Properties

Label 2394.2.o.b.1261.1
Level $2394$
Weight $2$
Character 2394.1261
Analytic conductor $19.116$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.o (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1161862439\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 798)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2394.1261
Dual form 2394.2.o.b.505.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 4.33013i) q^{19} +3.00000 q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-1.50000 - 2.59808i) q^{35} +8.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-3.00000 + 5.19615i) q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{49} +4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-9.00000 - 15.5885i) q^{55} +1.00000 q^{56} -6.00000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(6.50000 - 11.2583i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +15.0000 q^{65} +(-7.00000 + 12.1244i) q^{67} +6.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-1.50000 - 2.59808i) q^{71} +(2.00000 + 3.46410i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(4.00000 + 1.73205i) q^{76} +6.00000 q^{77} +(-4.00000 - 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 - 5.19615i) q^{82} -15.0000 q^{83} +(-9.00000 + 15.5885i) q^{85} +(2.00000 - 3.46410i) q^{86} +6.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} -6.00000 q^{94} +(-10.5000 + 7.79423i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8} - 3 q^{10} + 12 q^{11} - 5 q^{13} - q^{14} - q^{16} - 6 q^{17} - q^{19} + 6 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25} + 10 q^{26} - q^{28} + 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 3 q^{35} + 16 q^{37} - 7 q^{38} - 3 q^{40} + 6 q^{41} + 4 q^{43} - 6 q^{44} + 6 q^{46} + 6 q^{47} + 2 q^{49} + 8 q^{50} - 5 q^{52} + 12 q^{53} - 18 q^{55} + 2 q^{56} - 12 q^{58} - 9 q^{59} + 13 q^{61} + 4 q^{62} + 2 q^{64} + 30 q^{65} - 14 q^{67} + 12 q^{68} - 3 q^{70} - 3 q^{71} + 4 q^{73} - 8 q^{74} + 8 q^{76} + 12 q^{77} - 8 q^{79} - 3 q^{80} + 6 q^{82} - 30 q^{83} - 18 q^{85} + 4 q^{86} + 12 q^{88} - 6 q^{89} - 5 q^{91} - 3 q^{92} - 12 q^{94} - 21 q^{95} - 8 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(1009\) \(1711\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −0.500000 4.33013i −0.114708 0.993399i
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 5.00000 0.980581
\(27\) 0 0
\(28\) −0.500000 + 0.866025i −0.0944911 + 0.163663i
\(29\) 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
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) −1.50000 2.59808i −0.253546 0.439155i
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −3.50000 + 2.59808i −0.567775 + 0.421464i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 0 0
\(55\) −9.00000 15.5885i −1.21356 2.10195i
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 15.0000 1.86052
\(66\) 0 0
\(67\) −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) −1.50000 + 2.59808i −0.179284 + 0.310530i
\(71\) −1.50000 2.59808i −0.178017 0.308335i 0.763184 0.646181i \(-0.223635\pi\)
−0.941201 + 0.337846i \(0.890302\pi\)
\(72\) 0 0
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) 0 0
\(76\) 4.00000 + 1.73205i 0.458831 + 0.198680i
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −1.50000 + 2.59808i −0.167705 + 0.290474i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −15.0000 −1.64646 −0.823232 0.567705i \(-0.807831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(84\) 0 0
\(85\) −9.00000 + 15.5885i −0.976187 + 1.69081i
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 0 0
\(88\) 6.00000 0.639602
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 0 0
