Properties

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

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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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} - 7296 x - 2048\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.22430\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.22430 q^{5} -1.00000 q^{6} +1.37131 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.22430 q^{5} -1.00000 q^{6} +1.37131 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.22430 q^{10} +3.97219 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.37131 q^{14} -2.22430 q^{15} +1.00000 q^{16} +2.05875 q^{17} -1.00000 q^{18} -6.55850 q^{19} -2.22430 q^{20} +1.37131 q^{21} -3.97219 q^{22} -0.577248 q^{23} -1.00000 q^{24} -0.0525006 q^{25} +1.00000 q^{26} +1.00000 q^{27} +1.37131 q^{28} -3.79856 q^{29} +2.22430 q^{30} +2.84411 q^{31} -1.00000 q^{32} +3.97219 q^{33} -2.05875 q^{34} -3.05021 q^{35} +1.00000 q^{36} -3.41291 q^{37} +6.55850 q^{38} -1.00000 q^{39} +2.22430 q^{40} -6.35321 q^{41} -1.37131 q^{42} +12.0059 q^{43} +3.97219 q^{44} -2.22430 q^{45} +0.577248 q^{46} +2.35194 q^{47} +1.00000 q^{48} -5.11950 q^{49} +0.0525006 q^{50} +2.05875 q^{51} -1.00000 q^{52} -9.83809 q^{53} -1.00000 q^{54} -8.83534 q^{55} -1.37131 q^{56} -6.55850 q^{57} +3.79856 q^{58} +5.32093 q^{59} -2.22430 q^{60} +4.72419 q^{61} -2.84411 q^{62} +1.37131 q^{63} +1.00000 q^{64} +2.22430 q^{65} -3.97219 q^{66} +2.48532 q^{67} +2.05875 q^{68} -0.577248 q^{69} +3.05021 q^{70} -9.14181 q^{71} -1.00000 q^{72} +9.71266 q^{73} +3.41291 q^{74} -0.0525006 q^{75} -6.55850 q^{76} +5.44712 q^{77} +1.00000 q^{78} -1.40658 q^{79} -2.22430 q^{80} +1.00000 q^{81} +6.35321 q^{82} -12.3179 q^{83} +1.37131 q^{84} -4.57928 q^{85} -12.0059 q^{86} -3.79856 q^{87} -3.97219 q^{88} -17.1581 q^{89} +2.22430 q^{90} -1.37131 q^{91} -0.577248 q^{92} +2.84411 q^{93} -2.35194 q^{94} +14.5881 q^{95} -1.00000 q^{96} -14.8494 q^{97} +5.11950 q^{98} +3.97219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + 6q^{10} - 8q^{11} + 14q^{12} - 14q^{13} + 4q^{14} - 6q^{15} + 14q^{16} - 4q^{17} - 14q^{18} - q^{19} - 6q^{20} - 4q^{21} + 8q^{22} - 9q^{23} - 14q^{24} + 24q^{25} + 14q^{26} + 14q^{27} - 4q^{28} - 10q^{29} + 6q^{30} - 5q^{31} - 14q^{32} - 8q^{33} + 4q^{34} - 16q^{35} + 14q^{36} - 4q^{37} + q^{38} - 14q^{39} + 6q^{40} - 24q^{41} + 4q^{42} - 8q^{44} - 6q^{45} + 9q^{46} - 32q^{47} + 14q^{48} + 24q^{49} - 24q^{50} - 4q^{51} - 14q^{52} - 5q^{53} - 14q^{54} - 8q^{55} + 4q^{56} - q^{57} + 10q^{58} - 13q^{59} - 6q^{60} + 2q^{61} + 5q^{62} - 4q^{63} + 14q^{64} + 6q^{65} + 8q^{66} - 16q^{67} - 4q^{68} - 9q^{69} + 16q^{70} - 29q^{71} - 14q^{72} + 4q^{74} + 24q^{75} - q^{76} - 9q^{77} + 14q^{78} - 21q^{79} - 6q^{80} + 14q^{81} + 24q^{82} - 40q^{83} - 4q^{84} - 7q^{85} - 10q^{87} + 8q^{88} - 48q^{89} + 6q^{90} + 4q^{91} - 9q^{92} - 5q^{93} + 32q^{94} - 26q^{95} - 14q^{96} + 18q^{97} - 24q^{98} - 8q^{99} + O(q^{100}) \)

