Properties

Label 4010.2.a.k.1.1
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.07374\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.34293 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.34293 q^{6} +3.45446 q^{7} -1.00000 q^{8} +8.17517 q^{9} +1.00000 q^{10} +3.65066 q^{11} -3.34293 q^{12} +3.49629 q^{13} -3.45446 q^{14} +3.34293 q^{15} +1.00000 q^{16} +4.44571 q^{17} -8.17517 q^{18} -6.26283 q^{19} -1.00000 q^{20} -11.5480 q^{21} -3.65066 q^{22} -7.57267 q^{23} +3.34293 q^{24} +1.00000 q^{25} -3.49629 q^{26} -17.3002 q^{27} +3.45446 q^{28} -2.62514 q^{29} -3.34293 q^{30} +3.28327 q^{31} -1.00000 q^{32} -12.2039 q^{33} -4.44571 q^{34} -3.45446 q^{35} +8.17517 q^{36} -7.45793 q^{37} +6.26283 q^{38} -11.6879 q^{39} +1.00000 q^{40} +4.62987 q^{41} +11.5480 q^{42} -9.40958 q^{43} +3.65066 q^{44} -8.17517 q^{45} +7.57267 q^{46} -4.02949 q^{47} -3.34293 q^{48} +4.93327 q^{49} -1.00000 q^{50} -14.8617 q^{51} +3.49629 q^{52} +4.07029 q^{53} +17.3002 q^{54} -3.65066 q^{55} -3.45446 q^{56} +20.9362 q^{57} +2.62514 q^{58} +4.53317 q^{59} +3.34293 q^{60} -11.7429 q^{61} -3.28327 q^{62} +28.2408 q^{63} +1.00000 q^{64} -3.49629 q^{65} +12.2039 q^{66} -2.55592 q^{67} +4.44571 q^{68} +25.3149 q^{69} +3.45446 q^{70} +13.5208 q^{71} -8.17517 q^{72} -12.2418 q^{73} +7.45793 q^{74} -3.34293 q^{75} -6.26283 q^{76} +12.6111 q^{77} +11.6879 q^{78} -11.7450 q^{79} -1.00000 q^{80} +33.3079 q^{81} -4.62987 q^{82} -9.38947 q^{83} -11.5480 q^{84} -4.44571 q^{85} +9.40958 q^{86} +8.77564 q^{87} -3.65066 q^{88} +1.01654 q^{89} +8.17517 q^{90} +12.0778 q^{91} -7.57267 q^{92} -10.9757 q^{93} +4.02949 q^{94} +6.26283 q^{95} +3.34293 q^{96} +3.76457 q^{97} -4.93327 q^{98} +29.8448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −3.34293 −1.93004 −0.965020 0.262175i \(-0.915560\pi\)
−0.965020 + 0.262175i \(0.915560\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 3.34293 1.36474
\(7\) 3.45446 1.30566 0.652831 0.757504i \(-0.273581\pi\)
0.652831 + 0.757504i \(0.273581\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.17517 2.72506
\(10\) 1.00000 0.316228
\(11\) 3.65066 1.10072 0.550358 0.834929i \(-0.314491\pi\)
0.550358 + 0.834929i \(0.314491\pi\)
\(12\) −3.34293 −0.965020
\(13\) 3.49629 0.969697 0.484849 0.874598i \(-0.338875\pi\)
0.484849 + 0.874598i \(0.338875\pi\)
\(14\) −3.45446 −0.923242
\(15\) 3.34293 0.863140
\(16\) 1.00000 0.250000
\(17\) 4.44571 1.07824 0.539122 0.842228i \(-0.318756\pi\)
0.539122 + 0.842228i \(0.318756\pi\)
\(18\) −8.17517 −1.92691
\(19\) −6.26283 −1.43679 −0.718396 0.695635i \(-0.755123\pi\)
−0.718396 + 0.695635i \(0.755123\pi\)
\(20\) −1.00000 −0.223607
\(21\) −11.5480 −2.51998
\(22\) −3.65066 −0.778324
\(23\) −7.57267 −1.57901 −0.789506 0.613743i \(-0.789663\pi\)
−0.789506 + 0.613743i \(0.789663\pi\)
\(24\) 3.34293 0.682372
\(25\) 1.00000 0.200000
\(26\) −3.49629 −0.685679
\(27\) −17.3002 −3.32943
\(28\) 3.45446 0.652831
\(29\) −2.62514 −0.487475 −0.243738 0.969841i \(-0.578374\pi\)
−0.243738 + 0.969841i \(0.578374\pi\)
\(30\) −3.34293 −0.610332
\(31\) 3.28327 0.589692 0.294846 0.955545i \(-0.404732\pi\)
0.294846 + 0.955545i \(0.404732\pi\)
\(32\) −1.00000 −0.176777
\(33\) −12.2039 −2.12443
\(34\) −4.44571 −0.762433
\(35\) −3.45446 −0.583910
\(36\) 8.17517 1.36253
\(37\) −7.45793 −1.22608 −0.613038 0.790053i \(-0.710053\pi\)
−0.613038 + 0.790053i \(0.710053\pi\)
\(38\) 6.26283 1.01597
\(39\) −11.6879 −1.87156
\(40\) 1.00000 0.158114
\(41\) 4.62987 0.723064 0.361532 0.932360i \(-0.382254\pi\)
0.361532 + 0.932360i \(0.382254\pi\)
\(42\) 11.5480 1.78190
\(43\) −9.40958 −1.43495 −0.717474 0.696585i \(-0.754702\pi\)
−0.717474 + 0.696585i \(0.754702\pi\)
\(44\) 3.65066 0.550358
\(45\) −8.17517 −1.21868
\(46\) 7.57267 1.11653
\(47\) −4.02949 −0.587762 −0.293881 0.955842i \(-0.594947\pi\)
−0.293881 + 0.955842i \(0.594947\pi\)
\(48\) −3.34293 −0.482510
\(49\) 4.93327 0.704753
\(50\) −1.00000 −0.141421
\(51\) −14.8617 −2.08105
\(52\) 3.49629 0.484849
\(53\) 4.07029 0.559098 0.279549 0.960131i \(-0.409815\pi\)
0.279549 + 0.960131i \(0.409815\pi\)
\(54\) 17.3002 2.35426
\(55\) −3.65066 −0.492255
\(56\) −3.45446 −0.461621
\(57\) 20.9362 2.77307
\(58\) 2.62514 0.344697
\(59\) 4.53317 0.590169 0.295085 0.955471i \(-0.404652\pi\)
0.295085 + 0.955471i \(0.404652\pi\)
\(60\) 3.34293 0.431570
\(61\) −11.7429 −1.50352 −0.751762 0.659435i \(-0.770796\pi\)
−0.751762 + 0.659435i \(0.770796\pi\)
\(62\) −3.28327 −0.416975
\(63\) 28.2408 3.55800
\(64\) 1.00000 0.125000
\(65\) −3.49629 −0.433662
\(66\) 12.2039 1.50220
\(67\) −2.55592 −0.312255 −0.156128 0.987737i \(-0.549901\pi\)
−0.156128 + 0.987737i \(0.549901\pi\)
\(68\) 4.44571 0.539122
\(69\) 25.3149 3.04756
\(70\) 3.45446 0.412887
\(71\) 13.5208 1.60462 0.802311 0.596906i \(-0.203603\pi\)
0.802311 + 0.596906i \(0.203603\pi\)
\(72\) −8.17517 −0.963453
\(73\) −12.2418 −1.43279 −0.716395 0.697695i \(-0.754209\pi\)
−0.716395 + 0.697695i \(0.754209\pi\)
\(74\) 7.45793 0.866967
\(75\) −3.34293 −0.386008
