Properties

Label 1441.2.a.d.1.1
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66894 q^{2} +0.662508 q^{3} +5.12325 q^{4} -2.84363 q^{5} -1.76820 q^{6} -0.180196 q^{7} -8.33576 q^{8} -2.56108 q^{9} +O(q^{10})\) \(q-2.66894 q^{2} +0.662508 q^{3} +5.12325 q^{4} -2.84363 q^{5} -1.76820 q^{6} -0.180196 q^{7} -8.33576 q^{8} -2.56108 q^{9} +7.58947 q^{10} -1.00000 q^{11} +3.39419 q^{12} +1.26569 q^{13} +0.480932 q^{14} -1.88393 q^{15} +12.0012 q^{16} +1.06897 q^{17} +6.83538 q^{18} +4.26148 q^{19} -14.5686 q^{20} -0.119381 q^{21} +2.66894 q^{22} +9.55869 q^{23} -5.52251 q^{24} +3.08622 q^{25} -3.37804 q^{26} -3.68426 q^{27} -0.923187 q^{28} +2.29032 q^{29} +5.02809 q^{30} +5.97247 q^{31} -15.3589 q^{32} -0.662508 q^{33} -2.85301 q^{34} +0.512410 q^{35} -13.1211 q^{36} -9.40337 q^{37} -11.3736 q^{38} +0.838527 q^{39} +23.7038 q^{40} -9.00894 q^{41} +0.318621 q^{42} +8.24228 q^{43} -5.12325 q^{44} +7.28277 q^{45} -25.5116 q^{46} +0.606920 q^{47} +7.95087 q^{48} -6.96753 q^{49} -8.23694 q^{50} +0.708199 q^{51} +6.48442 q^{52} -11.1720 q^{53} +9.83308 q^{54} +2.84363 q^{55} +1.50207 q^{56} +2.82326 q^{57} -6.11273 q^{58} -10.4884 q^{59} -9.65182 q^{60} +3.71120 q^{61} -15.9402 q^{62} +0.461496 q^{63} +16.9896 q^{64} -3.59914 q^{65} +1.76820 q^{66} -2.18153 q^{67} +5.47658 q^{68} +6.33271 q^{69} -1.36759 q^{70} -9.13890 q^{71} +21.3486 q^{72} +0.113363 q^{73} +25.0970 q^{74} +2.04464 q^{75} +21.8326 q^{76} +0.180196 q^{77} -2.23798 q^{78} -9.53623 q^{79} -34.1268 q^{80} +5.24239 q^{81} +24.0443 q^{82} +7.25131 q^{83} -0.611619 q^{84} -3.03974 q^{85} -21.9982 q^{86} +1.51736 q^{87} +8.33576 q^{88} -7.31539 q^{89} -19.4373 q^{90} -0.228071 q^{91} +48.9715 q^{92} +3.95681 q^{93} -1.61983 q^{94} -12.1181 q^{95} -10.1754 q^{96} +0.678612 q^{97} +18.5959 q^{98} +2.56108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} + O(q^{10}) \) \( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66894 −1.88723 −0.943613 0.331050i \(-0.892597\pi\)
−0.943613 + 0.331050i \(0.892597\pi\)
\(3\) 0.662508 0.382499 0.191250 0.981541i \(-0.438746\pi\)
0.191250 + 0.981541i \(0.438746\pi\)
\(4\) 5.12325 2.56162
\(5\) −2.84363 −1.27171 −0.635854 0.771809i \(-0.719352\pi\)
−0.635854 + 0.771809i \(0.719352\pi\)
\(6\) −1.76820 −0.721863
\(7\) −0.180196 −0.0681076 −0.0340538 0.999420i \(-0.510842\pi\)
−0.0340538 + 0.999420i \(0.510842\pi\)
\(8\) −8.33576 −2.94714
\(9\) −2.56108 −0.853694
\(10\) 7.58947 2.40000
\(11\) −1.00000 −0.301511
\(12\) 3.39419 0.979819
\(13\) 1.26569 0.351038 0.175519 0.984476i \(-0.443840\pi\)
0.175519 + 0.984476i \(0.443840\pi\)
\(14\) 0.480932 0.128534
\(15\) −1.88393 −0.486428
\(16\) 12.0012 3.00029
\(17\) 1.06897 0.259262 0.129631 0.991562i \(-0.458621\pi\)
0.129631 + 0.991562i \(0.458621\pi\)
\(18\) 6.83538 1.61111
\(19\) 4.26148 0.977650 0.488825 0.872382i \(-0.337426\pi\)
0.488825 + 0.872382i \(0.337426\pi\)
\(20\) −14.5686 −3.25764
\(21\) −0.119381 −0.0260511
\(22\) 2.66894 0.569020
\(23\) 9.55869 1.99312 0.996562 0.0828456i \(-0.0264008\pi\)
0.996562 + 0.0828456i \(0.0264008\pi\)
\(24\) −5.52251 −1.12728
\(25\) 3.08622 0.617244
\(26\) −3.37804 −0.662488
\(27\) −3.68426 −0.709037
\(28\) −0.923187 −0.174466
\(29\) 2.29032 0.425302 0.212651 0.977128i \(-0.431790\pi\)
0.212651 + 0.977128i \(0.431790\pi\)
\(30\) 5.02809 0.917999
\(31\) 5.97247 1.07269 0.536344 0.844000i \(-0.319805\pi\)
0.536344 + 0.844000i \(0.319805\pi\)
\(32\) −15.3589 −2.71509
\(33\) −0.662508 −0.115328
\(34\) −2.85301 −0.489287
\(35\) 0.512410 0.0866130
\(36\) −13.1211 −2.18684
\(37\) −9.40337 −1.54590 −0.772952 0.634464i \(-0.781221\pi\)
−0.772952 + 0.634464i \(0.781221\pi\)
\(38\) −11.3736 −1.84505
\(39\) 0.838527 0.134272
\(40\) 23.7038 3.74790
\(41\) −9.00894 −1.40696 −0.703480 0.710715i \(-0.748371\pi\)
−0.703480 + 0.710715i \(0.748371\pi\)
\(42\) 0.318621 0.0491643
\(43\) 8.24228 1.25694 0.628468 0.777836i \(-0.283682\pi\)
0.628468 + 0.777836i \(0.283682\pi\)
\(44\) −5.12325 −0.772358
\(45\) 7.28277 1.08565
\(46\) −25.5116 −3.76148
\(47\) 0.606920 0.0885284 0.0442642 0.999020i \(-0.485906\pi\)
0.0442642 + 0.999020i \(0.485906\pi\)
\(48\) 7.95087 1.14761
\(49\) −6.96753 −0.995361
\(50\) −8.23694 −1.16488
\(51\) 0.708199 0.0991677
\(52\) 6.48442 0.899227
\(53\) −11.1720 −1.53459 −0.767295 0.641294i \(-0.778398\pi\)
−0.767295 + 0.641294i \(0.778398\pi\)
\(54\) 9.83308 1.33811
\(55\) 2.84363 0.383435
\(56\) 1.50207 0.200722
\(57\) 2.82326 0.373950
\(58\) −6.11273 −0.802641
\(59\) −10.4884 −1.36547 −0.682734 0.730667i \(-0.739209\pi\)
−0.682734 + 0.730667i \(0.739209\pi\)
\(60\) −9.65182 −1.24604
\(61\) 3.71120 0.475171 0.237585 0.971367i \(-0.423644\pi\)
0.237585 + 0.971367i \(0.423644\pi\)
\(62\) −15.9402 −2.02440
\(63\) 0.461496 0.0581431
\(64\) 16.9896 2.12370
\(65\) −3.59914 −0.446418
\(66\) 1.76820 0.217650
\(67\) −2.18153 −0.266517 −0.133258 0.991081i \(-0.542544\pi\)
−0.133258 + 0.991081i \(0.542544\pi\)
\(68\) 5.47658 0.664133
\(69\) 6.33271 0.762369
\(70\) −1.36759 −0.163458
\(71\) −9.13890 −1.08459 −0.542294 0.840189i \(-0.682444\pi\)
