Properties

Label 4033.2.a.f.1.19
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +O(q^{10})\) \(q-1.67574 q^{2} +1.31893 q^{3} +0.808091 q^{4} -4.46158 q^{5} -2.21019 q^{6} +0.153470 q^{7} +1.99732 q^{8} -1.26041 q^{9} +7.47643 q^{10} -2.02860 q^{11} +1.06582 q^{12} -0.641377 q^{13} -0.257174 q^{14} -5.88453 q^{15} -4.96317 q^{16} +4.82713 q^{17} +2.11212 q^{18} -5.72216 q^{19} -3.60536 q^{20} +0.202416 q^{21} +3.39940 q^{22} -7.85045 q^{23} +2.63434 q^{24} +14.9057 q^{25} +1.07478 q^{26} -5.61920 q^{27} +0.124017 q^{28} +3.40426 q^{29} +9.86092 q^{30} -9.46396 q^{31} +4.32231 q^{32} -2.67559 q^{33} -8.08899 q^{34} -0.684717 q^{35} -1.01853 q^{36} +1.00000 q^{37} +9.58884 q^{38} -0.845934 q^{39} -8.91123 q^{40} -6.28903 q^{41} -0.339196 q^{42} -4.53674 q^{43} -1.63929 q^{44} +5.62343 q^{45} +13.1553 q^{46} +6.13454 q^{47} -6.54610 q^{48} -6.97645 q^{49} -24.9780 q^{50} +6.36666 q^{51} -0.518291 q^{52} +1.29314 q^{53} +9.41630 q^{54} +9.05076 q^{55} +0.306529 q^{56} -7.54716 q^{57} -5.70464 q^{58} -2.52877 q^{59} -4.75524 q^{60} -7.78879 q^{61} +15.8591 q^{62} -0.193435 q^{63} +2.68328 q^{64} +2.86156 q^{65} +4.48358 q^{66} -5.17506 q^{67} +3.90076 q^{68} -10.3542 q^{69} +1.14740 q^{70} +6.99021 q^{71} -2.51745 q^{72} -3.90986 q^{73} -1.67574 q^{74} +19.6596 q^{75} -4.62403 q^{76} -0.311328 q^{77} +1.41756 q^{78} +2.27090 q^{79} +22.1436 q^{80} -3.63012 q^{81} +10.5388 q^{82} +1.48552 q^{83} +0.163571 q^{84} -21.5366 q^{85} +7.60239 q^{86} +4.48999 q^{87} -4.05177 q^{88} +16.3116 q^{89} -9.42339 q^{90} -0.0984319 q^{91} -6.34388 q^{92} -12.4823 q^{93} -10.2799 q^{94} +25.5299 q^{95} +5.70085 q^{96} -13.6877 q^{97} +11.6907 q^{98} +2.55687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67574 −1.18492 −0.592462 0.805598i \(-0.701844\pi\)
−0.592462 + 0.805598i \(0.701844\pi\)
\(3\) 1.31893 0.761487 0.380744 0.924681i \(-0.375668\pi\)
0.380744 + 0.924681i \(0.375668\pi\)
\(4\) 0.808091 0.404046
\(5\) −4.46158 −1.99528 −0.997640 0.0686650i \(-0.978126\pi\)
−0.997640 + 0.0686650i \(0.978126\pi\)
\(6\) −2.21019 −0.902305
\(7\) 0.153470 0.0580060 0.0290030 0.999579i \(-0.490767\pi\)
0.0290030 + 0.999579i \(0.490767\pi\)
\(8\) 1.99732 0.706161
\(9\) −1.26041 −0.420137
\(10\) 7.47643 2.36426
\(11\) −2.02860 −0.611646 −0.305823 0.952088i \(-0.598932\pi\)
−0.305823 + 0.952088i \(0.598932\pi\)
\(12\) 1.06582 0.307675
\(13\) −0.641377 −0.177886 −0.0889430 0.996037i \(-0.528349\pi\)
−0.0889430 + 0.996037i \(0.528349\pi\)
\(14\) −0.257174 −0.0687328
\(15\) −5.88453 −1.51938
\(16\) −4.96317 −1.24079
\(17\) 4.82713 1.17075 0.585375 0.810763i \(-0.300947\pi\)
0.585375 + 0.810763i \(0.300947\pi\)
\(18\) 2.11212 0.497831
\(19\) −5.72216 −1.31275 −0.656377 0.754433i \(-0.727912\pi\)
−0.656377 + 0.754433i \(0.727912\pi\)
\(20\) −3.60536 −0.806184
\(21\) 0.202416 0.0441709
\(22\) 3.39940 0.724754
\(23\) −7.85045 −1.63693 −0.818466 0.574555i \(-0.805175\pi\)
−0.818466 + 0.574555i \(0.805175\pi\)
\(24\) 2.63434 0.537732
\(25\) 14.9057 2.98114
\(26\) 1.07478 0.210781
\(27\) −5.61920 −1.08142
\(28\) 0.124017 0.0234371
\(29\) 3.40426 0.632155 0.316078 0.948733i \(-0.397634\pi\)
0.316078 + 0.948733i \(0.397634\pi\)
\(30\) 9.86092 1.80035
\(31\) −9.46396 −1.69978 −0.849889 0.526962i \(-0.823331\pi\)
−0.849889 + 0.526962i \(0.823331\pi\)
\(32\) 4.32231 0.764085
\(33\) −2.67559 −0.465760
\(34\) −8.08899 −1.38725
\(35\) −0.684717 −0.115738
\(36\) −1.01853 −0.169755
\(37\) 1.00000 0.164399
\(38\) 9.58884 1.55551
\(39\) −0.845934 −0.135458
\(40\) −8.91123 −1.40899
\(41\) −6.28903 −0.982182 −0.491091 0.871108i \(-0.663402\pi\)
−0.491091 + 0.871108i \(0.663402\pi\)
\(42\) −0.339196 −0.0523391
\(43\) −4.53674 −0.691847 −0.345924 0.938263i \(-0.612434\pi\)
−0.345924 + 0.938263i \(0.612434\pi\)
\(44\) −1.63929 −0.247133
\(45\) 5.62343 0.838292
\(46\) 13.1553 1.93964
\(47\) 6.13454 0.894814 0.447407 0.894330i \(-0.352348\pi\)
0.447407 + 0.894330i \(0.352348\pi\)
\(48\) −6.54610 −0.944848
\(49\) −6.97645 −0.996635
\(50\) −24.9780 −3.53243
\(51\) 6.36666 0.891511
\(52\) −0.518291 −0.0718740
\(53\) 1.29314 0.177626 0.0888130 0.996048i \(-0.471693\pi\)
0.0888130 + 0.996048i \(0.471693\pi\)
\(54\) 9.41630 1.28140
\(55\) 9.05076 1.22040
\(56\) 0.306529 0.0409616
\(57\) −7.54716 −0.999646
\(58\) −5.70464 −0.749056
\(59\) −2.52877 −0.329218 −0.164609 0.986359i \(-0.552636\pi\)
−0.164609 + 0.986359i \(0.552636\pi\)
\(60\) −4.75524 −0.613899
\(61\) −7.78879 −0.997253 −0.498626 0.866817i \(-0.666162\pi\)
−0.498626 + 0.866817i \(0.666162\pi\)
\(62\) 15.8591 2.01411
\(63\) −0.193435 −0.0243705
\(64\) 2.68328 0.335410
\(65\) 2.86156 0.354932
\(66\) 4.48358 0.551891
\(67\) −5.17506 −0.632234 −0.316117 0.948720i \(-0.602379\pi\)
−0.316117 + 0.948720i \(0.602379\pi\)
\(68\) 3.90076 0.473036
\(69\) −10.3542 −1.24650
\(70\) 1.14740 0.137141
\(71\) 6.99021 0.829585 0.414793 0.909916i \(-0.363854\pi\)
0.414793 + 0.909916i \(0.363854\pi\)
\(72\) −2.51745 −0.296685
\(73\) −3.90986 −0.457614 −0.228807 0.973472i \(-0.573482\pi\)
−0.228807 + 0.973472i \(0.573482\pi\)
