Properties

Label 1170.2.i.g.451.1
Level $1170$
Weight $2$
Character 1170.451
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1170.451
Dual form 1170.2.i.g.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 2.59808i) q^{13} -5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.00000 - 6.92820i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} +(2.50000 - 4.33013i) q^{28} +(-2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +8.00000 q^{34} +(2.50000 + 4.33013i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +1.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-9.00000 + 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(-4.00000 + 6.92820i) q^{68} -5.00000 q^{70} +(1.00000 + 1.73205i) q^{71} +(3.50000 + 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{76} -15.0000 q^{77} -2.00000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{85} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(-17.5000 - 4.33013i) q^{91} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(2.50000 + 4.33013i) q^{95} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 2q^{5} + 5q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 2q^{5} + 5q^{7} + 2q^{8} - q^{10} - 3q^{11} - 5q^{13} - 10q^{14} - q^{16} - 8q^{17} + 5q^{19} - q^{20} - 3q^{22} - 4q^{23} + 2q^{25} - 2q^{26} + 5q^{28} - 4q^{29} - 4q^{31} - q^{32} + 16q^{34} + 5q^{35} + 7q^{37} - 10q^{38} + 2q^{40} + 6q^{41} - 6q^{43} + 6q^{44} - 4q^{46} + 6q^{47} - 18q^{49} - q^{50} + 7q^{52} - 2q^{53} - 3q^{55} + 5q^{56} - 4q^{58} + 12q^{59} - 2q^{61} + 2q^{62} + 2q^{64} - 5q^{65} - 8q^{67} - 8q^{68} - 10q^{70} + 2q^{71} + 7q^{74} + 5q^{76} - 30q^{77} - 4q^{79} - q^{80} + 6q^{82} - 16q^{83} - 8q^{85} + 12q^{86} - 3q^{88} - 11q^{89} - 35q^{91} + 8q^{92} - 3q^{94} + 5q^{95} - 18q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.50000 + 4.33013i 0.944911 + 1.63663i 0.755929 + 0.654654i \(0.227186\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −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 −0.695113 0.718900i \(-0.744646\pi\)
−0.275029 0.961436i \(-0.588688\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −1.00000 3.46410i −0.196116 0.679366i
\(27\) 0 0
\(28\) 2.50000 4.33013i 0.472456 0.818317i
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 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
\(34\) 8.00000 1.37199
\(35\) 2.50000 + 4.33013i 0.422577 + 0.731925i
\(36\) 0 0
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) −5.00000 −0.811107
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) 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 0
\(49\) −9.00000 + 15.5885i −1.28571 + 2.22692i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 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 0
\(55\) −1.50000 + 2.59808i −0.202260 + 0.350325i
\(56\) 2.50000 + 4.33013i 0.334077 + 0.578638i
\(57\) 0 0
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 1.00000 1.73205i 0.127000 0.219971i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.50000 + 2.59808i −0.310087 + 0.322252i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) −4.00000 + 6.92820i −0.485071 + 0.840168i
\(69\) 0 0
\(70\) −5.00000 −0.597614
\(71\) 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(72\) 0 0
\(73\) 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
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) −4.00000 6.92820i −0.433861 0.751469i
\(86\) 6.00000 0.646997
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −5.50000 + 9.52628i −0.582999 + 1.00978i 0.412123 + 0.911128i \(0.364787\pi\)
−0.995122 + 0.0986553i \(0.968546\pi\)
\(90\) 0 0
\(91\) −17.5000 4.33013i −1.83450 0.453921i
