Properties

Label 8003.2.a.b.1.19
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +O(q^{10})\) \(q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +9.31479 q^{10} -5.50344 q^{11} +11.0371 q^{12} -4.82534 q^{13} +2.44599 q^{14} -12.5182 q^{15} +1.25726 q^{16} +6.98013 q^{17} -16.2685 q^{18} +2.80545 q^{19} -13.9054 q^{20} -3.28716 q^{21} +12.9084 q^{22} +5.55558 q^{23} -11.1008 q^{24} +10.7713 q^{25} +11.3179 q^{26} +12.4069 q^{27} -3.65143 q^{28} +2.52356 q^{29} +29.3616 q^{30} -4.92733 q^{31} +4.09443 q^{32} -17.3476 q^{33} -16.3720 q^{34} +4.14142 q^{35} +24.2861 q^{36} -4.19053 q^{37} -6.58023 q^{38} -15.2102 q^{39} +13.9857 q^{40} -2.26840 q^{41} +7.71010 q^{42} +0.103309 q^{43} -19.2700 q^{44} -27.5451 q^{45} -13.0307 q^{46} +13.3859 q^{47} +3.96307 q^{48} -5.91250 q^{49} -25.2644 q^{50} +22.0024 q^{51} -16.8957 q^{52} -1.00000 q^{53} -29.1005 q^{54} +21.8559 q^{55} +3.67253 q^{56} +8.84318 q^{57} -5.91906 q^{58} -11.5829 q^{59} -43.8317 q^{60} -5.00345 q^{61} +11.5571 q^{62} -7.23311 q^{63} -12.1181 q^{64} +19.1629 q^{65} +40.6892 q^{66} +9.25657 q^{67} +24.4406 q^{68} +17.5120 q^{69} -9.71378 q^{70} -4.37839 q^{71} -24.4264 q^{72} -5.17646 q^{73} +9.82897 q^{74} +33.9528 q^{75} +9.82314 q^{76} +5.73917 q^{77} +35.6757 q^{78} -3.52255 q^{79} -4.99299 q^{80} +18.3002 q^{81} +5.32057 q^{82} +12.2718 q^{83} -11.5098 q^{84} -27.7203 q^{85} -0.242314 q^{86} +7.95463 q^{87} +19.3814 q^{88} -8.95032 q^{89} +64.6075 q^{90} +5.03202 q^{91} +19.4526 q^{92} -15.5317 q^{93} -31.3968 q^{94} -11.1413 q^{95} +12.9062 q^{96} +12.3696 q^{97} +13.8679 q^{98} -38.1719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34552 −1.65853 −0.829266 0.558855i \(-0.811241\pi\)
−0.829266 + 0.558855i \(0.811241\pi\)
\(3\) 3.15214 1.81989 0.909945 0.414728i \(-0.136123\pi\)
0.909945 + 0.414728i \(0.136123\pi\)
\(4\) 3.50145 1.75073
\(5\) −3.97132 −1.77603 −0.888013 0.459818i \(-0.847915\pi\)
−0.888013 + 0.459818i \(0.847915\pi\)
\(6\) −7.39341 −3.01835
\(7\) −1.04283 −0.394154 −0.197077 0.980388i \(-0.563145\pi\)
−0.197077 + 0.980388i \(0.563145\pi\)
\(8\) −3.52168 −1.24510
\(9\) 6.93601 2.31200
\(10\) 9.31479 2.94560
\(11\) −5.50344 −1.65935 −0.829674 0.558248i \(-0.811474\pi\)
−0.829674 + 0.558248i \(0.811474\pi\)
\(12\) 11.0371 3.18613
\(13\) −4.82534 −1.33831 −0.669154 0.743124i \(-0.733343\pi\)
−0.669154 + 0.743124i \(0.733343\pi\)
\(14\) 2.44599 0.653717
\(15\) −12.5182 −3.23217
\(16\) 1.25726 0.314316
\(17\) 6.98013 1.69293 0.846465 0.532445i \(-0.178727\pi\)
0.846465 + 0.532445i \(0.178727\pi\)
\(18\) −16.2685 −3.83453
\(19\) 2.80545 0.643614 0.321807 0.946805i \(-0.395710\pi\)
0.321807 + 0.946805i \(0.395710\pi\)
\(20\) −13.9054 −3.10934
\(21\) −3.28716 −0.717318
\(22\) 12.9084 2.75208
\(23\) 5.55558 1.15842 0.579210 0.815179i \(-0.303361\pi\)
0.579210 + 0.815179i \(0.303361\pi\)
\(24\) −11.1008 −2.26595
\(25\) 10.7713 2.15427
\(26\) 11.3179 2.21962
\(27\) 12.4069 2.38770
\(28\) −3.65143 −0.690056
\(29\) 2.52356 0.468614 0.234307 0.972163i \(-0.424718\pi\)
0.234307 + 0.972163i \(0.424718\pi\)
\(30\) 29.3616 5.36066
\(31\) −4.92733 −0.884975 −0.442488 0.896775i \(-0.645904\pi\)
−0.442488 + 0.896775i \(0.645904\pi\)
\(32\) 4.09443 0.723800
\(33\) −17.3476 −3.01983
\(34\) −16.3720 −2.80778
\(35\) 4.14142 0.700028
\(36\) 24.2861 4.04768
\(37\) −4.19053 −0.688919 −0.344460 0.938801i \(-0.611938\pi\)
−0.344460 + 0.938801i \(0.611938\pi\)
\(38\) −6.58023 −1.06745
\(39\) −15.2102 −2.43557
\(40\) 13.9857 2.21134
\(41\) −2.26840 −0.354264 −0.177132 0.984187i \(-0.556682\pi\)
−0.177132 + 0.984187i \(0.556682\pi\)
\(42\) 7.71010 1.18969
\(43\) 0.103309 0.0157545 0.00787726 0.999969i \(-0.497493\pi\)
0.00787726 + 0.999969i \(0.497493\pi\)
\(44\) −19.2700 −2.90506
\(45\) −27.5451 −4.10618
\(46\) −13.0307 −1.92127
\(47\) 13.3859 1.95253 0.976267 0.216572i \(-0.0694876\pi\)
0.976267 + 0.216572i \(0.0694876\pi\)
\(48\) 3.96307 0.572021
\(49\) −5.91250 −0.844642
\(50\) −25.2644 −3.57292
\(51\) 22.0024 3.08095
\(52\) −16.8957 −2.34301
\(53\) −1.00000 −0.137361
\(54\) −29.1005 −3.96008
\(55\) 21.8559 2.94705
\(56\) 3.67253 0.490762
\(57\) 8.84318 1.17131
\(58\) −5.91906 −0.777211
\(59\) −11.5829 −1.50797 −0.753983 0.656894i \(-0.771870\pi\)
−0.753983 + 0.656894i \(0.771870\pi\)
\(60\) −43.8317 −5.65865
\(61\) −5.00345 −0.640626 −0.320313 0.947312i \(-0.603788\pi\)
−0.320313 + 0.947312i \(0.603788\pi\)
\(62\) 11.5571 1.46776
\(63\) −7.23311 −0.911286
\(64\) −12.1181 −1.51476
\(65\) 19.1629 2.37687
\(66\) 40.6892 5.00849
\(67\) 9.25657 1.13087 0.565435 0.824793i \(-0.308708\pi\)
0.565435 + 0.824793i \(0.308708\pi\)
\(68\) 24.4406 2.96386
\(69\) 17.5120 2.10820
\(70\) −9.71378 −1.16102
\(71\) −4.37839 −0.519619 −0.259809 0.965660i \(-0.583660\pi\)
−0.259809 + 0.965660i \(0.583660\pi\)
\(72\) −24.4264 −2.87868
\(73\) −5.17646 −0.605859 −0.302930 0.953013i \(-0.597965\pi\)
−0.302930 + 0.953013i \(0.597965\pi\)
\(74\) 9.82897 1.14259
\(75\) 33.9528 3.92054
