Properties

Label 1710.2.l.c.1261.1
Level $1710$
Weight $2$
Character 1710.1261
Analytic conductor $13.654$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
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 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1261
Dual form 1710.2.l.c.1531.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(-3.00000 + 5.19615i) q^{13} +(2.50000 + 4.33013i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 4.33013i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +6.00000 q^{26} +(2.50000 - 4.33013i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{34} +(-2.50000 - 4.33013i) q^{35} +7.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-2.50000 - 4.33013i) q^{41} +(-3.00000 - 5.19615i) q^{43} +(0.500000 - 0.866025i) q^{44} -7.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +18.0000 q^{49} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(5.50000 - 9.52628i) q^{53} +(-0.500000 - 0.866025i) q^{55} -5.00000 q^{56} -6.00000 q^{58} +(-4.00000 - 6.92820i) q^{59} +(2.00000 - 3.46410i) q^{61} +1.00000 q^{64} -6.00000 q^{65} +(-6.00000 + 10.3923i) q^{67} -4.00000 q^{68} +(-2.50000 + 4.33013i) q^{70} +(1.00000 + 1.73205i) q^{71} +(1.00000 + 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(4.00000 + 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 - 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 + 4.33013i) q^{82} +10.0000 q^{83} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 + 5.19615i) q^{86} -1.00000 q^{88} +(6.50000 - 11.2583i) q^{89} +(15.0000 - 25.9808i) q^{91} +(3.50000 + 6.06218i) q^{92} +8.00000 q^{94} +(3.50000 - 2.59808i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + q^{5} - 10q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + q^{5} - 10q^{7} + 2q^{8} + q^{10} - 2q^{11} - 6q^{13} + 5q^{14} - q^{16} + 4q^{17} - q^{19} - 2q^{20} + q^{22} + 7q^{23} - q^{25} + 12q^{26} + 5q^{28} + 6q^{29} - q^{32} + 4q^{34} - 5q^{35} + 14q^{37} - 7q^{38} + q^{40} - 5q^{41} - 6q^{43} + q^{44} - 14q^{46} - 8q^{47} + 36q^{49} + 2q^{50} - 6q^{52} + 11q^{53} - q^{55} - 10q^{56} - 12q^{58} - 8q^{59} + 4q^{61} + 2q^{64} - 12q^{65} - 12q^{67} - 8q^{68} - 5q^{70} + 2q^{71} + 2q^{73} - 7q^{74} + 8q^{76} + 10q^{77} - 10q^{79} + q^{80} - 5q^{82} + 20q^{83} - 4q^{85} - 6q^{86} - 2q^{88} + 13q^{89} + 30q^{91} + 7q^{92} + 16q^{94} + 7q^{95} - 2q^{97} - 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i \(0.479500\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) 2.50000 + 4.33013i 0.668153 + 1.15728i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) −0.500000 4.33013i −0.114708 0.993399i
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 0.500000 + 0.866025i 0.106600 + 0.184637i
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 6.00000 1.17670
\(27\) 0 0
\(28\) 2.50000 4.33013i 0.472456 0.818317i
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 2.00000 3.46410i 0.342997 0.594089i
\(35\) −2.50000 4.33013i −0.422577 0.731925i
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) −3.50000 + 2.59808i −0.567775 + 0.421464i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 0 0
\(43\) −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i \(-0.317920\pi\)
−0.998828 + 0.0484030i \(0.984587\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −7.00000 −1.03209
\(47\) −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 0 0
\(49\) 18.0000 2.57143
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i \(-0.560736\pi\)
0.945134 0.326683i \(-0.105931\pi\)
\(54\) 0 0
