Properties

Label 8007.2.a.f.1.6
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.6
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.28381 q^{2} -1.00000 q^{3} +3.21580 q^{4} +1.64317 q^{5} +2.28381 q^{6} +3.93496 q^{7} -2.77667 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.28381 q^{2} -1.00000 q^{3} +3.21580 q^{4} +1.64317 q^{5} +2.28381 q^{6} +3.93496 q^{7} -2.77667 q^{8} +1.00000 q^{9} -3.75270 q^{10} -0.343655 q^{11} -3.21580 q^{12} +0.744706 q^{13} -8.98670 q^{14} -1.64317 q^{15} -0.0902101 q^{16} -1.00000 q^{17} -2.28381 q^{18} -7.57478 q^{19} +5.28412 q^{20} -3.93496 q^{21} +0.784844 q^{22} -3.77572 q^{23} +2.77667 q^{24} -2.29998 q^{25} -1.70077 q^{26} -1.00000 q^{27} +12.6540 q^{28} +5.07234 q^{29} +3.75270 q^{30} -4.98225 q^{31} +5.75937 q^{32} +0.343655 q^{33} +2.28381 q^{34} +6.46581 q^{35} +3.21580 q^{36} +4.72599 q^{37} +17.2994 q^{38} -0.744706 q^{39} -4.56255 q^{40} -2.83772 q^{41} +8.98670 q^{42} -0.185855 q^{43} -1.10513 q^{44} +1.64317 q^{45} +8.62304 q^{46} +8.35281 q^{47} +0.0902101 q^{48} +8.48387 q^{49} +5.25274 q^{50} +1.00000 q^{51} +2.39483 q^{52} +8.10439 q^{53} +2.28381 q^{54} -0.564685 q^{55} -10.9261 q^{56} +7.57478 q^{57} -11.5843 q^{58} -7.50731 q^{59} -5.28412 q^{60} -14.1241 q^{61} +11.3785 q^{62} +3.93496 q^{63} -12.9729 q^{64} +1.22368 q^{65} -0.784844 q^{66} +2.48169 q^{67} -3.21580 q^{68} +3.77572 q^{69} -14.7667 q^{70} -1.23832 q^{71} -2.77667 q^{72} -9.29357 q^{73} -10.7933 q^{74} +2.29998 q^{75} -24.3590 q^{76} -1.35227 q^{77} +1.70077 q^{78} +9.60307 q^{79} -0.148231 q^{80} +1.00000 q^{81} +6.48081 q^{82} +14.1340 q^{83} -12.6540 q^{84} -1.64317 q^{85} +0.424458 q^{86} -5.07234 q^{87} +0.954217 q^{88} -3.05836 q^{89} -3.75270 q^{90} +2.93038 q^{91} -12.1420 q^{92} +4.98225 q^{93} -19.0763 q^{94} -12.4467 q^{95} -5.75937 q^{96} -6.82046 q^{97} -19.3756 q^{98} -0.343655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28381 −1.61490 −0.807450 0.589936i \(-0.799153\pi\)
−0.807450 + 0.589936i \(0.799153\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.21580 1.60790
\(5\) 1.64317 0.734849 0.367425 0.930053i \(-0.380240\pi\)
0.367425 + 0.930053i \(0.380240\pi\)
\(6\) 2.28381 0.932363
\(7\) 3.93496 1.48727 0.743637 0.668584i \(-0.233099\pi\)
0.743637 + 0.668584i \(0.233099\pi\)
\(8\) −2.77667 −0.981701
\(9\) 1.00000 0.333333
\(10\) −3.75270 −1.18671
\(11\) −0.343655 −0.103616 −0.0518079 0.998657i \(-0.516498\pi\)
−0.0518079 + 0.998657i \(0.516498\pi\)
\(12\) −3.21580 −0.928323
\(13\) 0.744706 0.206544 0.103272 0.994653i \(-0.467069\pi\)
0.103272 + 0.994653i \(0.467069\pi\)
\(14\) −8.98670 −2.40180
\(15\) −1.64317 −0.424265
\(16\) −0.0902101 −0.0225525
\(17\) −1.00000 −0.242536
\(18\) −2.28381 −0.538300
\(19\) −7.57478 −1.73777 −0.868887 0.495010i \(-0.835164\pi\)
−0.868887 + 0.495010i \(0.835164\pi\)
\(20\) 5.28412 1.18157
\(21\) −3.93496 −0.858678
\(22\) 0.784844 0.167329
\(23\) −3.77572 −0.787292 −0.393646 0.919262i \(-0.628786\pi\)
−0.393646 + 0.919262i \(0.628786\pi\)
\(24\) 2.77667 0.566786
\(25\) −2.29998 −0.459997
\(26\) −1.70077 −0.333548
\(27\) −1.00000 −0.192450
\(28\) 12.6540 2.39139
\(29\) 5.07234 0.941910 0.470955 0.882157i \(-0.343909\pi\)
0.470955 + 0.882157i \(0.343909\pi\)
\(30\) 3.75270 0.685146
\(31\) −4.98225 −0.894838 −0.447419 0.894324i \(-0.647657\pi\)
−0.447419 + 0.894324i \(0.647657\pi\)
\(32\) 5.75937 1.01812
\(33\) 0.343655 0.0598227
\(34\) 2.28381 0.391671
\(35\) 6.46581 1.09292
\(36\) 3.21580 0.535967
\(37\) 4.72599 0.776949 0.388474 0.921460i \(-0.373002\pi\)
0.388474 + 0.921460i \(0.373002\pi\)
\(38\) 17.2994 2.80633
\(39\) −0.744706 −0.119248
\(40\) −4.56255 −0.721402
\(41\) −2.83772 −0.443177 −0.221588 0.975140i \(-0.571124\pi\)
−0.221588 + 0.975140i \(0.571124\pi\)
\(42\) 8.98670 1.38668
\(43\) −0.185855 −0.0283426 −0.0141713 0.999900i \(-0.504511\pi\)
−0.0141713 + 0.999900i \(0.504511\pi\)
\(44\) −1.10513 −0.166604
\(45\) 1.64317 0.244950
\(46\) 8.62304 1.27140
\(47\) 8.35281 1.21838 0.609191 0.793023i \(-0.291494\pi\)
0.609191 + 0.793023i \(0.291494\pi\)
\(48\) 0.0902101 0.0130207
\(49\) 8.48387 1.21198
\(50\) 5.25274 0.742849
\(51\) 1.00000 0.140028
\(52\) 2.39483 0.332103
\(53\) 8.10439 1.11322 0.556611 0.830773i \(-0.312101\pi\)
0.556611 + 0.830773i \(0.312101\pi\)
\(54\) 2.28381 0.310788
\(55\) −0.564685 −0.0761420
\(56\) −10.9261 −1.46006
\(57\) 7.57478 1.00330
\(58\) −11.5843 −1.52109
\(59\) −7.50731 −0.977369 −0.488684 0.872461i \(-0.662523\pi\)
−0.488684 + 0.872461i \(0.662523\pi\)
\(60\) −5.28412 −0.682177
\(61\) −14.1241 −1.80840 −0.904201 0.427107i \(-0.859533\pi\)
−0.904201 + 0.427107i \(0.859533\pi\)
\(62\) 11.3785 1.44507
\(63\) 3.93496 0.495758
\(64\) −12.9729 −1.62161
\(65\) 1.22368 0.151779
\(66\) −0.784844 −0.0966076
\(67\) 2.48169 0.303187 0.151594 0.988443i \(-0.451559\pi\)
0.151594 + 0.988443i \(0.451559\pi\)
\(68\) −3.21580 −0.389974
\(69\) 3.77572 0.454543
\(70\) −14.7667 −1.76496
\(71\) −1.23832 −0.146962 −0.0734809 0.997297i \(-0.523411\pi\)
−0.0734809 + 0.997297i \(0.523411\pi\)
\(72\) −2.77667 −0.327234