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 2.50000 + 4.33013i 0.256495 + 0.444262i
\(96\) 0 0
\(97\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(98\) −9.00000 15.5885i −0.909137 1.57467i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −4.00000 + 6.92820i −0.398015 + 0.689382i −0.993481 0.113998i \(-0.963634\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) −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 −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) 0 0
\(112\) −5.00000 −0.472456
\(113\) 4.00000 + 6.92820i 0.376288 + 0.651751i 0.990519 0.137376i \(-0.0438669\pi\)
−0.614231 + 0.789127i \(0.710534\pi\)
\(114\) 0 0
\(115\) −2.00000 + 3.46410i −0.186501 + 0.323029i
\(116\) 4.00000 0.371391
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.5000 18.1865i 0.931724 1.61379i 0.151351 0.988480i \(-0.451638\pi\)
0.780373 0.625314i \(-0.215029\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.00000 3.46410i −0.0877058 0.303822i
\(131\) 19.0000 1.66004 0.830019 0.557735i \(-0.188330\pi\)
0.830019 + 0.557735i \(0.188330\pi\)
\(132\) 0 0
\(133\) −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 −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i \(-0.262608\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 2.50000 4.33013i 0.211289 0.365963i
\(141\) 0 0
\(142\) −2.00000 −0.167836
\(143\) −3.00000 10.3923i −0.250873 0.869048i
\(144\) 0 0
\(145\) −2.00000 + 3.46410i −0.166091 + 0.287678i
\(146\) 0 0
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i \(-0.192773\pi\)
−0.904076 + 0.427372i \(0.859440\pi\)
\(150\) 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
\(153\) 0 0
\(154\) 7.50000 12.9904i 0.604367 1.04679i
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 15.0000 1.19713 0.598565 0.801074i \(-0.295738\pi\)
0.598565 + 0.801074i \(0.295738\pi\)
\(158\) 1.00000 1.73205i 0.0795557 0.137795i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −20.0000 −1.57622
\(162\) 0 0
\(163\) 10.0000 + 17.3205i 0.783260 + 1.35665i 0.930033 + 0.367477i \(0.119778\pi\)
−0.146772 + 0.989170i \(0.546888\pi\)
\(164\) −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 −0.0499004 + 0.998754i \(0.515890\pi\)
−0.839996 + 0.542592i \(0.817443\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 8.00000 0.613572
\(171\) 0 0
\(172\) −3.00000 + 5.19615i −0.228748 + 0.396203i
\(173\) 2.50000 + 4.33013i 0.190071 + 0.329213i 0.945274 0.326278i \(-0.105795\pi\)
−0.755202 + 0.655492i \(0.772461\pi\)
\(174\) 0 0
\(175\) 2.50000 + 4.33013i 0.188982 + 0.327327i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) −5.50000 9.52628i −0.412242 0.714025i
\(179\) 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i \(-0.785571\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(180\) 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
\(183\) 0 0
\(184\) −2.00000 + 3.46410i −0.147442 + 0.255377i
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) 24.0000 1.75505
\(188\) −1.50000 2.59808i −0.109399 0.189484i
\(189\) 0 0
\(190\) −5.00000 −0.362738
\(191\) 1.00000 + 1.73205i 0.0723575 + 0.125327i 0.899934 0.436026i \(-0.143614\pi\)
−0.827577 + 0.561353i \(0.810281\pi\)
\(192\) 0 0
\(193\) −12.0000 + 20.7846i −0.863779 + 1.49611i 0.00447566 + 0.999990i \(0.498575\pi\)
−0.868255 + 0.496119i \(0.834758\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) 1.50000 2.59808i 0.106871 0.185105i −0.807630 0.589689i \(-0.799250\pi\)
0.914501 + 0.404584i \(0.132584\pi\)
\(198\) 0 0
\(199\) −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451330\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) −4.00000 6.92820i −0.281439 0.487467i
\(203\) −20.0000 −1.40372
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) 3.50000 6.06218i 0.243857 0.422372i
