Properties

Label 950.2.e.b.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
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 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.b.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -2.00000 q^{18} +(3.50000 - 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-0.500000 + 0.866025i) q^{24} +6.00000 q^{26} -5.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-5.00000 - 8.66025i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.50000 - 6.06218i) q^{34} +(1.00000 - 1.73205i) q^{36} +4.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +6.00000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{42} +(6.00000 - 10.3923i) q^{43} +2.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} -3.00000 q^{49} +(-3.50000 - 6.06218i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(2.50000 - 4.33013i) q^{54} -2.00000 q^{56} +(0.500000 + 4.33013i) q^{57} +10.0000 q^{58} +(0.500000 - 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(1.00000 - 1.73205i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-4.00000 - 6.92820i) q^{67} +7.00000 q^{68} +2.00000 q^{69} +(6.00000 - 10.3923i) q^{71} +(1.00000 + 1.73205i) q^{72} +(1.50000 - 2.59808i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 - 1.73205i) q^{76} +(-3.00000 + 5.19615i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} -13.0000 q^{83} -2.00000 q^{84} +(6.00000 + 10.3923i) q^{86} +10.0000 q^{87} +(6.50000 + 11.2583i) q^{89} +(6.00000 + 10.3923i) q^{91} +(-1.00000 + 1.73205i) q^{92} +(1.00000 - 1.73205i) q^{93} +1.00000 q^{96} +(-7.50000 + 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - 4q^{7} + 2q^{8} + 2q^{9} + 2q^{12} - 6q^{13} + 2q^{14} - q^{16} - 7q^{17} - 4q^{18} + 7q^{19} + 2q^{21} - 2q^{23} - q^{24} + 12q^{26} - 10q^{27} + 2q^{28} - 10q^{29} - 4q^{31} - q^{32} - 7q^{34} + 2q^{36} + 8q^{37} + q^{38} + 12q^{39} - 2q^{41} + 2q^{42} + 12q^{43} + 4q^{46} - q^{48} - 6q^{49} - 7q^{51} - 6q^{52} + 5q^{54} - 4q^{56} + q^{57} + 20q^{58} + q^{59} - 8q^{61} + 2q^{62} - 4q^{63} + 2q^{64} - 8q^{67} + 14q^{68} + 4q^{69} + 12q^{71} + 2q^{72} + 3q^{73} - 4q^{74} - 8q^{76} - 6q^{78} + 4q^{79} - q^{81} - 2q^{82} - 26q^{83} - 4q^{84} + 12q^{86} + 20q^{87} + 13q^{89} + 12q^{91} - 2q^{92} + 2q^{93} + 2q^{96} - 15q^{97} + 3q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i \(-0.853834\pi\)
0.0643593 0.997927i \(-0.479500\pi\)
\(14\) 1.00000 1.73205i 0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i \(0.489386\pi\)
−0.882213 + 0.470850i \(0.843947\pi\)
\(18\) −2.00000 −0.471405
\(19\) 3.50000 2.59808i 0.802955 0.596040i
\(20\) 0 0
\(21\) 1.00000 1.73205i 0.218218 0.377964i
\(22\) 0 0
\(23\) −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) −5.00000 −0.962250
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) −5.00000 8.66025i −0.928477 1.60817i −0.785872 0.618389i \(-0.787786\pi\)
−0.142605 0.989780i \(-0.545548\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.50000 6.06218i −0.600245 1.03965i
\(35\) 0 0
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0.500000 + 4.33013i 0.0811107 + 0.702439i
\(39\) 6.00000 0.960769
\(40\) 0 0
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 6.00000 10.3923i 0.914991 1.58481i 0.108078 0.994142i \(-0.465531\pi\)
0.806914 0.590669i \(-0.201136\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 2.00000 0.294884
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −3.50000 6.06218i −0.490098 0.848875i
\(52\) −3.00000 + 5.19615i −0.416025 + 0.720577i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 0.500000 + 4.33013i 0.0662266 + 0.573539i
\(58\) 10.0000 1.31306
\(59\) 0.500000 0.866025i 0.0650945 0.112747i −0.831641 0.555313i \(-0.812598\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 1.00000 1.73205i 0.127000 0.219971i