\(73\) −9.29357 −1.08773 −0.543865 0.839173i \(-0.683040\pi\)
−0.543865 + 0.839173i \(0.683040\pi\)
\(74\) −10.7933 −1.25469
\(75\) 2.29998 0.265579
\(76\) −24.3590 −2.79417
\(77\) −1.35227 −0.154105
\(78\) 1.70077 0.192574
\(79\) 9.60307 1.08043 0.540215 0.841527i \(-0.318343\pi\)
0.540215 + 0.841527i \(0.318343\pi\)
\(80\) −0.148231 −0.0165727
\(81\) 1.00000 0.111111
\(82\) 6.48081 0.715686
\(83\) 14.1340 1.55140 0.775702 0.631099i \(-0.217396\pi\)
0.775702 + 0.631099i \(0.217396\pi\)
\(84\) −12.6540 −1.38067
\(85\) −1.64317 −0.178227
\(86\) 0.424458 0.0457705
\(87\) −5.07234 −0.543812
\(88\) 0.954217 0.101720
\(89\) −3.05836 −0.324186 −0.162093 0.986776i \(-0.551824\pi\)
−0.162093 + 0.986776i \(0.551824\pi\)
\(90\) −3.75270 −0.395569
\(91\) 2.93038 0.307188
\(92\) −12.1420 −1.26589
\(93\) 4.98225 0.516635
\(94\) −19.0763 −1.96757
\(95\) −12.4467 −1.27700
\(96\) −5.75937 −0.587813
\(97\) −6.82046 −0.692513 −0.346257 0.938140i \(-0.612547\pi\)
−0.346257 + 0.938140i \(0.612547\pi\)
\(98\) −19.3756 −1.95723
\(99\) −0.343655 −0.0345386
\(100\) −7.39630 −0.739630
\(101\) 14.1430 1.40728 0.703639 0.710558i \(-0.251557\pi\)
0.703639 + 0.710558i \(0.251557\pi\)
\(102\) −2.28381 −0.226131
\(103\) 4.71884 0.464961 0.232480 0.972601i \(-0.425316\pi\)
0.232480 + 0.972601i \(0.425316\pi\)
\(104\) −2.06780 −0.202765
\(105\) −6.46581 −0.630998
\(106\) −18.5089 −1.79774
\(107\) −16.2355 −1.56955 −0.784774 0.619783i \(-0.787221\pi\)
−0.784774 + 0.619783i \(0.787221\pi\)
\(108\) −3.21580 −0.309441
\(109\) −18.7232 −1.79336 −0.896680 0.442680i \(-0.854028\pi\)
−0.896680 + 0.442680i \(0.854028\pi\)
\(110\) 1.28963 0.122962
\(111\) −4.72599 −0.448572
\(112\) −0.354973 −0.0335418
\(113\) −15.7168 −1.47851 −0.739255 0.673426i \(-0.764822\pi\)
−0.739255 + 0.673426i \(0.764822\pi\)
\(114\) −17.2994 −1.62024
\(115\) −6.20416 −0.578541
\(116\) 16.3116 1.51450
\(117\) 0.744706 0.0688481
\(118\) 17.1453 1.57835
\(119\) −3.93496 −0.360717
\(120\) 4.56255 0.416502
\(121\) −10.8819 −0.989264
\(122\) 32.2568 2.92039
\(123\) 2.83772 0.255868
\(124\) −16.0219 −1.43881
\(125\) −11.9951 −1.07288
\(126\) −8.98670 −0.800599
\(127\) −1.73892 −0.154305 −0.0771523 0.997019i \(-0.524583\pi\)
−0.0771523 + 0.997019i \(0.524583\pi\)
\(128\) 18.1089 1.60062
\(129\) 0.185855 0.0163636
\(130\) −2.79466 −0.245108
\(131\) −3.19032 −0.278739 −0.139370 0.990240i \(-0.544508\pi\)
−0.139370 + 0.990240i \(0.544508\pi\)
\(132\) 1.10513 0.0961890
\(133\) −29.8064 −2.58455
\(134\) −5.66773 −0.489617
\(135\) −1.64317 −0.141422
\(136\) 2.77667 0.238098
\(137\) 13.0663 1.11633 0.558164 0.829731i \(-0.311506\pi\)
0.558164 + 0.829731i \(0.311506\pi\)
\(138\) −8.62304 −0.734042
\(139\) 5.19269 0.440439 0.220219 0.975450i \(-0.429323\pi\)
0.220219 + 0.975450i \(0.429323\pi\)
\(140\) 20.7928 1.75731
\(141\) −8.35281 −0.703433
\(142\) 2.82810 0.237329
\(143\) −0.255922 −0.0214013
\(144\) −0.0902101 −0.00751751
\(145\) 8.33473 0.692161
\(146\) 21.2248 1.75658
\(147\) −8.48387 −0.699738
\(148\) 15.1979 1.24926
\(149\) 10.4192 0.853575 0.426788 0.904352i \(-0.359645\pi\)
0.426788 + 0.904352i \(0.359645\pi\)
\(150\) −5.25274 −0.428884
\(151\) 11.8289 0.962624 0.481312 0.876549i \(-0.340160\pi\)
0.481312 + 0.876549i \(0.340160\pi\)
\(152\) 21.0327 1.70598
\(153\) −1.00000 −0.0808452
\(154\) 3.08833 0.248864
\(155\) −8.18669 −0.657571
\(156\) −2.39483 −0.191740
\(157\) −1.00000 −0.0798087
\(158\) −21.9316 −1.74479
\(159\) −8.10439 −0.642720
\(160\) 9.46363 0.748166
\(161\) −14.8573 −1.17092
\(162\) −2.28381 −0.179433
\(163\) −2.45136 −0.192005 −0.0960027 0.995381i \(-0.530606\pi\)
−0.0960027 + 0.995381i \(0.530606\pi\)
\(164\) −9.12554 −0.712585
\(165\) 0.564685 0.0439606
\(166\) −32.2793 −2.50536
\(167\) 11.2918 0.873786 0.436893 0.899514i \(-0.356079\pi\)
0.436893 + 0.899514i \(0.356079\pi\)
\(168\) 10.9261 0.842965
\(169\) −12.4454 −0.957340
\(170\) 3.75270 0.287819
\(171\) −7.57478 −0.579258
\(172\) −0.597673 −0.0455721
\(173\) 1.69657 0.128988 0.0644939 0.997918i \(-0.479457\pi\)
0.0644939 + 0.997918i \(0.479457\pi\)
\(174\) 11.5843 0.878202
\(175\) −9.05033 −0.684141
\(176\) 0.0310012 0.00233680
\(177\) 7.50731 0.564284
\(178\) 6.98473 0.523528
\(179\) 5.23063 0.390955 0.195478 0.980708i \(-0.437374\pi\)
0.195478 + 0.980708i \(0.437374\pi\)
\(180\) 5.28412 0.393855
\(181\) −11.8843 −0.883352 −0.441676 0.897175i \(-0.645616\pi\)
−0.441676 + 0.897175i \(0.645616\pi\)
\(182\) −6.69245 −0.496077
\(183\) 14.1241 1.04408
\(184\) 10.4839 0.772886
\(185\) 7.76562 0.570940
\(186\) −11.3785 −0.834314
\(187\) 0.343655 0.0251305
\(188\) 26.8610 1.95904
\(189\) −3.93496 −0.286226
\(190\) 28.4259 2.06223
\(191\) −8.14955 −0.589681 −0.294840 0.955547i \(-0.595266\pi\)
−0.294840 + 0.955547i \(0.595266\pi\)
\(192\) 12.9729 0.936238
\(193\) −23.0373 −1.65826 −0.829131 0.559055i \(-0.811164\pi\)
−0.829131 + 0.559055i \(0.811164\pi\)
\(194\) 15.5767 1.11834
\(195\) −1.22368 −0.0876295
\(196\) 27.2825 1.94875
\(197\) −5.11546 −0.364462 −0.182231 0.983256i \(-0.558332\pi\)
−0.182231 + 0.983256i \(0.558332\pi\)
