Properties

Label 6017.2.a.f.1.14
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
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 1.14
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} +O(q^{10})\) \(q-2.30378 q^{2} +2.53807 q^{3} +3.30742 q^{4} +3.98214 q^{5} -5.84717 q^{6} -4.26603 q^{7} -3.01201 q^{8} +3.44182 q^{9} -9.17400 q^{10} -1.00000 q^{11} +8.39448 q^{12} +0.239607 q^{13} +9.82801 q^{14} +10.1070 q^{15} +0.324190 q^{16} +1.10862 q^{17} -7.92921 q^{18} +1.67372 q^{19} +13.1706 q^{20} -10.8275 q^{21} +2.30378 q^{22} -3.87775 q^{23} -7.64472 q^{24} +10.8575 q^{25} -0.552003 q^{26} +1.12137 q^{27} -14.1096 q^{28} -2.02650 q^{29} -23.2843 q^{30} +9.78699 q^{31} +5.27717 q^{32} -2.53807 q^{33} -2.55403 q^{34} -16.9879 q^{35} +11.3835 q^{36} -9.41514 q^{37} -3.85589 q^{38} +0.608140 q^{39} -11.9943 q^{40} +7.37283 q^{41} +24.9442 q^{42} +9.44813 q^{43} -3.30742 q^{44} +13.7058 q^{45} +8.93351 q^{46} +10.3308 q^{47} +0.822818 q^{48} +11.1990 q^{49} -25.0133 q^{50} +2.81377 q^{51} +0.792481 q^{52} +12.0331 q^{53} -2.58340 q^{54} -3.98214 q^{55} +12.8493 q^{56} +4.24802 q^{57} +4.66862 q^{58} +4.50186 q^{59} +33.4280 q^{60} -2.69193 q^{61} -22.5471 q^{62} -14.6829 q^{63} -12.8058 q^{64} +0.954149 q^{65} +5.84717 q^{66} -6.26446 q^{67} +3.66668 q^{68} -9.84203 q^{69} +39.1365 q^{70} +8.56057 q^{71} -10.3668 q^{72} -7.48196 q^{73} +21.6905 q^{74} +27.5571 q^{75} +5.53569 q^{76} +4.26603 q^{77} -1.40102 q^{78} -16.5502 q^{79} +1.29097 q^{80} -7.47934 q^{81} -16.9854 q^{82} -0.664294 q^{83} -35.8111 q^{84} +4.41470 q^{85} -21.7664 q^{86} -5.14341 q^{87} +3.01201 q^{88} -9.23046 q^{89} -31.5753 q^{90} -1.02217 q^{91} -12.8254 q^{92} +24.8401 q^{93} -23.7999 q^{94} +6.66499 q^{95} +13.3938 q^{96} -15.9767 q^{97} -25.8001 q^{98} -3.44182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30378 −1.62902 −0.814511 0.580149i \(-0.802994\pi\)
−0.814511 + 0.580149i \(0.802994\pi\)
\(3\) 2.53807 1.46536 0.732679 0.680575i \(-0.238270\pi\)
0.732679 + 0.680575i \(0.238270\pi\)
\(4\) 3.30742 1.65371
\(5\) 3.98214 1.78087 0.890434 0.455111i \(-0.150401\pi\)
0.890434 + 0.455111i \(0.150401\pi\)
\(6\) −5.84717 −2.38710
\(7\) −4.26603 −1.61241 −0.806204 0.591638i \(-0.798481\pi\)
−0.806204 + 0.591638i \(0.798481\pi\)
\(8\) −3.01201 −1.06491
\(9\) 3.44182 1.14727
\(10\) −9.17400 −2.90107
\(11\) −1.00000 −0.301511
\(12\) 8.39448 2.42328
\(13\) 0.239607 0.0664550 0.0332275 0.999448i \(-0.489421\pi\)
0.0332275 + 0.999448i \(0.489421\pi\)
\(14\) 9.82801 2.62665
\(15\) 10.1070 2.60961
\(16\) 0.324190 0.0810475
\(17\) 1.10862 0.268881 0.134440 0.990922i \(-0.457076\pi\)
0.134440 + 0.990922i \(0.457076\pi\)
\(18\) −7.92921 −1.86893
\(19\) 1.67372 0.383978 0.191989 0.981397i \(-0.438506\pi\)
0.191989 + 0.981397i \(0.438506\pi\)
\(20\) 13.1706 2.94504
\(21\) −10.8275 −2.36275
\(22\) 2.30378 0.491168
\(23\) −3.87775 −0.808568 −0.404284 0.914634i \(-0.632479\pi\)
−0.404284 + 0.914634i \(0.632479\pi\)
\(24\) −7.64472 −1.56047
\(25\) 10.8575 2.17149
\(26\) −0.552003 −0.108257
\(27\) 1.12137 0.215808
\(28\) −14.1096 −2.66645
\(29\) −2.02650 −0.376312 −0.188156 0.982139i \(-0.560251\pi\)
−0.188156 + 0.982139i \(0.560251\pi\)
\(30\) −23.2843 −4.25111
\(31\) 9.78699 1.75780 0.878898 0.477010i \(-0.158279\pi\)
0.878898 + 0.477010i \(0.158279\pi\)
\(32\) 5.27717 0.932880
\(33\) −2.53807 −0.441822
\(34\) −2.55403 −0.438012
\(35\) −16.9879 −2.87149
\(36\) 11.3835 1.89726
\(37\) −9.41514 −1.54784 −0.773920 0.633283i \(-0.781707\pi\)
−0.773920 + 0.633283i \(0.781707\pi\)
\(38\) −3.85589 −0.625508
\(39\) 0.608140 0.0973803
\(40\) −11.9943 −1.89646
\(41\) 7.37283 1.15144 0.575721 0.817646i \(-0.304721\pi\)
0.575721 + 0.817646i \(0.304721\pi\)
\(42\) 24.9442 3.84898
\(43\) 9.44813 1.44083 0.720413 0.693545i \(-0.243952\pi\)
0.720413 + 0.693545i \(0.243952\pi\)
\(44\) −3.30742 −0.498612
\(45\) 13.7058 2.04314
\(46\) 8.93351 1.31717
\(47\) 10.3308 1.50690 0.753452 0.657503i \(-0.228387\pi\)
0.753452 + 0.657503i \(0.228387\pi\)
\(48\) 0.822818 0.118764
\(49\) 11.1990 1.59986
\(50\) −25.0133 −3.53741
\(51\) 2.81377 0.394006
\(52\) 0.792481 0.109897
\(53\) 12.0331 1.65288 0.826438 0.563027i \(-0.190363\pi\)
0.826438 + 0.563027i \(0.190363\pi\)
\(54\) −2.58340 −0.351556
\(55\) −3.98214 −0.536952
\(56\) 12.8493 1.71707
\(57\) 4.24802 0.562665
\(58\) 4.66862 0.613020
\(59\) 4.50186 0.586092 0.293046 0.956098i \(-0.405331\pi\)
0.293046 + 0.956098i \(0.405331\pi\)
\(60\) 33.4280 4.31554
\(61\) −2.69193 −0.344666 −0.172333 0.985039i \(-0.555131\pi\)
−0.172333 + 0.985039i \(0.555131\pi\)
\(62\) −22.5471 −2.86349
\(63\) −14.6829 −1.84987
\(64\) −12.8058 −1.60073
\(65\) 0.954149 0.118348
\(66\) 5.84717 0.719737
\(67\) −6.26446 −0.765326 −0.382663 0.923888i \(-0.624993\pi\)
−0.382663 + 0.923888i \(0.624993\pi\)
\(68\) 3.66668 0.444651
\(69\) −9.84203 −1.18484
\(70\) 39.1365 4.67771
\(71\) 8.56057 1.01595 0.507976 0.861371i \(-0.330394\pi\)
0.507976 + 0.861371i \(0.330394\pi\)
\(72\) −10.3668 −1.22174
