Properties

Label 1170.2.bs.d.901.1
Level $1170$
Weight $2$
Character 1170.901
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.901
Dual form 1170.2.bs.d.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(2.59808 - 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.232051 - 0.133975i) q^{11} +(0.866025 + 3.50000i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.96410 - 2.86603i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.133975 + 0.232051i) q^{22} +(1.73205 - 3.00000i) q^{23} -1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +(2.59808 + 1.50000i) q^{28} +(0.732051 - 1.26795i) q^{29} +4.92820i q^{31} +(0.866025 - 0.500000i) q^{32} -4.00000i q^{34} +(-1.50000 - 2.59808i) q^{35} +(-5.13397 - 2.96410i) q^{37} -5.73205 q^{38} -1.00000 q^{40} +(3.46410 + 2.00000i) q^{41} +(-3.00000 - 5.19615i) q^{43} -0.267949i q^{44} +(-3.00000 + 1.73205i) q^{46} +6.46410i q^{47} +(1.00000 - 1.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-2.59808 + 2.50000i) q^{52} +0.267949 q^{53} +(-0.133975 + 0.232051i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(-1.26795 + 0.732051i) q^{58} +(9.92820 - 5.73205i) q^{59} +(0.267949 + 0.464102i) q^{61} +(2.46410 - 4.26795i) q^{62} -1.00000 q^{64} +(3.50000 - 0.866025i) q^{65} +(1.26795 + 0.732051i) q^{67} +(-2.00000 + 3.46410i) q^{68} +3.00000i q^{70} +(11.1962 - 6.46410i) q^{71} -6.92820i q^{73} +(2.96410 + 5.13397i) q^{74} +(4.96410 + 2.86603i) q^{76} -0.803848 q^{77} +3.07180 q^{79} +(0.866025 + 0.500000i) q^{80} +(-2.00000 - 3.46410i) q^{82} -9.46410i q^{83} +(3.46410 - 2.00000i) q^{85} +6.00000i q^{86} +(-0.133975 + 0.232051i) q^{88} +(12.2321 + 7.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +3.46410 q^{92} +(3.23205 - 5.59808i) q^{94} +(-2.86603 - 4.96410i) q^{95} +(7.26795 - 4.19615i) q^{97} +(-1.73205 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + O(q^{10}) \) \( 4q + 2q^{4} - 2q^{10} + 6q^{11} - 12q^{14} - 2q^{16} + 8q^{17} + 6q^{19} + 4q^{22} - 4q^{25} + 4q^{26} - 4q^{29} - 6q^{35} - 24q^{37} - 16q^{38} - 4q^{40} - 12q^{43} - 12q^{46} + 4q^{49} + 8q^{53} - 4q^{55} - 6q^{56} - 12q^{58} + 12q^{59} + 8q^{61} - 4q^{62} - 4q^{64} + 14q^{65} + 12q^{67} - 8q^{68} + 24q^{71} - 2q^{74} + 6q^{76} - 24q^{77} + 40q^{79} - 8q^{82} - 4q^{88} + 42q^{89} + 30q^{91} + 6q^{94} - 8q^{95} + 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.59808 1.50000i 0.981981 0.566947i 0.0791130 0.996866i \(-0.474791\pi\)
0.902867 + 0.429919i \(0.141458\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −0.232051 0.133975i −0.0699660 0.0403949i 0.464609 0.885516i \(-0.346195\pi\)
−0.534575 + 0.845121i \(0.679528\pi\)
\(12\) 0 0
\(13\) 0.866025 + 3.50000i 0.240192 + 0.970725i
\(14\) −3.00000 −0.801784
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) 4.96410 2.86603i 1.13884 0.657511i 0.192699 0.981258i \(-0.438276\pi\)
0.946144 + 0.323747i \(0.104943\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 0 0
\(22\) 0.133975 + 0.232051i 0.0285635 + 0.0494734i
\(23\) 1.73205 3.00000i 0.361158 0.625543i −0.626994 0.779024i \(-0.715715\pi\)
0.988152 + 0.153481i \(0.0490483\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 0 0
\(28\) 2.59808 + 1.50000i 0.490990 + 0.283473i
\(29\) 0.732051 1.26795i 0.135938 0.235452i −0.790017 0.613085i \(-0.789928\pi\)
0.925956 + 0.377633i \(0.123262\pi\)
\(30\) 0 0
\(31\) 4.92820i 0.885131i 0.896736 + 0.442566i \(0.145932\pi\)
−0.896736 + 0.442566i \(0.854068\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) −1.50000 2.59808i −0.253546 0.439155i
\(36\) 0 0
\(37\) −5.13397 2.96410i −0.844020 0.487295i 0.0146085 0.999893i \(-0.495350\pi\)
−0.858629 + 0.512598i \(0.828683\pi\)
\(38\) −5.73205 −0.929861
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 3.46410 + 2.00000i 0.541002 + 0.312348i 0.745485 0.666523i \(-0.232218\pi\)
−0.204483 + 0.978870i \(0.565551\pi\)
\(42\) 0 0
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) 0.267949i 0.0403949i
\(45\) 0 0
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) 6.46410i 0.942886i 0.881897 + 0.471443i \(0.156267\pi\)
−0.881897 + 0.471443i \(0.843733\pi\)
\(48\) 0 0
\(49\) 1.00000 1.73205i 0.142857 0.247436i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 0 0
\(52\) −2.59808 + 2.50000i −0.360288 + 0.346688i
\(53\) 0.267949 0.0368057 0.0184028 0.999831i \(-0.494142\pi\)
0.0184028 + 0.999831i \(0.494142\pi\)
\(54\) 0 0
\(55\) −0.133975 + 0.232051i −0.0180651 + 0.0312897i
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) 0 0
\(58\) −1.26795 + 0.732051i −0.166490 + 0.0961230i
