Properties

Label 260.2.a.b.1.2
Level $260$
Weight $2$
Character 260.1
Self dual yes
Analytic conductor $2.076$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.08613\) of defining polynomial
Character \(\chi\) \(=\) 260.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.35194 q^{3} +1.00000 q^{5} +4.17226 q^{7} -1.17226 q^{9} +O(q^{10})\) \(q+1.35194 q^{3} +1.00000 q^{5} +4.17226 q^{7} -1.17226 q^{9} -5.52420 q^{11} +1.00000 q^{13} +1.35194 q^{15} -0.703878 q^{17} +6.82032 q^{19} +5.64064 q^{21} -2.64806 q^{23} +1.00000 q^{25} -5.64064 q^{27} +8.17226 q^{29} -9.52420 q^{31} -7.46838 q^{33} +4.17226 q^{35} -6.87614 q^{37} +1.35194 q^{39} +0.703878 q^{41} -1.35194 q^{43} -1.17226 q^{45} -8.17226 q^{47} +10.4078 q^{49} -0.951601 q^{51} +5.04840 q^{53} -5.52420 q^{55} +9.22066 q^{57} -12.2281 q^{59} -0.172260 q^{61} -4.89098 q^{63} +1.00000 q^{65} +10.8761 q^{67} -3.58002 q^{69} -5.52420 q^{71} -11.2207 q^{73} +1.35194 q^{75} -23.0484 q^{77} +1.29612 q^{79} -4.10902 q^{81} -9.58002 q^{83} -0.703878 q^{85} +11.0484 q^{87} +11.7523 q^{89} +4.17226 q^{91} -12.8761 q^{93} +6.82032 q^{95} +18.3445 q^{97} +6.47580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9} + 3 q^{13} + 2 q^{15} + 2 q^{17} + 8 q^{19} - 8 q^{21} - 10 q^{23} + 3 q^{25} + 8 q^{27} + 10 q^{29} - 12 q^{31} - 12 q^{33} - 2 q^{35} - 2 q^{37} + 2 q^{39} - 2 q^{41} - 2 q^{43} + 11 q^{45} - 10 q^{47} + 23 q^{49} - 36 q^{51} - 18 q^{53} - 20 q^{57} - 16 q^{59} + 14 q^{61} - 50 q^{63} + 3 q^{65} + 14 q^{67} + 12 q^{69} + 14 q^{73} + 2 q^{75} - 36 q^{77} + 8 q^{79} + 23 q^{81} - 6 q^{83} + 2 q^{85} - 2 q^{89} - 2 q^{91} - 20 q^{93} + 8 q^{95} + 26 q^{97} + 36 q^{99}+O(q^{100}) \) 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 0
\(3\) 1.35194 0.780542 0.390271 0.920700i \(-0.372381\pi\)
0.390271 + 0.920700i \(0.372381\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 4.17226 1.57697 0.788483 0.615056i \(-0.210867\pi\)
0.788483 + 0.615056i \(0.210867\pi\)
\(8\) 0 0
\(9\) −1.17226 −0.390753
\(10\) 0 0
\(11\) −5.52420 −1.66561 −0.832804 0.553567i \(-0.813266\pi\)
−0.832804 + 0.553567i \(0.813266\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.35194 0.349069
\(16\) 0 0
\(17\) −0.703878 −0.170716 −0.0853578 0.996350i \(-0.527203\pi\)
−0.0853578 + 0.996350i \(0.527203\pi\)
\(18\) 0 0
\(19\) 6.82032 1.56469 0.782344 0.622846i \(-0.214024\pi\)
0.782344 + 0.622846i \(0.214024\pi\)
\(20\) 0 0
\(21\) 5.64064 1.23089
\(22\) 0 0
\(23\) −2.64806 −0.552159 −0.276079 0.961135i \(-0.589035\pi\)
−0.276079 + 0.961135i \(0.589035\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.64064 −1.08554
\(28\) 0 0
\(29\) 8.17226 1.51755 0.758775 0.651352i \(-0.225798\pi\)
0.758775 + 0.651352i \(0.225798\pi\)
\(30\) 0 0
\(31\) −9.52420 −1.71060 −0.855298 0.518136i \(-0.826626\pi\)
−0.855298 + 0.518136i \(0.826626\pi\)
\(32\) 0 0
\(33\) −7.46838 −1.30008
\(34\) 0 0
\(35\) 4.17226 0.705241
\(36\) 0 0
\(37\) −6.87614 −1.13043 −0.565215 0.824944i \(-0.691207\pi\)
−0.565215 + 0.824944i \(0.691207\pi\)
\(38\) 0 0
\(39\) 1.35194 0.216484
\(40\) 0 0
\(41\) 0.703878 0.109927 0.0549637 0.998488i \(-0.482496\pi\)
0.0549637 + 0.998488i \(0.482496\pi\)
\(42\) 0 0
\(43\) −1.35194 −0.206169 −0.103084 0.994673i \(-0.532871\pi\)
−0.103084 + 0.994673i \(0.532871\pi\)
\(44\) 0 0
\(45\) −1.17226 −0.174750
\(46\) 0 0
\(47\) −8.17226 −1.19205 −0.596023 0.802967i \(-0.703253\pi\)
−0.596023 + 0.802967i \(0.703253\pi\)
\(48\) 0 0
\(49\) 10.4078 1.48682
\(50\) 0 0
\(51\) −0.951601 −0.133251
\(52\) 0 0
\(53\) 5.04840 0.693451 0.346725 0.937967i \(-0.387294\pi\)
0.346725 + 0.937967i \(0.387294\pi\)
\(54\) 0 0
\(55\) −5.52420 −0.744883
\(56\) 0 0
\(57\) 9.22066 1.22131
\(58\) 0 0
\(59\) −12.2281 −1.59196 −0.795980 0.605323i \(-0.793044\pi\)
−0.795980 + 0.605323i \(0.793044\pi\)
\(60\) 0 0
\(61\) −0.172260 −0.0220557 −0.0110278 0.999939i \(-0.503510\pi\)
−0.0110278 + 0.999939i \(0.503510\pi\)
\(62\) 0 0
\(63\) −4.89098 −0.616205
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 10.8761 1.32873 0.664366 0.747407i \(-0.268702\pi\)
0.664366 + 0.747407i \(0.268702\pi\)
\(68\) 0 0
\(69\) −3.58002 −0.430983
\(70\) 0 0
