Properties

Label 950.2.e.c.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.c.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +4.00000 q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} -3.00000 q^{18} +(4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +2.00000 q^{26} +(-2.00000 - 3.46410i) q^{28} +(3.00000 + 5.19615i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(1.50000 - 2.59808i) q^{41} +(6.00000 - 10.3923i) q^{43} +(0.500000 + 0.866025i) q^{44} +4.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-1.00000 + 1.73205i) q^{52} +(2.00000 + 3.46410i) q^{53} +4.00000 q^{56} -6.00000 q^{58} +(-4.50000 + 7.79423i) q^{59} +(6.00000 + 10.3923i) q^{61} +(1.00000 - 1.73205i) q^{62} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} +(7.50000 + 12.9904i) q^{67} -3.00000 q^{68} +(-3.00000 + 5.19615i) q^{71} +(1.50000 + 2.59808i) q^{72} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 - 4.33013i) q^{76} -4.00000 q^{77} +(7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} -4.00000 q^{83} +(6.00000 + 10.3923i) q^{86} -1.00000 q^{88} +(0.500000 + 0.866025i) q^{89} +(-4.00000 - 6.92820i) q^{91} +(-2.00000 + 3.46410i) q^{92} -6.00000 q^{94} +(-0.500000 + 0.866025i) q^{97} +(-4.50000 + 7.79423i) q^{98} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 8q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 8q^{7} + 2q^{8} + 3q^{9} - 2q^{11} - 2q^{13} - 4q^{14} - q^{16} + 3q^{17} - 6q^{18} + 8q^{19} + q^{22} - 4q^{23} + 4q^{26} - 4q^{28} + 6q^{29} - 4q^{31} - q^{32} + 3q^{34} + 3q^{36} - 4q^{37} - 7q^{38} + 3q^{41} + 12q^{43} + q^{44} + 8q^{46} + 6q^{47} + 18q^{49} - 2q^{52} + 4q^{53} + 8q^{56} - 12q^{58} - 9q^{59} + 12q^{61} + 2q^{62} + 12q^{63} + 2q^{64} + 15q^{67} - 6q^{68} - 6q^{71} + 3q^{72} + 10q^{73} + 2q^{74} - q^{76} - 8q^{77} + 14q^{79} - 9q^{81} + 3q^{82} - 8q^{83} + 12q^{86} - 2q^{88} + q^{89} - 8q^{91} - 4q^{92} - 12q^{94} - q^{97} - 9q^{98} - 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −2.00000 + 3.46410i −0.534522 + 0.925820i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) −3.00000 −0.707107
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) 0.500000 0.866025i 0.106600 0.184637i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) −2.00000 3.46410i −0.377964 0.654654i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 0 0
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −3.50000 + 2.59808i −0.567775 + 0.421464i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) 6.00000 10.3923i 0.914991 1.58481i 0.108078 0.994142i \(-0.465531\pi\)
0.806914 0.590669i \(-0.201136\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 4.00000 0.534522
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) 6.00000 + 10.3923i 0.768221 + 1.33060i 0.938527 + 0.345207i \(0.112191\pi\)
−0.170305 + 0.985391i \(0.554475\pi\)
\(62\) 1.00000 1.73205i 0.127000 0.219971i
\(63\) 6.00000 + 10.3923i 0.755929 + 1.30931i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 7.50000 + 12.9904i 0.916271 + 1.58703i 0.805030 + 0.593234i \(0.202149\pi\)
0.111241 + 0.993793i \(0.464517\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 0 0
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 7.00000 12.1244i 0.787562 1.36410i −0.139895 0.990166i \(-0.544677\pi\)
0.927457 0.373930i \(-0.121990\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000 + 10.3923i 0.646997 + 1.12063i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 0.500000 + 0.866025i 0.0529999 + 0.0917985i 0.891308 0.453398i \(-0.149788\pi\)
