Properties

Label 6025.2.a.h.1.8
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.8
Root \(-0.342147\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.342147 q^{2}\) \(-2.18519 q^{3}\) \(-1.88294 q^{4}\) \(-0.747658 q^{6}\) \(-1.82459 q^{7}\) \(-1.32853 q^{8}\) \(+1.77508 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.342147 q^{2}\) \(-2.18519 q^{3}\) \(-1.88294 q^{4}\) \(-0.747658 q^{6}\) \(-1.82459 q^{7}\) \(-1.32853 q^{8}\) \(+1.77508 q^{9}\) \(+5.99218 q^{11}\) \(+4.11458 q^{12}\) \(-3.70515 q^{13}\) \(-0.624278 q^{14}\) \(+3.31132 q^{16}\) \(+1.64451 q^{17}\) \(+0.607337 q^{18}\) \(-3.15821 q^{19}\) \(+3.98709 q^{21}\) \(+2.05021 q^{22}\) \(+5.46015 q^{23}\) \(+2.90311 q^{24}\) \(-1.26771 q^{26}\) \(+2.67670 q^{27}\) \(+3.43559 q^{28}\) \(+7.24801 q^{29}\) \(-9.41700 q^{31}\) \(+3.79003 q^{32}\) \(-13.0941 q^{33}\) \(+0.562662 q^{34}\) \(-3.34236 q^{36}\) \(-1.27680 q^{37}\) \(-1.08057 q^{38}\) \(+8.09648 q^{39}\) \(-5.81239 q^{41}\) \(+1.36417 q^{42}\) \(-7.82887 q^{43}\) \(-11.2829 q^{44}\) \(+1.86817 q^{46}\) \(-2.61568 q^{47}\) \(-7.23587 q^{48}\) \(-3.67086 q^{49}\) \(-3.59356 q^{51}\) \(+6.97656 q^{52}\) \(-8.81076 q^{53}\) \(+0.915823 q^{54}\) \(+2.42403 q^{56}\) \(+6.90130 q^{57}\) \(+2.47989 q^{58}\) \(-7.78270 q^{59}\) \(+1.03194 q^{61}\) \(-3.22200 q^{62}\) \(-3.23879 q^{63}\) \(-5.32589 q^{64}\) \(-4.48010 q^{66}\) \(+8.39801 q^{67}\) \(-3.09650 q^{68}\) \(-11.9315 q^{69}\) \(+13.1691 q^{71}\) \(-2.35825 q^{72}\) \(+13.3963 q^{73}\) \(-0.436852 q^{74}\) \(+5.94670 q^{76}\) \(-10.9333 q^{77}\) \(+2.77018 q^{78}\) \(-10.6362 q^{79}\) \(-11.1743 q^{81}\) \(-1.98869 q^{82}\) \(-6.25636 q^{83}\) \(-7.50743 q^{84}\) \(-2.67862 q^{86}\) \(-15.8383 q^{87}\) \(-7.96082 q^{88}\) \(-3.94129 q^{89}\) \(+6.76039 q^{91}\) \(-10.2811 q^{92}\) \(+20.5780 q^{93}\) \(-0.894948 q^{94}\) \(-8.28195 q^{96}\) \(+2.22451 q^{97}\) \(-1.25598 q^{98}\) \(+10.6366 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342147 0.241934 0.120967 0.992657i \(-0.461400\pi\)
0.120967 + 0.992657i \(0.461400\pi\)
\(3\) −2.18519 −1.26162 −0.630811 0.775936i \(-0.717278\pi\)
−0.630811 + 0.775936i \(0.717278\pi\)
\(4\) −1.88294 −0.941468
\(5\) 0 0
\(6\) −0.747658 −0.305230
\(7\) −1.82459 −0.689631 −0.344815 0.938671i \(-0.612058\pi\)
−0.344815 + 0.938671i \(0.612058\pi\)
\(8\) −1.32853 −0.469708
\(9\) 1.77508 0.591692
\(10\) 0 0
\(11\) 5.99218 1.80671 0.903355 0.428894i \(-0.141096\pi\)
0.903355 + 0.428894i \(0.141096\pi\)
\(12\) 4.11458 1.18778
\(13\) −3.70515 −1.02762 −0.513812 0.857903i \(-0.671767\pi\)
−0.513812 + 0.857903i \(0.671767\pi\)
\(14\) −0.624278 −0.166845
\(15\) 0 0
\(16\) 3.31132 0.827829
\(17\) 1.64451 0.398851 0.199426 0.979913i \(-0.436092\pi\)
0.199426 + 0.979913i \(0.436092\pi\)
\(18\) 0.607337 0.143151
\(19\) −3.15821 −0.724543 −0.362271 0.932073i \(-0.617999\pi\)
−0.362271 + 0.932073i \(0.617999\pi\)
\(20\) 0 0
\(21\) 3.98709 0.870054
\(22\) 2.05021 0.437105
\(23\) 5.46015 1.13852 0.569260 0.822158i \(-0.307230\pi\)
0.569260 + 0.822158i \(0.307230\pi\)
\(24\) 2.90311 0.592594
\(25\) 0 0
\(26\) −1.26771 −0.248618
\(27\) 2.67670 0.515130
\(28\) 3.43559 0.649265
\(29\) 7.24801 1.34592 0.672961 0.739678i \(-0.265022\pi\)
0.672961 + 0.739678i \(0.265022\pi\)
\(30\) 0 0
\(31\) −9.41700 −1.69134 −0.845672 0.533703i \(-0.820800\pi\)
−0.845672 + 0.533703i \(0.820800\pi\)
\(32\) 3.79003 0.669988
\(33\) −13.0941 −2.27939
\(34\) 0.562662 0.0964958
\(35\) 0 0
\(36\) −3.34236 −0.557059
\(37\) −1.27680 −0.209904 −0.104952 0.994477i \(-0.533469\pi\)
−0.104952 + 0.994477i \(0.533469\pi\)
\(38\) −1.08057 −0.175292
\(39\) 8.09648 1.29647
\(40\) 0 0
\(41\) −5.81239 −0.907743 −0.453872 0.891067i \(-0.649958\pi\)
−0.453872 + 0.891067i \(0.649958\pi\)
\(42\) 1.36417 0.210496
\(43\) −7.82887 −1.19389 −0.596946 0.802281i \(-0.703619\pi\)
−0.596946 + 0.802281i \(0.703619\pi\)
\(44\) −11.2829 −1.70096
\(45\) 0 0
\(46\) 1.86817 0.275447
\(47\) −2.61568 −0.381537 −0.190768 0.981635i \(-0.561098\pi\)
−0.190768 + 0.981635i \(0.561098\pi\)
\(48\) −7.23587 −1.04441
\(49\) −3.67086 −0.524409
\(50\) 0 0
\(51\) −3.59356 −0.503200
\(52\) 6.97656 0.967475
\(53\) −8.81076 −1.21025 −0.605126 0.796130i \(-0.706877\pi\)
−0.605126 + 0.796130i \(0.706877\pi\)
\(54\) 0.915823 0.124628
\(55\) 0 0
\(56\) 2.42403 0.323925
\(57\) 6.90130 0.914100
\(58\) 2.47989 0.325625
\(59\) −7.78270 −1.01322 −0.506610 0.862175i \(-0.669102\pi\)
−0.506610 + 0.862175i \(0.669102\pi\)
\(60\) 0 0
\(61\) 1.03194 0.132127 0.0660635 0.997815i \(-0.478956\pi\)
0.0660635 + 0.997815i \(0.478956\pi\)
\(62\) −3.22200 −0.409194
\(63\) −3.23879 −0.408049
\(64\) −5.32589 −0.665736
\(65\) 0 0
\(66\) −4.48010 −0.551462
