Properties

Label 300.3.f.a.199.1
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.a.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 - 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -6.92820 q^{7} -8.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.73205 - 1.00000i) q^{2} -1.73205 q^{3} +(2.00000 + 3.46410i) q^{4} +(3.00000 + 1.73205i) q^{6} -6.92820 q^{7} -8.00000i q^{8} +3.00000 q^{9} -6.92820i q^{11} +(-3.46410 - 6.00000i) q^{12} -2.00000i q^{13} +(12.0000 + 6.92820i) q^{14} +(-8.00000 + 13.8564i) q^{16} +10.0000i q^{17} +(-5.19615 - 3.00000i) q^{18} +20.7846i q^{19} +12.0000 q^{21} +(-6.92820 + 12.0000i) q^{22} +27.7128 q^{23} +13.8564i q^{24} +(-2.00000 + 3.46410i) q^{26} -5.19615 q^{27} +(-13.8564 - 24.0000i) q^{28} +26.0000 q^{29} -6.92820i q^{31} +(27.7128 - 16.0000i) q^{32} +12.0000i q^{33} +(10.0000 - 17.3205i) q^{34} +(6.00000 + 10.3923i) q^{36} +26.0000i q^{37} +(20.7846 - 36.0000i) q^{38} +3.46410i q^{39} +58.0000 q^{41} +(-20.7846 - 12.0000i) q^{42} +48.4974 q^{43} +(24.0000 - 13.8564i) q^{44} +(-48.0000 - 27.7128i) q^{46} +69.2820 q^{47} +(13.8564 - 24.0000i) q^{48} -1.00000 q^{49} -17.3205i q^{51} +(6.92820 - 4.00000i) q^{52} +74.0000i q^{53} +(9.00000 + 5.19615i) q^{54} +55.4256i q^{56} -36.0000i q^{57} +(-45.0333 - 26.0000i) q^{58} -90.0666i q^{59} +26.0000 q^{61} +(-6.92820 + 12.0000i) q^{62} -20.7846 q^{63} -64.0000 q^{64} +(12.0000 - 20.7846i) q^{66} +6.92820 q^{67} +(-34.6410 + 20.0000i) q^{68} -48.0000 q^{69} -24.0000i q^{72} +46.0000i q^{73} +(26.0000 - 45.0333i) q^{74} +(-72.0000 + 41.5692i) q^{76} +48.0000i q^{77} +(3.46410 - 6.00000i) q^{78} +117.779i q^{79} +9.00000 q^{81} +(-100.459 - 58.0000i) q^{82} -48.4974 q^{83} +(24.0000 + 41.5692i) q^{84} +(-84.0000 - 48.4974i) q^{86} -45.0333 q^{87} -55.4256 q^{88} -82.0000 q^{89} +13.8564i q^{91} +(55.4256 + 96.0000i) q^{92} +12.0000i q^{93} +(-120.000 - 69.2820i) q^{94} +(-48.0000 + 27.7128i) q^{96} +2.00000i q^{97} +(1.73205 + 1.00000i) q^{98} -20.7846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{4} + 12q^{6} + 12q^{9} + O(q^{10}) \) \( 4q + 8q^{4} + 12q^{6} + 12q^{9} + 48q^{14} - 32q^{16} + 48q^{21} - 8q^{26} + 104q^{29} + 40q^{34} + 24q^{36} + 232q^{41} + 96q^{44} - 192q^{46} - 4q^{49} + 36q^{54} + 104q^{61} - 256q^{64} + 48q^{66} - 192q^{69} + 104q^{74} - 288q^{76} + 36q^{81} + 96q^{84} - 336q^{86} - 328q^{89} - 480q^{94} - 192q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 1.00000i −0.866025 0.500000i
\(3\) −1.73205 −0.577350
\(4\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(5\) 0 0
\(6\) 3.00000 + 1.73205i 0.500000 + 0.288675i
\(7\) −6.92820 −0.989743 −0.494872 0.868966i \(-0.664785\pi\)
−0.494872 + 0.868966i \(0.664785\pi\)
\(8\) 8.00000i 1.00000i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 6.92820i 0.629837i −0.949119 0.314918i \(-0.898023\pi\)
0.949119 0.314918i \(-0.101977\pi\)
\(12\) −3.46410 6.00000i −0.288675 0.500000i
\(13\) 2.00000i 0.153846i −0.997037 0.0769231i \(-0.975490\pi\)
0.997037 0.0769231i \(-0.0245096\pi\)
\(14\) 12.0000 + 6.92820i 0.857143 + 0.494872i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) 10.0000i 0.588235i 0.955769 + 0.294118i \(0.0950258\pi\)
−0.955769 + 0.294118i \(0.904974\pi\)
\(18\) −5.19615 3.00000i −0.288675 0.166667i
\(19\) 20.7846i 1.09393i 0.837157 + 0.546963i \(0.184216\pi\)
−0.837157 + 0.546963i \(0.815784\pi\)
\(20\) 0 0
\(21\) 12.0000 0.571429
\(22\) −6.92820 + 12.0000i −0.314918 + 0.545455i
\(23\) 27.7128 1.20490 0.602452 0.798155i \(-0.294190\pi\)
0.602452 + 0.798155i \(0.294190\pi\)
\(24\) 13.8564i 0.577350i
\(25\) 0 0
\(26\) −2.00000 + 3.46410i −0.0769231 + 0.133235i
\(27\) −5.19615 −0.192450
\(28\) −13.8564 24.0000i −0.494872 0.857143i
\(29\) 26.0000 0.896552 0.448276 0.893895i \(-0.352038\pi\)
0.448276 + 0.893895i \(0.352038\pi\)
\(30\) 0 0
\(31\) 6.92820i 0.223490i −0.993737 0.111745i \(-0.964356\pi\)
0.993737 0.111745i \(-0.0356441\pi\)
\(32\) 27.7128 16.0000i 0.866025 0.500000i
\(33\) 12.0000i 0.363636i
\(34\) 10.0000 17.3205i 0.294118 0.509427i
\(35\) 0 0
\(36\) 6.00000 + 10.3923i 0.166667 + 0.288675i
\(37\) 26.0000i 0.702703i 0.936244 + 0.351351i \(0.114278\pi\)
−0.936244 + 0.351351i \(0.885722\pi\)
\(38\) 20.7846 36.0000i 0.546963 0.947368i
\(39\) 3.46410i 0.0888231i
\(40\) 0 0
\(41\) 58.0000 1.41463 0.707317 0.706896i \(-0.249905\pi\)
0.707317 + 0.706896i \(0.249905\pi\)
\(42\) −20.7846 12.0000i −0.494872 0.285714i
\(43\) 48.4974 1.12785 0.563924 0.825827i \(-0.309291\pi\)
0.563924 + 0.825827i \(0.309291\pi\)
\(44\) 24.0000 13.8564i 0.545455 0.314918i
\(45\) 0 0
