Properties

Label 833.4.a.d.1.1
Level $833$
Weight $4$
Character 833.1
Self dual yes
Analytic conductor $49.149$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 833.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.1485910348\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Defining polynomial: \( x^{3} - 14x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.58966\) of defining polynomial
Character \(\chi\) \(=\) 833.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -0.885690 q^{5} +42.6523 q^{6} -46.9339 q^{8} +44.8316 q^{9} +O(q^{10})\) \(q-5.03251 q^{2} -8.47535 q^{3} +17.3261 q^{4} -0.885690 q^{5} +42.6523 q^{6} -46.9339 q^{8} +44.8316 q^{9} +4.45724 q^{10} -52.3720 q^{11} -146.845 q^{12} +8.06025 q^{13} +7.50653 q^{15} +97.5862 q^{16} +17.0000 q^{17} -225.616 q^{18} +66.5154 q^{19} -15.3456 q^{20} +263.563 q^{22} +180.226 q^{23} +397.782 q^{24} -124.216 q^{25} -40.5633 q^{26} -151.129 q^{27} -41.2800 q^{29} -37.7767 q^{30} +34.9114 q^{31} -115.632 q^{32} +443.871 q^{33} -85.5527 q^{34} +776.759 q^{36} +130.368 q^{37} -334.739 q^{38} -68.3134 q^{39} +41.5689 q^{40} +17.9081 q^{41} +277.620 q^{43} -907.405 q^{44} -39.7069 q^{45} -906.987 q^{46} -463.789 q^{47} -827.078 q^{48} +625.116 q^{50} -144.081 q^{51} +139.653 q^{52} -329.944 q^{53} +760.560 q^{54} +46.3853 q^{55} -563.741 q^{57} +207.742 q^{58} -678.656 q^{59} +130.059 q^{60} -340.280 q^{61} -175.692 q^{62} -198.770 q^{64} -7.13888 q^{65} -2233.79 q^{66} +15.3925 q^{67} +294.545 q^{68} -1527.48 q^{69} -670.203 q^{71} -2104.12 q^{72} -193.480 q^{73} -656.080 q^{74} +1052.77 q^{75} +1152.46 q^{76} +343.788 q^{78} +1080.15 q^{79} -86.4311 q^{80} +70.4207 q^{81} -90.1229 q^{82} +865.668 q^{83} -15.0567 q^{85} -1397.13 q^{86} +349.863 q^{87} +2458.02 q^{88} -1129.46 q^{89} +199.825 q^{90} +3122.61 q^{92} -295.886 q^{93} +2334.02 q^{94} -58.9120 q^{95} +980.023 q^{96} +379.412 q^{97} -2347.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 39 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 4 q^{3} + 25 q^{4} + 8 q^{5} + 74 q^{6} - 39 q^{8} + 59 q^{9} + 56 q^{10} - 28 q^{11} - 22 q^{12} - 30 q^{13} + 108 q^{15} + 137 q^{16} + 51 q^{17} - 103 q^{18} - 80 q^{19} + 168 q^{20} + 286 q^{22} + 142 q^{23} + 666 q^{24} - 223 q^{25} - 26 q^{26} + 20 q^{27} - 456 q^{29} + 400 q^{30} - 230 q^{31} - 71 q^{32} + 332 q^{33} + 17 q^{34} + 1313 q^{36} + 356 q^{37} - 724 q^{38} + 268 q^{39} + 424 q^{40} + 294 q^{41} + 556 q^{43} - 1122 q^{44} + 384 q^{45} - 704 q^{46} - 640 q^{47} - 774 q^{48} + 547 q^{50} - 68 q^{51} + 774 q^{52} + 302 q^{53} + 1100 q^{54} - 76 q^{55} - 720 q^{57} - 1304 q^{58} - 636 q^{59} + 1328 q^{60} + 84 q^{61} - 508 q^{62} - 919 q^{64} + 408 q^{65} - 2468 q^{66} + 1008 q^{67} + 425 q^{68} - 576 q^{69} - 402 q^{71} - 927 q^{72} - 838 q^{73} + 836 q^{74} + 1548 q^{75} + 908 q^{76} + 1308 q^{78} - 594 q^{79} + 40 q^{80} - 505 q^{81} - 358 q^{82} + 2396 q^{83} + 136 q^{85} - 1264 q^{86} - 1428 q^{87} + 1838 q^{88} + 170 q^{89} + 2008 q^{90} + 4896 q^{92} + 632 q^{93} + 2016 q^{94} - 472 q^{95} - 678 q^{96} + 270 q^{97} - 2920 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.03251 −1.77926 −0.889630 0.456681i \(-0.849038\pi\)
−0.889630 + 0.456681i \(0.849038\pi\)
\(3\) −8.47535 −1.63108 −0.815541 0.578699i \(-0.803561\pi\)
−0.815541 + 0.578699i \(0.803561\pi\)
\(4\) 17.3261 2.16577
\(5\) −0.885690 −0.0792185 −0.0396092 0.999215i \(-0.512611\pi\)
−0.0396092 + 0.999215i \(0.512611\pi\)
\(6\) 42.6523 2.90212
\(7\) 0 0
\(8\) −46.9339 −2.07421
\(9\) 44.8316 1.66043
\(10\) 4.45724 0.140950
\(11\) −52.3720 −1.43552 −0.717761 0.696289i \(-0.754833\pi\)
−0.717761 + 0.696289i \(0.754833\pi\)
\(12\) −146.845 −3.53255
\(13\) 8.06025 0.171962 0.0859811 0.996297i \(-0.472598\pi\)
0.0859811 + 0.996297i \(0.472598\pi\)
\(14\) 0 0
\(15\) 7.50653 0.129212
\(16\) 97.5862 1.52478
\(17\) 17.0000 0.242536
\(18\) −225.616 −2.95434
\(19\) 66.5154 0.803141 0.401570 0.915828i \(-0.368465\pi\)
0.401570 + 0.915828i \(0.368465\pi\)
\(20\) −15.3456 −0.171569
\(21\) 0 0
\(22\) 263.563 2.55417
\(23\) 180.226 1.63390 0.816948 0.576711i \(-0.195664\pi\)
0.816948 + 0.576711i \(0.195664\pi\)
\(24\) 397.782 3.38320
\(25\) −124.216 −0.993724
\(26\) −40.5633 −0.305966
\(27\) −151.129 −1.07722
\(28\) 0 0
\(29\) −41.2800 −0.264328 −0.132164 0.991228i \(-0.542193\pi\)
−0.132164 + 0.991228i \(0.542193\pi\)
\(30\) −37.7767 −0.229902
\(31\) 34.9114 0.202267 0.101133 0.994873i \(-0.467753\pi\)
0.101133 + 0.994873i \(0.467753\pi\)
\(32\) −115.632 −0.638783
\(33\) 443.871 2.34146
\(34\) −85.5527 −0.431534
\(35\) 0 0
\(36\) 776.759 3.59611
\(37\) 130.368 0.579255 0.289627 0.957139i \(-0.406469\pi\)
0.289627 + 0.957139i \(0.406469\pi\)
\(38\) −334.739 −1.42900
\(39\) −68.3134 −0.280485
\(40\) 41.5689 0.164315
\(41\) 17.9081 0.0682142 0.0341071 0.999418i \(-0.489141\pi\)
0.0341071 + 0.999418i \(0.489141\pi\)
\(42\) 0 0
\(43\) 277.620 0.984573 0.492287 0.870433i \(-0.336161\pi\)
0.492287 + 0.870433i \(0.336161\pi\)
\(44\) −907.405 −3.10901
\(45\) −39.7069 −0.131537
