Properties

Label 8034.2.a.ba.1.5
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492\)
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 1.5
Root \(0.924862\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.924862 q^{10} +2.47789 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.24556 q^{14} +0.924862 q^{15} +1.00000 q^{16} +0.549056 q^{17} -1.00000 q^{18} -4.66906 q^{19} -0.924862 q^{20} +4.24556 q^{21} -2.47789 q^{22} -2.37974 q^{23} +1.00000 q^{24} -4.14463 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.24556 q^{28} +7.33896 q^{29} -0.924862 q^{30} +8.34581 q^{31} -1.00000 q^{32} -2.47789 q^{33} -0.549056 q^{34} +3.92656 q^{35} +1.00000 q^{36} -9.19443 q^{37} +4.66906 q^{38} +1.00000 q^{39} +0.924862 q^{40} -0.968492 q^{41} -4.24556 q^{42} -11.3612 q^{43} +2.47789 q^{44} -0.924862 q^{45} +2.37974 q^{46} +2.40638 q^{47} -1.00000 q^{48} +11.0248 q^{49} +4.14463 q^{50} -0.549056 q^{51} -1.00000 q^{52} -10.3792 q^{53} +1.00000 q^{54} -2.29171 q^{55} +4.24556 q^{56} +4.66906 q^{57} -7.33896 q^{58} +3.20528 q^{59} +0.924862 q^{60} -6.92554 q^{61} -8.34581 q^{62} -4.24556 q^{63} +1.00000 q^{64} +0.924862 q^{65} +2.47789 q^{66} -2.85465 q^{67} +0.549056 q^{68} +2.37974 q^{69} -3.92656 q^{70} -7.09939 q^{71} -1.00000 q^{72} +7.73116 q^{73} +9.19443 q^{74} +4.14463 q^{75} -4.66906 q^{76} -10.5200 q^{77} -1.00000 q^{78} +11.8927 q^{79} -0.924862 q^{80} +1.00000 q^{81} +0.968492 q^{82} +7.46254 q^{83} +4.24556 q^{84} -0.507801 q^{85} +11.3612 q^{86} -7.33896 q^{87} -2.47789 q^{88} -0.591240 q^{89} +0.924862 q^{90} +4.24556 q^{91} -2.37974 q^{92} -8.34581 q^{93} -2.40638 q^{94} +4.31824 q^{95} +1.00000 q^{96} -7.00078 q^{97} -11.0248 q^{98} +2.47789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + q^{10} - q^{11} - 14q^{12} - 14q^{13} - 5q^{14} + q^{15} + 14q^{16} - 12q^{17} - 14q^{18} + 10q^{19} - q^{20} - 5q^{21} + q^{22} - q^{23} + 14q^{24} + 19q^{25} + 14q^{26} - 14q^{27} + 5q^{28} + 6q^{29} - q^{30} + 20q^{31} - 14q^{32} + q^{33} + 12q^{34} - 16q^{35} + 14q^{36} - 3q^{37} - 10q^{38} + 14q^{39} + q^{40} + q^{41} + 5q^{42} + 6q^{43} - q^{44} - q^{45} + q^{46} - 13q^{47} - 14q^{48} + 9q^{49} - 19q^{50} + 12q^{51} - 14q^{52} - 27q^{53} + 14q^{54} + 10q^{55} - 5q^{56} - 10q^{57} - 6q^{58} - 6q^{59} + q^{60} - 4q^{61} - 20q^{62} + 5q^{63} + 14q^{64} + q^{65} - q^{66} + 13q^{67} - 12q^{68} + q^{69} + 16q^{70} + 18q^{71} - 14q^{72} + 11q^{73} + 3q^{74} - 19q^{75} + 10q^{76} - 15q^{77} - 14q^{78} + 33q^{79} - q^{80} + 14q^{81} - q^{82} - 25q^{83} - 5q^{84} + 25q^{85} - 6q^{86} - 6q^{87} + q^{88} + 3q^{89} + q^{90} - 5q^{91} - q^{92} - 20q^{93} + 13q^{94} + 30q^{95} + 14q^{96} + 11q^{97} - 9q^{98} - q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −0.924862 −0.413611 −0.206805 0.978382i \(-0.566307\pi\)
−0.206805 + 0.978382i \(0.566307\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.24556 −1.60467 −0.802335 0.596874i \(-0.796409\pi\)
−0.802335 + 0.596874i \(0.796409\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.924862 0.292467
\(11\) 2.47789 0.747113 0.373556 0.927608i \(-0.378138\pi\)
0.373556 + 0.927608i \(0.378138\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) 4.24556 1.13467
\(15\) 0.924862 0.238798
\(16\) 1.00000 0.250000
\(17\) 0.549056 0.133166 0.0665828 0.997781i \(-0.478790\pi\)
0.0665828 + 0.997781i \(0.478790\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.66906 −1.07116 −0.535578 0.844486i \(-0.679906\pi\)
−0.535578 + 0.844486i \(0.679906\pi\)
\(20\) −0.924862 −0.206805
\(21\) 4.24556 0.926457
\(22\) −2.47789 −0.528288
\(23\) −2.37974 −0.496210 −0.248105 0.968733i \(-0.579808\pi\)
−0.248105 + 0.968733i \(0.579808\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.14463 −0.828926
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) −4.24556 −0.802335
\(29\) 7.33896 1.36281 0.681406 0.731906i \(-0.261369\pi\)
0.681406 + 0.731906i \(0.261369\pi\)
\(30\) −0.924862 −0.168856
\(31\) 8.34581 1.49895 0.749476 0.662032i \(-0.230306\pi\)
0.749476 + 0.662032i \(0.230306\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.47789 −0.431346
\(34\) −0.549056 −0.0941623
\(35\) 3.92656 0.663709
\(36\) 1.00000 0.166667
\(37\) −9.19443 −1.51155 −0.755777 0.654829i \(-0.772741\pi\)
−0.755777 + 0.654829i \(0.772741\pi\)
\(38\) 4.66906 0.757422
\(39\) 1.00000 0.160128
\(40\) 0.924862 0.146234
\(41\) −0.968492 −0.151253 −0.0756265 0.997136i \(-0.524096\pi\)
−0.0756265 + 0.997136i \(0.524096\pi\)
\(42\) −4.24556 −0.655104
\(43\) −11.3612 −1.73257 −0.866284 0.499553i \(-0.833498\pi\)
−0.866284 + 0.499553i \(0.833498\pi\)
\(44\) 2.47789 0.373556
\(45\) −0.924862 −0.137870
\(46\) 2.37974 0.350874
\(47\) 2.40638 0.351007 0.175503 0.984479i \(-0.443845\pi\)
0.175503 + 0.984479i \(0.443845\pi\)
\(48\) −1.00000 −0.144338
\(49\) 11.0248 1.57497
\(50\) 4.14463 0.586139
\(51\) −0.549056 −0.0768832
\(52\) −1.00000 −0.138675
\(53\) −10.3792 −1.42570 −0.712850 0.701317i \(-0.752596\pi\)
−0.712850 + 0.701317i \(0.752596\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.29171 −0.309014
\(56\) 4.24556 0.567337
\(57\) 4.66906 0.618433
\(58\) −7.33896 −0.963653
\(59\) 3.20528 0.417293 0.208646 0.977991i \(-0.433094\pi\)
