Properties

Label 525.2.r.e.424.1
Level $525$
Weight $2$
Character 525.424
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 424.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.424
Dual form 525.2.r.e.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-1.73205 + 1.00000i) q^{12} +1.00000i q^{13} +(-1.00000 - 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-1.73205 - 1.00000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(2.00000 - 1.73205i) q^{21} +4.00000i q^{22} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +(3.46410 + 4.00000i) q^{28} -4.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(-6.92820 - 4.00000i) q^{32} +(-1.73205 + 1.00000i) q^{33} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(0.500000 - 0.866025i) q^{39} -10.0000 q^{41} +(-1.73205 + 5.00000i) q^{42} +5.00000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(5.19615 - 3.00000i) q^{47} -4.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(1.73205 + 1.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(1.00000 + 1.73205i) q^{54} -1.00000i q^{57} +(6.92820 - 4.00000i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} -18.0000i q^{62} +(-2.59808 + 0.500000i) q^{63} +8.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-4.33013 - 2.50000i) q^{67} -6.00000 q^{71} +(2.59808 + 1.50000i) q^{73} +(3.00000 - 5.19615i) q^{74} +2.00000 q^{76} +(3.46410 + 4.00000i) q^{77} +2.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(17.3205 - 10.0000i) q^{82} +6.00000i q^{83} +(-1.00000 - 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(3.46410 + 2.00000i) q^{87} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(7.79423 - 4.50000i) q^{93} +(-6.00000 + 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{96} +6.00000i q^{97} +(13.8564 + 2.00000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + 8q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 4q^{4} + 8q^{6} + 2q^{9} + 4q^{11} - 4q^{14} + 8q^{16} + 2q^{19} + 8q^{21} - 4q^{26} - 16q^{29} - 18q^{31} + 8q^{36} + 2q^{39} - 40q^{41} - 8q^{44} - 22q^{49} + 4q^{54} - 24q^{59} - 20q^{61} + 32q^{64} + 8q^{66} - 24q^{71} + 12q^{74} + 8q^{76} - 2q^{79} - 2q^{81} - 4q^{84} - 20q^{86} + 32q^{89} - 10q^{91} - 24q^{94} + 16q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0 0
\(6\) 2.00000 0.816497
\(7\) −0.866025 + 2.50000i −0.327327 + 0.944911i
\(8\) 0 0
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) −1.73205 + 1.00000i −0.500000 + 0.288675i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) −1.00000 5.19615i −0.267261 1.38873i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) −1.73205 1.00000i −0.408248 0.235702i
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) 4.00000i 0.852803i
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) 3.46410 + 4.00000i 0.654654 + 0.755929i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −4.50000 + 7.79423i −0.808224 + 1.39988i 0.105869 + 0.994380i \(0.466238\pi\)
−0.914093 + 0.405505i \(0.867096\pi\)
\(32\) −6.92820 4.00000i −1.22474 0.707107i
\(33\) −1.73205 + 1.00000i −0.301511 + 0.174078i
\(34\) 0 0
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i \(-0.745980\pi\)
0.270998 + 0.962580i \(0.412646\pi\)
\(38\) −1.73205 1.00000i −0.280976 0.162221i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) −1.73205 + 5.00000i −0.267261 + 0.771517i
\(43\) 5.00000i 0.762493i 0.924473 + 0.381246i \(0.124505\pi\)
−0.924473 + 0.381246i \(0.875495\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 4.00000i 0.577350i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.73205 + 1.00000i 0.240192 + 0.138675i
\(53\) −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i \(-0.641688\pi\)
−0.996922 + 0.0783936i \(0.975021\pi\)
\(54\) 1.00000 + 1.73205i 0.136083 + 0.235702i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 6.92820 4.00000i 0.909718 0.525226i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 18.0000i 2.28600i
