Properties

Label 4034.2.a.d.1.15
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.22639 q^{3} +1.00000 q^{4} -1.99280 q^{5} -1.22639 q^{6} -0.468701 q^{7} +1.00000 q^{8} -1.49597 q^{9} -1.99280 q^{10} -3.45486 q^{11} -1.22639 q^{12} -1.26776 q^{13} -0.468701 q^{14} +2.44395 q^{15} +1.00000 q^{16} -2.46010 q^{17} -1.49597 q^{18} -5.31368 q^{19} -1.99280 q^{20} +0.574810 q^{21} -3.45486 q^{22} +5.20667 q^{23} -1.22639 q^{24} -1.02874 q^{25} -1.26776 q^{26} +5.51381 q^{27} -0.468701 q^{28} -7.19591 q^{29} +2.44395 q^{30} +2.21935 q^{31} +1.00000 q^{32} +4.23701 q^{33} -2.46010 q^{34} +0.934028 q^{35} -1.49597 q^{36} +2.86218 q^{37} -5.31368 q^{38} +1.55477 q^{39} -1.99280 q^{40} +1.05732 q^{41} +0.574810 q^{42} +9.41639 q^{43} -3.45486 q^{44} +2.98117 q^{45} +5.20667 q^{46} +10.8071 q^{47} -1.22639 q^{48} -6.78032 q^{49} -1.02874 q^{50} +3.01704 q^{51} -1.26776 q^{52} +13.2163 q^{53} +5.51381 q^{54} +6.88486 q^{55} -0.468701 q^{56} +6.51664 q^{57} -7.19591 q^{58} +9.17618 q^{59} +2.44395 q^{60} +11.1857 q^{61} +2.21935 q^{62} +0.701161 q^{63} +1.00000 q^{64} +2.52640 q^{65} +4.23701 q^{66} -14.5904 q^{67} -2.46010 q^{68} -6.38541 q^{69} +0.934028 q^{70} -9.48130 q^{71} -1.49597 q^{72} -8.28665 q^{73} +2.86218 q^{74} +1.26163 q^{75} -5.31368 q^{76} +1.61930 q^{77} +1.55477 q^{78} -7.53123 q^{79} -1.99280 q^{80} -2.27418 q^{81} +1.05732 q^{82} -12.5561 q^{83} +0.574810 q^{84} +4.90249 q^{85} +9.41639 q^{86} +8.82499 q^{87} -3.45486 q^{88} -11.0345 q^{89} +2.98117 q^{90} +0.594201 q^{91} +5.20667 q^{92} -2.72179 q^{93} +10.8071 q^{94} +10.5891 q^{95} -1.22639 q^{96} +1.02710 q^{97} -6.78032 q^{98} +5.16836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.22639 −0.708057 −0.354028 0.935235i \(-0.615188\pi\)
−0.354028 + 0.935235i \(0.615188\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.99280 −0.891208 −0.445604 0.895230i \(-0.647011\pi\)
−0.445604 + 0.895230i \(0.647011\pi\)
\(6\) −1.22639 −0.500672
\(7\) −0.468701 −0.177152 −0.0885761 0.996069i \(-0.528232\pi\)
−0.0885761 + 0.996069i \(0.528232\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.49597 −0.498656
\(10\) −1.99280 −0.630179
\(11\) −3.45486 −1.04168 −0.520840 0.853654i \(-0.674381\pi\)
−0.520840 + 0.853654i \(0.674381\pi\)
\(12\) −1.22639 −0.354028
\(13\) −1.26776 −0.351614 −0.175807 0.984425i \(-0.556253\pi\)
−0.175807 + 0.984425i \(0.556253\pi\)
\(14\) −0.468701 −0.125266
\(15\) 2.44395 0.631026
\(16\) 1.00000 0.250000
\(17\) −2.46010 −0.596661 −0.298331 0.954463i \(-0.596430\pi\)
−0.298331 + 0.954463i \(0.596430\pi\)
\(18\) −1.49597 −0.352603
\(19\) −5.31368 −1.21904 −0.609521 0.792770i \(-0.708638\pi\)
−0.609521 + 0.792770i \(0.708638\pi\)
\(20\) −1.99280 −0.445604
\(21\) 0.574810 0.125434
\(22\) −3.45486 −0.736579
\(23\) 5.20667 1.08567 0.542833 0.839841i \(-0.317352\pi\)
0.542833 + 0.839841i \(0.317352\pi\)
\(24\) −1.22639 −0.250336
\(25\) −1.02874 −0.205748
\(26\) −1.26776 −0.248629
\(27\) 5.51381 1.06113
\(28\) −0.468701 −0.0885761
\(29\) −7.19591 −1.33625 −0.668124 0.744050i \(-0.732902\pi\)
−0.668124 + 0.744050i \(0.732902\pi\)
\(30\) 2.44395 0.446203
\(31\) 2.21935 0.398607 0.199303 0.979938i \(-0.436132\pi\)
0.199303 + 0.979938i \(0.436132\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.23701 0.737569
\(34\) −2.46010 −0.421903
\(35\) 0.934028 0.157880
\(36\) −1.49597 −0.249328
\(37\) 2.86218 0.470539 0.235269 0.971930i \(-0.424403\pi\)
0.235269 + 0.971930i \(0.424403\pi\)
\(38\) −5.31368 −0.861993
\(39\) 1.55477 0.248963
\(40\) −1.99280 −0.315090
\(41\) 1.05732 0.165125 0.0825624 0.996586i \(-0.473690\pi\)
0.0825624 + 0.996586i \(0.473690\pi\)
\(42\) 0.574810 0.0886951
\(43\) 9.41639 1.43599 0.717993 0.696050i \(-0.245061\pi\)
0.717993 + 0.696050i \(0.245061\pi\)
\(44\) −3.45486 −0.520840
\(45\) 2.98117 0.444406
\(46\) 5.20667 0.767682
\(47\) 10.8071 1.57637 0.788187 0.615436i \(-0.211020\pi\)
0.788187 + 0.615436i \(0.211020\pi\)
\(48\) −1.22639 −0.177014
\(49\) −6.78032 −0.968617
\(50\) −1.02874 −0.145486
\(51\) 3.01704 0.422470
\(52\) −1.26776 −0.175807
\(53\) 13.2163 1.81540 0.907699 0.419621i \(-0.137837\pi\)
0.907699 + 0.419621i \(0.137837\pi\)
\(54\) 5.51381 0.750334
\(55\) 6.88486 0.928354
\(56\) −0.468701 −0.0626328
\(57\) 6.51664 0.863151
\(58\) −7.19591 −0.944870
\(59\) 9.17618 1.19464 0.597319 0.802004i \(-0.296233\pi\)
0.597319 + 0.802004i \(0.296233\pi\)
\(60\) 2.44395 0.315513
\(61\) 11.1857 1.43219 0.716094 0.698004i \(-0.245928\pi\)
0.716094 + 0.698004i \(0.245928\pi\)
\(62\) 2.21935 0.281858
\(63\) 0.701161 0.0883380
\(64\) 1.00000 0.125000
\(65\) 2.52640 0.313362
\(66\) 4.23701 0.521540
\(67\) −14.5904 −1.78250 −0.891251 0.453510i \(-0.850172\pi\)
−0.891251 + 0.453510i \(0.850172\pi\)
\(68\) −2.46010 −0.298331
\(69\) −6.38541 −0.768713
\(70\) 0.934028 0.111638
\(71\) −9.48130 −1.12522 −0.562612 0.826721i \(-0.690203\pi\)
−0.562612 + 0.826721i \(0.690203\pi\)
\(72\) −1.49597 −0.176301
\(73\) −8.28665 −0.969879 −0.484940 0.874548i \(-0.661158\pi\)
−0.484940 + 0.874548i \(0.661158\pi\)
\(74\) 2.86218 0.332721
\(75\) 1.26163 0.145681
