Properties

Label 950.2.e.l.201.4
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.39075800976.1
Defining polynomial: \(x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(1.51772 - 2.62877i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.l.501.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.51772 - 2.62877i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51772 + 2.62877i) q^{6} +4.93155 q^{7} +1.00000 q^{8} +(-3.10694 - 5.38138i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.51772 - 2.62877i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51772 + 2.62877i) q^{6} +4.93155 q^{7} +1.00000 q^{8} +(-3.10694 - 5.38138i) q^{9} +1.28233 q^{11} -3.03544 q^{12} +(-1.98349 - 3.43551i) q^{13} +(-2.46578 + 4.27085i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.10694 + 1.91728i) q^{17} +6.21388 q^{18} +(3.12466 - 3.03916i) q^{19} +(7.48471 - 12.9639i) q^{21} +(-0.641165 + 1.11053i) q^{22} +(3.84233 + 6.65511i) q^{23} +(1.51772 - 2.62877i) q^{24} +3.96699 q^{26} -9.75553 q^{27} +(-2.46578 - 4.27085i) q^{28} +(2.14116 + 3.70861i) q^{29} -4.14543 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.94622 - 3.37094i) q^{33} +(-1.10694 - 1.91728i) q^{34} +(-3.10694 + 5.38138i) q^{36} -9.38864 q^{37} +(1.06966 + 4.22562i) q^{38} -12.0415 q^{39} +(2.30005 - 3.98380i) q^{41} +(7.48471 + 12.9639i) q^{42} +(-3.32461 + 5.75839i) q^{43} +(-0.641165 - 1.11053i) q^{44} -7.68466 q^{46} +(3.46578 + 6.00290i) q^{47} +(1.51772 + 2.62877i) q^{48} +17.3202 q^{49} +(3.36005 + 5.81977i) q^{51} +(-1.98349 + 3.43551i) q^{52} +(-3.46578 - 6.00290i) q^{53} +(4.87777 - 8.44854i) q^{54} +4.93155 q^{56} +(-3.24689 - 12.8266i) q^{57} -4.28233 q^{58} +(3.15888 - 5.47135i) q^{59} +(-5.64238 - 9.77288i) q^{61} +(2.07272 - 3.59005i) q^{62} +(-15.3220 - 26.5385i) q^{63} +1.00000 q^{64} +(1.94622 + 3.37094i) q^{66} +(-0.965775 - 1.67277i) q^{67} +2.21388 q^{68} +23.3263 q^{69} +(-4.16010 + 7.20550i) q^{71} +(-3.10694 - 5.38138i) q^{72} +(-3.41383 + 5.91293i) q^{73} +(4.69432 - 8.13080i) q^{74} +(-4.19432 - 1.18645i) q^{76} +6.32387 q^{77} +(6.02077 - 10.4283i) q^{78} +(-1.76961 + 3.06506i) q^{79} +(-5.48533 + 9.50088i) q^{81} +(2.30005 + 3.98380i) q^{82} +3.28476 q^{83} -14.9694 q^{84} +(-3.32461 - 5.75839i) q^{86} +12.9987 q^{87} +1.28233 q^{88} +(-4.46699 - 7.73705i) q^{89} +(-9.78170 - 16.9424i) q^{91} +(3.84233 - 6.65511i) q^{92} +(-6.29160 + 10.8974i) q^{93} -6.93155 q^{94} -3.03544 q^{96} +(-1.07150 + 1.85590i) q^{97} +(-8.66010 + 14.9997i) q^{98} +(-3.98412 - 6.90070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + 10q^{11} - 2q^{12} + 9q^{13} - 6q^{14} - 4q^{16} + 5q^{17} + 22q^{18} - q^{21} - 5q^{22} + 6q^{23} + q^{24} - 18q^{26} + 16q^{27} - 6q^{28} + 17q^{29} + 22q^{31} - 4q^{32} - 4q^{33} + 5q^{34} - 11q^{36} - 8q^{37} - 36q^{39} + 7q^{41} - q^{42} - 13q^{43} - 5q^{44} - 12q^{46} + 14q^{47} + q^{48} + 44q^{49} - 9q^{51} + 9q^{52} - 14q^{53} - 8q^{54} + 12q^{56} - 48q^{57} - 34q^{58} + 14q^{59} - 9q^{61} - 11q^{62} - 45q^{63} + 8q^{64} - 4q^{66} + 6q^{67} - 10q^{68} + 54q^{69} + 14q^{71} - 11q^{72} - 11q^{73} + 4q^{74} - 10q^{77} + 18q^{78} - 17q^{79} - 36q^{81} + 7q^{82} - 46q^{83} + 2q^{84} - 13q^{86} - 2q^{87} + 10q^{88} + 14q^{89} - 25q^{91} + 6q^{92} + 13q^{93} - 28q^{94} - 2q^{96} - 17q^{97} - 22q^{98} - 60q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 1.51772 2.62877i 0.876255 1.51772i 0.0208358 0.999783i \(-0.493367\pi\)
0.855419 0.517936i \(-0.173299\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 1.51772 + 2.62877i 0.619606 + 1.07319i
\(7\) 4.93155 1.86395 0.931975 0.362521i \(-0.118084\pi\)
0.931975 + 0.362521i \(0.118084\pi\)
\(8\) 1.00000 0.353553
\(9\) −3.10694 5.38138i −1.03565 1.79379i
\(10\) 0 0
\(11\) 1.28233 0.386637 0.193318 0.981136i \(-0.438075\pi\)
0.193318 + 0.981136i \(0.438075\pi\)
\(12\) −3.03544 −0.876255
\(13\) −1.98349 3.43551i −0.550122 0.952840i −0.998265 0.0588778i \(-0.981248\pi\)
0.448143 0.893962i \(-0.352086\pi\)
\(14\) −2.46578 + 4.27085i −0.659006 + 1.14143i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.10694 + 1.91728i −0.268472 + 0.465008i −0.968468 0.249140i \(-0.919852\pi\)
0.699995 + 0.714148i \(0.253185\pi\)
\(18\) 6.21388 1.46463
\(19\) 3.12466 3.03916i 0.716846 0.697232i
\(20\) 0 0
\(21\) 7.48471 12.9639i 1.63330 2.82895i
\(22\) −0.641165 + 1.11053i −0.136697 + 0.236766i
\(23\) 3.84233 + 6.65511i 0.801181 + 1.38769i 0.918839 + 0.394632i \(0.129128\pi\)
−0.117658 + 0.993054i \(0.537539\pi\)
\(24\) 1.51772 2.62877i 0.309803 0.536595i
\(25\) 0 0
\(26\) 3.96699 0.777990
\(27\) −9.75553 −1.87745
\(28\) −2.46578 4.27085i −0.465988 0.807114i
\(29\) 2.14116 + 3.70861i 0.397604 + 0.688671i 0.993430 0.114443i \(-0.0365083\pi\)
−0.595825 + 0.803114i \(0.703175\pi\)
\(30\) 0 0
\(31\) −4.14543 −0.744541 −0.372271 0.928124i \(-0.621421\pi\)
−0.372271 + 0.928124i \(0.621421\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.94622 3.37094i 0.338793 0.586806i
\(34\) −1.10694 1.91728i −0.189839 0.328810i
\(35\) 0 0
\(36\) −3.10694 + 5.38138i −0.517823 + 0.896896i
