Properties

Label 4005.2.a.t.1.5
Level $4005$
Weight $2$
Character 4005.1
Self dual yes
Analytic conductor $31.980$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4005,2,Mod(1,4005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4005, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4005.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 19x^{8} - x^{7} + 128x^{6} + 14x^{5} - 358x^{4} - 59x^{3} + 344x^{2} + 71x - 21 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1335)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.167560\) of defining polynomial
Character \(\chi\) \(=\) 4005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.167560 q^{2} -1.97192 q^{4} +1.00000 q^{5} -2.76137 q^{7} +0.665537 q^{8} +O(q^{10})\) \(q-0.167560 q^{2} -1.97192 q^{4} +1.00000 q^{5} -2.76137 q^{7} +0.665537 q^{8} -0.167560 q^{10} -3.33531 q^{11} -4.89095 q^{13} +0.462697 q^{14} +3.83233 q^{16} -4.74870 q^{17} -2.12657 q^{19} -1.97192 q^{20} +0.558866 q^{22} -6.48422 q^{23} +1.00000 q^{25} +0.819530 q^{26} +5.44521 q^{28} +0.0885979 q^{29} -1.02003 q^{31} -1.97322 q^{32} +0.795695 q^{34} -2.76137 q^{35} +7.00644 q^{37} +0.356330 q^{38} +0.665537 q^{40} -5.31495 q^{41} +10.4989 q^{43} +6.57698 q^{44} +1.08650 q^{46} +4.77531 q^{47} +0.625170 q^{49} -0.167560 q^{50} +9.64458 q^{52} -3.53639 q^{53} -3.33531 q^{55} -1.83780 q^{56} -0.0148455 q^{58} +1.10447 q^{59} -1.87568 q^{61} +0.170917 q^{62} -7.33402 q^{64} -4.89095 q^{65} +12.8567 q^{67} +9.36408 q^{68} +0.462697 q^{70} -8.95798 q^{71} +4.33743 q^{73} -1.17400 q^{74} +4.19344 q^{76} +9.21003 q^{77} -0.560875 q^{79} +3.83233 q^{80} +0.890575 q^{82} +2.04236 q^{83} -4.74870 q^{85} -1.75920 q^{86} -2.21977 q^{88} +1.00000 q^{89} +13.5057 q^{91} +12.7864 q^{92} -0.800153 q^{94} -2.12657 q^{95} +10.5702 q^{97} -0.104754 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 18 q^{4} + 10 q^{5} + 9 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 18 q^{4} + 10 q^{5} + 9 q^{7} - 3 q^{8} - 4 q^{11} + 15 q^{13} + q^{14} + 22 q^{16} - 11 q^{17} + 14 q^{19} + 18 q^{20} + 10 q^{22} + 8 q^{23} + 10 q^{25} + 14 q^{26} + 36 q^{28} - 5 q^{29} - 8 q^{31} - q^{32} + 2 q^{34} + 9 q^{35} + 23 q^{37} - 8 q^{38} - 3 q^{40} - 13 q^{41} + 25 q^{43} + 8 q^{44} - 14 q^{46} + q^{47} + 21 q^{49} + 51 q^{52} - 9 q^{53} - 4 q^{55} - 15 q^{56} - 8 q^{58} + 15 q^{59} + 8 q^{61} + 8 q^{62} + 9 q^{64} + 15 q^{65} + 52 q^{67} + 28 q^{68} + q^{70} + 22 q^{71} + 34 q^{73} + 18 q^{74} + 14 q^{76} - 4 q^{77} - 3 q^{79} + 22 q^{80} + 17 q^{82} + 10 q^{83} - 11 q^{85} + 6 q^{86} + 4 q^{88} + 10 q^{89} + 18 q^{91} + 14 q^{92} - 43 q^{94} + 14 q^{95} + 34 q^{97} + 38 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.167560 −0.118483 −0.0592416 0.998244i \(-0.518868\pi\)
−0.0592416 + 0.998244i \(0.518868\pi\)
\(3\) 0 0
\(4\) −1.97192 −0.985962
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.76137 −1.04370 −0.521850 0.853037i \(-0.674758\pi\)
−0.521850 + 0.853037i \(0.674758\pi\)
\(8\) 0.665537 0.235303
\(9\) 0 0
\(10\) −0.167560 −0.0529873
\(11\) −3.33531 −1.00563 −0.502817 0.864393i \(-0.667703\pi\)
−0.502817 + 0.864393i \(0.667703\pi\)
\(12\) 0 0
\(13\) −4.89095 −1.35651 −0.678253 0.734829i \(-0.737263\pi\)
−0.678253 + 0.734829i \(0.737263\pi\)
\(14\) 0.462697 0.123661
\(15\) 0 0
\(16\) 3.83233 0.958082
\(17\) −4.74870 −1.15173 −0.575865 0.817545i \(-0.695335\pi\)
−0.575865 + 0.817545i \(0.695335\pi\)
\(18\) 0 0
\(19\) −2.12657 −0.487870 −0.243935 0.969792i \(-0.578438\pi\)
−0.243935 + 0.969792i \(0.578438\pi\)
\(20\) −1.97192 −0.440935
\(21\) 0 0
\(22\) 0.558866 0.119151
\(23\) −6.48422 −1.35205 −0.676027 0.736877i \(-0.736300\pi\)
−0.676027 + 0.736877i \(0.736300\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.819530 0.160723
\(27\) 0 0
\(28\) 5.44521 1.02905
\(29\) 0.0885979 0.0164522 0.00822611 0.999966i \(-0.497382\pi\)
0.00822611 + 0.999966i \(0.497382\pi\)
\(30\) 0 0
\(31\) −1.02003 −0.183203 −0.0916013 0.995796i \(-0.529199\pi\)
−0.0916013 + 0.995796i \(0.529199\pi\)
\(32\) −1.97322 −0.348820
\(33\) 0 0
\(34\) 0.795695 0.136461
\(35\) −2.76137 −0.466757
\(36\) 0 0
\(37\) 7.00644 1.15185 0.575925 0.817502i \(-0.304642\pi\)
0.575925 + 0.817502i \(0.304642\pi\)
\(38\) 0.356330 0.0578043
\(39\) 0 0
\(40\) 0.665537 0.105231
\(41\) −5.31495 −0.830056 −0.415028 0.909809i \(-0.636228\pi\)
−0.415028 + 0.909809i \(0.636228\pi\)
\(42\) 0 0
\(43\) 10.4989 1.60107 0.800533 0.599288i \(-0.204550\pi\)
0.800533 + 0.599288i \(0.204550\pi\)
\(44\) 6.57698 0.991517
\(45\) 0 0
\(46\) 1.08650 0.160196
\(47\) 4.77531 0.696551 0.348275 0.937392i \(-0.386767\pi\)
