Properties

Label 42.3.c.a.13.1
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 13.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.13
Dual form 42.3.c.a.13.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -5.91359i q^{5} +2.44949i q^{6} +(6.24264 - 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.73205i q^{3} +2.00000 q^{4} -5.91359i q^{5} +2.44949i q^{6} +(6.24264 - 3.16693i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +8.36308i q^{10} -1.75736 q^{11} -3.46410i q^{12} +18.7554i q^{13} +(-8.82843 + 4.47871i) q^{14} -10.2426 q^{15} +4.00000 q^{16} +23.4803i q^{17} +4.24264 q^{18} -23.0600i q^{19} -11.8272i q^{20} +(-5.48528 - 10.8126i) q^{21} +2.48528 q^{22} +18.7279 q^{23} +4.89898i q^{24} -9.97056 q^{25} -26.5241i q^{26} +5.19615i q^{27} +(12.4853 - 6.33386i) q^{28} +30.0000 q^{29} +14.4853 q^{30} +8.60927i q^{31} -5.65685 q^{32} +3.04384i q^{33} -33.2061i q^{34} +(-18.7279 - 36.9164i) q^{35} -6.00000 q^{36} -70.9117 q^{37} +32.6118i q^{38} +32.4853 q^{39} +16.7262i q^{40} +41.3951i q^{41} +(7.75736 + 15.2913i) q^{42} +10.4264 q^{43} -3.51472 q^{44} +17.7408i q^{45} -26.4853 q^{46} +38.6995i q^{47} -6.92820i q^{48} +(28.9411 - 39.5400i) q^{49} +14.1005 q^{50} +40.6690 q^{51} +37.5108i q^{52} -37.0294 q^{53} -7.34847i q^{54} +10.3923i q^{55} +(-17.6569 + 8.95743i) q^{56} -39.9411 q^{57} -42.4264 q^{58} -97.4872i q^{59} -20.4853 q^{60} +16.7262i q^{61} -12.1753i q^{62} +(-18.7279 + 9.50079i) q^{63} +8.00000 q^{64} +110.912 q^{65} -4.30463i q^{66} +60.9706 q^{67} +46.9606i q^{68} -32.4377i q^{69} +(26.4853 + 52.2077i) q^{70} -110.610 q^{71} +8.48528 q^{72} -56.7585i q^{73} +100.284 q^{74} +17.2695i q^{75} -46.1200i q^{76} +(-10.9706 + 5.56543i) q^{77} -45.9411 q^{78} -69.8234 q^{79} -23.6544i q^{80} +9.00000 q^{81} -58.5416i q^{82} +6.43583i q^{83} +(-10.9706 - 21.6251i) q^{84} +138.853 q^{85} -14.7452 q^{86} -51.9615i q^{87} +4.97056 q^{88} -42.0915i q^{89} -25.0892i q^{90} +(59.3970 + 117.083i) q^{91} +37.4558 q^{92} +14.9117 q^{93} -54.7293i q^{94} -136.368 q^{95} +9.79796i q^{96} +51.7153i q^{97} +(-40.9289 + 55.9180i) q^{98} +5.27208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{4} + 8q^{7} - 12q^{9} + O(q^{10}) \) \( 4q + 8q^{4} + 8q^{7} - 12q^{9} - 24q^{11} - 24q^{14} - 24q^{15} + 16q^{16} + 12q^{21} - 24q^{22} + 24q^{23} + 28q^{25} + 16q^{28} + 120q^{29} + 24q^{30} - 24q^{35} - 24q^{36} - 80q^{37} + 96q^{39} + 48q^{42} - 128q^{43} - 48q^{44} - 72q^{46} - 20q^{49} + 96q^{50} - 24q^{51} - 216q^{53} - 48q^{56} - 24q^{57} - 48q^{60} - 24q^{63} + 32q^{64} + 240q^{65} + 176q^{67} + 72q^{70} - 120q^{71} + 288q^{74} + 24q^{77} - 48q^{78} + 128q^{79} + 36q^{81} + 24q^{84} + 216q^{85} - 240q^{86} - 48q^{88} + 48q^{92} - 144q^{93} - 240q^{95} - 192q^{98} + 72q^{99} + O(q^{100}) \)

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
\(5\) 5.91359i 1.18272i −0.806408 0.591359i \(-0.798592\pi\)
0.806408 0.591359i \(-0.201408\pi\)
\(6\) 2.44949i 0.408248i
\(7\) 6.24264 3.16693i 0.891806 0.452418i
\(8\) −2.82843 −0.353553
\(9\) −3.00000 −0.333333
\(10\) 8.36308i 0.836308i
\(11\) −1.75736 −0.159760 −0.0798800 0.996804i \(-0.525454\pi\)
−0.0798800 + 0.996804i \(0.525454\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 18.7554i 1.44272i 0.692559 + 0.721361i \(0.256483\pi\)
−0.692559 + 0.721361i \(0.743517\pi\)
\(14\) −8.82843 + 4.47871i −0.630602 + 0.319908i
\(15\) −10.2426 −0.682843
\(16\) 4.00000 0.250000
\(17\) 23.4803i 1.38119i 0.723240 + 0.690597i \(0.242652\pi\)
−0.723240 + 0.690597i \(0.757348\pi\)
\(18\) 4.24264 0.235702
\(19\) 23.0600i 1.21369i −0.794822 0.606843i \(-0.792436\pi\)
0.794822 0.606843i \(-0.207564\pi\)
\(20\) 11.8272i 0.591359i
\(21\) −5.48528 10.8126i −0.261204 0.514884i
\(22\) 2.48528 0.112967
\(23\) 18.7279 0.814257 0.407129 0.913371i \(-0.366530\pi\)
0.407129 + 0.913371i \(0.366530\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −9.97056 −0.398823
\(26\) 26.5241i 1.02016i
\(27\) 5.19615i 0.192450i
\(28\) 12.4853 6.33386i 0.445903 0.226209i
\(29\) 30.0000 1.03448 0.517241 0.855840i \(-0.326959\pi\)
0.517241 + 0.855840i \(0.326959\pi\)
\(30\) 14.4853 0.482843
\(31\) 8.60927i 0.277718i 0.990312 + 0.138859i \(0.0443435\pi\)
−0.990312 + 0.138859i \(0.955656\pi\)
\(32\) −5.65685 −0.176777
\(33\) 3.04384i 0.0922374i
\(34\) 33.2061i 0.976651i
\(35\) −18.7279 36.9164i −0.535083 1.05476i
\(36\) −6.00000 −0.166667
\(37\) −70.9117 −1.91653 −0.958266 0.285878i \(-0.907715\pi\)
−0.958266 + 0.285878i \(0.907715\pi\)
\(38\) 32.6118i 0.858205i
\(39\) 32.4853 0.832956
