Properties

Label 230.4.a.h.1.3
Level $230$
Weight $4$
Character 230.1
Self dual yes
Analytic conductor $13.570$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 68 x^{2} - 111 x + 342\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.58997\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +0.589969 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.17994 q^{6} -18.5077 q^{7} -8.00000 q^{8} -26.6519 q^{9} +10.0000 q^{10} +47.9296 q^{11} +2.35988 q^{12} +42.3717 q^{13} +37.0155 q^{14} -2.94985 q^{15} +16.0000 q^{16} +1.70534 q^{17} +53.3039 q^{18} +21.4208 q^{19} -20.0000 q^{20} -10.9190 q^{21} -95.8592 q^{22} -23.0000 q^{23} -4.71976 q^{24} +25.0000 q^{25} -84.7434 q^{26} -31.6530 q^{27} -74.0310 q^{28} +57.6332 q^{29} +5.89969 q^{30} +295.699 q^{31} -32.0000 q^{32} +28.2770 q^{33} -3.41069 q^{34} +92.5387 q^{35} -106.608 q^{36} -7.85184 q^{37} -42.8416 q^{38} +24.9980 q^{39} +40.0000 q^{40} +465.929 q^{41} +21.8380 q^{42} +182.374 q^{43} +191.718 q^{44} +133.260 q^{45} +46.0000 q^{46} +449.193 q^{47} +9.43951 q^{48} -0.463605 q^{49} -50.0000 q^{50} +1.00610 q^{51} +169.487 q^{52} -368.316 q^{53} +63.3060 q^{54} -239.648 q^{55} +148.062 q^{56} +12.6376 q^{57} -115.266 q^{58} -377.032 q^{59} -11.7994 q^{60} +849.042 q^{61} -591.398 q^{62} +493.267 q^{63} +64.0000 q^{64} -211.858 q^{65} -56.5540 q^{66} +92.3424 q^{67} +6.82138 q^{68} -13.5693 q^{69} -185.077 q^{70} -626.854 q^{71} +213.215 q^{72} +439.227 q^{73} +15.7037 q^{74} +14.7492 q^{75} +85.6831 q^{76} -887.068 q^{77} -49.9960 q^{78} +641.707 q^{79} -80.0000 q^{80} +700.928 q^{81} -931.859 q^{82} -609.932 q^{83} -43.6760 q^{84} -8.52672 q^{85} -364.747 q^{86} +34.0018 q^{87} -383.437 q^{88} +1122.87 q^{89} -266.519 q^{90} -784.204 q^{91} -92.0000 q^{92} +174.453 q^{93} -898.386 q^{94} -107.104 q^{95} -18.8790 q^{96} -1428.80 q^{97} +0.927209 q^{98} -1277.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{2} - 4q^{3} + 16q^{4} - 20q^{5} + 8q^{6} - q^{7} - 32q^{8} + 32q^{9} + O(q^{10}) \) \( 4q - 8q^{2} - 4q^{3} + 16q^{4} - 20q^{5} + 8q^{6} - q^{7} - 32q^{8} + 32q^{9} + 40q^{10} - 39q^{11} - 16q^{12} - 20q^{13} + 2q^{14} + 20q^{15} + 64q^{16} - 23q^{17} - 64q^{18} + 53q^{19} - 80q^{20} + 300q^{21} + 78q^{22} - 92q^{23} + 32q^{24} + 100q^{25} + 40q^{26} + 137q^{27} - 4q^{28} + 161q^{29} - 40q^{30} + 388q^{31} - 128q^{32} + 87q^{33} + 46q^{34} + 5q^{35} + 128q^{36} + 466q^{37} - 106q^{38} + 1047q^{39} + 160q^{40} + 484q^{41} - 600q^{42} + 894q^{43} - 156q^{44} - 160q^{45} + 184q^{46} - 265q^{47} - 64q^{48} + 1643q^{49} - 200q^{50} + 1825q^{51} - 80q^{52} + 576q^{53} - 274q^{54} + 195q^{55} + 8q^{56} + 178q^{57} - 322q^{58} - 94q^{59} + 80q^{60} + 1153q^{61} - 776q^{62} + 60q^{63} + 256q^{64} + 100q^{65} - 174q^{66} - 1472q^{67} - 92q^{68} + 92q^{69} - 10q^{70} + 200q^{71} - 256q^{72} + 1147q^{73} - 932q^{74} - 100q^{75} + 212q^{76} - 2176q^{77} - 2094q^{78} - 908q^{79} - 320q^{80} - 1056q^{81} - 968q^{82} - 1048q^{83} + 1200q^{84} + 115q^{85} - 1788q^{86} - 2167q^{87} + 312q^{88} - 1784q^{89} + 320q^{90} + 2329q^{91} - 368q^{92} + 1483q^{93} + 530q^{94} - 265q^{95} + 128q^{96} - 2047q^{97} - 3286q^{98} - 2665q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0.589969 0.113540 0.0567698 0.998387i \(-0.481920\pi\)
0.0567698 + 0.998387i \(0.481920\pi\)
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) −1.17994 −0.0802847
\(7\) −18.5077 −0.999324 −0.499662 0.866220i \(-0.666542\pi\)
−0.499662 + 0.866220i \(0.666542\pi\)
\(8\) −8.00000 −0.353553
\(9\) −26.6519 −0.987109
\(10\) 10.0000 0.316228
\(11\) 47.9296 1.31376 0.656878 0.753997i \(-0.271877\pi\)
0.656878 + 0.753997i \(0.271877\pi\)
\(12\) 2.35988 0.0567698
\(13\) 42.3717 0.903984 0.451992 0.892022i \(-0.350714\pi\)
0.451992 + 0.892022i \(0.350714\pi\)
\(14\) 37.0155 0.706629
\(15\) −2.94985 −0.0507765
\(16\) 16.0000 0.250000
\(17\) 1.70534 0.0243298 0.0121649 0.999926i \(-0.496128\pi\)
0.0121649 + 0.999926i \(0.496128\pi\)
\(18\) 53.3039 0.697991
\(19\) 21.4208 0.258645 0.129323 0.991603i \(-0.458720\pi\)
0.129323 + 0.991603i \(0.458720\pi\)
\(20\) −20.0000 −0.223607
\(21\) −10.9190 −0.113463
\(22\) −95.8592 −0.928966
\(23\) −23.0000 −0.208514
\(24\) −4.71976 −0.0401423
\(25\) 25.0000 0.200000
\(26\) −84.7434 −0.639213
\(27\) −31.6530 −0.225616
\(28\) −74.0310 −0.499662
\(29\) 57.6332 0.369042 0.184521 0.982829i \(-0.440927\pi\)
0.184521 + 0.982829i \(0.440927\pi\)
\(30\) 5.89969 0.0359044
\(31\) 295.699 1.71320 0.856599 0.515983i \(-0.172573\pi\)
0.856599 + 0.515983i \(0.172573\pi\)
\(32\) −32.0000 −0.176777
\(33\) 28.2770 0.149163
\(34\) −3.41069 −0.0172038
\(35\) 92.5387 0.446911
\(36\) −106.608 −0.493554
\(37\) −7.85184 −0.0348874 −0.0174437 0.999848i \(-0.505553\pi\)
−0.0174437 + 0.999848i \(0.505553\pi\)
\(38\) −42.8416 −0.182890
\(39\) 24.9980 0.102638
\(40\) 40.0000 0.158114
\(41\) 465.929 1.77478 0.887390 0.461020i \(-0.152516\pi\)
0.887390 + 0.461020i \(0.152516\pi\)
\(42\) 21.8380 0.0802304
\(43\) 182.374 0.646784 0.323392 0.946265i \(-0.395177\pi\)
0.323392 + 0.946265i \(0.395177\pi\)
\(44\) 191.718 0.656878
\(45\) 133.260 0.441448
\(46\) 46.0000 0.147442
\(47\) 449.193 1.39408 0.697038 0.717035i \(-0.254501\pi\)
0.697038 + 0.717035i \(0.254501\pi\)
\(48\) 9.43951 0.0283849
\(49\) −0.463605 −0.00135162