\(73\) −7.48196 −0.875697 −0.437849 0.899049i \(-0.644259\pi\)
−0.437849 + 0.899049i \(0.644259\pi\)
\(74\) 21.6905 2.52146
\(75\) 27.5571 3.18202
\(76\) 5.53569 0.634988
\(77\) 4.26603 0.486159
\(78\) −1.40102 −0.158635
\(79\) −16.5502 −1.86204 −0.931021 0.364965i \(-0.881081\pi\)
−0.931021 + 0.364965i \(0.881081\pi\)
\(80\) 1.29097 0.144335
\(81\) −7.47934 −0.831037
\(82\) −16.9854 −1.87572
\(83\) −0.664294 −0.0729157 −0.0364578 0.999335i \(-0.511607\pi\)
−0.0364578 + 0.999335i \(0.511607\pi\)
\(84\) −35.8111 −3.90731
\(85\) 4.41470 0.478841
\(86\) −21.7664 −2.34714
\(87\) −5.14341 −0.551432
\(88\) 3.01201 0.321082
\(89\) −9.23046 −0.978427 −0.489213 0.872164i \(-0.662716\pi\)
−0.489213 + 0.872164i \(0.662716\pi\)
\(90\) −31.5753 −3.32832
\(91\) −1.02217 −0.107153
\(92\) −12.8254 −1.33714
\(93\) 24.8401 2.57580
\(94\) −23.7999 −2.45478
\(95\) 6.66499 0.683814
\(96\) 13.3938 1.36700
\(97\) −15.9767 −1.62219 −0.811096 0.584913i \(-0.801128\pi\)
−0.811096 + 0.584913i \(0.801128\pi\)
\(98\) −25.8001 −2.60620
\(99\) −3.44182 −0.345916
\(100\) 35.9102 3.59102
\(101\) −16.5539 −1.64718 −0.823589 0.567187i \(-0.808032\pi\)
−0.823589 + 0.567187i \(0.808032\pi\)
\(102\) −6.48231 −0.641845
\(103\) 13.2353 1.30411 0.652056 0.758171i \(-0.273907\pi\)
0.652056 + 0.758171i \(0.273907\pi\)
\(104\) −0.721700 −0.0707685
\(105\) −43.1167 −4.20775
\(106\) −27.7217 −2.69257
\(107\) 14.5438 1.40600 0.703001 0.711189i \(-0.251843\pi\)
0.703001 + 0.711189i \(0.251843\pi\)
\(108\) 3.70885 0.356884
\(109\) 13.4304 1.28640 0.643202 0.765697i \(-0.277606\pi\)
0.643202 + 0.765697i \(0.277606\pi\)
\(110\) 9.17400 0.874707
\(111\) −23.8963 −2.26814
\(112\) −1.38300 −0.130682
\(113\) 19.8752 1.86970 0.934852 0.355038i \(-0.115532\pi\)
0.934852 + 0.355038i \(0.115532\pi\)
\(114\) −9.78653 −0.916593
\(115\) −15.4418 −1.43995
\(116\) −6.70249 −0.622311
\(117\) 0.824684 0.0762420
\(118\) −10.3713 −0.954757
\(119\) −4.72942 −0.433545
\(120\) −30.4424 −2.77899
\(121\) 1.00000 0.0909091
\(122\) 6.20162 0.561469
\(123\) 18.7128 1.68727
\(124\) 32.3697 2.90689
\(125\) 23.3253 2.08628
\(126\) 33.8262 3.01348
\(127\) 15.4483 1.37082 0.685408 0.728160i \(-0.259624\pi\)
0.685408 + 0.728160i \(0.259624\pi\)
\(128\) 18.9475 1.67474
\(129\) 23.9800 2.11133
\(130\) −2.19815 −0.192791
\(131\) 14.2948 1.24894 0.624471 0.781048i \(-0.285315\pi\)
0.624471 + 0.781048i \(0.285315\pi\)
\(132\) −8.39448 −0.730646
\(133\) −7.14014 −0.619128
\(134\) 14.4320 1.24673
\(135\) 4.46546 0.384326
\(136\) −3.33919 −0.286333
\(137\) −10.8970 −0.930993 −0.465496 0.885050i \(-0.654124\pi\)
−0.465496 + 0.885050i \(0.654124\pi\)
\(138\) 22.6739 1.93013
\(139\) −5.23250 −0.443815 −0.221907 0.975068i \(-0.571228\pi\)
−0.221907 + 0.975068i \(0.571228\pi\)
\(140\) −56.1863 −4.74861
\(141\) 26.2204 2.20815
\(142\) −19.7217 −1.65501
\(143\) −0.239607 −0.0200369
\(144\) 1.11580 0.0929836
\(145\) −8.06982 −0.670162
\(146\) 17.2368 1.42653
\(147\) 28.4239 2.34436
\(148\) −31.1398 −2.55968
\(149\) 3.87854 0.317742 0.158871 0.987299i \(-0.449215\pi\)
0.158871 + 0.987299i \(0.449215\pi\)
\(150\) −63.4855 −5.18357
\(151\) −9.03658 −0.735386 −0.367693 0.929947i \(-0.619852\pi\)
−0.367693 + 0.929947i \(0.619852\pi\)
\(152\) −5.04127 −0.408901
\(153\) 3.81568 0.308480
\(154\) −9.82801 −0.791963
\(155\) 38.9732 3.13040
\(156\) 2.01138 0.161039
\(157\) 15.2715 1.21880 0.609398 0.792865i \(-0.291411\pi\)
0.609398 + 0.792865i \(0.291411\pi\)
\(158\) 38.1281 3.03331
\(159\) 30.5410 2.42206
\(160\) 21.0144 1.66134
\(161\) 16.5426 1.30374
\(162\) 17.2308 1.35378
\(163\) 21.7300 1.70202 0.851012 0.525147i \(-0.175990\pi\)
0.851012 + 0.525147i \(0.175990\pi\)
\(164\) 24.3850 1.90415
\(165\) −10.1070 −0.786827
\(166\) 1.53039 0.118781
\(167\) 11.8949 0.920453 0.460226 0.887802i \(-0.347768\pi\)
0.460226 + 0.887802i \(0.347768\pi\)
\(168\) 32.6126 2.51612
\(169\) −12.9426 −0.995584
\(170\) −10.1705 −0.780043
\(171\) 5.76064 0.440527
\(172\) 31.2489 2.38271
\(173\) 8.79578 0.668731 0.334366 0.942443i \(-0.391478\pi\)
0.334366 + 0.942443i \(0.391478\pi\)
\(174\) 11.8493 0.898294
\(175\) −46.3183 −3.50133
\(176\) −0.324190 −0.0244367
\(177\) 11.4261 0.858835
\(178\) 21.2650 1.59388
\(179\) −19.2364 −1.43780 −0.718899 0.695114i \(-0.755354\pi\)
−0.718899 + 0.695114i \(0.755354\pi\)
\(180\) 45.3309 3.37877
\(181\) −9.55691 −0.710359 −0.355180 0.934798i \(-0.615580\pi\)
−0.355180 + 0.934798i \(0.615580\pi\)
\(182\) 2.35486 0.174554
\(183\) −6.83232 −0.505059
\(184\) 11.6799 0.861050
\(185\) −37.4925 −2.75650
\(186\) −57.2263 −4.19603
\(187\) −1.10862 −0.0810706
\(188\) 34.1683 2.49198
\(189\) −4.78380 −0.347970
\(190\) −15.3547 −1.11395
\(191\) −2.32991 −0.168586 −0.0842931 0.996441i \(-0.526863\pi\)
−0.0842931 + 0.996441i \(0.526863\pi\)
\(192\) −32.5021 −2.34564
\(193\) 5.77583 0.415753 0.207877 0.978155i \(-0.433345\pi\)
0.207877 + 0.978155i \(0.433345\pi\)
\(194\) 36.8069 2.64258
\(195\) 2.42170 0.173422
\(196\) 37.0398 2.64570
\(197\) −19.4656 −1.38686 −0.693432 0.720522i \(-0.743902\pi\)