\(37\) −9.38864 −1.54348 −0.771742 0.635936i \(-0.780614\pi\)
−0.771742 + 0.635936i \(0.780614\pi\)
\(38\) 1.06966 + 4.22562i 0.173522 + 0.685485i
\(39\) −12.0415 −1.92819
\(40\) 0 0
\(41\) 2.30005 3.98380i 0.359207 0.622165i −0.628621 0.777711i \(-0.716380\pi\)
0.987829 + 0.155546i \(0.0497138\pi\)
\(42\) 7.48471 + 12.9639i 1.15492 + 2.00037i
\(43\) −3.32461 + 5.75839i −0.506998 + 0.878147i 0.492969 + 0.870047i \(0.335912\pi\)
−0.999967 + 0.00809994i \(0.997422\pi\)
\(44\) −0.641165 1.11053i −0.0966592 0.167419i
\(45\) 0 0
\(46\) −7.68466 −1.13304
\(47\) 3.46578 + 6.00290i 0.505535 + 0.875613i 0.999979 + 0.00640345i \(0.00203829\pi\)
−0.494444 + 0.869209i \(0.664628\pi\)
\(48\) 1.51772 + 2.62877i 0.219064 + 0.379430i
\(49\) 17.3202 2.47431
\(50\) 0 0
\(51\) 3.36005 + 5.81977i 0.470501 + 0.814931i
\(52\) −1.98349 + 3.43551i −0.275061 + 0.476420i
\(53\) −3.46578 6.00290i −0.476061 0.824562i 0.523563 0.851987i \(-0.324602\pi\)
−0.999624 + 0.0274254i \(0.991269\pi\)
\(54\) 4.87777 8.44854i 0.663780 1.14970i
\(55\) 0 0
\(56\) 4.93155 0.659006
\(57\) −3.24689 12.8266i −0.430061 1.69892i
\(58\) −4.28233 −0.562297
\(59\) 3.15888 5.47135i 0.411252 0.712309i −0.583775 0.811915i \(-0.698425\pi\)
0.995027 + 0.0996066i \(0.0317584\pi\)
\(60\) 0 0
\(61\) −5.64238 9.77288i −0.722432 1.25129i −0.960022 0.279924i \(-0.909691\pi\)
0.237590 0.971366i \(-0.423643\pi\)
\(62\) 2.07272 3.59005i 0.263235 0.455937i
\(63\) −15.3220 26.5385i −1.93039 3.34354i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.94622 + 3.37094i 0.239563 + 0.414935i
\(67\) −0.965775 1.67277i −0.117988 0.204362i 0.800982 0.598688i \(-0.204311\pi\)
−0.918970 + 0.394327i \(0.870978\pi\)
\(68\) 2.21388 0.268472
\(69\) 23.3263 2.80816
\(70\) 0 0
\(71\) −4.16010 + 7.20550i −0.493713 + 0.855135i −0.999974 0.00724489i \(-0.997694\pi\)
0.506261 + 0.862380i \(0.331027\pi\)
\(72\) −3.10694 5.38138i −0.366156 0.634202i
\(73\) −3.41383 + 5.91293i −0.399559 + 0.692056i −0.993671 0.112326i \(-0.964170\pi\)
0.594113 + 0.804382i \(0.297503\pi\)
\(74\) 4.69432 8.13080i 0.545704 0.945187i
\(75\) 0 0
\(76\) −4.19432 1.18645i −0.481122 0.136095i
\(77\) 6.32387 0.720672
\(78\) 6.02077 10.4283i 0.681718 1.18077i
\(79\) −1.76961 + 3.06506i −0.199097 + 0.344846i −0.948236 0.317567i \(-0.897134\pi\)
0.749139 + 0.662413i \(0.230468\pi\)
\(80\) 0 0
\(81\) −5.48533 + 9.50088i −0.609482 + 1.05565i
\(82\) 2.30005 + 3.98380i 0.253998 + 0.439937i
\(83\) 3.28476 0.360549 0.180274 0.983616i \(-0.442301\pi\)
0.180274 + 0.983616i \(0.442301\pi\)
\(84\) −14.9694 −1.63330
\(85\) 0 0
\(86\) −3.32461 5.75839i −0.358502 0.620944i
\(87\) 12.9987 1.39361
\(88\) 1.28233 0.136697
\(89\) −4.46699 7.73705i −0.473500 0.820126i 0.526040 0.850460i \(-0.323676\pi\)
−0.999540 + 0.0303341i \(0.990343\pi\)
\(90\) 0 0
\(91\) −9.78170 16.9424i −1.02540 1.77605i
\(92\) 3.84233 6.65511i 0.400591 0.693843i
\(93\) −6.29160 + 10.8974i −0.652408 + 1.13000i
\(94\) −6.93155 −0.714935
\(95\) 0 0
\(96\) −3.03544 −0.309803
\(97\) −1.07150 + 1.85590i −0.108795 + 0.188438i −0.915282 0.402813i \(-0.868032\pi\)
0.806488 + 0.591251i \(0.201366\pi\)
\(98\) −8.66010 + 14.9997i −0.874802 + 1.51520i
\(99\) −3.98412 6.90070i −0.400419 0.693547i
\(100\) 0 0
\(101\) −5.27267 9.13253i −0.524650 0.908720i −0.999588 0.0287012i \(-0.990863\pi\)
0.474938 0.880019i \(-0.342470\pi\)
\(102\) −6.72010 −0.665389
\(103\) 3.64311 0.358967 0.179483 0.983761i \(-0.442557\pi\)
0.179483 + 0.983761i \(0.442557\pi\)
\(104\) −1.98349 3.43551i −0.194498 0.336880i
\(105\) 0 0
\(106\) 6.93155 0.673252
\(107\) −5.07456 −0.490576 −0.245288 0.969450i \(-0.578883\pi\)
−0.245288 + 0.969450i \(0.578883\pi\)
\(108\) 4.87777 + 8.44854i 0.469363 + 0.812961i
\(109\) −2.37155 + 4.10765i −0.227153 + 0.393441i −0.956963 0.290209i \(-0.906275\pi\)
0.729810 + 0.683650i \(0.239609\pi\)
\(110\) 0 0
\(111\) −14.2493 + 24.6805i −1.35249 + 2.34257i
\(112\) −2.46578 + 4.27085i −0.232994 + 0.403557i
\(113\) 12.4414 1.17039 0.585196 0.810892i \(-0.301017\pi\)
0.585196 + 0.810892i \(0.301017\pi\)
\(114\) 12.7316 + 3.60140i 1.19242 + 0.337302i
\(115\) 0 0
\(116\) 2.14116 3.70861i 0.198802 0.344335i
\(117\) −12.3252 + 21.3479i −1.13946 + 1.97361i
\(118\) 3.15888 + 5.47135i 0.290799 + 0.503678i
\(119\) −5.45893 + 9.45515i −0.500419 + 0.866752i
\(120\) 0 0
\(121\) −9.35563 −0.850512
\(122\) 11.2848 1.02167
\(123\) −6.98165 12.0926i −0.629514 1.09035i
\(124\) 2.07272 + 3.59005i 0.186135 + 0.322396i
\(125\) 0 0
\(126\) 30.6441 2.72999
\(127\) 1.94806 + 3.37413i 0.172862 + 0.299406i 0.939419 0.342770i \(-0.111365\pi\)
−0.766557 + 0.642176i \(0.778032\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 10.0916 + 17.4792i 0.888520 + 1.53896i
\(130\) 0 0
\(131\) 5.41504 9.37913i 0.473115 0.819459i −0.526412 0.850230i \(-0.676463\pi\)
0.999526 + 0.0307711i \(0.00979629\pi\)
\(132\) −3.89243 −0.338793
\(133\) 15.4094 14.9878i 1.33617 1.29961i
\(134\) 1.93155 0.166861
\(135\) 0 0
\(136\) −1.10694 + 1.91728i −0.0949193 + 0.164405i
\(137\) 10.2994 + 17.8391i 0.879939 + 1.52410i 0.851407 + 0.524506i \(0.175750\pi\)