\(207\) 0 0
\(208\) −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 −0.483499 0.875345i \(-0.660634\pi\)
0.999820 0.0189499i \(-0.00603229\pi\)
\(212\) 0.500000 + 0.866025i 0.0343401 + 0.0594789i
\(213\) 0 0
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) −5.00000 8.66025i −0.339422 0.587896i
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 0 0
\(220\) 3.00000 0.202260
\(221\) 28.0000 + 6.92820i 1.88348 + 0.466041i
\(222\) 0 0
\(223\) 1.50000 2.59808i 0.100447 0.173980i −0.811422 0.584461i \(-0.801306\pi\)
0.911869 + 0.410481i \(0.134639\pi\)
\(224\) 2.50000 4.33013i 0.167038 0.289319i
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −2.00000 3.46410i −0.131876 0.228416i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 3.00000 0.195698
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 20.0000 + 34.6410i 1.29641 + 2.24544i
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i \(0.131273\pi\)
−0.110963 + 0.993825i \(0.535394\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) −9.00000 + 15.5885i −0.574989 + 0.995910i
\(246\) 0 0
\(247\) −17.5000 4.33013i −1.11350 0.275519i
\(248\) −2.00000 −0.127000
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 7.50000 + 12.9904i 0.473396 + 0.819946i 0.999536 0.0304521i \(-0.00969471\pi\)
−0.526140 + 0.850398i \(0.676361\pi\)
\(252\) 0 0
\(253\) −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 0.0147291 0.999892i \(-0.495311\pi\)
0.858567 0.512702i \(-0.171355\pi\)
\(258\) 0 0
\(259\) 35.0000 2.17479
\(260\) 3.50000 + 0.866025i 0.217061 + 0.0537086i
\(261\) 0 0
\(262\) −9.50000 + 16.4545i −0.586912 + 1.01656i
\(263\) −7.50000 + 12.9904i −0.462470 + 0.801021i −0.999083 0.0428069i \(-0.986370\pi\)
0.536614 + 0.843828i \(0.319703\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) −12.5000 21.6506i −0.766424 1.32749i
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) 2.00000 + 3.46410i 0.121942 + 0.211210i 0.920534 0.390664i \(-0.127754\pi\)
−0.798591 + 0.601874i \(0.794421\pi\)
\(270\) 0 0
\(271\) −2.00000 + 3.46410i −0.121491 + 0.210429i −0.920356 0.391082i \(-0.872101\pi\)
0.798865 + 0.601511i \(0.205434\pi\)
\(272\) 8.00000 0.485071
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 7.50000 + 12.9904i 0.450631 + 0.780516i 0.998425 0.0560969i \(-0.0178656\pi\)
−0.547794 + 0.836613i \(0.684532\pi\)
\(278\) 7.00000 0.419832
\(279\) 0 0
\(280\) 2.50000 + 4.33013i 0.149404 + 0.258775i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 5.00000 8.66025i 0.297219 0.514799i −0.678280 0.734804i \(-0.737274\pi\)
0.975499 + 0.220005i \(0.0706075\pi\)
\(284\) 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 0
\(289\) −23.5000 + 40.7032i −1.38235 + 2.39431i
\(290\) −2.00000 3.46410i −0.117444 0.203419i
\(291\) 0 0
\(292\) 0 0
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) 6.00000 + 10.3923i 0.349334 + 0.605063i
\(296\) 3.50000 6.06218i 0.203433 0.352357i
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) −5.00000 −0.286770
\(305\) −1.00000 1.73205i −0.0572598 0.0991769i
\(306\) 0 0
\(307\) −6.00000 −0.342438 −0.171219 0.985233i \(-0.554771\pi\)
−0.171219 + 0.985233i \(0.554771\pi\)
\(308\) 7.50000 + 12.9904i 0.427352 + 0.740196i
\(309\) 0 0
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −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 0
\(319\) −6.00000 10.3923i −0.335936 0.581857i
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 10.0000 17.3205i 0.557278 0.965234i
\(323\) 20.0000 34.6410i 1.11283 1.92748i
\(324\) 0 0
\(325\) −2.50000 + 2.59808i −0.138675 + 0.144115i
\(326\) −20.0000 −1.10770
\(327\) 0 0