\(40\) 16.7262i 0.418154i
\(41\) 41.3951i 1.00964i 0.863225 + 0.504819i \(0.168441\pi\)
−0.863225 + 0.504819i \(0.831559\pi\)
\(42\) 7.75736 + 15.2913i 0.184699 + 0.364078i
\(43\) 10.4264 0.242475 0.121237 0.992624i \(-0.461314\pi\)
0.121237 + 0.992624i \(0.461314\pi\)
\(44\) −3.51472 −0.0798800
\(45\) 17.7408i 0.394239i
\(46\) −26.4853 −0.575767
\(47\) 38.6995i 0.823393i 0.911321 + 0.411696i \(0.135064\pi\)
−0.911321 + 0.411696i \(0.864936\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 28.9411 39.5400i 0.590635 0.806939i
\(50\) 14.1005 0.282010
\(51\) 40.6690 0.797432
\(52\) 37.5108i 0.721361i
\(53\) −37.0294 −0.698669 −0.349334 0.936998i \(-0.613592\pi\)
−0.349334 + 0.936998i \(0.613592\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 10.3923i 0.188951i
\(56\) −17.6569 + 8.95743i −0.315301 + 0.159954i
\(57\) −39.9411 −0.700721
\(58\) −42.4264 −0.731490
\(59\) 97.4872i 1.65233i −0.563431 0.826163i \(-0.690519\pi\)
0.563431 0.826163i \(-0.309481\pi\)
\(60\) −20.4853 −0.341421
\(61\) 16.7262i 0.274199i 0.990557 + 0.137100i \(0.0437781\pi\)
−0.990557 + 0.137100i \(0.956222\pi\)
\(62\) 12.1753i 0.196376i
\(63\) −18.7279 + 9.50079i −0.297269 + 0.150806i
\(64\) 8.00000 0.125000
\(65\) 110.912 1.70633
\(66\) 4.30463i 0.0652217i
\(67\) 60.9706 0.910008 0.455004 0.890489i \(-0.349638\pi\)
0.455004 + 0.890489i \(0.349638\pi\)
\(68\) 46.9606i 0.690597i
\(69\) 32.4377i 0.470112i
\(70\) 26.4853 + 52.2077i 0.378361 + 0.745824i
\(71\) −110.610 −1.55789 −0.778945 0.627092i \(-0.784245\pi\)
−0.778945 + 0.627092i \(0.784245\pi\)
\(72\) 8.48528 0.117851
\(73\) 56.7585i 0.777514i −0.921340 0.388757i \(-0.872905\pi\)
0.921340 0.388757i \(-0.127095\pi\)
\(74\) 100.284 1.35519
\(75\) 17.2695i 0.230260i
\(76\) 46.1200i 0.606843i
\(77\) −10.9706 + 5.56543i −0.142475 + 0.0722783i
\(78\) −45.9411 −0.588989
\(79\) −69.8234 −0.883840 −0.441920 0.897054i \(-0.645703\pi\)
−0.441920 + 0.897054i \(0.645703\pi\)
\(80\) 23.6544i 0.295680i
\(81\) 9.00000 0.111111
\(82\) 58.5416i 0.713922i
\(83\) 6.43583i 0.0775401i 0.999248 + 0.0387701i \(0.0123440\pi\)
−0.999248 + 0.0387701i \(0.987656\pi\)
\(84\) −10.9706 21.6251i −0.130602 0.257442i
\(85\) 138.853 1.63356
\(86\) −14.7452 −0.171455
\(87\) 51.9615i 0.597259i
\(88\) 4.97056 0.0564837
\(89\) 42.0915i 0.472938i −0.971639 0.236469i \(-0.924010\pi\)
0.971639 0.236469i \(-0.0759901\pi\)
\(90\) 25.0892i 0.278769i
\(91\) 59.3970 + 117.083i 0.652714 + 1.28663i
\(92\) 37.4558 0.407129
\(93\) 14.9117 0.160341
\(94\) 54.7293i 0.582227i
\(95\) −136.368 −1.43545
\(96\) 9.79796i 0.102062i
\(97\) 51.7153i 0.533148i 0.963814 + 0.266574i \(0.0858916\pi\)
−0.963814 + 0.266574i \(0.914108\pi\)
\(98\) −40.9289 + 55.9180i −0.417642 + 0.570592i
\(99\) 5.27208 0.0532533
\(100\) −19.9411 −0.199411
\(101\) 6.60991i 0.0654447i 0.999464 + 0.0327223i \(0.0104177\pi\)
−0.999464 + 0.0327223i \(0.989582\pi\)
\(102\) −57.5147 −0.563870
\(103\) 175.871i 1.70748i 0.520696 + 0.853742i \(0.325673\pi\)
−0.520696 + 0.853742i \(0.674327\pi\)
\(104\) 53.0482i 0.510079i
\(105\) −63.9411 + 32.4377i −0.608963 + 0.308931i
\(106\) 52.3675 0.494033
\(107\) −46.2426 −0.432174 −0.216087 0.976374i \(-0.569330\pi\)
−0.216087 + 0.976374i \(0.569330\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −35.9411 −0.329735 −0.164868 0.986316i \(-0.552720\pi\)
−0.164868 + 0.986316i \(0.552720\pi\)
\(110\) 14.6969i 0.133609i
\(111\) 122.823i 1.10651i
\(112\) 24.9706 12.6677i 0.222951 0.113105i
\(113\) −73.0294 −0.646278 −0.323139 0.946351i \(-0.604738\pi\)
−0.323139 + 0.946351i \(0.604738\pi\)
\(114\) 56.4853 0.495485
\(115\) 110.749i 0.963037i
\(116\) 60.0000 0.517241
\(117\) 56.2662i 0.480907i
\(118\) 137.868i 1.16837i
\(119\) 74.3604 + 146.579i 0.624877 + 1.23176i
\(120\) 28.9706 0.241421
\(121\) −117.912 −0.974477
\(122\) 23.6544i 0.193888i
\(123\) 71.6985 0.582915
\(124\) 17.2185i 0.138859i
\(125\) 88.8780i 0.711024i
\(126\) 26.4853 13.4361i 0.210201 0.106636i
\(127\) 89.9411 0.708198 0.354099 0.935208i \(-0.384788\pi\)
0.354099 + 0.935208i \(0.384788\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 18.0591i 0.139993i
\(130\) −156.853 −1.20656
\(131\) 12.1753i 0.0929415i 0.998920 + 0.0464708i \(0.0147974\pi\)
−0.998920 + 0.0464708i \(0.985203\pi\)
\(132\) 6.08767i 0.0461187i
\(133\) −73.0294 143.955i −0.549094 1.08237i
\(134\) −86.2254 −0.643473
\(135\) 30.7279 0.227614
\(136\) 66.4123i 0.488326i
\(137\) 165.765 1.20996 0.604980 0.796241i \(-0.293181\pi\)
0.604980 + 0.796241i \(0.293181\pi\)
\(138\) 45.8739i 0.332419i
