Properties

Label 570.4.a.s.1.2
Level $570$
Weight $4$
Character 570.1
Self dual yes
Analytic conductor $33.631$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.6310887033\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 410 x^{2} + 4362 x - 12540\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-24.2310\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -1.42654 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} -1.42654 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -25.0356 q^{11} +12.0000 q^{12} +47.9099 q^{13} -2.85307 q^{14} +15.0000 q^{15} +16.0000 q^{16} +77.5665 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} -4.27961 q^{21} -50.0711 q^{22} -53.1968 q^{23} +24.0000 q^{24} +25.0000 q^{25} +95.8198 q^{26} +27.0000 q^{27} -5.70614 q^{28} +56.8795 q^{29} +30.0000 q^{30} +227.206 q^{31} +32.0000 q^{32} -75.1067 q^{33} +155.133 q^{34} -7.13268 q^{35} +36.0000 q^{36} +202.303 q^{37} +38.0000 q^{38} +143.730 q^{39} +40.0000 q^{40} +372.234 q^{41} -8.55922 q^{42} -154.460 q^{43} -100.142 q^{44} +45.0000 q^{45} -106.394 q^{46} -619.202 q^{47} +48.0000 q^{48} -340.965 q^{49} +50.0000 q^{50} +232.700 q^{51} +191.640 q^{52} +285.434 q^{53} +54.0000 q^{54} -125.178 q^{55} -11.4123 q^{56} +57.0000 q^{57} +113.759 q^{58} +121.716 q^{59} +60.0000 q^{60} +58.9035 q^{61} +454.412 q^{62} -12.8388 q^{63} +64.0000 q^{64} +239.549 q^{65} -150.213 q^{66} -74.7191 q^{67} +310.266 q^{68} -159.590 q^{69} -14.2654 q^{70} -267.374 q^{71} +72.0000 q^{72} -144.347 q^{73} +404.607 q^{74} +75.0000 q^{75} +76.0000 q^{76} +35.7141 q^{77} +287.459 q^{78} -368.934 q^{79} +80.0000 q^{80} +81.0000 q^{81} +744.469 q^{82} +208.538 q^{83} -17.1184 q^{84} +387.833 q^{85} -308.919 q^{86} +170.638 q^{87} -200.284 q^{88} +944.352 q^{89} +90.0000 q^{90} -68.3452 q^{91} -212.787 q^{92} +681.618 q^{93} -1238.40 q^{94} +95.0000 q^{95} +96.0000 q^{96} +326.833 q^{97} -681.930 q^{98} -225.320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + O(q^{10}) \) \( 4q + 8q^{2} + 12q^{3} + 16q^{4} + 20q^{5} + 24q^{6} + 36q^{7} + 32q^{8} + 36q^{9} + 40q^{10} + 54q^{11} + 48q^{12} + 46q^{13} + 72q^{14} + 60q^{15} + 64q^{16} + 14q^{17} + 72q^{18} + 76q^{19} + 80q^{20} + 108q^{21} + 108q^{22} + 104q^{23} + 96q^{24} + 100q^{25} + 92q^{26} + 108q^{27} + 144q^{28} + 14q^{29} + 120q^{30} + 30q^{31} + 128q^{32} + 162q^{33} + 28q^{34} + 180q^{35} + 144q^{36} + 30q^{37} + 152q^{38} + 138q^{39} + 160q^{40} - 36q^{41} + 216q^{42} + 102q^{43} + 216q^{44} + 180q^{45} + 208q^{46} + 408q^{47} + 192q^{48} + 480q^{49} + 200q^{50} + 42q^{51} + 184q^{52} - 176q^{53} + 216q^{54} + 270q^{55} + 288q^{56} + 228q^{57} + 28q^{58} + 66q^{59} + 240q^{60} + 60q^{61} + 60q^{62} + 324q^{63} + 256q^{64} + 230q^{65} + 324q^{66} - 152q^{67} + 56q^{68} + 312q^{69} + 360q^{70} + 172q^{71} + 288q^{72} + 284q^{73} + 60q^{74} + 300q^{75} + 304q^{76} - 300q^{77} + 276q^{78} + 554q^{79} + 320q^{80} + 324q^{81} - 72q^{82} - 394q^{83} + 432q^{84} + 70q^{85} + 204q^{86} + 42q^{87} + 432q^{88} - 60q^{89} + 360q^{90} + 32q^{91} + 416q^{92} + 90q^{93} + 816q^{94} + 380q^{95} + 384q^{96} - 922q^{97} + 960q^{98} + 486q^{99} + O(q^{100}) \)

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
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 6.00000 0.408248
\(7\) −1.42654 −0.0770257 −0.0385129 0.999258i \(-0.512262\pi\)
−0.0385129 + 0.999258i \(0.512262\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) −25.0356 −0.686228 −0.343114 0.939294i \(-0.611482\pi\)
−0.343114 + 0.939294i \(0.611482\pi\)
\(12\) 12.0000 0.288675
\(13\) 47.9099 1.02214 0.511070 0.859539i \(-0.329249\pi\)
0.511070 + 0.859539i \(0.329249\pi\)
\(14\) −2.85307 −0.0544654
\(15\) 15.0000 0.258199
\(16\) 16.0000 0.250000
\(17\) 77.5665 1.10663 0.553313 0.832973i \(-0.313363\pi\)
0.553313 + 0.832973i \(0.313363\pi\)
\(18\) 18.0000 0.235702
\(19\) 19.0000 0.229416
\(20\) 20.0000 0.223607
\(21\) −4.27961 −0.0444708
\(22\) −50.0711 −0.485236
\(23\) −53.1968 −0.482274 −0.241137 0.970491i \(-0.577520\pi\)
−0.241137 + 0.970491i \(0.577520\pi\)
\(24\) 24.0000 0.204124
\(25\) 25.0000 0.200000
\(26\) 95.8198 0.722762
\(27\) 27.0000 0.192450
\(28\) −5.70614 −0.0385129
\(29\) 56.8795 0.364215 0.182108 0.983279i \(-0.441708\pi\)
0.182108 + 0.983279i \(0.441708\pi\)
\(30\) 30.0000 0.182574
\(31\) 227.206 1.31637 0.658184 0.752857i \(-0.271325\pi\)
0.658184 + 0.752857i \(0.271325\pi\)
\(32\) 32.0000 0.176777
\(33\) −75.1067 −0.396194
\(34\) 155.133 0.782503
\(35\) −7.13268 −0.0344469
\(36\) 36.0000 0.166667
\(37\) 202.303 0.898878 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(38\) 38.0000 0.162221
\(39\) 143.730 0.590132
\(40\) 40.0000 0.158114
\(41\) 372.234 1.41788 0.708942 0.705267i \(-0.249173\pi\)
0.708942 + 0.705267i \(0.249173\pi\)
\(42\) −8.55922 −0.0314456
\(43\) −154.460 −0.547787 −0.273894 0.961760i \(-0.588312\pi\)
−0.273894 + 0.961760i \(0.588312\pi\)
\(44\) −100.142 −0.343114
\(45\) 45.0000 0.149071
\(46\) −106.394 −0.341019
\(47\) −619.202 −1.92170 −0.960850 0.277069i \(-0.910637\pi\)
−0.960850 + 0.277069i \(0.910637\pi\)
\(48\) 48.0000 0.144338
\(49\) −340.965 −0.994067
\(50\) 50.0000 0.141421
\(51\) 232.700 0.638911
\(52\) 191.640 0.511070