\(198\) 0.784844 0.0557764
\(199\) 15.1202 1.07184 0.535922 0.844267i \(-0.319964\pi\)
0.535922 + 0.844267i \(0.319964\pi\)
\(200\) 6.38630 0.451580
\(201\) −2.48169 −0.175045
\(202\) −32.2999 −2.27261
\(203\) 19.9594 1.40088
\(204\) 3.21580 0.225151
\(205\) −4.66286 −0.325668
\(206\) −10.7769 −0.750865
\(207\) −3.77572 −0.262431
\(208\) −0.0671800 −0.00465809
\(209\) 2.60311 0.180061
\(210\) 14.7667 1.01900
\(211\) 3.68584 0.253744 0.126872 0.991919i \(-0.459506\pi\)
0.126872 + 0.991919i \(0.459506\pi\)
\(212\) 26.0621 1.78995
\(213\) 1.23832 0.0848484
\(214\) 37.0789 2.53466
\(215\) −0.305392 −0.0208275
\(216\) 2.77667 0.188929
\(217\) −19.6049 −1.33087
\(218\) 42.7603 2.89610
\(219\) 9.29357 0.628002
\(220\) −1.81592 −0.122429
\(221\) −0.744706 −0.0500943
\(222\) 10.7933 0.724398
\(223\) 16.2493 1.08814 0.544068 0.839041i \(-0.316883\pi\)
0.544068 + 0.839041i \(0.316883\pi\)
\(224\) 22.6628 1.51422
\(225\) −2.29998 −0.153332
\(226\) 35.8942 2.38765
\(227\) −12.9106 −0.856903 −0.428452 0.903565i \(-0.640941\pi\)
−0.428452 + 0.903565i \(0.640941\pi\)
\(228\) 24.3590 1.61322
\(229\) −22.3888 −1.47949 −0.739747 0.672885i \(-0.765055\pi\)
−0.739747 + 0.672885i \(0.765055\pi\)
\(230\) 14.1691 0.934286
\(231\) 1.35227 0.0889726
\(232\) −14.0842 −0.924674
\(233\) −27.3862 −1.79413 −0.897065 0.441898i \(-0.854305\pi\)
−0.897065 + 0.441898i \(0.854305\pi\)
\(234\) −1.70077 −0.111183
\(235\) 13.7251 0.895327
\(236\) −24.1420 −1.57151
\(237\) −9.60307 −0.623787
\(238\) 8.98670 0.582521
\(239\) −26.4691 −1.71214 −0.856071 0.516858i \(-0.827102\pi\)
−0.856071 + 0.516858i \(0.827102\pi\)
\(240\) 0.148231 0.00956825
\(241\) 5.03232 0.324160 0.162080 0.986778i \(-0.448180\pi\)
0.162080 + 0.986778i \(0.448180\pi\)
\(242\) 24.8522 1.59756
\(243\) −1.00000 −0.0641500
\(244\) −45.4203 −2.90773
\(245\) 13.9405 0.890624
\(246\) −6.48081 −0.413202
\(247\) −5.64098 −0.358927
\(248\) 13.8341 0.878464
\(249\) −14.1340 −0.895703
\(250\) 27.3946 1.73259
\(251\) 14.7615 0.931736 0.465868 0.884854i \(-0.345742\pi\)
0.465868 + 0.884854i \(0.345742\pi\)
\(252\) 12.6540 0.797130
\(253\) 1.29755 0.0815760
\(254\) 3.97138 0.249186
\(255\) 1.64317 0.102899
\(256\) −15.4117 −0.963229
\(257\) −3.34200 −0.208468 −0.104234 0.994553i \(-0.533239\pi\)
−0.104234 + 0.994553i \(0.533239\pi\)
\(258\) −0.424458 −0.0264256
\(259\) 18.5966 1.15554
\(260\) 3.93511 0.244045
\(261\) 5.07234 0.313970
\(262\) 7.28609 0.450136
\(263\) −15.8904 −0.979843 −0.489921 0.871767i \(-0.662975\pi\)
−0.489921 + 0.871767i \(0.662975\pi\)
\(264\) −0.954217 −0.0587280
\(265\) 13.3169 0.818051
\(266\) 68.0723 4.17378
\(267\) 3.05836 0.187169
\(268\) 7.98064 0.487495
\(269\) −16.1573 −0.985127 −0.492564 0.870276i \(-0.663940\pi\)
−0.492564 + 0.870276i \(0.663940\pi\)
\(270\) 3.75270 0.228382
\(271\) 0.735116 0.0446551 0.0223276 0.999751i \(-0.492892\pi\)
0.0223276 + 0.999751i \(0.492892\pi\)
\(272\) 0.0902101 0.00546979
\(273\) −2.93038 −0.177355
\(274\) −29.8410 −1.80276
\(275\) 0.790401 0.0476630
\(276\) 12.1420 0.730861
\(277\) 21.7686 1.30795 0.653974 0.756517i \(-0.273101\pi\)
0.653974 + 0.756517i \(0.273101\pi\)
\(278\) −11.8591 −0.711264
\(279\) −4.98225 −0.298279
\(280\) −17.9534 −1.07292
\(281\) 28.2341 1.68431 0.842153 0.539239i \(-0.181288\pi\)
0.842153 + 0.539239i \(0.181288\pi\)
\(282\) 19.0763 1.13597
\(283\) −22.8906 −1.36071 −0.680353 0.732885i \(-0.738174\pi\)
−0.680353 + 0.732885i \(0.738174\pi\)
\(284\) −3.98220 −0.236300
\(285\) 12.4467 0.737277
\(286\) 0.584478 0.0345609
\(287\) −11.1663 −0.659125
\(288\) 5.75937 0.339374
\(289\) 1.00000 0.0588235
\(290\) −19.0350 −1.11777
\(291\) 6.82046 0.399823
\(292\) −29.8863 −1.74896
\(293\) −22.7044 −1.32641 −0.663203 0.748439i \(-0.730804\pi\)
−0.663203 + 0.748439i \(0.730804\pi\)
\(294\) 19.3756 1.13001
\(295\) −12.3358 −0.718219
\(296\) −13.1225 −0.762732
\(297\) 0.343655 0.0199409
\(298\) −23.7955 −1.37844
\(299\) −2.81180 −0.162611
\(300\) 7.39630 0.427026
\(301\) −0.731330 −0.0421532
\(302\) −27.0150 −1.55454
\(303\) −14.1430 −0.812492
\(304\) 0.683322 0.0391912
\(305\) −23.2083 −1.32890
\(306\) 2.28381 0.130557
\(307\) −21.9407 −1.25222 −0.626112 0.779733i \(-0.715355\pi\)
−0.626112 + 0.779733i \(0.715355\pi\)
\(308\) −4.34863 −0.247786
\(309\) −4.71884 −0.268445
\(310\) 18.6969 1.06191
\(311\) −6.35520 −0.360370 −0.180185 0.983633i \(-0.557670\pi\)
−0.180185 + 0.983633i \(0.557670\pi\)
\(312\) 2.06780 0.117066
\(313\) −14.8247 −0.837939 −0.418970 0.908000i \(-0.637609\pi\)
−0.418970 + 0.908000i \(0.637609\pi\)
\(314\) 2.28381 0.128883
\(315\) 6.46581 0.364307
\(316\) 30.8816 1.73723
\(317\) −11.3622 −0.638167 −0.319083 0.947727i \(-0.603375\pi\)
−0.319083 + 0.947727i \(0.603375\pi\)
\(318\) 18.5089 1.03793
\(319\) −1.74313 −0.0975968
\(320\) −21.3167 −1.19164
\(321\) 16.2355 0.906178
\(322\) 33.9313 1.89092
\(323\) 7.57478 0.421472
\(324\) 3.21580 0.178656
\(325\) −1.71281 −0.0950097
\(326\) 5.59845 0.310070
\(327\) 18.7232 1.03540
\(328\) 7.87940 0.435067
\(329\) 32.8679 1.81207
\(330\) −1.28963 −0.0709920
