Properties

Label 6001.2.a.d.1.11
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 1.11
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43959 q^{2} +2.16595 q^{3} +3.95162 q^{4} -1.55175 q^{5} -5.28403 q^{6} -2.38051 q^{7} -4.76117 q^{8} +1.69132 q^{9} +O(q^{10})\) \(q-2.43959 q^{2} +2.16595 q^{3} +3.95162 q^{4} -1.55175 q^{5} -5.28403 q^{6} -2.38051 q^{7} -4.76117 q^{8} +1.69132 q^{9} +3.78564 q^{10} -0.331488 q^{11} +8.55900 q^{12} +2.10394 q^{13} +5.80748 q^{14} -3.36101 q^{15} +3.71207 q^{16} +1.00000 q^{17} -4.12615 q^{18} +5.24243 q^{19} -6.13193 q^{20} -5.15606 q^{21} +0.808697 q^{22} -4.52995 q^{23} -10.3124 q^{24} -2.59207 q^{25} -5.13276 q^{26} -2.83452 q^{27} -9.40687 q^{28} +2.32694 q^{29} +8.19949 q^{30} -6.94962 q^{31} +0.466385 q^{32} -0.717986 q^{33} -2.43959 q^{34} +3.69395 q^{35} +6.68347 q^{36} -1.77681 q^{37} -12.7894 q^{38} +4.55702 q^{39} +7.38813 q^{40} +10.3883 q^{41} +12.5787 q^{42} -5.51062 q^{43} -1.30992 q^{44} -2.62451 q^{45} +11.0512 q^{46} -10.5314 q^{47} +8.04015 q^{48} -1.33317 q^{49} +6.32361 q^{50} +2.16595 q^{51} +8.31398 q^{52} +12.7771 q^{53} +6.91508 q^{54} +0.514387 q^{55} +11.3340 q^{56} +11.3548 q^{57} -5.67680 q^{58} +7.29560 q^{59} -13.2814 q^{60} +4.86741 q^{61} +16.9542 q^{62} -4.02621 q^{63} -8.56193 q^{64} -3.26479 q^{65} +1.75160 q^{66} -7.11782 q^{67} +3.95162 q^{68} -9.81163 q^{69} -9.01175 q^{70} +12.7376 q^{71} -8.05267 q^{72} +1.53418 q^{73} +4.33471 q^{74} -5.61430 q^{75} +20.7161 q^{76} +0.789112 q^{77} -11.1173 q^{78} +13.5494 q^{79} -5.76020 q^{80} -11.2134 q^{81} -25.3433 q^{82} +5.47710 q^{83} -20.3748 q^{84} -1.55175 q^{85} +13.4437 q^{86} +5.04003 q^{87} +1.57827 q^{88} +10.2065 q^{89} +6.40274 q^{90} -5.00845 q^{91} -17.9007 q^{92} -15.0525 q^{93} +25.6923 q^{94} -8.13494 q^{95} +1.01016 q^{96} -14.7667 q^{97} +3.25240 q^{98} -0.560654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43959 −1.72505 −0.862527 0.506011i \(-0.831119\pi\)
−0.862527 + 0.506011i \(0.831119\pi\)
\(3\) 2.16595 1.25051 0.625255 0.780421i \(-0.284995\pi\)
0.625255 + 0.780421i \(0.284995\pi\)
\(4\) 3.95162 1.97581
\(5\) −1.55175 −0.693963 −0.346982 0.937872i \(-0.612793\pi\)
−0.346982 + 0.937872i \(0.612793\pi\)
\(6\) −5.28403 −2.15720
\(7\) −2.38051 −0.899748 −0.449874 0.893092i \(-0.648531\pi\)
−0.449874 + 0.893092i \(0.648531\pi\)
\(8\) −4.76117 −1.68333
\(9\) 1.69132 0.563775
\(10\) 3.78564 1.19712
\(11\) −0.331488 −0.0999475 −0.0499738 0.998751i \(-0.515914\pi\)
−0.0499738 + 0.998751i \(0.515914\pi\)
\(12\) 8.55900 2.47077
\(13\) 2.10394 0.583528 0.291764 0.956490i \(-0.405758\pi\)
0.291764 + 0.956490i \(0.405758\pi\)
\(14\) 5.80748 1.55211
\(15\) −3.36101 −0.867808
\(16\) 3.71207 0.928018
\(17\) 1.00000 0.242536
\(18\) −4.12615 −0.972542
\(19\) 5.24243 1.20270 0.601348 0.798987i \(-0.294630\pi\)
0.601348 + 0.798987i \(0.294630\pi\)
\(20\) −6.13193 −1.37114
\(21\) −5.15606 −1.12514
\(22\) 0.808697 0.172415
\(23\) −4.52995 −0.944560 −0.472280 0.881449i \(-0.656569\pi\)
−0.472280 + 0.881449i \(0.656569\pi\)
\(24\) −10.3124 −2.10502
\(25\) −2.59207 −0.518415
\(26\) −5.13276 −1.00662
\(27\) −2.83452 −0.545504
\(28\) −9.40687 −1.77773
\(29\) 2.32694 0.432102 0.216051 0.976382i \(-0.430682\pi\)
0.216051 + 0.976382i \(0.430682\pi\)
\(30\) 8.19949 1.49702
\(31\) −6.94962 −1.24819 −0.624094 0.781349i \(-0.714532\pi\)
−0.624094 + 0.781349i \(0.714532\pi\)
\(32\) 0.466385 0.0824460
\(33\) −0.717986 −0.124985
\(34\) −2.43959 −0.418387
\(35\) 3.69395 0.624392
\(36\) 6.68347 1.11391
\(37\) −1.77681 −0.292107 −0.146053 0.989277i \(-0.546657\pi\)
−0.146053 + 0.989277i \(0.546657\pi\)
\(38\) −12.7894 −2.07472
\(39\) 4.55702 0.729708
\(40\) 7.38813 1.16817
\(41\) 10.3883 1.62238 0.811191 0.584781i \(-0.198820\pi\)
0.811191 + 0.584781i \(0.198820\pi\)
\(42\) 12.5787 1.94093
\(43\) −5.51062 −0.840362 −0.420181 0.907440i \(-0.638033\pi\)
−0.420181 + 0.907440i \(0.638033\pi\)
\(44\) −1.30992 −0.197477
\(45\) −2.62451 −0.391239
\(46\) 11.0512 1.62942
\(47\) −10.5314 −1.53616 −0.768079 0.640355i \(-0.778787\pi\)
−0.768079 + 0.640355i \(0.778787\pi\)
\(48\) 8.04015 1.16049
\(49\) −1.33317 −0.190453
\(50\) 6.32361 0.894294
\(51\) 2.16595 0.303293
\(52\) 8.31398 1.15294
\(53\) 12.7771 1.75506 0.877532 0.479519i \(-0.159189\pi\)
0.877532 + 0.479519i \(0.159189\pi\)
\(54\) 6.91508 0.941024
\(55\) 0.514387 0.0693599
\(56\) 11.3340 1.51457
\(57\) 11.3548 1.50398
\(58\) −5.67680 −0.745400
\(59\) 7.29560 0.949806 0.474903 0.880038i \(-0.342483\pi\)
0.474903 + 0.880038i \(0.342483\pi\)
\(60\) −13.2814 −1.71462
\(61\) 4.86741 0.623209 0.311604 0.950212i \(-0.399134\pi\)
0.311604 + 0.950212i \(0.399134\pi\)
\(62\) 16.9542 2.15319
\(63\) −4.02621 −0.507255
\(64\) −8.56193 −1.07024
\(65\) −3.26479 −0.404947
\(66\) 1.75160 0.215606
\(67\) −7.11782 −0.869580 −0.434790 0.900532i \(-0.643177\pi\)
−0.434790 + 0.900532i \(0.643177\pi\)
\(68\) 3.95162 0.479205
\(69\) −9.81163 −1.18118
\(70\) −9.01175 −1.07711
\(71\) 12.7376 1.51168 0.755839 0.654758i \(-0.227229\pi\)
