Properties

Label 4730.2.a.be.1.12
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 12
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(3.12850\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.12850 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.12850 q^{6} -0.193657 q^{7} +1.00000 q^{8} +6.78751 q^{9} +1.00000 q^{10} -1.00000 q^{11} +3.12850 q^{12} +6.24972 q^{13} -0.193657 q^{14} +3.12850 q^{15} +1.00000 q^{16} +4.69491 q^{17} +6.78751 q^{18} -3.31827 q^{19} +1.00000 q^{20} -0.605855 q^{21} -1.00000 q^{22} -4.24972 q^{23} +3.12850 q^{24} +1.00000 q^{25} +6.24972 q^{26} +11.8492 q^{27} -0.193657 q^{28} -3.16019 q^{29} +3.12850 q^{30} -4.43189 q^{31} +1.00000 q^{32} -3.12850 q^{33} +4.69491 q^{34} -0.193657 q^{35} +6.78751 q^{36} -9.89168 q^{37} -3.31827 q^{38} +19.5522 q^{39} +1.00000 q^{40} -6.26146 q^{41} -0.605855 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.78751 q^{45} -4.24972 q^{46} +5.29078 q^{47} +3.12850 q^{48} -6.96250 q^{49} +1.00000 q^{50} +14.6880 q^{51} +6.24972 q^{52} +9.92110 q^{53} +11.8492 q^{54} -1.00000 q^{55} -0.193657 q^{56} -10.3812 q^{57} -3.16019 q^{58} +13.1950 q^{59} +3.12850 q^{60} -11.8849 q^{61} -4.43189 q^{62} -1.31445 q^{63} +1.00000 q^{64} +6.24972 q^{65} -3.12850 q^{66} -12.5688 q^{67} +4.69491 q^{68} -13.2952 q^{69} -0.193657 q^{70} +7.75245 q^{71} +6.78751 q^{72} -5.20439 q^{73} -9.89168 q^{74} +3.12850 q^{75} -3.31827 q^{76} +0.193657 q^{77} +19.5522 q^{78} -4.61249 q^{79} +1.00000 q^{80} +16.7077 q^{81} -6.26146 q^{82} -1.70199 q^{83} -0.605855 q^{84} +4.69491 q^{85} +1.00000 q^{86} -9.88665 q^{87} -1.00000 q^{88} -5.37533 q^{89} +6.78751 q^{90} -1.21030 q^{91} -4.24972 q^{92} -13.8652 q^{93} +5.29078 q^{94} -3.31827 q^{95} +3.12850 q^{96} -2.37063 q^{97} -6.96250 q^{98} -6.78751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + O(q^{10}) \) \( 12q + 12q^{2} + 3q^{3} + 12q^{4} + 12q^{5} + 3q^{6} + 8q^{7} + 12q^{8} + 25q^{9} + 12q^{10} - 12q^{11} + 3q^{12} + 16q^{13} + 8q^{14} + 3q^{15} + 12q^{16} + 18q^{17} + 25q^{18} - 4q^{19} + 12q^{20} + 4q^{21} - 12q^{22} + 8q^{23} + 3q^{24} + 12q^{25} + 16q^{26} + 6q^{27} + 8q^{28} + 20q^{29} + 3q^{30} + 5q^{31} + 12q^{32} - 3q^{33} + 18q^{34} + 8q^{35} + 25q^{36} + 19q^{37} - 4q^{38} + 6q^{39} + 12q^{40} + 16q^{41} + 4q^{42} + 12q^{43} - 12q^{44} + 25q^{45} + 8q^{46} - q^{47} + 3q^{48} + 52q^{49} + 12q^{50} + q^{51} + 16q^{52} + 11q^{53} + 6q^{54} - 12q^{55} + 8q^{56} + 9q^{57} + 20q^{58} - 11q^{59} + 3q^{60} + 18q^{61} + 5q^{62} + 15q^{63} + 12q^{64} + 16q^{65} - 3q^{66} - 10q^{67} + 18q^{68} + 8q^{70} - 2q^{71} + 25q^{72} + 29q^{73} + 19q^{74} + 3q^{75} - 4q^{76} - 8q^{77} + 6q^{78} + 2q^{79} + 12q^{80} - 8q^{81} + 16q^{82} + 26q^{83} + 4q^{84} + 18q^{85} + 12q^{86} - 4q^{87} - 12q^{88} + 41q^{89} + 25q^{90} - 4q^{91} + 8q^{92} + 5q^{93} - q^{94} - 4q^{95} + 3q^{96} - 7q^{97} + 52q^{98} - 25q^{99} + O(q^{100}) \)

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
\(3\) 3.12850 1.80624 0.903120 0.429388i \(-0.141271\pi\)
0.903120 + 0.429388i \(0.141271\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 3.12850 1.27720
\(7\) −0.193657 −0.0731954 −0.0365977 0.999330i \(-0.511652\pi\)
−0.0365977 + 0.999330i \(0.511652\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.78751 2.26250
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 3.12850 0.903120
\(13\) 6.24972 1.73336 0.866680 0.498865i \(-0.166250\pi\)
0.866680 + 0.498865i \(0.166250\pi\)
\(14\) −0.193657 −0.0517569
\(15\) 3.12850 0.807775
\(16\) 1.00000 0.250000
\(17\) 4.69491 1.13868 0.569341 0.822101i \(-0.307198\pi\)
0.569341 + 0.822101i \(0.307198\pi\)
\(18\) 6.78751 1.59983
\(19\) −3.31827 −0.761262 −0.380631 0.924727i \(-0.624293\pi\)
−0.380631 + 0.924727i \(0.624293\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.605855 −0.132208
\(22\) −1.00000 −0.213201
\(23\) −4.24972 −0.886127 −0.443064 0.896490i \(-0.646108\pi\)
−0.443064 + 0.896490i \(0.646108\pi\)
\(24\) 3.12850 0.638602
\(25\) 1.00000 0.200000
\(26\) 6.24972 1.22567
\(27\) 11.8492 2.28038
\(28\) −0.193657 −0.0365977
\(29\) −3.16019 −0.586832 −0.293416 0.955985i \(-0.594792\pi\)
−0.293416 + 0.955985i \(0.594792\pi\)
\(30\) 3.12850 0.571183
\(31\) −4.43189 −0.795991 −0.397995 0.917387i \(-0.630294\pi\)
−0.397995 + 0.917387i \(0.630294\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.12850 −0.544602
\(34\) 4.69491 0.805170
\(35\) −0.193657 −0.0327340
\(36\) 6.78751 1.13125
\(37\) −9.89168 −1.62618 −0.813091 0.582137i \(-0.802217\pi\)
−0.813091 + 0.582137i \(0.802217\pi\)
\(38\) −3.31827 −0.538294
\(39\) 19.5522 3.13086
\(40\) 1.00000 0.158114
\(41\) −6.26146 −0.977875 −0.488938 0.872319i \(-0.662615\pi\)
−0.488938 + 0.872319i \(0.662615\pi\)
\(42\) −0.605855 −0.0934855
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 6.78751 1.01182
\(46\) −4.24972 −0.626587
\(47\) 5.29078 0.771739 0.385869 0.922553i \(-0.373902\pi\)
0.385869 + 0.922553i \(0.373902\pi\)
\(48\) 3.12850 0.451560
\(49\) −6.96250 −0.994642
\(50\) 1.00000 0.141421
\(51\) 14.6880 2.05673
\(52\) 6.24972 0.866680
\(53\) 9.92110 1.36277 0.681384 0.731926i \(-0.261379\pi\)
0.681384 + 0.731926i \(0.261379\pi\)
\(54\) 11.8492 1.61247