\(59\) 9.92820 5.73205i 1.29254 0.746249i 0.313438 0.949609i \(-0.398519\pi\)
0.979104 + 0.203359i \(0.0651859\pi\)
\(60\) 0 0
\(61\) 0.267949 + 0.464102i 0.0343074 + 0.0594221i 0.882669 0.469995i \(-0.155744\pi\)
−0.848362 + 0.529417i \(0.822411\pi\)
\(62\) 2.46410 4.26795i 0.312941 0.542030i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.50000 0.866025i 0.434122 0.107417i
\(66\) 0 0
\(67\) 1.26795 + 0.732051i 0.154905 + 0.0894342i 0.575449 0.817838i \(-0.304827\pi\)
−0.420544 + 0.907272i \(0.638161\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0 0
\(70\) 3.00000i 0.358569i
\(71\) 11.1962 6.46410i 1.32874 0.767148i 0.343634 0.939104i \(-0.388342\pi\)
0.985105 + 0.171956i \(0.0550086\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 2.96410 + 5.13397i 0.344570 + 0.596812i
\(75\) 0 0
\(76\) 4.96410 + 2.86603i 0.569422 + 0.328756i
\(77\) −0.803848 −0.0916069
\(78\) 0 0
\(79\) 3.07180 0.345604 0.172802 0.984957i \(-0.444718\pi\)
0.172802 + 0.984957i \(0.444718\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) 9.46410i 1.03882i −0.854525 0.519410i \(-0.826152\pi\)
0.854525 0.519410i \(-0.173848\pi\)
\(84\) 0 0
\(85\) 3.46410 2.00000i 0.375735 0.216930i
\(86\) 6.00000i 0.646997i
\(87\) 0 0
\(88\) −0.133975 + 0.232051i −0.0142817 + 0.0247367i
\(89\) 12.2321 + 7.06218i 1.29659 + 0.748589i 0.979814 0.199910i \(-0.0640648\pi\)
0.316780 + 0.948499i \(0.397398\pi\)
\(90\) 0 0
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 3.46410 0.361158
\(93\) 0 0
\(94\) 3.23205 5.59808i 0.333361 0.577397i
\(95\) −2.86603 4.96410i −0.294048 0.509306i
\(96\) 0 0
\(97\) 7.26795 4.19615i 0.737948 0.426055i −0.0833745 0.996518i \(-0.526570\pi\)
0.821323 + 0.570464i \(0.193236\pi\)
\(98\) −1.73205 + 1.00000i −0.174964 + 0.101015i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 6.19615 10.7321i 0.616540 1.06788i −0.373572 0.927601i \(-0.621867\pi\)
0.990112 0.140278i \(-0.0447996\pi\)
\(102\) 0 0
\(103\) −11.5885 −1.14184 −0.570922 0.821004i \(-0.693414\pi\)
−0.570922 + 0.821004i \(0.693414\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 0 0
\(106\) −0.232051 0.133975i −0.0225388 0.0130128i
\(107\) −6.46410 + 11.1962i −0.624908 + 1.08237i 0.363650 + 0.931536i \(0.381530\pi\)
−0.988559 + 0.150837i \(0.951803\pi\)
\(108\) 0 0
\(109\) 10.3923i 0.995402i −0.867349 0.497701i \(-0.834178\pi\)
0.867349 0.497701i \(-0.165822\pi\)
\(110\) 0.232051 0.133975i 0.0221252 0.0127740i
\(111\) 0 0
\(112\) 3.00000i 0.283473i
\(113\) −6.00000 10.3923i −0.564433 0.977626i −0.997102 0.0760733i \(-0.975762\pi\)
0.432670 0.901553i \(-0.357572\pi\)
\(114\) 0 0
\(115\) −3.00000 1.73205i −0.279751 0.161515i
\(116\) 1.46410 0.135938
\(117\) 0 0
\(118\) −11.4641 −1.05536
\(119\) 10.3923 + 6.00000i 0.952661 + 0.550019i
\(120\) 0 0
\(121\) −5.46410 9.46410i −0.496737 0.860373i
\(122\) 0.535898i 0.0485180i
\(123\) 0 0
\(124\) −4.26795 + 2.46410i −0.383273 + 0.221283i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 6.33013 10.9641i 0.561708 0.972907i −0.435640 0.900121i \(-0.643478\pi\)
0.997348 0.0727855i \(-0.0231889\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.46410 1.00000i −0.303822 0.0877058i
\(131\) −14.3205 −1.25119 −0.625594 0.780149i \(-0.715143\pi\)
−0.625594 + 0.780149i \(0.715143\pi\)
\(132\) 0 0
\(133\) 8.59808 14.8923i 0.745548 1.29133i
\(134\) −0.732051 1.26795i −0.0632396 0.109534i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) −11.6603 + 6.73205i −0.996203 + 0.575158i −0.907123 0.420867i \(-0.861726\pi\)
−0.0890802 + 0.996024i \(0.528393\pi\)
\(138\) 0 0
\(139\) 9.89230 + 17.1340i 0.839054 + 1.45328i 0.890686 + 0.454619i \(0.150224\pi\)
−0.0516319 + 0.998666i \(0.516442\pi\)
\(140\) 1.50000 2.59808i 0.126773 0.219578i
\(141\) 0 0
\(142\) −12.9282 −1.08491
\(143\) 0.267949 0.928203i 0.0224070 0.0776203i
\(144\) 0 0
\(145\) −1.26795 0.732051i −0.105297 0.0607935i
\(146\) −3.46410 + 6.00000i −0.286691 + 0.496564i
\(147\) 0 0
\(148\) 5.92820i 0.487295i
\(149\) −16.2679 + 9.39230i −1.33272 + 0.769448i −0.985716 0.168415i \(-0.946135\pi\)
−0.347006 + 0.937863i \(0.612802\pi\)
\(150\) 0 0
\(151\) 22.7846i 1.85419i 0.374832 + 0.927093i \(0.377700\pi\)
−0.374832 + 0.927093i \(0.622300\pi\)
\(152\) −2.86603 4.96410i −0.232465 0.402642i
\(153\) 0 0
\(154\) 0.696152 + 0.401924i 0.0560976 + 0.0323879i
\(155\) 4.92820 0.395843
\(156\) 0 0
\(157\) 21.1962 1.69164 0.845819 0.533471i \(-0.179113\pi\)
0.845819 + 0.533471i \(0.179113\pi\)
\(158\) −2.66025 1.53590i −0.211638 0.122190i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 10.3923i 0.819028i
