Properties

Label 1950.2.i.i.601.1
Level $1950$
Weight $2$
Character 1950.601
Analytic conductor $15.571$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 601.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1950.601
Dual form 1950.2.i.i.451.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.00000 + 6.92820i) q^{17} +1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} -5.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.50000 - 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.50000 + 4.33013i) q^{42} +(3.00000 - 5.19615i) q^{43} -3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} -8.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} +5.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-2.50000 - 4.33013i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} -15.0000 q^{77} +(3.50000 - 0.866025i) q^{78} -2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} -6.00000 q^{86} +(-2.00000 + 3.46410i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} +4.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} - 5q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{6} - 5q^{7} + 2q^{8} - q^{9} + 3q^{11} - 2q^{12} + 5q^{13} + 10q^{14} - q^{16} - 8q^{17} + 2q^{18} + 5q^{19} - 10q^{21} + 3q^{22} - 4q^{23} + q^{24} + 2q^{26} - 2q^{27} - 5q^{28} + 4q^{29} - 4q^{31} - q^{32} - 3q^{33} + 16q^{34} - q^{36} - 7q^{37} - 10q^{38} - 2q^{39} - 6q^{41} + 5q^{42} + 6q^{43} - 6q^{44} - 4q^{46} + 6q^{47} + q^{48} - 18q^{49} - 16q^{51} - 7q^{52} - 2q^{53} + q^{54} - 5q^{56} + 10q^{57} + 4q^{58} - 12q^{59} - 2q^{61} + 2q^{62} - 5q^{63} + 2q^{64} + 6q^{66} + 8q^{67} - 8q^{68} + 4q^{69} - 2q^{71} - q^{72} - 7q^{74} + 5q^{76} - 30q^{77} + 7q^{78} - 4q^{79} - q^{81} - 6q^{82} - 16q^{83} + 5q^{84} - 12q^{86} - 4q^{87} + 3q^{88} + 11q^{89} - 35q^{91} + 8q^{92} - 2q^{93} - 3q^{94} - 2q^{96} - 18q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −2.50000 + 4.33013i −0.944911 + 1.63663i −0.188982 + 0.981981i \(0.560519\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) 5.00000 1.33631
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.00000 + 6.92820i −0.970143 + 1.68034i −0.275029 + 0.961436i \(0.588688\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) −5.00000 −1.09109
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) −1.00000 −0.192450
\(28\) −2.50000 4.33013i −0.472456 0.818317i
\(29\) 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i \(-0.0455477\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(30\) 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
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) −5.00000 −0.811107
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) 0 0
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 2.50000 + 4.33013i 0.385758 + 0.668153i
\(43\) 3.00000 5.19615i 0.457496 0.792406i −0.541332 0.840809i \(-0.682080\pi\)
0.998828 + 0.0484030i \(0.0154132\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −2.00000 + 3.46410i −0.294884 + 0.510754i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −9.00000 15.5885i −1.28571 2.22692i
\(50\) 0 0
\(51\) −8.00000 −1.12022
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.50000 + 4.33013i −0.334077 + 0.578638i
\(57\) 5.00000 0.662266
\(58\) 2.00000 3.46410i 0.262613 0.454859i
\(59\) −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
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 1.00000 + 1.73205i 0.127000 + 0.219971i
\(63\) −2.50000 4.33013i −0.314970 0.545545i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) −4.00000 6.92820i −0.485071 0.840168i
\(69\) 2.00000 3.46410i 0.240772 0.417029i
\(70\) 0 0
\(71\) −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i \(-0.871199\pi\)
0.800566 + 0.599245i \(0.204532\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 0 0
