Properties

Label 4009.2.a.c.1.18
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.89239 q^{2}\) \(-0.431235 q^{3}\) \(+1.58115 q^{4}\) \(+3.97235 q^{5}\) \(+0.816065 q^{6}\) \(-2.66937 q^{7}\) \(+0.792636 q^{8}\) \(-2.81404 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.89239 q^{2}\) \(-0.431235 q^{3}\) \(+1.58115 q^{4}\) \(+3.97235 q^{5}\) \(+0.816065 q^{6}\) \(-2.66937 q^{7}\) \(+0.792636 q^{8}\) \(-2.81404 q^{9}\) \(-7.51724 q^{10}\) \(-2.92001 q^{11}\) \(-0.681845 q^{12}\) \(+1.55018 q^{13}\) \(+5.05149 q^{14}\) \(-1.71301 q^{15}\) \(-4.66227 q^{16}\) \(-1.96101 q^{17}\) \(+5.32526 q^{18}\) \(+1.00000 q^{19}\) \(+6.28087 q^{20}\) \(+1.15112 q^{21}\) \(+5.52581 q^{22}\) \(-6.26871 q^{23}\) \(-0.341812 q^{24}\) \(+10.7796 q^{25}\) \(-2.93355 q^{26}\) \(+2.50721 q^{27}\) \(-4.22066 q^{28}\) \(+8.06876 q^{29}\) \(+3.24170 q^{30}\) \(-4.58316 q^{31}\) \(+7.23757 q^{32}\) \(+1.25921 q^{33}\) \(+3.71099 q^{34}\) \(-10.6037 q^{35}\) \(-4.44940 q^{36}\) \(+8.58707 q^{37}\) \(-1.89239 q^{38}\) \(-0.668492 q^{39}\) \(+3.14863 q^{40}\) \(+8.34308 q^{41}\) \(-2.17838 q^{42}\) \(+6.30592 q^{43}\) \(-4.61697 q^{44}\) \(-11.1783 q^{45}\) \(+11.8628 q^{46}\) \(+3.37259 q^{47}\) \(+2.01053 q^{48}\) \(+0.125532 q^{49}\) \(-20.3992 q^{50}\) \(+0.845653 q^{51}\) \(+2.45106 q^{52}\) \(-3.53695 q^{53}\) \(-4.74463 q^{54}\) \(-11.5993 q^{55}\) \(-2.11584 q^{56}\) \(-0.431235 q^{57}\) \(-15.2693 q^{58}\) \(+1.15247 q^{59}\) \(-2.70853 q^{60}\) \(-2.16887 q^{61}\) \(+8.67313 q^{62}\) \(+7.51170 q^{63}\) \(-4.37177 q^{64}\) \(+6.15787 q^{65}\) \(-2.38292 q^{66}\) \(-7.38999 q^{67}\) \(-3.10064 q^{68}\) \(+2.70328 q^{69}\) \(+20.0663 q^{70}\) \(-3.50612 q^{71}\) \(-2.23051 q^{72}\) \(-12.4025 q^{73}\) \(-16.2501 q^{74}\) \(-4.64852 q^{75}\) \(+1.58115 q^{76}\) \(+7.79459 q^{77}\) \(+1.26505 q^{78}\) \(-10.7182 q^{79}\) \(-18.5202 q^{80}\) \(+7.36091 q^{81}\) \(-15.7884 q^{82}\) \(+11.4521 q^{83}\) \(+1.82010 q^{84}\) \(-7.78980 q^{85}\) \(-11.9333 q^{86}\) \(-3.47953 q^{87}\) \(-2.31451 q^{88}\) \(+2.08592 q^{89}\) \(+21.1538 q^{90}\) \(-4.13801 q^{91}\) \(-9.91174 q^{92}\) \(+1.97642 q^{93}\) \(-6.38226 q^{94}\) \(+3.97235 q^{95}\) \(-3.12109 q^{96}\) \(-3.23881 q^{97}\) \(-0.237556 q^{98}\) \(+8.21702 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89239 −1.33812 −0.669061 0.743207i \(-0.733304\pi\)
−0.669061 + 0.743207i \(0.733304\pi\)
\(3\) −0.431235 −0.248973 −0.124487 0.992221i \(-0.539728\pi\)
−0.124487 + 0.992221i \(0.539728\pi\)
\(4\) 1.58115 0.790573
\(5\) 3.97235 1.77649 0.888245 0.459371i \(-0.151925\pi\)
0.888245 + 0.459371i \(0.151925\pi\)
\(6\) 0.816065 0.333157
\(7\) −2.66937 −1.00893 −0.504463 0.863433i \(-0.668310\pi\)
−0.504463 + 0.863433i \(0.668310\pi\)
\(8\) 0.792636 0.280239
\(9\) −2.81404 −0.938012
\(10\) −7.51724 −2.37716
\(11\) −2.92001 −0.880417 −0.440208 0.897896i \(-0.645095\pi\)
−0.440208 + 0.897896i \(0.645095\pi\)
\(12\) −0.681845 −0.196832
\(13\) 1.55018 0.429943 0.214972 0.976620i \(-0.431034\pi\)
0.214972 + 0.976620i \(0.431034\pi\)
\(14\) 5.05149 1.35007
\(15\) −1.71301 −0.442299
\(16\) −4.66227 −1.16557
\(17\) −1.96101 −0.475614 −0.237807 0.971312i \(-0.576429\pi\)
−0.237807 + 0.971312i \(0.576429\pi\)
\(18\) 5.32526 1.25518
\(19\) 1.00000 0.229416
\(20\) 6.28087 1.40444
\(21\) 1.15112 0.251196
\(22\) 5.52581 1.17811
\(23\) −6.26871 −1.30712 −0.653558 0.756877i \(-0.726724\pi\)
−0.653558 + 0.756877i \(0.726724\pi\)
\(24\) −0.341812 −0.0697721
\(25\) 10.7796 2.15591
\(26\) −2.93355 −0.575317
\(27\) 2.50721 0.482513
\(28\) −4.22066 −0.797630
\(29\) 8.06876 1.49833 0.749166 0.662383i \(-0.230455\pi\)
0.749166 + 0.662383i \(0.230455\pi\)
\(30\) 3.24170 0.591850
\(31\) −4.58316 −0.823159 −0.411580 0.911374i \(-0.635023\pi\)
−0.411580 + 0.911374i \(0.635023\pi\)
\(32\) 7.23757 1.27943
\(33\) 1.25921 0.219200
\(34\) 3.71099 0.636430
\(35\) −10.6037 −1.79235
\(36\) −4.44940 −0.741567
\(37\) 8.58707 1.41171 0.705853 0.708358i \(-0.250564\pi\)
0.705853 + 0.708358i \(0.250564\pi\)
\(38\) −1.89239 −0.306986
\(39\) −0.668492 −0.107044
\(40\) 3.14863 0.497842
\(41\) 8.34308 1.30297 0.651485 0.758662i \(-0.274146\pi\)
0.651485 + 0.758662i \(0.274146\pi\)
\(42\) −2.17838 −0.336131
\(43\) 6.30592 0.961643 0.480822 0.876818i \(-0.340338\pi\)
0.480822 + 0.876818i \(0.340338\pi\)
\(44\) −4.61697 −0.696034
\(45\) −11.1783 −1.66637
\(46\) 11.8628 1.74908
\(47\) 3.37259 0.491943 0.245971 0.969277i \(-0.420893\pi\)
0.245971 + 0.969277i \(0.420893\pi\)
\(48\) 2.01053 0.290195
\(49\) 0.125532 0.0179331
\(50\) −20.3992 −2.88488
\(51\) 0.845653 0.118415
\(52\) 2.45106 0.339901
\(53\) −3.53695 −0.485837 −0.242919 0.970047i \(-0.578105\pi\)
−0.242919 + 0.970047i \(0.578105\pi\)
\(54\) −4.74463 −0.645662
\(55\) −11.5993 −1.56405
\(56\) −2.11584 −0.282741
\(57\) −0.431235 −0.0571184
\(58\) −15.2693 −2.00495
\(59\) 1.15247 0.150039 0.0750194 0.997182i \(-0.476098\pi\)
0.0750194 + 0.997182i \(0.476098\pi\)
\(60\) −2.70853 −0.349669
\(61\) −2.16887 −0.277695 −0.138848 0.990314i \(-0.544340\pi\)
−0.138848 + 0.990314i \(0.544340\pi\)
\(62\) 8.67313 1.10149
