Properties

Label 950.2.e.n.501.3
Level $950$
Weight $2$
Character 950.501
Analytic conductor $7.586$
Analytic rank $0$
Dimension $10$
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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.3
Root \(0.341187 + 0.590953i\) of defining polynomial
Character \(\chi\) \(=\) 950.501
Dual form 950.2.e.n.201.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.341187 + 0.590953i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.341187 - 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 - 2.19482i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.341187 + 0.590953i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.341187 - 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 - 2.19482i) q^{9} -4.31087 q^{11} -0.682374 q^{12} +(-3.14836 + 5.45312i) q^{13} +(0.158813 + 0.275072i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0669268 + 0.115921i) q^{17} -2.53437 q^{18} +(-4.05310 + 1.60387i) q^{19} +(-0.108370 - 0.187702i) q^{21} +(2.15544 + 3.73333i) q^{22} +(-1.98955 + 3.44600i) q^{23} +(0.341187 + 0.590953i) q^{24} +6.29672 q^{26} +3.77651 q^{27} +(0.158813 - 0.275072i) q^{28} +(4.57435 - 7.92301i) q^{29} -2.98584 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.47081 - 2.54753i) q^{33} +(0.0669268 - 0.115921i) q^{34} +(1.26718 + 2.19482i) q^{36} -5.07323 q^{37} +(3.41554 + 2.70815i) q^{38} -4.29672 q^{39} +(0.433073 + 0.750105i) q^{41} +(-0.108370 + 0.187702i) q^{42} +(-2.85199 - 4.93979i) q^{43} +(2.15544 - 3.73333i) q^{44} +3.97909 q^{46} +(-6.48617 + 11.2344i) q^{47} +(0.341187 - 0.590953i) q^{48} -6.89911 q^{49} +(-0.0456691 + 0.0791012i) q^{51} +(-3.14836 - 5.45312i) q^{52} +(-3.96261 + 6.86344i) q^{53} +(-1.88825 - 3.27055i) q^{54} -0.317626 q^{56} +(-2.33068 - 1.84797i) q^{57} -9.14871 q^{58} +(4.80717 + 8.32627i) q^{59} +(-3.08711 + 5.34704i) q^{61} +(1.49292 + 2.58582i) q^{62} +(-0.402490 + 0.697133i) q^{63} +1.00000 q^{64} +(-1.47081 + 2.54753i) q^{66} +(0.295518 - 0.511852i) q^{67} -0.133854 q^{68} -2.71523 q^{69} +(-5.83073 - 10.0991i) q^{71} +(1.26718 - 2.19482i) q^{72} +(4.13048 + 7.15420i) q^{73} +(2.53661 + 4.39354i) q^{74} +(0.637555 - 4.31202i) q^{76} +1.36924 q^{77} +(2.14836 + 3.72107i) q^{78} +(1.66112 + 2.87714i) q^{79} +(-2.51305 - 4.35273i) q^{81} +(0.433073 - 0.750105i) q^{82} -4.20708 q^{83} +0.216740 q^{84} +(-2.85199 + 4.93979i) q^{86} +6.24284 q^{87} -4.31087 q^{88} +(1.85992 - 3.22147i) q^{89} +(1.00000 - 1.73205i) q^{91} +(-1.98955 - 3.44600i) q^{92} +(-1.01873 - 1.76450i) q^{93} +12.9723 q^{94} -0.682374 q^{96} +(-2.42830 - 4.20594i) q^{97} +(3.44956 + 5.97481i) q^{98} +(-5.46266 + 9.46161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} + O(q^{10}) \) \( 10q - 5q^{2} - 5q^{4} - 10q^{7} + 10q^{8} - 5q^{9} - 6q^{11} - 2q^{13} + 5q^{14} - 5q^{16} + 4q^{17} + 10q^{18} + 11q^{19} + 20q^{21} + 3q^{22} + 13q^{23} + 4q^{26} + 36q^{27} + 5q^{28} + 2q^{29} - 8q^{31} - 5q^{32} + 2q^{33} + 4q^{34} - 5q^{36} + 10q^{37} - 13q^{38} + 16q^{39} + q^{41} + 20q^{42} + 3q^{44} - 26q^{46} - 10q^{47} - 20q^{49} + 4q^{51} - 2q^{52} + 5q^{53} - 18q^{54} - 10q^{56} - 10q^{57} - 4q^{58} + 22q^{59} - 2q^{61} + 4q^{62} + 23q^{63} + 10q^{64} + 2q^{66} + 4q^{67} - 8q^{68} - 24q^{69} - 22q^{71} - 5q^{72} + 26q^{73} - 5q^{74} + 2q^{76} + 10q^{77} - 8q^{78} + 2q^{79} - 5q^{81} + q^{82} + 12q^{83} - 40q^{84} - 20q^{87} - 6q^{88} - q^{89} + 10q^{91} + 13q^{92} + 6q^{93} + 20q^{94} + 8q^{97} + 10q^{98} + 13q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 0.341187 + 0.590953i 0.196984 + 0.341187i 0.947549 0.319610i \(-0.103552\pi\)
−0.750565 + 0.660797i \(0.770218\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.341187 0.590953i 0.139289 0.241256i
\(7\) −0.317626 −0.120051 −0.0600256 0.998197i \(-0.519118\pi\)
−0.0600256 + 0.998197i \(0.519118\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.26718 2.19482i 0.422394 0.731608i
\(10\) 0 0
\(11\) −4.31087 −1.29978 −0.649889 0.760029i \(-0.725184\pi\)
−0.649889 + 0.760029i \(0.725184\pi\)
\(12\) −0.682374 −0.196984
\(13\) −3.14836 + 5.45312i −0.873198 + 1.51242i −0.0145275 + 0.999894i \(0.504624\pi\)
−0.858670 + 0.512528i \(0.828709\pi\)
\(14\) 0.158813 + 0.275072i 0.0424445 + 0.0735161i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.0669268 + 0.115921i 0.0162321 + 0.0281149i 0.874027 0.485877i \(-0.161500\pi\)
−0.857795 + 0.513992i \(0.828166\pi\)
\(18\) −2.53437 −0.597356
\(19\) −4.05310 + 1.60387i −0.929844 + 0.367953i
\(20\) 0 0
\(21\) −0.108370 0.187702i −0.0236482 0.0409599i
\(22\) 2.15544 + 3.73333i 0.459541 + 0.795948i
\(23\) −1.98955 + 3.44600i −0.414849 + 0.718540i −0.995413 0.0956753i \(-0.969499\pi\)
0.580564 + 0.814215i \(0.302832\pi\)
\(24\) 0.341187 + 0.590953i 0.0696445 + 0.120628i
\(25\) 0 0
\(26\) 6.29672 1.23489
\(27\) 3.77651 0.726789
\(28\) 0.158813 0.275072i 0.0300128 0.0519837i
\(29\) 4.57435 7.92301i 0.849436 1.47127i −0.0322757 0.999479i \(-0.510275\pi\)
0.881712 0.471788i \(-0.156391\pi\)
\(30\) 0 0
\(31\) −2.98584 −0.536274 −0.268137 0.963381i \(-0.586408\pi\)
−0.268137 + 0.963381i \(0.586408\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.47081 2.54753i −0.256036 0.443467i