\(76\) −6.26283 −0.718396
\(77\) 12.6111 1.43716
\(78\) 11.6879 1.32339
\(79\) −11.7450 −1.32142 −0.660708 0.750643i \(-0.729744\pi\)
−0.660708 + 0.750643i \(0.729744\pi\)
\(80\) −1.00000 −0.111803
\(81\) 33.3079 3.70088
\(82\) −4.62987 −0.511284
\(83\) −9.38947 −1.03063 −0.515314 0.857001i \(-0.672325\pi\)
−0.515314 + 0.857001i \(0.672325\pi\)
\(84\) −11.5480 −1.25999
\(85\) −4.44571 −0.482205
\(86\) 9.40958 1.01466
\(87\) 8.77564 0.940848
\(88\) −3.65066 −0.389162
\(89\) 1.01654 0.107753 0.0538763 0.998548i \(-0.482842\pi\)
0.0538763 + 0.998548i \(0.482842\pi\)
\(90\) 8.17517 0.861739
\(91\) 12.0778 1.26610
\(92\) −7.57267 −0.789506
\(93\) −10.9757 −1.13813
\(94\) 4.02949 0.415610
\(95\) 6.26283 0.642553
\(96\) 3.34293 0.341186
\(97\) 3.76457 0.382234 0.191117 0.981567i \(-0.438789\pi\)
0.191117 + 0.981567i \(0.438789\pi\)
\(98\) −4.93327 −0.498336
\(99\) 29.8448 2.99951
\(100\) 1.00000 0.100000
\(101\) 9.63337 0.958556 0.479278 0.877663i \(-0.340899\pi\)
0.479278 + 0.877663i \(0.340899\pi\)
\(102\) 14.8617 1.47153
\(103\) −13.3052 −1.31100 −0.655498 0.755197i \(-0.727541\pi\)
−0.655498 + 0.755197i \(0.727541\pi\)
\(104\) −3.49629 −0.342840
\(105\) 11.5480 1.12697
\(106\) −4.07029 −0.395342
\(107\) −8.65878 −0.837076 −0.418538 0.908199i \(-0.637457\pi\)
−0.418538 + 0.908199i \(0.637457\pi\)
\(108\) −17.3002 −1.66472
\(109\) −9.64624 −0.923942 −0.461971 0.886895i \(-0.652858\pi\)
−0.461971 + 0.886895i \(0.652858\pi\)
\(110\) 3.65066 0.348077
\(111\) 24.9313 2.36638
\(112\) 3.45446 0.326415
\(113\) −9.31138 −0.875941 −0.437971 0.898989i \(-0.644303\pi\)
−0.437971 + 0.898989i \(0.644303\pi\)
\(114\) −20.9362 −1.96085
\(115\) 7.57267 0.706155
\(116\) −2.62514 −0.243738
\(117\) 28.5828 2.64248
\(118\) −4.53317 −0.417313
\(119\) 15.3575 1.40782
\(120\) −3.34293 −0.305166
\(121\) 2.32733 0.211575
\(122\) 11.7429 1.06315
\(123\) −15.4773 −1.39554
\(124\) 3.28327 0.294846
\(125\) −1.00000 −0.0894427
\(126\) −28.2408 −2.51589
\(127\) −7.95062 −0.705503 −0.352752 0.935717i \(-0.614754\pi\)
−0.352752 + 0.935717i \(0.614754\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 31.4556 2.76951
\(130\) 3.49629 0.306645
\(131\) 12.6694 1.10693 0.553467 0.832871i \(-0.313304\pi\)
0.553467 + 0.832871i \(0.313304\pi\)
\(132\) −12.2039 −1.06221
\(133\) −21.6347 −1.87596
\(134\) 2.55592 0.220798
\(135\) 17.3002 1.48897
\(136\) −4.44571 −0.381217
\(137\) 0.305403 0.0260923 0.0130462 0.999915i \(-0.495847\pi\)
0.0130462 + 0.999915i \(0.495847\pi\)
\(138\) −25.3149 −2.15495
\(139\) 4.21702 0.357683 0.178841 0.983878i \(-0.442765\pi\)
0.178841 + 0.983878i \(0.442765\pi\)
\(140\) −3.45446 −0.291955
\(141\) 13.4703 1.13440
\(142\) −13.5208 −1.13464
\(143\) 12.7638 1.06736
\(144\) 8.17517 0.681264
\(145\) 2.62514 0.218006
\(146\) 12.2418 1.01314
\(147\) −16.4916 −1.36020
\(148\) −7.45793 −0.613038
\(149\) −10.9607 −0.897937 −0.448968 0.893548i \(-0.648208\pi\)
−0.448968 + 0.893548i \(0.648208\pi\)
\(150\) 3.34293 0.272949
\(151\) −5.55463 −0.452030 −0.226015 0.974124i \(-0.572570\pi\)
−0.226015 + 0.974124i \(0.572570\pi\)
\(152\) 6.26283 0.507983
\(153\) 36.3445 2.93828
\(154\) −12.6111 −1.01623
\(155\) −3.28327 −0.263718
\(156\) −11.6879 −0.935778
\(157\) −10.1392 −0.809193 −0.404597 0.914495i \(-0.632588\pi\)
−0.404597 + 0.914495i \(0.632588\pi\)
\(158\) 11.7450 0.934382
\(159\) −13.6067 −1.07908
\(160\) 1.00000 0.0790569
\(161\) −26.1595 −2.06166
\(162\) −33.3079 −2.61692
\(163\) 11.3585 0.889668 0.444834 0.895613i \(-0.353263\pi\)
0.444834 + 0.895613i \(0.353263\pi\)
\(164\) 4.62987 0.361532
\(165\) 12.2039 0.950072
\(166\) 9.38947 0.728764
\(167\) 10.1324 0.784071 0.392036 0.919950i \(-0.371771\pi\)
0.392036 + 0.919950i \(0.371771\pi\)
\(168\) 11.5480 0.890948
\(169\) −0.775935 −0.0596873
\(170\) 4.44571 0.340971
\(171\) −51.1997 −3.91534
\(172\) −9.40958 −0.717474
\(173\) −17.6077 −1.33869 −0.669344 0.742953i \(-0.733425\pi\)
−0.669344 + 0.742953i \(0.733425\pi\)
\(174\) −8.77564 −0.665280
\(175\) 3.45446 0.261132
\(176\) 3.65066 0.275179
\(177\) −15.1541 −1.13905
\(178\) −1.01654 −0.0761926
\(179\) −24.2483 −1.81241 −0.906203 0.422843i \(-0.861032\pi\)
−0.906203 + 0.422843i \(0.861032\pi\)
\(180\) −8.17517 −0.609341
\(181\) −5.16159 −0.383658 −0.191829 0.981428i \(-0.561442\pi\)
−0.191829 + 0.981428i \(0.561442\pi\)
\(182\) −12.0778 −0.895266
\(183\) 39.2557 2.90186
\(184\) 7.57267 0.558265
\(185\) 7.45793 0.548318
\(186\) 10.9757 0.804779
\(187\) 16.2298 1.18684
\(188\) −4.02949 −0.293881
\(189\) −59.7629 −4.34711
\(190\) −6.26283 −0.454353
\(191\) −14.8898 −1.07739 −0.538695 0.842501i \(-0.681083\pi\)
−0.538695 + 0.842501i \(0.681083\pi\)
\(192\) −3.34293 −0.241255
\(193\) 10.3403 0.744312 0.372156 0.928170i \(-0.378619\pi\)
0.372156 + 0.928170i \(0.378619\pi\)
\(194\) −3.76457 −0.270280
\(195\) 11.6879 0.836985
\(196\) 4.93327 0.352376
\(197\) 26.7271 1.90423 0.952114 0.305744i \(-0.0989052\pi\)
0.952114 + 0.305744i \(0.0989052\pi\)
\(198\) −29.8448 −2.12098