\(91\) −2.50000 + 4.33013i −0.262071 + 0.453921i
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) −10.5000 + 7.79423i −1.07728 + 0.799671i
\(96\) 0 0
\(97\) −4.00000 6.92820i −0.406138 0.703452i 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) −0.500000 0.866025i −0.0505076 0.0874818i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −2.50000 + 4.33013i −0.245145 + 0.424604i
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 2.00000 + 3.46410i 0.191565 + 0.331801i 0.945769 0.324840i \(-0.105310\pi\)
−0.754204 + 0.656640i \(0.771977\pi\)
\(110\) −9.00000 + 15.5885i −0.858116 + 1.48630i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −21.0000 −1.97551 −0.987757 0.156001i \(-0.950140\pi\)
−0.987757 + 0.156001i \(0.950140\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) −4.50000 + 7.79423i −0.414259 + 0.717517i
\(119\) −3.00000 5.19615i −0.275010 0.476331i
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) −13.0000 −1.17696
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 6.50000 11.2583i 0.576782 0.999015i −0.419064 0.907957i \(-0.637642\pi\)
0.995846 0.0910585i \(-0.0290250\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −7.50000 12.9904i −0.657794 1.13933i
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) −0.500000 4.33013i −0.0433555 0.375470i
\(134\) 14.0000 1.20942
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 3.00000 0.253546
\(141\) 0 0
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) −15.0000 + 25.9808i −1.25436 + 2.17262i
\(144\) 0 0
\(145\) −18.0000 −1.49482
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) 0 0
\(148\) −4.00000 + 6.92820i −0.328798 + 0.569495i
\(149\) −12.0000 20.7846i −0.983078 1.70274i −0.650183 0.759778i \(-0.725308\pi\)
−0.332896 0.942964i \(-0.608026\pi\)
\(150\) 0 0
\(151\) −19.0000 −1.54620 −0.773099 0.634285i \(-0.781294\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) −0.500000 4.33013i −0.0405554 0.351220i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) 6.00000 + 10.3923i 0.481932 + 0.834730i
\(156\) 0 0
\(157\) −8.50000 14.7224i −0.678374 1.17498i −0.975470 0.220131i \(-0.929352\pi\)
0.297097 0.954847i \(-0.403982\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) −1.50000 + 2.59808i −0.118217 + 0.204757i
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 7.50000 + 12.9904i 0.582113 + 1.00825i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 18.0000 1.38054
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 7.50000 + 12.9904i 0.570214 + 0.987640i 0.996544 + 0.0830722i \(0.0264732\pi\)
−0.426329 + 0.904568i \(0.640193\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −2.50000 + 4.33013i −0.185824 + 0.321856i −0.943854 0.330364i \(-0.892829\pi\)
0.758030 + 0.652219i \(0.226162\pi\)
\(182\) 5.00000 0.370625
\(183\) 0 0
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) −12.0000 20.7846i −0.882258 1.52811i
\(186\) 0 0
\(187\) −18.0000 31.1769i −1.31629 2.27988i
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) 0 0
\(190\) 12.0000 + 5.19615i 0.870572 + 0.376969i
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i \(-0.548670\pi\)
0.932075 0.362267i \(-0.117997\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 3.00000 5.19615i 0.210559 0.364698i
\(204\) 0 0
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) −3.00000 25.9808i −0.207514 1.79713i
\(210\) 0 0
\(211\) 5.00000 + 8.66025i 0.344214 + 0.596196i 0.985211 0.171347i \(-0.0548120\pi\)
−0.640996 + 0.767544i \(0.721479\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) 0 0
\(215\) 6.00000 10.3923i 0.409197 0.708749i