\(46\) −48.0000 27.7128i −1.04348 0.602452i
\(47\) 69.2820 1.47409 0.737043 0.675846i \(-0.236222\pi\)
0.737043 + 0.675846i \(0.236222\pi\)
\(48\) 13.8564 24.0000i 0.288675 0.500000i
\(49\) −1.00000 −0.0204082
\(50\) 0 0
\(51\) 17.3205i 0.339618i
\(52\) 6.92820 4.00000i 0.133235 0.0769231i
\(53\) 74.0000i 1.39623i 0.715987 + 0.698113i \(0.245977\pi\)
−0.715987 + 0.698113i \(0.754023\pi\)
\(54\) 9.00000 + 5.19615i 0.166667 + 0.0962250i
\(55\) 0 0
\(56\) 55.4256i 0.989743i
\(57\) 36.0000i 0.631579i
\(58\) −45.0333 26.0000i −0.776437 0.448276i
\(59\) 90.0666i 1.52655i −0.646072 0.763277i \(-0.723589\pi\)
0.646072 0.763277i \(-0.276411\pi\)
\(60\) 0 0
\(61\) 26.0000 0.426230 0.213115 0.977027i \(-0.431639\pi\)
0.213115 + 0.977027i \(0.431639\pi\)
\(62\) −6.92820 + 12.0000i −0.111745 + 0.193548i
\(63\) −20.7846 −0.329914
\(64\) −64.0000 −1.00000
\(65\) 0 0
\(66\) 12.0000 20.7846i 0.181818 0.314918i
\(67\) 6.92820 0.103406 0.0517030 0.998663i \(-0.483535\pi\)
0.0517030 + 0.998663i \(0.483535\pi\)
\(68\) −34.6410 + 20.0000i −0.509427 + 0.294118i
\(69\) −48.0000 −0.695652
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 24.0000i 0.333333i
\(73\) 46.0000i 0.630137i 0.949069 + 0.315068i \(0.102027\pi\)
−0.949069 + 0.315068i \(0.897973\pi\)
\(74\) 26.0000 45.0333i 0.351351 0.608558i
\(75\) 0 0
\(76\) −72.0000 + 41.5692i −0.947368 + 0.546963i
\(77\) 48.0000i 0.623377i
\(78\) 3.46410 6.00000i 0.0444116 0.0769231i
\(79\) 117.779i 1.49088i 0.666573 + 0.745440i \(0.267760\pi\)
−0.666573 + 0.745440i \(0.732240\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −100.459 58.0000i −1.22511 0.707317i
\(83\) −48.4974 −0.584306 −0.292153 0.956372i \(-0.594372\pi\)
−0.292153 + 0.956372i \(0.594372\pi\)
\(84\) 24.0000 + 41.5692i 0.285714 + 0.494872i
\(85\) 0 0
\(86\) −84.0000 48.4974i −0.976744 0.563924i
\(87\) −45.0333 −0.517624
\(88\) −55.4256 −0.629837
\(89\) −82.0000 −0.921348 −0.460674 0.887569i \(-0.652392\pi\)
−0.460674 + 0.887569i \(0.652392\pi\)
\(90\) 0 0
\(91\) 13.8564i 0.152268i
\(92\) 55.4256 + 96.0000i 0.602452 + 1.04348i
\(93\) 12.0000i 0.129032i
\(94\) −120.000 69.2820i −1.27660 0.737043i
\(95\) 0 0
\(96\) −48.0000 + 27.7128i −0.500000 + 0.288675i
\(97\) 2.00000i 0.0206186i 0.999947 + 0.0103093i \(0.00328160\pi\)
−0.999947 + 0.0103093i \(0.996718\pi\)
\(98\) 1.73205 + 1.00000i 0.0176740 + 0.0102041i
\(99\) 20.7846i 0.209946i
\(100\) 0 0
\(101\) −74.0000 −0.732673 −0.366337 0.930482i \(-0.619388\pi\)
−0.366337 + 0.930482i \(0.619388\pi\)
\(102\) −17.3205 + 30.0000i −0.169809 + 0.294118i
\(103\) 76.2102 0.739905 0.369953 0.929051i \(-0.379374\pi\)
0.369953 + 0.929051i \(0.379374\pi\)
\(104\) −16.0000 −0.153846
\(105\) 0 0
\(106\) 74.0000 128.172i 0.698113 1.20917i
\(107\) 20.7846 0.194249 0.0971243 0.995272i \(-0.469036\pi\)
0.0971243 + 0.995272i \(0.469036\pi\)
\(108\) −10.3923 18.0000i −0.0962250 0.166667i
\(109\) 46.0000 0.422018 0.211009 0.977484i \(-0.432325\pi\)
0.211009 + 0.977484i \(0.432325\pi\)
\(110\) 0 0
\(111\) 45.0333i 0.405706i
\(112\) 55.4256 96.0000i 0.494872 0.857143i
\(113\) 110.000i 0.973451i 0.873555 + 0.486726i \(0.161809\pi\)
−0.873555 + 0.486726i \(0.838191\pi\)
\(114\) −36.0000 + 62.3538i −0.315789 + 0.546963i
\(115\) 0 0
\(116\) 52.0000 + 90.0666i 0.448276 + 0.776437i
\(117\) 6.00000i 0.0512821i
\(118\) −90.0666 + 156.000i −0.763277 + 1.32203i
\(119\) 69.2820i 0.582202i
\(120\) 0 0
\(121\) 73.0000 0.603306
\(122\) −45.0333 26.0000i −0.369126 0.213115i
\(123\) −100.459 −0.816739
\(124\) 24.0000 13.8564i 0.193548 0.111745i
\(125\) 0 0
\(126\) 36.0000 + 20.7846i 0.285714 + 0.164957i
\(127\) −145.492 −1.14561 −0.572804 0.819692i \(-0.694144\pi\)
−0.572804 + 0.819692i \(0.694144\pi\)
\(128\) 110.851 + 64.0000i 0.866025 + 0.500000i
\(129\) −84.0000 −0.651163
\(130\) 0 0
\(131\) 117.779i 0.899080i −0.893260 0.449540i \(-0.851588\pi\)
0.893260 0.449540i \(-0.148412\pi\)
\(132\) −41.5692 + 24.0000i −0.314918 + 0.181818i
\(133\) 144.000i 1.08271i
\(134\) −12.0000 6.92820i −0.0895522 0.0517030i
\(135\) 0 0
\(136\) 80.0000 0.588235
\(137\) 10.0000i 0.0729927i 0.999334 + 0.0364964i \(0.0116197\pi\)
−0.999334 + 0.0364964i \(0.988380\pi\)
\(138\) 83.1384 + 48.0000i 0.602452 + 0.347826i
\(139\) 48.4974i 0.348902i 0.984666 + 0.174451i \(0.0558151\pi\)
−0.984666 + 0.174451i \(0.944185\pi\)
\(140\) 0 0
\(141\) −120.000 −0.851064
\(142\) 0 0
\(143\) −13.8564 −0.0968979
\(144\) −24.0000 + 41.5692i −0.166667 + 0.288675i
\(145\) 0 0
\(146\) 46.0000 79.6743i 0.315068 0.545715i
\(147\) 1.73205 0.0117827
\(148\) −90.0666 + 52.0000i −0.608558 + 0.351351i
