Properties

Label 1134.2.e.l.919.1
Level $1134$
Weight $2$
Character 1134.919
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 919.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.919
Dual form 1134.2.e.l.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(-2.50000 + 0.866025i) q^{14} +1.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(2.00000 + 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 0.866025i) q^{28} +(2.50000 + 4.33013i) q^{29} +3.00000 q^{31} +1.00000 q^{32} +(2.00000 + 3.46410i) q^{34} +(2.00000 + 1.73205i) q^{35} +(2.00000 - 3.46410i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} -6.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{50} +(4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} -11.0000 q^{59} -6.00000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +(2.00000 + 3.46410i) q^{68} +(2.00000 + 1.73205i) q^{70} +2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(2.50000 - 12.9904i) q^{77} +3.00000 q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.50000 + 6.06218i) q^{83} +(2.00000 - 3.46410i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.00000 + 3.46410i) q^{92} -6.00000 q^{94} +8.00000 q^{95} +(-3.50000 - 6.06218i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{4} - q^{5} - 5q^{7} + 2q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{4} - q^{5} - 5q^{7} + 2q^{8} - q^{10} - 5q^{11} - 5q^{14} + 2q^{16} + 4q^{17} - 8q^{19} - q^{20} - 5q^{22} + 4q^{23} + 4q^{25} - 5q^{28} + 5q^{29} + 6q^{31} + 2q^{32} + 4q^{34} + 4q^{35} + 4q^{37} - 8q^{38} - q^{40} - 2q^{43} - 5q^{44} + 4q^{46} - 12q^{47} + 11q^{49} + 4q^{50} + 9q^{53} + 10q^{55} - 5q^{56} + 5q^{58} - 22q^{59} - 12q^{61} + 6q^{62} + 2q^{64} - 4q^{67} + 4q^{68} + 4q^{70} + 4q^{71} - 10q^{73} + 4q^{74} - 8q^{76} + 5q^{77} + 6q^{79} - q^{80} + 7q^{83} + 4q^{85} - 2q^{86} - 5q^{88} + 6q^{89} + 4q^{92} - 12q^{94} + 16q^{95} - 7q^{97} + 11q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 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
\(19\) −4.00000 + 6.92820i −0.917663 + 1.58944i −0.114708 + 0.993399i \(0.536593\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) −2.50000 + 0.866025i −0.472456 + 0.163663i
\(29\) 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i \(-0.0129948\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −4.00000 + 6.92820i −0.648886 + 1.12390i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) −1.00000 1.73205i −0.152499 0.264135i 0.779647 0.626219i \(-0.215399\pi\)
−0.932145 + 0.362084i \(0.882065\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 0 0
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 3.00000 0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 0 0
\(70\) 2.00000 + 1.73205i 0.239046 + 0.207020i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) −4.00000 + 6.92820i −0.458831 + 0.794719i
\(77\) 2.50000 12.9904i 0.284901 1.48039i
\(78\) 0 0
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 0 0
\(82\) 0 0
\(83\) 3.50000 + 6.06218i 0.384175 + 0.665410i 0.991654 0.128925i \(-0.0411526\pi\)
−0.607479 + 0.794335i \(0.707819\pi\)
\(84\) 0 0
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) −2.50000 + 4.33013i −0.266501 + 0.461593i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.00000 + 3.46410i 0.208514 + 0.361158i
\(93\) 0 0
\(94\) −6.00000 −0.618853
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) −3.50000 6.06218i −0.355371 0.615521i 0.631810 0.775123i \(-0.282312\pi\)
−0.987181 + 0.159602i \(0.948979\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.50000 + 7.79423i 0.437079 + 0.757042i