−0.838308 + 0.545197i \(0.816455\pi\)
\(90\) 0 0
\(91\) −4.00000 6.92820i −0.419314 0.726273i
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) 0 0
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) −4.50000 + 7.79423i −0.454569 + 0.787336i
\(99\) −1.50000 2.59808i −0.150756 0.261116i
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) 5.00000 0.483368 0.241684 0.970355i \(-0.422300\pi\)
0.241684 + 0.970355i \(0.422300\pi\)
\(108\) 0 0
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.00000 + 3.46410i −0.188982 + 0.327327i
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) −4.50000 7.79423i −0.414259 0.717517i
\(119\) 6.00000 10.3923i 0.550019 0.952661i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −12.0000 −1.08643
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 0 0
\(126\) −12.0000 −1.06904
\(127\) −3.00000 5.19615i −0.266207 0.461084i 0.701672 0.712500i \(-0.252437\pi\)
−0.967879 + 0.251416i \(0.919104\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.50000 + 6.06218i −0.305796 + 0.529655i −0.977438 0.211221i \(-0.932256\pi\)
0.671642 + 0.740876i \(0.265589\pi\)
\(132\) 0 0
\(133\) 16.0000 + 6.92820i 1.38738 + 0.600751i
\(134\) −15.0000 −1.29580
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i \(-0.0986536\pi\)
−0.740308 + 0.672268i \(0.765320\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) 5.00000 + 8.66025i 0.413803 + 0.716728i
\(147\) 0 0
\(148\) 1.00000 + 1.73205i 0.0821995 + 0.142374i
\(149\) 8.00000 13.8564i 0.655386 1.13516i −0.326411 0.945228i \(-0.605840\pi\)
0.981797 0.189933i \(-0.0608272\pi\)
\(150\) 0 0
\(151\) 14.0000 1.13930 0.569652 0.821886i \(-0.307078\pi\)
0.569652 + 0.821886i \(0.307078\pi\)
\(152\) 4.00000 + 1.73205i 0.324443 + 0.140488i
\(153\) 9.00000 0.727607
\(154\) 2.00000 3.46410i 0.161165 0.279145i
\(155\) 0 0
\(156\) 0 0
\(157\) −3.00000 + 5.19615i −0.239426 + 0.414698i −0.960550 0.278108i \(-0.910293\pi\)
0.721124 + 0.692806i \(0.243626\pi\)
\(158\) 7.00000 + 12.1244i 0.556890 + 0.964562i
\(159\) 0 0
\(160\) 0 0
\(161\) −8.00000 13.8564i −0.630488 1.09204i
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) 1.00000 0.0783260 0.0391630 0.999233i \(-0.487531\pi\)
0.0391630 + 0.999233i \(0.487531\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) 4.00000 + 6.92820i 0.309529 + 0.536120i 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 1.50000 + 12.9904i 0.114708 + 0.993399i
\(172\) −12.0000 −0.914991
\(173\) −2.00000 + 3.46410i −0.152057 + 0.263371i −0.931984 0.362500i \(-0.881923\pi\)
0.779926 + 0.625871i \(0.215256\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) 0 0
\(178\) −1.00000 −0.0749532
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) −7.00000 12.1244i −0.520306 0.901196i −0.999721 0.0236082i \(-0.992485\pi\)
0.479415 0.877588i \(-0.340849\pi\)
\(182\) 8.00000 0.592999
\(183\) 0 0
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) 0 0
\(186\) 0 0
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) 3.00000 5.19615i 0.218797 0.378968i
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i \(-0.703766\pi\)
0.993215 + 0.116289i \(0.0370998\pi\)
\(194\) −0.500000 0.866025i −0.0358979 0.0621770i
\(195\) 0 0
\(196\) −4.50000 7.79423i −0.321429 0.556731i
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 3.00000 0.213201
\(199\) −9.00000 15.5885i −0.637993 1.10504i −0.985873 0.167497i \(-0.946431\pi\)