\(331\) −21.8740 −1.20230 −0.601151 0.799135i \(-0.705291\pi\)
−0.601151 + 0.799135i \(0.705291\pi\)
\(332\) 45.4521 2.49451
\(333\) 4.72599 0.258983
\(334\) −25.7884 −1.41108
\(335\) 4.07785 0.222797
\(336\) 0.354973 0.0193653
\(337\) 31.6522 1.72421 0.862103 0.506734i \(-0.169147\pi\)
0.862103 + 0.506734i \(0.169147\pi\)
\(338\) 28.4230 1.54601
\(339\) 15.7168 0.853618
\(340\) −5.28412 −0.286572
\(341\) 1.71217 0.0927194
\(342\) 17.2994 0.935444
\(343\) 5.83897 0.315275
\(344\) 0.516058 0.0278240
\(345\) 6.20416 0.334021
\(346\) −3.87465 −0.208303
\(347\) 15.0487 0.807856 0.403928 0.914791i \(-0.367645\pi\)
0.403928 + 0.914791i \(0.367645\pi\)
\(348\) −16.3116 −0.874396
\(349\) −10.8723 −0.581982 −0.290991 0.956726i \(-0.593985\pi\)
−0.290991 + 0.956726i \(0.593985\pi\)
\(350\) 20.6693 1.10482
\(351\) −0.744706 −0.0397494
\(352\) −1.97923 −0.105494
\(353\) −8.45806 −0.450177 −0.225088 0.974338i \(-0.572267\pi\)
−0.225088 + 0.974338i \(0.572267\pi\)
\(354\) −17.1453 −0.911263
\(355\) −2.03478 −0.107995
\(356\) −9.83510 −0.521259
\(357\) 3.93496 0.208260
\(358\) −11.9458 −0.631354
\(359\) 16.6960 0.881183 0.440591 0.897708i \(-0.354769\pi\)
0.440591 + 0.897708i \(0.354769\pi\)
\(360\) −4.56255 −0.240467
\(361\) 38.3773 2.01986
\(362\) 27.1415 1.42653
\(363\) 10.8819 0.571152
\(364\) 9.42354 0.493928
\(365\) −15.2709 −0.799318
\(366\) −32.2568 −1.68609
\(367\) −25.1638 −1.31354 −0.656770 0.754091i \(-0.728078\pi\)
−0.656770 + 0.754091i \(0.728078\pi\)
\(368\) 0.340608 0.0177554
\(369\) −2.83772 −0.147726
\(370\) −17.7352 −0.922011
\(371\) 31.8904 1.65567
\(372\) 16.0219 0.830698
\(373\) 4.42595 0.229167 0.114583 0.993414i \(-0.463447\pi\)
0.114583 + 0.993414i \(0.463447\pi\)
\(374\) −0.784844 −0.0405833
\(375\) 11.9951 0.619426
\(376\) −23.1930 −1.19609
\(377\) 3.77740 0.194546
\(378\) 8.98670 0.462226
\(379\) 21.9939 1.12975 0.564877 0.825175i \(-0.308924\pi\)
0.564877 + 0.825175i \(0.308924\pi\)
\(380\) −40.0261 −2.05329
\(381\) 1.73892 0.0890878
\(382\) 18.6121 0.952275
\(383\) 8.03045 0.410337 0.205168 0.978727i \(-0.434226\pi\)
0.205168 + 0.978727i \(0.434226\pi\)
\(384\) −18.1089 −0.924118
\(385\) −2.22201 −0.113244
\(386\) 52.6129 2.67793
\(387\) −0.185855 −0.00944753
\(388\) −21.9333 −1.11349
\(389\) 13.8051 0.699947 0.349973 0.936760i \(-0.386191\pi\)
0.349973 + 0.936760i \(0.386191\pi\)
\(390\) 2.79466 0.141513
\(391\) 3.77572 0.190946
\(392\) −23.5569 −1.18980
\(393\) 3.19032 0.160930
\(394\) 11.6828 0.588569
\(395\) 15.7795 0.793953
\(396\) −1.10513 −0.0555347
\(397\) 20.1434 1.01097 0.505483 0.862836i \(-0.331314\pi\)
0.505483 + 0.862836i \(0.331314\pi\)
\(398\) −34.5318 −1.73092
\(399\) 29.8064 1.49219
\(400\) 0.207482 0.0103741
\(401\) 9.08698 0.453782 0.226891 0.973920i \(-0.427144\pi\)
0.226891 + 0.973920i \(0.427144\pi\)
\(402\) 5.66773 0.282681
\(403\) −3.71031 −0.184824
\(404\) 45.4810 2.26277
\(405\) 1.64317 0.0816499
\(406\) −45.5836 −2.26228
\(407\) −1.62411 −0.0805042
\(408\) −2.77667 −0.137466
\(409\) 21.5349 1.06483 0.532416 0.846483i \(-0.321284\pi\)
0.532416 + 0.846483i \(0.321284\pi\)
\(410\) 10.6491 0.525921
\(411\) −13.0663 −0.644512
\(412\) 15.1749 0.747612
\(413\) −29.5409 −1.45361
\(414\) 8.62304 0.423799
\(415\) 23.2245 1.14005
\(416\) 4.28903 0.210287
\(417\) −5.19269 −0.254287
\(418\) −5.94502 −0.290781
\(419\) 12.9785 0.634042 0.317021 0.948419i \(-0.397317\pi\)
0.317021 + 0.948419i \(0.397317\pi\)
\(420\) −20.7928 −1.01458
\(421\) −30.2124 −1.47246 −0.736232 0.676729i \(-0.763397\pi\)
−0.736232 + 0.676729i \(0.763397\pi\)
\(422\) −8.41777 −0.409771
\(423\) 8.35281 0.406127
\(424\) −22.5032 −1.09285
\(425\) 2.29998 0.111566
\(426\) −2.82810 −0.137022
\(427\) −55.5776 −2.68959
\(428\) −52.2103 −2.52368
\(429\) 0.255922 0.0123560
\(430\) 0.697457 0.0336344
\(431\) 0.789997 0.0380528 0.0190264 0.999819i \(-0.493943\pi\)
0.0190264 + 0.999819i \(0.493943\pi\)
\(432\) 0.0902101 0.00434024
\(433\) −11.6288 −0.558845 −0.279423 0.960168i \(-0.590143\pi\)
−0.279423 + 0.960168i \(0.590143\pi\)
\(434\) 44.7740 2.14922
\(435\) −8.33473 −0.399620
\(436\) −60.2102 −2.88355
\(437\) 28.6003 1.36814
\(438\) −21.2248 −1.01416
\(439\) 3.63175 0.173334 0.0866670 0.996237i \(-0.472378\pi\)
0.0866670 + 0.996237i \(0.472378\pi\)
\(440\) 1.56794 0.0747488
\(441\) 8.48387 0.403994
\(442\) 1.70077 0.0808973
\(443\) −23.4637 −1.11479 −0.557396 0.830247i \(-0.688199\pi\)
−0.557396 + 0.830247i \(0.688199\pi\)
\(444\) −15.1979 −0.721259
\(445\) −5.02542 −0.238228
\(446\) −37.1104 −1.75723
\(447\) −10.4192 −0.492812
\(448\) −51.0478 −2.41178
\(449\) −5.79842 −0.273644 −0.136822 0.990596i \(-0.543689\pi\)
−0.136822 + 0.990596i \(0.543689\pi\)
\(450\) 5.25274 0.247616
\(451\) 0.975195 0.0459202
\(452\) −50.5421 −2.37730
\(453\) −11.8289 −0.555771
\(454\) 29.4853 1.38381
\(455\) 4.81512 0.225737
\(456\) −21.0327 −0.984945
\(457\) −26.5566 −1.24226 −0.621132 0.783706i \(-0.713327\pi\)
−0.621132 + 0.783706i \(0.713327\pi\)
\(458\) 51.1319 2.38924
\(459\) 1.00000 0.0466760
\(460\) −19.9514 −0.930237