\(76\) 9.82314 1.12679
\(77\) 5.73917 0.654039
\(78\) 35.6757 4.03948
\(79\) −3.52255 −0.396318 −0.198159 0.980170i \(-0.563496\pi\)
−0.198159 + 0.980170i \(0.563496\pi\)
\(80\) −4.99299 −0.558233
\(81\) 18.3002 2.03335
\(82\) 5.32057 0.587558
\(83\) 12.2718 1.34700 0.673501 0.739186i \(-0.264790\pi\)
0.673501 + 0.739186i \(0.264790\pi\)
\(84\) −11.5098 −1.25583
\(85\) −27.7203 −3.00669
\(86\) −0.242314 −0.0261294
\(87\) 7.95463 0.852826
\(88\) 19.3814 2.06606
\(89\) −8.95032 −0.948732 −0.474366 0.880328i \(-0.657323\pi\)
−0.474366 + 0.880328i \(0.657323\pi\)
\(90\) 64.6075 6.81023
\(91\) 5.03202 0.527500
\(92\) 19.4526 2.02807
\(93\) −15.5317 −1.61056
\(94\) −31.3968 −3.23834
\(95\) −11.1413 −1.14308
\(96\) 12.9062 1.31724
\(97\) 12.3696 1.25595 0.627973 0.778235i \(-0.283885\pi\)
0.627973 + 0.778235i \(0.283885\pi\)
\(98\) 13.8679 1.40087
\(99\) −38.1719 −3.83642
\(100\) 37.7154 3.77154
\(101\) 10.1738 1.01233 0.506167 0.862436i \(-0.331062\pi\)
0.506167 + 0.862436i \(0.331062\pi\)
\(102\) −51.6069 −5.10985
\(103\) −14.1633 −1.39555 −0.697776 0.716316i \(-0.745827\pi\)
−0.697776 + 0.716316i \(0.745827\pi\)
\(104\) 16.9933 1.66633
\(105\) 13.0544 1.27398
\(106\) 2.34552 0.227817
\(107\) −12.2679 −1.18599 −0.592993 0.805207i \(-0.702054\pi\)
−0.592993 + 0.805207i \(0.702054\pi\)
\(108\) 43.4420 4.18021
\(109\) 6.13508 0.587634 0.293817 0.955862i \(-0.405074\pi\)
0.293817 + 0.955862i \(0.405074\pi\)
\(110\) −51.2634 −4.88777
\(111\) −13.2092 −1.25376
\(112\) −1.31112 −0.123889
\(113\) 15.4606 1.45441 0.727205 0.686420i \(-0.240819\pi\)
0.727205 + 0.686420i \(0.240819\pi\)
\(114\) −20.7418 −1.94265
\(115\) −22.0630 −2.05738
\(116\) 8.83614 0.820415
\(117\) −33.4686 −3.09417
\(118\) 27.1679 2.50101
\(119\) −7.27911 −0.667275
\(120\) 44.0850 4.02439
\(121\) 19.2878 1.75344
\(122\) 11.7357 1.06250
\(123\) −7.15031 −0.644722
\(124\) −17.2528 −1.54935
\(125\) −22.9199 −2.05001
\(126\) 16.9654 1.51140
\(127\) −9.88057 −0.876759 −0.438379 0.898790i \(-0.644447\pi\)
−0.438379 + 0.898790i \(0.644447\pi\)
\(128\) 20.2343 1.78848
\(129\) 0.325646 0.0286715
\(130\) −44.9470 −3.94211
\(131\) −12.4196 −1.08511 −0.542553 0.840021i \(-0.682542\pi\)
−0.542553 + 0.840021i \(0.682542\pi\)
\(132\) −60.7419 −5.28690
\(133\) −2.92562 −0.253683
\(134\) −21.7114 −1.87558
\(135\) −49.2716 −4.24062
\(136\) −24.5818 −2.10787
\(137\) 14.5989 1.24727 0.623633 0.781717i \(-0.285656\pi\)
0.623633 + 0.781717i \(0.285656\pi\)
\(138\) −41.0747 −3.49651
\(139\) 10.2468 0.869125 0.434563 0.900642i \(-0.356903\pi\)
0.434563 + 0.900642i \(0.356903\pi\)
\(140\) 14.5010 1.22556
\(141\) 42.1943 3.55340
\(142\) 10.2696 0.861804
\(143\) 26.5559 2.22072
\(144\) 8.72039 0.726699
\(145\) −10.0219 −0.832271
\(146\) 12.1415 1.00484
\(147\) −18.6370 −1.53716
\(148\) −14.6730 −1.20611
\(149\) −6.64792 −0.544619 −0.272310 0.962210i \(-0.587787\pi\)
−0.272310 + 0.962210i \(0.587787\pi\)
\(150\) −79.6370 −6.50233
\(151\) −1.00000 −0.0813788
\(152\) −9.87990 −0.801366
\(153\) 48.4142 3.91406
\(154\) −13.4613 −1.08474
\(155\) 19.5680 1.57174
\(156\) −53.2576 −4.26402
\(157\) −6.63538 −0.529561 −0.264780 0.964309i \(-0.585299\pi\)
−0.264780 + 0.964309i \(0.585299\pi\)
\(158\) 8.26221 0.657306
\(159\) −3.15214 −0.249981
\(160\) −16.2603 −1.28549
\(161\) −5.79355 −0.456596
\(162\) −42.9234 −3.37238
\(163\) 24.6232 1.92864 0.964319 0.264742i \(-0.0852868\pi\)
0.964319 + 0.264742i \(0.0852868\pi\)
\(164\) −7.94269 −0.620220
\(165\) 68.8929 5.36330
\(166\) −28.7837 −2.23404
\(167\) −3.06144 −0.236901 −0.118451 0.992960i \(-0.537793\pi\)
−0.118451 + 0.992960i \(0.537793\pi\)
\(168\) 11.5763 0.893134
\(169\) 10.2839 0.791067
\(170\) 65.0184 4.98669
\(171\) 19.4586 1.48804
\(172\) 0.361733 0.0275819
\(173\) −8.88290 −0.675355 −0.337677 0.941262i \(-0.609641\pi\)
−0.337677 + 0.941262i \(0.609641\pi\)
\(174\) −18.6577 −1.41444
\(175\) −11.2327 −0.849115
\(176\) −6.91927 −0.521560
\(177\) −36.5110 −2.74433
\(178\) 20.9931 1.57350
\(179\) −1.87234 −0.139945 −0.0699726 0.997549i \(-0.522291\pi\)
−0.0699726 + 0.997549i \(0.522291\pi\)
\(180\) −96.4478 −7.18879
\(181\) −20.2306 −1.50373 −0.751865 0.659317i \(-0.770845\pi\)
−0.751865 + 0.659317i \(0.770845\pi\)
\(182\) −11.8027 −0.874874
\(183\) −15.7716 −1.16587
\(184\) −19.5650 −1.44235
\(185\) 16.6419 1.22354
\(186\) 36.4298 2.67116
\(187\) −38.4147 −2.80916
\(188\) 46.8701 3.41835
\(189\) −12.9383 −0.941123
\(190\) 26.1322 1.89583
\(191\) 13.1056 0.948286 0.474143 0.880448i \(-0.342758\pi\)
0.474143 + 0.880448i \(0.342758\pi\)
\(192\) −38.1980 −2.75670
\(193\) 19.1966 1.38180 0.690902 0.722948i \(-0.257214\pi\)
0.690902 + 0.722948i \(0.257214\pi\)
\(194\) −29.0132 −2.08303
\(195\) 60.4043 4.32564
\(196\) −20.7023 −1.47874
\(197\) 24.5624 1.75000 0.875001 0.484121i \(-0.160861\pi\)
0.875001 + 0.484121i \(0.160861\pi\)
\(198\) 89.5328 6.36282
\(199\) −19.2496 −1.36457 −0.682285 0.731086i \(-0.739014\pi\)
−0.682285 + 0.731086i \(0.739014\pi\)
\(200\) −37.9333 −2.68229