−0.693432 + 0.720522i \(0.743902\pi\)
\(198\) 7.92921 0.563504
\(199\) −17.5635 −1.24505 −0.622523 0.782601i \(-0.713892\pi\)
−0.622523 + 0.782601i \(0.713892\pi\)
\(200\) −32.7029 −2.31244
\(201\) −15.8997 −1.12148
\(202\) 38.1367 2.68329
\(203\) 8.64512 0.606768
\(204\) 9.30631 0.651572
\(205\) 29.3597 2.05057
\(206\) −30.4913 −2.12443
\(207\) −13.3465 −0.927648
\(208\) 0.0776781 0.00538601
\(209\) −1.67372 −0.115774
\(210\) 99.3315 6.85452
\(211\) −4.06736 −0.280009 −0.140004 0.990151i \(-0.544712\pi\)
−0.140004 + 0.990151i \(0.544712\pi\)
\(212\) 39.7986 2.73338
\(213\) 21.7274 1.48873
\(214\) −33.5058 −2.29041
\(215\) 37.6238 2.56592
\(216\) −3.37759 −0.229816
\(217\) −41.7516 −2.83428
\(218\) −30.9409 −2.09558
\(219\) −18.9898 −1.28321
\(220\) −13.1706 −0.887963
\(221\) 0.265634 0.0178685
\(222\) 55.0520 3.69485
\(223\) 25.8060 1.72810 0.864049 0.503408i \(-0.167921\pi\)
0.864049 + 0.503408i \(0.167921\pi\)
\(224\) −22.5125 −1.50418
\(225\) 37.3695 2.49130
\(226\) −45.7882 −3.04579
\(227\) −1.95544 −0.129787 −0.0648936 0.997892i \(-0.520671\pi\)
−0.0648936 + 0.997892i \(0.520671\pi\)
\(228\) 14.0500 0.930484
\(229\) 19.8009 1.30848 0.654241 0.756286i \(-0.272988\pi\)
0.654241 + 0.756286i \(0.272988\pi\)
\(230\) 35.5745 2.34571
\(231\) 10.8275 0.712397
\(232\) 6.10385 0.400738
\(233\) 16.9713 1.11183 0.555915 0.831239i \(-0.312368\pi\)
0.555915 + 0.831239i \(0.312368\pi\)
\(234\) −1.89989 −0.124200
\(235\) 41.1388 2.68360
\(236\) 14.8896 0.969227
\(237\) −42.0056 −2.72856
\(238\) 10.8956 0.706254
\(239\) 11.9663 0.774035 0.387017 0.922072i \(-0.373505\pi\)
0.387017 + 0.922072i \(0.373505\pi\)
\(240\) 3.27658 0.211502
\(241\) 20.5162 1.32156 0.660781 0.750579i \(-0.270225\pi\)
0.660781 + 0.750579i \(0.270225\pi\)
\(242\) −2.30378 −0.148093
\(243\) −22.3472 −1.43357
\(244\) −8.90334 −0.569978
\(245\) 44.5960 2.84914
\(246\) −43.1102 −2.74861
\(247\) 0.401035 0.0255172
\(248\) −29.4786 −1.87189
\(249\) −1.68603 −0.106848
\(250\) −53.7364 −3.39859
\(251\) 17.6380 1.11330 0.556649 0.830748i \(-0.312087\pi\)
0.556649 + 0.830748i \(0.312087\pi\)
\(252\) −48.5625 −3.05915
\(253\) 3.87775 0.243792
\(254\) −35.5896 −2.23309
\(255\) 11.2048 0.701674
\(256\) −18.0394 −1.12746
\(257\) 1.88561 0.117621 0.0588107 0.998269i \(-0.481269\pi\)
0.0588107 + 0.998269i \(0.481269\pi\)
\(258\) −55.2448 −3.43939
\(259\) 40.1653 2.49575
\(260\) 3.15577 0.195713
\(261\) −6.97485 −0.431733
\(262\) −32.9321 −2.03455
\(263\) 14.5005 0.894141 0.447071 0.894499i \(-0.352467\pi\)
0.447071 + 0.894499i \(0.352467\pi\)
\(264\) 7.64472 0.470500
\(265\) 47.9176 2.94356
\(266\) 16.4493 1.00857
\(267\) −23.4276 −1.43375
\(268\) −20.7192 −1.26563
\(269\) 25.1358 1.53256 0.766278 0.642509i \(-0.222107\pi\)
0.766278 + 0.642509i \(0.222107\pi\)
\(270\) −10.2875 −0.626075
\(271\) 18.0695 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(272\) 0.359405 0.0217921
\(273\) −2.59434 −0.157017
\(274\) 25.1043 1.51661
\(275\) −10.8575 −0.654730
\(276\) −32.5517 −1.95938
\(277\) −7.02113 −0.421859 −0.210929 0.977501i \(-0.567649\pi\)
−0.210929 + 0.977501i \(0.567649\pi\)
\(278\) 12.0545 0.722984
\(279\) 33.6851 2.01667
\(280\) 51.1679 3.05787
\(281\) −13.0086 −0.776025 −0.388013 0.921654i \(-0.626838\pi\)
−0.388013 + 0.921654i \(0.626838\pi\)
\(282\) −60.4060 −3.59713
\(283\) 14.3409 0.852477 0.426239 0.904611i \(-0.359838\pi\)
0.426239 + 0.904611i \(0.359838\pi\)
\(284\) 28.3134 1.68009
\(285\) 16.9162 1.00203
\(286\) 0.552003 0.0326406
\(287\) −31.4527 −1.85659
\(288\) 18.1631 1.07027
\(289\) −15.7710 −0.927703
\(290\) 18.5911 1.09171
\(291\) −40.5501 −2.37709
\(292\) −24.7460 −1.44815
\(293\) 6.30326 0.368240 0.184120 0.982904i \(-0.441056\pi\)
0.184120 + 0.982904i \(0.441056\pi\)
\(294\) −65.4825 −3.81902
\(295\) 17.9271 1.04375
\(296\) 28.3586 1.64831
\(297\) −1.12137 −0.0650686
\(298\) −8.93531 −0.517609
\(299\) −0.929137 −0.0537334
\(300\) 91.1428 5.26213
\(301\) −40.3060 −2.32320
\(302\) 20.8183 1.19796
\(303\) −42.0151 −2.41370
\(304\) 0.542603 0.0311204
\(305\) −10.7197 −0.613805
\(306\) −8.79051 −0.502520
\(307\) −3.30017 −0.188350 −0.0941752 0.995556i \(-0.530021\pi\)
−0.0941752 + 0.995556i \(0.530021\pi\)
\(308\) 14.1096 0.803966
\(309\) 33.5922 1.91099
\(310\) −89.7859 −5.09950
\(311\) −13.7765 −0.781195 −0.390597 0.920562i \(-0.627732\pi\)
−0.390597 + 0.920562i \(0.627732\pi\)
\(312\) −1.83173 −0.103701
\(313\) −12.8179 −0.724513 −0.362256 0.932079i \(-0.617994\pi\)
−0.362256 + 0.932079i \(0.617994\pi\)
\(314\) −35.1822 −1.98544
\(315\) −58.4694 −3.29438
\(316\) −54.7384 −3.07928
\(317\) −17.3093 −0.972188 −0.486094 0.873906i \(-0.661579\pi\)
−0.486094 + 0.873906i \(0.661579\pi\)
\(318\) −70.3598 −3.94558
\(319\) 2.02650 0.113462
\(320\) −50.9947 −2.85069
\(321\) 36.9132 2.06030
\(322\) −38.1106 −2.12382
\(323\) 1.85552 0.103244
\(324\) −24.7373 −1.37429
\(325\) 2.60153 0.144307
\(326\) −50.0612 −2.77263
\(327\) 34.0875 1.88504
\(328\) −22.2071 −1.22618
\(329\) −44.0715 −2.42974
