Properties

Label 4598.2.a.bv.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.258228.1
Defining polynomial: \(x^{4} - 2 x^{3} - 12 x^{2} + 6 x + 24\)
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 1.1
Root \(4.19461\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.19461 q^{3} +1.00000 q^{4} -4.19461 q^{5} -3.19461 q^{6} +1.32286 q^{7} +1.00000 q^{8} +7.20555 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.19461 q^{3} +1.00000 q^{4} -4.19461 q^{5} -3.19461 q^{6} +1.32286 q^{7} +1.00000 q^{8} +7.20555 q^{9} -4.19461 q^{10} -3.19461 q^{12} -3.52841 q^{13} +1.32286 q^{14} +13.4002 q^{15} +1.00000 q^{16} -2.32286 q^{17} +7.20555 q^{18} +1.00000 q^{19} -4.19461 q^{20} -4.22603 q^{21} +2.52841 q^{23} -3.19461 q^{24} +12.5948 q^{25} -3.52841 q^{26} -13.4351 q^{27} +1.32286 q^{28} -10.4002 q^{29} +13.4002 q^{30} -6.38923 q^{31} +1.00000 q^{32} -2.32286 q^{34} -5.54889 q^{35} +7.20555 q^{36} +7.84034 q^{37} +1.00000 q^{38} +11.2719 q^{39} -4.19461 q^{40} +2.34334 q^{41} -4.22603 q^{42} -11.4461 q^{43} -30.2245 q^{45} +2.52841 q^{46} -6.20555 q^{47} -3.19461 q^{48} -5.25004 q^{49} +12.5948 q^{50} +7.42064 q^{51} -3.52841 q^{52} +4.40017 q^{53} -13.4351 q^{54} +1.32286 q^{56} -3.19461 q^{57} -10.4002 q^{58} -6.72303 q^{59} +13.4002 q^{60} -8.60572 q^{61} -6.38923 q^{62} +9.53195 q^{63} +1.00000 q^{64} +14.8003 q^{65} +6.21509 q^{67} -2.32286 q^{68} -8.07730 q^{69} -5.54889 q^{70} -10.7326 q^{71} +7.20555 q^{72} -1.67714 q^{73} +7.84034 q^{74} -40.2354 q^{75} +1.00000 q^{76} +11.2719 q^{78} +5.65666 q^{79} -4.19461 q^{80} +21.3033 q^{81} +2.34334 q^{82} -1.80539 q^{83} -4.22603 q^{84} +9.74350 q^{85} -11.4461 q^{86} +33.2245 q^{87} +6.04589 q^{89} -30.2245 q^{90} -4.66760 q^{91} +2.52841 q^{92} +20.4111 q^{93} -6.20555 q^{94} -4.19461 q^{95} -3.19461 q^{96} -10.0000 q^{97} -5.25004 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98} + O(q^{100}) \)

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
\(3\) −3.19461 −1.84441 −0.922205 0.386700i \(-0.873615\pi\)
−0.922205 + 0.386700i \(0.873615\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.19461 −1.87589 −0.937944 0.346787i \(-0.887273\pi\)
−0.937944 + 0.346787i \(0.887273\pi\)
\(6\) −3.19461 −1.30420
\(7\) 1.32286 0.499995 0.249997 0.968247i \(-0.419570\pi\)
0.249997 + 0.968247i \(0.419570\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.20555 2.40185
\(10\) −4.19461 −1.32645
\(11\) 0 0
\(12\) −3.19461 −0.922205
\(13\) −3.52841 −0.978606 −0.489303 0.872114i \(-0.662749\pi\)
−0.489303 + 0.872114i \(0.662749\pi\)
\(14\) 1.32286 0.353550
\(15\) 13.4002 3.45991
\(16\) 1.00000 0.250000
\(17\) −2.32286 −0.563377 −0.281688 0.959506i \(-0.590894\pi\)
−0.281688 + 0.959506i \(0.590894\pi\)
\(18\) 7.20555 1.69837
\(19\) 1.00000 0.229416
\(20\) −4.19461 −0.937944
\(21\) −4.22603 −0.922195
\(22\) 0 0
\(23\) 2.52841 0.527211 0.263605 0.964631i \(-0.415088\pi\)
0.263605 + 0.964631i \(0.415088\pi\)
\(24\) −3.19461 −0.652098
\(25\) 12.5948 2.51896
\(26\) −3.52841 −0.691979
\(27\) −13.4351 −2.58559
\(28\) 1.32286 0.249997
\(29\) −10.4002 −1.93126 −0.965631 0.259916i \(-0.916305\pi\)
−0.965631 + 0.259916i \(0.916305\pi\)
\(30\) 13.4002 2.44652
\(31\) −6.38923 −1.14754 −0.573769 0.819017i \(-0.694519\pi\)
−0.573769 + 0.819017i \(0.694519\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.32286 −0.398367
\(35\) −5.54889 −0.937934
\(36\) 7.20555 1.20093
\(37\) 7.84034 1.28894 0.644472 0.764628i \(-0.277077\pi\)
0.644472 + 0.764628i \(0.277077\pi\)
\(38\) 1.00000 0.162221
\(39\) 11.2719 1.80495
\(40\) −4.19461 −0.663227
\(41\) 2.34334 0.365968 0.182984 0.983116i \(-0.441424\pi\)
0.182984 + 0.983116i \(0.441424\pi\)
\(42\) −4.22603 −0.652091
\(43\) −11.4461 −1.74551 −0.872753 0.488161i \(-0.837668\pi\)
−0.872753 + 0.488161i \(0.837668\pi\)
\(44\) 0 0
\(45\) −30.2245 −4.50560
\(46\) 2.52841 0.372794
\(47\) −6.20555 −0.905173 −0.452586 0.891721i \(-0.649499\pi\)
−0.452586 + 0.891721i \(0.649499\pi\)
\(48\) −3.19461 −0.461103
\(49\) −5.25004 −0.750005
\(50\) 12.5948 1.78117
\(51\) 7.42064 1.03910
\(52\) −3.52841 −0.489303
\(53\) 4.40017 0.604409 0.302205 0.953243i \(-0.402277\pi\)
0.302205 + 0.953243i \(0.402277\pi\)
\(54\) −13.4351 −1.82829
\(55\) 0 0
\(56\) 1.32286 0.176775
\(57\) −3.19461 −0.423137
\(58\) −10.4002 −1.36561
\(59\) −6.72303 −0.875264 −0.437632 0.899154i \(-0.644183\pi\)
−0.437632 + 0.899154i \(0.644183\pi\)
\(60\) 13.4002 1.72995
\(61\) −8.60572 −1.10185 −0.550925 0.834555i \(-0.685725\pi\)
−0.550925 + 0.834555i \(0.685725\pi\)
\(62\) −6.38923 −0.811433
\(63\) 9.53195 1.20091
\(64\) 1.00000 0.125000
\(65\) 14.8003 1.83576
\(66\) 0 0
\(67\) 6.21509 0.759294 0.379647 0.925131i \(-0.376045\pi\)
0.379647 + 0.925131i \(0.376045\pi\)
\(68\) −2.32286 −0.281688
\(69\) −8.07730 −0.972393
\(70\) −5.54889 −0.663219
\(71\) −10.7326 −1.27372 −0.636861 0.770979i \(-0.719767\pi\)