\(67\) 8.39801 1.02598 0.512990 0.858395i \(-0.328538\pi\)
0.512990 + 0.858395i \(0.328538\pi\)
\(68\) −3.09650 −0.375505
\(69\) −11.9315 −1.43638
\(70\) 0 0
\(71\) 13.1691 1.56288 0.781440 0.623981i \(-0.214486\pi\)
0.781440 + 0.623981i \(0.214486\pi\)
\(72\) −2.35825 −0.277923
\(73\) 13.3963 1.56792 0.783959 0.620813i \(-0.213197\pi\)
0.783959 + 0.620813i \(0.213197\pi\)
\(74\) −0.436852 −0.0507830
\(75\) 0 0
\(76\) 5.94670 0.682133
\(77\) −10.9333 −1.24596
\(78\) 2.77018 0.313662
\(79\) −10.6362 −1.19666 −0.598332 0.801248i \(-0.704170\pi\)
−0.598332 + 0.801248i \(0.704170\pi\)
\(80\) 0 0
\(81\) −11.1743 −1.24159
\(82\) −1.98869 −0.219614
\(83\) −6.25636 −0.686725 −0.343362 0.939203i \(-0.611566\pi\)
−0.343362 + 0.939203i \(0.611566\pi\)
\(84\) −7.50743 −0.819128
\(85\) 0 0
\(86\) −2.67862 −0.288844
\(87\) −15.8383 −1.69805
\(88\) −7.96082 −0.848626
\(89\) −3.94129 −0.417776 −0.208888 0.977940i \(-0.566984\pi\)
−0.208888 + 0.977940i \(0.566984\pi\)
\(90\) 0 0
\(91\) 6.76039 0.708681
\(92\) −10.2811 −1.07188
\(93\) 20.5780 2.13384
\(94\) −0.894948 −0.0923069
\(95\) 0 0
\(96\) −8.28195 −0.845273
\(97\) 2.22451 0.225865 0.112933 0.993603i \(-0.463976\pi\)
0.112933 + 0.993603i \(0.463976\pi\)
\(98\) −1.25598 −0.126873
\(99\) 10.6366 1.06902
\(100\) 0 0
\(101\) −4.24027 −0.421923 −0.210962 0.977494i \(-0.567659\pi\)
−0.210962 + 0.977494i \(0.567659\pi\)
\(102\) −1.22953 −0.121741
\(103\) −0.164858 −0.0162439 −0.00812196 0.999967i \(-0.502585\pi\)
−0.00812196 + 0.999967i \(0.502585\pi\)
\(104\) 4.92242 0.482683
\(105\) 0 0
\(106\) −3.01458 −0.292801
\(107\) −9.28536 −0.897650 −0.448825 0.893620i \(-0.648157\pi\)
−0.448825 + 0.893620i \(0.648157\pi\)
\(108\) −5.04005 −0.484979
\(109\) 12.1952 1.16809 0.584044 0.811722i \(-0.301470\pi\)
0.584044 + 0.811722i \(0.301470\pi\)
\(110\) 0 0
\(111\) 2.79005 0.264820
\(112\) −6.04180 −0.570897
\(113\) −13.1834 −1.24019 −0.620093 0.784528i \(-0.712905\pi\)
−0.620093 + 0.784528i \(0.712905\pi\)
\(114\) 2.36126 0.221152
\(115\) 0 0
\(116\) −13.6475 −1.26714
\(117\) −6.57693 −0.608037
\(118\) −2.66283 −0.245133
\(119\) −3.00055 −0.275060
\(120\) 0 0
\(121\) 24.9062 2.26420
\(122\) 0.353077 0.0319661
\(123\) 12.7012 1.14523
\(124\) 17.7316 1.59235
\(125\) 0 0
\(126\) −1.10814 −0.0987212
\(127\) 11.7563 1.04321 0.521603 0.853188i \(-0.325334\pi\)
0.521603 + 0.853188i \(0.325334\pi\)
\(128\) −9.40229 −0.831053
\(129\) 17.1076 1.50624
\(130\) 0 0
\(131\) 14.0839 1.23051 0.615257 0.788326i \(-0.289052\pi\)
0.615257 + 0.788326i \(0.289052\pi\)
\(132\) 24.6553 2.14597
\(133\) 5.76244 0.499667
\(134\) 2.87335 0.248220
\(135\) 0 0
\(136\) −2.18478 −0.187343
\(137\) 12.3993 1.05935 0.529673 0.848202i \(-0.322315\pi\)
0.529673 + 0.848202i \(0.322315\pi\)
\(138\) −4.08232 −0.347510
\(139\) −10.5456 −0.894464 −0.447232 0.894418i \(-0.647590\pi\)
−0.447232 + 0.894418i \(0.647590\pi\)
\(140\) 0 0
\(141\) 5.71578 0.481356
\(142\) 4.50575 0.378114
\(143\) −22.2019 −1.85662
\(144\) 5.87784 0.489820
\(145\) 0 0
\(146\) 4.58350 0.379333
\(147\) 8.02156 0.661607
\(148\) 2.40412 0.197618
\(149\) −9.30604 −0.762380 −0.381190 0.924497i \(-0.624486\pi\)
−0.381190 + 0.924497i \(0.624486\pi\)
\(150\) 0 0
\(151\) 10.2870 0.837143 0.418572 0.908184i \(-0.362531\pi\)
0.418572 + 0.908184i \(0.362531\pi\)
\(152\) 4.19579 0.340323
\(153\) 2.91912 0.235997
\(154\) −3.74079 −0.301441
\(155\) 0 0
\(156\) −15.2451 −1.22059
\(157\) 4.23848 0.338268 0.169134 0.985593i \(-0.445903\pi\)
0.169134 + 0.985593i \(0.445903\pi\)
\(158\) −3.63914 −0.289514
\(159\) 19.2532 1.52688
\(160\) 0 0
\(161\) −9.96254 −0.785159
\(162\) −3.82326 −0.300384
\(163\) 6.42582 0.503309 0.251655 0.967817i \(-0.419025\pi\)
0.251655 + 0.967817i \(0.419025\pi\)
\(164\) 10.9444 0.854611
\(165\) 0 0
\(166\) −2.14060 −0.166142
\(167\) −3.96260 −0.306636 −0.153318 0.988177i \(-0.548996\pi\)
−0.153318 + 0.988177i \(0.548996\pi\)
\(168\) −5.29698 −0.408671
\(169\) 0.728137 0.0560105
\(170\) 0 0
\(171\) −5.60606 −0.428706
\(172\) 14.7413 1.12401
\(173\) 8.45221 0.642610 0.321305 0.946976i \(-0.395879\pi\)
0.321305 + 0.946976i \(0.395879\pi\)
\(174\) −5.41903 −0.410816
\(175\) 0 0
\(176\) 19.8420 1.49565
\(177\) 17.0067 1.27830
\(178\) −1.34850 −0.101074
\(179\) −10.5847 −0.791138 −0.395569 0.918436i \(-0.629453\pi\)
−0.395569 + 0.918436i \(0.629453\pi\)
\(180\) 0 0
\(181\) −19.4914 −1.44879 −0.724394 0.689387i \(-0.757880\pi\)
−0.724394 + 0.689387i \(0.757880\pi\)
\(182\) 2.31305 0.171454
\(183\) −2.25500 −0.166694
\(184\) −7.25400 −0.534772
\(185\) 0 0
\(186\) 7.04070 0.516249
\(187\) 9.85417 0.720608
\(188\) 4.92517 0.359205
\(189\) −4.88388 −0.355250
\(190\) 0 0
\(191\) −2.21537 −0.160298 −0.0801491 0.996783i \(-0.525540\pi\)
