Properties

Label 6001.2.a.d.1.2
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.70572 q^{2} -1.68319 q^{3} +5.32093 q^{4} +1.67453 q^{5} +4.55424 q^{6} +1.84178 q^{7} -8.98553 q^{8} -0.166876 q^{9} +O(q^{10})\) \(q-2.70572 q^{2} -1.68319 q^{3} +5.32093 q^{4} +1.67453 q^{5} +4.55424 q^{6} +1.84178 q^{7} -8.98553 q^{8} -0.166876 q^{9} -4.53081 q^{10} +0.558914 q^{11} -8.95614 q^{12} -5.94381 q^{13} -4.98335 q^{14} -2.81855 q^{15} +13.6705 q^{16} +1.00000 q^{17} +0.451519 q^{18} +3.04694 q^{19} +8.91007 q^{20} -3.10007 q^{21} -1.51227 q^{22} -5.10489 q^{23} +15.1243 q^{24} -2.19595 q^{25} +16.0823 q^{26} +5.33045 q^{27} +9.80000 q^{28} +10.3641 q^{29} +7.62622 q^{30} -7.50364 q^{31} -19.0175 q^{32} -0.940757 q^{33} -2.70572 q^{34} +3.08412 q^{35} -0.887934 q^{36} +2.24859 q^{37} -8.24418 q^{38} +10.0046 q^{39} -15.0465 q^{40} -9.13228 q^{41} +8.38792 q^{42} -6.30731 q^{43} +2.97394 q^{44} -0.279438 q^{45} +13.8124 q^{46} -10.2645 q^{47} -23.0100 q^{48} -3.60784 q^{49} +5.94163 q^{50} -1.68319 q^{51} -31.6266 q^{52} -5.57774 q^{53} -14.4227 q^{54} +0.935918 q^{55} -16.5494 q^{56} -5.12858 q^{57} -28.0424 q^{58} +12.6599 q^{59} -14.9973 q^{60} +9.95044 q^{61} +20.3028 q^{62} -0.307348 q^{63} +24.1150 q^{64} -9.95309 q^{65} +2.54543 q^{66} +2.73060 q^{67} +5.32093 q^{68} +8.59249 q^{69} -8.34477 q^{70} -4.00977 q^{71} +1.49947 q^{72} -8.56730 q^{73} -6.08406 q^{74} +3.69620 q^{75} +16.2126 q^{76} +1.02940 q^{77} -27.0696 q^{78} +4.26844 q^{79} +22.8916 q^{80} -8.47153 q^{81} +24.7094 q^{82} +2.46846 q^{83} -16.4952 q^{84} +1.67453 q^{85} +17.0658 q^{86} -17.4447 q^{87} -5.02214 q^{88} +16.5008 q^{89} +0.756082 q^{90} -10.9472 q^{91} -27.1628 q^{92} +12.6300 q^{93} +27.7730 q^{94} +5.10220 q^{95} +32.0100 q^{96} -17.2729 q^{97} +9.76182 q^{98} -0.0932691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70572 −1.91323 −0.956617 0.291347i \(-0.905897\pi\)
−0.956617 + 0.291347i \(0.905897\pi\)
\(3\) −1.68319 −0.971789 −0.485895 0.874017i \(-0.661506\pi\)
−0.485895 + 0.874017i \(0.661506\pi\)
\(4\) 5.32093 2.66047
\(5\) 1.67453 0.748873 0.374436 0.927253i \(-0.377836\pi\)
0.374436 + 0.927253i \(0.377836\pi\)
\(6\) 4.55424 1.85926
\(7\) 1.84178 0.696128 0.348064 0.937471i \(-0.386839\pi\)
0.348064 + 0.937471i \(0.386839\pi\)
\(8\) −8.98553 −3.17686
\(9\) −0.166876 −0.0556252
\(10\) −4.53081 −1.43277
\(11\) 0.558914 0.168519 0.0842594 0.996444i \(-0.473148\pi\)
0.0842594 + 0.996444i \(0.473148\pi\)
\(12\) −8.95614 −2.58541
\(13\) −5.94381 −1.64852 −0.824258 0.566214i \(-0.808408\pi\)
−0.824258 + 0.566214i \(0.808408\pi\)
\(14\) −4.98335 −1.33186
\(15\) −2.81855 −0.727747
\(16\) 13.6705 3.41762
\(17\) 1.00000 0.242536
\(18\) 0.451519 0.106424
\(19\) 3.04694 0.699017 0.349508 0.936933i \(-0.386349\pi\)
0.349508 + 0.936933i \(0.386349\pi\)
\(20\) 8.91007 1.99235
\(21\) −3.10007 −0.676490
\(22\) −1.51227 −0.322416
\(23\) −5.10489 −1.06444 −0.532221 0.846605i \(-0.678643\pi\)
−0.532221 + 0.846605i \(0.678643\pi\)
\(24\) 15.1243 3.08724
\(25\) −2.19595 −0.439190
\(26\) 16.0823 3.15400
\(27\) 5.33045 1.02585
\(28\) 9.80000 1.85203
\(29\) 10.3641 1.92457 0.962283 0.272052i \(-0.0877022\pi\)
0.962283 + 0.272052i \(0.0877022\pi\)
\(30\) 7.62622 1.39235
\(31\) −7.50364 −1.34769 −0.673847 0.738871i \(-0.735359\pi\)
−0.673847 + 0.738871i \(0.735359\pi\)
\(32\) −19.0175 −3.36184
\(33\) −0.940757 −0.163765
\(34\) −2.70572 −0.464028
\(35\) 3.08412 0.521311
\(36\) −0.887934 −0.147989
\(37\) 2.24859 0.369666 0.184833 0.982770i \(-0.440826\pi\)
0.184833 + 0.982770i \(0.440826\pi\)
\(38\) −8.24418 −1.33738
\(39\) 10.0046 1.60201
\(40\) −15.0465 −2.37907
\(41\) −9.13228 −1.42622 −0.713111 0.701051i \(-0.752715\pi\)
−0.713111 + 0.701051i \(0.752715\pi\)
\(42\) 8.38792 1.29428
\(43\) −6.30731 −0.961856 −0.480928 0.876760i \(-0.659700\pi\)
−0.480928 + 0.876760i \(0.659700\pi\)
\(44\) 2.97394 0.448339
\(45\) −0.279438 −0.0416562
\(46\) 13.8124 2.03653
\(47\) −10.2645 −1.49724 −0.748618 0.663002i \(-0.769282\pi\)
−0.748618 + 0.663002i \(0.769282\pi\)
\(48\) −23.0100 −3.32121
\(49\) −3.60784 −0.515406
\(50\) 5.94163 0.840273
\(51\) −1.68319 −0.235694
\(52\) −31.6266 −4.38582
\(53\) −5.57774 −0.766162 −0.383081 0.923715i \(-0.625137\pi\)
−0.383081 + 0.923715i \(0.625137\pi\)
\(54\) −14.4227 −1.96268
\(55\) 0.935918 0.126199
\(56\) −16.5494 −2.21150
\(57\) −5.12858 −0.679297
\(58\) −28.0424 −3.68215
\(59\) 12.6599 1.64818 0.824089 0.566460i \(-0.191687\pi\)
0.824089 + 0.566460i \(0.191687\pi\)
\(60\) −14.9973 −1.93615
\(61\) 9.95044 1.27402 0.637012 0.770854i \(-0.280170\pi\)
0.637012 + 0.770854i \(0.280170\pi\)
\(62\) 20.3028 2.57845
\(63\) −0.307348 −0.0387223
\(64\) 24.1150 3.01438
\(65\) −9.95309 −1.23453
\(66\) 2.54543 0.313321
\(67\) 2.73060 0.333596 0.166798 0.985991i \(-0.446657\pi\)
0.166798 + 0.985991i \(0.446657\pi\)
\(68\) 5.32093 0.645258
\(69\) 8.59249 1.03441
\(70\) −8.34477 −0.997391
\(71\) −4.00977 −0.475872 −0.237936 0.971281i \(-0.576471\pi\)
−0.237936 + 0.971281i \(0.576471\pi\)
