Properties

Label 2001.2.a.i.1.3
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.9780654445\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 5 x^{5} + 18 x^{4} + 4 x^{3} - 26 x^{2} + x + 8\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.44008\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} -1.05791 q^{10} -2.70213 q^{11} +0.0738306 q^{12} -2.87193 q^{13} -5.38039 q^{14} +0.734622 q^{15} -4.14221 q^{16} -2.75120 q^{17} -1.44008 q^{18} -5.54463 q^{19} +0.0542376 q^{20} +3.73618 q^{21} +3.89128 q^{22} +1.00000 q^{23} +2.77384 q^{24} -4.46033 q^{25} +4.13581 q^{26} +1.00000 q^{27} +0.275844 q^{28} -1.00000 q^{29} -1.05791 q^{30} -10.2606 q^{31} +0.417438 q^{32} -2.70213 q^{33} +3.96194 q^{34} +2.74468 q^{35} +0.0738306 q^{36} -11.4951 q^{37} +7.98471 q^{38} -2.87193 q^{39} +2.03772 q^{40} -1.81028 q^{41} -5.38039 q^{42} +0.181163 q^{43} -0.199500 q^{44} +0.734622 q^{45} -1.44008 q^{46} -6.02453 q^{47} -4.14221 q^{48} +6.95901 q^{49} +6.42323 q^{50} -2.75120 q^{51} -0.212037 q^{52} -0.662081 q^{53} -1.44008 q^{54} -1.98504 q^{55} +10.3635 q^{56} -5.54463 q^{57} +1.44008 q^{58} -0.174372 q^{59} +0.0542376 q^{60} -5.37843 q^{61} +14.7760 q^{62} +3.73618 q^{63} +7.68328 q^{64} -2.10978 q^{65} +3.89128 q^{66} +15.9959 q^{67} -0.203123 q^{68} +1.00000 q^{69} -3.95255 q^{70} +12.0047 q^{71} +2.77384 q^{72} +0.990842 q^{73} +16.5538 q^{74} -4.46033 q^{75} -0.409363 q^{76} -10.0956 q^{77} +4.13581 q^{78} -2.96323 q^{79} -3.04296 q^{80} +1.00000 q^{81} +2.60694 q^{82} +1.08995 q^{83} +0.275844 q^{84} -2.02109 q^{85} -0.260889 q^{86} -1.00000 q^{87} -7.49527 q^{88} +5.21337 q^{89} -1.05791 q^{90} -10.7300 q^{91} +0.0738306 q^{92} -10.2606 q^{93} +8.67580 q^{94} -4.07320 q^{95} +0.417438 q^{96} -3.97122 q^{97} -10.0215 q^{98} -2.70213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + 3q^{10} - 4q^{11} + 5q^{12} - 18q^{13} - 2q^{14} - 3q^{15} - 7q^{16} - 3q^{17} - 3q^{18} - 4q^{19} - 2q^{20} - 5q^{21} - 26q^{22} + 7q^{23} - 6q^{24} - 8q^{25} - 7q^{26} + 7q^{27} - 6q^{28} - 7q^{29} + 3q^{30} - 22q^{31} + 5q^{32} - 4q^{33} + 9q^{34} + 3q^{35} + 5q^{36} - 25q^{37} + 14q^{38} - 18q^{39} - 10q^{40} - 13q^{41} - 2q^{42} - 2q^{43} + 4q^{44} - 3q^{45} - 3q^{46} - 25q^{47} - 7q^{48} - 8q^{49} + 19q^{50} - 3q^{51} - 12q^{52} - 5q^{53} - 3q^{54} - 15q^{55} + 18q^{56} - 4q^{57} + 3q^{58} + 11q^{59} - 2q^{60} - 33q^{61} + 28q^{62} - 5q^{63} - 14q^{64} - 2q^{65} - 26q^{66} + 8q^{67} + 12q^{68} + 7q^{69} - 22q^{70} - 6q^{71} - 6q^{72} + 15q^{73} + 34q^{74} - 8q^{75} - 28q^{76} - q^{77} - 7q^{78} - 15q^{79} - 12q^{80} + 7q^{81} - 14q^{82} + 21q^{83} - 6q^{84} - 28q^{85} - 12q^{86} - 7q^{87} - 13q^{88} + 8q^{89} + 3q^{90} + 6q^{91} + 5q^{92} - 22q^{93} - 35q^{94} - 25q^{95} + 5q^{96} + 13q^{97} + q^{98} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44008 −1.01829 −0.509145 0.860681i \(-0.670038\pi\)
−0.509145 + 0.860681i \(0.670038\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.0738306 0.0369153
\(5\) 0.734622 0.328533 0.164266 0.986416i \(-0.447474\pi\)
0.164266 + 0.986416i \(0.447474\pi\)
\(6\) −1.44008 −0.587910
\(7\) 3.73618 1.41214 0.706071 0.708141i \(-0.250466\pi\)
0.706071 + 0.708141i \(0.250466\pi\)
\(8\) 2.77384 0.980700
\(9\) 1.00000 0.333333
\(10\) −1.05791 −0.334542
\(11\) −2.70213 −0.814723 −0.407361 0.913267i \(-0.633551\pi\)
−0.407361 + 0.913267i \(0.633551\pi\)
\(12\) 0.0738306 0.0213131
\(13\) −2.87193 −0.796531 −0.398265 0.917270i \(-0.630388\pi\)
−0.398265 + 0.917270i \(0.630388\pi\)
\(14\) −5.38039 −1.43797
\(15\) 0.734622 0.189678
\(16\) −4.14221 −1.03555
\(17\) −2.75120 −0.667263 −0.333632 0.942704i \(-0.608274\pi\)
−0.333632 + 0.942704i \(0.608274\pi\)
\(18\) −1.44008 −0.339430
\(19\) −5.54463 −1.27202 −0.636012 0.771679i \(-0.719417\pi\)
−0.636012 + 0.771679i \(0.719417\pi\)
\(20\) 0.0542376 0.0121279
\(21\) 3.73618 0.815300
\(22\) 3.89128 0.829625
\(23\) 1.00000 0.208514
\(24\) 2.77384 0.566207
\(25\) −4.46033 −0.892066
\(26\) 4.13581 0.811099
\(27\) 1.00000 0.192450
\(28\) 0.275844 0.0521296
\(29\) −1.00000 −0.185695
\(30\) −1.05791 −0.193148
\(31\) −10.2606 −1.84285 −0.921425 0.388557i \(-0.872974\pi\)
−0.921425 + 0.388557i \(0.872974\pi\)
\(32\) 0.417438 0.0737933
\(33\) −2.70213 −0.470380
\(34\) 3.96194 0.679468
\(35\) 2.74468 0.463935
\(36\) 0.0738306 0.0123051
\(37\) −11.4951 −1.88978 −0.944888 0.327394i \(-0.893829\pi\)
−0.944888 + 0.327394i \(0.893829\pi\)
\(38\) 7.98471 1.29529
\(39\) −2.87193 −0.459877
\(40\) 2.03772 0.322192
\(41\) −1.81028 −0.282718 −0.141359 0.989958i \(-0.545147\pi\)
−0.141359 + 0.989958i \(0.545147\pi\)
\(42\) −5.38039 −0.830212
\(43\) 0.181163 0.0276271 0.0138136 0.999905i \(-0.495603\pi\)
0.0138136 + 0.999905i \(0.495603\pi\)
\(44\) −0.199500 −0.0300757
\(45\) 0.734622 0.109511
\(46\) −1.44008 −0.212328
\(47\) −6.02453 −0.878768 −0.439384 0.898299i \(-0.644803\pi\)
−0.439384 + 0.898299i \(0.644803\pi\)
\(48\) −4.14221 −0.597877
\(49\) 6.95901 0.994144
\(50\) 6.42323 0.908382
\(51\) −2.75120 −0.385245
\(52\) −0.212037 −0.0294042
\(53\) −0.662081 −0.0909438 −0.0454719 0.998966i \(-0.514479\pi\)
−0.0454719 + 0.998966i \(0.514479\pi\)
\(54\) −1.44008 −0.195970
\(55\) −1.98504 −0.267663
\(56\) 10.3635 1.38489
\(57\) −5.54463 −0.734404