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 5.00000 0.476731
\(111\) 0 0
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) −8.00000 + 13.8564i −0.752577 + 1.30350i 0.193993 + 0.981003i \(0.437856\pi\)
−0.946570 + 0.322498i \(0.895477\pi\)
\(114\) 0 0
\(115\) 2.00000 3.46410i 0.186501 0.323029i
\(116\) 2.50000 + 4.33013i 0.232119 + 0.402042i
\(117\) 0 0
\(118\) −11.0000 −1.01263
\(119\) −8.00000 6.92820i −0.733359 0.635107i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −6.00000 −0.543214
\(123\) 0 0
\(124\) 3.00000 0.269408
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 0 0
\(133\) 4.00000 20.7846i 0.346844 1.80225i
\(134\) −2.00000 −0.172774
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i \(-0.806105\pi\)
0.905577 + 0.424182i \(0.139438\pi\)
\(138\) 0 0
\(139\) 7.00000 12.1244i 0.593732 1.02837i −0.399992 0.916519i \(-0.630987\pi\)
0.993724 0.111856i \(-0.0356795\pi\)
\(140\) 2.00000 + 1.73205i 0.169031 + 0.146385i
\(141\) 0 0
\(142\) 2.00000 0.167836
\(143\) 0 0
\(144\) 0 0
\(145\) 2.50000 4.33013i 0.207614 0.359597i
\(146\) −5.00000 8.66025i −0.413803 0.716728i
\(147\) 0 0
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i \(0.447961\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) −4.00000 + 6.92820i −0.324443 + 0.561951i
\(153\) 0 0
\(154\) 2.50000 12.9904i 0.201456 1.04679i
\(155\) −1.50000 2.59808i −0.120483 0.208683i
\(156\) 0 0
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 3.00000 0.238667
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −8.00000 6.92820i −0.630488 0.546019i
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.50000 + 6.06218i 0.271653 + 0.470516i
\(167\) 7.00000 12.1244i 0.541676 0.938211i −0.457132 0.889399i \(-0.651123\pi\)
0.998808 0.0488118i \(-0.0155435\pi\)
\(168\) 0 0
\(169\) 6.50000 + 11.2583i 0.500000 + 0.866025i
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 0 0
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 22.0000 1.67263 0.836315 0.548250i \(-0.184706\pi\)
0.836315 + 0.548250i \(0.184706\pi\)
\(174\) 0 0
\(175\) −2.00000 + 10.3923i −0.151186 + 0.785584i
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) −20.0000 −1.46254
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 0 0
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 0 0
\(202\) −5.00000 + 8.66025i −0.351799 + 0.609333i
\(203\) −10.0000 8.66025i −0.701862 0.607831i
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) 0 0
\(208\) 0 0
\(209\) −20.0000 34.6410i −1.38343 2.39617i
\(210\) 0 0
\(211\) −1.00000 + 1.73205i −0.0688428 + 0.119239i −0.898392 0.439194i \(-0.855264\pi\)
0.829549 + 0.558433i \(0.188597\pi\)
\(212\) 4.50000 + 7.79423i 0.309061 + 0.535310i
\(213\) 0 0
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) 0 0
\(217\) −7.50000 + 2.59808i −0.509133 + 0.176369i
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 0 0
\(220\) 5.00000 0.337100
\(221\) 0 0
\(222\) 0 0
\(223\) 3.50000 + 6.06218i 0.234377 + 0.405953i 0.959092 0.283096i \(-0.0913615\pi\)
−0.724714 + 0.689050i \(0.758028\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i \(0.0631241\pi\)
−0.319582 + 0.947559i \(0.603543\pi\)
\(230\) 2.00000 3.46410i 0.131876 0.228416i
\(231\) 0 0
\(232\) 2.50000 + 4.33013i 0.164133 + 0.284287i
\(233\) 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) 0 0
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −11.0000 −0.716039
\(237\) 0 0
\(238\) −8.00000 6.92820i −0.518563 0.449089i