0.755839 + 0.654758i \(0.227229\pi\)
\(72\) −8.05267 −0.949017
\(73\) 1.53418 0.179562 0.0897811 0.995962i \(-0.471383\pi\)
0.0897811 + 0.995962i \(0.471383\pi\)
\(74\) 4.33471 0.503899
\(75\) −5.61430 −0.648283
\(76\) 20.7161 2.37630
\(77\) 0.789112 0.0899276
\(78\) −11.1173 −1.25879
\(79\) 13.5494 1.52443 0.762213 0.647326i \(-0.224113\pi\)
0.762213 + 0.647326i \(0.224113\pi\)
\(80\) −5.76020 −0.644010
\(81\) −11.2134 −1.24593
\(82\) −25.3433 −2.79870
\(83\) 5.47710 0.601190 0.300595 0.953752i \(-0.402815\pi\)
0.300595 + 0.953752i \(0.402815\pi\)
\(84\) −20.3748 −2.22307
\(85\) −1.55175 −0.168311
\(86\) 13.4437 1.44967
\(87\) 5.04003 0.540348
\(88\) 1.57827 0.168244
\(89\) 10.2065 1.08189 0.540946 0.841057i \(-0.318066\pi\)
0.540946 + 0.841057i \(0.318066\pi\)
\(90\) 6.40274 0.674908
\(91\) −5.00845 −0.525029
\(92\) −17.9007 −1.86627
\(93\) −15.0525 −1.56087
\(94\) 25.6923 2.64995
\(95\) −8.13494 −0.834628
\(96\) 1.01016 0.103100
\(97\) −14.7667 −1.49933 −0.749667 0.661816i \(-0.769786\pi\)
−0.749667 + 0.661816i \(0.769786\pi\)
\(98\) 3.25240 0.328542
\(99\) −0.560654 −0.0563479
\(100\) −10.2429 −1.02429
\(101\) −16.6313 −1.65488 −0.827438 0.561558i \(-0.810202\pi\)
−0.827438 + 0.561558i \(0.810202\pi\)
\(102\) −5.28403 −0.523197
\(103\) 11.2320 1.10672 0.553362 0.832941i \(-0.313345\pi\)
0.553362 + 0.832941i \(0.313345\pi\)
\(104\) −10.0172 −0.982269
\(105\) 8.00091 0.780809
\(106\) −31.1708 −3.02758
\(107\) 2.82459 0.273063 0.136532 0.990636i \(-0.456405\pi\)
0.136532 + 0.990636i \(0.456405\pi\)
\(108\) −11.2010 −1.07781
\(109\) 5.72740 0.548586 0.274293 0.961646i \(-0.411556\pi\)
0.274293 + 0.961646i \(0.411556\pi\)
\(110\) −1.25490 −0.119650
\(111\) −3.84849 −0.365282
\(112\) −8.83662 −0.834982
\(113\) 3.53328 0.332383 0.166192 0.986093i \(-0.446853\pi\)
0.166192 + 0.986093i \(0.446853\pi\)
\(114\) −27.7012 −2.59445
\(115\) 7.02935 0.655490
\(116\) 9.19519 0.853752
\(117\) 3.55845 0.328979
\(118\) −17.7983 −1.63847
\(119\) −2.38051 −0.218221
\(120\) 16.0023 1.46080
\(121\) −10.8901 −0.990010
\(122\) −11.8745 −1.07507
\(123\) 22.5005 2.02880
\(124\) −27.4623 −2.46618
\(125\) 11.7810 1.05372
\(126\) 9.82233 0.875043
\(127\) −3.49919 −0.310503 −0.155251 0.987875i \(-0.549619\pi\)
−0.155251 + 0.987875i \(0.549619\pi\)
\(128\) 19.9549 1.76378
\(129\) −11.9357 −1.05088
\(130\) 7.96476 0.698556
\(131\) −17.2951 −1.51108 −0.755539 0.655104i \(-0.772625\pi\)
−0.755539 + 0.655104i \(0.772625\pi\)
\(132\) −2.83721 −0.246947
\(133\) −12.4797 −1.08212
\(134\) 17.3646 1.50007
\(135\) 4.39847 0.378560
\(136\) −4.76117 −0.408267
\(137\) −8.67248 −0.740940 −0.370470 0.928844i \(-0.620803\pi\)
−0.370470 + 0.928844i \(0.620803\pi\)
\(138\) 23.9364 2.03760
\(139\) 8.75419 0.742520 0.371260 0.928529i \(-0.378926\pi\)
0.371260 + 0.928529i \(0.378926\pi\)
\(140\) 14.5971 1.23368
\(141\) −22.8104 −1.92098
\(142\) −31.0746 −2.60772
\(143\) −0.697432 −0.0583222
\(144\) 6.27831 0.523193
\(145\) −3.61083 −0.299863
\(146\) −3.74278 −0.309754
\(147\) −2.88758 −0.238164
\(148\) −7.02130 −0.577147
\(149\) 4.48786 0.367660 0.183830 0.982958i \(-0.441150\pi\)
0.183830 + 0.982958i \(0.441150\pi\)
\(150\) 13.6966 1.11832
\(151\) −3.82712 −0.311447 −0.155723 0.987801i \(-0.549771\pi\)
−0.155723 + 0.987801i \(0.549771\pi\)
\(152\) −24.9601 −2.02453
\(153\) 1.69132 0.136735
\(154\) −1.92511 −0.155130
\(155\) 10.7841 0.866197
\(156\) 18.0076 1.44176
\(157\) −2.12060 −0.169242 −0.0846212 0.996413i \(-0.526968\pi\)
−0.0846212 + 0.996413i \(0.526968\pi\)
\(158\) −33.0550 −2.62972
\(159\) 27.6744 2.19472
\(160\) −0.723712 −0.0572145
\(161\) 10.7836 0.849866
\(162\) 27.3561 2.14930
\(163\) 4.53145 0.354931 0.177465 0.984127i \(-0.443210\pi\)
0.177465 + 0.984127i \(0.443210\pi\)
\(164\) 41.0507 3.20552
\(165\) 1.11413 0.0867353
\(166\) −13.3619 −1.03708
\(167\) 6.19738 0.479568 0.239784 0.970826i \(-0.422923\pi\)
0.239784 + 0.970826i \(0.422923\pi\)
\(168\) 24.5488 1.89398
\(169\) −8.57343 −0.659495
\(170\) 3.78564 0.290345
\(171\) 8.86666 0.678050
\(172\) −21.7759 −1.66040
\(173\) 3.11966 0.237183 0.118592 0.992943i \(-0.462162\pi\)
0.118592 + 0.992943i \(0.462162\pi\)
\(174\) −12.2956 −0.932130
\(175\) 6.17046 0.466443
\(176\) −1.23051 −0.0927531
\(177\) 15.8019 1.18774
\(178\) −24.8998 −1.86632
\(179\) 19.3913 1.44938 0.724688 0.689077i \(-0.241984\pi\)
0.724688 + 0.689077i \(0.241984\pi\)
\(180\) −10.3711 −0.773014
\(181\) 8.82501 0.655958 0.327979 0.944685i \(-0.393633\pi\)
0.327979 + 0.944685i \(0.393633\pi\)
\(182\) 12.2186 0.905703
\(183\) 10.5426 0.779328
\(184\) 21.5678 1.59000
\(185\) 2.75717 0.202711
\(186\) 36.7220 2.69259
\(187\) −0.331488 −0.0242408
\(188\) −41.6160 −3.03516
\(189\) 6.74761 0.490816
\(190\) 19.8460 1.43978
\(191\) 22.7893 1.64898 0.824490 0.565877i \(-0.191462\pi\)
0.824490 + 0.565877i \(0.191462\pi\)
\(192\) −18.5447 −1.33835
\(193\) −10.7670 −0.775023 −0.387511 0.921865i \(-0.626665\pi\)
−0.387511 + 0.921865i \(0.626665\pi\)
\(194\) 36.0248 2.58643
\(195\) −7.07136 −0.506391
\(196\) −5.26819 −0.376300
