Properties

Label 1134.2.h.l.541.1
Level $1134$
Weight $2$
Character 1134.541
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.541
Dual form 1134.2.h.l.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -5.00000 q^{11} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{22} +4.00000 q^{23} -4.00000 q^{25} +(-2.50000 + 0.866025i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(2.00000 - 3.46410i) q^{37} -8.00000 q^{38} +1.00000 q^{40} +(-1.00000 + 1.73205i) q^{43} +(2.50000 - 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} -5.00000 q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +4.00000 q^{68} +(0.500000 - 2.59808i) q^{70} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +4.00000 q^{74} +(-4.00000 - 6.92820i) q^{76} +(-10.0000 - 8.66025i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.50000 + 6.06218i) q^{83} +(2.00000 + 3.46410i) q^{85} -2.00000 q^{86} +5.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 + 3.46410i) q^{92} +(3.00000 - 5.19615i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-3.50000 + 6.06218i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} - q^{10} - 10q^{11} - q^{14} - q^{16} - 4q^{17} - 8q^{19} + q^{20} - 5q^{22} + 8q^{23} - 8q^{25} - 5q^{28} - 5q^{29} - 3q^{31} + q^{32} + 4q^{34} - 4q^{35} + 4q^{37} - 16q^{38} + 2q^{40} - 2q^{43} + 5q^{44} + 4q^{46} - 6q^{47} + 2q^{49} - 4q^{50} - 9q^{53} + 10q^{55} - 4q^{56} - 10q^{58} - 11q^{59} + 6q^{61} - 6q^{62} + 2q^{64} + 2q^{67} + 8q^{68} + q^{70} - 4q^{71} - 10q^{73} + 8q^{74} - 8q^{76} - 20q^{77} - 3q^{79} + q^{80} - 7q^{83} + 4q^{85} - 4q^{86} + 10q^{88} - 6q^{89} - 4q^{92} + 6q^{94} + 8q^{95} - 7q^{97} - 11q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) −0.500000 + 2.59808i −0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 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
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 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 \(-0.987005\pi\)
0.534928 + 0.844897i \(0.320339\pi\)
\(30\) 0 0
\(31\) −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i \(-0.920161\pi\)
0.699301 + 0.714827i \(0.253495\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 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 \(0.0600231\pi\)
\(38\) −8.00000 −1.29777
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) −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 \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) −5.50000 + 9.52628i −0.716039 + 1.24022i 0.246518 + 0.969138i \(0.420713\pi\)
−0.962557 + 0.271078i \(0.912620\pi\)
\(60\) 0 0
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) −3.00000 −0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0.500000 2.59808i 0.0597614 0.310530i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) −10.0000 8.66025i −1.13961 0.986928i
\(78\) 0 0
\(79\) −1.50000 2.59808i −0.168763 0.292306i 0.769222 0.638982i \(-0.220644\pi\)
−0.937985 + 0.346675i \(0.887311\pi\)
\(80\) 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 \(-0.958847\pi\)
0.607479 + 0.794335i \(0.292181\pi\)
\(84\) 0 0
\(85\) 2.00000 + 3.46410i 0.216930 + 0.375735i
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 5.00000 0.533002
\(89\) −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
\(91\) 0 0
\(92\) −2.00000 + 3.46410i −0.208514 + 0.361158i
\(93\) 0 0
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) −3.50000 + 6.06218i −0.355371 + 0.615521i −0.987181 0.159602i \(-0.948979\pi\)
0.631810 + 0.775123i \(0.282312\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 2.50000 + 4.33013i 0.238366 + 0.412861i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) 8.00000 + 13.8564i 0.752577 + 1.30350i 0.946570 + 0.322498i \(0.104523\pi\)
−0.193993 + 0.981003i \(0.562144\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) −2.50000 4.33013i −0.232119 0.402042i
\(117\) 0 0
\(118\) −11.0000 −1.01263
\(119\) 2.00000 10.3923i 0.183340 0.952661i
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) −3.00000 + 5.19615i −0.271607 + 0.470438i
\(123\) 0 0
\(124\) −1.50000 2.59808i −0.134704 0.233314i
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) −20.0000 + 6.92820i −1.73422 + 0.600751i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 7.00000 + 12.1244i 0.593732 + 1.02837i 0.993724 + 0.111856i \(0.0356795\pi\)