\(139\) 220.514i 1.58643i −0.608941 0.793215i \(-0.708406\pi\)
0.608941 0.793215i \(-0.291594\pi\)
\(140\) −37.4558 73.8329i −0.267542 0.527378i
\(141\) 67.0294 0.475386
\(142\) 156.426 1.10159
\(143\) 32.9600i 0.230489i
\(144\) −12.0000 −0.0833333
\(145\) 177.408i 1.22350i
\(146\) 80.2687i 0.549786i
\(147\) −68.4853 50.1275i −0.465886 0.341003i
\(148\) −141.823 −0.958266
\(149\) 210.853 1.41512 0.707560 0.706653i \(-0.249796\pi\)
0.707560 + 0.706653i \(0.249796\pi\)
\(150\) 24.4228i 0.162819i
\(151\) −72.3675 −0.479255 −0.239628 0.970865i \(-0.577025\pi\)
−0.239628 + 0.970865i \(0.577025\pi\)
\(152\) 65.2236i 0.429103i
\(153\) 70.4409i 0.460398i
\(154\) 15.5147 7.87071i 0.100745 0.0511085i
\(155\) 50.9117 0.328463
\(156\) 64.9706 0.416478
\(157\) 233.674i 1.48837i 0.667974 + 0.744184i \(0.267162\pi\)
−0.667974 + 0.744184i \(0.732838\pi\)
\(158\) 98.7452 0.624969
\(159\) 64.1369i 0.403377i
\(160\) 33.4523i 0.209077i
\(161\) 116.912 59.3100i 0.726160 0.368385i
\(162\) −12.7279 −0.0785674
\(163\) −73.0883 −0.448395 −0.224197 0.974544i \(-0.571976\pi\)
−0.224197 + 0.974544i \(0.571976\pi\)
\(164\) 82.7903i 0.504819i
\(165\) 18.0000 0.109091
\(166\) 9.10164i 0.0548292i
\(167\) 39.3958i 0.235903i −0.993019 0.117951i \(-0.962367\pi\)
0.993019 0.117951i \(-0.0376327\pi\)
\(168\) 15.5147 + 30.5826i 0.0923495 + 0.182039i
\(169\) −182.765 −1.08145
\(170\) −196.368 −1.15510
\(171\) 69.1801i 0.404562i
\(172\) 20.8528 0.121237
\(173\) 23.8284i 0.137737i 0.997626 + 0.0688683i \(0.0219388\pi\)
−0.997626 + 0.0688683i \(0.978061\pi\)
\(174\) 73.4847i 0.422326i
\(175\) −62.2426 + 31.5761i −0.355672 + 0.180435i
\(176\) −7.02944 −0.0399400
\(177\) −168.853 −0.953971
\(178\) 59.5263i 0.334417i
\(179\) −12.9045 −0.0720924 −0.0360462 0.999350i \(-0.511476\pi\)
−0.0360462 + 0.999350i \(0.511476\pi\)
\(180\) 35.4815i 0.197120i
\(181\) 65.3678i 0.361148i 0.983561 + 0.180574i \(0.0577955\pi\)
−0.983561 + 0.180574i \(0.942204\pi\)
\(182\) −84.0000 165.581i −0.461538 0.909783i
\(183\) 28.9706 0.158309
\(184\) −52.9706 −0.287883
\(185\) 419.343i 2.26672i
\(186\) −21.0883 −0.113378
\(187\) 41.2633i 0.220659i
\(188\) 77.3989i 0.411696i
\(189\) 16.4558 + 32.4377i 0.0870680 + 0.171628i
\(190\) 192.853 1.01501
\(191\) −100.066 −0.523906 −0.261953 0.965081i \(-0.584367\pi\)
−0.261953 + 0.965081i \(0.584367\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) 78.9117 0.408869 0.204434 0.978880i \(-0.434464\pi\)
0.204434 + 0.978880i \(0.434464\pi\)
\(194\) 73.1365i 0.376992i
\(195\) 192.105i 0.985152i
\(196\) 57.8823 79.0800i 0.295318 0.403469i
\(197\) −183.941 −0.933711 −0.466856 0.884334i \(-0.654613\pi\)
−0.466856 + 0.884334i \(0.654613\pi\)
\(198\) −7.45584 −0.0376558
\(199\) 170.029i 0.854419i 0.904153 + 0.427210i \(0.140503\pi\)
−0.904153 + 0.427210i \(0.859497\pi\)
\(200\) 28.2010 0.141005
\(201\) 105.604i 0.525394i
\(202\) 9.34783i 0.0462764i
\(203\) 187.279 95.0079i 0.922558 0.468019i
\(204\) 81.3381 0.398716
\(205\) 244.794 1.19412
\(206\) 248.719i 1.20737i
\(207\) −56.1838 −0.271419
\(208\) 75.0215i 0.360680i
\(209\) 40.5247i 0.193898i
\(210\) 90.4264 45.8739i 0.430602 0.218447i
\(211\) 21.5736 0.102245 0.0511223 0.998692i \(-0.483720\pi\)
0.0511223 + 0.998692i \(0.483720\pi\)
\(212\) −74.0589 −0.349334
\(213\) 191.582i 0.899448i
\(214\) 65.3970 0.305593
\(215\) 61.6575i 0.286779i
\(216\) 14.6969i 0.0680414i
\(217\) 27.2649 + 53.7446i 0.125645 + 0.247671i
\(218\) 50.8284 0.233158
\(219\) −98.3087 −0.448898
\(220\) 20.7846i 0.0944755i
\(221\) −440.382 −1.99268
\(222\) 173.697i 0.782421i
\(223\) 119.359i 0.535240i −0.963525 0.267620i \(-0.913763\pi\)
0.963525 0.267620i \(-0.0862372\pi\)
\(224\) −35.3137 + 17.9149i −0.157650 + 0.0799770i
\(225\) 29.9117 0.132941
\(226\) 103.279 0.456988
\(227\) 169.843i 0.748207i −0.927387 0.374103i \(-0.877951\pi\)
0.927387 0.374103i \(-0.122049\pi\)
\(228\) −79.8823 −0.350361
\(229\) 110.011i 0.480396i −0.970724 0.240198i \(-0.922788\pi\)
0.970724 0.240198i \(-0.0772124\pi\)
\(230\) 156.623i 0.680970i
\(231\) 9.63961 + 19.0016i 0.0417299 + 0.0822579i
\(232\) −84.8528 −0.365745
\(233\) 57.2649 0.245772 0.122886 0.992421i \(-0.460785\pi\)
0.122886 + 0.992421i \(0.460785\pi\)
\(234\) 79.5724i 0.340053i
\(235\) 228.853 0.973842
\(236\) 194.974i 0.826163i
\(237\) 120.938i 0.510285i
\(238\) −105.161 207.294i −0.441855 0.870983i
\(239\) 281.522 1.17792 0.588958 0.808164i \(-0.299538\pi\)
0.588958 + 0.808164i \(0.299538\pi\)
\(240\) −40.9706 −0.170711
\(241\) 168.306i 0.698366i 0.937055 + 0.349183i \(0.113541\pi\)
