Properties

Label 23.2.a.a.1.1
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 1.1
Root \(1.61803\)
Character \(\chi\) = 23.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.61803 q^{2}\) \(+2.23607 q^{3}\) \(+0.618034 q^{4}\) \(-3.23607 q^{5}\) \(-3.61803 q^{6}\) \(-1.23607 q^{7}\) \(+2.23607 q^{8}\) \(+2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.61803 q^{2}\) \(+2.23607 q^{3}\) \(+0.618034 q^{4}\) \(-3.23607 q^{5}\) \(-3.61803 q^{6}\) \(-1.23607 q^{7}\) \(+2.23607 q^{8}\) \(+2.00000 q^{9}\) \(+5.23607 q^{10}\) \(-0.763932 q^{11}\) \(+1.38197 q^{12}\) \(+3.00000 q^{13}\) \(+2.00000 q^{14}\) \(-7.23607 q^{15}\) \(-4.85410 q^{16}\) \(+5.23607 q^{17}\) \(-3.23607 q^{18}\) \(-2.00000 q^{19}\) \(-2.00000 q^{20}\) \(-2.76393 q^{21}\) \(+1.23607 q^{22}\) \(+1.00000 q^{23}\) \(+5.00000 q^{24}\) \(+5.47214 q^{25}\) \(-4.85410 q^{26}\) \(-2.23607 q^{27}\) \(-0.763932 q^{28}\) \(-3.00000 q^{29}\) \(+11.7082 q^{30}\) \(-6.70820 q^{31}\) \(+3.38197 q^{32}\) \(-1.70820 q^{33}\) \(-8.47214 q^{34}\) \(+4.00000 q^{35}\) \(+1.23607 q^{36}\) \(+3.23607 q^{37}\) \(+3.23607 q^{38}\) \(+6.70820 q^{39}\) \(-7.23607 q^{40}\) \(+5.47214 q^{41}\) \(+4.47214 q^{42}\) \(-0.472136 q^{44}\) \(-6.47214 q^{45}\) \(-1.61803 q^{46}\) \(+2.23607 q^{47}\) \(-10.8541 q^{48}\) \(-5.47214 q^{49}\) \(-8.85410 q^{50}\) \(+11.7082 q^{51}\) \(+1.85410 q^{52}\) \(-8.47214 q^{53}\) \(+3.61803 q^{54}\) \(+2.47214 q^{55}\) \(-2.76393 q^{56}\) \(-4.47214 q^{57}\) \(+4.85410 q^{58}\) \(-2.47214 q^{59}\) \(-4.47214 q^{60}\) \(+10.9443 q^{61}\) \(+10.8541 q^{62}\) \(-2.47214 q^{63}\) \(+4.23607 q^{64}\) \(-9.70820 q^{65}\) \(+2.76393 q^{66}\) \(-7.23607 q^{67}\) \(+3.23607 q^{68}\) \(+2.23607 q^{69}\) \(-6.47214 q^{70}\) \(+7.76393 q^{71}\) \(+4.47214 q^{72}\) \(+15.4721 q^{73}\) \(-5.23607 q^{74}\) \(+12.2361 q^{75}\) \(-1.23607 q^{76}\) \(+0.944272 q^{77}\) \(-10.8541 q^{78}\) \(+6.94427 q^{79}\) \(+15.7082 q^{80}\) \(-11.0000 q^{81}\) \(-8.85410 q^{82}\) \(-13.2361 q^{83}\) \(-1.70820 q^{84}\) \(-16.9443 q^{85}\) \(-6.70820 q^{87}\) \(-1.70820 q^{88}\) \(-1.52786 q^{89}\) \(+10.4721 q^{90}\) \(-3.70820 q^{91}\) \(+0.618034 q^{92}\) \(-15.0000 q^{93}\) \(-3.61803 q^{94}\) \(+6.47214 q^{95}\) \(+7.56231 q^{96}\) \(+4.29180 q^{97}\) \(+8.85410 q^{98}\) \(-1.52786 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut -\mathstrut 15q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 11q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut -\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 11q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut +\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut -\mathstrut 30q^{93} \) \(\mathstrut -\mathstrut 5q^{94} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 11q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 −1.14412 −0.572061 0.820211i \(-0.693856\pi\)
−0.572061 + 0.820211i \(0.693856\pi\)
\(3\) 2.23607 1.29099 0.645497 0.763763i \(-0.276650\pi\)
0.645497 + 0.763763i \(0.276650\pi\)
\(4\) 0.618034 0.309017
\(5\) −3.23607 −1.44721 −0.723607 0.690212i \(-0.757517\pi\)
−0.723607 + 0.690212i \(0.757517\pi\)
\(6\) −3.61803 −1.47706
\(7\) −1.23607 −0.467190 −0.233595 0.972334i \(-0.575049\pi\)
−0.233595 + 0.972334i \(0.575049\pi\)
\(8\) 2.23607 0.790569
\(9\) 2.00000 0.666667
\(10\) 5.23607 1.65579
\(11\) −0.763932 −0.230334 −0.115167 0.993346i \(-0.536740\pi\)
−0.115167 + 0.993346i \(0.536740\pi\)
\(12\) 1.38197 0.398939
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 2.00000 0.534522
\(15\) −7.23607 −1.86834
\(16\) −4.85410 −1.21353
\(17\) 5.23607 1.26993 0.634967 0.772540i \(-0.281014\pi\)
0.634967 + 0.772540i \(0.281014\pi\)
\(18\) −3.23607 −0.762749
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) −2.76393 −0.603139
\(22\) 1.23607 0.263531
\(23\) 1.00000 0.208514
\(24\) 5.00000 1.02062
\(25\) 5.47214 1.09443
\(26\) −4.85410 −0.951968
\(27\) −2.23607 −0.430331
\(28\) −0.763932 −0.144370
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 11.7082 2.13762
\(31\) −6.70820 −1.20483 −0.602414 0.798183i \(-0.705795\pi\)
−0.602414 + 0.798183i \(0.705795\pi\)
\(32\) 3.38197 0.597853
\(33\) −1.70820 −0.297360
\(34\) −8.47214 −1.45296
\(35\) 4.00000 0.676123
\(36\) 1.23607 0.206011
\(37\) 3.23607 0.532006 0.266003 0.963972i \(-0.414297\pi\)
0.266003 + 0.963972i \(0.414297\pi\)
\(38\) 3.23607 0.524960
\(39\) 6.70820 1.07417
\(40\) −7.23607 −1.14412
\(41\) 5.47214 0.854604 0.427302 0.904109i \(-0.359464\pi\)
0.427302 + 0.904109i \(0.359464\pi\)
\(42\) 4.47214 0.690066
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −0.472136 −0.0711772
\(45\) −6.47214 −0.964809
\(46\) −1.61803 −0.238566
\(47\) 2.23607 0.326164 0.163082 0.986613i \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) −10.8541 −1.56665
\(49\) −5.47214 −0.781734
\(50\) −8.85410 −1.25216
\(51\) 11.7082 1.63948
\(52\) 1.85410 0.257118
\(53\) −8.47214 −1.16374 −0.581869 0.813283i \(-0.697678\pi\)
−0.581869 + 0.813283i \(0.697678\pi\)
\(54\) 3.61803 0.492352
\(55\) 2.47214 0.333343