\(63\) −2.00000 3.46410i −0.251976 0.436436i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 7.00000 0.848875
\(69\) 2.00000 0.240772
\(70\) 0 0
\(71\) 6.00000 10.3923i 0.712069 1.23334i −0.252010 0.967725i \(-0.581092\pi\)
0.964079 0.265615i \(-0.0855750\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) 0 0
\(78\) −3.00000 + 5.19615i −0.339683 + 0.588348i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) −13.0000 −1.42694 −0.713468 0.700688i \(-0.752876\pi\)
−0.713468 + 0.700688i \(0.752876\pi\)
\(84\) −2.00000 −0.218218
\(85\) 0 0
\(86\) 6.00000 + 10.3923i 0.646997 + 1.12063i
\(87\) 10.0000 1.07211
\(88\) 0 0
\(89\) 6.50000 + 11.2583i 0.688999 + 1.19338i 0.972162 + 0.234309i \(0.0752827\pi\)
−0.283164 + 0.959072i \(0.591384\pi\)
\(90\) 0 0
\(91\) 6.00000 + 10.3923i 0.628971 + 1.08941i
\(92\) −1.00000 + 1.73205i −0.104257 + 0.180579i
\(93\) 1.00000 1.73205i 0.103695 0.179605i
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −7.50000 + 12.9904i −0.761510 + 1.31897i 0.180563 + 0.983563i \(0.442208\pi\)
−0.942072 + 0.335410i \(0.891125\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 7.00000 0.693103
\(103\) 12.0000 1.18240 0.591198 0.806527i \(-0.298655\pi\)
0.591198 + 0.806527i \(0.298655\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 0 0
\(106\) 0 0
\(107\) 15.0000 1.45010 0.725052 0.688694i \(-0.241816\pi\)
0.725052 + 0.688694i \(0.241816\pi\)
\(108\) 2.50000 + 4.33013i 0.240563 + 0.416667i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) −2.00000 + 3.46410i −0.189832 + 0.328798i
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) −4.00000 1.73205i −0.374634 0.162221i
\(115\) 0 0
\(116\) −5.00000 + 8.66025i −0.464238 + 0.804084i
\(117\) 6.00000 10.3923i 0.554700 0.960769i
\(118\) 0.500000 + 0.866025i 0.0460287 + 0.0797241i
\(119\) 7.00000 12.1244i 0.641689 1.11144i
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 8.00000 0.724286
\(123\) −1.00000 1.73205i −0.0901670 0.156174i
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 4.00000 0.356348
\(127\) −6.00000 10.3923i −0.532414 0.922168i −0.999284 0.0378419i \(-0.987952\pi\)
0.466870 0.884326i \(-0.345382\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 6.00000 + 10.3923i 0.528271 + 0.914991i
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.0436852 + 0.0756650i −0.887041 0.461690i \(-0.847243\pi\)
0.843356 + 0.537355i \(0.180577\pi\)
\(132\) 0 0
\(133\) −7.00000 + 5.19615i −0.606977 + 0.450564i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) −3.50000 + 6.06218i −0.300123 + 0.519827i
\(137\) −7.50000 12.9904i −0.640768 1.10984i −0.985262 0.171054i \(-0.945283\pi\)
0.344493 0.938789i \(-0.388051\pi\)
\(138\) −1.00000 + 1.73205i −0.0851257 + 0.147442i
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) −2.00000 3.46410i −0.164399 0.284747i
\(149\) −8.00000 + 13.8564i −0.655386 + 1.13516i 0.326411 + 0.945228i \(0.394160\pi\)
−0.981797 + 0.189933i \(0.939173\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) 3.50000 2.59808i 0.283887 0.210732i
\(153\) −14.0000 −1.13183
\(154\) 0 0
\(155\) 0 0
\(156\) −3.00000 5.19615i −0.240192 0.416025i
\(157\) −3.00000 + 5.19615i −0.239426 + 0.414698i −0.960550 0.278108i \(-0.910293\pi\)
0.721124 + 0.692806i \(0.243626\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 0 0
\(160\) 0 0
\(161\) 2.00000 + 3.46410i 0.157622 + 0.273009i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 6.50000 11.2583i 0.504498 0.873816i
\(167\) −5.00000 8.66025i −0.386912 0.670151i 0.605121 0.796134i \(-0.293125\pi\)
−0.992032 + 0.125983i \(0.959791\pi\)
\(168\) 1.00000 1.73205i 0.0771517 0.133631i
\(169\) −11.5000 + 19.9186i −0.884615 + 1.53220i
\(170\) 0 0