\(74\) −1.67574 −0.194800
\(75\) 19.6596 2.27010
\(76\) −4.62403 −0.530413
\(77\) −0.311328 −0.0354791
\(78\) 1.41756 0.160507
\(79\) 2.27090 0.255496 0.127748 0.991807i \(-0.459225\pi\)
0.127748 + 0.991807i \(0.459225\pi\)
\(80\) 22.1436 2.47573
\(81\) −3.63012 −0.403347
\(82\) 10.5388 1.16381
\(83\) 1.48552 0.163057 0.0815283 0.996671i \(-0.474020\pi\)
0.0815283 + 0.996671i \(0.474020\pi\)
\(84\) 0.163571 0.0178470
\(85\) −21.5366 −2.33597
\(86\) 7.60239 0.819786
\(87\) 4.48999 0.481378
\(88\) −4.05177 −0.431920
\(89\) 16.3116 1.72903 0.864515 0.502607i \(-0.167626\pi\)
0.864515 + 0.502607i \(0.167626\pi\)
\(90\) −9.42339 −0.993312
\(91\) −0.0984319 −0.0103185
\(92\) −6.34388 −0.661395
\(93\) −12.4823 −1.29436
\(94\) −10.2799 −1.06029
\(95\) 25.5299 2.61931
\(96\) 5.70085 0.581840
\(97\) −13.6877 −1.38978 −0.694889 0.719117i \(-0.744546\pi\)
−0.694889 + 0.719117i \(0.744546\pi\)
\(98\) 11.6907 1.18094
\(99\) 2.55687 0.256975
\(100\) 12.0452 1.20452
\(101\) 0.406458 0.0404441 0.0202220 0.999796i \(-0.493563\pi\)
0.0202220 + 0.999796i \(0.493563\pi\)
\(102\) −10.6688 −1.05637
\(103\) −12.1679 −1.19894 −0.599470 0.800397i \(-0.704622\pi\)
−0.599470 + 0.800397i \(0.704622\pi\)
\(104\) −1.28104 −0.125616
\(105\) −0.903097 −0.0881332
\(106\) −2.16696 −0.210473
\(107\) −19.0438 −1.84103 −0.920516 0.390706i \(-0.872231\pi\)
−0.920516 + 0.390706i \(0.872231\pi\)
\(108\) −4.54083 −0.436941
\(109\) −1.00000 −0.0957826
\(110\) −15.1667 −1.44609
\(111\) 1.31893 0.125188
\(112\) −0.761696 −0.0719735
\(113\) −10.5792 −0.995203 −0.497602 0.867406i \(-0.665786\pi\)
−0.497602 + 0.867406i \(0.665786\pi\)
\(114\) 12.6470 1.18450
\(115\) 35.0254 3.26614
\(116\) 2.75095 0.255419
\(117\) 0.808400 0.0747366
\(118\) 4.23756 0.390099
\(119\) 0.740817 0.0679106
\(120\) −11.7533 −1.07293
\(121\) −6.88479 −0.625890
\(122\) 13.0520 1.18167
\(123\) −8.29482 −0.747919
\(124\) −7.64774 −0.686787
\(125\) −44.1951 −3.95293
\(126\) 0.324146 0.0288772
\(127\) 4.01781 0.356523 0.178261 0.983983i \(-0.442953\pi\)
0.178261 + 0.983983i \(0.442953\pi\)
\(128\) −13.1411 −1.16152
\(129\) −5.98367 −0.526833
\(130\) −4.79521 −0.420568
\(131\) 11.8040 1.03132 0.515662 0.856792i \(-0.327546\pi\)
0.515662 + 0.856792i \(0.327546\pi\)
\(132\) −2.16212 −0.188188
\(133\) −0.878178 −0.0761477
\(134\) 8.67203 0.749150
\(135\) 25.0705 2.15773
\(136\) 9.64134 0.826738
\(137\) 6.89832 0.589363 0.294682 0.955596i \(-0.404786\pi\)
0.294682 + 0.955596i \(0.404786\pi\)
\(138\) 17.3510 1.47701
\(139\) 19.1239 1.62207 0.811033 0.585000i \(-0.198905\pi\)
0.811033 + 0.585000i \(0.198905\pi\)
\(140\) −0.553314 −0.0467635
\(141\) 8.09105 0.681389
\(142\) −11.7137 −0.982996
\(143\) 1.30110 0.108803
\(144\) 6.25564 0.521303
\(145\) −15.1884 −1.26133
\(146\) 6.55189 0.542238
\(147\) −9.20148 −0.758925
\(148\) 0.808091 0.0664247
\(149\) 5.79483 0.474731 0.237365 0.971420i \(-0.423716\pi\)
0.237365 + 0.971420i \(0.423716\pi\)
\(150\) −32.9444 −2.68990
\(151\) 10.8220 0.880680 0.440340 0.897831i \(-0.354858\pi\)
0.440340 + 0.897831i \(0.354858\pi\)
\(152\) −11.4290 −0.927016
\(153\) −6.08417 −0.491876
\(154\) 0.521704 0.0420401
\(155\) 42.2242 3.39153
\(156\) −0.683592 −0.0547312
\(157\) 8.58264 0.684969 0.342485 0.939523i \(-0.388732\pi\)
0.342485 + 0.939523i \(0.388732\pi\)
\(158\) −3.80542 −0.302743
\(159\) 1.70556 0.135260
\(160\) −19.2844 −1.52456
\(161\) −1.20481 −0.0949520
\(162\) 6.08313 0.477936
\(163\) −2.78158 −0.217870 −0.108935 0.994049i \(-0.534744\pi\)
−0.108935 + 0.994049i \(0.534744\pi\)
\(164\) −5.08211 −0.396846
\(165\) 11.9374 0.929322
\(166\) −2.48933 −0.193210
\(167\) 5.14086 0.397812 0.198906 0.980019i \(-0.436261\pi\)
0.198906 + 0.980019i \(0.436261\pi\)
\(168\) 0.404291 0.0311917
\(169\) −12.5886 −0.968357
\(170\) 36.0897 2.76795
\(171\) 7.21229 0.551537
\(172\) −3.66610 −0.279538
\(173\) 8.64474 0.657247 0.328624 0.944461i \(-0.393415\pi\)
0.328624 + 0.944461i \(0.393415\pi\)
\(174\) −7.52405 −0.570396
\(175\) 2.28757 0.172924
\(176\) 10.0683 0.758925
\(177\) −3.33529 −0.250695
\(178\) −27.3340 −2.04877
\(179\) 11.9934 0.896429 0.448215 0.893926i \(-0.352060\pi\)
0.448215 + 0.893926i \(0.352060\pi\)
\(180\) 4.54424 0.338708
\(181\) 10.1340 0.753254 0.376627 0.926365i \(-0.377084\pi\)
0.376627 + 0.926365i \(0.377084\pi\)
\(182\) 0.164946 0.0122266
\(183\) −10.2729 −0.759395
\(184\) −15.6799 −1.15594
\(185\) −4.46158 −0.328022
\(186\) 20.9171 1.53372
\(187\) −9.79230 −0.716084
\(188\) 4.95726 0.361546
\(189\) −0.862377 −0.0627287
\(190\) −42.7814 −3.10369
\(191\) 17.7409 1.28368 0.641842 0.766837i \(-0.278171\pi\)
0.641842 + 0.766837i \(0.278171\pi\)
\(192\) 3.53907 0.255411
\(193\) 8.06832 0.580771 0.290385 0.956910i \(-0.406217\pi\)
0.290385 + 0.956910i \(0.406217\pi\)
\(194\) 22.9370 1.64678
\(195\) 3.77420 0.270276
\(196\) −5.63760 −0.402686
\(197\) −4.70969 −0.335551 −0.167776 0.985825i \(-0.553658\pi\)
−0.167776 + 0.985825i \(0.553658\pi\)
\(198\) −4.28464 −0.304496
\(199\) 11.2513 0.797585 0.398793 0.917041i \(-0.369429\pi\)
0.398793 + 0.917041i \(0.369429\pi\)