−0.636861 + 0.770979i \(0.719767\pi\)
\(72\) 7.20555 0.849183
\(73\) −1.67714 −0.196294 −0.0981471 0.995172i \(-0.531292\pi\)
−0.0981471 + 0.995172i \(0.531292\pi\)
\(74\) 7.84034 0.911420
\(75\) −40.2354 −4.64599
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 11.2719 1.27629
\(79\) 5.65666 0.636424 0.318212 0.948020i \(-0.396918\pi\)
0.318212 + 0.948020i \(0.396918\pi\)
\(80\) −4.19461 −0.468972
\(81\) 21.3033 2.36704
\(82\) 2.34334 0.258778
\(83\) −1.80539 −0.198167 −0.0990835 0.995079i \(-0.531591\pi\)
−0.0990835 + 0.995079i \(0.531591\pi\)
\(84\) −4.22603 −0.461098
\(85\) 9.74350 1.05683
\(86\) −11.4461 −1.23426
\(87\) 33.2245 3.56204
\(88\) 0 0
\(89\) 6.04589 0.640863 0.320431 0.947272i \(-0.396172\pi\)
0.320431 + 0.947272i \(0.396172\pi\)
\(90\) −30.2245 −3.18594
\(91\) −4.66760 −0.489298
\(92\) 2.52841 0.263605
\(93\) 20.4111 2.11653
\(94\) −6.20555 −0.640054
\(95\) −4.19461 −0.430358
\(96\) −3.19461 −0.326049
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −5.25004 −0.530334
\(99\) 0 0
\(100\) 12.5948 1.25948
\(101\) 18.9949 1.89007 0.945034 0.326973i \(-0.106028\pi\)
0.945034 + 0.326973i \(0.106028\pi\)
\(102\) 7.42064 0.734753
\(103\) 20.0459 1.97518 0.987590 0.157054i \(-0.0501996\pi\)
0.987590 + 0.157054i \(0.0501996\pi\)
\(104\) −3.52841 −0.345989
\(105\) 17.7266 1.72994
\(106\) 4.40017 0.427382
\(107\) 0.849872 0.0821603 0.0410801 0.999156i \(-0.486920\pi\)
0.0410801 + 0.999156i \(0.486920\pi\)
\(108\) −13.4351 −1.29279
\(109\) 8.72303 0.835514 0.417757 0.908559i \(-0.362816\pi\)
0.417757 + 0.908559i \(0.362816\pi\)
\(110\) 0 0
\(111\) −25.0468 −2.37734
\(112\) 1.32286 0.124999
\(113\) 3.65666 0.343990 0.171995 0.985098i \(-0.444979\pi\)
0.171995 + 0.985098i \(0.444979\pi\)
\(114\) −3.19461 −0.299203
\(115\) −10.6057 −0.988988
\(116\) −10.4002 −0.965631
\(117\) −25.4242 −2.35047
\(118\) −6.72303 −0.618905
\(119\) −3.07282 −0.281685
\(120\) 13.4002 1.22326
\(121\) 0 0
\(122\) −8.60572 −0.779125
\(123\) −7.48606 −0.674995
\(124\) −6.38923 −0.573769
\(125\) −31.8572 −2.84939
\(126\) 9.53195 0.849173
\(127\) −0.256496 −0.0227603 −0.0113802 0.999935i \(-0.503623\pi\)
−0.0113802 + 0.999935i \(0.503623\pi\)
\(128\) 1.00000 0.0883883
\(129\) 36.5657 3.21943
\(130\) 14.8003 1.29807
\(131\) −3.70255 −0.323493 −0.161747 0.986832i \(-0.551713\pi\)
−0.161747 + 0.986832i \(0.551713\pi\)
\(132\) 0 0
\(133\) 1.32286 0.114707
\(134\) 6.21509 0.536902
\(135\) 56.3551 4.85028
\(136\) −2.32286 −0.199184
\(137\) −5.12319 −0.437704 −0.218852 0.975758i \(-0.570231\pi\)
−0.218852 + 0.975758i \(0.570231\pi\)
\(138\) −8.07730 −0.687586
\(139\) 6.36735 0.540071 0.270036 0.962850i \(-0.412965\pi\)
0.270036 + 0.962850i \(0.412965\pi\)
\(140\) −5.54889 −0.468967
\(141\) 19.8243 1.66951
\(142\) −10.7326 −0.900657
\(143\) 0 0
\(144\) 7.20555 0.600463
\(145\) 43.6247 3.62283
\(146\) −1.67714 −0.138801
\(147\) 16.7718 1.38332
\(148\) 7.84034 0.644472
\(149\) −13.7244 −1.12435 −0.562175 0.827019i \(-0.690035\pi\)
−0.562175 + 0.827019i \(0.690035\pi\)
\(150\) −40.2354 −3.28521
\(151\) −4.98906 −0.406004 −0.203002 0.979178i \(-0.565070\pi\)
−0.203002 + 0.979178i \(0.565070\pi\)
\(152\) 1.00000 0.0811107
\(153\) −16.7375 −1.35315
\(154\) 0 0
\(155\) 26.8003 2.15265
\(156\) 11.2719 0.902476
\(157\) 2.04000 0.162810 0.0814050 0.996681i \(-0.474059\pi\)
0.0814050 + 0.996681i \(0.474059\pi\)
\(158\) 5.65666 0.450020
\(159\) −14.0568 −1.11478
\(160\) −4.19461 −0.331613
\(161\) 3.34474 0.263603
\(162\) 21.3033 1.67375
\(163\) 6.15461 0.482066 0.241033 0.970517i \(-0.422514\pi\)
0.241033 + 0.970517i \(0.422514\pi\)
\(164\) 2.34334 0.182984
\(165\) 0 0
\(166\) −1.80539 −0.140125
\(167\) 3.74350 0.289681 0.144841 0.989455i \(-0.453733\pi\)
0.144841 + 0.989455i \(0.453733\pi\)
\(168\) −4.22603 −0.326045
\(169\) −0.550294 −0.0423303
\(170\) 9.74350 0.747293
\(171\) 7.20555 0.551022
\(172\) −11.4461 −0.872753
\(173\) 9.08684 0.690860 0.345430 0.938445i \(-0.387733\pi\)
0.345430 + 0.938445i \(0.387733\pi\)
\(174\) 33.2245 2.51874
\(175\) 16.6611 1.25946
\(176\) 0 0
\(177\) 21.4775 1.61435
\(178\) 6.04589 0.453158
\(179\) 8.76751 0.655315 0.327657 0.944797i \(-0.393741\pi\)
0.327657 + 0.944797i \(0.393741\pi\)
\(180\) −30.2245 −2.25280
\(181\) 19.6807 1.46285 0.731426 0.681920i \(-0.238855\pi\)
0.731426 + 0.681920i \(0.238855\pi\)
\(182\) −4.66760 −0.345986
\(183\) 27.4919 2.03226
\(184\) 2.52841 0.186397
\(185\) −32.8872 −2.41791
\(186\) 20.4111 1.49661
\(187\) 0 0
\(188\) −6.20555 −0.452586
\(189\) −17.7728 −1.29278
\(190\) −4.19461 −0.304309
\(191\) −9.47747 −0.685766 −0.342883 0.939378i \(-0.611403\pi\)
−0.342883 + 0.939378i \(0.611403\pi\)
\(192\) −3.19461 −0.230551
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) −10.0000 −0.717958
\(195\) −47.2813 −3.38589
\(196\) −5.25004 −0.375003
\(197\) −24.5438 −1.74868 −0.874338 0.485318i \(-0.838704\pi\)