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 2.00000 3.46410i 0.135457 0.234619i
\(219\) 0 0
\(220\) 18.0000 1.21356
\(221\) 30.0000 2.01802
\(222\) 0 0
\(223\) 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 10.5000 + 18.1865i 0.698450 + 1.20975i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) −4.50000 7.79423i −0.296721 0.513936i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −10.5000 18.1865i −0.687878 1.19144i −0.972523 0.232806i \(-0.925209\pi\)
0.284645 0.958633i \(-0.408124\pi\)
\(234\) 0 0
\(235\) −18.0000 −1.17419
\(236\) 9.00000 0.585850
\(237\) 0 0
\(238\) −3.00000 + 5.19615i −0.194461 + 0.336817i
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 0 0
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) −12.5000 21.6506i −0.803530 1.39176i
\(243\) 0 0
\(244\) 6.50000 + 11.2583i 0.416120 + 0.720741i
\(245\) −1.50000 2.59808i −0.0958315 0.165985i
\(246\) 0 0
\(247\) 20.0000 + 8.66025i 1.27257 + 0.551039i
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 1.50000 2.59808i 0.0946792 0.163989i −0.814795 0.579748i \(-0.803151\pi\)
0.909475 + 0.415759i \(0.136484\pi\)
\(252\) 0 0
\(253\) −9.00000 + 15.5885i −0.565825 + 0.980038i
\(254\) −13.0000 −0.815693
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) −7.50000 + 12.9904i −0.465130 + 0.805629i
\(261\) 0 0
\(262\) −7.50000 + 12.9904i −0.463352 + 0.802548i
\(263\) −7.50000 12.9904i −0.462470 0.801021i 0.536614 0.843828i \(-0.319703\pi\)
−0.999083 + 0.0428069i \(0.986370\pi\)
\(264\) 0 0
\(265\) −36.0000 −2.21146
\(266\) −3.50000 + 2.59808i −0.214599 + 0.159298i
\(267\) 0 0
\(268\) −7.00000 12.1244i −0.427593 0.740613i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) 3.00000 0.181237
\(275\) −12.0000 + 20.7846i −0.723627 + 1.25336i
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) −1.50000 2.59808i −0.0896421 0.155265i
\(281\) 3.00000 5.19615i 0.178965 0.309976i −0.762561 0.646916i \(-0.776058\pi\)
0.941526 + 0.336939i \(0.109392\pi\)
\(282\) 0 0
\(283\) 3.50000 + 6.06218i 0.208053 + 0.360359i 0.951101 0.308879i \(-0.0999539\pi\)
−0.743048 + 0.669238i \(0.766621\pi\)
\(284\) 3.00000 0.178017
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 3.00000 + 5.19615i 0.177084 + 0.306719i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 9.00000 + 15.5885i 0.528498 + 0.915386i
\(291\) 0 0
\(292\) −4.00000 −0.234082
\(293\) 27.0000 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(294\) 0 0
\(295\) −13.5000 + 23.3827i −0.786000 + 1.36139i
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) −12.0000 + 20.7846i −0.695141 + 1.20402i
\(299\) −7.50000 12.9904i −0.433736 0.751253i
\(300\) 0 0
\(301\) 2.00000 + 3.46410i 0.115278 + 0.199667i
\(302\) 9.50000 + 16.4545i 0.546664 + 0.946849i
\(303\) 0 0
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) −39.0000 −2.23313
\(306\) 0 0
\(307\) 12.5000 + 21.6506i 0.713413 + 1.23567i 0.963569 + 0.267461i \(0.0861848\pi\)
−0.250156 + 0.968206i \(0.580482\pi\)
\(308\) −3.00000 + 5.19615i −0.170941 + 0.296078i
\(309\) 0 0
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 8.00000 13.8564i 0.452187 0.783210i −0.546335 0.837567i \(-0.683977\pi\)
0.998522 + 0.0543564i \(0.0173107\pi\)
\(314\) −8.50000 + 14.7224i −0.479683 + 0.830835i
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) 3.00000 0.167183
\(323\) −21.0000 + 15.5885i −1.16847 + 0.867365i
\(324\) 0 0
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) −7.00000 12.1244i −0.387694 0.671506i
\(327\) 0 0
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 7.50000 12.9904i 0.411616 0.712940i
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 42.0000 2.29471
\(336\) 0 0