0.347879 0.937539i \(-0.386902\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 12.0000 + 20.7846i 0.842235 + 1.45879i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.00000 + 3.46410i −0.139347 + 0.241355i
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 2.00000 0.138675
\(209\) −4.00000 1.73205i −0.276686 0.119808i
\(210\) 0 0
\(211\) 2.50000 4.33013i 0.172107 0.298098i −0.767049 0.641588i \(-0.778276\pi\)
0.939156 + 0.343490i \(0.111609\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 0 0
\(214\) −2.50000 + 4.33013i −0.170896 + 0.296001i
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) −5.00000 8.66025i −0.338643 0.586546i
\(219\) 0 0
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 0 0
\(223\) −11.0000 + 19.0526i −0.736614 + 1.27585i 0.217397 + 0.976083i \(0.430243\pi\)
−0.954011 + 0.299770i \(0.903090\pi\)
\(224\) −2.00000 3.46410i −0.133631 0.231455i
\(225\) 0 0
\(226\) 9.00000 15.5885i 0.598671 1.03693i
\(227\) −19.0000 −1.26107 −0.630537 0.776159i \(-0.717165\pi\)
−0.630537 + 0.776159i \(0.717165\pi\)
\(228\) 0 0
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 8.50000 14.7224i 0.556854 0.964499i −0.440903 0.897555i \(-0.645342\pi\)
0.997757 0.0669439i \(-0.0213249\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) 9.00000 0.585850
\(237\) 0 0
\(238\) 6.00000 + 10.3923i 0.388922 + 0.673633i
\(239\) −14.0000 −0.905585 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 0 0
\(241\) −10.5000 18.1865i −0.676364 1.17150i −0.976068 0.217465i \(-0.930221\pi\)
0.299704 0.954032i \(-0.403112\pi\)
\(242\) 5.00000 8.66025i 0.321412 0.556702i
\(243\) 0 0
\(244\) 6.00000 10.3923i 0.384111 0.665299i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.00000 8.66025i −0.0636285 0.551039i
\(248\) −2.00000 −0.127000
\(249\) 0 0
\(250\) 0 0
\(251\) 13.5000 + 23.3827i 0.852112 + 1.47590i 0.879298 + 0.476272i \(0.158012\pi\)
−0.0271858 + 0.999630i \(0.508655\pi\)
\(252\) 6.00000 10.3923i 0.377964 0.654654i
\(253\) 2.00000 + 3.46410i 0.125739 + 0.217786i
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −15.5000 26.8468i −0.966863 1.67466i −0.704523 0.709681i \(-0.748839\pi\)
−0.262341 0.964975i \(-0.584494\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) −9.00000 + 15.5885i −0.557086 + 0.964901i
\(262\) −3.50000 6.06218i −0.216231 0.374523i
\(263\) 5.00000 8.66025i 0.308313 0.534014i −0.669680 0.742650i \(-0.733569\pi\)
0.977993 + 0.208635i \(0.0669022\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −14.0000 + 10.3923i −0.858395 + 0.637193i
\(267\) 0 0
\(268\) 7.50000 12.9904i 0.458135 0.793514i
\(269\) −4.00000 + 6.92820i −0.243884 + 0.422420i −0.961817 0.273692i \(-0.911755\pi\)
0.717933 + 0.696112i \(0.245088\pi\)
\(270\) 0 0
\(271\) 6.00000 10.3923i 0.364474 0.631288i −0.624218 0.781251i \(-0.714582\pi\)
0.988692 + 0.149963i \(0.0479155\pi\)
\(272\) 1.50000 + 2.59808i 0.0909509 + 0.157532i
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −5.00000 −0.299880
\(279\) −3.00000 5.19615i −0.179605 0.311086i
\(280\) 0 0
\(281\) −7.50000 12.9904i −0.447412 0.774941i 0.550804 0.834634i \(-0.314321\pi\)
−0.998217 + 0.0596933i \(0.980988\pi\)
\(282\) 0 0
\(283\) −0.500000 + 0.866025i −0.0297219 + 0.0514799i −0.880504 0.474039i \(-0.842796\pi\)
0.850782 + 0.525519i \(0.176129\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) −2.00000 −0.118262
\(287\) 6.00000 10.3923i 0.354169 0.613438i