−0.874338 + 0.485318i \(0.838704\pi\)
\(198\) 0 0
\(199\) 20.1991 1.43188 0.715938 0.698164i \(-0.245999\pi\)
0.715938 + 0.698164i \(0.245999\pi\)
\(200\) 12.5948 0.890585
\(201\) −19.8548 −1.40045
\(202\) 18.9949 1.33648
\(203\) −13.7580 −0.965621
\(204\) 7.42064 0.519549
\(205\) −9.82940 −0.686515
\(206\) 20.0459 1.39666
\(207\) 18.2186 1.26628
\(208\) −3.52841 −0.244652
\(209\) 0 0
\(210\) 17.7266 1.22325
\(211\) 1.88129 0.129513 0.0647566 0.997901i \(-0.479373\pi\)
0.0647566 + 0.997901i \(0.479373\pi\)
\(212\) 4.40017 0.302205
\(213\) 34.2864 2.34926
\(214\) 0.849872 0.0580961
\(215\) 48.0118 3.27438
\(216\) −13.4351 −0.914144
\(217\) −8.45206 −0.573763
\(218\) 8.72303 0.590798
\(219\) 5.35781 0.362047
\(220\) 0 0
\(221\) 8.19602 0.551324
\(222\) −25.0468 −1.68103
\(223\) 20.0868 1.34511 0.672557 0.740045i \(-0.265196\pi\)
0.672557 + 0.740045i \(0.265196\pi\)
\(224\) 1.32286 0.0883874
\(225\) 90.7523 6.05016
\(226\) 3.65666 0.243238
\(227\) 3.55029 0.235641 0.117821 0.993035i \(-0.462409\pi\)
0.117821 + 0.993035i \(0.462409\pi\)
\(228\) −3.19461 −0.211568
\(229\) 7.72162 0.510259 0.255130 0.966907i \(-0.417882\pi\)
0.255130 + 0.966907i \(0.417882\pi\)
\(230\) −10.6057 −0.699320
\(231\) 0 0
\(232\) −10.4002 −0.682804
\(233\) −21.9081 −1.43525 −0.717624 0.696431i \(-0.754770\pi\)
−0.717624 + 0.696431i \(0.754770\pi\)
\(234\) −25.4242 −1.66203
\(235\) 26.0299 1.69800
\(236\) −6.72303 −0.437632
\(237\) −18.0708 −1.17383
\(238\) −3.07282 −0.199182
\(239\) 17.6676 1.14282 0.571411 0.820664i \(-0.306396\pi\)
0.571411 + 0.820664i \(0.306396\pi\)
\(240\) 13.4002 0.864977
\(241\) 17.0999 1.10150 0.550751 0.834670i \(-0.314341\pi\)
0.550751 + 0.834670i \(0.314341\pi\)
\(242\) 0 0
\(243\) −27.7506 −1.78020
\(244\) −8.60572 −0.550925
\(245\) 22.0219 1.40693
\(246\) −7.48606 −0.477294
\(247\) −3.52841 −0.224508
\(248\) −6.38923 −0.405716
\(249\) 5.76751 0.365501
\(250\) −31.8572 −2.01482
\(251\) 13.4461 0.848707 0.424354 0.905497i \(-0.360501\pi\)
0.424354 + 0.905497i \(0.360501\pi\)
\(252\) 9.53195 0.600456
\(253\) 0 0
\(254\) −0.256496 −0.0160940
\(255\) −31.1267 −1.94923
\(256\) 1.00000 0.0625000
\(257\) 10.1546 0.633427 0.316714 0.948521i \(-0.397421\pi\)
0.316714 + 0.948521i \(0.397421\pi\)
\(258\) 36.5657 2.27648
\(259\) 10.3717 0.644465
\(260\) 14.8003 0.917878
\(261\) −74.9389 −4.63860
\(262\) −3.70255 −0.228744
\(263\) 24.9081 1.53590 0.767950 0.640510i \(-0.221277\pi\)
0.767950 + 0.640510i \(0.221277\pi\)
\(264\) 0 0
\(265\) −18.4570 −1.13380
\(266\) 1.32286 0.0811098
\(267\) −19.3143 −1.18201
\(268\) 6.21509 0.379647
\(269\) −29.4761 −1.79719 −0.898594 0.438781i \(-0.855410\pi\)
−0.898594 + 0.438781i \(0.855410\pi\)
\(270\) 56.3551 3.42966
\(271\) −2.99046 −0.181658 −0.0908289 0.995867i \(-0.528952\pi\)
−0.0908289 + 0.995867i \(0.528952\pi\)
\(272\) −2.32286 −0.140844
\(273\) 14.9112 0.902466
\(274\) −5.12319 −0.309503
\(275\) 0 0
\(276\) −8.07730 −0.486197
\(277\) −16.8622 −1.01315 −0.506576 0.862195i \(-0.669089\pi\)
−0.506576 + 0.862195i \(0.669089\pi\)
\(278\) 6.36735 0.381888
\(279\) −46.0379 −2.75622
\(280\) −5.54889 −0.331610
\(281\) −0.989060 −0.0590024 −0.0295012 0.999565i \(-0.509392\pi\)
−0.0295012 + 0.999565i \(0.509392\pi\)
\(282\) 19.8243 1.18052
\(283\) −5.97812 −0.355362 −0.177681 0.984088i \(-0.556860\pi\)
−0.177681 + 0.984088i \(0.556860\pi\)
\(284\) −10.7326 −0.636861
\(285\) 13.4002 0.793757
\(286\) 0 0
\(287\) 3.09991 0.182982
\(288\) 7.20555 0.424591
\(289\) −11.6043 −0.682607
\(290\) 43.6247 2.56173
\(291\) 31.9461 1.87272
\(292\) −1.67714 −0.0981471
\(293\) 14.5489 0.849955 0.424978 0.905204i \(-0.360282\pi\)
0.424978 + 0.905204i \(0.360282\pi\)
\(294\) 16.7718 0.978154
\(295\) 28.2005 1.64190
\(296\) 7.84034 0.455710
\(297\) 0 0
\(298\) −13.7244 −0.795035
\(299\) −8.92129 −0.515932
\(300\) −40.2354 −2.32299
\(301\) −15.1415 −0.872744
\(302\) −4.98906 −0.287088
\(303\) −60.6815 −3.48606
\(304\) 1.00000 0.0573539
\(305\) 36.0977 2.06695
\(306\) −16.7375 −0.956819
\(307\) 9.69161 0.553129 0.276565 0.960995i \(-0.410804\pi\)
0.276565 + 0.960995i \(0.410804\pi\)
\(308\) 0 0
\(309\) −64.0389 −3.64304
\(310\) 26.8003 1.52216
\(311\) −18.8229 −1.06735 −0.533675 0.845689i \(-0.679190\pi\)
−0.533675 + 0.845689i \(0.679190\pi\)
\(312\) 11.2719 0.638147
\(313\) 27.1800 1.53631 0.768153 0.640267i \(-0.221176\pi\)
0.768153 + 0.640267i \(0.221176\pi\)
\(314\) 2.04000 0.115124
\(315\) −39.9828 −2.25278
\(316\) 5.65666 0.318212
\(317\) −14.3697 −0.807083 −0.403541 0.914961i \(-0.632221\pi\)
−0.403541 + 0.914961i \(0.632221\pi\)
\(318\) −14.0568 −0.788268
\(319\) 0 0
\(320\) −4.19461 −0.234486
\(321\) −2.71501 −0.151537
\(322\) 3.34474 0.186395
\(323\) −2.32286 −0.129247
\(324\) 21.3033 1.18352
\(325\) −44.4396 −2.46507
\(326\) 6.15461 0.340872
\(327\) −27.8667 −1.54103
\(328\) 2.34334 0.129389
\(329\) −8.20909 −0.452582
\(330\) 0 0