\(58\) 1.44008 0.189092
\(59\) −0.174372 −0.0227013 −0.0113506 0.999936i \(-0.503613\pi\)
−0.0113506 + 0.999936i \(0.503613\pi\)
\(60\) 0.0542376 0.00700204
\(61\) −5.37843 −0.688637 −0.344318 0.938853i \(-0.611890\pi\)
−0.344318 + 0.938853i \(0.611890\pi\)
\(62\) 14.7760 1.87656
\(63\) 3.73618 0.470714
\(64\) 7.68328 0.960410
\(65\) −2.10978 −0.261686
\(66\) 3.89128 0.478984
\(67\) 15.9959 1.95421 0.977106 0.212754i \(-0.0682432\pi\)
0.977106 + 0.212754i \(0.0682432\pi\)
\(68\) −0.203123 −0.0246322
\(69\) 1.00000 0.120386
\(70\) −3.95255 −0.472420
\(71\) 12.0047 1.42469 0.712347 0.701828i \(-0.247632\pi\)
0.712347 + 0.701828i \(0.247632\pi\)
\(72\) 2.77384 0.326900
\(73\) 0.990842 0.115969 0.0579847 0.998317i \(-0.481533\pi\)
0.0579847 + 0.998317i \(0.481533\pi\)
\(74\) 16.5538 1.92434
\(75\) −4.46033 −0.515035
\(76\) −0.409363 −0.0469572
\(77\) −10.0956 −1.15050
\(78\) 4.13581 0.468288
\(79\) −2.96323 −0.333390 −0.166695 0.986009i \(-0.553309\pi\)
−0.166695 + 0.986009i \(0.553309\pi\)
\(80\) −3.04296 −0.340213
\(81\) 1.00000 0.111111
\(82\) 2.60694 0.287889
\(83\) 1.08995 0.119638 0.0598189 0.998209i \(-0.480948\pi\)
0.0598189 + 0.998209i \(0.480948\pi\)
\(84\) 0.275844 0.0300971
\(85\) −2.02109 −0.219218
\(86\) −0.260889 −0.0281324
\(87\) −1.00000 −0.107211
\(88\) −7.49527 −0.798999
\(89\) 5.21337 0.552617 0.276308 0.961069i \(-0.410889\pi\)
0.276308 + 0.961069i \(0.410889\pi\)
\(90\) −1.05791 −0.111514
\(91\) −10.7300 −1.12481
\(92\) 0.0738306 0.00769737
\(93\) −10.2606 −1.06397
\(94\) 8.67580 0.894841
\(95\) −4.07320 −0.417902
\(96\) 0.417438 0.0426046
\(97\) −3.97122 −0.403217 −0.201608 0.979466i \(-0.564617\pi\)
−0.201608 + 0.979466i \(0.564617\pi\)
\(98\) −10.0215 −1.01233
\(99\) −2.70213 −0.271574
\(100\) −0.329309 −0.0329309
\(101\) 18.4855 1.83938 0.919688 0.392650i \(-0.128442\pi\)
0.919688 + 0.392650i \(0.128442\pi\)
\(102\) 3.96194 0.392291
\(103\) −2.24948 −0.221648 −0.110824 0.993840i \(-0.535349\pi\)
−0.110824 + 0.993840i \(0.535349\pi\)
\(104\) −7.96627 −0.781157
\(105\) 2.74468 0.267853
\(106\) 0.953449 0.0926072
\(107\) −12.9231 −1.24932 −0.624660 0.780897i \(-0.714762\pi\)
−0.624660 + 0.780897i \(0.714762\pi\)
\(108\) 0.0738306 0.00710435
\(109\) 16.2725 1.55863 0.779313 0.626635i \(-0.215568\pi\)
0.779313 + 0.626635i \(0.215568\pi\)
\(110\) 2.85862 0.272559
\(111\) −11.4951 −1.09106
\(112\) −15.4760 −1.46235
\(113\) −11.3227 −1.06515 −0.532573 0.846384i \(-0.678775\pi\)
−0.532573 + 0.846384i \(0.678775\pi\)
\(114\) 7.98471 0.747836
\(115\) 0.734622 0.0685038
\(116\) −0.0738306 −0.00685500
\(117\) −2.87193 −0.265510
\(118\) 0.251109 0.0231165
\(119\) −10.2790 −0.942270
\(120\) 2.03772 0.186018
\(121\) −3.69849 −0.336227
\(122\) 7.74536 0.701232
\(123\) −1.81028 −0.163227
\(124\) −0.757543 −0.0680294
\(125\) −6.94976 −0.621606
\(126\) −5.38039 −0.479323
\(127\) −9.54485 −0.846968 −0.423484 0.905903i \(-0.639193\pi\)
−0.423484 + 0.905903i \(0.639193\pi\)
\(128\) −11.8994 −1.05177
\(129\) 0.181163 0.0159505
\(130\) 3.03826 0.266473
\(131\) 15.3632 1.34229 0.671146 0.741326i \(-0.265803\pi\)
0.671146 + 0.741326i \(0.265803\pi\)
\(132\) −0.199500 −0.0173642
\(133\) −20.7157 −1.79628
\(134\) −23.0354 −1.98995
\(135\) 0.734622 0.0632262
\(136\) −7.63137 −0.654385
\(137\) 15.4197 1.31739 0.658697 0.752408i \(-0.271108\pi\)
0.658697 + 0.752408i \(0.271108\pi\)
\(138\) −1.44008 −0.122588
\(139\) −16.2808 −1.38092 −0.690461 0.723370i \(-0.742592\pi\)
−0.690461 + 0.723370i \(0.742592\pi\)
\(140\) 0.202641 0.0171263
\(141\) −6.02453 −0.507357
\(142\) −17.2877 −1.45075
\(143\) 7.76033 0.648952
\(144\) −4.14221 −0.345184
\(145\) −0.734622 −0.0610070
\(146\) −1.42689 −0.118090
\(147\) 6.95901 0.573969
\(148\) −0.848687 −0.0697617
\(149\) −11.2442 −0.921159 −0.460580 0.887618i \(-0.652358\pi\)
−0.460580 + 0.887618i \(0.652358\pi\)
\(150\) 6.42323 0.524455
\(151\) −13.0268 −1.06011 −0.530053 0.847965i \(-0.677828\pi\)
−0.530053 + 0.847965i \(0.677828\pi\)
\(152\) −15.3799 −1.24747
\(153\) −2.75120 −0.222421
\(154\) 14.5385 1.17155
\(155\) −7.53762 −0.605436
\(156\) −0.212037 −0.0169765
\(157\) 5.40186 0.431116 0.215558 0.976491i \(-0.430843\pi\)
0.215558 + 0.976491i \(0.430843\pi\)
\(158\) 4.26729 0.339488
\(159\) −0.662081 −0.0525064
\(160\) 0.306659 0.0242435
\(161\) 3.73618 0.294452
\(162\) −1.44008 −0.113143
\(163\) 5.91249 0.463102 0.231551 0.972823i \(-0.425620\pi\)
0.231551 + 0.972823i \(0.425620\pi\)
\(164\) −0.133654 −0.0104366
\(165\) −1.98504 −0.154535
\(166\) −1.56962 −0.121826
\(167\) −0.341562 −0.0264308 −0.0132154 0.999913i \(-0.504207\pi\)
−0.0132154 + 0.999913i \(0.504207\pi\)
\(168\) 10.3635 0.799565
\(169\) −4.75201 −0.365539
\(170\) 2.91053 0.223227
\(171\) −5.54463 −0.424008
\(172\) 0.0133754 0.00101986
\(173\) 13.8093 1.04990 0.524950 0.851133i \(-0.324084\pi\)
0.524950 + 0.851133i \(0.324084\pi\)
\(174\) 1.44008 0.109172
\(175\) −16.6646 −1.25972
\(176\) 11.1928 0.843688
\(177\) −0.174372 −0.0131066
\(178\) −7.50768 −0.562724
\(179\) 15.3349 1.14619 0.573093 0.819490i \(-0.305743\pi\)
0.573093 + 0.819490i \(0.305743\pi\)
\(180\) 0.0542376 0.00404263
\(181\) −4.64338 −0.345139 −0.172570 0.984997i \(-0.555207\pi\)
−0.172570 + 0.984997i \(0.555207\pi\)
\(182\) 15.4521 1.14539
