Properties

Label 6017.2.a.c.1.4
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70820 q^{2}\) \(+2.96568 q^{3}\) \(+5.33437 q^{4}\) \(-1.26109 q^{5}\) \(-8.03167 q^{6}\) \(+1.85077 q^{7}\) \(-9.03015 q^{8}\) \(+5.79526 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70820 q^{2}\) \(+2.96568 q^{3}\) \(+5.33437 q^{4}\) \(-1.26109 q^{5}\) \(-8.03167 q^{6}\) \(+1.85077 q^{7}\) \(-9.03015 q^{8}\) \(+5.79526 q^{9}\) \(+3.41529 q^{10}\) \(+1.00000 q^{11}\) \(+15.8200 q^{12}\) \(-5.34816 q^{13}\) \(-5.01227 q^{14}\) \(-3.73999 q^{15}\) \(+13.7868 q^{16}\) \(+3.21050 q^{17}\) \(-15.6947 q^{18}\) \(-7.60704 q^{19}\) \(-6.72713 q^{20}\) \(+5.48880 q^{21}\) \(-2.70820 q^{22}\) \(-3.07950 q^{23}\) \(-26.7805 q^{24}\) \(-3.40965 q^{25}\) \(+14.4839 q^{26}\) \(+8.28984 q^{27}\) \(+9.87270 q^{28}\) \(-0.603421 q^{29}\) \(+10.1287 q^{30}\) \(+3.99164 q^{31}\) \(-19.2770 q^{32}\) \(+2.96568 q^{33}\) \(-8.69469 q^{34}\) \(-2.33399 q^{35}\) \(+30.9140 q^{36}\) \(-0.667363 q^{37}\) \(+20.6014 q^{38}\) \(-15.8609 q^{39}\) \(+11.3878 q^{40}\) \(+0.907812 q^{41}\) \(-14.8648 q^{42}\) \(-7.50474 q^{43}\) \(+5.33437 q^{44}\) \(-7.30835 q^{45}\) \(+8.33991 q^{46}\) \(+2.39940 q^{47}\) \(+40.8871 q^{48}\) \(-3.57465 q^{49}\) \(+9.23402 q^{50}\) \(+9.52132 q^{51}\) \(-28.5291 q^{52}\) \(+11.9695 q^{53}\) \(-22.4506 q^{54}\) \(-1.26109 q^{55}\) \(-16.7127 q^{56}\) \(-22.5600 q^{57}\) \(+1.63419 q^{58}\) \(+2.90667 q^{59}\) \(-19.9505 q^{60}\) \(+0.749237 q^{61}\) \(-10.8102 q^{62}\) \(+10.7257 q^{63}\) \(+24.6326 q^{64}\) \(+6.74452 q^{65}\) \(-8.03167 q^{66}\) \(-6.13031 q^{67}\) \(+17.1260 q^{68}\) \(-9.13281 q^{69}\) \(+6.32093 q^{70}\) \(-11.1018 q^{71}\) \(-52.3321 q^{72}\) \(+2.46272 q^{73}\) \(+1.80736 q^{74}\) \(-10.1119 q^{75}\) \(-40.5787 q^{76}\) \(+1.85077 q^{77}\) \(+42.9547 q^{78}\) \(-11.2992 q^{79}\) \(-17.3864 q^{80}\) \(+7.19924 q^{81}\) \(-2.45854 q^{82}\) \(-7.98386 q^{83}\) \(+29.2793 q^{84}\) \(-4.04874 q^{85}\) \(+20.3244 q^{86}\) \(-1.78955 q^{87}\) \(-9.03015 q^{88}\) \(+3.27238 q^{89}\) \(+19.7925 q^{90}\) \(-9.89823 q^{91}\) \(-16.4272 q^{92}\) \(+11.8379 q^{93}\) \(-6.49807 q^{94}\) \(+9.59317 q^{95}\) \(-57.1695 q^{96}\) \(-4.16250 q^{97}\) \(+9.68087 q^{98}\) \(+5.79526 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70820 −1.91499 −0.957495 0.288451i \(-0.906860\pi\)
−0.957495 + 0.288451i \(0.906860\pi\)
\(3\) 2.96568 1.71224 0.856118 0.516780i \(-0.172870\pi\)
0.856118 + 0.516780i \(0.172870\pi\)
\(4\) 5.33437 2.66718
\(5\) −1.26109 −0.563977 −0.281989 0.959418i \(-0.590994\pi\)
−0.281989 + 0.959418i \(0.590994\pi\)
\(6\) −8.03167 −3.27891
\(7\) 1.85077 0.699526 0.349763 0.936838i \(-0.386262\pi\)
0.349763 + 0.936838i \(0.386262\pi\)
\(8\) −9.03015 −3.19264
\(9\) 5.79526 1.93175
\(10\) 3.41529 1.08001
\(11\) 1.00000 0.301511
\(12\) 15.8200 4.56685
\(13\) −5.34816 −1.48331 −0.741657 0.670780i \(-0.765960\pi\)
−0.741657 + 0.670780i \(0.765960\pi\)
\(14\) −5.01227 −1.33958
\(15\) −3.73999 −0.965662
\(16\) 13.7868 3.44669
\(17\) 3.21050 0.778661 0.389330 0.921098i \(-0.372706\pi\)
0.389330 + 0.921098i \(0.372706\pi\)
\(18\) −15.6947 −3.69929
\(19\) −7.60704 −1.74517 −0.872587 0.488459i \(-0.837559\pi\)
−0.872587 + 0.488459i \(0.837559\pi\)
\(20\) −6.72713 −1.50423
\(21\) 5.48880 1.19775
\(22\) −2.70820 −0.577391
\(23\) −3.07950 −0.642120 −0.321060 0.947059i \(-0.604039\pi\)
−0.321060 + 0.947059i \(0.604039\pi\)
\(24\) −26.7805 −5.46655
\(25\) −3.40965 −0.681930
\(26\) 14.4839 2.84053
\(27\) 8.28984 1.59538
\(28\) 9.87270 1.86576
\(29\) −0.603421 −0.112053 −0.0560263 0.998429i \(-0.517843\pi\)
−0.0560263 + 0.998429i \(0.517843\pi\)
\(30\) 10.1287 1.84923
\(31\) 3.99164 0.716920 0.358460 0.933545i \(-0.383302\pi\)
0.358460 + 0.933545i \(0.383302\pi\)
\(32\) −19.2770 −3.40773
\(33\) 2.96568 0.516259
\(34\) −8.69469 −1.49113
\(35\) −2.33399 −0.394517
\(36\) 30.9140 5.15234
\(37\) −0.667363 −0.109714 −0.0548569 0.998494i \(-0.517470\pi\)
−0.0548569 + 0.998494i \(0.517470\pi\)
\(38\) 20.6014 3.34199
\(39\) −15.8609 −2.53978
\(40\) 11.3878 1.80058
\(41\) 0.907812 0.141776 0.0708882 0.997484i \(-0.477417\pi\)
0.0708882 + 0.997484i \(0.477417\pi\)
\(42\) −14.8648 −2.29369
\(43\) −7.50474 −1.14446 −0.572231 0.820093i \(-0.693922\pi\)
−0.572231 + 0.820093i \(0.693922\pi\)
\(44\) 5.33437 0.804186
\(45\) −7.30835 −1.08946
\(46\) 8.33991 1.22965
\(47\) 2.39940 0.349989 0.174994 0.984569i \(-0.444009\pi\)
0.174994 + 0.984569i \(0.444009\pi\)
\(48\) 40.8871 5.90154
\(49\) −3.57465 −0.510664
\(50\) 9.23402 1.30589
\(51\) 9.52132 1.33325
\(52\) −28.5291 −3.95627
\(53\) 11.9695 1.64414 0.822070 0.569386i \(-0.192819\pi\)
0.822070 + 0.569386i \(0.192819\pi\)
\(54\) −22.4506 −3.05514
\(55\) −1.26109 −0.170046
\(56\) −16.7127 −2.23333
\(57\) −22.5600 −2.98815
\(58\) 1.63419 0.214579
\(59\) 2.90667 0.378416 0.189208 0.981937i \(-0.439408\pi\)
0.189208 + 0.981937i \(0.439408\pi\)
\(60\) −19.9505 −2.57560
\(61\) 0.749237 0.0959299 0.0479650 0.998849i \(-0.484726\pi\)
0.0479650 + 0.998849i \(0.484726\pi\)
\(62\) −10.8102 −1.37290