\(288\) 1.50000 2.59808i 0.0883883 0.153093i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) −10.0000 −0.585206
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 8.00000 + 13.8564i 0.463428 + 0.802680i
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 0 0
\(301\) 24.0000 41.5692i 1.38334 2.39601i
\(302\) −7.00000 + 12.1244i −0.402805 + 0.697678i
\(303\) 0 0
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) 0 0
\(306\) −4.50000 + 7.79423i −0.257248 + 0.445566i
\(307\) −2.00000 + 3.46410i −0.114146 + 0.197707i −0.917438 0.397879i \(-0.869747\pi\)
0.803292 + 0.595585i \(0.203080\pi\)
\(308\) 2.00000 + 3.46410i 0.113961 + 0.197386i
\(309\) 0 0
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) −2.50000 4.33013i −0.141308 0.244753i 0.786681 0.617359i \(-0.211798\pi\)
−0.927990 + 0.372606i \(0.878464\pi\)
\(314\) −3.00000 5.19615i −0.169300 0.293236i
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 0 0
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) 16.0000 0.891645
\(323\) 10.5000 7.79423i 0.584236 0.433682i
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) −8.00000 −0.437741
\(335\) 0 0
\(336\) 0 0
\(337\) 4.50000 7.79423i 0.245131 0.424579i −0.717038 0.697034i \(-0.754502\pi\)
0.962168 + 0.272456i \(0.0878358\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) −12.0000 5.19615i −0.648886 0.280976i
\(343\) 8.00000 0.431959
\(344\) 6.00000 10.3923i 0.323498 0.560316i
\(345\) 0 0
\(346\) −2.00000 3.46410i −0.107521 0.186231i
\(347\) −13.5000 + 23.3827i −0.724718 + 1.25525i 0.234372 + 0.972147i \(0.424697\pi\)
−0.959090 + 0.283101i \(0.908637\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −17.0000 −0.904819 −0.452409 0.891810i \(-0.649435\pi\)
−0.452409 + 0.891810i \(0.649435\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.500000 0.866025i 0.0264999 0.0458993i
\(357\) 0 0
\(358\) 10.0000 17.3205i 0.528516 0.915417i
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) −4.00000 + 6.92820i −0.209657 + 0.363137i
\(365\) 0 0
\(366\) 0 0
\(367\) 17.0000 + 29.4449i 0.887393 + 1.53701i 0.842946 + 0.537998i \(0.180819\pi\)
0.0444464 + 0.999012i \(0.485848\pi\)
\(368\) 4.00000 0.208514
\(369\) 9.00000 0.468521
\(370\) 0 0
\(371\) 8.00000 + 13.8564i 0.415339 + 0.719389i
\(372\) 0 0
\(373\) −38.0000 −1.96757 −0.983783 0.179364i \(-0.942596\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) −1.50000 2.59808i −0.0775632 0.134343i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 6.00000 10.3923i 0.309016 0.535231i
\(378\) 0 0
\(379\) −9.00000 −0.462299 −0.231149 0.972918i \(-0.574249\pi\)
−0.231149 + 0.972918i \(0.574249\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i \(-0.949767\pi\)
0.629890 + 0.776684i \(0.283100\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5.50000 + 9.52628i 0.279943 + 0.484875i
\(387\) 36.0000 1.82998
\(388\) 1.00000 0.0507673
\(389\) −1.00000 1.73205i −0.0507020 0.0878185i 0.839561 0.543266i \(-0.182813\pi\)
−0.890263 + 0.455448i \(0.849479\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 9.00000 0.454569
\(393\) 0 0
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) 0 0
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) −19.0000 + 32.9090i −0.953583 + 1.65165i −0.216004 + 0.976392i \(0.569302\pi\)
−0.737579 + 0.675261i \(0.764031\pi\)
\(398\) 18.0000 0.902258
\(399\) 0 0
\(400\) 0 0
\(401\) −16.5000 + 28.5788i −0.823971 + 1.42716i 0.0787327 + 0.996896i \(0.474913\pi\)
