Properties

Label 23.2.a.a.1.2
Level 23
Weight 2
Character 23.1
Self dual Yes
Analytic conductor 0.184
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 23.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.183655924649\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\)
Character \(\chi\) = 23.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.618034 q^{2}\) \(-2.23607 q^{3}\) \(-1.61803 q^{4}\) \(+1.23607 q^{5}\) \(-1.38197 q^{6}\) \(+3.23607 q^{7}\) \(-2.23607 q^{8}\) \(+2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.618034 q^{2}\) \(-2.23607 q^{3}\) \(-1.61803 q^{4}\) \(+1.23607 q^{5}\) \(-1.38197 q^{6}\) \(+3.23607 q^{7}\) \(-2.23607 q^{8}\) \(+2.00000 q^{9}\) \(+0.763932 q^{10}\) \(-5.23607 q^{11}\) \(+3.61803 q^{12}\) \(+3.00000 q^{13}\) \(+2.00000 q^{14}\) \(-2.76393 q^{15}\) \(+1.85410 q^{16}\) \(+0.763932 q^{17}\) \(+1.23607 q^{18}\) \(-2.00000 q^{19}\) \(-2.00000 q^{20}\) \(-7.23607 q^{21}\) \(-3.23607 q^{22}\) \(+1.00000 q^{23}\) \(+5.00000 q^{24}\) \(-3.47214 q^{25}\) \(+1.85410 q^{26}\) \(+2.23607 q^{27}\) \(-5.23607 q^{28}\) \(-3.00000 q^{29}\) \(-1.70820 q^{30}\) \(+6.70820 q^{31}\) \(+5.61803 q^{32}\) \(+11.7082 q^{33}\) \(+0.472136 q^{34}\) \(+4.00000 q^{35}\) \(-3.23607 q^{36}\) \(-1.23607 q^{37}\) \(-1.23607 q^{38}\) \(-6.70820 q^{39}\) \(-2.76393 q^{40}\) \(-3.47214 q^{41}\) \(-4.47214 q^{42}\) \(+8.47214 q^{44}\) \(+2.47214 q^{45}\) \(+0.618034 q^{46}\) \(-2.23607 q^{47}\) \(-4.14590 q^{48}\) \(+3.47214 q^{49}\) \(-2.14590 q^{50}\) \(-1.70820 q^{51}\) \(-4.85410 q^{52}\) \(+0.472136 q^{53}\) \(+1.38197 q^{54}\) \(-6.47214 q^{55}\) \(-7.23607 q^{56}\) \(+4.47214 q^{57}\) \(-1.85410 q^{58}\) \(+6.47214 q^{59}\) \(+4.47214 q^{60}\) \(-6.94427 q^{61}\) \(+4.14590 q^{62}\) \(+6.47214 q^{63}\) \(-0.236068 q^{64}\) \(+3.70820 q^{65}\) \(+7.23607 q^{66}\) \(-2.76393 q^{67}\) \(-1.23607 q^{68}\) \(-2.23607 q^{69}\) \(+2.47214 q^{70}\) \(+12.2361 q^{71}\) \(-4.47214 q^{72}\) \(+6.52786 q^{73}\) \(-0.763932 q^{74}\) \(+7.76393 q^{75}\) \(+3.23607 q^{76}\) \(-16.9443 q^{77}\) \(-4.14590 q^{78}\) \(-10.9443 q^{79}\) \(+2.29180 q^{80}\) \(-11.0000 q^{81}\) \(-2.14590 q^{82}\) \(-8.76393 q^{83}\) \(+11.7082 q^{84}\) \(+0.944272 q^{85}\) \(+6.70820 q^{87}\) \(+11.7082 q^{88}\) \(-10.4721 q^{89}\) \(+1.52786 q^{90}\) \(+9.70820 q^{91}\) \(-1.61803 q^{92}\) \(-15.0000 q^{93}\) \(-1.38197 q^{94}\) \(-2.47214 q^{95}\) \(-12.5623 q^{96}\) \(+17.7082 q^{97}\) \(+2.14590 q^{98}\) \(-10.4721 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut -\mathstrut 15q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 11q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut -\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 11q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut +\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut -\mathstrut 30q^{93} \) \(\mathstrut -\mathstrut 5q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 11q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 0.437016 0.218508 0.975835i \(-0.429881\pi\)
0.218508 + 0.975835i \(0.429881\pi\)
\(3\) −2.23607 −1.29099 −0.645497 0.763763i \(-0.723350\pi\)
−0.645497 + 0.763763i \(0.723350\pi\)
\(4\) −1.61803 −0.809017
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) −1.38197 −0.564185
\(7\) 3.23607 1.22312 0.611559 0.791199i \(-0.290543\pi\)
0.611559 + 0.791199i \(0.290543\pi\)
\(8\) −2.23607 −0.790569
\(9\) 2.00000 0.666667
\(10\) 0.763932 0.241577
\(11\) −5.23607 −1.57873 −0.789367 0.613922i \(-0.789591\pi\)
−0.789367 + 0.613922i \(0.789591\pi\)
\(12\) 3.61803 1.04444
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 2.00000 0.534522
\(15\) −2.76393 −0.713644
\(16\) 1.85410 0.463525
\(17\) 0.763932 0.185281 0.0926404 0.995700i \(-0.470469\pi\)
0.0926404 + 0.995700i \(0.470469\pi\)
\(18\) 1.23607 0.291344
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) −7.23607 −1.57904
\(22\) −3.23607 −0.689932
\(23\) 1.00000 0.208514
\(24\) 5.00000 1.02062
\(25\) −3.47214 −0.694427
\(26\) 1.85410 0.363619
\(27\) 2.23607 0.430331
\(28\) −5.23607 −0.989524
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) −1.70820 −0.311874
\(31\) 6.70820 1.20483 0.602414 0.798183i \(-0.294205\pi\)
0.602414 + 0.798183i \(0.294205\pi\)
\(32\) 5.61803 0.993137
\(33\) 11.7082 2.03814
\(34\) 0.472136 0.0809706
\(35\) 4.00000 0.676123
\(36\) −3.23607 −0.539345
\(37\) −1.23607 −0.203208 −0.101604 0.994825i \(-0.532398\pi\)
−0.101604 + 0.994825i \(0.532398\pi\)
\(38\) −1.23607 −0.200517
\(39\) −6.70820 −1.07417
\(40\) −2.76393 −0.437016
\(41\) −3.47214 −0.542257 −0.271128 0.962543i \(-0.587397\pi\)
−0.271128 + 0.962543i \(0.587397\pi\)
\(42\) −4.47214 −0.690066
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 8.47214 1.27722
\(45\) 2.47214 0.368524
\(46\) 0.618034 0.0911241
\(47\) −2.23607 −0.326164 −0.163082 0.986613i \(-0.552144\pi\)
−0.163082 + 0.986613i \(0.552144\pi\)
\(48\) −4.14590 −0.598409
\(49\) 3.47214 0.496019
\(50\) −2.14590 −0.303476
\(51\) −1.70820 −0.239196
\(52\) −4.85410 −0.673143
\(53\) 0.472136 0.0648529 0.0324264 0.999474i \(-0.489677\pi\)