\(34\) 0.0669268 0.115921i 0.0114778 0.0198802i
\(35\) 0 0
\(36\) 1.26718 + 2.19482i 0.211197 + 0.365804i
\(37\) −5.07323 −0.834033 −0.417017 0.908899i \(-0.636924\pi\)
−0.417017 + 0.908899i \(0.636924\pi\)
\(38\) 3.41554 + 2.70815i 0.554074 + 0.439320i
\(39\) −4.29672 −0.688026
\(40\) 0 0
\(41\) 0.433073 + 0.750105i 0.0676347 + 0.117147i 0.897860 0.440282i \(-0.145121\pi\)
−0.830225 + 0.557428i \(0.811788\pi\)
\(42\) −0.108370 + 0.187702i −0.0167218 + 0.0289631i
\(43\) −2.85199 4.93979i −0.434925 0.753311i 0.562365 0.826889i \(-0.309892\pi\)
−0.997289 + 0.0735777i \(0.976558\pi\)
\(44\) 2.15544 3.73333i 0.324944 0.562820i
\(45\) 0 0
\(46\) 3.97909 0.586685
\(47\) −6.48617 + 11.2344i −0.946105 + 1.63870i −0.192582 + 0.981281i \(0.561686\pi\)
−0.753523 + 0.657421i \(0.771647\pi\)
\(48\) 0.341187 0.590953i 0.0492461 0.0852968i
\(49\) −6.89911 −0.985588
\(50\) 0 0
\(51\) −0.0456691 + 0.0791012i −0.00639495 + 0.0110764i
\(52\) −3.14836 5.45312i −0.436599 0.756211i
\(53\) −3.96261 + 6.86344i −0.544306 + 0.942766i 0.454344 + 0.890826i \(0.349874\pi\)
−0.998650 + 0.0519397i \(0.983460\pi\)
\(54\) −1.88825 3.27055i −0.256959 0.445066i
\(55\) 0 0
\(56\) −0.317626 −0.0424445
\(57\) −2.33068 1.84797i −0.308706 0.244770i
\(58\) −9.14871 −1.20128
\(59\) 4.80717 + 8.32627i 0.625841 + 1.08399i 0.988378 + 0.152018i \(0.0485772\pi\)
−0.362537 + 0.931969i \(0.618089\pi\)
\(60\) 0 0
\(61\) −3.08711 + 5.34704i −0.395264 + 0.684618i −0.993135 0.116975i \(-0.962680\pi\)
0.597871 + 0.801593i \(0.296014\pi\)
\(62\) 1.49292 + 2.58582i 0.189601 + 0.328399i
\(63\) −0.402490 + 0.697133i −0.0507090 + 0.0878305i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.47081 + 2.54753i −0.181045 + 0.313579i
\(67\) 0.295518 0.511852i 0.0361033 0.0625327i −0.847409 0.530940i \(-0.821839\pi\)
0.883512 + 0.468408i \(0.155172\pi\)
\(68\) −0.133854 −0.0162321
\(69\) −2.71523 −0.326875
\(70\) 0 0
\(71\) −5.83073 10.0991i −0.691981 1.19855i −0.971188 0.238315i \(-0.923405\pi\)
0.279207 0.960231i \(-0.409928\pi\)
\(72\) 1.26718 2.19482i 0.149339 0.258663i
\(73\) 4.13048 + 7.15420i 0.483436 + 0.837335i 0.999819 0.0190222i \(-0.00605532\pi\)
−0.516383 + 0.856358i \(0.672722\pi\)
\(74\) 2.53661 + 4.39354i 0.294875 + 0.510739i
\(75\) 0 0
\(76\) 0.637555 4.31202i 0.0731326 0.494623i
\(77\) 1.36924 0.156040
\(78\) 2.14836 + 3.72107i 0.243254 + 0.421328i
\(79\) 1.66112 + 2.87714i 0.186890 + 0.323703i 0.944212 0.329339i \(-0.106826\pi\)
−0.757322 + 0.653042i \(0.773492\pi\)
\(80\) 0 0
\(81\) −2.51305 4.35273i −0.279228 0.483637i
\(82\) 0.433073 0.750105i 0.0478249 0.0828352i
\(83\) −4.20708 −0.461787 −0.230894 0.972979i \(-0.574165\pi\)
−0.230894 + 0.972979i \(0.574165\pi\)
\(84\) 0.216740 0.0236482
\(85\) 0 0
\(86\) −2.85199 + 4.93979i −0.307538 + 0.532672i
\(87\) 6.24284 0.669303
\(88\) −4.31087 −0.459541
\(89\) 1.85992 3.22147i 0.197151 0.341476i −0.750453 0.660924i \(-0.770164\pi\)
0.947604 + 0.319449i \(0.103498\pi\)
\(90\) 0 0
\(91\) 1.00000 1.73205i 0.104828 0.181568i
\(92\) −1.98955 3.44600i −0.207425 0.359270i
\(93\) −1.01873 1.76450i −0.105638 0.182970i
\(94\) 12.9723 1.33799
\(95\) 0 0
\(96\) −0.682374 −0.0696445
\(97\) −2.42830 4.20594i −0.246556 0.427048i 0.716012 0.698088i \(-0.245966\pi\)
−0.962568 + 0.271040i \(0.912632\pi\)
\(98\) 3.44956 + 5.97481i 0.348458 + 0.603547i
\(99\) −5.46266 + 9.46161i −0.549018 + 0.950928i
\(100\) 0 0
\(101\) 1.25638 2.17611i 0.125014 0.216531i −0.796724 0.604343i \(-0.793436\pi\)
0.921739 + 0.387812i \(0.126769\pi\)
\(102\) 0.0913382 0.00904383
\(103\) −4.03297 −0.397380 −0.198690 0.980062i \(-0.563669\pi\)
−0.198690 + 0.980062i \(0.563669\pi\)
\(104\) −3.14836 + 5.45312i −0.308722 + 0.534722i
\(105\) 0 0
\(106\) 7.92522 0.769765
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) −1.88825 + 3.27055i −0.181697 + 0.314709i
\(109\) 2.93197 + 5.07832i 0.280832 + 0.486415i 0.971590 0.236671i \(-0.0760564\pi\)
−0.690758 + 0.723086i \(0.742723\pi\)
\(110\) 0 0
\(111\) −1.73092 2.99804i −0.164292 0.284561i
\(112\) 0.158813 + 0.275072i 0.0150064 + 0.0259919i
\(113\) 18.0853 1.70132 0.850660 0.525716i \(-0.176202\pi\)
0.850660 + 0.525716i \(0.176202\pi\)
\(114\) −0.435051 + 2.94241i −0.0407463 + 0.275582i
\(115\) 0 0
\(116\) 4.57435 + 7.92301i 0.424718 + 0.735633i
\(117\) 7.97909 + 13.8202i 0.737667 + 1.27768i
\(118\) 4.80717 8.32627i 0.442536 0.766495i
\(119\) −0.0212577 0.0368194i −0.00194869 0.00337523i
\(120\) 0 0
\(121\) 7.58363 0.689421
\(122\) 6.17422 0.558988
\(123\) −0.295518 + 0.511852i −0.0266460 + 0.0461522i
\(124\) 1.49292 2.58582i 0.134068 0.232213i
\(125\) 0 0
\(126\) 0.804980 0.0717133
\(127\) 8.94845 15.4992i 0.794047 1.37533i −0.129396 0.991593i \(-0.541304\pi\)
0.923443 0.383736i \(-0.125363\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 1.94613 3.37079i 0.171347 0.296781i
\(130\) 0 0
\(131\) 5.90509 + 10.2279i 0.515930 + 0.893617i 0.999829 + 0.0184931i \(0.00588686\pi\)
−0.483899 + 0.875124i \(0.660780\pi\)
\(132\) 2.94163 0.256036
\(133\) 1.28737 0.509431i 0.111629 0.0441733i
\(134\) −0.591036 −0.0510577
\(135\) 0 0
\(136\) 0.0669268 + 0.115921i 0.00573892 + 0.00994011i