\(461\) −10.1533 −0.472888 −0.236444 0.971645i \(-0.575982\pi\)
−0.236444 + 0.971645i \(0.575982\pi\)
\(462\) −3.08833 −0.143682
\(463\) 31.2143 1.45065 0.725326 0.688405i \(-0.241689\pi\)
0.725326 + 0.688405i \(0.241689\pi\)
\(464\) −0.457576 −0.0212424
\(465\) 8.18669 0.379649
\(466\) 62.5450 2.89734
\(467\) −10.6906 −0.494701 −0.247350 0.968926i \(-0.579560\pi\)
−0.247350 + 0.968926i \(0.579560\pi\)
\(468\) 2.39483 0.110701
\(469\) 9.76536 0.450922
\(470\) −31.3456 −1.44586
\(471\) 1.00000 0.0460776
\(472\) 20.8453 0.959484
\(473\) 0.0638700 0.00293674
\(474\) 21.9316 1.00735
\(475\) 17.4219 0.799371
\(476\) −12.6540 −0.579997
\(477\) 8.10439 0.371074
\(478\) 60.4504 2.76494
\(479\) 5.50305 0.251441 0.125720 0.992066i \(-0.459876\pi\)
0.125720 + 0.992066i \(0.459876\pi\)
\(480\) −9.46363 −0.431954
\(481\) 3.51947 0.160474
\(482\) −11.4929 −0.523486
\(483\) 14.8573 0.676030
\(484\) −34.9941 −1.59064
\(485\) −11.2072 −0.508893
\(486\) 2.28381 0.103596
\(487\) 9.02380 0.408907 0.204454 0.978876i \(-0.434458\pi\)
0.204454 + 0.978876i \(0.434458\pi\)
\(488\) 39.2179 1.77531
\(489\) 2.45136 0.110854
\(490\) −31.8374 −1.43827
\(491\) −7.47171 −0.337194 −0.168597 0.985685i \(-0.553924\pi\)
−0.168597 + 0.985685i \(0.553924\pi\)
\(492\) 9.12554 0.411411
\(493\) −5.07234 −0.228447
\(494\) 12.8830 0.579631
\(495\) −0.564685 −0.0253807
\(496\) 0.449449 0.0201809
\(497\) −4.87274 −0.218572
\(498\) 32.2793 1.44647
\(499\) −36.9614 −1.65462 −0.827311 0.561745i \(-0.810130\pi\)
−0.827311 + 0.561745i \(0.810130\pi\)
\(500\) −38.5740 −1.72508
\(501\) −11.2918 −0.504480
\(502\) −33.7125 −1.50466
\(503\) 27.2962 1.21708 0.608538 0.793525i \(-0.291756\pi\)
0.608538 + 0.793525i \(0.291756\pi\)
\(504\) −10.9261 −0.486686
\(505\) 23.2393 1.03414
\(506\) −2.96335 −0.131737
\(507\) 12.4454 0.552720
\(508\) −5.59204 −0.248107
\(509\) 18.2765 0.810093 0.405047 0.914296i \(-0.367255\pi\)
0.405047 + 0.914296i \(0.367255\pi\)
\(510\) −3.75270 −0.166172
\(511\) −36.5698 −1.61775
\(512\) −1.02052 −0.0451011
\(513\) 7.57478 0.334435
\(514\) 7.63251 0.336656
\(515\) 7.75386 0.341676
\(516\) 0.597673 0.0263111
\(517\) −2.87048 −0.126244
\(518\) −42.4711 −1.86607
\(519\) −1.69657 −0.0744712
\(520\) −3.39776 −0.149001
\(521\) −32.9305 −1.44271 −0.721355 0.692566i \(-0.756480\pi\)
−0.721355 + 0.692566i \(0.756480\pi\)
\(522\) −11.5843 −0.507030
\(523\) 17.1929 0.751793 0.375896 0.926662i \(-0.377335\pi\)
0.375896 + 0.926662i \(0.377335\pi\)
\(524\) −10.2594 −0.448186
\(525\) 9.05033 0.394989
\(526\) 36.2907 1.58235
\(527\) 4.98225 0.217030
\(528\) −0.0310012 −0.00134915
\(529\) −8.74393 −0.380171
\(530\) −30.4133 −1.32107
\(531\) −7.50731 −0.325790
\(532\) −95.8516 −4.15570
\(533\) −2.11326 −0.0915356
\(534\) −6.98473 −0.302259
\(535\) −26.6778 −1.15338
\(536\) −6.89085 −0.297639
\(537\) −5.23063 −0.225718
\(538\) 36.9002 1.59088
\(539\) −2.91553 −0.125581
\(540\) −5.28412 −0.227392
\(541\) −26.7196 −1.14876 −0.574382 0.818588i \(-0.694758\pi\)
−0.574382 + 0.818588i \(0.694758\pi\)
\(542\) −1.67887 −0.0721136
\(543\) 11.8843 0.510004
\(544\) −5.75937 −0.246931
\(545\) −30.7655 −1.31785
\(546\) 6.69245 0.286410
\(547\) −9.68769 −0.414216 −0.207108 0.978318i \(-0.566405\pi\)
−0.207108 + 0.978318i \(0.566405\pi\)
\(548\) 42.0186 1.79495
\(549\) −14.1241 −0.602801
\(550\) −1.80513 −0.0769710
\(551\) −38.4219 −1.63683
\(552\) −10.4839 −0.446226
\(553\) 37.7877 1.60689
\(554\) −49.7154 −2.11221
\(555\) −7.76562 −0.329632
\(556\) 16.6987 0.708182
\(557\) 15.7084 0.665586 0.332793 0.943000i \(-0.392009\pi\)
0.332793 + 0.943000i \(0.392009\pi\)
\(558\) 11.3785 0.481691
\(559\) −0.138407 −0.00585400
\(560\) −0.583281 −0.0246481
\(561\) −0.343655 −0.0145091
\(562\) −64.4814 −2.71998
\(563\) −0.931120 −0.0392420 −0.0196210 0.999807i \(-0.506246\pi\)
−0.0196210 + 0.999807i \(0.506246\pi\)
\(564\) −26.8610 −1.13105
\(565\) −25.8254 −1.08648
\(566\) 52.2779 2.19740
\(567\) 3.93496 0.165253
\(568\) 3.43841 0.144273
\(569\) −8.07417 −0.338487 −0.169243 0.985574i \(-0.554132\pi\)
−0.169243 + 0.985574i \(0.554132\pi\)
\(570\) −28.4259 −1.19063
\(571\) −10.2170 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(572\) −0.822995 −0.0344111
\(573\) 8.14955 0.340452
\(574\) 25.5017 1.06442
\(575\) 8.68410 0.362152
\(576\) −12.9729 −0.540537
\(577\) 3.95276 0.164556 0.0822778 0.996609i \(-0.473781\pi\)
0.0822778 + 0.996609i \(0.473781\pi\)
\(578\) −2.28381 −0.0949941
\(579\) 23.0373 0.957398
\(580\) 26.8029 1.11293
\(581\) 55.6165 2.30736
\(582\) −15.5767 −0.645674
\(583\) −2.78511 −0.115348
\(584\) 25.8052 1.06783
\(585\) 1.22368 0.0505929
\(586\) 51.8527 2.14201
\(587\) −4.52030 −0.186573 −0.0932863 0.995639i \(-0.529737\pi\)
−0.0932863 + 0.995639i \(0.529737\pi\)
\(588\) −27.2825 −1.12511
\(589\) 37.7394 1.55503
\(590\) 28.1727 1.15985
\(591\) 5.11546 0.210422
\(592\) −0.426332 −0.0175222
\(593\) −5.17192 −0.212385 −0.106193 0.994346i \(-0.533866\pi\)
−0.106193 + 0.994346i \(0.533866\pi\)
\(594\) −0.784844 −0.0322025
\(595\) −6.46581 −0.265072
\(596\) 33.5062 1.37247
\(597\) −15.1202 −0.618830
