Properties

Label 126.2.g.c.109.1
Level $126$
Weight $2$
Character 126.109
Analytic conductor $1.006$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00611506547\)
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 109.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.2.g.c.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 - 0.866025i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(4.00000 - 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(-4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.50000 - 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 + 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(0.500000 - 0.866025i) q^{80} +7.00000 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + q^{5} + q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + q^{5} + q^{7} - 2q^{8} - q^{10} + 5q^{11} - 4q^{14} - q^{16} - 4q^{17} - 8q^{19} - 2q^{20} + 10q^{22} - 4q^{23} + 4q^{25} - 5q^{28} + 10q^{29} - 3q^{31} + q^{32} - 8q^{34} - 4q^{35} + 4q^{37} + 8q^{38} - q^{40} + 4q^{43} + 5q^{44} + 4q^{46} - 6q^{47} - 13q^{49} + 8q^{50} - 9q^{53} + 10q^{55} - q^{56} + 5q^{58} - 11q^{59} + 6q^{61} - 6q^{62} + 2q^{64} + 2q^{67} - 4q^{68} - 5q^{70} - 4q^{71} - 10q^{73} - 4q^{74} + 16q^{76} + 25q^{77} - 3q^{79} + q^{80} + 14q^{83} - 8q^{85} + 2q^{86} - 5q^{88} - 6q^{89} + 8q^{92} + 6q^{94} + 8q^{95} + 14q^{97} - 11q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) −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 \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −4.00000 6.92820i −0.917663 1.58944i −0.802955 0.596040i \(-0.796740\pi\)
−0.114708 0.993399i \(-0.536593\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 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
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 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
\(34\) −4.00000 −0.685994
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 0 0
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 4.00000 6.92820i 0.648886 1.12390i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 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
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 0 0
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) −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 \(0.127682\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 0 0
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) −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 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) 8.00000 0.917663
\(77\) 12.5000 + 4.33013i 1.42451 + 0.493464i
\(78\) 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
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 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 \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −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 −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 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
\(106\) −9.00000 −0.874157
\(107\) 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i \(-0.120345\pi\)
−0.784366 + 0.620298i \(0.787012\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 2.50000 + 4.33013i 0.238366 + 0.412861i
\(111\) 0 0
\(112\) 2.00000 1.73205i 0.188982 0.163663i
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 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
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −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
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 0 0
\(133\) 16.0000 13.8564i 1.38738 1.20150i
\(134\) 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 −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) −0.500000 2.59808i −0.0422577 0.219578i
\(141\) 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
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 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
\(155\) −3.00000 −0.240966
\(156\) 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
\(160\) 1.00000 0.0790569
\(161\) 8.00000 6.92820i 0.630488 0.546019i
\(162\) 0 0
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.50000 + 6.06218i 0.271653 + 0.470516i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −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
\(175\) 10.0000 + 3.46410i 0.755929 + 0.261861i
\(176\) −5.00000 −0.376889
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 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
\(185\) −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 \(0.224262\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) −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 −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 2.50000 + 12.9904i 0.175466 + 0.911746i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) 0 0
\(208\) 0 0
\(209\) −40.0000 −2.76686
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) −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
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) −2.50000 + 4.33013i −0.168550 + 0.291937i
\(221\) 0 0
\(222\) 0 0
\(223\) −7.00000 −0.468755 −0.234377 0.972146i \(-0.575305\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(224\) 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 −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i \(0.0631241\pi\)
−0.319582 + 0.947559i \(0.603543\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −2.00000 3.46410i −0.131024 0.226941i 0.793047 0.609160i \(-0.208493\pi\)
−0.924072 + 0.382219i \(0.875160\pi\)
\(234\) 0 0
\(235\) 3.00000 5.19615i 0.195698 0.338960i
\(236\) −5.50000 9.52628i −0.358020 0.620108i
\(237\) 0 0
\(238\) −2.00000 10.3923i −0.129641 0.673633i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 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
