Properties

Label 4030.2.a.n.1.5
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.178838\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.178838 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.178838 q^{6} -4.63233 q^{7} +1.00000 q^{8} -2.96802 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.178838 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.178838 q^{6} -4.63233 q^{7} +1.00000 q^{8} -2.96802 q^{9} -1.00000 q^{10} +5.33531 q^{11} +0.178838 q^{12} -1.00000 q^{13} -4.63233 q^{14} -0.178838 q^{15} +1.00000 q^{16} -6.03643 q^{17} -2.96802 q^{18} -0.663724 q^{19} -1.00000 q^{20} -0.828437 q^{21} +5.33531 q^{22} -1.20734 q^{23} +0.178838 q^{24} +1.00000 q^{25} -1.00000 q^{26} -1.06731 q^{27} -4.63233 q^{28} +7.03585 q^{29} -0.178838 q^{30} -1.00000 q^{31} +1.00000 q^{32} +0.954158 q^{33} -6.03643 q^{34} +4.63233 q^{35} -2.96802 q^{36} +6.84984 q^{37} -0.663724 q^{38} -0.178838 q^{39} -1.00000 q^{40} +7.35666 q^{41} -0.828437 q^{42} +12.4429 q^{43} +5.33531 q^{44} +2.96802 q^{45} -1.20734 q^{46} +0.326660 q^{47} +0.178838 q^{48} +14.4585 q^{49} +1.00000 q^{50} -1.07955 q^{51} -1.00000 q^{52} +12.3242 q^{53} -1.06731 q^{54} -5.33531 q^{55} -4.63233 q^{56} -0.118699 q^{57} +7.03585 q^{58} +10.9205 q^{59} -0.178838 q^{60} -11.0097 q^{61} -1.00000 q^{62} +13.7488 q^{63} +1.00000 q^{64} +1.00000 q^{65} +0.954158 q^{66} -3.23660 q^{67} -6.03643 q^{68} -0.215919 q^{69} +4.63233 q^{70} -9.94396 q^{71} -2.96802 q^{72} +1.10218 q^{73} +6.84984 q^{74} +0.178838 q^{75} -0.663724 q^{76} -24.7149 q^{77} -0.178838 q^{78} +15.7918 q^{79} -1.00000 q^{80} +8.71317 q^{81} +7.35666 q^{82} -8.93682 q^{83} -0.828437 q^{84} +6.03643 q^{85} +12.4429 q^{86} +1.25828 q^{87} +5.33531 q^{88} -0.384321 q^{89} +2.96802 q^{90} +4.63233 q^{91} -1.20734 q^{92} -0.178838 q^{93} +0.326660 q^{94} +0.663724 q^{95} +0.178838 q^{96} -17.7548 q^{97} +14.4585 q^{98} -15.8353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.178838 0.103252 0.0516262 0.998666i \(-0.483560\pi\)
0.0516262 + 0.998666i \(0.483560\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.178838 0.0730104
\(7\) −4.63233 −1.75086 −0.875428 0.483349i \(-0.839420\pi\)
−0.875428 + 0.483349i \(0.839420\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.96802 −0.989339
\(10\) −1.00000 −0.316228
\(11\) 5.33531 1.60866 0.804328 0.594185i \(-0.202525\pi\)
0.804328 + 0.594185i \(0.202525\pi\)
\(12\) 0.178838 0.0516262
\(13\) −1.00000 −0.277350
\(14\) −4.63233 −1.23804
\(15\) −0.178838 −0.0461758
\(16\) 1.00000 0.250000
\(17\) −6.03643 −1.46405 −0.732025 0.681278i \(-0.761425\pi\)
−0.732025 + 0.681278i \(0.761425\pi\)
\(18\) −2.96802 −0.699568
\(19\) −0.663724 −0.152269 −0.0761343 0.997098i \(-0.524258\pi\)
−0.0761343 + 0.997098i \(0.524258\pi\)
\(20\) −1.00000 −0.223607
\(21\) −0.828437 −0.180780
\(22\) 5.33531 1.13749
\(23\) −1.20734 −0.251748 −0.125874 0.992046i \(-0.540174\pi\)
−0.125874 + 0.992046i \(0.540174\pi\)
\(24\) 0.178838 0.0365052
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) −1.06731 −0.205404
\(28\) −4.63233 −0.875428
\(29\) 7.03585 1.30652 0.653262 0.757132i \(-0.273400\pi\)
0.653262 + 0.757132i \(0.273400\pi\)
\(30\) −0.178838 −0.0326513
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 0.954158 0.166098
\(34\) −6.03643 −1.03524
\(35\) 4.63233 0.783006
\(36\) −2.96802 −0.494669
\(37\) 6.84984 1.12611 0.563053 0.826421i \(-0.309627\pi\)
0.563053 + 0.826421i \(0.309627\pi\)
\(38\) −0.663724 −0.107670
\(39\) −0.178838 −0.0286370
\(40\) −1.00000 −0.158114
\(41\) 7.35666 1.14892 0.574459 0.818534i \(-0.305213\pi\)
0.574459 + 0.818534i \(0.305213\pi\)
\(42\) −0.828437 −0.127831
\(43\) 12.4429 1.89753 0.948763 0.315989i \(-0.102336\pi\)
0.948763 + 0.315989i \(0.102336\pi\)
\(44\) 5.33531 0.804328
\(45\) 2.96802 0.442446
\(46\) −1.20734 −0.178013
\(47\) 0.326660 0.0476482 0.0238241 0.999716i \(-0.492416\pi\)
0.0238241 + 0.999716i \(0.492416\pi\)
\(48\) 0.178838 0.0258131
\(49\) 14.4585 2.06549
\(50\) 1.00000 0.141421
\(51\) −1.07955 −0.151167
\(52\) −1.00000 −0.138675
\(53\) 12.3242 1.69286 0.846430 0.532500i \(-0.178747\pi\)
0.846430 + 0.532500i \(0.178747\pi\)
\(54\) −1.06731 −0.145242
\(55\) −5.33531 −0.719413
\(56\) −4.63233 −0.619021
\(57\) −0.118699 −0.0157221
\(58\) 7.03585 0.923852
\(59\) 10.9205 1.42173 0.710865 0.703328i \(-0.248304\pi\)
0.710865 + 0.703328i \(0.248304\pi\)
\(60\) −0.178838 −0.0230879
\(61\) −11.0097 −1.40964 −0.704822 0.709384i \(-0.748973\pi\)
−0.704822 + 0.709384i \(0.748973\pi\)
\(62\) −1.00000 −0.127000
\(63\) 13.7488 1.73219
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 0.954158 0.117449
\(67\) −3.23660 −0.395414 −0.197707 0.980261i \(-0.563349\pi\)
−0.197707 + 0.980261i \(0.563349\pi\)
\(68\) −6.03643 −0.732025
\(69\) −0.215919 −0.0259936
\(70\) 4.63233 0.553669
\(71\) −9.94396 −1.18013 −0.590066 0.807355i \(-0.700898\pi\)
−0.590066 + 0.807355i \(0.700898\pi\)
\(72\) −2.96802 −0.349784
\(73\) 1.10218 0.129000 0.0645002 0.997918i \(-0.479455\pi\)
0.0645002 + 0.997918i \(0.479455\pi\)
\(74\) 6.84984 0.796277
\(75\) 0.178838 0.0206505
