Properties

Label 966.4.a.m.1.4
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.9958450655\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(18.8692\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -20.2887 q^{10} -47.7648 q^{11} -12.0000 q^{12} -77.2742 q^{13} +14.0000 q^{14} -30.4330 q^{15} +16.0000 q^{16} -26.2302 q^{17} -18.0000 q^{18} +54.9670 q^{19} +40.5774 q^{20} +21.0000 q^{21} +95.5296 q^{22} -23.0000 q^{23} +24.0000 q^{24} -22.0923 q^{25} +154.548 q^{26} -27.0000 q^{27} -28.0000 q^{28} -52.9111 q^{29} +60.8660 q^{30} -97.0969 q^{31} -32.0000 q^{32} +143.294 q^{33} +52.4605 q^{34} -71.0104 q^{35} +36.0000 q^{36} +295.495 q^{37} -109.934 q^{38} +231.823 q^{39} -81.1547 q^{40} +365.501 q^{41} -42.0000 q^{42} +392.207 q^{43} -191.059 q^{44} +91.2991 q^{45} +46.0000 q^{46} +79.9862 q^{47} -48.0000 q^{48} +49.0000 q^{49} +44.1847 q^{50} +78.6907 q^{51} -309.097 q^{52} -146.138 q^{53} +54.0000 q^{54} -484.542 q^{55} +56.0000 q^{56} -164.901 q^{57} +105.822 q^{58} -19.0284 q^{59} -121.732 q^{60} +89.2284 q^{61} +194.194 q^{62} -63.0000 q^{63} +64.0000 q^{64} -783.896 q^{65} -286.589 q^{66} -1020.99 q^{67} -104.921 q^{68} +69.0000 q^{69} +142.021 q^{70} -121.668 q^{71} -72.0000 q^{72} -749.764 q^{73} -590.991 q^{74} +66.2770 q^{75} +219.868 q^{76} +334.354 q^{77} -463.645 q^{78} +548.871 q^{79} +162.309 q^{80} +81.0000 q^{81} -731.003 q^{82} +73.0846 q^{83} +84.0000 q^{84} -266.088 q^{85} -784.414 q^{86} +158.733 q^{87} +382.118 q^{88} +1089.25 q^{89} -182.598 q^{90} +540.919 q^{91} -92.0000 q^{92} +291.291 q^{93} -159.972 q^{94} +557.604 q^{95} +96.0000 q^{96} +724.274 q^{97} -98.0000 q^{98} -429.883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 10.1443 0.907337 0.453669 0.891170i \(-0.350115\pi\)
0.453669 + 0.891170i \(0.350115\pi\)
\(6\) 6.00000 0.408248
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −20.2887 −0.641584
\(11\) −47.7648 −1.30924 −0.654619 0.755959i \(-0.727171\pi\)
−0.654619 + 0.755959i \(0.727171\pi\)
\(12\) −12.0000 −0.288675
\(13\) −77.2742 −1.64862 −0.824308 0.566142i \(-0.808435\pi\)
−0.824308 + 0.566142i \(0.808435\pi\)
\(14\) 14.0000 0.267261
\(15\) −30.4330 −0.523852
\(16\) 16.0000 0.250000
\(17\) −26.2302 −0.374222 −0.187111 0.982339i \(-0.559912\pi\)
−0.187111 + 0.982339i \(0.559912\pi\)
\(18\) −18.0000 −0.235702
\(19\) 54.9670 0.663700 0.331850 0.943332i \(-0.392327\pi\)
0.331850 + 0.943332i \(0.392327\pi\)
\(20\) 40.5774 0.453669
\(21\) 21.0000 0.218218
\(22\) 95.5296 0.925772
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) −22.0923 −0.176739
\(26\) 154.548 1.16575
\(27\) −27.0000 −0.192450
\(28\) −28.0000 −0.188982
\(29\) −52.9111 −0.338805 −0.169402 0.985547i \(-0.554184\pi\)
−0.169402 + 0.985547i \(0.554184\pi\)
\(30\) 60.8660 0.370419
\(31\) −97.0969 −0.562552 −0.281276 0.959627i \(-0.590758\pi\)
−0.281276 + 0.959627i \(0.590758\pi\)
\(32\) −32.0000 −0.176777
\(33\) 143.294 0.755889
\(34\) 52.4605 0.264615
\(35\) −71.0104 −0.342941
\(36\) 36.0000 0.166667
\(37\) 295.495 1.31295 0.656475 0.754348i \(-0.272047\pi\)
0.656475 + 0.754348i \(0.272047\pi\)
\(38\) −109.934 −0.469307
\(39\) 231.823 0.951829
\(40\) −81.1547 −0.320792
\(41\) 365.501 1.39224 0.696119 0.717927i \(-0.254909\pi\)
0.696119 + 0.717927i \(0.254909\pi\)
\(42\) −42.0000 −0.154303
\(43\) 392.207 1.39095 0.695477 0.718548i \(-0.255193\pi\)
0.695477 + 0.718548i \(0.255193\pi\)
\(44\) −191.059 −0.654619
\(45\) 91.2991 0.302446
\(46\) 46.0000 0.147442
\(47\) 79.9862 0.248238 0.124119 0.992267i \(-0.460390\pi\)
0.124119 + 0.992267i \(0.460390\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) 44.1847 0.124973
\(51\) 78.6907 0.216057
\(52\) −309.097 −0.824308
\(53\) −146.138 −0.378747 −0.189373 0.981905i \(-0.560646\pi\)
−0.189373 + 0.981905i \(0.560646\pi\)
\(54\) 54.0000 0.136083
\(55\) −484.542 −1.18792
\(56\) 56.0000 0.133631
\(57\) −164.901 −0.383188
\(58\) 105.822 0.239571
\(59\) −19.0284 −0.0419879 −0.0209939 0.999780i \(-0.506683\pi\)
−0.0209939 + 0.999780i \(0.506683\pi\)
\(60\) −121.732 −0.261926
\(61\) 89.2284 0.187287 0.0936436 0.995606i \(-0.470149\pi\)
0.0936436 + 0.995606i \(0.470149\pi\)
\(62\) 194.194 0.397784
\(63\) −63.0000 −0.125988
\(64\) 64.0000 0.125000
\(65\) −783.896 −1.49585
\(66\) −286.589 −0.534495
\(67\) −1020.99 −1.86169 −0.930845 0.365415i \(-0.880927\pi\)
−0.930845 + 0.365415i \(0.880927\pi\)
\(68\) −104.921 −0.187111
\(69\) 69.0000 0.120386
\(70\) 142.021 0.242496
\(71\) −121.668 −0.203370 −0.101685 0.994817i \(-0.532423\pi\)
−0.101685 + 0.994817i \(0.532423\pi\)
\(72\) −72.0000 −0.117851
\(73\) −749.764 −1.20210 −0.601049 0.799212i \(-0.705250\pi\)
−0.601049 + 0.799212i \(0.705250\pi\)
\(74\) −590.991 −0.928395
\(75\) 66.2770 0.102040
\(76\) 219.868 0.331850
\(77\) 334.354 0.494846
\(78\) −463.645 −0.673045
\(79\) 548.871 0.781681 0.390840 0.920459i \(-0.372184\pi\)
0.390840 + 0.920459i \(0.372184\pi\)
\(80\) 162.309 0.226834
\(81\) 81.0000 0.111111
\(82\) −731.003 −0.984461
\(83\) 73.0846 0.0966516 0.0483258 0.998832i \(-0.484611\pi\)