−0.937055 + 0.349183i \(0.886459\pi\)
\(242\) 166.752 0.689059
\(243\) 15.5885i 0.0641500i
\(244\) 33.4523i 0.137100i
\(245\) −233.823 171.146i −0.954381 0.698555i
\(246\) −101.397 −0.412183
\(247\) 432.500 1.75101
\(248\) 24.3507i 0.0981882i
\(249\) 11.1472 0.0447678
\(250\) 125.692i 0.502770i
\(251\) 106.096i 0.422695i 0.977411 + 0.211348i \(0.0677852\pi\)
−0.977411 + 0.211348i \(0.932215\pi\)
\(252\) −37.4558 + 19.0016i −0.148634 + 0.0754031i
\(253\) −32.9117 −0.130086
\(254\) −127.196 −0.500771
\(255\) 240.500i 0.943138i
\(256\) 16.0000 0.0625000
\(257\) 290.462i 1.13020i −0.825021 0.565102i \(-0.808837\pi\)
0.825021 0.565102i \(-0.191163\pi\)
\(258\) 25.5394i 0.0989898i
\(259\) −442.676 + 224.572i −1.70917 + 0.867074i
\(260\) 221.823 0.853167
\(261\) −90.0000 −0.344828
\(262\) 17.2185i 0.0657196i
\(263\) −89.0223 −0.338488 −0.169244 0.985574i \(-0.554133\pi\)
−0.169244 + 0.985574i \(0.554133\pi\)
\(264\) 8.60927i 0.0326109i
\(265\) 218.977i 0.826328i
\(266\) 103.279 + 203.584i 0.388268 + 0.765352i
\(267\) −72.9045 −0.273051
\(268\) 121.941 0.455004
\(269\) 191.498i 0.711888i 0.934507 + 0.355944i \(0.115841\pi\)
−0.934507 + 0.355944i \(0.884159\pi\)
\(270\) −43.4558 −0.160948
\(271\) 217.440i 0.802362i −0.915999 0.401181i \(-0.868600\pi\)
0.915999 0.401181i \(-0.131400\pi\)
\(272\) 93.9211i 0.345298i
\(273\) 202.794 102.879i 0.742835 0.376845i
\(274\) −234.426 −0.855571
\(275\) 17.5219 0.0637159
\(276\) 64.8754i 0.235056i
\(277\) 290.676 1.04937 0.524686 0.851296i \(-0.324183\pi\)
0.524686 + 0.851296i \(0.324183\pi\)
\(278\) 311.854i 1.12178i
\(279\) 25.8278i 0.0925728i
\(280\) 52.9706 + 104.415i 0.189181 + 0.372912i
\(281\) 18.8528 0.0670919 0.0335459 0.999437i \(-0.489320\pi\)
0.0335459 + 0.999437i \(0.489320\pi\)
\(282\) −94.7939 −0.336149
\(283\) 401.734i 1.41955i −0.704426 0.709777i \(-0.748796\pi\)
0.704426 0.709777i \(-0.251204\pi\)
\(284\) −221.220 −0.778945
\(285\) 236.195i 0.828756i
\(286\) 46.6124i 0.162980i
\(287\) 131.095 + 258.415i 0.456779 + 0.900401i
\(288\) 16.9706 0.0589256
\(289\) −262.324 −0.907695
\(290\) 250.892i 0.865146i
\(291\) 89.5736 0.307813
\(292\) 113.517i 0.388757i
\(293\) 280.893i 0.958679i −0.877629 0.479340i \(-0.840876\pi\)
0.877629 0.479340i \(-0.159124\pi\)
\(294\) 96.8528 + 70.8910i 0.329431 + 0.241126i
\(295\) −576.500 −1.95424
\(296\) 200.569 0.677596
\(297\) 9.13151i 0.0307458i
\(298\) −298.191 −1.00064
\(299\) 351.249i 1.17475i
\(300\) 34.5390i 0.115130i
\(301\) 65.0883 33.0197i 0.216240 0.109700i
\(302\) 102.343 0.338885
\(303\) 11.4487 0.0377845
\(304\) 92.2401i 0.303421i
\(305\) 98.9117 0.324301
\(306\) 99.6184i 0.325550i
\(307\) 152.318i 0.496151i 0.968741 + 0.248076i \(0.0797982\pi\)
−0.968741 + 0.248076i \(0.920202\pi\)
\(308\) −21.9411 + 11.1309i −0.0712374 + 0.0361392i
\(309\) 304.617 0.985817
\(310\) −72.0000 −0.232258
\(311\) 283.156i 0.910470i −0.890371 0.455235i \(-0.849555\pi\)
0.890371 0.455235i \(-0.150445\pi\)
\(312\) −91.8823 −0.294494
\(313\) 48.5819i 0.155214i 0.996984 + 0.0776069i \(0.0247279\pi\)
−0.996984 + 0.0776069i \(0.975272\pi\)
\(314\) 330.465i 1.05244i
\(315\) 56.1838 + 110.749i 0.178361 + 0.351585i
\(316\) −139.647 −0.441920
\(317\) −578.029 −1.82343 −0.911717 0.410819i \(-0.865243\pi\)
−0.911717 + 0.410819i \(0.865243\pi\)
\(318\) 90.7032i 0.285230i
\(319\) −52.7208 −0.165269
\(320\) 47.3087i 0.147840i
\(321\) 80.0946i 0.249516i
\(322\) −165.338 + 83.8770i −0.513472 + 0.260488i
\(323\) 541.456 1.67633
\(324\) 18.0000 0.0555556
\(325\) 187.002i 0.575390i
\(326\) 103.362 0.317063
\(327\) 62.2519i 0.190373i
\(328\) 117.083i 0.356961i
\(329\) 122.558 + 241.587i 0.372518 + 0.734307i
\(330\) −25.4558 −0.0771389
\(331\) 332.368 1.00413 0.502066 0.864829i \(-0.332574\pi\)
0.502066 + 0.864829i \(0.332574\pi\)
\(332\) 12.8717i 0.0387701i
\(333\) 212.735 0.638844
\(334\) 55.7141i 0.166809i
\(335\) 360.555i 1.07628i
\(336\) −21.9411 43.2503i −0.0653010 0.128721i
\(337\) 88.1766 0.261652 0.130826 0.991405i \(-0.458237\pi\)
0.130826 + 0.991405i \(0.458237\pi\)
\(338\) 258.468 0.764698
\(339\) 126.491i 0.373129i
\(340\) 277.706 0.816781
\(341\) 15.1296i 0.0443683i
\(342\) 97.8354i 0.286068i
\(343\) 55.4487 338.488i 0.161658 0.986847i
\(344\) −29.4903 −0.0857277
\(345\) −191.823 −0.556010
\(346\) 33.6985i 0.0973945i
\(347\) −320.080 −0.922422 −0.461211 0.887291i \(-0.652585\pi\)
−0.461211 + 0.887291i \(0.652585\pi\)
\(348\) 103.923i 0.298629i
\(349\) 333.046i 0.954287i −0.878825 0.477143i \(-0.841672\pi\)
0.878825 0.477143i \(-0.158328\pi\)
\(350\) 88.0244 44.6553i 0.251498 0.127587i