\(330\) 23.2843 1.28176
\(331\) 1.17681 0.0646833 0.0323416 0.999477i \(-0.489704\pi\)
0.0323416 + 0.999477i \(0.489704\pi\)
\(332\) −2.19710 −0.120581
\(333\) −32.4052 −1.77580
\(334\) −27.4032 −1.49944
\(335\) −24.9460 −1.36295
\(336\) −3.51017 −0.191495
\(337\) 23.7231 1.29228 0.646139 0.763220i \(-0.276383\pi\)
0.646139 + 0.763220i \(0.276383\pi\)
\(338\) 29.8169 1.62183
\(339\) 50.4448 2.73978
\(340\) 14.6013 0.791865
\(341\) −9.78699 −0.529995
\(342\) −13.2713 −0.717628
\(343\) −17.9131 −0.967214
\(344\) −28.4579 −1.53435
\(345\) −39.1924 −2.11005
\(346\) −20.2636 −1.08938
\(347\) −27.9352 −1.49964 −0.749819 0.661642i \(-0.769860\pi\)
−0.749819 + 0.661642i \(0.769860\pi\)
\(348\) −17.0114 −0.911908
\(349\) 19.8487 1.06248 0.531239 0.847222i \(-0.321726\pi\)
0.531239 + 0.847222i \(0.321726\pi\)
\(350\) 106.707 5.70375
\(351\) 0.268688 0.0143415
\(352\) −5.27717 −0.281274
\(353\) 0.222781 0.0118574 0.00592872 0.999982i \(-0.498113\pi\)
0.00592872 + 0.999982i \(0.498113\pi\)
\(354\) −26.3232 −1.39906
\(355\) 34.0894 1.80928
\(356\) −30.5290 −1.61803
\(357\) −12.0036 −0.635299
\(358\) 44.3166 2.34220
\(359\) −9.35655 −0.493820 −0.246910 0.969038i \(-0.579415\pi\)
−0.246910 + 0.969038i \(0.579415\pi\)
\(360\) −41.2821 −2.17576
\(361\) −16.1987 −0.852561
\(362\) 22.0171 1.15719
\(363\) 2.53807 0.133214
\(364\) −3.38075 −0.177199
\(365\) −29.7942 −1.55950
\(366\) 15.7402 0.822752
\(367\) 8.82606 0.460717 0.230358 0.973106i \(-0.426010\pi\)
0.230358 + 0.973106i \(0.426010\pi\)
\(368\) −1.25713 −0.0655324
\(369\) 25.3759 1.32102
\(370\) 86.3745 4.49040
\(371\) −51.3337 −2.66511
\(372\) 82.1567 4.25963
\(373\) 13.7180 0.710293 0.355147 0.934811i \(-0.384431\pi\)
0.355147 + 0.934811i \(0.384431\pi\)
\(374\) 2.55403 0.132066
\(375\) 59.2013 3.05714
\(376\) −31.1165 −1.60471
\(377\) −0.485564 −0.0250078
\(378\) 11.0208 0.566851
\(379\) −28.4038 −1.45901 −0.729503 0.683978i \(-0.760248\pi\)
−0.729503 + 0.683978i \(0.760248\pi\)
\(380\) 22.0439 1.13083
\(381\) 39.2089 2.00873
\(382\) 5.36760 0.274630
\(383\) 7.06772 0.361143 0.180572 0.983562i \(-0.442205\pi\)
0.180572 + 0.983562i \(0.442205\pi\)
\(384\) 48.0902 2.45410
\(385\) 16.9879 0.865786
\(386\) −13.3063 −0.677271
\(387\) 32.5188 1.65302
\(388\) −52.8418 −2.68263
\(389\) 23.4828 1.19063 0.595313 0.803494i \(-0.297028\pi\)
0.595313 + 0.803494i \(0.297028\pi\)
\(390\) −5.57908 −0.282508
\(391\) −4.29897 −0.217408
\(392\) −33.7316 −1.70370
\(393\) 36.2812 1.83015
\(394\) 44.8445 2.25923
\(395\) −65.9053 −3.31605
\(396\) −11.3835 −0.572045
\(397\) 1.47453 0.0740047 0.0370024 0.999315i \(-0.488219\pi\)
0.0370024 + 0.999315i \(0.488219\pi\)
\(398\) 40.4626 2.02821
\(399\) −18.1222 −0.907244
\(400\) 3.51988 0.175994
\(401\) −14.5488 −0.726531 −0.363265 0.931686i \(-0.618338\pi\)
−0.363265 + 0.931686i \(0.618338\pi\)
\(402\) 36.6294 1.82691
\(403\) 2.34503 0.116814
\(404\) −54.7508 −2.72396
\(405\) −29.7838 −1.47997
\(406\) −19.9165 −0.988438
\(407\) 9.41514 0.466691
\(408\) −8.47511 −0.419581
\(409\) −19.0056 −0.939766 −0.469883 0.882729i \(-0.655704\pi\)
−0.469883 + 0.882729i \(0.655704\pi\)
\(410\) −67.6383 −3.34042
\(411\) −27.6574 −1.36424
\(412\) 43.7747 2.15662
\(413\) −19.2051 −0.945020
\(414\) 30.7475 1.51116
\(415\) −2.64531 −0.129853
\(416\) 1.26445 0.0619945
\(417\) −13.2805 −0.650347
\(418\) 3.85589 0.188598
\(419\) −30.1199 −1.47146 −0.735728 0.677277i \(-0.763160\pi\)
−0.735728 + 0.677277i \(0.763160\pi\)
\(420\) −142.605 −6.95841
\(421\) −14.8792 −0.725169 −0.362585 0.931951i \(-0.618106\pi\)
−0.362585 + 0.931951i \(0.618106\pi\)
\(422\) 9.37033 0.456140
\(423\) 35.5568 1.72883
\(424\) −36.2439 −1.76016
\(425\) 12.0368 0.583873
\(426\) −50.0551 −2.42518
\(427\) 11.4838 0.555742
\(428\) 48.1025 2.32512
\(429\) −0.608140 −0.0293613
\(430\) −86.6771 −4.17994
\(431\) 16.7160 0.805182 0.402591 0.915380i \(-0.368110\pi\)
0.402591 + 0.915380i \(0.368110\pi\)
\(432\) 0.363537 0.0174907
\(433\) −21.0529 −1.01174 −0.505869 0.862610i \(-0.668828\pi\)
−0.505869 + 0.862610i \(0.668828\pi\)
\(434\) 96.1867 4.61711
\(435\) −20.4818 −0.982027
\(436\) 44.4201 2.12734
\(437\) −6.49027 −0.310472
\(438\) 43.7483 2.09038
\(439\) 18.1058 0.864141 0.432071 0.901840i \(-0.357783\pi\)
0.432071 + 0.901840i \(0.357783\pi\)
\(440\) 11.9943 0.571805
\(441\) 38.5449 1.83547
\(442\) −0.611963 −0.0291081
\(443\) −2.68647 −0.127638 −0.0638191 0.997961i \(-0.520328\pi\)
−0.0638191 + 0.997961i \(0.520328\pi\)
\(444\) −79.0352 −3.75085
\(445\) −36.7570 −1.74245
\(446\) −59.4514 −2.81511
\(447\) 9.84402 0.465606
\(448\) 54.6300 2.58103
\(449\) 12.7497 0.601697 0.300848 0.953672i \(-0.402730\pi\)
0.300848 + 0.953672i \(0.402730\pi\)
\(450\) −86.0912 −4.05838
\(451\) −7.37283 −0.347173
\(452\) 65.7357 3.09195
\(453\) −22.9355 −1.07760
\(454\) 4.50491 0.211426
\(455\) −4.07043 −0.190825
\(456\) −12.7951 −0.599186
\(457\) 26.6427 1.24629 0.623147 0.782105i \(-0.285854\pi\)
0.623147 + 0.782105i \(0.285854\pi\)
\(458\) −45.6171 −2.13155
\(459\) 1.24318 0.0580266