\(137\) 7.91554 13.7101i 0.676270 1.17133i −0.299825 0.953994i \(-0.596928\pi\)
0.976096 0.217341i \(-0.0697382\pi\)
\(138\) 1.35762 + 2.35146i 0.115568 + 0.200169i
\(139\) −0.583681 + 1.01096i −0.0495071 + 0.0857489i −0.889717 0.456512i \(-0.849098\pi\)
0.840210 + 0.542261i \(0.182432\pi\)
\(140\) 0 0
\(141\) −8.85199 −0.745472
\(142\) −5.83073 + 10.0991i −0.489304 + 0.847500i
\(143\) 13.5722 23.5077i 1.13496 1.96581i
\(144\) −2.53437 −0.211197
\(145\) 0 0
\(146\) 4.13048 7.15420i 0.341841 0.592086i
\(147\) −2.35389 4.07705i −0.194145 0.336270i
\(148\) 2.53661 4.39354i 0.208508 0.361147i
\(149\) 6.07575 + 10.5235i 0.497745 + 0.862120i 0.999997 0.00260182i \(-0.000828187\pi\)
−0.502252 + 0.864722i \(0.667495\pi\)
\(150\) 0 0
\(151\) −20.3803 −1.65853 −0.829263 0.558859i \(-0.811239\pi\)
−0.829263 + 0.558859i \(0.811239\pi\)
\(152\) −4.05310 + 1.60387i −0.328750 + 0.130091i
\(153\) 0.339234 0.0274254
\(154\) −0.684622 1.18580i −0.0551684 0.0955545i
\(155\) 0 0
\(156\) 2.14836 3.72107i 0.172006 0.297924i
\(157\) −2.46121 4.26294i −0.196426 0.340220i 0.750941 0.660369i \(-0.229600\pi\)
−0.947367 + 0.320149i \(0.896267\pi\)
\(158\) 1.66112 2.87714i 0.132151 0.228893i
\(159\) −5.40796 −0.428879
\(160\) 0 0
\(161\) 0.631931 1.09454i 0.0498032 0.0862616i
\(162\) −2.51305 + 4.35273i −0.197444 + 0.341983i
\(163\) −1.43727 −0.112576 −0.0562880 0.998415i \(-0.517927\pi\)
−0.0562880 + 0.998415i \(0.517927\pi\)
\(164\) −0.866146 −0.0676347
\(165\) 0 0
\(166\) 2.10354 + 3.64344i 0.163266 + 0.282786i
\(167\) −4.68750 + 8.11899i −0.362730 + 0.628266i −0.988409 0.151814i \(-0.951488\pi\)
0.625680 + 0.780080i \(0.284822\pi\)
\(168\) −0.108370 0.187702i −0.00836091 0.0144815i
\(169\) −13.3243 23.0784i −1.02495 1.77526i
\(170\) 0 0
\(171\) −1.61580 + 10.9282i −0.123563 + 0.835703i
\(172\) 5.70398 0.434925
\(173\) −3.88263 6.72491i −0.295191 0.511286i 0.679838 0.733362i \(-0.262050\pi\)
−0.975029 + 0.222076i \(0.928717\pi\)
\(174\) −3.12142 5.40646i −0.236634 0.409863i
\(175\) 0 0
\(176\) 2.15544 + 3.73333i 0.162472 + 0.281410i
\(177\) −3.28029 + 5.68163i −0.246562 + 0.427057i
\(178\) −3.71984 −0.278814
\(179\) −1.12249 −0.0838992 −0.0419496 0.999120i \(-0.513357\pi\)
−0.0419496 + 0.999120i \(0.513357\pi\)
\(180\) 0 0
\(181\) −7.89198 + 13.6693i −0.586606 + 1.01603i 0.408067 + 0.912952i \(0.366203\pi\)
−0.994673 + 0.103080i \(0.967130\pi\)
\(182\) −2.00000 −0.148250
\(183\) −4.21313 −0.311444
\(184\) −1.98955 + 3.44600i −0.146671 + 0.254042i
\(185\) 0 0
\(186\) −1.01873 + 1.76450i −0.0746970 + 0.129379i
\(187\) −0.288513 0.499719i −0.0210982 0.0365431i
\(188\) −6.48617 11.2344i −0.473053 0.819351i
\(189\) −1.19952 −0.0872520
\(190\) 0 0
\(191\) 18.2974 1.32395 0.661977 0.749524i \(-0.269717\pi\)
0.661977 + 0.749524i \(0.269717\pi\)
\(192\) 0.341187 + 0.590953i 0.0246231 + 0.0426484i
\(193\) −0.558777 0.967830i −0.0402216 0.0696659i 0.845214 0.534428i \(-0.179473\pi\)
−0.885435 + 0.464762i \(0.846140\pi\)
\(194\) −2.42830 + 4.20594i −0.174342 + 0.301969i
\(195\) 0 0
\(196\) 3.44956 5.97481i 0.246397 0.426772i
\(197\) 16.2594 1.15843 0.579217 0.815173i \(-0.303358\pi\)
0.579217 + 0.815173i \(0.303358\pi\)
\(198\) 10.9253 0.776429
\(199\) 6.89911 11.9496i 0.489065 0.847086i −0.510856 0.859667i \(-0.670671\pi\)
0.999921 + 0.0125807i \(0.00400467\pi\)
\(200\) 0 0
\(201\) 0.403308 0.0284471
\(202\) −2.51276 −0.176797
\(203\) −1.45293 + 2.51655i −0.101976 + 0.176627i
\(204\) −0.0456691 0.0791012i −0.00319748 0.00553819i
\(205\) 0 0
\(206\) 2.01648 + 3.49265i 0.140495 + 0.243345i
\(207\) 5.04224 + 8.73341i 0.350460 + 0.607014i
\(208\) 6.29672 0.436599
\(209\) 17.4724 6.91409i 1.20859 0.478257i
\(210\) 0 0
\(211\) 0.584458 + 1.01231i 0.0402358 + 0.0696904i 0.885442 0.464750i \(-0.153856\pi\)
−0.845206 + 0.534440i \(0.820522\pi\)
\(212\) −3.96261 6.86344i −0.272153 0.471383i
\(213\) 3.97874 6.89138i 0.272619 0.472190i
\(214\) 5.00000 + 8.66025i 0.341793 + 0.592003i
\(215\) 0 0
\(216\) 3.77651 0.256959
\(217\) 0.948381 0.0643803
\(218\) 2.93197 5.07832i 0.198578 0.343947i
\(219\) −2.81853 + 4.88184i −0.190459 + 0.329884i
\(220\) 0 0
\(221\) −0.842838 −0.0566954
\(222\) −1.73092 + 2.99804i −0.116172 + 0.201215i
\(223\) −3.15881 5.47122i −0.211530 0.366380i 0.740664 0.671876i \(-0.234511\pi\)
−0.952193 + 0.305496i \(0.901178\pi\)
\(224\) 0.158813 0.275072i 0.0106111 0.0183790i
\(225\) 0 0
\(226\) −9.04264 15.6623i −0.601508 1.04184i
\(227\) 3.77942 0.250849 0.125424 0.992103i \(-0.459971\pi\)
0.125424 + 0.992103i \(0.459971\pi\)
\(228\) 2.76573 1.09444i 0.183165 0.0724811i
\(229\) 5.43628 0.359239 0.179620 0.983736i \(-0.442513\pi\)
0.179620 + 0.983736i \(0.442513\pi\)
\(230\) 0 0
\(231\) 0.467169 + 0.809160i 0.0307374 + 0.0532388i
\(232\) 4.57435 7.92301i 0.300321 0.520171i
\(233\) −1.22461 2.12109i −0.0802270 0.138957i 0.823120 0.567867i \(-0.192231\pi\)
−0.903347 + 0.428910i \(0.858898\pi\)
\(234\) 7.97909 13.8202i 0.521610 0.903454i
\(235\) 0 0
\(236\) −9.61434 −0.625841
\(237\) −1.13350 + 1.96329i −0.0736289 + 0.127529i
\(238\) −0.0212577 + 0.0368194i −0.00137793 + 0.00238664i
\(239\) −9.45899 −0.611851 −0.305926 0.952055i \(-0.598966\pi\)
−0.305926 + 0.952055i \(0.598966\pi\)