0.348275 + 0.937392i \(0.386767\pi\)
\(48\) 0 0
\(49\) 0.625170 0.0893101
\(50\) −0.167560 −0.0236966
\(51\) 0 0
\(52\) 9.64458 1.33746
\(53\) −3.53639 −0.485760 −0.242880 0.970056i \(-0.578092\pi\)
−0.242880 + 0.970056i \(0.578092\pi\)
\(54\) 0 0
\(55\) −3.33531 −0.449733
\(56\) −1.83780 −0.245586
\(57\) 0 0
\(58\) −0.0148455 −0.00194931
\(59\) 1.10447 0.143789 0.0718946 0.997412i \(-0.477095\pi\)
0.0718946 + 0.997412i \(0.477095\pi\)
\(60\) 0 0
\(61\) −1.87568 −0.240157 −0.120078 0.992764i \(-0.538315\pi\)
−0.120078 + 0.992764i \(0.538315\pi\)
\(62\) 0.170917 0.0217064
\(63\) 0 0
\(64\) −7.33402 −0.916753
\(65\) −4.89095 −0.606648
\(66\) 0 0
\(67\) 12.8567 1.57070 0.785350 0.619052i \(-0.212483\pi\)
0.785350 + 0.619052i \(0.212483\pi\)
\(68\) 9.36408 1.13556
\(69\) 0 0
\(70\) 0.462697 0.0553028
\(71\) −8.95798 −1.06312 −0.531558 0.847022i \(-0.678393\pi\)
−0.531558 + 0.847022i \(0.678393\pi\)
\(72\) 0 0
\(73\) 4.33743 0.507657 0.253829 0.967249i \(-0.418310\pi\)
0.253829 + 0.967249i \(0.418310\pi\)
\(74\) −1.17400 −0.136475
\(75\) 0 0
\(76\) 4.19344 0.481021
\(77\) 9.21003 1.04958
\(78\) 0 0
\(79\) −0.560875 −0.0631033 −0.0315517 0.999502i \(-0.510045\pi\)
−0.0315517 + 0.999502i \(0.510045\pi\)
\(80\) 3.83233 0.428467
\(81\) 0 0
\(82\) 0.890575 0.0983476
\(83\) 2.04236 0.224179 0.112089 0.993698i \(-0.464246\pi\)
0.112089 + 0.993698i \(0.464246\pi\)
\(84\) 0 0
\(85\) −4.74870 −0.515069
\(86\) −1.75920 −0.189699
\(87\) 0 0
\(88\) −2.21977 −0.236629
\(89\) 1.00000 0.106000
\(90\) 0 0
\(91\) 13.5057 1.41579
\(92\) 12.7864 1.33307
\(93\) 0 0
\(94\) −0.800153 −0.0825295
\(95\) −2.12657 −0.218182
\(96\) 0 0
\(97\) 10.5702 1.07324 0.536621 0.843824i \(-0.319701\pi\)
0.536621 + 0.843824i \(0.319701\pi\)
\(98\) −0.104754 −0.0105817
\(99\) 0 0
\(100\) −1.97192 −0.197192
\(101\) −6.50558 −0.647329 −0.323664 0.946172i \(-0.604915\pi\)
−0.323664 + 0.946172i \(0.604915\pi\)
\(102\) 0 0
\(103\) −18.3709 −1.81014 −0.905072 0.425259i \(-0.860183\pi\)
−0.905072 + 0.425259i \(0.860183\pi\)
\(104\) −3.25511 −0.319190
\(105\) 0 0
\(106\) 0.592559 0.0575544
\(107\) −8.39617 −0.811689 −0.405844 0.913942i \(-0.633022\pi\)
−0.405844 + 0.913942i \(0.633022\pi\)
\(108\) 0 0
\(109\) −12.1755 −1.16620 −0.583100 0.812401i \(-0.698160\pi\)
−0.583100 + 0.812401i \(0.698160\pi\)
\(110\) 0.558866 0.0532858
\(111\) 0 0
\(112\) −10.5825 −0.999951
\(113\) −0.762011 −0.0716840 −0.0358420 0.999357i \(-0.511411\pi\)
−0.0358420 + 0.999357i \(0.511411\pi\)
\(114\) 0 0
\(115\) −6.48422 −0.604657
\(116\) −0.174708 −0.0162213
\(117\) 0 0
\(118\) −0.185065 −0.0170366
\(119\) 13.1129 1.20206
\(120\) 0 0
\(121\) 0.124299 0.0112999
\(122\) 0.314290 0.0284545
\(123\) 0 0
\(124\) 2.01142 0.180631
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 17.5917 1.56101 0.780505 0.625150i \(-0.214962\pi\)
0.780505 + 0.625150i \(0.214962\pi\)
\(128\) 5.17533 0.457439
\(129\) 0 0
\(130\) 0.819530 0.0718775
\(131\) 16.4645 1.43851 0.719254 0.694747i \(-0.244484\pi\)
0.719254 + 0.694747i \(0.244484\pi\)
\(132\) 0 0
\(133\) 5.87226 0.509190
\(134\) −2.15428 −0.186101
\(135\) 0 0
\(136\) −3.16044 −0.271005
\(137\) 10.0200 0.856063 0.428031 0.903764i \(-0.359207\pi\)
0.428031 + 0.903764i \(0.359207\pi\)
\(138\) 0 0
\(139\) 9.15475 0.776496 0.388248 0.921555i \(-0.373080\pi\)
0.388248 + 0.921555i \(0.373080\pi\)
\(140\) 5.44521 0.460204
\(141\) 0 0
\(142\) 1.50100 0.125961
\(143\) 16.3128 1.36415
\(144\) 0 0
\(145\) 0.0885979 0.00735766
\(146\) −0.726781 −0.0601488
\(147\) 0 0
\(148\) −13.8162 −1.13568
\(149\) 0.754909 0.0618446 0.0309223 0.999522i \(-0.490156\pi\)
0.0309223 + 0.999522i \(0.490156\pi\)
\(150\) 0 0
\(151\) 20.3641 1.65720 0.828602 0.559839i \(-0.189137\pi\)
0.828602 + 0.559839i \(0.189137\pi\)
\(152\) −1.41531 −0.114797
\(153\) 0 0
\(154\) −1.54324 −0.124358
\(155\) −1.02003 −0.0819307
\(156\) 0 0
\(157\) −18.7103 −1.49324 −0.746620 0.665250i \(-0.768325\pi\)
−0.746620 + 0.665250i \(0.768325\pi\)
\(158\) 0.0939804 0.00747668
\(159\) 0 0
\(160\) −1.97322 −0.155997
\(161\) 17.9053 1.41114
\(162\) 0 0
\(163\) −9.39787 −0.736098 −0.368049 0.929806i \(-0.619974\pi\)
−0.368049 + 0.929806i \(0.619974\pi\)
\(164\) 10.4807 0.818403
\(165\) 0 0
\(166\) −0.342219 −0.0265614
\(167\) 17.2812 1.33726 0.668629 0.743596i \(-0.266881\pi\)
0.668629 + 0.743596i \(0.266881\pi\)
\(168\) 0 0
\(169\) 10.9214 0.840107
\(170\) 0.795695 0.0610270
\(171\) 0 0
\(172\) −20.7030 −1.57859
\(173\) −14.9919 −1.13981 −0.569905 0.821710i \(-0.693020\pi\)
−0.569905 + 0.821710i \(0.693020\pi\)
\(174\) 0 0
\(175\) −2.76137 −0.208740
\(176\) −12.7820 −0.963480
\(177\) 0 0
