Properties

Label 8034.2.a.ba.1.3
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.09495\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.09495 q^{10} -2.08878 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.97310 q^{14} +3.09495 q^{15} +1.00000 q^{16} +3.07102 q^{17} -1.00000 q^{18} -6.35933 q^{19} -3.09495 q^{20} -3.97310 q^{21} +2.08878 q^{22} +0.753374 q^{23} +1.00000 q^{24} +4.57874 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.97310 q^{28} -7.73052 q^{29} -3.09495 q^{30} +5.41795 q^{31} -1.00000 q^{32} +2.08878 q^{33} -3.07102 q^{34} -12.2966 q^{35} +1.00000 q^{36} +6.26162 q^{37} +6.35933 q^{38} +1.00000 q^{39} +3.09495 q^{40} -3.19603 q^{41} +3.97310 q^{42} +4.21307 q^{43} -2.08878 q^{44} -3.09495 q^{45} -0.753374 q^{46} -9.09805 q^{47} -1.00000 q^{48} +8.78553 q^{49} -4.57874 q^{50} -3.07102 q^{51} -1.00000 q^{52} +1.78997 q^{53} +1.00000 q^{54} +6.46468 q^{55} -3.97310 q^{56} +6.35933 q^{57} +7.73052 q^{58} +3.06235 q^{59} +3.09495 q^{60} -7.26725 q^{61} -5.41795 q^{62} +3.97310 q^{63} +1.00000 q^{64} +3.09495 q^{65} -2.08878 q^{66} -4.59049 q^{67} +3.07102 q^{68} -0.753374 q^{69} +12.2966 q^{70} +6.81056 q^{71} -1.00000 q^{72} -1.90860 q^{73} -6.26162 q^{74} -4.57874 q^{75} -6.35933 q^{76} -8.29894 q^{77} -1.00000 q^{78} +3.61660 q^{79} -3.09495 q^{80} +1.00000 q^{81} +3.19603 q^{82} +11.1151 q^{83} -3.97310 q^{84} -9.50467 q^{85} -4.21307 q^{86} +7.73052 q^{87} +2.08878 q^{88} -10.2078 q^{89} +3.09495 q^{90} -3.97310 q^{91} +0.753374 q^{92} -5.41795 q^{93} +9.09805 q^{94} +19.6818 q^{95} +1.00000 q^{96} +14.6236 q^{97} -8.78553 q^{98} -2.08878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + q^{10} - q^{11} - 14q^{12} - 14q^{13} - 5q^{14} + q^{15} + 14q^{16} - 12q^{17} - 14q^{18} + 10q^{19} - q^{20} - 5q^{21} + q^{22} - q^{23} + 14q^{24} + 19q^{25} + 14q^{26} - 14q^{27} + 5q^{28} + 6q^{29} - q^{30} + 20q^{31} - 14q^{32} + q^{33} + 12q^{34} - 16q^{35} + 14q^{36} - 3q^{37} - 10q^{38} + 14q^{39} + q^{40} + q^{41} + 5q^{42} + 6q^{43} - q^{44} - q^{45} + q^{46} - 13q^{47} - 14q^{48} + 9q^{49} - 19q^{50} + 12q^{51} - 14q^{52} - 27q^{53} + 14q^{54} + 10q^{55} - 5q^{56} - 10q^{57} - 6q^{58} - 6q^{59} + q^{60} - 4q^{61} - 20q^{62} + 5q^{63} + 14q^{64} + q^{65} - q^{66} + 13q^{67} - 12q^{68} + q^{69} + 16q^{70} + 18q^{71} - 14q^{72} + 11q^{73} + 3q^{74} - 19q^{75} + 10q^{76} - 15q^{77} - 14q^{78} + 33q^{79} - q^{80} + 14q^{81} - q^{82} - 25q^{83} - 5q^{84} + 25q^{85} - 6q^{86} - 6q^{87} + q^{88} + 3q^{89} + q^{90} - 5q^{91} - q^{92} - 20q^{93} + 13q^{94} + 30q^{95} + 14q^{96} + 11q^{97} - 9q^{98} - q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −3.09495 −1.38411 −0.692053 0.721847i \(-0.743293\pi\)
−0.692053 + 0.721847i \(0.743293\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.97310 1.50169 0.750846 0.660478i \(-0.229646\pi\)
0.750846 + 0.660478i \(0.229646\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.09495 0.978710
\(11\) −2.08878 −0.629791 −0.314896 0.949126i \(-0.601969\pi\)
−0.314896 + 0.949126i \(0.601969\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −3.97310 −1.06186
\(15\) 3.09495 0.799114
\(16\) 1.00000 0.250000
\(17\) 3.07102 0.744832 0.372416 0.928066i \(-0.378529\pi\)
0.372416 + 0.928066i \(0.378529\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.35933 −1.45893 −0.729465 0.684018i \(-0.760231\pi\)
−0.729465 + 0.684018i \(0.760231\pi\)
\(20\) −3.09495 −0.692053
\(21\) −3.97310 −0.867002
\(22\) 2.08878 0.445329
\(23\) 0.753374 0.157089 0.0785447 0.996911i \(-0.474973\pi\)
0.0785447 + 0.996911i \(0.474973\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.57874 0.915748
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 3.97310 0.750846
\(29\) −7.73052 −1.43552 −0.717761 0.696290i \(-0.754833\pi\)
−0.717761 + 0.696290i \(0.754833\pi\)
\(30\) −3.09495 −0.565059
\(31\) 5.41795 0.973092 0.486546 0.873655i \(-0.338257\pi\)
0.486546 + 0.873655i \(0.338257\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.08878 0.363610
\(34\) −3.07102 −0.526676
\(35\) −12.2966 −2.07850
\(36\) 1.00000 0.166667
\(37\) 6.26162 1.02940 0.514702 0.857369i \(-0.327903\pi\)
0.514702 + 0.857369i \(0.327903\pi\)
\(38\) 6.35933 1.03162
\(39\) 1.00000 0.160128
\(40\) 3.09495 0.489355
\(41\) −3.19603 −0.499136 −0.249568 0.968357i \(-0.580289\pi\)
−0.249568 + 0.968357i \(0.580289\pi\)
\(42\) 3.97310 0.613063
\(43\) 4.21307 0.642486 0.321243 0.946997i \(-0.395899\pi\)
0.321243 + 0.946997i \(0.395899\pi\)
\(44\) −2.08878 −0.314896
\(45\) −3.09495 −0.461368
\(46\) −0.753374 −0.111079
\(47\) −9.09805 −1.32709 −0.663544 0.748138i \(-0.730948\pi\)
−0.663544 + 0.748138i \(0.730948\pi\)
\(48\) −1.00000 −0.144338
\(49\) 8.78553 1.25508
\(50\) −4.57874 −0.647532
\(51\) −3.07102 −0.430029
\(52\) −1.00000 −0.138675
\(53\) 1.78997 0.245872 0.122936 0.992415i \(-0.460769\pi\)
0.122936 + 0.992415i \(0.460769\pi\)
\(54\) 1.00000 0.136083
\(55\) 6.46468 0.871697
\(56\) −3.97310 −0.530928
\(57\) 6.35933 0.842314
\(58\) 7.73052 1.01507
\(59\) 3.06235 0.398684 0.199342 0.979930i \(-0.436120\pi\)
0.199342 + 0.979930i \(0.436120\pi\)
\(60\) 3.09495 0.399557
