Properties

Label 630.2.m.a.323.1
Level 630
Weight 2
Character 630.323
Analytic conductor 5.031
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 323.1
Root \(-0.707107 - 0.707107i\) of \(x^{4} + 1\)
Character \(\chi\) \(=\) 630.323
Dual form 630.2.m.a.197.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.707107 + 2.12132i) q^{10} +0.585786i q^{11} +(4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(0.585786 + 0.585786i) q^{17} -2.82843i q^{19} +(1.00000 - 2.00000i) q^{20} +(0.414214 - 0.414214i) q^{22} +(4.82843 - 4.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} -5.65685i q^{26} +(-0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(0.707107 + 0.707107i) q^{32} -0.828427i q^{34} +(2.12132 - 0.707107i) q^{35} +(6.24264 - 6.24264i) q^{37} +(-2.00000 + 2.00000i) q^{38} +(-2.12132 + 0.707107i) q^{40} -3.17157i q^{41} +(6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(9.24264 + 9.24264i) q^{47} -1.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(-4.00000 + 4.00000i) q^{52} +(-2.58579 + 2.58579i) q^{53} +(0.585786 - 1.17157i) q^{55} +1.00000i q^{56} +(-0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(-1.24264 - 1.24264i) q^{62} -1.00000i q^{64} +(-4.00000 - 12.0000i) q^{65} +(8.41421 - 8.41421i) q^{67} +(-0.585786 + 0.585786i) q^{68} +(-2.00000 - 1.00000i) q^{70} +1.17157i q^{71} +(7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(-0.414214 - 0.414214i) q^{77} -5.65685i q^{79} +(2.00000 + 1.00000i) q^{80} +(-2.24264 + 2.24264i) q^{82} +(-0.828427 + 0.828427i) q^{83} +(-0.585786 - 1.75736i) q^{85} -8.58579i q^{86} +(0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(4.82843 + 4.82843i) q^{92} -13.0711i q^{94} +(-2.82843 + 5.65685i) q^{95} +(-4.58579 + 4.58579i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{5} + O(q^{10}) \) \( 4q - 8q^{5} + 16q^{13} + 4q^{14} - 4q^{16} + 8q^{17} + 4q^{20} - 4q^{22} + 8q^{23} + 12q^{25} - 8q^{29} + 24q^{31} + 8q^{37} - 8q^{38} - 4q^{43} - 8q^{44} - 16q^{46} + 20q^{47} - 16q^{52} - 16q^{53} + 8q^{55} - 8q^{58} + 12q^{62} - 16q^{65} + 28q^{67} - 8q^{68} - 8q^{70} - 24q^{74} + 4q^{77} + 8q^{80} + 8q^{82} + 8q^{83} - 8q^{85} - 4q^{88} + 24q^{89} + 8q^{92} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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
\(5\) −2.00000 1.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) 0.707107 + 2.12132i 0.223607 + 0.670820i
\(11\) 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 \(0.0370621\pi\)
0.116171 + 0.993229i \(0.462938\pi\)
\(14\) 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 \(-0.217968\pi\)
−0.632492 + 0.774567i \(0.717968\pi\)
\(18\) 0 0
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) 0.414214 0.414214i 0.0883106 0.0883106i
\(23\) 4.82843 4.82843i 1.00680 1.00680i 0.00681991 0.999977i \(-0.497829\pi\)
0.999977 0.00681991i \(-0.00217086\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 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
\(35\) 2.12132 0.707107i 0.358569 0.119523i