\(162\) 0 0
\(163\) −2.53590 + 1.46410i −0.198627 + 0.114677i −0.596015 0.802973i \(-0.703250\pi\)
0.397388 + 0.917651i \(0.369917\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −4.73205 + 8.19615i −0.367278 + 0.636145i
\(167\) 0.401924 + 0.232051i 0.0311018 + 0.0179566i 0.515470 0.856907i \(-0.327617\pi\)
−0.484368 + 0.874864i \(0.660951\pi\)
\(168\) 0 0
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) 3.00000 5.19615i 0.228748 0.396203i
\(173\) −1.06218 1.83975i −0.0807559 0.139873i 0.822819 0.568304i \(-0.192400\pi\)
−0.903575 + 0.428430i \(0.859067\pi\)
\(174\) 0 0
\(175\) −2.59808 + 1.50000i −0.196396 + 0.113389i
\(176\) 0.232051 0.133975i 0.0174915 0.0100987i
\(177\) 0 0
\(178\) −7.06218 12.2321i −0.529333 0.916831i
\(179\) 4.53590 7.85641i 0.339029 0.587215i −0.645221 0.763996i \(-0.723235\pi\)
0.984250 + 0.176780i \(0.0565682\pi\)
\(180\) 0 0
\(181\) 16.9282 1.25826 0.629132 0.777299i \(-0.283411\pi\)
0.629132 + 0.777299i \(0.283411\pi\)
\(182\) −2.59808 10.5000i −0.192582 0.778312i
\(183\) 0 0
\(184\) −3.00000 1.73205i −0.221163 0.127688i
\(185\) −2.96410 + 5.13397i −0.217925 + 0.377457i
\(186\) 0 0
\(187\) 1.07180i 0.0783775i
\(188\) −5.59808 + 3.23205i −0.408282 + 0.235722i
\(189\) 0 0
\(190\) 5.73205i 0.415847i
\(191\) −8.66025 15.0000i −0.626634 1.08536i −0.988222 0.153024i \(-0.951099\pi\)
0.361588 0.932338i \(-0.382235\pi\)
\(192\) 0 0
\(193\) −8.53590 4.92820i −0.614427 0.354740i 0.160269 0.987073i \(-0.448764\pi\)
−0.774696 + 0.632334i \(0.782097\pi\)
\(194\) −8.39230 −0.602532
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 9.86603 + 5.69615i 0.702925 + 0.405834i 0.808436 0.588584i \(-0.200314\pi\)
−0.105511 + 0.994418i \(0.533648\pi\)
\(198\) 0 0
\(199\) 12.4641 + 21.5885i 0.883557 + 1.53037i 0.847359 + 0.531021i \(0.178191\pi\)
0.0361978 + 0.999345i \(0.488475\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) −10.7321 + 6.19615i −0.755104 + 0.435960i
\(203\) 4.39230i 0.308279i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 10.0359 + 5.79423i 0.699234 + 0.403703i
\(207\) 0 0
\(208\) −3.46410 1.00000i −0.240192 0.0693375i
\(209\) −1.53590 −0.106240
\(210\) 0 0
\(211\) 4.03590 6.99038i 0.277843 0.481238i −0.693006 0.720932i \(-0.743714\pi\)
0.970848 + 0.239694i \(0.0770473\pi\)
\(212\) 0.133975 + 0.232051i 0.00920141 + 0.0159373i
\(213\) 0 0
\(214\) 11.1962 6.46410i 0.765353 0.441877i
\(215\) −5.19615 + 3.00000i −0.354375 + 0.204598i
\(216\) 0 0
\(217\) 7.39230 + 12.8038i 0.501822 + 0.869182i
\(218\) −5.19615 + 9.00000i −0.351928 + 0.609557i
\(219\) 0 0
\(220\) −0.267949 −0.0180651
\(221\) −10.3923 + 10.0000i −0.699062 + 0.672673i
\(222\) 0 0
\(223\) −16.3301 9.42820i −1.09355 0.631359i −0.159028 0.987274i \(-0.550836\pi\)
−0.934518 + 0.355915i \(0.884169\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) −5.66025 + 3.26795i −0.375684 + 0.216901i −0.675939 0.736958i \(-0.736262\pi\)
0.300255 + 0.953859i \(0.402928\pi\)
\(228\) 0 0
\(229\) 4.53590i 0.299741i 0.988706 + 0.149870i \(0.0478856\pi\)
−0.988706 + 0.149870i \(0.952114\pi\)
\(230\) 1.73205 + 3.00000i 0.114208 + 0.197814i
\(231\) 0 0
\(232\) −1.26795 0.732051i −0.0832449 0.0480615i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 6.46410 0.421671
\(236\) 9.92820 + 5.73205i 0.646271 + 0.373125i
\(237\) 0 0
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) 3.46410i 0.224074i 0.993704 + 0.112037i \(0.0357375\pi\)
−0.993704 + 0.112037i \(0.964262\pi\)
\(240\) 0 0
\(241\) −21.8205 + 12.5981i −1.40558 + 0.811513i −0.994958 0.100291i \(-0.968023\pi\)
−0.410624 + 0.911805i \(0.634689\pi\)
\(242\) 10.9282i 0.702492i
\(243\) 0 0
\(244\) −0.267949 + 0.464102i −0.0171537 + 0.0297111i
\(245\) −1.73205 1.00000i −0.110657 0.0638877i
\(246\) 0 0
\(247\) 14.3301 + 14.8923i 0.911804 + 0.947575i
\(248\) 4.92820 0.312941
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 9.76795 + 16.9186i 0.616547 + 1.06789i 0.990111 + 0.140287i \(0.0448025\pi\)
−0.373563 + 0.927605i \(0.621864\pi\)
\(252\) 0 0
\(253\) −0.803848 + 0.464102i −0.0505375 + 0.0291778i
\(254\) −10.9641 + 6.33013i −0.687949 + 0.397187i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.26795 12.5885i 0.453362 0.785246i −0.545230 0.838286i \(-0.683558\pi\)
0.998592 + 0.0530400i \(0.0168911\pi\)
\(258\) 0 0
\(259\) −17.7846 −1.10508
\(260\) 2.50000 + 2.59808i 0.155043 + 0.161126i
\(261\) 0 0
\(262\) 12.4019 + 7.16025i 0.766193 + 0.442362i
\(263\) −12.2583 + 21.2321i −0.755881 + 1.30922i 0.189054 + 0.981967i \(0.439458\pi\)