\(76\) −0.663724 −0.0761343
\(77\) −24.7149 −2.81652
\(78\) −0.178838 −0.0202494
\(79\) 15.7918 1.77671 0.888356 0.459156i \(-0.151848\pi\)
0.888356 + 0.459156i \(0.151848\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.71317 0.968131
\(82\) 7.35666 0.812407
\(83\) −8.93682 −0.980944 −0.490472 0.871457i \(-0.663176\pi\)
−0.490472 + 0.871457i \(0.663176\pi\)
\(84\) −0.828437 −0.0903899
\(85\) 6.03643 0.654743
\(86\) 12.4429 1.34175
\(87\) 1.25828 0.134902
\(88\) 5.33531 0.568746
\(89\) −0.384321 −0.0407379 −0.0203690 0.999793i \(-0.506484\pi\)
−0.0203690 + 0.999793i \(0.506484\pi\)
\(90\) 2.96802 0.312856
\(91\) 4.63233 0.485600
\(92\) −1.20734 −0.125874
\(93\) −0.178838 −0.0185447
\(94\) 0.326660 0.0336924
\(95\) 0.663724 0.0680966
\(96\) 0.178838 0.0182526
\(97\) −17.7548 −1.80273 −0.901365 0.433060i \(-0.857434\pi\)
−0.901365 + 0.433060i \(0.857434\pi\)
\(98\) 14.4585 1.46053
\(99\) −15.8353 −1.59151
\(100\) 1.00000 0.100000
\(101\) 5.33151 0.530505 0.265252 0.964179i \(-0.414545\pi\)
0.265252 + 0.964179i \(0.414545\pi\)
\(102\) −1.07955 −0.106891
\(103\) 0.761610 0.0750436 0.0375218 0.999296i \(-0.488054\pi\)
0.0375218 + 0.999296i \(0.488054\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0.828437 0.0808472
\(106\) 12.3242 1.19703
\(107\) −17.9697 −1.73720 −0.868598 0.495518i \(-0.834978\pi\)
−0.868598 + 0.495518i \(0.834978\pi\)
\(108\) −1.06731 −0.102702
\(109\) 11.9278 1.14248 0.571238 0.820785i \(-0.306463\pi\)
0.571238 + 0.820785i \(0.306463\pi\)
\(110\) −5.33531 −0.508702
\(111\) 1.22501 0.116273
\(112\) −4.63233 −0.437714
\(113\) −13.8676 −1.30455 −0.652277 0.757981i \(-0.726186\pi\)
−0.652277 + 0.757981i \(0.726186\pi\)
\(114\) −0.118699 −0.0111172
\(115\) 1.20734 0.112585
\(116\) 7.03585 0.653262
\(117\) 2.96802 0.274393
\(118\) 10.9205 1.00532
\(119\) 27.9627 2.56334
\(120\) −0.178838 −0.0163256
\(121\) 17.4655 1.58778
\(122\) −11.0097 −0.996769
\(123\) 1.31565 0.118628
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 13.7488 1.22484
\(127\) 18.4024 1.63295 0.816473 0.577384i \(-0.195926\pi\)
0.816473 + 0.577384i \(0.195926\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.22527 0.195924
\(130\) 1.00000 0.0877058
\(131\) −7.02881 −0.614110 −0.307055 0.951692i \(-0.599344\pi\)
−0.307055 + 0.951692i \(0.599344\pi\)
\(132\) 0.954158 0.0830488
\(133\) 3.07459 0.266600
\(134\) −3.23660 −0.279600
\(135\) 1.06731 0.0918594
\(136\) −6.03643 −0.517620
\(137\) 15.3912 1.31496 0.657480 0.753472i \(-0.271622\pi\)
0.657480 + 0.753472i \(0.271622\pi\)
\(138\) −0.215919 −0.0183802
\(139\) −5.33060 −0.452136 −0.226068 0.974112i \(-0.572587\pi\)
−0.226068 + 0.974112i \(0.572587\pi\)
\(140\) 4.63233 0.391503
\(141\) 0.0584192 0.00491979
\(142\) −9.94396 −0.834479
\(143\) −5.33531 −0.446161
\(144\) −2.96802 −0.247335
\(145\) −7.03585 −0.584295
\(146\) 1.10218 0.0912170
\(147\) 2.58573 0.213267
\(148\) 6.84984 0.563053
\(149\) 8.14501 0.667265 0.333633 0.942703i \(-0.391726\pi\)
0.333633 + 0.942703i \(0.391726\pi\)
\(150\) 0.178838 0.0146021
\(151\) −4.82349 −0.392530 −0.196265 0.980551i \(-0.562881\pi\)
−0.196265 + 0.980551i \(0.562881\pi\)
\(152\) −0.663724 −0.0538351
\(153\) 17.9162 1.44844
\(154\) −24.7149 −1.99158
\(155\) 1.00000 0.0803219
\(156\) −0.178838 −0.0143185
\(157\) −9.18398 −0.732961 −0.366481 0.930426i \(-0.619437\pi\)
−0.366481 + 0.930426i \(0.619437\pi\)
\(158\) 15.7918 1.25632
\(159\) 2.20404 0.174792
\(160\) −1.00000 −0.0790569
\(161\) 5.59280 0.440774
\(162\) 8.71317 0.684572
\(163\) 4.50771 0.353071 0.176536 0.984294i \(-0.443511\pi\)
0.176536 + 0.984294i \(0.443511\pi\)
\(164\) 7.35666 0.574459
\(165\) −0.954158 −0.0742811
\(166\) −8.93682 −0.693632
\(167\) 4.88428 0.377957 0.188979 0.981981i \(-0.439482\pi\)
0.188979 + 0.981981i \(0.439482\pi\)
\(168\) −0.828437 −0.0639153
\(169\) 1.00000 0.0769231
\(170\) 6.03643 0.462973
\(171\) 1.96994 0.150645
\(172\) 12.4429 0.948763
\(173\) 3.37554 0.256637 0.128319 0.991733i \(-0.459042\pi\)
0.128319 + 0.991733i \(0.459042\pi\)
\(174\) 1.25828 0.0953899
\(175\) −4.63233 −0.350171
\(176\) 5.33531 0.402164
\(177\) 1.95301 0.146797
\(178\) −0.384321 −0.0288061
\(179\) −20.3213 −1.51888 −0.759441 0.650576i \(-0.774527\pi\)
−0.759441 + 0.650576i \(0.774527\pi\)
\(180\) 2.96802 0.221223
\(181\) 16.0859 1.19565 0.597827 0.801625i \(-0.296031\pi\)
0.597827 + 0.801625i \(0.296031\pi\)
\(182\) 4.63233 0.343371
\(183\) −1.96895 −0.145549
\(184\) −1.20734 −0.0890064
\(185\) −6.84984 −0.503610
\(186\) −0.178838 −0.0131131
\(187\) −32.2062 −2.35515
\(188\) 0.326660 0.0238241
\(189\) 4.94413 0.359632
\(190\) 0.663724 0.0481516
\(191\) 3.94669 0.285572 0.142786 0.989754i \(-0.454394\pi\)
0.142786 + 0.989754i \(0.454394\pi\)
\(192\) 0.178838 0.0129065
\(193\) −1.51907 −0.109345 −0.0546725 0.998504i \(-0.517411\pi\)
−0.0546725 + 0.998504i \(0.517411\pi\)
\(194\) −17.7548 −1.27472
\(195\) 0.178838 0.0128069
\(196\) 14.4585 1.03275
\(197\) 19.1945 1.36755 0.683776 0.729692i \(-0.260336\pi\)
0.683776 + 0.729692i \(0.260336\pi\)
\(198\) −15.8353 −1.12537