\(63\) 10.7257 1.35131
\(64\) 24.6326 3.07908
\(65\) 6.74452 0.836555
\(66\) −8.03167 −0.988630
\(67\) −6.13031 −0.748937 −0.374468 0.927240i \(-0.622175\pi\)
−0.374468 + 0.927240i \(0.622175\pi\)
\(68\) 17.1260 2.07683
\(69\) −9.13281 −1.09946
\(70\) 6.32093 0.755495
\(71\) −11.1018 −1.31754 −0.658770 0.752344i \(-0.728923\pi\)
−0.658770 + 0.752344i \(0.728923\pi\)
\(72\) −52.3321 −6.16739
\(73\) 2.46272 0.288239 0.144120 0.989560i \(-0.453965\pi\)
0.144120 + 0.989560i \(0.453965\pi\)
\(74\) 1.80736 0.210101
\(75\) −10.1119 −1.16762
\(76\) −40.5787 −4.65470
\(77\) 1.85077 0.210915
\(78\) 42.9547 4.86366
\(79\) −11.2992 −1.27125 −0.635627 0.771996i \(-0.719258\pi\)
−0.635627 + 0.771996i \(0.719258\pi\)
\(80\) −17.3864 −1.94385
\(81\) 7.19924 0.799916
\(82\) −2.45854 −0.271500
\(83\) −7.98386 −0.876343 −0.438171 0.898891i \(-0.644374\pi\)
−0.438171 + 0.898891i \(0.644374\pi\)
\(84\) 29.2793 3.19463
\(85\) −4.04874 −0.439147
\(86\) 20.3244 2.19163
\(87\) −1.78955 −0.191860
\(88\) −9.03015 −0.962617
\(89\) 3.27238 0.346872 0.173436 0.984845i \(-0.444513\pi\)
0.173436 + 0.984845i \(0.444513\pi\)
\(90\) 19.7925 2.08631
\(91\) −9.89823 −1.03762
\(92\) −16.4272 −1.71265
\(93\) 11.8379 1.22754
\(94\) −6.49807 −0.670225
\(95\) 9.59317 0.984239
\(96\) −57.1695 −5.83484
\(97\) −4.16250 −0.422638 −0.211319 0.977417i \(-0.567776\pi\)
−0.211319 + 0.977417i \(0.567776\pi\)
\(98\) 9.68087 0.977915
\(99\) 5.79526 0.582445
\(100\) −18.1883 −1.81883
\(101\) 5.79334 0.576459 0.288230 0.957561i \(-0.406933\pi\)
0.288230 + 0.957561i \(0.406933\pi\)
\(102\) −25.7857 −2.55316
\(103\) −9.57292 −0.943248 −0.471624 0.881800i \(-0.656332\pi\)
−0.471624 + 0.881800i \(0.656332\pi\)
\(104\) 48.2947 4.73569
\(105\) −6.92188 −0.675506
\(106\) −32.4159 −3.14851
\(107\) −14.5234 −1.40403 −0.702016 0.712161i \(-0.747716\pi\)
−0.702016 + 0.712161i \(0.747716\pi\)
\(108\) 44.2211 4.25517
\(109\) −2.66667 −0.255421 −0.127711 0.991811i \(-0.540763\pi\)
−0.127711 + 0.991811i \(0.540763\pi\)
\(110\) 3.41529 0.325635
\(111\) −1.97919 −0.187856
\(112\) 25.5161 2.41105
\(113\) 11.9363 1.12287 0.561434 0.827521i \(-0.310250\pi\)
0.561434 + 0.827521i \(0.310250\pi\)
\(114\) 61.0972 5.72227
\(115\) 3.88353 0.362141
\(116\) −3.21887 −0.298865
\(117\) −30.9940 −2.86540
\(118\) −7.87186 −0.724663
\(119\) 5.94190 0.544693
\(120\) 33.7727 3.08301
\(121\) 1.00000 0.0909091
\(122\) −2.02909 −0.183705
\(123\) 2.69228 0.242755
\(124\) 21.2929 1.91216
\(125\) 10.6053 0.948570
\(126\) −29.0474 −2.58775
\(127\) 16.0814 1.42700 0.713499 0.700657i \(-0.247109\pi\)
0.713499 + 0.700657i \(0.247109\pi\)
\(128\) −28.1561 −2.48867
\(129\) −22.2566 −1.95959
\(130\) −18.2655 −1.60199
\(131\) 14.0716 1.22944 0.614722 0.788744i \(-0.289268\pi\)
0.614722 + 0.788744i \(0.289268\pi\)
\(132\) 15.8200 1.37696
\(133\) −14.0789 −1.22079
\(134\) 16.6021 1.43421
\(135\) −10.4543 −0.899759
\(136\) −28.9913 −2.48598
\(137\) −11.9734 −1.02295 −0.511477 0.859297i \(-0.670902\pi\)
−0.511477 + 0.859297i \(0.670902\pi\)
\(138\) 24.7335 2.10546
\(139\) −1.75295 −0.148684 −0.0743418 0.997233i \(-0.523686\pi\)
−0.0743418 + 0.997233i \(0.523686\pi\)
\(140\) −12.4504 −1.05225
\(141\) 7.11586 0.599264
\(142\) 30.0659 2.52308
\(143\) −5.34816 −0.447236
\(144\) 79.8978 6.65815
\(145\) 0.760970 0.0631951
\(146\) −6.66954 −0.551975
\(147\) −10.6013 −0.874377
\(148\) −3.55996 −0.292627
\(149\) 3.31700 0.271739 0.135870 0.990727i \(-0.456617\pi\)
0.135870 + 0.990727i \(0.456617\pi\)
\(150\) 27.3852 2.23599
\(151\) −15.4234 −1.25514 −0.627570 0.778561i \(-0.715950\pi\)
−0.627570 + 0.778561i \(0.715950\pi\)
\(152\) 68.6927 5.57171
\(153\) 18.6057 1.50418
\(154\) −5.01227 −0.403900
\(155\) −5.03383 −0.404327
\(156\) −84.6081 −6.77407
\(157\) −10.9000 −0.869917 −0.434958 0.900451i \(-0.643237\pi\)
−0.434958 + 0.900451i \(0.643237\pi\)
\(158\) 30.6004 2.43444
\(159\) 35.4978 2.81516
\(160\) 24.3101 1.92188
\(161\) −5.69945 −0.449179
\(162\) −19.4970 −1.53183
\(163\) −0.449109 −0.0351769 −0.0175885 0.999845i \(-0.505599\pi\)
−0.0175885 + 0.999845i \(0.505599\pi\)
\(164\) 4.84260 0.378144
\(165\) −3.73999 −0.291158
\(166\) 21.6219 1.67819
\(167\) −21.3714 −1.65377 −0.826885 0.562371i \(-0.809889\pi\)
−0.826885 + 0.562371i \(0.809889\pi\)
\(168\) −49.5647 −3.82400
\(169\) 15.6028 1.20022
\(170\) 10.9648 0.840962
\(171\) −44.0847 −3.37124
\(172\) −40.0330 −3.05249
\(173\) 15.3758 1.16900 0.584499 0.811394i \(-0.301291\pi\)
0.584499 + 0.811394i \(0.301291\pi\)
\(174\) 4.84648 0.367411
\(175\) −6.31048 −0.477027
\(176\) 13.7868 1.03922
\(177\) 8.62026 0.647938
\(178\) −8.86229 −0.664256
\(179\) −16.8159 −1.25688 −0.628438 0.777860i \(-0.716305\pi\)
−0.628438 + 0.777860i \(0.716305\pi\)
\(180\) −38.9854 −2.90580
\(181\) −1.97496 −0.146798 −0.0733988 0.997303i \(-0.523385\pi\)
−0.0733988 + 0.997303i \(0.523385\pi\)
\(182\) 26.8064 1.98702
\(183\) 2.22200 0.164255
\(184\) 27.8083 2.05006
\(185\) 0.841606 0.0618761
\(186\) −32.0596 −2.35072
\(187\) 3.21050 0.234775
\(188\) 12.7993 0.933485
\(189\) 15.3426 1.11601
\(190\) −25.9803 −1.88481