\(55\) −0.500000 0.866025i −0.0674200 0.116775i
\(56\) −5.00000 −0.668153
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) −2.50000 + 4.33013i −0.298807 + 0.517549i
\(71\) 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
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 0 0
\(76\) 4.00000 + 1.73205i 0.458831 + 0.198680i
\(77\) 5.00000 0.569803
\(78\) 0 0
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 0 0
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) 0 0
\(85\) −2.00000 + 3.46410i −0.216930 + 0.375735i
\(86\) −3.00000 + 5.19615i −0.323498 + 0.560316i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 6.50000 11.2583i 0.688999 1.19338i −0.283164 0.959072i \(-0.591384\pi\)
0.972162 0.234309i \(-0.0752827\pi\)
\(90\) 0 0
\(91\) 15.0000 25.9808i 1.57243 2.72352i
\(92\) 3.50000 + 6.06218i 0.364900 + 0.632026i
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) 3.50000 2.59808i 0.359092 0.266557i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) −9.00000 15.5885i −0.909137 1.57467i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) 15.0000 1.47799 0.738997 0.673709i \(-0.235300\pi\)
0.738997 + 0.673709i \(0.235300\pi\)
\(104\) −3.00000 + 5.19615i −0.294174 + 0.509525i
\(105\) 0 0
\(106\) −11.0000 −1.06841
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 0 0
\(112\) 2.50000 + 4.33013i 0.236228 + 0.409159i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) 7.00000 0.652753
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) −4.00000 + 6.92820i −0.368230 + 0.637793i
\(119\) −10.0000 17.3205i −0.916698 1.58777i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −4.00000 −0.362143
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 2.50000 4.33013i 0.221839 0.384237i −0.733527 0.679660i \(-0.762127\pi\)
0.955366 + 0.295423i \(0.0954607\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 2.50000 + 21.6506i 0.216777 + 1.87735i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 5.00000 0.422577
\(141\) 0 0
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) 0 0
\(148\) −3.50000 + 6.06218i −0.287698 + 0.498308i
\(149\) −2.00000 3.46410i −0.163846 0.283790i 0.772399 0.635138i \(-0.219057\pi\)
−0.936245 + 0.351348i \(0.885723\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) −0.500000 4.33013i −0.0405554 0.351220i
\(153\) 0 0
\(154\) −2.50000 4.33013i −0.201456 0.348932i
\(155\) 0 0
\(156\) 0 0
\(157\) −4.50000 7.79423i −0.359139 0.622047i 0.628678 0.777666i \(-0.283596\pi\)
−0.987817 + 0.155618i \(0.950263\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) −17.5000 + 30.3109i −1.37919 + 2.38883i
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −5.00000 8.66025i −0.388075 0.672166i
\(167\) 10.5000 18.1865i 0.812514 1.40732i −0.0985846 0.995129i \(-0.531432\pi\)
0.911099 0.412188i \(-0.135235\pi\)
\(168\) 0 0
\(169\) −11.5000 19.9186i −0.884615 1.53220i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 6.00000 0.457496
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 0 0
\(175\) 2.50000 4.33013i 0.188982 0.327327i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 0 0
\(178\) −13.0000 −0.974391
\(179\) −7.00000 −0.523205 −0.261602 0.965176i \(-0.584251\pi\)
−0.261602 + 0.965176i \(0.584251\pi\)
\(180\) 0 0
\(181\) −9.00000 + 15.5885i −0.668965 + 1.15868i 0.309229 + 0.950988i \(0.399929\pi\)
−0.978194 + 0.207693i \(0.933404\pi\)
\(182\) −30.0000 −2.22375
\(183\) 0 0
\(184\) 3.50000 6.06218i 0.258023 0.446910i
\(185\) 3.50000 + 6.06218i 0.257325 + 0.445700i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) −4.00000 6.92820i −0.291730 0.505291i
