 0 0
\(666\) 0 0
\(667\) −4.00000 4.00000i −0.154881 0.154881i
\(668\) 10.4142 + 10.4142i 0.402938 + 0.402938i
\(669\) 0 0
\(670\) 0 0
\(671\) 33.7990i 1.30480i
\(672\) 0 0
\(673\) −14.6569 + 14.6569i −0.564980 + 0.564980i −0.930718 0.365738i \(-0.880817\pi\)
0.365738 + 0.930718i \(0.380817\pi\)
\(674\) −22.3848 −0.862229
\(675\) 0 0
\(676\) −19.0000 −0.730769
\(677\) 10.1716 10.1716i 0.390925 0.390925i −0.484092 0.875017i \(-0.660850\pi\)
0.875017 + 0.484092i \(0.160850\pi\)
\(678\) 0 0
\(679\) 10.4853i 0.402388i
\(680\) 0 0
\(681\) 0 0
\(682\) 24.7279 + 24.7279i 0.946881 + 0.946881i
\(683\) −12.3848 12.3848i −0.473890 0.473890i 0.429281 0.903171i \(-0.358767\pi\)
−0.903171 + 0.429281i \(0.858767\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −8.07107 + 8.07107i −0.307707 + 0.307707i
\(689\) 43.3137 1.65012
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 5.48528 5.48528i 0.208519 0.208519i
\(693\) 0 0
\(694\) 12.0000i 0.455514i
\(695\) 0 0
\(696\) 0 0
\(697\) −30.1421 30.1421i −1.14171 1.14171i
\(698\) −5.14214 5.14214i −0.194633 0.194633i
\(699\) 0 0
\(700\) 0 0
\(701\) 35.1716i 1.32841i 0.747550 + 0.664206i \(0.231230\pi\)
−0.747550 + 0.664206i \(0.768770\pi\)
\(702\) 0 0
\(703\) 6.34315 6.34315i 0.239236 0.239236i
\(704\) −3.41421 −0.128678
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) 4.48528 4.48528i 0.168686 0.168686i
\(708\) 0 0
\(709\) 35.1716i 1.32090i 0.750872 + 0.660448i \(0.229634\pi\)
−0.750872 + 0.660448i \(0.770366\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.24264 + 6.24264i 0.233953 + 0.233953i
\(713\) −8.48528 8.48528i −0.317776 0.317776i
\(714\) 0 0
\(715\) 0 0
\(716\) 19.4142i 0.725543i
\(717\) 0 0
\(718\) 11.1716 11.1716i 0.416919 0.416919i
\(719\) 6.62742 0.247161 0.123580 0.992335i \(-0.460562\pi\)
0.123580 + 0.992335i \(0.460562\pi\)
\(720\) 0 0
\(721\) −6.48528 −0.241524
\(722\) 7.77817 7.77817i 0.289474 0.289474i
\(723\) 0 0
\(724\) 4.92893i 0.183182i
\(725\) 0 0
\(726\) 0 0
\(727\) −22.6274 22.6274i −0.839204 0.839204i 0.149550 0.988754i \(-0.452218\pi\)
−0.988754 + 0.149550i \(0.952218\pi\)
\(728\) −4.00000 4.00000i −0.148250 0.148250i
\(729\) 0 0
\(730\) 0 0
\(731\) 55.1127i 2.03842i
\(732\) 0 0
\(733\) 31.5563 31.5563i 1.16556 1.16556i 0.182321 0.983239i \(-0.441639\pi\)
0.983239 0.182321i \(-0.0583611\pi\)
\(734\) 2.48528 0.0917334
\(735\) 0 0
\(736\) 1.17157 0.0431847
\(737\) 19.0711 19.0711i 0.702492 0.702492i
\(738\) 0 0
\(739\) 43.4558i 1.59855i −0.600966 0.799275i \(-0.705217\pi\)
0.600966 0.799275i \(-0.294783\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 5.41421 + 5.41421i 0.198762 + 0.198762i
\(743\) 31.1127 + 31.1127i 1.14141 + 1.14141i 0.988192 + 0.153222i \(0.0489651\pi\)
0.153222 + 0.988192i \(0.451035\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 4.34315i 0.159014i
\(747\) 0 0
\(748\) 11.6569 11.6569i 0.426217 0.426217i
\(749\) 15.3137 0.559551
\(750\) 0 0
\(751\) 31.5147 1.14999 0.574994 0.818157i \(-0.305004\pi\)
0.574994 + 0.818157i \(0.305004\pi\)
\(752\) −0.757359 + 0.757359i −0.0276181 + 0.0276181i
\(753\) 0 0
\(754\) 27.3137i 0.994707i
\(755\) 0 0
\(756\) 0 0
\(757\) −7.55635 7.55635i −0.274640 0.274640i 0.556325 0.830965i \(-0.312211\pi\)
−0.830965 + 0.556325i \(0.812211\pi\)
\(758\) 9.75736 + 9.75736i 0.354403 + 0.354403i
\(759\) 0 0
\(760\) 0 0
\(761\) 14.9706i 0.542682i −0.962483 0.271341i \(-0.912533\pi\)
0.962483 0.271341i \(-0.0874672\pi\)
\(762\) 0 0
\(763\) −9.41421 + 9.41421i −0.340817 + 0.340817i
\(764\) −25.6569 −0.928232
\(765\) 0 0
\(766\) 2.24264 0.0810299
\(767\) −11.3137 + 11.3137i −0.408514 + 0.408514i
\(768\) 0 0
\(769\) 37.5980i 1.35582i −0.735146 0.677909i \(-0.762886\pi\)
0.735146 0.677909i \(-0.237114\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.48528 3.48528i −0.125438 0.125438i
\(773\) −32.9411 32.9411i −1.18481 1.18481i −0.978483 0.206327i \(-0.933849\pi\)
−0.206327 0.978483i \(-0.566151\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 10.4853i 0.376400i
\(777\) 0 0
\(778\) −21.0711 + 21.0711i −0.755434 + 0.755434i
\(779\) −24.9706 −0.894663
\(780\) 0 0
\(781\) −23.3137 −0.834230
\(782\) −4.00000 + 4.00000i −0.143040 + 0.143040i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 32.4853 + 32.4853i 1.15798 + 1.15798i 0.984910 + 0.173065i \(0.0553670\pi\)
0.173065 + 0.984910i \(0.444633\pi\)
\(788\) 1.75736 + 1.75736i 0.0626033 + 0.0626033i
\(789\) 0 0
\(790\) 0 0
\(791\) 16.0000i 0.568895i
\(792\) 0 0
\(793\) −39.5980 + 39.5980i −1.40617 + 1.40617i
\(794\) 21.3137 0.756395
\(795\) 0 0
\(796\) 23.8995 0.847095
\(797\) 25.8284 25.8284i 0.914890 0.914890i −0.0817621 0.996652i \(-0.526055\pi\)
0.996652 + 0.0817621i \(0.0260548\pi\)
\(798\) 0 0
\(799\) 5.17157i 0.182957i
\(800\) 0 0
\(801\) 0 0
\(802\) −19.0000 19.0000i −0.670913 0.670913i
\(803\) 24.1421 + 24.1421i 0.851957 + 0.851957i
\(804\) 0 0