−0.542294 + 0.840189i \(0.682444\pi\)
\(72\) 21.3486 2.51595
\(73\) 0.113363 0.0132682 0.00663408 0.999978i \(-0.497888\pi\)
0.00663408 + 0.999978i \(0.497888\pi\)
\(74\) 25.0970 2.91747
\(75\) 2.04464 0.236095
\(76\) 21.8326 2.50437
\(77\) 0.180196 0.0205352
\(78\) −2.23798 −0.253401
\(79\) −9.53623 −1.07291 −0.536455 0.843929i \(-0.680237\pi\)
−0.536455 + 0.843929i \(0.680237\pi\)
\(80\) −34.1268 −3.81550
\(81\) 5.24239 0.582488
\(82\) 24.0443 2.65525
\(83\) 7.25131 0.795935 0.397968 0.917400i \(-0.369716\pi\)
0.397968 + 0.917400i \(0.369716\pi\)
\(84\) −0.611619 −0.0667331
\(85\) −3.03974 −0.329706
\(86\) −21.9982 −2.37212
\(87\) 1.51736 0.162678
\(88\) 8.33576 0.888595
\(89\) −7.31539 −0.775429 −0.387715 0.921779i \(-0.626735\pi\)
−0.387715 + 0.921779i \(0.626735\pi\)
\(90\) −19.4373 −2.04887
\(91\) −0.228071 −0.0239083
\(92\) 48.9715 5.10563
\(93\) 3.95681 0.410302
\(94\) −1.61983 −0.167073
\(95\) −12.1181 −1.24329
\(96\) −10.1754 −1.03852
\(97\) 0.678612 0.0689026 0.0344513 0.999406i \(-0.489032\pi\)
0.0344513 + 0.999406i \(0.489032\pi\)
\(98\) 18.5959 1.87847
\(99\) 2.56108 0.257399
\(100\) 15.8115 1.58115
\(101\) −6.51509 −0.648276 −0.324138 0.946010i \(-0.605074\pi\)
−0.324138 + 0.946010i \(0.605074\pi\)
\(102\) −1.89014 −0.187152
\(103\) 5.49441 0.541380 0.270690 0.962667i \(-0.412748\pi\)
0.270690 + 0.962667i \(0.412748\pi\)
\(104\) −10.5504 −1.03456
\(105\) 0.339476 0.0331294
\(106\) 29.8174 2.89612
\(107\) 11.5650 1.11803 0.559017 0.829156i \(-0.311179\pi\)
0.559017 + 0.829156i \(0.311179\pi\)
\(108\) −18.8754 −1.81628
\(109\) −5.69337 −0.545326 −0.272663 0.962110i \(-0.587904\pi\)
−0.272663 + 0.962110i \(0.587904\pi\)
\(110\) −7.58947 −0.723628
\(111\) −6.22981 −0.591307
\(112\) −2.16256 −0.204343
\(113\) −7.99372 −0.751986 −0.375993 0.926622i \(-0.622698\pi\)
−0.375993 + 0.926622i \(0.622698\pi\)
\(114\) −7.53512 −0.705729
\(115\) −27.1814 −2.53467
\(116\) 11.7339 1.08946
\(117\) −3.24152 −0.299679
\(118\) 27.9928 2.57695
\(119\) −0.192623 −0.0176577
\(120\) 15.7040 1.43357
\(121\) 1.00000 0.0909091
\(122\) −9.90498 −0.896755
\(123\) −5.96849 −0.538161
\(124\) 30.5984 2.74782
\(125\) 5.44208 0.486755
\(126\) −1.23171 −0.109729
\(127\) 5.80674 0.515265 0.257632 0.966243i \(-0.417058\pi\)
0.257632 + 0.966243i \(0.417058\pi\)
\(128\) −14.6265 −1.29281
\(129\) 5.46058 0.480777
\(130\) 9.60588 0.842492
\(131\) −1.00000 −0.0873704
\(132\) −3.39419 −0.295427
\(133\) −0.767900 −0.0665854
\(134\) 5.82238 0.502977
\(135\) 10.4767 0.901688
\(136\) −8.91065 −0.764082
\(137\) −16.9267 −1.44615 −0.723073 0.690772i \(-0.757271\pi\)
−0.723073 + 0.690772i \(0.757271\pi\)
\(138\) −16.9016 −1.43876
\(139\) −11.1716 −0.947567 −0.473783 0.880641i \(-0.657112\pi\)
−0.473783 + 0.880641i \(0.657112\pi\)
\(140\) 2.62520 0.221870
\(141\) 0.402089 0.0338620
\(142\) 24.3912 2.04686
\(143\) −1.26569 −0.105842
\(144\) −30.7360 −2.56133
\(145\) −6.51282 −0.540860
\(146\) −0.302560 −0.0250400
\(147\) −4.61605 −0.380725
\(148\) −48.1758 −3.96002
\(149\) 12.6405 1.03555 0.517776 0.855516i \(-0.326760\pi\)
0.517776 + 0.855516i \(0.326760\pi\)
\(150\) −5.45704 −0.445565
\(151\) −17.9789 −1.46310 −0.731551 0.681786i \(-0.761203\pi\)
−0.731551 + 0.681786i \(0.761203\pi\)
\(152\) −35.5226 −2.88127
\(153\) −2.73771 −0.221331
\(154\) −0.480932 −0.0387546
\(155\) −16.9835 −1.36415
\(156\) 4.29598 0.343954
\(157\) −23.7423 −1.89484 −0.947421 0.319990i \(-0.896320\pi\)
−0.947421 + 0.319990i \(0.896320\pi\)
\(158\) 25.4516 2.02482
\(159\) −7.40153 −0.586980
\(160\) 43.6749 3.45280
\(161\) −1.72244 −0.135747
\(162\) −13.9916 −1.09929
\(163\) 12.1771 0.953782 0.476891 0.878962i \(-0.341764\pi\)
0.476891 + 0.878962i \(0.341764\pi\)
\(164\) −46.1550 −3.60410
\(165\) 1.88393 0.146663
\(166\) −19.3533 −1.50211
\(167\) −15.5110 −1.20028 −0.600138 0.799896i \(-0.704888\pi\)
−0.600138 + 0.799896i \(0.704888\pi\)
\(168\) 0.995133 0.0767762
\(169\) −11.3980 −0.876772
\(170\) 8.11289 0.622230
\(171\) −10.9140 −0.834614
\(172\) 42.2272 3.21979
\(173\) −10.7995 −0.821073 −0.410537 0.911844i \(-0.634659\pi\)
−0.410537 + 0.911844i \(0.634659\pi\)
\(174\) −4.04974 −0.307010
\(175\) −0.556124 −0.0420390
\(176\) −12.0012 −0.904621
\(177\) −6.94863 −0.522291
\(178\) 19.5243 1.46341
\(179\) 0.731463 0.0546721 0.0273361 0.999626i \(-0.491298\pi\)
0.0273361 + 0.999626i \(0.491298\pi\)
\(180\) 37.3114 2.78103
\(181\) 1.88798 0.140332 0.0701661 0.997535i \(-0.477647\pi\)
0.0701661 + 0.997535i \(0.477647\pi\)
\(182\) 0.608708 0.0451205
\(183\) 2.45870 0.181752
\(184\) −79.6790 −5.87401
\(185\) 26.7397 1.96594
\(186\) −10.5605 −0.774333
\(187\) −1.06897 −0.0781705
\(188\) 3.10940 0.226776
\(189\) 0.663889 0.0482908
\(190\) 32.3424 2.34636
\(191\) 10.0783 0.729242 0.364621 0.931156i \(-0.381199\pi\)
0.364621 + 0.931156i \(0.381199\pi\)
\(192\) 11.2557 0.812313
\(193\) −15.5597 −1.12001 −0.560007 0.828488i \(-0.689201\pi\)
−0.560007 + 0.828488i \(0.689201\pi\)
\(194\) −1.81117 −0.130035
\(195\) −2.38446 −0.170755
\(196\) −35.6964 −2.54974
\(197\) 5.45420 0.388596 0.194298 0.980943i \(-0.437757\pi\)