\(53\) 285.434 0.739761 0.369880 0.929079i \(-0.379399\pi\)
0.369880 + 0.929079i \(0.379399\pi\)
\(54\) 54.0000 0.136083
\(55\) −125.178 −0.306890
\(56\) −11.4123 −0.0272327
\(57\) 57.0000 0.132453
\(58\) 113.759 0.257539
\(59\) 121.716 0.268578 0.134289 0.990942i \(-0.457125\pi\)
0.134289 + 0.990942i \(0.457125\pi\)
\(60\) 60.0000 0.129099
\(61\) 58.9035 0.123637 0.0618183 0.998087i \(-0.480310\pi\)
0.0618183 + 0.998087i \(0.480310\pi\)
\(62\) 454.412 0.930813
\(63\) −12.8388 −0.0256752
\(64\) 64.0000 0.125000
\(65\) 239.549 0.457115
\(66\) −150.213 −0.280151
\(67\) −74.7191 −0.136245 −0.0681223 0.997677i \(-0.521701\pi\)
−0.0681223 + 0.997677i \(0.521701\pi\)
\(68\) 310.266 0.553313
\(69\) −159.590 −0.278441
\(70\) −14.2654 −0.0243577
\(71\) −267.374 −0.446922 −0.223461 0.974713i \(-0.571736\pi\)
−0.223461 + 0.974713i \(0.571736\pi\)
\(72\) 72.0000 0.117851
\(73\) −144.347 −0.231433 −0.115716 0.993282i \(-0.536916\pi\)
−0.115716 + 0.993282i \(0.536916\pi\)
\(74\) 404.607 0.635603
\(75\) 75.0000 0.115470
\(76\) 76.0000 0.114708
\(77\) 35.7141 0.0528572
\(78\) 287.459 0.417287
\(79\) −368.934 −0.525421 −0.262711 0.964875i \(-0.584616\pi\)
−0.262711 + 0.964875i \(0.584616\pi\)
\(80\) 80.0000 0.111803
\(81\) 81.0000 0.111111
\(82\) 744.469 1.00260
\(83\) 208.538 0.275783 0.137891 0.990447i \(-0.455967\pi\)
0.137891 + 0.990447i \(0.455967\pi\)
\(84\) −17.1184 −0.0222354
\(85\) 387.833 0.494898
\(86\) −308.919 −0.387344
\(87\) 170.638 0.210280
\(88\) −200.284 −0.242618
\(89\) 944.352 1.12473 0.562366 0.826888i \(-0.309891\pi\)
0.562366 + 0.826888i \(0.309891\pi\)
\(90\) 90.0000 0.105409
\(91\) −68.3452 −0.0787310
\(92\) −212.787 −0.241137
\(93\) 681.618 0.760005
\(94\) −1238.40 −1.35885
\(95\) 95.0000 0.102598
\(96\) 96.0000 0.102062
\(97\) 326.833 0.342112 0.171056 0.985261i \(-0.445282\pi\)
0.171056 + 0.985261i \(0.445282\pi\)
\(98\) −681.930 −0.702912
\(99\) −225.320 −0.228743
\(100\) 100.000 0.100000
\(101\) −1442.06 −1.42069 −0.710346 0.703853i \(-0.751462\pi\)
−0.710346 + 0.703853i \(0.751462\pi\)
\(102\) 465.399 0.451778
\(103\) 457.652 0.437804 0.218902 0.975747i \(-0.429753\pi\)
0.218902 + 0.975747i \(0.429753\pi\)
\(104\) 383.279 0.361381
\(105\) −21.3980 −0.0198880
\(106\) 570.867 0.523090
\(107\) −1930.95 −1.74459 −0.872297 0.488976i \(-0.837371\pi\)
−0.872297 + 0.488976i \(0.837371\pi\)
\(108\) 108.000 0.0962250
\(109\) 106.028 0.0931707 0.0465854 0.998914i \(-0.485166\pi\)
0.0465854 + 0.998914i \(0.485166\pi\)
\(110\) −250.356 −0.217004
\(111\) 606.910 0.518967
\(112\) −22.8246 −0.0192564
\(113\) 129.473 0.107786 0.0538930 0.998547i \(-0.482837\pi\)
0.0538930 + 0.998547i \(0.482837\pi\)
\(114\) 114.000 0.0936586
\(115\) −265.984 −0.215679
\(116\) 227.518 0.182108
\(117\) 431.189 0.340713
\(118\) 243.432 0.189913
\(119\) −110.651 −0.0852387
\(120\) 120.000 0.0912871
\(121\) −704.221 −0.529092
\(122\) 117.807 0.0874242
\(123\) 1116.70 0.818616
\(124\) 908.824 0.658184
\(125\) 125.000 0.0894427
\(126\) −25.6777 −0.0181551
\(127\) 1048.71 0.732737 0.366368 0.930470i \(-0.380601\pi\)
0.366368 + 0.930470i \(0.380601\pi\)
\(128\) 128.000 0.0883883
\(129\) −463.379 −0.316265
\(130\) 479.099 0.323229
\(131\) 1409.26 0.939904 0.469952 0.882692i \(-0.344271\pi\)
0.469952 + 0.882692i \(0.344271\pi\)
\(132\) −300.427 −0.198097
\(133\) −27.1042 −0.0176709
\(134\) −149.438 −0.0963394
\(135\) 135.000 0.0860663
\(136\) 620.532 0.391251
\(137\) −734.235 −0.457883 −0.228941 0.973440i \(-0.573526\pi\)
−0.228941 + 0.973440i \(0.573526\pi\)
\(138\) −319.181 −0.196887
\(139\) 2039.11 1.24428 0.622139 0.782907i \(-0.286264\pi\)
0.622139 + 0.782907i \(0.286264\pi\)
\(140\) −28.5307 −0.0172235
\(141\) −1857.61 −1.10949
\(142\) −534.749 −0.316022
\(143\) −1199.45 −0.701420
\(144\) 144.000 0.0833333
\(145\) 284.397 0.162882
\(146\) −288.695 −0.163648
\(147\) −1022.89 −0.573925
\(148\) 809.214 0.449439
\(149\) −1834.97 −1.00890 −0.504452 0.863440i \(-0.668305\pi\)
−0.504452 + 0.863440i \(0.668305\pi\)
\(150\) 150.000 0.0816497
\(151\) −1945.41 −1.04844 −0.524222 0.851582i \(-0.675644\pi\)
−0.524222 + 0.851582i \(0.675644\pi\)
\(152\) 152.000 0.0811107
\(153\) 698.099 0.368875
\(154\) 71.4283 0.0373757
\(155\) 1136.03 0.588698
\(156\) 574.919 0.295066
\(157\) −1320.80 −0.671411 −0.335706 0.941967i \(-0.608975\pi\)
−0.335706 + 0.941967i \(0.608975\pi\)
\(158\) −737.867 −0.371529
\(159\) 856.301 0.427101
\(160\) 160.000 0.0790569
\(161\) 75.8871 0.0371475
\(162\) 162.000 0.0785674
\(163\) −2910.40 −1.39853 −0.699263 0.714864i \(-0.746488\pi\)
−0.699263 + 0.714864i \(0.746488\pi\)
\(164\) 1488.94 0.708942
\(165\) −375.533 −0.177183
\(166\) 417.075 0.195008
\(167\) 2037.32 0.944027 0.472014 0.881591i \(-0.343527\pi\)
0.472014 + 0.881591i \(0.343527\pi\)
\(168\) −34.2369 −0.0157228
\(169\) 98.3562 0.0447684
\(170\) 775.665 0.349946
\(171\) 171.000 0.0764719
\(172\) −617.838 −0.273894
\(173\) −1586.95 −0.697419 −0.348709 0.937231i \(-0.613380\pi\)
−0.348709 + 0.937231i \(0.613380\pi\)
\(174\) 341.277 0.148690
\(175\) −35.6634 −0.0154051
\(176\) −400.569 −0.171557
\(177\) 365.148 0.155063
\(178\) 1888.70 0.795306
\(179\) −181.231 −0.0756749 −0.0378375 0.999284i \(-0.512047\pi\)
−0.0378375 + 0.999284i \(0.512047\pi\)