\(240\) 0 0
\(241\) 8.43540 14.6105i 0.543372 0.941148i −0.455335 0.890320i \(-0.650481\pi\)
0.998707 0.0508279i \(-0.0161860\pi\)
\(242\) −3.79182 6.56762i −0.243747 0.422183i
\(243\) 7.37960 12.7819i 0.473402 0.819956i
\(244\) −3.08711 5.34704i −0.197632 0.342309i
\(245\) 0 0
\(246\) 0.591036 0.0376831
\(247\) 4.01451 27.1516i 0.255437 1.72761i
\(248\) −2.98584 −0.189601
\(249\) −1.43540 2.48619i −0.0909649 0.157556i
\(250\) 0 0
\(251\) −1.32814 + 2.30040i −0.0838311 + 0.145200i −0.904893 0.425640i \(-0.860049\pi\)
0.821061 + 0.570840i \(0.193382\pi\)
\(252\) −0.402490 0.697133i −0.0253545 0.0439152i
\(253\) 8.57668 14.8553i 0.539211 0.933942i
\(254\) −17.8969 −1.12295
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.12373 + 1.94635i −0.0700961 + 0.121410i −0.898943 0.438065i \(-0.855664\pi\)
0.828847 + 0.559475i \(0.188997\pi\)
\(258\) −3.89225 −0.242321
\(259\) 1.61139 0.100127
\(260\) 0 0
\(261\) −11.5931 20.0798i −0.717594 1.24291i
\(262\) 5.90509 10.2279i 0.364818 0.631883i
\(263\) 15.9289 + 27.5897i 0.982219 + 1.70125i 0.653695 + 0.756758i \(0.273218\pi\)
0.328524 + 0.944496i \(0.393449\pi\)
\(264\) −1.47081 2.54753i −0.0905224 0.156789i
\(265\) 0 0
\(266\) −1.08486 0.860178i −0.0665173 0.0527409i
\(267\) 2.53832 0.155343
\(268\) 0.295518 + 0.511852i 0.0180516 + 0.0312663i
\(269\) 5.44763 + 9.43558i 0.332148 + 0.575297i 0.982933 0.183965i \(-0.0588933\pi\)
−0.650785 + 0.759262i \(0.725560\pi\)
\(270\) 0 0
\(271\) 5.96631 + 10.3340i 0.362428 + 0.627743i 0.988360 0.152134i \(-0.0486147\pi\)
−0.625932 + 0.779877i \(0.715281\pi\)
\(272\) 0.0669268 0.115921i 0.00405803 0.00702872i
\(273\) 1.36475 0.0825983
\(274\) −15.8311 −0.956391
\(275\) 0 0
\(276\) 1.35762 2.35146i 0.0817188 0.141541i
\(277\) −15.9065 −0.955730 −0.477865 0.878433i \(-0.658589\pi\)
−0.477865 + 0.878433i \(0.658589\pi\)
\(278\) 1.16736 0.0700137
\(279\) −3.78361 + 6.55341i −0.226519 + 0.392342i
\(280\) 0 0
\(281\) 10.4921 18.1729i 0.625909 1.08411i −0.362455 0.932001i \(-0.618062\pi\)
0.988364 0.152105i \(-0.0486052\pi\)
\(282\) 4.42600 + 7.66605i 0.263564 + 0.456507i
\(283\) 6.43083 + 11.1385i 0.382273 + 0.662116i 0.991387 0.130967i \(-0.0418081\pi\)
−0.609114 + 0.793083i \(0.708475\pi\)
\(284\) 11.6615 0.691981
\(285\) 0 0
\(286\) −27.1444 −1.60508
\(287\) −0.137555 0.238253i −0.00811963 0.0140636i
\(288\) 1.26718 + 2.19482i 0.0746695 + 0.129331i
\(289\) 8.49104 14.7069i 0.499473 0.865113i
\(290\) 0 0
\(291\) 1.65701 2.87002i 0.0971356 0.168244i
\(292\) −8.26096 −0.483436
\(293\) −12.1278 −0.708511 −0.354255 0.935149i \(-0.615266\pi\)
−0.354255 + 0.935149i \(0.615266\pi\)
\(294\) −2.35389 + 4.07705i −0.137282 + 0.237779i
\(295\) 0 0
\(296\) −5.07323 −0.294875
\(297\) −16.2801 −0.944664
\(298\) 6.07575 10.5235i 0.351959 0.609611i
\(299\) −12.5276 21.6985i −0.724491 1.25485i
\(300\) 0 0
\(301\) 0.905866 + 1.56901i 0.0522132 + 0.0904360i
\(302\) 10.1902 + 17.6499i 0.586377 + 1.01564i
\(303\) 1.71464 0.0985035
\(304\) 3.41554 + 2.70815i 0.195895 + 0.155323i
\(305\) 0 0
\(306\) −0.169617 0.293785i −0.00969635 0.0167946i
\(307\) −9.08409 15.7341i −0.518456 0.897992i −0.999770 0.0214442i \(-0.993174\pi\)
0.481314 0.876548i \(-0.340160\pi\)
\(308\) −0.684622 + 1.18580i −0.0390100 + 0.0675673i
\(309\) −1.37600 2.38330i −0.0782777 0.135581i
\(310\) 0 0
\(311\) 19.4766 1.10442 0.552210 0.833705i \(-0.313785\pi\)
0.552210 + 0.833705i \(0.313785\pi\)
\(312\) −4.29672 −0.243254
\(313\) 5.98987 10.3748i 0.338568 0.586416i −0.645596 0.763679i \(-0.723391\pi\)
0.984164 + 0.177263i \(0.0567243\pi\)
\(314\) −2.46121 + 4.26294i −0.138894 + 0.240572i
\(315\) 0 0
\(316\) −3.32223 −0.186890
\(317\) 0.564654 0.978009i 0.0317141 0.0549305i −0.849733 0.527214i \(-0.823237\pi\)
0.881447 + 0.472283i \(0.156570\pi\)
\(318\) 2.70398 + 4.68343i 0.151632 + 0.262634i
\(319\) −19.7195 + 34.1551i −1.10408 + 1.91232i
\(320\) 0 0
\(321\) −3.41187 5.90953i −0.190432 0.329838i
\(322\) −1.26386 −0.0704323
\(323\) −0.457182 0.362495i −0.0254383 0.0201698i
\(324\) 5.02610 0.279228
\(325\) 0 0
\(326\) 0.718637 + 1.24472i 0.0398016 + 0.0689385i
\(327\) −2.00070 + 3.46532i −0.110639 + 0.191632i
\(328\) 0.433073 + 0.750105i 0.0239125 + 0.0414176i
\(329\) 2.06017 3.56833i 0.113581 0.196728i
\(330\) 0 0
\(331\) −14.3080 −0.786437 −0.393218 0.919445i \(-0.628638\pi\)
−0.393218 + 0.919445i \(0.628638\pi\)
\(332\) 2.10354 3.64344i 0.115447 0.199960i
\(333\) −6.42871 + 11.1348i −0.352291 + 0.610186i
\(334\) 9.37500 0.512977
\(335\) 0 0
\(336\) −0.108370 + 0.187702i −0.00591206 + 0.0102400i
\(337\) −13.8589 24.0043i −0.754941 1.30760i −0.945404 0.325901i \(-0.894332\pi\)
0.190463 0.981694i \(-0.439001\pi\)
\(338\) −13.3243 + 23.0784i −0.724748 + 1.25530i
\(339\) 6.17047 + 10.6876i 0.335134 + 0.580469i
\(340\) 0 0
\(341\) 12.8716 0.697036
\(342\) 10.2720 4.06480i 0.555448 0.219799i
\(343\) 4.41472 0.238372
\(344\) −2.85199 4.93979i −0.153769 0.266336i
\(345\) 0 0
\(346\) −3.88263 + 6.72491i −0.208731 + 0.361534i
\(347\) 15.7098 + 27.2102i 0.843346 + 1.46072i 0.887050 + 0.461673i \(0.152751\pi\)
−0.0437044 + 0.999045i \(0.513916\pi\)
\(348\) −3.12142 + 5.40646i −0.167326 + 0.289817i
