Properties

Label 1050.2.o.a.949.1
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.a.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(4.00000 + 6.92820i) q^{19} +(2.50000 + 0.866025i) q^{21} -5.00000i q^{22} +(-3.46410 + 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.33013 + 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(3.46410 - 2.00000i) q^{37} +(-6.92820 - 4.00000i) q^{38} +(-2.59808 + 0.500000i) q^{42} +2.00000i q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(5.19615 - 3.00000i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} +8.00000i q^{57} +(-4.33013 + 2.50000i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000i q^{62} +(1.73205 + 2.00000i) q^{63} -1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} -4.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(-4.33013 + 12.5000i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-1.00000 - 1.73205i) q^{86} +(4.33013 + 2.50000i) q^{87} +(-4.33013 - 2.50000i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000i q^{92} +(-2.59808 + 1.50000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} -7.00000i q^{97} +(-4.33013 + 5.50000i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} - 10q^{11} - 8q^{14} - 2q^{16} + 16q^{19} + 10q^{21} - 2q^{24} + 20q^{29} - 6q^{31} + 16q^{34} + 4q^{36} + 10q^{44} + 8q^{46} + 26q^{49} - 8q^{51} - 2q^{54} + 2q^{56} - 22q^{59} + 12q^{61} - 4q^{64} + 10q^{66} - 16q^{69} + 8q^{71} - 8q^{74} + 32q^{76} + 6q^{79} - 2q^{81} + 8q^{84} - 4q^{86} - 12q^{89} - 12q^{94} + 2q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 2.59808 0.500000i 0.981981 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 4.00000 + 6.92820i 0.917663 + 1.58944i 0.802955 + 0.596040i \(0.203260\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 2.50000 + 0.866025i 0.545545 + 0.188982i
\(22\) 5.00000i 1.06600i
\(23\) −3.46410 + 2.00000i −0.722315 + 0.417029i −0.815604 0.578610i \(-0.803595\pi\)
0.0932891 + 0.995639i \(0.470262\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0.866025 2.50000i 0.163663 0.472456i
\(29\) 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 \(0.253495\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −4.33013 + 2.50000i −0.753778 + 0.435194i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.46410 2.00000i 0.569495 0.328798i −0.187453 0.982274i \(-0.560023\pi\)
0.756948 + 0.653476i \(0.226690\pi\)
\(38\) −6.92820 4.00000i −1.12390 0.648886i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −2.59808 + 0.500000i −0.400892 + 0.0771517i
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) 7.79423 + 4.50000i 1.07062 + 0.618123i 0.928351 0.371706i \(-0.121227\pi\)
0.142269 + 0.989828i \(0.454560\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) 8.00000i 1.05963i
\(58\) −4.33013 + 2.50000i −0.568574 + 0.328266i
\(59\) −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 \(0.707841\pi\)
\(62\) 3.00000i 0.381000i
\(63\) 1.73205 + 2.00000i 0.218218 + 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 2.50000 4.33013i 0.307729 0.533002i
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −8.66025 5.00000i −1.01361 0.585206i −0.101361 0.994850i \(-0.532320\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) 8.00000 0.917663
\(77\) −4.33013 + 12.5000i −0.493464 + 1.42451i
\(78\) 0 0
\(79\) 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i \(-0.112689\pi\)
−0.769222 + 0.638982i \(0.779356\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 7.00000i 0.768350i −0.923260 0.384175i \(-0.874486\pi\)
0.923260 0.384175i \(-0.125514\pi\)
\(84\) 2.00000 1.73205i 0.218218 0.188982i
\(85\) 0 0