\(197\) 15.3605 1.09439 0.547195 0.837005i \(-0.315696\pi\)
0.547195 + 0.837005i \(0.315696\pi\)
\(198\) 1.36777 0.0972031
\(199\) 11.0101 0.780487 0.390244 0.920712i \(-0.372391\pi\)
0.390244 + 0.920712i \(0.372391\pi\)
\(200\) 12.3413 0.872661
\(201\) −15.4168 −1.08742
\(202\) 40.5736 2.85475
\(203\) −5.53931 −0.388783
\(204\) 8.55900 0.599250
\(205\) −16.1201 −1.12587
\(206\) −27.4016 −1.90916
\(207\) −7.66162 −0.532519
\(208\) 7.80998 0.541525
\(209\) −1.73781 −0.120207
\(210\) −19.5190 −1.34694
\(211\) −8.86005 −0.609951 −0.304976 0.952360i \(-0.598648\pi\)
−0.304976 + 0.952360i \(0.598648\pi\)
\(212\) 50.4901 3.46767
\(213\) 27.5890 1.89037
\(214\) −6.89084 −0.471048
\(215\) 8.55110 0.583180
\(216\) 13.4956 0.918261
\(217\) 16.5436 1.12305
\(218\) −13.9725 −0.946340
\(219\) 3.32295 0.224544
\(220\) 2.03266 0.137042
\(221\) 2.10394 0.141526
\(222\) 9.38874 0.630131
\(223\) 17.8274 1.19381 0.596907 0.802311i \(-0.296396\pi\)
0.596907 + 0.802311i \(0.296396\pi\)
\(224\) −1.11023 −0.0741806
\(225\) −4.38404 −0.292269
\(226\) −8.61978 −0.573379
\(227\) 7.98163 0.529759 0.264880 0.964281i \(-0.414668\pi\)
0.264880 + 0.964281i \(0.414668\pi\)
\(228\) 44.8700 2.97159
\(229\) 21.9464 1.45026 0.725129 0.688613i \(-0.241780\pi\)
0.725129 + 0.688613i \(0.241780\pi\)
\(230\) −17.1488 −1.13076
\(231\) 1.70917 0.112455
\(232\) −11.0790 −0.727369
\(233\) −20.4183 −1.33765 −0.668825 0.743420i \(-0.733202\pi\)
−0.668825 + 0.743420i \(0.733202\pi\)
\(234\) −8.68117 −0.567506
\(235\) 16.3420 1.06604
\(236\) 28.8295 1.87664
\(237\) 29.3473 1.90631
\(238\) 5.80748 0.376443
\(239\) −12.9302 −0.836383 −0.418192 0.908359i \(-0.637336\pi\)
−0.418192 + 0.908359i \(0.637336\pi\)
\(240\) −12.4763 −0.805341
\(241\) −1.52327 −0.0981223 −0.0490611 0.998796i \(-0.515623\pi\)
−0.0490611 + 0.998796i \(0.515623\pi\)
\(242\) 26.5675 1.70782
\(243\) −15.7840 −1.01255
\(244\) 19.2342 1.23134
\(245\) 2.06875 0.132168
\(246\) −54.8922 −3.49980
\(247\) 11.0298 0.701808
\(248\) 33.0883 2.10111
\(249\) 11.8631 0.751794
\(250\) −28.7409 −1.81773
\(251\) −4.23907 −0.267568 −0.133784 0.991011i \(-0.542713\pi\)
−0.133784 + 0.991011i \(0.542713\pi\)
\(252\) −15.9101 −1.00224
\(253\) 1.50163 0.0944064
\(254\) 8.53660 0.535634
\(255\) −3.36101 −0.210474
\(256\) −31.5579 −1.97237
\(257\) −16.9061 −1.05457 −0.527286 0.849688i \(-0.676790\pi\)
−0.527286 + 0.849688i \(0.676790\pi\)
\(258\) 29.1183 1.81283
\(259\) 4.22972 0.262822
\(260\) −12.9012 −0.800099
\(261\) 3.93561 0.243608
\(262\) 42.1930 2.60669
\(263\) 19.2945 1.18975 0.594876 0.803818i \(-0.297201\pi\)
0.594876 + 0.803818i \(0.297201\pi\)
\(264\) 3.41845 0.210391
\(265\) −19.8268 −1.21795
\(266\) 30.4453 1.86672
\(267\) 22.1068 1.35292
\(268\) −28.1269 −1.71812
\(269\) −6.66760 −0.406531 −0.203265 0.979124i \(-0.565155\pi\)
−0.203265 + 0.979124i \(0.565155\pi\)
\(270\) −10.7305 −0.653036
\(271\) 26.7375 1.62419 0.812093 0.583528i \(-0.198328\pi\)
0.812093 + 0.583528i \(0.198328\pi\)
\(272\) 3.71207 0.225077
\(273\) −10.8480 −0.656553
\(274\) 21.1573 1.27816
\(275\) 0.859243 0.0518143
\(276\) −38.7719 −2.33379
\(277\) 5.83031 0.350309 0.175155 0.984541i \(-0.443957\pi\)
0.175155 + 0.984541i \(0.443957\pi\)
\(278\) −21.3567 −1.28089
\(279\) −11.7541 −0.703697
\(280\) −17.5875 −1.05106
\(281\) 3.63894 0.217081 0.108540 0.994092i \(-0.465382\pi\)
0.108540 + 0.994092i \(0.465382\pi\)
\(282\) 55.6481 3.31379
\(283\) −24.9066 −1.48054 −0.740272 0.672308i \(-0.765303\pi\)
−0.740272 + 0.672308i \(0.765303\pi\)
\(284\) 50.3343 2.98679
\(285\) −17.6199 −1.04371
\(286\) 1.70145 0.100609
\(287\) −24.7295 −1.45974
\(288\) 0.788808 0.0464810
\(289\) 1.00000 0.0588235
\(290\) 8.80896 0.517280
\(291\) −31.9839 −1.87493
\(292\) 6.06250 0.354781
\(293\) 24.0302 1.40386 0.701929 0.712247i \(-0.252322\pi\)
0.701929 + 0.712247i \(0.252322\pi\)
\(294\) 7.04453 0.410845
\(295\) −11.3209 −0.659131
\(296\) 8.45971 0.491711
\(297\) 0.939611 0.0545218
\(298\) −10.9486 −0.634233
\(299\) −9.53075 −0.551178
\(300\) −22.1856 −1.28088
\(301\) 13.1181 0.756114
\(302\) 9.33662 0.537262
\(303\) −36.0225 −2.06944
\(304\) 19.4603 1.11612
\(305\) −7.55301 −0.432484
\(306\) −4.12615 −0.235876
\(307\) −1.58616 −0.0905268 −0.0452634 0.998975i \(-0.514413\pi\)
−0.0452634 + 0.998975i \(0.514413\pi\)
\(308\) 3.11827 0.177680
\(309\) 24.3279 1.38397
\(310\) −26.3087 −1.49424
\(311\) 0.859062 0.0487130 0.0243565 0.999703i \(-0.492246\pi\)
0.0243565 + 0.999703i \(0.492246\pi\)
\(312\) −21.6967 −1.22834
\(313\) 5.90864 0.333976 0.166988 0.985959i \(-0.446596\pi\)
0.166988 + 0.985959i \(0.446596\pi\)
\(314\) 5.17341 0.291952
\(315\) 6.24767 0.352017
\(316\) 53.5421 3.01198
\(317\) 19.0085 1.06762 0.533812 0.845603i \(-0.320759\pi\)
0.533812 + 0.845603i \(0.320759\pi\)
\(318\) −67.5144 −3.78602
\(319\) −0.771354 −0.0431876
\(320\) 13.2860 0.742708
\(321\) 6.11790 0.341468
\(322\) −26.3076 −1.46606
\(323\) 5.24243 0.291697
\(324\) −44.3111 −2.46173
\(325\) −5.45357 −0.302510
\(326\) −11.0549 −0.612275
\(327\) 12.4052 0.686012