−0.0801491 + 0.996783i \(0.525540\pi\)
\(192\) 11.6381 0.839908
\(193\) 8.84755 0.636861 0.318430 0.947946i \(-0.396844\pi\)
0.318430 + 0.947946i \(0.396844\pi\)
\(194\) 0.761111 0.0546446
\(195\) 0 0
\(196\) 6.91200 0.493714
\(197\) −6.19744 −0.441549 −0.220775 0.975325i \(-0.570859\pi\)
−0.220775 + 0.975325i \(0.570859\pi\)
\(198\) 3.63927 0.258632
\(199\) 20.2303 1.43409 0.717043 0.697028i \(-0.245495\pi\)
0.717043 + 0.697028i \(0.245495\pi\)
\(200\) 0 0
\(201\) −18.3513 −1.29440
\(202\) −1.45080 −0.102078
\(203\) −13.2247 −0.928190
\(204\) 6.76645 0.473746
\(205\) 0 0
\(206\) −0.0564056 −0.00392996
\(207\) 9.69219 0.673653
\(208\) −12.2689 −0.850697
\(209\) −18.9245 −1.30904
\(210\) 0 0
\(211\) 1.96502 0.135278 0.0676388 0.997710i \(-0.478453\pi\)
0.0676388 + 0.997710i \(0.478453\pi\)
\(212\) 16.5901 1.13941
\(213\) −28.7769 −1.97176
\(214\) −3.17696 −0.217172
\(215\) 0 0
\(216\) −3.55608 −0.241961
\(217\) 17.1822 1.16640
\(218\) 4.17255 0.282600
\(219\) −29.2735 −1.97812
\(220\) 0 0
\(221\) −6.09314 −0.409869
\(222\) 0.954606 0.0640690
\(223\) −21.4906 −1.43911 −0.719557 0.694433i \(-0.755655\pi\)
−0.719557 + 0.694433i \(0.755655\pi\)
\(224\) −6.91525 −0.462045
\(225\) 0 0
\(226\) −4.51065 −0.300044
\(227\) −20.7806 −1.37925 −0.689627 0.724165i \(-0.742226\pi\)
−0.689627 + 0.724165i \(0.742226\pi\)
\(228\) −12.9947 −0.860595
\(229\) 28.4761 1.88176 0.940878 0.338746i \(-0.110003\pi\)
0.940878 + 0.338746i \(0.110003\pi\)
\(230\) 0 0
\(231\) 23.8914 1.57194
\(232\) −9.62924 −0.632190
\(233\) 2.19220 0.143616 0.0718079 0.997418i \(-0.477123\pi\)
0.0718079 + 0.997418i \(0.477123\pi\)
\(234\) −2.25028 −0.147105
\(235\) 0 0
\(236\) 14.6543 0.953915
\(237\) 23.2421 1.50974
\(238\) −1.02663 −0.0665465
\(239\) 25.2449 1.63296 0.816478 0.577377i \(-0.195924\pi\)
0.816478 + 0.577377i \(0.195924\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 8.52158 0.547788
\(243\) 16.3880 1.05129
\(244\) −1.94309 −0.124393
\(245\) 0 0
\(246\) 4.34568 0.277071
\(247\) 11.7016 0.744557
\(248\) 12.5108 0.794437
\(249\) 13.6714 0.866388
\(250\) 0 0
\(251\) 21.2167 1.33919 0.669593 0.742728i \(-0.266468\pi\)
0.669593 + 0.742728i \(0.266468\pi\)
\(252\) 6.09843 0.384165
\(253\) 32.7182 2.05698
\(254\) 4.02240 0.252388
\(255\) 0 0
\(256\) 7.43481 0.464676
\(257\) −19.1130 −1.19224 −0.596119 0.802896i \(-0.703292\pi\)
−0.596119 + 0.802896i \(0.703292\pi\)
\(258\) 5.85332 0.364412
\(259\) 2.32963 0.144756
\(260\) 0 0
\(261\) 12.8658 0.796372
\(262\) 4.81876 0.297704
\(263\) 12.7792 0.787999 0.394000 0.919111i \(-0.371091\pi\)
0.394000 + 0.919111i \(0.371091\pi\)
\(264\) 17.3959 1.07065
\(265\) 0 0
\(266\) 1.97160 0.120887
\(267\) 8.61249 0.527076
\(268\) −15.8129 −0.965927
\(269\) 1.65545 0.100934 0.0504672 0.998726i \(-0.483929\pi\)
0.0504672 + 0.998726i \(0.483929\pi\)
\(270\) 0 0
\(271\) −17.0226 −1.03405 −0.517023 0.855971i \(-0.672960\pi\)
−0.517023 + 0.855971i \(0.672960\pi\)
\(272\) 5.44548 0.330181
\(273\) −14.7728 −0.894088
\(274\) 4.24239 0.256292
\(275\) 0 0
\(276\) 22.4662 1.35231
\(277\) −16.8245 −1.01089 −0.505443 0.862860i \(-0.668671\pi\)
−0.505443 + 0.862860i \(0.668671\pi\)
\(278\) −3.60814 −0.216402
\(279\) −16.7159 −1.00076
\(280\) 0 0
\(281\) −16.1664 −0.964405 −0.482203 0.876060i \(-0.660163\pi\)
−0.482203 + 0.876060i \(0.660163\pi\)
\(282\) 1.95564 0.116456
\(283\) −2.53878 −0.150915 −0.0754573 0.997149i \(-0.524042\pi\)
−0.0754573 + 0.997149i \(0.524042\pi\)
\(284\) −24.7965 −1.47140
\(285\) 0 0
\(286\) −7.59632 −0.449180
\(287\) 10.6052 0.626008
\(288\) 6.72759 0.396427
\(289\) −14.2956 −0.840918
\(290\) 0 0
\(291\) −4.86100 −0.284957
\(292\) −25.2243 −1.47614
\(293\) 22.8971 1.33767 0.668833 0.743413i \(-0.266794\pi\)
0.668833 + 0.743413i \(0.266794\pi\)
\(294\) 2.74455 0.160065
\(295\) 0 0
\(296\) 1.69627 0.0985935
\(297\) 16.0392 0.930691
\(298\) −3.18403 −0.184446
\(299\) −20.2307 −1.16997
\(300\) 0 0
\(301\) 14.2845 0.823345
\(302\) 3.51966 0.202534
\(303\) 9.26583 0.532308
\(304\) −10.4578 −0.599798
\(305\) 0 0
\(306\) 0.998769 0.0570958
\(307\) 4.71512 0.269106 0.134553 0.990906i \(-0.457040\pi\)
0.134553 + 0.990906i \(0.457040\pi\)
\(308\) 20.5867 1.17303
\(309\) 0.360246 0.0204937
\(310\) 0 0
\(311\) 4.63908 0.263058 0.131529 0.991312i \(-0.458011\pi\)
0.131529 + 0.991312i \(0.458011\pi\)
\(312\) −10.7564 −0.608964
\(313\) 5.04057 0.284910 0.142455 0.989801i \(-0.454500\pi\)
0.142455 + 0.989801i \(0.454500\pi\)
\(314\) 1.45018 0.0818386
\(315\) 0 0
\(316\) 20.0272 1.12662
\(317\) 28.0992 1.57821 0.789105 0.614259i \(-0.210545\pi\)
0.789105 + 0.614259i \(0.210545\pi\)
\(318\) 6.58744 0.369405
\(319\) 43.4314 2.43169
\(320\) 0 0
\(321\) 20.2903 1.13250