0.194298 + 0.980943i \(0.437757\pi\)
\(198\) −6.83538 −0.485769
\(199\) −22.7176 −1.61041 −0.805206 0.592996i \(-0.797945\pi\)
−0.805206 + 0.592996i \(0.797945\pi\)
\(200\) −25.7260 −1.81910
\(201\) −1.44528 −0.101942
\(202\) 17.3884 1.22344
\(203\) −0.412706 −0.0289663
\(204\) 3.62828 0.254030
\(205\) 25.6181 1.78924
\(206\) −14.6642 −1.02171
\(207\) −24.4806 −1.70152
\(208\) 15.1897 1.05322
\(209\) −4.26148 −0.294772
\(210\) −0.906040 −0.0625227
\(211\) 13.9394 0.959628 0.479814 0.877370i \(-0.340704\pi\)
0.479814 + 0.877370i \(0.340704\pi\)
\(212\) −57.2369 −3.93104
\(213\) −6.05460 −0.414854
\(214\) −30.8664 −2.10998
\(215\) −23.4380 −1.59846
\(216\) 30.7111 2.08963
\(217\) −1.07621 −0.0730582
\(218\) 15.1953 1.02915
\(219\) 0.0751041 0.00507507
\(220\) 14.5686 0.982215
\(221\) 1.35297 0.0910109
\(222\) 16.6270 1.11593
\(223\) 13.7324 0.919588 0.459794 0.888025i \(-0.347923\pi\)
0.459794 + 0.888025i \(0.347923\pi\)
\(224\) 2.76760 0.184918
\(225\) −7.90406 −0.526937
\(226\) 21.3348 1.41917
\(227\) 12.1230 0.804631 0.402316 0.915501i \(-0.368205\pi\)
0.402316 + 0.915501i \(0.368205\pi\)
\(228\) 14.4643 0.957920
\(229\) −24.2714 −1.60390 −0.801950 0.597392i \(-0.796204\pi\)
−0.801950 + 0.597392i \(0.796204\pi\)
\(230\) 72.5454 4.78350
\(231\) 0.119381 0.00785470
\(232\) −19.0916 −1.25342
\(233\) 19.6855 1.28964 0.644819 0.764336i \(-0.276933\pi\)
0.644819 + 0.764336i \(0.276933\pi\)
\(234\) 8.65144 0.565562
\(235\) −1.72585 −0.112582
\(236\) −53.7345 −3.49782
\(237\) −6.31783 −0.410387
\(238\) 0.514100 0.0333242
\(239\) 21.0603 1.36227 0.681137 0.732156i \(-0.261486\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(240\) −22.6093 −1.45942
\(241\) −18.6749 −1.20295 −0.601477 0.798890i \(-0.705421\pi\)
−0.601477 + 0.798890i \(0.705421\pi\)
\(242\) −2.66894 −0.171566
\(243\) 14.5259 0.931838
\(244\) 19.0134 1.21721
\(245\) 19.8131 1.26581
\(246\) 15.9296 1.01563
\(247\) 5.39369 0.343192
\(248\) −49.7851 −3.16136
\(249\) 4.80405 0.304445
\(250\) −14.5246 −0.918616
\(251\) 17.4636 1.10229 0.551146 0.834409i \(-0.314191\pi\)
0.551146 + 0.834409i \(0.314191\pi\)
\(252\) 2.36436 0.148941
\(253\) −9.55869 −0.600950
\(254\) −15.4978 −0.972421
\(255\) −2.01385 −0.126112
\(256\) 5.05804 0.316128
\(257\) −18.5944 −1.15989 −0.579943 0.814657i \(-0.696925\pi\)
−0.579943 + 0.814657i \(0.696925\pi\)
\(258\) −14.5740 −0.907335
\(259\) 1.69445 0.105288
\(260\) −18.4393 −1.14355
\(261\) −5.86570 −0.363078
\(262\) 2.66894 0.164888
\(263\) 12.8592 0.792929 0.396465 0.918050i \(-0.370237\pi\)
0.396465 + 0.918050i \(0.370237\pi\)
\(264\) 5.52251 0.339887
\(265\) 31.7690 1.95155
\(266\) 2.04948 0.125662
\(267\) −4.84650 −0.296601
\(268\) −11.1765 −0.682715
\(269\) −2.26025 −0.137810 −0.0689049 0.997623i \(-0.521950\pi\)
−0.0689049 + 0.997623i \(0.521950\pi\)
\(270\) −27.9616 −1.70169
\(271\) 19.6892 1.19603 0.598016 0.801484i \(-0.295956\pi\)
0.598016 + 0.801484i \(0.295956\pi\)
\(272\) 12.8288 0.777862
\(273\) −0.151099 −0.00914493
\(274\) 45.1764 2.72920
\(275\) −3.08622 −0.186106
\(276\) 32.4440 1.95290
\(277\) −14.1396 −0.849566 −0.424783 0.905295i \(-0.639650\pi\)
−0.424783 + 0.905295i \(0.639650\pi\)
\(278\) 29.8165 1.78827
\(279\) −15.2960 −0.915747
\(280\) −4.27132 −0.255260
\(281\) −11.6442 −0.694632 −0.347316 0.937748i \(-0.612907\pi\)
−0.347316 + 0.937748i \(0.612907\pi\)
\(282\) −1.07315 −0.0639053
\(283\) 0.146913 0.00873307 0.00436654 0.999990i \(-0.498610\pi\)
0.00436654 + 0.999990i \(0.498610\pi\)
\(284\) −46.8208 −2.77831
\(285\) −8.02831 −0.475556
\(286\) 3.37804 0.199748
\(287\) 1.62337 0.0958247
\(288\) 39.3353 2.31786
\(289\) −15.8573 −0.932783
\(290\) 17.3823 1.02073
\(291\) 0.449586 0.0263552
\(292\) 0.580788 0.0339880
\(293\) −1.48150 −0.0865502 −0.0432751 0.999063i \(-0.513779\pi\)
−0.0432751 + 0.999063i \(0.513779\pi\)
\(294\) 12.3200 0.718514
\(295\) 29.8250 1.73648
\(296\) 78.3842 4.55599
\(297\) 3.68426 0.213783
\(298\) −33.7368 −1.95432
\(299\) 12.0983 0.699662
\(300\) 10.4752 0.604787
\(301\) −1.48522 −0.0856069
\(302\) 47.9847 2.76121
\(303\) −4.31630 −0.247965
\(304\) 51.1426 2.93323
\(305\) −10.5533 −0.604279
\(306\) 7.30679 0.417701
\(307\) 4.15045 0.236879 0.118439 0.992961i \(-0.462211\pi\)
0.118439 + 0.992961i \(0.462211\pi\)
\(308\) 0.923187 0.0526035
\(309\) 3.64009 0.207077
\(310\) 45.3279 2.57445
\(311\) 0.958286 0.0543394 0.0271697 0.999631i \(-0.491351\pi\)
0.0271697 + 0.999631i \(0.491351\pi\)
\(312\) −6.98976 −0.395717
\(313\) 33.8258 1.91195 0.955975 0.293449i \(-0.0948029\pi\)
0.955975 + 0.293449i \(0.0948029\pi\)
\(314\) 63.3668 3.57599
\(315\) −1.31232 −0.0739411
\(316\) −48.8565 −2.74839
\(317\) 2.91347 0.163637 0.0818184 0.996647i \(-0.473927\pi\)
0.0818184 + 0.996647i \(0.473927\pi\)
\(318\) 19.7543 1.10776
\(319\) −2.29032 −0.128233
\(320\) −48.3121 −2.70073
\(321\) 7.66193 0.427647
\(322\) 4.59708 0.256185
\(323\) 4.55537 0.253468
\(324\) 26.8581 1.49212
\(325\) 3.90618 0.216676
\(326\) −32.4999 −1.80000
\(327\) −3.77190 −0.208587
\(328\) 75.0963 4.14650
\(329\) −0.109364 −0.00602946