\(56\) −2.76393 −0.369346
\(57\) −4.47214 −0.592349
\(58\) 4.85410 0.637375
\(59\) −2.47214 −0.321845 −0.160922 0.986967i \(-0.551447\pi\)
−0.160922 + 0.986967i \(0.551447\pi\)
\(60\) −4.47214 −0.577350
\(61\) 10.9443 1.40127 0.700635 0.713520i \(-0.252900\pi\)
0.700635 + 0.713520i \(0.252900\pi\)
\(62\) 10.8541 1.37847
\(63\) −2.47214 −0.311460
\(64\) 4.23607 0.529508
\(65\) −9.70820 −1.20415
\(66\) 2.76393 0.340217
\(67\) −7.23607 −0.884026 −0.442013 0.897009i \(-0.645736\pi\)
−0.442013 + 0.897009i \(0.645736\pi\)
\(68\) 3.23607 0.392431
\(69\) 2.23607 0.269191
\(70\) −6.47214 −0.773568
\(71\) 7.76393 0.921409 0.460705 0.887554i \(-0.347597\pi\)
0.460705 + 0.887554i \(0.347597\pi\)
\(72\) 4.47214 0.527046
\(73\) 15.4721 1.81088 0.905438 0.424478i \(-0.139542\pi\)
0.905438 + 0.424478i \(0.139542\pi\)
\(74\) −5.23607 −0.608681
\(75\) 12.2361 1.41290
\(76\) −1.23607 −0.141787
\(77\) 0.944272 0.107610
\(78\) −10.8541 −1.22899
\(79\) 6.94427 0.781292 0.390646 0.920541i \(-0.372252\pi\)
0.390646 + 0.920541i \(0.372252\pi\)
\(80\) 15.7082 1.75623
\(81\) −11.0000 −1.22222
\(82\) −8.85410 −0.977772
\(83\) −13.2361 −1.45285 −0.726424 0.687247i \(-0.758819\pi\)
−0.726424 + 0.687247i \(0.758819\pi\)
\(84\) −1.70820 −0.186380
\(85\) −16.9443 −1.83786
\(86\) 0 0
\(87\) −6.70820 −0.719195
\(88\) −1.70820 −0.182095
\(89\) −1.52786 −0.161953 −0.0809766 0.996716i \(-0.525804\pi\)
−0.0809766 + 0.996716i \(0.525804\pi\)
\(90\) 10.4721 1.10386
\(91\) −3.70820 −0.388725
\(92\) 0.618034 0.0644345
\(93\) −15.0000 −1.55543
\(94\) −3.61803 −0.373172
\(95\) 6.47214 0.664027
\(96\) 7.56231 0.771825
\(97\) 4.29180 0.435766 0.217883 0.975975i \(-0.430085\pi\)
0.217883 + 0.975975i \(0.430085\pi\)
\(98\) 8.85410 0.894399
\(99\) −1.52786 −0.153556
\(100\) 3.38197 0.338197
\(101\) −4.47214 −0.444994 −0.222497 0.974933i \(-0.571421\pi\)
−0.222497 + 0.974933i \(0.571421\pi\)
\(102\) −18.9443 −1.87576
\(103\) 18.1803 1.79136 0.895681 0.444697i \(-0.146689\pi\)
0.895681 + 0.444697i \(0.146689\pi\)
\(104\) 6.70820 0.657794
\(105\) 8.94427 0.872872
\(106\) 13.7082 1.33146
\(107\) −13.4164 −1.29701 −0.648507 0.761209i \(-0.724606\pi\)
−0.648507 + 0.761209i \(0.724606\pi\)
\(108\) −1.38197 −0.132980
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −4.00000 −0.381385
\(111\) 7.23607 0.686817
\(112\) 6.00000 0.566947
\(113\) 13.2361 1.24514 0.622572 0.782562i \(-0.286088\pi\)
0.622572 + 0.782562i \(0.286088\pi\)
\(114\) 7.23607 0.677720
\(115\) −3.23607 −0.301765
\(116\) −1.85410 −0.172149
\(117\) 6.00000 0.554700
\(118\) 4.00000 0.368230
\(119\) −6.47214 −0.593300
\(120\) −16.1803 −1.47706
\(121\) −10.4164 −0.946946
\(122\) −17.7082 −1.60323
\(123\) 12.2361 1.10329
\(124\) −4.14590 −0.372313
\(125\) −1.52786 −0.136656
\(126\) 4.00000 0.356348
\(127\) −20.7082 −1.83756 −0.918778 0.394775i \(-0.870823\pi\)
−0.918778 + 0.394775i \(0.870823\pi\)
\(128\) −13.6180 −1.20368
\(129\) 0 0
\(130\) 15.7082 1.37770
\(131\) 5.29180 0.462346 0.231173 0.972913i \(-0.425744\pi\)
0.231173 + 0.972913i \(0.425744\pi\)
\(132\) −1.05573 −0.0918893
\(133\) 2.47214 0.214361
\(134\) 11.7082 1.01143
\(135\) 7.23607 0.622782
\(136\) 11.7082 1.00397
\(137\) 13.8885 1.18658 0.593289 0.804989i \(-0.297829\pi\)
0.593289 + 0.804989i \(0.297829\pi\)
\(138\) −3.61803 −0.307988
\(139\) 2.70820 0.229707 0.114853 0.993382i \(-0.463360\pi\)
0.114853 + 0.993382i \(0.463360\pi\)
\(140\) 2.47214 0.208934
\(141\) 5.00000 0.421076
\(142\) −12.5623 −1.05421
\(143\) −2.29180 −0.191650
\(144\) −9.70820 −0.809017
\(145\) 9.70820 0.806222
\(146\) −25.0344 −2.07187
\(147\) −12.2361 −1.00921
\(148\) 2.00000 0.164399
\(149\) −11.8885 −0.973947 −0.486974 0.873417i \(-0.661899\pi\)
−0.486974 + 0.873417i \(0.661899\pi\)
\(150\) −19.7984 −1.61653
\(151\) −0.236068 −0.0192109 −0.00960547 0.999954i \(-0.503058\pi\)
−0.00960547 + 0.999954i \(0.503058\pi\)
\(152\) −4.47214 −0.362738
\(153\) 10.4721 0.846622
\(154\) −1.52786 −0.123119
\(155\) 21.7082 1.74364
\(156\) 4.14590 0.331937
\(157\) 15.4164 1.23036 0.615182 0.788385i \(-0.289083\pi\)
0.615182 + 0.788385i \(0.289083\pi\)
\(158\) −11.2361 −0.893894
\(159\) −18.9443 −1.50238
\(160\) −10.9443 −0.865221
\(161\) −1.23607 −0.0974158
\(162\) 17.7984 1.39837
\(163\) −10.2361 −0.801751 −0.400875 0.916133i \(-0.631294\pi\)
−0.400875 + 0.916133i \(0.631294\pi\)
\(164\) 3.38197 0.264087
\(165\) 5.52786 0.430344
\(166\) 21.4164 1.66224
\(167\) 10.4721 0.810358 0.405179 0.914237i \(-0.367209\pi\)
0.405179 + 0.914237i \(0.367209\pi\)
\(168\) −6.18034 −0.476824
\(169\) −4.00000 −0.307692
\(170\) 27.4164 2.10274
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) 5.05573 0.384380 0.192190 0.981358i \(-0.438441\pi\)
0.192190 + 0.981358i \(0.438441\pi\)
\(174\) 10.8541 0.822847
\(175\) −6.76393 −0.511305
\(176\) 3.70820 0.279516
\(177\) −5.52786 −0.415500
\(178\) 2.47214 0.185294
\(179\) −12.7082 −0.949856 −0.474928 0.880025i \(-0.657526\pi\)
−0.474928 + 0.880025i \(0.657526\pi\)
\(180\) −4.00000 −0.298142
\(181\) −14.6525 −1.08911 −0.544555 0.838725i \(-0.683301\pi\)
