Properties

Label 42.2.e.a.37.1
Level $42$
Weight $2$
Character 42.37
Analytic conductor $0.335$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.335371688489\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 42.37
Dual form 42.2.e.a.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +1.00000 q^{20} +(2.50000 - 0.866025i) q^{21} +5.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} -1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} -5.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(-1.50000 - 2.59808i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} -4.00000 q^{34} +(2.00000 + 1.73205i) q^{35} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-0.500000 + 2.59808i) q^{42} +2.00000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(2.00000 + 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} +(0.500000 - 0.866025i) q^{54} +5.00000 q^{55} +(0.500000 - 2.59808i) q^{56} -8.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{60} +(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} +(-2.50000 + 0.866025i) q^{70} +2.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} +8.00000 q^{76} +(-12.5000 + 4.33013i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} -7.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} -4.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +(-2.50000 - 4.33013i) q^{87} +(-2.50000 - 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} + 2q^{8} - q^{9} - q^{10} - 5q^{11} + q^{12} + 4q^{14} - 2q^{15} - q^{16} + 4q^{17} - q^{18} - 8q^{19} + 2q^{20} + 5q^{21} + 10q^{22} + 4q^{23} + q^{24} + 4q^{25} - 2q^{27} - 5q^{28} - 10q^{29} + q^{30} - 3q^{31} - q^{32} + 5q^{33} - 8q^{34} + 4q^{35} + 2q^{36} + 4q^{37} - 8q^{38} - q^{40} - q^{42} + 4q^{43} - 5q^{44} - q^{45} + 4q^{46} + 6q^{47} - 2q^{48} - 13q^{49} - 8q^{50} - 4q^{51} + 9q^{53} + q^{54} + 10q^{55} + q^{56} - 16q^{57} + 5q^{58} + 11q^{59} + q^{60} + 6q^{61} + 6q^{62} + 4q^{63} + 2q^{64} + 5q^{66} + 2q^{67} + 4q^{68} + 8q^{69} - 5q^{70} + 4q^{71} - q^{72} - 10q^{73} + 4q^{74} - 4q^{75} + 16q^{76} - 25q^{77} - 3q^{79} - q^{80} - q^{81} - 14q^{83} - 4q^{84} - 8q^{85} - 2q^{86} - 5q^{87} - 5q^{88} + 6q^{89} + 2q^{90} - 8q^{92} + 3q^{93} + 6q^{94} - 8q^{95} + q^{96} + 14q^{97} + 11q^{98} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) −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
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −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
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) −0.500000 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 \(0.796740\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 5.00000 1.06600
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 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 \(0.653672\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) −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
\(35\) 2.00000 + 1.73205i 0.338062 + 0.292770i
\(36\) 1.00000 0.166667
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −4.00000 6.92820i −0.648886 1.12390i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 0 0 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 \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −4.00000 −0.565685
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 5.00000 0.674200
\(56\) 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 \(0.579287\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 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 0.920623 0.390453i \(-0.127682\pi\)
−0.798454 + 0.602056i \(0.794348\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 4.00000 0.481543
\(70\) −2.50000 + 0.866025i −0.298807 + 0.103510i
\(71\) 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 \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 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 \(0.220644\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −7.00000 −0.768350 −0.384175 0.923260i \(-0.625514\pi\)
−0.384175 + 0.923260i \(0.625514\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) −4.00000 −0.433861
\(86\) −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 \(0.0636557\pi\)
\(90\) 1.00000 0.105409
\(91\) 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
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 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
\(99\) 5.00000 0.502519
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −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 −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 0 0
\(105\) −0.500000 + 2.59808i −0.0487950 + 0.253546i
\(106\) −9.00000 −0.874157
\(107\) −1.50000 + 2.59808i −0.145010 + 0.251166i −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) 0.500000 + 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 \(0.802798\pi\)
\(110\) −2.50000 + 4.33013i −0.238366 + 0.412861i
\(111\) 4.00000 0.379663
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 4.00000 6.92820i 0.374634 0.648886i
\(115\) 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
\(120\) −1.00000 −0.0912871
\(121\) −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
\(126\) −2.50000 + 0.866025i −0.222718 + 0.0771517i
\(127\) 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
\(129\) 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
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) −2.00000 + 3.46410i −0.170251 + 0.294884i
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0.500000 2.59808i 0.0422577 0.219578i
\(141\) 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
\(145\) 2.50000 4.33013i 0.207614 0.359597i
\(146\) 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 \(-0.0972370\pi\)
\(150\) −2.00000 3.46410i −0.163299 0.282843i
