Properties

Label 42.3.c.a.13.3
Level $42$
Weight $3$
Character 42.13
Analytic conductor $1.144$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 42.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14441711031\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 13.3
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.13
Dual form 42.3.c.a.13.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -1.01461i q^{5} -2.44949i q^{6} +(-2.24264 + 6.63103i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -1.43488i q^{10} -10.2426 q^{11} -3.46410i q^{12} +8.95743i q^{13} +(-3.17157 + 9.37769i) q^{14} -1.75736 q^{15} +4.00000 q^{16} -30.4085i q^{17} -4.24264 q^{18} +16.1318i q^{19} -2.02922i q^{20} +(11.4853 + 3.88437i) q^{21} -14.4853 q^{22} -6.72792 q^{23} -4.89898i q^{24} +23.9706 q^{25} +12.6677i q^{26} +5.19615i q^{27} +(-4.48528 + 13.2621i) q^{28} +30.0000 q^{29} -2.48528 q^{30} -50.1785i q^{31} +5.65685 q^{32} +17.7408i q^{33} -43.0041i q^{34} +(6.72792 + 2.27541i) q^{35} -6.00000 q^{36} +30.9117 q^{37} +22.8138i q^{38} +15.5147 q^{39} -2.86976i q^{40} +7.10228i q^{41} +(16.2426 + 5.49333i) q^{42} -74.4264 q^{43} -20.4853 q^{44} +3.04384i q^{45} -9.51472 q^{46} +58.2954i q^{47} -6.92820i q^{48} +(-38.9411 - 29.7420i) q^{49} +33.8995 q^{50} -52.6690 q^{51} +17.9149i q^{52} -70.9706 q^{53} +7.34847i q^{54} +10.3923i q^{55} +(-6.34315 + 18.7554i) q^{56} +27.9411 q^{57} +42.4264 q^{58} +0.492372i q^{59} -3.51472 q^{60} -2.86976i q^{61} -70.9631i q^{62} +(6.72792 - 19.8931i) q^{63} +8.00000 q^{64} +9.08831 q^{65} +25.0892i q^{66} +27.0294 q^{67} -60.8170i q^{68} +11.6531i q^{69} +(9.51472 + 3.21792i) q^{70} +50.6102 q^{71} -8.48528 q^{72} +70.6149i q^{73} +43.7157 q^{74} -41.5182i q^{75} +32.2636i q^{76} +(22.9706 - 67.9193i) q^{77} +21.9411 q^{78} +133.823 q^{79} -4.05845i q^{80} +9.00000 q^{81} +10.0441i q^{82} +104.415i q^{83} +(22.9706 + 7.76874i) q^{84} -30.8528 q^{85} -105.255 q^{86} -51.9615i q^{87} -28.9706 q^{88} -144.970i q^{89} +4.30463i q^{90} +(-59.3970 - 20.0883i) q^{91} -13.4558 q^{92} -86.9117 q^{93} +82.4421i q^{94} +16.3675 q^{95} -9.79796i q^{96} +100.705i q^{97} +(-55.0711 - 42.0616i) q^{98} +30.7279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{4} + 8q^{7} - 12q^{9} + O(q^{10}) \) \( 4q + 8q^{4} + 8q^{7} - 12q^{9} - 24q^{11} - 24q^{14} - 24q^{15} + 16q^{16} + 12q^{21} - 24q^{22} + 24q^{23} + 28q^{25} + 16q^{28} + 120q^{29} + 24q^{30} - 24q^{35} - 24q^{36} - 80q^{37} + 96q^{39} + 48q^{42} - 128q^{43} - 48q^{44} - 72q^{46} - 20q^{49} + 96q^{50} - 24q^{51} - 216q^{53} - 48q^{56} - 24q^{57} - 48q^{60} - 24q^{63} + 32q^{64} + 240q^{65} + 176q^{67} + 72q^{70} - 120q^{71} + 288q^{74} + 24q^{77} - 48q^{78} + 128q^{79} + 36q^{81} + 24q^{84} + 216q^{85} - 240q^{86} - 48q^{88} + 48q^{92} - 144q^{93} - 240q^{95} - 192q^{98} + 72q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 0.707107
\(3\) 1.73205i 0.577350i
\(4\) 2.00000 0.500000
\(5\) 1.01461i 0.202922i −0.994839 0.101461i \(-0.967648\pi\)
0.994839 0.101461i \(-0.0323518\pi\)
\(6\) 2.44949i 0.408248i
\(7\) −2.24264 + 6.63103i −0.320377 + 0.947290i
\(8\) 2.82843 0.353553
\(9\) −3.00000 −0.333333
\(10\) 1.43488i 0.143488i
\(11\) −10.2426 −0.931149 −0.465575 0.885009i \(-0.654152\pi\)
−0.465575 + 0.885009i \(0.654152\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 8.95743i 0.689033i 0.938780 + 0.344516i \(0.111957\pi\)
−0.938780 + 0.344516i \(0.888043\pi\)
\(14\) −3.17157 + 9.37769i −0.226541 + 0.669835i
\(15\) −1.75736 −0.117157
\(16\) 4.00000 0.250000
\(17\) 30.4085i 1.78873i −0.447333 0.894367i \(-0.647626\pi\)
0.447333 0.894367i \(-0.352374\pi\)
\(18\) −4.24264 −0.235702
\(19\) 16.1318i 0.849043i 0.905418 + 0.424521i \(0.139558\pi\)
−0.905418 + 0.424521i \(0.860442\pi\)
\(20\) 2.02922i 0.101461i
\(21\) 11.4853 + 3.88437i 0.546918 + 0.184970i
\(22\) −14.4853 −0.658422
\(23\) −6.72792 −0.292518 −0.146259 0.989246i \(-0.546723\pi\)
−0.146259 + 0.989246i \(0.546723\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 23.9706 0.958823
\(26\) 12.6677i 0.487220i
\(27\) 5.19615i 0.192450i
\(28\) −4.48528 + 13.2621i −0.160189 + 0.473645i
\(29\) 30.0000 1.03448 0.517241 0.855840i \(-0.326959\pi\)
0.517241 + 0.855840i \(0.326959\pi\)
\(30\) −2.48528 −0.0828427
\(31\) 50.1785i 1.61866i −0.587354 0.809330i \(-0.699830\pi\)
0.587354 0.809330i \(-0.300170\pi\)
\(32\) 5.65685 0.176777
\(33\) 17.7408i 0.537599i
\(34\) 43.0041i 1.26483i
\(35\) 6.72792 + 2.27541i 0.192226 + 0.0650117i
\(36\) −6.00000 −0.166667
\(37\) 30.9117 0.835451 0.417726 0.908573i \(-0.362827\pi\)