\(328\) −49.4605 −2.73100
\(329\) 25.0700 1.38215
\(330\) −2.71804 −0.149623
\(331\) −10.7889 −0.593012 −0.296506 0.955031i \(-0.595821\pi\)
−0.296506 + 0.955031i \(0.595821\pi\)
\(332\) 21.6434 1.18784
\(333\) −3.00517 −0.164682
\(334\) −15.1191 −0.827281
\(335\) 11.0451 0.603456
\(336\) −19.1396 −1.04415
\(337\) −1.75569 −0.0956388 −0.0478194 0.998856i \(-0.515227\pi\)
−0.0478194 + 0.998856i \(0.515227\pi\)
\(338\) 20.9157 1.13766
\(339\) 7.65290 0.415648
\(340\) −6.13193 −0.332550
\(341\) 2.30372 0.124753
\(342\) −21.6310 −1.16967
\(343\) 19.8372 1.07111
\(344\) 26.2370 1.41460
\(345\) 15.2252 0.819697
\(346\) −7.61071 −0.409154
\(347\) 28.4412 1.52680 0.763401 0.645924i \(-0.223528\pi\)
0.763401 + 0.645924i \(0.223528\pi\)
\(348\) 19.9163 1.06763
\(349\) −10.9018 −0.583562 −0.291781 0.956485i \(-0.594248\pi\)
−0.291781 + 0.956485i \(0.594248\pi\)
\(350\) −15.0534 −0.804639
\(351\) −5.96367 −0.318317
\(352\) −0.154601 −0.00824027
\(353\) −1.00000 −0.0532246
\(354\) −38.5502 −2.04892
\(355\) −19.7656 −1.04905
\(356\) 40.3324 2.13761
\(357\) −5.15606 −0.272887
\(358\) −47.3070 −2.50025
\(359\) 33.1572 1.74997 0.874985 0.484150i \(-0.160871\pi\)
0.874985 + 0.484150i \(0.160871\pi\)
\(360\) 12.4957 0.658583
\(361\) 8.48312 0.446480
\(362\) −21.5294 −1.13156
\(363\) −23.5874 −1.23802
\(364\) −19.7915 −1.03736
\(365\) −2.38066 −0.124610
\(366\) −25.7196 −1.34438
\(367\) 18.1359 0.946685 0.473343 0.880878i \(-0.343047\pi\)
0.473343 + 0.880878i \(0.343047\pi\)
\(368\) −16.8155 −0.876568
\(369\) 17.5700 0.914658
\(370\) −6.72638 −0.349688
\(371\) −30.4159 −1.57912
\(372\) −59.4818 −3.08399
\(373\) 27.4929 1.42353 0.711765 0.702418i \(-0.247896\pi\)
0.711765 + 0.702418i \(0.247896\pi\)
\(374\) 0.808697 0.0418167
\(375\) 25.5170 1.31769
\(376\) 50.1416 2.58585
\(377\) 4.89575 0.252144
\(378\) −16.4614 −0.846684
\(379\) 33.4884 1.72019 0.860093 0.510138i \(-0.170406\pi\)
0.860093 + 0.510138i \(0.170406\pi\)
\(380\) −32.1462 −1.64907
\(381\) −7.57905 −0.388287
\(382\) −55.5968 −2.84458
\(383\) 7.98791 0.408163 0.204082 0.978954i \(-0.434579\pi\)
0.204082 + 0.978954i \(0.434579\pi\)
\(384\) 43.2212 2.20562
\(385\) −1.22450 −0.0624065
\(386\) 26.2670 1.33696
\(387\) −9.32025 −0.473775
\(388\) −58.3525 −2.96240
\(389\) −22.7428 −1.15310 −0.576552 0.817060i \(-0.695602\pi\)
−0.576552 + 0.817060i \(0.695602\pi\)
\(390\) 17.2512 0.873551
\(391\) −4.52995 −0.229089
\(392\) 6.34745 0.320595
\(393\) −37.4602 −1.88962
\(394\) −37.4734 −1.88788
\(395\) −21.0253 −1.05790
\(396\) −2.21549 −0.111333
\(397\) 17.1611 0.861291 0.430645 0.902521i \(-0.358286\pi\)
0.430645 + 0.902521i \(0.358286\pi\)
\(398\) −26.8602 −1.34638
\(399\) −27.0303 −1.35321
\(400\) −9.62196 −0.481098
\(401\) 11.0439 0.551507 0.275754 0.961228i \(-0.411073\pi\)
0.275754 + 0.961228i \(0.411073\pi\)
\(402\) 37.6108 1.87585
\(403\) −14.6216 −0.728353
\(404\) −65.7206 −3.26972
\(405\) 17.4004 0.864632
\(406\) 13.5137 0.670672
\(407\) 0.588994 0.0291953
\(408\) −10.3124 −0.510541
\(409\) −34.7777 −1.71964 −0.859822 0.510594i \(-0.829426\pi\)
−0.859822 + 0.510594i \(0.829426\pi\)
\(410\) 39.3264 1.94219
\(411\) −18.7841 −0.926553
\(412\) 44.3847 2.18668
\(413\) −17.3672 −0.854587
\(414\) 18.6912 0.918624
\(415\) −8.49908 −0.417204
\(416\) 0.981247 0.0481096
\(417\) 18.9611 0.928529
\(418\) 4.23954 0.207363
\(419\) −2.52776 −0.123489 −0.0617447 0.998092i \(-0.519666\pi\)
−0.0617447 + 0.998092i \(0.519666\pi\)
\(420\) 31.6166 1.54273
\(421\) −30.6821 −1.49536 −0.747678 0.664061i \(-0.768831\pi\)
−0.747678 + 0.664061i \(0.768831\pi\)
\(422\) 21.6149 1.05220
\(423\) −17.8120 −0.866047
\(424\) −60.8337 −2.95434
\(425\) −2.59207 −0.125734
\(426\) −67.3060 −3.26099
\(427\) −11.5869 −0.560731
\(428\) 11.1617 0.539521
\(429\) −1.51060 −0.0729325
\(430\) −20.8612 −1.00602
\(431\) −41.0083 −1.97530 −0.987650 0.156675i \(-0.949923\pi\)
−0.987650 + 0.156675i \(0.949923\pi\)
\(432\) −10.5219 −0.506237
\(433\) −19.2570 −0.925433 −0.462717 0.886506i \(-0.653125\pi\)
−0.462717 + 0.886506i \(0.653125\pi\)
\(434\) −40.3598 −1.93733
\(435\) −7.82086 −0.374982
\(436\) 22.6325 1.08390
\(437\) −23.7480 −1.13602
\(438\) −8.10665 −0.387351
\(439\) −5.31344 −0.253597 −0.126798 0.991929i \(-0.540470\pi\)
−0.126798 + 0.991929i \(0.540470\pi\)
\(440\) −2.44908 −0.116755
\(441\) −2.25483 −0.107373
\(442\) −5.13276 −0.244141
\(443\) −3.88221 −0.184450 −0.0922248 0.995738i \(-0.529398\pi\)
−0.0922248 + 0.995738i \(0.529398\pi\)
\(444\) −15.2078 −0.721728
\(445\) −15.8380 −0.750793
\(446\) −43.4917 −2.05939
\(447\) 9.72046 0.459762
\(448\) 20.3818 0.962948
\(449\) 27.8395 1.31383 0.656914 0.753965i \(-0.271861\pi\)
0.656914 + 0.753965i \(0.271861\pi\)
\(450\) 10.6953 0.504180
\(451\) −3.44361 −0.162153
\(452\) 13.9622 0.656726
\(453\) −8.28934 −0.389467
\(454\) −19.4719 −0.913863
\(455\) 7.77186 0.364351
\(456\) −54.0622 −2.53170
\(457\) 7.88687 0.368932 0.184466 0.982839i \(-0.440944\pi\)
0.184466 + 0.982839i \(0.440944\pi\)
\(458\) −53.5403 −2.50177
