Properties

Label 4033.2.a.f.1.1
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +O(q^{10})\) \(q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +4.46684 q^{10} +3.88769 q^{11} +17.6881 q^{12} +3.80642 q^{13} +9.25654 q^{14} -5.03714 q^{15} +16.7659 q^{16} +1.84146 q^{17} -18.6820 q^{18} -6.95397 q^{19} -9.14036 q^{20} -10.4384 q^{21} -10.7636 q^{22} +4.09671 q^{23} -31.6839 q^{24} -2.39705 q^{25} -10.5386 q^{26} +11.7008 q^{27} -18.9414 q^{28} +3.22497 q^{29} +13.9461 q^{30} +1.83556 q^{31} -26.1224 q^{32} +12.1379 q^{33} -5.09834 q^{34} +5.39404 q^{35} +38.2284 q^{36} +1.00000 q^{37} +19.2531 q^{38} +11.8841 q^{39} +16.3727 q^{40} -2.86442 q^{41} +28.9001 q^{42} -1.93334 q^{43} +22.0253 q^{44} -10.8865 q^{45} -11.3423 q^{46} +7.27647 q^{47} +52.3453 q^{48} +4.17796 q^{49} +6.63657 q^{50} +5.74927 q^{51} +21.5648 q^{52} +5.78810 q^{53} -32.3954 q^{54} -6.27227 q^{55} +33.9288 q^{56} -21.7112 q^{57} -8.92879 q^{58} -12.5053 q^{59} -28.5374 q^{60} +7.02458 q^{61} -5.08200 q^{62} -22.5599 q^{63} +38.7920 q^{64} -6.14115 q^{65} -33.6055 q^{66} +14.0937 q^{67} +10.4326 q^{68} +12.7905 q^{69} -14.9342 q^{70} +2.13334 q^{71} -68.4769 q^{72} -3.64184 q^{73} -2.76864 q^{74} -7.48390 q^{75} -39.3970 q^{76} -12.9979 q^{77} -32.9029 q^{78} -9.58443 q^{79} -27.0495 q^{80} +16.2884 q^{81} +7.93055 q^{82} +9.85300 q^{83} -59.1374 q^{84} -2.97094 q^{85} +5.35272 q^{86} +10.0688 q^{87} -39.4530 q^{88} +14.5544 q^{89} +30.1409 q^{90} -12.7262 q^{91} +23.2095 q^{92} +5.73085 q^{93} -20.1460 q^{94} +11.2193 q^{95} -81.5577 q^{96} +2.55129 q^{97} -11.5673 q^{98} +26.2330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76864 −1.95773 −0.978864 0.204514i \(-0.934439\pi\)
−0.978864 + 0.204514i \(0.934439\pi\)
\(3\) 3.12213 1.80256 0.901282 0.433233i \(-0.142627\pi\)
0.901282 + 0.433233i \(0.142627\pi\)
\(4\) 5.66539 2.83270
\(5\) −1.61337 −0.721520 −0.360760 0.932659i \(-0.617483\pi\)
−0.360760 + 0.932659i \(0.617483\pi\)
\(6\) −8.64407 −3.52893
\(7\) −3.34335 −1.26367 −0.631833 0.775105i \(-0.717697\pi\)
−0.631833 + 0.775105i \(0.717697\pi\)
\(8\) −10.1482 −3.58792
\(9\) 6.74771 2.24924
\(10\) 4.46684 1.41254
\(11\) 3.88769 1.17218 0.586092 0.810245i \(-0.300666\pi\)
0.586092 + 0.810245i \(0.300666\pi\)
\(12\) 17.6881 5.10611
\(13\) 3.80642 1.05571 0.527855 0.849334i \(-0.322996\pi\)
0.527855 + 0.849334i \(0.322996\pi\)
\(14\) 9.25654 2.47391
\(15\) −5.03714 −1.30058
\(16\) 16.7659 4.19147
\(17\) 1.84146 0.446619 0.223309 0.974748i \(-0.428314\pi\)
0.223309 + 0.974748i \(0.428314\pi\)
\(18\) −18.6820 −4.40339
\(19\) −6.95397 −1.59535 −0.797676 0.603087i \(-0.793937\pi\)
−0.797676 + 0.603087i \(0.793937\pi\)
\(20\) −9.14036 −2.04385
\(21\) −10.4384 −2.27784
\(22\) −10.7636 −2.29482
\(23\) 4.09671 0.854223 0.427112 0.904199i \(-0.359531\pi\)
0.427112 + 0.904199i \(0.359531\pi\)
\(24\) −31.6839 −6.46745
\(25\) −2.39705 −0.479409
\(26\) −10.5386 −2.06679
\(27\) 11.7008 2.25183
\(28\) −18.9414 −3.57958
\(29\) 3.22497 0.598861 0.299431 0.954118i \(-0.403203\pi\)
0.299431 + 0.954118i \(0.403203\pi\)
\(30\) 13.9461 2.54619
\(31\) 1.83556 0.329676 0.164838 0.986321i \(-0.447290\pi\)
0.164838 + 0.986321i \(0.447290\pi\)
\(32\) −26.1224 −4.61784
\(33\) 12.1379 2.11293
\(34\) −5.09834 −0.874357
\(35\) 5.39404 0.911760
\(36\) 38.2284 6.37140
\(37\) 1.00000 0.164399
\(38\) 19.2531 3.12326
\(39\) 11.8841 1.90298
\(40\) 16.3727 2.58875
\(41\) −2.86442 −0.447347 −0.223673 0.974664i \(-0.571805\pi\)
−0.223673 + 0.974664i \(0.571805\pi\)
\(42\) 28.9001 4.45939
\(43\) −1.93334 −0.294831 −0.147416 0.989075i \(-0.547095\pi\)
−0.147416 + 0.989075i \(0.547095\pi\)
\(44\) 22.0253 3.32044
\(45\) −10.8865 −1.62287
\(46\) −11.3423 −1.67234
\(47\) 7.27647 1.06138 0.530691 0.847565i \(-0.321932\pi\)
0.530691 + 0.847565i \(0.321932\pi\)
\(48\) 52.3453 7.55539
\(49\) 4.17796 0.596852
\(50\) 6.63657 0.938553
\(51\) 5.74927 0.805058
\(52\) 21.5648 2.99051
\(53\) 5.78810 0.795057 0.397528 0.917590i \(-0.369868\pi\)
0.397528 + 0.917590i \(0.369868\pi\)
\(54\) −32.3954 −4.40846
\(55\) −6.27227 −0.845753
\(56\) 33.9288 4.53393
\(57\) −21.7112 −2.87572
\(58\) −8.92879 −1.17241
\(59\) −12.5053 −1.62805 −0.814023 0.580832i \(-0.802727\pi\)
−0.814023 + 0.580832i \(0.802727\pi\)
\(60\) −28.5374 −3.68416
\(61\) 7.02458 0.899405 0.449703 0.893178i \(-0.351530\pi\)
0.449703 + 0.893178i \(0.351530\pi\)
\(62\) −5.08200 −0.645415
\(63\) −22.5599 −2.84228
\(64\) 38.7920 4.84900
\(65\) −6.14115 −0.761716
\(66\) −33.6055 −4.13655
\(67\) 14.0937 1.72182 0.860909 0.508759i \(-0.169896\pi\)
0.860909 + 0.508759i \(0.169896\pi\)
\(68\) 10.4326 1.26513
\(69\) 12.7905 1.53979
\(70\) −14.9342 −1.78498
\(71\) 2.13334 0.253181 0.126590 0.991955i \(-0.459597\pi\)
0.126590 + 0.991955i \(0.459597\pi\)
\(72\) −68.4769 −8.07008
\(73\) −3.64184 −0.426245 −0.213123 0.977025i \(-0.568363\pi\)
−0.213123 + 0.977025i \(0.568363\pi\)
\(74\) −2.76864 −0.321848
\(75\) −7.48390 −0.864166
\(76\) −39.3970 −4.51915
