Properties

Label 8042.2.a.a.1.11
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.32940 q^{3}\) \(+1.00000 q^{4}\) \(-2.43485 q^{5}\) \(-2.32940 q^{6}\) \(+0.839554 q^{7}\) \(+1.00000 q^{8}\) \(+2.42611 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.32940 q^{3}\) \(+1.00000 q^{4}\) \(-2.43485 q^{5}\) \(-2.32940 q^{6}\) \(+0.839554 q^{7}\) \(+1.00000 q^{8}\) \(+2.42611 q^{9}\) \(-2.43485 q^{10}\) \(-5.28397 q^{11}\) \(-2.32940 q^{12}\) \(-0.826967 q^{13}\) \(+0.839554 q^{14}\) \(+5.67174 q^{15}\) \(+1.00000 q^{16}\) \(+1.19444 q^{17}\) \(+2.42611 q^{18}\) \(+3.71172 q^{19}\) \(-2.43485 q^{20}\) \(-1.95566 q^{21}\) \(-5.28397 q^{22}\) \(-1.07783 q^{23}\) \(-2.32940 q^{24}\) \(+0.928478 q^{25}\) \(-0.826967 q^{26}\) \(+1.33681 q^{27}\) \(+0.839554 q^{28}\) \(+8.71254 q^{29}\) \(+5.67174 q^{30}\) \(-1.57356 q^{31}\) \(+1.00000 q^{32}\) \(+12.3085 q^{33}\) \(+1.19444 q^{34}\) \(-2.04418 q^{35}\) \(+2.42611 q^{36}\) \(-1.49810 q^{37}\) \(+3.71172 q^{38}\) \(+1.92634 q^{39}\) \(-2.43485 q^{40}\) \(-0.609475 q^{41}\) \(-1.95566 q^{42}\) \(-2.45587 q^{43}\) \(-5.28397 q^{44}\) \(-5.90722 q^{45}\) \(-1.07783 q^{46}\) \(+4.85052 q^{47}\) \(-2.32940 q^{48}\) \(-6.29515 q^{49}\) \(+0.928478 q^{50}\) \(-2.78234 q^{51}\) \(-0.826967 q^{52}\) \(+3.68255 q^{53}\) \(+1.33681 q^{54}\) \(+12.8657 q^{55}\) \(+0.839554 q^{56}\) \(-8.64608 q^{57}\) \(+8.71254 q^{58}\) \(+2.81044 q^{59}\) \(+5.67174 q^{60}\) \(+14.9799 q^{61}\) \(-1.57356 q^{62}\) \(+2.03685 q^{63}\) \(+1.00000 q^{64}\) \(+2.01354 q^{65}\) \(+12.3085 q^{66}\) \(-6.07332 q^{67}\) \(+1.19444 q^{68}\) \(+2.51070 q^{69}\) \(-2.04418 q^{70}\) \(+10.5814 q^{71}\) \(+2.42611 q^{72}\) \(-12.0486 q^{73}\) \(-1.49810 q^{74}\) \(-2.16280 q^{75}\) \(+3.71172 q^{76}\) \(-4.43618 q^{77}\) \(+1.92634 q^{78}\) \(+11.2960 q^{79}\) \(-2.43485 q^{80}\) \(-10.3923 q^{81}\) \(-0.609475 q^{82}\) \(-1.64570 q^{83}\) \(-1.95566 q^{84}\) \(-2.90828 q^{85}\) \(-2.45587 q^{86}\) \(-20.2950 q^{87}\) \(-5.28397 q^{88}\) \(+3.88182 q^{89}\) \(-5.90722 q^{90}\) \(-0.694283 q^{91}\) \(-1.07783 q^{92}\) \(+3.66546 q^{93}\) \(+4.85052 q^{94}\) \(-9.03746 q^{95}\) \(-2.32940 q^{96}\) \(-8.04003 q^{97}\) \(-6.29515 q^{98}\) \(-12.8195 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.32940 −1.34488 −0.672440 0.740151i \(-0.734754\pi\)
−0.672440 + 0.740151i \(0.734754\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.43485 −1.08890 −0.544448 0.838794i \(-0.683261\pi\)
−0.544448 + 0.838794i \(0.683261\pi\)
\(6\) −2.32940 −0.950974
\(7\) 0.839554 0.317322 0.158661 0.987333i \(-0.449282\pi\)
0.158661 + 0.987333i \(0.449282\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.42611 0.808705
\(10\) −2.43485 −0.769966
\(11\) −5.28397 −1.59318 −0.796588 0.604522i \(-0.793364\pi\)
−0.796588 + 0.604522i \(0.793364\pi\)
\(12\) −2.32940 −0.672440
\(13\) −0.826967 −0.229359 −0.114680 0.993403i \(-0.536584\pi\)
−0.114680 + 0.993403i \(0.536584\pi\)
\(14\) 0.839554 0.224380
\(15\) 5.67174 1.46444
\(16\) 1.00000 0.250000
\(17\) 1.19444 0.289695 0.144847 0.989454i \(-0.453731\pi\)
0.144847 + 0.989454i \(0.453731\pi\)
\(18\) 2.42611 0.571841
\(19\) 3.71172 0.851526 0.425763 0.904835i \(-0.360006\pi\)
0.425763 + 0.904835i \(0.360006\pi\)
\(20\) −2.43485 −0.544448
\(21\) −1.95566 −0.426760
\(22\) −5.28397 −1.12655
\(23\) −1.07783 −0.224743 −0.112371 0.993666i \(-0.535845\pi\)
−0.112371 + 0.993666i \(0.535845\pi\)
\(24\) −2.32940 −0.475487
\(25\) 0.928478 0.185696
\(26\) −0.826967 −0.162182
\(27\) 1.33681 0.257269
\(28\) 0.839554 0.158661
\(29\) 8.71254 1.61788 0.808939 0.587893i \(-0.200042\pi\)
0.808939 + 0.587893i \(0.200042\pi\)
\(30\) 5.67174 1.03551
\(31\) −1.57356 −0.282620 −0.141310 0.989965i \(-0.545131\pi\)
−0.141310 + 0.989965i \(0.545131\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.3085 2.14263
\(34\) 1.19444 0.204845
\(35\) −2.04418 −0.345530
\(36\) 2.42611 0.404352
\(37\) −1.49810 −0.246286 −0.123143 0.992389i \(-0.539297\pi\)
−0.123143 + 0.992389i \(0.539297\pi\)
\(38\) 3.71172 0.602120
\(39\) 1.92634 0.308461
\(40\) −2.43485 −0.384983
\(41\) −0.609475 −0.0951839 −0.0475920 0.998867i \(-0.515155\pi\)
−0.0475920 + 0.998867i \(0.515155\pi\)
\(42\) −1.95566 −0.301765
\(43\) −2.45587 −0.374516 −0.187258 0.982311i \(-0.559960\pi\)
−0.187258 + 0.982311i \(0.559960\pi\)
\(44\) −5.28397 −0.796588
\(45\) −5.90722 −0.880596
\(46\) −1.07783 −0.158917
\(47\) 4.85052 0.707520 0.353760 0.935336i \(-0.384903\pi\)
0.353760 + 0.935336i \(0.384903\pi\)
\(48\) −2.32940 −0.336220
\(49\) −6.29515 −0.899307
\(50\) 0.928478 0.131307
\(51\) −2.78234 −0.389605
\(52\) −0.826967 −0.114680
\(53\) 3.68255 0.505838 0.252919 0.967488i \(-0.418609\pi\)
0.252919 + 0.967488i \(0.418609\pi\)
\(54\) 1.33681 0.181917
\(55\) 12.8657 1.73480
\(56\) 0.839554 0.112190
\(57\) −8.64608 −1.14520
\(58\) 8.71254 1.14401
\(59\) 2.81044 0.365888 0.182944 0.983123i \(-0.441437\pi\)
0.182944 + 0.983123i \(0.441437\pi\)
\(60\) 5.67174 0.732218
\(61\) 14.9799 1.91798 0.958992 0.283432i \(-0.0914730\pi\)
0.958992 + 0.283432i \(0.0914730\pi\)
\(62\) −1.57356 −0.199843
\(63\) 2.03685 0.256619
\(64\) 1.00000 0.125000