−0.544555 + 0.838725i \(0.683301\pi\)
\(182\) 6.00000 0.444750
\(183\) 24.4721 1.80903
\(184\) 2.23607 0.164845
\(185\) −10.4721 −0.769927
\(186\) 24.2705 1.77960
\(187\) −4.00000 −0.292509
\(188\) 1.38197 0.100790
\(189\) 2.76393 0.201046
\(190\) −10.4721 −0.759729
\(191\) −3.81966 −0.276381 −0.138190 0.990406i \(-0.544129\pi\)
−0.138190 + 0.990406i \(0.544129\pi\)
\(192\) 9.47214 0.683593
\(193\) −7.94427 −0.571841 −0.285921 0.958253i \(-0.592299\pi\)
−0.285921 + 0.958253i \(0.592299\pi\)
\(194\) −6.94427 −0.498570
\(195\) −21.7082 −1.55456
\(196\) −3.38197 −0.241569
\(197\) 7.47214 0.532368 0.266184 0.963922i \(-0.414237\pi\)
0.266184 + 0.963922i \(0.414237\pi\)
\(198\) 2.47214 0.175687
\(199\) −25.7082 −1.82241 −0.911203 0.411957i \(-0.864845\pi\)
−0.911203 + 0.411957i \(0.864845\pi\)
\(200\) 12.2361 0.865221
\(201\) −16.1803 −1.14127
\(202\) 7.23607 0.509128
\(203\) 3.70820 0.260265
\(204\) 7.23607 0.506626
\(205\) −17.7082 −1.23679
\(206\) −29.4164 −2.04954
\(207\) 2.00000 0.139010
\(208\) −14.5623 −1.00971
\(209\) 1.52786 0.105685
\(210\) −14.4721 −0.998672
\(211\) 3.41641 0.235195 0.117598 0.993061i \(-0.462481\pi\)
0.117598 + 0.993061i \(0.462481\pi\)
\(212\) −5.23607 −0.359615
\(213\) 17.3607 1.18953
\(214\) 21.7082 1.48394
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 8.29180 0.562884
\(218\) 0 0
\(219\) 34.5967 2.33783
\(220\) 1.52786 0.103009
\(221\) 15.7082 1.05665
\(222\) −11.7082 −0.785803
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) −4.18034 −0.279311
\(225\) 10.9443 0.729618
\(226\) −21.4164 −1.42460
\(227\) 10.1803 0.675693 0.337846 0.941201i \(-0.390302\pi\)
0.337846 + 0.941201i \(0.390302\pi\)
\(228\) −2.76393 −0.183046
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 5.23607 0.345256
\(231\) 2.11146 0.138924
\(232\) −6.70820 −0.440415
\(233\) −15.4721 −1.01361 −0.506807 0.862060i \(-0.669174\pi\)
−0.506807 + 0.862060i \(0.669174\pi\)
\(234\) −9.70820 −0.634645
\(235\) −7.23607 −0.472029
\(236\) −1.52786 −0.0994555
\(237\) 15.5279 1.00864
\(238\) 10.4721 0.678808
\(239\) 18.2361 1.17959 0.589797 0.807552i \(-0.299208\pi\)
0.589797 + 0.807552i \(0.299208\pi\)
\(240\) 35.1246 2.26728
\(241\) 17.1246 1.10309 0.551547 0.834144i \(-0.314038\pi\)
0.551547 + 0.834144i \(0.314038\pi\)
\(242\) 16.8541 1.08342
\(243\) −17.8885 −1.14755
\(244\) 6.76393 0.433016
\(245\) 17.7082 1.13134
\(246\) −19.7984 −1.26230
\(247\) −6.00000 −0.381771
\(248\) −15.0000 −0.952501
\(249\) −29.5967 −1.87562
\(250\) 2.47214 0.156352
\(251\) 15.7082 0.991493 0.495747 0.868467i \(-0.334895\pi\)
0.495747 + 0.868467i \(0.334895\pi\)
\(252\) −1.52786 −0.0962464
\(253\) −0.763932 −0.0480280
\(254\) 33.5066 2.10239
\(255\) −37.8885 −2.37267
\(256\) 13.5623 0.847644
\(257\) 1.47214 0.0918293 0.0459147 0.998945i \(-0.485380\pi\)
0.0459147 + 0.998945i \(0.485380\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) −6.00000 −0.372104
\(261\) −6.00000 −0.371391
\(262\) −8.56231 −0.528981
\(263\) −14.9443 −0.921503 −0.460752 0.887529i \(-0.652420\pi\)
−0.460752 + 0.887529i \(0.652420\pi\)
\(264\) −3.81966 −0.235084
\(265\) 27.4164 1.68418
\(266\) −4.00000 −0.245256
\(267\) −3.41641 −0.209081
\(268\) −4.47214 −0.273179
\(269\) 9.94427 0.606313 0.303156 0.952941i \(-0.401960\pi\)
0.303156 + 0.952941i \(0.401960\pi\)
\(270\) −11.7082 −0.712539
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −25.4164 −1.54110
\(273\) −8.29180 −0.501842
\(274\) −22.4721 −1.35759
\(275\) −4.18034 −0.252084
\(276\) 1.38197 0.0831846
\(277\) 6.52786 0.392221 0.196111 0.980582i \(-0.437169\pi\)
0.196111 + 0.980582i \(0.437169\pi\)
\(278\) −4.38197 −0.262813
\(279\) −13.4164 −0.803219
\(280\) 8.94427 0.534522
\(281\) −13.2361 −0.789598 −0.394799 0.918768i \(-0.629186\pi\)
−0.394799 + 0.918768i \(0.629186\pi\)
\(282\) −8.09017 −0.481763
\(283\) 14.2918 0.849559 0.424780 0.905297i \(-0.360352\pi\)
0.424780 + 0.905297i \(0.360352\pi\)
\(284\) 4.79837 0.284731
\(285\) 14.4721 0.857255
\(286\) 3.70820 0.219271
\(287\) −6.76393 −0.399262
\(288\) 6.76393 0.398569
\(289\) 10.4164 0.612730
\(290\) −15.7082 −0.922417
\(291\) 9.59675 0.562571
\(292\) 9.56231 0.559592
\(293\) −10.4721 −0.611789 −0.305894 0.952065i \(-0.598955\pi\)
−0.305894 + 0.952065i \(0.598955\pi\)
\(294\) 19.7984 1.15466
\(295\) 8.00000 0.465778
\(296\) 7.23607 0.420588
\(297\) 1.70820 0.0991200
\(298\) 19.2361 1.11432
\(299\) 3.00000 0.173494
\(300\) 7.56231 0.436610
\(301\) 0 0
\(302\) 0.381966 0.0219797
\(303\) −10.0000 −0.574485
\(304\) 9.70820 0.556804
\(305\) −35.4164 −2.02794
\(306\) −16.9443 −0.968640
\(307\) 18.4721 1.05426 0.527130 0.849785i \(-0.323268\pi\)
0.527130 + 0.849785i \(0.323268\pi\)
\(308\) 0.583592 0.0332532
\(309\) 40.6525 2.31264
\(310\) −35.1246 −1.99494
\(311\) −9.18034 −0.520569 −0.260285 0.965532i \(-0.583816\pi\)
−0.260285 + 0.965532i \(0.583816\pi\)
\(312\) 15.0000 0.849208
\(313\) −20.3607 −1.15085 −0.575427 0.817853i \(-0.695164\pi\)
−0.575427 + 0.817853i \(0.695164\pi\)
\(314\) −24.9443 −1.40769