0.417726 + 0.908573i \(0.362827\pi\)
\(38\) 22.8138i 0.600364i
\(39\) 15.5147 0.397813
\(40\) 2.86976i 0.0717439i
\(41\) 7.10228i 0.173226i 0.996242 + 0.0866132i \(0.0276044\pi\)
−0.996242 + 0.0866132i \(0.972396\pi\)
\(42\) 16.2426 + 5.49333i 0.386730 + 0.130793i
\(43\) −74.4264 −1.73085 −0.865423 0.501041i \(-0.832950\pi\)
−0.865423 + 0.501041i \(0.832950\pi\)
\(44\) −20.4853 −0.465575
\(45\) 3.04384i 0.0676408i
\(46\) −9.51472 −0.206842
\(47\) 58.2954i 1.24033i 0.784472 + 0.620164i \(0.212934\pi\)
−0.784472 + 0.620164i \(0.787066\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −38.9411 29.7420i −0.794717 0.606980i
\(50\) 33.8995 0.677990
\(51\) −52.6690 −1.03273
\(52\) 17.9149i 0.344516i
\(53\) −70.9706 −1.33907 −0.669534 0.742782i \(-0.733506\pi\)
−0.669534 + 0.742782i \(0.733506\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 10.3923i 0.188951i
\(56\) −6.34315 + 18.7554i −0.113270 + 0.334918i
\(57\) 27.9411 0.490195
\(58\) 42.4264 0.731490
\(59\) 0.492372i 0.00834529i 0.999991 + 0.00417265i \(0.00132820\pi\)
−0.999991 + 0.00417265i \(0.998672\pi\)
\(60\) −3.51472 −0.0585786
\(61\) 2.86976i 0.0470452i −0.999723 0.0235226i \(-0.992512\pi\)
0.999723 0.0235226i \(-0.00748816\pi\)
\(62\) 70.9631i 1.14457i
\(63\) 6.72792 19.8931i 0.106792 0.315763i
\(64\) 8.00000 0.125000
\(65\) 9.08831 0.139820
\(66\) 25.0892i 0.380140i
\(67\) 27.0294 0.403424 0.201712 0.979445i \(-0.435349\pi\)
0.201712 + 0.979445i \(0.435349\pi\)
\(68\) 60.8170i 0.894367i
\(69\) 11.6531i 0.168886i
\(70\) 9.51472 + 3.21792i 0.135925 + 0.0459702i
\(71\) 50.6102 0.712819 0.356410 0.934330i \(-0.384001\pi\)
0.356410 + 0.934330i \(0.384001\pi\)
\(72\) −8.48528 −0.117851
\(73\) 70.6149i 0.967328i 0.875254 + 0.483664i \(0.160694\pi\)
−0.875254 + 0.483664i \(0.839306\pi\)
\(74\) 43.7157 0.590753
\(75\) 41.5182i 0.553576i
\(76\) 32.2636i 0.424521i
\(77\) 22.9706 67.9193i 0.298319 0.882068i
\(78\) 21.9411 0.281296
\(79\) 133.823 1.69397 0.846983 0.531619i \(-0.178416\pi\)
0.846983 + 0.531619i \(0.178416\pi\)
\(80\) 4.05845i 0.0507306i
\(81\) 9.00000 0.111111
\(82\) 10.0441i 0.122490i
\(83\) 104.415i 1.25802i 0.777398 + 0.629009i \(0.216539\pi\)
−0.777398 + 0.629009i \(0.783461\pi\)
\(84\) 22.9706 + 7.76874i 0.273459 + 0.0924849i
\(85\) −30.8528 −0.362974
\(86\) −105.255 −1.22389
\(87\) 51.9615i 0.597259i
\(88\) −28.9706 −0.329211
\(89\) 144.970i 1.62888i −0.580250 0.814438i \(-0.697045\pi\)
0.580250 0.814438i \(-0.302955\pi\)
\(90\) 4.30463i 0.0478293i
\(91\) −59.3970 20.0883i −0.652714 0.220750i
\(92\) −13.4558 −0.146259
\(93\) −86.9117 −0.934534
\(94\) 82.4421i 0.877044i
\(95\) 16.3675 0.172290
\(96\) 9.79796i 0.102062i
\(97\) 100.705i 1.03820i 0.854714 + 0.519099i \(0.173732\pi\)
−0.854714 + 0.519099i \(0.826268\pi\)
\(98\) −55.0711 42.0616i −0.561950 0.429200i
\(99\) 30.7279 0.310383
\(100\) 47.9411 0.479411
\(101\) 138.882i 1.37507i 0.726150 + 0.687536i \(0.241308\pi\)
−0.726150 + 0.687536i \(0.758692\pi\)
\(102\) −74.4853 −0.730248
\(103\) 78.8760i 0.765787i −0.923793 0.382893i \(-0.874928\pi\)
0.923793 0.382893i \(-0.125072\pi\)
\(104\) 25.3354i 0.243610i
\(105\) 3.94113 11.6531i 0.0375345 0.110982i
\(106\) −100.368 −0.946864
\(107\) −37.7574 −0.352873 −0.176436 0.984312i \(-0.556457\pi\)
−0.176436 + 0.984312i \(0.556457\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 31.9411 0.293038 0.146519 0.989208i \(-0.453193\pi\)
0.146519 + 0.989208i \(0.453193\pi\)
\(110\) 14.6969i 0.133609i
\(111\) 53.5406i 0.482348i
\(112\) −8.97056 + 26.5241i −0.0800943 + 0.236823i
\(113\) −106.971 −0.946642 −0.473321 0.880890i \(-0.656945\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(114\) 39.5147 0.346620
\(115\) 6.82623i 0.0593585i
\(116\) 60.0000 0.517241
\(117\) 26.8723i 0.229678i
\(118\) 0.696320i 0.00590101i
\(119\) 201.640 + 68.1953i 1.69445 + 0.573070i
\(120\) −4.97056 −0.0414214
\(121\) −16.0883 −0.132961
\(122\) 4.05845i 0.0332660i
\(123\) 12.3015 0.100012
\(124\) 100.357i 0.809330i
\(125\) 49.6861i 0.397489i
\(126\) 9.51472 28.1331i 0.0755136 0.223278i
\(127\) 22.0589 0.173692 0.0868460 0.996222i \(-0.472321\pi\)
0.0868460 + 0.996222i \(0.472321\pi\)
\(128\) 11.3137 0.0883883
\(129\) 128.910i 0.999305i
\(130\) 12.8528 0.0988678
\(131\) 70.9631i 0.541703i 0.962621 + 0.270852i \(0.0873052\pi\)
−0.962621 + 0.270852i \(0.912695\pi\)
\(132\) 35.4815i 0.268800i
\(133\) −106.971 36.1779i −0.804290 0.272014i
\(134\) 38.2254 0.285264
\(135\) 5.27208 0.0390524
\(136\) 86.0082i 0.632413i
\(137\) −105.765 −0.772004 −0.386002 0.922498i \(-0.626144\pi\)
