Properties

Label 950.2.e.m.501.1
Level $950$
Weight $2$
Character 950.501
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 501.1
Root \(1.51772 + 2.62877i\) of defining polynomial
Character \(\chi\) \(=\) 950.501
Dual form 950.2.e.m.201.1

$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.51772 2.62877i −0.876255 1.51772i −0.855419 0.517936i \(-0.826701\pi\)
−0.0208358 0.999783i \(-0.506633\pi\)
\(4\) −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 \(-0.881916\pi\)
−0.931975 + 0.362521i \(0.881916\pi\)
\(8\) −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 −0.448143 0.893962i \(-0.647914\pi\)
0.998265 0.0588778i \(-0.0187522\pi\)
\(14\) −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 \(-0.0801478\pi\)
−0.699995 + 0.714148i \(0.746815\pi\)
\(18\) −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 0.117658 + 0.993054i \(0.462461\pi\)
−0.918839 + 0.394632i \(0.870872\pi\)
\(24\) 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 −0.595825 0.803114i \(-0.703175\pi\)
0.993430 + 0.114443i \(0.0365083\pi\)
\(30\) 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 \(-0.219386\pi\)
0.771742 + 0.635936i \(0.219386\pi\)
\(38\) −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 0.987829 0.155546i \(-0.0497138\pi\)
−0.628621 + 0.777711i \(0.716380\pi\)
\(42\) −7.48471 + 12.9639i −1.15492 + 2.00037i
\(43\) 3.32461 + 5.75839i 0.506998 + 0.878147i 0.999967 + 0.00809994i \(0.00257832\pi\)
−0.492969 + 0.870047i \(0.664088\pi\)
\(44\) −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 0.494444 + 0.869209i \(0.335372\pi\)
−0.999979 + 0.00640345i \(0.997962\pi\)
\(48\) −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 \(-0.675398\pi\)
0.999624 + 0.0274254i \(0.00873086\pi\)
\(54\) 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 0.995027 0.0996066i \(-0.0317584\pi\)
−0.583775 + 0.811915i \(0.698425\pi\)
\(60\) 0 0
\(61\) −5.64238 + 9.77288i −0.722432 + 1.25129i 0.237590 + 0.971366i \(0.423643\pi\)
−0.960022 + 0.279924i \(0.909691\pi\)
\(62\) −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 \(-0.795689\pi\)
0.918970 + 0.394327i \(0.129022\pi\)
\(68\) −2.21388 −0.268472
\(69\) 23.3263 2.80816
\(70\) 0 0
\(71\) −4.16010 7.20550i −0.493713 0.855135i 0.506261 0.862380i \(-0.331027\pi\)
−0.999974 + 0.00724489i \(0.997694\pi\)
\(72\) 3.10694 5.38138i 0.366156 0.634202i
\(73\) 3.41383 + 5.91293i 0.399559 + 0.692056i 0.993671 0.112326i \(-0.0358300\pi\)
−0.594113 + 0.804382i \(0.702497\pi\)
\(74\) 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 0.749139 0.662413i \(-0.230468\pi\)
−0.948236 + 0.317567i \(0.897134\pi\)
\(80\) 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 \(-0.557699\pi\)
−0.180274 + 0.983616i \(0.557699\pi\)
\(84\) −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 −0.999540 0.0303341i \(-0.990343\pi\)
0.526040 + 0.850460i \(0.323676\pi\)
\(90\) 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 \(-0.131968\pi\)
−0.806488 + 0.591251i \(0.798634\pi\)
\(98\) 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 0.474938 + 0.880019i \(0.342470\pi\)
−0.999588 + 0.0287012i \(0.990863\pi\)
\(102\) 6.72010 0.665389
\(103\) −3.64311 −0.358967 −0.179483 0.983761i \(-0.557443\pi\)
−0.179483 + 0.983761i \(0.557443\pi\)
\(104\) −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 \(-0.421117\pi\)
0.245288 + 0.969450i \(0.421117\pi\)
\(108\) −4.87777 + 8.44854i −0.469363 + 0.812961i
\(109\) −2.37155 4.10765i −0.227153 0.393441i 0.729810 0.683650i \(-0.239609\pi\)
−0.956963 + 0.290209i \(0.906275\pi\)
\(110\) 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 \(-0.698983\pi\)
−0.585196 + 0.810892i \(0.698983\pi\)
\(114\) 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 \(-0.888635\pi\)
0.766557 + 0.642176i \(0.221968\pi\)
\(128\) 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 0.999526 0.0307711i \(-0.00979629\pi\)