\(199\) −3.45167 −0.244682 −0.122341 0.992488i \(-0.539040\pi\)
−0.122341 + 0.992488i \(0.539040\pi\)
\(200\) 1.00000 0.0707107
\(201\) −0.578829 −0.0408274
\(202\) 5.33151 0.375124
\(203\) −32.5923 −2.28753
\(204\) −1.07955 −0.0755833
\(205\) −7.35666 −0.513811
\(206\) 0.761610 0.0530639
\(207\) 3.58341 0.249064
\(208\) −1.00000 −0.0693375
\(209\) −3.54117 −0.244948
\(210\) 0.828437 0.0571676
\(211\) 19.5039 1.34271 0.671353 0.741138i \(-0.265714\pi\)
0.671353 + 0.741138i \(0.265714\pi\)
\(212\) 12.3242 0.846430
\(213\) −1.77836 −0.121851
\(214\) −17.9697 −1.22838
\(215\) −12.4429 −0.848599
\(216\) −1.06731 −0.0726212
\(217\) 4.63233 0.314463
\(218\) 11.9278 0.807852
\(219\) 0.197112 0.0133196
\(220\) −5.33531 −0.359707
\(221\) 6.03643 0.406054
\(222\) 1.22501 0.0822175
\(223\) 21.7277 1.45500 0.727498 0.686110i \(-0.240683\pi\)
0.727498 + 0.686110i \(0.240683\pi\)
\(224\) −4.63233 −0.309510
\(225\) −2.96802 −0.197868
\(226\) −13.8676 −0.922459
\(227\) 15.9688 1.05989 0.529943 0.848033i \(-0.322213\pi\)
0.529943 + 0.848033i \(0.322213\pi\)
\(228\) −0.118699 −0.00786105
\(229\) 14.7883 0.977241 0.488620 0.872497i \(-0.337500\pi\)
0.488620 + 0.872497i \(0.337500\pi\)
\(230\) 1.20734 0.0796097
\(231\) −4.41997 −0.290813
\(232\) 7.03585 0.461926
\(233\) 6.09633 0.399384 0.199692 0.979859i \(-0.436006\pi\)
0.199692 + 0.979859i \(0.436006\pi\)
\(234\) 2.96802 0.194025
\(235\) −0.326660 −0.0213089
\(236\) 10.9205 0.710865
\(237\) 2.82417 0.183450
\(238\) 27.9627 1.81256
\(239\) 27.2233 1.76093 0.880464 0.474113i \(-0.157231\pi\)
0.880464 + 0.474113i \(0.157231\pi\)
\(240\) −0.178838 −0.0115440
\(241\) −8.85643 −0.570493 −0.285246 0.958454i \(-0.592075\pi\)
−0.285246 + 0.958454i \(0.592075\pi\)
\(242\) 17.4655 1.12273
\(243\) 4.76018 0.305366
\(244\) −11.0097 −0.704822
\(245\) −14.4585 −0.923717
\(246\) 1.31565 0.0838829
\(247\) 0.663724 0.0422317
\(248\) −1.00000 −0.0635001
\(249\) −1.59825 −0.101285
\(250\) −1.00000 −0.0632456
\(251\) −6.59287 −0.416139 −0.208069 0.978114i \(-0.566718\pi\)
−0.208069 + 0.978114i \(0.566718\pi\)
\(252\) 13.7488 0.866095
\(253\) −6.44154 −0.404976
\(254\) 18.4024 1.15467
\(255\) 1.07955 0.0676038
\(256\) 1.00000 0.0625000
\(257\) 3.16043 0.197142 0.0985710 0.995130i \(-0.468573\pi\)
0.0985710 + 0.995130i \(0.468573\pi\)
\(258\) 2.22527 0.138539
\(259\) −31.7307 −1.97165
\(260\) 1.00000 0.0620174
\(261\) −20.8825 −1.29260
\(262\) −7.02881 −0.434241
\(263\) 2.92844 0.180575 0.0902876 0.995916i \(-0.471221\pi\)
0.0902876 + 0.995916i \(0.471221\pi\)
\(264\) 0.954158 0.0587243
\(265\) −12.3242 −0.757070
\(266\) 3.07459 0.188515
\(267\) −0.0687313 −0.00420628
\(268\) −3.23660 −0.197707
\(269\) 16.7347 1.02033 0.510167 0.860075i \(-0.329584\pi\)
0.510167 + 0.860075i \(0.329584\pi\)
\(270\) 1.06731 0.0649544
\(271\) 28.1642 1.71085 0.855425 0.517926i \(-0.173296\pi\)
0.855425 + 0.517926i \(0.173296\pi\)
\(272\) −6.03643 −0.366013
\(273\) 0.828437 0.0501393
\(274\) 15.3912 0.929817
\(275\) 5.33531 0.321731
\(276\) −0.215919 −0.0129968
\(277\) −4.18271 −0.251315 −0.125657 0.992074i \(-0.540104\pi\)
−0.125657 + 0.992074i \(0.540104\pi\)
\(278\) −5.33060 −0.319708
\(279\) 2.96802 0.177691
\(280\) 4.63233 0.276835
\(281\) −29.5778 −1.76446 −0.882231 0.470816i \(-0.843959\pi\)
−0.882231 + 0.470816i \(0.843959\pi\)
\(282\) 0.0584192 0.00347881
\(283\) −21.8936 −1.30144 −0.650721 0.759317i \(-0.725533\pi\)
−0.650721 + 0.759317i \(0.725533\pi\)
\(284\) −9.94396 −0.590066
\(285\) 0.118699 0.00703113
\(286\) −5.33531 −0.315484
\(287\) −34.0785 −2.01159
\(288\) −2.96802 −0.174892
\(289\) 19.4385 1.14344
\(290\) −7.03585 −0.413159
\(291\) −3.17524 −0.186136
\(292\) 1.10218 0.0645002
\(293\) −31.6771 −1.85059 −0.925297 0.379242i \(-0.876185\pi\)
−0.925297 + 0.379242i \(0.876185\pi\)
\(294\) 2.58573 0.150803
\(295\) −10.9205 −0.635817
\(296\) 6.84984 0.398139
\(297\) −5.69443 −0.330424
\(298\) 8.14501 0.471828
\(299\) 1.20734 0.0698224
\(300\) 0.178838 0.0103252
\(301\) −57.6396 −3.32229
\(302\) −4.82349 −0.277560
\(303\) 0.953478 0.0547759
\(304\) −0.663724 −0.0380672
\(305\) 11.0097 0.630412
\(306\) 17.9162 1.02420
\(307\) −15.6792 −0.894860 −0.447430 0.894319i \(-0.647661\pi\)
−0.447430 + 0.894319i \(0.647661\pi\)
\(308\) −24.7149 −1.40826
\(309\) 0.136205 0.00774843
\(310\) 1.00000 0.0567962
\(311\) 1.60738 0.0911462 0.0455731 0.998961i \(-0.485489\pi\)
0.0455731 + 0.998961i \(0.485489\pi\)
\(312\) −0.178838 −0.0101247
\(313\) 33.2099 1.87714 0.938568 0.345096i \(-0.112154\pi\)
0.938568 + 0.345096i \(0.112154\pi\)
\(314\) −9.18398 −0.518282
\(315\) −13.7488 −0.774659
\(316\) 15.7918 0.888356
\(317\) −28.2205 −1.58502 −0.792511 0.609858i \(-0.791226\pi\)
−0.792511 + 0.609858i \(0.791226\pi\)
\(318\) 2.20404 0.123596
\(319\) 37.5384 2.10175
\(320\) −1.00000 −0.0559017
\(321\) −3.21367 −0.179370
\(322\) 5.59280 0.311675
\(323\) 4.00652 0.222929
\(324\) 8.71317 0.484065
\(325\) −1.00000 −0.0554700
\(326\) 4.50771 0.249659
\(327\) 2.13315 0.117963
\(328\) 7.35666 0.406204
\(329\) −1.51319 −0.0834251
\(330\) −0.954158 −0.0525246
\(331\) 15.1107 0.830558 0.415279 0.909694i \(-0.363684\pi\)