−0.386002 + 0.922498i \(0.626144\pi\)
\(138\) 16.4800i 0.119420i
\(139\) 181.322i 1.30447i −0.758015 0.652237i \(-0.773831\pi\)
0.758015 0.652237i \(-0.226169\pi\)
\(140\) 13.4558 + 4.55082i 0.0961132 + 0.0325059i
\(141\) 100.971 0.716103
\(142\) 71.5736 0.504039
\(143\) 91.7477i 0.641592i
\(144\) −12.0000 −0.0833333
\(145\) 30.4384i 0.209920i
\(146\) 99.8646i 0.684004i
\(147\) −51.5147 + 67.4480i −0.350440 + 0.458830i
\(148\) 61.8234 0.417726
\(149\) 41.1472 0.276156 0.138078 0.990421i \(-0.455908\pi\)
0.138078 + 0.990421i \(0.455908\pi\)
\(150\) 58.7156i 0.391438i
\(151\) 80.3675 0.532235 0.266118 0.963941i \(-0.414259\pi\)
0.266118 + 0.963941i \(0.414259\pi\)
\(152\) 45.6277i 0.300182i
\(153\) 91.2255i 0.596245i
\(154\) 32.4853 96.0523i 0.210943 0.623716i
\(155\) −50.9117 −0.328463
\(156\) 31.0294 0.198907
\(157\) 57.3106i 0.365036i 0.983203 + 0.182518i \(0.0584248\pi\)
−0.983203 + 0.182518i \(0.941575\pi\)
\(158\) 189.255 1.19782
\(159\) 122.925i 0.773111i
\(160\) 5.73951i 0.0358719i
\(161\) 15.0883 44.6131i 0.0937162 0.277100i
\(162\) 12.7279 0.0785674
\(163\) −174.912 −1.07308 −0.536539 0.843876i \(-0.680269\pi\)
−0.536539 + 0.843876i \(0.680269\pi\)
\(164\) 14.2046i 0.0866132i
\(165\) 18.0000 0.109091
\(166\) 147.666i 0.889552i
\(167\) 196.163i 1.17463i −0.809359 0.587315i \(-0.800185\pi\)
0.809359 0.587315i \(-0.199815\pi\)
\(168\) 32.4853 + 10.9867i 0.193365 + 0.0653967i
\(169\) 88.7645 0.525234
\(170\) −43.6325 −0.256662
\(171\) 48.3954i 0.283014i
\(172\) −148.853 −0.865423
\(173\) 38.5254i 0.222690i 0.993782 + 0.111345i \(0.0355159\pi\)
−0.993782 + 0.111345i \(0.964484\pi\)
\(174\) 73.4847i 0.422326i
\(175\) −53.7574 + 158.950i −0.307185 + 0.908283i
\(176\) −40.9706 −0.232787
\(177\) 0.852814 0.00481816
\(178\) 205.019i 1.15179i
\(179\) −191.095 −1.06757 −0.533786 0.845619i \(-0.679231\pi\)
−0.533786 + 0.845619i \(0.679231\pi\)
\(180\) 6.08767i 0.0338204i
\(181\) 120.793i 0.667367i −0.942685 0.333683i \(-0.891708\pi\)
0.942685 0.333683i \(-0.108292\pi\)
\(182\) −84.0000 28.4091i −0.461538 0.156094i
\(183\) −4.97056 −0.0271615
\(184\) −19.0294 −0.103421
\(185\) 31.3634i 0.169532i
\(186\) −122.912 −0.660816
\(187\) 311.463i 1.66558i
\(188\) 116.591i 0.620164i
\(189\) −34.4558 11.6531i −0.182306 0.0616566i
\(190\) 23.1472 0.121827
\(191\) 112.066 0.586733 0.293367 0.956000i \(-0.405224\pi\)
0.293367 + 0.956000i \(0.405224\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −22.9117 −0.118713 −0.0593567 0.998237i \(-0.518905\pi\)
−0.0593567 + 0.998237i \(0.518905\pi\)
\(194\) 142.419i 0.734116i
\(195\) 15.7414i 0.0807252i
\(196\) −77.8823 59.4841i −0.397358 0.303490i
\(197\) −116.059 −0.589131 −0.294566 0.955631i \(-0.595175\pi\)
−0.294566 + 0.955631i \(0.595175\pi\)
\(198\) 43.4558 0.219474
\(199\) 163.101i 0.819604i −0.912174 0.409802i \(-0.865598\pi\)
0.912174 0.409802i \(-0.134402\pi\)
\(200\) 67.7990 0.338995
\(201\) 46.8164i 0.232917i
\(202\) 196.409i 0.972323i
\(203\) −67.2792 + 198.931i −0.331425 + 0.979955i
\(204\) −105.338 −0.516363
\(205\) 7.20606 0.0351515
\(206\) 111.548i 0.541493i
\(207\) 20.1838 0.0975061
\(208\) 35.8297i 0.172258i
\(209\) 165.232i 0.790586i
\(210\) 5.57359 16.4800i 0.0265409 0.0784761i
\(211\) 106.426 0.504391 0.252195 0.967676i \(-0.418847\pi\)
0.252195 + 0.967676i \(0.418847\pi\)
\(212\) −141.941 −0.669534
\(213\) 87.6594i 0.411546i
\(214\) −53.3970 −0.249519
\(215\) 75.5139i 0.351228i
\(216\) 14.6969i 0.0680414i
\(217\) 332.735 + 112.532i 1.53334 + 0.518582i
\(218\) 45.1716 0.207209
\(219\) 122.309 0.558487
\(220\) 20.7846i 0.0944755i
\(221\) 272.382 1.23250
\(222\) 75.7179i 0.341071i
\(223\) 57.0047i 0.255627i 0.991798 + 0.127813i \(0.0407958\pi\)
−0.991798 + 0.127813i \(0.959204\pi\)
\(224\) −12.6863 + 37.5108i −0.0566352 + 0.167459i
\(225\) −71.9117 −0.319608
\(226\) −151.279 −0.669377
\(227\) 287.418i 1.26616i −0.774086 0.633080i \(-0.781790\pi\)
0.774086 0.633080i \(-0.218210\pi\)
\(228\) 55.8823 0.245098
\(229\) 139.405i 0.608754i −0.952552 0.304377i \(-0.901552\pi\)
0.952552 0.304377i \(-0.0984482\pi\)
\(230\) 9.65375i 0.0419728i
\(231\) −117.640 39.7862i −0.509262 0.172235i
\(232\) 84.8528 0.365745
\(233\) 362.735 1.55680 0.778401 0.627767i \(-0.216031\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(234\) 38.0031i 0.162407i
\(235\) 59.1472 0.251690
\(236\) 0.984744i 0.00417265i
\(237\) 231.789i 0.978012i
\(238\) 285.161 + 96.4427i 1.19816 + 0.405222i
\(239\) 18.4781 0.0773144 0.0386572 0.999253i \(-0.487692\pi\)
0.0386572 + 0.999253i \(0.487692\pi\)
\(240\) −7.02944 −0.0292893