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 4.33013 + 2.50000i 0.464238 + 0.268028i
\(88\) −4.33013 2.50000i −0.461593 0.266501i
\(89\) −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
\(92\) 4.00000i 0.417029i
\(93\) −2.59808 + 1.50000i −0.269408 + 0.155543i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) −5.00000 −0.502519
\(100\) 0 0
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 3.46410 + 2.00000i 0.342997 + 0.198030i
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) −1.73205 2.00000i −0.163663 0.188982i
\(113\) 16.0000i 1.50515i 0.658505 + 0.752577i \(0.271189\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −4.00000 6.92820i −0.374634 0.648886i
\(115\) 0 0
\(116\) 2.50000 4.33013i 0.232119 0.402042i
\(117\) 0 0
\(118\) 11.0000i 1.01263i
\(119\) −10.0000 3.46410i −0.916698 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −5.19615 3.00000i −0.470438 0.271607i
\(123\) 0 0
\(124\) 1.50000 + 2.59808i 0.134704 + 0.233314i
\(125\) 0 0
\(126\) −2.50000 0.866025i −0.222718 0.0771517i
\(127\) 9.00000i 0.798621i −0.916816 0.399310i \(-0.869250\pi\)
0.916816 0.399310i \(-0.130750\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −1.00000 + 1.73205i −0.0880451 + 0.152499i
\(130\) 0 0
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 13.8564 + 16.0000i 1.20150 + 1.38738i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) −1.73205 1.00000i −0.147979 0.0854358i 0.424182 0.905577i \(-0.360562\pi\)
−0.572161 + 0.820141i \(0.693895\pi\)
\(138\) 3.46410 2.00000i 0.294884 0.170251i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) −1.73205 + 1.00000i −0.145350 + 0.0839181i
\(143\) 0 0
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 6.92820 + 1.00000i 0.571429 + 0.0824786i
\(148\) 4.00000i 0.328798i
\(149\) −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 \(0.885372\pi\)
\(152\) −6.92820 + 4.00000i −0.561951 + 0.324443i
\(153\) 4.00000i 0.323381i
\(154\) −2.50000 12.9904i −0.201456 1.04679i
\(155\) 0 0
\(156\) 0 0
\(157\) −3.46410 2.00000i −0.276465 0.159617i 0.355357 0.934731i \(-0.384359\pi\)
−0.631822 + 0.775113i \(0.717693\pi\)
\(158\) −2.59808 1.50000i −0.206692 0.119334i
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) 0 0
\(161\) −8.00000 + 6.92820i −0.630488 + 0.546019i
\(162\) 1.00000i 0.0785674i
\(163\) −3.46410 + 2.00000i −0.271329 + 0.156652i −0.629492 0.777007i \(-0.716737\pi\)
0.358162 + 0.933659i \(0.383403\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.50000 + 6.06218i 0.271653 + 0.470516i
\(167\) 14.0000i 1.08335i 0.840587 + 0.541676i \(0.182210\pi\)
−0.840587 + 0.541676i \(0.817790\pi\)
\(168\) −0.866025 + 2.50000i −0.0668153 + 0.192879i
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) −4.00000 + 6.92820i −0.305888 + 0.529813i
\(172\) 1.73205 + 1.00000i 0.132068 + 0.0762493i
\(173\) 19.0526 11.0000i 1.44854 0.836315i 0.450145 0.892956i \(-0.351372\pi\)
0.998395 + 0.0566411i \(0.0180391\pi\)
\(174\) −5.00000 −0.379049
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) −9.52628 + 5.50000i −0.716039 + 0.413405i
\(178\) 5.19615 + 3.00000i 0.389468 + 0.224860i
\(179\) 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
\(183\) 6.00000i 0.443533i
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) 0 0
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) 17.3205 10.0000i 1.26660 0.731272i
\(188\) 6.00000i 0.437595i
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −4.33013 2.50000i −0.311689 0.179954i 0.335993 0.941865i \(-0.390928\pi\)
−0.647682 + 0.761911i \(0.724262\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 4.33013 2.50000i 0.307729 0.177667i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0 0