\(200\) 29.7715 2.10516
\(201\) −6.82556 −0.481438
\(202\) −0.681116 −0.0479232
\(203\) 0.522450 0.0366688
\(204\) 5.14484 0.360211
\(205\) 28.0590 1.95973
\(206\) 20.3902 1.42065
\(207\) 9.89480 0.687736
\(208\) 3.18326 0.220720
\(209\) 11.6080 0.802941
\(210\) 1.51335 0.104431
\(211\) −26.9066 −1.85232 −0.926162 0.377126i \(-0.876912\pi\)
−0.926162 + 0.377126i \(0.876912\pi\)
\(212\) 1.04497 0.0717690
\(213\) 9.21963 0.631719
\(214\) 31.9123 2.18148
\(215\) 20.2411 1.38043
\(216\) −11.2234 −0.763654
\(217\) −1.45243 −0.0985974
\(218\) 1.67574 0.113495
\(219\) −5.15684 −0.348467
\(220\) 7.31384 0.493099
\(221\) −3.09601 −0.208260
\(222\) −2.21019 −0.148338
\(223\) 15.3948 1.03091 0.515457 0.856915i \(-0.327622\pi\)
0.515457 + 0.856915i \(0.327622\pi\)
\(224\) 0.663344 0.0443215
\(225\) −18.7873 −1.25249
\(226\) 17.7279 1.17924
\(227\) 3.31210 0.219832 0.109916 0.993941i \(-0.464942\pi\)
0.109916 + 0.993941i \(0.464942\pi\)
\(228\) −6.09879 −0.403902
\(229\) −15.1489 −1.00107 −0.500535 0.865717i \(-0.666863\pi\)
−0.500535 + 0.865717i \(0.666863\pi\)
\(230\) −58.6934 −3.87013
\(231\) −0.410621 −0.0270169
\(232\) 6.79941 0.446403
\(233\) 28.5028 1.86728 0.933641 0.358211i \(-0.116613\pi\)
0.933641 + 0.358211i \(0.116613\pi\)
\(234\) −1.35466 −0.0885572
\(235\) −27.3697 −1.78540
\(236\) −2.04348 −0.133019
\(237\) 2.99516 0.194557
\(238\) −1.24141 −0.0804689
\(239\) 7.32458 0.473788 0.236894 0.971536i \(-0.423871\pi\)
0.236894 + 0.971536i \(0.423871\pi\)
\(240\) 29.2059 1.88524
\(241\) 13.4407 0.865792 0.432896 0.901444i \(-0.357492\pi\)
0.432896 + 0.901444i \(0.357492\pi\)
\(242\) 11.5371 0.741632
\(243\) 12.0697 0.774273
\(244\) −6.29405 −0.402935
\(245\) 31.1260 1.98857
\(246\) 13.8999 0.886227
\(247\) 3.67007 0.233521
\(248\) −18.9026 −1.20032
\(249\) 1.95930 0.124165
\(250\) 74.0593 4.68392
\(251\) −1.47113 −0.0928566 −0.0464283 0.998922i \(-0.514784\pi\)
−0.0464283 + 0.998922i \(0.514784\pi\)
\(252\) −0.156313 −0.00984680
\(253\) 15.9254 1.00122
\(254\) −6.73278 −0.422452
\(255\) −28.4054 −1.77881
\(256\) 16.6545 1.04090
\(257\) −17.6787 −1.10277 −0.551384 0.834252i \(-0.685900\pi\)
−0.551384 + 0.834252i \(0.685900\pi\)
\(258\) 10.0270 0.624257
\(259\) 0.153470 0.00953614
\(260\) 2.31240 0.143409
\(261\) −4.29077 −0.265592
\(262\) −19.7805 −1.22204
\(263\) 10.4354 0.643473 0.321737 0.946829i \(-0.395733\pi\)
0.321737 + 0.946829i \(0.395733\pi\)
\(264\) −5.34402 −0.328902
\(265\) −5.76944 −0.354414
\(266\) 1.47159 0.0902293
\(267\) 21.5140 1.31663
\(268\) −4.18192 −0.255451
\(269\) −9.05288 −0.551964 −0.275982 0.961163i \(-0.589003\pi\)
−0.275982 + 0.961163i \(0.589003\pi\)
\(270\) −42.0116 −2.55674
\(271\) 10.8294 0.657837 0.328919 0.944358i \(-0.393316\pi\)
0.328919 + 0.944358i \(0.393316\pi\)
\(272\) −23.9578 −1.45266
\(273\) −0.129825 −0.00785738
\(274\) −11.5598 −0.698351
\(275\) −30.2377 −1.82340
\(276\) −8.36716 −0.503644
\(277\) 18.4815 1.11045 0.555223 0.831702i \(-0.312633\pi\)
0.555223 + 0.831702i \(0.312633\pi\)
\(278\) −32.0466 −1.92203
\(279\) 11.9285 0.714140
\(280\) −1.36760 −0.0817299
\(281\) 1.60098 0.0955062 0.0477531 0.998859i \(-0.484794\pi\)
0.0477531 + 0.998859i \(0.484794\pi\)
\(282\) −13.5585 −0.807395
\(283\) 17.0393 1.01288 0.506442 0.862274i \(-0.330960\pi\)
0.506442 + 0.862274i \(0.330960\pi\)
\(284\) 5.64873 0.335190
\(285\) 33.6723 1.99457
\(286\) −2.18029 −0.128924
\(287\) −0.965175 −0.0569725
\(288\) −5.44790 −0.321021
\(289\) 6.30114 0.370655
\(290\) 25.4517 1.49458
\(291\) −18.0532 −1.05830
\(292\) −3.15952 −0.184897
\(293\) 8.59821 0.502313 0.251156 0.967947i \(-0.419189\pi\)
0.251156 + 0.967947i \(0.419189\pi\)
\(294\) 15.4192 0.899269
\(295\) 11.2823 0.656882
\(296\) 1.99732 0.116092
\(297\) 11.3991 0.661443
\(298\) −9.71060 −0.562520
\(299\) 5.03510 0.291187
\(300\) 15.8868 0.917224
\(301\) −0.696252 −0.0401313
\(302\) −18.1348 −1.04354
\(303\) 0.536091 0.0307976
\(304\) 28.4001 1.62886
\(305\) 34.7503 1.98980
\(306\) 10.1955 0.582836
\(307\) −2.71832 −0.155143 −0.0775713 0.996987i \(-0.524717\pi\)
−0.0775713 + 0.996987i \(0.524717\pi\)
\(308\) −0.251582 −0.0143352
\(309\) −16.0487 −0.912978
\(310\) −70.7566 −4.01871
\(311\) −0.471741 −0.0267500 −0.0133750 0.999911i \(-0.504258\pi\)
−0.0133750 + 0.999911i \(0.504258\pi\)
\(312\) −1.68961 −0.0956551
\(313\) −7.41533 −0.419139 −0.209570 0.977794i \(-0.567206\pi\)
−0.209570 + 0.977794i \(0.567206\pi\)
\(314\) −14.3822 −0.811636
\(315\) 0.863026 0.0486260
\(316\) 1.83509 0.103232
\(317\) −32.0167 −1.79824 −0.899120 0.437703i \(-0.855792\pi\)
−0.899120 + 0.437703i \(0.855792\pi\)
\(318\) −2.85807 −0.160273
\(319\) −6.90588 −0.386655
\(320\) −11.9717 −0.669238
\(321\) −25.1175 −1.40192
\(322\) 2.01894 0.112511
\(323\) −27.6216 −1.53691
\(324\) −2.93347 −0.162971
\(325\) −9.56018 −0.530303
\(326\) 4.66119 0.258159
\(327\) −1.31893 −0.0729372
\(328\) −12.5612 −0.693578
\(329\) 0.941465 0.0519046
\(330\) −20.0039 −1.10118
\(331\) −20.8827 −1.14782 −0.573910 0.818919i \(-0.694574\pi\)
−0.573910 + 0.818919i \(0.694574\pi\)
