Properties

Label 8021.2.a.a.1.7
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.51883 q^{2}\) \(-2.43350 q^{3}\) \(+4.34452 q^{4}\) \(-0.221192 q^{5}\) \(+6.12959 q^{6}\) \(-1.84924 q^{7}\) \(-5.90546 q^{8}\) \(+2.92194 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.51883 q^{2}\) \(-2.43350 q^{3}\) \(+4.34452 q^{4}\) \(-0.221192 q^{5}\) \(+6.12959 q^{6}\) \(-1.84924 q^{7}\) \(-5.90546 q^{8}\) \(+2.92194 q^{9}\) \(+0.557145 q^{10}\) \(-0.570132 q^{11}\) \(-10.5724 q^{12}\) \(+1.00000 q^{13}\) \(+4.65793 q^{14}\) \(+0.538271 q^{15}\) \(+6.18583 q^{16}\) \(-2.72385 q^{17}\) \(-7.35988 q^{18}\) \(+0.725895 q^{19}\) \(-0.960972 q^{20}\) \(+4.50014 q^{21}\) \(+1.43607 q^{22}\) \(+9.23887 q^{23}\) \(+14.3710 q^{24}\) \(-4.95107 q^{25}\) \(-2.51883 q^{26}\) \(+0.189961 q^{27}\) \(-8.03407 q^{28}\) \(-5.17059 q^{29}\) \(-1.35581 q^{30}\) \(-1.94484 q^{31}\) \(-3.77015 q^{32}\) \(+1.38742 q^{33}\) \(+6.86093 q^{34}\) \(+0.409037 q^{35}\) \(+12.6944 q^{36}\) \(+3.04393 q^{37}\) \(-1.82841 q^{38}\) \(-2.43350 q^{39}\) \(+1.30624 q^{40}\) \(-10.8334 q^{41}\) \(-11.3351 q^{42}\) \(+1.96107 q^{43}\) \(-2.47695 q^{44}\) \(-0.646308 q^{45}\) \(-23.2712 q^{46}\) \(-6.01145 q^{47}\) \(-15.0532 q^{48}\) \(-3.58031 q^{49}\) \(+12.4709 q^{50}\) \(+6.62850 q^{51}\) \(+4.34452 q^{52}\) \(+8.41021 q^{53}\) \(-0.478479 q^{54}\) \(+0.126109 q^{55}\) \(+10.9206 q^{56}\) \(-1.76647 q^{57}\) \(+13.0238 q^{58}\) \(+12.7351 q^{59}\) \(+2.33853 q^{60}\) \(+4.56498 q^{61}\) \(+4.89874 q^{62}\) \(-5.40337 q^{63}\) \(-2.87528 q^{64}\) \(-0.221192 q^{65}\) \(-3.49468 q^{66}\) \(-7.92183 q^{67}\) \(-11.8338 q^{68}\) \(-22.4828 q^{69}\) \(-1.03030 q^{70}\) \(-1.61023 q^{71}\) \(-17.2554 q^{72}\) \(+10.2770 q^{73}\) \(-7.66716 q^{74}\) \(+12.0485 q^{75}\) \(+3.15367 q^{76}\) \(+1.05431 q^{77}\) \(+6.12959 q^{78}\) \(-9.24103 q^{79}\) \(-1.36825 q^{80}\) \(-9.22809 q^{81}\) \(+27.2875 q^{82}\) \(+16.4887 q^{83}\) \(+19.5509 q^{84}\) \(+0.602493 q^{85}\) \(-4.93960 q^{86}\) \(+12.5826 q^{87}\) \(+3.36689 q^{88}\) \(+12.2808 q^{89}\) \(+1.62794 q^{90}\) \(-1.84924 q^{91}\) \(+40.1385 q^{92}\) \(+4.73279 q^{93}\) \(+15.1418 q^{94}\) \(-0.160562 q^{95}\) \(+9.17467 q^{96}\) \(-8.85175 q^{97}\) \(+9.01819 q^{98}\) \(-1.66589 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51883 −1.78108 −0.890542 0.454901i \(-0.849675\pi\)
−0.890542 + 0.454901i \(0.849675\pi\)
\(3\) −2.43350 −1.40498 −0.702492 0.711692i \(-0.747929\pi\)
−0.702492 + 0.711692i \(0.747929\pi\)
\(4\) 4.34452 2.17226
\(5\) −0.221192 −0.0989199 −0.0494599 0.998776i \(-0.515750\pi\)
−0.0494599 + 0.998776i \(0.515750\pi\)
\(6\) 6.12959 2.50239
\(7\) −1.84924 −0.698948 −0.349474 0.936946i \(-0.613640\pi\)
−0.349474 + 0.936946i \(0.613640\pi\)
\(8\) −5.90546 −2.08790
\(9\) 2.92194 0.973980
\(10\) 0.557145 0.176185
\(11\) −0.570132 −0.171901 −0.0859507 0.996299i \(-0.527393\pi\)
−0.0859507 + 0.996299i \(0.527393\pi\)
\(12\) −10.5724 −3.05199
\(13\) 1.00000 0.277350
\(14\) 4.65793 1.24488
\(15\) 0.538271 0.138981
\(16\) 6.18583 1.54646
\(17\) −2.72385 −0.660631 −0.330315 0.943871i \(-0.607155\pi\)
−0.330315 + 0.943871i \(0.607155\pi\)
\(18\) −7.35988 −1.73474
\(19\) 0.725895 0.166532 0.0832659 0.996527i \(-0.473465\pi\)
0.0832659 + 0.996527i \(0.473465\pi\)
\(20\) −0.960972 −0.214880
\(21\) 4.50014 0.982010
\(22\) 1.43607 0.306171
\(23\) 9.23887 1.92644 0.963218 0.268720i \(-0.0866005\pi\)
0.963218 + 0.268720i \(0.0866005\pi\)
\(24\) 14.3710 2.93346
\(25\) −4.95107 −0.990215
\(26\) −2.51883 −0.493984
\(27\) 0.189961 0.0365579
\(28\) −8.03407 −1.51830
\(29\) −5.17059 −0.960154 −0.480077 0.877226i \(-0.659391\pi\)
−0.480077 + 0.877226i \(0.659391\pi\)
\(30\) −1.35581 −0.247537
\(31\) −1.94484 −0.349304 −0.174652 0.984630i \(-0.555880\pi\)
−0.174652 + 0.984630i \(0.555880\pi\)
\(32\) −3.77015 −0.666474
\(33\) 1.38742 0.241519
\(34\) 6.86093 1.17664
\(35\) 0.409037 0.0691398
\(36\) 12.6944 2.11574
\(37\) 3.04393 0.500419 0.250210 0.968192i \(-0.419500\pi\)
0.250210 + 0.968192i \(0.419500\pi\)
\(38\) −1.82841 −0.296607
\(39\) −2.43350 −0.389672
\(40\) 1.30624 0.206534
\(41\) −10.8334 −1.69189 −0.845946 0.533269i \(-0.820963\pi\)
−0.845946 + 0.533269i \(0.820963\pi\)
\(42\) −11.3351 −1.74904
\(43\) 1.96107 0.299060 0.149530 0.988757i \(-0.452224\pi\)
0.149530 + 0.988757i \(0.452224\pi\)
\(44\) −2.47695 −0.373415
\(45\) −0.646308 −0.0963460
\(46\) −23.2712 −3.43115
\(47\) −6.01145 −0.876860 −0.438430 0.898765i \(-0.644465\pi\)
−0.438430 + 0.898765i \(0.644465\pi\)
\(48\) −15.0532 −2.17275
\(49\) −3.58031 −0.511472
\(50\) 12.4709 1.76366
\(51\) 6.62850 0.928176
\(52\) 4.34452 0.602477
\(53\) 8.41021 1.15523 0.577615 0.816309i \(-0.303983\pi\)
0.577615 + 0.816309i \(0.303983\pi\)
\(54\) −0.478479 −0.0651127
\(55\) 0.126109 0.0170045
\(56\) 10.9206 1.45933
\(57\) −1.76647 −0.233975
\(58\) 13.0238 1.71011
\(59\) 12.7351 1.65797 0.828987 0.559268i \(-0.188918\pi\)
0.828987 + 0.559268i \(0.188918\pi\)
\(60\) 2.33853 0.301903
\(61\) 4.56498 0.584486 0.292243 0.956344i \(-0.405598\pi\)
0.292243 + 0.956344i \(0.405598\pi\)
\(62\) 4.89874 0.622141