0.0285321 + 0.999593i \(0.490917\pi\)
\(138\) −11.6632 + 20.2012i −0.992833 + 1.71964i
\(139\) 3.39427 + 5.87905i 0.287898 + 0.498655i 0.973308 0.229503i \(-0.0737101\pi\)
−0.685409 + 0.728158i \(0.740377\pi\)
\(140\) 0 0
\(141\) 21.0403 1.77191
\(142\) −4.16010 7.20550i −0.349108 0.604672i
\(143\) −2.54349 4.40546i −0.212698 0.368403i
\(144\) 6.21388 0.517823
\(145\) 0 0
\(146\) −3.41383 5.91293i −0.282531 0.489358i
\(147\) 26.2872 45.5307i 2.16813 3.75531i
\(148\) 4.69432 + 8.13080i 0.385871 + 0.668348i
\(149\) −11.3790 + 19.7090i −0.932202 + 1.61462i −0.152654 + 0.988280i \(0.548782\pi\)
−0.779548 + 0.626342i \(0.784551\pi\)
\(150\) 0 0
\(151\) 11.5478 0.939743 0.469872 0.882735i \(-0.344300\pi\)
0.469872 + 0.882735i \(0.344300\pi\)
\(152\) 3.12466 3.03916i 0.253443 0.246509i
\(153\) 13.7568 1.11217
\(154\) −3.16194 + 5.47664i −0.254796 + 0.441320i
\(155\) 0 0
\(156\) 6.02077 + 10.4283i 0.482048 + 0.834931i
\(157\) −5.44927 + 9.43841i −0.434899 + 0.753267i −0.997287 0.0736060i \(-0.976549\pi\)
0.562388 + 0.826873i \(0.309883\pi\)
\(158\) −1.76961 3.06506i −0.140783 0.243843i
\(159\) −21.0403 −1.66860
\(160\) 0 0
\(161\) 18.9486 + 32.8200i 1.49336 + 2.58658i
\(162\) −5.48533 9.50088i −0.430969 0.746460i
\(163\) 11.8240 0.926126 0.463063 0.886325i \(-0.346750\pi\)
0.463063 + 0.886325i \(0.346750\pi\)
\(164\) −4.60010 −0.359207
\(165\) 0 0
\(166\) −1.64238 + 2.84468i −0.127473 + 0.220790i
\(167\) 8.83549 + 15.3035i 0.683710 + 1.18422i 0.973840 + 0.227234i \(0.0729682\pi\)
−0.290130 + 0.956987i \(0.593698\pi\)
\(168\) 7.48471 12.9639i 0.577458 1.00019i
\(169\) −1.36850 + 2.37031i −0.105269 + 0.182331i
\(170\) 0 0
\(171\) −26.0630 7.37248i −1.99309 0.563787i
\(172\) 6.64922 0.506998
\(173\) −6.22855 + 10.7882i −0.473548 + 0.820208i −0.999541 0.0302799i \(-0.990360\pi\)
0.525994 + 0.850488i \(0.323693\pi\)
\(174\) −6.49937 + 11.2572i −0.492716 + 0.853409i
\(175\) 0 0
\(176\) −0.641165 + 1.11053i −0.0483296 + 0.0837094i
\(177\) −9.58859 16.6079i −0.720723 1.24833i
\(178\) 8.93398 0.669630
\(179\) 13.7971 1.03124 0.515621 0.856817i \(-0.327561\pi\)
0.515621 + 0.856817i \(0.327561\pi\)
\(180\) 0 0
\(181\) 6.96883 + 12.0704i 0.517989 + 0.897183i 0.999782 + 0.0208980i \(0.00665251\pi\)
−0.481793 + 0.876285i \(0.660014\pi\)
\(182\) 19.5634 1.45014
\(183\) −34.2542 −2.53214
\(184\) 3.84233 + 6.65511i 0.283260 + 0.490621i
\(185\) 0 0
\(186\) −6.29160 10.8974i −0.461322 0.799034i
\(187\) −1.41946 + 2.45858i −0.103801 + 0.179789i
\(188\) 3.46578 6.00290i 0.252768 0.437806i
\(189\) −48.1099 −3.49948
\(190\) 0 0
\(191\) 4.28233 0.309859 0.154929 0.987926i \(-0.450485\pi\)
0.154929 + 0.987926i \(0.450485\pi\)
\(192\) 1.51772 2.62877i 0.109532 0.189715i
\(193\) 4.80310 8.31922i 0.345735 0.598830i −0.639752 0.768581i \(-0.720963\pi\)
0.985487 + 0.169751i \(0.0542963\pi\)
\(194\) −1.07150 1.85590i −0.0769294 0.133246i
\(195\) 0 0
\(196\) −8.66010 14.9997i −0.618578 1.07141i
\(197\) −23.7834 −1.69450 −0.847248 0.531197i \(-0.821742\pi\)
−0.847248 + 0.531197i \(0.821742\pi\)
\(198\) 7.96824 0.566278
\(199\) −7.51588 13.0179i −0.532786 0.922813i −0.999267 0.0382818i \(-0.987812\pi\)
0.466481 0.884531i \(-0.345522\pi\)
\(200\) 0 0
\(201\) −5.86310 −0.413551
\(202\) 10.5453 0.741967
\(203\) 10.5593 + 18.2892i 0.741115 + 1.28365i
\(204\) 3.36005 5.81977i 0.235250 0.407466i
\(205\) 0 0
\(206\) −1.82156 + 3.15503i −0.126914 + 0.219821i
\(207\) 23.8758 41.3541i 1.65948 2.87431i
\(208\) 3.96699 0.275061
\(209\) 4.00684 3.89721i 0.277159 0.269576i
\(210\) 0 0
\(211\) −9.73281 + 16.8577i −0.670034 + 1.16053i 0.307859 + 0.951432i \(0.400387\pi\)
−0.977894 + 0.209102i \(0.932946\pi\)
\(212\) −3.46578 + 6.00290i −0.238030 + 0.412281i
\(213\) 12.6277 + 21.8718i 0.865237 + 1.49863i
\(214\) 2.53728 4.39469i 0.173445 0.300415i
\(215\) 0 0
\(216\) −9.75553 −0.663780
\(217\) −20.4434 −1.38779
\(218\) −2.37155 4.10765i −0.160622 0.278205i
\(219\) 10.3625 + 17.9483i 0.700231 + 1.21284i
\(220\) 0 0
\(221\) 8.78244 0.590771
\(222\) −14.2493 24.6805i −0.956352 1.65645i
\(223\) −2.82582 + 4.89447i −0.189231 + 0.327758i −0.944994 0.327087i \(-0.893933\pi\)
0.755763 + 0.654845i \(0.227266\pi\)
\(224\) −2.46578 4.27085i −0.164752 0.285358i
\(225\) 0 0
\(226\) −6.22072 + 10.7746i −0.413796 + 0.716716i
\(227\) −8.45952 −0.561478 −0.280739 0.959784i \(-0.590580\pi\)
−0.280739 + 0.959784i \(0.590580\pi\)
\(228\) −9.48471 + 9.22519i −0.628140 + 0.610953i
\(229\) 1.54291 0.101958 0.0509791 0.998700i \(-0.483766\pi\)
0.0509791 + 0.998700i \(0.483766\pi\)
\(230\) 0 0
\(231\) 9.59786 16.6240i 0.631493 1.09378i
\(232\) 2.14116 + 3.70861i 0.140574 + 0.243482i
\(233\) −2.04631 + 3.54432i −0.134058 + 0.232196i −0.925237 0.379389i \(-0.876134\pi\)
0.791179 + 0.611585i \(0.209468\pi\)
\(234\) −12.3252 21.3479i −0.805723 1.39555i
\(235\) 0 0
\(236\) −6.31777 −0.411252
\(237\) 5.37155 + 9.30380i 0.348920 + 0.604347i
\(238\) −5.45893 9.45515i −0.353850 0.612886i
\(239\) 25.1442 1.62644 0.813221 0.581955i \(-0.197712\pi\)
0.813221 + 0.581955i \(0.197712\pi\)
\(240\) 0 0