\(351\) −97.4558 −0.277652
\(352\) 9.94113 0.0282418
\(353\) 655.712i 1.85754i −0.370654 0.928771i \(-0.620866\pi\)
0.370654 0.928771i \(-0.379134\pi\)
\(354\) 238.794 0.674559
\(355\) 654.103i 1.84254i
\(356\) 84.1829i 0.236469i
\(357\) 253.882 128.796i 0.711155 0.360773i
\(358\) 18.2498 0.0509770
\(359\) −97.7574 −0.272305 −0.136152 0.990688i \(-0.543474\pi\)
−0.136152 + 0.990688i \(0.543474\pi\)
\(360\) 50.1785i 0.139385i
\(361\) −170.765 −0.473032
\(362\) 92.4440i 0.255370i
\(363\) 204.229i 0.562614i
\(364\) 118.794 + 234.166i 0.326357 + 0.643314i
\(365\) −335.647 −0.919580
\(366\) −40.9706 −0.111941
\(367\) 321.057i 0.874815i −0.899263 0.437408i \(-0.855897\pi\)
0.899263 0.437408i \(-0.144103\pi\)
\(368\) 74.9117 0.203564
\(369\) 124.185i 0.336546i
\(370\) 593.040i 1.60281i
\(371\) −231.161 + 117.270i −0.623077 + 0.316091i
\(372\) 29.8234 0.0801704
\(373\) 187.470 0.502601 0.251300 0.967909i \(-0.419142\pi\)
0.251300 + 0.967909i \(0.419142\pi\)
\(374\) 58.3551i 0.156030i
\(375\) −153.941 −0.410510
\(376\) 109.459i 0.291113i
\(377\) 562.662i 1.49247i
\(378\) −23.2721 45.8739i −0.0615663 0.121359i
\(379\) −357.103 −0.942223 −0.471112 0.882074i \(-0.656147\pi\)
−0.471112 + 0.882074i \(0.656147\pi\)
\(380\) −272.735 −0.717724
\(381\) 155.783i 0.408878i
\(382\) 141.515 0.370457
\(383\) 622.230i 1.62462i 0.583225 + 0.812311i \(0.301791\pi\)
−0.583225 + 0.812311i \(0.698209\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 32.9117 + 64.8754i 0.0854849 + 0.168508i
\(386\) −111.598 −0.289114
\(387\) −31.2792 −0.0808249
\(388\) 103.431i 0.266574i
\(389\) 227.470 0.584756 0.292378 0.956303i \(-0.405553\pi\)
0.292378 + 0.956303i \(0.405553\pi\)
\(390\) 271.677i 0.696608i
\(391\) 439.737i 1.12465i
\(392\) −81.8579 + 111.836i −0.208821 + 0.285296i
\(393\) 21.0883 0.0536598
\(394\) 260.132 0.660234
\(395\) 412.907i 1.04533i
\(396\) 10.5442 0.0266267
\(397\) 720.329i 1.81443i 0.420666 + 0.907216i \(0.361796\pi\)
−0.420666 + 0.907216i \(0.638204\pi\)
\(398\) 240.458i 0.604166i
\(399\) −249.338 + 126.491i −0.624908 + 0.317019i
\(400\) −39.8823 −0.0997056
\(401\) 697.176 1.73859 0.869296 0.494291i \(-0.164572\pi\)
0.869296 + 0.494291i \(0.164572\pi\)
\(402\) 149.347i 0.371509i
\(403\) −161.470 −0.400670
\(404\) 13.2198i 0.0327223i
\(405\) 53.2223i 0.131413i
\(406\) −264.853 + 134.361i −0.652347 + 0.330939i
\(407\) 124.617 0.306185
\(408\) −115.029 −0.281935
\(409\) 102.386i 0.250333i 0.992136 + 0.125166i \(0.0399465\pi\)
−0.992136 + 0.125166i \(0.960053\pi\)
\(410\) −346.191 −0.844368
\(411\) 287.113i 0.698571i
\(412\) 351.742i 0.853742i
\(413\) −308.735 608.578i −0.747543 1.47355i
\(414\) 79.4558 0.191922
\(415\) 38.0589 0.0917081
\(416\) 106.096i 0.255040i
\(417\) −381.941 −0.915926
\(418\) 57.3106i 0.137107i
\(419\) 391.426i 0.934191i 0.884207 + 0.467095i \(0.154700\pi\)
−0.884207 + 0.467095i \(0.845300\pi\)
\(420\) −127.882 + 64.8754i −0.304482 + 0.154465i
\(421\) 354.441 0.841902 0.420951 0.907083i \(-0.361696\pi\)
0.420951 + 0.907083i \(0.361696\pi\)
\(422\) −30.5097 −0.0722978
\(423\) 116.098i 0.274464i
\(424\) 104.735 0.247017
\(425\) 234.112i 0.550851i
\(426\) 270.938i 0.636006i
\(427\) 52.9706 + 104.415i 0.124053 + 0.244533i
\(428\) −92.4853 −0.216087
\(429\) −57.0883 −0.133073
\(430\) 87.1969i 0.202783i
\(431\) 585.286 1.35797 0.678987 0.734151i \(-0.262419\pi\)
0.678987 + 0.734151i \(0.262419\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 392.207i 0.905789i −0.891564 0.452895i \(-0.850391\pi\)
0.891564 0.452895i \(-0.149609\pi\)
\(434\) −38.5584 76.0063i −0.0888443 0.175130i
\(435\) −307.279 −0.706389
\(436\) −71.8823 −0.164868
\(437\) 431.866i 0.988252i
\(438\) 139.029 0.317419
\(439\) 392.513i 0.894106i −0.894507 0.447053i \(-0.852473\pi\)
0.894507 0.447053i \(-0.147527\pi\)
\(440\) 29.3939i 0.0668043i
\(441\) −86.8234 + 118.620i −0.196878 + 0.268980i
\(442\) 622.794 1.40904
\(443\) −814.742 −1.83915 −0.919574 0.392918i \(-0.871466\pi\)
−0.919574 + 0.392918i \(0.871466\pi\)
\(444\) 245.645i 0.553255i
\(445\) −248.912 −0.559352
\(446\) 168.798i 0.378472i
\(447\) 365.208i 0.817020i
\(448\) 49.9411 25.3354i 0.111476 0.0565523i
\(449\) 180.323 0.401610 0.200805 0.979631i \(-0.435644\pi\)
0.200805 + 0.979631i \(0.435644\pi\)
\(450\) −42.3015 −0.0940034
\(451\) 72.7461i 0.161300i
\(452\) −146.059 −0.323139
\(453\) 125.344i 0.276698i
\(454\) 240.194i 0.529062i
\(455\) 692.382 351.249i 1.52172 0.771977i
\(456\) 112.971 0.247742
\(457\) 280.177 0.613078 0.306539 0.951858i \(-0.400829\pi\)
