Properties

Label 930.2.a.p.1.2
Level $930$
Weight $2$
Character 930.1
Self dual yes
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 930.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.56155 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.56155 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.56155 q^{11} -1.00000 q^{12} +2.00000 q^{13} +2.56155 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.12311 q^{17} +1.00000 q^{18} -7.68466 q^{19} +1.00000 q^{20} -2.56155 q^{21} +2.56155 q^{22} +1.43845 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +2.56155 q^{28} +7.12311 q^{29} -1.00000 q^{30} +1.00000 q^{31} +1.00000 q^{32} -2.56155 q^{33} -3.12311 q^{34} +2.56155 q^{35} +1.00000 q^{36} -3.12311 q^{37} -7.68466 q^{38} -2.00000 q^{39} +1.00000 q^{40} +7.12311 q^{41} -2.56155 q^{42} +12.8078 q^{43} +2.56155 q^{44} +1.00000 q^{45} +1.43845 q^{46} +5.12311 q^{47} -1.00000 q^{48} -0.438447 q^{49} +1.00000 q^{50} +3.12311 q^{51} +2.00000 q^{52} +7.43845 q^{53} -1.00000 q^{54} +2.56155 q^{55} +2.56155 q^{56} +7.68466 q^{57} +7.12311 q^{58} -13.1231 q^{59} -1.00000 q^{60} +6.00000 q^{61} +1.00000 q^{62} +2.56155 q^{63} +1.00000 q^{64} +2.00000 q^{65} -2.56155 q^{66} -15.3693 q^{67} -3.12311 q^{68} -1.43845 q^{69} +2.56155 q^{70} -7.68466 q^{71} +1.00000 q^{72} -10.8078 q^{73} -3.12311 q^{74} -1.00000 q^{75} -7.68466 q^{76} +6.56155 q^{77} -2.00000 q^{78} -4.31534 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.12311 q^{82} +14.2462 q^{83} -2.56155 q^{84} -3.12311 q^{85} +12.8078 q^{86} -7.12311 q^{87} +2.56155 q^{88} -13.6847 q^{89} +1.00000 q^{90} +5.12311 q^{91} +1.43845 q^{92} -1.00000 q^{93} +5.12311 q^{94} -7.68466 q^{95} -1.00000 q^{96} -6.00000 q^{97} -0.438447 q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + q^{11} - 2 q^{12} + 4 q^{13} + q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} + 2 q^{20} - q^{21} + q^{22} + 7 q^{23} - 2 q^{24} + 2 q^{25} + 4 q^{26} - 2 q^{27} + q^{28} + 6 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} - q^{33} + 2 q^{34} + q^{35} + 2 q^{36} + 2 q^{37} - 3 q^{38} - 4 q^{39} + 2 q^{40} + 6 q^{41} - q^{42} + 5 q^{43} + q^{44} + 2 q^{45} + 7 q^{46} + 2 q^{47} - 2 q^{48} - 5 q^{49} + 2 q^{50} - 2 q^{51} + 4 q^{52} + 19 q^{53} - 2 q^{54} + q^{55} + q^{56} + 3 q^{57} + 6 q^{58} - 18 q^{59} - 2 q^{60} + 12 q^{61} + 2 q^{62} + q^{63} + 2 q^{64} + 4 q^{65} - q^{66} - 6 q^{67} + 2 q^{68} - 7 q^{69} + q^{70} - 3 q^{71} + 2 q^{72} - q^{73} + 2 q^{74} - 2 q^{75} - 3 q^{76} + 9 q^{77} - 4 q^{78} - 21 q^{79} + 2 q^{80} + 2 q^{81} + 6 q^{82} + 12 q^{83} - q^{84} + 2 q^{85} + 5 q^{86} - 6 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} + 2 q^{91} + 7 q^{92} - 2 q^{93} + 2 q^{94} - 3 q^{95} - 2 q^{96} - 12 q^{97} - 5 q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) 2.56155 0.968176 0.484088 0.875019i \(-0.339151\pi\)
0.484088 + 0.875019i \(0.339151\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 2.56155 0.772337 0.386169 0.922428i \(-0.373798\pi\)
0.386169 + 0.922428i \(0.373798\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 2.56155 0.684604
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −3.12311 −0.757464 −0.378732 0.925506i \(-0.623640\pi\)
−0.378732 + 0.925506i \(0.623640\pi\)
\(18\) 1.00000 0.235702
\(19\) −7.68466 −1.76298 −0.881491 0.472201i \(-0.843460\pi\)
−0.881491 + 0.472201i \(0.843460\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.56155 −0.558977
\(22\) 2.56155 0.546125
\(23\) 1.43845 0.299937 0.149968 0.988691i \(-0.452083\pi\)
0.149968 + 0.988691i \(0.452083\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) 2.56155 0.484088
\(29\) 7.12311 1.32273 0.661364 0.750065i \(-0.269978\pi\)
0.661364 + 0.750065i \(0.269978\pi\)
\(30\) −1.00000 −0.182574
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) −2.56155 −0.445909
\(34\) −3.12311 −0.535608
\(35\) 2.56155 0.432981
\(36\) 1.00000 0.166667
\(37\) −3.12311 −0.513435 −0.256718 0.966486i \(-0.582641\pi\)
−0.256718 + 0.966486i \(0.582641\pi\)
\(38\) −7.68466 −1.24662
\(39\) −2.00000 −0.320256
\(40\) 1.00000 0.158114
\(41\) 7.12311 1.11244 0.556221 0.831034i \(-0.312251\pi\)
0.556221 + 0.831034i \(0.312251\pi\)
\(42\) −2.56155 −0.395256
\(43\) 12.8078 1.95317 0.976583 0.215142i \(-0.0690213\pi\)
0.976583 + 0.215142i \(0.0690213\pi\)
\(44\) 2.56155 0.386169
\(45\) 1.00000 0.149071
\(46\) 1.43845 0.212087
\(47\) 5.12311 0.747282 0.373641 0.927573i \(-0.378109\pi\)
0.373641 + 0.927573i \(0.378109\pi\)
\(48\) −1.00000 −0.144338
\(49\) −0.438447 −0.0626353
\(50\) 1.00000 0.141421
\(51\) 3.12311 0.437322
\(52\) 2.00000 0.277350
\(53\) 7.43845 1.02175 0.510875 0.859655i \(-0.329322\pi\)
0.510875 + 0.859655i \(0.329322\pi\)
\(54\) −1.00000 −0.136083
\(55\) 2.56155 0.345400
\(56\) 2.56155 0.342302
\(57\) 7.68466 1.01786
\(58\) 7.12311 0.935310
\(59\) −13.1231 −1.70848 −0.854241 0.519877i \(-0.825978\pi\)
−0.854241 + 0.519877i \(0.825978\pi\)
\(60\) −1.00000 −0.129099
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 1.00000 0.127000