\(201\) 29.1780 2.05806
\(202\) −23.8629 −1.67899
\(203\) −2.63166 −0.184706
\(204\) 77.0402 5.39390
\(205\) 9.00852 0.629183
\(206\) 33.2203 2.31457
\(207\) 38.5336 2.67827
\(208\) −6.06672 −0.420651
\(209\) −15.4396 −1.06798
\(210\) −30.6192 −2.11293
\(211\) −16.5678 −1.14057 −0.570287 0.821446i \(-0.693168\pi\)
−0.570287 + 0.821446i \(0.693168\pi\)
\(212\) −3.50145 −0.240481
\(213\) −13.8013 −0.945650
\(214\) 28.7747 1.96700
\(215\) −0.410274 −0.0279805
\(216\) −43.6930 −2.97293
\(217\) 5.13839 0.348817
\(218\) −14.3899 −0.974609
\(219\) −16.3170 −1.10260
\(220\) 76.5273 5.15947
\(221\) −33.6815 −2.26566
\(222\) 30.9823 2.07940
\(223\) −5.81768 −0.389581 −0.194790 0.980845i \(-0.562403\pi\)
−0.194790 + 0.980845i \(0.562403\pi\)
\(224\) −4.26981 −0.285289
\(225\) 74.7102 4.98068
\(226\) −36.2631 −2.41219
\(227\) 8.09810 0.537490 0.268745 0.963211i \(-0.413391\pi\)
0.268745 + 0.963211i \(0.413391\pi\)
\(228\) 30.9640 2.05064
\(229\) −15.9430 −1.05354 −0.526772 0.850007i \(-0.676598\pi\)
−0.526772 + 0.850007i \(0.676598\pi\)
\(230\) 51.7491 3.41223
\(231\) 18.0907 1.19028
\(232\) −8.88719 −0.583473
\(233\) −15.8721 −1.03982 −0.519909 0.854222i \(-0.674034\pi\)
−0.519909 + 0.854222i \(0.674034\pi\)
\(234\) 78.5011 5.13178
\(235\) −53.1596 −3.46775
\(236\) −40.5570 −2.64004
\(237\) −11.1036 −0.721256
\(238\) 17.0733 1.10670
\(239\) 14.1564 0.915703 0.457852 0.889029i \(-0.348619\pi\)
0.457852 + 0.889029i \(0.348619\pi\)
\(240\) −15.7386 −1.01592
\(241\) −12.9146 −0.831904 −0.415952 0.909387i \(-0.636552\pi\)
−0.415952 + 0.909387i \(0.636552\pi\)
\(242\) −45.2399 −2.90813
\(243\) 20.4642 1.31278
\(244\) −17.5193 −1.12156
\(245\) 23.4804 1.50011
\(246\) 16.7712 1.06929
\(247\) −13.5372 −0.861354
\(248\) 17.3525 1.10189
\(249\) 38.6824 2.45140
\(250\) 53.7589 3.40001
\(251\) 13.0071 0.821000 0.410500 0.911861i \(-0.365354\pi\)
0.410500 + 0.911861i \(0.365354\pi\)
\(252\) −25.3264 −1.59541
\(253\) −30.5748 −1.92222
\(254\) 23.1751 1.45413
\(255\) −87.3783 −5.47184
\(256\) −23.2238 −1.45149
\(257\) 6.84507 0.426984 0.213492 0.976945i \(-0.431516\pi\)
0.213492 + 0.976945i \(0.431516\pi\)
\(258\) −0.763808 −0.0475526
\(259\) 4.37003 0.271541
\(260\) 67.0981 4.16125
\(261\) 17.5035 1.08344
\(262\) 29.1304 1.79968
\(263\) −10.3701 −0.639448 −0.319724 0.947511i \(-0.603590\pi\)
−0.319724 + 0.947511i \(0.603590\pi\)
\(264\) 61.0928 3.76000
\(265\) 3.97132 0.243956
\(266\) 6.86209 0.420741
\(267\) −28.2127 −1.72659
\(268\) 32.4114 1.97984
\(269\) −20.4535 −1.24707 −0.623535 0.781795i \(-0.714304\pi\)
−0.623535 + 0.781795i \(0.714304\pi\)
\(270\) 115.567 7.03320
\(271\) 0.574480 0.0348972 0.0174486 0.999848i \(-0.494446\pi\)
0.0174486 + 0.999848i \(0.494446\pi\)
\(272\) 8.77586 0.532115
\(273\) 15.8617 0.959992
\(274\) −34.2419 −2.06863
\(275\) −59.2794 −3.57468
\(276\) 61.3174 3.69087
\(277\) 7.36175 0.442325 0.221162 0.975237i \(-0.429015\pi\)
0.221162 + 0.975237i \(0.429015\pi\)
\(278\) −24.0341 −1.44147
\(279\) −34.1760 −2.04607
\(280\) −14.5848 −0.871607
\(281\) −29.8642 −1.78155 −0.890774 0.454446i \(-0.849837\pi\)
−0.890774 + 0.454446i \(0.849837\pi\)
\(282\) −98.9674 −5.89342
\(283\) −27.3521 −1.62591 −0.812956 0.582324i \(-0.802143\pi\)
−0.812956 + 0.582324i \(0.802143\pi\)
\(284\) −15.3307 −0.909710
\(285\) −35.1190 −2.08027
\(286\) −62.2874 −3.68313
\(287\) 2.36556 0.139635
\(288\) 28.3990 1.67343
\(289\) 31.7222 1.86601
\(290\) 23.5065 1.38035
\(291\) 38.9908 2.28568
\(292\) −18.1251 −1.06069
\(293\) −13.1653 −0.769124 −0.384562 0.923099i \(-0.625648\pi\)
−0.384562 + 0.923099i \(0.625648\pi\)
\(294\) 43.7135 2.54942
\(295\) 45.9994 2.67819
\(296\) 14.7577 0.857776
\(297\) −68.2804 −3.96203
\(298\) 15.5928 0.903268
\(299\) −26.8076 −1.55032
\(300\) 118.884 6.86379
\(301\) −0.107734 −0.00620971
\(302\) 2.34552 0.134969
\(303\) 32.0694 1.84234
\(304\) 3.52719 0.202298
\(305\) 19.8703 1.13777
\(306\) −113.556 −6.49159
\(307\) −26.6418 −1.52053 −0.760265 0.649613i \(-0.774931\pi\)
−0.760265 + 0.649613i \(0.774931\pi\)
\(308\) 20.0954 1.14504
\(309\) −44.6448 −2.53975
\(310\) −45.8971 −2.60678
\(311\) −13.8513 −0.785438 −0.392719 0.919659i \(-0.628465\pi\)
−0.392719 + 0.919659i \(0.628465\pi\)
\(312\) 53.5653 3.03254
\(313\) −29.9143 −1.69086 −0.845429 0.534088i \(-0.820655\pi\)
−0.845429 + 0.534088i \(0.820655\pi\)
\(314\) 15.5634 0.878293
\(315\) 28.7249 1.61847
\(316\) −12.3341 −0.693845
\(317\) −35.5414 −1.99620 −0.998101 0.0615969i \(-0.980381\pi\)
−0.998101 + 0.0615969i \(0.980381\pi\)
\(318\) 7.39341 0.414602
\(319\) −13.8883 −0.777594
\(320\) 48.1248 2.69026
\(321\) −38.6703 −2.15837
\(322\) 13.5889 0.757278
\(323\) 19.5824 1.08959
\(324\) 64.0772 3.55985
\(325\) −51.9754 −2.88308
\(326\) −57.7542 −3.19871
\(327\) 19.3386 1.06943
\(328\) 7.98858 0.441095
\(329\) −13.9593 −0.769599
\(330\) −161.589 −8.89521
\(331\) −23.7422 −1.30499 −0.652494 0.757794i \(-0.726277\pi\)
−0.652494 + 0.757794i \(0.726277\pi\)
\(332\) 42.9690 2.35823