\(180\) 180.000 0.0745356
\(181\) 1253.68 0.514837 0.257418 0.966300i \(-0.417128\pi\)
0.257418 + 0.966300i \(0.417128\pi\)
\(182\) −136.690 −0.0556712
\(183\) 176.711 0.0713816
\(184\) −425.574 −0.170510
\(185\) 1011.52 0.401990
\(186\) 1363.24 0.537405
\(187\) −1941.92 −0.759397
\(188\) −2476.81 −0.960850
\(189\) −38.5165 −0.0148236
\(190\) 190.000 0.0725476
\(191\) −3973.74 −1.50539 −0.752696 0.658368i \(-0.771247\pi\)
−0.752696 + 0.658368i \(0.771247\pi\)
\(192\) 192.000 0.0721688
\(193\) −935.873 −0.349045 −0.174522 0.984653i \(-0.555838\pi\)
−0.174522 + 0.984653i \(0.555838\pi\)
\(194\) 653.666 0.241910
\(195\) 718.648 0.263915
\(196\) −1363.86 −0.497034
\(197\) −2980.01 −1.07775 −0.538875 0.842386i \(-0.681151\pi\)
−0.538875 + 0.842386i \(0.681151\pi\)
\(198\) −450.640 −0.161745
\(199\) 3191.54 1.13690 0.568448 0.822719i \(-0.307544\pi\)
0.568448 + 0.822719i \(0.307544\pi\)
\(200\) 200.000 0.0707107
\(201\) −224.157 −0.0786608
\(202\) −2884.11 −1.00458
\(203\) −81.1406 −0.0280540
\(204\) 930.798 0.319455
\(205\) 1861.17 0.634097
\(206\) 915.304 0.309574
\(207\) −478.771 −0.160758
\(208\) 766.558 0.255535
\(209\) −475.676 −0.157431
\(210\) −42.7961 −0.0140629
\(211\) −1823.32 −0.594894 −0.297447 0.954738i \(-0.596135\pi\)
−0.297447 + 0.954738i \(0.596135\pi\)
\(212\) 1141.73 0.369880
\(213\) −802.123 −0.258031
\(214\) −3861.89 −1.23361
\(215\) −772.298 −0.244978
\(216\) 216.000 0.0680414
\(217\) −324.118 −0.101394
\(218\) 212.055 0.0658817
\(219\) −433.042 −0.133618
\(220\) −500.711 −0.153445
\(221\) 3716.20 1.13113
\(222\) 1213.82 0.366965
\(223\) 2856.95 0.857917 0.428959 0.903324i \(-0.358881\pi\)
0.428959 + 0.903324i \(0.358881\pi\)
\(224\) −45.6492 −0.0136164
\(225\) 225.000 0.0666667
\(226\) 258.946 0.0762162
\(227\) −1951.42 −0.570574 −0.285287 0.958442i \(-0.592089\pi\)
−0.285287 + 0.958442i \(0.592089\pi\)
\(228\) 228.000 0.0662266
\(229\) 165.507 0.0477598 0.0238799 0.999715i \(-0.492398\pi\)
0.0238799 + 0.999715i \(0.492398\pi\)
\(230\) −531.968 −0.152508
\(231\) 107.142 0.0305171
\(232\) 455.036 0.128770
\(233\) 1854.43 0.521408 0.260704 0.965419i \(-0.416045\pi\)
0.260704 + 0.965419i \(0.416045\pi\)
\(234\) 862.378 0.240921
\(235\) −3096.01 −0.859410
\(236\) 486.864 0.134289
\(237\) −1106.80 −0.303352
\(238\) −221.303 −0.0602728
\(239\) −5765.67 −1.56046 −0.780231 0.625492i \(-0.784898\pi\)
−0.780231 + 0.625492i \(0.784898\pi\)
\(240\) 240.000 0.0645497
\(241\) −5302.82 −1.41736 −0.708681 0.705529i \(-0.750710\pi\)
−0.708681 + 0.705529i \(0.750710\pi\)
\(242\) −1408.44 −0.374124
\(243\) 243.000 0.0641500
\(244\) 235.614 0.0618183
\(245\) −1704.82 −0.444560
\(246\) 2233.41 0.578849
\(247\) 910.288 0.234495
\(248\) 1817.65 0.465406
\(249\) 625.613 0.159223
\(250\) 250.000 0.0632456
\(251\) −1801.62 −0.453057 −0.226528 0.974005i \(-0.572738\pi\)
−0.226528 + 0.974005i \(0.572738\pi\)
\(252\) −51.3553 −0.0128376
\(253\) 1331.81 0.330950
\(254\) 2097.41 0.518123
\(255\) 1163.50 0.285730
\(256\) 256.000 0.0625000
\(257\) −5776.67 −1.40210 −0.701048 0.713114i \(-0.747284\pi\)
−0.701048 + 0.713114i \(0.747284\pi\)
\(258\) −926.757 −0.223633
\(259\) −288.593 −0.0692367
\(260\) 958.198 0.228557
\(261\) 511.915 0.121405
\(262\) 2818.52 0.664612
\(263\) −4580.68 −1.07398 −0.536990 0.843589i \(-0.680439\pi\)
−0.536990 + 0.843589i \(0.680439\pi\)
\(264\) −600.853 −0.140076
\(265\) 1427.17 0.330831
\(266\) −54.2084 −0.0124952
\(267\) 2833.06 0.649364
\(268\) −298.876 −0.0681223
\(269\) 6820.48 1.54592 0.772960 0.634455i \(-0.218775\pi\)
0.772960 + 0.634455i \(0.218775\pi\)
\(270\) 270.000 0.0608581
\(271\) −388.570 −0.0870995 −0.0435498 0.999051i \(-0.513867\pi\)
−0.0435498 + 0.999051i \(0.513867\pi\)
\(272\) 1241.06 0.276657
\(273\) −205.036 −0.0454554
\(274\) −1468.47 −0.323772
\(275\) −625.889 −0.137246
\(276\) −638.361 −0.139220
\(277\) 6307.17 1.36809 0.684045 0.729440i \(-0.260219\pi\)
0.684045 + 0.729440i \(0.260219\pi\)
\(278\) 4078.21 0.879838
\(279\) 2044.85 0.438789
\(280\) −57.0614 −0.0121788
\(281\) −8388.14 −1.78076 −0.890381 0.455215i \(-0.849562\pi\)
−0.890381 + 0.455215i \(0.849562\pi\)
\(282\) −3715.21 −0.784531
\(283\) 5889.76 1.23714 0.618569 0.785731i \(-0.287713\pi\)
0.618569 + 0.785731i \(0.287713\pi\)
\(284\) −1069.50 −0.223461
\(285\) 285.000 0.0592349
\(286\) −2398.90 −0.495979
\(287\) −531.006 −0.109214
\(288\) 288.000 0.0589256
\(289\) 1103.57 0.224622
\(290\) 568.795 0.115175
\(291\) 980.499 0.197518
\(292\) −577.389 −0.115716
\(293\) −8914.74 −1.77749 −0.888746 0.458401i \(-0.848422\pi\)
−0.888746 + 0.458401i \(0.848422\pi\)
\(294\) −2045.79 −0.405826
\(295\) 608.580 0.120112
\(296\) 1618.43 0.317801
\(297\) −675.960 −0.132065
\(298\) −3669.94 −0.713402
\(299\) −2548.65 −0.492951
\(300\) 300.000 0.0577350
\(301\) 220.342 0.0421937
\(302\) −3890.82 −0.741362
\(303\) −4326.17 −0.820237
\(304\) 304.000 0.0573539
\(305\) 294.518 0.0552919
\(306\) 1396.20 0.260834
\(307\) 832.485 0.154764 0.0773818 0.997002i \(-0.475344\pi\)
0.0773818 + 0.997002i \(0.475344\pi\)
\(308\) 142.857 0.0264286
\(309\) 1372.96 0.252766
\(310\) 2272.06 0.416272
\(311\) −6887.18 −1.25574 −0.627872 0.778317i \(-0.716074\pi\)
−0.627872 + 0.778317i \(0.716074\pi\)
\(312\) 1149.84 0.208643
