Properties

Label 4598.2.a.cc.1.9
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $10$
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: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 418)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.12868\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} -2.12868 q^{6} +0.813941 q^{7} -1.00000 q^{8} +1.53127 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} -2.12868 q^{6} +0.813941 q^{7} -1.00000 q^{8} +1.53127 q^{9} +0.444747 q^{10} +2.12868 q^{12} +0.531472 q^{13} -0.813941 q^{14} -0.946723 q^{15} +1.00000 q^{16} -5.88116 q^{17} -1.53127 q^{18} -1.00000 q^{19} -0.444747 q^{20} +1.73262 q^{21} +6.69536 q^{23} -2.12868 q^{24} -4.80220 q^{25} -0.531472 q^{26} -3.12645 q^{27} +0.813941 q^{28} -4.16686 q^{29} +0.946723 q^{30} -5.80088 q^{31} -1.00000 q^{32} +5.88116 q^{34} -0.361998 q^{35} +1.53127 q^{36} +2.37532 q^{37} +1.00000 q^{38} +1.13133 q^{39} +0.444747 q^{40} -10.2569 q^{41} -1.73262 q^{42} -10.2461 q^{43} -0.681029 q^{45} -6.69536 q^{46} +6.33722 q^{47} +2.12868 q^{48} -6.33750 q^{49} +4.80220 q^{50} -12.5191 q^{51} +0.531472 q^{52} +9.31823 q^{53} +3.12645 q^{54} -0.813941 q^{56} -2.12868 q^{57} +4.16686 q^{58} +3.37870 q^{59} -0.946723 q^{60} -4.76838 q^{61} +5.80088 q^{62} +1.24637 q^{63} +1.00000 q^{64} -0.236370 q^{65} -1.23043 q^{67} -5.88116 q^{68} +14.2523 q^{69} +0.361998 q^{70} -11.5841 q^{71} -1.53127 q^{72} +12.3402 q^{73} -2.37532 q^{74} -10.2223 q^{75} -1.00000 q^{76} -1.13133 q^{78} -3.46996 q^{79} -0.444747 q^{80} -11.2490 q^{81} +10.2569 q^{82} -12.8659 q^{83} +1.73262 q^{84} +2.61563 q^{85} +10.2461 q^{86} -8.86991 q^{87} +7.40160 q^{89} +0.681029 q^{90} +0.432587 q^{91} +6.69536 q^{92} -12.3482 q^{93} -6.33722 q^{94} +0.444747 q^{95} -2.12868 q^{96} -14.2295 q^{97} +6.33750 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20} + q^{21} + 14 q^{23} - 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} - 11 q^{28} - 16 q^{29} - q^{30} + 12 q^{31} - 10 q^{32} + 12 q^{34} + 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} - 11 q^{39} + 3 q^{40} + 5 q^{41} - q^{42} - 22 q^{43} - 2 q^{45} - 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} - 5 q^{50} - 8 q^{51} - 11 q^{52} + 2 q^{53} - 2 q^{54} + 11 q^{56} - 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} - 35 q^{61} - 12 q^{62} - 38 q^{63} + 10 q^{64} - 4 q^{65} + 9 q^{67} - 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} + q^{74} - 15 q^{75} - 10 q^{76} + 11 q^{78} - 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} - 7 q^{83} + q^{84} - 35 q^{85} + 22 q^{86} - 8 q^{87} + 22 q^{89} + 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} - 8 q^{94} + 3 q^{95} - 2 q^{96} + 32 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 2.12868 1.22899 0.614497 0.788919i \(-0.289359\pi\)
0.614497 + 0.788919i \(0.289359\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.444747 −0.198897 −0.0994485 0.995043i \(-0.531708\pi\)
−0.0994485 + 0.995043i \(0.531708\pi\)
\(6\) −2.12868 −0.869029
\(7\) 0.813941 0.307641 0.153820 0.988099i \(-0.450842\pi\)
0.153820 + 0.988099i \(0.450842\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.53127 0.510424
\(10\) 0.444747 0.140641
\(11\) 0 0
\(12\) 2.12868 0.614497
\(13\) 0.531472 0.147404 0.0737019 0.997280i \(-0.476519\pi\)
0.0737019 + 0.997280i \(0.476519\pi\)
\(14\) −0.813941 −0.217535
\(15\) −0.946723 −0.244443
\(16\) 1.00000 0.250000
\(17\) −5.88116 −1.42639 −0.713196 0.700965i \(-0.752753\pi\)
−0.713196 + 0.700965i \(0.752753\pi\)
\(18\) −1.53127 −0.360924
\(19\) −1.00000 −0.229416
\(20\) −0.444747 −0.0994485
\(21\) 1.73262 0.378089
\(22\) 0 0
\(23\) 6.69536 1.39608 0.698040 0.716059i \(-0.254056\pi\)
0.698040 + 0.716059i \(0.254056\pi\)
\(24\) −2.12868 −0.434515
\(25\) −4.80220 −0.960440
\(26\) −0.531472 −0.104230
\(27\) −3.12645 −0.601685
\(28\) 0.813941 0.153820
\(29\) −4.16686 −0.773767 −0.386883 0.922129i \(-0.626448\pi\)
−0.386883 + 0.922129i \(0.626448\pi\)
\(30\) 0.946723 0.172847
\(31\) −5.80088 −1.04187 −0.520934 0.853597i \(-0.674416\pi\)
−0.520934 + 0.853597i \(0.674416\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 5.88116 1.00861
\(35\) −0.361998 −0.0611888
\(36\) 1.53127 0.255212
\(37\) 2.37532 0.390500 0.195250 0.980754i \(-0.437448\pi\)
0.195250 + 0.980754i \(0.437448\pi\)
\(38\) 1.00000 0.162221
\(39\) 1.13133 0.181158
\(40\) 0.444747 0.0703207
\(41\) −10.2569 −1.60186 −0.800932 0.598755i \(-0.795662\pi\)
−0.800932 + 0.598755i \(0.795662\pi\)
\(42\) −1.73262 −0.267349
\(43\) −10.2461 −1.56252 −0.781258 0.624208i \(-0.785422\pi\)
−0.781258 + 0.624208i \(0.785422\pi\)
\(44\) 0 0
\(45\) −0.681029 −0.101522
\(46\) −6.69536 −0.987177
\(47\) 6.33722 0.924379 0.462189 0.886781i \(-0.347064\pi\)
0.462189 + 0.886781i \(0.347064\pi\)
\(48\) 2.12868 0.307248
\(49\) −6.33750 −0.905357
\(50\) 4.80220 0.679134
\(51\) −12.5191 −1.75302
\(52\) 0.531472 0.0737019
\(53\) 9.31823 1.27996 0.639979 0.768392i \(-0.278943\pi\)
0.639979 + 0.768392i \(0.278943\pi\)
\(54\) 3.12645 0.425456
\(55\) 0 0