\(189\) 0 0
\(190\) −4.00000 1.73205i −0.290191 0.125656i
\(191\) 14.0000 1.01300 0.506502 0.862239i \(-0.330938\pi\)
0.506502 + 0.862239i \(0.330938\pi\)
\(192\) 0 0
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 0 0
\(196\) −9.00000 + 15.5885i −0.642857 + 1.11346i
\(197\) −1.00000 −0.0712470 −0.0356235 0.999365i \(-0.511342\pi\)
−0.0356235 + 0.999365i \(0.511342\pi\)
\(198\) 0 0
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −2.00000 −0.140720
\(203\) −15.0000 + 25.9808i −1.05279 + 1.82349i
\(204\) 0 0
\(205\) 2.50000 4.33013i 0.174608 0.302429i
\(206\) −7.50000 12.9904i −0.522550 0.905083i
\(207\) 0 0
\(208\) 6.00000 0.416025
\(209\) 0.500000 + 4.33013i 0.0345857 + 0.299521i
\(210\) 0 0
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 5.50000 + 9.52628i 0.377742 + 0.654268i
\(213\) 0 0
\(214\) −2.00000 3.46410i −0.136717 0.236801i
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) 0 0
\(217\) 0 0
\(218\) 8.00000 13.8564i 0.541828 0.938474i
\(219\) 0 0
\(220\) 1.00000 0.0674200
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) 10.5000 + 18.1865i 0.703132 + 1.21786i 0.967361 + 0.253401i \(0.0815490\pi\)
−0.264229 + 0.964460i \(0.585118\pi\)
\(224\) 2.50000 4.33013i 0.167038 0.289319i
\(225\) 0 0
\(226\) 2.00000 + 3.46410i 0.133038 + 0.230429i
\(227\) −2.00000 −0.132745 −0.0663723 0.997795i \(-0.521143\pi\)
−0.0663723 + 0.997795i \(0.521143\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −3.50000 6.06218i −0.230783 0.399728i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) −10.0000 + 17.3205i −0.648204 + 1.12272i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i \(-0.517406\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) 0 0
\(244\) 2.00000 + 3.46410i 0.128037 + 0.221766i
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) 0 0
\(247\) 24.0000 + 10.3923i 1.52708 + 0.661247i
\(248\) 0 0
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 0 0
\(253\) −3.50000 + 6.06218i −0.220043 + 0.381126i
\(254\) −5.00000 −0.313728
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 0 0
\(259\) −35.0000 −2.17479
\(260\) 3.00000 5.19615i 0.186052 0.322252i
\(261\) 0 0
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) 10.5000 + 18.1865i 0.647458 + 1.12143i 0.983728 + 0.179664i \(0.0575011\pi\)
−0.336270 + 0.941766i \(0.609166\pi\)
\(264\) 0 0
\(265\) 11.0000 0.675725
\(266\) 17.5000 12.9904i 1.07299 0.796491i
\(267\) 0 0
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) 16.0000 + 27.7128i 0.975537 + 1.68968i 0.678151 + 0.734923i \(0.262782\pi\)
0.297386 + 0.954757i \(0.403885\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 2.00000 3.46410i 0.121268 0.210042i
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 0 0
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) −16.0000 −0.959616
\(279\) 0 0
\(280\) −2.50000 4.33013i −0.149404 0.258775i
\(281\) −5.50000 + 9.52628i −0.328102 + 0.568290i −0.982135 0.188176i \(-0.939742\pi\)
0.654033 + 0.756466i \(0.273076\pi\)
\(282\) 0 0
\(283\) −11.0000 19.0526i −0.653882 1.13256i −0.982173 0.187980i \(-0.939806\pi\)
0.328291 0.944577i \(-0.393527\pi\)
\(284\) −2.00000 −0.118678
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 12.5000 + 21.6506i 0.737852 + 1.27800i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 0 0
\(292\) −2.00000 −0.117041
\(293\) −5.00000 −0.292103 −0.146052 0.989277i \(-0.546657\pi\)
−0.146052 + 0.989277i \(0.546657\pi\)
\(294\) 0 0
