Properties

Label 1050.2.i.l.751.1
Level $1050$
Weight $2$
Character 1050.751
Analytic conductor $8.384$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(1\)
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 751.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1050.751
Dual form 1050.2.i.l.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +(2.50000 - 0.866025i) q^{21} -5.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(4.00000 + 6.92820i) q^{38} +(0.500000 - 2.59808i) q^{42} -2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 + 5.19615i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.50000 - 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +8.00000 q^{57} +(-2.50000 + 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} -3.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 + 4.33013i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 - 4.33013i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-1.00000 + 1.73205i) q^{86} +(2.50000 + 4.33013i) q^{87} +(2.50000 + 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} -7.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{6} - q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{6} - q^{7} - 2q^{8} - q^{9} - 5q^{11} - q^{12} + 4q^{14} - q^{16} - 4q^{17} + q^{18} - 8q^{19} + 5q^{21} - 10q^{22} - 4q^{23} + q^{24} + 2q^{27} + 5q^{28} - 10q^{29} - 3q^{31} + q^{32} - 5q^{33} - 8q^{34} + 2q^{36} - 4q^{37} + 8q^{38} + q^{42} - 4q^{43} - 5q^{44} + 4q^{46} - 6q^{47} + 2q^{48} - 13q^{49} - 4q^{51} - 9q^{53} + q^{54} + q^{56} + 16q^{57} - 5q^{58} + 11q^{59} + 6q^{61} - 6q^{62} - 4q^{63} + 2q^{64} + 5q^{66} - 2q^{67} - 4q^{68} + 8q^{69} + 4q^{71} + q^{72} + 10q^{73} + 4q^{74} + 16q^{76} + 25q^{77} - 3q^{79} - q^{81} + 14q^{83} - 4q^{84} - 2q^{86} + 5q^{87} + 5q^{88} + 6q^{89} + 8q^{92} - 3q^{93} + 6q^{94} + q^{96} - 14q^{97} - 11q^{98} + 10q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 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 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −4.00000 + 6.92820i −0.917663 + 1.58944i −0.114708 + 0.993399i \(0.536593\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) −5.00000 −1.06600
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) −1.50000 2.59808i −0.269408 0.466628i 0.699301 0.714827i \(-0.253495\pi\)
−0.968709 + 0.248199i \(0.920161\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 4.00000 + 6.92820i 0.648886 + 1.12390i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0.500000 2.59808i 0.0771517 0.400892i
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −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 −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 8.00000 1.05963
\(58\) −2.50000 + 4.33013i −0.328266 + 0.568574i
\(59\) 5.50000 + 9.52628i 0.716039 + 1.24022i 0.962557 + 0.271078i \(0.0873801\pi\)
−0.246518 + 0.969138i \(0.579287\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) −3.00000 −0.381000
\(63\) −2.00000 1.73205i −0.251976 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.50000 + 4.33013i 0.307729 + 0.533002i
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 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 −0.937985 0.346675i \(-0.887311\pi\)
0.769222 + 0.638982i \(0.220644\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 0 0
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) 2.50000 + 4.33013i 0.268028 + 0.464238i
\(88\) 2.50000 + 4.33013i 0.266501 + 0.461593i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 2.00000 + 3.46410i 0.198030 + 0.342997i
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 4.00000 6.92820i 0.374634 0.648886i
\(115\) 0 0
\(116\) 2.50000 + 4.33013i 0.232119 + 0.402042i
\(117\) 0 0
\(118\) 11.0000 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
\(125\) 0 0
\(126\) −2.50000 + 0.866025i −0.222718 + 0.0771517i
\(127\) −9.00000 −0.798621 −0.399310 0.916816i \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.0436852 + 0.0756650i −0.887041 0.461690i \(-0.847243\pi\)