\(239\) 6.00000 10.3923i 0.388108 0.672222i −0.604087 0.796918i \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i \(-0.535394\pi\)
0.916159 0.400815i \(-0.131273\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) −6.50000 2.59808i −0.415270 0.165985i
\(246\) 0 0
\(247\) 0 0
\(248\) 3.00000 0.190500
\(249\) 0 0
\(250\) −9.00000 −0.569210
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 9.00000 0.564710
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) −2.00000 + 10.3923i −0.124274 + 0.645746i
\(260\) 0 0
\(261\) 0 0
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) 15.0000 25.9808i 0.924940 1.60204i 0.133281 0.991078i \(-0.457449\pi\)
0.791658 0.610964i \(-0.209218\pi\)
\(264\) 0 0
\(265\) 4.50000 7.79423i 0.276433 0.478796i
\(266\) 4.00000 20.7846i 0.245256 1.27439i
\(267\) 0 0
\(268\) −2.00000 −0.122169
\(269\) −15.5000 26.8468i −0.945052 1.63688i −0.755648 0.654978i \(-0.772678\pi\)
−0.189404 0.981899i \(-0.560656\pi\)
\(270\) 0 0
\(271\) −7.50000 + 12.9904i −0.455593 + 0.789109i −0.998722 0.0505395i \(-0.983906\pi\)
0.543130 + 0.839649i \(0.317239\pi\)
\(272\) 2.00000 + 3.46410i 0.121268 + 0.210042i
\(273\) 0 0
\(274\) 1.00000 1.73205i 0.0604122 0.104637i
\(275\) 10.0000 + 17.3205i 0.603023 + 1.04447i
\(276\) 0 0
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) 7.00000 12.1244i 0.419832 0.727171i
\(279\) 0 0
\(280\) 2.00000 + 1.73205i 0.119523 + 0.103510i
\(281\) −1.00000 1.73205i −0.0596550 0.103325i 0.834656 0.550772i \(-0.185667\pi\)
−0.894311 + 0.447447i \(0.852333\pi\)
\(282\) 0 0
\(283\) 10.0000 0.594438 0.297219 0.954809i \(-0.403941\pi\)
0.297219 + 0.954809i \(0.403941\pi\)
\(284\) 2.00000 0.118678
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 2.50000 4.33013i 0.146805 0.254274i
\(291\) 0 0
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 10.5000 18.1865i 0.613417 1.06247i −0.377244 0.926114i \(-0.623128\pi\)
0.990660 0.136355i \(-0.0435386\pi\)
\(294\) 0 0
\(295\) 5.50000 + 9.52628i 0.320222 + 0.554641i
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) 0 0
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) 0 0
\(300\) 0 0
\(301\) 4.00000 + 3.46410i 0.230556 + 0.199667i
\(302\) −9.50000 + 16.4545i −0.546664 + 0.946849i
\(303\) 0 0
\(304\) −4.00000 + 6.92820i −0.229416 + 0.397360i
\(305\) 3.00000 + 5.19615i 0.171780 + 0.297531i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 2.50000 12.9904i 0.142451 0.740196i
\(309\) 0 0
\(310\) −1.50000 2.59808i −0.0851943 0.147561i
\(311\) −32.0000 −1.81455 −0.907277 0.420534i \(-0.861843\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) 0 0
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) −25.0000 −1.39973
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) −8.00000 6.92820i −0.445823 0.386094i
\(323\) −32.0000 −1.78053
\(324\) 0 0
\(325\) 0 0
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 0 0
\(328\) 0 0
\(329\) 15.0000 5.19615i 0.826977 0.286473i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 3.50000 + 6.06218i 0.192087 + 0.332705i
\(333\) 0 0
\(334\) 7.00000 12.1244i 0.383023 0.663415i
\(335\) 1.00000 + 1.73205i 0.0546358 + 0.0946320i
\(336\) 0 0
\(337\) −4.50000 + 7.79423i −0.245131 + 0.424579i −0.962168 0.272456i \(-0.912164\pi\)
0.717038 + 0.697034i \(0.245498\pi\)
\(338\) 6.50000 + 11.2583i 0.353553 + 0.612372i
\(339\) 0 0
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −1.00000 1.73205i −0.0539164 0.0933859i
\(345\) 0 0
\(346\) 22.0000 1.18273
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) 7.00000 + 12.1244i 0.374701 + 0.649002i 0.990282 0.139072i \(-0.0444119\pi\)
