Properties

Label 8007.2.a.f.1.46
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.46
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.47221 q^{2} -1.00000 q^{3} +4.11184 q^{4} +2.50638 q^{5} -2.47221 q^{6} -1.59545 q^{7} +5.22093 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.47221 q^{2} -1.00000 q^{3} +4.11184 q^{4} +2.50638 q^{5} -2.47221 q^{6} -1.59545 q^{7} +5.22093 q^{8} +1.00000 q^{9} +6.19631 q^{10} -4.88370 q^{11} -4.11184 q^{12} -3.74615 q^{13} -3.94430 q^{14} -2.50638 q^{15} +4.68357 q^{16} -1.00000 q^{17} +2.47221 q^{18} -5.54146 q^{19} +10.3058 q^{20} +1.59545 q^{21} -12.0735 q^{22} +5.99527 q^{23} -5.22093 q^{24} +1.28194 q^{25} -9.26130 q^{26} -1.00000 q^{27} -6.56026 q^{28} -3.31756 q^{29} -6.19631 q^{30} -2.69692 q^{31} +1.13693 q^{32} +4.88370 q^{33} -2.47221 q^{34} -3.99881 q^{35} +4.11184 q^{36} +6.21888 q^{37} -13.6997 q^{38} +3.74615 q^{39} +13.0856 q^{40} +1.59975 q^{41} +3.94430 q^{42} +8.43316 q^{43} -20.0810 q^{44} +2.50638 q^{45} +14.8216 q^{46} +2.21983 q^{47} -4.68357 q^{48} -4.45453 q^{49} +3.16922 q^{50} +1.00000 q^{51} -15.4036 q^{52} -13.5884 q^{53} -2.47221 q^{54} -12.2404 q^{55} -8.32975 q^{56} +5.54146 q^{57} -8.20172 q^{58} +11.3430 q^{59} -10.3058 q^{60} -6.89417 q^{61} -6.66736 q^{62} -1.59545 q^{63} -6.55641 q^{64} -9.38929 q^{65} +12.0735 q^{66} -3.64490 q^{67} -4.11184 q^{68} -5.99527 q^{69} -9.88592 q^{70} -13.4958 q^{71} +5.22093 q^{72} -7.03042 q^{73} +15.3744 q^{74} -1.28194 q^{75} -22.7856 q^{76} +7.79171 q^{77} +9.26130 q^{78} -6.59345 q^{79} +11.7388 q^{80} +1.00000 q^{81} +3.95492 q^{82} +1.65622 q^{83} +6.56026 q^{84} -2.50638 q^{85} +20.8486 q^{86} +3.31756 q^{87} -25.4974 q^{88} -14.5094 q^{89} +6.19631 q^{90} +5.97682 q^{91} +24.6516 q^{92} +2.69692 q^{93} +5.48791 q^{94} -13.8890 q^{95} -1.13693 q^{96} -5.29458 q^{97} -11.0125 q^{98} -4.88370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.47221 1.74812 0.874060 0.485818i \(-0.161478\pi\)
0.874060 + 0.485818i \(0.161478\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.11184 2.05592
\(5\) 2.50638 1.12089 0.560443 0.828193i \(-0.310631\pi\)
0.560443 + 0.828193i \(0.310631\pi\)
\(6\) −2.47221 −1.00928
\(7\) −1.59545 −0.603025 −0.301512 0.953462i \(-0.597491\pi\)
−0.301512 + 0.953462i \(0.597491\pi\)
\(8\) 5.22093 1.84588
\(9\) 1.00000 0.333333
\(10\) 6.19631 1.95944
\(11\) −4.88370 −1.47249 −0.736245 0.676715i \(-0.763403\pi\)
−0.736245 + 0.676715i \(0.763403\pi\)
\(12\) −4.11184 −1.18699
\(13\) −3.74615 −1.03900 −0.519498 0.854472i \(-0.673881\pi\)
−0.519498 + 0.854472i \(0.673881\pi\)
\(14\) −3.94430 −1.05416
\(15\) −2.50638 −0.647144
\(16\) 4.68357 1.17089
\(17\) −1.00000 −0.242536
\(18\) 2.47221 0.582706
\(19\) −5.54146 −1.27130 −0.635649 0.771978i \(-0.719268\pi\)
−0.635649 + 0.771978i \(0.719268\pi\)
\(20\) 10.3058 2.30446
\(21\) 1.59545 0.348157
\(22\) −12.0735 −2.57409
\(23\) 5.99527 1.25010 0.625051 0.780584i \(-0.285078\pi\)
0.625051 + 0.780584i \(0.285078\pi\)
\(24\) −5.22093 −1.06572
\(25\) 1.28194 0.256388
\(26\) −9.26130 −1.81629
\(27\) −1.00000 −0.192450
\(28\) −6.56026 −1.23977
\(29\) −3.31756 −0.616056 −0.308028 0.951377i \(-0.599669\pi\)
−0.308028 + 0.951377i \(0.599669\pi\)
\(30\) −6.19631 −1.13129
\(31\) −2.69692 −0.484381 −0.242190 0.970229i \(-0.577866\pi\)
−0.242190 + 0.970229i \(0.577866\pi\)
\(32\) 1.13693 0.200982
\(33\) 4.88370 0.850143
\(34\) −2.47221 −0.423981
\(35\) −3.99881 −0.675923
\(36\) 4.11184 0.685307
\(37\) 6.21888 1.02238 0.511189 0.859469i \(-0.329205\pi\)
0.511189 + 0.859469i \(0.329205\pi\)
\(38\) −13.6997 −2.22238
\(39\) 3.74615 0.599865
\(40\) 13.0856 2.06902
\(41\) 1.59975 0.249838 0.124919 0.992167i \(-0.460133\pi\)
0.124919 + 0.992167i \(0.460133\pi\)
\(42\) 3.94430 0.608619
\(43\) 8.43316 1.28604 0.643022 0.765847i \(-0.277680\pi\)
0.643022 + 0.765847i \(0.277680\pi\)
\(44\) −20.0810 −3.02732
\(45\) 2.50638 0.373629
\(46\) 14.8216 2.18533
\(47\) 2.21983 0.323796 0.161898 0.986807i \(-0.448238\pi\)
0.161898 + 0.986807i \(0.448238\pi\)
\(48\) −4.68357 −0.676015
\(49\) −4.45453 −0.636361
\(50\) 3.16922 0.448196
\(51\) 1.00000 0.140028
\(52\) −15.4036 −2.13610
\(53\) −13.5884 −1.86651 −0.933255 0.359216i \(-0.883044\pi\)
−0.933255 + 0.359216i \(0.883044\pi\)
\(54\) −2.47221 −0.336426
\(55\) −12.2404 −1.65049
\(56\) −8.32975 −1.11311
\(57\) 5.54146 0.733985
\(58\) −8.20172 −1.07694
\(59\) 11.3430 1.47674 0.738369 0.674397i \(-0.235597\pi\)
0.738369 + 0.674397i \(0.235597\pi\)
\(60\) −10.3058 −1.33048
\(61\) −6.89417 −0.882708 −0.441354 0.897333i \(-0.645502\pi\)
−0.441354 + 0.897333i \(0.645502\pi\)
\(62\) −6.66736 −0.846756
\(63\) −1.59545 −0.201008
\(64\) −6.55641 −0.819551
\(65\) −9.38929 −1.16460
\(66\) 12.0735 1.48615
\(67\) −3.64490 −0.445296 −0.222648 0.974899i \(-0.571470\pi\)
−0.222648 + 0.974899i \(0.571470\pi\)
\(68\) −4.11184 −0.498634
\(69\) −5.99527 −0.721746
\(70\) −9.88592 −1.18159
\(71\) −13.4958 −1.60166 −0.800828 0.598895i \(-0.795607\pi\)
−0.800828 + 0.598895i \(0.795607\pi\)
\(72\) 5.22093 0.615292