\(71\) −5.52420 −0.655602 −0.327801 0.944747i \(-0.606308\pi\)
−0.327801 + 0.944747i \(0.606308\pi\)
\(72\) 0 0
\(73\) −11.2207 −1.31328 −0.656639 0.754205i \(-0.728023\pi\)
−0.656639 + 0.754205i \(0.728023\pi\)
\(74\) 0 0
\(75\) 1.35194 0.156108
\(76\) 0 0
\(77\) −23.0484 −2.62661
\(78\) 0 0
\(79\) 1.29612 0.145825 0.0729125 0.997338i \(-0.476771\pi\)
0.0729125 + 0.997338i \(0.476771\pi\)
\(80\) 0 0
\(81\) −4.10902 −0.456558
\(82\) 0 0
\(83\) −9.58002 −1.05154 −0.525772 0.850626i \(-0.676223\pi\)
−0.525772 + 0.850626i \(0.676223\pi\)
\(84\) 0 0
\(85\) −0.703878 −0.0763463
\(86\) 0 0
\(87\) 11.0484 1.18451
\(88\) 0 0
\(89\) 11.7523 1.24574 0.622869 0.782326i \(-0.285967\pi\)
0.622869 + 0.782326i \(0.285967\pi\)
\(90\) 0 0
\(91\) 4.17226 0.437372
\(92\) 0 0
\(93\) −12.8761 −1.33519
\(94\) 0 0
\(95\) 6.82032 0.699750
\(96\) 0 0
\(97\) 18.3445 1.86260 0.931302 0.364248i \(-0.118674\pi\)
0.931302 + 0.364248i \(0.118674\pi\)
\(98\) 0 0
\(99\) 6.47580 0.650842
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −10.9926 −1.08313 −0.541566 0.840658i \(-0.682168\pi\)
−0.541566 + 0.840658i \(0.682168\pi\)
\(104\) 0 0
\(105\) 5.64064 0.550470
\(106\) 0 0
\(107\) 6.99258 0.675998 0.337999 0.941146i \(-0.390250\pi\)
0.337999 + 0.941146i \(0.390250\pi\)
\(108\) 0 0
\(109\) 3.40776 0.326404 0.163202 0.986593i \(-0.447818\pi\)
0.163202 + 0.986593i \(0.447818\pi\)
\(110\) 0 0
\(111\) −9.29612 −0.882349
\(112\) 0 0
\(113\) 3.64064 0.342483 0.171241 0.985229i \(-0.445222\pi\)
0.171241 + 0.985229i \(0.445222\pi\)
\(114\) 0 0
\(115\) −2.64806 −0.246933
\(116\) 0 0
\(117\) −1.17226 −0.108376
\(118\) 0 0
\(119\) −2.93676 −0.269213
\(120\) 0 0
\(121\) 19.5168 1.77425
\(122\) 0 0
\(123\) 0.951601 0.0858030
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.69646 −0.505479 −0.252740 0.967534i \(-0.581332\pi\)
−0.252740 + 0.967534i \(0.581332\pi\)
\(128\) 0 0
\(129\) −1.82774 −0.160923
\(130\) 0 0
\(131\) 17.7523 1.55102 0.775512 0.631333i \(-0.217492\pi\)
0.775512 + 0.631333i \(0.217492\pi\)
\(132\) 0 0
\(133\) 28.4562 2.46746
\(134\) 0 0
\(135\) −5.64064 −0.485469
\(136\) 0 0
\(137\) −8.93676 −0.763519 −0.381760 0.924262i \(-0.624682\pi\)
−0.381760 + 0.924262i \(0.624682\pi\)
\(138\) 0 0
\(139\) 13.2961 1.12776 0.563881 0.825856i \(-0.309308\pi\)
0.563881 + 0.825856i \(0.309308\pi\)
\(140\) 0 0
\(141\) −11.0484 −0.930443
\(142\) 0 0
\(143\) −5.52420 −0.461957
\(144\) 0 0
\(145\) 8.17226 0.678669
\(146\) 0 0
\(147\) 14.0707 1.16053
\(148\) 0 0
\(149\) −8.93676 −0.732128 −0.366064 0.930590i \(-0.619295\pi\)
−0.366064 + 0.930590i \(0.619295\pi\)
\(150\) 0 0
\(151\) 2.93196 0.238599 0.119300 0.992858i \(-0.461935\pi\)
0.119300 + 0.992858i \(0.461935\pi\)
\(152\) 0 0
\(153\) 0.825129 0.0667077
\(154\) 0 0
\(155\) −9.52420 −0.765002
\(156\) 0 0
\(157\) 0.592243 0.0472662 0.0236331 0.999721i \(-0.492477\pi\)
0.0236331 + 0.999721i \(0.492477\pi\)
\(158\) 0 0
\(159\) 6.82513 0.541268
\(160\) 0 0
\(161\) −11.0484 −0.870736
\(162\) 0 0
\(163\) 16.6284 1.30244 0.651219 0.758890i \(-0.274258\pi\)
0.651219 + 0.758890i \(0.274258\pi\)
\(164\) 0 0
\(165\) −7.46838 −0.581413
\(166\) 0 0
\(167\) −3.82774 −0.296199 −0.148100 0.988972i \(-0.547316\pi\)
−0.148100 + 0.988972i \(0.547316\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −7.99519 −0.611408
\(172\) 0 0
\(173\) 14.1116 1.07289 0.536444 0.843936i \(-0.319767\pi\)
0.536444 + 0.843936i \(0.319767\pi\)
\(174\) 0 0
\(175\) 4.17226 0.315393
\(176\) 0 0
\(177\) −16.5316 −1.24259
\(178\) 0 0
\(179\) 5.75228 0.429945 0.214973 0.976620i \(-0.431034\pi\)
0.214973 + 0.976620i \(0.431034\pi\)
\(180\) 0 0
\(181\) 2.76450 0.205484 0.102742 0.994708i \(-0.467238\pi\)
0.102742 + 0.994708i \(0.467238\pi\)
\(182\) 0 0
\(183\) −0.232886 −0.0172154
\(184\) 0 0
\(185\) −6.87614 −0.505544
\(186\) 0 0
\(187\) 3.88836 0.284345
\(188\) 0 0
\(189\) −23.5342 −1.71186
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −14.3445 −1.03254 −0.516271 0.856426i \(-0.672680\pi\)
−0.516271 + 0.856426i \(0.672680\pi\)
\(194\) 0 0
\(195\) 1.35194 0.0968144
\(196\) 0 0
\(197\) −7.40776 −0.527781 −0.263890 0.964553i \(-0.585006\pi\)
−0.263890 + 0.964553i \(0.585006\pi\)
\(198\) 0 0