−0.399992 + 0.916519i \(0.630987\pi\)
\(140\) 2.50000 0.866025i 0.211289 0.0731925i
\(141\) 0 0
\(142\) −1.00000 1.73205i −0.0839181 0.145350i
\(143\) 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
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 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
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 1.50000 2.59808i 0.119334 0.206692i
\(159\) 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
\(166\) −7.00000 −0.543305
\(167\) −7.00000 12.1244i −0.541676 0.938211i −0.998808 0.0488118i \(-0.984457\pi\)
0.457132 0.889399i \(-0.348877\pi\)
\(168\) 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
\(173\) 11.0000 + 19.0526i 0.836315 + 1.44854i 0.892956 + 0.450145i \(0.148628\pi\)
−0.0566411 + 0.998395i \(0.518039\pi\)
\(174\) 0 0
\(175\) −8.00000 6.92820i −0.604743 0.523723i
\(176\) 2.50000 + 4.33013i 0.188445 + 0.326396i
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) 10.0000 + 17.3205i 0.731272 + 1.26660i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) −5.00000 8.66025i −0.351799 0.609333i
\(203\) −12.5000 + 4.33013i −0.877328 + 0.303915i
\(204\) 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 0.829549 0.558433i \(-0.188597\pi\)
−0.898392 + 0.439194i \(0.855264\pi\)
\(212\) 9.00000 0.618123
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) 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
\(220\) −2.50000 + 4.33013i −0.168550 + 0.291937i
\(221\) 0 0
\(222\) 0 0
\(223\) 3.50000 6.06218i 0.234377 0.405953i −0.724714 0.689050i \(-0.758028\pi\)
0.959092 + 0.283096i \(0.0913615\pi\)
\(224\) 2.50000 0.866025i 0.167038 0.0578638i
\(225\) 0 0
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) −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 −0.924072 0.382219i \(-0.875160\pi\)
0.793047 + 0.609160i \(0.208493\pi\)
\(234\) 0 0
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −5.50000 9.52628i −0.358020 0.620108i
\(237\) 0 0
\(238\) 10.0000 3.46410i 0.648204 0.224544i
\(239\) −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i \(-0.293538\pi\)
−0.992195 + 0.124696i \(0.960204\pi\)
\(240\) 0 0
\(241\) −25.0000 −1.61039 −0.805196 0.593009i \(-0.797940\pi\)
−0.805196 + 0.593009i \(0.797940\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) −1.00000 6.92820i −0.0638877 0.442627i
\(246\) 0 0
\(247\) 0 0
\(248\) 1.50000 2.59808i 0.0952501 0.164978i
\(249\) 0 0
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 4.50000 + 7.79423i 0.282355 + 0.489053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 10.0000 3.46410i 0.621370 0.215249i
\(260\) 0 0
\(261\) 0 0
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) 30.0000 1.84988 0.924940 0.380114i \(-0.124115\pi\)
0.924940 + 0.380114i \(0.124115\pi\)
\(264\) 0 0
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) −16.0000 13.8564i −0.981023 0.849591i
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 15.5000 + 26.8468i 0.945052 + 1.63688i 0.755648 + 0.654978i \(0.227322\pi\)
0.189404 + 0.981899i \(0.439344\pi\)
\(270\) 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
\(275\) 20.0000 1.20605
\(276\) 0 0
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) −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 \(-0.814333\pi\)
0.894311 + 0.447447i \(0.147667\pi\)
\(282\) 0 0
\(283\) −5.00000 + 8.66025i −0.297219 + 0.514799i −0.975499 0.220005i \(-0.929393\pi\)
0.678280 + 0.734804i \(0.262726\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 5.00000 0.293610
\(291\) 0 0
\(292\) 10.0000 0.585206
\(293\) −10.5000 18.1865i −0.613417 1.06247i −0.990660 0.136355i \(-0.956461\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(294\) 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
\(301\) −5.00000 + 1.73205i −0.288195 + 0.0998337i
\(302\) 9.50000 + 16.4545i 0.546664 + 0.946849i
\(303\) 0 0
\(304\) 8.00000 0.458831
\(305\) −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 \(0.205351\pi\)
\(308\) 12.5000 4.33013i 0.712254 0.246732i
\(309\) 0 0
\(310\) 3.00000 0.170389
\(311\) −16.0000 + 27.7128i −0.907277 + 1.57145i −0.0894452 + 0.995992i \(0.528509\pi\)
−0.817832 + 0.575458i \(0.804824\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) 0 0