\(77\) −12.9979 −1.48125
\(78\) −32.9029 −3.72553
\(79\) −9.58443 −1.07833 −0.539166 0.842199i \(-0.681261\pi\)
−0.539166 + 0.842199i \(0.681261\pi\)
\(80\) −27.0495 −3.02423
\(81\) 16.2884 1.80982
\(82\) 7.93055 0.875783
\(83\) 9.85300 1.08151 0.540754 0.841181i \(-0.318139\pi\)
0.540754 + 0.841181i \(0.318139\pi\)
\(84\) −59.1374 −6.45242
\(85\) −2.97094 −0.322244
\(86\) 5.35272 0.577199
\(87\) 10.0688 1.07949
\(88\) −39.4530 −4.20570
\(89\) 14.5544 1.54277 0.771383 0.636371i \(-0.219565\pi\)
0.771383 + 0.636371i \(0.219565\pi\)
\(90\) 30.1409 3.17713
\(91\) −12.7262 −1.33407
\(92\) 23.2095 2.41976
\(93\) 5.73085 0.594261
\(94\) −20.1460 −2.07790
\(95\) 11.2193 1.15108
\(96\) −81.5577 −8.32395
\(97\) 2.55129 0.259045 0.129522 0.991577i \(-0.458656\pi\)
0.129522 + 0.991577i \(0.458656\pi\)
\(98\) −11.5673 −1.16847
\(99\) 26.2330 2.63652
\(100\) −13.5802 −1.35802
\(101\) 1.73108 0.172249 0.0861246 0.996284i \(-0.472552\pi\)
0.0861246 + 0.996284i \(0.472552\pi\)
\(102\) −15.9177 −1.57608
\(103\) −14.2240 −1.40153 −0.700767 0.713390i \(-0.747159\pi\)
−0.700767 + 0.713390i \(0.747159\pi\)
\(104\) −38.6282 −3.78780
\(105\) 16.8409 1.64350
\(106\) −16.0252 −1.55650
\(107\) 9.11248 0.880937 0.440468 0.897768i \(-0.354812\pi\)
0.440468 + 0.897768i \(0.354812\pi\)
\(108\) 66.2898 6.37874
\(109\) −1.00000 −0.0957826
\(110\) 17.3657 1.65575
\(111\) 3.12213 0.296340
\(112\) −56.0542 −5.29662
\(113\) −3.16377 −0.297622 −0.148811 0.988866i \(-0.547545\pi\)
−0.148811 + 0.988866i \(0.547545\pi\)
\(114\) 60.1107 5.62988
\(115\) −6.60950 −0.616339
\(116\) 18.2707 1.69639
\(117\) 25.6846 2.37454
\(118\) 34.6226 3.18727
\(119\) −6.15662 −0.564377
\(120\) 51.1178 4.66639
\(121\) 4.11415 0.374014
\(122\) −19.4486 −1.76079
\(123\) −8.94309 −0.806371
\(124\) 10.3991 0.933871
\(125\) 11.9342 1.06742
\(126\) 62.4604 5.56441
\(127\) 14.3425 1.27269 0.636346 0.771404i \(-0.280445\pi\)
0.636346 + 0.771404i \(0.280445\pi\)
\(128\) −55.1563 −4.87518
\(129\) −6.03613 −0.531452
\(130\) 17.0027 1.49123
\(131\) −9.83339 −0.859147 −0.429574 0.903032i \(-0.641336\pi\)
−0.429574 + 0.903032i \(0.641336\pi\)
\(132\) 68.7659 5.98530
\(133\) 23.2495 2.01599
\(134\) −39.0204 −3.37085
\(135\) −18.8777 −1.62474
\(136\) −18.6874 −1.60243
\(137\) −8.50721 −0.726820 −0.363410 0.931629i \(-0.618388\pi\)
−0.363410 + 0.931629i \(0.618388\pi\)
\(138\) −35.4123 −3.01449
\(139\) 10.1041 0.857019 0.428509 0.903537i \(-0.359039\pi\)
0.428509 + 0.903537i \(0.359039\pi\)
\(140\) 30.5594 2.58274
\(141\) 22.7181 1.91321
\(142\) −5.90646 −0.495659
\(143\) 14.7982 1.23749
\(144\) 113.131 9.42761
\(145\) −5.20306 −0.432090
\(146\) 10.0830 0.834472
\(147\) 13.0441 1.07586
\(148\) 5.66539 0.465692
\(149\) 14.7565 1.20890 0.604450 0.796643i \(-0.293393\pi\)
0.604450 + 0.796643i \(0.293393\pi\)
\(150\) 20.7203 1.69180
\(151\) −18.5105 −1.50636 −0.753182 0.657813i \(-0.771482\pi\)
−0.753182 + 0.657813i \(0.771482\pi\)
\(152\) 70.5701 5.72399
\(153\) 12.4256 1.00455
\(154\) 35.9866 2.89988
\(155\) −2.96143 −0.237867
\(156\) 67.3283 5.39058
\(157\) 1.29859 0.103639 0.0518195 0.998656i \(-0.483498\pi\)
0.0518195 + 0.998656i \(0.483498\pi\)
\(158\) 26.5359 2.11108
\(159\) 18.0712 1.43314
\(160\) 42.1451 3.33186
\(161\) −13.6967 −1.07945
\(162\) −45.0968 −3.54314
\(163\) −10.0122 −0.784213 −0.392106 0.919920i \(-0.628254\pi\)
−0.392106 + 0.919920i \(0.628254\pi\)
\(164\) −16.2280 −1.26720
\(165\) −19.5829 −1.52452
\(166\) −27.2795 −2.11730
\(167\) 24.2850 1.87923 0.939614 0.342237i \(-0.111185\pi\)
0.939614 + 0.342237i \(0.111185\pi\)
\(168\) 105.930 8.17270
\(169\) 1.48881 0.114524
\(170\) 8.22549 0.630866
\(171\) −46.9234 −3.58832
\(172\) −10.9531 −0.835167
\(173\) −25.2346 −1.91855 −0.959275 0.282473i \(-0.908845\pi\)
−0.959275 + 0.282473i \(0.908845\pi\)
\(174\) −27.8769 −2.11334
\(175\) 8.01416 0.605813
\(176\) 65.1806 4.91317
\(177\) −39.0431 −2.93466
\(178\) −40.2960 −3.02031
\(179\) 23.2089 1.73472 0.867358 0.497685i \(-0.165817\pi\)
0.867358 + 0.497685i \(0.165817\pi\)
\(180\) −61.6764 −4.59709
\(181\) 12.8021 0.951574 0.475787 0.879560i \(-0.342163\pi\)
0.475787 + 0.879560i \(0.342163\pi\)
\(182\) 35.2342 2.61174
\(183\) 21.9317 1.62123
\(184\) −41.5741 −3.06488
\(185\) −1.61337 −0.118617
\(186\) −15.8667 −1.16340
\(187\) 7.15901 0.523519
\(188\) 41.2241 3.00658
\(189\) −39.1199 −2.84556
\(190\) −31.0623 −2.25350
\(191\) 21.2022 1.53414 0.767068 0.641566i \(-0.221715\pi\)
0.767068 + 0.641566i \(0.221715\pi\)
\(192\) 121.114 8.74063
\(193\) −8.81889 −0.634798 −0.317399 0.948292i \(-0.602809\pi\)
−0.317399 + 0.948292i \(0.602809\pi\)
\(194\) −7.06362 −0.507139
\(195\) −19.1735 −1.37304
\(196\) 23.6698 1.69070
\(197\) 17.5294 1.24892 0.624461 0.781056i \(-0.285319\pi\)
0.624461 + 0.781056i \(0.285319\pi\)
\(198\) −72.6299 −5.16158
\(199\) −14.0884 −0.998697 −0.499348 0.866401i \(-0.666427\pi\)
−0.499348 + 0.866401i \(0.666427\pi\)
\(200\) 24.3256 1.72008
\(201\) 44.0023 3.10369