0.0483258 + 0.998832i \(0.484611\pi\)
\(84\) 84.0000 0.109109
\(85\) −266.088 −0.339545
\(86\) −784.414 −0.983553
\(87\) 158.733 0.195609
\(88\) 382.118 0.462886
\(89\) 1089.25 1.29731 0.648655 0.761082i \(-0.275332\pi\)
0.648655 + 0.761082i \(0.275332\pi\)
\(90\) −182.598 −0.213861
\(91\) 540.919 0.623118
\(92\) −92.0000 −0.104257
\(93\) 291.291 0.324790
\(94\) −159.972 −0.175531
\(95\) 557.604 0.602200
\(96\) 96.0000 0.102062
\(97\) 724.274 0.758132 0.379066 0.925370i \(-0.376245\pi\)
0.379066 + 0.925370i \(0.376245\pi\)
\(98\) −98.0000 −0.101015
\(99\) −429.883 −0.436413
\(100\) −88.3694 −0.0883694
\(101\) −159.521 −0.157158 −0.0785788 0.996908i \(-0.525038\pi\)
−0.0785788 + 0.996908i \(0.525038\pi\)
\(102\) −157.381 −0.152775
\(103\) −184.341 −0.176347 −0.0881733 0.996105i \(-0.528103\pi\)
−0.0881733 + 0.996105i \(0.528103\pi\)
\(104\) 618.194 0.582874
\(105\) 213.031 0.197997
\(106\) 292.276 0.267814
\(107\) 488.616 0.441461 0.220730 0.975335i \(-0.429156\pi\)
0.220730 + 0.975335i \(0.429156\pi\)
\(108\) −108.000 −0.0962250
\(109\) 786.623 0.691237 0.345618 0.938375i \(-0.387669\pi\)
0.345618 + 0.938375i \(0.387669\pi\)
\(110\) 969.085 0.839987
\(111\) −886.486 −0.758032
\(112\) −112.000 −0.0944911
\(113\) 986.714 0.821436 0.410718 0.911762i \(-0.365278\pi\)
0.410718 + 0.911762i \(0.365278\pi\)
\(114\) 329.802 0.270955
\(115\) −233.320 −0.189193
\(116\) −211.644 −0.169402
\(117\) −695.468 −0.549539
\(118\) 38.0568 0.0296899
\(119\) 183.612 0.141442
\(120\) 243.464 0.185209
\(121\) 950.476 0.714107
\(122\) −178.457 −0.132432
\(123\) −1096.50 −0.803809
\(124\) −388.387 −0.281276
\(125\) −1492.15 −1.06770
\(126\) 126.000 0.0890871
\(127\) 653.081 0.456311 0.228156 0.973625i \(-0.426731\pi\)
0.228156 + 0.973625i \(0.426731\pi\)
\(128\) −128.000 −0.0883883
\(129\) −1176.62 −0.803068
\(130\) 1567.79 1.05773
\(131\) 1747.44 1.16545 0.582727 0.812668i \(-0.301986\pi\)
0.582727 + 0.812668i \(0.301986\pi\)
\(132\) 573.178 0.377945
\(133\) −384.769 −0.250855
\(134\) 2041.97 1.31641
\(135\) −273.897 −0.174617
\(136\) 209.842 0.132307
\(137\) 1512.55 0.943251 0.471626 0.881799i \(-0.343667\pi\)
0.471626 + 0.881799i \(0.343667\pi\)
\(138\) −138.000 −0.0851257
\(139\) −581.410 −0.354781 −0.177390 0.984141i \(-0.556766\pi\)
−0.177390 + 0.984141i \(0.556766\pi\)
\(140\) −284.042 −0.171471
\(141\) −239.958 −0.143320
\(142\) 243.335 0.143804
\(143\) 3690.99 2.15843
\(144\) 144.000 0.0833333
\(145\) −536.748 −0.307410
\(146\) 1499.53 0.850012
\(147\) −147.000 −0.0824786
\(148\) 1181.98 0.656475
\(149\) 2846.52 1.56508 0.782538 0.622603i \(-0.213925\pi\)
0.782538 + 0.622603i \(0.213925\pi\)
\(150\) −132.554 −0.0721533
\(151\) −2712.86 −1.46205 −0.731025 0.682351i \(-0.760958\pi\)
−0.731025 + 0.682351i \(0.760958\pi\)
\(152\) −439.736 −0.234653
\(153\) −236.072 −0.124741
\(154\) −668.707 −0.349909
\(155\) −984.984 −0.510424
\(156\) 927.290 0.475914
\(157\) 2744.44 1.39510 0.697549 0.716537i \(-0.254274\pi\)
0.697549 + 0.716537i \(0.254274\pi\)
\(158\) −1097.74 −0.552732
\(159\) 438.413 0.218669
\(160\) −324.619 −0.160396
\(161\) 161.000 0.0788110
\(162\) −162.000 −0.0785674
\(163\) −2844.94 −1.36707 −0.683536 0.729917i \(-0.739559\pi\)
−0.683536 + 0.729917i \(0.739559\pi\)
\(164\) 1462.01 0.696119
\(165\) 1453.63 0.685847
\(166\) −146.169 −0.0683430
\(167\) −495.312 −0.229511 −0.114756 0.993394i \(-0.536609\pi\)
−0.114756 + 0.993394i \(0.536609\pi\)
\(168\) −168.000 −0.0771517
\(169\) 3774.30 1.71793
\(170\) 532.177 0.240095
\(171\) 494.703 0.221233
\(172\) 1568.83 0.695477
\(173\) 3565.79 1.56706 0.783532 0.621351i \(-0.213416\pi\)
0.783532 + 0.621351i \(0.213416\pi\)
\(174\) −317.467 −0.138317
\(175\) 154.646 0.0668010
\(176\) −764.237 −0.327310
\(177\) 57.0852 0.0242417
\(178\) −2178.51 −0.917337
\(179\) −490.581 −0.204848 −0.102424 0.994741i \(-0.532660\pi\)
−0.102424 + 0.994741i \(0.532660\pi\)
\(180\) 365.196 0.151223
\(181\) 235.990 0.0969115 0.0484558 0.998825i \(-0.484570\pi\)
0.0484558 + 0.998825i \(0.484570\pi\)
\(182\) −1081.84 −0.440611
\(183\) −267.685 −0.108130
\(184\) 184.000 0.0737210
\(185\) 2997.60 1.19129
\(186\) −582.581 −0.229661
\(187\) 1252.88 0.489946
\(188\) 319.945 0.124119
\(189\) 189.000 0.0727393
\(190\) −1115.21 −0.425820
\(191\) 306.490 0.116109 0.0580546 0.998313i \(-0.481510\pi\)
0.0580546 + 0.998313i \(0.481510\pi\)
\(192\) −192.000 −0.0721688
\(193\) −1142.78 −0.426213 −0.213106 0.977029i \(-0.568358\pi\)
−0.213106 + 0.977029i \(0.568358\pi\)
\(194\) −1448.55 −0.536081
\(195\) 2351.69 0.863630
\(196\) 196.000 0.0714286
\(197\) 3109.77 1.12468 0.562340 0.826906i \(-0.309901\pi\)
0.562340 + 0.826906i \(0.309901\pi\)
\(198\) 859.766 0.308591
\(199\) 886.066 0.315636 0.157818 0.987468i \(-0.449554\pi\)
0.157818 + 0.987468i \(0.449554\pi\)
\(200\) 176.739 0.0624866
\(201\) 3062.96 1.07485
\(202\) 319.042 0.111127
\(203\) 370.378 0.128056
\(204\) 314.763 0.108028
\(205\) 3707.77 1.26323
\(206\) 368.683 0.124696
\(207\) −207.000 −0.0695048
\(208\) −1236.39 −0.412154