\(349\) 23.4539 1.25546 0.627729 0.778432i \(-0.283985\pi\)
0.627729 + 0.778432i \(0.283985\pi\)
\(350\) 0 0
\(351\) −11.8898 + 20.5937i −0.634631 + 1.09921i
\(352\) 2.15544 3.73333i 0.114885 0.198987i
\(353\) −17.3468 −0.923277 −0.461638 0.887068i \(-0.652738\pi\)
−0.461638 + 0.887068i \(0.652738\pi\)
\(354\) 6.56058 0.348691
\(355\) 0 0
\(356\) 1.85992 + 3.22147i 0.0985755 + 0.170738i
\(357\) 0.0145057 0.0251246i 0.000767722 0.00132973i
\(358\) 0.561247 + 0.972108i 0.0296628 + 0.0513775i
\(359\) −0.402934 0.697902i −0.0212660 0.0368339i 0.855197 0.518304i \(-0.173436\pi\)
−0.876463 + 0.481470i \(0.840103\pi\)
\(360\) 0 0
\(361\) 13.8552 13.0013i 0.729221 0.684279i
\(362\) 15.7840 0.829587
\(363\) 2.58744 + 4.48157i 0.135805 + 0.235222i
\(364\) 1.00000 + 1.73205i 0.0524142 + 0.0907841i
\(365\) 0 0
\(366\) 2.10657 + 3.64868i 0.110112 + 0.190720i
\(367\) −1.26908 + 2.19811i −0.0662455 + 0.114740i −0.897246 0.441531i \(-0.854435\pi\)
0.831000 + 0.556272i \(0.187769\pi\)
\(368\) 3.97909 0.207425
\(369\) 2.19513 0.114274
\(370\) 0 0
\(371\) 1.25863 2.18001i 0.0653446 0.113180i
\(372\) 2.03746 0.105638
\(373\) −12.4012 −0.642110 −0.321055 0.947060i \(-0.604038\pi\)
−0.321055 + 0.947060i \(0.604038\pi\)
\(374\) −0.288513 + 0.499719i −0.0149186 + 0.0258399i
\(375\) 0 0
\(376\) −6.48617 + 11.2344i −0.334499 + 0.579369i
\(377\) 28.8034 + 49.8890i 1.48345 + 2.56941i
\(378\) 0.599758 + 1.03881i 0.0308482 + 0.0534307i
\(379\) −12.6756 −0.651100 −0.325550 0.945525i \(-0.605549\pi\)
−0.325550 + 0.945525i \(0.605549\pi\)
\(380\) 0 0
\(381\) 12.2124 0.625660
\(382\) −9.14871 15.8460i −0.468089 0.810753i
\(383\) −7.97632 13.8154i −0.407571 0.705934i 0.587046 0.809554i \(-0.300291\pi\)
−0.994617 + 0.103620i \(0.966957\pi\)
\(384\) 0.341187 0.590953i 0.0174111 0.0301570i
\(385\) 0 0
\(386\) −0.558777 + 0.967830i −0.0284410 + 0.0492612i
\(387\) −14.4560 −0.734839
\(388\) 4.85660 0.246556
\(389\) 13.0991 22.6883i 0.664150 1.15034i −0.315365 0.948971i \(-0.602127\pi\)
0.979515 0.201372i \(-0.0645399\pi\)
\(390\) 0 0
\(391\) −0.532616 −0.0269355
\(392\) −6.89911 −0.348458
\(393\) −4.02948 + 6.97926i −0.203260 + 0.352057i
\(394\) −8.12970 14.0811i −0.409568 0.709393i
\(395\) 0 0
\(396\) −5.46266 9.46161i −0.274509 0.475464i
\(397\) 15.0639 + 26.0914i 0.756034 + 1.30949i 0.944858 + 0.327479i \(0.106199\pi\)
−0.188824 + 0.982011i \(0.560468\pi\)
\(398\) −13.7982 −0.691643
\(399\) 0.740283 + 0.586963i 0.0370605 + 0.0293849i
\(400\) 0 0
\(401\) 1.08591 + 1.88085i 0.0542278 + 0.0939254i 0.891865 0.452302i \(-0.149397\pi\)
−0.837637 + 0.546227i \(0.816064\pi\)
\(402\) −0.201654 0.349275i −0.0100576 0.0174202i
\(403\) 9.40051 16.2822i 0.468273 0.811072i
\(404\) 1.25638 + 2.17611i 0.0625072 + 0.108266i
\(405\) 0 0
\(406\) 2.90587 0.144216
\(407\) 21.8700 1.08406
\(408\) −0.0456691 + 0.0791012i −0.00226096 + 0.00391609i
\(409\) −16.0832 + 27.8569i −0.795262 + 1.37743i 0.127410 + 0.991850i \(0.459333\pi\)
−0.922673 + 0.385584i \(0.874000\pi\)
\(410\) 0 0
\(411\) 10.8027 0.532859
\(412\) 2.01648 3.49265i 0.0993450 0.172071i
\(413\) −1.52688 2.64464i −0.0751329 0.130134i
\(414\) 5.04224 8.73341i 0.247812 0.429224i
\(415\) 0 0
\(416\) −3.14836 5.45312i −0.154361 0.267361i
\(417\) −0.796577 −0.0390085
\(418\) −14.7240 11.6745i −0.720173 0.571018i
\(419\) −9.99674 −0.488373 −0.244186 0.969728i \(-0.578521\pi\)
−0.244186 + 0.969728i \(0.578521\pi\)
\(420\) 0 0
\(421\) 19.0856 + 33.0572i 0.930173 + 1.61111i 0.783023 + 0.621993i \(0.213677\pi\)
0.147150 + 0.989114i \(0.452990\pi\)
\(422\) 0.584458 1.01231i 0.0284510 0.0492785i
\(423\) 16.4383 + 28.4720i 0.799259 + 1.38436i
\(424\) −3.96261 + 6.86344i −0.192441 + 0.333318i
\(425\) 0 0
\(426\) −7.95748 −0.385541
\(427\) 0.980546 1.69836i 0.0474520 0.0821892i
\(428\) 5.00000 8.66025i 0.241684 0.418609i
\(429\) 18.5226 0.894280
\(430\) 0 0
\(431\) −1.73649 + 3.00769i −0.0836437 + 0.144875i −0.904812 0.425810i \(-0.859989\pi\)
0.821169 + 0.570685i \(0.193322\pi\)
\(432\) −1.88825 3.27055i −0.0908487 0.157355i
\(433\) 5.54742 9.60841i 0.266592 0.461751i −0.701388 0.712780i \(-0.747436\pi\)
0.967979 + 0.251029i \(0.0807691\pi\)
\(434\) −0.474191 0.821322i −0.0227619 0.0394247i
\(435\) 0 0
\(436\) −5.86394 −0.280832
\(437\) 2.53689 17.1579i 0.121356 0.820775i
\(438\) 5.63706 0.269349
\(439\) 6.51914 + 11.2915i 0.311141 + 0.538913i 0.978610 0.205725i \(-0.0659554\pi\)
−0.667468 + 0.744638i \(0.732622\pi\)
\(440\) 0 0
\(441\) −8.74244 + 15.1423i −0.416307 + 0.721064i
\(442\) 0.421419 + 0.729919i 0.0200449 + 0.0347187i
\(443\) −7.51250 + 13.0120i −0.356930 + 0.618221i −0.987446 0.157955i \(-0.949510\pi\)
0.630516 + 0.776176i \(0.282843\pi\)
\(444\) 3.46184 0.164292
\(445\) 0 0
\(446\) −3.15881 + 5.47122i −0.149574 + 0.259070i
\(447\) −4.14594 + 7.18097i −0.196096 + 0.339648i
\(448\) −0.317626 −0.0150064
\(449\) 14.4251 0.680761 0.340381 0.940288i \(-0.389444\pi\)
0.340381 + 0.940288i \(0.389444\pi\)
\(450\) 0 0
\(451\) −1.86692 3.23361i −0.0879100 0.152265i
\(452\) −9.04264 + 15.6623i −0.425330 + 0.736693i
\(453\) −6.95350 12.0438i −0.326704 0.565868i
\(454\) −1.88971 3.27307i −0.0886884 0.153613i
\(455\) 0 0