\(322\) −3.40865 −0.189957
\(323\) −5.19369 −0.288985
\(324\) 21.0405 1.16892
\(325\) 0 0
\(326\) 2.19858 0.121768
\(327\) −26.6489 −1.47369
\(328\) 7.72197 0.426374
\(329\) 4.77256 0.263120
\(330\) 0 0
\(331\) 29.6777 1.63124 0.815618 0.578590i \(-0.196397\pi\)
0.815618 + 0.578590i \(0.196397\pi\)
\(332\) 11.7803 0.646529
\(333\) −2.26641 −0.124199
\(334\) −1.35579 −0.0741857
\(335\) 0 0
\(336\) 13.2025 0.720256
\(337\) 12.2225 0.665799 0.332900 0.942962i \(-0.391973\pi\)
0.332900 + 0.942962i \(0.391973\pi\)
\(338\) 0.249130 0.0135509
\(339\) 28.8082 1.56465
\(340\) 0 0
\(341\) −56.4284 −3.05577
\(342\) −1.91810 −0.103719
\(343\) 19.4700 1.05128
\(344\) 10.4009 0.560780
\(345\) 0 0
\(346\) 2.89190 0.155469
\(347\) 17.9815 0.965296 0.482648 0.875814i \(-0.339675\pi\)
0.482648 + 0.875814i \(0.339675\pi\)
\(348\) 29.8225 1.59866
\(349\) 26.2848 1.40699 0.703496 0.710699i \(-0.251621\pi\)
0.703496 + 0.710699i \(0.251621\pi\)
\(350\) 0 0
\(351\) −9.91756 −0.529360
\(352\) 22.7105 1.21047
\(353\) 13.7610 0.732424 0.366212 0.930531i \(-0.380654\pi\)
0.366212 + 0.930531i \(0.380654\pi\)
\(354\) 5.81879 0.309265
\(355\) 0 0
\(356\) 7.42120 0.393323
\(357\) 6.55679 0.347022
\(358\) −3.62152 −0.191403
\(359\) −1.32555 −0.0699598 −0.0349799 0.999388i \(-0.511137\pi\)
−0.0349799 + 0.999388i \(0.511137\pi\)
\(360\) 0 0
\(361\) −9.02572 −0.475038
\(362\) −6.66894 −0.350511
\(363\) −54.4249 −2.85657
\(364\) −12.7294 −0.667200
\(365\) 0 0
\(366\) −0.771541 −0.0403291
\(367\) −6.05979 −0.316319 −0.158159 0.987414i \(-0.550556\pi\)
−0.158159 + 0.987414i \(0.550556\pi\)
\(368\) 18.0803 0.942500
\(369\) −10.3174 −0.537105
\(370\) 0 0
\(371\) 16.0760 0.834627
\(372\) −38.7470 −2.00894
\(373\) −20.4445 −1.05858 −0.529288 0.848442i \(-0.677541\pi\)
−0.529288 + 0.848442i \(0.677541\pi\)
\(374\) 3.37157 0.174340
\(375\) 0 0
\(376\) 3.47503 0.179211
\(377\) −26.8550 −1.38310
\(378\) −1.67100 −0.0859471
\(379\) 35.4042 1.81859 0.909296 0.416150i \(-0.136621\pi\)
0.909296 + 0.416150i \(0.136621\pi\)
\(380\) 0 0
\(381\) −25.6899 −1.31613
\(382\) −0.757981 −0.0387817
\(383\) −6.79327 −0.347120 −0.173560 0.984823i \(-0.555527\pi\)
−0.173560 + 0.984823i \(0.555527\pi\)
\(384\) 20.5458 1.04848
\(385\) 0 0
\(386\) 3.02716 0.154079
\(387\) −13.8969 −0.706417
\(388\) −4.18862 −0.212645
\(389\) 24.6869 1.25168 0.625838 0.779953i \(-0.284757\pi\)
0.625838 + 0.779953i \(0.284757\pi\)
\(390\) 0 0
\(391\) 8.97924 0.454100
\(392\) 4.87687 0.246319
\(393\) −30.7760 −1.55245
\(394\) −2.12043 −0.106826
\(395\) 0 0
\(396\) −20.0280 −1.00644
\(397\) −14.3804 −0.721730 −0.360865 0.932618i \(-0.617518\pi\)
−0.360865 + 0.932618i \(0.617518\pi\)
\(398\) 6.92173 0.346955
\(399\) −12.5921 −0.630391
\(400\) 0 0
\(401\) 7.62276 0.380663 0.190331 0.981720i \(-0.439044\pi\)
0.190331 + 0.981720i \(0.439044\pi\)
\(402\) −6.27883 −0.313160
\(403\) 34.8914 1.73806
\(404\) 7.98416 0.397227
\(405\) 0 0
\(406\) −4.52478 −0.224561
\(407\) −7.65079 −0.379236
\(408\) 4.77417 0.236357
\(409\) 5.12423 0.253377 0.126688 0.991943i \(-0.459565\pi\)
0.126688 + 0.991943i \(0.459565\pi\)
\(410\) 0 0
\(411\) −27.0949 −1.33649
\(412\) 0.310416 0.0152931
\(413\) 14.2002 0.698748
\(414\) 3.31615 0.162980
\(415\) 0 0
\(416\) −14.0426 −0.688496
\(417\) 23.0441 1.12848
\(418\) −6.47498 −0.316701
\(419\) 13.3513 0.652254 0.326127 0.945326i \(-0.394256\pi\)
0.326127 + 0.945326i \(0.394256\pi\)
\(420\) 0 0
\(421\) 27.8059 1.35518 0.677588 0.735442i \(-0.263025\pi\)
0.677588 + 0.735442i \(0.263025\pi\)
\(422\) 0.672326 0.0327283
\(423\) −4.64304 −0.225752
\(424\) 11.7054 0.568465
\(425\) 0 0
\(426\) −9.84594 −0.477038
\(427\) −1.88288 −0.0911188
\(428\) 17.4837 0.845109
\(429\) 48.5155 2.34235
\(430\) 0 0
\(431\) 18.5717 0.894567 0.447283 0.894392i \(-0.352392\pi\)
0.447283 + 0.894392i \(0.352392\pi\)
\(432\) 8.86339 0.426440
\(433\) 7.19376 0.345710 0.172855 0.984947i \(-0.444701\pi\)
0.172855 + 0.984947i \(0.444701\pi\)
\(434\) 5.87883 0.282193
\(435\) 0 0
\(436\) −22.9628 −1.09972
\(437\) −17.2443 −0.824906
\(438\) −10.0158 −0.478575
\(439\) −16.2866 −0.777315 −0.388657 0.921382i \(-0.627061\pi\)
−0.388657 + 0.921382i \(0.627061\pi\)
\(440\) 0 0
\(441\) −6.51607 −0.310289
\(442\) −2.08475 −0.0991614
\(443\) 37.0915 1.76227 0.881135 0.472864i \(-0.156780\pi\)
0.881135 + 0.472864i \(0.156780\pi\)
\(444\) −5.25348 −0.249319
\(445\) 0 0
\(446\) −7.35293 −0.348171
\(447\) 20.3355 0.961837
\(448\) 9.71757 0.459112
\(449\) −17.1059 −0.807275 −0.403638 0.914919i \(-0.632254\pi\)
−0.403638 + 0.914919i \(0.632254\pi\)
\(450\) 0 0
\(451\) −34.8289 −1.64003
\(452\) 24.8234 1.16760
\(453\) −22.4791 −1.05616
\(454\) −7.11001 −0.333689
\(455\) 0 0
\(456\) −9.16861 −0.429360