\(63\) 2.56155 0.322725
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) −2.56155 −0.315305
\(67\) −15.3693 −1.87766 −0.938830 0.344380i \(-0.888089\pi\)
−0.938830 + 0.344380i \(0.888089\pi\)
\(68\) −3.12311 −0.378732
\(69\) −1.43845 −0.173169
\(70\) 2.56155 0.306164
\(71\) −7.68466 −0.912001 −0.456001 0.889979i \(-0.650719\pi\)
−0.456001 + 0.889979i \(0.650719\pi\)
\(72\) 1.00000 0.117851
\(73\) −10.8078 −1.26495 −0.632477 0.774580i \(-0.717962\pi\)
−0.632477 + 0.774580i \(0.717962\pi\)
\(74\) −3.12311 −0.363054
\(75\) −1.00000 −0.115470
\(76\) −7.68466 −0.881491
\(77\) 6.56155 0.747758
\(78\) −2.00000 −0.226455
\(79\) −4.31534 −0.485514 −0.242757 0.970087i \(-0.578052\pi\)
−0.242757 + 0.970087i \(0.578052\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 7.12311 0.786615
\(83\) 14.2462 1.56372 0.781862 0.623451i \(-0.214270\pi\)
0.781862 + 0.623451i \(0.214270\pi\)
\(84\) −2.56155 −0.279488
\(85\) −3.12311 −0.338748
\(86\) 12.8078 1.38110
\(87\) −7.12311 −0.763677
\(88\) 2.56155 0.273062
\(89\) −13.6847 −1.45057 −0.725285 0.688448i \(-0.758292\pi\)
−0.725285 + 0.688448i \(0.758292\pi\)
\(90\) 1.00000 0.105409
\(91\) 5.12311 0.537047
\(92\) 1.43845 0.149968
\(93\) −1.00000 −0.103695
\(94\) 5.12311 0.528408
\(95\) −7.68466 −0.788429
\(96\) −1.00000 −0.102062
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −0.438447 −0.0442899
\(99\) 2.56155 0.257446
\(100\) 1.00000 0.100000
\(101\) −0.561553 −0.0558766 −0.0279383 0.999610i \(-0.508894\pi\)
−0.0279383 + 0.999610i \(0.508894\pi\)
\(102\) 3.12311 0.309234
\(103\) −1.75379 −0.172806 −0.0864030 0.996260i \(-0.527537\pi\)
−0.0864030 + 0.996260i \(0.527537\pi\)
\(104\) 2.00000 0.196116
\(105\) −2.56155 −0.249982
\(106\) 7.43845 0.722486
\(107\) −2.56155 −0.247635 −0.123817 0.992305i \(-0.539514\pi\)
−0.123817 + 0.992305i \(0.539514\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 5.36932 0.514287 0.257144 0.966373i \(-0.417219\pi\)
0.257144 + 0.966373i \(0.417219\pi\)
\(110\) 2.56155 0.244234
\(111\) 3.12311 0.296432
\(112\) 2.56155 0.242044
\(113\) −1.68466 −0.158479 −0.0792397 0.996856i \(-0.525249\pi\)
−0.0792397 + 0.996856i \(0.525249\pi\)
\(114\) 7.68466 0.719734
\(115\) 1.43845 0.134136
\(116\) 7.12311 0.661364
\(117\) 2.00000 0.184900
\(118\) −13.1231 −1.20808
\(119\) −8.00000 −0.733359
\(120\) −1.00000 −0.0912871
\(121\) −4.43845 −0.403495
\(122\) 6.00000 0.543214
\(123\) −7.12311 −0.642269
\(124\) 1.00000 0.0898027
\(125\) 1.00000 0.0894427
\(126\) 2.56155 0.228201
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000 0.0883883
\(129\) −12.8078 −1.12766
\(130\) 2.00000 0.175412
\(131\) −15.3693 −1.34282 −0.671412 0.741085i \(-0.734312\pi\)
−0.671412 + 0.741085i \(0.734312\pi\)
\(132\) −2.56155 −0.222955
\(133\) −19.6847 −1.70688
\(134\) −15.3693 −1.32771
\(135\) −1.00000 −0.0860663
\(136\) −3.12311 −0.267804
\(137\) 20.2462 1.72975 0.864875 0.501987i \(-0.167397\pi\)
0.864875 + 0.501987i \(0.167397\pi\)
\(138\) −1.43845 −0.122449
\(139\) −17.1231 −1.45236 −0.726181 0.687503i \(-0.758707\pi\)
−0.726181 + 0.687503i \(0.758707\pi\)
\(140\) 2.56155 0.216491
\(141\) −5.12311 −0.431443
\(142\) −7.68466 −0.644882
\(143\) 5.12311 0.428416
\(144\) 1.00000 0.0833333
\(145\) 7.12311 0.591542
\(146\) −10.8078 −0.894457
\(147\) 0.438447 0.0361625
\(148\) −3.12311 −0.256718
\(149\) 17.0540 1.39712 0.698558 0.715553i \(-0.253825\pi\)
0.698558 + 0.715553i \(0.253825\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −7.68466 −0.623308
\(153\) −3.12311 −0.252488
\(154\) 6.56155 0.528745
\(155\) 1.00000 0.0803219
\(156\) −2.00000 −0.160128
\(157\) 17.0540 1.36106 0.680528 0.732722i \(-0.261751\pi\)
0.680528 + 0.732722i \(0.261751\pi\)
\(158\) −4.31534 −0.343310
\(159\) −7.43845 −0.589907
\(160\) 1.00000 0.0790569
\(161\) 3.68466 0.290392
\(162\) 1.00000 0.0785674
\(163\) −15.3693 −1.20382 −0.601909 0.798565i \(-0.705593\pi\)
−0.601909 + 0.798565i \(0.705593\pi\)
\(164\) 7.12311 0.556221
\(165\) −2.56155 −0.199417
\(166\) 14.2462 1.10572
\(167\) −6.56155 −0.507748 −0.253874 0.967237i \(-0.581705\pi\)
−0.253874 + 0.967237i \(0.581705\pi\)
\(168\) −2.56155 −0.197628
\(169\) −9.00000 −0.692308
\(170\) −3.12311 −0.239531
\(171\) −7.68466 −0.587661
\(172\) 12.8078 0.976583
\(173\) 8.24621 0.626948 0.313474 0.949597i \(-0.398507\pi\)
0.313474 + 0.949597i \(0.398507\pi\)
\(174\) −7.12311 −0.540001
\(175\) 2.56155 0.193635
\(176\) 2.56155 0.193084
\(177\) 13.1231 0.986393
\(178\) −13.6847 −1.02571
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 0.0745356
\(181\) −13.0540 −0.970294 −0.485147 0.874433i \(-0.661234\pi\)
−0.485147 + 0.874433i \(0.661234\pi\)
\(182\) 5.12311 0.379750
\(183\) −6.00000 −0.443533
\(184\) 1.43845 0.106044
\(185\) −3.12311 −0.229615
\(186\) −1.00000 −0.0733236
\(187\) −8.00000 −0.585018
\(188\) 5.12311 0.373641
\(189\) −2.56155 −0.186326
\(190\) −7.68466 −0.557504
\(191\) −14.2462 −1.03082 −0.515410 0.856944i \(-0.672360\pi\)
−0.515410 + 0.856944i \(0.672360\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.4924 1.04319 0.521594 0.853194i \(-0.325338\pi\)