\(191\) −14.6931 −1.06315 −0.531577 0.847010i \(-0.678400\pi\)
−0.531577 + 0.847010i \(0.678400\pi\)
\(192\) 73.0525 5.27211
\(193\) −0.662869 −0.0477143 −0.0238572 0.999715i \(-0.507595\pi\)
−0.0238572 + 0.999715i \(0.507595\pi\)
\(194\) 11.2729 0.809347
\(195\) 20.0021 1.43238
\(196\) −19.0685 −1.36203
\(197\) −16.1645 −1.15167 −0.575837 0.817564i \(-0.695324\pi\)
−0.575837 + 0.817564i \(0.695324\pi\)
\(198\) −15.6947 −1.11538
\(199\) −20.0997 −1.42483 −0.712413 0.701760i \(-0.752398\pi\)
−0.712413 + 0.701760i \(0.752398\pi\)
\(200\) 30.7896 2.17716
\(201\) −18.1805 −1.28236
\(202\) −15.6896 −1.10391
\(203\) −1.11679 −0.0783836
\(204\) 50.7902 3.55603
\(205\) −1.14483 −0.0799587
\(206\) 25.9254 1.80631
\(207\) −17.8465 −1.24042
\(208\) −73.7338 −5.11252
\(209\) −7.60704 −0.526190
\(210\) 18.7459 1.29359
\(211\) 22.3700 1.54001 0.770006 0.638036i \(-0.220253\pi\)
0.770006 + 0.638036i \(0.220253\pi\)
\(212\) 63.8498 4.38523
\(213\) −32.9244 −2.25594
\(214\) 39.3324 2.68871
\(215\) 9.46416 0.645450
\(216\) −74.8585 −5.09348
\(217\) 7.38762 0.501504
\(218\) 7.22190 0.489129
\(219\) 7.30363 0.493534
\(220\) −6.72713 −0.453543
\(221\) −17.1703 −1.15500
\(222\) 5.36004 0.359742
\(223\) −27.0966 −1.81452 −0.907262 0.420567i \(-0.861831\pi\)
−0.907262 + 0.420567i \(0.861831\pi\)
\(224\) −35.6774 −2.38380
\(225\) −19.7598 −1.31732
\(226\) −32.3258 −2.15028
\(227\) −27.6172 −1.83302 −0.916509 0.400013i \(-0.869005\pi\)
−0.916509 + 0.400013i \(0.869005\pi\)
\(228\) −120.344 −7.96995
\(229\) 10.4911 0.693269 0.346634 0.938000i \(-0.387324\pi\)
0.346634 + 0.938000i \(0.387324\pi\)
\(230\) −10.5174 −0.693496
\(231\) 5.48880 0.361136
\(232\) 5.44898 0.357743
\(233\) −18.5041 −1.21224 −0.606121 0.795372i \(-0.707275\pi\)
−0.606121 + 0.795372i \(0.707275\pi\)
\(234\) 83.9380 5.48720
\(235\) −3.02587 −0.197386
\(236\) 15.5053 1.00931
\(237\) −33.5097 −2.17669
\(238\) −16.0919 −1.04308
\(239\) −25.5943 −1.65556 −0.827779 0.561054i \(-0.810396\pi\)
−0.827779 + 0.561054i \(0.810396\pi\)
\(240\) −51.5624 −3.32834
\(241\) −12.0435 −0.775792 −0.387896 0.921703i \(-0.626798\pi\)
−0.387896 + 0.921703i \(0.626798\pi\)
\(242\) −2.70820 −0.174090
\(243\) −3.51887 −0.225736
\(244\) 3.99671 0.255863
\(245\) 4.50796 0.288003
\(246\) −7.29124 −0.464873
\(247\) 40.6837 2.58864
\(248\) −36.0451 −2.28887
\(249\) −23.6776 −1.50051
\(250\) −28.7214 −1.81650
\(251\) 18.6971 1.18015 0.590075 0.807348i \(-0.299098\pi\)
0.590075 + 0.807348i \(0.299098\pi\)
\(252\) 57.2148 3.60420
\(253\) −3.07950 −0.193606
\(254\) −43.5518 −2.73268
\(255\) −12.0073 −0.751924
\(256\) 26.9873 1.68670
\(257\) 2.23407 0.139357 0.0696786 0.997569i \(-0.477803\pi\)
0.0696786 + 0.997569i \(0.477803\pi\)
\(258\) 60.2755 3.75259
\(259\) −1.23514 −0.0767477
\(260\) 35.9778 2.23125
\(261\) −3.49698 −0.216458
\(262\) −38.1089 −2.35437
\(263\) 18.3853 1.13369 0.566843 0.823826i \(-0.308165\pi\)
0.566843 + 0.823826i \(0.308165\pi\)
\(264\) −26.7805 −1.64823
\(265\) −15.0947 −0.927258
\(266\) 38.1285 2.33781
\(267\) 9.70485 0.593927
\(268\) −32.7013 −1.99755
\(269\) 28.4063 1.73196 0.865981 0.500078i \(-0.166695\pi\)
0.865981 + 0.500078i \(0.166695\pi\)
\(270\) 28.3122 1.72303
\(271\) −10.7111 −0.650654 −0.325327 0.945602i \(-0.605474\pi\)
−0.325327 + 0.945602i \(0.605474\pi\)
\(272\) 44.2624 2.68380
\(273\) −29.3550 −1.77664
\(274\) 32.4264 1.95895
\(275\) −3.40965 −0.205609
\(276\) −48.7177 −2.93246
\(277\) −3.22663 −0.193869 −0.0969346 0.995291i \(-0.530904\pi\)
−0.0969346 + 0.995291i \(0.530904\pi\)
\(278\) 4.74736 0.284728
\(279\) 23.1326 1.38491
\(280\) 21.0763 1.25955
\(281\) 32.7063 1.95109 0.975547 0.219791i \(-0.0705376\pi\)
0.975547 + 0.219791i \(0.0705376\pi\)
\(282\) −19.2712 −1.14758
\(283\) 25.4567 1.51324 0.756622 0.653853i \(-0.226849\pi\)
0.756622 + 0.653853i \(0.226849\pi\)
\(284\) −59.2211 −3.51412
\(285\) 28.4503 1.68525
\(286\) 14.4839 0.856452
\(287\) 1.68015 0.0991763
\(288\) −111.715 −6.58289
\(289\) −6.69268 −0.393687
\(290\) −2.06086 −0.121018
\(291\) −12.3446 −0.723656
\(292\) 13.1370 0.768787
\(293\) −17.5954 −1.02794 −0.513968 0.857809i \(-0.671825\pi\)
−0.513968 + 0.857809i \(0.671825\pi\)
\(294\) 28.7104 1.67442
\(295\) −3.66558 −0.213418
\(296\) 6.02639 0.350277
\(297\) 8.28984 0.481025
\(298\) −8.98311 −0.520378
\(299\) 16.4697 0.952465
\(300\) −53.9407 −3.11427
\(301\) −13.8896 −0.800581
\(302\) 41.7697 2.40358
\(303\) 17.1812 0.987034
\(304\) −104.876 −6.01507
\(305\) −0.944856 −0.0541023
\(306\) −50.3880 −2.88049
\(307\) −18.9693 −1.08264 −0.541318 0.840818i \(-0.682074\pi\)
−0.541318 + 0.840818i \(0.682074\pi\)
\(308\) 9.87270 0.562549
\(309\) −28.3902 −1.61506
\(310\) 13.6326 0.774282
\(311\) −9.47818 −0.537458 −0.268729 0.963216i \(-0.586604\pi\)
−0.268729 + 0.963216i \(0.586604\pi\)
\(312\) 143.227 8.10861
\(313\) 24.2524 1.37083 0.685414 0.728153i \(-0.259621\pi\)
0.685414 + 0.728153i \(0.259621\pi\)
\(314\) 29.5195 1.66588
\(315\) −13.5261 −0.762109
\(316\) −60.2739 −3.39067
\(317\) 23.9063 1.34271 0.671355 0.741136i \(-0.265713\pi\)