\(73\) −7.03042 −0.822848 −0.411424 0.911444i \(-0.634969\pi\)
−0.411424 + 0.911444i \(0.634969\pi\)
\(74\) 15.3744 1.78724
\(75\) −1.28194 −0.148025
\(76\) −22.7856 −2.61369
\(77\) 7.79171 0.887948
\(78\) 9.26130 1.04864
\(79\) −6.59345 −0.741821 −0.370911 0.928669i \(-0.620954\pi\)
−0.370911 + 0.928669i \(0.620954\pi\)
\(80\) 11.7388 1.31244
\(81\) 1.00000 0.111111
\(82\) 3.95492 0.436747
\(83\) 1.65622 0.181794 0.0908970 0.995860i \(-0.471027\pi\)
0.0908970 + 0.995860i \(0.471027\pi\)
\(84\) 6.56026 0.715783
\(85\) −2.50638 −0.271855
\(86\) 20.8486 2.24816
\(87\) 3.31756 0.355680
\(88\) −25.4974 −2.71804
\(89\) −14.5094 −1.53799 −0.768995 0.639254i \(-0.779243\pi\)
−0.768995 + 0.639254i \(0.779243\pi\)
\(90\) 6.19631 0.653148
\(91\) 5.97682 0.626541
\(92\) 24.6516 2.57011
\(93\) 2.69692 0.279657
\(94\) 5.48791 0.566034
\(95\) −13.8890 −1.42498
\(96\) −1.13693 −0.116037
\(97\) −5.29458 −0.537583 −0.268792 0.963198i \(-0.586624\pi\)
−0.268792 + 0.963198i \(0.586624\pi\)
\(98\) −11.0125 −1.11244
\(99\) −4.88370 −0.490830
\(100\) 5.27113 0.527113
\(101\) 12.7297 1.26665 0.633325 0.773886i \(-0.281689\pi\)
0.633325 + 0.773886i \(0.281689\pi\)
\(102\) 2.47221 0.244786
\(103\) 1.36407 0.134406 0.0672030 0.997739i \(-0.478593\pi\)
0.0672030 + 0.997739i \(0.478593\pi\)
\(104\) −19.5584 −1.91786
\(105\) 3.99881 0.390244
\(106\) −33.5934 −3.26288
\(107\) −8.23301 −0.795915 −0.397958 0.917404i \(-0.630281\pi\)
−0.397958 + 0.917404i \(0.630281\pi\)
\(108\) −4.11184 −0.395662
\(109\) −1.75758 −0.168346 −0.0841729 0.996451i \(-0.526825\pi\)
−0.0841729 + 0.996451i \(0.526825\pi\)
\(110\) −30.2609 −2.88526
\(111\) −6.21888 −0.590270
\(112\) −7.47242 −0.706077
\(113\) −11.6046 −1.09167 −0.545836 0.837892i \(-0.683788\pi\)
−0.545836 + 0.837892i \(0.683788\pi\)
\(114\) 13.6997 1.28309
\(115\) 15.0264 1.40122
\(116\) −13.6413 −1.26656
\(117\) −3.74615 −0.346332
\(118\) 28.0424 2.58151
\(119\) 1.59545 0.146255
\(120\) −13.0856 −1.19455
\(121\) 12.8505 1.16823
\(122\) −17.0439 −1.54308
\(123\) −1.59975 −0.144244
\(124\) −11.0893 −0.995849
\(125\) −9.31887 −0.833505
\(126\) −3.94430 −0.351387
\(127\) 9.34079 0.828861 0.414431 0.910081i \(-0.363981\pi\)
0.414431 + 0.910081i \(0.363981\pi\)
\(128\) −18.4827 −1.63366
\(129\) −8.43316 −0.742498
\(130\) −23.2123 −2.03586
\(131\) 2.25937 0.197402 0.0987011 0.995117i \(-0.468531\pi\)
0.0987011 + 0.995117i \(0.468531\pi\)
\(132\) 20.0810 1.74783
\(133\) 8.84115 0.766625
\(134\) −9.01098 −0.778430
\(135\) −2.50638 −0.215715
\(136\) −5.22093 −0.447691
\(137\) 11.2060 0.957394 0.478697 0.877980i \(-0.341109\pi\)
0.478697 + 0.877980i \(0.341109\pi\)
\(138\) −14.8216 −1.26170
\(139\) 13.5241 1.14710 0.573548 0.819172i \(-0.305566\pi\)
0.573548 + 0.819172i \(0.305566\pi\)
\(140\) −16.4425 −1.38964
\(141\) −2.21983 −0.186944
\(142\) −33.3645 −2.79989
\(143\) 18.2951 1.52991
\(144\) 4.68357 0.390297
\(145\) −8.31507 −0.690529
\(146\) −17.3807 −1.43844
\(147\) 4.45453 0.367403
\(148\) 25.5711 2.10193
\(149\) −19.7181 −1.61537 −0.807683 0.589617i \(-0.799279\pi\)
−0.807683 + 0.589617i \(0.799279\pi\)
\(150\) −3.16922 −0.258766
\(151\) −11.3901 −0.926909 −0.463455 0.886121i \(-0.653390\pi\)
−0.463455 + 0.886121i \(0.653390\pi\)
\(152\) −28.9316 −2.34666
\(153\) −1.00000 −0.0808452
\(154\) 19.2628 1.55224
\(155\) −6.75950 −0.542936
\(156\) 15.4036 1.23328
\(157\) −1.00000 −0.0798087
\(158\) −16.3004 −1.29679
\(159\) 13.5884 1.07763
\(160\) 2.84957 0.225279
\(161\) −9.56518 −0.753842
\(162\) 2.47221 0.194235
\(163\) 4.67176 0.365921 0.182960 0.983120i \(-0.441432\pi\)
0.182960 + 0.983120i \(0.441432\pi\)
\(164\) 6.57791 0.513648
\(165\) 12.2404 0.952914
\(166\) 4.09454 0.317798
\(167\) 18.9495 1.46636 0.733179 0.680036i \(-0.238036\pi\)
0.733179 + 0.680036i \(0.238036\pi\)
\(168\) 8.32975 0.642654
\(169\) 1.03368 0.0795136
\(170\) −6.19631 −0.475235
\(171\) −5.54146 −0.423766
\(172\) 34.6758 2.64401
\(173\) −21.8285 −1.65959 −0.829794 0.558070i \(-0.811542\pi\)
−0.829794 + 0.558070i \(0.811542\pi\)
\(174\) 8.20172 0.621771
\(175\) −2.04527 −0.154608
\(176\) −22.8731 −1.72413
\(177\) −11.3430 −0.852595
\(178\) −35.8703 −2.68859
\(179\) 7.99352 0.597464 0.298732 0.954337i \(-0.403436\pi\)
0.298732 + 0.954337i \(0.403436\pi\)
\(180\) 10.3058 0.768152
\(181\) 13.7293 1.02049 0.510245 0.860029i \(-0.329555\pi\)
0.510245 + 0.860029i \(0.329555\pi\)
\(182\) 14.7760 1.09527
\(183\) 6.89417 0.509632
\(184\) 31.3009 2.30753
\(185\) 15.5869 1.14597
\(186\) 6.66736 0.488875
\(187\) 4.88370 0.357131
\(188\) 9.12761 0.665699
\(189\) 1.59545 0.116052
\(190\) −34.3366 −2.49104
\(191\) 17.8356 1.29054 0.645270 0.763954i \(-0.276745\pi\)
0.645270 + 0.763954i \(0.276745\pi\)
\(192\) 6.55641 0.473168
\(193\) 20.3824 1.46716 0.733579 0.679604i \(-0.237848\pi\)
0.733579 + 0.679604i \(0.237848\pi\)
\(194\) −13.0893 −0.939760
\(195\) 9.38929 0.672381
\(196\) −18.3163 −1.30831
\(197\) −3.58164 −0.255181 −0.127591 0.991827i \(-0.540724\pi\)
−0.127591 + 0.991827i \(0.540724\pi\)
\(198\) −12.0735 −0.858030