\(72\) 1.49947 0.176714
\(73\) −8.56730 −1.00273 −0.501363 0.865237i \(-0.667168\pi\)
−0.501363 + 0.865237i \(0.667168\pi\)
\(74\) −6.08406 −0.707257
\(75\) 3.69620 0.426800
\(76\) 16.2126 1.85971
\(77\) 1.02940 0.117311
\(78\) −27.0696 −3.06502
\(79\) 4.26844 0.480238 0.240119 0.970744i \(-0.422814\pi\)
0.240119 + 0.970744i \(0.422814\pi\)
\(80\) 22.8916 2.55936
\(81\) −8.47153 −0.941281
\(82\) 24.7094 2.72870
\(83\) 2.46846 0.270949 0.135474 0.990781i \(-0.456744\pi\)
0.135474 + 0.990781i \(0.456744\pi\)
\(84\) −16.4952 −1.79978
\(85\) 1.67453 0.181628
\(86\) 17.0658 1.84026
\(87\) −17.4447 −1.87027
\(88\) −5.02214 −0.535361
\(89\) 16.5008 1.74909 0.874543 0.484947i \(-0.161161\pi\)
0.874543 + 0.484947i \(0.161161\pi\)
\(90\) 0.756082 0.0796981
\(91\) −10.9472 −1.14758
\(92\) −27.1628 −2.83192
\(93\) 12.6300 1.30967
\(94\) 27.7730 2.86456
\(95\) 5.10220 0.523475
\(96\) 32.0100 3.26701
\(97\) −17.2729 −1.75379 −0.876896 0.480680i \(-0.840390\pi\)
−0.876896 + 0.480680i \(0.840390\pi\)
\(98\) 9.76182 0.986092
\(99\) −0.0932691 −0.00937389
\(100\) −11.6845 −1.16845
\(101\) 1.41292 0.140591 0.0702953 0.997526i \(-0.477606\pi\)
0.0702953 + 0.997526i \(0.477606\pi\)
\(102\) 4.55424 0.450937
\(103\) 9.36344 0.922607 0.461304 0.887242i \(-0.347382\pi\)
0.461304 + 0.887242i \(0.347382\pi\)
\(104\) 53.4083 5.23711
\(105\) −5.19115 −0.506605
\(106\) 15.0918 1.46585
\(107\) 15.3345 1.48244 0.741219 0.671264i \(-0.234248\pi\)
0.741219 + 0.671264i \(0.234248\pi\)
\(108\) 28.3630 2.72923
\(109\) 11.9365 1.14331 0.571655 0.820494i \(-0.306302\pi\)
0.571655 + 0.820494i \(0.306302\pi\)
\(110\) −2.53233 −0.241449
\(111\) −3.78480 −0.359237
\(112\) 25.1780 2.37910
\(113\) 18.9746 1.78498 0.892491 0.451066i \(-0.148956\pi\)
0.892491 + 0.451066i \(0.148956\pi\)
\(114\) 13.8765 1.29965
\(115\) −8.54829 −0.797132
\(116\) 55.1467 5.12024
\(117\) 0.991877 0.0916991
\(118\) −34.2542 −3.15335
\(119\) 1.84178 0.168836
\(120\) 25.3262 2.31195
\(121\) −10.6876 −0.971601
\(122\) −26.9231 −2.43751
\(123\) 15.3714 1.38599
\(124\) −39.9264 −3.58549
\(125\) −12.0498 −1.07777
\(126\) 0.831600 0.0740848
\(127\) −0.796633 −0.0706897 −0.0353449 0.999375i \(-0.511253\pi\)
−0.0353449 + 0.999375i \(0.511253\pi\)
\(128\) −27.2136 −2.40537
\(129\) 10.6164 0.934722
\(130\) 26.9303 2.36194
\(131\) −2.10806 −0.184182 −0.0920910 0.995751i \(-0.529355\pi\)
−0.0920910 + 0.995751i \(0.529355\pi\)
\(132\) −5.00571 −0.435691
\(133\) 5.61180 0.486605
\(134\) −7.38825 −0.638248
\(135\) 8.92600 0.768228
\(136\) −8.98553 −0.770503
\(137\) 0.742855 0.0634664 0.0317332 0.999496i \(-0.489897\pi\)
0.0317332 + 0.999496i \(0.489897\pi\)
\(138\) −23.2489 −1.97908
\(139\) −17.5100 −1.48518 −0.742591 0.669745i \(-0.766403\pi\)
−0.742591 + 0.669745i \(0.766403\pi\)
\(140\) 16.4104 1.38693
\(141\) 17.2771 1.45500
\(142\) 10.8493 0.910455
\(143\) −3.32208 −0.277806
\(144\) −2.28127 −0.190106
\(145\) 17.3550 1.44125
\(146\) 23.1807 1.91845
\(147\) 6.07268 0.500866
\(148\) 11.9646 0.983484
\(149\) 8.93805 0.732234 0.366117 0.930569i \(-0.380687\pi\)
0.366117 + 0.930569i \(0.380687\pi\)
\(150\) −10.0009 −0.816569
\(151\) −11.9902 −0.975745 −0.487873 0.872915i \(-0.662227\pi\)
−0.487873 + 0.872915i \(0.662227\pi\)
\(152\) −27.3784 −2.22068
\(153\) −0.166876 −0.0134911
\(154\) −2.78526 −0.224443
\(155\) −12.5651 −1.00925
\(156\) 53.2336 4.26210
\(157\) 22.5925 1.80308 0.901539 0.432698i \(-0.142438\pi\)
0.901539 + 0.432698i \(0.142438\pi\)
\(158\) −11.5492 −0.918807
\(159\) 9.38839 0.744548
\(160\) −31.8453 −2.51759
\(161\) −9.40209 −0.740988
\(162\) 22.9216 1.80089
\(163\) 8.50494 0.666158 0.333079 0.942899i \(-0.391912\pi\)
0.333079 + 0.942899i \(0.391912\pi\)
\(164\) −48.5923 −3.79442
\(165\) −1.57533 −0.122639
\(166\) −6.67897 −0.518388
\(167\) 9.31309 0.720668 0.360334 0.932823i \(-0.382663\pi\)
0.360334 + 0.932823i \(0.382663\pi\)
\(168\) 27.8557 2.14912
\(169\) 22.3289 1.71761
\(170\) −4.53081 −0.347498
\(171\) −0.508461 −0.0388830
\(172\) −33.5608 −2.55899
\(173\) −5.73546 −0.436059 −0.218030 0.975942i \(-0.569963\pi\)
−0.218030 + 0.975942i \(0.569963\pi\)
\(174\) 47.2006 3.57827
\(175\) −4.04446 −0.305732
\(176\) 7.64062 0.575933
\(177\) −21.3090 −1.60168
\(178\) −44.6467 −3.34641
\(179\) −3.87463 −0.289604 −0.144802 0.989461i \(-0.546254\pi\)
−0.144802 + 0.989461i \(0.546254\pi\)
\(180\) −1.48687 −0.110825
\(181\) 6.29550 0.467941 0.233970 0.972244i \(-0.424828\pi\)
0.233970 + 0.972244i \(0.424828\pi\)
\(182\) 29.6201 2.19559
\(183\) −16.7485 −1.23808
\(184\) 45.8701 3.38159
\(185\) 3.76533 0.276833
\(186\) −34.1734 −2.50571
\(187\) 0.558914 0.0408718
\(188\) −54.6169 −3.98335
\(189\) 9.81752 0.714120
\(190\) −13.8051 −1.00153
\(191\) −23.4761 −1.69867 −0.849334 0.527856i \(-0.822996\pi\)
−0.849334 + 0.527856i \(0.822996\pi\)
\(192\) −40.5901 −2.92934
\(193\) 17.3210 1.24679 0.623397 0.781905i \(-0.285752\pi\)
0.623397 + 0.781905i \(0.285752\pi\)
\(194\) 46.7355 3.35542
\(195\) 16.7529 1.19970
\(196\) −19.1971 −1.37122
\(197\) 8.87078 0.632017 0.316008 0.948756i \(-0.397657\pi\)