0.671355 + 0.741136i \(0.265713\pi\)
\(318\) −96.1352 −5.39100
\(319\) −0.603421 −0.0337851
\(320\) −31.0640 −1.73653
\(321\) −43.0718 −2.40403
\(322\) 15.4353 0.860174
\(323\) −24.4224 −1.35890
\(324\) 38.4034 2.13352
\(325\) 18.2354 1.01152
\(326\) 1.21628 0.0673635
\(327\) −7.90850 −0.437341
\(328\) −8.19768 −0.452641
\(329\) 4.44075 0.244826
\(330\) 10.1287 0.557565
\(331\) 1.13048 0.0621370 0.0310685 0.999517i \(-0.490109\pi\)
0.0310685 + 0.999517i \(0.490109\pi\)
\(332\) −42.5889 −2.33737
\(333\) −3.86754 −0.211940
\(334\) 57.8782 3.16695
\(335\) 7.73089 0.422383
\(336\) 75.6727 4.12828
\(337\) 26.7203 1.45555 0.727775 0.685816i \(-0.240555\pi\)
0.727775 + 0.685816i \(0.240555\pi\)
\(338\) −42.2557 −2.29841
\(339\) 35.3991 1.92262
\(340\) −21.5975 −1.17129
\(341\) 3.99164 0.216160
\(342\) 119.390 6.45590
\(343\) −19.5713 −1.05675
\(344\) 67.7689 3.65385
\(345\) 11.5173 0.620071
\(346\) −41.6407 −2.23862
\(347\) −13.3911 −0.718871 −0.359435 0.933170i \(-0.617031\pi\)
−0.359435 + 0.933170i \(0.617031\pi\)
\(348\) −9.54614 −0.511727
\(349\) 4.38597 0.234776 0.117388 0.993086i \(-0.462548\pi\)
0.117388 + 0.993086i \(0.462548\pi\)
\(350\) 17.0901 0.913502
\(351\) −44.3354 −2.36645
\(352\) −19.2770 −1.02747
\(353\) 2.18438 0.116263 0.0581313 0.998309i \(-0.481486\pi\)
0.0581313 + 0.998309i \(0.481486\pi\)
\(354\) −23.3454 −1.24080
\(355\) 14.0004 0.743063
\(356\) 17.4561 0.925172
\(357\) 17.6218 0.932644
\(358\) 45.5408 2.40690
\(359\) 2.27025 0.119819 0.0599096 0.998204i \(-0.480919\pi\)
0.0599096 + 0.998204i \(0.480919\pi\)
\(360\) 65.9955 3.47827
\(361\) 38.8670 2.04563
\(362\) 5.34859 0.281116
\(363\) 2.96568 0.155658
\(364\) −52.8008 −2.76751
\(365\) −3.10571 −0.162560
\(366\) −6.01762 −0.314546
\(367\) −10.7058 −0.558841 −0.279420 0.960169i \(-0.590142\pi\)
−0.279420 + 0.960169i \(0.590142\pi\)
\(368\) −42.4563 −2.21319
\(369\) 5.26101 0.273877
\(370\) −2.27924 −0.118492
\(371\) 22.1529 1.15012
\(372\) 63.1479 3.27407
\(373\) −4.26136 −0.220645 −0.110322 0.993896i \(-0.535188\pi\)
−0.110322 + 0.993896i \(0.535188\pi\)
\(374\) −8.69469 −0.449592
\(375\) 31.4520 1.62418
\(376\) −21.6670 −1.11739
\(377\) 3.22720 0.166209
\(378\) −41.5509 −2.13715
\(379\) 36.3236 1.86582 0.932910 0.360110i \(-0.117261\pi\)
0.932910 + 0.360110i \(0.117261\pi\)
\(380\) 51.1735 2.62515
\(381\) 47.6924 2.44336
\(382\) 39.7919 2.03593
\(383\) −21.7319 −1.11045 −0.555224 0.831701i \(-0.687368\pi\)
−0.555224 + 0.831701i \(0.687368\pi\)
\(384\) −83.5021 −4.26120
\(385\) −2.33399 −0.118951
\(386\) 1.79518 0.0913724
\(387\) −43.4919 −2.21082
\(388\) −22.2043 −1.12725
\(389\) −11.2709 −0.571460 −0.285730 0.958310i \(-0.592236\pi\)
−0.285730 + 0.958310i \(0.592236\pi\)
\(390\) −54.1698 −2.74299
\(391\) −9.88673 −0.499993
\(392\) 32.2796 1.63037
\(393\) 41.7320 2.10510
\(394\) 43.7768 2.20544
\(395\) 14.2493 0.716959
\(396\) 30.9140 1.55349
\(397\) 10.1721 0.510522 0.255261 0.966872i \(-0.417839\pi\)
0.255261 + 0.966872i \(0.417839\pi\)
\(398\) 54.4340 2.72853
\(399\) −41.7535 −2.09029
\(400\) −47.0080 −2.35040
\(401\) 22.6399 1.13058 0.565292 0.824891i \(-0.308764\pi\)
0.565292 + 0.824891i \(0.308764\pi\)
\(402\) 49.2366 2.45570
\(403\) −21.3480 −1.06342
\(404\) 30.9038 1.53752
\(405\) −9.07891 −0.451134
\(406\) 3.02451 0.150104
\(407\) −0.667363 −0.0330800
\(408\) −85.9789 −4.25659
\(409\) −15.6624 −0.774454 −0.387227 0.921984i \(-0.626567\pi\)
−0.387227 + 0.921984i \(0.626567\pi\)
\(410\) 3.10045 0.153120
\(411\) −35.5092 −1.75154
\(412\) −51.0655 −2.51582
\(413\) 5.37959 0.264712
\(414\) 48.3319 2.37538
\(415\) 10.0684 0.494237
\(416\) 103.097 5.05473
\(417\) −5.19870 −0.254582
\(418\) 20.6014 1.00765
\(419\) −16.9011 −0.825673 −0.412836 0.910805i \(-0.635462\pi\)
−0.412836 + 0.910805i \(0.635462\pi\)
\(420\) −36.9238 −1.80170
\(421\) −9.78715 −0.476996 −0.238498 0.971143i \(-0.576655\pi\)
−0.238498 + 0.971143i \(0.576655\pi\)
\(422\) −60.5824 −2.94911
\(423\) 13.9052 0.676092
\(424\) −108.087 −5.24915
\(425\) −10.9467 −0.530992
\(426\) 89.1659 4.32010
\(427\) 1.38667 0.0671055
\(428\) −77.4732 −3.74481
\(429\) −15.8609 −0.765773
\(430\) −25.6309 −1.23603
\(431\) 0.102479 0.00493624 0.00246812 0.999997i \(-0.499214\pi\)
0.00246812 + 0.999997i \(0.499214\pi\)
\(432\) 114.290 5.49878
\(433\) 17.3195 0.832323 0.416161 0.909291i \(-0.363375\pi\)
0.416161 + 0.909291i \(0.363375\pi\)
\(434\) −20.0072 −0.960376
\(435\) 2.25679 0.108205
\(436\) −14.2250 −0.681255
\(437\) 23.4259 1.12061
\(438\) −19.7797 −0.945112
\(439\) 0.0191838 0.000915595 0 0.000457797 1.00000i \(-0.499854\pi\)
0.000457797 1.00000i \(0.499854\pi\)
\(440\) 11.3878 0.542894
\(441\) −20.7160 −0.986476
\(442\) 46.5006 2.21181
\(443\) 20.2494 0.962077 0.481038 0.876700i \(-0.340260\pi\)
0.481038 + 0.876700i \(0.340260\pi\)
\(444\) −10.5577 −0.501047
\(445\) −4.12678 −0.195628
\(446\) 73.3831 3.47479
\(447\) 9.83716 0.465282
\(448\) 45.5894 2.15390
\(449\) 11.8043 0.557077 0.278539 0.960425i \(-0.410150\pi\)
0.278539 + 0.960425i \(0.410150\pi\)
\(450\) 53.5135 2.52265
\(451\) 0.907812 0.0427472