0.521594 + 0.853194i \(0.325338\pi\)
\(194\) −6.00000 −0.430775
\(195\) −2.00000 −0.143223
\(196\) −0.438447 −0.0313177
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 2.56155 0.182042
\(199\) −16.8078 −1.19147 −0.595735 0.803181i \(-0.703139\pi\)
−0.595735 + 0.803181i \(0.703139\pi\)
\(200\) 1.00000 0.0707107
\(201\) 15.3693 1.08407
\(202\) −0.561553 −0.0395107
\(203\) 18.2462 1.28063
\(204\) 3.12311 0.218661
\(205\) 7.12311 0.497499
\(206\) −1.75379 −0.122192
\(207\) 1.43845 0.0999790
\(208\) 2.00000 0.138675
\(209\) −19.6847 −1.36162
\(210\) −2.56155 −0.176764
\(211\) −23.6847 −1.63052 −0.815260 0.579096i \(-0.803406\pi\)
−0.815260 + 0.579096i \(0.803406\pi\)
\(212\) 7.43845 0.510875
\(213\) 7.68466 0.526544
\(214\) −2.56155 −0.175104
\(215\) 12.8078 0.873482
\(216\) −1.00000 −0.0680414
\(217\) 2.56155 0.173890
\(218\) 5.36932 0.363656
\(219\) 10.8078 0.730321
\(220\) 2.56155 0.172700
\(221\) −6.24621 −0.420166
\(222\) 3.12311 0.209609
\(223\) −21.1231 −1.41451 −0.707254 0.706960i \(-0.750066\pi\)
−0.707254 + 0.706960i \(0.750066\pi\)
\(224\) 2.56155 0.171151
\(225\) 1.00000 0.0666667
\(226\) −1.68466 −0.112062
\(227\) 7.68466 0.510049 0.255024 0.966935i \(-0.417917\pi\)
0.255024 + 0.966935i \(0.417917\pi\)
\(228\) 7.68466 0.508929
\(229\) −16.5616 −1.09442 −0.547209 0.836996i \(-0.684310\pi\)
−0.547209 + 0.836996i \(0.684310\pi\)
\(230\) 1.43845 0.0948484
\(231\) −6.56155 −0.431718
\(232\) 7.12311 0.467655
\(233\) −17.0540 −1.11724 −0.558622 0.829423i \(-0.688670\pi\)
−0.558622 + 0.829423i \(0.688670\pi\)
\(234\) 2.00000 0.130744
\(235\) 5.12311 0.334195
\(236\) −13.1231 −0.854241
\(237\) 4.31534 0.280312
\(238\) −8.00000 −0.518563
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 12.2462 0.788848 0.394424 0.918929i \(-0.370944\pi\)
0.394424 + 0.918929i \(0.370944\pi\)
\(242\) −4.43845 −0.285314
\(243\) −1.00000 −0.0641500
\(244\) 6.00000 0.384111
\(245\) −0.438447 −0.0280114
\(246\) −7.12311 −0.454153
\(247\) −15.3693 −0.977926
\(248\) 1.00000 0.0635001
\(249\) −14.2462 −0.902817
\(250\) 1.00000 0.0632456
\(251\) 16.4924 1.04099 0.520496 0.853864i \(-0.325747\pi\)
0.520496 + 0.853864i \(0.325747\pi\)
\(252\) 2.56155 0.161363
\(253\) 3.68466 0.231652
\(254\) 0 0
\(255\) 3.12311 0.195576
\(256\) 1.00000 0.0625000
\(257\) −1.68466 −0.105086 −0.0525431 0.998619i \(-0.516733\pi\)
−0.0525431 + 0.998619i \(0.516733\pi\)
\(258\) −12.8078 −0.797377
\(259\) −8.00000 −0.497096
\(260\) 2.00000 0.124035
\(261\) 7.12311 0.440909
\(262\) −15.3693 −0.949520
\(263\) −20.4924 −1.26362 −0.631808 0.775125i \(-0.717687\pi\)
−0.631808 + 0.775125i \(0.717687\pi\)
\(264\) −2.56155 −0.157653
\(265\) 7.43845 0.456940
\(266\) −19.6847 −1.20694
\(267\) 13.6847 0.837487
\(268\) −15.3693 −0.938830
\(269\) −0.246211 −0.0150118 −0.00750588 0.999972i \(-0.502389\pi\)
−0.00750588 + 0.999972i \(0.502389\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 27.0540 1.64341 0.821706 0.569912i \(-0.193023\pi\)
0.821706 + 0.569912i \(0.193023\pi\)
\(272\) −3.12311 −0.189366
\(273\) −5.12311 −0.310064
\(274\) 20.2462 1.22312
\(275\) 2.56155 0.154467
\(276\) −1.43845 −0.0865843
\(277\) −5.36932 −0.322611 −0.161305 0.986905i \(-0.551570\pi\)
−0.161305 + 0.986905i \(0.551570\pi\)
\(278\) −17.1231 −1.02698
\(279\) 1.00000 0.0598684
\(280\) 2.56155 0.153082
\(281\) 4.87689 0.290931 0.145466 0.989363i \(-0.453532\pi\)
0.145466 + 0.989363i \(0.453532\pi\)
\(282\) −5.12311 −0.305077
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −7.68466 −0.456001
\(285\) 7.68466 0.455200
\(286\) 5.12311 0.302936
\(287\) 18.2462 1.07704
\(288\) 1.00000 0.0589256
\(289\) −7.24621 −0.426248
\(290\) 7.12311 0.418283
\(291\) 6.00000 0.351726
\(292\) −10.8078 −0.632477
\(293\) 26.4924 1.54770 0.773852 0.633367i \(-0.218327\pi\)
0.773852 + 0.633367i \(0.218327\pi\)
\(294\) 0.438447 0.0255708
\(295\) −13.1231 −0.764057
\(296\) −3.12311 −0.181527
\(297\) −2.56155 −0.148636
\(298\) 17.0540 0.987910
\(299\) 2.87689 0.166375
\(300\) −1.00000 −0.0577350
\(301\) 32.8078 1.89101
\(302\) 0 0
\(303\) 0.561553 0.0322604
\(304\) −7.68466 −0.440745
\(305\) 6.00000 0.343559
\(306\) −3.12311 −0.178536
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 6.56155 0.373879
\(309\) 1.75379 0.0997696
\(310\) 1.00000 0.0567962
\(311\) −1.75379 −0.0994482 −0.0497241 0.998763i \(-0.515834\pi\)
−0.0497241 + 0.998763i \(0.515834\pi\)
\(312\) −2.00000 −0.113228
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 17.0540 0.962412
\(315\) 2.56155 0.144327
\(316\) −4.31534 −0.242757
\(317\) 16.8769 0.947901 0.473950 0.880552i \(-0.342828\pi\)
0.473950 + 0.880552i \(0.342828\pi\)
\(318\) −7.43845 −0.417127
\(319\) 18.2462 1.02159
\(320\) 1.00000 0.0559017
\(321\) 2.56155 0.142972
\(322\) 3.68466 0.205338
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −15.3693 −0.851228
\(327\) −5.36932 −0.296924
\(328\) 7.12311 0.393308
\(329\) 13.1231 0.723500
\(330\) −2.56155 −0.141009