\(46\) −906.987 −2.90713
\(47\) −463.789 −1.43937 −0.719687 0.694299i \(-0.755715\pi\)
−0.719687 + 0.694299i \(0.755715\pi\)
\(48\) −827.078 −2.48705
\(49\) 0 0
\(50\) 625.116 1.76809
\(51\) −144.081 −0.395596
\(52\) 139.653 0.372431
\(53\) −329.944 −0.855118 −0.427559 0.903987i \(-0.640626\pi\)
−0.427559 + 0.903987i \(0.640626\pi\)
\(54\) 760.560 1.91665
\(55\) 46.3853 0.113720
\(56\) 0 0
\(57\) −563.741 −1.30999
\(58\) 207.742 0.470308
\(59\) −678.656 −1.49752 −0.748759 0.662843i \(-0.769350\pi\)
−0.748759 + 0.662843i \(0.769350\pi\)
\(60\) 130.059 0.279843
\(61\) −340.280 −0.714237 −0.357118 0.934059i \(-0.616241\pi\)
−0.357118 + 0.934059i \(0.616241\pi\)
\(62\) −175.692 −0.359885
\(63\) 0 0
\(64\) −198.770 −0.388223
\(65\) −7.13888 −0.0136226
\(66\) −2233.79 −4.16606
\(67\) 15.3925 0.0280671 0.0140336 0.999902i \(-0.495533\pi\)
0.0140336 + 0.999902i \(0.495533\pi\)
\(68\) 294.545 0.525276
\(69\) −1527.48 −2.66502
\(70\) 0 0
\(71\) −670.203 −1.12026 −0.560130 0.828405i \(-0.689249\pi\)
−0.560130 + 0.828405i \(0.689249\pi\)
\(72\) −2104.12 −3.44408
\(73\) −193.480 −0.310207 −0.155103 0.987898i \(-0.549571\pi\)
−0.155103 + 0.987898i \(0.549571\pi\)
\(74\) −656.080 −1.03065
\(75\) 1052.77 1.62085
\(76\) 1152.46 1.73942
\(77\) 0 0
\(78\) 343.788 0.499055
\(79\) 1080.15 1.53831 0.769156 0.639061i \(-0.220677\pi\)
0.769156 + 0.639061i \(0.220677\pi\)
\(80\) −86.4311 −0.120791
\(81\) 70.4207 0.0965990
\(82\) −90.1229 −0.121371
\(83\) 865.668 1.14481 0.572406 0.819970i \(-0.306010\pi\)
0.572406 + 0.819970i \(0.306010\pi\)
\(84\) 0 0
\(85\) −15.0567 −0.0192133
\(86\) −1397.13 −1.75181
\(87\) 349.863 0.431141
\(88\) 2458.02 2.97757
\(89\) −1129.46 −1.34520 −0.672599 0.740008i \(-0.734822\pi\)
−0.672599 + 0.740008i \(0.734822\pi\)
\(90\) 199.825 0.234038
\(91\) 0 0
\(92\) 3122.61 3.53864
\(93\) −295.886 −0.329914
\(94\) 2334.02 2.56102
\(95\) −58.9120 −0.0636236
\(96\) 980.023 1.04191
\(97\) 379.412 0.397149 0.198574 0.980086i \(-0.436369\pi\)
0.198574 + 0.980086i \(0.436369\pi\)
\(98\) 0 0
\(99\) −2347.92 −2.38359
\(100\) −2152.18 −2.15218
\(101\) −131.732 −0.129780 −0.0648902 0.997892i \(-0.520670\pi\)
−0.0648902 + 0.997892i \(0.520670\pi\)
\(102\) 725.089 0.703868
\(103\) −195.988 −0.187488 −0.0937442 0.995596i \(-0.529884\pi\)
−0.0937442 + 0.995596i \(0.529884\pi\)
\(104\) −378.299 −0.356685
\(105\) 0 0
\(106\) 1660.45 1.52148
\(107\) −485.147 −0.438326 −0.219163 0.975688i \(-0.570333\pi\)
−0.219163 + 0.975688i \(0.570333\pi\)
\(108\) −2618.49 −2.33300
\(109\) −1255.12 −1.10292 −0.551460 0.834201i \(-0.685929\pi\)
−0.551460 + 0.834201i \(0.685929\pi\)
\(110\) −233.435 −0.202337
\(111\) −1104.92 −0.944812
\(112\) 0 0
\(113\) −1013.35 −0.843612 −0.421806 0.906686i \(-0.638604\pi\)
−0.421806 + 0.906686i \(0.638604\pi\)
\(114\) 2837.03 2.33081
\(115\) −159.624 −0.129435
\(116\) −715.224 −0.572473
\(117\) 361.354 0.285531
\(118\) 3415.34 2.66447
\(119\) 0 0
\(120\) −352.311 −0.268012
\(121\) 1411.83 1.06073
\(122\) 1712.46 1.27081
\(123\) −151.778 −0.111263
\(124\) 604.880 0.438063
\(125\) 220.728 0.157940
\(126\) 0 0
\(127\) 1927.72 1.34691 0.673456 0.739227i \(-0.264809\pi\)
0.673456 + 0.739227i \(0.264809\pi\)
\(128\) 1925.37 1.32953
\(129\) −2352.93 −1.60592
\(130\) 35.9265 0.0242381
\(131\) 406.738 0.271274 0.135637 0.990759i \(-0.456692\pi\)
0.135637 + 0.990759i \(0.456692\pi\)
\(132\) 7690.58 5.07105
\(133\) 0 0
\(134\) −77.4631 −0.0499387
\(135\) 133.854 0.0853355
\(136\) −797.877 −0.503069
\(137\) −130.552 −0.0814149 −0.0407074 0.999171i \(-0.512961\pi\)
−0.0407074 + 0.999171i \(0.512961\pi\)
\(138\) 7687.03 4.74177
\(139\) −2073.54 −1.26529 −0.632644 0.774443i \(-0.718030\pi\)
−0.632644 + 0.774443i \(0.718030\pi\)
\(140\) 0 0
\(141\) 3930.78 2.34774
\(142\) 3372.80 1.99323
\(143\) −422.131 −0.246856
\(144\) 4374.95 2.53180
\(145\) 36.5613 0.0209397
\(146\) 973.689 0.551939
\(147\) 0 0
\(148\) 2258.78 1.25453
\(149\) −1852.73 −1.01867 −0.509334 0.860569i \(-0.670108\pi\)
−0.509334 + 0.860569i \(0.670108\pi\)
\(150\) −5298.08 −2.88391
\(151\) 2050.86 1.10527 0.552637 0.833422i \(-0.313622\pi\)
0.552637 + 0.833422i \(0.313622\pi\)
\(152\) −3121.83 −1.66588
\(153\) 762.138 0.402714
\(154\) 0 0
\(155\) −30.9207 −0.0160233
\(156\) −1183.61 −0.607465
\(157\) 262.991 0.133688 0.0668438 0.997763i \(-0.478707\pi\)
0.0668438 + 0.997763i \(0.478707\pi\)
\(158\) −5435.88 −2.73706
\(159\) 2796.39 1.39477
\(160\) 102.414 0.0506035
\(161\) 0 0
\(162\) −354.393 −0.171875
\(163\) −1444.98 −0.694354 −0.347177 0.937800i \(-0.612860\pi\)
−0.347177 + 0.937800i \(0.612860\pi\)
\(164\) 310.279 0.147736
\(165\) −393.132 −0.185487
\(166\) −4356.48 −2.03692
\(167\) 501.565 0.232409 0.116204 0.993225i \(-0.462927\pi\)
0.116204 + 0.993225i \(0.462927\pi\)
\(168\) 0 0
\(169\) −2132.03 −0.970429
\(170\) 75.7731 0.0341855
\(171\) 2981.99 1.33356
\(172\) 4810.08 2.13236
\(173\) 2590.14 1.13829 0.569146 0.822237i \(-0.307274\pi\)
0.569146 + 0.822237i \(0.307274\pi\)
\(174\) −1760.69 −0.767112
\(175\) 0 0
\(176\) −5110.79 −2.18886