\(452\) 63.6724 2.99490
\(453\) −45.7409 −2.14909
\(454\) 74.7930 3.51021
\(455\) 12.4826 0.585192
\(456\) 203.721 9.54009
\(457\) 29.4288 1.37662 0.688310 0.725416i \(-0.258353\pi\)
0.688310 + 0.725416i \(0.258353\pi\)
\(458\) −28.4119 −1.32760
\(459\) 26.6145 1.24226
\(460\) 20.7162 0.965897
\(461\) 29.6630 1.38154 0.690771 0.723074i \(-0.257271\pi\)
0.690771 + 0.723074i \(0.257271\pi\)
\(462\) −14.8648 −0.691572
\(463\) −3.98757 −0.185318 −0.0926591 0.995698i \(-0.529537\pi\)
−0.0926591 + 0.995698i \(0.529537\pi\)
\(464\) −8.31922 −0.386210
\(465\) −14.9287 −0.692303
\(466\) 50.1128 2.32143
\(467\) −41.2377 −1.90825 −0.954127 0.299402i \(-0.903213\pi\)
−0.954127 + 0.299402i \(0.903213\pi\)
\(468\) −165.333 −7.64254
\(469\) −11.3458 −0.523901
\(470\) 8.19467 0.377992
\(471\) −32.3260 −1.48950
\(472\) −26.2477 −1.20815
\(473\) −7.50474 −0.345068
\(474\) 90.7510 4.16833
\(475\) 25.9373 1.19009
\(476\) 31.6963 1.45280
\(477\) 69.3665 3.17607
\(478\) 69.3146 3.17038
\(479\) −3.12730 −0.142890 −0.0714449 0.997445i \(-0.522761\pi\)
−0.0714449 + 0.997445i \(0.522761\pi\)
\(480\) 72.0960 3.29072
\(481\) 3.56917 0.162740
\(482\) 32.6164 1.48563
\(483\) −16.9027 −0.769101
\(484\) 5.33437 0.242471
\(485\) 5.24929 0.238358
\(486\) 9.52982 0.432282
\(487\) −5.68093 −0.257427 −0.128714 0.991682i \(-0.541085\pi\)
−0.128714 + 0.991682i \(0.541085\pi\)
\(488\) −6.76572 −0.306270
\(489\) −1.33191 −0.0602312
\(490\) −12.2085 −0.551522
\(491\) 28.0152 1.26431 0.632155 0.774842i \(-0.282171\pi\)
0.632155 + 0.774842i \(0.282171\pi\)
\(492\) 14.3616 0.647472
\(493\) −1.93728 −0.0872509
\(494\) −110.180 −4.95722
\(495\) −7.30835 −0.328486
\(496\) 55.0318 2.47100
\(497\) −20.5469 −0.921654
\(498\) 64.1237 2.87345
\(499\) 29.8915 1.33813 0.669063 0.743206i \(-0.266696\pi\)
0.669063 + 0.743206i \(0.266696\pi\)
\(500\) 56.5728 2.53001
\(501\) −63.3808 −2.83164
\(502\) −50.6355 −2.25997
\(503\) 17.1935 0.766619 0.383310 0.923620i \(-0.374784\pi\)
0.383310 + 0.923620i \(0.374784\pi\)
\(504\) −96.8547 −4.31425
\(505\) −7.30594 −0.325110
\(506\) 8.33991 0.370754
\(507\) 46.2731 2.05506
\(508\) 85.7844 3.80607
\(509\) −11.4147 −0.505949 −0.252975 0.967473i \(-0.581409\pi\)
−0.252975 + 0.967473i \(0.581409\pi\)
\(510\) 32.5181 1.43993
\(511\) 4.55793 0.201631
\(512\) −16.7748 −0.741348
\(513\) −63.0611 −2.78422
\(514\) −6.05031 −0.266868
\(515\) 12.0723 0.531970
\(516\) −118.725 −5.22658
\(517\) 2.39940 0.105526
\(518\) 3.34500 0.146971
\(519\) 45.5996 2.00160
\(520\) −60.9041 −2.67082
\(521\) 38.0825 1.66843 0.834213 0.551442i \(-0.185922\pi\)
0.834213 + 0.551442i \(0.185922\pi\)
\(522\) 9.47054 0.414514
\(523\) −6.71485 −0.293620 −0.146810 0.989165i \(-0.546901\pi\)
−0.146810 + 0.989165i \(0.546901\pi\)
\(524\) 75.0633 3.27916
\(525\) −18.7149 −0.816783
\(526\) −49.7911 −2.17100
\(527\) 12.8152 0.558238
\(528\) 40.8871 1.77938
\(529\) −13.5167 −0.587682
\(530\) 40.8794 1.77569
\(531\) 16.8449 0.731007
\(532\) −75.1020 −3.25608
\(533\) −4.85513 −0.210299
\(534\) −26.2827 −1.13736
\(535\) 18.3154 0.791842
\(536\) 55.3576 2.39109
\(537\) −49.8704 −2.15207
\(538\) −76.9300 −3.31669
\(539\) −3.57465 −0.153971
\(540\) −55.7668 −2.39982
\(541\) −36.0432 −1.54962 −0.774810 0.632194i \(-0.782154\pi\)
−0.774810 + 0.632194i \(0.782154\pi\)
\(542\) 29.0079 1.24600
\(543\) −5.85710 −0.251352
\(544\) −61.8889 −2.65347
\(545\) 3.36292 0.144052
\(546\) 79.4993 3.40225
\(547\) 1.00000 0.0427569
\(548\) −63.8704 −2.72841
\(549\) 4.34202 0.185313
\(550\) 9.23402 0.393740
\(551\) 4.59025 0.195551
\(552\) 82.4706 3.51018
\(553\) −20.9122 −0.889275
\(554\) 8.73836 0.371258
\(555\) 2.49594 0.105947
\(556\) −9.35091 −0.396567
\(557\) −15.7749 −0.668404 −0.334202 0.942501i \(-0.608467\pi\)
−0.334202 + 0.942501i \(0.608467\pi\)
\(558\) −62.6478 −2.65209
\(559\) 40.1366 1.69760
\(560\) −32.1782 −1.35978
\(561\) 9.52132 0.401990
\(562\) −88.5753 −3.73632
\(563\) 9.12226 0.384458 0.192229 0.981350i \(-0.438428\pi\)
0.192229 + 0.981350i \(0.438428\pi\)
\(564\) 37.9586 1.59835
\(565\) −15.0527 −0.633272
\(566\) −68.9419 −2.89784
\(567\) 13.3242 0.559562
\(568\) 100.251 4.20643
\(569\) 11.6914 0.490130 0.245065 0.969507i \(-0.421191\pi\)
0.245065 + 0.969507i \(0.421191\pi\)
\(570\) −77.0491 −3.22723
\(571\) 3.59023 0.150246 0.0751231 0.997174i \(-0.476065\pi\)
0.0751231 + 0.997174i \(0.476065\pi\)
\(572\) −28.5291 −1.19286
\(573\) −43.5750 −1.82037
\(574\) −4.55020 −0.189922
\(575\) 10.5000 0.437880
\(576\) 142.752 5.94802
\(577\) −39.3583 −1.63851 −0.819255 0.573430i \(-0.805613\pi\)
−0.819255 + 0.573430i \(0.805613\pi\)
\(578\) 18.1252 0.753907
\(579\) −1.96586 −0.0816982
\(580\) 4.05929 0.168553
\(581\) −14.7763 −0.613024
\(582\) 33.4318 1.38579
\(583\) 11.9695 0.495727
\(584\) −22.2387 −0.920244
\(585\) 39.0863 1.61602
\(586\) 47.6520 1.96849
\(587\) −30.1683 −1.24518 −0.622590 0.782548i \(-0.713920\pi\)
−0.622590 + 0.782548i \(0.713920\pi\)
\(588\) −56.5510 −2.33212
\(589\) −30.3646 −1.25115
\(590\) 9.92714 0.408694
\(591\) −47.9388 −1.97194
\(592\) −9.20077 −0.378149