0.306539 + 0.951858i \(0.400829\pi\)
\(458\) 155.579i 0.339691i
\(459\) −122.007 −0.265811
\(460\) 221.499i 0.481519i
\(461\) 406.297i 0.881338i 0.897670 + 0.440669i \(0.145259\pi\)
−0.897670 + 0.440669i \(0.854741\pi\)
\(462\) −13.6325 26.8723i −0.0295075 0.0581651i
\(463\) 457.470 0.988056 0.494028 0.869446i \(-0.335524\pi\)
0.494028 + 0.869446i \(0.335524\pi\)
\(464\) 120.000 0.258621
\(465\) 88.1816i 0.189638i
\(466\) −80.9848 −0.173787
\(467\) 643.711i 1.37840i −0.724573 0.689198i \(-0.757963\pi\)
0.724573 0.689198i \(-0.242037\pi\)
\(468\) 112.532i 0.240454i
\(469\) 380.617 193.089i 0.811551 0.411705i
\(470\) −323.647 −0.688610
\(471\) 404.735 0.859310
\(472\) 275.735i 0.584185i
\(473\) −18.3229 −0.0387377
\(474\) 171.032i 0.360826i
\(475\) 229.921i 0.484045i
\(476\) 148.721 + 293.158i 0.312439 + 0.615878i
\(477\) 111.088 0.232890
\(478\) −398.132 −0.832912
\(479\) 168.535i 0.351847i 0.984404 + 0.175924i \(0.0562912\pi\)
−0.984404 + 0.175924i \(0.943709\pi\)
\(480\) 57.9411 0.120711
\(481\) 1329.98i 2.76502i
\(482\) 238.021i 0.493819i
\(483\) −102.728 202.497i −0.212687 0.419248i
\(484\) −235.823 −0.487238
\(485\) 305.823 0.630564
\(486\) 22.0454i 0.0453609i
\(487\) −2.77965 −0.00570771 −0.00285385 0.999996i \(-0.500908\pi\)
−0.00285385 + 0.999996i \(0.500908\pi\)
\(488\) 47.3087i 0.0969441i
\(489\) 126.593i 0.258881i
\(490\) 330.676 + 242.037i 0.674849 + 0.493953i
\(491\) −247.477 −0.504027 −0.252014 0.967724i \(-0.581093\pi\)
−0.252014 + 0.967724i \(0.581093\pi\)
\(492\) 143.397 0.291457
\(493\) 704.409i 1.42882i
\(494\) −611.647 −1.23815
\(495\) 31.1769i 0.0629837i
\(496\) 34.4371i 0.0694296i
\(497\) −690.500 + 350.295i −1.38934 + 0.704818i
\(498\) −15.7645 −0.0316556
\(499\) −483.426 −0.968789 −0.484394 0.874850i \(-0.660960\pi\)
−0.484394 + 0.874850i \(0.660960\pi\)
\(500\) 177.756i 0.355512i
\(501\) −68.2355 −0.136199
\(502\) 150.043i 0.298891i
\(503\) 58.7033i 0.116706i 0.998296 + 0.0583532i \(0.0185849\pi\)
−0.998296 + 0.0583532i \(0.981415\pi\)
\(504\) 52.9706 26.8723i 0.105100 0.0533180i
\(505\) 39.0883 0.0774026
\(506\) 46.5442 0.0919845
\(507\) 316.557i 0.624374i
\(508\) 179.882 0.354099
\(509\) 68.8793i 0.135323i 0.997708 + 0.0676614i \(0.0215537\pi\)
−0.997708 + 0.0676614i \(0.978446\pi\)
\(510\) 340.119i 0.666899i
\(511\) −179.750 354.323i −0.351762 0.693392i
\(512\) −22.6274 −0.0441942
\(513\) 119.823 0.233574
\(514\) 410.776i 0.799175i
\(515\) 1040.03 2.01947
\(516\) 36.1181i 0.0699964i
\(517\) 68.0089i 0.131545i
\(518\) 626.039 317.593i 1.20857 0.613114i
\(519\) 41.2721 0.0795223
\(520\) −313.706 −0.603280
\(521\) 292.720i 0.561843i 0.959731 + 0.280922i \(0.0906401\pi\)
−0.959731 + 0.280922i \(0.909360\pi\)
\(522\) 127.279 0.243830
\(523\) 493.056i 0.942746i 0.881934 + 0.471373i \(0.156241\pi\)
−0.881934 + 0.471373i \(0.843759\pi\)
\(524\) 24.3507i 0.0464708i
\(525\) 54.6913 + 107.807i 0.104174 + 0.205347i
\(526\) 125.897 0.239347
\(527\) −202.148 −0.383583
\(528\) 12.1753i 0.0230594i
\(529\) −178.265 −0.336985
\(530\) 309.680i 0.584302i
\(531\) 292.462i 0.550775i
\(532\) −146.059 287.911i −0.274547 0.541186i
\(533\) −776.382 −1.45663
\(534\) 103.103 0.193076
\(535\) 273.460i 0.511140i
\(536\) −172.451 −0.321737
\(537\) 22.3513i 0.0416226i
\(538\) 270.819i 0.503381i
\(539\) −50.8600 + 69.4860i −0.0943598 + 0.128916i
\(540\) 61.4558 0.113807
\(541\) −1037.85 −1.91840 −0.959198 0.282736i \(-0.908758\pi\)
−0.959198 + 0.282736i \(0.908758\pi\)
\(542\) 307.507i 0.567356i
\(543\) 113.220 0.208509
\(544\) 132.825i 0.244163i
\(545\) 212.541i 0.389984i
\(546\) −286.794 + 145.492i −0.525264 + 0.266469i
\(547\) −130.530 −0.238629 −0.119314 0.992857i \(-0.538070\pi\)
−0.119314 + 0.992857i \(0.538070\pi\)
\(548\) 331.529 0.604980
\(549\) 50.1785i 0.0913998i
\(550\) −24.7797 −0.0450539
\(551\) 691.801i 1.25554i
\(552\) 91.7477i 0.166210i
\(553\) −435.882 + 221.126i −0.788214 + 0.399866i
\(554\) −411.078 −0.742018
\(555\) 726.323 1.30869
\(556\) 441.028i 0.793215i
\(557\) 665.147 1.19416 0.597080 0.802182i \(-0.296327\pi\)
0.597080 + 0.802182i \(0.296327\pi\)
\(558\) 36.5260i 0.0654588i
\(559\) 195.551i 0.349823i
\(560\) −74.9117 147.666i −0.133771 0.263689i
\(561\) −71.4701 −0.127398
\(562\) −26.6619 −0.0474411
\(563\) 829.295i 1.47299i 0.676441 + 0.736497i \(0.263521\pi\)
−0.676441 + 0.736497i \(0.736479\pi\)
\(564\) 134.059 0.237693
\(565\) 431.866i 0.764365i
\(566\) 568.137i 1.00378i
\(567\) 56.1838 28.5024i 0.0990895 0.0502687i
\(568\) 312.853 0.550797
\(569\) 706.971 1.24248 0.621240 0.783621i \(-0.286629\pi\)