\(330\) −5.02809 −0.276787
\(331\) −22.4524 −1.23409 −0.617047 0.786927i \(-0.711671\pi\)
−0.617047 + 0.786927i \(0.711671\pi\)
\(332\) 37.1503 2.03889
\(333\) 24.0828 1.31973
\(334\) 41.3979 2.26519
\(335\) 6.20347 0.338932
\(336\) −1.43271 −0.0781609
\(337\) −29.1518 −1.58800 −0.793999 0.607918i \(-0.792005\pi\)
−0.793999 + 0.607918i \(0.792005\pi\)
\(338\) 30.4207 1.65467
\(339\) −5.29591 −0.287634
\(340\) −15.5733 −0.844583
\(341\) −5.97247 −0.323427
\(342\) 29.1288 1.57511
\(343\) 2.51689 0.135899
\(344\) −68.7056 −3.70436
\(345\) −18.0079 −0.969511
\(346\) 28.8233 1.54955
\(347\) 25.3829 1.36263 0.681313 0.731993i \(-0.261409\pi\)
0.681313 + 0.731993i \(0.261409\pi\)
\(348\) 7.77379 0.416719
\(349\) 2.23701 0.119744 0.0598721 0.998206i \(-0.480931\pi\)
0.0598721 + 0.998206i \(0.480931\pi\)
\(350\) 1.48426 0.0793371
\(351\) −4.66312 −0.248899
\(352\) 15.3589 0.818630
\(353\) −1.35804 −0.0722810 −0.0361405 0.999347i \(-0.511506\pi\)
−0.0361405 + 0.999347i \(0.511506\pi\)
\(354\) 18.5455 0.985681
\(355\) 25.9876 1.37928
\(356\) −37.4785 −1.98636
\(357\) −0.127614 −0.00675407
\(358\) −1.95223 −0.103179
\(359\) −9.99224 −0.527370 −0.263685 0.964609i \(-0.584938\pi\)
−0.263685 + 0.964609i \(0.584938\pi\)
\(360\) −60.7074 −3.19956
\(361\) −0.839826 −0.0442014
\(362\) −5.03890 −0.264839
\(363\) 0.662508 0.0347727
\(364\) −1.16846 −0.0612442
\(365\) −0.322363 −0.0168733
\(366\) −6.56213 −0.343008
\(367\) 0.326523 0.0170444 0.00852218 0.999964i \(-0.497287\pi\)
0.00852218 + 0.999964i \(0.497287\pi\)
\(368\) 114.715 5.97995
\(369\) 23.0726 1.20111
\(370\) −71.3666 −3.71017
\(371\) 2.01315 0.104517
\(372\) 20.2717 1.05104
\(373\) 10.5955 0.548614 0.274307 0.961642i \(-0.411552\pi\)
0.274307 + 0.961642i \(0.411552\pi\)
\(374\) 2.85301 0.147526
\(375\) 3.60542 0.186183
\(376\) −5.05914 −0.260905
\(377\) 2.89883 0.149297
\(378\) −1.77188 −0.0911356
\(379\) −31.9187 −1.63955 −0.819776 0.572684i \(-0.805902\pi\)
−0.819776 + 0.572684i \(0.805902\pi\)
\(380\) −62.0838 −3.18483
\(381\) 3.84701 0.197088
\(382\) −26.8985 −1.37624
\(383\) −2.92341 −0.149379 −0.0746896 0.997207i \(-0.523797\pi\)
−0.0746896 + 0.997207i \(0.523797\pi\)
\(384\) −9.69017 −0.494499
\(385\) −0.512410 −0.0261148
\(386\) 41.5280 2.11372
\(387\) −21.1092 −1.07304
\(388\) 3.47669 0.176502
\(389\) −15.1610 −0.768691 −0.384346 0.923189i \(-0.625573\pi\)
−0.384346 + 0.923189i \(0.625573\pi\)
\(390\) 6.36398 0.322252
\(391\) 10.2179 0.516742
\(392\) 58.0797 2.93347
\(393\) −0.662508 −0.0334191
\(394\) −14.5569 −0.733368
\(395\) 27.1175 1.36443
\(396\) 13.1211 0.659358
\(397\) 4.83712 0.242768 0.121384 0.992606i \(-0.461267\pi\)
0.121384 + 0.992606i \(0.461267\pi\)
\(398\) 60.6321 3.03921
\(399\) −0.508740 −0.0254689
\(400\) 37.0382 1.85191
\(401\) −26.7555 −1.33611 −0.668054 0.744113i \(-0.732873\pi\)
−0.668054 + 0.744113i \(0.732873\pi\)
\(402\) 3.85738 0.192388
\(403\) 7.55927 0.376554
\(404\) −33.3784 −1.66064
\(405\) −14.9074 −0.740756
\(406\) 1.10149 0.0546660
\(407\) 9.40337 0.466108
\(408\) −5.90338 −0.292261
\(409\) 1.54562 0.0764262 0.0382131 0.999270i \(-0.487833\pi\)
0.0382131 + 0.999270i \(0.487833\pi\)
\(410\) −68.3731 −3.37671
\(411\) −11.2141 −0.553150
\(412\) 28.1492 1.38681
\(413\) 1.88996 0.0929988
\(414\) 65.3373 3.21115
\(415\) −20.6200 −1.01220
\(416\) −19.4395 −0.953099
\(417\) −7.40131 −0.362444
\(418\) 11.3736 0.556302
\(419\) −17.6173 −0.860660 −0.430330 0.902672i \(-0.641603\pi\)
−0.430330 + 0.902672i \(0.641603\pi\)
\(420\) 1.73922 0.0848651
\(421\) −8.41029 −0.409892 −0.204946 0.978773i \(-0.565702\pi\)
−0.204946 + 0.978773i \(0.565702\pi\)
\(422\) −37.2034 −1.81104
\(423\) −1.55437 −0.0755762
\(424\) 93.1270 4.52265
\(425\) 3.29906 0.160028
\(426\) 16.1594 0.782924
\(427\) −0.668743 −0.0323627
\(428\) 59.2505 2.86398
\(429\) −0.838527 −0.0404844
\(430\) 62.5546 3.01665
\(431\) −27.4707 −1.32322 −0.661609 0.749849i \(-0.730126\pi\)
−0.661609 + 0.749849i \(0.730126\pi\)
\(432\) −44.2154 −2.12732
\(433\) −15.5514 −0.747353 −0.373676 0.927559i \(-0.621903\pi\)
−0.373676 + 0.927559i \(0.621903\pi\)
\(434\) 2.87235 0.137877
\(435\) −4.31480 −0.206879
\(436\) −29.1685 −1.39692
\(437\) 40.7341 1.94858
\(438\) −0.200448 −0.00957780
\(439\) −11.0150 −0.525718 −0.262859 0.964834i \(-0.584665\pi\)
−0.262859 + 0.964834i \(0.584665\pi\)
\(440\) −23.7038 −1.13003
\(441\) 17.8444 0.849734
\(442\) −3.61101 −0.171758
\(443\) 3.05301 0.145053 0.0725265 0.997366i \(-0.476894\pi\)
0.0725265 + 0.997366i \(0.476894\pi\)
\(444\) −31.9168 −1.51471
\(445\) 20.8022 0.986121
\(446\) −36.6509 −1.73547
\(447\) 8.37444 0.396098
\(448\) −3.06145 −0.144640
\(449\) 18.3110 0.864151 0.432075 0.901837i \(-0.357781\pi\)
0.432075 + 0.901837i \(0.357781\pi\)
\(450\) 21.0955 0.994450
\(451\) 9.00894 0.424214
\(452\) −40.9538 −1.92631
\(453\) −11.9112 −0.559636
\(454\) −32.3555 −1.51852
\(455\) 0.648549 0.0304045
\(456\) −23.5340 −1.10208
\(457\) 4.10981 0.192249 0.0961245 0.995369i \(-0.469355\pi\)
0.0961245 + 0.995369i \(0.469355\pi\)
\(458\) 64.7789 3.02692
\(459\) −3.93835 −0.183827