\(328\) 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 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) 4.00000 + 6.92820i 0.219529 + 0.380235i
\(333\) 0 0
\(334\) −11.5000 19.9186i −0.629252 1.08990i
\(335\) −4.00000 + 6.92820i −0.218543 + 0.378528i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 11.5000 + 6.06218i 0.625518 + 0.329739i
\(339\) 0 0
\(340\) −4.00000 + 6.92820i −0.216930 + 0.375735i
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 0 0
\(343\) −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 0.567363 0.823468i \(-0.307964\pi\)
−0.996826 + 0.0796169i \(0.974630\pi\)
\(348\) 0 0
\(349\) −4.00000 + 6.92820i −0.214115 + 0.370858i −0.952998 0.302975i \(-0.902020\pi\)
0.738883 + 0.673833i \(0.235353\pi\)
\(350\) −5.00000 −0.267261
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 8.00000 13.8564i 0.425797 0.737502i −0.570697 0.821160i \(-0.693327\pi\)
0.996495 + 0.0836583i \(0.0266604\pi\)
\(354\) 0 0
\(355\) 1.00000 + 1.73205i 0.0530745 + 0.0919277i
\(356\) 11.0000 0.582999
\(357\) 0 0
\(358\) 2.00000 + 3.46410i 0.105703 + 0.183083i
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 0 0
\(364\) 5.00000 + 17.3205i 0.262071 + 0.907841i
\(365\) 0 0
\(366\) 0 0
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 0 0
\(370\) 3.50000 + 6.06218i 0.181956 + 0.315158i
\(371\) −2.50000 4.33013i −0.129794 0.224809i
\(372\) 0 0
\(373\) −19.0000 32.9090i −0.983783 1.70396i −0.647225 0.762299i \(-0.724071\pi\)
−0.336557 0.941663i \(-0.609263\pi\)
\(374\) −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
\(378\) 0 0
\(379\) 12.5000 21.6506i 0.642082 1.11212i −0.342885 0.939377i \(-0.611404\pi\)
0.984967 0.172741i \(-0.0552624\pi\)
\(380\) 2.50000 4.33013i 0.128247 0.222131i
\(381\) 0 0
\(382\) −2.00000 −0.102329
\(383\) −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i \(-0.912926\pi\)
0.247451 0.968900i \(-0.420407\pi\)
\(384\) 0 0
\(385\) −15.0000 −0.764471
\(386\) −12.0000 20.7846i −0.610784 1.05791i
\(387\) 0 0
\(388\) 0 0
\(389\) 32.0000 1.62246 0.811232 0.584724i \(-0.198797\pi\)
0.811232 + 0.584724i \(0.198797\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) −9.00000 + 15.5885i −0.454569 + 0.787336i
\(393\) 0 0
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) −2.00000 −0.100631
\(396\) 0 0
\(397\) −12.5000 21.6506i −0.627357 1.08661i −0.988080 0.153941i \(-0.950803\pi\)
0.360723 0.932673i \(-0.382530\pi\)
\(398\) 22.0000 1.10276
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −9.50000 + 16.4545i −0.474407 + 0.821698i −0.999571 0.0293039i \(-0.990671\pi\)
0.525163 + 0.851002i \(0.324004\pi\)
\(402\) 0 0
\(403\) 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
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 3.00000 + 5.19615i 0.148159 + 0.256620i
\(411\) 0 0
\(412\) 3.50000 + 6.06218i 0.172433 + 0.298662i
\(413\) −30.0000 + 51.9615i −1.47620 + 2.55686i
\(414\) 0 0
\(415\) −8.00000 −0.392705
\(416\) 3.50000 + 0.866025i 0.171602 + 0.0424604i
\(417\) 0 0
\(418\) 7.50000 12.9904i 0.366837 0.635380i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 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
\(423\) 0 0
\(424\) −1.00000 −0.0485643
\(425\) −4.00000 6.92820i −0.194029 0.336067i
\(426\) 0 0
\(427\) 5.00000 8.66025i 0.241967 0.419099i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) −8.00000 13.8564i −0.384455 0.665896i 0.607238 0.794520i \(-0.292277\pi\)
−0.991693 + 0.128624i \(0.958944\pi\)
\(434\) 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 −0.960323 0.278889i \(-0.910034\pi\)
0.721686 + 0.692220i \(0.243367\pi\)
\(440\) −1.50000 + 2.59808i −0.0715097 + 0.123858i
\(441\) 0 0
\(442\) −20.0000 + 20.7846i −0.951303 + 0.988623i
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) −5.50000 + 9.52628i −0.260725 + 0.451589i