−0.615581 + 0.788074i \(0.711079\pi\)
\(350\) −2.00000 + 10.3923i −0.106904 + 0.555492i
\(351\) 0 0
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) −1.00000 1.73205i −0.0530745 0.0919277i
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) −6.00000 10.3923i −0.317110 0.549250i
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 2.00000 + 3.46410i 0.104257 + 0.180579i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) −18.0000 15.5885i −0.934513 0.809312i
\(372\) 0 0
\(373\) 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i \(0.144109\pi\)
−0.0708063 + 0.997490i \(0.522557\pi\)
\(374\) −20.0000 −1.03418
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 8.00000 0.410391
\(381\) 0 0
\(382\) 24.0000 1.22795
\(383\) 17.0000 + 29.4449i 0.868659 + 1.50456i 0.863367 + 0.504576i \(0.168351\pi\)
0.00529229 + 0.999986i \(0.498315\pi\)
\(384\) 0 0
\(385\) −12.5000 + 4.33013i −0.637059 + 0.220684i
\(386\) 5.00000 0.254493
\(387\) 0 0
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) 0 0
\(391\) −8.00000 + 13.8564i −0.404577 + 0.700749i
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) −18.0000 + 31.1769i −0.903394 + 1.56472i −0.0803356 + 0.996768i \(0.525599\pi\)
−0.823058 + 0.567957i \(0.807734\pi\)
\(398\) 2.00000 + 3.46410i 0.100251 + 0.173640i
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) 0 0
\(406\) −10.0000 8.66025i −0.496292 0.429801i
\(407\) 10.0000 + 17.3205i 0.495682 + 0.858546i
\(408\) 0 0
\(409\) −25.0000 −1.23617 −0.618085 0.786111i \(-0.712091\pi\)
−0.618085 + 0.786111i \(0.712091\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 6.92820i −0.197066 0.341328i
\(413\) 27.5000 9.52628i 1.35319 0.468758i
\(414\) 0 0
\(415\) 3.50000 6.06218i 0.171808 0.297581i
\(416\) 0 0
\(417\) 0 0
\(418\) −20.0000 34.6410i −0.978232 1.69435i
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) −15.0000 25.9808i −0.731055 1.26622i −0.956433 0.291953i \(-0.905695\pi\)
0.225377 0.974272i \(-0.427639\pi\)
\(422\) −1.00000 + 1.73205i −0.0486792 + 0.0843149i
\(423\) 0 0
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 16.0000 0.776114
\(426\) 0 0
\(427\) 15.0000 5.19615i 0.725901 0.251459i
\(428\) −1.50000 + 2.59808i −0.0725052 + 0.125583i
\(429\) 0 0
\(430\) −1.00000 + 1.73205i −0.0482243 + 0.0835269i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −7.50000 + 2.59808i −0.360012 + 0.124712i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −32.0000 −1.53077
\(438\) 0 0
\(439\) 15.0000 0.715911 0.357955 0.933739i \(-0.383474\pi\)
0.357955 + 0.933739i \(0.383474\pi\)
\(440\) 5.00000 0.238366
\(441\) 0 0
\(442\) 0 0
\(443\) 17.0000 0.807694 0.403847 0.914826i \(-0.367673\pi\)
0.403847 + 0.914826i \(0.367673\pi\)
\(444\) 0 0
\(445\) −6.00000 −0.284427
\(446\) 3.50000 + 6.06218i 0.165730 + 0.287052i
\(447\) 0 0
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −8.00000 + 13.8564i −0.376288 + 0.651751i
\(453\) 0 0
\(454\) −1.50000 + 2.59808i −0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) 31.0000 1.45012 0.725059 0.688686i \(-0.241812\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 10.0000 + 17.3205i 0.467269 + 0.809334i
\(459\) 0 0
\(460\) 2.00000 3.46410i 0.0932505 0.161515i
\(461\) 7.00000 + 12.1244i 0.326023 + 0.564688i 0.981719 0.190337i \(-0.0609581\pi\)
−0.655696 + 0.755025i \(0.727625\pi\)
\(462\) 0 0
\(463\) −8.00000 + 13.8564i −0.371792 + 0.643962i −0.989841 0.142177i \(-0.954590\pi\)
0.618050 + 0.786139i \(0.287923\pi\)
\(464\) 2.50000 + 4.33013i 0.116060 + 0.201021i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 10.0000 17.3205i 0.462745 0.801498i −0.536352 0.843995i \(-0.680198\pi\)
