Properties

Label 230.2.a.d.1.1
Level $230$
Weight $2$
Character 230.1
Self dual yes
Analytic conductor $1.837$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.83655924649\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
Defining polynomial: \(x^{3} - x^{2} - 9 x + 12\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.11903\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} -1.00000 q^{10} +4.33763 q^{11} -3.11903 q^{12} -3.72833 q^{13} +4.50973 q^{14} +3.11903 q^{15} +1.00000 q^{16} +1.11903 q^{17} +6.72833 q^{18} +4.50973 q^{19} -1.00000 q^{20} -14.0660 q^{21} +4.33763 q^{22} -1.00000 q^{23} -3.11903 q^{24} +1.00000 q^{25} -3.72833 q^{26} -11.6288 q^{27} +4.50973 q^{28} -8.23805 q^{29} +3.11903 q^{30} +1.72833 q^{31} +1.00000 q^{32} -13.5292 q^{33} +1.11903 q^{34} -4.50973 q^{35} +6.72833 q^{36} -0.781399 q^{37} +4.50973 q^{38} +11.6288 q^{39} -1.00000 q^{40} +3.90043 q^{41} -14.0660 q^{42} +8.00000 q^{43} +4.33763 q^{44} -6.72833 q^{45} -1.00000 q^{46} -11.4567 q^{47} -3.11903 q^{48} +13.3376 q^{49} +1.00000 q^{50} -3.49027 q^{51} -3.72833 q^{52} -6.00000 q^{53} -11.6288 q^{54} -4.33763 q^{55} +4.50973 q^{56} -14.0660 q^{57} -8.23805 q^{58} -2.23805 q^{59} +3.11903 q^{60} +3.55623 q^{61} +1.72833 q^{62} +30.3429 q^{63} +1.00000 q^{64} +3.72833 q^{65} -13.5292 q^{66} +2.43720 q^{67} +1.11903 q^{68} +3.11903 q^{69} -4.50973 q^{70} +7.11903 q^{71} +6.72833 q^{72} -9.45665 q^{73} -0.781399 q^{74} -3.11903 q^{75} +4.50973 q^{76} +19.5615 q^{77} +11.6288 q^{78} -14.9133 q^{79} -1.00000 q^{80} +16.0854 q^{81} +3.90043 q^{82} +2.78140 q^{83} -14.0660 q^{84} -1.11903 q^{85} +8.00000 q^{86} +25.6947 q^{87} +4.33763 q^{88} -7.69471 q^{89} -6.72833 q^{90} -16.8137 q^{91} -1.00000 q^{92} -5.39070 q^{93} -11.4567 q^{94} -4.50973 q^{95} -3.11903 q^{96} -0.642920 q^{97} +13.3376 q^{98} +29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + q^{3} + 3q^{4} - 3q^{5} + q^{6} + 3q^{7} + 3q^{8} + 10q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + q^{3} + 3q^{4} - 3q^{5} + q^{6} + 3q^{7} + 3q^{8} + 10q^{9} - 3q^{10} + 3q^{11} + q^{12} - q^{13} + 3q^{14} - q^{15} + 3q^{16} - 7q^{17} + 10q^{18} + 3q^{19} - 3q^{20} - 22q^{21} + 3q^{22} - 3q^{23} + q^{24} + 3q^{25} - q^{26} - 14q^{27} + 3q^{28} - 4q^{29} - q^{30} - 5q^{31} + 3q^{32} - 9q^{33} - 7q^{34} - 3q^{35} + 10q^{36} - 2q^{37} + 3q^{38} + 14q^{39} - 3q^{40} + q^{41} - 22q^{42} + 24q^{43} + 3q^{44} - 10q^{45} - 3q^{46} - 14q^{47} + q^{48} + 30q^{49} + 3q^{50} - 21q^{51} - q^{52} - 18q^{53} - 14q^{54} - 3q^{55} + 3q^{56} - 22q^{57} - 4q^{58} + 14q^{59} - q^{60} + q^{61} - 5q^{62} + 8q^{63} + 3q^{64} + q^{65} - 9q^{66} + 8q^{67} - 7q^{68} - q^{69} - 3q^{70} + 11q^{71} + 10q^{72} - 8q^{73} - 2q^{74} + q^{75} + 3q^{76} - 24q^{77} + 14q^{78} - 4q^{79} - 3q^{80} + 7q^{81} + q^{82} + 8q^{83} - 22q^{84} + 7q^{85} + 24q^{86} + 36q^{87} + 3q^{88} + 18q^{89} - 10q^{90} + q^{91} - 3q^{92} - 16q^{93} - 14q^{94} - 3q^{95} + q^{96} - 33q^{97} + 30q^{98} + 57q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.11903 −1.80077 −0.900385 0.435093i \(-0.856715\pi\)
−0.900385 + 0.435093i \(0.856715\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −3.11903 −1.27334
\(7\) 4.50973 1.70452 0.852258 0.523122i \(-0.175233\pi\)
0.852258 + 0.523122i \(0.175233\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.72833 2.24278
\(10\) −1.00000 −0.316228
\(11\) 4.33763 1.30784 0.653922 0.756562i \(-0.273122\pi\)
0.653922 + 0.756562i \(0.273122\pi\)
\(12\) −3.11903 −0.900385
\(13\) −3.72833 −1.03405 −0.517026 0.855970i \(-0.672961\pi\)
−0.517026 + 0.855970i \(0.672961\pi\)
\(14\) 4.50973 1.20527
\(15\) 3.11903 0.805329
\(16\) 1.00000 0.250000
\(17\) 1.11903 0.271404 0.135702 0.990750i \(-0.456671\pi\)
0.135702 + 0.990750i \(0.456671\pi\)
\(18\) 6.72833 1.58588
\(19\) 4.50973 1.03460 0.517301 0.855803i \(-0.326937\pi\)
0.517301 + 0.855803i \(0.326937\pi\)
\(20\) −1.00000 −0.223607
\(21\) −14.0660 −3.06944
\(22\) 4.33763 0.924785
\(23\) −1.00000 −0.208514
\(24\) −3.11903 −0.636669
\(25\) 1.00000 0.200000
\(26\) −3.72833 −0.731185
\(27\) −11.6288 −2.23795
\(28\) 4.50973 0.852258
\(29\) −8.23805 −1.52977 −0.764884 0.644168i \(-0.777204\pi\)
−0.764884 + 0.644168i \(0.777204\pi\)
\(30\) 3.11903 0.569454
\(31\) 1.72833 0.310417 0.155208 0.987882i \(-0.450395\pi\)
0.155208 + 0.987882i \(0.450395\pi\)
\(32\) 1.00000 0.176777
\(33\) −13.5292 −2.35513
\(34\) 1.11903 0.191911
\(35\) −4.50973 −0.762283
\(36\) 6.72833 1.12139
\(37\) −0.781399 −0.128461 −0.0642306 0.997935i \(-0.520459\pi\)
−0.0642306 + 0.997935i \(0.520459\pi\)
\(38\) 4.50973 0.731574
\(39\) 11.6288 1.86209
\(40\) −1.00000 −0.158114
\(41\) 3.90043 0.609144 0.304572 0.952489i \(-0.401487\pi\)
0.304572 + 0.952489i \(0.401487\pi\)
\(42\) −14.0660 −2.17042
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 4.33763 0.653922
\(45\) −6.72833 −1.00300
\(46\) −1.00000 −0.147442
\(47\) −11.4567 −1.67112 −0.835562 0.549396i \(-0.814858\pi\)
−0.835562 + 0.549396i \(0.814858\pi\)
\(48\) −3.11903 −0.450193
\(49\) 13.3376 1.90538
\(50\) 1.00000 0.141421
\(51\) −3.49027 −0.488736
\(52\) −3.72833 −0.517026
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −11.6288 −1.58247