\(241\) 178.104i 0.739021i 0.929227 + 0.369510i \(0.120475\pi\)
−0.929227 + 0.369510i \(0.879525\pi\)
\(242\) −22.7523 −0.0940178
\(243\) 15.5885i 0.0641500i
\(244\) 5.73951i 0.0235226i
\(245\) −30.1766 + 39.5101i −0.123170 + 0.161266i
\(246\) 17.3970 0.0707194
\(247\) −144.500 −0.585018
\(248\) 141.926i 0.572283i
\(249\) 180.853 0.726317
\(250\) 70.2668i 0.281067i
\(251\) 50.6709i 0.201876i −0.994893 0.100938i \(-0.967816\pi\)
0.994893 0.100938i \(-0.0321844\pi\)
\(252\) 13.4558 39.7862i 0.0533962 0.157882i
\(253\) 68.9117 0.272378
\(254\) 31.1960 0.122819
\(255\) 53.4386i 0.209563i
\(256\) 16.0000 0.0625000
\(257\) 187.584i 0.729898i −0.931028 0.364949i \(-0.881086\pi\)
0.931028 0.364949i \(-0.118914\pi\)
\(258\) 182.307i 0.706615i
\(259\) −69.3238 + 204.976i −0.267659 + 0.791414i
\(260\) 18.1766 0.0699101
\(261\) −90.0000 −0.344828
\(262\) 100.357i 0.383042i
\(263\) −402.978 −1.53223 −0.766117 0.642701i \(-0.777814\pi\)
−0.766117 + 0.642701i \(0.777814\pi\)
\(264\) 50.1785i 0.190070i
\(265\) 72.0076i 0.271727i
\(266\) −151.279 51.1632i −0.568719 0.192343i
\(267\) −251.095 −0.940432
\(268\) 54.0589 0.201712
\(269\) 480.538i 1.78639i 0.449674 + 0.893193i \(0.351540\pi\)
−0.449674 + 0.893193i \(0.648460\pi\)
\(270\) 7.45584 0.0276142
\(271\) 37.3068i 0.137664i 0.997628 + 0.0688318i \(0.0219272\pi\)
−0.997628 + 0.0688318i \(0.978073\pi\)
\(272\) 121.634i 0.447184i
\(273\) −34.7939 + 102.879i −0.127450 + 0.376845i
\(274\) −149.574 −0.545889
\(275\) −245.522 −0.892807
\(276\) 23.3062i 0.0844428i
\(277\) −82.6762 −0.298470 −0.149235 0.988802i \(-0.547681\pi\)
−0.149235 + 0.988802i \(0.547681\pi\)
\(278\) 256.428i 0.922403i
\(279\) 150.535i 0.539554i
\(280\) 19.0294 + 6.43583i 0.0679623 + 0.0229851i
\(281\) −150.853 −0.536843 −0.268421 0.963302i \(-0.586502\pi\)
−0.268421 + 0.963302i \(0.586502\pi\)
\(282\) 142.794 0.506361
\(283\) 284.158i 1.00409i −0.864841 0.502046i \(-0.832581\pi\)
0.864841 0.502046i \(-0.167419\pi\)
\(284\) 101.220 0.356410
\(285\) 28.3494i 0.0994716i
\(286\) 129.751i 0.453674i
\(287\) −47.0955 15.9279i −0.164096 0.0554978i
\(288\) −16.9706 −0.0589256
\(289\) −635.676 −2.19957
\(290\) 43.0463i 0.148436i
\(291\) 174.426 0.599403
\(292\) 141.230i 0.483664i
\(293\) 537.237i 1.83357i 0.399379 + 0.916786i \(0.369226\pi\)
−0.399379 + 0.916786i \(0.630774\pi\)
\(294\) −72.8528 + 95.3859i −0.247799 + 0.324442i
\(295\) 0.499567 0.00169345
\(296\) 87.4315 0.295377
\(297\) 53.2223i 0.179200i
\(298\) 58.1909 0.195272
\(299\) 60.2649i 0.201555i
\(300\) 83.0365i 0.276788i
\(301\) 166.912 493.524i 0.554524 1.63961i
\(302\) 113.657 0.376347
\(303\) 240.551 0.793899
\(304\) 64.5273i 0.212261i
\(305\) −2.91169 −0.00954652
\(306\) 129.012i 0.421609i
\(307\) 34.7430i 0.113169i 0.998398 + 0.0565847i \(0.0180211\pi\)
−0.998398 + 0.0565847i \(0.981979\pi\)
\(308\) 45.9411 135.839i 0.149159 0.441034i
\(309\) −136.617 −0.442127
\(310\) −72.0000 −0.232258
\(311\) 89.1664i 0.286709i 0.989671 + 0.143354i \(0.0457888\pi\)
−0.989671 + 0.143354i \(0.954211\pi\)
\(312\) 43.8823 0.140648
\(313\) 519.700i 1.66038i −0.557479 0.830191i \(-0.688231\pi\)
0.557479 0.830191i \(-0.311769\pi\)
\(314\) 81.0495i 0.258119i
\(315\) −20.1838 6.82623i −0.0640754 0.0216706i
\(316\) 267.647 0.846983
\(317\) 542.029 1.70987 0.854935 0.518736i \(-0.173597\pi\)
0.854935 + 0.518736i \(0.173597\pi\)
\(318\) 173.842i 0.546672i
\(319\) −307.279 −0.963258
\(320\) 8.11689i 0.0253653i
\(321\) 65.3977i 0.203731i
\(322\) 21.3381 63.0924i 0.0662674 0.195939i
\(323\) 490.544 1.51871
\(324\) 18.0000 0.0555556
\(325\) 214.715i 0.660660i
\(326\) −247.362 −0.758781
\(327\) 55.3237i 0.169185i
\(328\) 20.0883i 0.0612448i
\(329\) −386.558 130.736i −1.17495 0.397373i
\(330\) 25.4558 0.0771389
\(331\) 179.632 0.542696 0.271348 0.962481i \(-0.412531\pi\)
0.271348 + 0.962481i \(0.412531\pi\)
\(332\) 208.831i 0.629009i
\(333\) −92.7351 −0.278484
\(334\) 277.417i 0.830588i
\(335\) 27.4244i 0.0818638i
\(336\) 45.9411 + 15.5375i 0.136730 + 0.0462425i
\(337\) 291.823 0.865945 0.432972 0.901407i \(-0.357465\pi\)
0.432972 + 0.901407i \(0.357465\pi\)
\(338\) 125.532 0.371396
\(339\) 185.278i 0.546544i
\(340\) −61.7056 −0.181487
\(341\) 513.960i 1.50721i
\(342\) 68.4415i 0.200121i
\(343\) 284.551 191.519i 0.829596 0.558365i
\(344\) −210.510 −0.611947
\(345\) 11.8234 0.0342707
\(346\) 54.4831i 0.157466i
\(347\) 452.080 1.30283 0.651413 0.758724i \(-0.274177\pi\)
0.651413 + 0.758724i \(0.274177\pi\)
\(348\) 103.923i 0.298629i
\(349\) 235.067i 0.673543i −0.941586 0.336772i \(-0.890665\pi\)
0.941586 0.336772i \(-0.109335\pi\)