\(151\) −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
\(155\) 3.00000 0.240966
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −1.50000 2.59808i −0.119334 0.206692i
\(159\) −4.50000 + 7.79423i −0.356873 + 0.618123i
\(160\) 1.00000 0.0790569
\(161\) −8.00000 6.92820i −0.630488 0.546019i
\(162\) 1.00000 0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 2.50000 + 4.33013i 0.194625 + 0.337100i
\(166\) 3.50000 6.06218i 0.271653 0.470516i
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 2.50000 0.866025i 0.192879 0.0668153i
\(169\) −13.0000 −1.00000
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) −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 \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 5.00000 0.379049
\(175\) 10.0000 3.46410i 0.755929 0.261861i
\(176\) 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 \(0.981361\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 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
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) 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
\(190\) 8.00000 0.580381
\(191\) −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 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −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 \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −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 \(0.788052\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) −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
\(210\) −2.00000 1.73205i −0.138013 0.119523i
\(211\) 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
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) −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
\(220\) −2.50000 4.33013i −0.168550 0.291937i
\(221\) 0 0
\(222\) −2.00000 + 3.46410i −0.134231 + 0.232495i
\(223\) −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
\(225\) −4.00000 −0.266667
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) −1.50000 2.59808i −0.0995585 0.172440i 0.811943 0.583736i \(-0.198410\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(228\) 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 \(-0.0631241\pi\)
\(230\) −4.00000 −0.263752
\(231\) −10.0000 8.66025i −0.657952 0.569803i
\(232\) −5.00000 −0.328266
\(233\) 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i \(-0.791507\pi\)
0.924072 + 0.382219i \(0.124840\pi\)
\(234\) 0 0
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) 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 \(0.626871\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 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
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) 0 0
\(247\) 0 0
\(248\) −1.50000 2.59808i −0.0952501 0.164978i
\(249\) −3.50000 6.06218i −0.221803 0.384175i
\(250\) 4.50000 7.79423i 0.284605 0.492950i
\(251\) 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
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) −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 \(0.209218\pi\)
0.133281 + 0.991078i \(0.457449\pi\)
\(264\) 2.50000 4.33013i 0.153864 0.266501i
\(265\) −9.00000 −0.552866
\(266\) −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 \(-0.560656\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −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
\(275\) 10.0000 17.3205i 0.603023 1.04447i
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 7.00000 12.1244i 0.419832 0.727171i
\(279\) 3.00000 0.179605
\(280\) 2.00000 + 1.73205i 0.119523 + 0.103510i
\(281\) 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 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 4.00000 6.92820i 0.236940 0.410391i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 2.50000 + 4.33013i 0.146805 + 0.254274i
\(291\) 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 \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 6.50000 + 2.59808i 0.379088 + 0.151523i
\(295\) −11.0000 −0.640445
\(296\) 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
\(300\) 4.00000 0.230940
\(301\) 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
\(305\) 3.00000 + 5.19615i 0.171780 + 0.297531i
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) 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
\(309\) −8.00000 −0.455104
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) 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 −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) −4.00000 −0.225733
\(315\) −2.50000 + 0.866025i −0.140859 + 0.0487950i
\(316\) 3.00000 0.168763
\(317\) −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i \(-0.860182\pi\)
0.820822 + 0.571184i \(0.193516\pi\)
\(318\) −4.50000 7.79423i −0.252347 0.437079i
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −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
\(330\) −5.00000 −0.275241
\(331\) 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
\(335\) −2.00000 −0.109272
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) 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
\(339\) 8.00000 + 13.8564i 0.434500 + 0.752577i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −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
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) −11.0000 19.0526i −0.591364 1.02427i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) −2.50000 + 4.33013i −0.134014 + 0.232119i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −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 −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) −5.50000 9.52628i −0.292322 0.506316i
\(355\) −1.00000 + 1.73205i −0.0530745 + 0.0919277i
