Properties

Label 3150.2.m.b.2843.2
Level 3150
Weight 2
Character 3150.2843
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 2843.2
Root \(0.707107 + 0.707107i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.b.1457.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +0.585786i q^{11} +(-4.00000 - 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-0.585786 - 0.585786i) q^{17} -2.82843i q^{19} +(-0.414214 + 0.414214i) q^{22} +(-4.82843 + 4.82843i) q^{23} -5.65685i q^{26} +(0.707107 + 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(-0.707107 - 0.707107i) q^{32} -0.828427i q^{34} +(-6.24264 + 6.24264i) q^{37} +(2.00000 - 2.00000i) q^{38} -3.17157i q^{41} +(-6.07107 - 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(-9.24264 - 9.24264i) q^{47} -1.00000i q^{49} +(4.00000 - 4.00000i) q^{52} +(2.58579 - 2.58579i) q^{53} +1.00000i q^{56} +(0.585786 + 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(1.24264 + 1.24264i) q^{62} -1.00000i q^{64} +(-8.41421 + 8.41421i) q^{67} +(0.585786 - 0.585786i) q^{68} +1.17157i q^{71} +(-7.07107 - 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(0.414214 + 0.414214i) q^{77} -5.65685i q^{79} +(2.24264 - 2.24264i) q^{82} +(0.828427 - 0.828427i) q^{83} -8.58579i q^{86} +(-0.414214 - 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(-4.82843 - 4.82843i) q^{92} -13.0711i q^{94} +(4.58579 - 4.58579i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q - 16q^{13} + 4q^{14} - 4q^{16} - 8q^{17} + 4q^{22} - 8q^{23} - 8q^{29} + 24q^{31} - 8q^{37} + 8q^{38} + 4q^{43} - 8q^{44} - 16q^{46} - 20q^{47} + 16q^{52} + 16q^{53} + 8q^{58} - 12q^{62} - 28q^{67} + 8q^{68} - 24q^{74} - 4q^{77} - 8q^{82} - 8q^{83} + 4q^{88} + 24q^{89} - 8q^{92} + 24q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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
\(11\) 0.585786i 0.176621i 0.996093 + 0.0883106i \(0.0281468\pi\)
−0.996093 + 0.0883106i \(0.971853\pi\)
\(12\) 0 0
\(13\) −4.00000 4.00000i −1.10940 1.10940i −0.993229 0.116171i \(-0.962938\pi\)
−0.116171 0.993229i \(-0.537062\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −0.585786 0.585786i −0.142074 0.142074i 0.632492 0.774567i \(-0.282032\pi\)
−0.774567 + 0.632492i \(0.782032\pi\)
\(18\) 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
\(22\) −0.414214 + 0.414214i −0.0883106 + 0.0883106i
\(23\) −4.82843 + 4.82843i −1.00680 + 1.00680i −0.00681991 + 0.999977i \(0.502171\pi\)
−0.999977 + 0.00681991i \(0.997829\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 5.65685i 1.10940i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 0.828427 0.153835 0.0769175 0.997037i \(-0.475492\pi\)
0.0769175 + 0.997037i \(0.475492\pi\)
\(30\) 0 0
\(31\) 1.75736 0.315631 0.157816 0.987469i \(-0.449555\pi\)
0.157816 + 0.987469i \(0.449555\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 0.828427i 0.142074i
\(35\) 0 0
\(36\) 0 0
\(37\) −6.24264 + 6.24264i −1.02628 + 1.02628i −0.0266387 + 0.999645i \(0.508480\pi\)
−0.999645 + 0.0266387i \(0.991520\pi\)
\(38\) 2.00000 2.00000i 0.324443 0.324443i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.17157i 0.495316i −0.968847 0.247658i \(-0.920339\pi\)
0.968847 0.247658i \(-0.0796610\pi\)
\(42\) 0 0
\(43\) −6.07107 6.07107i −0.925829 0.925829i 0.0716040 0.997433i \(-0.477188\pi\)
−0.997433 + 0.0716040i \(0.977188\pi\)
\(44\) −0.585786 −0.0883106
\(45\) 0 0
\(46\) −6.82843 −1.00680
\(47\) −9.24264 9.24264i −1.34818 1.34818i −0.887640 0.460537i \(-0.847657\pi\)
−0.460537 0.887640i \(-0.652343\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.00000 4.00000i 0.554700 0.554700i
\(53\) 2.58579 2.58579i 0.355185 0.355185i −0.506849 0.862035i \(-0.669190\pi\)
0.862035 + 0.506849i \(0.169190\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 0.585786 + 0.585786i 0.0769175 + 0.0769175i
\(59\) 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 \(-0.718485\pi\)
−0.633750 + 0.773538i \(0.718485\pi\)
\(62\) 1.24264 + 1.24264i 0.157816 + 0.157816i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −8.41421 + 8.41421i −1.02796 + 1.02796i −0.0283621 + 0.999598i \(0.509029\pi\)