\(295\) 4.00000 6.92820i 0.232889 0.403376i
\(296\) 7.00000 0.406867
\(297\) 0 0
\(298\) −2.00000 + 3.46410i −0.115857 + 0.200670i
\(299\) 21.0000 + 36.3731i 1.21446 + 2.10351i
\(300\) 0 0
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) 10.0000 + 17.3205i 0.575435 + 0.996683i
\(303\) 0 0
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) 4.00000 0.229039
\(306\) 0 0
\(307\) −9.00000 15.5885i −0.513657 0.889680i −0.999875 0.0158424i \(-0.994957\pi\)
0.486217 0.873838i \(-0.338376\pi\)
\(308\) −2.50000 + 4.33013i −0.142451 + 0.246732i
\(309\) 0 0
\(310\) 0 0
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 0 0
\(313\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) −4.50000 + 7.79423i −0.253950 + 0.439854i
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) 0 0
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 35.0000 1.95047
\(323\) 14.0000 10.3923i 0.778981 0.578243i
\(324\) 0 0
\(325\) −3.00000 5.19615i −0.166410 0.288231i
\(326\) 5.00000 + 8.66025i 0.276924 + 0.479647i
\(327\) 0 0
\(328\) −2.50000 4.33013i −0.138039 0.239091i
\(329\) 20.0000 34.6410i 1.10264 1.90982i
\(330\) 0 0
\(331\) 15.0000 0.824475 0.412237 0.911077i \(-0.364747\pi\)
0.412237 + 0.911077i \(0.364747\pi\)
\(332\) −5.00000 + 8.66025i −0.274411 + 0.475293i
\(333\) 0 0
\(334\) −21.0000 −1.14907
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) −11.5000 + 19.9186i −0.625518 + 1.08343i
\(339\) 0 0
\(340\) −2.00000 3.46410i −0.108465 0.187867i
\(341\) 0 0
\(342\) 0 0
\(343\) −55.0000 −2.96972
\(344\) −3.00000 5.19615i −0.161749 0.280158i
\(345\) 0 0
\(346\) −4.50000 + 7.79423i −0.241921 + 0.419020i
\(347\) −1.00000 1.73205i −0.0536828 0.0929814i 0.837935 0.545770i \(-0.183763\pi\)
−0.891618 + 0.452788i \(0.850429\pi\)
\(348\) 0 0
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) −5.00000 −0.267261
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −36.0000 −1.91609 −0.958043 0.286623i \(-0.907467\pi\)
−0.958043 + 0.286623i \(0.907467\pi\)
\(354\) 0 0
\(355\) −1.00000 + 1.73205i −0.0530745 + 0.0919277i
\(356\) 6.50000 + 11.2583i 0.344499 + 0.596690i
\(357\) 0 0
\(358\) 3.50000 + 6.06218i 0.184981 + 0.320396i
\(359\) −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) 0 0
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 18.0000 0.946059
\(363\) 0 0
\(364\) 15.0000 + 25.9808i 0.786214 + 1.36176i
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) −7.00000 −0.364900
\(369\) 0 0
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) −27.5000 + 47.6314i −1.42773 + 2.47290i
\(372\) 0 0
\(373\) 5.00000 0.258890 0.129445 0.991587i \(-0.458680\pi\)
0.129445 + 0.991587i \(0.458680\pi\)
\(374\) −2.00000 + 3.46410i −0.103418 + 0.179124i
\(375\) 0 0
\(376\) −4.00000 + 6.92820i −0.206284 + 0.357295i
\(377\) 18.0000 + 31.1769i 0.927047 + 1.60569i
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0.500000 + 4.33013i 0.0256495 + 0.222131i
\(381\) 0 0
\(382\) −7.00000 12.1244i −0.358151 0.620336i
\(383\) 16.0000 + 27.7128i 0.817562 + 1.41606i 0.907474 + 0.420109i \(0.138008\pi\)
−0.0899119 + 0.995950i \(0.528659\pi\)
\(384\) 0 0
\(385\) 2.50000 + 4.33013i 0.127412 + 0.220684i
\(386\) 2.00000 3.46410i 0.101797 0.176318i
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) 0 0
\(391\) 28.0000 1.41602
\(392\) 18.0000 0.909137
\(393\) 0 0
\(394\) 0.500000 + 0.866025i 0.0251896 + 0.0436297i
\(395\) 5.00000 8.66025i 0.251577 0.435745i
\(396\) 0 0
\(397\) 16.5000 + 28.5788i 0.828111 + 1.43433i 0.899518 + 0.436884i \(0.143918\pi\)