\(55\) −4.33763 −0.584886
\(56\) 4.50973 0.602637
\(57\) −14.0660 −1.86308
\(58\) −8.23805 −1.08171
\(59\) −2.23805 −0.291370 −0.145685 0.989331i \(-0.546539\pi\)
−0.145685 + 0.989331i \(0.546539\pi\)
\(60\) 3.11903 0.402665
\(61\) 3.55623 0.455329 0.227664 0.973740i \(-0.426891\pi\)
0.227664 + 0.973740i \(0.426891\pi\)
\(62\) 1.72833 0.219498
\(63\) 30.3429 3.82285
\(64\) 1.00000 0.125000
\(65\) 3.72833 0.462442
\(66\) −13.5292 −1.66533
\(67\) 2.43720 0.297752 0.148876 0.988856i \(-0.452435\pi\)
0.148876 + 0.988856i \(0.452435\pi\)
\(68\) 1.11903 0.135702
\(69\) 3.11903 0.375487
\(70\) −4.50973 −0.539015
\(71\) 7.11903 0.844873 0.422437 0.906393i \(-0.361175\pi\)
0.422437 + 0.906393i \(0.361175\pi\)
\(72\) 6.72833 0.792941
\(73\) −9.45665 −1.10682 −0.553409 0.832910i \(-0.686673\pi\)
−0.553409 + 0.832910i \(0.686673\pi\)
\(74\) −0.781399 −0.0908357
\(75\) −3.11903 −0.360154
\(76\) 4.50973 0.517301
\(77\) 19.5615 2.22924
\(78\) 11.6288 1.31670
\(79\) −14.9133 −1.67788 −0.838939 0.544225i \(-0.816824\pi\)
−0.838939 + 0.544225i \(0.816824\pi\)
\(80\) −1.00000 −0.111803
\(81\) 16.0854 1.78727
\(82\) 3.90043 0.430730
\(83\) 2.78140 0.305298 0.152649 0.988280i \(-0.451220\pi\)
0.152649 + 0.988280i \(0.451220\pi\)
\(84\) −14.0660 −1.53472
\(85\) −1.11903 −0.121375
\(86\) 8.00000 0.862662
\(87\) 25.6947 2.75476
\(88\) 4.33763 0.462393
\(89\) −7.69471 −0.815637 −0.407819 0.913063i \(-0.633710\pi\)
−0.407819 + 0.913063i \(0.633710\pi\)
\(90\) −6.72833 −0.709228
\(91\) −16.8137 −1.76256
\(92\) −1.00000 −0.104257
\(93\) −5.39070 −0.558989
\(94\) −11.4567 −1.18166
\(95\) −4.50973 −0.462688
\(96\) −3.11903 −0.318334
\(97\) −0.642920 −0.0652786 −0.0326393 0.999467i \(-0.510391\pi\)
−0.0326393 + 0.999467i \(0.510391\pi\)
\(98\) 13.3376 1.34730
\(99\) 29.1850 2.93320
\(100\) 1.00000 0.100000
\(101\) −8.23805 −0.819717 −0.409858 0.912149i \(-0.634422\pi\)
−0.409858 + 0.912149i \(0.634422\pi\)
\(102\) −3.49027 −0.345589
\(103\) 12.3376 1.21566 0.607831 0.794066i \(-0.292040\pi\)
0.607831 + 0.794066i \(0.292040\pi\)
\(104\) −3.72833 −0.365593
\(105\) 14.0660 1.37270
\(106\) −6.00000 −0.582772
\(107\) −15.9328 −1.54028 −0.770139 0.637876i \(-0.779813\pi\)
−0.770139 + 0.637876i \(0.779813\pi\)
\(108\) −11.6288 −1.11898
\(109\) −1.49027 −0.142742 −0.0713712 0.997450i \(-0.522737\pi\)
−0.0713712 + 0.997450i \(0.522737\pi\)
\(110\) −4.33763 −0.413577
\(111\) 2.43720 0.231329
\(112\) 4.50973 0.426129
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −14.0660 −1.31740
\(115\) 1.00000 0.0932505
\(116\) −8.23805 −0.764884
\(117\) −25.0854 −2.31915
\(118\) −2.23805 −0.206030
\(119\) 5.04650 0.462612
\(120\) 3.11903 0.284727
\(121\) 7.81502 0.710456
\(122\) 3.55623 0.321966
\(123\) −12.1655 −1.09693
\(124\) 1.72833 0.155208
\(125\) −1.00000 −0.0894427
\(126\) 30.3429 2.70316
\(127\) −0.675256 −0.0599193 −0.0299597 0.999551i \(-0.509538\pi\)
−0.0299597 + 0.999551i \(0.509538\pi\)
\(128\) 1.00000 0.0883883
\(129\) −24.9522 −2.19692
\(130\) 3.72833 0.326996
\(131\) −13.6947 −1.19651 −0.598256 0.801305i \(-0.704139\pi\)
−0.598256 + 0.801305i \(0.704139\pi\)
\(132\) −13.5292 −1.17756
\(133\) 20.3376 1.76350
\(134\) 2.43720 0.210542
\(135\) 11.6288 1.00084
\(136\) 1.11903 0.0959557
\(137\) 7.52918 0.643261 0.321631 0.946865i \(-0.395769\pi\)
0.321631 + 0.946865i \(0.395769\pi\)
\(138\) 3.11903 0.265509
\(139\) 4.67526 0.396550 0.198275 0.980146i \(-0.436466\pi\)
0.198275 + 0.980146i \(0.436466\pi\)
\(140\) −4.50973 −0.381141
\(141\) 35.7336 3.00931
\(142\) 7.11903 0.597415
\(143\) −16.1721 −1.35238
\(144\) 6.72833 0.560694
\(145\) 8.23805 0.684133
\(146\) −9.45665 −0.782638
\(147\) −41.6004 −3.43114
\(148\) −0.781399 −0.0642306
\(149\) 7.52918 0.616814 0.308407 0.951254i \(-0.400204\pi\)
0.308407 + 0.951254i \(0.400204\pi\)
\(150\) −3.11903 −0.254667
\(151\) −13.3571 −1.08698 −0.543492 0.839414i \(-0.682898\pi\)
−0.543492 + 0.839414i \(0.682898\pi\)
\(152\) 4.50973 0.365787
\(153\) 7.52918 0.608698
\(154\) 19.5615 1.57631
\(155\) −1.72833 −0.138823
\(156\) 11.6288 0.931045
\(157\) 16.2381 1.29594 0.647969 0.761667i \(-0.275619\pi\)
0.647969 + 0.761667i \(0.275619\pi\)
\(158\) −14.9133 −1.18644
\(159\) 18.7142 1.48413
\(160\) −1.00000 −0.0790569
\(161\) −4.50973 −0.355416
\(162\) 16.0854 1.26379
\(163\) −3.29112 −0.257781 −0.128890 0.991659i \(-0.541142\pi\)
−0.128890 + 0.991659i \(0.541142\pi\)
\(164\) 3.90043 0.304572
\(165\) 13.5292 1.05325
\(166\) 2.78140 0.215878
\(167\) 22.9133 1.77309 0.886543 0.462647i \(-0.153100\pi\)
0.886543 + 0.462647i \(0.153100\pi\)
\(168\) −14.0660 −1.08521
\(169\) 0.900425 0.0692635
\(170\) −1.11903 −0.0858254
\(171\) 30.3429 2.32038
\(172\) 8.00000 0.609994
\(173\) 0.575681 0.0437683 0.0218841 0.999761i \(-0.493034\pi\)
0.0218841 + 0.999761i \(0.493034\pi\)
\(174\) 25.6947 1.94791
\(175\) 4.50973 0.340903
\(176\) 4.33763 0.326961
\(177\) 6.98055 0.524690
\(178\) −7.69471 −0.576743
\(179\) 5.01945 0.375171 0.187586 0.982248i \(-0.439934\pi\)
0.187586 + 0.982248i \(0.439934\pi\)
\(180\) −6.72833 −0.501500
\(181\) −11.5292 −0.856957 −0.428479 0.903552i \(-0.640950\pi\)
−0.428479 + 0.903552i \(0.640950\pi\)
\(182\) −16.8137 −1.24632
\(183\) −11.0920 −0.819942
\(184\) −1.00000 −0.0737210