−0.999598 + 0.0283621i \(0.990971\pi\)
\(68\) 0.585786 0.585786i 0.0710370 0.0710370i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.17157i 0.139040i 0.997581 + 0.0695201i \(0.0221468\pi\)
−0.997581 + 0.0695201i \(0.977853\pi\)
\(72\) 0 0
\(73\) −7.07107 7.07107i −0.827606 0.827606i 0.159579 0.987185i \(-0.448986\pi\)
−0.987185 + 0.159579i \(0.948986\pi\)
\(74\) −8.82843 −1.02628
\(75\) 0 0
\(76\) 2.82843 0.324443
\(77\) 0.414214 + 0.414214i 0.0472040 + 0.0472040i
\(78\) 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
\(82\) 2.24264 2.24264i 0.247658 0.247658i
\(83\) 0.828427 0.828427i 0.0909317 0.0909317i −0.660178 0.751109i \(-0.729519\pi\)
0.751109 + 0.660178i \(0.229519\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.58579i 0.925829i
\(87\) 0 0
\(88\) −0.414214 0.414214i −0.0441553 0.0441553i
\(89\) 3.17157 0.336186 0.168093 0.985771i \(-0.446239\pi\)
0.168093 + 0.985771i \(0.446239\pi\)
\(90\) 0 0
\(91\) −5.65685 −0.592999
\(92\) −4.82843 4.82843i −0.503398 0.503398i
\(93\) 0 0
\(94\) 13.0711i 1.34818i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.58579 4.58579i 0.465616 0.465616i −0.434875 0.900491i \(-0.643207\pi\)
0.900491 + 0.434875i \(0.143207\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 17.6569i 1.75692i 0.477813 + 0.878461i \(0.341429\pi\)
−0.477813 + 0.878461i \(0.658571\pi\)
\(102\) 0 0
\(103\) 7.41421 + 7.41421i 0.730544 + 0.730544i 0.970728 0.240183i \(-0.0772076\pi\)
−0.240183 + 0.970728i \(0.577208\pi\)
\(104\) 5.65685 0.554700
\(105\) 0 0
\(106\) 3.65685 0.355185
\(107\) 5.17157 + 5.17157i 0.499955 + 0.499955i 0.911424 0.411469i \(-0.134984\pi\)
−0.411469 + 0.911424i \(0.634984\pi\)
\(108\) 0 0
\(109\) 9.31371i 0.892091i −0.895010 0.446046i \(-0.852832\pi\)
0.895010 0.446046i \(-0.147168\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 11.3137 11.3137i 1.06430 1.06430i 0.0665190 0.997785i \(-0.478811\pi\)
0.997785 0.0665190i \(-0.0211893\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.828427i 0.0769175i
\(117\) 0 0
\(118\) 2.00000 + 2.00000i 0.184115 + 0.184115i
\(119\) −0.828427 −0.0759418
\(120\) 0 0
\(121\) 10.6569 0.968805
\(122\) −7.00000 7.00000i −0.633750 0.633750i
\(123\) 0 0
\(124\) 1.75736i 0.157816i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.65685 + 7.65685i −0.679436 + 0.679436i −0.959873 0.280437i \(-0.909521\pi\)
0.280437 + 0.959873i \(0.409521\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 16.4853i 1.44033i 0.693805 + 0.720163i \(0.255933\pi\)
−0.693805 + 0.720163i \(0.744067\pi\)
\(132\) 0 0
\(133\) −2.00000 2.00000i −0.173422 0.173422i
\(134\) −11.8995 −1.02796
\(135\) 0 0
\(136\) 0.828427 0.0710370
\(137\) −12.0000 12.0000i −1.02523 1.02523i −0.999673 0.0255558i \(-0.991864\pi\)
−0.0255558 0.999673i \(-0.508136\pi\)
\(138\) 0 0
\(139\) 17.6569i 1.49763i −0.662776 0.748817i \(-0.730622\pi\)
0.662776 0.748817i \(-0.269378\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.828427 + 0.828427i −0.0695201 + 0.0695201i
\(143\) 2.34315 2.34315i 0.195944 0.195944i
\(144\) 0 0
\(145\) 0 0
\(146\) 10.0000i 0.827606i
\(147\) 0 0
\(148\) −6.24264 6.24264i −0.513142 0.513142i
\(149\) −8.14214 −0.667030 −0.333515 0.942745i \(-0.608235\pi\)
−0.333515 + 0.942745i \(0.608235\pi\)
\(150\) 0 0
\(151\) −18.8284 −1.53224 −0.766118 0.642700i \(-0.777814\pi\)
−0.766118 + 0.642700i \(0.777814\pi\)
\(152\) 2.00000 + 2.00000i 0.162221 + 0.162221i
\(153\) 0 0
\(154\) 0.585786i 0.0472040i
\(155\) 0 0
\(156\) 0 0
\(157\) 9.65685 9.65685i 0.770701 0.770701i −0.207528 0.978229i \(-0.566542\pi\)
0.978229 + 0.207528i \(0.0665419\pi\)
\(158\) 4.00000 4.00000i 0.318223 0.318223i
\(159\) 0 0
\(160\) 0 0
\(161\) 6.82843i 0.538155i
\(162\) 0 0
\(163\) −11.7279 11.7279i −0.918602 0.918602i 0.0783260 0.996928i \(-0.475042\pi\)
−0.996928 + 0.0783260i \(0.975042\pi\)
\(164\) 3.17157 0.247658
\(165\) 0 0
\(166\) 1.17157 0.0909317
\(167\) 7.58579 + 7.58579i 0.587006 + 0.587006i 0.936819 0.349814i \(-0.113755\pi\)