\(199\) −0.620373 −0.0439771 −0.0219885 0.999758i \(-0.507000\pi\)
−0.0219885 + 0.999758i \(0.507000\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.54426 0.602665
\(202\) −9.63337 −0.677802
\(203\) −9.06842 −0.636478
\(204\) −14.8617 −1.04053
\(205\) −4.62987 −0.323364
\(206\) 13.3052 0.927014
\(207\) −61.9079 −4.30290
\(208\) 3.49629 0.242424
\(209\) −22.8635 −1.58150
\(210\) −11.5480 −0.796888
\(211\) −4.78650 −0.329516 −0.164758 0.986334i \(-0.552684\pi\)
−0.164758 + 0.986334i \(0.552684\pi\)
\(212\) 4.07029 0.279549
\(213\) −45.1990 −3.09699
\(214\) 8.65878 0.591902
\(215\) 9.40958 0.641728
\(216\) 17.3002 1.17713
\(217\) 11.3419 0.769938
\(218\) 9.64624 0.653326
\(219\) 40.9233 2.76534
\(220\) −3.65066 −0.246128
\(221\) 15.5435 1.04557
\(222\) −24.9313 −1.67328
\(223\) −27.9906 −1.87439 −0.937195 0.348806i \(-0.886587\pi\)
−0.937195 + 0.348806i \(0.886587\pi\)
\(224\) −3.45446 −0.230811
\(225\) 8.17517 0.545012
\(226\) 9.31138 0.619384
\(227\) −4.43698 −0.294493 −0.147246 0.989100i \(-0.547041\pi\)
−0.147246 + 0.989100i \(0.547041\pi\)
\(228\) 20.9362 1.38653
\(229\) 27.5641 1.82149 0.910744 0.412972i \(-0.135509\pi\)
0.910744 + 0.412972i \(0.135509\pi\)
\(230\) −7.57267 −0.499327
\(231\) −42.1578 −2.77378
\(232\) 2.62514 0.172349
\(233\) −11.9986 −0.786057 −0.393029 0.919526i \(-0.628573\pi\)
−0.393029 + 0.919526i \(0.628573\pi\)
\(234\) −28.5828 −1.86852
\(235\) 4.02949 0.262855
\(236\) 4.53317 0.295085
\(237\) 39.2627 2.55039
\(238\) −15.3575 −0.995480
\(239\) 20.7284 1.34081 0.670406 0.741995i \(-0.266120\pi\)
0.670406 + 0.741995i \(0.266120\pi\)
\(240\) 3.34293 0.215785
\(241\) 21.3272 1.37381 0.686904 0.726748i \(-0.258969\pi\)
0.686904 + 0.726748i \(0.258969\pi\)
\(242\) −2.32733 −0.149606
\(243\) −59.4453 −3.81342
\(244\) −11.7429 −0.751762
\(245\) −4.93327 −0.315175
\(246\) 15.4773 0.986798
\(247\) −21.8967 −1.39325
\(248\) −3.28327 −0.208488
\(249\) 31.3883 1.98915
\(250\) 1.00000 0.0632456
\(251\) 13.0329 0.822630 0.411315 0.911493i \(-0.365070\pi\)
0.411315 + 0.911493i \(0.365070\pi\)
\(252\) 28.2408 1.77900
\(253\) −27.6453 −1.73804
\(254\) 7.95062 0.498866
\(255\) 14.8617 0.930676
\(256\) 1.00000 0.0625000
\(257\) 9.04869 0.564442 0.282221 0.959349i \(-0.408929\pi\)
0.282221 + 0.959349i \(0.408929\pi\)
\(258\) −31.4556 −1.95834
\(259\) −25.7631 −1.60084
\(260\) −3.49629 −0.216831
\(261\) −21.4609 −1.32840
\(262\) −12.6694 −0.782721
\(263\) 18.8162 1.16025 0.580127 0.814526i \(-0.303003\pi\)
0.580127 + 0.814526i \(0.303003\pi\)
\(264\) 12.2039 0.751098
\(265\) −4.07029 −0.250036
\(266\) 21.6347 1.32651
\(267\) −3.39821 −0.207967
\(268\) −2.55592 −0.156128
\(269\) −22.5925 −1.37749 −0.688744 0.725005i \(-0.741838\pi\)
−0.688744 + 0.725005i \(0.741838\pi\)
\(270\) −17.3002 −1.05286
\(271\) 22.2738 1.35304 0.676518 0.736426i \(-0.263488\pi\)
0.676518 + 0.736426i \(0.263488\pi\)
\(272\) 4.44571 0.269561
\(273\) −40.3752 −2.44362
\(274\) −0.305403 −0.0184501
\(275\) 3.65066 0.220143
\(276\) 25.3149 1.52378
\(277\) 28.2150 1.69527 0.847637 0.530576i \(-0.178024\pi\)
0.847637 + 0.530576i \(0.178024\pi\)
\(278\) −4.21702 −0.252920
\(279\) 26.8413 1.60694
\(280\) 3.45446 0.206443
\(281\) −11.5833 −0.691000 −0.345500 0.938419i \(-0.612291\pi\)
−0.345500 + 0.938419i \(0.612291\pi\)
\(282\) −13.4703 −0.802145
\(283\) −11.3650 −0.675579 −0.337789 0.941222i \(-0.609679\pi\)
−0.337789 + 0.941222i \(0.609679\pi\)
\(284\) 13.5208 0.802311
\(285\) −20.9362 −1.24015
\(286\) −12.7638 −0.754738
\(287\) 15.9937 0.944078
\(288\) −8.17517 −0.481727
\(289\) 2.76436 0.162610
\(290\) −2.62514 −0.154153
\(291\) −12.5847 −0.737727
\(292\) −12.2418 −0.716395
\(293\) 2.36108 0.137936 0.0689678 0.997619i \(-0.478029\pi\)
0.0689678 + 0.997619i \(0.478029\pi\)
\(294\) 16.4916 0.961808
\(295\) −4.53317 −0.263932
\(296\) 7.45793 0.433484
\(297\) −63.1573 −3.66476
\(298\) 10.9607 0.634937
\(299\) −26.4763 −1.53116
\(300\) −3.34293 −0.193004
\(301\) −32.5050 −1.87356
\(302\) 5.55463 0.319633
\(303\) −32.2037 −1.85005
\(304\) −6.26283 −0.359198
\(305\) 11.7429 0.672396
\(306\) −36.3445 −2.07768
\(307\) −6.48616 −0.370185 −0.185092 0.982721i \(-0.559258\pi\)
−0.185092 + 0.982721i \(0.559258\pi\)
\(308\) 12.6111 0.718581
\(309\) 44.4782 2.53028
\(310\) 3.28327 0.186477
\(311\) −25.2762 −1.43328 −0.716640 0.697443i \(-0.754321\pi\)
−0.716640 + 0.697443i \(0.754321\pi\)
\(312\) 11.6879 0.661695
\(313\) 7.61926 0.430666 0.215333 0.976541i \(-0.430916\pi\)
0.215333 + 0.976541i \(0.430916\pi\)
\(314\) 10.1392 0.572186
\(315\) −28.2408 −1.59119
\(316\) −11.7450 −0.660708
\(317\) 16.5917 0.931884 0.465942 0.884815i \(-0.345716\pi\)
0.465942 + 0.884815i \(0.345716\pi\)
\(318\) 13.6067 0.763026
\(319\) −9.58348 −0.536572
\(320\) −1.00000 −0.0559017
\(321\) 28.9457 1.61559
\(322\) 26.1595 1.45781
\(323\) −27.8427 −1.54921
\(324\) 33.3079 1.85044
\(325\) 3.49629 0.193939
\(326\) −11.3585 −0.629090
\(327\) 32.2467 1.78325
\(328\) −4.62987 −0.255642
\(329\) −13.9197 −0.767418
\(330\) −12.2039 −0.671803