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
\(5\) −2.22430 −0.994736 −0.497368 0.867540i \(-0.665700\pi\)
−0.497368 + 0.867540i \(0.665700\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.37131 0.518308 0.259154 0.965836i \(-0.416556\pi\)
0.259154 + 0.965836i \(0.416556\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.22430 0.703385
\(11\) 3.97219 1.19766 0.598830 0.800876i \(-0.295632\pi\)
0.598830 + 0.800876i \(0.295632\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350
\(14\) −1.37131 −0.366499
\(15\) −2.22430 −0.574311
\(16\) 1.00000 0.250000
\(17\) 2.05875 0.499321 0.249660 0.968333i \(-0.419681\pi\)
0.249660 + 0.968333i \(0.419681\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.55850 −1.50462 −0.752311 0.658808i \(-0.771061\pi\)
−0.752311 + 0.658808i \(0.771061\pi\)
\(20\) −2.22430 −0.497368
\(21\) 1.37131 0.299245
\(22\) −3.97219 −0.846874
\(23\) −0.577248 −0.120365 −0.0601823 0.998187i \(-0.519168\pi\)
−0.0601823 + 0.998187i \(0.519168\pi\)
\(24\) −1.00000 −0.204124
\(25\) −0.0525006 −0.0105001
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 1.37131 0.259154
\(29\) −3.79856 −0.705375 −0.352687 0.935741i \(-0.614732\pi\)
−0.352687 + 0.935741i \(0.614732\pi\)
\(30\) 2.22430 0.406099
\(31\) 2.84411 0.510818 0.255409 0.966833i \(-0.417790\pi\)
0.255409 + 0.966833i \(0.417790\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.97219 0.691470
\(34\) −2.05875 −0.353073
\(35\) −3.05021 −0.515579
\(36\) 1.00000 0.166667
\(37\) −3.41291 −0.561079 −0.280540 0.959842i \(-0.590513\pi\)
−0.280540 + 0.959842i \(0.590513\pi\)
\(38\) 6.55850 1.06393
\(39\) −1.00000 −0.160128
\(40\) 2.22430 0.351692
\(41\) −6.35321 −0.992205 −0.496103 0.868264i \(-0.665236\pi\)
−0.496103 + 0.868264i \(0.665236\pi\)
\(42\) −1.37131 −0.211598
\(43\) 12.0059 1.83088 0.915438 0.402460i \(-0.131845\pi\)
0.915438 + 0.402460i \(0.131845\pi\)
\(44\) 3.97219 0.598830
\(45\) −2.22430 −0.331579
\(46\) 0.577248 0.0851106
\(47\) 2.35194 0.343066 0.171533 0.985178i \(-0.445128\pi\)
0.171533 + 0.985178i \(0.445128\pi\)
\(48\) 1.00000 0.144338
\(49\) −5.11950 −0.731357
\(50\) 0.0525006 0.00742471
\(51\) 2.05875 0.288283
\(52\) −1.00000 −0.138675
\(53\) −9.83809 −1.35137 −0.675683 0.737192i \(-0.736151\pi\)
−0.675683 + 0.737192i \(0.736151\pi\)
\(54\) −1.00000 −0.136083
\(55\) −8.83534 −1.19136
\(56\) −1.37131 −0.183249
\(57\) −6.55850 −0.868694
\(58\) 3.79856 0.498775
\(59\) 5.32093 0.692727 0.346363 0.938100i \(-0.387416\pi\)
0.346363 + 0.938100i \(0.387416\pi\)
\(60\) −2.22430 −0.287156
\(61\) 4.72419 0.604870 0.302435 0.953170i \(-0.402200\pi\)