\(199\) 1.75228 0.124216 0.0621078 0.998069i \(-0.480218\pi\)
0.0621078 + 0.998069i \(0.480218\pi\)
\(200\) 0 0
\(201\) 14.7039 1.03713
\(202\) 0 0
\(203\) 34.0968 2.39313
\(204\) 0 0
\(205\) 0.703878 0.0491610
\(206\) 0 0
\(207\) 3.10422 0.215758
\(208\) 0 0
\(209\) −37.6768 −2.60616
\(210\) 0 0
\(211\) −9.75228 −0.671374 −0.335687 0.941974i \(-0.608969\pi\)
−0.335687 + 0.941974i \(0.608969\pi\)
\(212\) 0 0
\(213\) −7.46838 −0.511725
\(214\) 0 0
\(215\) −1.35194 −0.0922015
\(216\) 0 0
\(217\) −39.7374 −2.69755
\(218\) 0 0
\(219\) −15.1696 −1.02507
\(220\) 0 0
\(221\) −0.703878 −0.0473480
\(222\) 0 0
\(223\) 2.76450 0.185125 0.0925624 0.995707i \(-0.470494\pi\)
0.0925624 + 0.995707i \(0.470494\pi\)
\(224\) 0 0
\(225\) −1.17226 −0.0781507
\(226\) 0 0
\(227\) 17.8129 1.18228 0.591142 0.806568i \(-0.298677\pi\)
0.591142 + 0.806568i \(0.298677\pi\)
\(228\) 0 0
\(229\) 10.1116 0.668196 0.334098 0.942538i \(-0.391568\pi\)
0.334098 + 0.942538i \(0.391568\pi\)
\(230\) 0 0
\(231\) −31.1600 −2.05018
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −8.17226 −0.533099
\(236\) 0 0
\(237\) 1.75228 0.113823
\(238\) 0 0
\(239\) 9.86872 0.638354 0.319177 0.947695i \(-0.396593\pi\)
0.319177 + 0.947695i \(0.396593\pi\)
\(240\) 0 0
\(241\) −1.88836 −0.121640 −0.0608201 0.998149i \(-0.519372\pi\)
−0.0608201 + 0.998149i \(0.519372\pi\)
\(242\) 0 0
\(243\) 11.3668 0.729179
\(244\) 0 0
\(245\) 10.4078 0.664927
\(246\) 0 0
\(247\) 6.82032 0.433967
\(248\) 0 0
\(249\) −12.9516 −0.820774
\(250\) 0 0
\(251\) 2.35936 0.148921 0.0744607 0.997224i \(-0.476276\pi\)
0.0744607 + 0.997224i \(0.476276\pi\)
\(252\) 0 0
\(253\) 14.6284 0.919681
\(254\) 0 0
\(255\) −0.951601 −0.0595916
\(256\) 0 0
\(257\) −1.65548 −0.103266 −0.0516330 0.998666i \(-0.516443\pi\)
−0.0516330 + 0.998666i \(0.516443\pi\)
\(258\) 0 0
\(259\) −28.6890 −1.78265
\(260\) 0 0
\(261\) −9.58002 −0.592988
\(262\) 0 0
\(263\) −16.6332 −1.02565 −0.512824 0.858494i \(-0.671401\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(264\) 0 0
\(265\) 5.04840 0.310121
\(266\) 0 0
\(267\) 15.8884 0.972352
\(268\) 0 0
\(269\) 16.0968 0.981439 0.490720 0.871318i \(-0.336734\pi\)
0.490720 + 0.871318i \(0.336734\pi\)
\(270\) 0 0
\(271\) −10.4758 −0.636360 −0.318180 0.948030i \(-0.603072\pi\)
−0.318180 + 0.948030i \(0.603072\pi\)
\(272\) 0 0
\(273\) 5.64064 0.341387
\(274\) 0 0
\(275\) −5.52420 −0.333122
\(276\) 0 0
\(277\) 17.3929 1.04504 0.522520 0.852627i \(-0.324992\pi\)
0.522520 + 0.852627i \(0.324992\pi\)
\(278\) 0 0
\(279\) 11.1648 0.668422
\(280\) 0 0
\(281\) 11.2961 0.673870 0.336935 0.941528i \(-0.390610\pi\)
0.336935 + 0.941528i \(0.390610\pi\)
\(282\) 0 0
\(283\) 9.24030 0.549279 0.274640 0.961547i \(-0.411441\pi\)
0.274640 + 0.961547i \(0.411441\pi\)
\(284\) 0 0
\(285\) 9.22066 0.546185
\(286\) 0 0
\(287\) 2.93676 0.173352
\(288\) 0 0
\(289\) −16.5046 −0.970856
\(290\) 0 0
\(291\) 24.8007 1.45384
\(292\) 0 0
\(293\) −16.4051 −0.958399 −0.479199 0.877706i \(-0.659073\pi\)
−0.479199 + 0.877706i \(0.659073\pi\)
\(294\) 0 0
\(295\) −12.2281 −0.711946
\(296\) 0 0
\(297\) 31.1600 1.80809
\(298\) 0 0
\(299\) −2.64806 −0.153141
\(300\) 0 0
\(301\) −5.64064 −0.325121
\(302\) 0 0
\(303\) 8.11164 0.466001
\(304\) 0 0
\(305\) −0.172260 −0.00986360
\(306\) 0 0
\(307\) −15.1090 −0.862318 −0.431159 0.902276i \(-0.641895\pi\)
−0.431159 + 0.902276i \(0.641895\pi\)
\(308\) 0 0
\(309\) −14.8613 −0.845430
\(310\) 0 0
\(311\) −8.11164 −0.459969 −0.229984 0.973194i \(-0.573867\pi\)
−0.229984 + 0.973194i \(0.573867\pi\)
\(312\) 0 0
\(313\) −1.39292 −0.0787325 −0.0393662 0.999225i \(-0.512534\pi\)
−0.0393662 + 0.999225i \(0.512534\pi\)
\(314\) 0 0
\(315\) −4.89098 −0.275575
\(316\) 0 0
\(317\) −29.8129 −1.67446 −0.837230 0.546851i \(-0.815826\pi\)
−0.837230 + 0.546851i \(0.815826\pi\)
\(318\) 0 0
\(319\) −45.1452 −2.52765
\(320\) 0 0
\(321\) 9.45355 0.527645
\(322\) 0 0
\(323\) −4.80068 −0.267117
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 4.60708 0.254772
\(328\) 0 0
\(329\) −34.0968 −1.87982
\(330\) 0 0
\(331\) −19.1648 −1.05339 −0.526697 0.850053i \(-0.676570\pi\)
−0.526697 + 0.850053i \(0.676570\pi\)
\(332\) 0 0
\(333\) 8.06063 0.441720
\(334\) 0 0