\(331\) 18.9635 1.04233 0.521165 0.853456i \(-0.325498\pi\)
0.521165 + 0.853456i \(0.325498\pi\)
\(332\) −1.80539 −0.0990835
\(333\) 56.4940 3.09585
\(334\) 3.74350 0.204835
\(335\) −26.0699 −1.42435
\(336\) −4.22603 −0.230549
\(337\) 30.1595 1.64290 0.821448 0.570284i \(-0.193167\pi\)
0.821448 + 0.570284i \(0.193167\pi\)
\(338\) −0.550294 −0.0299320
\(339\) −11.6816 −0.634459
\(340\) 9.74350 0.528416
\(341\) 0 0
\(342\) 7.20555 0.389632
\(343\) −16.2051 −0.874993
\(344\) −11.4461 −0.617130
\(345\) 33.8812 1.82410
\(346\) 9.08684 0.488512
\(347\) 23.5997 1.26690 0.633450 0.773784i \(-0.281638\pi\)
0.633450 + 0.773784i \(0.281638\pi\)
\(348\) 33.2245 1.78102
\(349\) −29.2086 −1.56350 −0.781751 0.623591i \(-0.785673\pi\)
−0.781751 + 0.623591i \(0.785673\pi\)
\(350\) 16.6611 0.890576
\(351\) 47.4046 2.53027
\(352\) 0 0
\(353\) −10.2274 −0.544351 −0.272176 0.962248i \(-0.587743\pi\)
−0.272176 + 0.962248i \(0.587743\pi\)
\(354\) 21.4775 1.14151
\(355\) 45.0190 2.38936
\(356\) 6.04589 0.320431
\(357\) 9.81648 0.519543
\(358\) 8.76751 0.463377
\(359\) 0.876807 0.0462761 0.0231380 0.999732i \(-0.492634\pi\)
0.0231380 + 0.999732i \(0.492634\pi\)
\(360\) −30.2245 −1.59297
\(361\) 1.00000 0.0526316
\(362\) 19.6807 1.03439
\(363\) 0 0
\(364\) −4.66760 −0.244649
\(365\) 7.03495 0.368226
\(366\) 27.4919 1.43703
\(367\) 10.5030 0.548252 0.274126 0.961694i \(-0.411611\pi\)
0.274126 + 0.961694i \(0.411611\pi\)
\(368\) 2.52841 0.131803
\(369\) 16.8850 0.879000
\(370\) −32.8872 −1.70972
\(371\) 5.82081 0.302201
\(372\) 20.4111 1.05827
\(373\) 34.9249 1.80834 0.904172 0.427168i \(-0.140489\pi\)
0.904172 + 0.427168i \(0.140489\pi\)
\(374\) 0 0
\(375\) 101.771 5.25545
\(376\) −6.20555 −0.320027
\(377\) 36.6961 1.88994
\(378\) −17.7728 −0.914134
\(379\) −13.9695 −0.717567 −0.358783 0.933421i \(-0.616808\pi\)
−0.358783 + 0.933421i \(0.616808\pi\)
\(380\) −4.19461 −0.215179
\(381\) 0.819406 0.0419794
\(382\) −9.47747 −0.484910
\(383\) 35.3223 1.80488 0.902442 0.430811i \(-0.141772\pi\)
0.902442 + 0.430811i \(0.141772\pi\)
\(384\) −3.19461 −0.163024
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) −82.4752 −4.19245
\(388\) −10.0000 −0.507673
\(389\) 12.5838 0.638026 0.319013 0.947750i \(-0.396649\pi\)
0.319013 + 0.947750i \(0.396649\pi\)
\(390\) −47.2813 −2.39418
\(391\) −5.87315 −0.297018
\(392\) −5.25004 −0.265167
\(393\) 11.8282 0.596655
\(394\) −24.5438 −1.23650
\(395\) −23.7275 −1.19386
\(396\) 0 0
\(397\) 0.924098 0.0463792 0.0231896 0.999731i \(-0.492618\pi\)
0.0231896 + 0.999731i \(0.492618\pi\)
\(398\) 20.1991 1.01249
\(399\) −4.22603 −0.211566
\(400\) 12.5948 0.629739
\(401\) −2.30238 −0.114976 −0.0574878 0.998346i \(-0.518309\pi\)
−0.0574878 + 0.998346i \(0.518309\pi\)
\(402\) −19.8548 −0.990268
\(403\) 22.5438 1.12299
\(404\) 18.9949 0.945034
\(405\) −89.3592 −4.44030
\(406\) −13.7580 −0.682797
\(407\) 0 0
\(408\) 7.42064 0.367377
\(409\) −11.4870 −0.567996 −0.283998 0.958825i \(-0.591661\pi\)
−0.283998 + 0.958825i \(0.591661\pi\)
\(410\) −9.82940 −0.485439
\(411\) 16.3666 0.807306
\(412\) 20.0459 0.987590
\(413\) −8.89363 −0.437627
\(414\) 18.2186 0.895396
\(415\) 7.57290 0.371739
\(416\) −3.52841 −0.172995
\(417\) −20.3412 −0.996113
\(418\) 0 0
\(419\) 6.21369 0.303558 0.151779 0.988414i \(-0.451500\pi\)
0.151779 + 0.988414i \(0.451500\pi\)
\(420\) 17.7266 0.864968
\(421\) 12.5934 0.613764 0.306882 0.951748i \(-0.400714\pi\)
0.306882 + 0.951748i \(0.400714\pi\)
\(422\) 1.88129 0.0915797
\(423\) −44.7144 −2.17409
\(424\) 4.40017 0.213691
\(425\) −29.2559 −1.41912
\(426\) 34.2864 1.66118
\(427\) −11.3842 −0.550919
\(428\) 0.849872 0.0410801
\(429\) 0 0
\(430\) 48.0118 2.31533
\(431\) 24.4570 1.17805 0.589026 0.808114i \(-0.299512\pi\)
0.589026 + 0.808114i \(0.299512\pi\)
\(432\) −13.4351 −0.646397
\(433\) 16.3892 0.787616 0.393808 0.919193i \(-0.371157\pi\)
0.393808 + 0.919193i \(0.371157\pi\)
\(434\) −8.45206 −0.405712
\(435\) −139.364 −6.68199
\(436\) 8.72303 0.417757
\(437\) 2.52841 0.120950
\(438\) 5.35781 0.256006
\(439\) −31.8353 −1.51942 −0.759708 0.650265i \(-0.774658\pi\)
−0.759708 + 0.650265i \(0.774658\pi\)
\(440\) 0 0
\(441\) −37.8294 −1.80140
\(442\) 8.19602 0.389845
\(443\) −14.7594 −0.701239 −0.350620 0.936518i \(-0.614029\pi\)
−0.350620 + 0.936518i \(0.614029\pi\)
\(444\) −25.0468 −1.18867
\(445\) −25.3602 −1.20219
\(446\) 20.0868 0.951140
\(447\) 43.8442 2.07376
\(448\) 1.32286 0.0624993
\(449\) 1.44605 0.0682435 0.0341218 0.999418i \(-0.489137\pi\)
0.0341218 + 0.999418i \(0.489137\pi\)
\(450\) 90.7523 4.27811
\(451\) 0 0
\(452\) 3.65666 0.171995
\(453\) 15.9381 0.748838
\(454\) 3.55029 0.166624
\(455\) 19.5788 0.917868
\(456\) −3.19461 −0.149601
\(457\) 9.58524 0.448379 0.224189 0.974546i \(-0.428027\pi\)
0.224189 + 0.974546i \(0.428027\pi\)
\(458\) 7.72162 0.360808
\(459\) 31.2079 1.45666
\(460\) −10.6057 −0.494494