\(55\) −1.00000 −0.134840
\(56\) −0.193657 −0.0258785
\(57\) −10.3812 −1.37502
\(58\) −3.16019 −0.414953
\(59\) 13.1950 1.71784 0.858921 0.512108i \(-0.171135\pi\)
0.858921 + 0.512108i \(0.171135\pi\)
\(60\) 3.12850 0.403888
\(61\) −11.8849 −1.52170 −0.760850 0.648927i \(-0.775218\pi\)
−0.760850 + 0.648927i \(0.775218\pi\)
\(62\) −4.43189 −0.562851
\(63\) −1.31445 −0.165605
\(64\) 1.00000 0.125000
\(65\) 6.24972 0.775182
\(66\) −3.12850 −0.385092
\(67\) −12.5688 −1.53552 −0.767762 0.640735i \(-0.778630\pi\)
−0.767762 + 0.640735i \(0.778630\pi\)
\(68\) 4.69491 0.569341
\(69\) −13.2952 −1.60056
\(70\) −0.193657 −0.0231464
\(71\) 7.75245 0.920047 0.460023 0.887907i \(-0.347841\pi\)
0.460023 + 0.887907i \(0.347841\pi\)
\(72\) 6.78751 0.799915
\(73\) −5.20439 −0.609128 −0.304564 0.952492i \(-0.598511\pi\)
−0.304564 + 0.952492i \(0.598511\pi\)
\(74\) −9.89168 −1.14988
\(75\) 3.12850 0.361248
\(76\) −3.31827 −0.380631
\(77\) 0.193657 0.0220692
\(78\) 19.5522 2.21385
\(79\) −4.61249 −0.518946 −0.259473 0.965750i \(-0.583549\pi\)
−0.259473 + 0.965750i \(0.583549\pi\)
\(80\) 1.00000 0.111803
\(81\) 16.7077 1.85641
\(82\) −6.26146 −0.691462
\(83\) −1.70199 −0.186818 −0.0934089 0.995628i \(-0.529776\pi\)
−0.0934089 + 0.995628i \(0.529776\pi\)
\(84\) −0.605855 −0.0661042
\(85\) 4.69491 0.509234
\(86\) 1.00000 0.107833
\(87\) −9.88665 −1.05996
\(88\) −1.00000 −0.106600
\(89\) −5.37533 −0.569784 −0.284892 0.958560i \(-0.591958\pi\)
−0.284892 + 0.958560i \(0.591958\pi\)
\(90\) 6.78751 0.715466
\(91\) −1.21030 −0.126874
\(92\) −4.24972 −0.443064
\(93\) −13.8652 −1.43775
\(94\) 5.29078 0.545702
\(95\) −3.31827 −0.340447
\(96\) 3.12850 0.319301
\(97\) −2.37063 −0.240701 −0.120350 0.992731i \(-0.538402\pi\)
−0.120350 + 0.992731i \(0.538402\pi\)
\(98\) −6.96250 −0.703318
\(99\) −6.78751 −0.682170
\(100\) 1.00000 0.100000
\(101\) 17.5532 1.74661 0.873305 0.487174i \(-0.161972\pi\)
0.873305 + 0.487174i \(0.161972\pi\)
\(102\) 14.6880 1.45433
\(103\) −9.75744 −0.961429 −0.480714 0.876877i \(-0.659623\pi\)
−0.480714 + 0.876877i \(0.659623\pi\)
\(104\) 6.24972 0.612835
\(105\) −0.605855 −0.0591254
\(106\) 9.92110 0.963622
\(107\) −11.3919 −1.10130 −0.550648 0.834737i \(-0.685619\pi\)
−0.550648 + 0.834737i \(0.685619\pi\)
\(108\) 11.8492 1.14019
\(109\) 19.5074 1.86847 0.934236 0.356657i \(-0.116083\pi\)
0.934236 + 0.356657i \(0.116083\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −30.9461 −2.93727
\(112\) −0.193657 −0.0182988
\(113\) −16.1060 −1.51513 −0.757564 0.652761i \(-0.773611\pi\)
−0.757564 + 0.652761i \(0.773611\pi\)
\(114\) −10.3812 −0.972287
\(115\) −4.24972 −0.396288
\(116\) −3.16019 −0.293416
\(117\) 42.4200 3.92173
\(118\) 13.1950 1.21470
\(119\) −0.909200 −0.0833463
\(120\) 3.12850 0.285592
\(121\) 1.00000 0.0909091
\(122\) −11.8849 −1.07600
\(123\) −19.5890 −1.76628
\(124\) −4.43189 −0.397995
\(125\) 1.00000 0.0894427
\(126\) −1.31445 −0.117100
\(127\) 16.6647 1.47876 0.739378 0.673290i \(-0.235120\pi\)
0.739378 + 0.673290i \(0.235120\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.12850 0.275449
\(130\) 6.24972 0.548137
\(131\) −10.7205 −0.936651 −0.468326 0.883556i \(-0.655143\pi\)
−0.468326 + 0.883556i \(0.655143\pi\)
\(132\) −3.12850 −0.272301
\(133\) 0.642604 0.0557209
\(134\) −12.5688 −1.08578
\(135\) 11.8492 1.01982
\(136\) 4.69491 0.402585
\(137\) 1.88001 0.160620 0.0803102 0.996770i \(-0.474409\pi\)
0.0803102 + 0.996770i \(0.474409\pi\)
\(138\) −13.2952 −1.13177
\(139\) 20.1904 1.71253 0.856266 0.516536i \(-0.172779\pi\)
0.856266 + 0.516536i \(0.172779\pi\)
\(140\) −0.193657 −0.0163670
\(141\) 16.5522 1.39395
\(142\) 7.75245 0.650571
\(143\) −6.24972 −0.522628
\(144\) 6.78751 0.565626
\(145\) −3.16019 −0.262439
\(146\) −5.20439 −0.430718
\(147\) −21.7822 −1.79656
\(148\) −9.89168 −0.813091
\(149\) 9.04828 0.741264 0.370632 0.928780i \(-0.379141\pi\)
0.370632 + 0.928780i \(0.379141\pi\)
\(150\) 3.12850 0.255441
\(151\) −5.17559 −0.421183 −0.210592 0.977574i \(-0.567539\pi\)
−0.210592 + 0.977574i \(0.567539\pi\)
\(152\) −3.31827 −0.269147
\(153\) 31.8667 2.57627
\(154\) 0.193657 0.0156053
\(155\) −4.43189 −0.355978
\(156\) 19.5522 1.56543
\(157\) 8.79226 0.701699 0.350850 0.936432i \(-0.385893\pi\)
0.350850 + 0.936432i \(0.385893\pi\)
\(158\) −4.61249 −0.366950
\(159\) 31.0381 2.46148
\(160\) 1.00000 0.0790569
\(161\) 0.822986 0.0648604
\(162\) 16.7077 1.31268
\(163\) −0.776503 −0.0608204 −0.0304102 0.999538i \(-0.509681\pi\)
−0.0304102 + 0.999538i \(0.509681\pi\)
\(164\) −6.26146 −0.488938
\(165\) −3.12850 −0.243553
\(166\) −1.70199 −0.132100
\(167\) −6.07340 −0.469974 −0.234987 0.971999i \(-0.575505\pi\)
−0.234987 + 0.971999i \(0.575505\pi\)
\(168\) −0.605855 −0.0467427
\(169\) 26.0590 2.00454
\(170\) 4.69491 0.360083
\(171\) −22.5227 −1.72236
\(172\) 1.00000 0.0762493
\(173\) −17.3693 −1.32056 −0.660282 0.751017i \(-0.729563\pi\)
−0.660282 + 0.751017i \(0.729563\pi\)
\(174\) −9.88665 −0.749505
\(175\) −0.193657 −0.0146391
\(176\) −1.00000 −0.0753778
\(177\) 41.2805 3.10284
\(178\) −5.37533 −0.402898
\(179\) −8.69359 −0.649790 −0.324895 0.945750i \(-0.605329\pi\)
−0.324895 + 0.945750i \(0.605329\pi\)
\(180\) 6.78751 0.505911