\(63\) −2.59808 + 0.500000i −0.327327 + 0.0629941i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 2.00000 3.46410i 0.246183 0.426401i
\(67\) −4.33013 2.50000i −0.529009 0.305424i 0.211604 0.977356i \(-0.432131\pi\)
−0.740613 + 0.671932i \(0.765465\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 2.59808 + 1.50000i 0.304082 + 0.175562i 0.644275 0.764794i \(-0.277159\pi\)
−0.340193 + 0.940356i \(0.610493\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 3.46410 + 4.00000i 0.394771 + 0.455842i
\(78\) 2.00000i 0.226455i
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 17.3205 10.0000i 1.91273 1.10432i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −1.00000 5.19615i −0.109109 0.566947i
\(85\) 0 0
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 3.46410 + 2.00000i 0.371391 + 0.214423i
\(88\) 0 0
\(89\) 8.00000 + 13.8564i 0.847998 + 1.46878i 0.882992 + 0.469389i \(0.155526\pi\)
−0.0349934 + 0.999388i \(0.511141\pi\)
\(90\) 0 0
\(91\) −2.50000 0.866025i −0.262071 0.0907841i
\(92\) 0 0
\(93\) 7.79423 4.50000i 0.808224 0.466628i
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) 0 0
\(96\) 4.00000 + 6.92820i 0.408248 + 0.707107i
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 13.8564 + 2.00000i 1.39971 + 0.202031i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) −6.06218 + 3.50000i −0.597324 + 0.344865i −0.767988 0.640464i \(-0.778742\pi\)
0.170664 + 0.985329i \(0.445409\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 24.0000 2.33109
\(107\) 6.92820 4.00000i 0.669775 0.386695i −0.126217 0.992003i \(-0.540283\pi\)
0.795991 + 0.605308i \(0.206950\pi\)
\(108\) −1.73205 1.00000i −0.166667 0.0962250i
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) −10.3923 + 2.00000i −0.981981 + 0.188982i
\(113\) 10.0000i 0.940721i 0.882474 + 0.470360i \(0.155876\pi\)
−0.882474 + 0.470360i \(0.844124\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 0 0
\(116\) −4.00000 + 6.92820i −0.371391 + 0.643268i
\(117\) −0.866025 + 0.500000i −0.0800641 + 0.0462250i
\(118\) 24.0000i 2.20938i
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 17.3205 + 10.0000i 1.56813 + 0.905357i
\(123\) 8.66025 + 5.00000i 0.780869 + 0.450835i
\(124\) 9.00000 + 15.5885i 0.808224 + 1.39988i
\(125\) 0 0
\(126\) 4.00000 3.46410i 0.356348 0.308607i
\(127\) 15.0000i 1.33103i 0.746382 + 0.665517i \(0.231789\pi\)
−0.746382 + 0.665517i \(0.768211\pi\)
\(128\) 0 0
\(129\) 2.50000 4.33013i 0.220113 0.381246i
\(130\) 0 0
\(131\) 7.00000 + 12.1244i 0.611593 + 1.05931i 0.990972 + 0.134069i \(0.0428042\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(132\) 4.00000i 0.348155i
\(133\) −2.59808 + 0.500000i −0.225282 + 0.0433555i
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) 0 0
\(139\) 3.00000 0.254457 0.127228 0.991873i \(-0.459392\pi\)
0.127228 + 0.991873i \(0.459392\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 10.3923 6.00000i 0.872103 0.503509i
\(143\) 1.73205 + 1.00000i 0.144841 + 0.0836242i
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 6.00000i 0.493197i
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −10.0000 3.46410i −0.805823 0.279145i
\(155\) 0 0
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) −12.1244 7.00000i −0.967629 0.558661i −0.0691164 0.997609i \(-0.522018\pi\)
−0.898513 + 0.438948i \(0.855351\pi\)
\(158\) 1.73205 + 1.00000i 0.137795 + 0.0795557i
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 2.00000i 0.157135i
\(163\) 3.46410 2.00000i 0.271329 0.156652i −0.358162 0.933659i \(-0.616597\pi\)
0.629492 + 0.777007i \(0.283263\pi\)
\(164\) −10.0000 + 17.3205i −0.780869 + 1.35250i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 14.0000i 1.08335i 0.840587 + 0.541676i \(0.182210\pi\)