0.0324264 + 0.999474i \(0.489677\pi\)
\(54\) 1.38197 0.188062
\(55\) −6.47214 −0.872703
\(56\) −7.23607 −0.966960
\(57\) 4.47214 0.592349
\(58\) −1.85410 −0.243456
\(59\) 6.47214 0.842600 0.421300 0.906921i \(-0.361574\pi\)
0.421300 + 0.906921i \(0.361574\pi\)
\(60\) 4.47214 0.577350
\(61\) −6.94427 −0.889123 −0.444561 0.895748i \(-0.646640\pi\)
−0.444561 + 0.895748i \(0.646640\pi\)
\(62\) 4.14590 0.526530
\(63\) 6.47214 0.815412
\(64\) −0.236068 −0.0295085
\(65\) 3.70820 0.459946
\(66\) 7.23607 0.890698
\(67\) −2.76393 −0.337668 −0.168834 0.985644i \(-0.554000\pi\)
−0.168834 + 0.985644i \(0.554000\pi\)
\(68\) −1.23607 −0.149895
\(69\) −2.23607 −0.269191
\(70\) 2.47214 0.295477
\(71\) 12.2361 1.45215 0.726077 0.687613i \(-0.241342\pi\)
0.726077 + 0.687613i \(0.241342\pi\)
\(72\) −4.47214 −0.527046
\(73\) 6.52786 0.764029 0.382014 0.924156i \(-0.375230\pi\)
0.382014 + 0.924156i \(0.375230\pi\)
\(74\) −0.763932 −0.0888053
\(75\) 7.76393 0.896502
\(76\) 3.23607 0.371202
\(77\) −16.9443 −1.93098
\(78\) −4.14590 −0.469431
\(79\) −10.9443 −1.23133 −0.615663 0.788009i \(-0.711112\pi\)
−0.615663 + 0.788009i \(0.711112\pi\)
\(80\) 2.29180 0.256231
\(81\) −11.0000 −1.22222
\(82\) −2.14590 −0.236975
\(83\) −8.76393 −0.961967 −0.480983 0.876730i \(-0.659720\pi\)
−0.480983 + 0.876730i \(0.659720\pi\)
\(84\) 11.7082 1.27747
\(85\) 0.944272 0.102421
\(86\) 0 0
\(87\) 6.70820 0.719195
\(88\) 11.7082 1.24810
\(89\) −10.4721 −1.11004 −0.555022 0.831836i \(-0.687290\pi\)
−0.555022 + 0.831836i \(0.687290\pi\)
\(90\) 1.52786 0.161051
\(91\) 9.70820 1.01770
\(92\) −1.61803 −0.168692
\(93\) −15.0000 −1.55543
\(94\) −1.38197 −0.142539
\(95\) −2.47214 −0.253636
\(96\) −12.5623 −1.28213
\(97\) 17.7082 1.79800 0.898998 0.437953i \(-0.144296\pi\)
0.898998 + 0.437953i \(0.144296\pi\)
\(98\) 2.14590 0.216768
\(99\) −10.4721 −1.05249
\(100\) 5.61803 0.561803
\(101\) 4.47214 0.444994 0.222497 0.974933i \(-0.428579\pi\)
0.222497 + 0.974933i \(0.428579\pi\)
\(102\) −1.05573 −0.104533
\(103\) −4.18034 −0.411901 −0.205951 0.978562i \(-0.566029\pi\)
−0.205951 + 0.978562i \(0.566029\pi\)
\(104\) −6.70820 −0.657794
\(105\) −8.94427 −0.872872
\(106\) 0.291796 0.0283417
\(107\) 13.4164 1.29701 0.648507 0.761209i \(-0.275394\pi\)
0.648507 + 0.761209i \(0.275394\pi\)
\(108\) −3.61803 −0.348145
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −4.00000 −0.381385
\(111\) 2.76393 0.262341
\(112\) 6.00000 0.566947
\(113\) 8.76393 0.824441 0.412221 0.911084i \(-0.364753\pi\)
0.412221 + 0.911084i \(0.364753\pi\)
\(114\) 2.76393 0.258866
\(115\) 1.23607 0.115264
\(116\) 4.85410 0.450692
\(117\) 6.00000 0.554700
\(118\) 4.00000 0.368230
\(119\) 2.47214 0.226620
\(120\) 6.18034 0.564185
\(121\) 16.4164 1.49240
\(122\) −4.29180 −0.388561
\(123\) 7.76393 0.700050
\(124\) −10.8541 −0.974727
\(125\) −10.4721 −0.936656
\(126\) 4.00000 0.356348
\(127\) −7.29180 −0.647042 −0.323521 0.946221i \(-0.604867\pi\)
−0.323521 + 0.946221i \(0.604867\pi\)
\(128\) −11.3820 −1.00603
\(129\) 0 0
\(130\) 2.29180 0.201004
\(131\) 18.7082 1.63454 0.817272 0.576253i \(-0.195486\pi\)
0.817272 + 0.576253i \(0.195486\pi\)
\(132\) −18.9443 −1.64889
\(133\) −6.47214 −0.561205
\(134\) −1.70820 −0.147566
\(135\) 2.76393 0.237881
\(136\) −1.70820 −0.146477
\(137\) −21.8885 −1.87006 −0.935032 0.354563i \(-0.884630\pi\)
−0.935032 + 0.354563i \(0.884630\pi\)
\(138\) −1.38197 −0.117641
\(139\) −10.7082 −0.908258 −0.454129 0.890936i \(-0.650049\pi\)
−0.454129 + 0.890936i \(0.650049\pi\)
\(140\) −6.47214 −0.546995
\(141\) 5.00000 0.421076
\(142\) 7.56231 0.634615
\(143\) −15.7082 −1.31359
\(144\) 3.70820 0.309017
\(145\) −3.70820 −0.307950
\(146\) 4.03444 0.333893
\(147\) −7.76393 −0.640358
\(148\) 2.00000 0.164399
\(149\) 23.8885 1.95703 0.978513 0.206186i \(-0.0661051\pi\)
0.978513 + 0.206186i \(0.0661051\pi\)
\(150\) 4.79837 0.391786
\(151\) 4.23607 0.344726 0.172363 0.985033i \(-0.444860\pi\)
0.172363 + 0.985033i \(0.444860\pi\)
\(152\) 4.47214 0.362738
\(153\) 1.52786 0.123520
\(154\) −10.4721 −0.843869
\(155\) 8.29180 0.666013
\(156\) 10.8541 0.869024
\(157\) −11.4164 −0.911129 −0.455564 0.890203i \(-0.650562\pi\)
−0.455564 + 0.890203i \(0.650562\pi\)
\(158\) −6.76393 −0.538110
\(159\) −1.05573 −0.0837247
\(160\) 6.94427 0.548993
\(161\) 3.23607 0.255038
\(162\) −6.79837 −0.534131
\(163\) −5.76393 −0.451466 −0.225733 0.974189i \(-0.572478\pi\)
−0.225733 + 0.974189i \(0.572478\pi\)
\(164\) 5.61803 0.438695
\(165\) 14.4721 1.12665
\(166\) −5.41641 −0.420395
\(167\) 1.52786 0.118230 0.0591148 0.998251i \(-0.481172\pi\)
0.0591148 + 0.998251i \(0.481172\pi\)
\(168\) 16.1803 1.24834
\(169\) −4.00000 −0.307692
\(170\) 0.583592 0.0447595
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) 22.9443 1.74442 0.872210 0.489131i \(-0.162686\pi\)
0.872210 + 0.489131i \(0.162686\pi\)
\(174\) 4.14590 0.314300
\(175\) −11.2361 −0.849367
\(176\) −9.70820 −0.731783
\(177\) −14.4721 −1.08779
\(178\) −6.47214 −0.485107
\(179\) 0.708204 0.0529336 0.0264668 0.999650i \(-0.491574\pi\)