\(63\) 7.51170 0.946386
\(64\) −4.37177 −0.546472
\(65\) 6.15787 0.763789
\(66\) −2.38292 −0.293317
\(67\) −7.38999 −0.902831 −0.451416 0.892314i \(-0.649081\pi\)
−0.451416 + 0.892314i \(0.649081\pi\)
\(68\) −3.10064 −0.376007
\(69\) 2.70328 0.325437
\(70\) 20.0663 2.39838
\(71\) −3.50612 −0.416100 −0.208050 0.978118i \(-0.566712\pi\)
−0.208050 + 0.978118i \(0.566712\pi\)
\(72\) −2.23051 −0.262868
\(73\) −12.4025 −1.45160 −0.725802 0.687904i \(-0.758531\pi\)
−0.725802 + 0.687904i \(0.758531\pi\)
\(74\) −16.2501 −1.88904
\(75\) −4.64852 −0.536765
\(76\) 1.58115 0.181370
\(77\) 7.79459 0.888276
\(78\) 1.26505 0.143239
\(79\) −10.7182 −1.20589 −0.602944 0.797784i \(-0.706006\pi\)
−0.602944 + 0.797784i \(0.706006\pi\)
\(80\) −18.5202 −2.07062
\(81\) 7.36091 0.817879
\(82\) −15.7884 −1.74353
\(83\) 11.4521 1.25704 0.628518 0.777795i \(-0.283662\pi\)
0.628518 + 0.777795i \(0.283662\pi\)
\(84\) 1.82010 0.198589
\(85\) −7.78980 −0.844923
\(86\) −11.9333 −1.28680
\(87\) −3.47953 −0.373045
\(88\) −2.31451 −0.246727
\(89\) 2.08592 0.221107 0.110554 0.993870i \(-0.464738\pi\)
0.110554 + 0.993870i \(0.464738\pi\)
\(90\) 21.1538 2.22981
\(91\) −4.13801 −0.433781
\(92\) −9.91174 −1.03337
\(93\) 1.97642 0.204945
\(94\) −6.38226 −0.658280
\(95\) 3.97235 0.407555
\(96\) −3.12109 −0.318545
\(97\) −3.23881 −0.328852 −0.164426 0.986389i \(-0.552577\pi\)
−0.164426 + 0.986389i \(0.552577\pi\)
\(98\) −0.237556 −0.0239967
\(99\) 8.21702 0.825842
\(100\) 17.0441 1.70441
\(101\) −8.66946 −0.862643 −0.431322 0.902198i \(-0.641953\pi\)
−0.431322 + 0.902198i \(0.641953\pi\)
\(102\) −1.60031 −0.158454
\(103\) −17.3840 −1.71289 −0.856447 0.516234i \(-0.827333\pi\)
−0.856447 + 0.516234i \(0.827333\pi\)
\(104\) 1.22873 0.120487
\(105\) 4.57267 0.446247
\(106\) 6.69329 0.650110
\(107\) −13.7047 −1.32488 −0.662440 0.749115i \(-0.730479\pi\)
−0.662440 + 0.749115i \(0.730479\pi\)
\(108\) 3.96427 0.381462
\(109\) 8.52053 0.816118 0.408059 0.912955i \(-0.366206\pi\)
0.408059 + 0.912955i \(0.366206\pi\)
\(110\) 21.9504 2.09289
\(111\) −3.70304 −0.351477
\(112\) 12.4453 1.17597
\(113\) −7.74204 −0.728310 −0.364155 0.931338i \(-0.618642\pi\)
−0.364155 + 0.931338i \(0.618642\pi\)
\(114\) 0.816065 0.0764315
\(115\) −24.9015 −2.32208
\(116\) 12.7579 1.18454
\(117\) −4.36227 −0.403292
\(118\) −2.18093 −0.200770
\(119\) 5.23465 0.479859
\(120\) −1.35780 −0.123949
\(121\) −2.47353 −0.224866
\(122\) 4.10435 0.371591
\(123\) −3.59782 −0.324405
\(124\) −7.24664 −0.650768
\(125\) 22.9585 2.05347
\(126\) −14.2151 −1.26638
\(127\) −0.746775 −0.0662656 −0.0331328 0.999451i \(-0.510548\pi\)
−0.0331328 + 0.999451i \(0.510548\pi\)
\(128\) −6.20203 −0.548187
\(129\) −2.71933 −0.239424
\(130\) −11.6531 −1.02204
\(131\) −0.288153 −0.0251761 −0.0125880 0.999921i \(-0.504007\pi\)
−0.0125880 + 0.999921i \(0.504007\pi\)
\(132\) 1.99100 0.173294
\(133\) −2.66937 −0.231464
\(134\) 13.9848 1.20810
\(135\) 9.95953 0.857180
\(136\) −1.55436 −0.133286
\(137\) −8.17721 −0.698627 −0.349313 0.937006i \(-0.613585\pi\)
−0.349313 + 0.937006i \(0.613585\pi\)
\(138\) −5.11567 −0.435475
\(139\) −5.55725 −0.471360 −0.235680 0.971831i \(-0.575732\pi\)
−0.235680 + 0.971831i \(0.575732\pi\)
\(140\) −16.7660 −1.41698
\(141\) −1.45438 −0.122481
\(142\) 6.63496 0.556793
\(143\) −4.52655 −0.378529
\(144\) 13.1198 1.09332
\(145\) 32.0519 2.66177
\(146\) 23.4704 1.94242
\(147\) −0.0541337 −0.00446487
\(148\) 13.5774 1.11606
\(149\) −2.53650 −0.207798 −0.103899 0.994588i \(-0.533132\pi\)
−0.103899 + 0.994588i \(0.533132\pi\)
\(150\) 8.79683 0.718258
\(151\) −0.252628 −0.0205586 −0.0102793 0.999947i \(-0.503272\pi\)
−0.0102793 + 0.999947i \(0.503272\pi\)
\(152\) 0.792636 0.0642913
\(153\) 5.51834 0.446132
\(154\) −14.7504 −1.18862
\(155\) −18.2059 −1.46233
\(156\) −1.05698 −0.0846264
\(157\) −16.8917 −1.34810 −0.674050 0.738685i \(-0.735447\pi\)
−0.674050 + 0.738685i \(0.735447\pi\)
\(158\) 20.2830 1.61363
\(159\) 1.52525 0.120961
\(160\) 28.7502 2.27290
\(161\) 16.7335 1.31878
\(162\) −13.9297 −1.09442
\(163\) 18.6982 1.46456 0.732279 0.681004i \(-0.238456\pi\)
0.732279 + 0.681004i \(0.238456\pi\)
\(164\) 13.1916 1.03009
\(165\) 5.00203 0.389407
\(166\) −21.6719 −1.68207
\(167\) 14.3754 1.11240 0.556202 0.831047i \(-0.312258\pi\)
0.556202 + 0.831047i \(0.312258\pi\)
\(168\) 0.912423 0.0703949
\(169\) −10.5969 −0.815149
\(170\) 14.7414 1.13061
\(171\) −2.81404 −0.215195
\(172\) 9.97057 0.760249
\(173\) −16.8972 −1.28467 −0.642336 0.766423i \(-0.722035\pi\)
−0.642336 + 0.766423i \(0.722035\pi\)
\(174\) 6.58463 0.499180
\(175\) −28.7747 −2.17516
\(176\) 13.6139 1.02619
\(177\) −0.496985 −0.0373557
\(178\) −3.94738 −0.295869
\(179\) −10.4442 −0.780637 −0.390319 0.920680i \(-0.627635\pi\)
−0.390319 + 0.920680i \(0.627635\pi\)
\(180\) −17.6746 −1.31739
\(181\) 8.68371 0.645455 0.322727 0.946492i \(-0.395400\pi\)
0.322727 + 0.946492i \(0.395400\pi\)
\(182\) 7.83073 0.580452
\(183\) 0.935292 0.0691388
\(184\) −4.96880 −0.366305
\(185\) 34.1109 2.50788
\(186\) −3.74015 −0.274241
\(187\) 5.72616 0.418738
\(188\) 5.33255 0.388917
\(189\) −6.69268 −0.486821