0.999097 + 0.0424970i \(0.0135313\pi\)
\(468\) 0 0
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) 3.00000 + 5.19615i 0.138380 + 0.239681i
\(471\) 0 0
\(472\) −11.0000 −0.506316
\(473\) 10.0000 0.459800
\(474\) 0 0
\(475\) 16.0000 + 27.7128i 0.734130 + 1.27155i
\(476\) −8.00000 6.92820i −0.366679 0.317554i
\(477\) 0 0
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) −19.0000 + 32.9090i −0.868132 + 1.50365i −0.00422900 + 0.999991i \(0.501346\pi\)
−0.863903 + 0.503658i \(0.831987\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 12.5000 21.6506i 0.569359 0.986159i
\(483\) 0 0
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) −3.50000 + 6.06218i −0.158927 + 0.275269i
\(486\) 0 0
\(487\) −2.50000 4.33013i −0.113286 0.196217i 0.803807 0.594890i \(-0.202804\pi\)
−0.917093 + 0.398673i \(0.869471\pi\)
\(488\) −6.00000 −0.271607
\(489\) 0 0
\(490\) −6.50000 2.59808i −0.293640 0.117369i
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) −5.00000 + 1.73205i −0.224281 + 0.0776931i
\(498\) 0 0
\(499\) −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) −9.00000 −0.402492
\(501\) 0 0
\(502\) 21.0000 0.937276
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −20.0000 −0.889108
\(507\) 0 0
\(508\) 9.00000 0.399310
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 0 0
\(511\) 20.0000 + 17.3205i 0.884748 + 0.766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) −4.00000 + 6.92820i −0.176261 + 0.305293i
\(516\) 0 0
\(517\) 15.0000 25.9808i 0.659699 1.14263i
\(518\) −2.00000 + 10.3923i −0.0878750 + 0.456612i
\(519\) 0 0
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) −4.00000 + 6.92820i −0.174908 + 0.302949i −0.940129 0.340818i \(-0.889296\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) −0.500000 0.866025i −0.0218426 0.0378325i
\(525\) 0 0
\(526\) 15.0000 25.9808i 0.654031 1.13282i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) 4.00000 20.7846i 0.173422 0.901127i
\(533\) 0 0
\(534\) 0 0
\(535\) 3.00000 0.129701
\(536\) −2.00000 −0.0863868
\(537\) 0 0
\(538\) −15.5000 26.8468i −0.668252 1.15745i
\(539\) 5.00000 + 34.6410i 0.215365 + 1.49209i
\(540\) 0 0
\(541\) 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i \(-0.706865\pi\)
0.992036 + 0.125952i \(0.0401986\pi\)
\(542\) −7.50000 + 12.9904i −0.322153 + 0.557985i
\(543\) 0 0
\(544\) 2.00000 + 3.46410i 0.0857493 + 0.148522i
\(545\) 1.00000 1.73205i 0.0428353 0.0741929i
\(546\) 0 0
\(547\) 6.00000 + 10.3923i 0.256541 + 0.444343i 0.965313 0.261095i \(-0.0840836\pi\)
−0.708772 + 0.705438i \(0.750750\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) 0 0
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) −40.0000 −1.70406
\(552\) 0 0
\(553\) −7.50000 + 2.59808i −0.318932 + 0.110481i
\(554\) 8.00000 13.8564i 0.339887 0.588702i
\(555\) 0 0
\(556\) 7.00000 12.1244i 0.296866 0.514187i
\(557\) 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i \(-0.00465919\pi\)
−0.512622 + 0.858614i \(0.671326\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2.00000 + 1.73205i 0.0845154 + 0.0731925i
\(561\) 0 0
\(562\) −1.00000 1.73205i −0.0421825 0.0730622i
\(563\) 17.0000 0.716465 0.358232 0.933632i \(-0.383380\pi\)
0.358232 + 0.933632i \(0.383380\pi\)
\(564\) 0 0
\(565\) 16.0000 0.673125
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) 2.00000 0.0839181
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −30.0000 −1.25546 −0.627730 0.778431i \(-0.716016\pi\)