\(456\) −2.33068 1.84797i −0.109144 0.0865392i
\(457\) −32.1773 −1.50519 −0.752596 0.658483i \(-0.771199\pi\)
−0.752596 + 0.658483i \(0.771199\pi\)
\(458\) −2.71814 4.70795i −0.127010 0.219988i
\(459\) 0.252750 + 0.437775i 0.0117973 + 0.0204336i
\(460\) 0 0
\(461\) 7.75530 + 13.4326i 0.361200 + 0.625617i 0.988159 0.153435i \(-0.0490337\pi\)
−0.626958 + 0.779053i \(0.715700\pi\)
\(462\) 0.467169 0.809160i 0.0217347 0.0376455i
\(463\) −30.1477 −1.40108 −0.700541 0.713612i \(-0.747058\pi\)
−0.700541 + 0.713612i \(0.747058\pi\)
\(464\) −9.14871 −0.424718
\(465\) 0 0
\(466\) −1.22461 + 2.12109i −0.0567290 + 0.0982576i
\(467\) −34.5731 −1.59985 −0.799927 0.600098i \(-0.795128\pi\)
−0.799927 + 0.600098i \(0.795128\pi\)
\(468\) −15.9582 −0.737667
\(469\) −0.0938641 + 0.162577i −0.00433424 + 0.00750713i
\(470\) 0 0
\(471\) 1.67947 2.90892i 0.0773858 0.134036i
\(472\) 4.80717 + 8.32627i 0.221268 + 0.383247i
\(473\) 12.2946 + 21.2948i 0.565305 + 0.979137i
\(474\) 2.26701 0.104127
\(475\) 0 0
\(476\) 0.0425153 0.00194869
\(477\) 10.0427 + 17.3945i 0.459824 + 0.796438i
\(478\) 4.72950 + 8.19173i 0.216322 + 0.374681i
\(479\) −15.4238 + 26.7148i −0.704732 + 1.22063i 0.262056 + 0.965053i \(0.415600\pi\)
−0.966788 + 0.255579i \(0.917734\pi\)
\(480\) 0 0
\(481\) 15.9723 27.6649i 0.728276 1.26141i
\(482\) −16.8708 −0.768444
\(483\) 0.862427 0.0392418
\(484\) −3.79182 + 6.56762i −0.172355 + 0.298528i
\(485\) 0 0
\(486\) −14.7592 −0.669491
\(487\) −30.7745 −1.39453 −0.697263 0.716815i \(-0.745599\pi\)
−0.697263 + 0.716815i \(0.745599\pi\)
\(488\) −3.08711 + 5.34704i −0.139747 + 0.242049i
\(489\) −0.490380 0.849362i −0.0221757 0.0384095i
\(490\) 0 0
\(491\) 12.8571 + 22.2692i 0.580234 + 1.00499i 0.995451 + 0.0952719i \(0.0303720\pi\)
−0.415218 + 0.909722i \(0.636295\pi\)
\(492\) −0.295518 0.511852i −0.0133230 0.0230761i
\(493\) 1.22459 0.0551526
\(494\) −25.5212 + 10.0991i −1.14825 + 0.454381i
\(495\) 0 0
\(496\) 1.49292 + 2.58582i 0.0670342 + 0.116107i
\(497\) 1.85199 + 3.20774i 0.0830732 + 0.143887i
\(498\) −1.43540 + 2.48619i −0.0643219 + 0.111409i
\(499\) 0.201106 + 0.348326i 0.00900274 + 0.0155932i 0.870492 0.492183i \(-0.163801\pi\)
−0.861489 + 0.507776i \(0.830468\pi\)
\(500\) 0 0
\(501\) −6.39726 −0.285808
\(502\) 2.65627 0.118555
\(503\) −20.2327 + 35.0441i −0.902133 + 1.56254i −0.0774136 + 0.996999i \(0.524666\pi\)
−0.824720 + 0.565542i \(0.808667\pi\)
\(504\) −0.402490 + 0.697133i −0.0179283 + 0.0310528i
\(505\) 0 0
\(506\) −17.1534 −0.762560
\(507\) 9.09218 15.7481i 0.403798 0.699399i
\(508\) 8.94845 + 15.4992i 0.397023 + 0.687665i
\(509\) 5.72694 9.91935i 0.253842 0.439668i −0.710738 0.703457i \(-0.751639\pi\)
0.964580 + 0.263789i \(0.0849723\pi\)
\(510\) 0 0
\(511\) −1.31195 2.27236i −0.0580371 0.100523i
\(512\) 1.00000 0.0441942
\(513\) −15.3066 + 6.05703i −0.675801 + 0.267425i
\(514\) 2.24745 0.0991308
\(515\) 0 0
\(516\) 1.94613 + 3.37079i 0.0856734 + 0.148391i
\(517\) 27.9611 48.4300i 1.22973 2.12995i
\(518\) −0.805694 1.39550i −0.0354002 0.0613149i
\(519\) 2.64941 4.58891i 0.116296 0.201431i
\(520\) 0 0
\(521\) 1.66822 0.0730860 0.0365430 0.999332i \(-0.488365\pi\)
0.0365430 + 0.999332i \(0.488365\pi\)
\(522\) −11.5931 + 20.0798i −0.507416 + 0.878870i
\(523\) −21.9775 + 38.0662i −0.961011 + 1.66452i −0.241039 + 0.970515i \(0.577488\pi\)
−0.719971 + 0.694004i \(0.755845\pi\)
\(524\) −11.8102 −0.515930
\(525\) 0 0
\(526\) 15.9289 27.5897i 0.694534 1.20297i
\(527\) −0.199833 0.346121i −0.00870486 0.0150773i
\(528\) −1.47081 + 2.54753i −0.0640090 + 0.110867i
\(529\) 3.58341 + 6.20665i 0.155800 + 0.269854i
\(530\) 0 0
\(531\) 24.3663 1.05741
\(532\) −0.202504 + 1.36961i −0.00877966 + 0.0593801i
\(533\) −5.45388 −0.236234
\(534\) −1.26916 2.19825i −0.0549220 0.0951276i
\(535\) 0 0
\(536\) 0.295518 0.511852i 0.0127644 0.0221086i
\(537\) −0.382981 0.663342i −0.0165268 0.0286253i
\(538\) 5.44763 9.43558i 0.234864 0.406797i
\(539\) 29.7412 1.28104
\(540\) 0 0
\(541\) 14.7202 25.4961i 0.632870 1.09616i −0.354092 0.935211i \(-0.615210\pi\)
0.986962 0.160953i \(-0.0514567\pi\)
\(542\) 5.96631 10.3340i 0.256275 0.443881i
\(543\) −10.7706 −0.462209
\(544\) −0.133854 −0.00573892
\(545\) 0 0
\(546\) −0.682374 1.18191i −0.0292029 0.0505809i
\(547\) −10.2026 + 17.6714i −0.436231 + 0.755574i −0.997395 0.0721302i \(-0.977020\pi\)
0.561164 + 0.827704i \(0.310354\pi\)
\(548\) 7.91554 + 13.7101i 0.338135 + 0.585667i
\(549\) 7.82387 + 13.5513i 0.333915 + 0.578357i
\(550\) 0 0
\(551\) −5.83281 + 39.4494i −0.248486 + 1.68060i
\(552\) −2.71523 −0.115568
\(553\) −0.527613 0.913853i −0.0224364 0.0388610i
\(554\) 7.95326 + 13.7754i 0.337902 + 0.585263i
\(555\) 0 0
\(556\) −0.583681 1.01096i −0.0247536 0.0428744i
\(557\) 2.30575 3.99368i 0.0976977 0.169217i −0.813034 0.582217i \(-0.802185\pi\)
0.910731 + 0.412999i \(0.135519\pi\)
\(558\) 7.56722 0.320346
\(559\) 35.9164 1.51910
\(560\) 0 0
\(561\) 0.196874 0.340995i 0.00831202 0.0143968i
\(562\) −20.9843 −0.885169
\(563\) −5.13495 −0.216412 −0.108206 0.994128i \(-0.534511\pi\)
−0.108206 + 0.994128i \(0.534511\pi\)
\(564\) 4.42600 7.66605i 0.186368 0.322799i
\(565\) 0 0
\(566\) 6.43083 11.1385i 0.270308 0.468187i