\(337\) −2.50000 4.33013i −0.136184 0.235877i 0.789865 0.613280i \(-0.210150\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 0 0
\(340\) −9.00000 15.5885i −0.488094 0.845403i
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 0 0
\(346\) 7.50000 12.9904i 0.403202 0.698367i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) −3.00000 + 5.19615i −0.159901 + 0.276956i
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 0 0
\(355\) −4.50000 + 7.79423i −0.238835 + 0.413675i
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) 0 0
\(358\) 3.00000 + 5.19615i 0.158555 + 0.274625i
\(359\) 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 0 0
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 5.00000 0.262794
\(363\) 0 0
\(364\) −2.50000 4.33013i −0.131036 0.226960i
\(365\) 6.00000 10.3923i 0.314054 0.543958i
\(366\) 0 0
\(367\) −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i \(0.404077\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) −12.0000 + 20.7846i −0.623850 + 1.08054i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) −16.0000 −0.828449 −0.414224 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) −18.0000 + 31.1769i −0.930758 + 1.61212i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 15.0000 + 25.9808i 0.772539 + 1.33808i
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −1.50000 12.9904i −0.0769484 0.666392i
\(381\) 0 0
\(382\) −7.50000 12.9904i −0.383733 0.664646i
\(383\) 3.00000 + 5.19615i 0.153293 + 0.265511i 0.932436 0.361335i \(-0.117679\pi\)
−0.779143 + 0.626846i \(0.784346\pi\)
\(384\) 0 0
\(385\) −9.00000 15.5885i −0.458682 0.794461i
\(386\) −2.50000 + 4.33013i −0.127247 + 0.220398i
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 0 0
\(395\) −12.0000 + 20.7846i −0.603786 + 1.04579i
\(396\) 0 0
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) −22.0000 −1.10276
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −3.00000 5.19615i −0.149256 0.258518i
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) 48.0000 2.37927
\(408\) 0 0
\(409\) 17.0000 29.4449i 0.840596 1.45595i −0.0487958 0.998809i \(-0.515538\pi\)
0.889392 0.457146i \(-0.151128\pi\)
\(410\) −18.0000 −0.888957
\(411\) 0 0
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) −4.50000 7.79423i −0.221431 0.383529i
\(414\) 0 0
\(415\) 22.5000 + 38.9711i 1.10448 + 1.91302i
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 0 0
\(418\) −21.0000 + 15.5885i −1.02714 + 0.762456i
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 5.00000 8.66025i 0.243396 0.421575i
\(423\) 0 0
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) 24.0000 1.16417
\(426\) 0 0
\(427\) 6.50000 11.2583i 0.314557 0.544829i
\(428\) 0 0
\(429\) 0 0
\(430\) −12.0000 −0.578691
\(431\) 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i \(-0.637159\pi\)
0.995706 0.0925683i \(-0.0295076\pi\)
\(432\) 0 0
\(433\) −4.00000 + 6.92820i −0.192228 + 0.332948i −0.945988 0.324201i \(-0.894905\pi\)
0.753760 + 0.657149i \(0.228238\pi\)
\(434\) 2.00000 + 3.46410i 0.0960031 + 0.166282i
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) 12.0000 + 5.19615i 0.574038 + 0.248566i
\(438\) 0 0
\(439\) 11.0000 + 19.0526i 0.525001 + 0.909329i 0.999576 + 0.0291138i \(0.00926853\pi\)
−0.474575 + 0.880215i \(0.657398\pi\)
\(440\) −9.00000 15.5885i −0.429058 0.743151i
\(441\) 0 0
\(442\) −15.0000 25.9808i −0.713477 1.23578i
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) 0 0
\(445\) 18.0000 0.853282
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 0 0
\(451\) 18.0000 + 31.1769i 0.847587 + 1.46806i
\(452\) 10.5000 18.1865i 0.493878 0.855423i
\(453\) 0 0