\(241\) −13.7170 23.7586i −0.883592 1.53043i −0.847319 0.531085i \(-0.821784\pi\)
−0.0362738 0.999342i \(-0.511549\pi\)
\(242\) 4.67782 8.10221i 0.300701 0.520830i
\(243\) 2.01709 + 3.49370i 0.129396 + 0.224121i
\(244\) −5.64238 + 9.77288i −0.361216 + 0.625645i
\(245\) 0 0
\(246\) 13.9633 0.890268
\(247\) −16.6388 4.70665i −1.05870 0.299477i
\(248\) −4.14543 −0.263235
\(249\) 4.98533 8.63485i 0.315933 0.547212i
\(250\) 0 0
\(251\) −2.30263 3.98826i −0.145340 0.251737i 0.784159 0.620559i \(-0.213094\pi\)
−0.929500 + 0.368822i \(0.879761\pi\)
\(252\) −15.3220 + 26.5385i −0.965197 + 1.67177i
\(253\) 4.92713 + 8.53404i 0.309766 + 0.536531i
\(254\) −3.89611 −0.244464
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.86247 + 17.0823i 0.615204 + 1.06556i 0.990349 + 0.138599i \(0.0442598\pi\)
−0.375144 + 0.926966i \(0.622407\pi\)
\(258\) −20.1833 −1.25656
\(259\) −46.3006 −2.87698
\(260\) 0 0
\(261\) 13.3049 23.0448i 0.823555 1.42644i
\(262\) 5.41504 + 9.37913i 0.334543 + 0.579445i
\(263\) −4.16010 + 7.20550i −0.256523 + 0.444310i −0.965308 0.261114i \(-0.915910\pi\)
0.708785 + 0.705424i \(0.249243\pi\)
\(264\) 1.94622 3.37094i 0.119781 0.207467i
\(265\) 0 0
\(266\) 5.27509 + 20.8388i 0.323437 + 1.27771i
\(267\) −27.1185 −1.65963
\(268\) −0.965775 + 1.67277i −0.0589941 + 0.102181i
\(269\) −7.67281 + 13.2897i −0.467820 + 0.810287i −0.999324 0.0367683i \(-0.988294\pi\)
0.531504 + 0.847056i \(0.321627\pi\)
\(270\) 0 0
\(271\) −1.68039 + 2.91052i −0.102077 + 0.176802i −0.912540 0.408987i \(-0.865882\pi\)
0.810463 + 0.585789i \(0.199215\pi\)
\(272\) −1.10694 1.91728i −0.0671181 0.116252i
\(273\) −59.3835 −3.59405
\(274\) −20.5988 −1.24442
\(275\) 0 0
\(276\) −11.6632 20.2012i −0.702039 1.21597i
\(277\) 31.2517 1.87774 0.938868 0.344278i \(-0.111876\pi\)
0.938868 + 0.344278i \(0.111876\pi\)
\(278\) −6.78855 −0.407150
\(279\) 12.8796 + 22.3081i 0.771082 + 1.33555i
\(280\) 0 0
\(281\) −1.46699 2.54090i −0.0875132 0.151577i 0.818946 0.573870i \(-0.194559\pi\)
−0.906459 + 0.422293i \(0.861225\pi\)
\(282\) −10.5201 + 18.2214i −0.626465 + 1.08507i
\(283\) 7.34660 12.7247i 0.436710 0.756404i −0.560724 0.828003i \(-0.689477\pi\)
0.997433 + 0.0715995i \(0.0228103\pi\)
\(284\) 8.32019 0.493713
\(285\) 0 0
\(286\) 5.08699 0.300800
\(287\) 11.3428 19.6463i 0.669545 1.15969i
\(288\) −3.10694 + 5.38138i −0.183078 + 0.317101i
\(289\) 6.04937 + 10.4778i 0.355845 + 0.616342i
\(290\) 0 0
\(291\) 3.25248 + 5.63346i 0.190664 + 0.330239i
\(292\) 6.82766 0.399559
\(293\) −8.58320 −0.501436 −0.250718 0.968060i \(-0.580667\pi\)
−0.250718 + 0.968060i \(0.580667\pi\)
\(294\) 26.2872 + 45.5307i 1.53310 + 2.65541i
\(295\) 0 0
\(296\) −9.38864 −0.545704
\(297\) −12.5098 −0.725893
\(298\) −11.3790 19.7090i −0.659167 1.14171i
\(299\) 15.2425 26.4007i 0.881495 1.52679i
\(300\) 0 0
\(301\) −16.3955 + 28.3978i −0.945020 + 1.63682i
\(302\) −5.77388 + 10.0007i −0.332249 + 0.575473i
\(303\) −32.0097 −1.83891
\(304\) 1.06966 + 4.22562i 0.0613493 + 0.242356i
\(305\) 0 0
\(306\) −6.87839 + 11.9137i −0.393212 + 0.681063i
\(307\) 2.66757 4.62036i 0.152246 0.263698i −0.779807 0.626020i \(-0.784683\pi\)
0.932053 + 0.362322i \(0.118016\pi\)
\(308\) −3.16194 5.47664i −0.180168 0.312060i
\(309\) 5.52922 9.57689i 0.314546 0.544810i
\(310\) 0 0
\(311\) 23.2933 1.32084 0.660421 0.750896i \(-0.270378\pi\)
0.660421 + 0.750896i \(0.270378\pi\)
\(312\) −12.0415 −0.681718
\(313\) −5.35699 9.27859i −0.302795 0.524457i 0.673973 0.738756i \(-0.264586\pi\)
−0.976768 + 0.214299i \(0.931253\pi\)
\(314\) −5.44927 9.43841i −0.307520 0.532640i
\(315\) 0 0
\(316\) 3.53923 0.199097
\(317\) −7.16267 12.4061i −0.402296 0.696797i 0.591707 0.806153i \(-0.298454\pi\)
−0.994003 + 0.109356i \(0.965121\pi\)
\(318\) 10.5201 18.2214i 0.589940 1.02181i
\(319\) 2.74568 + 4.75566i 0.153729 + 0.266266i
\(320\) 0 0
\(321\) −7.70175 + 13.3398i −0.429870 + 0.744556i
\(322\) −37.8973 −2.11193
\(323\) 2.36810 + 9.35501i 0.131765 + 0.520527i
\(324\) 10.9707 0.609482
\(325\) 0 0
\(326\) −5.91199 + 10.2399i −0.327435 + 0.567134i
\(327\) 7.19870 + 12.4685i 0.398089 + 0.689510i
\(328\) 2.30005 3.98380i 0.126999 0.219969i
\(329\) 17.0916 + 29.6036i 0.942293 + 1.63210i
\(330\) 0 0
\(331\) −10.5695 −0.580953 −0.290476 0.956882i \(-0.593814\pi\)
−0.290476 + 0.956882i \(0.593814\pi\)
\(332\) −1.64238 2.84468i −0.0901372 0.156122i
\(333\) 29.1700 + 50.5238i 1.59850 + 2.76869i
\(334\) −17.6710 −0.966913
\(335\) 0 0
\(336\) 7.48471 + 12.9639i 0.408324 + 0.707238i
\(337\) −5.85931 + 10.1486i −0.319177 + 0.552831i −0.980317 0.197432i \(-0.936740\pi\)
0.661140 + 0.750263i \(0.270073\pi\)
\(338\) −1.36850 2.37031i −0.0744365 0.128928i
\(339\) 18.8826 32.7057i 1.02556 1.77633i
\(340\) 0 0
\(341\) −5.31581 −0.287867
\(342\) 19.4163 18.8850i 1.04991 1.02118i
\(343\) 50.8946 2.74805
\(344\) −3.32461 + 5.75839i −0.179251 + 0.310472i
\(345\) 0 0
\(346\) −6.22855 10.7882i −0.334849 0.579975i
\(347\) −10.4505 + 18.1008i −0.561011 + 0.971700i 0.436397 + 0.899754i \(0.356254\pi\)
−0.997409 + 0.0719459i \(0.977079\pi\)
\(348\) −6.49937 11.2572i −0.348403 0.603452i