\(76\) −5.31368 −0.609521
\(77\) 1.61930 0.184536
\(78\) 1.55477 0.176043
\(79\) −7.53123 −0.847330 −0.423665 0.905819i \(-0.639257\pi\)
−0.423665 + 0.905819i \(0.639257\pi\)
\(80\) −1.99280 −0.222802
\(81\) −2.27418 −0.252686
\(82\) 1.05732 0.116761
\(83\) −12.5561 −1.37821 −0.689104 0.724662i \(-0.741996\pi\)
−0.689104 + 0.724662i \(0.741996\pi\)
\(84\) 0.574810 0.0627169
\(85\) 4.90249 0.531750
\(86\) 9.41639 1.01540
\(87\) 8.82499 0.946139
\(88\) −3.45486 −0.368290
\(89\) −11.0345 −1.16965 −0.584827 0.811158i \(-0.698838\pi\)
−0.584827 + 0.811158i \(0.698838\pi\)
\(90\) 2.98117 0.314243
\(91\) 0.594201 0.0622892
\(92\) 5.20667 0.542833
\(93\) −2.72179 −0.282236
\(94\) 10.8071 1.11466
\(95\) 10.5891 1.08642
\(96\) −1.22639 −0.125168
\(97\) 1.02710 0.104286 0.0521431 0.998640i \(-0.483395\pi\)
0.0521431 + 0.998640i \(0.483395\pi\)
\(98\) −6.78032 −0.684916
\(99\) 5.16836 0.519440
\(100\) −1.02874 −0.102874
\(101\) 5.56064 0.553305 0.276652 0.960970i \(-0.410775\pi\)
0.276652 + 0.960970i \(0.410775\pi\)
\(102\) 3.01704 0.298731
\(103\) 17.3209 1.70668 0.853341 0.521354i \(-0.174573\pi\)
0.853341 + 0.521354i \(0.174573\pi\)
\(104\) −1.26776 −0.124314
\(105\) −1.14548 −0.111788
\(106\) 13.2163 1.28368
\(107\) 4.27354 0.413139 0.206570 0.978432i \(-0.433770\pi\)
0.206570 + 0.978432i \(0.433770\pi\)
\(108\) 5.51381 0.530567
\(109\) 9.01216 0.863209 0.431604 0.902063i \(-0.357948\pi\)
0.431604 + 0.902063i \(0.357948\pi\)
\(110\) 6.88486 0.656446
\(111\) −3.51014 −0.333168
\(112\) −0.468701 −0.0442881
\(113\) 1.97136 0.185450 0.0927252 0.995692i \(-0.470442\pi\)
0.0927252 + 0.995692i \(0.470442\pi\)
\(114\) 6.51664 0.610340
\(115\) −10.3759 −0.967555
\(116\) −7.19591 −0.668124
\(117\) 1.89653 0.175335
\(118\) 9.17618 0.844736
\(119\) 1.15305 0.105700
\(120\) 2.44395 0.223101
\(121\) 0.936076 0.0850978
\(122\) 11.1857 1.01271
\(123\) −1.29668 −0.116918
\(124\) 2.21935 0.199303
\(125\) 12.0141 1.07457
\(126\) 0.701161 0.0624644
\(127\) 18.0401 1.60080 0.800402 0.599464i \(-0.204620\pi\)
0.800402 + 0.599464i \(0.204620\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.5482 −1.01676
\(130\) 2.52640 0.221580
\(131\) −10.7284 −0.937346 −0.468673 0.883372i \(-0.655268\pi\)
−0.468673 + 0.883372i \(0.655268\pi\)
\(132\) 4.23701 0.368784
\(133\) 2.49053 0.215956
\(134\) −14.5904 −1.26042
\(135\) −10.9879 −0.945691
\(136\) −2.46010 −0.210952
\(137\) −0.261550 −0.0223458 −0.0111729 0.999938i \(-0.503557\pi\)
−0.0111729 + 0.999938i \(0.503557\pi\)
\(138\) −6.38541 −0.543562
\(139\) 20.8819 1.77118 0.885591 0.464466i \(-0.153754\pi\)
0.885591 + 0.464466i \(0.153754\pi\)
\(140\) 0.934028 0.0789398
\(141\) −13.2537 −1.11616
\(142\) −9.48130 −0.795653
\(143\) 4.37995 0.366270
\(144\) −1.49597 −0.124664
\(145\) 14.3400 1.19087
\(146\) −8.28665 −0.685808
\(147\) 8.31532 0.685836
\(148\) 2.86218 0.235269
\(149\) 5.09400 0.417317 0.208658 0.977989i \(-0.433090\pi\)
0.208658 + 0.977989i \(0.433090\pi\)
\(150\) 1.26163 0.103012
\(151\) −12.1959 −0.992489 −0.496244 0.868183i \(-0.665288\pi\)
−0.496244 + 0.868183i \(0.665288\pi\)
\(152\) −5.31368 −0.430996
\(153\) 3.68023 0.297529
\(154\) 1.61930 0.130487
\(155\) −4.42272 −0.355242
\(156\) 1.55477 0.124481
\(157\) 22.6683 1.80913 0.904564 0.426337i \(-0.140196\pi\)
0.904564 + 0.426337i \(0.140196\pi\)
\(158\) −7.53123 −0.599153
\(159\) −16.2083 −1.28540
\(160\) −1.99280 −0.157545
\(161\) −2.44037 −0.192328
\(162\) −2.27418 −0.178676
\(163\) 3.49835 0.274012 0.137006 0.990570i \(-0.456252\pi\)
0.137006 + 0.990570i \(0.456252\pi\)
\(164\) 1.05732 0.0825624
\(165\) −8.44352 −0.657327
\(166\) −12.5561 −0.974541
\(167\) 1.11061 0.0859412 0.0429706 0.999076i \(-0.486318\pi\)
0.0429706 + 0.999076i \(0.486318\pi\)
\(168\) 0.574810 0.0443475
\(169\) −11.3928 −0.876367
\(170\) 4.90249 0.376004
\(171\) 7.94909 0.607882
\(172\) 9.41639 0.717993
\(173\) −4.81367 −0.365977 −0.182988 0.983115i \(-0.558577\pi\)
−0.182988 + 0.983115i \(0.558577\pi\)
\(174\) 8.82499 0.669021
\(175\) 0.482170 0.0364486
\(176\) −3.45486 −0.260420
\(177\) −11.2536 −0.845871
\(178\) −11.0345 −0.827071
\(179\) −0.366851 −0.0274198 −0.0137099 0.999906i \(-0.504364\pi\)
−0.0137099 + 0.999906i \(0.504364\pi\)
\(180\) 2.98117 0.222203
\(181\) 16.7553 1.24541 0.622706 0.782456i \(-0.286033\pi\)
0.622706 + 0.782456i \(0.286033\pi\)
\(182\) 0.594201 0.0440451
\(183\) −13.7181 −1.01407
\(184\) 5.20667 0.383841
\(185\) −5.70375 −0.419348
\(186\) −2.72179 −0.199571
\(187\) 8.49930 0.621530
\(188\) 10.8071 0.788187
\(189\) −2.58433 −0.187982
\(190\) 10.5891 0.768215
\(191\) 14.6870 1.06271 0.531357 0.847148i \(-0.321682\pi\)
0.531357 + 0.847148i \(0.321682\pi\)
\(192\) −1.22639 −0.0885071
\(193\) −1.48909 −0.107187 −0.0535935 0.998563i \(-0.517068\pi\)
−0.0535935 + 0.998563i \(0.517068\pi\)
\(194\) 1.02710 0.0737415
\(195\) −3.09835 −0.221878
\(196\) −6.78032 −0.484309
\(197\) 11.1774 0.796358 0.398179 0.917308i \(-0.369642\pi\)
0.398179 + 0.917308i \(0.369642\pi\)
\(198\) 5.16836 0.367300
\(199\) −5.08108 −0.360188 −0.180094 0.983649i \(-0.557640\pi\)