−0.0714068 + 0.997447i \(0.522749\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 + 1.73205i 0.0497519 + 0.0861727i
\(405\) 0 0
\(406\) 30.0000 1.48888
\(407\) −7.00000 −0.346977
\(408\) 0 0
\(409\) 1.50000 2.59808i 0.0741702 0.128467i −0.826555 0.562856i \(-0.809703\pi\)
0.900725 + 0.434389i \(0.143036\pi\)
\(410\) −5.00000 −0.246932
\(411\) 0 0
\(412\) −7.50000 + 12.9904i −0.369498 + 0.639990i
\(413\) 20.0000 + 34.6410i 0.984136 + 1.70457i
\(414\) 0 0
\(415\) 5.00000 + 8.66025i 0.245440 + 0.425115i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 0 0
\(418\) 3.50000 2.59808i 0.171191 0.127076i
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) 4.00000 + 6.92820i 0.194948 + 0.337660i 0.946883 0.321577i \(-0.104213\pi\)
−0.751935 + 0.659237i \(0.770879\pi\)
\(422\) −6.50000 + 11.2583i −0.316415 + 0.548047i
\(423\) 0 0
\(424\) 5.50000 9.52628i 0.267104 0.462637i
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) −10.0000 + 17.3205i −0.483934 + 0.838198i
\(428\) −2.00000 + 3.46410i −0.0966736 + 0.167444i
\(429\) 0 0
\(430\) −6.00000 −0.289346
\(431\) −2.00000 + 3.46410i −0.0963366 + 0.166860i −0.910166 0.414244i \(-0.864046\pi\)
0.813829 + 0.581104i \(0.197379\pi\)
\(432\) 0 0
\(433\) −3.00000 + 5.19615i −0.144171 + 0.249711i −0.929063 0.369921i \(-0.879385\pi\)
0.784892 + 0.619632i \(0.212718\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −28.0000 12.1244i −1.33942 0.579987i
\(438\) 0 0
\(439\) 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i \(0.109922\pi\)
−0.177325 + 0.984152i \(0.556744\pi\)
\(440\) −0.500000 0.866025i −0.0238366 0.0412861i
\(441\) 0 0
\(442\) 12.0000 + 20.7846i 0.570782 + 0.988623i
\(443\) 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i \(-0.640223\pi\)
0.996551 0.0829786i \(-0.0264433\pi\)
\(444\) 0 0
\(445\) 13.0000 0.616259
\(446\) 10.5000 18.1865i 0.497189 0.861157i
\(447\) 0 0
\(448\) −5.00000 −0.236228
\(449\) 39.0000 1.84052 0.920262 0.391303i \(-0.127976\pi\)
0.920262 + 0.391303i \(0.127976\pi\)
\(450\) 0 0
\(451\) 2.50000 + 4.33013i 0.117720 + 0.203898i
\(452\) 2.00000 3.46410i 0.0940721 0.162938i
\(453\) 0 0
\(454\) 1.00000 + 1.73205i 0.0469323 + 0.0812892i
\(455\) 30.0000 1.40642
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −5.00000 8.66025i −0.233635 0.404667i
\(459\) 0 0
\(460\) −3.50000 + 6.06218i −0.163188 + 0.282650i
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) 0 0
\(463\) −9.00000 −0.418265 −0.209133 0.977887i \(-0.567064\pi\)
−0.209133 + 0.977887i \(0.567064\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) −38.0000 −1.75843 −0.879215 0.476425i \(-0.841932\pi\)
−0.879215 + 0.476425i \(0.841932\pi\)
\(468\) 0 0
\(469\) 30.0000 51.9615i 1.38527 2.39936i
\(470\) 4.00000 + 6.92820i 0.184506 + 0.319574i
\(471\) 0 0
\(472\) −4.00000 6.92820i −0.184115 0.318896i
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 0 0
\(475\) 4.00000 + 1.73205i 0.183533 + 0.0794719i
\(476\) 20.0000 0.916698
\(477\) 0 0
\(478\) 0 0
\(479\) 21.0000 36.3731i 0.959514 1.66193i 0.235833 0.971794i \(-0.424218\pi\)
0.723681 0.690134i \(-0.242449\pi\)
\(480\) 0 0
\(481\) −21.0000 + 36.3731i −0.957518 + 1.65847i
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) −13.0000 −0.589086 −0.294543 0.955638i \(-0.595167\pi\)
−0.294543 + 0.955638i \(0.595167\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 0 0
\(490\) 9.00000 15.5885i 0.406579 0.704215i
\(491\) −16.5000 28.5788i −0.744635 1.28974i −0.950365 0.311136i \(-0.899290\pi\)
0.205731 0.978609i \(-0.434043\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) −3.00000 25.9808i −0.134976 1.16893i