\(185\) 0.781399 0.0574496
\(186\) −5.39070 −0.395265
\(187\) 4.85392 0.354954
\(188\) −11.4567 −0.835562
\(189\) −52.4425 −3.81463
\(190\) −4.50973 −0.327170
\(191\) −18.7142 −1.35411 −0.677055 0.735933i \(-0.736744\pi\)
−0.677055 + 0.735933i \(0.736744\pi\)
\(192\) −3.11903 −0.225096
\(193\) 23.4956 1.69125 0.845624 0.533780i \(-0.179229\pi\)
0.845624 + 0.533780i \(0.179229\pi\)
\(194\) −0.642920 −0.0461590
\(195\) −11.6288 −0.832752
\(196\) 13.3376 0.952688
\(197\) −18.1385 −1.29231 −0.646157 0.763205i \(-0.723625\pi\)
−0.646157 + 0.763205i \(0.723625\pi\)
\(198\) 29.1850 2.07409
\(199\) −23.2575 −1.64868 −0.824340 0.566094i \(-0.808454\pi\)
−0.824340 + 0.566094i \(0.808454\pi\)
\(200\) 1.00000 0.0707107
\(201\) −7.60170 −0.536183
\(202\) −8.23805 −0.579627
\(203\) −37.1514 −2.60751
\(204\) −3.49027 −0.244368
\(205\) −3.90043 −0.272418
\(206\) 12.3376 0.859603
\(207\) −6.72833 −0.467651
\(208\) −3.72833 −0.258513
\(209\) 19.5615 1.35310
\(210\) 14.0660 0.970643
\(211\) 4.34420 0.299067 0.149533 0.988757i \(-0.452223\pi\)
0.149533 + 0.988757i \(0.452223\pi\)
\(212\) −6.00000 −0.412082
\(213\) −22.2044 −1.52142
\(214\) −15.9328 −1.08914
\(215\) −8.00000 −0.545595
\(216\) −11.6288 −0.791236
\(217\) 7.79428 0.529110
\(218\) −1.49027 −0.100934
\(219\) 29.4956 1.99313
\(220\) −4.33763 −0.292443
\(221\) −4.17210 −0.280646
\(222\) 2.43720 0.163574
\(223\) 12.4761 0.835462 0.417731 0.908571i \(-0.362825\pi\)
0.417731 + 0.908571i \(0.362825\pi\)
\(224\) 4.50973 0.301319
\(225\) 6.72833 0.448555
\(226\) −6.00000 −0.399114
\(227\) 15.9328 1.05749 0.528747 0.848779i \(-0.322662\pi\)
0.528747 + 0.848779i \(0.322662\pi\)
\(228\) −14.0660 −0.931541
\(229\) −3.56280 −0.235436 −0.117718 0.993047i \(-0.537558\pi\)
−0.117718 + 0.993047i \(0.537558\pi\)
\(230\) 1.00000 0.0659380
\(231\) −61.0129 −4.01435
\(232\) −8.23805 −0.540855
\(233\) −27.4956 −1.80129 −0.900647 0.434552i \(-0.856907\pi\)
−0.900647 + 0.434552i \(0.856907\pi\)
\(234\) −25.0854 −1.63988
\(235\) 11.4567 0.747350
\(236\) −2.23805 −0.145685
\(237\) 46.5150 3.02147
\(238\) 5.04650 0.327116
\(239\) 10.0389 0.649363 0.324681 0.945823i \(-0.394743\pi\)
0.324681 + 0.945823i \(0.394743\pi\)
\(240\) 3.11903 0.201332
\(241\) −23.6947 −1.52631 −0.763155 0.646215i \(-0.776351\pi\)
−0.763155 + 0.646215i \(0.776351\pi\)
\(242\) 7.81502 0.502368
\(243\) −15.2846 −0.980505
\(244\) 3.55623 0.227664
\(245\) −13.3376 −0.852110
\(246\) −12.1655 −0.775646
\(247\) −16.8137 −1.06983
\(248\) 1.72833 0.109749
\(249\) −8.67526 −0.549772
\(250\) −1.00000 −0.0632456
\(251\) 12.4425 0.785363 0.392681 0.919675i \(-0.371548\pi\)
0.392681 + 0.919675i \(0.371548\pi\)
\(252\) 30.3429 1.91142
\(253\) −4.33763 −0.272704
\(254\) −0.675256 −0.0423693
\(255\) 3.49027 0.218569
\(256\) 1.00000 0.0625000
\(257\) 5.45665 0.340377 0.170188 0.985412i \(-0.445562\pi\)
0.170188 + 0.985412i \(0.445562\pi\)
\(258\) −24.9522 −1.55346
\(259\) −3.52389 −0.218964
\(260\) 3.72833 0.231221
\(261\) −55.4283 −3.43093
\(262\) −13.6947 −0.846062
\(263\) 0.138479 0.00853895 0.00426948 0.999991i \(-0.498641\pi\)
0.00426948 + 0.999991i \(0.498641\pi\)
\(264\) −13.5292 −0.832663
\(265\) 6.00000 0.368577
\(266\) 20.3376 1.24698
\(267\) 24.0000 1.46878
\(268\) 2.43720 0.148876
\(269\) 14.6753 0.894766 0.447383 0.894342i \(-0.352356\pi\)
0.447383 + 0.894342i \(0.352356\pi\)
\(270\) 11.6288 0.707703
\(271\) −8.31058 −0.504832 −0.252416 0.967619i \(-0.581225\pi\)
−0.252416 + 0.967619i \(0.581225\pi\)
\(272\) 1.11903 0.0678510
\(273\) 52.4425 3.17396
\(274\) 7.52918 0.454854
\(275\) 4.33763 0.261569
\(276\) 3.11903 0.187743
\(277\) 12.9133 0.775886 0.387943 0.921683i \(-0.373186\pi\)
0.387943 + 0.921683i \(0.373186\pi\)
\(278\) 4.67526 0.280403
\(279\) 11.6288 0.696195
\(280\) −4.50973 −0.269508
\(281\) 2.67526 0.159592 0.0797962 0.996811i \(-0.474573\pi\)
0.0797962 + 0.996811i \(0.474573\pi\)
\(282\) 35.7336 2.12791
\(283\) 0.742495 0.0441367 0.0220684 0.999756i \(-0.492975\pi\)
0.0220684 + 0.999756i \(0.492975\pi\)
\(284\) 7.11903 0.422437
\(285\) 14.0660 0.833195
\(286\) −16.1721 −0.956276
\(287\) 17.5898 1.03830
\(288\) 6.72833 0.396470
\(289\) −15.7478 −0.926340
\(290\) 8.23805 0.483755
\(291\) 2.00528 0.117552
\(292\) −9.45665 −0.553409
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −41.6004 −2.42619
\(295\) 2.23805 0.130305
\(296\) −0.781399 −0.0454179
\(297\) −50.4412 −2.92690
\(298\) 7.52918 0.436154
\(299\) 3.72833 0.215615
\(300\) −3.11903 −0.180077
\(301\) 36.0778 2.07949
\(302\) −13.3571 −0.768614
\(303\) 25.6947 1.47612
\(304\) 4.50973 0.258651
\(305\) −3.55623 −0.203629
\(306\) 7.52918 0.430414
\(307\) 30.5084 1.74121 0.870604 0.491984i \(-0.163728\pi\)
0.870604 + 0.491984i \(0.163728\pi\)
\(308\) 19.5615 1.11462
\(309\) −38.4814 −2.18913
\(310\) −1.72833 −0.0981624
\(311\) 5.56280 0.315437 0.157719 0.987484i \(-0.449586\pi\)
0.157719 + 0.987484i \(0.449586\pi\)
\(312\) 11.6288 0.658348
\(313\) 4.07252 0.230193 0.115096 0.993354i \(-0.463282\pi\)
0.115096 + 0.993354i \(0.463282\pi\)
\(314\) 16.2381 0.916366
\(315\) −30.3429 −1.70963
\(316\) −14.9133 −0.838939
\(317\) −6.16553 −0.346291 −0.173145 0.984896i \(-0.555393\pi\)
−0.173145 + 0.984896i \(0.555393\pi\)