\(190\) −7.51724 −0.545358
\(191\) −20.7391 −1.50063 −0.750316 0.661080i \(-0.770099\pi\)
−0.750316 + 0.661080i \(0.770099\pi\)
\(192\) 1.88526 0.136057
\(193\) −2.83556 −0.204108 −0.102054 0.994779i \(-0.532541\pi\)
−0.102054 + 0.994779i \(0.532541\pi\)
\(194\) 6.12910 0.440044
\(195\) −2.65549 −0.190163
\(196\) 0.198484 0.0141775
\(197\) 0.931748 0.0663843 0.0331921 0.999449i \(-0.489433\pi\)
0.0331921 + 0.999449i \(0.489433\pi\)
\(198\) −15.5498 −1.10508
\(199\) −4.76979 −0.338122 −0.169061 0.985606i \(-0.554073\pi\)
−0.169061 + 0.985606i \(0.554073\pi\)
\(200\) 8.54428 0.604172
\(201\) 3.18682 0.224781
\(202\) 16.4060 1.15432
\(203\) −21.5385 −1.51171
\(204\) 1.33710 0.0936158
\(205\) 33.1416 2.31471
\(206\) 32.8973 2.29206
\(207\) 17.6404 1.22609
\(208\) −7.22737 −0.501128
\(209\) −2.92001 −0.201982
\(210\) −8.65328 −0.597133
\(211\) 1.00000 0.0688428
\(212\) −5.59243 −0.384090
\(213\) 1.51196 0.103598
\(214\) 25.9346 1.77285
\(215\) 25.0493 1.70835
\(216\) 1.98731 0.135219
\(217\) 12.2341 0.830508
\(218\) −16.1242 −1.09207
\(219\) 5.34839 0.361411
\(220\) −18.3402 −1.23650
\(221\) −3.03992 −0.204487
\(222\) 7.00761 0.470320
\(223\) −21.2792 −1.42496 −0.712481 0.701691i \(-0.752429\pi\)
−0.712481 + 0.701691i \(0.752429\pi\)
\(224\) −19.3197 −1.29085
\(225\) −30.3341 −2.02227
\(226\) 14.6510 0.974568
\(227\) 5.41960 0.359712 0.179856 0.983693i \(-0.442437\pi\)
0.179856 + 0.983693i \(0.442437\pi\)
\(228\) −0.681845 −0.0451563
\(229\) 22.6413 1.49618 0.748089 0.663598i \(-0.230972\pi\)
0.748089 + 0.663598i \(0.230972\pi\)
\(230\) 47.1234 3.10722
\(231\) −3.36130 −0.221157
\(232\) 6.39559 0.419891
\(233\) 26.0017 1.70343 0.851715 0.524006i \(-0.175563\pi\)
0.851715 + 0.524006i \(0.175563\pi\)
\(234\) 8.25512 0.539654
\(235\) 13.3971 0.873931
\(236\) 1.82222 0.118617
\(237\) 4.62204 0.300234
\(238\) −9.90600 −0.642111
\(239\) 2.91530 0.188575 0.0942875 0.995545i \(-0.469943\pi\)
0.0942875 + 0.995545i \(0.469943\pi\)
\(240\) 7.98654 0.515529
\(241\) −18.3673 −1.18314 −0.591570 0.806254i \(-0.701491\pi\)
−0.591570 + 0.806254i \(0.701491\pi\)
\(242\) 4.68088 0.300898
\(243\) −10.6959 −0.686144
\(244\) −3.42930 −0.219538
\(245\) 0.498657 0.0318580
\(246\) 6.80849 0.434093
\(247\) 1.55018 0.0986357
\(248\) −3.63278 −0.230682
\(249\) −4.93856 −0.312969
\(250\) −43.4464 −2.74779
\(251\) −1.77480 −0.112025 −0.0560123 0.998430i \(-0.517839\pi\)
−0.0560123 + 0.998430i \(0.517839\pi\)
\(252\) 11.8771 0.748187
\(253\) 18.3047 1.15081
\(254\) 1.41319 0.0886715
\(255\) 3.35923 0.210363
\(256\) 20.4802 1.28001
\(257\) 29.6639 1.85038 0.925191 0.379502i \(-0.123905\pi\)
0.925191 + 0.379502i \(0.123905\pi\)
\(258\) 5.14603 0.320378
\(259\) −22.9221 −1.42431
\(260\) 9.73649 0.603831
\(261\) −22.7058 −1.40545
\(262\) 0.545299 0.0336887
\(263\) −18.5302 −1.14262 −0.571311 0.820733i \(-0.693565\pi\)
−0.571311 + 0.820733i \(0.693565\pi\)
\(264\) 0.998096 0.0614285
\(265\) −14.0500 −0.863085
\(266\) 5.05149 0.309727
\(267\) −0.899522 −0.0550499
\(268\) −11.6847 −0.713754
\(269\) −12.7956 −0.780161 −0.390080 0.920781i \(-0.627553\pi\)
−0.390080 + 0.920781i \(0.627553\pi\)
\(270\) −18.8473 −1.14701
\(271\) −18.6582 −1.13340 −0.566702 0.823923i \(-0.691781\pi\)
−0.566702 + 0.823923i \(0.691781\pi\)
\(272\) 9.14274 0.554360
\(273\) 1.78445 0.108000
\(274\) 15.4745 0.934848
\(275\) −31.4765 −1.89810
\(276\) 4.27428 0.257282
\(277\) −9.93806 −0.597120 −0.298560 0.954391i \(-0.596506\pi\)
−0.298560 + 0.954391i \(0.596506\pi\)
\(278\) 10.5165 0.630737
\(279\) 12.8972 0.772134
\(280\) −8.40485 −0.502286
\(281\) −2.85464 −0.170294 −0.0851468 0.996368i \(-0.527136\pi\)
−0.0851468 + 0.996368i \(0.527136\pi\)
\(282\) 2.75225 0.163894
\(283\) 7.89406 0.469253 0.234627 0.972086i \(-0.424613\pi\)
0.234627 + 0.972086i \(0.424613\pi\)
\(284\) −5.54369 −0.328958
\(285\) −1.71301 −0.101470
\(286\) 8.56601 0.506519
\(287\) −22.2708 −1.31460
\(288\) −20.3668 −1.20012
\(289\) −13.1545 −0.773792
\(290\) −60.6548 −3.56177
\(291\) 1.39669 0.0818753
\(292\) −19.6102 −1.14760
\(293\) −29.3435 −1.71427 −0.857133 0.515096i \(-0.827756\pi\)
−0.857133 + 0.515096i \(0.827756\pi\)
\(294\) 0.102442 0.00597455
\(295\) 4.57802 0.266542
\(296\) 6.80642 0.395615
\(297\) −7.32110 −0.424813
\(298\) 4.80004 0.278059
\(299\) −9.71764 −0.561985
\(300\) −7.34999 −0.424352
\(301\) −16.8328 −0.970227
\(302\) 0.478071 0.0275099
\(303\) 3.73857 0.214775
\(304\) −4.66227 −0.267399
\(305\) −8.61551 −0.493323
\(306\) −10.4429 −0.596979
\(307\) 21.8870 1.24916 0.624579 0.780962i \(-0.285271\pi\)
0.624579 + 0.780962i \(0.285271\pi\)
\(308\) 12.3244 0.702247
\(309\) 7.49658 0.426465
\(310\) 34.4527 1.95678
\(311\) 6.66403 0.377882 0.188941 0.981988i \(-0.439494\pi\)
0.188941 + 0.981988i \(0.439494\pi\)
\(312\) −0.529871 −0.0299980
\(313\) 9.76104 0.551726 0.275863 0.961197i \(-0.411036\pi\)
0.275863 + 0.961197i \(0.411036\pi\)
\(314\) 31.9656 1.80392
\(315\) 29.8391 1.68124
\(316\) −16.9470 −0.953342
\(317\) −7.69015 −0.431922 −0.215961 0.976402i \(-0.569288\pi\)
−0.215961 + 0.976402i \(0.569288\pi\)
\(318\) −2.88638 −0.161860
\(319\) −23.5609 −1.31916