\(149\) 2.00000 0.0134228 0.00671141 0.999977i \(-0.497864\pi\)
0.00671141 + 0.999977i \(0.497864\pi\)
\(150\) 0 0
\(151\) 90.0666i 0.596468i 0.954493 + 0.298234i \(0.0963975\pi\)
−0.954493 + 0.298234i \(0.903602\pi\)
\(152\) 166.277 1.09393
\(153\) 30.0000i 0.196078i
\(154\) 48.0000 83.1384i 0.311688 0.539860i
\(155\) 0 0
\(156\) −12.0000 + 6.92820i −0.0769231 + 0.0444116i
\(157\) 214.000i 1.36306i −0.731791 0.681529i \(-0.761315\pi\)
0.731791 0.681529i \(-0.238685\pi\)
\(158\) 117.779 204.000i 0.745440 1.29114i
\(159\) 128.172i 0.806112i
\(160\) 0 0
\(161\) −192.000 −1.19255
\(162\) −15.5885 9.00000i −0.0962250 0.0555556i
\(163\) −20.7846 −0.127513 −0.0637565 0.997965i \(-0.520308\pi\)
−0.0637565 + 0.997965i \(0.520308\pi\)
\(164\) 116.000 + 200.918i 0.707317 + 1.22511i
\(165\) 0 0
\(166\) 84.0000 + 48.4974i 0.506024 + 0.292153i
\(167\) 96.9948 0.580807 0.290404 0.956904i \(-0.406210\pi\)
0.290404 + 0.956904i \(0.406210\pi\)
\(168\) 96.0000i 0.571429i
\(169\) 165.000 0.976331
\(170\) 0 0
\(171\) 62.3538i 0.364642i
\(172\) 96.9948 + 168.000i 0.563924 + 0.976744i
\(173\) 334.000i 1.93064i −0.261077 0.965318i \(-0.584078\pi\)
0.261077 0.965318i \(-0.415922\pi\)
\(174\) 78.0000 + 45.0333i 0.448276 + 0.258812i
\(175\) 0 0
\(176\) 96.0000 + 55.4256i 0.545455 + 0.314918i
\(177\) 156.000i 0.881356i
\(178\) 142.028 + 82.0000i 0.797911 + 0.460674i
\(179\) 187.061i 1.04504i −0.852628 0.522518i \(-0.824993\pi\)
0.852628 0.522518i \(-0.175007\pi\)
\(180\) 0 0
\(181\) 2.00000 0.0110497 0.00552486 0.999985i \(-0.498241\pi\)
0.00552486 + 0.999985i \(0.498241\pi\)
\(182\) 13.8564 24.0000i 0.0761341 0.131868i
\(183\) −45.0333 −0.246084
\(184\) 221.703i 1.20490i
\(185\) 0 0
\(186\) 12.0000 20.7846i 0.0645161 0.111745i
\(187\) 69.2820 0.370492
\(188\) 138.564 + 240.000i 0.737043 + 1.27660i
\(189\) 36.0000 0.190476
\(190\) 0 0
\(191\) 221.703i 1.16075i 0.814351 + 0.580373i \(0.197093\pi\)
−0.814351 + 0.580373i \(0.802907\pi\)
\(192\) 110.851 0.577350
\(193\) 290.000i 1.50259i −0.659966 0.751295i \(-0.729429\pi\)
0.659966 0.751295i \(-0.270571\pi\)
\(194\) 2.00000 3.46410i 0.0103093 0.0178562i
\(195\) 0 0
\(196\) −2.00000 3.46410i −0.0102041 0.0176740i
\(197\) 26.0000i 0.131980i −0.997820 0.0659898i \(-0.978980\pi\)
0.997820 0.0659898i \(-0.0210205\pi\)
\(198\) −20.7846 + 36.0000i −0.104973 + 0.181818i
\(199\) 394.908i 1.98446i 0.124416 + 0.992230i \(0.460294\pi\)
−0.124416 + 0.992230i \(0.539706\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.0597015
\(202\) 128.172 + 74.0000i 0.634514 + 0.366337i
\(203\) −180.133 −0.887356
\(204\) 60.0000 34.6410i 0.294118 0.169809i
\(205\) 0 0
\(206\) −132.000 76.2102i −0.640777 0.369953i
\(207\) 83.1384 0.401635
\(208\) 27.7128 + 16.0000i 0.133235 + 0.0769231i
\(209\) 144.000 0.688995
\(210\) 0 0
\(211\) 242.487i 1.14923i 0.818425 + 0.574614i \(0.194848\pi\)
−0.818425 + 0.574614i \(0.805152\pi\)
\(212\) −256.344 + 148.000i −1.20917 + 0.698113i
\(213\) 0 0
\(214\) −36.0000 20.7846i −0.168224 0.0971243i
\(215\) 0 0
\(216\) 41.5692i 0.192450i
\(217\) 48.0000i 0.221198i
\(218\) −79.6743 46.0000i −0.365479 0.211009i
\(219\) 79.6743i 0.363810i
\(220\) 0 0
\(221\) 20.0000 0.0904977
\(222\) −45.0333 + 78.0000i −0.202853 + 0.351351i
\(223\) 339.482 1.52234 0.761170 0.648552i \(-0.224625\pi\)
0.761170 + 0.648552i \(0.224625\pi\)
\(224\) −192.000 + 110.851i −0.857143 + 0.494872i
\(225\) 0 0
\(226\) 110.000 190.526i 0.486726 0.843034i
\(227\) −284.056 −1.25135 −0.625675 0.780084i \(-0.715176\pi\)
−0.625675 + 0.780084i \(0.715176\pi\)
\(228\) 124.708 72.0000i 0.546963 0.315789i
\(229\) 142.000 0.620087 0.310044 0.950722i \(-0.399656\pi\)
0.310044 + 0.950722i \(0.399656\pi\)
\(230\) 0 0
\(231\) 83.1384i 0.359907i
\(232\) 208.000i 0.896552i
\(233\) 82.0000i 0.351931i −0.984396 0.175966i \(-0.943695\pi\)
0.984396 0.175966i \(-0.0563048\pi\)
\(234\) −6.00000 + 10.3923i −0.0256410 + 0.0444116i
\(235\) 0 0
\(236\) 312.000 180.133i 1.32203 0.763277i
\(237\) 204.000i 0.860759i
\(238\) −69.2820 + 120.000i −0.291101 + 0.504202i
\(239\) 387.979i 1.62334i 0.584113 + 0.811672i \(0.301442\pi\)
−0.584113 + 0.811672i \(0.698558\pi\)
\(240\) 0 0
\(241\) −46.0000 −0.190871 −0.0954357 0.995436i \(-0.530424\pi\)
−0.0954357 + 0.995436i \(0.530424\pi\)
\(242\) −126.440 73.0000i −0.522478 0.301653i
\(243\) −15.5885 −0.0641500
\(244\) 52.0000 + 90.0666i 0.213115 + 0.369126i
\(245\) 0 0
\(246\) 174.000 + 100.459i 0.707317 + 0.408370i
\(247\) 41.5692 0.168296
\(248\) −55.4256 −0.223490
\(249\) 84.0000 0.337349
\(250\) 0 0
\(251\) 145.492i 0.579650i −0.957080 0.289825i \(-0.906403\pi\)