\(201\) −1.00000 1.73205i −0.0705346 0.122169i
\(202\) 10.0000i 0.703598i
\(203\) 12.9904 2.50000i 0.911746 0.175466i
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) −3.46410 2.00000i −0.240772 0.139010i
\(208\) 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 \(0.478069\pi\)
\(212\) 7.79423 4.50000i 0.535310 0.309061i
\(213\) 1.73205 + 1.00000i 0.118678 + 0.0685189i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −2.59808 + 7.50000i −0.176369 + 0.509133i
\(218\) 2.00000i 0.135457i
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 0 0
\(221\) 0 0
\(222\) −3.46410 + 2.00000i −0.232495 + 0.134231i
\(223\) 7.00000i 0.468755i −0.972146 0.234377i \(-0.924695\pi\)
0.972146 0.234377i \(-0.0753051\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −8.00000 13.8564i −0.532152 0.921714i
\(227\) 2.59808 + 1.50000i 0.172440 + 0.0995585i 0.583736 0.811943i \(-0.301590\pi\)
−0.411296 + 0.911502i \(0.634924\pi\)
\(228\) 6.92820 + 4.00000i 0.458831 + 0.264906i
\(229\) −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i \(-0.936876\pi\)
0.319582 0.947559i \(-0.396457\pi\)
\(230\) 0 0
\(231\) −10.0000 + 8.66025i −0.657952 + 0.569803i
\(232\) 5.00000i 0.328266i
\(233\) −3.46410 + 2.00000i −0.226941 + 0.131024i −0.609160 0.793047i \(-0.708493\pi\)
0.382219 + 0.924072i \(0.375160\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.50000 + 9.52628i 0.358020 + 0.620108i
\(237\) 3.00000i 0.194871i
\(238\) 10.3923 2.00000i 0.673633 0.129641i
\(239\) 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 \(-0.131273\pi\)
\(242\) 12.1244 + 7.00000i 0.779383 + 0.449977i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −2.59808 1.50000i −0.164978 0.0952501i
\(249\) 3.50000 6.06218i 0.221803 0.384175i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 2.59808 0.500000i 0.163663 0.0314970i
\(253\) 20.0000i 1.25739i
\(254\) 4.50000 + 7.79423i 0.282355 + 0.489053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.19615 3.00000i 0.324127 0.187135i −0.329104 0.944294i \(-0.606747\pi\)
0.653231 + 0.757159i \(0.273413\pi\)
\(258\) 2.00000i 0.124515i
\(259\) 8.00000 6.92820i 0.497096 0.430498i
\(260\) 0 0
\(261\) 2.50000 + 4.33013i 0.154746 + 0.268028i
\(262\) 0.866025 + 0.500000i 0.0535032 + 0.0308901i
\(263\) 25.9808 + 15.0000i 1.60204 + 0.924940i 0.991078 + 0.133281i \(0.0425514\pi\)
0.610964 + 0.791658i \(0.290782\pi\)
\(264\) −2.50000 4.33013i −0.153864 0.266501i
\(265\) 0 0
\(266\) −20.0000 6.92820i −1.22628 0.424795i
\(267\) 6.00000i 0.367194i
\(268\) −1.73205 + 1.00000i −0.105802 + 0.0610847i
\(269\) 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 \(0.983906\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) −2.00000 + 3.46410i −0.120386 + 0.208514i
\(277\) −13.8564 8.00000i −0.832551 0.480673i 0.0221745 0.999754i \(-0.492941\pi\)
−0.854725 + 0.519081i \(0.826274\pi\)
\(278\) −12.1244 + 7.00000i −0.727171 + 0.419832i
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −5.19615 + 3.00000i −0.309426 + 0.178647i
\(283\) −8.66025 5.00000i −0.514799 0.297219i 0.220005 0.975499i \(-0.429393\pi\)
−0.734804 + 0.678280i \(0.762726\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) −8.66025 + 5.00000i −0.506803 + 0.292603i
\(293\) 21.0000i 1.22683i −0.789760 0.613417i \(-0.789795\pi\)
0.789760 0.613417i \(-0.210205\pi\)
\(294\) −6.50000 + 2.59808i −0.379088 + 0.151523i
\(295\) 0 0
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) −4.33013 2.50000i −0.251259 0.145065i
\(298\) 15.5885 + 9.00000i 0.903015 + 0.521356i
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 + 5.19615i 0.0576390 + 0.299501i
\(302\) 19.0000i 1.09333i