\(202\) −4.79275 −0.337217
\(203\) −10.7822 −0.756761
\(204\) 32.5718 2.28049
\(205\) 4.62136 0.322769
\(206\) 39.3813 2.74382
\(207\) 27.6434 1.92135
\(208\) 63.8180 4.42498
\(209\) −27.0349 −1.87004
\(210\) −46.6265 −3.21753
\(211\) −16.2991 −1.12208 −0.561038 0.827790i \(-0.689598\pi\)
−0.561038 + 0.827790i \(0.689598\pi\)
\(212\) 32.7919 2.25215
\(213\) 6.66057 0.456375
\(214\) −25.2292 −1.72463
\(215\) 3.11918 0.212726
\(216\) −118.742 −8.07937
\(217\) −6.13690 −0.416600
\(218\) 2.76864 0.187516
\(219\) −11.3703 −0.768335
\(220\) −35.5349 −2.39576
\(221\) 7.00935 0.471500
\(222\) −8.64407 −0.580152
\(223\) 11.5553 0.773797 0.386899 0.922122i \(-0.373546\pi\)
0.386899 + 0.922122i \(0.373546\pi\)
\(224\) 87.3364 5.83541
\(225\) −16.1746 −1.07830
\(226\) 8.75934 0.582663
\(227\) 0.204192 0.0135527 0.00677635 0.999977i \(-0.497843\pi\)
0.00677635 + 0.999977i \(0.497843\pi\)
\(228\) −123.003 −8.14605
\(229\) 4.75914 0.314493 0.157246 0.987559i \(-0.449738\pi\)
0.157246 + 0.987559i \(0.449738\pi\)
\(230\) 18.2994 1.20662
\(231\) −40.5812 −2.67004
\(232\) −32.7275 −2.14867
\(233\) −20.4066 −1.33688 −0.668442 0.743764i \(-0.733038\pi\)
−0.668442 + 0.743764i \(0.733038\pi\)
\(234\) −71.1115 −4.64870
\(235\) −11.7396 −0.765809
\(236\) −70.8472 −4.61176
\(237\) −29.9238 −1.94376
\(238\) 17.0455 1.10490
\(239\) 23.8903 1.54534 0.772668 0.634811i \(-0.218922\pi\)
0.772668 + 0.634811i \(0.218922\pi\)
\(240\) −84.4522 −5.45136
\(241\) −10.3426 −0.666224 −0.333112 0.942887i \(-0.608099\pi\)
−0.333112 + 0.942887i \(0.608099\pi\)
\(242\) −11.3906 −0.732217
\(243\) 15.7521 1.01050
\(244\) 39.7970 2.54774
\(245\) −6.74059 −0.430640
\(246\) 24.7602 1.57865
\(247\) −26.4697 −1.68423
\(248\) −18.6275 −1.18285
\(249\) 30.7624 1.94949
\(250\) −33.0414 −2.08972
\(251\) 1.75869 0.111008 0.0555038 0.998458i \(-0.482323\pi\)
0.0555038 + 0.998458i \(0.482323\pi\)
\(252\) −127.811 −8.05132
\(253\) 15.9268 1.00131
\(254\) −39.7093 −2.49158
\(255\) −9.27568 −0.580865
\(256\) 75.1243 4.69527
\(257\) 30.8732 1.92582 0.962908 0.269828i \(-0.0869670\pi\)
0.962908 + 0.269828i \(0.0869670\pi\)
\(258\) 16.7119 1.04044
\(259\) −3.34335 −0.207745
\(260\) −34.7920 −2.15771
\(261\) 21.7611 1.34698
\(262\) 27.2252 1.68198
\(263\) 7.80846 0.481491 0.240745 0.970588i \(-0.422608\pi\)
0.240745 + 0.970588i \(0.422608\pi\)
\(264\) −123.177 −7.58104
\(265\) −9.33833 −0.573649
\(266\) −64.3697 −3.94676
\(267\) 45.4408 2.78093
\(268\) 79.8462 4.87739
\(269\) 11.2276 0.684558 0.342279 0.939598i \(-0.388801\pi\)
0.342279 + 0.939598i \(0.388801\pi\)
\(270\) 52.2657 3.18079
\(271\) 0.492152 0.0298961 0.0149480 0.999888i \(-0.495242\pi\)
0.0149480 + 0.999888i \(0.495242\pi\)
\(272\) 30.8736 1.87199
\(273\) −39.7328 −2.40474
\(274\) 23.5534 1.42291
\(275\) −9.31898 −0.561956
\(276\) 72.4630 4.36176
\(277\) 26.2559 1.57757 0.788783 0.614672i \(-0.210712\pi\)
0.788783 + 0.614672i \(0.210712\pi\)
\(278\) −27.9747 −1.67781
\(279\) 12.3858 0.741518
\(280\) −54.7397 −3.27132
\(281\) −18.9457 −1.13021 −0.565103 0.825021i \(-0.691163\pi\)
−0.565103 + 0.825021i \(0.691163\pi\)
\(282\) −62.8984 −3.74554
\(283\) 22.5710 1.34170 0.670852 0.741591i \(-0.265928\pi\)
0.670852 + 0.741591i \(0.265928\pi\)
\(284\) 12.0862 0.717185
\(285\) 35.0282 2.07489
\(286\) −40.9709 −2.42266
\(287\) 9.57674 0.565297
\(288\) −176.267 −10.3866
\(289\) −13.6090 −0.800532
\(290\) 14.4054 0.845915
\(291\) 7.96547 0.466944
\(292\) −20.6325 −1.20742
\(293\) 19.5955 1.14478 0.572392 0.819980i \(-0.306016\pi\)
0.572392 + 0.819980i \(0.306016\pi\)
\(294\) −36.1146 −2.10625
\(295\) 20.1756 1.17467
\(296\) −10.1482 −0.589850
\(297\) 45.4892 2.63955
\(298\) −40.8555 −2.36670
\(299\) 15.5938 0.901812
\(300\) −42.3992 −2.44792
\(301\) 6.46381 0.372568
\(302\) 51.2490 2.94905
\(303\) 5.40467 0.310490
\(304\) −116.590 −6.68687
\(305\) −11.3332 −0.648938
\(306\) −34.4021 −1.96664
\(307\) 33.6617 1.92117 0.960586 0.277982i \(-0.0896657\pi\)
0.960586 + 0.277982i \(0.0896657\pi\)
\(308\) −73.6382 −4.19593
\(309\) −44.4093 −2.52635
\(310\) 8.19914 0.465680
\(311\) −0.765802 −0.0434246 −0.0217123 0.999764i \(-0.506912\pi\)
−0.0217123 + 0.999764i \(0.506912\pi\)
\(312\) −120.602 −6.82776
\(313\) −8.97560 −0.507331 −0.253665 0.967292i \(-0.581636\pi\)
−0.253665 + 0.967292i \(0.581636\pi\)
\(314\) −3.59534 −0.202897
\(315\) 36.3974 2.05076
\(316\) −54.2995 −3.05459
\(317\) −11.1037 −0.623645 −0.311823 0.950140i \(-0.600939\pi\)
−0.311823 + 0.950140i \(0.600939\pi\)
\(318\) −50.0328 −2.80570
\(319\) 12.5377 0.701975
\(320\) −62.5857 −3.49865
\(321\) 28.4504 1.58794
\(322\) 37.9214 2.11327
\(323\) −12.8054 −0.712513
\(324\) 92.2803 5.12668
\(325\) −9.12416 −0.506117
\(326\) 27.7201 1.53527
\(327\) −3.12213 −0.172654
\(328\) 29.0686 1.60504
\(329\) −24.3278 −1.34123
\(330\) 54.2180 2.98460
\(331\) 18.3752 1.00999 0.504996 0.863122i \(-0.331494\pi\)
0.504996 + 0.863122i \(0.331494\pi\)
\(332\) 55.8211 3.06358
\(333\) 6.74771 0.369772