\(61\) −7.26725 −0.930476 −0.465238 0.885186i \(-0.654031\pi\)
−0.465238 + 0.885186i \(0.654031\pi\)
\(62\) −5.41795 −0.688080
\(63\) 3.97310 0.500564
\(64\) 1.00000 0.125000
\(65\) 3.09495 0.383882
\(66\) −2.08878 −0.257111
\(67\) −4.59049 −0.560818 −0.280409 0.959881i \(-0.590470\pi\)
−0.280409 + 0.959881i \(0.590470\pi\)
\(68\) 3.07102 0.372416
\(69\) −0.753374 −0.0906956
\(70\) 12.2966 1.46972
\(71\) 6.81056 0.808265 0.404133 0.914700i \(-0.367573\pi\)
0.404133 + 0.914700i \(0.367573\pi\)
\(72\) −1.00000 −0.117851
\(73\) −1.90860 −0.223385 −0.111693 0.993743i \(-0.535627\pi\)
−0.111693 + 0.993743i \(0.535627\pi\)
\(74\) −6.26162 −0.727898
\(75\) −4.57874 −0.528707
\(76\) −6.35933 −0.729465
\(77\) −8.29894 −0.945752
\(78\) −1.00000 −0.113228
\(79\) 3.61660 0.406899 0.203450 0.979085i \(-0.434785\pi\)
0.203450 + 0.979085i \(0.434785\pi\)
\(80\) −3.09495 −0.346026
\(81\) 1.00000 0.111111
\(82\) 3.19603 0.352942
\(83\) 11.1151 1.22004 0.610021 0.792385i \(-0.291161\pi\)
0.610021 + 0.792385i \(0.291161\pi\)
\(84\) −3.97310 −0.433501
\(85\) −9.50467 −1.03093
\(86\) −4.21307 −0.454306
\(87\) 7.73052 0.828799
\(88\) 2.08878 0.222665
\(89\) −10.2078 −1.08202 −0.541011 0.841015i \(-0.681958\pi\)
−0.541011 + 0.841015i \(0.681958\pi\)
\(90\) 3.09495 0.326237
\(91\) −3.97310 −0.416494
\(92\) 0.753374 0.0785447
\(93\) −5.41795 −0.561815
\(94\) 9.09805 0.938392
\(95\) 19.6818 2.01931
\(96\) 1.00000 0.102062
\(97\) 14.6236 1.48480 0.742402 0.669955i \(-0.233686\pi\)
0.742402 + 0.669955i \(0.233686\pi\)
\(98\) −8.78553 −0.887473
\(99\) −2.08878 −0.209930
\(100\) 4.57874 0.457874
\(101\) −2.52140 −0.250888 −0.125444 0.992101i \(-0.540036\pi\)
−0.125444 + 0.992101i \(0.540036\pi\)
\(102\) 3.07102 0.304076
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) 12.2966 1.20002
\(106\) −1.78997 −0.173858
\(107\) −11.8799 −1.14847 −0.574236 0.818690i \(-0.694701\pi\)
−0.574236 + 0.818690i \(0.694701\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 1.43249 0.137207 0.0686036 0.997644i \(-0.478146\pi\)
0.0686036 + 0.997644i \(0.478146\pi\)
\(110\) −6.46468 −0.616383
\(111\) −6.26162 −0.594326
\(112\) 3.97310 0.375423
\(113\) 14.4197 1.35649 0.678244 0.734836i \(-0.262741\pi\)
0.678244 + 0.734836i \(0.262741\pi\)
\(114\) −6.35933 −0.595606
\(115\) −2.33166 −0.217428
\(116\) −7.73052 −0.717761
\(117\) −1.00000 −0.0924500
\(118\) −3.06235 −0.281912
\(119\) 12.2015 1.11851
\(120\) −3.09495 −0.282529
\(121\) −6.63700 −0.603363
\(122\) 7.26725 0.657946
\(123\) 3.19603 0.288176
\(124\) 5.41795 0.486546
\(125\) 1.30378 0.116614
\(126\) −3.97310 −0.353952
\(127\) −12.9427 −1.14848 −0.574238 0.818688i \(-0.694702\pi\)
−0.574238 + 0.818688i \(0.694702\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.21307 −0.370940
\(130\) −3.09495 −0.271445
\(131\) −10.3348 −0.902953 −0.451476 0.892283i \(-0.649102\pi\)
−0.451476 + 0.892283i \(0.649102\pi\)
\(132\) 2.08878 0.181805
\(133\) −25.2663 −2.19086
\(134\) 4.59049 0.396558
\(135\) 3.09495 0.266371
\(136\) −3.07102 −0.263338
\(137\) 8.59513 0.734331 0.367166 0.930156i \(-0.380328\pi\)
0.367166 + 0.930156i \(0.380328\pi\)
\(138\) 0.753374 0.0641315
\(139\) −8.32306 −0.705952 −0.352976 0.935632i \(-0.614830\pi\)
−0.352976 + 0.935632i \(0.614830\pi\)
\(140\) −12.2966 −1.03925
\(141\) 9.09805 0.766194
\(142\) −6.81056 −0.571530
\(143\) 2.08878 0.174673
\(144\) 1.00000 0.0833333
\(145\) 23.9256 1.98691
\(146\) 1.90860 0.157957
\(147\) −8.78553 −0.724619
\(148\) 6.26162 0.514702
\(149\) 2.51358 0.205921 0.102960 0.994685i \(-0.467169\pi\)
0.102960 + 0.994685i \(0.467169\pi\)
\(150\) 4.57874 0.373853
\(151\) 14.7689 1.20188 0.600939 0.799295i \(-0.294794\pi\)
0.600939 + 0.799295i \(0.294794\pi\)
\(152\) 6.35933 0.515810
\(153\) 3.07102 0.248277
\(154\) 8.29894 0.668747
\(155\) −16.7683 −1.34686
\(156\) 1.00000 0.0800641
\(157\) 1.41185 0.112678 0.0563389 0.998412i \(-0.482057\pi\)
0.0563389 + 0.998412i \(0.482057\pi\)
\(158\) −3.61660 −0.287721
\(159\) −1.78997 −0.141954
\(160\) 3.09495 0.244678
\(161\) 2.99323 0.235900
\(162\) −1.00000 −0.0785674
\(163\) 12.2897 0.962607 0.481303 0.876554i \(-0.340164\pi\)
0.481303 + 0.876554i \(0.340164\pi\)
\(164\) −3.19603 −0.249568
\(165\) −6.46468 −0.503275
\(166\) −11.1151 −0.862700
\(167\) −2.97526 −0.230233 −0.115116 0.993352i \(-0.536724\pi\)
−0.115116 + 0.993352i \(0.536724\pi\)
\(168\) 3.97310 0.306531
\(169\) 1.00000 0.0769231
\(170\) 9.50467 0.728975
\(171\) −6.35933 −0.486310
\(172\) 4.21307 0.321243
\(173\) −23.4486 −1.78276 −0.891382 0.453253i \(-0.850263\pi\)
−0.891382 + 0.453253i \(0.850263\pi\)
\(174\) −7.73052 −0.586049
\(175\) 18.1918 1.37517
\(176\) −2.08878 −0.157448
\(177\) −3.06235 −0.230180
\(178\) 10.2078 0.765105
\(179\) −13.5864 −1.01549 −0.507747 0.861506i \(-0.669521\pi\)
−0.507747 + 0.861506i \(0.669521\pi\)
\(180\) −3.09495 −0.230684
\(181\) −11.7992 −0.877030 −0.438515 0.898724i \(-0.644495\pi\)
−0.438515 + 0.898724i \(0.644495\pi\)
\(182\) 3.97310 0.294506
\(183\) 7.26725 0.537210
\(184\) −0.753374 −0.0555395
\(185\) −19.3794 −1.42480
\(186\) 5.41795 0.397263
\(187\) −6.41469 −0.469088
\(188\) −9.09805 −0.663544
\(189\) −3.97310 −0.289001