\(209\) −2625.49 −0.868942
\(210\) −426.062 −0.140005
\(211\) 393.347 0.128337 0.0641686 0.997939i \(-0.479560\pi\)
0.0641686 + 0.997939i \(0.479560\pi\)
\(212\) −584.551 −0.189373
\(213\) 365.003 0.117416
\(214\) −977.233 −0.312160
\(215\) 3978.68 1.26206
\(216\) 216.000 0.0680414
\(217\) 679.678 0.212625
\(218\) −1573.25 −0.488778
\(219\) 2249.29 0.694032
\(220\) −1938.17 −0.593961
\(221\) 2026.92 0.616948
\(222\) 1772.97 0.536009
\(223\) −4935.73 −1.48216 −0.741079 0.671418i \(-0.765685\pi\)
−0.741079 + 0.671418i \(0.765685\pi\)
\(224\) 224.000 0.0668153
\(225\) −198.831 −0.0589129
\(226\) −1973.43 −0.580843
\(227\) 67.8077 0.0198262 0.00991311 0.999951i \(-0.496845\pi\)
0.00991311 + 0.999951i \(0.496845\pi\)
\(228\) −659.605 −0.191594
\(229\) 4500.59 1.29872 0.649361 0.760481i \(-0.275037\pi\)
0.649361 + 0.760481i \(0.275037\pi\)
\(230\) 466.640 0.133780
\(231\) −1003.06 −0.285699
\(232\) 423.289 0.119786
\(233\) −5112.93 −1.43759 −0.718797 0.695220i \(-0.755307\pi\)
−0.718797 + 0.695220i \(0.755307\pi\)
\(234\) 1390.94 0.388582
\(235\) 811.407 0.225236
\(236\) −76.1135 −0.0209939
\(237\) −1646.61 −0.451303
\(238\) −367.223 −0.100015
\(239\) 4432.35 1.19960 0.599801 0.800149i \(-0.295246\pi\)
0.599801 + 0.800149i \(0.295246\pi\)
\(240\) −486.928 −0.130963
\(241\) 2451.90 0.655355 0.327678 0.944790i \(-0.393734\pi\)
0.327678 + 0.944790i \(0.393734\pi\)
\(242\) −1900.95 −0.504950
\(243\) −243.000 −0.0641500
\(244\) 356.914 0.0936436
\(245\) 497.073 0.129620
\(246\) 2193.01 0.568379
\(247\) −4247.53 −1.09419
\(248\) 776.775 0.198892
\(249\) −219.254 −0.0558018
\(250\) 2984.31 0.754977
\(251\) 1628.07 0.409414 0.204707 0.978823i \(-0.434376\pi\)
0.204707 + 0.978823i \(0.434376\pi\)
\(252\) −252.000 −0.0629941
\(253\) 1098.59 0.272995
\(254\) −1306.16 −0.322661
\(255\) 798.265 0.196037
\(256\) 256.000 0.0625000
\(257\) 5757.66 1.39748 0.698741 0.715375i \(-0.253744\pi\)
0.698741 + 0.715375i \(0.253744\pi\)
\(258\) 2353.24 0.567855
\(259\) −2068.47 −0.496248
\(260\) −3135.58 −0.747925
\(261\) −476.200 −0.112935
\(262\) −3494.88 −0.824101
\(263\) 1559.25 0.365580 0.182790 0.983152i \(-0.441487\pi\)
0.182790 + 0.983152i \(0.441487\pi\)
\(264\) −1146.36 −0.267247
\(265\) −1482.47 −0.343651
\(266\) 769.539 0.177381
\(267\) −3267.76 −0.749003
\(268\) −4083.94 −0.930845
\(269\) 6369.88 1.44379 0.721893 0.692005i \(-0.243272\pi\)
0.721893 + 0.692005i \(0.243272\pi\)
\(270\) 547.794 0.123473
\(271\) −5526.08 −1.23869 −0.619346 0.785119i \(-0.712602\pi\)
−0.619346 + 0.785119i \(0.712602\pi\)
\(272\) −419.684 −0.0935554
\(273\) −1622.76 −0.359757
\(274\) −3025.09 −0.666979
\(275\) 1055.24 0.231393
\(276\) 276.000 0.0601929
\(277\) 7349.07 1.59409 0.797045 0.603920i \(-0.206395\pi\)
0.797045 + 0.603920i \(0.206395\pi\)
\(278\) 1162.82 0.250868
\(279\) −873.872 −0.187517
\(280\) 568.083 0.121248
\(281\) 3432.00 0.728598 0.364299 0.931282i \(-0.381309\pi\)
0.364299 + 0.931282i \(0.381309\pi\)
\(282\) 479.917 0.101343
\(283\) −8732.86 −1.83433 −0.917163 0.398512i \(-0.869527\pi\)
−0.917163 + 0.398512i \(0.869527\pi\)
\(284\) −486.670 −0.101685
\(285\) −1672.81 −0.347680
\(286\) −7381.97 −1.52624
\(287\) −2558.51 −0.526216
\(288\) −288.000 −0.0589256
\(289\) −4224.97 −0.859958
\(290\) 1073.50 0.217372
\(291\) −2172.82 −0.437708
\(292\) −2999.05 −0.601049
\(293\) −5749.95 −1.14647 −0.573235 0.819391i \(-0.694312\pi\)
−0.573235 + 0.819391i \(0.694312\pi\)
\(294\) 294.000 0.0583212
\(295\) −193.030 −0.0380972
\(296\) −2363.96 −0.464198
\(297\) 1289.65 0.251963
\(298\) −5693.05 −1.10668
\(299\) 1777.31 0.343760
\(300\) 265.108 0.0510201
\(301\) −2745.45 −0.525731
\(302\) 5425.72 1.03382
\(303\) 478.562 0.0907349
\(304\) 879.473 0.165925
\(305\) 905.163 0.169933
\(306\) 472.144 0.0882049
\(307\) 2069.88 0.384802 0.192401 0.981316i \(-0.438373\pi\)
0.192401 + 0.981316i \(0.438373\pi\)
\(308\) 1337.41 0.247423
\(309\) 553.024 0.101814
\(310\) 1969.97 0.360925
\(311\) 8128.54 1.48208 0.741040 0.671460i \(-0.234333\pi\)
0.741040 + 0.671460i \(0.234333\pi\)
\(312\) −1854.58 −0.336522
\(313\) −2147.81 −0.387865 −0.193932 0.981015i \(-0.562124\pi\)
−0.193932 + 0.981015i \(0.562124\pi\)
\(314\) −5488.89 −0.986483
\(315\) −639.093 −0.114314
\(316\) 2195.48 0.390840
\(317\) −5908.90 −1.04693 −0.523465 0.852047i \(-0.675361\pi\)
−0.523465 + 0.852047i \(0.675361\pi\)
\(318\) −876.827 −0.154623
\(319\) 2527.29 0.443577
\(320\) 649.238 0.113417
\(321\) −1465.85 −0.254878
\(322\) −322.000 −0.0557278
\(323\) −1441.80 −0.248371
\(324\) 324.000 0.0555556
\(325\) 1707.17 0.291374
\(326\) 5689.87 0.966665
\(327\) −2359.87 −0.399086
\(328\) −2924.01 −0.492230
\(329\) −559.903 −0.0938251
\(330\) −2907.25 −0.484967
\(331\) −278.062 −0.0461742 −0.0230871 0.999733i \(-0.507350\pi\)
−0.0230871 + 0.999733i \(0.507350\pi\)
\(332\) 292.339 0.0483258
\(333\) 2659.46 0.437650
\(334\) 990.624 0.162289
\(335\) −10357.2 −1.68918
\(336\) 336.000 0.0545545
\(337\) −8355.18 −1.35055 −0.675275 0.737566i \(-0.735975\pi\)
−0.675275 + 0.737566i \(0.735975\pi\)