0.0264668 + 0.999650i \(0.491574\pi\)
\(180\) −4.00000 −0.298142
\(181\) 16.6525 1.23777 0.618884 0.785482i \(-0.287585\pi\)
0.618884 + 0.785482i \(0.287585\pi\)
\(182\) 6.00000 0.444750
\(183\) 15.5279 1.14785
\(184\) −2.23607 −0.164845
\(185\) −1.52786 −0.112331
\(186\) −9.27051 −0.679747
\(187\) −4.00000 −0.292509
\(188\) 3.61803 0.263872
\(189\) 7.23607 0.526346
\(190\) −1.52786 −0.110843
\(191\) −26.1803 −1.89434 −0.947171 0.320728i \(-0.896073\pi\)
−0.947171 + 0.320728i \(0.896073\pi\)
\(192\) 0.527864 0.0380953
\(193\) 9.94427 0.715804 0.357902 0.933759i \(-0.383492\pi\)
0.357902 + 0.933759i \(0.383492\pi\)
\(194\) 10.9443 0.785753
\(195\) −8.29180 −0.593788
\(196\) −5.61803 −0.401288
\(197\) −1.47214 −0.104885 −0.0524427 0.998624i \(-0.516701\pi\)
−0.0524427 + 0.998624i \(0.516701\pi\)
\(198\) −6.47214 −0.459955
\(199\) −12.2918 −0.871342 −0.435671 0.900106i \(-0.643489\pi\)
−0.435671 + 0.900106i \(0.643489\pi\)
\(200\) 7.76393 0.548993
\(201\) 6.18034 0.435928
\(202\) 2.76393 0.194470
\(203\) −9.70820 −0.681382
\(204\) 2.76393 0.193514
\(205\) −4.29180 −0.299752
\(206\) −2.58359 −0.180007
\(207\) 2.00000 0.139010
\(208\) 5.56231 0.385677
\(209\) 10.4721 0.724373
\(210\) −5.52786 −0.381459
\(211\) −23.4164 −1.61205 −0.806026 0.591880i \(-0.798386\pi\)
−0.806026 + 0.591880i \(0.798386\pi\)
\(212\) −0.763932 −0.0524671
\(213\) −27.3607 −1.87472
\(214\) 8.29180 0.566816
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 21.7082 1.47365
\(218\) 0 0
\(219\) −14.5967 −0.986357
\(220\) 10.4721 0.706031
\(221\) 2.29180 0.154163
\(222\) 1.70820 0.114647
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 18.1803 1.21473
\(225\) −6.94427 −0.462951
\(226\) 5.41641 0.360294
\(227\) −12.1803 −0.808438 −0.404219 0.914662i \(-0.632457\pi\)
−0.404219 + 0.914662i \(0.632457\pi\)
\(228\) −7.23607 −0.479220
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 0.763932 0.0503722
\(231\) 37.8885 2.49288
\(232\) 6.70820 0.440415
\(233\) −6.52786 −0.427655 −0.213827 0.976871i \(-0.568593\pi\)
−0.213827 + 0.976871i \(0.568593\pi\)
\(234\) 3.70820 0.242413
\(235\) −2.76393 −0.180299
\(236\) −10.4721 −0.681678
\(237\) 24.4721 1.58964
\(238\) 1.52786 0.0990367
\(239\) 13.7639 0.890315 0.445157 0.895452i \(-0.353148\pi\)
0.445157 + 0.895452i \(0.353148\pi\)
\(240\) −5.12461 −0.330792
\(241\) −23.1246 −1.48959 −0.744794 0.667295i \(-0.767452\pi\)
−0.744794 + 0.667295i \(0.767452\pi\)
\(242\) 10.1459 0.652203
\(243\) 17.8885 1.14755
\(244\) 11.2361 0.719316
\(245\) 4.29180 0.274193
\(246\) 4.79837 0.305933
\(247\) −6.00000 −0.381771
\(248\) −15.0000 −0.952501
\(249\) 19.5967 1.24189
\(250\) −6.47214 −0.409334
\(251\) 2.29180 0.144657 0.0723284 0.997381i \(-0.476957\pi\)
0.0723284 + 0.997381i \(0.476957\pi\)
\(252\) −10.4721 −0.659683
\(253\) −5.23607 −0.329189
\(254\) −4.50658 −0.282768
\(255\) −2.11146 −0.132225
\(256\) −6.56231 −0.410144
\(257\) −7.47214 −0.466099 −0.233050 0.972465i \(-0.574870\pi\)
−0.233050 + 0.972465i \(0.574870\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) −6.00000 −0.372104
\(261\) −6.00000 −0.371391
\(262\) 11.5623 0.714322
\(263\) 2.94427 0.181552 0.0907758 0.995871i \(-0.471065\pi\)
0.0907758 + 0.995871i \(0.471065\pi\)
\(264\) −26.1803 −1.61129
\(265\) 0.583592 0.0358498
\(266\) −4.00000 −0.245256
\(267\) 23.4164 1.43306
\(268\) 4.47214 0.273179
\(269\) −7.94427 −0.484371 −0.242185 0.970230i \(-0.577864\pi\)
−0.242185 + 0.970230i \(0.577864\pi\)
\(270\) 1.70820 0.103958
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 1.41641 0.0858823
\(273\) −21.7082 −1.31384
\(274\) −13.5279 −0.817248
\(275\) 18.1803 1.09632
\(276\) 3.61803 0.217780
\(277\) 15.4721 0.929631 0.464815 0.885408i \(-0.346121\pi\)
0.464815 + 0.885408i \(0.346121\pi\)
\(278\) −6.61803 −0.396923
\(279\) 13.4164 0.803219
\(280\) −8.94427 −0.534522
\(281\) −8.76393 −0.522812 −0.261406 0.965229i \(-0.584186\pi\)
−0.261406 + 0.965229i \(0.584186\pi\)
\(282\) 3.09017 0.184017
\(283\) 27.7082 1.64708 0.823541 0.567257i \(-0.191995\pi\)
0.823541 + 0.567257i \(0.191995\pi\)
\(284\) −19.7984 −1.17482
\(285\) 5.52786 0.327442
\(286\) −9.70820 −0.574058
\(287\) −11.2361 −0.663244
\(288\) 11.2361 0.662092
\(289\) −16.4164 −0.965671
\(290\) −2.29180 −0.134579
\(291\) −39.5967 −2.32120
\(292\) −10.5623 −0.618112
\(293\) −1.52786 −0.0892588 −0.0446294 0.999004i \(-0.514211\pi\)
−0.0446294 + 0.999004i \(0.514211\pi\)
\(294\) −4.79837 −0.279847
\(295\) 8.00000 0.465778
\(296\) 2.76393 0.160650
\(297\) −11.7082 −0.679379
\(298\) 14.7639 0.855252
\(299\) 3.00000 0.173494
\(300\) −12.5623 −0.725285
\(301\) 0 0
\(302\) 2.61803 0.150651
\(303\) −10.0000 −0.574485
\(304\) −3.70820 −0.212680
\(305\) −8.58359 −0.491495
\(306\) 0.944272 0.0539804
\(307\) 9.52786 0.543784 0.271892 0.962328i \(-0.412351\pi\)
0.271892 + 0.962328i \(0.412351\pi\)
\(308\) 27.4164 1.56219
\(309\) 9.34752 0.531762
\(310\) 5.12461 0.291058
\(311\) 13.1803 0.747389 0.373694 0.927552i \(-0.378091\pi\)
0.373694 + 0.927552i \(0.378091\pi\)
\(312\) 15.0000 0.849208
\(313\) 24.3607 1.37695 0.688474 0.725261i \(-0.258281\pi\)