0.316008 + 0.948756i \(0.397657\pi\)
\(198\) 0.252360 0.0179345
\(199\) −4.83354 −0.342640 −0.171320 0.985215i \(-0.554803\pi\)
−0.171320 + 0.985215i \(0.554803\pi\)
\(200\) 19.7318 1.39525
\(201\) −4.59612 −0.324185
\(202\) −3.82296 −0.268983
\(203\) 19.0884 1.33974
\(204\) −8.95614 −0.627055
\(205\) −15.2923 −1.06806
\(206\) −25.3349 −1.76516
\(207\) 0.851882 0.0592099
\(208\) −81.2547 −5.63400
\(209\) 1.70298 0.117797
\(210\) 14.0458 0.969254
\(211\) −10.8548 −0.747274 −0.373637 0.927575i \(-0.621889\pi\)
−0.373637 + 0.927575i \(0.621889\pi\)
\(212\) −29.6788 −2.03835
\(213\) 6.74920 0.462447
\(214\) −41.4908 −2.83625
\(215\) −10.5618 −0.720308
\(216\) −47.8969 −3.25897
\(217\) −13.8201 −0.938167
\(218\) −32.2969 −2.18742
\(219\) 14.4204 0.974439
\(220\) 4.97996 0.335749
\(221\) −5.94381 −0.399824
\(222\) 10.2406 0.687305
\(223\) −2.67295 −0.178994 −0.0894969 0.995987i \(-0.528526\pi\)
−0.0894969 + 0.995987i \(0.528526\pi\)
\(224\) −35.0260 −2.34027
\(225\) 0.366450 0.0244300
\(226\) −51.3400 −3.41509
\(227\) 27.1408 1.80140 0.900698 0.434446i \(-0.143056\pi\)
0.900698 + 0.434446i \(0.143056\pi\)
\(228\) −27.2888 −1.80725
\(229\) −11.8184 −0.780985 −0.390492 0.920606i \(-0.627695\pi\)
−0.390492 + 0.920606i \(0.627695\pi\)
\(230\) 23.1293 1.52510
\(231\) −1.73267 −0.114001
\(232\) −93.1269 −6.11408
\(233\) 12.4933 0.818465 0.409232 0.912430i \(-0.365797\pi\)
0.409232 + 0.912430i \(0.365797\pi\)
\(234\) −2.68374 −0.175442
\(235\) −17.1883 −1.12124
\(236\) 67.3625 4.38493
\(237\) −7.18460 −0.466690
\(238\) −4.98335 −0.323023
\(239\) 25.5242 1.65102 0.825511 0.564385i \(-0.190887\pi\)
0.825511 + 0.564385i \(0.190887\pi\)
\(240\) −38.5309 −2.48716
\(241\) 9.73478 0.627072 0.313536 0.949576i \(-0.398486\pi\)
0.313536 + 0.949576i \(0.398486\pi\)
\(242\) 28.9177 1.85890
\(243\) −1.73217 −0.111119
\(244\) 52.9457 3.38950
\(245\) −6.04144 −0.385973
\(246\) −41.5906 −2.65172
\(247\) −18.1105 −1.15234
\(248\) 67.4242 4.28144
\(249\) −4.15488 −0.263305
\(250\) 32.6035 2.06203
\(251\) 26.7548 1.68875 0.844374 0.535754i \(-0.179973\pi\)
0.844374 + 0.535754i \(0.179973\pi\)
\(252\) −1.63538 −0.103019
\(253\) −2.85319 −0.179379
\(254\) 2.15547 0.135246
\(255\) −2.81855 −0.176504
\(256\) 25.4025 1.58766
\(257\) 12.0435 0.751251 0.375625 0.926772i \(-0.377428\pi\)
0.375625 + 0.926772i \(0.377428\pi\)
\(258\) −28.7250 −1.78834
\(259\) 4.14141 0.257335
\(260\) −52.9597 −3.28442
\(261\) −1.72952 −0.107054
\(262\) 5.70382 0.352383
\(263\) −11.4025 −0.703110 −0.351555 0.936167i \(-0.614347\pi\)
−0.351555 + 0.936167i \(0.614347\pi\)
\(264\) 8.45320 0.520259
\(265\) −9.34010 −0.573758
\(266\) −15.1840 −0.930990
\(267\) −27.7740 −1.69974
\(268\) 14.5294 0.887521
\(269\) −9.82240 −0.598882 −0.299441 0.954115i \(-0.596800\pi\)
−0.299441 + 0.954115i \(0.596800\pi\)
\(270\) −24.1513 −1.46980
\(271\) 16.4673 1.00032 0.500159 0.865934i \(-0.333275\pi\)
0.500159 + 0.865934i \(0.333275\pi\)
\(272\) 13.6705 0.828895
\(273\) 18.4262 1.11520
\(274\) −2.00996 −0.121426
\(275\) −1.22735 −0.0740117
\(276\) 45.7201 2.75203
\(277\) −23.1278 −1.38962 −0.694808 0.719196i \(-0.744510\pi\)
−0.694808 + 0.719196i \(0.744510\pi\)
\(278\) 47.3773 2.84150
\(279\) 1.25217 0.0749657
\(280\) −27.7124 −1.65613
\(281\) −10.0091 −0.597095 −0.298548 0.954395i \(-0.596502\pi\)
−0.298548 + 0.954395i \(0.596502\pi\)
\(282\) −46.7472 −2.78375
\(283\) −2.72899 −0.162222 −0.0811109 0.996705i \(-0.525847\pi\)
−0.0811109 + 0.996705i \(0.525847\pi\)
\(284\) −21.3357 −1.26604
\(285\) −8.58796 −0.508707
\(286\) 8.98862 0.531508
\(287\) −16.8197 −0.992833
\(288\) 3.17355 0.187003
\(289\) 1.00000 0.0588235
\(290\) −46.9578 −2.75746
\(291\) 29.0735 1.70432
\(292\) −45.5860 −2.66772
\(293\) 4.60430 0.268986 0.134493 0.990915i \(-0.457059\pi\)
0.134493 + 0.990915i \(0.457059\pi\)
\(294\) −16.4310 −0.958274
\(295\) 21.1994 1.23428
\(296\) −20.2048 −1.17438
\(297\) 2.97926 0.172874
\(298\) −24.1839 −1.40094
\(299\) 30.3425 1.75475
\(300\) 19.6672 1.13549
\(301\) −11.6167 −0.669575
\(302\) 32.4420 1.86683
\(303\) −2.37821 −0.136624
\(304\) 41.6532 2.38897
\(305\) 16.6623 0.954082
\(306\) 0.451519 0.0258116
\(307\) 12.7085 0.725314 0.362657 0.931923i \(-0.381870\pi\)
0.362657 + 0.931923i \(0.381870\pi\)
\(308\) 5.47735 0.312101
\(309\) −15.7604 −0.896580
\(310\) 33.9976 1.93093
\(311\) 23.0931 1.30949 0.654746 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(312\) −89.8962 −5.08937
\(313\) −14.7436 −0.833359 −0.416680 0.909053i \(-0.636806\pi\)
−0.416680 + 0.909053i \(0.636806\pi\)
\(314\) −61.1290 −3.44971
\(315\) −0.514664 −0.0289980
\(316\) 22.7121 1.27766
\(317\) −19.0331 −1.06900 −0.534502 0.845167i \(-0.679501\pi\)
−0.534502 + 0.845167i \(0.679501\pi\)
\(318\) −25.4024 −1.42449
\(319\) 5.79264 0.324325
\(320\) 40.3813 2.25739
\(321\) −25.8108 −1.44062
\(322\) 25.4394 1.41768
\(323\) 3.04694 0.169536
\(324\) −45.0764 −2.50425
\(325\) 13.0523 0.724011
\(326\) −23.0120 −1.27452
\(327\) −20.0914 −1.11106
\(328\) 82.0584 4.53092