\(338\) −7548.60 −1.21476
\(339\) −2960.14 −0.474256
\(340\) −1064.35 −0.169773
\(341\) 4637.81 0.736515
\(342\) −989.407 −0.156436
\(343\) −343.000 −0.0539949
\(344\) −3137.66 −0.491776
\(345\) 699.960 0.109231
\(346\) −7131.58 −1.10808
\(347\) 6786.89 1.04997 0.524984 0.851112i \(-0.324071\pi\)
0.524984 + 0.851112i \(0.324071\pi\)
\(348\) 634.933 0.0978046
\(349\) −7005.57 −1.07450 −0.537249 0.843424i \(-0.680536\pi\)
−0.537249 + 0.843424i \(0.680536\pi\)
\(350\) −309.293 −0.0472354
\(351\) 2086.40 0.317276
\(352\) 1528.47 0.231443
\(353\) 2040.58 0.307674 0.153837 0.988096i \(-0.450837\pi\)
0.153837 + 0.988096i \(0.450837\pi\)
\(354\) −114.170 −0.0171415
\(355\) −1234.24 −0.184525
\(356\) 4357.01 0.648655
\(357\) −550.835 −0.0816619
\(358\) 981.162 0.144849
\(359\) 5503.62 0.809109 0.404555 0.914514i \(-0.367427\pi\)
0.404555 + 0.914514i \(0.367427\pi\)
\(360\) −730.393 −0.106931
\(361\) −3837.62 −0.559502
\(362\) −471.980 −0.0685268
\(363\) −2851.43 −0.412290
\(364\) 2163.68 0.311559
\(365\) −7605.86 −1.09071
\(366\) 535.370 0.0764597
\(367\) −5167.28 −0.734959 −0.367479 0.930032i \(-0.619779\pi\)
−0.367479 + 0.930032i \(0.619779\pi\)
\(368\) −368.000 −0.0521286
\(369\) 3289.51 0.464079
\(370\) −5995.21 −0.842368
\(371\) 1022.96 0.143153
\(372\) 1165.16 0.162395
\(373\) −956.629 −0.132795 −0.0663973 0.997793i \(-0.521150\pi\)
−0.0663973 + 0.997793i \(0.521150\pi\)
\(374\) −2505.76 −0.346444
\(375\) 4476.46 0.616436
\(376\) −639.889 −0.0877653
\(377\) 4088.66 0.558559
\(378\) −378.000 −0.0514344
\(379\) 13701.1 1.85694 0.928468 0.371413i \(-0.121127\pi\)
0.928468 + 0.371413i \(0.121127\pi\)
\(380\) 2230.42 0.301100
\(381\) −1959.24 −0.263451
\(382\) −612.980 −0.0821015
\(383\) −5039.42 −0.672330 −0.336165 0.941803i \(-0.609130\pi\)
−0.336165 + 0.941803i \(0.609130\pi\)
\(384\) 384.000 0.0510310
\(385\) 3391.80 0.448992
\(386\) 2285.56 0.301378
\(387\) 3529.86 0.463651
\(388\) 2897.09 0.379066
\(389\) −5545.34 −0.722776 −0.361388 0.932415i \(-0.617697\pi\)
−0.361388 + 0.932415i \(0.617697\pi\)
\(390\) −4703.37 −0.610679
\(391\) 603.296 0.0780306
\(392\) −392.000 −0.0505076
\(393\) −5242.32 −0.672875
\(394\) −6219.54 −0.795269
\(395\) 5567.93 0.709248
\(396\) −1719.53 −0.218206
\(397\) 3102.14 0.392171 0.196085 0.980587i \(-0.437177\pi\)
0.196085 + 0.980587i \(0.437177\pi\)
\(398\) −1772.13 −0.223188
\(399\) 1154.31 0.144831
\(400\) −353.478 −0.0441847
\(401\) 10715.5 1.33443 0.667214 0.744866i \(-0.267487\pi\)
0.667214 + 0.744866i \(0.267487\pi\)
\(402\) −6125.91 −0.760031
\(403\) 7503.08 0.927432
\(404\) −638.083 −0.0785788
\(405\) 821.692 0.100815
\(406\) −740.755 −0.0905494
\(407\) −14114.3 −1.71896
\(408\) −629.526 −0.0763877
\(409\) 11550.2 1.39638 0.698190 0.715913i \(-0.253989\pi\)
0.698190 + 0.715913i \(0.253989\pi\)
\(410\) −7415.54 −0.893238
\(411\) −4537.64 −0.544586
\(412\) −737.365 −0.0881733
\(413\) 133.199 0.0158699
\(414\) 414.000 0.0491473
\(415\) 741.396 0.0876956
\(416\) 2472.77 0.291437
\(417\) 1744.23 0.204833
\(418\) 5250.98 0.614435
\(419\) 2239.70 0.261137 0.130569 0.991439i \(-0.458320\pi\)
0.130569 + 0.991439i \(0.458320\pi\)
\(420\) 852.125 0.0989986
\(421\) 5738.65 0.664334 0.332167 0.943221i \(-0.392220\pi\)
0.332167 + 0.943221i \(0.392220\pi\)
\(422\) −786.695 −0.0907481
\(423\) 719.875 0.0827460
\(424\) 1169.10 0.133907
\(425\) 579.488 0.0661395
\(426\) −730.005 −0.0830255
\(427\) −624.599 −0.0707879
\(428\) 1954.47 0.220730
\(429\) −11073.0 −1.24617
\(430\) −7957.36 −0.892414
\(431\) 2493.21 0.278640 0.139320 0.990247i \(-0.455508\pi\)
0.139320 + 0.990247i \(0.455508\pi\)
\(432\) −432.000 −0.0481125
\(433\) 4175.42 0.463414 0.231707 0.972786i \(-0.425569\pi\)
0.231707 + 0.972786i \(0.425569\pi\)
\(434\) −1359.36 −0.150348
\(435\) 1610.24 0.177483
\(436\) 3146.49 0.345618
\(437\) −1264.24 −0.138391
\(438\) −4498.58 −0.490755
\(439\) −10892.5 −1.18422 −0.592109 0.805858i \(-0.701704\pi\)
−0.592109 + 0.805858i \(0.701704\pi\)
\(440\) 3876.34 0.419994
\(441\) 441.000 0.0476190
\(442\) −4053.84 −0.436248
\(443\) −10500.1 −1.12612 −0.563062 0.826415i \(-0.690377\pi\)
−0.563062 + 0.826415i \(0.690377\pi\)
\(444\) −3545.94 −0.379016
\(445\) 11049.8 1.17710
\(446\) 9871.47 1.04804
\(447\) −8539.57 −0.903597
\(448\) −448.000 −0.0472456
\(449\) 5069.81 0.532871 0.266435 0.963853i \(-0.414154\pi\)
0.266435 + 0.963853i \(0.414154\pi\)
\(450\) 397.662 0.0416577
\(451\) −17458.1 −1.82277
\(452\) 3946.86 0.410718
\(453\) 8138.58 0.844114
\(454\) −135.615 −0.0140193
\(455\) 5487.27 0.565379
\(456\) 1319.21 0.135477
\(457\) 1772.04 0.181384 0.0906919 0.995879i \(-0.471092\pi\)
0.0906919 + 0.995879i \(0.471092\pi\)
\(458\) −9001.17 −0.918334
\(459\) 708.216 0.0720190
\(460\) −933.279 −0.0945965
\(461\) −12009.1 −1.21328 −0.606639 0.794977i \(-0.707483\pi\)
−0.606639 + 0.794977i \(0.707483\pi\)
\(462\) 2006.12 0.202020
\(463\) 13558.0 1.36089 0.680446 0.732799i \(-0.261786\pi\)
0.680446 + 0.732799i \(0.261786\pi\)
\(464\) −846.577 −0.0847012
\(465\) 2954.95 0.294694