\(178\) −0.167560 −0.0125592
\(179\) 11.1785 0.835522 0.417761 0.908557i \(-0.362815\pi\)
0.417761 + 0.908557i \(0.362815\pi\)
\(180\) 0 0
\(181\) −4.51645 −0.335705 −0.167852 0.985812i \(-0.553683\pi\)
−0.167852 + 0.985812i \(0.553683\pi\)
\(182\) −2.26303 −0.167747
\(183\) 0 0
\(184\) −4.31549 −0.318142
\(185\) 7.00644 0.515123
\(186\) 0 0
\(187\) 15.8384 1.15822
\(188\) −9.41655 −0.686772
\(189\) 0 0
\(190\) 0.356330 0.0258509
\(191\) −24.7702 −1.79231 −0.896153 0.443744i \(-0.853650\pi\)
−0.896153 + 0.443744i \(0.853650\pi\)
\(192\) 0 0
\(193\) 27.4522 1.97605 0.988026 0.154288i \(-0.0493083\pi\)
0.988026 + 0.154288i \(0.0493083\pi\)
\(194\) −1.77115 −0.127161
\(195\) 0 0
\(196\) −1.23279 −0.0880563
\(197\) −8.84300 −0.630038 −0.315019 0.949085i \(-0.602011\pi\)
−0.315019 + 0.949085i \(0.602011\pi\)
\(198\) 0 0
\(199\) −12.1238 −0.859430 −0.429715 0.902964i \(-0.641386\pi\)
−0.429715 + 0.902964i \(0.641386\pi\)
\(200\) 0.665537 0.0470606
\(201\) 0 0
\(202\) 1.09008 0.0766976
\(203\) −0.244652 −0.0171712
\(204\) 0 0
\(205\) −5.31495 −0.371212
\(206\) 3.07824 0.214471
\(207\) 0 0
\(208\) −18.7437 −1.29964
\(209\) 7.09279 0.490618
\(210\) 0 0
\(211\) −1.68837 −0.116232 −0.0581161 0.998310i \(-0.518509\pi\)
−0.0581161 + 0.998310i \(0.518509\pi\)
\(212\) 6.97349 0.478941
\(213\) 0 0
\(214\) 1.40687 0.0961714
\(215\) 10.4989 0.716019
\(216\) 0 0
\(217\) 2.81668 0.191209
\(218\) 2.04013 0.138175
\(219\) 0 0
\(220\) 6.57698 0.443420
\(221\) 23.2257 1.56233
\(222\) 0 0
\(223\) 19.5451 1.30884 0.654418 0.756133i \(-0.272914\pi\)
0.654418 + 0.756133i \(0.272914\pi\)
\(224\) 5.44880 0.364063
\(225\) 0 0
\(226\) 0.127683 0.00849334
\(227\) 7.16828 0.475776 0.237888 0.971293i \(-0.423545\pi\)
0.237888 + 0.971293i \(0.423545\pi\)
\(228\) 0 0
\(229\) 7.47217 0.493775 0.246887 0.969044i \(-0.420592\pi\)
0.246887 + 0.969044i \(0.420592\pi\)
\(230\) 1.08650 0.0716416
\(231\) 0 0
\(232\) 0.0589652 0.00387126
\(233\) −25.9048 −1.69708 −0.848540 0.529131i \(-0.822518\pi\)
−0.848540 + 0.529131i \(0.822518\pi\)
\(234\) 0 0
\(235\) 4.77531 0.311507
\(236\) −2.17792 −0.141771
\(237\) 0 0
\(238\) −2.19721 −0.142424
\(239\) 22.6981 1.46822 0.734110 0.679030i \(-0.237599\pi\)
0.734110 + 0.679030i \(0.237599\pi\)
\(240\) 0 0
\(241\) 3.37348 0.217305 0.108653 0.994080i \(-0.465346\pi\)
0.108653 + 0.994080i \(0.465346\pi\)
\(242\) −0.0208275 −0.00133885
\(243\) 0 0
\(244\) 3.69871 0.236785
\(245\) 0.625170 0.0399407
\(246\) 0 0
\(247\) 10.4010 0.661798
\(248\) −0.678867 −0.0431081
\(249\) 0 0
\(250\) −0.167560 −0.0105975
\(251\) 0.179341 0.0113199 0.00565996 0.999984i \(-0.498198\pi\)
0.00565996 + 0.999984i \(0.498198\pi\)
\(252\) 0 0
\(253\) 21.6269 1.35967
\(254\) −2.94767 −0.184953
\(255\) 0 0
\(256\) 13.8009 0.862554
\(257\) 19.0232 1.18663 0.593316 0.804970i \(-0.297818\pi\)
0.593316 + 0.804970i \(0.297818\pi\)
\(258\) 0 0
\(259\) −19.3474 −1.20219
\(260\) 9.64458 0.598131
\(261\) 0 0
\(262\) −2.75879 −0.170439
\(263\) −9.99555 −0.616352 −0.308176 0.951329i \(-0.599719\pi\)
−0.308176 + 0.951329i \(0.599719\pi\)
\(264\) 0 0
\(265\) −3.53639 −0.217239
\(266\) −0.983959 −0.0603304
\(267\) 0 0
\(268\) −25.3525 −1.54865
\(269\) −21.4992 −1.31083 −0.655414 0.755269i \(-0.727506\pi\)
−0.655414 + 0.755269i \(0.727506\pi\)
\(270\) 0 0
\(271\) −5.04650 −0.306553 −0.153277 0.988183i \(-0.548983\pi\)
−0.153277 + 0.988183i \(0.548983\pi\)
\(272\) −18.1986 −1.10345
\(273\) 0 0
\(274\) −1.67895 −0.101429
\(275\) −3.33531 −0.201127
\(276\) 0 0
\(277\) −1.35611 −0.0814805 −0.0407402 0.999170i \(-0.512972\pi\)
−0.0407402 + 0.999170i \(0.512972\pi\)
\(278\) −1.53397 −0.0920017
\(279\) 0 0
\(280\) −1.83780 −0.109829
\(281\) 11.5826 0.690961 0.345481 0.938426i \(-0.387716\pi\)
0.345481 + 0.938426i \(0.387716\pi\)
\(282\) 0 0
\(283\) 10.0608 0.598053 0.299027 0.954245i \(-0.403338\pi\)
0.299027 + 0.954245i \(0.403338\pi\)
\(284\) 17.6644 1.04819
\(285\) 0 0
\(286\) −2.73339 −0.161629
\(287\) 14.6765 0.866329
\(288\) 0 0
\(289\) 5.55019 0.326482
\(290\) −0.0148455 −0.000871758 0
\(291\) 0 0
\(292\) −8.55307 −0.500531
\(293\) 7.91473 0.462383 0.231192 0.972908i \(-0.425738\pi\)
0.231192 + 0.972908i \(0.425738\pi\)
\(294\) 0 0
\(295\) 1.10447 0.0643045
\(296\) 4.66304 0.271034
\(297\) 0 0
\(298\) −0.126493 −0.00732754
\(299\) 31.7140 1.83407
\(300\) 0 0
\(301\) −28.9913 −1.67103
\(302\) −3.41221 −0.196351
\(303\) 0 0
\(304\) −8.14973 −0.467419
\(305\) −1.87568 −0.107401
\(306\) 0 0
\(307\) −5.68306 −0.324349 −0.162175 0.986762i \(-0.551851\pi\)
−0.162175 + 0.986762i \(0.551851\pi\)
\(308\) −18.1615 −1.03485
\(309\) 0 0
\(310\) 0.170917 0.00970741