\(318\) 18.7142 1.04944
\(319\) −35.7336 −2.00070
\(320\) −1.00000 −0.0559017
\(321\) 49.6947 2.77369
\(322\) −4.50973 −0.251317
\(323\) 5.04650 0.280795
\(324\) 16.0854 0.893634
\(325\) −3.72833 −0.206810
\(326\) −3.29112 −0.182279
\(327\) 4.64820 0.257046
\(328\) 3.90043 0.215365
\(329\) −51.6664 −2.84846
\(330\) 13.5292 0.744757
\(331\) 27.5886 1.51640 0.758202 0.652019i \(-0.226078\pi\)
0.758202 + 0.652019i \(0.226078\pi\)
\(332\) 2.78140 0.152649
\(333\) −5.25751 −0.288110
\(334\) 22.9133 1.25376
\(335\) −2.43720 −0.133159
\(336\) −14.0660 −0.767361
\(337\) −17.4230 −0.949093 −0.474547 0.880230i \(-0.657388\pi\)
−0.474547 + 0.880230i \(0.657388\pi\)
\(338\) 0.900425 0.0489767
\(339\) 18.7142 1.01641
\(340\) −1.11903 −0.0606877
\(341\) 7.49684 0.405977
\(342\) 30.3429 1.64076
\(343\) 28.5810 1.54323
\(344\) 8.00000 0.431331
\(345\) −3.11903 −0.167923
\(346\) 0.575681 0.0309488
\(347\) 4.88097 0.262024 0.131012 0.991381i \(-0.458177\pi\)
0.131012 + 0.991381i \(0.458177\pi\)
\(348\) 25.6947 1.37738
\(349\) 24.0389 1.28677 0.643387 0.765542i \(-0.277529\pi\)
0.643387 + 0.765542i \(0.277529\pi\)
\(350\) 4.50973 0.241055
\(351\) 43.3558 2.31416
\(352\) 4.33763 0.231196
\(353\) −14.3442 −0.763464 −0.381732 0.924273i \(-0.624672\pi\)
−0.381732 + 0.924273i \(0.624672\pi\)
\(354\) 6.98055 0.371012
\(355\) −7.11903 −0.377839
\(356\) −7.69471 −0.407819
\(357\) −15.7402 −0.833059
\(358\) 5.01945 0.265286
\(359\) 26.7814 1.41347 0.706734 0.707479i \(-0.250168\pi\)
0.706734 + 0.707479i \(0.250168\pi\)
\(360\) −6.72833 −0.354614
\(361\) 1.33763 0.0704015
\(362\) −11.5292 −0.605960
\(363\) −24.3752 −1.27937
\(364\) −16.8137 −0.881279
\(365\) 9.45665 0.494984
\(366\) −11.0920 −0.579787
\(367\) −20.4761 −1.06884 −0.534422 0.845218i \(-0.679471\pi\)
−0.534422 + 0.845218i \(0.679471\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 26.2433 1.36617
\(370\) 0.781399 0.0406230
\(371\) −27.0584 −1.40480
\(372\) −5.39070 −0.279495
\(373\) −3.89386 −0.201616 −0.100808 0.994906i \(-0.532143\pi\)
−0.100808 + 0.994906i \(0.532143\pi\)
\(374\) 4.85392 0.250990
\(375\) 3.11903 0.161066
\(376\) −11.4567 −0.590832
\(377\) 30.7142 1.58186
\(378\) −52.4425 −2.69735
\(379\) −30.3765 −1.56034 −0.780169 0.625569i \(-0.784867\pi\)
−0.780169 + 0.625569i \(0.784867\pi\)
\(380\) −4.50973 −0.231344
\(381\) 2.10614 0.107901
\(382\) −18.7142 −0.957500
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −3.11903 −0.159167
\(385\) −19.5615 −0.996947
\(386\) 23.4956 1.19589
\(387\) 53.8266 2.73616
\(388\) −0.642920 −0.0326393
\(389\) −18.6818 −0.947206 −0.473603 0.880738i \(-0.657047\pi\)
−0.473603 + 0.880738i \(0.657047\pi\)
\(390\) −11.6288 −0.588845
\(391\) −1.11903 −0.0565916
\(392\) 13.3376 0.673652
\(393\) 42.7142 2.15464
\(394\) −18.1385 −0.913803
\(395\) 14.9133 0.750370
\(396\) 29.1850 1.46660
\(397\) −28.5757 −1.43417 −0.717086 0.696985i \(-0.754525\pi\)
−0.717086 + 0.696985i \(0.754525\pi\)
\(398\) −23.2575 −1.16579
\(399\) −63.4336 −3.17565
\(400\) 1.00000 0.0500000
\(401\) 12.1061 0.604552 0.302276 0.953220i \(-0.402254\pi\)
0.302276 + 0.953220i \(0.402254\pi\)
\(402\) −7.60170 −0.379138
\(403\) −6.44377 −0.320987
\(404\) −8.23805 −0.409858
\(405\) −16.0854 −0.799290
\(406\) −37.1514 −1.84379
\(407\) −3.38942 −0.168007
\(408\) −3.49027 −0.172794
\(409\) 25.2911 1.25057 0.625283 0.780398i \(-0.284984\pi\)
0.625283 + 0.780398i \(0.284984\pi\)
\(410\) −3.90043 −0.192628
\(411\) −23.4837 −1.15837
\(412\) 12.3376 0.607831
\(413\) −10.0930 −0.496644
\(414\) −6.72833 −0.330679
\(415\) −2.78140 −0.136533
\(416\) −3.72833 −0.182796
\(417\) −14.5822 −0.714096
\(418\) 19.5615 0.956785
\(419\) −17.3505 −0.847628 −0.423814 0.905749i \(-0.639309\pi\)
−0.423814 + 0.905749i \(0.639309\pi\)
\(420\) 14.0660 0.686348
\(421\) 21.4230 1.04409 0.522047 0.852916i \(-0.325168\pi\)
0.522047 + 0.852916i \(0.325168\pi\)
\(422\) 4.34420 0.211472
\(423\) −77.0841 −3.74796
\(424\) −6.00000 −0.291386
\(425\) 1.11903 0.0542808
\(426\) −22.2044 −1.07581
\(427\) 16.0376 0.776115
\(428\) −15.9328 −0.770139
\(429\) 50.4412 2.43532
\(430\) −8.00000 −0.385794
\(431\) 22.5822 1.08775 0.543874 0.839167i \(-0.316957\pi\)
0.543874 + 0.839167i \(0.316957\pi\)
\(432\) −11.6288 −0.559489
\(433\) 1.01417 0.0487378 0.0243689 0.999703i \(-0.492242\pi\)
0.0243689 + 0.999703i \(0.492242\pi\)
\(434\) 7.79428 0.374138
\(435\) −25.6947 −1.23197
\(436\) −1.49027 −0.0713712
\(437\) −4.50973 −0.215729
\(438\) 29.4956 1.40935
\(439\) −26.7478 −1.27660 −0.638301 0.769787i \(-0.720362\pi\)
−0.638301 + 0.769787i \(0.720362\pi\)
\(440\) −4.33763 −0.206788
\(441\) 89.7399 4.27333
\(442\) −4.17210 −0.198446
\(443\) 10.2044 0.484827 0.242414 0.970173i \(-0.422061\pi\)
0.242414 + 0.970173i \(0.422061\pi\)
\(444\) 2.43720 0.115665
\(445\) 7.69471 0.364764
\(446\) 12.4761 0.590761
\(447\) −23.4837 −1.11074
\(448\) 4.50973 0.213065
\(449\) 38.7867 1.83046 0.915228 0.402936i \(-0.132010\pi\)
0.915228 + 0.402936i \(0.132010\pi\)
\(450\) 6.72833 0.317176
\(451\) 16.9186 0.796665
\(452\) −6.00000 −0.282216
\(453\) 41.6611 1.95741
\(454\) 15.9328 0.747762
\(455\) 16.8137 0.788240
\(456\) −14.0660 −0.658699
\(457\) 34.9522 1.63500 0.817498 0.575932i \(-0.195361\pi\)