\(56\) −0.813941 −0.108768
\(57\) −2.12868 −0.281950
\(58\) 4.16686 0.547136
\(59\) 3.37870 0.439869 0.219935 0.975515i \(-0.429416\pi\)
0.219935 + 0.975515i \(0.429416\pi\)
\(60\) −0.946723 −0.122221
\(61\) −4.76838 −0.610529 −0.305264 0.952268i \(-0.598745\pi\)
−0.305264 + 0.952268i \(0.598745\pi\)
\(62\) 5.80088 0.736712
\(63\) 1.24637 0.157027
\(64\) 1.00000 0.125000
\(65\) −0.236370 −0.0293181
\(66\) 0 0
\(67\) −1.23043 −0.150321 −0.0751604 0.997171i \(-0.523947\pi\)
−0.0751604 + 0.997171i \(0.523947\pi\)
\(68\) −5.88116 −0.713196
\(69\) 14.2523 1.71577
\(70\) 0.361998 0.0432670
\(71\) −11.5841 −1.37479 −0.687393 0.726286i \(-0.741245\pi\)
−0.687393 + 0.726286i \(0.741245\pi\)
\(72\) −1.53127 −0.180462
\(73\) 12.3402 1.44431 0.722155 0.691731i \(-0.243152\pi\)
0.722155 + 0.691731i \(0.243152\pi\)
\(74\) −2.37532 −0.276125
\(75\) −10.2223 −1.18037
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −1.13133 −0.128098
\(79\) −3.46996 −0.390401 −0.195200 0.980763i \(-0.562536\pi\)
−0.195200 + 0.980763i \(0.562536\pi\)
\(80\) −0.444747 −0.0497242
\(81\) −11.2490 −1.24989
\(82\) 10.2569 1.13269
\(83\) −12.8659 −1.41222 −0.706110 0.708102i \(-0.749551\pi\)
−0.706110 + 0.708102i \(0.749551\pi\)
\(84\) 1.73262 0.189044
\(85\) 2.61563 0.283705
\(86\) 10.2461 1.10487
\(87\) −8.86991 −0.950954
\(88\) 0 0
\(89\) 7.40160 0.784568 0.392284 0.919844i \(-0.371685\pi\)
0.392284 + 0.919844i \(0.371685\pi\)
\(90\) 0.681029 0.0717867
\(91\) 0.432587 0.0453474
\(92\) 6.69536 0.698040
\(93\) −12.3482 −1.28045
\(94\) −6.33722 −0.653635
\(95\) 0.444747 0.0456301
\(96\) −2.12868 −0.217257
\(97\) −14.2295 −1.44479 −0.722395 0.691481i \(-0.756959\pi\)
−0.722395 + 0.691481i \(0.756959\pi\)
\(98\) 6.33750 0.640184
\(99\) 0 0
\(100\) −4.80220 −0.480220
\(101\) 3.50507 0.348767 0.174384 0.984678i \(-0.444207\pi\)
0.174384 + 0.984678i \(0.444207\pi\)
\(102\) 12.5191 1.23958
\(103\) 0.694123 0.0683939 0.0341970 0.999415i \(-0.489113\pi\)
0.0341970 + 0.999415i \(0.489113\pi\)
\(104\) −0.531472 −0.0521151
\(105\) −0.770577 −0.0752007
\(106\) −9.31823 −0.905067
\(107\) 8.63080 0.834371 0.417185 0.908821i \(-0.363017\pi\)
0.417185 + 0.908821i \(0.363017\pi\)
\(108\) −3.12645 −0.300843
\(109\) 8.10360 0.776184 0.388092 0.921621i \(-0.373134\pi\)
0.388092 + 0.921621i \(0.373134\pi\)
\(110\) 0 0
\(111\) 5.05629 0.479922
\(112\) 0.813941 0.0769102
\(113\) 4.66260 0.438620 0.219310 0.975655i \(-0.429619\pi\)
0.219310 + 0.975655i \(0.429619\pi\)
\(114\) 2.12868 0.199369
\(115\) −2.97774 −0.277676
\(116\) −4.16686 −0.386883
\(117\) 0.813828 0.0752384
\(118\) −3.37870 −0.311034
\(119\) −4.78692 −0.438816
\(120\) 0.946723 0.0864236
\(121\) 0 0
\(122\) 4.76838 0.431709
\(123\) −21.8337 −1.96868
\(124\) −5.80088 −0.520934
\(125\) 4.35950 0.389925
\(126\) −1.24637 −0.111035
\(127\) 5.75512 0.510684 0.255342 0.966851i \(-0.417812\pi\)
0.255342 + 0.966851i \(0.417812\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.8107 −1.92032
\(130\) 0.236370 0.0207311
\(131\) −0.970302 −0.0847756 −0.0423878 0.999101i \(-0.513497\pi\)
−0.0423878 + 0.999101i \(0.513497\pi\)
\(132\) 0 0
\(133\) −0.813941 −0.0705777
\(134\) 1.23043 0.106293
\(135\) 1.39048 0.119673
\(136\) 5.88116 0.504305
\(137\) 2.14682 0.183415 0.0917077 0.995786i \(-0.470767\pi\)
0.0917077 + 0.995786i \(0.470767\pi\)
\(138\) −14.2523 −1.21323
\(139\) −9.78816 −0.830221 −0.415110 0.909771i \(-0.636257\pi\)
−0.415110 + 0.909771i \(0.636257\pi\)
\(140\) −0.361998 −0.0305944
\(141\) 13.4899 1.13606
\(142\) 11.5841 0.972120
\(143\) 0 0
\(144\) 1.53127 0.127606
\(145\) 1.85320 0.153900
\(146\) −12.3402 −1.02128
\(147\) −13.4905 −1.11268
\(148\) 2.37532 0.195250
\(149\) 1.24923 0.102341 0.0511703 0.998690i \(-0.483705\pi\)
0.0511703 + 0.998690i \(0.483705\pi\)
\(150\) 10.2223 0.834651
\(151\) −13.8527 −1.12732 −0.563659 0.826008i \(-0.690607\pi\)
−0.563659 + 0.826008i \(0.690607\pi\)
\(152\) 1.00000 0.0811107
\(153\) −9.00566 −0.728065
\(154\) 0 0
\(155\) 2.57992 0.207224
\(156\) 1.13133 0.0905791
\(157\) 17.3097 1.38146 0.690731 0.723112i \(-0.257289\pi\)
0.690731 + 0.723112i \(0.257289\pi\)
\(158\) 3.46996 0.276055
\(159\) 19.8355 1.57306
\(160\) 0.444747 0.0351603
\(161\) 5.44963 0.429491
\(162\) 11.2490 0.883807
\(163\) −9.97325 −0.781165 −0.390583 0.920568i \(-0.627726\pi\)
−0.390583 + 0.920568i \(0.627726\pi\)
\(164\) −10.2569 −0.800932
\(165\) 0 0
\(166\) 12.8659 0.998590
\(167\) 22.8982 1.77191 0.885957 0.463768i \(-0.153503\pi\)
0.885957 + 0.463768i \(0.153503\pi\)
\(168\) −1.73262 −0.133675
\(169\) −12.7175 −0.978272
\(170\) −2.61563 −0.200610
\(171\) −1.53127 −0.117099
\(172\) −10.2461 −0.781258
\(173\) −7.74923 −0.589163 −0.294581 0.955626i \(-0.595180\pi\)
−0.294581 + 0.955626i \(0.595180\pi\)
\(174\) 8.86991 0.672426
\(175\) −3.90871 −0.295471
\(176\) 0 0
\(177\) 7.19216 0.540596
\(178\) −7.40160 −0.554773
\(179\) 13.1788 0.985032 0.492516 0.870303i \(-0.336077\pi\)
0.492516 + 0.870303i \(0.336077\pi\)
\(180\) −0.681029 −0.0507609
\(181\) −9.16172 −0.680985 −0.340493 0.940247i \(-0.610594\pi\)