\(332\) 1.20043 0.0658823
\(333\) −1.26041 −0.0690702
\(334\) −8.61473 −0.471377
\(335\) 23.0889 1.26148
\(336\) −1.00463 −0.0548069
\(337\) 14.3925 0.784008 0.392004 0.919964i \(-0.371782\pi\)
0.392004 + 0.919964i \(0.371782\pi\)
\(338\) 21.0952 1.14743
\(339\) −13.9532 −0.757835
\(340\) −17.4035 −0.943840
\(341\) 19.1986 1.03966
\(342\) −12.0859 −0.653530
\(343\) −2.14496 −0.115817
\(344\) −9.06135 −0.488555
\(345\) 46.1962 2.48712
\(346\) −14.4863 −0.778788
\(347\) −16.6072 −0.891519 −0.445760 0.895153i \(-0.647066\pi\)
−0.445760 + 0.895153i \(0.647066\pi\)
\(348\) 3.62832 0.194499
\(349\) −17.6196 −0.943158 −0.471579 0.881824i \(-0.656316\pi\)
−0.471579 + 0.881824i \(0.656316\pi\)
\(350\) −3.83337 −0.204902
\(351\) 3.60403 0.192369
\(352\) −8.76824 −0.467349
\(353\) −31.4761 −1.67530 −0.837652 0.546204i \(-0.816072\pi\)
−0.837652 + 0.546204i \(0.816072\pi\)
\(354\) 5.58906 0.297055
\(355\) −31.1874 −1.65525
\(356\) 13.1813 0.698607
\(357\) 0.977089 0.0517130
\(358\) −20.0978 −1.06220
\(359\) 6.20620 0.327551 0.163775 0.986498i \(-0.447633\pi\)
0.163775 + 0.986498i \(0.447633\pi\)
\(360\) 11.2318 0.591969
\(361\) 13.7432 0.723325
\(362\) −16.9819 −0.892549
\(363\) −9.08058 −0.476607
\(364\) −0.0795419 −0.00416913
\(365\) 17.4441 0.913068
\(366\) 17.2147 0.899826
\(367\) 6.05050 0.315833 0.157917 0.987452i \(-0.449522\pi\)
0.157917 + 0.987452i \(0.449522\pi\)
\(368\) 38.9631 2.03109
\(369\) 7.92677 0.412651
\(370\) 7.47643 0.388681
\(371\) 0.198457 0.0103034
\(372\) −10.0869 −0.522980
\(373\) 9.37059 0.485191 0.242595 0.970128i \(-0.422001\pi\)
0.242595 + 0.970128i \(0.422001\pi\)
\(374\) 16.4093 0.848505
\(375\) −58.2904 −3.01010
\(376\) 12.2527 0.631883
\(377\) −2.18341 −0.112452
\(378\) 1.44512 0.0743287
\(379\) 3.05433 0.156890 0.0784452 0.996918i \(-0.475004\pi\)
0.0784452 + 0.996918i \(0.475004\pi\)
\(380\) 20.6305 1.05832
\(381\) 5.29922 0.271487
\(382\) −29.7290 −1.52107
\(383\) 17.6483 0.901785 0.450893 0.892578i \(-0.351106\pi\)
0.450893 + 0.892578i \(0.351106\pi\)
\(384\) −17.3323 −0.884483
\(385\) 1.38902 0.0707908
\(386\) −13.5204 −0.688169
\(387\) 5.71817 0.290671
\(388\) −11.0609 −0.561534
\(389\) −0.0515818 −0.00261530 −0.00130765 0.999999i \(-0.500416\pi\)
−0.00130765 + 0.999999i \(0.500416\pi\)
\(390\) −6.32457 −0.320257
\(391\) −37.8951 −1.91644
\(392\) −13.9342 −0.703785
\(393\) 15.5688 0.785340
\(394\) 7.89219 0.397603
\(395\) −10.1318 −0.509786
\(396\) 2.06618 0.103830
\(397\) 7.63554 0.383217 0.191608 0.981471i \(-0.438630\pi\)
0.191608 + 0.981471i \(0.438630\pi\)
\(398\) −18.8542 −0.945078
\(399\) −1.15826 −0.0579855
\(400\) −73.9795 −3.69898
\(401\) −12.8734 −0.642868 −0.321434 0.946932i \(-0.604165\pi\)
−0.321434 + 0.946932i \(0.604165\pi\)
\(402\) 11.4378 0.570468
\(403\) 6.06997 0.302367
\(404\) 0.328455 0.0163412
\(405\) 16.1961 0.804790
\(406\) −0.875489 −0.0434498
\(407\) −2.02860 −0.100554
\(408\) 12.7163 0.629550
\(409\) −18.0254 −0.891299 −0.445649 0.895208i \(-0.647027\pi\)
−0.445649 + 0.895208i \(0.647027\pi\)
\(410\) −47.0195 −2.32213
\(411\) 9.09843 0.448792
\(412\) −9.83279 −0.484427
\(413\) −0.388090 −0.0190966
\(414\) −16.5811 −0.814916
\(415\) −6.62775 −0.325343
\(416\) −2.77223 −0.135920
\(417\) 25.2231 1.23518
\(418\) −19.4519 −0.951424
\(419\) 33.6446 1.64365 0.821824 0.569741i \(-0.192957\pi\)
0.821824 + 0.569741i \(0.192957\pi\)
\(420\) −0.729784 −0.0356098
\(421\) 5.64937 0.275334 0.137667 0.990479i \(-0.456040\pi\)
0.137667 + 0.990479i \(0.456040\pi\)
\(422\) 45.0883 2.19486
\(423\) −7.73205 −0.375945
\(424\) 2.58282 0.125433
\(425\) 71.9517 3.49017
\(426\) −15.4497 −0.748539
\(427\) −1.19534 −0.0578467
\(428\) −15.3891 −0.743861
\(429\) 1.71606 0.0828522
\(430\) −33.9187 −1.63570
\(431\) 26.3292 1.26824 0.634118 0.773237i \(-0.281363\pi\)
0.634118 + 0.773237i \(0.281363\pi\)
\(432\) 27.8891 1.34181
\(433\) 4.76137 0.228817 0.114409 0.993434i \(-0.463503\pi\)
0.114409 + 0.993434i \(0.463503\pi\)
\(434\) 2.43389 0.116830
\(435\) −20.0325 −0.960484
\(436\) −0.808091 −0.0387005
\(437\) 44.9216 2.14889
\(438\) 8.64151 0.412907
\(439\) 13.1522 0.627722 0.313861 0.949469i \(-0.398377\pi\)
0.313861 + 0.949469i \(0.398377\pi\)
\(440\) 18.0773 0.861801
\(441\) 8.79320 0.418724
\(442\) 5.18809 0.246772
\(443\) 11.2474 0.534380 0.267190 0.963644i \(-0.413905\pi\)
0.267190 + 0.963644i \(0.413905\pi\)
\(444\) 1.06582 0.0505815
\(445\) −72.7757 −3.44990
\(446\) −25.7977 −1.22156
\(447\) 7.64300 0.361501
\(448\) 0.411802 0.0194558
\(449\) −35.2363 −1.66290 −0.831451 0.555598i \(-0.812489\pi\)
−0.831451 + 0.555598i \(0.812489\pi\)
\(450\) 31.4826 1.48410
\(451\) 12.7579 0.600747
\(452\) −8.54892 −0.402107
\(453\) 14.2735 0.670626
\(454\) −5.55020 −0.260484
\(455\) 0.439162 0.0205882
\(456\) −15.0741 −0.705911
\(457\) −16.9482 −0.792801 −0.396401 0.918078i \(-0.629741\pi\)
−0.396401 + 0.918078i \(0.629741\pi\)
\(458\) 25.3856 1.18619
\(459\) −27.1246 −1.26607
\(460\) 28.3037 1.31967
\(461\) 16.6647 0.776155 0.388077 0.921627i \(-0.373139\pi\)
0.388077 + 0.921627i \(0.373139\pi\)