\(181\) −9.10022 −0.676414 −0.338207 0.941072i \(-0.609820\pi\)
−0.338207 + 0.941072i \(0.609820\pi\)
\(182\) −1.21030 −0.0897134
\(183\) −37.1818 −2.74856
\(184\) −4.24972 −0.313293
\(185\) −9.89168 −0.727250
\(186\) −13.8652 −1.01664
\(187\) −4.69491 −0.343326
\(188\) 5.29078 0.385869
\(189\) −2.29468 −0.166913
\(190\) −3.31827 −0.240732
\(191\) −15.7633 −1.14060 −0.570298 0.821438i \(-0.693172\pi\)
−0.570298 + 0.821438i \(0.693172\pi\)
\(192\) 3.12850 0.225780
\(193\) 27.7551 1.99786 0.998930 0.0462583i \(-0.0147297\pi\)
0.998930 + 0.0462583i \(0.0147297\pi\)
\(194\) −2.37063 −0.170201
\(195\) 19.5522 1.40016
\(196\) −6.96250 −0.497321
\(197\) −3.09129 −0.220246 −0.110123 0.993918i \(-0.535124\pi\)
−0.110123 + 0.993918i \(0.535124\pi\)
\(198\) −6.78751 −0.482367
\(199\) 5.65969 0.401205 0.200603 0.979673i \(-0.435710\pi\)
0.200603 + 0.979673i \(0.435710\pi\)
\(200\) 1.00000 0.0707107
\(201\) −39.3215 −2.77353
\(202\) 17.5532 1.23504
\(203\) 0.611992 0.0429534
\(204\) 14.6880 1.02837
\(205\) −6.26146 −0.437319
\(206\) −9.75744 −0.679833
\(207\) −28.8450 −2.00487
\(208\) 6.24972 0.433340
\(209\) 3.31827 0.229529
\(210\) −0.605855 −0.0418080
\(211\) 19.6553 1.35313 0.676563 0.736385i \(-0.263469\pi\)
0.676563 + 0.736385i \(0.263469\pi\)
\(212\) 9.92110 0.681384
\(213\) 24.2535 1.66182
\(214\) −11.3919 −0.778734
\(215\) 1.00000 0.0681994
\(216\) 11.8492 0.806237
\(217\) 0.858265 0.0582628
\(218\) 19.5074 1.32121
\(219\) −16.2819 −1.10023
\(220\) −1.00000 −0.0674200
\(221\) 29.3418 1.97375
\(222\) −30.9461 −2.07697
\(223\) 0.836405 0.0560098 0.0280049 0.999608i \(-0.491085\pi\)
0.0280049 + 0.999608i \(0.491085\pi\)
\(224\) −0.193657 −0.0129392
\(225\) 6.78751 0.452500
\(226\) −16.1060 −1.07136
\(227\) 22.7464 1.50973 0.754867 0.655878i \(-0.227701\pi\)
0.754867 + 0.655878i \(0.227701\pi\)
\(228\) −10.3812 −0.687511
\(229\) 2.59628 0.171567 0.0857836 0.996314i \(-0.472661\pi\)
0.0857836 + 0.996314i \(0.472661\pi\)
\(230\) −4.24972 −0.280218
\(231\) 0.605855 0.0398623
\(232\) −3.16019 −0.207477
\(233\) −25.8388 −1.69275 −0.846377 0.532585i \(-0.821221\pi\)
−0.846377 + 0.532585i \(0.821221\pi\)
\(234\) 42.4200 2.77308
\(235\) 5.29078 0.345132
\(236\) 13.1950 0.858921
\(237\) −14.4302 −0.937340
\(238\) −0.909200 −0.0589347
\(239\) −18.2999 −1.18372 −0.591860 0.806041i \(-0.701606\pi\)
−0.591860 + 0.806041i \(0.701606\pi\)
\(240\) 3.12850 0.201944
\(241\) 21.1752 1.36401 0.682007 0.731346i \(-0.261107\pi\)
0.682007 + 0.731346i \(0.261107\pi\)
\(242\) 1.00000 0.0642824
\(243\) 16.7225 1.07275
\(244\) −11.8849 −0.760850
\(245\) −6.96250 −0.444818
\(246\) −19.5890 −1.24895
\(247\) −20.7382 −1.31954
\(248\) −4.43189 −0.281425
\(249\) −5.32468 −0.337438
\(250\) 1.00000 0.0632456
\(251\) −22.4564 −1.41743 −0.708717 0.705492i \(-0.750726\pi\)
−0.708717 + 0.705492i \(0.750726\pi\)
\(252\) −1.31445 −0.0828023
\(253\) 4.24972 0.267177
\(254\) 16.6647 1.04564
\(255\) 14.6880 0.919799
\(256\) 1.00000 0.0625000
\(257\) 20.9293 1.30553 0.652766 0.757560i \(-0.273609\pi\)
0.652766 + 0.757560i \(0.273609\pi\)
\(258\) 3.12850 0.194772
\(259\) 1.91559 0.119029
\(260\) 6.24972 0.387591
\(261\) −21.4498 −1.32771
\(262\) −10.7205 −0.662313
\(263\) 12.9753 0.800090 0.400045 0.916495i \(-0.368994\pi\)
0.400045 + 0.916495i \(0.368994\pi\)
\(264\) −3.12850 −0.192546
\(265\) 9.92110 0.609448
\(266\) 0.642604 0.0394006
\(267\) −16.8167 −1.02917
\(268\) −12.5688 −0.767762
\(269\) 23.9968 1.46311 0.731555 0.681783i \(-0.238795\pi\)
0.731555 + 0.681783i \(0.238795\pi\)
\(270\) 11.8492 0.721120
\(271\) −16.9027 −1.02677 −0.513383 0.858160i \(-0.671608\pi\)
−0.513383 + 0.858160i \(0.671608\pi\)
\(272\) 4.69491 0.284671
\(273\) −3.78642 −0.229165
\(274\) 1.88001 0.113576
\(275\) −1.00000 −0.0603023
\(276\) −13.2952 −0.800279
\(277\) 7.18000 0.431405 0.215702 0.976459i \(-0.430796\pi\)
0.215702 + 0.976459i \(0.430796\pi\)
\(278\) 20.1904 1.21094
\(279\) −30.0815 −1.80093
\(280\) −0.193657 −0.0115732
\(281\) 15.7186 0.937692 0.468846 0.883280i \(-0.344670\pi\)
0.468846 + 0.883280i \(0.344670\pi\)
\(282\) 16.5522 0.985668
\(283\) −6.09885 −0.362539 −0.181269 0.983433i \(-0.558021\pi\)
−0.181269 + 0.983433i \(0.558021\pi\)
\(284\) 7.75245 0.460023
\(285\) −10.3812 −0.614929
\(286\) −6.24972 −0.369554
\(287\) 1.21257 0.0715759
\(288\) 6.78751 0.399958
\(289\) 5.04215 0.296597
\(290\) −3.16019 −0.185573
\(291\) −7.41650 −0.434763
\(292\) −5.20439 −0.304564
\(293\) 16.1455 0.943228 0.471614 0.881805i \(-0.343672\pi\)
0.471614 + 0.881805i \(0.343672\pi\)
\(294\) −21.7822 −1.27036
\(295\) 13.1950 0.768242
\(296\) −9.89168 −0.574942
\(297\) −11.8492 −0.687561
\(298\) 9.04828 0.524153
\(299\) −26.5595 −1.53598
\(300\) 3.12850 0.180624
\(301\) −0.193657 −0.0111622
\(302\) −5.17559 −0.297822
\(303\) 54.9152 3.15480
\(304\) −3.31827 −0.190316
\(305\) −11.8849 −0.680525
\(306\) 31.8667 1.82170
\(307\) 30.3281 1.73091 0.865457 0.500983i \(-0.167028\pi\)
0.865457 + 0.500983i \(0.167028\pi\)
\(308\) 0.193657 0.0110346
\(309\) −30.5261 −1.73657
\(310\) −4.43189 −0.251714
\(311\) 14.5883 0.827224 0.413612 0.910453i \(-0.364267\pi\)
0.413612 + 0.910453i \(0.364267\pi\)
\(312\) 19.5522 1.10693
\(313\) −29.5597 −1.67081 −0.835407 0.549632i \(-0.814768\pi\)