\(177\) 5751.85 2.44257
\(178\) 5684.02 2.39346
\(179\) 2165.65 0.904294 0.452147 0.891943i \(-0.350658\pi\)
0.452147 + 0.891943i \(0.350658\pi\)
\(180\) −687.968 −0.284878
\(181\) 1925.56 0.790750 0.395375 0.918520i \(-0.370615\pi\)
0.395375 + 0.918520i \(0.370615\pi\)
\(182\) 0 0
\(183\) 2884.00 1.16498
\(184\) −8458.69 −3.38904
\(185\) −115.466 −0.0458877
\(186\) 1489.05 0.587003
\(187\) −890.324 −0.348165
\(188\) −8035.68 −3.11735
\(189\) 0 0
\(190\) 296.475 0.113203
\(191\) −2783.52 −1.05449 −0.527247 0.849712i \(-0.676776\pi\)
−0.527247 + 0.849712i \(0.676776\pi\)
\(192\) 1684.65 0.633223
\(193\) 2258.27 0.842246 0.421123 0.907004i \(-0.361636\pi\)
0.421123 + 0.907004i \(0.361636\pi\)
\(194\) −1909.39 −0.706631
\(195\) 60.5045 0.0222196
\(196\) 0 0
\(197\) −1270.70 −0.459560 −0.229780 0.973243i \(-0.573801\pi\)
−0.229780 + 0.973243i \(0.573801\pi\)
\(198\) 11815.9 4.24102
\(199\) 4794.36 1.70786 0.853928 0.520392i \(-0.174214\pi\)
0.853928 + 0.520392i \(0.174214\pi\)
\(200\) 5829.92 2.06119
\(201\) −130.457 −0.0457798
\(202\) 662.942 0.230913
\(203\) 0 0
\(204\) −2496.37 −0.856769
\(205\) −15.8611 −0.00540383
\(206\) 986.313 0.333591
\(207\) 8079.80 2.71297
\(208\) 786.569 0.262205
\(209\) −3483.54 −1.15293
\(210\) 0 0
\(211\) −2807.00 −0.915837 −0.457918 0.888994i \(-0.651405\pi\)
−0.457918 + 0.888994i \(0.651405\pi\)
\(212\) −5716.66 −1.85199
\(213\) 5680.21 1.82724
\(214\) 2441.50 0.779896
\(215\) −245.885 −0.0779964
\(216\) 7093.09 2.23437
\(217\) 0 0
\(218\) 6316.38 1.96238
\(219\) 1639.81 0.505973
\(220\) 803.679 0.246291
\(221\) 137.024 0.0417070
\(222\) 5560.51 1.68107
\(223\) −4684.30 −1.40665 −0.703327 0.710866i \(-0.748303\pi\)
−0.703327 + 0.710866i \(0.748303\pi\)
\(224\) 0 0
\(225\) −5568.79 −1.65001
\(226\) 5099.70 1.50101
\(227\) 1395.72 0.408095 0.204047 0.978961i \(-0.434590\pi\)
0.204047 + 0.978961i \(0.434590\pi\)
\(228\) −9767.47 −2.83713
\(229\) −894.638 −0.258163 −0.129082 0.991634i \(-0.541203\pi\)
−0.129082 + 0.991634i \(0.541203\pi\)
\(230\) 803.309 0.230298
\(231\) 0 0
\(232\) 1937.43 0.548270
\(233\) 1196.13 0.336313 0.168156 0.985760i \(-0.446219\pi\)
0.168156 + 0.985760i \(0.446219\pi\)
\(234\) −1818.52 −0.508035
\(235\) 410.773 0.114025
\(236\) −11758.5 −3.24328
\(237\) −9154.67 −2.50911
\(238\) 0 0
\(239\) 4948.82 1.33938 0.669691 0.742639i \(-0.266426\pi\)
0.669691 + 0.742639i \(0.266426\pi\)
\(240\) 732.534 0.197020
\(241\) 6702.73 1.79154 0.895770 0.444518i \(-0.146625\pi\)
0.895770 + 0.444518i \(0.146625\pi\)
\(242\) −7105.03 −1.88731
\(243\) 3483.65 0.919656
\(244\) −5895.75 −1.54687
\(245\) 0 0
\(246\) 763.824 0.197966
\(247\) 536.130 0.138110
\(248\) −1638.53 −0.419543
\(249\) −7336.85 −1.86728
\(250\) −1110.81 −0.281016
\(251\) 4756.08 1.19602 0.598010 0.801489i \(-0.295958\pi\)
0.598010 + 0.801489i \(0.295958\pi\)
\(252\) 0 0
\(253\) −9438.77 −2.34550
\(254\) −9701.29 −2.39651
\(255\) 127.611 0.0313385
\(256\) −8099.28 −1.97736
\(257\) −2892.84 −0.702143 −0.351071 0.936349i \(-0.614183\pi\)
−0.351071 + 0.936349i \(0.614183\pi\)
\(258\) 11841.1 2.85735
\(259\) 0 0
\(260\) −123.689 −0.0295034
\(261\) −1850.65 −0.438898
\(262\) −2046.92 −0.482667
\(263\) 5415.48 1.26971 0.634853 0.772633i \(-0.281061\pi\)
0.634853 + 0.772633i \(0.281061\pi\)
\(264\) −20832.6 −4.85666
\(265\) 292.228 0.0677412
\(266\) 0 0
\(267\) 9572.58 2.19413
\(268\) 266.693 0.0607869
\(269\) −5787.00 −1.31167 −0.655835 0.754904i \(-0.727683\pi\)
−0.655835 + 0.754904i \(0.727683\pi\)
\(270\) −673.620 −0.151834
\(271\) −5465.13 −1.22503 −0.612515 0.790459i \(-0.709842\pi\)
−0.612515 + 0.790459i \(0.709842\pi\)
\(272\) 1658.97 0.369815
\(273\) 0 0
\(274\) 657.006 0.144858
\(275\) 6505.42 1.42651
\(276\) −26465.3 −5.77182
\(277\) −1207.65 −0.261952 −0.130976 0.991386i \(-0.541811\pi\)
−0.130976 + 0.991386i \(0.541811\pi\)
\(278\) 10435.1 2.25128
\(279\) 1565.13 0.335850
\(280\) 0 0
\(281\) −1197.18 −0.254155 −0.127077 0.991893i \(-0.540560\pi\)
−0.127077 + 0.991893i \(0.540560\pi\)
\(282\) −19781.7 −4.17724
\(283\) −3164.73 −0.664748 −0.332374 0.943148i \(-0.607850\pi\)
−0.332374 + 0.943148i \(0.607850\pi\)
\(284\) −11612.0 −2.42622
\(285\) 499.300 0.103775
\(286\) 2124.38 0.439221
\(287\) 0 0
\(288\) −5183.98 −1.06066
\(289\) 289.000 0.0588235
\(290\) −183.995 −0.0372571
\(291\) −3215.65 −0.647782
\(292\) −3352.26 −0.671836
\(293\) −7456.21 −1.48668 −0.743339 0.668915i \(-0.766759\pi\)
−0.743339 + 0.668915i \(0.766759\pi\)
\(294\) 0 0
\(295\) 601.079 0.118631
\(296\) −6118.70 −1.20149
\(297\) 7914.94 1.54637
\(298\) 9323.89 1.81248
\(299\) 1452.66 0.280969
\(300\) 18240.5 3.51038
\(301\) 0 0
\(302\) −10321.0 −1.96657
\(303\) 1116.47 0.211683
\(304\) 6490.98 1.22462
\(305\) 301.383 0.0565808
\(306\) −3835.46 −0.716532
\(307\) 6535.48 1.21498 0.607491 0.794327i \(-0.292176\pi\)
0.607491 + 0.794327i \(0.292176\pi\)
\(308\) 0 0
\(309\) 1661.07 0.305809
\(310\) 155.608 0.0285096
\(311\) 8935.89 1.62928 0.814642 0.579963i \(-0.196933\pi\)
0.814642 + 0.579963i \(0.196933\pi\)
\(312\) 3206.22 0.581783