\(303\) −8.66025 + 5.00000i −0.497519 + 0.287242i
\(304\) 4.00000 6.92820i 0.229416 0.397360i
\(305\) 0 0
\(306\) 2.00000 + 3.46410i 0.114332 + 0.198030i
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 8.66025 + 10.0000i 0.493464 + 0.569803i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 16.0000 27.7128i 0.907277 1.57145i 0.0894452 0.995992i \(-0.471491\pi\)
0.817832 0.575458i \(-0.195176\pi\)
\(312\) 0 0
\(313\) 0.866025 0.500000i 0.0489506 0.0282617i −0.475325 0.879810i \(-0.657669\pi\)
0.524276 + 0.851549i \(0.324336\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) −2.59808 + 1.50000i −0.145922 + 0.0842484i −0.571184 0.820822i \(-0.693516\pi\)
0.425261 + 0.905071i \(0.360182\pi\)
\(318\) −7.79423 4.50000i −0.437079 0.252347i
\(319\) −12.5000 + 21.6506i −0.699866 + 1.21220i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) 3.46410 10.0000i 0.193047 0.557278i
\(323\) 32.0000i 1.78053i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) −1.73205 + 1.00000i −0.0957826 + 0.0553001i
\(328\) 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 \(0.798271\pi\)
\(332\) −6.06218 3.50000i −0.332705 0.192087i
\(333\) 3.46410 + 2.00000i 0.189832 + 0.109599i
\(334\) −7.00000 12.1244i −0.383023 0.663415i
\(335\) 0 0
\(336\) −0.500000 2.59808i −0.0272772 0.141737i
\(337\) 9.00000i 0.490261i −0.969490 0.245131i \(-0.921169\pi\)
0.969490 0.245131i \(-0.0788309\pi\)
\(338\) −11.2583 + 6.50000i −0.612372 + 0.353553i
\(339\) −8.00000 + 13.8564i −0.434500 + 0.752577i
\(340\) 0 0
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 8.00000i 0.432590i
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) −11.0000 + 19.0526i −0.591364 + 1.02427i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 4.33013 2.50000i 0.232119 0.134014i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.33013 + 2.50000i −0.230797 + 0.133250i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 5.50000 9.52628i 0.292322 0.506316i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −6.92820 8.00000i −0.366679 0.423405i
\(358\) 12.0000i 0.634220i
\(359\) 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
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 0 0
\(366\) −3.00000 5.19615i −0.156813 0.271607i
\(367\) 14.7224 + 8.50000i 0.768505 + 0.443696i 0.832341 0.554264i \(-0.187000\pi\)
−0.0638362 + 0.997960i \(0.520334\pi\)
\(368\) 3.46410 + 2.00000i 0.180579 + 0.104257i
\(369\) 0 0
\(370\) 0 0
\(371\) 22.5000 + 7.79423i 1.16814 + 0.404656i
\(372\) 3.00000i 0.155543i
\(373\) −27.7128 + 16.0000i −1.43492 + 0.828449i −0.997490 0.0708063i \(-0.977443\pi\)
−0.437425 + 0.899255i \(0.644109\pi\)
\(374\) −10.0000 + 17.3205i −0.517088 + 0.895622i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 0 0
\(378\) −1.73205 2.00000i −0.0890871 0.102869i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 4.50000 7.79423i 0.230542 0.399310i
\(382\) 20.7846 + 12.0000i 1.06343 + 0.613973i
\(383\) −29.4449 + 17.0000i −1.50456 + 0.868659i −0.504576 + 0.863367i \(0.668351\pi\)
−0.999986 + 0.00529229i \(0.998315\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) −1.73205 + 1.00000i −0.0880451 + 0.0508329i
\(388\) −6.06218 3.50000i −0.307760 0.177686i
\(389\) −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
\(392\) 2.59808 + 6.50000i 0.131223 + 0.328300i
\(393\) 1.00000i 0.0504433i
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) −2.50000 + 4.33013i −0.125630 + 0.217597i
\(397\) −31.1769 + 18.0000i −1.56472 + 0.903394i −0.567957 + 0.823058i \(0.692266\pi\)
−0.996768 + 0.0803356i \(0.974401\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 4.00000 + 20.7846i 0.200250 + 1.04053i
\(400\) 0 0