\(335\) 10.8761 0.594227
\(336\) 0 0
\(337\) 11.6406 0.634106 0.317053 0.948408i \(-0.397307\pi\)
0.317053 + 0.948408i \(0.397307\pi\)
\(338\) 0 0
\(339\) 4.92193 0.267322
\(340\) 0 0
\(341\) 52.6136 2.84919
\(342\) 0 0
\(343\) 14.2180 0.767702
\(344\) 0 0
\(345\) −3.58002 −0.192742
\(346\) 0 0
\(347\) −22.7597 −1.22180 −0.610902 0.791706i \(-0.709193\pi\)
−0.610902 + 0.791706i \(0.709193\pi\)
\(348\) 0 0
\(349\) 1.04840 0.0561195 0.0280598 0.999606i \(-0.491067\pi\)
0.0280598 + 0.999606i \(0.491067\pi\)
\(350\) 0 0
\(351\) −5.64064 −0.301075
\(352\) 0 0
\(353\) 4.40515 0.234462 0.117231 0.993105i \(-0.462598\pi\)
0.117231 + 0.993105i \(0.462598\pi\)
\(354\) 0 0
\(355\) −5.52420 −0.293194
\(356\) 0 0
\(357\) −3.97033 −0.210132
\(358\) 0 0
\(359\) 24.2281 1.27871 0.639355 0.768912i \(-0.279202\pi\)
0.639355 + 0.768912i \(0.279202\pi\)
\(360\) 0 0
\(361\) 27.5168 1.44825
\(362\) 0 0
\(363\) 26.3855 1.38488
\(364\) 0 0
\(365\) −11.2207 −0.587316
\(366\) 0 0
\(367\) −27.3371 −1.42699 −0.713493 0.700663i \(-0.752888\pi\)
−0.713493 + 0.700663i \(0.752888\pi\)
\(368\) 0 0
\(369\) −0.825129 −0.0429545
\(370\) 0 0
\(371\) 21.0632 1.09355
\(372\) 0 0
\(373\) 22.6890 1.17479 0.587397 0.809299i \(-0.300153\pi\)
0.587397 + 0.809299i \(0.300153\pi\)
\(374\) 0 0
\(375\) 1.35194 0.0698138
\(376\) 0 0
\(377\) 8.17226 0.420893
\(378\) 0 0
\(379\) 30.3249 1.55768 0.778842 0.627220i \(-0.215807\pi\)
0.778842 + 0.627220i \(0.215807\pi\)
\(380\) 0 0
\(381\) −7.70127 −0.394548
\(382\) 0 0
\(383\) −5.23550 −0.267521 −0.133761 0.991014i \(-0.542705\pi\)
−0.133761 + 0.991014i \(0.542705\pi\)
\(384\) 0 0
\(385\) −23.0484 −1.17466
\(386\) 0 0
\(387\) 1.58482 0.0805612
\(388\) 0 0
\(389\) 23.8735 1.21044 0.605218 0.796060i \(-0.293086\pi\)
0.605218 + 0.796060i \(0.293086\pi\)
\(390\) 0 0
\(391\) 1.86391 0.0942621
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) 1.29612 0.0652150
\(396\) 0 0
\(397\) 39.2207 1.96843 0.984214 0.176981i \(-0.0566332\pi\)
0.984214 + 0.176981i \(0.0566332\pi\)
\(398\) 0 0
\(399\) 38.4710 1.92596
\(400\) 0 0
\(401\) 31.0336 1.54974 0.774871 0.632119i \(-0.217815\pi\)
0.774871 + 0.632119i \(0.217815\pi\)
\(402\) 0 0
\(403\) −9.52420 −0.474434
\(404\) 0 0
\(405\) −4.10902 −0.204179
\(406\) 0 0
\(407\) 37.9852 1.88285
\(408\) 0 0
\(409\) −18.1116 −0.895563 −0.447781 0.894143i \(-0.647786\pi\)
−0.447781 + 0.894143i \(0.647786\pi\)
\(410\) 0 0
\(411\) −12.0820 −0.595959
\(412\) 0 0
\(413\) −51.0187 −2.51047
\(414\) 0 0
\(415\) −9.58002 −0.470265
\(416\) 0 0
\(417\) 17.9755 0.880266
\(418\) 0 0
\(419\) −23.0484 −1.12599 −0.562994 0.826461i \(-0.690351\pi\)
−0.562994 + 0.826461i \(0.690351\pi\)
\(420\) 0 0
\(421\) −34.9123 −1.70152 −0.850761 0.525553i \(-0.823859\pi\)
−0.850761 + 0.525553i \(0.823859\pi\)
\(422\) 0 0
\(423\) 9.58002 0.465796
\(424\) 0 0
\(425\) −0.703878 −0.0341431
\(426\) 0 0
\(427\) −0.718715 −0.0347811
\(428\) 0 0
\(429\) −7.46838 −0.360577
\(430\) 0 0
\(431\) 6.47580 0.311928 0.155964 0.987763i \(-0.450152\pi\)
0.155964 + 0.987763i \(0.450152\pi\)
\(432\) 0 0
\(433\) −24.8155 −1.19256 −0.596279 0.802777i \(-0.703355\pi\)
−0.596279 + 0.802777i \(0.703355\pi\)
\(434\) 0 0
\(435\) 11.0484 0.529730
\(436\) 0 0
\(437\) −18.0606 −0.863957
\(438\) 0 0
\(439\) 10.8155 0.516196 0.258098 0.966119i \(-0.416904\pi\)
0.258098 + 0.966119i \(0.416904\pi\)
\(440\) 0 0
\(441\) −12.2006 −0.580981
\(442\) 0 0
\(443\) 18.0410 0.857153 0.428576 0.903506i \(-0.359015\pi\)
0.428576 + 0.903506i \(0.359015\pi\)
\(444\) 0 0
\(445\) 11.7523 0.557111
\(446\) 0 0
\(447\) −12.0820 −0.571457
\(448\) 0 0
\(449\) 27.1452 1.28106 0.640531 0.767933i \(-0.278714\pi\)
0.640531 + 0.767933i \(0.278714\pi\)
\(450\) 0 0
\(451\) −3.88836 −0.183096
\(452\) 0 0
\(453\) 3.96383 0.186237
\(454\) 0 0
\(455\) 4.17226 0.195599
\(456\) 0 0
\(457\) −3.75228 −0.175524 −0.0877621 0.996141i \(-0.527972\pi\)
−0.0877621 + 0.996141i \(0.527972\pi\)
\(458\) 0 0
\(459\) 3.97033 0.185319
\(460\) 0 0
\(461\) 36.3297 1.69204 0.846021 0.533150i \(-0.178992\pi\)
0.846021 + 0.533150i \(0.178992\pi\)
\(462\) 0 0
\(463\) −29.4684 −1.36951 −0.684756 0.728772i \(-0.740091\pi\)
−0.684756 + 0.728772i \(0.740091\pi\)
\(464\) 0 0