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) −15.0000 −1.70941
\(78\) 3.50000 0.866025i 0.396297 0.0980581i
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 2.50000 4.33013i 0.272772 0.472456i
\(85\) 0 0
\(86\) −6.00000 −0.646997
\(87\) −2.00000 + 3.46410i −0.214423 + 0.371391i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 0 0
\(91\) −17.5000 + 4.33013i −1.83450 + 0.453921i
\(92\) 4.00000 0.417029
\(93\) −1.00000 1.73205i −0.103695 0.179605i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(98\) −9.00000 + 15.5885i −0.909137 + 1.57467i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i \(-0.0363659\pi\)
−0.595466 + 0.803380i \(0.703033\pi\)
\(102\) 4.00000 + 6.92820i 0.396059 + 0.685994i
\(103\) 7.00000 0.689730 0.344865 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 0 0
\(106\) 0.500000 + 0.866025i 0.0485643 + 0.0841158i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 5.00000 0.472456
\(113\) 4.00000 6.92820i 0.376288 0.651751i −0.614231 0.789127i \(-0.710534\pi\)
0.990519 + 0.137376i \(0.0438669\pi\)
\(114\) −2.50000 4.33013i −0.234146 0.405554i
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) −3.50000 + 0.866025i −0.323575 + 0.0800641i
\(118\) 12.0000 1.10469
\(119\) −20.0000 34.6410i −1.83340 3.17554i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 2.00000 0.181071
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 0 0
\(126\) −2.50000 + 4.33013i −0.222718 + 0.385758i
\(127\) −10.5000 18.1865i −0.931724 1.61379i −0.780373 0.625314i \(-0.784971\pi\)
−0.151351 0.988480i \(-0.548362\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 6.00000 0.528271
\(130\) 0 0
\(131\) −19.0000 −1.66004 −0.830019 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(132\) −1.50000 2.59808i −0.130558 0.226134i
\(133\) 12.5000 + 21.6506i 1.08389 + 1.87735i
\(134\) 4.00000 6.92820i 0.345547 0.598506i
\(135\) 0 0
\(136\) −4.00000 + 6.92820i −0.342997 + 0.594089i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) −4.00000 −0.340503
\(139\) −3.50000 + 6.06218i −0.296866 + 0.514187i −0.975417 0.220366i \(-0.929275\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) 2.00000 0.167836
\(143\) −3.00000 + 10.3923i −0.250873 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 0 0
\(147\) 9.00000 15.5885i 0.742307 1.28571i
\(148\) 7.00000 0.575396
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0 0
\(151\) 22.0000 1.79033 0.895167 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) −4.00000 6.92820i −0.323381 0.560112i
\(154\) 7.50000 + 12.9904i 0.604367 + 1.04679i
\(155\) 0 0
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) −15.0000 −1.19713 −0.598565 0.801074i \(-0.704262\pi\)
−0.598565 + 0.801074i \(0.704262\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 0 0
\(161\) 20.0000 1.57622
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 4.00000 + 6.92820i 0.310460 + 0.537733i
\(167\) −11.5000 19.9186i −0.889897 1.54135i −0.839996 0.542592i \(-0.817443\pi\)
−0.0499004 0.998754i \(-0.515890\pi\)
\(168\) −5.00000 −0.385758
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 2.50000 + 4.33013i 0.191180 + 0.331133i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 2.50000 4.33013i 0.190071 0.329213i −0.755202 0.655492i \(-0.772461\pi\)
0.945274 + 0.326278i \(0.105795\pi\)
\(174\) 4.00000 0.303239
\(175\) 0 0
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −12.0000 −0.901975
\(178\) 5.50000 9.52628i 0.412242 0.714025i
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 12.5000 + 12.9904i 0.926562 + 0.962911i
\(183\) −2.00000 −0.147844
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) 0 0
\(186\) −1.00000 + 1.73205i −0.0733236 + 0.127000i
\(187\) −24.0000 −1.75505
\(188\) −1.50000 + 2.59808i −0.109399 + 0.189484i