\(50\) −50.0000 −0.141421
\(51\) 1.00610 0.00276240
\(52\) 169.487 0.451992
\(53\) −368.316 −0.954567 −0.477283 0.878749i \(-0.658379\pi\)
−0.477283 + 0.878749i \(0.658379\pi\)
\(54\) 63.3060 0.159534
\(55\) −239.648 −0.587529
\(56\) 148.062 0.353314
\(57\) 12.6376 0.0293665
\(58\) −115.266 −0.260952
\(59\) −377.032 −0.831955 −0.415977 0.909375i \(-0.636560\pi\)
−0.415977 + 0.909375i \(0.636560\pi\)
\(60\) −11.7994 −0.0253882
\(61\) 849.042 1.78211 0.891055 0.453896i \(-0.149966\pi\)
0.891055 + 0.453896i \(0.149966\pi\)
\(62\) −591.398 −1.21141
\(63\) 493.267 0.986441
\(64\) 64.0000 0.125000
\(65\) −211.858 −0.404274
\(66\) −56.5540 −0.105474
\(67\) 92.3424 0.168379 0.0841897 0.996450i \(-0.473170\pi\)
0.0841897 + 0.996450i \(0.473170\pi\)
\(68\) 6.82138 0.0121649
\(69\) −13.5693 −0.0236747
\(70\) −185.077 −0.316014
\(71\) −626.854 −1.04780 −0.523901 0.851779i \(-0.675524\pi\)
−0.523901 + 0.851779i \(0.675524\pi\)
\(72\) 213.215 0.348996
\(73\) 439.227 0.704214 0.352107 0.935960i \(-0.385465\pi\)
0.352107 + 0.935960i \(0.385465\pi\)
\(74\) 15.7037 0.0246691
\(75\) 14.7492 0.0227079
\(76\) 85.6831 0.129323
\(77\) −887.068 −1.31287
\(78\) −49.9960 −0.0725761
\(79\) 641.707 0.913894 0.456947 0.889494i \(-0.348943\pi\)
0.456947 + 0.889494i \(0.348943\pi\)
\(80\) −80.0000 −0.111803
\(81\) 700.928 0.961492
\(82\) −931.859 −1.25496
\(83\) −609.932 −0.806611 −0.403306 0.915065i \(-0.632139\pi\)
−0.403306 + 0.915065i \(0.632139\pi\)
\(84\) −43.6760 −0.0567315
\(85\) −8.52672 −0.0108806
\(86\) −364.747 −0.457346
\(87\) 34.0018 0.0419009
\(88\) −383.437 −0.464483
\(89\) 1122.87 1.33735 0.668673 0.743557i \(-0.266863\pi\)
0.668673 + 0.743557i \(0.266863\pi\)
\(90\) −266.519 −0.312151
\(91\) −784.204 −0.903373
\(92\) −92.0000 −0.104257
\(93\) 174.453 0.194516
\(94\) −898.386 −0.985760
\(95\) −107.104 −0.115670
\(96\) −18.8790 −0.0200712
\(97\) −1428.80 −1.49559 −0.747795 0.663930i \(-0.768887\pi\)
−0.747795 + 0.663930i \(0.768887\pi\)
\(98\) 0.927209 0.000955737 0
\(99\) −1277.42 −1.29682
\(100\) 100.000 0.100000
\(101\) −1512.15 −1.48975 −0.744875 0.667204i \(-0.767491\pi\)
−0.744875 + 0.667204i \(0.767491\pi\)
\(102\) −2.01220 −0.00195331
\(103\) 957.279 0.915762 0.457881 0.889013i \(-0.348609\pi\)
0.457881 + 0.889013i \(0.348609\pi\)
\(104\) −338.974 −0.319607
\(105\) 54.5950 0.0507422
\(106\) 736.631 0.674981
\(107\) −1742.16 −1.57403 −0.787013 0.616936i \(-0.788374\pi\)
−0.787013 + 0.616936i \(0.788374\pi\)
\(108\) −126.612 −0.112808
\(109\) 1166.77 1.02529 0.512644 0.858601i \(-0.328666\pi\)
0.512644 + 0.858601i \(0.328666\pi\)
\(110\) 479.296 0.415446
\(111\) −4.63234 −0.00396111
\(112\) −296.124 −0.249831
\(113\) −393.287 −0.327410 −0.163705 0.986509i \(-0.552345\pi\)
−0.163705 + 0.986509i \(0.552345\pi\)
\(114\) −25.2752 −0.0207653
\(115\) 115.000 0.0932505
\(116\) 230.533 0.184521
\(117\) −1129.29 −0.892331
\(118\) 754.063 0.588281
\(119\) −31.5621 −0.0243134
\(120\) 23.5988 0.0179522
\(121\) 966.245 0.725954
\(122\) −1698.08 −1.26014
\(123\) 274.884 0.201508
\(124\) 1182.80 0.856599
\(125\) −125.000 −0.0894427
\(126\) −986.534 −0.697519
\(127\) −1067.87 −0.746127 −0.373063 0.927806i \(-0.621693\pi\)
−0.373063 + 0.927806i \(0.621693\pi\)
\(128\) −128.000 −0.0883883
\(129\) 107.595 0.0734357
\(130\) 423.717 0.285865
\(131\) −175.497 −0.117047 −0.0585237 0.998286i \(-0.518639\pi\)
−0.0585237 + 0.998286i \(0.518639\pi\)
\(132\) 113.108 0.0745817
\(133\) −396.450 −0.258471
\(134\) −184.685 −0.119062
\(135\) 158.265 0.100898
\(136\) −13.6428 −0.00860189
\(137\) 475.898 0.296779 0.148389 0.988929i \(-0.452591\pi\)
0.148389 + 0.988929i \(0.452591\pi\)
\(138\) 27.1386 0.0167405
\(139\) 153.167 0.0934638 0.0467319 0.998907i \(-0.485119\pi\)
0.0467319 + 0.998907i \(0.485119\pi\)
\(140\) 370.155 0.223456
\(141\) 265.010 0.158283
\(142\) 1253.71 0.740907
\(143\) 2030.86 1.18761
\(144\) −426.431 −0.246777
\(145\) −288.166 −0.165041
\(146\) −878.454 −0.497954
\(147\) −0.273513 −0.000153462 0
\(148\) −31.4074 −0.0174437
\(149\) 506.906 0.278707 0.139353 0.990243i \(-0.455498\pi\)
0.139353 + 0.990243i \(0.455498\pi\)
\(150\) −29.4985 −0.0160569
\(151\) 2437.84 1.31383 0.656916 0.753964i \(-0.271861\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(152\) −171.366 −0.0914450
\(153\) −45.4507 −0.0240162
\(154\) 1774.14 0.928338
\(155\) −1478.50 −0.766166
\(156\) 99.9920 0.0513190
\(157\) 255.966 0.130117 0.0650584 0.997881i \(-0.479277\pi\)
0.0650584 + 0.997881i \(0.479277\pi\)
\(158\) −1283.41 −0.646221
\(159\) −217.295 −0.108381
\(160\) 160.000 0.0790569
\(161\) 425.678 0.208373
\(162\) −1401.86 −0.679878
\(163\) 321.632 0.154553 0.0772767 0.997010i \(-0.475378\pi\)
0.0772767 + 0.997010i \(0.475378\pi\)
\(164\) 1863.72 0.887390
\(165\) −141.385 −0.0667079
\(166\) 1219.86 0.570360
\(167\) −2926.22 −1.35591 −0.677957 0.735102i \(-0.737134\pi\)
−0.677957 + 0.735102i \(0.737134\pi\)
\(168\) 87.3520 0.0401152
\(169\) −401.640 −0.182813
\(170\) 17.0534 0.00769376
\(171\) −570.905 −0.255311
\(172\) 729.495 0.323392
\(173\) 1811.84 0.796254 0.398127 0.917330i \(-0.369660\pi\)
0.398127 + 0.917330i \(0.369660\pi\)
\(174\) −68.0037 −0.0296284
\(175\) −462.693 −0.199865
\(176\) 766.873 0.328439
\(177\) −222.437 −0.0944599
\(178\) −2245.74 −0.945646
\(179\) 912.664 0.381093 0.190547 0.981678i \(-0.438974\pi\)