\(331\) −16.0676 −0.883157 −0.441578 0.897223i \(-0.645581\pi\)
−0.441578 + 0.897223i \(0.645581\pi\)
\(332\) −9.38947 −0.515314
\(333\) −60.9699 −3.34113
\(334\) −10.1324 −0.554422
\(335\) 2.55592 0.139645
\(336\) −11.5480 −0.629995
\(337\) −32.4640 −1.76843 −0.884213 0.467084i \(-0.845305\pi\)
−0.884213 + 0.467084i \(0.845305\pi\)
\(338\) 0.775935 0.0422053
\(339\) 31.1273 1.69060
\(340\) −4.44571 −0.241103
\(341\) 11.9861 0.649083
\(342\) 51.1997 2.76856
\(343\) −7.13943 −0.385493
\(344\) 9.40958 0.507331
\(345\) −25.3149 −1.36291
\(346\) 17.6077 0.946595
\(347\) −25.8709 −1.38882 −0.694410 0.719579i \(-0.744335\pi\)
−0.694410 + 0.719579i \(0.744335\pi\)
\(348\) 8.77564 0.470424
\(349\) 16.1470 0.864330 0.432165 0.901794i \(-0.357750\pi\)
0.432165 + 0.901794i \(0.357750\pi\)
\(350\) −3.45446 −0.184648
\(351\) −60.4867 −3.22854
\(352\) −3.65066 −0.194581
\(353\) 26.9240 1.43302 0.716511 0.697576i \(-0.245738\pi\)
0.716511 + 0.697576i \(0.245738\pi\)
\(354\) 15.1541 0.805430
\(355\) −13.5208 −0.717609
\(356\) 1.01654 0.0538763
\(357\) −51.3391 −2.71715
\(358\) 24.2483 1.28156
\(359\) 9.66274 0.509980 0.254990 0.966944i \(-0.417928\pi\)
0.254990 + 0.966944i \(0.417928\pi\)
\(360\) 8.17517 0.430869
\(361\) 20.2230 1.06437
\(362\) 5.16159 0.271287
\(363\) −7.78009 −0.408349
\(364\) 12.0778 0.633048
\(365\) 12.2418 0.640763
\(366\) −39.2557 −2.05193
\(367\) 23.3113 1.21684 0.608419 0.793616i \(-0.291804\pi\)
0.608419 + 0.793616i \(0.291804\pi\)
\(368\) −7.57267 −0.394753
\(369\) 37.8500 1.97039
\(370\) −7.45793 −0.387719
\(371\) 14.0606 0.729992
\(372\) −10.9757 −0.569065
\(373\) 18.7188 0.969223 0.484612 0.874729i \(-0.338961\pi\)
0.484612 + 0.874729i \(0.338961\pi\)
\(374\) −16.2298 −0.839223
\(375\) 3.34293 0.172628
\(376\) 4.02949 0.207805
\(377\) −9.17824 −0.472704
\(378\) 59.7629 3.07387
\(379\) −28.5930 −1.46872 −0.734362 0.678758i \(-0.762519\pi\)
−0.734362 + 0.678758i \(0.762519\pi\)
\(380\) 6.26283 0.321276
\(381\) 26.5784 1.36165
\(382\) 14.8898 0.761830
\(383\) −4.40398 −0.225033 −0.112516 0.993650i \(-0.535891\pi\)
−0.112516 + 0.993650i \(0.535891\pi\)
\(384\) 3.34293 0.170593
\(385\) −12.6111 −0.642719
\(386\) −10.3403 −0.526308
\(387\) −76.9250 −3.91032
\(388\) 3.76457 0.191117
\(389\) −24.5618 −1.24533 −0.622667 0.782487i \(-0.713951\pi\)
−0.622667 + 0.782487i \(0.713951\pi\)
\(390\) −11.6879 −0.591838
\(391\) −33.6659 −1.70256
\(392\) −4.93327 −0.249168
\(393\) −42.3530 −2.13643
\(394\) −26.7271 −1.34649
\(395\) 11.7450 0.590955
\(396\) 29.8448 1.49976
\(397\) 15.5751 0.781691 0.390845 0.920456i \(-0.372183\pi\)
0.390845 + 0.920456i \(0.372183\pi\)
\(398\) 0.620373 0.0310965
\(399\) 72.3232 3.62069
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −8.54426 −0.426149
\(403\) 11.4793 0.571823
\(404\) 9.63337 0.479278
\(405\) −33.3079 −1.65508
\(406\) 9.06842 0.450058
\(407\) −27.2264 −1.34956
\(408\) 14.8617 0.735764
\(409\) −22.2350 −1.09945 −0.549724 0.835346i \(-0.685267\pi\)
−0.549724 + 0.835346i \(0.685267\pi\)
\(410\) 4.62987 0.228653
\(411\) −1.02094 −0.0503593
\(412\) −13.3052 −0.655498
\(413\) 15.6597 0.770561
\(414\) 61.9079 3.04261
\(415\) 9.38947 0.460911
\(416\) −3.49629 −0.171420
\(417\) −14.0972 −0.690343
\(418\) 22.8635 1.11829
\(419\) 21.5003 1.05036 0.525179 0.850992i \(-0.323998\pi\)
0.525179 + 0.850992i \(0.323998\pi\)
\(420\) 11.5480 0.563485
\(421\) −35.3921 −1.72490 −0.862452 0.506139i \(-0.831072\pi\)
−0.862452 + 0.506139i \(0.831072\pi\)
\(422\) 4.78650 0.233003
\(423\) −32.9418 −1.60168
\(424\) −4.07029 −0.197671
\(425\) 4.44571 0.215649
\(426\) 45.1990 2.18990
\(427\) −40.5653 −1.96309
\(428\) −8.65878 −0.418538
\(429\) −42.6684 −2.06005
\(430\) −9.40958 −0.453770
\(431\) 17.4615 0.841089 0.420544 0.907272i \(-0.361839\pi\)
0.420544 + 0.907272i \(0.361839\pi\)
\(432\) −17.3002 −0.832358
\(433\) 25.5592 1.22830 0.614149 0.789190i \(-0.289499\pi\)
0.614149 + 0.789190i \(0.289499\pi\)
\(434\) −11.3419 −0.544429
\(435\) −8.77564 −0.420760
\(436\) −9.64624 −0.461971
\(437\) 47.4264 2.26871
\(438\) −40.9233 −1.95539
\(439\) 0.954774 0.0455689 0.0227844 0.999740i \(-0.492747\pi\)
0.0227844 + 0.999740i \(0.492747\pi\)
\(440\) 3.65066 0.174038
\(441\) 40.3303 1.92049
\(442\) −15.5435 −0.739330
\(443\) −22.2117 −1.05531 −0.527654 0.849459i \(-0.676928\pi\)
−0.527654 + 0.849459i \(0.676928\pi\)
\(444\) 24.9313 1.18319
\(445\) −1.01654 −0.0481884
\(446\) 27.9906 1.32539
\(447\) 36.6409 1.73305
\(448\) 3.45446 0.163208
\(449\) −10.9315 −0.515891 −0.257945 0.966159i \(-0.583045\pi\)
−0.257945 + 0.966159i \(0.583045\pi\)
\(450\) −8.17517 −0.385381
\(451\) 16.9021 0.795888
\(452\) −9.31138 −0.437971
\(453\) 18.5687 0.872436
\(454\) 4.43698 0.208238
\(455\) −12.0778 −0.566216
\(456\) −20.9362 −0.980427
\(457\) 18.8479 0.881667 0.440833 0.897589i \(-0.354683\pi\)
0.440833 + 0.897589i \(0.354683\pi\)
\(458\) −27.5641 −1.28799
\(459\) −76.9119 −3.58994
\(460\) 7.57267 0.353078
\(461\) −13.9256 −0.648580 −0.324290 0.945958i \(-0.605125\pi\)