\(171\) 8.00000 + 3.46410i 0.611775 + 0.264906i
\(172\) −12.0000 −0.914991
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −5.00000 + 8.66025i −0.379049 + 0.656532i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 + 0.866025i 0.0375823 + 0.0650945i
\(178\) −13.0000 −0.974391
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) −10.0000 17.3205i −0.743294 1.28742i −0.950988 0.309229i \(-0.899929\pi\)
0.207693 0.978194i \(-0.433404\pi\)
\(182\) −12.0000 −0.889499
\(183\) 8.00000 0.591377
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) 0 0
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 0 0
\(188\) 0 0
\(189\) 10.0000 0.727393
\(190\) 0 0
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) −7.50000 12.9904i −0.538469 0.932655i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 4.00000 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(198\) 0 0
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) 0 0
\(201\) 8.00000 0.564276
\(202\) 2.00000 0.140720
\(203\) 10.0000 + 17.3205i 0.701862 + 1.21566i
\(204\) −3.50000 + 6.06218i −0.245049 + 0.424437i
\(205\) 0 0
\(206\) −6.00000 + 10.3923i −0.418040 + 0.724066i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 0 0
\(211\) −11.5000 + 19.9186i −0.791693 + 1.37125i 0.133226 + 0.991086i \(0.457467\pi\)
−0.924918 + 0.380166i \(0.875867\pi\)
\(212\) 0 0
\(213\) 6.00000 + 10.3923i 0.411113 + 0.712069i
\(214\) −7.50000 + 12.9904i −0.512689 + 0.888004i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 4.00000 0.271538
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 1.50000 + 2.59808i 0.101361 + 0.175562i
\(220\) 0 0
\(221\) 42.0000 2.82523
\(222\) −2.00000 3.46410i −0.134231 0.232495i
\(223\) 1.00000 1.73205i 0.0669650 0.115987i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440884i \(0.145335\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) −0.500000 + 0.866025i −0.0332595 + 0.0576072i
\(227\) 13.0000 0.862840 0.431420 0.902151i \(-0.358013\pi\)
0.431420 + 0.902151i \(0.358013\pi\)
\(228\) 3.50000 2.59808i 0.231793 0.172062i
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −5.00000 8.66025i −0.328266 0.568574i
\(233\) −6.50000 + 11.2583i −0.425829 + 0.737558i −0.996497 0.0836229i \(-0.973351\pi\)
0.570668 + 0.821181i \(0.306684\pi\)
\(234\) 6.00000 + 10.3923i 0.392232 + 0.679366i
\(235\) 0 0
\(236\) −1.00000 −0.0650945
\(237\) 2.00000 + 3.46410i 0.129914 + 0.225018i
\(238\) 7.00000 + 12.1244i 0.453743 + 0.785905i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 5.50000 9.52628i 0.353553 0.612372i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −4.00000 + 6.92820i −0.256074 + 0.443533i
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) −24.0000 10.3923i −1.52708 0.661247i
\(248\) −2.00000 −0.127000
\(249\) 6.50000 11.2583i 0.411921 0.713468i
\(250\) 0 0
\(251\) 10.0000 + 17.3205i 0.631194 + 1.09326i 0.987308 + 0.158818i \(0.0507683\pi\)
−0.356113 + 0.934443i \(0.615898\pi\)
\(252\) −2.00000 + 3.46410i −0.125988 + 0.218218i
\(253\) 0 0
\(254\) 12.0000 0.752947
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) −12.0000 −0.747087
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 10.0000 17.3205i 0.618984 1.07211i
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) −7.00000 + 12.1244i −0.431638 + 0.747620i −0.997015 0.0772134i \(-0.975398\pi\)
0.565376 + 0.824833i \(0.308731\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 8.66025i −0.0613139 0.530994i
\(267\) −13.0000 −0.795587
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) −13.0000 + 22.5167i −0.792624 + 1.37287i 0.131713 + 0.991288i \(0.457952\pi\)
−0.924337 + 0.381577i \(0.875381\pi\)
\(270\) 0 0
\(271\) −13.0000 + 22.5167i −0.789694 + 1.36779i 0.136461 + 0.990645i \(0.456427\pi\)
−0.926155 + 0.377144i \(0.876906\pi\)