\(465\) −12.8761 −0.597117
\(466\) 0 0
\(467\) −17.5848 −0.813729 −0.406864 0.913489i \(-0.633378\pi\)
−0.406864 + 0.913489i \(0.633378\pi\)
\(468\) 0 0
\(469\) 45.3781 2.09537
\(470\) 0 0
\(471\) 0.800677 0.0368932
\(472\) 0 0
\(473\) 7.46838 0.343397
\(474\) 0 0
\(475\) 6.82032 0.312938
\(476\) 0 0
\(477\) −5.91804 −0.270968
\(478\) 0 0
\(479\) −11.2765 −0.515235 −0.257618 0.966247i \(-0.582938\pi\)
−0.257618 + 0.966247i \(0.582938\pi\)
\(480\) 0 0
\(481\) −6.87614 −0.313525
\(482\) 0 0
\(483\) −14.9368 −0.679646
\(484\) 0 0
\(485\) 18.3445 0.832982
\(486\) 0 0
\(487\) −26.1574 −1.18531 −0.592653 0.805458i \(-0.701919\pi\)
−0.592653 + 0.805458i \(0.701919\pi\)
\(488\) 0 0
\(489\) 22.4806 1.01661
\(490\) 0 0
\(491\) 0.456156 0.0205860 0.0102930 0.999947i \(-0.496724\pi\)
0.0102930 + 0.999947i \(0.496724\pi\)
\(492\) 0 0
\(493\) −5.75228 −0.259070
\(494\) 0 0
\(495\) 6.47580 0.291066
\(496\) 0 0
\(497\) −23.0484 −1.03386
\(498\) 0 0
\(499\) −12.4610 −0.557829 −0.278915 0.960316i \(-0.589975\pi\)
−0.278915 + 0.960316i \(0.589975\pi\)
\(500\) 0 0
\(501\) −5.17487 −0.231196
\(502\) 0 0
\(503\) −11.7933 −0.525835 −0.262918 0.964818i \(-0.584685\pi\)
−0.262918 + 0.964818i \(0.584685\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 1.35194 0.0600417
\(508\) 0 0
\(509\) −29.0484 −1.28755 −0.643774 0.765216i \(-0.722632\pi\)
−0.643774 + 0.765216i \(0.722632\pi\)
\(510\) 0 0
\(511\) −46.8155 −2.07100
\(512\) 0 0
\(513\) −38.4710 −1.69854
\(514\) 0 0
\(515\) −10.9926 −0.484391
\(516\) 0 0
\(517\) 45.1452 1.98548
\(518\) 0 0
\(519\) 19.0781 0.837434
\(520\) 0 0
\(521\) −15.3323 −0.671720 −0.335860 0.941912i \(-0.609027\pi\)
−0.335860 + 0.941912i \(0.609027\pi\)
\(522\) 0 0
\(523\) 15.4487 0.675526 0.337763 0.941231i \(-0.390330\pi\)
0.337763 + 0.941231i \(0.390330\pi\)
\(524\) 0 0
\(525\) 5.64064 0.246178
\(526\) 0 0
\(527\) 6.70388 0.292026
\(528\) 0 0
\(529\) −15.9878 −0.695121
\(530\) 0 0
\(531\) 14.3345 0.622064
\(532\) 0 0
\(533\) 0.703878 0.0304884
\(534\) 0 0
\(535\) 6.99258 0.302316
\(536\) 0 0
\(537\) 7.77673 0.335591
\(538\) 0 0
\(539\) −57.4945 −2.47646
\(540\) 0 0
\(541\) −38.8007 −1.66817 −0.834086 0.551635i \(-0.814004\pi\)
−0.834086 + 0.551635i \(0.814004\pi\)
\(542\) 0 0
\(543\) 3.73744 0.160389
\(544\) 0 0
\(545\) 3.40776 0.145972
\(546\) 0 0
\(547\) 14.9926 0.641036 0.320518 0.947242i \(-0.396143\pi\)
0.320518 + 0.947242i \(0.396143\pi\)
\(548\) 0 0
\(549\) 0.201934 0.00861833
\(550\) 0 0
\(551\) 55.7374 2.37449
\(552\) 0 0
\(553\) 5.40776 0.229961
\(554\) 0 0
\(555\) −9.29612 −0.394598
\(556\) 0 0
\(557\) −26.3807 −1.11779 −0.558893 0.829240i \(-0.688774\pi\)
−0.558893 + 0.829240i \(0.688774\pi\)
\(558\) 0 0
\(559\) −1.35194 −0.0571809
\(560\) 0 0
\(561\) 5.25683 0.221944
\(562\) 0 0
\(563\) −42.0410 −1.77182 −0.885908 0.463861i \(-0.846464\pi\)
−0.885908 + 0.463861i \(0.846464\pi\)
\(564\) 0 0
\(565\) 3.64064 0.153163
\(566\) 0 0
\(567\) −17.1439 −0.719977
\(568\) 0 0
\(569\) 30.2691 1.26894 0.634472 0.772945i \(-0.281217\pi\)
0.634472 + 0.772945i \(0.281217\pi\)
\(570\) 0 0
\(571\) −12.1116 −0.506856 −0.253428 0.967354i \(-0.581558\pi\)
−0.253428 + 0.967354i \(0.581558\pi\)
\(572\) 0 0
\(573\) 16.2233 0.677737
\(574\) 0 0
\(575\) −2.64806 −0.110432
\(576\) 0 0
\(577\) −8.40515 −0.349911 −0.174955 0.984576i \(-0.555978\pi\)
−0.174955 + 0.984576i \(0.555978\pi\)
\(578\) 0 0
\(579\) −19.3929 −0.805942
\(580\) 0 0
\(581\) −39.9703 −1.65825
\(582\) 0 0
\(583\) −27.8884 −1.15502
\(584\) 0 0
\(585\) −1.17226 −0.0484670
\(586\) 0 0
\(587\) 47.4439 1.95822 0.979110 0.203330i \(-0.0651764\pi\)
0.979110 + 0.203330i \(0.0651764\pi\)
\(588\) 0 0
\(589\) −64.9581 −2.67655
\(590\) 0 0
\(591\) −10.0148 −0.411955
\(592\) 0 0
\(593\) 32.4413 1.33221 0.666103 0.745860i \(-0.267961\pi\)
0.666103 + 0.745860i \(0.267961\pi\)
\(594\) 0 0
\(595\) −2.93676 −0.120396
\(596\) 0 0
\(597\) 2.36897 0.0969556
\(598\) 0 0
\(599\) −34.6742 −1.41675 −0.708375 0.705836i \(-0.750571\pi\)
−0.708375 + 0.705836i \(0.750571\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −12.7497 −0.519207
\(604\) 0 0
\(605\) 19.5168 0.793470
\(606\) 0 0
\(607\) −2.30354 −0.0934978 −0.0467489 0.998907i \(-0.514886\pi\)