\(313\) 2628.71 0.474707 0.237353 0.971423i \(-0.423720\pi\)
0.237353 + 0.971423i \(0.423720\pi\)
\(314\) −1323.50 −0.237865
\(315\) 0 0
\(316\) 18714.9 3.33163
\(317\) 4268.54 0.756293 0.378147 0.925746i \(-0.376562\pi\)
0.378147 + 0.925746i \(0.376562\pi\)
\(318\) −14072.9 −2.48166
\(319\) 2161.92 0.379449
\(320\) 176.048 0.0307544
\(321\) 4111.79 0.714946
\(322\) 0 0
\(323\) 1130.76 0.194790
\(324\) 1220.12 0.209211
\(325\) −1001.21 −0.170883
\(326\) 7271.89 1.23544
\(327\) 10637.5 1.79895
\(328\) −840.500 −0.141490
\(329\) 0 0
\(330\) 1978.44 0.330029
\(331\) 992.298 0.164778 0.0823892 0.996600i \(-0.473745\pi\)
0.0823892 + 0.996600i \(0.473745\pi\)
\(332\) 14998.7 2.47940
\(333\) 5844.63 0.961812
\(334\) −2524.13 −0.413516
\(335\) −13.6330 −0.00222344
\(336\) 0 0
\(337\) 8042.26 1.29997 0.649985 0.759947i \(-0.274775\pi\)
0.649985 + 0.759947i \(0.274775\pi\)
\(338\) 10729.5 1.72665
\(339\) 8588.52 1.37600
\(340\) −260.875 −0.0416116
\(341\) −1828.38 −0.290359
\(342\) −15006.9 −2.37275
\(343\) 0 0
\(344\) −13029.8 −2.04221
\(345\) 1352.87 0.211119
\(346\) −13034.9 −2.02532
\(347\) −7414.16 −1.14701 −0.573506 0.819202i \(-0.694417\pi\)
−0.573506 + 0.819202i \(0.694417\pi\)
\(348\) 6061.78 0.933751
\(349\) 859.194 0.131781 0.0658905 0.997827i \(-0.479011\pi\)
0.0658905 + 0.997827i \(0.479011\pi\)
\(350\) 0 0
\(351\) −1218.14 −0.185241
\(352\) 6055.89 0.916988
\(353\) −569.084 −0.0858053 −0.0429027 0.999079i \(-0.513661\pi\)
−0.0429027 + 0.999079i \(0.513661\pi\)
\(354\) −28946.3 −4.34598
\(355\) 593.592 0.0887453
\(356\) −19569.2 −2.91339
\(357\) 0 0
\(358\) −10898.7 −1.60897
\(359\) −5005.21 −0.735835 −0.367918 0.929858i \(-0.619929\pi\)
−0.367918 + 0.929858i \(0.619929\pi\)
\(360\) 1863.60 0.272834
\(361\) −2434.71 −0.354965
\(362\) −9690.40 −1.40695
\(363\) −11965.7 −1.73013
\(364\) 0 0
\(365\) 171.363 0.0245741
\(366\) −14513.7 −2.07280
\(367\) 10975.3 1.56105 0.780523 0.625127i \(-0.214953\pi\)
0.780523 + 0.625127i \(0.214953\pi\)
\(368\) 17587.5 2.49134
\(369\) 802.851 0.113265
\(370\) 581.083 0.0816462
\(371\) 0 0
\(372\) −5126.57 −0.714517
\(373\) −3211.72 −0.445835 −0.222918 0.974837i \(-0.571558\pi\)
−0.222918 + 0.974837i \(0.571558\pi\)
\(374\) 4480.56 0.619477
\(375\) −1870.74 −0.257613
\(376\) 21767.4 2.98556
\(377\) −332.727 −0.0454544
\(378\) 0 0
\(379\) 8051.48 1.09123 0.545616 0.838035i \(-0.316296\pi\)
0.545616 + 0.838035i \(0.316296\pi\)
\(380\) −1020.72 −0.137794
\(381\) −16338.1 −2.19692
\(382\) 14008.1 1.87622
\(383\) 2584.16 0.344763 0.172382 0.985030i \(-0.444854\pi\)
0.172382 + 0.985030i \(0.444854\pi\)
\(384\) −16318.2 −2.16858
\(385\) 0 0
\(386\) −11364.7 −1.49858
\(387\) 12446.2 1.63482
\(388\) 6573.74 0.860132
\(389\) −5174.31 −0.674417 −0.337208 0.941430i \(-0.609483\pi\)
−0.337208 + 0.941430i \(0.609483\pi\)
\(390\) −304.489 −0.0395344
\(391\) 3063.83 0.396278
\(392\) 0 0
\(393\) −3447.25 −0.442470
\(394\) 6394.79 0.817677
\(395\) −956.680 −0.121863
\(396\) −40680.4 −5.16230
\(397\) 5149.36 0.650980 0.325490 0.945545i \(-0.394471\pi\)
0.325490 + 0.945545i \(0.394471\pi\)
\(398\) −24127.7 −3.03872
\(399\) 0 0
\(400\) −12121.7 −1.51522
\(401\) 8700.49 1.08350 0.541748 0.840541i \(-0.317763\pi\)
0.541748 + 0.840541i \(0.317763\pi\)
\(402\) 656.527 0.0814542
\(403\) 281.394 0.0347823
\(404\) −2282.41 −0.281074
\(405\) −62.3709 −0.00765243
\(406\) 0 0
\(407\) −6827.65 −0.831533
\(408\) 6762.29 0.820547
\(409\) −12346.0 −1.49260 −0.746299 0.665611i \(-0.768171\pi\)
−0.746299 + 0.665611i \(0.768171\pi\)
\(410\) 79.8209 0.00961482
\(411\) 1106.48 0.132794
\(412\) −3395.72 −0.406056
\(413\) 0 0
\(414\) −40661.7 −4.82708
\(415\) −766.713 −0.0906903
\(416\) −932.023 −0.109847
\(417\) 17574.0 2.06379
\(418\) 17531.0 2.05136
\(419\) 5763.33 0.671974 0.335987 0.941867i \(-0.390930\pi\)
0.335987 + 0.941867i \(0.390930\pi\)
\(420\) 0 0
\(421\) −1876.12 −0.217188 −0.108594 0.994086i \(-0.534635\pi\)
−0.108594 + 0.994086i \(0.534635\pi\)
\(422\) 14126.2 1.62951
\(423\) −20792.4 −2.38998
\(424\) 15485.6 1.77369
\(425\) −2111.66 −0.241014
\(426\) −28585.7 −3.25113
\(427\) 0 0
\(428\) −8405.72 −0.949313
\(429\) 3577.71 0.402642
\(430\) 1237.42 0.138776
\(431\) 83.9299 0.00937996 0.00468998 0.999989i \(-0.498507\pi\)
0.00468998 + 0.999989i \(0.498507\pi\)
\(432\) −14748.1 −1.64252
\(433\) 15345.0 1.70308 0.851539 0.524291i \(-0.175669\pi\)
0.851539 + 0.524291i \(0.175669\pi\)
\(434\) 0 0
\(435\) −309.870 −0.0341543
\(436\) −21746.3 −2.38867
\(437\) 11987.8 1.31225
\(438\) −8252.36 −0.900258
\(439\) −3064.74 −0.333194 −0.166597 0.986025i \(-0.553278\pi\)
−0.166597 + 0.986025i \(0.553278\pi\)
\(440\) −2177.05 −0.235879
\(441\) 0 0
\(442\) −689.575 −0.0742076
\(443\) −1792.97 −0.192295 −0.0961474 0.995367i \(-0.530652\pi\)
−0.0961474 + 0.995367i \(0.530652\pi\)
\(444\) −19144.0 −2.04624
\(445\) 1000.35 0.106564
\(446\) 23573.8 2.50281
\(447\) 15702.6 1.66153
\(448\) 0 0
\(449\) 2499.19 0.262681 0.131341 0.991337i \(-0.458072\pi\)
0.131341 + 0.991337i \(0.458072\pi\)
\(450\) 28025.0 2.93580