\(331\) −6.24621 −0.343323 −0.171661 0.985156i \(-0.554914\pi\)
−0.171661 + 0.985156i \(0.554914\pi\)
\(332\) 14.2462 0.781862
\(333\) −3.12311 −0.171145
\(334\) −6.56155 −0.359032
\(335\) −15.3693 −0.839715
\(336\) −2.56155 −0.139744
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) −9.00000 −0.489535
\(339\) 1.68466 0.0914981
\(340\) −3.12311 −0.169374
\(341\) 2.56155 0.138716
\(342\) −7.68466 −0.415539
\(343\) −19.0540 −1.02882
\(344\) 12.8078 0.690548
\(345\) −1.43845 −0.0774434
\(346\) 8.24621 0.443319
\(347\) 14.2462 0.764777 0.382388 0.924002i \(-0.375102\pi\)
0.382388 + 0.924002i \(0.375102\pi\)
\(348\) −7.12311 −0.381839
\(349\) 5.36932 0.287413 0.143706 0.989620i \(-0.454098\pi\)
0.143706 + 0.989620i \(0.454098\pi\)
\(350\) 2.56155 0.136921
\(351\) −2.00000 −0.106752
\(352\) 2.56155 0.136531
\(353\) −0.246211 −0.0131045 −0.00655225 0.999979i \(-0.502086\pi\)
−0.00655225 + 0.999979i \(0.502086\pi\)
\(354\) 13.1231 0.697485
\(355\) −7.68466 −0.407859
\(356\) −13.6847 −0.725285
\(357\) 8.00000 0.423405
\(358\) −12.0000 −0.634220
\(359\) −31.6847 −1.67225 −0.836126 0.548537i \(-0.815185\pi\)
−0.836126 + 0.548537i \(0.815185\pi\)
\(360\) 1.00000 0.0527046
\(361\) 40.0540 2.10810
\(362\) −13.0540 −0.686102
\(363\) 4.43845 0.232958
\(364\) 5.12311 0.268524
\(365\) −10.8078 −0.565704
\(366\) −6.00000 −0.313625
\(367\) 15.3693 0.802272 0.401136 0.916019i \(-0.368616\pi\)
0.401136 + 0.916019i \(0.368616\pi\)
\(368\) 1.43845 0.0749842
\(369\) 7.12311 0.370814
\(370\) −3.12311 −0.162363
\(371\) 19.0540 0.989233
\(372\) −1.00000 −0.0518476
\(373\) −5.68466 −0.294340 −0.147170 0.989111i \(-0.547017\pi\)
−0.147170 + 0.989111i \(0.547017\pi\)
\(374\) −8.00000 −0.413670
\(375\) −1.00000 −0.0516398
\(376\) 5.12311 0.264204
\(377\) 14.2462 0.733717
\(378\) −2.56155 −0.131752
\(379\) −7.05398 −0.362338 −0.181169 0.983452i \(-0.557988\pi\)
−0.181169 + 0.983452i \(0.557988\pi\)
\(380\) −7.68466 −0.394215
\(381\) 0 0
\(382\) −14.2462 −0.728900
\(383\) −10.2462 −0.523557 −0.261778 0.965128i \(-0.584309\pi\)
−0.261778 + 0.965128i \(0.584309\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 6.56155 0.334408
\(386\) 14.4924 0.737645
\(387\) 12.8078 0.651055
\(388\) −6.00000 −0.304604
\(389\) 7.75379 0.393133 0.196566 0.980491i \(-0.437021\pi\)
0.196566 + 0.980491i \(0.437021\pi\)
\(390\) −2.00000 −0.101274
\(391\) −4.49242 −0.227192
\(392\) −0.438447 −0.0221449
\(393\) 15.3693 0.775279
\(394\) 6.00000 0.302276
\(395\) −4.31534 −0.217128
\(396\) 2.56155 0.128723
\(397\) 9.05398 0.454406 0.227203 0.973847i \(-0.427042\pi\)
0.227203 + 0.973847i \(0.427042\pi\)
\(398\) −16.8078 −0.842497
\(399\) 19.6847 0.985466
\(400\) 1.00000 0.0500000
\(401\) −13.6847 −0.683379 −0.341690 0.939813i \(-0.610999\pi\)
−0.341690 + 0.939813i \(0.610999\pi\)
\(402\) 15.3693 0.766552
\(403\) 2.00000 0.0996271
\(404\) −0.561553 −0.0279383
\(405\) 1.00000 0.0496904
\(406\) 18.2462 0.905544
\(407\) −8.00000 −0.396545
\(408\) 3.12311 0.154617
\(409\) −37.3693 −1.84779 −0.923897 0.382642i \(-0.875014\pi\)
−0.923897 + 0.382642i \(0.875014\pi\)
\(410\) 7.12311 0.351785
\(411\) −20.2462 −0.998672
\(412\) −1.75379 −0.0864030
\(413\) −33.6155 −1.65411
\(414\) 1.43845 0.0706958
\(415\) 14.2462 0.699319
\(416\) 2.00000 0.0980581
\(417\) 17.1231 0.838522
\(418\) −19.6847 −0.962808
\(419\) 5.75379 0.281091 0.140545 0.990074i \(-0.455114\pi\)
0.140545 + 0.990074i \(0.455114\pi\)
\(420\) −2.56155 −0.124991
\(421\) −14.4924 −0.706317 −0.353159 0.935563i \(-0.614892\pi\)
−0.353159 + 0.935563i \(0.614892\pi\)
\(422\) −23.6847 −1.15295
\(423\) 5.12311 0.249094
\(424\) 7.43845 0.361243
\(425\) −3.12311 −0.151493
\(426\) 7.68466 0.372323
\(427\) 15.3693 0.743773
\(428\) −2.56155 −0.123817
\(429\) −5.12311 −0.247346
\(430\) 12.8078 0.617645
\(431\) −30.2462 −1.45691 −0.728454 0.685094i \(-0.759761\pi\)
−0.728454 + 0.685094i \(0.759761\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 35.3002 1.69642 0.848209 0.529661i \(-0.177681\pi\)
0.848209 + 0.529661i \(0.177681\pi\)
\(434\) 2.56155 0.122958
\(435\) −7.12311 −0.341527
\(436\) 5.36932 0.257144
\(437\) −11.0540 −0.528783
\(438\) 10.8078 0.516415
\(439\) 9.61553 0.458924 0.229462 0.973318i \(-0.426303\pi\)
0.229462 + 0.973318i \(0.426303\pi\)
\(440\) 2.56155 0.122117
\(441\) −0.438447 −0.0208784
\(442\) −6.24621 −0.297102
\(443\) 23.0540 1.09533 0.547664 0.836699i \(-0.315517\pi\)
0.547664 + 0.836699i \(0.315517\pi\)
\(444\) 3.12311 0.148216
\(445\) −13.6847 −0.648715
\(446\) −21.1231 −1.00021
\(447\) −17.0540 −0.806625
\(448\) 2.56155 0.121022
\(449\) 10.4924 0.495168 0.247584 0.968866i \(-0.420363\pi\)
0.247584 + 0.968866i \(0.420363\pi\)
\(450\) 1.00000 0.0471405
\(451\) 18.2462 0.859181
\(452\) −1.68466 −0.0792397
\(453\) 0 0
\(454\) 7.68466 0.360659
\(455\) 5.12311 0.240175
\(456\) 7.68466 0.359867
\(457\) −24.7386 −1.15722 −0.578612 0.815603i \(-0.696406\pi\)
−0.578612 + 0.815603i \(0.696406\pi\)
\(458\) −16.5616 −0.773871
\(459\) 3.12311 0.145774
\(460\) 1.43845 0.0670679
\(461\) 9.36932 0.436373 0.218186 0.975907i \(-0.429986\pi\)