\(183\) −5.37843 −0.397585
\(184\) 2.77384 0.204490
\(185\) −8.44452 −0.620853
\(186\) 14.7760 1.08343
\(187\) 7.43409 0.543635
\(188\) −0.444795 −0.0324400
\(189\) 3.73618 0.271767
\(190\) 5.86574 0.425545
\(191\) 9.85469 0.713060 0.356530 0.934284i \(-0.383960\pi\)
0.356530 + 0.934284i \(0.383960\pi\)
\(192\) 7.68328 0.554493
\(193\) −21.2787 −1.53167 −0.765837 0.643035i \(-0.777675\pi\)
−0.765837 + 0.643035i \(0.777675\pi\)
\(194\) 5.71888 0.410592
\(195\) −2.10978 −0.151085
\(196\) 0.513788 0.0366991
\(197\) 9.61747 0.685216 0.342608 0.939478i \(-0.388690\pi\)
0.342608 + 0.939478i \(0.388690\pi\)
\(198\) 3.89128 0.276542
\(199\) 4.39951 0.311873 0.155936 0.987767i \(-0.450161\pi\)
0.155936 + 0.987767i \(0.450161\pi\)
\(200\) −12.3722 −0.874849
\(201\) 15.9959 1.12826
\(202\) −26.6206 −1.87302
\(203\) −3.73618 −0.262228
\(204\) −0.203123 −0.0142214
\(205\) −1.32987 −0.0928821
\(206\) 3.23944 0.225702
\(207\) 1.00000 0.0695048
\(208\) 11.8961 0.824849
\(209\) 14.9823 1.03635
\(210\) −3.95255 −0.272752
\(211\) 1.95120 0.134326 0.0671630 0.997742i \(-0.478605\pi\)
0.0671630 + 0.997742i \(0.478605\pi\)
\(212\) −0.0488818 −0.00335722
\(213\) 12.0047 0.822547
\(214\) 18.6103 1.27217
\(215\) 0.133086 0.00907641
\(216\) 2.77384 0.188736
\(217\) −38.3352 −2.60236
\(218\) −23.4337 −1.58713
\(219\) 0.990842 0.0669549
\(220\) −0.146557 −0.00988087
\(221\) 7.90125 0.531495
\(222\) 16.5538 1.11102
\(223\) 5.60600 0.375406 0.187703 0.982226i \(-0.439896\pi\)
0.187703 + 0.982226i \(0.439896\pi\)
\(224\) 1.55962 0.104207
\(225\) −4.46033 −0.297355
\(226\) 16.3055 1.08463
\(227\) −5.99730 −0.398055 −0.199027 0.979994i \(-0.563778\pi\)
−0.199027 + 0.979994i \(0.563778\pi\)
\(228\) −0.409363 −0.0271107
\(229\) −14.2127 −0.939199 −0.469599 0.882880i \(-0.655602\pi\)
−0.469599 + 0.882880i \(0.655602\pi\)
\(230\) −1.05791 −0.0697568
\(231\) −10.0956 −0.664244
\(232\) −2.77384 −0.182111
\(233\) −28.3893 −1.85985 −0.929923 0.367755i \(-0.880126\pi\)
−0.929923 + 0.367755i \(0.880126\pi\)
\(234\) 4.13581 0.270366
\(235\) −4.42575 −0.288704
\(236\) −0.0128740 −0.000838024 0
\(237\) −2.96323 −0.192483
\(238\) 14.8025 0.959504
\(239\) 20.3486 1.31624 0.658121 0.752912i \(-0.271352\pi\)
0.658121 + 0.752912i \(0.271352\pi\)
\(240\) −3.04296 −0.196422
\(241\) 19.2101 1.23743 0.618715 0.785615i \(-0.287654\pi\)
0.618715 + 0.785615i \(0.287654\pi\)
\(242\) 5.32613 0.342376
\(243\) 1.00000 0.0641500
\(244\) −0.397093 −0.0254212
\(245\) 5.11224 0.326609
\(246\) 2.60694 0.166213
\(247\) 15.9238 1.01321
\(248\) −28.4611 −1.80728
\(249\) 1.08995 0.0690729
\(250\) 10.0082 0.632975
\(251\) −1.27973 −0.0807761 −0.0403880 0.999184i \(-0.512859\pi\)
−0.0403880 + 0.999184i \(0.512859\pi\)
\(252\) 0.275844 0.0173765
\(253\) −2.70213 −0.169881
\(254\) 13.7453 0.862460
\(255\) −2.02109 −0.126565
\(256\) 1.76955 0.110597
\(257\) −21.5611 −1.34494 −0.672472 0.740123i \(-0.734767\pi\)
−0.672472 + 0.740123i \(0.734767\pi\)
\(258\) −0.260889 −0.0162423
\(259\) −42.9475 −2.66863
\(260\) −0.155767 −0.00966023
\(261\) −1.00000 −0.0618984
\(262\) −22.1243 −1.36684
\(263\) 14.7781 0.911258 0.455629 0.890170i \(-0.349414\pi\)
0.455629 + 0.890170i \(0.349414\pi\)
\(264\) −7.49527 −0.461302
\(265\) −0.486379 −0.0298780
\(266\) 29.8323 1.82913
\(267\) 5.21337 0.319053
\(268\) 1.18099 0.0721403
\(269\) 9.78238 0.596442 0.298221 0.954497i \(-0.403607\pi\)
0.298221 + 0.954497i \(0.403607\pi\)
\(270\) −1.05791 −0.0643826
\(271\) 1.60503 0.0974985 0.0487492 0.998811i \(-0.484476\pi\)
0.0487492 + 0.998811i \(0.484476\pi\)
\(272\) 11.3960 0.690986
\(273\) −10.7300 −0.649412
\(274\) −22.2056 −1.34149
\(275\) 12.0524 0.726787
\(276\) 0.0738306 0.00444408
\(277\) 2.04019 0.122583 0.0612917 0.998120i \(-0.480478\pi\)
0.0612917 + 0.998120i \(0.480478\pi\)
\(278\) 23.4457 1.40618
\(279\) −10.2606 −0.614283
\(280\) 7.61328 0.454981
\(281\) −6.40945 −0.382356 −0.191178 0.981555i \(-0.561231\pi\)
−0.191178 + 0.981555i \(0.561231\pi\)
\(282\) 8.67580 0.516636
\(283\) −6.25421 −0.371774 −0.185887 0.982571i \(-0.559516\pi\)
−0.185887 + 0.982571i \(0.559516\pi\)
\(284\) 0.886313 0.0525930
\(285\) −4.07320 −0.241276
\(286\) −11.1755 −0.660821
\(287\) −6.76351 −0.399238
\(288\) 0.417438 0.0245978
\(289\) −9.43092 −0.554760
\(290\) 1.05791 0.0621228
\(291\) −3.97122 −0.232797
\(292\) 0.0731545 0.00428104
\(293\) −16.3014 −0.952338 −0.476169 0.879354i \(-0.657975\pi\)
−0.476169 + 0.879354i \(0.657975\pi\)
\(294\) −10.0215 −0.584467
\(295\) −0.128097 −0.00745811
\(296\) −31.8854 −1.85330
\(297\) −2.70213 −0.156793
\(298\) 16.1925 0.938008
\(299\) −2.87193 −0.166088
\(300\) −0.329309 −0.0190127
\(301\) 0.676857 0.0390134
\(302\) 18.7596 1.07949
\(303\) 18.4855 1.06196
\(304\) 22.9670 1.31725
\(305\) −3.95111 −0.226240
\(306\) 3.96194 0.226489
\(307\) 6.13524 0.350157 0.175078 0.984555i \(-0.443982\pi\)
0.175078 + 0.984555i \(0.443982\pi\)
\(308\) −0.745367 −0.0424712
\(309\) −2.24948 −0.127969
\(310\) 10.8548 0.616510
\(311\) −0.302171 −0.0171346 −0.00856728 0.999963i \(-0.502727\pi\)
−0.00856728 + 0.999963i \(0.502727\pi\)
\(312\) −7.96627 −0.451001
\(313\) 21.6672 1.22471 0.612353 0.790585i \(-0.290223\pi\)
0.612353 + 0.790585i \(0.290223\pi\)
\(314\) −7.77912 −0.439001