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 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
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 0 0
\(259\) −8.00000 + 6.92820i −0.497096 + 0.430498i
\(260\) 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 \(0.542551\pi\)
−0.791658 + 0.610964i \(0.790782\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 20.0000 + 6.92820i 1.22628 + 0.424795i
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 15.5000 26.8468i 0.945052 1.63688i 0.189404 0.981899i \(-0.439344\pi\)
0.755648 0.654978i \(-0.227322\pi\)
\(270\) 0 0
\(271\) −7.50000 12.9904i −0.455593 0.789109i 0.543130 0.839649i \(-0.317239\pi\)
−0.998722 + 0.0505395i \(0.983906\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −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
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 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
\(290\) −2.50000 + 4.33013i −0.146805 + 0.254274i
\(291\) 0 0
\(292\) −5.00000 8.66025i −0.292603 0.506803i
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 0 0
\(295\) −11.0000 −0.640445
\(296\) −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
\(301\) 1.00000 + 5.19615i 0.0576390 + 0.299501i
\(302\) −19.0000 −1.09333
\(303\) 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 \(0.205351\pi\)
\(308\) −10.0000 + 8.66025i −0.569803 + 0.493464i
\(309\) 0 0
\(310\) −1.50000 2.59808i −0.0851943 0.147561i
\(311\) −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
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 10.0000 + 3.46410i 0.557278 + 0.193047i
\(323\) 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
\(329\) 12.0000 10.3923i 0.661581 0.572946i
\(330\) 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
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) −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
\(344\) −2.00000 −0.107833
\(345\) 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
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 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 \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) −1.00000 1.73205i −0.0530745 0.0919277i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 5.00000 + 8.66025i 0.263890 + 0.457071i 0.967272 0.253741i \(-0.0816611\pi\)
−0.703382 + 0.710812i \(0.748328\pi\)
\(360\) 0 0
\(361\) −22.5000 + 38.9711i −1.18421 + 2.05111i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) 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
\(371\) −22.5000 7.79423i −1.16814 0.404656i
\(372\) 0 0
\(373\) 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i \(0.144109\pi\)
−0.0708063 + 0.997490i \(0.522557\pi\)
\(374\) −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
\(383\) −17.0000 29.4449i −0.868659 1.50456i −0.863367 0.504576i \(-0.831649\pi\)
−0.00529229 0.999986i \(-0.501685\pi\)
\(384\) 0 0
\(385\) 2.50000 + 12.9904i 0.127412 + 0.662051i
\(386\) −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 −0.890263 0.455448i \(-0.849479\pi\)
0.839561 + 0.543266i \(0.182813\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 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 −0.823058 0.567957i \(-0.807734\pi\)
−0.0803356 0.996768i \(-0.525599\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) 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
\(407\) 20.0000 0.991363
\(408\) 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
\(412\) 8.00000 0.394132
\(413\) −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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 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
\(427\) −12.0000 + 10.3923i −0.580721 + 0.502919i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) −1.00000 + 1.73205i −0.0482243 + 0.0835269i
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −1.50000 7.79423i −0.0720023 0.374135i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −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
\(446\) −3.50000 6.06218i −0.165730 0.287052i
\(447\) 0 0
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) −16.0000 −0.755087 −0.377543 0.925992i \(-0.623231\pi\)
−0.377543 + 0.925992i \(0.623231\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 8.00000 13.8564i 0.376288 0.651751i
\(453\) 0 0
\(454\) 3.00000 0.140797
\(455\) 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
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −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 \(-0.319802\pi\)
−0.999097 + 0.0424970i \(0.986469\pi\)
\(468\) 0 0
\(469\) 5.00000 + 1.73205i 0.230879 + 0.0799787i
\(470\) 6.00000 0.276759
\(471\) 0 0
\(472\) 5.50000 9.52628i 0.253158 0.438483i
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) 0 0
\(475\) −32.0000 −1.46826
\(476\) 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 \(-0.498654\pi\)
0.863903 0.503658i \(-0.168013\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 25.0000 1.13872
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 0 0
\(487\) −2.50000 + 4.33013i −0.113286 + 0.196217i −0.917093 0.398673i \(-0.869471\pi\)
0.803807 + 0.594890i \(0.202804\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) 0 0
\(490\) 1.00000 6.92820i 0.0451754 0.312984i
\(491\) −9.00000 −0.406164 −0.203082 0.979162i \(-0.565096\pi\)
−0.203082 + 0.979162i \(0.565096\pi\)
\(492\) 0 0
\(493\) −10.0000 + 17.3205i −0.450377 + 0.780076i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) −1.00000 5.19615i −0.0448561 0.233079i
\(498\) 0 0
\(499\) −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) −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
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) −25.0000 8.66025i −1.10593 0.383107i
\(512\) −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
\(517\) −30.0000 −1.31940