\(190\) −19.6818 −1.42787
\(191\) 12.0182 0.869604 0.434802 0.900526i \(-0.356818\pi\)
0.434802 + 0.900526i \(0.356818\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 2.88551 0.207703 0.103852 0.994593i \(-0.466883\pi\)
0.103852 + 0.994593i \(0.466883\pi\)
\(194\) −14.6236 −1.04991
\(195\) −3.09495 −0.221634
\(196\) 8.78553 0.627538
\(197\) 15.7583 1.12273 0.561367 0.827567i \(-0.310275\pi\)
0.561367 + 0.827567i \(0.310275\pi\)
\(198\) 2.08878 0.148443
\(199\) −0.965819 −0.0684651 −0.0342326 0.999414i \(-0.510899\pi\)
−0.0342326 + 0.999414i \(0.510899\pi\)
\(200\) −4.57874 −0.323766
\(201\) 4.59049 0.323789
\(202\) 2.52140 0.177405
\(203\) −30.7141 −2.15571
\(204\) −3.07102 −0.215014
\(205\) 9.89156 0.690856
\(206\) −1.00000 −0.0696733
\(207\) 0.753374 0.0523631
\(208\) −1.00000 −0.0693375
\(209\) 13.2832 0.918821
\(210\) −12.2966 −0.848544
\(211\) 7.71356 0.531023 0.265512 0.964108i \(-0.414459\pi\)
0.265512 + 0.964108i \(0.414459\pi\)
\(212\) 1.78997 0.122936
\(213\) −6.81056 −0.466652
\(214\) 11.8799 0.812092
\(215\) −13.0392 −0.889269
\(216\) 1.00000 0.0680414
\(217\) 21.5261 1.46128
\(218\) −1.43249 −0.0970202
\(219\) 1.90860 0.128972
\(220\) 6.46468 0.435849
\(221\) −3.07102 −0.206579
\(222\) 6.26162 0.420252
\(223\) 11.7910 0.789583 0.394791 0.918771i \(-0.370817\pi\)
0.394791 + 0.918771i \(0.370817\pi\)
\(224\) −3.97310 −0.265464
\(225\) 4.57874 0.305249
\(226\) −14.4197 −0.959182
\(227\) 2.29930 0.152610 0.0763048 0.997085i \(-0.475688\pi\)
0.0763048 + 0.997085i \(0.475688\pi\)
\(228\) 6.35933 0.421157
\(229\) −14.0302 −0.927139 −0.463569 0.886061i \(-0.653432\pi\)
−0.463569 + 0.886061i \(0.653432\pi\)
\(230\) 2.33166 0.153745
\(231\) 8.29894 0.546030
\(232\) 7.73052 0.507534
\(233\) −7.93621 −0.519918 −0.259959 0.965620i \(-0.583709\pi\)
−0.259959 + 0.965620i \(0.583709\pi\)
\(234\) 1.00000 0.0653720
\(235\) 28.1581 1.83683
\(236\) 3.06235 0.199342
\(237\) −3.61660 −0.234923
\(238\) −12.2015 −0.790904
\(239\) −14.3211 −0.926354 −0.463177 0.886266i \(-0.653291\pi\)
−0.463177 + 0.886266i \(0.653291\pi\)
\(240\) 3.09495 0.199778
\(241\) −14.4962 −0.933784 −0.466892 0.884314i \(-0.654626\pi\)
−0.466892 + 0.884314i \(0.654626\pi\)
\(242\) 6.63700 0.426642
\(243\) −1.00000 −0.0641500
\(244\) −7.26725 −0.465238
\(245\) −27.1908 −1.73716
\(246\) −3.19603 −0.203771
\(247\) 6.35933 0.404634
\(248\) −5.41795 −0.344040
\(249\) −11.1151 −0.704392
\(250\) −1.30378 −0.0824584
\(251\) −9.08432 −0.573397 −0.286699 0.958021i \(-0.592558\pi\)
−0.286699 + 0.958021i \(0.592558\pi\)
\(252\) 3.97310 0.250282
\(253\) −1.57363 −0.0989335
\(254\) 12.9427 0.812095
\(255\) 9.50467 0.595205
\(256\) 1.00000 0.0625000
\(257\) 17.0807 1.06547 0.532733 0.846283i \(-0.321165\pi\)
0.532733 + 0.846283i \(0.321165\pi\)
\(258\) 4.21307 0.262294
\(259\) 24.8780 1.54585
\(260\) 3.09495 0.191941
\(261\) −7.73052 −0.478507
\(262\) 10.3348 0.638484
\(263\) 3.31151 0.204196 0.102098 0.994774i \(-0.467444\pi\)
0.102098 + 0.994774i \(0.467444\pi\)
\(264\) −2.08878 −0.128556
\(265\) −5.53989 −0.340313
\(266\) 25.2663 1.54917
\(267\) 10.2078 0.624706
\(268\) −4.59049 −0.280409
\(269\) 7.49680 0.457088 0.228544 0.973534i \(-0.426603\pi\)
0.228544 + 0.973534i \(0.426603\pi\)
\(270\) −3.09495 −0.188353
\(271\) −4.30922 −0.261766 −0.130883 0.991398i \(-0.541781\pi\)
−0.130883 + 0.991398i \(0.541781\pi\)
\(272\) 3.07102 0.186208
\(273\) 3.97310 0.240463
\(274\) −8.59513 −0.519251
\(275\) −9.56398 −0.576730
\(276\) −0.753374 −0.0453478
\(277\) 7.46649 0.448618 0.224309 0.974518i \(-0.427987\pi\)
0.224309 + 0.974518i \(0.427987\pi\)
\(278\) 8.32306 0.499184
\(279\) 5.41795 0.324364
\(280\) 12.2966 0.734860
\(281\) −24.4370 −1.45779 −0.728895 0.684626i \(-0.759966\pi\)
−0.728895 + 0.684626i \(0.759966\pi\)
\(282\) −9.09805 −0.541781
\(283\) 5.72108 0.340083 0.170042 0.985437i \(-0.445610\pi\)
0.170042 + 0.985437i \(0.445610\pi\)
\(284\) 6.81056 0.404133
\(285\) −19.6818 −1.16585
\(286\) −2.08878 −0.123512
\(287\) −12.6981 −0.749547
\(288\) −1.00000 −0.0589256
\(289\) −7.56883 −0.445225
\(290\) −23.9256 −1.40496
\(291\) −14.6236 −0.857252
\(292\) −1.90860 −0.111693
\(293\) 21.1961 1.23829 0.619145 0.785276i \(-0.287479\pi\)
0.619145 + 0.785276i \(0.287479\pi\)
\(294\) 8.78553 0.512383
\(295\) −9.47783 −0.551821
\(296\) −6.26162 −0.363949
\(297\) 2.08878 0.121203
\(298\) −2.51358 −0.145608
\(299\) −0.753374 −0.0435688
\(300\) −4.57874 −0.264354
\(301\) 16.7389 0.964816
\(302\) −14.7689 −0.849856
\(303\) 2.52140 0.144850
\(304\) −6.35933 −0.364733
\(305\) 22.4918 1.28788
\(306\) −3.07102 −0.175559
\(307\) 1.23481 0.0704743 0.0352371 0.999379i \(-0.488781\pi\)
0.0352371 + 0.999379i \(0.488781\pi\)
\(308\) −8.29894 −0.472876
\(309\) −1.00000 −0.0568880
\(310\) 16.7683 0.952375
\(311\) −19.4195 −1.10118 −0.550589 0.834777i \(-0.685597\pi\)
−0.550589 + 0.834777i \(0.685597\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 8.68698 0.491017 0.245508 0.969394i \(-0.421045\pi\)
0.245508 + 0.969394i \(0.421045\pi\)
\(314\) −1.41185 −0.0796753
\(315\) −12.2966 −0.692833
\(316\) 3.61660 0.203450
\(317\) 10.3957 0.583878 0.291939 0.956437i \(-0.405700\pi\)