\(459\) −2.83452 −0.132304
\(460\) 27.7773 1.29512
\(461\) 40.1192 1.86854 0.934269 0.356568i \(-0.116053\pi\)
0.934269 + 0.356568i \(0.116053\pi\)
\(462\) −4.16969 −0.193992
\(463\) 19.2785 0.895949 0.447974 0.894046i \(-0.352146\pi\)
0.447974 + 0.894046i \(0.352146\pi\)
\(464\) 8.63777 0.400998
\(465\) 23.3577 1.08319
\(466\) 49.8125 2.30752
\(467\) 38.9346 1.80168 0.900838 0.434155i \(-0.142953\pi\)
0.900838 + 0.434155i \(0.142953\pi\)
\(468\) 14.0616 0.649999
\(469\) 16.9440 0.782403
\(470\) −39.8679 −1.83897
\(471\) −4.59311 −0.211639
\(472\) −34.7356 −1.59883
\(473\) 1.82671 0.0839921
\(474\) −71.5954 −3.28849
\(475\) −13.5888 −0.623496
\(476\) −9.40687 −0.431163
\(477\) 21.6101 0.989460
\(478\) 31.5444 1.44281
\(479\) 22.0684 1.00833 0.504165 0.863607i \(-0.331800\pi\)
0.504165 + 0.863607i \(0.331800\pi\)
\(480\) −1.56752 −0.0715473
\(481\) −3.73831 −0.170452
\(482\) 3.71615 0.169266
\(483\) 23.3567 1.06277
\(484\) −43.0336 −1.95607
\(485\) 22.9142 1.04048
\(486\) 38.5067 1.74670
\(487\) −11.5562 −0.523662 −0.261831 0.965114i \(-0.584326\pi\)
−0.261831 + 0.965114i \(0.584326\pi\)
\(488\) −23.1746 −1.04906
\(489\) 9.81489 0.443845
\(490\) −5.04691 −0.227996
\(491\) −21.5999 −0.974788 −0.487394 0.873182i \(-0.662053\pi\)
−0.487394 + 0.873182i \(0.662053\pi\)
\(492\) 88.9136 4.00853
\(493\) 2.32694 0.104800
\(494\) −26.9082 −1.21066
\(495\) 0.869995 0.0391034
\(496\) −25.7975 −1.15834
\(497\) −30.3220 −1.36013
\(498\) −28.9412 −1.29688
\(499\) 18.1598 0.812943 0.406471 0.913664i \(-0.366759\pi\)
0.406471 + 0.913664i \(0.366759\pi\)
\(500\) 46.5540 2.08196
\(501\) 13.4232 0.599704
\(502\) 10.3416 0.461569
\(503\) 22.4046 0.998974 0.499487 0.866321i \(-0.333522\pi\)
0.499487 + 0.866321i \(0.333522\pi\)
\(504\) 19.1695 0.853876
\(505\) 25.8076 1.14842
\(506\) −3.66336 −0.162856
\(507\) −18.5696 −0.824704
\(508\) −13.8275 −0.613494
\(509\) 26.3574 1.16827 0.584136 0.811656i \(-0.301433\pi\)
0.584136 + 0.811656i \(0.301433\pi\)
\(510\) 8.19949 0.363080
\(511\) −3.65213 −0.161561
\(512\) 37.0788 1.63867
\(513\) −14.8598 −0.656076
\(514\) 41.2440 1.81919
\(515\) −17.4293 −0.768025
\(516\) −47.1654 −2.07634
\(517\) 3.49103 0.153535
\(518\) −10.3188 −0.453383
\(519\) 6.75702 0.296600
\(520\) 15.5442 0.681658
\(521\) −21.1260 −0.925547 −0.462773 0.886477i \(-0.653146\pi\)
−0.462773 + 0.886477i \(0.653146\pi\)
\(522\) −9.60130 −0.420238
\(523\) 23.7845 1.04002 0.520011 0.854159i \(-0.325928\pi\)
0.520011 + 0.854159i \(0.325928\pi\)
\(524\) −68.3436 −2.98560
\(525\) 13.3649 0.583291
\(526\) −47.0708 −2.05239
\(527\) −6.94962 −0.302730
\(528\) −2.66522 −0.115989
\(529\) −2.47955 −0.107806
\(530\) 48.3693 2.10103
\(531\) 12.3392 0.535477
\(532\) −49.3149 −2.13807
\(533\) 21.8564 0.946706
\(534\) −53.9317 −2.33385
\(535\) −4.38305 −0.189496
\(536\) 33.8891 1.46379
\(537\) 42.0006 1.81246
\(538\) 16.2662 0.701287
\(539\) 0.441931 0.0190353
\(540\) 17.3811 0.747962
\(541\) 41.4113 1.78041 0.890205 0.455561i \(-0.150561\pi\)
0.890205 + 0.455561i \(0.150561\pi\)
\(542\) −65.2286 −2.80181
\(543\) 19.1145 0.820281
\(544\) 0.466385 0.0199961
\(545\) −8.88749 −0.380698
\(546\) 26.4648 1.13259
\(547\) 15.4934 0.662452 0.331226 0.943551i \(-0.392538\pi\)
0.331226 + 0.943551i \(0.392538\pi\)
\(548\) −34.2704 −1.46396
\(549\) 8.23238 0.351349
\(550\) −2.09620 −0.0893824
\(551\) 12.1988 0.519688
\(552\) 46.7148 1.98831
\(553\) −32.2545 −1.37160
\(554\) −14.2236 −0.604303
\(555\) 5.97188 0.253492
\(556\) 34.5932 1.46708
\(557\) −37.9758 −1.60909 −0.804543 0.593895i \(-0.797590\pi\)
−0.804543 + 0.593895i \(0.797590\pi\)
\(558\) 28.6751 1.21392
\(559\) −11.5940 −0.490375
\(560\) 13.7122 0.579447
\(561\) −0.717986 −0.0303134
\(562\) −8.87754 −0.374476
\(563\) −5.40724 −0.227888 −0.113944 0.993487i \(-0.536348\pi\)
−0.113944 + 0.993487i \(0.536348\pi\)
\(564\) −90.1380 −3.79549
\(565\) −5.48277 −0.230662
\(566\) 60.7620 2.55402
\(567\) 26.6936 1.12103
\(568\) −60.6459 −2.54465
\(569\) 28.2550 1.18451 0.592256 0.805750i \(-0.298237\pi\)
0.592256 + 0.805750i \(0.298237\pi\)
\(570\) 42.9853 1.80046
\(571\) −15.9031 −0.665522 −0.332761 0.943011i \(-0.607980\pi\)
−0.332761 + 0.943011i \(0.607980\pi\)
\(572\) −2.75599 −0.115234
\(573\) 49.3605 2.06206
\(574\) 60.3299 2.51812
\(575\) 11.7420 0.489674
\(576\) −14.4810 −0.603375
\(577\) −7.60304 −0.316519 −0.158259 0.987398i \(-0.550588\pi\)
−0.158259 + 0.987398i \(0.550588\pi\)
\(578\) −2.43959 −0.101474
\(579\) −23.3207 −0.969173
\(580\) −14.2686 −0.592473
\(581\) −13.0383 −0.540919
\(582\) 78.0278 3.23436
\(583\) −4.23545 −0.175414
\(584\) −7.30448 −0.302262
\(585\) −5.52182 −0.228299
\(586\) −58.6239 −2.42173
\(587\) 0.467879 0.0193114 0.00965572 0.999953i \(-0.496926\pi\)
0.00965572 + 0.999953i \(0.496926\pi\)
\(588\) −11.4106 −0.470566
\(589\) −36.4329 −1.50119
\(590\) 27.6185 1.13704
\(591\) 33.2700 1.36854
\(592\) −6.59566 −0.271080
\(593\) −40.2234 −1.65178 −0.825889 0.563832i \(-0.809326\pi\)
−0.825889 + 0.563832i \(0.809326\pi\)
\(594\) −2.29227 −0.0940530
\(595\) 3.69395 0.151437