\(320\) −17.3662 −0.970801
\(321\) 5.90993 0.329860
\(322\) −31.6663 −1.76469
\(323\) −1.96101 −0.109113
\(324\) 11.6387 0.646593
\(325\) 16.7103 0.926921
\(326\) −35.3844 −1.95976
\(327\) −3.67435 −0.203192
\(328\) 6.61302 0.365143
\(329\) −9.00268 −0.496334
\(330\) −9.46579 −0.521075
\(331\) −21.2827 −1.16980 −0.584901 0.811104i \(-0.698867\pi\)
−0.584901 + 0.811104i \(0.698867\pi\)
\(332\) 18.1075 0.993779
\(333\) −24.1643 −1.32420
\(334\) −27.2039 −1.48853
\(335\) −29.3556 −1.60387
\(336\) −5.36685 −0.292786
\(337\) −6.59326 −0.359158 −0.179579 0.983744i \(-0.557473\pi\)
−0.179579 + 0.983744i \(0.557473\pi\)
\(338\) 20.0536 1.09077
\(339\) 3.33864 0.181330
\(340\) −12.3168 −0.667973
\(341\) 13.3829 0.724724
\(342\) 5.32526 0.287957
\(343\) 18.3505 0.990834
\(344\) 4.99830 0.269490
\(345\) 10.7384 0.578135
\(346\) 31.9762 1.71905
\(347\) −34.8761 −1.87224 −0.936122 0.351675i \(-0.885612\pi\)
−0.936122 + 0.351675i \(0.885612\pi\)
\(348\) −5.50164 −0.294919
\(349\) −28.0182 −1.49978 −0.749891 0.661561i \(-0.769894\pi\)
−0.749891 + 0.661561i \(0.769894\pi\)
\(350\) 54.4529 2.91063
\(351\) 3.88664 0.207453
\(352\) −21.1338 −1.12643
\(353\) 14.3987 0.766365 0.383183 0.923673i \(-0.374828\pi\)
0.383183 + 0.923673i \(0.374828\pi\)
\(354\) 0.940490 0.0499865
\(355\) −13.9275 −0.739198
\(356\) 3.29815 0.174802
\(357\) −2.25736 −0.119472
\(358\) 19.7645 1.04459
\(359\) −31.1781 −1.64552 −0.822759 0.568390i \(-0.807567\pi\)
−0.822759 + 0.568390i \(0.807567\pi\)
\(360\) −8.86036 −0.466982
\(361\) 1.00000 0.0526316
\(362\) −16.4330 −0.863698
\(363\) 1.06667 0.0559856
\(364\) −6.54279 −0.342936
\(365\) −49.2671 −2.57876
\(366\) −1.76994 −0.0925162
\(367\) 23.0055 1.20088 0.600438 0.799671i \(-0.294993\pi\)
0.600438 + 0.799671i \(0.294993\pi\)
\(368\) 29.2264 1.52353
\(369\) −23.4777 −1.22220
\(370\) −64.5511 −3.35585
\(371\) 9.44142 0.490174
\(372\) 3.12500 0.162024
\(373\) −9.84297 −0.509650 −0.254825 0.966987i \(-0.582018\pi\)
−0.254825 + 0.966987i \(0.582018\pi\)
\(374\) −10.8361 −0.560324
\(375\) −9.90049 −0.511259
\(376\) 2.67324 0.137862
\(377\) 12.5080 0.644197
\(378\) 12.6652 0.651426
\(379\) 19.9138 1.02290 0.511452 0.859312i \(-0.329108\pi\)
0.511452 + 0.859312i \(0.329108\pi\)
\(380\) 6.28087 0.322202
\(381\) 0.322035 0.0164984
\(382\) 39.2466 2.00803
\(383\) −13.4333 −0.686410 −0.343205 0.939260i \(-0.611513\pi\)
−0.343205 + 0.939260i \(0.611513\pi\)
\(384\) 2.67453 0.136484
\(385\) 30.9629 1.57801
\(386\) 5.36598 0.273121
\(387\) −17.7451 −0.902033
\(388\) −5.12104 −0.259981
\(389\) −6.83937 −0.346770 −0.173385 0.984854i \(-0.555470\pi\)
−0.173385 + 0.984854i \(0.555470\pi\)
\(390\) 5.02522 0.254462
\(391\) 12.2930 0.621682
\(392\) 0.0995011 0.00502557
\(393\) 0.124262 0.00626817
\(394\) −1.76323 −0.0888303
\(395\) −42.5763 −2.14225
\(396\) 12.9923 0.652888
\(397\) 18.3971 0.923324 0.461662 0.887056i \(-0.347253\pi\)
0.461662 + 0.887056i \(0.347253\pi\)
\(398\) 9.02631 0.452448
\(399\) 1.15112 0.0576283
\(400\) −50.2573 −2.51286
\(401\) −8.37620 −0.418288 −0.209144 0.977885i \(-0.567068\pi\)
−0.209144 + 0.977885i \(0.567068\pi\)
\(402\) −6.03071 −0.300785
\(403\) −7.10473 −0.353912
\(404\) −13.7077 −0.681983
\(405\) 29.2401 1.45295
\(406\) 40.7593 2.02285
\(407\) −25.0744 −1.24289
\(408\) 0.670295 0.0331846
\(409\) −24.9165 −1.23204 −0.616020 0.787731i \(-0.711256\pi\)
−0.616020 + 0.787731i \(0.711256\pi\)
\(410\) −62.7169 −3.09737
\(411\) 3.52630 0.173939
\(412\) −27.4866 −1.35417
\(413\) −3.07637 −0.151378
\(414\) −33.3825 −1.64066
\(415\) 45.4919 2.23311
\(416\) 11.2195 0.550084
\(417\) 2.39648 0.117356
\(418\) 5.52581 0.270276
\(419\) −3.30379 −0.161401 −0.0807005 0.996738i \(-0.525716\pi\)
−0.0807005 + 0.996738i \(0.525716\pi\)
\(420\) 7.23006 0.352791
\(421\) −17.4464 −0.850287 −0.425144 0.905126i \(-0.639776\pi\)
−0.425144 + 0.905126i \(0.639776\pi\)
\(422\) −1.89239 −0.0921202
\(423\) −9.49059 −0.461448
\(424\) −2.80351 −0.136151
\(425\) −21.1388 −1.02538
\(426\) −2.86122 −0.138627
\(427\) 5.78952 0.280174
\(428\) −21.6691 −1.04741
\(429\) 1.95201 0.0942437
\(430\) −47.4031 −2.28598
\(431\) 29.6915 1.43019 0.715094 0.699028i \(-0.246384\pi\)
0.715094 + 0.699028i \(0.246384\pi\)
\(432\) −11.6893 −0.562402
\(433\) −1.25365 −0.0602466 −0.0301233 0.999546i \(-0.509590\pi\)
−0.0301233 + 0.999546i \(0.509590\pi\)
\(434\) −23.1518 −1.11132
\(435\) −13.8219 −0.662710
\(436\) 13.4722 0.645201
\(437\) −6.26871 −0.299873
\(438\) −10.1212 −0.483612
\(439\) −31.5486 −1.50573 −0.752866 0.658173i \(-0.771329\pi\)
−0.752866 + 0.658173i \(0.771329\pi\)
\(440\) −9.19404 −0.438308
\(441\) −0.353251 −0.0168215
\(442\) 5.75271 0.273629
\(443\) 17.8480 0.847983 0.423992 0.905666i \(-0.360629\pi\)
0.423992 + 0.905666i \(0.360629\pi\)
\(444\) −5.85505 −0.277868
\(445\) 8.28602 0.392795
\(446\) 40.2686 1.90678
\(447\) 1.09382 0.0517361
\(448\) 11.6699 0.551350
\(449\) −30.3609 −1.43282 −0.716411 0.697679i \(-0.754216\pi\)
−0.716411 + 0.697679i \(0.754216\pi\)
\(450\) 57.4040 2.70605
\(451\) −24.3619 −1.14716
\(452\) −12.2413 −0.575782
\(453\) 0.108942 0.00511854