0.415279 + 0.909694i \(0.363684\pi\)
\(332\) −8.93682 −0.490472
\(333\) −20.3304 −1.11410
\(334\) 4.88428 0.267256
\(335\) 3.23660 0.176835
\(336\) −0.828437 −0.0451950
\(337\) −17.3733 −0.946385 −0.473193 0.880959i \(-0.656899\pi\)
−0.473193 + 0.880959i \(0.656899\pi\)
\(338\) 1.00000 0.0543928
\(339\) −2.48006 −0.134698
\(340\) 6.03643 0.327372
\(341\) −5.33531 −0.288923
\(342\) 1.96994 0.106522
\(343\) −34.5500 −1.86553
\(344\) 12.4429 0.670877
\(345\) 0.215919 0.0116247
\(346\) 3.37554 0.181470
\(347\) 5.03025 0.270038 0.135019 0.990843i \(-0.456890\pi\)
0.135019 + 0.990843i \(0.456890\pi\)
\(348\) 1.25828 0.0674508
\(349\) 3.33672 0.178611 0.0893053 0.996004i \(-0.471535\pi\)
0.0893053 + 0.996004i \(0.471535\pi\)
\(350\) −4.63233 −0.247608
\(351\) 1.06731 0.0569688
\(352\) 5.33531 0.284373
\(353\) 10.8928 0.579768 0.289884 0.957062i \(-0.406383\pi\)
0.289884 + 0.957062i \(0.406383\pi\)
\(354\) 1.95301 0.103801
\(355\) 9.94396 0.527771
\(356\) −0.384321 −0.0203690
\(357\) 5.00081 0.264671
\(358\) −20.3213 −1.07401
\(359\) −14.7587 −0.778937 −0.389468 0.921040i \(-0.627341\pi\)
−0.389468 + 0.921040i \(0.627341\pi\)
\(360\) 2.96802 0.156428
\(361\) −18.5595 −0.976814
\(362\) 16.0859 0.845456
\(363\) 3.12351 0.163942
\(364\) 4.63233 0.242800
\(365\) −1.10218 −0.0576907
\(366\) −1.96895 −0.102919
\(367\) 19.5687 1.02148 0.510739 0.859736i \(-0.329372\pi\)
0.510739 + 0.859736i \(0.329372\pi\)
\(368\) −1.20734 −0.0629370
\(369\) −21.8347 −1.13667
\(370\) −6.84984 −0.356106
\(371\) −57.0898 −2.96395
\(372\) −0.178838 −0.00927233
\(373\) −23.4343 −1.21338 −0.606690 0.794938i \(-0.707503\pi\)
−0.606690 + 0.794938i \(0.707503\pi\)
\(374\) −32.2062 −1.66535
\(375\) −0.178838 −0.00923517
\(376\) 0.326660 0.0168462
\(377\) −7.03585 −0.362365
\(378\) 4.94413 0.254299
\(379\) −9.95784 −0.511500 −0.255750 0.966743i \(-0.582322\pi\)
−0.255750 + 0.966743i \(0.582322\pi\)
\(380\) 0.663724 0.0340483
\(381\) 3.29105 0.168605
\(382\) 3.94669 0.201930
\(383\) 15.5114 0.792598 0.396299 0.918122i \(-0.370294\pi\)
0.396299 + 0.918122i \(0.370294\pi\)
\(384\) 0.178838 0.00912630
\(385\) 24.7149 1.25959
\(386\) −1.51907 −0.0773187
\(387\) −36.9308 −1.87730
\(388\) −17.7548 −0.901365
\(389\) 5.09129 0.258139 0.129069 0.991636i \(-0.458801\pi\)
0.129069 + 0.991636i \(0.458801\pi\)
\(390\) 0.178838 0.00905583
\(391\) 7.28804 0.368572
\(392\) 14.4585 0.730263
\(393\) −1.25702 −0.0634083
\(394\) 19.1945 0.967006
\(395\) −15.7918 −0.794569
\(396\) −15.8353 −0.795753
\(397\) 23.7475 1.19185 0.595926 0.803039i \(-0.296785\pi\)
0.595926 + 0.803039i \(0.296785\pi\)
\(398\) −3.45167 −0.173016
\(399\) 0.549854 0.0275271
\(400\) 1.00000 0.0500000
\(401\) −7.89202 −0.394109 −0.197054 0.980393i \(-0.563138\pi\)
−0.197054 + 0.980393i \(0.563138\pi\)
\(402\) −0.578829 −0.0288694
\(403\) 1.00000 0.0498135
\(404\) 5.33151 0.265252
\(405\) −8.71317 −0.432961
\(406\) −32.5923 −1.61753
\(407\) 36.5460 1.81152
\(408\) −1.07955 −0.0534455
\(409\) −37.3652 −1.84759 −0.923796 0.382886i \(-0.874930\pi\)
−0.923796 + 0.382886i \(0.874930\pi\)
\(410\) −7.35666 −0.363320
\(411\) 2.75254 0.135773
\(412\) 0.761610 0.0375218
\(413\) −50.5874 −2.48924
\(414\) 3.58341 0.176115
\(415\) 8.93682 0.438691
\(416\) −1.00000 −0.0490290
\(417\) −0.953316 −0.0466841
\(418\) −3.54117 −0.173204
\(419\) −16.2972 −0.796168 −0.398084 0.917349i \(-0.630325\pi\)
−0.398084 + 0.917349i \(0.630325\pi\)
\(420\) 0.828437 0.0404236
\(421\) −11.5930 −0.565008 −0.282504 0.959266i \(-0.591165\pi\)
−0.282504 + 0.959266i \(0.591165\pi\)
\(422\) 19.5039 0.949436
\(423\) −0.969531 −0.0471402
\(424\) 12.3242 0.598516
\(425\) −6.03643 −0.292810
\(426\) −1.77836 −0.0861619
\(427\) 51.0004 2.46808
\(428\) −17.9697 −0.868598
\(429\) −0.954158 −0.0460672
\(430\) −12.4429 −0.600050
\(431\) 16.9740 0.817610 0.408805 0.912622i \(-0.365946\pi\)
0.408805 + 0.912622i \(0.365946\pi\)
\(432\) −1.06731 −0.0513510
\(433\) 26.3107 1.26441 0.632205 0.774801i \(-0.282150\pi\)
0.632205 + 0.774801i \(0.282150\pi\)
\(434\) 4.63233 0.222359
\(435\) −1.25828 −0.0603298
\(436\) 11.9278 0.571238
\(437\) 0.801341 0.0383333
\(438\) 0.197112 0.00941837
\(439\) 26.8813 1.28298 0.641488 0.767133i \(-0.278318\pi\)
0.641488 + 0.767133i \(0.278318\pi\)
\(440\) −5.33531 −0.254351
\(441\) −42.9130 −2.04347
\(442\) 6.03643 0.287124
\(443\) −4.26704 −0.202733 −0.101366 0.994849i \(-0.532321\pi\)
−0.101366 + 0.994849i \(0.532321\pi\)
\(444\) 1.22501 0.0581365
\(445\) 0.384321 0.0182186
\(446\) 21.7277 1.02884
\(447\) 1.45664 0.0688967
\(448\) −4.63233 −0.218857
\(449\) 0.342985 0.0161865 0.00809323 0.999967i \(-0.497424\pi\)
0.00809323 + 0.999967i \(0.497424\pi\)
\(450\) −2.96802 −0.139914
\(451\) 39.2501 1.84821
\(452\) −13.8676 −0.652277
\(453\) −0.862624 −0.0405296
\(454\) 15.9688 0.749453
\(455\) −4.63233 −0.217167
\(456\) −0.118699 −0.00555860
\(457\) −12.6480 −0.591649 −0.295824 0.955242i \(-0.595594\pi\)
−0.295824 + 0.955242i \(0.595594\pi\)
\(458\) 14.7883 0.691013
\(459\) 6.44274 0.300722
\(460\) 1.20734 0.0562926