\(189\) 2.50000 4.33013i 0.181848 0.314970i
\(190\) 0 0
\(191\) −1.00000 + 1.73205i −0.0723575 + 0.125327i −0.899934 0.436026i \(-0.856386\pi\)
0.827577 + 0.561353i \(0.189719\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 12.0000 + 20.7846i 0.863779 + 1.49611i 0.868255 + 0.496119i \(0.165242\pi\)
−0.00447566 + 0.999990i \(0.501425\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) 1.50000 + 2.59808i 0.106871 + 0.185105i 0.914501 0.404584i \(-0.132584\pi\)
−0.807630 + 0.589689i \(0.799250\pi\)
\(198\) 1.50000 + 2.59808i 0.106600 + 0.184637i
\(199\) −11.0000 + 19.0526i −0.779769 + 1.35060i 0.152305 + 0.988334i \(0.451330\pi\)
−0.932075 + 0.362267i \(0.882003\pi\)
\(200\) 0 0
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 4.00000 6.92820i 0.281439 0.487467i
\(203\) −20.0000 −1.40372
\(204\) 4.00000 6.92820i 0.280056 0.485071i
\(205\) 0 0
\(206\) −3.50000 6.06218i −0.243857 0.422372i
\(207\) 4.00000 0.278019
\(208\) 1.00000 3.46410i 0.0693375 0.240192i
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i \(0.00603229\pi\)
−0.483499 + 0.875345i \(0.660634\pi\)
\(212\) 0.500000 0.866025i 0.0343401 0.0594789i
\(213\) −2.00000 −0.137038
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 5.00000 8.66025i 0.339422 0.587896i
\(218\) −7.00000 12.1244i −0.474100 0.821165i
\(219\) 0 0
\(220\) 0 0
\(221\) −28.0000 + 6.92820i −1.88348 + 0.466041i
\(222\) −7.00000 −0.469809
\(223\) −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i \(-0.198694\pi\)
−0.911869 + 0.410481i \(0.865361\pi\)
\(224\) −2.50000 4.33013i −0.167038 0.289319i
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) −2.50000 + 4.33013i −0.165567 + 0.286770i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −7.50000 12.9904i −0.493464 0.854704i
\(232\) 2.00000 + 3.46410i 0.131306 + 0.227429i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 2.50000 + 2.59808i 0.163430 + 0.169842i
\(235\) 0 0
\(236\) −6.00000 10.3923i −0.390567 0.676481i
\(237\) −1.00000 1.73205i −0.0649570 0.112509i
\(238\) −20.0000 + 34.6410i −1.29641 + 2.24544i
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 17.5000 4.33013i 1.11350 0.275519i
\(248\) −2.00000 −0.127000
\(249\) −4.00000 6.92820i −0.253490 0.439057i
\(250\) 0 0
\(251\) −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i \(-0.990305\pi\)
0.526140 + 0.850398i \(0.323639\pi\)
\(252\) 5.00000 0.314970
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) −10.5000 + 18.1865i −0.658829 + 1.14112i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.0000 + 24.2487i 0.873296 + 1.51259i 0.858567 + 0.512702i \(0.171355\pi\)
0.0147291 + 0.999892i \(0.495311\pi\)
\(258\) −3.00000 5.19615i −0.186772 0.323498i
\(259\) 35.0000 2.17479
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 9.50000 + 16.4545i 0.586912 + 1.01656i
\(263\) −7.50000 12.9904i −0.462470 0.801021i 0.536614 0.843828i \(-0.319703\pi\)
−0.999083 + 0.0428069i \(0.986370\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 12.5000 21.6506i 0.766424 1.32749i
\(267\) −5.50000 + 9.52628i −0.336595 + 0.582999i
\(268\) −8.00000 −0.488678
\(269\) −2.00000 + 3.46410i −0.121942 + 0.211210i −0.920534 0.390664i \(-0.872246\pi\)
0.798591 + 0.601874i \(0.205579\pi\)
\(270\) 0 0
\(271\) −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i \(-0.205434\pi\)
−0.920356 + 0.391082i \(0.872101\pi\)
\(272\) 8.00000 0.485071
\(273\) −12.5000 12.9904i −0.756534 0.786214i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 2.00000 + 3.46410i 0.120386 + 0.208514i
\(277\) −7.50000 + 12.9904i −0.450631 + 0.780516i −0.998425 0.0560969i \(-0.982134\pi\)
0.547794 + 0.836613i \(0.315468\pi\)
\(278\) 7.00000 0.419832
\(279\) 1.00000 1.73205i 0.0598684 0.103695i
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) −5.00000 8.66025i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 0 0