\(333\) −29.0656 −1.59278
\(334\) 7.18066 0.392908
\(335\) −36.7608 −2.00845
\(336\) −4.13283 −0.225464
\(337\) 14.5673 0.793530 0.396765 0.917920i \(-0.370133\pi\)
0.396765 + 0.917920i \(0.370133\pi\)
\(338\) −24.1210 −1.31201
\(339\) 48.7340 2.64687
\(340\) −97.0613 −5.26389
\(341\) 27.1173 1.46848
\(342\) −45.6405 −2.46796
\(343\) 13.4656 0.727074
\(344\) −0.363823 −0.0196160
\(345\) −69.5457 −3.74421
\(346\) 20.8350 1.12010
\(347\) 8.79001 0.471873 0.235936 0.971769i \(-0.424184\pi\)
0.235936 + 0.971769i \(0.424184\pi\)
\(348\) 27.8528 1.49307
\(349\) −4.51073 −0.241454 −0.120727 0.992686i \(-0.538523\pi\)
−0.120727 + 0.992686i \(0.538523\pi\)
\(350\) 26.3466 1.40828
\(351\) −59.8673 −3.19548
\(352\) −22.5334 −1.20104
\(353\) −26.9852 −1.43628 −0.718140 0.695899i \(-0.755006\pi\)
−0.718140 + 0.695899i \(0.755006\pi\)
\(354\) 85.6371 4.55156
\(355\) 17.3880 0.922857
\(356\) −31.3391 −1.66097
\(357\) −22.9448 −1.21437
\(358\) 4.39160 0.232103
\(359\) −1.42982 −0.0754631 −0.0377315 0.999288i \(-0.512013\pi\)
−0.0377315 + 0.999288i \(0.512013\pi\)
\(360\) 97.0050 5.11261
\(361\) −11.1295 −0.585761
\(362\) 47.4513 2.49398
\(363\) 60.7980 3.19107
\(364\) 17.6194 0.923507
\(365\) 20.5574 1.07602
\(366\) 36.9925 1.93363
\(367\) 10.4541 0.545700 0.272850 0.962057i \(-0.412034\pi\)
0.272850 + 0.962057i \(0.412034\pi\)
\(368\) 6.98483 0.364109
\(369\) −15.7336 −0.819060
\(370\) −39.0339 −2.02928
\(371\) 1.04283 0.0541412
\(372\) −54.3834 −2.81965
\(373\) −8.75035 −0.453076 −0.226538 0.974002i \(-0.572741\pi\)
−0.226538 + 0.974002i \(0.572741\pi\)
\(374\) 90.1023 4.65908
\(375\) −72.2467 −3.73080
\(376\) −47.1409 −2.43110
\(377\) −12.1770 −0.627150
\(378\) 30.3470 1.56088
\(379\) −22.0649 −1.13340 −0.566699 0.823925i \(-0.691780\pi\)
−0.566699 + 0.823925i \(0.691780\pi\)
\(380\) −39.0108 −2.00121
\(381\) −31.1450 −1.59561
\(382\) −30.7393 −1.57276
\(383\) −8.02210 −0.409910 −0.204955 0.978771i \(-0.565705\pi\)
−0.204955 + 0.978771i \(0.565705\pi\)
\(384\) 63.7815 3.25484
\(385\) −22.7921 −1.16159
\(386\) −45.0260 −2.29177
\(387\) 0.716554 0.0364245
\(388\) 43.3117 2.19882
\(389\) −0.885811 −0.0449124 −0.0224562 0.999748i \(-0.507149\pi\)
−0.0224562 + 0.999748i \(0.507149\pi\)
\(390\) −141.679 −7.17421
\(391\) 38.7787 1.96112
\(392\) 20.8219 1.05167
\(393\) −39.1484 −1.97478
\(394\) −57.6117 −2.90243
\(395\) 13.9892 0.703872
\(396\) −133.657 −6.71652
\(397\) −35.9632 −1.80494 −0.902470 0.430754i \(-0.858248\pi\)
−0.902470 + 0.430754i \(0.858248\pi\)
\(398\) 45.1504 2.26318
\(399\) −9.22196 −0.461676
\(400\) 13.5424 0.677121
\(401\) −2.38362 −0.119032 −0.0595160 0.998227i \(-0.518956\pi\)
−0.0595160 + 0.998227i \(0.518956\pi\)
\(402\) −68.4376 −3.41336
\(403\) 23.7760 1.18437
\(404\) 35.6232 1.77232
\(405\) −72.6758 −3.61129
\(406\) 6.17260 0.306341
\(407\) 23.0623 1.14316
\(408\) −77.4853 −3.83610
\(409\) 0.0752741 0.00372206 0.00186103 0.999998i \(-0.499408\pi\)
0.00186103 + 0.999998i \(0.499408\pi\)
\(410\) −21.1296 −1.04352
\(411\) 46.0178 2.26989
\(412\) −49.5921 −2.44323
\(413\) 12.0790 0.594371
\(414\) −90.3812 −4.44199
\(415\) −48.7351 −2.39231
\(416\) −19.7570 −0.968667
\(417\) 32.2995 1.58171
\(418\) 36.2139 1.77128
\(419\) 7.32288 0.357746 0.178873 0.983872i \(-0.442755\pi\)
0.178873 + 0.983872i \(0.442755\pi\)
\(420\) 45.7092 2.23038
\(421\) 15.1602 0.738862 0.369431 0.929258i \(-0.379553\pi\)
0.369431 + 0.929258i \(0.379553\pi\)
\(422\) 38.8600 1.89168
\(423\) 92.8447 4.51426
\(424\) 3.52168 0.171028
\(425\) 75.1854 3.64703
\(426\) 32.3712 1.56839
\(427\) 5.21776 0.252505
\(428\) −42.9556 −2.07634
\(429\) 83.7081 4.04147
\(430\) 0.962305 0.0464065
\(431\) 33.1437 1.59648 0.798238 0.602342i \(-0.205766\pi\)
0.798238 + 0.602342i \(0.205766\pi\)
\(432\) 15.5987 0.750493
\(433\) 6.80192 0.326879 0.163440 0.986553i \(-0.447741\pi\)
0.163440 + 0.986553i \(0.447741\pi\)
\(434\) −12.0522 −0.578523
\(435\) −31.5904 −1.51464
\(436\) 21.4817 1.02879
\(437\) 15.5859 0.745575
\(438\) 38.2717 1.82869
\(439\) −2.27086 −0.108382 −0.0541912 0.998531i \(-0.517258\pi\)
−0.0541912 + 0.998531i \(0.517258\pi\)
\(440\) −76.9695 −3.66938
\(441\) −41.0091 −1.95282
\(442\) 79.0005 3.75767
\(443\) 17.9739 0.853966 0.426983 0.904260i \(-0.359576\pi\)
0.426983 + 0.904260i \(0.359576\pi\)
\(444\) −46.2513 −2.19499
\(445\) 35.5445 1.68497
\(446\) 13.6455 0.646132
\(447\) −20.9552 −0.991147
\(448\) 12.6372 0.597049
\(449\) −11.7656 −0.555255 −0.277628 0.960689i \(-0.589548\pi\)
−0.277628 + 0.960689i \(0.589548\pi\)
\(450\) −175.234 −8.26061
\(451\) 12.4840 0.587848
\(452\) 54.1345 2.54627
\(453\) −3.15214 −0.148101
\(454\) −18.9942 −0.891444
\(455\) −19.9838 −0.936853
\(456\) −31.1429 −1.45840
\(457\) −30.7963 −1.44059 −0.720295 0.693668i \(-0.755994\pi\)
−0.720295 + 0.693668i \(0.755994\pi\)
\(458\) 37.3946 1.74733
\(459\) 86.6015 4.04221
\(460\) −77.2525 −3.60191
\(461\) 6.98632 0.325385 0.162693 0.986677i \(-0.447982\pi\)
0.162693 + 0.986677i \(0.447982\pi\)