−0.526412 + 0.850230i \(0.676463\pi\)
\(132\) 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 −0.0285321 + 0.999593i \(0.509083\pi\)
−0.851407 + 0.524506i \(0.824250\pi\)
\(138\) 11.6632 + 20.2012i 0.992833 + 1.71964i
\(139\) 3.39427 5.87905i 0.287898 0.498655i −0.685409 0.728158i \(-0.740377\pi\)
0.973308 + 0.229503i \(0.0737101\pi\)
\(140\) 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 −0.779548 0.626342i \(-0.784551\pi\)
−0.152654 0.988280i \(-0.548782\pi\)
\(150\) 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 \(-0.0234507\pi\)
−0.562388 + 0.826873i \(0.690117\pi\)
\(158\) 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 \(-0.653250\pi\)
−0.463063 + 0.886325i \(0.653250\pi\)
\(164\) −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 0.290130 + 0.956987i \(0.406302\pi\)
−0.973840 + 0.227234i \(0.927032\pi\)
\(168\) −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 \(-0.00963987\pi\)
−0.525994 + 0.850488i \(0.676307\pi\)
\(174\) −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 −0.481793 0.876285i \(-0.660014\pi\)
0.999782 0.0208980i \(-0.00665251\pi\)
\(182\) −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 \(-0.279037\pi\)
−0.985487 + 0.169751i \(0.945704\pi\)
\(194\) −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 \(-0.178258\pi\)
0.847248 + 0.531197i \(0.178258\pi\)
\(198\) −7.96824 −0.566278
\(199\) −7.51588 + 13.0179i −0.532786 + 0.922813i 0.466481 + 0.884531i \(0.345522\pi\)
−0.999267 + 0.0382818i \(0.987812\pi\)
\(200\) 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 −0.977894 0.209102i \(-0.932946\pi\)
0.307859 0.951432i \(-0.400387\pi\)
\(212\) 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 \(-0.106067\pi\)
−0.755763 + 0.654845i \(0.772734\pi\)
\(224\) −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 \(-0.409420\pi\)
0.280739 + 0.959784i \(0.409420\pi\)
\(228\) 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 \(-0.123866\pi\)
−0.791179 + 0.611585i \(0.790532\pi\)
\(234\) −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 −0.0362738 + 0.999342i \(0.511549\pi\)
−0.847319 + 0.531085i \(0.821784\pi\)
\(242\) −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 −0.929500 0.368822i \(-0.879761\pi\)
0.784159 + 0.620559i \(0.213094\pi\)
\(252\) 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 0.375144 + 0.926966i \(0.377593\pi\)
−0.990349 + 0.138599i \(0.955740\pi\)
\(258\) 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 \(-0.0840899\pi\)
−0.708785 + 0.705424i \(0.750757\pi\)
\(264\) 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 0.531504 0.847056i \(-0.321627\pi\)
−0.999324 + 0.0367683i \(0.988294\pi\)
\(270\) 0 0
\(271\) −1.68039 2.91052i −0.102077 0.176802i 0.810463 0.585789i \(-0.199215\pi\)
−0.912540 + 0.408987i \(0.865882\pi\)
\(272\) 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 \(-0.888124\pi\)
−0.938868 + 0.344278i \(0.888124\pi\)
\(278\) 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 −0.906459 0.422293i \(-0.861225\pi\)
0.818946 + 0.573870i \(0.194559\pi\)
\(282\) 10.5201 + 18.2214i 0.626465 + 1.08507i
\(283\) −7.34660 12.7247i −0.436710 0.756404i 0.560724 0.828003i \(-0.310523\pi\)
−0.997433 + 0.0715995i \(0.977190\pi\)
\(284\) 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 \(-0.419333\pi\)
0.250718 + 0.968060i \(0.419333\pi\)
\(294\) 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 \(-0.215317\pi\)
−0.932053 + 0.362322i \(0.881984\pi\)
\(308\) 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 \(-0.735414\pi\)
0.976768 + 0.214299i \(0.0687468\pi\)
\(314\) −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 \(-0.701546\pi\)
0.994003 + 0.109356i \(0.0348790\pi\)
\(318\) −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 \(-0.0632602\pi\)