\(466\) 10225.9 1.01653
\(467\) 7489.21 0.742097 0.371048 0.928614i \(-0.378998\pi\)
0.371048 + 0.928614i \(0.378998\pi\)
\(468\) −2781.87 −0.274769
\(469\) 7146.90 0.703652
\(470\) −1622.81 −0.159266
\(471\) −8233.33 −0.805460
\(472\) 152.227 0.0148450
\(473\) −18733.7 −1.82109
\(474\) 3293.22 0.319120
\(475\) −1214.35 −0.117302
\(476\) 734.447 0.0707212
\(477\) −1315.24 −0.126249
\(478\) −8864.71 −0.848247
\(479\) −13665.4 −1.30352 −0.651761 0.758424i \(-0.725969\pi\)
−0.651761 + 0.758424i \(0.725969\pi\)
\(480\) 973.857 0.0926047
\(481\) −22834.2 −2.16455
\(482\) −4903.79 −0.463406
\(483\) −483.000 −0.0455016
\(484\) 3801.90 0.357053
\(485\) 7347.28 0.687882
\(486\) 486.000 0.0453609
\(487\) 687.947 0.0640121 0.0320060 0.999488i \(-0.489810\pi\)
0.0320060 + 0.999488i \(0.489810\pi\)
\(488\) −713.827 −0.0662161
\(489\) 8534.81 0.789279
\(490\) −994.145 −0.0916549
\(491\) 7748.27 0.712168 0.356084 0.934454i \(-0.384112\pi\)
0.356084 + 0.934454i \(0.384112\pi\)
\(492\) −4386.02 −0.401904
\(493\) 1387.87 0.126788
\(494\) 8495.07 0.773707
\(495\) −4360.88 −0.395974
\(496\) −1553.55 −0.140638
\(497\) 851.673 0.0768667
\(498\) 438.508 0.0394578
\(499\) −11221.2 −1.00667 −0.503335 0.864091i \(-0.667894\pi\)
−0.503335 + 0.864091i \(0.667894\pi\)
\(500\) −5968.62 −0.533850
\(501\) 1485.94 0.132508
\(502\) −3256.14 −0.289499
\(503\) 12631.4 1.11969 0.559845 0.828597i \(-0.310861\pi\)
0.559845 + 0.828597i \(0.310861\pi\)
\(504\) 504.000 0.0445435
\(505\) −1618.23 −0.142595
\(506\) −2197.18 −0.193037
\(507\) −11322.9 −0.991850
\(508\) 2612.32 0.228156
\(509\) −10373.2 −0.903307 −0.451653 0.892193i \(-0.649166\pi\)
−0.451653 + 0.892193i \(0.649166\pi\)
\(510\) −1596.53 −0.138619
\(511\) 5248.34 0.454350
\(512\) −512.000 −0.0441942
\(513\) −1484.11 −0.127729
\(514\) −11515.3 −0.988169
\(515\) −1870.02 −0.160006
\(516\) −4706.48 −0.401534
\(517\) −3820.52 −0.325003
\(518\) 4136.93 0.350900
\(519\) −10697.4 −0.904745
\(520\) 6271.17 0.528863
\(521\) −18433.9 −1.55010 −0.775051 0.631898i \(-0.782276\pi\)
−0.775051 + 0.631898i \(0.782276\pi\)
\(522\) 952.400 0.0798571
\(523\) 10811.1 0.903894 0.451947 0.892045i \(-0.350730\pi\)
0.451947 + 0.892045i \(0.350730\pi\)
\(524\) 6989.76 0.582727
\(525\) −463.939 −0.0385676
\(526\) −3118.50 −0.258504
\(527\) 2546.87 0.210519
\(528\) 2292.71 0.188972
\(529\) 529.000 0.0434783
\(530\) 2964.94 0.242998
\(531\) −171.255 −0.0139960
\(532\) −1539.08 −0.125428
\(533\) −28243.8 −2.29527
\(534\) 6535.52 0.529625
\(535\) 4956.69 0.400554
\(536\) 8167.88 0.658207
\(537\) 1471.74 0.118269
\(538\) −12739.8 −1.02091
\(539\) −2340.48 −0.187034
\(540\) −1095.59 −0.0873086
\(541\) 7964.67 0.632954 0.316477 0.948600i \(-0.397500\pi\)
0.316477 + 0.948600i \(0.397500\pi\)
\(542\) 11052.2 0.875887
\(543\) −707.969 −0.0559519
\(544\) 839.368 0.0661537
\(545\) 7979.77 0.627185
\(546\) 3245.52 0.254387
\(547\) −19077.6 −1.49122 −0.745611 0.666382i \(-0.767842\pi\)
−0.745611 + 0.666382i \(0.767842\pi\)
\(548\) 6050.18 0.471626
\(549\) 803.055 0.0624291
\(550\) −2110.47 −0.163620
\(551\) −2908.37 −0.224865
\(552\) −552.000 −0.0425628
\(553\) −3842.09 −0.295447
\(554\) −14698.1 −1.12719
\(555\) −8992.81 −0.687790
\(556\) −2325.64 −0.177390
\(557\) 18414.8 1.40083 0.700414 0.713737i \(-0.252999\pi\)
0.700414 + 0.713737i \(0.252999\pi\)
\(558\) 1747.74 0.132595
\(559\) −30307.5 −2.29315
\(560\) −1136.17 −0.0857353
\(561\) −3758.65 −0.282870
\(562\) −6864.00 −0.515196
\(563\) −8660.61 −0.648314 −0.324157 0.946003i \(-0.605081\pi\)
−0.324157 + 0.946003i \(0.605081\pi\)
\(564\) −959.834 −0.0716601
\(565\) 10009.6 0.745320
\(566\) 17465.7 1.29706
\(567\) −567.000 −0.0419961
\(568\) 973.341 0.0719022
\(569\) 14435.5 1.06357 0.531783 0.846881i \(-0.321522\pi\)
0.531783 + 0.846881i \(0.321522\pi\)
\(570\) 3345.63 0.245847
\(571\) 15744.4 1.15391 0.576954 0.816776i \(-0.304241\pi\)
0.576954 + 0.816776i \(0.304241\pi\)
\(572\) 14763.9 1.07922
\(573\) −919.470 −0.0670356
\(574\) 5117.02 0.372091
\(575\) 508.124 0.0368526
\(576\) 576.000 0.0416667
\(577\) 14990.4 1.08156 0.540780 0.841164i \(-0.318129\pi\)
0.540780 + 0.841164i \(0.318129\pi\)
\(578\) 8449.95 0.608082
\(579\) 3428.34 0.246074
\(580\) −2146.99 −0.153705
\(581\) −511.592 −0.0365309
\(582\) 4345.64 0.309506
\(583\) 6980.24 0.495870
\(584\) 5998.11 0.425006
\(585\) −7055.06 −0.498617
\(586\) 11499.9 0.810677
\(587\) −6469.75 −0.454915 −0.227457 0.973788i \(-0.573041\pi\)
−0.227457 + 0.973788i \(0.573041\pi\)
\(588\) −588.000 −0.0412393
\(589\) −5337.13 −0.373366
\(590\) 386.061 0.0269388
\(591\) −9329.31 −0.649334
\(592\) 4727.92 0.328237
\(593\) −2693.71 −0.186539 −0.0932693 0.995641i \(-0.529732\pi\)
−0.0932693 + 0.995641i \(0.529732\pi\)
\(594\) −2579.30 −0.178165
\(595\) 1862.62 0.128336
\(596\) 11386.1 0.782538
\(597\) −2658.20 −0.182233
\(598\) −3554.61 −0.243075
\(599\) 15387.1 1.04958 0.524790 0.851232i \(-0.324144\pi\)
0.524790 + 0.851232i \(0.324144\pi\)
\(600\) −530.216 −0.0360767
\(601\) −5907.39 −0.400944 −0.200472 0.979699i \(-0.564248\pi\)