−0.835407 + 0.549632i \(0.814768\pi\)
\(314\) 8.79226 0.496176
\(315\) −1.31445 −0.0740607
\(316\) −4.61249 −0.259473
\(317\) −4.24315 −0.238319 −0.119160 0.992875i \(-0.538020\pi\)
−0.119160 + 0.992875i \(0.538020\pi\)
\(318\) 31.0381 1.74053
\(319\) 3.16019 0.176937
\(320\) 1.00000 0.0559017
\(321\) −35.6396 −1.98921
\(322\) 0.822986 0.0458632
\(323\) −15.5789 −0.866836
\(324\) 16.7077 0.928207
\(325\) 6.24972 0.346672
\(326\) −0.776503 −0.0430065
\(327\) 61.0289 3.37491
\(328\) −6.26146 −0.345731
\(329\) −1.02459 −0.0564877
\(330\) −3.12850 −0.172218
\(331\) −27.2051 −1.49533 −0.747663 0.664079i \(-0.768824\pi\)
−0.747663 + 0.664079i \(0.768824\pi\)
\(332\) −1.70199 −0.0934089
\(333\) −67.1398 −3.67924
\(334\) −6.07340 −0.332322
\(335\) −12.5688 −0.686707
\(336\) −0.605855 −0.0330521
\(337\) −19.5564 −1.06530 −0.532651 0.846335i \(-0.678804\pi\)
−0.532651 + 0.846335i \(0.678804\pi\)
\(338\) 26.0590 1.41742
\(339\) −50.3877 −2.73668
\(340\) 4.69491 0.254617
\(341\) 4.43189 0.240000
\(342\) −22.5227 −1.21789
\(343\) 2.70393 0.145999
\(344\) 1.00000 0.0539164
\(345\) −13.2952 −0.715792
\(346\) −17.3693 −0.933780
\(347\) −12.1096 −0.650079 −0.325040 0.945700i \(-0.605378\pi\)
−0.325040 + 0.945700i \(0.605378\pi\)
\(348\) −9.88665 −0.529980
\(349\) −14.2454 −0.762536 −0.381268 0.924465i \(-0.624513\pi\)
−0.381268 + 0.924465i \(0.624513\pi\)
\(350\) −0.193657 −0.0103514
\(351\) 74.0542 3.95272
\(352\) −1.00000 −0.0533002
\(353\) −19.8649 −1.05730 −0.528650 0.848840i \(-0.677302\pi\)
−0.528650 + 0.848840i \(0.677302\pi\)
\(354\) 41.2805 2.19404
\(355\) 7.75245 0.411457
\(356\) −5.37533 −0.284892
\(357\) −2.84443 −0.150543
\(358\) −8.69359 −0.459471
\(359\) −14.7650 −0.779267 −0.389633 0.920970i \(-0.627398\pi\)
−0.389633 + 0.920970i \(0.627398\pi\)
\(360\) 6.78751 0.357733
\(361\) −7.98912 −0.420480
\(362\) −9.10022 −0.478297
\(363\) 3.12850 0.164204
\(364\) −1.21030 −0.0634370
\(365\) −5.20439 −0.272410
\(366\) −37.1818 −1.94352
\(367\) −22.7348 −1.18675 −0.593373 0.804928i \(-0.702204\pi\)
−0.593373 + 0.804928i \(0.702204\pi\)
\(368\) −4.24972 −0.221532
\(369\) −42.4997 −2.21244
\(370\) −9.89168 −0.514244
\(371\) −1.92129 −0.0997483
\(372\) −13.8652 −0.718875
\(373\) −18.7567 −0.971183 −0.485592 0.874186i \(-0.661396\pi\)
−0.485592 + 0.874186i \(0.661396\pi\)
\(374\) −4.69491 −0.242768
\(375\) 3.12850 0.161555
\(376\) 5.29078 0.272851
\(377\) −19.7503 −1.01719
\(378\) −2.29468 −0.118026
\(379\) 7.68533 0.394769 0.197384 0.980326i \(-0.436755\pi\)
0.197384 + 0.980326i \(0.436755\pi\)
\(380\) −3.31827 −0.170223
\(381\) 52.1356 2.67099
\(382\) −15.7633 −0.806523
\(383\) 38.7917 1.98217 0.991083 0.133248i \(-0.0425408\pi\)
0.991083 + 0.133248i \(0.0425408\pi\)
\(384\) 3.12850 0.159651
\(385\) 0.193657 0.00986966
\(386\) 27.7551 1.41270
\(387\) 6.78751 0.345028
\(388\) −2.37063 −0.120350
\(389\) −19.1490 −0.970895 −0.485447 0.874266i \(-0.661343\pi\)
−0.485447 + 0.874266i \(0.661343\pi\)
\(390\) 19.5522 0.990066
\(391\) −19.9520 −1.00902
\(392\) −6.96250 −0.351659
\(393\) −33.5390 −1.69182
\(394\) −3.09129 −0.155737
\(395\) −4.61249 −0.232079
\(396\) −6.78751 −0.341085
\(397\) 17.7274 0.889714 0.444857 0.895602i \(-0.353254\pi\)
0.444857 + 0.895602i \(0.353254\pi\)
\(398\) 5.65969 0.283695
\(399\) 2.01039 0.100645
\(400\) 1.00000 0.0500000
\(401\) −19.4462 −0.971099 −0.485550 0.874209i \(-0.661380\pi\)
−0.485550 + 0.874209i \(0.661380\pi\)
\(402\) −39.3215 −1.96118
\(403\) −27.6981 −1.37974
\(404\) 17.5532 0.873305
\(405\) 16.7077 0.830214
\(406\) 0.611992 0.0303726
\(407\) 9.89168 0.490312
\(408\) 14.6880 0.727165
\(409\) 25.0290 1.23760 0.618802 0.785547i \(-0.287618\pi\)
0.618802 + 0.785547i \(0.287618\pi\)
\(410\) −6.26146 −0.309231
\(411\) 5.88162 0.290119
\(412\) −9.75744 −0.480714
\(413\) −2.55530 −0.125738
\(414\) −28.8450 −1.41765
\(415\) −1.70199 −0.0835474
\(416\) 6.24972 0.306418
\(417\) 63.1658 3.09324
\(418\) 3.31827 0.162302
\(419\) −27.0833 −1.32310 −0.661552 0.749899i \(-0.730102\pi\)
−0.661552 + 0.749899i \(0.730102\pi\)
\(420\) −0.605855 −0.0295627
\(421\) 31.7825 1.54899 0.774493 0.632583i \(-0.218005\pi\)
0.774493 + 0.632583i \(0.218005\pi\)
\(422\) 19.6553 0.956804
\(423\) 35.9112 1.74606
\(424\) 9.92110 0.481811
\(425\) 4.69491 0.227736
\(426\) 24.2535 1.17509
\(427\) 2.30158 0.111381
\(428\) −11.3919 −0.550648
\(429\) −19.5522 −0.943991
\(430\) 1.00000 0.0482243
\(431\) −7.44734 −0.358726 −0.179363 0.983783i \(-0.557404\pi\)
−0.179363 + 0.983783i \(0.557404\pi\)
\(432\) 11.8492 0.570096
\(433\) −6.15585 −0.295831 −0.147916 0.989000i \(-0.547256\pi\)
−0.147916 + 0.989000i \(0.547256\pi\)
\(434\) 0.858265 0.0411981
\(435\) −9.88665 −0.474028
\(436\) 19.5074 0.934236
\(437\) 14.1017 0.674575
\(438\) −16.2819 −0.777980
\(439\) −14.2070 −0.678062 −0.339031 0.940775i \(-0.610099\pi\)
−0.339031 + 0.940775i \(0.610099\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −47.2580 −2.25038
\(442\) 29.3418 1.39565
\(443\) −16.9314 −0.804434 −0.402217 0.915544i \(-0.631760\pi\)
−0.402217 + 0.915544i \(0.631760\pi\)
\(444\) −30.9461 −1.46864
\(445\) −5.37533 −0.254815
\(446\) 0.836405 0.0396049
\(447\) 28.3075 1.33890