\(313\) 4101.88 0.740740 0.370370 0.928884i \(-0.379231\pi\)
0.370370 + 0.928884i \(0.379231\pi\)
\(314\) −2641.61 −0.474760
\(315\) −64.1941 −0.0114823
\(316\) −1475.73 −0.262711
\(317\) −8821.41 −1.56296 −0.781482 0.623928i \(-0.785536\pi\)
−0.781482 + 0.623928i \(0.785536\pi\)
\(318\) 1712.60 0.302006
\(319\) −1424.01 −0.249935
\(320\) 320.000 0.0559017
\(321\) −5792.84 −1.00724
\(322\) 151.774 0.0262672
\(323\) 1473.76 0.253877
\(324\) 324.000 0.0555556
\(325\) 1197.75 0.204428
\(326\) −5820.79 −0.988907
\(327\) 318.083 0.0537922
\(328\) 2977.87 0.501298
\(329\) 883.314 0.148020
\(330\) −751.067 −0.125287
\(331\) 11.2463 0.00186752 0.000933762 1.00000i \(-0.499703\pi\)
0.000933762 1.00000i \(0.499703\pi\)
\(332\) 834.151 0.137891
\(333\) 1820.73 0.299626
\(334\) 4074.64 0.667528
\(335\) −373.595 −0.0609304
\(336\) −68.4737 −0.0111177
\(337\) 1806.72 0.292042 0.146021 0.989281i \(-0.453353\pi\)
0.146021 + 0.989281i \(0.453353\pi\)
\(338\) 196.712 0.0316560
\(339\) 388.419 0.0622302
\(340\) 1551.33 0.247449
\(341\) −5688.23 −0.903328
\(342\) 342.000 0.0540738
\(343\) 975.701 0.153594
\(344\) −1235.68 −0.193672
\(345\) −797.952 −0.124523
\(346\) −3173.90 −0.493149
\(347\) −7543.99 −1.16710 −0.583548 0.812078i \(-0.698336\pi\)
−0.583548 + 0.812078i \(0.698336\pi\)
\(348\) 682.553 0.105140
\(349\) −2044.40 −0.313566 −0.156783 0.987633i \(-0.550112\pi\)
−0.156783 + 0.987633i \(0.550112\pi\)
\(350\) −71.3268 −0.0108931
\(351\) 1293.57 0.196711
\(352\) −801.138 −0.121309
\(353\) 9260.33 1.39625 0.698127 0.715974i \(-0.254017\pi\)
0.698127 + 0.715974i \(0.254017\pi\)
\(354\) 730.296 0.109646
\(355\) −1336.87 −0.199870
\(356\) 3777.41 0.562366
\(357\) −331.954 −0.0492126
\(358\) −362.461 −0.0535103
\(359\) 1381.51 0.203101 0.101551 0.994830i \(-0.467620\pi\)
0.101551 + 0.994830i \(0.467620\pi\)
\(360\) 360.000 0.0527046
\(361\) 361.000 0.0526316
\(362\) 2507.36 0.364045
\(363\) −2112.66 −0.305471
\(364\) −273.381 −0.0393655
\(365\) −721.737 −0.103500
\(366\) 353.421 0.0504744
\(367\) −5516.48 −0.784626 −0.392313 0.919832i \(-0.628325\pi\)
−0.392313 + 0.919832i \(0.628325\pi\)
\(368\) −851.149 −0.120568
\(369\) 3350.11 0.472628
\(370\) 2023.03 0.284250
\(371\) −407.181 −0.0569806
\(372\) 2726.47 0.380003
\(373\) 6540.47 0.907916 0.453958 0.891023i \(-0.350012\pi\)
0.453958 + 0.891023i \(0.350012\pi\)
\(374\) −3883.84 −0.536975
\(375\) 375.000 0.0516398
\(376\) −4953.62 −0.679424
\(377\) 2725.09 0.372279
\(378\) −77.0330 −0.0104819
\(379\) 7414.01 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(380\) 380.000 0.0512989
\(381\) 3146.12 0.423046
\(382\) −7947.49 −1.06447
\(383\) 10865.9 1.44966 0.724830 0.688928i \(-0.241918\pi\)
0.724830 + 0.688928i \(0.241918\pi\)
\(384\) 384.000 0.0510310
\(385\) 178.571 0.0236384
\(386\) −1871.75 −0.246812
\(387\) −1390.14 −0.182596
\(388\) 1307.33 0.171056
\(389\) 7966.01 1.03828 0.519142 0.854688i \(-0.326251\pi\)
0.519142 + 0.854688i \(0.326251\pi\)
\(390\) 1437.30 0.186616
\(391\) −4126.29 −0.533697
\(392\) −2727.72 −0.351456
\(393\) 4227.77 0.542654
\(394\) −5960.02 −0.762085
\(395\) −1844.67 −0.234975
\(396\) −901.280 −0.114371
\(397\) 6918.42 0.874624 0.437312 0.899310i \(-0.355931\pi\)
0.437312 + 0.899310i \(0.355931\pi\)
\(398\) 6383.08 0.803907
\(399\) −81.3126 −0.0102023
\(400\) 400.000 0.0500000
\(401\) −8342.55 −1.03892 −0.519460 0.854494i \(-0.673867\pi\)
−0.519460 + 0.854494i \(0.673867\pi\)
\(402\) −448.314 −0.0556216
\(403\) 10885.4 1.34551
\(404\) −5768.22 −0.710346
\(405\) 405.000 0.0496904
\(406\) −162.281 −0.0198371
\(407\) −5064.78 −0.616835
\(408\) 1861.60 0.225889
\(409\) 7411.37 0.896012 0.448006 0.894031i \(-0.352134\pi\)
0.448006 + 0.894031i \(0.352134\pi\)
\(410\) 3722.34 0.448374
\(411\) −2202.71 −0.264359
\(412\) 1830.61 0.218902
\(413\) −173.632 −0.0206874
\(414\) −957.542 −0.113673
\(415\) 1042.69 0.123334
\(416\) 1533.12 0.180690
\(417\) 6117.32 0.718385
\(418\) −951.351 −0.111321
\(419\) −4893.15 −0.570516 −0.285258 0.958451i \(-0.592079\pi\)
−0.285258 + 0.958451i \(0.592079\pi\)
\(420\) −85.5922 −0.00994398
\(421\) −6436.10 −0.745074 −0.372537 0.928017i \(-0.621512\pi\)
−0.372537 + 0.928017i \(0.621512\pi\)
\(422\) −3646.65 −0.420654
\(423\) −5572.82 −0.640567
\(424\) 2283.47 0.261545
\(425\) 1939.16 0.221325
\(426\) −1604.25 −0.182455
\(427\) −84.0280 −0.00952319
\(428\) −7723.78 −0.872297
\(429\) −3598.35 −0.404965
\(430\) −1544.60 −0.173226
\(431\) −4367.77 −0.488140 −0.244070 0.969758i \(-0.578483\pi\)
−0.244070 + 0.969758i \(0.578483\pi\)
\(432\) 432.000 0.0481125
\(433\) 9988.53 1.10859 0.554293 0.832321i \(-0.312989\pi\)
0.554293 + 0.832321i \(0.312989\pi\)
\(434\) −648.235 −0.0716965
\(435\) 853.192 0.0940400
\(436\) 424.111 0.0465854
\(437\) −1010.74 −0.110641
\(438\) −866.084 −0.0944820
\(439\) 1046.65 0.113790 0.0568950 0.998380i \(-0.481880\pi\)
0.0568950 + 0.998380i \(0.481880\pi\)
\(440\) −1001.42 −0.108502
\(441\) −3068.68 −0.331356
\(442\) 7432.41 0.799827
\(443\) 13768.1 1.47662 0.738311 0.674460i \(-0.235624\pi\)
0.738311 + 0.674460i \(0.235624\pi\)
\(444\) 2427.64 0.259484
\(445\) 4721.76 0.502995
\(446\) 5713.90 0.606639
\(447\) −5504.91 −0.582491
\(448\) −91.2983 −0.00962821