\(272\) −3.50000 6.06218i −0.212219 0.367574i
\(273\) −12.0000 −0.726273
\(274\) 15.0000 0.906183
\(275\) 0 0
\(276\) −1.00000 1.73205i −0.0601929 0.104257i
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 0 0
\(279\) −2.00000 3.46410i −0.119737 0.207390i
\(280\) 0 0
\(281\) −3.50000 6.06218i −0.208792 0.361639i 0.742542 0.669800i \(-0.233620\pi\)
−0.951334 + 0.308160i \(0.900287\pi\)
\(282\) 0 0
\(283\) 14.0000 24.2487i 0.832214 1.44144i −0.0640654 0.997946i \(-0.520407\pi\)
0.896279 0.443491i \(-0.146260\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) 0 0
\(287\) 2.00000 3.46410i 0.118056 0.204479i
\(288\) 1.00000 1.73205i 0.0589256 0.102062i
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) −3.00000 −0.175562
\(293\) 32.0000 1.86946 0.934730 0.355359i \(-0.115641\pi\)
0.934730 + 0.355359i \(0.115641\pi\)
\(294\) 1.50000 + 2.59808i 0.0874818 + 0.151523i
\(295\) 0 0
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) −8.00000 13.8564i −0.463428 0.802680i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) 6.00000 10.3923i 0.345261 0.598010i
\(303\) 2.00000 0.114897
\(304\) 0.500000 + 4.33013i 0.0286770 + 0.248350i
\(305\) 0 0
\(306\) 7.00000 12.1244i 0.400163 0.693103i
\(307\) 9.50000 16.4545i 0.542194 0.939107i −0.456584 0.889680i \(-0.650927\pi\)
0.998778 0.0494267i \(-0.0157394\pi\)
\(308\) 0 0
\(309\) −6.00000 + 10.3923i −0.341328 + 0.591198i
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 6.00000 0.339683
\(313\) −5.50000 9.52628i −0.310878 0.538457i 0.667674 0.744453i \(-0.267290\pi\)
−0.978553 + 0.205996i \(0.933957\pi\)
\(314\) −3.00000 5.19615i −0.169300 0.293236i
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −7.50000 + 12.9904i −0.418609 + 0.725052i
\(322\) −4.00000 −0.222911
\(323\) 3.50000 + 30.3109i 0.194745 + 1.68654i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) −1.00000 + 1.73205i −0.0552158 + 0.0956365i
\(329\) 0 0
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) 6.50000 + 11.2583i 0.356734 + 0.617881i
\(333\) 4.00000 + 6.92820i 0.219199 + 0.379663i
\(334\) 10.0000 0.547176
\(335\) 0 0
\(336\) 1.00000 + 1.73205i 0.0545545 + 0.0944911i
\(337\) 11.0000 19.0526i 0.599208 1.03786i −0.393730 0.919226i \(-0.628816\pi\)
0.992938 0.118633i \(-0.0378512\pi\)
\(338\) −11.5000 19.9186i −0.625518 1.08343i
\(339\) −0.500000 + 0.866025i −0.0271563 + 0.0470360i
\(340\) 0 0
\(341\) 0 0
\(342\) −7.00000 + 5.19615i −0.378517 + 0.280976i
\(343\) 20.0000 1.07990
\(344\) 6.00000 10.3923i 0.323498 0.560316i
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) −5.00000 8.66025i −0.268028 0.464238i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 0 0
\(351\) 15.0000 + 25.9808i 0.800641 + 1.38675i
\(352\) 0 0
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 0 0
\(356\) 6.50000 11.2583i 0.344499 0.596690i
\(357\) 7.00000 + 12.1244i 0.370479 + 0.641689i
\(358\) 4.50000 7.79423i 0.237832 0.411938i
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) 20.0000 1.05118
\(363\) 5.50000 9.52628i 0.288675 0.500000i
\(364\) 6.00000 10.3923i 0.314485 0.544705i
\(365\) 0 0
\(366\) −4.00000 + 6.92820i −0.209083 + 0.362143i
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) 2.00000 0.104257
\(369\) −4.00000 −0.208232
\(370\) 0 0
\(371\) 0 0
\(372\) −2.00000 −0.103695
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −30.0000 + 51.9615i −1.54508 + 2.67615i
\(378\) −5.00000 + 8.66025i −0.257172 + 0.445435i
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 12.0000 0.614779
\(382\) 5.00000 8.66025i 0.255822 0.443097i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −5.50000 9.52628i −0.279943 0.484875i
\(387\) 24.0000 1.21999
\(388\) 15.0000 0.761510
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) −3.00000 −0.151523