0.957080 0.289825i \(-0.0935972\pi\)
\(252\) −41.5692 72.0000i −0.164957 0.285714i
\(253\) 192.000i 0.758893i
\(254\) 252.000 + 145.492i 0.992126 + 0.572804i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) 254.000i 0.988327i −0.869369 0.494163i \(-0.835474\pi\)
0.869369 0.494163i \(-0.164526\pi\)
\(258\) 145.492 + 84.0000i 0.563924 + 0.325581i
\(259\) 180.133i 0.695495i
\(260\) 0 0
\(261\) 78.0000 0.298851
\(262\) −117.779 + 204.000i −0.449540 + 0.778626i
\(263\) −152.420 −0.579546 −0.289773 0.957095i \(-0.593580\pi\)
−0.289773 + 0.957095i \(0.593580\pi\)
\(264\) 96.0000 0.363636
\(265\) 0 0
\(266\) −144.000 + 249.415i −0.541353 + 0.937652i
\(267\) 142.028 0.531941
\(268\) 13.8564 + 24.0000i 0.0517030 + 0.0895522i
\(269\) −262.000 −0.973978 −0.486989 0.873408i \(-0.661905\pi\)
−0.486989 + 0.873408i \(0.661905\pi\)
\(270\) 0 0
\(271\) 20.7846i 0.0766960i −0.999264 0.0383480i \(-0.987790\pi\)
0.999264 0.0383480i \(-0.0122095\pi\)
\(272\) −138.564 80.0000i −0.509427 0.294118i
\(273\) 24.0000i 0.0879121i
\(274\) 10.0000 17.3205i 0.0364964 0.0632135i
\(275\) 0 0
\(276\) −96.0000 166.277i −0.347826 0.602452i
\(277\) 290.000i 1.04693i 0.852047 + 0.523466i \(0.175361\pi\)
−0.852047 + 0.523466i \(0.824639\pi\)
\(278\) 48.4974 84.0000i 0.174451 0.302158i
\(279\) 20.7846i 0.0744968i
\(280\) 0 0
\(281\) 226.000 0.804270 0.402135 0.915580i \(-0.368268\pi\)
0.402135 + 0.915580i \(0.368268\pi\)
\(282\) 207.846 + 120.000i 0.737043 + 0.425532i
\(283\) −297.913 −1.05270 −0.526348 0.850269i \(-0.676439\pi\)
−0.526348 + 0.850269i \(0.676439\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 24.0000 + 13.8564i 0.0839161 + 0.0484490i
\(287\) −401.836 −1.40012
\(288\) 83.1384 48.0000i 0.288675 0.166667i
\(289\) 189.000 0.653979
\(290\) 0 0
\(291\) 3.46410i 0.0119041i
\(292\) −159.349 + 92.0000i −0.545715 + 0.315068i
\(293\) 362.000i 1.23549i 0.786377 + 0.617747i \(0.211955\pi\)
−0.786377 + 0.617747i \(0.788045\pi\)
\(294\) −3.00000 1.73205i −0.0102041 0.00589133i
\(295\) 0 0
\(296\) 208.000 0.702703
\(297\) 36.0000i 0.121212i
\(298\) −3.46410 2.00000i −0.0116245 0.00671141i
\(299\) 55.4256i 0.185370i
\(300\) 0 0
\(301\) −336.000 −1.11628
\(302\) 90.0666 156.000i 0.298234 0.516556i
\(303\) 128.172 0.423009
\(304\) −288.000 166.277i −0.947368 0.546963i
\(305\) 0 0
\(306\) 30.0000 51.9615i 0.0980392 0.169809i
\(307\) 145.492 0.473916 0.236958 0.971520i \(-0.423850\pi\)
0.236958 + 0.971520i \(0.423850\pi\)
\(308\) −166.277 + 96.0000i −0.539860 + 0.311688i
\(309\) −132.000 −0.427184
\(310\) 0 0
\(311\) 235.559i 0.757424i 0.925515 + 0.378712i \(0.123633\pi\)
−0.925515 + 0.378712i \(0.876367\pi\)
\(312\) 27.7128 0.0888231
\(313\) 478.000i 1.52716i 0.645715 + 0.763578i \(0.276559\pi\)
−0.645715 + 0.763578i \(0.723441\pi\)
\(314\) −214.000 + 370.659i −0.681529 + 1.18044i
\(315\) 0 0
\(316\) −408.000 + 235.559i −1.29114 + 0.745440i
\(317\) 170.000i 0.536278i −0.963380 0.268139i \(-0.913591\pi\)
0.963380 0.268139i \(-0.0864086\pi\)
\(318\) −128.172 + 222.000i −0.403056 + 0.698113i
\(319\) 180.133i 0.564681i
\(320\) 0 0
\(321\) −36.0000 −0.112150
\(322\) 332.554 + 192.000i 1.03278 + 0.596273i
\(323\) −207.846 −0.643486
\(324\) 18.0000 + 31.1769i 0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) 36.0000 + 20.7846i 0.110429 + 0.0637565i
\(327\) −79.6743 −0.243652
\(328\) 464.000i 1.41463i
\(329\) −480.000 −1.45897
\(330\) 0 0
\(331\) 408.764i 1.23494i −0.786596 0.617468i \(-0.788158\pi\)
0.786596 0.617468i \(-0.211842\pi\)
\(332\) −96.9948 168.000i −0.292153 0.506024i
\(333\) 78.0000i 0.234234i
\(334\) −168.000 96.9948i −0.502994 0.290404i
\(335\) 0 0
\(336\) −96.0000 + 166.277i −0.285714 + 0.494872i
\(337\) 338.000i 1.00297i 0.865167 + 0.501484i \(0.167212\pi\)
−0.865167 + 0.501484i \(0.832788\pi\)
\(338\) −285.788 165.000i −0.845528 0.488166i
\(339\) 190.526i 0.562022i
\(340\) 0 0
\(341\) −48.0000 −0.140762
\(342\) 62.3538 108.000i 0.182321 0.315789i
\(343\) 346.410 1.00994
\(344\) 387.979i 1.12785i
\(345\) 0 0
\(346\) −334.000 + 578.505i −0.965318 + 1.67198i
\(347\) 200.918 0.579014 0.289507 0.957176i \(-0.406509\pi\)
0.289507 + 0.957176i \(0.406509\pi\)
\(348\) −90.0666 156.000i −0.258812 0.448276i
\(349\) −506.000 −1.44986 −0.724928 0.688824i \(-0.758127\pi\)
−0.724928 + 0.688824i \(0.758127\pi\)
\(350\) 0 0
\(351\) 10.3923i 0.0296077i
\(352\) −110.851 192.000i −0.314918 0.545455i
\(353\) 178.000i 0.504249i −0.967695 0.252125i \(-0.918871\pi\)
0.967695 0.252125i \(-0.0811293\pi\)
\(354\) 156.000 270.200i 0.440678 0.763277i
\(355\) 0 0