0.688474 + 0.725261i \(0.258281\pi\)
\(314\) −7.05573 −0.398178
\(315\) 8.00000 0.450749
\(316\) 17.7082 0.996164
\(317\) 25.4164 1.42753 0.713764 0.700386i \(-0.246989\pi\)
0.713764 + 0.700386i \(0.246989\pi\)
\(318\) −0.652476 −0.0365890
\(319\) 15.7082 0.879491
\(320\) −0.291796 −0.0163119
\(321\) −30.0000 −1.67444
\(322\) 2.00000 0.111456
\(323\) −1.52786 −0.0850126
\(324\) 17.7984 0.988799
\(325\) −10.4164 −0.577798
\(326\) −3.56231 −0.197298
\(327\) 0 0
\(328\) 7.76393 0.428691
\(329\) −7.23607 −0.398937
\(330\) 8.94427 0.492366
\(331\) −19.6525 −1.08020 −0.540099 0.841602i \(-0.681613\pi\)
−0.540099 + 0.841602i \(0.681613\pi\)
\(332\) 14.1803 0.778247
\(333\) −2.47214 −0.135472
\(334\) 0.944272 0.0516683
\(335\) −3.41641 −0.186658
\(336\) −13.4164 −0.731925
\(337\) 23.4164 1.27557 0.637787 0.770213i \(-0.279850\pi\)
0.637787 + 0.770213i \(0.279850\pi\)
\(338\) −2.47214 −0.134466
\(339\) −19.5967 −1.06435
\(340\) −1.52786 −0.0828601
\(341\) −35.1246 −1.90210
\(342\) −2.47214 −0.133678
\(343\) −11.4164 −0.616428
\(344\) 0 0
\(345\) −2.76393 −0.148805
\(346\) 14.1803 0.762340
\(347\) −9.88854 −0.530845 −0.265422 0.964132i \(-0.585511\pi\)
−0.265422 + 0.964132i \(0.585511\pi\)
\(348\) −10.8541 −0.581841
\(349\) 24.4164 1.30698 0.653490 0.756935i \(-0.273304\pi\)
0.653490 + 0.756935i \(0.273304\pi\)
\(350\) −6.94427 −0.371187
\(351\) 6.70820 0.358057
\(352\) −29.4164 −1.56790
\(353\) 9.36068 0.498219 0.249109 0.968475i \(-0.419862\pi\)
0.249109 + 0.968475i \(0.419862\pi\)
\(354\) −8.94427 −0.475383
\(355\) 15.1246 0.802731
\(356\) 16.9443 0.898045
\(357\) −5.52786 −0.292566
\(358\) 0.437694 0.0231329
\(359\) −19.8885 −1.04968 −0.524839 0.851202i \(-0.675874\pi\)
−0.524839 + 0.851202i \(0.675874\pi\)
\(360\) −5.52786 −0.291344
\(361\) −15.0000 −0.789474
\(362\) 10.2918 0.540925
\(363\) −36.7082 −1.92668
\(364\) −15.7082 −0.823334
\(365\) 8.06888 0.422345
\(366\) 9.59675 0.501630
\(367\) −4.18034 −0.218212 −0.109106 0.994030i \(-0.534799\pi\)
−0.109106 + 0.994030i \(0.534799\pi\)
\(368\) 1.85410 0.0966517
\(369\) −6.94427 −0.361504
\(370\) −0.944272 −0.0490904
\(371\) 1.52786 0.0793227
\(372\) 24.2705 1.25837
\(373\) 7.70820 0.399116 0.199558 0.979886i \(-0.436049\pi\)
0.199558 + 0.979886i \(0.436049\pi\)
\(374\) −2.47214 −0.127831
\(375\) 23.4164 1.20922
\(376\) 5.00000 0.257855
\(377\) −9.00000 −0.463524
\(378\) 4.47214 0.230022
\(379\) 24.3607 1.25132 0.625662 0.780094i \(-0.284829\pi\)
0.625662 + 0.780094i \(0.284829\pi\)
\(380\) 4.00000 0.205196
\(381\) 16.3050 0.835328
\(382\) −16.1803 −0.827858
\(383\) 7.05573 0.360531 0.180265 0.983618i \(-0.442304\pi\)
0.180265 + 0.983618i \(0.442304\pi\)
\(384\) 25.4508 1.29878
\(385\) −20.9443 −1.06742
\(386\) 6.14590 0.312818
\(387\) 0 0
\(388\) −28.6525 −1.45461
\(389\) 25.5279 1.29431 0.647157 0.762357i \(-0.275958\pi\)
0.647157 + 0.762357i \(0.275958\pi\)
\(390\) −5.12461 −0.259495
\(391\) 0.763932 0.0386337
\(392\) −7.76393 −0.392138
\(393\) −41.8328 −2.11019
\(394\) −0.909830 −0.0458366
\(395\) −13.5279 −0.680661
\(396\) 16.9443 0.851482
\(397\) −24.4164 −1.22542 −0.612712 0.790306i \(-0.709922\pi\)
−0.612712 + 0.790306i \(0.709922\pi\)
\(398\) −7.59675 −0.380791
\(399\) 14.4721 0.724513
\(400\) −6.43769 −0.321885
\(401\) −14.1803 −0.708132 −0.354066 0.935220i \(-0.615201\pi\)
−0.354066 + 0.935220i \(0.615201\pi\)
\(402\) 3.81966 0.190507
\(403\) 20.1246 1.00248
\(404\) −7.23607 −0.360008
\(405\) −13.5967 −0.675628
\(406\) −6.00000 −0.297775
\(407\) 6.47214 0.320812
\(408\) 3.81966 0.189101
\(409\) 21.3607 1.05622 0.528109 0.849177i \(-0.322901\pi\)
0.528109 + 0.849177i \(0.322901\pi\)
\(410\) −2.65248 −0.130996
\(411\) 48.9443 2.41424
\(412\) 6.76393 0.333235
\(413\) 20.9443 1.03060
\(414\) 1.23607 0.0607494
\(415\) −10.8328 −0.531762
\(416\) 16.8541 0.826340
\(417\) 23.9443 1.17256
\(418\) 6.47214 0.316563
\(419\) −4.58359 −0.223923 −0.111962 0.993713i \(-0.535713\pi\)
−0.111962 + 0.993713i \(0.535713\pi\)
\(420\) 14.4721 0.706168
\(421\) −10.2918 −0.501591 −0.250796 0.968040i \(-0.580692\pi\)
−0.250796 + 0.968040i \(0.580692\pi\)
\(422\) −14.4721 −0.704493
\(423\) −4.47214 −0.217443
\(424\) −1.05573 −0.0512707
\(425\) −2.65248 −0.128664
\(426\) −16.9098 −0.819284
\(427\) −22.4721 −1.08750
\(428\) −21.7082 −1.04931
\(429\) 35.1246 1.69583
\(430\) 0 0
\(431\) −17.5279 −0.844288 −0.422144 0.906529i \(-0.638722\pi\)
−0.422144 + 0.906529i \(0.638722\pi\)
\(432\) 4.14590 0.199470
\(433\) 17.8197 0.856358 0.428179 0.903694i \(-0.359155\pi\)
0.428179 + 0.903694i \(0.359155\pi\)
\(434\) 13.4164 0.644008
\(435\) 8.29180 0.397561
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) −9.02129 −0.431054
\(439\) −18.7082 −0.892894 −0.446447 0.894810i \(-0.647311\pi\)
−0.446447 + 0.894810i \(0.647311\pi\)
\(440\) 14.4721 0.689932
\(441\) 6.94427 0.330680
\(442\) 1.41641 0.0673717
\(443\) 38.1246 1.81135 0.905677 0.423967i \(-0.139363\pi\)
0.905677 + 0.423967i \(0.139363\pi\)
\(444\) −4.47214 −0.212238
\(445\) −12.9443 −0.613617
\(446\) 2.47214 0.117059
\(447\) −53.4164 −2.52651