\(461\) −11.1326 −0.518497 −0.259249 0.965811i \(-0.583475\pi\)
−0.259249 + 0.965811i \(0.583475\pi\)
\(462\) −4.41997 −0.205636
\(463\) −36.7366 −1.70730 −0.853648 0.520850i \(-0.825615\pi\)
−0.853648 + 0.520850i \(0.825615\pi\)
\(464\) 7.03585 0.326631
\(465\) 0.178838 0.00829343
\(466\) 6.09633 0.282407
\(467\) 15.6133 0.722497 0.361249 0.932470i \(-0.382351\pi\)
0.361249 + 0.932470i \(0.382351\pi\)
\(468\) 2.96802 0.137197
\(469\) 14.9930 0.692313
\(470\) −0.326660 −0.0150677
\(471\) −1.64245 −0.0756800
\(472\) 10.9205 0.502658
\(473\) 66.3868 3.05247
\(474\) 2.82417 0.129718
\(475\) −0.663724 −0.0304537
\(476\) 27.9627 1.28167
\(477\) −36.5785 −1.67481
\(478\) 27.2233 1.24516
\(479\) −4.03715 −0.184462 −0.0922310 0.995738i \(-0.529400\pi\)
−0.0922310 + 0.995738i \(0.529400\pi\)
\(480\) −0.178838 −0.00816281
\(481\) −6.84984 −0.312326
\(482\) −8.85643 −0.403399
\(483\) 1.00021 0.0455110
\(484\) 17.4655 0.793888
\(485\) 17.7548 0.806205
\(486\) 4.76018 0.215926
\(487\) 40.9020 1.85344 0.926722 0.375747i \(-0.122614\pi\)
0.926722 + 0.375747i \(0.122614\pi\)
\(488\) −11.0097 −0.498385
\(489\) 0.806152 0.0364554
\(490\) −14.4585 −0.653167
\(491\) 30.5529 1.37883 0.689417 0.724365i \(-0.257867\pi\)
0.689417 + 0.724365i \(0.257867\pi\)
\(492\) 1.31565 0.0593142
\(493\) −42.4714 −1.91282
\(494\) 0.663724 0.0298623
\(495\) 15.8353 0.711743
\(496\) −1.00000 −0.0449013
\(497\) 46.0637 2.06624
\(498\) −1.59825 −0.0716191
\(499\) 26.9218 1.20519 0.602593 0.798048i \(-0.294134\pi\)
0.602593 + 0.798048i \(0.294134\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0.873497 0.0390250
\(502\) −6.59287 −0.294254
\(503\) −36.0604 −1.60785 −0.803926 0.594730i \(-0.797259\pi\)
−0.803926 + 0.594730i \(0.797259\pi\)
\(504\) 13.7488 0.612421
\(505\) −5.33151 −0.237249
\(506\) −6.44154 −0.286361
\(507\) 0.178838 0.00794249
\(508\) 18.4024 0.816473
\(509\) −30.9960 −1.37387 −0.686936 0.726718i \(-0.741045\pi\)
−0.686936 + 0.726718i \(0.741045\pi\)
\(510\) 1.07955 0.0478031
\(511\) −5.10566 −0.225861
\(512\) 1.00000 0.0441942
\(513\) 0.708399 0.0312766
\(514\) 3.16043 0.139400
\(515\) −0.761610 −0.0335605
\(516\) 2.22527 0.0979620
\(517\) 1.74283 0.0766496
\(518\) −31.7307 −1.39417
\(519\) 0.603675 0.0264984
\(520\) 1.00000 0.0438529
\(521\) −8.33312 −0.365081 −0.182540 0.983198i \(-0.558432\pi\)
−0.182540 + 0.983198i \(0.558432\pi\)
\(522\) −20.8825 −0.914003
\(523\) −4.55325 −0.199100 −0.0995498 0.995033i \(-0.531740\pi\)
−0.0995498 + 0.995033i \(0.531740\pi\)
\(524\) −7.02881 −0.307055
\(525\) −0.828437 −0.0361560
\(526\) 2.92844 0.127686
\(527\) 6.03643 0.262951
\(528\) 0.954158 0.0415244
\(529\) −21.5423 −0.936623
\(530\) −12.3242 −0.535329
\(531\) −32.4123 −1.40657
\(532\) 3.07459 0.133300
\(533\) −7.35666 −0.318652
\(534\) −0.0687313 −0.00297429
\(535\) 17.9697 0.776898
\(536\) −3.23660 −0.139800
\(537\) −3.63422 −0.156828
\(538\) 16.7347 0.721485
\(539\) 77.1404 3.32267
\(540\) 1.06731 0.0459297
\(541\) 20.1042 0.864347 0.432173 0.901791i \(-0.357747\pi\)
0.432173 + 0.901791i \(0.357747\pi\)
\(542\) 28.1642 1.20975
\(543\) 2.87677 0.123454
\(544\) −6.03643 −0.258810
\(545\) −11.9278 −0.510930
\(546\) 0.828437 0.0354539
\(547\) −12.6527 −0.540992 −0.270496 0.962721i \(-0.587188\pi\)
−0.270496 + 0.962721i \(0.587188\pi\)
\(548\) 15.3912 0.657480
\(549\) 32.6769 1.39462
\(550\) 5.33531 0.227498
\(551\) −4.66986 −0.198943
\(552\) −0.215919 −0.00919012
\(553\) −73.1526 −3.11076
\(554\) −4.18271 −0.177706
\(555\) −1.22501 −0.0519989
\(556\) −5.33060 −0.226068
\(557\) 9.98212 0.422956 0.211478 0.977383i \(-0.432172\pi\)
0.211478 + 0.977383i \(0.432172\pi\)
\(558\) 2.96802 0.125646
\(559\) −12.4429 −0.526279
\(560\) 4.63233 0.195752
\(561\) −5.75971 −0.243175
\(562\) −29.5778 −1.24766
\(563\) 42.7653 1.80234 0.901171 0.433464i \(-0.142709\pi\)
0.901171 + 0.433464i \(0.142709\pi\)
\(564\) 0.0584192 0.00245989
\(565\) 13.8676 0.583414
\(566\) −21.8936 −0.920258
\(567\) −40.3623 −1.69506
\(568\) −9.94396 −0.417239
\(569\) 17.3053 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(570\) 0.118699 0.00497176
\(571\) 35.4528 1.48365 0.741827 0.670592i \(-0.233960\pi\)
0.741827 + 0.670592i \(0.233960\pi\)
\(572\) −5.33531 −0.223081
\(573\) 0.705819 0.0294860
\(574\) −34.0785 −1.42241
\(575\) −1.20734 −0.0503496
\(576\) −2.96802 −0.123667
\(577\) 13.3304 0.554953 0.277477 0.960732i \(-0.410502\pi\)
0.277477 + 0.960732i \(0.410502\pi\)
\(578\) 19.4385 0.808536
\(579\) −0.271668 −0.0112901
\(580\) −7.03585 −0.292148
\(581\) 41.3983 1.71749
\(582\) −3.17524 −0.131618
\(583\) 65.7535 2.72323
\(584\) 1.10218 0.0456085
\(585\) −2.96802 −0.122712
\(586\) −31.6771 −1.30857
\(587\) 19.6700 0.811868 0.405934 0.913902i \(-0.366946\pi\)
0.405934 + 0.913902i \(0.366946\pi\)
\(588\) 2.58573 0.106634
\(589\) 0.663724 0.0273483
\(590\) −10.9205 −0.449591
\(591\) 3.43271 0.141203
\(592\) 6.84984 0.281527
\(593\) 24.8311 1.01969 0.509845 0.860266i \(-0.329703\pi\)
0.509845 + 0.860266i \(0.329703\pi\)
\(594\) −5.69443 −0.233645
\(595\) −27.9627 −1.14636
\(596\) 8.14501 0.333633
\(597\) −0.617290 −0.0252640