0.208646 + 0.977991i \(0.433094\pi\)
\(60\) 0.924862 0.119399
\(61\) −6.92554 −0.886725 −0.443363 0.896342i \(-0.646215\pi\)
−0.443363 + 0.896342i \(0.646215\pi\)
\(62\) −8.34581 −1.05992
\(63\) −4.24556 −0.534890
\(64\) 1.00000 0.125000
\(65\) 0.924862 0.114715
\(66\) 2.47789 0.305007
\(67\) −2.85465 −0.348751 −0.174376 0.984679i \(-0.555791\pi\)
−0.174376 + 0.984679i \(0.555791\pi\)
\(68\) 0.549056 0.0665828
\(69\) 2.37974 0.286487
\(70\) −3.92656 −0.469313
\(71\) −7.09939 −0.842543 −0.421271 0.906935i \(-0.638416\pi\)
−0.421271 + 0.906935i \(0.638416\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.73116 0.904863 0.452432 0.891799i \(-0.350557\pi\)
0.452432 + 0.891799i \(0.350557\pi\)
\(74\) 9.19443 1.06883
\(75\) 4.14463 0.478581
\(76\) −4.66906 −0.535578
\(77\) −10.5200 −1.19887
\(78\) −1.00000 −0.113228
\(79\) 11.8927 1.33804 0.669018 0.743246i \(-0.266715\pi\)
0.669018 + 0.743246i \(0.266715\pi\)
\(80\) −0.924862 −0.103403
\(81\) 1.00000 0.111111
\(82\) 0.968492 0.106952
\(83\) 7.46254 0.819120 0.409560 0.912283i \(-0.365682\pi\)
0.409560 + 0.912283i \(0.365682\pi\)
\(84\) 4.24556 0.463228
\(85\) −0.507801 −0.0550788
\(86\) 11.3612 1.22511
\(87\) −7.33896 −0.786819
\(88\) −2.47789 −0.264144
\(89\) −0.591240 −0.0626713 −0.0313357 0.999509i \(-0.509976\pi\)
−0.0313357 + 0.999509i \(0.509976\pi\)
\(90\) 0.924862 0.0974890
\(91\) 4.24556 0.445056
\(92\) −2.37974 −0.248105
\(93\) −8.34581 −0.865420
\(94\) −2.40638 −0.248199
\(95\) 4.31824 0.443042
\(96\) 1.00000 0.102062
\(97\) −7.00078 −0.710821 −0.355411 0.934710i \(-0.615659\pi\)
−0.355411 + 0.934710i \(0.615659\pi\)
\(98\) −11.0248 −1.11367
\(99\) 2.47789 0.249038
\(100\) −4.14463 −0.414463
\(101\) −16.7023 −1.66194 −0.830971 0.556316i \(-0.812215\pi\)
−0.830971 + 0.556316i \(0.812215\pi\)
\(102\) 0.549056 0.0543646
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) −3.92656 −0.383193
\(106\) 10.3792 1.00812
\(107\) −15.5404 −1.50234 −0.751172 0.660107i \(-0.770511\pi\)
−0.751172 + 0.660107i \(0.770511\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.53988 −0.243277 −0.121638 0.992574i \(-0.538815\pi\)
−0.121638 + 0.992574i \(0.538815\pi\)
\(110\) 2.29171 0.218506
\(111\) 9.19443 0.872697
\(112\) −4.24556 −0.401168
\(113\) −0.761050 −0.0715936 −0.0357968 0.999359i \(-0.511397\pi\)
−0.0357968 + 0.999359i \(0.511397\pi\)
\(114\) −4.66906 −0.437298
\(115\) 2.20093 0.205238
\(116\) 7.33896 0.681406
\(117\) −1.00000 −0.0924500
\(118\) −3.20528 −0.295070
\(119\) −2.33105 −0.213687
\(120\) −0.924862 −0.0844280
\(121\) −4.86005 −0.441823
\(122\) 6.92554 0.627009
\(123\) 0.968492 0.0873260
\(124\) 8.34581 0.749476
\(125\) 8.45752 0.756464
\(126\) 4.24556 0.378224
\(127\) 7.62232 0.676372 0.338186 0.941079i \(-0.390187\pi\)
0.338186 + 0.941079i \(0.390187\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.3612 1.00030
\(130\) −0.924862 −0.0811158
\(131\) −17.1454 −1.49800 −0.749002 0.662567i \(-0.769467\pi\)
−0.749002 + 0.662567i \(0.769467\pi\)
\(132\) −2.47789 −0.215673
\(133\) 19.8228 1.71885
\(134\) 2.85465 0.246604
\(135\) 0.924862 0.0795994
\(136\) −0.549056 −0.0470812
\(137\) −2.30953 −0.197316 −0.0986581 0.995121i \(-0.531455\pi\)
−0.0986581 + 0.995121i \(0.531455\pi\)
\(138\) −2.37974 −0.202577
\(139\) −5.43429 −0.460931 −0.230465 0.973081i \(-0.574025\pi\)
−0.230465 + 0.973081i \(0.574025\pi\)
\(140\) 3.92656 0.331855
\(141\) −2.40638 −0.202654
\(142\) 7.09939 0.595768
\(143\) −2.47789 −0.207212
\(144\) 1.00000 0.0833333
\(145\) −6.78753 −0.563674
\(146\) −7.73116 −0.639835
\(147\) −11.0248 −0.909308
\(148\) −9.19443 −0.755777
\(149\) −18.1116 −1.48376 −0.741879 0.670533i \(-0.766065\pi\)
−0.741879 + 0.670533i \(0.766065\pi\)
\(150\) −4.14463 −0.338408
\(151\) 18.4752 1.50349 0.751745 0.659454i \(-0.229213\pi\)
0.751745 + 0.659454i \(0.229213\pi\)
\(152\) 4.66906 0.378711
\(153\) 0.549056 0.0443885
\(154\) 10.5200 0.847729
\(155\) −7.71872 −0.619983
\(156\) 1.00000 0.0800641
\(157\) −2.42290 −0.193368 −0.0966840 0.995315i \(-0.530824\pi\)
−0.0966840 + 0.995315i \(0.530824\pi\)
\(158\) −11.8927 −0.946135
\(159\) 10.3792 0.823128
\(160\) 0.924862 0.0731168
\(161\) 10.1033 0.796254
\(162\) −1.00000 −0.0785674
\(163\) −0.347587 −0.0272251 −0.0136126 0.999907i \(-0.504333\pi\)
−0.0136126 + 0.999907i \(0.504333\pi\)
\(164\) −0.968492 −0.0756265
\(165\) 2.29171 0.178409
\(166\) −7.46254 −0.579206
\(167\) −2.09894 −0.162421 −0.0812106 0.996697i \(-0.525879\pi\)
−0.0812106 + 0.996697i \(0.525879\pi\)
\(168\) −4.24556 −0.327552
\(169\) 1.00000 0.0769231
\(170\) 0.507801 0.0389466
\(171\) −4.66906 −0.357052
\(172\) −11.3612 −0.866284
\(173\) −6.76812 −0.514570 −0.257285 0.966336i \(-0.582828\pi\)
−0.257285 + 0.966336i \(0.582828\pi\)
\(174\) 7.33896 0.556365
\(175\) 17.5963 1.33015
\(176\) 2.47789 0.186778
\(177\) −3.20528 −0.240924
\(178\) 0.591240 0.0443153
\(179\) 18.8614 1.40976 0.704882 0.709325i \(-0.251000\pi\)
0.704882 + 0.709325i \(0.251000\pi\)
\(180\) −0.924862 −0.0689351
\(181\) −21.5859 −1.60447 −0.802234 0.597010i \(-0.796355\pi\)
−0.802234 + 0.597010i \(0.796355\pi\)
\(182\) −4.24556 −0.314702
\(183\) 6.92554 0.511951
\(184\) 2.37974 0.175437
\(185\) 8.50358 0.625195