\(448\) −0.763932 −0.0360924
\(449\) −14.9443 −0.705264 −0.352632 0.935762i \(-0.614713\pi\)
−0.352632 + 0.935762i \(0.614713\pi\)
\(450\) −4.29180 −0.202317
\(451\) 18.1803 0.856079
\(452\) −14.1803 −0.666987
\(453\) −9.47214 −0.445040
\(454\) −7.52786 −0.353300
\(455\) 12.0000 0.562569
\(456\) −10.0000 −0.468293
\(457\) −5.12461 −0.239719 −0.119860 0.992791i \(-0.538244\pi\)
−0.119860 + 0.992791i \(0.538244\pi\)
\(458\) −7.41641 −0.346546
\(459\) 1.70820 0.0797321
\(460\) −2.00000 −0.0932505
\(461\) −1.47214 −0.0685642 −0.0342821 0.999412i \(-0.510914\pi\)
−0.0342821 + 0.999412i \(0.510914\pi\)
\(462\) 23.4164 1.08943
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) −5.56231 −0.258224
\(465\) −18.5410 −0.859819
\(466\) −4.03444 −0.186892
\(467\) −13.0557 −0.604147 −0.302074 0.953285i \(-0.597679\pi\)
−0.302074 + 0.953285i \(0.597679\pi\)
\(468\) −9.70820 −0.448762
\(469\) −8.94427 −0.413008
\(470\) −1.70820 −0.0787936
\(471\) 25.5279 1.17626
\(472\) −14.4721 −0.666134
\(473\) 0 0
\(474\) 15.1246 0.694696
\(475\) 6.94427 0.318625
\(476\) −4.00000 −0.183340
\(477\) 0.944272 0.0432352
\(478\) 8.50658 0.389082
\(479\) 31.5967 1.44369 0.721846 0.692054i \(-0.243294\pi\)
0.721846 + 0.692054i \(0.243294\pi\)
\(480\) −15.5279 −0.708747
\(481\) −3.70820 −0.169080
\(482\) −14.2918 −0.650973
\(483\) −7.23607 −0.329252
\(484\) −26.5623 −1.20738
\(485\) 21.8885 0.993908
\(486\) 11.0557 0.501498
\(487\) −14.7082 −0.666492 −0.333246 0.942840i \(-0.608144\pi\)
−0.333246 + 0.942840i \(0.608144\pi\)
\(488\) 15.5279 0.702913
\(489\) 12.8885 0.582840
\(490\) 2.65248 0.119827
\(491\) 8.34752 0.376718 0.188359 0.982100i \(-0.439683\pi\)
0.188359 + 0.982100i \(0.439683\pi\)
\(492\) −12.5623 −0.566352
\(493\) −2.29180 −0.103217
\(494\) −3.70820 −0.166840
\(495\) −12.9443 −0.581802
\(496\) 12.4377 0.558469
\(497\) 39.5967 1.77616
\(498\) 12.1115 0.542727
\(499\) 19.2918 0.863619 0.431810 0.901965i \(-0.357875\pi\)
0.431810 + 0.901965i \(0.357875\pi\)
\(500\) 16.9443 0.757771
\(501\) −3.41641 −0.152634
\(502\) 1.41641 0.0632174
\(503\) −26.9443 −1.20139 −0.600693 0.799480i \(-0.705109\pi\)
−0.600693 + 0.799480i \(0.705109\pi\)
\(504\) −14.4721 −0.644640
\(505\) 5.52786 0.245987
\(506\) −3.23607 −0.143861
\(507\) 8.94427 0.397229
\(508\) 11.7984 0.523468
\(509\) −28.3050 −1.25459 −0.627297 0.778780i \(-0.715839\pi\)
−0.627297 + 0.778780i \(0.715839\pi\)
\(510\) −1.30495 −0.0577842
\(511\) 21.1246 0.934498
\(512\) 18.7082 0.826794
\(513\) −4.47214 −0.197450
\(514\) −4.61803 −0.203693
\(515\) −5.16718 −0.227693
\(516\) 0 0
\(517\) 11.7082 0.514926
\(518\) −2.47214 −0.108619
\(519\) −51.3050 −2.25204
\(520\) −8.29180 −0.363619
\(521\) 31.4164 1.37638 0.688189 0.725532i \(-0.258406\pi\)
0.688189 + 0.725532i \(0.258406\pi\)
\(522\) −3.70820 −0.162304
\(523\) 41.1246 1.79825 0.899127 0.437688i \(-0.144203\pi\)
0.899127 + 0.437688i \(0.144203\pi\)
\(524\) −30.2705 −1.32237
\(525\) 25.1246 1.09653
\(526\) 1.81966 0.0793410
\(527\) 5.12461 0.223232
\(528\) 21.7082 0.944728
\(529\) 1.00000 0.0434783
\(530\) 0.360680 0.0156669
\(531\) 12.9443 0.561734
\(532\) 10.4721 0.454025
\(533\) −10.4164 −0.451185
\(534\) 14.4721 0.626271
\(535\) 16.5836 0.716971
\(536\) 6.18034 0.266950
\(537\) −1.58359 −0.0683370
\(538\) −4.90983 −0.211678
\(539\) −18.1803 −0.783083
\(540\) −4.47214 −0.192450
\(541\) −34.4164 −1.47968 −0.739838 0.672785i \(-0.765098\pi\)
−0.739838 + 0.672785i \(0.765098\pi\)
\(542\) 4.94427 0.212375
\(543\) −37.2361 −1.59795
\(544\) 4.29180 0.184009
\(545\) 0 0
\(546\) −13.4164 −0.574169
\(547\) −29.5410 −1.26308 −0.631541 0.775342i \(-0.717577\pi\)
−0.631541 + 0.775342i \(0.717577\pi\)
\(548\) 35.4164 1.51291
\(549\) −13.8885 −0.592749
\(550\) 11.2361 0.479108
\(551\) 6.00000 0.255609
\(552\) 5.00000 0.212814
\(553\) −35.4164 −1.50606
\(554\) 9.56231 0.406263
\(555\) 3.41641 0.145018
\(556\) 17.3262 0.734796
\(557\) −7.41641 −0.314243 −0.157122 0.987579i \(-0.550221\pi\)
−0.157122 + 0.987579i \(0.550221\pi\)
\(558\) 8.29180 0.351020
\(559\) 0 0
\(560\) 7.41641 0.313400
\(561\) 8.94427 0.377627
\(562\) −5.41641 −0.228477
\(563\) −32.9443 −1.38844 −0.694218 0.719765i \(-0.744250\pi\)
−0.694218 + 0.719765i \(0.744250\pi\)
\(564\) −8.09017 −0.340658
\(565\) 10.8328 0.455740
\(566\) 17.1246 0.719801
\(567\) −35.5967 −1.49492
\(568\) −27.3607 −1.14803
\(569\) −22.1803 −0.929848 −0.464924 0.885351i \(-0.653918\pi\)
−0.464924 + 0.885351i \(0.653918\pi\)
\(570\) 3.41641 0.143098
\(571\) −14.2918 −0.598093 −0.299047 0.954239i \(-0.596669\pi\)
−0.299047 + 0.954239i \(0.596669\pi\)
\(572\) 25.4164 1.06271
\(573\) 58.5410 2.44559
\(574\) −6.94427 −0.289848
\(575\) −3.47214 −0.144798
\(576\) −0.472136 −0.0196723
\(577\) 22.8885 0.952863 0.476431 0.879212i \(-0.341930\pi\)
0.476431 + 0.879212i \(0.341930\pi\)
\(578\) −10.1459 −0.422014
\(579\) −22.2361 −0.924099
\(580\) 6.00000 0.249136
\(581\) −28.3607 −1.17660
\(582\) −24.4721 −1.01440
\(583\) −2.47214 −0.102385
\(584\) −14.5967 −0.604018
\(585\) 7.41641 0.306631
\(586\) −0.944272 −0.0390075