−0.0467489 + 0.998907i \(0.514886\pi\)
\(608\) 0 0
\(609\) 46.0968 1.86794
\(610\) 0 0
\(611\) −8.17226 −0.330614
\(612\) 0 0
\(613\) −15.8735 −0.641126 −0.320563 0.947227i \(-0.603872\pi\)
−0.320563 + 0.947227i \(0.603872\pi\)
\(614\) 0 0
\(615\) 0.951601 0.0383722
\(616\) 0 0
\(617\) 10.3445 0.416455 0.208227 0.978080i \(-0.433231\pi\)
0.208227 + 0.978080i \(0.433231\pi\)
\(618\) 0 0
\(619\) 37.1500 1.49318 0.746592 0.665282i \(-0.231689\pi\)
0.746592 + 0.665282i \(0.231689\pi\)
\(620\) 0 0
\(621\) 14.9368 0.599392
\(622\) 0 0
\(623\) 49.0336 1.96449
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −50.9368 −2.03422
\(628\) 0 0
\(629\) 4.83997 0.192982
\(630\) 0 0
\(631\) 10.2132 0.406583 0.203291 0.979118i \(-0.434836\pi\)
0.203291 + 0.979118i \(0.434836\pi\)
\(632\) 0 0
\(633\) −13.1845 −0.524036
\(634\) 0 0
\(635\) −5.69646 −0.226057
\(636\) 0 0
\(637\) 10.4078 0.412370
\(638\) 0 0
\(639\) 6.47580 0.256179
\(640\) 0 0
\(641\) −16.0968 −0.635785 −0.317893 0.948127i \(-0.602975\pi\)
−0.317893 + 0.948127i \(0.602975\pi\)
\(642\) 0 0
\(643\) −18.0458 −0.711656 −0.355828 0.934551i \(-0.615801\pi\)
−0.355828 + 0.934551i \(0.615801\pi\)
\(644\) 0 0
\(645\) −1.82774 −0.0719672
\(646\) 0 0
\(647\) −43.5700 −1.71291 −0.856456 0.516219i \(-0.827339\pi\)
−0.856456 + 0.516219i \(0.827339\pi\)
\(648\) 0 0
\(649\) 67.5503 2.65158
\(650\) 0 0
\(651\) −53.7226 −2.10555
\(652\) 0 0
\(653\) −22.3445 −0.874409 −0.437204 0.899362i \(-0.644031\pi\)
−0.437204 + 0.899362i \(0.644031\pi\)
\(654\) 0 0
\(655\) 17.7523 0.693639
\(656\) 0 0
\(657\) 13.1535 0.513168
\(658\) 0 0
\(659\) 28.9219 1.12664 0.563319 0.826239i \(-0.309524\pi\)
0.563319 + 0.826239i \(0.309524\pi\)
\(660\) 0 0
\(661\) −18.6890 −0.726919 −0.363460 0.931610i \(-0.618405\pi\)
−0.363460 + 0.931610i \(0.618405\pi\)
\(662\) 0 0
\(663\) −0.951601 −0.0369571
\(664\) 0 0
\(665\) 28.4562 1.10348
\(666\) 0 0
\(667\) −21.6406 −0.837929
\(668\) 0 0
\(669\) 3.73744 0.144498
\(670\) 0 0
\(671\) 0.951601 0.0367361
\(672\) 0 0
\(673\) 23.5194 0.906606 0.453303 0.891357i \(-0.350246\pi\)
0.453303 + 0.891357i \(0.350246\pi\)
\(674\) 0 0
\(675\) −5.64064 −0.217108
\(676\) 0 0
\(677\) −8.35936 −0.321276 −0.160638 0.987013i \(-0.551355\pi\)
−0.160638 + 0.987013i \(0.551355\pi\)
\(678\) 0 0
\(679\) 76.5381 2.93726
\(680\) 0 0
\(681\) 24.0820 0.922823
\(682\) 0 0
\(683\) −11.9394 −0.456847 −0.228424 0.973562i \(-0.573357\pi\)
−0.228424 + 0.973562i \(0.573357\pi\)
\(684\) 0 0
\(685\) −8.93676 −0.341456
\(686\) 0 0
\(687\) 13.6703 0.521555
\(688\) 0 0
\(689\) 5.04840 0.192329
\(690\) 0 0
\(691\) 15.4274 0.586886 0.293443 0.955977i \(-0.405199\pi\)
0.293443 + 0.955977i \(0.405199\pi\)
\(692\) 0 0
\(693\) 27.0187 1.02636
\(694\) 0 0
\(695\) 13.2961 0.504351
\(696\) 0 0
\(697\) −0.495445 −0.0187663
\(698\) 0 0
\(699\) −8.11164 −0.306810
\(700\) 0 0
\(701\) 37.2813 1.40809 0.704047 0.710153i \(-0.251374\pi\)
0.704047 + 0.710153i \(0.251374\pi\)
\(702\) 0 0
\(703\) −46.8975 −1.76877
\(704\) 0 0
\(705\) −11.0484 −0.416107
\(706\) 0 0
\(707\) 25.0336 0.941484
\(708\) 0 0
\(709\) −11.9852 −0.450112 −0.225056 0.974346i \(-0.572257\pi\)
−0.225056 + 0.974346i \(0.572257\pi\)
\(710\) 0 0
\(711\) −1.51939 −0.0569817
\(712\) 0 0
\(713\) 25.2207 0.944521
\(714\) 0 0
\(715\) −5.52420 −0.206593
\(716\) 0 0
\(717\) 13.3419 0.498263
\(718\) 0 0
\(719\) 23.6258 0.881094 0.440547 0.897730i \(-0.354785\pi\)
0.440547 + 0.897730i \(0.354785\pi\)
\(720\) 0 0
\(721\) −45.8639 −1.70806
\(722\) 0 0
\(723\) −2.55295 −0.0949454
\(724\) 0 0
\(725\) 8.17226 0.303510
\(726\) 0 0
\(727\) 22.1526 0.821595 0.410798 0.911727i \(-0.365250\pi\)
0.410798 + 0.911727i \(0.365250\pi\)
\(728\) 0 0
\(729\) 27.6943 1.02571
\(730\) 0 0
\(731\) 0.951601 0.0351962
\(732\) 0 0
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) 0 0
\(735\) 14.0707 0.519004
\(736\) 0 0
\(737\) −60.0820 −2.21315
\(738\) 0 0
\(739\) −19.0436 −0.700530 −0.350265 0.936651i \(-0.613908\pi\)
−0.350265 + 0.936651i \(0.613908\pi\)
\(740\) 0 0
\(741\) 9.22066 0.338729
\(742\) 0 0
\(743\) 6.26906 0.229989 0.114995 0.993366i \(-0.463315\pi\)
0.114995 + 0.993366i \(0.463315\pi\)
\(744\) 0 0