\(334\) −67.2364 −3.67901
\(335\) −22.7383 −1.24233
\(336\) −175.008 −9.54749
\(337\) 20.6948 1.12732 0.563658 0.826008i \(-0.309394\pi\)
0.563658 + 0.826008i \(0.309394\pi\)
\(338\) −4.12199 −0.224207
\(339\) −9.87769 −0.536483
\(340\) −16.8316 −0.912819
\(341\) 7.13608 0.386440
\(342\) 129.914 7.02495
\(343\) 9.43505 0.509445
\(344\) 19.6198 1.05783
\(345\) −20.6357 −1.11099
\(346\) 69.8656 3.75600
\(347\) −0.106910 −0.00573921 −0.00286961 0.999996i \(-0.500913\pi\)
−0.00286961 + 0.999996i \(0.500913\pi\)
\(348\) 57.0436 3.05786
\(349\) −27.1790 −1.45486 −0.727429 0.686183i \(-0.759285\pi\)
−0.727429 + 0.686183i \(0.759285\pi\)
\(350\) −22.1884 −1.18602
\(351\) 44.5382 2.37728
\(352\) −101.556 −5.41295
\(353\) −30.9054 −1.64493 −0.822463 0.568819i \(-0.807401\pi\)
−0.822463 + 0.568819i \(0.807401\pi\)
\(354\) 108.096 5.74526
\(355\) −3.44186 −0.182675
\(356\) 82.4565 4.37019
\(357\) −19.2218 −1.01732
\(358\) −64.2572 −3.39610
\(359\) 32.8630 1.73444 0.867221 0.497924i \(-0.165904\pi\)
0.867221 + 0.497924i \(0.165904\pi\)
\(360\) 110.478 5.82272
\(361\) 29.3578 1.54515
\(362\) −35.4445 −1.86292
\(363\) 12.8449 0.674184
\(364\) −72.0987 −3.77900
\(365\) 5.87563 0.307544
\(366\) −60.7210 −3.17394
\(367\) −16.4096 −0.856572 −0.428286 0.903643i \(-0.640882\pi\)
−0.428286 + 0.903643i \(0.640882\pi\)
\(368\) 68.6850 3.58045
\(369\) −19.3282 −1.00619
\(370\) 4.46684 0.232220
\(371\) −19.3516 −1.00469
\(372\) 32.4675 1.68336
\(373\) −27.6209 −1.43016 −0.715079 0.699043i \(-0.753609\pi\)
−0.715079 + 0.699043i \(0.753609\pi\)
\(374\) −19.8208 −1.02491
\(375\) 37.2600 1.92410
\(376\) −73.8429 −3.80816
\(377\) 12.2756 0.632224
\(378\) 108.309 5.57082
\(379\) −11.3449 −0.582749 −0.291374 0.956609i \(-0.594113\pi\)
−0.291374 + 0.956609i \(0.594113\pi\)
\(380\) 63.5618 3.26065
\(381\) 44.7792 2.29411
\(382\) −58.7013 −3.00342
\(383\) 37.6711 1.92490 0.962452 0.271452i \(-0.0875040\pi\)
0.962452 + 0.271452i \(0.0875040\pi\)
\(384\) −172.205 −8.78782
\(385\) 20.9704 1.06875
\(386\) 24.4164 1.24276
\(387\) −13.0456 −0.663144
\(388\) 14.4541 0.733794
\(389\) 3.22236 0.163380 0.0816902 0.996658i \(-0.473968\pi\)
0.0816902 + 0.996658i \(0.473968\pi\)
\(390\) 53.0845 2.68804
\(391\) 7.54391 0.381512
\(392\) −42.3987 −2.14146
\(393\) −30.7011 −1.54867
\(394\) −48.5328 −2.44505
\(395\) 15.4632 0.778038
\(396\) 148.620 7.46845
\(397\) −3.41350 −0.171319 −0.0856594 0.996324i \(-0.527300\pi\)
−0.0856594 + 0.996324i \(0.527300\pi\)
\(398\) 39.0056 1.95518
\(399\) 72.5881 3.63395
\(400\) −40.1886 −2.00943
\(401\) −27.5181 −1.37419 −0.687095 0.726568i \(-0.741114\pi\)
−0.687095 + 0.726568i \(0.741114\pi\)
\(402\) −121.827 −6.07617
\(403\) 6.98689 0.348042
\(404\) 9.80726 0.487929
\(405\) −26.2792 −1.30582
\(406\) 29.8520 1.48153
\(407\) 3.88769 0.192706
\(408\) −58.3445 −2.88848
\(409\) 12.6710 0.626540 0.313270 0.949664i \(-0.398575\pi\)
0.313270 + 0.949664i \(0.398575\pi\)
\(410\) −12.7949 −0.631895
\(411\) −26.5606 −1.31014
\(412\) −80.5847 −3.97012
\(413\) 41.8094 2.05731
\(414\) −76.5348 −3.76148
\(415\) −15.8965 −0.780329
\(416\) −99.4329 −4.87510
\(417\) 31.5463 1.54483
\(418\) 74.8501 3.66104
\(419\) −24.5440 −1.19905 −0.599527 0.800355i \(-0.704645\pi\)
−0.599527 + 0.800355i \(0.704645\pi\)
\(420\) 95.4104 4.65555
\(421\) 21.5089 1.04828 0.524140 0.851632i \(-0.324387\pi\)
0.524140 + 0.851632i \(0.324387\pi\)
\(422\) 45.1264 2.19672
\(423\) 49.0995 2.38730
\(424\) −58.7386 −2.85260
\(425\) −4.41406 −0.214113
\(426\) −18.4407 −0.893457
\(427\) −23.4856 −1.13655
\(428\) 51.6258 2.49543
\(429\) 46.2019 2.23065
\(430\) −8.63590 −0.416460
\(431\) −20.0907 −0.967734 −0.483867 0.875142i \(-0.660768\pi\)
−0.483867 + 0.875142i \(0.660768\pi\)
\(432\) 196.175 9.43847
\(433\) 12.6758 0.609158 0.304579 0.952487i \(-0.401484\pi\)
0.304579 + 0.952487i \(0.401484\pi\)
\(434\) 16.9909 0.815589
\(435\) −16.2446 −0.778870
\(436\) −5.66539 −0.271323
\(437\) −28.4884 −1.36279
\(438\) 31.4804 1.50419
\(439\) −17.8879 −0.853742 −0.426871 0.904313i \(-0.640384\pi\)
−0.426871 + 0.904313i \(0.640384\pi\)
\(440\) 63.6521 3.03449
\(441\) 28.1917 1.34246
\(442\) −19.4064 −0.923068
\(443\) 2.23203 0.106047 0.0530235 0.998593i \(-0.483114\pi\)
0.0530235 + 0.998593i \(0.483114\pi\)
\(444\) 17.6881 0.839440
\(445\) −23.4816 −1.11314
\(446\) −31.9924 −1.51488
\(447\) 46.0717 2.17912
\(448\) −129.695 −6.12751
\(449\) −34.4729 −1.62688 −0.813438 0.581652i \(-0.802407\pi\)
−0.813438 + 0.581652i \(0.802407\pi\)
\(450\) 44.7816 2.11103
\(451\) −11.1360 −0.524372
\(452\) −17.9240 −0.843073
\(453\) −57.7922 −2.71532
\(454\) −0.565335 −0.0265325
\(455\) 20.5320 0.962554
\(456\) 220.329 10.3179
\(457\) 17.3065 0.809562 0.404781 0.914414i \(-0.367348\pi\)
0.404781 + 0.914414i \(0.367348\pi\)
\(458\) −13.1764 −0.615691
\(459\) 21.5466 1.00571
\(460\) −37.4454 −1.74590
\(461\) 21.8186 1.01619 0.508097 0.861300i \(-0.330349\pi\)
0.508097 + 0.861300i \(0.330349\pi\)
\(462\) 112.355 5.22722