\(598\) 1.20734 0.0493719
\(599\) −18.9916 −0.775977 −0.387989 0.921664i \(-0.626830\pi\)
−0.387989 + 0.921664i \(0.626830\pi\)
\(600\) 0.178838 0.00730104
\(601\) −32.2369 −1.31497 −0.657486 0.753467i \(-0.728380\pi\)
−0.657486 + 0.753467i \(0.728380\pi\)
\(602\) −57.6396 −2.34922
\(603\) 9.60630 0.391199
\(604\) −4.82349 −0.196265
\(605\) −17.4655 −0.710075
\(606\) 0.953478 0.0387324
\(607\) −22.8430 −0.927169 −0.463585 0.886053i \(-0.653437\pi\)
−0.463585 + 0.886053i \(0.653437\pi\)
\(608\) −0.663724 −0.0269175
\(609\) −5.82876 −0.236193
\(610\) 11.0097 0.445769
\(611\) −0.326660 −0.0132152
\(612\) 17.9162 0.724221
\(613\) 48.2963 1.95067 0.975335 0.220728i \(-0.0708432\pi\)
0.975335 + 0.220728i \(0.0708432\pi\)
\(614\) −15.6792 −0.632761
\(615\) −1.31565 −0.0530522
\(616\) −24.7149 −0.995792
\(617\) 14.6017 0.587844 0.293922 0.955829i \(-0.405039\pi\)
0.293922 + 0.955829i \(0.405039\pi\)
\(618\) 0.136205 0.00547897
\(619\) −14.6378 −0.588342 −0.294171 0.955753i \(-0.595043\pi\)
−0.294171 + 0.955753i \(0.595043\pi\)
\(620\) 1.00000 0.0401610
\(621\) 1.28861 0.0517100
\(622\) 1.60738 0.0644501
\(623\) 1.78030 0.0713262
\(624\) −0.178838 −0.00715926
\(625\) 1.00000 0.0400000
\(626\) 33.2099 1.32733
\(627\) −0.633297 −0.0252914
\(628\) −9.18398 −0.366481
\(629\) −41.3486 −1.64868
\(630\) −13.7488 −0.547766
\(631\) 6.72848 0.267857 0.133928 0.990991i \(-0.457241\pi\)
0.133928 + 0.990991i \(0.457241\pi\)
\(632\) 15.7918 0.628162
\(633\) 3.48805 0.138637
\(634\) −28.2205 −1.12078
\(635\) −18.4024 −0.730275
\(636\) 2.20404 0.0873959
\(637\) −14.4585 −0.572865
\(638\) 37.5384 1.48616
\(639\) 29.5139 1.16755
\(640\) −1.00000 −0.0395285
\(641\) 21.2546 0.839508 0.419754 0.907638i \(-0.362116\pi\)
0.419754 + 0.907638i \(0.362116\pi\)
\(642\) −3.21367 −0.126833
\(643\) −15.5072 −0.611543 −0.305772 0.952105i \(-0.598914\pi\)
−0.305772 + 0.952105i \(0.598914\pi\)
\(644\) 5.59280 0.220387
\(645\) −2.22527 −0.0876198
\(646\) 4.00652 0.157635
\(647\) −7.68131 −0.301983 −0.150992 0.988535i \(-0.548247\pi\)
−0.150992 + 0.988535i \(0.548247\pi\)
\(648\) 8.71317 0.342286
\(649\) 58.2643 2.28708
\(650\) −1.00000 −0.0392232
\(651\) 0.828437 0.0324690
\(652\) 4.50771 0.176536
\(653\) −34.2319 −1.33960 −0.669799 0.742543i \(-0.733620\pi\)
−0.669799 + 0.742543i \(0.733620\pi\)
\(654\) 2.13315 0.0834126
\(655\) 7.02881 0.274638
\(656\) 7.35666 0.287229
\(657\) −3.27129 −0.127625
\(658\) −1.51319 −0.0589904
\(659\) −1.15499 −0.0449919 −0.0224960 0.999747i \(-0.507161\pi\)
−0.0224960 + 0.999747i \(0.507161\pi\)
\(660\) −0.954158 −0.0371405
\(661\) 1.95963 0.0762207 0.0381103 0.999274i \(-0.487866\pi\)
0.0381103 + 0.999274i \(0.487866\pi\)
\(662\) 15.1107 0.587293
\(663\) 1.07955 0.0419261
\(664\) −8.93682 −0.346816
\(665\) −3.07459 −0.119227
\(666\) −20.3304 −0.787788
\(667\) −8.49467 −0.328915
\(668\) 4.88428 0.188979
\(669\) 3.88575 0.150232
\(670\) 3.23660 0.125041
\(671\) −58.7400 −2.26763
\(672\) −0.828437 −0.0319577
\(673\) −33.5909 −1.29483 −0.647417 0.762136i \(-0.724151\pi\)
−0.647417 + 0.762136i \(0.724151\pi\)
\(674\) −17.3733 −0.669195
\(675\) −1.06731 −0.0410808
\(676\) 1.00000 0.0384615
\(677\) 8.34855 0.320861 0.160430 0.987047i \(-0.448712\pi\)
0.160430 + 0.987047i \(0.448712\pi\)
\(678\) −2.48006 −0.0952460
\(679\) 82.2462 3.15632
\(680\) 6.03643 0.231487
\(681\) 2.85583 0.109436
\(682\) −5.33531 −0.204300
\(683\) 0.0400037 0.00153070 0.000765350 1.00000i \(-0.499756\pi\)
0.000765350 1.00000i \(0.499756\pi\)
\(684\) 1.96994 0.0753227
\(685\) −15.3912 −0.588068
\(686\) −34.5500 −1.31913
\(687\) 2.64472 0.100902
\(688\) 12.4429 0.474381
\(689\) −12.3242 −0.469515
\(690\) 0.215919 0.00821989
\(691\) 16.2070 0.616542 0.308271 0.951299i \(-0.400250\pi\)
0.308271 + 0.951299i \(0.400250\pi\)
\(692\) 3.37554 0.128319
\(693\) 73.3543 2.78650
\(694\) 5.03025 0.190946
\(695\) 5.33060 0.202201
\(696\) 1.25828 0.0476949
\(697\) −44.4080 −1.68207
\(698\) 3.33672 0.126297
\(699\) 1.09026 0.0412373
\(700\) −4.63233 −0.175086
\(701\) −21.9164 −0.827772 −0.413886 0.910329i \(-0.635829\pi\)
−0.413886 + 0.910329i \(0.635829\pi\)
\(702\) 1.06731 0.0402830
\(703\) −4.54640 −0.171471
\(704\) 5.33531 0.201082
\(705\) −0.0584192 −0.00220020
\(706\) 10.8928 0.409958
\(707\) −24.6973 −0.928837
\(708\) 1.95301 0.0733985
\(709\) −36.5413 −1.37234 −0.686169 0.727442i \(-0.740709\pi\)
−0.686169 + 0.727442i \(0.740709\pi\)
\(710\) 9.94396 0.373190
\(711\) −46.8702 −1.75777
\(712\) −0.384321 −0.0144030
\(713\) 1.20734 0.0452153
\(714\) 5.00081 0.187151
\(715\) 5.33531 0.199529
\(716\) −20.3213 −0.759441
\(717\) 4.86857 0.181820
\(718\) −14.7587 −0.550791
\(719\) −0.635175 −0.0236880 −0.0118440 0.999930i \(-0.503770\pi\)
−0.0118440 + 0.999930i \(0.503770\pi\)
\(720\) 2.96802 0.110611
\(721\) −3.52803 −0.131391
\(722\) −18.5595 −0.690712
\(723\) −1.58387 −0.0589047
\(724\) 16.0859 0.597827
\(725\) 7.03585 0.261305
\(726\) 3.12351 0.115924
\(727\) −23.1672 −0.859223 −0.429611 0.903014i \(-0.641349\pi\)
−0.429611 + 0.903014i \(0.641349\pi\)
\(728\) 4.63233 0.171685
\(729\) −25.2882 −0.936601