−0.902703 + 0.430263i \(0.858421\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.00000 3.46410i −0.0985329 0.170664i
\(413\) −18.0000 + 31.1769i −0.885722 + 1.53412i
\(414\) 6.00000 + 10.3923i 0.294884 + 0.510754i
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 3.50000 2.59808i 0.171191 0.127076i
\(419\) 29.0000 1.41674 0.708371 0.705840i \(-0.249430\pi\)
0.708371 + 0.705840i \(0.249430\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) 2.50000 + 4.33013i 0.121698 + 0.210787i
\(423\) −9.00000 + 15.5885i −0.437595 + 0.757937i
\(424\) 2.00000 + 3.46410i 0.0971286 + 0.168232i
\(425\) 0 0
\(426\) 0 0
\(427\) 24.0000 + 41.5692i 1.16144 + 2.01168i
\(428\) −2.50000 4.33013i −0.120842 0.209305i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 0 0
\(433\) −14.5000 25.1147i −0.696826 1.20694i −0.969561 0.244848i \(-0.921262\pi\)
0.272736 0.962089i \(-0.412071\pi\)
\(434\) 4.00000 6.92820i 0.192006 0.332564i
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) −2.00000 17.3205i −0.0956730 0.828552i
\(438\) 0 0
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) 13.5000 + 23.3827i 0.642857 + 1.11346i
\(442\) 3.00000 5.19615i 0.142695 0.247156i
\(443\) −10.5000 18.1865i −0.498870 0.864068i 0.501129 0.865373i \(-0.332918\pi\)
−0.999999 + 0.00130426i \(0.999585\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.0000 19.0526i −0.520865 0.902165i
\(447\) 0 0
\(448\) 4.00000 0.188982
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) −1.50000 + 2.59808i −0.0706322 + 0.122339i
\(452\) 9.00000 + 15.5885i 0.423324 + 0.733219i
\(453\) 0 0
\(454\) 9.50000 16.4545i 0.445857 0.772247i
\(455\) 0 0
\(456\) 0 0
\(457\) −14.0000 −0.654892 −0.327446 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(458\) 9.00000 15.5885i 0.420542 0.728401i
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 8.50000 + 14.7224i 0.393755 + 0.682003i
\(467\) −5.00000 −0.231372 −0.115686 0.993286i \(-0.536907\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(468\) −6.00000 −0.277350
\(469\) 30.0000 + 51.9615i 1.38527 + 2.39936i
\(470\) 0 0
\(471\) 0 0
\(472\) −4.50000 + 7.79423i −0.207129 + 0.358758i
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 0 0
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) 7.00000 12.1244i 0.320173 0.554555i
\(479\) 15.0000 + 25.9808i 0.685367 + 1.18709i 0.973321 + 0.229447i \(0.0736918\pi\)
−0.287954 + 0.957644i \(0.592975\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 21.0000 0.956524
\(483\) 0 0
\(484\) 5.00000 + 8.66025i 0.227273 + 0.393648i
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 6.00000 + 10.3923i 0.271607 + 0.470438i
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 8.00000 + 3.46410i 0.359937 + 0.155857i
\(495\) 0 0
\(496\) 1.00000 1.73205i 0.0449013 0.0777714i
\(497\) −12.0000 + 20.7846i −0.538274 + 0.932317i
\(498\) 0 0
\(499\) 13.5000 23.3827i 0.604343 1.04675i −0.387812 0.921739i \(-0.626769\pi\)
0.992155 0.125014i \(-0.0398977\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −27.0000 −1.20507
\(503\) −18.0000 31.1769i −0.802580 1.39011i −0.917912 0.396783i \(-0.870127\pi\)
0.115332 0.993327i \(-0.463207\pi\)
\(504\) 6.00000 + 10.3923i 0.267261 + 0.462910i
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) 0 0
\(508\) −3.00000 + 5.19615i −0.133103 + 0.230542i
\(509\) 11.0000 + 19.0526i 0.487566 + 0.844490i 0.999898 0.0142980i \(-0.00455136\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(510\) 0 0