\(65\) 2.01354 0.249749
\(66\) 12.3085 1.51507
\(67\) −6.07332 −0.741974 −0.370987 0.928638i \(-0.620981\pi\)
−0.370987 + 0.928638i \(0.620981\pi\)
\(68\) 1.19444 0.144847
\(69\) 2.51070 0.302252
\(70\) −2.04418 −0.244327
\(71\) 10.5814 1.25578 0.627891 0.778301i \(-0.283918\pi\)
0.627891 + 0.778301i \(0.283918\pi\)
\(72\) 2.42611 0.285920
\(73\) −12.0486 −1.41018 −0.705090 0.709118i \(-0.749093\pi\)
−0.705090 + 0.709118i \(0.749093\pi\)
\(74\) −1.49810 −0.174151
\(75\) −2.16280 −0.249739
\(76\) 3.71172 0.425763
\(77\) −4.43618 −0.505549
\(78\) 1.92634 0.218115
\(79\) 11.2960 1.27089 0.635447 0.772145i \(-0.280816\pi\)
0.635447 + 0.772145i \(0.280816\pi\)
\(80\) −2.43485 −0.272224
\(81\) −10.3923 −1.15470
\(82\) −0.609475 −0.0673052
\(83\) −1.64570 −0.180639 −0.0903195 0.995913i \(-0.528789\pi\)
−0.0903195 + 0.995913i \(0.528789\pi\)
\(84\) −1.95566 −0.213380
\(85\) −2.90828 −0.315448
\(86\) −2.45587 −0.264823
\(87\) −20.2950 −2.17585
\(88\) −5.28397 −0.563273
\(89\) 3.88182 0.411472 0.205736 0.978608i \(-0.434041\pi\)
0.205736 + 0.978608i \(0.434041\pi\)
\(90\) −5.90722 −0.622675
\(91\) −0.694283 −0.0727806
\(92\) −1.07783 −0.112371
\(93\) 3.66546 0.380090
\(94\) 4.85052 0.500292
\(95\) −9.03746 −0.927224
\(96\) −2.32940 −0.237744
\(97\) −8.04003 −0.816342 −0.408171 0.912906i \(-0.633833\pi\)
−0.408171 + 0.912906i \(0.633833\pi\)
\(98\) −6.29515 −0.635906
\(99\) −12.8195 −1.28841
\(100\) 0.928478 0.0928478
\(101\) −12.2146 −1.21540 −0.607699 0.794167i \(-0.707907\pi\)
−0.607699 + 0.794167i \(0.707907\pi\)
\(102\) −2.78234 −0.275492
\(103\) −1.71547 −0.169030 −0.0845150 0.996422i \(-0.526934\pi\)
−0.0845150 + 0.996422i \(0.526934\pi\)
\(104\) −0.826967 −0.0810908
\(105\) 4.76173 0.464697
\(106\) 3.68255 0.357681
\(107\) 17.9762 1.73782 0.868911 0.494968i \(-0.164820\pi\)
0.868911 + 0.494968i \(0.164820\pi\)
\(108\) 1.33681 0.128635
\(109\) −1.80745 −0.173122 −0.0865610 0.996247i \(-0.527588\pi\)
−0.0865610 + 0.996247i \(0.527588\pi\)
\(110\) 12.8657 1.22669
\(111\) 3.48968 0.331226
\(112\) 0.839554 0.0793304
\(113\) −10.3727 −0.975785 −0.487892 0.872904i \(-0.662234\pi\)
−0.487892 + 0.872904i \(0.662234\pi\)
\(114\) −8.64608 −0.809779
\(115\) 2.62435 0.244722
\(116\) 8.71254 0.808939
\(117\) −2.00632 −0.185484
\(118\) 2.81044 0.258722
\(119\) 1.00280 0.0919264
\(120\) 5.67174 0.517756
\(121\) 16.9203 1.53821
\(122\) 14.9799 1.35622
\(123\) 1.41971 0.128011
\(124\) −1.57356 −0.141310
\(125\) 9.91353 0.886693
\(126\) 2.03685 0.181457
\(127\) −0.603915 −0.0535888 −0.0267944 0.999641i \(-0.508530\pi\)
−0.0267944 + 0.999641i \(0.508530\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.72070 0.503680
\(130\) 2.01354 0.176599
\(131\) −13.6610 −1.19357 −0.596784 0.802402i \(-0.703555\pi\)
−0.596784 + 0.802402i \(0.703555\pi\)
\(132\) 12.3085 1.07132
\(133\) 3.11618 0.270208
\(134\) −6.07332 −0.524655
\(135\) −3.25493 −0.280140
\(136\) 1.19444 0.102423
\(137\) −5.93477 −0.507042 −0.253521 0.967330i \(-0.581589\pi\)
−0.253521 + 0.967330i \(0.581589\pi\)
\(138\) 2.51070 0.213725
\(139\) −1.81978 −0.154352 −0.0771759 0.997017i \(-0.524590\pi\)
−0.0771759 + 0.997017i \(0.524590\pi\)
\(140\) −2.04418 −0.172765
\(141\) −11.2988 −0.951531
\(142\) 10.5814 0.887972
\(143\) 4.36967 0.365410
\(144\) 2.42611 0.202176
\(145\) −21.2137 −1.76170
\(146\) −12.0486 −0.997148
\(147\) 14.6639 1.20946
\(148\) −1.49810 −0.123143
\(149\) 13.0036 1.06529 0.532646 0.846338i \(-0.321198\pi\)
0.532646 + 0.846338i \(0.321198\pi\)
\(150\) −2.16280 −0.176592
\(151\) −9.41130 −0.765881 −0.382940 0.923773i \(-0.625089\pi\)
−0.382940 + 0.923773i \(0.625089\pi\)
\(152\) 3.71172 0.301060
\(153\) 2.89785 0.234278
\(154\) −4.43618 −0.357477
\(155\) 3.83138 0.307744
\(156\) 1.92634 0.154230
\(157\) −7.04207 −0.562018 −0.281009 0.959705i \(-0.590669\pi\)
−0.281009 + 0.959705i \(0.590669\pi\)
\(158\) 11.2960 0.898658
\(159\) −8.57815 −0.680291
\(160\) −2.43485 −0.192492
\(161\) −0.904895 −0.0713157
\(162\) −10.3923 −0.816497
\(163\) 6.87365 0.538386 0.269193 0.963086i \(-0.413243\pi\)
0.269193 + 0.963086i \(0.413243\pi\)
\(164\) −0.609475 −0.0475920
\(165\) −29.9693 −2.33310
\(166\) −1.64570 −0.127731
\(167\) −5.22780 −0.404539 −0.202270 0.979330i \(-0.564832\pi\)
−0.202270 + 0.979330i \(0.564832\pi\)
\(168\) −1.95566 −0.150882
\(169\) −12.3161 −0.947394
\(170\) −2.90828 −0.223055
\(171\) 9.00504 0.688633
\(172\) −2.45587 −0.187258
\(173\) 11.4441 0.870077 0.435038 0.900412i \(-0.356735\pi\)
0.435038 + 0.900412i \(0.356735\pi\)
\(174\) −20.2950 −1.53856
\(175\) 0.779508 0.0589252
\(176\) −5.28397 −0.398294
\(177\) −6.54664 −0.492075
\(178\) 3.88182 0.290955
\(179\) −1.65368 −0.123602 −0.0618009 0.998088i \(-0.519684\pi\)
−0.0618009 + 0.998088i \(0.519684\pi\)
\(180\) −5.90722 −0.440298
\(181\) −8.36335 −0.621643 −0.310821 0.950468i \(-0.600604\pi\)
−0.310821 + 0.950468i \(0.600604\pi\)
\(182\) −0.694283 −0.0514637
\(183\) −34.8943 −2.57946
\(184\) −1.07783 −0.0794585
\(185\) 3.64765 0.268180
\(186\) 3.66546 0.268764
\(187\) −6.31139 −0.461535
\(188\) 4.85052 0.353760
\(189\) 1.12232 0.0816371
\(190\) −9.03746 −0.655646