−0.180094 + 0.983649i \(0.557640\pi\)
\(200\) −1.02874 −0.0727428
\(201\) 17.8935 1.26211
\(202\) 5.56064 0.391245
\(203\) 3.37273 0.236719
\(204\) 3.01704 0.211235
\(205\) −2.10702 −0.147161
\(206\) 17.3209 1.20681
\(207\) −7.78902 −0.541374
\(208\) −1.26776 −0.0879035
\(209\) 18.3580 1.26985
\(210\) −1.14548 −0.0790458
\(211\) 16.1157 1.10945 0.554727 0.832033i \(-0.312823\pi\)
0.554727 + 0.832033i \(0.312823\pi\)
\(212\) 13.2163 0.907699
\(213\) 11.6278 0.796722
\(214\) 4.27354 0.292133
\(215\) −18.7650 −1.27976
\(216\) 5.51381 0.375167
\(217\) −1.04021 −0.0706141
\(218\) 9.01216 0.610381
\(219\) 10.1627 0.686729
\(220\) 6.88486 0.464177
\(221\) 3.11882 0.209795
\(222\) −3.51014 −0.235585
\(223\) −14.0246 −0.939158 −0.469579 0.882890i \(-0.655594\pi\)
−0.469579 + 0.882890i \(0.655594\pi\)
\(224\) −0.468701 −0.0313164
\(225\) 1.53896 0.102597
\(226\) 1.97136 0.131133
\(227\) −11.6235 −0.771478 −0.385739 0.922608i \(-0.626054\pi\)
−0.385739 + 0.922608i \(0.626054\pi\)
\(228\) 6.51664 0.431575
\(229\) −7.63220 −0.504350 −0.252175 0.967682i \(-0.581146\pi\)
−0.252175 + 0.967682i \(0.581146\pi\)
\(230\) −10.3759 −0.684165
\(231\) −1.98589 −0.130662
\(232\) −7.19591 −0.472435
\(233\) 3.48540 0.228336 0.114168 0.993461i \(-0.463580\pi\)
0.114168 + 0.993461i \(0.463580\pi\)
\(234\) 1.89653 0.123980
\(235\) −21.5364 −1.40488
\(236\) 9.17618 0.597319
\(237\) 9.23623 0.599957
\(238\) 1.15305 0.0747411
\(239\) −20.7109 −1.33967 −0.669837 0.742508i \(-0.733636\pi\)
−0.669837 + 0.742508i \(0.733636\pi\)
\(240\) 2.44395 0.157756
\(241\) −2.17768 −0.140276 −0.0701382 0.997537i \(-0.522344\pi\)
−0.0701382 + 0.997537i \(0.522344\pi\)
\(242\) 0.936076 0.0601732
\(243\) −13.7524 −0.882217
\(244\) 11.1857 0.716094
\(245\) 13.5118 0.863240
\(246\) −1.29668 −0.0826733
\(247\) 6.73649 0.428632
\(248\) 2.21935 0.140929
\(249\) 15.3986 0.975850
\(250\) 12.0141 0.759837
\(251\) −26.2146 −1.65465 −0.827324 0.561724i \(-0.810138\pi\)
−0.827324 + 0.561724i \(0.810138\pi\)
\(252\) 0.701161 0.0441690
\(253\) −17.9883 −1.13092
\(254\) 18.0401 1.13194
\(255\) −6.01236 −0.376509
\(256\) 1.00000 0.0625000
\(257\) 10.8492 0.676754 0.338377 0.941011i \(-0.390122\pi\)
0.338377 + 0.941011i \(0.390122\pi\)
\(258\) −11.5482 −0.718958
\(259\) −1.34150 −0.0833570
\(260\) 2.52640 0.156681
\(261\) 10.7649 0.666328
\(262\) −10.7284 −0.662804
\(263\) −11.5792 −0.714003 −0.357001 0.934104i \(-0.616201\pi\)
−0.357001 + 0.934104i \(0.616201\pi\)
\(264\) 4.23701 0.260770
\(265\) −26.3375 −1.61790
\(266\) 2.49053 0.152704
\(267\) 13.5326 0.828182
\(268\) −14.5904 −0.891251
\(269\) −7.95732 −0.485166 −0.242583 0.970131i \(-0.577995\pi\)
−0.242583 + 0.970131i \(0.577995\pi\)
\(270\) −10.9879 −0.668704
\(271\) 15.3230 0.930806 0.465403 0.885099i \(-0.345909\pi\)
0.465403 + 0.885099i \(0.345909\pi\)
\(272\) −2.46010 −0.149165
\(273\) −0.728723 −0.0441043
\(274\) −0.261550 −0.0158008
\(275\) 3.55415 0.214323
\(276\) −6.38541 −0.384357
\(277\) 23.9857 1.44116 0.720581 0.693371i \(-0.243875\pi\)
0.720581 + 0.693371i \(0.243875\pi\)
\(278\) 20.8819 1.25241
\(279\) −3.32007 −0.198768
\(280\) 0.934028 0.0558188
\(281\) −0.496586 −0.0296238 −0.0148119 0.999890i \(-0.504715\pi\)
−0.0148119 + 0.999890i \(0.504715\pi\)
\(282\) −13.2537 −0.789245
\(283\) 18.5242 1.10115 0.550575 0.834786i \(-0.314408\pi\)
0.550575 + 0.834786i \(0.314408\pi\)
\(284\) −9.48130 −0.562612
\(285\) −12.9864 −0.769247
\(286\) 4.37995 0.258992
\(287\) −0.495564 −0.0292522
\(288\) −1.49597 −0.0881507
\(289\) −10.9479 −0.643995
\(290\) 14.3400 0.842076
\(291\) −1.25962 −0.0738405
\(292\) −8.28665 −0.484940
\(293\) 9.03198 0.527654 0.263827 0.964570i \(-0.415015\pi\)
0.263827 + 0.964570i \(0.415015\pi\)
\(294\) 8.31532 0.484959
\(295\) −18.2863 −1.06467
\(296\) 2.86218 0.166361
\(297\) −19.0495 −1.10536
\(298\) 5.09400 0.295088
\(299\) −6.60083 −0.381736
\(300\) 1.26163 0.0728405
\(301\) −4.41347 −0.254388
\(302\) −12.1959 −0.701796
\(303\) −6.81952 −0.391771
\(304\) −5.31368 −0.304760
\(305\) −22.2910 −1.27638
\(306\) 3.68023 0.210385
\(307\) 18.3884 1.04948 0.524741 0.851262i \(-0.324162\pi\)
0.524741 + 0.851262i \(0.324162\pi\)
\(308\) 1.61930 0.0922680
\(309\) −21.2422 −1.20843
\(310\) −4.42272 −0.251194
\(311\) −0.472049 −0.0267674 −0.0133837 0.999910i \(-0.504260\pi\)
−0.0133837 + 0.999910i \(0.504260\pi\)
\(312\) 1.55477 0.0880216
\(313\) 26.2113 1.48155 0.740775 0.671753i \(-0.234459\pi\)
0.740775 + 0.671753i \(0.234459\pi\)
\(314\) 22.6683 1.27925
\(315\) −1.39728 −0.0787276
\(316\) −7.53123 −0.423665
\(317\) 15.1408 0.850391 0.425195 0.905102i \(-0.360205\pi\)
0.425195 + 0.905102i \(0.360205\pi\)
\(318\) −16.2083 −0.908918
\(319\) 24.8609 1.39194
\(320\) −1.99280 −0.111401
\(321\) −5.24103 −0.292526
\(322\) −2.44037 −0.135997
\(323\) 13.0722 0.727355
\(324\) −2.27418 −0.126343
\(325\) 1.30420 0.0723438
\(326\) 3.49835 0.193756
\(327\) −11.0524 −0.611201
\(328\) 1.05732 0.0583805
\(329\) −5.06528 −0.279258
\(330\) −8.44352 −0.464801
\(331\) −27.5801 −1.51594 −0.757970 0.652290i \(-0.773809\pi\)