\(311\) 32.8960 1.86536 0.932679 0.360706i \(-0.117464\pi\)
0.932679 + 0.360706i \(0.117464\pi\)
\(312\) 0 0
\(313\) 5.66481 0.320194 0.160097 0.987101i \(-0.448819\pi\)
0.160097 + 0.987101i \(0.448819\pi\)
\(314\) 3.13510 0.176924
\(315\) 0 0
\(316\) 1.10600 0.0622175
\(317\) 19.8605 1.11548 0.557738 0.830017i \(-0.311670\pi\)
0.557738 + 0.830017i \(0.311670\pi\)
\(318\) 0 0
\(319\) −0.295502 −0.0165449
\(320\) −7.33402 −0.409984
\(321\) 0 0
\(322\) −3.00023 −0.167196
\(323\) 10.0985 0.561894
\(324\) 0 0
\(325\) −4.89095 −0.271301
\(326\) 1.57471 0.0872151
\(327\) 0 0
\(328\) −3.53730 −0.195315
\(329\) −13.1864 −0.726990
\(330\) 0 0
\(331\) −19.2500 −1.05807 −0.529037 0.848599i \(-0.677447\pi\)
−0.529037 + 0.848599i \(0.677447\pi\)
\(332\) −4.02739 −0.221032
\(333\) 0 0
\(334\) −2.89564 −0.158443
\(335\) 12.8567 0.702439
\(336\) 0 0
\(337\) 30.1877 1.64443 0.822215 0.569177i \(-0.192738\pi\)
0.822215 + 0.569177i \(0.192738\pi\)
\(338\) −1.82999 −0.0995385
\(339\) 0 0
\(340\) 9.36408 0.507839
\(341\) 3.40211 0.184235
\(342\) 0 0
\(343\) 17.6033 0.950487
\(344\) 6.98741 0.376736
\(345\) 0 0
\(346\) 2.51204 0.135048
\(347\) −20.5587 −1.10365 −0.551824 0.833960i \(-0.686068\pi\)
−0.551824 + 0.833960i \(0.686068\pi\)
\(348\) 0 0
\(349\) 11.1762 0.598249 0.299124 0.954214i \(-0.403305\pi\)
0.299124 + 0.954214i \(0.403305\pi\)
\(350\) 0.462697 0.0247322
\(351\) 0 0
\(352\) 6.58131 0.350785
\(353\) −25.6908 −1.36738 −0.683691 0.729772i \(-0.739626\pi\)
−0.683691 + 0.729772i \(0.739626\pi\)
\(354\) 0 0
\(355\) −8.95798 −0.475440
\(356\) −1.97192 −0.104512
\(357\) 0 0
\(358\) −1.87308 −0.0989952
\(359\) −26.2724 −1.38660 −0.693301 0.720648i \(-0.743844\pi\)
−0.693301 + 0.720648i \(0.743844\pi\)
\(360\) 0 0
\(361\) −14.4777 −0.761983
\(362\) 0.756778 0.0397753
\(363\) 0 0
\(364\) −26.6323 −1.39591
\(365\) 4.33743 0.227031
\(366\) 0 0
\(367\) 36.7123 1.91636 0.958182 0.286160i \(-0.0923788\pi\)
0.958182 + 0.286160i \(0.0923788\pi\)
\(368\) −24.8497 −1.29538
\(369\) 0 0
\(370\) −1.17400 −0.0610334
\(371\) 9.76528 0.506988
\(372\) 0 0
\(373\) −28.5774 −1.47968 −0.739842 0.672781i \(-0.765100\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(374\) −2.65389 −0.137229
\(375\) 0 0
\(376\) 3.17815 0.163900
\(377\) −0.433328 −0.0223175
\(378\) 0 0
\(379\) −15.7598 −0.809529 −0.404764 0.914421i \(-0.632646\pi\)
−0.404764 + 0.914421i \(0.632646\pi\)
\(380\) 4.19344 0.215119
\(381\) 0 0
\(382\) 4.15050 0.212358
\(383\) 29.3120 1.49777 0.748886 0.662699i \(-0.230589\pi\)
0.748886 + 0.662699i \(0.230589\pi\)
\(384\) 0 0
\(385\) 9.21003 0.469387
\(386\) −4.59990 −0.234129
\(387\) 0 0
\(388\) −20.8436 −1.05818
\(389\) 7.63643 0.387182 0.193591 0.981082i \(-0.437987\pi\)
0.193591 + 0.981082i \(0.437987\pi\)
\(390\) 0 0
\(391\) 30.7916 1.55720
\(392\) 0.416074 0.0210149
\(393\) 0 0
\(394\) 1.48174 0.0746488
\(395\) −0.560875 −0.0282207
\(396\) 0 0
\(397\) 17.2875 0.867634 0.433817 0.901001i \(-0.357166\pi\)
0.433817 + 0.901001i \(0.357166\pi\)
\(398\) 2.03146 0.101828
\(399\) 0 0
\(400\) 3.83233 0.191616
\(401\) −27.7710 −1.38682 −0.693408 0.720545i \(-0.743892\pi\)
−0.693408 + 0.720545i \(0.743892\pi\)
\(402\) 0 0
\(403\) 4.98891 0.248515
\(404\) 12.8285 0.638242
\(405\) 0 0
\(406\) 0.0409939 0.00203450
\(407\) −23.3686 −1.15834
\(408\) 0 0
\(409\) 5.94849 0.294134 0.147067 0.989127i \(-0.453017\pi\)
0.147067 + 0.989127i \(0.453017\pi\)
\(410\) 0.890575 0.0439824
\(411\) 0 0
\(412\) 36.2261 1.78473
\(413\) −3.04984 −0.150073
\(414\) 0 0
\(415\) 2.04236 0.100256
\(416\) 9.65093 0.473176
\(417\) 0 0
\(418\) −1.18847 −0.0581300
\(419\) −22.5429 −1.10129 −0.550646 0.834739i \(-0.685619\pi\)
−0.550646 + 0.834739i \(0.685619\pi\)
\(420\) 0 0
\(421\) −8.87459 −0.432521 −0.216261 0.976336i \(-0.569386\pi\)
−0.216261 + 0.976336i \(0.569386\pi\)
\(422\) 0.282904 0.0137716
\(423\) 0 0
\(424\) −2.35360 −0.114301
\(425\) −4.74870 −0.230346
\(426\) 0 0
\(427\) 5.17946 0.250652
\(428\) 16.5566 0.800294
\(429\) 0 0
\(430\) −1.75920 −0.0848361
\(431\) 28.2077 1.35872 0.679358 0.733807i \(-0.262258\pi\)
0.679358 + 0.733807i \(0.262258\pi\)
\(432\) 0 0
\(433\) −19.1190 −0.918801 −0.459400 0.888229i \(-0.651936\pi\)
−0.459400 + 0.888229i \(0.651936\pi\)
\(434\) −0.471964 −0.0226550
\(435\) 0 0
\(436\) 24.0091 1.14983
\(437\) 13.7892 0.659626
\(438\) 0 0
\(439\) 1.00432 0.0479334 0.0239667 0.999713i \(-0.492370\pi\)
0.0239667 + 0.999713i \(0.492370\pi\)
\(440\) −2.21977 −0.105824
\(441\) 0 0
\(442\) −3.89170 −0.185110
\(443\) −12.4989 −0.593841 −0.296920 0.954902i \(-0.595960\pi\)
−0.296920 + 0.954902i \(0.595960\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) −3.27498 −0.155075