\(63\) −5.40337 −0.680761
\(64\) −2.87528 −0.359410
\(65\) −0.221192 −0.0274354
\(66\) −3.49468 −0.430165
\(67\) −7.92183 −0.967805 −0.483903 0.875122i \(-0.660781\pi\)
−0.483903 + 0.875122i \(0.660781\pi\)
\(68\) −11.8338 −1.43506
\(69\) −22.4828 −2.70661
\(70\) −1.03030 −0.123144
\(71\) −1.61023 −0.191099 −0.0955495 0.995425i \(-0.530461\pi\)
−0.0955495 + 0.995425i \(0.530461\pi\)
\(72\) −17.2554 −2.03357
\(73\) 10.2770 1.20284 0.601418 0.798934i \(-0.294603\pi\)
0.601418 + 0.798934i \(0.294603\pi\)
\(74\) −7.66716 −0.891289
\(75\) 12.0485 1.39124
\(76\) 3.15367 0.361751
\(77\) 1.05431 0.120150
\(78\) 6.12959 0.694039
\(79\) −9.24103 −1.03970 −0.519849 0.854258i \(-0.674012\pi\)
−0.519849 + 0.854258i \(0.674012\pi\)
\(80\) −1.36825 −0.152975
\(81\) −9.22809 −1.02534
\(82\) 27.2875 3.01340
\(83\) 16.4887 1.80987 0.904937 0.425545i \(-0.139918\pi\)
0.904937 + 0.425545i \(0.139918\pi\)
\(84\) 19.5509 2.13318
\(85\) 0.602493 0.0653495
\(86\) −4.93960 −0.532651
\(87\) 12.5826 1.34900
\(88\) 3.36689 0.358912
\(89\) 12.2808 1.30176 0.650879 0.759182i \(-0.274401\pi\)
0.650879 + 0.759182i \(0.274401\pi\)
\(90\) 1.62794 0.171600
\(91\) −1.84924 −0.193853
\(92\) 40.1385 4.18472
\(93\) 4.73279 0.490767
\(94\) 15.1418 1.56176
\(95\) −0.160562 −0.0164733
\(96\) 9.17467 0.936386
\(97\) −8.85175 −0.898759 −0.449380 0.893341i \(-0.648355\pi\)
−0.449380 + 0.893341i \(0.648355\pi\)
\(98\) 9.01819 0.910975
\(99\) −1.66589 −0.167429
\(100\) −21.5101 −2.15101
\(101\) −7.08468 −0.704952 −0.352476 0.935821i \(-0.614660\pi\)
−0.352476 + 0.935821i \(0.614660\pi\)
\(102\) −16.6961 −1.65316
\(103\) −4.57406 −0.450696 −0.225348 0.974278i \(-0.572352\pi\)
−0.225348 + 0.974278i \(0.572352\pi\)
\(104\) −5.90546 −0.579078
\(105\) −0.995392 −0.0971403
\(106\) −21.1839 −2.05756
\(107\) −16.3395 −1.57959 −0.789797 0.613368i \(-0.789814\pi\)
−0.789797 + 0.613368i \(0.789814\pi\)
\(108\) 0.825288 0.0794134
\(109\) 5.94027 0.568975 0.284487 0.958680i \(-0.408177\pi\)
0.284487 + 0.958680i \(0.408177\pi\)
\(110\) −0.317646 −0.0302864
\(111\) −7.40742 −0.703081
\(112\) −11.4391 −1.08089
\(113\) 2.62243 0.246697 0.123349 0.992363i \(-0.460637\pi\)
0.123349 + 0.992363i \(0.460637\pi\)
\(114\) 4.44944 0.416728
\(115\) −2.04356 −0.190563
\(116\) −22.4637 −2.08570
\(117\) 2.92194 0.270133
\(118\) −32.0777 −2.95299
\(119\) 5.03706 0.461746
\(120\) −3.17874 −0.290178
\(121\) −10.6749 −0.970450
\(122\) −11.4984 −1.04102
\(123\) 26.3631 2.37708
\(124\) −8.44942 −0.758780
\(125\) 2.20109 0.196872
\(126\) 13.6102 1.21249
\(127\) 4.62182 0.410120 0.205060 0.978749i \(-0.434261\pi\)
0.205060 + 0.978749i \(0.434261\pi\)
\(128\) 14.7826 1.30661
\(129\) −4.77226 −0.420174
\(130\) 0.557145 0.0488648
\(131\) −11.0299 −0.963691 −0.481845 0.876256i \(-0.660033\pi\)
−0.481845 + 0.876256i \(0.660033\pi\)
\(132\) 6.02767 0.524642
\(133\) −1.34236 −0.116397
\(134\) 19.9538 1.72374
\(135\) −0.0420177 −0.00361631
\(136\) 16.0856 1.37933
\(137\) 2.40317 0.205316 0.102658 0.994717i \(-0.467265\pi\)
0.102658 + 0.994717i \(0.467265\pi\)
\(138\) 56.6305 4.82071
\(139\) −1.55707 −0.132069 −0.0660345 0.997817i \(-0.521035\pi\)
−0.0660345 + 0.997817i \(0.521035\pi\)
\(140\) 1.77707 0.150190
\(141\) 14.6289 1.23197
\(142\) 4.05590 0.340363
\(143\) −0.570132 −0.0476769
\(144\) 18.0746 1.50622
\(145\) 1.14369 0.0949783
\(146\) −25.8862 −2.14235
\(147\) 8.71269 0.718610
\(148\) 13.2244 1.08704
\(149\) 11.1268 0.911541 0.455770 0.890097i \(-0.349364\pi\)
0.455770 + 0.890097i \(0.349364\pi\)
\(150\) −30.3481 −2.47791
\(151\) 8.31701 0.676829 0.338414 0.940997i \(-0.390109\pi\)
0.338414 + 0.940997i \(0.390109\pi\)
\(152\) −4.28675 −0.347701
\(153\) −7.95893 −0.643441
\(154\) −2.65564 −0.213997
\(155\) 0.430183 0.0345532
\(156\) −10.5724 −0.846470
\(157\) −10.5305 −0.840423 −0.420212 0.907426i \(-0.638044\pi\)
−0.420212 + 0.907426i \(0.638044\pi\)
\(158\) 23.2766 1.85179
\(159\) −20.4663 −1.62308
\(160\) 0.833925 0.0659276
\(161\) −17.0849 −1.34648
\(162\) 23.2440 1.82622
\(163\) −4.92927 −0.386090 −0.193045 0.981190i \(-0.561836\pi\)
−0.193045 + 0.981190i \(0.561836\pi\)
\(164\) −47.0659 −3.67523
\(165\) −0.306886 −0.0238910
\(166\) −41.5324 −3.22354
\(167\) −15.5438 −1.20281 −0.601406 0.798944i \(-0.705393\pi\)
−0.601406 + 0.798944i \(0.705393\pi\)
\(168\) −26.5754 −2.05033
\(169\) 1.00000 0.0769231
\(170\) −1.51758 −0.116393
\(171\) 2.12102 0.162199
\(172\) 8.51989 0.649636
\(173\) 15.5327 1.18093 0.590465 0.807063i \(-0.298944\pi\)
0.590465 + 0.807063i \(0.298944\pi\)
\(174\) −31.6936 −2.40268
\(175\) 9.15573 0.692108
\(176\) −3.52674 −0.265838
\(177\) −30.9910 −2.32943
\(178\) −30.9332 −2.31854
\(179\) 7.93161 0.592836 0.296418 0.955058i \(-0.404208\pi\)
0.296418 + 0.955058i \(0.404208\pi\)
\(180\) −2.80790 −0.209289
\(181\) −7.42017 −0.551537 −0.275769 0.961224i \(-0.588932\pi\)
−0.275769 + 0.961224i \(0.588932\pi\)
\(182\) 4.65793 0.345269
\(183\) −11.1089 −0.821194
\(184\) −54.5598 −4.02220
\(185\) −0.673292 −0.0495014
\(186\) −11.9211 −0.874097
\(187\) 1.55296 0.113563
\(188\) −26.1169 −1.90477
\(189\) −0.351283 −0.0255521