\(598\) 6.42163 0.262600
\(599\) −31.7199 −1.29604 −0.648021 0.761622i \(-0.724403\pi\)
−0.648021 + 0.761622i \(0.724403\pi\)
\(600\) −6.38630 −0.260720
\(601\) −16.6431 −0.678888 −0.339444 0.940626i \(-0.610239\pi\)
−0.339444 + 0.940626i \(0.610239\pi\)
\(602\) 1.67022 0.0680732
\(603\) 2.48169 0.101062
\(604\) 38.0395 1.54781
\(605\) −17.8808 −0.726960
\(606\) 32.2999 1.31209
\(607\) −42.2975 −1.71680 −0.858401 0.512979i \(-0.828542\pi\)
−0.858401 + 0.512979i \(0.828542\pi\)
\(608\) −43.6259 −1.76927
\(609\) −19.9594 −0.808797
\(610\) 53.0034 2.14605
\(611\) 6.22038 0.251650
\(612\) −3.21580 −0.129991
\(613\) −11.7368 −0.474046 −0.237023 0.971504i \(-0.576172\pi\)
−0.237023 + 0.971504i \(0.576172\pi\)
\(614\) 50.1085 2.02222
\(615\) 4.66286 0.188025
\(616\) 3.75480 0.151285
\(617\) −5.37427 −0.216360 −0.108180 0.994131i \(-0.534502\pi\)
−0.108180 + 0.994131i \(0.534502\pi\)
\(618\) 10.7769 0.433512
\(619\) 23.5041 0.944710 0.472355 0.881408i \(-0.343404\pi\)
0.472355 + 0.881408i \(0.343404\pi\)
\(620\) −26.3268 −1.05731
\(621\) 3.77572 0.151514
\(622\) 14.5141 0.581962
\(623\) −12.0345 −0.482153
\(624\) 0.0671800 0.00268935
\(625\) −8.21015 −0.328406
\(626\) 33.8568 1.35319
\(627\) −2.60311 −0.103958
\(628\) −3.21580 −0.128325
\(629\) −4.72599 −0.188438
\(630\) −14.7667 −0.588320
\(631\) −31.6032 −1.25810 −0.629051 0.777364i \(-0.716556\pi\)
−0.629051 + 0.777364i \(0.716556\pi\)
\(632\) −26.6646 −1.06066
\(633\) −3.68584 −0.146499
\(634\) 25.9492 1.03058
\(635\) −2.85735 −0.113391
\(636\) −26.0621 −1.03343
\(637\) 6.31799 0.250328
\(638\) 3.98099 0.157609
\(639\) −1.23832 −0.0489873
\(640\) 29.7561 1.17621
\(641\) −12.1560 −0.480132 −0.240066 0.970757i \(-0.577169\pi\)
−0.240066 + 0.970757i \(0.577169\pi\)
\(642\) −37.0789 −1.46339
\(643\) 25.8277 1.01854 0.509272 0.860606i \(-0.329915\pi\)
0.509272 + 0.860606i \(0.329915\pi\)
\(644\) −47.7782 −1.88272
\(645\) 0.305392 0.0120248
\(646\) −17.2994 −0.680635
\(647\) 8.69894 0.341991 0.170995 0.985272i \(-0.445302\pi\)
0.170995 + 0.985272i \(0.445302\pi\)
\(648\) −2.77667 −0.109078
\(649\) 2.57993 0.101271
\(650\) 3.91174 0.153431
\(651\) 19.6049 0.768377
\(652\) −7.88310 −0.308726
\(653\) −17.8507 −0.698553 −0.349276 0.937020i \(-0.613573\pi\)
−0.349276 + 0.937020i \(0.613573\pi\)
\(654\) −42.7603 −1.67206
\(655\) −5.24224 −0.204831
\(656\) 0.255991 0.00999476
\(657\) −9.29357 −0.362577
\(658\) −75.0642 −2.92631
\(659\) 29.0028 1.12979 0.564894 0.825163i \(-0.308917\pi\)
0.564894 + 0.825163i \(0.308917\pi\)
\(660\) 1.81592 0.0706844
\(661\) −21.9879 −0.855229 −0.427615 0.903961i \(-0.640646\pi\)
−0.427615 + 0.903961i \(0.640646\pi\)
\(662\) 49.9561 1.94160
\(663\) 0.744706 0.0289220
\(664\) −39.2454 −1.52302
\(665\) −48.9771 −1.89925
\(666\) −10.7933 −0.418232
\(667\) −19.1517 −0.741558
\(668\) 36.3122 1.40496
\(669\) −16.2493 −0.628235
\(670\) −9.31305 −0.359795
\(671\) 4.85381 0.187379
\(672\) −22.6628 −0.874238
\(673\) −26.6462 −1.02713 −0.513567 0.858049i \(-0.671676\pi\)
−0.513567 + 0.858049i \(0.671676\pi\)
\(674\) −72.2877 −2.78442
\(675\) 2.29998 0.0885264
\(676\) −40.0220 −1.53931
\(677\) 5.43009 0.208695 0.104348 0.994541i \(-0.466725\pi\)
0.104348 + 0.994541i \(0.466725\pi\)
\(678\) −35.8942 −1.37851
\(679\) −26.8382 −1.02996
\(680\) 4.56255 0.174966
\(681\) 12.9106 0.494733
\(682\) −3.91029 −0.149733
\(683\) 20.0529 0.767303 0.383652 0.923478i \(-0.374666\pi\)
0.383652 + 0.923478i \(0.374666\pi\)
\(684\) −24.3590 −0.931390
\(685\) 21.4702 0.820333
\(686\) −13.3351 −0.509137
\(687\) 22.3888 0.854186
\(688\) 0.0167660 0.000639197 0
\(689\) 6.03538 0.229930
\(690\) −14.1691 −0.539410
\(691\) 6.41006 0.243850 0.121925 0.992539i \(-0.461093\pi\)
0.121925 + 0.992539i \(0.461093\pi\)
\(692\) 5.45584 0.207400
\(693\) −1.35227 −0.0513684
\(694\) −34.3684 −1.30461
\(695\) 8.53249 0.323656
\(696\) 14.0842 0.533861
\(697\) 2.83772 0.107486
\(698\) 24.8304 0.939843
\(699\) 27.3862 1.03584
\(700\) −29.1041 −1.10003
\(701\) −17.2133 −0.650137 −0.325068 0.945691i \(-0.605387\pi\)
−0.325068 + 0.945691i \(0.605387\pi\)
\(702\) 1.70077 0.0641914
\(703\) −35.7984 −1.35016
\(704\) 4.45820 0.168025
\(705\) −13.7251 −0.516917
\(706\) 19.3166 0.726991
\(707\) 55.6519 2.09301
\(708\) 24.1420 0.907314
\(709\) 28.4357 1.06793 0.533963 0.845508i \(-0.320702\pi\)
0.533963 + 0.845508i \(0.320702\pi\)
\(710\) 4.64705 0.174401
\(711\) 9.60307 0.360143
\(712\) 8.49207 0.318254
\(713\) 18.8116 0.704499
\(714\) −8.98670 −0.336319
\(715\) −0.420524 −0.0157267
\(716\) 16.8207 0.628618
\(717\) 26.4691 0.988506
\(718\) −38.1306 −1.42302
\(719\) 14.7261 0.549191 0.274595 0.961560i \(-0.411456\pi\)
0.274595 + 0.961560i \(0.411456\pi\)
\(720\) −0.148231 −0.00552423
\(721\) 18.5684 0.691524
\(722\) −87.6467 −3.26187
\(723\) −5.03232 −0.187154
\(724\) −38.2175 −1.42034
\(725\) −11.6663 −0.433275
\(726\) −24.8522 −0.922353
\(727\) 26.8968 0.997546 0.498773 0.866733i \(-0.333784\pi\)
0.498773 + 0.866733i \(0.333784\pi\)
\(728\) −8.13671 −0.301567
\(729\) 1.00000 0.0370370
\(730\) 34.8760 1.29082
\(731\) 0.185855 0.00687409