\(315\) 8.00000 0.450749
\(316\) 4.29180 0.241432
\(317\) −1.41641 −0.0795534 −0.0397767 0.999209i \(-0.512665\pi\)
−0.0397767 + 0.999209i \(0.512665\pi\)
\(318\) 30.6525 1.71891
\(319\) 2.29180 0.128316
\(320\) −13.7082 −0.766312
\(321\) −30.0000 −1.67444
\(322\) 2.00000 0.111456
\(323\) −10.4721 −0.582685
\(324\) −6.79837 −0.377687
\(325\) 16.4164 0.910618
\(326\) 16.5623 0.917301
\(327\) 0 0
\(328\) 12.2361 0.675624
\(329\) −2.76393 −0.152381
\(330\) −8.94427 −0.492366
\(331\) 11.6525 0.640478 0.320239 0.947337i \(-0.396237\pi\)
0.320239 + 0.947337i \(0.396237\pi\)
\(332\) −8.18034 −0.448954
\(333\) 6.47214 0.354671
\(334\) −16.9443 −0.927149
\(335\) 23.4164 1.27938
\(336\) 13.4164 0.731925
\(337\) −3.41641 −0.186104 −0.0930518 0.995661i \(-0.529662\pi\)
−0.0930518 + 0.995661i \(0.529662\pi\)
\(338\) 6.47214 0.352038
\(339\) 29.5967 1.60747
\(340\) −10.4721 −0.567931
\(341\) 5.12461 0.277513
\(342\) 6.47214 0.349973
\(343\) 15.4164 0.832408
\(344\) 0 0
\(345\) −7.23607 −0.389577
\(346\) −8.18034 −0.439778
\(347\) 25.8885 1.38977 0.694885 0.719121i \(-0.255455\pi\)
0.694885 + 0.719121i \(0.255455\pi\)
\(348\) −4.14590 −0.222243
\(349\) −2.41641 −0.129347 −0.0646737 0.997906i \(-0.520601\pi\)
−0.0646737 + 0.997906i \(0.520601\pi\)
\(350\) 10.9443 0.584996
\(351\) −6.70820 −0.358057
\(352\) −2.58359 −0.137706
\(353\) −35.3607 −1.88206 −0.941030 0.338324i \(-0.890140\pi\)
−0.941030 + 0.338324i \(0.890140\pi\)
\(354\) 8.94427 0.475383
\(355\) −25.1246 −1.33348
\(356\) −0.944272 −0.0500463
\(357\) −14.4721 −0.765947
\(358\) 20.5623 1.08675
\(359\) 15.8885 0.838565 0.419283 0.907856i \(-0.362282\pi\)
0.419283 + 0.907856i \(0.362282\pi\)
\(360\) −14.4721 −0.762749
\(361\) −15.0000 −0.789474
\(362\) 23.7082 1.24608
\(363\) −23.2918 −1.22250
\(364\) −2.29180 −0.120123
\(365\) −50.0689 −2.62073
\(366\) −39.5967 −2.06976
\(367\) 18.1803 0.949006 0.474503 0.880254i \(-0.342628\pi\)
0.474503 + 0.880254i \(0.342628\pi\)
\(368\) −4.85410 −0.253038
\(369\) 10.9443 0.569736
\(370\) 16.9443 0.880891
\(371\) 10.4721 0.543686
\(372\) −9.27051 −0.480654
\(373\) −5.70820 −0.295560 −0.147780 0.989020i \(-0.547213\pi\)
−0.147780 + 0.989020i \(0.547213\pi\)
\(374\) 6.47214 0.334666
\(375\) −3.41641 −0.176423
\(376\) 5.00000 0.257855
\(377\) −9.00000 −0.463524
\(378\) −4.47214 −0.230022
\(379\) −20.3607 −1.04586 −0.522929 0.852376i \(-0.675161\pi\)
−0.522929 + 0.852376i \(0.675161\pi\)
\(380\) 4.00000 0.205196
\(381\) −46.3050 −2.37227
\(382\) 6.18034 0.316214
\(383\) 24.9443 1.27459 0.637296 0.770619i \(-0.280053\pi\)
0.637296 + 0.770619i \(0.280053\pi\)
\(384\) −30.4508 −1.55394
\(385\) −3.05573 −0.155734
\(386\) 12.8541 0.654257
\(387\) 0 0
\(388\) 2.65248 0.134659
\(389\) 34.4721 1.74781 0.873903 0.486100i \(-0.161581\pi\)
0.873903 + 0.486100i \(0.161581\pi\)
\(390\) 35.1246 1.77860
\(391\) 5.23607 0.264799
\(392\) −12.2361 −0.618015
\(393\) 11.8328 0.596887
\(394\) −12.0902 −0.609094
\(395\) −22.4721 −1.13070
\(396\) −0.944272 −0.0474514
\(397\) 2.41641 0.121276 0.0606380 0.998160i \(-0.480686\pi\)
0.0606380 + 0.998160i \(0.480686\pi\)
\(398\) 41.5967 2.08506
\(399\) 5.52786 0.276739
\(400\) −26.5623 −1.32812
\(401\) 8.18034 0.408507 0.204253 0.978918i \(-0.434523\pi\)
0.204253 + 0.978918i \(0.434523\pi\)
\(402\) 26.1803 1.30576
\(403\) −20.1246 −1.00248
\(404\) −2.76393 −0.137511
\(405\) 35.5967 1.76882
\(406\) −6.00000 −0.297775
\(407\) −2.47214 −0.122539
\(408\) 26.1803 1.29612
\(409\) −23.3607 −1.15511 −0.577556 0.816351i \(-0.695993\pi\)
−0.577556 + 0.816351i \(0.695993\pi\)
\(410\) 28.6525 1.41504
\(411\) 31.0557 1.53187
\(412\) 11.2361 0.553561
\(413\) 3.05573 0.150363
\(414\) −3.23607 −0.159044
\(415\) 42.8328 2.10258
\(416\) 10.1459 0.497444
\(417\) 6.05573 0.296550
\(418\) −2.47214 −0.120916
\(419\) −31.4164 −1.53479 −0.767396 0.641173i \(-0.778448\pi\)
−0.767396 + 0.641173i \(0.778448\pi\)
\(420\) 5.52786 0.269732
\(421\) −23.7082 −1.15547 −0.577734 0.816225i \(-0.696063\pi\)
−0.577734 + 0.816225i \(0.696063\pi\)
\(422\) −5.52786 −0.269092
\(423\) 4.47214 0.217443
\(424\) −18.9443 −0.920015
\(425\) 28.6525 1.38985
\(426\) −28.0902 −1.36097
\(427\) −13.5279 −0.654659
\(428\) −8.29180 −0.400799
\(429\) −5.12461 −0.247419
\(430\) 0 0
\(431\) −26.4721 −1.27512 −0.637559 0.770402i \(-0.720056\pi\)
−0.637559 + 0.770402i \(0.720056\pi\)
\(432\) 10.8541 0.522218
\(433\) 40.1803 1.93094 0.965472 0.260507i \(-0.0838897\pi\)
0.965472 + 0.260507i \(0.0838897\pi\)
\(434\) −13.4164 −0.644008
\(435\) 21.7082 1.04083
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) −55.9787 −2.67477
\(439\) −5.29180 −0.252564 −0.126282 0.991994i \(-0.540304\pi\)
−0.126282 + 0.991994i \(0.540304\pi\)
\(440\) 5.52786 0.263531
\(441\) −10.9443 −0.521156
\(442\) −25.4164 −1.20894
\(443\) −2.12461 −0.100943 −0.0504717 0.998725i \(-0.516072\pi\)
−0.0504717 + 0.998725i \(0.516072\pi\)
\(444\) 4.47214 0.212238
\(445\) 4.94427 0.234381
\(446\) −6.47214 −0.306465
\(447\) −26.5836 −1.25736
\(448\) −5.23607 −0.247381