\(191\) −9.06744 −0.656097 −0.328048 0.944661i \(-0.606391\pi\)
−0.328048 + 0.944661i \(0.606391\pi\)
\(192\) −2.32940 −0.168110
\(193\) −4.66340 −0.335679 −0.167839 0.985814i \(-0.553679\pi\)
−0.167839 + 0.985814i \(0.553679\pi\)
\(194\) −8.04003 −0.577241
\(195\) −4.69034 −0.335882
\(196\) −6.29515 −0.449654
\(197\) −13.6852 −0.975033 −0.487516 0.873114i \(-0.662097\pi\)
−0.487516 + 0.873114i \(0.662097\pi\)
\(198\) −12.8195 −0.911043
\(199\) −12.0896 −0.857007 −0.428504 0.903540i \(-0.640959\pi\)
−0.428504 + 0.903540i \(0.640959\pi\)
\(200\) 0.928478 0.0656533
\(201\) 14.1472 0.997866
\(202\) −12.2146 −0.859416
\(203\) 7.31465 0.513388
\(204\) −2.78234 −0.194803
\(205\) 1.48398 0.103645
\(206\) −1.71547 −0.119522
\(207\) −2.61493 −0.181750
\(208\) −0.826967 −0.0573398
\(209\) −19.6126 −1.35663
\(210\) 4.76173 0.328590
\(211\) −6.42797 −0.442520 −0.221260 0.975215i \(-0.571017\pi\)
−0.221260 + 0.975215i \(0.571017\pi\)
\(212\) 3.68255 0.252919
\(213\) −24.6484 −1.68888
\(214\) 17.9762 1.22883
\(215\) 5.97966 0.407809
\(216\) 1.33681 0.0909585
\(217\) −1.32109 −0.0896814
\(218\) −1.80745 −0.122416
\(219\) 28.0660 1.89652
\(220\) 12.8657 0.867402
\(221\) −0.987764 −0.0664442
\(222\) 3.48968 0.234212
\(223\) 24.1728 1.61873 0.809364 0.587308i \(-0.199812\pi\)
0.809364 + 0.587308i \(0.199812\pi\)
\(224\) 0.839554 0.0560950
\(225\) 2.25259 0.150173
\(226\) −10.3727 −0.689984
\(227\) −17.2841 −1.14719 −0.573593 0.819140i \(-0.694451\pi\)
−0.573593 + 0.819140i \(0.694451\pi\)
\(228\) −8.64608 −0.572600
\(229\) 29.0334 1.91858 0.959291 0.282419i \(-0.0911369\pi\)
0.959291 + 0.282419i \(0.0911369\pi\)
\(230\) 2.62435 0.173044
\(231\) 10.3336 0.679903
\(232\) 8.71254 0.572006
\(233\) 9.67858 0.634065 0.317032 0.948415i \(-0.397314\pi\)
0.317032 + 0.948415i \(0.397314\pi\)
\(234\) −2.00632 −0.131157
\(235\) −11.8103 −0.770417
\(236\) 2.81044 0.182944
\(237\) −26.3128 −1.70920
\(238\) 1.00280 0.0650018
\(239\) −22.7208 −1.46968 −0.734842 0.678239i \(-0.762744\pi\)
−0.734842 + 0.678239i \(0.762744\pi\)
\(240\) 5.67174 0.366109
\(241\) −28.6211 −1.84365 −0.921824 0.387610i \(-0.873301\pi\)
−0.921824 + 0.387610i \(0.873301\pi\)
\(242\) 16.9203 1.08768
\(243\) 20.1974 1.29567
\(244\) 14.9799 0.958992
\(245\) 15.3277 0.979252
\(246\) 1.41971 0.0905175
\(247\) −3.06947 −0.195305
\(248\) −1.57356 −0.0999213
\(249\) 3.83350 0.242938
\(250\) 9.91353 0.626987
\(251\) 9.58402 0.604938 0.302469 0.953159i \(-0.402189\pi\)
0.302469 + 0.953159i \(0.402189\pi\)
\(252\) 2.03685 0.128310
\(253\) 5.69521 0.358055
\(254\) −0.603915 −0.0378930
\(255\) 6.77456 0.424240
\(256\) 1.00000 0.0625000
\(257\) −29.3218 −1.82905 −0.914523 0.404533i \(-0.867434\pi\)
−0.914523 + 0.404533i \(0.867434\pi\)
\(258\) 5.72070 0.356155
\(259\) −1.25774 −0.0781519
\(260\) 2.01354 0.124874
\(261\) 21.1376 1.30839
\(262\) −13.6610 −0.843980
\(263\) −6.18250 −0.381229 −0.190615 0.981665i \(-0.561048\pi\)
−0.190615 + 0.981665i \(0.561048\pi\)
\(264\) 12.3085 0.757535
\(265\) −8.96645 −0.550805
\(266\) 3.11618 0.191066
\(267\) −9.04232 −0.553381
\(268\) −6.07332 −0.370987
\(269\) 5.97166 0.364099 0.182049 0.983289i \(-0.441727\pi\)
0.182049 + 0.983289i \(0.441727\pi\)
\(270\) −3.25493 −0.198089
\(271\) 15.4945 0.941222 0.470611 0.882341i \(-0.344034\pi\)
0.470611 + 0.882341i \(0.344034\pi\)
\(272\) 1.19444 0.0724237
\(273\) 1.61726 0.0978813
\(274\) −5.93477 −0.358533
\(275\) −4.90605 −0.295846
\(276\) 2.51070 0.151126
\(277\) 17.7529 1.06667 0.533334 0.845905i \(-0.320939\pi\)
0.533334 + 0.845905i \(0.320939\pi\)
\(278\) −1.81978 −0.109143
\(279\) −3.81764 −0.228556
\(280\) −2.04418 −0.122163
\(281\) −10.3974 −0.620258 −0.310129 0.950694i \(-0.600372\pi\)
−0.310129 + 0.950694i \(0.600372\pi\)
\(282\) −11.2988 −0.672834
\(283\) 6.89539 0.409889 0.204944 0.978774i \(-0.434299\pi\)
0.204944 + 0.978774i \(0.434299\pi\)
\(284\) 10.5814 0.627891
\(285\) 21.0519 1.24701
\(286\) 4.36967 0.258384
\(287\) −0.511687 −0.0302039
\(288\) 2.42611 0.142960
\(289\) −15.5733 −0.916077
\(290\) −21.2137 −1.24571
\(291\) 18.7285 1.09788
\(292\) −12.0486 −0.705090
\(293\) 8.75954 0.511738 0.255869 0.966711i \(-0.417638\pi\)
0.255869 + 0.966711i \(0.417638\pi\)
\(294\) 14.6639 0.855218
\(295\) −6.84298 −0.398414
\(296\) −1.49810 −0.0870753
\(297\) −7.06367 −0.409876
\(298\) 13.0036 0.753276
\(299\) 0.891328 0.0515468
\(300\) −2.16280 −0.124869
\(301\) −2.06183 −0.118842
\(302\) −9.41130 −0.541560
\(303\) 28.4527 1.63457
\(304\) 3.71172 0.212881
\(305\) −36.4739 −2.08849
\(306\) 2.89785 0.165659
\(307\) −2.88547 −0.164683 −0.0823413 0.996604i \(-0.526240\pi\)
−0.0823413 + 0.996604i \(0.526240\pi\)
\(308\) −4.43618 −0.252775
\(309\) 3.99601 0.227325
\(310\) 3.83138 0.217608
\(311\) 31.2564 1.77239 0.886195 0.463313i \(-0.153339\pi\)
0.886195 + 0.463313i \(0.153339\pi\)
\(312\) 1.92634 0.109057
\(313\) −29.2113 −1.65112 −0.825559 0.564316i \(-0.809140\pi\)
−0.825559 + 0.564316i \(0.809140\pi\)
\(314\) −7.04207 −0.397407
\(315\) −4.95943 −0.279432
\(316\) 11.2960 0.635447
\(317\) 19.4126 1.09032 0.545159 0.838333i \(-0.316469\pi\)
0.545159 + 0.838333i \(0.316469\pi\)
\(318\) −8.57815 −0.481039