−0.324290 + 0.945958i \(0.605125\pi\)
\(462\) 42.1578 1.96136
\(463\) −7.79458 −0.362245 −0.181123 0.983461i \(-0.557973\pi\)
−0.181123 + 0.983461i \(0.557973\pi\)
\(464\) −2.62514 −0.121869
\(465\) 10.9757 0.508987
\(466\) 11.9986 0.555826
\(467\) −30.0377 −1.38998 −0.694990 0.719019i \(-0.744591\pi\)
−0.694990 + 0.719019i \(0.744591\pi\)
\(468\) 28.5828 1.32124
\(469\) −8.82931 −0.407700
\(470\) −4.02949 −0.185867
\(471\) 33.8945 1.56178
\(472\) −4.53317 −0.208656
\(473\) −34.3512 −1.57947
\(474\) −39.2627 −1.80340
\(475\) −6.26283 −0.287358
\(476\) 15.3575 0.703911
\(477\) 33.2753 1.52357
\(478\) −20.7284 −0.948097
\(479\) −12.4327 −0.568063 −0.284032 0.958815i \(-0.591672\pi\)
−0.284032 + 0.958815i \(0.591672\pi\)
\(480\) −3.34293 −0.152583
\(481\) −26.0751 −1.18892
\(482\) −21.3272 −0.971429
\(483\) 87.4493 3.97908
\(484\) 2.32733 0.105788
\(485\) −3.76457 −0.170940
\(486\) 59.4453 2.69650
\(487\) −15.1280 −0.685515 −0.342758 0.939424i \(-0.611361\pi\)
−0.342758 + 0.939424i \(0.611361\pi\)
\(488\) 11.7429 0.531576
\(489\) −37.9707 −1.71710
\(490\) 4.93327 0.222862
\(491\) −28.3599 −1.27986 −0.639932 0.768431i \(-0.721038\pi\)
−0.639932 + 0.768431i \(0.721038\pi\)
\(492\) −15.4773 −0.697772
\(493\) −11.6706 −0.525617
\(494\) 21.8967 0.985178
\(495\) −29.8448 −1.34142
\(496\) 3.28327 0.147423
\(497\) 46.7070 2.09509
\(498\) −31.3883 −1.40654
\(499\) 12.2680 0.549190 0.274595 0.961560i \(-0.411456\pi\)
0.274595 + 0.961560i \(0.411456\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −33.8720 −1.51329
\(502\) −13.0329 −0.581687
\(503\) −0.349538 −0.0155851 −0.00779257 0.999970i \(-0.502480\pi\)
−0.00779257 + 0.999970i \(0.502480\pi\)
\(504\) −28.2408 −1.25794
\(505\) −9.63337 −0.428679
\(506\) 27.6453 1.22898
\(507\) 2.59390 0.115199
\(508\) −7.95062 −0.352752
\(509\) 14.2824 0.633058 0.316529 0.948583i \(-0.397483\pi\)
0.316529 + 0.948583i \(0.397483\pi\)
\(510\) −14.8617 −0.658087
\(511\) −42.2886 −1.87074
\(512\) −1.00000 −0.0441942
\(513\) 108.348 4.78370
\(514\) −9.04869 −0.399121
\(515\) 13.3052 0.586295
\(516\) 31.4556 1.38475
\(517\) −14.7103 −0.646958
\(518\) 25.7631 1.13197
\(519\) 58.8612 2.58372
\(520\) 3.49629 0.153323
\(521\) −2.68168 −0.117486 −0.0587432 0.998273i \(-0.518709\pi\)
−0.0587432 + 0.998273i \(0.518709\pi\)
\(522\) 21.4609 0.939320
\(523\) 0.564206 0.0246710 0.0123355 0.999924i \(-0.496073\pi\)
0.0123355 + 0.999924i \(0.496073\pi\)
\(524\) 12.6694 0.553467
\(525\) −11.5480 −0.503996
\(526\) −18.8162 −0.820424
\(527\) 14.5965 0.635832
\(528\) −12.2039 −0.531107
\(529\) 34.3454 1.49328
\(530\) 4.07029 0.176802
\(531\) 37.0595 1.60824
\(532\) −21.6347 −0.937982
\(533\) 16.1874 0.701154
\(534\) 3.39821 0.147055
\(535\) 8.65878 0.374352
\(536\) 2.55592 0.110399
\(537\) 81.0605 3.49802
\(538\) 22.5925 0.974031
\(539\) 18.0097 0.775733
\(540\) 17.3002 0.744484
\(541\) −0.472310 −0.0203062 −0.0101531 0.999948i \(-0.503232\pi\)
−0.0101531 + 0.999948i \(0.503232\pi\)
\(542\) −22.2738 −0.956740
\(543\) 17.2548 0.740475
\(544\) −4.44571 −0.190608
\(545\) 9.64624 0.413200
\(546\) 40.3752 1.72790
\(547\) −10.3468 −0.442399 −0.221199 0.975229i \(-0.570997\pi\)
−0.221199 + 0.975229i \(0.570997\pi\)
\(548\) 0.305403 0.0130462
\(549\) −96.0002 −4.09719
\(550\) −3.65066 −0.155665
\(551\) 16.4408 0.700401
\(552\) −25.3149 −1.07747
\(553\) −40.5726 −1.72532
\(554\) −28.2150 −1.19874
\(555\) −24.9313 −1.05828
\(556\) 4.21702 0.178841
\(557\) 19.3194 0.818591 0.409296 0.912402i \(-0.365774\pi\)
0.409296 + 0.912402i \(0.365774\pi\)
\(558\) −26.8413 −1.13628
\(559\) −32.8987 −1.39146
\(560\) −3.45446 −0.145977
\(561\) −54.2550 −2.29065
\(562\) 11.5833 0.488610
\(563\) 31.5587 1.33004 0.665020 0.746825i \(-0.268423\pi\)
0.665020 + 0.746825i \(0.268423\pi\)
\(564\) 13.4703 0.567202
\(565\) 9.31138 0.391733
\(566\) 11.3650 0.477706
\(567\) 115.061 4.83210
\(568\) −13.5208 −0.567320
\(569\) 5.72419 0.239970 0.119985 0.992776i \(-0.461715\pi\)
0.119985 + 0.992776i \(0.461715\pi\)
\(570\) 20.9362 0.876921
\(571\) 33.3106 1.39400 0.697002 0.717069i \(-0.254517\pi\)
0.697002 + 0.717069i \(0.254517\pi\)
\(572\) 12.7638 0.533681
\(573\) 49.7756 2.07941
\(574\) −15.9937 −0.667564
\(575\) −7.57267 −0.315802
\(576\) 8.17517 0.340632
\(577\) −28.0651 −1.16836 −0.584182 0.811623i \(-0.698584\pi\)
−0.584182 + 0.811623i \(0.698584\pi\)
\(578\) −2.76436 −0.114982
\(579\) −34.5669 −1.43655
\(580\) 2.62514 0.109003
\(581\) −32.4355 −1.34565
\(582\) 12.5847 0.521652
\(583\) 14.8593 0.615408
\(584\) 12.2418 0.506568
\(585\) −28.5828 −1.18175
\(586\) −2.36108 −0.0975352
\(587\) 7.95389 0.328292 0.164146 0.986436i \(-0.447513\pi\)
0.164146 + 0.986436i \(0.447513\pi\)
\(588\) −16.4916 −0.680101
\(589\) −20.5625 −0.847265
\(590\) 4.53317 0.186628
\(591\) −89.3468 −3.67524
\(592\) −7.45793 −0.306519
\(593\) 19.8773 0.816264 0.408132 0.912923i \(-0.366180\pi\)
0.408132 + 0.912923i \(0.366180\pi\)
\(594\) 63.1573 2.59138
\(595\) −15.3575 −0.629597
\(596\) −10.9607 −0.448968