\(349\) 35.4817 1.89929 0.949647 0.313322i \(-0.101442\pi\)
0.949647 + 0.313322i \(0.101442\pi\)
\(350\) 0 0
\(351\) 19.3500 + 33.5153i 1.03283 + 1.78891i
\(352\) −0.641165 1.11053i −0.0341742 0.0591915i
\(353\) −14.2984 −0.761029 −0.380515 0.924775i \(-0.624253\pi\)
−0.380515 + 0.924775i \(0.624253\pi\)
\(354\) 19.1772 1.01926
\(355\) 0 0
\(356\) −4.46699 + 7.73705i −0.236750 + 0.410063i
\(357\) 16.5702 + 28.7005i 0.876990 + 1.51899i
\(358\) −6.89854 + 11.9486i −0.364599 + 0.631504i
\(359\) −2.11073 + 3.65589i −0.111400 + 0.192951i −0.916335 0.400413i \(-0.868867\pi\)
0.804935 + 0.593363i \(0.202200\pi\)
\(360\) 0 0
\(361\) 0.526988 18.9927i 0.0277362 0.999615i
\(362\) −13.9377 −0.732547
\(363\) −14.1992 + 24.5938i −0.745266 + 1.29084i
\(364\) −9.78170 + 16.9424i −0.512700 + 0.888023i
\(365\) 0 0
\(366\) 17.1271 29.6650i 0.895247 1.55061i
\(367\) −7.08238 12.2670i −0.369697 0.640334i 0.619821 0.784743i \(-0.287205\pi\)
−0.989518 + 0.144409i \(0.953872\pi\)
\(368\) −7.68466 −0.400591
\(369\) −28.5845 −1.48805
\(370\) 0 0
\(371\) −17.0916 29.6036i −0.887354 1.53694i
\(372\) 12.5832 0.652408
\(373\) 16.6541 0.862315 0.431158 0.902277i \(-0.358105\pi\)
0.431158 + 0.902277i \(0.358105\pi\)
\(374\) −1.41946 2.45858i −0.0733987 0.127130i
\(375\) 0 0
\(376\) 3.46578 + 6.00290i 0.178734 + 0.309576i
\(377\) 8.49398 14.7120i 0.437462 0.757706i
\(378\) 24.0550 41.6644i 1.23725 2.14299i
\(379\) 3.36689 0.172946 0.0864728 0.996254i \(-0.472440\pi\)
0.0864728 + 0.996254i \(0.472440\pi\)
\(380\) 0 0
\(381\) 11.8264 0.605885
\(382\) −2.14116 + 3.70861i −0.109552 + 0.189749i
\(383\) −4.16010 + 7.20550i −0.212571 + 0.368184i −0.952518 0.304481i \(-0.901517\pi\)
0.739947 + 0.672665i \(0.234850\pi\)
\(384\) 1.51772 + 2.62877i 0.0774508 + 0.134149i
\(385\) 0 0
\(386\) 4.80310 + 8.31922i 0.244471 + 0.423437i
\(387\) 41.3175 2.10028
\(388\) 2.14301 0.108795
\(389\) −12.4076 21.4905i −0.629089 1.08961i −0.987735 0.156140i \(-0.950095\pi\)
0.358646 0.933474i \(-0.383239\pi\)
\(390\) 0 0
\(391\) −17.0129 −0.860380
\(392\) 17.3202 0.874802
\(393\) −16.4370 28.4698i −0.829138 1.43611i
\(394\) 11.8917 20.5970i 0.599095 1.03766i
\(395\) 0 0
\(396\) −3.98412 + 6.90070i −0.200210 + 0.346773i
\(397\) 6.15043 10.6529i 0.308681 0.534652i −0.669393 0.742909i \(-0.733446\pi\)
0.978074 + 0.208257i \(0.0667790\pi\)
\(398\) 15.0318 0.753474
\(399\) −16.0122 63.2550i −0.801613 3.16671i
\(400\) 0 0
\(401\) 7.52320 13.0306i 0.375691 0.650715i −0.614740 0.788730i \(-0.710739\pi\)
0.990430 + 0.138015i \(0.0440722\pi\)
\(402\) 2.93155 5.07759i 0.146212 0.253247i
\(403\) 8.22244 + 14.2417i 0.409589 + 0.709429i
\(404\) −5.27267 + 9.13253i −0.262325 + 0.454360i
\(405\) 0 0
\(406\) −21.1185 −1.04809
\(407\) −12.0393 −0.596768
\(408\) 3.36005 + 5.81977i 0.166347 + 0.288122i
\(409\) −13.0170 22.5461i −0.643648 1.11483i −0.984612 0.174755i \(-0.944087\pi\)
0.340964 0.940077i \(-0.389247\pi\)
\(410\) 0 0
\(411\) 62.5265 3.08420
\(412\) −1.82156 3.15503i −0.0897417 0.155437i
\(413\) 15.5782 26.9822i 0.766553 1.32771i
\(414\) 23.8758 + 41.3541i 1.17343 + 2.03244i
\(415\) 0 0
\(416\) −1.98349 + 3.43551i −0.0972488 + 0.168440i
\(417\) 20.6062 1.00909
\(418\) 1.37166 + 5.41863i 0.0670901 + 0.265034i
\(419\) 9.69640 0.473700 0.236850 0.971546i \(-0.423885\pi\)
0.236850 + 0.971546i \(0.423885\pi\)
\(420\) 0 0
\(421\) −9.04154 + 15.6604i −0.440658 + 0.763242i −0.997738 0.0672166i \(-0.978588\pi\)
0.557080 + 0.830459i \(0.311921\pi\)
\(422\) −9.73281 16.8577i −0.473786 0.820621i
\(423\) 21.5359 37.3013i 1.04711 1.81365i
\(424\) −3.46578 6.00290i −0.168313 0.291527i
\(425\) 0 0
\(426\) −25.2554 −1.22363
\(427\) −27.8257 48.1955i −1.34658 2.33234i
\(428\) 2.53728 + 4.39469i 0.122644 + 0.212426i
\(429\) −15.4412 −0.745510
\(430\) 0 0
\(431\) 9.08981 + 15.7440i 0.437841 + 0.758362i 0.997523 0.0703453i \(-0.0224101\pi\)
−0.559682 + 0.828707i \(0.689077\pi\)
\(432\) 4.87777 8.44854i 0.234682 0.406481i
\(433\) −2.35699 4.08243i −0.113270 0.196189i 0.803817 0.594877i \(-0.202799\pi\)
−0.917087 + 0.398687i \(0.869466\pi\)
\(434\) 10.2217 17.7045i 0.490657 0.849844i
\(435\) 0 0
\(436\) 4.74310 0.227153
\(437\) 32.2319 + 9.11749i 1.54186 + 0.436149i
\(438\) −20.7249 −0.990276
\(439\) 7.08554 12.2725i 0.338174 0.585735i −0.645915 0.763409i \(-0.723524\pi\)
0.984089 + 0.177674i \(0.0568573\pi\)
\(440\) 0 0
\(441\) −53.8128 93.2065i −2.56251 4.43841i
\(442\) −4.39122 + 7.60581i −0.208869 + 0.361772i
\(443\) 6.24811 + 10.8220i 0.296856 + 0.514170i 0.975415 0.220376i \(-0.0707284\pi\)
−0.678559 + 0.734546i \(0.737395\pi\)
\(444\) 28.4986 1.35249
\(445\) 0 0
\(446\) −2.82582 4.89447i −0.133807 0.231760i
\(447\) 34.5402 + 59.8253i 1.63369 + 2.82964i
\(448\) 4.93155 0.232994
\(449\) −29.3326 −1.38429 −0.692146 0.721757i \(-0.743335\pi\)
−0.692146 + 0.721757i \(0.743335\pi\)
\(450\) 0 0
\(451\) 2.94942 5.10855i 0.138883 0.240552i
\(452\) −6.22072 10.7746i −0.292598 0.506795i
\(453\) 17.5263 30.3564i 0.823455 1.42627i
\(454\) 4.22976 7.32616i 0.198512 0.343834i
\(455\) 0 0
\(456\) −3.24689 12.8266i −0.152050 0.600660i