\(460\) −139.257 −6.49288
\(461\) −37.4058 −1.74216 −0.871081 0.491140i \(-0.836580\pi\)
−0.871081 + 0.491140i \(0.836580\pi\)
\(462\) −0.318621 −0.0148236
\(463\) 20.7765 0.965565 0.482782 0.875740i \(-0.339626\pi\)
0.482782 + 0.875740i \(0.339626\pi\)
\(464\) 27.4865 1.27603
\(465\) −11.2517 −0.521785
\(466\) −52.5393 −2.43384
\(467\) 29.7623 1.37723 0.688616 0.725126i \(-0.258218\pi\)
0.688616 + 0.725126i \(0.258218\pi\)
\(468\) −16.6071 −0.767665
\(469\) 0.393103 0.0181518
\(470\) 4.60620 0.212468
\(471\) −15.7295 −0.724775
\(472\) 87.4285 4.02422
\(473\) −8.24228 −0.378980
\(474\) 16.8619 0.774493
\(475\) 13.1518 0.603448
\(476\) −0.986856 −0.0452325
\(477\) 28.6124 1.31007
\(478\) −56.2086 −2.57092
\(479\) −25.1599 −1.14958 −0.574791 0.818300i \(-0.694917\pi\)
−0.574791 + 0.818300i \(0.694917\pi\)
\(480\) 28.9350 1.32070
\(481\) −11.9017 −0.542671
\(482\) 49.8421 2.27025
\(483\) −1.14113 −0.0519231
\(484\) 5.12325 0.232875
\(485\) −1.92972 −0.0876240
\(486\) −38.7688 −1.75859
\(487\) 0.510256 0.0231219 0.0115610 0.999933i \(-0.496320\pi\)
0.0115610 + 0.999933i \(0.496320\pi\)
\(488\) −30.9357 −1.40039
\(489\) 8.06741 0.364821
\(490\) −52.8799 −2.38887
\(491\) −36.4422 −1.64461 −0.822307 0.569044i \(-0.807313\pi\)
−0.822307 + 0.569044i \(0.807313\pi\)
\(492\) −30.5781 −1.37857
\(493\) 2.44828 0.110265
\(494\) −14.3954 −0.647681
\(495\) −7.28277 −0.327336
\(496\) 71.6766 3.21837
\(497\) 1.64679 0.0738687
\(498\) −12.8217 −0.574556
\(499\) 42.6858 1.91088 0.955439 0.295190i \(-0.0953830\pi\)
0.955439 + 0.295190i \(0.0953830\pi\)
\(500\) 27.8811 1.24688
\(501\) −10.2762 −0.459105
\(502\) −46.6093 −2.08027
\(503\) −42.0874 −1.87658 −0.938292 0.345845i \(-0.887592\pi\)
−0.938292 + 0.345845i \(0.887592\pi\)
\(504\) −3.84692 −0.171356
\(505\) 18.5265 0.824418
\(506\) 25.5116 1.13413
\(507\) −7.55130 −0.335365
\(508\) 29.7493 1.31991
\(509\) 21.2665 0.942621 0.471310 0.881967i \(-0.343781\pi\)
0.471310 + 0.881967i \(0.343781\pi\)
\(510\) 5.37486 0.238003
\(511\) −0.0204276 −0.000903663 0
\(512\) 15.7534 0.696207
\(513\) −15.7004 −0.693189
\(514\) 49.6274 2.18897
\(515\) −15.6240 −0.688478
\(516\) 27.9759 1.23157
\(517\) −0.606920 −0.0266923
\(518\) −4.52238 −0.198702
\(519\) −7.15478 −0.314060
\(520\) 30.0015 1.31565
\(521\) 37.9890 1.66433 0.832164 0.554530i \(-0.187102\pi\)
0.832164 + 0.554530i \(0.187102\pi\)
\(522\) 15.6552 0.685210
\(523\) 8.24453 0.360508 0.180254 0.983620i \(-0.442308\pi\)
0.180254 + 0.983620i \(0.442308\pi\)
\(524\) −5.12325 −0.223810
\(525\) −0.368436 −0.0160799
\(526\) −34.3203 −1.49644
\(527\) 6.38437 0.278107
\(528\) −7.95087 −0.346017
\(529\) 68.3686 2.97255
\(530\) −84.7895 −3.68302
\(531\) 26.8616 1.16569
\(532\) −3.93414 −0.170567
\(533\) −11.4025 −0.493896
\(534\) 12.9350 0.559754
\(535\) −32.8866 −1.42181
\(536\) 18.1847 0.785461
\(537\) 0.484600 0.0209121
\(538\) 6.03247 0.260078
\(539\) 6.96753 0.300113
\(540\) 53.6746 2.30979
\(541\) 26.3614 1.13336 0.566682 0.823937i \(-0.308227\pi\)
0.566682 + 0.823937i \(0.308227\pi\)
\(542\) −52.5492 −2.25718
\(543\) 1.25080 0.0536770
\(544\) −16.4181 −0.703921
\(545\) 16.1898 0.693495
\(546\) 0.403274 0.0172585
\(547\) −20.8575 −0.891801 −0.445901 0.895082i \(-0.647117\pi\)
−0.445901 + 0.895082i \(0.647117\pi\)
\(548\) −86.7197 −3.70448
\(549\) −9.50469 −0.405650
\(550\) 8.23694 0.351224
\(551\) 9.76015 0.415796
\(552\) −52.7880 −2.24680
\(553\) 1.71839 0.0730733
\(554\) 37.7377 1.60332
\(555\) 17.7153 0.751971
\(556\) −57.2351 −2.42731
\(557\) −9.69854 −0.410940 −0.205470 0.978663i \(-0.565872\pi\)
−0.205470 + 0.978663i \(0.565872\pi\)
\(558\) 40.8241 1.72822
\(559\) 10.4321 0.441232
\(560\) 6.14951 0.259864
\(561\) −0.708199 −0.0299002
\(562\) 31.0776 1.31093
\(563\) 21.0211 0.885934 0.442967 0.896538i \(-0.353926\pi\)
0.442967 + 0.896538i \(0.353926\pi\)
\(564\) 2.06000 0.0867418
\(565\) 22.7312 0.956308
\(566\) −0.392102 −0.0164813
\(567\) −0.944657 −0.0396719
\(568\) 76.1797 3.19643
\(569\) 33.0683 1.38630 0.693148 0.720795i \(-0.256223\pi\)
0.693148 + 0.720795i \(0.256223\pi\)
\(570\) 21.4271 0.897482
\(571\) −6.48596 −0.271429 −0.135715 0.990748i \(-0.543333\pi\)
−0.135715 + 0.990748i \(0.543333\pi\)
\(572\) −6.48442 −0.271127
\(573\) 6.67697 0.278935
\(574\) −4.33269 −0.180843
\(575\) 29.5002 1.23024
\(576\) −43.5118 −1.81299
\(577\) 39.7547 1.65501 0.827504 0.561459i \(-0.189760\pi\)
0.827504 + 0.561459i \(0.189760\pi\)
\(578\) 42.3222 1.76037
\(579\) −10.3084 −0.428404
\(580\) −33.3668 −1.38548
\(581\) −1.30666 −0.0542092
\(582\) −1.19992 −0.0497382
\(583\) 11.1720 0.462697
\(584\) −0.944969 −0.0391031
\(585\) 9.21769 0.381105
\(586\) 3.95404 0.163340
\(587\) −32.0146 −1.32138 −0.660692 0.750657i \(-0.729737\pi\)
−0.660692 + 0.750657i \(0.729737\pi\)
\(588\) −23.6491 −0.975274
\(589\) 25.4515 1.04871
\(590\) −79.6012 −3.27713
\(591\) 3.61345 0.148638
\(592\) −112.851 −4.63816
\(593\) −6.33312 −0.260070 −0.130035 0.991509i \(-0.541509\pi\)
−0.130035 + 0.991509i \(0.541509\pi\)
\(594\) −9.83308 −0.403456
\(595\) 0.547749 0.0224555
\(596\) 64.7605 2.65269