\(190\) 0.404429 0.0293404
\(191\) 5.40208 0.390881 0.195440 0.980716i \(-0.437386\pi\)
0.195440 + 0.980716i \(0.437386\pi\)
\(192\) 6.99700 0.504965
\(193\) 19.0924 1.37430 0.687151 0.726515i \(-0.258861\pi\)
0.687151 + 0.726515i \(0.258861\pi\)
\(194\) 22.2961 1.60077
\(195\) 0.538271 0.0385464
\(196\) −15.5547 −1.11105
\(197\) 4.96836 0.353981 0.176990 0.984213i \(-0.443364\pi\)
0.176990 + 0.984213i \(0.443364\pi\)
\(198\) 4.19611 0.298204
\(199\) −12.2242 −0.866553 −0.433276 0.901261i \(-0.642643\pi\)
−0.433276 + 0.901261i \(0.642643\pi\)
\(200\) 29.2384 2.06747
\(201\) 19.2778 1.35975
\(202\) 17.8451 1.25558
\(203\) 9.56166 0.671097
\(204\) 28.7977 2.01624
\(205\) 2.39626 0.167362
\(206\) 11.5213 0.802727
\(207\) 26.9954 1.87631
\(208\) 6.18583 0.428910
\(209\) −0.413857 −0.0286271
\(210\) 2.50723 0.173015
\(211\) 18.0902 1.24538 0.622691 0.782468i \(-0.286039\pi\)
0.622691 + 0.782468i \(0.286039\pi\)
\(212\) 36.5383 2.50946
\(213\) 3.91850 0.268491
\(214\) 41.1564 2.81339
\(215\) −0.433771 −0.0295830
\(216\) −1.12180 −0.0763291
\(217\) 3.59649 0.244145
\(218\) −14.9626 −1.01339
\(219\) −25.0092 −1.68997
\(220\) 0.547881 0.0369381
\(221\) −2.72385 −0.183226
\(222\) 18.6581 1.25225
\(223\) −9.93760 −0.665471 −0.332736 0.943020i \(-0.607972\pi\)
−0.332736 + 0.943020i \(0.607972\pi\)
\(224\) 6.97191 0.465831
\(225\) −14.4667 −0.964449
\(226\) −6.60545 −0.439388
\(227\) −1.44380 −0.0958283 −0.0479142 0.998851i \(-0.515257\pi\)
−0.0479142 + 0.998851i \(0.515257\pi\)
\(228\) −7.67446 −0.508254
\(229\) 3.36100 0.222101 0.111051 0.993815i \(-0.464578\pi\)
0.111051 + 0.993815i \(0.464578\pi\)
\(230\) 5.14739 0.339409
\(231\) −2.56567 −0.168809
\(232\) 30.5347 2.00470
\(233\) 13.8966 0.910400 0.455200 0.890389i \(-0.349568\pi\)
0.455200 + 0.890389i \(0.349568\pi\)
\(234\) −7.35988 −0.481130
\(235\) 1.32968 0.0867389
\(236\) 55.3281 3.60155
\(237\) 22.4881 1.46076
\(238\) −12.6875 −0.822409
\(239\) −8.83495 −0.571485 −0.285743 0.958306i \(-0.592240\pi\)
−0.285743 + 0.958306i \(0.592240\pi\)
\(240\) 3.32965 0.214928
\(241\) 10.5701 0.680883 0.340441 0.940266i \(-0.389424\pi\)
0.340441 + 0.940266i \(0.389424\pi\)
\(242\) 26.8884 1.72845
\(243\) 21.8867 1.40403
\(244\) 19.8327 1.26966
\(245\) 0.791934 0.0505948
\(246\) −66.4043 −4.23378
\(247\) 0.725895 0.0461876
\(248\) 11.4852 0.729311
\(249\) −40.1254 −2.54284
\(250\) −5.54419 −0.350645
\(251\) 10.9621 0.691923 0.345961 0.938249i \(-0.387553\pi\)
0.345961 + 0.938249i \(0.387553\pi\)
\(252\) −23.4751 −1.47879
\(253\) −5.26738 −0.331157
\(254\) −11.6416 −0.730459
\(255\) −1.46617 −0.0918151
\(256\) −31.4845 −1.96778
\(257\) 22.1898 1.38416 0.692080 0.721821i \(-0.256695\pi\)
0.692080 + 0.721821i \(0.256695\pi\)
\(258\) 12.0205 0.748366
\(259\) −5.62896 −0.349767
\(260\) −0.960972 −0.0595969
\(261\) −15.1081 −0.935170
\(262\) 27.7826 1.71641
\(263\) −4.69101 −0.289260 −0.144630 0.989486i \(-0.546199\pi\)
−0.144630 + 0.989486i \(0.546199\pi\)
\(264\) −8.19335 −0.504266
\(265\) −1.86027 −0.114275
\(266\) 3.38117 0.207313
\(267\) −29.8853 −1.82895
\(268\) −34.4165 −2.10233
\(269\) 27.3934 1.67021 0.835104 0.550092i \(-0.185407\pi\)
0.835104 + 0.550092i \(0.185407\pi\)
\(270\) 0.105836 0.00644095
\(271\) −6.28478 −0.381773 −0.190887 0.981612i \(-0.561136\pi\)
−0.190887 + 0.981612i \(0.561136\pi\)
\(272\) −16.8493 −1.02164
\(273\) 4.50014 0.272361
\(274\) −6.05317 −0.365686
\(275\) 2.82277 0.170219
\(276\) −97.6771 −5.87947
\(277\) 16.3770 0.983996 0.491998 0.870596i \(-0.336267\pi\)
0.491998 + 0.870596i \(0.336267\pi\)
\(278\) 3.92200 0.235226
\(279\) −5.68272 −0.340215
\(280\) −2.41555 −0.144357
\(281\) −8.13368 −0.485215 −0.242607 0.970125i \(-0.578003\pi\)
−0.242607 + 0.970125i \(0.578003\pi\)
\(282\) −36.8477 −2.19425
\(283\) 15.6804 0.932104 0.466052 0.884757i \(-0.345676\pi\)
0.466052 + 0.884757i \(0.345676\pi\)
\(284\) −6.99567 −0.415117
\(285\) 0.390728 0.0231447
\(286\) 1.43607 0.0849165
\(287\) 20.0336 1.18254
\(288\) −11.0161 −0.649133
\(289\) −9.58063 −0.563567
\(290\) −2.88077 −0.169164
\(291\) 21.5408 1.26274
\(292\) 44.6488 2.61287
\(293\) 18.8635 1.10202 0.551008 0.834500i \(-0.314243\pi\)
0.551008 + 0.834500i \(0.314243\pi\)
\(294\) −21.9458 −1.27991
\(295\) −2.81691 −0.164007
\(296\) −17.9758 −1.04482
\(297\) −0.108303 −0.00628436
\(298\) −28.0265 −1.62353
\(299\) 9.23887 0.534297
\(300\) 52.3448 3.02213
\(301\) −3.62648 −0.209027
\(302\) −20.9492 −1.20549
\(303\) 17.2406 0.990447
\(304\) 4.49026 0.257534
\(305\) −1.00974 −0.0578173
\(306\) 20.0472 1.14602
\(307\) −22.7774 −1.29997 −0.649987 0.759945i \(-0.725226\pi\)
−0.649987 + 0.759945i \(0.725226\pi\)
\(308\) 4.58048 0.260997
\(309\) 11.1310 0.633220
\(310\) −1.08356 −0.0615421
\(311\) −9.62933 −0.546029 −0.273014 0.962010i \(-0.588021\pi\)
−0.273014 + 0.962010i \(0.588021\pi\)
\(312\) 14.3710 0.813595
\(313\) −30.0545 −1.69878 −0.849391 0.527765i \(-0.823030\pi\)
−0.849391 + 0.527765i \(0.823030\pi\)
\(314\) 26.5245 1.49686
\(315\) 1.19518 0.0673408
\(316\) −40.1479 −2.25849
\(317\) −9.99419 −0.561330 −0.280665 0.959806i \(-0.590555\pi\)
−0.280665 + 0.959806i \(0.590555\pi\)
