Properties

Label 3150.2.m.b.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.b.2843.2

$q$-expansion

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

Character values

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

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

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
\(11\) 0.585786i 0.176621i −0.996093 0.0883106i \(-0.971853\pi\)
0.996093 0.0883106i \(-0.0281468\pi\)
\(12\) 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
\(17\) −0.585786 + 0.585786i −0.142074 + 0.142074i −0.774567 0.632492i \(-0.782032\pi\)
0.632492 + 0.774567i \(0.282032\pi\)
\(18\) 0 0
\(19\) 2.82843i 0.648886i 0.945905 + 0.324443i \(0.105177\pi\)
−0.945905 + 0.324443i \(0.894823\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.414214 0.414214i −0.0883106 0.0883106i
\(23\) −4.82843 4.82843i −1.00680 1.00680i −0.999977 0.00681991i \(-0.997829\pi\)
−0.00681991 0.999977i \(-0.502171\pi\)
\(24\) 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 −0.999645 0.0266387i \(-0.991520\pi\)
−0.0266387 0.999645i \(-0.508480\pi\)
\(38\) 2.00000 + 2.00000i 0.324443 + 0.324443i
\(39\) 0 0
\(40\) 0 0
\(41\) 3.17157i 0.495316i 0.968847 + 0.247658i \(0.0796610\pi\)
−0.968847 + 0.247658i \(0.920339\pi\)
\(42\) 0 0
\(43\) −6.07107 + 6.07107i −0.925829 + 0.925829i −0.997433 0.0716040i \(-0.977188\pi\)
0.0716040 + 0.997433i \(0.477188\pi\)
\(44\) −0.585786 −0.0883106
\(45\) 0 0
\(46\) −6.82843 −1.00680
\(47\) −9.24264 + 9.24264i −1.34818 + 1.34818i −0.460537 + 0.887640i \(0.652343\pi\)
−0.887640 + 0.460537i \(0.847657\pi\)
\(48\) 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 0.862035 0.506849i \(-0.169190\pi\)
−0.506849 + 0.862035i \(0.669190\pi\)
\(54\) 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 −0.999598 0.0283621i \(-0.990971\pi\)
−0.0283621 0.999598i \(-0.509029\pi\)
\(68\) 0.585786 + 0.585786i 0.0710370 + 0.0710370i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.17157i 0.139040i −0.997581 0.0695201i \(-0.977853\pi\)
0.997581 0.0695201i \(-0.0221468\pi\)
\(72\) 0 0
\(73\) −7.07107 + 7.07107i −0.827606 + 0.827606i −0.987185 0.159579i \(-0.948986\pi\)
0.159579 + 0.987185i \(0.448986\pi\)
\(74\) −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 \(0.103086\pi\)
−0.948016 + 0.318223i \(0.896914\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.24264 + 2.24264i 0.247658 + 0.247658i
\(83\) 0.828427 + 0.828427i 0.0909317 + 0.0909317i 0.751109 0.660178i \(-0.229519\pi\)
−0.660178 + 0.751109i \(0.729519\pi\)
\(84\) 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 0.900491 0.434875i \(-0.143207\pi\)
−0.434875 + 0.900491i \(0.643207\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 17.6569i 1.75692i −0.477813 0.878461i \(-0.658571\pi\)
0.477813 0.878461i \(-0.341429\pi\)
\(102\) 0 0
\(103\) 7.41421 7.41421i 0.730544 0.730544i −0.240183 0.970728i \(-0.577208\pi\)
0.970728 + 0.240183i \(0.0772076\pi\)
\(104\) 5.65685 0.554700
\(105\) 0 0
\(106\) 3.65685 0.355185
\(107\) 5.17157 5.17157i 0.499955 0.499955i −0.411469 0.911424i \(-0.634984\pi\)
0.911424 + 0.411469i \(0.134984\pi\)
\(108\) 0 0
\(109\) 9.31371i 0.892091i 0.895010 + 0.446046i \(0.147168\pi\)
−0.895010 + 0.446046i \(0.852832\pi\)
\(110\) 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
\(116\) 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 0.280437 0.959873i \(-0.409521\pi\)
−0.959873 + 0.280437i \(0.909521\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 16.4853i 1.44033i −0.693805 0.720163i \(-0.744067\pi\)
0.693805 0.720163i \(-0.255933\pi\)
\(132\) 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 −0.0255558 + 0.999673i \(0.508136\pi\)
−0.999673 + 0.0255558i \(0.991864\pi\)
\(138\) 0 0
\(139\) 17.6569i 1.49763i 0.662776 + 0.748817i \(0.269378\pi\)