\(447\) 0 0
\(448\) 20.2520 0.956815
\(449\) 16.2680 0.767735 0.383867 0.923388i \(-0.374592\pi\)
0.383867 + 0.923388i \(0.374592\pi\)
\(450\) 0 0
\(451\) 17.7270 0.834732
\(452\) 1.50263 0.0706777
\(453\) 0 0
\(454\) −1.20112 −0.0563714
\(455\) 13.5057 0.633158
\(456\) 0 0
\(457\) 0.351528 0.0164438 0.00822189 0.999966i \(-0.497383\pi\)
0.00822189 + 0.999966i \(0.497383\pi\)
\(458\) −1.25204 −0.0585040
\(459\) 0 0
\(460\) 12.7864 0.596168
\(461\) 12.5064 0.582482 0.291241 0.956650i \(-0.405932\pi\)
0.291241 + 0.956650i \(0.405932\pi\)
\(462\) 0 0
\(463\) −19.1522 −0.890080 −0.445040 0.895511i \(-0.646811\pi\)
−0.445040 + 0.895511i \(0.646811\pi\)
\(464\) 0.339536 0.0157626
\(465\) 0 0
\(466\) 4.34062 0.201075
\(467\) 32.9017 1.52251 0.761255 0.648452i \(-0.224583\pi\)
0.761255 + 0.648452i \(0.224583\pi\)
\(468\) 0 0
\(469\) −35.5022 −1.63934
\(470\) −0.800153 −0.0369083
\(471\) 0 0
\(472\) 0.735064 0.0338340
\(473\) −35.0171 −1.61009
\(474\) 0 0
\(475\) −2.12657 −0.0975739
\(476\) −25.8577 −1.18519
\(477\) 0 0
\(478\) −3.80331 −0.173959
\(479\) 16.9068 0.772494 0.386247 0.922395i \(-0.373771\pi\)
0.386247 + 0.922395i \(0.373771\pi\)
\(480\) 0 0
\(481\) −34.2681 −1.56249
\(482\) −0.565262 −0.0257470
\(483\) 0 0
\(484\) −0.245108 −0.0111413
\(485\) 10.5702 0.479968
\(486\) 0 0
\(487\) −35.5619 −1.61147 −0.805733 0.592279i \(-0.798228\pi\)
−0.805733 + 0.592279i \(0.798228\pi\)
\(488\) −1.24834 −0.0565096
\(489\) 0 0
\(490\) −0.104754 −0.00473230
\(491\) −20.4192 −0.921505 −0.460753 0.887529i \(-0.652421\pi\)
−0.460753 + 0.887529i \(0.652421\pi\)
\(492\) 0 0
\(493\) −0.420725 −0.0189485
\(494\) −1.74279 −0.0784119
\(495\) 0 0
\(496\) −3.90909 −0.175523
\(497\) 24.7363 1.10957
\(498\) 0 0
\(499\) −25.6453 −1.14804 −0.574022 0.818840i \(-0.694617\pi\)
−0.574022 + 0.818840i \(0.694617\pi\)
\(500\) −1.97192 −0.0881871
\(501\) 0 0
\(502\) −0.0300505 −0.00134122
\(503\) 18.9559 0.845201 0.422601 0.906316i \(-0.361117\pi\)
0.422601 + 0.906316i \(0.361117\pi\)
\(504\) 0 0
\(505\) −6.50558 −0.289494
\(506\) −3.62381 −0.161098
\(507\) 0 0
\(508\) −34.6895 −1.53910
\(509\) −32.3589 −1.43428 −0.717141 0.696929i \(-0.754549\pi\)
−0.717141 + 0.696929i \(0.754549\pi\)
\(510\) 0 0
\(511\) −11.9772 −0.529842
\(512\) −12.6631 −0.559637
\(513\) 0 0
\(514\) −3.18753 −0.140596
\(515\) −18.3709 −0.809521
\(516\) 0 0
\(517\) −15.9271 −0.700475
\(518\) 3.24185 0.142439
\(519\) 0 0
\(520\) −3.25511 −0.142746
\(521\) 8.27462 0.362518 0.181259 0.983435i \(-0.441983\pi\)
0.181259 + 0.983435i \(0.441983\pi\)
\(522\) 0 0
\(523\) 15.9288 0.696519 0.348260 0.937398i \(-0.386773\pi\)
0.348260 + 0.937398i \(0.386773\pi\)
\(524\) −32.4667 −1.41831
\(525\) 0 0
\(526\) 1.67486 0.0730273
\(527\) 4.84382 0.211000
\(528\) 0 0
\(529\) 19.0451 0.828048
\(530\) 0.592559 0.0257391
\(531\) 0 0
\(532\) −11.5796 −0.502041
\(533\) 25.9952 1.12598
\(534\) 0 0
\(535\) −8.39617 −0.362998
\(536\) 8.55664 0.369590
\(537\) 0 0
\(538\) 3.60241 0.155311
\(539\) −2.08514 −0.0898132
\(540\) 0 0
\(541\) 2.14871 0.0923804 0.0461902 0.998933i \(-0.485292\pi\)
0.0461902 + 0.998933i \(0.485292\pi\)
\(542\) 0.845594 0.0363214
\(543\) 0 0
\(544\) 9.37024 0.401746
\(545\) −12.1755 −0.521540
\(546\) 0 0
\(547\) 19.0513 0.814576 0.407288 0.913300i \(-0.366475\pi\)
0.407288 + 0.913300i \(0.366475\pi\)
\(548\) −19.7586 −0.844045
\(549\) 0 0
\(550\) 0.558866 0.0238301
\(551\) −0.188410 −0.00802654
\(552\) 0 0
\(553\) 1.54878 0.0658610
\(554\) 0.227230 0.00965406
\(555\) 0 0
\(556\) −18.0525 −0.765595
\(557\) −6.15992 −0.261004 −0.130502 0.991448i \(-0.541659\pi\)
−0.130502 + 0.991448i \(0.541659\pi\)
\(558\) 0 0
\(559\) −51.3496 −2.17186
\(560\) −10.5825 −0.447192
\(561\) 0 0
\(562\) −1.94079 −0.0818672
\(563\) −14.3245 −0.603704 −0.301852 0.953355i \(-0.597605\pi\)
−0.301852 + 0.953355i \(0.597605\pi\)
\(564\) 0 0
\(565\) −0.762011 −0.0320580
\(566\) −1.68579 −0.0708592
\(567\) 0 0
\(568\) −5.96187 −0.250154
\(569\) −6.91851 −0.290039 −0.145020 0.989429i \(-0.546324\pi\)
−0.145020 + 0.989429i \(0.546324\pi\)
\(570\) 0 0
\(571\) 19.0087 0.795490 0.397745 0.917496i \(-0.369793\pi\)
0.397745 + 0.917496i \(0.369793\pi\)
\(572\) −32.1677 −1.34500
\(573\) 0 0
\(574\) −2.45921 −0.102645
\(575\) −6.48422 −0.270411
\(576\) 0 0
\(577\) 10.2198 0.425458 0.212729 0.977111i \(-0.431765\pi\)
0.212729 + 0.977111i \(0.431765\pi\)
\(578\) −0.929992 −0.0386826
\(579\) 0 0
\(580\) −0.174708 −0.00725437
\(581\) −5.63973 −0.233975
\(582\) 0 0
\(583\) 11.7950 0.488497
\(584\) 2.88672 0.119453
\(585\) 0 0
\(586\) −1.32620 −0.0547846