0.817498 + 0.575932i \(0.195361\pi\)
\(458\) −3.56280 −0.166479
\(459\) −13.0129 −0.607389
\(460\) 1.00000 0.0466252
\(461\) 16.3700 0.762425 0.381213 0.924487i \(-0.375507\pi\)
0.381213 + 0.924487i \(0.375507\pi\)
\(462\) −61.0129 −2.83858
\(463\) 29.2186 1.35790 0.678952 0.734183i \(-0.262435\pi\)
0.678952 + 0.734183i \(0.262435\pi\)
\(464\) −8.23805 −0.382442
\(465\) 5.39070 0.249988
\(466\) −27.4956 −1.27371
\(467\) 24.2770 1.12340 0.561702 0.827340i \(-0.310147\pi\)
0.561702 + 0.827340i \(0.310147\pi\)
\(468\) −25.0854 −1.15957
\(469\) 10.9911 0.507523
\(470\) 11.4567 0.528456
\(471\) −50.6469 −2.33369
\(472\) −2.23805 −0.103015
\(473\) 34.7010 1.59555
\(474\) 46.5150 2.13651
\(475\) 4.50973 0.206920
\(476\) 5.04650 0.231306
\(477\) −40.3700 −1.84841
\(478\) 10.0389 0.459169
\(479\) 24.6080 1.12437 0.562185 0.827012i \(-0.309961\pi\)
0.562185 + 0.827012i \(0.309961\pi\)
\(480\) 3.11903 0.142363
\(481\) 2.91331 0.132835
\(482\) −23.6947 −1.07926
\(483\) 14.0660 0.640023
\(484\) 7.81502 0.355228
\(485\) 0.642920 0.0291935
\(486\) −15.2846 −0.693322
\(487\) −30.2381 −1.37022 −0.685108 0.728441i \(-0.740245\pi\)
−0.685108 + 0.728441i \(0.740245\pi\)
\(488\) 3.55623 0.160983
\(489\) 10.2651 0.464204
\(490\) −13.3376 −0.602533
\(491\) 12.3311 0.556493 0.278246 0.960510i \(-0.410247\pi\)
0.278246 + 0.960510i \(0.410247\pi\)
\(492\) −12.1655 −0.548464
\(493\) −9.21860 −0.415185
\(494\) −16.8137 −0.756486
\(495\) −29.1850 −1.31177
\(496\) 1.72833 0.0776042
\(497\) 32.1049 1.44010
\(498\) −8.67526 −0.388748
\(499\) −26.9133 −1.20481 −0.602403 0.798192i \(-0.705790\pi\)
−0.602403 + 0.798192i \(0.705790\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −71.4672 −3.19292
\(502\) 12.4425 0.555335
\(503\) 20.5097 0.914483 0.457242 0.889342i \(-0.348837\pi\)
0.457242 + 0.889342i \(0.348837\pi\)
\(504\) 30.3429 1.35158
\(505\) 8.23805 0.366589
\(506\) −4.33763 −0.192831
\(507\) −2.80845 −0.124728
\(508\) −0.675256 −0.0299597
\(509\) −36.7142 −1.62733 −0.813663 0.581336i \(-0.802530\pi\)
−0.813663 + 0.581336i \(0.802530\pi\)
\(510\) 3.49027 0.154552
\(511\) −42.6469 −1.88659
\(512\) 1.00000 0.0441942
\(513\) −52.4425 −2.31539
\(514\) 5.45665 0.240683
\(515\) −12.3376 −0.543661
\(516\) −24.9522 −1.09846
\(517\) −49.6947 −2.18557
\(518\) −3.52389 −0.154831
\(519\) −1.79557 −0.0788166
\(520\) 3.72833 0.163498
\(521\) −4.91331 −0.215256 −0.107628 0.994191i \(-0.534326\pi\)
−0.107628 + 0.994191i \(0.534326\pi\)
\(522\) −55.4283 −2.42603
\(523\) −0.344196 −0.0150506 −0.00752531 0.999972i \(-0.502395\pi\)
−0.00752531 + 0.999972i \(0.502395\pi\)
\(524\) −13.6947 −0.598256
\(525\) −14.0660 −0.613889
\(526\) 0.138479 0.00603795
\(527\) 1.93404 0.0842483
\(528\) −13.5292 −0.588782
\(529\) 1.00000 0.0434783
\(530\) 6.00000 0.260623
\(531\) −15.0584 −0.653477
\(532\) 20.3376 0.881748
\(533\) −14.5421 −0.629887
\(534\) 24.0000 1.03858
\(535\) 15.9328 0.688833
\(536\) 2.43720 0.105271
\(537\) −15.6558 −0.675598
\(538\) 14.6753 0.632695
\(539\) 57.8537 2.49193
\(540\) 11.6288 0.500422
\(541\) −6.13191 −0.263631 −0.131816 0.991274i \(-0.542081\pi\)
−0.131816 + 0.991274i \(0.542081\pi\)
\(542\) −8.31058 −0.356970
\(543\) 35.9598 1.54318
\(544\) 1.11903 0.0479779
\(545\) 1.49027 0.0638363
\(546\) 52.4425 2.24433
\(547\) −9.18498 −0.392721 −0.196361 0.980532i \(-0.562912\pi\)
−0.196361 + 0.980532i \(0.562912\pi\)
\(548\) 7.52918 0.321631
\(549\) 23.9275 1.02120
\(550\) 4.33763 0.184957
\(551\) −37.1514 −1.58270
\(552\) 3.11903 0.132755
\(553\) −67.2549 −2.85997
\(554\) 12.9133 0.548634
\(555\) −2.43720 −0.103454
\(556\) 4.67526 0.198275
\(557\) −4.30529 −0.182421 −0.0912105 0.995832i \(-0.529074\pi\)
−0.0912105 + 0.995832i \(0.529074\pi\)
\(558\) 11.6288 0.492284
\(559\) −29.8266 −1.26153
\(560\) −4.50973 −0.190571
\(561\) −15.1395 −0.639191
\(562\) 2.67526 0.112849
\(563\) 11.1256 0.468888 0.234444 0.972130i \(-0.424673\pi\)
0.234444 + 0.972130i \(0.424673\pi\)
\(564\) 35.7336 1.50466
\(565\) 6.00000 0.252422
\(566\) 0.742495 0.0312094
\(567\) 72.5408 3.04643
\(568\) 7.11903 0.298708
\(569\) −16.0389 −0.672386 −0.336193 0.941793i \(-0.609139\pi\)
−0.336193 + 0.941793i \(0.609139\pi\)
\(570\) 14.0660 0.589158
\(571\) 17.9004 0.749109 0.374555 0.927205i \(-0.377796\pi\)
0.374555 + 0.927205i \(0.377796\pi\)
\(572\) −16.1721 −0.676189
\(573\) 58.3700 2.43844
\(574\) 17.5898 0.734186
\(575\) −1.00000 −0.0417029
\(576\) 6.72833 0.280347
\(577\) −9.12559 −0.379903 −0.189952 0.981793i \(-0.560833\pi\)
−0.189952 + 0.981793i \(0.560833\pi\)
\(578\) −15.7478 −0.655021
\(579\) −73.2833 −3.04555
\(580\) 8.23805 0.342067
\(581\) 12.5433 0.520386
\(582\) 2.00528 0.0831217
\(583\) −26.0258 −1.07788
\(584\) −9.45665 −0.391319
\(585\) 25.0854 1.03715
\(586\) −6.00000 −0.247858
\(587\) −33.6340 −1.38823 −0.694113 0.719866i \(-0.744203\pi\)
−0.694113 + 0.719866i \(0.744203\pi\)
\(588\) −41.6004 −1.71557
\(589\) 7.79428 0.321158
\(590\) 2.23805 0.0921392
\(591\) 56.5744 2.32716
\(592\) −0.781399 −0.0321153
\(593\) −17.4567 −0.716859 −0.358429 0.933557i \(-0.616688\pi\)
−0.358429 + 0.933557i \(0.616688\pi\)
\(594\) −50.4412 −2.06963
\(595\) −5.04650 −0.206886
\(596\) 7.52918 0.308407