0.190547 + 0.981678i \(0.438974\pi\)
\(180\) 533.039 0.220724
\(181\) 3670.55 1.50735 0.753673 0.657249i \(-0.228280\pi\)
0.753673 + 0.657249i \(0.228280\pi\)
\(182\) 1568.41 0.638781
\(183\) 500.909 0.202340
\(184\) 184.000 0.0737210
\(185\) 39.2592 0.0156021
\(186\) −348.907 −0.137544
\(187\) 81.7364 0.0319634
\(188\) 1796.77 0.697038
\(189\) 585.826 0.225463
\(190\) 214.208 0.0817909
\(191\) −1840.96 −0.697419 −0.348710 0.937231i \(-0.613380\pi\)
−0.348710 + 0.937231i \(0.613380\pi\)
\(192\) 37.7580 0.0141925
\(193\) −611.817 −0.228184 −0.114092 0.993470i \(-0.536396\pi\)
−0.114092 + 0.993470i \(0.536396\pi\)
\(194\) 2857.59 1.05754
\(195\) −124.990 −0.0459011
\(196\) −1.85442 −0.000675808 0
\(197\) 2830.26 1.02359 0.511796 0.859107i \(-0.328980\pi\)
0.511796 + 0.859107i \(0.328980\pi\)
\(198\) 2554.83 0.916990
\(199\) −1162.74 −0.414195 −0.207097 0.978320i \(-0.566402\pi\)
−0.207097 + 0.978320i \(0.566402\pi\)
\(200\) −200.000 −0.0707107
\(201\) 54.4792 0.0191177
\(202\) 3024.31 1.05341
\(203\) −1066.66 −0.368792
\(204\) 4.02440 0.00138120
\(205\) −2329.65 −0.793705
\(206\) −1914.56 −0.647542
\(207\) 612.995 0.205826
\(208\) 677.947 0.225996
\(209\) 1026.69 0.339797
\(210\) −109.190 −0.0358801
\(211\) 1399.58 0.456641 0.228320 0.973586i \(-0.426677\pi\)
0.228320 + 0.973586i \(0.426677\pi\)
\(212\) −1473.26 −0.477283
\(213\) −369.825 −0.118967
\(214\) 3484.32 1.11300
\(215\) −911.869 −0.289251
\(216\) 253.224 0.0797672
\(217\) −5472.72 −1.71204
\(218\) −2333.54 −0.724988
\(219\) 259.130 0.0799562
\(220\) −958.592 −0.293765
\(221\) 72.2583 0.0219938
\(222\) 9.26469 0.00280092
\(223\) 4257.98 1.27863 0.639317 0.768943i \(-0.279217\pi\)
0.639317 + 0.768943i \(0.279217\pi\)
\(224\) 592.248 0.176657
\(225\) −666.298 −0.197422
\(226\) 786.574 0.231514
\(227\) −4025.03 −1.17688 −0.588438 0.808542i \(-0.700257\pi\)
−0.588438 + 0.808542i \(0.700257\pi\)
\(228\) 50.5504 0.0146833
\(229\) 3623.04 1.04549 0.522745 0.852489i \(-0.324908\pi\)
0.522745 + 0.852489i \(0.324908\pi\)
\(230\) −230.000 −0.0659380
\(231\) −523.343 −0.149063
\(232\) −461.066 −0.130476
\(233\) 6502.81 1.82838 0.914192 0.405282i \(-0.132827\pi\)
0.914192 + 0.405282i \(0.132827\pi\)
\(234\) 2258.58 0.630973
\(235\) −2245.96 −0.623449
\(236\) −1508.13 −0.415977
\(237\) 378.587 0.103763
\(238\) 63.1241 0.0171921
\(239\) −2690.07 −0.728059 −0.364030 0.931387i \(-0.618599\pi\)
−0.364030 + 0.931387i \(0.618599\pi\)
\(240\) −47.1976 −0.0126941
\(241\) −44.6958 −0.0119465 −0.00597326 0.999982i \(-0.501901\pi\)
−0.00597326 + 0.999982i \(0.501901\pi\)
\(242\) −1932.49 −0.513327
\(243\) 1268.16 0.334783
\(244\) 3396.17 0.891055
\(245\) 2.31802 0.000604461 0
\(246\) −549.768 −0.142488
\(247\) 907.635 0.233811
\(248\) −2365.59 −0.605707
\(249\) −359.841 −0.0915824
\(250\) 250.000 0.0632456
\(251\) −6801.41 −1.71036 −0.855181 0.518329i \(-0.826554\pi\)
−0.855181 + 0.518329i \(0.826554\pi\)
\(252\) 1973.07 0.493221
\(253\) −1102.38 −0.273937
\(254\) 2135.74 0.527591
\(255\) −5.03050 −0.00123538
\(256\) 256.000 0.0625000
\(257\) 5576.00 1.35339 0.676695 0.736263i \(-0.263411\pi\)
0.676695 + 0.736263i \(0.263411\pi\)
\(258\) −215.190 −0.0519269
\(259\) 145.320 0.0348638
\(260\) −847.434 −0.202137
\(261\) −1536.04 −0.364285
\(262\) 350.993 0.0827651
\(263\) −5669.58 −1.32928 −0.664641 0.747163i \(-0.731415\pi\)
−0.664641 + 0.747163i \(0.731415\pi\)
\(264\) −226.216 −0.0527372
\(265\) 1841.58 0.426895
\(266\) 792.900 0.182766
\(267\) 662.458 0.151842
\(268\) 369.370 0.0841897
\(269\) 6040.21 1.36906 0.684532 0.728983i \(-0.260006\pi\)
0.684532 + 0.728983i \(0.260006\pi\)
\(270\) −316.530 −0.0713459
\(271\) −6899.26 −1.54650 −0.773248 0.634104i \(-0.781369\pi\)
−0.773248 + 0.634104i \(0.781369\pi\)
\(272\) 27.2855 0.00608245
\(273\) −462.657 −0.102569
\(274\) −951.795 −0.209854
\(275\) 1198.24 0.262751
\(276\) −54.2772 −0.0118373
\(277\) 5617.68 1.21853 0.609267 0.792965i \(-0.291464\pi\)
0.609267 + 0.792965i \(0.291464\pi\)
\(278\) −306.334 −0.0660889
\(279\) −7880.96 −1.69111
\(280\) −740.310 −0.158007
\(281\) 3069.89 0.651723 0.325861 0.945418i \(-0.394346\pi\)
0.325861 + 0.945418i \(0.394346\pi\)
\(282\) −530.020 −0.111923
\(283\) 1404.86 0.295089 0.147544 0.989055i \(-0.452863\pi\)
0.147544 + 0.989055i \(0.452863\pi\)
\(284\) −2507.42 −0.523901
\(285\) −63.1880 −0.0131331
\(286\) −4061.72 −0.839770
\(287\) −8623.30 −1.77358
\(288\) 852.862 0.174498
\(289\) −4910.09 −0.999408
\(290\) 576.332 0.116701
\(291\) −842.946 −0.169809
\(292\) 1756.91 0.352107
\(293\) −2407.05 −0.479936 −0.239968 0.970781i \(-0.577137\pi\)
−0.239968 + 0.970781i \(0.577137\pi\)
\(294\) 0.547025 0.000108514 0
\(295\) 1885.16 0.372062
\(296\) 62.8147 0.0123346
\(297\) −1517.12 −0.296404
\(298\) −1013.81 −0.197076
\(299\) −974.549 −0.188494
\(300\) 58.9969 0.0113540
\(301\) −3375.33 −0.646347
\(302\) −4875.68 −0.929020
\(303\) −892.124 −0.169146
\(304\) 342.732 0.0646614
\(305\) −4245.21 −0.796984
\(306\) 90.9015 0.0169820
\(307\) −459.743 −0.0854689 −0.0427344 0.999086i \(-0.513607\pi\)
−0.0427344 + 0.999086i \(0.513607\pi\)
\(308\) −3548.27 −0.656434
\(309\) 564.765 0.103975
\(310\) 2956.99 0.541761
\(311\) 4119.48 0.751107 0.375553 0.926801i \(-0.377453\pi\)
0.375553 + 0.926801i \(0.377453\pi\)
\(312\) −199.984 −0.0362880