\(462\) −42.4320 −1.97412
\(463\) −30.6727 −1.42548 −0.712741 0.701427i \(-0.752546\pi\)
−0.712741 + 0.701427i \(0.752546\pi\)
\(464\) 3.17278 0.147293
\(465\) 61.6811 2.86039
\(466\) 37.2283 1.72457
\(467\) −7.67184 −0.355010 −0.177505 0.984120i \(-0.556803\pi\)
−0.177505 + 0.984120i \(0.556803\pi\)
\(468\) −117.189 −5.41705
\(469\) −9.65306 −0.445737
\(470\) 124.687 5.75137
\(471\) −20.9157 −0.963743
\(472\) 40.7913 1.87757
\(473\) −0.568556 −0.0261423
\(474\) 26.0437 1.19623
\(475\) 30.2185 1.38652
\(476\) −25.4875 −1.16822
\(477\) −6.93601 −0.317578
\(478\) −33.2041 −1.51872
\(479\) −24.3706 −1.11352 −0.556761 0.830673i \(-0.687956\pi\)
−0.556761 + 0.830673i \(0.687956\pi\)
\(480\) −51.2547 −2.33945
\(481\) 20.2207 0.921986
\(482\) 30.2915 1.37974
\(483\) −18.2621 −0.830955
\(484\) 67.5354 3.06979
\(485\) −49.1237 −2.23059
\(486\) −47.9992 −2.17729
\(487\) −25.0511 −1.13517 −0.567586 0.823314i \(-0.692123\pi\)
−0.567586 + 0.823314i \(0.692123\pi\)
\(488\) 17.6205 0.797645
\(489\) 77.6159 3.50991
\(490\) −55.0737 −2.48798
\(491\) −43.4091 −1.95902 −0.979512 0.201384i \(-0.935456\pi\)
−0.979512 + 0.201384i \(0.935456\pi\)
\(492\) −25.0365 −1.12873
\(493\) 17.6148 0.793331
\(494\) 31.7518 1.42858
\(495\) 151.593 6.81358
\(496\) −6.19496 −0.278162
\(497\) 4.56593 0.204810
\(498\) −90.7302 −4.06572
\(499\) −18.1571 −0.812823 −0.406411 0.913690i \(-0.633220\pi\)
−0.406411 + 0.913690i \(0.633220\pi\)
\(500\) −80.2528 −3.58901
\(501\) −9.65010 −0.431134
\(502\) −30.5083 −1.36165
\(503\) −3.95074 −0.176155 −0.0880773 0.996114i \(-0.528072\pi\)
−0.0880773 + 0.996114i \(0.528072\pi\)
\(504\) 25.4727 1.13464
\(505\) −40.4035 −1.79793
\(506\) 71.7137 3.18806
\(507\) 32.4162 1.43966
\(508\) −34.5963 −1.53496
\(509\) −17.0282 −0.754759 −0.377380 0.926059i \(-0.623175\pi\)
−0.377380 + 0.926059i \(0.623175\pi\)
\(510\) 204.947 9.07522
\(511\) 5.39819 0.238802
\(512\) 14.0031 0.618857
\(513\) 34.8068 1.53676
\(514\) −16.0552 −0.708166
\(515\) 56.2469 2.47854
\(516\) 1.14023 0.0501960
\(517\) −73.6684 −3.23993
\(518\) −10.2500 −0.450358
\(519\) −28.0002 −1.22907
\(520\) −67.4858 −2.95945
\(521\) 16.9285 0.741652 0.370826 0.928702i \(-0.379075\pi\)
0.370826 + 0.928702i \(0.379075\pi\)
\(522\) −41.0547 −1.79691
\(523\) −37.9676 −1.66021 −0.830103 0.557610i \(-0.811718\pi\)
−0.830103 + 0.557610i \(0.811718\pi\)
\(524\) −43.4867 −1.89973
\(525\) −35.4072 −1.54530
\(526\) 24.3233 1.06054
\(527\) −34.3934 −1.49820
\(528\) −21.8105 −0.949181
\(529\) 7.86451 0.341935
\(530\) −9.31479 −0.404609
\(531\) −80.3391 −3.48642
\(532\) −10.2439 −0.444130
\(533\) 10.9458 0.474114
\(534\) 66.1733 2.86360
\(535\) 48.7199 2.10634
\(536\) −32.5987 −1.40805
\(537\) −5.90188 −0.254685
\(538\) 47.9740 2.06831
\(539\) 32.5391 1.40156
\(540\) −172.522 −7.42417
\(541\) −0.869907 −0.0374002 −0.0187001 0.999825i \(-0.505953\pi\)
−0.0187001 + 0.999825i \(0.505953\pi\)
\(542\) −1.34745 −0.0578780
\(543\) −63.7698 −2.73662
\(544\) 28.5797 1.22534
\(545\) −24.3643 −1.04365
\(546\) −37.2038 −1.59218
\(547\) 41.6084 1.77905 0.889523 0.456890i \(-0.151037\pi\)
0.889523 + 0.456890i \(0.151037\pi\)
\(548\) 51.1173 2.18362
\(549\) −34.7039 −1.48113
\(550\) 139.041 5.92873
\(551\) 7.07973 0.301607
\(552\) −61.6717 −2.62492
\(553\) 3.67344 0.156210
\(554\) −17.2671 −0.733610
\(555\) 52.4578 2.22671
\(556\) 35.8788 1.52160
\(557\) 20.4343 0.865829 0.432914 0.901435i \(-0.357485\pi\)
0.432914 + 0.901435i \(0.357485\pi\)
\(558\) 80.1605 3.39346
\(559\) −0.498502 −0.0210844
\(560\) 5.20686 0.220030
\(561\) −121.089 −5.11237
\(562\) 70.0470 2.95475
\(563\) 30.5117 1.28591 0.642957 0.765903i \(-0.277708\pi\)
0.642957 + 0.765903i \(0.277708\pi\)
\(564\) 147.741 6.22103
\(565\) −61.3989 −2.58307
\(566\) 64.1548 2.69663
\(567\) −19.0841 −0.801455
\(568\) 15.4193 0.646979
\(569\) 27.8902 1.16922 0.584610 0.811314i \(-0.301248\pi\)
0.584610 + 0.811314i \(0.301248\pi\)
\(570\) 82.3723 3.45020
\(571\) −8.26252 −0.345776 −0.172888 0.984942i \(-0.555310\pi\)
−0.172888 + 0.984942i \(0.555310\pi\)
\(572\) 92.9843 3.88787
\(573\) 41.3106 1.72578
\(574\) −5.54847 −0.231589
\(575\) 59.8411 2.49555
\(576\) −84.0512 −3.50213
\(577\) −4.44259 −0.184948 −0.0924738 0.995715i \(-0.529477\pi\)
−0.0924738 + 0.995715i \(0.529477\pi\)
\(578\) −74.4050 −3.09484
\(579\) 60.5105 2.51473
\(580\) −35.0911 −1.45708
\(581\) −12.7974 −0.530926
\(582\) −91.4537 −3.79088
\(583\) 5.50344 0.227929
\(584\) 18.2299 0.754357
\(585\) 132.914 5.49533
\(586\) 30.8794 1.27562
\(587\) −4.97345 −0.205276 −0.102638 0.994719i \(-0.532728\pi\)
−0.102638 + 0.994719i \(0.532728\pi\)
\(588\) −65.2567 −2.69114
\(589\) −13.8234 −0.569582
\(590\) −107.892 −4.44186
\(591\) 77.4244 3.18481
\(592\) −5.26860 −0.216538
\(593\) −5.21919 −0.214326 −0.107163 0.994241i \(-0.534177\pi\)
−0.107163 + 0.994241i \(0.534177\pi\)
\(594\) 160.153 6.57115
\(595\) 28.9077 1.18510
\(596\) −23.2774 −0.953479
\(597\) −60.6776 −2.48337
\(598\) 62.8776 2.57126