\(186\) 8.34581 0.611945
\(187\) 1.36050 0.0994897
\(188\) 2.40638 0.175503
\(189\) 4.24556 0.308819
\(190\) −4.31824 −0.313278
\(191\) 5.01170 0.362634 0.181317 0.983425i \(-0.441964\pi\)
0.181317 + 0.983425i \(0.441964\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 8.23014 0.592418 0.296209 0.955123i \(-0.404277\pi\)
0.296209 + 0.955123i \(0.404277\pi\)
\(194\) 7.00078 0.502626
\(195\) −0.924862 −0.0662307
\(196\) 11.0248 0.787484
\(197\) −0.479465 −0.0341605 −0.0170802 0.999854i \(-0.505437\pi\)
−0.0170802 + 0.999854i \(0.505437\pi\)
\(198\) −2.47789 −0.176096
\(199\) −12.7103 −0.901007 −0.450504 0.892775i \(-0.648756\pi\)
−0.450504 + 0.892775i \(0.648756\pi\)
\(200\) 4.14463 0.293070
\(201\) 2.85465 0.201352
\(202\) 16.7023 1.17517
\(203\) −31.1580 −2.18686
\(204\) −0.549056 −0.0384416
\(205\) 0.895721 0.0625599
\(206\) −1.00000 −0.0696733
\(207\) −2.37974 −0.165403
\(208\) −1.00000 −0.0693375
\(209\) −11.5694 −0.800275
\(210\) 3.92656 0.270958
\(211\) 10.6225 0.731286 0.365643 0.930755i \(-0.380849\pi\)
0.365643 + 0.930755i \(0.380849\pi\)
\(212\) −10.3792 −0.712850
\(213\) 7.09939 0.486442
\(214\) 15.5404 1.06232
\(215\) 10.5075 0.716609
\(216\) 1.00000 0.0680414
\(217\) −35.4326 −2.40532
\(218\) 2.53988 0.172023
\(219\) −7.73116 −0.522423
\(220\) −2.29171 −0.154507
\(221\) −0.549056 −0.0369335
\(222\) −9.19443 −0.617090
\(223\) 19.4059 1.29951 0.649756 0.760143i \(-0.274871\pi\)
0.649756 + 0.760143i \(0.274871\pi\)
\(224\) 4.24556 0.283668
\(225\) −4.14463 −0.276309
\(226\) 0.761050 0.0506243
\(227\) −7.36686 −0.488956 −0.244478 0.969655i \(-0.578617\pi\)
−0.244478 + 0.969655i \(0.578617\pi\)
\(228\) 4.66906 0.309216
\(229\) 2.87706 0.190122 0.0950608 0.995471i \(-0.469695\pi\)
0.0950608 + 0.995471i \(0.469695\pi\)
\(230\) −2.20093 −0.145125
\(231\) 10.5200 0.692168
\(232\) −7.33896 −0.481827
\(233\) 21.3454 1.39838 0.699190 0.714936i \(-0.253544\pi\)
0.699190 + 0.714936i \(0.253544\pi\)
\(234\) 1.00000 0.0653720
\(235\) −2.22557 −0.145180
\(236\) 3.20528 0.208646
\(237\) −11.8927 −0.772516
\(238\) 2.33105 0.151100
\(239\) −4.40691 −0.285059 −0.142530 0.989791i \(-0.545524\pi\)
−0.142530 + 0.989791i \(0.545524\pi\)
\(240\) 0.924862 0.0596996
\(241\) 3.62912 0.233772 0.116886 0.993145i \(-0.462709\pi\)
0.116886 + 0.993145i \(0.462709\pi\)
\(242\) 4.86005 0.312416
\(243\) −1.00000 −0.0641500
\(244\) −6.92554 −0.443363
\(245\) −10.1964 −0.651424
\(246\) −0.968492 −0.0617488
\(247\) 4.66906 0.297085
\(248\) −8.34581 −0.529960
\(249\) −7.46254 −0.472919
\(250\) −8.45752 −0.534901
\(251\) 15.8324 0.999332 0.499666 0.866218i \(-0.333456\pi\)
0.499666 + 0.866218i \(0.333456\pi\)
\(252\) −4.24556 −0.267445
\(253\) −5.89674 −0.370725
\(254\) −7.62232 −0.478267
\(255\) 0.507801 0.0317997
\(256\) 1.00000 0.0625000
\(257\) −27.4973 −1.71523 −0.857617 0.514289i \(-0.828056\pi\)
−0.857617 + 0.514289i \(0.828056\pi\)
\(258\) −11.3612 −0.707318
\(259\) 39.0355 2.42555
\(260\) 0.924862 0.0573575
\(261\) 7.33896 0.454270
\(262\) 17.1454 1.05925
\(263\) −16.7345 −1.03190 −0.515948 0.856620i \(-0.672560\pi\)
−0.515948 + 0.856620i \(0.672560\pi\)
\(264\) 2.47789 0.152504
\(265\) 9.59937 0.589685
\(266\) −19.8228 −1.21541
\(267\) 0.591240 0.0361833
\(268\) −2.85465 −0.174376
\(269\) 10.8418 0.661035 0.330517 0.943800i \(-0.392777\pi\)
0.330517 + 0.943800i \(0.392777\pi\)
\(270\) −0.924862 −0.0562853
\(271\) 17.9774 1.09205 0.546026 0.837769i \(-0.316140\pi\)
0.546026 + 0.837769i \(0.316140\pi\)
\(272\) 0.549056 0.0332914
\(273\) −4.24556 −0.256953
\(274\) 2.30953 0.139524
\(275\) −10.2699 −0.619301
\(276\) 2.37974 0.143244
\(277\) 25.6652 1.54207 0.771036 0.636792i \(-0.219739\pi\)
0.771036 + 0.636792i \(0.219739\pi\)
\(278\) 5.43429 0.325927
\(279\) 8.34581 0.499651
\(280\) −3.92656 −0.234657
\(281\) 23.1458 1.38076 0.690380 0.723447i \(-0.257443\pi\)
0.690380 + 0.723447i \(0.257443\pi\)
\(282\) 2.40638 0.143298
\(283\) −16.1782 −0.961694 −0.480847 0.876805i \(-0.659671\pi\)
−0.480847 + 0.876805i \(0.659671\pi\)
\(284\) −7.09939 −0.421271
\(285\) −4.31824 −0.255790
\(286\) 2.47789 0.146521
\(287\) 4.11179 0.242711
\(288\) −1.00000 −0.0589256
\(289\) −16.6985 −0.982267
\(290\) 6.78753 0.398577
\(291\) 7.00078 0.410393
\(292\) 7.73116 0.452432
\(293\) 25.8709 1.51139 0.755696 0.654923i \(-0.227299\pi\)
0.755696 + 0.654923i \(0.227299\pi\)
\(294\) 11.0248 0.642978
\(295\) −2.96445 −0.172597
\(296\) 9.19443 0.534415
\(297\) −2.47789 −0.143782
\(298\) 18.1116 1.04918
\(299\) 2.37974 0.137624
\(300\) 4.14463 0.239290
\(301\) 48.2347 2.78020
\(302\) −18.4752 −1.06313
\(303\) 16.7023 0.959523
\(304\) −4.66906 −0.267789
\(305\) 6.40517 0.366759
\(306\) −0.549056 −0.0313874
\(307\) 3.15586 0.180114 0.0900572 0.995937i \(-0.471295\pi\)
0.0900572 + 0.995937i \(0.471295\pi\)
\(308\) −10.5200 −0.599435
\(309\) −1.00000 −0.0568880
\(310\) 7.71872 0.438394
\(311\) 6.63267 0.376104 0.188052 0.982159i \(-0.439783\pi\)
0.188052 + 0.982159i \(0.439783\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −8.29547 −0.468888 −0.234444 0.972130i \(-0.575327\pi\)
−0.234444 + 0.972130i \(0.575327\pi\)
\(314\) 2.42290 0.136732
\(315\) 3.92656 0.221236
\(316\) 11.8927 0.669018