−0.340493 + 0.940247i \(0.610594\pi\)
\(182\) −0.432587 −0.0320655
\(183\) −10.1503 −0.750335
\(184\) −6.69536 −0.493589
\(185\) −1.05642 −0.0776692
\(186\) 12.3482 0.905414
\(187\) 0 0
\(188\) 6.33722 0.462189
\(189\) −2.54475 −0.185103
\(190\) −0.444747 −0.0322653
\(191\) −14.5629 −1.05373 −0.526865 0.849949i \(-0.676633\pi\)
−0.526865 + 0.849949i \(0.676633\pi\)
\(192\) 2.12868 0.153624
\(193\) −2.43059 −0.174958 −0.0874789 0.996166i \(-0.527881\pi\)
−0.0874789 + 0.996166i \(0.527881\pi\)
\(194\) 14.2295 1.02162
\(195\) −0.503157 −0.0360318
\(196\) −6.33750 −0.452679
\(197\) −10.9047 −0.776928 −0.388464 0.921464i \(-0.626994\pi\)
−0.388464 + 0.921464i \(0.626994\pi\)
\(198\) 0 0
\(199\) −15.3004 −1.08461 −0.542307 0.840180i \(-0.682449\pi\)
−0.542307 + 0.840180i \(0.682449\pi\)
\(200\) 4.80220 0.339567
\(201\) −2.61919 −0.184743
\(202\) −3.50507 −0.246616
\(203\) −3.39158 −0.238042
\(204\) −12.5191 −0.876512
\(205\) 4.56174 0.318606
\(206\) −0.694123 −0.0483618
\(207\) 10.2524 0.712593
\(208\) 0.531472 0.0368509
\(209\) 0 0
\(210\) 0.770577 0.0531749
\(211\) −5.61110 −0.386284 −0.193142 0.981171i \(-0.561868\pi\)
−0.193142 + 0.981171i \(0.561868\pi\)
\(212\) 9.31823 0.639979
\(213\) −24.6589 −1.68960
\(214\) −8.63080 −0.589989
\(215\) 4.55693 0.310780
\(216\) 3.12645 0.212728
\(217\) −4.72157 −0.320521
\(218\) −8.10360 −0.548845
\(219\) 26.2683 1.77505
\(220\) 0 0
\(221\) −3.12567 −0.210255
\(222\) −5.05629 −0.339356
\(223\) −23.9862 −1.60624 −0.803118 0.595821i \(-0.796827\pi\)
−0.803118 + 0.595821i \(0.796827\pi\)
\(224\) −0.813941 −0.0543838
\(225\) −7.35348 −0.490232
\(226\) −4.66260 −0.310151
\(227\) −3.52771 −0.234142 −0.117071 0.993124i \(-0.537351\pi\)
−0.117071 + 0.993124i \(0.537351\pi\)
\(228\) −2.12868 −0.140975
\(229\) −19.5717 −1.29334 −0.646669 0.762771i \(-0.723838\pi\)
−0.646669 + 0.762771i \(0.723838\pi\)
\(230\) 2.97774 0.196347
\(231\) 0 0
\(232\) 4.16686 0.273568
\(233\) 19.2019 1.25796 0.628980 0.777422i \(-0.283473\pi\)
0.628980 + 0.777422i \(0.283473\pi\)
\(234\) −0.813828 −0.0532016
\(235\) −2.81846 −0.183856
\(236\) 3.37870 0.219935
\(237\) −7.38643 −0.479800
\(238\) 4.78692 0.310290
\(239\) −19.3799 −1.25358 −0.626790 0.779188i \(-0.715632\pi\)
−0.626790 + 0.779188i \(0.715632\pi\)
\(240\) −0.946723 −0.0611107
\(241\) 5.20964 0.335582 0.167791 0.985823i \(-0.446337\pi\)
0.167791 + 0.985823i \(0.446337\pi\)
\(242\) 0 0
\(243\) −14.5662 −0.934423
\(244\) −4.76838 −0.305264
\(245\) 2.81858 0.180073
\(246\) 21.8337 1.39207
\(247\) −0.531472 −0.0338167
\(248\) 5.80088 0.368356
\(249\) −27.3874 −1.73561
\(250\) −4.35950 −0.275719
\(251\) 13.5993 0.858382 0.429191 0.903214i \(-0.358799\pi\)
0.429191 + 0.903214i \(0.358799\pi\)
\(252\) 1.24637 0.0785137
\(253\) 0 0
\(254\) −5.75512 −0.361108
\(255\) 5.56783 0.348671
\(256\) 1.00000 0.0625000
\(257\) −10.9529 −0.683224 −0.341612 0.939841i \(-0.610973\pi\)
−0.341612 + 0.939841i \(0.610973\pi\)
\(258\) 21.8107 1.35787
\(259\) 1.93337 0.120134
\(260\) −0.236370 −0.0146591
\(261\) −6.38060 −0.394949
\(262\) 0.970302 0.0599454
\(263\) 27.8602 1.71793 0.858966 0.512032i \(-0.171107\pi\)
0.858966 + 0.512032i \(0.171107\pi\)
\(264\) 0 0
\(265\) −4.14426 −0.254580
\(266\) 0.813941 0.0499060
\(267\) 15.7556 0.964228
\(268\) −1.23043 −0.0751604
\(269\) 12.9191 0.787693 0.393847 0.919176i \(-0.371144\pi\)
0.393847 + 0.919176i \(0.371144\pi\)
\(270\) −1.39048 −0.0846218
\(271\) 8.10604 0.492407 0.246203 0.969218i \(-0.420817\pi\)
0.246203 + 0.969218i \(0.420817\pi\)
\(272\) −5.88116 −0.356598
\(273\) 0.920838 0.0557317
\(274\) −2.14682 −0.129694
\(275\) 0 0
\(276\) 14.2523 0.857886
\(277\) 23.4635 1.40979 0.704893 0.709313i \(-0.250995\pi\)
0.704893 + 0.709313i \(0.250995\pi\)
\(278\) 9.78816 0.587055
\(279\) −8.88272 −0.531795
\(280\) 0.361998 0.0216335
\(281\) −14.3704 −0.857269 −0.428634 0.903478i \(-0.641005\pi\)
−0.428634 + 0.903478i \(0.641005\pi\)
\(282\) −13.4899 −0.803312
\(283\) −11.6889 −0.694833 −0.347416 0.937711i \(-0.612941\pi\)
−0.347416 + 0.937711i \(0.612941\pi\)
\(284\) −11.5841 −0.687393
\(285\) 0.946723 0.0560791
\(286\) 0 0
\(287\) −8.34854 −0.492799
\(288\) −1.53127 −0.0902311
\(289\) 17.5881 1.03459
\(290\) −1.85320 −0.108824
\(291\) −30.2901 −1.77564
\(292\) 12.3402 0.722155
\(293\) 24.6851 1.44212 0.721059 0.692874i \(-0.243656\pi\)
0.721059 + 0.692874i \(0.243656\pi\)
\(294\) 13.4905 0.786782
\(295\) −1.50267 −0.0874886
\(296\) −2.37532 −0.138063
\(297\) 0 0
\(298\) −1.24923 −0.0723657
\(299\) 3.55839 0.205787
\(300\) −10.2223 −0.590187
\(301\) −8.33973 −0.480694
\(302\) 13.8527 0.797134
\(303\) 7.46117 0.428633
\(304\) −1.00000 −0.0573539
\(305\) 2.12072 0.121432
\(306\) 9.00566 0.514819
\(307\) −11.2527 −0.642226 −0.321113 0.947041i \(-0.604057\pi\)
−0.321113 + 0.947041i \(0.604057\pi\)
\(308\) 0 0
\(309\) 1.47756 0.0840557
\(310\) −2.57992 −0.146530
\(311\) 3.40711 0.193199 0.0965996 0.995323i \(-0.469203\pi\)
0.0965996 + 0.995323i \(0.469203\pi\)
\(312\) −1.13133 −0.0640491
\(313\) 20.6424 1.16678 0.583388 0.812194i \(-0.301727\pi\)