\(597\) −15.0506 −0.615981
\(598\) −32.2896 −1.32042
\(599\) −26.6386 −1.08843 −0.544213 0.838947i \(-0.683172\pi\)
−0.544213 + 0.838947i \(0.683172\pi\)
\(600\) −17.0437 −0.695805
\(601\) 4.32699 0.176502 0.0882508 0.996098i \(-0.471872\pi\)
0.0882508 + 0.996098i \(0.471872\pi\)
\(602\) 3.96397 0.161560
\(603\) 5.58709 0.227524
\(604\) −92.1104 −3.74792
\(605\) −2.84363 −0.115610
\(606\) 11.5200 0.467966
\(607\) −44.3947 −1.80193 −0.900963 0.433896i \(-0.857138\pi\)
−0.900963 + 0.433896i \(0.857138\pi\)
\(608\) −65.4514 −2.65441
\(609\) −0.273421 −0.0110796
\(610\) 28.1661 1.14041
\(611\) 0.768170 0.0310768
\(612\) −14.0260 −0.566966
\(613\) −48.2696 −1.94959 −0.974796 0.223097i \(-0.928383\pi\)
−0.974796 + 0.223097i \(0.928383\pi\)
\(614\) −11.0773 −0.447044
\(615\) 16.9722 0.684384
\(616\) −1.50207 −0.0605201
\(617\) 17.2782 0.695596 0.347798 0.937570i \(-0.386930\pi\)
0.347798 + 0.937570i \(0.386930\pi\)
\(618\) −9.71518 −0.390802
\(619\) −27.0441 −1.08699 −0.543497 0.839411i \(-0.682900\pi\)
−0.543497 + 0.839411i \(0.682900\pi\)
\(620\) −87.0106 −3.49443
\(621\) −35.2167 −1.41320
\(622\) −2.55761 −0.102551
\(623\) 1.31820 0.0528126
\(624\) 10.0633 0.402854
\(625\) −30.9063 −1.23625
\(626\) −90.2792 −3.60828
\(627\) −2.82326 −0.112750
\(628\) −121.638 −4.85387
\(629\) −10.0519 −0.400795
\(630\) 3.50251 0.139544
\(631\) −30.6954 −1.22197 −0.610983 0.791644i \(-0.709226\pi\)
−0.610983 + 0.791644i \(0.709226\pi\)
\(632\) 79.4917 3.16201
\(633\) 9.23497 0.367057
\(634\) −7.77588 −0.308820
\(635\) −16.5122 −0.655267
\(636\) −37.9199 −1.50362
\(637\) −8.81870 −0.349410
\(638\) 6.11273 0.242005
\(639\) 23.4055 0.925907
\(640\) 41.5923 1.64408
\(641\) 37.7102 1.48946 0.744731 0.667364i \(-0.232578\pi\)
0.744731 + 0.667364i \(0.232578\pi\)
\(642\) −20.4492 −0.807067
\(643\) −19.4955 −0.768826 −0.384413 0.923161i \(-0.625596\pi\)
−0.384413 + 0.923161i \(0.625596\pi\)
\(644\) −8.82446 −0.347733
\(645\) −15.5278 −0.611408
\(646\) −12.1580 −0.478351
\(647\) 8.71222 0.342513 0.171256 0.985227i \(-0.445217\pi\)
0.171256 + 0.985227i \(0.445217\pi\)
\(648\) −43.6993 −1.71667
\(649\) 10.4884 0.411704
\(650\) −10.4254 −0.408917
\(651\) −0.713001 −0.0279447
\(652\) 62.3862 2.44323
\(653\) −18.3713 −0.718925 −0.359463 0.933159i \(-0.617040\pi\)
−0.359463 + 0.933159i \(0.617040\pi\)
\(654\) 10.0670 0.393650
\(655\) 2.84363 0.111110
\(656\) −108.118 −4.22129
\(657\) −0.290333 −0.0113270
\(658\) 0.291887 0.0113789
\(659\) 27.3948 1.06715 0.533575 0.845753i \(-0.320848\pi\)
0.533575 + 0.845753i \(0.320848\pi\)
\(660\) 9.65182 0.375697
\(661\) −20.9725 −0.815736 −0.407868 0.913041i \(-0.633728\pi\)
−0.407868 + 0.913041i \(0.633728\pi\)
\(662\) 59.9240 2.32901
\(663\) 0.896357 0.0348116
\(664\) −60.4452 −2.34573
\(665\) 2.18362 0.0846772
\(666\) −64.2756 −2.49063
\(667\) 21.8925 0.847680
\(668\) −79.4666 −3.07466
\(669\) 9.09782 0.351742
\(670\) −16.5567 −0.639641
\(671\) −3.71120 −0.143269
\(672\) 1.83356 0.0707311
\(673\) −15.0610 −0.580560 −0.290280 0.956942i \(-0.593748\pi\)
−0.290280 + 0.956942i \(0.593748\pi\)
\(674\) 77.8044 2.99691
\(675\) −11.3704 −0.437648
\(676\) −58.3950 −2.24596
\(677\) −28.4929 −1.09507 −0.547535 0.836783i \(-0.684434\pi\)
−0.547535 + 0.836783i \(0.684434\pi\)
\(678\) 14.1345 0.542831
\(679\) −0.122283 −0.00469279
\(680\) 25.3386 0.971689
\(681\) 8.03158 0.307771
\(682\) 15.9402 0.610381
\(683\) 2.01408 0.0770668 0.0385334 0.999257i \(-0.487731\pi\)
0.0385334 + 0.999257i \(0.487731\pi\)
\(684\) −55.9151 −2.13797
\(685\) 48.1332 1.83908
\(686\) −6.71743 −0.256473
\(687\) −16.0800 −0.613490
\(688\) 98.9169 3.77117
\(689\) −14.1402 −0.538700
\(690\) 48.0619 1.82969
\(691\) 0.625992 0.0238139 0.0119069 0.999929i \(-0.496210\pi\)
0.0119069 + 0.999929i \(0.496210\pi\)
\(692\) −55.3287 −2.10328
\(693\) −0.461496 −0.0175308
\(694\) −67.7454 −2.57158
\(695\) 31.7680 1.20503
\(696\) −12.6483 −0.479433
\(697\) −9.63025 −0.364772
\(698\) −5.97043 −0.225984
\(699\) 13.0418 0.493285
\(700\) −2.84916 −0.107688
\(701\) −29.9973 −1.13298 −0.566490 0.824068i \(-0.691699\pi\)
−0.566490 + 0.824068i \(0.691699\pi\)
\(702\) 12.4456 0.469728
\(703\) −40.0722 −1.51135
\(704\) −16.9896 −0.640319
\(705\) −1.14339 −0.0430627
\(706\) 3.62452 0.136411
\(707\) 1.17399 0.0441525
\(708\) −35.5995 −1.33791
\(709\) −7.47402 −0.280693 −0.140346 0.990102i \(-0.544822\pi\)
−0.140346 + 0.990102i \(0.544822\pi\)
\(710\) −69.3595 −2.60301
\(711\) 24.4231 0.915937
\(712\) 60.9793 2.28530
\(713\) 57.0890 2.13800
\(714\) 0.340595 0.0127465
\(715\) 3.59914 0.134600
\(716\) 3.74747 0.140049
\(717\) 13.9526 0.521069
\(718\) 26.6687 0.995267
\(719\) 8.84215 0.329756 0.164878 0.986314i \(-0.447277\pi\)
0.164878 + 0.986314i \(0.447277\pi\)
\(720\) 87.4016 3.25727
\(721\) −0.990069 −0.0368721
\(722\) 2.24145 0.0834180
\(723\) −12.3722 −0.460129
\(724\) 9.67257 0.359478
\(725\) 7.06843 0.262515
\(726\) −1.76820 −0.0656239
\(727\) −11.2206 −0.416148 −0.208074 0.978113i \(-0.566719\pi\)
−0.208074 + 0.978113i \(0.566719\pi\)
\(728\) 1.90115 0.0704612
\(729\) −6.10365 −0.226061