\(36\) 0 0
\(37\) 6.24264 6.24264i 1.02628 1.02628i 0.0266387 0.999645i \(-0.491520\pi\)
0.999645 0.0266387i \(-0.00848036\pi\)
\(38\) −2.00000 + 2.00000i −0.324443 + 0.324443i
\(39\) 0 0
\(40\) −2.12132 + 0.707107i −0.335410 + 0.111803i
\(41\) 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 0.997433 0.0716040i \(-0.0228118\pi\)
−0.0716040 + 0.997433i \(0.522812\pi\)
\(44\) −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 \(0.152343\pi\)
0.460537 + 0.887640i \(0.347657\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0.707107 4.94975i 0.100000 0.700000i
\(51\) 0 0
\(52\) −4.00000 + 4.00000i −0.554700 + 0.554700i
\(53\) −2.58579 + 2.58579i −0.355185 + 0.355185i −0.862035 0.506849i \(-0.830810\pi\)
0.506849 + 0.862035i \(0.330810\pi\)
\(54\) 0 0
\(55\) 0.585786 1.17157i 0.0789874 0.157975i
\(56\) 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
\(65\) −4.00000 12.0000i −0.496139 1.48842i
\(66\) 0 0
\(67\) 8.41421 8.41421i 1.02796 1.02796i 0.0283621 0.999598i \(-0.490971\pi\)
0.999598 0.0283621i \(-0.00902914\pi\)
\(68\) −0.585786 + 0.585786i −0.0710370 + 0.0710370i
\(69\) 0 0
\(70\) −2.00000 1.00000i −0.239046 0.119523i
\(71\) 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 0.987185 0.159579i \(-0.0510137\pi\)
−0.159579 + 0.987185i \(0.551014\pi\)
\(74\) −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 \(-0.103086\pi\)
\(80\) 2.00000 + 1.00000i 0.223607 + 0.111803i
\(81\) 0 0
\(82\) −2.24264 + 2.24264i −0.247658 + 0.247658i
\(83\) −0.828427 + 0.828427i −0.0909317 + 0.0909317i −0.751109 0.660178i \(-0.770481\pi\)
0.660178 + 0.751109i \(0.270481\pi\)
\(84\) 0 0
\(85\) −0.585786 1.75736i −0.0635375 0.190612i
\(86\) 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
\(95\) −2.82843 + 5.65685i −0.290191 + 0.580381i
\(96\) 0 0
\(97\) −4.58579 + 4.58579i −0.465616 + 0.465616i −0.900491 0.434875i \(-0.856793\pi\)
0.434875 + 0.900491i \(0.356793\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) −4.00000 + 3.00000i −0.400000 + 0.300000i
\(101\) 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 0.240183 0.970728i \(-0.422792\pi\)
−0.970728 + 0.240183i \(0.922792\pi\)
\(104\) 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 \(-0.365016\pi\)
−0.911424 + 0.411469i \(0.865016\pi\)
\(108\) 0 0
\(109\) 9.31371i 0.892091i −0.895010 0.446046i \(-0.852832\pi\)
0.895010 0.446046i \(-0.147168\pi\)
\(110\) −1.24264 + 0.414214i −0.118481 + 0.0394937i
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) −11.3137 + 11.3137i −1.06430 + 1.06430i −0.0665190 + 0.997785i \(0.521189\pi\)
−0.997785 + 0.0665190i \(0.978811\pi\)
\(114\) 0 0
\(115\) −14.4853 + 4.82843i −1.35076 + 0.450253i
\(116\) 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
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 7.65685 7.65685i 0.679436 0.679436i −0.280437 0.959873i \(-0.590479\pi\)
0.959873 + 0.280437i \(0.0904792\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −5.65685 + 11.3137i −0.496139 + 0.992278i