−0.840587 + 0.541676i \(0.817790\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) 8.66025 + 5.00000i 0.660338 + 0.381246i
\(173\) 6.92820 4.00000i 0.526742 0.304114i −0.212947 0.977064i \(-0.568306\pi\)
0.739689 + 0.672949i \(0.234973\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0 0
\(176\) 8.00000 0.603023
\(177\) 10.3923 6.00000i 0.781133 0.450988i
\(178\) −27.7128 16.0000i −2.07716 1.19925i
\(179\) 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i \(-0.809520\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) 5.19615 1.00000i 0.385164 0.0741249i
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) 0 0
\(186\) −9.00000 + 15.5885i −0.659912 + 1.14300i
\(187\) 0 0
\(188\) 12.0000i 0.875190i
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 0 0
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) −6.92820 4.00000i −0.500000 0.288675i
\(193\) −9.52628 5.50000i −0.685717 0.395899i 0.116289 0.993215i \(-0.462900\pi\)
−0.802005 + 0.597317i \(0.796234\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 0 0
\(196\) −13.0000 + 5.19615i −0.928571 + 0.371154i
\(197\) 16.0000i 1.13995i −0.821661 0.569976i \(-0.806952\pi\)
0.821661 0.569976i \(-0.193048\pi\)
\(198\) −3.46410 + 2.00000i −0.246183 + 0.142134i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 2.50000 + 4.33013i 0.176336 + 0.305424i
\(202\) 4.00000i 0.281439i
\(203\) 3.46410 10.0000i 0.243132 0.701862i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 0 0
\(208\) −3.46410 + 2.00000i −0.240192 + 0.138675i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −20.7846 + 12.0000i −1.42749 + 0.824163i
\(213\) 5.19615 + 3.00000i 0.356034 + 0.205557i
\(214\) −8.00000 + 13.8564i −0.546869 + 0.947204i
\(215\) 0 0
\(216\) 0 0
\(217\) −15.5885 18.0000i −1.05821 1.22192i
\(218\) 18.0000i 1.21911i
\(219\) −1.50000 2.59808i −0.101361 0.175562i
\(220\) 0 0
\(221\) 0 0
\(222\) −5.19615 + 3.00000i −0.348743 + 0.201347i
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 16.0000 13.8564i 1.06904 0.925820i
\(225\) 0 0
\(226\) −10.0000 17.3205i −0.665190 1.15214i
\(227\) 15.5885 + 9.00000i 1.03464 + 0.597351i 0.918311 0.395860i \(-0.129553\pi\)
0.116331 + 0.993210i \(0.462887\pi\)
\(228\) −1.73205 1.00000i −0.114708 0.0662266i
\(229\) −9.50000 16.4545i −0.627778 1.08734i −0.987997 0.154475i \(-0.950631\pi\)
0.360219 0.932868i \(-0.382702\pi\)
\(230\) 0 0
\(231\) −1.00000 5.19615i −0.0657952 0.341882i
\(232\) 0 0
\(233\) 5.19615 3.00000i 0.340411 0.196537i −0.320043 0.947403i \(-0.603697\pi\)
0.660454 + 0.750867i \(0.270364\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) 0 0
\(236\) 12.0000 + 20.7846i 0.781133 + 1.35296i
\(237\) 1.00000i 0.0649570i
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −12.1244 7.00000i −0.779383 0.449977i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −20.0000 −1.28037
\(245\) 0 0
\(246\) −20.0000 −1.27515
\(247\) −0.866025 + 0.500000i −0.0551039 + 0.0318142i
\(248\) 0 0
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) −1.73205 + 5.00000i −0.109109 + 0.314970i
\(253\) 0 0
\(254\) −15.0000 25.9808i −0.941184 1.63018i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −22.5167 + 13.0000i −1.40455 + 0.810918i −0.994855 0.101305i \(-0.967698\pi\)
−0.409695 + 0.912222i \(0.634365\pi\)
\(258\) 10.0000i 0.622573i
\(259\) −1.50000 7.79423i −0.0932055 0.484310i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) −24.2487 14.0000i −1.49809 0.864923i
\(263\) −3.46410 2.00000i −0.213606 0.123325i 0.389380 0.921077i \(-0.372689\pi\)
−0.602986 + 0.797752i \(0.706023\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) 16.0000i 0.979184i
\(268\) −8.66025 + 5.00000i −0.529009 + 0.305424i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 0 0
\(273\) 1.73205 + 2.00000i 0.104828 + 0.121046i
\(274\) 24.0000 1.44989
\(275\) 0 0
\(276\) 0 0