\(460\) −51.0724 −2.38127
\(461\) −38.1924 −1.77880 −0.889400 0.457131i \(-0.848877\pi\)
−0.889400 + 0.457131i \(0.848877\pi\)
\(462\) −24.9442 −1.16051
\(463\) 10.6895 0.496784 0.248392 0.968660i \(-0.420098\pi\)
0.248392 + 0.968660i \(0.420098\pi\)
\(464\) −0.656971 −0.0304991
\(465\) 98.9169 4.58716
\(466\) −39.0983 −1.81119
\(467\) −7.36289 −0.340714 −0.170357 0.985382i \(-0.554492\pi\)
−0.170357 + 0.985382i \(0.554492\pi\)
\(468\) 2.72758 0.126082
\(469\) 26.7244 1.23402
\(470\) −94.7748 −4.37164
\(471\) 38.7601 1.78597
\(472\) −13.5597 −0.624135
\(473\) −9.44813 −0.434425
\(474\) 96.7719 4.44488
\(475\) 18.1724 0.833805
\(476\) −15.6422 −0.716958
\(477\) 41.4158 1.89630
\(478\) −27.5677 −1.26092
\(479\) 32.8567 1.50126 0.750631 0.660722i \(-0.229750\pi\)
0.750631 + 0.660722i \(0.229750\pi\)
\(480\) 53.3362 2.43445
\(481\) −2.25593 −0.102862
\(482\) −47.2648 −2.15285
\(483\) 41.9864 1.91045
\(484\) 3.30742 0.150337
\(485\) −63.6217 −2.88891
\(486\) 51.4832 2.33532
\(487\) 2.62659 0.119022 0.0595112 0.998228i \(-0.481046\pi\)
0.0595112 + 0.998228i \(0.481046\pi\)
\(488\) 8.10813 0.367038
\(489\) 55.1523 2.49407
\(490\) −102.740 −4.64130
\(491\) 13.8747 0.626158 0.313079 0.949727i \(-0.398640\pi\)
0.313079 + 0.949727i \(0.398640\pi\)
\(492\) 61.8910 2.79026
\(493\) −2.24663 −0.101183
\(494\) −0.923898 −0.0415681
\(495\) −13.7058 −0.616031
\(496\) 3.17284 0.142465
\(497\) −36.5196 −1.63813
\(498\) 3.88424 0.174057
\(499\) 5.30974 0.237697 0.118848 0.992912i \(-0.462080\pi\)
0.118848 + 0.992912i \(0.462080\pi\)
\(500\) 77.1466 3.45010
\(501\) 30.1901 1.34879
\(502\) −40.6340 −1.81359
\(503\) −18.1124 −0.807593 −0.403797 0.914849i \(-0.632310\pi\)
−0.403797 + 0.914849i \(0.632310\pi\)
\(504\) 44.2251 1.96994
\(505\) −65.9201 −2.93341
\(506\) −8.93351 −0.397143
\(507\) −32.8492 −1.45889
\(508\) 51.0940 2.26693
\(509\) −14.9004 −0.660449 −0.330225 0.943902i \(-0.607125\pi\)
−0.330225 + 0.943902i \(0.607125\pi\)
\(510\) −25.8135 −1.14304
\(511\) 31.9183 1.41198
\(512\) 3.66373 0.161916
\(513\) 1.87686 0.0828655
\(514\) −4.34405 −0.191608
\(515\) 52.7049 2.32245
\(516\) 79.3121 3.49152
\(517\) −10.3308 −0.454348
\(518\) −92.5321 −4.06563
\(519\) 22.3244 0.979930
\(520\) −2.87391 −0.126029
\(521\) 4.83008 0.211610 0.105805 0.994387i \(-0.466258\pi\)
0.105805 + 0.994387i \(0.466258\pi\)
\(522\) 16.0686 0.703302
\(523\) −21.5141 −0.940747 −0.470373 0.882467i \(-0.655881\pi\)
−0.470373 + 0.882467i \(0.655881\pi\)
\(524\) 47.2789 2.06539
\(525\) −117.559 −5.13071
\(526\) −33.4061 −1.45658
\(527\) 10.8501 0.472637
\(528\) −0.822818 −0.0358086
\(529\) −7.96302 −0.346218
\(530\) −110.392 −4.79512
\(531\) 15.4946 0.672408
\(532\) −23.6154 −1.02386
\(533\) 1.76658 0.0765191
\(534\) 53.9721 2.33560
\(535\) 57.9155 2.50391
\(536\) 18.8687 0.815002
\(537\) −48.8235 −2.10689
\(538\) −57.9074 −2.49657
\(539\) −11.1990 −0.482375
\(540\) 14.7692 0.635564
\(541\) −1.61904 −0.0696081 −0.0348040 0.999394i \(-0.511081\pi\)
−0.0348040 + 0.999394i \(0.511081\pi\)
\(542\) −41.6281 −1.78808
\(543\) −24.2561 −1.04093
\(544\) 5.85039 0.250833
\(545\) 53.4820 2.29092
\(546\) 5.97681 0.255784
\(547\) 1.00000 0.0427569
\(548\) −36.0409 −1.53959
\(549\) −9.26514 −0.395426
\(550\) 25.0133 1.06657
\(551\) −3.39180 −0.144495
\(552\) 29.6443 1.26175
\(553\) 70.6036 3.00237
\(554\) 16.1752 0.687217
\(555\) −95.1587 −4.03926
\(556\) −17.3061 −0.733941
\(557\) −15.9533 −0.675962 −0.337981 0.941153i \(-0.609744\pi\)
−0.337981 + 0.941153i \(0.609744\pi\)
\(558\) −77.6031 −3.28520
\(559\) 2.26384 0.0957501
\(560\) −5.50732 −0.232727
\(561\) −2.81377 −0.118797
\(562\) 29.9689 1.26416
\(563\) −5.52511 −0.232856 −0.116428 0.993199i \(-0.537144\pi\)
−0.116428 + 0.993199i \(0.537144\pi\)
\(564\) 86.7217 3.65164
\(565\) 79.1460 3.32970
\(566\) −33.0383 −1.38870
\(567\) 31.9071 1.33997
\(568\) −25.7846 −1.08190
\(569\) 30.1646 1.26456 0.632282 0.774738i \(-0.282118\pi\)
0.632282 + 0.774738i \(0.282118\pi\)
\(570\) −38.9714 −1.63233
\(571\) −39.3044 −1.64484 −0.822418 0.568884i \(-0.807376\pi\)
−0.822418 + 0.568884i \(0.807376\pi\)
\(572\) −0.792481 −0.0331353
\(573\) −5.91347 −0.247039
\(574\) 72.4602 3.02443
\(575\) −42.1026 −1.75580
\(576\) −44.0754 −1.83647
\(577\) 20.9956 0.874058 0.437029 0.899447i \(-0.356031\pi\)
0.437029 + 0.899447i \(0.356031\pi\)
\(578\) 36.3329 1.51125
\(579\) 14.6595 0.609228
\(580\) −26.6903 −1.10825
\(581\) 2.83390 0.117570
\(582\) 93.4187 3.87233
\(583\) −12.0331 −0.498361
\(584\) 22.5358 0.932537
\(585\) 3.28401 0.135777
\(586\) −14.5214 −0.599872
\(587\) 0.0321604 0.00132740 0.000663701 1.00000i \(-0.499789\pi\)
0.000663701 1.00000i \(0.499789\pi\)
\(588\) 94.0098 3.87690
\(589\) 16.3807 0.674954
\(590\) −41.3001 −1.70030
\(591\) −49.4050 −2.03225
\(592\) −3.05229 −0.125449
\(593\) −12.0995 −0.496865 −0.248433 0.968649i \(-0.579915\pi\)
−0.248433 + 0.968649i \(0.579915\pi\)
\(594\) 2.58340 0.105998
\(595\) −18.8332 −0.772087
\(596\) 12.8280 0.525453
\(597\) −44.5776 −1.82444