\(319\) −46.0368 −2.57756
\(320\) −2.43485 −0.136112
\(321\) −41.8737 −2.33716
\(322\) −0.904895 −0.0504278
\(323\) 4.43343 0.246683
\(324\) −10.3923 −0.577351
\(325\) −0.767821 −0.0425910
\(326\) 6.87365 0.380696
\(327\) 4.21027 0.232828
\(328\) −0.609475 −0.0336526
\(329\) 4.07227 0.224511
\(330\) −29.9693 −1.64975
\(331\) −8.75448 −0.481190 −0.240595 0.970626i \(-0.577342\pi\)
−0.240595 + 0.970626i \(0.577342\pi\)
\(332\) −1.64570 −0.0903195
\(333\) −3.63456 −0.199173
\(334\) −5.22780 −0.286053
\(335\) 14.7876 0.807933
\(336\) −1.95566 −0.106690
\(337\) −24.9438 −1.35878 −0.679388 0.733779i \(-0.737755\pi\)
−0.679388 + 0.733779i \(0.737755\pi\)
\(338\) −12.3161 −0.669909
\(339\) 24.1623 1.31231
\(340\) −2.90828 −0.157724
\(341\) 8.31465 0.450264
\(342\) 9.00504 0.486937
\(343\) −11.1620 −0.602691
\(344\) −2.45587 −0.132411
\(345\) −6.11316 −0.329121
\(346\) 11.4441 0.615237
\(347\) −29.1632 −1.56556 −0.782782 0.622296i \(-0.786200\pi\)
−0.782782 + 0.622296i \(0.786200\pi\)
\(348\) −20.2950 −1.08793
\(349\) 0.661633 0.0354164 0.0177082 0.999843i \(-0.494363\pi\)
0.0177082 + 0.999843i \(0.494363\pi\)
\(350\) 0.779508 0.0416664
\(351\) −1.10550 −0.0590071
\(352\) −5.28397 −0.281636
\(353\) 21.1964 1.12817 0.564086 0.825716i \(-0.309229\pi\)
0.564086 + 0.825716i \(0.309229\pi\)
\(354\) −6.54664 −0.347950
\(355\) −25.7641 −1.36742
\(356\) 3.88182 0.205736
\(357\) −2.33592 −0.123630
\(358\) −1.65368 −0.0873996
\(359\) −31.5311 −1.66415 −0.832073 0.554666i \(-0.812846\pi\)
−0.832073 + 0.554666i \(0.812846\pi\)
\(360\) −5.90722 −0.311338
\(361\) −5.22317 −0.274904
\(362\) −8.36335 −0.439568
\(363\) −39.4142 −2.06871
\(364\) −0.694283 −0.0363903
\(365\) 29.3364 1.53554
\(366\) −34.8943 −1.82395
\(367\) −17.7182 −0.924884 −0.462442 0.886650i \(-0.653027\pi\)
−0.462442 + 0.886650i \(0.653027\pi\)
\(368\) −1.07783 −0.0561857
\(369\) −1.47865 −0.0769757
\(370\) 3.64765 0.189632
\(371\) 3.09170 0.160513
\(372\) 3.66546 0.190045
\(373\) −26.0262 −1.34759 −0.673794 0.738920i \(-0.735336\pi\)
−0.673794 + 0.738920i \(0.735336\pi\)
\(374\) −6.31139 −0.326354
\(375\) −23.0926 −1.19250
\(376\) 4.85052 0.250146
\(377\) −7.20498 −0.371075
\(378\) 1.12232 0.0577262
\(379\) −0.634769 −0.0326059 −0.0163029 0.999867i \(-0.505190\pi\)
−0.0163029 + 0.999867i \(0.505190\pi\)
\(380\) −9.03746 −0.463612
\(381\) 1.40676 0.0720706
\(382\) −9.06744 −0.463931
\(383\) 8.55509 0.437145 0.218572 0.975821i \(-0.429860\pi\)
0.218572 + 0.975821i \(0.429860\pi\)
\(384\) −2.32940 −0.118872
\(385\) 10.8014 0.550491
\(386\) −4.66340 −0.237361
\(387\) −5.95821 −0.302873
\(388\) −8.04003 −0.408171
\(389\) 7.48402 0.379455 0.189728 0.981837i \(-0.439240\pi\)
0.189728 + 0.981837i \(0.439240\pi\)
\(390\) −4.69034 −0.237504
\(391\) −1.28740 −0.0651068
\(392\) −6.29515 −0.317953
\(393\) 31.8220 1.60521
\(394\) −13.6852 −0.689452
\(395\) −27.5039 −1.38387
\(396\) −12.8195 −0.644205
\(397\) −0.224964 −0.0112906 −0.00564532 0.999984i \(-0.501797\pi\)
−0.00564532 + 0.999984i \(0.501797\pi\)
\(398\) −12.0896 −0.605996
\(399\) −7.25885 −0.363397
\(400\) 0.928478 0.0464239
\(401\) 11.8662 0.592569 0.296284 0.955100i \(-0.404252\pi\)
0.296284 + 0.955100i \(0.404252\pi\)
\(402\) 14.1472 0.705598
\(403\) 1.30128 0.0648215
\(404\) −12.2146 −0.607699
\(405\) 25.3037 1.25735
\(406\) 7.31465 0.363020
\(407\) 7.91592 0.392377
\(408\) −2.78234 −0.137746
\(409\) −1.66699 −0.0824275 −0.0412137 0.999150i \(-0.513122\pi\)
−0.0412137 + 0.999150i \(0.513122\pi\)
\(410\) 1.48398 0.0732884
\(411\) 13.8245 0.681911
\(412\) −1.71547 −0.0845150
\(413\) 2.35951 0.116104
\(414\) −2.61493 −0.128517
\(415\) 4.00703 0.196697
\(416\) −0.826967 −0.0405454
\(417\) 4.23900 0.207585
\(418\) −19.6126 −0.959283
\(419\) −12.6731 −0.619122 −0.309561 0.950880i \(-0.600182\pi\)
−0.309561 + 0.950880i \(0.600182\pi\)
\(420\) 4.76173 0.232349
\(421\) −25.5422 −1.24485 −0.622426 0.782679i \(-0.713853\pi\)
−0.622426 + 0.782679i \(0.713853\pi\)
\(422\) −6.42797 −0.312909
\(423\) 11.7679 0.572175
\(424\) 3.68255 0.178841
\(425\) 1.10901 0.0537951
\(426\) −24.6484 −1.19422
\(427\) 12.5765 0.608618
\(428\) 17.9762 0.868911
\(429\) −10.1787 −0.491433
\(430\) 5.97966 0.288365
\(431\) 30.7220 1.47982 0.739912 0.672703i \(-0.234867\pi\)
0.739912 + 0.672703i \(0.234867\pi\)
\(432\) 1.33681 0.0643174
\(433\) 2.16933 0.104252 0.0521258 0.998641i \(-0.483400\pi\)
0.0521258 + 0.998641i \(0.483400\pi\)
\(434\) −1.32109 −0.0634143
\(435\) 49.4152 2.36928
\(436\) −1.80745 −0.0865610
\(437\) −4.00059 −0.191374
\(438\) 28.0660 1.34104
\(439\) 11.2301 0.535984 0.267992 0.963421i \(-0.413640\pi\)
0.267992 + 0.963421i \(0.413640\pi\)
\(440\) 12.8657 0.613346
\(441\) −15.2728 −0.727274
\(442\) −0.987764 −0.0469831
\(443\) −15.0579 −0.715423 −0.357711 0.933832i \(-0.616443\pi\)
−0.357711 + 0.933832i \(0.616443\pi\)
\(444\) 3.48968 0.165613
\(445\) −9.45164 −0.448051
\(446\) 24.1728 1.14461
\(447\) −30.2905 −1.43269
\(448\) 0.839554 0.0396652
\(449\) −4.70643 −0.222110 −0.111055 0.993814i \(-0.535423\pi\)
−0.111055 + 0.993814i \(0.535423\pi\)
\(450\) 2.25259 0.106188
\(451\) 3.22044 0.151645