\(449\) 7217.73 0.758632 0.379316 0.925267i \(-0.376159\pi\)
0.379316 + 0.925267i \(0.376159\pi\)
\(450\) 450.000 0.0471405
\(451\) −9319.09 −0.972991
\(452\) 517.893 0.0538930
\(453\) −5836.23 −0.605320
\(454\) −3902.84 −0.403457
\(455\) −341.726 −0.0352096
\(456\) 456.000 0.0468293
\(457\) 374.066 0.0382890 0.0191445 0.999817i \(-0.493906\pi\)
0.0191445 + 0.999817i \(0.493906\pi\)
\(458\) 331.014 0.0337713
\(459\) 2094.30 0.212970
\(460\) −1063.94 −0.107840
\(461\) 2993.07 0.302388 0.151194 0.988504i \(-0.451688\pi\)
0.151194 + 0.988504i \(0.451688\pi\)
\(462\) 214.285 0.0215789
\(463\) 9736.06 0.977264 0.488632 0.872490i \(-0.337496\pi\)
0.488632 + 0.872490i \(0.337496\pi\)
\(464\) 910.071 0.0910539
\(465\) 3408.09 0.339885
\(466\) 3708.87 0.368691
\(467\) −14488.1 −1.43560 −0.717802 0.696247i \(-0.754852\pi\)
−0.717802 + 0.696247i \(0.754852\pi\)
\(468\) 1724.76 0.170357
\(469\) 106.589 0.0104943
\(470\) −6192.02 −0.607695
\(471\) −3962.41 −0.387640
\(472\) 973.728 0.0949565
\(473\) 3866.98 0.375907
\(474\) −2213.60 −0.214502
\(475\) 475.000 0.0458831
\(476\) −442.606 −0.0426193
\(477\) 2568.90 0.246587
\(478\) −11531.3 −1.10341
\(479\) 4836.79 0.461375 0.230687 0.973028i \(-0.425903\pi\)
0.230687 + 0.973028i \(0.425903\pi\)
\(480\) 480.000 0.0456435
\(481\) 9692.33 0.918778
\(482\) −10605.6 −1.00223
\(483\) 227.661 0.0214471
\(484\) −2816.88 −0.264546
\(485\) 1634.16 0.152997
\(486\) 486.000 0.0453609
\(487\) 13699.4 1.27470 0.637351 0.770574i \(-0.280030\pi\)
0.637351 + 0.770574i \(0.280030\pi\)
\(488\) 471.228 0.0437121
\(489\) −8731.19 −0.807439
\(490\) −3409.65 −0.314352
\(491\) −4403.43 −0.404733 −0.202367 0.979310i \(-0.564863\pi\)
−0.202367 + 0.979310i \(0.564863\pi\)
\(492\) 4466.81 0.409308
\(493\) 4411.94 0.403050
\(494\) 1820.58 0.165813
\(495\) −1126.60 −0.102297
\(496\) 3635.30 0.329092
\(497\) 381.419 0.0344245
\(498\) 1251.23 0.112588
\(499\) −9821.98 −0.881146 −0.440573 0.897717i \(-0.645225\pi\)
−0.440573 + 0.897717i \(0.645225\pi\)
\(500\) 500.000 0.0447214
\(501\) 6111.96 0.545035
\(502\) −3603.24 −0.320360
\(503\) 3619.79 0.320871 0.160436 0.987046i \(-0.448710\pi\)
0.160436 + 0.987046i \(0.448710\pi\)
\(504\) −102.711 −0.00907757
\(505\) −7210.28 −0.635353
\(506\) 2663.62 0.234017
\(507\) 295.069 0.0258470
\(508\) 4194.82 0.366368
\(509\) 1647.73 0.143486 0.0717431 0.997423i \(-0.477144\pi\)
0.0717431 + 0.997423i \(0.477144\pi\)
\(510\) 2327.00 0.202041
\(511\) 205.917 0.0178263
\(512\) 512.000 0.0441942
\(513\) 513.000 0.0441511
\(514\) −11553.3 −0.991432
\(515\) 2288.26 0.195792
\(516\) −1853.51 −0.158133
\(517\) 15502.1 1.31872
\(518\) −577.186 −0.0489577
\(519\) −4760.84 −0.402655
\(520\) 1916.40 0.161614
\(521\) −4445.53 −0.373824 −0.186912 0.982377i \(-0.559848\pi\)
−0.186912 + 0.982377i \(0.559848\pi\)
\(522\) 1023.83 0.0858464
\(523\) 13101.8 1.09541 0.547706 0.836671i \(-0.315501\pi\)
0.547706 + 0.836671i \(0.315501\pi\)
\(524\) 5637.03 0.469952
\(525\) −106.990 −0.00889416
\(526\) −9161.36 −0.759418
\(527\) 17623.6 1.45673
\(528\) −1201.71 −0.0990484
\(529\) −9337.10 −0.767412
\(530\) 2854.34 0.233933
\(531\) 1095.44 0.0895258
\(532\) −108.417 −0.00883546
\(533\) 17833.7 1.44927
\(534\) 5666.11 0.459170
\(535\) −9654.73 −0.780206
\(536\) −597.752 −0.0481697
\(537\) −543.692 −0.0436910
\(538\) 13641.0 1.09313
\(539\) 8536.25 0.682156
\(540\) 540.000 0.0430331
\(541\) 6187.61 0.491731 0.245865 0.969304i \(-0.420928\pi\)
0.245865 + 0.969304i \(0.420928\pi\)
\(542\) −777.141 −0.0615887
\(543\) 3761.05 0.297241
\(544\) 2482.13 0.195626
\(545\) 530.138 0.0416672
\(546\) −410.071 −0.0321418
\(547\) 24661.4 1.92769 0.963843 0.266471i \(-0.0858576\pi\)
0.963843 + 0.266471i \(0.0858576\pi\)
\(548\) −2936.94 −0.228941
\(549\) 530.132 0.0412122
\(550\) −1251.78 −0.0970472
\(551\) 1080.71 0.0835568
\(552\) −1276.72 −0.0984437
\(553\) 526.297 0.0404709
\(554\) 12614.3 0.967386
\(555\) 3034.55 0.232089
\(556\) 8156.43 0.622139
\(557\) −8519.73 −0.648101 −0.324051 0.946040i \(-0.605045\pi\)
−0.324051 + 0.946040i \(0.605045\pi\)
\(558\) 4089.71 0.310271
\(559\) −7400.14 −0.559915
\(560\) −114.123 −0.00861174
\(561\) −5825.76 −0.438438
\(562\) −16776.3 −1.25919
\(563\) 6774.09 0.507094 0.253547 0.967323i \(-0.418403\pi\)
0.253547 + 0.967323i \(0.418403\pi\)
\(564\) −7430.43 −0.554747
\(565\) 647.366 0.0482033
\(566\) 11779.5 0.874788
\(567\) −115.549 −0.00855841
\(568\) −2138.99 −0.158011
\(569\) 15993.1 1.17833 0.589163 0.808014i \(-0.299458\pi\)
0.589163 + 0.808014i \(0.299458\pi\)
\(570\) 570.000 0.0418854
\(571\) 18145.5 1.32989 0.664945 0.746893i \(-0.268455\pi\)
0.664945 + 0.746893i \(0.268455\pi\)
\(572\) −4797.80 −0.350710
\(573\) −11921.2 −0.869139
\(574\) −1062.01 −0.0772256
\(575\) −1329.92 −0.0964548
\(576\) 576.000 0.0416667
\(577\) 4834.40 0.348802 0.174401 0.984675i \(-0.444201\pi\)
0.174401 + 0.984675i \(0.444201\pi\)
\(578\) 2207.13 0.158831
\(579\) −2807.62 −0.201521
\(580\) 1137.59 0.0814411
\(581\) −297.487 −0.0212424
\(582\) 1961.00 0.139667
\(583\) −7145.99 −0.507644
\(584\) −1154.78 −0.0818238
\(585\) 2155.94 0.152372
\(586\) −17829.5 −1.25688
\(587\) −1688.46 −0.118723 −0.0593614 0.998237i \(-0.518906\pi\)
−0.0593614 + 0.998237i \(0.518906\pi\)