\(598\) 2.14053 0.0875328
\(599\) 5.95315 0.243239 0.121620 0.992577i \(-0.461191\pi\)
0.121620 + 0.992577i \(0.461191\pi\)
\(600\) −83.0023 −3.38855
\(601\) −24.9138 −1.01626 −0.508128 0.861281i \(-0.669662\pi\)
−0.508128 + 0.861281i \(0.669662\pi\)
\(602\) 92.8563 3.78454
\(603\) −21.5612 −0.878038
\(604\) −29.8878 −1.21612
\(605\) 3.98214 0.161897
\(606\) 96.7937 3.93198
\(607\) −44.4229 −1.80307 −0.901535 0.432706i \(-0.857559\pi\)
−0.901535 + 0.432706i \(0.857559\pi\)
\(608\) 8.83250 0.358205
\(609\) 21.9419 0.889132
\(610\) 24.6958 0.999902
\(611\) 2.47533 0.100141
\(612\) 12.6201 0.510136
\(613\) −35.1906 −1.42133 −0.710667 0.703529i \(-0.751607\pi\)
−0.710667 + 0.703529i \(0.751607\pi\)
\(614\) 7.60287 0.306827
\(615\) 74.5170 3.00481
\(616\) −12.8493 −0.517715
\(617\) −19.4229 −0.781936 −0.390968 0.920404i \(-0.627860\pi\)
−0.390968 + 0.920404i \(0.627860\pi\)
\(618\) −77.3891 −3.11305
\(619\) −38.8990 −1.56348 −0.781741 0.623603i \(-0.785668\pi\)
−0.781741 + 0.623603i \(0.785668\pi\)
\(620\) 128.901 5.17678
\(621\) −4.34840 −0.174495
\(622\) 31.7381 1.27258
\(623\) 39.3774 1.57762
\(624\) 0.197153 0.00789243
\(625\) 38.5973 1.54389
\(626\) 29.5298 1.18025
\(627\) −4.24802 −0.169650
\(628\) 50.5092 2.01554
\(629\) −10.4378 −0.416184
\(630\) 134.701 5.36661
\(631\) 20.4180 0.812829 0.406414 0.913689i \(-0.366779\pi\)
0.406414 + 0.913689i \(0.366779\pi\)
\(632\) 49.8494 1.98290
\(633\) −10.3233 −0.410313
\(634\) 39.8769 1.58372
\(635\) 61.5174 2.44124
\(636\) 101.012 4.00538
\(637\) 2.68336 0.106319
\(638\) −4.66862 −0.184833
\(639\) 29.4639 1.16558
\(640\) 75.4518 2.98249
\(641\) 30.2787 1.19594 0.597969 0.801519i \(-0.295974\pi\)
0.597969 + 0.801519i \(0.295974\pi\)
\(642\) −85.0401 −3.35627
\(643\) 27.9713 1.10308 0.551540 0.834148i \(-0.314040\pi\)
0.551540 + 0.834148i \(0.314040\pi\)
\(644\) 54.7134 2.15601
\(645\) 95.4920 3.75999
\(646\) −4.27473 −0.168187
\(647\) −24.2473 −0.953261 −0.476630 0.879104i \(-0.658142\pi\)
−0.476630 + 0.879104i \(0.658142\pi\)
\(648\) 22.5279 0.884978
\(649\) −4.50186 −0.176714
\(650\) −5.99335 −0.235079
\(651\) −105.969 −4.15324
\(652\) 71.8702 2.81465
\(653\) −25.5506 −0.999871 −0.499935 0.866063i \(-0.666643\pi\)
−0.499935 + 0.866063i \(0.666643\pi\)
\(654\) −78.5302 −3.07077
\(655\) 56.9239 2.22420
\(656\) 2.39020 0.0933215
\(657\) −25.7516 −1.00466
\(658\) 101.531 3.95810
\(659\) −13.0434 −0.508097 −0.254049 0.967191i \(-0.581762\pi\)
−0.254049 + 0.967191i \(0.581762\pi\)
\(660\) −33.4280 −1.30118
\(661\) 13.0702 0.508373 0.254186 0.967155i \(-0.418192\pi\)
0.254186 + 0.967155i \(0.418192\pi\)
\(662\) −2.71111 −0.105370
\(663\) 0.674198 0.0261837
\(664\) 2.00086 0.0776485
\(665\) −28.4331 −1.10259
\(666\) 74.6547 2.89281
\(667\) 7.85828 0.304274
\(668\) 39.3413 1.52216
\(669\) 65.4975 2.53228
\(670\) 57.4702 2.22027
\(671\) 2.69193 0.103921
\(672\) −57.1385 −2.20417
\(673\) 0.853595 0.0329037 0.0164518 0.999865i \(-0.494763\pi\)
0.0164518 + 0.999865i \(0.494763\pi\)
\(674\) −54.6528 −2.10515
\(675\) 12.1753 0.468626
\(676\) −42.8066 −1.64641
\(677\) −30.8462 −1.18552 −0.592759 0.805380i \(-0.701961\pi\)
−0.592759 + 0.805380i \(0.701961\pi\)
\(678\) −116.214 −4.46317
\(679\) 68.1572 2.61563
\(680\) −13.2971 −0.509922
\(681\) −4.96305 −0.190185
\(682\) 22.5471 0.863374
\(683\) −0.692076 −0.0264815 −0.0132408 0.999912i \(-0.504215\pi\)
−0.0132408 + 0.999912i \(0.504215\pi\)
\(684\) 19.0529 0.728504
\(685\) −43.3934 −1.65798
\(686\) 41.2678 1.57561
\(687\) 50.2562 1.91739
\(688\) 3.06299 0.116775
\(689\) 2.88322 0.109842
\(690\) 90.2908 3.43731
\(691\) 40.9031 1.55603 0.778014 0.628247i \(-0.216227\pi\)
0.778014 + 0.628247i \(0.216227\pi\)
\(692\) 29.0914 1.10589
\(693\) 14.6829 0.557757
\(694\) 64.3566 2.44294
\(695\) −20.8366 −0.790376
\(696\) 15.4920 0.587224
\(697\) 8.17369 0.309600
\(698\) −45.7272 −1.73080
\(699\) 43.0745 1.62923
\(700\) −153.194 −5.79019
\(701\) 23.4308 0.884969 0.442485 0.896776i \(-0.354097\pi\)
0.442485 + 0.896776i \(0.354097\pi\)
\(702\) −0.619000 −0.0233626
\(703\) −15.7583 −0.594336
\(704\) 12.8058 0.482638
\(705\) 104.413 3.93243
\(706\) −0.513239 −0.0193160
\(707\) 70.6196 2.65592
\(708\) 37.7908 1.42026
\(709\) 4.87997 0.183271 0.0916356 0.995793i \(-0.470791\pi\)
0.0916356 + 0.995793i \(0.470791\pi\)
\(710\) −78.5346 −2.94735
\(711\) −56.9628 −2.13627
\(712\) 27.8023 1.04193
\(713\) −37.9516 −1.42130
\(714\) 27.6537 1.03492
\(715\) −0.954149 −0.0356832
\(716\) −63.6230 −2.37770
\(717\) 30.3713 1.13424
\(718\) 21.5555 0.804443
\(719\) −51.5845 −1.92378 −0.961889 0.273442i \(-0.911838\pi\)
−0.961889 + 0.273442i \(0.911838\pi\)
\(720\) 4.44329 0.165592
\(721\) −56.4622 −2.10276
\(722\) 37.3182 1.38884
\(723\) 52.0715 1.93656
\(724\) −31.6087 −1.17473
\(725\) −22.0027 −0.817159
\(726\) −5.84717 −0.217009
\(727\) 29.3422 1.08824 0.544120 0.839007i \(-0.316863\pi\)
0.544120 + 0.839007i \(0.316863\pi\)
\(728\) 3.07879 0.114108
\(729\) −34.2809 −1.26966
\(730\) 68.6395 2.54046
\(731\) 10.4744 0.387410