\(393\) −0.500000 0.866025i −0.0252217 0.0436852i
\(394\) −2.00000 + 3.46410i −0.100759 + 0.174519i
\(395\) 0 0
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −16.0000 −0.802008
\(399\) −1.00000 8.66025i −0.0500626 0.433555i
\(400\) 0 0
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) −4.00000 + 6.92820i −0.199502 + 0.345547i
\(403\) 6.00000 + 10.3923i 0.298881 + 0.517678i
\(404\) −1.00000 + 1.73205i −0.0497519 + 0.0861727i
\(405\) 0 0
\(406\) −20.0000 −0.992583
\(407\) 0 0
\(408\) −3.50000 6.06218i −0.173276 0.300123i
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) 0 0
\(411\) 15.0000 0.739895
\(412\) −6.00000 10.3923i −0.295599 0.511992i
\(413\) −1.00000 + 1.73205i −0.0492068 + 0.0852286i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) 0 0
\(416\) −3.00000 + 5.19615i −0.147087 + 0.254762i
\(417\) 0 0
\(418\) 0 0
\(419\) 13.0000 0.635092 0.317546 0.948243i \(-0.397141\pi\)
0.317546 + 0.948243i \(0.397141\pi\)
\(420\) 0 0
\(421\) −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i \(0.477489\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(422\) −11.5000 19.9186i −0.559811 0.969622i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 8.00000 + 13.8564i 0.387147 + 0.670559i
\(428\) −7.50000 12.9904i −0.362526 0.627914i
\(429\) 0 0
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 2.50000 4.33013i 0.120281 0.208333i
\(433\) 10.5000 + 18.1865i 0.504598 + 0.873989i 0.999986 + 0.00531724i \(0.00169254\pi\)
−0.495388 + 0.868672i \(0.664974\pi\)
\(434\) −2.00000 + 3.46410i −0.0960031 + 0.166282i
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −8.00000 3.46410i −0.382692 0.165710i
\(438\) −3.00000 −0.143346
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) −3.00000 5.19615i −0.142857 0.247436i
\(442\) −21.0000 + 36.3731i −0.998868 + 1.73009i
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 4.00000 0.189832
\(445\) 0 0
\(446\) 1.00000 + 1.73205i 0.0473514 + 0.0820150i
\(447\) −8.00000 13.8564i −0.378387 0.655386i
\(448\) −2.00000 −0.0944911
\(449\) 41.0000 1.93491 0.967455 0.253044i \(-0.0814317\pi\)
0.967455 + 0.253044i \(0.0814317\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.500000 0.866025i −0.0235180 0.0407344i
\(453\) 6.00000 10.3923i 0.281905 0.488273i
\(454\) −6.50000 + 11.2583i −0.305060 + 0.528380i
\(455\) 0 0
\(456\) 0.500000 + 4.33013i 0.0234146 + 0.202777i
\(457\) 11.0000 0.514558 0.257279 0.966337i \(-0.417174\pi\)
0.257279 + 0.966337i \(0.417174\pi\)
\(458\) 9.00000 15.5885i 0.420542 0.728401i
\(459\) 17.5000 30.3109i 0.816830 1.41479i
\(460\) 0 0
\(461\) −1.00000 + 1.73205i −0.0465746 + 0.0806696i −0.888373 0.459123i \(-0.848164\pi\)
0.841798 + 0.539792i \(0.181497\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) −6.50000 11.2583i −0.301107 0.521532i
\(467\) 23.0000 1.06431 0.532157 0.846646i \(-0.321382\pi\)
0.532157 + 0.846646i \(0.321382\pi\)
\(468\) −12.0000 −0.554700
\(469\) 8.00000 + 13.8564i 0.369406 + 0.639829i
\(470\) 0 0
\(471\) −3.00000 5.19615i −0.138233 0.239426i
\(472\) 0.500000 0.866025i 0.0230144 0.0398621i
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) −14.0000 −0.641689
\(477\) 0 0
\(478\) 3.00000 5.19615i 0.137217 0.237666i
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) 0 0
\(481\) −12.0000 20.7846i −0.547153 0.947697i
\(482\) 14.0000 0.637683
\(483\) −4.00000 −0.182006
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −4.00000 6.92820i −0.181071 0.313625i
\(489\) 6.00000 10.3923i 0.271329 0.469956i
\(490\) 0 0
\(491\) −4.00000 + 6.92820i −0.180517 + 0.312665i −0.942057 0.335453i \(-0.891111\pi\)
0.761539 + 0.648119i \(0.224444\pi\)
\(492\) −1.00000 + 1.73205i −0.0450835 + 0.0780869i
\(493\) 70.0000 3.15264