\(315\) 2.74468 0.154645
\(316\) −0.218777 −0.0123072
\(317\) −7.71514 −0.433326 −0.216663 0.976247i \(-0.569517\pi\)
−0.216663 + 0.976247i \(0.569517\pi\)
\(318\) 0.953449 0.0534668
\(319\) 2.70213 0.151290
\(320\) 5.64430 0.315526
\(321\) −12.9231 −0.721295
\(322\) −5.38039 −0.299837
\(323\) 15.2544 0.848775
\(324\) 0.0738306 0.00410170
\(325\) 12.8098 0.710558
\(326\) −8.51446 −0.471573
\(327\) 16.2725 0.899873
\(328\) −5.02142 −0.277261
\(329\) −22.5087 −1.24094
\(330\) 2.85862 0.157362
\(331\) −15.6398 −0.859642 −0.429821 0.902914i \(-0.641423\pi\)
−0.429821 + 0.902914i \(0.641423\pi\)
\(332\) 0.0804719 0.00441647
\(333\) −11.4951 −0.629925
\(334\) 0.491876 0.0269143
\(335\) 11.7509 0.642023
\(336\) −15.4760 −0.844286
\(337\) 22.0539 1.20135 0.600675 0.799493i \(-0.294898\pi\)
0.600675 + 0.799493i \(0.294898\pi\)
\(338\) 6.84327 0.372225
\(339\) −11.3227 −0.614962
\(340\) −0.149218 −0.00809249
\(341\) 27.7253 1.50141
\(342\) 7.98471 0.431764
\(343\) −0.153162 −0.00826999
\(344\) 0.502517 0.0270939
\(345\) 0.734622 0.0395507
\(346\) −19.8865 −1.06910
\(347\) −3.22284 −0.173011 −0.0865055 0.996251i \(-0.527570\pi\)
−0.0865055 + 0.996251i \(0.527570\pi\)
\(348\) −0.0738306 −0.00395774
\(349\) 12.2805 0.657362 0.328681 0.944441i \(-0.393396\pi\)
0.328681 + 0.944441i \(0.393396\pi\)
\(350\) 23.9983 1.28276
\(351\) −2.87193 −0.153292
\(352\) −1.12797 −0.0601211
\(353\) 23.4425 1.24772 0.623860 0.781536i \(-0.285564\pi\)
0.623860 + 0.781536i \(0.285564\pi\)
\(354\) 0.251109 0.0133463
\(355\) 8.81890 0.468058
\(356\) 0.384907 0.0204000
\(357\) −10.2790 −0.544020
\(358\) −22.0835 −1.16715
\(359\) −3.94790 −0.208362 −0.104181 0.994558i \(-0.533222\pi\)
−0.104181 + 0.994558i \(0.533222\pi\)
\(360\) 2.03772 0.107397
\(361\) 11.7429 0.618047
\(362\) 6.68683 0.351452
\(363\) −3.69849 −0.194121
\(364\) −0.792206 −0.0415229
\(365\) 0.727894 0.0380997
\(366\) 7.74536 0.404857
\(367\) −8.80947 −0.459850 −0.229925 0.973208i \(-0.573848\pi\)
−0.229925 + 0.973208i \(0.573848\pi\)
\(368\) −4.14221 −0.215928
\(369\) −1.81028 −0.0942393
\(370\) 12.1608 0.632209
\(371\) −2.47365 −0.128426
\(372\) −0.757543 −0.0392768
\(373\) 15.8227 0.819267 0.409634 0.912250i \(-0.365657\pi\)
0.409634 + 0.912250i \(0.365657\pi\)
\(374\) −10.7057 −0.553578
\(375\) −6.94976 −0.358884
\(376\) −16.7111 −0.861807
\(377\) 2.87193 0.147912
\(378\) −5.38039 −0.276737
\(379\) 10.4466 0.536605 0.268302 0.963335i \(-0.413537\pi\)
0.268302 + 0.963335i \(0.413537\pi\)
\(380\) −0.300727 −0.0154270
\(381\) −9.54485 −0.488997
\(382\) −14.1915 −0.726102
\(383\) −8.85503 −0.452471 −0.226236 0.974073i \(-0.572642\pi\)
−0.226236 + 0.974073i \(0.572642\pi\)
\(384\) −11.8994 −0.607239
\(385\) −7.41647 −0.377978
\(386\) 30.6430 1.55969
\(387\) 0.181163 0.00920903
\(388\) −0.293198 −0.0148849
\(389\) 18.5823 0.942158 0.471079 0.882091i \(-0.343865\pi\)
0.471079 + 0.882091i \(0.343865\pi\)
\(390\) 3.03826 0.153848
\(391\) −2.75120 −0.139134
\(392\) 19.3032 0.974957
\(393\) 15.3632 0.774972
\(394\) −13.8499 −0.697749
\(395\) −2.17685 −0.109529
\(396\) −0.199500 −0.0100252
\(397\) −21.6225 −1.08520 −0.542602 0.839990i \(-0.682561\pi\)
−0.542602 + 0.839990i \(0.682561\pi\)
\(398\) −6.33564 −0.317577
\(399\) −20.7157 −1.03708
\(400\) 18.4756 0.923781
\(401\) −25.2586 −1.26135 −0.630677 0.776045i \(-0.717223\pi\)
−0.630677 + 0.776045i \(0.717223\pi\)
\(402\) −23.0354 −1.14890
\(403\) 29.4676 1.46789
\(404\) 1.36480 0.0679011
\(405\) 0.734622 0.0365036
\(406\) 5.38039 0.267024
\(407\) 31.0611 1.53964
\(408\) −7.63137 −0.377809
\(409\) 2.31715 0.114576 0.0572878 0.998358i \(-0.481755\pi\)
0.0572878 + 0.998358i \(0.481755\pi\)
\(410\) 1.91512 0.0945809
\(411\) 15.4197 0.760598
\(412\) −0.166081 −0.00818221
\(413\) −0.651483 −0.0320574
\(414\) −1.44008 −0.0707761
\(415\) 0.800703 0.0393050
\(416\) −1.19885 −0.0587787
\(417\) −16.2808 −0.797276
\(418\) −21.5757 −1.05530
\(419\) −6.36432 −0.310917 −0.155459 0.987842i \(-0.549686\pi\)
−0.155459 + 0.987842i \(0.549686\pi\)
\(420\) 0.202641 0.00988787
\(421\) −5.84235 −0.284739 −0.142369 0.989814i \(-0.545472\pi\)
−0.142369 + 0.989814i \(0.545472\pi\)
\(422\) −2.80988 −0.136783
\(423\) −6.02453 −0.292923
\(424\) −1.83651 −0.0891886
\(425\) 12.2712 0.595243
\(426\) −17.2877 −0.837592
\(427\) −20.0947 −0.972453
\(428\) −0.954118 −0.0461190
\(429\) 7.76033 0.374672
\(430\) −0.191655 −0.00924242
\(431\) −17.3297 −0.834744 −0.417372 0.908736i \(-0.637049\pi\)
−0.417372 + 0.908736i \(0.637049\pi\)
\(432\) −4.14221 −0.199292
\(433\) −13.9592 −0.670835 −0.335417 0.942070i \(-0.608877\pi\)
−0.335417 + 0.942070i \(0.608877\pi\)
\(434\) 55.2058 2.64996
\(435\) −0.734622 −0.0352224
\(436\) 1.20141 0.0575371
\(437\) −5.54463 −0.265236
\(438\) −1.42689 −0.0681795
\(439\) 14.7239 0.702733 0.351367 0.936238i \(-0.385717\pi\)
0.351367 + 0.936238i \(0.385717\pi\)
\(440\) −5.50619 −0.262497
\(441\) 6.95901 0.331381
\(442\) −11.3784 −0.541217
\(443\) −39.8806 −1.89479 −0.947393 0.320073i \(-0.896293\pi\)
−0.947393 + 0.320073i \(0.896293\pi\)
\(444\) −0.848687 −0.0402769
\(445\) 3.82986 0.181553
\(446\) −8.07309 −0.382272
\(447\) −11.2442 −0.531832
\(448\) 28.7061 1.35623
\(449\) 13.8427 0.653277 0.326639 0.945149i \(-0.394084\pi\)