\(457\) 9.35857 0.437776 0.218888 0.975750i \(-0.429757\pi\)
0.218888 + 0.975750i \(0.429757\pi\)
\(458\) 9.74302 0.455262
\(459\) 4.40184 0.205460
\(460\) 0 0
\(461\) −15.8670 −0.738999 −0.369500 0.929231i \(-0.620471\pi\)
−0.369500 + 0.929231i \(0.620471\pi\)
\(462\) 8.17435 0.380305
\(463\) 6.99749 0.325201 0.162601 0.986692i \(-0.448012\pi\)
0.162601 + 0.986692i \(0.448012\pi\)
\(464\) 24.0005 1.11419
\(465\) 0 0
\(466\) 0.750055 0.0347456
\(467\) 24.2782 1.12346 0.561729 0.827321i \(-0.310136\pi\)
0.561729 + 0.827321i \(0.310136\pi\)
\(468\) 12.3839 0.572447
\(469\) −15.3229 −0.707547
\(470\) 0 0
\(471\) −9.26191 −0.426766
\(472\) 10.3396 0.475918
\(473\) −46.9120 −2.15702
\(474\) 7.95222 0.365258
\(475\) 0 0
\(476\) 5.64984 0.258960
\(477\) −15.6398 −0.716096
\(478\) 8.63746 0.395068
\(479\) 8.93171 0.408100 0.204050 0.978960i \(-0.434589\pi\)
0.204050 + 0.978960i \(0.434589\pi\)
\(480\) 0 0
\(481\) 4.73072 0.215702
\(482\) 0.342147 0.0155844
\(483\) 21.7701 0.990574
\(484\) −46.8968 −2.13167
\(485\) 0 0
\(486\) 5.60711 0.254344
\(487\) −34.5963 −1.56771 −0.783855 0.620944i \(-0.786750\pi\)
−0.783855 + 0.620944i \(0.786750\pi\)
\(488\) −1.37097 −0.0620611
\(489\) −14.0417 −0.634987
\(490\) 0 0
\(491\) 34.3798 1.55154 0.775770 0.631016i \(-0.217362\pi\)
0.775770 + 0.631016i \(0.217362\pi\)
\(492\) −23.9156 −1.07820
\(493\) 11.9194 0.536823
\(494\) 4.00368 0.180134
\(495\) 0 0
\(496\) −31.1827 −1.40014
\(497\) −24.0281 −1.07781
\(498\) 4.67762 0.209609
\(499\) 38.3126 1.71511 0.857554 0.514394i \(-0.171983\pi\)
0.857554 + 0.514394i \(0.171983\pi\)
\(500\) 0 0
\(501\) 8.65906 0.386858
\(502\) 7.25923 0.323995
\(503\) 12.6073 0.562132 0.281066 0.959688i \(-0.409312\pi\)
0.281066 + 0.959688i \(0.409312\pi\)
\(504\) 4.30285 0.191664
\(505\) 0 0
\(506\) 11.1944 0.497653
\(507\) −1.59112 −0.0706641
\(508\) −22.1364 −0.982146
\(509\) −19.0748 −0.845476 −0.422738 0.906252i \(-0.638931\pi\)
−0.422738 + 0.906252i \(0.638931\pi\)
\(510\) 0 0
\(511\) −24.4428 −1.08128
\(512\) 21.3484 0.943474
\(513\) −8.45356 −0.373234
\(514\) −6.53947 −0.288444
\(515\) 0 0
\(516\) −32.2125 −1.41808
\(517\) −15.6737 −0.689326
\(518\) 0.797076 0.0350215
\(519\) −18.4697 −0.810731
\(520\) 0 0
\(521\) 11.5960 0.508028 0.254014 0.967201i \(-0.418249\pi\)
0.254014 + 0.967201i \(0.418249\pi\)
\(522\) 4.40199 0.192670
\(523\) 26.2727 1.14883 0.574413 0.818566i \(-0.305230\pi\)
0.574413 + 0.818566i \(0.305230\pi\)
\(524\) −26.5190 −1.15849
\(525\) 0 0
\(526\) 4.37236 0.190644
\(527\) −15.4863 −0.674594
\(528\) −43.3586 −1.88694
\(529\) 6.81324 0.296228
\(530\) 0 0
\(531\) −13.8149 −0.599515
\(532\) −10.8503 −0.470420
\(533\) 21.5358 0.932819
\(534\) 2.94674 0.127518
\(535\) 0 0
\(536\) −11.1570 −0.481911
\(537\) 23.1296 0.998118
\(538\) 0.566406 0.0244195
\(539\) −21.9965 −0.947455
\(540\) 0 0
\(541\) −15.1441 −0.651097 −0.325548 0.945525i \(-0.605549\pi\)
−0.325548 + 0.945525i \(0.605549\pi\)
\(542\) −5.82421 −0.250171
\(543\) 42.5926 1.82782
\(544\) 6.23272 0.267226
\(545\) 0 0
\(546\) −5.05446 −0.216311
\(547\) −34.7331 −1.48508 −0.742540 0.669802i \(-0.766379\pi\)
−0.742540 + 0.669802i \(0.766379\pi\)
\(548\) −23.3471 −0.997339
\(549\) 1.83178 0.0781785
\(550\) 0 0
\(551\) −22.8907 −0.975178
\(552\) 15.8514 0.674680
\(553\) 19.4067 0.825256
\(554\) −5.75645 −0.244568
\(555\) 0 0
\(556\) 19.8566 0.842109
\(557\) −34.1470 −1.44685 −0.723427 0.690401i \(-0.757434\pi\)
−0.723427 + 0.690401i \(0.757434\pi\)
\(558\) −5.71930 −0.242117
\(559\) 29.0071 1.22687
\(560\) 0 0
\(561\) −21.5333 −0.909136
\(562\) −5.53128 −0.233323
\(563\) 19.2900 0.812975 0.406488 0.913656i \(-0.366753\pi\)
0.406488 + 0.913656i \(0.366753\pi\)
\(564\) −10.7624 −0.453181
\(565\) 0 0
\(566\) −0.868635 −0.0365114
\(567\) 20.3886 0.856241
\(568\) −17.4955 −0.734097
\(569\) −33.4263 −1.40130 −0.700652 0.713503i \(-0.747107\pi\)
−0.700652 + 0.713503i \(0.747107\pi\)
\(570\) 0 0
\(571\) 3.07936 0.128867 0.0644336 0.997922i \(-0.479476\pi\)
0.0644336 + 0.997922i \(0.479476\pi\)
\(572\) 41.8048 1.74795
\(573\) 4.84101 0.202236
\(574\) 3.62855 0.151453
\(575\) 0 0
\(576\) −9.45386 −0.393911
\(577\) 5.95435 0.247883 0.123941 0.992290i \(-0.460447\pi\)
0.123941 + 0.992290i \(0.460447\pi\)
\(578\) −4.89120 −0.203447
\(579\) −19.3336 −0.803478
\(580\) 0 0
\(581\) 11.4153 0.473587
\(582\) −1.66318 −0.0689408
\(583\) −52.7957 −2.18657
\(584\) −17.7974 −0.736463
\(585\) 0 0
\(586\) 7.83419 0.323627
\(587\) −42.0432 −1.73531 −0.867655 0.497167i \(-0.834374\pi\)
−0.867655 + 0.497167i \(0.834374\pi\)
\(588\) −15.1041 −0.622881
\(589\) 29.7409 1.22545
\(590\) 0 0
\(591\) 13.5426 0.557068
\(592\) −4.22788 −0.173765
\(593\) −40.9908 −1.68329 −0.841645 0.540031i \(-0.818413\pi\)