\(494\) 21.0000 15.5885i 0.944835 0.701358i
\(495\) 0 0
\(496\) 1.00000 1.73205i 0.0449013 0.0777714i
\(497\) −12.0000 + 20.7846i −0.538274 + 0.932317i
\(498\) 6.50000 + 11.2583i 0.291272 + 0.504498i
\(499\) 16.5000 28.5788i 0.738641 1.27936i −0.214466 0.976732i \(-0.568801\pi\)
0.953107 0.302633i \(-0.0978656\pi\)
\(500\) 0 0
\(501\) 10.0000 0.446767
\(502\) −20.0000 −0.892644
\(503\) −4.00000 6.92820i −0.178351 0.308913i 0.762965 0.646440i \(-0.223743\pi\)
−0.941316 + 0.337527i \(0.890410\pi\)
\(504\) −2.00000 3.46410i −0.0890871 0.154303i
\(505\) 0 0
\(506\) 0 0
\(507\) −11.5000 19.9186i −0.510733 0.884615i
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) −3.00000 + 5.19615i −0.132712 + 0.229864i
\(512\) 1.00000 0.0441942
\(513\) −17.5000 + 12.9904i −0.772644 + 0.573539i
\(514\) −15.0000 −0.661622
\(515\) 0 0
\(516\) 6.00000 10.3923i 0.264135 0.457496i
\(517\) 0 0
\(518\) 4.00000 6.92820i 0.175750 0.304408i
\(519\) −3.00000 5.19615i −0.131685 0.228086i
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 10.0000 + 17.3205i 0.437688 + 0.758098i
\(523\) 14.5000 + 25.1147i 0.634041 + 1.09819i 0.986718 + 0.162446i \(0.0519382\pi\)
−0.352677 + 0.935745i \(0.614728\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0 0
\(526\) −7.00000 12.1244i −0.305215 0.528647i
\(527\) 7.00000 12.1244i 0.304925 0.528145i
\(528\) 0 0
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 8.00000 + 3.46410i 0.346844 + 0.150188i
\(533\) 12.0000 0.519778
\(534\) 6.50000 11.2583i 0.281283 0.487196i
\(535\) 0 0
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) 4.50000 7.79423i 0.194189 0.336346i
\(538\) −13.0000 22.5167i −0.560470 0.970762i
\(539\) 0 0
\(540\) 0 0
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) −13.0000 22.5167i −0.558398 0.967173i
\(543\) 20.0000 0.858282
\(544\) 7.00000 0.300123
\(545\) 0 0
\(546\) 6.00000 10.3923i 0.256776 0.444750i
\(547\) 0.500000 + 0.866025i 0.0213785 + 0.0370286i 0.876517 0.481371i \(-0.159861\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) −7.50000 + 12.9904i −0.320384 + 0.554922i
\(549\) 8.00000 13.8564i 0.341432 0.591377i
\(550\) 0 0
\(551\) −40.0000 17.3205i −1.70406 0.737878i
\(552\) 2.00000 0.0851257
\(553\) −4.00000 + 6.92820i −0.170097 + 0.294617i
\(554\) 11.0000 19.0526i 0.467345 0.809466i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) 4.00000 0.169334
\(559\) −72.0000 −3.04528
\(560\) 0 0
\(561\) 0 0
\(562\) 7.00000 0.295277
\(563\) −43.0000 −1.81223 −0.906117 0.423027i \(-0.860967\pi\)
−0.906117 + 0.423027i \(0.860967\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 + 24.2487i 0.588464 + 1.01925i
\(567\) 1.00000 1.73205i 0.0419961 0.0727393i
\(568\) 6.00000 10.3923i 0.251754 0.436051i
\(569\) 1.00000 0.0419222 0.0209611 0.999780i \(-0.493327\pi\)
0.0209611 + 0.999780i \(0.493327\pi\)
\(570\) 0 0
\(571\) 1.00000 0.0418487 0.0209243 0.999781i \(-0.493339\pi\)
0.0209243 + 0.999781i \(0.493339\pi\)
\(572\) 0 0
\(573\) 5.00000 8.66025i 0.208878 0.361787i
\(574\) 2.00000 + 3.46410i 0.0834784 + 0.144589i
\(575\) 0 0
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 32.0000 1.33102
\(579\) −5.50000 9.52628i −0.228572 0.395899i
\(580\) 0 0
\(581\) 26.0000 1.07866
\(582\) 15.0000 0.621770
\(583\) 0 0
\(584\) 1.50000 2.59808i 0.0620704 0.107509i
\(585\) 0 0
\(586\) −16.0000 + 27.7128i −0.660954 + 1.14481i
\(587\) −22.5000 + 38.9711i −0.928674 + 1.60851i −0.143132 + 0.989704i \(0.545717\pi\)
−0.785543 + 0.618808i \(0.787616\pi\)
\(588\) −3.00000 −0.123718
\(589\) −7.00000 + 5.19615i −0.288430 + 0.214104i
\(590\) 0 0
\(591\) −2.00000 + 3.46410i −0.0822690 + 0.142494i
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 7.00000 + 12.1244i 0.287456 + 0.497888i 0.973202 0.229953i \(-0.0738573\pi\)