\(462\) 0.688093 0.0320130
\(463\) 17.1884 0.798812 0.399406 0.916774i \(-0.369216\pi\)
0.399406 + 0.916774i \(0.369216\pi\)
\(464\) −16.8959 −0.784373
\(465\) 55.6910 2.58261
\(466\) −47.7632 −2.21259
\(467\) 17.9660 0.831368 0.415684 0.909509i \(-0.363542\pi\)
0.415684 + 0.909509i \(0.363542\pi\)
\(468\) 0.653260 0.0301970
\(469\) −0.794214 −0.0366734
\(470\) 45.8644 2.11557
\(471\) 11.3199 0.521595
\(472\) −5.05078 −0.232481
\(473\) 9.20323 0.423165
\(474\) −5.01910 −0.230535
\(475\) −85.2929 −3.91351
\(476\) 0.598647 0.0274390
\(477\) −1.62989 −0.0746274
\(478\) −12.2741 −0.561403
\(479\) −17.3024 −0.790565 −0.395282 0.918560i \(-0.629353\pi\)
−0.395282 + 0.918560i \(0.629353\pi\)
\(480\) −25.4348 −1.16093
\(481\) −0.641377 −0.0292443
\(482\) −22.5231 −1.02590
\(483\) −1.58906 −0.0723047
\(484\) −5.56353 −0.252888
\(485\) 61.0689 2.77300
\(486\) −20.2257 −0.917454
\(487\) −27.9162 −1.26500 −0.632502 0.774559i \(-0.717972\pi\)
−0.632502 + 0.774559i \(0.717972\pi\)
\(488\) −15.5567 −0.704221
\(489\) −3.66872 −0.165905
\(490\) −52.1589 −2.35630
\(491\) 37.1406 1.67613 0.838065 0.545570i \(-0.183687\pi\)
0.838065 + 0.545570i \(0.183687\pi\)
\(492\) −6.70297 −0.302193
\(493\) 16.4328 0.740095
\(494\) −6.15006 −0.276704
\(495\) −11.4077 −0.512737
\(496\) 46.9712 2.10907
\(497\) 1.07278 0.0481210
\(498\) −3.28327 −0.147127
\(499\) −17.6921 −0.792007 −0.396004 0.918249i \(-0.629603\pi\)
−0.396004 + 0.918249i \(0.629603\pi\)
\(500\) −35.7137 −1.59716
\(501\) 6.78046 0.302929
\(502\) 2.46522 0.110028
\(503\) 24.1713 1.07774 0.538872 0.842388i \(-0.318851\pi\)
0.538872 + 0.842388i \(0.318851\pi\)
\(504\) −0.386352 −0.0172095
\(505\) −1.81344 −0.0806972
\(506\) −26.6868 −1.18637
\(507\) −16.6036 −0.737391
\(508\) 3.24675 0.144051
\(509\) 12.9107 0.572256 0.286128 0.958191i \(-0.407632\pi\)
0.286128 + 0.958191i \(0.407632\pi\)
\(510\) 47.5999 2.10776
\(511\) −0.600044 −0.0265444
\(512\) −1.62626 −0.0718712
\(513\) 32.1540 1.41963
\(514\) 29.6248 1.30670
\(515\) 54.2882 2.39222
\(516\) −4.83535 −0.212864
\(517\) −12.4445 −0.547309
\(518\) −0.257174 −0.0112996
\(519\) 11.4018 0.500485
\(520\) 5.71546 0.250639
\(521\) 39.7298 1.74059 0.870297 0.492528i \(-0.163927\pi\)
0.870297 + 0.492528i \(0.163927\pi\)
\(522\) 7.19020 0.314706
\(523\) 35.6685 1.55968 0.779838 0.625982i \(-0.215302\pi\)
0.779838 + 0.625982i \(0.215302\pi\)
\(524\) 9.53874 0.416702
\(525\) 3.01716 0.131680
\(526\) −17.4869 −0.762467
\(527\) −45.6837 −1.99001
\(528\) 13.2794 0.577912
\(529\) 38.6296 1.67955
\(530\) 9.66805 0.419953
\(531\) 3.18730 0.138317
\(532\) −0.709648 −0.0307671
\(533\) 4.03364 0.174716
\(534\) −36.0517 −1.56011
\(535\) 84.9653 3.67337
\(536\) −10.3363 −0.446459
\(537\) 15.8185 0.682619
\(538\) 15.1702 0.654035
\(539\) 14.1524 0.609588
\(540\) 20.2593 0.871820
\(541\) −22.8304 −0.981556 −0.490778 0.871285i \(-0.663287\pi\)
−0.490778 + 0.871285i \(0.663287\pi\)
\(542\) −18.1472 −0.779487
\(543\) 13.3661 0.573593
\(544\) 20.8644 0.894552
\(545\) 4.46158 0.191113
\(546\) 0.217553 0.00931040
\(547\) −12.1051 −0.517575 −0.258788 0.965934i \(-0.583323\pi\)
−0.258788 + 0.965934i \(0.583323\pi\)
\(548\) 5.57447 0.238130
\(549\) 9.81709 0.418983
\(550\) 50.6704 2.16059
\(551\) −19.4797 −0.829865
\(552\) −20.6808 −0.880231
\(553\) 0.348514 0.0148203
\(554\) −30.9701 −1.31579
\(555\) −5.88453 −0.249784
\(556\) 15.4538 0.655389
\(557\) −18.1528 −0.769160 −0.384580 0.923092i \(-0.625654\pi\)
−0.384580 + 0.923092i \(0.625654\pi\)
\(558\) −19.9890 −0.846202
\(559\) 2.90976 0.123070
\(560\) 3.39837 0.143607
\(561\) −12.9154 −0.545289
\(562\) −2.68281 −0.113168
\(563\) −26.8044 −1.12967 −0.564836 0.825203i \(-0.691061\pi\)
−0.564836 + 0.825203i \(0.691061\pi\)
\(564\) 6.53831 0.275312
\(565\) 47.1998 1.98571
\(566\) −28.5534 −1.20019
\(567\) −0.557114 −0.0233966
\(568\) 13.9617 0.585821
\(569\) 1.27982 0.0536526 0.0268263 0.999640i \(-0.491460\pi\)
0.0268263 + 0.999640i \(0.491460\pi\)
\(570\) −56.4258 −2.36342
\(571\) 19.9893 0.836527 0.418264 0.908326i \(-0.362639\pi\)
0.418264 + 0.908326i \(0.362639\pi\)
\(572\) 1.05140 0.0439614
\(573\) 23.3990 0.977509
\(574\) 1.61738 0.0675081
\(575\) −117.016 −4.87992
\(576\) −3.38204 −0.140918
\(577\) −23.2353 −0.967297 −0.483648 0.875262i \(-0.660689\pi\)
−0.483648 + 0.875262i \(0.660689\pi\)
\(578\) −10.5590 −0.439198
\(579\) 10.6416 0.442249
\(580\) −12.2736 −0.509633
\(581\) 0.227981 0.00945826
\(582\) 30.2524 1.25400
\(583\) −2.62326 −0.108644
\(584\) −7.80925 −0.323149
\(585\) −3.60674 −0.149120
\(586\) −14.4083 −0.595202
\(587\) −39.7308 −1.63987 −0.819933 0.572460i \(-0.805989\pi\)
−0.819933 + 0.572460i \(0.805989\pi\)
\(588\) −7.43563 −0.306640
\(589\) 54.1543 2.23139
\(590\) −18.9062 −0.778356
\(591\) −6.21177 −0.255518
\(592\) −4.96317 −0.203985
\(593\) 35.8883 1.47376 0.736879 0.676025i \(-0.236299\pi\)
0.736879 + 0.676025i \(0.236299\pi\)
\(594\) −19.1019 −0.783760
\(595\) −3.30521 −0.135501
\(596\) 4.68275 0.191813
\(597\) 14.8398 0.607351
\(598\) −8.43750 −0.345035