\(588\) −4091.58 −0.286962
\(589\) 4316.91 0.301996
\(590\) 1217.16 0.0849317
\(591\) −8940.02 −0.622239
\(592\) 3236.86 0.224719
\(593\) 2635.53 0.182509 0.0912547 0.995828i \(-0.470912\pi\)
0.0912547 + 0.995828i \(0.470912\pi\)
\(594\) −1351.92 −0.0933838
\(595\) −553.257 −0.0381199
\(596\) −7339.88 −0.504452
\(597\) 9574.62 0.656387
\(598\) −5097.30 −0.348569
\(599\) −6322.28 −0.431254 −0.215627 0.976476i \(-0.569180\pi\)
−0.215627 + 0.976476i \(0.569180\pi\)
\(600\) 600.000 0.0408248
\(601\) 12769.4 0.866680 0.433340 0.901231i \(-0.357335\pi\)
0.433340 + 0.901231i \(0.357335\pi\)
\(602\) 440.684 0.0298355
\(603\) −672.471 −0.0454149
\(604\) −7781.63 −0.524222
\(605\) −3521.10 −0.236617
\(606\) −8652.33 −0.579995
\(607\) 9057.11 0.605629 0.302814 0.953050i \(-0.402074\pi\)
0.302814 + 0.953050i \(0.402074\pi\)
\(608\) 608.000 0.0405554
\(609\) −243.422 −0.0161970
\(610\) 589.035 0.0390973
\(611\) −29665.9 −1.96425
\(612\) 2792.39 0.184438
\(613\) 26446.5 1.74252 0.871259 0.490823i \(-0.163304\pi\)
0.871259 + 0.490823i \(0.163304\pi\)
\(614\) 1664.97 0.109434
\(615\) 5583.52 0.366096
\(616\) 285.713 0.0186878
\(617\) 29028.1 1.89405 0.947023 0.321164i \(-0.104074\pi\)
0.947023 + 0.321164i \(0.104074\pi\)
\(618\) 2745.91 0.178733
\(619\) −17102.9 −1.11054 −0.555270 0.831670i \(-0.687385\pi\)
−0.555270 + 0.831670i \(0.687385\pi\)
\(620\) 4544.12 0.294349
\(621\) −1436.31 −0.0928136
\(622\) −13774.4 −0.887945
\(623\) −1347.15 −0.0866333
\(624\) 2299.67 0.147533
\(625\) 625.000 0.0400000
\(626\) 8203.75 0.523783
\(627\) −1427.03 −0.0908931
\(628\) −5283.21 −0.335706
\(629\) 15692.0 0.994722
\(630\) −128.388 −0.00811922
\(631\) −20126.3 −1.26976 −0.634879 0.772612i \(-0.718950\pi\)
−0.634879 + 0.772612i \(0.718950\pi\)
\(632\) −2951.47 −0.185764
\(633\) −5469.97 −0.343462
\(634\) −17642.8 −1.10518
\(635\) 5243.53 0.327690
\(636\) 3425.20 0.213551
\(637\) −16335.6 −1.01607
\(638\) −2848.02 −0.176731
\(639\) −2406.37 −0.148974
\(640\) 640.000 0.0395285
\(641\) 8332.13 0.513415 0.256708 0.966489i \(-0.417362\pi\)
0.256708 + 0.966489i \(0.417362\pi\)
\(642\) −11585.7 −0.712228
\(643\) −3074.94 −0.188591 −0.0942953 0.995544i \(-0.530060\pi\)
−0.0942953 + 0.995544i \(0.530060\pi\)
\(644\) 303.549 0.0185737
\(645\) −2316.89 −0.141438
\(646\) 2947.53 0.179518
\(647\) 15252.7 0.926810 0.463405 0.886147i \(-0.346628\pi\)
0.463405 + 0.886147i \(0.346628\pi\)
\(648\) 648.000 0.0392837
\(649\) −3047.23 −0.184305
\(650\) 2395.49 0.144552
\(651\) −972.353 −0.0585400
\(652\) −11641.6 −0.699263
\(653\) 4429.48 0.265450 0.132725 0.991153i \(-0.457627\pi\)
0.132725 + 0.991153i \(0.457627\pi\)
\(654\) 636.166 0.0380368
\(655\) 7046.29 0.420338
\(656\) 5955.75 0.354471
\(657\) −1299.13 −0.0771442
\(658\) 1766.63 0.104666
\(659\) −5914.18 −0.349596 −0.174798 0.984604i \(-0.555927\pi\)
−0.174798 + 0.984604i \(0.555927\pi\)
\(660\) −1502.13 −0.0885916
\(661\) 19512.3 1.14817 0.574086 0.818795i \(-0.305358\pi\)
0.574086 + 0.818795i \(0.305358\pi\)
\(662\) 22.4925 0.00132054
\(663\) 11148.6 0.653056
\(664\) 1668.30 0.0975040
\(665\) −135.521 −0.00790267
\(666\) 3641.46 0.211868
\(667\) −3025.80 −0.175652
\(668\) 8149.28 0.472014
\(669\) 8570.85 0.495319
\(670\) −747.191 −0.0430843
\(671\) −1474.68 −0.0848428
\(672\) −136.947 −0.00786140
\(673\) −16026.9 −0.917968 −0.458984 0.888445i \(-0.651786\pi\)
−0.458984 + 0.888445i \(0.651786\pi\)
\(674\) 3613.44 0.206505
\(675\) 675.000 0.0384900
\(676\) 393.425 0.0223842
\(677\) 14762.4 0.838060 0.419030 0.907972i \(-0.362370\pi\)
0.419030 + 0.907972i \(0.362370\pi\)
\(678\) 776.839 0.0440034
\(679\) −466.239 −0.0263514
\(680\) 3102.66 0.174973
\(681\) −5854.26 −0.329421
\(682\) −11376.5 −0.638749
\(683\) 309.727 0.0173519 0.00867596 0.999962i \(-0.497238\pi\)
0.00867596 + 0.999962i \(0.497238\pi\)
\(684\) 684.000 0.0382360
\(685\) −3671.18 −0.204771
\(686\) 1951.40 0.108608
\(687\) 496.521 0.0275742
\(688\) −2471.35 −0.136947
\(689\) 13675.1 0.756139
\(690\) −1595.90 −0.0880507
\(691\) −16718.4 −0.920404 −0.460202 0.887814i \(-0.652223\pi\)
−0.460202 + 0.887814i \(0.652223\pi\)
\(692\) −6347.79 −0.348709
\(693\) 321.427 0.0176191
\(694\) −15088.0 −0.825262
\(695\) 10195.5 0.556458
\(696\) 1365.11 0.0743452
\(697\) 28872.9 1.56907
\(698\) −4088.81 −0.221724
\(699\) 5563.30 0.301035
\(700\) −142.654 −0.00770257
\(701\) 23477.6 1.26496 0.632479 0.774578i \(-0.282038\pi\)
0.632479 + 0.774578i \(0.282038\pi\)
\(702\) 2587.13 0.139096
\(703\) 3843.77 0.206217
\(704\) −1602.28 −0.0857785
\(705\) −9288.03 −0.496181
\(706\) 18520.7 0.987300
\(707\) 2057.14 0.109430
\(708\) 1460.59 0.0775316
\(709\) −3168.51 −0.167836 −0.0839182 0.996473i \(-0.526743\pi\)
−0.0839182 + 0.996473i \(0.526743\pi\)
\(710\) −2673.74 −0.141329
\(711\) −3320.40 −0.175140
\(712\) 7554.82 0.397653
\(713\) −12086.6 −0.634850
\(714\) −663.909 −0.0347985
\(715\) −5997.25 −0.313685
\(716\) −724.923 −0.0378375
\(717\) −17297.0 −0.900933
\(718\) 2763.02 0.143614
\(719\) −14421.4 −0.748022 −0.374011 0.927424i \(-0.622018\pi\)
−0.374011 + 0.927424i \(0.622018\pi\)
\(720\) 720.000 0.0372678
\(721\) −652.857 −0.0337221
\(722\) 722.000 0.0372161
\(723\) −15908.5 −0.818315
\(724\) 5014.73 0.257418
\(725\) 1421.99 0.0728431