0.291939 + 0.956437i \(0.405700\pi\)
\(318\) 1.78997 0.100377
\(319\) 16.1474 0.904079
\(320\) −3.09495 −0.173013
\(321\) 11.8799 0.663071
\(322\) −2.99323 −0.166806
\(323\) −19.5296 −1.08666
\(324\) 1.00000 0.0555556
\(325\) −4.57874 −0.253983
\(326\) −12.2897 −0.680666
\(327\) −1.43249 −0.0792167
\(328\) 3.19603 0.176471
\(329\) −36.1475 −1.99288
\(330\) 6.46468 0.355869
\(331\) −29.7538 −1.63542 −0.817709 0.575632i \(-0.804756\pi\)
−0.817709 + 0.575632i \(0.804756\pi\)
\(332\) 11.1151 0.610021
\(333\) 6.26162 0.343135
\(334\) 2.97526 0.162799
\(335\) 14.2074 0.776231
\(336\) −3.97310 −0.216750
\(337\) 16.0791 0.875887 0.437943 0.899003i \(-0.355707\pi\)
0.437943 + 0.899003i \(0.355707\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −14.4197 −0.783169
\(340\) −9.50467 −0.515463
\(341\) −11.3169 −0.612845
\(342\) 6.35933 0.343873
\(343\) 7.09411 0.383046
\(344\) −4.21307 −0.227153
\(345\) 2.33166 0.125532
\(346\) 23.4486 1.26060
\(347\) 18.2402 0.979187 0.489594 0.871951i \(-0.337145\pi\)
0.489594 + 0.871951i \(0.337145\pi\)
\(348\) 7.73052 0.414399
\(349\) 21.2293 1.13638 0.568190 0.822897i \(-0.307644\pi\)
0.568190 + 0.822897i \(0.307644\pi\)
\(350\) −18.1918 −0.972392
\(351\) 1.00000 0.0533761
\(352\) 2.08878 0.111332
\(353\) −12.0968 −0.643847 −0.321923 0.946766i \(-0.604329\pi\)
−0.321923 + 0.946766i \(0.604329\pi\)
\(354\) 3.06235 0.162762
\(355\) −21.0784 −1.11872
\(356\) −10.2078 −0.541011
\(357\) −12.2015 −0.645771
\(358\) 13.5864 0.718062
\(359\) −10.2784 −0.542474 −0.271237 0.962513i \(-0.587433\pi\)
−0.271237 + 0.962513i \(0.587433\pi\)
\(360\) 3.09495 0.163118
\(361\) 21.4411 1.12848
\(362\) 11.7992 0.620154
\(363\) 6.63700 0.348352
\(364\) −3.97310 −0.208247
\(365\) 5.90704 0.309189
\(366\) −7.26725 −0.379865
\(367\) −9.96267 −0.520047 −0.260024 0.965602i \(-0.583730\pi\)
−0.260024 + 0.965602i \(0.583730\pi\)
\(368\) 0.753374 0.0392723
\(369\) −3.19603 −0.166379
\(370\) 19.3794 1.00749
\(371\) 7.11175 0.369224
\(372\) −5.41795 −0.280908
\(373\) 14.6558 0.758848 0.379424 0.925223i \(-0.376122\pi\)
0.379424 + 0.925223i \(0.376122\pi\)
\(374\) 6.41469 0.331696
\(375\) −1.30378 −0.0673270
\(376\) 9.09805 0.469196
\(377\) 7.73052 0.398142
\(378\) 3.97310 0.204354
\(379\) 35.2468 1.81051 0.905253 0.424874i \(-0.139682\pi\)
0.905253 + 0.424874i \(0.139682\pi\)
\(380\) 19.6818 1.00966
\(381\) 12.9427 0.663073
\(382\) −12.0182 −0.614903
\(383\) 7.70592 0.393754 0.196877 0.980428i \(-0.436920\pi\)
0.196877 + 0.980428i \(0.436920\pi\)
\(384\) 1.00000 0.0510310
\(385\) 25.6848 1.30902
\(386\) −2.88551 −0.146868
\(387\) 4.21307 0.214162
\(388\) 14.6236 0.742402
\(389\) 4.86896 0.246866 0.123433 0.992353i \(-0.460610\pi\)
0.123433 + 0.992353i \(0.460610\pi\)
\(390\) 3.09495 0.156719
\(391\) 2.31363 0.117005
\(392\) −8.78553 −0.443736
\(393\) 10.3348 0.521320
\(394\) −15.7583 −0.793893
\(395\) −11.1932 −0.563192
\(396\) −2.08878 −0.104965
\(397\) 29.0682 1.45889 0.729446 0.684039i \(-0.239778\pi\)
0.729446 + 0.684039i \(0.239778\pi\)
\(398\) 0.965819 0.0484121
\(399\) 25.2663 1.26490
\(400\) 4.57874 0.228937
\(401\) 33.5973 1.67777 0.838884 0.544311i \(-0.183209\pi\)
0.838884 + 0.544311i \(0.183209\pi\)
\(402\) −4.59049 −0.228953
\(403\) −5.41795 −0.269887
\(404\) −2.52140 −0.125444
\(405\) −3.09495 −0.153789
\(406\) 30.7141 1.52432
\(407\) −13.0791 −0.648309
\(408\) 3.07102 0.152038
\(409\) 32.1938 1.59188 0.795941 0.605375i \(-0.206977\pi\)
0.795941 + 0.605375i \(0.206977\pi\)
\(410\) −9.89156 −0.488509
\(411\) −8.59513 −0.423966
\(412\) 1.00000 0.0492665
\(413\) 12.1670 0.598700
\(414\) −0.753374 −0.0370263
\(415\) −34.4008 −1.68867
\(416\) 1.00000 0.0490290
\(417\) 8.32306 0.407582
\(418\) −13.2832 −0.649705
\(419\) 10.2866 0.502534 0.251267 0.967918i \(-0.419153\pi\)
0.251267 + 0.967918i \(0.419153\pi\)
\(420\) 12.2966 0.600011
\(421\) 3.55842 0.173427 0.0867135 0.996233i \(-0.472364\pi\)
0.0867135 + 0.996233i \(0.472364\pi\)
\(422\) −7.71356 −0.375490
\(423\) −9.09805 −0.442362
\(424\) −1.78997 −0.0869288
\(425\) 14.0614 0.682078
\(426\) 6.81056 0.329973
\(427\) −28.8735 −1.39729
\(428\) −11.8799 −0.574236
\(429\) −2.08878 −0.100847
\(430\) 13.0392 0.628808
\(431\) 34.3904 1.65653 0.828264 0.560339i \(-0.189329\pi\)
0.828264 + 0.560339i \(0.189329\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 28.3588 1.36284 0.681418 0.731894i \(-0.261364\pi\)
0.681418 + 0.731894i \(0.261364\pi\)
\(434\) −21.5261 −1.03328
\(435\) −23.9256 −1.14715
\(436\) 1.43249 0.0686036
\(437\) −4.79096 −0.229182
\(438\) −1.90860 −0.0911966
\(439\) −9.92285 −0.473592 −0.236796 0.971559i \(-0.576097\pi\)
−0.236796 + 0.971559i \(0.576097\pi\)
\(440\) −6.46468 −0.308191
\(441\) 8.78553 0.418359
\(442\) 3.07102 0.146074
\(443\) 23.5320 1.11804 0.559020 0.829154i \(-0.311177\pi\)
0.559020 + 0.829154i \(0.311177\pi\)
\(444\) −6.26162 −0.297163
\(445\) 31.5926 1.49763
\(446\) −11.7910 −0.558319
\(447\) −2.51358 −0.118888
\(448\) 3.97310 0.187711
\(449\) −26.6482 −1.25761 −0.628804 0.777564i \(-0.716455\pi\)
−0.628804 + 0.777564i \(0.716455\pi\)
\(450\) −4.57874 −0.215844
\(451\) 6.67580 0.314351
\(452\) 14.4197 0.678244
\(453\) −14.7689 −0.693904