0.302435 + 0.953170i \(0.402200\pi\)
\(62\) −2.84411 −0.361203
\(63\) 1.37131 0.172769
\(64\) 1.00000 0.125000
\(65\) 2.22430 0.275890
\(66\) −3.97219 −0.488943
\(67\) 2.48532 0.303630 0.151815 0.988409i \(-0.451488\pi\)
0.151815 + 0.988409i \(0.451488\pi\)
\(68\) 2.05875 0.249660
\(69\) −0.577248 −0.0694925
\(70\) 3.05021 0.364570
\(71\) −9.14181 −1.08493 −0.542466 0.840077i \(-0.682509\pi\)
−0.542466 + 0.840077i \(0.682509\pi\)
\(72\) −1.00000 −0.117851
\(73\) 9.71266 1.13678 0.568390 0.822759i \(-0.307566\pi\)
0.568390 + 0.822759i \(0.307566\pi\)
\(74\) 3.41291 0.396743
\(75\) −0.0525006 −0.00606225
\(76\) −6.55850 −0.752311
\(77\) 5.44712 0.620757
\(78\) 1.00000 0.113228
\(79\) −1.40658 −0.158252 −0.0791261 0.996865i \(-0.525213\pi\)
−0.0791261 + 0.996865i \(0.525213\pi\)
\(80\) −2.22430 −0.248684
\(81\) 1.00000 0.111111
\(82\) 6.35321 0.701595
\(83\) −12.3179 −1.35207 −0.676034 0.736870i \(-0.736303\pi\)
−0.676034 + 0.736870i \(0.736303\pi\)
\(84\) 1.37131 0.149623
\(85\) −4.57928 −0.496693
\(86\) −12.0059 −1.29462
\(87\) −3.79856 −0.407248
\(88\) −3.97219 −0.423437
\(89\) −17.1581 −1.81875 −0.909377 0.415974i \(-0.863441\pi\)
−0.909377 + 0.415974i \(0.863441\pi\)
\(90\) 2.22430 0.234462
\(91\) −1.37131 −0.143753
\(92\) −0.577248 −0.0601823
\(93\) 2.84411 0.294921
\(94\) −2.35194 −0.242584
\(95\) 14.5881 1.49670
\(96\) −1.00000 −0.102062
\(97\) −14.8494 −1.50773 −0.753863 0.657032i \(-0.771812\pi\)
−0.753863 + 0.657032i \(0.771812\pi\)
\(98\) 5.11950 0.517148
\(99\) 3.97219 0.399220
\(100\) −0.0525006 −0.00525006
\(101\) 7.50888 0.747161 0.373581 0.927598i \(-0.378130\pi\)
0.373581 + 0.927598i \(0.378130\pi\)
\(102\) −2.05875 −0.203847
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) −3.05021 −0.297670
\(106\) 9.83809 0.955560
\(107\) −10.7285 −1.03716 −0.518582 0.855028i \(-0.673540\pi\)
−0.518582 + 0.855028i \(0.673540\pi\)
\(108\) 1.00000 0.0962250
\(109\) −14.9243 −1.42949 −0.714745 0.699385i \(-0.753457\pi\)
−0.714745 + 0.699385i \(0.753457\pi\)
\(110\) 8.83534 0.842416
\(111\) −3.41291 −0.323939
\(112\) 1.37131 0.129577
\(113\) −5.51653 −0.518952 −0.259476 0.965750i \(-0.583550\pi\)
−0.259476 + 0.965750i \(0.583550\pi\)
\(114\) 6.55850 0.614260
\(115\) 1.28397 0.119731
\(116\) −3.79856 −0.352687
\(117\) −1.00000 −0.0924500
\(118\) −5.32093 −0.489832
\(119\) 2.82320 0.258802
\(120\) 2.22430 0.203050
\(121\) 4.77831 0.434392
\(122\) −4.72419 −0.427708
\(123\) −6.35321 −0.572850
\(124\) 2.84411 0.255409
\(125\) 11.2383 1.00518
\(126\) −1.37131 −0.122166
\(127\) −0.708893 −0.0629041 −0.0314520 0.999505i \(-0.510013\pi\)
−0.0314520 + 0.999505i \(0.510013\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.0059 1.05706
\(130\) −2.22430 −0.195084
\(131\) 9.30987 0.813407 0.406704 0.913560i \(-0.366678\pi\)