\(593\) 5.38500 0.221136 0.110568 0.993869i \(-0.464733\pi\)
0.110568 + 0.993869i \(0.464733\pi\)
\(594\) −22.4506 −0.921159
\(595\) −7.49329 −0.307195
\(596\) 17.6941 0.724779
\(597\) −59.6092 −2.43964
\(598\) −44.6032 −1.82396
\(599\) 8.98567 0.367145 0.183572 0.983006i \(-0.441234\pi\)
0.183572 + 0.983006i \(0.441234\pi\)
\(600\) 91.3122 3.72780
\(601\) −1.08029 −0.0440660 −0.0220330 0.999757i \(-0.507014\pi\)
−0.0220330 + 0.999757i \(0.507014\pi\)
\(602\) 37.6157 1.53310
\(603\) −35.5267 −1.44676
\(604\) −82.2741 −3.34769
\(605\) −1.26109 −0.0512707
\(606\) −46.5302 −1.89016
\(607\) −22.1977 −0.900978 −0.450489 0.892782i \(-0.648750\pi\)
−0.450489 + 0.892782i \(0.648750\pi\)
\(608\) 146.641 5.94708
\(609\) −3.31206 −0.134211
\(610\) 2.55886 0.103605
\(611\) −12.8324 −0.519143
\(612\) 99.2496 4.01193
\(613\) −28.9653 −1.16990 −0.584949 0.811070i \(-0.698885\pi\)
−0.584949 + 0.811070i \(0.698885\pi\)
\(614\) 51.3727 2.07323
\(615\) −3.39521 −0.136908
\(616\) −16.7127 −0.673376
\(617\) 16.1433 0.649905 0.324953 0.945730i \(-0.394652\pi\)
0.324953 + 0.945730i \(0.394652\pi\)
\(618\) 76.8865 3.09283
\(619\) −41.7313 −1.67732 −0.838660 0.544655i \(-0.816661\pi\)
−0.838660 + 0.544655i \(0.816661\pi\)
\(620\) −26.8523 −1.07841
\(621\) −25.5285 −1.02443
\(622\) 25.6688 1.02923
\(623\) 6.05644 0.242646
\(624\) −218.671 −8.75384
\(625\) 3.67393 0.146957
\(626\) −65.6805 −2.62512
\(627\) −22.5600 −0.900961
\(628\) −58.1448 −2.32023
\(629\) −2.14257 −0.0854299
\(630\) 36.6314 1.45943
\(631\) −21.3161 −0.848582 −0.424291 0.905526i \(-0.639477\pi\)
−0.424291 + 0.905526i \(0.639477\pi\)
\(632\) 102.033 4.05866
\(633\) 66.3422 2.63686
\(634\) −64.7430 −2.57127
\(635\) −20.2802 −0.804794
\(636\) 189.358 7.50854
\(637\) 19.1178 0.757474
\(638\) 1.63419 0.0646981
\(639\) −64.3378 −2.54516
\(640\) 35.5075 1.40356
\(641\) −10.1135 −0.399457 −0.199729 0.979851i \(-0.564006\pi\)
−0.199729 + 0.979851i \(0.564006\pi\)
\(642\) 116.647 4.60370
\(643\) −26.2851 −1.03658 −0.518292 0.855204i \(-0.673432\pi\)
−0.518292 + 0.855204i \(0.673432\pi\)
\(644\) −30.4029 −1.19804
\(645\) 28.0677 1.10516
\(646\) 66.1408 2.60228
\(647\) −13.8508 −0.544530 −0.272265 0.962222i \(-0.587773\pi\)
−0.272265 + 0.962222i \(0.587773\pi\)
\(648\) −65.0102 −2.55384
\(649\) 2.90667 0.114097
\(650\) −49.3850 −1.93704
\(651\) 21.9093 0.858694
\(652\) −2.39571 −0.0938234
\(653\) −30.5105 −1.19397 −0.596985 0.802253i \(-0.703635\pi\)
−0.596985 + 0.802253i \(0.703635\pi\)
\(654\) 21.4178 0.837504
\(655\) −17.7456 −0.693379
\(656\) 12.5158 0.488659
\(657\) 14.2721 0.556807
\(658\) −12.0264 −0.468840
\(659\) 37.8830 1.47571 0.737855 0.674959i \(-0.235839\pi\)
0.737855 + 0.674959i \(0.235839\pi\)
\(660\) −19.9505 −0.776573
\(661\) 41.1371 1.60005 0.800023 0.599969i \(-0.204820\pi\)
0.800023 + 0.599969i \(0.204820\pi\)
\(662\) −3.06158 −0.118992
\(663\) −50.9216 −1.97763
\(664\) 72.0955 2.79785
\(665\) 17.7548 0.688500
\(666\) 10.4741 0.405863
\(667\) 1.85823 0.0719511
\(668\) −114.003 −4.41091
\(669\) −80.3599 −3.10689
\(670\) −20.9368 −0.808860
\(671\) 0.749237 0.0289240
\(672\) −105.808 −4.08162
\(673\) 40.9094 1.57694 0.788471 0.615072i \(-0.210873\pi\)
0.788471 + 0.615072i \(0.210873\pi\)
\(674\) −72.3641 −2.78736
\(675\) −28.2654 −1.08794
\(676\) 83.2313 3.20121
\(677\) 0.586737 0.0225501 0.0112751 0.999936i \(-0.496411\pi\)
0.0112751 + 0.999936i \(0.496411\pi\)
\(678\) −95.8680 −3.68179
\(679\) −7.70383 −0.295646
\(680\) 36.5607 1.40204
\(681\) −81.9038 −3.13856
\(682\) −10.8102 −0.413943
\(683\) 6.99564 0.267681 0.133840 0.991003i \(-0.457269\pi\)
0.133840 + 0.991003i \(0.457269\pi\)
\(684\) −235.164 −8.99173
\(685\) 15.0995 0.576923
\(686\) 53.0029 2.02366
\(687\) 31.1131 1.18704
\(688\) −103.466 −3.94460
\(689\) −64.0150 −2.43878
\(690\) −31.1912 −1.18743
\(691\) 40.5622 1.54306 0.771530 0.636193i \(-0.219492\pi\)
0.771530 + 0.636193i \(0.219492\pi\)
\(692\) 82.0200 3.11793
\(693\) 10.7257 0.407436
\(694\) 36.2658 1.37663
\(695\) 2.21064 0.0838542
\(696\) 16.1599 0.612541
\(697\) 2.91453 0.110396
\(698\) −11.8781 −0.449593
\(699\) −54.8772 −2.07565
\(700\) −33.6624 −1.27232
\(701\) −11.9868 −0.452736 −0.226368 0.974042i \(-0.572685\pi\)
−0.226368 + 0.974042i \(0.572685\pi\)
\(702\) 120.069 4.53173
\(703\) 5.07666 0.191470
\(704\) 24.6326 0.928377
\(705\) −8.97376 −0.337971
\(706\) −5.91574 −0.222642
\(707\) 10.7222 0.403248
\(708\) 45.9836 1.72817
\(709\) −28.1864 −1.05856 −0.529281 0.848447i \(-0.677538\pi\)
−0.529281 + 0.848447i \(0.677538\pi\)
\(710\) −37.9159 −1.42296
\(711\) −65.4815 −2.45575
\(712\) −29.5501 −1.10744
\(713\) −12.2923 −0.460349
\(714\) −47.7234 −1.78600
\(715\) 6.74452 0.252231
\(716\) −89.7020 −3.35232
\(717\) −75.9046 −2.83471
\(718\) −6.14829 −0.229452
\(719\) −28.2604 −1.05393 −0.526967 0.849886i \(-0.676671\pi\)
−0.526967 + 0.849886i \(0.676671\pi\)
\(720\) −100.758 −3.75505
\(721\) −17.7173 −0.659826
\(722\) −105.260 −3.91736
\(723\) −35.7173 −1.32834
\(724\) −10.5352 −0.391536
\(725\) 2.05745 0.0764119
\(726\) −8.03167 −0.298083