\(587\) −24.7082 −1.01982 −0.509908 0.860229i \(-0.670321\pi\)
−0.509908 + 0.860229i \(0.670321\pi\)
\(588\) 12.5623 0.518061
\(589\) −13.4164 −0.552813
\(590\) 4.94427 0.203552
\(591\) 3.29180 0.135406
\(592\) −2.29180 −0.0941922
\(593\) −2.94427 −0.120907 −0.0604534 0.998171i \(-0.519255\pi\)
−0.0604534 + 0.998171i \(0.519255\pi\)
\(594\) −7.23607 −0.296899
\(595\) 3.05573 0.125273
\(596\) −38.6525 −1.58327
\(597\) 27.4853 1.12490
\(598\) 1.85410 0.0758199
\(599\) 33.8885 1.38465 0.692324 0.721587i \(-0.256587\pi\)
0.692324 + 0.721587i \(0.256587\pi\)
\(600\) −17.3607 −0.708747
\(601\) 46.8885 1.91262 0.956312 0.292349i \(-0.0944368\pi\)
0.956312 + 0.292349i \(0.0944368\pi\)
\(602\) 0 0
\(603\) −5.52786 −0.225112
\(604\) −6.85410 −0.278889
\(605\) 20.2918 0.824979
\(606\) −6.18034 −0.251059
\(607\) 26.4721 1.07447 0.537235 0.843432i \(-0.319469\pi\)
0.537235 + 0.843432i \(0.319469\pi\)
\(608\) −11.2361 −0.455683
\(609\) 21.7082 0.879661
\(610\) −5.30495 −0.214791
\(611\) −6.70820 −0.271385
\(612\) −2.47214 −0.0999302
\(613\) 5.70820 0.230552 0.115276 0.993333i \(-0.463225\pi\)
0.115276 + 0.993333i \(0.463225\pi\)
\(614\) 5.88854 0.237642
\(615\) 9.59675 0.386978
\(616\) 37.8885 1.52657
\(617\) −7.52786 −0.303060 −0.151530 0.988453i \(-0.548420\pi\)
−0.151530 + 0.988453i \(0.548420\pi\)
\(618\) 5.77709 0.232389
\(619\) 19.4164 0.780411 0.390206 0.920728i \(-0.372404\pi\)
0.390206 + 0.920728i \(0.372404\pi\)
\(620\) −13.4164 −0.538816
\(621\) 2.23607 0.0897303
\(622\) 8.14590 0.326621
\(623\) −33.8885 −1.35772
\(624\) −12.4377 −0.497906
\(625\) 4.41641 0.176656
\(626\) 15.0557 0.601748
\(627\) −23.4164 −0.935161
\(628\) 18.4721 0.737118
\(629\) −0.944272 −0.0376506
\(630\) 4.94427 0.196985
\(631\) 12.3607 0.492071 0.246035 0.969261i \(-0.420872\pi\)
0.246035 + 0.969261i \(0.420872\pi\)
\(632\) 24.4721 0.973449
\(633\) 52.3607 2.08115
\(634\) 15.7082 0.623852
\(635\) −9.01316 −0.357676
\(636\) 1.70820 0.0677347
\(637\) 10.4164 0.412713
\(638\) 9.70820 0.384351
\(639\) 24.4721 0.968103
\(640\) −14.0689 −0.556121
\(641\) −17.3050 −0.683504 −0.341752 0.939790i \(-0.611020\pi\)
−0.341752 + 0.939790i \(0.611020\pi\)
\(642\) −18.5410 −0.731756
\(643\) −29.5967 −1.16718 −0.583591 0.812048i \(-0.698353\pi\)
−0.583591 + 0.812048i \(0.698353\pi\)
\(644\) −5.23607 −0.206330
\(645\) 0 0
\(646\) −0.944272 −0.0371519
\(647\) 6.70820 0.263727 0.131863 0.991268i \(-0.457904\pi\)
0.131863 + 0.991268i \(0.457904\pi\)
\(648\) 24.5967 0.966252
\(649\) −33.8885 −1.33024
\(650\) −6.43769 −0.252507
\(651\) −48.5410 −1.90247
\(652\) 9.32624 0.365244
\(653\) −38.3050 −1.49899 −0.749494 0.662011i \(-0.769703\pi\)
−0.749494 + 0.662011i \(0.769703\pi\)
\(654\) 0 0
\(655\) 23.1246 0.903553
\(656\) −6.43769 −0.251350
\(657\) 13.0557 0.509352
\(658\) −4.47214 −0.174342
\(659\) −10.6525 −0.414962 −0.207481 0.978239i \(-0.566526\pi\)
−0.207481 + 0.978239i \(0.566526\pi\)
\(660\) −23.4164 −0.911482
\(661\) −22.9443 −0.892429 −0.446214 0.894926i \(-0.647228\pi\)
−0.446214 + 0.894926i \(0.647228\pi\)
\(662\) −12.1459 −0.472064
\(663\) −5.12461 −0.199023
\(664\) 19.5967 0.760501
\(665\) −8.00000 −0.310227
\(666\) −1.52786 −0.0592035
\(667\) −3.00000 −0.116160
\(668\) −2.47214 −0.0956498
\(669\) −8.94427 −0.345806
\(670\) −2.11146 −0.0815727
\(671\) 36.3607 1.40369
\(672\) −40.6525 −1.56820
\(673\) 3.00000 0.115642 0.0578208 0.998327i \(-0.481585\pi\)
0.0578208 + 0.998327i \(0.481585\pi\)
\(674\) 14.4721 0.557446
\(675\) −7.76393 −0.298834
\(676\) 6.47214 0.248928
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −12.1115 −0.465138
\(679\) 57.3050 2.19916
\(680\) −2.11146 −0.0809706
\(681\) 27.2361 1.04369
\(682\) −21.7082 −0.831250
\(683\) 26.5967 1.01770 0.508848 0.860856i \(-0.330071\pi\)
0.508848 + 0.860856i \(0.330071\pi\)
\(684\) 6.47214 0.247468
\(685\) −27.0557 −1.03375
\(686\) −7.05573 −0.269389
\(687\) 26.8328 1.02374
\(688\) 0 0
\(689\) 1.41641 0.0539608
\(690\) −1.70820 −0.0650302
\(691\) 7.05573 0.268413 0.134206 0.990953i \(-0.457152\pi\)
0.134206 + 0.990953i \(0.457152\pi\)
\(692\) −37.1246 −1.41127
\(693\) −33.8885 −1.28732
\(694\) −6.11146 −0.231988
\(695\) −13.2361 −0.502073
\(696\) −15.0000 −0.568574
\(697\) −2.65248 −0.100470
\(698\) 15.0902 0.571171
\(699\) 14.5967 0.552100
\(700\) 18.1803 0.687152
\(701\) −3.81966 −0.144267 −0.0721333 0.997395i \(-0.522981\pi\)
−0.0721333 + 0.997395i \(0.522981\pi\)
\(702\) 4.14590 0.156477
\(703\) 2.47214 0.0932384
\(704\) 1.23607 0.0465861
\(705\) 6.18034 0.232765
\(706\) 5.78522 0.217730
\(707\) 14.4721 0.544281
\(708\) 23.4164 0.880042
\(709\) −42.0689 −1.57993 −0.789965 0.613152i \(-0.789901\pi\)
−0.789965 + 0.613152i \(0.789901\pi\)
\(710\) 9.34752 0.350806
\(711\) −21.8885 −0.820885
\(712\) 23.4164 0.877567
\(713\) 6.70820 0.251224
\(714\) −3.41641 −0.127856
\(715\) −19.4164 −0.726132
\(716\) −1.14590 −0.0428242
\(717\) −30.7771 −1.14939
\(718\) −12.2918 −0.458726
\(719\) −3.05573 −0.113959 −0.0569797 0.998375i \(-0.518147\pi\)
−0.0569797 + 0.998375i \(0.518147\pi\)
\(720\) 4.58359 0.170820
\(721\) −13.5279 −0.503804