−0.685746 + 0.727841i \(0.740524\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.0000 0.655386
\(597\) −16.0000 −0.654836
\(598\) −6.00000 10.3923i −0.245358 0.424973i
\(599\) 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 0 0
\(601\) 35.0000 1.42768 0.713840 0.700309i \(-0.246954\pi\)
0.713840 + 0.700309i \(0.246954\pi\)
\(602\) −12.0000 20.7846i −0.489083 0.847117i
\(603\) 8.00000 13.8564i 0.325785 0.564276i
\(604\) 6.00000 + 10.3923i 0.244137 + 0.422857i
\(605\) 0 0
\(606\) −1.00000 + 1.73205i −0.0406222 + 0.0703598i
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) −4.00000 1.73205i −0.162221 0.0702439i
\(609\) −20.0000 −0.810441
\(610\) 0 0
\(611\) 0 0
\(612\) 7.00000 + 12.1244i 0.282958 + 0.490098i
\(613\) 7.00000 12.1244i 0.282727 0.489698i −0.689328 0.724449i \(-0.742094\pi\)
0.972056 + 0.234751i \(0.0754275\pi\)
\(614\) 9.50000 + 16.4545i 0.383389 + 0.664049i
\(615\) 0 0
\(616\) 0 0
\(617\) 3.50000 + 6.06218i 0.140905 + 0.244054i 0.927838 0.372985i \(-0.121666\pi\)
−0.786933 + 0.617039i \(0.788332\pi\)
\(618\) −6.00000 10.3923i −0.241355 0.418040i
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 5.00000 + 8.66025i 0.200643 + 0.347524i
\(622\) −15.0000 + 25.9808i −0.601445 + 1.04173i
\(623\) −13.0000 22.5167i −0.520834 0.902111i
\(624\) −3.00000 + 5.19615i −0.120096 + 0.208013i
\(625\) 0 0
\(626\) 11.0000 0.439648
\(627\) 0 0
\(628\) 6.00000 0.239426
\(629\) −14.0000 + 24.2487i −0.558217 + 0.966859i
\(630\) 0 0
\(631\) −24.0000 41.5692i −0.955425 1.65484i −0.733393 0.679805i \(-0.762064\pi\)
−0.222032 0.975039i \(-0.571269\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) −11.5000 19.9186i −0.457084 0.791693i
\(634\) −24.0000 −0.953162
\(635\) 0 0
\(636\) 0 0
\(637\) 9.00000 + 15.5885i 0.356593 + 0.617637i
\(638\) 0 0
\(639\) 24.0000 0.949425
\(640\) 0 0
\(641\) 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) −7.50000 12.9904i −0.296001 0.512689i
\(643\) 12.5000 21.6506i 0.492952 0.853818i −0.507015 0.861937i \(-0.669251\pi\)
0.999967 + 0.00811944i \(0.00258453\pi\)
\(644\) 2.00000 3.46410i 0.0788110 0.136505i
\(645\) 0 0
\(646\) −28.0000 12.1244i −1.10165 0.477026i
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) −2.00000 + 3.46410i −0.0783862 + 0.135769i
\(652\) 6.00000 + 10.3923i 0.234978 + 0.406994i
\(653\) −12.0000 −0.469596 −0.234798 0.972044i \(-0.575443\pi\)
−0.234798 + 0.972044i \(0.575443\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 0 0
\(656\) −1.00000 1.73205i −0.0390434 0.0676252i
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) −1.50000 2.59808i −0.0584317 0.101207i 0.835330 0.549749i \(-0.185277\pi\)
−0.893762 + 0.448542i \(0.851943\pi\)
\(660\) 0 0
\(661\) 2.00000 + 3.46410i 0.0777910 + 0.134738i 0.902297 0.431116i \(-0.141880\pi\)
−0.824506 + 0.565854i \(0.808547\pi\)
\(662\) 8.50000 14.7224i 0.330362 0.572204i
\(663\) −21.0000 + 36.3731i −0.815572 + 1.41261i
\(664\) −13.0000 −0.504498
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) −10.0000 + 17.3205i −0.387202 + 0.670653i
\(668\) −5.00000 + 8.66025i −0.193456 + 0.335075i
\(669\) 1.00000 + 1.73205i 0.0386622 + 0.0669650i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 11.0000 + 19.0526i 0.423704 + 0.733877i
\(675\) 0 0
\(676\) 23.0000 0.884615
\(677\) 26.0000 0.999261 0.499631 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) −0.500000 0.866025i −0.0192024 0.0332595i
\(679\) 15.0000 25.9808i 0.575647 0.997050i
\(680\) 0 0
\(681\) −6.50000 + 11.2583i −0.249081 + 0.431420i
\(682\) 0 0
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) −1.00000 8.66025i −0.0382360 0.331133i
\(685\) 0 0
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 9.00000 15.5885i 0.343371 0.594737i
\(688\) 6.00000 + 10.3923i 0.228748 + 0.396203i
\(689\) 0 0
\(690\) 0 0