\(356\) −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 \(0.251672\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) 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
\(372\) −3.00000 −0.155543
\(373\) 16.0000 27.7128i 0.828449 1.43492i −0.0708063 0.997490i \(-0.522557\pi\)
0.899255 0.437425i \(-0.144109\pi\)
\(374\) 10.0000 + 17.3205i 0.517088 + 0.895622i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) 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 \(0.365203\pi\)
\(380\) −4.00000 + 6.92820i −0.205196 + 0.355409i
\(381\) 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 \(-0.498315\pi\)
0.863367 0.504576i \(-0.168351\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 2.50000 12.9904i 0.127412 0.662051i
\(386\) 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
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) −2.50000 4.33013i −0.125630 0.217597i
\(397\) −18.0000 + 31.1769i −0.903394 + 1.56472i −0.0803356 + 0.996768i \(0.525599\pi\)
−0.823058 + 0.567957i \(0.807734\pi\)
\(398\) −4.00000 −0.200502
\(399\) −4.00000 + 20.7846i −0.200250 + 1.04053i
\(400\) −4.00000 −0.200000
\(401\) −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
\(405\) 1.00000 0.0496904
\(406\) −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
\(415\) 3.50000 6.06218i 0.171808 0.297581i
\(416\) 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 \(0.5\pi\)
\(420\) 2.50000 0.866025i 0.121988 0.0422577i
\(421\) 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
\(425\) −8.00000 + 13.8564i −0.388057 + 0.672134i
\(426\) −2.00000 −0.0969003
\(427\) −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 \(-0.259993\pi\)
−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 \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 1.50000 7.79423i 0.0720023 0.374135i
\(435\) 5.00000 0.239732
\(436\) 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 \(0.283193\pi\)
\(440\) 5.00000 0.238366
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 0 0
\(443\) −8.50000 + 14.7224i −0.403847 + 0.699484i −0.994187 0.107671i \(-0.965661\pi\)
0.590339 + 0.807155i \(0.298994\pi\)
\(444\) −2.00000 3.46410i −0.0949158 0.164399i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) 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 \(0.376769\pi\)
\(450\) 2.00000 3.46410i 0.0942809 0.163299i
\(451\) 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 \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 10.0000 + 17.3205i 0.467269 + 0.809334i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 2.00000 3.46410i 0.0932505 0.161515i
\(461\) −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 \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 2.50000 4.33013i 0.116060 0.201021i
\(465\) 1.50000 + 2.59808i 0.0695608 + 0.120483i
\(466\) 2.00000 + 3.46410i 0.0926482 + 0.160471i
\(467\) 10.0000 17.3205i 0.462745 0.801498i −0.536352 0.843995i \(-0.680198\pi\)
0.999097 + 0.0424970i \(0.0135313\pi\)
\(468\) 0 0
\(469\) 5.00000 1.73205i 0.230879 0.0799787i
\(470\) −6.00000 −0.276759
\(471\) −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
\(475\) −32.0000 −1.46826
\(476\) −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 \(-0.501346\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 0 0
\(482\) −25.0000 −1.13872
\(483\) 2.00000 10.3923i 0.0910032 0.472866i
\(484\) 14.0000 0.636364
\(485\) −3.50000 + 6.06218i −0.158927 + 0.275269i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −2.50000 4.33013i −0.113286 0.196217i 0.803807 0.594890i \(-0.202804\pi\)
−0.917093 + 0.398673i \(0.869471\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) 4.00000 0.180886
\(490\) 1.00000 + 6.92820i 0.0451754 + 0.312984i
\(491\) 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
\(495\) −2.50000 + 4.33013i −0.112367 + 0.194625i
\(496\) 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 \(0.238523\pi\)
\(500\) 4.50000 + 7.79423i 0.201246 + 0.348569i
\(501\) −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
\(505\) 10.0000 0.444994
\(506\) 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 \(0.274536\pi\)
\(510\) 4.00000 0.177123
\(511\) −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
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 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 −0.940129 0.340818i \(-0.889296\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) 1.00000 0.0436852
\(525\) 8.00000 + 6.92820i 0.349149 + 0.302372i
\(526\) −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
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) −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
\(535\) −1.50000 2.59808i −0.0648507 0.112325i
\(536\) 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
\(540\) −1.00000 −0.0430331
\(541\) 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
\(545\) −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
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) 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
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 7.00000 + 12.1244i 0.296866 + 0.514187i
\(557\) 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i \(-0.00465919\pi\)
−0.512622 + 0.858614i \(0.671326\pi\)
\(558\) −1.50000 + 2.59808i −0.0635001 + 0.109985i
\(559\) 0 0
\(560\) −2.50000 + 0.866025i −0.105644 + 0.0365963i
\(561\) 20.0000 0.844401
\(562\) −1.00000 + 1.73205i −0.0421825 + 0.0730622i
\(563\) −8.50000 14.7224i −0.358232 0.620477i 0.629433 0.777055i \(-0.283287\pi\)
−0.987666 + 0.156578i \(0.949954\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) −8.00000 + 13.8564i −0.336563 + 0.582943i
\(566\) 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 \(0.998872\pi\)
\(570\) 4.00000 + 6.92820i 0.167542 + 0.290191i