−0.200472 + 0.979699i \(0.564248\pi\)
\(602\) 5490.90 0.371748
\(603\) −9188.87 −0.620563
\(604\) −10851.4 −0.731025
\(605\) 9641.95 0.647936
\(606\) −957.125 −0.0641593
\(607\) 6209.90 0.415243 0.207621 0.978209i \(-0.433428\pi\)
0.207621 + 0.978209i \(0.433428\pi\)
\(608\) −1758.95 −0.117327
\(609\) −1111.13 −0.0739333
\(610\) −1810.33 −0.120161
\(611\) −6180.87 −0.409249
\(612\) −944.289 −0.0623703
\(613\) 4419.34 0.291183 0.145592 0.989345i \(-0.453491\pi\)
0.145592 + 0.989345i \(0.453491\pi\)
\(614\) −4139.75 −0.272096
\(615\) −11123.3 −0.729326
\(616\) −2674.83 −0.174954
\(617\) −9736.05 −0.635265 −0.317633 0.948214i \(-0.602888\pi\)
−0.317633 + 0.948214i \(0.602888\pi\)
\(618\) −1106.05 −0.0719932
\(619\) 16608.5 1.07844 0.539218 0.842166i \(-0.318720\pi\)
0.539218 + 0.842166i \(0.318720\pi\)
\(620\) −3939.93 −0.255212
\(621\) 621.000 0.0401286
\(622\) −16257.1 −1.04799
\(623\) −7624.77 −0.490337
\(624\) 3709.16 0.237957
\(625\) −12375.4 −0.792025
\(626\) 4295.63 0.274262
\(627\) 7876.47 0.501684
\(628\) 10977.8 0.697549
\(629\) −7750.91 −0.491334
\(630\) 1278.19 0.0808320
\(631\) 15115.7 0.953640 0.476820 0.879001i \(-0.341789\pi\)
0.476820 + 0.879001i \(0.341789\pi\)
\(632\) −4390.96 −0.276366
\(633\) −1180.04 −0.0740955
\(634\) 11817.8 0.740291
\(635\) 6625.07 0.414028
\(636\) 1753.65 0.109335
\(637\) −3786.44 −0.235517
\(638\) −5054.58 −0.313656
\(639\) −1095.01 −0.0677901
\(640\) −1298.48 −0.0801981
\(641\) −11613.9 −0.715633 −0.357816 0.933792i \(-0.616479\pi\)
−0.357816 + 0.933792i \(0.616479\pi\)
\(642\) 2931.70 0.180226
\(643\) −13410.3 −0.822471 −0.411236 0.911529i \(-0.634903\pi\)
−0.411236 + 0.911529i \(0.634903\pi\)
\(644\) 644.000 0.0394055
\(645\) −11936.0 −0.728653
\(646\) 2883.60 0.175625
\(647\) −8032.34 −0.488074 −0.244037 0.969766i \(-0.578472\pi\)
−0.244037 + 0.969766i \(0.578472\pi\)
\(648\) −648.000 −0.0392837
\(649\) 908.887 0.0549722
\(650\) −3414.34 −0.206033
\(651\) −2039.03 −0.122759
\(652\) −11379.7 −0.683536
\(653\) 29290.6 1.75533 0.877664 0.479276i \(-0.159101\pi\)
0.877664 + 0.479276i \(0.159101\pi\)
\(654\) 4719.74 0.282196
\(655\) 17726.6 1.05746
\(656\) 5848.02 0.348059
\(657\) −6747.87 −0.400699
\(658\) 1119.81 0.0663444
\(659\) −8361.11 −0.494237 −0.247119 0.968985i \(-0.579484\pi\)
−0.247119 + 0.968985i \(0.579484\pi\)
\(660\) 5814.51 0.342923
\(661\) 12471.7 0.733877 0.366938 0.930245i \(-0.380406\pi\)
0.366938 + 0.930245i \(0.380406\pi\)
\(662\) 556.124 0.0326501
\(663\) −6080.76 −0.356195
\(664\) −584.677 −0.0341715
\(665\) −3903.23 −0.227610
\(666\) −5318.92 −0.309465
\(667\) 1216.96 0.0706457
\(668\) −1981.25 −0.114756
\(669\) 14807.2 0.855724
\(670\) 20714.4 1.19443
\(671\) −4261.98 −0.245204
\(672\) −672.000 −0.0385758
\(673\) −18614.5 −1.06617 −0.533087 0.846061i \(-0.678968\pi\)
−0.533087 + 0.846061i \(0.678968\pi\)
\(674\) 16710.4 0.954983
\(675\) 596.493 0.0340134
\(676\) 15097.2 0.858967
\(677\) 10930.2 0.620504 0.310252 0.950654i \(-0.399587\pi\)
0.310252 + 0.950654i \(0.399587\pi\)
\(678\) 5920.29 0.335350
\(679\) −5069.92 −0.286547
\(680\) 2128.71 0.120047
\(681\) −203.423 −0.0114467
\(682\) −9275.62 −0.520795
\(683\) 18745.1 1.05016 0.525082 0.851052i \(-0.324035\pi\)
0.525082 + 0.851052i \(0.324035\pi\)
\(684\) 1978.81 0.110617
\(685\) 15343.8 0.855847
\(686\) 686.000 0.0381802
\(687\) −13501.8 −0.749817
\(688\) 6275.31 0.347738
\(689\) 11292.7 0.624408
\(690\) −1399.92 −0.0772377
\(691\) −26682.8 −1.46898 −0.734488 0.678622i \(-0.762577\pi\)
−0.734488 + 0.678622i \(0.762577\pi\)
\(692\) 14263.2 0.783532
\(693\) 3009.18 0.164949
\(694\) −13573.8 −0.742440
\(695\) −5898.02 −0.321906
\(696\) −1269.87 −0.0691583
\(697\) −9587.19 −0.521005
\(698\) 14011.1 0.759784
\(699\) 15338.8 0.829995
\(700\) 618.586 0.0334005
\(701\) −16576.7 −0.893144 −0.446572 0.894748i \(-0.647355\pi\)
−0.446572 + 0.894748i \(0.647355\pi\)
\(702\) −4172.81 −0.224348
\(703\) 16242.5 0.871405
\(704\) −3056.95 −0.163655
\(705\) −2434.22 −0.130040
\(706\) −4081.15 −0.217558
\(707\) 1116.65 0.0594000
\(708\) 228.341 0.0121209
\(709\) 10566.8 0.559723 0.279862 0.960040i \(-0.409711\pi\)
0.279862 + 0.960040i \(0.409711\pi\)
\(710\) 2468.47 0.130479
\(711\) 4939.84 0.260560
\(712\) −8714.03 −0.458669
\(713\) 2233.23 0.117300
\(714\) 1101.67 0.0577436
\(715\) 37442.6 1.95843
\(716\) −1962.32 −0.102424
\(717\) −13297.1 −0.692591
\(718\) −11007.2 −0.572127
\(719\) −26143.1 −1.35601 −0.678006 0.735056i \(-0.737156\pi\)
−0.678006 + 0.735056i \(0.737156\pi\)
\(720\) 1460.79 0.0756115
\(721\) 1290.39 0.0666527
\(722\) 7675.25 0.395628
\(723\) −7355.69 −0.378369
\(724\) 943.959 0.0484558
\(725\) 1168.93 0.0598800
\(726\) 5702.86 0.291533
\(727\) −30744.5 −1.56843 −0.784216 0.620488i \(-0.786934\pi\)
−0.784216 + 0.620488i \(0.786934\pi\)
\(728\) −4327.36 −0.220306
\(729\) 729.000 0.0370370
\(730\) 15211.7 0.771248
\(731\) −10287.7 −0.520525
\(732\) −1070.74 −0.0540652
\(733\) −5053.21 −0.254631 −0.127316 0.991862i \(-0.540636\pi\)