\(448\) −0.193657 −0.00914942
\(449\) 3.31895 0.156631 0.0783155 0.996929i \(-0.475046\pi\)
0.0783155 + 0.996929i \(0.475046\pi\)
\(450\) 6.78751 0.319966
\(451\) 6.26146 0.294840
\(452\) −16.1060 −0.757564
\(453\) −16.1918 −0.760758
\(454\) 22.7464 1.06754
\(455\) −1.21030 −0.0567397
\(456\) −10.3812 −0.486144
\(457\) 11.2382 0.525700 0.262850 0.964837i \(-0.415338\pi\)
0.262850 + 0.964837i \(0.415338\pi\)
\(458\) 2.59628 0.121316
\(459\) 55.6310 2.59663
\(460\) −4.24972 −0.198144
\(461\) 33.5807 1.56401 0.782004 0.623274i \(-0.214198\pi\)
0.782004 + 0.623274i \(0.214198\pi\)
\(462\) 0.605855 0.0281869
\(463\) −35.3657 −1.64359 −0.821793 0.569787i \(-0.807026\pi\)
−0.821793 + 0.569787i \(0.807026\pi\)
\(464\) −3.16019 −0.146708
\(465\) −13.8652 −0.642982
\(466\) −25.8388 −1.19696
\(467\) −41.6956 −1.92944 −0.964721 0.263273i \(-0.915198\pi\)
−0.964721 + 0.263273i \(0.915198\pi\)
\(468\) 42.4200 1.96087
\(469\) 2.43403 0.112393
\(470\) 5.29078 0.244045
\(471\) 27.5066 1.26744
\(472\) 13.1950 0.607349
\(473\) −1.00000 −0.0459800
\(474\) −14.4302 −0.662800
\(475\) −3.31827 −0.152252
\(476\) −0.909200 −0.0416731
\(477\) 67.3395 3.08326
\(478\) −18.2999 −0.837017
\(479\) 10.6458 0.486420 0.243210 0.969974i \(-0.421800\pi\)
0.243210 + 0.969974i \(0.421800\pi\)
\(480\) 3.12850 0.142796
\(481\) −61.8202 −2.81876
\(482\) 21.1752 0.964503
\(483\) 2.57471 0.117153
\(484\) 1.00000 0.0454545
\(485\) −2.37063 −0.107645
\(486\) 16.7225 0.758547
\(487\) 26.0432 1.18013 0.590064 0.807356i \(-0.299102\pi\)
0.590064 + 0.807356i \(0.299102\pi\)
\(488\) −11.8849 −0.538002
\(489\) −2.42929 −0.109856
\(490\) −6.96250 −0.314534
\(491\) −2.01820 −0.0910800 −0.0455400 0.998963i \(-0.514501\pi\)
−0.0455400 + 0.998963i \(0.514501\pi\)
\(492\) −19.5890 −0.883138
\(493\) −14.8368 −0.668215
\(494\) −20.7382 −0.933057
\(495\) −6.78751 −0.305076
\(496\) −4.43189 −0.198998
\(497\) −1.50131 −0.0673432
\(498\) −5.32468 −0.238604
\(499\) 41.1976 1.84426 0.922129 0.386881i \(-0.126448\pi\)
0.922129 + 0.386881i \(0.126448\pi\)
\(500\) 1.00000 0.0447214
\(501\) −19.0006 −0.848885
\(502\) −22.4564 −1.00228
\(503\) 13.7250 0.611966 0.305983 0.952037i \(-0.401015\pi\)
0.305983 + 0.952037i \(0.401015\pi\)
\(504\) −1.31445 −0.0585501
\(505\) 17.5532 0.781108
\(506\) 4.24972 0.188923
\(507\) 81.5255 3.62067
\(508\) 16.6647 0.739378
\(509\) 6.02206 0.266923 0.133462 0.991054i \(-0.457391\pi\)
0.133462 + 0.991054i \(0.457391\pi\)
\(510\) 14.6880 0.650396
\(511\) 1.00786 0.0445853
\(512\) 1.00000 0.0441942
\(513\) −39.3188 −1.73597
\(514\) 20.9293 0.923150
\(515\) −9.75744 −0.429964
\(516\) 3.12850 0.137724
\(517\) −5.29078 −0.232688
\(518\) 1.91559 0.0841662
\(519\) −54.3399 −2.38526
\(520\) 6.24972 0.274068
\(521\) 10.1266 0.443655 0.221828 0.975086i \(-0.428798\pi\)
0.221828 + 0.975086i \(0.428798\pi\)
\(522\) −21.4498 −0.938832
\(523\) −22.7197 −0.993465 −0.496732 0.867904i \(-0.665467\pi\)
−0.496732 + 0.867904i \(0.665467\pi\)
\(524\) −10.7205 −0.468326
\(525\) −0.605855 −0.0264417
\(526\) 12.9753 0.565749
\(527\) −20.8073 −0.906381
\(528\) −3.12850 −0.136150
\(529\) −4.93990 −0.214778
\(530\) 9.92110 0.430945
\(531\) 89.5611 3.88662
\(532\) 0.642604 0.0278604
\(533\) −39.1323 −1.69501
\(534\) −16.8167 −0.727730
\(535\) −11.3919 −0.492515
\(536\) −12.5688 −0.542890
\(537\) −27.1979 −1.17368
\(538\) 23.9968 1.03457
\(539\) 6.96250 0.299896
\(540\) 11.8492 0.509909
\(541\) 13.8163 0.594010 0.297005 0.954876i \(-0.404012\pi\)
0.297005 + 0.954876i \(0.404012\pi\)
\(542\) −16.9027 −0.726033
\(543\) −28.4700 −1.22177
\(544\) 4.69491 0.201292
\(545\) 19.5074 0.835606
\(546\) −3.78642 −0.162044
\(547\) −17.3469 −0.741700 −0.370850 0.928693i \(-0.620934\pi\)
−0.370850 + 0.928693i \(0.620934\pi\)
\(548\) 1.88001 0.0803102
\(549\) −80.6686 −3.44285
\(550\) −1.00000 −0.0426401
\(551\) 10.4863 0.446733
\(552\) −13.2952 −0.565883
\(553\) 0.893240 0.0379844
\(554\) 7.18000 0.305049
\(555\) −30.9461 −1.31359
\(556\) 20.1904 0.856266
\(557\) −34.7817 −1.47375 −0.736873 0.676031i \(-0.763698\pi\)
−0.736873 + 0.676031i \(0.763698\pi\)
\(558\) −30.0815 −1.27345
\(559\) 6.24972 0.264335
\(560\) −0.193657 −0.00818349
\(561\) −14.6880 −0.620128
\(562\) 15.7186 0.663048
\(563\) 29.9031 1.26027 0.630134 0.776487i \(-0.283000\pi\)
0.630134 + 0.776487i \(0.283000\pi\)
\(564\) 16.5522 0.696973
\(565\) −16.1060 −0.677586
\(566\) −6.09885 −0.256354
\(567\) −3.23556 −0.135881
\(568\) 7.75245 0.325286
\(569\) 37.5427 1.57387 0.786937 0.617034i \(-0.211666\pi\)
0.786937 + 0.617034i \(0.211666\pi\)
\(570\) −10.3812 −0.434820
\(571\) −6.33780 −0.265229 −0.132614 0.991168i \(-0.542337\pi\)
−0.132614 + 0.991168i \(0.542337\pi\)
\(572\) −6.24972 −0.261314
\(573\) −49.3156 −2.06019
\(574\) 1.21257 0.0506118
\(575\) −4.24972 −0.177225
\(576\) 6.78751 0.282813
\(577\) 0.991396 0.0412724 0.0206362 0.999787i \(-0.493431\pi\)
0.0206362 + 0.999787i \(0.493431\pi\)
\(578\) 5.04215 0.209726
\(579\) 86.8319 3.60861
\(580\) −3.16019 −0.131220
\(581\) 0.329602 0.0136742
\(582\) −7.41650 −0.307424
\(583\) −9.92110 −0.410890
\(584\) −5.20439 −0.215359
\(585\) 42.4200 1.75385
\(586\) 16.1455 0.666963
\(587\) −35.4653 −1.46381 −0.731906 0.681406i \(-0.761369\pi\)