\(691\) 37.0000 1.40755 0.703773 0.710425i \(-0.251497\pi\)
0.703773 + 0.710425i \(0.251497\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 6.00000 + 10.3923i 0.227757 + 0.394486i
\(695\) 0 0
\(696\) 10.0000 0.379049
\(697\) −7.00000 12.1244i −0.265144 0.459243i
\(698\) −8.00000 + 13.8564i −0.302804 + 0.524473i
\(699\) −6.50000 11.2583i −0.245853 0.425829i
\(700\) 0 0
\(701\) 12.0000 20.7846i 0.453234 0.785024i −0.545351 0.838208i \(-0.683604\pi\)
0.998585 + 0.0531839i \(0.0169370\pi\)
\(702\) −30.0000 −1.13228
\(703\) 14.0000 10.3923i 0.528020 0.391953i
\(704\) 0 0
\(705\) 0 0
\(706\) 1.50000 2.59808i 0.0564532 0.0977799i
\(707\) 2.00000 + 3.46410i 0.0752177 + 0.130281i
\(708\) 0.500000 0.866025i 0.0187912 0.0325472i
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 6.50000 + 11.2583i 0.243598 + 0.421924i
\(713\) 2.00000 + 3.46410i 0.0749006 + 0.129732i
\(714\) −14.0000 −0.523937
\(715\) 0 0
\(716\) 4.50000 + 7.79423i 0.168173 + 0.291284i
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) −16.0000 + 27.7128i −0.596699 + 1.03351i 0.396605 + 0.917989i \(0.370188\pi\)
−0.993305 + 0.115524i \(0.963145\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 13.0000 + 13.8564i 0.483810 + 0.515682i
\(723\) 14.0000 0.520666
\(724\) −10.0000 + 17.3205i −0.371647 + 0.643712i
\(725\) 0 0
\(726\) 5.50000 + 9.52628i 0.204124 + 0.353553i
\(727\) 7.00000 12.1244i 0.259616 0.449667i −0.706523 0.707690i \(-0.749737\pi\)
0.966139 + 0.258022i \(0.0830708\pi\)
\(728\) 6.00000 + 10.3923i 0.222375 + 0.385164i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 42.0000 + 72.7461i 1.55343 + 2.69061i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −1.00000 + 1.73205i −0.0368605 + 0.0638442i
\(737\) 0 0
\(738\) 2.00000 3.46410i 0.0736210 0.127515i
\(739\) −23.5000 + 40.7032i −0.864461 + 1.49729i 0.00311943 + 0.999995i \(0.499007\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(740\) 0 0
\(741\) 21.0000 15.5885i 0.771454 0.572656i
\(742\) 0 0
\(743\) −13.0000 + 22.5167i −0.476924 + 0.826056i −0.999650 0.0264443i \(-0.991582\pi\)
0.522727 + 0.852500i \(0.324915\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) −13.0000 22.5167i −0.475645 0.823842i
\(748\) 0 0
\(749\) −30.0000 −1.09618
\(750\) 0 0
\(751\) 13.0000 + 22.5167i 0.474377 + 0.821645i 0.999570 0.0293387i \(-0.00934013\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(752\) 0 0
\(753\) −20.0000 −0.728841
\(754\) −30.0000 51.9615i −1.09254 1.89233i
\(755\) 0 0
\(756\) −5.00000 8.66025i −0.181848 0.314970i
\(757\) −16.0000 + 27.7128i −0.581530 + 1.00724i 0.413768 + 0.910382i \(0.364212\pi\)
−0.995298 + 0.0968571i \(0.969121\pi\)
\(758\) 0.500000 0.866025i 0.0181608 0.0314555i
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −6.00000 + 10.3923i −0.217357 + 0.376473i
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) 5.00000 + 8.66025i 0.180894 + 0.313317i
\(765\) 0 0
\(766\) 6.00000 + 10.3923i 0.216789 + 0.375489i
\(767\) −6.00000 −0.216647
\(768\) 1.00000 0.0360844
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) 0 0
\(771\) −15.0000 −0.540212
\(772\) 11.0000 0.395899
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) −12.0000 + 20.7846i −0.431331 + 0.747087i
\(775\) 0 0
\(776\) −7.50000 + 12.9904i −0.269234 + 0.466328i
\(777\) 4.00000 6.92820i 0.143499 0.248548i
\(778\) 18.0000 0.645331
\(779\) 1.00000 + 8.66025i 0.0358287 + 0.310286i
\(780\) 0 0
\(781\) 0 0
\(782\) −7.00000 + 12.1244i −0.250319 + 0.433566i
\(783\) 25.0000 + 43.3013i 0.893427 + 1.54746i
\(784\) 1.50000 2.59808i 0.0535714 0.0927884i
\(785\) 0 0
\(786\) 1.00000 0.0356688
\(787\) −29.0000 −1.03374 −0.516869 0.856064i \(-0.672903\pi\)
−0.516869 + 0.856064i \(0.672903\pi\)
\(788\) −2.00000 3.46410i −0.0712470 0.123404i