Properties

Label 950.2.e.g.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.g.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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −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 \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −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 \(0.146166\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 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 \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) 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 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) −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 \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −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 \(0.534469\pi\)
−0.806914 + 0.590669i \(0.798864\pi\)
\(44\) 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 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) −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 −0.940356 0.340193i \(-0.889507\pi\)
0.764794 + 0.644275i \(0.222841\pi\)
\(74\) −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 \(-0.247124\pi\)
0.713468 + 0.700688i \(0.247124\pi\)
\(84\) −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 \(-0.557792\pi\)
0.942072 0.335410i \(-0.108875\pi\)
\(98\) −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 \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) −3.00000 5.19615i −0.294174 0.509525i
\(105\) 0 0
\(106\) 0 0
\(107\) −15.0000 −1.45010 −0.725052 0.688694i \(-0.758184\pi\)
−0.725052 + 0.688694i \(0.758184\pi\)
\(108\) −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 \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) −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 \(0.0120483\pi\)
−0.466870 + 0.884326i \(0.654618\pi\)
\(128\) 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 \(0.0547174\pi\)
−0.344493 + 0.938789i \(0.611949\pi\)
\(138\) 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 −0.721124 0.692806i \(-0.756374\pi\)
0.960550 + 0.278108i \(0.0897074\pi\)
\(158\) −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 \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 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 0.992032 0.125983i \(-0.0402085\pi\)
−0.605121 + 0.796134i \(0.706875\pi\)
\(168\) −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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −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 −0.597317 0.802005i \(-0.703766\pi\)
0.993215 + 0.116289i \(0.0370998\pi\)
\(194\) −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 \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) 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 −0.897564 0.440884i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(224\) 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 \(-0.641987\pi\)
−0.431420 + 0.902151i \(0.641987\pi\)
\(228\) −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 −0.570668 0.821181i \(-0.693316\pi\)
0.996497 + 0.0836229i \(0.0266491\pi\)
\(234\) 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 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) 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 −0.565376 0.824833i \(-0.691269\pi\)
0.997015 + 0.0772134i \(0.0246023\pi\)
\(264\) 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 \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 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 \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) −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 \(-0.884359\pi\)
−0.934730 + 0.355359i \(0.884359\pi\)
\(294\) 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 \(0.349073\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) 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 0.978553 0.205996i \(-0.0660435\pi\)
−0.667674 + 0.744453i \(0.732710\pi\)
\(314\) −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 \(-0.931247\pi\)
0.302777 0.953062i \(-0.402086\pi\)
\(318\) 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 \(0.371184\pi\)
−0.992938 + 0.118633i \(0.962149\pi\)
\(338\) 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 −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 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 \(-0.474560\pi\)
0.0798369 + 0.996808i \(0.474560\pi\)
\(354\) −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 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) −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 \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 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 −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) −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 −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) 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 \(-0.998307\pi\)
0.495388 0.868672i \(-0.335026\pi\)
\(434\) −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 \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 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 \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) −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 \(-0.329196\pi\)
0.511213 + 0.859454i \(0.329196\pi\)
\(464\) 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 \(-0.678618\pi\)
−0.532157 + 0.846646i \(0.678618\pi\)
\(468\) 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 \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 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 0.941316 0.337527i \(-0.109590\pi\)
−0.762965 + 0.646440i \(0.776257\pi\)
\(504\) −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 \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) 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 0.855138 0.518400i \(-0.173472\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(548\) 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 0.844062 0.536246i \(-0.180158\pi\)
−0.886433 + 0.462856i \(0.846825\pi\)
\(558\) −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 \(-0.139033\pi\)
0.906117 + 0.423027i \(0.139033\pi\)
\(564\) 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 \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) −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 \(-0.454283\pi\)
0.785543 0.618808i \(-0.212384\pi\)
\(588\) 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 0.685746 0.727841i \(-0.259476\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(594\) 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 \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) 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 −0.972056 0.234751i \(-0.924572\pi\)
0.689328 + 0.724449i \(0.257906\pi\)
\(614\) 9.50000 + 16.4545i 0.383389 + 0.664049i
\(615\) 0 0
\(616\) 0 0
\(617\) −3.50000 6.06218i −0.140905 0.244054i 0.786933 0.617039i \(-0.211668\pi\)
−0.927838 + 0.372985i \(0.878334\pi\)
\(618\) 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 −0.999967 0.00811944i \(-0.997415\pi\)
0.507015 + 0.861937i \(0.330749\pi\)
\(644\) 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 \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 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 \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) −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 \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 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 \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) 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 \(-0.592651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(684\) −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 −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) −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 \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) −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 −0.522727 0.852500i \(-0.675085\pi\)
0.999650 + 0.0264443i \(0.00841845\pi\)
\(744\) 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 \(-0.635788\pi\)
0.995298 0.0968571i \(-0.0308790\pi\)
\(758\) −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 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) −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 \(-0.327097\pi\)
0.516869 + 0.856064i \(0.327097\pi\)
\(788\) 2.00000 + 3.46410i 0.0712470 + 0.123404i
\(789\) −7.00000 12.1244i