\(511\) 20.0000 34.6410i 0.884748 1.53243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 31.0000 1.36735
\(515\) 0 0
\(516\) 0 0
\(517\) −3.00000 5.19615i −0.131940 0.228527i
\(518\) 4.00000 6.92820i 0.175750 0.304408i
\(519\) 0 0
\(520\) 0 0
\(521\) 45.0000 1.97149 0.985743 0.168259i \(-0.0538144\pi\)
0.985743 + 0.168259i \(0.0538144\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −4.50000 7.79423i −0.196771 0.340818i 0.750708 0.660634i \(-0.229712\pi\)
−0.947480 + 0.319816i \(0.896379\pi\)
\(524\) 7.00000 0.305796
\(525\) 0 0
\(526\) 5.00000 + 8.66025i 0.218010 + 0.377605i
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −27.0000 −1.17170
\(532\) −2.00000 17.3205i −0.0867110 0.750939i
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 0 0
\(536\) 7.50000 + 12.9904i 0.323951 + 0.561099i
\(537\) 0 0
\(538\) −4.00000 6.92820i −0.172452 0.298696i
\(539\) −9.00000 −0.387657
\(540\) 0 0
\(541\) 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i \(-0.152977\pi\)
−0.843728 + 0.536771i \(0.819644\pi\)
\(542\) 6.00000 + 10.3923i 0.257722 + 0.446388i
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 0 0
\(546\) 0 0
\(547\) 3.50000 + 6.06218i 0.149649 + 0.259200i 0.931098 0.364770i \(-0.118852\pi\)
−0.781449 + 0.623970i \(0.785519\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) −18.0000 + 31.1769i −0.768221 + 1.33060i
\(550\) 0 0
\(551\) 3.00000 + 25.9808i 0.127804 + 1.10682i
\(552\) 0 0
\(553\) 28.0000 48.4974i 1.19068 2.06232i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 0 0
\(556\) 2.50000 4.33013i 0.106024 0.183638i
\(557\) −18.0000 31.1769i −0.762684 1.32101i −0.941462 0.337119i \(-0.890548\pi\)
0.178778 0.983890i \(-0.442786\pi\)
\(558\) 6.00000 0.254000
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 15.0000 0.632737
\(563\) −31.0000 −1.30649 −0.653247 0.757145i \(-0.726594\pi\)
−0.653247 + 0.757145i \(0.726594\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.500000 0.866025i −0.0210166 0.0364018i
\(567\) −18.0000 + 31.1769i −0.755929 + 1.30931i
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) 45.0000 1.88650 0.943249 0.332086i \(-0.107752\pi\)
0.943249 + 0.332086i \(0.107752\pi\)
\(570\) 0 0
\(571\) 3.00000 0.125546 0.0627730 0.998028i \(-0.480006\pi\)
0.0627730 + 0.998028i \(0.480006\pi\)
\(572\) 1.00000 1.73205i 0.0418121 0.0724207i
\(573\) 0 0
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) 0 0
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −1.00000 −0.0416305 −0.0208153 0.999783i \(-0.506626\pi\)
−0.0208153 + 0.999783i \(0.506626\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 0 0
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) 0 0
\(586\) 12.0000 20.7846i 0.495715 0.858604i
\(587\) 10.5000 18.1865i 0.433381 0.750639i −0.563781 0.825925i \(-0.690654\pi\)
0.997162 + 0.0752860i \(0.0239870\pi\)
\(588\) 0 0
\(589\) −8.00000 3.46410i −0.329634 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 16.5000 + 28.5788i 0.677574 + 1.17359i 0.975709 + 0.219069i \(0.0703019\pi\)
−0.298136 + 0.954524i \(0.596365\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.0000 −0.655386
\(597\) 0 0
\(598\) −4.00000 6.92820i −0.163572 0.283315i
\(599\) 16.0000 + 27.7128i 0.653742 + 1.13231i 0.982208 + 0.187799i \(0.0601353\pi\)
−0.328465 + 0.944516i \(0.606531\pi\)
\(600\) 0 0
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) 24.0000 + 41.5692i 0.978167 + 1.69423i