−0.662776 + 0.748817i \(0.730622\pi\)
\(140\) 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 0.978229 0.207528i \(-0.0665419\pi\)
−0.207528 + 0.978229i \(0.566542\pi\)
\(158\) 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 −0.996928 0.0783260i \(-0.975042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 3.17157 0.247658
\(165\) 0 0
\(166\) 1.17157 0.0909317
\(167\) 7.58579 7.58579i 0.587006 0.587006i −0.349814 0.936819i \(-0.613755\pi\)
0.936819 + 0.349814i \(0.113755\pi\)
\(168\) 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 0.992821 0.119611i \(-0.0381648\pi\)
−0.119611 + 0.992821i \(0.538165\pi\)
\(174\) 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 \(0.173665\pi\)
−0.854825 + 0.518917i \(0.826335\pi\)
\(192\) 0 0
\(193\) −13.4853 + 13.4853i −0.970692 + 0.970692i −0.999583 0.0288908i \(-0.990802\pi\)
0.0288908 + 0.999583i \(0.490802\pi\)
\(194\) 6.48528 0.465616
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 10.2426 10.2426i 0.729758 0.729758i −0.240813 0.970571i \(-0.577414\pi\)
0.970571 + 0.240813i \(0.0774142\pi\)
\(198\) 0 0
\(199\) 4.10051i 0.290677i 0.989382 + 0.145339i \(0.0464271\pi\)
−0.989382 + 0.145339i \(0.953573\pi\)
\(200\) 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 −0.908231 0.418469i \(-0.862567\pi\)
0.418469 + 0.908231i \(0.362567\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) −1.17157 + 1.17157i −0.0777600 + 0.0777600i −0.744917 0.667157i \(-0.767511\pi\)
0.667157 + 0.744917i \(0.267511\pi\)
\(228\) 0 0
\(229\) 8.24264i 0.544689i −0.962200 0.272345i \(-0.912201\pi\)
0.962200 0.272345i \(-0.0877990\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.585786 0.585786i −0.0384588 0.0384588i
\(233\) −14.8284 14.8284i −0.971443 0.971443i 0.0281608 0.999603i \(-0.491035\pi\)
−0.999603 + 0.0281608i \(0.991035\pi\)
\(234\) 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 \(0.317653\pi\)
−0.542038 + 0.840354i \(0.682347\pi\)
\(252\) 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 −0.922224 0.386657i \(-0.873630\pi\)
0.386657 + 0.922224i \(0.373630\pi\)
\(258\) 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 0.430465 0.902607i \(-0.358349\pi\)
−0.902607 + 0.430465i \(0.858349\pi\)
\(264\) 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 0.767389 0.641182i \(-0.221556\pi\)
−0.641182 + 0.767389i \(0.721556\pi\)
\(278\) 12.4853 + 12.4853i 0.748817 + 0.748817i
\(279\) 0 0
\(280\) 0 0
\(281\) 19.0711i 1.13768i 0.822447 + 0.568842i \(0.192609\pi\)
−0.822447 + 0.568842i \(0.807391\pi\)
\(282\) 0 0
\(283\) 21.3137 21.3137i 1.26697 1.26697i 0.319322 0.947646i \(-0.396545\pi\)
0.947646 0.319322i \(-0.103455\pi\)
\(284\) −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 0.407477 0.913216i \(-0.366409\pi\)
−0.913216 + 0.407477i \(0.866409\pi\)
\(294\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) −0.414214 0.414214i −0.0236020 0.0236020i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.82843i 0.273795i 0.990585 + 0.136897i \(0.0437131\pi\)
−0.990585 + 0.136897i \(0.956287\pi\)
\(312\) 0 0
\(313\) −2.24264 + 2.24264i −0.126762 + 0.126762i −0.767641 0.640880i \(-0.778570\pi\)
0.640880 + 0.767641i \(0.278570\pi\)
\(314\) 13.6569 0.770701
\(315\) 0 0
\(316\) 5.65685 0.318223
\(317\) 24.7279 24.7279i 1.38886 1.38886i 0.561132 0.827726i \(-0.310366\pi\)
0.827726 0.561132i \(-0.189634\pi\)
\(318\) 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 0.373535 0.927616i \(-0.378146\pi\)
−0.927616 + 0.373535i \(0.878146\pi\)
\(338\) −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 −0.441666 0.897180i \(-0.645612\pi\)
0.897180 + 0.441666i \(0.145612\pi\)
\(348\) 0 0
\(349\) 32.7279i 1.75189i −0.482415 0.875943i \(-0.660240\pi\)