\(313\) 1684.15 0.304133 0.152066 0.988370i \(-0.451407\pi\)
0.152066 + 0.988370i \(0.451407\pi\)
\(314\) −511.933 −0.0920065
\(315\) −2466.34 −0.441150
\(316\) 2566.83 0.456947
\(317\) 8686.47 1.53906 0.769528 0.638613i \(-0.220492\pi\)
0.769528 + 0.638613i \(0.220492\pi\)
\(318\) 434.590 0.0766371
\(319\) 2762.34 0.484831
\(320\) −320.000 −0.0559017
\(321\) −1027.82 −0.178714
\(322\) −851.356 −0.147342
\(323\) 36.5298 0.00629279
\(324\) 2803.71 0.480746
\(325\) 1059.29 0.180797
\(326\) −643.265 −0.109286
\(327\) 688.360 0.116411
\(328\) −3727.44 −0.627479
\(329\) −8313.55 −1.39313
\(330\) 282.770 0.0471696
\(331\) 4307.91 0.715359 0.357680 0.933844i \(-0.383568\pi\)
0.357680 + 0.933844i \(0.383568\pi\)
\(332\) −2439.73 −0.403306
\(333\) 209.267 0.0344377
\(334\) 5852.44 0.958776
\(335\) −461.712 −0.0753015
\(336\) −174.704 −0.0283657
\(337\) −290.156 −0.0469015 −0.0234507 0.999725i \(-0.507465\pi\)
−0.0234507 + 0.999725i \(0.507465\pi\)
\(338\) 803.280 0.129268
\(339\) −232.027 −0.0371740
\(340\) −34.1069 −0.00544031
\(341\) 14172.7 2.25072
\(342\) 1141.81 0.180532
\(343\) 6356.73 1.00067
\(344\) −1458.99 −0.228673
\(345\) 67.8465 0.0105876
\(346\) −3623.69 −0.563037
\(347\) 1042.94 0.161349 0.0806743 0.996741i \(-0.474293\pi\)
0.0806743 + 0.996741i \(0.474293\pi\)
\(348\) 136.007 0.0209505
\(349\) −1819.56 −0.279080 −0.139540 0.990216i \(-0.544562\pi\)
−0.139540 + 0.990216i \(0.544562\pi\)
\(350\) 925.387 0.141326
\(351\) −1341.19 −0.203953
\(352\) −1533.75 −0.232241
\(353\) −4514.29 −0.680656 −0.340328 0.940307i \(-0.610538\pi\)
−0.340328 + 0.940307i \(0.610538\pi\)
\(354\) 444.874 0.0667932
\(355\) 3134.27 0.468591
\(356\) 4491.47 0.668673
\(357\) −18.6207 −0.00276053
\(358\) −1825.33 −0.269474
\(359\) 11527.9 1.69476 0.847379 0.530988i \(-0.178179\pi\)
0.847379 + 0.530988i \(0.178179\pi\)
\(360\) −1066.08 −0.156076
\(361\) −6400.15 −0.933103
\(362\) −7341.10 −1.06585
\(363\) 570.055 0.0824246
\(364\) −3136.82 −0.451686
\(365\) −2196.13 −0.314934
\(366\) −1001.82 −0.143076
\(367\) 6894.09 0.980568 0.490284 0.871563i \(-0.336893\pi\)
0.490284 + 0.871563i \(0.336893\pi\)
\(368\) −368.000 −0.0521286
\(369\) −12417.9 −1.75190
\(370\) −78.5184 −0.0110324
\(371\) 6816.69 0.953922
\(372\) 697.814 0.0972580
\(373\) 7733.25 1.07349 0.536746 0.843744i \(-0.319653\pi\)
0.536746 + 0.843744i \(0.319653\pi\)
\(374\) −163.473 −0.0226016
\(375\) −73.7462 −0.0101553
\(376\) −3593.54 −0.492880
\(377\) 2442.02 0.333608
\(378\) −1171.65 −0.159427
\(379\) −9495.72 −1.28697 −0.643486 0.765458i \(-0.722512\pi\)
−0.643486 + 0.765458i \(0.722512\pi\)
\(380\) −428.416 −0.0578349
\(381\) −630.011 −0.0847150
\(382\) 3681.92 0.493150
\(383\) −12877.0 −1.71797 −0.858987 0.511998i \(-0.828906\pi\)
−0.858987 + 0.511998i \(0.828906\pi\)
\(384\) −75.5161 −0.0100356
\(385\) 4435.34 0.587132
\(386\) 1223.63 0.161351
\(387\) −4860.61 −0.638447
\(388\) −5715.18 −0.747795
\(389\) −8200.40 −1.06884 −0.534418 0.845221i \(-0.679469\pi\)
−0.534418 + 0.845221i \(0.679469\pi\)
\(390\) 249.980 0.0324570
\(391\) −39.2229 −0.00507312
\(392\) 3.70884 0.000477869 0
\(393\) −103.538 −0.0132895
\(394\) −5660.52 −0.723789
\(395\) −3208.53 −0.408706
\(396\) −5109.66 −0.648410
\(397\) 7842.68 0.991468 0.495734 0.868475i \(-0.334899\pi\)
0.495734 + 0.868475i \(0.334899\pi\)
\(398\) 2325.49 0.292880
\(399\) −233.893 −0.0293467
\(400\) 400.000 0.0500000
\(401\) −14534.2 −1.80999 −0.904993 0.425427i \(-0.860124\pi\)
−0.904993 + 0.425427i \(0.860124\pi\)
\(402\) −108.958 −0.0135183
\(403\) 12529.3 1.54870
\(404\) −6048.61 −0.744875
\(405\) −3504.64 −0.429992
\(406\) 2133.32 0.260776
\(407\) −376.335 −0.0458335
\(408\) −8.04881 −0.000976655 0
\(409\) 13388.0 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(410\) 4659.29 0.561234
\(411\) 280.765 0.0336962
\(412\) 3829.12 0.457881
\(413\) 6978.00 0.831393
\(414\) −1225.99 −0.145541
\(415\) 3049.66 0.360727
\(416\) −1355.89 −0.159803
\(417\) 90.3640 0.0106119
\(418\) −2053.38 −0.240273
\(419\) −3103.10 −0.361805 −0.180903 0.983501i \(-0.557902\pi\)
−0.180903 + 0.983501i \(0.557902\pi\)
\(420\) 218.380 0.0253711
\(421\) −6075.82 −0.703367 −0.351684 0.936119i \(-0.614391\pi\)
−0.351684 + 0.936119i \(0.614391\pi\)
\(422\) −2799.16 −0.322894
\(423\) −11971.9 −1.37610
\(424\) 2946.53 0.337490
\(425\) 42.6336 0.00486596
\(426\) 739.649 0.0841224
\(427\) −15713.8 −1.78090
\(428\) −6968.63 −0.787013
\(429\) 1198.14 0.134841
\(430\) 1823.74 0.204531
\(431\) 14120.3 1.57808 0.789040 0.614341i \(-0.210578\pi\)
0.789040 + 0.614341i \(0.210578\pi\)
\(432\) −506.448 −0.0564039
\(433\) 8555.96 0.949592 0.474796 0.880096i \(-0.342522\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(434\) 10945.4 1.21060
\(435\) −170.009 −0.0187387
\(436\) 4667.09 0.512644
\(437\) −492.678 −0.0539313
\(438\) −518.261 −0.0565376
\(439\) −10894.1 −1.18439 −0.592194 0.805796i \(-0.701738\pi\)
−0.592194 + 0.805796i \(0.701738\pi\)
\(440\) 1917.18 0.207723
\(441\) 12.3560 0.00133419
\(442\) −144.517 −0.0155519
\(443\) 16120.5 1.72891 0.864456 0.502708i \(-0.167663\pi\)
0.864456 + 0.502708i \(0.167663\pi\)
\(444\) −18.5294 −0.00198055
\(445\) −5614.34 −0.598079
\(446\) −8515.96 −0.904130
\(447\) 299.059 0.0316443
\(448\) −1184.50 −0.124915
\(449\) 4811.29 0.505699 0.252849 0.967506i \(-0.418632\pi\)