\(131\) 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 \(0.00813555\pi\)
0.0255558 + 0.999673i \(0.491864\pi\)
\(138\) 0 0
\(139\) 17.6569i 1.49763i −0.662776 0.748817i \(-0.730622\pi\)
0.662776 0.748817i \(-0.269378\pi\)
\(140\) 0.707107 + 2.12132i 0.0597614 + 0.179284i
\(141\) 0 0
\(142\) 0.828427 0.828427i 0.0695201 0.0695201i
\(143\) −2.34315 + 2.34315i −0.195944 + 0.195944i
\(144\) 0 0
\(145\) −1.65685 0.828427i −0.137594 0.0687971i
\(146\) 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
\(155\) −3.51472 1.75736i −0.282309 0.141154i
\(156\) 0 0
\(157\) −9.65685 + 9.65685i −0.770701 + 0.770701i −0.978229 0.207528i \(-0.933458\pi\)
0.207528 + 0.978229i \(0.433458\pi\)
\(158\) −4.00000 + 4.00000i −0.318223 + 0.318223i
\(159\) 0 0
\(160\) −0.707107 2.12132i −0.0559017 0.167705i
\(161\) 6.82843i 0.538155i
\(162\) 0 0
\(163\) 11.7279 + 11.7279i 0.918602 + 0.918602i 0.996928 0.0783260i \(-0.0249575\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 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 \(-0.386245\pi\)
−0.936819 + 0.349814i \(0.886245\pi\)
\(168\) 0 0
\(169\) 19.0000i 1.46154i
\(170\) −0.828427 + 1.65685i −0.0635375 + 0.127075i
\(171\) 0 0
\(172\) −6.07107 + 6.07107i −0.462915 + 0.462915i
\(173\) −11.4853 + 11.4853i −0.873210 + 0.873210i −0.992821 0.119611i \(-0.961835\pi\)
0.119611 + 0.992821i \(0.461835\pi\)
\(174\) 0 0
\(175\) −4.94975 0.707107i −0.374166 0.0534522i
\(176\) 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
\(185\) −18.7279 + 6.24264i −1.37690 + 0.458968i
\(186\) 0 0
\(187\) −0.343146 + 0.343146i −0.0250933 + 0.0250933i
\(188\) −9.24264 + 9.24264i −0.674089 + 0.674089i
\(189\) 0 0
\(190\) 6.00000 2.00000i 0.435286 0.145095i
\(191\) 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 0.999583 0.0288908i \(-0.00919750\pi\)
−0.0288908 + 0.999583i \(0.509198\pi\)
\(194\) 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 \(-0.422586\pi\)
−0.970571 + 0.240813i \(0.922586\pi\)
\(198\) 0 0
\(199\) 4.10051i 0.290677i −0.989382 0.145339i \(-0.953573\pi\)
0.989382 0.145339i \(-0.0464271\pi\)
\(200\) 4.94975 + 0.707107i 0.350000 + 0.0500000i
\(201\) 0 0
\(202\) 12.4853 12.4853i 0.878461 0.878461i
\(203\) −0.585786 + 0.585786i −0.0411141 + 0.0411141i
\(204\) 0 0
\(205\) −3.17157 + 6.34315i −0.221512 + 0.443025i
\(206\) 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
\(215\) −6.07107 18.2132i −0.414043 1.24213i
\(216\) 0 0
\(217\) −1.24264 + 1.24264i −0.0843559 + 0.0843559i
\(218\) −6.58579 + 6.58579i −0.446046 + 0.446046i
\(219\) 0 0
\(220\) 1.17157 + 0.585786i 0.0789874 + 0.0394937i
\(221\) 4.68629i 0.315234i
\(222\) 0 0
\(223\) 7.31371 + 7.31371i 0.489762 + 0.489762i 0.908231 0.418469i \(-0.137433\pi\)
−0.418469 + 0.908231i \(0.637433\pi\)
\(224\) −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 \(-0.232489\pi\)
−0.667157 + 0.744917i \(0.732489\pi\)
\(228\) 0 0
\(229\) 8.24264i 0.544689i 0.962200 + 0.272345i \(0.0877990\pi\)
−0.962200 + 0.272345i \(0.912201\pi\)