\(452\) −10.3727 −0.487892
\(453\) 21.9227 1.03002
\(454\) −17.2841 −0.811183
\(455\) 1.69047 0.0792506
\(456\) −8.64608 −0.404890
\(457\) −33.9258 −1.58698 −0.793491 0.608582i \(-0.791739\pi\)
−0.793491 + 0.608582i \(0.791739\pi\)
\(458\) 29.0334 1.35664
\(459\) 1.59674 0.0745296
\(460\) 2.62435 0.122361
\(461\) −14.5339 −0.676909 −0.338455 0.940983i \(-0.609904\pi\)
−0.338455 + 0.940983i \(0.609904\pi\)
\(462\) 10.3336 0.480764
\(463\) 17.3313 0.805453 0.402726 0.915320i \(-0.368063\pi\)
0.402726 + 0.915320i \(0.368063\pi\)
\(464\) 8.71254 0.404470
\(465\) −8.92483 −0.413879
\(466\) 9.67858 0.448351
\(467\) 6.04447 0.279705 0.139852 0.990172i \(-0.455337\pi\)
0.139852 + 0.990172i \(0.455337\pi\)
\(468\) −2.00632 −0.0927420
\(469\) −5.09888 −0.235444
\(470\) −11.8103 −0.544767
\(471\) 16.4038 0.755847
\(472\) 2.81044 0.129361
\(473\) 12.9767 0.596670
\(474\) −26.3128 −1.20859
\(475\) 3.44625 0.158125
\(476\) 1.00280 0.0459632
\(477\) 8.93429 0.409073
\(478\) −22.7208 −1.03922
\(479\) 32.2044 1.47146 0.735728 0.677277i \(-0.236840\pi\)
0.735728 + 0.677277i \(0.236840\pi\)
\(480\) 5.67174 0.258878
\(481\) 1.23888 0.0564880
\(482\) −28.6211 −1.30366
\(483\) 2.10786 0.0959111
\(484\) 16.9203 0.769105
\(485\) 19.5762 0.888912
\(486\) 20.1974 0.916175
\(487\) −31.7527 −1.43885 −0.719426 0.694569i \(-0.755595\pi\)
−0.719426 + 0.694569i \(0.755595\pi\)
\(488\) 14.9799 0.678110
\(489\) −16.0115 −0.724065
\(490\) 15.3277 0.692436
\(491\) −23.6489 −1.06726 −0.533629 0.845718i \(-0.679172\pi\)
−0.533629 + 0.845718i \(0.679172\pi\)
\(492\) 1.41971 0.0640055
\(493\) 10.4066 0.468691
\(494\) −3.06947 −0.138102
\(495\) 31.2135 1.40294
\(496\) −1.57356 −0.0706550
\(497\) 8.88367 0.398487
\(498\) 3.83350 0.171783
\(499\) −24.6965 −1.10557 −0.552783 0.833325i \(-0.686434\pi\)
−0.552783 + 0.833325i \(0.686434\pi\)
\(500\) 9.91353 0.443347
\(501\) 12.1777 0.544057
\(502\) 9.58402 0.427756
\(503\) −6.93249 −0.309105 −0.154552 0.987985i \(-0.549393\pi\)
−0.154552 + 0.987985i \(0.549393\pi\)
\(504\) 2.03685 0.0907287
\(505\) 29.7407 1.32344
\(506\) 5.69521 0.253183
\(507\) 28.6892 1.27413
\(508\) −0.603915 −0.0267944
\(509\) −15.2412 −0.675556 −0.337778 0.941226i \(-0.609675\pi\)
−0.337778 + 0.941226i \(0.609675\pi\)
\(510\) 6.77456 0.299983
\(511\) −10.1154 −0.447480
\(512\) 1.00000 0.0441942
\(513\) 4.96186 0.219072
\(514\) −29.3218 −1.29333
\(515\) 4.17690 0.184056
\(516\) 5.72070 0.251840
\(517\) −25.6300 −1.12720
\(518\) −1.25774 −0.0552618
\(519\) −26.6578 −1.17015
\(520\) 2.01354 0.0882994
\(521\) 20.9887 0.919532 0.459766 0.888040i \(-0.347933\pi\)
0.459766 + 0.888040i \(0.347933\pi\)
\(522\) 21.1376 0.925168
\(523\) −11.2784 −0.493170 −0.246585 0.969121i \(-0.579308\pi\)
−0.246585 + 0.969121i \(0.579308\pi\)
\(524\) −13.6610 −0.596784
\(525\) −1.81579 −0.0792474
\(526\) −6.18250 −0.269570
\(527\) −1.87953 −0.0818736
\(528\) 12.3085 0.535658
\(529\) −21.8383 −0.949491
\(530\) −8.96645 −0.389478
\(531\) 6.81844 0.295895
\(532\) 3.11618 0.135104
\(533\) 0.504015 0.0218313
\(534\) −9.04232 −0.391300
\(535\) −43.7692 −1.89231
\(536\) −6.07332 −0.262327
\(537\) 3.85208 0.166230
\(538\) 5.97166 0.257457
\(539\) 33.2634 1.43275
\(540\) −3.25493 −0.140070
\(541\) −40.0672 −1.72263 −0.861313 0.508075i \(-0.830357\pi\)
−0.861313 + 0.508075i \(0.830357\pi\)
\(542\) 15.4945 0.665545
\(543\) 19.4816 0.836036
\(544\) 1.19444 0.0512113
\(545\) 4.40085 0.188512
\(546\) 1.61726 0.0692125
\(547\) 19.0009 0.812420 0.406210 0.913780i \(-0.366850\pi\)
0.406210 + 0.913780i \(0.366850\pi\)
\(548\) −5.93477 −0.253521
\(549\) 36.3430 1.55108
\(550\) −4.90605 −0.209195
\(551\) 32.3385 1.37767
\(552\) 2.51070 0.106862
\(553\) 9.48356 0.403282
\(554\) 17.7529 0.754248
\(555\) −8.49683 −0.360671
\(556\) −1.81978 −0.0771759
\(557\) −8.37592 −0.354899 −0.177450 0.984130i \(-0.556785\pi\)
−0.177450 + 0.984130i \(0.556785\pi\)
\(558\) −3.81764 −0.161614
\(559\) 2.03092 0.0858988
\(560\) −2.04418 −0.0863826
\(561\) 14.7018 0.620709
\(562\) −10.3974 −0.438589
\(563\) −29.2806 −1.23403 −0.617015 0.786952i \(-0.711658\pi\)
−0.617015 + 0.786952i \(0.711658\pi\)
\(564\) −11.2988 −0.475765
\(565\) 25.2560 1.06253
\(566\) 6.89539 0.289835
\(567\) −8.72491 −0.366412
\(568\) 10.5814 0.443986
\(569\) −35.7409 −1.49834 −0.749168 0.662380i \(-0.769546\pi\)
−0.749168 + 0.662380i \(0.769546\pi\)
\(570\) 21.0519 0.881766
\(571\) 39.1562 1.63864 0.819319 0.573338i \(-0.194352\pi\)
0.819319 + 0.573338i \(0.194352\pi\)
\(572\) 4.36967 0.182705
\(573\) 21.1217 0.882372
\(574\) −0.511687 −0.0213574
\(575\) −1.00074 −0.0417337
\(576\) 2.42611 0.101088
\(577\) 19.5386 0.813402 0.406701 0.913561i \(-0.366679\pi\)
0.406701 + 0.913561i \(0.366679\pi\)
\(578\) −15.5733 −0.647764
\(579\) 10.8629 0.451448
\(580\) −21.2137 −0.880851
\(581\) −1.38165 −0.0573206
\(582\) 18.7285 0.776320
\(583\) −19.4585 −0.805889
\(584\) −12.0486 −0.498574
\(585\) 4.88507 0.201973
\(586\) 8.75954 0.361853
\(587\) 6.93614 0.286285 0.143143 0.989702i \(-0.454279\pi\)
0.143143 + 0.989702i \(0.454279\pi\)
\(588\) 14.6639 0.604730
\(589\) −5.84061 −0.240658
\(590\) −6.84298 −0.281721
\(591\) 31.8784 1.31130