\(199\) −8.42779 −0.597430 −0.298715 0.954342i \(-0.596558\pi\)
−0.298715 + 0.954342i \(0.596558\pi\)
\(200\) 6.69291 0.473260
\(201\) 3.64490 0.257092
\(202\) 31.4705 2.21426
\(203\) 5.29302 0.371497
\(204\) 4.11184 0.287887
\(205\) 4.00957 0.280041
\(206\) 3.37228 0.234958
\(207\) 5.99527 0.416700
\(208\) −17.5454 −1.21655
\(209\) 27.0628 1.87198
\(210\) 9.88592 0.682193
\(211\) 12.5035 0.860774 0.430387 0.902644i \(-0.358377\pi\)
0.430387 + 0.902644i \(0.358377\pi\)
\(212\) −55.8733 −3.83740
\(213\) 13.4958 0.924716
\(214\) −20.3538 −1.39135
\(215\) 21.1367 1.44151
\(216\) −5.22093 −0.355239
\(217\) 4.30281 0.292094
\(218\) −4.34512 −0.294288
\(219\) 7.03042 0.475072
\(220\) −50.3306 −3.39329
\(221\) 3.74615 0.251994
\(222\) −15.3744 −1.03186
\(223\) 29.0755 1.94704 0.973518 0.228609i \(-0.0734177\pi\)
0.973518 + 0.228609i \(0.0734177\pi\)
\(224\) −1.81392 −0.121197
\(225\) 1.28194 0.0854625
\(226\) −28.6891 −1.90837
\(227\) −20.0385 −1.33000 −0.665001 0.746843i \(-0.731569\pi\)
−0.665001 + 0.746843i \(0.731569\pi\)
\(228\) 22.7856 1.50902
\(229\) 22.2994 1.47358 0.736792 0.676119i \(-0.236340\pi\)
0.736792 + 0.676119i \(0.236340\pi\)
\(230\) 37.1486 2.44950
\(231\) −7.79171 −0.512657
\(232\) −17.3208 −1.13716
\(233\) −2.76491 −0.181135 −0.0905676 0.995890i \(-0.528868\pi\)
−0.0905676 + 0.995890i \(0.528868\pi\)
\(234\) −9.26130 −0.605430
\(235\) 5.56375 0.362939
\(236\) 46.6408 3.03606
\(237\) 6.59345 0.428291
\(238\) 3.94430 0.255671
\(239\) −5.50752 −0.356252 −0.178126 0.984008i \(-0.557003\pi\)
−0.178126 + 0.984008i \(0.557003\pi\)
\(240\) −11.7388 −0.757736
\(241\) −12.3269 −0.794046 −0.397023 0.917809i \(-0.629957\pi\)
−0.397023 + 0.917809i \(0.629957\pi\)
\(242\) 31.7692 2.04220
\(243\) −1.00000 −0.0641500
\(244\) −28.3478 −1.81478
\(245\) −11.1647 −0.713289
\(246\) −3.95492 −0.252156
\(247\) 20.7592 1.32088
\(248\) −14.0804 −0.894108
\(249\) −1.65622 −0.104959
\(250\) −23.0383 −1.45707
\(251\) −18.4414 −1.16401 −0.582005 0.813185i \(-0.697732\pi\)
−0.582005 + 0.813185i \(0.697732\pi\)
\(252\) −6.56026 −0.413257
\(253\) −29.2791 −1.84076
\(254\) 23.0924 1.44895
\(255\) 2.50638 0.156956
\(256\) −32.5804 −2.03627
\(257\) 24.4376 1.52437 0.762187 0.647357i \(-0.224126\pi\)
0.762187 + 0.647357i \(0.224126\pi\)
\(258\) −20.8486 −1.29798
\(259\) −9.92193 −0.616519
\(260\) −38.6073 −2.39432
\(261\) −3.31756 −0.205352
\(262\) 5.58565 0.345083
\(263\) 20.7441 1.27914 0.639569 0.768733i \(-0.279113\pi\)
0.639569 + 0.768733i \(0.279113\pi\)
\(264\) 25.4974 1.56926
\(265\) −34.0577 −2.09215
\(266\) 21.8572 1.34015
\(267\) 14.5094 0.887959
\(268\) −14.9873 −0.915494
\(269\) 7.89442 0.481331 0.240666 0.970608i \(-0.422634\pi\)
0.240666 + 0.970608i \(0.422634\pi\)
\(270\) −6.19631 −0.377095
\(271\) −27.9905 −1.70030 −0.850152 0.526537i \(-0.823490\pi\)
−0.850152 + 0.526537i \(0.823490\pi\)
\(272\) −4.68357 −0.283983
\(273\) −5.97682 −0.361733
\(274\) 27.7037 1.67364
\(275\) −6.26060 −0.377528
\(276\) −24.6516 −1.48385
\(277\) −22.4096 −1.34646 −0.673230 0.739433i \(-0.735094\pi\)
−0.673230 + 0.739433i \(0.735094\pi\)
\(278\) 33.4344 2.00526
\(279\) −2.69692 −0.161460
\(280\) −20.8775 −1.24767
\(281\) −3.49732 −0.208633 −0.104316 0.994544i \(-0.533265\pi\)
−0.104316 + 0.994544i \(0.533265\pi\)
\(282\) −5.48791 −0.326800
\(283\) 0.857084 0.0509483 0.0254742 0.999675i \(-0.491890\pi\)
0.0254742 + 0.999675i \(0.491890\pi\)
\(284\) −55.4926 −3.29288
\(285\) 13.8890 0.822714
\(286\) 45.2294 2.67447
\(287\) −2.55232 −0.150659
\(288\) 1.13693 0.0669942
\(289\) 1.00000 0.0588235
\(290\) −20.5566 −1.20713
\(291\) 5.29458 0.310374
\(292\) −28.9080 −1.69171
\(293\) 10.5660 0.617275 0.308637 0.951180i \(-0.400127\pi\)
0.308637 + 0.951180i \(0.400127\pi\)
\(294\) 11.0125 0.642265
\(295\) 28.4299 1.65526
\(296\) 32.4683 1.88718
\(297\) 4.88370 0.283381
\(298\) −48.7473 −2.82385
\(299\) −22.4592 −1.29885
\(300\) −5.27113 −0.304329
\(301\) −13.4547 −0.775517
\(302\) −28.1587 −1.62035
\(303\) −12.7297 −0.731301
\(304\) −25.9538 −1.48855
\(305\) −17.2794 −0.989416
\(306\) −2.47221 −0.141327
\(307\) 21.6768 1.23716 0.618581 0.785721i \(-0.287708\pi\)
0.618581 + 0.785721i \(0.287708\pi\)
\(308\) 32.0383 1.82555
\(309\) −1.36407 −0.0775993
\(310\) −16.7109 −0.949117
\(311\) 25.6294 1.45331 0.726655 0.687003i \(-0.241074\pi\)
0.726655 + 0.687003i \(0.241074\pi\)
\(312\) 19.5584 1.10728
\(313\) −29.3253 −1.65756 −0.828781 0.559573i \(-0.810965\pi\)
−0.828781 + 0.559573i \(0.810965\pi\)
\(314\) −2.47221 −0.139515
\(315\) −3.99881 −0.225308
\(316\) −27.1112 −1.52513
\(317\) −20.7740 −1.16678 −0.583391 0.812191i \(-0.698274\pi\)
−0.583391 + 0.812191i \(0.698274\pi\)
\(318\) 33.5934 1.88383
\(319\) 16.2020 0.907136
\(320\) −16.4328 −0.918624
\(321\) 8.23301 0.459522
\(322\) −23.6472 −1.31781
\(323\) 5.54146 0.308335
\(324\) 4.11184 0.228436
\(325\) −4.80234 −0.266386
\(326\) 11.5496 0.639673
\(327\) 1.75758 0.0971945
\(328\) 8.35216 0.461171
\(329\) −3.54164 −0.195257
\(330\) 30.2609 1.66581