\(463\) 36.0980 1.67762 0.838809 0.544426i \(-0.183252\pi\)
0.838809 + 0.544426i \(0.183252\pi\)
\(464\) 54.0694 2.51011
\(465\) −9.24596 −0.428771
\(466\) 56.4988 2.61725
\(467\) 7.60070 0.351718 0.175859 0.984415i \(-0.443730\pi\)
0.175859 + 0.984415i \(0.443730\pi\)
\(468\) 145.513 6.72635
\(469\) −47.1201 −2.17580
\(470\) 32.5028 1.49924
\(471\) 4.05438 0.186816
\(472\) 126.905 5.84130
\(473\) −7.51622 −0.345596
\(474\) 82.8485 3.80536
\(475\) 16.6690 0.764827
\(476\) −34.8797 −1.59871
\(477\) 39.0564 1.78827
\(478\) −66.1438 −3.02534
\(479\) −22.9636 −1.04923 −0.524616 0.851339i \(-0.675791\pi\)
−0.524616 + 0.851339i \(0.675791\pi\)
\(480\) 131.583 6.00589
\(481\) 3.80642 0.173558
\(482\) 28.6349 1.30428
\(483\) −42.7630 −1.94578
\(484\) 23.3083 1.05947
\(485\) −4.11617 −0.186906
\(486\) −43.6119 −1.97828
\(487\) 23.7112 1.07446 0.537229 0.843436i \(-0.319471\pi\)
0.537229 + 0.843436i \(0.319471\pi\)
\(488\) −71.2866 −3.22699
\(489\) −31.2593 −1.41359
\(490\) 18.6623 0.843076
\(491\) −6.19229 −0.279454 −0.139727 0.990190i \(-0.544623\pi\)
−0.139727 + 0.990190i \(0.544623\pi\)
\(492\) −50.6661 −2.28420
\(493\) 5.93863 0.267463
\(494\) 73.2853 3.29726
\(495\) −42.3235 −1.90230
\(496\) 30.7747 1.38183
\(497\) −7.13249 −0.319936
\(498\) −85.1701 −3.81656
\(499\) −40.9988 −1.83536 −0.917680 0.397321i \(-0.869940\pi\)
−0.917680 + 0.397321i \(0.869940\pi\)
\(500\) 67.6116 3.02368
\(501\) 75.8209 3.38743
\(502\) −4.86919 −0.217323
\(503\) 18.0643 0.805446 0.402723 0.915322i \(-0.368064\pi\)
0.402723 + 0.915322i \(0.368064\pi\)
\(504\) 228.942 10.1979
\(505\) −2.79287 −0.124281
\(506\) −44.0955 −1.96028
\(507\) 4.64827 0.206437
\(508\) 81.2560 3.60515
\(509\) 21.2323 0.941103 0.470552 0.882373i \(-0.344055\pi\)
0.470552 + 0.882373i \(0.344055\pi\)
\(510\) 25.6810 1.13718
\(511\) 12.1759 0.538632
\(512\) −97.6798 −4.31688
\(513\) −81.3673 −3.59245
\(514\) −85.4769 −3.77022
\(515\) 22.9486 1.01123
\(516\) −34.1971 −1.50544
\(517\) 28.2887 1.24414
\(518\) 9.25654 0.406709
\(519\) −78.7857 −3.45831
\(520\) 62.3214 2.73297
\(521\) −10.1868 −0.446292 −0.223146 0.974785i \(-0.571633\pi\)
−0.223146 + 0.974785i \(0.571633\pi\)
\(522\) −60.2488 −2.63702
\(523\) −12.5749 −0.549863 −0.274932 0.961464i \(-0.588655\pi\)
−0.274932 + 0.961464i \(0.588655\pi\)
\(524\) −55.7100 −2.43370
\(525\) 25.0213 1.09202
\(526\) −21.6189 −0.942627
\(527\) 3.38010 0.147239
\(528\) 203.502 8.85631
\(529\) −6.21696 −0.270302
\(530\) 25.8545 1.12305
\(531\) −84.3818 −3.66186
\(532\) 131.718 5.71069
\(533\) −10.9032 −0.472269
\(534\) −125.809 −5.44431
\(535\) −14.7018 −0.635613
\(536\) −143.025 −6.17774
\(537\) 72.4613 3.12693
\(538\) −31.0852 −1.34018
\(539\) 16.2426 0.699620
\(540\) −106.950 −4.60239
\(541\) −32.3227 −1.38966 −0.694831 0.719173i \(-0.744521\pi\)
−0.694831 + 0.719173i \(0.744521\pi\)
\(542\) −1.36259 −0.0585284
\(543\) 39.9699 1.71527
\(544\) −48.1033 −2.06241
\(545\) 1.61337 0.0691090
\(546\) 110.006 4.70782
\(547\) 19.7943 0.846342 0.423171 0.906050i \(-0.360917\pi\)
0.423171 + 0.906050i \(0.360917\pi\)
\(548\) −48.1967 −2.05886
\(549\) 47.3998 2.02297
\(550\) 25.8010 1.10016
\(551\) −22.4263 −0.955394
\(552\) −129.800 −5.52465
\(553\) 32.0441 1.36265
\(554\) −72.6933 −3.08844
\(555\) −5.03714 −0.213815
\(556\) 57.2437 2.42767
\(557\) −28.9516 −1.22672 −0.613358 0.789805i \(-0.710182\pi\)
−0.613358 + 0.789805i \(0.710182\pi\)
\(558\) −34.2919 −1.45169
\(559\) −7.35909 −0.311256
\(560\) 90.4359 3.82162
\(561\) 22.3514 0.943676
\(562\) 52.4539 2.21263
\(563\) −0.477589 −0.0201280 −0.0100640 0.999949i \(-0.503204\pi\)
−0.0100640 + 0.999949i \(0.503204\pi\)
\(564\) 128.707 5.41954
\(565\) 5.10431 0.214740
\(566\) −62.4910 −2.62669
\(567\) −54.4578 −2.28701
\(568\) −21.6495 −0.908393
\(569\) −12.6469 −0.530186 −0.265093 0.964223i \(-0.585403\pi\)
−0.265093 + 0.964223i \(0.585403\pi\)
\(570\) −96.9806 −4.06207
\(571\) 20.4305 0.854990 0.427495 0.904018i \(-0.359396\pi\)
0.427495 + 0.904018i \(0.359396\pi\)
\(572\) 83.8375 3.50542
\(573\) 66.1960 2.76538
\(574\) −26.5146 −1.10670
\(575\) −9.82001 −0.409523
\(576\) 261.757 10.9065
\(577\) 34.5195 1.43706 0.718532 0.695494i \(-0.244814\pi\)
0.718532 + 0.695494i \(0.244814\pi\)
\(578\) 37.6786 1.56722
\(579\) −27.5337 −1.14426
\(580\) −29.4774 −1.22398
\(581\) −32.9420 −1.36666
\(582\) −22.0536 −0.914149
\(583\) 22.5024 0.931952
\(584\) 36.9580 1.52933
\(585\) −41.4387 −1.71328
\(586\) −54.2531 −2.24117
\(587\) 5.38327 0.222191 0.111096 0.993810i \(-0.464564\pi\)
0.111096 + 0.993810i \(0.464564\pi\)
\(588\) 73.9002 3.04759
\(589\) −12.7644 −0.525949
\(590\) −55.8590 −2.29968
\(591\) 54.7292 2.25126
\(592\) 16.7659 0.689074
\(593\) −13.9864 −0.574353 −0.287176 0.957878i \(-0.592717\pi\)
−0.287176 + 0.957878i \(0.592717\pi\)
\(594\) −125.944 −5.16752
\(595\) 9.93289 0.407209
\(596\) 83.6013 3.42444
\(597\) −43.9857 −1.80021
\(598\) −43.1737 −1.76550
\(599\) −42.3275 −1.72945 −0.864727 0.502241i \(-0.832509\pi\)