\(592\) −1.49810 −0.0615716
\(593\) 34.9109 1.43362 0.716810 0.697268i \(-0.245601\pi\)
0.716810 + 0.697268i \(0.245601\pi\)
\(594\) −7.06367 −0.289826
\(595\) −2.44166 −0.100098
\(596\) 13.0036 0.532646
\(597\) 28.1615 1.15257
\(598\) 0.891328 0.0364491
\(599\) −6.07663 −0.248284 −0.124142 0.992264i \(-0.539618\pi\)
−0.124142 + 0.992264i \(0.539618\pi\)
\(600\) −2.16280 −0.0882959
\(601\) −10.3947 −0.424010 −0.212005 0.977269i \(-0.567999\pi\)
−0.212005 + 0.977269i \(0.567999\pi\)
\(602\) −2.06183 −0.0840340
\(603\) −14.7346 −0.600038
\(604\) −9.41130 −0.382940
\(605\) −41.1984 −1.67495
\(606\) 28.4527 1.15581
\(607\) −33.3950 −1.35546 −0.677731 0.735310i \(-0.737037\pi\)
−0.677731 + 0.735310i \(0.737037\pi\)
\(608\) 3.71172 0.150530
\(609\) −17.0388 −0.690445
\(610\) −36.4739 −1.47678
\(611\) −4.01121 −0.162276
\(612\) 2.89785 0.117139
\(613\) 8.51003 0.343717 0.171859 0.985122i \(-0.445023\pi\)
0.171859 + 0.985122i \(0.445023\pi\)
\(614\) −2.88547 −0.116448
\(615\) −3.45678 −0.139391
\(616\) −4.43618 −0.178739
\(617\) 5.27523 0.212373 0.106186 0.994346i \(-0.466136\pi\)
0.106186 + 0.994346i \(0.466136\pi\)
\(618\) 3.99601 0.160743
\(619\) −18.7411 −0.753267 −0.376634 0.926362i \(-0.622918\pi\)
−0.376634 + 0.926362i \(0.622918\pi\)
\(620\) 3.83138 0.153872
\(621\) −1.44085 −0.0578194
\(622\) 31.2564 1.25327
\(623\) 3.25900 0.130569
\(624\) 1.92634 0.0771152
\(625\) −28.7803 −1.15121
\(626\) −29.2113 −1.16752
\(627\) 45.6856 1.82451
\(628\) −7.04207 −0.281009
\(629\) −1.78940 −0.0713479
\(630\) −4.95943 −0.197588
\(631\) −9.07510 −0.361274 −0.180637 0.983550i \(-0.557816\pi\)
−0.180637 + 0.983550i \(0.557816\pi\)
\(632\) 11.2960 0.449329
\(633\) 14.9733 0.595137
\(634\) 19.4126 0.770972
\(635\) 1.47044 0.0583527
\(636\) −8.57815 −0.340146
\(637\) 5.20588 0.206264
\(638\) −46.0368 −1.82261
\(639\) 25.6717 1.01556
\(640\) −2.43485 −0.0962458
\(641\) −38.7985 −1.53245 −0.766225 0.642573i \(-0.777867\pi\)
−0.766225 + 0.642573i \(0.777867\pi\)
\(642\) −41.8737 −1.65262
\(643\) −45.6826 −1.80154 −0.900772 0.434291i \(-0.856999\pi\)
−0.900772 + 0.434291i \(0.856999\pi\)
\(644\) −0.904895 −0.0356578
\(645\) −13.9290 −0.548455
\(646\) 4.43343 0.174431
\(647\) −7.20417 −0.283225 −0.141613 0.989922i \(-0.545229\pi\)
−0.141613 + 0.989922i \(0.545229\pi\)
\(648\) −10.3923 −0.408249
\(649\) −14.8503 −0.582924
\(650\) −0.767821 −0.0301164
\(651\) 3.07735 0.120611
\(652\) 6.87365 0.269193
\(653\) −7.03589 −0.275336 −0.137668 0.990478i \(-0.543961\pi\)
−0.137668 + 0.990478i \(0.543961\pi\)
\(654\) 4.21027 0.164635
\(655\) 33.2625 1.29967
\(656\) −0.609475 −0.0237960
\(657\) −29.2312 −1.14042
\(658\) 4.07227 0.158754
\(659\) 21.4415 0.835243 0.417621 0.908621i \(-0.362864\pi\)
0.417621 + 0.908621i \(0.362864\pi\)
\(660\) −29.9693 −1.16655
\(661\) 48.3581 1.88091 0.940456 0.339915i \(-0.110398\pi\)
0.940456 + 0.339915i \(0.110398\pi\)
\(662\) −8.75448 −0.340252
\(663\) 2.30090 0.0893595
\(664\) −1.64570 −0.0638655
\(665\) −7.58743 −0.294228
\(666\) −3.63456 −0.140836
\(667\) −9.39062 −0.363606
\(668\) −5.22780 −0.202270
\(669\) −56.3081 −2.17700
\(670\) 14.7876 0.571295
\(671\) −79.1535 −3.05569
\(672\) −1.95566 −0.0754412
\(673\) 20.5451 0.791956 0.395978 0.918260i \(-0.370406\pi\)
0.395978 + 0.918260i \(0.370406\pi\)
\(674\) −24.9438 −0.960800
\(675\) 1.24120 0.0477738
\(676\) −12.3161 −0.473697
\(677\) 30.6479 1.17789 0.588947 0.808172i \(-0.299543\pi\)
0.588947 + 0.808172i \(0.299543\pi\)
\(678\) 24.1623 0.927947
\(679\) −6.75004 −0.259043
\(680\) −2.90828 −0.111528
\(681\) 40.2616 1.54283
\(682\) 8.31465 0.318384
\(683\) 20.5442 0.786102 0.393051 0.919517i \(-0.371420\pi\)
0.393051 + 0.919517i \(0.371420\pi\)
\(684\) 9.00504 0.344316
\(685\) 14.4503 0.552116
\(686\) −11.1620 −0.426167
\(687\) −67.6305 −2.58026
\(688\) −2.45587 −0.0936291
\(689\) −3.04535 −0.116019
\(690\) −6.11316 −0.232724
\(691\) 9.15226 0.348168 0.174084 0.984731i \(-0.444304\pi\)
0.174084 + 0.984731i \(0.444304\pi\)
\(692\) 11.4441 0.435038
\(693\) −10.7627 −0.408840
\(694\) −29.1632 −1.10702
\(695\) 4.43089 0.168073
\(696\) −20.2950 −0.769280
\(697\) −0.727982 −0.0275743
\(698\) 0.661633 0.0250432
\(699\) −22.5453 −0.852742
\(700\) 0.779508 0.0294626
\(701\) −43.0248 −1.62502 −0.812512 0.582945i \(-0.801900\pi\)
−0.812512 + 0.582945i \(0.801900\pi\)
\(702\) −1.10550 −0.0417243
\(703\) −5.56052 −0.209719
\(704\) −5.28397 −0.199147
\(705\) 27.5108 1.03612
\(706\) 21.1964 0.797738
\(707\) −10.2548 −0.385672
\(708\) −6.54664 −0.246038
\(709\) −36.0122 −1.35247 −0.676233 0.736688i \(-0.736389\pi\)
−0.676233 + 0.736688i \(0.736389\pi\)
\(710\) −25.7641 −0.966910
\(711\) 27.4053 1.02778
\(712\) 3.88182 0.145477
\(713\) 1.69603 0.0635168
\(714\) −2.33592 −0.0874196
\(715\) −10.6395 −0.397893
\(716\) −1.65368 −0.0618009
\(717\) 52.9258 1.97655
\(718\) −31.5311 −1.17673
\(719\) −46.1319 −1.72043 −0.860214 0.509932i \(-0.829670\pi\)
−0.860214 + 0.509932i \(0.829670\pi\)
\(720\) −5.90722 −0.220149
\(721\) −1.44023 −0.0536369
\(722\) −5.22317 −0.194386
\(723\) 66.6701 2.47949
\(724\) −8.36335 −0.310821
\(725\) 8.08941 0.300433