\(356\) −164.000 284.056i −0.460674 0.797911i
\(357\) 120.000i 0.336134i
\(358\) −187.061 + 324.000i −0.522518 + 0.905028i
\(359\) 166.277i 0.463167i 0.972815 + 0.231583i \(0.0743906\pi\)
−0.972815 + 0.231583i \(0.925609\pi\)
\(360\) 0 0
\(361\) −71.0000 −0.196676
\(362\) −3.46410 2.00000i −0.00956934 0.00552486i
\(363\) −126.440 −0.348319
\(364\) −48.0000 + 27.7128i −0.131868 + 0.0761341i
\(365\) 0 0
\(366\) 78.0000 + 45.0333i 0.213115 + 0.123042i
\(367\) 200.918 0.547460 0.273730 0.961807i \(-0.411742\pi\)
0.273730 + 0.961807i \(0.411742\pi\)
\(368\) −221.703 + 384.000i −0.602452 + 1.04348i
\(369\) 174.000 0.471545
\(370\) 0 0
\(371\) 512.687i 1.38191i
\(372\) −41.5692 + 24.0000i −0.111745 + 0.0645161i
\(373\) 310.000i 0.831099i 0.909571 + 0.415550i \(0.136411\pi\)
−0.909571 + 0.415550i \(0.863589\pi\)
\(374\) −120.000 69.2820i −0.320856 0.185246i
\(375\) 0 0
\(376\) 554.256i 1.47409i
\(377\) 52.0000i 0.137931i
\(378\) −62.3538 36.0000i −0.164957 0.0952381i
\(379\) 436.477i 1.15165i −0.817572 0.575827i \(-0.804680\pi\)
0.817572 0.575827i \(-0.195320\pi\)
\(380\) 0 0
\(381\) 252.000 0.661417
\(382\) 221.703 384.000i 0.580373 1.00524i
\(383\) 609.682 1.59186 0.795929 0.605390i \(-0.206983\pi\)
0.795929 + 0.605390i \(0.206983\pi\)
\(384\) −192.000 110.851i −0.500000 0.288675i
\(385\) 0 0
\(386\) −290.000 + 502.295i −0.751295 + 1.30128i
\(387\) 145.492 0.375949
\(388\) −6.92820 + 4.00000i −0.0178562 + 0.0103093i
\(389\) 578.000 1.48586 0.742931 0.669368i \(-0.233435\pi\)
0.742931 + 0.669368i \(0.233435\pi\)
\(390\) 0 0
\(391\) 277.128i 0.708768i
\(392\) 8.00000i 0.0204082i
\(393\) 204.000i 0.519084i
\(394\) −26.0000 + 45.0333i −0.0659898 + 0.114298i
\(395\) 0 0
\(396\) 72.0000 41.5692i 0.181818 0.104973i
\(397\) 26.0000i 0.0654912i 0.999464 + 0.0327456i \(0.0104251\pi\)
−0.999464 + 0.0327456i \(0.989575\pi\)
\(398\) 394.908 684.000i 0.992230 1.71859i
\(399\) 249.415i 0.625101i
\(400\) 0 0
\(401\) 250.000 0.623441 0.311721 0.950174i \(-0.399095\pi\)
0.311721 + 0.950174i \(0.399095\pi\)
\(402\) 20.7846 + 12.0000i 0.0517030 + 0.0298507i
\(403\) −13.8564 −0.0343831
\(404\) −148.000 256.344i −0.366337 0.634514i
\(405\) 0 0
\(406\) 312.000 + 180.133i 0.768473 + 0.443678i
\(407\) 180.133 0.442588
\(408\) −138.564 −0.339618
\(409\) −290.000 −0.709046 −0.354523 0.935047i \(-0.615357\pi\)
−0.354523 + 0.935047i \(0.615357\pi\)
\(410\) 0 0
\(411\) 17.3205i 0.0421424i
\(412\) 152.420 + 264.000i 0.369953 + 0.640777i
\(413\) 624.000i 1.51090i
\(414\) −144.000 83.1384i −0.347826 0.200817i
\(415\) 0 0
\(416\) −32.0000 55.4256i −0.0769231 0.133235i
\(417\) 84.0000i 0.201439i
\(418\) −249.415 144.000i −0.596687 0.344498i
\(419\) 339.482i 0.810219i −0.914268 0.405110i \(-0.867233\pi\)
0.914268 0.405110i \(-0.132767\pi\)
\(420\) 0 0
\(421\) 674.000 1.60095 0.800475 0.599366i \(-0.204581\pi\)
0.800475 + 0.599366i \(0.204581\pi\)
\(422\) 242.487 420.000i 0.574614 0.995261i
\(423\) 207.846 0.491362
\(424\) 592.000 1.39623
\(425\) 0 0
\(426\) 0 0
\(427\) −180.133 −0.421858
\(428\) 41.5692 + 72.0000i 0.0971243 + 0.168224i
\(429\) 24.0000 0.0559441
\(430\) 0 0
\(431\) 540.400i 1.25383i −0.779088 0.626914i \(-0.784318\pi\)
0.779088 0.626914i \(-0.215682\pi\)
\(432\) 41.5692 72.0000i 0.0962250 0.166667i
\(433\) 334.000i 0.771363i 0.922632 + 0.385681i \(0.126034\pi\)
−0.922632 + 0.385681i \(0.873966\pi\)
\(434\) 48.0000 83.1384i 0.110599 0.191563i
\(435\) 0 0
\(436\) 92.0000 + 159.349i 0.211009 + 0.365479i
\(437\) 576.000i 1.31808i
\(438\) −79.6743 + 138.000i −0.181905 + 0.315068i
\(439\) 117.779i 0.268290i 0.990962 + 0.134145i \(0.0428288\pi\)
−0.990962 + 0.134145i \(0.957171\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.00680272
\(442\) −34.6410 20.0000i −0.0783733 0.0452489i
\(443\) 76.2102 0.172032 0.0860161 0.996294i \(-0.472586\pi\)
0.0860161 + 0.996294i \(0.472586\pi\)
\(444\) 156.000 90.0666i 0.351351 0.202853i
\(445\) 0 0
\(446\) −588.000 339.482i −1.31839 0.761170i
\(447\) −3.46410 −0.00774967
\(448\) 443.405 0.989743
\(449\) −394.000 −0.877506 −0.438753 0.898608i \(-0.644580\pi\)
−0.438753 + 0.898608i \(0.644580\pi\)
\(450\) 0 0
\(451\) 401.836i 0.890988i
\(452\) −381.051 + 220.000i −0.843034 + 0.486726i
\(453\) 156.000i 0.344371i
\(454\) 492.000 + 284.056i 1.08370 + 0.625675i
\(455\) 0 0
\(456\) −288.000 −0.631579
\(457\) 478.000i 1.04595i −0.852347 0.522976i \(-0.824822\pi\)
0.852347 0.522976i \(-0.175178\pi\)
\(458\) −245.951 142.000i −0.537011 0.310044i
\(459\) 51.9615i 0.113206i
\(460\) 0 0
\(461\) 142.000 0.308026 0.154013 0.988069i \(-0.450780\pi\)
0.154013 + 0.988069i \(0.450780\pi\)