\(571\) 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
\(575\) 16.0000 0.667246
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) 2.50000 4.33013i 0.103896 0.179954i
\(580\) −5.00000 −0.207614
\(581\) −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 \(-0.243084\pi\)
0.722302 + 0.691577i \(0.243084\pi\)
\(588\) −5.50000 + 4.33013i −0.226816 + 0.178571i
\(589\) 24.0000 0.988903
\(590\) 5.50000 9.52628i 0.226431 0.392191i
\(591\) 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 \(0.431449\pi\)
−0.952869 + 0.303383i \(0.901884\pi\)
\(594\) −5.00000 −0.205152
\(595\) −2.00000 + 10.3923i −0.0819920 + 0.426043i
\(596\) −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 \(0.623343\pi\)
\(600\) −2.00000 + 3.46410i −0.0816497 + 0.141421i
\(601\) 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
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 5.00000 + 8.66025i 0.203111 + 0.351799i
\(607\) 13.5000 23.3827i 0.547948 0.949074i −0.450467 0.892793i \(-0.648742\pi\)
0.998415 0.0562808i \(-0.0179242\pi\)
\(608\) 8.00000 0.324443
\(609\) −12.5000 + 4.33013i −0.506526 + 0.175466i
\(610\) −6.00000 −0.242933
\(611\) 0 0
\(612\) 2.00000 + 3.46410i 0.0808452 + 0.140028i
\(613\) −6.00000 10.3923i −0.242338 0.419741i 0.719042 0.694967i \(-0.244581\pi\)
−0.961380 + 0.275225i \(0.911248\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 0 0
\(616\) −12.5000 + 4.33013i −0.503639 + 0.174466i
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 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 \(0.897742\pi\)
\(620\) −1.50000 2.59808i −0.0602414 0.104341i
\(621\) −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
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) −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
\(630\) 0.500000 2.59808i 0.0199205 0.103510i
\(631\) −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
\(635\) −4.50000 + 7.79423i −0.178577 + 0.309305i
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) −25.0000 −0.989759
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −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 \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) −2.00000 + 10.3923i −0.0788110 + 0.409514i
\(645\) −2.00000 −0.0787499
\(646\) 16.0000 27.7128i 0.629512 1.09035i
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) −0.500000 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 \(-0.557013\pi\)
0.941248 0.337715i \(-0.109654\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) −0.500000 0.866025i −0.0195366 0.0338384i
\(656\) 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 \(0.784318\pi\)
\(660\) 2.50000 4.33013i 0.0973124 0.168550i
\(661\) −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
\(665\) −20.0000 + 6.92820i −0.775567 + 0.268664i
\(666\) −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
\(670\) 1.00000 1.73205i 0.0386334 0.0669150i
\(671\) −30.0000 −1.15814
\(672\) −2.00000 1.73205i −0.0771517 0.0668153i
\(673\) −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
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i \(-0.659695\pi\)
0.999760 0.0219013i \(-0.00697196\pi\)
\(678\) −16.0000 −0.614476
\(679\) 3.50000 18.1865i 0.134318 0.697935i
\(680\) −4.00000 −0.153393
\(681\) 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 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) −4.00000 + 6.92820i −0.152944 + 0.264906i
\(685\) −2.00000 −0.0764161
\(686\) −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
\(690\) −2.00000 3.46410i −0.0761387 0.131876i
\(691\) −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
\(695\) 7.00000 12.1244i 0.265525 0.459903i
\(696\) −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
\(700\) −8.00000 6.92820i −0.302372 0.261861i
\(701\) −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
\(705\) −3.00000 + 5.19615i −0.112987 + 0.195698i
\(706\) 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 \(0.913748\pi\)
\(710\) −1.00000 1.73205i −0.0375293 0.0650027i
\(711\) −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 \(0.130979\pi\)
\(720\) 1.00000 0.0372678
\(721\) 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
\(725\) −10.0000 17.3205i −0.371391 0.643268i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) 7.00000 0.259616 0.129808 0.991539i \(-0.458564\pi\)
0.129808 + 0.991539i \(0.458564\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) 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 −0.805289 0.592883i \(-0.797990\pi\)
0.916096 + 0.400959i \(0.131323\pi\)
\(734\) 17.0000 0.627481
\(735\) 6.50000 + 2.59808i 0.239756 + 0.0958315i
\(736\) −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 \(0.647281\pi\)
\(740\) 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 \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) 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
\(750\) 9.00000 0.328634
\(751\) −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
\(755\) 19.0000 0.691481
\(756\) 2.50000 0.866025i 0.0909241 0.0314970i
\(757\) −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
\(759\) −10.0000 17.3205i −0.362977 0.628695i
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) −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
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) 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 \(0.717382\pi\)
\(770\) 10.0000 + 8.66025i 0.360375 + 0.312094i
\(771\) 6.00000 0.216085
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) −5.00000 8.66025i −0.179838 0.311488i 0.761987 0.647592i \(-0.224224\pi\)
−0.941825 + 0.336104i \(0.890891\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 6.00000 10.3923i 0.215526 0.373303i
\(776\) 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