\(451\) −937.885 −0.0979231
\(452\) −17557.5 −1.82707
\(453\) −17381.7 −1.80279
\(454\) −7024.00 −0.726107
\(455\) 0 0
\(456\) 26458.6 2.71719
\(457\) 14784.4 1.51331 0.756656 0.653813i \(-0.226832\pi\)
0.756656 + 0.653813i \(0.226832\pi\)
\(458\) 4502.28 0.459340
\(459\) −2569.20 −0.261263
\(460\) −2765.67 −0.280326
\(461\) 17746.9 1.79297 0.896483 0.443078i \(-0.146113\pi\)
0.896483 + 0.443078i \(0.146113\pi\)
\(462\) 0 0
\(463\) 18486.4 1.85559 0.927793 0.373096i \(-0.121704\pi\)
0.927793 + 0.373096i \(0.121704\pi\)
\(464\) −4028.36 −0.403043
\(465\) 262.064 0.0261353
\(466\) −6019.52 −0.598388
\(467\) −7406.57 −0.733908 −0.366954 0.930239i \(-0.619599\pi\)
−0.366954 + 0.930239i \(0.619599\pi\)
\(468\) 6260.87 0.618395
\(469\) 0 0
\(470\) −2067.22 −0.202880
\(471\) −2228.94 −0.218055
\(472\) 31852.0 3.10616
\(473\) −14539.5 −1.41338
\(474\) 46071.0 4.46437
\(475\) −8262.24 −0.798101
\(476\) 0 0
\(477\) −14791.9 −1.41986
\(478\) −24905.0 −2.38311
\(479\) 18550.9 1.76955 0.884775 0.466019i \(-0.154312\pi\)
0.884775 + 0.466019i \(0.154312\pi\)
\(480\) −867.997 −0.0825384
\(481\) 1050.80 0.0996100
\(482\) −33731.6 −3.18762
\(483\) 0 0
\(484\) 24461.5 2.29729
\(485\) −336.041 −0.0314615
\(486\) −17531.5 −1.63631
\(487\) 10203.4 0.949406 0.474703 0.880146i \(-0.342556\pi\)
0.474703 + 0.880146i \(0.342556\pi\)
\(488\) 15970.7 1.48147
\(489\) 12246.7 1.13255
\(490\) 0 0
\(491\) −1247.46 −0.114658 −0.0573290 0.998355i \(-0.518258\pi\)
−0.0573290 + 0.998355i \(0.518258\pi\)
\(492\) −2629.73 −0.240970
\(493\) −701.760 −0.0641089
\(494\) −2698.08 −0.245734
\(495\) 2079.53 0.188824
\(496\) 3406.87 0.308413
\(497\) 0 0
\(498\) 36922.7 3.32238
\(499\) 70.0303 0.00628254 0.00314127 0.999995i \(-0.499000\pi\)
0.00314127 + 0.999995i \(0.499000\pi\)
\(500\) 3824.36 0.342061
\(501\) −4250.94 −0.379078
\(502\) −23935.0 −2.12803
\(503\) −1444.29 −0.128028 −0.0640138 0.997949i \(-0.520390\pi\)
−0.0640138 + 0.997949i \(0.520390\pi\)
\(504\) 0 0
\(505\) 116.674 0.0102810
\(506\) 47500.7 4.17325
\(507\) 18069.7 1.58285
\(508\) 33400.0 2.91710
\(509\) −14272.8 −1.24289 −0.621445 0.783458i \(-0.713454\pi\)
−0.621445 + 0.783458i \(0.713454\pi\)
\(510\) −642.204 −0.0557593
\(511\) 0 0
\(512\) 25356.7 2.18871
\(513\) −10052.4 −0.865157
\(514\) 14558.3 1.24929
\(515\) 173.585 0.0148525
\(516\) −40767.2 −3.47805
\(517\) 24289.6 2.06625
\(518\) 0 0
\(519\) −21952.3 −1.85665
\(520\) 335.055 0.0282561
\(521\) −14874.0 −1.25075 −0.625376 0.780324i \(-0.715054\pi\)
−0.625376 + 0.780324i \(0.715054\pi\)
\(522\) 9313.42 0.780914
\(523\) 8142.90 0.680811 0.340406 0.940279i \(-0.389436\pi\)
0.340406 + 0.940279i \(0.389436\pi\)
\(524\) 7047.21 0.587517
\(525\) 0 0
\(526\) −27253.4 −2.25914
\(527\) 593.494 0.0490569
\(528\) 43315.7 3.57022
\(529\) 20314.2 1.66962
\(530\) −1470.64 −0.120529
\(531\) −30425.3 −2.48652
\(532\) 0 0
\(533\) 144.344 0.0117303
\(534\) −48174.1 −3.90393
\(535\) 429.689 0.0347235
\(536\) −722.432 −0.0582170
\(537\) −18354.7 −1.47498
\(538\) 29123.1 2.33380
\(539\) 0 0
\(540\) 2319.17 0.184817
\(541\) 3179.67 0.252689 0.126344 0.991986i \(-0.459676\pi\)
0.126344 + 0.991986i \(0.459676\pi\)
\(542\) 27503.3 2.17965
\(543\) −16319.8 −1.28978
\(544\) −1965.75 −0.154928
\(545\) 1111.64 0.0873716
\(546\) 0 0
\(547\) 2107.07 0.164702 0.0823509 0.996603i \(-0.473757\pi\)
0.0823509 + 0.996603i \(0.473757\pi\)
\(548\) −2261.97 −0.176326
\(549\) −15255.3 −1.18594
\(550\) −32738.6 −2.53814
\(551\) −2745.76 −0.212292
\(552\) 71690.4 5.52780
\(553\) 0 0
\(554\) 6077.51 0.466081
\(555\) 978.614 0.0748466
\(556\) −35926.4 −2.74032
\(557\) 467.382 0.0355540 0.0177770 0.999842i \(-0.494341\pi\)
0.0177770 + 0.999842i \(0.494341\pi\)
\(558\) −7876.55 −0.597565
\(559\) 2237.69 0.169309
\(560\) 0 0
\(561\) 7545.81 0.567887
\(562\) 6024.80 0.452208
\(563\) −14612.6 −1.09387 −0.546935 0.837175i \(-0.684206\pi\)
−0.546935 + 0.837175i \(0.684206\pi\)
\(564\) 68105.2 5.08466
\(565\) 897.515 0.0668297
\(566\) 15926.5 1.18276
\(567\) 0 0
\(568\) 31455.3 2.32365
\(569\) 11602.3 0.854821 0.427410 0.904058i \(-0.359426\pi\)
0.427410 + 0.904058i \(0.359426\pi\)
\(570\) −2512.73 −0.184643
\(571\) −10534.9 −0.772104 −0.386052 0.922477i \(-0.626161\pi\)
−0.386052 + 0.922477i \(0.626161\pi\)
\(572\) −7313.91 −0.534633
\(573\) 23591.3 1.71997
\(574\) 0 0
\(575\) −22386.8 −1.62364
\(576\) −8911.18 −0.644617
\(577\) −14404.7 −1.03930 −0.519650 0.854379i \(-0.673938\pi\)
−0.519650 + 0.854379i \(0.673938\pi\)
\(578\) −1454.40 −0.104662
\(579\) −19139.6 −1.37377
\(580\) 633.466 0.0453504
\(581\) 0 0
\(582\) 16182.8 1.15257
\(583\) 17279.8 1.22754
\(584\) 9080.77 0.643433
\(585\) −320.047 −0.0226194
\(586\) 37523.5 2.64519
\(587\) 11004.9 0.773799 0.386900 0.922122i \(-0.373546\pi\)
0.386900 + 0.922122i \(0.373546\pi\)
\(588\) 0 0
\(589\) 2322.14 0.162449
\(590\) −3024.94 −0.211076
\(591\) 10769.6 0.749581
\(592\) 12722.2 0.883239
\(593\) −1853.59 −0.128361 −0.0641804 0.997938i \(-0.520443\pi\)
−0.0641804 + 0.997938i \(0.520443\pi\)
\(594\) −39832.0 −2.75139
\(595\) 0 0