\(449\) 2.94427 0.138949 0.0694744 0.997584i \(-0.477868\pi\)
0.0694744 + 0.997584i \(0.477868\pi\)
\(450\) −17.7082 −0.834773
\(451\) −4.18034 −0.196845
\(452\) 8.18034 0.384771
\(453\) −0.527864 −0.0248012
\(454\) −16.4721 −0.773076
\(455\) 12.0000 0.562569
\(456\) −10.0000 −0.468293
\(457\) 35.1246 1.64306 0.821530 0.570165i \(-0.193121\pi\)
0.821530 + 0.570165i \(0.193121\pi\)
\(458\) 19.4164 0.907269
\(459\) −11.7082 −0.546492
\(460\) −2.00000 −0.0932505
\(461\) 7.47214 0.348012 0.174006 0.984745i \(-0.444329\pi\)
0.174006 + 0.984745i \(0.444329\pi\)
\(462\) −3.41641 −0.158946
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 14.5623 0.676038
\(465\) 48.5410 2.25104
\(466\) 25.0344 1.15970
\(467\) −30.9443 −1.43193 −0.715965 0.698136i \(-0.754013\pi\)
−0.715965 + 0.698136i \(0.754013\pi\)
\(468\) 3.70820 0.171412
\(469\) 8.94427 0.413008
\(470\) 11.7082 0.540059
\(471\) 34.4721 1.58839
\(472\) −5.52786 −0.254441
\(473\) 0 0
\(474\) −25.1246 −1.15401
\(475\) −10.9443 −0.502158
\(476\) −4.00000 −0.183340
\(477\) −16.9443 −0.775825
\(478\) −29.5066 −1.34960
\(479\) −17.5967 −0.804016 −0.402008 0.915636i \(-0.631688\pi\)
−0.402008 + 0.915636i \(0.631688\pi\)
\(480\) −24.4721 −1.11700
\(481\) 9.70820 0.442656
\(482\) −27.7082 −1.26207
\(483\) −2.76393 −0.125763
\(484\) −6.43769 −0.292622
\(485\) −13.8885 −0.630646
\(486\) 28.9443 1.31294
\(487\) −1.29180 −0.0585369 −0.0292684 0.999572i \(-0.509318\pi\)
−0.0292684 + 0.999572i \(0.509318\pi\)
\(488\) 24.4721 1.10780
\(489\) −22.8885 −1.03506
\(490\) −28.6525 −1.29439
\(491\) 39.6525 1.78949 0.894746 0.446576i \(-0.147357\pi\)
0.894746 + 0.446576i \(0.147357\pi\)
\(492\) 7.56231 0.340935
\(493\) −15.7082 −0.707462
\(494\) 9.70820 0.436793
\(495\) 4.94427 0.222228
\(496\) 32.5623 1.46209
\(497\) −9.59675 −0.430473
\(498\) 47.8885 2.14594
\(499\) 32.7082 1.46422 0.732110 0.681186i \(-0.238536\pi\)
0.732110 + 0.681186i \(0.238536\pi\)
\(500\) −0.944272 −0.0422291
\(501\) 23.4164 1.04617
\(502\) −25.4164 −1.13439
\(503\) −9.05573 −0.403775 −0.201887 0.979409i \(-0.564708\pi\)
−0.201887 + 0.979409i \(0.564708\pi\)
\(504\) −5.52786 −0.246231
\(505\) 14.4721 0.644002
\(506\) 1.23607 0.0549499
\(507\) −8.94427 −0.397229
\(508\) −12.7984 −0.567836
\(509\) 34.3050 1.52054 0.760270 0.649607i \(-0.225067\pi\)
0.760270 + 0.649607i \(0.225067\pi\)
\(510\) 61.3050 2.71463
\(511\) −19.1246 −0.846023
\(512\) 5.29180 0.233867
\(513\) 4.47214 0.197450
\(514\) −2.38197 −0.105064
\(515\) −58.8328 −2.59248
\(516\) 0 0
\(517\) −1.70820 −0.0751267
\(518\) 6.47214 0.284369
\(519\) 11.3050 0.496232
\(520\) −21.7082 −0.951968
\(521\) 4.58359 0.200811 0.100405 0.994947i \(-0.467986\pi\)
0.100405 + 0.994947i \(0.467986\pi\)
\(522\) 9.70820 0.424917
\(523\) 0.875388 0.0382781 0.0191390 0.999817i \(-0.493907\pi\)
0.0191390 + 0.999817i \(0.493907\pi\)
\(524\) 3.27051 0.142873
\(525\) −15.1246 −0.660092
\(526\) 24.1803 1.05431
\(527\) −35.1246 −1.53005
\(528\) 8.29180 0.360854
\(529\) 1.00000 0.0434783
\(530\) −44.3607 −1.92690
\(531\) −4.94427 −0.214563
\(532\) 1.52786 0.0662413
\(533\) 16.4164 0.711074
\(534\) 5.52786 0.239214
\(535\) 43.4164 1.87705
\(536\) −16.1803 −0.698884
\(537\) −28.4164 −1.22626
\(538\) −16.0902 −0.693696
\(539\) 4.18034 0.180060
\(540\) 4.47214 0.192450
\(541\) −7.58359 −0.326044 −0.163022 0.986622i \(-0.552124\pi\)
−0.163022 + 0.986622i \(0.552124\pi\)
\(542\) −12.9443 −0.556004
\(543\) −32.7639 −1.40603
\(544\) 17.7082 0.759233
\(545\) 0 0
\(546\) 13.4164 0.574169
\(547\) 37.5410 1.60514 0.802569 0.596559i \(-0.203466\pi\)
0.802569 + 0.596559i \(0.203466\pi\)
\(548\) 8.58359 0.366673
\(549\) 21.8885 0.934180
\(550\) 6.76393 0.288415
\(551\) 6.00000 0.255609
\(552\) 5.00000 0.212814
\(553\) −8.58359 −0.365011
\(554\) −10.5623 −0.448749
\(555\) −23.4164 −0.993971
\(556\) 1.67376 0.0709833
\(557\) 19.4164 0.822700 0.411350 0.911478i \(-0.365057\pi\)
0.411350 + 0.911478i \(0.365057\pi\)
\(558\) 21.7082 0.918982
\(559\) 0 0
\(560\) −19.4164 −0.820493
\(561\) −8.94427 −0.377627
\(562\) 21.4164 0.903397
\(563\) −15.0557 −0.634523 −0.317262 0.948338i \(-0.602763\pi\)
−0.317262 + 0.948338i \(0.602763\pi\)
\(564\) 3.09017 0.130120
\(565\) −42.8328 −1.80199
\(566\) −23.1246 −0.972000
\(567\) 13.5967 0.571010
\(568\) 17.3607 0.728438
\(569\) 0.180340 0.00756024 0.00378012 0.999993i \(-0.498797\pi\)
0.00378012 + 0.999993i \(0.498797\pi\)
\(570\) −23.4164 −0.980805
\(571\) −27.7082 −1.15955 −0.579776 0.814776i \(-0.696860\pi\)
−0.579776 + 0.814776i \(0.696860\pi\)
\(572\) −1.41641 −0.0592230
\(573\) −8.54102 −0.356806
\(574\) 10.9443 0.456805
\(575\) 5.47214 0.228204
\(576\) 8.47214 0.353006
\(577\) −12.8885 −0.536557 −0.268279 0.963341i \(-0.586455\pi\)
−0.268279 + 0.963341i \(0.586455\pi\)
\(578\) −16.8541 −0.701038
\(579\) −17.7639 −0.738244
\(580\) 6.00000 0.249136
\(581\) 16.3607 0.678755
\(582\) −15.5279 −0.643651
\(583\) 6.47214 0.268048
\(584\) 34.5967 1.43162
\(585\) −19.4164 −0.802770
\(586\) 16.9443 0.699961
\(587\) −11.2918 −0.466062 −0.233031 0.972469i \(-0.574864\pi\)