−0.349814 + 0.936819i \(0.613755\pi\)
\(168\) 0 0
\(169\) 19.0000i 1.46154i
\(170\) 0 0
\(171\) 0 0
\(172\) 6.07107 6.07107i 0.462915 0.462915i
\(173\) 11.4853 11.4853i 0.873210 0.873210i −0.119611 0.992821i \(-0.538165\pi\)
0.992821 + 0.119611i \(0.0381648\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.585786i 0.0441553i
\(177\) 0 0
\(178\) 2.24264 + 2.24264i 0.168093 + 0.168093i
\(179\) 16.5858 1.23968 0.619840 0.784728i \(-0.287198\pi\)
0.619840 + 0.784728i \(0.287198\pi\)
\(180\) 0 0
\(181\) −19.0711 −1.41754 −0.708771 0.705439i \(-0.750750\pi\)
−0.708771 + 0.705439i \(0.750750\pi\)
\(182\) −4.00000 4.00000i −0.296500 0.296500i
\(183\) 0 0
\(184\) 6.82843i 0.503398i
\(185\) 0 0
\(186\) 0 0
\(187\) 0.343146 0.343146i 0.0250933 0.0250933i
\(188\) 9.24264 9.24264i 0.674089 0.674089i
\(189\) 0 0
\(190\) 0 0
\(191\) 14.3431i 1.03783i −0.854825 0.518917i \(-0.826335\pi\)
0.854825 0.518917i \(-0.173665\pi\)
\(192\) 0 0
\(193\) −13.4853 13.4853i −0.970692 0.970692i 0.0288908 0.999583i \(-0.490802\pi\)
−0.999583 + 0.0288908i \(0.990802\pi\)
\(194\) 6.48528 0.465616
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 10.2426 + 10.2426i 0.729758 + 0.729758i 0.970571 0.240813i \(-0.0774142\pi\)
−0.240813 + 0.970571i \(0.577414\pi\)
\(198\) 0 0
\(199\) 4.10051i 0.290677i −0.989382 0.145339i \(-0.953573\pi\)
0.989382 0.145339i \(-0.0464271\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −12.4853 + 12.4853i −0.878461 + 0.878461i
\(203\) 0.585786 0.585786i 0.0411141 0.0411141i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.4853i 0.730544i
\(207\) 0 0
\(208\) 4.00000 + 4.00000i 0.277350 + 0.277350i
\(209\) 1.65685 0.114607
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 2.58579 + 2.58579i 0.177593 + 0.177593i
\(213\) 0 0
\(214\) 7.31371i 0.499955i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.24264 1.24264i 0.0843559 0.0843559i
\(218\) 6.58579 6.58579i 0.446046 0.446046i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.68629i 0.315234i
\(222\) 0 0
\(223\) −7.31371 7.31371i −0.489762 0.489762i 0.418469 0.908231i \(-0.362567\pi\)
−0.908231 + 0.418469i \(0.862567\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) −1.17157 1.17157i −0.0777600 0.0777600i 0.667157 0.744917i \(-0.267511\pi\)
−0.744917 + 0.667157i \(0.767511\pi\)
\(228\) 0 0
\(229\) 8.24264i 0.544689i 0.962200 + 0.272345i \(0.0877990\pi\)
−0.962200 + 0.272345i \(0.912201\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.585786 + 0.585786i −0.0384588 + 0.0384588i
\(233\) −14.8284 + 14.8284i −0.971443 + 0.971443i −0.999603 0.0281608i \(-0.991035\pi\)
0.0281608 + 0.999603i \(0.491035\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.82843i 0.184115i
\(237\) 0 0
\(238\) −0.585786 0.585786i −0.0379709 0.0379709i
\(239\) 13.6569 0.883388 0.441694 0.897166i \(-0.354378\pi\)
0.441694 + 0.897166i \(0.354378\pi\)
\(240\) 0 0
\(241\) −4.14214 −0.266818 −0.133409 0.991061i \(-0.542592\pi\)
−0.133409 + 0.991061i \(0.542592\pi\)
\(242\) 7.53553 + 7.53553i 0.484402 + 0.484402i
\(243\) 0 0
\(244\) 9.89949i 0.633750i
\(245\) 0 0
\(246\) 0 0
\(247\) −11.3137 + 11.3137i −0.719874 + 0.719874i
\(248\) −1.24264 + 1.24264i −0.0789078 + 0.0789078i
\(249\) 0 0
\(250\) 0 0
\(251\) 26.6274i 1.68071i −0.542038 0.840354i \(-0.682347\pi\)
0.542038 0.840354i \(-0.317653\pi\)
\(252\) 0 0
\(253\) −2.82843 2.82843i −0.177822 0.177822i
\(254\) −10.8284 −0.679436
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −8.58579 8.58579i −0.535567 0.535567i 0.386657 0.922224i \(-0.373630\pi\)
−0.922224 + 0.386657i \(0.873630\pi\)
\(258\) 0 0
\(259\) 8.82843i 0.548572i
\(260\) 0 0
\(261\) 0 0
\(262\) −11.6569 + 11.6569i −0.720163 + 0.720163i
\(263\) −7.65685 + 7.65685i −0.472142 + 0.472142i −0.902607 0.430465i \(-0.858349\pi\)
0.430465 + 0.902607i \(0.358349\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.82843i 0.173422i
\(267\) 0 0
\(268\) −8.41421 8.41421i −0.513980 0.513980i
\(269\) 5.65685 0.344904 0.172452 0.985018i \(-0.444831\pi\)