\(329\) −18.9050 −1.04227
\(330\) 4.26240 0.234637
\(331\) 17.6338 0.969243 0.484621 0.874724i \(-0.338957\pi\)
0.484621 + 0.874724i \(0.338957\pi\)
\(332\) 13.1345 0.720850
\(333\) −0.375235 −0.0205627
\(334\) −25.1986 −1.37881
\(335\) 4.57247 0.249821
\(336\) −42.3794 −2.31198
\(337\) −18.9768 −1.03373 −0.516867 0.856065i \(-0.672902\pi\)
−0.516867 + 0.856065i \(0.672902\pi\)
\(338\) −60.4158 −3.28618
\(339\) −31.9379 −1.73463
\(340\) 8.91007 0.483216
\(341\) −4.19389 −0.227112
\(342\) 1.37575 0.0743922
\(343\) −19.5373 −1.05492
\(344\) 56.6745 3.05569
\(345\) 14.3884 0.774645
\(346\) 15.5186 0.834283
\(347\) −8.10286 −0.434984 −0.217492 0.976062i \(-0.569788\pi\)
−0.217492 + 0.976062i \(0.569788\pi\)
\(348\) −92.8223 −4.97580
\(349\) −17.5405 −0.938919 −0.469460 0.882954i \(-0.655551\pi\)
−0.469460 + 0.882954i \(0.655551\pi\)
\(350\) 10.9432 0.584938
\(351\) −31.6832 −1.69112
\(352\) −10.6291 −0.566534
\(353\) −1.00000 −0.0532246
\(354\) 57.6562 3.06440
\(355\) −6.71448 −0.356368
\(356\) 87.7999 4.65339
\(357\) −3.10007 −0.164073
\(358\) 10.4837 0.554080
\(359\) −15.1653 −0.800394 −0.400197 0.916429i \(-0.631058\pi\)
−0.400197 + 0.916429i \(0.631058\pi\)
\(360\) 2.51090 0.132336
\(361\) −9.71614 −0.511376
\(362\) −17.0339 −0.895280
\(363\) 17.9893 0.944192
\(364\) −58.2493 −3.05310
\(365\) −14.3462 −0.750914
\(366\) 45.3167 2.36874
\(367\) −13.4345 −0.701273 −0.350636 0.936512i \(-0.614035\pi\)
−0.350636 + 0.936512i \(0.614035\pi\)
\(368\) −69.7863 −3.63786
\(369\) 1.52395 0.0793339
\(370\) −10.1879 −0.529646
\(371\) −10.2730 −0.533347
\(372\) 67.2036 3.48435
\(373\) −21.9548 −1.13678 −0.568388 0.822761i \(-0.692433\pi\)
−0.568388 + 0.822761i \(0.692433\pi\)
\(374\) −1.51227 −0.0781974
\(375\) 20.2821 1.04737
\(376\) 92.2322 4.75651
\(377\) −61.6023 −3.17268
\(378\) −26.5635 −1.36628
\(379\) 16.1879 0.831519 0.415759 0.909475i \(-0.363516\pi\)
0.415759 + 0.909475i \(0.363516\pi\)
\(380\) 27.1485 1.39269
\(381\) 1.34088 0.0686955
\(382\) 63.5197 3.24995
\(383\) 14.6384 0.747990 0.373995 0.927431i \(-0.377988\pi\)
0.373995 + 0.927431i \(0.377988\pi\)
\(384\) 45.8057 2.33751
\(385\) 1.72376 0.0878508
\(386\) −46.8659 −2.38541
\(387\) 1.05254 0.0535034
\(388\) −91.9077 −4.66591
\(389\) 18.7351 0.949910 0.474955 0.880010i \(-0.342464\pi\)
0.474955 + 0.880010i \(0.342464\pi\)
\(390\) −45.3288 −2.29531
\(391\) −5.10489 −0.258165
\(392\) 32.4184 1.63737
\(393\) 3.54826 0.178986
\(394\) −24.0019 −1.20920
\(395\) 7.14764 0.359637
\(396\) −0.496279 −0.0249389
\(397\) 37.6712 1.89066 0.945332 0.326109i \(-0.105738\pi\)
0.945332 + 0.326109i \(0.105738\pi\)
\(398\) 13.0782 0.655551
\(399\) −9.44573 −0.472878
\(400\) −30.0197 −1.50098
\(401\) 9.06349 0.452609 0.226304 0.974057i \(-0.427336\pi\)
0.226304 + 0.974057i \(0.427336\pi\)
\(402\) 12.4358 0.620242
\(403\) 44.6002 2.22169
\(404\) 7.51805 0.374037
\(405\) −14.1858 −0.704899
\(406\) −51.6479 −2.56324
\(407\) 1.25677 0.0622956
\(408\) 15.1243 0.748766
\(409\) 9.74733 0.481975 0.240987 0.970528i \(-0.422529\pi\)
0.240987 + 0.970528i \(0.422529\pi\)
\(410\) 41.3767 2.04345
\(411\) −1.25037 −0.0616760
\(412\) 49.8223 2.45457
\(413\) 23.3168 1.14734
\(414\) −2.30496 −0.113282
\(415\) 4.13351 0.202906
\(416\) 113.036 5.54206
\(417\) 29.4727 1.44328
\(418\) −4.60779 −0.225374
\(419\) 10.4581 0.510911 0.255456 0.966821i \(-0.417775\pi\)
0.255456 + 0.966821i \(0.417775\pi\)
\(420\) −27.6218 −1.34781
\(421\) 31.5548 1.53789 0.768945 0.639315i \(-0.220782\pi\)
0.768945 + 0.639315i \(0.220782\pi\)
\(422\) 29.3700 1.42971
\(423\) 1.71290 0.0832840
\(424\) 50.1190 2.43399
\(425\) −2.19595 −0.106519
\(426\) −18.2615 −0.884770
\(427\) 18.3265 0.886884
\(428\) 81.5936 3.94398
\(429\) 5.59168 0.269969
\(430\) 28.5773 1.37812
\(431\) −21.2979 −1.02589 −0.512943 0.858423i \(-0.671445\pi\)
−0.512943 + 0.858423i \(0.671445\pi\)
\(432\) 72.8698 3.50595
\(433\) −26.5276 −1.27483 −0.637417 0.770519i \(-0.719997\pi\)
−0.637417 + 0.770519i \(0.719997\pi\)
\(434\) 37.3933 1.79493
\(435\) −29.2117 −1.40060
\(436\) 63.5134 3.04174
\(437\) −15.5543 −0.744063
\(438\) −39.0175 −1.86433
\(439\) 10.8375 0.517247 0.258624 0.965978i \(-0.416731\pi\)
0.258624 + 0.965978i \(0.416731\pi\)
\(440\) −8.40972 −0.400918
\(441\) 0.602061 0.0286696
\(442\) 16.0823 0.764957
\(443\) 21.5202 1.02246 0.511229 0.859445i \(-0.329191\pi\)
0.511229 + 0.859445i \(0.329191\pi\)
\(444\) −20.1387 −0.955739
\(445\) 27.6312 1.30984
\(446\) 7.23225 0.342457
\(447\) −15.0444 −0.711577
\(448\) 44.4146 2.09839
\(449\) −26.0648 −1.23007 −0.615036 0.788499i \(-0.710859\pi\)
−0.615036 + 0.788499i \(0.710859\pi\)
\(450\) −0.991513 −0.0467404
\(451\) −5.10416 −0.240345
\(452\) 100.963 4.74889
\(453\) 20.1817 0.948219
\(454\) −73.4354 −3.44649
\(455\) −18.3314 −0.859390
\(456\) 46.0830 2.15803
\(457\) −25.4756 −1.19170 −0.595848 0.803097i \(-0.703184\pi\)
−0.595848 + 0.803097i \(0.703184\pi\)
\(458\) 31.9774 1.49421
\(459\) 5.33045 0.248804
\(460\) −45.4849 −2.12074