−0.233031 + 0.972469i \(0.574864\pi\)
\(588\) −7.56231 −0.311864
\(589\) 13.4164 0.552813
\(590\) −12.9443 −0.532907
\(591\) 16.7082 0.687284
\(592\) −15.7082 −0.645603
\(593\) 14.9443 0.613688 0.306844 0.951760i \(-0.400727\pi\)
0.306844 + 0.951760i \(0.400727\pi\)
\(594\) −2.76393 −0.113406
\(595\) 20.9443 0.858631
\(596\) −7.34752 −0.300966
\(597\) −57.4853 −2.35272
\(598\) −4.85410 −0.198499
\(599\) −1.88854 −0.0771638 −0.0385819 0.999255i \(-0.512284\pi\)
−0.0385819 + 0.999255i \(0.512284\pi\)
\(600\) 27.3607 1.11700
\(601\) 11.1115 0.453246 0.226623 0.973983i \(-0.427232\pi\)
0.226623 + 0.973983i \(0.427232\pi\)
\(602\) 0 0
\(603\) −14.4721 −0.589351
\(604\) −0.145898 −0.00593651
\(605\) 33.7082 1.37043
\(606\) 16.1803 0.657281
\(607\) 17.5279 0.711434 0.355717 0.934594i \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(608\) −6.76393 −0.274314
\(609\) 8.29180 0.336001
\(610\) 57.3050 2.32021
\(611\) 6.70820 0.271385
\(612\) 6.47214 0.261621
\(613\) −7.70820 −0.311331 −0.155666 0.987810i \(-0.549752\pi\)
−0.155666 + 0.987810i \(0.549752\pi\)
\(614\) −29.8885 −1.20620
\(615\) −39.5967 −1.59669
\(616\) 2.11146 0.0850730
\(617\) −16.4721 −0.663143 −0.331572 0.943430i \(-0.607579\pi\)
−0.331572 + 0.943430i \(0.607579\pi\)
\(618\) −65.7771 −2.64594
\(619\) −7.41641 −0.298091 −0.149045 0.988830i \(-0.547620\pi\)
−0.149045 + 0.988830i \(0.547620\pi\)
\(620\) 13.4164 0.538816
\(621\) −2.23607 −0.0897303
\(622\) 14.8541 0.595595
\(623\) 1.88854 0.0756629
\(624\) −32.5623 −1.30354
\(625\) −22.4164 −0.896656
\(626\) 32.9443 1.31672
\(627\) 3.41641 0.136438
\(628\) 9.52786 0.380203
\(629\) 16.9443 0.675612
\(630\) −12.9443 −0.515712
\(631\) −32.3607 −1.28826 −0.644129 0.764917i \(-0.722780\pi\)
−0.644129 + 0.764917i \(0.722780\pi\)
\(632\) 15.5279 0.617665
\(633\) 7.63932 0.303636
\(634\) 2.29180 0.0910188
\(635\) 67.0132 2.65934
\(636\) −11.7082 −0.464260
\(637\) −16.4164 −0.650442
\(638\) −3.70820 −0.146809
\(639\) 15.5279 0.614273
\(640\) 44.0689 1.74198
\(641\) 45.3050 1.78944 0.894719 0.446629i \(-0.147376\pi\)
0.894719 + 0.446629i \(0.147376\pi\)
\(642\) 48.5410 1.91576
\(643\) 19.5967 0.772820 0.386410 0.922327i \(-0.373715\pi\)
0.386410 + 0.922327i \(0.373715\pi\)
\(644\) −0.763932 −0.0301031
\(645\) 0 0
\(646\) 16.9443 0.666663
\(647\) −6.70820 −0.263727 −0.131863 0.991268i \(-0.542096\pi\)
−0.131863 + 0.991268i \(0.542096\pi\)
\(648\) −24.5967 −0.966252
\(649\) 1.88854 0.0741318
\(650\) −26.5623 −1.04186
\(651\) 18.5410 0.726680
\(652\) −6.32624 −0.247755
\(653\) 24.3050 0.951126 0.475563 0.879682i \(-0.342244\pi\)
0.475563 + 0.879682i \(0.342244\pi\)
\(654\) 0 0
\(655\) −17.1246 −0.669114
\(656\) −26.5623 −1.03708
\(657\) 30.9443 1.20725
\(658\) 4.47214 0.174342
\(659\) 20.6525 0.804506 0.402253 0.915528i \(-0.368227\pi\)
0.402253 + 0.915528i \(0.368227\pi\)
\(660\) 3.41641 0.132983
\(661\) −5.05573 −0.196645 −0.0983225 0.995155i \(-0.531348\pi\)
−0.0983225 + 0.995155i \(0.531348\pi\)
\(662\) −18.8541 −0.732785
\(663\) 35.1246 1.36413
\(664\) −29.5967 −1.14858
\(665\) −8.00000 −0.310227
\(666\) −10.4721 −0.405787
\(667\) −3.00000 −0.116160
\(668\) 6.47214 0.250414
\(669\) 8.94427 0.345806
\(670\) −37.8885 −1.46376
\(671\) −8.36068 −0.322760
\(672\) −9.34752 −0.360589
\(673\) 3.00000 0.115642 0.0578208 0.998327i \(-0.481585\pi\)
0.0578208 + 0.998327i \(0.481585\pi\)
\(674\) 5.52786 0.212925
\(675\) −12.2361 −0.470966
\(676\) −2.47214 −0.0950822
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −47.8885 −1.83915
\(679\) −5.30495 −0.203585
\(680\) −37.8885 −1.45296
\(681\) 22.7639 0.872316
\(682\) −8.29180 −0.317509
\(683\) −22.5967 −0.864641 −0.432320 0.901720i \(-0.642305\pi\)
−0.432320 + 0.901720i \(0.642305\pi\)
\(684\) −2.47214 −0.0945245
\(685\) −44.9443 −1.71723
\(686\) −24.9443 −0.952377
\(687\) −26.8328 −1.02374
\(688\) 0 0
\(689\) −25.4164 −0.968288
\(690\) 11.7082 0.445724
\(691\) 24.9443 0.948925 0.474462 0.880276i \(-0.342642\pi\)
0.474462 + 0.880276i \(0.342642\pi\)
\(692\) 3.12461 0.118780
\(693\) 1.88854 0.0717398
\(694\) −41.8885 −1.59007
\(695\) −8.76393 −0.332435
\(696\) −15.0000 −0.568574
\(697\) 28.6525 1.08529
\(698\) 3.90983 0.147989
\(699\) −34.5967 −1.30857
\(700\) −4.18034 −0.158002
\(701\) −26.1803 −0.988818 −0.494409 0.869229i \(-0.664615\pi\)
−0.494409 + 0.869229i \(0.664615\pi\)
\(702\) 10.8541 0.409662
\(703\) −6.47214 −0.244101
\(704\) −3.23607 −0.121964
\(705\) −16.1803 −0.609387
\(706\) 57.2148 2.15331
\(707\) 5.52786 0.207897
\(708\) −3.41641 −0.128396
\(709\) 16.0689 0.603480 0.301740 0.953390i \(-0.402433\pi\)
0.301740 + 0.953390i \(0.402433\pi\)
\(710\) 40.6525 1.52566
\(711\) 13.8885 0.520861
\(712\) −3.41641 −0.128035
\(713\) −6.70820 −0.251224
\(714\) 23.4164 0.876337
\(715\) 7.41641 0.277358
\(716\) −7.85410 −0.293522
\(717\) 40.7771 1.52285
\(718\) −25.7082 −0.959422
\(719\) −20.9443 −0.781090 −0.390545 0.920584i \(-0.627713\pi\)
−0.390545 + 0.920584i \(0.627713\pi\)
\(720\) 31.4164 1.17082
\(721\) −22.4721 −0.836906
\(722\) 24.2705 0.903255