−0.661140 + 0.750263i \(0.729927\pi\)
\(338\) 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 0.997409 + 0.0719459i \(0.0229209\pi\)
−0.436397 + 0.899754i \(0.643746\pi\)
\(348\) 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 \(-0.375747\pi\)
0.380515 + 0.924775i \(0.375747\pi\)
\(354\) 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 0.804935 0.593363i \(-0.202200\pi\)
−0.916335 + 0.400413i \(0.868867\pi\)
\(360\) 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 \(-0.712795\pi\)
0.989518 + 0.144409i \(0.0461281\pi\)
\(368\) 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 \(-0.641895\pi\)
−0.431158 + 0.902277i \(0.641895\pi\)
\(374\) −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 \(-0.0984830\pi\)
−0.739947 + 0.672665i \(0.765150\pi\)
\(384\) 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 0.358646 + 0.933474i \(0.383239\pi\)
−0.987735 + 0.156140i \(0.950095\pi\)
\(390\) 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 \(-0.266554\pi\)
−0.978074 + 0.208257i \(0.933221\pi\)
\(398\) −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 0.990430 0.138015i \(-0.0440722\pi\)
−0.614740 + 0.788730i \(0.710739\pi\)
\(402\) −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 0.340964 + 0.940077i \(0.389247\pi\)
−0.984612 + 0.174755i \(0.944087\pi\)
\(410\) 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 0.557080 0.830459i \(-0.311921\pi\)
−0.997738 + 0.0672166i \(0.978588\pi\)
\(422\) 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 −0.559682 0.828707i \(-0.689077\pi\)
0.997523 + 0.0703453i \(0.0224101\pi\)
\(432\) −4.87777 8.44854i −0.234682 0.406481i
\(433\) 2.35699 4.08243i 0.113270 0.196189i −0.803817 0.594877i \(-0.797201\pi\)
0.917087 + 0.398687i \(0.130534\pi\)
\(434\) 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 0.984089 0.177674i \(-0.0568573\pi\)
−0.645915 + 0.763409i \(0.723524\pi\)
\(440\) 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 \(-0.929272\pi\)
0.678559 + 0.734546i \(0.262605\pi\)
\(444\) 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 \(-0.289927\pi\)
0.613087 + 0.790015i \(0.289927\pi\)
\(458\) 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 0.730489 0.682925i \(-0.239292\pi\)
−0.956674 + 0.291160i \(0.905959\pi\)
\(462\) −9.59786 + 16.6240i −0.446533 + 0.773418i
\(463\) 5.34146 0.248239 0.124119 0.992267i \(-0.460389\pi\)
0.124119 + 0.992267i \(0.460389\pi\)
\(464\) −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 \(-0.252048\pi\)
0.702543 + 0.711641i \(0.252048\pi\)
\(468\) −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 −0.887861 0.460111i \(-0.847810\pi\)
0.842399 + 0.538855i \(0.181143\pi\)
\(480\) 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 \(-0.730216\pi\)
−0.661820 + 0.749663i \(0.730216\pi\)
\(488\) 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 0.991245 0.132035i \(-0.0421511\pi\)
−0.609968 + 0.792426i \(0.708818\pi\)
\(492\) 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 0.851588 0.524212i \(-0.175640\pi\)
−0.879775 + 0.475390i \(0.842307\pi\)
\(500\) 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 \(-0.768020\pi\)
0.949734 + 0.313058i \(0.101353\pi\)
\(504\) −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 0.172440 + 0.985020i \(0.444835\pi\)
−0.939272 + 0.343172i \(0.888498\pi\)
\(510\) 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 −0.488009 0.872839i \(-0.662277\pi\)
0.999905 0.0137910i \(-0.00438994\pi\)
\(524\) −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 −0.929698 0.368322i \(-0.879932\pi\)
0.783826 + 0.620981i \(0.213266\pi\)
\(542\) 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 0.376043 + 0.926602i \(0.377284\pi\)
−0.990483 + 0.137638i \(0.956049\pi\)
\(548\) −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 \(-0.758677\pi\)