\(596\) 17.7343 0.726426
\(597\) 23.8473 0.976007
\(598\) 23.2512 0.950811
\(599\) 13.1977 0.539243 0.269621 0.962966i \(-0.413101\pi\)
0.269621 + 0.962966i \(0.413101\pi\)
\(600\) 26.7306 1.09127
\(601\) 45.1815 1.84299 0.921496 0.388389i \(-0.126968\pi\)
0.921496 + 0.388389i \(0.126968\pi\)
\(602\) −32.0028 −1.30434
\(603\) −12.0385 −0.490247
\(604\) −15.1233 −0.615360
\(605\) 16.8987 0.687031
\(606\) 87.8803 3.56989
\(607\) −37.8514 −1.53634 −0.768171 0.640245i \(-0.778833\pi\)
−0.768171 + 0.640245i \(0.778833\pi\)
\(608\) 2.44499 0.0991575
\(609\) −11.9978 −0.486177
\(610\) 18.4263 0.746058
\(611\) −22.1574 −0.896392
\(612\) 6.68347 0.270163
\(613\) −22.6989 −0.916798 −0.458399 0.888746i \(-0.651577\pi\)
−0.458399 + 0.888746i \(0.651577\pi\)
\(614\) 3.86958 0.156164
\(615\) −34.9152 −1.40792
\(616\) −3.75709 −0.151377
\(617\) −35.0940 −1.41283 −0.706415 0.707798i \(-0.749689\pi\)
−0.706415 + 0.707798i \(0.749689\pi\)
\(618\) −59.3503 −2.38742
\(619\) 42.7451 1.71807 0.859035 0.511916i \(-0.171064\pi\)
0.859035 + 0.511916i \(0.171064\pi\)
\(620\) 42.6145 1.71144
\(621\) 12.8402 0.515261
\(622\) −2.09576 −0.0840325
\(623\) −24.2968 −0.973430
\(624\) 16.9160 0.677182
\(625\) −5.32077 −0.212831
\(626\) −14.4147 −0.576127
\(627\) −3.76400 −0.150320
\(628\) −8.37981 −0.334391
\(629\) −1.77681 −0.0708462
\(630\) −15.2418 −0.607248
\(631\) 43.0293 1.71297 0.856485 0.516172i \(-0.172643\pi\)
0.856485 + 0.516172i \(0.172643\pi\)
\(632\) −64.5109 −2.56611
\(633\) −19.1904 −0.762750
\(634\) −46.3730 −1.84171
\(635\) 5.42986 0.215477
\(636\) 109.359 4.33636
\(637\) −2.80492 −0.111135
\(638\) 1.88179 0.0745009
\(639\) 21.5434 0.852246
\(640\) −30.9649 −1.22400
\(641\) 22.7599 0.898961 0.449480 0.893290i \(-0.351609\pi\)
0.449480 + 0.893290i \(0.351609\pi\)
\(642\) −14.9252 −0.589051
\(643\) 46.8753 1.84858 0.924290 0.381690i \(-0.124658\pi\)
0.924290 + 0.381690i \(0.124658\pi\)
\(644\) 42.6127 1.67917
\(645\) 18.5212 0.729273
\(646\) −12.7894 −0.503193
\(647\) 3.43619 0.135091 0.0675453 0.997716i \(-0.478483\pi\)
0.0675453 + 0.997716i \(0.478483\pi\)
\(648\) 53.3888 2.09731
\(649\) −2.41841 −0.0949308
\(650\) 13.3045 0.521846
\(651\) 35.8326 1.40439
\(652\) 17.9066 0.701276
\(653\) −25.9230 −1.01445 −0.507223 0.861815i \(-0.669328\pi\)
−0.507223 + 0.861815i \(0.669328\pi\)
\(654\) −30.2638 −1.18341
\(655\) 26.8376 1.04863
\(656\) 38.5622 1.50560
\(657\) 2.59480 0.101233
\(658\) −61.1607 −2.38429
\(659\) −7.01835 −0.273396 −0.136698 0.990613i \(-0.543649\pi\)
−0.136698 + 0.990613i \(0.543649\pi\)
\(660\) 4.40264 0.171372
\(661\) 42.6116 1.65740 0.828700 0.559693i \(-0.189081\pi\)
0.828700 + 0.559693i \(0.189081\pi\)
\(662\) 26.3205 1.02298
\(663\) 4.55702 0.176980
\(664\) −26.0774 −1.01200
\(665\) 19.3653 0.750955
\(666\) 7.33140 0.284086
\(667\) −10.5409 −0.408147
\(668\) 24.4897 0.947536
\(669\) 38.6133 1.49288
\(670\) −26.9455 −1.04099
\(671\) −1.61349 −0.0622882
\(672\) −2.40471 −0.0927636
\(673\) −19.6109 −0.755946 −0.377973 0.925817i \(-0.623379\pi\)
−0.377973 + 0.925817i \(0.623379\pi\)
\(674\) 4.28318 0.164982
\(675\) 7.34729 0.282797
\(676\) −33.8790 −1.30304
\(677\) −37.3753 −1.43645 −0.718224 0.695812i \(-0.755045\pi\)
−0.718224 + 0.695812i \(0.755045\pi\)
\(678\) −18.6700 −0.717016
\(679\) 35.1523 1.34902
\(680\) 7.38813 0.283322
\(681\) 17.2878 0.662469
\(682\) −5.62014 −0.215206
\(683\) 31.0519 1.18817 0.594084 0.804403i \(-0.297515\pi\)
0.594084 + 0.804403i \(0.297515\pi\)
\(684\) 35.0377 1.33970
\(685\) 13.4575 0.514185
\(686\) −48.3947 −1.84772
\(687\) 47.5347 1.81356
\(688\) −20.4558 −0.779871
\(689\) 26.8822 1.02413
\(690\) −37.1433 −1.41402
\(691\) −37.1209 −1.41215 −0.706073 0.708139i \(-0.749535\pi\)
−0.706073 + 0.708139i \(0.749535\pi\)
\(692\) 12.3277 0.468629
\(693\) 1.33464 0.0506989
\(694\) −69.3850 −2.63382
\(695\) −13.5843 −0.515282
\(696\) −23.9964 −0.909582
\(697\) 10.3883 0.393485
\(698\) 26.5960 1.00668
\(699\) −44.2250 −1.67274
\(700\) 24.3833 0.921603
\(701\) 50.5494 1.90922 0.954611 0.297854i \(-0.0962709\pi\)
0.954611 + 0.297854i \(0.0962709\pi\)
\(702\) 14.5489 0.549114
\(703\) −9.31483 −0.351316
\(704\) 2.83818 0.106968
\(705\) 35.3960 1.33309
\(706\) 2.43959 0.0918154
\(707\) 39.5910 1.48897
\(708\) 62.4431 2.34675
\(709\) 1.08277 0.0406644 0.0203322 0.999793i \(-0.493528\pi\)
0.0203322 + 0.999793i \(0.493528\pi\)
\(710\) 48.2200 1.80967
\(711\) 22.9164 0.859433
\(712\) −48.5951 −1.82118
\(713\) 31.4814 1.17899
\(714\) 12.5787 0.470746
\(715\) 1.08224 0.0404735
\(716\) 76.6272 2.86369
\(717\) −28.0061 −1.04591
\(718\) −80.8901 −3.01879
\(719\) −51.0688 −1.90454 −0.952272 0.305250i \(-0.901260\pi\)
−0.952272 + 0.305250i \(0.901260\pi\)
\(720\) −9.74237 −0.363077
\(721\) −26.7379 −0.995772
\(722\) −20.6954 −0.770202
\(723\) −3.29932 −0.122703
\(724\) 34.8731 1.29605
\(725\) −6.03161 −0.224008
\(726\) 57.5437 2.13565
\(727\) 30.7699 1.14119 0.570596 0.821231i \(-0.306712\pi\)
0.570596 + 0.821231i \(0.306712\pi\)
\(728\) 23.8461 0.883794