\(454\) −10.2560 −0.481339
\(455\) −16.4376 −0.770608
\(456\) −0.341812 −0.0160068
\(457\) 7.24655 0.338979 0.169490 0.985532i \(-0.445788\pi\)
0.169490 + 0.985532i \(0.445788\pi\)
\(458\) −42.8462 −2.00207
\(459\) −4.91666 −0.229490
\(460\) −39.3729 −1.83577
\(461\) −0.629689 −0.0293275 −0.0146638 0.999892i \(-0.504668\pi\)
−0.0146638 + 0.999892i \(0.504668\pi\)
\(462\) 6.36089 0.295935
\(463\) 26.8896 1.24966 0.624832 0.780759i \(-0.285167\pi\)
0.624832 + 0.780759i \(0.285167\pi\)
\(464\) −37.6187 −1.74641
\(465\) 7.85102 0.364082
\(466\) −49.2054 −2.27940
\(467\) −25.0649 −1.15987 −0.579933 0.814664i \(-0.696921\pi\)
−0.579933 + 0.814664i \(0.696921\pi\)
\(468\) −6.89738 −0.318832
\(469\) 19.7266 0.910891
\(470\) −25.3526 −1.16943
\(471\) 7.28427 0.335641
\(472\) 0.913490 0.0420468
\(473\) −18.4134 −0.846647
\(474\) −8.74671 −0.401750
\(475\) 10.7796 0.494601
\(476\) 8.27674 0.379364
\(477\) 9.95310 0.455721
\(478\) −5.51689 −0.252337
\(479\) −23.3100 −1.06506 −0.532530 0.846411i \(-0.678759\pi\)
−0.532530 + 0.846411i \(0.678759\pi\)
\(480\) −12.3981 −0.565891
\(481\) 13.3115 0.606953
\(482\) 34.7580 1.58319
\(483\) −7.21606 −0.328342
\(484\) −3.91100 −0.177773
\(485\) −12.8657 −0.584202
\(486\) 20.2409 0.918145
\(487\) 18.4438 0.835767 0.417883 0.908501i \(-0.362772\pi\)
0.417883 + 0.908501i \(0.362772\pi\)
\(488\) −1.71912 −0.0778211
\(489\) −8.06333 −0.364636
\(490\) −0.943654 −0.0426299
\(491\) −9.24161 −0.417068 −0.208534 0.978015i \(-0.566869\pi\)
−0.208534 + 0.978015i \(0.566869\pi\)
\(492\) −5.68868 −0.256466
\(493\) −15.8229 −0.712627
\(494\) −2.93355 −0.131987
\(495\) 32.6409 1.46710
\(496\) 21.3679 0.959448
\(497\) 9.35914 0.419815
\(498\) 9.34569 0.418790
\(499\) 29.0119 1.29875 0.649376 0.760468i \(-0.275030\pi\)
0.649376 + 0.760468i \(0.275030\pi\)
\(500\) 36.3007 1.62342
\(501\) −6.19918 −0.276959
\(502\) 3.35862 0.149903
\(503\) −0.439864 −0.0196126 −0.00980629 0.999952i \(-0.503121\pi\)
−0.00980629 + 0.999952i \(0.503121\pi\)
\(504\) 5.95405 0.265214
\(505\) −34.4381 −1.53248
\(506\) −34.6397 −1.53992
\(507\) 4.56976 0.202950
\(508\) −1.18076 −0.0523878
\(509\) −40.4136 −1.79130 −0.895651 0.444758i \(-0.853290\pi\)
−0.895651 + 0.444758i \(0.853290\pi\)
\(510\) −6.35698 −0.281492
\(511\) 33.1069 1.46456
\(512\) −26.3525 −1.16463
\(513\) 2.50721 0.110696
\(514\) −56.1357 −2.47604
\(515\) −69.0553 −3.04294
\(516\) −4.29966 −0.189282
\(517\) −9.84800 −0.433115
\(518\) 43.3775 1.90590
\(519\) 7.28667 0.319849
\(520\) 4.88095 0.214044
\(521\) 19.4698 0.852987 0.426493 0.904491i \(-0.359749\pi\)
0.426493 + 0.904491i \(0.359749\pi\)
\(522\) 42.9682 1.88067
\(523\) 19.7990 0.865748 0.432874 0.901454i \(-0.357499\pi\)
0.432874 + 0.901454i \(0.357499\pi\)
\(524\) −0.455612 −0.0199035
\(525\) 12.4086 0.541557
\(526\) 35.0664 1.52897
\(527\) 8.98760 0.391506
\(528\) −5.87078 −0.255493
\(529\) 16.2967 0.708551
\(530\) 26.5881 1.15491
\(531\) −3.24309 −0.140738
\(532\) −4.22066 −0.182989
\(533\) 12.9333 0.560203
\(534\) 1.70225 0.0736635
\(535\) −54.4398 −2.35364
\(536\) −5.85757 −0.253009
\(537\) 4.50391 0.194358
\(538\) 24.2143 1.04395
\(539\) −0.366555 −0.0157886
\(540\) 15.7475 0.677663
\(541\) 14.4034 0.619251 0.309625 0.950859i \(-0.399796\pi\)
0.309625 + 0.950859i \(0.399796\pi\)
\(542\) 35.3086 1.51663
\(543\) −3.74471 −0.160701
\(544\) −14.1929 −0.608516
\(545\) 33.8465 1.44983
\(546\) −3.37688 −0.144517
\(547\) 5.80940 0.248392 0.124196 0.992258i \(-0.460365\pi\)
0.124196 + 0.992258i \(0.460365\pi\)
\(548\) −12.9294 −0.552315
\(549\) 6.10328 0.260482
\(550\) 59.5658 2.53990
\(551\) 8.06876 0.343741
\(552\) 2.14272 0.0912002
\(553\) 28.6107 1.21665
\(554\) 18.8067 0.799020
\(555\) −14.7098 −0.624395
\(556\) −8.78682 −0.372644
\(557\) −23.5050 −0.995938 −0.497969 0.867195i \(-0.665921\pi\)
−0.497969 + 0.867195i \(0.665921\pi\)
\(558\) −24.4065 −1.03321
\(559\) 9.77532 0.413452
\(560\) 49.4372 2.08910
\(561\) −2.46932 −0.104255
\(562\) 5.40210 0.227874
\(563\) 6.15833 0.259543 0.129771 0.991544i \(-0.458576\pi\)
0.129771 + 0.991544i \(0.458576\pi\)
\(564\) −2.29958 −0.0968299
\(565\) −30.7541 −1.29383
\(566\) −14.9387 −0.627919
\(567\) −19.6490 −0.825180
\(568\) −2.77908 −0.116608
\(569\) −4.45139 −0.186612 −0.0933060 0.995637i \(-0.529743\pi\)
−0.0933060 + 0.995637i \(0.529743\pi\)
\(570\) 3.24170 0.135780
\(571\) −17.1721 −0.718631 −0.359315 0.933216i \(-0.616990\pi\)
−0.359315 + 0.933216i \(0.616990\pi\)
\(572\) −7.15714 −0.299255
\(573\) 8.94343 0.373617
\(574\) 42.1450 1.75910
\(575\) −67.5740 −2.81803
\(576\) 12.3023 0.512597
\(577\) 7.52251 0.313166 0.156583 0.987665i \(-0.449952\pi\)
0.156583 + 0.987665i \(0.449952\pi\)
\(578\) 24.8934 1.03543
\(579\) 1.22279 0.0508174
\(580\) 50.6788 2.10432
\(581\) −30.5700 −1.26826
\(582\) −2.64308 −0.109559
\(583\) 10.3279 0.427739
\(584\) −9.83067 −0.406796
\(585\) −17.3285 −0.716444
\(586\) 55.5294 2.29390
\(587\) 41.1449 1.69823 0.849117 0.528205i \(-0.177135\pi\)
0.849117 + 0.528205i \(0.177135\pi\)
\(588\) −0.0855933 −0.00352981
\(589\) −4.58316 −0.188846
\(590\) −8.66340 −0.356667