0.621240 + 0.783621i \(0.286629\pi\)
\(570\) 334.031i 0.586019i
\(571\) −366.912 −0.642577 −0.321289 0.946981i \(-0.604116\pi\)
−0.321289 + 0.946981i \(0.604116\pi\)
\(572\) 65.9199i 0.115245i
\(573\) 173.319i 0.302477i
\(574\) −185.397 365.454i −0.322991 0.636679i
\(575\) −186.728 −0.324744
\(576\) −24.0000 −0.0416667
\(577\) 390.357i 0.676528i −0.941051 0.338264i \(-0.890160\pi\)
0.941051 0.338264i \(-0.109840\pi\)
\(578\) 370.982 0.641837
\(579\) 136.679i 0.236061i
\(580\) 354.815i 0.611751i
\(581\) 20.3818 + 40.1766i 0.0350806 + 0.0691507i
\(582\) −126.676 −0.217657
\(583\) 65.0740 0.111619
\(584\) 160.537i 0.274893i
\(585\) −332.735 −0.568778
\(586\) 397.243i 0.677889i
\(587\) 702.499i 1.19676i −0.801212 0.598381i \(-0.795811\pi\)
0.801212 0.598381i \(-0.204189\pi\)
\(588\) −136.971 100.255i −0.232943 0.170502i
\(589\) 198.530 0.337063
\(590\) 815.294 1.38185
\(591\) 318.595i 0.539078i
\(592\) −283.647 −0.479133
\(593\) 942.519i 1.58941i 0.606997 + 0.794704i \(0.292374\pi\)
−0.606997 + 0.794704i \(0.707626\pi\)
\(594\) 12.9139i 0.0217406i
\(595\) 866.808 439.737i 1.45682 0.739054i
\(596\) 421.706 0.707560
\(597\) 294.500 0.493299
\(598\) 496.742i 0.830672i
\(599\) −952.109 −1.58950 −0.794749 0.606939i \(-0.792397\pi\)
−0.794749 + 0.606939i \(0.792397\pi\)
\(600\) 48.8456i 0.0814093i
\(601\) 729.804i 1.21432i 0.794581 + 0.607158i \(0.207690\pi\)
−0.794581 + 0.607158i \(0.792310\pi\)
\(602\) −92.0488 + 46.6969i −0.152905 + 0.0775696i
\(603\) −182.912 −0.303336
\(604\) −144.735 −0.239628
\(605\) 697.282i 1.15253i
\(606\) −16.1909 −0.0267177
\(607\) 1006.34i 1.65789i −0.559332 0.828944i \(-0.688942\pi\)
0.559332 0.828944i \(-0.311058\pi\)
\(608\) 130.447i 0.214551i
\(609\) −164.558 324.377i −0.270211 0.532639i
\(610\) −139.882 −0.229315
\(611\) −725.823 −1.18793
\(612\) 140.882i 0.230199i
\(613\) −199.588 −0.325592 −0.162796 0.986660i \(-0.552051\pi\)
−0.162796 + 0.986660i \(0.552051\pi\)
\(614\) 215.411i 0.350832i
\(615\) 423.996i 0.689424i
\(616\) 31.0294 15.7414i 0.0503725 0.0255542i
\(617\) −353.294 −0.572599 −0.286299 0.958140i \(-0.592425\pi\)
−0.286299 + 0.958140i \(0.592425\pi\)
\(618\) −430.794 −0.697078
\(619\) 56.2064i 0.0908020i −0.998969 0.0454010i \(-0.985543\pi\)
0.998969 0.0454010i \(-0.0144566\pi\)
\(620\) 101.823 0.164231
\(621\) 97.3131i 0.156704i
\(622\) 400.443i 0.643799i
\(623\) −133.301 262.762i −0.213966 0.421769i
\(624\) 129.941 0.208239
\(625\) −774.852 −1.23976
\(626\) 68.7052i 0.109753i
\(627\) 70.1909 0.111947
\(628\) 467.348i 0.744184i
\(629\) 1665.03i 2.64710i
\(630\) −79.4558 156.623i −0.126120 0.248608i
\(631\) 807.322 1.27943 0.639716 0.768611i \(-0.279052\pi\)
0.639716 + 0.768611i \(0.279052\pi\)
\(632\) 197.490 0.312485
\(633\) 37.3666i 0.0590309i
\(634\) 817.456 1.28936
\(635\) 531.875i 0.837599i
\(636\) 128.274i 0.201688i
\(637\) 741.588 + 542.802i 1.16419 + 0.852122i
\(638\) 74.5584 0.116863
\(639\) 331.831 0.519297
\(640\) 66.9046i 0.104539i
\(641\) 1016.35 1.58557 0.792786 0.609500i \(-0.208630\pi\)
0.792786 + 0.609500i \(0.208630\pi\)
\(642\) 113.271i 0.176434i
\(643\) 404.688i 0.629375i −0.949195 0.314687i \(-0.898100\pi\)
0.949195 0.314687i \(-0.101900\pi\)
\(644\) 233.823 118.620i 0.363080 0.184193i
\(645\) −106.794 −0.165572
\(646\) −765.734 −1.18535
\(647\) 940.604i 1.45379i −0.686747 0.726896i \(-0.740962\pi\)
0.686747 0.726896i \(-0.259038\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 171.320i 0.263975i
\(650\) 264.460i 0.406862i
\(651\) 93.0883 47.2243i 0.142993 0.0725411i
\(652\) −146.177 −0.224197
\(653\) 731.970 1.12093 0.560467 0.828177i \(-0.310622\pi\)
0.560467 + 0.828177i \(0.310622\pi\)
\(654\) 88.0374i 0.134614i
\(655\) 72.0000 0.109924
\(656\) 165.581i 0.252409i
\(657\) 170.276i 0.259171i
\(658\) −173.324 341.655i −0.263410 0.519233i
\(659\) 904.316 1.37225 0.686127 0.727481i \(-0.259309\pi\)
0.686127 + 0.727481i \(0.259309\pi\)
\(660\) 36.0000 0.0545455
\(661\) 335.881i 0.508141i −0.967186 0.254070i \(-0.918231\pi\)
0.967186 0.254070i \(-0.0817695\pi\)
\(662\) −470.039 −0.710028
\(663\) 762.764i 1.15047i
\(664\) 18.2033i 0.0274146i
\(665\) −851.294 + 431.866i −1.28014 + 0.649423i
\(666\) −300.853 −0.451731
\(667\) 561.838 0.842335
\(668\) 78.7916i 0.117951i
\(669\) −206.735 −0.309021
\(670\) 509.902i 0.761047i
\(671\) 29.3939i 0.0438061i
\(672\) 31.0294 + 61.1651i 0.0461748 + 0.0910195i
\(673\) 1191.44 1.77034 0.885171 0.465266i \(-0.154041\pi\)
0.885171 + 0.465266i \(0.154041\pi\)
\(674\) −124.701 −0.185016
\(675\) 51.8086i 0.0767534i