\(350\) −76.0244 + 224.789i −0.217213 + 0.642253i
\(351\) −46.5442 −0.132604
\(352\) −57.9411 −0.164605
\(353\) 25.2458i 0.0715179i 0.999360 + 0.0357590i \(0.0113849\pi\)
−0.999360 + 0.0357590i \(0.988615\pi\)
\(354\) 1.20606 0.00340695
\(355\) 51.3497i 0.144647i
\(356\) 289.940i 0.814438i
\(357\) 118.118 349.250i 0.330862 0.978291i
\(358\) −270.250 −0.754888
\(359\) −106.243 −0.295941 −0.147970 0.988992i \(-0.547274\pi\)
−0.147970 + 0.988992i \(0.547274\pi\)
\(360\) 8.60927i 0.0239146i
\(361\) 100.765 0.279126
\(362\) 170.828i 0.471900i
\(363\) 27.8658i 0.0767652i
\(364\) −118.794 40.1766i −0.326357 0.110375i
\(365\) 71.6468 0.196292
\(366\) −7.02944 −0.0192061
\(367\) 286.416i 0.780426i 0.920725 + 0.390213i \(0.127599\pi\)
−0.920725 + 0.390213i \(0.872401\pi\)
\(368\) −26.9117 −0.0731296
\(369\) 21.3068i 0.0577421i
\(370\) 44.3545i 0.119877i
\(371\) 159.161 470.608i 0.429007 1.26849i
\(372\) −173.823 −0.467267
\(373\) −423.470 −1.13531 −0.567654 0.823267i \(-0.692149\pi\)
−0.567654 + 0.823267i \(0.692149\pi\)
\(374\) 440.476i 1.17774i
\(375\) −86.0589 −0.229490
\(376\) 164.884i 0.438522i
\(377\) 268.723i 0.712793i
\(378\) −48.7279 16.4800i −0.128910 0.0435978i
\(379\) 101.103 0.266761 0.133381 0.991065i \(-0.457417\pi\)
0.133381 + 0.991065i \(0.457417\pi\)
\(380\) 32.7351 0.0861449
\(381\) 38.2071i 0.100281i
\(382\) 158.485 0.414883
\(383\) 220.394i 0.575442i −0.957714 0.287721i \(-0.907102\pi\)
0.957714 0.287721i \(-0.0928976\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −68.9117 23.3062i −0.178991 0.0605356i
\(386\) −32.4020 −0.0839431
\(387\) 223.279 0.576949
\(388\) 201.410i 0.519099i
\(389\) −383.470 −0.985784 −0.492892 0.870090i \(-0.664060\pi\)
−0.492892 + 0.870090i \(0.664060\pi\)
\(390\) 22.2617i 0.0570813i
\(391\) 204.586i 0.523238i
\(392\) −110.142 84.1232i −0.280975 0.214600i
\(393\) 122.912 0.312752
\(394\) −164.132 −0.416579
\(395\) 135.779i 0.343744i
\(396\) 61.4558 0.155192
\(397\) 485.178i 1.22211i 0.791588 + 0.611056i \(0.209255\pi\)
−0.791588 + 0.611056i \(0.790745\pi\)
\(398\) 230.660i 0.579548i
\(399\) −62.6619 + 185.278i −0.157047 + 0.464357i
\(400\) 95.8823 0.239706
\(401\) −253.176 −0.631361 −0.315680 0.948866i \(-0.602233\pi\)
−0.315680 + 0.948866i \(0.602233\pi\)
\(402\) 66.2083i 0.164697i
\(403\) 449.470 1.11531
\(404\) 277.765i 0.687536i
\(405\) 9.13151i 0.0225469i
\(406\) −95.1472 + 281.331i −0.234353 + 0.692933i
\(407\) −316.617 −0.777930
\(408\) −148.971 −0.365124
\(409\) 5.39135i 0.0131818i −0.999978 0.00659089i \(-0.997902\pi\)
0.999978 0.00659089i \(-0.00209796\pi\)
\(410\) 10.1909 0.0248559
\(411\) 183.189i 0.445717i
\(412\) 157.752i 0.382893i
\(413\) −3.26494 1.10421i −0.00790541 0.00267364i
\(414\) 28.5442 0.0689472
\(415\) 105.941 0.255280
\(416\) 50.6709i 0.121805i
\(417\) −314.059 −0.753139
\(418\) 233.674i 0.559028i
\(419\) 294.431i 0.702700i −0.936244 0.351350i \(-0.885723\pi\)
0.936244 0.351350i \(-0.114277\pi\)
\(420\) 7.88225 23.3062i 0.0187673 0.0554910i
\(421\) −290.441 −0.689883 −0.344941 0.938624i \(-0.612101\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(422\) 150.510 0.356658
\(423\) 174.886i 0.413442i
\(424\) −200.735 −0.473432
\(425\) 728.909i 1.71508i
\(426\) 123.969i 0.291007i
\(427\) 19.0294 + 6.43583i 0.0445654 + 0.0150722i
\(428\) −75.5147 −0.176436
\(429\) −158.912 −0.370424
\(430\) 106.793i 0.248355i
\(431\) 50.7136 0.117665 0.0588325 0.998268i \(-0.481262\pi\)
0.0588325 + 0.998268i \(0.481262\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 724.761i 1.67381i 0.547347 + 0.836906i \(0.315638\pi\)
−0.547347 + 0.836906i \(0.684362\pi\)
\(434\) 470.558 + 159.145i 1.08424 + 0.366693i
\(435\) −52.7208 −0.121197
\(436\) 63.8823 0.146519
\(437\) 108.534i 0.248361i
\(438\) 172.971 0.394910
\(439\) 371.728i 0.846761i 0.905952 + 0.423381i \(0.139157\pi\)
−0.905952 + 0.423381i \(0.860843\pi\)
\(440\) 29.3939i 0.0668043i
\(441\) 116.823 + 89.2261i 0.264906 + 0.202327i
\(442\) 385.206 0.871507
\(443\) −229.258 −0.517512 −0.258756 0.965943i \(-0.583313\pi\)
−0.258756 + 0.965943i \(0.583313\pi\)
\(444\) 107.081i 0.241174i
\(445\) −147.088 −0.330536
\(446\) 80.6168i 0.180755i
\(447\) 71.2690i 0.159439i
\(448\) −17.9411 + 53.0482i −0.0400472 + 0.118411i
\(449\) −600.323 −1.33702 −0.668511 0.743702i \(-0.733068\pi\)
−0.668511 + 0.743702i \(0.733068\pi\)
\(450\) −101.698 −0.225997
\(451\) 72.7461i 0.161300i
\(452\) −213.941 −0.473321
\(453\) 139.201i 0.307286i
\(454\) 406.471i 0.895311i
\(455\) −20.3818 + 60.2649i −0.0447952 + 0.132450i
\(456\) 79.0294 0.173310