\(597\) 2.07386 0.0848775
\(598\) 26.4763 1.08270
\(599\) −0.352831 −0.0144163 −0.00720814 0.999974i \(-0.502294\pi\)
−0.00720814 + 0.999974i \(0.502294\pi\)
\(600\) 3.34293 0.136474
\(601\) −6.66728 −0.271964 −0.135982 0.990711i \(-0.543419\pi\)
−0.135982 + 0.990711i \(0.543419\pi\)
\(602\) 32.5050 1.32480
\(603\) −20.8951 −0.850914
\(604\) −5.55463 −0.226015
\(605\) −2.32733 −0.0946194
\(606\) 32.2037 1.30818
\(607\) −32.8036 −1.33146 −0.665729 0.746194i \(-0.731879\pi\)
−0.665729 + 0.746194i \(0.731879\pi\)
\(608\) 6.26283 0.253991
\(609\) 30.3151 1.22843
\(610\) −11.7429 −0.475456
\(611\) −14.0883 −0.569951
\(612\) 36.3445 1.46914
\(613\) 16.3431 0.660090 0.330045 0.943965i \(-0.392936\pi\)
0.330045 + 0.943965i \(0.392936\pi\)
\(614\) 6.48616 0.261760
\(615\) 15.4773 0.624106
\(616\) −12.6111 −0.508114
\(617\) 28.0275 1.12834 0.564172 0.825657i \(-0.309195\pi\)
0.564172 + 0.825657i \(0.309195\pi\)
\(618\) −44.4782 −1.78917
\(619\) 20.9690 0.842815 0.421407 0.906871i \(-0.361536\pi\)
0.421407 + 0.906871i \(0.361536\pi\)
\(620\) −3.28327 −0.131859
\(621\) 131.009 5.25721
\(622\) 25.2762 1.01348
\(623\) 3.51158 0.140688
\(624\) −11.6879 −0.467889
\(625\) 1.00000 0.0400000
\(626\) −7.61926 −0.304527
\(627\) 76.4309 3.05236
\(628\) −10.1392 −0.404597
\(629\) −33.1558 −1.32201
\(630\) 28.2408 1.12514
\(631\) −34.5444 −1.37519 −0.687594 0.726095i \(-0.741333\pi\)
−0.687594 + 0.726095i \(0.741333\pi\)
\(632\) 11.7450 0.467191
\(633\) 16.0009 0.635979
\(634\) −16.5917 −0.658941
\(635\) 7.95062 0.315511
\(636\) −13.6067 −0.539541
\(637\) 17.2482 0.683397
\(638\) 9.58348 0.379414
\(639\) 110.535 4.37269
\(640\) 1.00000 0.0395285
\(641\) 37.2692 1.47205 0.736023 0.676956i \(-0.236701\pi\)
0.736023 + 0.676956i \(0.236701\pi\)
\(642\) −28.9457 −1.14240
\(643\) 16.9416 0.668112 0.334056 0.942553i \(-0.391583\pi\)
0.334056 + 0.942553i \(0.391583\pi\)
\(644\) −26.1595 −1.03083
\(645\) −31.4556 −1.23856
\(646\) 27.8427 1.09546
\(647\) −26.5263 −1.04286 −0.521428 0.853296i \(-0.674600\pi\)
−0.521428 + 0.853296i \(0.674600\pi\)
\(648\) −33.3079 −1.30846
\(649\) 16.5491 0.649608
\(650\) −3.49629 −0.137136
\(651\) −37.9152 −1.48601
\(652\) 11.3585 0.444834
\(653\) −29.6548 −1.16048 −0.580242 0.814444i \(-0.697042\pi\)
−0.580242 + 0.814444i \(0.697042\pi\)
\(654\) −32.2467 −1.26095
\(655\) −12.6694 −0.495036
\(656\) 4.62987 0.180766
\(657\) −100.079 −3.90444
\(658\) 13.9197 0.542646
\(659\) −43.3932 −1.69036 −0.845180 0.534481i \(-0.820507\pi\)
−0.845180 + 0.534481i \(0.820507\pi\)
\(660\) 12.2039 0.475036
\(661\) −8.56314 −0.333068 −0.166534 0.986036i \(-0.553257\pi\)
−0.166534 + 0.986036i \(0.553257\pi\)
\(662\) 16.0676 0.624486
\(663\) −51.9609 −2.01799
\(664\) 9.38947 0.364382
\(665\) 21.6347 0.838957
\(666\) 60.9699 2.36254
\(667\) 19.8793 0.769729
\(668\) 10.1324 0.392036
\(669\) 93.5706 3.61765
\(670\) −2.55592 −0.0987438
\(671\) −42.8693 −1.65495
\(672\) 11.5480 0.445474
\(673\) 27.5521 1.06205 0.531027 0.847355i \(-0.321806\pi\)
0.531027 + 0.847355i \(0.321806\pi\)
\(674\) 32.4640 1.25047
\(675\) −17.3002 −0.665886
\(676\) −0.775935 −0.0298437
\(677\) 11.9822 0.460515 0.230258 0.973130i \(-0.426043\pi\)
0.230258 + 0.973130i \(0.426043\pi\)
\(678\) −31.1273 −1.19544
\(679\) 13.0045 0.499068
\(680\) 4.44571 0.170485
\(681\) 14.8325 0.568383
\(682\) −11.9861 −0.458971
\(683\) −36.5333 −1.39791 −0.698954 0.715166i \(-0.746351\pi\)
−0.698954 + 0.715166i \(0.746351\pi\)
\(684\) −51.1997 −1.95767
\(685\) −0.305403 −0.0116688
\(686\) 7.13943 0.272585
\(687\) −92.1449 −3.51555
\(688\) −9.40958 −0.358737
\(689\) 14.2309 0.542155
\(690\) 25.3149 0.963722
\(691\) 29.2002 1.11083 0.555413 0.831575i \(-0.312560\pi\)
0.555413 + 0.831575i \(0.312560\pi\)
\(692\) −17.6077 −0.669344
\(693\) 103.098 3.91635
\(694\) 25.8709 0.982044
\(695\) −4.21702 −0.159961
\(696\) −8.77564 −0.332640
\(697\) 20.5831 0.779640
\(698\) −16.1470 −0.611174
\(699\) 40.1106 1.51712
\(700\) 3.45446 0.130566
\(701\) 12.8440 0.485112 0.242556 0.970137i \(-0.422014\pi\)
0.242556 + 0.970137i \(0.422014\pi\)
\(702\) 60.4867 2.28292
\(703\) 46.7078 1.76162
\(704\) 3.65066 0.137589
\(705\) −13.4703 −0.507321
\(706\) −26.9240 −1.01330
\(707\) 33.2781 1.25155
\(708\) −15.1541 −0.569525
\(709\) −36.5289 −1.37187 −0.685936 0.727662i \(-0.740607\pi\)
−0.685936 + 0.727662i \(0.740607\pi\)
\(710\) 13.5208 0.507426
\(711\) −96.0174 −3.60093
\(712\) −1.01654 −0.0380963
\(713\) −24.8631 −0.931131
\(714\) 51.3391 1.92132
\(715\) −12.7638 −0.477338
\(716\) −24.2483 −0.906203
\(717\) −69.2937 −2.58782
\(718\) −9.66274 −0.360610
\(719\) 29.5026 1.10026 0.550130 0.835079i \(-0.314578\pi\)
0.550130 + 0.835079i \(0.314578\pi\)
\(720\) −8.17517 −0.304671
\(721\) −45.9621 −1.71172
\(722\) −20.2230 −0.752623
\(723\) −71.2955 −2.65151
\(724\) −5.16159 −0.191829
\(725\) −2.62514 −0.0974951
\(726\) 7.78009 0.288746
\(727\) 35.2323 1.30670 0.653348 0.757058i \(-0.273364\pi\)
0.653348 + 0.757058i \(0.273364\pi\)
\(728\) −12.0778 −0.447633