\(230\) 13.6569 + 6.82843i 0.900506 + 0.450253i
\(231\) 0 0
\(232\) 0.585786 0.585786i 0.0384588 0.0384588i
\(233\) 14.8284 14.8284i 0.971443 0.971443i −0.0281608 0.999603i \(-0.508965\pi\)
0.999603 + 0.0281608i \(0.00896506\pi\)
\(234\) 0 0
\(235\) −9.24264 27.7279i −0.602923 1.80877i
\(236\) 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
\(245\) −1.00000 + 2.00000i −0.0638877 + 0.127775i
\(246\) 0 0
\(247\) 11.3137 11.3137i 0.719874 0.719874i
\(248\) 1.24264 1.24264i 0.0789078 0.0789078i
\(249\) 0 0
\(250\) −6.36396 + 9.19239i −0.402492 + 0.581378i
\(251\) 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 0.922224 0.386657i \(-0.126370\pi\)
−0.386657 + 0.922224i \(0.626370\pi\)
\(258\) 0 0
\(259\) 8.82843i 0.548572i
\(260\) 12.0000 4.00000i 0.744208 0.248069i
\(261\) 0 0
\(262\) 11.6569 11.6569i 0.720163 0.720163i
\(263\) 7.65685 7.65685i 0.472142 0.472142i −0.430465 0.902607i \(-0.641651\pi\)
0.902607 + 0.430465i \(0.141651\pi\)
\(264\) 0 0
\(265\) 7.75736 2.58579i 0.476531 0.158844i
\(266\) 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
\(275\) −2.34315 + 1.75736i −0.141297 + 0.105973i
\(276\) 0 0
\(277\) −2.10051 + 2.10051i −0.126207 + 0.126207i −0.767389 0.641182i \(-0.778444\pi\)
0.641182 + 0.767389i \(0.278444\pi\)
\(278\) −12.4853 + 12.4853i −0.748817 + 0.748817i
\(279\) 0 0
\(280\) 1.00000 2.00000i 0.0597614 0.119523i
\(281\) 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 \(-0.896545\pi\)
−0.319322 0.947646i \(-0.603455\pi\)
\(284\) −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
\(290\) 0.585786 + 1.75736i 0.0343986 + 0.103196i
\(291\) 0 0
\(292\) −7.07107 + 7.07107i −0.413803 + 0.413803i
\(293\) 8.65685 8.65685i 0.505739 0.505739i −0.407477 0.913216i \(-0.633591\pi\)
0.913216 + 0.407477i \(0.133591\pi\)
\(294\) 0 0
\(295\) −5.65685 2.82843i −0.329355 0.164677i
\(296\) 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
\(305\) 19.7990 + 9.89949i 1.13369 + 0.566843i
\(306\) 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
\(310\) 1.24264 + 3.72792i 0.0705772 + 0.211732i
\(311\) 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 0.767641 0.640880i \(-0.221430\pi\)
−0.640880 + 0.767641i \(0.721430\pi\)
\(314\) 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 \(-0.810366\pi\)
−0.561132 0.827726i \(-0.689634\pi\)
\(318\) 0 0
\(319\) 0.485281i 0.0271705i
\(320\) −1.00000 + 2.00000i −0.0559017 + 0.111803i
\(321\) 0 0
\(322\) 4.82843 4.82843i 0.269078 0.269078i
\(323\) 1.65685 1.65685i 0.0921898 0.0921898i
\(324\) 0 0
\(325\) −4.00000 + 28.0000i −0.221880 + 1.55316i
\(326\) 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
\(335\) −25.2426 + 8.41421i −1.37915 + 0.459718i
\(336\) 0 0
\(337\) 10.1716 10.1716i 0.554081 0.554081i −0.373535 0.927616i \(-0.621854\pi\)
0.927616 + 0.373535i \(0.121854\pi\)
\(338\) 13.4350 13.4350i 0.730769 0.730769i
\(339\) 0 0
\(340\) 1.75736 0.585786i 0.0953062 0.0317687i
\(341\) 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 \(-0.354388\pi\)