\(722\) −9.27051 −0.345013
\(723\) 51.7082 1.92305
\(724\) −26.9443 −1.00138
\(725\) 10.4164 0.386856
\(726\) −22.6869 −0.841990
\(727\) −27.7082 −1.02764 −0.513820 0.857898i \(-0.671770\pi\)
−0.513820 + 0.857898i \(0.671770\pi\)
\(728\) −21.7082 −0.804560
\(729\) −7.00000 −0.259259
\(730\) 4.98684 0.184571
\(731\) 0 0
\(732\) −25.1246 −0.928632
\(733\) −31.2361 −1.15373 −0.576865 0.816839i \(-0.695724\pi\)
−0.576865 + 0.816839i \(0.695724\pi\)
\(734\) −2.58359 −0.0953621
\(735\) −9.59675 −0.353981
\(736\) 5.61803 0.207083
\(737\) 14.4721 0.533088
\(738\) −4.29180 −0.157983
\(739\) 26.8197 0.986577 0.493289 0.869866i \(-0.335795\pi\)
0.493289 + 0.869866i \(0.335795\pi\)
\(740\) 2.47214 0.0908775
\(741\) 13.4164 0.492864
\(742\) 0.944272 0.0346653
\(743\) 41.1246 1.50872 0.754358 0.656463i \(-0.227948\pi\)
0.754358 + 0.656463i \(0.227948\pi\)
\(744\) 33.5410 1.22967
\(745\) 29.5279 1.08182
\(746\) 4.76393 0.174420
\(747\) −17.5279 −0.641311
\(748\) 6.47214 0.236645
\(749\) 43.4164 1.58640
\(750\) 14.4721 0.528448
\(751\) 0.360680 0.0131614 0.00658070 0.999978i \(-0.497905\pi\)
0.00658070 + 0.999978i \(0.497905\pi\)
\(752\) −4.14590 −0.151185
\(753\) −5.12461 −0.186751
\(754\) −5.56231 −0.202567
\(755\) 5.23607 0.190560
\(756\) −11.7082 −0.425823
\(757\) 1.59675 0.0580348 0.0290174 0.999579i \(-0.490762\pi\)
0.0290174 + 0.999579i \(0.490762\pi\)
\(758\) 15.0557 0.546849
\(759\) 11.7082 0.424981
\(760\) 5.52786 0.200517
\(761\) 46.3050 1.67855 0.839277 0.543705i \(-0.182979\pi\)
0.839277 + 0.543705i \(0.182979\pi\)
\(762\) 10.0770 0.365052
\(763\) 0 0
\(764\) 42.3607 1.53256
\(765\) 1.88854 0.0682804
\(766\) 4.36068 0.157558
\(767\) 19.4164 0.701086
\(768\) 14.6738 0.529494
\(769\) −23.1246 −0.833895 −0.416947 0.908931i \(-0.636900\pi\)
−0.416947 + 0.908931i \(0.636900\pi\)
\(770\) −12.9443 −0.466479
\(771\) 16.7082 0.601731
\(772\) −16.0902 −0.579098
\(773\) −5.52786 −0.198823 −0.0994117 0.995046i \(-0.531696\pi\)
−0.0994117 + 0.995046i \(0.531696\pi\)
\(774\) 0 0
\(775\) −23.2918 −0.836666
\(776\) −39.5967 −1.42144
\(777\) 8.94427 0.320874
\(778\) 15.7771 0.565636
\(779\) 6.94427 0.248804
\(780\) 13.4164 0.480384
\(781\) −64.0689 −2.29256
\(782\) 0.472136 0.0168835
\(783\) −6.70820 −0.239732
\(784\) 6.43769 0.229918
\(785\) −14.1115 −0.503659
\(786\) −25.8541 −0.922185
\(787\) 24.5836 0.876310 0.438155 0.898899i \(-0.355632\pi\)
0.438155 + 0.898899i \(0.355632\pi\)
\(788\) 2.38197 0.0848540
\(789\) −6.58359 −0.234382
\(790\) −8.36068 −0.297460
\(791\) 28.3607 1.00839
\(792\) 23.4164 0.832066
\(793\) −20.8328 −0.739795
\(794\) −15.0902 −0.535530
\(795\) −1.30495 −0.0462819
\(796\) 19.8885 0.704931
\(797\) −34.3607 −1.21712 −0.608559 0.793509i \(-0.708252\pi\)
−0.608559 + 0.793509i \(0.708252\pi\)
\(798\) 8.94427 0.316624
\(799\) −1.70820 −0.0604319
\(800\) −19.5066 −0.689662
\(801\) −20.9443 −0.740029
\(802\) −8.76393 −0.309465
\(803\) −34.1803 −1.20620
\(804\) −10.0000 −0.352673
\(805\) 4.00000 0.140981
\(806\) 12.4377 0.438099
\(807\) 17.7639 0.625320
\(808\) −10.0000 −0.351799
\(809\) 12.1115 0.425816 0.212908 0.977072i \(-0.431707\pi\)
0.212908 + 0.977072i \(0.431707\pi\)
\(810\) −8.40325 −0.295260
\(811\) −24.3475 −0.854957 −0.427479 0.904025i \(-0.640598\pi\)
−0.427479 + 0.904025i \(0.640598\pi\)
\(812\) 15.7082 0.551250
\(813\) −17.8885 −0.627379
\(814\) 4.00000 0.140200
\(815\) −7.12461 −0.249564
\(816\) −3.16718 −0.110874
\(817\) 0 0
\(818\) 13.2016 0.461584
\(819\) 19.4164 0.678464
\(820\) 6.94427 0.242504
\(821\) −38.9443 −1.35916 −0.679582 0.733599i \(-0.737839\pi\)
−0.679582 + 0.733599i \(0.737839\pi\)
\(822\) 30.2492 1.05506
\(823\) −39.5410 −1.37831 −0.689157 0.724612i \(-0.742019\pi\)
−0.689157 + 0.724612i \(0.742019\pi\)
\(824\) 9.34752 0.325636
\(825\) −40.6525 −1.41534
\(826\) 12.9443 0.450389
\(827\) 1.52786 0.0531290 0.0265645 0.999647i \(-0.491543\pi\)
0.0265645 + 0.999647i \(0.491543\pi\)
\(828\) −3.23607 −0.112461
\(829\) 40.2492 1.39791 0.698957 0.715164i \(-0.253648\pi\)
0.698957 + 0.715164i \(0.253648\pi\)
\(830\) −6.69505 −0.232389
\(831\) −34.5967 −1.20015
\(832\) −0.708204 −0.0245526
\(833\) 2.65248 0.0919028
\(834\) 14.7984 0.512426
\(835\) 1.88854 0.0653558
\(836\) −16.9443 −0.586030
\(837\) 15.0000 0.518476
\(838\) −2.83282 −0.0978580
\(839\) −41.1246 −1.41978 −0.709890 0.704313i \(-0.751255\pi\)
−0.709890 + 0.704313i \(0.751255\pi\)
\(840\) 20.0000 0.690066
\(841\) −20.0000 −0.689655
\(842\) −6.36068 −0.219204
\(843\) 19.5967 0.674948
\(844\) 37.8885 1.30418
\(845\) −4.94427 −0.170088
\(846\) −2.76393 −0.0950259
\(847\) 53.1246 1.82538
\(848\) 0.875388 0.0300610
\(849\) −61.9574 −2.12637
\(850\) −1.63932 −0.0562282
\(851\) −1.23607 −0.0423719
\(852\) 44.2705 1.51668
\(853\) −10.5836 −0.362375 −0.181188 0.983449i \(-0.557994\pi\)
−0.181188 + 0.983449i \(0.557994\pi\)
\(854\) −13.8885 −0.475256
\(855\) −4.94427 −0.169091
\(856\) −30.0000 −1.02538
\(857\) 1.47214 0.0502872 0.0251436 0.999684i \(-0.491996\pi\)
0.0251436 + 0.999684i \(0.491996\pi\)
\(858\) 21.7082 0.741106