−0.944935 + 0.327258i \(0.893875\pi\)
\(264\) 0 0
\(265\) 0.267949i 0.0164600i
\(266\) −14.8923 + 8.59808i −0.913106 + 0.527182i
\(267\) 0 0
\(268\) 1.46410i 0.0894342i
\(269\) −8.53590 14.7846i −0.520443 0.901434i −0.999717 0.0237685i \(-0.992434\pi\)
0.479275 0.877665i \(-0.340900\pi\)
\(270\) 0 0
\(271\) 21.1244 + 12.1962i 1.28321 + 0.740863i 0.977434 0.211239i \(-0.0677499\pi\)
0.305779 + 0.952103i \(0.401083\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) 13.4641 0.813396
\(275\) 0.232051 + 0.133975i 0.0139932 + 0.00807897i
\(276\) 0 0
\(277\) −5.79423 10.0359i −0.348141 0.602999i 0.637778 0.770220i \(-0.279854\pi\)
−0.985919 + 0.167222i \(0.946520\pi\)
\(278\) 19.7846i 1.18660i
\(279\) 0 0
\(280\) −2.59808 + 1.50000i −0.155265 + 0.0896421i
\(281\) 6.92820i 0.413302i 0.978415 + 0.206651i \(0.0662565\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(282\) 0 0
\(283\) 3.19615 5.53590i 0.189992 0.329075i −0.755256 0.655430i \(-0.772487\pi\)
0.945247 + 0.326355i \(0.105821\pi\)
\(284\) 11.1962 + 6.46410i 0.664369 + 0.383574i
\(285\) 0 0
\(286\) −0.696152 + 0.669873i −0.0411644 + 0.0396104i
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0.732051 + 1.26795i 0.0429875 + 0.0744565i
\(291\) 0 0
\(292\) 6.00000 3.46410i 0.351123 0.202721i
\(293\) −25.3301 + 14.6244i −1.47980 + 0.854364i −0.999738 0.0228698i \(-0.992720\pi\)
−0.480063 + 0.877234i \(0.659386\pi\)
\(294\) 0 0
\(295\) −5.73205 9.92820i −0.333733 0.578042i
\(296\) −2.96410 + 5.13397i −0.172285 + 0.298406i
\(297\) 0 0
\(298\) 18.7846 1.08816
\(299\) 12.0000 + 3.46410i 0.693978 + 0.200334i
\(300\) 0 0
\(301\) −15.5885 9.00000i −0.898504 0.518751i
\(302\) 11.3923 19.7321i 0.655553 1.13545i
\(303\) 0 0
\(304\) 5.73205i 0.328756i
\(305\) 0.464102 0.267949i 0.0265744 0.0153427i
\(306\) 0 0
\(307\) 28.2487i 1.61224i 0.591753 + 0.806120i \(0.298436\pi\)
−0.591753 + 0.806120i \(0.701564\pi\)
\(308\) −0.401924 0.696152i −0.0229017 0.0396670i
\(309\) 0 0
\(310\) −4.26795 2.46410i −0.242403 0.139952i
\(311\) −18.9282 −1.07332 −0.536660 0.843799i \(-0.680314\pi\)
−0.536660 + 0.843799i \(0.680314\pi\)
\(312\) 0 0
\(313\) −33.3205 −1.88339 −0.941693 0.336473i \(-0.890766\pi\)
−0.941693 + 0.336473i \(0.890766\pi\)
\(314\) −18.3564 10.5981i −1.03591 0.598084i
\(315\) 0 0
\(316\) 1.53590 + 2.66025i 0.0864010 + 0.149651i
\(317\) 30.4641i 1.71103i 0.517774 + 0.855517i \(0.326761\pi\)
−0.517774 + 0.855517i \(0.673239\pi\)
\(318\) 0 0
\(319\) −0.339746 + 0.196152i −0.0190221 + 0.0109824i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −5.19615 + 9.00000i −0.289570 + 0.501550i
\(323\) 19.8564 + 11.4641i 1.10484 + 0.637880i
\(324\) 0 0
\(325\) −0.866025 3.50000i −0.0480384 0.194145i
\(326\) 2.92820 0.162178
\(327\) 0 0
\(328\) 2.00000 3.46410i 0.110432 0.191273i
\(329\) 9.69615 + 16.7942i 0.534566 + 0.925896i
\(330\) 0 0
\(331\) 12.4641 7.19615i 0.685089 0.395536i −0.116681 0.993169i \(-0.537225\pi\)
0.801770 + 0.597633i \(0.203892\pi\)
\(332\) 8.19615 4.73205i 0.449822 0.259705i
\(333\) 0 0
\(334\) −0.232051 0.401924i −0.0126973 0.0219923i
\(335\) 0.732051 1.26795i 0.0399962 0.0692755i
\(336\) 0 0
\(337\) −26.3923 −1.43768 −0.718840 0.695175i \(-0.755327\pi\)
−0.718840 + 0.695175i \(0.755327\pi\)
\(338\) 12.9904 + 0.500000i 0.706584 + 0.0271964i
\(339\) 0 0
\(340\) 3.46410 + 2.00000i 0.187867 + 0.108465i
\(341\) 0.660254 1.14359i 0.0357548 0.0619291i
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) −5.19615 + 3.00000i −0.280158 + 0.161749i
\(345\) 0 0
\(346\) 2.12436i 0.114206i
\(347\) 2.19615 + 3.80385i 0.117896 + 0.204201i 0.918934 0.394412i \(-0.129052\pi\)
−0.801038 + 0.598614i \(0.795719\pi\)
\(348\) 0 0
\(349\) −9.12436 5.26795i −0.488416 0.281987i 0.235501 0.971874i \(-0.424327\pi\)
−0.723917 + 0.689887i \(0.757660\pi\)
\(350\) 3.00000 0.160357
\(351\) 0 0
\(352\) −0.267949 −0.0142817
\(353\) −6.58846 3.80385i −0.350668 0.202458i 0.314311 0.949320i \(-0.398226\pi\)
−0.664980 + 0.746862i \(0.731560\pi\)
\(354\) 0 0
\(355\) −6.46410 11.1962i −0.343079 0.594230i
\(356\) 14.1244i 0.748589i
\(357\) 0 0
\(358\) −7.85641 + 4.53590i −0.415224 + 0.239730i
\(359\) 0.928203i 0.0489887i 0.999700 + 0.0244943i \(0.00779757\pi\)
−0.999700 + 0.0244943i \(0.992202\pi\)
\(360\) 0 0
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) −14.6603 8.46410i −0.770526 0.444863i
\(363\) 0 0
\(364\) −3.00000 + 10.3923i −0.157243 + 0.544705i
\(365\) −6.92820 −0.362639
\(366\) 0 0
\(367\) −10.6603 + 18.4641i −0.556461 + 0.963818i 0.441328 + 0.897346i \(0.354508\pi\)