\(446\) 1.50000 + 2.59808i 0.0710271 + 0.123022i
\(447\) 0 0
\(448\) 2.50000 + 4.33013i 0.118114 + 0.204579i
\(449\) −13.5000 23.3827i −0.637104 1.10350i −0.986065 0.166360i \(-0.946799\pi\)
0.348961 0.937137i \(-0.386535\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 4.00000 6.92820i 0.188144 0.325875i
\(453\) 0 0
\(454\) 0 0
\(455\) −17.5000 4.33013i −0.820413 0.202999i
\(456\) 0 0
\(457\) −15.0000 + 25.9808i −0.701670 + 1.21533i 0.266209 + 0.963915i \(0.414229\pi\)
−0.967880 + 0.251414i \(0.919105\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) 4.00000 + 6.92820i 0.186299 + 0.322679i 0.944013 0.329907i \(-0.107017\pi\)
−0.757715 + 0.652586i \(0.773684\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −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 \(0.312606\pi\)
\(468\) 0 0
\(469\) −40.0000 −1.84703
\(470\) −1.50000 + 2.59808i −0.0691898 + 0.119840i
\(471\) 0 0
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) 18.0000 0.827641
\(474\) 0 0
\(475\) 2.50000 + 4.33013i 0.114708 + 0.198680i
\(476\) −40.0000 −1.83340
\(477\) 0 0
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) −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
\(481\) 7.00000 + 24.2487i 0.319173 + 1.10565i
\(482\) −25.0000 −1.13872
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) −18.5000 32.0429i −0.838315 1.45200i −0.891303 0.453409i \(-0.850208\pi\)
0.0529875 0.998595i \(-0.483126\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) 0 0
\(490\) −9.00000 15.5885i −0.406579 0.704215i
\(491\) 10.5000 18.1865i 0.473858 0.820747i −0.525694 0.850674i \(-0.676194\pi\)
0.999552 + 0.0299272i \(0.00952753\pi\)
\(492\) 0 0
\(493\) 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
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) −15.0000 −0.669483
\(503\) −5.50000 9.52628i −0.245233 0.424756i 0.716964 0.697110i \(-0.245531\pi\)
−0.962197 + 0.272354i \(0.912198\pi\)
\(504\) 0 0
\(505\) −4.00000 + 6.92820i −0.177998 + 0.308301i
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −21.0000 −0.931724
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 14.0000 + 24.2487i 0.617514 + 1.06956i
\(515\) −7.00000 −0.308457
\(516\) 0 0
\(517\) −4.50000 + 7.79423i −0.197910 + 0.342790i
\(518\) −17.5000 + 30.3109i −0.768906 + 1.33178i
\(519\) 0 0
\(520\) −2.50000 + 2.59808i −0.109632 + 0.113933i
\(521\) −5.00000 −0.219054 −0.109527 0.993984i \(-0.534934\pi\)
−0.109527 + 0.993984i \(0.534934\pi\)
\(522\) 0 0
\(523\) 5.00000 8.66025i 0.218635 0.378686i −0.735756 0.677247i \(-0.763173\pi\)
0.954391 + 0.298560i \(0.0965063\pi\)
\(524\) −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
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0.500000 0.866025i 0.0217186 0.0376177i
\(531\) 0 0
\(532\) 25.0000 1.08389
\(533\) 6.00000 + 20.7846i 0.259889 + 0.900281i
\(534\) 0 0
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 0 0
\(538\) −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
\(543\) 0 0
\(544\) −4.00000 + 6.92820i −0.171499 + 0.297044i
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) 6.00000 0.256541 0.128271 0.991739i \(-0.459057\pi\)
0.128271 + 0.991739i \(0.459057\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 0 0
\(550\) −1.50000 2.59808i −0.0639602 0.110782i
\(551\) −20.0000 −0.852029
\(552\) 0 0
\(553\) −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 −0.662240 0.749291i \(-0.730394\pi\)
0.980026 + 0.198871i \(0.0637276\pi\)
\(558\) 0 0
\(559\) 21.0000 + 5.19615i 0.888205 + 0.219774i
\(560\) −5.00000 −0.211289
\(561\) 0 0
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i \(0.107454\pi\)
−0.184950 + 0.982748i \(0.559212\pi\)