0.406704 + 0.913560i \(0.366678\pi\)
\(132\) 3.97219 0.345735
\(133\) −8.99376 −0.779858
\(134\) −2.48532 −0.214699
\(135\) −2.22430 −0.191437
\(136\) −2.05875 −0.176537
\(137\) −10.1749 −0.869302 −0.434651 0.900599i \(-0.643128\pi\)
−0.434651 + 0.900599i \(0.643128\pi\)
\(138\) 0.577248 0.0491386
\(139\) 4.75647 0.403438 0.201719 0.979443i \(-0.435347\pi\)
0.201719 + 0.979443i \(0.435347\pi\)
\(140\) −3.05021 −0.257790
\(141\) 2.35194 0.198069
\(142\) 9.14181 0.767163
\(143\) −3.97219 −0.332171
\(144\) 1.00000 0.0833333
\(145\) 8.44913 0.701662
\(146\) −9.71266 −0.803826
\(147\) −5.11950 −0.422249
\(148\) −3.41291 −0.280540
\(149\) 12.5814 1.03071 0.515355 0.856977i \(-0.327660\pi\)
0.515355 + 0.856977i \(0.327660\pi\)
\(150\) 0.0525006 0.00428666
\(151\) 16.7636 1.36420 0.682102 0.731257i \(-0.261066\pi\)
0.682102 + 0.731257i \(0.261066\pi\)
\(152\) 6.55850 0.531965
\(153\) 2.05875 0.166440
\(154\) −5.44712 −0.438941
\(155\) −6.32616 −0.508129
\(156\) −1.00000 −0.0800641
\(157\) −0.478623 −0.0381983 −0.0190991 0.999818i \(-0.506080\pi\)
−0.0190991 + 0.999818i \(0.506080\pi\)
\(158\) 1.40658 0.111901
\(159\) −9.83809 −0.780211
\(160\) 2.22430 0.175846
\(161\) −0.791588 −0.0623859
\(162\) −1.00000 −0.0785674
\(163\) −2.15078 −0.168462 −0.0842310 0.996446i \(-0.526843\pi\)
−0.0842310 + 0.996446i \(0.526843\pi\)
\(164\) −6.35321 −0.496103
\(165\) −8.83534 −0.687830
\(166\) 12.3179 0.956057
\(167\) −6.59412 −0.510268 −0.255134 0.966906i \(-0.582120\pi\)
−0.255134 + 0.966906i \(0.582120\pi\)
\(168\) −1.37131 −0.105799
\(169\) 1.00000 0.0769231
\(170\) 4.57928 0.351215
\(171\) −6.55850 −0.501541
\(172\) 12.0059 0.915438
\(173\) −19.9171 −1.51427 −0.757134 0.653260i \(-0.773401\pi\)
−0.757134 + 0.653260i \(0.773401\pi\)
\(174\) 3.79856 0.287968
\(175\) −0.0719948 −0.00544230
\(176\) 3.97219 0.299415
\(177\) 5.32093 0.399946
\(178\) 17.1581 1.28605
\(179\) −5.92624 −0.442948 −0.221474 0.975166i \(-0.571087\pi\)
−0.221474 + 0.975166i \(0.571087\pi\)
\(180\) −2.22430 −0.165789
\(181\) 8.59434 0.638812 0.319406 0.947618i \(-0.396517\pi\)
0.319406 + 0.947618i \(0.396517\pi\)
\(182\) 1.37131 0.101649
\(183\) 4.72419 0.349222
\(184\) 0.577248 0.0425553
\(185\) 7.59133 0.558126
\(186\) −2.84411 −0.208541
\(187\) 8.17776 0.598017
\(188\) 2.35194 0.171533
\(189\) 1.37131 0.0997484
\(190\) −14.5881 −1.05833
\(191\) −7.69976 −0.557135 −0.278567 0.960417i \(-0.589860\pi\)
−0.278567 + 0.960417i \(0.589860\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.7819 1.20799 0.603993 0.796989i \(-0.293575\pi\)
0.603993 + 0.796989i \(0.293575\pi\)
\(194\) 14.8494 1.06612
\(195\) 2.22430 0.159285
\(196\) −5.11950 −0.365679
\(197\) −19.5782 −1.39489 −0.697445 0.716639i \(-0.745680\pi\)
−0.697445 + 0.716639i \(0.745680\pi\)