0.843356 + 0.537355i \(0.180577\pi\)
\(132\) 5.00000 0.435194
\(133\) −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 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) 2.00000 3.46410i 0.170251 0.294884i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 1.00000 + 6.92820i 0.0824786 + 0.571429i
\(148\) 4.00000 0.328798
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) −9.50000 16.4545i −0.773099 1.33905i −0.935857 0.352381i \(-0.885372\pi\)
0.162758 0.986666i \(-0.447961\pi\)
\(152\) 4.00000 6.92820i 0.324443 0.561951i
\(153\) 4.00000 0.323381
\(154\) 2.50000 12.9904i 0.201456 1.04679i
\(155\) 0 0
\(156\) 0 0
\(157\) −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) 1.50000 + 2.59808i 0.119334 + 0.206692i
\(159\) −4.50000 + 7.79423i −0.356873 + 0.618123i
\(160\) 0 0
\(161\) −8.00000 6.92820i −0.630488 0.546019i
\(162\) −1.00000 −0.0785674
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 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 \(0.317790\pi\)
\(168\) −2.50000 + 0.866025i −0.192879 + 0.0668153i
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −4.00000 6.92820i −0.305888 0.529813i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) 11.0000 19.0526i 0.836315 1.44854i −0.0566411 0.998395i \(-0.518039\pi\)
0.892956 0.450145i \(-0.148628\pi\)
\(174\) 5.00000 0.379049
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) 5.50000 9.52628i 0.413405 0.716039i
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 0 0
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) −10.0000 + 17.3205i −0.731272 + 1.26660i
\(188\) 6.00000 0.437595
\(189\) −0.500000 + 2.59808i −0.0363696 + 0.188982i
\(190\) 0 0
\(191\) −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) −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 \(0.522698\pi\)
\(198\) 2.50000 4.33013i 0.177667 0.307729i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0 0
\(201\) −1.00000 + 1.73205i −0.0705346 + 0.122169i
\(202\) −10.0000 −0.703598
\(203\) 2.50000 12.9904i 0.175466 0.911746i
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 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
\(213\) −1.00000 1.73205i −0.0685189 0.118678i
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 7.50000 2.59808i 0.509133 0.176369i
\(218\) 2.00000 0.135457
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 0 0
\(221\) 0 0
\(222\) 2.00000 3.46410i 0.134231 0.232495i
\(223\) 7.00000 0.468755 0.234377 0.972146i \(-0.424695\pi\)
0.234377 + 0.972146i \(0.424695\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) −4.00000 6.92820i −0.264906 0.458831i
\(229\) 10.0000 17.3205i 0.660819 1.14457i −0.319582 0.947559i \(-0.603543\pi\)
0.980401 0.197013i \(-0.0631241\pi\)
\(230\) 0 0
\(231\) −10.0000 8.66025i −0.657952 0.569803i
\(232\) 5.00000 0.328266
\(233\) −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
\(235\) 0 0
\(236\) 5.50000 9.52628i 0.358020 0.620108i
\(237\) 3.00000 0.194871
\(238\) 2.00000 10.3923i 0.129641 0.673633i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i \(0.131273\pi\)
−0.110963 + 0.993825i \(0.535394\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −6.00000 −0.384111
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) −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 \(0.269387\pi\)
\(252\) −0.500000 + 2.59808i −0.0314970 + 0.163663i
\(253\) 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 −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 2.00000 0.124515
\(259\) −8.00000 6.92820i −0.497096 0.430498i
\(260\) 0 0
\(261\) 2.50000 4.33013i 0.154746 0.268028i
\(262\) 0.500000 + 0.866025i 0.0308901 + 0.0535032i
\(263\) −15.0000 25.9808i −0.924940 1.60204i −0.791658 0.610964i \(-0.790782\pi\)
−0.133281 0.991078i \(-0.542551\pi\)
\(264\) 2.50000 4.33013i 0.153864 0.266501i
\(265\) 0 0
\(266\) −20.0000 + 6.92820i −1.22628 + 0.424795i