0.583388 + 0.812194i \(0.301727\pi\)
\(314\) −17.3097 −0.976840
\(315\) −0.554318 −0.0312323
\(316\) −3.46996 −0.195200
\(317\) −26.2022 −1.47166 −0.735832 0.677165i \(-0.763209\pi\)
−0.735832 + 0.677165i \(0.763209\pi\)
\(318\) −19.8355 −1.11232
\(319\) 0 0
\(320\) −0.444747 −0.0248621
\(321\) 18.3722 1.02544
\(322\) −5.44963 −0.303696
\(323\) 5.88116 0.327237
\(324\) −11.2490 −0.624946
\(325\) −2.55223 −0.141572
\(326\) 9.97325 0.552367
\(327\) 17.2500 0.953925
\(328\) 10.2569 0.566344
\(329\) 5.15813 0.284377
\(330\) 0 0
\(331\) 22.7831 1.25227 0.626137 0.779713i \(-0.284635\pi\)
0.626137 + 0.779713i \(0.284635\pi\)
\(332\) −12.8659 −0.706110
\(333\) 3.63726 0.199321
\(334\) −22.8982 −1.25293
\(335\) 0.547230 0.0298984
\(336\) 1.73262 0.0945222
\(337\) −16.6810 −0.908670 −0.454335 0.890831i \(-0.650123\pi\)
−0.454335 + 0.890831i \(0.650123\pi\)
\(338\) 12.7175 0.691743
\(339\) 9.92517 0.539061
\(340\) 2.61563 0.141852
\(341\) 0 0
\(342\) 1.53127 0.0828017
\(343\) −10.8559 −0.586166
\(344\) 10.2461 0.552433
\(345\) −6.33866 −0.341262
\(346\) 7.74923 0.416601
\(347\) 24.8615 1.33463 0.667317 0.744774i \(-0.267443\pi\)
0.667317 + 0.744774i \(0.267443\pi\)
\(348\) −8.86991 −0.475477
\(349\) 19.5583 1.04693 0.523467 0.852046i \(-0.324638\pi\)
0.523467 + 0.852046i \(0.324638\pi\)
\(350\) 3.90871 0.208929
\(351\) −1.66162 −0.0886907
\(352\) 0 0
\(353\) −17.1793 −0.914360 −0.457180 0.889374i \(-0.651141\pi\)
−0.457180 + 0.889374i \(0.651141\pi\)
\(354\) −7.19216 −0.382259
\(355\) 5.15201 0.273441
\(356\) 7.40160 0.392284
\(357\) −10.1898 −0.539302
\(358\) −13.1788 −0.696523
\(359\) 19.0190 1.00379 0.501893 0.864930i \(-0.332637\pi\)
0.501893 + 0.864930i \(0.332637\pi\)
\(360\) 0.681029 0.0358934
\(361\) 1.00000 0.0526316
\(362\) 9.16172 0.481529
\(363\) 0 0
\(364\) 0.432587 0.0226737
\(365\) −5.48827 −0.287269
\(366\) 10.1503 0.530567
\(367\) 4.19576 0.219017 0.109509 0.993986i \(-0.465072\pi\)
0.109509 + 0.993986i \(0.465072\pi\)
\(368\) 6.69536 0.349020
\(369\) −15.7062 −0.817630
\(370\) 1.05642 0.0549204
\(371\) 7.58450 0.393767
\(372\) −12.3482 −0.640225
\(373\) −30.5753 −1.58313 −0.791564 0.611086i \(-0.790733\pi\)
−0.791564 + 0.611086i \(0.790733\pi\)
\(374\) 0 0
\(375\) 9.27997 0.479216
\(376\) −6.33722 −0.326817
\(377\) −2.21457 −0.114056
\(378\) 2.54475 0.130888
\(379\) 27.9152 1.43391 0.716954 0.697121i \(-0.245536\pi\)
0.716954 + 0.697121i \(0.245536\pi\)
\(380\) 0.444747 0.0228150
\(381\) 12.2508 0.627627
\(382\) 14.5629 0.745100
\(383\) −13.3334 −0.681304 −0.340652 0.940189i \(-0.610648\pi\)
−0.340652 + 0.940189i \(0.610648\pi\)
\(384\) −2.12868 −0.108629
\(385\) 0 0
\(386\) 2.43059 0.123714
\(387\) −15.6896 −0.797546
\(388\) −14.2295 −0.722395
\(389\) −6.00531 −0.304481 −0.152241 0.988343i \(-0.548649\pi\)
−0.152241 + 0.988343i \(0.548649\pi\)
\(390\) 0.503157 0.0254783
\(391\) −39.3765 −1.99136
\(392\) 6.33750 0.320092
\(393\) −2.06546 −0.104189
\(394\) 10.9047 0.549371
\(395\) 1.54325 0.0776495
\(396\) 0 0
\(397\) −27.7223 −1.39134 −0.695671 0.718360i \(-0.744893\pi\)
−0.695671 + 0.718360i \(0.744893\pi\)
\(398\) 15.3004 0.766938
\(399\) −1.73262 −0.0867395
\(400\) −4.80220 −0.240110
\(401\) 29.1632 1.45634 0.728170 0.685396i \(-0.240371\pi\)
0.728170 + 0.685396i \(0.240371\pi\)
\(402\) 2.61919 0.130633
\(403\) −3.08300 −0.153575
\(404\) 3.50507 0.174384
\(405\) 5.00297 0.248600
\(406\) 3.39158 0.168321
\(407\) 0 0
\(408\) 12.5191 0.619788
\(409\) 11.2326 0.555415 0.277708 0.960666i \(-0.410425\pi\)
0.277708 + 0.960666i \(0.410425\pi\)
\(410\) −4.56174 −0.225288
\(411\) 4.56990 0.225416
\(412\) 0.694123 0.0341970
\(413\) 2.75006 0.135322
\(414\) −10.2524 −0.503879
\(415\) 5.72208 0.280886
\(416\) −0.531472 −0.0260575
\(417\) −20.8358 −1.02034
\(418\) 0 0
\(419\) −20.2013 −0.986897 −0.493449 0.869775i \(-0.664264\pi\)
−0.493449 + 0.869775i \(0.664264\pi\)
\(420\) −0.770577 −0.0376003
\(421\) −12.7072 −0.619311 −0.309656 0.950849i \(-0.600214\pi\)
−0.309656 + 0.950849i \(0.600214\pi\)
\(422\) 5.61110 0.273144
\(423\) 9.70401 0.471825
\(424\) −9.31823 −0.452533
\(425\) 28.2425 1.36996
\(426\) 24.6589 1.19473
\(427\) −3.88118 −0.187824
\(428\) 8.63080 0.417185
\(429\) 0 0
\(430\) −4.55693 −0.219754
\(431\) −31.5802 −1.52117 −0.760583 0.649240i \(-0.775087\pi\)
−0.760583 + 0.649240i \(0.775087\pi\)
\(432\) −3.12645 −0.150421
\(433\) 21.2373 1.02060 0.510299 0.859997i \(-0.329535\pi\)
0.510299 + 0.859997i \(0.329535\pi\)
\(434\) 4.72157 0.226643
\(435\) 3.94487 0.189142
\(436\) 8.10360 0.388092
\(437\) −6.69536 −0.320283
\(438\) −26.2683 −1.25515
\(439\) 23.1919 1.10689 0.553445 0.832886i \(-0.313313\pi\)
0.553445 + 0.832886i \(0.313313\pi\)
\(440\) 0 0
\(441\) −9.70444 −0.462116
\(442\) 3.12567 0.148673
\(443\) −16.6453 −0.790843 −0.395421 0.918500i \(-0.629401\pi\)
−0.395421 + 0.918500i \(0.629401\pi\)
\(444\) 5.05629 0.239961
\(445\) −3.29184 −0.156048
\(446\) 23.9862 1.13578
\(447\) 2.65920 0.125776
\(448\) 0.813941 0.0384551
\(449\) −2.23355 −0.105408 −0.0527038 0.998610i \(-0.516784\pi\)
−0.0527038 + 0.998610i \(0.516784\pi\)