−0.897180 + 0.441666i \(0.854388\pi\)
\(348\) 0 0
\(349\) 32.7279i 1.75189i 0.482415 + 0.875943i \(0.339760\pi\)
−0.482415 + 0.875943i \(0.660240\pi\)
\(350\) 3.00000 + 4.00000i 0.160357 + 0.213809i
\(351\) 0 0
\(352\) −0.414214 + 0.414214i −0.0220777 + 0.0220777i
\(353\) 18.3848 18.3848i 0.978523 0.978523i −0.0212513 0.999774i \(-0.506765\pi\)
0.999774 + 0.0212513i \(0.00676499\pi\)
\(354\) 0 0
\(355\) 1.17157 2.34315i 0.0621806 0.124361i
\(356\) 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
\(365\) −7.07107 21.2132i −0.370117 1.11035i
\(366\) 0 0
\(367\) −10.2426 + 10.2426i −0.534661 + 0.534661i −0.921956 0.387295i \(-0.873410\pi\)
0.387295 + 0.921956i \(0.373410\pi\)
\(368\) −4.82843 + 4.82843i −0.251699 + 0.251699i
\(369\) 0 0
\(370\) 17.6569 + 8.82843i 0.917936 + 0.458968i
\(371\) 3.65685i 0.189854i
\(372\) 0 0
\(373\) −11.0711 11.0711i −0.573238 0.573238i 0.359794 0.933032i \(-0.382847\pi\)
−0.933032 + 0.359794i \(0.882847\pi\)
\(374\) 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 \(0.769452\pi\)
\(380\) −5.65685 2.82843i −0.290191 0.145095i
\(381\) 0 0
\(382\) −10.1421 + 10.1421i −0.518917 + 0.518917i
\(383\) 4.41421 4.41421i 0.225556 0.225556i −0.585277 0.810833i \(-0.699014\pi\)
0.810833 + 0.585277i \(0.199014\pi\)
\(384\) 0 0
\(385\) 0.414214 + 1.24264i 0.0211103 + 0.0633308i
\(386\) 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
\(395\) −5.65685 + 11.3137i −0.284627 + 0.569254i
\(396\) 0 0
\(397\) −0.928932 + 0.928932i −0.0466218 + 0.0466218i −0.730033 0.683412i \(-0.760495\pi\)
0.683412 + 0.730033i \(0.260495\pi\)
\(398\) −2.89949 + 2.89949i −0.145339 + 0.145339i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) 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 \(-0.0795217\pi\)
\(410\) 6.72792 2.24264i 0.332268 0.110756i
\(411\) 0 0
\(412\) 7.41421 7.41421i 0.365272 0.365272i
\(413\) −2.00000 + 2.00000i −0.0984136 + 0.0984136i
\(414\) 0 0
\(415\) 2.48528 0.828427i 0.121998 0.0406659i
\(416\) 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
\(425\) −0.585786 + 4.10051i −0.0284148 + 0.198904i
\(426\) 0 0
\(427\) 7.00000 7.00000i 0.338754 0.338754i
\(428\) 5.17157 5.17157i 0.249977 0.249977i
\(429\) 0 0
\(430\) −8.58579 + 17.1716i −0.414043 + 0.828087i
\(431\) 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 0.993190 0.116505i \(-0.0371690\pi\)
−0.116505 + 0.993190i \(0.537169\pi\)
\(434\) 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 \(-0.0296637\pi\)
\(440\) −0.414214 1.24264i −0.0197469 0.0592406i
\(441\) 0 0
\(442\) 3.31371 3.31371i 0.157617 0.157617i
\(443\) −3.51472 + 3.51472i −0.166989 + 0.166989i −0.785655 0.618665i \(-0.787674\pi\)
0.618665 + 0.785655i \(0.287674\pi\)
\(444\) 0 0
\(445\) −6.34315 3.17157i −0.300694 0.150347i
\(446\) 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
\(455\) 11.3137 + 5.65685i 0.530395 + 0.265197i
\(456\) 0 0
\(457\) 2.17157 2.17157i 0.101582 0.101582i −0.654489 0.756071i \(-0.727116\pi\)
0.756071 + 0.654489i \(0.227116\pi\)