−0.757970 + 0.652290i \(0.773809\pi\)
\(332\) −12.5561 −0.689104
\(333\) −4.28172 −0.234637
\(334\) 1.11061 0.0607696
\(335\) 29.0758 1.58858
\(336\) 0.574810 0.0313584
\(337\) 16.0622 0.874962 0.437481 0.899228i \(-0.355871\pi\)
0.437481 + 0.899228i \(0.355871\pi\)
\(338\) −11.3928 −0.619685
\(339\) −2.41766 −0.131309
\(340\) 4.90249 0.265875
\(341\) −7.66755 −0.415221
\(342\) 7.94909 0.429838
\(343\) 6.45885 0.348745
\(344\) 9.41639 0.507698
\(345\) 12.7249 0.685084
\(346\) −4.81367 −0.258785
\(347\) −2.01697 −0.108277 −0.0541383 0.998533i \(-0.517241\pi\)
−0.0541383 + 0.998533i \(0.517241\pi\)
\(348\) 8.82499 0.473069
\(349\) 17.0248 0.911317 0.455658 0.890155i \(-0.349404\pi\)
0.455658 + 0.890155i \(0.349404\pi\)
\(350\) 0.482170 0.0257731
\(351\) −6.99020 −0.373109
\(352\) −3.45486 −0.184145
\(353\) 27.5866 1.46829 0.734143 0.678995i \(-0.237584\pi\)
0.734143 + 0.678995i \(0.237584\pi\)
\(354\) −11.2536 −0.598121
\(355\) 18.8944 1.00281
\(356\) −11.0345 −0.584827
\(357\) −1.41409 −0.0748415
\(358\) −0.366851 −0.0193887
\(359\) −33.2045 −1.75247 −0.876233 0.481888i \(-0.839951\pi\)
−0.876233 + 0.481888i \(0.839951\pi\)
\(360\) 2.98117 0.157121
\(361\) 9.23520 0.486063
\(362\) 16.7553 0.880640
\(363\) −1.14799 −0.0602540
\(364\) 0.594201 0.0311446
\(365\) 16.5137 0.864364
\(366\) −13.7181 −0.717056
\(367\) −2.21268 −0.115501 −0.0577505 0.998331i \(-0.518393\pi\)
−0.0577505 + 0.998331i \(0.518393\pi\)
\(368\) 5.20667 0.271417
\(369\) −1.58171 −0.0823405
\(370\) −5.70375 −0.296524
\(371\) −6.19449 −0.321602
\(372\) −2.72179 −0.141118
\(373\) 0.285462 0.0147807 0.00739034 0.999973i \(-0.497648\pi\)
0.00739034 + 0.999973i \(0.497648\pi\)
\(374\) 8.49930 0.439488
\(375\) −14.7340 −0.760858
\(376\) 10.8071 0.557332
\(377\) 9.12271 0.469844
\(378\) −2.58433 −0.132923
\(379\) 14.7529 0.757804 0.378902 0.925437i \(-0.376302\pi\)
0.378902 + 0.925437i \(0.376302\pi\)
\(380\) 10.5891 0.543210
\(381\) −22.1242 −1.13346
\(382\) 14.6870 0.751453
\(383\) 5.84673 0.298754 0.149377 0.988780i \(-0.452273\pi\)
0.149377 + 0.988780i \(0.452273\pi\)
\(384\) −1.22639 −0.0625839
\(385\) −3.22694 −0.164460
\(386\) −1.48909 −0.0757926
\(387\) −14.0866 −0.716063
\(388\) 1.02710 0.0521431
\(389\) −22.9421 −1.16321 −0.581606 0.813471i \(-0.697575\pi\)
−0.581606 + 0.813471i \(0.697575\pi\)
\(390\) −3.09835 −0.156891
\(391\) −12.8089 −0.647775
\(392\) −6.78032 −0.342458
\(393\) 13.1572 0.663694
\(394\) 11.1774 0.563110
\(395\) 15.0083 0.755147
\(396\) 5.16836 0.259720
\(397\) −27.6353 −1.38698 −0.693489 0.720467i \(-0.743927\pi\)
−0.693489 + 0.720467i \(0.743927\pi\)
\(398\) −5.08108 −0.254691
\(399\) −3.05436 −0.152909
\(400\) −1.02874 −0.0514369
\(401\) −23.4743 −1.17225 −0.586125 0.810221i \(-0.699347\pi\)
−0.586125 + 0.810221i \(0.699347\pi\)
\(402\) 17.8935 0.892448
\(403\) −2.81361 −0.140156
\(404\) 5.56064 0.276652
\(405\) 4.53199 0.225196
\(406\) 3.37273 0.167386
\(407\) −9.88843 −0.490151
\(408\) 3.01704 0.149366
\(409\) −19.5672 −0.967538 −0.483769 0.875196i \(-0.660733\pi\)
−0.483769 + 0.875196i \(0.660733\pi\)
\(410\) −2.10702 −0.104058
\(411\) 0.320763 0.0158221
\(412\) 17.3209 0.853341
\(413\) −4.30088 −0.211633
\(414\) −7.78902 −0.382809
\(415\) 25.0218 1.22827
\(416\) −1.26776 −0.0621572
\(417\) −25.6094 −1.25410
\(418\) 18.3580 0.897921
\(419\) −37.7940 −1.84636 −0.923179 0.384370i \(-0.874419\pi\)
−0.923179 + 0.384370i \(0.874419\pi\)
\(420\) −1.14548 −0.0558938
\(421\) 5.94735 0.289856 0.144928 0.989442i \(-0.453705\pi\)
0.144928 + 0.989442i \(0.453705\pi\)
\(422\) 16.1157 0.784502
\(423\) −16.1670 −0.786068
\(424\) 13.2163 0.641840
\(425\) 2.53080 0.122762
\(426\) 11.6278 0.563367
\(427\) −5.24277 −0.253715
\(428\) 4.27354 0.206570
\(429\) −5.37152 −0.259340
\(430\) −18.7650 −0.904929
\(431\) −18.5632 −0.894157 −0.447078 0.894495i \(-0.647535\pi\)
−0.447078 + 0.894495i \(0.647535\pi\)
\(432\) 5.51381 0.265283
\(433\) 29.0746 1.39724 0.698618 0.715495i \(-0.253799\pi\)
0.698618 + 0.715495i \(0.253799\pi\)
\(434\) −1.04021 −0.0499317
\(435\) −17.5865 −0.843207
\(436\) 9.01216 0.431604
\(437\) −27.6666 −1.32347
\(438\) 10.1627 0.485591
\(439\) 12.4853 0.595890 0.297945 0.954583i \(-0.403699\pi\)
0.297945 + 0.954583i \(0.403699\pi\)
\(440\) 6.88486 0.328223
\(441\) 10.1431 0.483007
\(442\) 3.11882 0.148347
\(443\) 10.6334 0.505210 0.252605 0.967570i \(-0.418713\pi\)
0.252605 + 0.967570i \(0.418713\pi\)
\(444\) −3.51014 −0.166584
\(445\) 21.9896 1.04241
\(446\) −14.0246 −0.664085
\(447\) −6.24723 −0.295484
\(448\) −0.468701 −0.0221440
\(449\) −13.8383 −0.653068 −0.326534 0.945186i \(-0.605881\pi\)
−0.326534 + 0.945186i \(0.605881\pi\)
\(450\) 1.53896 0.0725472
\(451\) −3.65288 −0.172007
\(452\) 1.97136 0.0927252
\(453\) 14.9569 0.702738
\(454\) −11.6235 −0.545517
\(455\) −1.18413 −0.0555127
\(456\) 6.51664 0.305170
\(457\) −19.8523 −0.928652 −0.464326 0.885664i \(-0.653703\pi\)
−0.464326 + 0.885664i \(0.653703\pi\)
\(458\) −7.63220 −0.356629
\(459\) −13.5645 −0.633137
\(460\) −10.3759 −0.483778
\(461\) 28.4002 1.32273 0.661366 0.750064i \(-0.269977\pi\)