0.218186 + 0.975907i \(0.429986\pi\)
\(462\) −6.56155 −0.305271
\(463\) 30.7386 1.42855 0.714273 0.699867i \(-0.246758\pi\)
0.714273 + 0.699867i \(0.246758\pi\)
\(464\) 7.12311 0.330682
\(465\) −1.00000 −0.0463739
\(466\) −17.0540 −0.790010
\(467\) −9.75379 −0.451352 −0.225676 0.974202i \(-0.572459\pi\)
−0.225676 + 0.974202i \(0.572459\pi\)
\(468\) 2.00000 0.0924500
\(469\) −39.3693 −1.81791
\(470\) 5.12311 0.236311
\(471\) −17.0540 −0.785806
\(472\) −13.1231 −0.604040
\(473\) 32.8078 1.50850
\(474\) 4.31534 0.198210
\(475\) −7.68466 −0.352596
\(476\) −8.00000 −0.366679
\(477\) 7.43845 0.340583
\(478\) 24.0000 1.09773
\(479\) 10.5616 0.482570 0.241285 0.970454i \(-0.422431\pi\)
0.241285 + 0.970454i \(0.422431\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −6.24621 −0.284803
\(482\) 12.2462 0.557800
\(483\) −3.68466 −0.167658
\(484\) −4.43845 −0.201748
\(485\) −6.00000 −0.272446
\(486\) −1.00000 −0.0453609
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) 6.00000 0.271607
\(489\) 15.3693 0.695025
\(490\) −0.438447 −0.0198070
\(491\) −25.9309 −1.17024 −0.585122 0.810945i \(-0.698953\pi\)
−0.585122 + 0.810945i \(0.698953\pi\)
\(492\) −7.12311 −0.321134
\(493\) −22.2462 −1.00192
\(494\) −15.3693 −0.691498
\(495\) 2.56155 0.115133
\(496\) 1.00000 0.0449013
\(497\) −19.6847 −0.882978
\(498\) −14.2462 −0.638388
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 1.00000 0.0447214
\(501\) 6.56155 0.293149
\(502\) 16.4924 0.736093
\(503\) 26.2462 1.17026 0.585130 0.810939i \(-0.301043\pi\)
0.585130 + 0.810939i \(0.301043\pi\)
\(504\) 2.56155 0.114101
\(505\) −0.561553 −0.0249888
\(506\) 3.68466 0.163803
\(507\) 9.00000 0.399704
\(508\) 0 0
\(509\) 19.6155 0.869443 0.434721 0.900565i \(-0.356847\pi\)
0.434721 + 0.900565i \(0.356847\pi\)
\(510\) 3.12311 0.138293
\(511\) −27.6847 −1.22470
\(512\) 1.00000 0.0441942
\(513\) 7.68466 0.339286
\(514\) −1.68466 −0.0743071
\(515\) −1.75379 −0.0772812
\(516\) −12.8078 −0.563830
\(517\) 13.1231 0.577154
\(518\) −8.00000 −0.351500
\(519\) −8.24621 −0.361968
\(520\) 2.00000 0.0877058
\(521\) −32.2462 −1.41273 −0.706366 0.707847i \(-0.749667\pi\)
−0.706366 + 0.707847i \(0.749667\pi\)
\(522\) 7.12311 0.311770
\(523\) −22.4233 −0.980502 −0.490251 0.871581i \(-0.663095\pi\)
−0.490251 + 0.871581i \(0.663095\pi\)
\(524\) −15.3693 −0.671412
\(525\) −2.56155 −0.111795
\(526\) −20.4924 −0.893512
\(527\) −3.12311 −0.136045
\(528\) −2.56155 −0.111477
\(529\) −20.9309 −0.910038
\(530\) 7.43845 0.323105
\(531\) −13.1231 −0.569494
\(532\) −19.6847 −0.853438
\(533\) 14.2462 0.617072
\(534\) 13.6847 0.592193
\(535\) −2.56155 −0.110746
\(536\) −15.3693 −0.663853
\(537\) 12.0000 0.517838
\(538\) −0.246211 −0.0106149
\(539\) −1.12311 −0.0483756
\(540\) −1.00000 −0.0430331
\(541\) 19.7538 0.849282 0.424641 0.905362i \(-0.360400\pi\)
0.424641 + 0.905362i \(0.360400\pi\)
\(542\) 27.0540 1.16207
\(543\) 13.0540 0.560200
\(544\) −3.12311 −0.133902
\(545\) 5.36932 0.229996
\(546\) −5.12311 −0.219249
\(547\) 26.8769 1.14917 0.574587 0.818444i \(-0.305163\pi\)
0.574587 + 0.818444i \(0.305163\pi\)
\(548\) 20.2462 0.864875
\(549\) 6.00000 0.256074
\(550\) 2.56155 0.109225
\(551\) −54.7386 −2.33194
\(552\) −1.43845 −0.0612244
\(553\) −11.0540 −0.470063
\(554\) −5.36932 −0.228120
\(555\) 3.12311 0.132568
\(556\) −17.1231 −0.726181
\(557\) −26.8078 −1.13588 −0.567941 0.823069i \(-0.692260\pi\)
−0.567941 + 0.823069i \(0.692260\pi\)
\(558\) 1.00000 0.0423334
\(559\) 25.6155 1.08342
\(560\) 2.56155 0.108245
\(561\) 8.00000 0.337760
\(562\) 4.87689 0.205719
\(563\) 16.4924 0.695073 0.347536 0.937667i \(-0.387018\pi\)
0.347536 + 0.937667i \(0.387018\pi\)
\(564\) −5.12311 −0.215722
\(565\) −1.68466 −0.0708741
\(566\) 0 0
\(567\) 2.56155 0.107575
\(568\) −7.68466 −0.322441
\(569\) 30.8078 1.29153 0.645764 0.763537i \(-0.276539\pi\)
0.645764 + 0.763537i \(0.276539\pi\)
\(570\) 7.68466 0.321875
\(571\) 41.1231 1.72095 0.860474 0.509494i \(-0.170167\pi\)
0.860474 + 0.509494i \(0.170167\pi\)
\(572\) 5.12311 0.214208
\(573\) 14.2462 0.595144
\(574\) 18.2462 0.761582
\(575\) 1.43845 0.0599874
\(576\) 1.00000 0.0416667
\(577\) 15.1231 0.629583 0.314792 0.949161i \(-0.398065\pi\)
0.314792 + 0.949161i \(0.398065\pi\)
\(578\) −7.24621 −0.301403
\(579\) −14.4924 −0.602285
\(580\) 7.12311 0.295771
\(581\) 36.4924 1.51396
\(582\) 6.00000 0.248708
\(583\) 19.0540 0.789135
\(584\) −10.8078 −0.447228
\(585\) 2.00000 0.0826898
\(586\) 26.4924 1.09439
\(587\) −0.492423 −0.0203245 −0.0101622 0.999948i \(-0.503235\pi\)
−0.0101622 + 0.999948i \(0.503235\pi\)
\(588\) 0.438447 0.0180813
\(589\) −7.68466 −0.316641
\(590\) −13.1231 −0.540270
\(591\) −6.00000 −0.246807
\(592\) −3.12311 −0.128359
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) −2.56155 −0.105102
\(595\) −8.00000 −0.327968
\(596\) 17.0540 0.698558
\(597\) 16.8078 0.687896
\(598\) 2.87689 0.117645
\(599\) 38.4233 1.56993 0.784967 0.619538i \(-0.212680\pi\)
0.784967 + 0.619538i \(0.212680\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 32.8078 1.33714