\(319\) 12.5000 21.6506i 0.699866 1.21220i
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) −2.00000 + 10.3923i −0.111456 + 0.579141i
\(323\) 32.0000 1.78053
\(324\) 0 0
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) 0 0
\(329\) 3.00000 15.5885i 0.165395 0.859419i
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −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 0.717038 0.697034i \(-0.245498\pi\)
−0.962168 + 0.272456i \(0.912164\pi\)
\(338\) 13.0000 0.707107
\(339\) 0 0
\(340\) −4.00000 −0.216930
\(341\) 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
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i \(-0.711079\pi\)
0.990282 + 0.139072i \(0.0444119\pi\)
\(350\) 2.00000 10.3923i 0.106904 0.555492i
\(351\) 0 0
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) 2.00000 0.106149
\(356\) −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 −0.703382 0.710812i \(-0.748328\pi\)
0.967272 + 0.253741i \(0.0816611\pi\)
\(360\) 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
\(367\) 17.0000 0.887393 0.443696 0.896177i \(-0.353667\pi\)
0.443696 + 0.896177i \(0.353667\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 4.50000 23.3827i 0.233628 1.21397i
\(372\) 0 0
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) −10.0000 + 17.3205i −0.517088 + 0.895622i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 4.00000 + 6.92820i 0.205196 + 0.355409i
\(381\) 0 0
\(382\) −12.0000 + 20.7846i −0.613973 + 1.06343i
\(383\) 34.0000 1.73732 0.868659 0.495410i \(-0.164982\pi\)
0.868659 + 0.495410i \(0.164982\pi\)
\(384\) 0 0
\(385\) 10.0000 + 8.66025i 0.509647 + 0.441367i
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) −8.00000 13.8564i −0.404577 0.700749i
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 0 0
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) 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
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 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
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 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
\(418\) 40.0000 1.95646
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) −15.0000 + 25.9808i −0.731055 + 1.26622i 0.225377 + 0.974272i \(0.427639\pi\)
−0.956433 + 0.291953i \(0.905695\pi\)
\(422\) 1.00000 1.73205i 0.0486792 0.0843149i
\(423\) 0 0
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 8.00000 + 13.8564i 0.388057 + 0.672134i
\(426\) 0 0
\(427\) −3.00000 + 15.5885i −0.145180 + 0.754378i
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) 0 0
\(430\) 2.00000 0.0964486
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −6.00000 5.19615i −0.288009 0.249423i
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −16.0000 + 27.7128i −0.765384 + 1.32568i
\(438\) 0 0
\(439\) −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i \(-0.283193\pi\)
−0.987619 + 0.156871i \(0.949859\pi\)
\(440\) −5.00000 −0.238366
\(441\) 0 0
\(442\) 0 0
\(443\) 8.50000 + 14.7224i 0.403847 + 0.699484i 0.994187 0.107671i \(-0.0343394\pi\)
−0.590339 + 0.807155i \(0.701006\pi\)
\(444\) 0 0
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) 7.00000 0.331460
\(447\) 0 0
\(448\) 2.00000 + 1.73205i 0.0944911 + 0.0818317i
\(449\) −16.0000 −0.755087 −0.377543 0.925992i \(-0.623231\pi\)
−0.377543 + 0.925992i \(0.623231\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −16.0000 −0.752577
\(453\) 0 0
\(454\) −1.50000 2.59808i −0.0703985 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) −15.5000 26.8468i −0.725059 1.25584i −0.958950 0.283577i \(-0.908479\pi\)
0.233890 0.972263i \(-0.424854\pi\)
\(458\) −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 \(-0.939042\pi\)
0.655696 + 0.755025i \(0.272375\pi\)
\(462\) 0 0
\(463\) −8.00000 13.8564i −0.371792 0.643962i 0.618050 0.786139i \(-0.287923\pi\)
−0.989841 + 0.142177i \(0.954590\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) −4.00000 −0.185296
\(467\) −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) −3.00000 + 5.19615i −0.138380 + 0.239681i
\(471\) 0 0
\(472\) 5.50000 9.52628i 0.253158 0.438483i
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) 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