0.172452 + 0.985018i \(0.444831\pi\)
\(270\) 0 0
\(271\) 4.10051 0.249088 0.124544 0.992214i \(-0.460253\pi\)
0.124544 + 0.992214i \(0.460253\pi\)
\(272\) 0.585786 + 0.585786i 0.0355185 + 0.0355185i
\(273\) 0 0
\(274\) 16.9706i 1.02523i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.10051 2.10051i 0.126207 0.126207i −0.641182 0.767389i \(-0.721556\pi\)
0.767389 + 0.641182i \(0.221556\pi\)
\(278\) 12.4853 12.4853i 0.748817 0.748817i
\(279\) 0 0
\(280\) 0 0
\(281\) 19.0711i 1.13768i −0.822447 0.568842i \(-0.807391\pi\)
0.822447 0.568842i \(-0.192609\pi\)
\(282\) 0 0
\(283\) 21.3137 + 21.3137i 1.26697 + 1.26697i 0.947646 + 0.319322i \(0.103455\pi\)
0.319322 + 0.947646i \(0.396545\pi\)
\(284\) −1.17157 −0.0695201
\(285\) 0 0
\(286\) 3.31371 0.195944
\(287\) −2.24264 2.24264i −0.132379 0.132379i
\(288\) 0 0
\(289\) 16.3137i 0.959630i
\(290\) 0 0
\(291\) 0 0
\(292\) 7.07107 7.07107i 0.413803 0.413803i
\(293\) −8.65685 + 8.65685i −0.505739 + 0.505739i −0.913216 0.407477i \(-0.866409\pi\)
0.407477 + 0.913216i \(0.366409\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.82843i 0.513142i
\(297\) 0 0
\(298\) −5.75736 5.75736i −0.333515 0.333515i
\(299\) 38.6274 2.23388
\(300\) 0 0
\(301\) −8.58579 −0.494877
\(302\) −13.3137 13.3137i −0.766118 0.766118i
\(303\) 0 0
\(304\) 2.82843i 0.162221i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) −0.414214 + 0.414214i −0.0236020 + 0.0236020i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.82843i 0.273795i −0.990585 0.136897i \(-0.956287\pi\)
0.990585 0.136897i \(-0.0437131\pi\)
\(312\) 0 0
\(313\) −2.24264 2.24264i −0.126762 0.126762i 0.640880 0.767641i \(-0.278570\pi\)
−0.767641 + 0.640880i \(0.778570\pi\)
\(314\) 13.6569 0.770701
\(315\) 0 0
\(316\) 5.65685 0.318223
\(317\) 24.7279 + 24.7279i 1.38886 + 1.38886i 0.827726 + 0.561132i \(0.189634\pi\)
0.561132 + 0.827726i \(0.310366\pi\)
\(318\) 0 0
\(319\) 0.485281i 0.0271705i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.82843 + 4.82843i −0.269078 + 0.269078i
\(323\) −1.65685 + 1.65685i −0.0921898 + 0.0921898i
\(324\) 0 0
\(325\) 0 0
\(326\) 16.5858i 0.918602i
\(327\) 0 0
\(328\) 2.24264 + 2.24264i 0.123829 + 0.123829i
\(329\) −13.0711 −0.720631
\(330\) 0 0
\(331\) 18.6274 1.02386 0.511928 0.859029i \(-0.328932\pi\)
0.511928 + 0.859029i \(0.328932\pi\)
\(332\) 0.828427 + 0.828427i 0.0454658 + 0.0454658i
\(333\) 0 0
\(334\) 10.7279i 0.587006i
\(335\) 0 0
\(336\) 0 0
\(337\) −10.1716 + 10.1716i −0.554081 + 0.554081i −0.927616 0.373535i \(-0.878146\pi\)
0.373535 + 0.927616i \(0.378146\pi\)
\(338\) −13.4350 + 13.4350i −0.730769 + 0.730769i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.02944i 0.0557472i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 8.58579 0.462915
\(345\) 0 0
\(346\) 16.2426 0.873210
\(347\) 8.48528 + 8.48528i 0.455514 + 0.455514i 0.897180 0.441666i \(-0.145612\pi\)
−0.441666 + 0.897180i \(0.645612\pi\)
\(348\) 0 0
\(349\) 32.7279i 1.75189i 0.482415 + 0.875943i \(0.339760\pi\)
−0.482415 + 0.875943i \(0.660240\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.414214 0.414214i 0.0220777 0.0220777i
\(353\) −18.3848 + 18.3848i −0.978523 + 0.978523i −0.999774 0.0212513i \(-0.993235\pi\)
0.0212513 + 0.999774i \(0.493235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.17157i 0.168093i
\(357\) 0 0
\(358\) 11.7279 + 11.7279i 0.619840 + 0.619840i
\(359\) 23.7990 1.25606 0.628031 0.778188i \(-0.283861\pi\)
0.628031 + 0.778188i \(0.283861\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) −13.4853 13.4853i −0.708771 0.708771i
\(363\) 0 0
\(364\) 5.65685i 0.296500i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.2426 10.2426i 0.534661 0.534661i −0.387295 0.921956i \(-0.626590\pi\)
0.921956 + 0.387295i \(0.126590\pi\)
\(368\) 4.82843 4.82843i 0.251699 0.251699i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.65685i 0.189854i
\(372\) 0 0
\(373\) 11.0711 + 11.0711i 0.573238 + 0.573238i 0.933032 0.359794i \(-0.117153\pi\)
−0.359794 + 0.933032i \(0.617153\pi\)
\(374\) 0.485281 0.0250933