\(596\) −32100.7 −2.20620
\(597\) −40633.9 −2.78565
\(598\) −7310.53 −0.499916
\(599\) 19074.7 1.30112 0.650559 0.759456i \(-0.274535\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(600\) −49410.7 −3.36197
\(601\) 27776.0 1.88520 0.942600 0.333923i \(-0.108373\pi\)
0.942600 + 0.333923i \(0.108373\pi\)
\(602\) 0 0
\(603\) 690.073 0.0466035
\(604\) 35533.4 2.39377
\(605\) −1250.44 −0.0840291
\(606\) −5618.67 −0.376638
\(607\) −18728.3 −1.25232 −0.626159 0.779695i \(-0.715374\pi\)
−0.626159 + 0.779695i \(0.715374\pi\)
\(608\) −7691.32 −0.513033
\(609\) 0 0
\(610\) −1516.71 −0.100672
\(611\) −3738.25 −0.247518
\(612\) 13204.9 0.872184
\(613\) −24405.3 −1.60802 −0.804012 0.594613i \(-0.797305\pi\)
−0.804012 + 0.594613i \(0.797305\pi\)
\(614\) −32889.8 −2.16177
\(615\) 134.428 0.00881409
\(616\) 0 0
\(617\) −22516.4 −1.46917 −0.734584 0.678518i \(-0.762623\pi\)
−0.734584 + 0.678518i \(0.762623\pi\)
\(618\) −8359.35 −0.544114
\(619\) 5146.53 0.334179 0.167089 0.985942i \(-0.446563\pi\)
0.167089 + 0.985942i \(0.446563\pi\)
\(620\) −535.736 −0.0347027
\(621\) −27237.4 −1.76006
\(622\) −44969.9 −2.89892
\(623\) 0 0
\(624\) −6666.45 −0.427679
\(625\) 15331.4 0.981213
\(626\) −13229.0 −0.844627
\(627\) 29524.3 1.88052
\(628\) 4556.62 0.289536
\(629\) 2216.26 0.140490
\(630\) 0 0
\(631\) −3858.77 −0.243447 −0.121724 0.992564i \(-0.538842\pi\)
−0.121724 + 0.992564i \(0.538842\pi\)
\(632\) −50695.8 −3.19078
\(633\) 23790.3 1.49381
\(634\) −21481.5 −1.34564
\(635\) −1707.36 −0.106700
\(636\) 48450.7 3.02075
\(637\) 0 0
\(638\) −10879.9 −0.675138
\(639\) −30046.3 −1.86011
\(640\) −1705.28 −0.105324
\(641\) 18689.3 1.15161 0.575805 0.817587i \(-0.304689\pi\)
0.575805 + 0.817587i \(0.304689\pi\)
\(642\) −20692.6 −1.27208
\(643\) −26473.5 −1.62366 −0.811831 0.583893i \(-0.801529\pi\)
−0.811831 + 0.583893i \(0.801529\pi\)
\(644\) 0 0
\(645\) 2083.96 0.127219
\(646\) −5690.57 −0.346583
\(647\) −14397.7 −0.874855 −0.437427 0.899254i \(-0.644110\pi\)
−0.437427 + 0.899254i \(0.644110\pi\)
\(648\) −3305.12 −0.200366
\(649\) 35542.6 2.14972
\(650\) 5038.59 0.304046
\(651\) 0 0
\(652\) −25036.0 −1.50381
\(653\) 20939.5 1.25486 0.627431 0.778672i \(-0.284107\pi\)
0.627431 + 0.778672i \(0.284107\pi\)
\(654\) −53533.6 −3.20081
\(655\) −360.244 −0.0214899
\(656\) 1747.59 0.104012
\(657\) −8674.02 −0.515077
\(658\) 0 0
\(659\) 4031.76 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(660\) −6811.47 −0.401721
\(661\) −6691.52 −0.393752 −0.196876 0.980428i \(-0.563080\pi\)
−0.196876 + 0.980428i \(0.563080\pi\)
\(662\) −4993.75 −0.293184
\(663\) −1161.33 −0.0680275
\(664\) −40629.2 −2.37458
\(665\) 0 0
\(666\) −29413.1 −1.71131
\(667\) −7439.71 −0.431884
\(668\) 8690.19 0.503344
\(669\) 39701.1 2.29437
\(670\) 68.6083 0.00395607
\(671\) 17821.2 1.02530
\(672\) 0 0
\(673\) 10319.2 0.591048 0.295524 0.955335i \(-0.404506\pi\)
0.295524 + 0.955335i \(0.404506\pi\)
\(674\) −40472.7 −2.31298
\(675\) 18772.6 1.07046
\(676\) −36939.9 −2.10172
\(677\) 19813.3 1.12480 0.562398 0.826866i \(-0.309879\pi\)
0.562398 + 0.826866i \(0.309879\pi\)
\(678\) −43221.8 −2.44826
\(679\) 0 0
\(680\) 706.671 0.0398524
\(681\) −11829.3 −0.665636
\(682\) 9201.33 0.516624
\(683\) 5924.61 0.331916 0.165958 0.986133i \(-0.446928\pi\)
0.165958 + 0.986133i \(0.446928\pi\)
\(684\) 51666.4 2.88818
\(685\) 115.629 0.00644957
\(686\) 0 0
\(687\) 7582.38 0.421085
\(688\) 27091.9 1.50126
\(689\) −2659.43 −0.147048
\(690\) −6808.33 −0.375636
\(691\) −1973.16 −0.108629 −0.0543143 0.998524i \(-0.517297\pi\)
−0.0543143 + 0.998524i \(0.517297\pi\)
\(692\) 44877.1 2.46528
\(693\) 0 0
\(694\) 37311.8 2.04083
\(695\) 1836.51 0.100234
\(696\) −16420.4 −0.894274
\(697\) 304.439 0.0165444
\(698\) −4323.90 −0.234473
\(699\) −10137.6 −0.548554
\(700\) 0 0
\(701\) −12840.1 −0.691815 −0.345907 0.938269i \(-0.612429\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(702\) 6130.30 0.329591
\(703\) 8671.50 0.465223
\(704\) 10410.0 0.557302
\(705\) −3481.45 −0.185984
\(706\) 2863.92 0.152670
\(707\) 0 0
\(708\) 99657.5 5.29005
\(709\) −27749.7 −1.46990 −0.734952 0.678119i \(-0.762796\pi\)
−0.734952 + 0.678119i \(0.762796\pi\)
\(710\) −2987.26 −0.157901
\(711\) 48425.0 2.55426
\(712\) 53010.0 2.79022
\(713\) 6291.92 0.330483
\(714\) 0 0
\(715\) 373.877 0.0195555
\(716\) 37522.4 1.95849
\(717\) −41943.0 −2.18464
\(718\) 25188.8 1.30924
\(719\) −16888.3 −0.875979 −0.437989 0.898980i \(-0.644309\pi\)
−0.437989 + 0.898980i \(0.644309\pi\)
\(720\) −3874.85 −0.200565
\(721\) 0 0
\(722\) 12252.7 0.631575
\(723\) −56808.0 −2.92215
\(724\) 33362.6 1.71258
\(725\) 5127.62 0.262669
\(726\) 60217.6 3.07835
\(727\) −2135.25 −0.108930 −0.0544649 0.998516i \(-0.517345\pi\)
−0.0544649 + 0.998516i \(0.517345\pi\)
\(728\) 0 0
\(729\) −31426.5 −1.59663
\(730\) −862.386 −0.0437238
\(731\) 4719.54 0.238794
\(732\) 49968.6 2.52308
\(733\) −4795.27 −0.241633 −0.120817 0.992675i \(-0.538551\pi\)
−0.120817 + 0.992675i \(0.538551\pi\)
\(734\) −55233.1 −2.77751
\(735\) 0 0
\(736\) −20839.9 −1.04371