−0.731906 + 0.681406i \(0.761369\pi\)
\(588\) −21.7822 −0.898281
\(589\) 14.7062 0.605958
\(590\) 13.1950 0.543229
\(591\) −9.67111 −0.397816
\(592\) −9.89168 −0.406545
\(593\) −11.2684 −0.462739 −0.231370 0.972866i \(-0.574321\pi\)
−0.231370 + 0.972866i \(0.574321\pi\)
\(594\) −11.8492 −0.486179
\(595\) −0.909200 −0.0372736
\(596\) 9.04828 0.370632
\(597\) 17.7063 0.724673
\(598\) −26.5595 −1.08610
\(599\) −29.5386 −1.20692 −0.603458 0.797395i \(-0.706211\pi\)
−0.603458 + 0.797395i \(0.706211\pi\)
\(600\) 3.12850 0.127720
\(601\) 37.8682 1.54468 0.772338 0.635211i \(-0.219087\pi\)
0.772338 + 0.635211i \(0.219087\pi\)
\(602\) −0.193657 −0.00789286
\(603\) −85.3109 −3.47413
\(604\) −5.17559 −0.210592
\(605\) 1.00000 0.0406558
\(606\) 54.9152 2.23078
\(607\) 18.0637 0.733182 0.366591 0.930382i \(-0.380525\pi\)
0.366591 + 0.930382i \(0.380525\pi\)
\(608\) −3.31827 −0.134573
\(609\) 1.91462 0.0775841
\(610\) −11.8849 −0.481204
\(611\) 33.0659 1.33770
\(612\) 31.8667 1.28814
\(613\) 24.6658 0.996244 0.498122 0.867107i \(-0.334023\pi\)
0.498122 + 0.867107i \(0.334023\pi\)
\(614\) 30.3281 1.22394
\(615\) −19.5890 −0.789903
\(616\) 0.193657 0.00780265
\(617\) −18.3689 −0.739503 −0.369751 0.929131i \(-0.620557\pi\)
−0.369751 + 0.929131i \(0.620557\pi\)
\(618\) −30.5261 −1.22794
\(619\) 21.3251 0.857127 0.428564 0.903512i \(-0.359020\pi\)
0.428564 + 0.903512i \(0.359020\pi\)
\(620\) −4.43189 −0.177989
\(621\) −50.3558 −2.02071
\(622\) 14.5883 0.584936
\(623\) 1.04097 0.0417055
\(624\) 19.5522 0.782716
\(625\) 1.00000 0.0400000
\(626\) −29.5597 −1.18144
\(627\) 10.3812 0.414585
\(628\) 8.79226 0.350850
\(629\) −46.4405 −1.85170
\(630\) −1.31445 −0.0523688
\(631\) 1.17951 0.0469556 0.0234778 0.999724i \(-0.492526\pi\)
0.0234778 + 0.999724i \(0.492526\pi\)
\(632\) −4.61249 −0.183475
\(633\) 61.4916 2.44407
\(634\) −4.24315 −0.168517
\(635\) 16.6647 0.661320
\(636\) 31.0381 1.23074
\(637\) −43.5136 −1.72407
\(638\) 3.16019 0.125113
\(639\) 52.6198 2.08161
\(640\) 1.00000 0.0395285
\(641\) 25.6176 1.01184 0.505918 0.862582i \(-0.331154\pi\)
0.505918 + 0.862582i \(0.331154\pi\)
\(642\) −35.6396 −1.40658
\(643\) −14.0320 −0.553366 −0.276683 0.960961i \(-0.589235\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(644\) 0.822986 0.0324302
\(645\) 3.12850 0.123185
\(646\) −15.5789 −0.612945
\(647\) 2.39495 0.0941551 0.0470775 0.998891i \(-0.485009\pi\)
0.0470775 + 0.998891i \(0.485009\pi\)
\(648\) 16.7077 0.656342
\(649\) −13.1950 −0.517949
\(650\) 6.24972 0.245134
\(651\) 2.68508 0.105237
\(652\) −0.776503 −0.0304102
\(653\) −6.55041 −0.256337 −0.128169 0.991752i \(-0.540910\pi\)
−0.128169 + 0.991752i \(0.540910\pi\)
\(654\) 61.0289 2.38642
\(655\) −10.7205 −0.418883
\(656\) −6.26146 −0.244469
\(657\) −35.3248 −1.37815
\(658\) −1.02459 −0.0399428
\(659\) −42.3962 −1.65152 −0.825760 0.564021i \(-0.809254\pi\)
−0.825760 + 0.564021i \(0.809254\pi\)
\(660\) −3.12850 −0.121777
\(661\) 25.8356 1.00489 0.502444 0.864610i \(-0.332434\pi\)
0.502444 + 0.864610i \(0.332434\pi\)
\(662\) −27.2051 −1.05735
\(663\) 91.7959 3.56506
\(664\) −1.70199 −0.0660500
\(665\) 0.642604 0.0249191
\(666\) −67.1398 −2.60162
\(667\) 13.4299 0.520008
\(668\) −6.07340 −0.234987
\(669\) 2.61669 0.101167
\(670\) −12.5688 −0.485575
\(671\) 11.8849 0.458810
\(672\) −0.605855 −0.0233714
\(673\) −6.73500 −0.259615 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(674\) −19.5564 −0.753283
\(675\) 11.8492 0.456076
\(676\) 26.0590 1.00227
\(677\) 21.7097 0.834373 0.417186 0.908821i \(-0.363016\pi\)
0.417186 + 0.908821i \(0.363016\pi\)
\(678\) −50.3877 −1.93513
\(679\) 0.459088 0.0176182
\(680\) 4.69491 0.180041
\(681\) 71.1622 2.72694
\(682\) 4.43189 0.169706
\(683\) −49.9877 −1.91272 −0.956362 0.292184i \(-0.905618\pi\)
−0.956362 + 0.292184i \(0.905618\pi\)
\(684\) −22.5227 −0.861179
\(685\) 1.88001 0.0718316
\(686\) 2.70393 0.103237
\(687\) 8.12247 0.309891
\(688\) 1.00000 0.0381246
\(689\) 62.0040 2.36217
\(690\) −13.2952 −0.506141
\(691\) −15.1962 −0.578091 −0.289046 0.957315i \(-0.593338\pi\)
−0.289046 + 0.957315i \(0.593338\pi\)
\(692\) −17.3693 −0.660282
\(693\) 1.31445 0.0499317
\(694\) −12.1096 −0.459675
\(695\) 20.1904 0.765867
\(696\) −9.88665 −0.374752
\(697\) −29.3970 −1.11349
\(698\) −14.2454 −0.539194
\(699\) −80.8365 −3.05752
\(700\) −0.193657 −0.00731954
\(701\) −11.7539 −0.443938 −0.221969 0.975054i \(-0.571248\pi\)
−0.221969 + 0.975054i \(0.571248\pi\)
\(702\) 74.0542 2.79500
\(703\) 32.8232 1.23795
\(704\) −1.00000 −0.0376889
\(705\) 16.5522 0.623391
\(706\) −19.8649 −0.747625
\(707\) −3.39930 −0.127844
\(708\) 41.2805 1.55142
\(709\) 18.5238 0.695676 0.347838 0.937555i \(-0.386916\pi\)
0.347838 + 0.937555i \(0.386916\pi\)
\(710\) 7.75245 0.290944
\(711\) −31.3073 −1.17412
\(712\) −5.37533 −0.201449
\(713\) 18.8343 0.705349
\(714\) −2.84443 −0.106450
\(715\) −6.24972 −0.233726
\(716\) −8.69359 −0.324895
\(717\) −57.2512 −2.13808
\(718\) −14.7650 −0.551025
\(719\) −25.4450 −0.948939 −0.474469 0.880272i \(-0.657360\pi\)
−0.474469 + 0.880272i \(0.657360\pi\)
\(720\) 6.78751 0.252955
\(721\) 1.88959 0.0703721
\(722\) −7.98912 −0.297324
\(723\) 66.2466 2.46374