\(375\) 0 0
\(376\) 13.0711 0.674089
\(377\) −3.31371 3.31371i −0.170665 0.170665i
\(378\) 0 0
\(379\) 25.7990i 1.32521i 0.748971 + 0.662603i \(0.230548\pi\)
−0.748971 + 0.662603i \(0.769452\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 10.1421 10.1421i 0.518917 0.518917i
\(383\) −4.41421 + 4.41421i −0.225556 + 0.225556i −0.810833 0.585277i \(-0.800986\pi\)
0.585277 + 0.810833i \(0.300986\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.0711i 0.970692i
\(387\) 0 0
\(388\) 4.58579 + 4.58579i 0.232808 + 0.232808i
\(389\) −9.79899 −0.496829 −0.248414 0.968654i \(-0.579909\pi\)
−0.248414 + 0.968654i \(0.579909\pi\)
\(390\) 0 0
\(391\) 5.65685 0.286079
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 14.4853i 0.729758i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.928932 0.928932i 0.0466218 0.0466218i −0.683412 0.730033i \(-0.739505\pi\)
0.730033 + 0.683412i \(0.239505\pi\)
\(398\) 2.89949 2.89949i 0.145339 0.145339i
\(399\) 0 0
\(400\) 0 0
\(401\) 26.8701i 1.34183i 0.741536 + 0.670913i \(0.234098\pi\)
−0.741536 + 0.670913i \(0.765902\pi\)
\(402\) 0 0
\(403\) −7.02944 7.02944i −0.350161 0.350161i
\(404\) −17.6569 −0.878461
\(405\) 0 0
\(406\) 0.828427 0.0411141
\(407\) −3.65685 3.65685i −0.181264 0.181264i
\(408\) 0 0
\(409\) 10.0000i 0.494468i −0.968956 0.247234i \(-0.920478\pi\)
0.968956 0.247234i \(-0.0795217\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7.41421 + 7.41421i −0.365272 + 0.365272i
\(413\) 2.00000 2.00000i 0.0984136 0.0984136i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.65685i 0.277350i
\(417\) 0 0
\(418\) 1.17157 + 1.17157i 0.0573035 + 0.0573035i
\(419\) −18.6274 −0.910009 −0.455004 0.890489i \(-0.650362\pi\)
−0.455004 + 0.890489i \(0.650362\pi\)
\(420\) 0 0
\(421\) −40.6274 −1.98006 −0.990030 0.140860i \(-0.955013\pi\)
−0.990030 + 0.140860i \(0.955013\pi\)
\(422\) −2.82843 2.82843i −0.137686 0.137686i
\(423\) 0 0
\(424\) 3.65685i 0.177593i
\(425\) 0 0
\(426\) 0 0
\(427\) −7.00000 + 7.00000i −0.338754 + 0.338754i
\(428\) −5.17157 + 5.17157i −0.249977 + 0.249977i
\(429\) 0 0
\(430\) 0 0
\(431\) 26.1421i 1.25922i 0.776910 + 0.629611i \(0.216786\pi\)
−0.776910 + 0.629611i \(0.783214\pi\)
\(432\) 0 0
\(433\) −18.2426 18.2426i −0.876685 0.876685i 0.116505 0.993190i \(-0.462831\pi\)
−0.993190 + 0.116505i \(0.962831\pi\)
\(434\) 1.75736 0.0843559
\(435\) 0 0
\(436\) 9.31371 0.446046
\(437\) 13.6569 + 13.6569i 0.653296 + 0.653296i
\(438\) 0 0
\(439\) 3.89949i 0.186113i −0.995661 0.0930564i \(-0.970336\pi\)
0.995661 0.0930564i \(-0.0296637\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −3.31371 + 3.31371i −0.157617 + 0.157617i
\(443\) 3.51472 3.51472i 0.166989 0.166989i −0.618665 0.785655i \(-0.712326\pi\)
0.785655 + 0.618665i \(0.212326\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 10.3431i 0.489762i
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) −16.7279 −0.789439 −0.394720 0.918802i \(-0.629158\pi\)
−0.394720 + 0.918802i \(0.629158\pi\)
\(450\) 0 0
\(451\) 1.85786 0.0874834
\(452\) 11.3137 + 11.3137i 0.532152 + 0.532152i
\(453\) 0 0
\(454\) 1.65685i 0.0777600i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.17157 + 2.17157i −0.101582 + 0.101582i −0.756071 0.654489i \(-0.772884\pi\)
0.654489 + 0.756071i \(0.272884\pi\)
\(458\) −5.82843 + 5.82843i −0.272345 + 0.272345i
\(459\) 0 0
\(460\) 0 0
\(461\) 5.31371i 0.247484i −0.992314 0.123742i \(-0.960510\pi\)
0.992314 0.123742i \(-0.0394895\pi\)
\(462\) 0 0
\(463\) 19.7990 + 19.7990i 0.920137 + 0.920137i 0.997039 0.0769016i \(-0.0245027\pi\)
−0.0769016 + 0.997039i \(0.524503\pi\)
\(464\) −0.828427 −0.0384588
\(465\) 0 0
\(466\) −20.9706 −0.971443
\(467\) 14.0000 + 14.0000i 0.647843 + 0.647843i 0.952471 0.304629i \(-0.0985323\pi\)
−0.304629 + 0.952471i \(0.598532\pi\)
\(468\) 0 0
\(469\) 11.8995i 0.549468i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.00000 + 2.00000i −0.0920575 + 0.0920575i
\(473\) 3.55635 3.55635i 0.163521 0.163521i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.828427i 0.0379709i