\(727\) −0.523961 −0.0194326 −0.00971632 0.999953i \(-0.503093\pi\)
−0.00971632 + 0.999953i \(0.503093\pi\)
\(728\) 89.3825 3.31273
\(729\) −32.0336 −1.18643
\(730\) 8.41090 0.311302
\(731\) −24.0940 −0.891148
\(732\) 11.8529 0.438098
\(733\) 1.22762 0.0453433 0.0226716 0.999743i \(-0.492783\pi\)
0.0226716 + 0.999743i \(0.492783\pi\)
\(734\) 28.9936 1.07017
\(735\) 13.3692 0.493129
\(736\) 59.3636 2.18817
\(737\) −6.13031 −0.225813
\(738\) −14.2479 −0.524472
\(739\) 8.01240 0.294741 0.147370 0.989081i \(-0.452919\pi\)
0.147370 + 0.989081i \(0.452919\pi\)
\(740\) 4.48944 0.165035
\(741\) 120.655 4.43236
\(742\) −59.9944 −2.20247
\(743\) 17.6933 0.649104 0.324552 0.945868i \(-0.394786\pi\)
0.324552 + 0.945868i \(0.394786\pi\)
\(744\) −106.898 −3.91908
\(745\) −4.18304 −0.153255
\(746\) 11.5406 0.422532
\(747\) −46.2685 −1.69288
\(748\) 17.1260 0.626188
\(749\) −26.8795 −0.982156
\(750\) −85.1785 −3.11028
\(751\) −6.38702 −0.233066 −0.116533 0.993187i \(-0.537178\pi\)
−0.116533 + 0.993187i \(0.537178\pi\)
\(752\) 33.0800 1.20630
\(753\) 55.4496 2.02070
\(754\) −8.73990 −0.318288
\(755\) 19.4503 0.707870
\(756\) 81.8431 2.97660
\(757\) 41.2391 1.49886 0.749430 0.662084i \(-0.230328\pi\)
0.749430 + 0.662084i \(0.230328\pi\)
\(758\) −98.3718 −3.57303
\(759\) −9.13281 −0.331500
\(760\) −86.6278 −3.14232
\(761\) 23.6428 0.857051 0.428525 0.903530i \(-0.359033\pi\)
0.428525 + 0.903530i \(0.359033\pi\)
\(762\) −129.161 −4.67900
\(763\) −4.93540 −0.178674
\(764\) −78.3783 −2.83563
\(765\) −23.4635 −0.848324
\(766\) 58.8544 2.12650
\(767\) −15.5454 −0.561310
\(768\) 80.0356 2.88804
\(769\) 15.5818 0.561894 0.280947 0.959723i \(-0.409351\pi\)
0.280947 + 0.959723i \(0.409351\pi\)
\(770\) 6.32093 0.227790
\(771\) 6.62552 0.238612
\(772\) −3.53599 −0.127263
\(773\) 43.2206 1.55454 0.777268 0.629170i \(-0.216605\pi\)
0.777268 + 0.629170i \(0.216605\pi\)
\(774\) 117.785 4.23369
\(775\) −13.6101 −0.488889
\(776\) 37.5880 1.34933
\(777\) −3.66302 −0.131410
\(778\) 30.5240 1.09434
\(779\) −6.90576 −0.247425
\(780\) 106.699 3.82042
\(781\) −11.1018 −0.397253
\(782\) 26.7753 0.957482
\(783\) −5.00227 −0.178766
\(784\) −49.2827 −1.76010
\(785\) 13.7459 0.490613
\(786\) −113.019 −4.03124
\(787\) 36.7308 1.30931 0.654655 0.755927i \(-0.272814\pi\)
0.654655 + 0.755927i \(0.272814\pi\)
\(788\) −86.2275 −3.07173
\(789\) 54.5249 1.94114
\(790\) −38.5899 −1.37297
\(791\) 22.0913 0.785475
\(792\) −52.3321 −1.85954
\(793\) −4.00704 −0.142294
\(794\) −27.5480 −0.977643
\(795\) −44.7660 −1.58768
\(796\) −107.219 −3.80028
\(797\) −29.4984 −1.04489 −0.522443 0.852674i \(-0.674979\pi\)
−0.522443 + 0.852674i \(0.674979\pi\)
\(798\) 113.077 4.00288
\(799\) 7.70329 0.272523
\(800\) 65.7279 2.32383
\(801\) 18.9643 0.670071
\(802\) −61.3135 −2.16506
\(803\) 2.46272 0.0869074
\(804\) −96.9817 −3.42028
\(805\) 7.18753 0.253327
\(806\) 57.8146 2.03643
\(807\) 84.2439 2.96553
\(808\) −52.3148 −1.84043
\(809\) 45.9270 1.61471 0.807354 0.590067i \(-0.200899\pi\)
0.807354 + 0.590067i \(0.200899\pi\)
\(810\) 24.5875 0.863918
\(811\) 20.9065 0.734127 0.367063 0.930196i \(-0.380363\pi\)
0.367063 + 0.930196i \(0.380363\pi\)
\(812\) −5.95740 −0.209064
\(813\) −31.7658 −1.11407
\(814\) 1.80736 0.0633478
\(815\) 0.566368 0.0198390
\(816\) 131.268 4.59530
\(817\) 57.0888 1.99728
\(818\) 42.4169 1.48307
\(819\) −57.3628 −2.00442
\(820\) −6.10697 −0.213265
\(821\) −12.5474 −0.437906 −0.218953 0.975735i \(-0.570264\pi\)
−0.218953 + 0.975735i \(0.570264\pi\)
\(822\) 96.1662 3.35418
\(823\) −38.7451 −1.35057 −0.675284 0.737558i \(-0.735979\pi\)
−0.675284 + 0.737558i \(0.735979\pi\)
\(824\) 86.4449 3.01145
\(825\) −10.1119 −0.352052
\(826\) −14.5690 −0.506921
\(827\) −33.6839 −1.17130 −0.585652 0.810562i \(-0.699162\pi\)
−0.585652 + 0.810562i \(0.699162\pi\)
\(828\) −95.1997 −3.30842
\(829\) 35.6829 1.23932 0.619659 0.784871i \(-0.287271\pi\)
0.619659 + 0.784871i \(0.287271\pi\)
\(830\) −27.2672 −0.946459
\(831\) −9.56914 −0.331950
\(832\) −131.739 −4.56724
\(833\) −11.4764 −0.397634
\(834\) 14.0791 0.487521
\(835\) 26.9513 0.932689
\(836\) −40.5787 −1.40344
\(837\) 33.0901 1.14376
\(838\) 45.7716 1.58115
\(839\) 22.7138 0.784166 0.392083 0.919930i \(-0.371755\pi\)
0.392083 + 0.919930i \(0.371755\pi\)
\(840\) 62.5056 2.15665
\(841\) −28.6359 −0.987444
\(842\) 26.5056 0.913443
\(843\) 96.9964 3.34073
\(844\) 119.330 4.10750
\(845\) −19.6766 −0.676896
\(846\) −37.6580 −1.29471
\(847\) 1.85077 0.0635933
\(848\) 165.021 5.66684
\(849\) 75.4964 2.59103
\(850\) 29.6458 1.01684
\(851\) 2.05514 0.0704494
\(852\) −175.631 −6.01701
\(853\) 12.5561 0.429912 0.214956 0.976624i \(-0.431039\pi\)
0.214956 + 0.976624i \(0.431039\pi\)
\(854\) −3.75537 −0.128506
\(855\) 55.5949 1.90131
\(856\) 131.149 4.48257
\(857\) −5.87810 −0.200792 −0.100396 0.994948i \(-0.532011\pi\)
−0.100396 + 0.994948i \(0.532011\pi\)
\(858\) 42.9547 1.46645
\(859\) 44.7161 1.52569 0.762847 0.646579i \(-0.223801\pi\)
0.762847 + 0.646579i \(0.223801\pi\)
\(860\) 50.4853 1.72154
\(861\) 4.98280 0.169813
\(862\) −0.277534 −0.00945286