\(726\) −39.4142 −1.46280
\(727\) 17.3359 0.642953 0.321476 0.946918i \(-0.395821\pi\)
0.321476 + 0.946918i \(0.395821\pi\)
\(728\) −0.694283 −0.0257318
\(729\) −15.8710 −0.587816
\(730\) 29.3364 1.08579
\(731\) −2.93339 −0.108495
\(732\) −34.8943 −1.28973
\(733\) −7.93149 −0.292956 −0.146478 0.989214i \(-0.546794\pi\)
−0.146478 + 0.989214i \(0.546794\pi\)
\(734\) −17.7182 −0.653992
\(735\) −35.7044 −1.31698
\(736\) −1.07783 −0.0397293
\(737\) 32.0912 1.18209
\(738\) −1.47865 −0.0544300
\(739\) −3.96053 −0.145691 −0.0728453 0.997343i \(-0.523208\pi\)
−0.0728453 + 0.997343i \(0.523208\pi\)
\(740\) 3.64765 0.134090
\(741\) 7.15002 0.262662
\(742\) 3.09170 0.113500
\(743\) −8.63437 −0.316764 −0.158382 0.987378i \(-0.550628\pi\)
−0.158382 + 0.987378i \(0.550628\pi\)
\(744\) 3.66546 0.134382
\(745\) −31.6617 −1.15999
\(746\) −26.0262 −0.952888
\(747\) −3.99265 −0.146084
\(748\) −6.31139 −0.230767
\(749\) 15.0920 0.551448
\(750\) −23.0926 −0.843223
\(751\) 12.2092 0.445519 0.222759 0.974873i \(-0.428494\pi\)
0.222759 + 0.974873i \(0.428494\pi\)
\(752\) 4.85052 0.176880
\(753\) −22.3250 −0.813569
\(754\) −7.20498 −0.262390
\(755\) 22.9151 0.833965
\(756\) 1.12232 0.0408186
\(757\) −17.9274 −0.651583 −0.325791 0.945442i \(-0.605631\pi\)
−0.325791 + 0.945442i \(0.605631\pi\)
\(758\) −0.634769 −0.0230558
\(759\) −13.2664 −0.481541
\(760\) −9.03746 −0.327823
\(761\) −27.4872 −0.996408 −0.498204 0.867060i \(-0.666007\pi\)
−0.498204 + 0.867060i \(0.666007\pi\)
\(762\) 1.40676 0.0509616
\(763\) −1.51745 −0.0549353
\(764\) −9.06744 −0.328048
\(765\) −7.05583 −0.255104
\(766\) 8.55509 0.309108
\(767\) −2.32414 −0.0839197
\(768\) −2.32940 −0.0840551
\(769\) −27.7383 −1.00027 −0.500134 0.865948i \(-0.666716\pi\)
−0.500134 + 0.865948i \(0.666716\pi\)
\(770\) 10.8014 0.389256
\(771\) 68.3024 2.45985
\(772\) −4.66340 −0.167839
\(773\) 30.2622 1.08846 0.544229 0.838937i \(-0.316822\pi\)
0.544229 + 0.838937i \(0.316822\pi\)
\(774\) −5.95821 −0.214164
\(775\) −1.46102 −0.0524813
\(776\) −8.04003 −0.288620
\(777\) 2.92977 0.105105
\(778\) 7.48402 0.268315
\(779\) −2.26220 −0.0810516
\(780\) −4.69034 −0.167941
\(781\) −55.9118 −2.00068
\(782\) −1.28740 −0.0460375
\(783\) 11.6470 0.416231
\(784\) −6.29515 −0.224827
\(785\) 17.1464 0.611980
\(786\) 31.8220 1.13505
\(787\) −0.118372 −0.00421949 −0.00210974 0.999998i \(-0.500672\pi\)
−0.00210974 + 0.999998i \(0.500672\pi\)
\(788\) −13.6852 −0.487516
\(789\) 14.4015 0.512708
\(790\) −27.5039 −0.978545
\(791\) −8.70847 −0.309638
\(792\) −12.8195 −0.455521
\(793\) −12.3879 −0.439908
\(794\) −0.224964 −0.00798369
\(795\) 20.8865 0.740767
\(796\) −12.0896 −0.428504
\(797\) 27.8852 0.987743 0.493872 0.869535i \(-0.335581\pi\)
0.493872 + 0.869535i \(0.335581\pi\)
\(798\) −7.25885 −0.256960
\(799\) 5.79366 0.204965
\(800\) 0.928478 0.0328267
\(801\) 9.41774 0.332760
\(802\) 11.8662 0.419010
\(803\) 63.6643 2.24666
\(804\) 14.1472 0.498933
\(805\) 2.20328 0.0776554
\(806\) 1.30128 0.0458358
\(807\) −13.9104 −0.489669
\(808\) −12.2146 −0.429708
\(809\) −8.48860 −0.298443 −0.149222 0.988804i \(-0.547677\pi\)
−0.149222 + 0.988804i \(0.547677\pi\)
\(810\) 25.3037 0.889081
\(811\) 37.6517 1.32213 0.661065 0.750328i \(-0.270105\pi\)
0.661065 + 0.750328i \(0.270105\pi\)
\(812\) 7.31465 0.256694
\(813\) −36.0929 −1.26583
\(814\) 7.91592 0.277453
\(815\) −16.7363 −0.586246
\(816\) −2.78234 −0.0974013
\(817\) −9.11548 −0.318910
\(818\) −1.66699 −0.0582850
\(819\) −1.68441 −0.0588580
\(820\) 1.48398 0.0518227
\(821\) 26.1360 0.912151 0.456076 0.889941i \(-0.349255\pi\)
0.456076 + 0.889941i \(0.349255\pi\)
\(822\) 13.8245 0.482184
\(823\) −16.2827 −0.567579 −0.283789 0.958887i \(-0.591592\pi\)
−0.283789 + 0.958887i \(0.591592\pi\)
\(824\) −1.71547 −0.0597611
\(825\) 11.4282 0.397878
\(826\) 2.35951 0.0820980
\(827\) 37.4397 1.30191 0.650953 0.759118i \(-0.274370\pi\)
0.650953 + 0.759118i \(0.274370\pi\)
\(828\) −2.61493 −0.0908752
\(829\) −17.3493 −0.602566 −0.301283 0.953535i \(-0.597415\pi\)
−0.301283 + 0.953535i \(0.597415\pi\)
\(830\) 4.00703 0.139086
\(831\) −41.3536 −1.43454
\(832\) −0.826967 −0.0286699
\(833\) −7.51919 −0.260525
\(834\) 4.23900 0.146785
\(835\) 12.7289 0.440502
\(836\) −19.6126 −0.678315
\(837\) −2.10356 −0.0727095
\(838\) −12.6731 −0.437785
\(839\) 26.6947 0.921604 0.460802 0.887503i \(-0.347562\pi\)
0.460802 + 0.887503i \(0.347562\pi\)
\(840\) 4.76173 0.164295
\(841\) 46.9084 1.61753
\(842\) −25.5422 −0.880243
\(843\) 24.2198 0.834174
\(844\) −6.42797 −0.221260
\(845\) 29.9879 1.03161
\(846\) 11.7679 0.404589
\(847\) 14.2055 0.488107
\(848\) 3.68255 0.126459
\(849\) −16.0621 −0.551251
\(850\) 1.10901 0.0380389
\(851\) 1.61470 0.0553510
\(852\) −24.6484 −0.844439
\(853\) −56.4901 −1.93419 −0.967093 0.254424i \(-0.918114\pi\)
−0.967093 + 0.254424i \(0.918114\pi\)
\(854\) 12.5765 0.430358
\(855\) −21.9259 −0.749850
\(856\) 17.9762 0.614413
\(857\) 21.1982 0.724118 0.362059 0.932155i \(-0.382074\pi\)
0.362059 + 0.932155i \(0.382074\pi\)
\(858\) −10.1787 −0.347495
\(859\) 32.9341 1.12370 0.561849 0.827240i \(-0.310090\pi\)
0.561849 + 0.827240i \(0.310090\pi\)
\(860\) 5.97966 0.203905