\(732\) −22.5973 −0.835222
\(733\) 23.5474 0.869742 0.434871 0.900493i \(-0.356794\pi\)
0.434871 + 0.900493i \(0.356794\pi\)
\(734\) −20.3333 −0.750517
\(735\) 113.188 4.17500
\(736\) −20.4636 −0.754297
\(737\) 6.26446 0.230754
\(738\) −58.4607 −2.15197
\(739\) −8.33389 −0.306567 −0.153284 0.988182i \(-0.548985\pi\)
−0.153284 + 0.988182i \(0.548985\pi\)
\(740\) −124.003 −4.55845
\(741\) 1.01786 0.0373919
\(742\) 118.262 4.34152
\(743\) −24.2424 −0.889369 −0.444684 0.895687i \(-0.646684\pi\)
−0.444684 + 0.895687i \(0.646684\pi\)
\(744\) −74.8188 −2.74299
\(745\) 15.4449 0.565857
\(746\) −31.6034 −1.15708
\(747\) −2.28638 −0.0836542
\(748\) −3.66668 −0.134067
\(749\) −62.0443 −2.26705
\(750\) −136.387 −4.98015
\(751\) 8.55298 0.312103 0.156051 0.987749i \(-0.450123\pi\)
0.156051 + 0.987749i \(0.450123\pi\)
\(752\) 3.34914 0.122131
\(753\) 44.7664 1.63138
\(754\) 1.11863 0.0407383
\(755\) −35.9850 −1.30963
\(756\) −15.8220 −0.575442
\(757\) −25.0608 −0.910852 −0.455426 0.890274i \(-0.650513\pi\)
−0.455426 + 0.890274i \(0.650513\pi\)
\(758\) 65.4362 2.37675
\(759\) 9.84203 0.357243
\(760\) −20.0751 −0.728199
\(761\) 8.47099 0.307073 0.153537 0.988143i \(-0.450934\pi\)
0.153537 + 0.988143i \(0.450934\pi\)
\(762\) −90.3289 −3.27227
\(763\) −57.2947 −2.07421
\(764\) −7.70598 −0.278793
\(765\) 15.1946 0.549362
\(766\) −16.2825 −0.588310
\(767\) 1.07868 0.0389488
\(768\) −45.7852 −1.65213
\(769\) −40.0278 −1.44344 −0.721720 0.692185i \(-0.756648\pi\)
−0.721720 + 0.692185i \(0.756648\pi\)
\(770\) −39.1365 −1.41038
\(771\) 4.78583 0.172357
\(772\) 19.1031 0.687536
\(773\) −50.1623 −1.80421 −0.902106 0.431514i \(-0.857980\pi\)
−0.902106 + 0.431514i \(0.857980\pi\)
\(774\) −74.9162 −2.69281
\(775\) 106.262 3.81704
\(776\) 48.1222 1.72748
\(777\) 101.942 3.65717
\(778\) −54.0993 −1.93955
\(779\) 12.3400 0.442128
\(780\) 8.00959 0.286789
\(781\) −8.56057 −0.306321
\(782\) 9.90390 0.354163
\(783\) −2.27246 −0.0812111
\(784\) 3.63060 0.129664
\(785\) 60.8132 2.17052
\(786\) −83.5841 −2.98135
\(787\) 52.3215 1.86506 0.932530 0.361092i \(-0.117596\pi\)
0.932530 + 0.361092i \(0.117596\pi\)
\(788\) −64.3808 −2.29347
\(789\) 36.8034 1.31024
\(790\) 151.831 5.40192
\(791\) −84.7883 −3.01472
\(792\) 10.3668 0.368369
\(793\) −0.645005 −0.0229048
\(794\) −3.39701 −0.120555
\(795\) 121.619 4.31336
\(796\) −58.0900 −2.05895
\(797\) −26.2201 −0.928762 −0.464381 0.885635i \(-0.653723\pi\)
−0.464381 + 0.885635i \(0.653723\pi\)
\(798\) 41.7496 1.47792
\(799\) 11.4530 0.405177
\(800\) 57.2967 2.02574
\(801\) −31.7696 −1.12252
\(802\) 33.5172 1.18353
\(803\) 7.48196 0.264033
\(804\) −52.5869 −1.85460
\(805\) 65.8751 2.32179
\(806\) −5.40245 −0.190293
\(807\) 63.7965 2.24574
\(808\) 49.8607 1.75409
\(809\) −14.7187 −0.517483 −0.258742 0.965947i \(-0.583308\pi\)
−0.258742 + 0.965947i \(0.583308\pi\)
\(810\) 68.6154 2.41090
\(811\) −4.44788 −0.156186 −0.0780931 0.996946i \(-0.524883\pi\)
−0.0780931 + 0.996946i \(0.524883\pi\)
\(812\) 28.5930 1.00342
\(813\) 45.8616 1.60844
\(814\) −21.6905 −0.760250
\(815\) 86.5319 3.03108
\(816\) 0.912195 0.0319332
\(817\) 15.8135 0.553245
\(818\) 43.7848 1.53090
\(819\) −3.51812 −0.122933
\(820\) 97.1047 3.39104
\(821\) −30.8260 −1.07583 −0.537917 0.842998i \(-0.680789\pi\)
−0.537917 + 0.842998i \(0.680789\pi\)
\(822\) 63.7166 2.22237
\(823\) −10.3276 −0.359999 −0.179999 0.983667i \(-0.557610\pi\)
−0.179999 + 0.983667i \(0.557610\pi\)
\(824\) −39.8649 −1.38876
\(825\) −27.5571 −0.959414
\(826\) 44.2443 1.53946
\(827\) 13.6156 0.473460 0.236730 0.971576i \(-0.423924\pi\)
0.236730 + 0.971576i \(0.423924\pi\)
\(828\) −44.1426 −1.53406
\(829\) 35.6558 1.23838 0.619189 0.785242i \(-0.287462\pi\)
0.619189 + 0.785242i \(0.287462\pi\)
\(830\) 6.09423 0.211534
\(831\) −17.8201 −0.618174
\(832\) −3.06837 −0.106376
\(833\) 12.4155 0.430171
\(834\) 30.5953 1.05943
\(835\) 47.3671 1.63921
\(836\) −5.53569 −0.191456
\(837\) 10.9749 0.379347
\(838\) 69.3898 2.39703
\(839\) 16.5368 0.570914 0.285457 0.958392i \(-0.407855\pi\)
0.285457 + 0.958392i \(0.407855\pi\)
\(840\) 129.868 4.48087
\(841\) −24.8933 −0.858389
\(842\) 34.2785 1.18132
\(843\) −33.0167 −1.13715
\(844\) −13.4525 −0.463053
\(845\) −51.5393 −1.77300
\(846\) −81.9151 −2.81630
\(847\) −4.26603 −0.146582
\(848\) 3.90102 0.133961
\(849\) 36.3982 1.24918
\(850\) −27.7303 −0.951141
\(851\) 36.5096 1.25153
\(852\) 71.8615 2.46193
\(853\) 54.0237 1.84974 0.924868 0.380289i \(-0.124176\pi\)
0.924868 + 0.380289i \(0.124176\pi\)
\(854\) −26.4563 −0.905316
\(855\) 22.9397 0.784521
\(856\) −43.8061 −1.49726
\(857\) −20.3714 −0.695873 −0.347936 0.937518i \(-0.613118\pi\)
−0.347936 + 0.937518i \(0.613118\pi\)
\(858\) 1.40102 0.0478301
\(859\) 20.8255 0.710558 0.355279 0.934760i \(-0.384386\pi\)
0.355279 + 0.934760i \(0.384386\pi\)
\(860\) 124.438 4.24329
\(861\) −79.8292 −2.72057
\(862\) −38.5101 −1.31166
\(863\) 4.32385 0.147186 0.0735928 0.997288i \(-0.476553\pi\)
0.0735928 + 0.997288i \(0.476553\pi\)
\(864\) 5.91766 0.201323