\(461\) 26.0947 1.21535 0.607677 0.794184i \(-0.292102\pi\)
0.607677 + 0.794184i \(0.292102\pi\)
\(462\) 4.68812 0.218111
\(463\) −3.16113 −0.146910 −0.0734551 0.997299i \(-0.523403\pi\)
−0.0734551 + 0.997299i \(0.523403\pi\)
\(464\) 141.682 6.57743
\(465\) 21.1494 0.980779
\(466\) −33.8035 −1.56592
\(467\) −16.0676 −0.743518 −0.371759 0.928329i \(-0.621245\pi\)
−0.371759 + 0.928329i \(0.621245\pi\)
\(468\) 5.27771 0.243962
\(469\) 5.02917 0.232226
\(470\) 46.5067 2.14519
\(471\) −38.0274 −1.75221
\(472\) −113.756 −5.23604
\(473\) −3.52524 −0.162091
\(474\) 19.4395 0.892887
\(475\) −6.69093 −0.307001
\(476\) 9.80000 0.449182
\(477\) 0.930789 0.0426179
\(478\) −69.0614 −3.15879
\(479\) −14.3527 −0.655793 −0.327896 0.944714i \(-0.606340\pi\)
−0.327896 + 0.944714i \(0.606340\pi\)
\(480\) 53.6017 2.44657
\(481\) −13.3652 −0.609400
\(482\) −26.3396 −1.19974
\(483\) 15.8255 0.720085
\(484\) −56.8681 −2.58491
\(485\) −28.9239 −1.31337
\(486\) 4.68678 0.212596
\(487\) −15.7570 −0.714016 −0.357008 0.934101i \(-0.616203\pi\)
−0.357008 + 0.934101i \(0.616203\pi\)
\(488\) −89.4100 −4.04740
\(489\) −14.3154 −0.647365
\(490\) 16.3465 0.738458
\(491\) 23.5945 1.06481 0.532403 0.846491i \(-0.321289\pi\)
0.532403 + 0.846491i \(0.321289\pi\)
\(492\) 81.7900 3.68738
\(493\) 10.3641 0.466776
\(494\) 49.0019 2.20470
\(495\) −0.156182 −0.00701985
\(496\) −102.578 −4.60590
\(497\) −7.38512 −0.331268
\(498\) 11.2420 0.503764
\(499\) 18.8159 0.842317 0.421158 0.906987i \(-0.361624\pi\)
0.421158 + 0.906987i \(0.361624\pi\)
\(500\) −64.1164 −2.86737
\(501\) −15.6757 −0.700338
\(502\) −72.3911 −3.23097
\(503\) 8.56359 0.381832 0.190916 0.981606i \(-0.438854\pi\)
0.190916 + 0.981606i \(0.438854\pi\)
\(504\) 2.76169 0.123015
\(505\) 2.36597 0.105284
\(506\) 7.71995 0.343194
\(507\) −37.5837 −1.66915
\(508\) −4.23883 −0.188068
\(509\) 32.9734 1.46152 0.730761 0.682634i \(-0.239166\pi\)
0.730761 + 0.682634i \(0.239166\pi\)
\(510\) 7.62622 0.337695
\(511\) −15.7791 −0.698026
\(512\) −14.3049 −0.632193
\(513\) 16.2416 0.717083
\(514\) −32.5863 −1.43732
\(515\) 15.6794 0.690916
\(516\) 56.4892 2.48680
\(517\) −5.73699 −0.252312
\(518\) −11.2055 −0.492342
\(519\) 9.65387 0.423758
\(520\) 89.4338 3.92193
\(521\) −0.0432643 −0.00189545 −0.000947723 1.00000i \(-0.500302\pi\)
−0.000947723 1.00000i \(0.500302\pi\)
\(522\) 4.67959 0.204820
\(523\) 11.7577 0.514129 0.257065 0.966394i \(-0.417245\pi\)
0.257065 + 0.966394i \(0.417245\pi\)
\(524\) −11.2168 −0.490010
\(525\) 6.80759 0.297107
\(526\) 30.8521 1.34521
\(527\) −7.50364 −0.326864
\(528\) −12.8606 −0.559686
\(529\) 3.05989 0.133039
\(530\) 25.2717 1.09773
\(531\) −2.11263 −0.0916803
\(532\) 29.8600 1.29460
\(533\) 54.2805 2.35115
\(534\) 75.1489 3.25201
\(535\) 25.6780 1.11016
\(536\) −24.5359 −1.05979
\(537\) 6.52174 0.281434
\(538\) 26.5767 1.14580
\(539\) −2.01647 −0.0868556
\(540\) 47.4947 2.04384
\(541\) −36.9614 −1.58910 −0.794548 0.607202i \(-0.792292\pi\)
−0.794548 + 0.607202i \(0.792292\pi\)
\(542\) −44.5559 −1.91384
\(543\) −10.5965 −0.454740
\(544\) −19.0175 −0.815367
\(545\) 19.9880 0.856194
\(546\) −49.8562 −2.13365
\(547\) −7.10790 −0.303912 −0.151956 0.988387i \(-0.548557\pi\)
−0.151956 + 0.988387i \(0.548557\pi\)
\(548\) 3.95269 0.168850
\(549\) −1.66049 −0.0708678
\(550\) 3.32086 0.141602
\(551\) 31.5788 1.34530
\(552\) −77.2081 −3.28619
\(553\) 7.86154 0.334307
\(554\) 62.5774 2.65866
\(555\) −6.33776 −0.269023
\(556\) −93.1698 −3.95128
\(557\) 4.84879 0.205450 0.102725 0.994710i \(-0.467244\pi\)
0.102725 + 0.994710i \(0.467244\pi\)
\(558\) −3.38804 −0.143427
\(559\) 37.4895 1.58564
\(560\) 42.1614 1.78164
\(561\) −0.940757 −0.0397188
\(562\) 27.0820 1.14238
\(563\) 22.4760 0.947249 0.473624 0.880727i \(-0.342945\pi\)
0.473624 + 0.880727i \(0.342945\pi\)
\(564\) 91.9305 3.87097
\(565\) 31.7736 1.33672
\(566\) 7.38390 0.310369
\(567\) −15.6027 −0.655252
\(568\) 36.0299 1.51178
\(569\) 27.6309 1.15835 0.579174 0.815204i \(-0.303375\pi\)
0.579174 + 0.815204i \(0.303375\pi\)
\(570\) 23.2366 0.973276
\(571\) −18.4759 −0.773192 −0.386596 0.922249i \(-0.626349\pi\)
−0.386596 + 0.922249i \(0.626349\pi\)
\(572\) −17.6766 −0.739094
\(573\) 39.5146 1.65075
\(574\) 45.5093 1.89952
\(575\) 11.2101 0.467492
\(576\) −4.02421 −0.167675
\(577\) −12.5598 −0.522871 −0.261435 0.965221i \(-0.584196\pi\)
−0.261435 + 0.965221i \(0.584196\pi\)
\(578\) −2.70572 −0.112543
\(579\) −29.1546 −1.21162
\(580\) 92.3448 3.83441
\(581\) 4.54636 0.188615
\(582\) −78.6647 −3.26076
\(583\) −3.11748 −0.129113
\(584\) 76.9817 3.18552
\(585\) 1.66093 0.0686709
\(586\) −12.4579 −0.514633
\(587\) −22.3296 −0.921641 −0.460821 0.887493i \(-0.652445\pi\)
−0.460821 + 0.887493i \(0.652445\pi\)
\(588\) 32.3123 1.33254
\(589\) −22.8632 −0.942060
\(590\) −57.3597 −2.36146
\(591\) −14.9312 −0.614187
\(592\) 30.7393 1.26338
\(593\) 22.8713 0.939210 0.469605 0.882877i \(-0.344396\pi\)
0.469605 + 0.882877i \(0.344396\pi\)
\(594\) −8.06105 −0.330749
\(595\) 3.08412 0.126437
\(596\) 47.5588 1.94808
\(597\) 8.13575 0.332974