\(730\) −1.10218 −0.0407935
\(731\) −75.1108 −2.77807
\(732\) −1.96895 −0.0727746
\(733\) 28.9507 1.06932 0.534659 0.845068i \(-0.320440\pi\)
0.534659 + 0.845068i \(0.320440\pi\)
\(734\) 19.5687 0.722294
\(735\) −2.58573 −0.0953759
\(736\) −1.20734 −0.0445032
\(737\) −17.2683 −0.636086
\(738\) −21.8347 −0.803746
\(739\) 4.15374 0.152798 0.0763989 0.997077i \(-0.475658\pi\)
0.0763989 + 0.997077i \(0.475658\pi\)
\(740\) −6.84984 −0.251805
\(741\) 0.118699 0.00436052
\(742\) −57.0898 −2.09583
\(743\) 2.66887 0.0979114 0.0489557 0.998801i \(-0.484411\pi\)
0.0489557 + 0.998801i \(0.484411\pi\)
\(744\) −0.178838 −0.00655653
\(745\) −8.14501 −0.298410
\(746\) −23.4343 −0.857990
\(747\) 26.5246 0.970486
\(748\) −32.2062 −1.17758
\(749\) 83.2415 3.04158
\(750\) −0.178838 −0.00653025
\(751\) 2.49405 0.0910090 0.0455045 0.998964i \(-0.485510\pi\)
0.0455045 + 0.998964i \(0.485510\pi\)
\(752\) 0.326660 0.0119120
\(753\) −1.17906 −0.0429673
\(754\) −7.03585 −0.256230
\(755\) 4.82349 0.175545
\(756\) 4.94413 0.179816
\(757\) −43.2745 −1.57284 −0.786419 0.617693i \(-0.788068\pi\)
−0.786419 + 0.617693i \(0.788068\pi\)
\(758\) −9.95784 −0.361685
\(759\) −1.15199 −0.0418147
\(760\) 0.663724 0.0240758
\(761\) 11.3170 0.410242 0.205121 0.978737i \(-0.434241\pi\)
0.205121 + 0.978737i \(0.434241\pi\)
\(762\) 3.29105 0.119222
\(763\) −55.2534 −2.00031
\(764\) 3.94669 0.142786
\(765\) −17.9162 −0.647763
\(766\) 15.5114 0.560451
\(767\) −10.9205 −0.394317
\(768\) 0.178838 0.00645327
\(769\) 42.9251 1.54792 0.773959 0.633236i \(-0.218274\pi\)
0.773959 + 0.633236i \(0.218274\pi\)
\(770\) 24.7149 0.890663
\(771\) 0.565205 0.0203554
\(772\) −1.51907 −0.0546725
\(773\) 29.2341 1.05148 0.525739 0.850646i \(-0.323789\pi\)
0.525739 + 0.850646i \(0.323789\pi\)
\(774\) −36.9308 −1.32745
\(775\) −1.00000 −0.0359211
\(776\) −17.7548 −0.637361
\(777\) −5.67466 −0.203577
\(778\) 5.09129 0.182532
\(779\) −4.88279 −0.174944
\(780\) 0.178838 0.00640344
\(781\) −53.0541 −1.89843
\(782\) 7.28804 0.260620
\(783\) −7.50943 −0.268365
\(784\) 14.4585 0.516374
\(785\) 9.18398 0.327790
\(786\) −1.25702 −0.0448364
\(787\) 5.72717 0.204151 0.102076 0.994777i \(-0.467452\pi\)
0.102076 + 0.994777i \(0.467452\pi\)
\(788\) 19.1945 0.683776
\(789\) 0.523716 0.0186448
\(790\) −15.7918 −0.561845
\(791\) 64.2392 2.28408
\(792\) −15.8353 −0.562683
\(793\) 11.0097 0.390965
\(794\) 23.7475 0.842767
\(795\) −2.20404 −0.0781692
\(796\) −3.45167 −0.122341
\(797\) −51.1198 −1.81075 −0.905377 0.424608i \(-0.860412\pi\)
−0.905377 + 0.424608i \(0.860412\pi\)
\(798\) 0.549854 0.0194646
\(799\) −1.97186 −0.0697593
\(800\) 1.00000 0.0353553
\(801\) 1.14067 0.0403036
\(802\) −7.89202 −0.278677
\(803\) 5.88047 0.207517
\(804\) −0.578829 −0.0204137
\(805\) −5.59280 −0.197120
\(806\) 1.00000 0.0352235
\(807\) 2.99281 0.105352
\(808\) 5.33151 0.187562
\(809\) −39.5674 −1.39112 −0.695558 0.718470i \(-0.744843\pi\)
−0.695558 + 0.718470i \(0.744843\pi\)
\(810\) −8.71317 −0.306150
\(811\) −11.7083 −0.411136 −0.205568 0.978643i \(-0.565904\pi\)
−0.205568 + 0.978643i \(0.565904\pi\)
\(812\) −32.5923 −1.14377
\(813\) 5.03683 0.176649
\(814\) 36.5460 1.28094
\(815\) −4.50771 −0.157898
\(816\) −1.07955 −0.0377916
\(817\) −8.25865 −0.288934
\(818\) −37.3652 −1.30644
\(819\) −13.7488 −0.480423
\(820\) −7.35666 −0.256906
\(821\) −21.6045 −0.754001 −0.377000 0.926213i \(-0.623044\pi\)
−0.377000 + 0.926213i \(0.623044\pi\)
\(822\) 2.75254 0.0960058
\(823\) −15.1764 −0.529015 −0.264507 0.964384i \(-0.585209\pi\)
−0.264507 + 0.964384i \(0.585209\pi\)
\(824\) 0.761610 0.0265319
\(825\) 0.954158 0.0332195
\(826\) −50.5874 −1.76016
\(827\) 18.6439 0.648311 0.324155 0.946004i \(-0.394920\pi\)
0.324155 + 0.946004i \(0.394920\pi\)
\(828\) 3.58341 0.124532
\(829\) −29.6882 −1.03111 −0.515557 0.856855i \(-0.672415\pi\)
−0.515557 + 0.856855i \(0.672415\pi\)
\(830\) 8.93682 0.310202
\(831\) −0.748028 −0.0259488
\(832\) −1.00000 −0.0346688
\(833\) −87.2775 −3.02399
\(834\) −0.953316 −0.0330106
\(835\) −4.88428 −0.169028
\(836\) −3.54117 −0.122474
\(837\) 1.06731 0.0368916
\(838\) −16.2972 −0.562976
\(839\) 20.8238 0.718919 0.359459 0.933161i \(-0.382961\pi\)
0.359459 + 0.933161i \(0.382961\pi\)
\(840\) 0.828437 0.0285838
\(841\) 20.5031 0.707005
\(842\) −11.5930 −0.399521
\(843\) −5.28964 −0.182185
\(844\) 19.5039 0.671353
\(845\) −1.00000 −0.0344010
\(846\) −0.969531 −0.0333332
\(847\) −80.9061 −2.77997
\(848\) 12.3242 0.423215
\(849\) −3.91542 −0.134377
\(850\) −6.03643 −0.207048
\(851\) −8.27009 −0.283495
\(852\) −1.77836 −0.0609257
\(853\) 45.2753 1.55020 0.775098 0.631841i \(-0.217700\pi\)
0.775098 + 0.631841i \(0.217700\pi\)
\(854\) 51.0004 1.74520
\(855\) −1.96994 −0.0673706
\(856\) −17.9697 −0.614191
\(857\) 52.3546 1.78840 0.894200 0.447668i \(-0.147745\pi\)
0.894200 + 0.447668i \(0.147745\pi\)
\(858\) −0.954158 −0.0325744
\(859\) 29.1940 0.996087 0.498043 0.867152i \(-0.334052\pi\)
0.498043 + 0.867152i \(0.334052\pi\)
\(860\) −12.4429 −0.424300
\(861\) −6.09453 −0.207701
\(862\) 16.9740 0.578137
\(863\) 17.6919 0.602239 0.301120 0.953586i \(-0.402640\pi\)