\(730\) 0.860368 0.0318436
\(731\) 8.81072 0.325876
\(732\) 12.5965 0.465581
\(733\) −17.4756 −0.645475 −0.322737 0.946489i \(-0.604603\pi\)
−0.322737 + 0.946489i \(0.604603\pi\)
\(734\) −0.871471 −0.0321666
\(735\) 13.1263 0.484171
\(736\) −146.811 −5.41151
\(737\) 2.18153 0.0803578
\(738\) −61.5795 −2.26677
\(739\) −6.07460 −0.223458 −0.111729 0.993739i \(-0.535639\pi\)
−0.111729 + 0.993739i \(0.535639\pi\)
\(740\) 136.994 5.03600
\(741\) 3.57336 0.131271
\(742\) −5.37297 −0.197248
\(743\) 15.2685 0.560148 0.280074 0.959978i \(-0.409641\pi\)
0.280074 + 0.959978i \(0.409641\pi\)
\(744\) −32.9830 −1.20922
\(745\) −35.9449 −1.31692
\(746\) −28.2787 −1.03536
\(747\) −18.5712 −0.679485
\(748\) −5.47658 −0.200243
\(749\) −2.08397 −0.0761466
\(750\) −9.62266 −0.351370
\(751\) 22.9599 0.837819 0.418909 0.908028i \(-0.362413\pi\)
0.418909 + 0.908028i \(0.362413\pi\)
\(752\) 7.28374 0.265611
\(753\) 11.5698 0.421626
\(754\) −7.73680 −0.281757
\(755\) 51.1253 1.86064
\(756\) 3.40126 0.123703
\(757\) 50.1162 1.82150 0.910752 0.412954i \(-0.135503\pi\)
0.910752 + 0.412954i \(0.135503\pi\)
\(758\) 85.1891 3.09421
\(759\) −6.33271 −0.229863
\(760\) 101.013 3.66413
\(761\) −11.2089 −0.406321 −0.203161 0.979145i \(-0.565121\pi\)
−0.203161 + 0.979145i \(0.565121\pi\)
\(762\) −10.2674 −0.371950
\(763\) 1.02592 0.0371408
\(764\) 51.6337 1.86804
\(765\) 7.78503 0.281468
\(766\) 7.80240 0.281912
\(767\) −13.2750 −0.479331
\(768\) 3.35099 0.120919
\(769\) −13.8992 −0.501217 −0.250609 0.968088i \(-0.580631\pi\)
−0.250609 + 0.968088i \(0.580631\pi\)
\(770\) 1.36759 0.0492846
\(771\) −12.3189 −0.443656
\(772\) −79.7163 −2.86905
\(773\) 39.5745 1.42340 0.711698 0.702485i \(-0.247926\pi\)
0.711698 + 0.702485i \(0.247926\pi\)
\(774\) 56.3391 2.02507
\(775\) 18.4323 0.662110
\(776\) −5.65674 −0.203065
\(777\) 1.12259 0.0402725
\(778\) 40.4637 1.45069
\(779\) −38.3914 −1.37551
\(780\) −12.2162 −0.437409
\(781\) 9.13890 0.327016
\(782\) −27.2710 −0.975210
\(783\) −8.43815 −0.301555
\(784\) −83.6184 −2.98637
\(785\) 67.5143 2.40969
\(786\) 1.76820 0.0630694
\(787\) 48.7837 1.73895 0.869476 0.493975i \(-0.164457\pi\)
0.869476 + 0.493975i \(0.164457\pi\)
\(788\) 27.9432 0.995435
\(789\) 8.51929 0.303295
\(790\) −72.3750 −2.57499
\(791\) 1.44044 0.0512160
\(792\) −21.3486 −0.758589
\(793\) 4.69721 0.166803
\(794\) −12.9100 −0.458158
\(795\) 21.0472 0.746468
\(796\) −116.388 −4.12527
\(797\) 8.16406 0.289186 0.144593 0.989491i \(-0.453813\pi\)
0.144593 + 0.989491i \(0.453813\pi\)
\(798\) 1.35780 0.0480655
\(799\) 0.648777 0.0229521
\(800\) −47.4008 −1.67587
\(801\) 18.7353 0.661980
\(802\) 71.4090 2.52154
\(803\) −0.113363 −0.00400050
\(804\) −7.40454 −0.261138
\(805\) 4.89797 0.172631
\(806\) −20.1752 −0.710642
\(807\) −1.49743 −0.0527121
\(808\) 54.3083 1.91056
\(809\) 44.8773 1.57780 0.788900 0.614521i \(-0.210651\pi\)
0.788900 + 0.614521i \(0.210651\pi\)
\(810\) 39.7870 1.39797
\(811\) 42.1321 1.47946 0.739730 0.672904i \(-0.234953\pi\)
0.739730 + 0.672904i \(0.234953\pi\)
\(812\) −2.11440 −0.0742008
\(813\) 13.0442 0.457481
\(814\) −25.0970 −0.879651
\(815\) −34.6271 −1.21293
\(816\) 8.49921 0.297532
\(817\) 35.1243 1.22884
\(818\) −4.12518 −0.144234
\(819\) 0.584109 0.0204104
\(820\) 131.248 4.58337
\(821\) −25.8471 −0.902068 −0.451034 0.892507i \(-0.648945\pi\)
−0.451034 + 0.892507i \(0.648945\pi\)
\(822\) 29.9297 1.04392
\(823\) −10.1326 −0.353202 −0.176601 0.984283i \(-0.556510\pi\)
−0.176601 + 0.984283i \(0.556510\pi\)
\(824\) −45.8001 −1.59552
\(825\) −2.04464 −0.0711854
\(826\) −5.04419 −0.175510
\(827\) 35.1488 1.22225 0.611123 0.791536i \(-0.290718\pi\)
0.611123 + 0.791536i \(0.290718\pi\)
\(828\) −125.420 −4.35865
\(829\) 20.8882 0.725478 0.362739 0.931891i \(-0.381842\pi\)
0.362739 + 0.931891i \(0.381842\pi\)
\(830\) 55.0337 1.91025
\(831\) −9.36759 −0.324958
\(832\) 21.5035 0.745499
\(833\) −7.44805 −0.258060
\(834\) 19.7537 0.684013
\(835\) 44.1075 1.52640
\(836\) −21.8326 −0.755096
\(837\) −22.0042 −0.760575
\(838\) 47.0195 1.62426
\(839\) 20.6064 0.711411 0.355706 0.934598i \(-0.384241\pi\)
0.355706 + 0.934598i \(0.384241\pi\)
\(840\) −2.82979 −0.0976369
\(841\) −23.7544 −0.819118
\(842\) 22.4466 0.773560
\(843\) −7.71435 −0.265696
\(844\) 71.4150 2.45821
\(845\) 32.4118 1.11500
\(846\) 4.14853 0.142629
\(847\) −0.180196 −0.00619160
\(848\) −134.077 −4.60422
\(849\) 0.0973311 0.00334039
\(850\) −8.80501 −0.302009
\(851\) −89.8839 −3.08118
\(852\) −31.0192 −1.06270
\(853\) 3.22405 0.110389 0.0551947 0.998476i \(-0.482422\pi\)
0.0551947 + 0.998476i \(0.482422\pi\)
\(854\) 1.78484 0.0610758
\(855\) 31.0353 1.06139
\(856\) −96.4033 −3.29500
\(857\) 39.1244 1.33646 0.668232 0.743953i \(-0.267051\pi\)
0.668232 + 0.743953i \(0.267051\pi\)
\(858\) 2.23798 0.0764033
\(859\) 24.4225 0.833284 0.416642 0.909071i \(-0.363207\pi\)
0.416642 + 0.909071i \(0.363207\pi\)
\(860\) −120.078 −4.09464
\(861\) 1.07550 0.0366529
\(862\) 73.3178 2.49721
\(863\) −0.592122 −0.0201561 −0.0100780 0.999949i \(-0.503208\pi\)
−0.0100780 + 0.999949i \(0.503208\pi\)