0.661366 + 0.750064i \(0.269977\pi\)
\(462\) −1.98589 −0.0923919
\(463\) 10.2596 0.476806 0.238403 0.971166i \(-0.423376\pi\)
0.238403 + 0.971166i \(0.423376\pi\)
\(464\) −7.19591 −0.334062
\(465\) 5.42398 0.251531
\(466\) 3.48540 0.161458
\(467\) 36.2596 1.67789 0.838947 0.544214i \(-0.183172\pi\)
0.838947 + 0.544214i \(0.183172\pi\)
\(468\) 1.89653 0.0876673
\(469\) 6.83853 0.315774
\(470\) −21.5364 −0.993398
\(471\) −27.8002 −1.28097
\(472\) 9.17618 0.422368
\(473\) −32.5323 −1.49584
\(474\) 9.23623 0.424234
\(475\) 5.46639 0.250815
\(476\) 1.15305 0.0528499
\(477\) −19.7712 −0.905259
\(478\) −20.7109 −0.947293
\(479\) 19.3438 0.883842 0.441921 0.897054i \(-0.354297\pi\)
0.441921 + 0.897054i \(0.354297\pi\)
\(480\) 2.44395 0.111551
\(481\) −3.62856 −0.165448
\(482\) −2.17768 −0.0991904
\(483\) 2.99285 0.136179
\(484\) 0.936076 0.0425489
\(485\) −2.04681 −0.0929407
\(486\) −13.7524 −0.623822
\(487\) −10.6202 −0.481248 −0.240624 0.970618i \(-0.577352\pi\)
−0.240624 + 0.970618i \(0.577352\pi\)
\(488\) 11.1857 0.506355
\(489\) −4.29034 −0.194016
\(490\) 13.5118 0.610403
\(491\) 26.9304 1.21535 0.607676 0.794185i \(-0.292102\pi\)
0.607676 + 0.794185i \(0.292102\pi\)
\(492\) −1.29668 −0.0584589
\(493\) 17.7026 0.797287
\(494\) 6.73649 0.303089
\(495\) −10.2995 −0.462929
\(496\) 2.21935 0.0996517
\(497\) 4.44389 0.199336
\(498\) 15.3986 0.690030
\(499\) 8.48031 0.379631 0.189815 0.981820i \(-0.439211\pi\)
0.189815 + 0.981820i \(0.439211\pi\)
\(500\) 12.0141 0.537286
\(501\) −1.36204 −0.0608513
\(502\) −26.2146 −1.17001
\(503\) −28.6508 −1.27748 −0.638739 0.769424i \(-0.720544\pi\)
−0.638739 + 0.769424i \(0.720544\pi\)
\(504\) 0.701161 0.0312322
\(505\) −11.0813 −0.493110
\(506\) −17.9883 −0.799679
\(507\) 13.9720 0.620518
\(508\) 18.0401 0.800402
\(509\) 41.4837 1.83873 0.919366 0.393404i \(-0.128703\pi\)
0.919366 + 0.393404i \(0.128703\pi\)
\(510\) −6.01236 −0.266232
\(511\) 3.88396 0.171816
\(512\) 1.00000 0.0441942
\(513\) −29.2986 −1.29357
\(514\) 10.8492 0.478537
\(515\) −34.5172 −1.52101
\(516\) −11.5482 −0.508380
\(517\) −37.3369 −1.64208
\(518\) −1.34150 −0.0589423
\(519\) 5.90344 0.259132
\(520\) 2.52640 0.110790
\(521\) −21.7332 −0.952149 −0.476075 0.879405i \(-0.657941\pi\)
−0.476075 + 0.879405i \(0.657941\pi\)
\(522\) 10.7649 0.471165
\(523\) 42.3559 1.85210 0.926048 0.377406i \(-0.123184\pi\)
0.926048 + 0.377406i \(0.123184\pi\)
\(524\) −10.7284 −0.468673
\(525\) −0.591329 −0.0258077
\(526\) −11.5792 −0.504876
\(527\) −5.45982 −0.237833
\(528\) 4.23701 0.184392
\(529\) 4.10945 0.178672
\(530\) −26.3375 −1.14403
\(531\) −13.7273 −0.595713
\(532\) 2.49053 0.107978
\(533\) −1.34043 −0.0580603
\(534\) 13.5326 0.585613
\(535\) −8.51633 −0.368193
\(536\) −14.5904 −0.630210
\(537\) 0.449903 0.0194147
\(538\) −7.95732 −0.343064
\(539\) 23.4251 1.00899
\(540\) −10.9879 −0.472845
\(541\) 14.9391 0.642282 0.321141 0.947031i \(-0.395934\pi\)
0.321141 + 0.947031i \(0.395934\pi\)
\(542\) 15.3230 0.658179
\(543\) −20.5486 −0.881823
\(544\) −2.46010 −0.105476
\(545\) −17.9595 −0.769299
\(546\) −0.728723 −0.0311864
\(547\) −23.8414 −1.01938 −0.509692 0.860357i \(-0.670241\pi\)
−0.509692 + 0.860357i \(0.670241\pi\)
\(548\) −0.261550 −0.0111729
\(549\) −16.7335 −0.714169
\(550\) 3.55415 0.151549
\(551\) 38.2368 1.62894
\(552\) −6.38541 −0.271781
\(553\) 3.52989 0.150106
\(554\) 23.9857 1.01906
\(555\) 6.99502 0.296922
\(556\) 20.8819 0.885591
\(557\) −25.4238 −1.07724 −0.538621 0.842548i \(-0.681055\pi\)
−0.538621 + 0.842548i \(0.681055\pi\)
\(558\) −3.32007 −0.140550
\(559\) −11.9378 −0.504913
\(560\) 0.934028 0.0394699
\(561\) −10.4235 −0.440079
\(562\) −0.496586 −0.0209472
\(563\) −31.7593 −1.33849 −0.669247 0.743040i \(-0.733383\pi\)
−0.669247 + 0.743040i \(0.733383\pi\)
\(564\) −13.2537 −0.558081
\(565\) −3.92854 −0.165275
\(566\) 18.5242 0.778631
\(567\) 1.06591 0.0447639
\(568\) −9.48130 −0.397826
\(569\) 1.91690 0.0803607 0.0401803 0.999192i \(-0.487207\pi\)
0.0401803 + 0.999192i \(0.487207\pi\)
\(570\) −12.9864 −0.543940
\(571\) 43.9925 1.84103 0.920514 0.390709i \(-0.127770\pi\)
0.920514 + 0.390709i \(0.127770\pi\)
\(572\) 4.37995 0.183135
\(573\) −18.0120 −0.752462
\(574\) −0.495564 −0.0206845
\(575\) −5.35630 −0.223373
\(576\) −1.49597 −0.0623320
\(577\) −40.7671 −1.69716 −0.848578 0.529070i \(-0.822541\pi\)
−0.848578 + 0.529070i \(0.822541\pi\)
\(578\) −10.9479 −0.455373
\(579\) 1.82620 0.0758944
\(580\) 14.3400 0.595437
\(581\) 5.88504 0.244153
\(582\) −1.25962 −0.0522131
\(583\) −45.6605 −1.89106
\(584\) −8.28665 −0.342904
\(585\) −3.77942 −0.156260
\(586\) 9.03198 0.373107
\(587\) −34.9801 −1.44378 −0.721891 0.692007i \(-0.756727\pi\)
−0.721891 + 0.692007i \(0.756727\pi\)
\(588\) 8.31532 0.342918
\(589\) −11.7929 −0.485918
\(590\) −18.2863 −0.752836
\(591\) −13.7079 −0.563867
\(592\) 2.86218 0.117635
\(593\) −12.4676 −0.511983 −0.255992 0.966679i \(-0.582402\pi\)
−0.255992 + 0.966679i \(0.582402\pi\)
\(594\) −19.0495 −0.781609
\(595\) −2.29780 −0.0942006
\(596\) 5.09400 0.208658
\(597\) 6.23138 0.255033
\(598\) −6.60083 −0.269928