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 1.73205 + 1.00000i 0.0863868 + 0.0498755i
\(403\) 0 0
\(404\) 5.00000 + 8.66025i 0.248759 + 0.430864i
\(405\) 0 0
\(406\) −10.0000 + 8.66025i −0.496292 + 0.429801i
\(407\) 20.0000i 0.991363i
\(408\) 3.46410 2.00000i 0.171499 0.0990148i
\(409\) −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) 0 0
\(411\) −1.00000 1.73205i −0.0493264 0.0854358i
\(412\) 8.00000i 0.394132i
\(413\) −9.52628 + 27.5000i −0.468758 + 1.35319i
\(414\) 4.00000 0.196589
\(415\) 0 0
\(416\) 0 0
\(417\) 12.1244 + 7.00000i 0.593732 + 0.342791i
\(418\) 34.6410 20.0000i 1.69435 0.978232i
\(419\) 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 \(0.239028\pi\)
\(422\) −1.73205 + 1.00000i −0.0843149 + 0.0486792i
\(423\) 5.19615 + 3.00000i 0.252646 + 0.145865i
\(424\) −4.50000 + 7.79423i −0.218539 + 0.378521i
\(425\) 0 0
\(426\) −2.00000 −0.0969003
\(427\) 10.3923 + 12.0000i 0.502919 + 0.580721i
\(428\) 3.00000i 0.145010i
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) −1.50000 7.79423i −0.0720023 0.374135i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −27.7128 16.0000i −1.32568 0.765384i
\(438\) 8.66025 + 5.00000i 0.413803 + 0.238909i
\(439\) 7.50000 + 12.9904i 0.357955 + 0.619997i 0.987619 0.156871i \(-0.0501406\pi\)
−0.629664 + 0.776868i \(0.716807\pi\)
\(440\) 0 0
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 0 0
\(443\) 14.7224 8.50000i 0.699484 0.403847i −0.107671 0.994187i \(-0.534339\pi\)
0.807155 + 0.590339i \(0.201006\pi\)
\(444\) 2.00000 3.46410i 0.0949158 0.164399i
\(445\) 0 0
\(446\) 3.50000 + 6.06218i 0.165730 + 0.287052i
\(447\) 18.0000i 0.851371i
\(448\) −2.59808 + 0.500000i −0.122748 + 0.0236228i
\(449\) −16.0000 −0.755087 −0.377543 0.925992i \(-0.623231\pi\)
−0.377543 + 0.925992i \(0.623231\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 13.8564 + 8.00000i 0.651751 + 0.376288i
\(453\) −16.4545 + 9.50000i −0.773099 + 0.446349i
\(454\) −3.00000 −0.140797
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) −26.8468 + 15.5000i −1.25584 + 0.725059i −0.972263 0.233890i \(-0.924854\pi\)
−0.283577 + 0.958950i \(0.591521\pi\)
\(458\) 17.3205 + 10.0000i 0.809334 + 0.467269i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 4.33013 12.5000i 0.201456 0.581553i
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) −2.50000 4.33013i −0.116060 0.201021i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 17.3205 10.0000i 0.801498 0.462745i −0.0424970 0.999097i \(-0.513531\pi\)
0.843995 + 0.536352i \(0.180198\pi\)
\(468\) 0 0
\(469\) −5.00000 1.73205i −0.230879 0.0799787i
\(470\) 0 0
\(471\) −2.00000 3.46410i −0.0921551 0.159617i
\(472\) −9.52628 5.50000i −0.438483 0.253158i
\(473\) −8.66025 5.00000i −0.398199 0.229900i
\(474\) −1.50000 2.59808i −0.0688973 0.119334i
\(475\) 0 0
\(476\) −8.00000 + 6.92820i −0.366679 + 0.317554i
\(477\) 9.00000i 0.412082i
\(478\) −10.3923 + 6.00000i −0.475333 + 0.274434i
\(479\) 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
\(482\) 25.0000i 1.13872i
\(483\) −10.3923 + 2.00000i −0.472866 + 0.0910032i
\(484\) −14.0000 −0.636364
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 4.33013 + 2.50000i 0.196217 + 0.113286i 0.594890 0.803807i \(-0.297196\pi\)
−0.398673 + 0.917093i \(0.630529\pi\)
\(488\) −5.19615 + 3.00000i −0.235219 + 0.135804i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 9.00000 0.406164 0.203082 0.979162i \(-0.434904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(492\) 0 0
\(493\) −17.3205 10.0000i −0.780076 0.450377i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) 5.19615 1.00000i 0.233079 0.0448561i
\(498\) 7.00000i 0.313678i