\(457\) 483.823 1.05869 0.529347 0.848405i \(-0.322437\pi\)
0.529347 + 0.848405i \(0.322437\pi\)
\(458\) 197.148i 0.430454i
\(459\) 158.007 0.344242
\(460\) 13.6525i 0.0296793i
\(461\) 274.661i 0.595794i −0.954598 0.297897i \(-0.903715\pi\)
0.954598 0.297897i \(-0.0962852\pi\)
\(462\) −166.368 56.2662i −0.360103 0.121788i
\(463\) −153.470 −0.331469 −0.165734 0.986170i \(-0.552999\pi\)
−0.165734 + 0.986170i \(0.552999\pi\)
\(464\) 120.000 0.258621
\(465\) 88.1816i 0.189638i
\(466\) 512.985 1.10083
\(467\) 61.7420i 0.132210i 0.997813 + 0.0661049i \(0.0210572\pi\)
−0.997813 + 0.0661049i \(0.978943\pi\)
\(468\) 53.7446i 0.114839i
\(469\) −60.6173 + 179.233i −0.129248 + 0.382160i
\(470\) 83.6468 0.177972
\(471\) 99.2649 0.210754
\(472\) 1.39264i 0.00295051i
\(473\) 762.323 1.61168
\(474\) 327.799i 0.691559i
\(475\) 386.689i 0.814082i
\(476\) 403.279 + 136.391i 0.847225 + 0.286535i
\(477\) 212.912 0.446356
\(478\) 26.1320 0.0546695
\(479\) 556.514i 1.16182i −0.813966 0.580912i \(-0.802696\pi\)
0.813966 0.580912i \(-0.197304\pi\)
\(480\) −9.94113 −0.0207107
\(481\) 276.889i 0.575653i
\(482\) 251.877i 0.522567i
\(483\) −77.2721 26.1337i −0.159984 0.0541071i
\(484\) −32.1766 −0.0664806
\(485\) 102.177 0.210673
\(486\) 22.0454i 0.0453609i
\(487\) −325.220 −0.667804 −0.333902 0.942608i \(-0.608365\pi\)
−0.333902 + 0.942608i \(0.608365\pi\)
\(488\) 8.11689i 0.0166330i
\(489\) 302.956i 0.619542i
\(490\) −42.6762 + 55.8758i −0.0870943 + 0.114032i
\(491\) 643.477 1.31054 0.655272 0.755393i \(-0.272554\pi\)
0.655272 + 0.755393i \(0.272554\pi\)
\(492\) 24.6030 0.0500062
\(493\) 912.255i 1.85042i
\(494\) −204.353 −0.413671
\(495\) 31.1769i 0.0629837i
\(496\) 200.714i 0.404665i
\(497\) −113.500 + 335.598i −0.228371 + 0.675247i
\(498\) 255.765 0.513583
\(499\) 755.426 1.51388 0.756939 0.653485i \(-0.226694\pi\)
0.756939 + 0.653485i \(0.226694\pi\)
\(500\) 99.3722i 0.198744i
\(501\) −339.765 −0.678173
\(502\) 71.6594i 0.142748i
\(503\) 509.409i 1.01274i 0.862316 + 0.506371i \(0.169013\pi\)
−0.862316 + 0.506371i \(0.830987\pi\)
\(504\) 19.0294 56.2662i 0.0377568 0.111639i
\(505\) 140.912 0.279033
\(506\) 97.4558 0.192600
\(507\) 153.745i 0.303244i
\(508\) 44.1177 0.0868460
\(509\) 769.433i 1.51166i 0.654770 + 0.755828i \(0.272766\pi\)
−0.654770 + 0.755828i \(0.727234\pi\)
\(510\) 75.5737i 0.148184i
\(511\) −468.250 158.364i −0.916340 0.309910i
\(512\) 22.6274 0.0441942
\(513\) −83.8234 −0.163398
\(514\) 265.283i 0.516116i
\(515\) −80.0286 −0.155395
\(516\) 257.821i 0.499652i
\(517\) 597.099i 1.15493i
\(518\) −98.0387 + 289.880i −0.189264 + 0.559615i
\(519\) 66.7279 0.128570
\(520\) 25.7056 0.0494339
\(521\) 535.207i 1.02727i −0.858009 0.513635i \(-0.828299\pi\)
0.858009 0.513635i \(-0.171701\pi\)
\(522\) −127.279 −0.243830
\(523\) 839.466i 1.60510i −0.596586 0.802549i \(-0.703477\pi\)
0.596586 0.802549i \(-0.296523\pi\)
\(524\) 141.926i 0.270852i
\(525\) 275.309 + 93.1105i 0.524397 + 0.177353i
\(526\) −569.897 −1.08345
\(527\) −1525.85 −2.89535
\(528\) 70.9631i 0.134400i
\(529\) −483.735 −0.914433
\(530\) 101.834i 0.192140i
\(531\) 1.47712i 0.00278176i
\(532\) −213.941 72.3557i −0.402145 0.136007i
\(533\) −63.6182 −0.119359
\(534\) −355.103 −0.664986
\(535\) 38.3091i 0.0716057i
\(536\) 76.4508 0.142632
\(537\) 330.987i 0.616363i
\(538\) 679.583i 1.26317i
\(539\) 398.860 + 304.637i 0.740000 + 0.565189i
\(540\) 10.5442 0.0195262
\(541\) 285.852 0.528377 0.264188 0.964471i \(-0.414896\pi\)
0.264188 + 0.964471i \(0.414896\pi\)
\(542\) 52.7598i 0.0973428i
\(543\) −209.220 −0.385305
\(544\) 172.016i 0.316207i
\(545\) 32.4078i 0.0594639i
\(546\) −49.2061 + 145.492i −0.0901210 + 0.266469i
\(547\) −741.470 −1.35552 −0.677761 0.735283i \(-0.737049\pi\)
−0.677761 + 0.735283i \(0.737049\pi\)
\(548\) −211.529 −0.386002
\(549\) 8.60927i 0.0156817i
\(550\) −347.220 −0.631310
\(551\) 483.954i 0.878320i
\(552\) 32.9600i 0.0597101i
\(553\) −300.118 + 887.387i −0.542708 + 1.60468i
\(554\) −116.922 −0.211050
\(555\) −54.3229 −0.0978792
\(556\) 362.644i 0.652237i
\(557\) 834.853 1.49884 0.749419 0.662096i \(-0.230333\pi\)
0.749419 + 0.662096i \(0.230333\pi\)
\(558\) 212.889i 0.381522i
\(559\) 666.669i 1.19261i
\(560\) 26.9117 + 9.10164i 0.0480566 + 0.0162529i
\(561\) 539.470 0.961622
\(562\) −213.338 −0.379605
\(563\) 417.781i 0.742062i 0.928620 + 0.371031i \(0.120996\pi\)
−0.928620 + 0.371031i \(0.879004\pi\)
\(564\) 201.941 0.358052
\(565\) 108.534i 0.192095i
\(566\) 401.861i 0.710001i
\(567\) −20.1838 + 59.6793i −0.0355975 + 0.105254i
\(568\) 143.147 0.252020