\(458\) 5.82843 5.82843i 0.272345 0.272345i
\(459\) 0 0
\(460\) −4.82843 14.4853i −0.225127 0.675380i
\(461\) 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 0.0769016 0.997039i \(-0.475497\pi\)
−0.997039 + 0.0769016i \(0.975497\pi\)
\(464\) −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 \(-0.401468\pi\)
−0.952471 + 0.304629i \(0.901468\pi\)
\(468\) 0 0
\(469\) 11.8995i 0.549468i
\(470\) −13.0711 + 26.1421i −0.602923 + 1.20585i
\(471\) 0 0
\(472\) 2.00000 2.00000i 0.0920575 0.0920575i
\(473\) −3.55635 + 3.55635i −0.163521 + 0.163521i
\(474\) 0 0
\(475\) 11.3137 8.48528i 0.519109 0.389331i
\(476\) 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
\(485\) 13.7574 4.58579i 0.624690 0.208230i
\(486\) 0 0
\(487\) 18.9706 18.9706i 0.859638 0.859638i −0.131657 0.991295i \(-0.542030\pi\)
0.991295 + 0.131657i \(0.0420298\pi\)
\(488\) −7.00000 + 7.00000i −0.316875 + 0.316875i
\(489\) 0 0
\(490\) 2.12132 0.707107i 0.0958315 0.0319438i
\(491\) 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 \(0.824060\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 0 0
\(502\) −18.8284 + 18.8284i −0.840354 + 0.840354i
\(503\) −16.5563 + 16.5563i −0.738211 + 0.738211i −0.972232 0.234021i \(-0.924812\pi\)
0.234021 + 0.972232i \(0.424812\pi\)
\(504\) 0 0
\(505\) 17.6569 35.3137i 0.785720 1.57144i
\(506\) 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
\(515\) 7.41421 + 22.2426i 0.326709 + 0.980128i
\(516\) 0 0
\(517\) −5.41421 + 5.41421i −0.238117 + 0.238117i
\(518\) 6.24264 6.24264i 0.274286 0.274286i
\(519\) 0 0
\(520\) −11.3137 5.65685i −0.496139 0.248069i
\(521\) 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 \(-0.963847\pi\)
−0.113334 0.993557i \(-0.536153\pi\)
\(524\) −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
\(530\) −7.31371 3.65685i −0.317687 0.158844i
\(531\) 0 0
\(532\) −2.00000 + 2.00000i −0.0867110 + 0.0867110i
\(533\) 12.6863 12.6863i 0.549504 0.549504i
\(534\) 0 0
\(535\) 5.17157 + 15.5147i 0.223587 + 0.670760i
\(536\) 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
\(545\) −9.31371 + 18.6274i −0.398955 + 0.797911i
\(546\) 0 0
\(547\) −12.5563 + 12.5563i −0.536871 + 0.536871i −0.922608 0.385738i \(-0.873947\pi\)
0.385738 + 0.922608i \(0.373947\pi\)
\(548\) −12.0000 + 12.0000i −0.512615 + 0.512615i
\(549\) 0 0
\(550\) 2.89949 + 0.414214i 0.123635 + 0.0176621i
\(551\) 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 \(-0.177306\pi\)
−0.528661 + 0.848833i \(0.677306\pi\)
\(558\) 0 0
\(559\) 48.5685i 2.05423i
\(560\) −2.12132 + 0.707107i −0.0896421 + 0.0298807i
\(561\) 0 0
\(562\) −13.4853 + 13.4853i −0.568842 + 0.568842i
\(563\) 6.68629 6.68629i 0.281794 0.281794i −0.552030 0.833824i \(-0.686147\pi\)
0.833824 + 0.552030i \(0.186147\pi\)
\(564\) 0 0
\(565\) 33.9411 11.3137i 1.42791 0.475971i
\(566\) 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
\(575\) 33.7990 + 4.82843i 1.40952 + 0.201359i
\(576\) 0 0
\(577\) −10.7279 + 10.7279i −0.446609 + 0.446609i −0.894226 0.447616i \(-0.852273\pi\)