\(499\) 5.00000 + 8.66025i 0.223831 + 0.387686i 0.955968 0.293471i \(-0.0948104\pi\)
−0.732137 + 0.681157i \(0.761477\pi\)
\(500\) 0 0
\(501\) −7.00000 + 12.1244i −0.312737 + 0.541676i
\(502\) −18.1865 + 10.5000i −0.811705 + 0.468638i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) 10.0000 + 17.3205i 0.444554 + 0.769991i
\(507\) 11.2583 + 6.50000i 0.500000 + 0.288675i
\(508\) −7.79423 4.50000i −0.345813 0.199655i
\(509\) 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
\(512\) 1.00000i 0.0441942i
\(513\) −6.92820 + 4.00000i −0.305888 + 0.176604i
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) 0 0
\(516\) 1.00000 + 1.73205i 0.0440225 + 0.0762493i
\(517\) 30.0000i 1.31940i
\(518\) −3.46410 + 10.0000i −0.152204 + 0.439375i
\(519\) 22.0000 0.965693
\(520\) 0 0
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) −4.33013 2.50000i −0.189525 0.109422i
\(523\) 6.92820 4.00000i 0.302949 0.174908i −0.340818 0.940129i \(-0.610704\pi\)
0.643767 + 0.765222i \(0.277371\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) 10.3923 6.00000i 0.452696 0.261364i
\(528\) 4.33013 + 2.50000i 0.188445 + 0.108799i
\(529\) −3.50000 + 6.06218i −0.152174 + 0.263573i
\(530\) 0 0
\(531\) −11.0000 −0.477359
\(532\) 20.7846 4.00000i 0.901127 0.173422i
\(533\) 0 0
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) 0 0
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 10.3923 6.00000i 0.448461 0.258919i
\(538\) 31.0000i 1.33650i
\(539\) −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 \(0.706865\pi\)
\(542\) 12.9904 + 7.50000i 0.557985 + 0.322153i
\(543\) 0 0
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000i 0.513083i 0.966533 + 0.256541i \(0.0825830\pi\)
−0.966533 + 0.256541i \(0.917417\pi\)
\(548\) −1.73205 + 1.00000i −0.0739895 + 0.0427179i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) 20.0000 + 34.6410i 0.852029 + 1.47576i
\(552\) 4.00000i 0.170251i
\(553\) 5.19615 + 6.00000i 0.220963 + 0.255146i
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) 7.00000 12.1244i 0.296866 0.514187i
\(557\) −19.9186 11.5000i −0.843978 0.487271i 0.0146368 0.999893i \(-0.495341\pi\)
−0.858614 + 0.512622i \(0.828674\pi\)
\(558\) 2.59808 1.50000i 0.109985 0.0635001i
\(559\) 0 0
\(560\) 0 0
\(561\) 20.0000 0.844401
\(562\) −1.73205 + 1.00000i −0.0730622 + 0.0421825i
\(563\) −14.7224 8.50000i −0.620477 0.358232i 0.156578 0.987666i \(-0.449954\pi\)
−0.777055 + 0.629433i \(0.783287\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) 0 0
\(566\) 10.0000 0.420331
\(567\) −0.866025 + 2.50000i −0.0363696 + 0.104990i
\(568\) 2.00000i 0.0839181i
\(569\) 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
\(573\) 24.0000i 1.00261i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 26.8468 + 15.5000i 1.11765 + 0.645273i 0.940799 0.338965i \(-0.110077\pi\)
0.176847 + 0.984238i \(0.443410\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) −2.50000 4.33013i −0.103896 0.179954i
\(580\) 0 0
\(581\) −3.50000 18.1865i −0.145204 0.754505i
\(582\) 7.00000i 0.290159i
\(583\) −38.9711 + 22.5000i −1.61402 + 0.931855i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) 0 0
\(586\) 10.5000 + 18.1865i 0.433751 + 0.751279i
\(587\) 35.0000i 1.44460i −0.691577 0.722302i \(-0.743084\pi\)
0.691577 0.722302i \(-0.256916\pi\)
\(588\) 4.33013 5.50000i 0.178571 0.226816i
\(589\) −24.0000 −0.988903
\(590\) 0 0
\(591\) 1.00000 1.73205i 0.0411345 0.0712470i
\(592\) −3.46410 2.00000i −0.142374 0.0821995i
\(593\) 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i \(-0.401884\pi\)
0.976900 + 0.213697i \(0.0685507\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) −3.46410 + 2.00000i −0.141776 + 0.0818546i