\(569\) 673.029 1.18283 0.591414 0.806368i \(-0.298570\pi\)
0.591414 + 0.806368i \(0.298570\pi\)
\(570\) 40.0921i 0.0703370i
\(571\) −265.088 −0.464253 −0.232126 0.972686i \(-0.574568\pi\)
−0.232126 + 0.972686i \(0.574568\pi\)
\(572\) 183.495i 0.320796i
\(573\) 194.104i 0.338750i
\(574\) −66.6030 22.5254i −0.116033 0.0392429i
\(575\) −161.272 −0.280473
\(576\) −24.0000 −0.0416667
\(577\) 468.740i 0.812375i −0.913790 0.406188i \(-0.866858\pi\)
0.913790 0.406188i \(-0.133142\pi\)
\(578\) −898.982 −1.55533
\(579\) 39.6842i 0.0685392i
\(580\) 60.8767i 0.104960i
\(581\) −692.382 234.166i −1.19171 0.403040i
\(582\) 246.676 0.423842
\(583\) 726.926 1.24687
\(584\) 199.729i 0.342002i
\(585\) −27.2649 −0.0466067
\(586\) 759.767i 1.29653i
\(587\) 120.530i 0.205332i 0.994716 + 0.102666i \(0.0327372\pi\)
−0.994716 + 0.102666i \(0.967263\pi\)
\(588\) −103.029 + 134.896i −0.175220 + 0.229415i
\(589\) 809.470 1.37431
\(590\) 0.706494 0.00119745
\(591\) 201.020i 0.340135i
\(592\) 123.647 0.208863
\(593\) 561.468i 0.946826i −0.880841 0.473413i \(-0.843022\pi\)
0.880841 0.473413i \(-0.156978\pi\)
\(594\) 75.2677i 0.126713i
\(595\) 69.1918 204.586i 0.116289 0.343842i
\(596\) 82.2944 0.138078
\(597\) −282.500 −0.473199
\(598\) 85.2274i 0.142521i
\(599\) 940.109 1.56946 0.784732 0.619835i \(-0.212801\pi\)
0.784732 + 0.619835i \(0.212801\pi\)
\(600\) 117.431i 0.195719i
\(601\) 563.527i 0.937649i −0.883291 0.468824i \(-0.844678\pi\)
0.883291 0.468824i \(-0.155322\pi\)
\(602\) 236.049 697.948i 0.392108 1.15938i
\(603\) −81.0883 −0.134475
\(604\) 160.735 0.266118
\(605\) 16.3234i 0.0269808i
\(606\) 340.191 0.561371
\(607\) 306.589i 0.505089i 0.967585 + 0.252544i \(0.0812674\pi\)
−0.967585 + 0.252544i \(0.918733\pi\)
\(608\) 91.2553i 0.150091i
\(609\) 344.558 + 116.531i 0.565777 + 0.191348i
\(610\) −4.11775 −0.00675041
\(611\) −522.177 −0.854626
\(612\) 182.451i 0.298122i
\(613\) 275.588 0.449572 0.224786 0.974408i \(-0.427832\pi\)
0.224786 + 0.974408i \(0.427832\pi\)
\(614\) 49.1340i 0.0800228i
\(615\) 12.4813i 0.0202947i
\(616\) 64.9706 192.105i 0.105472 0.311858i
\(617\) 461.294 0.747639 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(618\) −193.206 −0.312631
\(619\) 374.904i 0.605660i 0.953045 + 0.302830i \(0.0979315\pi\)
−0.953045 + 0.302830i \(0.902068\pi\)
\(620\) −101.823 −0.164231
\(621\) 34.9593i 0.0562952i
\(622\) 126.100i 0.202734i
\(623\) 961.301 + 325.116i 1.54302 + 0.521855i
\(624\) 62.0589 0.0994533
\(625\) 548.852 0.878163
\(626\) 734.966i 1.17407i
\(627\) −286.191 −0.456445
\(628\) 114.621i 0.182518i
\(629\) 939.978i 1.49440i
\(630\) −28.5442 9.65375i −0.0453082 0.0153234i
\(631\) −1127.32 −1.78656 −0.893282 0.449496i \(-0.851603\pi\)
−0.893282 + 0.449496i \(0.851603\pi\)
\(632\) 378.510 0.598908
\(633\) 184.336i 0.291210i
\(634\) 766.544 1.20906
\(635\) 22.3812i 0.0352460i
\(636\) 245.849i 0.386555i
\(637\) 266.412 348.812i 0.418229 0.547586i
\(638\) −434.558 −0.681126
\(639\) −151.831 −0.237606
\(640\) 11.4790i 0.0179360i
\(641\) −884.352 −1.37964 −0.689822 0.723979i \(-0.742311\pi\)
−0.689822 + 0.723979i \(0.742311\pi\)
\(642\) 92.4863i 0.144060i
\(643\) 300.765i 0.467753i 0.972266 + 0.233876i \(0.0751411\pi\)
−0.972266 + 0.233876i \(0.924859\pi\)
\(644\) 30.1766 89.2261i 0.0468581 0.138550i
\(645\) 130.794 0.202781
\(646\) 693.734 1.07389
\(647\) 940.604i 1.45379i 0.686747 + 0.726896i \(0.259038\pi\)
−0.686747 + 0.726896i \(0.740962\pi\)
\(648\) 25.4558 0.0392837
\(649\) 5.04319i 0.00777071i
\(650\) 303.652i 0.467157i
\(651\) 194.912 576.314i 0.299404 0.885275i
\(652\) −349.823 −0.536539
\(653\) −455.970 −0.698269 −0.349135 0.937073i \(-0.613524\pi\)
−0.349135 + 0.937073i \(0.613524\pi\)
\(654\) 78.2395i 0.119632i
\(655\) 72.0000 0.109924
\(656\) 28.4091i 0.0433066i
\(657\) 211.845i 0.322443i
\(658\) −546.676 184.888i −0.830815 0.280985i
\(659\) 403.684 0.612571 0.306285 0.951940i \(-0.400914\pi\)
0.306285 + 0.951940i \(0.400914\pi\)
\(660\) 36.0000 0.0545455
\(661\) 1153.41i 1.74495i 0.488663 + 0.872473i \(0.337485\pi\)
−0.488663 + 0.872473i \(0.662515\pi\)
\(662\) 254.039 0.383744
\(663\) 471.779i 0.711582i
\(664\) 295.331i 0.444776i
\(665\) −36.7065 + 108.534i −0.0551977 + 0.163208i
\(666\) −131.147 −0.196918
\(667\) −201.838 −0.302605
\(668\) 392.326i 0.587315i
\(669\) 98.7351 0.147586
\(670\) 38.7839i 0.0578865i
\(671\) 29.3939i 0.0438061i
\(672\) 64.9706 + 21.9733i 0.0966824 + 0.0326984i
\(673\) −607.440 −0.902585 −0.451293 0.892376i \(-0.649037\pi\)
−0.451293 + 0.892376i \(0.649037\pi\)
\(674\) 412.701 0.612315
\(675\) 124.555i 0.184525i