\(859\) −16.7082 −0.570077 −0.285038 0.958516i \(-0.592006\pi\)
−0.285038 + 0.958516i \(0.592006\pi\)
\(860\) 0 0
\(861\) 25.1246 0.856244
\(862\) −10.8328 −0.368967
\(863\) −21.5410 −0.733265 −0.366632 0.930366i \(-0.619489\pi\)
−0.366632 + 0.930366i \(0.619489\pi\)
\(864\) 12.5623 0.427378
\(865\) 28.3607 0.964292
\(866\) 11.0132 0.374242
\(867\) 36.7082 1.24668
\(868\) −35.1246 −1.19221
\(869\) 57.3050 1.94394
\(870\) 5.12461 0.173741
\(871\) −8.29180 −0.280957
\(872\) 0 0
\(873\) 35.4164 1.19866
\(874\) −1.23607 −0.0418106
\(875\) −33.8885 −1.14564
\(876\) 23.6180 0.797979
\(877\) −36.4721 −1.23158 −0.615788 0.787912i \(-0.711162\pi\)
−0.615788 + 0.787912i \(0.711162\pi\)
\(878\) −11.5623 −0.390209
\(879\) 3.41641 0.115233
\(880\) −12.0000 −0.404520
\(881\) 44.1803 1.48847 0.744237 0.667916i \(-0.232813\pi\)
0.744237 + 0.667916i \(0.232813\pi\)
\(882\) 4.29180 0.144512
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) −3.70820 −0.124720
\(885\) −17.8885 −0.601317
\(886\) 23.5623 0.791591
\(887\) 23.0689 0.774577 0.387289 0.921959i \(-0.373412\pi\)
0.387289 + 0.921959i \(0.373412\pi\)
\(888\) −6.18034 −0.207399
\(889\) −23.5967 −0.791410
\(890\) −8.00000 −0.268161
\(891\) 57.5967 1.92956
\(892\) −6.47214 −0.216703
\(893\) 4.47214 0.149654
\(894\) −33.0132 −1.10413
\(895\) 0.875388 0.0292610
\(896\) −36.8328 −1.23050
\(897\) −6.70820 −0.223980
\(898\) −9.23607 −0.308212
\(899\) −20.1246 −0.671193
\(900\) 11.2361 0.374536
\(901\) 0.360680 0.0120160
\(902\) 11.2361 0.374120
\(903\) 0 0
\(904\) −19.5967 −0.651778
\(905\) 20.5836 0.684222
\(906\) −5.85410 −0.194490
\(907\) −40.2492 −1.33645 −0.668227 0.743958i \(-0.732946\pi\)
−0.668227 + 0.743958i \(0.732946\pi\)
\(908\) 19.7082 0.654040
\(909\) 8.94427 0.296663
\(910\) 7.41641 0.245852
\(911\) 31.3050 1.03718 0.518590 0.855023i \(-0.326457\pi\)
0.518590 + 0.855023i \(0.326457\pi\)
\(912\) 8.29180 0.274569
\(913\) 45.8885 1.51869
\(914\) −3.16718 −0.104761
\(915\) 19.1935 0.634517
\(916\) 19.4164 0.641536
\(917\) 60.5410 1.99924
\(918\) 1.05573 0.0348442
\(919\) 41.1246 1.35658 0.678288 0.734796i \(-0.262722\pi\)
0.678288 + 0.734796i \(0.262722\pi\)
\(920\) −2.76393 −0.0911241
\(921\) −21.3050 −0.702022
\(922\) −0.909830 −0.0299637
\(923\) 36.7082 1.20827
\(924\) −61.3050 −2.01678
\(925\) 4.29180 0.141113
\(926\) −12.3607 −0.406197
\(927\) −8.36068 −0.274601
\(928\) −16.8541 −0.553263
\(929\) −24.0557 −0.789243 −0.394621 0.918844i \(-0.629124\pi\)
−0.394621 + 0.918844i \(0.629124\pi\)
\(930\) −11.4590 −0.375755
\(931\) −6.94427 −0.227589
\(932\) 10.5623 0.345980
\(933\) −29.4721 −0.964874
\(934\) −8.06888 −0.264022
\(935\) −4.94427 −0.161695
\(936\) −13.4164 −0.438529
\(937\) 34.1803 1.11662 0.558312 0.829631i \(-0.311449\pi\)
0.558312 + 0.829631i \(0.311449\pi\)
\(938\) −5.52786 −0.180491
\(939\) −54.4721 −1.77763
\(940\) 4.47214 0.145865
\(941\) 6.65248 0.216865 0.108432 0.994104i \(-0.465417\pi\)
0.108432 + 0.994104i \(0.465417\pi\)
\(942\) 15.7771 0.514045
\(943\) −3.47214 −0.113068
\(944\) 12.0000 0.390567
\(945\) 8.94427 0.290957
\(946\) 0 0
\(947\) −10.8197 −0.351592 −0.175796 0.984427i \(-0.556250\pi\)
−0.175796 + 0.984427i \(0.556250\pi\)
\(948\) −39.5967 −1.28604
\(949\) 19.5836 0.635710
\(950\) 4.29180 0.139244
\(951\) −56.8328 −1.84293
\(952\) −5.52786 −0.179159
\(953\) 20.4721 0.663158 0.331579 0.943428i \(-0.392419\pi\)
0.331579 + 0.943428i \(0.392419\pi\)
\(954\) 0.583592 0.0188945
\(955\) −32.3607 −1.04717
\(956\) −22.2705 −0.720280
\(957\) −35.1246 −1.13542
\(958\) 19.5279 0.630917
\(959\) −70.8328 −2.28731
\(960\) 0.652476 0.0210586
\(961\) 14.0000 0.451613
\(962\) −2.29180 −0.0738905
\(963\) 26.8328 0.864675
\(964\) 37.4164 1.20510
\(965\) 12.2918 0.395687
\(966\) −4.47214 −0.143889
\(967\) 27.5410 0.885659 0.442830 0.896606i \(-0.353975\pi\)
0.442830 + 0.896606i \(0.353975\pi\)
\(968\) −36.7082 −1.17985
\(969\) 3.41641 0.109751
\(970\) 13.5279 0.434354
\(971\) 16.4721 0.528616 0.264308 0.964438i \(-0.414856\pi\)
0.264308 + 0.964438i \(0.414856\pi\)
\(972\) −28.9443 −0.928388
\(973\) −34.6525 −1.11091
\(974\) −9.09017 −0.291268
\(975\) 23.2918 0.745934
\(976\) −12.8754 −0.412131
\(977\) −23.3475 −0.746953 −0.373477 0.927640i \(-0.621834\pi\)
−0.373477 + 0.927640i \(0.621834\pi\)
\(978\) 7.96556 0.254710
\(979\) 54.8328 1.75246
\(980\) −6.94427 −0.221827
\(981\) 0 0
\(982\) 5.15905 0.164632
\(983\) −40.4721 −1.29086 −0.645430 0.763819i \(-0.723322\pi\)
−0.645430 + 0.763819i \(0.723322\pi\)
\(984\) −17.3607 −0.553438
\(985\) −1.81966 −0.0579792
\(986\) −1.41641 −0.0451076
\(987\) 16.1803 0.515026
\(988\) 9.70820 0.308859
\(989\) 0 0
\(990\) −8.00000 −0.254257
\(991\) 24.0000 0.762385 0.381193 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) 37.6869 1.19656
\(993\) 43.9443 1.39453
\(994\) 24.4721 0.776209
\(995\) −15.1935 −0.481666
\(996\) −31.7082 −1.00471
\(997\) 16.8328 0.533101 0.266550 0.963821i \(-0.414116\pi\)
0.266550 + 0.963821i \(0.414116\pi\)
\(998\) 11.9230 0.377416
\(999\) −2.76393 −0.0874469
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 \(a_p\))