\(461\) −9.91624 −0.461845 −0.230923 0.972972i \(-0.574174\pi\)
−0.230923 + 0.972972i \(0.574174\pi\)
\(462\) 0 0
\(463\) 3.22743 0.149992 0.0749958 0.997184i \(-0.476106\pi\)
0.0749958 + 0.997184i \(0.476106\pi\)
\(464\) −10.4002 −0.482816
\(465\) −85.6167 −3.97038
\(466\) −21.9081 −1.01487
\(467\) 36.0118 1.66643 0.833213 0.552952i \(-0.186499\pi\)
0.833213 + 0.552952i \(0.186499\pi\)
\(468\) −25.4242 −1.17523
\(469\) 8.22170 0.379643
\(470\) 26.0299 1.20067
\(471\) −6.51702 −0.300288
\(472\) −6.72303 −0.309452
\(473\) 0 0
\(474\) −18.0708 −0.830021
\(475\) 12.5948 0.577888
\(476\) −3.07282 −0.140843
\(477\) 31.7056 1.45170
\(478\) 17.6676 0.808097
\(479\) −7.68668 −0.351213 −0.175607 0.984460i \(-0.556189\pi\)
−0.175607 + 0.984460i \(0.556189\pi\)
\(480\) 13.4002 0.611631
\(481\) −27.6640 −1.26137
\(482\) 17.0999 0.778880
\(483\) −10.6852 −0.486191
\(484\) 0 0
\(485\) 41.9461 1.90468
\(486\) −27.7506 −1.25879
\(487\) −34.6356 −1.56949 −0.784745 0.619819i \(-0.787206\pi\)
−0.784745 + 0.619819i \(0.787206\pi\)
\(488\) −8.60572 −0.389563
\(489\) −19.6616 −0.889128
\(490\) 22.0219 0.994847
\(491\) 33.1458 1.49585 0.747924 0.663784i \(-0.231051\pi\)
0.747924 + 0.663784i \(0.231051\pi\)
\(492\) −7.48606 −0.337498
\(493\) 24.1581 1.08803
\(494\) −3.52841 −0.158751
\(495\) 0 0
\(496\) −6.38923 −0.286885
\(497\) −14.1977 −0.636854
\(498\) 5.76751 0.258448
\(499\) −22.9949 −1.02940 −0.514698 0.857372i \(-0.672096\pi\)
−0.514698 + 0.857372i \(0.672096\pi\)
\(500\) −31.8572 −1.42470
\(501\) −11.9590 −0.534291
\(502\) 13.4461 0.600127
\(503\) 7.30098 0.325535 0.162767 0.986664i \(-0.447958\pi\)
0.162767 + 0.986664i \(0.447958\pi\)
\(504\) 9.53195 0.424587
\(505\) −79.6764 −3.54556
\(506\) 0 0
\(507\) 1.75798 0.0780744
\(508\) −0.256496 −0.0113802
\(509\) −38.3213 −1.69856 −0.849282 0.527940i \(-0.822965\pi\)
−0.849282 + 0.527940i \(0.822965\pi\)
\(510\) −31.1267 −1.37831
\(511\) −2.21862 −0.0981461
\(512\) 1.00000 0.0441942
\(513\) −13.4351 −0.593175
\(514\) 10.1546 0.447901
\(515\) −84.0847 −3.70522
\(516\) 36.5657 1.60972
\(517\) 0 0
\(518\) 10.3717 0.455705
\(519\) −29.0289 −1.27423
\(520\) 14.8003 0.649037
\(521\) 8.17649 0.358219 0.179109 0.983829i \(-0.442678\pi\)
0.179109 + 0.983829i \(0.442678\pi\)
\(522\) −74.9389 −3.27999
\(523\) 24.3806 1.06609 0.533045 0.846087i \(-0.321047\pi\)
0.533045 + 0.846087i \(0.321047\pi\)
\(524\) −3.70255 −0.161747
\(525\) −53.2259 −2.32297
\(526\) 24.9081 1.08604
\(527\) 14.8413 0.646497
\(528\) 0 0
\(529\) −16.6071 −0.722049
\(530\) −18.4570 −0.801721
\(531\) −48.4431 −2.10225
\(532\) 1.32286 0.0573533
\(533\) −8.26827 −0.358138
\(534\) −19.3143 −0.835810
\(535\) −3.56489 −0.154123
\(536\) 6.21509 0.268451
\(537\) −28.0088 −1.20867
\(538\) −29.4761 −1.27080
\(539\) 0 0
\(540\) 56.3551 2.42514
\(541\) −41.5788 −1.78761 −0.893806 0.448454i \(-0.851975\pi\)
−0.893806 + 0.448454i \(0.851975\pi\)
\(542\) −2.99046 −0.128451
\(543\) −62.8721 −2.69810
\(544\) −2.32286 −0.0995919
\(545\) −36.5897 −1.56733
\(546\) 14.9112 0.638140
\(547\) −6.05778 −0.259012 −0.129506 0.991579i \(-0.541339\pi\)
−0.129506 + 0.991579i \(0.541339\pi\)
\(548\) −5.12319 −0.218852
\(549\) −62.0090 −2.64648
\(550\) 0 0
\(551\) −10.4002 −0.443062
\(552\) −8.07730 −0.343793
\(553\) 7.48298 0.318209
\(554\) −16.8622 −0.716407
\(555\) 105.062 4.45962
\(556\) 6.36735 0.270036
\(557\) −30.0527 −1.27337 −0.636687 0.771122i \(-0.719696\pi\)
−0.636687 + 0.771122i \(0.719696\pi\)
\(558\) −46.0379 −1.94894
\(559\) 40.3864 1.70816
\(560\) −5.54889 −0.234483
\(561\) 0 0
\(562\) −0.989060 −0.0417210
\(563\) −29.4410 −1.24079 −0.620395 0.784289i \(-0.713028\pi\)
−0.620395 + 0.784289i \(0.713028\pi\)
\(564\) 19.8243 0.834755
\(565\) −15.3383 −0.645286
\(566\) −5.97812 −0.251279
\(567\) 28.1814 1.18351
\(568\) −10.7326 −0.450328
\(569\) −30.5438 −1.28046 −0.640232 0.768182i \(-0.721162\pi\)
−0.640232 + 0.768182i \(0.721162\pi\)
\(570\) 13.4002 0.561271
\(571\) 2.95399 0.123621 0.0618104 0.998088i \(-0.480313\pi\)
0.0618104 + 0.998088i \(0.480313\pi\)
\(572\) 0 0
\(573\) 30.2769 1.26483
\(574\) 3.09991 0.129388
\(575\) 31.8448 1.32802
\(576\) 7.20555 0.300231
\(577\) −4.69021 −0.195256 −0.0976280 0.995223i \(-0.531126\pi\)
−0.0976280 + 0.995223i \(0.531126\pi\)
\(578\) −11.6043 −0.482676
\(579\) −25.5569 −1.06211
\(580\) 43.6247 1.81142
\(581\) −2.38828 −0.0990824
\(582\) 31.9461 1.32421
\(583\) 0 0
\(584\) −1.67714 −0.0694005
\(585\) 106.645 4.40921
\(586\) 14.5489 0.601009
\(587\) −11.8273 −0.488164 −0.244082 0.969755i \(-0.578487\pi\)
−0.244082 + 0.969755i \(0.578487\pi\)
\(588\) 16.7718 0.691659
\(589\) −6.38923 −0.263263
\(590\) 28.2005 1.16100
\(591\) 78.4081 3.22528
\(592\) 7.84034 0.322236
\(593\) −24.9621 −1.02507 −0.512536 0.858666i \(-0.671294\pi\)
−0.512536 + 0.858666i \(0.671294\pi\)
\(594\) 0 0
\(595\) 12.8893 0.528410
\(596\) −13.7244 −0.562175
\(597\) −64.5283 −2.64097