\(317\) 1.19753 0.0672602 0.0336301 0.999434i \(-0.489293\pi\)
0.0336301 + 0.999434i \(0.489293\pi\)
\(318\) −10.3792 −0.582039
\(319\) 18.1852 1.01817
\(320\) −0.924862 −0.0517014
\(321\) 15.5404 0.867378
\(322\) −10.1033 −0.563037
\(323\) −2.56358 −0.142641
\(324\) 1.00000 0.0555556
\(325\) 4.14463 0.229903
\(326\) 0.347587 0.0192511
\(327\) 2.53988 0.140456
\(328\) 0.968492 0.0534760
\(329\) −10.2164 −0.563250
\(330\) −2.29171 −0.126154
\(331\) 15.5698 0.855791 0.427896 0.903828i \(-0.359255\pi\)
0.427896 + 0.903828i \(0.359255\pi\)
\(332\) 7.46254 0.409560
\(333\) −9.19443 −0.503852
\(334\) 2.09894 0.114849
\(335\) 2.64016 0.144247
\(336\) 4.24556 0.231614
\(337\) −12.9559 −0.705752 −0.352876 0.935670i \(-0.614796\pi\)
−0.352876 + 0.935670i \(0.614796\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 0.761050 0.0413346
\(340\) −0.507801 −0.0275394
\(341\) 20.6800 1.11989
\(342\) 4.66906 0.252474
\(343\) −17.0874 −0.922633
\(344\) 11.3612 0.612555
\(345\) −2.20093 −0.118494
\(346\) 6.76812 0.363856
\(347\) 30.5303 1.63895 0.819476 0.573113i \(-0.194264\pi\)
0.819476 + 0.573113i \(0.194264\pi\)
\(348\) −7.33896 −0.393410
\(349\) 5.81081 0.311046 0.155523 0.987832i \(-0.450294\pi\)
0.155523 + 0.987832i \(0.450294\pi\)
\(350\) −17.5963 −0.940560
\(351\) 1.00000 0.0533761
\(352\) −2.47789 −0.132072
\(353\) −21.3783 −1.13785 −0.568926 0.822389i \(-0.692641\pi\)
−0.568926 + 0.822389i \(0.692641\pi\)
\(354\) 3.20528 0.170359
\(355\) 6.56596 0.348485
\(356\) −0.591240 −0.0313357
\(357\) 2.33105 0.123372
\(358\) −18.8614 −0.996854
\(359\) 6.87350 0.362769 0.181385 0.983412i \(-0.441942\pi\)
0.181385 + 0.983412i \(0.441942\pi\)
\(360\) 0.924862 0.0487445
\(361\) 2.80016 0.147377
\(362\) 21.5859 1.13453
\(363\) 4.86005 0.255087
\(364\) 4.24556 0.222528
\(365\) −7.15025 −0.374261
\(366\) −6.92554 −0.362004
\(367\) 23.9000 1.24757 0.623786 0.781595i \(-0.285594\pi\)
0.623786 + 0.781595i \(0.285594\pi\)
\(368\) −2.37974 −0.124053
\(369\) −0.968492 −0.0504177
\(370\) −8.50358 −0.442080
\(371\) 44.0657 2.28778
\(372\) −8.34581 −0.432710
\(373\) −19.9817 −1.03461 −0.517307 0.855800i \(-0.673066\pi\)
−0.517307 + 0.855800i \(0.673066\pi\)
\(374\) −1.36050 −0.0703499
\(375\) −8.45752 −0.436745
\(376\) −2.40638 −0.124100
\(377\) −7.33896 −0.377976
\(378\) −4.24556 −0.218368
\(379\) −9.19649 −0.472392 −0.236196 0.971705i \(-0.575901\pi\)
−0.236196 + 0.971705i \(0.575901\pi\)
\(380\) 4.31824 0.221521
\(381\) −7.62232 −0.390503
\(382\) −5.01170 −0.256421
\(383\) −20.1021 −1.02717 −0.513586 0.858038i \(-0.671683\pi\)
−0.513586 + 0.858038i \(0.671683\pi\)
\(384\) 1.00000 0.0510310
\(385\) 9.72958 0.495865
\(386\) −8.23014 −0.418903
\(387\) −11.3612 −0.577522
\(388\) −7.00078 −0.355411
\(389\) 21.9274 1.11176 0.555882 0.831261i \(-0.312381\pi\)
0.555882 + 0.831261i \(0.312381\pi\)
\(390\) 0.924862 0.0468322
\(391\) −1.30661 −0.0660782
\(392\) −11.0248 −0.556835
\(393\) 17.1454 0.864874
\(394\) 0.479465 0.0241551
\(395\) −10.9991 −0.553426
\(396\) 2.47789 0.124519
\(397\) 28.3446 1.42258 0.711288 0.702900i \(-0.248112\pi\)
0.711288 + 0.702900i \(0.248112\pi\)
\(398\) 12.7103 0.637108
\(399\) −19.8228 −0.992381
\(400\) −4.14463 −0.207232
\(401\) −21.8488 −1.09108 −0.545539 0.838086i \(-0.683675\pi\)
−0.545539 + 0.838086i \(0.683675\pi\)
\(402\) −2.85465 −0.142377
\(403\) −8.34581 −0.415734
\(404\) −16.7023 −0.830971
\(405\) −0.924862 −0.0459568
\(406\) 31.1580 1.54635
\(407\) −22.7828 −1.12930
\(408\) 0.549056 0.0271823
\(409\) 2.98848 0.147771 0.0738854 0.997267i \(-0.476460\pi\)
0.0738854 + 0.997267i \(0.476460\pi\)
\(410\) −0.895721 −0.0442365
\(411\) 2.30953 0.113921
\(412\) 1.00000 0.0492665
\(413\) −13.6082 −0.669617
\(414\) 2.37974 0.116958
\(415\) −6.90182 −0.338797
\(416\) 1.00000 0.0490290
\(417\) 5.43429 0.266118
\(418\) 11.5694 0.565880
\(419\) 7.64382 0.373425 0.186713 0.982415i \(-0.440217\pi\)
0.186713 + 0.982415i \(0.440217\pi\)
\(420\) −3.92656 −0.191596
\(421\) 6.62472 0.322869 0.161435 0.986883i \(-0.448388\pi\)
0.161435 + 0.986883i \(0.448388\pi\)
\(422\) −10.6225 −0.517097
\(423\) 2.40638 0.117002
\(424\) 10.3792 0.504061
\(425\) −2.27563 −0.110384
\(426\) −7.09939 −0.343967
\(427\) 29.4028 1.42290
\(428\) −15.5404 −0.751172
\(429\) 2.47789 0.119634
\(430\) −10.5075 −0.506719
\(431\) −23.7953 −1.14618 −0.573089 0.819493i \(-0.694255\pi\)
−0.573089 + 0.819493i \(0.694255\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 9.20725 0.442472 0.221236 0.975220i \(-0.428991\pi\)
0.221236 + 0.975220i \(0.428991\pi\)
\(434\) 35.4326 1.70082
\(435\) 6.78753 0.325437
\(436\) −2.53988 −0.121638
\(437\) 11.1112 0.531519
\(438\) 7.73116 0.369409
\(439\) −1.68419 −0.0803819 −0.0401910 0.999192i \(-0.512797\pi\)
−0.0401910 + 0.999192i \(0.512797\pi\)
\(440\) 2.29171 0.109253
\(441\) 11.0248 0.524989
\(442\) 0.549056 0.0261159
\(443\) −4.58842 −0.218003 −0.109001 0.994042i \(-0.534765\pi\)
−0.109001 + 0.994042i \(0.534765\pi\)
\(444\) 9.19443 0.436348
\(445\) 0.546816 0.0259215
\(446\) −19.4059 −0.918894
\(447\) 18.1116 0.856648
\(448\) −4.24556 −0.200584
\(449\) 5.14126 0.242631 0.121316 0.992614i \(-0.461289\pi\)
0.121316 + 0.992614i \(0.461289\pi\)
\(450\) 4.14463 0.195380