\(597\) 72.5408 2.96890
\(598\) 3.72833 0.152463
\(599\) −11.5951 −0.473764 −0.236882 0.971538i \(-0.576126\pi\)
−0.236882 + 0.971538i \(0.576126\pi\)
\(600\) −3.11903 −0.127334
\(601\) −31.6611 −1.29148 −0.645741 0.763556i \(-0.723452\pi\)
−0.645741 + 0.763556i \(0.723452\pi\)
\(602\) 36.0778 1.47042
\(603\) 16.3983 0.667790
\(604\) −13.3571 −0.543492
\(605\) −7.81502 −0.317726
\(606\) 25.6947 1.04378
\(607\) −36.0778 −1.46435 −0.732177 0.681115i \(-0.761495\pi\)
−0.732177 + 0.681115i \(0.761495\pi\)
\(608\) 4.50973 0.182894
\(609\) 115.876 4.69554
\(610\) −3.55623 −0.143988
\(611\) 42.7142 1.72803
\(612\) 7.52918 0.304349
\(613\) −32.0389 −1.29404 −0.647020 0.762473i \(-0.723985\pi\)
−0.647020 + 0.762473i \(0.723985\pi\)
\(614\) 30.5084 1.23122
\(615\) 12.1655 0.490562
\(616\) 19.5615 0.788156
\(617\) −13.3960 −0.539302 −0.269651 0.962958i \(-0.586908\pi\)
−0.269651 + 0.962958i \(0.586908\pi\)
\(618\) −38.4814 −1.54795
\(619\) 37.1309 1.49242 0.746208 0.665713i \(-0.231872\pi\)
0.746208 + 0.665713i \(0.231872\pi\)
\(620\) −1.72833 −0.0694113
\(621\) 11.6288 0.466646
\(622\) 5.56280 0.223048
\(623\) −34.7010 −1.39027
\(624\) 11.6288 0.465523
\(625\) 1.00000 0.0400000
\(626\) 4.07252 0.162771
\(627\) −61.0129 −2.43662
\(628\) 16.2381 0.647969
\(629\) −0.874406 −0.0348648
\(630\) −30.3429 −1.20889
\(631\) 11.1125 0.442380 0.221190 0.975231i \(-0.429006\pi\)
0.221190 + 0.975231i \(0.429006\pi\)
\(632\) −14.9133 −0.593220
\(633\) −13.5497 −0.538551
\(634\) −6.16553 −0.244864
\(635\) 0.675256 0.0267967
\(636\) 18.7142 0.742065
\(637\) −49.7270 −1.97026
\(638\) −35.7336 −1.41471
\(639\) 47.8991 1.89486
\(640\) −1.00000 −0.0395285
\(641\) 12.3831 0.489103 0.244552 0.969636i \(-0.421359\pi\)
0.244552 + 0.969636i \(0.421359\pi\)
\(642\) 49.6947 1.96129
\(643\) −37.4956 −1.47868 −0.739340 0.673332i \(-0.764862\pi\)
−0.739340 + 0.673332i \(0.764862\pi\)
\(644\) −4.50973 −0.177708
\(645\) 24.9522 0.982492
\(646\) 5.04650 0.198552
\(647\) 14.5691 0.572771 0.286385 0.958114i \(-0.407546\pi\)
0.286385 + 0.958114i \(0.407546\pi\)
\(648\) 16.0854 0.631894
\(649\) −9.70784 −0.381066
\(650\) −3.72833 −0.146237
\(651\) −24.3106 −0.952807
\(652\) −3.29112 −0.128890
\(653\) −4.41672 −0.172840 −0.0864198 0.996259i \(-0.527543\pi\)
−0.0864198 + 0.996259i \(0.527543\pi\)
\(654\) 4.64820 0.181759
\(655\) 13.6947 0.535097
\(656\) 3.90043 0.152286
\(657\) −63.6275 −2.48234
\(658\) −51.6664 −2.01416
\(659\) −31.8655 −1.24130 −0.620652 0.784086i \(-0.713132\pi\)
−0.620652 + 0.784086i \(0.713132\pi\)
\(660\) 13.5292 0.526623
\(661\) 33.1190 1.28818 0.644090 0.764949i \(-0.277236\pi\)
0.644090 + 0.764949i \(0.277236\pi\)
\(662\) 27.5886 1.07226
\(663\) 13.0129 0.505379
\(664\) 2.78140 0.107939
\(665\) −20.3376 −0.788659
\(666\) −5.25751 −0.203724
\(667\) 8.23805 0.318979
\(668\) 22.9133 0.886543
\(669\) −38.9133 −1.50448
\(670\) −2.43720 −0.0941574
\(671\) 15.4256 0.595499
\(672\) −14.0660 −0.542606
\(673\) 19.3505 0.745907 0.372954 0.927850i \(-0.378345\pi\)
0.372954 + 0.927850i \(0.378345\pi\)
\(674\) −17.4230 −0.671110
\(675\) −11.6288 −0.447591
\(676\) 0.900425 0.0346317
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 18.7142 0.718713
\(679\) −2.89939 −0.111268
\(680\) −1.11903 −0.0429127
\(681\) −49.6947 −1.90431
\(682\) 7.49684 0.287069
\(683\) 38.3495 1.46740 0.733701 0.679472i \(-0.237791\pi\)
0.733701 + 0.679472i \(0.237791\pi\)
\(684\) 30.3429 1.16019
\(685\) −7.52918 −0.287675
\(686\) 28.5810 1.09123
\(687\) 11.1125 0.423967
\(688\) 8.00000 0.304997
\(689\) 22.3700 0.852228
\(690\) −3.11903 −0.118739
\(691\) −21.0195 −0.799618 −0.399809 0.916599i \(-0.630923\pi\)
−0.399809 + 0.916599i \(0.630923\pi\)
\(692\) 0.575681 0.0218841
\(693\) 131.616 4.99969
\(694\) 4.88097 0.185279
\(695\) −4.67526 −0.177343
\(696\) 25.6947 0.973955
\(697\) 4.36468 0.165324
\(698\) 24.0389 0.909886
\(699\) 85.7594 3.24372
\(700\) 4.50973 0.170452
\(701\) 19.3169 0.729589 0.364794 0.931088i \(-0.381139\pi\)
0.364794 + 0.931088i \(0.381139\pi\)
\(702\) 43.3558 1.63636
\(703\) −3.52389 −0.132906
\(704\) 4.33763 0.163481
\(705\) −35.7336 −1.34581
\(706\) −14.3442 −0.539851
\(707\) −37.1514 −1.39722
\(708\) 6.98055 0.262345
\(709\) 12.2315 0.459363 0.229682 0.973266i \(-0.426232\pi\)
0.229682 + 0.973266i \(0.426232\pi\)
\(710\) −7.11903 −0.267172
\(711\) −100.342 −3.76311
\(712\) −7.69471 −0.288371
\(713\) −1.72833 −0.0647264
\(714\) −15.7402 −0.589061
\(715\) 16.1721 0.604802
\(716\) 5.01945 0.187586
\(717\) −31.3116 −1.16935
\(718\) 26.7814 0.999473
\(719\) −40.6416 −1.51568 −0.757839 0.652442i \(-0.773745\pi\)
−0.757839 + 0.652442i \(0.773745\pi\)
\(720\) −6.72833 −0.250750
\(721\) 55.6393 2.07212
\(722\) 1.33763 0.0497814
\(723\) 73.9044 2.74854
\(724\) −11.5292 −0.428479
\(725\) −8.23805 −0.305954
\(726\) −24.3752 −0.904650
\(727\) −23.4501 −0.869716 −0.434858 0.900499i \(-0.643201\pi\)
−0.434858 + 0.900499i \(0.643201\pi\)
\(728\) −16.8137 −0.623158
\(729\) −0.583281 −0.0216030
\(730\) 9.45665 0.350006
\(731\) 8.95221 0.331110
\(732\) −11.0920 −0.409971
\(733\) −12.5150 −0.462252 −0.231126 0.972924i \(-0.574241\pi\)
−0.231126 + 0.972924i \(0.574241\pi\)
\(734\) −20.4761 −0.755787
\(735\) 41.6004 1.53445