0.326639 + 0.945149i \(0.394084\pi\)
\(450\) 6.42323 0.302794
\(451\) 4.89160 0.230337
\(452\) −0.835958 −0.0393202
\(453\) −13.0268 −0.612052
\(454\) 8.63659 0.405335
\(455\) −7.88252 −0.369538
\(456\) −15.3799 −0.720230
\(457\) 16.5018 0.771924 0.385962 0.922515i \(-0.373870\pi\)
0.385962 + 0.922515i \(0.373870\pi\)
\(458\) 20.4674 0.956377
\(459\) −2.75120 −0.128415
\(460\) 0.0542376 0.00252884
\(461\) 32.0920 1.49468 0.747338 0.664445i \(-0.231332\pi\)
0.747338 + 0.664445i \(0.231332\pi\)
\(462\) 14.5385 0.676393
\(463\) 1.18030 0.0548530 0.0274265 0.999624i \(-0.491269\pi\)
0.0274265 + 0.999624i \(0.491269\pi\)
\(464\) 4.14221 0.192297
\(465\) −7.53762 −0.349549
\(466\) 40.8829 1.89386
\(467\) 18.8983 0.874507 0.437254 0.899338i \(-0.355951\pi\)
0.437254 + 0.899338i \(0.355951\pi\)
\(468\) −0.212037 −0.00980139
\(469\) 59.7635 2.75962
\(470\) 6.37343 0.293984
\(471\) 5.40186 0.248905
\(472\) −0.483679 −0.0222631
\(473\) −0.489526 −0.0225084
\(474\) 4.26729 0.196003
\(475\) 24.7309 1.13473
\(476\) −0.758901 −0.0347842
\(477\) −0.662081 −0.0303146
\(478\) −29.3036 −1.34032
\(479\) 15.2872 0.698490 0.349245 0.937031i \(-0.386438\pi\)
0.349245 + 0.937031i \(0.386438\pi\)
\(480\) 0.306659 0.0139970
\(481\) 33.0130 1.50526
\(482\) −27.6641 −1.26006
\(483\) 3.73618 0.170002
\(484\) −0.273062 −0.0124119
\(485\) −2.91735 −0.132470
\(486\) −1.44008 −0.0653234
\(487\) −22.1203 −1.00237 −0.501183 0.865341i \(-0.667102\pi\)
−0.501183 + 0.865341i \(0.667102\pi\)
\(488\) −14.9189 −0.675346
\(489\) 5.91249 0.267372
\(490\) −7.36203 −0.332583
\(491\) −33.8069 −1.52568 −0.762842 0.646585i \(-0.776197\pi\)
−0.762842 + 0.646585i \(0.776197\pi\)
\(492\) −0.133654 −0.00602558
\(493\) 2.75120 0.123908
\(494\) −22.9315 −1.03174
\(495\) −1.98504 −0.0892211
\(496\) 42.5014 1.90837
\(497\) 44.8516 2.01187
\(498\) −1.56962 −0.0703363
\(499\) 25.1393 1.12539 0.562695 0.826664i \(-0.309764\pi\)
0.562695 + 0.826664i \(0.309764\pi\)
\(500\) −0.513105 −0.0229468
\(501\) −0.341562 −0.0152599
\(502\) 1.84292 0.0822535
\(503\) −40.7380 −1.81642 −0.908209 0.418518i \(-0.862550\pi\)
−0.908209 + 0.418518i \(0.862550\pi\)
\(504\) 10.3635 0.461629
\(505\) 13.5798 0.604295
\(506\) 3.89128 0.172989
\(507\) −4.75201 −0.211044
\(508\) −0.704702 −0.0312661
\(509\) 25.6947 1.13890 0.569450 0.822026i \(-0.307156\pi\)
0.569450 + 0.822026i \(0.307156\pi\)
\(510\) 2.91053 0.128880
\(511\) 3.70196 0.163765
\(512\) 21.2505 0.939149
\(513\) −5.54463 −0.244801
\(514\) 31.0497 1.36954
\(515\) −1.65252 −0.0728187
\(516\) 0.0133754 0.000588818 0
\(517\) 16.2791 0.715952
\(518\) 61.8479 2.71744
\(519\) 13.8093 0.606160
\(520\) −5.85220 −0.256636
\(521\) −38.8339 −1.70134 −0.850671 0.525698i \(-0.823804\pi\)
−0.850671 + 0.525698i \(0.823804\pi\)
\(522\) 1.44008 0.0630306
\(523\) 27.7980 1.21552 0.607762 0.794119i \(-0.292068\pi\)
0.607762 + 0.794119i \(0.292068\pi\)
\(524\) 1.13428 0.0495511
\(525\) −16.6646 −0.727302
\(526\) −21.2817 −0.927925
\(527\) 28.2288 1.22967
\(528\) 11.1928 0.487104
\(529\) 1.00000 0.0434783
\(530\) 0.700425 0.0304245
\(531\) −0.174372 −0.00756709
\(532\) −1.52945 −0.0663102
\(533\) 5.19899 0.225193
\(534\) −7.50768 −0.324889
\(535\) −9.49356 −0.410443
\(536\) 44.3701 1.91650
\(537\) 15.3349 0.661751
\(538\) −14.0874 −0.607351
\(539\) −18.8041 −0.809952
\(540\) 0.0542376 0.00233401
\(541\) −34.1038 −1.46624 −0.733118 0.680101i \(-0.761936\pi\)
−0.733118 + 0.680101i \(0.761936\pi\)
\(542\) −2.31137 −0.0992818
\(543\) −4.64338 −0.199266
\(544\) −1.14845 −0.0492396
\(545\) 11.9541 0.512059
\(546\) 15.4521 0.661290
\(547\) 9.35076 0.399810 0.199905 0.979815i \(-0.435937\pi\)
0.199905 + 0.979815i \(0.435937\pi\)
\(548\) 1.13845 0.0486320
\(549\) −5.37843 −0.229546
\(550\) −17.3564 −0.740080
\(551\) 5.54463 0.236209
\(552\) 2.77384 0.118062
\(553\) −11.0712 −0.470793
\(554\) −2.93804 −0.124826
\(555\) −8.44452 −0.358450
\(556\) −1.20202 −0.0509772
\(557\) −12.7997 −0.542341 −0.271170 0.962531i \(-0.587411\pi\)
−0.271170 + 0.962531i \(0.587411\pi\)
\(558\) 14.7760 0.625519
\(559\) −0.520288 −0.0220058
\(560\) −11.3690 −0.480429
\(561\) 7.43409 0.313868
\(562\) 9.23012 0.389349
\(563\) 24.8909 1.04903 0.524513 0.851402i \(-0.324247\pi\)
0.524513 + 0.851402i \(0.324247\pi\)
\(564\) −0.444795 −0.0187292
\(565\) −8.31786 −0.349935
\(566\) 9.00656 0.378574
\(567\) 3.73618 0.156905
\(568\) 33.2990 1.39720
\(569\) −36.1179 −1.51414 −0.757072 0.653332i \(-0.773371\pi\)
−0.757072 + 0.653332i \(0.773371\pi\)
\(570\) 5.86574 0.245689
\(571\) −24.7666 −1.03645 −0.518226 0.855244i \(-0.673407\pi\)
−0.518226 + 0.855244i \(0.673407\pi\)
\(572\) 0.572950 0.0239563
\(573\) 9.85469 0.411686
\(574\) 9.74000 0.406540
\(575\) −4.46033 −0.186009
\(576\) 7.68328 0.320137
\(577\) 21.4822 0.894315 0.447157 0.894455i \(-0.352436\pi\)
0.447157 + 0.894455i \(0.352436\pi\)
\(578\) 13.5813 0.564907
\(579\) −21.2787 −0.884312
\(580\) −0.0542376 −0.00225209
\(581\) 4.07225 0.168946
\(582\) 5.71888 0.237055
\(583\) 1.78903 0.0740940
\(584\) 2.74844 0.113731
\(585\) −2.10978 −0.0872288
\(586\) 23.4753 0.969756
\(587\) 47.2043 1.94833 0.974164 0.225840i \(-0.0725127\pi\)
0.974164 + 0.225840i \(0.0725127\pi\)
\(588\) 0.513788 0.0211882
\(589\) 56.8909 2.34415