−0.127316 + 0.991862i \(0.540636\pi\)
\(734\) 10334.6 0.519694
\(735\) −1491.22 −0.0748359
\(736\) 736.000 0.0368605
\(737\) 48767.1 2.43740
\(738\) −6579.03 −0.328154
\(739\) 15337.4 0.763460 0.381730 0.924274i \(-0.375328\pi\)
0.381730 + 0.924274i \(0.375328\pi\)
\(740\) 11990.4 0.595644
\(741\) 12742.6 0.631729
\(742\) −2045.93 −0.101224
\(743\) 40357.0 1.99267 0.996336 0.0855253i \(-0.0272568\pi\)
0.996336 + 0.0855253i \(0.0272568\pi\)
\(744\) −2330.32 −0.114830
\(745\) 28876.1 1.42005
\(746\) 1913.26 0.0938999
\(747\) 657.762 0.0322172
\(748\) 5011.53 0.244973
\(749\) −3420.31 −0.166857
\(750\) −8952.93 −0.435886
\(751\) 15971.2 0.776027 0.388013 0.921654i \(-0.373161\pi\)
0.388013 + 0.921654i \(0.373161\pi\)
\(752\) 1279.78 0.0620595
\(753\) −4884.21 −0.236375
\(754\) −8177.32 −0.394961
\(755\) −27520.2 −1.32657
\(756\) 756.000 0.0363696
\(757\) −18896.1 −0.907251 −0.453626 0.891192i \(-0.649870\pi\)
−0.453626 + 0.891192i \(0.649870\pi\)
\(758\) −27402.2 −1.31305
\(759\) −3295.77 −0.157614
\(760\) −4460.84 −0.212910
\(761\) 10130.8 0.482577 0.241289 0.970453i \(-0.422430\pi\)
0.241289 + 0.970453i \(0.422430\pi\)
\(762\) 3918.48 0.186288
\(763\) −5506.36 −0.261263
\(764\) 1225.96 0.0580546
\(765\) −2394.80 −0.113182
\(766\) 10078.8 0.475409
\(767\) 1470.40 0.0692219
\(768\) −768.000 −0.0360844
\(769\) 9225.09 0.432594 0.216297 0.976328i \(-0.430602\pi\)
0.216297 + 0.976328i \(0.430602\pi\)
\(770\) −6783.59 −0.317485
\(771\) −17273.0 −0.806837
\(772\) −4571.12 −0.213106
\(773\) 1879.77 0.0874652 0.0437326 0.999043i \(-0.486075\pi\)
0.0437326 + 0.999043i \(0.486075\pi\)
\(774\) −7059.73 −0.327851
\(775\) 2145.10 0.0994247
\(776\) −5794.19 −0.268040
\(777\) 6205.40 0.286509
\(778\) 11090.7 0.511080
\(779\) 20090.5 0.924029
\(780\) 9406.75 0.431815
\(781\) 5811.43 0.266260
\(782\) −1206.59 −0.0551760
\(783\) 1428.60 0.0652030
\(784\) 784.000 0.0357143
\(785\) 27840.6 1.26582
\(786\) 10484.6 0.475795
\(787\) −1579.70 −0.0715506 −0.0357753 0.999360i \(-0.511390\pi\)
−0.0357753 + 0.999360i \(0.511390\pi\)
\(788\) 12439.1 0.562340
\(789\) −4677.75 −0.211068
\(790\) −11135.9 −0.501514
\(791\) −6907.00 −0.310474
\(792\) 3439.07 0.154295
\(793\) −6895.05 −0.308765
\(794\) −6204.27 −0.277307
\(795\) 4447.41 0.198407
\(796\) 3544.27 0.157818
\(797\) 10146.4 0.450946 0.225473 0.974249i \(-0.427607\pi\)
0.225473 + 0.974249i \(0.427607\pi\)
\(798\) −2308.62 −0.102411
\(799\) −2098.06 −0.0928960
\(800\) 706.955 0.0312433
\(801\) 9803.28 0.432437
\(802\) −21431.0 −0.943583
\(803\) 35812.3 1.57383
\(804\) 12251.8 0.537423
\(805\) 1633.24 0.0715082
\(806\) −15006.2 −0.655794
\(807\) −19109.6 −0.833570
\(808\) 1276.17 0.0555636
\(809\) −9235.53 −0.401365 −0.200682 0.979656i \(-0.564316\pi\)
−0.200682 + 0.979656i \(0.564316\pi\)
\(810\) −1643.38 −0.0712872
\(811\) 31367.8 1.35817 0.679083 0.734062i \(-0.262378\pi\)
0.679083 + 0.734062i \(0.262378\pi\)
\(812\) 1481.51 0.0640281
\(813\) 16578.2 0.715159
\(814\) 28228.5 1.21549
\(815\) −28860.0 −1.24040
\(816\) 1259.05 0.0540142
\(817\) 21558.5 0.923176
\(818\) −23100.3 −0.987390
\(819\) 4868.27 0.207706
\(820\) 14831.1 0.631615
\(821\) −1449.02 −0.0615971 −0.0307985 0.999526i \(-0.509805\pi\)
−0.0307985 + 0.999526i \(0.509805\pi\)
\(822\) 9075.27 0.385081
\(823\) −6671.39 −0.282564 −0.141282 0.989969i \(-0.545122\pi\)
−0.141282 + 0.989969i \(0.545122\pi\)
\(824\) 1474.73 0.0623479
\(825\) −3165.71 −0.133595
\(826\) −266.397 −0.0112217
\(827\) −19290.9 −0.811139 −0.405570 0.914064i \(-0.632927\pi\)
−0.405570 + 0.914064i \(0.632927\pi\)
\(828\) −828.000 −0.0347524
\(829\) −17190.7 −0.720213 −0.360107 0.932911i \(-0.617260\pi\)
−0.360107 + 0.932911i \(0.617260\pi\)
\(830\) −1482.79 −0.0620102
\(831\) −22047.2 −0.920348
\(832\) −4945.55 −0.206077
\(833\) −1285.28 −0.0534602
\(834\) −3488.46 −0.144839
\(835\) −5024.61 −0.208244
\(836\) −10502.0 −0.434471
\(837\) 2621.62 0.108263
\(838\) −4479.40 −0.184652
\(839\) −47293.3 −1.94606 −0.973032 0.230670i \(-0.925908\pi\)
−0.973032 + 0.230670i \(0.925908\pi\)
\(840\) −1704.25 −0.0700026
\(841\) −21589.4 −0.885211
\(842\) −11477.3 −0.469755
\(843\) −10296.0 −0.420656
\(844\) 1573.39 0.0641686
\(845\) 38287.8 1.55875
\(846\) −1439.75 −0.0585102
\(847\) −6653.33 −0.269907
\(848\) −2338.20 −0.0946866
\(849\) 26198.6 1.05905
\(850\) −1158.98 −0.0467677
\(851\) −6796.39 −0.273769
\(852\) 1460.01 0.0587079
\(853\) −29185.6 −1.17151 −0.585754 0.810489i \(-0.699202\pi\)
−0.585754 + 0.810489i \(0.699202\pi\)
\(854\) 1249.20 0.0500546
\(855\) 5018.44 0.200733
\(856\) −3908.93 −0.156080
\(857\) −3922.80 −0.156360 −0.0781798 0.996939i \(-0.524911\pi\)
−0.0781798 + 0.996939i \(0.524911\pi\)
\(858\) 22145.9 0.881176
\(859\) 18335.8 0.728300 0.364150 0.931340i \(-0.381359\pi\)
0.364150 + 0.931340i \(0.381359\pi\)
\(860\) 15914.7 0.631032
\(861\) 7675.53 0.303811
\(862\) −4986.42 −0.197028
\(863\) −30425.0 −1.20009 −0.600045 0.799966i \(-0.704851\pi\)
−0.600045 + 0.799966i \(0.704851\pi\)
\(864\) 864.000 0.0340207
\(865\) 36172.6 1.42186