\(318\) 51.5511 2.89084
\(319\) 2.94792 0.165052
\(320\) 0.635988 0.0355528
\(321\) 39.7621 2.21931
\(322\) 43.0340 2.39819
\(323\) −1.97723 −0.110016
\(324\) −40.0916 −2.22731
\(325\) −4.95107 −0.274636
\(326\) 12.4160 0.687660
\(327\) −14.4557 −0.799400
\(328\) 63.9762 3.53249
\(329\) 11.1166 0.612879
\(330\) 0.772994 0.0425519
\(331\) −1.61217 −0.0886128 −0.0443064 0.999018i \(-0.514108\pi\)
−0.0443064 + 0.999018i \(0.514108\pi\)
\(332\) 71.6357 3.93152
\(333\) 8.89418 0.487398
\(334\) 39.1521 2.14231
\(335\) 1.75224 0.0957352
\(336\) 27.8371 1.51864
\(337\) 26.2381 1.42928 0.714640 0.699493i \(-0.246591\pi\)
0.714640 + 0.699493i \(0.246591\pi\)
\(338\) −2.51883 −0.137006
\(339\) −6.38168 −0.346605
\(340\) 2.61754 0.141956
\(341\) 1.10882 0.0600459
\(342\) −5.34250 −0.288889
\(343\) 19.5655 1.05644
\(344\) −11.5810 −0.624406
\(345\) 4.97301 0.267738
\(346\) −39.1243 −2.10334
\(347\) −9.84301 −0.528401 −0.264200 0.964468i \(-0.585108\pi\)
−0.264200 + 0.964468i \(0.585108\pi\)
\(348\) 54.6656 2.93038
\(349\) 32.5097 1.74020 0.870102 0.492872i \(-0.164053\pi\)
0.870102 + 0.492872i \(0.164053\pi\)
\(350\) −23.0618 −1.23270
\(351\) 0.189961 0.0101393
\(352\) 2.14948 0.114568
\(353\) 35.8101 1.90598 0.952991 0.303000i \(-0.0979882\pi\)
0.952991 + 0.303000i \(0.0979882\pi\)
\(354\) 78.0612 4.14891
\(355\) 0.356169 0.0189035
\(356\) 53.3540 2.82776
\(357\) −12.2577 −0.648746
\(358\) −19.9784 −1.05589
\(359\) 12.8975 0.680706 0.340353 0.940298i \(-0.389453\pi\)
0.340353 + 0.940298i \(0.389453\pi\)
\(360\) 3.81675 0.201160
\(361\) −18.4731 −0.972267
\(362\) 18.6902 0.982334
\(363\) 25.9775 1.36347
\(364\) −8.03407 −0.421100
\(365\) −2.27319 −0.118984
\(366\) 27.9815 1.46262
\(367\) 28.5603 1.49084 0.745419 0.666596i \(-0.232249\pi\)
0.745419 + 0.666596i \(0.232249\pi\)
\(368\) 57.1500 2.97915
\(369\) −31.6545 −1.64787
\(370\) 1.69591 0.0881662
\(371\) −15.5525 −0.807446
\(372\) 20.5617 1.06607
\(373\) 0.246560 0.0127664 0.00638318 0.999980i \(-0.497968\pi\)
0.00638318 + 0.999980i \(0.497968\pi\)
\(374\) −3.91164 −0.202266
\(375\) −5.35637 −0.276602
\(376\) 35.5004 1.83079
\(377\) −5.17059 −0.266299
\(378\) 0.884823 0.0455104
\(379\) −10.8613 −0.557905 −0.278953 0.960305i \(-0.589987\pi\)
−0.278953 + 0.960305i \(0.589987\pi\)
\(380\) −0.697565 −0.0357843
\(381\) −11.2472 −0.576212
\(382\) −13.6069 −0.696192
\(383\) 22.8063 1.16535 0.582674 0.812706i \(-0.302006\pi\)
0.582674 + 0.812706i \(0.302006\pi\)
\(384\) −35.9736 −1.83577
\(385\) −0.233205 −0.0118852
\(386\) −48.0906 −2.44775
\(387\) 5.73012 0.291278
\(388\) −38.4566 −1.95234
\(389\) −17.0529 −0.864618 −0.432309 0.901726i \(-0.642301\pi\)
−0.432309 + 0.901726i \(0.642301\pi\)
\(390\) −1.35581 −0.0686543
\(391\) −25.1653 −1.27266
\(392\) 21.1434 1.06790
\(393\) 26.8414 1.35397
\(394\) −12.5145 −0.630470
\(395\) 2.04404 0.102847
\(396\) −7.23751 −0.363698
\(397\) 26.8577 1.34795 0.673975 0.738754i \(-0.264585\pi\)
0.673975 + 0.738754i \(0.264585\pi\)
\(398\) 30.7908 1.54340
\(399\) 3.26663 0.163536
\(400\) −30.6265 −1.53132
\(401\) 23.9948 1.19824 0.599122 0.800658i \(-0.295516\pi\)
0.599122 + 0.800658i \(0.295516\pi\)
\(402\) −48.5575 −2.42183
\(403\) −1.94484 −0.0968796
\(404\) −30.7796 −1.53134
\(405\) 2.04118 0.101427
\(406\) −24.0842 −1.19528
\(407\) −1.73544 −0.0860228
\(408\) −39.1444 −1.93793
\(409\) 3.97701 0.196650 0.0983251 0.995154i \(-0.468651\pi\)
0.0983251 + 0.995154i \(0.468651\pi\)
\(410\) −6.03577 −0.298085
\(411\) −5.84811 −0.288466
\(412\) −19.8721 −0.979028
\(413\) −23.5504 −1.15884
\(414\) −67.9969 −3.34187
\(415\) −3.64717 −0.179033
\(416\) −3.77015 −0.184847
\(417\) 3.78914 0.185555
\(418\) 1.04244 0.0509872
\(419\) −7.30573 −0.356908 −0.178454 0.983948i \(-0.557110\pi\)
−0.178454 + 0.983948i \(0.557110\pi\)
\(420\) −4.32450 −0.211014
\(421\) −17.6314 −0.859301 −0.429650 0.902995i \(-0.641363\pi\)
−0.429650 + 0.902995i \(0.641363\pi\)
\(422\) −45.5663 −2.21813
\(423\) −17.5651 −0.854044
\(424\) −49.6661 −2.41200
\(425\) 13.4860 0.654167
\(426\) −9.87004 −0.478205
\(427\) −8.44176 −0.408525
\(428\) −70.9871 −3.43129
\(429\) 1.38742 0.0669852
\(430\) 1.09260 0.0526897
\(431\) −10.8027 −0.520348 −0.260174 0.965562i \(-0.583780\pi\)
−0.260174 + 0.965562i \(0.583780\pi\)
\(432\) 1.17506 0.0565353
\(433\) 0.408217 0.0196177 0.00980883 0.999952i \(-0.496878\pi\)
0.00980883 + 0.999952i \(0.496878\pi\)
\(434\) −9.05895 −0.434844
\(435\) −2.78317 −0.133443
\(436\) 25.8076 1.23596
\(437\) 6.70645 0.320813
\(438\) 62.9940 3.00997
\(439\) −19.1821 −0.915510 −0.457755 0.889078i \(-0.651346\pi\)
−0.457755 + 0.889078i \(0.651346\pi\)
\(440\) −0.744729 −0.0355036
\(441\) −10.4614 −0.498164
\(442\) 6.86093 0.326341
\(443\) 15.8699 0.754001 0.377001 0.926213i \(-0.376955\pi\)
0.377001 + 0.926213i \(0.376955\pi\)
\(444\) −32.1817 −1.52728
\(445\) −2.71640 −0.128770
\(446\) 25.0312 1.18526
\(447\) −27.0770 −1.28070
\(448\) 5.31709 0.251209
\(449\) −26.3949 −1.24565 −0.622825 0.782361i \(-0.714015\pi\)
−0.622825 + 0.782361i \(0.714015\pi\)
\(450\) 36.4393 1.71777
\(451\) 6.17647 0.290839
\(452\) 11.3932 0.535890