−0.841645 + 0.540031i \(0.818413\pi\)
\(594\) 5.48778 0.225166
\(595\) 0 0
\(596\) 17.5227 0.717757
\(597\) −44.2071 −1.80928
\(598\) −6.92186 −0.283056
\(599\) −27.0862 −1.10671 −0.553356 0.832945i \(-0.686653\pi\)
−0.553356 + 0.832945i \(0.686653\pi\)
\(600\) 0 0
\(601\) −3.03033 −0.123610 −0.0618049 0.998088i \(-0.519686\pi\)
−0.0618049 + 0.998088i \(0.519686\pi\)
\(602\) 4.88740 0.199195
\(603\) 14.9071 0.607064
\(604\) −19.3697 −0.788144
\(605\) 0 0
\(606\) 3.17027 0.128784
\(607\) −0.560838 −0.0227637 −0.0113818 0.999935i \(-0.503623\pi\)
−0.0113818 + 0.999935i \(0.503623\pi\)
\(608\) −11.9697 −0.485435
\(609\) 28.8985 1.17103
\(610\) 0 0
\(611\) 9.69150 0.392076
\(612\) −5.49652 −0.222184
\(613\) −23.7388 −0.958801 −0.479401 0.877596i \(-0.659146\pi\)
−0.479401 + 0.877596i \(0.659146\pi\)
\(614\) 1.61326 0.0651061
\(615\) 0 0
\(616\) 14.5252 0.585239
\(617\) 10.2411 0.412290 0.206145 0.978521i \(-0.433908\pi\)
0.206145 + 0.978521i \(0.433908\pi\)
\(618\) 0.123257 0.00495813
\(619\) −27.8348 −1.11878 −0.559388 0.828906i \(-0.688964\pi\)
−0.559388 + 0.828906i \(0.688964\pi\)
\(620\) 0 0
\(621\) 14.6152 0.586486
\(622\) 1.58725 0.0636428
\(623\) 7.19125 0.288111
\(624\) 26.8100 1.07326
\(625\) 0 0
\(626\) 1.72462 0.0689295
\(627\) 41.3538 1.65151
\(628\) −7.98079 −0.318468
\(629\) −2.09970 −0.0837204
\(630\) 0 0
\(631\) 23.0564 0.917861 0.458931 0.888472i \(-0.348233\pi\)
0.458931 + 0.888472i \(0.348233\pi\)
\(632\) 14.1305 0.562082
\(633\) −4.29396 −0.170669
\(634\) 9.61406 0.381823
\(635\) 0 0
\(636\) −36.2526 −1.43751
\(637\) 13.6011 0.538895
\(638\) 14.8599 0.588310
\(639\) 23.3761 0.924744
\(640\) 0 0
\(641\) 35.6143 1.40668 0.703340 0.710853i \(-0.251691\pi\)
0.703340 + 0.710853i \(0.251691\pi\)
\(642\) 6.94227 0.273990
\(643\) 28.2806 1.11528 0.557639 0.830084i \(-0.311707\pi\)
0.557639 + 0.830084i \(0.311707\pi\)
\(644\) 18.7588 0.739201
\(645\) 0 0
\(646\) −1.77700 −0.0699153
\(647\) −14.5953 −0.573802 −0.286901 0.957960i \(-0.592625\pi\)
−0.286901 + 0.957960i \(0.592625\pi\)
\(648\) 14.8455 0.583186
\(649\) −46.6353 −1.83060
\(650\) 0 0
\(651\) −37.5464 −1.47156
\(652\) −12.0994 −0.473850
\(653\) 28.0718 1.09853 0.549267 0.835647i \(-0.314907\pi\)
0.549267 + 0.835647i \(0.314907\pi\)
\(654\) −9.11783 −0.356535
\(655\) 0 0
\(656\) −19.2467 −0.751457
\(657\) 23.7794 0.927724
\(658\) 1.63292 0.0636577
\(659\) −2.33181 −0.0908343 −0.0454172 0.998968i \(-0.514462\pi\)
−0.0454172 + 0.998968i \(0.514462\pi\)
\(660\) 0 0
\(661\) −21.3409 −0.830063 −0.415031 0.909807i \(-0.636229\pi\)
−0.415031 + 0.909807i \(0.636229\pi\)
\(662\) 10.1542 0.394652
\(663\) 13.3147 0.517100
\(664\) 8.31179 0.322560
\(665\) 0 0
\(666\) −0.775446 −0.0300479
\(667\) 39.5752 1.53236
\(668\) 7.46133 0.288687
\(669\) 46.9611 1.81562
\(670\) 0 0
\(671\) 6.18360 0.238715
\(672\) 15.1112 0.582926
\(673\) 25.0948 0.967333 0.483667 0.875252i \(-0.339305\pi\)
0.483667 + 0.875252i \(0.339305\pi\)
\(674\) 4.18187 0.161080
\(675\) 0 0
\(676\) −1.37103 −0.0527321
\(677\) 7.78669 0.299267 0.149633 0.988742i \(-0.452191\pi\)
0.149633 + 0.988742i \(0.452191\pi\)
\(678\) 9.85664 0.378542
\(679\) −4.05883 −0.155764
\(680\) 0 0
\(681\) 45.4096 1.74010
\(682\) −19.3068 −0.739295
\(683\) −2.68470 −0.102727 −0.0513636 0.998680i \(-0.516357\pi\)
−0.0513636 + 0.998680i \(0.516357\pi\)
\(684\) 10.5559 0.403613
\(685\) 0 0
\(686\) 6.66159 0.254341
\(687\) −62.2259 −2.37407
\(688\) −25.9239 −0.988339
\(689\) 32.6452 1.24368
\(690\) 0 0
\(691\) −46.3260 −1.76232 −0.881162 0.472814i \(-0.843238\pi\)
−0.881162 + 0.472814i \(0.843238\pi\)
\(692\) −15.9150 −0.604996
\(693\) −19.4074 −0.737227
\(694\) 6.15230 0.233538
\(695\) 0 0
\(696\) 21.0418 0.797586
\(697\) −9.55851 −0.362054
\(698\) 8.99326 0.340400
\(699\) −4.79039 −0.181189
\(700\) 0 0
\(701\) 4.33233 0.163630 0.0818150 0.996648i \(-0.473928\pi\)
0.0818150 + 0.996648i \(0.473928\pi\)
\(702\) −3.39326 −0.128070
\(703\) 4.03239 0.152084
\(704\) −31.9137 −1.20279
\(705\) 0 0
\(706\) 4.70829 0.177199
\(707\) 7.73677 0.290971
\(708\) −32.0225 −1.20348
\(709\) −45.2491 −1.69936 −0.849682 0.527295i \(-0.823206\pi\)
−0.849682 + 0.527295i \(0.823206\pi\)
\(710\) 0 0
\(711\) −18.8800 −0.708057
\(712\) 5.23614 0.196233
\(713\) −51.4182 −1.92563
\(714\) 2.24338 0.0839566
\(715\) 0 0
\(716\) 19.9303 0.744831
\(717\) −55.1650 −2.06017
\(718\) −0.453533 −0.0169257
\(719\) 34.3560 1.28126 0.640632 0.767848i \(-0.278672\pi\)
0.640632 + 0.767848i \(0.278672\pi\)
\(720\) 0 0
\(721\) 0.300798 0.0112023
\(722\) −3.08812 −0.114928
\(723\) −2.18519 −0.0812683
\(724\) 36.7011 1.36399
\(725\) 0 0
\(726\) −18.6213 −0.691102
\(727\) 29.1579 1.08141 0.540703 0.841213i \(-0.318158\pi\)