\(454\) −2.29930 −0.107911
\(455\) 12.2966 0.576472
\(456\) −6.35933 −0.297803
\(457\) −3.70020 −0.173088 −0.0865440 0.996248i \(-0.527582\pi\)
−0.0865440 + 0.996248i \(0.527582\pi\)
\(458\) 14.0302 0.655586
\(459\) −3.07102 −0.143343
\(460\) −2.33166 −0.108714
\(461\) 35.5552 1.65597 0.827985 0.560750i \(-0.189487\pi\)
0.827985 + 0.560750i \(0.189487\pi\)
\(462\) −8.29894 −0.386101
\(463\) −13.5000 −0.627398 −0.313699 0.949523i \(-0.601568\pi\)
−0.313699 + 0.949523i \(0.601568\pi\)
\(464\) −7.73052 −0.358880
\(465\) 16.7683 0.777611
\(466\) 7.93621 0.367638
\(467\) 22.0480 1.02026 0.510129 0.860098i \(-0.329598\pi\)
0.510129 + 0.860098i \(0.329598\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −18.2385 −0.842176
\(470\) −28.1581 −1.29883
\(471\) −1.41185 −0.0650546
\(472\) −3.06235 −0.140956
\(473\) −8.80017 −0.404632
\(474\) 3.61660 0.166116
\(475\) −29.1177 −1.33601
\(476\) 12.2015 0.559254
\(477\) 1.78997 0.0819573
\(478\) 14.3211 0.655031
\(479\) −8.97508 −0.410082 −0.205041 0.978753i \(-0.565733\pi\)
−0.205041 + 0.978753i \(0.565733\pi\)
\(480\) −3.09495 −0.141265
\(481\) −6.26162 −0.285505
\(482\) 14.4962 0.660285
\(483\) −2.99323 −0.136197
\(484\) −6.63700 −0.301682
\(485\) −45.2594 −2.05513
\(486\) 1.00000 0.0453609
\(487\) −4.81808 −0.218328 −0.109164 0.994024i \(-0.534817\pi\)
−0.109164 + 0.994024i \(0.534817\pi\)
\(488\) 7.26725 0.328973
\(489\) −12.2897 −0.555761
\(490\) 27.1908 1.22836
\(491\) 36.5073 1.64755 0.823775 0.566917i \(-0.191864\pi\)
0.823775 + 0.566917i \(0.191864\pi\)
\(492\) 3.19603 0.144088
\(493\) −23.7406 −1.06922
\(494\) −6.35933 −0.286120
\(495\) 6.46468 0.290566
\(496\) 5.41795 0.243273
\(497\) 27.0591 1.21376
\(498\) 11.1151 0.498080
\(499\) 2.73918 0.122622 0.0613112 0.998119i \(-0.480472\pi\)
0.0613112 + 0.998119i \(0.480472\pi\)
\(500\) 1.30378 0.0583069
\(501\) 2.97526 0.132925
\(502\) 9.08432 0.405453
\(503\) 11.9691 0.533678 0.266839 0.963741i \(-0.414021\pi\)
0.266839 + 0.963741i \(0.414021\pi\)
\(504\) −3.97310 −0.176976
\(505\) 7.80361 0.347256
\(506\) 1.57363 0.0699565
\(507\) −1.00000 −0.0444116
\(508\) −12.9427 −0.574238
\(509\) −14.3296 −0.635150 −0.317575 0.948233i \(-0.602869\pi\)
−0.317575 + 0.948233i \(0.602869\pi\)
\(510\) −9.50467 −0.420874
\(511\) −7.58308 −0.335456
\(512\) −1.00000 −0.0441942
\(513\) 6.35933 0.280771
\(514\) −17.0807 −0.753399
\(515\) −3.09495 −0.136380
\(516\) −4.21307 −0.185470
\(517\) 19.0038 0.835788
\(518\) −24.8780 −1.09308
\(519\) 23.4486 1.02928
\(520\) −3.09495 −0.135723
\(521\) 24.2921 1.06426 0.532128 0.846664i \(-0.321392\pi\)
0.532128 + 0.846664i \(0.321392\pi\)
\(522\) 7.73052 0.338356
\(523\) 21.3771 0.934754 0.467377 0.884058i \(-0.345199\pi\)
0.467377 + 0.884058i \(0.345199\pi\)
\(524\) −10.3348 −0.451476
\(525\) −18.1918 −0.793955
\(526\) −3.31151 −0.144388
\(527\) 16.6386 0.724790
\(528\) 2.08878 0.0909025
\(529\) −22.4324 −0.975323
\(530\) 5.53989 0.240637
\(531\) 3.06235 0.132895
\(532\) −25.2663 −1.09543
\(533\) 3.19603 0.138435
\(534\) −10.2078 −0.441734
\(535\) 36.7677 1.58961
\(536\) 4.59049 0.198279
\(537\) 13.5864 0.586295
\(538\) −7.49680 −0.323210
\(539\) −18.3511 −0.790436
\(540\) 3.09495 0.133186
\(541\) 32.1472 1.38212 0.691059 0.722799i \(-0.257145\pi\)
0.691059 + 0.722799i \(0.257145\pi\)
\(542\) 4.30922 0.185097
\(543\) 11.7992 0.506354
\(544\) −3.07102 −0.131669
\(545\) −4.43348 −0.189909
\(546\) −3.97310 −0.170033
\(547\) −4.02482 −0.172089 −0.0860445 0.996291i \(-0.527423\pi\)
−0.0860445 + 0.996291i \(0.527423\pi\)
\(548\) 8.59513 0.367166
\(549\) −7.26725 −0.310159
\(550\) 9.56398 0.407810
\(551\) 49.1609 2.09433
\(552\) 0.753374 0.0320657
\(553\) 14.3691 0.611037
\(554\) −7.46649 −0.317221
\(555\) 19.3794 0.822611
\(556\) −8.32306 −0.352976
\(557\) 34.5232 1.46279 0.731397 0.681952i \(-0.238869\pi\)
0.731397 + 0.681952i \(0.238869\pi\)
\(558\) −5.41795 −0.229360
\(559\) −4.21307 −0.178194
\(560\) −12.2966 −0.519625
\(561\) 6.41469 0.270828
\(562\) 24.4370 1.03081
\(563\) 43.5433 1.83513 0.917566 0.397582i \(-0.130151\pi\)
0.917566 + 0.397582i \(0.130151\pi\)
\(564\) 9.09805 0.383097
\(565\) −44.6282 −1.87752
\(566\) −5.72108 −0.240475
\(567\) 3.97310 0.166855
\(568\) −6.81056 −0.285765
\(569\) 22.9529 0.962234 0.481117 0.876657i \(-0.340231\pi\)
0.481117 + 0.876657i \(0.340231\pi\)
\(570\) 19.6818 0.824381
\(571\) 10.0139 0.419070 0.209535 0.977801i \(-0.432805\pi\)
0.209535 + 0.977801i \(0.432805\pi\)
\(572\) 2.08878 0.0873363
\(573\) −12.0182 −0.502066
\(574\) 12.6981 0.530010
\(575\) 3.44950 0.143854
\(576\) 1.00000 0.0416667
\(577\) −4.63353 −0.192896 −0.0964481 0.995338i \(-0.530748\pi\)
−0.0964481 + 0.995338i \(0.530748\pi\)
\(578\) 7.56883 0.314822
\(579\) −2.88551 −0.119918
\(580\) 23.9256 0.993457
\(581\) 44.1615 1.83213
\(582\) 14.6236 0.606169
\(583\) −3.73886 −0.154848
\(584\) 1.90860 0.0789786
\(585\) 3.09495 0.127961
\(586\) −21.1961 −0.875604
\(587\) 8.19409 0.338206 0.169103 0.985598i \(-0.445913\pi\)
0.169103 + 0.985598i \(0.445913\pi\)
\(588\) −8.78553 −0.362309
\(589\) −34.4545 −1.41967
\(590\) 9.47783 0.390196
\(591\) −15.7583 −0.648211
\(592\) 6.26162 0.257351