\(567\) 0.798210 + 1.38254i 0.0335217 + 0.0580612i
\(568\) −5.83073 10.0991i −0.244652 0.423750i
\(569\) −23.0698 −0.967135 −0.483568 0.875307i \(-0.660659\pi\)
−0.483568 + 0.875307i \(0.660659\pi\)
\(570\) 0 0
\(571\) −24.7009 −1.03370 −0.516850 0.856076i \(-0.672896\pi\)
−0.516850 + 0.856076i \(0.672896\pi\)
\(572\) 13.5722 + 23.5077i 0.567481 + 0.982906i
\(573\) 6.24284 + 10.8129i 0.260799 + 0.451716i
\(574\) −0.137555 + 0.238253i −0.00574144 + 0.00994447i
\(575\) 0 0
\(576\) 1.26718 2.19482i 0.0527993 0.0914510i
\(577\) −34.0569 −1.41781 −0.708903 0.705306i \(-0.750810\pi\)
−0.708903 + 0.705306i \(0.750810\pi\)
\(578\) −16.9821 −0.706362
\(579\) 0.381295 0.660422i 0.0158461 0.0274462i
\(580\) 0 0
\(581\) 1.33628 0.0554381
\(582\) −3.31402 −0.137370
\(583\) 17.0823 29.5874i 0.707477 1.22539i
\(584\) 4.13048 + 7.15420i 0.170920 + 0.296043i
\(585\) 0 0
\(586\) 6.06388 + 10.5029i 0.250496 + 0.433873i
\(587\) −18.9701 32.8572i −0.782981 1.35616i −0.930198 0.367059i \(-0.880365\pi\)
0.147216 0.989104i \(-0.452969\pi\)
\(588\) 4.70778 0.194145
\(589\) 12.1019 4.78891i 0.498651 0.197324i
\(590\) 0 0
\(591\) 5.54750 + 9.60855i 0.228194 + 0.395243i
\(592\) 2.53661 + 4.39354i 0.104254 + 0.180574i
\(593\) −4.85602 + 8.41087i −0.199413 + 0.345393i −0.948338 0.317261i \(-0.897237\pi\)
0.748925 + 0.662654i \(0.230570\pi\)
\(594\) 8.14003 + 14.0989i 0.333989 + 0.578486i
\(595\) 0 0
\(596\) −12.1515 −0.497745
\(597\) 9.41556 0.385353
\(598\) −12.5276 + 21.6985i −0.512292 + 0.887316i
\(599\) 7.71001 13.3541i 0.315023 0.545635i −0.664420 0.747360i \(-0.731321\pi\)
0.979442 + 0.201725i \(0.0646546\pi\)
\(600\) 0 0
\(601\) −21.9383 −0.894881 −0.447441 0.894314i \(-0.647664\pi\)
−0.447441 + 0.894314i \(0.647664\pi\)
\(602\) 0.905866 1.56901i 0.0369203 0.0639479i
\(603\) −0.748951 1.29722i −0.0304996 0.0528269i
\(604\) 10.1902 17.6499i 0.414631 0.718163i
\(605\) 0 0
\(606\) −0.857320 1.48492i −0.0348263 0.0603209i
\(607\) 22.2900 0.904724 0.452362 0.891834i \(-0.350582\pi\)
0.452362 + 0.891834i \(0.350582\pi\)
\(608\) 0.637555 4.31202i 0.0258563 0.174876i
\(609\) −1.98289 −0.0803507
\(610\) 0 0
\(611\) −40.8416 70.7397i −1.65227 2.86182i
\(612\) −0.169617 + 0.293785i −0.00685636 + 0.0118756i
\(613\) 12.6028 + 21.8287i 0.509023 + 0.881654i 0.999945 + 0.0104504i \(0.00332654\pi\)
−0.490922 + 0.871203i \(0.663340\pi\)
\(614\) −9.08409 + 15.7341i −0.366604 + 0.634977i
\(615\) 0 0
\(616\) 1.36924 0.0551684
\(617\) −9.51333 + 16.4776i −0.382992 + 0.663362i −0.991488 0.130195i \(-0.958440\pi\)
0.608496 + 0.793557i \(0.291773\pi\)
\(618\) −1.37600 + 2.38330i −0.0553507 + 0.0958702i
\(619\) −33.9075 −1.36286 −0.681429 0.731884i \(-0.738641\pi\)
−0.681429 + 0.731884i \(0.738641\pi\)
\(620\) 0 0
\(621\) −7.51354 + 13.0138i −0.301508 + 0.522227i
\(622\) −9.73832 16.8673i −0.390471 0.676316i
\(623\) −0.590758 + 1.02322i −0.0236682 + 0.0409946i
\(624\) 2.14836 + 3.72107i 0.0860032 + 0.148962i
\(625\) 0 0
\(626\) −11.9797 −0.478807
\(627\) 10.0473 + 7.96637i 0.401249 + 0.318146i
\(628\) 4.92242 0.196426
\(629\) −0.339535 0.588091i −0.0135381 0.0234487i
\(630\) 0 0
\(631\) −4.27169 + 7.39878i −0.170053 + 0.294541i −0.938438 0.345447i \(-0.887727\pi\)
0.768385 + 0.639988i \(0.221061\pi\)
\(632\) 1.66112 + 2.87714i 0.0660757 + 0.114446i
\(633\) −0.398819 + 0.690775i −0.0158516 + 0.0274558i
\(634\) −1.12931 −0.0448505
\(635\) 0 0
\(636\) 2.70398 4.68343i 0.107220 0.185710i
\(637\) 21.7209 37.6217i 0.860613 1.49063i
\(638\) 39.4389 1.56140
\(639\) −29.5544 −1.16915
\(640\) 0 0
\(641\) −1.86302 3.22684i −0.0735847 0.127453i 0.826885 0.562371i \(-0.190111\pi\)
−0.900470 + 0.434918i \(0.856777\pi\)
\(642\) −3.41187 + 5.90953i −0.134656 + 0.233231i
\(643\) −16.1350 27.9466i −0.636300 1.10210i −0.986238 0.165332i \(-0.947131\pi\)
0.349938 0.936773i \(-0.386203\pi\)
\(644\) 0.631931 + 1.09454i 0.0249016 + 0.0431308i
\(645\) 0 0
\(646\) −0.0853390 + 0.577179i −0.00335762 + 0.0227088i
\(647\) 48.1241 1.89195 0.945977 0.324234i \(-0.105107\pi\)
0.945977 + 0.324234i \(0.105107\pi\)
\(648\) −2.51305 4.35273i −0.0987220 0.170992i
\(649\) −20.7231 35.8935i −0.813453 1.40894i
\(650\) 0 0
\(651\) 0.323575 + 0.560449i 0.0126819 + 0.0219657i
\(652\) 0.718637 1.24472i 0.0281440 0.0487469i
\(653\) 13.9774 0.546979 0.273489 0.961875i \(-0.411822\pi\)
0.273489 + 0.961875i \(0.411822\pi\)
\(654\) 4.00140 0.156467
\(655\) 0 0
\(656\) 0.433073 0.750105i 0.0169087 0.0292867i
\(657\) 20.9363 0.816802
\(658\) −4.12035 −0.160628
\(659\) 6.24517 10.8170i 0.243277 0.421369i −0.718369 0.695663i \(-0.755111\pi\)
0.961646 + 0.274294i \(0.0884441\pi\)
\(660\) 0 0
\(661\) −14.2429 + 24.6695i −0.553986 + 0.959531i 0.443996 + 0.896029i \(0.353560\pi\)
−0.997982 + 0.0635024i \(0.979773\pi\)
\(662\) 7.15398 + 12.3911i 0.278047 + 0.481592i
\(663\) −0.287566 0.498078i −0.0111681 0.0193438i
\(664\) −4.20708 −0.163266
\(665\) 0 0
\(666\) 12.8574 0.498215
\(667\) 18.2018 + 31.5264i 0.704776 + 1.22071i
\(668\) −4.68750 8.11899i −0.181365 0.314133i
\(669\) 2.15549 3.73342i 0.0833362 0.144342i
\(670\) 0 0
\(671\) 13.3082 23.0504i 0.513755 0.889851i
\(672\) 0.216740 0.00836091
\(673\) 31.6748 1.22097 0.610486 0.792027i \(-0.290974\pi\)