\(453\) −20.2395 −0.950934
\(454\) 3.63669 0.170678
\(455\) 0.409037 0.0191759
\(456\) 10.4318 0.488514
\(457\) 4.92449 0.230358 0.115179 0.993345i \(-0.463256\pi\)
0.115179 + 0.993345i \(0.463256\pi\)
\(458\) −8.46580 −0.395581
\(459\) −0.517424 −0.0241513
\(460\) −8.87829 −0.413952
\(461\) 34.8301 1.62220 0.811101 0.584907i \(-0.198869\pi\)
0.811101 + 0.584907i \(0.198869\pi\)
\(462\) 6.46250 0.300663
\(463\) −0.487675 −0.0226642 −0.0113321 0.999936i \(-0.503607\pi\)
−0.0113321 + 0.999936i \(0.503607\pi\)
\(464\) −31.9844 −1.48484
\(465\) −1.04685 −0.0485466
\(466\) −35.0033 −1.62150
\(467\) −37.9178 −1.75463 −0.877313 0.479918i \(-0.840666\pi\)
−0.877313 + 0.479918i \(0.840666\pi\)
\(468\) 12.6944 0.586800
\(469\) 14.6494 0.676445
\(470\) −3.34925 −0.154489
\(471\) 25.6259 1.18078
\(472\) −75.2069 −3.46168
\(473\) −1.11807 −0.0514088
\(474\) −56.6438 −2.60173
\(475\) −3.59396 −0.164902
\(476\) 21.8836 1.00303
\(477\) 24.5741 1.12517
\(478\) 22.2538 1.01786
\(479\) −11.6961 −0.534406 −0.267203 0.963640i \(-0.586099\pi\)
−0.267203 + 0.963640i \(0.586099\pi\)
\(480\) −2.02936 −0.0926272
\(481\) 3.04393 0.138791
\(482\) −26.6244 −1.21271
\(483\) 41.5762 1.89178
\(484\) −46.3776 −2.10807
\(485\) 1.95793 0.0889051
\(486\) −55.1290 −2.50070
\(487\) −14.6131 −0.662182 −0.331091 0.943599i \(-0.607417\pi\)
−0.331091 + 0.943599i \(0.607417\pi\)
\(488\) −26.9583 −1.22035
\(489\) 11.9954 0.542451
\(490\) −1.99475 −0.0901136
\(491\) −4.38216 −0.197764 −0.0988821 0.995099i \(-0.531527\pi\)
−0.0988821 + 0.995099i \(0.531527\pi\)
\(492\) 114.535 5.16364
\(493\) 14.0839 0.634307
\(494\) −1.82841 −0.0822640
\(495\) 0.368481 0.0165620
\(496\) −12.0305 −0.540184
\(497\) 2.97770 0.133568
\(498\) 101.069 4.52902
\(499\) 8.36464 0.374453 0.187226 0.982317i \(-0.440050\pi\)
0.187226 + 0.982317i \(0.440050\pi\)
\(500\) 9.56270 0.427657
\(501\) 37.8258 1.68993
\(502\) −27.6117 −1.23237
\(503\) 30.5505 1.36218 0.681089 0.732201i \(-0.261507\pi\)
0.681089 + 0.732201i \(0.261507\pi\)
\(504\) 31.9094 1.42136
\(505\) 1.56707 0.0697338
\(506\) 13.2676 0.589819
\(507\) −2.43350 −0.108076
\(508\) 20.0796 0.890888
\(509\) 0.301504 0.0133639 0.00668196 0.999978i \(-0.497873\pi\)
0.00668196 + 0.999978i \(0.497873\pi\)
\(510\) 3.69304 0.163530
\(511\) −19.0047 −0.840720
\(512\) 49.7388 2.19817
\(513\) 0.137891 0.00608806
\(514\) −55.8923 −2.46530
\(515\) 1.01174 0.0445828
\(516\) −20.7332 −0.912728
\(517\) 3.42732 0.150734
\(518\) 14.1784 0.622964
\(519\) −37.7989 −1.65919
\(520\) 1.30624 0.0572823
\(521\) −23.4929 −1.02924 −0.514621 0.857418i \(-0.672067\pi\)
−0.514621 + 0.857418i \(0.672067\pi\)
\(522\) 38.0549 1.66562
\(523\) 19.8954 0.869965 0.434983 0.900439i \(-0.356754\pi\)
0.434983 + 0.900439i \(0.356754\pi\)
\(524\) −47.9198 −2.09339
\(525\) −22.2805 −0.972401
\(526\) 11.8159 0.515197
\(527\) 5.29747 0.230761
\(528\) 8.58234 0.373498
\(529\) 62.3567 2.71116
\(530\) 4.68570 0.203534
\(531\) 37.2113 1.61483
\(532\) −5.83189 −0.252845
\(533\) −10.8334 −0.469246
\(534\) 75.2760 3.25751
\(535\) 3.61415 0.156253
\(536\) 46.7820 2.02068
\(537\) −19.3016 −0.832925
\(538\) −68.9995 −2.97478
\(539\) 2.04125 0.0879228
\(540\) −0.182547 −0.00785556
\(541\) −7.50470 −0.322652 −0.161326 0.986901i \(-0.551577\pi\)
−0.161326 + 0.986901i \(0.551577\pi\)
\(542\) 15.8303 0.679970
\(543\) 18.0570 0.774901
\(544\) 10.2693 0.440294
\(545\) −1.31394 −0.0562829
\(546\) −11.3351 −0.485097
\(547\) 19.3190 0.826020 0.413010 0.910727i \(-0.364478\pi\)
0.413010 + 0.910727i \(0.364478\pi\)
\(548\) 10.4406 0.446001
\(549\) 13.3386 0.569278
\(550\) −7.11008 −0.303175
\(551\) −3.75331 −0.159896
\(552\) 132.771 5.65112
\(553\) 17.0889 0.726694
\(554\) −41.2508 −1.75258
\(555\) 1.63846 0.0695487
\(556\) −6.76473 −0.286889
\(557\) 22.6330 0.958992 0.479496 0.877544i \(-0.340819\pi\)
0.479496 + 0.877544i \(0.340819\pi\)
\(558\) 14.3138 0.605952
\(559\) 1.96107 0.0829443
\(560\) 2.53023 0.106922
\(561\) −3.77912 −0.159555
\(562\) 20.4874 0.864208
\(563\) −10.2983 −0.434020 −0.217010 0.976169i \(-0.569630\pi\)
−0.217010 + 0.976169i \(0.569630\pi\)
\(564\) 63.5555 2.67617
\(565\) −0.580059 −0.0244033
\(566\) −39.4964 −1.66016
\(567\) 17.0650 0.716661
\(568\) 9.50914 0.398995
\(569\) −5.28019 −0.221357 −0.110678 0.993856i \(-0.535302\pi\)
−0.110678 + 0.993856i \(0.535302\pi\)
\(570\) −0.984179 −0.0412227
\(571\) −19.4225 −0.812808 −0.406404 0.913694i \(-0.633217\pi\)
−0.406404 + 0.913694i \(0.633217\pi\)
\(572\) −2.47695 −0.103567
\(573\) −13.1460 −0.549181
\(574\) −50.4612 −2.10621
\(575\) −45.7423 −1.90759
\(576\) −8.40139 −0.350058
\(577\) −32.0820 −1.33559 −0.667796 0.744344i \(-0.732762\pi\)
−0.667796 + 0.744344i \(0.732762\pi\)
\(578\) 24.1320 1.00376
\(579\) −46.4614 −1.93087
\(580\) 4.96879 0.206318
\(581\) −30.4917 −1.26501
\(582\) −54.2576 −2.24905
\(583\) −4.79493 −0.198586
\(584\) −60.6907 −2.51140
\(585\) −0.646308 −0.0267216
\(586\) −47.5139 −1.96278
\(587\) 10.4229 0.430198 0.215099 0.976592i \(-0.430993\pi\)
0.215099 + 0.976592i \(0.430993\pi\)
\(588\) 37.8525 1.56101
\(589\) −1.41175 −0.0581703