\(457\) −26.2126 −1.22617 −0.613087 0.790015i \(-0.710073\pi\)
−0.613087 + 0.790015i \(0.710073\pi\)
\(458\) −0.771454 + 1.33620i −0.0360477 + 0.0624364i
\(459\) 10.7988 18.7041i 0.504044 0.873031i
\(460\) 0 0
\(461\) −4.85641 + 8.41155i −0.226186 + 0.391765i −0.956674 0.291160i \(-0.905959\pi\)
0.730489 + 0.682925i \(0.239292\pi\)
\(462\) 9.59786 + 16.6240i 0.446533 + 0.773418i
\(463\) −5.34146 −0.248239 −0.124119 0.992267i \(-0.539611\pi\)
−0.124119 + 0.992267i \(0.539611\pi\)
\(464\) −4.28233 −0.198802
\(465\) 0 0
\(466\) −2.04631 3.54432i −0.0947936 0.164187i
\(467\) −30.3642 −1.40509 −0.702543 0.711641i \(-0.747952\pi\)
−0.702543 + 0.711641i \(0.747952\pi\)
\(468\) 24.6504 1.13946
\(469\) −4.76277 8.24936i −0.219924 0.380920i
\(470\) 0 0
\(471\) 16.5409 + 28.6497i 0.762165 + 1.32011i
\(472\) 3.15888 5.47135i 0.145399 0.251839i
\(473\) −4.26325 + 7.38416i −0.196024 + 0.339524i
\(474\) −10.7431 −0.493447
\(475\) 0 0
\(476\) 10.9179 0.500419
\(477\) −21.5359 + 37.3013i −0.986062 + 1.70791i
\(478\) −12.5721 + 21.7755i −0.575034 + 0.995988i
\(479\) −0.994997 1.72339i −0.0454626 0.0787435i 0.842399 0.538855i \(-0.181143\pi\)
−0.887861 + 0.460111i \(0.847810\pi\)
\(480\) 0 0
\(481\) 18.6223 + 32.2548i 0.849105 + 1.47069i
\(482\) 27.4341 1.24959
\(483\) 115.035 5.23427
\(484\) 4.67782 + 8.10221i 0.212628 + 0.368282i
\(485\) 0 0
\(486\) −4.03418 −0.182994
\(487\) 29.2102 1.32364 0.661820 0.749663i \(-0.269784\pi\)
0.661820 + 0.749663i \(0.269784\pi\)
\(488\) −5.64238 9.77288i −0.255418 0.442398i
\(489\) 17.9455 31.0825i 0.811523 1.40560i
\(490\) 0 0
\(491\) 8.44853 14.6333i 0.381277 0.660391i −0.609968 0.792426i \(-0.708818\pi\)
0.991245 + 0.132035i \(0.0421511\pi\)
\(492\) −6.98165 + 12.0926i −0.314757 + 0.545176i
\(493\) −9.48057 −0.426983
\(494\) 12.3955 12.0563i 0.557699 0.542439i
\(495\) 0 0
\(496\) 2.07272 3.59005i 0.0930677 0.161198i
\(497\) −20.5157 + 35.5343i −0.920256 + 1.59393i
\(498\) 4.98533 + 8.63485i 0.223398 + 0.386937i
\(499\) −0.629662 + 1.09061i −0.0281875 + 0.0488222i −0.879775 0.475390i \(-0.842307\pi\)
0.851588 + 0.524212i \(0.175640\pi\)
\(500\) 0 0
\(501\) 53.6391 2.39642
\(502\) 4.60525 0.205542
\(503\) −4.56966 7.91489i −0.203751 0.352907i 0.745983 0.665965i \(-0.231980\pi\)
−0.949734 + 0.313058i \(0.898647\pi\)
\(504\) −15.3220 26.5385i −0.682498 1.18212i
\(505\) 0 0
\(506\) −9.85427 −0.438076
\(507\) 4.15399 + 7.19492i 0.184485 + 0.319538i
\(508\) 1.94806 3.37413i 0.0864310 0.149703i
\(509\) −17.3005 29.9654i −0.766832 1.32819i −0.939272 0.343172i \(-0.888498\pi\)
0.172440 0.985020i \(-0.444835\pi\)
\(510\) 0 0
\(511\) −16.8355 + 29.1599i −0.744758 + 1.28996i
\(512\) 1.00000 0.0441942
\(513\) −30.4827 + 29.6486i −1.34584 + 1.30902i
\(514\) −19.7249 −0.870030
\(515\) 0 0
\(516\) 10.0916 17.4792i 0.444260 0.769481i
\(517\) 4.44427 + 7.69770i 0.195459 + 0.338544i
\(518\) 23.1503 40.0975i 1.01717 1.76178i
\(519\) 18.9064 + 32.7468i 0.829897 + 1.43742i
\(520\) 0 0
\(521\) 23.2542 1.01878 0.509392 0.860535i \(-0.329870\pi\)
0.509392 + 0.860535i \(0.329870\pi\)
\(522\) 13.3049 + 23.0448i 0.582342 + 1.00865i
\(523\) −11.7066 20.2765i −0.511896 0.886630i −0.999905 0.0137910i \(-0.995610\pi\)
0.488009 0.872839i \(-0.337723\pi\)
\(524\) −10.8301 −0.473115
\(525\) 0 0
\(526\) −4.16010 7.20550i −0.181389 0.314175i
\(527\) 4.58874 7.94794i 0.199889 0.346218i
\(528\) 1.94622 + 3.37094i 0.0846982 + 0.146702i
\(529\) −18.0270 + 31.2237i −0.783782 + 1.35755i
\(530\) 0 0
\(531\) −39.2579 −1.70365
\(532\) −20.6845 5.85105i −0.896787 0.253675i
\(533\) −18.2485 −0.790432
\(534\) 13.5593 23.4853i 0.586767 1.01631i
\(535\) 0 0
\(536\) −0.965775 1.67277i −0.0417151 0.0722527i
\(537\) 20.9401 36.2693i 0.903631 1.56514i
\(538\) −7.67281 13.2897i −0.330798 0.572960i
\(539\) 22.2102 0.956661
\(540\) 0 0
\(541\) −3.39291 5.87669i −0.145873 0.252659i 0.783826 0.620981i \(-0.213266\pi\)
−0.929698 + 0.368322i \(0.879932\pi\)
\(542\) −1.68039 2.91052i −0.0721790 0.125018i
\(543\) 42.3069 1.81556
\(544\) 2.21388 0.0949193
\(545\) 0 0
\(546\) 29.6917 51.4276i 1.27069 2.20090i
\(547\) 14.3705 + 24.8905i 0.614439 + 1.06424i 0.990483 + 0.137638i \(0.0439511\pi\)
−0.376043 + 0.926602i \(0.622716\pi\)
\(548\) 10.2994 17.8391i 0.439969 0.762049i
\(549\) −35.0611 + 60.7275i −1.49637 + 2.59179i
\(550\) 0 0
\(551\) 17.9615 + 5.08078i 0.765184 + 0.216449i
\(552\) 23.3263 0.992833
\(553\) −8.72694 + 15.1155i −0.371107 + 0.642777i
\(554\) −15.6259 + 27.0648i −0.663880 + 1.14987i
\(555\) 0 0
\(556\) 3.39427 5.87905i 0.143949 0.249327i
\(557\) −5.48471 9.49979i −0.232394 0.402519i 0.726118 0.687570i \(-0.241323\pi\)
−0.958512 + 0.285051i \(0.907989\pi\)
\(558\) −25.7592 −1.09047
\(559\) 26.3774 1.11564
\(560\) 0 0
\(561\) 4.30869 + 7.46287i 0.181913 + 0.315083i
\(562\) 2.93398 0.123762
\(563\) −1.10389 −0.0465233 −0.0232616 0.999729i \(-0.507405\pi\)
−0.0232616 + 0.999729i \(0.507405\pi\)
\(564\) −10.5201 18.2214i −0.442978 0.767260i
\(565\) 0 0
\(566\) 7.34660 + 12.7247i 0.308800 + 0.534858i
\(567\) −27.0512 + 46.8541i −1.13604 + 1.96769i