0.252849 + 0.967506i \(0.418632\pi\)
\(450\) 1332.60 0.139598
\(451\) 22331.8 2.33163
\(452\) −1573.15 −0.163705
\(453\) 1438.25 0.149172
\(454\) 8050.06 0.832177
\(455\) 3921.02 0.404001
\(456\) −101.101 −0.0103826
\(457\) −226.329 −0.0231667 −0.0115834 0.999933i \(-0.503687\pi\)
−0.0115834 + 0.999933i \(0.503687\pi\)
\(458\) −7246.08 −0.739273
\(459\) −53.9793 −0.00548919
\(460\) 460.000 0.0466252
\(461\) −4349.17 −0.439395 −0.219697 0.975568i \(-0.570507\pi\)
−0.219697 + 0.975568i \(0.570507\pi\)
\(462\) 1046.69 0.105403
\(463\) −989.313 −0.0993030 −0.0496515 0.998767i \(-0.515811\pi\)
−0.0496515 + 0.998767i \(0.515811\pi\)
\(464\) 922.131 0.0922605
\(465\) −872.267 −0.0869902
\(466\) −13005.6 −1.29286
\(467\) 8512.91 0.843535 0.421767 0.906704i \(-0.361410\pi\)
0.421767 + 0.906704i \(0.361410\pi\)
\(468\) −4517.15 −0.446165
\(469\) −1709.05 −0.168266
\(470\) 4491.93 0.440845
\(471\) 151.012 0.0147734
\(472\) 3016.25 0.294140
\(473\) 8741.10 0.849717
\(474\) −757.175 −0.0733717
\(475\) 535.519 0.0517291
\(476\) −126.248 −0.0121567
\(477\) 9816.33 0.942261
\(478\) 5380.14 0.514816
\(479\) −12058.6 −1.15025 −0.575125 0.818065i \(-0.695047\pi\)
−0.575125 + 0.818065i \(0.695047\pi\)
\(480\) 94.3951 0.00897610
\(481\) −332.696 −0.0315377
\(482\) 89.3916 0.00844746
\(483\) 251.137 0.0236587
\(484\) 3864.98 0.362977
\(485\) 7143.98 0.668848
\(486\) −2536.31 −0.236727
\(487\) 11605.3 1.07985 0.539924 0.841714i \(-0.318453\pi\)
0.539924 + 0.841714i \(0.318453\pi\)
\(488\) −6792.34 −0.630071
\(489\) 189.753 0.0175479
\(490\) −4.63605 −0.000427419 0
\(491\) −4651.88 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(492\) 1099.54 0.100754
\(493\) 98.2845 0.00897872
\(494\) −1815.27 −0.165330
\(495\) 6387.08 0.579955
\(496\) 4731.19 0.428300
\(497\) 11601.6 1.04709
\(498\) 719.682 0.0647585
\(499\) −7953.03 −0.713480 −0.356740 0.934204i \(-0.616112\pi\)
−0.356740 + 0.934204i \(0.616112\pi\)
\(500\) −500.000 −0.0447214
\(501\) −1726.38 −0.153950
\(502\) 13602.8 1.20941
\(503\) −11805.6 −1.04649 −0.523245 0.852182i \(-0.675279\pi\)
−0.523245 + 0.852182i \(0.675279\pi\)
\(504\) −3946.14 −0.348760
\(505\) 7560.76 0.666237
\(506\) 2204.76 0.193703
\(507\) −236.955 −0.0207565
\(508\) −4271.48 −0.373063
\(509\) −2732.89 −0.237983 −0.118991 0.992895i \(-0.537966\pi\)
−0.118991 + 0.992895i \(0.537966\pi\)
\(510\) 10.0610 0.000873547 0
\(511\) −8129.09 −0.703738
\(512\) −512.000 −0.0441942
\(513\) −678.032 −0.0583545
\(514\) −11152.0 −0.956992
\(515\) −4786.40 −0.409541
\(516\) 430.380 0.0367178
\(517\) 21529.6 1.83147
\(518\) −290.640 −0.0246525
\(519\) 1068.93 0.0904065
\(520\) 1694.87 0.142932
\(521\) 14710.9 1.23704 0.618518 0.785771i \(-0.287733\pi\)
0.618518 + 0.785771i \(0.287733\pi\)
\(522\) 3072.07 0.257588
\(523\) −7034.35 −0.588127 −0.294064 0.955786i \(-0.595008\pi\)
−0.294064 + 0.955786i \(0.595008\pi\)
\(524\) −701.987 −0.0585237
\(525\) −272.975 −0.0226926
\(526\) 11339.2 0.939944
\(527\) 504.269 0.0416818
\(528\) 452.432 0.0372908
\(529\) 529.000 0.0434783
\(530\) −3683.16 −0.301861
\(531\) 10048.6 0.821230
\(532\) −1585.80 −0.129235
\(533\) 19742.2 1.60437
\(534\) −1324.92 −0.107368
\(535\) 8710.79 0.703926
\(536\) −738.739 −0.0595311
\(537\) 538.444 0.0432692
\(538\) −12080.4 −0.968075
\(539\) −22.2204 −0.00177569
\(540\) 633.060 0.0504492
\(541\) 1552.90 0.123409 0.0617045 0.998094i \(-0.480346\pi\)
0.0617045 + 0.998094i \(0.480346\pi\)
\(542\) 13798.5 1.09354
\(543\) 2165.51 0.171144
\(544\) −54.5710 −0.00430094
\(545\) −5833.86 −0.458523
\(546\) 925.313 0.0725270
\(547\) 174.657 0.0136523 0.00682614 0.999977i \(-0.497827\pi\)
0.00682614 + 0.999977i \(0.497827\pi\)
\(548\) 1903.59 0.148389
\(549\) −22628.6 −1.75914
\(550\) −2396.48 −0.185793
\(551\) 1234.55 0.0954510
\(552\) 108.554 0.00837026
\(553\) −11876.5 −0.913276
\(554\) −11235.4 −0.861633
\(555\) 23.1617 0.00177146
\(556\) 612.669 0.0467319
\(557\) −1990.63 −0.151429 −0.0757143 0.997130i \(-0.524124\pi\)
−0.0757143 + 0.997130i \(0.524124\pi\)
\(558\) 15761.9 1.19580
\(559\) 7727.48 0.584683
\(560\) 1480.62 0.111728
\(561\) 48.2220 0.00362912
\(562\) −6139.78 −0.460838
\(563\) 208.006 0.0155709 0.00778543 0.999970i \(-0.497522\pi\)
0.00778543 + 0.999970i \(0.497522\pi\)
\(564\) 1060.04 0.0791414
\(565\) 1966.44 0.146422
\(566\) −2809.71 −0.208659
\(567\) −12972.6 −0.960842
\(568\) 5014.83 0.370454
\(569\) −3003.05 −0.221256 −0.110628 0.993862i \(-0.535286\pi\)
−0.110628 + 0.993862i \(0.535286\pi\)
\(570\) 126.376 0.00928651
\(571\) −10796.1 −0.791249 −0.395624 0.918412i \(-0.629472\pi\)
−0.395624 + 0.918412i \(0.629472\pi\)
\(572\) 8123.43 0.593807
\(573\) −1086.11 −0.0791847
\(574\) 17246.6 1.25411
\(575\) −575.000 −0.0417029
\(576\) −1705.72 −0.123389
\(577\) −26011.3 −1.87671 −0.938357 0.345667i \(-0.887653\pi\)
−0.938357 + 0.345667i \(0.887653\pi\)
\(578\) 9820.18 0.706688
\(579\) −360.953 −0.0259079
\(580\) −1152.66 −0.0825203
\(581\) 11288.5 0.806066
\(582\) 1685.89 0.120073
\(583\) −17653.2 −1.25407
\(584\) −3513.81 −0.248977
\(585\) 5646.44 0.399062
\(586\) 4814.09 0.339366
\(587\) −2774.97 −0.195120 −0.0975598 0.995230i \(-0.531104\pi\)
−0.0975598 + 0.995230i \(0.531104\pi\)
\(588\) −1.09405 −7.67311e−5 0
\(589\) 6334.11 0.443111
\(590\) −3770.32 −0.263087