\(593\) −24.9784 −1.02574 −0.512871 0.858466i \(-0.671418\pi\)
−0.512871 + 0.858466i \(0.671418\pi\)
\(594\) −2.08878 −0.0857037
\(595\) −37.7630 −1.54813
\(596\) 2.51358 0.102960
\(597\) 0.965819 0.0395283
\(598\) 0.753374 0.0308078
\(599\) −34.4558 −1.40782 −0.703912 0.710287i \(-0.748565\pi\)
−0.703912 + 0.710287i \(0.748565\pi\)
\(600\) 4.57874 0.186926
\(601\) −15.7186 −0.641177 −0.320588 0.947219i \(-0.603881\pi\)
−0.320588 + 0.947219i \(0.603881\pi\)
\(602\) −16.7389 −0.682228
\(603\) −4.59049 −0.186939
\(604\) 14.7689 0.600939
\(605\) 20.5412 0.835118
\(606\) −2.52140 −0.102425
\(607\) −21.8966 −0.888754 −0.444377 0.895840i \(-0.646575\pi\)
−0.444377 + 0.895840i \(0.646575\pi\)
\(608\) 6.35933 0.257905
\(609\) 30.7141 1.24460
\(610\) −22.4918 −0.910666
\(611\) 9.09805 0.368068
\(612\) 3.07102 0.124139
\(613\) 29.8462 1.20548 0.602738 0.797939i \(-0.294077\pi\)
0.602738 + 0.797939i \(0.294077\pi\)
\(614\) −1.23481 −0.0498328
\(615\) −9.89156 −0.398866
\(616\) 8.29894 0.334374
\(617\) 41.6456 1.67659 0.838293 0.545219i \(-0.183554\pi\)
0.838293 + 0.545219i \(0.183554\pi\)
\(618\) 1.00000 0.0402259
\(619\) −13.6457 −0.548468 −0.274234 0.961663i \(-0.588424\pi\)
−0.274234 + 0.961663i \(0.588424\pi\)
\(620\) −16.7683 −0.673431
\(621\) −0.753374 −0.0302319
\(622\) 19.4195 0.778650
\(623\) −40.5565 −1.62486
\(624\) 1.00000 0.0400320
\(625\) −26.9288 −1.07715
\(626\) −8.68698 −0.347201
\(627\) −13.2832 −0.530482
\(628\) 1.41185 0.0563389
\(629\) 19.2296 0.766733
\(630\) 12.2966 0.489907
\(631\) 39.0625 1.55506 0.777528 0.628849i \(-0.216474\pi\)
0.777528 + 0.628849i \(0.216474\pi\)
\(632\) −3.61660 −0.143861
\(633\) −7.71356 −0.306587
\(634\) −10.3957 −0.412864
\(635\) 40.0570 1.58961
\(636\) −1.78997 −0.0709771
\(637\) −8.78553 −0.348096
\(638\) −16.1474 −0.639280
\(639\) 6.81056 0.269422
\(640\) 3.09495 0.122339
\(641\) 1.74733 0.0690153 0.0345076 0.999404i \(-0.489014\pi\)
0.0345076 + 0.999404i \(0.489014\pi\)
\(642\) −11.8799 −0.468862
\(643\) −14.0947 −0.555842 −0.277921 0.960604i \(-0.589645\pi\)
−0.277921 + 0.960604i \(0.589645\pi\)
\(644\) 2.99323 0.117950
\(645\) 13.0392 0.513420
\(646\) 19.5296 0.768383
\(647\) −28.2107 −1.10908 −0.554538 0.832158i \(-0.687105\pi\)
−0.554538 + 0.832158i \(0.687105\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.39658 −0.251088
\(650\) 4.57874 0.179593
\(651\) −21.5261 −0.843673
\(652\) 12.2897 0.481303
\(653\) −42.2473 −1.65326 −0.826632 0.562743i \(-0.809746\pi\)
−0.826632 + 0.562743i \(0.809746\pi\)
\(654\) 1.43249 0.0560146
\(655\) 31.9856 1.24978
\(656\) −3.19603 −0.124784
\(657\) −1.90860 −0.0744617
\(658\) 36.1475 1.40918
\(659\) 27.3069 1.06372 0.531862 0.846831i \(-0.321492\pi\)
0.531862 + 0.846831i \(0.321492\pi\)
\(660\) −6.46468 −0.251637
\(661\) 45.6838 1.77689 0.888447 0.458980i \(-0.151785\pi\)
0.888447 + 0.458980i \(0.151785\pi\)
\(662\) 29.7538 1.15642
\(663\) 3.07102 0.119269
\(664\) −11.1151 −0.431350
\(665\) 78.1979 3.03239
\(666\) −6.26162 −0.242633
\(667\) −5.82398 −0.225505
\(668\) −2.97526 −0.115116
\(669\) −11.7910 −0.455866
\(670\) −14.2074 −0.548879
\(671\) 15.1797 0.586005
\(672\) 3.97310 0.153266
\(673\) −34.7742 −1.34045 −0.670224 0.742159i \(-0.733802\pi\)
−0.670224 + 0.742159i \(0.733802\pi\)
\(674\) −16.0791 −0.619346
\(675\) −4.57874 −0.176236
\(676\) 1.00000 0.0384615
\(677\) 3.69503 0.142012 0.0710059 0.997476i \(-0.477379\pi\)
0.0710059 + 0.997476i \(0.477379\pi\)
\(678\) 14.4197 0.553784
\(679\) 58.1011 2.22972
\(680\) 9.50467 0.364487
\(681\) −2.29930 −0.0881092
\(682\) 11.3169 0.433347
\(683\) −19.4471 −0.744125 −0.372062 0.928208i \(-0.621349\pi\)
−0.372062 + 0.928208i \(0.621349\pi\)
\(684\) −6.35933 −0.243155
\(685\) −26.6015 −1.01639
\(686\) −7.09411 −0.270854
\(687\) 14.0302 0.535284
\(688\) 4.21307 0.160622
\(689\) −1.78997 −0.0681926
\(690\) −2.33166 −0.0887647
\(691\) −10.0287 −0.381508 −0.190754 0.981638i \(-0.561093\pi\)
−0.190754 + 0.981638i \(0.561093\pi\)
\(692\) −23.4486 −0.891382
\(693\) −8.29894 −0.315251
\(694\) −18.2402 −0.692390
\(695\) 25.7595 0.977113
\(696\) −7.73052 −0.293025
\(697\) −9.81506 −0.371772
\(698\) −21.2293 −0.803542
\(699\) 7.93621 0.300175
\(700\) 18.1918 0.687585
\(701\) 31.8042 1.20123 0.600613 0.799540i \(-0.294923\pi\)
0.600613 + 0.799540i \(0.294923\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −39.8197 −1.50183
\(704\) −2.08878 −0.0787239
\(705\) −28.1581 −1.06049
\(706\) 12.0968 0.455269
\(707\) −10.0178 −0.376757
\(708\) −3.06235 −0.115090
\(709\) −23.5901 −0.885943 −0.442972 0.896536i \(-0.646076\pi\)
−0.442972 + 0.896536i \(0.646076\pi\)
\(710\) 21.0784 0.791057
\(711\) 3.61660 0.135633
\(712\) 10.2078 0.382553
\(713\) 4.08174 0.152862
\(714\) 12.2015 0.456629
\(715\) −6.46468 −0.241765
\(716\) −13.5864 −0.507747
\(717\) 14.3211 0.534831
\(718\) 10.2784 0.383587
\(719\) 28.8301 1.07518 0.537590 0.843206i \(-0.319335\pi\)
0.537590 + 0.843206i \(0.319335\pi\)
\(720\) −3.09495 −0.115342
\(721\) 3.97310 0.147966
\(722\) −21.4411 −0.797954
\(723\) 14.4962 0.539121
\(724\) −11.7992 −0.438515
\(725\) −35.3960 −1.31458
\(726\) −6.63700 −0.246322
\(727\) 51.5821 1.91308 0.956538 0.291608i \(-0.0941904\pi\)