\(590\) 7.09532 0.292110
\(591\) −12.0905 −0.497338
\(592\) 18.8292 0.773877
\(593\) 36.0999 1.48244 0.741222 0.671260i \(-0.234247\pi\)
0.741222 + 0.671260i \(0.234247\pi\)
\(594\) 0.272796 0.0111930
\(595\) −1.11416 −0.0456759
\(596\) 48.3405 1.98010
\(597\) 29.7477 1.21749
\(598\) −23.2712 −0.951629
\(599\) 37.9352 1.54999 0.774996 0.631966i \(-0.217752\pi\)
0.774996 + 0.631966i \(0.217752\pi\)
\(600\) −71.1517 −2.90476
\(601\) −24.4848 −0.998755 −0.499377 0.866385i \(-0.666438\pi\)
−0.499377 + 0.866385i \(0.666438\pi\)
\(602\) 9.13451 0.372295
\(603\) −23.1471 −0.942623
\(604\) 36.1334 1.47025
\(605\) 2.36121 0.0959968
\(606\) −43.4262 −1.76407
\(607\) −33.6918 −1.36751 −0.683753 0.729713i \(-0.739654\pi\)
−0.683753 + 0.729713i \(0.739654\pi\)
\(608\) −2.73673 −0.110989
\(609\) −23.2683 −0.942881
\(610\) 2.54336 0.102977
\(611\) −6.01145 −0.243197
\(612\) −34.5777 −1.39772
\(613\) 0.00186567 7.53535e−5 0 3.76768e−5 1.00000i \(-0.499988\pi\)
3.76768e−5 1.00000i \(0.499988\pi\)
\(614\) 57.3724 2.31536
\(615\) −5.83130 −0.235141
\(616\) −6.22620 −0.250861
\(617\) 1.00000 0.0402585
\(618\) −28.0371 −1.12782
\(619\) −39.5169 −1.58832 −0.794158 0.607711i \(-0.792088\pi\)
−0.794158 + 0.607711i \(0.792088\pi\)
\(620\) 1.86894 0.0750585
\(621\) 1.75502 0.0704265
\(622\) 24.2547 0.972524
\(623\) −22.7101 −0.909861
\(624\) −15.0532 −0.602612
\(625\) 24.2685 0.970740
\(626\) 75.7023 3.02567
\(627\) 1.00712 0.0402206
\(628\) −45.7499 −1.82562
\(629\) −8.29122 −0.330592
\(630\) −3.01046 −0.119940
\(631\) 5.96338 0.237398 0.118699 0.992930i \(-0.462128\pi\)
0.118699 + 0.992930i \(0.462128\pi\)
\(632\) 54.5726 2.17078
\(633\) −44.0226 −1.74974
\(634\) 25.1737 0.999775
\(635\) −1.02231 −0.0405691
\(636\) −88.9161 −3.52575
\(637\) −3.58031 −0.141857
\(638\) −7.42532 −0.293971
\(639\) −4.70499 −0.186126
\(640\) −3.26980 −0.129250
\(641\) −3.04033 −0.120086 −0.0600428 0.998196i \(-0.519124\pi\)
−0.0600428 + 0.998196i \(0.519124\pi\)
\(642\) −100.154 −3.95277
\(643\) −34.8329 −1.37368 −0.686838 0.726811i \(-0.741002\pi\)
−0.686838 + 0.726811i \(0.741002\pi\)
\(644\) −74.2257 −2.92490
\(645\) 1.05558 0.0415636
\(646\) 4.98032 0.195948
\(647\) −2.21360 −0.0870256 −0.0435128 0.999053i \(-0.513855\pi\)
−0.0435128 + 0.999053i \(0.513855\pi\)
\(648\) 54.4961 2.14081
\(649\) −7.26072 −0.285008
\(650\) 12.4709 0.489150
\(651\) −8.75206 −0.343020
\(652\) −21.4153 −0.838689
\(653\) −28.7597 −1.12545 −0.562726 0.826643i \(-0.690247\pi\)
−0.562726 + 0.826643i \(0.690247\pi\)
\(654\) 36.4114 1.42380
\(655\) 2.43973 0.0953282
\(656\) −67.0135 −2.61644
\(657\) 30.0289 1.17154
\(658\) −28.0009 −1.09159
\(659\) 21.6371 0.842864 0.421432 0.906860i \(-0.361528\pi\)
0.421432 + 0.906860i \(0.361528\pi\)
\(660\) −1.33327 −0.0518975
\(661\) 13.0069 0.505909 0.252955 0.967478i \(-0.418598\pi\)
0.252955 + 0.967478i \(0.418598\pi\)
\(662\) 4.06078 0.157827
\(663\) 6.62850 0.257430
\(664\) −97.3736 −3.77883
\(665\) 0.296918 0.0115140
\(666\) −22.4030 −0.868097
\(667\) −47.7704 −1.84968
\(668\) −67.5302 −2.61282
\(669\) 24.1832 0.934976
\(670\) −4.41360 −0.170512
\(671\) −2.60264 −0.100474
\(672\) −16.9662 −0.654485
\(673\) −17.9639 −0.692456 −0.346228 0.938150i \(-0.612538\pi\)
−0.346228 + 0.938150i \(0.612538\pi\)
\(674\) −66.0893 −2.54567
\(675\) −0.940509 −0.0362002
\(676\) 4.34452 0.167097
\(677\) −0.826149 −0.0317515 −0.0158757 0.999874i \(-0.505054\pi\)
−0.0158757 + 0.999874i \(0.505054\pi\)
\(678\) 16.0744 0.617334
\(679\) 16.3690 0.628185
\(680\) −3.55800 −0.136443
\(681\) 3.51349 0.134637
\(682\) −2.79293 −0.106947
\(683\) 21.0033 0.803670 0.401835 0.915712i \(-0.368373\pi\)
0.401835 + 0.915712i \(0.368373\pi\)
\(684\) 9.21483 0.352338
\(685\) −0.531560 −0.0203099
\(686\) −49.2823 −1.88161
\(687\) −8.17900 −0.312048
\(688\) 12.1308 0.462483
\(689\) 8.41021 0.320403
\(690\) −12.5262 −0.476864
\(691\) −23.2297 −0.883699 −0.441850 0.897089i \(-0.645678\pi\)
−0.441850 + 0.897089i \(0.645678\pi\)
\(692\) 67.4822 2.56529
\(693\) 3.08064 0.117024
\(694\) 24.7929 0.941126
\(695\) 0.344411 0.0130643
\(696\) −74.3063 −2.81657
\(697\) 29.5086 1.11772
\(698\) −81.8865 −3.09945
\(699\) −33.8175 −1.27910
\(700\) 39.7773 1.50344
\(701\) −21.3033 −0.804613 −0.402307 0.915505i \(-0.631791\pi\)
−0.402307 + 0.915505i \(0.631791\pi\)
\(702\) −0.478479 −0.0180590
\(703\) 2.20958 0.0833357
\(704\) 1.63929 0.0617831
\(705\) −3.23579 −0.121867
\(706\) −90.1998 −3.39471
\(707\) 13.1013 0.492725
\(708\) −134.641 −5.06012
\(709\) −35.1976 −1.32188 −0.660938 0.750441i \(-0.729841\pi\)
−0.660938 + 0.750441i \(0.729841\pi\)
\(710\) −0.897130 −0.0336687
\(711\) −27.0017 −1.01264
\(712\) −72.5235 −2.71793
\(713\) −17.9682 −0.672913
\(714\) 30.8751 1.15547
\(715\) 0.126109 0.00471619
\(716\) 34.4590 1.28779
\(717\) 21.4999 0.802928
\(718\) −32.4867 −1.21239
\(719\) −8.73898 −0.325909 −0.162954 0.986634i \(-0.552102\pi\)
−0.162954 + 0.986634i \(0.552102\pi\)
\(720\) −3.99795 −0.148995
\(721\) 8.45854 0.315013
\(722\) 46.5306 1.73169
\(723\) −25.7225 −0.956629
\(724\) −32.2371 −1.19808
\(725\) 25.6000 0.950759
\(726\) −65.4331 −2.42845