\(599\) −26.9746 −1.10215 −0.551076 0.834455i \(-0.685783\pi\)
−0.551076 + 0.834455i \(0.685783\pi\)
\(600\) 39.2667 1.60306
\(601\) −40.1900 −1.63939 −0.819693 0.572803i \(-0.805856\pi\)
−0.819693 + 0.572803i \(0.805856\pi\)
\(602\) 1.16673 0.0475526
\(603\) 6.52271 0.265625
\(604\) 8.74514 0.355835
\(605\) 30.7170 1.24882
\(606\) −0.898347 −0.0364929
\(607\) 26.9356 1.09328 0.546641 0.837367i \(-0.315906\pi\)
0.546641 + 0.837367i \(0.315906\pi\)
\(608\) −24.7330 −1.00306
\(609\) 0.689078 0.0279228
\(610\) −58.2324 −2.35776
\(611\) −3.93455 −0.159175
\(612\) −4.91656 −0.198740
\(613\) −23.5851 −0.952594 −0.476297 0.879284i \(-0.658021\pi\)
−0.476297 + 0.879284i \(0.658021\pi\)
\(614\) 4.55518 0.183832
\(615\) 37.0080 1.49231
\(616\) −0.621824 −0.0250540
\(617\) −44.2803 −1.78266 −0.891330 0.453355i \(-0.850227\pi\)
−0.891330 + 0.453355i \(0.850227\pi\)
\(618\) 26.8934 1.08181
\(619\) −23.7990 −0.956562 −0.478281 0.878207i \(-0.658740\pi\)
−0.478281 + 0.878207i \(0.658740\pi\)
\(620\) 34.1210 1.37033
\(621\) 44.1133 1.77021
\(622\) 0.790513 0.0316967
\(623\) 2.50334 0.100294
\(624\) 4.19852 0.168075
\(625\) 122.651 4.90606
\(626\) 12.4261 0.496648
\(627\) 15.3102 0.611429
\(628\) 6.93555 0.276759
\(629\) 4.82713 0.192470
\(630\) −1.44620 −0.0576181
\(631\) −9.24950 −0.368217 −0.184108 0.982906i \(-0.558940\pi\)
−0.184108 + 0.982906i \(0.558940\pi\)
\(632\) 4.53572 0.180421
\(633\) −35.4880 −1.41052
\(634\) 53.6516 2.13078
\(635\) −17.9258 −0.711363
\(636\) 1.37825 0.0546512
\(637\) 4.47453 0.177287
\(638\) 11.5724 0.458157
\(639\) −8.81055 −0.348540
\(640\) 58.6301 2.31756
\(641\) 18.8887 0.746060 0.373030 0.927819i \(-0.378319\pi\)
0.373030 + 0.927819i \(0.378319\pi\)
\(642\) 42.0903 1.66117
\(643\) −40.3848 −1.59262 −0.796311 0.604887i \(-0.793218\pi\)
−0.796311 + 0.604887i \(0.793218\pi\)
\(644\) −0.973592 −0.0383649
\(645\) 26.6966 1.05118
\(646\) 46.2865 1.82112
\(647\) 6.12486 0.240793 0.120397 0.992726i \(-0.461583\pi\)
0.120397 + 0.992726i \(0.461583\pi\)
\(648\) −7.25054 −0.284828
\(649\) 5.12987 0.201365
\(650\) 16.0203 0.628369
\(651\) −1.91566 −0.0750806
\(652\) −2.24777 −0.0880294
\(653\) −31.4355 −1.23017 −0.615084 0.788462i \(-0.710878\pi\)
−0.615084 + 0.788462i \(0.710878\pi\)
\(654\) 2.21019 0.0864251
\(655\) −52.6647 −2.05778
\(656\) 31.2135 1.21868
\(657\) 4.92803 0.192261
\(658\) −1.57765 −0.0615031
\(659\) 22.0639 0.859487 0.429744 0.902951i \(-0.358604\pi\)
0.429744 + 0.902951i \(0.358604\pi\)
\(660\) 9.64647 0.375488
\(661\) 13.1323 0.510788 0.255394 0.966837i \(-0.417795\pi\)
0.255394 + 0.966837i \(0.417795\pi\)
\(662\) 34.9940 1.36008
\(663\) −4.08343 −0.158587
\(664\) 2.96706 0.115144
\(665\) 3.91806 0.151936
\(666\) 2.11212 0.0818429
\(667\) −26.7250 −1.03480
\(668\) 4.15428 0.160734
\(669\) 20.3048 0.785028
\(670\) −38.6910 −1.49476
\(671\) 15.8003 0.609965
\(672\) 0.874907 0.0337503
\(673\) 3.38035 0.130303 0.0651514 0.997875i \(-0.479247\pi\)
0.0651514 + 0.997875i \(0.479247\pi\)
\(674\) −24.1180 −0.928990
\(675\) −83.7582 −3.22385
\(676\) −10.1728 −0.391260
\(677\) 24.8002 0.953147 0.476574 0.879135i \(-0.341879\pi\)
0.476574 + 0.879135i \(0.341879\pi\)
\(678\) 23.3819 0.897976
\(679\) −2.10065 −0.0806155
\(680\) −43.0156 −1.64957
\(681\) 4.36844 0.167399
\(682\) −32.1717 −1.23192
\(683\) 36.7428 1.40593 0.702963 0.711226i \(-0.251860\pi\)
0.702963 + 0.711226i \(0.251860\pi\)
\(684\) 5.82818 0.222846
\(685\) −30.7774 −1.17594
\(686\) 3.59439 0.137234
\(687\) −19.9804 −0.762301
\(688\) 22.5166 0.858439
\(689\) −0.829389 −0.0315972
\(690\) −77.4127 −2.94705
\(691\) 17.0966 0.650384 0.325192 0.945648i \(-0.394571\pi\)
0.325192 + 0.945648i \(0.394571\pi\)
\(692\) 6.98574 0.265558
\(693\) 0.392402 0.0149061
\(694\) 27.8292 1.05638
\(695\) −85.3228 −3.23648
\(696\) 8.96798 0.339930
\(697\) −30.3579 −1.14989
\(698\) 29.5259 1.11757
\(699\) 37.5933 1.42191
\(700\) 1.84857 0.0698692
\(701\) −21.0036 −0.793295 −0.396647 0.917971i \(-0.629826\pi\)
−0.396647 + 0.917971i \(0.629826\pi\)
\(702\) −6.03940 −0.227942
\(703\) −5.72216 −0.215816
\(704\) −5.44331 −0.205152
\(705\) −36.0989 −1.35956
\(706\) 52.7457 1.98511
\(707\) 0.0623789 0.00234600
\(708\) −2.69521 −0.101292
\(709\) −48.1637 −1.80883 −0.904413 0.426659i \(-0.859691\pi\)
−0.904413 + 0.426659i \(0.859691\pi\)
\(710\) 52.2618 1.96135
\(711\) −2.86227 −0.107343
\(712\) 32.5796 1.22097
\(713\) 74.2963 2.78242
\(714\) −1.63734 −0.0612760
\(715\) −5.80495 −0.217093
\(716\) 9.69176 0.362198
\(717\) 9.66064 0.360783
\(718\) −10.3999 −0.388123
\(719\) 24.7294 0.922249 0.461125 0.887335i \(-0.347446\pi\)
0.461125 + 0.887335i \(0.347446\pi\)
\(720\) −27.9100 −1.04015
\(721\) −1.86741 −0.0695458
\(722\) −23.0299 −0.857085
\(723\) 17.7274 0.659289
\(724\) 8.18919 0.304349
\(725\) 50.7429 1.88454
\(726\) 15.2167 0.564743
\(727\) 43.8033 1.62457 0.812287 0.583258i \(-0.198222\pi\)
0.812287 + 0.583258i \(0.198222\pi\)
\(728\) −0.196600 −0.00728650
\(729\) 26.8095 0.992946
\(730\) −29.2318 −1.08192
\(731\) −21.8994 −0.809980
\(732\) −8.30144 −0.306830