\(286\) 10.5000 2.59808i 0.620878 0.153627i
\(287\) 30.0000 1.77084
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −23.5000 40.7032i −1.38235 2.39431i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.50000 + 7.79423i −0.262893 + 0.455344i −0.967009 0.254741i \(-0.918010\pi\)
0.704117 + 0.710084i \(0.251343\pi\)
\(294\) −18.0000 −1.04978
\(295\) 0 0
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) −2.00000 −0.115857
\(299\) 4.00000 13.8564i 0.231326 0.801337i
\(300\) 0 0
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) −11.0000 19.0526i −0.632979 1.09635i
\(303\) −4.00000 + 6.92820i −0.229794 + 0.398015i
\(304\) −5.00000 −0.286770
\(305\) 0 0
\(306\) −4.00000 + 6.92820i −0.228665 + 0.396059i
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) 7.50000 12.9904i 0.427352 0.740196i
\(309\) 3.50000 + 6.06218i 0.199108 + 0.344865i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −1.00000 + 3.46410i −0.0566139 + 0.196116i
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 7.50000 + 12.9904i 0.423249 + 0.733090i
\(315\) 0 0
\(316\) 1.00000 1.73205i 0.0562544 0.0974355i
\(317\) 23.0000 1.29181 0.645904 0.763418i \(-0.276480\pi\)
0.645904 + 0.763418i \(0.276480\pi\)
\(318\) −0.500000 + 0.866025i −0.0280386 + 0.0485643i
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) 0 0
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) −10.0000 17.3205i −0.557278 0.965234i
\(323\) 20.0000 + 34.6410i 1.11283 + 1.92748i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 20.0000 1.10770
\(327\) 7.00000 + 12.1244i 0.387101 + 0.670478i
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) −7.50000 + 12.9904i −0.413488 + 0.716183i
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 4.00000 6.92820i 0.219529 0.380235i
\(333\) 7.00000 0.383598
\(334\) −11.5000 + 19.9186i −0.629252 + 1.08990i
\(335\) 0 0
\(336\) 2.50000 + 4.33013i 0.136386 + 0.236228i
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 11.5000 6.06218i 0.625518 0.329739i
\(339\) 8.00000 0.434500
\(340\) 0 0
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) 2.50000 4.33013i 0.135185 0.234146i
\(343\) 55.0000 2.96972
\(344\) 3.00000 5.19615i 0.161749 0.280158i
\(345\) 0 0
\(346\) −5.00000 −0.268802
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) −2.00000 3.46410i −0.107211 0.185695i
\(349\) −4.00000 6.92820i −0.214115 0.370858i 0.738883 0.673833i \(-0.235353\pi\)
−0.952998 + 0.302975i \(0.902020\pi\)
\(350\) 0 0
\(351\) −2.50000 2.59808i −0.133440 0.138675i
\(352\) −3.00000 −0.159901
\(353\) 8.00000 + 13.8564i 0.425797 + 0.737502i 0.996495 0.0836583i \(-0.0266604\pi\)
−0.570697 + 0.821160i \(0.693327\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 0 0
\(356\) −11.0000 −0.582999
\(357\) 20.0000 34.6410i 1.05851 1.83340i
\(358\) −2.00000 + 3.46410i −0.105703 + 0.183083i
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) 2.00000 0.104973
\(364\) 5.00000 17.3205i 0.262071 0.907841i
\(365\) 0 0
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 2.50000 4.33013i 0.129794 0.224809i
\(372\) 2.00000 0.103695
\(373\) 19.0000 32.9090i 0.983783 1.70396i 0.336557 0.941663i \(-0.390737\pi\)
0.647225 0.762299i \(-0.275929\pi\)
\(374\) 12.0000 + 20.7846i 0.620505 + 1.07475i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) −4.00000 + 13.8564i −0.206010 + 0.713641i
\(378\) −5.00000 −0.257172
\(379\) 12.5000 + 21.6506i 0.642082 + 1.11212i 0.984967 + 0.172741i \(0.0552624\pi\)
−0.342885 + 0.939377i \(0.611404\pi\)
\(380\) 0 0
\(381\) 10.5000 18.1865i 0.537931 0.931724i
\(382\) 2.00000 0.102329
\(383\) −14.0000 + 24.2487i −0.715367 + 1.23905i 0.247451 + 0.968900i \(0.420407\pi\)
−0.962818 + 0.270151i \(0.912926\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) 12.0000 20.7846i 0.610784 1.05791i