\(745\) −8.93676 −0.327418
\(746\) 0 0
\(747\) 11.2303 0.410894
\(748\) 0 0
\(749\) 29.1749 1.06603
\(750\) 0 0
\(751\) −20.9219 −0.763452 −0.381726 0.924276i \(-0.624670\pi\)
−0.381726 + 0.924276i \(0.624670\pi\)
\(752\) 0 0
\(753\) 3.18971 0.116239
\(754\) 0 0
\(755\) 2.93196 0.106705
\(756\) 0 0
\(757\) −48.8975 −1.77721 −0.888604 0.458674i \(-0.848324\pi\)
−0.888604 + 0.458674i \(0.848324\pi\)
\(758\) 0 0
\(759\) 19.7767 0.717850
\(760\) 0 0
\(761\) −4.09680 −0.148509 −0.0742544 0.997239i \(-0.523658\pi\)
−0.0742544 + 0.997239i \(0.523658\pi\)
\(762\) 0 0
\(763\) 14.2180 0.514728
\(764\) 0 0
\(765\) 0.825129 0.0298326
\(766\) 0 0
\(767\) −12.2281 −0.441530
\(768\) 0 0
\(769\) −28.7858 −1.03804 −0.519022 0.854761i \(-0.673704\pi\)
−0.519022 + 0.854761i \(0.673704\pi\)
\(770\) 0 0
\(771\) −2.23811 −0.0806035
\(772\) 0 0
\(773\) 7.22066 0.259709 0.129855 0.991533i \(-0.458549\pi\)
0.129855 + 0.991533i \(0.458549\pi\)
\(774\) 0 0
\(775\) −9.52420 −0.342119
\(776\) 0 0
\(777\) −38.7858 −1.39143
\(778\) 0 0
\(779\) 4.80068 0.172002
\(780\) 0 0
\(781\) 30.5168 1.09198
\(782\) 0 0
\(783\) −46.0968 −1.64737
\(784\) 0 0
\(785\) 0.592243 0.0211381
\(786\) 0 0
\(787\) 41.5800 1.48217 0.741084 0.671413i \(-0.234312\pi\)
0.741084 + 0.671413i \(0.234312\pi\)
\(788\) 0 0
\(789\) −22.4871 −0.800562
\(790\) 0 0
\(791\) 15.1897 0.540084
\(792\) 0 0
\(793\) −0.172260 −0.00611715
\(794\) 0 0
\(795\) 6.82513 0.242062
\(796\) 0 0
\(797\) 19.4078 0.687458 0.343729 0.939069i \(-0.388310\pi\)
0.343729 + 0.939069i \(0.388310\pi\)
\(798\) 0 0
\(799\) 5.75228 0.203501
\(800\) 0 0
\(801\) −13.7767 −0.486777
\(802\) 0 0
\(803\) 61.9852 2.18741
\(804\) 0 0
\(805\) −11.0484 −0.389405
\(806\) 0 0
\(807\) 21.7619 0.766055
\(808\) 0 0
\(809\) 43.7981 1.53986 0.769929 0.638130i \(-0.220292\pi\)
0.769929 + 0.638130i \(0.220292\pi\)
\(810\) 0 0
\(811\) −5.75709 −0.202159 −0.101079 0.994878i \(-0.532230\pi\)
−0.101079 + 0.994878i \(0.532230\pi\)
\(812\) 0 0
\(813\) −14.1626 −0.496706
\(814\) 0 0
\(815\) 16.6284 0.582468
\(816\) 0 0
\(817\) −9.22066 −0.322590
\(818\) 0 0
\(819\) −4.89098 −0.170905
\(820\) 0 0
\(821\) −32.9368 −1.14950 −0.574750 0.818329i \(-0.694901\pi\)
−0.574750 + 0.818329i \(0.694901\pi\)
\(822\) 0 0
\(823\) −57.0894 −1.99001 −0.995005 0.0998217i \(-0.968173\pi\)
−0.995005 + 0.0998217i \(0.968173\pi\)
\(824\) 0 0
\(825\) −7.46838 −0.260016
\(826\) 0 0
\(827\) −27.4535 −0.954653 −0.477327 0.878726i \(-0.658394\pi\)
−0.477327 + 0.878726i \(0.658394\pi\)
\(828\) 0 0
\(829\) 10.4200 0.361901 0.180950 0.983492i \(-0.442083\pi\)
0.180950 + 0.983492i \(0.442083\pi\)
\(830\) 0 0
\(831\) 23.5142 0.815698
\(832\) 0 0
\(833\) −7.32580 −0.253824
\(834\) 0 0
\(835\) −3.82774 −0.132464
\(836\) 0 0
\(837\) 53.7226 1.85692
\(838\) 0 0
\(839\) 40.1984 1.38780 0.693902 0.720070i \(-0.255890\pi\)
0.693902 + 0.720070i \(0.255890\pi\)
\(840\) 0 0
\(841\) 37.7858 1.30296
\(842\) 0 0
\(843\) 15.2717 0.525984
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) 81.4291 2.79794
\(848\) 0 0
\(849\) 12.4923 0.428736
\(850\) 0 0
\(851\) 18.2084 0.624177
\(852\) 0 0
\(853\) 34.8761 1.19414 0.597068 0.802191i \(-0.296332\pi\)
0.597068 + 0.802191i \(0.296332\pi\)
\(854\) 0 0
\(855\) −7.99519 −0.273430
\(856\) 0 0
\(857\) 25.1600 0.859450 0.429725 0.902960i \(-0.358610\pi\)
0.429725 + 0.902960i \(0.358610\pi\)
\(858\) 0 0
\(859\) −15.0484 −0.513445 −0.256722 0.966485i \(-0.582643\pi\)
−0.256722 + 0.966485i \(0.582643\pi\)
\(860\) 0 0
\(861\) 3.97033 0.135308
\(862\) 0 0
\(863\) 2.29873 0.0782498 0.0391249 0.999234i \(-0.487543\pi\)
0.0391249 + 0.999234i \(0.487543\pi\)
\(864\) 0 0
\(865\) 14.1116 0.479810
\(866\) 0 0
\(867\) −22.3132 −0.757794
\(868\) 0 0
\(869\) −7.16003 −0.242888
\(870\) 0 0
\(871\) 10.8761 0.368524
\(872\) 0 0
\(873\) −21.5046 −0.727819
\(874\) 0 0
\(875\) 4.17226 0.141048
\(876\) 0 0
\(877\) −10.0000 −0.337676 −0.168838 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) 0 0
\(879\) −22.1788 −0.748071
\(880\) 0 0
\(881\) −48.1426 −1.62196 −0.810982 0.585070i \(-0.801067\pi\)
−0.810982 + 0.585070i \(0.801067\pi\)
\(882\) 0 0
\(883\) −12.8565 −0.432655 −0.216328 0.976321i \(-0.569408\pi\)