−0.627730 + 0.778431i \(0.716016\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.0000 0.667246
\(576\) 0 0
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) 0.500000 0.866025i 0.0207973 0.0360219i
\(579\) 0 0
\(580\) 2.50000 4.33013i 0.103807 0.179799i
\(581\) −14.0000 12.1244i −0.580818 0.503003i
\(582\) 0 0
\(583\) −45.0000 −1.86371
\(584\) −5.00000 8.66025i −0.206901 0.358364i
\(585\) 0 0
\(586\) 10.5000 18.1865i 0.433751 0.751279i
\(587\) −17.5000 30.3109i −0.722302 1.25106i −0.960075 0.279743i \(-0.909751\pi\)
0.237773 0.971321i \(-0.423583\pi\)
\(588\) 0 0
\(589\) −12.0000 + 20.7846i −0.494451 + 0.856415i
\(590\) 5.50000 + 9.52628i 0.226431 + 0.392191i
\(591\) 0 0
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) −18.0000 + 31.1769i −0.739171 + 1.28028i 0.213697 + 0.976900i \(0.431449\pi\)
−0.952869 + 0.303383i \(0.901884\pi\)
\(594\) 0 0
\(595\) −2.00000 + 10.3923i −0.0819920 + 0.426043i
\(596\) 9.00000 + 15.5885i 0.368654 + 0.638528i
\(597\) 0 0
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −17.5000 30.3109i −0.713840 1.23641i −0.963405 0.268049i \(-0.913621\pi\)
0.249565 0.968358i \(-0.419712\pi\)
\(602\) 4.00000 + 3.46410i 0.163028 + 0.141186i
\(603\) 0 0
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) 13.5000 + 23.3827i 0.547948 + 0.949074i 0.998415 + 0.0562808i \(0.0179242\pi\)
−0.450467 + 0.892793i \(0.648742\pi\)
\(608\) −4.00000 + 6.92820i −0.162221 + 0.280976i
\(609\) 0 0
\(610\) 3.00000 + 5.19615i 0.121466 + 0.210386i
\(611\) 0 0
\(612\) 0 0
\(613\) −6.00000 10.3923i −0.242338 0.419741i 0.719042 0.694967i \(-0.244581\pi\)
−0.961380 + 0.275225i \(0.911248\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) 2.50000 12.9904i 0.100728 0.523397i
\(617\) −1.00000 + 1.73205i −0.0402585 + 0.0697297i −0.885453 0.464730i \(-0.846151\pi\)
0.845194 + 0.534460i \(0.179485\pi\)
\(618\) 0 0
\(619\) −5.00000 + 8.66025i −0.200967 + 0.348085i −0.948840 0.315757i \(-0.897742\pi\)
0.747873 + 0.663842i \(0.231075\pi\)
\(620\) −1.50000 2.59808i −0.0602414 0.104341i
\(621\) 0 0
\(622\) −32.0000 −1.28308
\(623\) −3.00000 + 15.5885i −0.120192 + 0.624538i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 1.00000 0.0399680
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) 3.00000 0.119334
\(633\) 0 0
\(634\) 3.00000 0.119145
\(635\) −4.50000 7.79423i −0.178577 0.309305i
\(636\) 0 0
\(637\) 0 0
\(638\) −25.0000 −0.989759
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i \(0.338307\pi\)
−0.999878 + 0.0156233i \(0.995027\pi\)
\(642\) 0 0
\(643\) −7.00000 + 12.1244i −0.276053 + 0.478138i −0.970400 0.241502i \(-0.922360\pi\)
0.694347 + 0.719640i \(0.255693\pi\)
\(644\) −8.00000 6.92820i −0.315244 0.273009i
\(645\) 0 0
\(646\) −32.0000 −1.25902
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) 27.5000 47.6314i 1.07947 1.86970i
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i \(0.109654\pi\)
−0.178154 + 0.984003i \(0.557013\pi\)
\(654\) 0 0
\(655\) −0.500000 + 0.866025i −0.0195366 + 0.0338384i
\(656\) 0 0
\(657\) 0 0
\(658\) 15.0000 5.19615i 0.584761 0.202567i
\(659\) 20.0000 + 34.6410i 0.779089 + 1.34942i 0.932467 + 0.361255i \(0.117652\pi\)
−0.153378 + 0.988168i \(0.549015\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) 3.50000 + 6.06218i 0.135826 + 0.235258i
\(665\) −20.0000 + 6.92820i −0.775567 + 0.268664i
\(666\) 0 0
\(667\) −10.0000 + 17.3205i −0.387202 + 0.670653i
\(668\) 7.00000 12.1244i 0.270838 0.469105i
\(669\) 0 0
\(670\) 1.00000 + 1.73205i 0.0386334 + 0.0669150i
\(671\) 15.0000 25.9808i 0.579069 1.00298i
\(672\) 0 0