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 0 0
\(389\) −32.0000 −1.62246 −0.811232 0.584724i \(-0.801203\pi\)
−0.811232 + 0.584724i \(0.801203\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) −9.00000 15.5885i −0.454569 0.787336i
\(393\) −9.50000 16.4545i −0.479212 0.830019i
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 0 0
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 12.5000 21.6506i 0.627357 1.08661i −0.360723 0.932673i \(-0.617470\pi\)
0.988080 0.153941i \(-0.0491966\pi\)
\(398\) 22.0000 1.10276
\(399\) −12.5000 + 21.6506i −0.625783 + 1.08389i
\(400\) 0 0
\(401\) 9.50000 + 16.4545i 0.474407 + 0.821698i 0.999571 0.0293039i \(-0.00932905\pi\)
−0.525163 + 0.851002i \(0.675996\pi\)
\(402\) 8.00000 0.399004
\(403\) −5.00000 5.19615i −0.249068 0.258839i
\(404\) −8.00000 −0.398015
\(405\) 0 0
\(406\) 10.0000 + 17.3205i 0.496292 + 0.859602i
\(407\) 10.5000 18.1865i 0.520466 0.901473i
\(408\) −8.00000 −0.396059
\(409\) −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) −3.50000 + 6.06218i −0.172433 + 0.298662i
\(413\) −30.0000 51.9615i −1.47620 2.55686i
\(414\) −2.00000 3.46410i −0.0982946 0.170251i
\(415\) 0 0
\(416\) −3.50000 + 0.866025i −0.171602 + 0.0424604i
\(417\) −7.00000 −0.342791
\(418\) −7.50000 12.9904i −0.366837 0.635380i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) 12.0000 0.584844 0.292422 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) 7.50000 12.9904i 0.365094 0.632362i
\(423\) −1.50000 + 2.59808i −0.0729325 + 0.126323i
\(424\) −1.00000 −0.0485643
\(425\) 0 0
\(426\) 1.00000 + 1.73205i 0.0484502 + 0.0839181i
\(427\) −5.00000 8.66025i −0.241967 0.419099i
\(428\) 6.00000 0.290021
\(429\) −10.5000 + 2.59808i −0.506945 + 0.125436i
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 8.00000 13.8564i 0.384455 0.665896i −0.607238 0.794520i \(-0.707723\pi\)
0.991693 + 0.128624i \(0.0410559\pi\)
\(434\) −10.0000 −0.480015
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) −20.0000 −0.956730
\(438\) 0 0
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 20.0000 + 20.7846i 0.951303 + 0.988623i
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) 0 0
\(446\) −1.50000 + 2.59808i −0.0710271 + 0.123022i
\(447\) 2.00000 0.0945968
\(448\) −2.50000 + 4.33013i −0.118114 + 0.204579i
\(449\) 13.5000 23.3827i 0.637104 1.10350i −0.348961 0.937137i \(-0.613465\pi\)
0.986065 0.166360i \(-0.0532013\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 4.00000 + 6.92820i 0.188144 + 0.325875i
\(453\) 11.0000 + 19.0526i 0.516825 + 0.895167i
\(454\) 0 0
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) 15.0000 + 25.9808i 0.701670 + 1.21533i 0.967880 + 0.251414i \(0.0808954\pi\)
−0.266209 + 0.963915i \(0.585771\pi\)
\(458\) −7.00000 12.1244i −0.327089 0.566534i
\(459\) 4.00000 6.92820i 0.186704 0.323381i
\(460\) 0 0
\(461\) −4.00000 + 6.92820i −0.186299 + 0.322679i −0.944013 0.329907i \(-0.892983\pi\)
0.757715 + 0.652586i \(0.226316\pi\)
\(462\) −7.50000 + 12.9904i −0.348932 + 0.604367i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 2.00000 3.46410i 0.0928477 0.160817i
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 1.00000 3.46410i 0.0462250 0.160128i
\(469\) −40.0000 −1.84703
\(470\) 0 0
\(471\) −7.50000 12.9904i −0.345582 0.598565i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) 18.0000 0.827641
\(474\) −1.00000 + 1.73205i −0.0459315 + 0.0795557i
\(475\) 0 0
\(476\) 40.0000 1.83340
\(477\) 0.500000 0.866025i 0.0228934 0.0396526i
\(478\) 9.00000 + 15.5885i 0.411650 + 0.712999i
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 0 0
\(481\) 7.00000 24.2487i 0.319173 1.10565i
\(482\) −25.0000 −1.13872
\(483\) 10.0000 + 17.3205i 0.455016 + 0.788110i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 18.5000 32.0429i 0.838315 1.45200i −0.0529875 0.998595i \(-0.516874\pi\)