\(598\) −82.0984 −3.35725
\(599\) 39.9728 1.63324 0.816622 0.577173i \(-0.195844\pi\)
0.816622 + 0.577173i \(0.195844\pi\)
\(600\) −33.2123 −1.35589
\(601\) −24.4201 −0.996116 −0.498058 0.867144i \(-0.665953\pi\)
−0.498058 + 0.867144i \(0.665953\pi\)
\(602\) 31.4315 1.28105
\(603\) −0.455671 −0.0185563
\(604\) −63.7989 −2.59594
\(605\) −17.8967 −0.727606
\(606\) 6.43477 0.261395
\(607\) 43.2923 1.75718 0.878590 0.477578i \(-0.158485\pi\)
0.878590 + 0.477578i \(0.158485\pi\)
\(608\) −57.9451 −2.34999
\(609\) −32.1294 −1.30195
\(610\) −45.0836 −1.82538
\(611\) 61.0104 2.46822
\(612\) −0.887934 −0.0358926
\(613\) 42.8854 1.73212 0.866062 0.499937i \(-0.166643\pi\)
0.866062 + 0.499937i \(0.166643\pi\)
\(614\) −34.3857 −1.38770
\(615\) 25.7398 1.03793
\(616\) −9.24968 −0.372680
\(617\) −14.8844 −0.599224 −0.299612 0.954061i \(-0.596857\pi\)
−0.299612 + 0.954061i \(0.596857\pi\)
\(618\) 42.6434 1.71537
\(619\) 5.76151 0.231574 0.115787 0.993274i \(-0.463061\pi\)
0.115787 + 0.993274i \(0.463061\pi\)
\(620\) −66.8579 −2.68508
\(621\) −27.2114 −1.09195
\(622\) −62.4836 −2.50537
\(623\) 30.3910 1.21759
\(624\) 136.767 5.47506
\(625\) −9.19807 −0.367923
\(626\) 39.8922 1.59441
\(627\) −2.86643 −0.114474
\(628\) 120.213 4.79703
\(629\) 2.24859 0.0896571
\(630\) 1.39254 0.0554801
\(631\) 31.7660 1.26458 0.632292 0.774730i \(-0.282114\pi\)
0.632292 + 0.774730i \(0.282114\pi\)
\(632\) −38.3542 −1.52565
\(633\) 18.2706 0.726193
\(634\) 51.4982 2.04525
\(635\) −1.33399 −0.0529376
\(636\) 49.9550 1.98085
\(637\) 21.4443 0.849655
\(638\) −15.6733 −0.620511
\(639\) 0.669133 0.0264705
\(640\) −45.5701 −1.80132
\(641\) −14.8411 −0.586187 −0.293094 0.956084i \(-0.594685\pi\)
−0.293094 + 0.956084i \(0.594685\pi\)
\(642\) 69.8368 2.75624
\(643\) 12.8523 0.506846 0.253423 0.967356i \(-0.418444\pi\)
0.253423 + 0.967356i \(0.418444\pi\)
\(644\) −50.0279 −1.97138
\(645\) 17.7775 0.699988
\(646\) −8.24418 −0.324363
\(647\) 36.2423 1.42483 0.712416 0.701757i \(-0.247601\pi\)
0.712416 + 0.701757i \(0.247601\pi\)
\(648\) 76.1211 2.99032
\(649\) 7.07579 0.277749
\(650\) −35.3159 −1.38520
\(651\) 23.2618 0.911701
\(652\) 45.2542 1.77229
\(653\) −40.3711 −1.57984 −0.789922 0.613207i \(-0.789879\pi\)
−0.789922 + 0.613207i \(0.789879\pi\)
\(654\) 54.3617 2.12571
\(655\) −3.53001 −0.137929
\(656\) −124.843 −4.87429
\(657\) 1.42967 0.0557769
\(658\) 51.1517 1.99410
\(659\) −8.69629 −0.338760 −0.169380 0.985551i \(-0.554176\pi\)
−0.169380 + 0.985551i \(0.554176\pi\)
\(660\) −8.38221 −0.326277
\(661\) −27.1239 −1.05500 −0.527498 0.849556i \(-0.676870\pi\)
−0.527498 + 0.849556i \(0.676870\pi\)
\(662\) −47.7123 −1.85439
\(663\) 10.0046 0.388545
\(664\) −22.1804 −0.860767
\(665\) 9.39714 0.364405
\(666\) 1.01528 0.0393413
\(667\) −52.9076 −2.04859
\(668\) 49.5543 1.91731
\(669\) 4.49908 0.173944
\(670\) −12.3718 −0.477966
\(671\) 5.56144 0.214697
\(672\) 58.9554 2.27425
\(673\) −12.0292 −0.463691 −0.231846 0.972753i \(-0.574476\pi\)
−0.231846 + 0.972753i \(0.574476\pi\)
\(674\) 51.3461 1.97778
\(675\) −11.7054 −0.450541
\(676\) 118.811 4.56964
\(677\) 15.7253 0.604371 0.302186 0.953249i \(-0.402284\pi\)
0.302186 + 0.953249i \(0.402284\pi\)
\(678\) 86.4150 3.31875
\(679\) −31.8128 −1.22086
\(680\) −15.0465 −0.577008
\(681\) −45.6830 −1.75058
\(682\) 11.3475 0.434518
\(683\) −33.9234 −1.29804 −0.649021 0.760770i \(-0.724821\pi\)
−0.649021 + 0.760770i \(0.724821\pi\)
\(684\) −2.70549 −0.103447
\(685\) 1.24393 0.0475283
\(686\) 52.8626 2.01830
\(687\) 19.8927 0.758953
\(688\) −86.2240 −3.28726
\(689\) 33.1530 1.26303
\(690\) −38.9310 −1.48208
\(691\) 10.5284 0.400517 0.200259 0.979743i \(-0.435822\pi\)
0.200259 + 0.979743i \(0.435822\pi\)
\(692\) −30.5180 −1.16012
\(693\) −0.171781 −0.00652543
\(694\) 21.9241 0.832227
\(695\) −29.3211 −1.11221
\(696\) 156.750 5.94160
\(697\) −9.13228 −0.345910
\(698\) 47.4596 1.79637
\(699\) −21.0286 −0.795375
\(700\) −21.5203 −0.813391
\(701\) 8.19886 0.309667 0.154833 0.987941i \(-0.450516\pi\)
0.154833 + 0.987941i \(0.450516\pi\)
\(702\) 85.7259 3.23552
\(703\) 6.85132 0.258403
\(704\) 13.4782 0.507980
\(705\) 28.9311 1.08961
\(706\) 2.70572 0.101831
\(707\) 2.60229 0.0978691
\(708\) −113.384 −4.26122
\(709\) 50.7481 1.90589 0.952943 0.303149i \(-0.0980380\pi\)
0.952943 + 0.303149i \(0.0980380\pi\)
\(710\) 18.1675 0.681815
\(711\) −0.712299 −0.0267133
\(712\) −148.269 −5.55661
\(713\) 38.3052 1.43454
\(714\) 8.38792 0.313910
\(715\) −5.56292 −0.208041
\(716\) −20.6167 −0.770481
\(717\) −42.9620 −1.60445
\(718\) 41.0331 1.53134
\(719\) 6.22781 0.232258 0.116129 0.993234i \(-0.462951\pi\)
0.116129 + 0.993234i \(0.462951\pi\)
\(720\) −3.82005 −0.142365
\(721\) 17.2454 0.642253
\(722\) 26.2892 0.978382
\(723\) −16.3855 −0.609382
\(724\) 33.4979 1.24494
\(725\) −22.7590 −0.845249
\(726\) −48.6740 −1.80646
\(727\) −28.4762 −1.05612 −0.528061 0.849206i \(-0.677081\pi\)
−0.528061 + 0.849206i \(0.677081\pi\)
\(728\) 98.3664 3.64570
\(729\) 28.3301 1.04926
\(730\) 38.8168 1.43668
\(731\) −6.30731 −0.233284