\(267\) −6.00000 −0.367194
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) −15.5000 26.8468i −0.945052 1.63688i −0.755648 0.654978i \(-0.772678\pi\)
−0.189404 0.981899i \(-0.560656\pi\)
\(270\) 0 0
\(271\) −7.50000 + 12.9904i −0.455593 + 0.789109i −0.998722 0.0505395i \(-0.983906\pi\)
0.543130 + 0.839649i \(0.317239\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) −8.00000 13.8564i −0.480673 0.832551i 0.519081 0.854725i \(-0.326274\pi\)
−0.999754 + 0.0221745i \(0.992941\pi\)
\(278\) −7.00000 + 12.1244i −0.419832 + 0.727171i
\(279\) 3.00000 0.179605
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 3.00000 5.19615i 0.178647 0.309426i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 21.0000 1.22683 0.613417 0.789760i \(-0.289795\pi\)
0.613417 + 0.789760i \(0.289795\pi\)
\(294\) 6.50000 + 2.59808i 0.379088 + 0.151523i
\(295\) 0 0
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) −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
\(303\) −5.00000 + 8.66025i −0.287242 + 0.497519i
\(304\) −4.00000 6.92820i −0.229416 0.397360i
\(305\) 0 0
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −10.0000 8.66025i −0.569803 0.493464i
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 16.0000 + 27.7128i 0.907277 + 1.57145i 0.817832 + 0.575458i \(0.195176\pi\)
0.0894452 + 0.995992i \(0.471491\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i \(-0.806484\pi\)
0.905071 + 0.425261i \(0.139818\pi\)
\(318\) 4.50000 + 7.79423i 0.252347 + 0.437079i
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) 0 0
\(321\) −3.00000 −0.167444
\(322\) −10.0000 + 3.46410i −0.557278 + 0.193047i
\(323\) 32.0000 1.78053
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 0 0
\(329\) −12.0000 10.3923i −0.661581 0.572946i
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −3.50000 6.06218i −0.192087 0.332705i
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) 7.00000 12.1244i 0.383023 0.663415i
\(335\) 0 0
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) −6.50000 + 11.2583i −0.353553 + 0.612372i
\(339\) 8.00000 + 13.8564i 0.434500 + 0.752577i
\(340\) 0 0
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) −8.00000 −0.432590
\(343\) 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 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 2.50000 4.33013i 0.134014 0.232119i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.50000 4.33013i 0.133250 0.230797i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) −5.50000 9.52628i −0.292322 0.506316i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −8.00000 6.92820i −0.423405 0.366679i
\(358\) −12.0000 −0.634220
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 0 0
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) 8.50000 + 14.7224i 0.443696 + 0.768505i 0.997960 0.0638362i \(-0.0203335\pi\)
−0.554264 + 0.832341i \(0.687000\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 0 0
\(370\) 0 0
\(371\) 22.5000 7.79423i 1.16814 0.404656i
\(372\) 3.00000 0.155543
\(373\) −16.0000 + 27.7128i −0.828449 + 1.43492i 0.0708063 + 0.997490i \(0.477443\pi\)
−0.899255 + 0.437425i \(0.855891\pi\)
\(374\) 10.0000 + 17.3205i 0.517088 + 0.895622i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 0 0
\(378\) 2.00000 + 1.73205i 0.102869 + 0.0890871i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 4.50000 + 7.79423i 0.230542 + 0.399310i
\(382\) 12.0000 + 20.7846i 0.613973 + 1.06343i
\(383\) −17.0000 + 29.4449i −0.868659 + 1.50456i −0.00529229 + 0.999986i \(0.501685\pi\)
−0.863367 + 0.504576i \(0.831649\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) 1.00000 1.73205i 0.0508329 0.0880451i
\(388\) 3.50000 + 6.06218i 0.177686 + 0.307760i
\(389\) 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i \(-0.150521\pi\)
−0.839561 + 0.543266i \(0.817187\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) 1.00000 0.0504433
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 0 0