\(598\) 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 \(0.246954\pi\)
\(602\) −3.46410 4.00000i −0.141186 0.163028i
\(603\) 2.00000i 0.0814463i
\(604\) 9.50000 + 16.4545i 0.386550 + 0.669523i
\(605\) 0 0
\(606\) 5.00000 8.66025i 0.203111 0.351799i
\(607\) 23.3827 13.5000i 0.949074 0.547948i 0.0562808 0.998415i \(-0.482076\pi\)
0.892793 + 0.450467i \(0.148742\pi\)
\(608\) 8.00000i 0.324443i
\(609\) 12.5000 + 4.33013i 0.506526 + 0.175466i
\(610\) 0 0
\(611\) 0 0
\(612\) −3.46410 2.00000i −0.140028 0.0808452i
\(613\) −10.3923 6.00000i −0.419741 0.242338i 0.275225 0.961380i \(-0.411248\pi\)
−0.694967 + 0.719042i \(0.744581\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) −12.5000 4.33013i −0.503639 0.174466i
\(617\) 2.00000i 0.0805170i −0.999189 0.0402585i \(-0.987182\pi\)
0.999189 0.0402585i \(-0.0128181\pi\)
\(618\) −6.92820 + 4.00000i −0.278693 + 0.160904i
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 32.0000i 1.28308i
\(623\) −10.3923 12.0000i −0.416359 0.480770i
\(624\) 0 0
\(625\) 0 0
\(626\) −0.500000 + 0.866025i −0.0199840 + 0.0346133i
\(627\) −34.6410 20.0000i −1.38343 0.798723i
\(628\) −3.46410 + 2.00000i −0.138233 + 0.0798087i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −19.0000 −0.756378 −0.378189 0.925728i \(-0.623453\pi\)
−0.378189 + 0.925728i \(0.623453\pi\)
\(632\) −2.59808 + 1.50000i −0.103346 + 0.0596668i
\(633\) 1.73205 + 1.00000i 0.0688428 + 0.0397464i
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) 0 0
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) 25.0000i 0.989759i
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i \(0.338307\pi\)
−0.999878 + 0.0156233i \(0.995027\pi\)
\(642\) 2.59808 1.50000i 0.102538 0.0592003i
\(643\) 14.0000i 0.552106i 0.961142 + 0.276053i \(0.0890266\pi\)
−0.961142 + 0.276053i \(0.910973\pi\)
\(644\) 2.00000 + 10.3923i 0.0788110 + 0.409514i
\(645\) 0 0
\(646\) 16.0000 + 27.7128i 0.629512 + 1.09035i
\(647\) −15.5885 9.00000i −0.612845 0.353827i 0.161233 0.986916i \(-0.448453\pi\)
−0.774078 + 0.633090i \(0.781786\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −27.5000 47.6314i −1.07947 1.86970i
\(650\) 0 0
\(651\) −6.00000 + 5.19615i −0.235159 + 0.203653i
\(652\) 4.00000i 0.156652i
\(653\) −33.7750 + 19.5000i −1.32172 + 0.763094i −0.984003 0.178154i \(-0.942987\pi\)
−0.337715 + 0.941248i \(0.609654\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 0 0
\(656\) 0 0
\(657\) 10.0000i 0.390137i
\(658\) −5.19615 + 15.0000i −0.202567 + 0.584761i
\(659\) 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 \(0.228968\pi\)
\(662\) −3.46410 2.00000i −0.134636 0.0777322i
\(663\) 0 0
\(664\) 7.00000 0.271653
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) −17.3205 + 10.0000i −0.670653 + 0.387202i
\(668\) 12.1244 + 7.00000i 0.469105 + 0.270838i
\(669\) 3.50000 6.06218i 0.135318 0.234377i
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 1.73205 + 2.00000i 0.0668153 + 0.0771517i
\(673\) 19.0000i 0.732396i −0.930537 0.366198i \(-0.880659\pi\)
0.930537 0.366198i \(-0.119341\pi\)
\(674\) 4.50000 + 7.79423i 0.173334 + 0.300222i
\(675\) 0 0
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 23.3827 13.5000i 0.898670 0.518847i 0.0219013 0.999760i \(-0.493028\pi\)
0.876768 + 0.480913i \(0.159695\pi\)
\(678\) 16.0000i 0.614476i
\(679\) −3.50000 18.1865i −0.134318 0.697935i
\(680\) 0 0
\(681\) 1.50000 + 2.59808i 0.0574801 + 0.0995585i
\(682\) 12.9904 + 7.50000i 0.497427 + 0.287190i
\(683\) 7.79423 + 4.50000i 0.298238 + 0.172188i 0.641651 0.766997i \(-0.278250\pi\)
−0.343413 + 0.939184i \(0.611583\pi\)
\(684\) 4.00000 + 6.92820i 0.152944 + 0.264906i
\(685\) 0 0