−0.864727 + 0.502241i \(0.832509\pi\)
\(600\) 75.9479 3.10056
\(601\) 15.3659 0.626789 0.313394 0.949623i \(-0.398534\pi\)
0.313394 + 0.949623i \(0.398534\pi\)
\(602\) −17.8960 −0.729386
\(603\) 95.1000 3.87277
\(604\) −104.869 −4.26707
\(605\) −6.63764 −0.269858
\(606\) −14.9636 −0.607855
\(607\) −30.1097 −1.22211 −0.611057 0.791587i \(-0.709255\pi\)
−0.611057 + 0.791587i \(0.709255\pi\)
\(608\) 181.655 7.36708
\(609\) −33.6634 −1.36411
\(610\) 31.3777 1.27044
\(611\) 27.6973 1.12051
\(612\) 70.3959 2.84559
\(613\) −46.3485 −1.87200 −0.936000 0.352000i \(-0.885502\pi\)
−0.936000 + 0.352000i \(0.885502\pi\)
\(614\) −93.1972 −3.76113
\(615\) 14.4285 0.581812
\(616\) 131.905 5.31460
\(617\) 24.7591 0.996764 0.498382 0.866957i \(-0.333928\pi\)
0.498382 + 0.866957i \(0.333928\pi\)
\(618\) 122.953 4.94591
\(619\) 13.7396 0.552240 0.276120 0.961123i \(-0.410951\pi\)
0.276120 + 0.961123i \(0.410951\pi\)
\(620\) −16.7776 −0.673806
\(621\) 47.9349 1.92356
\(622\) 2.12023 0.0850136
\(623\) −48.6605 −1.94954
\(624\) 199.248 7.97631
\(625\) −7.26893 −0.290757
\(626\) 24.8502 0.993215
\(627\) −84.4066 −3.37087
\(628\) 7.35704 0.293578
\(629\) 1.84146 0.0734236
\(630\) −100.772 −4.01483
\(631\) 8.02661 0.319534 0.159767 0.987155i \(-0.448926\pi\)
0.159767 + 0.987155i \(0.448926\pi\)
\(632\) 97.2644 3.86897
\(633\) −50.8879 −2.02261
\(634\) 30.7422 1.22093
\(635\) −23.1397 −0.918273
\(636\) 102.380 4.05965
\(637\) 15.9031 0.630102
\(638\) −34.7124 −1.37428
\(639\) 14.3952 0.569463
\(640\) 88.9874 3.51754
\(641\) 12.9124 0.510009 0.255005 0.966940i \(-0.417923\pi\)
0.255005 + 0.966940i \(0.417923\pi\)
\(642\) −78.7689 −3.10876
\(643\) 4.69458 0.185136 0.0925681 0.995706i \(-0.470492\pi\)
0.0925681 + 0.995706i \(0.470492\pi\)
\(644\) −77.5973 −3.05776
\(645\) 9.73849 0.383453
\(646\) 35.4537 1.39491
\(647\) −28.9482 −1.13807 −0.569036 0.822313i \(-0.692683\pi\)
−0.569036 + 0.822313i \(0.692683\pi\)
\(648\) −165.298 −6.49350
\(649\) −48.6166 −1.90837
\(650\) 25.2616 0.990840
\(651\) −19.1602 −0.750948
\(652\) −56.7228 −2.22144
\(653\) −35.6751 −1.39607 −0.698037 0.716062i \(-0.745943\pi\)
−0.698037 + 0.716062i \(0.745943\pi\)
\(654\) 8.64407 0.338010
\(655\) 15.8649 0.619892
\(656\) −48.0245 −1.87504
\(657\) −24.5741 −0.958726
\(658\) 67.3550 2.62577
\(659\) −12.1829 −0.474578 −0.237289 0.971439i \(-0.576259\pi\)
−0.237289 + 0.971439i \(0.576259\pi\)
\(660\) −110.945 −4.31851
\(661\) 34.9982 1.36127 0.680635 0.732622i \(-0.261704\pi\)
0.680635 + 0.732622i \(0.261704\pi\)
\(662\) −50.8744 −1.97729
\(663\) 21.8841 0.849908
\(664\) −99.9900 −3.88036
\(665\) −37.5100 −1.45458
\(666\) −18.6820 −0.723913
\(667\) 13.2118 0.511561
\(668\) 137.584 5.32328
\(669\) 36.0770 1.39482
\(670\) 62.9542 2.43213
\(671\) 27.3094 1.05427
\(672\) 272.676 10.5187
\(673\) 28.9217 1.11485 0.557424 0.830228i \(-0.311790\pi\)
0.557424 + 0.830228i \(0.311790\pi\)
\(674\) −57.2965 −2.20698
\(675\) −28.0474 −1.07955
\(676\) 8.43471 0.324412
\(677\) 2.75805 0.106000 0.0530002 0.998595i \(-0.483122\pi\)
0.0530002 + 0.998595i \(0.483122\pi\)
\(678\) 27.3478 1.05029
\(679\) −8.52985 −0.327346
\(680\) 30.1496 1.15619
\(681\) 0.637514 0.0244296
\(682\) −19.7573 −0.756545
\(683\) 9.78543 0.374429 0.187215 0.982319i \(-0.440054\pi\)
0.187215 + 0.982319i \(0.440054\pi\)
\(684\) −265.839 −10.1646
\(685\) 13.7252 0.524415
\(686\) −26.1223 −0.997354
\(687\) 14.8587 0.566893
\(688\) −32.4141 −1.23578
\(689\) 22.0319 0.839349
\(690\) 57.1330 2.17502
\(691\) −3.52814 −0.134217 −0.0671084 0.997746i \(-0.521377\pi\)
−0.0671084 + 0.997746i \(0.521377\pi\)
\(692\) −142.964 −5.43467
\(693\) −87.7060 −3.33168
\(694\) 0.295995 0.0112358
\(695\) −16.3016 −0.618356
\(696\) −102.180 −3.87311
\(697\) −5.27470 −0.199793
\(698\) 75.2489 2.84821
\(699\) −63.7122 −2.40982
\(700\) 45.4034 1.71609
\(701\) 35.7474 1.35016 0.675081 0.737744i \(-0.264109\pi\)
0.675081 + 0.737744i \(0.264109\pi\)
\(702\) −123.311 −4.65406
\(703\) −6.95397 −0.262274
\(704\) 150.811 5.68392
\(705\) −36.6526 −1.38042
\(706\) 85.5659 3.22032
\(707\) −5.78761 −0.217665
\(708\) −221.194 −8.31299
\(709\) 3.75615 0.141065 0.0705325 0.997509i \(-0.477530\pi\)
0.0705325 + 0.997509i \(0.477530\pi\)
\(710\) 9.52929 0.357628
\(711\) −64.6729 −2.42542
\(712\) −147.701 −5.53532
\(713\) 7.51975 0.281617
\(714\) 53.2183 1.99164
\(715\) −23.8749 −0.892870
\(716\) 131.488 4.91392
\(717\) 74.5887 2.78556
\(718\) −90.9859 −3.39556
\(719\) −1.18679 −0.0442599 −0.0221300 0.999755i \(-0.507045\pi\)
−0.0221300 + 0.999755i \(0.507045\pi\)
\(720\) −182.522 −6.80220
\(721\) 47.5558 1.77107
\(722\) −81.2812 −3.02497
\(723\) −32.2909 −1.20091
\(724\) 72.5290 2.69552
\(725\) −7.73040 −0.287100
\(726\) −35.5630 −1.31987
\(727\) 18.0752 0.670370 0.335185 0.942152i \(-0.391201\pi\)
0.335185 + 0.942152i \(0.391201\pi\)
\(728\) 129.147 4.78652
\(729\) 0.314846 0.0116610
\(730\) −16.2675 −0.602088
\(731\) −3.56015 −0.131677
\(732\) 124.251 4.59247