\(599\) 3.68277 0.150474 0.0752370 0.997166i \(-0.476029\pi\)
0.0752370 + 0.997166i \(0.476029\pi\)
\(600\) −119.571 −4.88147
\(601\) −15.9179 −0.649305 −0.324653 0.945833i \(-0.605247\pi\)
−0.324653 + 0.945833i \(0.605247\pi\)
\(602\) 0.252693 0.0102990
\(603\) 64.2036 2.61457
\(604\) −3.50145 −0.142472
\(605\) −76.5980 −3.11415
\(606\) −75.2193 −3.05557
\(607\) −31.5212 −1.27941 −0.639704 0.768622i \(-0.720943\pi\)
−0.639704 + 0.768622i \(0.720943\pi\)
\(608\) 11.4867 0.465848
\(609\) −8.29536 −0.336145
\(610\) −46.6061 −1.88702
\(611\) −64.5914 −2.61309
\(612\) 169.520 6.85244
\(613\) 15.4872 0.625523 0.312761 0.949832i \(-0.398746\pi\)
0.312761 + 0.949832i \(0.398746\pi\)
\(614\) 62.4889 2.52185
\(615\) 28.3962 1.14504
\(616\) −20.2115 −0.814346
\(617\) −12.3772 −0.498285 −0.249143 0.968467i \(-0.580149\pi\)
−0.249143 + 0.968467i \(0.580149\pi\)
\(618\) 104.715 4.21226
\(619\) −25.5839 −1.02830 −0.514151 0.857700i \(-0.671893\pi\)
−0.514151 + 0.857700i \(0.671893\pi\)
\(620\) 68.5164 2.75169
\(621\) 68.9274 2.76596
\(622\) 32.4886 1.30267
\(623\) 9.33370 0.373947
\(624\) −19.1232 −0.765539
\(625\) 37.1652 1.48661
\(626\) 70.1646 2.80434
\(627\) −48.6679 −1.94361
\(628\) −23.2335 −0.927116
\(629\) −29.2505 −1.16629
\(630\) −67.3749 −2.68428
\(631\) 43.4395 1.72930 0.864650 0.502374i \(-0.167540\pi\)
0.864650 + 0.502374i \(0.167540\pi\)
\(632\) 12.4053 0.493457
\(633\) −52.2241 −2.07572
\(634\) 83.3629 3.31076
\(635\) 39.2389 1.55715
\(636\) −11.0371 −0.437649
\(637\) 28.5298 1.13039
\(638\) 32.5752 1.28966
\(639\) −30.3685 −1.20136
\(640\) −80.3569 −3.17639
\(641\) 34.6308 1.36784 0.683918 0.729559i \(-0.260275\pi\)
0.683918 + 0.729559i \(0.260275\pi\)
\(642\) 90.7019 3.57972
\(643\) 3.66932 0.144704 0.0723519 0.997379i \(-0.476950\pi\)
0.0723519 + 0.997379i \(0.476950\pi\)
\(644\) −20.2858 −0.799374
\(645\) −1.29324 −0.0509214
\(646\) −45.9308 −1.80712
\(647\) −31.2028 −1.22671 −0.613354 0.789808i \(-0.710180\pi\)
−0.613354 + 0.789808i \(0.710180\pi\)
\(648\) −64.4475 −2.53174
\(649\) 63.7458 2.50224
\(650\) 121.909 4.78167
\(651\) 16.1969 0.634808
\(652\) 86.2170 3.37652
\(653\) −10.4249 −0.407959 −0.203980 0.978975i \(-0.565388\pi\)
−0.203980 + 0.978975i \(0.565388\pi\)
\(654\) −45.3591 −1.77368
\(655\) 49.3222 1.92718
\(656\) −2.85197 −0.111351
\(657\) −35.9040 −1.40075
\(658\) 32.7417 1.27640
\(659\) −47.1818 −1.83794 −0.918971 0.394326i \(-0.870978\pi\)
−0.918971 + 0.394326i \(0.870978\pi\)
\(660\) 241.225 9.38968
\(661\) 8.45099 0.328705 0.164353 0.986402i \(-0.447446\pi\)
0.164353 + 0.986402i \(0.447446\pi\)
\(662\) 55.6877 2.16436
\(663\) −106.169 −4.12326
\(664\) −43.2173 −1.67716
\(665\) 11.6185 0.450548
\(666\) 68.1738 2.64168
\(667\) 14.0199 0.542851
\(668\) −10.7195 −0.414749
\(669\) −18.3382 −0.708995
\(670\) 86.2230 3.33108
\(671\) 27.5362 1.06302
\(672\) −13.4591 −0.519195
\(673\) 33.6766 1.29814 0.649069 0.760729i \(-0.275158\pi\)
0.649069 + 0.760729i \(0.275158\pi\)
\(674\) −34.1678 −1.31609
\(675\) 133.639 5.14375
\(676\) 36.0085 1.38494
\(677\) 18.7060 0.718929 0.359465 0.933159i \(-0.382959\pi\)
0.359465 + 0.933159i \(0.382959\pi\)
\(678\) −114.307 −4.38992
\(679\) −12.8995 −0.495036
\(680\) 97.6221 3.74364
\(681\) 25.5264 0.978173
\(682\) −63.6040 −2.43552
\(683\) 40.0938 1.53415 0.767073 0.641560i \(-0.221713\pi\)
0.767073 + 0.641560i \(0.221713\pi\)
\(684\) 68.1334 2.60515
\(685\) −57.9768 −2.21518
\(686\) −31.5838 −1.20587
\(687\) −50.2546 −1.91733
\(688\) 0.129887 0.00495190
\(689\) 4.82534 0.183831
\(690\) 163.121 6.20989
\(691\) 0.481014 0.0182987 0.00914933 0.999958i \(-0.497088\pi\)
0.00914933 + 0.999958i \(0.497088\pi\)
\(692\) −31.1031 −1.18236
\(693\) 39.8069 1.51214
\(694\) −20.6171 −0.782616
\(695\) −40.6934 −1.54359
\(696\) −28.0137 −1.06186
\(697\) −15.8337 −0.599744
\(698\) 10.5800 0.400459
\(699\) −50.0312 −1.89235
\(700\) −39.3309 −1.48657
\(701\) −14.8744 −0.561800 −0.280900 0.959737i \(-0.590633\pi\)
−0.280900 + 0.959737i \(0.590633\pi\)
\(702\) 140.420 5.29980
\(703\) −11.7563 −0.443398
\(704\) 66.6911 2.51352
\(705\) −167.567 −6.31093
\(706\) 63.2944 2.38211
\(707\) −10.6096 −0.399016
\(708\) −127.841 −4.80458
\(709\) −19.6190 −0.736808 −0.368404 0.929666i \(-0.620096\pi\)
−0.368404 + 0.929666i \(0.620096\pi\)
\(710\) −40.7838 −1.53059
\(711\) −24.4325 −0.916289
\(712\) 31.5202 1.18127
\(713\) −27.3742 −1.02517
\(714\) 53.8175 2.01407
\(715\) −105.462 −3.94406
\(716\) −6.55590 −0.245006
\(717\) 44.6231 1.66648
\(718\) 3.35367 0.125158
\(719\) 8.32799 0.310582 0.155291 0.987869i \(-0.450369\pi\)
0.155291 + 0.987869i \(0.450369\pi\)
\(720\) −34.6314 −1.29064
\(721\) 14.7700 0.550062
\(722\) 26.1043 0.971503
\(723\) −40.7087 −1.51397
\(724\) −70.8365 −2.63262
\(725\) 27.1822 1.00952
\(726\) −142.603 −5.29248
\(727\) 37.2688 1.38222 0.691112 0.722747i \(-0.257121\pi\)
0.691112 + 0.722747i \(0.257121\pi\)
\(728\) −17.7212 −0.656791
\(729\) 9.60563 0.355764
\(730\) −48.2177 −1.78462
\(731\) 0.721112 0.0266713