\(865\) 35.0261 1.19092
\(866\) 48.5013 1.64814
\(867\) −40.0278 −1.35942
\(868\) −138.090 −4.68708
\(869\) 16.5502 0.561427
\(870\) 47.1857 1.59974
\(871\) −1.50101 −0.0508597
\(872\) −40.4527 −1.36990
\(873\) −54.9890 −1.86110
\(874\) 14.9522 0.505765
\(875\) −99.5064 −3.36393
\(876\) −62.8071 −2.12206
\(877\) 3.44140 0.116208 0.0581038 0.998311i \(-0.481495\pi\)
0.0581038 + 0.998311i \(0.481495\pi\)
\(878\) −41.7118 −1.40770
\(879\) 15.9981 0.539604
\(880\) −1.29097 −0.0435186
\(881\) −28.9444 −0.975162 −0.487581 0.873078i \(-0.662121\pi\)
−0.487581 + 0.873078i \(0.662121\pi\)
\(882\) −88.7992 −2.99003
\(883\) −32.6872 −1.10001 −0.550006 0.835161i \(-0.685375\pi\)
−0.550006 + 0.835161i \(0.685375\pi\)
\(884\) 0.878563 0.0295493
\(885\) 45.5002 1.52947
\(886\) 6.18905 0.207925
\(887\) 40.4964 1.35974 0.679868 0.733334i \(-0.262037\pi\)
0.679868 + 0.733334i \(0.262037\pi\)
\(888\) 71.9761 2.41536
\(889\) −65.9029 −2.21031
\(890\) 84.6802 2.83849
\(891\) 7.47934 0.250567
\(892\) 85.3513 2.85777
\(893\) 17.2909 0.578617
\(894\) −22.6785 −0.758482
\(895\) −76.6022 −2.56053
\(896\) −80.8307 −2.70036
\(897\) −2.35822 −0.0787386
\(898\) −29.3726 −0.980177
\(899\) −19.8334 −0.661480
\(900\) 123.597 4.11988
\(901\) 13.3402 0.444427
\(902\) 16.9854 0.565552
\(903\) −102.300 −3.40432
\(904\) −59.8645 −1.99106
\(905\) −38.0570 −1.26506
\(906\) 52.8385 1.75544
\(907\) −0.0280674 −0.000931963 0 −0.000465982 1.00000i \(-0.500148\pi\)
−0.000465982 1.00000i \(0.500148\pi\)
\(908\) −6.46746 −0.214630
\(909\) −56.9757 −1.88976
\(910\) 9.37739 0.310857
\(911\) −30.2306 −1.00158 −0.500792 0.865568i \(-0.666958\pi\)
−0.500792 + 0.865568i \(0.666958\pi\)
\(912\) 1.37717 0.0456025
\(913\) 0.664294 0.0219849
\(914\) −61.3791 −2.03024
\(915\) −27.2073 −0.899445
\(916\) 65.4900 2.16385
\(917\) −60.9820 −2.01380
\(918\) −2.86402 −0.0945266
\(919\) 41.4350 1.36682 0.683408 0.730037i \(-0.260497\pi\)
0.683408 + 0.730037i \(0.260497\pi\)
\(920\) 46.5109 1.53342
\(921\) −8.37606 −0.276001
\(922\) 87.9871 2.89770
\(923\) 2.05117 0.0675151
\(924\) 35.8111 1.17810
\(925\) −102.225 −3.36113
\(926\) −24.6264 −0.809272
\(927\) 45.5535 1.49617
\(928\) −10.6942 −0.351054
\(929\) −30.6298 −1.00493 −0.502466 0.864597i \(-0.667574\pi\)
−0.502466 + 0.864597i \(0.667574\pi\)
\(930\) −227.883 −7.47259
\(931\) 18.7440 0.614309
\(932\) 56.1314 1.83864
\(933\) −34.9658 −1.14473
\(934\) 16.9625 0.555030
\(935\) −4.41470 −0.144376
\(936\) −2.48396 −0.0811908
\(937\) −7.37277 −0.240858 −0.120429 0.992722i \(-0.538427\pi\)
−0.120429 + 0.992722i \(0.538427\pi\)
\(938\) −61.5672 −2.01024
\(939\) −32.5329 −1.06167
\(940\) 136.063 4.43789
\(941\) 9.42733 0.307322 0.153661 0.988124i \(-0.450894\pi\)
0.153661 + 0.988124i \(0.450894\pi\)
\(942\) −89.2949 −2.90939
\(943\) −28.5900 −0.931019
\(944\) 1.45946 0.0475013
\(945\) −19.0498 −0.619690
\(946\) 21.7664 0.707688
\(947\) −18.0487 −0.586505 −0.293253 0.956035i \(-0.594738\pi\)
−0.293253 + 0.956035i \(0.594738\pi\)
\(948\) −138.930 −4.51224
\(949\) −1.79273 −0.0581944
\(950\) −41.8652 −1.35829
\(951\) −43.9323 −1.42460
\(952\) 14.2451 0.461686
\(953\) −19.6596 −0.636838 −0.318419 0.947950i \(-0.603152\pi\)
−0.318419 + 0.947950i \(0.603152\pi\)
\(954\) −95.4132 −3.08912
\(955\) −9.27802 −0.300230
\(956\) 39.5776 1.28003
\(957\) 5.14341 0.166263
\(958\) −75.6947 −2.44559
\(959\) 46.4869 1.50114
\(960\) −129.428 −4.17728
\(961\) 64.7853 2.08985
\(962\) 5.19718 0.167564
\(963\) 50.0571 1.61307
\(964\) 67.8555 2.18548
\(965\) 23.0002 0.740402
\(966\) −96.7275 −3.11216
\(967\) −28.4547 −0.915041 −0.457520 0.889199i \(-0.651262\pi\)
−0.457520 + 0.889199i \(0.651262\pi\)
\(968\) −3.01201 −0.0968098
\(969\) 4.70946 0.151290
\(970\) 146.571 4.70610
\(971\) 53.1850 1.70679 0.853394 0.521267i \(-0.174540\pi\)
0.853394 + 0.521267i \(0.174540\pi\)
\(972\) −73.9117 −2.37072
\(973\) 22.3220 0.715610
\(974\) −6.05111 −0.193890
\(975\) 6.60286 0.211461
\(976\) −0.872696 −0.0279343
\(977\) 16.5598 0.529794 0.264897 0.964277i \(-0.414662\pi\)
0.264897 + 0.964277i \(0.414662\pi\)
\(978\) −127.059 −4.06290
\(979\) 9.23046 0.295007
\(980\) 147.498 4.71165
\(981\) 46.2252 1.47586
\(982\) −31.9644 −1.02002
\(983\) 26.1604 0.834386 0.417193 0.908818i \(-0.363014\pi\)
0.417193 + 0.908818i \(0.363014\pi\)
\(984\) −56.3632 −1.79679
\(985\) −77.5147 −2.46982
\(986\) 5.17574 0.164829
\(987\) −111.857 −3.56044
\(988\) 1.32639 0.0421981
\(989\) −36.6375 −1.16501
\(990\) 31.5753 1.00353
\(991\) 32.8391 1.04317 0.521584 0.853200i \(-0.325341\pi\)
0.521584 + 0.853200i \(0.325341\pi\)
\(992\) 51.6476 1.63981
\(993\) 2.98683 0.0947841
\(994\) 84.1333 2.66855
\(995\) −69.9406 −2.21727
\(996\) −5.57640 −0.176695
\(997\) −35.0668 −1.11058 −0.555289 0.831657i \(-0.687392\pi\)
−0.555289 + 0.831657i \(0.687392\pi\)
\(998\) −12.2325 −0.387213
\(999\) −10.5579 −0.334036
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 6017.2.a.f.1.14 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.14 121 1.1 even 1 trivial