0.540703 + 0.841213i \(0.318158\pi\)
\(728\) −8.98141 −0.332873
\(729\) −2.28799 −0.0847405
\(730\) 0 0
\(731\) −12.8746 −0.476185
\(732\) 4.24602 0.156937
\(733\) −36.8326 −1.36044 −0.680222 0.733007i \(-0.738116\pi\)
−0.680222 + 0.733007i \(0.738116\pi\)
\(734\) −2.07334 −0.0765283
\(735\) 0 0
\(736\) 20.6941 0.762795
\(737\) 50.3224 1.85365
\(738\) −3.53008 −0.129944
\(739\) 24.4258 0.898517 0.449258 0.893402i \(-0.351688\pi\)
0.449258 + 0.893402i \(0.351688\pi\)
\(740\) 0 0
\(741\) −25.5704 −0.939350
\(742\) 5.50037 0.201925
\(743\) 24.4245 0.896049 0.448024 0.894021i \(-0.352128\pi\)
0.448024 + 0.894021i \(0.352128\pi\)
\(744\) −27.3386 −1.00228
\(745\) 0 0
\(746\) −6.99503 −0.256106
\(747\) −11.1055 −0.406330
\(748\) −18.5548 −0.678429
\(749\) 16.9420 0.619047
\(750\) 0 0
\(751\) −30.0598 −1.09690 −0.548449 0.836184i \(-0.684781\pi\)
−0.548449 + 0.836184i \(0.684781\pi\)
\(752\) −8.66136 −0.315847
\(753\) −46.3627 −1.68955
\(754\) −9.18835 −0.334620
\(755\) 0 0
\(756\) 9.19603 0.334456
\(757\) −5.79087 −0.210473 −0.105236 0.994447i \(-0.533560\pi\)
−0.105236 + 0.994447i \(0.533560\pi\)
\(758\) 12.1134 0.439980
\(759\) −71.4956 −2.59513
\(760\) 0 0
\(761\) 2.42691 0.0879754 0.0439877 0.999032i \(-0.485994\pi\)
0.0439877 + 0.999032i \(0.485994\pi\)
\(762\) −8.78972 −0.318418
\(763\) −22.2512 −0.805549
\(764\) 4.17139 0.150916
\(765\) 0 0
\(766\) −2.32430 −0.0839803
\(767\) 28.8361 1.04121
\(768\) −16.2465 −0.586246
\(769\) 22.0750 0.796045 0.398022 0.917376i \(-0.369697\pi\)
0.398022 + 0.917376i \(0.369697\pi\)
\(770\) 0 0
\(771\) 41.7657 1.50416
\(772\) −16.6594 −0.599584
\(773\) −28.7802 −1.03515 −0.517576 0.855637i \(-0.673166\pi\)
−0.517576 + 0.855637i \(0.673166\pi\)
\(774\) −4.75476 −0.170906
\(775\) 0 0
\(776\) −2.95534 −0.106091
\(777\) −5.09070 −0.182628
\(778\) 8.44655 0.302824
\(779\) 18.3567 0.657699
\(780\) 0 0
\(781\) 78.9113 2.82367
\(782\) 3.07222 0.109862
\(783\) 19.4007 0.693325
\(784\) −12.1554 −0.434121
\(785\) 0 0
\(786\) −10.5299 −0.375590
\(787\) 53.4388 1.90489 0.952443 0.304715i \(-0.0985613\pi\)
0.952443 + 0.304715i \(0.0985613\pi\)
\(788\) 11.6694 0.415704
\(789\) −27.9250 −0.994158
\(790\) 0 0
\(791\) 24.0543 0.855271
\(792\) −14.1311 −0.502125
\(793\) −3.82351 −0.135777
\(794\) −4.92020 −0.174611
\(795\) 0 0
\(796\) −38.0923 −1.35015
\(797\) −10.4149 −0.368914 −0.184457 0.982841i \(-0.559053\pi\)
−0.184457 + 0.982841i \(0.559053\pi\)
\(798\) −4.30833 −0.152513
\(799\) −4.30151 −0.152176
\(800\) 0 0
\(801\) −6.99609 −0.247195
\(802\) 2.60810 0.0920954
\(803\) 80.2730 2.83277
\(804\) 34.5543 1.21864
\(805\) 0 0
\(806\) 11.9380 0.420498
\(807\) −3.61747 −0.127341
\(808\) 5.63335 0.198181
\(809\) −25.9467 −0.912237 −0.456118 0.889919i \(-0.650761\pi\)
−0.456118 + 0.889919i \(0.650761\pi\)
\(810\) 0 0
\(811\) −11.1712 −0.392275 −0.196137 0.980576i \(-0.562840\pi\)
−0.196137 + 0.980576i \(0.562840\pi\)
\(812\) 24.9012 0.873861
\(813\) 37.1976 1.30458
\(814\) −2.61769 −0.0917501
\(815\) 0 0
\(816\) −11.8994 −0.416563
\(817\) 24.7252 0.865026
\(818\) 1.75324 0.0613005
\(819\) 12.0002 0.419321
\(820\) 0 0
\(821\) 18.3232 0.639484 0.319742 0.947505i \(-0.396404\pi\)
0.319742 + 0.947505i \(0.396404\pi\)
\(822\) −9.27045 −0.323344
\(823\) −21.1230 −0.736301 −0.368150 0.929766i \(-0.620009\pi\)
−0.368150 + 0.929766i \(0.620009\pi\)
\(824\) 0.219019 0.00762989
\(825\) 0 0
\(826\) 4.85857 0.169051
\(827\) −47.5383 −1.65307 −0.826534 0.562887i \(-0.809690\pi\)
−0.826534 + 0.562887i \(0.809690\pi\)
\(828\) −18.2498 −0.634223
\(829\) 15.8701 0.551190 0.275595 0.961274i \(-0.411125\pi\)
0.275595 + 0.961274i \(0.411125\pi\)
\(830\) 0 0
\(831\) 36.7648 1.27536
\(832\) 19.7332 0.684126
\(833\) −6.03676 −0.209161
\(834\) 7.88448 0.273017
\(835\) 0 0
\(836\) 35.6337 1.23242
\(837\) −25.2065 −0.871262
\(838\) 4.56811 0.157803
\(839\) 34.3114 1.18456 0.592281 0.805732i \(-0.298228\pi\)
0.592281 + 0.805732i \(0.298228\pi\)
\(840\) 0 0
\(841\) 23.5337 0.811507
\(842\) 9.51370 0.327864
\(843\) 35.3267 1.21672
\(844\) −3.70001 −0.127360
\(845\) 0 0
\(846\) −1.58860 −0.0546173
\(847\) −45.4437 −1.56146
\(848\) −29.1752 −1.00188
\(849\) 5.54772 0.190397
\(850\) 0 0
\(851\) −6.97150 −0.238980
\(852\) 54.1851 1.85635
\(853\) 45.8466 1.56976 0.784879 0.619649i \(-0.212725\pi\)
0.784879 + 0.619649i \(0.212725\pi\)
\(854\) −0.644221 −0.0220448
\(855\) 0 0
\(856\) 12.3359 0.421633
\(857\) −21.7254 −0.742125 −0.371063 0.928608i \(-0.621007\pi\)
−0.371063 + 0.928608i \(0.621007\pi\)
\(858\) 16.5994 0.566696
\(859\) 52.5363 1.79252 0.896258 0.443534i \(-0.146275\pi\)
0.896258 + 0.443534i \(0.146275\pi\)
\(860\) 0 0
\(861\) −23.1745 −0.789786
\(862\) 6.35425 0.216427