\(568\) −4.16010 + 7.20550i −0.174554 + 0.302336i
\(569\) −3.17844 −0.133247 −0.0666236 0.997778i \(-0.521223\pi\)
−0.0666236 + 0.997778i \(0.521223\pi\)
\(570\) 0 0
\(571\) −33.3717 −1.39656 −0.698282 0.715823i \(-0.746052\pi\)
−0.698282 + 0.715823i \(0.746052\pi\)
\(572\) −2.54349 + 4.40546i −0.106349 + 0.184202i
\(573\) 6.49937 11.2572i 0.271515 0.470278i
\(574\) 11.3428 + 19.6463i 0.473440 + 0.820021i
\(575\) 0 0
\(576\) −3.10694 5.38138i −0.129456 0.224224i
\(577\) −6.96331 −0.289886 −0.144943 0.989440i \(-0.546300\pi\)
−0.144943 + 0.989440i \(0.546300\pi\)
\(578\) −12.0987 −0.503241
\(579\) −14.5795 25.2525i −0.605904 1.04946i
\(580\) 0 0
\(581\) 16.1989 0.672045
\(582\) −6.50496 −0.269639
\(583\) −4.44427 7.69770i −0.184063 0.318806i
\(584\) −3.41383 + 5.91293i −0.141265 + 0.244679i
\(585\) 0 0
\(586\) 4.29160 7.43327i 0.177284 0.307065i
\(587\) 5.49500 9.51761i 0.226803 0.392834i −0.730056 0.683387i \(-0.760506\pi\)
0.956859 + 0.290553i \(0.0938394\pi\)
\(588\) −52.5744 −2.16813
\(589\) −12.9531 + 12.5986i −0.533722 + 0.519118i
\(590\) 0 0
\(591\) −36.0965 + 62.5210i −1.48481 + 2.57177i
\(592\) 4.69432 8.13080i 0.192935 0.334174i
\(593\) 19.3949 + 33.5929i 0.796451 + 1.37949i 0.921914 + 0.387396i \(0.126625\pi\)
−0.125462 + 0.992098i \(0.540041\pi\)
\(594\) 6.25491 10.8338i 0.256642 0.444517i
\(595\) 0 0
\(596\) 22.7580 0.932202
\(597\) −45.6280 −1.86743
\(598\) 15.2425 + 26.4007i 0.623311 + 1.07961i
\(599\) −1.47262 2.55065i −0.0601696 0.104217i 0.834372 0.551202i \(-0.185831\pi\)
−0.894541 + 0.446986i \(0.852497\pi\)
\(600\) 0 0
\(601\) −9.62059 −0.392432 −0.196216 0.980561i \(-0.562865\pi\)
−0.196216 + 0.980561i \(0.562865\pi\)
\(602\) −16.3955 28.3978i −0.668230 1.15741i
\(603\) −6.00121 + 10.3944i −0.244388 + 0.423293i
\(604\) −5.77388 10.0007i −0.234936 0.406921i
\(605\) 0 0
\(606\) 16.0049 27.7212i 0.650153 1.12610i
\(607\) −32.8499 −1.33334 −0.666668 0.745355i \(-0.732280\pi\)
−0.666668 + 0.745355i \(0.732280\pi\)
\(608\) −4.19432 1.18645i −0.170102 0.0481170i
\(609\) 64.1040 2.59762
\(610\) 0 0
\(611\) 13.7487 23.8134i 0.556212 0.963388i
\(612\) −6.87839 11.9137i −0.278043 0.481584i
\(613\) 5.29101 9.16430i 0.213702 0.370143i −0.739168 0.673521i \(-0.764781\pi\)
0.952870 + 0.303378i \(0.0981145\pi\)
\(614\) 2.66757 + 4.62036i 0.107654 + 0.186463i
\(615\) 0 0
\(616\) 6.32387 0.254796
\(617\) 14.0478 + 24.3314i 0.565542 + 0.979547i 0.996999 + 0.0774134i \(0.0246661\pi\)
−0.431458 + 0.902133i \(0.642001\pi\)
\(618\) 5.52922 + 9.57689i 0.222418 + 0.385239i
\(619\) 2.32903 0.0936115 0.0468058 0.998904i \(-0.485096\pi\)
0.0468058 + 0.998904i \(0.485096\pi\)
\(620\) 0 0
\(621\) −37.4840 64.9241i −1.50418 2.60532i
\(622\) −11.6466 + 20.1726i −0.466988 + 0.808847i
\(623\) −22.0292 38.1557i −0.882580 1.52867i
\(624\) 6.02077 10.4283i 0.241024 0.417465i
\(625\) 0 0
\(626\) 10.7140 0.428217
\(627\) −4.16359 16.4479i −0.166278 0.656867i
\(628\) 10.8985 0.434899
\(629\) 10.3927 18.0006i 0.414383 0.717732i
\(630\) 0 0
\(631\) 6.20704 + 10.7509i 0.247098 + 0.427987i 0.962719 0.270502i \(-0.0871896\pi\)
−0.715621 + 0.698489i \(0.753856\pi\)
\(632\) −1.76961 + 3.06506i −0.0703914 + 0.121922i
\(633\) 29.5433 + 51.1706i 1.17424 + 2.03385i
\(634\) 14.3253 0.568932
\(635\) 0 0
\(636\) 10.5201 + 18.2214i 0.417151 + 0.722526i
\(637\) −34.3545 59.5037i −1.36117 2.35762i
\(638\) −5.49136 −0.217405
\(639\) 51.7007 2.04525
\(640\) 0 0
\(641\) 11.2279 19.4473i 0.443476 0.768123i −0.554469 0.832205i \(-0.687078\pi\)
0.997945 + 0.0640815i \(0.0204118\pi\)
\(642\) −7.70175 13.3398i −0.303964 0.526481i
\(643\) 15.5465 26.9274i 0.613096 1.06191i −0.377619 0.925961i \(-0.623257\pi\)
0.990715 0.135952i \(-0.0434094\pi\)
\(644\) 18.9486 32.8200i 0.746681 1.29329i
\(645\) 0 0
\(646\) −9.28573 2.62667i −0.365342 0.103345i
\(647\) −23.8320 −0.936934 −0.468467 0.883481i \(-0.655194\pi\)
−0.468467 + 0.883481i \(0.655194\pi\)
\(648\) −5.48533 + 9.50088i −0.215484 + 0.373230i
\(649\) 4.05073 7.01607i 0.159005 0.275405i
\(650\) 0 0
\(651\) −31.0273 + 53.7409i −1.21606 + 2.10627i
\(652\) −5.91199 10.2399i −0.231531 0.401024i
\(653\) −25.2762 −0.989135 −0.494568 0.869139i \(-0.664674\pi\)
−0.494568 + 0.869139i \(0.664674\pi\)
\(654\) −14.3974 −0.562983
\(655\) 0 0
\(656\) 2.30005 + 3.98380i 0.0898018 + 0.155541i
\(657\) 42.4263 1.65521
\(658\) −34.1833 −1.33260
\(659\) 0.0195595 + 0.0338780i 0.000761929 + 0.00131970i 0.866406 0.499340i \(-0.166424\pi\)
−0.865644 + 0.500660i \(0.833091\pi\)
\(660\) 0 0
\(661\) 12.9014 + 22.3458i 0.501805 + 0.869151i 0.999998 + 0.00208512i \(0.000663715\pi\)
−0.498193 + 0.867066i \(0.666003\pi\)
\(662\) 5.28476 9.15346i 0.205398 0.355760i
\(663\) 13.3293 23.0870i 0.517666 0.896624i
\(664\) 3.28476 0.127473
\(665\) 0 0
\(666\) −58.3399 −2.26063
\(667\) −16.4541 + 28.4994i −0.637106 + 1.10350i
\(668\) 8.83549 15.3035i 0.341855 0.592111i
\(669\) 8.57761 + 14.8569i 0.331630 + 0.574399i
\(670\) 0 0
\(671\) −7.23539 12.5321i −0.279319 0.483795i
\(672\) −14.9694 −0.577458
\(673\) −24.6682 −0.950891 −0.475445 0.879745i \(-0.657713\pi\)