\(729\) −0.547221 −0.0202674
\(730\) 5.80785 0.214958
\(731\) −5.51062 −0.203818
\(732\) 41.6602 1.53981
\(733\) 28.6093 1.05671 0.528355 0.849023i \(-0.322809\pi\)
0.528355 + 0.849023i \(0.322809\pi\)
\(734\) −44.2442 −1.63308
\(735\) 4.48080 0.165277
\(736\) −2.11270 −0.0778752
\(737\) 2.35947 0.0869123
\(738\) −42.8637 −1.57783
\(739\) 30.7075 1.12959 0.564797 0.825230i \(-0.308955\pi\)
0.564797 + 0.825230i \(0.308955\pi\)
\(740\) 10.8953 0.400519
\(741\) 23.8899 0.877618
\(742\) 74.2025 2.72406
\(743\) −45.4232 −1.66642 −0.833208 0.552960i \(-0.813498\pi\)
−0.833208 + 0.552960i \(0.813498\pi\)
\(744\) 71.6674 2.62746
\(745\) −6.96403 −0.255142
\(746\) −67.0716 −2.45567
\(747\) 9.26355 0.338936
\(748\) −1.30992 −0.0478953
\(749\) −6.72395 −0.245688
\(750\) −62.2511 −2.27309
\(751\) −23.9748 −0.874851 −0.437426 0.899255i \(-0.644110\pi\)
−0.437426 + 0.899255i \(0.644110\pi\)
\(752\) −39.0932 −1.42558
\(753\) −9.18160 −0.334596
\(754\) −11.9436 −0.434962
\(755\) 5.93873 0.216133
\(756\) 26.6640 0.969760
\(757\) 4.67479 0.169908 0.0849540 0.996385i \(-0.472926\pi\)
0.0849540 + 0.996385i \(0.472926\pi\)
\(758\) −81.6982 −2.96741
\(759\) 3.25244 0.118056
\(760\) 38.7318 1.40495
\(761\) 2.06117 0.0747174 0.0373587 0.999302i \(-0.488106\pi\)
0.0373587 + 0.999302i \(0.488106\pi\)
\(762\) 18.4898 0.669815
\(763\) −13.6341 −0.493589
\(764\) 90.0549 3.25807
\(765\) −2.62451 −0.0948894
\(766\) −19.4873 −0.704103
\(767\) 15.3495 0.554239
\(768\) −68.3528 −2.46647
\(769\) −35.6933 −1.28713 −0.643567 0.765390i \(-0.722546\pi\)
−0.643567 + 0.765390i \(0.722546\pi\)
\(770\) 2.98729 0.107654
\(771\) −36.6177 −1.31875
\(772\) −42.5469 −1.53130
\(773\) 31.8253 1.14468 0.572339 0.820017i \(-0.306036\pi\)
0.572339 + 0.820017i \(0.306036\pi\)
\(774\) 22.7376 0.817287
\(775\) 18.0139 0.647079
\(776\) 70.3068 2.52387
\(777\) 9.16136 0.328662
\(778\) 55.4832 1.98917
\(779\) 54.4601 1.95123
\(780\) −27.9433 −1.00053
\(781\) −4.22237 −0.151088
\(782\) 11.0512 0.395192
\(783\) −6.59577 −0.235713
\(784\) −4.94883 −0.176744
\(785\) 3.29064 0.117448
\(786\) 91.3877 3.25969
\(787\) 12.6426 0.450660 0.225330 0.974282i \(-0.427654\pi\)
0.225330 + 0.974282i \(0.427654\pi\)
\(788\) 60.6988 2.16231
\(789\) 41.7909 1.48780
\(790\) 51.2931 1.82493
\(791\) −8.41101 −0.299061
\(792\) 2.66937 0.0948519
\(793\) 10.2408 0.363660
\(794\) −41.8661 −1.48577
\(795\) −42.9438 −1.52306
\(796\) 43.5079 1.54210
\(797\) 2.72698 0.0965946 0.0482973 0.998833i \(-0.484621\pi\)
0.0482973 + 0.998833i \(0.484621\pi\)
\(798\) 65.9430 2.33436
\(799\) −10.5314 −0.372573
\(800\) −1.20890 −0.0427412
\(801\) 17.2626 0.609943
\(802\) −26.9427 −0.951379
\(803\) −0.508563 −0.0179468
\(804\) −60.9214 −2.14853
\(805\) −16.7334 −0.589776
\(806\) 35.6707 1.25645
\(807\) −14.4417 −0.508371
\(808\) 79.1843 2.78570
\(809\) 6.76133 0.237716 0.118858 0.992911i \(-0.462077\pi\)
0.118858 + 0.992911i \(0.462077\pi\)
\(810\) −42.4499 −1.49154
\(811\) 20.9359 0.735160 0.367580 0.929992i \(-0.380186\pi\)
0.367580 + 0.929992i \(0.380186\pi\)
\(812\) −21.8893 −0.768162
\(813\) 57.9119 2.03106
\(814\) −1.43691 −0.0503635
\(815\) −7.03168 −0.246309
\(816\) 8.04015 0.281461
\(817\) −28.8891 −1.01070
\(818\) 84.8434 2.96648
\(819\) −8.47092 −0.295998
\(820\) −63.7004 −2.22451
\(821\) 0.350697 0.0122394 0.00611970 0.999981i \(-0.498052\pi\)
0.00611970 + 0.999981i \(0.498052\pi\)
\(822\) 45.8257 1.59835
\(823\) −53.5640 −1.86712 −0.933561 0.358418i \(-0.883316\pi\)
−0.933561 + 0.358418i \(0.883316\pi\)
\(824\) −53.4775 −1.86298
\(825\) 1.86107 0.0647943
\(826\) 42.3690 1.47421
\(827\) 47.7563 1.66065 0.830325 0.557280i \(-0.188155\pi\)
0.830325 + 0.557280i \(0.188155\pi\)
\(828\) −30.2758 −1.05216
\(829\) −29.1769 −1.01335 −0.506677 0.862136i \(-0.669126\pi\)
−0.506677 + 0.862136i \(0.669126\pi\)
\(830\) 20.7343 0.719699
\(831\) 12.6281 0.438065
\(832\) −18.0138 −0.624516
\(833\) −1.33317 −0.0461917
\(834\) −46.2574 −1.60176
\(835\) −9.61678 −0.332803
\(836\) −6.86715 −0.237505
\(837\) 19.6988 0.680892
\(838\) 6.16672 0.213026
\(839\) −43.5378 −1.50309 −0.751546 0.659681i \(-0.770692\pi\)
−0.751546 + 0.659681i \(0.770692\pi\)
\(840\) −38.0936 −1.31436
\(841\) −23.5853 −0.813288
\(842\) 74.8520 2.57957
\(843\) 7.88175 0.271462
\(844\) −35.0116 −1.20515
\(845\) 13.3038 0.457665
\(846\) 43.4539 1.49398
\(847\) 25.9240 0.890760
\(848\) 47.4293 1.62873
\(849\) −53.9463 −1.85143
\(850\) 6.32361 0.216898
\(851\) 8.04888 0.275912
\(852\) 109.021 3.73501
\(853\) 43.1562 1.47764 0.738820 0.673903i \(-0.235383\pi\)
0.738820 + 0.673903i \(0.235383\pi\)
\(854\) 28.2674 0.967291
\(855\) −13.7588 −0.470542
\(856\) −13.4483 −0.459654
\(857\) 32.1463 1.09810 0.549048 0.835791i \(-0.314990\pi\)
0.549048 + 0.835791i \(0.314990\pi\)
\(858\) 3.68525 0.125813
\(859\) 32.1165 1.09580 0.547900 0.836544i \(-0.315427\pi\)
0.547900 + 0.836544i \(0.315427\pi\)
\(860\) 33.7907 1.15225
\(861\) −53.5627 −1.82541
\(862\) 100.044 3.40750
\(863\) 9.50292 0.323483 0.161741 0.986833i \(-0.448289\pi\)