0.956538 + 0.291608i \(0.0941904\pi\)
\(728\) 3.97310 0.147253
\(729\) 1.00000 0.0370370
\(730\) −5.90704 −0.218629
\(731\) 12.9384 0.478544
\(732\) 7.26725 0.268605
\(733\) −3.58288 −0.132337 −0.0661683 0.997808i \(-0.521077\pi\)
−0.0661683 + 0.997808i \(0.521077\pi\)
\(734\) 9.96267 0.367729
\(735\) 27.1908 1.00295
\(736\) −0.753374 −0.0277697
\(737\) 9.58853 0.353198
\(738\) 3.19603 0.117647
\(739\) 14.7686 0.543272 0.271636 0.962400i \(-0.412435\pi\)
0.271636 + 0.962400i \(0.412435\pi\)
\(740\) −19.3794 −0.712402
\(741\) −6.35933 −0.233616
\(742\) −7.11175 −0.261081
\(743\) −1.95971 −0.0718946 −0.0359473 0.999354i \(-0.511445\pi\)
−0.0359473 + 0.999354i \(0.511445\pi\)
\(744\) 5.41795 0.198632
\(745\) −7.77943 −0.285016
\(746\) −14.6558 −0.536586
\(747\) 11.1151 0.406681
\(748\) −6.41469 −0.234544
\(749\) −47.2000 −1.72465
\(750\) 1.30378 0.0476074
\(751\) −22.9151 −0.836185 −0.418092 0.908405i \(-0.637301\pi\)
−0.418092 + 0.908405i \(0.637301\pi\)
\(752\) −9.09805 −0.331772
\(753\) 9.08432 0.331051
\(754\) −7.73052 −0.281529
\(755\) −45.7091 −1.66353
\(756\) −3.97310 −0.144500
\(757\) −36.3906 −1.32264 −0.661319 0.750105i \(-0.730003\pi\)
−0.661319 + 0.750105i \(0.730003\pi\)
\(758\) −35.2468 −1.28022
\(759\) 1.57363 0.0571193
\(760\) −19.6818 −0.713935
\(761\) 39.0269 1.41473 0.707363 0.706851i \(-0.249885\pi\)
0.707363 + 0.706851i \(0.249885\pi\)
\(762\) −12.9427 −0.468863
\(763\) 5.69141 0.206043
\(764\) 12.0182 0.434802
\(765\) −9.50467 −0.343642
\(766\) −7.70592 −0.278426
\(767\) −3.06235 −0.110575
\(768\) −1.00000 −0.0360844
\(769\) 36.6546 1.32180 0.660900 0.750474i \(-0.270175\pi\)
0.660900 + 0.750474i \(0.270175\pi\)
\(770\) −25.6848 −0.925617
\(771\) −17.0807 −0.615147
\(772\) 2.88551 0.103852
\(773\) −21.9360 −0.788984 −0.394492 0.918899i \(-0.629079\pi\)
−0.394492 + 0.918899i \(0.629079\pi\)
\(774\) −4.21307 −0.151435
\(775\) 24.8074 0.891107
\(776\) −14.6236 −0.524957
\(777\) −24.8780 −0.892495
\(778\) −4.86896 −0.174561
\(779\) 20.3246 0.728204
\(780\) −3.09495 −0.110817
\(781\) −14.2258 −0.509038
\(782\) −2.31363 −0.0827352
\(783\) 7.73052 0.276266
\(784\) 8.78553 0.313769
\(785\) −4.36961 −0.155958
\(786\) −10.3348 −0.368629
\(787\) 50.9715 1.81694 0.908469 0.417953i \(-0.137252\pi\)
0.908469 + 0.417953i \(0.137252\pi\)
\(788\) 15.7583 0.561367
\(789\) −3.31151 −0.117893
\(790\) 11.1932 0.398237
\(791\) 57.2908 2.03703
\(792\) 2.08878 0.0742216
\(793\) 7.26725 0.258068
\(794\) −29.0682 −1.03159
\(795\) 5.53989 0.196480
\(796\) −0.965819 −0.0342326
\(797\) 0.459944 0.0162920 0.00814602 0.999967i \(-0.497407\pi\)
0.00814602 + 0.999967i \(0.497407\pi\)
\(798\) −25.2663 −0.894416
\(799\) −27.9403 −0.988457
\(800\) −4.57874 −0.161883
\(801\) −10.2078 −0.360674
\(802\) −33.5973 −1.18636
\(803\) 3.98666 0.140686
\(804\) 4.59049 0.161894
\(805\) −9.26392 −0.326510
\(806\) 5.41795 0.190839
\(807\) −7.49680 −0.263900
\(808\) 2.52140 0.0887024
\(809\) 33.4757 1.17694 0.588472 0.808518i \(-0.299730\pi\)
0.588472 + 0.808518i \(0.299730\pi\)
\(810\) 3.09495 0.108746
\(811\) 11.1170 0.390372 0.195186 0.980766i \(-0.437469\pi\)
0.195186 + 0.980766i \(0.437469\pi\)
\(812\) −30.7141 −1.07786
\(813\) 4.30922 0.151131
\(814\) 13.0791 0.458424
\(815\) −38.0362 −1.33235
\(816\) −3.07102 −0.107507
\(817\) −26.7923 −0.937343
\(818\) −32.1938 −1.12563
\(819\) −3.97310 −0.138831
\(820\) 9.89156 0.345428
\(821\) 7.06169 0.246455 0.123227 0.992378i \(-0.460676\pi\)
0.123227 + 0.992378i \(0.460676\pi\)
\(822\) 8.59513 0.299789
\(823\) 39.6732 1.38292 0.691460 0.722415i \(-0.256968\pi\)
0.691460 + 0.722415i \(0.256968\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 9.56398 0.332975
\(826\) −12.1670 −0.423345
\(827\) −2.94176 −0.102295 −0.0511476 0.998691i \(-0.516288\pi\)
−0.0511476 + 0.998691i \(0.516288\pi\)
\(828\) 0.753374 0.0261816
\(829\) 4.67196 0.162264 0.0811319 0.996703i \(-0.474146\pi\)
0.0811319 + 0.996703i \(0.474146\pi\)
\(830\) 34.4008 1.19407
\(831\) −7.46649 −0.259010
\(832\) −1.00000 −0.0346688
\(833\) 26.9806 0.934821
\(834\) −8.32306 −0.288204
\(835\) 9.20830 0.318666
\(836\) 13.2832 0.459411
\(837\) −5.41795 −0.187272
\(838\) −10.2866 −0.355345
\(839\) 35.8053 1.23614 0.618068 0.786124i \(-0.287916\pi\)
0.618068 + 0.786124i \(0.287916\pi\)
\(840\) −12.2966 −0.424272
\(841\) 30.7610 1.06072
\(842\) −3.55842 −0.122631
\(843\) 24.4370 0.841655
\(844\) 7.71356 0.265512
\(845\) −3.09495 −0.106470
\(846\) 9.09805 0.312797
\(847\) −26.3695 −0.906065
\(848\) 1.78997 0.0614680
\(849\) −5.72108 −0.196347
\(850\) −14.0614 −0.482302
\(851\) 4.71734 0.161708
\(852\) −6.81056 −0.233326
\(853\) −29.8185 −1.02097 −0.510483 0.859888i \(-0.670533\pi\)
−0.510483 + 0.859888i \(0.670533\pi\)
\(854\) 28.8735 0.988031
\(855\) 19.6818 0.673105
\(856\) 11.8799 0.406046
\(857\) −32.8346 −1.12161 −0.560804 0.827949i \(-0.689508\pi\)
−0.560804 + 0.827949i \(0.689508\pi\)
\(858\) 2.08878 0.0713098
\(859\) −37.4820 −1.27887 −0.639434 0.768846i \(-0.720831\pi\)
−0.639434 + 0.768846i \(0.720831\pi\)
\(860\) −13.0392 −0.444634
\(861\) 12.6981 0.432751
\(862\) −34.3904 −1.17134