\(479\) −38.0000 −1.73626 −0.868132 0.496333i \(-0.834679\pi\)
−0.868132 + 0.496333i \(0.834679\pi\)
\(480\) 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 \(0.869471\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) 0 0
\(490\) 5.50000 4.33013i 0.248465 0.195615i
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) 0 0
\(493\) 20.0000 0.900755
\(494\) 0 0
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) −4.00000 3.46410i −0.179425 0.155386i
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 0 0
\(502\) −10.5000 18.1865i −0.468638 0.811705i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −10.0000 17.3205i −0.444554 0.769991i
\(507\) 0 0
\(508\) −4.50000 + 7.79423i −0.199655 + 0.345813i
\(509\) −15.0000 −0.664863 −0.332432 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) 5.00000 25.9808i 0.221187 1.14932i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 15.0000 + 25.9808i 0.659699 + 1.14263i
\(518\) 8.00000 + 6.92820i 0.351500 + 0.304408i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) 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
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −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
\(535\) −1.50000 + 2.59808i −0.0648507 + 0.112325i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 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 \(0.0401986\pi\)
\(542\) −15.0000 −0.644305
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) −1.00000 1.73205i −0.0428353 0.0741929i
\(546\) 0 0
\(547\) 6.00000 10.3923i 0.256541 0.444343i −0.708772 0.705438i \(-0.750750\pi\)
0.965313 + 0.261095i \(0.0840836\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) −20.0000 34.6410i −0.852029 1.47576i
\(552\) 0 0
\(553\) 1.50000 7.79423i 0.0637865 0.331444i
\(554\) −8.00000 13.8564i −0.339887 0.588702i
\(555\) 0 0
\(556\) −14.0000 −0.593732
\(557\) −11.5000 19.9186i −0.487271 0.843978i 0.512622 0.858614i \(-0.328674\pi\)
−0.999893 + 0.0146368i \(0.995341\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.500000 + 2.59808i −0.0211289 + 0.109789i
\(561\) 0 0
\(562\) 2.00000 0.0843649
\(563\) 8.50000 14.7224i 0.358232 0.620477i −0.629433 0.777055i \(-0.716713\pi\)
0.987666 + 0.156578i \(0.0500463\pi\)
\(564\) 0 0
\(565\) −8.00000 13.8564i −0.336563 0.582943i
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) 2.00000 0.0839181
\(569\) 12.0000 + 20.7846i 0.503066 + 0.871336i 0.999994 + 0.00354413i \(0.00112814\pi\)
−0.496928 + 0.867792i \(0.665539\pi\)
\(570\) 0 0
\(571\) 15.0000 25.9808i 0.627730 1.08726i −0.360276 0.932846i \(-0.617317\pi\)
0.988006 0.154415i \(-0.0493493\pi\)
\(572\) 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 \(-0.389923\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 2.50000 + 4.33013i 0.103807 + 0.179799i
\(581\) −17.5000 + 6.06218i −0.726022 + 0.251502i
\(582\) 0 0
\(583\) 22.5000 + 38.9711i 0.931855 + 1.61402i
\(584\) 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 −0.237773 0.971321i \(-0.576417\pi\)
0.960075 0.279743i \(-0.0902494\pi\)
\(588\) 0 0
\(589\) −12.0000 20.7846i −0.494451 0.856415i
\(590\) 11.0000 0.452863
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 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
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) −4.00000 3.46410i −0.163028 0.141186i
\(603\) 0 0
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) −27.0000 −1.09590 −0.547948 0.836512i \(-0.684591\pi\)
−0.547948 + 0.836512i \(0.684591\pi\)
\(608\) 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 \(0.911248\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) 10.0000 + 8.66025i 0.402911 + 0.348932i
\(617\) 1.00000 + 1.73205i 0.0402585 + 0.0697297i 0.885453 0.464730i \(-0.153849\pi\)
−0.845194 + 0.534460i \(0.820515\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 1.50000 + 2.59808i 0.0602414 + 0.104341i
\(621\) 0 0
\(622\) −32.0000 −1.28308
\(623\) −15.0000 + 5.19615i −0.600962 + 0.208179i
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0.500000 0.866025i 0.0199840 0.0346133i
\(627\) 0 0
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) 1.50000 + 2.59808i 0.0596668 + 0.103346i
\(633\) 0 0
\(634\) −1.50000 + 2.59808i −0.0595726 + 0.103183i
\(635\) −9.00000 −0.357154