\(723\) 38.2918 1.42409
\(724\) −9.05573 −0.336553
\(725\) −16.4164 −0.609690
\(726\) 37.6869 1.39869
\(727\) −14.2918 −0.530053 −0.265027 0.964241i \(-0.585381\pi\)
−0.265027 + 0.964241i \(0.585381\pi\)
\(728\) −8.29180 −0.307314
\(729\) −7.00000 −0.259259
\(730\) 81.0132 2.99843
\(731\) 0 0
\(732\) 15.1246 0.559022
\(733\) −26.7639 −0.988548 −0.494274 0.869306i \(-0.664566\pi\)
−0.494274 + 0.869306i \(0.664566\pi\)
\(734\) −29.4164 −1.08578
\(735\) 39.5967 1.46055
\(736\) 3.38197 0.124661
\(737\) 5.52786 0.203621
\(738\) −17.7082 −0.651848
\(739\) 49.1803 1.80913 0.904564 0.426338i \(-0.140197\pi\)
0.904564 + 0.426338i \(0.140197\pi\)
\(740\) −6.47214 −0.237920
\(741\) −13.4164 −0.492864
\(742\) −16.9443 −0.622044
\(743\) 0.875388 0.0321149 0.0160574 0.999871i \(-0.494889\pi\)
0.0160574 + 0.999871i \(0.494889\pi\)
\(744\) −33.5410 −1.22967
\(745\) 38.4721 1.40951
\(746\) 9.23607 0.338156
\(747\) −26.4721 −0.968565
\(748\) −2.47214 −0.0903902
\(749\) 16.5836 0.605951
\(750\) 5.52786 0.201849
\(751\) −44.3607 −1.61874 −0.809372 0.587296i \(-0.800192\pi\)
−0.809372 + 0.587296i \(0.800192\pi\)
\(752\) −10.8541 −0.395808
\(753\) 35.1246 1.28001
\(754\) 14.5623 0.530328
\(755\) 0.763932 0.0278023
\(756\) 1.70820 0.0621268
\(757\) −47.5967 −1.72993 −0.864967 0.501829i \(-0.832661\pi\)
−0.864967 + 0.501829i \(0.832661\pi\)
\(758\) 32.9443 1.19659
\(759\) −1.70820 −0.0620039
\(760\) 14.4721 0.524960
\(761\) −16.3050 −0.591054 −0.295527 0.955334i \(-0.595495\pi\)
−0.295527 + 0.955334i \(0.595495\pi\)
\(762\) 74.9230 2.71417
\(763\) 0 0
\(764\) −2.36068 −0.0854064
\(765\) −33.8885 −1.22524
\(766\) −40.3607 −1.45829
\(767\) −7.41641 −0.267791
\(768\) 30.3262 1.09430
\(769\) 17.1246 0.617529 0.308765 0.951138i \(-0.400084\pi\)
0.308765 + 0.951138i \(0.400084\pi\)
\(770\) 4.94427 0.178179
\(771\) 3.29180 0.118551
\(772\) −4.90983 −0.176709
\(773\) −14.4721 −0.520527 −0.260263 0.965538i \(-0.583809\pi\)
−0.260263 + 0.965538i \(0.583809\pi\)
\(774\) 0 0
\(775\) −36.7082 −1.31860
\(776\) 9.59675 0.344503
\(777\) −8.94427 −0.320874
\(778\) −55.7771 −1.99971
\(779\) −10.9443 −0.392119
\(780\) −13.4164 −0.480384
\(781\) −5.93112 −0.212232
\(782\) −8.47214 −0.302963
\(783\) 6.70820 0.239732
\(784\) 26.5623 0.948654
\(785\) −49.8885 −1.78060
\(786\) −19.1459 −0.682912
\(787\) 51.4164 1.83280 0.916399 0.400267i \(-0.131083\pi\)
0.916399 + 0.400267i \(0.131083\pi\)
\(788\) 4.61803 0.164511
\(789\) −33.4164 −1.18966
\(790\) 36.3607 1.29365
\(791\) −16.3607 −0.581719
\(792\) −3.41641 −0.121397
\(793\) 32.8328 1.16593
\(794\) −3.90983 −0.138755
\(795\) 61.3050 2.17426
\(796\) −15.8885 −0.563155
\(797\) 10.3607 0.366994 0.183497 0.983020i \(-0.441258\pi\)
0.183497 + 0.983020i \(0.441258\pi\)
\(798\) −8.94427 −0.316624
\(799\) 11.7082 0.414206
\(800\) 18.5066 0.654306
\(801\) −3.05573 −0.107969
\(802\) −13.2361 −0.467382
\(803\) −11.8197 −0.417107
\(804\) −10.0000 −0.352673
\(805\) 4.00000 0.140981
\(806\) 32.5623 1.14696
\(807\) 22.2361 0.782747
\(808\) −10.0000 −0.351799
\(809\) 47.8885 1.68367 0.841836 0.539734i \(-0.181475\pi\)
0.841836 + 0.539734i \(0.181475\pi\)
\(810\) −57.5967 −2.02374
\(811\) −55.6525 −1.95422 −0.977111 0.212728i \(-0.931765\pi\)
−0.977111 + 0.212728i \(0.931765\pi\)
\(812\) 2.29180 0.0804263
\(813\) 17.8885 0.627379
\(814\) 4.00000 0.140200
\(815\) 33.1246 1.16030
\(816\) −56.8328 −1.98955
\(817\) 0 0
\(818\) 37.7984 1.32159
\(819\) −7.41641 −0.259150
\(820\) −10.9443 −0.382191
\(821\) −21.0557 −0.734850 −0.367425 0.930053i \(-0.619761\pi\)
−0.367425 + 0.930053i \(0.619761\pi\)
\(822\) −50.2492 −1.75264
\(823\) 27.5410 0.960020 0.480010 0.877263i \(-0.340633\pi\)
0.480010 + 0.877263i \(0.340633\pi\)
\(824\) 40.6525 1.41620
\(825\) −9.34752 −0.325439
\(826\) −4.94427 −0.172033
\(827\) 10.4721 0.364152 0.182076 0.983284i \(-0.441718\pi\)
0.182076 + 0.983284i \(0.441718\pi\)
\(828\) 1.23607 0.0429563
\(829\) −40.2492 −1.39791 −0.698957 0.715164i \(-0.746352\pi\)
−0.698957 + 0.715164i \(0.746352\pi\)
\(830\) −69.3050 −2.40561
\(831\) 14.5967 0.506356
\(832\) 12.7082 0.440578
\(833\) −28.6525 −0.992749
\(834\) −9.79837 −0.339290
\(835\) −33.8885 −1.17276
\(836\) 0.944272 0.0326583
\(837\) 15.0000 0.518476
\(838\) 50.8328 1.75599
\(839\) −0.875388 −0.0302218 −0.0151109 0.999886i \(-0.504810\pi\)
−0.0151109 + 0.999886i \(0.504810\pi\)
\(840\) 20.0000 0.690066
\(841\) −20.0000 −0.689655
\(842\) 38.3607 1.32200
\(843\) −29.5967 −1.01937
\(844\) 2.11146 0.0726793
\(845\) 12.9443 0.445296
\(846\) −7.23607 −0.248781
\(847\) 12.8754 0.442404
\(848\) 41.1246 1.41222
\(849\) 31.9574 1.09678
\(850\) −46.3607 −1.59016
\(851\) 3.23607 0.110931
\(852\) 10.7295 0.367586
\(853\) −37.4164 −1.28111 −0.640557 0.767911i \(-0.721296\pi\)
−0.640557 + 0.767911i \(0.721296\pi\)
\(854\) 21.8885 0.749011
\(855\) 12.9443 0.442685
\(856\) −30.0000 −1.02538
\(857\) −7.47214 −0.255243 −0.127622 0.991823i \(-0.540734\pi\)
−0.127622 + 0.991823i \(0.540734\pi\)
\(858\) 8.29180 0.283077
\(859\) −3.29180 −0.112315 −0.0561573 0.998422i \(-0.517885\pi\)