0.482415 0.875943i \(-0.339760\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.414214 + 0.414214i 0.0220777 + 0.0220777i
\(353\) −18.3848 18.3848i −0.978523 0.978523i 0.0212513 0.999774i \(-0.493235\pi\)
−0.999774 + 0.0212513i \(0.993235\pi\)
\(354\) 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 0.921956 0.387295i \(-0.126590\pi\)
−0.387295 + 0.921956i \(0.626590\pi\)
\(368\) 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 −0.359794 0.933032i \(-0.617153\pi\)
0.933032 + 0.359794i \(0.117153\pi\)
\(374\) 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 \(-0.769452\pi\)
0.748971 0.662603i \(-0.230548\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 10.1421 + 10.1421i 0.518917 + 0.518917i
\(383\) −4.41421 4.41421i −0.225556 0.225556i 0.585277 0.810833i \(-0.300986\pi\)
−0.810833 + 0.585277i \(0.800986\pi\)
\(384\) 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 0.730033 0.683412i \(-0.239505\pi\)
−0.683412 + 0.730033i \(0.739505\pi\)
\(398\) 2.89949 + 2.89949i 0.145339 + 0.145339i
\(399\) 0 0
\(400\) 0 0
\(401\) 26.8701i 1.34183i −0.741536 0.670913i \(-0.765902\pi\)
0.741536 0.670913i \(-0.234098\pi\)
\(402\) 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 \(0.0795217\pi\)
−0.968956 + 0.247234i \(0.920478\pi\)
\(410\) 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 \(-0.783214\pi\)
0.776910 0.629611i \(-0.216786\pi\)
\(432\) 0 0
\(433\) −18.2426 + 18.2426i −0.876685 + 0.876685i −0.993190 0.116505i \(-0.962831\pi\)
0.116505 + 0.993190i \(0.462831\pi\)
\(434\) 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 \(0.0296637\pi\)
−0.995661 + 0.0930564i \(0.970336\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −3.31371 3.31371i −0.157617 0.157617i
\(443\) 3.51472 + 3.51472i 0.166989 + 0.166989i 0.785655 0.618665i \(-0.212326\pi\)
−0.618665 + 0.785655i \(0.712326\pi\)
\(444\) 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 0.654489 0.756071i \(-0.272884\pi\)
−0.756071 + 0.654489i \(0.772884\pi\)
\(458\) −5.82843 5.82843i −0.272345 0.272345i
\(459\) 0 0
\(460\) 0 0
\(461\) 5.31371i 0.247484i 0.992314 + 0.123742i \(0.0394895\pi\)
−0.992314 + 0.123742i \(0.960510\pi\)
\(462\) 0 0
\(463\) 19.7990 19.7990i 0.920137 0.920137i −0.0769016 0.997039i \(-0.524503\pi\)
0.997039 + 0.0769016i \(0.0245027\pi\)
\(464\) −0.828427 −0.0384588
\(465\) 0 0
\(466\) −20.9706 −0.971443
\(467\) 14.0000 14.0000i 0.647843 0.647843i −0.304629 0.952471i \(-0.598532\pi\)
0.952471 + 0.304629i \(0.0985323\pi\)
\(468\) 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 0.131657 0.991295i \(-0.457970\pi\)
−0.991295 + 0.131657i \(0.957970\pi\)
\(488\) 7.00000 + 7.00000i 0.316875 + 0.316875i
\(489\) 0 0
\(490\) 0 0
\(491\) 26.7279i 1.20621i 0.797660 + 0.603107i \(0.206071\pi\)
−0.797660 + 0.603107i \(0.793929\pi\)
\(492\) 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 \(-0.824060\pi\)
0.851094 0.525014i \(-0.175940\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.8284 + 18.8284i 0.840354 + 0.840354i
\(503\) 16.5563 + 16.5563i 0.738211 + 0.738211i 0.972232 0.234021i \(-0.0751883\pi\)
−0.234021 + 0.972232i \(0.575188\pi\)
\(504\) 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 \(-0.613696\pi\)
0.349640 0.936884i \(-0.386304\pi\)
\(522\) 0 0
\(523\) 25.3137 25.3137i 1.10689 1.10689i 0.113334 0.993557i \(-0.463847\pi\)
0.993557 0.113334i \(-0.0361531\pi\)
\(524\) −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 0.922608 0.385738i \(-0.126053\pi\)
−0.385738 + 0.922608i \(0.626053\pi\)
\(548\) 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 −0.848833 0.528661i \(-0.822694\pi\)
0.528661 + 0.848833i \(0.322694\pi\)
\(558\) 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 0.552030 0.833824i \(-0.313853\pi\)
−0.833824 + 0.552030i \(0.813853\pi\)