\(603\) −22.5000 + 38.9711i −0.916271 + 1.58703i
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) 0 0
\(606\) 0 0
\(607\) 4.00000 0.162355 0.0811775 0.996700i \(-0.474132\pi\)
0.0811775 + 0.996700i \(0.474132\pi\)
\(608\) −0.500000 4.33013i −0.0202777 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) −4.50000 7.79423i −0.181902 0.315063i
\(613\) −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i \(-0.938064\pi\)
0.658012 + 0.753007i \(0.271397\pi\)
\(614\) −2.00000 3.46410i −0.0807134 0.139800i
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) 6.50000 + 11.2583i 0.261680 + 0.453243i 0.966689 0.255956i \(-0.0823901\pi\)
−0.705008 + 0.709199i \(0.749057\pi\)
\(618\) 0 0
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 10.0000 17.3205i 0.400963 0.694489i
\(623\) 2.00000 + 3.46410i 0.0801283 + 0.138786i
\(624\) 0 0
\(625\) 0 0
\(626\) 5.00000 0.199840
\(627\) 0 0
\(628\) 6.00000 0.239426
\(629\) −3.00000 + 5.19615i −0.119618 + 0.207184i
\(630\) 0 0
\(631\) 2.00000 + 3.46410i 0.0796187 + 0.137904i 0.903085 0.429461i \(-0.141296\pi\)
−0.823467 + 0.567365i \(0.807963\pi\)
\(632\) 7.00000 12.1244i 0.278445 0.482281i
\(633\) 0 0
\(634\) 12.0000 0.476581
\(635\) 0 0
\(636\) 0 0
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 6.00000 0.237542
\(639\) −18.0000 −0.712069
\(640\) 0 0
\(641\) −20.5000 + 35.5070i −0.809701 + 1.40244i 0.103370 + 0.994643i \(0.467038\pi\)
−0.913071 + 0.407801i \(0.866296\pi\)
\(642\) 0 0
\(643\) 24.5000 42.4352i 0.966186 1.67348i 0.259791 0.965665i \(-0.416346\pi\)
0.706395 0.707818i \(-0.250320\pi\)
\(644\) −8.00000 + 13.8564i −0.315244 + 0.546019i
\(645\) 0 0
\(646\) 1.50000 + 12.9904i 0.0590167 + 0.511100i
\(647\) 36.0000 1.41531 0.707653 0.706560i \(-0.249754\pi\)
0.707653 + 0.706560i \(0.249754\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.500000 0.866025i −0.0195815 0.0339162i
\(653\) 20.0000 0.782660 0.391330 0.920250i \(-0.372015\pi\)
0.391330 + 0.920250i \(0.372015\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 30.0000 1.17041
\(658\) −24.0000 −0.935617
\(659\) −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) 0 0
\(661\) −15.0000 25.9808i −0.583432 1.01053i −0.995069 0.0991864i \(-0.968376\pi\)
0.411636 0.911348i \(-0.364957\pi\)
\(662\) −10.0000 + 17.3205i −0.388661 + 0.673181i
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 12.0000 20.7846i 0.464642 0.804783i
\(668\) 4.00000 6.92820i 0.154765 0.268060i
\(669\) 0 0
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 4.50000 + 7.79423i 0.173334 + 0.300222i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.00000 + 1.73205i −0.0382920 + 0.0663237i
\(683\) 25.0000 0.956598 0.478299 0.878197i \(-0.341253\pi\)
0.478299 + 0.878197i \(0.341253\pi\)
\(684\) 10.5000 7.79423i 0.401478 0.298020i
\(685\) 0 0
\(686\) −4.00000 + 6.92820i −0.152721 + 0.264520i
\(687\) 0 0
\(688\) 6.00000 + 10.3923i 0.228748 + 0.396203i
\(689\) 4.00000 6.92820i 0.152388 0.263944i
\(690\) 0 0
\(691\) −27.0000 −1.02713 −0.513564 0.858051i \(-0.671675\pi\)
−0.513564 + 0.858051i \(0.671675\pi\)
\(692\) 4.00000 0.152057
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) −13.5000 23.3827i −0.512453 0.887595i
\(695\) 0 0
\(696\) 0 0
\(697\) −4.50000 7.79423i −0.170450 0.295227i
\(698\) −7.00000 + 12.1244i −0.264954 + 0.458914i
\(699\) 0 0
\(700\) 0 0
\(701\) 12.0000 20.7846i 0.453234 0.785024i −0.545351 0.838208i \(-0.683604\pi\)
0.998585 + 0.0531839i \(0.0169370\pi\)