\(198\) −3.97219 −0.282291
\(199\) 19.3299 1.37026 0.685130 0.728421i \(-0.259745\pi\)
0.685130 + 0.728421i \(0.259745\pi\)
\(200\) 0.0525006 0.00371236
\(201\) 2.48532 0.175301
\(202\) −7.50888 −0.528323
\(203\) −5.20902 −0.365601
\(204\) 2.05875 0.144142
\(205\) 14.1314 0.986982
\(206\) −1.00000 −0.0696733
\(207\) −0.577248 −0.0401215
\(208\) −1.00000 −0.0693375
\(209\) −26.0516 −1.80203
\(210\) 3.05021 0.210484
\(211\) 15.3213 1.05476 0.527380 0.849629i \(-0.323174\pi\)
0.527380 + 0.849629i \(0.323174\pi\)
\(212\) −9.83809 −0.675683
\(213\) −9.14181 −0.626386
\(214\) 10.7285 0.733386
\(215\) −26.7046 −1.82124
\(216\) −1.00000 −0.0680414
\(217\) 3.90017 0.264761
\(218\) 14.9243 1.01080
\(219\) 9.71266 0.656321
\(220\) −8.83534 −0.595678
\(221\) −2.05875 −0.138487
\(222\) 3.41291 0.229060
\(223\) 3.09661 0.207364 0.103682 0.994610i \(-0.466938\pi\)
0.103682 + 0.994610i \(0.466938\pi\)
\(224\) −1.37131 −0.0916247
\(225\) −0.0525006 −0.00350004
\(226\) 5.51653 0.366954
\(227\) 6.51896 0.432679 0.216339 0.976318i \(-0.430588\pi\)
0.216339 + 0.976318i \(0.430588\pi\)
\(228\) −6.55850 −0.434347
\(229\) −2.09643 −0.138536 −0.0692678 0.997598i \(-0.522066\pi\)
−0.0692678 + 0.997598i \(0.522066\pi\)
\(230\) −1.28397 −0.0846626
\(231\) 5.44712 0.358394
\(232\) 3.79856 0.249388
\(233\) 16.0235 1.04973 0.524866 0.851185i \(-0.324116\pi\)
0.524866 + 0.851185i \(0.324116\pi\)
\(234\) 1.00000 0.0653720
\(235\) −5.23142 −0.341260
\(236\) 5.32093 0.346363
\(237\) −1.40658 −0.0913669
\(238\) −2.82320 −0.183001
\(239\) 3.86885 0.250255 0.125128 0.992141i \(-0.460066\pi\)
0.125128 + 0.992141i \(0.460066\pi\)
\(240\) −2.22430 −0.143578
\(241\) 18.4872 1.19086 0.595432 0.803406i \(-0.296981\pi\)
0.595432 + 0.803406i \(0.296981\pi\)
\(242\) −4.77831 −0.307161
\(243\) 1.00000 0.0641500
\(244\) 4.72419 0.302435
\(245\) 11.3873 0.727507
\(246\) 6.35321 0.405066
\(247\) 6.55850 0.417307
\(248\) −2.84411 −0.180601
\(249\) −12.3179 −0.780617
\(250\) −11.2383 −0.710770
\(251\) −13.1469 −0.829822 −0.414911 0.909862i \(-0.636187\pi\)
−0.414911 + 0.909862i \(0.636187\pi\)
\(252\) 1.37131 0.0863846
\(253\) −2.29294 −0.144156
\(254\) 0.708893 0.0444799
\(255\) −4.57928 −0.286766
\(256\) 1.00000 0.0625000
\(257\) −13.3601 −0.833379 −0.416690 0.909049i \(-0.636810\pi\)
−0.416690 + 0.909049i \(0.636810\pi\)
\(258\) −12.0059 −0.747452
\(259\) −4.68017 −0.290812
\(260\) 2.22430 0.137945
\(261\) −3.79856 −0.235125
\(262\) −9.30987 −0.575166
\(263\) 9.94191 0.613045 0.306522 0.951863i \(-0.400835\pi\)
0.306522 + 0.951863i \(0.400835\pi\)
\(264\) −3.97219 −0.244472
\(265\) 21.8828 1.34425
\(266\) 8.99376 0.551443
\(267\) −17.1581 −1.05006
\(268\) 2.48532 0.151815
\(269\) 15.0666 0.918628 0.459314 0.888274i \(-0.348095\pi\)
0.459314 + 0.888274i \(0.348095\pi\)