\(277\) 11.2583 + 6.50000i 0.676448 + 0.390547i 0.798515 0.601975i \(-0.205619\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(278\) −5.19615 + 3.00000i −0.311645 + 0.179928i
\(279\) −9.00000 −0.538816
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 10.3923 6.00000i 0.618853 0.357295i
\(283\) 9.52628 + 5.50000i 0.566279 + 0.326941i 0.755662 0.654962i \(-0.227315\pi\)
−0.189383 + 0.981903i \(0.560649\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) 8.66025 25.0000i 0.511199 1.47570i
\(288\) 8.00000i 0.471405i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 0 0
\(291\) 3.00000 5.19615i 0.175863 0.304604i
\(292\) 5.19615 3.00000i 0.304082 0.175562i
\(293\) 8.00000i 0.467365i 0.972313 + 0.233682i \(0.0750776\pi\)
−0.972313 + 0.233682i \(0.924922\pi\)
\(294\) −11.0000 8.66025i −0.641533 0.505076i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.73205 1.00000i −0.100504 0.0580259i
\(298\) 20.7846 + 12.0000i 1.20402 + 0.695141i
\(299\) 0 0
\(300\) 0 0
\(301\) −12.5000 4.33013i −0.720488 0.249584i
\(302\) 32.0000i 1.84139i
\(303\) 1.73205 1.00000i 0.0995037 0.0574485i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 17.0000i 0.970241i 0.874447 + 0.485121i \(0.161224\pi\)
−0.874447 + 0.485121i \(0.838776\pi\)
\(308\) 10.3923 2.00000i 0.592157 0.113961i
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) −0.866025 + 0.500000i −0.0489506 + 0.0282617i −0.524276 0.851549i \(-0.675664\pi\)
0.475325 + 0.879810i \(0.342331\pi\)
\(314\) 28.0000 1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −20.7846 + 12.0000i −1.16738 + 0.673987i −0.953062 0.302777i \(-0.902086\pi\)
−0.214318 + 0.976764i \(0.568753\pi\)
\(318\) −20.7846 12.0000i −1.16554 0.672927i
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 0 0
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) −7.79423 + 4.50000i −0.431022 + 0.248851i
\(328\) 0 0
\(329\) 3.00000 + 15.5885i 0.165395 + 0.859419i
\(330\) 0 0
\(331\) 12.5000 + 21.6506i 0.687062 + 1.19003i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.285722 + 0.958313i \(0.592233\pi\)
\(332\) 10.3923 + 6.00000i 0.570352 + 0.329293i
\(333\) −2.59808 1.50000i −0.142374 0.0821995i
\(334\) −14.0000 24.2487i −0.766046 1.32683i
\(335\) 0 0
\(336\) 10.0000 + 3.46410i 0.545545 + 0.188982i
\(337\) 13.0000i 0.708155i −0.935216 0.354078i \(-0.884795\pi\)
0.935216 0.354078i \(-0.115205\pi\)
\(338\) −20.7846 + 12.0000i −1.13053 + 0.652714i
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) 0 0
\(341\) 9.00000 + 15.5885i 0.487377 + 0.844162i
\(342\) 2.00000i 0.108148i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.00000 + 13.8564i −0.430083 + 0.744925i
\(347\) 27.7128 + 16.0000i 1.48770 + 0.858925i 0.999902 0.0140303i \(-0.00446613\pi\)
0.487800 + 0.872955i \(0.337799\pi\)
\(348\) 6.92820 4.00000i 0.371391 0.214423i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) −13.8564 + 8.00000i −0.738549 + 0.426401i
\(353\) −29.4449 17.0000i −1.56719 0.904819i −0.996495 0.0836583i \(-0.973340\pi\)
−0.570697 0.821160i \(-0.693327\pi\)
\(354\) −12.0000 + 20.7846i −0.637793 + 1.10469i
\(355\) 0 0
\(356\) 32.0000 1.69600
\(357\) 0 0
\(358\) 4.00000i 0.211407i
\(359\) 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i \(0.0103087\pi\)
−0.471696 + 0.881761i \(0.656358\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −22.5167 + 13.0000i −1.18345 + 0.683265i
\(363\) 7.00000i 0.367405i
\(364\) −4.00000 + 3.46410i −0.209657 + 0.181568i
\(365\) 0 0
\(366\) −10.0000 17.3205i −0.522708 0.905357i
\(367\) −7.79423 4.50000i −0.406855 0.234898i 0.282582 0.959243i \(-0.408809\pi\)
−0.689438 + 0.724345i \(0.742142\pi\)
\(368\) 0 0
\(369\) −5.00000 8.66025i −0.260290 0.450835i
\(370\) 0 0
\(371\) 24.0000 20.7846i 1.24602 1.07908i
\(372\) 18.0000i 0.933257i
\(373\) 19.9186 11.5000i 1.03135 0.595447i 0.113975 0.993484i \(-0.463641\pi\)