\(599\) 0.735309 0.0300439 0.0150220 0.999887i \(-0.495218\pi\)
0.0150220 + 0.999887i \(0.495218\pi\)
\(600\) 1.26163 0.0515060
\(601\) 37.9668 1.54870 0.774350 0.632758i \(-0.218077\pi\)
0.774350 + 0.632758i \(0.218077\pi\)
\(602\) −4.41347 −0.179880
\(603\) 21.8268 0.888855
\(604\) −12.1959 −0.496244
\(605\) −1.86541 −0.0758399
\(606\) −6.81952 −0.277024
\(607\) −6.91276 −0.280580 −0.140290 0.990110i \(-0.544804\pi\)
−0.140290 + 0.990110i \(0.544804\pi\)
\(608\) −5.31368 −0.215498
\(609\) −4.13628 −0.167611
\(610\) −22.2910 −0.902535
\(611\) −13.7008 −0.554275
\(612\) 3.68023 0.148764
\(613\) 42.0624 1.69888 0.849441 0.527683i \(-0.176939\pi\)
0.849441 + 0.527683i \(0.176939\pi\)
\(614\) 18.3884 0.742096
\(615\) 2.58403 0.104198
\(616\) 1.61930 0.0652433
\(617\) −38.5018 −1.55003 −0.775013 0.631946i \(-0.782257\pi\)
−0.775013 + 0.631946i \(0.782257\pi\)
\(618\) −21.2422 −0.854487
\(619\) 21.7947 0.876003 0.438001 0.898974i \(-0.355686\pi\)
0.438001 + 0.898974i \(0.355686\pi\)
\(620\) −4.42272 −0.177621
\(621\) 28.7086 1.15204
\(622\) −0.472049 −0.0189274
\(623\) 5.17188 0.207207
\(624\) 1.55477 0.0622407
\(625\) −18.7980 −0.751920
\(626\) 26.2113 1.04761
\(627\) −22.5141 −0.899127
\(628\) 22.6683 0.904564
\(629\) −7.04123 −0.280752
\(630\) −1.39728 −0.0556688
\(631\) −27.9156 −1.11130 −0.555651 0.831416i \(-0.687531\pi\)
−0.555651 + 0.831416i \(0.687531\pi\)
\(632\) −7.53123 −0.299576
\(633\) −19.7642 −0.785556
\(634\) 15.1408 0.601317
\(635\) −35.9504 −1.42665
\(636\) −16.2083 −0.642702
\(637\) 8.59584 0.340580
\(638\) 24.8609 0.984252
\(639\) 14.1837 0.561099
\(640\) −1.99280 −0.0787724
\(641\) −0.211616 −0.00835835 −0.00417917 0.999991i \(-0.501330\pi\)
−0.00417917 + 0.999991i \(0.501330\pi\)
\(642\) −5.24103 −0.206847
\(643\) −36.7885 −1.45080 −0.725398 0.688330i \(-0.758344\pi\)
−0.725398 + 0.688330i \(0.758344\pi\)
\(644\) −2.44037 −0.0961641
\(645\) 23.0132 0.906145
\(646\) 13.0722 0.514318
\(647\) 25.0198 0.983631 0.491815 0.870700i \(-0.336334\pi\)
0.491815 + 0.870700i \(0.336334\pi\)
\(648\) −2.27418 −0.0893381
\(649\) −31.7024 −1.24443
\(650\) 1.30420 0.0511548
\(651\) 1.27570 0.0499988
\(652\) 3.49835 0.137006
\(653\) −0.663535 −0.0259661 −0.0129831 0.999916i \(-0.504133\pi\)
−0.0129831 + 0.999916i \(0.504133\pi\)
\(654\) −11.0524 −0.432184
\(655\) 21.3796 0.835371
\(656\) 1.05732 0.0412812
\(657\) 12.3966 0.483636
\(658\) −5.06528 −0.197465
\(659\) −20.3893 −0.794254 −0.397127 0.917764i \(-0.629993\pi\)
−0.397127 + 0.917764i \(0.629993\pi\)
\(660\) −8.44352 −0.328664
\(661\) 25.3599 0.986386 0.493193 0.869920i \(-0.335830\pi\)
0.493193 + 0.869920i \(0.335830\pi\)
\(662\) −27.5801 −1.07193
\(663\) −3.82489 −0.148546
\(664\) −12.5561 −0.487270
\(665\) −4.96313 −0.192462
\(666\) −4.28172 −0.165913
\(667\) −37.4668 −1.45072
\(668\) 1.11061 0.0429706
\(669\) 17.1997 0.664977
\(670\) 29.0758 1.12330
\(671\) −38.6452 −1.49188
\(672\) 0.574810 0.0221738
\(673\) 22.6291 0.872288 0.436144 0.899877i \(-0.356344\pi\)
0.436144 + 0.899877i \(0.356344\pi\)
\(674\) 16.0622 0.618692
\(675\) −5.67227 −0.218326
\(676\) −11.3928 −0.438184
\(677\) 38.5144 1.48023 0.740114 0.672481i \(-0.234772\pi\)
0.740114 + 0.672481i \(0.234772\pi\)
\(678\) −2.41766 −0.0928498
\(679\) −0.481402 −0.0184745
\(680\) 4.90249 0.188002
\(681\) 14.2549 0.546250
\(682\) −7.66755 −0.293606
\(683\) −29.6764 −1.13554 −0.567768 0.823189i \(-0.692193\pi\)
−0.567768 + 0.823189i \(0.692193\pi\)
\(684\) 7.94909 0.303941
\(685\) 0.521218 0.0199147
\(686\) 6.45885 0.246600
\(687\) 9.36005 0.357108
\(688\) 9.41639 0.358997
\(689\) −16.7551 −0.638320
\(690\) 12.7249 0.484427
\(691\) 17.2758 0.657204 0.328602 0.944469i \(-0.393423\pi\)
0.328602 + 0.944469i \(0.393423\pi\)
\(692\) −4.81367 −0.182988
\(693\) −2.42242 −0.0920200
\(694\) −2.01697 −0.0765631
\(695\) −41.6136 −1.57849
\(696\) 8.82499 0.334511
\(697\) −2.60110 −0.0985236
\(698\) 17.0248 0.644398
\(699\) −4.27446 −0.161675
\(700\) 0.482170 0.0182243
\(701\) 7.14664 0.269925 0.134962 0.990851i \(-0.456909\pi\)
0.134962 + 0.990851i \(0.456909\pi\)
\(702\) −6.99020 −0.263828
\(703\) −15.2087 −0.573607
\(704\) −3.45486 −0.130210
\(705\) 26.4120 0.994732
\(706\) 27.5866 1.03823
\(707\) −2.60628 −0.0980191
\(708\) −11.2536 −0.422935
\(709\) 3.34637 0.125676 0.0628378 0.998024i \(-0.479985\pi\)
0.0628378 + 0.998024i \(0.479985\pi\)
\(710\) 18.8944 0.709093
\(711\) 11.2665 0.422526
\(712\) −11.0345 −0.413535
\(713\) 11.5554 0.432754
\(714\) −1.41409 −0.0529209
\(715\) −8.72837 −0.326423
\(716\) −0.366851 −0.0137099
\(717\) 25.3996 0.948565
\(718\) −33.2045 −1.23918
\(719\) 30.2300 1.12739 0.563693 0.825984i \(-0.309380\pi\)
0.563693 + 0.825984i \(0.309380\pi\)
\(720\) 2.98117 0.111102
\(721\) −8.11833 −0.302342
\(722\) 9.23520 0.343699
\(723\) 2.67068 0.0993236
\(724\) 16.7553 0.622706
\(725\) 7.40271 0.274930
\(726\) −1.14799 −0.0426060
\(727\) −24.9277 −0.924515 −0.462258 0.886746i \(-0.652960\pi\)
−0.462258 + 0.886746i \(0.652960\pi\)
\(728\) 0.594201 0.0220226
\(729\) 23.6883 0.877346
\(730\) 16.5137 0.611198