\(451\) −2.39982 −0.113003
\(452\) −0.761050 −0.0357968
\(453\) −18.4752 −0.868040
\(454\) 7.36686 0.345744
\(455\) −3.92656 −0.184080
\(456\) −4.66906 −0.218649
\(457\) 20.4298 0.955665 0.477833 0.878451i \(-0.341423\pi\)
0.477833 + 0.878451i \(0.341423\pi\)
\(458\) −2.87706 −0.134436
\(459\) −0.549056 −0.0256277
\(460\) 2.20093 0.102619
\(461\) −6.15593 −0.286710 −0.143355 0.989671i \(-0.545789\pi\)
−0.143355 + 0.989671i \(0.545789\pi\)
\(462\) −10.5200 −0.489436
\(463\) 15.7448 0.731722 0.365861 0.930670i \(-0.380775\pi\)
0.365861 + 0.930670i \(0.380775\pi\)
\(464\) 7.33896 0.340703
\(465\) 7.71872 0.357947
\(466\) −21.3454 −0.988804
\(467\) 32.0932 1.48510 0.742549 0.669791i \(-0.233617\pi\)
0.742549 + 0.669791i \(0.233617\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 12.1196 0.559631
\(470\) 2.22557 0.102658
\(471\) 2.42290 0.111641
\(472\) −3.20528 −0.147535
\(473\) −28.1518 −1.29442
\(474\) 11.8927 0.546251
\(475\) 19.3515 0.887910
\(476\) −2.33105 −0.106843
\(477\) −10.3792 −0.475233
\(478\) 4.40691 0.201567
\(479\) 41.1788 1.88151 0.940753 0.339093i \(-0.110120\pi\)
0.940753 + 0.339093i \(0.110120\pi\)
\(480\) −0.924862 −0.0422140
\(481\) 9.19443 0.419230
\(482\) −3.62912 −0.165302
\(483\) −10.1033 −0.459718
\(484\) −4.86005 −0.220911
\(485\) 6.47475 0.294003
\(486\) 1.00000 0.0453609
\(487\) 5.83363 0.264347 0.132174 0.991227i \(-0.457804\pi\)
0.132174 + 0.991227i \(0.457804\pi\)
\(488\) 6.92554 0.313505
\(489\) 0.347587 0.0157184
\(490\) 10.1964 0.460626
\(491\) 8.06550 0.363991 0.181995 0.983299i \(-0.441744\pi\)
0.181995 + 0.983299i \(0.441744\pi\)
\(492\) 0.968492 0.0436630
\(493\) 4.02950 0.181480
\(494\) −4.66906 −0.210071
\(495\) −2.29171 −0.103005
\(496\) 8.34581 0.374738
\(497\) 30.1409 1.35200
\(498\) 7.46254 0.334404
\(499\) −1.14142 −0.0510970 −0.0255485 0.999674i \(-0.508133\pi\)
−0.0255485 + 0.999674i \(0.508133\pi\)
\(500\) 8.45752 0.378232
\(501\) 2.09894 0.0937739
\(502\) −15.8324 −0.706635
\(503\) −31.0106 −1.38270 −0.691348 0.722522i \(-0.742983\pi\)
−0.691348 + 0.722522i \(0.742983\pi\)
\(504\) 4.24556 0.189112
\(505\) 15.4473 0.687397
\(506\) 5.89674 0.262142
\(507\) −1.00000 −0.0444116
\(508\) 7.62232 0.338186
\(509\) −8.44767 −0.374436 −0.187218 0.982318i \(-0.559947\pi\)
−0.187218 + 0.982318i \(0.559947\pi\)
\(510\) −0.507801 −0.0224858
\(511\) −32.8231 −1.45201
\(512\) −1.00000 −0.0441942
\(513\) 4.66906 0.206144
\(514\) 27.4973 1.21285
\(515\) −0.924862 −0.0407543
\(516\) 11.3612 0.500149
\(517\) 5.96275 0.262241
\(518\) −39.0355 −1.71512
\(519\) 6.76812 0.297087
\(520\) −0.924862 −0.0405579
\(521\) −12.4275 −0.544459 −0.272230 0.962232i \(-0.587761\pi\)
−0.272230 + 0.962232i \(0.587761\pi\)
\(522\) −7.33896 −0.321218
\(523\) 19.8778 0.869195 0.434597 0.900625i \(-0.356891\pi\)
0.434597 + 0.900625i \(0.356891\pi\)
\(524\) −17.1454 −0.749002
\(525\) −17.5963 −0.767964
\(526\) 16.7345 0.729660
\(527\) 4.58232 0.199609
\(528\) −2.47789 −0.107836
\(529\) −17.3368 −0.753775
\(530\) −9.59937 −0.416970
\(531\) 3.20528 0.139098
\(532\) 19.8228 0.859427
\(533\) 0.968492 0.0419500
\(534\) −0.591240 −0.0255855
\(535\) 14.3727 0.621386
\(536\) 2.85465 0.123302
\(537\) −18.8614 −0.813928
\(538\) −10.8418 −0.467422
\(539\) 27.3182 1.17668
\(540\) 0.924862 0.0397997
\(541\) −22.9394 −0.986243 −0.493122 0.869960i \(-0.664144\pi\)
−0.493122 + 0.869960i \(0.664144\pi\)
\(542\) −17.9774 −0.772197
\(543\) 21.5859 0.926340
\(544\) −0.549056 −0.0235406
\(545\) 2.34904 0.100622
\(546\) 4.24556 0.181693
\(547\) −29.0471 −1.24196 −0.620981 0.783825i \(-0.713266\pi\)
−0.620981 + 0.783825i \(0.713266\pi\)
\(548\) −2.30953 −0.0986581
\(549\) −6.92554 −0.295575
\(550\) 10.2699 0.437912
\(551\) −34.2661 −1.45978
\(552\) −2.37974 −0.101289
\(553\) −50.4913 −2.14711
\(554\) −25.6652 −1.09041
\(555\) −8.50358 −0.360957
\(556\) −5.43429 −0.230465
\(557\) −1.52392 −0.0645706 −0.0322853 0.999479i \(-0.510279\pi\)
−0.0322853 + 0.999479i \(0.510279\pi\)
\(558\) −8.34581 −0.353306
\(559\) 11.3612 0.480528
\(560\) 3.92656 0.165927
\(561\) −1.36050 −0.0574404
\(562\) −23.1458 −0.976345
\(563\) −28.0389 −1.18170 −0.590850 0.806781i \(-0.701207\pi\)
−0.590850 + 0.806781i \(0.701207\pi\)
\(564\) −2.40638 −0.101327
\(565\) 0.703866 0.0296119
\(566\) 16.1782 0.680020
\(567\) −4.24556 −0.178297
\(568\) 7.09939 0.297884
\(569\) −32.8020 −1.37513 −0.687566 0.726122i \(-0.741321\pi\)
−0.687566 + 0.726122i \(0.741321\pi\)
\(570\) 4.31824 0.180871
\(571\) 42.3562 1.77255 0.886277 0.463156i \(-0.153283\pi\)
0.886277 + 0.463156i \(0.153283\pi\)
\(572\) −2.47789 −0.103606
\(573\) −5.01170 −0.209367
\(574\) −4.11179 −0.171623
\(575\) 9.86315 0.411322
\(576\) 1.00000 0.0416667
\(577\) 30.3341 1.26283 0.631413 0.775447i \(-0.282475\pi\)
0.631413 + 0.775447i \(0.282475\pi\)
\(578\) 16.6985 0.694568
\(579\) −8.23014 −0.342033
\(580\) −6.78753 −0.281837
\(581\) −31.6827 −1.31442
\(582\) −7.00078 −0.290191
\(583\) −25.7187 −1.06516
\(584\) −7.73116 −0.319918
\(585\) 0.924862 0.0382383
\(586\) −25.8709 −1.06872
\(587\) 12.0373 0.496834 0.248417 0.968653i \(-0.420090\pi\)
0.248417 + 0.968653i \(0.420090\pi\)
\(588\) −11.0248 −0.454654
\(589\) −38.9671 −1.60561
\(590\) 2.96445 0.122044