0.891303 0.453409i \(-0.149792\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) −32.0000 −1.44121
\(494\) −12.5000 12.9904i −0.562402 0.584465i
\(495\) 0 0
\(496\) 1.00000 + 1.73205i 0.0449013 + 0.0777714i
\(497\) −5.00000 8.66025i −0.224281 0.388465i
\(498\) −4.00000 + 6.92820i −0.179244 + 0.310460i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 11.5000 19.9186i 0.513782 0.889897i
\(502\) 15.0000 0.669483
\(503\) −5.50000 + 9.52628i −0.245233 + 0.424756i −0.962197 0.272354i \(-0.912198\pi\)
0.716964 + 0.697110i \(0.245531\pi\)
\(504\) −2.50000 4.33013i −0.111359 0.192879i
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) −11.5000 + 6.06218i −0.510733 + 0.269231i
\(508\) 21.0000 0.931724
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) 14.0000 24.2487i 0.617514 1.06956i
\(515\) 0 0
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) 4.50000 + 7.79423i 0.197910 + 0.342790i
\(518\) −17.5000 30.3109i −0.768906 1.33178i
\(519\) 5.00000 0.219476
\(520\) 0 0
\(521\) 5.00000 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(522\) 2.00000 + 3.46410i 0.0875376 + 0.151620i
\(523\) −5.00000 8.66025i −0.218635 0.378686i 0.735756 0.677247i \(-0.236827\pi\)
−0.954391 + 0.298560i \(0.903494\pi\)
\(524\) 9.50000 16.4545i 0.415009 0.718817i
\(525\) 0 0
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) 8.00000 13.8564i 0.348485 0.603595i
\(528\) 3.00000 0.130558
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −6.00000 10.3923i −0.260378 0.450988i
\(532\) −25.0000 −1.08389
\(533\) 6.00000 20.7846i 0.259889 0.900281i
\(534\) 11.0000 0.476017
\(535\) 0 0
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) 2.00000 3.46410i 0.0863064 0.149487i
\(538\) 4.00000 0.172452
\(539\) 27.0000 46.7654i 1.16297 2.01433i
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) −2.00000 + 3.46410i −0.0859074 + 0.148796i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) −4.00000 6.92820i −0.171499 0.297044i
\(545\) 0 0
\(546\) −5.00000 + 17.3205i −0.213980 + 0.741249i
\(547\) −6.00000 −0.256541 −0.128271 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) 20.0000 0.852029
\(552\) 2.00000 3.46410i 0.0851257 0.147442i
\(553\) 5.00000 8.66025i 0.212622 0.368271i
\(554\) 15.0000 0.637289
\(555\) 0 0
\(556\) −3.50000 6.06218i −0.148433 0.257094i
\(557\) 7.50000 + 12.9904i 0.317785 + 0.550420i 0.980026 0.198871i \(-0.0637276\pi\)
−0.662240 + 0.749291i \(0.730394\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 21.0000 5.19615i 0.888205 0.219774i
\(560\) 0 0
\(561\) −12.0000 20.7846i −0.506640 0.877527i
\(562\) −9.00000 15.5885i −0.379642 0.657559i
\(563\) 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(564\) −3.00000 −0.126323
\(565\) 0 0
\(566\) −5.00000 + 8.66025i −0.210166 + 0.364018i
\(567\) 5.00000 0.209980
\(568\) −1.00000 + 1.73205i −0.0419591 + 0.0726752i
\(569\) 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i \(-0.0648579\pi\)
−0.664897 + 0.746935i \(0.731525\pi\)
\(570\) 0 0
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) −7.50000 7.79423i −0.313591 0.325893i
\(573\) −2.00000 −0.0835512
\(574\) −15.0000 25.9808i −0.626088 1.08442i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −23.5000 + 40.7032i −0.977471 + 1.69303i
\(579\) −12.0000 + 20.7846i −0.498703 + 0.863779i
\(580\) 0 0
\(581\) 20.0000 34.6410i 0.829740 1.43715i
\(582\) 0 0
\(583\) −1.50000 2.59808i −0.0621237 0.107601i
\(584\) 0 0
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) 9.00000 + 15.5885i 0.371154 + 0.642857i
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) 0 0
\(591\) −1.50000 + 2.59808i −0.0617018 + 0.106871i
\(592\) −3.50000 + 6.06218i −0.143849 + 0.249154i