\(731\) −23.1652 −0.856798
\(732\) −13.7181 −0.507035
\(733\) −34.7321 −1.28286 −0.641430 0.767182i \(-0.721658\pi\)
−0.641430 + 0.767182i \(0.721658\pi\)
\(734\) −2.21268 −0.0816715
\(735\) −16.5708 −0.611222
\(736\) 5.20667 0.191921
\(737\) 50.4079 1.85680
\(738\) −1.58171 −0.0582235
\(739\) 32.8629 1.20888 0.604441 0.796650i \(-0.293396\pi\)
0.604441 + 0.796650i \(0.293396\pi\)
\(740\) −5.70375 −0.209674
\(741\) −8.26156 −0.303496
\(742\) −6.19449 −0.227407
\(743\) −19.9724 −0.732717 −0.366358 0.930474i \(-0.619396\pi\)
−0.366358 + 0.930474i \(0.619396\pi\)
\(744\) −2.72179 −0.0997856
\(745\) −10.1513 −0.371916
\(746\) 0.285462 0.0104515
\(747\) 18.7835 0.687252
\(748\) 8.49930 0.310765
\(749\) −2.00301 −0.0731885
\(750\) −14.7340 −0.538008
\(751\) 38.3818 1.40057 0.700286 0.713862i \(-0.253056\pi\)
0.700286 + 0.713862i \(0.253056\pi\)
\(752\) 10.8071 0.394093
\(753\) 32.1493 1.17158
\(754\) 9.12271 0.332230
\(755\) 24.3040 0.884514
\(756\) −2.58433 −0.0939910
\(757\) 4.98078 0.181030 0.0905148 0.995895i \(-0.471149\pi\)
0.0905148 + 0.995895i \(0.471149\pi\)
\(758\) 14.7529 0.535849
\(759\) 22.0607 0.800753
\(760\) 10.5891 0.384108
\(761\) 29.1946 1.05830 0.529152 0.848527i \(-0.322510\pi\)
0.529152 + 0.848527i \(0.322510\pi\)
\(762\) −22.1242 −0.801477
\(763\) −4.22401 −0.152919
\(764\) 14.6870 0.531357
\(765\) −7.33397 −0.265160
\(766\) 5.84673 0.211251
\(767\) −11.6332 −0.420051
\(768\) −1.22639 −0.0442535
\(769\) −23.1290 −0.834052 −0.417026 0.908895i \(-0.636928\pi\)
−0.417026 + 0.908895i \(0.636928\pi\)
\(770\) −3.22694 −0.116291
\(771\) −13.3053 −0.479180
\(772\) −1.48909 −0.0535935
\(773\) −5.18341 −0.186434 −0.0932171 0.995646i \(-0.529715\pi\)
−0.0932171 + 0.995646i \(0.529715\pi\)
\(774\) −14.0866 −0.506333
\(775\) −2.28313 −0.0820124
\(776\) 1.02710 0.0368707
\(777\) 1.64521 0.0590215
\(778\) −22.9421 −0.822514
\(779\) −5.61823 −0.201294
\(780\) −3.09835 −0.110939
\(781\) 32.7566 1.17212
\(782\) −12.8089 −0.458046
\(783\) −39.6769 −1.41794
\(784\) −6.78032 −0.242154
\(785\) −45.1735 −1.61231
\(786\) 13.1572 0.469303
\(787\) −38.5988 −1.37590 −0.687949 0.725759i \(-0.741489\pi\)
−0.687949 + 0.725759i \(0.741489\pi\)
\(788\) 11.1774 0.398179
\(789\) 14.2006 0.505554
\(790\) 15.0083 0.533970
\(791\) −0.923980 −0.0328530
\(792\) 5.16836 0.183650
\(793\) −14.1809 −0.503577
\(794\) −27.6353 −0.980742
\(795\) 32.3000 1.14556
\(796\) −5.08108 −0.180094
\(797\) −17.2442 −0.610820 −0.305410 0.952221i \(-0.598793\pi\)
−0.305410 + 0.952221i \(0.598793\pi\)
\(798\) −3.05436 −0.108123
\(799\) −26.5864 −0.940561
\(800\) −1.02874 −0.0363714
\(801\) 16.5073 0.583255
\(802\) −23.4743 −0.828906
\(803\) 28.6292 1.01030
\(804\) 17.8935 0.631056
\(805\) 4.86318 0.171405
\(806\) −2.81361 −0.0991051
\(807\) 9.75877 0.343525
\(808\) 5.56064 0.195623
\(809\) −39.6251 −1.39314 −0.696571 0.717488i \(-0.745292\pi\)
−0.696571 + 0.717488i \(0.745292\pi\)
\(810\) 4.53199 0.159238
\(811\) −15.3270 −0.538202 −0.269101 0.963112i \(-0.586727\pi\)
−0.269101 + 0.963112i \(0.586727\pi\)
\(812\) 3.37273 0.118360
\(813\) −18.7920 −0.659063
\(814\) −9.88843 −0.346589
\(815\) −6.97152 −0.244202
\(816\) 3.01704 0.105617
\(817\) −50.0357 −1.75053
\(818\) −19.5672 −0.684153
\(819\) −0.888906 −0.0310609
\(820\) −2.10702 −0.0735803
\(821\) −31.4855 −1.09885 −0.549425 0.835543i \(-0.685153\pi\)
−0.549425 + 0.835543i \(0.685153\pi\)
\(822\) 0.320763 0.0111879
\(823\) 50.9733 1.77682 0.888409 0.459052i \(-0.151811\pi\)
0.888409 + 0.459052i \(0.151811\pi\)
\(824\) 17.3209 0.603403
\(825\) −4.35877 −0.151753
\(826\) −4.30088 −0.149647
\(827\) −14.6151 −0.508218 −0.254109 0.967176i \(-0.581782\pi\)
−0.254109 + 0.967176i \(0.581782\pi\)
\(828\) −7.78902 −0.270687
\(829\) 35.5328 1.23411 0.617053 0.786922i \(-0.288326\pi\)
0.617053 + 0.786922i \(0.288326\pi\)
\(830\) 25.0218 0.868519
\(831\) −29.4158 −1.02042
\(832\) −1.26776 −0.0439518
\(833\) 16.6802 0.577936
\(834\) −25.6094 −0.886781
\(835\) −2.21322 −0.0765916
\(836\) 18.3580 0.634926
\(837\) 12.2371 0.422975
\(838\) −37.7940 −1.30557
\(839\) 48.5533 1.67625 0.838124 0.545480i \(-0.183653\pi\)
0.838124 + 0.545480i \(0.183653\pi\)
\(840\) −1.14548 −0.0395229
\(841\) 22.7812 0.785557
\(842\) 5.94735 0.204959
\(843\) 0.609008 0.0209753
\(844\) 16.1157 0.554727
\(845\) 22.7036 0.781026
\(846\) −16.1670 −0.555834
\(847\) −0.438739 −0.0150753
\(848\) 13.2163 0.453850
\(849\) −22.7179 −0.779677
\(850\) 2.53080 0.0868056
\(851\) 14.9024 0.510848
\(852\) 11.6278 0.398361
\(853\) 25.2425 0.864288 0.432144 0.901805i \(-0.357757\pi\)
0.432144 + 0.901805i \(0.357757\pi\)
\(854\) −5.24277 −0.179404
\(855\) −15.8410 −0.541750
\(856\) 4.27354 0.146067
\(857\) 34.5179 1.17911 0.589554 0.807729i \(-0.299303\pi\)
0.589554 + 0.807729i \(0.299303\pi\)
\(858\) −5.37152 −0.183381
\(859\) −17.7314 −0.604989 −0.302495 0.953151i \(-0.597819\pi\)
−0.302495 + 0.953151i \(0.597819\pi\)
\(860\) −18.7650 −0.639882
\(861\) 0.607755 0.0207122
\(862\) −18.5632 −0.632264
\(863\) 24.6702 0.839785 0.419892 0.907574i \(-0.362068\pi\)
0.419892 + 0.907574i \(0.362068\pi\)