\(863\) −34.9347 −1.18919 −0.594595 0.804026i \(-0.702688\pi\)
−0.594595 + 0.804026i \(0.702688\pi\)
\(864\) −159.804 −5.43663
\(865\) −19.3903 −0.659289
\(866\) −46.9048 −1.59389
\(867\) −19.8484 −0.674086
\(868\) 39.4083 1.33760
\(869\) −11.2992 −0.383298
\(870\) −6.11185 −0.207211
\(871\) 32.7859 1.11091
\(872\) 24.0805 0.815467
\(873\) −24.1228 −0.816432
\(874\) −63.4420 −2.14596
\(875\) 19.6281 0.663549
\(876\) 38.9603 1.31635
\(877\) −45.9861 −1.55284 −0.776421 0.630215i \(-0.782967\pi\)
−0.776421 + 0.630215i \(0.782967\pi\)
\(878\) −0.0519538 −0.00175335
\(879\) −52.1824 −1.76007
\(880\) −17.3864 −0.586094
\(881\) −2.04730 −0.0689753 −0.0344876 0.999405i \(-0.510980\pi\)
−0.0344876 + 0.999405i \(0.510980\pi\)
\(882\) 56.1031 1.88909
\(883\) 15.5665 0.523853 0.261926 0.965088i \(-0.415642\pi\)
0.261926 + 0.965088i \(0.415642\pi\)
\(884\) −91.5926 −3.08059
\(885\) −10.8709 −0.365423
\(886\) −54.8394 −1.84237
\(887\) 5.24540 0.176123 0.0880616 0.996115i \(-0.471933\pi\)
0.0880616 + 0.996115i \(0.471933\pi\)
\(888\) 17.8723 0.599757
\(889\) 29.7631 0.998222
\(890\) 11.1762 0.374626
\(891\) 7.19924 0.241184
\(892\) −144.543 −4.83967
\(893\) −18.2523 −0.610792
\(894\) −26.6410 −0.891010
\(895\) 21.2063 0.708850
\(896\) −52.1106 −1.74089
\(897\) 48.8437 1.63084
\(898\) −31.9683 −1.06680
\(899\) −2.40864 −0.0803327
\(900\) −105.406 −3.51353
\(901\) 38.4282 1.28023
\(902\) −2.45854 −0.0818604
\(903\) −41.1920 −1.37078
\(904\) −107.786 −3.58491
\(905\) 2.49060 0.0827905
\(906\) 123.876 4.11549
\(907\) 21.4012 0.710617 0.355308 0.934749i \(-0.384376\pi\)
0.355308 + 0.934749i \(0.384376\pi\)
\(908\) −147.320 −4.88900
\(909\) 33.5739 1.11358
\(910\) −33.8054 −1.12064
\(911\) 8.09467 0.268189 0.134094 0.990969i \(-0.457188\pi\)
0.134094 + 0.990969i \(0.457188\pi\)
\(912\) −311.030 −10.2992
\(913\) −7.98386 −0.264227
\(914\) −79.6992 −2.63621
\(915\) −2.80214 −0.0926359
\(916\) 55.9632 1.84908
\(917\) 26.0434 0.860028
\(918\) −72.0776 −2.37892
\(919\) 22.2669 0.734517 0.367258 0.930119i \(-0.380297\pi\)
0.367258 + 0.930119i \(0.380297\pi\)
\(920\) −35.0689 −1.15619
\(921\) −56.2569 −1.85373
\(922\) −80.3333 −2.64564
\(923\) 59.3742 1.95433
\(924\) 29.2793 0.963217
\(925\) 2.27547 0.0748171
\(926\) 10.7992 0.354883
\(927\) −55.4775 −1.82212
\(928\) 11.6322 0.381845
\(929\) −55.4811 −1.82028 −0.910138 0.414305i \(-0.864025\pi\)
−0.910138 + 0.414305i \(0.864025\pi\)
\(930\) 40.4300 1.32575
\(931\) 27.1925 0.891197
\(932\) −98.7076 −3.23328
\(933\) −28.1093 −0.920256
\(934\) 111.680 3.65429
\(935\) −4.04874 −0.132408
\(936\) 279.880 9.14818
\(937\) −25.5277 −0.833953 −0.416976 0.908917i \(-0.636910\pi\)
−0.416976 + 0.908917i \(0.636910\pi\)
\(938\) 30.7268 1.00326
\(939\) 71.9250 2.34718
\(940\) −16.1411 −0.526464
\(941\) 1.17540 0.0383169 0.0191584 0.999816i \(-0.493901\pi\)
0.0191584 + 0.999816i \(0.493901\pi\)
\(942\) 87.5454 2.85238
\(943\) −2.79561 −0.0910374
\(944\) 40.0736 1.30428
\(945\) −19.3484 −0.629404
\(946\) 20.3244 0.660802
\(947\) 50.2495 1.63289 0.816444 0.577424i \(-0.195942\pi\)
0.816444 + 0.577424i \(0.195942\pi\)
\(948\) −178.753 −5.80563
\(949\) −13.1710 −0.427549
\(950\) −70.2435 −2.27900
\(951\) 70.8983 2.29904
\(952\) −53.6563 −1.73901
\(953\) −43.3113 −1.40299 −0.701495 0.712675i \(-0.747484\pi\)
−0.701495 + 0.712675i \(0.747484\pi\)
\(954\) −187.859 −6.08215
\(955\) 18.5293 0.599595
\(956\) −136.530 −4.41568
\(957\) −1.78955 −0.0578481
\(958\) 8.46936 0.273633
\(959\) −22.1600 −0.715583
\(960\) −92.1259 −2.97335
\(961\) −15.0668 −0.486025
\(962\) −9.66604 −0.311645
\(963\) −84.1669 −2.71224
\(964\) −64.2447 −2.06918
\(965\) 0.835938 0.0269098
\(966\) 45.7761 1.47282
\(967\) 6.88835 0.221514 0.110757 0.993847i \(-0.464672\pi\)
0.110757 + 0.993847i \(0.464672\pi\)
\(968\) −9.03015 −0.290240
\(969\) −72.4290 −2.32676
\(970\) −14.2162 −0.456453
\(971\) −39.6340 −1.27192 −0.635958 0.771723i \(-0.719395\pi\)
−0.635958 + 0.771723i \(0.719395\pi\)
\(972\) −18.7710 −0.602079
\(973\) −3.24432 −0.104008
\(974\) 15.3851 0.492971
\(975\) 54.0802 1.73195
\(976\) 10.3295 0.330641
\(977\) −28.0212 −0.896479 −0.448240 0.893914i \(-0.647949\pi\)
−0.448240 + 0.893914i \(0.647949\pi\)
\(978\) 3.60710 0.115342
\(979\) 3.27238 0.104586
\(980\) 24.0471 0.768156
\(981\) −15.4541 −0.493410
\(982\) −75.8710 −2.42114
\(983\) 55.6586 1.77523 0.887617 0.460582i \(-0.152359\pi\)
0.887617 + 0.460582i \(0.152359\pi\)
\(984\) −24.3117 −0.775029
\(985\) 20.3849 0.649518
\(986\) 5.24656 0.167085
\(987\) 13.1698 0.419200
\(988\) 217.022 6.90438
\(989\) 23.1108 0.734881
\(990\) 19.7925 0.629047
\(991\) −56.2914 −1.78816 −0.894078 0.447912i \(-0.852168\pi\)
−0.894078 + 0.447912i \(0.852168\pi\)
\(992\) −76.9471 −2.44307
\(993\) 3.35265 0.106393
\(994\) 55.6452 1.76496
\(995\) 25.3475 0.803570
\(996\) −126.305 −4.00213
\(997\) −11.5970 −0.367279 −0.183640 0.982994i \(-0.558788\pi\)
−0.183640 + 0.982994i \(0.558788\pi\)
\(998\) −80.9522 −2.56250
\(999\) −5.53234 −0.175035
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 \(a_p\))