\(396\) −2.50000 4.33013i −0.125630 0.217597i
\(397\) 18.0000 31.1769i 0.903394 1.56472i 0.0803356 0.996768i \(-0.474401\pi\)
0.823058 0.567957i \(-0.192266\pi\)
\(398\) 4.00000 0.200502
\(399\) −4.00000 + 20.7846i −0.200250 + 1.04053i
\(400\) 0 0
\(401\) −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i \(0.371202\pi\)
−0.992932 + 0.118686i \(0.962132\pi\)
\(402\) 1.00000 + 1.73205i 0.0498755 + 0.0863868i
\(403\) 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
\(408\) 2.00000 3.46410i 0.0990148 0.171499i
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) −8.00000 −0.394132
\(413\) −27.5000 + 9.52628i −1.35319 + 0.468758i
\(414\) −4.00000 −0.196589
\(415\) 0 0
\(416\) 0 0
\(417\) 7.00000 + 12.1244i 0.342791 + 0.593732i
\(418\) 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
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 0 0
\(426\) −2.00000 −0.0969003
\(427\) 12.0000 + 10.3923i 0.580721 + 0.502919i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 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
\(438\) −5.00000 8.66025i −0.238909 0.413803i
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 0 0
\(443\) 8.50000 14.7224i 0.403847 0.699484i −0.590339 0.807155i \(-0.701006\pi\)
0.994187 + 0.107671i \(0.0343394\pi\)
\(444\) −2.00000 3.46410i −0.0949158 0.164399i
\(445\) 0 0
\(446\) 3.50000 6.06218i 0.165730 0.287052i
\(447\) −18.0000 −0.851371
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 8.00000 + 13.8564i 0.376288 + 0.651751i
\(453\) −9.50000 + 16.4545i −0.446349 + 0.773099i
\(454\) 3.00000 0.140797
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) 15.5000 26.8468i 0.725059 1.25584i −0.233890 0.972263i \(-0.575146\pi\)
0.958950 0.283577i \(-0.0915211\pi\)
\(458\) −10.0000 17.3205i −0.467269 0.809334i
\(459\) −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 \(0.605709\pi\)
\(462\) −12.5000 + 4.33013i −0.581553 + 0.201456i
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 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 −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) 0 0
\(471\) −2.00000 + 3.46410i −0.0921551 + 0.159617i
\(472\) −5.50000 9.52628i −0.253158 0.438483i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 1.50000 2.59808i 0.0688973 0.119334i
\(475\) 0 0
\(476\) −8.00000 6.92820i −0.366679 0.317554i
\(477\) 9.00000 0.412082
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) −19.0000 32.9090i −0.868132 1.50365i −0.863903 0.503658i \(-0.831987\pi\)
−0.00422900 0.999991i \(-0.501346\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 25.0000 1.13872
\(483\) −2.00000 + 10.3923i −0.0910032 + 0.472866i
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 2.50000 + 4.33013i 0.113286 + 0.196217i 0.917093 0.398673i \(-0.130529\pi\)
−0.803807 + 0.594890i \(0.797196\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) 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
\(493\) 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
\(498\) −7.00000 −0.313678
\(499\) −5.00000 + 8.66025i −0.223831 + 0.387686i −0.955968 0.293471i \(-0.905190\pi\)
0.732137 + 0.681157i \(0.238523\pi\)
\(500\) 0 0
\(501\) −7.00000 12.1244i −0.312737 0.541676i
\(502\) 10.5000 18.1865i 0.468638 0.811705i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 2.00000 + 1.73205i 0.0890871 + 0.0771517i
\(505\) 0 0
\(506\) 10.0000 17.3205i 0.444554 0.769991i
\(507\) 6.50000 + 11.2583i 0.288675 + 0.500000i
\(508\) 4.50000 + 7.79423i 0.199655 + 0.345813i
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 0 0
\(511\) −25.0000 + 8.66025i −1.10593 + 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 0 0
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) 30.0000 1.31940
\(518\) −10.0000 + 3.46410i −0.439375 + 0.152204i
\(519\) −22.0000 −0.965693
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) −2.50000 4.33013i −0.109422 0.189525i
\(523\) 4.00000 6.92820i 0.174908 0.302949i −0.765222 0.643767i \(-0.777371\pi\)