\(737\) −806.138 −0.0402910
\(738\) −4040.36 −0.201528
\(739\) −32747.6 −1.63010 −0.815048 0.579393i \(-0.803290\pi\)
−0.815048 + 0.579393i \(0.803290\pi\)
\(740\) −2000.58 −0.0993821
\(741\) −4543.89 −0.225269
\(742\) 0 0
\(743\) 12299.4 0.607298 0.303649 0.952784i \(-0.401795\pi\)
0.303649 + 0.952784i \(0.401795\pi\)
\(744\) 13887.1 0.684309
\(745\) 1640.94 0.0806974
\(746\) 16163.0 0.793257
\(747\) 38809.3 1.90088
\(748\) −15425.9 −0.754046
\(749\) 0 0
\(750\) 9414.54 0.458361
\(751\) 30102.6 1.46266 0.731332 0.682021i \(-0.238899\pi\)
0.731332 + 0.682021i \(0.238899\pi\)
\(752\) −45259.4 −2.19474
\(753\) −40309.4 −1.95081
\(754\) 1674.45 0.0808753
\(755\) −1816.42 −0.0875581
\(756\) 0 0
\(757\) 38826.3 1.86416 0.932078 0.362257i \(-0.117994\pi\)
0.932078 + 0.362257i \(0.117994\pi\)
\(758\) −40519.2 −1.94159
\(759\) 79996.9 3.82570
\(760\) 2764.97 0.131968
\(761\) −19981.6 −0.951815 −0.475907 0.879495i \(-0.657880\pi\)
−0.475907 + 0.879495i \(0.657880\pi\)
\(762\) 82221.8 3.90890
\(763\) 0 0
\(764\) −48227.7 −2.28379
\(765\) −675.017 −0.0319024
\(766\) −13004.8 −0.613424
\(767\) −5470.14 −0.257517
\(768\) 68644.2 3.22524
\(769\) 22407.7 1.05077 0.525384 0.850865i \(-0.323922\pi\)
0.525384 + 0.850865i \(0.323922\pi\)
\(770\) 0 0
\(771\) 24517.9 1.14525
\(772\) 39127.0 1.82411
\(773\) 6902.77 0.321184 0.160592 0.987021i \(-0.448660\pi\)
0.160592 + 0.987021i \(0.448660\pi\)
\(774\) −62635.4 −2.90876
\(775\) −4336.54 −0.200997
\(776\) −17807.3 −0.823768
\(777\) 0 0
\(778\) 26039.8 1.19996
\(779\) 1191.17 0.0547856
\(780\) 1048.31 0.0481225
\(781\) 35099.9 1.60816
\(782\) −15418.8 −0.705082
\(783\) 6238.62 0.284738
\(784\) 0 0
\(785\) −232.928 −0.0105905
\(786\) 17348.3 0.787270
\(787\) 22185.9 1.00488 0.502442 0.864611i \(-0.332435\pi\)
0.502442 + 0.864611i \(0.332435\pi\)
\(788\) −22016.3 −0.995301
\(789\) −45898.1 −2.07099
\(790\) 4814.50 0.216826
\(791\) 0 0
\(792\) 110197. 4.94405
\(793\) −2742.74 −0.122822
\(794\) −25914.2 −1.15826
\(795\) −2476.73 −0.110491
\(796\) 83067.8 3.69882
\(797\) 16291.1 0.724040 0.362020 0.932170i \(-0.382087\pi\)
0.362020 + 0.932170i \(0.382087\pi\)
\(798\) 0 0
\(799\) −7884.41 −0.349100
\(800\) 14363.3 0.634775
\(801\) −50635.5 −2.23361
\(802\) −43785.3 −1.92782
\(803\) 10132.9 0.445309
\(804\) −2260.32 −0.0991485
\(805\) 0 0
\(806\) −1416.12 −0.0618867
\(807\) 49046.8 2.13944
\(808\) 6182.70 0.269191
\(809\) 17696.8 0.769082 0.384541 0.923108i \(-0.374360\pi\)
0.384541 + 0.923108i \(0.374360\pi\)
\(810\) 313.882 0.0136157
\(811\) 3095.34 0.134022 0.0670111 0.997752i \(-0.478654\pi\)
0.0670111 + 0.997752i \(0.478654\pi\)
\(812\) 0 0
\(813\) 46318.9 1.99812
\(814\) 34360.2 1.47951
\(815\) 1279.81 0.0550057
\(816\) −14060.3 −0.603198
\(817\) 18466.0 0.790751
\(818\) 62131.5 2.65572
\(819\) 0 0
\(820\) −274.811 −0.0117034
\(821\) 12323.5 0.523864 0.261932 0.965086i \(-0.415640\pi\)
0.261932 + 0.965086i \(0.415640\pi\)
\(822\) −5568.36 −0.236276
\(823\) −34436.5 −1.45854 −0.729271 0.684225i \(-0.760140\pi\)
−0.729271 + 0.684225i \(0.760140\pi\)
\(824\) 9198.50 0.388889
\(825\) −55135.7 −2.32676
\(826\) 0 0
\(827\) 18761.6 0.788880 0.394440 0.918922i \(-0.370939\pi\)
0.394440 + 0.918922i \(0.370939\pi\)
\(828\) 139992. 5.87567
\(829\) −22423.8 −0.939457 −0.469728 0.882811i \(-0.655648\pi\)
−0.469728 + 0.882811i \(0.655648\pi\)
\(830\) 3858.49 0.161362
\(831\) 10235.3 0.427265
\(832\) −1602.13 −0.0667596
\(833\) 0 0
\(834\) −88441.1 −3.67202
\(835\) −444.231 −0.0184111
\(836\) −60356.4 −2.49697
\(837\) −5276.13 −0.217885
\(838\) −29004.0 −1.19562
\(839\) −9128.63 −0.375632 −0.187816 0.982204i \(-0.560141\pi\)
−0.187816 + 0.982204i \(0.560141\pi\)
\(840\) 0 0
\(841\) −22685.0 −0.930131
\(842\) 9441.58 0.386435
\(843\) 10146.5 0.414547
\(844\) −48634.4 −1.98349
\(845\) 1888.32 0.0768759
\(846\) 104638. 4.25240
\(847\) 0 0
\(848\) −32198.0 −1.30387
\(849\) 26822.2 1.08426
\(850\) 10627.0 0.428826
\(851\) 23495.7 0.946442
\(852\) 98416.1 3.95737
\(853\) −27204.8 −1.09200 −0.545999 0.837786i \(-0.683850\pi\)
−0.545999 + 0.837786i \(0.683850\pi\)
\(854\) 0 0
\(855\) −2641.12 −0.105643
\(856\) 22769.8 0.909179
\(857\) 38060.0 1.51704 0.758520 0.651649i \(-0.225923\pi\)
0.758520 + 0.651649i \(0.225923\pi\)
\(858\) −18004.9 −0.716405
\(859\) 33326.2 1.32372 0.661860 0.749627i \(-0.269767\pi\)
0.661860 + 0.749627i \(0.269767\pi\)
\(860\) −4260.24 −0.168922
\(861\) 0 0
\(862\) −422.378 −0.0166894
\(863\) −41724.2 −1.64578 −0.822890 0.568201i \(-0.807640\pi\)
−0.822890 + 0.568201i \(0.807640\pi\)
\(864\) 17475.4 0.688108
\(865\) −2294.06 −0.0901737
\(866\) −77223.8 −3.03022
\(867\) −2449.38 −0.0959460
\(868\) 0 0
\(869\) −56569.7 −2.20828
\(870\) 1559.42 0.0607694
\(871\) 124.068 0.00482649
\(872\) 58907.5 2.28768
\(873\) 17009.6 0.659438
\(874\) −60328.6 −2.33483
\(875\) 0 0
\(876\) 28411.6 1.09582
\(877\) −49337.3 −1.89966 −0.949830 0.312767i \(-0.898744\pi\)
−0.949830 + 0.312767i \(0.898744\pi\)
\(878\) 15423.3 0.592838
\(879\) 63194.0 2.42489
\(880\) 4526.57 0.173398