\(591\) 0.479465 0.0197226
\(592\) −9.19443 −0.377889
\(593\) 13.7264 0.563676 0.281838 0.959462i \(-0.409056\pi\)
0.281838 + 0.959462i \(0.409056\pi\)
\(594\) 2.47789 0.101669
\(595\) 2.15590 0.0883833
\(596\) −18.1116 −0.741879
\(597\) 12.7103 0.520197
\(598\) −2.37974 −0.0973149
\(599\) −7.25685 −0.296507 −0.148253 0.988949i \(-0.547365\pi\)
−0.148253 + 0.988949i \(0.547365\pi\)
\(600\) −4.14463 −0.169204
\(601\) 23.7190 0.967517 0.483758 0.875202i \(-0.339271\pi\)
0.483758 + 0.875202i \(0.339271\pi\)
\(602\) −48.2347 −1.96590
\(603\) −2.85465 −0.116250
\(604\) 18.4752 0.751745
\(605\) 4.49488 0.182743
\(606\) −16.7023 −0.678485
\(607\) 24.7564 1.00483 0.502416 0.864626i \(-0.332445\pi\)
0.502416 + 0.864626i \(0.332445\pi\)
\(608\) 4.66906 0.189356
\(609\) 31.1580 1.26259
\(610\) −6.40517 −0.259338
\(611\) −2.40638 −0.0973517
\(612\) 0.549056 0.0221943
\(613\) 37.8561 1.52899 0.764496 0.644629i \(-0.222988\pi\)
0.764496 + 0.644629i \(0.222988\pi\)
\(614\) −3.15586 −0.127360
\(615\) −0.895721 −0.0361190
\(616\) 10.5200 0.423864
\(617\) 6.05777 0.243877 0.121938 0.992538i \(-0.461089\pi\)
0.121938 + 0.992538i \(0.461089\pi\)
\(618\) 1.00000 0.0402259
\(619\) −30.3573 −1.22016 −0.610081 0.792339i \(-0.708863\pi\)
−0.610081 + 0.792339i \(0.708863\pi\)
\(620\) −7.71872 −0.309991
\(621\) 2.37974 0.0954958
\(622\) −6.63267 −0.265946
\(623\) 2.51015 0.100567
\(624\) 1.00000 0.0400320
\(625\) 12.9011 0.516044
\(626\) 8.29547 0.331554
\(627\) 11.5694 0.462039
\(628\) −2.42290 −0.0966840
\(629\) −5.04826 −0.201287
\(630\) −3.92656 −0.156438
\(631\) −0.227520 −0.00905741 −0.00452871 0.999990i \(-0.501442\pi\)
−0.00452871 + 0.999990i \(0.501442\pi\)
\(632\) −11.8927 −0.473067
\(633\) −10.6225 −0.422208
\(634\) −1.19753 −0.0475601
\(635\) −7.04960 −0.279755
\(636\) 10.3792 0.411564
\(637\) −11.0248 −0.436817
\(638\) −18.1852 −0.719957
\(639\) −7.09939 −0.280848
\(640\) 0.924862 0.0365584
\(641\) −32.0388 −1.26546 −0.632728 0.774374i \(-0.718065\pi\)
−0.632728 + 0.774374i \(0.718065\pi\)
\(642\) −15.5404 −0.613329
\(643\) 10.9375 0.431334 0.215667 0.976467i \(-0.430807\pi\)
0.215667 + 0.976467i \(0.430807\pi\)
\(644\) 10.1033 0.398127
\(645\) −10.5075 −0.413734
\(646\) 2.56358 0.100863
\(647\) 0.956751 0.0376137 0.0188069 0.999823i \(-0.494013\pi\)
0.0188069 + 0.999823i \(0.494013\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 7.94235 0.311764
\(650\) −4.14463 −0.162566
\(651\) 35.4326 1.38871
\(652\) −0.347587 −0.0136126
\(653\) 40.7145 1.59328 0.796641 0.604453i \(-0.206608\pi\)
0.796641 + 0.604453i \(0.206608\pi\)
\(654\) −2.53988 −0.0993173
\(655\) 15.8572 0.619591
\(656\) −0.968492 −0.0378133
\(657\) 7.73116 0.301621
\(658\) 10.2164 0.398278
\(659\) 1.62392 0.0632589 0.0316295 0.999500i \(-0.489930\pi\)
0.0316295 + 0.999500i \(0.489930\pi\)
\(660\) 2.29171 0.0892046
\(661\) −28.9108 −1.12450 −0.562251 0.826967i \(-0.690064\pi\)
−0.562251 + 0.826967i \(0.690064\pi\)
\(662\) −15.5698 −0.605136
\(663\) 0.549056 0.0213236
\(664\) −7.46254 −0.289603
\(665\) −18.3333 −0.710937
\(666\) 9.19443 0.356277
\(667\) −17.4648 −0.676241
\(668\) −2.09894 −0.0812106
\(669\) −19.4059 −0.750274
\(670\) −2.64016 −0.101998
\(671\) −17.1608 −0.662483
\(672\) −4.24556 −0.163776
\(673\) 28.5791 1.10164 0.550821 0.834624i \(-0.314315\pi\)
0.550821 + 0.834624i \(0.314315\pi\)
\(674\) 12.9559 0.499042
\(675\) 4.14463 0.159527
\(676\) 1.00000 0.0384615
\(677\) −7.90647 −0.303870 −0.151935 0.988390i \(-0.548550\pi\)
−0.151935 + 0.988390i \(0.548550\pi\)
\(678\) −0.761050 −0.0292279
\(679\) 29.7222 1.14063
\(680\) 0.507801 0.0194733
\(681\) 7.36686 0.282299
\(682\) −20.6800 −0.791879
\(683\) 29.6214 1.13343 0.566716 0.823913i \(-0.308214\pi\)
0.566716 + 0.823913i \(0.308214\pi\)
\(684\) −4.66906 −0.178526
\(685\) 2.13599 0.0816121
\(686\) 17.0874 0.652400
\(687\) −2.87706 −0.109767
\(688\) −11.3612 −0.433142
\(689\) 10.3792 0.395418
\(690\) 2.20093 0.0837881
\(691\) −7.71057 −0.293324 −0.146662 0.989187i \(-0.546853\pi\)
−0.146662 + 0.989187i \(0.546853\pi\)
\(692\) −6.76812 −0.257285
\(693\) −10.5200 −0.399623
\(694\) −30.5303 −1.15891
\(695\) 5.02597 0.190646
\(696\) 7.33896 0.278183
\(697\) −0.531756 −0.0201417
\(698\) −5.81081 −0.219942
\(699\) −21.3454 −0.807355
\(700\) 17.5963 0.665077
\(701\) 25.3023 0.955654 0.477827 0.878454i \(-0.341425\pi\)
0.477827 + 0.878454i \(0.341425\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 42.9294 1.61911
\(704\) 2.47789 0.0933891
\(705\) 2.22557 0.0838198
\(706\) 21.3783 0.804582
\(707\) 70.9107 2.66687
\(708\) −3.20528 −0.120462
\(709\) −13.7359 −0.515861 −0.257930 0.966164i \(-0.583041\pi\)
−0.257930 + 0.966164i \(0.583041\pi\)
\(710\) −6.56596 −0.246416
\(711\) 11.8927 0.446012
\(712\) 0.591240 0.0221577
\(713\) −19.8609 −0.743796
\(714\) −2.33105 −0.0872373
\(715\) 2.29171 0.0857050
\(716\) 18.8614 0.704882
\(717\) 4.40691 0.164579
\(718\) −6.87350 −0.256517
\(719\) −8.94794 −0.333702 −0.166851 0.985982i \(-0.553360\pi\)
−0.166851 + 0.985982i \(0.553360\pi\)
\(720\) −0.924862 −0.0344676
\(721\) −4.24556 −0.158113
\(722\) −2.80016 −0.104211
\(723\) −3.62912 −0.134968
\(724\) −21.5859 −0.802234
\(725\) −30.4173 −1.12967