\(495\) 0 0
\(496\) 0 0
\(497\) −5.00000 8.66025i −0.224281 0.388465i
\(498\) 0 0
\(499\) 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i \(-0.116587\pi\)
−0.776989 + 0.629515i \(0.783254\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) 0.500000 0.866025i 0.0222939 0.0386142i −0.854663 0.519183i \(-0.826236\pi\)
0.876957 + 0.480569i \(0.159570\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 7.00000 0.311188
\(507\) 0 0
\(508\) 2.50000 + 4.33013i 0.110920 + 0.192118i
\(509\) 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i \(-0.819220\pi\)
0.887336 + 0.461123i \(0.152553\pi\)
\(510\) 0 0
\(511\) −5.00000 8.66025i −0.221187 0.383107i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) 7.50000 + 12.9904i 0.330489 + 0.572425i
\(516\) 0 0
\(517\) 4.00000 6.92820i 0.175920 0.304702i
\(518\) 17.5000 + 30.3109i 0.768906 + 1.33178i
\(519\) 0 0
\(520\) −6.00000 −0.263117
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 0 0
\(523\) 7.00000 12.1244i 0.306089 0.530161i −0.671414 0.741082i \(-0.734313\pi\)
0.977503 + 0.210921i \(0.0676463\pi\)
\(524\) 3.00000 0.131056
\(525\) 0 0
\(526\) 10.5000 18.1865i 0.457822 0.792971i
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) −5.50000 9.52628i −0.238905 0.413795i
\(531\) 0 0
\(532\) −20.0000 8.66025i −0.867110 0.375470i
\(533\) 30.0000 1.29944
\(534\) 0 0
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) −6.00000 + 10.3923i −0.259161 + 0.448879i
\(537\) 0 0
\(538\) 16.0000 27.7128i 0.689809 1.19478i
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) −8.00000 + 13.8564i −0.342682 + 0.593543i
\(546\) 0 0
\(547\) −7.00000 + 12.1244i −0.299298 + 0.518400i −0.975976 0.217880i \(-0.930086\pi\)
0.676677 + 0.736280i \(0.263419\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 0 0
\(550\) −1.00000 −0.0426401
\(551\) −24.0000 10.3923i −1.02243 0.442727i
\(552\) 0 0
\(553\) 25.0000 + 43.3013i 1.06311 + 1.84136i
\(554\) 7.00000 + 12.1244i 0.297402 + 0.515115i
\(555\) 0 0
\(556\) 8.00000 + 13.8564i 0.339276 + 0.587643i
\(557\) 0.500000 0.866025i 0.0211857 0.0366947i −0.855238 0.518235i \(-0.826589\pi\)
0.876424 + 0.481540i \(0.159923\pi\)
\(558\) 0 0
\(559\) 36.0000 1.52264
\(560\) −2.50000 + 4.33013i −0.105644 + 0.182981i
\(561\) 0 0
\(562\) 11.0000 0.464007
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) −11.0000 + 19.0526i −0.462364 + 0.800839i
\(567\) 0 0
\(568\) 1.00000 + 1.73205i 0.0419591 + 0.0726752i
\(569\) −33.0000 −1.38343 −0.691716 0.722170i \(-0.743145\pi\)
−0.691716 + 0.722170i \(0.743145\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) 12.5000 21.6506i 0.521740 0.903680i
\(575\) 3.50000 + 6.06218i 0.145960 + 0.252810i
\(576\) 0 0
\(577\) −32.0000 −1.33218 −0.666089 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 0 0
\(580\) −3.00000 + 5.19615i −0.124568 + 0.215758i
\(581\) −50.0000 −2.07435
\(582\) 0 0
\(583\) −5.50000 + 9.52628i −0.227787 + 0.394538i
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 2.50000 + 4.33013i 0.103274 + 0.178876i
\(587\) −10.0000 17.3205i −0.412744 0.714894i 0.582445 0.812870i \(-0.302096\pi\)
−0.995189 + 0.0979766i \(0.968763\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −8.00000 −0.329355
\(591\) 0 0
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) 11.0000 19.0526i 0.451716 0.782395i −0.546777 0.837278i \(-0.684145\pi\)
0.998493 + 0.0548835i \(0.0174787\pi\)
\(594\) 0 0
\(595\) 10.0000 17.3205i 0.409960 0.710072i
\(596\) 4.00000 0.163846
\(597\) 0 0