0.917370 + 0.398036i \(0.130308\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000i 0.206010i
\(378\) −5.19615 + 1.00000i −0.267261 + 0.0514344i
\(379\) −3.00000 −0.154100 −0.0770498 0.997027i \(-0.524550\pi\)
−0.0770498 + 0.997027i \(0.524550\pi\)
\(380\) 0 0
\(381\) 7.50000 12.9904i 0.384237 0.665517i
\(382\) 17.3205 + 10.0000i 0.886194 + 0.511645i
\(383\) −10.3923 + 6.00000i −0.531022 + 0.306586i −0.741433 0.671027i \(-0.765853\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −4.33013 + 2.50000i −0.220113 + 0.127082i
\(388\) 10.3923 + 6.00000i 0.527589 + 0.304604i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 14.0000i 0.706207i
\(394\) 16.0000 + 27.7128i 0.806068 + 1.39615i
\(395\) 0 0
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) 7.79423 4.50000i 0.391181 0.225849i −0.291491 0.956574i \(-0.594151\pi\)
0.682672 + 0.730725i \(0.260818\pi\)
\(398\) 0 0
\(399\) 2.50000 + 0.866025i 0.125157 + 0.0433555i
\(400\) 0 0
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) −8.66025 5.00000i −0.431934 0.249377i
\(403\) −7.79423 4.50000i −0.388258 0.224161i
\(404\) 2.00000 + 3.46410i 0.0995037 + 0.172345i
\(405\) 0 0
\(406\) 4.00000 + 20.7846i 0.198517 + 1.03152i
\(407\) 6.00000i 0.297409i
\(408\) 0 0
\(409\) 2.50000 4.33013i 0.123617 0.214111i −0.797574 0.603220i \(-0.793884\pi\)
0.921192 + 0.389109i \(0.127217\pi\)
\(410\) 0 0
\(411\) 6.00000 + 10.3923i 0.295958 + 0.512615i
\(412\) 14.0000i 0.689730i
\(413\) −20.7846 24.0000i −1.02274 1.18096i
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 6.92820i 0.196116 0.339683i
\(417\) −2.59808 1.50000i −0.127228 0.0734553i
\(418\) −3.46410 + 2.00000i −0.169435 + 0.0978232i
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) −6.92820 + 4.00000i −0.337260 + 0.194717i
\(423\) 5.19615 + 3.00000i 0.252646 + 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 25.9808 5.00000i 1.25730 0.241967i
\(428\) 16.0000i 0.773389i
\(429\) −1.00000 1.73205i −0.0482805 0.0836242i
\(430\) 0 0
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) 3.46410 2.00000i 0.166667 0.0962250i
\(433\) 31.0000i 1.48976i 0.667196 + 0.744882i \(0.267494\pi\)
−0.667196 + 0.744882i \(0.732506\pi\)
\(434\) 45.0000 + 15.5885i 2.16007 + 0.748270i
\(435\) 0 0
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) 0 0
\(438\) 5.19615 + 3.00000i 0.248282 + 0.143346i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) 10.3923 6.00000i 0.493753 0.285069i −0.232377 0.972626i \(-0.574650\pi\)
0.726130 + 0.687557i \(0.241317\pi\)
\(444\) 3.00000 5.19615i 0.142374 0.246598i
\(445\) 0 0
\(446\) −16.0000 27.7128i −0.757622 1.31224i
\(447\) 12.0000i 0.567581i
\(448\) −6.92820 + 20.0000i −0.327327 + 0.944911i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −10.0000 + 17.3205i −0.470882 + 0.815591i
\(452\) 17.3205 + 10.0000i 0.814688 + 0.470360i
\(453\) −13.8564 + 8.00000i −0.651031 + 0.375873i
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 9.52628 5.50000i 0.445621 0.257279i −0.260358 0.965512i \(-0.583841\pi\)
0.705979 + 0.708233i \(0.250507\pi\)
\(458\) 32.9090 + 19.0000i 1.53773 + 0.887812i
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 6.92820 + 8.00000i 0.322329 + 0.372194i
\(463\) 17.0000i 0.790057i −0.918669 0.395029i \(-0.870735\pi\)
0.918669 0.395029i \(-0.129265\pi\)
\(464\) −8.00000 13.8564i −0.371391 0.643268i
\(465\) 0 0
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) −5.19615 + 3.00000i −0.240449 + 0.138823i −0.615383 0.788228i \(-0.710999\pi\)
0.374934 + 0.927052i \(0.377665\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 10.0000 8.66025i 0.461757 0.399893i
\(470\) 0 0
\(471\) 7.00000 + 12.1244i 0.322543 + 0.558661i
\(472\) 0 0
\(473\) 8.66025 + 5.00000i 0.398199 + 0.229900i
\(474\) −1.00000 1.73205i −0.0459315 0.0795557i
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000i 0.549442i
\(478\) 10.3923 6.00000i 0.475333 0.274434i