\(591\) 1669.77 0.116218
\(592\) −125.629 −0.00872185
\(593\) −2384.07 −0.165096 −0.0825481 0.996587i \(-0.526306\pi\)
−0.0825481 + 0.996587i \(0.526306\pi\)
\(594\) 3034.23 0.209589
\(595\) 157.810 0.0108733
\(596\) 2027.62 0.139353
\(597\) −685.984 −0.0470276
\(598\) 1949.10 0.133285
\(599\) −1090.87 −0.0744102 −0.0372051 0.999308i \(-0.511845\pi\)
−0.0372051 + 0.999308i \(0.511845\pi\)
\(600\) −117.994 −0.00802847
\(601\) −5192.37 −0.352414 −0.176207 0.984353i \(-0.556383\pi\)
−0.176207 + 0.984353i \(0.556383\pi\)
\(602\) 6750.65 0.457036
\(603\) −2461.10 −0.166209
\(604\) 9751.36 0.656916
\(605\) −4831.22 −0.324657
\(606\) 1784.25 0.119604
\(607\) 1205.44 0.0806054 0.0403027 0.999188i \(-0.487168\pi\)
0.0403027 + 0.999188i \(0.487168\pi\)
\(608\) −685.465 −0.0457225
\(609\) −629.297 −0.0418726
\(610\) 8490.42 0.563553
\(611\) 19033.1 1.26022
\(612\) −181.803 −0.0120081
\(613\) −14243.2 −0.938466 −0.469233 0.883075i \(-0.655469\pi\)
−0.469233 + 0.883075i \(0.655469\pi\)
\(614\) 919.487 0.0604356
\(615\) −1374.42 −0.0901170
\(616\) 7096.55 0.464169
\(617\) −422.492 −0.0275671 −0.0137835 0.999905i \(-0.504388\pi\)
−0.0137835 + 0.999905i \(0.504388\pi\)
\(618\) −1129.53 −0.0735217
\(619\) −8826.35 −0.573119 −0.286560 0.958062i \(-0.592512\pi\)
−0.286560 + 0.958062i \(0.592512\pi\)
\(620\) −5913.98 −0.383083
\(621\) 728.019 0.0470441
\(622\) −8238.96 −0.531113
\(623\) −20781.7 −1.33644
\(624\) 399.968 0.0256595
\(625\) 625.000 0.0400000
\(626\) −3368.29 −0.215054
\(627\) 605.715 0.0385804
\(628\) 1023.87 0.0650584
\(629\) −13.3901 −0.000848804 0
\(630\) 4932.67 0.311940
\(631\) −19684.1 −1.24186 −0.620929 0.783867i \(-0.713244\pi\)
−0.620929 + 0.783867i \(0.713244\pi\)
\(632\) −5133.65 −0.323110
\(633\) 825.710 0.0518468
\(634\) −17372.9 −1.08828
\(635\) 5339.35 0.333678
\(636\) −869.180 −0.0541906
\(637\) −19.6437 −0.00122184
\(638\) −5524.67 −0.342827
\(639\) 16706.9 1.03429
\(640\) 640.000 0.0395285
\(641\) 15113.1 0.931253 0.465626 0.884981i \(-0.345829\pi\)
0.465626 + 0.884981i \(0.345829\pi\)
\(642\) 2055.64 0.126370
\(643\) −16917.8 −1.03760 −0.518798 0.854897i \(-0.673620\pi\)
−0.518798 + 0.854897i \(0.673620\pi\)
\(644\) 1702.71 0.104187
\(645\) −537.975 −0.0328414
\(646\) −73.0596 −0.00444968
\(647\) 19564.5 1.18881 0.594405 0.804166i \(-0.297388\pi\)
0.594405 + 0.804166i \(0.297388\pi\)
\(648\) −5607.42 −0.339939
\(649\) −18071.0 −1.09299
\(650\) −2118.58 −0.127843
\(651\) −3228.74 −0.194384
\(652\) 1286.53 0.0772767
\(653\) −22735.0 −1.36247 −0.681233 0.732067i \(-0.738556\pi\)
−0.681233 + 0.732067i \(0.738556\pi\)
\(654\) −1376.72 −0.0823149
\(655\) 877.483 0.0523452
\(656\) 7454.87 0.443695
\(657\) −11706.2 −0.695136
\(658\) 16627.1 0.985094
\(659\) −30730.7 −1.81654 −0.908269 0.418388i \(-0.862595\pi\)
−0.908269 + 0.418388i \(0.862595\pi\)
\(660\) −565.540 −0.0333539
\(661\) −29204.3 −1.71848 −0.859240 0.511573i \(-0.829063\pi\)
−0.859240 + 0.511573i \(0.829063\pi\)
\(662\) −8615.81 −0.505835
\(663\) 42.6302 0.00249716
\(664\) 4879.45 0.285180
\(665\) 1982.25 0.115592
\(666\) −418.533 −0.0243511
\(667\) −1325.56 −0.0769506
\(668\) −11704.9 −0.677957
\(669\) 2512.08 0.145176
\(670\) 923.424 0.0532462
\(671\) 40694.2 2.34126
\(672\) 349.408 0.0200576
\(673\) −17530.1 −1.00406 −0.502032 0.864849i \(-0.667414\pi\)
−0.502032 + 0.864849i \(0.667414\pi\)
\(674\) 580.312 0.0331644
\(675\) −791.325 −0.0451231
\(676\) −1606.56 −0.0914064
\(677\) −20553.4 −1.16681 −0.583407 0.812180i \(-0.698281\pi\)
−0.583407 + 0.812180i \(0.698281\pi\)
\(678\) 464.055 0.0262860
\(679\) 26443.8 1.49458
\(680\) 68.2138 0.00384688
\(681\) −2374.65 −0.133622
\(682\) −28345.5 −1.59150
\(683\) 13174.8 0.738098 0.369049 0.929410i \(-0.379684\pi\)
0.369049 + 0.929410i \(0.379684\pi\)
\(684\) −2283.62 −0.127656
\(685\) −2379.49 −0.132723
\(686\) −12713.5 −0.707584
\(687\) 2137.48 0.118705
\(688\) 2917.98 0.161696
\(689\) −15606.2 −0.862913
\(690\) −135.693 −0.00748658
\(691\) −14800.8 −0.814831 −0.407415 0.913243i \(-0.633570\pi\)
−0.407415 + 0.913243i \(0.633570\pi\)
\(692\) 7247.38 0.398127
\(693\) 23642.1 1.29594
\(694\) −2085.88 −0.114091
\(695\) −765.836 −0.0417983
\(696\) −272.015 −0.0148142
\(697\) 794.570 0.0431800
\(698\) 3639.13 0.197339
\(699\) 3836.46 0.207594
\(700\) −1850.77 −0.0999324
\(701\) −12311.5 −0.663336 −0.331668 0.943396i \(-0.607611\pi\)
−0.331668 + 0.943396i \(0.607611\pi\)
\(702\) 2682.38 0.144217
\(703\) −168.192 −0.00902347
\(704\) 3067.49 0.164219
\(705\) −1325.05 −0.0707862
\(706\) 9028.59 0.481297
\(707\) 27986.5 1.48874
\(708\) −889.749 −0.0472299
\(709\) 3893.89 0.206260 0.103130 0.994668i \(-0.467114\pi\)
0.103130 + 0.994668i \(0.467114\pi\)
\(710\) −6268.54 −0.331344
\(711\) −17102.7 −0.902113
\(712\) −8982.94 −0.472823
\(713\) −6801.08 −0.357227
\(714\) 37.2413 0.00195199
\(715\) −10154.3 −0.531117
\(716\) 3650.65 0.190547
\(717\) −1587.06 −0.0826636
\(718\) −23055.8 −1.19838
\(719\) −19942.5 −1.03440 −0.517198 0.855866i \(-0.673025\pi\)
−0.517198 + 0.855866i \(0.673025\pi\)
\(720\) 2132.15 0.110362
\(721\) −17717.1 −0.915143
\(722\) 12800.3 0.659803
\(723\) −26.3692 −0.00135640
\(724\) 14682.2 0.753673
\(725\) 1440.83 0.0738084
\(726\) −1140.11 −0.0582830
\(727\) 36167.0 1.84506 0.922530 0.385926i \(-0.126118\pi\)
0.922530 + 0.385926i \(0.126118\pi\)