\(591\) −0.401802 −0.0165279
\(592\) −40.0352 −1.64544
\(593\) −44.7769 −1.83877 −0.919384 0.393361i \(-0.871312\pi\)
−0.919384 + 0.393361i \(0.871312\pi\)
\(594\) 13.8544 0.568452
\(595\) 20.7939 0.852465
\(596\) −4.01057 −0.164279
\(597\) 2.05690 0.0841833
\(598\) 18.3896 0.752005
\(599\) 25.3682 1.03651 0.518257 0.855225i \(-0.326581\pi\)
0.518257 + 0.855225i \(0.326581\pi\)
\(600\) −3.68459 −0.150423
\(601\) 14.2376 0.580763 0.290381 0.956911i \(-0.406218\pi\)
0.290381 + 0.956911i \(0.406218\pi\)
\(602\) 31.8543 1.29828
\(603\) 20.7957 0.846867
\(604\) −0.399441 −0.0162530
\(605\) −9.82571 −0.399472
\(606\) −7.07484 −0.287396
\(607\) 22.4003 0.909201 0.454601 0.890695i \(-0.349782\pi\)
0.454601 + 0.890695i \(0.349782\pi\)
\(608\) 7.23757 0.293522
\(609\) 9.28815 0.376375
\(610\) 16.3039 0.660127
\(611\) 5.22813 0.211507
\(612\) 8.72530 0.352700
\(613\) 37.4461 1.51244 0.756218 0.654320i \(-0.227045\pi\)
0.756218 + 0.654320i \(0.227045\pi\)
\(614\) −41.4188 −1.67153
\(615\) −14.2918 −0.576302
\(616\) 6.17827 0.248930
\(617\) −12.0902 −0.486732 −0.243366 0.969935i \(-0.578252\pi\)
−0.243366 + 0.969935i \(0.578252\pi\)
\(618\) −14.1865 −0.570663
\(619\) −4.32161 −0.173700 −0.0868501 0.996221i \(-0.527680\pi\)
−0.0868501 + 0.996221i \(0.527680\pi\)
\(620\) −28.7862 −1.15608
\(621\) −15.7170 −0.630701
\(622\) −12.6109 −0.505653
\(623\) −5.56810 −0.223081
\(624\) 3.11669 0.124767
\(625\) 37.3013 1.49205
\(626\) −18.4717 −0.738278
\(627\) 1.25921 0.0502880
\(628\) −26.7082 −1.06577
\(629\) −16.8393 −0.671427
\(630\) −56.4673 −2.24971
\(631\) −8.99677 −0.358156 −0.179078 0.983835i \(-0.557311\pi\)
−0.179078 + 0.983835i \(0.557311\pi\)
\(632\) −8.49560 −0.337937
\(633\) −0.431235 −0.0171400
\(634\) 14.5528 0.577965
\(635\) −2.96645 −0.117720
\(636\) 2.41165 0.0956281
\(637\) 0.194597 0.00771023
\(638\) 44.5864 1.76519
\(639\) 9.86636 0.390307
\(640\) −24.6366 −0.973849
\(641\) 7.61792 0.300890 0.150445 0.988618i \(-0.451929\pi\)
0.150445 + 0.988618i \(0.451929\pi\)
\(642\) −11.1839 −0.441393
\(643\) 24.0500 0.948441 0.474220 0.880406i \(-0.342730\pi\)
0.474220 + 0.880406i \(0.342730\pi\)
\(644\) 26.4581 1.04259
\(645\) −10.8021 −0.425333
\(646\) 3.71099 0.146007
\(647\) 19.1015 0.750956 0.375478 0.926831i \(-0.377479\pi\)
0.375478 + 0.926831i \(0.377479\pi\)
\(648\) 5.83453 0.229202
\(649\) −3.36523 −0.132097
\(650\) −31.6224 −1.24033
\(651\) −5.27578 −0.206774
\(652\) 29.5646 1.15784
\(653\) −25.6284 −1.00292 −0.501458 0.865182i \(-0.667203\pi\)
−0.501458 + 0.865182i \(0.667203\pi\)
\(654\) 6.95330 0.271896
\(655\) −1.14465 −0.0447250
\(656\) −38.8977 −1.51870
\(657\) 34.9011 1.36162
\(658\) 17.0366 0.664156
\(659\) −22.5265 −0.877509 −0.438754 0.898607i \(-0.644580\pi\)
−0.438754 + 0.898607i \(0.644580\pi\)
\(660\) 7.90893 0.307855
\(661\) 50.5326 1.96549 0.982745 0.184964i \(-0.0592170\pi\)
0.982745 + 0.184964i \(0.0592170\pi\)
\(662\) 40.2752 1.56534
\(663\) 1.31092 0.0509118
\(664\) 9.07738 0.352271
\(665\) −10.6037 −0.411193
\(666\) 45.7284 1.77194
\(667\) −50.5807 −1.95849
\(668\) 22.7296 0.879436
\(669\) 9.17634 0.354778
\(670\) 55.5524 2.14618
\(671\) 6.33313 0.244488
\(672\) 8.33134 0.321388
\(673\) 1.03113 0.0397471 0.0198736 0.999803i \(-0.493674\pi\)
0.0198736 + 0.999803i \(0.493674\pi\)
\(674\) 12.4770 0.480597
\(675\) 27.0267 1.04026
\(676\) −16.7553 −0.644435
\(677\) −11.9146 −0.457917 −0.228958 0.973436i \(-0.573532\pi\)
−0.228958 + 0.973436i \(0.573532\pi\)
\(678\) −6.31801 −0.242642
\(679\) 8.64559 0.331787
\(680\) −6.17448 −0.236780
\(681\) −2.33712 −0.0895587
\(682\) −25.3256 −0.969769
\(683\) 44.0075 1.68390 0.841950 0.539555i \(-0.181408\pi\)
0.841950 + 0.539555i \(0.181408\pi\)
\(684\) −4.44940 −0.170127
\(685\) −32.4828 −1.24110
\(686\) −34.7263 −1.32586
\(687\) −9.76370 −0.372509
\(688\) −29.3999 −1.12086
\(689\) −5.48291 −0.208882
\(690\) −20.3212 −0.773616
\(691\) 21.2501 0.808393 0.404196 0.914672i \(-0.367551\pi\)
0.404196 + 0.914672i \(0.367551\pi\)
\(692\) −26.7170 −1.01563
\(693\) −21.9343 −0.833214
\(694\) 65.9991 2.50529
\(695\) −22.0754 −0.837366
\(696\) −2.75800 −0.104542
\(697\) −16.3608 −0.619710
\(698\) 53.0215 2.00689
\(699\) −11.2128 −0.424109
\(700\) −45.4969 −1.71962
\(701\) −13.6685 −0.516250 −0.258125 0.966111i \(-0.583105\pi\)
−0.258125 + 0.966111i \(0.583105\pi\)
\(702\) −7.35504 −0.277598
\(703\) 8.58707 0.323868
\(704\) 12.7656 0.481123
\(705\) −5.77730 −0.217586
\(706\) −27.2480 −1.02549
\(707\) 23.1420 0.870344
\(708\) −0.785806 −0.0295324
\(709\) 4.88290 0.183381 0.0916906 0.995788i \(-0.470773\pi\)
0.0916906 + 0.995788i \(0.470773\pi\)
\(710\) 26.3564 0.989137
\(711\) 30.1613 1.13114
\(712\) 1.65338 0.0619629
\(713\) 28.7305 1.07596
\(714\) 4.27181 0.159869
\(715\) −17.9811 −0.672453
\(716\) −16.5138 −0.617151
\(717\) −1.25718 −0.0469502
\(718\) 59.0012 2.20191
\(719\) 20.7888 0.775291 0.387646 0.921808i \(-0.373288\pi\)
0.387646 + 0.921808i \(0.373288\pi\)
\(720\) 52.1164 1.94227
\(721\) 46.4043 1.72819
\(722\) −1.89239 −0.0704275
\(723\) 7.92060 0.294570
\(724\) 13.7302 0.510279
\(725\) 86.9778 3.23027
\(726\) −2.01856 −0.0749157