\(331\) −24.4356 −1.34310 −0.671551 0.740958i \(-0.734372\pi\)
−0.671551 + 0.740958i \(0.734372\pi\)
\(332\) 6.81013 0.373754
\(333\) 6.21888 0.340792
\(334\) 46.8473 2.56337
\(335\) −9.13551 −0.499126
\(336\) 7.47242 0.407654
\(337\) −14.0045 −0.762873 −0.381436 0.924395i \(-0.624570\pi\)
−0.381436 + 0.924395i \(0.624570\pi\)
\(338\) 2.55547 0.138999
\(339\) 11.6046 0.630277
\(340\) −10.3058 −0.558913
\(341\) 13.1709 0.713246
\(342\) −13.6997 −0.740794
\(343\) 18.2752 0.986766
\(344\) 44.0289 2.37388
\(345\) −15.0264 −0.808996
\(346\) −53.9647 −2.90116
\(347\) 17.2275 0.924820 0.462410 0.886666i \(-0.346985\pi\)
0.462410 + 0.886666i \(0.346985\pi\)
\(348\) 13.6413 0.731250
\(349\) 17.9965 0.963331 0.481666 0.876355i \(-0.340032\pi\)
0.481666 + 0.876355i \(0.340032\pi\)
\(350\) −5.05635 −0.270273
\(351\) 3.74615 0.199955
\(352\) −5.55241 −0.295945
\(353\) −6.73491 −0.358463 −0.179232 0.983807i \(-0.557361\pi\)
−0.179232 + 0.983807i \(0.557361\pi\)
\(354\) −28.0424 −1.49044
\(355\) −33.8256 −1.79527
\(356\) −59.6603 −3.16199
\(357\) −1.59545 −0.0844404
\(358\) 19.7617 1.04444
\(359\) 17.7930 0.939077 0.469538 0.882912i \(-0.344420\pi\)
0.469538 + 0.882912i \(0.344420\pi\)
\(360\) 13.0856 0.689673
\(361\) 11.7078 0.616201
\(362\) 33.9417 1.78394
\(363\) −12.8505 −0.674476
\(364\) 24.5757 1.28812
\(365\) −17.6209 −0.922320
\(366\) 17.0439 0.890898
\(367\) −11.5179 −0.601232 −0.300616 0.953745i \(-0.597192\pi\)
−0.300616 + 0.953745i \(0.597192\pi\)
\(368\) 28.0793 1.46373
\(369\) 1.59975 0.0832795
\(370\) 38.5341 2.00329
\(371\) 21.6797 1.12555
\(372\) 11.0893 0.574954
\(373\) 29.1916 1.51148 0.755741 0.654871i \(-0.227277\pi\)
0.755741 + 0.654871i \(0.227277\pi\)
\(374\) 12.0735 0.624308
\(375\) 9.31887 0.481225
\(376\) 11.5896 0.597688
\(377\) 12.4281 0.640080
\(378\) 3.94430 0.202873
\(379\) −34.4011 −1.76707 −0.883534 0.468367i \(-0.844842\pi\)
−0.883534 + 0.468367i \(0.844842\pi\)
\(380\) −57.1094 −2.92965
\(381\) −9.34079 −0.478543
\(382\) 44.0935 2.25602
\(383\) 18.0949 0.924607 0.462304 0.886722i \(-0.347023\pi\)
0.462304 + 0.886722i \(0.347023\pi\)
\(384\) 18.4827 0.943191
\(385\) 19.5290 0.995289
\(386\) 50.3897 2.56477
\(387\) 8.43316 0.428682
\(388\) −21.7705 −1.10523
\(389\) 1.16669 0.0591537 0.0295769 0.999563i \(-0.490584\pi\)
0.0295769 + 0.999563i \(0.490584\pi\)
\(390\) 23.2123 1.17540
\(391\) −5.99527 −0.303194
\(392\) −23.2568 −1.17464
\(393\) −2.25937 −0.113970
\(394\) −8.85459 −0.446088
\(395\) −16.5257 −0.831498
\(396\) −20.0810 −1.00911
\(397\) 31.2261 1.56719 0.783596 0.621271i \(-0.213383\pi\)
0.783596 + 0.621271i \(0.213383\pi\)
\(398\) −20.8353 −1.04438
\(399\) −8.84115 −0.442611
\(400\) 6.00404 0.300202
\(401\) −18.1287 −0.905306 −0.452653 0.891687i \(-0.649522\pi\)
−0.452653 + 0.891687i \(0.649522\pi\)
\(402\) 9.01098 0.449427
\(403\) 10.1031 0.503270
\(404\) 52.3425 2.60413
\(405\) 2.50638 0.124543
\(406\) 13.0855 0.649421
\(407\) −30.3711 −1.50544
\(408\) 5.22093 0.258475
\(409\) 38.0413 1.88102 0.940511 0.339762i \(-0.110347\pi\)
0.940511 + 0.339762i \(0.110347\pi\)
\(410\) 9.91252 0.489544
\(411\) −11.2060 −0.552752
\(412\) 5.60885 0.276328
\(413\) −18.0973 −0.890509
\(414\) 14.8216 0.728442
\(415\) 4.15112 0.203771
\(416\) −4.25911 −0.208820
\(417\) −13.5241 −0.662277
\(418\) 66.9051 3.27244
\(419\) 20.8824 1.02017 0.510086 0.860123i \(-0.329614\pi\)
0.510086 + 0.860123i \(0.329614\pi\)
\(420\) 16.4425 0.802311
\(421\) 27.6867 1.34937 0.674684 0.738107i \(-0.264280\pi\)
0.674684 + 0.738107i \(0.264280\pi\)
\(422\) 30.9112 1.50474
\(423\) 2.21983 0.107932
\(424\) −70.9440 −3.44535
\(425\) −1.28194 −0.0621831
\(426\) 33.3645 1.61651
\(427\) 10.9993 0.532295
\(428\) −33.8528 −1.63634
\(429\) −18.2951 −0.883295
\(430\) 52.2544 2.51993
\(431\) −17.3693 −0.836649 −0.418325 0.908298i \(-0.637383\pi\)
−0.418325 + 0.908298i \(0.637383\pi\)
\(432\) −4.68357 −0.225338
\(433\) 10.6305 0.510871 0.255436 0.966826i \(-0.417781\pi\)
0.255436 + 0.966826i \(0.417781\pi\)
\(434\) 10.6375 0.510615
\(435\) 8.31507 0.398677
\(436\) −7.22690 −0.346106
\(437\) −33.2226 −1.58925
\(438\) 17.3807 0.830482
\(439\) −14.2172 −0.678548 −0.339274 0.940688i \(-0.610181\pi\)
−0.339274 + 0.940688i \(0.610181\pi\)
\(440\) −63.9063 −3.04661
\(441\) −4.45453 −0.212120
\(442\) 9.26130 0.440515
\(443\) −22.9230 −1.08911 −0.544553 0.838727i \(-0.683301\pi\)
−0.544553 + 0.838727i \(0.683301\pi\)
\(444\) −25.5711 −1.21355
\(445\) −36.3660 −1.72391
\(446\) 71.8808 3.40365
\(447\) 19.7181 0.932632
\(448\) 10.4604 0.494210
\(449\) −18.2541 −0.861463 −0.430731 0.902480i \(-0.641744\pi\)
−0.430731 + 0.902480i \(0.641744\pi\)
\(450\) 3.16922 0.149399
\(451\) −7.81268 −0.367885
\(452\) −47.7164 −2.24439
\(453\) 11.3901 0.535151
\(454\) −49.5394 −2.32500
\(455\) 14.9802 0.702281
\(456\) 28.9316 1.35485
\(457\) −36.9837 −1.73003 −0.865013 0.501749i \(-0.832690\pi\)
−0.865013 + 0.501749i \(0.832690\pi\)
\(458\) 55.1288 2.57600
\(459\) 1.00000 0.0466760
\(460\) 61.7863 2.88080
\(461\) −35.8595 −1.67015 −0.835073 0.550140i \(-0.814574\pi\)