\(564\) 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 0.894226 0.447616i \(-0.147727\pi\)
−0.447616 + 0.894226i \(0.647727\pi\)
\(578\) 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 −0.971536 0.236893i \(-0.923871\pi\)
0.236893 + 0.971536i \(0.423871\pi\)
\(588\) 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 0.958370 0.285528i \(-0.0921690\pi\)
−0.285528 + 0.958370i \(0.592169\pi\)
\(594\) 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 0.839780 0.542926i \(-0.182684\pi\)
−0.542926 + 0.839780i \(0.682684\pi\)
\(608\) −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 −0.499777 0.866154i \(-0.666585\pi\)
0.866154 + 0.499777i \(0.166585\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.585786 −0.0236020
\(617\) −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
\(619\) 17.8579i 0.717768i 0.933382 + 0.358884i \(0.116843\pi\)
−0.933382 + 0.358884i \(0.883157\pi\)
\(620\) 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 \(0.137597\pi\)
−0.908016 + 0.418936i \(0.862403\pi\)
\(642\) 0 0
\(643\) 10.9706 10.9706i 0.432637 0.432637i −0.456888 0.889524i \(-0.651036\pi\)
0.889524 + 0.456888i \(0.151036\pi\)
\(644\) −6.82843 −0.269078
\(645\) 0 0
\(646\) −2.34315 −0.0921898
\(647\) 33.2426 33.2426i 1.30690 1.30690i 0.383264 0.923639i \(-0.374800\pi\)
0.923639 0.383264i \(-0.125200\pi\)
\(648\) 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 0.371197 0.928554i \(-0.378948\pi\)
−0.928554 + 0.371197i \(0.878948\pi\)
\(654\) 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 −0.768599 0.639731i \(-0.779046\pi\)
0.639731 + 0.768599i \(0.279046\pi\)
\(674\) −14.3848 −0.554081
\(675\) 0 0
\(676\) −19.0000 −0.730769
\(677\) −15.8284 + 15.8284i −0.608336 + 0.608336i −0.942511 0.334175i \(-0.891542\pi\)
0.334175 + 0.942511i \(0.391542\pi\)
\(678\) 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 0.0648383 0.997896i \(-0.479347\pi\)
−0.997896 + 0.0648383i \(0.979347\pi\)
\(684\) 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 \(-0.719740\pi\)
0.636794 0.771034i \(-0.280260\pi\)
\(702\) 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 \(0.278089\pi\)
−0.642039 + 0.766672i \(0.721911\pi\)
\(710\) 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 0.988754 0.149550i \(-0.0477824\pi\)
−0.149550 + 0.988754i \(0.547782\pi\)
\(728\) 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 −0.698866 0.715253i \(-0.746312\pi\)
0.715253 + 0.698866i \(0.246312\pi\)
\(734\) 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 \(0.0437890\pi\)
−0.990553 + 0.137134i \(0.956211\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.58579 + 2.58579i 0.0949272 + 0.0949272i
\(743\) 31.1127 + 31.1127i 1.14141 + 1.14141i 0.988192 + 0.153222i \(0.0489651\pi\)
0.153222 + 0.988192i \(0.451035\pi\)
\(744\) 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 0.990884 0.134714i \(-0.0430117\pi\)
−0.134714 + 0.990884i \(0.543012\pi\)
\(758\) −18.2426 18.2426i −0.662603 0.662603i
\(759\) 0 0
\(760\) 0 0
\(761\) 18.9706i 0.687682i −0.939028 0.343841i \(-0.888272\pi\)
0.939028 0.343841i \(-0.111728\pi\)
\(762\) 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 \(0.269961\pi\)
−0.661403 + 0.750031i \(0.730039\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.4853 + 13.4853i 0.485346 + 0.485346i
\(773\) −34.9411 34.9411i −1.25674 1.25674i −0.952638 0.304107i \(-0.901642\pi\)
−0.304107 0.952638i \(-0.598358\pi\)
\(774\) 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 0.927317 0.374277i \(-0.122109\pi\)
−0.374277 + 0.927317i \(0.622109\pi\)
\(788\) −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 −0.967476 0.252962i \(-0.918595\pi\)
0.252962 + 0.967476i \(0.418595\pi\)
\(798\) 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
\(805\) 0