\(727\) 8.74126 0.324195 0.162098 0.986775i \(-0.448174\pi\)
0.162098 + 0.986775i \(0.448174\pi\)
\(728\) 10.9206 0.404745
\(729\) −25.5771 −0.947300
\(730\) 5.72580 0.211921
\(731\) −5.34165 −0.197568
\(732\) −48.2629 −1.78385
\(733\) −24.1822 −0.893189 −0.446594 0.894736i \(-0.647363\pi\)
−0.446594 + 0.894736i \(0.647363\pi\)
\(734\) −71.9388 −2.65531
\(735\) −1.92717 −0.0710849
\(736\) −34.8319 −1.28392
\(737\) 4.51649 0.166367
\(738\) 79.7325 2.93499
\(739\) −52.8767 −1.94510 −0.972550 0.232695i \(-0.925246\pi\)
−0.972550 + 0.232695i \(0.925246\pi\)
\(740\) −2.92513 −0.107530
\(741\) −1.76647 −0.0648929
\(742\) 39.1742 1.43813
\(743\) 42.1241 1.54538 0.772691 0.634782i \(-0.218910\pi\)
0.772691 + 0.634782i \(0.218910\pi\)
\(744\) −27.9493 −1.02467
\(745\) −2.46115 −0.0901695
\(746\) −0.621042 −0.0227380
\(747\) 48.1791 1.76278
\(748\) 6.74685 0.246689
\(749\) 30.2156 1.10405
\(750\) 13.4918 0.492651
\(751\) −18.7486 −0.684145 −0.342073 0.939673i \(-0.611129\pi\)
−0.342073 + 0.939673i \(0.611129\pi\)
\(752\) −37.1858 −1.35603
\(753\) −26.6764 −0.972140
\(754\) 13.0238 0.474300
\(755\) −1.83965 −0.0669518
\(756\) −1.52616 −0.0555058
\(757\) −30.3567 −1.10333 −0.551667 0.834065i \(-0.686008\pi\)
−0.551667 + 0.834065i \(0.686008\pi\)
\(758\) 27.3577 0.993676
\(759\) 12.8182 0.465271
\(760\) 0.948192 0.0343946
\(761\) 50.4071 1.82726 0.913629 0.406550i \(-0.133268\pi\)
0.913629 + 0.406550i \(0.133268\pi\)
\(762\) 28.3299 1.02628
\(763\) −10.9850 −0.397683
\(764\) 23.4695 0.849095
\(765\) 1.76045 0.0636491
\(766\) −57.4453 −2.07558
\(767\) 12.7351 0.459839
\(768\) 76.6176 2.76470
\(769\) 36.5832 1.31922 0.659611 0.751607i \(-0.270721\pi\)
0.659611 + 0.751607i \(0.270721\pi\)
\(770\) 0.587405 0.0211686
\(771\) −53.9989 −1.94472
\(772\) 82.9474 2.98534
\(773\) −27.5777 −0.991902 −0.495951 0.868350i \(-0.665181\pi\)
−0.495951 + 0.868350i \(0.665181\pi\)
\(774\) −14.4332 −0.518791
\(775\) 9.62907 0.345886
\(776\) 52.2737 1.87652
\(777\) 13.6981 0.491417
\(778\) 42.9535 1.53996
\(779\) −7.86391 −0.281754
\(780\) 2.33853 0.0837327
\(781\) 0.918043 0.0328502
\(782\) 63.3872 2.26672
\(783\) −0.982207 −0.0351012
\(784\) −22.1472 −0.790970
\(785\) 2.32925 0.0831346
\(786\) −67.6090 −2.41153
\(787\) 13.9134 0.495961 0.247980 0.968765i \(-0.420233\pi\)
0.247980 + 0.968765i \(0.420233\pi\)
\(788\) 21.5851 0.768939
\(789\) 11.4156 0.406406
\(790\) −5.14859 −0.183179
\(791\) −4.84950 −0.172428
\(792\) 9.83786 0.349573
\(793\) 4.56498 0.162107
\(794\) −67.6501 −2.40081
\(795\) 4.52697 0.160555
\(796\) −53.1084 −1.88238
\(797\) −24.5998 −0.871369 −0.435685 0.900099i \(-0.643494\pi\)
−0.435685 + 0.900099i \(0.643494\pi\)
\(798\) −8.22809 −0.291271
\(799\) 16.3743 0.579281
\(800\) 18.6663 0.659953
\(801\) 35.8836 1.26789
\(802\) −60.4390 −2.13417
\(803\) −5.85927 −0.206769
\(804\) 83.7528 2.95373
\(805\) 3.77904 0.133193
\(806\) 4.89874 0.172551
\(807\) −66.6620 −2.34661
\(808\) 41.8383 1.47187
\(809\) −8.80674 −0.309629 −0.154814 0.987944i \(-0.549478\pi\)
−0.154814 + 0.987944i \(0.549478\pi\)
\(810\) −5.14138 −0.180650
\(811\) −48.2903 −1.69570 −0.847851 0.530235i \(-0.822104\pi\)
−0.847851 + 0.530235i \(0.822104\pi\)
\(812\) 41.5409 1.45780
\(813\) 15.2940 0.536385
\(814\) 4.37129 0.153214
\(815\) 1.09031 0.0381920
\(816\) 41.0028 1.43538
\(817\) 1.42353 0.0498030
\(818\) −10.0174 −0.350251
\(819\) −5.40337 −0.188809
\(820\) 10.4106 0.363553
\(821\) −8.02008 −0.279903 −0.139951 0.990158i \(-0.544695\pi\)
−0.139951 + 0.990158i \(0.544695\pi\)
\(822\) 14.7304 0.513782
\(823\) −46.9705 −1.63729 −0.818644 0.574302i \(-0.805274\pi\)
−0.818644 + 0.574302i \(0.805274\pi\)
\(824\) 27.0119 0.941005
\(825\) −6.86922 −0.239155
\(826\) 59.3194 2.06399
\(827\) −45.7058 −1.58935 −0.794674 0.607037i \(-0.792358\pi\)
−0.794674 + 0.607037i \(0.792358\pi\)
\(828\) 117.282 4.07584
\(829\) −34.2326 −1.18895 −0.594474 0.804115i \(-0.702640\pi\)
−0.594474 + 0.804115i \(0.702640\pi\)
\(830\) 9.18662 0.318872
\(831\) −39.8534 −1.38250
\(832\) −2.87528 −0.0996824
\(833\) 9.75222 0.337894
\(834\) −9.54421 −0.330489
\(835\) 3.43815 0.118982
\(836\) −1.79801 −0.0621854
\(837\) −0.369444 −0.0127698
\(838\) 18.4019 0.635684
\(839\) 12.2617 0.423322 0.211661 0.977343i \(-0.432113\pi\)
0.211661 + 0.977343i \(0.432113\pi\)
\(840\) 5.87825 0.202819
\(841\) −2.26504 −0.0781047
\(842\) 44.4105 1.53049
\(843\) 19.7933 0.681719
\(844\) 78.5934 2.70530
\(845\) −0.221192 −0.00760922
\(846\) 44.2436 1.52112
\(847\) 19.7406 0.678294
\(848\) 52.0241 1.78651
\(849\) −38.1584 −1.30959
\(850\) −33.9690 −1.16513
\(851\) 28.1225 0.964026
\(852\) 17.0240 0.583232
\(853\) 33.6911 1.15356 0.576781 0.816899i \(-0.304309\pi\)
0.576781 + 0.816899i \(0.304309\pi\)
\(854\) 21.2634 0.727618
\(855\) −0.469152 −0.0160447
\(856\) 96.4920 3.29803
\(857\) 0.603596 0.0206184 0.0103092 0.999947i \(-0.496718\pi\)
0.0103092 + 0.999947i \(0.496718\pi\)
\(858\) −3.49468 −0.119306
\(859\) 1.05988 0.0361626 0.0180813 0.999837i \(-0.494244\pi\)
0.0180813 + 0.999837i \(0.494244\pi\)
\(860\) −1.88453 −0.0642619
\(861\) −48.7517 −1.66145
\(862\) 27.2102 0.926783