\(724\) −9.10022 −0.338207
\(725\) −3.16019 −0.117366
\(726\) 3.12850 0.116109
\(727\) −4.50040 −0.166911 −0.0834554 0.996512i \(-0.526596\pi\)
−0.0834554 + 0.996512i \(0.526596\pi\)
\(728\) −1.21030 −0.0448567
\(729\) 2.19309 0.0812255
\(730\) −5.20439 −0.192623
\(731\) 4.69491 0.173647
\(732\) −37.1818 −1.37428
\(733\) 14.0557 0.519158 0.259579 0.965722i \(-0.416416\pi\)
0.259579 + 0.965722i \(0.416416\pi\)
\(734\) −22.7348 −0.839155
\(735\) −21.7822 −0.803447
\(736\) −4.24972 −0.156647
\(737\) 12.5688 0.462978
\(738\) −42.4997 −1.56443
\(739\) −34.9736 −1.28652 −0.643262 0.765646i \(-0.722420\pi\)
−0.643262 + 0.765646i \(0.722420\pi\)
\(740\) −9.89168 −0.363625
\(741\) −64.8795 −2.38341
\(742\) −1.92129 −0.0705327
\(743\) −51.3368 −1.88336 −0.941682 0.336505i \(-0.890755\pi\)
−0.941682 + 0.336505i \(0.890755\pi\)
\(744\) −13.8652 −0.508322
\(745\) 9.04828 0.331503
\(746\) −18.7567 −0.686730
\(747\) −11.5523 −0.422676
\(748\) −4.69491 −0.171663
\(749\) 2.20612 0.0806098
\(750\) 3.12850 0.114237
\(751\) −21.2244 −0.774488 −0.387244 0.921977i \(-0.626573\pi\)
−0.387244 + 0.921977i \(0.626573\pi\)
\(752\) 5.29078 0.192935
\(753\) −70.2548 −2.56023
\(754\) −19.7503 −0.719263
\(755\) −5.17559 −0.188359
\(756\) −2.29468 −0.0834567
\(757\) −0.637315 −0.0231636 −0.0115818 0.999933i \(-0.503687\pi\)
−0.0115818 + 0.999933i \(0.503687\pi\)
\(758\) 7.68533 0.279144
\(759\) 13.2952 0.482587
\(760\) −3.31827 −0.120366
\(761\) −6.81940 −0.247203 −0.123602 0.992332i \(-0.539444\pi\)
−0.123602 + 0.992332i \(0.539444\pi\)
\(762\) 52.1356 1.88867
\(763\) −3.77774 −0.136763
\(764\) −15.7633 −0.570298
\(765\) 31.8667 1.15214
\(766\) 38.7917 1.40160
\(767\) 82.4650 2.97764
\(768\) 3.12850 0.112890
\(769\) 42.2996 1.52536 0.762680 0.646775i \(-0.223883\pi\)
0.762680 + 0.646775i \(0.223883\pi\)
\(770\) 0.193657 0.00697890
\(771\) 65.4772 2.35810
\(772\) 27.7551 0.998930
\(773\) 33.6663 1.21089 0.605446 0.795886i \(-0.292995\pi\)
0.605446 + 0.795886i \(0.292995\pi\)
\(774\) 6.78751 0.243972
\(775\) −4.43189 −0.159198
\(776\) −2.37063 −0.0851005
\(777\) 5.99292 0.214995
\(778\) −19.1490 −0.686526
\(779\) 20.7772 0.744419
\(780\) 19.5522 0.700082
\(781\) −7.75245 −0.277405
\(782\) −19.9520 −0.713483
\(783\) −37.4457 −1.33820
\(784\) −6.96250 −0.248661
\(785\) 8.79226 0.313809
\(786\) −33.5390 −1.19630
\(787\) 36.0197 1.28396 0.641982 0.766720i \(-0.278112\pi\)
0.641982 + 0.766720i \(0.278112\pi\)
\(788\) −3.09129 −0.110123
\(789\) 40.5932 1.44515
\(790\) −4.61249 −0.164105
\(791\) 3.11904 0.110900
\(792\) −6.78751 −0.241184
\(793\) −74.2770 −2.63766
\(794\) 17.7274 0.629123
\(795\) 31.0381 1.10081
\(796\) 5.65969 0.200603
\(797\) −2.98746 −0.105821 −0.0529107 0.998599i \(-0.516850\pi\)
−0.0529107 + 0.998599i \(0.516850\pi\)
\(798\) 2.01039 0.0711669
\(799\) 24.8397 0.878765
\(800\) 1.00000 0.0353553
\(801\) −36.4851 −1.28914
\(802\) −19.4462 −0.686671
\(803\) 5.20439 0.183659
\(804\) −39.3215 −1.38676
\(805\) 0.822986 0.0290065
\(806\) −27.6981 −0.975623
\(807\) 75.0739 2.64273
\(808\) 17.5532 0.617520
\(809\) −38.1914 −1.34274 −0.671370 0.741123i \(-0.734294\pi\)
−0.671370 + 0.741123i \(0.734294\pi\)
\(810\) 16.7077 0.587050
\(811\) 4.18912 0.147100 0.0735499 0.997292i \(-0.476567\pi\)
0.0735499 + 0.997292i \(0.476567\pi\)
\(812\) 0.611992 0.0214767
\(813\) −52.8801 −1.85459
\(814\) 9.89168 0.346703
\(815\) −0.776503 −0.0271997
\(816\) 14.6880 0.514183
\(817\) −3.31827 −0.116091
\(818\) 25.0290 0.875119
\(819\) −8.21492 −0.287053
\(820\) −6.26146 −0.218659
\(821\) 36.3985 1.27032 0.635158 0.772383i \(-0.280935\pi\)
0.635158 + 0.772383i \(0.280935\pi\)
\(822\) 5.88162 0.205145
\(823\) 33.1651 1.15606 0.578032 0.816014i \(-0.303821\pi\)
0.578032 + 0.816014i \(0.303821\pi\)
\(824\) −9.75744 −0.339916
\(825\) −3.12850 −0.108920
\(826\) −2.55530 −0.0889103
\(827\) 38.0894 1.32450 0.662250 0.749283i \(-0.269602\pi\)
0.662250 + 0.749283i \(0.269602\pi\)
\(828\) −28.8450 −1.00243
\(829\) 35.6095 1.23677 0.618384 0.785876i \(-0.287788\pi\)
0.618384 + 0.785876i \(0.287788\pi\)
\(830\) −1.70199 −0.0590770
\(831\) 22.4626 0.779220
\(832\) 6.24972 0.216670
\(833\) −32.6883 −1.13258
\(834\) 63.1658 2.18725
\(835\) −6.07340 −0.210179
\(836\) 3.31827 0.114765
\(837\) −52.5144 −1.81516
\(838\) −27.0833 −0.935576
\(839\) 8.12212 0.280407 0.140203 0.990123i \(-0.455224\pi\)
0.140203 + 0.990123i \(0.455224\pi\)
\(840\) −0.605855 −0.0209040
\(841\) −19.0132 −0.655628
\(842\) 31.7825 1.09530
\(843\) 49.1756 1.69370
\(844\) 19.6553 0.676563
\(845\) 26.0590 0.896456
\(846\) 35.9112 1.23465
\(847\) −0.193657 −0.00665412
\(848\) 9.92110 0.340692
\(849\) −19.0802 −0.654832
\(850\) 4.69491 0.161034
\(851\) 42.0368 1.44100
\(852\) 24.2535 0.830912
\(853\) 38.9334 1.33306 0.666528 0.745480i \(-0.267780\pi\)
0.666528 + 0.745480i \(0.267780\pi\)
\(854\) 2.30158 0.0787586
\(855\) −22.5227 −0.770262
\(856\) −11.3919 −0.389367
\(857\) 10.7332 0.366640 0.183320 0.983053i \(-0.441316\pi\)
0.183320 + 0.983053i \(0.441316\pi\)
\(858\) −19.5522 −0.667502
\(859\) −29.2949 −0.999528 −0.499764 0.866162i \(-0.666580\pi\)
−0.499764 + 0.866162i \(0.666580\pi\)
\(860\) 1.00000 0.0340997
\(861\) 3.79353 0.129283
\(862\) −7.44734 −0.253657