\(587\) 43.0236 1.77578 0.887888 0.460060i \(-0.152172\pi\)
0.887888 + 0.460060i \(0.152172\pi\)
\(588\) 0 0
\(589\) 2.16917 0.0893790
\(590\) −0.185065 −0.00761900
\(591\) 0 0
\(592\) 26.8510 1.10357
\(593\) −14.8859 −0.611290 −0.305645 0.952146i \(-0.598872\pi\)
−0.305645 + 0.952146i \(0.598872\pi\)
\(594\) 0 0
\(595\) 13.1129 0.537578
\(596\) −1.48862 −0.0609764
\(597\) 0 0
\(598\) −5.31401 −0.217306
\(599\) −45.1669 −1.84547 −0.922735 0.385436i \(-0.874051\pi\)
−0.922735 + 0.385436i \(0.874051\pi\)
\(600\) 0 0
\(601\) 38.4553 1.56862 0.784311 0.620368i \(-0.213017\pi\)
0.784311 + 0.620368i \(0.213017\pi\)
\(602\) 4.85780 0.197989
\(603\) 0 0
\(604\) −40.1564 −1.63394
\(605\) 0.124299 0.00505346
\(606\) 0 0
\(607\) 29.5466 1.19926 0.599629 0.800278i \(-0.295315\pi\)
0.599629 + 0.800278i \(0.295315\pi\)
\(608\) 4.19620 0.170178
\(609\) 0 0
\(610\) 0.314290 0.0127252
\(611\) −23.3558 −0.944875
\(612\) 0 0
\(613\) 40.1853 1.62307 0.811534 0.584306i \(-0.198633\pi\)
0.811534 + 0.584306i \(0.198633\pi\)
\(614\) 0.952256 0.0384299
\(615\) 0 0
\(616\) 6.12962 0.246969
\(617\) −8.08517 −0.325497 −0.162748 0.986668i \(-0.552036\pi\)
−0.162748 + 0.986668i \(0.552036\pi\)
\(618\) 0 0
\(619\) −12.4190 −0.499161 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(620\) 2.01142 0.0807805
\(621\) 0 0
\(622\) −5.51206 −0.221014
\(623\) −2.76137 −0.110632
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −0.949197 −0.0379376
\(627\) 0 0
\(628\) 36.8952 1.47228
\(629\) −33.2715 −1.32662
\(630\) 0 0
\(631\) −8.89333 −0.354038 −0.177019 0.984207i \(-0.556645\pi\)
−0.177019 + 0.984207i \(0.556645\pi\)
\(632\) −0.373283 −0.0148484
\(633\) 0 0
\(634\) −3.32783 −0.132165
\(635\) 17.5917 0.698105
\(636\) 0 0
\(637\) −3.05768 −0.121150
\(638\) 0.0495144 0.00196029
\(639\) 0 0
\(640\) 5.17533 0.204573
\(641\) −16.8770 −0.666603 −0.333302 0.942820i \(-0.608163\pi\)
−0.333302 + 0.942820i \(0.608163\pi\)
\(642\) 0 0
\(643\) 4.09389 0.161447 0.0807235 0.996737i \(-0.474277\pi\)
0.0807235 + 0.996737i \(0.474277\pi\)
\(644\) −35.3080 −1.39133
\(645\) 0 0
\(646\) −1.69210 −0.0665750
\(647\) −15.1293 −0.594795 −0.297397 0.954754i \(-0.596119\pi\)
−0.297397 + 0.954754i \(0.596119\pi\)
\(648\) 0 0
\(649\) −3.68374 −0.144599
\(650\) 0.819530 0.0321446
\(651\) 0 0
\(652\) 18.5319 0.725764
\(653\) 7.52805 0.294595 0.147298 0.989092i \(-0.452942\pi\)
0.147298 + 0.989092i \(0.452942\pi\)
\(654\) 0 0
\(655\) 16.4645 0.643320
\(656\) −20.3686 −0.795262
\(657\) 0 0
\(658\) 2.20952 0.0861361
\(659\) 2.57821 0.100433 0.0502164 0.998738i \(-0.484009\pi\)
0.0502164 + 0.998738i \(0.484009\pi\)
\(660\) 0 0
\(661\) −11.1301 −0.432910 −0.216455 0.976293i \(-0.569449\pi\)
−0.216455 + 0.976293i \(0.569449\pi\)
\(662\) 3.22553 0.125364
\(663\) 0 0
\(664\) 1.35927 0.0527499
\(665\) 5.87226 0.227716
\(666\) 0 0
\(667\) −0.574488 −0.0222443
\(668\) −34.0772 −1.31849
\(669\) 0 0
\(670\) −2.15428 −0.0832271
\(671\) 6.25599 0.241510
\(672\) 0 0
\(673\) −13.4043 −0.516698 −0.258349 0.966052i \(-0.583178\pi\)
−0.258349 + 0.966052i \(0.583178\pi\)
\(674\) −5.05827 −0.194837
\(675\) 0 0
\(676\) −21.5362 −0.828314
\(677\) −48.9734 −1.88220 −0.941101 0.338127i \(-0.890207\pi\)
−0.941101 + 0.338127i \(0.890207\pi\)
\(678\) 0 0
\(679\) −29.1883 −1.12014
\(680\) −3.16044 −0.121197
\(681\) 0 0
\(682\) −0.570060 −0.0218287
\(683\) −31.9190 −1.22135 −0.610673 0.791883i \(-0.709101\pi\)
−0.610673 + 0.791883i \(0.709101\pi\)
\(684\) 0 0
\(685\) 10.0200 0.382843
\(686\) −2.94961 −0.112617
\(687\) 0 0
\(688\) 40.2352 1.53395
\(689\) 17.2963 0.658937
\(690\) 0 0
\(691\) −14.3516 −0.545960 −0.272980 0.962020i \(-0.588009\pi\)
−0.272980 + 0.962020i \(0.588009\pi\)
\(692\) 29.5628 1.12381
\(693\) 0 0
\(694\) 3.44483 0.130764
\(695\) 9.15475 0.347260
\(696\) 0 0
\(697\) 25.2391 0.956000
\(698\) −1.87269 −0.0708824
\(699\) 0 0
\(700\) 5.44521 0.205810
\(701\) 35.0461 1.32367 0.661836 0.749649i \(-0.269778\pi\)
0.661836 + 0.749649i \(0.269778\pi\)
\(702\) 0 0
\(703\) −14.8997 −0.561953
\(704\) 24.4613 0.921918
\(705\) 0 0
\(706\) 4.30476 0.162012
\(707\) 17.9643 0.675617
\(708\) 0 0
\(709\) 31.0084 1.16455 0.582273 0.812993i \(-0.302164\pi\)
0.582273 + 0.812993i \(0.302164\pi\)
\(710\) 1.50100 0.0563316
\(711\) 0 0
\(712\) 0.665537 0.0249421
\(713\) 6.61409 0.247700
\(714\) 0 0
\(715\) 16.3128 0.610066
\(716\) −22.0432 −0.823793
\(717\) 0 0
\(718\) 4.40221 0.164289
\(719\) −14.2269 −0.530572 −0.265286 0.964170i \(-0.585466\pi\)
−0.265286 + 0.964170i \(0.585466\pi\)
\(720\) 0 0
\(721\) 50.7290 1.88925
\(722\) 2.42589 0.0902822
\(723\) 0 0
\(724\) 8.90609 0.330992