\(733\) 51.8337 1.91452 0.957261 0.289227i \(-0.0933981\pi\)
0.957261 + 0.289227i \(0.0933981\pi\)
\(734\) −10.1390 −0.374239
\(735\) 41.0531 1.51427
\(736\) −33.9321 −1.25075
\(737\) 10.4981 0.386703
\(738\) −13.2832 −0.488961
\(739\) −20.4067 −0.750672 −0.375336 0.926889i \(-0.622473\pi\)
−0.375336 + 0.926889i \(0.622473\pi\)
\(740\) −3.60536 −0.132536
\(741\) 4.84058 0.177823
\(742\) −0.332562 −0.0122087
\(743\) 5.00059 0.183454 0.0917270 0.995784i \(-0.470761\pi\)
0.0917270 + 0.995784i \(0.470761\pi\)
\(744\) −24.9313 −0.914025
\(745\) −25.8541 −0.947221
\(746\) −15.7026 −0.574915
\(747\) −1.87236 −0.0685061
\(748\) −7.91307 −0.289331
\(749\) −2.92264 −0.106791
\(750\) 97.6794 3.56675
\(751\) 21.4224 0.781716 0.390858 0.920451i \(-0.372178\pi\)
0.390858 + 0.920451i \(0.372178\pi\)
\(752\) −30.4468 −1.11028
\(753\) −1.94032 −0.0707091
\(754\) 3.65883 0.133247
\(755\) −48.2831 −1.75720
\(756\) −0.696879 −0.0253452
\(757\) −31.0047 −1.12689 −0.563443 0.826155i \(-0.690524\pi\)
−0.563443 + 0.826155i \(0.690524\pi\)
\(758\) −5.11825 −0.185903
\(759\) 21.0046 0.762418
\(760\) 50.9915 1.84966
\(761\) 32.8588 1.19113 0.595566 0.803306i \(-0.296928\pi\)
0.595566 + 0.803306i \(0.296928\pi\)
\(762\) −8.88010 −0.321692
\(763\) −0.153470 −0.00555597
\(764\) 14.3362 0.518667
\(765\) 27.1450 0.981430
\(766\) −29.5739 −1.06855
\(767\) 1.62190 0.0585633
\(768\) 21.9661 0.792634
\(769\) 31.8058 1.14695 0.573473 0.819224i \(-0.305596\pi\)
0.573473 + 0.819224i \(0.305596\pi\)
\(770\) −2.32762 −0.0838817
\(771\) −23.3170 −0.839743
\(772\) 6.51994 0.234658
\(773\) −40.1636 −1.44458 −0.722292 0.691588i \(-0.756911\pi\)
−0.722292 + 0.691588i \(0.756911\pi\)
\(774\) −9.58214 −0.344423
\(775\) −141.067 −5.06727
\(776\) −27.3388 −0.981407
\(777\) 0.202416 0.00726164
\(778\) 0.0864375 0.00309893
\(779\) 35.9869 1.28936
\(780\) 3.04990 0.109204
\(781\) −14.1803 −0.507412
\(782\) 63.5022 2.27083
\(783\) −19.1292 −0.683623
\(784\) 34.6253 1.23662
\(785\) −38.2921 −1.36670
\(786\) −26.0891 −0.930568
\(787\) −27.0310 −0.963551 −0.481775 0.876295i \(-0.660008\pi\)
−0.481775 + 0.876295i \(0.660008\pi\)
\(788\) −3.80586 −0.135578
\(789\) 13.7636 0.489996
\(790\) 16.9782 0.604057
\(791\) −1.62358 −0.0577278
\(792\) 5.10690 0.181466
\(793\) 4.99555 0.177397
\(794\) −12.7951 −0.454083
\(795\) −7.60951 −0.269881
\(796\) 9.09209 0.322261
\(797\) −3.57575 −0.126660 −0.0633298 0.997993i \(-0.520172\pi\)
−0.0633298 + 0.997993i \(0.520172\pi\)
\(798\) 1.94094 0.0687084
\(799\) 29.6122 1.04760
\(800\) 64.4271 2.27784
\(801\) −20.5594 −0.726430
\(802\) 21.5725 0.761750
\(803\) 7.93153 0.279898
\(804\) −5.51568 −0.194523
\(805\) 5.37534 0.189456
\(806\) −10.1717 −0.358281
\(807\) −11.9402 −0.420313
\(808\) 0.811828 0.0285600
\(809\) −1.95987 −0.0689055 −0.0344527 0.999406i \(-0.510969\pi\)
−0.0344527 + 0.999406i \(0.510969\pi\)
\(810\) −27.1404 −0.953616
\(811\) 41.9428 1.47281 0.736406 0.676540i \(-0.236522\pi\)
0.736406 + 0.676540i \(0.236522\pi\)
\(812\) 0.422187 0.0148159
\(813\) 14.2832 0.500934
\(814\) 3.39940 0.119149
\(815\) 12.4102 0.434712
\(816\) −31.5988 −1.10618
\(817\) 25.9600 0.908225
\(818\) 30.2058 1.05612
\(819\) 0.124065 0.00433517
\(820\) 22.6742 0.791819
\(821\) −48.2157 −1.68274 −0.841370 0.540459i \(-0.818251\pi\)
−0.841370 + 0.540459i \(0.818251\pi\)
\(822\) −15.2466 −0.531785
\(823\) −15.0514 −0.524660 −0.262330 0.964978i \(-0.584491\pi\)
−0.262330 + 0.964978i \(0.584491\pi\)
\(824\) −24.3033 −0.846645
\(825\) −39.8815 −1.38850
\(826\) 0.650336 0.0226281
\(827\) 13.6704 0.475366 0.237683 0.971343i \(-0.423612\pi\)
0.237683 + 0.971343i \(0.423612\pi\)
\(828\) 7.99590 0.277877
\(829\) −0.116293 −0.00403903 −0.00201952 0.999998i \(-0.500643\pi\)
−0.00201952 + 0.999998i \(0.500643\pi\)
\(830\) 11.1064 0.385507
\(831\) 24.3759 0.845590
\(832\) −1.72100 −0.0596648
\(833\) −33.6762 −1.16681
\(834\) −42.2673 −1.46360
\(835\) −22.9364 −0.793746
\(836\) 9.38030 0.324425
\(837\) 53.1799 1.83817
\(838\) −56.3795 −1.94760
\(839\) 23.6555 0.816678 0.408339 0.912830i \(-0.366108\pi\)
0.408339 + 0.912830i \(0.366108\pi\)
\(840\) −1.80378 −0.0622362
\(841\) −17.4110 −0.600380
\(842\) −9.46686 −0.326249
\(843\) 2.11158 0.0727267
\(844\) −21.7429 −0.748423
\(845\) 56.1652 1.93214
\(846\) 12.9569 0.445466
\(847\) −1.05661 −0.0363054
\(848\) −6.41806 −0.220397
\(849\) 22.4738 0.771298
\(850\) −120.572 −4.13559
\(851\) −7.85045 −0.269110
\(852\) 7.45030 0.255243
\(853\) −13.9385 −0.477245 −0.238622 0.971112i \(-0.576696\pi\)
−0.238622 + 0.971112i \(0.576696\pi\)
\(854\) 2.00308 0.0685439
\(855\) −32.1782 −1.10047
\(856\) −38.0366 −1.30006
\(857\) −38.0360 −1.29929 −0.649643 0.760240i \(-0.725082\pi\)
−0.649643 + 0.760240i \(0.725082\pi\)
\(858\) −2.87567 −0.0981736
\(859\) −16.9867 −0.579578 −0.289789 0.957091i \(-0.593585\pi\)
−0.289789 + 0.957091i \(0.593585\pi\)
\(860\) 16.3566 0.557756
\(861\) −1.27300 −0.0433838
\(862\) −44.1209 −1.50276
\(863\) 1.32622 0.0451449 0.0225725 0.999745i \(-0.492814\pi\)
0.0225725 + 0.999745i \(0.492814\pi\)
\(864\) −24.2880 −0.826293