\(726\) −4225.33 −0.216001
\(727\) −28761.1 −1.46725 −0.733623 0.679556i \(-0.762172\pi\)
−0.733623 + 0.679556i \(0.762172\pi\)
\(728\) −546.761 −0.0278356
\(729\) 729.000 0.0370370
\(730\) −1443.47 −0.0731854
\(731\) −11980.9 −0.606196
\(732\) 706.843 0.0356908
\(733\) 8200.75 0.413236 0.206618 0.978422i \(-0.433754\pi\)
0.206618 + 0.978422i \(0.433754\pi\)
\(734\) −11033.0 −0.554814
\(735\) −5114.47 −0.256667
\(736\) −1702.30 −0.0852548
\(737\) 1870.63 0.0934948
\(738\) 6700.22 0.334198
\(739\) −32707.5 −1.62810 −0.814050 0.580795i \(-0.802742\pi\)
−0.814050 + 0.580795i \(0.802742\pi\)
\(740\) 4046.07 0.200995
\(741\) 2730.86 0.135386
\(742\) −814.363 −0.0402914
\(743\) 8322.15 0.410915 0.205458 0.978666i \(-0.434132\pi\)
0.205458 + 0.978666i \(0.434132\pi\)
\(744\) 5452.94 0.268702
\(745\) −9174.85 −0.451195
\(746\) 13080.9 0.641994
\(747\) 1876.84 0.0919276
\(748\) −7767.68 −0.379699
\(749\) 2754.56 0.134379
\(750\) 750.000 0.0365148
\(751\) −24764.3 −1.20328 −0.601640 0.798767i \(-0.705486\pi\)
−0.601640 + 0.798767i \(0.705486\pi\)
\(752\) −9907.23 −0.480425
\(753\) −5404.86 −0.261573
\(754\) 5450.18 0.263241
\(755\) −9727.04 −0.468879
\(756\) −154.066 −0.00741180
\(757\) −3561.84 −0.171014 −0.0855068 0.996338i \(-0.527251\pi\)
−0.0855068 + 0.996338i \(0.527251\pi\)
\(758\) 14828.0 0.710525
\(759\) 3995.43 0.191074
\(760\) 760.000 0.0362738
\(761\) −31092.5 −1.48108 −0.740540 0.672012i \(-0.765430\pi\)
−0.740540 + 0.672012i \(0.765430\pi\)
\(762\) 6292.23 0.299139
\(763\) −151.252 −0.00717654
\(764\) −15895.0 −0.752696
\(765\) 3490.49 0.164966
\(766\) 21731.7 1.02506
\(767\) 5831.40 0.274524
\(768\) 768.000 0.0360844
\(769\) −41882.9 −1.96403 −0.982014 0.188808i \(-0.939538\pi\)
−0.982014 + 0.188808i \(0.939538\pi\)
\(770\) 357.141 0.0167149
\(771\) −17330.0 −0.809501
\(772\) −3743.49 −0.174522
\(773\) 31224.7 1.45288 0.726438 0.687232i \(-0.241174\pi\)
0.726438 + 0.687232i \(0.241174\pi\)
\(774\) −2780.27 −0.129115
\(775\) 5680.15 0.263274
\(776\) 2614.66 0.120955
\(777\) −865.780 −0.0399738
\(778\) 15932.0 0.734178
\(779\) 7072.45 0.325285
\(780\) 2874.59 0.131958
\(781\) 6693.86 0.306690
\(782\) −8252.58 −0.377381
\(783\) 1535.75 0.0700933
\(784\) −5455.44 −0.248517
\(785\) −6604.02 −0.300264
\(786\) 8455.55 0.383714
\(787\) −22817.9 −1.03351 −0.516754 0.856134i \(-0.672860\pi\)
−0.516754 + 0.856134i \(0.672860\pi\)
\(788\) −11920.0 −0.538875
\(789\) −13742.0 −0.620063
\(790\) −3689.34 −0.166153
\(791\) −184.698 −0.00830229
\(792\) −1802.56 −0.0808727
\(793\) 2822.06 0.126374
\(794\) 13836.8 0.618453
\(795\) 4281.50 0.191005
\(796\) 12766.2 0.568448
\(797\) 2821.26 0.125388 0.0626939 0.998033i \(-0.480031\pi\)
0.0626939 + 0.998033i \(0.480031\pi\)
\(798\) −162.625 −0.00721412
\(799\) −48029.4 −2.12660
\(800\) 800.000 0.0353553
\(801\) 8499.17 0.374911
\(802\) −16685.1 −0.734628
\(803\) 3613.82 0.158815
\(804\) −896.629 −0.0393304
\(805\) 379.436 0.0166129
\(806\) 21770.8 0.951420
\(807\) 20461.5 0.892537
\(808\) −11536.4 −0.502290
\(809\) −31661.2 −1.37596 −0.687979 0.725730i \(-0.741502\pi\)
−0.687979 + 0.725730i \(0.741502\pi\)
\(810\) 810.000 0.0351364
\(811\) −28492.1 −1.23365 −0.616826 0.787099i \(-0.711582\pi\)
−0.616826 + 0.787099i \(0.711582\pi\)
\(812\) −324.562 −0.0140270
\(813\) −1165.71 −0.0502869
\(814\) −10129.6 −0.436168
\(815\) −14552.0 −0.625440
\(816\) 3723.19 0.159728
\(817\) −2934.73 −0.125671
\(818\) 14822.7 0.633576
\(819\) −615.107 −0.0262437
\(820\) 7444.69 0.317048
\(821\) 28632.0 1.21713 0.608565 0.793504i \(-0.291745\pi\)
0.608565 + 0.793504i \(0.291745\pi\)
\(822\) −4405.41 −0.186930
\(823\) −38182.5 −1.61720 −0.808601 0.588357i \(-0.799775\pi\)
−0.808601 + 0.588357i \(0.799775\pi\)
\(824\) 3661.21 0.154787
\(825\) −1877.67 −0.0792387
\(826\) −347.265 −0.0146282
\(827\) −17951.5 −0.754819 −0.377409 0.926046i \(-0.623185\pi\)
−0.377409 + 0.926046i \(0.623185\pi\)
\(828\) −1915.08 −0.0803790
\(829\) 4911.32 0.205762 0.102881 0.994694i \(-0.467194\pi\)
0.102881 + 0.994694i \(0.467194\pi\)
\(830\) 2085.38 0.0872102
\(831\) 18921.5 0.789867
\(832\) 3066.23 0.127767
\(833\) −26447.5 −1.10006
\(834\) 12234.6 0.507975
\(835\) 10186.6 0.422182
\(836\) −1902.70 −0.0787157
\(837\) 6134.56 0.253335
\(838\) −9786.31 −0.403416
\(839\) 15319.0 0.630357 0.315178 0.949032i \(-0.397936\pi\)
0.315178 + 0.949032i \(0.397936\pi\)
\(840\) −171.184 −0.00703145
\(841\) −21153.7 −0.867347
\(842\) −12872.2 −0.526847
\(843\) −25164.4 −1.02812
\(844\) −7293.29 −0.297447
\(845\) 491.781 0.0200210
\(846\) −11145.6 −0.452949
\(847\) 1004.60 0.0407537
\(848\) 4566.94 0.184940
\(849\) 17669.3 0.714262
\(850\) 3878.33 0.156501
\(851\) −10761.9 −0.433505
\(852\) −3208.49 −0.129015
\(853\) 22295.1 0.894923 0.447462 0.894303i \(-0.352328\pi\)
0.447462 + 0.894303i \(0.352328\pi\)
\(854\) −168.056 −0.00673391
\(855\) 855.000 0.0341993
\(856\) −15447.6 −0.616807
\(857\) −29462.8 −1.17436 −0.587182 0.809455i \(-0.699763\pi\)
−0.587182 + 0.809455i \(0.699763\pi\)
\(858\) −7196.70 −0.286354
\(859\) 17304.6 0.687339 0.343669 0.939091i \(-0.388330\pi\)
0.343669 + 0.939091i \(0.388330\pi\)
\(860\) −3089.19 −0.122489
\(861\) −1593.02 −0.0630545
\(862\) −8735.55 −0.345167