\(732\) 45.4203 1.67878
\(733\) −17.9577 −0.663282 −0.331641 0.943406i \(-0.607602\pi\)
−0.331641 + 0.943406i \(0.607602\pi\)
\(734\) 57.4695 2.12124
\(735\) −13.9405 −0.514202
\(736\) −21.7458 −0.801559
\(737\) −0.852847 −0.0314150
\(738\) 6.48081 0.238562
\(739\) −15.0489 −0.553582 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(740\) 24.9727 0.918016
\(741\) 5.64098 0.207227
\(742\) −72.8317 −2.67374
\(743\) −7.99002 −0.293125 −0.146563 0.989201i \(-0.546821\pi\)
−0.146563 + 0.989201i \(0.546821\pi\)
\(744\) −13.8341 −0.507181
\(745\) 17.1206 0.627249
\(746\) −10.1080 −0.370081
\(747\) 14.1340 0.517135
\(748\) 1.10513 0.0404075
\(749\) −63.8860 −2.33435
\(750\) −27.3946 −1.00031
\(751\) 2.65760 0.0969774 0.0484887 0.998824i \(-0.484560\pi\)
0.0484887 + 0.998824i \(0.484560\pi\)
\(752\) −0.753508 −0.0274776
\(753\) −14.7615 −0.537938
\(754\) −8.62687 −0.314172
\(755\) 19.4370 0.707383
\(756\) −12.6540 −0.460223
\(757\) −15.5147 −0.563891 −0.281945 0.959430i \(-0.590980\pi\)
−0.281945 + 0.959430i \(0.590980\pi\)
\(758\) −50.2301 −1.82444
\(759\) −1.29755 −0.0470979
\(760\) 34.5603 1.25363
\(761\) −9.83730 −0.356602 −0.178301 0.983976i \(-0.557060\pi\)
−0.178301 + 0.983976i \(0.557060\pi\)
\(762\) −3.97138 −0.143868
\(763\) −73.6750 −2.66721
\(764\) −26.2074 −0.948149
\(765\) −1.64317 −0.0594090
\(766\) −18.3401 −0.662653
\(767\) −5.59074 −0.201870
\(768\) 15.4117 0.556121
\(769\) −4.02433 −0.145121 −0.0725606 0.997364i \(-0.523117\pi\)
−0.0725606 + 0.997364i \(0.523117\pi\)
\(770\) 5.07465 0.182878
\(771\) 3.34200 0.120359
\(772\) −74.0835 −2.66632
\(773\) 52.4555 1.88669 0.943347 0.331809i \(-0.107659\pi\)
0.943347 + 0.331809i \(0.107659\pi\)
\(774\) 0.424458 0.0152568
\(775\) 11.4591 0.411623
\(776\) 18.9382 0.679841
\(777\) −18.5966 −0.667148
\(778\) −31.5283 −1.13034
\(779\) 21.4951 0.770141
\(780\) −3.93511 −0.140900
\(781\) 0.425556 0.0152276
\(782\) −8.62304 −0.308359
\(783\) −5.07234 −0.181271
\(784\) −0.765331 −0.0273332
\(785\) −1.64317 −0.0586473
\(786\) −7.28609 −0.259886
\(787\) 27.9913 0.997784 0.498892 0.866664i \(-0.333740\pi\)
0.498892 + 0.866664i \(0.333740\pi\)
\(788\) −16.4503 −0.586019
\(789\) 15.8904 0.565712
\(790\) −36.0374 −1.28215
\(791\) −61.8448 −2.19895
\(792\) 0.954217 0.0339066
\(793\) −10.5183 −0.373515
\(794\) −46.0037 −1.63261
\(795\) −13.3169 −0.472302
\(796\) 48.6237 1.72342
\(797\) 21.5375 0.762897 0.381448 0.924390i \(-0.375425\pi\)
0.381448 + 0.924390i \(0.375425\pi\)
\(798\) −68.0723 −2.40973
\(799\) −8.35281 −0.295501
\(800\) −13.2464 −0.468333
\(801\) −3.05836 −0.108062
\(802\) −20.7530 −0.732813
\(803\) 3.19378 0.112706
\(804\) −7.98064 −0.281456
\(805\) −24.4131 −0.860449
\(806\) 8.47365 0.298472
\(807\) 16.1573 0.568764
\(808\) −39.2704 −1.38153
\(809\) 16.7563 0.589122 0.294561 0.955633i \(-0.404827\pi\)
0.294561 + 0.955633i \(0.404827\pi\)
\(810\) −3.75270 −0.131856
\(811\) 5.50520 0.193314 0.0966569 0.995318i \(-0.469185\pi\)
0.0966569 + 0.995318i \(0.469185\pi\)
\(812\) 64.1856 2.25247
\(813\) −0.735116 −0.0257816
\(814\) 3.70917 0.130006
\(815\) −4.02801 −0.141095
\(816\) −0.0902101 −0.00315799
\(817\) 1.40781 0.0492530
\(818\) −49.1817 −1.71960
\(819\) 2.93038 0.102396
\(820\) −14.9948 −0.523642
\(821\) 0.976847 0.0340922 0.0170461 0.999855i \(-0.494574\pi\)
0.0170461 + 0.999855i \(0.494574\pi\)
\(822\) 29.8410 1.04082
\(823\) −27.6090 −0.962389 −0.481195 0.876614i \(-0.659797\pi\)
−0.481195 + 0.876614i \(0.659797\pi\)
\(824\) −13.1027 −0.456453
\(825\) −0.790401 −0.0275182
\(826\) 67.4660 2.34744
\(827\) −16.3078 −0.567077 −0.283539 0.958961i \(-0.591508\pi\)
−0.283539 + 0.958961i \(0.591508\pi\)
\(828\) −12.1420 −0.421963
\(829\) 46.7561 1.62391 0.811954 0.583722i \(-0.198404\pi\)
0.811954 + 0.583722i \(0.198404\pi\)
\(830\) −53.0405 −1.84106
\(831\) −21.7686 −0.755144
\(832\) −9.66099 −0.334934
\(833\) −8.48387 −0.293949
\(834\) 11.8591 0.410649
\(835\) 18.5544 0.642101
\(836\) 8.37110 0.289521
\(837\) 4.98225 0.172212
\(838\) −29.6405 −1.02391
\(839\) 35.8232 1.23676 0.618378 0.785881i \(-0.287790\pi\)
0.618378 + 0.785881i \(0.287790\pi\)
\(840\) 17.9534 0.619452
\(841\) −3.27139 −0.112806
\(842\) 68.9996 2.37788
\(843\) −28.2341 −0.972434
\(844\) 11.8529 0.407995
\(845\) −20.4500 −0.703500
\(846\) −19.0763 −0.655855
\(847\) −42.8198 −1.47131
\(848\) −0.731097 −0.0251060
\(849\) 22.8906 0.785604
\(850\) −5.25274 −0.180167
\(851\) −17.8440 −0.611686
\(852\) 3.98220 0.136428
\(853\) 22.0479 0.754906 0.377453 0.926029i \(-0.376800\pi\)
0.377453 + 0.926029i \(0.376800\pi\)
\(854\) 126.929 4.34342
\(855\) −12.4467 −0.425667
\(856\) 45.0807 1.54083
\(857\) 36.8458 1.25863 0.629314 0.777151i \(-0.283336\pi\)
0.629314 + 0.777151i \(0.283336\pi\)
\(858\) −0.584478 −0.0199537
\(859\) −46.3277 −1.58068 −0.790341 0.612667i \(-0.790097\pi\)
−0.790341 + 0.612667i \(0.790097\pi\)
\(860\) −0.982080 −0.0334886
\(861\) 11.1663 0.380546
\(862\) −1.80421 −0.0614515
\(863\) −34.1582 −1.16276 −0.581379 0.813633i \(-0.697487\pi\)
−0.581379 + 0.813633i \(0.697487\pi\)