\(702\) 0 0
\(703\) −8.00000 3.46410i −0.301726 0.130651i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 8.50000 14.7224i 0.319902 0.554086i
\(707\) −20.0000 34.6410i −0.752177 1.30281i
\(708\) 0 0
\(709\) −10.0000 17.3205i −0.375558 0.650485i 0.614852 0.788642i \(-0.289216\pi\)
−0.990410 + 0.138157i \(0.955882\pi\)
\(710\) 0 0
\(711\) 42.0000 1.57512
\(712\) 0.500000 + 0.866025i 0.0187383 + 0.0324557i
\(713\) 4.00000 + 6.92820i 0.149801 + 0.259463i
\(714\) 0 0
\(715\) 0 0
\(716\) 10.0000 + 17.3205i 0.373718 + 0.647298i
\(717\) 0 0
\(718\) −5.00000 8.66025i −0.186598 0.323198i
\(719\) −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i \(-0.981028\pi\)
0.550700 + 0.834703i \(0.314361\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) −18.5000 + 4.33013i −0.688499 + 0.161151i
\(723\) 0 0
\(724\) −7.00000 + 12.1244i −0.260153 + 0.450598i
\(725\) 0 0
\(726\) 0 0
\(727\) −16.0000 + 27.7128i −0.593407 + 1.02781i 0.400362 + 0.916357i \(0.368884\pi\)
−0.993770 + 0.111454i \(0.964449\pi\)
\(728\) −4.00000 6.92820i −0.148250 0.256776i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −18.0000 31.1769i −0.665754 1.15312i
\(732\) 0 0
\(733\) −24.0000 −0.886460 −0.443230 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(734\) −34.0000 −1.25496
\(735\) 0 0
\(736\) −2.00000 + 3.46410i −0.0737210 + 0.127688i
\(737\) −7.50000 12.9904i −0.276266 0.478507i
\(738\) −4.50000 + 7.79423i −0.165647 + 0.286910i
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −16.0000 −0.587378
\(743\) 15.0000 25.9808i 0.550297 0.953142i −0.447956 0.894055i \(-0.647848\pi\)
0.998253 0.0590862i \(-0.0188187\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 19.0000 32.9090i 0.695639 1.20488i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 3.00000 0.109691
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) 22.0000 + 38.1051i 0.802791 + 1.39048i 0.917772 + 0.397108i \(0.129986\pi\)
−0.114981 + 0.993368i \(0.536681\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) 3.00000 5.19615i 0.109037 0.188857i −0.806343 0.591448i \(-0.798557\pi\)
0.915380 + 0.402590i \(0.131890\pi\)
\(758\) 4.50000 7.79423i 0.163447 0.283099i
\(759\) 0 0
\(760\) 0 0
\(761\) 17.0000 0.616250 0.308125 0.951346i \(-0.400299\pi\)
0.308125 + 0.951346i \(0.400299\pi\)
\(762\) 0 0
\(763\) −20.0000 + 34.6410i −0.724049 + 1.25409i
\(764\) −6.00000 10.3923i −0.217072 0.375980i
\(765\) 0 0
\(766\) −7.00000 12.1244i −0.252920 0.438071i
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) −12.5000 21.6506i −0.450762 0.780742i 0.547672 0.836693i \(-0.315514\pi\)
−0.998434 + 0.0559513i \(0.982181\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.0000 −0.395899
\(773\) 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i \(-0.0246123\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(774\) −18.0000 + 31.1769i −0.646997 + 1.12063i
\(775\) 0 0
\(776\) −0.500000 + 0.866025i −0.0179490 + 0.0310885i
\(777\) 0 0
\(778\) 2.00000 0.0717035
\(779\) 10.5000 7.79423i 0.376202 0.279257i
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) 6.00000 10.3923i 0.214560 0.371628i
\(783\) 0 0
\(784\) −4.50000 + 7.79423i −0.160714 + 0.278365i
\(785\) 0 0
\(786\) 0 0
\(787\) 3.00000 0.106938 0.0534692 0.998569i \(-0.482972\pi\)
0.0534692 + 0.998569i \(0.482972\pi\)
\(788\) −4.00000 6.92820i −0.142494 0.246807i
\(789\) 0 0
\(790\) 0 0
\(791\) −72.0000 −2.56003
\(792\) −1.50000 2.59808i −0.0533002 0.0923186i