\(729\) 98.7977 3.65918
\(730\) −12.2418 −0.453088
\(731\) −41.8323 −1.54722
\(732\) 39.2557 1.45093
\(733\) −43.3304 −1.60045 −0.800223 0.599703i \(-0.795285\pi\)
−0.800223 + 0.599703i \(0.795285\pi\)
\(734\) −23.3113 −0.860434
\(735\) 16.4916 0.608301
\(736\) 7.57267 0.279132
\(737\) −9.33080 −0.343704
\(738\) −37.8500 −1.39328
\(739\) 21.8997 0.805592 0.402796 0.915290i \(-0.368038\pi\)
0.402796 + 0.915290i \(0.368038\pi\)
\(740\) 7.45793 0.274159
\(741\) 73.1991 2.68903
\(742\) −14.0606 −0.516183
\(743\) 29.8275 1.09426 0.547132 0.837047i \(-0.315720\pi\)
0.547132 + 0.837047i \(0.315720\pi\)
\(744\) 10.9757 0.402390
\(745\) 10.9607 0.401569
\(746\) −18.7188 −0.685344
\(747\) −76.7605 −2.80852
\(748\) 16.2298 0.593420
\(749\) −29.9114 −1.09294
\(750\) −3.34293 −0.122066
\(751\) −41.1292 −1.50083 −0.750413 0.660970i \(-0.770145\pi\)
−0.750413 + 0.660970i \(0.770145\pi\)
\(752\) −4.02949 −0.146940
\(753\) −43.5681 −1.58771
\(754\) 9.17824 0.334252
\(755\) 5.55463 0.202154
\(756\) −59.7629 −2.17356
\(757\) 6.82806 0.248170 0.124085 0.992272i \(-0.460400\pi\)
0.124085 + 0.992272i \(0.460400\pi\)
\(758\) 28.5930 1.03854
\(759\) 92.4162 3.35449
\(760\) −6.26283 −0.227177
\(761\) −54.4981 −1.97555 −0.987777 0.155872i \(-0.950181\pi\)
−0.987777 + 0.155872i \(0.950181\pi\)
\(762\) −26.5784 −0.962832
\(763\) −33.3225 −1.20636
\(764\) −14.8898 −0.538695
\(765\) −36.3445 −1.31404
\(766\) 4.40398 0.159122
\(767\) 15.8493 0.572285
\(768\) −3.34293 −0.120628
\(769\) 11.2232 0.404719 0.202359 0.979311i \(-0.435139\pi\)
0.202359 + 0.979311i \(0.435139\pi\)
\(770\) 12.6111 0.454471
\(771\) −30.2491 −1.08940
\(772\) 10.3403 0.372156
\(773\) 50.1349 1.80323 0.901613 0.432544i \(-0.142384\pi\)
0.901613 + 0.432544i \(0.142384\pi\)
\(774\) 76.9250 2.76501
\(775\) 3.28327 0.117938
\(776\) −3.76457 −0.135140
\(777\) 86.1242 3.08969
\(778\) 24.5618 0.880584
\(779\) −28.9961 −1.03889
\(780\) 11.6879 0.418492
\(781\) 49.3598 1.76623
\(782\) 33.6659 1.20389
\(783\) 45.4155 1.62302
\(784\) 4.93327 0.176188
\(785\) 10.1392 0.361882
\(786\) 42.3530 1.51068
\(787\) −26.6032 −0.948303 −0.474152 0.880443i \(-0.657245\pi\)
−0.474152 + 0.880443i \(0.657245\pi\)
\(788\) 26.7271 0.952114
\(789\) −62.9011 −2.23934
\(790\) −11.7450 −0.417868
\(791\) −32.1658 −1.14368
\(792\) −29.8448 −1.06049
\(793\) −41.0566 −1.45796
\(794\) −15.5751 −0.552739
\(795\) 13.6067 0.482580
\(796\) −0.620373 −0.0219885
\(797\) 36.3267 1.28676 0.643379 0.765548i \(-0.277532\pi\)
0.643379 + 0.765548i \(0.277532\pi\)
\(798\) −72.3232 −2.56021
\(799\) −17.9140 −0.633750
\(800\) −1.00000 −0.0353553
\(801\) 8.31036 0.293632
\(802\) 1.00000 0.0353112
\(803\) −44.6905 −1.57709
\(804\) 8.54426 0.301333
\(805\) 26.1595 0.922000
\(806\) −11.4793 −0.404340
\(807\) 75.5251 2.65861
\(808\) −9.63337 −0.338901
\(809\) −44.2243 −1.55484 −0.777421 0.628980i \(-0.783473\pi\)
−0.777421 + 0.628980i \(0.783473\pi\)
\(810\) 33.3079 1.17032
\(811\) 3.63339 0.127585 0.0637927 0.997963i \(-0.479680\pi\)
0.0637927 + 0.997963i \(0.479680\pi\)
\(812\) −9.06842 −0.318239
\(813\) −74.4596 −2.61141
\(814\) 27.2264 0.954284
\(815\) −11.3585 −0.397872
\(816\) −14.8617 −0.520264
\(817\) 58.9306 2.06172
\(818\) 22.2350 0.777427
\(819\) 98.7380 3.45019
\(820\) −4.62987 −0.161682
\(821\) 20.5307 0.716528 0.358264 0.933620i \(-0.383369\pi\)
0.358264 + 0.933620i \(0.383369\pi\)
\(822\) 1.02094 0.0356094
\(823\) 18.6824 0.651227 0.325614 0.945503i \(-0.394429\pi\)
0.325614 + 0.945503i \(0.394429\pi\)
\(824\) 13.3052 0.463507
\(825\) −12.2039 −0.424885
\(826\) −15.6597 −0.544869
\(827\) 43.2438 1.50373 0.751867 0.659315i \(-0.229153\pi\)
0.751867 + 0.659315i \(0.229153\pi\)
\(828\) −61.9079 −2.15145
\(829\) 7.38348 0.256439 0.128219 0.991746i \(-0.459074\pi\)
0.128219 + 0.991746i \(0.459074\pi\)
\(830\) −9.38947 −0.325913
\(831\) −94.3207 −3.27195
\(832\) 3.49629 0.121212
\(833\) 21.9319 0.759895
\(834\) 14.0972 0.488146
\(835\) −10.1324 −0.350647
\(836\) −22.8635 −0.790750
\(837\) −56.8013 −1.96334
\(838\) −21.5003 −0.742716
\(839\) 33.9771 1.17302 0.586509 0.809942i \(-0.300502\pi\)
0.586509 + 0.809942i \(0.300502\pi\)
\(840\) −11.5480 −0.398444
\(841\) −22.1087 −0.762368
\(842\) 35.3921 1.21969
\(843\) 38.7220 1.33366
\(844\) −4.78650 −0.164758
\(845\) 0.775935 0.0266930
\(846\) 32.9418 1.13256
\(847\) 8.03966 0.276246
\(848\) 4.07029 0.139774
\(849\) 37.9924 1.30389
\(850\) −4.44571 −0.152487
\(851\) 56.4765 1.93599
\(852\) −45.1990 −1.54849
\(853\) 39.3182 1.34623 0.673114 0.739539i \(-0.264956\pi\)
0.673114 + 0.739539i \(0.264956\pi\)
\(854\) 40.5653 1.38812
\(855\) 51.1997 1.75099
\(856\) 8.65878 0.295951
\(857\) −55.1736 −1.88469 −0.942347 0.334636i \(-0.891387\pi\)
−0.942347 + 0.334636i \(0.891387\pi\)
\(858\) 42.6684 1.45668
\(859\) 23.4800 0.801129 0.400564 0.916269i \(-0.368814\pi\)
0.400564 + 0.916269i \(0.368814\pi\)
\(860\) 9.40958 0.320864
\(861\) −53.4658 −1.82211
\(862\) −17.4615 −0.594740
\(863\) 35.4240 1.20585 0.602923 0.797799i \(-0.294003\pi\)