\(603\) −15.3693 −0.625887
\(604\) 0 0
\(605\) −4.43845 −0.180449
\(606\) 0.561553 0.0228115
\(607\) 7.05398 0.286312 0.143156 0.989700i \(-0.454275\pi\)
0.143156 + 0.989700i \(0.454275\pi\)
\(608\) −7.68466 −0.311654
\(609\) −18.2462 −0.739374
\(610\) 6.00000 0.242933
\(611\) 10.2462 0.414517
\(612\) −3.12311 −0.126244
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) −7.12311 −0.287231
\(616\) 6.56155 0.264372
\(617\) −15.4384 −0.621528 −0.310764 0.950487i \(-0.600585\pi\)
−0.310764 + 0.950487i \(0.600585\pi\)
\(618\) 1.75379 0.0705477
\(619\) 11.3693 0.456971 0.228486 0.973547i \(-0.426623\pi\)
0.228486 + 0.973547i \(0.426623\pi\)
\(620\) 1.00000 0.0401610
\(621\) −1.43845 −0.0577229
\(622\) −1.75379 −0.0703205
\(623\) −35.0540 −1.40441
\(624\) −2.00000 −0.0800641
\(625\) 1.00000 0.0400000
\(626\) −10.0000 −0.399680
\(627\) 19.6847 0.786130
\(628\) 17.0540 0.680528
\(629\) 9.75379 0.388909
\(630\) 2.56155 0.102055
\(631\) 29.3002 1.16642 0.583211 0.812321i \(-0.301796\pi\)
0.583211 + 0.812321i \(0.301796\pi\)
\(632\) −4.31534 −0.171655
\(633\) 23.6847 0.941381
\(634\) 16.8769 0.670267
\(635\) 0 0
\(636\) −7.43845 −0.294954
\(637\) −0.876894 −0.0347438
\(638\) 18.2462 0.722374
\(639\) −7.68466 −0.304000
\(640\) 1.00000 0.0395285
\(641\) −5.50758 −0.217536 −0.108768 0.994067i \(-0.534691\pi\)
−0.108768 + 0.994067i \(0.534691\pi\)
\(642\) 2.56155 0.101096
\(643\) −7.05398 −0.278182 −0.139091 0.990280i \(-0.544418\pi\)
−0.139091 + 0.990280i \(0.544418\pi\)
\(644\) 3.68466 0.145196
\(645\) −12.8078 −0.504305
\(646\) 24.0000 0.944267
\(647\) −45.9309 −1.80573 −0.902864 0.429925i \(-0.858540\pi\)
−0.902864 + 0.429925i \(0.858540\pi\)
\(648\) 1.00000 0.0392837
\(649\) −33.6155 −1.31952
\(650\) 2.00000 0.0784465
\(651\) −2.56155 −0.100395
\(652\) −15.3693 −0.601909
\(653\) 40.2462 1.57496 0.787478 0.616343i \(-0.211386\pi\)
0.787478 + 0.616343i \(0.211386\pi\)
\(654\) −5.36932 −0.209957
\(655\) −15.3693 −0.600529
\(656\) 7.12311 0.278111
\(657\) −10.8078 −0.421651
\(658\) 13.1231 0.511592
\(659\) −30.7386 −1.19741 −0.598704 0.800971i \(-0.704317\pi\)
−0.598704 + 0.800971i \(0.704317\pi\)
\(660\) −2.56155 −0.0997083
\(661\) 26.4924 1.03044 0.515218 0.857059i \(-0.327711\pi\)
0.515218 + 0.857059i \(0.327711\pi\)
\(662\) −6.24621 −0.242766
\(663\) 6.24621 0.242583
\(664\) 14.2462 0.552860
\(665\) −19.6847 −0.763338
\(666\) −3.12311 −0.121018
\(667\) 10.2462 0.396735
\(668\) −6.56155 −0.253874
\(669\) 21.1231 0.816666
\(670\) −15.3693 −0.593769
\(671\) 15.3693 0.593326
\(672\) −2.56155 −0.0988140
\(673\) 11.7538 0.453075 0.226538 0.974002i \(-0.427259\pi\)
0.226538 + 0.974002i \(0.427259\pi\)
\(674\) −10.0000 −0.385186
\(675\) −1.00000 −0.0384900
\(676\) −9.00000 −0.346154
\(677\) 32.4233 1.24613 0.623064 0.782171i \(-0.285888\pi\)
0.623064 + 0.782171i \(0.285888\pi\)
\(678\) 1.68466 0.0646989
\(679\) −15.3693 −0.589820
\(680\) −3.12311 −0.119766
\(681\) −7.68466 −0.294477
\(682\) 2.56155 0.0980869
\(683\) 31.6847 1.21238 0.606190 0.795320i \(-0.292697\pi\)
0.606190 + 0.795320i \(0.292697\pi\)
\(684\) −7.68466 −0.293830
\(685\) 20.2462 0.773568
\(686\) −19.0540 −0.727484
\(687\) 16.5616 0.631863
\(688\) 12.8078 0.488291
\(689\) 14.8769 0.566765
\(690\) −1.43845 −0.0547607
\(691\) 15.0540 0.572680 0.286340 0.958128i \(-0.407561\pi\)
0.286340 + 0.958128i \(0.407561\pi\)
\(692\) 8.24621 0.313474
\(693\) 6.56155 0.249253
\(694\) 14.2462 0.540779
\(695\) −17.1231 −0.649516
\(696\) −7.12311 −0.270001
\(697\) −22.2462 −0.842635
\(698\) 5.36932 0.203232
\(699\) 17.0540 0.645041
\(700\) 2.56155 0.0968176
\(701\) 5.19224 0.196108 0.0980540 0.995181i \(-0.468738\pi\)
0.0980540 + 0.995181i \(0.468738\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 24.0000 0.905177
\(704\) 2.56155 0.0965422
\(705\) −5.12311 −0.192947
\(706\) −0.246211 −0.00926628
\(707\) −1.43845 −0.0540984
\(708\) 13.1231 0.493197
\(709\) 17.0540 0.640475 0.320238 0.947337i \(-0.396237\pi\)
0.320238 + 0.947337i \(0.396237\pi\)
\(710\) −7.68466 −0.288400
\(711\) −4.31534 −0.161838
\(712\) −13.6847 −0.512854
\(713\) 1.43845 0.0538703
\(714\) 8.00000 0.299392
\(715\) 5.12311 0.191593
\(716\) −12.0000 −0.448461
\(717\) −24.0000 −0.896296
\(718\) −31.6847 −1.18246
\(719\) −34.8769 −1.30069 −0.650344 0.759640i \(-0.725375\pi\)
−0.650344 + 0.759640i \(0.725375\pi\)
\(720\) 1.00000 0.0372678
\(721\) −4.49242 −0.167307
\(722\) 40.0540 1.49065
\(723\) −12.2462 −0.455441
\(724\) −13.0540 −0.485147
\(725\) 7.12311 0.264546
\(726\) 4.43845 0.164726
\(727\) 23.0540 0.855025 0.427512 0.904010i \(-0.359390\pi\)
0.427512 + 0.904010i \(0.359390\pi\)
\(728\) 5.12311 0.189875
\(729\) 1.00000 0.0370370
\(730\) −10.8078 −0.400013
\(731\) −40.0000 −1.47945
\(732\) −6.00000 −0.221766
\(733\) −6.49242 −0.239803 −0.119902 0.992786i \(-0.538258\pi\)
−0.119902 + 0.992786i \(0.538258\pi\)
\(734\) 15.3693 0.567292
\(735\) 0.438447 0.0161724
\(736\) 1.43845 0.0530219
\(737\) −39.3693 −1.45019
\(738\) 7.12311 0.262205