−0.997788 + 0.0664722i \(0.978826\pi\)
\(368\) 1.73205 + 3.00000i 0.0902894 + 0.156386i
\(369\) 0 0
\(370\) 5.13397 2.96410i 0.266903 0.154096i
\(371\) 0.696152 0.401924i 0.0361424 0.0208668i
\(372\) 0 0
\(373\) −4.53590 7.85641i −0.234860 0.406789i 0.724372 0.689409i \(-0.242130\pi\)
−0.959232 + 0.282620i \(0.908796\pi\)
\(374\) −0.535898 + 0.928203i −0.0277106 + 0.0479962i
\(375\) 0 0
\(376\) 6.46410 0.333361
\(377\) 5.07180 + 1.46410i 0.261211 + 0.0754051i
\(378\) 0 0
\(379\) −8.42820 4.86603i −0.432928 0.249951i 0.267665 0.963512i \(-0.413748\pi\)
−0.700593 + 0.713561i \(0.747081\pi\)
\(380\) 2.86603 4.96410i 0.147024 0.254653i
\(381\) 0 0
\(382\) 17.3205i 0.886194i
\(383\) −4.14359 + 2.39230i −0.211728 + 0.122241i −0.602114 0.798410i \(-0.705675\pi\)
0.390386 + 0.920651i \(0.372341\pi\)
\(384\) 0 0
\(385\) 0.803848i 0.0409679i
\(386\) 4.92820 + 8.53590i 0.250839 + 0.434466i
\(387\) 0 0
\(388\) 7.26795 + 4.19615i 0.368974 + 0.213027i
\(389\) −17.8564 −0.905356 −0.452678 0.891674i \(-0.649531\pi\)
−0.452678 + 0.891674i \(0.649531\pi\)
\(390\) 0 0
\(391\) 13.8564 0.700749
\(392\) −1.73205 1.00000i −0.0874818 0.0505076i
\(393\) 0 0
\(394\) −5.69615 9.86603i −0.286968 0.497043i
\(395\) 3.07180i 0.154559i
\(396\) 0 0
\(397\) −5.13397 + 2.96410i −0.257667 + 0.148764i −0.623270 0.782007i \(-0.714196\pi\)
0.365603 + 0.930771i \(0.380863\pi\)
\(398\) 24.9282i 1.24954i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 19.1603 + 11.0622i 0.956817 + 0.552419i 0.895192 0.445681i \(-0.147038\pi\)
0.0616254 + 0.998099i \(0.480372\pi\)
\(402\) 0 0
\(403\) −17.2487 + 4.26795i −0.859220 + 0.212602i
\(404\) 12.3923 0.616540
\(405\) 0 0
\(406\) −2.19615 + 3.80385i −0.108993 + 0.188782i
\(407\) 0.794229 + 1.37564i 0.0393685 + 0.0681882i
\(408\) 0 0
\(409\) −33.8205 + 19.5263i −1.67232 + 0.965512i −0.705980 + 0.708232i \(0.749493\pi\)
−0.966337 + 0.257280i \(0.917174\pi\)
\(410\) −3.46410 + 2.00000i −0.171080 + 0.0987730i
\(411\) 0 0
\(412\) −5.79423 10.0359i −0.285461 0.494433i
\(413\) 17.1962 29.7846i 0.846167 1.46560i
\(414\) 0 0
\(415\) −9.46410 −0.464574
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) 0 0
\(418\) 1.33013 + 0.767949i 0.0650586 + 0.0375616i
\(419\) 4.92820 8.53590i 0.240758 0.417006i −0.720172 0.693795i \(-0.755937\pi\)
0.960931 + 0.276790i \(0.0892705\pi\)
\(420\) 0 0
\(421\) 21.8564i 1.06522i −0.846362 0.532608i \(-0.821212\pi\)
0.846362 0.532608i \(-0.178788\pi\)
\(422\) −6.99038 + 4.03590i −0.340286 + 0.196464i
\(423\) 0 0
\(424\) 0.267949i 0.0130128i
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) 0 0
\(427\) 1.39230 + 0.803848i 0.0673784 + 0.0389009i
\(428\) −12.9282 −0.624908
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 12.0000 + 6.92820i 0.578020 + 0.333720i 0.760346 0.649518i \(-0.225029\pi\)
−0.182326 + 0.983238i \(0.558363\pi\)
\(432\) 0 0
\(433\) 4.39230 + 7.60770i 0.211081 + 0.365602i 0.952053 0.305933i \(-0.0989684\pi\)
−0.740972 + 0.671536i \(0.765635\pi\)
\(434\) 14.7846i 0.709684i
\(435\) 0 0
\(436\) 9.00000 5.19615i 0.431022 0.248851i
\(437\) 19.8564i 0.949861i
\(438\) 0 0
\(439\) 6.66025 11.5359i 0.317877 0.550578i −0.662168 0.749355i \(-0.730364\pi\)
0.980045 + 0.198777i \(0.0636969\pi\)
\(440\) 0.232051 + 0.133975i 0.0110626 + 0.00638699i
\(441\) 0 0
\(442\) 14.0000 3.46410i 0.665912 0.164771i
\(443\) 19.8564 0.943406 0.471703 0.881757i \(-0.343639\pi\)
0.471703 + 0.881757i \(0.343639\pi\)
\(444\) 0 0
\(445\) 7.06218 12.2321i 0.334779 0.579855i
\(446\) 9.42820 + 16.3301i 0.446438 + 0.773254i
\(447\) 0 0
\(448\) −2.59808 + 1.50000i −0.122748 + 0.0708683i
\(449\) 5.30385 3.06218i 0.250304 0.144513i −0.369599 0.929191i \(-0.620505\pi\)
0.619903 + 0.784678i \(0.287172\pi\)
\(450\) 0 0
\(451\) −0.535898 0.928203i −0.0252345 0.0437074i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) 0 0
\(454\) 6.53590 0.306745
\(455\) 7.79423 7.50000i 0.365399 0.351605i
\(456\) 0 0
\(457\) −6.46410 3.73205i −0.302378 0.174578i 0.341133 0.940015i \(-0.389189\pi\)
−0.643511 + 0.765437i \(0.722523\pi\)
\(458\) 2.26795 3.92820i 0.105974 0.183553i
\(459\) 0 0
\(460\) 3.46410i 0.161515i
\(461\) 10.0526 5.80385i 0.468194 0.270312i −0.247289 0.968942i \(-0.579540\pi\)
0.715484 + 0.698630i \(0.246206\pi\)
\(462\) 0 0
\(463\) 40.7846i 1.89542i 0.319131 + 0.947711i \(0.396609\pi\)
−0.319131 + 0.947711i \(0.603391\pi\)
\(464\) 0.732051 + 1.26795i 0.0339846 + 0.0588631i
\(465\) 0 0
\(466\) 15.5885 + 9.00000i 0.722121 + 0.416917i
\(467\) −24.3923 −1.12874 −0.564371 0.825522i \(-0.690881\pi\)
−0.564371 + 0.825522i \(0.690881\pi\)