\(477\) 0 0
\(478\) 9.65685 + 9.65685i 0.441694 + 0.441694i
\(479\) 19.1716 0.875972 0.437986 0.898982i \(-0.355692\pi\)
0.437986 + 0.898982i \(0.355692\pi\)
\(480\) 0 0
\(481\) 49.9411 2.27712
\(482\) −2.92893 2.92893i −0.133409 0.133409i
\(483\) 0 0
\(484\) 10.6569i 0.484402i
\(485\) 0 0
\(486\) 0 0
\(487\) −18.9706 + 18.9706i −0.859638 + 0.859638i −0.991295 0.131657i \(-0.957970\pi\)
0.131657 + 0.991295i \(0.457970\pi\)
\(488\) 7.00000 7.00000i 0.316875 0.316875i
\(489\) 0 0
\(490\) 0 0
\(491\) 26.7279i 1.20621i −0.797660 0.603107i \(-0.793929\pi\)
0.797660 0.603107i \(-0.206071\pi\)
\(492\) 0 0
\(493\) −0.485281 0.485281i −0.0218560 0.0218560i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) −1.75736 −0.0789078
\(497\) 0.828427 + 0.828427i 0.0371600 + 0.0371600i
\(498\) 0 0
\(499\) 23.4558i 1.05003i 0.851094 + 0.525014i \(0.175940\pi\)
−0.851094 + 0.525014i \(0.824060\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.8284 18.8284i 0.840354 0.840354i
\(503\) 16.5563 16.5563i 0.738211 0.738211i −0.234021 0.972232i \(-0.575188\pi\)
0.972232 + 0.234021i \(0.0751883\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.00000i 0.177822i
\(507\) 0 0
\(508\) −7.65685 7.65685i −0.339718 0.339718i
\(509\) −18.3431 −0.813046 −0.406523 0.913641i \(-0.633259\pi\)
−0.406523 + 0.913641i \(0.633259\pi\)
\(510\) 0 0
\(511\) −10.0000 −0.442374
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 12.1421i 0.535567i
\(515\) 0 0
\(516\) 0 0
\(517\) 5.41421 5.41421i 0.238117 0.238117i
\(518\) −6.24264 + 6.24264i −0.274286 + 0.274286i
\(519\) 0 0
\(520\) 0 0
\(521\) 42.7696i 1.87377i 0.349640 + 0.936884i \(0.386304\pi\)
−0.349640 + 0.936884i \(0.613696\pi\)
\(522\) 0 0
\(523\) 25.3137 + 25.3137i 1.10689 + 1.10689i 0.993557 + 0.113334i \(0.0361531\pi\)
0.113334 + 0.993557i \(0.463847\pi\)
\(524\) −16.4853 −0.720163
\(525\) 0 0
\(526\) −10.8284 −0.472142
\(527\) −1.02944 1.02944i −0.0448430 0.0448430i
\(528\) 0 0
\(529\) 23.6274i 1.02728i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000 2.00000i 0.0867110 0.0867110i
\(533\) −12.6863 + 12.6863i −0.549504 + 0.549504i
\(534\) 0 0
\(535\) 0 0
\(536\) 11.8995i 0.513980i
\(537\) 0 0
\(538\) 4.00000 + 4.00000i 0.172452 + 0.172452i
\(539\) 0.585786 0.0252316
\(540\) 0 0
\(541\) −29.1127 −1.25165 −0.625826 0.779962i \(-0.715238\pi\)
−0.625826 + 0.779962i \(0.715238\pi\)
\(542\) 2.89949 + 2.89949i 0.124544 + 0.124544i
\(543\) 0 0
\(544\) 0.828427i 0.0355185i
\(545\) 0 0
\(546\) 0 0
\(547\) 12.5563 12.5563i 0.536871 0.536871i −0.385738 0.922608i \(-0.626053\pi\)
0.922608 + 0.385738i \(0.126053\pi\)
\(548\) 12.0000 12.0000i 0.512615 0.512615i
\(549\) 0 0
\(550\) 0 0
\(551\) 2.34315i 0.0998214i
\(552\) 0 0
\(553\) −4.00000 4.00000i −0.170097 0.170097i
\(554\) 2.97056 0.126207
\(555\) 0 0
\(556\) 17.6569 0.748817
\(557\) −7.55635 7.55635i −0.320173 0.320173i 0.528661 0.848833i \(-0.322694\pi\)
−0.848833 + 0.528661i \(0.822694\pi\)
\(558\) 0 0
\(559\) 48.5685i 2.05423i
\(560\) 0 0
\(561\) 0 0
\(562\) 13.4853 13.4853i 0.568842 0.568842i
\(563\) −6.68629 + 6.68629i −0.281794 + 0.281794i −0.833824 0.552030i \(-0.813853\pi\)
0.552030 + 0.833824i \(0.313853\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 30.1421i 1.26697i
\(567\) 0 0
\(568\) −0.828427 0.828427i −0.0347600 0.0347600i
\(569\) −14.1005 −0.591124 −0.295562 0.955324i \(-0.595507\pi\)
−0.295562 + 0.955324i \(0.595507\pi\)
\(570\) 0 0
\(571\) −11.0294 −0.461568 −0.230784 0.973005i \(-0.574129\pi\)
−0.230784 + 0.973005i \(0.574129\pi\)
\(572\) 2.34315 + 2.34315i 0.0979718 + 0.0979718i
\(573\) 0 0
\(574\) 3.17157i 0.132379i
\(575\) 0 0
\(576\) 0 0
\(577\) 10.7279 10.7279i 0.446609 0.446609i −0.447616 0.894226i \(-0.647727\pi\)
0.894226 + 0.447616i \(0.147727\pi\)
\(578\) 11.5355 11.5355i 0.479815 0.479815i
\(579\) 0 0
\(580\) 0 0
\(581\) 1.17157i 0.0486050i
\(582\) 0 0
\(583\) 1.51472 + 1.51472i 0.0627332 + 0.0627332i
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) −12.2426 −0.505739
\(587\) −17.7990 17.7990i −0.734643 0.734643i 0.236893 0.971536i \(-0.423871\pi\)