\(732\) −55.2234 −2.04112
\(733\) 28.2789 1.04451 0.522253 0.852791i \(-0.325092\pi\)
0.522253 + 0.852791i \(0.325092\pi\)
\(734\) −24.5203 −0.905060
\(735\) 74.0136 2.73003
\(736\) 22.7470 0.838464
\(737\) −50.9429 −1.87651
\(738\) 36.9035 1.35844
\(739\) 17.1794 0.631955 0.315977 0.948767i \(-0.397668\pi\)
0.315977 + 0.948767i \(0.397668\pi\)
\(740\) 58.2709 2.14208
\(741\) −42.6713 −1.56757
\(742\) −2.44599 −0.0897949
\(743\) −40.0252 −1.46838 −0.734191 0.678943i \(-0.762438\pi\)
−0.734191 + 0.678943i \(0.762438\pi\)
\(744\) 54.6976 2.00531
\(745\) 26.4010 0.967258
\(746\) 20.5241 0.751441
\(747\) 85.1171 3.11427
\(748\) −134.507 −4.91807
\(749\) 12.7934 0.467462
\(750\) 169.456 6.18765
\(751\) 39.3096 1.43443 0.717213 0.696854i \(-0.245417\pi\)
0.717213 + 0.696854i \(0.245417\pi\)
\(752\) 16.8296 0.613712
\(753\) 41.0002 1.49413
\(754\) 28.5615 1.04015
\(755\) 3.97132 0.144531
\(756\) −45.3028 −1.64765
\(757\) 6.63238 0.241058 0.120529 0.992710i \(-0.461541\pi\)
0.120529 + 0.992710i \(0.461541\pi\)
\(758\) 51.7536 1.87978
\(759\) −96.3762 −3.49823
\(760\) 39.2362 1.42325
\(761\) −18.3538 −0.665325 −0.332663 0.943046i \(-0.607947\pi\)
−0.332663 + 0.943046i \(0.607947\pi\)
\(762\) 73.0511 2.64636
\(763\) −6.39787 −0.231618
\(764\) 45.8885 1.66019
\(765\) −192.268 −6.95147
\(766\) 18.8160 0.679849
\(767\) 55.8914 2.01812
\(768\) −73.2047 −2.64155
\(769\) 21.4488 0.773463 0.386732 0.922192i \(-0.373604\pi\)
0.386732 + 0.922192i \(0.373604\pi\)
\(770\) 53.4592 1.92653
\(771\) 21.5766 0.777064
\(772\) 67.2161 2.41916
\(773\) −36.9424 −1.32872 −0.664362 0.747411i \(-0.731297\pi\)
−0.664362 + 0.747411i \(0.731297\pi\)
\(774\) −1.68069 −0.0604112
\(775\) −53.0740 −1.90648
\(776\) −43.5619 −1.56378
\(777\) 13.7750 0.494174
\(778\) 2.07769 0.0744887
\(779\) −6.36387 −0.228009
\(780\) 211.503 7.57302
\(781\) 24.0962 0.862229
\(782\) −90.9561 −3.25258
\(783\) 31.3095 1.11891
\(784\) −7.43357 −0.265484
\(785\) 26.3512 0.940514
\(786\) 91.8233 3.27523
\(787\) 22.1028 0.787878 0.393939 0.919137i \(-0.371112\pi\)
0.393939 + 0.919137i \(0.371112\pi\)
\(788\) 86.0042 3.06377
\(789\) −32.6881 −1.16373
\(790\) −32.8118 −1.16739
\(791\) −16.1228 −0.573262
\(792\) 134.429 4.77674
\(793\) 24.1433 0.857354
\(794\) 84.3522 2.99355
\(795\) 12.5182 0.443973
\(796\) −67.4017 −2.38899
\(797\) −10.8488 −0.384285 −0.192142 0.981367i \(-0.561544\pi\)
−0.192142 + 0.981367i \(0.561544\pi\)
\(798\) 21.6303 0.765704
\(799\) 93.4353 3.30550
\(800\) 44.1026 1.55926
\(801\) −62.0795 −2.19347
\(802\) 5.59081 0.197418
\(803\) 28.4883 1.00533
\(804\) 102.165 3.60310
\(805\) 23.0080 0.810926
\(806\) −55.7671 −1.96431
\(807\) −64.4723 −2.26953
\(808\) −35.8290 −1.26046
\(809\) −5.86806 −0.206310 −0.103155 0.994665i \(-0.532894\pi\)
−0.103155 + 0.994665i \(0.532894\pi\)
\(810\) 170.462 5.98944
\(811\) −10.4415 −0.366651 −0.183325 0.983052i \(-0.558686\pi\)
−0.183325 + 0.983052i \(0.558686\pi\)
\(812\) −9.21462 −0.323370
\(813\) 1.81084 0.0635090
\(814\) −54.0931 −1.89596
\(815\) −97.7865 −3.42531
\(816\) 27.6628 0.968391
\(817\) 0.289829 0.0101398
\(818\) −0.176557 −0.00617316
\(819\) 34.9022 1.21958
\(820\) 31.5429 1.10153
\(821\) 51.5650 1.79963 0.899815 0.436271i \(-0.143701\pi\)
0.899815 + 0.436271i \(0.143701\pi\)
\(822\) −107.935 −3.76468
\(823\) 52.6092 1.83384 0.916920 0.399071i \(-0.130667\pi\)
0.916920 + 0.399071i \(0.130667\pi\)
\(824\) 49.8786 1.73761
\(825\) −186.857 −6.50554
\(826\) −28.3316 −0.985783
\(827\) 2.56059 0.0890405 0.0445203 0.999008i \(-0.485824\pi\)
0.0445203 + 0.999008i \(0.485824\pi\)
\(828\) 134.923 4.68891
\(829\) −26.3995 −0.916894 −0.458447 0.888722i \(-0.651594\pi\)
−0.458447 + 0.888722i \(0.651594\pi\)
\(830\) 114.309 3.96772
\(831\) 23.2053 0.804983
\(832\) 58.4739 2.02722
\(833\) −41.2700 −1.42992
\(834\) −75.7591 −2.62332
\(835\) 12.1579 0.420743
\(836\) −54.0611 −1.86974
\(837\) −61.1328 −2.11306
\(838\) −17.1760 −0.593333
\(839\) 29.7082 1.02564 0.512821 0.858496i \(-0.328601\pi\)
0.512821 + 0.858496i \(0.328601\pi\)
\(840\) −45.9733 −1.58623
\(841\) −22.6316 −0.780401
\(842\) −35.5585 −1.22543
\(843\) −94.1362 −3.24222
\(844\) −58.0113 −1.99683
\(845\) −40.8405 −1.40496
\(846\) −217.769 −7.48705
\(847\) −20.1140 −0.691125
\(848\) −1.25726 −0.0431746
\(849\) −86.2177 −2.95898
\(850\) −176.349 −6.04871
\(851\) −23.2809 −0.798058
\(852\) −48.3246 −1.65557
\(853\) −2.99792 −0.102647 −0.0513234 0.998682i \(-0.516344\pi\)
−0.0513234 + 0.998682i \(0.516344\pi\)
\(854\) −12.2384 −0.418788
\(855\) −77.2763 −2.64279
\(856\) 43.2038 1.47667
\(857\) −30.2001 −1.03162 −0.515808 0.856704i \(-0.672508\pi\)
−0.515808 + 0.856704i \(0.672508\pi\)
\(858\) −196.339 −6.70290
\(859\) 8.94004 0.305030 0.152515 0.988301i \(-0.451263\pi\)
0.152515 + 0.988301i \(0.451263\pi\)
\(860\) −1.43655 −0.0489861
\(861\) 7.45659 0.254120
\(862\) −77.7391 −2.64780
\(863\) −4.85757 −0.165353 −0.0826767 0.996576i \(-0.526347\pi\)
−0.0826767 + 0.996576i \(0.526347\pi\)
\(864\) 50.7991 1.72822