\(564\) 0 0
\(565\) 4.00000 + 6.92820i 0.168281 + 0.291472i
\(566\) 5.00000 + 8.66025i 0.210166 + 0.364018i
\(567\) 0 0
\(568\) 1.00000 + 1.73205i 0.0419591 + 0.0726752i
\(569\) −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i \(-0.935142\pi\)
0.664897 + 0.746935i \(0.268475\pi\)
\(570\) 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
\(573\) 0 0
\(574\) −15.0000 + 25.9808i −0.626088 + 1.08442i
\(575\) −2.00000 + 3.46410i −0.0834058 + 0.144463i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −23.5000 40.7032i −0.977471 1.69303i
\(579\) 0 0
\(580\) 4.00000 0.166091
\(581\) −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 −0.618322 0.785925i \(-0.712187\pi\)
0.989792 + 0.142520i \(0.0455206\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) −12.0000 −0.494032
\(591\) 0 0
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) −20.0000 −0.821302 −0.410651 0.911793i \(-0.634698\pi\)
−0.410651 + 0.911793i \(0.634698\pi\)
\(594\) 0 0
\(595\) 20.0000 34.6410i 0.819920 1.42014i
\(596\) −1.00000 + 1.73205i −0.0409616 + 0.0709476i
\(597\) 0 0
\(598\) 14.0000 + 3.46410i 0.572503 + 0.141658i
\(599\) −34.0000 −1.38920 −0.694601 0.719395i \(-0.744419\pi\)
−0.694601 + 0.719395i \(0.744419\pi\)
\(600\) 0 0
\(601\) −18.5000 + 32.0429i −0.754631 + 1.30706i 0.190927 + 0.981604i \(0.438851\pi\)
−0.945558 + 0.325455i \(0.894483\pi\)
\(602\) 15.0000 + 25.9808i 0.611354 + 1.05890i
\(603\) 0 0
\(604\) −11.0000 19.0526i −0.447584 0.775238i
\(605\) 1.00000 + 1.73205i 0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 14.5000 + 25.1147i 0.588537 + 1.01938i 0.994424 + 0.105453i \(0.0336291\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) −7.50000 + 7.79423i −0.303418 + 0.315321i
\(612\) 0 0
\(613\) −12.5000 + 21.6506i −0.504870 + 0.874461i 0.495114 + 0.868828i \(0.335126\pi\)
−0.999984 + 0.00563283i \(0.998207\pi\)
\(614\) 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 0.690021 0.723789i \(-0.257601\pi\)
−0.971830 + 0.235681i \(0.924268\pi\)
\(618\) 0 0
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 1.00000 + 1.73205i 0.0401610 + 0.0695608i
\(621\) 0 0
\(622\) −6.00000 + 10.3923i −0.240578 + 0.416693i
\(623\) −55.0000 −2.20353
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) 0 0
\(628\) −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 0.721530 0.692383i \(-0.243439\pi\)
−0.960386 + 0.278672i \(0.910106\pi\)
\(632\) −2.00000 −0.0795557
\(633\) 0 0
\(634\) −11.5000 + 19.9186i −0.456723 + 0.791068i
\(635\) 10.5000 18.1865i 0.416680 0.721711i
\(636\) 0 0
\(637\) −18.0000 62.3538i −0.713186 2.47055i
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i \(0.0123508\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(642\) 0 0
\(643\) 22.0000 + 38.1051i 0.867595 + 1.50272i 0.864447 + 0.502724i \(0.167669\pi\)
0.00314839 + 0.999995i \(0.498998\pi\)
\(644\) 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 −0.835033 0.550200i \(-0.814551\pi\)
0.894004 + 0.448059i \(0.147885\pi\)
\(648\) 0 0
\(649\) −36.0000 −1.41312
\(650\) −1.00000 3.46410i −0.0392232 0.135873i
\(651\) 0 0
\(652\) 10.0000 17.3205i 0.391630 0.678323i
\(653\) 13.5000 23.3827i 0.528296 0.915035i −0.471160 0.882048i \(-0.656165\pi\)
0.999456 0.0329874i \(-0.0105021\pi\)
\(654\) 0 0
\(655\) 19.0000 0.742391
\(656\) 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 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) −12.5000 + 21.6506i −0.484729 + 0.839576i
\(666\) 0 0
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) 23.0000 0.889897
\(669\) 0 0
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) 16.0000 27.7128i 0.616755 1.06825i −0.373319 0.927703i \(-0.621780\pi\)
0.990074 0.140548i \(-0.0448863\pi\)