\(864\) 5.51381 0.187584
\(865\) 9.59270 0.326162
\(866\) 29.0746 0.987995
\(867\) 13.4264 0.455985
\(868\) −1.04021 −0.0353070
\(869\) 26.0194 0.882647
\(870\) −17.5865 −0.596237
\(871\) 18.4972 0.626753
\(872\) 9.01216 0.305190
\(873\) −1.53651 −0.0520029
\(874\) −27.6666 −0.935837
\(875\) −5.63101 −0.190363
\(876\) 10.1627 0.343365
\(877\) 11.8329 0.399567 0.199784 0.979840i \(-0.435976\pi\)
0.199784 + 0.979840i \(0.435976\pi\)
\(878\) 12.4853 0.421358
\(879\) −11.0767 −0.373609
\(880\) 6.88486 0.232089
\(881\) 5.19631 0.175068 0.0875340 0.996162i \(-0.472101\pi\)
0.0875340 + 0.996162i \(0.472101\pi\)
\(882\) 10.1431 0.341537
\(883\) 41.1552 1.38498 0.692492 0.721426i \(-0.256513\pi\)
0.692492 + 0.721426i \(0.256513\pi\)
\(884\) 3.11882 0.104897
\(885\) 22.4262 0.753847
\(886\) 10.6334 0.357237
\(887\) 49.2283 1.65293 0.826463 0.562992i \(-0.190350\pi\)
0.826463 + 0.562992i \(0.190350\pi\)
\(888\) −3.51014 −0.117793
\(889\) −8.45543 −0.283586
\(890\) 21.9896 0.737092
\(891\) 7.85697 0.263218
\(892\) −14.0246 −0.469579
\(893\) −57.4253 −1.92166
\(894\) −6.24723 −0.208939
\(895\) 0.731062 0.0244367
\(896\) −0.468701 −0.0156582
\(897\) 8.09519 0.270290
\(898\) −13.8383 −0.461789
\(899\) −15.9702 −0.532637
\(900\) 1.53896 0.0512986
\(901\) −32.5134 −1.08318
\(902\) −3.65288 −0.121628
\(903\) 5.41264 0.180121
\(904\) 1.97136 0.0655666
\(905\) −33.3900 −1.10992
\(906\) 14.9569 0.496911
\(907\) −31.0853 −1.03217 −0.516085 0.856538i \(-0.672611\pi\)
−0.516085 + 0.856538i \(0.672611\pi\)
\(908\) −11.6235 −0.385739
\(909\) −8.31854 −0.275909
\(910\) −1.18413 −0.0392534
\(911\) −55.7799 −1.84807 −0.924035 0.382309i \(-0.875129\pi\)
−0.924035 + 0.382309i \(0.875129\pi\)
\(912\) 6.51664 0.215788
\(913\) 43.3795 1.43565
\(914\) −19.8523 −0.656656
\(915\) 27.3374 0.903747
\(916\) −7.63220 −0.252175
\(917\) 5.02842 0.166053
\(918\) −13.5645 −0.447696
\(919\) 22.9204 0.756073 0.378037 0.925791i \(-0.376599\pi\)
0.378037 + 0.925791i \(0.376599\pi\)
\(920\) −10.3759 −0.342082
\(921\) −22.5514 −0.743093
\(922\) 28.4002 0.935312
\(923\) 12.0200 0.395644
\(924\) −1.98589 −0.0653309
\(925\) −2.94443 −0.0968123
\(926\) 10.2596 0.337153
\(927\) −25.9115 −0.851047
\(928\) −7.19591 −0.236217
\(929\) 13.5354 0.444084 0.222042 0.975037i \(-0.428728\pi\)
0.222042 + 0.975037i \(0.428728\pi\)
\(930\) 5.42398 0.177859
\(931\) 36.0285 1.18078
\(932\) 3.48540 0.114168
\(933\) 0.578916 0.0189529
\(934\) 36.2596 1.18645
\(935\) −16.9374 −0.553913
\(936\) 1.89653 0.0619901
\(937\) −16.2354 −0.530389 −0.265194 0.964195i \(-0.585436\pi\)
−0.265194 + 0.964195i \(0.585436\pi\)
\(938\) 6.83853 0.223286
\(939\) −32.1453 −1.04902
\(940\) −21.5364 −0.702438
\(941\) 57.8556 1.88604 0.943020 0.332737i \(-0.107972\pi\)
0.943020 + 0.332737i \(0.107972\pi\)
\(942\) −27.8002 −0.905779
\(943\) 5.50509 0.179271
\(944\) 9.17618 0.298659
\(945\) 5.15005 0.167531
\(946\) −32.5323 −1.05772
\(947\) 7.41463 0.240943 0.120472 0.992717i \(-0.461559\pi\)
0.120472 + 0.992717i \(0.461559\pi\)
\(948\) 9.23623 0.299979
\(949\) 10.5055 0.341023
\(950\) 5.46639 0.177353
\(951\) −18.5685 −0.602125
\(952\) 1.15305 0.0373705
\(953\) 28.1055 0.910426 0.455213 0.890382i \(-0.349563\pi\)
0.455213 + 0.890382i \(0.349563\pi\)
\(954\) −19.7712 −0.640115
\(955\) −29.2683 −0.947100
\(956\) −20.7109 −0.669837
\(957\) −30.4891 −0.985574
\(958\) 19.3438 0.624970
\(959\) 0.122589 0.00395860
\(960\) 2.44395 0.0788782
\(961\) −26.0745 −0.841113
\(962\) −3.62856 −0.116990
\(963\) −6.39308 −0.206014
\(964\) −2.17768 −0.0701382
\(965\) 2.96746 0.0955259
\(966\) 2.99285 0.0962933
\(967\) −54.4429 −1.75077 −0.875383 0.483430i \(-0.839391\pi\)
−0.875383 + 0.483430i \(0.839391\pi\)
\(968\) 0.936076 0.0300866
\(969\) −16.0316 −0.515009
\(970\) −2.04681 −0.0657190
\(971\) −26.5135 −0.850860 −0.425430 0.904991i \(-0.639877\pi\)
−0.425430 + 0.904991i \(0.639877\pi\)
\(972\) −13.7524 −0.441108
\(973\) −9.78738 −0.313769
\(974\) −10.6202 −0.340293
\(975\) −1.59945 −0.0512235
\(976\) 11.1857 0.358047
\(977\) 55.0904 1.76250 0.881250 0.472651i \(-0.156703\pi\)
0.881250 + 0.472651i \(0.156703\pi\)
\(978\) −4.29034 −0.137190
\(979\) 38.1227 1.21841
\(980\) 13.5118 0.431620
\(981\) −13.4819 −0.430444
\(982\) 26.9304 0.859384
\(983\) −15.8480 −0.505472 −0.252736 0.967535i \(-0.581330\pi\)
−0.252736 + 0.967535i \(0.581330\pi\)
\(984\) −1.29668 −0.0413367
\(985\) −22.2744 −0.709721
\(986\) 17.7026 0.563767
\(987\) 6.21201 0.197730
\(988\) 6.73649 0.214316
\(989\) 49.0281 1.55900
\(990\) −10.2995 −0.327340
\(991\) −0.00674818 −0.000214363 0 −0.000107182 1.00000i \(-0.500034\pi\)
−0.000107182 1.00000i \(0.500034\pi\)
\(992\) 2.21935 0.0704644
\(993\) 33.8240 1.07337
\(994\) 4.44389 0.140952
\(995\) 10.1256 0.321002
\(996\) 15.3986 0.487925
\(997\) −42.5804 −1.34854 −0.674268 0.738487i \(-0.735541\pi\)
−0.674268 + 0.738487i \(0.735541\pi\)
\(998\) 8.48031 0.268439
\(999\) 15.7815 0.499304
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 4034.2.a.d.1.15 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.15 52 1.1 even 1 trivial