\(468\) 0 0
\(469\) 4.39230 0.202818
\(470\) −5.59808 3.23205i −0.258220 0.149083i
\(471\) 0 0
\(472\) −5.73205 9.92820i −0.263839 0.456983i
\(473\) 1.60770i 0.0739219i
\(474\) 0 0
\(475\) −4.96410 + 2.86603i −0.227769 + 0.131502i
\(476\) 12.0000i 0.550019i
\(477\) 0 0
\(478\) 1.73205 3.00000i 0.0792222 0.137217i
\(479\) 19.2679 + 11.1244i 0.880375 + 0.508285i 0.870782 0.491669i \(-0.163613\pi\)
0.00959301 + 0.999954i \(0.496946\pi\)
\(480\) 0 0
\(481\) 5.92820 20.5359i 0.270303 0.936356i
\(482\) 25.1962 1.14765
\(483\) 0 0
\(484\) 5.46410 9.46410i 0.248368 0.430186i
\(485\) −4.19615 7.26795i −0.190537 0.330021i
\(486\) 0 0
\(487\) 18.1865 10.5000i 0.824110 0.475800i −0.0277214 0.999616i \(-0.508825\pi\)
0.851832 + 0.523815i \(0.175492\pi\)
\(488\) 0.464102 0.267949i 0.0210089 0.0121295i
\(489\) 0 0
\(490\) 1.00000 + 1.73205i 0.0451754 + 0.0782461i
\(491\) 2.69615 4.66987i 0.121676 0.210748i −0.798753 0.601659i \(-0.794507\pi\)
0.920429 + 0.390911i \(0.127840\pi\)
\(492\) 0 0
\(493\) 5.85641 0.263759
\(494\) −4.96410 20.0622i −0.223345 0.902640i
\(495\) 0 0
\(496\) −4.26795 2.46410i −0.191637 0.110641i
\(497\) 19.3923 33.5885i 0.869864 1.50665i
\(498\) 0 0
\(499\) 33.3205i 1.49163i −0.666153 0.745815i \(-0.732060\pi\)
0.666153 0.745815i \(-0.267940\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 19.5359i 0.871930i
\(503\) 1.86603 + 3.23205i 0.0832020 + 0.144110i 0.904624 0.426211i \(-0.140152\pi\)
−0.821422 + 0.570321i \(0.806819\pi\)
\(504\) 0 0
\(505\) −10.7321 6.19615i −0.477570 0.275725i
\(506\) 0.928203 0.0412637
\(507\) 0 0
\(508\) 12.6603 0.561708
\(509\) −25.3923 14.6603i −1.12549 0.649804i −0.182696 0.983169i \(-0.558483\pi\)
−0.942798 + 0.333365i \(0.891816\pi\)
\(510\) 0 0
\(511\) −10.3923 18.0000i −0.459728 0.796273i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −12.5885 + 7.26795i −0.555253 + 0.320575i
\(515\) 11.5885i 0.510648i
\(516\) 0 0
\(517\) 0.866025 1.50000i 0.0380878 0.0659699i
\(518\) 15.4019 + 8.89230i 0.676722 + 0.390705i
\(519\) 0 0
\(520\) −0.866025 3.50000i −0.0379777 0.153485i
\(521\) 6.60770 0.289488 0.144744 0.989469i \(-0.453764\pi\)
0.144744 + 0.989469i \(0.453764\pi\)
\(522\) 0 0
\(523\) 20.8564 36.1244i 0.911987 1.57961i 0.100733 0.994913i \(-0.467881\pi\)
0.811254 0.584694i \(-0.198786\pi\)
\(524\) −7.16025 12.4019i −0.312797 0.541781i
\(525\) 0 0
\(526\) 21.2321 12.2583i 0.925761 0.534489i
\(527\) −17.0718 + 9.85641i −0.743659 + 0.429352i
\(528\) 0 0
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) −0.133975 + 0.232051i −0.00581948 + 0.0100796i
\(531\) 0 0
\(532\) 17.1962 0.745548
\(533\) −4.00000 + 13.8564i −0.173259 + 0.600188i
\(534\) 0 0
\(535\) 11.1962 + 6.46410i 0.484052 + 0.279467i
\(536\) 0.732051 1.26795i 0.0316198 0.0547671i
\(537\) 0 0
\(538\) 17.0718i 0.736017i
\(539\) −0.464102 + 0.267949i −0.0199903 + 0.0115414i
\(540\) 0 0
\(541\) 14.7846i 0.635640i −0.948151 0.317820i \(-0.897049\pi\)
0.948151 0.317820i \(-0.102951\pi\)
\(542\) −12.1962 21.1244i −0.523870 0.907369i
\(543\) 0 0
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) −10.3923 −0.445157
\(546\) 0 0
\(547\) −5.32051 −0.227488 −0.113744 0.993510i \(-0.536284\pi\)
−0.113744 + 0.993510i \(0.536284\pi\)
\(548\) −11.6603 6.73205i −0.498101 0.287579i
\(549\) 0 0
\(550\) −0.133975 0.232051i −0.00571270 0.00989468i
\(551\) 8.39230i 0.357524i
\(552\) 0 0
\(553\) 7.98076 4.60770i 0.339377 0.195939i
\(554\) 11.5885i 0.492346i
\(555\) 0 0
\(556\) −9.89230 + 17.1340i −0.419527 + 0.726642i
\(557\) 19.5788 + 11.3038i 0.829582 + 0.478959i 0.853710 0.520749i \(-0.174347\pi\)
−0.0241275 + 0.999709i \(0.507681\pi\)
\(558\) 0 0
\(559\) 15.5885 15.0000i 0.659321 0.634432i
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 3.46410 6.00000i 0.146124 0.253095i
\(563\) −7.66025 13.2679i −0.322841 0.559177i 0.658232 0.752815i \(-0.271305\pi\)
−0.981073 + 0.193638i \(0.937971\pi\)
\(564\) 0 0
\(565\) −10.3923 + 6.00000i −0.437208 + 0.252422i
\(566\) −5.53590 + 3.19615i −0.232691 + 0.134344i
\(567\) 0 0
\(568\) −6.46410 11.1962i −0.271228 0.469780i
\(569\) −8.16025 + 14.1340i −0.342096 + 0.592527i −0.984822 0.173569i \(-0.944470\pi\)
0.642726 + 0.766096i \(0.277803\pi\)
\(570\) 0 0
\(571\) 10.8564 0.454326 0.227163 0.973857i \(-0.427055\pi\)
0.227163 + 0.973857i \(0.427055\pi\)
\(572\) 0.937822 0.232051i 0.0392123 0.00970253i
\(573\) 0 0
\(574\) −10.3923 6.00000i −0.433766 0.250435i
\(575\) −1.73205 + 3.00000i −0.0722315 + 0.125109i
\(576\) 0 0
\(577\) 9.32051i 0.388018i 0.981000 + 0.194009i \(0.0621491\pi\)