\(450\) 7.35348 0.346646
\(451\) 0 0
\(452\) 4.66260 0.219310
\(453\) −29.4880 −1.38547
\(454\) 3.52771 0.165564
\(455\) −0.192392 −0.00901946
\(456\) 2.12868 0.0996845
\(457\) 12.4265 0.581288 0.290644 0.956831i \(-0.406131\pi\)
0.290644 + 0.956831i \(0.406131\pi\)
\(458\) 19.5717 0.914527
\(459\) 18.3871 0.858239
\(460\) −2.97774 −0.138838
\(461\) 31.8148 1.48176 0.740881 0.671636i \(-0.234408\pi\)
0.740881 + 0.671636i \(0.234408\pi\)
\(462\) 0 0
\(463\) −0.0722953 −0.00335985 −0.00167992 0.999999i \(-0.500535\pi\)
−0.00167992 + 0.999999i \(0.500535\pi\)
\(464\) −4.16686 −0.193442
\(465\) 5.49183 0.254677
\(466\) −19.2019 −0.889511
\(467\) −33.8105 −1.56456 −0.782281 0.622925i \(-0.785944\pi\)
−0.782281 + 0.622925i \(0.785944\pi\)
\(468\) 0.813828 0.0376192
\(469\) −1.00150 −0.0462449
\(470\) 2.81846 0.130006
\(471\) 36.8467 1.69781
\(472\) −3.37870 −0.155517
\(473\) 0 0
\(474\) 7.38643 0.339270
\(475\) 4.80220 0.220340
\(476\) −4.78692 −0.219408
\(477\) 14.2688 0.653321
\(478\) 19.3799 0.886415
\(479\) −7.68378 −0.351081 −0.175540 0.984472i \(-0.556167\pi\)
−0.175540 + 0.984472i \(0.556167\pi\)
\(480\) 0.946723 0.0432118
\(481\) 1.26241 0.0575611
\(482\) −5.20964 −0.237293
\(483\) 11.6005 0.527842
\(484\) 0 0
\(485\) 6.32854 0.287364
\(486\) 14.5662 0.660737
\(487\) −30.3683 −1.37612 −0.688059 0.725654i \(-0.741537\pi\)
−0.688059 + 0.725654i \(0.741537\pi\)
\(488\) 4.76838 0.215854
\(489\) −21.2298 −0.960047
\(490\) −2.81858 −0.127331
\(491\) 10.1148 0.456473 0.228236 0.973606i \(-0.426704\pi\)
0.228236 + 0.973606i \(0.426704\pi\)
\(492\) −21.8337 −0.984340
\(493\) 24.5060 1.10369
\(494\) 0.531472 0.0239120
\(495\) 0 0
\(496\) −5.80088 −0.260467
\(497\) −9.42882 −0.422940
\(498\) 27.3874 1.22726
\(499\) −18.6624 −0.835445 −0.417723 0.908575i \(-0.637172\pi\)
−0.417723 + 0.908575i \(0.637172\pi\)
\(500\) 4.35950 0.194963
\(501\) 48.7428 2.17767
\(502\) −13.5993 −0.606968
\(503\) −13.3397 −0.594790 −0.297395 0.954755i \(-0.596118\pi\)
−0.297395 + 0.954755i \(0.596118\pi\)
\(504\) −1.24637 −0.0555176
\(505\) −1.55887 −0.0693688
\(506\) 0 0
\(507\) −27.0716 −1.20229
\(508\) 5.75512 0.255342
\(509\) 35.1855 1.55957 0.779784 0.626048i \(-0.215329\pi\)
0.779784 + 0.626048i \(0.215329\pi\)
\(510\) −5.56783 −0.246548
\(511\) 10.0442 0.444329
\(512\) −1.00000 −0.0441942
\(513\) 3.12645 0.138036
\(514\) 10.9529 0.483113
\(515\) −0.308709 −0.0136033
\(516\) −21.8107 −0.960161
\(517\) 0 0
\(518\) −1.93337 −0.0849474
\(519\) −16.4956 −0.724077
\(520\) 0.236370 0.0103655
\(521\) −27.1020 −1.18736 −0.593679 0.804702i \(-0.702325\pi\)
−0.593679 + 0.804702i \(0.702325\pi\)
\(522\) 6.38060 0.279271
\(523\) 12.2389 0.535169 0.267584 0.963534i \(-0.413775\pi\)
0.267584 + 0.963534i \(0.413775\pi\)
\(524\) −0.970302 −0.0423878
\(525\) −8.32039 −0.363131
\(526\) −27.8602 −1.21476
\(527\) 34.1159 1.48611
\(528\) 0 0
\(529\) 21.8279 0.949038
\(530\) 4.14426 0.180015
\(531\) 5.17371 0.224520
\(532\) −0.813941 −0.0352888
\(533\) −5.45127 −0.236121
\(534\) −15.7556 −0.681812
\(535\) −3.83852 −0.165954
\(536\) 1.23043 0.0531464
\(537\) 28.0535 1.21060
\(538\) −12.9191 −0.556983
\(539\) 0 0
\(540\) 1.39048 0.0598367
\(541\) 44.6953 1.92160 0.960801 0.277238i \(-0.0894189\pi\)
0.960801 + 0.277238i \(0.0894189\pi\)
\(542\) −8.10604 −0.348184
\(543\) −19.5024 −0.836926
\(544\) 5.88116 0.252153
\(545\) −3.60405 −0.154381
\(546\) −0.920838 −0.0394082
\(547\) −2.84216 −0.121522 −0.0607610 0.998152i \(-0.519353\pi\)
−0.0607610 + 0.998152i \(0.519353\pi\)
\(548\) 2.14682 0.0917077
\(549\) −7.30169 −0.311629
\(550\) 0 0
\(551\) 4.16686 0.177514
\(552\) −14.2523 −0.606617
\(553\) −2.82434 −0.120103
\(554\) −23.4635 −0.996870
\(555\) −2.24877 −0.0954550
\(556\) −9.78816 −0.415110
\(557\) −31.6341 −1.34038 −0.670189 0.742190i \(-0.733787\pi\)
−0.670189 + 0.742190i \(0.733787\pi\)
\(558\) 8.88272 0.376036
\(559\) −5.44551 −0.230321
\(560\) −0.361998 −0.0152972
\(561\) 0 0
\(562\) 14.3704 0.606180
\(563\) −4.38903 −0.184976 −0.0924878 0.995714i \(-0.529482\pi\)
−0.0924878 + 0.995714i \(0.529482\pi\)
\(564\) 13.4899 0.568028
\(565\) −2.07368 −0.0872402
\(566\) 11.6889 0.491321
\(567\) −9.15605 −0.384518
\(568\) 11.5841 0.486060
\(569\) −38.8116 −1.62707 −0.813534 0.581517i \(-0.802459\pi\)
−0.813534 + 0.581517i \(0.802459\pi\)
\(570\) −0.946723 −0.0396539
\(571\) −22.3077 −0.933547 −0.466774 0.884377i \(-0.654584\pi\)
−0.466774 + 0.884377i \(0.654584\pi\)
\(572\) 0 0
\(573\) −30.9996 −1.29503
\(574\) 8.34854 0.348462
\(575\) −32.1525 −1.34085
\(576\) 1.53127 0.0638030
\(577\) 19.6493 0.818009 0.409005 0.912532i \(-0.365876\pi\)
0.409005 + 0.912532i \(0.365876\pi\)
\(578\) −17.5881 −0.731567
\(579\) −5.17395 −0.215022
\(580\) 1.85320 0.0769499
\(581\) −10.4721 −0.434457
\(582\) 30.2901 1.25556
\(583\) 0 0
\(584\) −12.3402 −0.510641
\(585\) −0.361948 −0.0149647
\(586\) −24.6851 −1.01973
\(587\) 40.5186 1.67238 0.836191 0.548439i \(-0.184778\pi\)
0.836191 + 0.548439i \(0.184778\pi\)
\(588\) −13.4905 −0.556339
\(589\) 5.80088 0.239021
\(590\) 1.50267 0.0618638