−0.835073 + 0.550140i \(0.814574\pi\)
\(462\) −19.2628 −0.896186
\(463\) −2.33188 −0.108372 −0.0541859 0.998531i \(-0.517256\pi\)
−0.0541859 + 0.998531i \(0.517256\pi\)
\(464\) −15.5380 −0.721335
\(465\) 6.75950 0.313464
\(466\) −6.83544 −0.316646
\(467\) −15.3340 −0.709573 −0.354787 0.934947i \(-0.615446\pi\)
−0.354787 + 0.934947i \(0.615446\pi\)
\(468\) −15.4036 −0.712032
\(469\) 5.81528 0.268525
\(470\) 13.7548 0.634460
\(471\) 1.00000 0.0460776
\(472\) 59.2212 2.72588
\(473\) −41.1850 −1.89369
\(474\) 16.3004 0.748703
\(475\) −7.10381 −0.325945
\(476\) 6.56026 0.300689
\(477\) −13.5884 −0.622170
\(478\) −13.6158 −0.622771
\(479\) −24.9571 −1.14032 −0.570160 0.821534i \(-0.693119\pi\)
−0.570160 + 0.821534i \(0.693119\pi\)
\(480\) −2.84957 −0.130065
\(481\) −23.2969 −1.06225
\(482\) −30.4747 −1.38809
\(483\) 9.56518 0.435231
\(484\) 52.8392 2.40178
\(485\) −13.2702 −0.602570
\(486\) −2.47221 −0.112142
\(487\) 28.0174 1.26959 0.634795 0.772680i \(-0.281084\pi\)
0.634795 + 0.772680i \(0.281084\pi\)
\(488\) −35.9940 −1.62937
\(489\) −4.67176 −0.211264
\(490\) −27.6016 −1.24691
\(491\) 42.8879 1.93551 0.967753 0.251903i \(-0.0810563\pi\)
0.967753 + 0.251903i \(0.0810563\pi\)
\(492\) −6.57791 −0.296555
\(493\) 3.31756 0.149415
\(494\) 51.3211 2.30905
\(495\) −12.2404 −0.550165
\(496\) −12.6312 −0.567158
\(497\) 21.5319 0.965838
\(498\) −4.09454 −0.183481
\(499\) −13.2647 −0.593808 −0.296904 0.954907i \(-0.595954\pi\)
−0.296904 + 0.954907i \(0.595954\pi\)
\(500\) −38.3178 −1.71362
\(501\) −18.9495 −0.846602
\(502\) −45.5911 −2.03483
\(503\) 3.06201 0.136528 0.0682642 0.997667i \(-0.478254\pi\)
0.0682642 + 0.997667i \(0.478254\pi\)
\(504\) −8.32975 −0.371037
\(505\) 31.9054 1.41977
\(506\) −72.3842 −3.21787
\(507\) −1.03368 −0.0459072
\(508\) 38.4079 1.70407
\(509\) 6.23880 0.276530 0.138265 0.990395i \(-0.455847\pi\)
0.138265 + 0.990395i \(0.455847\pi\)
\(510\) 6.19631 0.274377
\(511\) 11.2167 0.496198
\(512\) −43.5803 −1.92599
\(513\) 5.54146 0.244662
\(514\) 60.4149 2.66479
\(515\) 3.41888 0.150654
\(516\) −34.6758 −1.52652
\(517\) −10.8410 −0.476786
\(518\) −24.5291 −1.07775
\(519\) 21.8285 0.958164
\(520\) −49.0208 −2.14970
\(521\) −27.8660 −1.22083 −0.610416 0.792081i \(-0.708998\pi\)
−0.610416 + 0.792081i \(0.708998\pi\)
\(522\) −8.20172 −0.358980
\(523\) 31.7178 1.38692 0.693461 0.720494i \(-0.256085\pi\)
0.693461 + 0.720494i \(0.256085\pi\)
\(524\) 9.29018 0.405844
\(525\) 2.04527 0.0892630
\(526\) 51.2840 2.23609
\(527\) 2.69692 0.117480
\(528\) 22.8731 0.995425
\(529\) 12.9433 0.562753
\(530\) −84.1978 −3.65732
\(531\) 11.3430 0.492246
\(532\) 36.3534 1.57612
\(533\) −5.99290 −0.259581
\(534\) 35.8703 1.55226
\(535\) −20.6350 −0.892131
\(536\) −19.0298 −0.821962
\(537\) −7.99352 −0.344946
\(538\) 19.5167 0.841424
\(539\) 21.7546 0.937035
\(540\) −10.3058 −0.443493
\(541\) 32.1001 1.38009 0.690045 0.723767i \(-0.257591\pi\)
0.690045 + 0.723767i \(0.257591\pi\)
\(542\) −69.1986 −2.97233
\(543\) −13.7293 −0.589180
\(544\) −1.13693 −0.0487454
\(545\) −4.40517 −0.188697
\(546\) −14.7760 −0.632353
\(547\) 14.2156 0.607817 0.303909 0.952701i \(-0.401708\pi\)
0.303909 + 0.952701i \(0.401708\pi\)
\(548\) 46.0774 1.96833
\(549\) −6.89417 −0.294236
\(550\) −15.4775 −0.659964
\(551\) 18.3841 0.783191
\(552\) −31.3009 −1.33225
\(553\) 10.5195 0.447337
\(554\) −55.4012 −2.35377
\(555\) −15.5869 −0.661626
\(556\) 55.6089 2.35834
\(557\) 16.0857 0.681575 0.340787 0.940140i \(-0.389306\pi\)
0.340787 + 0.940140i \(0.389306\pi\)
\(558\) −6.66736 −0.282252
\(559\) −31.5919 −1.33620
\(560\) −18.7287 −0.791433
\(561\) −4.88370 −0.206190
\(562\) −8.64613 −0.364715
\(563\) 23.3257 0.983062 0.491531 0.870860i \(-0.336437\pi\)
0.491531 + 0.870860i \(0.336437\pi\)
\(564\) −9.12761 −0.384342
\(565\) −29.0856 −1.22364
\(566\) 2.11889 0.0890638
\(567\) −1.59545 −0.0670028
\(568\) −70.4606 −2.95646
\(569\) 14.3464 0.601433 0.300717 0.953714i \(-0.402774\pi\)
0.300717 + 0.953714i \(0.402774\pi\)
\(570\) 34.3366 1.43820
\(571\) −8.74837 −0.366108 −0.183054 0.983103i \(-0.558598\pi\)
−0.183054 + 0.983103i \(0.558598\pi\)
\(572\) 75.2265 3.14538
\(573\) −17.8356 −0.745094
\(574\) −6.30989 −0.263370
\(575\) 7.68557 0.320510
\(576\) −6.55641 −0.273184
\(577\) −36.3599 −1.51368 −0.756841 0.653599i \(-0.773258\pi\)
−0.756841 + 0.653599i \(0.773258\pi\)
\(578\) 2.47221 0.102831
\(579\) −20.3824 −0.847064
\(580\) −34.1903 −1.41967
\(581\) −2.64243 −0.109626
\(582\) 13.0893 0.542571
\(583\) 66.3616 2.74842
\(584\) −36.7053 −1.51888
\(585\) −9.38929 −0.388199
\(586\) 26.1215 1.07907
\(587\) 6.92468 0.285812 0.142906 0.989736i \(-0.454355\pi\)
0.142906 + 0.989736i \(0.454355\pi\)
\(588\) 18.3163 0.755352
\(589\) 14.9449 0.615793
\(590\) 70.2849 2.89358
\(591\) 3.58164 0.147329
\(592\) 29.1265 1.19709
\(593\) 20.0460 0.823191 0.411596 0.911367i \(-0.364972\pi\)
0.411596 + 0.911367i \(0.364972\pi\)
\(594\) 12.0735 0.495384
\(595\) 3.99881 0.163935
\(596\) −81.0776 −3.32107
\(597\) 8.42779 0.344926