0.602923 + 0.797799i \(0.294003\pi\)
\(864\) 17.3002 0.588566
\(865\) 17.6077 0.598679
\(866\) −25.5592 −0.868538
\(867\) −9.24107 −0.313843
\(868\) 11.3419 0.384969
\(869\) −42.8770 −1.45450
\(870\) 8.77564 0.297522
\(871\) −8.93624 −0.302793
\(872\) 9.64624 0.326663
\(873\) 30.7760 1.04161
\(874\) −47.4264 −1.60422
\(875\) −3.45446 −0.116782
\(876\) 40.9233 1.38267
\(877\) −20.9567 −0.707656 −0.353828 0.935310i \(-0.615120\pi\)
−0.353828 + 0.935310i \(0.615120\pi\)
\(878\) −0.954774 −0.0322221
\(879\) −7.89291 −0.266221
\(880\) −3.65066 −0.123064
\(881\) −16.7761 −0.565200 −0.282600 0.959238i \(-0.591197\pi\)
−0.282600 + 0.959238i \(0.591197\pi\)
\(882\) −40.3303 −1.35799
\(883\) 20.5408 0.691253 0.345626 0.938372i \(-0.387666\pi\)
0.345626 + 0.938372i \(0.387666\pi\)
\(884\) 15.5435 0.522785
\(885\) 15.1541 0.509399
\(886\) 22.2117 0.746216
\(887\) −24.4967 −0.822517 −0.411259 0.911519i \(-0.634911\pi\)
−0.411259 + 0.911519i \(0.634911\pi\)
\(888\) −24.9313 −0.836641
\(889\) −27.4651 −0.921149
\(890\) 1.01654 0.0340744
\(891\) 121.596 4.07362
\(892\) −27.9906 −0.937195
\(893\) 25.2360 0.844491
\(894\) −36.6409 −1.22545
\(895\) 24.2483 0.810533
\(896\) −3.45446 −0.115405
\(897\) 88.5083 2.95521
\(898\) 10.9315 0.364790
\(899\) −8.61902 −0.287460
\(900\) 8.17517 0.272506
\(901\) 18.0953 0.602843
\(902\) −16.9021 −0.562778
\(903\) 108.662 3.61604
\(904\) 9.31138 0.309692
\(905\) 5.16159 0.171577
\(906\) −18.5687 −0.616905
\(907\) −44.9621 −1.49294 −0.746471 0.665418i \(-0.768254\pi\)
−0.746471 + 0.665418i \(0.768254\pi\)
\(908\) −4.43698 −0.147246
\(909\) 78.7545 2.61212
\(910\) 12.0778 0.400375
\(911\) −37.0311 −1.22689 −0.613447 0.789736i \(-0.710218\pi\)
−0.613447 + 0.789736i \(0.710218\pi\)
\(912\) 20.9362 0.693267
\(913\) −34.2778 −1.13443
\(914\) −18.8479 −0.623433
\(915\) −39.2557 −1.29775
\(916\) 27.5641 0.910744
\(917\) 43.7660 1.44528
\(918\) 76.9119 2.53847
\(919\) −0.942269 −0.0310826 −0.0155413 0.999879i \(-0.504947\pi\)
−0.0155413 + 0.999879i \(0.504947\pi\)
\(920\) −7.57267 −0.249664
\(921\) 21.6828 0.714472
\(922\) 13.9256 0.458615
\(923\) 47.2726 1.55600
\(924\) −42.1578 −1.38689
\(925\) −7.45793 −0.245215
\(926\) 7.79458 0.256146
\(927\) −108.772 −3.57254
\(928\) 2.62514 0.0861743
\(929\) 28.8335 0.945996 0.472998 0.881063i \(-0.343172\pi\)
0.472998 + 0.881063i \(0.343172\pi\)
\(930\) −10.9757 −0.359908
\(931\) −30.8962 −1.01258
\(932\) −11.9986 −0.393029
\(933\) 84.4965 2.76629
\(934\) 30.0377 0.982864
\(935\) −16.2298 −0.530771
\(936\) −28.5828 −0.934258
\(937\) −37.0807 −1.21137 −0.605686 0.795704i \(-0.707101\pi\)
−0.605686 + 0.795704i \(0.707101\pi\)
\(938\) 8.82931 0.288287
\(939\) −25.4707 −0.831204
\(940\) 4.02949 0.131427
\(941\) 19.3937 0.632217 0.316108 0.948723i \(-0.397624\pi\)
0.316108 + 0.948723i \(0.397624\pi\)
\(942\) −33.8945 −1.10434
\(943\) −35.0605 −1.14173
\(944\) 4.53317 0.147542
\(945\) 59.7629 1.94409
\(946\) 34.3512 1.11685
\(947\) −59.4392 −1.93151 −0.965757 0.259449i \(-0.916459\pi\)
−0.965757 + 0.259449i \(0.916459\pi\)
\(948\) 39.2627 1.27519
\(949\) −42.8008 −1.38937
\(950\) 6.26283 0.203193
\(951\) −55.4649 −1.79857
\(952\) −15.3575 −0.497740
\(953\) −32.8523 −1.06419 −0.532095 0.846685i \(-0.678595\pi\)
−0.532095 + 0.846685i \(0.678595\pi\)
\(954\) −33.2753 −1.07733
\(955\) 14.8898 0.481824
\(956\) 20.7284 0.670406
\(957\) 32.0369 1.03561
\(958\) 12.4327 0.401681
\(959\) 1.05500 0.0340678
\(960\) 3.34293 0.107893
\(961\) −20.2202 −0.652263
\(962\) 26.0751 0.840696
\(963\) −70.7870 −2.28108
\(964\) 21.3272 0.686904
\(965\) −10.3403 −0.332866
\(966\) −87.4493 −2.81363
\(967\) −3.24879 −0.104474 −0.0522370 0.998635i \(-0.516635\pi\)
−0.0522370 + 0.998635i \(0.516635\pi\)
\(968\) −2.32733 −0.0748032
\(969\) 93.0763 2.99004
\(970\) 3.76457 0.120873
\(971\) −13.5736 −0.435598 −0.217799 0.975994i \(-0.569888\pi\)
−0.217799 + 0.975994i \(0.569888\pi\)
\(972\) −59.4453 −1.90671
\(973\) 14.5675 0.467013
\(974\) 15.1280 0.484733
\(975\) −11.6879 −0.374311
\(976\) −11.7429 −0.375881
\(977\) −21.3061 −0.681644 −0.340822 0.940128i \(-0.610705\pi\)
−0.340822 + 0.940128i \(0.610705\pi\)
\(978\) 37.9707 1.21417
\(979\) 3.71103 0.118605
\(980\) −4.93327 −0.157588
\(981\) −78.8597 −2.51780
\(982\) 28.3599 0.905001
\(983\) 60.6251 1.93364 0.966821 0.255456i \(-0.0822257\pi\)
0.966821 + 0.255456i \(0.0822257\pi\)
\(984\) 15.4773 0.493399
\(985\) −26.7271 −0.851596
\(986\) 11.6706 0.371668
\(987\) 46.5326 1.48115
\(988\) −21.8967 −0.696626
\(989\) 71.2557 2.26580
\(990\) 29.8448 0.948530
\(991\) 17.5578 0.557741 0.278870 0.960329i \(-0.410040\pi\)
0.278870 + 0.960329i \(0.410040\pi\)
\(992\) −3.28327 −0.104244
\(993\) 53.7130 1.70453
\(994\) −46.7070 −1.48146
\(995\) 0.620373 0.0196671
\(996\) 31.3883 0.994577
\(997\) 26.6488 0.843976 0.421988 0.906602i \(-0.361333\pi\)
0.421988 + 0.906602i \(0.361333\pi\)
\(998\) −12.2680 −0.388336
\(999\) 129.024 4.08214
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 \(a_p\))