\(727\) 43.3897 1.60923 0.804617 0.593794i \(-0.202371\pi\)
0.804617 + 0.593794i \(0.202371\pi\)
\(728\) −3.27993 −0.121562
\(729\) −17.4703 −0.647048
\(730\) 93.2327 3.45070
\(731\) −12.3659 −0.457371
\(732\) 1.47883 0.0546592
\(733\) 50.5500 1.86711 0.933553 0.358439i \(-0.116691\pi\)
0.933553 + 0.358439i \(0.116691\pi\)
\(734\) −43.5354 −1.60692
\(735\) −0.215038 −0.00793180
\(736\) −45.3702 −1.67237
\(737\) 21.5789 0.794868
\(738\) 44.4291 1.63546
\(739\) −32.1331 −1.18203 −0.591017 0.806659i \(-0.701273\pi\)
−0.591017 + 0.806659i \(0.701273\pi\)
\(740\) 53.9342 1.98266
\(741\) −0.668492 −0.0245577
\(742\) −17.8669 −0.655913
\(743\) 34.7049 1.27320 0.636599 0.771195i \(-0.280341\pi\)
0.636599 + 0.771195i \(0.280341\pi\)
\(744\) 1.56658 0.0574336
\(745\) −10.0758 −0.369151
\(746\) 18.6268 0.681974
\(747\) −32.2268 −1.17912
\(748\) 9.05390 0.331043
\(749\) 36.5828 1.33671
\(750\) 18.7356 0.684128
\(751\) −23.1989 −0.846540 −0.423270 0.906003i \(-0.639118\pi\)
−0.423270 + 0.906003i \(0.639118\pi\)
\(752\) −15.7239 −0.573392
\(753\) 0.765357 0.0278911
\(754\) −23.6701 −0.862015
\(755\) −1.00353 −0.0365221
\(756\) −10.5821 −0.384867
\(757\) −26.6271 −0.967777 −0.483888 0.875130i \(-0.660776\pi\)
−0.483888 + 0.875130i \(0.660776\pi\)
\(758\) −37.6847 −1.36877
\(759\) −7.89362 −0.286520
\(760\) 3.14863 0.114213
\(761\) 48.4487 1.75626 0.878131 0.478420i \(-0.158790\pi\)
0.878131 + 0.478420i \(0.158790\pi\)
\(762\) −0.609417 −0.0220768
\(763\) −22.7444 −0.823404
\(764\) −32.7916 −1.18636
\(765\) 21.9208 0.792548
\(766\) 25.4211 0.918501
\(767\) 1.78654 0.0645082
\(768\) −8.83178 −0.318689
\(769\) 7.31530 0.263796 0.131898 0.991263i \(-0.457893\pi\)
0.131898 + 0.991263i \(0.457893\pi\)
\(770\) −58.5938 −2.11158
\(771\) −12.7921 −0.460696
\(772\) −4.48343 −0.161362
\(773\) −28.3452 −1.01951 −0.509754 0.860320i \(-0.670263\pi\)
−0.509754 + 0.860320i \(0.670263\pi\)
\(774\) 33.5806 1.20703
\(775\) −49.4045 −1.77466
\(776\) −2.56720 −0.0921571
\(777\) 9.88479 0.354615
\(778\) 12.9428 0.464021
\(779\) 8.34308 0.298922
\(780\) −4.19871 −0.150338
\(781\) 10.2379 0.366342
\(782\) −23.2631 −0.831887
\(783\) 20.2301 0.722965
\(784\) −0.585264 −0.0209023
\(785\) −67.0996 −2.39489
\(786\) −0.235152 −0.00838759
\(787\) 10.4549 0.372676 0.186338 0.982486i \(-0.440338\pi\)
0.186338 + 0.982486i \(0.440338\pi\)
\(788\) 1.47323 0.0524816
\(789\) 7.99087 0.284483
\(790\) 80.5710 2.86659
\(791\) 20.6664 0.734811
\(792\) 6.51311 0.231433
\(793\) −3.36214 −0.119393
\(794\) −34.8145 −1.23552
\(795\) 6.05885 0.214885
\(796\) −7.54174 −0.267310
\(797\) −13.7938 −0.488603 −0.244302 0.969699i \(-0.578559\pi\)
−0.244302 + 0.969699i \(0.578559\pi\)
\(798\) −2.17838 −0.0771137
\(799\) −6.61367 −0.233975
\(800\) 78.0179 2.75835
\(801\) −5.86986 −0.207401
\(802\) 15.8511 0.559720
\(803\) 36.2155 1.27802
\(804\) 5.03883 0.177706
\(805\) 66.4713 2.34281
\(806\) 13.4449 0.473577
\(807\) 5.51790 0.194239
\(808\) −6.87173 −0.241746
\(809\) −1.78829 −0.0628729 −0.0314365 0.999506i \(-0.510008\pi\)
−0.0314365 + 0.999506i \(0.510008\pi\)
\(810\) −55.3338 −1.94423
\(811\) −17.3843 −0.610445 −0.305222 0.952281i \(-0.598731\pi\)
−0.305222 + 0.952281i \(0.598731\pi\)
\(812\) −34.0555 −1.19511
\(813\) 8.04606 0.282188
\(814\) 47.4505 1.66314
\(815\) 74.2760 2.60177
\(816\) −3.94266 −0.138021
\(817\) 6.30592 0.220616
\(818\) 47.1517 1.64862
\(819\) 11.6445 0.406892
\(820\) 52.4018 1.82995
\(821\) 11.4029 0.397966 0.198983 0.980003i \(-0.436236\pi\)
0.198983 + 0.980003i \(0.436236\pi\)
\(822\) −6.67314 −0.232752
\(823\) −19.2968 −0.672644 −0.336322 0.941747i \(-0.609183\pi\)
−0.336322 + 0.941747i \(0.609183\pi\)
\(824\) −13.7792 −0.480020
\(825\) 13.5737 0.472577
\(826\) 5.82170 0.202563
\(827\) 13.5234 0.470254 0.235127 0.971965i \(-0.424449\pi\)
0.235127 + 0.971965i \(0.424449\pi\)
\(828\) 27.8920 0.969314
\(829\) 33.5736 1.16606 0.583029 0.812451i \(-0.301867\pi\)
0.583029 + 0.812451i \(0.301867\pi\)
\(830\) −86.0886 −2.98818
\(831\) 4.28564 0.148667
\(832\) −6.77704 −0.234952
\(833\) −0.246169 −0.00852925
\(834\) −4.53508 −0.157037
\(835\) 57.1042 1.97617
\(836\) −4.61697 −0.159681
\(837\) −11.4910 −0.397186
\(838\) 6.25207 0.215974
\(839\) −41.0171 −1.41607 −0.708034 0.706179i \(-0.750417\pi\)
−0.708034 + 0.706179i \(0.750417\pi\)
\(840\) 3.62446 0.125056
\(841\) 36.1049 1.24500
\(842\) 33.0155 1.13779
\(843\) 1.23102 0.0423986
\(844\) 1.58115 0.0544253
\(845\) −42.0947 −1.44810
\(846\) 17.9599 0.617474
\(847\) 6.60275 0.226873
\(848\) 16.4902 0.566276
\(849\) −3.40419 −0.116832
\(850\) 40.0029 1.37209
\(851\) −53.8298 −1.84526
\(852\) 2.39063 0.0819017
\(853\) 10.3099 0.353005 0.176503 0.984300i \(-0.443522\pi\)
0.176503 + 0.984300i \(0.443522\pi\)
\(854\) −10.9560 −0.374908
\(855\) −11.1783 −0.382291
\(856\) −10.8628 −0.371283
\(857\) −47.1413 −1.61032 −0.805158 0.593060i \(-0.797920\pi\)
−0.805158 + 0.593060i \(0.797920\pi\)
\(858\) −3.69396 −0.126110
\(859\) −56.7810 −1.93734 −0.968672 0.248345i \(-0.920113\pi\)
−0.968672 + 0.248345i \(0.920113\pi\)
\(860\) 39.6066 1.35057
\(861\) 9.60392 0.327301