\(590\) 0.184470 0.00759452
\(591\) 9.61747 0.395610
\(592\) 47.6149 1.95696
\(593\) −30.4167 −1.24906 −0.624532 0.780999i \(-0.714710\pi\)
−0.624532 + 0.780999i \(0.714710\pi\)
\(594\) 3.89128 0.159661
\(595\) −7.55114 −0.309567
\(596\) −0.830165 −0.0340049
\(597\) 4.39951 0.180060
\(598\) 4.13581 0.169126
\(599\) 3.07961 0.125829 0.0629147 0.998019i \(-0.479960\pi\)
0.0629147 + 0.998019i \(0.479960\pi\)
\(600\) −12.3722 −0.505094
\(601\) −22.7054 −0.926171 −0.463086 0.886314i \(-0.653258\pi\)
−0.463086 + 0.886314i \(0.653258\pi\)
\(602\) −0.974728 −0.0397269
\(603\) 15.9959 0.651404
\(604\) −0.961776 −0.0391341
\(605\) −2.71699 −0.110461
\(606\) −26.6206 −1.08139
\(607\) 23.3283 0.946868 0.473434 0.880829i \(-0.343014\pi\)
0.473434 + 0.880829i \(0.343014\pi\)
\(608\) −2.31454 −0.0938670
\(609\) −3.73618 −0.151397
\(610\) 5.68991 0.230378
\(611\) 17.3020 0.699965
\(612\) −0.203123 −0.00821074
\(613\) −10.1942 −0.411739 −0.205869 0.978579i \(-0.566002\pi\)
−0.205869 + 0.978579i \(0.566002\pi\)
\(614\) −8.83524 −0.356561
\(615\) −1.32987 −0.0536255
\(616\) −28.0036 −1.12830
\(617\) −35.5944 −1.43298 −0.716489 0.697599i \(-0.754252\pi\)
−0.716489 + 0.697599i \(0.754252\pi\)
\(618\) 3.23944 0.130309
\(619\) 24.9632 1.00336 0.501678 0.865055i \(-0.332716\pi\)
0.501678 + 0.865055i \(0.332716\pi\)
\(620\) −0.556507 −0.0223499
\(621\) 1.00000 0.0401286
\(622\) 0.435151 0.0174480
\(623\) 19.4781 0.780373
\(624\) 11.8961 0.476227
\(625\) 17.1962 0.687848
\(626\) −31.2026 −1.24711
\(627\) 14.9823 0.598336
\(628\) 0.398823 0.0159148
\(629\) 31.6252 1.26098
\(630\) −3.95255 −0.157473
\(631\) −47.0960 −1.87486 −0.937431 0.348172i \(-0.886802\pi\)
−0.937431 + 0.348172i \(0.886802\pi\)
\(632\) −8.21953 −0.326955
\(633\) 1.95120 0.0775531
\(634\) 11.1104 0.441251
\(635\) −7.01185 −0.278257
\(636\) −0.0488818 −0.00193829
\(637\) −19.9858 −0.791866
\(638\) −3.89128 −0.154057
\(639\) 12.0047 0.474898
\(640\) −8.74156 −0.345541
\(641\) −21.9528 −0.867084 −0.433542 0.901133i \(-0.642736\pi\)
−0.433542 + 0.901133i \(0.642736\pi\)
\(642\) 18.6103 0.734488
\(643\) −40.4333 −1.59454 −0.797268 0.603626i \(-0.793722\pi\)
−0.797268 + 0.603626i \(0.793722\pi\)
\(644\) 0.275844 0.0108698
\(645\) 0.133086 0.00524027
\(646\) −21.9675 −0.864300
\(647\) 7.21645 0.283708 0.141854 0.989888i \(-0.454694\pi\)
0.141854 + 0.989888i \(0.454694\pi\)
\(648\) 2.77384 0.108967
\(649\) 0.471175 0.0184952
\(650\) −18.4471 −0.723554
\(651\) −38.3352 −1.50248
\(652\) 0.436523 0.0170956
\(653\) 13.4765 0.527377 0.263689 0.964608i \(-0.415061\pi\)
0.263689 + 0.964608i \(0.415061\pi\)
\(654\) −23.4337 −0.916332
\(655\) 11.2862 0.440987
\(656\) 7.49855 0.292769
\(657\) 0.990842 0.0386564
\(658\) 32.4143 1.26364
\(659\) 37.3480 1.45487 0.727435 0.686177i \(-0.240712\pi\)
0.727435 + 0.686177i \(0.240712\pi\)
\(660\) −0.146557 −0.00570472
\(661\) 50.2592 1.95486 0.977428 0.211268i \(-0.0677592\pi\)
0.977428 + 0.211268i \(0.0677592\pi\)
\(662\) 22.5226 0.875366
\(663\) 7.90125 0.306859
\(664\) 3.02335 0.117329
\(665\) −15.2182 −0.590137
\(666\) 16.5538 0.641447
\(667\) −1.00000 −0.0387202
\(668\) −0.0252177 −0.000975703 0
\(669\) 5.60600 0.216740
\(670\) −16.9223 −0.653765
\(671\) 14.5332 0.561048
\(672\) 1.55962 0.0601637
\(673\) −32.0250 −1.23447 −0.617236 0.786778i \(-0.711748\pi\)
−0.617236 + 0.786778i \(0.711748\pi\)
\(674\) −31.7593 −1.22332
\(675\) −4.46033 −0.171678
\(676\) −0.350844 −0.0134940
\(677\) 47.4069 1.82200 0.910998 0.412412i \(-0.135314\pi\)
0.910998 + 0.412412i \(0.135314\pi\)
\(678\) 16.3055 0.626210
\(679\) −14.8372 −0.569399
\(680\) −5.60617 −0.214987
\(681\) −5.99730 −0.229817
\(682\) −39.9267 −1.52887
\(683\) −6.12035 −0.234189 −0.117094 0.993121i \(-0.537358\pi\)
−0.117094 + 0.993121i \(0.537358\pi\)
\(684\) −0.409363 −0.0156524
\(685\) 11.3276 0.432807
\(686\) 0.220566 0.00842126
\(687\) −14.2127 −0.542247
\(688\) −0.750415 −0.0286093
\(689\) 1.90145 0.0724395
\(690\) −1.05791 −0.0402741
\(691\) −46.8351 −1.78169 −0.890845 0.454307i \(-0.849887\pi\)
−0.890845 + 0.454307i \(0.849887\pi\)
\(692\) 1.01955 0.0387574
\(693\) −10.0956 −0.383501
\(694\) 4.64114 0.176175
\(695\) −11.9603 −0.453678
\(696\) −2.77384 −0.105142
\(697\) 4.98043 0.188647
\(698\) −17.6850 −0.669386
\(699\) −28.3893 −1.07378
\(700\) −1.23036 −0.0465031
\(701\) −8.62132 −0.325623 −0.162811 0.986657i \(-0.552056\pi\)
−0.162811 + 0.986657i \(0.552056\pi\)
\(702\) 4.13581 0.156096
\(703\) 63.7358 2.40384
\(704\) −20.7612 −0.782468
\(705\) −4.42575 −0.166683
\(706\) −33.7591 −1.27054
\(707\) 69.0651 2.59746
\(708\) −0.0128740 −0.000483834 0
\(709\) −23.5240 −0.883463 −0.441731 0.897147i \(-0.645636\pi\)
−0.441731 + 0.897147i \(0.645636\pi\)
\(710\) −12.6999 −0.476619
\(711\) −2.96323 −0.111130
\(712\) 14.4611 0.541951
\(713\) −10.2606 −0.384261
\(714\) 14.8025 0.553970
\(715\) 5.70091 0.213202
\(716\) 1.13219 0.0423118
\(717\) 20.3486 0.759932
\(718\) 5.68529 0.212173
\(719\) −14.1926 −0.529294 −0.264647 0.964345i \(-0.585255\pi\)
−0.264647 + 0.964345i \(0.585255\pi\)
\(720\) −3.04296 −0.113404
\(721\) −8.40447 −0.312999
\(722\) −16.9107 −0.629351
\(723\) 19.2101 0.714431
\(724\) −0.342823 −0.0127409
\(725\) 4.46033 0.165653
\(726\) 5.32613 0.197671