\(598\) 21.0000 36.3731i 0.858754 1.48741i
\(599\) 4.00000 6.92820i 0.163436 0.283079i −0.772663 0.634816i \(-0.781076\pi\)
0.936099 + 0.351738i \(0.114409\pi\)
\(600\) 0 0
\(601\) −3.00000 −0.122373 −0.0611863 0.998126i \(-0.519488\pi\)
−0.0611863 + 0.998126i \(0.519488\pi\)
\(602\) 15.0000 25.9808i 0.611354 1.05890i
\(603\) 0 0
\(604\) 10.0000 17.3205i 0.406894 0.704761i
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 0 0
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) 4.00000 + 1.73205i 0.162221 + 0.0702439i
\(609\) 0 0
\(610\) −2.00000 3.46410i −0.0809776 0.140257i
\(611\) −24.0000 41.5692i −0.970936 1.68171i
\(612\) 0 0
\(613\) −17.5000 30.3109i −0.706818 1.22425i −0.966031 0.258425i \(-0.916796\pi\)
0.259213 0.965820i \(-0.416537\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) 24.0000 41.5692i 0.966204 1.67351i 0.259858 0.965647i \(-0.416324\pi\)
0.706346 0.707867i \(-0.250342\pi\)
\(618\) 0 0
\(619\) 43.0000 1.72832 0.864158 0.503221i \(-0.167852\pi\)
0.864158 + 0.503221i \(0.167852\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −10.0000 17.3205i −0.400963 0.694489i
\(623\) −32.5000 + 56.2917i −1.30209 + 2.25528i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 9.00000 0.359139
\(629\) 14.0000 + 24.2487i 0.558217 + 0.966859i
\(630\) 0 0
\(631\) −19.0000 + 32.9090i −0.756378 + 1.31009i 0.188308 + 0.982110i \(0.439700\pi\)
−0.944686 + 0.327975i \(0.893634\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) 0 0
\(634\) −3.00000 −0.119145
\(635\) 5.00000 0.198419
\(636\) 0 0
\(637\) −54.0000 + 93.5307i −2.13956 + 3.70582i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) 0 0
\(643\) 22.0000 + 38.1051i 0.867595 + 1.50272i 0.864447 + 0.502724i \(0.167669\pi\)
0.00314839 + 0.999995i \(0.498998\pi\)
\(644\) −17.5000 30.3109i −0.689597 1.19442i
\(645\) 0 0
\(646\) −16.0000 6.92820i −0.629512 0.272587i
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 0 0
\(649\) 4.00000 + 6.92820i 0.157014 + 0.271956i
\(650\) −3.00000 + 5.19615i −0.117670 + 0.203810i
\(651\) 0 0
\(652\) 5.00000 8.66025i 0.195815 0.339162i
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) 0 0
\(658\) −40.0000 −1.55936
\(659\) −5.50000 + 9.52628i −0.214250 + 0.371091i −0.953040 0.302844i \(-0.902064\pi\)
0.738791 + 0.673935i \(0.235397\pi\)
\(660\) 0 0
\(661\) 10.0000 17.3205i 0.388955 0.673690i −0.603354 0.797473i \(-0.706170\pi\)
0.992309 + 0.123784i \(0.0395028\pi\)
\(662\) −7.50000 12.9904i −0.291496 0.504885i
\(663\) 0 0
\(664\) 10.0000 0.388075
\(665\) −17.5000 + 12.9904i −0.678621 + 0.503745i
\(666\) 0 0
\(667\) −21.0000 36.3731i −0.813123 1.40837i
\(668\) 10.5000 + 18.1865i 0.406257 + 0.703658i
\(669\) 0 0
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) −2.00000 + 3.46410i −0.0772091 + 0.133730i
\(672\) 0 0
\(673\) −40.0000 −1.54189 −0.770943 0.636904i \(-0.780215\pi\)
−0.770943 + 0.636904i \(0.780215\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) −21.0000 −0.807096 −0.403548 0.914959i \(-0.632223\pi\)
−0.403548 + 0.914959i \(0.632223\pi\)
\(678\) 0 0
\(679\) 5.00000 + 8.66025i 0.191882 + 0.332350i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 27.5000 + 47.6314i 1.04995 + 1.81858i
\(687\) 0 0
\(688\) −3.00000 + 5.19615i −0.114374 + 0.198101i
\(689\) 33.0000 + 57.1577i 1.25720 + 2.17753i
\(690\) 0 0
\(691\) 1.00000 0.0380418 0.0190209 0.999819i \(-0.493945\pi\)
0.0190209 + 0.999819i \(0.493945\pi\)
\(692\) 9.00000 0.342129
\(693\) 0 0
\(694\) −1.00000 + 1.73205i −0.0379595 + 0.0657477i
\(695\) 16.0000 0.606915
\(696\) 0 0