\(864\) −5.75937 −0.195938
\(865\) 2.78776 0.0947866
\(866\) 26.5581 0.902480
\(867\) −1.00000 −0.0339618
\(868\) −63.0456 −2.13991
\(869\) −3.30014 −0.111950
\(870\) 19.0350 0.645346
\(871\) 1.84813 0.0626216
\(872\) 51.9882 1.76054
\(873\) −6.82046 −0.230838
\(874\) −65.3177 −2.20940
\(875\) −47.2003 −1.59566
\(876\) 29.8863 1.00977
\(877\) 14.2785 0.482151 0.241076 0.970506i \(-0.422500\pi\)
0.241076 + 0.970506i \(0.422500\pi\)
\(878\) −8.29424 −0.279917
\(879\) 22.7044 0.765801
\(880\) 0.0509402 0.00171720
\(881\) −2.72212 −0.0917107 −0.0458554 0.998948i \(-0.514601\pi\)
−0.0458554 + 0.998948i \(0.514601\pi\)
\(882\) −19.3756 −0.652410
\(883\) 8.36424 0.281479 0.140740 0.990047i \(-0.455052\pi\)
0.140740 + 0.990047i \(0.455052\pi\)
\(884\) −2.39483 −0.0805468
\(885\) 12.3358 0.414664
\(886\) 53.5866 1.80028
\(887\) −22.1991 −0.745374 −0.372687 0.927957i \(-0.621564\pi\)
−0.372687 + 0.927957i \(0.621564\pi\)
\(888\) 13.1225 0.440363
\(889\) −6.84259 −0.229493
\(890\) 11.4771 0.384714
\(891\) −0.343655 −0.0115129
\(892\) 52.2547 1.74962
\(893\) −63.2707 −2.11727
\(894\) 23.7955 0.795842
\(895\) 8.59482 0.287293
\(896\) 71.2579 2.38056
\(897\) 2.81180 0.0938833
\(898\) 13.2425 0.441908
\(899\) −25.2716 −0.842856
\(900\) −7.39630 −0.246543
\(901\) −8.10439 −0.269996
\(902\) −2.22716 −0.0741565
\(903\) 0.731330 0.0243372
\(904\) 43.6403 1.45146
\(905\) −19.5279 −0.649130
\(906\) 27.0150 0.897515
\(907\) 11.0560 0.367108 0.183554 0.983010i \(-0.441240\pi\)
0.183554 + 0.983010i \(0.441240\pi\)
\(908\) −41.5178 −1.37782
\(909\) 14.1430 0.469093
\(910\) −10.9968 −0.364542
\(911\) −6.18810 −0.205021 −0.102510 0.994732i \(-0.532687\pi\)
−0.102510 + 0.994732i \(0.532687\pi\)
\(912\) −0.683322 −0.0226271
\(913\) −4.85721 −0.160750
\(914\) 60.6502 2.00613
\(915\) 23.2083 0.767242
\(916\) −71.9980 −2.37888
\(917\) −12.5538 −0.414562
\(918\) −2.28381 −0.0753771
\(919\) −32.5750 −1.07455 −0.537274 0.843407i \(-0.680546\pi\)
−0.537274 + 0.843407i \(0.680546\pi\)
\(920\) 17.2269 0.567955
\(921\) 21.9407 0.722972
\(922\) 23.1883 0.763667
\(923\) −0.922185 −0.0303541
\(924\) 4.34863 0.143059
\(925\) −10.8697 −0.357394
\(926\) −71.2877 −2.34266
\(927\) 4.71884 0.154987
\(928\) 29.2134 0.958978
\(929\) 30.0554 0.986084 0.493042 0.870005i \(-0.335885\pi\)
0.493042 + 0.870005i \(0.335885\pi\)
\(930\) −18.6969 −0.613095
\(931\) −64.2635 −2.10615
\(932\) −88.0687 −2.88479
\(933\) 6.35520 0.208060
\(934\) 24.4153 0.798892
\(935\) 0.564685 0.0184672
\(936\) −2.06780 −0.0675882
\(937\) 35.5638 1.16182 0.580909 0.813969i \(-0.302697\pi\)
0.580909 + 0.813969i \(0.302697\pi\)
\(938\) −22.3023 −0.728194
\(939\) 14.8247 0.483785
\(940\) 44.1373 1.43960
\(941\) 18.7705 0.611902 0.305951 0.952047i \(-0.401026\pi\)
0.305951 + 0.952047i \(0.401026\pi\)
\(942\) −2.28381 −0.0744107
\(943\) 10.7144 0.348910
\(944\) 0.677235 0.0220421
\(945\) −6.46581 −0.210333
\(946\) −0.145867 −0.00474255
\(947\) −52.5018 −1.70608 −0.853039 0.521847i \(-0.825243\pi\)
−0.853039 + 0.521847i \(0.825243\pi\)
\(948\) −30.8816 −1.00299
\(949\) −6.92098 −0.224664
\(950\) −39.7883 −1.29090
\(951\) 11.3622 0.368446
\(952\) 10.9261 0.354116
\(953\) −31.7200 −1.02751 −0.513756 0.857936i \(-0.671746\pi\)
−0.513756 + 0.857936i \(0.671746\pi\)
\(954\) −18.5089 −0.599248
\(955\) −13.3911 −0.433326
\(956\) −85.1194 −2.75296
\(957\) 1.74313 0.0563475
\(958\) −12.5679 −0.406052
\(959\) 51.4152 1.66029
\(960\) 21.3167 0.687994
\(961\) −6.17722 −0.199265
\(962\) −8.03782 −0.259150
\(963\) −16.2355 −0.523182
\(964\) 16.1829 0.521218
\(965\) −37.8543 −1.21857
\(966\) −33.9313 −1.09172
\(967\) 0.957467 0.0307901 0.0153950 0.999881i \(-0.495099\pi\)
0.0153950 + 0.999881i \(0.495099\pi\)
\(968\) 30.2155 0.971162
\(969\) −7.57478 −0.243337
\(970\) 25.5952 0.821811
\(971\) −40.2360 −1.29124 −0.645618 0.763660i \(-0.723400\pi\)
−0.645618 + 0.763660i \(0.723400\pi\)
\(972\) −3.21580 −0.103147
\(973\) 20.4330 0.655052
\(974\) −20.6087 −0.660345
\(975\) 1.71281 0.0548539
\(976\) 1.27413 0.0407840
\(977\) −24.2585 −0.776099 −0.388050 0.921639i \(-0.626851\pi\)
−0.388050 + 0.921639i \(0.626851\pi\)
\(978\) −5.59845 −0.179019
\(979\) 1.05102 0.0335908
\(980\) 44.8298 1.43204
\(981\) −18.7232 −0.597786
\(982\) 17.0640 0.544534
\(983\) −8.98399 −0.286545 −0.143272 0.989683i \(-0.545763\pi\)
−0.143272 + 0.989683i \(0.545763\pi\)
\(984\) −7.87940 −0.251186
\(985\) −8.40559 −0.267824
\(986\) 11.5843 0.368918
\(987\) −32.8679 −1.04620
\(988\) −18.1403 −0.577120
\(989\) 0.701736 0.0223139
\(990\) 1.28963 0.0409873
\(991\) 21.5905 0.685845 0.342922 0.939364i \(-0.388583\pi\)
0.342922 + 0.939364i \(0.388583\pi\)
\(992\) −28.6946 −0.911054
\(993\) 21.8740 0.694150
\(994\) 11.1284 0.352972
\(995\) 24.8451 0.787644
\(996\) −45.4521 −1.44020
\(997\) −42.2012 −1.33653 −0.668263 0.743925i \(-0.732962\pi\)
−0.668263 + 0.743925i \(0.732962\pi\)
\(998\) 84.4130 2.67205
\(999\) −4.72599 −0.149524
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.1.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.6 48 1.1 even 1 trivial