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 15.0000 0.703211
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −2.50000 4.33013i −0.116817 0.202334i
\(459\) 0 0
\(460\) −4.50000 + 7.79423i −0.209814 + 0.363408i
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −10.5000 + 18.1865i −0.486403 + 0.842475i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −7.00000 + 12.1244i −0.323230 + 0.559851i
\(470\) 9.00000 + 15.5885i 0.415139 + 0.719042i
\(471\) 0 0
\(472\) −4.50000 7.79423i −0.207129 0.358758i
\(473\) 12.0000 + 20.7846i 0.551761 + 0.955677i
\(474\) 0 0
\(475\) 16.0000 + 6.92820i 0.734130 + 0.317888i
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) −4.50000 7.79423i −0.205825 0.356500i
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 0 0
\(481\) −20.0000 + 34.6410i −0.911922 + 1.57949i
\(482\) 8.00000 0.364390
\(483\) 0 0
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) −12.0000 + 20.7846i −0.544892 + 0.943781i
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 6.50000 11.2583i 0.294241 0.509641i
\(489\) 0 0
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) −15.0000 25.9808i −0.676941 1.17250i −0.975898 0.218229i \(-0.929972\pi\)
0.298957 0.954267i \(-0.403361\pi\)
\(492\) 0 0
\(493\) −36.0000 −1.62136
\(494\) −2.50000 21.6506i −0.112480 0.974108i
\(495\) 0 0
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) −1.50000 2.59808i −0.0672842 0.116540i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) −3.00000 −0.133897
\(503\) 12.0000 20.7846i 0.535054 0.926740i −0.464107 0.885779i \(-0.653625\pi\)
0.999161 0.0409609i \(-0.0130419\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 18.0000 0.800198
\(507\) 0 0
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) 2.00000 + 3.46410i 0.0884748 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.00000 0.264649
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) 0 0
\(517\) 18.0000 31.1769i 0.791639 1.37116i
\(518\) −4.00000 6.92820i −0.175750 0.304408i
\(519\) 0 0
\(520\) 15.0000 0.657794
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 15.0000 0.655278
\(525\) 0 0
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) 12.0000 + 20.7846i 0.522728 + 0.905392i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 18.0000 + 31.1769i 0.781870 + 1.35424i
\(531\) 0 0
\(532\) 4.00000 + 1.73205i 0.173422 + 0.0750939i
\(533\) −30.0000 −1.29944
\(534\) 0 0
\(535\) 0 0
\(536\) −7.00000 + 12.1244i −0.302354 + 0.523692i
\(537\) 0 0
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) 6.00000 0.258438
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) −1.00000 + 1.73205i −0.0429537 + 0.0743980i
\(543\) 0 0
\(544\) 6.00000 0.257248
\(545\) 6.00000 10.3923i 0.257012 0.445157i
\(546\) 0 0
\(547\) 11.0000 19.0526i 0.470326 0.814629i −0.529098 0.848561i \(-0.677470\pi\)
0.999424 + 0.0339321i \(0.0108030\pi\)
\(548\) −1.50000 2.59808i −0.0640768 0.110984i
\(549\) 0 0
\(550\) 24.0000 1.02336
\(551\) −24.0000 10.3923i −1.02243 0.442727i
\(552\) 0 0
\(553\) −4.00000 6.92820i −0.170097 0.294617i
\(554\) 2.00000 + 3.46410i 0.0849719 + 0.147176i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) −1.50000 + 2.59808i −0.0633866 + 0.109789i
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) −15.0000 −0.632175 −0.316087 0.948730i \(-0.602369\pi\)
−0.316087 + 0.948730i \(0.602369\pi\)
\(564\) 0 0
\(565\) 31.5000 + 54.5596i 1.32521 + 2.29534i
\(566\) 3.50000 6.06218i 0.147116 0.254812i
\(567\) 0 0
\(568\) −1.50000 2.59808i −0.0629386 0.109013i
\(569\) 39.0000 1.63497 0.817483 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −15.0000 25.9808i −0.627182 1.08631i
\(573\) 0 0