−0.971536 + 0.236893i \(0.923871\pi\)
\(588\) 0 0
\(589\) 4.97056i 0.204808i
\(590\) 0 0
\(591\) 0 0
\(592\) 6.24264 6.24264i 0.256571 0.256571i
\(593\) 16.3848 16.3848i 0.672842 0.672842i −0.285528 0.958370i \(-0.592169\pi\)
0.958370 + 0.285528i \(0.0921690\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.14214i 0.333515i
\(597\) 0 0
\(598\) 27.3137 + 27.3137i 1.11694 + 1.11694i
\(599\) −15.3137 −0.625701 −0.312851 0.949802i \(-0.601284\pi\)
−0.312851 + 0.949802i \(0.601284\pi\)
\(600\) 0 0
\(601\) −4.14214 −0.168961 −0.0844806 0.996425i \(-0.526923\pi\)
−0.0844806 + 0.996425i \(0.526923\pi\)
\(602\) −6.07107 6.07107i −0.247438 0.247438i
\(603\) 0 0
\(604\) 18.8284i 0.766118i
\(605\) 0 0
\(606\) 0 0
\(607\) 7.31371 7.31371i 0.296854 0.296854i −0.542926 0.839780i \(-0.682684\pi\)
0.839780 + 0.542926i \(0.182684\pi\)
\(608\) −2.00000 + 2.00000i −0.0811107 + 0.0811107i
\(609\) 0 0
\(610\) 0 0
\(611\) 73.9411i 2.99134i
\(612\) 0 0
\(613\) 9.07107 + 9.07107i 0.366377 + 0.366377i 0.866154 0.499777i \(-0.166585\pi\)
−0.499777 + 0.866154i \(0.666585\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.585786 −0.0236020
\(617\) −24.0416 24.0416i −0.967880 0.967880i 0.0316203 0.999500i \(-0.489933\pi\)
−0.999500 + 0.0316203i \(0.989933\pi\)
\(618\) 0 0
\(619\) 17.8579i 0.717768i −0.933382 0.358884i \(-0.883157\pi\)
0.933382 0.358884i \(-0.116843\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 3.41421 3.41421i 0.136897 0.136897i
\(623\) 2.24264 2.24264i 0.0898495 0.0898495i
\(624\) 0 0
\(625\) 0 0
\(626\) 3.17157i 0.126762i
\(627\) 0 0
\(628\) 9.65685 + 9.65685i 0.385350 + 0.385350i
\(629\) 7.31371 0.291617
\(630\) 0 0
\(631\) −0.201010 −0.00800209 −0.00400104 0.999992i \(-0.501274\pi\)
−0.00400104 + 0.999992i \(0.501274\pi\)
\(632\) 4.00000 + 4.00000i 0.159111 + 0.159111i
\(633\) 0 0
\(634\) 34.9706i 1.38886i
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 + 4.00000i −0.158486 + 0.158486i
\(638\) −0.343146 + 0.343146i −0.0135853 + 0.0135853i
\(639\) 0 0
\(640\) 0 0
\(641\) 21.2132i 0.837871i −0.908016 0.418936i \(-0.862403\pi\)
0.908016 0.418936i \(-0.137597\pi\)
\(642\) 0 0
\(643\) 10.9706 + 10.9706i 0.432637 + 0.432637i 0.889524 0.456888i \(-0.151036\pi\)
−0.456888 + 0.889524i \(0.651036\pi\)
\(644\) −6.82843 −0.269078
\(645\) 0 0
\(646\) −2.34315 −0.0921898
\(647\) 33.2426 + 33.2426i 1.30690 + 1.30690i 0.923639 + 0.383264i \(0.125200\pi\)
0.383264 + 0.923639i \(0.374800\pi\)
\(648\) 0 0
\(649\) 1.65685i 0.0650372i
\(650\) 0 0
\(651\) 0 0
\(652\) 11.7279 11.7279i 0.459301 0.459301i
\(653\) −14.2426 + 14.2426i −0.557358 + 0.557358i −0.928554 0.371197i \(-0.878948\pi\)
0.371197 + 0.928554i \(0.378948\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.17157i 0.123829i
\(657\) 0 0
\(658\) −9.24264 9.24264i −0.360316 0.360316i
\(659\) −26.7279 −1.04117 −0.520586 0.853809i \(-0.674286\pi\)
−0.520586 + 0.853809i \(0.674286\pi\)
\(660\) 0 0
\(661\) 40.0416 1.55744 0.778719 0.627372i \(-0.215870\pi\)
0.778719 + 0.627372i \(0.215870\pi\)
\(662\) 13.1716 + 13.1716i 0.511928 + 0.511928i
\(663\) 0 0
\(664\) 1.17157i 0.0454658i
\(665\) 0 0
\(666\) 0 0
\(667\) −4.00000 + 4.00000i −0.154881 + 0.154881i
\(668\) −7.58579 + 7.58579i −0.293503 + 0.293503i
\(669\) 0 0
\(670\) 0 0
\(671\) 5.79899i 0.223868i
\(672\) 0 0
\(673\) −3.34315 3.34315i −0.128869 0.128869i 0.639731 0.768599i \(-0.279046\pi\)
−0.768599 + 0.639731i \(0.779046\pi\)
\(674\) −14.3848 −0.554081
\(675\) 0 0
\(676\) −19.0000 −0.730769
\(677\) −15.8284 15.8284i −0.608336 0.608336i 0.334175 0.942511i \(-0.391542\pi\)
−0.942511 + 0.334175i \(0.891542\pi\)
\(678\) 0 0
\(679\) 6.48528i 0.248882i
\(680\) 0 0
\(681\) 0 0
\(682\) −0.727922 + 0.727922i −0.0278736 + 0.0278736i
\(683\) −24.3848 + 24.3848i −0.933058 + 0.933058i −0.997896 0.0648383i \(-0.979347\pi\)
0.0648383 + 0.997896i \(0.479347\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 6.07107 + 6.07107i 0.231457 + 0.231457i
\(689\) −20.6863 −0.788085