\(593\) −20.0000 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 1.00000 + 1.73205i 0.0409616 + 0.0709476i
\(597\) −22.0000 −0.900400
\(598\) −14.0000 + 3.46410i −0.572503 + 0.141658i
\(599\) 34.0000 1.38920 0.694601 0.719395i \(-0.255581\pi\)
0.694601 + 0.719395i \(0.255581\pi\)
\(600\) 0 0
\(601\) −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i \(-0.894483\pi\)
0.190927 0.981604i \(-0.438851\pi\)
\(602\) 15.0000 25.9808i 0.611354 1.05890i
\(603\) −8.00000 −0.325785
\(604\) −11.0000 + 19.0526i −0.447584 + 0.775238i
\(605\) 0 0
\(606\) 8.00000 0.324978
\(607\) −14.5000 + 25.1147i −0.588537 + 1.01938i 0.405887 + 0.913923i \(0.366962\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) −10.0000 17.3205i −0.405220 0.701862i
\(610\) 0 0
\(611\) 7.50000 + 7.79423i 0.303418 + 0.315321i
\(612\) 8.00000 0.323381
\(613\) 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i \(0.00179300\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(614\) −3.00000 5.19615i −0.121070 0.209700i
\(615\) 0 0
\(616\) −15.0000 −0.604367
\(617\) −7.00000 + 12.1244i −0.281809 + 0.488108i −0.971830 0.235681i \(-0.924268\pi\)
0.690021 + 0.723789i \(0.257601\pi\)
\(618\) 3.50000 6.06218i 0.140791 0.243857i
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 0 0
\(621\) 2.00000 + 3.46410i 0.0802572 + 0.139010i
\(622\) 6.00000 + 10.3923i 0.240578 + 0.416693i
\(623\) −55.0000 −2.20353
\(624\) 3.50000 0.866025i 0.140112 0.0346688i
\(625\) 0 0
\(626\) −3.00000 5.19615i −0.119904 0.207680i
\(627\) 7.50000 + 12.9904i 0.299521 + 0.518786i
\(628\) 7.50000 12.9904i 0.299283 0.518373i
\(629\) 56.0000 2.23287
\(630\) 0 0
\(631\) −6.00000 + 10.3923i −0.238856 + 0.413711i −0.960386 0.278672i \(-0.910106\pi\)
0.721530 + 0.692383i \(0.243439\pi\)
\(632\) −2.00000 −0.0795557
\(633\) −7.50000 + 12.9904i −0.298098 + 0.516321i
\(634\) −11.5000 19.9186i −0.456723 0.791068i
\(635\) 0 0
\(636\) 1.00000 0.0396526
\(637\) 18.0000 62.3538i 0.713186 2.47055i
\(638\) 12.0000 0.475085
\(639\) −1.00000 1.73205i −0.0395594 0.0685189i
\(640\) 0 0
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) −6.00000 −0.236801
\(643\) −22.0000 + 38.1051i −0.867595 + 1.50272i −0.00314839 + 0.999995i \(0.501002\pi\)
−0.864447 + 0.502724i \(0.832331\pi\)
\(644\) −10.0000 + 17.3205i −0.394055 + 0.682524i
\(645\) 0 0
\(646\) 20.0000 34.6410i 0.786889 1.36293i
\(647\) 1.50000 + 2.59808i 0.0589711 + 0.102141i 0.894004 0.448059i \(-0.147885\pi\)
−0.835033 + 0.550200i \(0.814551\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 10.0000 0.391931
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 13.5000 + 23.3827i 0.528296 + 0.915035i 0.999456 + 0.0329874i \(0.0105021\pi\)
−0.471160 + 0.882048i \(0.656165\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) 15.0000 0.584761
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 4.00000 0.155464
\(663\) −20.0000 20.7846i −0.776736 0.807207i
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 23.0000 0.889897
\(669\) 1.50000 2.59808i 0.0579934 0.100447i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) 2.50000 4.33013i 0.0964396 0.167038i
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 22.0000 0.845529 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) −4.00000 6.92820i −0.153619 0.266076i
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) 15.0000 25.9808i 0.573959 0.994126i −0.422195 0.906505i \(-0.638740\pi\)
0.996154 0.0876211i \(-0.0279265\pi\)
\(684\) −5.00000 −0.191180
\(685\) 0 0
\(686\) −27.5000 47.6314i −1.04995 1.81858i
\(687\) 7.00000 + 12.1244i 0.267067 + 0.462573i
\(688\) −6.00000 −0.228748
\(689\) −2.50000 2.59808i −0.0952424 0.0989788i
\(690\) 0 0
\(691\) −8.50000 14.7224i −0.323355 0.560068i 0.657823 0.753173i \(-0.271478\pi\)
−0.981178 + 0.193105i \(0.938144\pi\)
\(692\) 2.50000 + 4.33013i 0.0950357 + 0.164607i