\(518\) −10.0000 3.46410i −0.439375 0.152204i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 0 0
\(523\) −4.00000 6.92820i −0.174908 0.302949i 0.765222 0.643767i \(-0.222629\pi\)
−0.940129 + 0.340818i \(0.889296\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) −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
\(535\) −1.50000 + 2.59808i −0.0648507 + 0.112325i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 31.0000 1.33650
\(539\) −5.00000 + 34.6410i −0.215365 + 1.49209i
\(540\) 0 0
\(541\) 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 7.50000 12.9904i 0.322153 0.557985i
\(543\) 0 0
\(544\) 2.00000 + 3.46410i 0.0857493 + 0.148522i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −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
\(553\) 6.00000 5.19615i 0.255146 0.220963i
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) 7.00000 12.1244i 0.296866 0.514187i
\(557\) −11.5000 + 19.9186i −0.487271 + 0.843978i −0.999893 0.0146368i \(-0.995341\pi\)
0.512622 + 0.858614i \(0.328674\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) 0 0
\(562\) −1.00000 1.73205i −0.0421825 0.0730622i
\(563\) 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 0.338965 + 0.940799i \(0.389923\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) 0 0
\(580\) −5.00000 −0.207614
\(581\) 3.50000 + 18.1865i 0.145204 + 0.754505i
\(582\) 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
\(587\) −35.0000 −1.44460 −0.722302 0.691577i \(-0.756916\pi\)
−0.722302 + 0.691577i \(0.756916\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) −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 0.952869 + 0.303383i \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) 0 0
\(595\) −2.00000 10.3923i −0.0819920 0.426043i
\(596\) 18.0000 0.737309
\(597\) 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
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) −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 \(0.648742\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) −6.00000 −0.242933
\(611\) 0 0
\(612\) 0 0
\(613\) −6.00000 + 10.3923i −0.242338 + 0.419741i −0.961380 0.275225i \(-0.911248\pi\)
0.719042 + 0.694967i \(0.244581\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) −12.5000 4.33013i −0.503639 0.174466i
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 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
\(623\) 12.0000 10.3923i 0.480770 0.416359i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 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
\(635\) 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 \(-0.661693\pi\)
0.999878 0.0156233i \(-0.00497325\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 2.00000 + 10.3923i 0.0788110 + 0.409514i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) 0 0
\(649\) 27.5000 + 47.6314i 1.07947 + 1.86970i
\(650\) 0 0
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i \(-0.890346\pi\)
0.178154 0.984003i \(-0.442987\pi\)
\(654\) 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
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 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
\(664\) −7.00000 −0.271653
\(665\) 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
\(671\) 30.0000 1.15814
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 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
\(679\) 3.50000 + 18.1865i 0.134318 + 0.697935i
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 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
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 0 0
\(700\) −8.00000 + 6.92820i −0.302372 + 0.261861i
\(701\) 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
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 25.0000 + 8.66025i 0.940222 + 0.325702i
\(708\) 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
\(713\) 12.0000 0.449404
\(714\) 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 \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) −45.0000 −1.67473
\(723\) 0 0
\(724\) 0 0
\(725\) 10.0000 17.3205i 0.371391 0.643268i
\(726\) 0 0
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 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 \(0.797990\pi\)
\(734\) −17.0000 −0.627481
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −5.00000 8.66025i −0.184177 0.319005i
\(738\) 0 0
\(739\) 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i \(-0.647281\pi\)
0.998146 0.0608653i \(-0.0193860\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) −4.50000 23.3827i −0.165200 0.858405i
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) 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
\(749\) −6.00000 + 5.19615i −0.219235 + 0.189863i
\(750\) 0 0
\(751\) −22.5000 38.9711i −0.821037 1.42208i −0.904911 0.425601i \(-0.860063\pi\)
0.0838743 0.996476i \(-0.473271\pi\)
\(752\) −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
\(761\) 4.00000 + 6.92820i 0.145000 + 0.251147i 0.929373 0.369142i \(-0.120348\pi\)
−0.784373 + 0.620289i \(0.787015\pi\)
\(762\) 0 0
\(763\) 5.00000 + 1.73205i 0.181012 + 0.0627044i
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 17.0000 29.4449i 0.614235 1.06389i
\(767\) 0 0
\(768\) 0 0
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) −10.0000 + 8.66025i −0.360375 + 0.312094i
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i \(-0.775776\pi\)
0.941825 + 0.336104i \(0.109109\pi\)
\(774\) 0 0
\(775\) 6.00000 + 10.3923i 0.215526 + 0.373303i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) −2.00000 −0.0717035
\(779\) 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
\(785\) 4.00000 0.142766
\(786\) 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
\(790\) 3.00000 0.106735
\(791\) −8.00000 41.5692i −0.284447 1.47803i
\(792\) 0 0
\(793\) 0 0