\(866\) −8350.85 −0.327683
\(867\) 12674.9 0.496497
\(868\) 2718.71 0.106312
\(869\) −26216.7 −1.02341
\(870\) −3220.49 −0.125500
\(871\) 78895.8 3.06921
\(872\) −6292.98 −0.244389
\(873\) 6518.46 0.252711
\(874\) 2528.48 0.0978573
\(875\) 10445.1 0.403552
\(876\) 8997.16 0.347016
\(877\) −23.1326 −0.000890685 0 −0.000445343 1.00000i \(-0.500142\pi\)
−0.000445343 1.00000i \(0.500142\pi\)
\(878\) 21785.0 0.837368
\(879\) 17249.9 0.661915
\(880\) −7752.68 −0.296980
\(881\) 41825.9 1.59949 0.799744 0.600341i \(-0.204968\pi\)
0.799744 + 0.600341i \(0.204968\pi\)
\(882\) −882.000 −0.0336718
\(883\) 25536.2 0.973230 0.486615 0.873617i \(-0.338232\pi\)
0.486615 + 0.873617i \(0.338232\pi\)
\(884\) 8107.68 0.308474
\(885\) 579.091 0.0219954
\(886\) 21000.1 0.796289
\(887\) −16939.0 −0.641213 −0.320606 0.947213i \(-0.603887\pi\)
−0.320606 + 0.947213i \(0.603887\pi\)
\(888\) 7091.89 0.268005
\(889\) −4571.56 −0.172469
\(890\) −22099.5 −0.832334
\(891\) −3868.95 −0.145471
\(892\) −19742.9 −0.741079
\(893\) 4396.60 0.164756
\(894\) 17079.1 0.638940
\(895\) −4976.62 −0.185866
\(896\) 896.000 0.0334077
\(897\) −5331.92 −0.198470
\(898\) −10139.6 −0.376797
\(899\) 5137.50 0.190595
\(900\) −795.324 −0.0294565
\(901\) 3833.23 0.141735
\(902\) 34916.2 1.28889
\(903\) 8236.35 0.303531
\(904\) −7893.71 −0.290421
\(905\) 2393.96 0.0879314
\(906\) −16277.2 −0.596879
\(907\) −53400.9 −1.95496 −0.977479 0.211032i \(-0.932318\pi\)
−0.977479 + 0.211032i \(0.932318\pi\)
\(908\) 271.231 0.00991311
\(909\) −1435.69 −0.0523858
\(910\) −10974.5 −0.399783
\(911\) −5253.70 −0.191068 −0.0955339 0.995426i \(-0.530456\pi\)
−0.0955339 + 0.995426i \(0.530456\pi\)
\(912\) −2638.42 −0.0957969
\(913\) −3490.87 −0.126540
\(914\) −3544.07 −0.128258
\(915\) −2715.49 −0.0981107
\(916\) 18002.3 0.649361
\(917\) −12232.1 −0.440500
\(918\) −1416.43 −0.0509251
\(919\) 23492.6 0.843253 0.421627 0.906770i \(-0.361459\pi\)
0.421627 + 0.906770i \(0.361459\pi\)
\(920\) 1866.56 0.0668898
\(921\) −6209.63 −0.222165
\(922\) 24018.3 0.857917
\(923\) 9401.76 0.335279
\(924\) −4012.24 −0.142850
\(925\) −6528.18 −0.232049
\(926\) −27116.0 −0.962295
\(927\) −1659.07 −0.0587822
\(928\) 1693.15 0.0598928
\(929\) 4184.83 0.147793 0.0738966 0.997266i \(-0.476457\pi\)
0.0738966 + 0.997266i \(0.476457\pi\)
\(930\) −5909.90 −0.208380
\(931\) 2693.39 0.0948143
\(932\) −20451.7 −0.718797
\(933\) −24385.6 −0.855680
\(934\) −14978.4 −0.524742
\(935\) 12709.7 0.444546
\(936\) 5563.74 0.194291
\(937\) −24593.9 −0.857470 −0.428735 0.903430i \(-0.641041\pi\)
−0.428735 + 0.903430i \(0.641041\pi\)
\(938\) −14293.8 −0.497557
\(939\) 6443.44 0.223934
\(940\) 3245.63 0.112618
\(941\) 6895.77 0.238890 0.119445 0.992841i \(-0.461888\pi\)
0.119445 + 0.992841i \(0.461888\pi\)
\(942\) 16466.7 0.569546
\(943\) −8406.53 −0.290302
\(944\) −304.454 −0.0104970
\(945\) 1917.28 0.0659991
\(946\) 37467.4 1.28771
\(947\) 780.389 0.0267785 0.0133892 0.999910i \(-0.495738\pi\)
0.0133892 + 0.999910i \(0.495738\pi\)
\(948\) −6586.45 −0.225652
\(949\) 57937.4 1.98180
\(950\) 2428.70 0.0829447
\(951\) 17726.7 0.604445
\(952\) −1468.89 −0.0500075
\(953\) 27383.7 0.930791 0.465396 0.885103i \(-0.345912\pi\)
0.465396 + 0.885103i \(0.345912\pi\)
\(954\) 2630.48 0.0892714
\(955\) 3109.14 0.105350
\(956\) 17729.4 0.599801
\(957\) −7581.86 −0.256099
\(958\) 27330.8 0.921729
\(959\) −10587.8 −0.356516
\(960\) −1947.71 −0.0654814
\(961\) −20363.2 −0.683535
\(962\) 45668.3 1.53057
\(963\) 4397.55 0.147154
\(964\) 9807.59 0.327678
\(965\) −11592.7 −0.386719
\(966\) 966.000 0.0321745
\(967\) 1541.70 0.0512698 0.0256349 0.999671i \(-0.491839\pi\)
0.0256349 + 0.999671i \(0.491839\pi\)
\(968\) −7603.81 −0.252475
\(969\) 4325.40 0.143397
\(970\) −14694.6 −0.486406
\(971\) 25166.5 0.831753 0.415876 0.909421i \(-0.363475\pi\)
0.415876 + 0.909421i \(0.363475\pi\)
\(972\) −972.000 −0.0320750
\(973\) 4069.87 0.134095
\(974\) −1375.89 −0.0452634
\(975\) −5121.51 −0.168225
\(976\) 1427.65 0.0468218
\(977\) 33468.8 1.09597 0.547985 0.836488i \(-0.315395\pi\)
0.547985 + 0.836488i \(0.315395\pi\)
\(978\) −17069.6 −0.558105
\(979\) −52028.0 −1.69849
\(980\) 1988.29 0.0648098
\(981\) 7079.61 0.230412
\(982\) −15496.5 −0.503579
\(983\) −32986.5 −1.07030 −0.535150 0.844757i \(-0.679745\pi\)
−0.535150 + 0.844757i \(0.679745\pi\)
\(984\) 8772.04 0.284189
\(985\) 31546.6 1.02046
\(986\) −2775.74 −0.0896527
\(987\) 1679.71 0.0541699
\(988\) −16990.1 −0.547093
\(989\) −9020.76 −0.290034
\(990\) 8721.76 0.279996
\(991\) 15665.5 0.502152 0.251076 0.967967i \(-0.419216\pi\)
0.251076 + 0.967967i \(0.419216\pi\)
\(992\) 3107.10 0.0994461
\(993\) 834.186 0.0266587
\(994\) −1703.35 −0.0543530
\(995\) 8988.56 0.286388
\(996\) −877.016 −0.0279009
\(997\) −14588.1 −0.463400 −0.231700 0.972787i \(-0.574429\pi\)
−0.231700 + 0.972787i \(0.574429\pi\)
\(998\) 22442.3 0.711824
\(999\) −7978.37 −0.252677
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 966.4.a.m.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.m.1.4 5 1.1 even 1 trivial