\(865\) −38.5692 −1.31139
\(866\) −7.97881 −0.271131
\(867\) 8.31079 0.282249
\(868\) −1.17370 −0.0398378
\(869\) −4.60674 −0.156273
\(870\) 33.5691 1.13810
\(871\) 3.31916 0.112466
\(872\) −1.99732 −0.0676379
\(873\) 17.2522 0.583898
\(874\) −75.2767 −2.54627
\(875\) −6.78260 −0.229294
\(876\) −4.16720 −0.140797
\(877\) 15.2829 0.516066 0.258033 0.966136i \(-0.416926\pi\)
0.258033 + 0.966136i \(0.416926\pi\)
\(878\) −22.0397 −0.743803
\(879\) 11.3405 0.382505
\(880\) −44.9205 −1.51427
\(881\) −51.7188 −1.74245 −0.871225 0.490883i \(-0.836674\pi\)
−0.871225 + 0.490883i \(0.836674\pi\)
\(882\) −14.7351 −0.496156
\(883\) −41.5272 −1.39750 −0.698750 0.715366i \(-0.746260\pi\)
−0.698750 + 0.715366i \(0.746260\pi\)
\(884\) −2.50186 −0.0841465
\(885\) 14.8806 0.500207
\(886\) −18.8477 −0.633200
\(887\) 2.05411 0.0689702 0.0344851 0.999405i \(-0.489021\pi\)
0.0344851 + 0.999405i \(0.489021\pi\)
\(888\) 2.63434 0.0884027
\(889\) 0.616611 0.0206805
\(890\) 121.953 4.08787
\(891\) 7.36407 0.246705
\(892\) 12.4404 0.416537
\(893\) −35.1028 −1.17467
\(894\) −12.8076 −0.428352
\(895\) −53.5095 −1.78863
\(896\) −2.01676 −0.0673752
\(897\) 6.64097 0.221735
\(898\) 59.0467 1.97041
\(899\) −32.2178 −1.07452
\(900\) −15.1819 −0.506062
\(901\) 6.24214 0.207956
\(902\) −21.3789 −0.711840
\(903\) −0.918311 −0.0305595
\(904\) −21.1300 −0.702774
\(905\) −45.2136 −1.50295
\(906\) −23.9186 −0.794641
\(907\) −0.825008 −0.0273939 −0.0136970 0.999906i \(-0.504360\pi\)
−0.0136970 + 0.999906i \(0.504360\pi\)
\(908\) 2.67648 0.0888219
\(909\) −0.512305 −0.0169921
\(910\) −0.735919 −0.0243955
\(911\) 3.44846 0.114253 0.0571263 0.998367i \(-0.481806\pi\)
0.0571263 + 0.998367i \(0.481806\pi\)
\(912\) 37.4578 1.24035
\(913\) −3.01352 −0.0997328
\(914\) 28.4006 0.939409
\(915\) 45.8334 1.51521
\(916\) −12.2417 −0.404478
\(917\) 1.81156 0.0598230
\(918\) 45.4537 1.50019
\(919\) 7.79335 0.257079 0.128539 0.991704i \(-0.458971\pi\)
0.128539 + 0.991704i \(0.458971\pi\)
\(920\) 69.9571 2.30642
\(921\) −3.58528 −0.118139
\(922\) −27.9257 −0.919685
\(923\) −4.48336 −0.147572
\(924\) −0.331820 −0.0109161
\(925\) 14.9057 0.490096
\(926\) −28.8032 −0.946531
\(927\) 15.3366 0.503720
\(928\) 14.7143 0.483020
\(929\) −33.0017 −1.08275 −0.541376 0.840781i \(-0.682096\pi\)
−0.541376 + 0.840781i \(0.682096\pi\)
\(930\) −93.3234 −3.06019
\(931\) 39.9204 1.30834
\(932\) 23.0329 0.754467
\(933\) −0.622195 −0.0203698
\(934\) −30.1063 −0.985108
\(935\) 43.6891 1.42879
\(936\) 1.61464 0.0527760
\(937\) −27.5557 −0.900204 −0.450102 0.892977i \(-0.648612\pi\)
−0.450102 + 0.892977i \(0.648612\pi\)
\(938\) 1.33089 0.0434552
\(939\) −9.78034 −0.319169
\(940\) −22.1172 −0.721385
\(941\) −30.3946 −0.990835 −0.495418 0.868655i \(-0.664985\pi\)
−0.495418 + 0.868655i \(0.664985\pi\)
\(942\) −18.9692 −0.618051
\(943\) 49.3717 1.60776
\(944\) 12.5507 0.408492
\(945\) 3.84756 0.125161
\(946\) −15.4222 −0.501419
\(947\) −45.5105 −1.47889 −0.739446 0.673215i \(-0.764913\pi\)
−0.739446 + 0.673215i \(0.764913\pi\)
\(948\) 2.42037 0.0786098
\(949\) 2.50769 0.0814031
\(950\) 142.928 4.63721
\(951\) −42.2280 −1.36934
\(952\) 1.47965 0.0479558
\(953\) −29.2668 −0.948046 −0.474023 0.880513i \(-0.657199\pi\)
−0.474023 + 0.880513i \(0.657199\pi\)
\(954\) 2.73126 0.0884278
\(955\) −79.1523 −2.56131
\(956\) 5.91893 0.191432
\(957\) −9.10840 −0.294433
\(958\) 28.9942 0.936759
\(959\) 1.05868 0.0341866
\(960\) −15.7899 −0.509616
\(961\) 58.5665 1.88924
\(962\) 1.07478 0.0346523
\(963\) 24.0030 0.773486
\(964\) 10.8613 0.349819
\(965\) −35.9975 −1.15880
\(966\) 2.66284 0.0856756
\(967\) 13.4930 0.433906 0.216953 0.976182i \(-0.430388\pi\)
0.216953 + 0.976182i \(0.430388\pi\)
\(968\) −13.7512 −0.441979
\(969\) −36.4311 −1.17034
\(970\) −102.335 −3.28579
\(971\) −0.866740 −0.0278150 −0.0139075 0.999903i \(-0.504427\pi\)
−0.0139075 + 0.999903i \(0.504427\pi\)
\(972\) 9.75343 0.312841
\(973\) 2.93493 0.0940897
\(974\) 46.7802 1.49893
\(975\) −12.6092 −0.403819
\(976\) 38.6571 1.23738
\(977\) −22.6329 −0.724092 −0.362046 0.932160i \(-0.617922\pi\)
−0.362046 + 0.932160i \(0.617922\pi\)
\(978\) 6.14780 0.196585
\(979\) −33.0898 −1.05755
\(980\) 25.1526 0.803471
\(981\) 1.26041 0.0402419
\(982\) −62.2378 −1.98609
\(983\) 15.5448 0.495803 0.247901 0.968785i \(-0.420259\pi\)
0.247901 + 0.968785i \(0.420259\pi\)
\(984\) −16.5674 −0.528151
\(985\) 21.0127 0.669519
\(986\) −27.5370 −0.876957
\(987\) 1.24173 0.0395247
\(988\) 2.96575 0.0943530
\(989\) 35.6155 1.13251
\(990\) 19.1163 0.607555
\(991\) 16.2076 0.514851 0.257425 0.966298i \(-0.417126\pi\)
0.257425 + 0.966298i \(0.417126\pi\)
\(992\) −40.9062 −1.29877
\(993\) −27.5430 −0.874049
\(994\) −1.79770 −0.0570197
\(995\) −50.1987 −1.59141
\(996\) 1.58329 0.0501685
\(997\) 39.7542 1.25903 0.629514 0.776990i \(-0.283254\pi\)
0.629514 + 0.776990i \(0.283254\pi\)
\(998\) 29.6473 0.938468
\(999\) −5.61920 −0.177784
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 4033.2.a.f.1.19 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.19 85 1.1 even 1 trivial