0.447616 + 0.894226i \(0.352273\pi\)
\(578\) −11.5355 + 11.5355i −0.479815 + 0.479815i
\(579\) 0 0
\(580\) 0.828427 1.65685i 0.0343986 0.0687971i
\(581\) 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 \(-0.0761290\pi\)
−0.236893 + 0.971536i \(0.576129\pi\)
\(588\) 0 0
\(589\) 4.97056i 0.204808i
\(590\) 2.00000 + 6.00000i 0.0823387 + 0.247016i
\(591\) 0 0
\(592\) −6.24264 + 6.24264i −0.256571 + 0.256571i
\(593\) −16.3848 + 16.3848i −0.672842 + 0.672842i −0.958370 0.285528i \(-0.907831\pi\)
0.285528 + 0.958370i \(0.407831\pi\)
\(594\) 0 0
\(595\) 1.65685 + 0.828427i 0.0679244 + 0.0339622i
\(596\) 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
\(605\) −21.3137 10.6569i −0.866525 0.433263i
\(606\) 0 0
\(607\) −7.31371 + 7.31371i −0.296854 + 0.296854i −0.839780 0.542926i \(-0.817316\pi\)
0.542926 + 0.839780i \(0.317316\pi\)
\(608\) 2.00000 2.00000i 0.0811107 0.0811107i
\(609\) 0 0
\(610\) −7.00000 21.0000i −0.283422 0.850265i
\(611\) 73.9411i 2.99134i
\(612\) 0 0
\(613\) −9.07107 9.07107i −0.366377 0.366377i 0.499777 0.866154i \(-0.333415\pi\)
−0.866154 + 0.499777i \(0.833415\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.585786 −0.0236020
\(617\) 24.0416 + 24.0416i 0.967880 + 0.967880i 0.999500 0.0316203i \(-0.0100667\pi\)
−0.0316203 + 0.999500i \(0.510067\pi\)
\(618\) 0 0
\(619\) 17.8579i 0.717768i −0.933382 0.358884i \(-0.883157\pi\)
0.933382 0.358884i \(-0.116843\pi\)
\(620\) 1.75736 3.51472i 0.0705772 0.141154i
\(621\) 0 0
\(622\) −3.41421 + 3.41421i −0.136897 + 0.136897i
\(623\) −2.24264 + 2.24264i −0.0898495 + 0.0898495i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 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
\(635\) −22.9706 + 7.65685i −0.911559 + 0.303853i
\(636\) 0 0
\(637\) 4.00000 4.00000i 0.158486 0.158486i
\(638\) 0.343146 0.343146i 0.0135853 0.0135853i
\(639\) 0 0
\(640\) 2.12132 0.707107i 0.0838525 0.0279508i
\(641\) 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 0.456888 0.889524i \(-0.348964\pi\)
−0.889524 + 0.456888i \(0.848964\pi\)
\(644\) −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 \(-0.874800\pi\)
−0.383264 0.923639i \(-0.625200\pi\)
\(648\) 0 0
\(649\) 1.65685i 0.0650372i
\(650\) 22.6274 16.9706i 0.887520 0.665640i
\(651\) 0 0
\(652\) −11.7279 + 11.7279i −0.459301 + 0.459301i
\(653\) 14.2426 14.2426i 0.557358 0.557358i −0.371197 0.928554i \(-0.621052\pi\)
0.928554 + 0.371197i \(0.121052\pi\)
\(654\) 0 0
\(655\) 16.4853 32.9706i 0.644133 1.28827i
\(656\) 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
\(665\) −2.00000 6.00000i −0.0775567 0.232670i
\(666\) 0 0
\(667\) 4.00000 4.00000i 0.154881 0.154881i
\(668\) 7.58579 7.58579i 0.293503 0.293503i
\(669\) 0 0
\(670\) 23.7990 + 11.8995i 0.919435 + 0.459718i
\(671\) 5.79899i 0.223868i
\(672\) 0 0
\(673\) 3.34315 + 3.34315i 0.128869 + 0.128869i 0.768599 0.639731i \(-0.220954\pi\)
−0.639731 + 0.768599i \(0.720954\pi\)
\(674\) −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 \(-0.108458\pi\)