0.958512 + 0.285051i \(0.0920106\pi\)
\(558\) 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 \(-0.492595\pi\)
0.0232616 + 0.999729i \(0.492595\pi\)
\(564\) −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 \(-0.453700\pi\)
0.144943 + 0.989440i \(0.453700\pi\)
\(578\) 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 \(-0.239494\pi\)
−0.956859 + 0.290553i \(0.906161\pi\)
\(588\) 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 0.125462 + 0.992098i \(0.459959\pi\)
−0.921914 + 0.387396i \(0.873375\pi\)
\(594\) 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 −0.894541 0.446986i \(-0.852497\pi\)
0.834372 + 0.551202i \(0.185831\pi\)
\(600\) 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 \(-0.267720\pi\)
0.666668 + 0.745355i \(0.267720\pi\)
\(608\) 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 \(-0.235219\pi\)
−0.952870 + 0.303378i \(0.901885\pi\)
\(614\) 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 0.431458 + 0.902133i \(0.357999\pi\)
−0.996999 + 0.0774134i \(0.975334\pi\)
\(618\) −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 −0.715621 0.698489i \(-0.753856\pi\)
0.962719 + 0.270502i \(0.0871896\pi\)
\(632\) 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 0.997945 0.0640815i \(-0.0204118\pi\)
−0.554469 + 0.832205i \(0.687078\pi\)
\(642\) 7.70175 13.3398i 0.303964 0.526481i
\(643\) −15.5465 26.9274i −0.613096 1.06191i −0.990715 0.135952i \(-0.956591\pi\)
0.377619 0.925961i \(-0.376743\pi\)
\(644\) 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 \(-0.344806\pi\)
0.468467 + 0.883481i \(0.344806\pi\)
\(648\) 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 \(-0.335326\pi\)
0.494568 + 0.869139i \(0.335326\pi\)
\(654\) −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 −0.865644 0.500660i \(-0.833091\pi\)
0.866406 + 0.499340i \(0.166424\pi\)
\(660\) 0 0
\(661\) 12.9014 22.3458i 0.501805 0.869151i −0.498193 0.867066i \(-0.666003\pi\)
0.999998 0.00208512i \(-0.000663715\pi\)
\(662\) −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 \(-0.342287\pi\)
0.475445 + 0.879745i \(0.342287\pi\)
\(674\) −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 \(-0.864531\pi\)
−0.910796 + 0.412858i \(0.864531\pi\)
\(678\) −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 \(-0.509815\pi\)
−0.0308284 + 0.999525i \(0.509815\pi\)
\(684\) 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 0.838395 0.545063i \(-0.183494\pi\)
−0.891236 + 0.453540i \(0.850161\pi\)
\(702\) 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 0.150643 + 0.988588i \(0.451866\pi\)
−0.931464 + 0.363834i \(0.881468\pi\)
\(710\) 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 0.620746 0.784012i \(-0.286830\pi\)
−0.989347 + 0.145575i \(0.953497\pi\)
\(720\) 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 \(-0.267312\pi\)
−0.978567 + 0.205928i \(0.933979\pi\)
\(728\) 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 \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(734\) 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 0.888379 0.459111i \(-0.151832\pi\)
−0.841792 + 0.539803i \(0.818499\pi\)
\(740\) 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 \(-0.288248\pi\)
−0.989986 + 0.141168i \(0.954914\pi\)
\(744\) −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 −0.979794 0.200008i \(-0.935903\pi\)
0.663109 + 0.748523i \(0.269236\pi\)
\(752\) 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 0.929773 + 0.368134i \(0.120003\pi\)
−0.146073 + 0.989274i \(0.546663\pi\)
\(758\) 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 −0.994946 0.100413i \(-0.967984\pi\)
0.584433 + 0.811442i \(0.301317\pi\)
\(770\) 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 \(-0.898362\pi\)
0.746578 + 0.665298i \(0.231696\pi\)
\(774\) −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
\(786\) 32.8741