0.940129 + 0.340818i \(0.110704\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0 0
\(526\) −30.0000 −1.30806
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) −2.50000 4.33013i −0.108799 0.188445i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −11.0000 −0.477359
\(532\) −4.00000 + 20.7846i −0.173422 + 0.901127i
\(533\) 0 0
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 0 0
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) −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 −0.605096 0.796152i \(-0.706865\pi\)
0.992036 + 0.125952i \(0.0401986\pi\)
\(542\) 7.50000 + 12.9904i 0.322153 + 0.557985i
\(543\) 0 0
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 0 0
\(551\) 20.0000 34.6410i 0.852029 1.47576i
\(552\) −4.00000 −0.170251
\(553\) −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 0.512622 0.858614i \(-0.328674\pi\)
−0.999893 + 0.0146368i \(0.995341\pi\)
\(558\) 1.50000 2.59808i 0.0635001 0.109985i
\(559\) 0 0
\(560\) 0 0
\(561\) 20.0000 0.844401
\(562\) 1.00000 1.73205i 0.0421825 0.0730622i
\(563\) 8.50000 + 14.7224i 0.358232 + 0.620477i 0.987666 0.156578i \(-0.0500463\pi\)
−0.629433 + 0.777055i \(0.716713\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) 0 0
\(566\) 10.0000 0.420331
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) −2.00000 −0.0839181
\(569\) −12.0000 + 20.7846i −0.503066 + 0.871336i 0.496928 + 0.867792i \(0.334461\pi\)
−0.999994 + 0.00354413i \(0.998872\pi\)
\(570\) 0 0
\(571\) 15.0000 + 25.9808i 0.627730 + 1.08726i 0.988006 + 0.154415i \(0.0493493\pi\)
−0.360276 + 0.932846i \(0.617317\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 2.50000 4.33013i 0.103896 0.179954i
\(580\) 0 0
\(581\) −3.50000 + 18.1865i −0.145204 + 0.754505i
\(582\) 7.00000 0.290159
\(583\) −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 \(0.756916\pi\)
\(588\) 5.50000 4.33013i 0.226816 0.178571i
\(589\) 24.0000 0.988903
\(590\) 0 0
\(591\) 1.00000 + 1.73205i 0.0411345 + 0.0712470i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 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
\(603\) 2.00000 0.0814463
\(604\) −9.50000 + 16.4545i −0.386550 + 0.669523i
\(605\) 0 0
\(606\) 5.00000 + 8.66025i 0.203111 + 0.351799i
\(607\) −13.5000 + 23.3827i −0.547948 + 0.949074i 0.450467 + 0.892793i \(0.351258\pi\)
−0.998415 + 0.0562808i \(0.982076\pi\)
\(608\) −8.00000 −0.324443
\(609\) −12.5000 + 4.33013i −0.506526 + 0.175466i
\(610\) 0 0
\(611\) 0 0
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) 6.00000 + 10.3923i 0.242338 + 0.419741i 0.961380 0.275225i \(-0.0887525\pi\)
−0.719042 + 0.694967i \(0.755419\pi\)
\(614\) −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 \(0.512818\pi\)
\(618\) −4.00000 + 6.92820i −0.160904 + 0.278693i
\(619\) −5.00000 8.66025i −0.200967 0.348085i 0.747873 0.663842i \(-0.231075\pi\)
−0.948840 + 0.315757i \(0.897742\pi\)
\(620\) 0 0
\(621\) −2.00000 + 3.46410i −0.0802572 + 0.139010i
\(622\) 32.0000 1.28308
\(623\) 12.0000 + 10.3923i 0.480770 + 0.416359i
\(624\) 0 0
\(625\) 0 0
\(626\) −0.500000 0.866025i −0.0199840 0.0346133i
\(627\) −20.0000 34.6410i −0.798723 1.38343i
\(628\) −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
\(633\) −1.00000 1.73205i −0.0397464 0.0688428i
\(634\) −1.50000 2.59808i −0.0595726 0.103183i
\(635\) 0 0
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) 25.0000 0.989759
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) −1.50000 + 2.59808i −0.0592003 + 0.102538i
\(643\) −14.0000 −0.552106 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(644\) −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 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 27.5000 47.6314i 1.07947 1.86970i
\(650\) 0 0
\(651\) −6.00000 5.19615i −0.235159 0.203653i
\(652\) 4.00000 0.156652
\(653\) −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i \(0.442987\pi\)
−0.941248 + 0.337715i \(0.890346\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) 0 0