\(736\) −1.00000 −0.0368605
\(737\) 10.5717 0.389413
\(738\) 26.2433 0.966031
\(739\) −21.3505 −0.785391 −0.392696 0.919668i \(-0.628457\pi\)
−0.392696 + 0.919668i \(0.628457\pi\)
\(740\) 0.781399 0.0287248
\(741\) 52.4425 1.92652
\(742\) −27.0584 −0.993343
\(743\) 24.9858 0.916641 0.458321 0.888787i \(-0.348451\pi\)
0.458321 + 0.888787i \(0.348451\pi\)
\(744\) −5.39070 −0.197633
\(745\) −7.52918 −0.275848
\(746\) −3.89386 −0.142564
\(747\) 18.7142 0.684715
\(748\) 4.85392 0.177477
\(749\) −71.8524 −2.62543
\(750\) 3.11903 0.113891
\(751\) −33.6275 −1.22708 −0.613542 0.789662i \(-0.710256\pi\)
−0.613542 + 0.789662i \(0.710256\pi\)
\(752\) −11.4567 −0.417781
\(753\) −38.8085 −1.41426
\(754\) 30.7142 1.11854
\(755\) 13.3571 0.486114
\(756\) −52.4425 −1.90731
\(757\) −37.1230 −1.34926 −0.674630 0.738156i \(-0.735697\pi\)
−0.674630 + 0.738156i \(0.735697\pi\)
\(758\) −30.3765 −1.10333
\(759\) 13.5292 0.491078
\(760\) −4.50973 −0.163585
\(761\) −3.87337 −0.140410 −0.0702048 0.997533i \(-0.522365\pi\)
−0.0702048 + 0.997533i \(0.522365\pi\)
\(762\) 2.10614 0.0762975
\(763\) −6.72073 −0.243307
\(764\) −18.7142 −0.677055
\(765\) −7.52918 −0.272218
\(766\) 0 0
\(767\) 8.34420 0.301291
\(768\) −3.11903 −0.112548
\(769\) 23.1645 0.835333 0.417667 0.908600i \(-0.362848\pi\)
0.417667 + 0.908600i \(0.362848\pi\)
\(770\) −19.5615 −0.704948
\(771\) −17.0195 −0.612941
\(772\) 23.4956 0.845624
\(773\) −8.78140 −0.315845 −0.157922 0.987452i \(-0.550480\pi\)
−0.157922 + 0.987452i \(0.550480\pi\)
\(774\) 53.8266 1.93476
\(775\) 1.72833 0.0620834
\(776\) −0.642920 −0.0230795
\(777\) 10.9911 0.394304
\(778\) −18.6818 −0.669776
\(779\) 17.5898 0.630222
\(780\) −11.6288 −0.416376
\(781\) 30.8797 1.10496
\(782\) −1.11903 −0.0400163
\(783\) 95.7983 3.42355
\(784\) 13.3376 0.476344
\(785\) −16.2381 −0.579561
\(786\) 42.7142 1.52356
\(787\) 49.6275 1.76903 0.884514 0.466513i \(-0.154490\pi\)
0.884514 + 0.466513i \(0.154490\pi\)
\(788\) −18.1385 −0.646157
\(789\) −0.431918 −0.0153767
\(790\) 14.9133 0.530592
\(791\) −27.0584 −0.962084
\(792\) 29.1850 1.03704
\(793\) −13.2588 −0.470833
\(794\) −28.5757 −1.01411
\(795\) −18.7142 −0.663723
\(796\) −23.2575 −0.824340
\(797\) 18.3311 0.649319 0.324660 0.945831i \(-0.394750\pi\)
0.324660 + 0.945831i \(0.394750\pi\)
\(798\) −63.4336 −2.24553
\(799\) −12.8203 −0.453550
\(800\) 1.00000 0.0353553
\(801\) −51.7725 −1.82929
\(802\) 12.1061 0.427483
\(803\) −41.0195 −1.44755
\(804\) −7.60170 −0.268091
\(805\) 4.50973 0.158947
\(806\) −6.44377 −0.226972
\(807\) −45.7725 −1.61127
\(808\) −8.23805 −0.289814
\(809\) −1.93933 −0.0681832 −0.0340916 0.999419i \(-0.510854\pi\)
−0.0340916 + 0.999419i \(0.510854\pi\)
\(810\) −16.0854 −0.565184
\(811\) −5.41775 −0.190243 −0.0951215 0.995466i \(-0.530324\pi\)
−0.0951215 + 0.995466i \(0.530324\pi\)
\(812\) −37.1514 −1.30376
\(813\) 25.9209 0.909086
\(814\) −3.38942 −0.118799
\(815\) 3.29112 0.115283
\(816\) −3.49027 −0.122184
\(817\) 36.0778 1.26220
\(818\) 25.2911 0.884283
\(819\) −113.128 −3.95302
\(820\) −3.90043 −0.136209
\(821\) 37.8655 1.32152 0.660758 0.750599i \(-0.270235\pi\)
0.660758 + 0.750599i \(0.270235\pi\)
\(822\) −23.4837 −0.819088
\(823\) 43.7336 1.52446 0.762229 0.647308i \(-0.224105\pi\)
0.762229 + 0.647308i \(0.224105\pi\)
\(824\) 12.3376 0.429802
\(825\) −13.5292 −0.471026
\(826\) −10.0930 −0.351181
\(827\) 28.1991 0.980581 0.490290 0.871559i \(-0.336891\pi\)
0.490290 + 0.871559i \(0.336891\pi\)
\(828\) −6.72833 −0.233826
\(829\) 1.12559 0.0390935 0.0195468 0.999809i \(-0.493778\pi\)
0.0195468 + 0.999809i \(0.493778\pi\)
\(830\) −2.78140 −0.0965438
\(831\) −40.2770 −1.39719
\(832\) −3.72833 −0.129256
\(833\) 14.9252 0.517126
\(834\) −14.5822 −0.504942
\(835\) −22.9133 −0.792948
\(836\) 19.5615 0.676549
\(837\) −20.0983 −0.694699
\(838\) −17.3505 −0.599364
\(839\) 39.9328 1.37863 0.689316 0.724461i \(-0.257911\pi\)
0.689316 + 0.724461i \(0.257911\pi\)
\(840\) 14.0660 0.485322
\(841\) 38.8655 1.34019
\(842\) 21.4230 0.738287
\(843\) −8.34420 −0.287389
\(844\) 4.34420 0.149533
\(845\) −0.900425 −0.0309756
\(846\) −77.0841 −2.65021
\(847\) 35.2436 1.21098
\(848\) −6.00000 −0.206041
\(849\) −2.31586 −0.0794801
\(850\) 1.11903 0.0383823
\(851\) 0.781399 0.0267860
\(852\) −22.2044 −0.760711
\(853\) 47.9921 1.64322 0.821610 0.570050i \(-0.193076\pi\)
0.821610 + 0.570050i \(0.193076\pi\)
\(854\) 16.0376 0.548796
\(855\) −30.3429 −1.03771
\(856\) −15.9328 −0.544571
\(857\) −43.4283 −1.48348 −0.741742 0.670686i \(-0.766000\pi\)
−0.741742 + 0.670686i \(0.766000\pi\)
\(858\) 50.4412 1.72203
\(859\) 32.5433 1.11036 0.555182 0.831729i \(-0.312648\pi\)
0.555182 + 0.831729i \(0.312648\pi\)
\(860\) −8.00000 −0.272798
\(861\) −54.8632 −1.86973
\(862\) 22.5822 0.769154
\(863\) 46.1036 1.56938 0.784692 0.619886i \(-0.212821\pi\)
0.784692 + 0.619886i \(0.212821\pi\)
\(864\) −11.6288 −0.395618
\(865\) −0.575681 −0.0195738
\(866\) 1.01417 0.0344628
\(867\) 49.1177 1.66813
\(868\) 7.79428 0.264555
\(869\) −64.6884 −2.19440
\(870\) −25.6947 −0.871132
\(871\) −9.08669 −0.307891
\(872\) −1.49027 −0.0504670
\(873\) −4.32578 −0.146405
\(874\) −4.50973 −0.152544
\(875\) −4.50973 −0.152457
\(876\) 29.4956 0.996563