\(598\) −55.5240 −2.27055
\(599\) −32.7945 −1.33995 −0.669973 0.742385i \(-0.733694\pi\)
−0.669973 + 0.742385i \(0.733694\pi\)
\(600\) −6.69291 −0.273237
\(601\) −8.30537 −0.338783 −0.169391 0.985549i \(-0.554180\pi\)
−0.169391 + 0.985549i \(0.554180\pi\)
\(602\) −33.2629 −1.35570
\(603\) −3.64490 −0.148432
\(604\) −46.8341 −1.90565
\(605\) 32.2082 1.30945
\(606\) −31.4705 −1.27840
\(607\) 37.1838 1.50924 0.754622 0.656160i \(-0.227820\pi\)
0.754622 + 0.656160i \(0.227820\pi\)
\(608\) −6.30025 −0.255509
\(609\) −5.29302 −0.214484
\(610\) −42.7184 −1.72962
\(611\) −8.31584 −0.336423
\(612\) −4.11184 −0.166211
\(613\) 10.5268 0.425172 0.212586 0.977142i \(-0.431811\pi\)
0.212586 + 0.977142i \(0.431811\pi\)
\(614\) 53.5898 2.16271
\(615\) −4.00957 −0.161682
\(616\) 40.6800 1.63904
\(617\) −14.9352 −0.601267 −0.300634 0.953740i \(-0.597198\pi\)
−0.300634 + 0.953740i \(0.597198\pi\)
\(618\) −3.37228 −0.135653
\(619\) 9.26278 0.372303 0.186151 0.982521i \(-0.440399\pi\)
0.186151 + 0.982521i \(0.440399\pi\)
\(620\) −27.7940 −1.11623
\(621\) −5.99527 −0.240582
\(622\) 63.3614 2.54056
\(623\) 23.1490 0.927447
\(624\) 17.5454 0.702377
\(625\) −29.7663 −1.19065
\(626\) −72.4983 −2.89762
\(627\) −27.0628 −1.08079
\(628\) −4.11184 −0.164080
\(629\) −6.21888 −0.247963
\(630\) −9.88592 −0.393865
\(631\) −28.0276 −1.11576 −0.557881 0.829921i \(-0.688386\pi\)
−0.557881 + 0.829921i \(0.688386\pi\)
\(632\) −34.4239 −1.36931
\(633\) −12.5035 −0.496968
\(634\) −51.3577 −2.03967
\(635\) 23.4116 0.929059
\(636\) 55.8733 2.21552
\(637\) 16.6873 0.661177
\(638\) 40.0547 1.58578
\(639\) −13.4958 −0.533885
\(640\) −46.3247 −1.83114
\(641\) 16.9974 0.671356 0.335678 0.941977i \(-0.391035\pi\)
0.335678 + 0.941977i \(0.391035\pi\)
\(642\) 20.3538 0.803299
\(643\) −38.6400 −1.52381 −0.761907 0.647686i \(-0.775737\pi\)
−0.761907 + 0.647686i \(0.775737\pi\)
\(644\) −39.3305 −1.54984
\(645\) −21.1367 −0.832257
\(646\) 13.6997 0.539007
\(647\) −27.0102 −1.06188 −0.530941 0.847409i \(-0.678162\pi\)
−0.530941 + 0.847409i \(0.678162\pi\)
\(648\) 5.22093 0.205097
\(649\) −55.3959 −2.17448
\(650\) −11.8724 −0.465674
\(651\) −4.30281 −0.168640
\(652\) 19.2096 0.752305
\(653\) 6.90725 0.270302 0.135151 0.990825i \(-0.456848\pi\)
0.135151 + 0.990825i \(0.456848\pi\)
\(654\) 4.34512 0.169908
\(655\) 5.66284 0.221266
\(656\) 7.49252 0.292534
\(657\) −7.03042 −0.274283
\(658\) −8.75570 −0.341333
\(659\) 10.8178 0.421403 0.210701 0.977550i \(-0.432425\pi\)
0.210701 + 0.977550i \(0.432425\pi\)
\(660\) 50.3306 1.95912
\(661\) −27.9516 −1.08719 −0.543595 0.839348i \(-0.682937\pi\)
−0.543595 + 0.839348i \(0.682937\pi\)
\(662\) −60.4101 −2.34790
\(663\) −3.74615 −0.145489
\(664\) 8.64702 0.335569
\(665\) 22.1593 0.859300
\(666\) 15.3744 0.595746
\(667\) −19.8897 −0.770132
\(668\) 77.9174 3.01472
\(669\) −29.0755 −1.12412
\(670\) −22.5849 −0.872533
\(671\) 33.6691 1.29978
\(672\) 1.81392 0.0699734
\(673\) −16.8896 −0.651048 −0.325524 0.945534i \(-0.605541\pi\)
−0.325524 + 0.945534i \(0.605541\pi\)
\(674\) −34.6221 −1.33359
\(675\) −1.28194 −0.0493418
\(676\) 4.25032 0.163474
\(677\) −21.0430 −0.808748 −0.404374 0.914594i \(-0.632511\pi\)
−0.404374 + 0.914594i \(0.632511\pi\)
\(678\) 28.6891 1.10180
\(679\) 8.44726 0.324176
\(680\) −13.0856 −0.501811
\(681\) 20.0385 0.767877
\(682\) 32.5614 1.24684
\(683\) 32.7088 1.25157 0.625784 0.779996i \(-0.284779\pi\)
0.625784 + 0.779996i \(0.284779\pi\)
\(684\) −22.7856 −0.871230
\(685\) 28.0865 1.07313
\(686\) 45.1801 1.72499
\(687\) −22.2994 −0.850774
\(688\) 39.4973 1.50582
\(689\) 50.9042 1.93930
\(690\) −37.1486 −1.41422
\(691\) −44.0088 −1.67417 −0.837087 0.547069i \(-0.815743\pi\)
−0.837087 + 0.547069i \(0.815743\pi\)
\(692\) −89.7553 −3.41198
\(693\) 7.79171 0.295983
\(694\) 42.5900 1.61670
\(695\) 33.8965 1.28577
\(696\) 17.3208 0.656542
\(697\) −1.59975 −0.0605947
\(698\) 44.4912 1.68402
\(699\) 2.76491 0.104578
\(700\) −8.40984 −0.317862
\(701\) −17.7496 −0.670392 −0.335196 0.942148i \(-0.608802\pi\)
−0.335196 + 0.942148i \(0.608802\pi\)
\(702\) 9.26130 0.349545
\(703\) −34.4617 −1.29975
\(704\) 32.0195 1.20678
\(705\) −5.56375 −0.209543
\(706\) −16.6501 −0.626636
\(707\) −20.3096 −0.763822
\(708\) −46.6408 −1.75287
\(709\) 0.947486 0.0355836 0.0177918 0.999842i \(-0.494336\pi\)
0.0177918 + 0.999842i \(0.494336\pi\)
\(710\) −83.6240 −3.13835
\(711\) −6.59345 −0.247274
\(712\) −75.7524 −2.83894
\(713\) −16.1688 −0.605525
\(714\) −3.94430 −0.147612
\(715\) 45.8544 1.71486
\(716\) 32.8681 1.22834
\(717\) 5.50752 0.205682
\(718\) 43.9880 1.64162
\(719\) −48.6762 −1.81532 −0.907658 0.419710i \(-0.862132\pi\)
−0.907658 + 0.419710i \(0.862132\pi\)
\(720\) 11.7388 0.437479
\(721\) −2.17631 −0.0810501
\(722\) 28.9442 1.07719
\(723\) 12.3269 0.458442
\(724\) 56.4527 2.09805
\(725\) −4.25291 −0.157949
\(726\) −31.7692 −1.17907
\(727\) 41.3146 1.53227 0.766137 0.642677i \(-0.222176\pi\)
0.766137 + 0.642677i \(0.222176\pi\)
\(728\) 31.2045 1.15652
\(729\) 1.00000 0.0370370
\(730\) −43.5626 −1.61233