\(726\) −4.86005 −0.180373
\(727\) 40.1106 1.48762 0.743809 0.668392i \(-0.233017\pi\)
0.743809 + 0.668392i \(0.233017\pi\)
\(728\) −4.24556 −0.157351
\(729\) 1.00000 0.0370370
\(730\) 7.15025 0.264643
\(731\) −6.23794 −0.230718
\(732\) 6.92554 0.255975
\(733\) 30.3820 1.12219 0.561093 0.827753i \(-0.310381\pi\)
0.561093 + 0.827753i \(0.310381\pi\)
\(734\) −23.9000 −0.882166
\(735\) 10.1964 0.376100
\(736\) 2.37974 0.0877185
\(737\) −7.07352 −0.260557
\(738\) 0.968492 0.0356507
\(739\) 48.9164 1.79942 0.899710 0.436489i \(-0.143778\pi\)
0.899710 + 0.436489i \(0.143778\pi\)
\(740\) 8.50358 0.312598
\(741\) −4.66906 −0.171522
\(742\) −44.0657 −1.61770
\(743\) 6.61259 0.242592 0.121296 0.992616i \(-0.461295\pi\)
0.121296 + 0.992616i \(0.461295\pi\)
\(744\) 8.34581 0.305972
\(745\) 16.7507 0.613699
\(746\) 19.9817 0.731583
\(747\) 7.46254 0.273040
\(748\) 1.36050 0.0497449
\(749\) 65.9775 2.41077
\(750\) 8.45752 0.308825
\(751\) 32.7253 1.19416 0.597081 0.802181i \(-0.296327\pi\)
0.597081 + 0.802181i \(0.296327\pi\)
\(752\) 2.40638 0.0877517
\(753\) −15.8324 −0.576965
\(754\) 7.33896 0.267269
\(755\) −17.0870 −0.621860
\(756\) 4.24556 0.154409
\(757\) −30.9809 −1.12602 −0.563010 0.826450i \(-0.690357\pi\)
−0.563010 + 0.826450i \(0.690357\pi\)
\(758\) 9.19649 0.334032
\(759\) 5.89674 0.214038
\(760\) −4.31824 −0.156639
\(761\) 0.601756 0.0218136 0.0109068 0.999941i \(-0.496528\pi\)
0.0109068 + 0.999941i \(0.496528\pi\)
\(762\) 7.62232 0.276128
\(763\) 10.7832 0.390379
\(764\) 5.01170 0.181317
\(765\) −0.507801 −0.0183596
\(766\) 20.1021 0.726320
\(767\) −3.20528 −0.115736
\(768\) −1.00000 −0.0360844
\(769\) 25.4331 0.917142 0.458571 0.888658i \(-0.348361\pi\)
0.458571 + 0.888658i \(0.348361\pi\)
\(770\) −9.72958 −0.350630
\(771\) 27.4973 0.990291
\(772\) 8.23014 0.296209
\(773\) 2.97235 0.106908 0.0534540 0.998570i \(-0.482977\pi\)
0.0534540 + 0.998570i \(0.482977\pi\)
\(774\) 11.3612 0.408370
\(775\) −34.5903 −1.24252
\(776\) 7.00078 0.251313
\(777\) −39.0355 −1.40039
\(778\) −21.9274 −0.786136
\(779\) 4.52195 0.162016
\(780\) −0.924862 −0.0331154
\(781\) −17.5915 −0.629474
\(782\) 1.30661 0.0467243
\(783\) −7.33896 −0.262273
\(784\) 11.0248 0.393742
\(785\) 2.24084 0.0799791
\(786\) −17.1454 −0.611558
\(787\) 49.4887 1.76408 0.882041 0.471173i \(-0.156169\pi\)
0.882041 + 0.471173i \(0.156169\pi\)
\(788\) −0.479465 −0.0170802
\(789\) 16.7345 0.595765
\(790\) 10.9991 0.391332
\(791\) 3.23108 0.114884
\(792\) −2.47789 −0.0880481
\(793\) 6.92554 0.245933
\(794\) −28.3446 −1.00591
\(795\) −9.59937 −0.340455
\(796\) −12.7103 −0.450504
\(797\) 24.3948 0.864107 0.432054 0.901848i \(-0.357789\pi\)
0.432054 + 0.901848i \(0.357789\pi\)
\(798\) 19.8228 0.701719
\(799\) 1.32124 0.0467420
\(800\) 4.14463 0.146535
\(801\) −0.591240 −0.0208904
\(802\) 21.8488 0.771508
\(803\) 19.1570 0.676035
\(804\) 2.85465 0.100676
\(805\) −9.34419 −0.329339
\(806\) 8.34581 0.293969
\(807\) −10.8418 −0.381649
\(808\) 16.7023 0.587585
\(809\) −16.6019 −0.583692 −0.291846 0.956465i \(-0.594270\pi\)
−0.291846 + 0.956465i \(0.594270\pi\)
\(810\) 0.924862 0.0324963
\(811\) −28.0278 −0.984189 −0.492094 0.870542i \(-0.663769\pi\)
−0.492094 + 0.870542i \(0.663769\pi\)
\(812\) −31.1580 −1.09343
\(813\) −17.9774 −0.630496
\(814\) 22.7828 0.798537
\(815\) 0.321470 0.0112606
\(816\) −0.549056 −0.0192208
\(817\) 53.0462 1.85585
\(818\) −2.98848 −0.104490
\(819\) 4.24556 0.148352
\(820\) 0.895721 0.0312799
\(821\) −8.96226 −0.312785 −0.156393 0.987695i \(-0.549987\pi\)
−0.156393 + 0.987695i \(0.549987\pi\)
\(822\) −2.30953 −0.0805540
\(823\) 29.9469 1.04388 0.521942 0.852981i \(-0.325208\pi\)
0.521942 + 0.852981i \(0.325208\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 10.2699 0.357554
\(826\) 13.6082 0.473491
\(827\) −26.2269 −0.911999 −0.455999 0.889980i \(-0.650718\pi\)
−0.455999 + 0.889980i \(0.650718\pi\)
\(828\) −2.37974 −0.0827017
\(829\) −36.2795 −1.26004 −0.630020 0.776579i \(-0.716953\pi\)
−0.630020 + 0.776579i \(0.716953\pi\)
\(830\) 6.90182 0.239566
\(831\) −25.6652 −0.890315
\(832\) −1.00000 −0.0346688
\(833\) 6.05322 0.209732
\(834\) −5.43429 −0.188174
\(835\) 1.94123 0.0671791
\(836\) −11.5694 −0.400137
\(837\) −8.34581 −0.288473
\(838\) −7.64382 −0.264051
\(839\) 43.7783 1.51139 0.755697 0.654921i \(-0.227298\pi\)
0.755697 + 0.654921i \(0.227298\pi\)
\(840\) 3.92656 0.135479
\(841\) 24.8604 0.857255
\(842\) −6.62472 −0.228303
\(843\) −23.1458 −0.797182
\(844\) 10.6225 0.365643
\(845\) −0.924862 −0.0318162
\(846\) −2.40638 −0.0827331
\(847\) 20.6336 0.708980
\(848\) −10.3792 −0.356425
\(849\) 16.1782 0.555234
\(850\) 2.27563 0.0780536
\(851\) 21.8804 0.750049
\(852\) 7.09939 0.243221
\(853\) 24.6685 0.844632 0.422316 0.906449i \(-0.361217\pi\)
0.422316 + 0.906449i \(0.361217\pi\)
\(854\) −29.4028 −1.00614
\(855\) 4.31824 0.147681
\(856\) 15.5404 0.531159
\(857\) 35.4427 1.21070 0.605350 0.795959i \(-0.293033\pi\)
0.605350 + 0.795959i \(0.293033\pi\)
\(858\) −2.47789 −0.0845938
\(859\) −5.55366 −0.189488 −0.0947442 0.995502i \(-0.530203\pi\)
−0.0947442 + 0.995502i \(0.530203\pi\)
\(860\) 10.5075 0.358304
\(861\) −4.11179 −0.140129
\(862\) 23.7953 0.810470