−0.981000 + 0.194009i \(0.937851\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 0 0
\(580\) 1.46410i 0.0607935i
\(581\) −14.1962 24.5885i −0.588956 1.02010i
\(582\) 0 0
\(583\) −0.0621778 0.0358984i −0.00257514 0.00148676i
\(584\) −6.92820 −0.286691
\(585\) 0 0
\(586\) 29.2487 1.20825
\(587\) 7.73205 + 4.46410i 0.319136 + 0.184253i 0.651007 0.759071i \(-0.274347\pi\)
−0.331871 + 0.943325i \(0.607680\pi\)
\(588\) 0 0
\(589\) 14.1244 + 24.4641i 0.581984 + 1.00803i
\(590\) 11.4641i 0.471970i
\(591\) 0 0
\(592\) 5.13397 2.96410i 0.211005 0.121824i
\(593\) 44.7846i 1.83908i −0.392992 0.919542i \(-0.628560\pi\)
0.392992 0.919542i \(-0.371440\pi\)
\(594\) 0 0
\(595\) 6.00000 10.3923i 0.245976 0.426043i
\(596\) −16.2679 9.39230i −0.666361 0.384724i
\(597\) 0 0
\(598\) −8.66025 9.00000i −0.354144 0.368037i
\(599\) −28.9282 −1.18197 −0.590987 0.806681i \(-0.701262\pi\)
−0.590987 + 0.806681i \(0.701262\pi\)
\(600\) 0 0
\(601\) −15.3564 + 26.5981i −0.626401 + 1.08496i 0.361867 + 0.932230i \(0.382139\pi\)
−0.988268 + 0.152729i \(0.951194\pi\)
\(602\) 9.00000 + 15.5885i 0.366813 + 0.635338i
\(603\) 0 0
\(604\) −19.7321 + 11.3923i −0.802886 + 0.463546i
\(605\) −9.46410 + 5.46410i −0.384770 + 0.222147i
\(606\) 0 0
\(607\) 10.7224 + 18.5718i 0.435210 + 0.753806i 0.997313 0.0732615i \(-0.0233408\pi\)
−0.562103 + 0.827067i \(0.690007\pi\)
\(608\) 2.86603 4.96410i 0.116233 0.201321i
\(609\) 0 0
\(610\) −0.535898 −0.0216979
\(611\) −22.6244 + 5.59808i −0.915283 + 0.226474i
\(612\) 0 0
\(613\) 38.9711 + 22.5000i 1.57403 + 0.908766i 0.995667 + 0.0929864i \(0.0296413\pi\)
0.578362 + 0.815780i \(0.303692\pi\)
\(614\) 14.1244 24.4641i 0.570013 0.987291i
\(615\) 0 0
\(616\) 0.803848i 0.0323879i
\(617\) 30.7128 17.7321i 1.23645 0.713865i 0.268084 0.963395i \(-0.413609\pi\)
0.968367 + 0.249530i \(0.0802761\pi\)
\(618\) 0 0
\(619\) 2.51666i 0.101153i −0.998720 0.0505766i \(-0.983894\pi\)
0.998720 0.0505766i \(-0.0161059\pi\)
\(620\) 2.46410 + 4.26795i 0.0989607 + 0.171405i
\(621\) 0 0
\(622\) 16.3923 + 9.46410i 0.657272 + 0.379476i
\(623\) 42.3731 1.69764
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 28.8564 + 16.6603i 1.15333 + 0.665878i
\(627\) 0 0
\(628\) 10.5981 + 18.3564i 0.422909 + 0.732500i
\(629\) 23.7128i 0.945492i
\(630\) 0 0
\(631\) −6.92820 + 4.00000i −0.275807 + 0.159237i −0.631524 0.775356i \(-0.717570\pi\)
0.355716 + 0.934594i \(0.384237\pi\)
\(632\) 3.07180i 0.122190i
\(633\) 0 0
\(634\) 15.2321 26.3827i 0.604942 1.04779i
\(635\) −10.9641 6.33013i −0.435097 0.251203i
\(636\) 0 0
\(637\) 6.92820 + 2.00000i 0.274505 + 0.0792429i
\(638\) 0.392305 0.0155315
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 7.23205 + 12.5263i 0.285649 + 0.494758i 0.972766 0.231788i \(-0.0744576\pi\)
−0.687117 + 0.726546i \(0.741124\pi\)
\(642\) 0 0
\(643\) 11.0718 6.39230i 0.436629 0.252088i −0.265538 0.964100i \(-0.585549\pi\)
0.702167 + 0.712013i \(0.252216\pi\)
\(644\) 9.00000 5.19615i 0.354650 0.204757i
\(645\) 0 0
\(646\) −11.4641 19.8564i −0.451049 0.781240i
\(647\) −17.8660 + 30.9449i −0.702386 + 1.21657i 0.265241 + 0.964182i \(0.414549\pi\)
−0.967627 + 0.252386i \(0.918785\pi\)
\(648\) 0 0
\(649\) −3.07180 −0.120579
\(650\) −1.00000 + 3.46410i −0.0392232 + 0.135873i
\(651\) 0 0
\(652\) −2.53590 1.46410i −0.0993134 0.0573386i
\(653\) −0.794229 + 1.37564i −0.0310806 + 0.0538331i −0.881147 0.472842i \(-0.843228\pi\)
0.850067 + 0.526675i \(0.176562\pi\)
\(654\) 0 0
\(655\) 14.3205i 0.559549i
\(656\) −3.46410 + 2.00000i −0.135250 + 0.0780869i
\(657\) 0 0
\(658\) 19.3923i 0.755991i
\(659\) −19.8564 34.3923i −0.773496 1.33973i −0.935636 0.352966i \(-0.885173\pi\)
0.162140 0.986768i \(-0.448160\pi\)
\(660\) 0 0
\(661\) −18.7128 10.8038i −0.727844 0.420221i 0.0897889 0.995961i \(-0.471381\pi\)
−0.817633 + 0.575740i \(0.804714\pi\)
\(662\) −14.3923 −0.559373
\(663\) 0 0
\(664\) −9.46410 −0.367278
\(665\) −14.8923 8.59808i −0.577499 0.333419i
\(666\) 0 0
\(667\) −2.53590 4.39230i −0.0981904 0.170071i
\(668\) 0.464102i 0.0179566i
\(669\) 0 0
\(670\) −1.26795 + 0.732051i −0.0489852 + 0.0282816i
\(671\) 0.143594i 0.00554337i
\(672\) 0 0
\(673\) 8.39230 14.5359i 0.323500 0.560318i −0.657708 0.753273i \(-0.728474\pi\)
0.981208 + 0.192955i \(0.0618072\pi\)
\(674\) 22.8564 + 13.1962i 0.880396 + 0.508297i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) −10.9282 −0.420005 −0.210002 0.977701i \(-0.567347\pi\)
−0.210002 + 0.977701i \(0.567347\pi\)
\(678\) 0 0
\(679\) 12.5885 21.8038i 0.483101 0.836755i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 0 0