\(674\) −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 \(0.361060\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.00000 6.92820i −0.153393 0.265684i
\(681\) 0 0
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) 15.0000 + 25.9808i 0.573959 + 0.994126i 0.996154 + 0.0876211i \(0.0279265\pi\)
−0.422195 + 0.906505i \(0.638740\pi\)
\(684\) 0 0
\(685\) −6.00000 10.3923i −0.229248 0.397070i
\(686\) 27.5000 47.6314i 1.04995 1.81858i
\(687\) 0 0
\(688\) 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 −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) 2.50000 4.33013i 0.0950357 0.164607i
\(693\) 0 0
\(694\) 16.0000 0.607352
\(695\) −3.50000 6.06218i −0.132763 0.229952i
\(696\) 0 0
\(697\) −48.0000 −1.81813
\(698\) −4.00000 6.92820i −0.151402 0.262236i
\(699\) 0 0
\(700\) 2.50000 4.33013i 0.0944911 0.163663i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) −16.0000 27.7128i −0.600893 1.04078i −0.992686 0.120723i \(-0.961479\pi\)
0.391794 0.920053i \(-0.371855\pi\)
\(710\) −2.00000 −0.0750587
\(711\) 0 0
\(712\) −5.50000 + 9.52628i −0.206121 + 0.357012i
\(713\) 4.00000 6.92820i 0.149801 0.259463i
\(714\) 0 0
\(715\) −3.00000 10.3923i −0.112194 0.388650i
\(716\) −4.00000 −0.149487
\(717\) 0 0
\(718\) −9.00000 + 15.5885i −0.335877 + 0.581756i
\(719\) −10.0000 17.3205i −0.372937 0.645946i 0.617079 0.786901i \(-0.288316\pi\)
−0.990016 + 0.140955i \(0.954983\pi\)
\(720\) 0 0
\(721\) −17.5000 30.3109i −0.651734 1.12884i
\(722\) −3.00000 5.19615i −0.111648 0.193381i
\(723\) 0 0
\(724\) 1.00000 + 1.73205i 0.0371647 + 0.0643712i
\(725\) −2.00000 + 3.46410i −0.0742781 + 0.128654i
\(726\) 0 0
\(727\) −11.0000 −0.407967 −0.203984 0.978974i \(-0.565389\pi\)
−0.203984 + 0.978974i \(0.565389\pi\)
\(728\) −17.5000 4.33013i −0.648593 0.160485i
\(729\) 0 0
\(730\) 0 0
\(731\) −24.0000 + 41.5692i −0.887672 + 1.53749i
\(732\) 0 0
\(733\) −43.0000 −1.58824 −0.794121 0.607760i \(-0.792068\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) 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
\(738\) 0 0
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) −7.00000 −0.257325
\(741\) 0 0
\(742\) 5.00000 0.183556
\(743\) −8.00000 + 13.8564i −0.293492 + 0.508342i −0.974633 0.223810i \(-0.928151\pi\)
0.681141 + 0.732152i \(0.261484\pi\)
\(744\) 0 0
\(745\) −1.00000 1.73205i −0.0366372 0.0634574i
\(746\) 38.0000 1.39128
\(747\) 0 0
\(748\) −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 −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 14.0000 + 3.46410i 0.509850 + 0.126155i
\(755\) 22.0000 0.800662
\(756\) 0 0
\(757\) −8.50000 + 14.7224i −0.308938 + 0.535096i −0.978130 0.207993i \(-0.933307\pi\)
0.669193 + 0.743089i \(0.266640\pi\)
\(758\) 12.5000 + 21.6506i 0.454020 + 0.786386i
\(759\) 0 0
\(760\) 2.50000 + 4.33013i 0.0906845 + 0.157070i
\(761\) 4.50000 + 7.79423i 0.163125 + 0.282541i 0.935988 0.352032i \(-0.114509\pi\)
−0.772863 + 0.634573i \(0.781176\pi\)
\(762\) 0 0
\(763\) 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
\(768\) 0 0
\(769\) 17.0000 29.4449i 0.613036 1.06181i −0.377690 0.925932i \(-0.623282\pi\)
0.990726 0.135877i \(-0.0433852\pi\)
\(770\) 7.50000 12.9904i 0.270281 0.468141i
\(771\) 0 0
\(772\) 24.0000 0.863779
\(773\) 0.500000 + 0.866025i 0.0179838 + 0.0311488i 0.874877 0.484345i \(-0.160942\pi\)
−0.856893 + 0.515494i \(0.827609\pi\)
\(774\) 0 0
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) −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
\(783\) 0 0
\(784\) −9.00000 15.5885i −0.321429 0.556731i
\(785\) 15.0000 0.535373
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) −3.00000 −0.106871
\(789\) 0 0
\(790\) 1.00000 1.73205i 0.0355784 0.0616236i