\(731\) −8.43316 −0.311912
\(732\) 28.3478 1.04776
\(733\) −32.2639 −1.19169 −0.595847 0.803098i \(-0.703183\pi\)
−0.595847 + 0.803098i \(0.703183\pi\)
\(734\) −28.4748 −1.05103
\(735\) 11.1647 0.411817
\(736\) 6.81620 0.251248
\(737\) 17.8006 0.655694
\(738\) 3.95492 0.145582
\(739\) 16.6915 0.614007 0.307004 0.951708i \(-0.400674\pi\)
0.307004 + 0.951708i \(0.400674\pi\)
\(740\) 64.0908 2.35602
\(741\) −20.7592 −0.762608
\(742\) 53.5967 1.96760
\(743\) −13.0508 −0.478787 −0.239394 0.970923i \(-0.576949\pi\)
−0.239394 + 0.970923i \(0.576949\pi\)
\(744\) 14.0804 0.516213
\(745\) −49.4209 −1.81064
\(746\) 72.1678 2.64225
\(747\) 1.65622 0.0605980
\(748\) 20.0810 0.734234
\(749\) 13.1354 0.479957
\(750\) 23.0383 0.841238
\(751\) 14.6647 0.535124 0.267562 0.963541i \(-0.413782\pi\)
0.267562 + 0.963541i \(0.413782\pi\)
\(752\) 10.3967 0.379130
\(753\) 18.4414 0.672042
\(754\) 30.7249 1.11894
\(755\) −28.5478 −1.03896
\(756\) 6.56026 0.238594
\(757\) −44.0438 −1.60080 −0.800400 0.599467i \(-0.795379\pi\)
−0.800400 + 0.599467i \(0.795379\pi\)
\(758\) −85.0470 −3.08905
\(759\) 29.2791 1.06276
\(760\) −72.5135 −2.63034
\(761\) 53.6313 1.94413 0.972066 0.234707i \(-0.0754132\pi\)
0.972066 + 0.234707i \(0.0754132\pi\)
\(762\) −23.0924 −0.836551
\(763\) 2.80414 0.101517
\(764\) 73.3373 2.65325
\(765\) −2.50638 −0.0906183
\(766\) 44.7345 1.61632
\(767\) −42.4928 −1.53432
\(768\) 32.5804 1.17564
\(769\) 2.30369 0.0830730 0.0415365 0.999137i \(-0.486775\pi\)
0.0415365 + 0.999137i \(0.486775\pi\)
\(770\) 48.2798 1.73988
\(771\) −24.4376 −0.880097
\(772\) 83.8093 3.01636
\(773\) −25.2634 −0.908660 −0.454330 0.890833i \(-0.650121\pi\)
−0.454330 + 0.890833i \(0.650121\pi\)
\(774\) 20.8486 0.749387
\(775\) −3.45728 −0.124189
\(776\) −27.6426 −0.992313
\(777\) 9.92193 0.355947
\(778\) 2.88432 0.103408
\(779\) −8.86494 −0.317619
\(780\) 38.6073 1.38236
\(781\) 65.9093 2.35842
\(782\) −14.8216 −0.530019
\(783\) 3.31756 0.118560
\(784\) −20.8631 −0.745110
\(785\) −2.50638 −0.0894565
\(786\) −5.58565 −0.199234
\(787\) 46.0316 1.64085 0.820425 0.571754i \(-0.193737\pi\)
0.820425 + 0.571754i \(0.193737\pi\)
\(788\) −14.7272 −0.524633
\(789\) −20.7441 −0.738511
\(790\) −40.8551 −1.45356
\(791\) 18.5147 0.658305
\(792\) −25.4974 −0.906012
\(793\) 25.8266 0.917131
\(794\) 77.1976 2.73964
\(795\) 34.0577 1.20790
\(796\) −34.6537 −1.22827
\(797\) −22.1643 −0.785100 −0.392550 0.919731i \(-0.628407\pi\)
−0.392550 + 0.919731i \(0.628407\pi\)
\(798\) −21.8572 −0.773737
\(799\) −2.21983 −0.0785321
\(800\) 1.45747 0.0515294
\(801\) −14.5094 −0.512664
\(802\) −44.8181 −1.58258
\(803\) 34.3344 1.21164
\(804\) 14.9873 0.528560
\(805\) −23.9740 −0.844972
\(806\) 24.9770 0.879776
\(807\) −7.89442 −0.277897
\(808\) 66.4608 2.33808
\(809\) −43.2647 −1.52111 −0.760554 0.649275i \(-0.775072\pi\)
−0.760554 + 0.649275i \(0.775072\pi\)
\(810\) 6.19631 0.217716
\(811\) −24.4397 −0.858196 −0.429098 0.903258i \(-0.641168\pi\)
−0.429098 + 0.903258i \(0.641168\pi\)
\(812\) 21.7641 0.763769
\(813\) 27.9905 0.981671
\(814\) −75.0839 −2.63169
\(815\) 11.7092 0.410156
\(816\) 4.68357 0.163958
\(817\) −46.7320 −1.63495
\(818\) 94.0463 3.28825
\(819\) 5.97682 0.208847
\(820\) 16.4867 0.575742
\(821\) −0.416979 −0.0145527 −0.00727633 0.999974i \(-0.502316\pi\)
−0.00727633 + 0.999974i \(0.502316\pi\)
\(822\) −27.7037 −0.966276
\(823\) 1.01442 0.0353603 0.0176802 0.999844i \(-0.494372\pi\)
0.0176802 + 0.999844i \(0.494372\pi\)
\(824\) 7.12172 0.248097
\(825\) 6.26060 0.217966
\(826\) −44.7404 −1.55672
\(827\) −21.4369 −0.745433 −0.372716 0.927945i \(-0.621574\pi\)
−0.372716 + 0.927945i \(0.621574\pi\)
\(828\) 24.6516 0.856703
\(829\) 3.72572 0.129399 0.0646997 0.997905i \(-0.479391\pi\)
0.0646997 + 0.997905i \(0.479391\pi\)
\(830\) 10.2625 0.356215
\(831\) 22.4096 0.777379
\(832\) 24.5613 0.851511
\(833\) 4.45453 0.154340
\(834\) −33.4344 −1.15774
\(835\) 47.4947 1.64362
\(836\) 111.278 3.84863
\(837\) 2.69692 0.0932191
\(838\) 51.6258 1.78338
\(839\) −22.7048 −0.783858 −0.391929 0.919995i \(-0.628192\pi\)
−0.391929 + 0.919995i \(0.628192\pi\)
\(840\) 20.8775 0.720343
\(841\) −17.9938 −0.620475
\(842\) 68.4475 2.35886
\(843\) 3.49732 0.120454
\(844\) 51.4123 1.76968
\(845\) 2.59079 0.0891258
\(846\) 5.48791 0.188678
\(847\) −20.5024 −0.704470
\(848\) −63.6422 −2.18548
\(849\) −0.857084 −0.0294150
\(850\) −3.16922 −0.108704
\(851\) 37.2839 1.27807
\(852\) 55.4926 1.90114
\(853\) 52.7749 1.80698 0.903489 0.428612i \(-0.140997\pi\)
0.903489 + 0.428612i \(0.140997\pi\)
\(854\) 27.1927 0.930516
\(855\) −13.8890 −0.474994
\(856\) −42.9840 −1.46916
\(857\) 30.8315 1.05318 0.526591 0.850119i \(-0.323470\pi\)
0.526591 + 0.850119i \(0.323470\pi\)
\(858\) −45.2294 −1.54411
\(859\) −0.580878 −0.0198193 −0.00990965 0.999951i \(-0.503154\pi\)
−0.00990965 + 0.999951i \(0.503154\pi\)
\(860\) 86.9108 2.96363
\(861\) 2.55232 0.0869829
\(862\) −42.9406 −1.46256
\(863\) 26.6726 0.907947 0.453973 0.891015i \(-0.350006\pi\)
0.453973 + 0.891015i \(0.350006\pi\)