\(877\) −24.0996 −0.813785 −0.406892 0.913476i \(-0.633388\pi\)
−0.406892 + 0.913476i \(0.633388\pi\)
\(878\) −26.7478 −0.902694
\(879\) 18.7142 0.631213
\(880\) −4.33763 −0.146221
\(881\) 2.34420 0.0789780 0.0394890 0.999220i \(-0.487427\pi\)
0.0394890 + 0.999220i \(0.487427\pi\)
\(882\) 89.7399 3.02170
\(883\) −41.0505 −1.38146 −0.690730 0.723113i \(-0.742711\pi\)
−0.690730 + 0.723113i \(0.742711\pi\)
\(884\) −4.17210 −0.140323
\(885\) −6.98055 −0.234649
\(886\) 10.2044 0.342825
\(887\) 54.7788 1.83929 0.919647 0.392747i \(-0.128475\pi\)
0.919647 + 0.392747i \(0.128475\pi\)
\(888\) 2.43720 0.0817872
\(889\) −3.04522 −0.102133
\(890\) 7.69471 0.257927
\(891\) 69.7725 2.33747
\(892\) 12.4761 0.417731
\(893\) −51.6664 −1.72895
\(894\) −23.4837 −0.785413
\(895\) −5.01945 −0.167782
\(896\) 4.50973 0.150659
\(897\) −11.6288 −0.388273
\(898\) 38.7867 1.29433
\(899\) −14.2381 −0.474866
\(900\) 6.72833 0.224278
\(901\) −6.71416 −0.223681
\(902\) 16.9186 0.563328
\(903\) −112.528 −3.74469
\(904\) −6.00000 −0.199557
\(905\) 11.5292 0.383243
\(906\) 41.6611 1.38410
\(907\) −10.1061 −0.335569 −0.167784 0.985824i \(-0.553661\pi\)
−0.167784 + 0.985824i \(0.553661\pi\)
\(908\) 15.9328 0.528747
\(909\) −55.4283 −1.83844
\(910\) 16.8137 0.557370
\(911\) −25.4178 −0.842128 −0.421064 0.907031i \(-0.638343\pi\)
−0.421064 + 0.907031i \(0.638343\pi\)
\(912\) −14.0660 −0.465770
\(913\) 12.0647 0.399282
\(914\) 34.9522 1.15612
\(915\) 11.0920 0.366689
\(916\) −3.56280 −0.117718
\(917\) −61.7594 −2.03947
\(918\) −13.0129 −0.429489
\(919\) 23.6017 0.778548 0.389274 0.921122i \(-0.372726\pi\)
0.389274 + 0.921122i \(0.372726\pi\)
\(920\) 1.00000 0.0329690
\(921\) −95.1566 −3.13552
\(922\) 16.3700 0.539116
\(923\) −26.5421 −0.873643
\(924\) −61.0129 −2.00718
\(925\) −0.781399 −0.0256922
\(926\) 29.2186 0.960183
\(927\) 83.0116 2.72646
\(928\) −8.23805 −0.270427
\(929\) −7.08669 −0.232507 −0.116253 0.993220i \(-0.537088\pi\)
−0.116253 + 0.993220i \(0.537088\pi\)
\(930\) 5.39070 0.176768
\(931\) 60.1490 1.97131
\(932\) −27.4956 −0.900647
\(933\) −17.3505 −0.568030
\(934\) 24.2770 0.794366
\(935\) −4.85392 −0.158740
\(936\) −25.0854 −0.819942
\(937\) 27.3169 0.892404 0.446202 0.894932i \(-0.352776\pi\)
0.446202 + 0.894932i \(0.352776\pi\)
\(938\) 10.9911 0.358873
\(939\) −12.7023 −0.414524
\(940\) 11.4567 0.373675
\(941\) 55.8979 1.82222 0.911109 0.412165i \(-0.135227\pi\)
0.911109 + 0.412165i \(0.135227\pi\)
\(942\) −50.6469 −1.65017
\(943\) −3.90043 −0.127015
\(944\) −2.23805 −0.0728424
\(945\) 52.4425 1.70595
\(946\) 34.7010 1.12823
\(947\) 37.5939 1.22164 0.610818 0.791771i \(-0.290841\pi\)
0.610818 + 0.791771i \(0.290841\pi\)
\(948\) 46.5150 1.51074
\(949\) 35.2575 1.14451
\(950\) 4.50973 0.146315
\(951\) 19.2305 0.623590
\(952\) 5.04650 0.163558
\(953\) −29.3828 −0.951804 −0.475902 0.879498i \(-0.657878\pi\)
−0.475902 + 0.879498i \(0.657878\pi\)
\(954\) −40.3700 −1.30703
\(955\) 18.7142 0.605576
\(956\) 10.0389 0.324681
\(957\) 111.454 3.60280
\(958\) 24.6080 0.795049
\(959\) 33.9545 1.09645
\(960\) 3.11903 0.100666
\(961\) −28.0129 −0.903641
\(962\) 2.91331 0.0939289
\(963\) −107.201 −3.45450
\(964\) −23.6947 −0.763155
\(965\) −23.4956 −0.756349
\(966\) 14.0660 0.452565
\(967\) −49.2292 −1.58310 −0.791552 0.611102i \(-0.790726\pi\)
−0.791552 + 0.611102i \(0.790726\pi\)
\(968\) 7.81502 0.251184
\(969\) −15.7402 −0.505647
\(970\) 0.642920 0.0206429
\(971\) 9.62347 0.308832 0.154416 0.988006i \(-0.450650\pi\)
0.154416 + 0.988006i \(0.450650\pi\)
\(972\) −15.2846 −0.490252
\(973\) 21.0841 0.675926
\(974\) −30.2381 −0.968890
\(975\) 11.6288 0.372418
\(976\) 3.55623 0.113832
\(977\) 18.9858 0.607411 0.303705 0.952766i \(-0.401776\pi\)
0.303705 + 0.952766i \(0.401776\pi\)
\(978\) 10.2651 0.328242
\(979\) −33.3768 −1.06673
\(980\) −13.3376 −0.426055
\(981\) −10.0271 −0.320139
\(982\) 12.3311 0.393500
\(983\) 4.33763 0.138349 0.0691744 0.997605i \(-0.477963\pi\)
0.0691744 + 0.997605i \(0.477963\pi\)
\(984\) −12.1655 −0.387823
\(985\) 18.1385 0.577940
\(986\) −9.21860 −0.293580
\(987\) 161.149 5.12942
\(988\) −16.8137 −0.534916
\(989\) −8.00000 −0.254385
\(990\) −29.1850 −0.927560
\(991\) 1.96766 0.0625049 0.0312524 0.999512i \(-0.490050\pi\)
0.0312524 + 0.999512i \(0.490050\pi\)
\(992\) 1.72833 0.0548744
\(993\) −86.0495 −2.73070
\(994\) 32.1049 1.01830
\(995\) 23.2575 0.737312
\(996\) −8.67526 −0.274886
\(997\) 3.96110 0.125449 0.0627246 0.998031i \(-0.480021\pi\)
0.0627246 + 0.998031i \(0.480021\pi\)
\(998\) −26.9133 −0.851926
\(999\) 9.08669 0.287490
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 230.2.a.d.1.1 3
3.2 odd 2 2070.2.a.z.1.3 3
4.3 odd 2 1840.2.a.r.1.3 3
5.2 odd 4 1150.2.b.j.599.6 6
5.3 odd 4 1150.2.b.j.599.1 6
5.4 even 2 1150.2.a.q.1.3 3
8.3 odd 2 7360.2.a.ce.1.1 3
8.5 even 2 7360.2.a.bz.1.3 3
20.19 odd 2 9200.2.a.cf.1.1 3
23.22 odd 2 5290.2.a.r.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.d.1.1 3 1.1 even 1 trivial
1150.2.a.q.1.3 3 5.4 even 2
1150.2.b.j.599.1 6 5.3 odd 4
1150.2.b.j.599.6 6 5.2 odd 4
1840.2.a.r.1.3 3 4.3 odd 2
2070.2.a.z.1.3 3 3.2 odd 2
5290.2.a.r.1.1 3 23.22 odd 2
7360.2.a.bz.1.3 3 8.5 even 2
7360.2.a.ce.1.1 3 8.3 odd 2
9200.2.a.cf.1.1 3 20.19 odd 2