\(863\) −26.6849 −0.908363 −0.454181 0.890909i \(-0.650068\pi\)
−0.454181 + 0.890909i \(0.650068\pi\)
\(864\) −0.716179 −0.0243649
\(865\) −3.43570 −0.116817
\(866\) −1.02823 −0.0349407
\(867\) 23.3145 0.791802
\(868\) 15.6250 0.530348
\(869\) 5.26861 0.178725
\(870\) 7.01035 0.237673
\(871\) −7.92183 −0.268421
\(872\) −35.0800 −1.18796
\(873\) −25.8643 −0.875373
\(874\) −16.8924 −0.571395
\(875\) −4.07035 −0.137603
\(876\) −108.653 −3.67105
\(877\) −50.2110 −1.69550 −0.847752 0.530393i \(-0.822044\pi\)
−0.847752 + 0.530393i \(0.822044\pi\)
\(878\) 48.3164 1.63060
\(879\) −45.9043 −1.54831
\(880\) 0.780086 0.0262967
\(881\) −41.5979 −1.40147 −0.700735 0.713422i \(-0.747144\pi\)
−0.700735 + 0.713422i \(0.747144\pi\)
\(882\) 26.3506 0.887272
\(883\) −38.4833 −1.29507 −0.647533 0.762037i \(-0.724199\pi\)
−0.647533 + 0.762037i \(0.724199\pi\)
\(884\) −11.8338 −0.398015
\(885\) 6.85495 0.230427
\(886\) −39.9736 −1.34294
\(887\) −9.38989 −0.315282 −0.157641 0.987497i \(-0.550389\pi\)
−0.157641 + 0.987497i \(0.550389\pi\)
\(888\) 43.7442 1.46796
\(889\) −8.54686 −0.286653
\(890\) 6.84216 0.229350
\(891\) 5.26123 0.176258
\(892\) −43.1741 −1.44558
\(893\) −4.36369 −0.146025
\(894\) 68.2026 2.28103
\(895\) −1.75440 −0.0586433
\(896\) −27.3367 −0.913254
\(897\) −22.4828 −0.750679
\(898\) 66.4843 2.21861
\(899\) 10.0560 0.335386
\(900\) −62.8511 −2.09504
\(901\) −22.9082 −0.763181
\(902\) −15.5575 −0.518008
\(903\) 8.82506 0.293680
\(904\) −15.4866 −0.515078
\(905\) 1.64128 0.0545580
\(906\) 50.9799 1.69369
\(907\) 37.4461 1.24338 0.621688 0.783265i \(-0.286447\pi\)
0.621688 + 0.783265i \(0.286447\pi\)
\(908\) −6.27262 −0.208164
\(909\) −20.7010 −0.686610
\(910\) −1.03030 −0.0341540
\(911\) −12.3835 −0.410283 −0.205142 0.978732i \(-0.565765\pi\)
−0.205142 + 0.978732i \(0.565765\pi\)
\(912\) −10.9271 −0.361832
\(913\) −9.40077 −0.311120
\(914\) −12.4040 −0.410287
\(915\) 2.45720 0.0812324
\(916\) 14.6019 0.482461
\(917\) 20.3970 0.673569
\(918\) 1.30331 0.0430155
\(919\) −48.5944 −1.60298 −0.801491 0.598007i \(-0.795960\pi\)
−0.801491 + 0.598007i \(0.795960\pi\)
\(920\) 12.0682 0.397875
\(921\) 55.4288 1.82644
\(922\) −87.7313 −2.88928
\(923\) −1.61023 −0.0530013
\(924\) −11.1466 −0.366697
\(925\) −15.0707 −0.495523
\(926\) 1.22837 0.0403668
\(927\) −13.3651 −0.438968
\(928\) 19.4939 0.639918
\(929\) −23.5622 −0.773051 −0.386526 0.922279i \(-0.626325\pi\)
−0.386526 + 0.922279i \(0.626325\pi\)
\(930\) 2.63685 0.0864656
\(931\) −2.59893 −0.0851764
\(932\) 60.3743 1.97763
\(933\) 23.4330 0.767162
\(934\) 95.5086 3.12514
\(935\) −0.343501 −0.0112337
\(936\) −17.2554 −0.564010
\(937\) 29.6586 0.968904 0.484452 0.874818i \(-0.339019\pi\)
0.484452 + 0.874818i \(0.339019\pi\)
\(938\) −36.8993 −1.20481
\(939\) 73.1378 2.38676
\(940\) 5.77684 0.188420
\(941\) 0.179871 0.00586362 0.00293181 0.999996i \(-0.499067\pi\)
0.00293181 + 0.999996i \(0.499067\pi\)
\(942\) −64.5475 −2.10307
\(943\) −100.088 −3.25932
\(944\) 78.7774 2.56399
\(945\) 0.0777008 0.00252761
\(946\) 2.81623 0.0915634
\(947\) −55.6536 −1.80850 −0.904250 0.427003i \(-0.859569\pi\)
−0.904250 + 0.427003i \(0.859569\pi\)
\(948\) 97.7000 3.17315
\(949\) 10.2770 0.333607
\(950\) 9.05259 0.293705
\(951\) 24.3209 0.788659
\(952\) −29.7462 −0.964078
\(953\) −44.7982 −1.45116 −0.725578 0.688140i \(-0.758427\pi\)
−0.725578 + 0.688140i \(0.758427\pi\)
\(954\) −61.8981 −2.00402
\(955\) −1.19490 −0.0386659
\(956\) −38.3836 −1.24142
\(957\) −7.17377 −0.231895
\(958\) 29.4604 0.951823
\(959\) −4.44403 −0.143505
\(960\) −1.54768 −0.0499511
\(961\) −27.2176 −0.877986
\(962\) −7.66716 −0.247199
\(963\) −47.7429 −1.53849
\(964\) 45.9222 1.47905
\(965\) −4.22308 −0.135946
\(966\) −104.723 −3.36942
\(967\) −21.1099 −0.678850 −0.339425 0.940633i \(-0.610232\pi\)
−0.339425 + 0.940633i \(0.610232\pi\)
\(968\) 63.0405 2.02620
\(969\) 4.81160 0.154571
\(970\) −4.93171 −0.158348
\(971\) −24.4654 −0.785134 −0.392567 0.919724i \(-0.628413\pi\)
−0.392567 + 0.919724i \(0.628413\pi\)
\(972\) 95.0873 3.04993
\(973\) 2.87940 0.0923094
\(974\) 36.8079 1.17940
\(975\) 12.0485 0.385859
\(976\) 28.2382 0.903883
\(977\) 5.96340 0.190786 0.0953930 0.995440i \(-0.469589\pi\)
0.0953930 + 0.995440i \(0.469589\pi\)
\(978\) −30.2144 −0.966151
\(979\) −7.00166 −0.223774
\(980\) 3.44057 0.109905
\(981\) 17.3571 0.554170
\(982\) 11.0379 0.352235
\(983\) −51.6942 −1.64879 −0.824395 0.566016i \(-0.808484\pi\)
−0.824395 + 0.566016i \(0.808484\pi\)
\(984\) −155.686 −4.96310
\(985\) −1.09896 −0.0350158
\(986\) −35.4750 −1.12975
\(987\) −27.0523 −0.861086
\(988\) 3.15367 0.100332
\(989\) 18.1180 0.576120
\(990\) −0.928143 −0.0294983
\(991\) 51.1752 1.62563 0.812816 0.582520i \(-0.197933\pi\)
0.812816 + 0.582520i \(0.197933\pi\)
\(992\) 7.33235 0.232802
\(993\) 3.92322 0.124500
\(994\) −7.50033 −0.237896
\(995\) 2.70390 0.0857193
\(996\) −174.326 −5.52372
\(997\) 17.4998 0.554223 0.277112 0.960838i \(-0.410623\pi\)
0.277112 + 0.960838i \(0.410623\pi\)
\(998\) −21.0691 −0.666932
\(999\) 0.578227 0.0182943
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 \(a_p\))