\(861\) 1.19192 0.0406207
\(862\) 30.7220 1.04639
\(863\) 31.6222 1.07643 0.538217 0.842806i \(-0.319098\pi\)
0.538217 + 0.842806i \(0.319098\pi\)
\(864\) 1.33681 0.0454792
\(865\) −27.8646 −0.947424
\(866\) 2.16933 0.0737170
\(867\) 36.2765 1.23201
\(868\) −1.32109 −0.0448407
\(869\) −59.6874 −2.02476
\(870\) 49.4152 1.67533
\(871\) 5.02243 0.170179
\(872\) −1.80745 −0.0612078
\(873\) −19.5060 −0.660179
\(874\) −4.00059 −0.135322
\(875\) 8.32294 0.281367
\(876\) 28.0660 0.948262
\(877\) −13.1255 −0.443215 −0.221608 0.975136i \(-0.571130\pi\)
−0.221608 + 0.975136i \(0.571130\pi\)
\(878\) 11.2301 0.378998
\(879\) −20.4045 −0.688227
\(880\) 12.8657 0.433701
\(881\) 41.6652 1.40373 0.701867 0.712308i \(-0.252350\pi\)
0.701867 + 0.712308i \(0.252350\pi\)
\(882\) −15.2728 −0.514260
\(883\) −7.85921 −0.264483 −0.132242 0.991217i \(-0.542218\pi\)
−0.132242 + 0.991217i \(0.542218\pi\)
\(884\) −0.987764 −0.0332221
\(885\) 15.9401 0.535819
\(886\) −15.0579 −0.505880
\(887\) 26.2520 0.881456 0.440728 0.897641i \(-0.354720\pi\)
0.440728 + 0.897641i \(0.354720\pi\)
\(888\) 3.48968 0.117106
\(889\) −0.507019 −0.0170049
\(890\) −9.45164 −0.316820
\(891\) 54.9126 1.83964
\(892\) 24.1728 0.809364
\(893\) 18.0037 0.602472
\(894\) −30.2905 −1.01307
\(895\) 4.02645 0.134590
\(896\) 0.839554 0.0280475
\(897\) −2.07626 −0.0693243
\(898\) −4.70643 −0.157055
\(899\) −13.7097 −0.457245
\(900\) 2.25259 0.0750865
\(901\) 4.39860 0.146539
\(902\) 3.22044 0.107229
\(903\) 4.80284 0.159828
\(904\) −10.3727 −0.344992
\(905\) 20.3635 0.676905
\(906\) 21.9227 0.728333
\(907\) 47.7509 1.58554 0.792772 0.609519i \(-0.208637\pi\)
0.792772 + 0.609519i \(0.208637\pi\)
\(908\) −17.2841 −0.573593
\(909\) −29.6340 −0.982898
\(910\) 1.69047 0.0560386
\(911\) −8.59572 −0.284789 −0.142395 0.989810i \(-0.545480\pi\)
−0.142395 + 0.989810i \(0.545480\pi\)
\(912\) −8.64608 −0.286300
\(913\) 8.69582 0.287790
\(914\) −33.9258 −1.12217
\(915\) 84.9623 2.80877
\(916\) 29.0334 0.959291
\(917\) −11.4692 −0.378745
\(918\) 1.59674 0.0527004
\(919\) 35.2148 1.16163 0.580815 0.814036i \(-0.302734\pi\)
0.580815 + 0.814036i \(0.302734\pi\)
\(920\) 2.62435 0.0865221
\(921\) 6.72142 0.221478
\(922\) −14.5339 −0.478647
\(923\) −8.75048 −0.288025
\(924\) 10.3336 0.339952
\(925\) −1.39095 −0.0457343
\(926\) 17.3313 0.569541
\(927\) −4.16192 −0.136695
\(928\) 8.71254 0.286003
\(929\) 55.6573 1.82606 0.913029 0.407894i \(-0.133737\pi\)
0.913029 + 0.407894i \(0.133737\pi\)
\(930\) −8.92483 −0.292657
\(931\) −23.3658 −0.765783
\(932\) 9.67858 0.317032
\(933\) −72.8088 −2.38365
\(934\) 6.04447 0.197781
\(935\) 15.3673 0.502564
\(936\) −2.00632 −0.0655785
\(937\) −10.4278 −0.340661 −0.170331 0.985387i \(-0.554484\pi\)
−0.170331 + 0.985387i \(0.554484\pi\)
\(938\) −5.09888 −0.166484
\(939\) 68.0447 2.22056
\(940\) −11.8103 −0.385208
\(941\) −0.429183 −0.0139910 −0.00699548 0.999976i \(-0.502227\pi\)
−0.00699548 + 0.999976i \(0.502227\pi\)
\(942\) 16.4038 0.534465
\(943\) 0.656909 0.0213919
\(944\) 2.81044 0.0914719
\(945\) −2.73269 −0.0888944
\(946\) 12.9767 0.421910
\(947\) −24.9345 −0.810263 −0.405132 0.914258i \(-0.632774\pi\)
−0.405132 + 0.914258i \(0.632774\pi\)
\(948\) −26.3128 −0.854600
\(949\) 9.96377 0.323438
\(950\) 3.44625 0.111811
\(951\) −45.2197 −1.46635
\(952\) 1.00280 0.0325009
\(953\) −9.58228 −0.310400 −0.155200 0.987883i \(-0.549602\pi\)
−0.155200 + 0.987883i \(0.549602\pi\)
\(954\) 8.93429 0.289258
\(955\) 22.0778 0.714422
\(956\) −22.7208 −0.734842
\(957\) 107.238 3.46652
\(958\) 32.2044 1.04048
\(959\) −4.98256 −0.160895
\(960\) 5.67174 0.183055
\(961\) −28.5239 −0.920126
\(962\) 1.23888 0.0399431
\(963\) 43.6122 1.40538
\(964\) −28.6211 −0.921824
\(965\) 11.3547 0.365520
\(966\) 2.10786 0.0678194
\(967\) −10.6500 −0.342482 −0.171241 0.985229i \(-0.554778\pi\)
−0.171241 + 0.985229i \(0.554778\pi\)
\(968\) 16.9203 0.543840
\(969\) −10.3272 −0.331759
\(970\) 19.5762 0.628555
\(971\) −26.7795 −0.859394 −0.429697 0.902973i \(-0.641380\pi\)
−0.429697 + 0.902973i \(0.641380\pi\)
\(972\) 20.1974 0.647833
\(973\) −1.52780 −0.0489791
\(974\) −31.7527 −1.01742
\(975\) 1.78856 0.0572799
\(976\) 14.9799 0.479496
\(977\) −13.8623 −0.443495 −0.221748 0.975104i \(-0.571176\pi\)
−0.221748 + 0.975104i \(0.571176\pi\)
\(978\) −16.0115 −0.511991
\(979\) −20.5114 −0.655548
\(980\) 15.3277 0.489626
\(981\) −4.38507 −0.140004
\(982\) −23.6489 −0.754666
\(983\) 39.6329 1.26409 0.632046 0.774931i \(-0.282215\pi\)
0.632046 + 0.774931i \(0.282215\pi\)
\(984\) 1.41971 0.0452587
\(985\) 33.3214 1.06171
\(986\) 10.4066 0.331414
\(987\) −9.48595 −0.301941
\(988\) −3.06947 −0.0976527
\(989\) 2.64700 0.0841698
\(990\) 31.2135 0.992031
\(991\) 40.3000 1.28017 0.640086 0.768303i \(-0.278899\pi\)
0.640086 + 0.768303i \(0.278899\pi\)
\(992\) −1.57356 −0.0499606
\(993\) 20.3927 0.647143
\(994\) 8.88367 0.281773
\(995\) 29.4363 0.933192
\(996\) 3.83350 0.121469
\(997\) −14.8039 −0.468844 −0.234422 0.972135i \(-0.575320\pi\)
−0.234422 + 0.972135i \(0.575320\pi\)
\(998\) −24.6965 −0.781753
\(999\) −2.00268 −0.0633619
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 \(a_p\))