\(864\) −1.13693 −0.0386791
\(865\) −54.7104 −1.86021
\(866\) 26.2810 0.893064
\(867\) −1.00000 −0.0339618
\(868\) 17.6925 0.600522
\(869\) 32.2004 1.09232
\(870\) 20.5566 0.696935
\(871\) 13.6544 0.462661
\(872\) −9.17621 −0.310746
\(873\) −5.29458 −0.179194
\(874\) −82.1334 −2.77820
\(875\) 14.8678 0.502625
\(876\) 28.9080 0.976710
\(877\) 35.2182 1.18923 0.594617 0.804009i \(-0.297304\pi\)
0.594617 + 0.804009i \(0.297304\pi\)
\(878\) −35.1479 −1.18618
\(879\) −10.5660 −0.356384
\(880\) −57.3288 −1.93255
\(881\) −55.4296 −1.86747 −0.933736 0.357962i \(-0.883472\pi\)
−0.933736 + 0.357962i \(0.883472\pi\)
\(882\) −11.0125 −0.370812
\(883\) 45.2445 1.52260 0.761299 0.648401i \(-0.224562\pi\)
0.761299 + 0.648401i \(0.224562\pi\)
\(884\) 15.4036 0.518079
\(885\) −28.4299 −0.955662
\(886\) −56.6706 −1.90389
\(887\) −6.10134 −0.204863 −0.102431 0.994740i \(-0.532662\pi\)
−0.102431 + 0.994740i \(0.532662\pi\)
\(888\) −32.4683 −1.08957
\(889\) −14.9028 −0.499824
\(890\) −89.9046 −3.01361
\(891\) −4.88370 −0.163610
\(892\) 119.554 4.00296
\(893\) −12.3011 −0.411642
\(894\) 48.7473 1.63035
\(895\) 20.0348 0.669690
\(896\) 29.4883 0.985135
\(897\) 22.4592 0.749892
\(898\) −45.1280 −1.50594
\(899\) 8.94719 0.298406
\(900\) 5.27113 0.175704
\(901\) 13.5884 0.452695
\(902\) −19.3146 −0.643106
\(903\) 13.4547 0.447745
\(904\) −60.5870 −2.01509
\(905\) 34.4108 1.14385
\(906\) 28.1587 0.935508
\(907\) −14.0834 −0.467631 −0.233816 0.972281i \(-0.575121\pi\)
−0.233816 + 0.972281i \(0.575121\pi\)
\(908\) −82.3951 −2.73438
\(909\) 12.7297 0.422217
\(910\) 37.0342 1.22767
\(911\) −18.5142 −0.613402 −0.306701 0.951806i \(-0.599225\pi\)
−0.306701 + 0.951806i \(0.599225\pi\)
\(912\) 25.9538 0.859417
\(913\) −8.08849 −0.267690
\(914\) −91.4317 −3.02429
\(915\) 17.2794 0.571240
\(916\) 91.6915 3.02957
\(917\) −3.60472 −0.119038
\(918\) 2.47221 0.0815952
\(919\) −1.19860 −0.0395383 −0.0197691 0.999805i \(-0.506293\pi\)
−0.0197691 + 0.999805i \(0.506293\pi\)
\(920\) 78.4519 2.58648
\(921\) −21.6768 −0.714276
\(922\) −88.6525 −2.91961
\(923\) 50.5573 1.66411
\(924\) −32.0383 −1.05398
\(925\) 7.97221 0.262125
\(926\) −5.76492 −0.189447
\(927\) 1.36407 0.0448020
\(928\) −3.77183 −0.123816
\(929\) 15.3912 0.504969 0.252485 0.967601i \(-0.418752\pi\)
0.252485 + 0.967601i \(0.418752\pi\)
\(930\) 16.7109 0.547973
\(931\) 24.6846 0.809005
\(932\) −11.3689 −0.372400
\(933\) −25.6294 −0.839069
\(934\) −37.9090 −1.24042
\(935\) 12.2404 0.400304
\(936\) −19.5584 −0.639287
\(937\) 12.9738 0.423834 0.211917 0.977288i \(-0.432029\pi\)
0.211917 + 0.977288i \(0.432029\pi\)
\(938\) 14.3766 0.469413
\(939\) 29.3253 0.956994
\(940\) 22.8773 0.746174
\(941\) −26.7806 −0.873023 −0.436512 0.899699i \(-0.643786\pi\)
−0.436512 + 0.899699i \(0.643786\pi\)
\(942\) 2.47221 0.0805491
\(943\) 9.59092 0.312323
\(944\) 53.1259 1.72910
\(945\) 3.99881 0.130081
\(946\) −101.818 −3.31039
\(947\) −34.0540 −1.10661 −0.553303 0.832980i \(-0.686633\pi\)
−0.553303 + 0.832980i \(0.686633\pi\)
\(948\) 27.1112 0.880532
\(949\) 26.3370 0.854937
\(950\) −17.5621 −0.569791
\(951\) 20.7740 0.673642
\(952\) 8.32975 0.269969
\(953\) 14.5859 0.472485 0.236242 0.971694i \(-0.424084\pi\)
0.236242 + 0.971694i \(0.424084\pi\)
\(954\) −33.5934 −1.08763
\(955\) 44.7028 1.44655
\(956\) −22.6461 −0.732426
\(957\) −16.2020 −0.523735
\(958\) −61.6993 −1.99341
\(959\) −17.8787 −0.577333
\(960\) 16.4328 0.530368
\(961\) −23.7266 −0.765375
\(962\) −57.5949 −1.85693
\(963\) −8.23301 −0.265305
\(964\) −50.6863 −1.63250
\(965\) 51.0861 1.64452
\(966\) 23.6472 0.760836
\(967\) −21.2818 −0.684375 −0.342188 0.939632i \(-0.611168\pi\)
−0.342188 + 0.939632i \(0.611168\pi\)
\(968\) 67.0915 2.15640
\(969\) −5.54146 −0.178017
\(970\) −32.8069 −1.05336
\(971\) 21.5909 0.692886 0.346443 0.938071i \(-0.387389\pi\)
0.346443 + 0.938071i \(0.387389\pi\)
\(972\) −4.11184 −0.131887
\(973\) −21.5770 −0.691728
\(974\) 69.2651 2.21940
\(975\) 4.80234 0.153798
\(976\) −32.2893 −1.03356
\(977\) −2.40610 −0.0769779 −0.0384889 0.999259i \(-0.512254\pi\)
−0.0384889 + 0.999259i \(0.512254\pi\)
\(978\) −11.5496 −0.369316
\(979\) 70.8594 2.26468
\(980\) −45.9076 −1.46647
\(981\) −1.75758 −0.0561152
\(982\) 106.028 3.38349
\(983\) 54.2149 1.72919 0.864594 0.502471i \(-0.167576\pi\)
0.864594 + 0.502471i \(0.167576\pi\)
\(984\) −8.35216 −0.266257
\(985\) −8.97696 −0.286030
\(986\) 8.20172 0.261196
\(987\) 3.54164 0.112732
\(988\) 85.3585 2.71562
\(989\) 50.5591 1.60769
\(990\) −30.2609 −0.961754
\(991\) −56.2103 −1.78558 −0.892790 0.450474i \(-0.851255\pi\)
−0.892790 + 0.450474i \(0.851255\pi\)
\(992\) −3.06620 −0.0973520
\(993\) 24.4356 0.775441
\(994\) 53.2315 1.68840
\(995\) −21.1232 −0.669651
\(996\) −6.81013 −0.215787
\(997\) 30.8626 0.977428 0.488714 0.872444i \(-0.337466\pi\)
0.488714 + 0.872444i \(0.337466\pi\)
\(998\) −32.7931 −1.03805
\(999\) −6.21888 −0.196757
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 8007.2.a.f.1.46 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.46 48 1.1 even 1 trivial