\(732\) −89.1175 −3.29388
\(733\) −34.4929 −1.27402 −0.637012 0.770854i \(-0.719830\pi\)
−0.637012 + 0.770854i \(0.719830\pi\)
\(734\) 36.3499 1.34170
\(735\) 10.1689 0.375085
\(736\) 97.0820 3.57849
\(737\) 1.52617 0.0562172
\(738\) −4.12340 −0.151784
\(739\) 37.6871 1.38634 0.693171 0.720773i \(-0.256213\pi\)
0.693171 + 0.720773i \(0.256213\pi\)
\(740\) 20.0351 0.736504
\(741\) 30.4833 1.11983
\(742\) 27.7958 1.02042
\(743\) 35.4670 1.30116 0.650578 0.759439i \(-0.274527\pi\)
0.650578 + 0.759439i \(0.274527\pi\)
\(744\) −113.488 −4.16066
\(745\) 14.9670 0.548350
\(746\) 59.4035 2.17492
\(747\) −0.411926 −0.0150716
\(748\) 2.97394 0.108738
\(749\) 28.2427 1.03197
\(750\) −54.8779 −2.00386
\(751\) 12.7504 0.465268 0.232634 0.972564i \(-0.425266\pi\)
0.232634 + 0.972564i \(0.425266\pi\)
\(752\) −140.321 −5.11698
\(753\) −45.0334 −1.64111
\(754\) 166.679 6.07008
\(755\) −20.0779 −0.730709
\(756\) 52.2384 1.89989
\(757\) 44.1110 1.60324 0.801621 0.597833i \(-0.203971\pi\)
0.801621 + 0.597833i \(0.203971\pi\)
\(758\) −43.8001 −1.59089
\(759\) 4.80246 0.174318
\(760\) −45.8460 −1.66301
\(761\) −39.8097 −1.44310 −0.721551 0.692361i \(-0.756570\pi\)
−0.721551 + 0.692361i \(0.756570\pi\)
\(762\) −3.62806 −0.131431
\(763\) 21.9844 0.795890
\(764\) −124.915 −4.51925
\(765\) −0.279438 −0.0101031
\(766\) −39.6076 −1.43108
\(767\) −75.2481 −2.71705
\(768\) −42.7573 −1.54287
\(769\) −37.3323 −1.34624 −0.673118 0.739535i \(-0.735045\pi\)
−0.673118 + 0.739535i \(0.735045\pi\)
\(770\) −4.66401 −0.168079
\(771\) −20.2714 −0.730057
\(772\) 92.1641 3.31706
\(773\) −24.3803 −0.876898 −0.438449 0.898756i \(-0.644472\pi\)
−0.438449 + 0.898756i \(0.644472\pi\)
\(774\) −2.84787 −0.102365
\(775\) 16.4776 0.591893
\(776\) 155.206 5.57156
\(777\) −6.97077 −0.250075
\(778\) −50.6921 −1.81740
\(779\) −27.8255 −0.996953
\(780\) 89.1413 3.19177
\(781\) −2.24111 −0.0801934
\(782\) 13.8124 0.493931
\(783\) 55.2453 1.97431
\(784\) −49.3209 −1.76146
\(785\) 37.8318 1.35028
\(786\) −9.60061 −0.342442
\(787\) −23.1559 −0.825419 −0.412709 0.910863i \(-0.635418\pi\)
−0.412709 + 0.910863i \(0.635418\pi\)
\(788\) 47.2008 1.68146
\(789\) 19.1926 0.683274
\(790\) −19.3395 −0.688070
\(791\) 34.9471 1.24258
\(792\) 0.838072 0.0297796
\(793\) −59.1436 −2.10025
\(794\) −101.928 −3.61728
\(795\) 15.7211 0.557572
\(796\) −25.7189 −0.911583
\(797\) 24.0008 0.850152 0.425076 0.905158i \(-0.360247\pi\)
0.425076 + 0.905158i \(0.360247\pi\)
\(798\) 25.5575 0.904726
\(799\) −10.2645 −0.363133
\(800\) 41.7614 1.47649
\(801\) −2.75359 −0.0972933
\(802\) −24.5233 −0.865947
\(803\) −4.78838 −0.168978
\(804\) −24.4556 −0.862484
\(805\) −15.7441 −0.554906
\(806\) −120.676 −4.25062
\(807\) 16.5329 0.581987
\(808\) −12.6958 −0.446637
\(809\) 36.7987 1.29378 0.646888 0.762585i \(-0.276070\pi\)
0.646888 + 0.762585i \(0.276070\pi\)
\(810\) 38.3829 1.34864
\(811\) 16.5578 0.581424 0.290712 0.956811i \(-0.406108\pi\)
0.290712 + 0.956811i \(0.406108\pi\)
\(812\) 101.568 3.56434
\(813\) −27.7176 −0.972098
\(814\) −3.40046 −0.119186
\(815\) 14.2418 0.498868
\(816\) −23.0100 −0.805511
\(817\) −19.2180 −0.672354
\(818\) −26.3736 −0.922131
\(819\) 1.82682 0.0638343
\(820\) −81.3692 −2.84154
\(821\) −29.4765 −1.02874 −0.514369 0.857569i \(-0.671974\pi\)
−0.514369 + 0.857569i \(0.671974\pi\)
\(822\) 3.38314 0.118001
\(823\) −1.35939 −0.0473853 −0.0236927 0.999719i \(-0.507542\pi\)
−0.0236927 + 0.999719i \(0.507542\pi\)
\(824\) −84.1355 −2.93100
\(825\) 2.06585 0.0719238
\(826\) −63.0887 −2.19514
\(827\) −36.8778 −1.28237 −0.641184 0.767388i \(-0.721556\pi\)
−0.641184 + 0.767388i \(0.721556\pi\)
\(828\) 4.53281 0.157526
\(829\) −6.54448 −0.227299 −0.113650 0.993521i \(-0.536254\pi\)
−0.113650 + 0.993521i \(0.536254\pi\)
\(830\) −11.1841 −0.388207
\(831\) 38.9285 1.35041
\(832\) −143.335 −4.96925
\(833\) −3.60784 −0.125004
\(834\) −79.7450 −2.76134
\(835\) 15.5950 0.539689
\(836\) 9.06144 0.313396
\(837\) −39.9978 −1.38253
\(838\) −28.2967 −0.977493
\(839\) 15.1254 0.522186 0.261093 0.965314i \(-0.415917\pi\)
0.261093 + 0.965314i \(0.415917\pi\)
\(840\) 46.6453 1.60941
\(841\) 78.4146 2.70395
\(842\) −85.3787 −2.94234
\(843\) 16.8473 0.580251
\(844\) −57.7576 −1.98810
\(845\) 37.3904 1.28627
\(846\) −4.63463 −0.159342
\(847\) −19.6843 −0.676359
\(848\) −76.2504 −2.61845
\(849\) 4.59341 0.157645
\(850\) 5.94163 0.203796
\(851\) −11.4788 −0.393488
\(852\) 35.9120 1.23033
\(853\) 29.0715 0.995388 0.497694 0.867353i \(-0.334180\pi\)
0.497694 + 0.867353i \(0.334180\pi\)
\(854\) −49.5865 −1.69682
\(855\) −0.851433 −0.0291184
\(856\) −137.788 −4.70950
\(857\) −3.36402 −0.114913 −0.0574564 0.998348i \(-0.518299\pi\)
−0.0574564 + 0.998348i \(0.518299\pi\)
\(858\) −15.1295 −0.516514
\(859\) 47.7323 1.62861 0.814303 0.580440i \(-0.197119\pi\)
0.814303 + 0.580440i \(0.197119\pi\)
\(860\) −56.1986 −1.91636
\(861\) 28.3107 0.964825
\(862\) 57.6263 1.96276
\(863\) −33.4504 −1.13867 −0.569333 0.822107i \(-0.692798\pi\)
−0.569333 + 0.822107i \(0.692798\pi\)