\(733\) −10.7342 −0.396478 −0.198239 0.980154i \(-0.563522\pi\)
−0.198239 + 0.980154i \(0.563522\pi\)
\(734\) 45.4323 1.67694
\(735\) −21.0450 −0.776256
\(736\) −107.016 −3.94467
\(737\) 54.7919 2.01829
\(738\) 53.5130 1.96984
\(739\) 15.1219 0.556270 0.278135 0.960542i \(-0.410284\pi\)
0.278135 + 0.960542i \(0.410284\pi\)
\(740\) −9.14036 −0.336006
\(741\) −82.6420 −3.03593
\(742\) 53.5778 1.96690
\(743\) 21.9608 0.805664 0.402832 0.915274i \(-0.368026\pi\)
0.402832 + 0.915274i \(0.368026\pi\)
\(744\) −58.1576 −2.13216
\(745\) −23.8076 −0.872245
\(746\) 76.4726 2.79986
\(747\) 66.4852 2.43257
\(748\) 40.5586 1.48297
\(749\) −30.4662 −1.11321
\(750\) −103.160 −3.76686
\(751\) −1.79937 −0.0656599 −0.0328299 0.999461i \(-0.510452\pi\)
−0.0328299 + 0.999461i \(0.510452\pi\)
\(752\) 121.997 4.44876
\(753\) 5.49087 0.200098
\(754\) −33.9867 −1.23772
\(755\) 29.8642 1.08687
\(756\) −221.630 −8.06060
\(757\) −27.8513 −1.01227 −0.506136 0.862454i \(-0.668927\pi\)
−0.506136 + 0.862454i \(0.668927\pi\)
\(758\) 31.4100 1.14086
\(759\) 49.7254 1.80492
\(760\) −113.855 −4.12997
\(761\) −44.4277 −1.61050 −0.805252 0.592932i \(-0.797970\pi\)
−0.805252 + 0.592932i \(0.797970\pi\)
\(762\) −123.978 −4.49124
\(763\) 3.34335 0.121037
\(764\) 120.119 4.34574
\(765\) −20.0470 −0.724803
\(766\) −104.298 −3.76844
\(767\) −47.6002 −1.71875
\(768\) 234.548 8.46352
\(769\) 8.70981 0.314084 0.157042 0.987592i \(-0.449804\pi\)
0.157042 + 0.987592i \(0.449804\pi\)
\(770\) −58.0595 −2.09232
\(771\) 96.3902 3.47141
\(772\) −49.9625 −1.79819
\(773\) 4.26867 0.153533 0.0767667 0.997049i \(-0.475540\pi\)
0.0767667 + 0.997049i \(0.475540\pi\)
\(774\) 36.1186 1.29826
\(775\) −4.39992 −0.158050
\(776\) −25.8909 −0.929431
\(777\) −10.4384 −0.374474
\(778\) −8.92158 −0.319854
\(779\) 19.9191 0.713675
\(780\) −108.625 −3.88941
\(781\) 8.29377 0.296774
\(782\) −20.8864 −0.746896
\(783\) 37.7348 1.34853
\(784\) 70.0472 2.50169
\(785\) −2.09511 −0.0747775
\(786\) 85.0005 3.03187
\(787\) 4.68347 0.166948 0.0834739 0.996510i \(-0.473398\pi\)
0.0834739 + 0.996510i \(0.473398\pi\)
\(788\) 99.3112 3.53781
\(789\) 24.3791 0.867917
\(790\) −42.8121 −1.52319
\(791\) 10.5776 0.376095
\(792\) −266.217 −9.45961
\(793\) 26.7385 0.949511
\(794\) 9.45078 0.335396
\(795\) −29.1555 −1.03404
\(796\) −79.8160 −2.82900
\(797\) −40.8931 −1.44851 −0.724254 0.689533i \(-0.757816\pi\)
−0.724254 + 0.689533i \(0.757816\pi\)
\(798\) −200.971 −7.11429
\(799\) 13.3993 0.474033
\(800\) 62.6167 2.21384
\(801\) 98.2090 3.47004
\(802\) 76.1879 2.69029
\(803\) −14.1584 −0.499638
\(804\) 249.290 8.79180
\(805\) 22.0978 0.778846
\(806\) −19.3442 −0.681371
\(807\) 35.0540 1.23396
\(808\) −17.5673 −0.618016
\(809\) −48.1269 −1.69205 −0.846025 0.533143i \(-0.821011\pi\)
−0.846025 + 0.533143i \(0.821011\pi\)
\(810\) 72.7577 2.55645
\(811\) 30.7336 1.07920 0.539601 0.841921i \(-0.318575\pi\)
0.539601 + 0.841921i \(0.318575\pi\)
\(812\) −61.0853 −2.14367
\(813\) 1.53656 0.0538896
\(814\) −10.7636 −0.377265
\(815\) 16.1533 0.565825
\(816\) 96.3915 3.37438
\(817\) 13.4444 0.470359
\(818\) −35.0815 −1.22660
\(819\) −85.8725 −3.00063
\(820\) 26.1818 0.914308
\(821\) −6.34502 −0.221443 −0.110721 0.993851i \(-0.535316\pi\)
−0.110721 + 0.993851i \(0.535316\pi\)
\(822\) 73.5369 2.56489
\(823\) −33.4548 −1.16616 −0.583080 0.812415i \(-0.698153\pi\)
−0.583080 + 0.812415i \(0.698153\pi\)
\(824\) 144.348 5.02859
\(825\) −29.0951 −1.01296
\(826\) −115.755 −4.02765
\(827\) −0.434651 −0.0151143 −0.00755715 0.999971i \(-0.502406\pi\)
−0.00755715 + 0.999971i \(0.502406\pi\)
\(828\) 156.611 5.44260
\(829\) 16.1239 0.560006 0.280003 0.959999i \(-0.409664\pi\)
0.280003 + 0.959999i \(0.409664\pi\)
\(830\) 44.0118 1.52767
\(831\) 81.9745 2.84366
\(832\) 147.658 5.11914
\(833\) 7.69353 0.266565
\(834\) −87.3406 −3.02436
\(835\) −39.1806 −1.35590
\(836\) −153.163 −5.29727
\(837\) 21.4775 0.742372
\(838\) 67.9537 2.34742
\(839\) −34.2038 −1.18085 −0.590423 0.807094i \(-0.701039\pi\)
−0.590423 + 0.807094i \(0.701039\pi\)
\(840\) −170.904 −5.89676
\(841\) −18.5996 −0.641365
\(842\) −59.5505 −2.05224
\(843\) −59.1509 −2.03727
\(844\) −92.3408 −3.17850
\(845\) −2.40200 −0.0826314
\(846\) −135.939 −4.67368
\(847\) −13.7550 −0.472629
\(848\) 97.0426 3.33246
\(849\) 70.4695 2.41851
\(850\) 12.2210 0.419175
\(851\) 4.09671 0.140433
\(852\) 37.7347 1.29277
\(853\) −7.51665 −0.257365 −0.128683 0.991686i \(-0.541075\pi\)
−0.128683 + 0.991686i \(0.541075\pi\)
\(854\) 65.0233 2.22505
\(855\) 75.7046 2.58904
\(856\) −92.4750 −3.16073
\(857\) 44.7278 1.52787 0.763937 0.645291i \(-0.223264\pi\)
0.763937 + 0.645291i \(0.223264\pi\)
\(858\) −127.917 −4.36700
\(859\) −2.95019 −0.100659 −0.0503296 0.998733i \(-0.516027\pi\)
−0.0503296 + 0.998733i \(0.516027\pi\)
\(860\) 17.6714 0.602589
\(861\) 29.8998 1.01898
\(862\) 55.6240 1.89456
\(863\) −19.7700 −0.672980 −0.336490 0.941687i \(-0.609240\pi\)
−0.336490 + 0.941687i \(0.609240\pi\)
\(864\) −305.654 −10.3986