0.610486 + 0.792027i \(0.290974\pi\)
\(674\) −13.8589 + 24.0043i −0.533824 + 0.924610i
\(675\) 0 0
\(676\) 26.6487 1.02495
\(677\) −49.3049 −1.89494 −0.947470 0.319844i \(-0.896369\pi\)
−0.947470 + 0.319844i \(0.896369\pi\)
\(678\) 6.17047 10.6876i 0.236975 0.410453i
\(679\) 0.771290 + 1.33591i 0.0295994 + 0.0512677i
\(680\) 0 0
\(681\) 1.28949 + 2.23346i 0.0494133 + 0.0855863i
\(682\) −6.43580 11.1471i −0.246440 0.426846i
\(683\) −4.26771 −0.163299 −0.0816496 0.996661i \(-0.526019\pi\)
−0.0816496 + 0.996661i \(0.526019\pi\)
\(684\) −8.65623 6.86344i −0.330979 0.262430i
\(685\) 0 0
\(686\) −2.20736 3.82326i −0.0842773 0.145973i
\(687\) 1.85479 + 3.21259i 0.0707645 + 0.122568i
\(688\) −2.85199 + 4.93979i −0.108731 + 0.188328i
\(689\) −24.9514 43.2172i −0.950574 1.64644i
\(690\) 0 0
\(691\) 0.249546 0.00949319 0.00474659 0.999989i \(-0.498489\pi\)
0.00474659 + 0.999989i \(0.498489\pi\)
\(692\) 7.76526 0.295191
\(693\) 1.73508 3.00525i 0.0659104 0.114160i
\(694\) 15.7098 27.2102i 0.596335 1.03288i
\(695\) 0 0
\(696\) 6.24284 0.236634
\(697\) −0.0579684 + 0.100404i −0.00219571 + 0.00380308i
\(698\) −11.7269 20.3117i −0.443871 0.768808i
\(699\) 0.835643 1.44738i 0.0316069 0.0547448i
\(700\) 0 0
\(701\) −4.08961 7.08341i −0.154462 0.267537i 0.778401 0.627768i \(-0.216031\pi\)
−0.932863 + 0.360231i \(0.882698\pi\)
\(702\) 23.7796 0.897504
\(703\) 20.5623 8.13680i 0.775521 0.306885i
\(704\) −4.31087 −0.162472
\(705\) 0 0
\(706\) 8.67340 + 15.0228i 0.326428 + 0.565389i
\(707\) −0.399058 + 0.691189i −0.0150081 + 0.0259948i
\(708\) −3.28029 5.68163i −0.123281 0.213529i
\(709\) 6.85226 11.8685i 0.257342 0.445730i −0.708187 0.706025i \(-0.750487\pi\)
0.965529 + 0.260295i \(0.0838200\pi\)
\(710\) 0 0
\(711\) 8.41975 0.315765
\(712\) 1.85992 3.22147i 0.0697034 0.120730i
\(713\) 5.94048 10.2892i 0.222473 0.385334i
\(714\) −0.0290114 −0.00108572
\(715\) 0 0
\(716\) 0.561247 0.972108i 0.0209748 0.0363294i
\(717\) −3.22729 5.58982i −0.120525 0.208756i
\(718\) −0.402934 + 0.697902i −0.0150374 + 0.0260455i
\(719\) −13.4178 23.2403i −0.500398 0.866715i −1.00000 0.000460027i \(-0.999854\pi\)
0.499602 0.866255i \(-0.333480\pi\)
\(720\) 0 0
\(721\) 1.28097 0.0477060
\(722\) −18.1870 5.49830i −0.676852 0.204626i
\(723\) 11.5122 0.428143
\(724\) −7.89198 13.6693i −0.293303 0.508016i
\(725\) 0 0
\(726\) 2.58744 4.48157i 0.0960288 0.166327i
\(727\) 14.5299 + 25.1665i 0.538883 + 0.933373i 0.998965 + 0.0454961i \(0.0144869\pi\)
−0.460081 + 0.887877i \(0.652180\pi\)
\(728\) 1.00000 1.73205i 0.0370625 0.0641941i
\(729\) −5.00701 −0.185445
\(730\) 0 0
\(731\) 0.381749 0.661209i 0.0141195 0.0244557i
\(732\) 2.10657 3.64868i 0.0778609 0.134859i
\(733\) −30.8850 −1.14076 −0.570381 0.821380i \(-0.693204\pi\)
−0.570381 + 0.821380i \(0.693204\pi\)
\(734\) 2.53816 0.0936852
\(735\) 0 0
\(736\) −1.98955 3.44600i −0.0733357 0.127021i
\(737\) −1.27394 + 2.20653i −0.0469262 + 0.0812786i
\(738\) −1.09757 1.90104i −0.0404020 0.0699782i
\(739\) 17.9491 + 31.0887i 0.660267 + 1.14362i 0.980545 + 0.196292i \(0.0628901\pi\)
−0.320279 + 0.947323i \(0.603777\pi\)
\(740\) 0 0
\(741\) 17.4150 6.89138i 0.639757 0.253161i
\(742\) −2.51725 −0.0924113
\(743\) 3.15432 + 5.46344i 0.115721 + 0.200434i 0.918068 0.396424i \(-0.129749\pi\)
−0.802347 + 0.596858i \(0.796416\pi\)
\(744\) −1.01873 1.76450i −0.0373485 0.0646895i
\(745\) 0 0
\(746\) 6.20061 + 10.7398i 0.227020 + 0.393211i
\(747\) −5.33114 + 9.23380i −0.195056 + 0.337847i
\(748\) 0.577026 0.0210982
\(749\) 3.17626 0.116058
\(750\) 0 0
\(751\) 20.3945 35.3242i 0.744204 1.28900i −0.206361 0.978476i \(-0.566162\pi\)
0.950566 0.310524i \(-0.100505\pi\)
\(752\) 12.9723 0.473053
\(753\) −1.81257 −0.0660537
\(754\) 28.8034 49.8890i 1.04896 1.81685i
\(755\) 0 0
\(756\) 0.599758 1.03881i 0.0218130 0.0377812i
\(757\) 9.72687 + 16.8474i 0.353529 + 0.612330i 0.986865 0.161547i \(-0.0516482\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(758\) 6.33778 + 10.9774i 0.230199 + 0.398716i
\(759\) 11.7050 0.424865
\(760\) 0 0
\(761\) −19.1465 −0.694058 −0.347029 0.937854i \(-0.612810\pi\)
−0.347029 + 0.937854i \(0.612810\pi\)
\(762\) −6.10619 10.5762i −0.221204 0.383137i
\(763\) −0.931269 1.61301i −0.0337142 0.0583947i
\(764\) −9.14871 + 15.8460i −0.330989 + 0.573289i
\(765\) 0 0
\(766\) −7.97632 + 13.8154i −0.288196 + 0.499170i
\(767\) −60.5388 −2.18593
\(768\) −0.682374 −0.0246231
\(769\) −13.3405 + 23.1064i −0.481070 + 0.833238i −0.999764 0.0217222i \(-0.993085\pi\)
0.518694 + 0.854960i \(0.326418\pi\)
\(770\) 0 0
\(771\) −1.53360 −0.0552314
\(772\) 1.11755 0.0402216
\(773\) 11.8521 20.5284i 0.426290 0.738356i −0.570250 0.821471i \(-0.693154\pi\)
0.996540 + 0.0831151i \(0.0264869\pi\)
\(774\) 7.22799 + 12.5192i 0.259805 + 0.449995i
\(775\) 0 0
\(776\) −2.42830 4.20594i −0.0871709 0.150984i
\(777\) 0.549785 + 0.952255i 0.0197234 + 0.0341620i
\(778\) −26.1982 −0.939250
\(779\) −2.95836 2.34565i −0.105994 0.0840418i
\(780\) 0 0
\(781\) 25.1356 + 43.5361i 0.899421 + 1.55784i
\(782\) 0.266308 + 0.461259i 0.00952315 + 0.0164946i
\(783\) 17.2751 29.9213i 0.617361 1.06930i
\(784\) 3.44956 + 5.97481i 0.123198 + 0.213386i
\(785\) 0 0