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 0 0
\(481\) −1.50000 2.59808i −0.0683941 0.118462i
\(482\) 28.0000i 1.27537i
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) −1.00000 + 1.73205i −0.0453609 + 0.0785674i
\(487\) 26.8468 + 15.5000i 1.21654 + 0.702372i 0.964177 0.265260i \(-0.0854576\pi\)
0.252367 + 0.967632i \(0.418791\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 17.3205 10.0000i 0.780869 0.450835i
\(493\) 0 0
\(494\) 1.00000 1.73205i 0.0449921 0.0779287i
\(495\) 0 0
\(496\) −36.0000 −1.61645
\(497\) 5.19615 15.0000i 0.233079 0.672842i
\(498\) 12.0000i 0.537733i
\(499\) 18.5000 + 32.0429i 0.828174 + 1.43444i 0.899469 + 0.436984i \(0.143953\pi\)
−0.0712957 + 0.997455i \(0.522713\pi\)
\(500\) 0 0
\(501\) 7.00000 12.1244i 0.312737 0.541676i
\(502\) 13.8564 8.00000i 0.618442 0.357057i
\(503\) 42.0000i 1.87269i −0.351085 0.936344i \(-0.614187\pi\)
0.351085 0.936344i \(-0.385813\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −10.3923 6.00000i −0.461538 0.266469i
\(508\) 25.9808 + 15.0000i 1.15271 + 0.665517i
\(509\) 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i \(-0.152553\pi\)
−0.843012 + 0.537895i \(0.819220\pi\)
\(510\) 0 0
\(511\) −6.00000 + 5.19615i −0.265424 + 0.229864i
\(512\) 32.0000i 1.41421i
\(513\) 0.866025 0.500000i 0.0382360 0.0220755i
\(514\) 26.0000 45.0333i 1.14681 1.98633i
\(515\) 0 0
\(516\) −5.00000 8.66025i −0.220113 0.381246i
\(517\) 12.0000i 0.527759i
\(518\) 10.3923 + 12.0000i 0.456612 + 0.527250i
\(519\) −8.00000 −0.351161
\(520\) 0 0
\(521\) −6.00000 + 10.3923i −0.262865 + 0.455295i −0.967002 0.254769i \(-0.918001\pi\)
0.704137 + 0.710064i \(0.251334\pi\)
\(522\) 6.92820 + 4.00000i 0.303239 + 0.175075i
\(523\) 26.8468 15.5000i 1.17393 0.677768i 0.219326 0.975652i \(-0.429614\pi\)
0.954602 + 0.297884i \(0.0962809\pi\)
\(524\) 28.0000 1.22319
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) −6.92820 4.00000i −0.301511 0.174078i
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) −1.73205 + 5.00000i −0.0750939 + 0.216777i
\(533\) 10.0000i 0.433148i
\(534\) 16.0000 + 27.7128i 0.692388 + 1.19925i
\(535\) 0 0
\(536\) 0 0
\(537\) −1.73205 + 1.00000i −0.0747435 + 0.0431532i
\(538\) 12.0000i 0.517357i
\(539\) −13.0000 + 5.19615i −0.559950 + 0.223814i
\(540\) 0 0
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 27.7128 + 16.0000i 1.19037 + 0.687259i
\(543\) −11.2583 6.50000i −0.483141 0.278942i
\(544\) 0 0
\(545\) 0 0
\(546\) −5.00000 1.73205i −0.213980 0.0741249i
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) −20.7846 + 12.0000i −0.887875 + 0.512615i
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) 0 0
\(551\) −2.00000 3.46410i −0.0852029 0.147576i
\(552\) 0 0
\(553\) 2.59808 0.500000i 0.110481 0.0212622i
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 3.00000 5.19615i 0.127228 0.220366i
\(557\) −1.73205 1.00000i −0.0733893 0.0423714i 0.462856 0.886433i \(-0.346825\pi\)
−0.536246 + 0.844062i \(0.680158\pi\)
\(558\) 15.5885 9.00000i 0.659912 0.381000i
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) 6.92820 4.00000i 0.292249 0.168730i
\(563\) 22.5167 + 13.0000i 0.948964 + 0.547885i 0.892759 0.450535i \(-0.148767\pi\)
0.0562051 + 0.998419i \(0.482100\pi\)
\(564\) −6.00000 + 10.3923i −0.252646 + 0.437595i
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) −1.73205 2.00000i −0.0727393 0.0839921i
\(568\) 0 0
\(569\) −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) 0 0
\(571\) 9.50000 16.4545i 0.397563 0.688599i −0.595862 0.803087i \(-0.703189\pi\)
0.993425 + 0.114488i \(0.0365228\pi\)
\(572\) 3.46410 2.00000i 0.144841 0.0836242i
\(573\) 10.0000i 0.417756i
\(574\) 10.0000 + 51.9615i 0.417392 + 2.16883i
\(575\) 0 0
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) −14.7224 8.50000i −0.612903 0.353860i 0.161198 0.986922i \(-0.448464\pi\)