\(865\) 40.7127 1.38427
\(866\) −35.0947 −1.19257
\(867\) −42.4892 −1.44301
\(868\) −34.7680 −1.18010
\(869\) −37.2613 −1.26400
\(870\) 44.9756 1.52482
\(871\) 53.6464 1.81774
\(872\) 10.1482 0.343660
\(873\) 17.2154 0.582652
\(874\) 78.8743 2.66796
\(875\) −39.9000 −1.34887
\(876\) −64.4173 −2.17646
\(877\) −28.3201 −0.956303 −0.478152 0.878277i \(-0.658693\pi\)
−0.478152 + 0.878277i \(0.658693\pi\)
\(878\) 49.5252 1.67139
\(879\) 61.1799 2.06355
\(880\) −105.160 −3.54495
\(881\) −21.2395 −0.715577 −0.357789 0.933803i \(-0.616469\pi\)
−0.357789 + 0.933803i \(0.616469\pi\)
\(882\) −78.0527 −2.62817
\(883\) 31.3857 1.05621 0.528107 0.849178i \(-0.322902\pi\)
0.528107 + 0.849178i \(0.322902\pi\)
\(884\) 39.7107 1.33562
\(885\) 62.9908 2.11741
\(886\) −6.17970 −0.207611
\(887\) −10.5544 −0.354381 −0.177191 0.984177i \(-0.556701\pi\)
−0.177191 + 0.984177i \(0.556701\pi\)
\(888\) −31.6839 −1.06324
\(889\) −47.9520 −1.60826
\(890\) 65.0123 2.17922
\(891\) 63.3244 2.12145
\(892\) 65.4651 2.19193
\(893\) −50.6004 −1.69328
\(894\) −127.556 −4.26612
\(895\) −37.4445 −1.25163
\(896\) 184.407 6.16060
\(897\) 48.6859 1.62557
\(898\) 95.4431 3.18498
\(899\) 5.91961 0.197430
\(900\) −91.6353 −3.05451
\(901\) 10.6585 0.355087
\(902\) 30.8315 1.02658
\(903\) 20.1809 0.671577
\(904\) 32.1064 1.06784
\(905\) −20.6545 −0.686579
\(906\) 160.006 5.31585
\(907\) −37.3604 −1.24053 −0.620266 0.784391i \(-0.712975\pi\)
−0.620266 + 0.784391i \(0.712975\pi\)
\(908\) 1.15683 0.0383907
\(909\) 11.6808 0.387429
\(910\) −56.8458 −1.88442
\(911\) −20.8312 −0.690169 −0.345085 0.938572i \(-0.612150\pi\)
−0.345085 + 0.938572i \(0.612150\pi\)
\(912\) −364.008 −12.0535
\(913\) 38.3055 1.26773
\(914\) −47.9154 −1.58490
\(915\) −35.3838 −1.16975
\(916\) 26.9624 0.890862
\(917\) 32.8764 1.08568
\(918\) −59.6548 −1.96890
\(919\) 49.6950 1.63929 0.819643 0.572874i \(-0.194172\pi\)
0.819643 + 0.572874i \(0.194172\pi\)
\(920\) 67.0743 2.21137
\(921\) 105.096 3.46304
\(922\) −60.4080 −1.98943
\(923\) 8.12038 0.267286
\(924\) −229.908 −7.56342
\(925\) −2.39705 −0.0788144
\(926\) −99.9426 −3.28432
\(927\) −95.9795 −3.15238
\(928\) −84.2440 −2.76545
\(929\) 25.5061 0.836827 0.418414 0.908257i \(-0.362586\pi\)
0.418414 + 0.908257i \(0.362586\pi\)
\(930\) 25.5988 0.839417
\(931\) −29.0534 −0.952188
\(932\) −115.612 −3.78699
\(933\) −2.39093 −0.0782756
\(934\) −21.0436 −0.688569
\(935\) −11.5501 −0.377729
\(936\) −260.652 −8.51966
\(937\) 7.39228 0.241495 0.120748 0.992683i \(-0.461471\pi\)
0.120748 + 0.992683i \(0.461471\pi\)
\(938\) 130.459 4.25963
\(939\) −28.0230 −0.914496
\(940\) −66.5096 −2.16930
\(941\) −28.9448 −0.943574 −0.471787 0.881712i \(-0.656391\pi\)
−0.471787 + 0.881712i \(0.656391\pi\)
\(942\) −11.2251 −0.365734
\(943\) −11.7347 −0.382134
\(944\) −209.662 −6.82391
\(945\) 63.1148 2.05312
\(946\) 20.8097 0.676583
\(947\) 0.591774 0.0192301 0.00961504 0.999954i \(-0.496939\pi\)
0.00961504 + 0.999954i \(0.496939\pi\)
\(948\) −169.530 −5.50609
\(949\) −13.8624 −0.449992
\(950\) −46.1506 −1.49732
\(951\) −34.6672 −1.12416
\(952\) 62.4784 2.02494
\(953\) −34.2049 −1.10801 −0.554003 0.832515i \(-0.686900\pi\)
−0.554003 + 0.832515i \(0.686900\pi\)
\(954\) −108.133 −3.50094
\(955\) −34.2069 −1.10691
\(956\) 135.348 4.37747
\(957\) 39.1443 1.26536
\(958\) 63.5780 2.05411
\(959\) 28.4425 0.918457
\(960\) −195.401 −6.30653
\(961\) −27.6307 −0.891314
\(962\) −10.5386 −0.339779
\(963\) 61.4883 1.98143
\(964\) −58.5947 −1.88721
\(965\) 14.2281 0.458019
\(966\) 118.395 3.80931
\(967\) −2.83106 −0.0910406 −0.0455203 0.998963i \(-0.514495\pi\)
−0.0455203 + 0.998963i \(0.514495\pi\)
\(968\) −41.7511 −1.34193
\(969\) −39.9803 −1.28435
\(970\) 11.3962 0.365910
\(971\) 10.2022 0.327404 0.163702 0.986510i \(-0.447656\pi\)
0.163702 + 0.986510i \(0.447656\pi\)
\(972\) 89.2418 2.86243
\(973\) −33.7815 −1.08299
\(974\) −65.6480 −2.10350
\(975\) −28.4868 −0.912309
\(976\) 117.773 3.76983
\(977\) 18.4032 0.588771 0.294386 0.955687i \(-0.404885\pi\)
0.294386 + 0.955687i \(0.404885\pi\)
\(978\) 86.5458 2.76743
\(979\) 56.5831 1.80840
\(980\) −38.1881 −1.21987
\(981\) −6.74771 −0.215438
\(982\) 17.1443 0.547095
\(983\) −22.6528 −0.722512 −0.361256 0.932467i \(-0.617652\pi\)
−0.361256 + 0.932467i \(0.617652\pi\)
\(984\) 90.7560 2.89319
\(985\) −28.2814 −0.901121
\(986\) −16.4420 −0.523619
\(987\) −75.9545 −2.41766
\(988\) −149.961 −4.77091
\(989\) −7.92032 −0.251852
\(990\) 117.179 3.72418
\(991\) −24.9346 −0.792073 −0.396036 0.918235i \(-0.629615\pi\)
−0.396036 + 0.918235i \(0.629615\pi\)
\(992\) −47.9492 −1.52239
\(993\) 57.3698 1.82058
\(994\) 19.7473 0.626348
\(995\) 22.7297 0.720579
\(996\) 174.281 5.52230
\(997\) 6.20822 0.196616 0.0983082 0.995156i \(-0.468657\pi\)
0.0983082 + 0.995156i \(0.468657\pi\)
\(998\) 113.511 3.59313
\(999\) 11.7008 0.370198
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 4033.2.a.f.1.1 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.1 85 1.1 even 1 trivial