\(739\) 52.9848 1.94908 0.974540 0.224216i \(-0.0719821\pi\)
0.974540 + 0.224216i \(0.0719821\pi\)
\(740\) −3.12311 −0.114808
\(741\) 15.3693 0.564606
\(742\) 19.0540 0.699493
\(743\) −50.4233 −1.84985 −0.924926 0.380148i \(-0.875873\pi\)
−0.924926 + 0.380148i \(0.875873\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 17.0540 0.624809
\(746\) −5.68466 −0.208130
\(747\) 14.2462 0.521242
\(748\) −8.00000 −0.292509
\(749\) −6.56155 −0.239754
\(750\) −1.00000 −0.0365148
\(751\) 45.1231 1.64657 0.823283 0.567631i \(-0.192140\pi\)
0.823283 + 0.567631i \(0.192140\pi\)
\(752\) 5.12311 0.186820
\(753\) −16.4924 −0.601017
\(754\) 14.2462 0.518816
\(755\) 0 0
\(756\) −2.56155 −0.0931628
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −7.05398 −0.256212
\(759\) −3.68466 −0.133745
\(760\) −7.68466 −0.278752
\(761\) −20.4233 −0.740344 −0.370172 0.928963i \(-0.620701\pi\)
−0.370172 + 0.928963i \(0.620701\pi\)
\(762\) 0 0
\(763\) 13.7538 0.497921
\(764\) −14.2462 −0.515410
\(765\) −3.12311 −0.112916
\(766\) −10.2462 −0.370211
\(767\) −26.2462 −0.947696
\(768\) −1.00000 −0.0360844
\(769\) −20.5616 −0.741469 −0.370734 0.928739i \(-0.620894\pi\)
−0.370734 + 0.928739i \(0.620894\pi\)
\(770\) 6.56155 0.236462
\(771\) 1.68466 0.0606715
\(772\) 14.4924 0.521594
\(773\) −11.4384 −0.411412 −0.205706 0.978614i \(-0.565949\pi\)
−0.205706 + 0.978614i \(0.565949\pi\)
\(774\) 12.8078 0.460366
\(775\) 1.00000 0.0359211
\(776\) −6.00000 −0.215387
\(777\) 8.00000 0.286998
\(778\) 7.75379 0.277987
\(779\) −54.7386 −1.96122
\(780\) −2.00000 −0.0716115
\(781\) −19.6847 −0.704372
\(782\) −4.49242 −0.160649
\(783\) −7.12311 −0.254559
\(784\) −0.438447 −0.0156588
\(785\) 17.0540 0.608682
\(786\) 15.3693 0.548205
\(787\) −17.9309 −0.639166 −0.319583 0.947558i \(-0.603543\pi\)
−0.319583 + 0.947558i \(0.603543\pi\)
\(788\) 6.00000 0.213741
\(789\) 20.4924 0.729550
\(790\) −4.31534 −0.153533
\(791\) −4.31534 −0.153436
\(792\) 2.56155 0.0910208
\(793\) 12.0000 0.426132
\(794\) 9.05398 0.321314
\(795\) −7.43845 −0.263815
\(796\) −16.8078 −0.595735
\(797\) −26.9848 −0.955852 −0.477926 0.878400i \(-0.658611\pi\)
−0.477926 + 0.878400i \(0.658611\pi\)
\(798\) 19.6847 0.696829
\(799\) −16.0000 −0.566039
\(800\) 1.00000 0.0353553
\(801\) −13.6847 −0.483524
\(802\) −13.6847 −0.483222
\(803\) −27.6847 −0.976970
\(804\) 15.3693 0.542034
\(805\) 3.68466 0.129867
\(806\) 2.00000 0.0704470
\(807\) 0.246211 0.00866705
\(808\) −0.561553 −0.0197554
\(809\) −37.6847 −1.32492 −0.662461 0.749096i \(-0.730488\pi\)
−0.662461 + 0.749096i \(0.730488\pi\)
\(810\) 1.00000 0.0351364
\(811\) −24.6695 −0.866263 −0.433132 0.901331i \(-0.642592\pi\)
−0.433132 + 0.901331i \(0.642592\pi\)
\(812\) 18.2462 0.640316
\(813\) −27.0540 −0.948824
\(814\) −8.00000 −0.280400
\(815\) −15.3693 −0.538364
\(816\) 3.12311 0.109331
\(817\) −98.4233 −3.44340
\(818\) −37.3693 −1.30659
\(819\) 5.12311 0.179016
\(820\) 7.12311 0.248750
\(821\) 19.6155 0.684587 0.342293 0.939593i \(-0.388796\pi\)
0.342293 + 0.939593i \(0.388796\pi\)
\(822\) −20.2462 −0.706168
\(823\) −25.6155 −0.892901 −0.446451 0.894808i \(-0.647312\pi\)
−0.446451 + 0.894808i \(0.647312\pi\)
\(824\) −1.75379 −0.0610961
\(825\) −2.56155 −0.0891818
\(826\) −33.6155 −1.16963
\(827\) 1.75379 0.0609852 0.0304926 0.999535i \(-0.490292\pi\)
0.0304926 + 0.999535i \(0.490292\pi\)
\(828\) 1.43845 0.0499895
\(829\) 24.4233 0.848256 0.424128 0.905602i \(-0.360581\pi\)
0.424128 + 0.905602i \(0.360581\pi\)
\(830\) 14.2462 0.494493
\(831\) 5.36932 0.186260
\(832\) 2.00000 0.0693375
\(833\) 1.36932 0.0474440
\(834\) 17.1231 0.592925
\(835\) −6.56155 −0.227072
\(836\) −19.6847 −0.680808
\(837\) −1.00000 −0.0345651
\(838\) 5.75379 0.198761
\(839\) 6.06913 0.209530 0.104765 0.994497i \(-0.466591\pi\)
0.104765 + 0.994497i \(0.466591\pi\)
\(840\) −2.56155 −0.0883820
\(841\) 21.7386 0.749608
\(842\) −14.4924 −0.499442
\(843\) −4.87689 −0.167969
\(844\) −23.6847 −0.815260
\(845\) −9.00000 −0.309609
\(846\) 5.12311 0.176136
\(847\) −11.3693 −0.390654
\(848\) 7.43845 0.255437
\(849\) 0 0
\(850\) −3.12311 −0.107122
\(851\) −4.49242 −0.153998
\(852\) 7.68466 0.263272
\(853\) 47.7926 1.63639 0.818194 0.574942i \(-0.194976\pi\)
0.818194 + 0.574942i \(0.194976\pi\)
\(854\) 15.3693 0.525927
\(855\) −7.68466 −0.262810
\(856\) −2.56155 −0.0875521
\(857\) 29.2311 0.998514 0.499257 0.866454i \(-0.333606\pi\)
0.499257 + 0.866454i \(0.333606\pi\)
\(858\) −5.12311 −0.174900
\(859\) 26.7386 0.912310 0.456155 0.889900i \(-0.349226\pi\)
0.456155 + 0.889900i \(0.349226\pi\)
\(860\) 12.8078 0.436741
\(861\) −18.2462 −0.621829
\(862\) −30.2462 −1.03019
\(863\) 39.5464 1.34618 0.673088 0.739563i \(-0.264968\pi\)
0.673088 + 0.739563i \(0.264968\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 8.24621 0.280380
\(866\) 35.3002 1.19955
\(867\) 7.24621 0.246094
\(868\) 2.56155 0.0869448
\(869\) −11.0540 −0.374980
\(870\) −7.12311 −0.241496
\(871\) −30.7386 −1.04154
\(872\) 5.36932 0.181828
\(873\) −6.00000 −0.203069
\(874\) −11.0540 −0.373906