\(636\) 0 0
\(637\) 0 0
\(638\) 25.0000 0.989759
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −26.0000 −1.02694 −0.513469 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(644\) −10.0000 + 3.46410i −0.394055 + 0.136505i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 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
\(653\) 39.0000 1.52619 0.763094 0.646288i \(-0.223679\pi\)
0.763094 + 0.646288i \(0.223679\pi\)
\(654\) 0 0
\(655\) 1.00000 0.0390732
\(656\) 0 0
\(657\) 0 0
\(658\) 15.0000 5.19615i 0.584761 0.202567i
\(659\) −20.0000 + 34.6410i −0.779089 + 1.34942i 0.153378 + 0.988168i \(0.450985\pi\)
−0.932467 + 0.361255i \(0.882348\pi\)
\(660\) 0 0
\(661\) −5.00000 + 8.66025i −0.194477 + 0.336845i −0.946729 0.322031i \(-0.895634\pi\)
0.752252 + 0.658876i \(0.228968\pi\)
\(662\) −2.00000 + 3.46410i −0.0777322 + 0.134636i
\(663\) 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
\(668\) 14.0000 0.541676
\(669\) 0 0
\(670\) −2.00000 −0.0772667
\(671\) −15.0000 25.9808i −0.579069 1.00298i
\(672\) 0 0
\(673\) 9.50000 16.4545i 0.366198 0.634274i −0.622770 0.782405i \(-0.713993\pi\)
0.988968 + 0.148132i \(0.0473259\pi\)
\(674\) 4.50000 7.79423i 0.173334 0.300222i
\(675\) 0 0
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i \(-0.993028\pi\)
0.480913 0.876768i \(-0.340305\pi\)
\(678\) 0 0
\(679\) −17.5000 + 6.06218i −0.671588 + 0.232645i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 0 0
\(682\) 15.0000 0.574380
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) 0 0
\(688\) 2.00000 0.0762493
\(689\) 0 0
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) 0 0
\(697\) 0 0
\(698\) 14.0000 0.529908
\(699\) 0 0
\(700\) 10.0000 3.46410i 0.377964 0.130931i
\(701\) 5.00000 0.188847 0.0944237 0.995532i \(-0.469899\pi\)
0.0944237 + 0.995532i \(0.469899\pi\)
\(702\) 0 0
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) −5.00000 −0.188445
\(705\) 0 0
\(706\) −12.0000 20.7846i −0.451626 0.782239i
\(707\) −20.0000 17.3205i −0.752177 0.651405i
\(708\) 0 0
\(709\) −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) 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
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 10.0000 0.373197
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 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
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) −3.50000 + 6.06218i −0.129808 + 0.224834i −0.923602 0.383353i \(-0.874769\pi\)
0.793794 + 0.608186i \(0.208103\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 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 \(0.647281\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) 22.5000 7.79423i 0.826001 0.286135i
\(743\) 15.0000 + 25.9808i 0.550297 + 0.953142i 0.998253 + 0.0590862i \(0.0188187\pi\)
−0.447956 + 0.894055i \(0.647848\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) −16.0000 27.7128i −0.585802 1.01464i
\(747\) 0 0
\(748\) −20.0000 −0.731272
\(749\) 7.50000 2.59808i 0.274044 0.0949316i
\(750\) 0 0
\(751\) 45.0000 1.64207 0.821037 0.570875i \(-0.193396\pi\)
0.821037 + 0.570875i \(0.193396\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) 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 \(0.938398\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) 0 0
\(760\) −4.00000 + 6.92820i −0.145095 + 0.251312i
\(761\) −8.00000 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) 0 0
\(763\) −1.00000 + 5.19615i −0.0362024 + 0.188113i
\(764\) −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 0.987334 + 0.158655i \(0.0507157\pi\)
−0.356268 + 0.934384i \(0.615951\pi\)
\(770\) −2.50000 + 12.9904i −0.0900937 + 0.468141i
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 5.00000 + 8.66025i 0.179838 + 0.311488i 0.941825 0.336104i \(-0.109109\pi\)
−0.761987 + 0.647592i \(0.775776\pi\)
\(774\) 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
\(781\) 10.0000 0.357828
\(782\) 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
\(787\) 9.00000 15.5885i 0.320815 0.555668i −0.659841 0.751405i \(-0.729376\pi\)
0.980656 + 0.195737i \(0.0627098\pi\)
\(788\) 1.00000 1.73205i 0.0356235 0.0617018i
\(789\) 0 0
\(790\) −1.50000 + 2.59808i −0.0533676 + 0.0924354i
\(791\) −8.00000 + 41.5692i −0.284447 + 1.47803i
\(792\) 0