−0.216328 + 0.976321i \(0.569408\pi\)
\(884\) 0 0
\(885\) −16.5316 −0.555704
\(886\) 0 0
\(887\) −32.5216 −1.09197 −0.545984 0.837796i \(-0.683844\pi\)
−0.545984 + 0.837796i \(0.683844\pi\)
\(888\) 0 0
\(889\) −23.7671 −0.797123
\(890\) 0 0
\(891\) 22.6991 0.760447
\(892\) 0 0
\(893\) −55.7374 −1.86518
\(894\) 0 0
\(895\) 5.75228 0.192277
\(896\) 0 0
\(897\) −3.58002 −0.119533
\(898\) 0 0
\(899\) −77.8342 −2.59592
\(900\) 0 0
\(901\) −3.55346 −0.118383
\(902\) 0 0
\(903\) −7.62581 −0.253771
\(904\) 0 0
\(905\) 2.76450 0.0918952
\(906\) 0 0
\(907\) −21.0894 −0.700261 −0.350131 0.936701i \(-0.613863\pi\)
−0.350131 + 0.936701i \(0.613863\pi\)
\(908\) 0 0
\(909\) −7.03356 −0.233289
\(910\) 0 0
\(911\) 43.1600 1.42996 0.714978 0.699147i \(-0.246437\pi\)
0.714978 + 0.699147i \(0.246437\pi\)
\(912\) 0 0
\(913\) 52.9219 1.75146
\(914\) 0 0
\(915\) −0.232886 −0.00769896
\(916\) 0 0
\(917\) 74.0671 2.44591
\(918\) 0 0
\(919\) 11.8884 0.392161 0.196080 0.980588i \(-0.437179\pi\)
0.196080 + 0.980588i \(0.437179\pi\)
\(920\) 0 0
\(921\) −20.4265 −0.673075
\(922\) 0 0
\(923\) −5.52420 −0.181831
\(924\) 0 0
\(925\) −6.87614 −0.226086
\(926\) 0 0
\(927\) 12.8862 0.423237
\(928\) 0 0
\(929\) −34.4265 −1.12950 −0.564748 0.825263i \(-0.691027\pi\)
−0.564748 + 0.825263i \(0.691027\pi\)
\(930\) 0 0
\(931\) 70.9842 2.32641
\(932\) 0 0
\(933\) −10.9664 −0.359025
\(934\) 0 0
\(935\) 3.88836 0.127163
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) −1.88314 −0.0614541
\(940\) 0 0
\(941\) −38.1116 −1.24240 −0.621202 0.783651i \(-0.713355\pi\)
−0.621202 + 0.783651i \(0.713355\pi\)
\(942\) 0 0
\(943\) −1.86391 −0.0606974
\(944\) 0 0
\(945\) −23.5342 −0.765569
\(946\) 0 0
\(947\) 13.9245 0.452487 0.226243 0.974071i \(-0.427356\pi\)
0.226243 + 0.974071i \(0.427356\pi\)
\(948\) 0 0
\(949\) −11.2207 −0.364238
\(950\) 0 0
\(951\) −40.3052 −1.30699
\(952\) 0 0
\(953\) −23.7523 −0.769412 −0.384706 0.923039i \(-0.625697\pi\)
−0.384706 + 0.923039i \(0.625697\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) 0 0
\(957\) −61.0336 −1.97293
\(958\) 0 0
\(959\) −37.2865 −1.20404
\(960\) 0 0
\(961\) 59.7104 1.92614
\(962\) 0 0
\(963\) −8.19713 −0.264149
\(964\) 0 0
\(965\) −14.3445 −0.461766
\(966\) 0 0
\(967\) −6.87614 −0.221122 −0.110561 0.993869i \(-0.535265\pi\)
−0.110561 + 0.993869i \(0.535265\pi\)
\(968\) 0 0
\(969\) −6.49022 −0.208496
\(970\) 0 0
\(971\) 6.24772 0.200499 0.100249 0.994962i \(-0.468036\pi\)
0.100249 + 0.994962i \(0.468036\pi\)
\(972\) 0 0
\(973\) 55.4749 1.77844
\(974\) 0 0
\(975\) 1.35194 0.0432967
\(976\) 0 0
\(977\) −34.5316 −1.10476 −0.552382 0.833591i \(-0.686281\pi\)
−0.552382 + 0.833591i \(0.686281\pi\)
\(978\) 0 0
\(979\) −64.9219 −2.07491
\(980\) 0 0
\(981\) −3.99478 −0.127543
\(982\) 0 0
\(983\) −11.5652 −0.368872 −0.184436 0.982845i \(-0.559046\pi\)
−0.184436 + 0.982845i \(0.559046\pi\)
\(984\) 0 0
\(985\) −7.40776 −0.236031
\(986\) 0 0
\(987\) −46.0968 −1.46728
\(988\) 0 0
\(989\) 3.58002 0.113838
\(990\) 0 0
\(991\) 3.77673 0.119972 0.0599859 0.998199i \(-0.480894\pi\)
0.0599859 + 0.998199i \(0.480894\pi\)
\(992\) 0 0
\(993\) −25.9097 −0.822220
\(994\) 0 0
\(995\) 1.75228 0.0555509
\(996\) 0 0
\(997\) 54.4265 1.72370 0.861852 0.507160i \(-0.169305\pi\)
0.861852 + 0.507160i \(0.169305\pi\)
\(998\) 0 0
\(999\) 38.7858 1.22713
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 260.2.a.b.1.2 3
3.2 odd 2 2340.2.a.n.1.3 3
4.3 odd 2 1040.2.a.o.1.2 3
5.2 odd 4 1300.2.c.f.1249.3 6
5.3 odd 4 1300.2.c.f.1249.4 6
5.4 even 2 1300.2.a.i.1.2 3
8.3 odd 2 4160.2.a.br.1.2 3
8.5 even 2 4160.2.a.bo.1.2 3
12.11 even 2 9360.2.a.da.1.1 3
13.5 odd 4 3380.2.f.h.3041.3 6
13.8 odd 4 3380.2.f.h.3041.4 6
13.12 even 2 3380.2.a.o.1.2 3
20.19 odd 2 5200.2.a.ci.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.a.b.1.2 3 1.1 even 1 trivial
1040.2.a.o.1.2 3 4.3 odd 2
1300.2.a.i.1.2 3 5.4 even 2
1300.2.c.f.1249.3 6 5.2 odd 4
1300.2.c.f.1249.4 6 5.3 odd 4
2340.2.a.n.1.3 3 3.2 odd 2
3380.2.a.o.1.2 3 13.12 even 2
3380.2.f.h.3041.3 6 13.5 odd 4
3380.2.f.h.3041.4 6 13.8 odd 4
4160.2.a.bo.1.2 3 8.5 even 2
4160.2.a.br.1.2 3 8.3 odd 2
5200.2.a.ci.1.2 3 20.19 odd 2
9360.2.a.da.1.1 3 12.11 even 2