\(727\) −4.28230 −0.158822 −0.0794108 0.996842i \(-0.525304\pi\)
−0.0794108 + 0.996842i \(0.525304\pi\)
\(728\) −29.7634 −1.10310
\(729\) 1.00000 0.0370370
\(730\) −1.04823 −0.0387966
\(731\) −0.498415 −0.0184345
\(732\) −0.397093 −0.0146770
\(733\) 12.6104 0.465774 0.232887 0.972504i \(-0.425183\pi\)
0.232887 + 0.972504i \(0.425183\pi\)
\(734\) 12.6863 0.468261
\(735\) 5.11224 0.188568
\(736\) 0.417438 0.0153870
\(737\) −43.2230 −1.59214
\(738\) 2.60694 0.0959629
\(739\) −14.4588 −0.531874 −0.265937 0.963990i \(-0.585681\pi\)
−0.265937 + 0.963990i \(0.585681\pi\)
\(740\) −0.623464 −0.0229190
\(741\) 15.9238 0.584975
\(742\) 3.56225 0.130774
\(743\) −52.1742 −1.91409 −0.957044 0.289944i \(-0.906363\pi\)
−0.957044 + 0.289944i \(0.906363\pi\)
\(744\) −28.4611 −1.04343
\(745\) −8.26022 −0.302631
\(746\) −22.7859 −0.834252
\(747\) 1.08995 0.0398793
\(748\) 0.548864 0.0200684
\(749\) −48.2828 −1.76422
\(750\) 10.0082 0.365448
\(751\) −29.7393 −1.08520 −0.542602 0.839990i \(-0.682561\pi\)
−0.542602 + 0.839990i \(0.682561\pi\)
\(752\) 24.9549 0.910010
\(753\) −1.27973 −0.0466361
\(754\) −4.13581 −0.150617
\(755\) −9.56976 −0.348279
\(756\) 0.275844 0.0100324
\(757\) 1.08267 0.0393504 0.0196752 0.999806i \(-0.493737\pi\)
0.0196752 + 0.999806i \(0.493737\pi\)
\(758\) −15.0439 −0.546419
\(759\) −2.70213 −0.0980811
\(760\) −11.2984 −0.409836
\(761\) −24.7614 −0.897599 −0.448799 0.893633i \(-0.648148\pi\)
−0.448799 + 0.893633i \(0.648148\pi\)
\(762\) 13.7453 0.497941
\(763\) 60.7970 2.20100
\(764\) 0.727578 0.0263228
\(765\) −2.02109 −0.0730726
\(766\) 12.7520 0.460747
\(767\) 0.500784 0.0180823
\(768\) 1.76955 0.0638531
\(769\) 38.2442 1.37912 0.689560 0.724229i \(-0.257804\pi\)
0.689560 + 0.724229i \(0.257804\pi\)
\(770\) 10.6803 0.384892
\(771\) −21.5611 −0.776504
\(772\) −1.57102 −0.0565422
\(773\) −4.36196 −0.156889 −0.0784444 0.996918i \(-0.524995\pi\)
−0.0784444 + 0.996918i \(0.524995\pi\)
\(774\) −0.260889 −0.00937747
\(775\) 45.7655 1.64394
\(776\) −11.0155 −0.395435
\(777\) −42.9475 −1.54073
\(778\) −26.7599 −0.959390
\(779\) 10.0373 0.359624
\(780\) −0.155767 −0.00557734
\(781\) −32.4382 −1.16073
\(782\) 3.96194 0.141679
\(783\) −1.00000 −0.0357371
\(784\) −28.8257 −1.02949
\(785\) 3.96833 0.141636
\(786\) −22.1243 −0.789147
\(787\) −54.5403 −1.94415 −0.972076 0.234666i \(-0.924600\pi\)
−0.972076 + 0.234666i \(0.924600\pi\)
\(788\) 0.710064 0.0252950
\(789\) 14.7781 0.526115
\(790\) 3.13485 0.111533
\(791\) −42.3034 −1.50414
\(792\) −7.49527 −0.266333
\(793\) 15.4465 0.548520
\(794\) 31.1382 1.10505
\(795\) −0.486379 −0.0172501
\(796\) 0.324818 0.0115129
\(797\) −14.1584 −0.501518 −0.250759 0.968050i \(-0.580680\pi\)
−0.250759 + 0.968050i \(0.580680\pi\)
\(798\) 29.8323 1.05605
\(799\) 16.5747 0.586369
\(800\) −1.86191 −0.0658286
\(801\) 5.21337 0.184206
\(802\) 36.3744 1.28442
\(803\) −2.67738 −0.0944829
\(804\) 1.18099 0.0416502
\(805\) 2.74468 0.0967371
\(806\) −42.4357 −1.49473
\(807\) 9.78238 0.344356
\(808\) 51.2758 1.80388
\(809\) −7.90499 −0.277925 −0.138962 0.990298i \(-0.544377\pi\)
−0.138962 + 0.990298i \(0.544377\pi\)
\(810\) −1.05791 −0.0371713
\(811\) −22.0093 −0.772853 −0.386426 0.922320i \(-0.626291\pi\)
−0.386426 + 0.922320i \(0.626291\pi\)
\(812\) −0.275844 −0.00968023
\(813\) 1.60503 0.0562908
\(814\) −44.7305 −1.56780
\(815\) 4.34345 0.152144
\(816\) 11.3960 0.398941
\(817\) −1.00448 −0.0351424
\(818\) −3.33688 −0.116671
\(819\) −10.7300 −0.374938
\(820\) −0.0981850 −0.00342877
\(821\) 1.48851 0.0519495 0.0259747 0.999663i \(-0.491731\pi\)
0.0259747 + 0.999663i \(0.491731\pi\)
\(822\) −22.2056 −0.774509
\(823\) 10.8193 0.377138 0.188569 0.982060i \(-0.439615\pi\)
0.188569 + 0.982060i \(0.439615\pi\)
\(824\) −6.23970 −0.217370
\(825\) 12.0524 0.419611
\(826\) 0.938188 0.0326437
\(827\) −11.1086 −0.386285 −0.193142 0.981171i \(-0.561868\pi\)
−0.193142 + 0.981171i \(0.561868\pi\)
\(828\) 0.0738306 0.00256579
\(829\) 37.1704 1.29098 0.645490 0.763769i \(-0.276653\pi\)
0.645490 + 0.763769i \(0.276653\pi\)
\(830\) −1.15308 −0.0400239
\(831\) 2.04019 0.0707736
\(832\) −22.0658 −0.764996
\(833\) −19.1456 −0.663355
\(834\) 23.4457 0.811858
\(835\) −0.250919 −0.00868340
\(836\) 1.10615 0.0382571
\(837\) −10.2606 −0.354657
\(838\) 9.16513 0.316604
\(839\) −32.0230 −1.10556 −0.552778 0.833328i \(-0.686432\pi\)
−0.552778 + 0.833328i \(0.686432\pi\)
\(840\) 7.61328 0.262683
\(841\) 1.00000 0.0344828
\(842\) 8.41345 0.289947
\(843\) −6.40945 −0.220753
\(844\) 0.144058 0.00495869
\(845\) −3.49093 −0.120092
\(846\) 8.67580 0.298280
\(847\) −13.8182 −0.474800
\(848\) 2.74248 0.0941771
\(849\) −6.25421 −0.214644
\(850\) −17.6716 −0.606130
\(851\) −11.4951 −0.394045
\(852\) 0.886313 0.0303646
\(853\) −34.0427 −1.16560 −0.582799 0.812616i \(-0.698043\pi\)
−0.582799 + 0.812616i \(0.698043\pi\)
\(854\) 28.9380 0.990239
\(855\) −4.07320 −0.139301
\(856\) −35.8465 −1.22521
\(857\) −8.43886 −0.288266 −0.144133 0.989558i \(-0.546039\pi\)
−0.144133 + 0.989558i \(0.546039\pi\)
\(858\) −11.1755 −0.381525
\(859\) 9.83616 0.335605 0.167803 0.985821i \(-0.446333\pi\)
0.167803 + 0.985821i \(0.446333\pi\)
\(860\) 0.00982584 0.000335058 0
\(861\) −6.76351 −0.230500
\(862\) 24.9562 0.850012
\(863\) −42.6331 −1.45125 −0.725624 0.688092i \(-0.758449\pi\)