\(598\) −8.92129 −0.364819
\(599\) −27.0131 −1.10372 −0.551862 0.833935i \(-0.686083\pi\)
−0.551862 + 0.833935i \(0.686083\pi\)
\(600\) −40.2354 −1.64261
\(601\) 7.24343 0.295466 0.147733 0.989027i \(-0.452802\pi\)
0.147733 + 0.989027i \(0.452802\pi\)
\(602\) −15.1415 −0.617123
\(603\) 44.7832 1.82371
\(604\) −4.98906 −0.203002
\(605\) 0 0
\(606\) −60.6815 −2.46502
\(607\) 27.4411 1.11380 0.556900 0.830579i \(-0.311991\pi\)
0.556900 + 0.830579i \(0.311991\pi\)
\(608\) 1.00000 0.0405554
\(609\) 43.9514 1.78100
\(610\) 36.0977 1.46155
\(611\) 21.8958 0.885808
\(612\) −16.7375 −0.676573
\(613\) −1.97011 −0.0795718 −0.0397859 0.999208i \(-0.512668\pi\)
−0.0397859 + 0.999208i \(0.512668\pi\)
\(614\) 9.69161 0.391122
\(615\) 31.4011 1.26622
\(616\) 0 0
\(617\) 2.42110 0.0974696 0.0487348 0.998812i \(-0.484481\pi\)
0.0487348 + 0.998812i \(0.484481\pi\)
\(618\) −64.0389 −2.57602
\(619\) 38.0118 1.52782 0.763911 0.645322i \(-0.223277\pi\)
0.763911 + 0.645322i \(0.223277\pi\)
\(620\) 26.8003 1.07633
\(621\) −33.9695 −1.36315
\(622\) −18.8229 −0.754731
\(623\) 7.99787 0.320428
\(624\) 11.2719 0.451238
\(625\) 70.6546 2.82618
\(626\) 27.1800 1.08633
\(627\) 0 0
\(628\) 2.04000 0.0814050
\(629\) −18.2120 −0.726160
\(630\) −39.9828 −1.59295
\(631\) 27.2873 1.08629 0.543146 0.839638i \(-0.317233\pi\)
0.543146 + 0.839638i \(0.317233\pi\)
\(632\) 5.65666 0.225010
\(633\) −6.00999 −0.238876
\(634\) −14.3697 −0.570694
\(635\) 1.07590 0.0426959
\(636\) −14.0568 −0.557389
\(637\) 18.5243 0.733960
\(638\) 0 0
\(639\) −77.3341 −3.05929
\(640\) −4.19461 −0.165807
\(641\) 0.589724 0.0232927 0.0116464 0.999932i \(-0.496293\pi\)
0.0116464 + 0.999932i \(0.496293\pi\)
\(642\) −2.71501 −0.107153
\(643\) 11.1197 0.438517 0.219258 0.975667i \(-0.429636\pi\)
0.219258 + 0.975667i \(0.429636\pi\)
\(644\) 3.34474 0.131801
\(645\) −153.379 −6.03929
\(646\) −2.32286 −0.0913918
\(647\) 9.19837 0.361625 0.180813 0.983518i \(-0.442127\pi\)
0.180813 + 0.983518i \(0.442127\pi\)
\(648\) 21.3033 0.836874
\(649\) 0 0
\(650\) −44.4396 −1.74306
\(651\) 27.0011 1.05825
\(652\) 6.15461 0.241033
\(653\) −12.9940 −0.508494 −0.254247 0.967139i \(-0.581828\pi\)
−0.254247 + 0.967139i \(0.581828\pi\)
\(654\) −27.8667 −1.08967
\(655\) 15.5308 0.606837
\(656\) 2.34334 0.0914920
\(657\) −12.0847 −0.471470
\(658\) −8.20909 −0.320023
\(659\) −2.11012 −0.0821988 −0.0410994 0.999155i \(-0.513086\pi\)
−0.0410994 + 0.999155i \(0.513086\pi\)
\(660\) 0 0
\(661\) 7.58665 0.295086 0.147543 0.989056i \(-0.452863\pi\)
0.147543 + 0.989056i \(0.452863\pi\)
\(662\) 18.9635 0.737038
\(663\) −26.1831 −1.01687
\(664\) −1.80539 −0.0700626
\(665\) −5.54889 −0.215177
\(666\) 56.4940 2.18910
\(667\) −26.2959 −1.01818
\(668\) 3.74350 0.144841
\(669\) −64.1697 −2.48094
\(670\) −26.0699 −1.00717
\(671\) 0 0
\(672\) −4.22603 −0.163023
\(673\) 33.2792 1.28282 0.641410 0.767199i \(-0.278350\pi\)
0.641410 + 0.767199i \(0.278350\pi\)
\(674\) 30.1595 1.16170
\(675\) −169.212 −6.51298
\(676\) −0.550294 −0.0211651
\(677\) −0.160391 −0.00616431 −0.00308216 0.999995i \(-0.500981\pi\)
−0.00308216 + 0.999995i \(0.500981\pi\)
\(678\) −11.6816 −0.448630
\(679\) −13.2286 −0.507668
\(680\) 9.74350 0.373646
\(681\) −11.3418 −0.434619
\(682\) 0 0
\(683\) 4.60477 0.176197 0.0880983 0.996112i \(-0.471921\pi\)
0.0880983 + 0.996112i \(0.471921\pi\)
\(684\) 7.20555 0.275511
\(685\) 21.4898 0.821084
\(686\) −16.2051 −0.618714
\(687\) −24.6676 −0.941128
\(688\) −11.4461 −0.436377
\(689\) −15.5256 −0.591479
\(690\) 33.8812 1.28983
\(691\) 6.54008 0.248796 0.124398 0.992232i \(-0.460300\pi\)
0.124398 + 0.992232i \(0.460300\pi\)
\(692\) 9.08684 0.345430
\(693\) 0 0
\(694\) 23.5997 0.895833
\(695\) −26.7086 −1.01311
\(696\) 33.2245 1.25937
\(697\) −5.44325 −0.206178
\(698\) −29.2086 −1.10556
\(699\) 69.9879 2.64719
\(700\) 16.6611 0.629732
\(701\) −12.3455 −0.466282 −0.233141 0.972443i \(-0.574900\pi\)
−0.233141 + 0.972443i \(0.574900\pi\)
\(702\) 47.4046 1.78917
\(703\) 7.84034 0.295704
\(704\) 0 0
\(705\) −83.1554 −3.13182
\(706\) −10.2274 −0.384915
\(707\) 25.1277 0.945023
\(708\) 21.4775 0.807173
\(709\) −26.2464 −0.985704 −0.492852 0.870113i \(-0.664046\pi\)
−0.492852 + 0.870113i \(0.664046\pi\)
\(710\) 45.0190 1.68953
\(711\) 40.7594 1.52860
\(712\) 6.04589 0.226579
\(713\) −16.1546 −0.604995
\(714\) 9.81648 0.367373
\(715\) 0 0
\(716\) 8.76751 0.327657
\(717\) −56.4412 −2.10783
\(718\) 0.876807 0.0327221
\(719\) 5.61032 0.209230 0.104615 0.994513i \(-0.466639\pi\)
0.104615 + 0.994513i \(0.466639\pi\)
\(720\) −30.2245 −1.12640
\(721\) 26.5179 0.987579
\(722\) 1.00000 0.0372161
\(723\) −54.6276 −2.03162
\(724\) 19.6807 0.731426
\(725\) −130.988 −4.86476
\(726\) 0 0
\(727\) −9.17060 −0.340119 −0.170059 0.985434i \(-0.554396\pi\)
−0.170059 + 0.985434i \(0.554396\pi\)
\(728\) −4.66760 −0.172993
\(729\) 24.7423 0.916382
\(730\) 7.03495 0.260375
\(731\) 26.5876 0.983378