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 20.0000i 0.763048i
\(688\) 1.73205 1.00000i 0.0660338 0.0381246i
\(689\) 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 \(0.881959\pi\)
\(692\) 22.0000i 0.836315i
\(693\) −12.9904 + 2.50000i −0.493464 + 0.0949671i
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) −2.50000 + 4.33013i −0.0947623 + 0.164133i
\(697\) 0 0
\(698\) −12.1244 + 7.00000i −0.458914 + 0.264954i
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) 0 0
\(703\) 27.7128 + 16.0000i 1.04521 + 0.603451i
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) −8.66025 + 25.0000i −0.325702 + 0.940222i
\(708\) 11.0000i 0.413405i
\(709\) 19.0000 + 32.9090i 0.713560 + 1.23592i 0.963512 + 0.267664i \(0.0862517\pi\)
−0.249952 + 0.968258i \(0.580415\pi\)
\(710\) 0 0
\(711\) −1.50000 + 2.59808i −0.0562544 + 0.0974355i
\(712\) 5.19615 3.00000i 0.194734 0.112430i
\(713\) 12.0000i 0.449404i
\(714\) 10.0000 + 3.46410i 0.374241 + 0.129641i
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 10.3923 + 6.00000i 0.388108 + 0.224074i
\(718\) −8.66025 5.00000i −0.323198 0.186598i
\(719\) −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
\(722\) 45.0000i 1.67473i
\(723\) 21.6506 12.5000i 0.805196 0.464880i
\(724\) 0 0
\(725\) 0 0
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 7.00000i 0.259616i −0.991539 0.129808i \(-0.958564\pi\)
0.991539 0.129808i \(-0.0414360\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 5.19615 + 3.00000i 0.192055 + 0.110883i
\(733\) −5.19615 + 3.00000i −0.191924 + 0.110808i −0.592883 0.805289i \(-0.702010\pi\)
0.400959 + 0.916096i \(0.368677\pi\)
\(734\) −17.0000 −0.627481
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 8.66025 5.00000i 0.319005 0.184177i
\(738\) 0 0
\(739\) −15.0000 + 25.9808i −0.551784 + 0.955718i 0.446362 + 0.894852i \(0.352719\pi\)
−0.998146 + 0.0608653i \(0.980614\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −23.3827 + 4.50000i −0.858405 + 0.165200i
\(743\) 30.0000i 1.10059i 0.834969 + 0.550297i \(0.185485\pi\)
−0.834969 + 0.550297i \(0.814515\pi\)
\(744\) −1.50000 2.59808i −0.0549927 0.0952501i
\(745\) 0 0
\(746\) 16.0000 27.7128i 0.585802 1.01464i
\(747\) 6.06218 3.50000i 0.221803 0.128058i
\(748\) 20.0000i 0.731272i
\(749\) −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 \(-0.473271\pi\)
\(752\) −5.19615 3.00000i −0.189484 0.109399i
\(753\) 18.1865 + 10.5000i 0.662754 + 0.382641i
\(754\) 0 0
\(755\) 0 0
\(756\) 2.50000 + 0.866025i 0.0909241 + 0.0314970i
\(757\) 54.0000i 1.96266i 0.192323 + 0.981332i \(0.438398\pi\)
−0.192323 + 0.981332i \(0.561602\pi\)
\(758\) 13.8564 8.00000i 0.503287 0.290573i
\(759\) 10.0000 17.3205i 0.362977 0.628695i
\(760\) 0 0
\(761\) −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i \(-0.212985\pi\)
−0.929373 + 0.369142i \(0.879652\pi\)
\(762\) 9.00000i 0.326036i
\(763\) −1.73205 + 5.00000i −0.0627044 + 0.181012i
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 17.0000 29.4449i 0.614235 1.06389i
\(767\) 0 0
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) −4.33013 + 2.50000i −0.155845 + 0.0899770i
\(773\) −8.66025 5.00000i −0.311488 0.179838i 0.336104 0.941825i \(-0.390891\pi\)
−0.647592 + 0.761987i \(0.724224\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) 10.3923 2.00000i 0.372822 0.0717496i
\(778\) 2.00000i 0.0717035i
\(779\) 0 0
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) −13.8564 + 8.00000i −0.495504 + 0.286079i
\(783\) 5.00000i 0.178685i
\(784\) −5.50000 4.33013i −0.196429 0.154647i
\(785\) 0 0
\(786\) 0.500000 + 0.866025i 0.0178344 + 0.0308901i
\(787\) −15.5885 9.00000i −0.555668 0.320815i 0.195737