−0.725624 + 0.688092i \(0.758449\pi\)
\(864\) 0.417438 0.0142015
\(865\) 10.1446 0.344926
\(866\) 20.1023 0.683104
\(867\) −9.43092 −0.320291
\(868\) −2.83031 −0.0960671
\(869\) 8.00704 0.271620
\(870\) 1.05791 0.0358666
\(871\) −45.9392 −1.55659
\(872\) 45.1374 1.52854
\(873\) −3.97122 −0.134406
\(874\) 7.98471 0.270087
\(875\) −25.9655 −0.877795
\(876\) 0.0731545 0.00247166
\(877\) 43.1875 1.45834 0.729170 0.684333i \(-0.239906\pi\)
0.729170 + 0.684333i \(0.239906\pi\)
\(878\) −21.2036 −0.715587
\(879\) −16.3014 −0.549832
\(880\) 8.22247 0.277179
\(881\) 5.46060 0.183972 0.0919861 0.995760i \(-0.470678\pi\)
0.0919861 + 0.995760i \(0.470678\pi\)
\(882\) −10.0215 −0.337442
\(883\) 17.9095 0.602703 0.301352 0.953513i \(-0.402562\pi\)
0.301352 + 0.953513i \(0.402562\pi\)
\(884\) 0.583354 0.0196203
\(885\) −0.128097 −0.00430594
\(886\) 57.4313 1.92944
\(887\) −36.8826 −1.23840 −0.619198 0.785235i \(-0.712542\pi\)
−0.619198 + 0.785235i \(0.712542\pi\)
\(888\) −31.8854 −1.07000
\(889\) −35.6612 −1.19604
\(890\) −5.51530 −0.184873
\(891\) −2.70213 −0.0905248
\(892\) 0.413894 0.0138582
\(893\) 33.4038 1.11781
\(894\) 16.1925 0.541559
\(895\) 11.2654 0.376560
\(896\) −44.4583 −1.48525
\(897\) −2.87193 −0.0958910
\(898\) −19.9346 −0.665226
\(899\) 10.2606 0.342209
\(900\) −0.329309 −0.0109770
\(901\) 1.82151 0.0606834
\(902\) −7.04430 −0.234550
\(903\) 0.676857 0.0225244
\(904\) −31.4072 −1.04459
\(905\) −3.41112 −0.113390
\(906\) 18.7596 0.623247
\(907\) −38.3059 −1.27193 −0.635964 0.771719i \(-0.719397\pi\)
−0.635964 + 0.771719i \(0.719397\pi\)
\(908\) −0.442784 −0.0146943
\(909\) 18.4855 0.613125
\(910\) 11.3515 0.376297
\(911\) −21.4837 −0.711787 −0.355894 0.934526i \(-0.615823\pi\)
−0.355894 + 0.934526i \(0.615823\pi\)
\(912\) 22.9670 0.760514
\(913\) −2.94519 −0.0974717
\(914\) −23.7640 −0.786042
\(915\) −3.95111 −0.130620
\(916\) −1.04933 −0.0346708
\(917\) 57.3997 1.89550
\(918\) 3.96194 0.130764
\(919\) −22.6683 −0.747759 −0.373880 0.927477i \(-0.621973\pi\)
−0.373880 + 0.927477i \(0.621973\pi\)
\(920\) 2.03772 0.0671817
\(921\) 6.13524 0.202163
\(922\) −46.2151 −1.52201
\(923\) −34.4766 −1.13481
\(924\) −0.745367 −0.0245208
\(925\) 51.2718 1.68581
\(926\) −1.69972 −0.0558563
\(927\) −2.24948 −0.0738828
\(928\) −0.417438 −0.0137031
\(929\) −21.5525 −0.707115 −0.353558 0.935413i \(-0.615028\pi\)
−0.353558 + 0.935413i \(0.615028\pi\)
\(930\) 10.8548 0.355942
\(931\) −38.5851 −1.26458
\(932\) −2.09600 −0.0686568
\(933\) −0.302171 −0.00989265
\(934\) −27.2150 −0.890502
\(935\) 5.46124 0.178602
\(936\) −7.96627 −0.260386
\(937\) 53.7168 1.75485 0.877425 0.479713i \(-0.159259\pi\)
0.877425 + 0.479713i \(0.159259\pi\)
\(938\) −86.0643 −2.81010
\(939\) 21.6672 0.707084
\(940\) −0.326756 −0.0106576
\(941\) 33.2298 1.08326 0.541631 0.840617i \(-0.317807\pi\)
0.541631 + 0.840617i \(0.317807\pi\)
\(942\) −7.77912 −0.253457
\(943\) −1.81028 −0.0589507
\(944\) 0.722284 0.0235084
\(945\) 2.74468 0.0892843
\(946\) 0.704957 0.0229201
\(947\) 6.93643 0.225404 0.112702 0.993629i \(-0.464050\pi\)
0.112702 + 0.993629i \(0.464050\pi\)
\(948\) −0.218777 −0.00710556
\(949\) −2.84563 −0.0923731
\(950\) −35.6144 −1.15548
\(951\) −7.71514 −0.250181
\(952\) −28.5121 −0.924084
\(953\) 34.3469 1.11261 0.556303 0.830979i \(-0.312219\pi\)
0.556303 + 0.830979i \(0.312219\pi\)
\(954\) 0.953449 0.0308691
\(955\) 7.23947 0.234264
\(956\) 1.50235 0.0485895
\(957\) 2.70213 0.0873475
\(958\) −22.0148 −0.711266
\(959\) 57.6107 1.86035
\(960\) 5.64430 0.182169
\(961\) 74.2789 2.39609
\(962\) −47.5414 −1.53280
\(963\) −12.9231 −0.416440
\(964\) 1.41829 0.0456801
\(965\) −15.6318 −0.503205
\(966\) −5.38039 −0.173111
\(967\) 22.8151 0.733685 0.366843 0.930283i \(-0.380439\pi\)
0.366843 + 0.930283i \(0.380439\pi\)
\(968\) −10.2590 −0.329737
\(969\) 15.2544 0.490041
\(970\) 4.20121 0.134893
\(971\) −43.7200 −1.40304 −0.701521 0.712649i \(-0.747495\pi\)
−0.701521 + 0.712649i \(0.747495\pi\)
\(972\) 0.0738306 0.00236812
\(973\) −60.8280 −1.95006
\(974\) 31.8550 1.02070
\(975\) 12.8098 0.410241
\(976\) 22.2786 0.713120
\(977\) −0.346127 −0.0110736 −0.00553679 0.999985i \(-0.501762\pi\)
−0.00553679 + 0.999985i \(0.501762\pi\)
\(978\) −8.51446 −0.272263
\(979\) −14.0872 −0.450229
\(980\) 0.377440 0.0120569
\(981\) 16.2725 0.519542
\(982\) 48.6846 1.55359
\(983\) −3.49735 −0.111548 −0.0557741 0.998443i \(-0.517763\pi\)
−0.0557741 + 0.998443i \(0.517763\pi\)
\(984\) −5.02142 −0.160077
\(985\) 7.06520 0.225116
\(986\) −3.96194 −0.126174
\(987\) −22.5087 −0.716459
\(988\) 1.17566 0.0374028
\(989\) 0.181163 0.00576065
\(990\) 2.85862 0.0908529
\(991\) −21.4825 −0.682414 −0.341207 0.939988i \(-0.610836\pi\)
−0.341207 + 0.939988i \(0.610836\pi\)
\(992\) −4.28315 −0.135990
\(993\) −15.6398 −0.496315
\(994\) −64.5899 −2.04867
\(995\) 3.23197 0.102460
\(996\) 0.0804719 0.00254985
\(997\) 15.2460 0.482845 0.241422 0.970420i \(-0.422386\pi\)
0.241422 + 0.970420i \(0.422386\pi\)
\(998\) −36.2026 −1.14597
\(999\) −11.4951 −0.363687
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2001.2.a.i.1.3 7
3.2 odd 2 6003.2.a.j.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.i.1.3 7 1.1 even 1 trivial
6003.2.a.j.1.5 7 3.2 odd 2