−0.774101 + 0.633062i \(0.781798\pi\)
\(578\) 29.4449 + 17.0000i 1.22474 + 0.707107i
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 12.0000i 0.497416i
\(583\) −20.7846 + 12.0000i −0.860811 + 0.496989i
\(584\) 0 0
\(585\) 0 0
\(586\) −8.00000 13.8564i −0.330477 0.572403i
\(587\) 16.0000i 0.660391i −0.943913 0.330195i \(-0.892885\pi\)
0.943913 0.330195i \(-0.107115\pi\)
\(588\) 13.8564 + 2.00000i 0.571429 + 0.0824786i
\(589\) −9.00000 −0.370839
\(590\) 0 0
\(591\) −8.00000 + 13.8564i −0.329076 + 0.569976i
\(592\) −10.3923 6.00000i −0.427121 0.246598i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) 25.9808 5.00000i 1.05890 0.203785i
\(603\) 5.00000i 0.203616i
\(604\) −16.0000 27.7128i −0.651031 1.12762i
\(605\) 0 0
\(606\) −2.00000 + 3.46410i −0.0812444 + 0.140720i
\(607\) −19.9186 + 11.5000i −0.808470 + 0.466771i −0.846424 0.532509i \(-0.821249\pi\)
0.0379540 + 0.999279i \(0.487916\pi\)
\(608\) 8.00000i 0.324443i
\(609\) −8.00000 + 6.92820i −0.324176 + 0.280745i
\(610\) 0 0
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 0 0
\(613\) −29.4449 17.0000i −1.18927 0.686624i −0.231127 0.972924i \(-0.574241\pi\)
−0.958140 + 0.286300i \(0.907575\pi\)
\(614\) −17.0000 29.4449i −0.686064 1.18830i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) −12.1244 + 7.00000i −0.487713 + 0.281581i
\(619\) −14.5000 + 25.1147i −0.582804 + 1.00945i 0.412341 + 0.911030i \(0.364711\pi\)
−0.995145 + 0.0984169i \(0.968622\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) −41.5692 + 8.00000i −1.66544 + 0.320513i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) 1.00000 1.73205i 0.0399680 0.0692267i
\(627\) −1.73205 1.00000i −0.0691714 0.0399362i
\(628\) −24.2487 + 14.0000i −0.967629 + 0.558661i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) −3.46410 2.00000i −0.137686 0.0794929i
\(634\) 24.0000 41.5692i 0.953162 1.65092i
\(635\) 0 0
\(636\) 24.0000 0.951662
\(637\) 4.33013 5.50000i 0.171566 0.217918i
\(638\) 16.0000i 0.633446i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 13.8564 8.00000i 0.546869 0.315735i
\(643\) 19.0000i 0.749287i −0.927169 0.374643i \(-0.877765\pi\)
0.927169 0.374643i \(-0.122235\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.73205 + 1.00000i 0.0680939 + 0.0393141i 0.533660 0.845699i \(-0.320816\pi\)
−0.465566 + 0.885013i \(0.654149\pi\)
\(648\) 0 0
\(649\) 12.0000 + 20.7846i 0.471041 + 0.815867i
\(650\) 0 0
\(651\) 4.50000 + 23.3827i 0.176369 + 0.916440i
\(652\) 8.00000i 0.313304i
\(653\) 15.5885 9.00000i 0.610023 0.352197i −0.162951 0.986634i \(-0.552101\pi\)
0.772975 + 0.634437i \(0.218768\pi\)
\(654\) 9.00000 15.5885i 0.351928 0.609557i
\(655\) 0 0
\(656\) −20.0000 34.6410i −0.780869 1.35250i
\(657\) 3.00000i 0.117041i
\(658\) −20.7846 24.0000i −0.810268 0.935617i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 20.5000 35.5070i 0.797358 1.38106i −0.123974 0.992286i \(-0.539564\pi\)
0.921331 0.388778i \(-0.127103\pi\)
\(662\) −43.3013 25.0000i −1.68295 0.971653i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) 24.2487 + 14.0000i 0.938211 + 0.541676i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) −20.7846 + 4.00000i −0.801784 + 0.154303i
\(673\) 41.0000i 1.58043i −0.612827 0.790217i \(-0.709968\pi\)
0.612827 0.790217i \(-0.290032\pi\)
\(674\) 13.0000 + 22.5167i 0.500741 + 0.867309i
\(675\) 0 0
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) −10.3923 + 6.00000i −0.399409 + 0.230599i −0.686229 0.727386i \(-0.740735\pi\)
0.286820 + 0.957984i \(0.407402\pi\)
\(678\) 20.0000i 0.768095i
\(679\) −15.0000 5.19615i −0.575647 0.199410i
\(680\) 0 0
\(681\) −9.00000 15.5885i −0.344881 0.597351i
\(682\) −31.1769 18.0000i −1.19383 0.689256i
\(683\) 10.3923 + 6.00000i 0.397650 + 0.229584i 0.685470 0.728101i \(-0.259597\pi\)
−0.287819 + 0.957685i \(0.592930\pi\)