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) −6.00000 10.3923i −0.250217 0.433389i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) 9.00000 15.5885i 0.373705 0.647275i
\(581\) −15.0000 −0.622305
\(582\) 0 0
\(583\) 36.0000 62.3538i 1.49097 2.58243i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −13.5000 23.3827i −0.557680 0.965930i
\(587\) 18.0000 + 31.1769i 0.742940 + 1.28681i 0.951151 + 0.308725i \(0.0999023\pi\)
−0.208212 + 0.978084i \(0.566764\pi\)
\(588\) 0 0
\(589\) 2.00000 + 17.3205i 0.0824086 + 0.713679i
\(590\) 27.0000 1.11157
\(591\) 0 0
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 9.00000 15.5885i 0.369586 0.640141i −0.619915 0.784669i \(-0.712833\pi\)
0.989501 + 0.144528i \(0.0461663\pi\)
\(594\) 0 0
\(595\) −9.00000 + 15.5885i −0.368964 + 0.639064i
\(596\) 24.0000 0.983078
\(597\) 0 0
\(598\) −7.50000 + 12.9904i −0.306698 + 0.531216i
\(599\) 4.50000 7.79423i 0.183865 0.318464i −0.759328 0.650708i \(-0.774472\pi\)
0.943193 + 0.332244i \(0.107806\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 2.00000 3.46410i 0.0815139 0.141186i
\(603\) 0 0
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) −37.5000 64.9519i −1.52459 2.64067i
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 4.00000 + 1.73205i 0.162221 + 0.0702439i
\(609\) 0 0
\(610\) 19.5000 + 33.7750i 0.789532 + 1.36751i
\(611\) 15.0000 + 25.9808i 0.606835 + 1.05107i
\(612\) 0 0
\(613\) 17.0000 + 29.4449i 0.686624 + 1.18927i 0.972924 + 0.231127i \(0.0742412\pi\)
−0.286300 + 0.958140i \(0.592425\pi\)
\(614\) 12.5000 21.6506i 0.504459 0.873749i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) −12.0000 −0.481932
\(621\) 0 0
\(622\) 0 0
\(623\) −3.00000 + 5.19615i −0.120192 + 0.208179i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) 17.0000 0.678374
\(629\) −24.0000 41.5692i −0.956943 1.65747i
\(630\) 0 0
\(631\) 20.0000 34.6410i 0.796187 1.37904i −0.125895 0.992044i \(-0.540180\pi\)
0.922082 0.386994i \(-0.126486\pi\)
\(632\) −4.00000 6.92820i −0.159111 0.275589i
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) −39.0000 −1.54767
\(636\) 0 0
\(637\) −2.50000 + 4.33013i −0.0990536 + 0.171566i
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 0 0
\(643\) −11.5000 19.9186i −0.453516 0.785512i 0.545086 0.838380i \(-0.316497\pi\)
−0.998602 + 0.0528680i \(0.983164\pi\)
\(644\) −1.50000 2.59808i −0.0591083 0.102379i
\(645\) 0 0
\(646\) 24.0000 + 10.3923i 0.944267 + 0.408880i
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 0 0
\(649\) −27.0000 46.7654i −1.05984 1.83570i
\(650\) −10.0000 + 17.3205i −0.392232 + 0.679366i
\(651\) 0 0
\(652\) −7.00000 + 12.1244i −0.274141 + 0.474826i
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 0 0
\(655\) −22.5000 + 38.9711i −0.879148 + 1.52273i
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 3.00000 5.19615i 0.116863 0.202413i −0.801660 0.597781i \(-0.796049\pi\)
0.918523 + 0.395367i \(0.129383\pi\)
\(660\) 0 0
\(661\) 24.5000 42.4352i 0.952940 1.65054i 0.213925 0.976850i \(-0.431375\pi\)
0.739014 0.673690i \(-0.235292\pi\)
\(662\) −4.00000 6.92820i −0.155464 0.269272i
\(663\) 0 0
\(664\) −15.0000 −0.582113
\(665\) −10.5000 + 7.79423i −0.407173 + 0.302247i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) −6.00000 10.3923i −0.232147 0.402090i
\(669\) 0 0
\(670\) −21.0000 36.3731i −0.811301 1.40521i
\(671\) 39.0000 67.5500i 1.50558 2.60774i
\(672\) 0 0
\(673\) −13.0000 −0.501113 −0.250557 0.968102i \(-0.580614\pi\)
−0.250557 + 0.968102i \(0.580614\pi\)
\(674\) −2.50000 + 4.33013i −0.0962964 + 0.166790i
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) 0 0
\(682\) 12.0000 + 20.7846i 0.459504 + 0.795884i