\(728\) 6273.63 0.319391
\(729\) −18176.9 −0.923481
\(730\) 4392.27 0.222692
\(731\) 311.010 0.0157361
\(732\) 2003.64 0.101170
\(733\) −11669.5 −0.588025 −0.294013 0.955802i \(-0.594991\pi\)
−0.294013 + 0.955802i \(0.594991\pi\)
\(734\) −13788.2 −0.693366
\(735\) 1.36756 6.86304e−5 0
\(736\) 736.000 0.0368605
\(737\) 4425.93 0.221209
\(738\) 24835.8 1.23878
\(739\) 75.0536 0.00373598 0.00186799 0.999998i \(-0.499405\pi\)
0.00186799 + 0.999998i \(0.499405\pi\)
\(740\) 157.037 0.00780106
\(741\) 535.477 0.0265469
\(742\) −13633.4 −0.674524
\(743\) 28279.8 1.39635 0.698173 0.715929i \(-0.253997\pi\)
0.698173 + 0.715929i \(0.253997\pi\)
\(744\) −1395.63 −0.0687718
\(745\) −2534.53 −0.124641
\(746\) −15466.5 −0.759074
\(747\) 16255.9 0.796213
\(748\) 326.946 0.0159817
\(749\) 32243.4 1.57296
\(750\) 147.492 0.00718088
\(751\) −17268.1 −0.839044 −0.419522 0.907745i \(-0.637802\pi\)
−0.419522 + 0.907745i \(0.637802\pi\)
\(752\) 7187.09 0.348519
\(753\) −4012.62 −0.194194
\(754\) −4884.03 −0.235897
\(755\) −12189.2 −0.587564
\(756\) 2343.30 0.112732
\(757\) −12525.8 −0.601400 −0.300700 0.953719i \(-0.597220\pi\)
−0.300700 + 0.953719i \(0.597220\pi\)
\(758\) 18991.4 0.910026
\(759\) −650.371 −0.0311027
\(760\) 856.831 0.0408954
\(761\) −18670.1 −0.889343 −0.444672 0.895694i \(-0.646680\pi\)
−0.444672 + 0.895694i \(0.646680\pi\)
\(762\) 1260.02 0.0599026
\(763\) −21594.3 −1.02460
\(764\) −7363.83 −0.348710
\(765\) 227.254 0.0107404
\(766\) 25754.0 1.21479
\(767\) −15975.5 −0.752074
\(768\) 151.032 0.00709623
\(769\) −32969.6 −1.54605 −0.773027 0.634373i \(-0.781258\pi\)
−0.773027 + 0.634373i \(0.781258\pi\)
\(770\) −8870.68 −0.415165
\(771\) 3289.67 0.153664
\(772\) −2447.27 −0.114092
\(773\) −23251.3 −1.08188 −0.540938 0.841062i \(-0.681931\pi\)
−0.540938 + 0.841062i \(0.681931\pi\)
\(774\) 9721.23 0.451450
\(775\) 7392.48 0.342640
\(776\) 11430.4 0.528771
\(777\) 85.7342 0.00395843
\(778\) 16400.8 0.755781
\(779\) 9980.57 0.459039
\(780\) −499.960 −0.0229506
\(781\) −30044.8 −1.37655
\(782\) 78.4458 0.00358723
\(783\) −1824.26 −0.0832617
\(784\) −7.41767 −0.000337904 0
\(785\) −1279.83 −0.0581900
\(786\) 207.075 0.00939712
\(787\) −29782.8 −1.34897 −0.674486 0.738288i \(-0.735635\pi\)
−0.674486 + 0.738288i \(0.735635\pi\)
\(788\) 11321.0 0.511796
\(789\) −3344.88 −0.150926
\(790\) 6417.07 0.288999
\(791\) 7278.86 0.327189
\(792\) 10219.3 0.458495
\(793\) 35975.3 1.61100
\(794\) −15685.4 −0.701073
\(795\) 1086.47 0.0484696
\(796\) −4650.98 −0.207097
\(797\) 35307.2 1.56919 0.784596 0.620008i \(-0.212871\pi\)
0.784596 + 0.620008i \(0.212871\pi\)
\(798\) 467.787 0.0207512
\(799\) 766.029 0.0339176
\(800\) −800.000 −0.0353553
\(801\) −29926.6 −1.32011
\(802\) 29068.4 1.27985
\(803\) 21052.0 0.925165
\(804\) 217.917 0.00955887
\(805\) −2128.39 −0.0931874
\(806\) −25058.5 −1.09510
\(807\) 3563.54 0.155443
\(808\) 12097.2 0.526706
\(809\) 7752.46 0.336912 0.168456 0.985709i \(-0.446122\pi\)
0.168456 + 0.985709i \(0.446122\pi\)
\(810\) 7009.28 0.304051
\(811\) 23471.6 1.01627 0.508137 0.861276i \(-0.330334\pi\)
0.508137 + 0.861276i \(0.330334\pi\)
\(812\) −4266.64 −0.184396
\(813\) −4070.35 −0.175589
\(814\) 752.671 0.0324092
\(815\) −1608.16 −0.0691184
\(816\) 16.0976 0.000690600 0
\(817\) 3906.59 0.167288
\(818\) −26776.0 −1.14450
\(819\) 20900.6 0.891727
\(820\) −9318.59 −0.396853
\(821\) 2467.55 0.104894 0.0524470 0.998624i \(-0.483298\pi\)
0.0524470 + 0.998624i \(0.483298\pi\)
\(822\) −561.530 −0.0238268
\(823\) 21984.5 0.931144 0.465572 0.885010i \(-0.345849\pi\)
0.465572 + 0.885010i \(0.345849\pi\)
\(824\) −7658.23 −0.323771
\(825\) 706.925 0.0298327
\(826\) −13956.0 −0.587883
\(827\) −587.293 −0.0246943 −0.0123472 0.999924i \(-0.503930\pi\)
−0.0123472 + 0.999924i \(0.503930\pi\)
\(828\) 2451.98 0.102913
\(829\) 41822.8 1.75219 0.876096 0.482137i \(-0.160139\pi\)
0.876096 + 0.482137i \(0.160139\pi\)
\(830\) −6099.32 −0.255073
\(831\) 3314.26 0.138352
\(832\) 2711.79 0.112998
\(833\) −0.790605 −3.28846e−5 0
\(834\) −180.728 −0.00750371
\(835\) 14631.1 0.606383
\(836\) 4106.76 0.169898
\(837\) −9359.77 −0.386524
\(838\) 6206.20 0.255835
\(839\) −10126.5 −0.416693 −0.208346 0.978055i \(-0.566808\pi\)
−0.208346 + 0.978055i \(0.566808\pi\)
\(840\) −436.760 −0.0179401
\(841\) −21067.4 −0.863808
\(842\) 12151.6 0.497356
\(843\) 1811.14 0.0739964
\(844\) 5598.33 0.228320
\(845\) 2008.20 0.0817564
\(846\) 23943.7 0.973052
\(847\) −17883.0 −0.725463
\(848\) −5893.05 −0.238642
\(849\) 828.822 0.0335043
\(850\) −85.2672 −0.00344075
\(851\) 180.592 0.00727453
\(852\) −1479.30 −0.0594835
\(853\) 11584.4 0.464995 0.232498 0.972597i \(-0.425310\pi\)
0.232498 + 0.972597i \(0.425310\pi\)
\(854\) 31427.7 1.25929
\(855\) 2854.53 0.114179
\(856\) 13937.3 0.556502
\(857\) −9221.47 −0.367561 −0.183780 0.982967i \(-0.558834\pi\)
−0.183780 + 0.982967i \(0.558834\pi\)
\(858\) −2396.29 −0.0953472
\(859\) 34654.2 1.37647 0.688235 0.725488i \(-0.258386\pi\)
0.688235 + 0.725488i \(0.258386\pi\)
\(860\) −3647.47 −0.144625
\(861\) −5087.48 −0.201372
\(862\) −28240.7 −1.11587
\(863\) 42887.7 1.69167 0.845837 0.533441i \(-0.179101\pi\)
0.845837 + 0.533441i \(0.179101\pi\)
\(864\) 1012.90 0.0398836
\(865\) −9059.22 −0.356096
\(866\) −17111.9 −0.671463
\(867\) −2896.80 −0.113472