\(682\) −1.14359 + 0.660254i −0.0437905 + 0.0252824i
\(683\) −35.7846 + 20.6603i −1.36926 + 0.790543i −0.990834 0.135089i \(-0.956868\pi\)
−0.378427 + 0.925631i \(0.623535\pi\)
\(684\) 0 0
\(685\) 6.73205 + 11.6603i 0.257218 + 0.445515i
\(686\) 7.50000 12.9904i 0.286351 0.495975i
\(687\) 0 0
\(688\) 6.00000 0.228748
\(689\) 0.232051 + 0.937822i 0.00884043 + 0.0357282i
\(690\) 0 0
\(691\) 13.0359 + 7.52628i 0.495909 + 0.286313i 0.727023 0.686614i \(-0.240904\pi\)
−0.231114 + 0.972927i \(0.574237\pi\)
\(692\) 1.06218 1.83975i 0.0403779 0.0699366i
\(693\) 0 0
\(694\) 4.39230i 0.166730i
\(695\) 17.1340 9.89230i 0.649929 0.375237i
\(696\) 0 0
\(697\) 16.0000i 0.606043i
\(698\) 5.26795 + 9.12436i 0.199395 + 0.345362i
\(699\) 0 0
\(700\) −2.59808 1.50000i −0.0981981 0.0566947i
\(701\) 4.39230 0.165895 0.0829475 0.996554i \(-0.473567\pi\)
0.0829475 + 0.996554i \(0.473567\pi\)
\(702\) 0 0
\(703\) −33.9808 −1.28161
\(704\) 0.232051 + 0.133975i 0.00874574 + 0.00504936i
\(705\) 0 0
\(706\) 3.80385 + 6.58846i 0.143160 + 0.247960i
\(707\) 37.1769i 1.39818i
\(708\) 0 0
\(709\) −23.6603 + 13.6603i −0.888579 + 0.513022i −0.873478 0.486864i \(-0.838141\pi\)
−0.0151019 + 0.999886i \(0.504807\pi\)
\(710\) 12.9282i 0.485187i
\(711\) 0 0
\(712\) 7.06218 12.2321i 0.264666 0.458415i
\(713\) 14.7846 + 8.53590i 0.553688 + 0.319672i
\(714\) 0 0
\(715\) −0.928203 0.267949i −0.0347128 0.0100207i
\(716\) 9.07180 0.339029
\(717\) 0 0
\(718\) 0.464102 0.803848i 0.0173201 0.0299993i
\(719\) 8.00000 + 13.8564i 0.298350 + 0.516757i 0.975759 0.218850i \(-0.0702305\pi\)
−0.677409 + 0.735607i \(0.736897\pi\)
\(720\) 0 0
\(721\) −30.1077 + 17.3827i −1.12127 + 0.647365i
\(722\) −12.0000 + 6.92820i −0.446594 + 0.257841i
\(723\) 0 0
\(724\) 8.46410 + 14.6603i 0.314566 + 0.544844i
\(725\) −0.732051 + 1.26795i −0.0271877 + 0.0470905i
\(726\) 0 0
\(727\) −4.66025 −0.172839 −0.0864196 0.996259i \(-0.527543\pi\)
−0.0864196 + 0.996259i \(0.527543\pi\)
\(728\) 7.79423 7.50000i 0.288873 0.277968i
\(729\) 0 0
\(730\) 6.00000 + 3.46410i 0.222070 + 0.128212i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) 20.8564i 0.770349i −0.922844 0.385174i \(-0.874141\pi\)
0.922844 0.385174i \(-0.125859\pi\)
\(734\) 18.4641 10.6603i 0.681522 0.393477i
\(735\) 0 0
\(736\) 3.46410i 0.127688i
\(737\) −0.196152 0.339746i −0.00722537 0.0125147i
\(738\) 0 0
\(739\) 31.0359 + 17.9186i 1.14167 + 0.659146i 0.946845 0.321691i \(-0.104251\pi\)
0.194829 + 0.980837i \(0.437585\pi\)
\(740\) −5.92820 −0.217925
\(741\) 0 0
\(742\) −0.803848 −0.0295102
\(743\) 9.46410 + 5.46410i 0.347204 + 0.200458i 0.663453 0.748218i \(-0.269090\pi\)
−0.316249 + 0.948676i \(0.602424\pi\)
\(744\) 0 0
\(745\) 9.39230 + 16.2679i 0.344107 + 0.596012i
\(746\) 9.07180i 0.332142i
\(747\) 0 0
\(748\) 0.928203 0.535898i 0.0339385 0.0195944i
\(749\) 38.7846i 1.41716i
\(750\) 0 0
\(751\) 10.5885 18.3397i 0.386378 0.669227i −0.605581 0.795784i \(-0.707059\pi\)
0.991959 + 0.126557i \(0.0403926\pi\)
\(752\) −5.59808 3.23205i −0.204141 0.117861i
\(753\) 0 0
\(754\) −3.66025 3.80385i −0.133299 0.138528i
\(755\) 22.7846 0.829217
\(756\) 0 0
\(757\) −10.8660 + 18.8205i −0.394932 + 0.684043i −0.993093 0.117334i \(-0.962565\pi\)
0.598160 + 0.801377i \(0.295899\pi\)
\(758\) 4.86603 + 8.42820i 0.176742 + 0.306126i
\(759\) 0 0
\(760\) −4.96410 + 2.86603i −0.180067 + 0.103962i
\(761\) −6.91154 + 3.99038i −0.250543 + 0.144651i −0.620013 0.784592i \(-0.712873\pi\)
0.369470 + 0.929243i \(0.379539\pi\)
\(762\) 0 0
\(763\) −15.5885 27.0000i −0.564340 0.977466i
\(764\) 8.66025 15.0000i 0.313317 0.542681i
\(765\) 0 0
\(766\) 4.78461 0.172875
\(767\) 28.6603 + 29.7846i 1.03486 + 1.07546i
\(768\) 0 0
\(769\) 13.6077 + 7.85641i 0.490706 + 0.283309i 0.724867 0.688889i \(-0.241901\pi\)
−0.234161 + 0.972198i \(0.575234\pi\)
\(770\) 0.401924 0.696152i 0.0144843 0.0250876i
\(771\) 0 0
\(772\) 9.85641i 0.354740i
\(773\) 28.2391 16.3038i 1.01569 0.586409i 0.102837 0.994698i \(-0.467208\pi\)
0.912852 + 0.408290i \(0.133875\pi\)
\(774\) 0 0
\(775\) 4.92820i 0.177026i
\(776\) −4.19615 7.26795i −0.150633 0.260904i
\(777\) 0 0
\(778\) 15.4641 + 8.92820i 0.554415 + 0.320092i
\(779\) 22.9282 0.821488
\(780\) 0 0
\(781\) −3.46410 −0.123955
\(782\) −12.0000 6.92820i −0.429119 0.247752i
\(783\) 0 0
\(784\) 1.00000 + 1.73205i 0.0357143 + 0.0618590i
\(785\) 21.1962i 0.756523i
\(786\) 0 0
\(787\) 1.26795 0.732051i 0.0451975 0.0260948i −0.477231 0.878778i \(-0.658359\pi\)
0.522428 + 0.852683i \(0.325026\pi\)
\(788\) 11.3923i 0.405834i
\(789\) 0 0