\(732\) 27.4919 1.01613
\(733\) 26.9140 0.994091 0.497045 0.867725i \(-0.334418\pi\)
0.497045 + 0.867725i \(0.334418\pi\)
\(734\) 10.5030 0.387673
\(735\) −70.3514 −2.59495
\(736\) 2.52841 0.0931986
\(737\) 0 0
\(738\) 16.8850 0.621547
\(739\) 43.4032 1.59661 0.798307 0.602251i \(-0.205729\pi\)
0.798307 + 0.602251i \(0.205729\pi\)
\(740\) −32.8872 −1.20896
\(741\) 11.2719 0.414084
\(742\) 5.82081 0.213689
\(743\) 18.0671 0.662817 0.331409 0.943487i \(-0.392476\pi\)
0.331409 + 0.943487i \(0.392476\pi\)
\(744\) 20.4111 0.748307
\(745\) 57.5687 2.10915
\(746\) 34.9249 1.27869
\(747\) −13.0088 −0.475967
\(748\) 0 0
\(749\) 1.12426 0.0410797
\(750\) 101.771 3.71616
\(751\) −44.0336 −1.60681 −0.803405 0.595432i \(-0.796981\pi\)
−0.803405 + 0.595432i \(0.796981\pi\)
\(752\) −6.20555 −0.226293
\(753\) −42.9549 −1.56537
\(754\) 36.6961 1.33639
\(755\) 20.9272 0.761618
\(756\) −17.7728 −0.646390
\(757\) 19.5489 0.710517 0.355258 0.934768i \(-0.384393\pi\)
0.355258 + 0.934768i \(0.384393\pi\)
\(758\) −13.9695 −0.507396
\(759\) 0 0
\(760\) −4.19461 −0.152155
\(761\) −36.8548 −1.33599 −0.667993 0.744168i \(-0.732846\pi\)
−0.667993 + 0.744168i \(0.732846\pi\)
\(762\) 0.819406 0.0296839
\(763\) 11.5394 0.417753
\(764\) −9.47747 −0.342883
\(765\) 70.2073 2.53835
\(766\) 35.3223 1.27625
\(767\) 23.7216 0.856538
\(768\) −3.19461 −0.115276
\(769\) −6.09778 −0.219892 −0.109946 0.993938i \(-0.535068\pi\)
−0.109946 + 0.993938i \(0.535068\pi\)
\(770\) 0 0
\(771\) −32.4400 −1.16830
\(772\) 8.00000 0.287926
\(773\) 3.70407 0.133226 0.0666131 0.997779i \(-0.478781\pi\)
0.0666131 + 0.997779i \(0.478781\pi\)
\(774\) −82.4752 −2.96451
\(775\) −80.4709 −2.89060
\(776\) −10.0000 −0.358979
\(777\) −33.1335 −1.18866
\(778\) 12.5838 0.451152
\(779\) 2.34334 0.0839588
\(780\) −47.2813 −1.69294
\(781\) 0 0
\(782\) −5.87315 −0.210024
\(783\) 139.727 4.99345
\(784\) −5.25004 −0.187501
\(785\) −8.55702 −0.305413
\(786\) 11.8282 0.421899
\(787\) −6.14367 −0.218998 −0.109499 0.993987i \(-0.534925\pi\)
−0.109499 + 0.993987i \(0.534925\pi\)
\(788\) −24.5438 −0.874338
\(789\) −79.5718 −2.83283
\(790\) −23.7275 −0.844187
\(791\) 4.83726 0.171993
\(792\) 0 0
\(793\) 30.3645 1.07828
\(794\) 0.924098 0.0327950
\(795\) 58.9630 2.09120
\(796\) 20.1991 0.715938
\(797\) 11.3957 0.403656 0.201828 0.979421i \(-0.435312\pi\)
0.201828 + 0.979421i \(0.435312\pi\)
\(798\) −4.22603 −0.149600
\(799\) 14.4146 0.509953
\(800\) 12.5948 0.445293
\(801\) 43.5640 1.53926
\(802\) −2.30238 −0.0813000
\(803\) 0 0
\(804\) −19.8548 −0.700225
\(805\) −14.0299 −0.494489
\(806\) 22.5438 0.794073
\(807\) 94.1646 3.31475
\(808\) 18.9949 0.668240
\(809\) −2.18367 −0.0767739 −0.0383869 0.999263i \(-0.512222\pi\)
−0.0383869 + 0.999263i \(0.512222\pi\)
\(810\) −89.3592 −3.13976
\(811\) 41.8142 1.46830 0.734148 0.678989i \(-0.237582\pi\)
0.734148 + 0.678989i \(0.237582\pi\)
\(812\) −13.7580 −0.482810
\(813\) 9.55337 0.335051
\(814\) 0 0
\(815\) −25.8162 −0.904302
\(816\) 7.42064 0.259774
\(817\) −11.4461 −0.400447
\(818\) −11.4870 −0.401634
\(819\) −33.6327 −1.17522
\(820\) −9.82940 −0.343257
\(821\) −7.65974 −0.267327 −0.133663 0.991027i \(-0.542674\pi\)
−0.133663 + 0.991027i \(0.542674\pi\)
\(822\) 16.3666 0.570851
\(823\) −13.8893 −0.484151 −0.242075 0.970257i \(-0.577828\pi\)
−0.242075 + 0.970257i \(0.577828\pi\)
\(824\) 20.0459 0.698332
\(825\) 0 0
\(826\) −8.89363 −0.309449
\(827\) −29.3887 −1.02194 −0.510972 0.859597i \(-0.670714\pi\)
−0.510972 + 0.859597i \(0.670714\pi\)
\(828\) 18.2186 0.633141
\(829\) 8.60432 0.298840 0.149420 0.988774i \(-0.452259\pi\)
0.149420 + 0.988774i \(0.452259\pi\)
\(830\) 7.57290 0.262859
\(831\) 53.8683 1.86867
\(832\) −3.52841 −0.122326
\(833\) 12.1951 0.422536
\(834\) −20.3412 −0.704358
\(835\) −15.7026 −0.543409
\(836\) 0 0
\(837\) 85.8400 2.96706
\(838\) 6.21369 0.214648
\(839\) 0.815377 0.0281499 0.0140750 0.999901i \(-0.495520\pi\)
0.0140750 + 0.999901i \(0.495520\pi\)
\(840\) 17.7266 0.611624
\(841\) 79.1635 2.72977
\(842\) 12.5934 0.433996
\(843\) 3.15966 0.108825
\(844\) 1.88129 0.0647566
\(845\) 2.30827 0.0794069
\(846\) −44.7144 −1.53731
\(847\) 0 0
\(848\) 4.40017 0.151102
\(849\) 19.0978 0.655434
\(850\) −29.2559 −1.00347
\(851\) 19.8236 0.679545
\(852\) 34.2864 1.17463
\(853\) −6.70856 −0.229697 −0.114848 0.993383i \(-0.536638\pi\)
−0.114848 + 0.993383i \(0.536638\pi\)
\(854\) −11.3842 −0.389558
\(855\) −30.2245 −1.03366
\(856\) 0.849872 0.0290480
\(857\) 17.6416 0.602626 0.301313 0.953525i \(-0.402575\pi\)
0.301313 + 0.953525i \(0.402575\pi\)
\(858\) 0 0
\(859\) 36.3520 1.24032 0.620158 0.784477i \(-0.287069\pi\)
0.620158 + 0.784477i \(0.287069\pi\)
\(860\) 48.0118 1.63719
\(861\) −9.90302 −0.337494
\(862\) 24.4570 0.833009
\(863\) 24.1984 0.823722 0.411861 0.911247i \(-0.364879\pi\)
0.411861 + 0.911247i \(0.364879\pi\)
\(864\) −13.4351 −0.457072
\(865\) −38.1158 −1.29598