\(875\) 2.56155 0.0865963
\(876\) 10.8078 0.365161
\(877\) −50.0000 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(878\) 9.61553 0.324508
\(879\) −26.4924 −0.893567
\(880\) 2.56155 0.0863499
\(881\) 9.50758 0.320318 0.160159 0.987091i \(-0.448799\pi\)
0.160159 + 0.987091i \(0.448799\pi\)
\(882\) −0.438447 −0.0147633
\(883\) 30.4233 1.02383 0.511913 0.859038i \(-0.328937\pi\)
0.511913 + 0.859038i \(0.328937\pi\)
\(884\) −6.24621 −0.210083
\(885\) 13.1231 0.441128
\(886\) 23.0540 0.774513
\(887\) −32.6307 −1.09563 −0.547816 0.836599i \(-0.684540\pi\)
−0.547816 + 0.836599i \(0.684540\pi\)
\(888\) 3.12311 0.104805
\(889\) 0 0
\(890\) −13.6847 −0.458711
\(891\) 2.56155 0.0858152
\(892\) −21.1231 −0.707254
\(893\) −39.3693 −1.31744
\(894\) −17.0540 −0.570370
\(895\) −12.0000 −0.401116
\(896\) 2.56155 0.0855755
\(897\) −2.87689 −0.0960567
\(898\) 10.4924 0.350137
\(899\) 7.12311 0.237569
\(900\) 1.00000 0.0333333
\(901\) −23.2311 −0.773939
\(902\) 18.2462 0.607532
\(903\) −32.8078 −1.09177
\(904\) −1.68466 −0.0560309
\(905\) −13.0540 −0.433929
\(906\) 0 0
\(907\) 24.0000 0.796907 0.398453 0.917189i \(-0.369547\pi\)
0.398453 + 0.917189i \(0.369547\pi\)
\(908\) 7.68466 0.255024
\(909\) −0.561553 −0.0186255
\(910\) 5.12311 0.169829
\(911\) −11.5076 −0.381263 −0.190632 0.981662i \(-0.561054\pi\)
−0.190632 + 0.981662i \(0.561054\pi\)
\(912\) 7.68466 0.254464
\(913\) 36.4924 1.20772
\(914\) −24.7386 −0.818281
\(915\) −6.00000 −0.198354
\(916\) −16.5616 −0.547209
\(917\) −39.3693 −1.30009
\(918\) 3.12311 0.103078
\(919\) −1.61553 −0.0532914 −0.0266457 0.999645i \(-0.508483\pi\)
−0.0266457 + 0.999645i \(0.508483\pi\)
\(920\) 1.43845 0.0474242
\(921\) 0 0
\(922\) 9.36932 0.308562
\(923\) −15.3693 −0.505887
\(924\) −6.56155 −0.215859
\(925\) −3.12311 −0.102687
\(926\) 30.7386 1.01013
\(927\) −1.75379 −0.0576020
\(928\) 7.12311 0.233827
\(929\) 7.43845 0.244048 0.122024 0.992527i \(-0.461062\pi\)
0.122024 + 0.992527i \(0.461062\pi\)
\(930\) −1.00000 −0.0327913
\(931\) 3.36932 0.110425
\(932\) −17.0540 −0.558622
\(933\) 1.75379 0.0574165
\(934\) −9.75379 −0.319154
\(935\) −8.00000 −0.261628
\(936\) 2.00000 0.0653720
\(937\) 41.3693 1.35148 0.675738 0.737142i \(-0.263825\pi\)
0.675738 + 0.737142i \(0.263825\pi\)
\(938\) −39.3693 −1.28545
\(939\) 10.0000 0.326338
\(940\) 5.12311 0.167097
\(941\) 2.63068 0.0857578 0.0428789 0.999080i \(-0.486347\pi\)
0.0428789 + 0.999080i \(0.486347\pi\)
\(942\) −17.0540 −0.555649
\(943\) 10.2462 0.333663
\(944\) −13.1231 −0.427121
\(945\) −2.56155 −0.0833273
\(946\) 32.8078 1.06667
\(947\) −9.12311 −0.296461 −0.148231 0.988953i \(-0.547358\pi\)
−0.148231 + 0.988953i \(0.547358\pi\)
\(948\) 4.31534 0.140156
\(949\) −21.6155 −0.701670
\(950\) −7.68466 −0.249323
\(951\) −16.8769 −0.547271
\(952\) −8.00000 −0.259281
\(953\) 16.1080 0.521788 0.260894 0.965367i \(-0.415983\pi\)
0.260894 + 0.965367i \(0.415983\pi\)
\(954\) 7.43845 0.240829
\(955\) −14.2462 −0.460997
\(956\) 24.0000 0.776215
\(957\) −18.2462 −0.589816
\(958\) 10.5616 0.341228
\(959\) 51.8617 1.67470
\(960\) −1.00000 −0.0322749
\(961\) 1.00000 0.0322581
\(962\) −6.24621 −0.201386
\(963\) −2.56155 −0.0825449
\(964\) 12.2462 0.394424
\(965\) 14.4924 0.466528
\(966\) −3.68466 −0.118552
\(967\) −42.2462 −1.35855 −0.679273 0.733885i \(-0.737705\pi\)
−0.679273 + 0.733885i \(0.737705\pi\)
\(968\) −4.43845 −0.142657
\(969\) −24.0000 −0.770991
\(970\) −6.00000 −0.192648
\(971\) −37.1231 −1.19134 −0.595669 0.803230i \(-0.703113\pi\)
−0.595669 + 0.803230i \(0.703113\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −43.8617 −1.40614
\(974\) 24.0000 0.769010
\(975\) −2.00000 −0.0640513
\(976\) 6.00000 0.192055
\(977\) 42.9848 1.37521 0.687604 0.726086i \(-0.258663\pi\)
0.687604 + 0.726086i \(0.258663\pi\)
\(978\) 15.3693 0.491457
\(979\) −35.0540 −1.12033
\(980\) −0.438447 −0.0140057
\(981\) 5.36932 0.171429
\(982\) −25.9309 −0.827487
\(983\) 40.9848 1.30721 0.653607 0.756834i \(-0.273255\pi\)
0.653607 + 0.756834i \(0.273255\pi\)
\(984\) −7.12311 −0.227076
\(985\) 6.00000 0.191176
\(986\) −22.2462 −0.708464
\(987\) −13.1231 −0.417713
\(988\) −15.3693 −0.488963
\(989\) 18.4233 0.585827
\(990\) 2.56155 0.0814115
\(991\) 35.6847 1.13356 0.566780 0.823869i \(-0.308189\pi\)
0.566780 + 0.823869i \(0.308189\pi\)
\(992\) 1.00000 0.0317500
\(993\) 6.24621 0.198218
\(994\) −19.6847 −0.624359
\(995\) −16.8078 −0.532842
\(996\) −14.2462 −0.451408
\(997\) −29.5076 −0.934514 −0.467257 0.884121i \(-0.654758\pi\)
−0.467257 + 0.884121i \(0.654758\pi\)
\(998\) 20.0000 0.633089
\(999\) 3.12311 0.0988107
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 930.2.a.p.1.2 2
3.2 odd 2 2790.2.a.be.1.2 2
4.3 odd 2 7440.2.a.bl.1.1 2
5.2 odd 4 4650.2.d.bd.3349.4 4
5.3 odd 4 4650.2.d.bd.3349.1 4
5.4 even 2 4650.2.a.ce.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.p.1.2 2 1.1 even 1 trivial
2790.2.a.be.1.2 2 3.2 odd 2
4650.2.a.ce.1.1 2 5.4 even 2
4650.2.d.bd.3349.1 4 5.3 odd 4
4650.2.d.bd.3349.4 4 5.2 odd 4
7440.2.a.bl.1.1 2 4.3 odd 2