\(462\) −83.1384 + 144.000i −0.179953 + 0.311688i
\(463\) −630.466 −1.36170 −0.680849 0.732423i \(-0.738389\pi\)
−0.680849 + 0.732423i \(0.738389\pi\)
\(464\) −208.000 + 360.267i −0.448276 + 0.776437i
\(465\) 0 0
\(466\) −82.0000 + 142.028i −0.175966 + 0.304781i
\(467\) 20.7846 0.0445067 0.0222533 0.999752i \(-0.492916\pi\)
0.0222533 + 0.999752i \(0.492916\pi\)
\(468\) 20.7846 12.0000i 0.0444116 0.0256410i
\(469\) −48.0000 −0.102345
\(470\) 0 0
\(471\) 370.659i 0.786962i
\(472\) −720.533 −1.52655
\(473\) 336.000i 0.710359i
\(474\) −204.000 + 353.338i −0.430380 + 0.745440i
\(475\) 0 0
\(476\) 240.000 138.564i 0.504202 0.291101i
\(477\) 222.000i 0.465409i
\(478\) 387.979 672.000i 0.811672 1.40586i
\(479\) 734.390i 1.53317i 0.642141 + 0.766586i \(0.278046\pi\)
−0.642141 + 0.766586i \(0.721954\pi\)
\(480\) 0 0
\(481\) 52.0000 0.108108
\(482\) 79.6743 + 46.0000i 0.165299 + 0.0954357i
\(483\) 332.554 0.688517
\(484\) 146.000 + 252.879i 0.301653 + 0.522478i
\(485\) 0 0
\(486\) 27.0000 + 15.5885i 0.0555556 + 0.0320750i
\(487\) 103.923 0.213394 0.106697 0.994292i \(-0.465972\pi\)
0.106697 + 0.994292i \(0.465972\pi\)
\(488\) 208.000i 0.426230i
\(489\) 36.0000 0.0736196
\(490\) 0 0
\(491\) 921.451i 1.87668i 0.345711 + 0.938341i \(0.387638\pi\)
−0.345711 + 0.938341i \(0.612362\pi\)
\(492\) −200.918 348.000i −0.408370 0.707317i
\(493\) 260.000i 0.527383i
\(494\) −72.0000 41.5692i −0.145749 0.0841482i
\(495\) 0 0
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) 0 0
\(498\) −145.492 84.0000i −0.292153 0.168675i
\(499\) 76.2102i 0.152726i −0.997080 0.0763630i \(-0.975669\pi\)
0.997080 0.0763630i \(-0.0243308\pi\)
\(500\) 0 0
\(501\) −168.000 −0.335329
\(502\) −145.492 + 252.000i −0.289825 + 0.501992i
\(503\) 581.969 1.15700 0.578498 0.815684i \(-0.303639\pi\)
0.578498 + 0.815684i \(0.303639\pi\)
\(504\) 166.277i 0.329914i
\(505\) 0 0
\(506\) −192.000 + 332.554i −0.379447 + 0.657221i
\(507\) −285.788 −0.563685
\(508\) −290.985 504.000i −0.572804 0.992126i
\(509\) 842.000 1.65422 0.827112 0.562037i \(-0.189982\pi\)
0.827112 + 0.562037i \(0.189982\pi\)
\(510\) 0 0
\(511\) 318.697i 0.623674i
\(512\) 512.000i 1.00000i
\(513\) 108.000i 0.210526i
\(514\) −254.000 + 439.941i −0.494163 + 0.855916i
\(515\) 0 0
\(516\) −168.000 290.985i −0.325581 0.563924i
\(517\) 480.000i 0.928433i
\(518\) −180.133 + 312.000i −0.347748 + 0.602317i
\(519\) 578.505i 1.11465i
\(520\) 0 0
\(521\) −326.000 −0.625720 −0.312860 0.949799i \(-0.601287\pi\)
−0.312860 + 0.949799i \(0.601287\pi\)
\(522\) −135.100 78.0000i −0.258812 0.149425i
\(523\) −311.769 −0.596117 −0.298058 0.954548i \(-0.596339\pi\)
−0.298058 + 0.954548i \(0.596339\pi\)
\(524\) 408.000 235.559i 0.778626 0.449540i
\(525\) 0 0
\(526\) 264.000 + 152.420i 0.501901 + 0.289773i
\(527\) 69.2820 0.131465
\(528\) −166.277 96.0000i −0.314918 0.181818i
\(529\) 239.000 0.451796
\(530\) 0 0
\(531\) 270.200i 0.508851i
\(532\) 498.831 288.000i 0.937652 0.541353i
\(533\) 116.000i 0.217636i
\(534\) −246.000 142.028i −0.460674 0.265970i
\(535\) 0 0
\(536\) 55.4256i 0.103406i
\(537\) 324.000i 0.603352i
\(538\) 453.797 + 262.000i 0.843489 + 0.486989i
\(539\) 6.92820i 0.0128538i
\(540\) 0 0
\(541\) 530.000 0.979667 0.489834 0.871816i \(-0.337058\pi\)
0.489834 + 0.871816i \(0.337058\pi\)
\(542\) −20.7846 + 36.0000i −0.0383480 + 0.0664207i
\(543\) −3.46410 −0.00637956
\(544\) 160.000 + 277.128i 0.294118 + 0.509427i
\(545\) 0 0
\(546\) −24.0000 + 41.5692i −0.0439560 + 0.0761341i
\(547\) −339.482 −0.620625 −0.310313 0.950635i \(-0.600434\pi\)
−0.310313 + 0.950635i \(0.600434\pi\)
\(548\) −34.6410 + 20.0000i −0.0632135 + 0.0364964i
\(549\) 78.0000 0.142077
\(550\) 0 0
\(551\) 540.400i 0.980762i
\(552\) 384.000i 0.695652i
\(553\) 816.000i 1.47559i
\(554\) 290.000 502.295i 0.523466 0.906669i
\(555\) 0 0
\(556\) −168.000 + 96.9948i −0.302158 + 0.174451i
\(557\) 766.000i 1.37522i 0.726078 + 0.687612i \(0.241341\pi\)
−0.726078 + 0.687612i \(0.758659\pi\)
\(558\) −20.7846 + 36.0000i −0.0372484 + 0.0645161i
\(559\) 96.9948i 0.173515i
\(560\) 0 0
\(561\) −120.000 −0.213904
\(562\) −391.443 226.000i −0.696519 0.402135i
\(563\) −491.902 −0.873717 −0.436858 0.899530i \(-0.643909\pi\)
−0.436858 + 0.899530i \(0.643909\pi\)
\(564\) −240.000 415.692i −0.425532 0.737043i
\(565\) 0 0
\(566\) 516.000 + 297.913i 0.911661 + 0.526348i
\(567\) −62.3538 −0.109971
\(568\) 0 0
\(569\) 422.000 0.741652 0.370826 0.928702i \(-0.379075\pi\)
0.370826 + 0.928702i \(0.379075\pi\)
\(570\) 0 0
\(571\) 284.056i 0.497472i 0.968571 + 0.248736i \(0.0800151\pi\)
−0.968571 + 0.248736i \(0.919985\pi\)