\(725\) 0.0885979 0.00329044
\(726\) 0 0
\(727\) 22.1412 0.821172 0.410586 0.911822i \(-0.365324\pi\)
0.410586 + 0.911822i \(0.365324\pi\)
\(728\) 8.98857 0.333138
\(729\) 0 0
\(730\) −0.726781 −0.0268994
\(731\) −49.8561 −1.84400
\(732\) 0 0
\(733\) −16.7772 −0.619679 −0.309839 0.950789i \(-0.600275\pi\)
−0.309839 + 0.950789i \(0.600275\pi\)
\(734\) −6.15152 −0.227057
\(735\) 0 0
\(736\) 12.7948 0.471623
\(737\) −42.8812 −1.57955
\(738\) 0 0
\(739\) −26.2549 −0.965802 −0.482901 0.875675i \(-0.660417\pi\)
−0.482901 + 0.875675i \(0.660417\pi\)
\(740\) −13.8162 −0.507892
\(741\) 0 0
\(742\) −1.63627 −0.0600695
\(743\) 5.64662 0.207154 0.103577 0.994621i \(-0.466971\pi\)
0.103577 + 0.994621i \(0.466971\pi\)
\(744\) 0 0
\(745\) 0.754909 0.0276577
\(746\) 4.78845 0.175317
\(747\) 0 0
\(748\) −31.2321 −1.14196
\(749\) 23.1849 0.847160
\(750\) 0 0
\(751\) −2.27816 −0.0831314 −0.0415657 0.999136i \(-0.513235\pi\)
−0.0415657 + 0.999136i \(0.513235\pi\)
\(752\) 18.3006 0.667353
\(753\) 0 0
\(754\) 0.0726086 0.00264425
\(755\) 20.3641 0.741124
\(756\) 0 0
\(757\) −48.3296 −1.75657 −0.878284 0.478139i \(-0.841311\pi\)
−0.878284 + 0.478139i \(0.841311\pi\)
\(758\) 2.64073 0.0959155
\(759\) 0 0
\(760\) −1.41531 −0.0513388
\(761\) 6.41780 0.232645 0.116323 0.993211i \(-0.462889\pi\)
0.116323 + 0.993211i \(0.462889\pi\)
\(762\) 0 0
\(763\) 33.6210 1.21716
\(764\) 48.8449 1.76715
\(765\) 0 0
\(766\) −4.91152 −0.177461
\(767\) −5.40189 −0.195051
\(768\) 0 0
\(769\) −27.7999 −1.00249 −0.501246 0.865305i \(-0.667125\pi\)
−0.501246 + 0.865305i \(0.667125\pi\)
\(770\) −1.54324 −0.0556144
\(771\) 0 0
\(772\) −54.1336 −1.94831
\(773\) −6.26657 −0.225393 −0.112696 0.993629i \(-0.535949\pi\)
−0.112696 + 0.993629i \(0.535949\pi\)
\(774\) 0 0
\(775\) −1.02003 −0.0366405
\(776\) 7.03486 0.252537
\(777\) 0 0
\(778\) −1.27956 −0.0458745
\(779\) 11.3026 0.404959
\(780\) 0 0
\(781\) 29.8776 1.06911
\(782\) −5.15946 −0.184502
\(783\) 0 0
\(784\) 2.39586 0.0855664
\(785\) −18.7103 −0.667798
\(786\) 0 0
\(787\) 28.3330 1.00996 0.504982 0.863130i \(-0.331499\pi\)
0.504982 + 0.863130i \(0.331499\pi\)
\(788\) 17.4377 0.621193
\(789\) 0 0
\(790\) 0.0939804 0.00334367
\(791\) 2.10420 0.0748166
\(792\) 0 0
\(793\) 9.17388 0.325774
\(794\) −2.89670 −0.102800
\(795\) 0 0
\(796\) 23.9071 0.847365
\(797\) −22.2283 −0.787366 −0.393683 0.919246i \(-0.628799\pi\)
−0.393683 + 0.919246i \(0.628799\pi\)
\(798\) 0 0
\(799\) −22.6765 −0.802238
\(800\) −1.97322 −0.0697639
\(801\) 0 0
\(802\) 4.65332 0.164314
\(803\) −14.4667 −0.510518
\(804\) 0 0
\(805\) 17.9053 0.631080
\(806\) −0.835944 −0.0294449
\(807\) 0 0
\(808\) −4.32970 −0.152318
\(809\) −21.9406 −0.771389 −0.385694 0.922627i \(-0.626038\pi\)
−0.385694 + 0.922627i \(0.626038\pi\)
\(810\) 0 0
\(811\) 6.38160 0.224088 0.112044 0.993703i \(-0.464260\pi\)
0.112044 + 0.993703i \(0.464260\pi\)
\(812\) 0.482434 0.0169301
\(813\) 0 0
\(814\) 3.91566 0.137244
\(815\) −9.39787 −0.329193
\(816\) 0 0
\(817\) −22.3267 −0.781112
\(818\) −0.996732 −0.0348499
\(819\) 0 0
\(820\) 10.4807 0.366001
\(821\) −29.9161 −1.04408 −0.522040 0.852921i \(-0.674829\pi\)
−0.522040 + 0.852921i \(0.674829\pi\)
\(822\) 0 0
\(823\) −41.5172 −1.44720 −0.723600 0.690220i \(-0.757514\pi\)
−0.723600 + 0.690220i \(0.757514\pi\)
\(824\) −12.2265 −0.425932
\(825\) 0 0
\(826\) 0.511033 0.0177811
\(827\) 23.8732 0.830153 0.415076 0.909787i \(-0.363755\pi\)
0.415076 + 0.909787i \(0.363755\pi\)
\(828\) 0 0
\(829\) 34.3129 1.19174 0.595868 0.803083i \(-0.296808\pi\)
0.595868 + 0.803083i \(0.296808\pi\)
\(830\) −0.342219 −0.0118786
\(831\) 0 0
\(832\) 35.8704 1.24358
\(833\) −2.96875 −0.102861
\(834\) 0 0
\(835\) 17.2812 0.598040
\(836\) −13.9864 −0.483731
\(837\) 0 0
\(838\) 3.77730 0.130485
\(839\) 20.4337 0.705451 0.352725 0.935727i \(-0.385255\pi\)
0.352725 + 0.935727i \(0.385255\pi\)
\(840\) 0 0
\(841\) −28.9922 −0.999729
\(842\) 1.48703 0.0512465
\(843\) 0 0
\(844\) 3.32934 0.114601
\(845\) 10.9214 0.375707
\(846\) 0 0
\(847\) −0.343235 −0.0117937
\(848\) −13.5526 −0.465398
\(849\) 0 0
\(850\) 0.795695 0.0272921
\(851\) −45.4313 −1.55736
\(852\) 0 0
\(853\) 16.6032 0.568482 0.284241 0.958753i \(-0.408258\pi\)
0.284241 + 0.958753i \(0.408258\pi\)
\(854\) −0.867873 −0.0296980
\(855\) 0 0
\(856\) −5.58797 −0.190993
\(857\) −37.1328 −1.26843 −0.634217 0.773155i \(-0.718677\pi\)
−0.634217 + 0.773155i \(0.718677\pi\)
\(858\) 0 0
\(859\) 36.9169 1.25959 0.629795 0.776762i \(-0.283139\pi\)
0.629795 + 0.776762i \(0.283139\pi\)
\(860\) −20.7030 −0.705967
\(861\) 0 0
\(862\) −4.72649 −0.160985
\(863\) 19.2588 0.655577 0.327788 0.944751i \(-0.393697\pi\)