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 11.4853 + 11.4853i 0.436605 + 0.436605i
\(693\) 0 0
\(694\) 12.0000i 0.455514i
\(695\) 0 0
\(696\) 0 0
\(697\) −1.85786 + 1.85786i −0.0703716 + 0.0703716i
\(698\) −23.1421 + 23.1421i −0.875943 + 0.875943i
\(699\) 0 0
\(700\) 0 0
\(701\) 40.8284i 1.54207i 0.636794 + 0.771034i \(0.280260\pi\)
−0.636794 + 0.771034i \(0.719740\pi\)
\(702\) 0 0
\(703\) 17.6569 + 17.6569i 0.665941 + 0.665941i
\(704\) 0.585786 0.0220777
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) 12.4853 + 12.4853i 0.469557 + 0.469557i
\(708\) 0 0
\(709\) 40.8284i 1.53334i −0.642039 0.766672i \(-0.721911\pi\)
0.642039 0.766672i \(-0.278089\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −2.24264 + 2.24264i −0.0840465 + 0.0840465i
\(713\) −8.48528 + 8.48528i −0.317776 + 0.317776i
\(714\) 0 0
\(715\) 0 0
\(716\) 16.5858i 0.619840i
\(717\) 0 0
\(718\) 16.8284 + 16.8284i 0.628031 + 0.628031i
\(719\) 38.6274 1.44056 0.720280 0.693684i \(-0.244013\pi\)
0.720280 + 0.693684i \(0.244013\pi\)
\(720\) 0 0
\(721\) 10.4853 0.390492
\(722\) 7.77817 + 7.77817i 0.289474 + 0.289474i
\(723\) 0 0
\(724\) 19.0711i 0.708771i
\(725\) 0 0
\(726\) 0 0
\(727\) 22.6274 22.6274i 0.839204 0.839204i −0.149550 0.988754i \(-0.547782\pi\)
0.988754 + 0.149550i \(0.0477824\pi\)
\(728\) 4.00000 4.00000i 0.148250 0.148250i
\(729\) 0 0
\(730\) 0 0
\(731\) 7.11270i 0.263073i
\(732\) 0 0
\(733\) 0.443651 + 0.443651i 0.0163866 + 0.0163866i 0.715253 0.698866i \(-0.246312\pi\)
−0.698866 + 0.715253i \(0.746312\pi\)
\(734\) 14.4853 0.534661
\(735\) 0 0
\(736\) 6.82843 0.251699
\(737\) −4.92893 4.92893i −0.181560 0.181560i
\(738\) 0 0
\(739\) 7.45584i 0.274268i −0.990553 0.137134i \(-0.956211\pi\)
0.990553 0.137134i \(-0.0437890\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.58579 2.58579i 0.0949272 0.0949272i
\(743\) 31.1127 31.1127i 1.14141 1.14141i 0.153222 0.988192i \(-0.451035\pi\)
0.988192 0.153222i \(-0.0489651\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 15.6569i 0.573238i
\(747\) 0 0
\(748\) 0.343146 + 0.343146i 0.0125467 + 0.0125467i
\(749\) 7.31371 0.267237
\(750\) 0 0
\(751\) 48.4853 1.76925 0.884627 0.466300i \(-0.154413\pi\)
0.884627 + 0.466300i \(0.154413\pi\)
\(752\) 9.24264 + 9.24264i 0.337044 + 0.337044i
\(753\) 0 0
\(754\) 4.68629i 0.170665i
\(755\) 0 0
\(756\) 0 0
\(757\) 23.5563 23.5563i 0.856170 0.856170i −0.134714 0.990884i \(-0.543012\pi\)
0.990884 + 0.134714i \(0.0430117\pi\)
\(758\) −18.2426 + 18.2426i −0.662603 + 0.662603i
\(759\) 0 0
\(760\) 0 0
\(761\) 18.9706i 0.687682i 0.939028 + 0.343841i \(0.111728\pi\)
−0.939028 + 0.343841i \(0.888272\pi\)
\(762\) 0 0
\(763\) −6.58579 6.58579i −0.238421 0.238421i
\(764\) 14.3431 0.518917
\(765\) 0 0
\(766\) −6.24264 −0.225556
\(767\) −11.3137 11.3137i −0.408514 0.408514i
\(768\) 0 0
\(769\) 41.5980i 1.50006i −0.661403 0.750031i \(-0.730039\pi\)
0.661403 0.750031i \(-0.269961\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.4853 13.4853i 0.485346 0.485346i
\(773\) −34.9411 + 34.9411i −1.25674 + 1.25674i −0.304107 + 0.952638i \(0.598358\pi\)
−0.952638 + 0.304107i \(0.901642\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.48528i 0.232808i
\(777\) 0 0
\(778\) −6.92893 6.92893i −0.248414 0.248414i
\(779\) −8.97056 −0.321404
\(780\) 0 0
\(781\) −0.686292 −0.0245574
\(782\) 4.00000 + 4.00000i 0.143040 + 0.143040i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 15.5147 15.5147i 0.553040 0.553040i −0.374277 0.927317i \(-0.622109\pi\)
0.927317 + 0.374277i \(0.122109\pi\)
\(788\) −10.2426 + 10.2426i −0.364879 + 0.364879i
\(789\) 0 0
\(790\) 0 0
\(791\) 16.0000i 0.568895i
\(792\) 0 0
\(793\) 39.5980 + 39.5980i 1.40617 + 1.40617i
\(794\) 1.31371 0.0466218
\(795\) 0 0
\(796\) 4.10051 0.145339
\(797\) −20.1716 20.1716i −0.714514 0.714514i 0.252962 0.967476i \(-0.418595\pi\)
−0.967476 + 0.252962i \(0.918595\pi\)
\(798\) 0 0
\(799\) 10.8284i 0.383082i
\(800\) 0 0
\(801\) 0 0
\(802\) −19.0000 + 19.0000i −0.670913 + 0.670913i
\(803\) 4.14214 4.14214i 0.146173 0.146173i
\(804\) 0 0
\(805\)