\(676\) 177.529 0.262617
\(677\) 1137.59i 1.68034i 0.542326 + 0.840168i \(0.317544\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(678\) 262.023i 0.386465i
\(679\) −667.779 225.845i −0.983474 0.332615i
\(680\) −87.2649 −0.128331
\(681\) −497.823 −0.731018
\(682\) 726.849i 1.06576i
\(683\) −818.111 −1.19782 −0.598910 0.800817i \(-0.704399\pi\)
−0.598910 + 0.800817i \(0.704399\pi\)
\(684\) 96.7909i 0.141507i
\(685\) 107.310i 0.156657i
\(686\) 402.416 270.849i 0.586613 0.394823i
\(687\) −241.456 −0.351464
\(688\) −297.706 −0.432712
\(689\) 635.714i 0.922661i
\(690\) 16.7208 0.0242330
\(691\) 204.280i 0.295630i −0.989015 0.147815i \(-0.952776\pi\)
0.989015 0.147815i \(-0.0472239\pi\)
\(692\) 77.0508i 0.111345i
\(693\) −68.9117 + 203.758i −0.0994397 + 0.294023i
\(694\) 639.338 0.921236
\(695\) −183.971 −0.264707
\(696\) 146.969i 0.211163i
\(697\) 215.970 0.309856
\(698\) 332.434i 0.476267i
\(699\) 628.276i 0.898821i
\(700\) −107.515 + 317.899i −0.153592 + 0.454142i
\(701\) −318.853 −0.454854 −0.227427 0.973795i \(-0.573031\pi\)
−0.227427 + 0.973795i \(0.573031\pi\)
\(702\) −65.8234 −0.0937655
\(703\) 498.662i 0.709334i
\(704\) −81.9411 −0.116394
\(705\) 102.446i 0.145313i
\(706\) 35.7030i 0.0505708i
\(707\) −920.933 311.463i −1.30259 0.440542i
\(708\) 1.70563 0.00240908
\(709\) −217.647 −0.306977 −0.153489 0.988150i \(-0.549051\pi\)
−0.153489 + 0.988150i \(0.549051\pi\)
\(710\) 72.6194i 0.102281i
\(711\) −401.470 −0.564656
\(712\) 410.037i 0.575895i
\(713\) 337.597i 0.473488i
\(714\) 167.044 493.914i 0.233955 0.691757i
\(715\) −93.0883 −0.130193
\(716\) −382.191 −0.533786
\(717\) 32.0051i 0.0446375i
\(718\) −150.250 −0.209262
\(719\) 1207.36i 1.67922i −0.543192 0.839609i \(-0.682784\pi\)
0.543192 0.839609i \(-0.317216\pi\)
\(720\) 12.1753i 0.0169102i
\(721\) 523.029 + 176.891i 0.725422 + 0.245341i
\(722\) 142.503 0.197372
\(723\) 308.485 0.426674
\(724\) 241.587i 0.333683i
\(725\) 719.117 0.991885
\(726\) 39.4082i 0.0542812i
\(727\) 123.231i 0.169506i −0.996402 0.0847528i \(-0.972990\pi\)
0.996402 0.0847528i \(-0.0270100\pi\)
\(728\) −168.000 56.8183i −0.230769 0.0780471i
\(729\) −27.0000 −0.0370370
\(730\) 101.324 0.138800
\(731\) 2263.19i 3.09603i
\(732\) −9.94113 −0.0135808
\(733\) 375.779i 0.512659i 0.966589 + 0.256330i \(0.0825133\pi\)
−0.966589 + 0.256330i \(0.917487\pi\)
\(734\) 405.054i 0.551844i
\(735\) 68.4335 + 52.2674i 0.0931069 + 0.0711122i
\(736\) −38.0589 −0.0517104
\(737\) −276.853 −0.375648
\(738\) 30.1324i 0.0408299i
\(739\) 722.530 0.977713 0.488856 0.872364i \(-0.337414\pi\)
0.488856 + 0.872364i \(0.337414\pi\)
\(740\) 62.7267i 0.0847659i
\(741\) 250.281i 0.337761i
\(742\) 225.088 665.540i 0.303354 0.896954i
\(743\) 1268.48 1.70724 0.853618 0.520899i \(-0.174403\pi\)
0.853618 + 0.520899i \(0.174403\pi\)
\(744\) −245.823 −0.330408
\(745\) 41.7484i 0.0560382i
\(746\) −598.877 −0.802784
\(747\) 313.246i 0.419339i
\(748\) 622.926i 0.832789i
\(749\) 84.6762 250.370i 0.113052 0.334273i
\(750\) −121.706 −0.162274
\(751\) 439.161 0.584769 0.292384 0.956301i \(-0.405551\pi\)
0.292384 + 0.956301i \(0.405551\pi\)
\(752\) 233.182i 0.310082i
\(753\) −87.7645 −0.116553
\(754\) 380.031i 0.504020i
\(755\) 81.5419i 0.108002i
\(756\) −68.9117 23.3062i −0.0911530 0.0308283i
\(757\) −668.530 −0.883131 −0.441565 0.897229i \(-0.645577\pi\)
−0.441565 + 0.897229i \(0.645577\pi\)
\(758\) 142.981 0.188629
\(759\) 119.359i 0.157258i
\(760\) 46.2944 0.0609136
\(761\) 880.116i 1.15653i −0.815851 0.578263i \(-0.803731\pi\)
0.815851 0.578263i \(-0.196269\pi\)
\(762\) 54.0330i 0.0709094i
\(763\) −71.6325 + 211.803i −0.0938827 + 0.277592i
\(764\) 224.132 0.293367
\(765\) 92.5584 0.120991
\(766\) 311.685i 0.406899i
\(767\) −4.41039 −0.00575018
\(768\) 27.7128i 0.0360844i
\(769\) 1163.41i 1.51289i 0.654059 + 0.756444i \(0.273065\pi\)
−0.654059 + 0.756444i \(0.726935\pi\)
\(770\) −97.4558 32.9600i −0.126566 0.0428051i
\(771\) −324.905 −0.421407
\(772\) −45.8234 −0.0593567
\(773\) 536.371i 0.693883i −0.937887 0.346941i \(-0.887220\pi\)
0.937887 0.346941i \(-0.112780\pi\)
\(774\) 315.765 0.407964
\(775\) 1202.81i 1.55201i
\(776\) 284.837i 0.367058i
\(777\) 355.029 + 120.072i 0.456923 + 0.154533i
\(778\) −542.309 −0.697055
\(779\) −114.573 −0.147077
\(780\) 31.4828i 0.0403626i
\(781\) −518.382 −0.663741
\(782\) 289.328i 0.369985i
\(783\) 155.885i 0.199086i
\(784\) −155.765 118.968i −0.198679 0.151745i
\(785\) 58.1481 0.0740740
\(786\) 173.823 0.221149
\(787\) 83.9192i 0.106632i 0.998578 + 0.0533159i \(0.0169790\pi\)
−0.998578 + 0.0533159i \(0.983021\pi\)