\(656\) 0 0
\(657\) −10.0000 −0.390137
\(658\) −15.0000 + 5.19615i −0.584761 + 0.202567i
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i \(-0.228968\pi\)
−0.946729 + 0.322031i \(0.895634\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 0 0
\(664\) −7.00000 −0.271653
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 10.0000 17.3205i 0.387202 0.670653i
\(668\) −7.00000 12.1244i −0.270838 0.469105i
\(669\) −3.50000 6.06218i −0.135318 0.234377i
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 2.00000 + 1.73205i 0.0771517 + 0.0668153i
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) −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 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 16.0000 0.614476
\(679\) 3.50000 18.1865i 0.134318 0.697935i
\(680\) 0 0
\(681\) 1.50000 2.59808i 0.0574801 0.0995585i
\(682\) 7.50000 + 12.9904i 0.287190 + 0.497427i
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) −4.00000 + 6.92820i −0.152944 + 0.264906i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) −20.0000 −0.763048
\(688\) 1.00000 1.73205i 0.0381246 0.0660338i
\(689\) 0 0
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −22.0000 −0.836315
\(693\) −2.50000 + 12.9904i −0.0949671 + 0.493464i
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) −2.50000 4.33013i −0.0947623 0.164133i
\(697\) 0 0
\(698\) −7.00000 + 12.1244i −0.264954 + 0.458914i
\(699\) 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
\(703\) −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
\(708\) −11.0000 −0.413405
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 0 0
\(711\) −1.50000 2.59808i −0.0562544 0.0974355i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 12.0000 0.449404
\(714\) −10.0000 + 3.46410i −0.374241 + 0.129641i
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) 5.00000 + 8.66025i 0.186598 + 0.323198i
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) 16.0000 + 13.8564i 0.595871 + 0.516040i
\(722\) −45.0000 −1.67473
\(723\) 12.5000 21.6506i 0.464880 0.805196i
\(724\) 0 0
\(725\) 0 0
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 3.00000 + 5.19615i 0.110883 + 0.192055i
\(733\) −3.00000 + 5.19615i −0.110808 + 0.191924i −0.916096 0.400959i \(-0.868677\pi\)
0.805289 + 0.592883i \(0.202010\pi\)
\(734\) 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 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) 0 0
\(741\) 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 \(0.685485\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 0 0
\(746\) 16.0000 + 27.7128i 0.585802 + 1.01464i
\(747\) −3.50000 + 6.06218i −0.128058 + 0.221803i
\(748\) 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 0.0838743 + 0.996476i \(0.473271\pi\)
−0.904911 + 0.425601i \(0.860063\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) −10.5000 18.1865i −0.382641 0.662754i
\(754\) 0 0
\(755\) 0 0
\(756\) 2.50000 0.866025i 0.0909241 0.0314970i
\(757\) 54.0000 1.96266 0.981332 0.192323i \(-0.0616021\pi\)
0.981332 + 0.192323i \(0.0616021\pi\)
\(758\) 8.00000 13.8564i 0.290573 0.503287i
\(759\) −10.0000 17.3205i −0.362977 0.628695i
\(760\) 0 0
\(761\) −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i \(-0.879652\pi\)
0.784373 + 0.620289i \(0.212985\pi\)
\(762\) 9.00000 0.326036
\(763\) −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
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 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 \(0.775776\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) −2.00000 + 10.3923i −0.0717496 + 0.372822i
\(778\) 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
\(783\) −5.00000 −0.178685
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 0 0
\(786\) 0.500000 0.866025i 0.0178344 0.0308901i
\(787\) −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i \(-0.270624\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)