\(868\) −21890.9 −0.856020
\(869\) 30756.7 1.20063
\(870\) 340.018 0.0132502
\(871\) 3912.70 0.152212
\(872\) −9334.17 −0.362494
\(873\) 38080.2 1.47631
\(874\) 985.356 0.0381352
\(875\) 2313.47 0.0893823
\(876\) 1036.52 0.0399781
\(877\) 45935.5 1.76868 0.884339 0.466846i \(-0.154610\pi\)
0.884339 + 0.466846i \(0.154610\pi\)
\(878\) 21788.2 0.837488
\(879\) −1420.08 −0.0544917
\(880\) −3834.37 −0.146882
\(881\) −71.9309 −0.00275075 −0.00137538 0.999999i \(-0.500438\pi\)
−0.00137538 + 0.999999i \(0.500438\pi\)
\(882\) −24.7119 −0.000943417 0
\(883\) 20003.8 0.762379 0.381189 0.924497i \(-0.375515\pi\)
0.381189 + 0.924497i \(0.375515\pi\)
\(884\) 289.033 0.0109969
\(885\) 1112.19 0.0422437
\(886\) −32241.0 −1.22253
\(887\) 26357.3 0.997737 0.498869 0.866678i \(-0.333749\pi\)
0.498869 + 0.866678i \(0.333749\pi\)
\(888\) 37.0588 0.00140046
\(889\) 19763.9 0.745623
\(890\) 11228.7 0.422906
\(891\) 33595.2 1.26317
\(892\) 17031.9 0.639317
\(893\) 9622.06 0.360571
\(894\) −598.118 −0.0223759
\(895\) −4563.32 −0.170430
\(896\) 2368.99 0.0883286
\(897\) −574.954 −0.0214015
\(898\) −9622.57 −0.357583
\(899\) 17042.1 0.632242
\(900\) −2665.19 −0.0987109
\(901\) −628.105 −0.0232244
\(902\) −44663.6 −1.64871
\(903\) −1991.34 −0.0733860
\(904\) 3146.30 0.115757
\(905\) −18352.7 −0.674106
\(906\) −2876.50 −0.105481
\(907\) −39300.4 −1.43875 −0.719377 0.694620i \(-0.755572\pi\)
−0.719377 + 0.694620i \(0.755572\pi\)
\(908\) −16100.1 −0.588438
\(909\) 40301.8 1.47055
\(910\) −7842.04 −0.285672
\(911\) 31099.2 1.13103 0.565513 0.824740i \(-0.308678\pi\)
0.565513 + 0.824740i \(0.308678\pi\)
\(912\) 202.202 0.00734163
\(913\) −29233.8 −1.05969
\(914\) 452.657 0.0163814
\(915\) −2504.54 −0.0904893
\(916\) 14492.2 0.522745
\(917\) 3248.05 0.116968
\(918\) 107.959 0.00388144
\(919\) 18935.8 0.679690 0.339845 0.940481i \(-0.389625\pi\)
0.339845 + 0.940481i \(0.389625\pi\)
\(920\) −920.000 −0.0329690
\(921\) −271.235 −0.00970411
\(922\) 8698.33 0.310699
\(923\) −26560.9 −0.947195
\(924\) −2093.37 −0.0745313
\(925\) −196.296 −0.00697748
\(926\) 1978.63 0.0702178
\(927\) −25513.3 −0.903957
\(928\) −1844.26 −0.0652380
\(929\) 40156.1 1.41817 0.709085 0.705123i \(-0.249108\pi\)
0.709085 + 0.705123i \(0.249108\pi\)
\(930\) 1744.53 0.0615113
\(931\) −9.93077 −0.000349590 0
\(932\) 26011.2 0.914192
\(933\) 2430.37 0.0852804
\(934\) −17025.8 −0.596469
\(935\) −408.682 −0.0142945
\(936\) 9034.30 0.315486
\(937\) 126.898 0.00442432 0.00221216 0.999998i \(-0.499296\pi\)
0.00221216 + 0.999998i \(0.499296\pi\)
\(938\) 3418.10 0.118982
\(939\) 993.594 0.0345311
\(940\) −8983.86 −0.311725
\(941\) −19266.6 −0.667452 −0.333726 0.942670i \(-0.608306\pi\)
−0.333726 + 0.942670i \(0.608306\pi\)
\(942\) −302.025 −0.0104464
\(943\) −10716.4 −0.370067
\(944\) −6032.51 −0.207989
\(945\) −2929.13 −0.100830
\(946\) −17482.2 −0.600840
\(947\) −54560.4 −1.87220 −0.936101 0.351732i \(-0.885593\pi\)
−0.936101 + 0.351732i \(0.885593\pi\)
\(948\) 1514.35 0.0518816
\(949\) 18610.8 0.636598
\(950\) −1071.04 −0.0365780
\(951\) 5124.75 0.174744
\(952\) 252.497 0.00859607
\(953\) −44976.2 −1.52877 −0.764387 0.644758i \(-0.776958\pi\)
−0.764387 + 0.644758i \(0.776958\pi\)
\(954\) −19632.7 −0.666279
\(955\) 9204.79 0.311895
\(956\) −10760.3 −0.364030
\(957\) 1629.69 0.0550476
\(958\) 24117.1 0.813350
\(959\) −8807.79 −0.296578
\(960\) −188.790 −0.00634706
\(961\) 57647.0 1.93505
\(962\) 665.391 0.0223005
\(963\) 46431.9 1.55374
\(964\) −178.783 −0.00597326
\(965\) 3059.08 0.102047
\(966\) −502.274 −0.0167292
\(967\) −39431.7 −1.31131 −0.655656 0.755059i \(-0.727608\pi\)
−0.655656 + 0.755059i \(0.727608\pi\)
\(968\) −7729.96 −0.256664
\(969\) 21.5515 0.000714482 0
\(970\) −14288.0 −0.472947
\(971\) 20249.9 0.669258 0.334629 0.942350i \(-0.391389\pi\)
0.334629 + 0.942350i \(0.391389\pi\)
\(972\) 5072.63 0.167392
\(973\) −2834.78 −0.0934006
\(974\) −23210.6 −0.763567
\(975\) 624.950 0.0205276
\(976\) 13584.7 0.445527
\(977\) −9673.55 −0.316770 −0.158385 0.987377i \(-0.550629\pi\)
−0.158385 + 0.987377i \(0.550629\pi\)
\(978\) −379.507 −0.0124083
\(979\) 53818.6 1.75695
\(980\) 9.27209 0.000302231 0
\(981\) −31096.7 −1.01207
\(982\) 9303.77 0.302337
\(983\) −17264.3 −0.560168 −0.280084 0.959975i \(-0.590362\pi\)
−0.280084 + 0.959975i \(0.590362\pi\)
\(984\) −2199.07 −0.0712438
\(985\) −14151.3 −0.457764
\(986\) −196.569 −0.00634891
\(987\) −4904.74 −0.158176
\(988\) 3630.54 0.116906
\(989\) −4194.60 −0.134864
\(990\) −12774.2 −0.410090
\(991\) 23892.9 0.765876 0.382938 0.923774i \(-0.374912\pi\)
0.382938 + 0.923774i \(0.374912\pi\)
\(992\) −9462.37 −0.302854
\(993\) 2541.53 0.0812217
\(994\) −23203.3 −0.740406
\(995\) 5813.72 0.185234
\(996\) −1439.36 −0.0457912
\(997\) −35830.2 −1.13817 −0.569083 0.822280i \(-0.692702\pi\)
−0.569083 + 0.822280i \(0.692702\pi\)
\(998\) 15906.1 0.504507
\(999\) 248.534 0.00787115
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 230.4.a.h.1.3 4
3.2 odd 2 2070.4.a.bj.1.2 4
4.3 odd 2 1840.4.a.m.1.2 4
5.2 odd 4 1150.4.b.n.599.2 8
5.3 odd 4 1150.4.b.n.599.7 8
5.4 even 2 1150.4.a.p.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.h.1.3 4 1.1 even 1 trivial
1150.4.a.p.1.2 4 5.4 even 2
1150.4.b.n.599.2 8 5.2 odd 4
1150.4.b.n.599.7 8 5.3 odd 4
1840.4.a.m.1.2 4 4.3 odd 2
2070.4.a.bj.1.2 4 3.2 odd 2