0.161741 + 0.986833i \(0.448289\pi\)
\(864\) −1.32198 −0.0449746
\(865\) −4.84093 −0.164597
\(866\) 46.9793 1.59642
\(867\) 2.16595 0.0735594
\(868\) 65.3742 2.21894
\(869\) −4.49147 −0.152363
\(870\) 19.0797 0.646864
\(871\) −14.9755 −0.507424
\(872\) −27.2691 −0.923448
\(873\) −24.9753 −0.845286
\(874\) 57.9354 1.95969
\(875\) −28.0448 −0.948086
\(876\) 13.1310 0.443657
\(877\) −36.3148 −1.22626 −0.613131 0.789981i \(-0.710090\pi\)
−0.613131 + 0.789981i \(0.710090\pi\)
\(878\) 12.9626 0.437468
\(879\) 52.0481 1.75554
\(880\) 1.90944 0.0643672
\(881\) −14.8202 −0.499307 −0.249653 0.968335i \(-0.580317\pi\)
−0.249653 + 0.968335i \(0.580317\pi\)
\(882\) 5.50086 0.185224
\(883\) 45.2575 1.52304 0.761518 0.648144i \(-0.224454\pi\)
0.761518 + 0.648144i \(0.224454\pi\)
\(884\) 8.31398 0.279629
\(885\) −24.5206 −0.824249
\(886\) 9.47103 0.318185
\(887\) 21.1357 0.709667 0.354834 0.934929i \(-0.384538\pi\)
0.354834 + 0.934929i \(0.384538\pi\)
\(888\) 18.3233 0.614889
\(889\) 8.32985 0.279374
\(890\) 38.6383 1.29516
\(891\) 3.71711 0.124528
\(892\) 70.4473 2.35875
\(893\) −55.2100 −1.84753
\(894\) −23.7140 −0.793115
\(895\) −30.0905 −1.00581
\(896\) −47.5028 −1.58696
\(897\) −20.6431 −0.689253
\(898\) −67.9172 −2.26642
\(899\) −16.1714 −0.539345
\(900\) −17.3241 −0.577469
\(901\) 12.7771 0.425665
\(902\) 8.40100 0.279723
\(903\) 28.4131 0.945528
\(904\) −16.8225 −0.559509
\(905\) −13.6942 −0.455210
\(906\) 20.2226 0.671852
\(907\) −21.3776 −0.709833 −0.354917 0.934898i \(-0.615491\pi\)
−0.354917 + 0.934898i \(0.615491\pi\)
\(908\) 31.5404 1.04670
\(909\) −28.1289 −0.932977
\(910\) −18.9602 −0.628524
\(911\) 32.7938 1.08651 0.543254 0.839569i \(-0.317192\pi\)
0.543254 + 0.839569i \(0.317192\pi\)
\(912\) 42.1499 1.39572
\(913\) −1.81559 −0.0600874
\(914\) −19.2408 −0.636428
\(915\) −16.3594 −0.540825
\(916\) 86.7238 2.86543
\(917\) 41.1711 1.35959
\(918\) 6.91508 0.228232
\(919\) −40.7384 −1.34383 −0.671917 0.740626i \(-0.734529\pi\)
−0.671917 + 0.740626i \(0.734529\pi\)
\(920\) −33.4679 −1.10340
\(921\) −3.43553 −0.113205
\(922\) −97.8747 −3.22333
\(923\) 26.7992 0.882107
\(924\) 6.75401 0.222190
\(925\) 4.60564 0.151432
\(926\) −47.0318 −1.54556
\(927\) 18.9970 0.623943
\(928\) 1.08525 0.0356251
\(929\) 36.9734 1.21306 0.606529 0.795061i \(-0.292561\pi\)
0.606529 + 0.795061i \(0.292561\pi\)
\(930\) −56.9833 −1.86856
\(931\) −6.98907 −0.229057
\(932\) −80.6855 −2.64294
\(933\) 1.86068 0.0609160
\(934\) −94.9845 −3.10799
\(935\) 0.514387 0.0168222
\(936\) −16.9424 −0.553778
\(937\) −38.3520 −1.25290 −0.626452 0.779460i \(-0.715494\pi\)
−0.626452 + 0.779460i \(0.715494\pi\)
\(938\) −41.3366 −1.34969
\(939\) 12.7978 0.417640
\(940\) 64.5775 2.10629
\(941\) −16.1699 −0.527123 −0.263561 0.964643i \(-0.584897\pi\)
−0.263561 + 0.964643i \(0.584897\pi\)
\(942\) 11.2053 0.365089
\(943\) −47.0586 −1.53244
\(944\) 27.0818 0.881437
\(945\) −10.4706 −0.340608
\(946\) −4.45643 −0.144891
\(947\) 40.4147 1.31330 0.656650 0.754195i \(-0.271973\pi\)
0.656650 + 0.754195i \(0.271973\pi\)
\(948\) 115.969 3.76651
\(949\) 3.22782 0.104780
\(950\) 33.1511 1.07556
\(951\) 41.1714 1.33507
\(952\) 11.3340 0.367337
\(953\) 43.5794 1.41167 0.705837 0.708374i \(-0.250571\pi\)
0.705837 + 0.708374i \(0.250571\pi\)
\(954\) −52.7200 −1.70687
\(955\) −35.3633 −1.14433
\(956\) −51.0952 −1.65254
\(957\) −1.67071 −0.0540065
\(958\) −53.8379 −1.73942
\(959\) 20.6449 0.666660
\(960\) 28.7767 0.928764
\(961\) 17.2972 0.557974
\(962\) 9.11997 0.294040
\(963\) 4.77729 0.153946
\(964\) −6.01938 −0.193871
\(965\) 16.7076 0.537837
\(966\) −56.9808 −1.83333
\(967\) 23.2942 0.749092 0.374546 0.927208i \(-0.377799\pi\)
0.374546 + 0.927208i \(0.377799\pi\)
\(968\) 51.8496 1.66651
\(969\) 11.3548 0.364770
\(970\) −55.9015 −1.79489
\(971\) 49.7542 1.59669 0.798343 0.602202i \(-0.205710\pi\)
0.798343 + 0.602202i \(0.205710\pi\)
\(972\) −62.3726 −2.00060
\(973\) −20.8394 −0.668081
\(974\) 28.1925 0.903345
\(975\) −11.8121 −0.378292
\(976\) 18.0682 0.578349
\(977\) −45.3176 −1.44984 −0.724919 0.688834i \(-0.758123\pi\)
−0.724919 + 0.688834i \(0.758123\pi\)
\(978\) −23.9443 −0.765656
\(979\) −3.38335 −0.108132
\(980\) 8.17491 0.261138
\(981\) 9.68689 0.309279
\(982\) 52.6949 1.68156
\(983\) 11.2505 0.358836 0.179418 0.983773i \(-0.442579\pi\)
0.179418 + 0.983773i \(0.442579\pi\)
\(984\) −107.129 −3.41514
\(985\) −23.8356 −0.759466
\(986\) −5.67680 −0.180786
\(987\) 54.3003 1.72840
\(988\) 43.5855 1.38664
\(989\) 24.9628 0.793772
\(990\) −2.12244 −0.0674554
\(991\) −26.8400 −0.852602 −0.426301 0.904581i \(-0.640184\pi\)
−0.426301 + 0.904581i \(0.640184\pi\)
\(992\) −3.24120 −0.102908
\(993\) −23.3682 −0.741567
\(994\) 73.9735 2.34630
\(995\) −17.0850 −0.541630
\(996\) 46.8785 1.48540
\(997\) 18.6420 0.590398 0.295199 0.955436i \(-0.404614\pi\)
0.295199 + 0.955436i \(0.404614\pi\)
\(998\) −44.3025 −1.40237
\(999\) 5.03642 0.159345
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.1.11 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.11 121 1.1 even 1 trivial