\(865\) 35.2768 1.19945
\(866\) −15.9540 −0.542140
\(867\) 99.9929 3.39594
\(868\) 17.9918 0.610682
\(869\) 19.3861 0.657630
\(870\) 74.0958 2.51208
\(871\) −44.6660 −1.51345
\(872\) −21.6058 −0.731664
\(873\) 85.7959 2.90375
\(874\) −36.5570 −1.23656
\(875\) 23.9016 0.808022
\(876\) −57.1331 −1.93035
\(877\) −17.8263 −0.601950 −0.300975 0.953632i \(-0.597312\pi\)
−0.300975 + 0.953632i \(0.597312\pi\)
\(878\) 5.32635 0.179755
\(879\) −41.4989 −1.39972
\(880\) 27.4786 0.926304
\(881\) 18.4207 0.620608 0.310304 0.950637i \(-0.399569\pi\)
0.310304 + 0.950637i \(0.399569\pi\)
\(882\) 96.1876 3.23881
\(883\) −23.6326 −0.795301 −0.397650 0.917537i \(-0.630174\pi\)
−0.397650 + 0.917537i \(0.630174\pi\)
\(884\) −117.934 −3.96655
\(885\) 144.997 4.87401
\(886\) −42.1581 −1.41633
\(887\) 53.5529 1.79813 0.899065 0.437815i \(-0.144248\pi\)
0.899065 + 0.437815i \(0.144248\pi\)
\(888\) 46.5185 1.56106
\(889\) 10.3038 0.345578
\(890\) −83.3703 −2.79458
\(891\) −100.714 −3.37404
\(892\) −20.3703 −0.682050
\(893\) 37.5534 1.25668
\(894\) 49.1508 1.64385
\(895\) 7.43565 0.248546
\(896\) −21.1010 −0.704936
\(897\) −84.5013 −2.82142
\(898\) 27.5965 0.920908
\(899\) −12.4344 −0.414712
\(900\) 261.594 8.71980
\(901\) −6.98013 −0.232542
\(902\) −29.2814 −0.974964
\(903\) −0.339595 −0.0113010
\(904\) −54.4473 −1.81089
\(905\) 80.3422 2.67066
\(906\) 7.39341 0.245630
\(907\) 27.9646 0.928548 0.464274 0.885692i \(-0.346315\pi\)
0.464274 + 0.885692i \(0.346315\pi\)
\(908\) 28.3551 0.940998
\(909\) 70.5658 2.34052
\(910\) 46.8723 1.55380
\(911\) −37.5412 −1.24380 −0.621898 0.783098i \(-0.713638\pi\)
−0.621898 + 0.783098i \(0.713638\pi\)
\(912\) 11.1182 0.368160
\(913\) −67.5369 −2.23515
\(914\) 72.2333 2.38926
\(915\) 62.6339 2.07061
\(916\) −55.8237 −1.84447
\(917\) 12.9516 0.427699
\(918\) −203.125 −6.70414
\(919\) −20.0748 −0.662205 −0.331102 0.943595i \(-0.607421\pi\)
−0.331102 + 0.943595i \(0.607421\pi\)
\(920\) 77.6988 2.56165
\(921\) −83.9789 −2.76720
\(922\) −16.3865 −0.539662
\(923\) 21.1272 0.695410
\(924\) 63.3437 2.08385
\(925\) −45.1377 −1.48412
\(926\) 71.9434 2.36421
\(927\) −98.2368 −3.22652
\(928\) 10.3326 0.339183
\(929\) −13.9540 −0.457815 −0.228907 0.973448i \(-0.573515\pi\)
−0.228907 + 0.973448i \(0.573515\pi\)
\(930\) −144.674 −4.74405
\(931\) −16.5872 −0.543624
\(932\) −55.5755 −1.82044
\(933\) −43.6614 −1.42941
\(934\) 17.9944 0.588796
\(935\) 152.557 4.98914
\(936\) 117.866 3.85256
\(937\) 23.9229 0.781528 0.390764 0.920491i \(-0.372211\pi\)
0.390764 + 0.920491i \(0.372211\pi\)
\(938\) 22.6414 0.739269
\(939\) −94.2942 −3.07718
\(940\) −186.136 −6.07108
\(941\) −4.86204 −0.158498 −0.0792490 0.996855i \(-0.525252\pi\)
−0.0792490 + 0.996855i \(0.525252\pi\)
\(942\) 49.0581 1.59840
\(943\) −12.6023 −0.410386
\(944\) −14.5628 −0.473978
\(945\) 51.3821 1.67146
\(946\) 1.33356 0.0433577
\(947\) 15.1351 0.491825 0.245913 0.969292i \(-0.420912\pi\)
0.245913 + 0.969292i \(0.420912\pi\)
\(948\) −38.8787 −1.26272
\(949\) 24.9782 0.810826
\(950\) −70.8779 −2.29958
\(951\) −112.031 −3.63287
\(952\) 25.6347 0.830826
\(953\) 26.6970 0.864801 0.432400 0.901682i \(-0.357667\pi\)
0.432400 + 0.901682i \(0.357667\pi\)
\(954\) 16.2685 0.526713
\(955\) −52.0463 −1.68418
\(956\) 49.5680 1.60315
\(957\) −43.7778 −1.41514
\(958\) 57.1617 1.84681
\(959\) −15.2242 −0.491615
\(960\) 151.696 4.89597
\(961\) −6.72138 −0.216819
\(962\) −47.4281 −1.52914
\(963\) −85.0905 −2.74200
\(964\) −45.2199 −1.45644
\(965\) −76.2359 −2.45412
\(966\) 42.8341 1.37816
\(967\) −12.7153 −0.408896 −0.204448 0.978877i \(-0.565540\pi\)
−0.204448 + 0.978877i \(0.565540\pi\)
\(968\) −67.9256 −2.18321
\(969\) 61.7265 1.98294
\(970\) 115.221 3.69951
\(971\) −17.7984 −0.571179 −0.285590 0.958352i \(-0.592189\pi\)
−0.285590 + 0.958352i \(0.592189\pi\)
\(972\) 71.6545 2.29832
\(973\) −10.6858 −0.342569
\(974\) 58.7577 1.88272
\(975\) −163.834 −5.24688
\(976\) −6.29065 −0.201359
\(977\) −46.3300 −1.48223 −0.741113 0.671380i \(-0.765702\pi\)
−0.741113 + 0.671380i \(0.765702\pi\)
\(978\) −182.049 −5.82130
\(979\) 49.2575 1.57428
\(980\) 82.2155 2.62628
\(981\) 42.5529 1.35861
\(982\) 101.817 3.24910
\(983\) 7.82079 0.249445 0.124722 0.992192i \(-0.460196\pi\)
0.124722 + 0.992192i \(0.460196\pi\)
\(984\) 25.1811 0.802745
\(985\) −97.5452 −3.10805
\(986\) −41.3158 −1.31576
\(987\) −44.0016 −1.40059
\(988\) −47.4000 −1.50799
\(989\) 0.573944 0.0182503
\(990\) −355.563 −11.3005
\(991\) −7.67415 −0.243777 −0.121889 0.992544i \(-0.538895\pi\)
−0.121889 + 0.992544i \(0.538895\pi\)
\(992\) −20.1746 −0.640545
\(993\) −74.8388 −2.37494
\(994\) −10.7095 −0.339684
\(995\) 76.4464 2.42351
\(996\) 135.445 4.29172
\(997\) 41.8751 1.32620 0.663099 0.748532i \(-0.269241\pi\)
0.663099 + 0.748532i \(0.269241\pi\)
\(998\) 42.5878 1.34809
\(999\) −51.9914 −1.64493
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 8003.2.a.b.1.19 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.19 153 1.1 even 1 trivial