\(676\) −365.529 −0.540723
\(677\) 1211.07i 1.78888i 0.447186 + 0.894441i \(0.352426\pi\)
−0.447186 + 0.894441i \(0.647574\pi\)
\(678\) 178.885i 0.263842i
\(679\) 163.779 + 322.840i 0.241206 + 0.475464i
\(680\) −392.735 −0.577552
\(681\) −294.177 −0.431977
\(682\) 21.3965i 0.0313731i
\(683\) −1233.89 −1.80657 −0.903287 0.429038i \(-0.858853\pi\)
−0.903287 + 0.429038i \(0.858853\pi\)
\(684\) 138.360i 0.202281i
\(685\) 980.264i 1.43104i
\(686\) −78.4163 + 478.695i −0.114309 + 0.697806i
\(687\) −190.544 −0.277357
\(688\) 41.7056 0.0606186
\(689\) 694.501i 1.00798i
\(690\) 271.279 0.393158
\(691\) 86.7045i 0.125477i −0.998030 0.0627384i \(-0.980017\pi\)
0.998030 0.0627384i \(-0.0199834\pi\)
\(692\) 47.6569i 0.0688683i
\(693\) 32.9117 16.6963i 0.0474916 0.0240928i
\(694\) 452.662 0.652251
\(695\) −1304.03 −1.87630
\(696\) 146.969i 0.211163i
\(697\) −971.970 −1.39450
\(698\) 470.998i 0.674783i
\(699\) 99.1858i 0.141897i
\(700\) −124.485 + 63.1521i −0.177836 + 0.0902173i
\(701\) −149.147 −0.212763 −0.106382 0.994325i \(-0.533927\pi\)
−0.106382 + 0.994325i \(0.533927\pi\)
\(702\) 137.823 0.196330
\(703\) 1635.22i 2.32607i
\(704\) −14.0589 −0.0199700
\(705\) 396.385i 0.562248i
\(706\) 927.317i 1.31348i
\(707\) 20.9331 + 41.2633i 0.0296084 + 0.0583639i
\(708\) −337.706 −0.476985
\(709\) 189.647 0.267485 0.133742 0.991016i \(-0.457301\pi\)
0.133742 + 0.991016i \(0.457301\pi\)
\(710\) 925.042i 1.30288i
\(711\) 209.470 0.294613
\(712\) 119.053i 0.167209i
\(713\) 161.234i 0.226134i
\(714\) −359.044 + 182.145i −0.502862 + 0.255105i
\(715\) −194.912 −0.272604
\(716\) −25.8091 −0.0360462
\(717\) 487.610i 0.680070i
\(718\) 138.250 0.192548
\(719\) 12.0064i 0.0166987i −0.999965 0.00834937i \(-0.997342\pi\)
0.999965 0.00834937i \(-0.00265772\pi\)
\(720\) 70.9631i 0.0985599i
\(721\) 556.971 + 1097.90i 0.772497 + 1.52274i
\(722\) 241.497 0.334484
\(723\) 291.515 0.403202
\(724\) 130.736i 0.180574i
\(725\) −299.117 −0.412575
\(726\) 288.823i 0.397828i
\(727\) 417.169i 0.573823i −0.957957 0.286911i \(-0.907371\pi\)
0.957957 0.286911i \(-0.0926286\pi\)
\(728\) −168.000 331.161i −0.230769 0.454892i
\(729\) −27.0000 −0.0370370
\(730\) 474.676 0.650241
\(731\) 244.815i 0.334904i
\(732\) 57.9411 0.0791545
\(733\) 1286.99i 1.75578i 0.478859 + 0.877892i \(0.341051\pi\)
−0.478859 + 0.877892i \(0.658949\pi\)
\(734\) 454.043i 0.618588i
\(735\) −296.434 + 404.994i −0.403311 + 0.551012i
\(736\) −105.941 −0.143942
\(737\) −107.147 −0.145383
\(738\) 175.625i 0.237974i
\(739\) 1333.47 1.80443 0.902213 0.431292i \(-0.141942\pi\)
0.902213 + 0.431292i \(0.141942\pi\)
\(740\) 838.685i 1.13336i
\(741\) 749.111i 1.01095i
\(742\) 326.912 165.844i 0.440582 0.223510i
\(743\) −776.476 −1.04506 −0.522528 0.852622i \(-0.675011\pi\)
−0.522528 + 0.852622i \(0.675011\pi\)
\(744\) −42.1766 −0.0566890
\(745\) 1246.90i 1.67369i
\(746\) −265.123 −0.355392
\(747\) 19.3075i 0.0258467i
\(748\) 82.5266i 0.110330i
\(749\) −288.676 + 146.447i −0.385415 + 0.195524i
\(750\) 217.706 0.290274
\(751\) 48.8385 0.0650313 0.0325157 0.999471i \(-0.489648\pi\)
0.0325157 + 0.999471i \(0.489648\pi\)
\(752\) 154.798i 0.205848i
\(753\) 183.765 0.244043
\(754\) 795.724i 1.05534i
\(755\) 427.952i 0.566824i
\(756\) 32.9117 + 64.8754i 0.0435340 + 0.0858141i
\(757\) −1279.47 −1.69019 −0.845093 0.534620i \(-0.820455\pi\)
−0.845093 + 0.534620i \(0.820455\pi\)
\(758\) 505.019 0.666252
\(759\) 57.0047i 0.0751050i
\(760\) 385.706 0.507507
\(761\) 1316.12i 1.72947i −0.502231 0.864734i \(-0.667487\pi\)
0.502231 0.864734i \(-0.332513\pi\)
\(762\) 220.310i 0.289121i
\(763\) −224.368 + 113.823i −0.294060 + 0.149178i
\(764\) −200.132 −0.261953
\(765\) −416.558 −0.544521
\(766\) 879.966i 1.14878i
\(767\) 1828.41 2.38385
\(768\) 27.7128i 0.0360844i
\(769\) 110.324i 0.143464i −0.997424 0.0717320i \(-0.977147\pi\)
0.997424 0.0717320i \(-0.0228526\pi\)
\(770\) −46.5442 91.7477i −0.0604470 0.119153i
\(771\) −503.095 −0.652523
\(772\) 157.823 0.204434
\(773\) 717.634i 0.928375i −0.885737 0.464187i \(-0.846346\pi\)
0.885737 0.464187i \(-0.153654\pi\)
\(774\) 44.2355 0.0571518
\(775\) 85.8392i 0.110760i
\(776\) 146.273i 0.188496i
\(777\) 388.971 + 766.738i 0.500606 + 0.986792i
\(778\) −321.691 −0.413485
\(779\) 954.573 1.22538
\(780\) 384.209i 0.492576i
\(781\) 194.382 0.248888
\(782\) 621.882i 0.795245i
\(783\) 155.885i 0.199086i
\(784\) 115.765 158.160i 0.147659 0.201735i
\(785\) 1381.85 1.76032
\(786\) −29.8234 −0.0379432
\(787\) 347.191i 0.441158i −0.975369 0.220579i \(-0.929205\pi\)
0.975369 0.220579i \(-0.0707946\pi\)