\(881\) −8845.46 −0.338265 −0.169132 0.985593i \(-0.554097\pi\)
−0.169132 + 0.985593i \(0.554097\pi\)
\(882\) 0 0
\(883\) 14724.2 0.561165 0.280582 0.959830i \(-0.409472\pi\)
0.280582 + 0.959830i \(0.409472\pi\)
\(884\) 2374.10 0.0903277
\(885\) −5094.36 −0.193497
\(886\) 9023.14 0.342143
\(887\) −3864.38 −0.146283 −0.0731415 0.997322i \(-0.523302\pi\)
−0.0731415 + 0.997322i \(0.523302\pi\)
\(888\) 51858.1 1.95974
\(889\) 0 0
\(890\) −5034.28 −0.189606
\(891\) −3688.07 −0.138670
\(892\) −81160.9 −3.04649
\(893\) −30849.1 −1.15602
\(894\) −79023.2 −2.95630
\(895\) −1918.10 −0.0716368
\(896\) 0 0
\(897\) −12311.8 −0.458283
\(898\) −12577.2 −0.467379
\(899\) −1441.14 −0.0534648
\(900\) −96485.6 −3.57354
\(901\) −5609.04 −0.207397
\(902\) 4719.92 0.174231
\(903\) 0 0
\(904\) 47560.6 1.74982
\(905\) −1705.45 −0.0626421
\(906\) 87473.7 3.20764
\(907\) −743.409 −0.0272155 −0.0136078 0.999907i \(-0.504332\pi\)
−0.0136078 + 0.999907i \(0.504332\pi\)
\(908\) 24182.5 0.883839
\(909\) −5905.76 −0.215491
\(910\) 0 0
\(911\) 16291.0 0.592475 0.296238 0.955114i \(-0.404268\pi\)
0.296238 + 0.955114i \(0.404268\pi\)
\(912\) −55013.4 −1.99745
\(913\) −45336.8 −1.64340
\(914\) −74402.5 −2.69258
\(915\) −2554.33 −0.0922879
\(916\) −15500.6 −0.559122
\(917\) 0 0
\(918\) 12929.5 0.464856
\(919\) −6188.99 −0.222150 −0.111075 0.993812i \(-0.535429\pi\)
−0.111075 + 0.993812i \(0.535429\pi\)
\(920\) 7491.78 0.268474
\(921\) −55390.5 −1.98174
\(922\) −89311.6 −3.19015
\(923\) −5402.00 −0.192643
\(924\) 0 0
\(925\) −16193.8 −0.575620
\(926\) −93033.0 −3.30157
\(927\) −8786.47 −0.311311
\(928\) 4773.30 0.168848
\(929\) 31661.7 1.11818 0.559089 0.829108i \(-0.311151\pi\)
0.559089 + 0.829108i \(0.311151\pi\)
\(930\) −1318.84 −0.0465015
\(931\) 0 0
\(932\) 20724.3 0.728376
\(933\) −75734.8 −2.65750
\(934\) 37273.6 1.30581
\(935\) 788.551 0.0275811
\(936\) −16959.8 −0.592251
\(937\) −35010.5 −1.22064 −0.610322 0.792153i \(-0.708960\pi\)
−0.610322 + 0.792153i \(0.708960\pi\)
\(938\) 0 0
\(939\) −22279.2 −0.774286
\(940\) 7117.12 0.246952
\(941\) 45625.8 1.58061 0.790307 0.612711i \(-0.209921\pi\)
0.790307 + 0.612711i \(0.209921\pi\)
\(942\) 11217.2 0.387977
\(943\) 3227.51 0.111455
\(944\) −66227.5 −2.28339
\(945\) 0 0
\(946\) 73170.2 2.51477
\(947\) −21508.4 −0.738044 −0.369022 0.929421i \(-0.620307\pi\)
−0.369022 + 0.929421i \(0.620307\pi\)
\(948\) −158615. −5.43416
\(949\) −1559.50 −0.0533439
\(950\) 41579.8 1.42003
\(951\) −36177.4 −1.23358
\(952\) 0 0
\(953\) 35686.7 1.21302 0.606509 0.795076i \(-0.292569\pi\)
0.606509 + 0.795076i \(0.292569\pi\)
\(954\) 74440.5 2.52631
\(955\) 2465.34 0.0835355
\(956\) 85744.0 2.90079
\(957\) −18323.0 −0.618912
\(958\) −93357.8 −3.14849
\(959\) 0 0
\(960\) −1492.07 −0.0501630
\(961\) −28572.2 −0.959088
\(962\) −5288.17 −0.177232
\(963\) −21749.9 −0.727810
\(964\) 116133. 3.88006
\(965\) −2000.12 −0.0667215
\(966\) 0 0
\(967\) −3731.33 −0.124086 −0.0620432 0.998073i \(-0.519762\pi\)
−0.0620432 + 0.998073i \(0.519762\pi\)
\(968\) −66262.5 −2.20016
\(969\) −9583.60 −0.317719
\(970\) 1691.13 0.0559782
\(971\) −17645.1 −0.583171 −0.291585 0.956545i \(-0.594183\pi\)
−0.291585 + 0.956545i \(0.594183\pi\)
\(972\) 60358.3 1.99176
\(973\) 0 0
\(974\) −51348.7 −1.68924
\(975\) 8485.59 0.278725
\(976\) −33206.7 −1.08906
\(977\) 24941.2 0.816723 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(978\) −61631.8 −2.01510
\(979\) 59152.1 1.93106
\(980\) 0 0
\(981\) −56268.9 −1.83132
\(982\) 6277.85 0.204006
\(983\) 22506.2 0.730252 0.365126 0.930958i \(-0.381026\pi\)
0.365126 + 0.930958i \(0.381026\pi\)
\(984\) 7123.53 0.230782
\(985\) 1125.44 0.0364057
\(986\) 3531.62 0.114066
\(987\) 0 0
\(988\) 9289.07 0.299114
\(989\) 50034.2 1.60869
\(990\) −10465.3 −0.335967
\(991\) 32694.1 1.04799 0.523997 0.851720i \(-0.324440\pi\)
0.523997 + 0.851720i \(0.324440\pi\)
\(992\) −4036.88 −0.129205
\(993\) −8410.08 −0.268767
\(994\) 0 0
\(995\) −4246.32 −0.135294
\(996\) −127119. −4.04410
\(997\) −18248.8 −0.579686 −0.289843 0.957074i \(-0.593603\pi\)
−0.289843 + 0.957074i \(0.593603\pi\)
\(998\) −352.428 −0.0111783
\(999\) −19702.5 −0.623983
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 833.4.a.d.1.1 3
7.6 odd 2 17.4.a.b.1.1 3
21.20 even 2 153.4.a.g.1.3 3
28.27 even 2 272.4.a.h.1.1 3
35.13 even 4 425.4.b.f.324.6 6
35.27 even 4 425.4.b.f.324.1 6
35.34 odd 2 425.4.a.g.1.3 3
56.13 odd 2 1088.4.a.v.1.1 3
56.27 even 2 1088.4.a.x.1.3 3
77.76 even 2 2057.4.a.e.1.3 3
84.83 odd 2 2448.4.a.bi.1.2 3
119.13 odd 4 289.4.b.b.288.6 6
119.55 odd 4 289.4.b.b.288.5 6
119.118 odd 2 289.4.a.b.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.a.b.1.1 3 7.6 odd 2
153.4.a.g.1.3 3 21.20 even 2
272.4.a.h.1.1 3 28.27 even 2
289.4.a.b.1.1 3 119.118 odd 2
289.4.b.b.288.5 6 119.55 odd 4
289.4.b.b.288.6 6 119.13 odd 4
425.4.a.g.1.3 3 35.34 odd 2
425.4.b.f.324.1 6 35.27 even 4
425.4.b.f.324.6 6 35.13 even 4
833.4.a.d.1.1 3 1.1 even 1 trivial
1088.4.a.v.1.1 3 56.13 odd 2
1088.4.a.x.1.3 3 56.27 even 2
2057.4.a.e.1.3 3 77.76 even 2
2448.4.a.bi.1.2 3 84.83 odd 2