\(591\) −23.2126 −0.954840
\(592\) 2.37532 0.0976250
\(593\) −11.8720 −0.487525 −0.243762 0.969835i \(-0.578382\pi\)
−0.243762 + 0.969835i \(0.578382\pi\)
\(594\) 0 0
\(595\) 2.12897 0.0872792
\(596\) 1.24923 0.0511703
\(597\) −32.5696 −1.33298
\(598\) −3.55839 −0.145514
\(599\) −37.2135 −1.52050 −0.760250 0.649630i \(-0.774924\pi\)
−0.760250 + 0.649630i \(0.774924\pi\)
\(600\) 10.2223 0.417325
\(601\) −17.3215 −0.706559 −0.353280 0.935518i \(-0.614934\pi\)
−0.353280 + 0.935518i \(0.614934\pi\)
\(602\) 8.33973 0.339902
\(603\) −1.88412 −0.0767274
\(604\) −13.8527 −0.563659
\(605\) 0 0
\(606\) −7.46117 −0.303089
\(607\) 0.942834 0.0382685 0.0191342 0.999817i \(-0.493909\pi\)
0.0191342 + 0.999817i \(0.493909\pi\)
\(608\) 1.00000 0.0405554
\(609\) −7.21959 −0.292552
\(610\) −2.12072 −0.0858656
\(611\) 3.36805 0.136257
\(612\) −9.00566 −0.364032
\(613\) −34.0246 −1.37424 −0.687121 0.726543i \(-0.741126\pi\)
−0.687121 + 0.726543i \(0.741126\pi\)
\(614\) 11.2527 0.454122
\(615\) 9.71048 0.391564
\(616\) 0 0
\(617\) −12.4983 −0.503162 −0.251581 0.967836i \(-0.580950\pi\)
−0.251581 + 0.967836i \(0.580950\pi\)
\(618\) −1.47756 −0.0594363
\(619\) −29.4196 −1.18247 −0.591237 0.806498i \(-0.701360\pi\)
−0.591237 + 0.806498i \(0.701360\pi\)
\(620\) 2.57992 0.103612
\(621\) −20.9327 −0.840001
\(622\) −3.40711 −0.136613
\(623\) 6.02447 0.241365
\(624\) 1.13133 0.0452895
\(625\) 22.0721 0.882885
\(626\) −20.6424 −0.825035
\(627\) 0 0
\(628\) 17.3097 0.690731
\(629\) −13.9696 −0.557006
\(630\) 0.554318 0.0220845
\(631\) 7.76186 0.308995 0.154497 0.987993i \(-0.450624\pi\)
0.154497 + 0.987993i \(0.450624\pi\)
\(632\) 3.46996 0.138028
\(633\) −11.9442 −0.474740
\(634\) 26.2022 1.04062
\(635\) −2.55957 −0.101573
\(636\) 19.8355 0.786530
\(637\) −3.36820 −0.133453
\(638\) 0 0
\(639\) −17.7385 −0.701724
\(640\) 0.444747 0.0175802
\(641\) 19.5247 0.771180 0.385590 0.922670i \(-0.373998\pi\)
0.385590 + 0.922670i \(0.373998\pi\)
\(642\) −18.3722 −0.725093
\(643\) −48.4409 −1.91032 −0.955162 0.296083i \(-0.904319\pi\)
−0.955162 + 0.296083i \(0.904319\pi\)
\(644\) 5.44963 0.214746
\(645\) 9.70023 0.381946
\(646\) −5.88116 −0.231391
\(647\) 32.0388 1.25958 0.629788 0.776767i \(-0.283142\pi\)
0.629788 + 0.776767i \(0.283142\pi\)
\(648\) 11.2490 0.441903
\(649\) 0 0
\(650\) 2.55223 0.100107
\(651\) −10.0507 −0.393919
\(652\) −9.97325 −0.390583
\(653\) −36.7648 −1.43872 −0.719359 0.694638i \(-0.755565\pi\)
−0.719359 + 0.694638i \(0.755565\pi\)
\(654\) −17.2500 −0.674527
\(655\) 0.431539 0.0168616
\(656\) −10.2569 −0.400466
\(657\) 18.8962 0.737211
\(658\) −5.15813 −0.201085
\(659\) −1.92517 −0.0749940 −0.0374970 0.999297i \(-0.511938\pi\)
−0.0374970 + 0.999297i \(0.511938\pi\)
\(660\) 0 0
\(661\) −0.375942 −0.0146225 −0.00731123 0.999973i \(-0.502327\pi\)
−0.00731123 + 0.999973i \(0.502327\pi\)
\(662\) −22.7831 −0.885491
\(663\) −6.65355 −0.258402
\(664\) 12.8659 0.499295
\(665\) 0.361998 0.0140377
\(666\) −3.63726 −0.140941
\(667\) −27.8986 −1.08024
\(668\) 22.8982 0.885957
\(669\) −51.0589 −1.97405
\(670\) −0.547230 −0.0211413
\(671\) 0 0
\(672\) −1.73262 −0.0668373
\(673\) −13.5595 −0.522681 −0.261340 0.965247i \(-0.584165\pi\)
−0.261340 + 0.965247i \(0.584165\pi\)
\(674\) 16.6810 0.642526
\(675\) 15.0138 0.577883
\(676\) −12.7175 −0.489136
\(677\) 46.1646 1.77425 0.887125 0.461530i \(-0.152699\pi\)
0.887125 + 0.461530i \(0.152699\pi\)
\(678\) −9.92517 −0.381174
\(679\) −11.5820 −0.444476
\(680\) −2.61563 −0.100305
\(681\) −7.50937 −0.287759
\(682\) 0 0
\(683\) 13.2284 0.506170 0.253085 0.967444i \(-0.418555\pi\)
0.253085 + 0.967444i \(0.418555\pi\)
\(684\) −1.53127 −0.0585497
\(685\) −0.954793 −0.0364808
\(686\) 10.8559 0.414482
\(687\) −41.6619 −1.58950
\(688\) −10.2461 −0.390629
\(689\) 4.95238 0.188671
\(690\) 6.33866 0.241309
\(691\) 30.8706 1.17437 0.587186 0.809452i \(-0.300236\pi\)
0.587186 + 0.809452i \(0.300236\pi\)
\(692\) −7.74923 −0.294581
\(693\) 0 0
\(694\) −24.8615 −0.943728
\(695\) 4.35325 0.165128
\(696\) 8.86991 0.336213
\(697\) 60.3227 2.28488
\(698\) −19.5583 −0.740294
\(699\) 40.8747 1.54602
\(700\) −3.90871 −0.147735
\(701\) −48.6574 −1.83777 −0.918883 0.394530i \(-0.870907\pi\)
−0.918883 + 0.394530i \(0.870907\pi\)
\(702\) 1.66162 0.0627138
\(703\) −2.37532 −0.0895868
\(704\) 0 0
\(705\) −5.99960 −0.225958
\(706\) 17.1793 0.646551
\(707\) 2.85292 0.107295
\(708\) 7.19216 0.270298
\(709\) −4.26738 −0.160265 −0.0801324 0.996784i \(-0.525534\pi\)
−0.0801324 + 0.996784i \(0.525534\pi\)
\(710\) −5.15201 −0.193352
\(711\) −5.31345 −0.199270
\(712\) −7.40160 −0.277387
\(713\) −38.8390 −1.45453
\(714\) 10.1898 0.381344
\(715\) 0 0
\(716\) 13.1788 0.492516
\(717\) −41.2535 −1.54064
\(718\) −19.0190 −0.709784
\(719\) 30.5349 1.13876 0.569379 0.822075i \(-0.307184\pi\)
0.569379 + 0.822075i \(0.307184\pi\)
\(720\) −0.681029 −0.0253804
\(721\) 0.564975 0.0210408
\(722\) −1.00000 −0.0372161
\(723\) 11.0897 0.412429
\(724\) −9.16172 −0.340493
\(725\) 20.0101 0.743157
\(726\) 0 0
\(727\) −3.87417 −0.143685 −0.0718425 0.997416i \(-0.522888\pi\)