0.327788 + 0.944751i \(0.393697\pi\)
\(864\) 0 0
\(865\) −14.9919 −0.509739
\(866\) 3.20359 0.108862
\(867\) 0 0
\(868\) −5.55428 −0.188524
\(869\) 1.87069 0.0634589
\(870\) 0 0
\(871\) −62.8817 −2.13066
\(872\) −8.10323 −0.274410
\(873\) 0 0
\(874\) −2.31052 −0.0781545
\(875\) −2.76137 −0.0933514
\(876\) 0 0
\(877\) 5.26192 0.177682 0.0888411 0.996046i \(-0.471684\pi\)
0.0888411 + 0.996046i \(0.471684\pi\)
\(878\) −0.168284 −0.00567930
\(879\) 0 0
\(880\) −12.7820 −0.430881
\(881\) −32.1477 −1.08308 −0.541541 0.840674i \(-0.682159\pi\)
−0.541541 + 0.840674i \(0.682159\pi\)
\(882\) 0 0
\(883\) 5.71530 0.192335 0.0961676 0.995365i \(-0.469342\pi\)
0.0961676 + 0.995365i \(0.469342\pi\)
\(884\) −45.7993 −1.54040
\(885\) 0 0
\(886\) 2.09432 0.0703601
\(887\) −0.829148 −0.0278401 −0.0139200 0.999903i \(-0.504431\pi\)
−0.0139200 + 0.999903i \(0.504431\pi\)
\(888\) 0 0
\(889\) −48.5772 −1.62923
\(890\) −0.167560 −0.00561664
\(891\) 0 0
\(892\) −38.5414 −1.29046
\(893\) −10.1551 −0.339826
\(894\) 0 0
\(895\) 11.1785 0.373657
\(896\) −14.2910 −0.477429
\(897\) 0 0
\(898\) −2.72587 −0.0909636
\(899\) −0.0903724 −0.00301409
\(900\) 0 0
\(901\) 16.7933 0.559465
\(902\) −2.97035 −0.0989017
\(903\) 0 0
\(904\) −0.507147 −0.0168675
\(905\) −4.51645 −0.150132
\(906\) 0 0
\(907\) −11.5923 −0.384916 −0.192458 0.981305i \(-0.561646\pi\)
−0.192458 + 0.981305i \(0.561646\pi\)
\(908\) −14.1353 −0.469096
\(909\) 0 0
\(910\) −2.26303 −0.0750186
\(911\) 50.4744 1.67229 0.836146 0.548507i \(-0.184804\pi\)
0.836146 + 0.548507i \(0.184804\pi\)
\(912\) 0 0
\(913\) −6.81192 −0.225442
\(914\) −0.0589022 −0.00194831
\(915\) 0 0
\(916\) −14.7346 −0.486843
\(917\) −45.4645 −1.50137
\(918\) 0 0
\(919\) 7.86726 0.259517 0.129759 0.991546i \(-0.458580\pi\)
0.129759 + 0.991546i \(0.458580\pi\)
\(920\) −4.31549 −0.142277
\(921\) 0 0
\(922\) −2.09558 −0.0690143
\(923\) 43.8130 1.44212
\(924\) 0 0
\(925\) 7.00644 0.230370
\(926\) 3.20916 0.105459
\(927\) 0 0
\(928\) −0.174823 −0.00573886
\(929\) −10.7076 −0.351305 −0.175652 0.984452i \(-0.556203\pi\)
−0.175652 + 0.984452i \(0.556203\pi\)
\(930\) 0 0
\(931\) −1.32947 −0.0435717
\(932\) 51.0823 1.67326
\(933\) 0 0
\(934\) −5.51303 −0.180392
\(935\) 15.8384 0.517971
\(936\) 0 0
\(937\) 27.0259 0.882896 0.441448 0.897287i \(-0.354465\pi\)
0.441448 + 0.897287i \(0.354465\pi\)
\(938\) 5.94877 0.194234
\(939\) 0 0
\(940\) −9.41655 −0.307134
\(941\) 22.0874 0.720029 0.360015 0.932947i \(-0.382772\pi\)
0.360015 + 0.932947i \(0.382772\pi\)
\(942\) 0 0
\(943\) 34.4633 1.12228
\(944\) 4.23268 0.137762
\(945\) 0 0
\(946\) 5.86748 0.190768
\(947\) 36.5249 1.18690 0.593449 0.804872i \(-0.297766\pi\)
0.593449 + 0.804872i \(0.297766\pi\)
\(948\) 0 0
\(949\) −21.2141 −0.688640
\(950\) 0.356330 0.0115609
\(951\) 0 0
\(952\) 8.72715 0.282848
\(953\) 44.9253 1.45527 0.727637 0.685962i \(-0.240618\pi\)
0.727637 + 0.685962i \(0.240618\pi\)
\(954\) 0 0
\(955\) −24.7702 −0.801544
\(956\) −44.7590 −1.44761
\(957\) 0 0
\(958\) −2.83292 −0.0915274
\(959\) −27.6688 −0.893473
\(960\) 0 0
\(961\) −29.9595 −0.966437
\(962\) 5.74198 0.185129
\(963\) 0 0
\(964\) −6.65225 −0.214255
\(965\) 27.4522 0.883717
\(966\) 0 0
\(967\) −37.0562 −1.19165 −0.595823 0.803116i \(-0.703174\pi\)
−0.595823 + 0.803116i \(0.703174\pi\)
\(968\) 0.0827254 0.00265890
\(969\) 0 0
\(970\) −1.77115 −0.0568681
\(971\) 31.3238 1.00523 0.502614 0.864511i \(-0.332372\pi\)
0.502614 + 0.864511i \(0.332372\pi\)
\(972\) 0 0
\(973\) −25.2797 −0.810429
\(974\) 5.95878 0.190931
\(975\) 0 0
\(976\) −7.18824 −0.230090
\(977\) 17.7676 0.568437 0.284219 0.958759i \(-0.408266\pi\)
0.284219 + 0.958759i \(0.408266\pi\)
\(978\) 0 0
\(979\) −3.33531 −0.106597
\(980\) −1.23279 −0.0393800
\(981\) 0 0
\(982\) 3.42145 0.109183
\(983\) 20.7240 0.660993 0.330496 0.943807i \(-0.392784\pi\)
0.330496 + 0.943807i \(0.392784\pi\)
\(984\) 0 0
\(985\) −8.84300 −0.281761
\(986\) 0.0704969 0.00224508
\(987\) 0 0
\(988\) −20.5099 −0.652507
\(989\) −68.0772 −2.16473
\(990\) 0 0
\(991\) 32.3041 1.02618 0.513088 0.858336i \(-0.328502\pi\)
0.513088 + 0.858336i \(0.328502\pi\)
\(992\) 2.01274 0.0639047
\(993\) 0 0
\(994\) −4.14482 −0.131466
\(995\) −12.1238 −0.384349
\(996\) 0 0
\(997\) 37.7989 1.19710 0.598551 0.801085i \(-0.295743\pi\)
0.598551 + 0.801085i \(0.295743\pi\)
\(998\) 4.29714 0.136024
\(999\) 0 0
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 4005.2.a.t.1.5 10
3.2 odd 2 1335.2.a.i.1.6 10
15.14 odd 2 6675.2.a.ba.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1335.2.a.i.1.6 10 3.2 odd 2
4005.2.a.t.1.5 10 1.1 even 1 trivial
6675.2.a.ba.1.5 10 15.14 odd 2