−0.475445 + 0.879745i \(0.657713\pi\)
\(674\) −5.85931 10.1486i −0.225692 0.390910i
\(675\) 0 0
\(676\) 2.73700 0.105269
\(677\) 47.3964 1.82159 0.910796 0.412858i \(-0.135469\pi\)
0.910796 + 0.412858i \(0.135469\pi\)
\(678\) 18.8826 + 32.7057i 0.725183 + 1.25605i
\(679\) −5.28417 + 9.15245i −0.202788 + 0.351239i
\(680\) 0 0
\(681\) −12.8392 + 22.2381i −0.491998 + 0.852165i
\(682\) 2.65790 4.60363i 0.101776 0.176282i
\(683\) 1.61136 0.0616569 0.0308284 0.999525i \(-0.490185\pi\)
0.0308284 + 0.999525i \(0.490185\pi\)
\(684\) 6.64675 + 26.2575i 0.254145 + 1.00398i
\(685\) 0 0
\(686\) −25.4473 + 44.0760i −0.971582 + 1.68283i
\(687\) 2.34170 4.05595i 0.0893415 0.154744i
\(688\) −3.32461 5.75839i −0.126750 0.219537i
\(689\) −13.7487 + 23.8134i −0.523783 + 0.907219i
\(690\) 0 0
\(691\) −30.9474 −1.17729 −0.588647 0.808391i \(-0.700339\pi\)
−0.588647 + 0.808391i \(0.700339\pi\)
\(692\) 12.4571 0.473548
\(693\) −19.6479 34.0312i −0.746362 1.29274i
\(694\) −10.4505 18.1008i −0.396695 0.687096i
\(695\) 0 0
\(696\) 12.9987 0.492716
\(697\) 5.09203 + 8.81966i 0.192874 + 0.334068i
\(698\) −17.7409 + 30.7281i −0.671502 + 1.16308i
\(699\) 6.21145 + 10.7586i 0.234939 + 0.406926i
\(700\) 0 0
\(701\) −1.39904 + 2.42321i −0.0528410 + 0.0915234i −0.891236 0.453540i \(-0.850161\pi\)
0.838395 + 0.545063i \(0.183494\pi\)
\(702\) −38.7001 −1.46064
\(703\) −29.3363 + 28.5336i −1.10644 + 1.07617i
\(704\) 1.28233 0.0483296
\(705\) 0 0
\(706\) 7.14922 12.3828i 0.269064 0.466033i
\(707\) −26.0024 45.0375i −0.977922 1.69381i
\(708\) −9.58859 + 16.6079i −0.360361 + 0.624164i
\(709\) −20.7910 36.0110i −0.780821 1.35242i −0.931464 0.363834i \(-0.881468\pi\)
0.150643 0.988588i \(-0.451866\pi\)
\(710\) 0 0
\(711\) 21.9923 0.824777
\(712\) −4.46699 7.73705i −0.167407 0.289958i
\(713\) −15.9281 27.5883i −0.596512 1.03319i
\(714\) −33.1405 −1.24025
\(715\) 0 0
\(716\) −6.89854 11.9486i −0.257811 0.446541i
\(717\) 38.1618 66.0982i 1.42518 2.46848i
\(718\) −2.11073 3.65589i −0.0787717 0.136437i
\(719\) −9.88375 + 17.1192i −0.368602 + 0.638437i −0.989347 0.145575i \(-0.953497\pi\)
0.620746 + 0.784012i \(0.286830\pi\)
\(720\) 0 0
\(721\) 17.9662 0.669096
\(722\) 16.1847 + 9.95273i 0.602331 + 0.370402i
\(723\) −83.2744 −3.09701
\(724\) 6.96883 12.0704i 0.258994 0.448592i
\(725\) 0 0
\(726\) −14.1992 24.5938i −0.526982 0.912760i
\(727\) 8.38398 14.5215i 0.310945 0.538572i −0.667622 0.744500i \(-0.732688\pi\)
0.978567 + 0.205928i \(0.0660213\pi\)
\(728\) −9.78170 16.9424i −0.362534 0.627927i
\(729\) −20.6665 −0.765426
\(730\) 0 0
\(731\) −7.36029 12.7484i −0.272230 0.471516i
\(732\) 17.1271 + 29.6650i 0.633035 + 1.09645i
\(733\) 7.20019 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(734\) 14.1648 0.522831
\(735\) 0 0
\(736\) 3.84233 6.65511i 0.141630 0.245311i
\(737\) −1.23844 2.14505i −0.0456186 0.0790138i
\(738\) 14.2922 24.7549i 0.526104 0.911239i
\(739\) 1.26645 2.19356i 0.0465872 0.0806914i −0.841792 0.539803i \(-0.818499\pi\)
0.888379 + 0.459111i \(0.151832\pi\)
\(740\) 0 0
\(741\) −37.6257 + 36.5962i −1.38222 + 1.34440i
\(742\) 34.1833 1.25491
\(743\) 10.1601 17.5978i 0.372738 0.645601i −0.617248 0.786769i \(-0.711752\pi\)
0.989986 + 0.141168i \(0.0450858\pi\)
\(744\) −6.29160 + 10.8974i −0.230661 + 0.399517i
\(745\) 0 0
\(746\) −8.32704 + 14.4228i −0.304874 + 0.528058i
\(747\) −10.2055 17.6765i −0.373401 0.646750i
\(748\) 2.83892 0.103801
\(749\) −25.0254 −0.914409
\(750\) 0 0
\(751\) −8.67855 15.0317i −0.316685 0.548514i 0.663109 0.748523i \(-0.269236\pi\)
−0.979794 + 0.200008i \(0.935903\pi\)
\(752\) −6.93155 −0.252768
\(753\) −13.9790 −0.509421
\(754\) 8.49398 + 14.7120i 0.309332 + 0.535779i
\(755\) 0 0
\(756\) 24.0550 + 41.6644i 0.874870 + 1.51532i
\(757\) −21.5624 + 37.3472i −0.783700 + 1.35741i 0.146073 + 0.989274i \(0.453337\pi\)
−0.929773 + 0.368134i \(0.879997\pi\)
\(758\) −1.68345 + 2.91581i −0.0611455 + 0.105907i
\(759\) 29.9120 1.08574
\(760\) 0 0
\(761\) 13.1711 0.477451 0.238726 0.971087i \(-0.423270\pi\)
0.238726 + 0.971087i \(0.423270\pi\)
\(762\) −5.91320 + 10.2420i −0.214213 + 0.371027i
\(763\) −11.6954 + 20.2571i −0.423403 + 0.733355i
\(764\) −2.14116 3.70861i −0.0774646 0.134173i
\(765\) 0 0
\(766\) −4.16010 7.20550i −0.150310 0.260345i
\(767\) −25.0625 −0.904955
\(768\) −3.03544 −0.109532
\(769\) −11.3839 19.7174i −0.410513 0.711029i 0.584433 0.811442i \(-0.301317\pi\)
−0.994946 + 0.100413i \(0.967984\pi\)
\(770\) 0 0
\(771\) 59.8738 2.15630
\(772\) −9.60620 −0.345735
\(773\) 5.64054 + 9.76970i 0.202876 + 0.351392i 0.949454 0.313906i \(-0.101638\pi\)
−0.746578 + 0.665298i \(0.768304\pi\)
\(774\) −20.6587 + 35.7820i −0.742563 + 1.28616i
\(775\) 0 0
\(776\) −1.07150 + 1.85590i −0.0384647 + 0.0666228i
\(777\) −70.2712 + 121.713i −2.52097 + 4.36644i
\(778\) 24.8151 0.889666
\(779\) −4.92055 19.4382i −0.176297 0.696447i
\(780\) 0 0
\(781\) −5.33462 + 9.23983i −0.190888 + 0.330627i
\(782\) 8.50646 14.7336i 0.304190 0.526873i
\(783\) −20.8882 36.1794i −0.746484 1.29295i
\(784\) −8.66010 + 14.9997i −0.309289 + 0.535705i
\(785\) 0 0
\(786\)