−0.0718425 + 0.997416i \(0.522888\pi\)
\(728\) −0.432587 −0.0160327
\(729\) 2.74030 0.101492
\(730\) 5.48827 0.203130
\(731\) 60.2590 2.22876
\(732\) −10.1503 −0.375168
\(733\) 23.0823 0.852566 0.426283 0.904590i \(-0.359823\pi\)
0.426283 + 0.904590i \(0.359823\pi\)
\(734\) −4.19576 −0.154868
\(735\) 5.99986 0.221308
\(736\) −6.69536 −0.246794
\(737\) 0 0
\(738\) 15.7062 0.578152
\(739\) −29.8163 −1.09681 −0.548404 0.836213i \(-0.684765\pi\)
−0.548404 + 0.836213i \(0.684765\pi\)
\(740\) −1.05642 −0.0388346
\(741\) −1.13133 −0.0415605
\(742\) −7.58450 −0.278436
\(743\) 2.86361 0.105056 0.0525279 0.998619i \(-0.483272\pi\)
0.0525279 + 0.998619i \(0.483272\pi\)
\(744\) 12.3482 0.452707
\(745\) −0.555589 −0.0203552
\(746\) 30.5753 1.11944
\(747\) −19.7012 −0.720831
\(748\) 0 0
\(749\) 7.02496 0.256687
\(750\) −9.27997 −0.338857
\(751\) −48.3540 −1.76446 −0.882232 0.470815i \(-0.843960\pi\)
−0.882232 + 0.470815i \(0.843960\pi\)
\(752\) 6.33722 0.231095
\(753\) 28.9486 1.05495
\(754\) 2.21457 0.0806498
\(755\) 6.16095 0.224220
\(756\) −2.54475 −0.0925515
\(757\) 22.8415 0.830188 0.415094 0.909778i \(-0.363749\pi\)
0.415094 + 0.909778i \(0.363749\pi\)
\(758\) −27.9152 −1.01393
\(759\) 0 0
\(760\) −0.444747 −0.0161327
\(761\) 23.6802 0.858408 0.429204 0.903208i \(-0.358794\pi\)
0.429204 + 0.903208i \(0.358794\pi\)
\(762\) −12.2508 −0.443799
\(763\) 6.59586 0.238786
\(764\) −14.5629 −0.526865
\(765\) 4.00524 0.144810
\(766\) 13.3334 0.481755
\(767\) 1.79568 0.0648383
\(768\) 2.12868 0.0768121
\(769\) −49.9760 −1.80218 −0.901090 0.433633i \(-0.857231\pi\)
−0.901090 + 0.433633i \(0.857231\pi\)
\(770\) 0 0
\(771\) −23.3152 −0.839678
\(772\) −2.43059 −0.0874789
\(773\) −33.4774 −1.20410 −0.602049 0.798459i \(-0.705649\pi\)
−0.602049 + 0.798459i \(0.705649\pi\)
\(774\) 15.6896 0.563950
\(775\) 27.8570 1.00065
\(776\) 14.2295 0.510810
\(777\) 4.11552 0.147644
\(778\) 6.00531 0.215301
\(779\) 10.2569 0.367493
\(780\) −0.503157 −0.0180159
\(781\) 0 0
\(782\) 39.3765 1.40810
\(783\) 13.0275 0.465564
\(784\) −6.33750 −0.226339
\(785\) −7.69842 −0.274768
\(786\) 2.06546 0.0736725
\(787\) 16.7744 0.597944 0.298972 0.954262i \(-0.403356\pi\)
0.298972 + 0.954262i \(0.403356\pi\)
\(788\) −10.9047 −0.388464
\(789\) 59.3054 2.11133
\(790\) −1.54325 −0.0549065
\(791\) 3.79508 0.134938
\(792\) 0 0
\(793\) −2.53426 −0.0899942
\(794\) 27.7223 0.983828
\(795\) −8.82179 −0.312877
\(796\) −15.3004 −0.542307
\(797\) 22.0845 0.782273 0.391136 0.920333i \(-0.372082\pi\)
0.391136 + 0.920333i \(0.372082\pi\)
\(798\) 1.73262 0.0613341
\(799\) −37.2702 −1.31853
\(800\) 4.80220 0.169783
\(801\) 11.3339 0.400462
\(802\) −29.1632 −1.02979
\(803\) 0 0
\(804\) −2.61919 −0.0923716
\(805\) −2.42371 −0.0854245
\(806\) 3.08300 0.108594
\(807\) 27.5007 0.968070
\(808\) −3.50507 −0.123308
\(809\) 29.1249 1.02398 0.511988 0.858993i \(-0.328909\pi\)
0.511988 + 0.858993i \(0.328909\pi\)
\(810\) −5.00297 −0.175786
\(811\) 30.3451 1.06556 0.532780 0.846254i \(-0.321147\pi\)
0.532780 + 0.846254i \(0.321147\pi\)
\(812\) −3.39158 −0.119021
\(813\) 17.2551 0.605164
\(814\) 0 0
\(815\) 4.43557 0.155371
\(816\) −12.5191 −0.438256
\(817\) 10.2461 0.358466
\(818\) −11.2326 −0.392738
\(819\) 0.662408 0.0231464
\(820\) 4.56174 0.159303
\(821\) 7.07451 0.246902 0.123451 0.992351i \(-0.460604\pi\)
0.123451 + 0.992351i \(0.460604\pi\)
\(822\) −4.56990 −0.159393
\(823\) −29.8242 −1.03961 −0.519803 0.854286i \(-0.673995\pi\)
−0.519803 + 0.854286i \(0.673995\pi\)
\(824\) −0.694123 −0.0241809
\(825\) 0 0
\(826\) −2.75006 −0.0956869
\(827\) 40.6914 1.41498 0.707490 0.706723i \(-0.249827\pi\)
0.707490 + 0.706723i \(0.249827\pi\)
\(828\) 10.2524 0.356296
\(829\) 14.0816 0.489073 0.244537 0.969640i \(-0.421364\pi\)
0.244537 + 0.969640i \(0.421364\pi\)
\(830\) −5.72208 −0.198616
\(831\) 49.9463 1.73262
\(832\) 0.531472 0.0184255
\(833\) 37.2719 1.29139
\(834\) 20.8358 0.721486
\(835\) −10.1839 −0.352428
\(836\) 0 0
\(837\) 18.1361 0.626877
\(838\) 20.2013 0.697842
\(839\) 49.4824 1.70832 0.854162 0.520007i \(-0.174071\pi\)
0.854162 + 0.520007i \(0.174071\pi\)
\(840\) 0.770577 0.0265874
\(841\) −11.6373 −0.401285
\(842\) 12.7072 0.437919
\(843\) −30.5901 −1.05358
\(844\) −5.61110 −0.193142
\(845\) 5.65609 0.194575
\(846\) −9.70401 −0.333631
\(847\) 0 0
\(848\) 9.31823 0.319989
\(849\) −24.8819 −0.853945
\(850\) −28.2425 −0.968710
\(851\) 15.9036 0.545169
\(852\) −24.6589 −0.844801
\(853\) 23.6652 0.810280 0.405140 0.914255i \(-0.367223\pi\)
0.405140 + 0.914255i \(0.367223\pi\)
\(854\) 3.88118 0.132811
\(855\) 0.681029 0.0232907
\(856\) −8.63080 −0.294995
\(857\) −17.6097 −0.601535 −0.300768 0.953697i \(-0.597243\pi\)
−0.300768 + 0.953697i \(0.597243\pi\)
\(858\) 0 0
\(859\) 35.6398 1.21602 0.608008 0.793931i \(-0.291969\pi\)
0.608008 + 0.793931i \(0.291969\pi\)
\(860\) 4.55693 0.155390
\(861\) −17.7714 −0.605647
\(862\) 31.5802 1.07563
\(863\) 32.1883 1.09570 0.547850 0.836576i \(-0.315446\pi\)
0.547850 + 0.836576i \(0.315446\pi\)
\(864\) 3.12645 0.106364
\(865\) 3.44645 0.117183