\(572\) −27.7128 48.0000i −0.0484490 0.0839161i
\(573\) 384.000i 0.670157i
\(574\) 696.000 + 401.836i 1.21254 + 0.700062i
\(575\) 0 0
\(576\) −192.000 −0.333333
\(577\) 46.0000i 0.0797227i −0.999205 0.0398614i \(-0.987308\pi\)
0.999205 0.0398614i \(-0.0126916\pi\)
\(578\) −327.358 189.000i −0.566363 0.326990i
\(579\) 502.295i 0.867521i
\(580\) 0 0
\(581\) 336.000 0.578313
\(582\) −3.46410 + 6.00000i −0.00595206 + 0.0103093i
\(583\) 512.687 0.879395
\(584\) 368.000 0.630137
\(585\) 0 0
\(586\) 362.000 627.002i 0.617747 1.06997i
\(587\) 630.466 1.07405 0.537024 0.843567i \(-0.319548\pi\)
0.537024 + 0.843567i \(0.319548\pi\)
\(588\) 3.46410 + 6.00000i 0.00589133 + 0.0102041i
\(589\) 144.000 0.244482
\(590\) 0 0
\(591\) 45.0333i 0.0761985i
\(592\) −360.267 208.000i −0.608558 0.351351i
\(593\) 82.0000i 0.138280i −0.997607 0.0691400i \(-0.977974\pi\)
0.997607 0.0691400i \(-0.0220255\pi\)
\(594\) 36.0000 62.3538i 0.0606061 0.104973i
\(595\) 0 0
\(596\) 4.00000 + 6.92820i 0.00671141 + 0.0116245i
\(597\) 684.000i 1.14573i
\(598\) −55.4256 + 96.0000i −0.0926850 + 0.160535i
\(599\) 55.4256i 0.0925303i 0.998929 + 0.0462651i \(0.0147319\pi\)
−0.998929 + 0.0462651i \(0.985268\pi\)
\(600\) 0 0
\(601\) −334.000 −0.555740 −0.277870 0.960619i \(-0.589629\pi\)
−0.277870 + 0.960619i \(0.589629\pi\)
\(602\) 581.969 + 336.000i 0.966726 + 0.558140i
\(603\) 20.7846 0.0344687
\(604\) −312.000 + 180.133i −0.516556 + 0.298234i
\(605\) 0 0
\(606\) −222.000 128.172i −0.366337 0.211505i
\(607\) −367.195 −0.604934 −0.302467 0.953160i \(-0.597810\pi\)
−0.302467 + 0.953160i \(0.597810\pi\)
\(608\) 332.554 + 576.000i 0.546963 + 0.947368i
\(609\) 312.000 0.512315
\(610\) 0 0
\(611\) 138.564i 0.226782i
\(612\) −103.923 + 60.0000i −0.169809 + 0.0980392i
\(613\) 214.000i 0.349103i 0.984648 + 0.174551i \(0.0558475\pi\)
−0.984648 + 0.174551i \(0.944152\pi\)
\(614\) −252.000 145.492i −0.410423 0.236958i
\(615\) 0 0
\(616\) 384.000 0.623377
\(617\) 1118.00i 1.81199i −0.423285 0.905997i \(-0.639123\pi\)
0.423285 0.905997i \(-0.360877\pi\)
\(618\) 228.631 + 132.000i 0.369953 + 0.213592i
\(619\) 672.036i 1.08568i −0.839836 0.542840i \(-0.817349\pi\)
0.839836 0.542840i \(-0.182651\pi\)
\(620\) 0 0
\(621\) −144.000 −0.231884
\(622\) 235.559 408.000i 0.378712 0.655949i
\(623\) 568.113 0.911898
\(624\) −48.0000 27.7128i −0.0769231 0.0444116i
\(625\) 0 0
\(626\) 478.000 827.920i 0.763578 1.32256i
\(627\) −249.415 −0.397792
\(628\) 741.318 428.000i 1.18044 0.681529i
\(629\) −260.000 −0.413355
\(630\) 0 0
\(631\) 145.492i 0.230574i 0.993332 + 0.115287i \(0.0367788\pi\)
−0.993332 + 0.115287i \(0.963221\pi\)
\(632\) 942.236 1.49088
\(633\) 420.000i 0.663507i
\(634\) −170.000 + 294.449i −0.268139 + 0.464430i
\(635\) 0 0
\(636\) 444.000 256.344i 0.698113 0.403056i
\(637\) 2.00000i 0.00313972i
\(638\) −180.133 + 312.000i −0.282341 + 0.489028i
\(639\) 0 0
\(640\) 0 0
\(641\) 10.0000 0.0156006 0.00780031 0.999970i \(-0.497517\pi\)
0.00780031 + 0.999970i \(0.497517\pi\)
\(642\) 62.3538 + 36.0000i 0.0971243 + 0.0560748i
\(643\) −1212.44 −1.88559 −0.942796 0.333370i \(-0.891814\pi\)
−0.942796 + 0.333370i \(0.891814\pi\)
\(644\) −384.000 665.108i −0.596273 1.03278i
\(645\) 0 0
\(646\) 360.000 + 207.846i 0.557276 + 0.321743i
\(647\) −332.554 −0.513993 −0.256997 0.966412i \(-0.582733\pi\)
−0.256997 + 0.966412i \(0.582733\pi\)
\(648\) 72.0000i 0.111111i
\(649\) −624.000 −0.961479
\(650\) 0 0
\(651\) 83.1384i 0.127709i
\(652\) −41.5692 72.0000i −0.0637565 0.110429i
\(653\) 670.000i 1.02603i −0.858379 0.513017i \(-0.828528\pi\)
0.858379 0.513017i \(-0.171472\pi\)
\(654\) 138.000 + 79.6743i 0.211009 + 0.121826i
\(655\) 0 0
\(656\) −464.000 + 803.672i −0.707317 + 1.22511i
\(657\) 138.000i 0.210046i
\(658\) 831.384 + 480.000i 1.26350 + 0.729483i
\(659\) 824.456i 1.25107i −0.780195 0.625536i \(-0.784880\pi\)
0.780195 0.625536i \(-0.215120\pi\)
\(660\) 0 0
\(661\) −1222.00 −1.84871 −0.924357 0.381529i \(-0.875398\pi\)
−0.924357 + 0.381529i \(0.875398\pi\)
\(662\) −408.764 + 708.000i −0.617468 + 1.06949i
\(663\) −34.6410 −0.0522489
\(664\) 387.979i 0.584306i
\(665\) 0 0
\(666\) 78.0000 135.100i 0.117117 0.202853i
\(667\) 720.533 1.08026
\(668\) 193.990 + 336.000i 0.290404 + 0.502994i
\(669\) −588.000 −0.878924
\(670\) 0 0
\(671\) 180.133i 0.268455i
\(672\) 332.554 192.000i 0.494872 0.285714i
\(673\) 334.000i 0.496285i 0.968724 + 0.248143i \(0.0798202\pi\)
−0.968724 + 0.248143i \(0.920180\pi\)
\(674\) 338.000 585.433i 0.501484 0.868595i
\(675\) 0 0
\(676\) 330.000 + 571.577i 0.488166 + 0.845528i