−0.0561573 + 0.998422i \(0.517885\pi\)
\(860\) 0 0
\(861\) −15.1246 −0.515445
\(862\) 42.8328 1.45889
\(863\) 45.5410 1.55023 0.775117 0.631818i \(-0.217691\pi\)
0.775117 + 0.631818i \(0.217691\pi\)
\(864\) −7.56231 −0.257275
\(865\) −16.3607 −0.556280
\(866\) −65.0132 −2.20924
\(867\) 23.2918 0.791031
\(868\) 5.12461 0.173941
\(869\) −5.30495 −0.179958
\(870\) −35.1246 −1.19084
\(871\) −21.7082 −0.735554
\(872\) 0 0
\(873\) 8.58359 0.290511
\(874\) 3.23607 0.109462
\(875\) 1.88854 0.0638444
\(876\) 21.3820 0.722430
\(877\) −27.5279 −0.929550 −0.464775 0.885429i \(-0.653865\pi\)
−0.464775 + 0.885429i \(0.653865\pi\)
\(878\) 8.56231 0.288964
\(879\) −23.4164 −0.789816
\(880\) −12.0000 −0.404520
\(881\) 21.8197 0.735123 0.367562 0.929999i \(-0.380193\pi\)
0.367562 + 0.929999i \(0.380193\pi\)
\(882\) 17.7082 0.596266
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 9.70820 0.326522
\(885\) 17.8885 0.601317
\(886\) 3.43769 0.115492
\(887\) −35.0689 −1.17750 −0.588749 0.808316i \(-0.700379\pi\)
−0.588749 + 0.808316i \(0.700379\pi\)
\(888\) 16.1803 0.542977
\(889\) 25.5967 0.858487
\(890\) −8.00000 −0.268161
\(891\) 8.40325 0.281520
\(892\) 2.47214 0.0827732
\(893\) −4.47214 −0.149654
\(894\) 43.0132 1.43858
\(895\) 41.1246 1.37464
\(896\) 16.8328 0.562345
\(897\) 6.70820 0.223980
\(898\) −4.76393 −0.158974
\(899\) 20.1246 0.671193
\(900\) 6.76393 0.225464
\(901\) −44.3607 −1.47787
\(902\) 6.76393 0.225214
\(903\) 0 0
\(904\) 29.5967 0.984373
\(905\) 47.4164 1.57617
\(906\) 0.854102 0.0283756
\(907\) 40.2492 1.33645 0.668227 0.743958i \(-0.267054\pi\)
0.668227 + 0.743958i \(0.267054\pi\)
\(908\) 6.29180 0.208801
\(909\) −8.94427 −0.296663
\(910\) −19.4164 −0.643648
\(911\) −31.3050 −1.03718 −0.518590 0.855023i \(-0.673543\pi\)
−0.518590 + 0.855023i \(0.673543\pi\)
\(912\) 21.7082 0.718830
\(913\) 10.1115 0.334640
\(914\) −56.8328 −1.87986
\(915\) −79.1935 −2.61806
\(916\) −7.41641 −0.245045
\(917\) −6.54102 −0.216003
\(918\) 18.9443 0.625254
\(919\) 0.875388 0.0288764 0.0144382 0.999896i \(-0.495404\pi\)
0.0144382 + 0.999896i \(0.495404\pi\)
\(920\) −7.23607 −0.238566
\(921\) 41.3050 1.36104
\(922\) −12.0902 −0.398169
\(923\) 23.2918 0.766659
\(924\) 1.30495 0.0429298
\(925\) 17.7082 0.582242
\(926\) 32.3607 1.06344
\(927\) 36.3607 1.19424
\(928\) −10.1459 −0.333055
\(929\) −41.9443 −1.37615 −0.688073 0.725641i \(-0.741543\pi\)
−0.688073 + 0.725641i \(0.741543\pi\)
\(930\) −78.5410 −2.57546
\(931\) 10.9443 0.358684
\(932\) −9.56231 −0.313224
\(933\) −20.5279 −0.672052
\(934\) 50.0689 1.63830
\(935\) 12.9443 0.423323
\(936\) 13.4164 0.438529
\(937\) 11.8197 0.386131 0.193066 0.981186i \(-0.438157\pi\)
0.193066 + 0.981186i \(0.438157\pi\)
\(938\) −14.4721 −0.472532
\(939\) −45.5279 −1.48575
\(940\) −4.47214 −0.145865
\(941\) −24.6525 −0.803648 −0.401824 0.915717i \(-0.631624\pi\)
−0.401824 + 0.915717i \(0.631624\pi\)
\(942\) −55.7771 −1.81732
\(943\) 5.47214 0.178197
\(944\) 12.0000 0.390567
\(945\) −8.94427 −0.290957
\(946\) 0 0
\(947\) −33.1803 −1.07822 −0.539108 0.842237i \(-0.681239\pi\)
−0.539108 + 0.842237i \(0.681239\pi\)
\(948\) 9.59675 0.311688
\(949\) 46.4164 1.50674
\(950\) 17.7082 0.574530
\(951\) −3.16718 −0.102703
\(952\) −14.4721 −0.469045
\(953\) 11.5279 0.373424 0.186712 0.982415i \(-0.440217\pi\)
0.186712 + 0.982415i \(0.440217\pi\)
\(954\) 27.4164 0.887639
\(955\) 12.3607 0.399982
\(956\) 11.2705 0.364514
\(957\) 5.12461 0.165655
\(958\) 28.4721 0.919893
\(959\) −17.1672 −0.554357
\(960\) −30.6525 −0.989304
\(961\) 14.0000 0.451613
\(962\) −15.7082 −0.506453
\(963\) −26.8328 −0.864675
\(964\) 10.5836 0.340875
\(965\) 25.7082 0.827576
\(966\) 4.47214 0.143889
\(967\) −39.5410 −1.27155 −0.635777 0.771873i \(-0.719320\pi\)
−0.635777 + 0.771873i \(0.719320\pi\)
\(968\) −23.2918 −0.748627
\(969\) −23.4164 −0.752243
\(970\) 22.4721 0.721537
\(971\) 7.52786 0.241581 0.120790 0.992678i \(-0.461457\pi\)
0.120790 + 0.992678i \(0.461457\pi\)
\(972\) −11.0557 −0.354613
\(973\) −3.34752 −0.107317
\(974\) 2.09017 0.0669734
\(975\) 36.7082 1.17560
\(976\) −53.1246 −1.70048
\(977\) −54.6525 −1.74849 −0.874244 0.485487i \(-0.838642\pi\)
−0.874244 + 0.485487i \(0.838642\pi\)
\(978\) 37.0344 1.18423
\(979\) 1.16718 0.0373034
\(980\) 10.9443 0.349602
\(981\) 0 0
\(982\) −64.1591 −2.04740
\(983\) −31.5279 −1.00558 −0.502791 0.864408i \(-0.667694\pi\)
−0.502791 + 0.864408i \(0.667694\pi\)
\(984\) 27.3607 0.872227
\(985\) −24.1803 −0.770450
\(986\) 25.4164 0.809423
\(987\) −6.18034 −0.196722
\(988\) −3.70820 −0.117974
\(989\) 0 0
\(990\) −8.00000 −0.254257
\(991\) 24.0000 0.762385 0.381193 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) −22.6869 −0.720310
\(993\) 26.0557 0.826854
\(994\) 15.5279 0.492514
\(995\) 83.1935 2.63741
\(996\) −18.2918 −0.579598
\(997\) −36.8328 −1.16651 −0.583253 0.812290i \(-0.698221\pi\)
−0.583253 + 0.812290i \(0.698221\pi\)
\(998\) −52.9230 −1.67525
\(999\) −7.23607 −0.228939
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 \(a_p\))