\(863\) 4.65550 0.158475 0.0792376 0.996856i \(-0.474751\pi\)
0.0792376 + 0.996856i \(0.474751\pi\)
\(864\) 11.8492 0.403118
\(865\) −17.3693 −0.590575
\(866\) −6.15585 −0.209184
\(867\) 15.7744 0.535726
\(868\) 0.858265 0.0291314
\(869\) 4.61249 0.156468
\(870\) −9.88665 −0.335189
\(871\) −78.5515 −2.66162
\(872\) 19.5074 0.660604
\(873\) −16.0906 −0.544586
\(874\) 14.1017 0.476997
\(875\) −0.193657 −0.00654679
\(876\) −16.2819 −0.550115
\(877\) 8.36090 0.282327 0.141164 0.989986i \(-0.454916\pi\)
0.141164 + 0.989986i \(0.454916\pi\)
\(878\) −14.2070 −0.479462
\(879\) 50.5111 1.70370
\(880\) −1.00000 −0.0337100
\(881\) 8.74262 0.294546 0.147273 0.989096i \(-0.452950\pi\)
0.147273 + 0.989096i \(0.452950\pi\)
\(882\) −47.2580 −1.59126
\(883\) −5.98650 −0.201462 −0.100731 0.994914i \(-0.532118\pi\)
−0.100731 + 0.994914i \(0.532118\pi\)
\(884\) 29.3418 0.986873
\(885\) 41.2805 1.38763
\(886\) −16.9314 −0.568821
\(887\) 13.1918 0.442937 0.221469 0.975167i \(-0.428915\pi\)
0.221469 + 0.975167i \(0.428915\pi\)
\(888\) −30.9461 −1.03848
\(889\) −3.22724 −0.108238
\(890\) −5.37533 −0.180181
\(891\) −16.7077 −0.559730
\(892\) 0.836405 0.0280049
\(893\) −17.5562 −0.587496
\(894\) 28.3075 0.946746
\(895\) −8.69359 −0.290595
\(896\) −0.193657 −0.00646962
\(897\) −83.0915 −2.77434
\(898\) 3.31895 0.110755
\(899\) 14.0056 0.467113
\(900\) 6.78751 0.226250
\(901\) 46.5786 1.55176
\(902\) 6.26146 0.208484
\(903\) −0.605855 −0.0201616
\(904\) −16.1060 −0.535679
\(905\) −9.10022 −0.302501
\(906\) −16.1918 −0.537937
\(907\) 5.91848 0.196520 0.0982600 0.995161i \(-0.468672\pi\)
0.0982600 + 0.995161i \(0.468672\pi\)
\(908\) 22.7464 0.754867
\(909\) 119.143 3.95171
\(910\) −1.21030 −0.0401211
\(911\) 19.1172 0.633381 0.316690 0.948529i \(-0.397428\pi\)
0.316690 + 0.948529i \(0.397428\pi\)
\(912\) −10.3812 −0.343756
\(913\) 1.70199 0.0563277
\(914\) 11.2382 0.371726
\(915\) −37.1818 −1.22919
\(916\) 2.59628 0.0857836
\(917\) 2.07609 0.0685585
\(918\) 55.6310 1.83610
\(919\) −14.5898 −0.481274 −0.240637 0.970615i \(-0.577356\pi\)
−0.240637 + 0.970615i \(0.577356\pi\)
\(920\) −4.24972 −0.140109
\(921\) 94.8813 3.12645
\(922\) 33.5807 1.10592
\(923\) 48.4506 1.59477
\(924\) 0.605855 0.0199312
\(925\) −9.89168 −0.325236
\(926\) −35.3657 −1.16219
\(927\) −66.2287 −2.17523
\(928\) −3.16019 −0.103738
\(929\) −16.7769 −0.550433 −0.275216 0.961382i \(-0.588749\pi\)
−0.275216 + 0.961382i \(0.588749\pi\)
\(930\) −13.8652 −0.454657
\(931\) 23.1034 0.757184
\(932\) −25.8388 −0.846377
\(933\) 45.6394 1.49417
\(934\) −41.6956 −1.36432
\(935\) −4.69491 −0.153540
\(936\) 42.4200 1.38654
\(937\) −34.4207 −1.12447 −0.562237 0.826976i \(-0.690059\pi\)
−0.562237 + 0.826976i \(0.690059\pi\)
\(938\) 2.43403 0.0794740
\(939\) −92.4776 −3.01789
\(940\) 5.29078 0.172566
\(941\) −29.7253 −0.969016 −0.484508 0.874787i \(-0.661001\pi\)
−0.484508 + 0.874787i \(0.661001\pi\)
\(942\) 27.5066 0.896213
\(943\) 26.6094 0.866522
\(944\) 13.1950 0.429461
\(945\) −2.29468 −0.0746459
\(946\) −1.00000 −0.0325128
\(947\) 27.0019 0.877443 0.438722 0.898623i \(-0.355431\pi\)
0.438722 + 0.898623i \(0.355431\pi\)
\(948\) −14.4302 −0.468670
\(949\) −32.5260 −1.05584
\(950\) −3.31827 −0.107659
\(951\) −13.2747 −0.430462
\(952\) −0.909200 −0.0294674
\(953\) 48.2152 1.56184 0.780922 0.624629i \(-0.214750\pi\)
0.780922 + 0.624629i \(0.214750\pi\)
\(954\) 67.3395 2.18020
\(955\) −15.7633 −0.510090
\(956\) −18.2999 −0.591860
\(957\) 9.88665 0.319590
\(958\) 10.6458 0.343951
\(959\) −0.364077 −0.0117567
\(960\) 3.12850 0.100972
\(961\) −11.3584 −0.366398
\(962\) −61.8202 −1.99316
\(963\) −77.3226 −2.49169
\(964\) 21.1752 0.682007
\(965\) 27.7551 0.893470
\(966\) 2.57471 0.0828400
\(967\) 58.8840 1.89358 0.946791 0.321848i \(-0.104304\pi\)
0.946791 + 0.321848i \(0.104304\pi\)
\(968\) 1.00000 0.0321412
\(969\) −48.7387 −1.56571
\(970\) −2.37063 −0.0761162
\(971\) 8.42518 0.270377 0.135188 0.990820i \(-0.456836\pi\)
0.135188 + 0.990820i \(0.456836\pi\)
\(972\) 16.7225 0.536374
\(973\) −3.91002 −0.125349
\(974\) 26.0432 0.834477
\(975\) 19.5522 0.626173
\(976\) −11.8849 −0.380425
\(977\) 31.0307 0.992759 0.496380 0.868106i \(-0.334662\pi\)
0.496380 + 0.868106i \(0.334662\pi\)
\(978\) −2.42929 −0.0776801
\(979\) 5.37533 0.171796
\(980\) −6.96250 −0.222409
\(981\) 132.407 4.22742
\(982\) −2.01820 −0.0644033
\(983\) −41.0262 −1.30853 −0.654267 0.756264i \(-0.727023\pi\)
−0.654267 + 0.756264i \(0.727023\pi\)
\(984\) −19.5890 −0.624473
\(985\) −3.09129 −0.0984968
\(986\) −14.8368 −0.472500
\(987\) −3.20544 −0.102030
\(988\) −20.7382 −0.659771
\(989\) −4.24972 −0.135133
\(990\) −6.78751 −0.215721
\(991\) 41.6398 1.32273 0.661366 0.750063i \(-0.269977\pi\)
0.661366 + 0.750063i \(0.269977\pi\)
\(992\) −4.43189 −0.140713
\(993\) −85.1110 −2.70092
\(994\) −1.50131 −0.0476188
\(995\) 5.65969 0.179424
\(996\) −5.32468 −0.168719
\(997\) −25.0395 −0.793007 −0.396504 0.918033i \(-0.629777\pi\)
−0.396504 + 0.918033i \(0.629777\pi\)
\(998\) 41.1976 1.30409
\(999\) −117.209 −3.70832
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 4730.2.a.be.1.12 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.be.1.12 12 1.1 even 1 trivial