\(683\) 30.0000 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 30.0000 + 51.9615i 1.14291 + 1.97958i
\(690\) 0 0
\(691\) −13.0000 −0.494543 −0.247272 0.968946i \(-0.579534\pi\)
−0.247272 + 0.968946i \(0.579534\pi\)
\(692\) −15.0000 −0.570214
\(693\) 0 0
\(694\) 6.00000 10.3923i 0.227757 0.394486i
\(695\) −12.0000 −0.455186
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) 0 0
\(700\) −2.00000 3.46410i −0.0755929 0.130931i
\(701\) −6.00000 10.3923i −0.226617 0.392512i 0.730186 0.683248i \(-0.239433\pi\)
−0.956803 + 0.290736i \(0.906100\pi\)
\(702\) 0 0
\(703\) −4.00000 34.6410i −0.150863 1.30651i
\(704\) 6.00000 0.226134
\(705\) 0 0
\(706\) −6.00000 10.3923i −0.225813 0.391120i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) 0 0
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 9.00000 0.337764
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) 90.0000 3.36581
\(716\) 3.00000 5.19615i 0.112115 0.194189i
\(717\) 0 0
\(718\) 6.00000 10.3923i 0.223918 0.387837i
\(719\) −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) 0 0
\(724\) −2.50000 4.33013i −0.0929118 0.160928i
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) −10.0000 17.3205i −0.370879 0.642382i 0.618822 0.785532i \(-0.287610\pi\)
−0.989701 + 0.143149i \(0.954277\pi\)
\(728\) −2.50000 + 4.33013i −0.0926562 + 0.160485i
\(729\) 0 0
\(730\) −12.0000 −0.444140
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) −1.00000 −0.0369358 −0.0184679 0.999829i \(-0.505879\pi\)
−0.0184679 + 0.999829i \(0.505879\pi\)
\(734\) 26.0000 0.959678
\(735\) 0 0
\(736\) −1.50000 2.59808i −0.0552907 0.0957664i
\(737\) −42.0000 + 72.7461i −1.54709 + 2.67964i
\(738\) 0 0
\(739\) 17.0000 + 29.4449i 0.625355 + 1.08315i 0.988472 + 0.151403i \(0.0483792\pi\)
−0.363117 + 0.931744i \(0.618287\pi\)
\(740\) 24.0000 0.882258
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) 10.5000 + 18.1865i 0.385208 + 0.667199i 0.991798 0.127815i \(-0.0407965\pi\)
−0.606590 + 0.795015i \(0.707463\pi\)
\(744\) 0 0
\(745\) −36.0000 + 62.3538i −1.31894 + 2.28447i
\(746\) 8.00000 + 13.8564i 0.292901 + 0.507319i
\(747\) 0 0
\(748\) 36.0000 1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) 15.0000 25.9808i 0.546268 0.946164i
\(755\) 28.5000 + 49.3634i 1.03722 + 1.79652i
\(756\) 0 0
\(757\) 14.0000 + 24.2487i 0.508839 + 0.881334i 0.999948 + 0.0102362i \(0.00325836\pi\)
−0.491109 + 0.871098i \(0.663408\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) 0 0
\(760\) −10.5000 + 7.79423i −0.380875 + 0.282726i
\(761\) −24.0000 −0.869999 −0.435000 0.900431i \(-0.643252\pi\)
−0.435000 + 0.900431i \(0.643252\pi\)
\(762\) 0 0
\(763\) 2.00000 + 3.46410i 0.0724049 + 0.125409i
\(764\) −7.50000 + 12.9904i −0.271340 + 0.469975i
\(765\) 0 0
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) 45.0000 1.62486
\(768\) 0 0
\(769\) 20.0000 34.6410i 0.721218 1.24919i −0.239293 0.970947i \(-0.576916\pi\)
0.960512 0.278240i \(-0.0897509\pi\)
\(770\) −9.00000 + 15.5885i −0.324337 + 0.561769i
\(771\) 0 0
\(772\) 5.00000 0.179954
\(773\) 22.5000 38.9711i 0.809269 1.40169i −0.104102 0.994567i \(-0.533197\pi\)
0.913371 0.407128i \(-0.133470\pi\)
\(774\) 0 0
\(775\) 8.00000 13.8564i 0.287368 0.497737i
\(776\) −4.00000 6.92820i −0.143592 0.248708i
\(777\) 0 0
\(778\) 0 0
\(779\) 21.0000 15.5885i 0.752403 0.558514i
\(780\) 0 0
\(781\) −9.00000 15.5885i −0.322045 0.557799i
\(782\) −9.00000 15.5885i −0.321839 0.557442i
\(783\) 0 0
\(784\) −0.500000 0.866025i −0.0178571 0.0309295i
\(785\) −25.5000 + 44.1673i −0.910134 + 1.57640i
\(786\) 0 0
\(787\) 29.0000 1.03374 0.516869 0.856064i \(-0.327097\pi\)
0.516869 + 0.856064i \(0.327097\pi\)