\(863\) −45.0178 −1.53242 −0.766211 0.642589i \(-0.777860\pi\)
−0.766211 + 0.642589i \(0.777860\pi\)
\(864\) 1.00000 0.0340207
\(865\) 6.25957 0.212832
\(866\) −9.20725 −0.312875
\(867\) 16.6985 0.567112
\(868\) −35.4326 −1.20266
\(869\) 29.4689 0.999664
\(870\) −6.78753 −0.230119
\(871\) 2.85465 0.0967262
\(872\) 2.53988 0.0860113
\(873\) −7.00078 −0.236940
\(874\) −11.1112 −0.375841
\(875\) −35.9069 −1.21387
\(876\) −7.73116 −0.261212
\(877\) 22.3613 0.755089 0.377545 0.925991i \(-0.376769\pi\)
0.377545 + 0.925991i \(0.376769\pi\)
\(878\) 1.68419 0.0568386
\(879\) −25.8709 −0.872602
\(880\) −2.29171 −0.0772535
\(881\) 16.0301 0.540067 0.270033 0.962851i \(-0.412965\pi\)
0.270033 + 0.962851i \(0.412965\pi\)
\(882\) −11.0248 −0.371223
\(883\) −11.1985 −0.376859 −0.188429 0.982087i \(-0.560340\pi\)
−0.188429 + 0.982087i \(0.560340\pi\)
\(884\) −0.549056 −0.0184668
\(885\) 2.96445 0.0996488
\(886\) 4.58842 0.154151
\(887\) 34.0707 1.14398 0.571992 0.820259i \(-0.306171\pi\)
0.571992 + 0.820259i \(0.306171\pi\)
\(888\) −9.19443 −0.308545
\(889\) −32.3610 −1.08535
\(890\) −0.546816 −0.0183293
\(891\) 2.47789 0.0830125
\(892\) 19.4059 0.649756
\(893\) −11.2355 −0.375983
\(894\) −18.1116 −0.605742
\(895\) −17.4442 −0.583094
\(896\) 4.24556 0.141834
\(897\) −2.37974 −0.0794573
\(898\) −5.14126 −0.171566
\(899\) 61.2496 2.04279
\(900\) −4.14463 −0.138154
\(901\) −5.69879 −0.189854
\(902\) 2.39982 0.0799052
\(903\) −48.2347 −1.60515
\(904\) 0.761050 0.0253121
\(905\) 19.9640 0.663625
\(906\) 18.4752 0.613797
\(907\) 10.0554 0.333885 0.166943 0.985967i \(-0.446610\pi\)
0.166943 + 0.985967i \(0.446610\pi\)
\(908\) −7.36686 −0.244478
\(909\) −16.7023 −0.553981
\(910\) 3.92656 0.130164
\(911\) 9.21796 0.305405 0.152702 0.988272i \(-0.451202\pi\)
0.152702 + 0.988272i \(0.451202\pi\)
\(912\) 4.66906 0.154608
\(913\) 18.4914 0.611975
\(914\) −20.4298 −0.675758
\(915\) −6.40517 −0.211748
\(916\) 2.87706 0.0950608
\(917\) 72.7920 2.40380
\(918\) 0.549056 0.0181215
\(919\) 51.7380 1.70668 0.853339 0.521356i \(-0.174574\pi\)
0.853339 + 0.521356i \(0.174574\pi\)
\(920\) −2.20093 −0.0725626
\(921\) −3.15586 −0.103989
\(922\) 6.15593 0.202735
\(923\) 7.09939 0.233679
\(924\) 10.5200 0.346084
\(925\) 38.1075 1.25297
\(926\) −15.7448 −0.517406
\(927\) 1.00000 0.0328443
\(928\) −7.33896 −0.240913
\(929\) 15.4283 0.506185 0.253092 0.967442i \(-0.418552\pi\)
0.253092 + 0.967442i \(0.418552\pi\)
\(930\) −7.71872 −0.253107
\(931\) −51.4754 −1.68704
\(932\) 21.3454 0.699190
\(933\) −6.63267 −0.217144
\(934\) −32.0932 −1.05012
\(935\) −1.25828 −0.0411500
\(936\) 1.00000 0.0326860
\(937\) −24.8677 −0.812392 −0.406196 0.913786i \(-0.633145\pi\)
−0.406196 + 0.913786i \(0.633145\pi\)
\(938\) −12.1196 −0.395719
\(939\) 8.29547 0.270713
\(940\) −2.22557 −0.0725901
\(941\) 20.6871 0.674379 0.337189 0.941437i \(-0.390524\pi\)
0.337189 + 0.941437i \(0.390524\pi\)
\(942\) −2.42290 −0.0789422
\(943\) 2.30476 0.0750533
\(944\) 3.20528 0.104323
\(945\) −3.92656 −0.127731
\(946\) 28.1518 0.915295
\(947\) −56.3540 −1.83126 −0.915629 0.402024i \(-0.868307\pi\)
−0.915629 + 0.402024i \(0.868307\pi\)
\(948\) −11.8927 −0.386258
\(949\) −7.73116 −0.250964
\(950\) −19.3515 −0.627847
\(951\) −1.19753 −0.0388327
\(952\) 2.33105 0.0755498
\(953\) 16.3780 0.530537 0.265268 0.964175i \(-0.414539\pi\)
0.265268 + 0.964175i \(0.414539\pi\)
\(954\) 10.3792 0.336041
\(955\) −4.63513 −0.149989
\(956\) −4.40691 −0.142530
\(957\) −18.1852 −0.587843
\(958\) −41.1788 −1.33043
\(959\) 9.80523 0.316627
\(960\) 0.924862 0.0298498
\(961\) 38.6526 1.24686
\(962\) −9.19443 −0.296440
\(963\) −15.5404 −0.500781
\(964\) 3.62912 0.116886
\(965\) −7.61174 −0.245031
\(966\) 10.1033 0.325069
\(967\) −6.28152 −0.202000 −0.101000 0.994886i \(-0.532204\pi\)
−0.101000 + 0.994886i \(0.532204\pi\)
\(968\) 4.86005 0.156208
\(969\) 2.56358 0.0823540
\(970\) −6.47475 −0.207892
\(971\) −16.8905 −0.542042 −0.271021 0.962573i \(-0.587361\pi\)
−0.271021 + 0.962573i \(0.587361\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 23.0716 0.739642
\(974\) −5.83363 −0.186922
\(975\) −4.14463 −0.132734
\(976\) −6.92554 −0.221681
\(977\) 52.3227 1.67395 0.836976 0.547240i \(-0.184321\pi\)
0.836976 + 0.547240i \(0.184321\pi\)
\(978\) −0.347587 −0.0111146
\(979\) −1.46503 −0.0468226
\(980\) −10.1964 −0.325712
\(981\) −2.53988 −0.0810922
\(982\) −8.06550 −0.257380
\(983\) −13.1119 −0.418205 −0.209102 0.977894i \(-0.567054\pi\)
−0.209102 + 0.977894i \(0.567054\pi\)
\(984\) −0.968492 −0.0308744
\(985\) 0.443439 0.0141291
\(986\) −4.02950 −0.128325
\(987\) 10.2164 0.325193
\(988\) 4.66906 0.148543
\(989\) 27.0367 0.859718
\(990\) 2.29171 0.0728353
\(991\) 23.5113 0.746861 0.373430 0.927658i \(-0.378181\pi\)
0.373430 + 0.927658i \(0.378181\pi\)
\(992\) −8.34581 −0.264980
\(993\) −15.5698 −0.494091
\(994\) −30.1409 −0.956011
\(995\) 11.7552 0.372666
\(996\) −7.46254 −0.236460
\(997\) −23.0393 −0.729662 −0.364831 0.931074i \(-0.618873\pi\)
−0.364831 + 0.931074i \(0.618873\pi\)
\(998\) 1.14142 0.0361311
\(999\) 9.19443 0.290899
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 8034.2.a.ba.1.5 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.ba.1.5 14 1.1 even 1 trivial