\(863\) −10150.3 −0.400373 −0.200186 0.979758i \(-0.564155\pi\)
−0.200186 + 0.979758i \(0.564155\pi\)
\(864\) 864.000 0.0340207
\(865\) −7934.74 −0.311895
\(866\) 19977.1 0.783889
\(867\) 3310.70 0.129685
\(868\) −1296.47 −0.0506971
\(869\) 9236.46 0.360558
\(870\) 1706.38 0.0664963
\(871\) −3579.78 −0.139261
\(872\) 848.222 0.0329408
\(873\) 2941.50 0.114037
\(874\) −2021.48 −0.0782351
\(875\) −178.317 −0.00688939
\(876\) −1732.17 −0.0668088
\(877\) −6744.84 −0.259700 −0.129850 0.991534i \(-0.541450\pi\)
−0.129850 + 0.991534i \(0.541450\pi\)
\(878\) 2093.30 0.0804617
\(879\) −26744.2 −1.02624
\(880\) −2002.84 −0.0767226
\(881\) −5709.33 −0.218334 −0.109167 0.994023i \(-0.534818\pi\)
−0.109167 + 0.994023i \(0.534818\pi\)
\(882\) −6137.37 −0.234304
\(883\) 19746.0 0.752557 0.376278 0.926507i \(-0.377204\pi\)
0.376278 + 0.926507i \(0.377204\pi\)
\(884\) 14864.8 0.565563
\(885\) 1825.74 0.0693464
\(886\) 27536.3 1.04413
\(887\) −25002.2 −0.946441 −0.473220 0.880944i \(-0.656909\pi\)
−0.473220 + 0.880944i \(0.656909\pi\)
\(888\) 4855.28 0.183483
\(889\) −1496.02 −0.0564396
\(890\) 9443.52 0.355672
\(891\) −2027.88 −0.0762475
\(892\) 11427.8 0.428959
\(893\) −11764.8 −0.440868
\(894\) −11009.8 −0.411883
\(895\) −906.153 −0.0338429
\(896\) −182.597 −0.00680818
\(897\) −7645.95 −0.284605
\(898\) 14435.5 0.536434
\(899\) 12923.4 0.479442
\(900\) 900.000 0.0333333
\(901\) 22140.1 0.818639
\(902\) −18638.2 −0.688009
\(903\) 661.026 0.0243606
\(904\) 1035.79 0.0381081
\(905\) 6268.41 0.230242
\(906\) −11672.5 −0.428026
\(907\) −42345.8 −1.55024 −0.775120 0.631814i \(-0.782311\pi\)
−0.775120 + 0.631814i \(0.782311\pi\)
\(908\) −7805.68 −0.285287
\(909\) −12978.5 −0.473564
\(910\) −683.452 −0.0248969
\(911\) 51843.6 1.88546 0.942731 0.333555i \(-0.108248\pi\)
0.942731 + 0.333555i \(0.108248\pi\)
\(912\) 912.000 0.0331133
\(913\) −5220.86 −0.189250
\(914\) 748.132 0.0270744
\(915\) 883.553 0.0319228
\(916\) 662.027 0.0238799
\(917\) −2010.36 −0.0723968
\(918\) 4188.59 0.150593
\(919\) 8118.80 0.291419 0.145710 0.989327i \(-0.453453\pi\)
0.145710 + 0.989327i \(0.453453\pi\)
\(920\) −2127.87 −0.0762542
\(921\) 2497.45 0.0893528
\(922\) 5986.13 0.213821
\(923\) −12809.9 −0.456817
\(924\) 428.570 0.0152586
\(925\) 5057.59 0.179776
\(926\) 19472.1 0.691030
\(927\) 4118.87 0.145935
\(928\) 1820.14 0.0643848
\(929\) 37130.5 1.31132 0.655658 0.755058i \(-0.272391\pi\)
0.655658 + 0.755058i \(0.272391\pi\)
\(930\) 6816.18 0.240335
\(931\) −6478.33 −0.228055
\(932\) 7417.74 0.260704
\(933\) −20661.5 −0.725004
\(934\) −28976.1 −1.01513
\(935\) −9709.61 −0.339613
\(936\) 3449.51 0.120460
\(937\) 21923.7 0.764373 0.382186 0.924085i \(-0.375171\pi\)
0.382186 + 0.924085i \(0.375171\pi\)
\(938\) 213.179 0.00742061
\(939\) 12305.6 0.427667
\(940\) −12384.0 −0.429705
\(941\) −31772.8 −1.10070 −0.550352 0.834933i \(-0.685507\pi\)
−0.550352 + 0.834933i \(0.685507\pi\)
\(942\) −7924.82 −0.274103
\(943\) −19801.7 −0.683808
\(944\) 1947.46 0.0671444
\(945\) −192.582 −0.00662932
\(946\) 7733.96 0.265806
\(947\) −29068.1 −0.997451 −0.498725 0.866760i \(-0.666198\pi\)
−0.498725 + 0.866760i \(0.666198\pi\)
\(948\) −4427.20 −0.151676
\(949\) −6915.66 −0.236556
\(950\) 950.000 0.0324443
\(951\) −26464.2 −0.902378
\(952\) −885.212 −0.0301364
\(953\) −46942.0 −1.59559 −0.797797 0.602926i \(-0.794001\pi\)
−0.797797 + 0.602926i \(0.794001\pi\)
\(954\) 5137.81 0.174363
\(955\) −19868.7 −0.673232
\(956\) −23062.7 −0.780231
\(957\) −4272.03 −0.144300
\(958\) 9673.58 0.326241
\(959\) 1047.41 0.0352687
\(960\) 960.000 0.0322749
\(961\) 21831.6 0.732825
\(962\) 19384.7 0.649674
\(963\) −17378.5 −0.581531
\(964\) −21211.3 −0.708681
\(965\) −4679.37 −0.156098
\(966\) 455.323 0.0151654
\(967\) 11665.7 0.387945 0.193972 0.981007i \(-0.437863\pi\)
0.193972 + 0.981007i \(0.437863\pi\)
\(968\) −5633.77 −0.187062
\(969\) 4421.29 0.146576
\(970\) 3268.33 0.108185
\(971\) −9003.84 −0.297577 −0.148788 0.988869i \(-0.547537\pi\)
−0.148788 + 0.988869i \(0.547537\pi\)
\(972\) 972.000 0.0320750
\(973\) −2908.86 −0.0958415
\(974\) 27398.8 0.901350
\(975\) 3593.24 0.118026
\(976\) 942.457 0.0309091
\(977\) 49676.5 1.62671 0.813353 0.581771i \(-0.197640\pi\)
0.813353 + 0.581771i \(0.197640\pi\)
\(978\) −17462.4 −0.570946
\(979\) −23642.4 −0.771822
\(980\) −6819.30 −0.222280
\(981\) 954.249 0.0310569
\(982\) −8806.86 −0.286190
\(983\) −4386.77 −0.142336 −0.0711681 0.997464i \(-0.522673\pi\)
−0.0711681 + 0.997464i \(0.522673\pi\)
\(984\) 8933.62 0.289424
\(985\) −14900.0 −0.481985
\(986\) 8823.88 0.285000
\(987\) 2649.94 0.0854596
\(988\) 3641.15 0.117247
\(989\) 8216.75 0.264184
\(990\) −2253.20 −0.0723347
\(991\) 45427.1 1.45614 0.728072 0.685500i \(-0.240416\pi\)
0.728072 + 0.685500i \(0.240416\pi\)
\(992\) 7270.59 0.232703
\(993\) 33.7388 0.00107822
\(994\) 762.838 0.0243418
\(995\) 15957.7 0.508435
\(996\) 2502.45 0.0796117
\(997\) 24933.7 0.792033 0.396016 0.918243i \(-0.370392\pi\)
0.396016 + 0.918243i \(0.370392\pi\)
\(998\) −19644.0 −0.623065
\(999\) 5462.19 0.172989
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 570.4.a.s.1.2 4
3.2 odd 2 1710.4.a.bc.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.4.a.s.1.2 4 1.1 even 1 trivial
1710.4.a.bc.1.2 4 3.2 odd 2