\(677\) 1006.00i 1.48597i 0.669309 + 0.742984i \(0.266590\pi\)
−0.669309 + 0.742984i \(0.733410\pi\)
\(678\) −190.526 + 330.000i −0.281011 + 0.486726i
\(679\) 13.8564i 0.0204071i
\(680\) 0 0
\(681\) 492.000 0.722467
\(682\) 83.1384 + 48.0000i 0.121904 + 0.0703812i
\(683\) 187.061 0.273882 0.136941 0.990579i \(-0.456273\pi\)
0.136941 + 0.990579i \(0.456273\pi\)
\(684\) −216.000 + 124.708i −0.315789 + 0.182321i
\(685\) 0 0
\(686\) −600.000 346.410i −0.874636 0.504971i
\(687\) −245.951 −0.358008
\(688\) −387.979 + 672.000i −0.563924 + 0.976744i
\(689\) 148.000 0.214804
\(690\) 0 0
\(691\) 990.733i 1.43377i −0.697193 0.716884i \(-0.745568\pi\)
0.697193 0.716884i \(-0.254432\pi\)
\(692\) 1157.01 668.000i 1.67198 0.965318i
\(693\) 144.000i 0.207792i
\(694\) −348.000 200.918i −0.501441 0.289507i
\(695\) 0 0
\(696\) 360.267i 0.517624i
\(697\) 580.000i 0.832138i
\(698\) 876.418 + 506.000i 1.25561 + 0.724928i
\(699\) 142.028i 0.203188i
\(700\) 0 0
\(701\) −1034.00 −1.47504 −0.737518 0.675328i \(-0.764002\pi\)
−0.737518 + 0.675328i \(0.764002\pi\)
\(702\) 10.3923 18.0000i 0.0148039 0.0256410i
\(703\) −540.400 −0.768705
\(704\) 443.405i 0.629837i
\(705\) 0 0
\(706\) −178.000 + 308.305i −0.252125 + 0.436693i
\(707\) 512.687 0.725158
\(708\) −540.400 + 312.000i −0.763277 + 0.440678i
\(709\) −530.000 −0.747532 −0.373766 0.927523i \(-0.621934\pi\)
−0.373766 + 0.927523i \(0.621934\pi\)
\(710\) 0 0
\(711\) 353.338i 0.496960i
\(712\) 656.000i 0.921348i
\(713\) 192.000i 0.269285i
\(714\) 120.000 207.846i 0.168067 0.291101i
\(715\) 0 0
\(716\) 648.000 374.123i 0.905028 0.522518i
\(717\) 672.000i 0.937238i
\(718\) 166.277 288.000i 0.231583 0.401114i
\(719\) 706.677i 0.982861i −0.870917 0.491430i \(-0.836474\pi\)
0.870917 0.491430i \(-0.163526\pi\)
\(720\) 0 0
\(721\) −528.000 −0.732316
\(722\) 122.976 + 71.0000i 0.170326 + 0.0983380i
\(723\) 79.6743 0.110200
\(724\) 4.00000 + 6.92820i 0.00552486 + 0.00956934i
\(725\) 0 0
\(726\) 219.000 + 126.440i 0.301653 + 0.174159i
\(727\) 242.487 0.333545 0.166772 0.985995i \(-0.446665\pi\)
0.166772 + 0.985995i \(0.446665\pi\)
\(728\) 110.851 0.152268
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 484.974i 0.663439i
\(732\) −90.0666 156.000i −0.123042 0.213115i
\(733\) 194.000i 0.264666i −0.991205 0.132333i \(-0.957753\pi\)
0.991205 0.132333i \(-0.0422468\pi\)
\(734\) −348.000 200.918i −0.474114 0.273730i
\(735\) 0 0
\(736\) 768.000 443.405i 1.04348 0.602452i
\(737\) 48.0000i 0.0651289i
\(738\) −301.377 174.000i −0.408370 0.235772i
\(739\) 1351.00i 1.82815i −0.405550 0.914073i \(-0.632920\pi\)
0.405550 0.914073i \(-0.367080\pi\)
\(740\) 0 0
\(741\) −72.0000 −0.0971660
\(742\) −512.687 + 888.000i −0.690953 + 1.19677i
\(743\) −678.964 −0.913814 −0.456907 0.889514i \(-0.651043\pi\)
−0.456907 + 0.889514i \(0.651043\pi\)
\(744\) 96.0000 0.129032
\(745\) 0 0
\(746\) 310.000 536.936i 0.415550 0.719753i
\(747\) −145.492 −0.194769
\(748\) 138.564 + 240.000i 0.185246 + 0.320856i
\(749\) −144.000 −0.192256
\(750\) 0 0
\(751\) 658.179i 0.876404i 0.898877 + 0.438202i \(0.144385\pi\)
−0.898877 + 0.438202i \(0.855615\pi\)
\(752\) −554.256 + 960.000i −0.737043 + 1.27660i
\(753\) 252.000i 0.334661i
\(754\) −52.0000 + 90.0666i −0.0689655 + 0.119452i
\(755\) 0 0
\(756\) 72.0000 + 124.708i 0.0952381 + 0.164957i
\(757\) 1006.00i 1.32893i −0.747319 0.664465i \(-0.768659\pi\)
0.747319 0.664465i \(-0.231341\pi\)
\(758\) −436.477 + 756.000i −0.575827 + 0.997361i
\(759\) 332.554i 0.438147i
\(760\) 0 0
\(761\) −758.000 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(762\) −436.477 252.000i −0.572804 0.330709i
\(763\) −318.697 −0.417690
\(764\) −768.000 + 443.405i −1.00524 + 0.580373i
\(765\) 0 0
\(766\) −1056.00 609.682i −1.37859 0.795929i
\(767\) −180.133 −0.234854
\(768\) 221.703 + 384.000i 0.288675 + 0.500000i
\(769\) −2.00000 −0.00260078 −0.00130039 0.999999i \(-0.500414\pi\)
−0.00130039 + 0.999999i \(0.500414\pi\)
\(770\) 0 0
\(771\) 439.941i 0.570611i
\(772\) 1004.59 580.000i 1.30128 0.751295i
\(773\) 262.000i 0.338939i −0.985535 0.169470i \(-0.945795\pi\)
0.985535 0.169470i \(-0.0542055\pi\)
\(774\) −252.000 145.492i −0.325581 0.187975i
\(775\) 0 0
\(776\) 16.0000 0.0206186
\(777\) 312.000i 0.401544i
\(778\) −1001.13 578.000i −1.28679 0.742931i
\(779\) 1205.51i 1.54751i
\(780\) 0 0
\(781\) 0 0
\(782\) 277.128 480.000i 0.354384 0.613811i
\(783\) −135.100 −0.172541
\(784\) 8.00000 13.8564i 0.0102041 0.0176740i
\(785\) 0 0
\(786\) 204.000 353.338i 0.259542 0.449540i
\(787\) −1447.99 −1.83989 −0.919946 0.392046i \(-0.871767\pi\)
−0.919946 + 0.392046i \(0.871767\pi\)