\(697\) 10.0000 17.3205i 0.378777 0.656061i
\(698\) −8.00000 13.8564i −0.302804 0.524473i
\(699\) 0 0
\(700\) 2.50000 + 4.33013i 0.0944911 + 0.163663i
\(701\) 17.0000 + 29.4449i 0.642081 + 1.11212i 0.984967 + 0.172740i \(0.0552621\pi\)
−0.342886 + 0.939377i \(0.611405\pi\)
\(702\) 0 0
\(703\) −3.50000 30.3109i −0.132005 1.14320i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 18.0000 + 31.1769i 0.677439 + 1.17336i
\(707\) −5.00000 + 8.66025i −0.188044 + 0.325702i
\(708\) 0 0
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 2.00000 0.0750587
\(711\) 0 0
\(712\) 6.50000 11.2583i 0.243598 0.421924i
\(713\) 0 0
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) 3.50000 6.06218i 0.130801 0.226554i
\(717\) 0 0
\(718\) −9.00000 + 15.5885i −0.335877 + 0.581756i
\(719\) −22.0000 38.1051i −0.820462 1.42108i −0.905339 0.424690i \(-0.860383\pi\)
0.0848774 0.996391i \(-0.472950\pi\)
\(720\) 0 0
\(721\) −75.0000 −2.79315
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) 0 0
\(724\) −9.00000 15.5885i −0.334482 0.579340i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 0 0
\(727\) −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i \(-0.964449\pi\)
0.400362 0.916357i \(-0.368884\pi\)
\(728\) 15.0000 25.9808i 0.555937 0.962911i
\(729\) 0 0
\(730\) 2.00000 0.0740233
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) 3.50000 + 6.06218i 0.129012 + 0.223455i
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i \(0.165674\pi\)
−0.00311943 + 0.999995i \(0.500993\pi\)
\(740\) −7.00000 −0.257325
\(741\) 0 0
\(742\) 55.0000 2.01911
\(743\) 7.50000 + 12.9904i 0.275148 + 0.476571i 0.970173 0.242415i \(-0.0779397\pi\)
−0.695024 + 0.718986i \(0.744606\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) −2.50000 4.33013i −0.0915315 0.158537i
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) −20.0000 −0.730784
\(750\) 0 0
\(751\) −20.0000 + 34.6410i −0.729810 + 1.26407i 0.227153 + 0.973859i \(0.427058\pi\)
−0.956963 + 0.290209i \(0.906275\pi\)
\(752\) 8.00000 0.291730
\(753\) 0 0
\(754\) 18.0000 31.1769i 0.655521 1.13540i
\(755\) −10.0000 17.3205i −0.363937 0.630358i
\(756\) 0 0
\(757\) 6.50000 + 11.2583i 0.236247 + 0.409191i 0.959634 0.281251i \(-0.0907494\pi\)
−0.723388 + 0.690442i \(0.757416\pi\)
\(758\) 2.00000 + 3.46410i 0.0726433 + 0.125822i
\(759\) 0 0
\(760\) 3.50000 2.59808i 0.126958 0.0942421i
\(761\) 31.0000 1.12375 0.561875 0.827222i \(-0.310080\pi\)
0.561875 + 0.827222i \(0.310080\pi\)
\(762\) 0 0
\(763\) −40.0000 69.2820i −1.44810 2.50818i
\(764\) −7.00000 + 12.1244i −0.253251 + 0.438644i
\(765\) 0 0
\(766\) 16.0000 27.7128i 0.578103 1.00130i
\(767\) 48.0000 1.73318
\(768\) 0 0
\(769\) −3.00000 + 5.19615i −0.108183 + 0.187378i −0.915034 0.403376i \(-0.867837\pi\)
0.806851 + 0.590755i \(0.201170\pi\)
\(770\) 2.50000 4.33013i 0.0900937 0.156047i
\(771\) 0 0
\(772\) −4.00000 −0.143963
\(773\) −10.5000 + 18.1865i −0.377659 + 0.654124i −0.990721 0.135910i \(-0.956604\pi\)
0.613062 + 0.790034i \(0.289937\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 0 0
\(778\) 10.0000 0.358517
\(779\) −17.5000 + 12.9904i −0.627003 + 0.465429i
\(780\) 0 0
\(781\) −1.00000 1.73205i −0.0357828 0.0619777i
\(782\) −14.0000 24.2487i −0.500639 0.867132i
\(783\) 0 0
\(784\) −9.00000 15.5885i −0.321429 0.556731i
\(785\) 4.50000 7.79423i 0.160612 0.278188i
\(786\) 0 0
\(787\) −26.0000 −0.926800 −0.463400 0.886149i \(-0.653371\pi\)
−0.463400 + 0.886149i \(0.653371\pi\)
\(788\) 0.500000 0.866025i 0.0178118 0.0308509i
\(789\) 0 0
\(790\) −10.0000