\(693\) 7.50000 12.9904i 0.284901 0.493464i
\(694\) 16.0000 0.607352
\(695\) 0 0
\(696\) −2.00000 + 3.46410i −0.0758098 + 0.131306i
\(697\) 48.0000 1.81813
\(698\) −4.00000 + 6.92820i −0.151402 + 0.262236i
\(699\) 7.00000 + 12.1244i 0.264764 + 0.458585i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −1.00000 + 3.46410i −0.0377426 + 0.130744i
\(703\) −35.0000 −1.32005
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 8.00000 13.8564i 0.301084 0.521493i
\(707\) −40.0000 −1.50435
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) −16.0000 + 27.7128i −0.600893 + 1.04078i 0.391794 + 0.920053i \(0.371855\pi\)
−0.992686 + 0.120723i \(0.961479\pi\)
\(710\) 0 0
\(711\) 1.00000 1.73205i 0.0375029 0.0649570i
\(712\) 5.50000 + 9.52628i 0.206121 + 0.357012i
\(713\) 4.00000 + 6.92820i 0.149801 + 0.259463i
\(714\) −40.0000 −1.49696
\(715\) 0 0
\(716\) 4.00000 0.149487
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) 10.0000 17.3205i 0.372937 0.645946i −0.617079 0.786901i \(-0.711684\pi\)
0.990016 + 0.140955i \(0.0450174\pi\)
\(720\) 0 0
\(721\) −17.5000 + 30.3109i −0.651734 + 1.12884i
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) 25.0000 0.929760
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 11.0000 0.407967 0.203984 0.978974i \(-0.434611\pi\)
0.203984 + 0.978974i \(0.434611\pi\)
\(728\) −17.5000 + 4.33013i −0.648593 + 0.160485i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) 1.00000 1.73205i 0.0369611 0.0640184i
\(733\) 43.0000 1.58824 0.794121 0.607760i \(-0.207932\pi\)
0.794121 + 0.607760i \(0.207932\pi\)
\(734\) −4.00000 + 6.92820i −0.147643 + 0.255725i
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) −12.0000 + 20.7846i −0.442026 + 0.765611i
\(738\) −3.00000 5.19615i −0.110432 0.191273i
\(739\) −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165831i \(0.946969\pi\)
\(740\) 0 0
\(741\) 12.5000 + 12.9904i 0.459199 + 0.477214i
\(742\) −5.00000 −0.183556
\(743\) −8.00000 13.8564i −0.293492 0.508342i 0.681141 0.732152i \(-0.261484\pi\)
−0.974633 + 0.223810i \(0.928151\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) 0 0
\(746\) −38.0000 −1.39128
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) 12.0000 20.7846i 0.438763 0.759961i
\(749\) 30.0000 1.09618
\(750\) 0 0
\(751\) 4.00000 + 6.92820i 0.145962 + 0.252814i 0.929731 0.368238i \(-0.120039\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) −15.0000 −0.546630
\(754\) 14.0000 3.46410i 0.509850 0.126155i
\(755\) 0 0
\(756\) 2.50000 + 4.33013i 0.0909241 + 0.157485i
\(757\) 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i \(-0.0666932\pi\)
−0.669193 + 0.743089i \(0.733360\pi\)
\(758\) 12.5000 21.6506i 0.454020 0.786386i
\(759\) 12.0000 0.435572
\(760\) 0 0
\(761\) −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i \(-0.885491\pi\)
0.772863 + 0.634573i \(0.218824\pi\)
\(762\) −21.0000 −0.760750
\(763\) −35.0000 + 60.6218i −1.26709 + 2.19466i
\(764\) −1.00000 1.73205i −0.0361787 0.0626634i
\(765\) 0 0
\(766\) 28.0000 1.01168
\(767\) −42.0000 + 10.3923i −1.51653 + 0.375244i
\(768\) −1.00000 −0.0360844
\(769\) 17.0000 + 29.4449i 0.613036 + 1.06181i 0.990726 + 0.135877i \(0.0433852\pi\)
−0.377690 + 0.925932i \(0.623282\pi\)
\(770\) 0 0
\(771\) −14.0000 + 24.2487i −0.504198 + 0.873296i
\(772\) −24.0000 −0.863779
\(773\) 0.500000 0.866025i 0.0179838 0.0311488i −0.856893 0.515494i \(-0.827609\pi\)
0.874877 + 0.484345i \(0.160942\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) 0 0
\(776\) 0 0
\(777\) 17.5000 + 30.3109i 0.627809 + 1.08740i
\(778\) 16.0000 + 27.7128i 0.573628 + 0.993552i
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) −16.0000 27.7128i −0.572159 0.991008i
\(783\) −2.00000 3.46410i −0.0714742 0.123797i
\(784\) −9.00000 + 15.5885i −0.321429 + 0.556731i
\(785\) 0 0
\(786\) −9.50000