0.301120 + 0.953586i \(0.402640\pi\)
\(864\) −1.06731 −0.0363106
\(865\) −3.37554 −0.114772
\(866\) 26.3107 0.894073
\(867\) 3.47635 0.118063
\(868\) 4.63233 0.157231
\(869\) 84.2539 2.85812
\(870\) −1.25828 −0.0426596
\(871\) 3.23660 0.109668
\(872\) 11.9278 0.403926
\(873\) 52.6966 1.78351
\(874\) 0.801341 0.0271058
\(875\) 4.63233 0.156601
\(876\) 0.197112 0.00665979
\(877\) −25.9751 −0.877117 −0.438559 0.898703i \(-0.644511\pi\)
−0.438559 + 0.898703i \(0.644511\pi\)
\(878\) 26.8813 0.907200
\(879\) −5.66507 −0.191078
\(880\) −5.33531 −0.179853
\(881\) 9.35799 0.315279 0.157639 0.987497i \(-0.449612\pi\)
0.157639 + 0.987497i \(0.449612\pi\)
\(882\) −42.9130 −1.44495
\(883\) 21.1305 0.711098 0.355549 0.934658i \(-0.384294\pi\)
0.355549 + 0.934658i \(0.384294\pi\)
\(884\) 6.03643 0.203027
\(885\) −1.95301 −0.0656496
\(886\) −4.26704 −0.143354
\(887\) 30.8744 1.03666 0.518331 0.855180i \(-0.326554\pi\)
0.518331 + 0.855180i \(0.326554\pi\)
\(888\) 1.22501 0.0411087
\(889\) −85.2458 −2.85905
\(890\) 0.384321 0.0128825
\(891\) 46.4875 1.55739
\(892\) 21.7277 0.727498
\(893\) −0.216812 −0.00725533
\(894\) 1.45664 0.0487173
\(895\) 20.3213 0.679265
\(896\) −4.63233 −0.154755
\(897\) 0.215919 0.00720932
\(898\) 0.342985 0.0114456
\(899\) −7.03585 −0.234659
\(900\) −2.96802 −0.0989339
\(901\) −74.3943 −2.47843
\(902\) 39.2501 1.30688
\(903\) −10.3082 −0.343034
\(904\) −13.8676 −0.461229
\(905\) −16.0859 −0.534713
\(906\) −0.862624 −0.0286588
\(907\) −25.3403 −0.841410 −0.420705 0.907197i \(-0.638217\pi\)
−0.420705 + 0.907197i \(0.638217\pi\)
\(908\) 15.9688 0.529943
\(909\) −15.8240 −0.524849
\(910\) −4.63233 −0.153560
\(911\) 47.5468 1.57530 0.787648 0.616125i \(-0.211298\pi\)
0.787648 + 0.616125i \(0.211298\pi\)
\(912\) −0.118699 −0.00393052
\(913\) −47.6807 −1.57800
\(914\) −12.6480 −0.418359
\(915\) 1.96895 0.0650915
\(916\) 14.7883 0.488620
\(917\) 32.5598 1.07522
\(918\) 6.44274 0.212642
\(919\) −47.8058 −1.57697 −0.788485 0.615055i \(-0.789134\pi\)
−0.788485 + 0.615055i \(0.789134\pi\)
\(920\) 1.20734 0.0398049
\(921\) −2.80404 −0.0923964
\(922\) −11.1326 −0.366633
\(923\) 9.94396 0.327310
\(924\) −4.41997 −0.145406
\(925\) 6.84984 0.225221
\(926\) −36.7366 −1.20724
\(927\) −2.26047 −0.0742436
\(928\) 7.03585 0.230963
\(929\) −42.0246 −1.37878 −0.689391 0.724390i \(-0.742122\pi\)
−0.689391 + 0.724390i \(0.742122\pi\)
\(930\) 0.178838 0.00586434
\(931\) −9.59642 −0.314510
\(932\) 6.09633 0.199692
\(933\) 0.287461 0.00941106
\(934\) 15.6133 0.510883
\(935\) 32.2062 1.05326
\(936\) 2.96802 0.0970127
\(937\) −30.8158 −1.00671 −0.503354 0.864080i \(-0.667901\pi\)
−0.503354 + 0.864080i \(0.667901\pi\)
\(938\) 14.9930 0.489539
\(939\) 5.93920 0.193819
\(940\) −0.326660 −0.0106545
\(941\) 14.0282 0.457306 0.228653 0.973508i \(-0.426568\pi\)
0.228653 + 0.973508i \(0.426568\pi\)
\(942\) −1.64245 −0.0535138
\(943\) −8.88200 −0.289238
\(944\) 10.9205 0.355433
\(945\) −4.94413 −0.160833
\(946\) 66.3868 2.15842
\(947\) −44.8909 −1.45876 −0.729379 0.684110i \(-0.760191\pi\)
−0.729379 + 0.684110i \(0.760191\pi\)
\(948\) 2.82417 0.0917248
\(949\) −1.10218 −0.0357783
\(950\) −0.663724 −0.0215340
\(951\) −5.04691 −0.163657
\(952\) 27.9627 0.906278
\(953\) 44.7485 1.44955 0.724773 0.688988i \(-0.241945\pi\)
0.724773 + 0.688988i \(0.241945\pi\)
\(954\) −36.5785 −1.18427
\(955\) −3.94669 −0.127712
\(956\) 27.2233 0.880464
\(957\) 6.71331 0.217010
\(958\) −4.03715 −0.130434
\(959\) −71.2972 −2.30231
\(960\) −0.178838 −0.00577198
\(961\) 1.00000 0.0322581
\(962\) −6.84984 −0.220848
\(963\) 53.3344 1.71868
\(964\) −8.85643 −0.285246
\(965\) 1.51907 0.0489006
\(966\) 1.00021 0.0321811
\(967\) −2.51505 −0.0808786 −0.0404393 0.999182i \(-0.512876\pi\)
−0.0404393 + 0.999182i \(0.512876\pi\)
\(968\) 17.4655 0.561364
\(969\) 0.716520 0.0230179
\(970\) 17.7548 0.570073
\(971\) −25.2644 −0.810773 −0.405386 0.914145i \(-0.632863\pi\)
−0.405386 + 0.914145i \(0.632863\pi\)
\(972\) 4.76018 0.152683
\(973\) 24.6931 0.791624
\(974\) 40.9020 1.31058
\(975\) −0.178838 −0.00572741
\(976\) −11.0097 −0.352411
\(977\) −41.9063 −1.34070 −0.670350 0.742045i \(-0.733856\pi\)
−0.670350 + 0.742045i \(0.733856\pi\)
\(978\) 0.806152 0.0257779
\(979\) −2.05047 −0.0655333
\(980\) −14.4585 −0.461859
\(981\) −35.4019 −1.13030
\(982\) 30.5529 0.974982
\(983\) 47.9142 1.52823 0.764113 0.645082i \(-0.223177\pi\)
0.764113 + 0.645082i \(0.223177\pi\)
\(984\) 1.31565 0.0419415
\(985\) −19.1945 −0.611588
\(986\) −42.4714 −1.35257
\(987\) −0.270617 −0.00861383
\(988\) 0.663724 0.0211159
\(989\) −15.0228 −0.477698
\(990\) 15.8353 0.503279
\(991\) −27.8008 −0.883120 −0.441560 0.897232i \(-0.645575\pi\)
−0.441560 + 0.897232i \(0.645575\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 2.70237 0.0857571
\(994\) 46.0637 1.46105
\(995\) 3.45167 0.109425
\(996\) −1.59825 −0.0506424
\(997\) −59.8817 −1.89647 −0.948236 0.317567i \(-0.897134\pi\)
−0.948236 + 0.317567i \(0.897134\pi\)
\(998\) 26.9218 0.852196
\(999\) −7.31090 −0.231307
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 \(a_p\))