\(864\) 56.5861 1.92510
\(865\) 30.7098 1.04417
\(866\) 41.5058 1.41042
\(867\) −10.5056 −0.356789
\(868\) −5.51371 −0.187147
\(869\) 9.53623 0.323494
\(870\) 11.5159 0.390427
\(871\) −2.76113 −0.0935574
\(872\) 47.4585 1.60715
\(873\) −1.73798 −0.0588217
\(874\) −108.717 −3.67741
\(875\) −0.980640 −0.0331517
\(876\) 0.384777 0.0130004
\(877\) −32.7827 −1.10699 −0.553497 0.832851i \(-0.686707\pi\)
−0.553497 + 0.832851i \(0.686707\pi\)
\(878\) 29.3984 0.992148
\(879\) −0.981507 −0.0331054
\(880\) 34.1268 1.15042
\(881\) 5.22039 0.175879 0.0879397 0.996126i \(-0.471972\pi\)
0.0879397 + 0.996126i \(0.471972\pi\)
\(882\) −47.6257 −1.60364
\(883\) −3.54486 −0.119294 −0.0596471 0.998220i \(-0.518998\pi\)
−0.0596471 + 0.998220i \(0.518998\pi\)
\(884\) 6.93162 0.233136
\(885\) 19.7593 0.664202
\(886\) −8.14831 −0.273748
\(887\) −49.8751 −1.67464 −0.837322 0.546710i \(-0.815880\pi\)
−0.837322 + 0.546710i \(0.815880\pi\)
\(888\) 51.9302 1.74266
\(889\) −1.04635 −0.0350934
\(890\) −55.5199 −1.86103
\(891\) −5.24239 −0.175627
\(892\) 70.3544 2.35564
\(893\) 2.58637 0.0865497
\(894\) −22.3509 −0.747526
\(895\) −2.08001 −0.0695271
\(896\) 2.63563 0.0880502
\(897\) 8.01522 0.267620
\(898\) −48.8711 −1.63085
\(899\) 13.6789 0.456216
\(900\) −40.4945 −1.34982
\(901\) −11.9425 −0.397862
\(902\) −24.0443 −0.800588
\(903\) −0.983973 −0.0327446
\(904\) 66.6338 2.21621
\(905\) −5.36870 −0.178462
\(906\) 31.7902 1.05616
\(907\) −26.4798 −0.879248 −0.439624 0.898182i \(-0.644888\pi\)
−0.439624 + 0.898182i \(0.644888\pi\)
\(908\) 62.1091 2.06116
\(909\) 16.6857 0.553430
\(910\) −1.73094 −0.0573801
\(911\) 5.91977 0.196131 0.0980653 0.995180i \(-0.468735\pi\)
0.0980653 + 0.995180i \(0.468735\pi\)
\(912\) 33.8824 1.12196
\(913\) −7.25131 −0.239983
\(914\) −10.9688 −0.362817
\(915\) −6.99163 −0.231136
\(916\) −124.348 −4.10858
\(917\) 0.180196 0.00595059
\(918\) 10.5112 0.346922
\(919\) 56.6534 1.86882 0.934412 0.356193i \(-0.115926\pi\)
0.934412 + 0.356193i \(0.115926\pi\)
\(920\) 226.577 7.47003
\(921\) 2.74971 0.0906060
\(922\) 99.8338 3.28785
\(923\) −11.5670 −0.380731
\(924\) 0.611619 0.0201208
\(925\) −29.0208 −0.954200
\(926\) −55.4512 −1.82224
\(927\) −14.0716 −0.462173
\(928\) −35.1767 −1.15473
\(929\) 9.37200 0.307485 0.153743 0.988111i \(-0.450867\pi\)
0.153743 + 0.988111i \(0.450867\pi\)
\(930\) 30.0301 0.984726
\(931\) −29.6920 −0.973115
\(932\) 100.853 3.30356
\(933\) 0.634872 0.0207848
\(934\) −79.4337 −2.59915
\(935\) 3.03974 0.0994102
\(936\) 27.0206 0.883195
\(937\) −13.7354 −0.448717 −0.224359 0.974507i \(-0.572029\pi\)
−0.224359 + 0.974507i \(0.572029\pi\)
\(938\) −1.04917 −0.0342566
\(939\) 22.4099 0.731319
\(940\) −8.84198 −0.288394
\(941\) 30.1259 0.982076 0.491038 0.871138i \(-0.336618\pi\)
0.491038 + 0.871138i \(0.336618\pi\)
\(942\) 41.9810 1.36782
\(943\) −86.1137 −2.80425
\(944\) −125.873 −4.09680
\(945\) −1.88785 −0.0614118
\(946\) 21.9982 0.715222
\(947\) −4.66649 −0.151641 −0.0758203 0.997121i \(-0.524158\pi\)
−0.0758203 + 0.997121i \(0.524158\pi\)
\(948\) −32.3678 −1.05126
\(949\) 0.143482 0.00465763
\(950\) −35.1015 −1.13884
\(951\) 1.93020 0.0625909
\(952\) 1.60566 0.0520398
\(953\) −0.513040 −0.0166190 −0.00830950 0.999965i \(-0.502645\pi\)
−0.00830950 + 0.999965i \(0.502645\pi\)
\(954\) −76.3648 −2.47240
\(955\) −28.6590 −0.927384
\(956\) 107.897 3.48963
\(957\) −1.51736 −0.0490492
\(958\) 67.1502 2.16952
\(959\) 3.05012 0.0984935
\(960\) −32.0071 −1.03303
\(961\) 4.67040 0.150658
\(962\) 31.7649 1.02414
\(963\) −29.6190 −0.954459
\(964\) −95.6759 −3.08151
\(965\) 44.2461 1.42433
\(966\) 3.04560 0.0979907
\(967\) 36.9166 1.18716 0.593579 0.804775i \(-0.297714\pi\)
0.593579 + 0.804775i \(0.297714\pi\)
\(968\) −8.33576 −0.267921
\(969\) 3.01797 0.0969512
\(970\) 5.15031 0.165366
\(971\) −43.1485 −1.38470 −0.692351 0.721561i \(-0.743425\pi\)
−0.692351 + 0.721561i \(0.743425\pi\)
\(972\) 74.4199 2.38702
\(973\) 2.01308 0.0645365
\(974\) −1.36184 −0.0436363
\(975\) 2.58788 0.0828784
\(976\) 44.5387 1.42565
\(977\) −7.36946 −0.235770 −0.117885 0.993027i \(-0.537611\pi\)
−0.117885 + 0.993027i \(0.537611\pi\)
\(978\) −21.5315 −0.688500
\(979\) 7.31539 0.233801
\(980\) 101.507 3.24253
\(981\) 14.5812 0.465541
\(982\) 97.2621 3.10376
\(983\) −16.8952 −0.538872 −0.269436 0.963018i \(-0.586837\pi\)
−0.269436 + 0.963018i \(0.586837\pi\)
\(984\) 49.7519 1.58603
\(985\) −15.5097 −0.494180
\(986\) −6.53431 −0.208095
\(987\) −0.0724548 −0.00230626
\(988\) 27.6332 0.879129
\(989\) 78.7854 2.50523
\(990\) 19.4373 0.617757
\(991\) 4.35617 0.138378 0.0691891 0.997604i \(-0.477959\pi\)
0.0691891 + 0.997604i \(0.477959\pi\)
\(992\) −91.7304 −2.91244
\(993\) −14.8749 −0.472040
\(994\) −4.39519 −0.139407
\(995\) 64.6005 2.04797
\(996\) 24.6124 0.779872
\(997\) −35.8096 −1.13410 −0.567051 0.823683i \(-0.691916\pi\)
−0.567051 + 0.823683i \(0.691916\pi\)
\(998\) −113.926 −3.60626
\(999\) 34.6445 1.09610
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 1441.2.a.d.1.1 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.d.1.1 23 1.1 even 1 trivial