\(864\) −101.372 −3.44873
\(865\) −9.60420 −0.326553
\(866\) 71.7762 2.43906
\(867\) −1.68319 −0.0571641
\(868\) −73.5357 −2.49596
\(869\) 2.38569 0.0809291
\(870\) 79.0389 2.67967
\(871\) −16.2302 −0.549939
\(872\) −107.256 −3.63214
\(873\) 2.88242 0.0975551
\(874\) 42.0856 1.42357
\(875\) −22.1932 −0.750266
\(876\) 76.7299 2.59246
\(877\) 29.8093 1.00659 0.503294 0.864115i \(-0.332121\pi\)
0.503294 + 0.864115i \(0.332121\pi\)
\(878\) −29.3234 −0.989616
\(879\) −7.74990 −0.261398
\(880\) 12.7944 0.431301
\(881\) 33.6299 1.13302 0.566510 0.824055i \(-0.308293\pi\)
0.566510 + 0.824055i \(0.308293\pi\)
\(882\) −1.62901 −0.0548516
\(883\) 44.1460 1.48563 0.742815 0.669497i \(-0.233490\pi\)
0.742815 + 0.669497i \(0.233490\pi\)
\(884\) −31.6266 −1.06372
\(885\) −35.6826 −1.19946
\(886\) −58.2278 −1.95620
\(887\) 20.6446 0.693179 0.346590 0.938017i \(-0.387340\pi\)
0.346590 + 0.938017i \(0.387340\pi\)
\(888\) 34.0084 1.14125
\(889\) −1.46722 −0.0492091
\(890\) −74.7623 −2.50604
\(891\) −4.73485 −0.158624
\(892\) −14.2226 −0.476207
\(893\) −31.2754 −1.04659
\(894\) 40.7061 1.36141
\(895\) −6.48819 −0.216876
\(896\) −50.1216 −1.67445
\(897\) −51.0721 −1.70525
\(898\) 70.5241 2.35342
\(899\) −77.7685 −2.59372
\(900\) 1.94986 0.0649953
\(901\) −5.57774 −0.185822
\(902\) 13.8104 0.459837
\(903\) 19.5531 0.650686
\(904\) −170.497 −5.67064
\(905\) 10.5420 0.350428
\(906\) −54.6061 −1.81417
\(907\) −7.98490 −0.265134 −0.132567 0.991174i \(-0.542322\pi\)
−0.132567 + 0.991174i \(0.542322\pi\)
\(908\) 144.414 4.79256
\(909\) −0.235782 −0.00782038
\(910\) 49.5997 1.64422
\(911\) 41.3573 1.37023 0.685114 0.728436i \(-0.259752\pi\)
0.685114 + 0.728436i \(0.259752\pi\)
\(912\) −70.1102 −2.32158
\(913\) 1.37966 0.0456599
\(914\) 68.9298 2.27999
\(915\) −28.0458 −0.927166
\(916\) −62.8852 −2.07778
\(917\) −3.88258 −0.128214
\(918\) −14.4227 −0.476021
\(919\) 0.0114048 0.000376210 0 0.000188105 1.00000i \(-0.499940\pi\)
0.000188105 1.00000i \(0.499940\pi\)
\(920\) 76.8109 2.53238
\(921\) −21.3908 −0.704852
\(922\) −70.6051 −2.32526
\(923\) 23.8333 0.784483
\(924\) −9.21942 −0.303297
\(925\) −4.93779 −0.162353
\(926\) 8.55314 0.281074
\(927\) −1.56253 −0.0513202
\(928\) −197.099 −6.47009
\(929\) 15.7644 0.517214 0.258607 0.965983i \(-0.416737\pi\)
0.258607 + 0.965983i \(0.416737\pi\)
\(930\) −57.2244 −1.87646
\(931\) −10.9929 −0.360277
\(932\) 66.4761 2.17750
\(933\) −38.8701 −1.27255
\(934\) 43.4744 1.42253
\(935\) 0.935918 0.0306078
\(936\) −8.91254 −0.291315
\(937\) 0.560104 0.0182978 0.00914890 0.999958i \(-0.497088\pi\)
0.00914890 + 0.999958i \(0.497088\pi\)
\(938\) −13.6075 −0.444302
\(939\) 24.8163 0.809850
\(940\) −91.4576 −2.98302
\(941\) −23.4047 −0.762971 −0.381485 0.924375i \(-0.624587\pi\)
−0.381485 + 0.924375i \(0.624587\pi\)
\(942\) 102.892 3.35239
\(943\) 46.6193 1.51813
\(944\) 173.067 5.63285
\(945\) 16.4397 0.534785
\(946\) 9.53833 0.310118
\(947\) −15.3214 −0.497879 −0.248939 0.968519i \(-0.580082\pi\)
−0.248939 + 0.968519i \(0.580082\pi\)
\(948\) −38.2288 −1.24161
\(949\) 50.9224 1.65301
\(950\) 18.1038 0.587365
\(951\) 32.0362 1.03885
\(952\) −16.5494 −0.536369
\(953\) −5.92208 −0.191835 −0.0959176 0.995389i \(-0.530579\pi\)
−0.0959176 + 0.995389i \(0.530579\pi\)
\(954\) −2.51846 −0.0815381
\(955\) −39.3114 −1.27209
\(956\) 135.813 4.39249
\(957\) −9.75010 −0.315176
\(958\) 38.8345 1.25469
\(959\) 1.36818 0.0441807
\(960\) −67.9694 −2.19370
\(961\) 25.3046 0.816277
\(962\) 36.1625 1.16593
\(963\) −2.55895 −0.0824609
\(964\) 51.7981 1.66831
\(965\) 29.0046 0.933691
\(966\) −42.8194 −1.37769
\(967\) 54.3939 1.74919 0.874594 0.484856i \(-0.161128\pi\)
0.874594 + 0.484856i \(0.161128\pi\)
\(968\) 96.0339 3.08665
\(969\) −5.12858 −0.164754
\(970\) 78.2601 2.51278
\(971\) 32.7652 1.05149 0.525743 0.850644i \(-0.323787\pi\)
0.525743 + 0.850644i \(0.323787\pi\)
\(972\) −9.21677 −0.295628
\(973\) −32.2497 −1.03388
\(974\) 42.6339 1.36608
\(975\) −21.9695 −0.703587
\(976\) 136.027 4.35413
\(977\) −19.2018 −0.614321 −0.307161 0.951658i \(-0.599379\pi\)
−0.307161 + 0.951658i \(0.599379\pi\)
\(978\) 38.7335 1.23856
\(979\) 9.22255 0.294754
\(980\) −32.1461 −1.02687
\(981\) −1.99191 −0.0635969
\(982\) −63.8403 −2.03722
\(983\) 3.24512 0.103503 0.0517517 0.998660i \(-0.483520\pi\)
0.0517517 + 0.998660i \(0.483520\pi\)
\(984\) −138.120 −4.40310
\(985\) 14.8544 0.473300
\(986\) −28.0424 −0.893051
\(987\) 31.8207 1.01286
\(988\) −96.3645 −3.06576
\(989\) 32.1981 1.02384
\(990\) 0.422585 0.0134306
\(991\) 20.0378 0.636521 0.318261 0.948003i \(-0.396901\pi\)
0.318261 + 0.948003i \(0.396901\pi\)
\(992\) 142.700 4.53074
\(993\) −29.6811 −0.941900
\(994\) 19.9821 0.633793
\(995\) −8.09390 −0.256594
\(996\) −22.1079 −0.700514
\(997\) 56.6327 1.79358 0.896788 0.442461i \(-0.145895\pi\)
0.896788 + 0.442461i \(0.145895\pi\)
\(998\) −50.9107 −1.61155
\(999\) 11.9860 0.379220
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 6001.2.a.d.1.2 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.2 121 1.1 even 1 trivial