\(863\) 4.29422 0.146177 0.0730884 0.997325i \(-0.476714\pi\)
0.0730884 + 0.997325i \(0.476714\pi\)
\(864\) 1.00000 0.0340207
\(865\) 72.5723 2.46753
\(866\) −28.3588 −0.963671
\(867\) 7.56883 0.257051
\(868\) 21.5261 0.730642
\(869\) −7.55428 −0.256262
\(870\) 23.9256 0.811154
\(871\) 4.59049 0.155543
\(872\) −1.43249 −0.0485101
\(873\) 14.6236 0.494935
\(874\) 4.79096 0.162056
\(875\) 5.18006 0.175118
\(876\) 1.90860 0.0644858
\(877\) −48.3566 −1.63289 −0.816444 0.577425i \(-0.804058\pi\)
−0.816444 + 0.577425i \(0.804058\pi\)
\(878\) 9.92285 0.334880
\(879\) −21.1961 −0.714927
\(880\) 6.46468 0.217924
\(881\) −33.8058 −1.13895 −0.569474 0.822010i \(-0.692853\pi\)
−0.569474 + 0.822010i \(0.692853\pi\)
\(882\) −8.78553 −0.295824
\(883\) −13.0623 −0.439581 −0.219790 0.975547i \(-0.570537\pi\)
−0.219790 + 0.975547i \(0.570537\pi\)
\(884\) −3.07102 −0.103290
\(885\) 9.47783 0.318594
\(886\) −23.5320 −0.790574
\(887\) −2.15806 −0.0724605 −0.0362302 0.999343i \(-0.511535\pi\)
−0.0362302 + 0.999343i \(0.511535\pi\)
\(888\) 6.26162 0.210126
\(889\) −51.4225 −1.72466
\(890\) −31.5926 −1.05899
\(891\) −2.08878 −0.0699768
\(892\) 11.7910 0.394791
\(893\) 57.8575 1.93613
\(894\) 2.51358 0.0840668
\(895\) 42.0492 1.40555
\(896\) −3.97310 −0.132732
\(897\) 0.753374 0.0251544
\(898\) 26.6482 0.889263
\(899\) −41.8836 −1.39690
\(900\) 4.57874 0.152625
\(901\) 5.49705 0.183133
\(902\) −6.67580 −0.222280
\(903\) −16.7389 −0.557037
\(904\) −14.4197 −0.479591
\(905\) 36.5181 1.21390
\(906\) 14.7689 0.490665
\(907\) −49.8857 −1.65643 −0.828213 0.560413i \(-0.810642\pi\)
−0.828213 + 0.560413i \(0.810642\pi\)
\(908\) 2.29930 0.0763048
\(909\) −2.52140 −0.0836295
\(910\) −12.2966 −0.407627
\(911\) 20.7445 0.687297 0.343648 0.939098i \(-0.388337\pi\)
0.343648 + 0.939098i \(0.388337\pi\)
\(912\) 6.35933 0.210578
\(913\) −23.2170 −0.768372
\(914\) 3.70020 0.122392
\(915\) −22.4918 −0.743556
\(916\) −14.0302 −0.463569
\(917\) −41.0611 −1.35596
\(918\) 3.07102 0.101359
\(919\) 36.8177 1.21451 0.607253 0.794509i \(-0.292272\pi\)
0.607253 + 0.794509i \(0.292272\pi\)
\(920\) 2.33166 0.0768725
\(921\) −1.23481 −0.0406883
\(922\) −35.5552 −1.17095
\(923\) −6.81056 −0.224172
\(924\) 8.29894 0.273015
\(925\) 28.6703 0.942674
\(926\) 13.5000 0.443637
\(927\) 1.00000 0.0328443
\(928\) 7.73052 0.253767
\(929\) −7.61626 −0.249881 −0.124941 0.992164i \(-0.539874\pi\)
−0.124941 + 0.992164i \(0.539874\pi\)
\(930\) −16.7683 −0.549854
\(931\) −55.8701 −1.83107
\(932\) −7.93621 −0.259959
\(933\) 19.4195 0.635765
\(934\) −22.0480 −0.721432
\(935\) 19.8532 0.649268
\(936\) 1.00000 0.0326860
\(937\) 46.9034 1.53227 0.766133 0.642682i \(-0.222178\pi\)
0.766133 + 0.642682i \(0.222178\pi\)
\(938\) 18.2385 0.595508
\(939\) −8.68698 −0.283489
\(940\) 28.1581 0.918414
\(941\) 41.6504 1.35776 0.678882 0.734248i \(-0.262465\pi\)
0.678882 + 0.734248i \(0.262465\pi\)
\(942\) 1.41185 0.0460006
\(943\) −2.40780 −0.0784089
\(944\) 3.06235 0.0996710
\(945\) 12.2966 0.400007
\(946\) 8.80017 0.286118
\(947\) 51.8176 1.68385 0.841923 0.539598i \(-0.181424\pi\)
0.841923 + 0.539598i \(0.181424\pi\)
\(948\) −3.61660 −0.117462
\(949\) 1.90860 0.0619559
\(950\) 29.1177 0.944703
\(951\) −10.3957 −0.337102
\(952\) −12.2015 −0.395452
\(953\) 3.94643 0.127837 0.0639186 0.997955i \(-0.479640\pi\)
0.0639186 + 0.997955i \(0.479640\pi\)
\(954\) −1.78997 −0.0579526
\(955\) −37.1957 −1.20362
\(956\) −14.3211 −0.463177
\(957\) −16.1474 −0.521970
\(958\) 8.97508 0.289972
\(959\) 34.1493 1.10274
\(960\) 3.09495 0.0998892
\(961\) −1.64584 −0.0530916
\(962\) 6.26162 0.201883
\(963\) −11.8799 −0.382824
\(964\) −14.4962 −0.466892
\(965\) −8.93051 −0.287483
\(966\) 2.99323 0.0963057
\(967\) 4.55096 0.146349 0.0731745 0.997319i \(-0.476687\pi\)
0.0731745 + 0.997319i \(0.476687\pi\)
\(968\) 6.63700 0.213321
\(969\) 19.5296 0.627382
\(970\) 45.2594 1.45319
\(971\) 42.2830 1.35693 0.678463 0.734634i \(-0.262646\pi\)
0.678463 + 0.734634i \(0.262646\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −33.0683 −1.06012
\(974\) 4.81808 0.154381
\(975\) 4.57874 0.146637
\(976\) −7.26725 −0.232619
\(977\) 42.7941 1.36910 0.684552 0.728964i \(-0.259998\pi\)
0.684552 + 0.728964i \(0.259998\pi\)
\(978\) 12.2897 0.392983
\(979\) 21.3218 0.681448
\(980\) −27.1908 −0.868579
\(981\) 1.43249 0.0457358
\(982\) −36.5073 −1.16499
\(983\) −19.0515 −0.607648 −0.303824 0.952728i \(-0.598263\pi\)
−0.303824 + 0.952728i \(0.598263\pi\)
\(984\) −3.19603 −0.101886
\(985\) −48.7713 −1.55398
\(986\) 23.7406 0.756055
\(987\) 36.1475 1.15059
\(988\) 6.35933 0.202317
\(989\) 3.17401 0.100928
\(990\) −6.46468 −0.205461
\(991\) 16.5441 0.525542 0.262771 0.964858i \(-0.415364\pi\)
0.262771 + 0.964858i \(0.415364\pi\)
\(992\) −5.41795 −0.172020
\(993\) 29.7538 0.944209
\(994\) −27.0591 −0.858261
\(995\) 2.98917 0.0947629
\(996\) −11.1151 −0.352196
\(997\) −7.78827 −0.246657 −0.123328 0.992366i \(-0.539357\pi\)
−0.123328 + 0.992366i \(0.539357\pi\)
\(998\) −2.73918 −0.0867071
\(999\) −6.26162 −0.198109
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 8034.2.a.ba.1.3 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.ba.1.3 14 1.1 even 1 trivial