\(684\) 1.00000 + 1.73205i 0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) −17.0000 + 32.9090i −0.649063 + 1.25647i
\(687\) 19.0000i 0.724895i
\(688\) −17.3205 + 10.0000i −0.660338 + 0.381246i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 18.5000 + 32.0429i 0.703773 + 1.21897i 0.967132 + 0.254273i \(0.0818362\pi\)
−0.263359 + 0.964698i \(0.584830\pi\)
\(692\) 16.0000i 0.608229i
\(693\) −1.73205 + 5.00000i −0.0657952 + 0.189934i
\(694\) −64.0000 −2.42941
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −24.2487 + 14.0000i −0.917827 + 0.529908i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −1.73205 + 1.00000i −0.0653720 + 0.0377426i
\(703\) −2.59808 1.50000i −0.0979883 0.0565736i
\(704\) 8.00000 13.8564i 0.301511 0.522233i
\(705\) 0 0
\(706\) 68.0000 2.55921
\(707\) −3.46410 4.00000i −0.130281 0.150435i
\(708\) 24.0000i 0.901975i
\(709\) 15.0000 + 25.9808i 0.563337 + 0.975728i 0.997202 + 0.0747503i \(0.0238160\pi\)
−0.433865 + 0.900978i \(0.642851\pi\)
\(710\) 0 0
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 5.19615 + 3.00000i 0.194054 + 0.112037i
\(718\) −34.6410 20.0000i −1.29279 0.746393i
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) 0 0
\(721\) −3.50000 18.1865i −0.130347 0.677302i
\(722\) 36.0000i 1.33978i
\(723\) 12.1244 7.00000i 0.450910 0.260333i
\(724\) 13.0000 22.5167i 0.483141 0.836825i
\(725\) 0 0
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 13.0000i 0.482143i 0.970507 + 0.241072i \(0.0774989\pi\)
−0.970507 + 0.241072i \(0.922501\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 17.3205 + 10.0000i 0.640184 + 0.369611i
\(733\) −12.9904 + 7.50000i −0.479811 + 0.277019i −0.720338 0.693624i \(-0.756013\pi\)
0.240527 + 0.970642i \(0.422680\pi\)
\(734\) 18.0000 0.664392
\(735\) 0 0
\(736\) 0 0
\(737\) −8.66025 + 5.00000i −0.319005 + 0.184177i
\(738\) 17.3205 + 10.0000i 0.637577 + 0.368105i
\(739\) −7.50000 + 12.9904i −0.275892 + 0.477859i −0.970360 0.241665i \(-0.922307\pi\)
0.694468 + 0.719524i \(0.255640\pi\)
\(740\) 0 0
\(741\) 1.00000 0.0367359
\(742\) −20.7846 + 60.0000i −0.763027 + 2.20267i
\(743\) 42.0000i 1.54083i 0.637542 + 0.770415i \(0.279951\pi\)
−0.637542 + 0.770415i \(0.720049\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −23.0000 + 39.8372i −0.842090 + 1.45854i
\(747\) −5.19615 + 3.00000i −0.190117 + 0.109764i
\(748\) 0 0
\(749\) 4.00000 + 20.7846i 0.146157 + 0.759453i
\(750\) 0 0
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 20.7846 + 12.0000i 0.757937 + 0.437595i
\(753\) 6.92820 + 4.00000i 0.252478 + 0.145768i
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) 0 0
\(756\) 4.00000 3.46410i 0.145479 0.125988i
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 5.19615 3.00000i 0.188733 0.108965i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 + 41.5692i 0.869999 + 1.50688i 0.861996 + 0.506915i \(0.169214\pi\)
0.00800331 + 0.999968i \(0.497452\pi\)
\(762\) 30.0000i 1.08679i
\(763\) 15.5885 + 18.0000i 0.564340 + 0.651644i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −10.3923 6.00000i −0.375244 0.216647i
\(768\) 13.8564 8.00000i 0.500000 0.288675i
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) −19.0526 + 11.0000i −0.685717 + 0.395899i
\(773\) 29.4449 + 17.0000i 1.05906 + 0.611448i 0.925172 0.379549i \(-0.123921\pi\)
0.133887 + 0.990997i \(0.457254\pi\)
\(774\) 5.00000 8.66025i 0.179721 0.311286i
\(775\) 0 0
\(776\) 0 0
\(777\) −2.59808 + 7.50000i −0.0932055 + 0.269061i
\(778\) 12.0000i 0.430221i
\(779\) −5.00000 8.66025i −0.179144 0.310286i
\(780\) 0 0
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 0 0
\(783\) 4.00000i 0.142948i
\(784\) 4.00000 27.7128i 0.142857 0.989743i
\(785\) 0 0
\(786\) 14.0000 + 24.2487i 0.499363 + 0.864923i
\(787\) 34.6410 + 20.0000i 1.23482 + 0.712923i 0.968031 0.250832i \(-0.0807042\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(788\) −27.7128