\(866\) −21.2373 −0.721672
\(867\) 37.4393 1.27151
\(868\) −4.72157 −0.160261
\(869\) 0 0
\(870\) −3.94487 −0.133743
\(871\) −0.653938 −0.0221578
\(872\) −8.10360 −0.274423
\(873\) −21.7893 −0.737455
\(874\) 6.69536 0.226474
\(875\) 3.54838 0.119957
\(876\) 26.2683 0.887524
\(877\) 29.1474 0.984238 0.492119 0.870528i \(-0.336222\pi\)
0.492119 + 0.870528i \(0.336222\pi\)
\(878\) −23.1919 −0.782689
\(879\) 52.5466 1.77235
\(880\) 0 0
\(881\) −17.4611 −0.588279 −0.294139 0.955763i \(-0.595033\pi\)
−0.294139 + 0.955763i \(0.595033\pi\)
\(882\) 9.70444 0.326765
\(883\) 10.2292 0.344239 0.172119 0.985076i \(-0.444939\pi\)
0.172119 + 0.985076i \(0.444939\pi\)
\(884\) −3.12567 −0.105128
\(885\) −3.19869 −0.107523
\(886\) 16.6453 0.559210
\(887\) −29.5730 −0.992966 −0.496483 0.868047i \(-0.665375\pi\)
−0.496483 + 0.868047i \(0.665375\pi\)
\(888\) −5.05629 −0.169678
\(889\) 4.68433 0.157107
\(890\) 3.29184 0.110343
\(891\) 0 0
\(892\) −23.9862 −0.803118
\(893\) −6.33722 −0.212067
\(894\) −2.65920 −0.0889369
\(895\) −5.86124 −0.195920
\(896\) −0.813941 −0.0271919
\(897\) 7.57468 0.252911
\(898\) 2.23355 0.0745344
\(899\) 24.1715 0.806163
\(900\) −7.35348 −0.245116
\(901\) −54.8020 −1.82572
\(902\) 0 0
\(903\) −17.7526 −0.590770
\(904\) −4.66260 −0.155076
\(905\) 4.07465 0.135446
\(906\) 29.4880 0.979673
\(907\) −11.7834 −0.391260 −0.195630 0.980678i \(-0.562675\pi\)
−0.195630 + 0.980678i \(0.562675\pi\)
\(908\) −3.52771 −0.117071
\(909\) 5.36722 0.178019
\(910\) 0.192392 0.00637772
\(911\) −48.6666 −1.61240 −0.806198 0.591646i \(-0.798478\pi\)
−0.806198 + 0.591646i \(0.798478\pi\)
\(912\) −2.12868 −0.0704876
\(913\) 0 0
\(914\) −12.4265 −0.411032
\(915\) 4.51434 0.149239
\(916\) −19.5717 −0.646669
\(917\) −0.789769 −0.0260805
\(918\) −18.3871 −0.606866
\(919\) −44.7874 −1.47740 −0.738700 0.674035i \(-0.764560\pi\)
−0.738700 + 0.674035i \(0.764560\pi\)
\(920\) 2.97774 0.0981733
\(921\) −23.9534 −0.789291
\(922\) −31.8148 −1.04776
\(923\) −6.15665 −0.202648
\(924\) 0 0
\(925\) −11.4068 −0.375052
\(926\) 0.0722953 0.00237577
\(927\) 1.06289 0.0349099
\(928\) 4.16686 0.136784
\(929\) 40.9518 1.34359 0.671793 0.740739i \(-0.265524\pi\)
0.671793 + 0.740739i \(0.265524\pi\)
\(930\) −5.49183 −0.180084
\(931\) 6.33750 0.207703
\(932\) 19.2019 0.628980
\(933\) 7.25263 0.237441
\(934\) 33.8105 1.10631
\(935\) 0 0
\(936\) −0.813828 −0.0266008
\(937\) 5.66048 0.184920 0.0924599 0.995716i \(-0.470527\pi\)
0.0924599 + 0.995716i \(0.470527\pi\)
\(938\) 1.00150 0.0327000
\(939\) 43.9410 1.43396
\(940\) −2.81846 −0.0919281
\(941\) −14.4380 −0.470664 −0.235332 0.971915i \(-0.575618\pi\)
−0.235332 + 0.971915i \(0.575618\pi\)
\(942\) −36.8467 −1.20053
\(943\) −68.6739 −2.23633
\(944\) 3.37870 0.109967
\(945\) 1.13177 0.0368164
\(946\) 0 0
\(947\) 6.99025 0.227153 0.113576 0.993529i \(-0.463769\pi\)
0.113576 + 0.993529i \(0.463769\pi\)
\(948\) −7.38643 −0.239900
\(949\) 6.55846 0.212897
\(950\) −4.80220 −0.155804
\(951\) −55.7761 −1.80866
\(952\) 4.78692 0.155145
\(953\) 16.6615 0.539718 0.269859 0.962900i \(-0.413023\pi\)
0.269859 + 0.962900i \(0.413023\pi\)
\(954\) −14.2688 −0.461968
\(955\) 6.47678 0.209584
\(956\) −19.3799 −0.626790
\(957\) 0 0
\(958\) 7.68378 0.248252
\(959\) 1.74739 0.0564261
\(960\) −0.946723 −0.0305554
\(961\) 2.65018 0.0854897
\(962\) −1.26241 −0.0407019
\(963\) 13.2161 0.425883
\(964\) 5.20964 0.167791
\(965\) 1.08100 0.0347986
\(966\) −11.6005 −0.373240
\(967\) 8.50933 0.273642 0.136821 0.990596i \(-0.456312\pi\)
0.136821 + 0.990596i \(0.456312\pi\)
\(968\) 0 0
\(969\) 12.5191 0.402172
\(970\) −6.32854 −0.203197
\(971\) −18.6734 −0.599257 −0.299628 0.954056i \(-0.596863\pi\)
−0.299628 + 0.954056i \(0.596863\pi\)
\(972\) −14.5662 −0.467211
\(973\) −7.96699 −0.255410
\(974\) 30.3683 0.973063
\(975\) −5.43288 −0.173992
\(976\) −4.76838 −0.152632
\(977\) −0.303786 −0.00971897 −0.00485948 0.999988i \(-0.501547\pi\)
−0.00485948 + 0.999988i \(0.501547\pi\)
\(978\) 21.2298 0.678856
\(979\) 0 0
\(980\) 2.81858 0.0900364
\(981\) 12.4088 0.396183
\(982\) −10.1148 −0.322775
\(983\) 45.9811 1.46657 0.733285 0.679922i \(-0.237986\pi\)
0.733285 + 0.679922i \(0.237986\pi\)
\(984\) 21.8337 0.696033
\(985\) 4.84984 0.154529
\(986\) −24.5060 −0.780430
\(987\) 10.9800 0.349497
\(988\) −0.531472 −0.0169084
\(989\) −68.6014 −2.18140
\(990\) 0 0
\(991\) 19.4299 0.617210 0.308605 0.951190i \(-0.400138\pi\)
0.308605 + 0.951190i \(0.400138\pi\)
\(992\) 5.80088 0.184178
\(993\) 48.4979 1.53904
\(994\) 9.42882 0.299064
\(995\) 6.80479 0.215726
\(996\) −27.3874 −0.867804
\(997\) −22.5459 −0.714035 −0.357018 0.934098i \(-0.616206\pi\)
−0.357018 + 0.934098i \(0.616206\pi\)
\(998\) 18.6624 0.590749
\(999\) −7.42631 −0.234958
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.cc.1.9 10
11.3 even 5 418.2.f.h.229.1 yes 20
11.4 even 5 418.2.f.h.115.1 20
11.10 odd 2 4598.2.a.cd.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.f.h.115.1 20 11.4 even 5
418.2.f.h.229.1 yes 20 11.3 even 5
4598.2.a.cc.1.9 10 1.1 even 1 trivial
4598.2.a.cd.1.9 10 11.10 odd 2