−0.334175 + 0.942511i \(0.608458\pi\)
\(678\) 0 0
\(679\) 6.48528i 0.248882i
\(680\) −1.65685 0.828427i −0.0635375 0.0317687i
\(681\) 0 0
\(682\) 0.727922 0.727922i 0.0278736 0.0278736i
\(683\) 24.3848 24.3848i 0.933058 0.933058i −0.0648383 0.997896i \(-0.520653\pi\)
0.997896 + 0.0648383i \(0.0206531\pi\)
\(684\) 0 0
\(685\) −12.0000 36.0000i −0.458496 1.37549i
\(686\) 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
\(695\) −17.6569 + 35.3137i −0.669763 + 1.33953i
\(696\) 0 0
\(697\) 1.85786 1.85786i 0.0703716 0.0703716i
\(698\) 23.1421 23.1421i 0.875943 0.875943i
\(699\) 0 0
\(700\) 0.707107 4.94975i 0.0267261 0.187083i
\(701\) 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 \(-0.278089\pi\)
\(710\) −2.48528 + 0.828427i −0.0932709 + 0.0310903i
\(711\) 0 0
\(712\) 2.24264 2.24264i 0.0840465 0.0840465i
\(713\) 8.48528 8.48528i 0.317776 0.317776i
\(714\) 0 0
\(715\) 7.02944 2.34315i 0.262886 0.0876287i
\(716\) 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
\(725\) 2.48528 + 3.31371i 0.0923010 + 0.123068i
\(726\) 0 0
\(727\) −22.6274 + 22.6274i −0.839204 + 0.839204i −0.988754 0.149550i \(-0.952218\pi\)
0.149550 + 0.988754i \(0.452218\pi\)
\(728\) −4.00000 + 4.00000i −0.148250 + 0.148250i
\(729\) 0 0
\(730\) −10.0000 + 20.0000i −0.370117 + 0.740233i
\(731\) 7.11270i 0.263073i
\(732\) 0 0
\(733\) −0.443651 0.443651i −0.0163866 0.0163866i 0.698866 0.715253i \(-0.253688\pi\)
−0.715253 + 0.698866i \(0.753688\pi\)
\(734\) 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 \(-0.0437890\pi\)
\(740\) −6.24264 18.7279i −0.229484 0.688452i
\(741\) 0 0
\(742\) −2.58579 + 2.58579i −0.0949272 + 0.0949272i
\(743\) −31.1127 + 31.1127i −1.14141 + 1.14141i −0.153222 + 0.988192i \(0.548965\pi\)
−0.988192 + 0.153222i \(0.951035\pi\)
\(744\) 0 0
\(745\) 16.2843 + 8.14214i 0.596610 + 0.298305i
\(746\) 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
\(755\) 37.6569 + 18.8284i 1.37047 + 0.685237i
\(756\) 0 0
\(757\) −23.5563 + 23.5563i −0.856170 + 0.856170i −0.990884 0.134714i \(-0.956988\pi\)
0.134714 + 0.990884i \(0.456988\pi\)
\(758\) 18.2426 18.2426i 0.662603 0.662603i
\(759\) 0 0
\(760\) 2.00000 + 6.00000i 0.0725476 + 0.217643i
\(761\) 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 \(-0.269961\pi\)
\(770\) 0.585786 1.17157i 0.0211103 0.0422206i
\(771\) 0 0
\(772\) −13.4853 + 13.4853i −0.485346 + 0.485346i
\(773\) 34.9411 34.9411i 1.25674 1.25674i 0.304107 0.952638i \(-0.401642\pi\)
0.952638 0.304107i \(-0.0983581\pi\)
\(774\) 0 0
\(775\) 5.27208 + 7.02944i 0.189379 + 0.252505i
\(776\) 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
\(785\) 28.9706 9.65685i 1.03400 0.344668i
\(786\) 0 0
\(787\) −15.5147 + 15.5147i −0.553040 + 0.553040i −0.927317 0.374277i \(-0.877891\pi\)
0.374277 + 0.927317i \(0.377891\pi\)
\(788\) 10.2426 10.2426i 0.364879 0.364879i
\(789\) 0 0
\(790\) 12.0000 4.00000i 0.426941 0.142314i
\(791\) 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 + 0.71451