\(863\) −32.9971 −1.12323 −0.561617 0.827397i \(-0.689821\pi\)
−0.561617 + 0.827397i \(0.689821\pi\)
\(864\) 10.1447 0.345131
\(865\) 0 0
\(866\) 2.46132 0.0836392
\(867\) 31.2387 1.06092
\(868\) −32.3529 −1.09813
\(869\) −63.7339 −2.16202
\(870\) 0 0
\(871\) −31.1159 −1.05432
\(872\) −16.2017 −0.548660
\(873\) 3.94868 0.133643
\(874\) −5.90008 −0.199573
\(875\) 0 0
\(876\) 55.1201 1.86234
\(877\) 21.4221 0.723372 0.361686 0.932300i \(-0.382201\pi\)
0.361686 + 0.932300i \(0.382201\pi\)
\(878\) −5.57239 −0.188059
\(879\) −50.0347 −1.68763
\(880\) 0 0
\(881\) −39.1162 −1.31786 −0.658929 0.752205i \(-0.728990\pi\)
−0.658929 + 0.752205i \(0.728990\pi\)
\(882\) −2.22945 −0.0750696
\(883\) 2.84717 0.0958150 0.0479075 0.998852i \(-0.484745\pi\)
0.0479075 + 0.998852i \(0.484745\pi\)
\(884\) 11.4730 0.385878
\(885\) 0 0
\(886\) 12.6907 0.426354
\(887\) 46.9262 1.57563 0.787814 0.615913i \(-0.211213\pi\)
0.787814 + 0.615913i \(0.211213\pi\)
\(888\) −3.70667 −0.124388
\(889\) −21.4505 −0.719428
\(890\) 0 0
\(891\) −66.9586 −2.24320
\(892\) 40.4653 1.35488
\(893\) 8.26088 0.276440
\(894\) 6.95773 0.232701
\(895\) 0 0
\(896\) 17.1553 0.573120
\(897\) 44.2080 1.47606
\(898\) −5.85272 −0.195308
\(899\) −68.2546 −2.27642
\(900\) 0 0
\(901\) −14.4893 −0.482710
\(902\) −11.9166 −0.396779
\(903\) −31.2144 −1.03875
\(904\) 17.5145 0.582525
\(905\) 0 0
\(906\) −7.69115 −0.255521
\(907\) −15.7164 −0.521856 −0.260928 0.965358i \(-0.584028\pi\)
−0.260928 + 0.965358i \(0.584028\pi\)
\(908\) 39.1285 1.29852
\(909\) −7.52681 −0.249649
\(910\) 0 0
\(911\) 0.0451186 0.00149485 0.000747423 1.00000i \(-0.499762\pi\)
0.000747423 1.00000i \(0.499762\pi\)
\(912\) 22.8524 0.756718
\(913\) −37.4892 −1.24071
\(914\) 3.20201 0.105913
\(915\) 0 0
\(916\) −53.6187 −1.77161
\(917\) −25.6973 −0.848601
\(918\) 1.50608 0.0497079
\(919\) −7.88987 −0.260263 −0.130131 0.991497i \(-0.541540\pi\)
−0.130131 + 0.991497i \(0.541540\pi\)
\(920\) 0 0
\(921\) −10.3035 −0.339511
\(922\) −5.42884 −0.178789
\(923\) −48.7933 −1.60605
\(924\) −44.9859 −1.47993
\(925\) 0 0
\(926\) 2.39417 0.0786773
\(927\) −0.292635 −0.00961140
\(928\) 27.4702 0.901752
\(929\) 25.6276 0.840815 0.420408 0.907335i \(-0.361887\pi\)
0.420408 + 0.907335i \(0.361887\pi\)
\(930\) 0 0
\(931\) 11.5934 0.379957
\(932\) −4.12777 −0.135210
\(933\) −10.1373 −0.331880
\(934\) 8.30670 0.271803
\(935\) 0 0
\(936\) 8.73767 0.285600
\(937\) 57.8627 1.89029 0.945146 0.326649i \(-0.105919\pi\)
0.945146 + 0.326649i \(0.105919\pi\)
\(938\) −5.24269 −0.171180
\(939\) −11.0146 −0.359449
\(940\) 0 0
\(941\) −14.1272 −0.460533 −0.230266 0.973128i \(-0.573960\pi\)
−0.230266 + 0.973128i \(0.573960\pi\)
\(942\) −3.16893 −0.103249
\(943\) −31.7365 −1.03348
\(944\) −25.7710 −0.838774
\(945\) 0 0
\(946\) −16.0508 −0.521857
\(947\) −22.5318 −0.732185 −0.366092 0.930578i \(-0.619305\pi\)
−0.366092 + 0.930578i \(0.619305\pi\)
\(948\) −43.7634 −1.42137
\(949\) −49.6353 −1.61123
\(950\) 0 0
\(951\) −61.4023 −1.99110
\(952\) 3.98633 0.129198
\(953\) 34.0142 1.10183 0.550914 0.834562i \(-0.314279\pi\)
0.550914 + 0.834562i \(0.314279\pi\)
\(954\) −5.35110 −0.173248
\(955\) 0 0
\(956\) −47.5345 −1.53737
\(957\) −94.9061 −3.06788
\(958\) 3.05596 0.0987335
\(959\) −22.6237 −0.730557
\(960\) 0 0
\(961\) 57.6799 1.86064
\(962\) 1.61860 0.0521858
\(963\) −16.4822 −0.531133
\(964\) −1.88294 −0.0606453
\(965\) 0 0
\(966\) 7.44857 0.239654
\(967\) 62.1874 1.99981 0.999906 0.0137093i \(-0.00436394\pi\)
0.999906 + 0.0137093i \(0.00436394\pi\)
\(968\) −33.0888 −1.06351
\(969\) 11.3492 0.364590
\(970\) 0 0
\(971\) 18.4346 0.591594 0.295797 0.955251i \(-0.404415\pi\)
0.295797 + 0.955251i \(0.404415\pi\)
\(972\) −30.8576 −0.989757
\(973\) 19.2414 0.616850
\(974\) −11.8370 −0.379283
\(975\) 0 0
\(976\) 3.41710 0.109379
\(977\) −25.2228 −0.806949 −0.403474 0.914991i \(-0.632198\pi\)
−0.403474 + 0.914991i \(0.632198\pi\)
\(978\) −4.80432 −0.153625
\(979\) −23.6169 −0.754800
\(980\) 0 0
\(981\) 21.6474 0.691148
\(982\) 11.7630 0.375371
\(983\) −12.7405 −0.406358 −0.203179 0.979142i \(-0.565127\pi\)
−0.203179 + 0.979142i \(0.565127\pi\)
\(984\) −16.8740 −0.537923
\(985\) 0 0
\(986\) 4.07819 0.129876
\(987\) −10.4290 −0.331958
\(988\) −22.0334 −0.700977
\(989\) −42.7468 −1.35927
\(990\) 0 0
\(991\) 15.6775 0.498011 0.249005 0.968502i \(-0.419896\pi\)
0.249005 + 0.968502i \(0.419896\pi\)
\(992\) −35.6907 −1.13318
\(993\) −64.8517 −2.05801
\(994\) −8.22116 −0.260759
\(995\) 0 0
\(996\) −25.7423 −0.815676
\(997\) −28.1048 −0.890088 −0.445044 0.895509i \(-0.646812\pi\)
−0.445044 + 0.895509i \(0.646812\pi\)
\(998\) 13.1085 0.414944
\(999\) −3.41759 −0.108128
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 \(a_p\))