\(866\) 16.3892 0.556929
\(867\) 37.0713 1.25901
\(868\) −8.45206 −0.286882
\(869\) 0 0
\(870\) −139.364 −4.72488
\(871\) −21.9294 −0.743050
\(872\) 8.72303 0.295399
\(873\) −72.0555 −2.43871
\(874\) 2.52841 0.0855249
\(875\) −42.1426 −1.42468
\(876\) 5.35781 0.181024
\(877\) 43.3477 1.46375 0.731874 0.681440i \(-0.238646\pi\)
0.731874 + 0.681440i \(0.238646\pi\)
\(878\) −31.8353 −1.07439
\(879\) −46.4781 −1.56767
\(880\) 0 0
\(881\) 1.34121 0.0451865 0.0225932 0.999745i \(-0.492808\pi\)
0.0225932 + 0.999745i \(0.492808\pi\)
\(882\) −37.8294 −1.27378
\(883\) 41.2924 1.38960 0.694800 0.719203i \(-0.255493\pi\)
0.694800 + 0.719203i \(0.255493\pi\)
\(884\) 8.19602 0.275662
\(885\) −90.0897 −3.02833
\(886\) −14.7594 −0.495851
\(887\) −8.18142 −0.274705 −0.137353 0.990522i \(-0.543859\pi\)
−0.137353 + 0.990522i \(0.543859\pi\)
\(888\) −25.0468 −0.840517
\(889\) −0.339309 −0.0113800
\(890\) −25.3602 −0.850075
\(891\) 0 0
\(892\) 20.0868 0.672557
\(893\) −6.20555 −0.207661
\(894\) 43.8442 1.46637
\(895\) −36.7763 −1.22930
\(896\) 1.32286 0.0441937
\(897\) 28.5001 0.951590
\(898\) 1.44605 0.0482555
\(899\) 66.4490 2.21620
\(900\) 90.7523 3.02508
\(901\) −10.2210 −0.340510
\(902\) 0 0
\(903\) 48.3714 1.60970
\(904\) 3.65666 0.121619
\(905\) −82.5528 −2.74415
\(906\) 15.9381 0.529508
\(907\) −4.76398 −0.158185 −0.0790927 0.996867i \(-0.525202\pi\)
−0.0790927 + 0.996867i \(0.525202\pi\)
\(908\) 3.55029 0.117821
\(909\) 136.869 4.53966
\(910\) 19.5788 0.649030
\(911\) 10.5589 0.349831 0.174916 0.984583i \(-0.444035\pi\)
0.174916 + 0.984583i \(0.444035\pi\)
\(912\) −3.19461 −0.105784
\(913\) 0 0
\(914\) 9.58524 0.317052
\(915\) −115.318 −3.81230
\(916\) 7.72162 0.255130
\(917\) −4.89796 −0.161745
\(918\) 31.2079 1.03001
\(919\) −37.5764 −1.23953 −0.619766 0.784787i \(-0.712773\pi\)
−0.619766 + 0.784787i \(0.712773\pi\)
\(920\) −10.6057 −0.349660
\(921\) −30.9609 −1.02020
\(922\) −9.91624 −0.326574
\(923\) 37.8689 1.24647
\(924\) 0 0
\(925\) 98.7473 3.24679
\(926\) 3.22743 0.106060
\(927\) 144.442 4.74409
\(928\) −10.4002 −0.341402
\(929\) −4.07590 −0.133726 −0.0668630 0.997762i \(-0.521299\pi\)
−0.0668630 + 0.997762i \(0.521299\pi\)
\(930\) −85.6167 −2.80748
\(931\) −5.25004 −0.172063
\(932\) −21.9081 −0.717624
\(933\) 60.1320 1.96863
\(934\) 36.0118 1.17834
\(935\) 0 0
\(936\) −25.4242 −0.831015
\(937\) 54.4273 1.77806 0.889030 0.457848i \(-0.151380\pi\)
0.889030 + 0.457848i \(0.151380\pi\)
\(938\) 8.22170 0.268448
\(939\) −86.8297 −2.83358
\(940\) 26.0299 0.849002
\(941\) 26.7152 0.870890 0.435445 0.900215i \(-0.356591\pi\)
0.435445 + 0.900215i \(0.356591\pi\)
\(942\) −6.51702 −0.212336
\(943\) 5.92493 0.192942
\(944\) −6.72303 −0.218816
\(945\) 74.5500 2.42511
\(946\) 0 0
\(947\) 56.9448 1.85046 0.925229 0.379409i \(-0.123873\pi\)
0.925229 + 0.379409i \(0.123873\pi\)
\(948\) −18.0708 −0.586914
\(949\) 5.91764 0.192095
\(950\) 12.5948 0.408629
\(951\) 45.9056 1.48859
\(952\) −3.07282 −0.0995908
\(953\) 0.764553 0.0247663 0.0123832 0.999923i \(-0.496058\pi\)
0.0123832 + 0.999923i \(0.496058\pi\)
\(954\) 31.7056 1.02651
\(955\) 39.7543 1.28642
\(956\) 17.6676 0.571411
\(957\) 0 0
\(958\) −7.68668 −0.248345
\(959\) −6.77727 −0.218850
\(960\) 13.4002 0.432489
\(961\) 9.82221 0.316846
\(962\) −27.6640 −0.891922
\(963\) 6.12380 0.197337
\(964\) 17.0999 0.550751
\(965\) −33.5569 −1.08023
\(966\) −10.6852 −0.343789
\(967\) 26.5510 0.853823 0.426912 0.904293i \(-0.359602\pi\)
0.426912 + 0.904293i \(0.359602\pi\)
\(968\) 0 0
\(969\) 7.42064 0.238385
\(970\) 41.9461 1.34681
\(971\) −35.6335 −1.14353 −0.571766 0.820416i \(-0.693742\pi\)
−0.571766 + 0.820416i \(0.693742\pi\)
\(972\) −27.7506 −0.890100
\(973\) 8.42312 0.270033
\(974\) −34.6356 −1.10980
\(975\) 141.967 4.54659
\(976\) −8.60572 −0.275462
\(977\) 23.8544 0.763168 0.381584 0.924334i \(-0.375379\pi\)
0.381584 + 0.924334i \(0.375379\pi\)
\(978\) −19.6616 −0.628709
\(979\) 0 0
\(980\) 22.0219 0.703463
\(981\) 62.8542 2.00678
\(982\) 33.1458 1.05772
\(983\) −21.5520 −0.687401 −0.343701 0.939079i \(-0.611681\pi\)
−0.343701 + 0.939079i \(0.611681\pi\)
\(984\) −7.48606 −0.238647
\(985\) 102.952 3.28032
\(986\) 24.1581 0.769352
\(987\) 26.2249 0.834746
\(988\) −3.52841 −0.112254
\(989\) −28.9404 −0.920250
\(990\) 0 0
\(991\) 14.0049 0.444881 0.222441 0.974946i \(-0.428598\pi\)
0.222441 + 0.974946i \(0.428598\pi\)
\(992\) −6.38923 −0.202858
\(993\) −60.5811 −1.92248
\(994\) −14.1977 −0.450323
\(995\) −84.7274 −2.68604
\(996\) 5.76751 0.182751
\(997\) −47.2733 −1.49716 −0.748581 0.663044i \(-0.769264\pi\)
−0.748581 + 0.663044i \(0.769264\pi\)
\(998\) −22.9949 −0.727892
\(999\) −105.336 −3.33268
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 4598.2.a.bv.1.1 yes 4
11.10 odd 2 4598.2.a.bs.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bs.1.1 4 11.10 odd 2
4598.2.a.bv.1.1 yes 4 1.1 even 1 trivial