\(862\) −56.1879 −1.91377
\(863\) −38.6274 −1.31489 −0.657446 0.753502i \(-0.728363\pi\)
−0.657446 + 0.753502i \(0.728363\pi\)
\(864\) 18.1461 0.617344
\(865\) −67.1217 −2.28221
\(866\) 2.37240 0.0806174
\(867\) 5.67266 0.192654
\(868\) 19.3440 0.656577
\(869\) 31.2972 1.06168
\(870\) 26.1565 0.886787
\(871\) −11.4558 −0.388166
\(872\) 6.75368 0.228708
\(873\) 9.11414 0.308467
\(874\) 11.8628 0.401267
\(875\) −61.2847 −2.07180
\(876\) 8.45658 0.285722
\(877\) −5.82626 −0.196739 −0.0983695 0.995150i \(-0.531363\pi\)
−0.0983695 + 0.995150i \(0.531363\pi\)
\(878\) 59.7023 2.01486
\(879\) 12.6539 0.426806
\(880\) 54.0791 1.82301
\(881\) 11.7275 0.395111 0.197555 0.980292i \(-0.436700\pi\)
0.197555 + 0.980292i \(0.436700\pi\)
\(882\) 0.668490 0.0225092
\(883\) −29.8526 −1.00462 −0.502310 0.864688i \(-0.667516\pi\)
−0.502310 + 0.864688i \(0.667516\pi\)
\(884\) −4.80655 −0.161662
\(885\) −1.97420 −0.0663620
\(886\) −33.7754 −1.13471
\(887\) −56.0411 −1.88168 −0.940838 0.338856i \(-0.889960\pi\)
−0.940838 + 0.338856i \(0.889960\pi\)
\(888\) −2.93516 −0.0984977
\(889\) 1.99342 0.0668571
\(890\) −15.6804 −0.525608
\(891\) −21.4940 −0.720075
\(892\) −33.6456 −1.12654
\(893\) 3.37259 0.112859
\(894\) −2.06994 −0.0692293
\(895\) −41.4881 −1.38679
\(896\) 16.5555 0.553081
\(897\) 4.19058 0.139919
\(898\) 57.4548 1.91729
\(899\) −36.9804 −1.23337
\(900\) −47.9627 −1.59876
\(901\) 6.93598 0.231071
\(902\) 46.1022 1.53504
\(903\) 7.25889 0.241561
\(904\) −6.13662 −0.204101
\(905\) 34.4947 1.14664
\(906\) −0.206161 −0.00684923
\(907\) −45.6727 −1.51654 −0.758268 0.651943i \(-0.773954\pi\)
−0.758268 + 0.651943i \(0.773954\pi\)
\(908\) 8.56918 0.284378
\(909\) 24.3962 0.809170
\(910\) 31.1064 1.03117
\(911\) 41.6338 1.37939 0.689695 0.724100i \(-0.257745\pi\)
0.689695 + 0.724100i \(0.257745\pi\)
\(912\) 2.01053 0.0665754
\(913\) −33.4404 −1.10672
\(914\) −13.7133 −0.453596
\(915\) 3.71531 0.122824
\(916\) 35.7992 1.18284
\(917\) 0.769188 0.0254008
\(918\) 9.30425 0.307086
\(919\) −46.5275 −1.53480 −0.767400 0.641169i \(-0.778450\pi\)
−0.767400 + 0.641169i \(0.778450\pi\)
\(920\) −19.7378 −0.650737
\(921\) −9.43843 −0.311007
\(922\) 1.19162 0.0392438
\(923\) −5.43513 −0.178899
\(924\) −5.31470 −0.174841
\(925\) 92.5649 3.04352
\(926\) −50.8856 −1.67220
\(927\) 48.9192 1.60672
\(928\) 58.3982 1.91701
\(929\) 4.90083 0.160791 0.0803955 0.996763i \(-0.474382\pi\)
0.0803955 + 0.996763i \(0.474382\pi\)
\(930\) −14.8572 −0.487187
\(931\) 0.125532 0.00411414
\(932\) 41.1125 1.34668
\(933\) −2.87376 −0.0940826
\(934\) 47.4326 1.55204
\(935\) 22.7463 0.743884
\(936\) −3.45769 −0.113018
\(937\) −17.7886 −0.581128 −0.290564 0.956856i \(-0.593843\pi\)
−0.290564 + 0.956856i \(0.593843\pi\)
\(938\) −37.3305 −1.21888
\(939\) −4.20930 −0.137365
\(940\) 21.1828 0.690906
\(941\) 29.5405 0.962992 0.481496 0.876448i \(-0.340094\pi\)
0.481496 + 0.876448i \(0.340094\pi\)
\(942\) −13.7847 −0.449129
\(943\) −52.3003 −1.70313
\(944\) −5.37313 −0.174880
\(945\) −26.5857 −0.864832
\(946\) 34.8453 1.13292
\(947\) 22.5425 0.732534 0.366267 0.930510i \(-0.380636\pi\)
0.366267 + 0.930510i \(0.380636\pi\)
\(948\) 7.30812 0.237357
\(949\) −19.2261 −0.624107
\(950\) −20.3992 −0.661836
\(951\) 3.31626 0.107537
\(952\) 4.14917 0.134475
\(953\) −2.55275 −0.0826918 −0.0413459 0.999145i \(-0.513165\pi\)
−0.0413459 + 0.999145i \(0.513165\pi\)
\(954\) −18.8352 −0.609811
\(955\) −82.3831 −2.66586
\(956\) 4.60951 0.149082
\(957\) 10.1603 0.328435
\(958\) 44.1116 1.42518
\(959\) 21.8280 0.704863
\(960\) 7.48891 0.241704
\(961\) −9.99466 −0.322409
\(962\) −25.1906 −0.812178
\(963\) 38.5655 1.24275
\(964\) −29.0413 −0.935358
\(965\) −11.2638 −0.362595
\(966\) 13.6556 0.439362
\(967\) 28.2237 0.907613 0.453806 0.891100i \(-0.350066\pi\)
0.453806 + 0.891100i \(0.350066\pi\)
\(968\) −1.96061 −0.0630162
\(969\) 0.845653 0.0271663
\(970\) 24.3470 0.781734
\(971\) −27.1250 −0.870483 −0.435241 0.900314i \(-0.643337\pi\)
−0.435241 + 0.900314i \(0.643337\pi\)
\(972\) −16.9118 −0.542447
\(973\) 14.8344 0.475568
\(974\) −34.9028 −1.11836
\(975\) −7.20606 −0.230779
\(976\) 10.1119 0.323673
\(977\) −32.2918 −1.03311 −0.516553 0.856255i \(-0.672785\pi\)
−0.516553 + 0.856255i \(0.672785\pi\)
\(978\) 15.2590 0.487928
\(979\) −6.09092 −0.194667
\(980\) 0.788449 0.0251861
\(981\) −23.9771 −0.765529
\(982\) 17.4887 0.558088
\(983\) 7.83824 0.250001 0.125001 0.992157i \(-0.460107\pi\)
0.125001 + 0.992157i \(0.460107\pi\)
\(984\) −2.85176 −0.0909109
\(985\) 3.70123 0.117931
\(986\) 29.9431 0.953582
\(987\) 3.88227 0.123574
\(988\) 2.45106 0.0779787
\(989\) −39.5299 −1.25698
\(990\) −61.7694 −1.96316
\(991\) 56.6231 1.79869 0.899346 0.437239i \(-0.144043\pi\)
0.899346 + 0.437239i \(0.144043\pi\)
\(992\) −33.1709 −1.05318
\(993\) 9.17783 0.291250
\(994\) −17.7111 −0.561764
\(995\) −18.9473 −0.600669
\(996\) −7.80858 −0.247424
\(997\) −40.2125 −1.27354 −0.636771 0.771053i \(-0.719730\pi\)
−0.636771 + 0.771053i \(0.719730\pi\)
\(998\) −54.9019 −1.73789
\(999\) 21.5296 0.681167
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 \(a_p\))