\(673\) 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) −4.50000 + 7.79423i −0.173334 + 0.300222i
\(675\) 0 0
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −27.0000 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) 0 0
\(679\) 14.0000 + 12.1244i 0.537271 + 0.465290i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 0 0
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) −10.0000 + 15.5885i −0.381802 + 0.595170i
\(687\) 0 0
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 0 0
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) 0 0
\(698\) 7.00000 + 12.1244i 0.264954 + 0.458914i
\(699\) 0 0
\(700\) −2.00000 + 10.3923i −0.0755929 + 0.392792i
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 0 0
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 0 0
\(706\) −12.0000 + 20.7846i −0.451626 + 0.782239i
\(707\) 5.00000 25.9808i 0.188044 0.977107i
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −1.00000 1.73205i −0.0375293 0.0650027i
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 0 0
\(718\) −5.00000 + 8.66025i −0.186598 + 0.323198i
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) 16.0000 + 13.8564i 0.595871 + 0.516040i
\(722\) −22.5000 38.9711i −0.837363 1.45036i
\(723\) 0 0
\(724\) 0 0
\(725\) 20.0000 0.742781
\(726\) 0 0
\(727\) −3.50000 6.06218i −0.129808 0.224834i 0.793794 0.608186i \(-0.208103\pi\)
−0.923602 + 0.383353i \(0.874769\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 0 0
\(733\) 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) −8.50000 + 14.7224i −0.313741 + 0.543415i
\(735\) 0 0
\(736\) 2.00000 + 3.46410i 0.0737210 + 0.127688i
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) 0 0
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) −18.0000 15.5885i −0.660801 0.572270i
\(743\) −15.0000 + 25.9808i −0.550297 + 0.953142i 0.447956 + 0.894055i \(0.352152\pi\)
−0.998253 + 0.0590862i \(0.981181\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 16.0000 + 27.7128i 0.585802 + 1.01464i
\(747\) 0 0
\(748\) −20.0000 −0.731272
\(749\) 1.50000 7.79423i 0.0548088 0.284795i
\(750\) 0 0
\(751\) −22.5000 38.9711i −0.821037 1.42208i −0.904911 0.425601i \(-0.860063\pi\)
0.0838743 0.996476i \(-0.473271\pi\)
\(752\) −6.00000 −0.218797
\(753\) 0 0
\(754\) 0 0
\(755\) 19.0000 0.691481
\(756\) 0 0
\(757\) −54.0000 −1.96266 −0.981332 0.192323i \(-0.938398\pi\)
−0.981332 + 0.192323i \(0.938398\pi\)
\(758\) 16.0000 0.581146
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i \(-0.212985\pi\)
−0.929373 + 0.369142i \(0.879652\pi\)
\(762\) 0 0
\(763\) −4.00000 3.46410i −0.144810 0.125409i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 17.0000 + 29.4449i 0.614235 + 1.06389i
\(767\) 0 0
\(768\) 0 0
\(769\) 17.5000 30.3109i 0.631066 1.09304i −0.356268 0.934384i \(-0.615951\pi\)
0.987334 0.158655i \(-0.0507157\pi\)
\(770\) −12.5000 + 4.33013i −0.450469 + 0.156047i
\(771\) 0 0
\(772\) 5.00000 0.179954
\(773\) −5.00000 8.66025i −0.179838 0.311488i 0.761987 0.647592i \(-0.224224\pi\)
−0.941825 + 0.336104i \(0.890891\pi\)
\(774\) 0 0
\(775\) 6.00000 10.3923i 0.215526 0.373303i
\(776\) −3.50000 6.06218i −0.125643 0.217620i
\(777\) 0 0
\(778\) 1.00000 1.73205i 0.0358517 0.0620970i
\(779\) 0 0
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 2.00000 + 3.46410i 0.0713831 + 0.123639i
\(786\) 0 0
\(787\) −18.0000 −0.641631 −0.320815 0.947142i \(-0.603957\pi\)
−0.320815 + 0.947142i \(0.603957\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) −1.50000 2.59808i −0.0533676 0.0924354i
\(791\) 8.00000 41.5692i 0.284447 1.47803i
\(792\) 0 0