\(270\) 2.22430 0.135366
\(271\) 9.46422 0.574910 0.287455 0.957794i \(-0.407191\pi\)
0.287455 + 0.957794i \(0.407191\pi\)
\(272\) 2.05875 0.124830
\(273\) −1.37131 −0.0829957
\(274\) 10.1749 0.614689
\(275\) −0.208543 −0.0125756
\(276\) −0.577248 −0.0347463
\(277\) −25.7673 −1.54821 −0.774104 0.633059i \(-0.781799\pi\)
−0.774104 + 0.633059i \(0.781799\pi\)
\(278\) −4.75647 −0.285274
\(279\) 2.84411 0.170273
\(280\) 3.05021 0.182285
\(281\) −0.119722 −0.00714203 −0.00357102 0.999994i \(-0.501137\pi\)
−0.00357102 + 0.999994i \(0.501137\pi\)
\(282\) −2.35194 −0.140056
\(283\) 30.8366 1.83304 0.916522 0.399985i \(-0.130985\pi\)
0.916522 + 0.399985i \(0.130985\pi\)
\(284\) −9.14181 −0.542466
\(285\) 14.5881 0.864122
\(286\) 3.97219 0.234881
\(287\) −8.71224 −0.514268
\(288\) −1.00000 −0.0589256
\(289\) −12.7615 −0.750679
\(290\) −8.44913 −0.496150
\(291\) −14.8494 −0.870486
\(292\) 9.71266 0.568390
\(293\) −6.70517 −0.391720 −0.195860 0.980632i \(-0.562750\pi\)
−0.195860 + 0.980632i \(0.562750\pi\)
\(294\) 5.11950 0.298575
\(295\) −11.8353 −0.689080
\(296\) 3.41291 0.198371
\(297\) 3.97219 0.230490
\(298\) −12.5814 −0.728822
\(299\) 0.577248 0.0333831
\(300\) −0.0525006 −0.00303113
\(301\) 16.4638 0.948957
\(302\) −16.7636 −0.964637
\(303\) 7.50888 0.431374
\(304\) −6.55850 −0.376156
\(305\) −10.5080 −0.601686
\(306\) −2.05875 −0.117691
\(307\) −28.1100 −1.60432 −0.802161 0.597108i \(-0.796316\pi\)
−0.802161 + 0.597108i \(0.796316\pi\)
\(308\) 5.44712 0.310378
\(309\) 1.00000 0.0568880
\(310\) 6.32616 0.359301
\(311\) −34.2660 −1.94305 −0.971525 0.236939i \(-0.923856\pi\)
−0.971525 + 0.236939i \(0.923856\pi\)
\(312\) 1.00000 0.0566139
\(313\) −10.9600 −0.619495 −0.309747 0.950819i \(-0.600244\pi\)
−0.309747 + 0.950819i \(0.600244\pi\)
\(314\) 0.478623 0.0270103
\(315\) −3.05021 −0.171860
\(316\) −1.40658 −0.0791261
\(317\) −22.3459 −1.25507 −0.627536 0.778588i \(-0.715936\pi\)
−0.627536 + 0.778588i \(0.715936\pi\)
\(318\) 9.83809 0.551693
\(319\) −15.0886 −0.844800
\(320\) −2.22430 −0.124342
\(321\) −10.7285 −0.598807
\(322\) 0.791588 0.0441135
\(323\) −13.5023 −0.751290
\(324\) 1.00000 0.0555556
\(325\) 0.0525006 0.00291221
\(326\) 2.15078 0.119121
\(327\) −14.9243 −0.825317
\(328\) 6.35321 0.350797
\(329\) 3.22525 0.177814
\(330\) 8.83534 0.486369
\(331\) −2.52085 −0.138559 −0.0692793 0.997597i \(-0.522070\pi\)
−0.0692793 + 0.997597i \(0.522070\pi\)
\(332\) −12.3179 −0.676034
\(333\) −3.41291 −0.187026
\(334\) 6.59412 0.360814
\(335\) −5.52809 −0.302032
\(336\) 1.37131 0.0748113
\(337\) −14.6487 −0.797963 −0.398981 0.916959i \(-0.630636\pi\)
−0.398981 + 0.916959i \(0.630636\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −5.51653 −0.299617
\(340\) −4.57928 −0.248346
\(341\) 11.2974 0.611787
\(342\) 6.55850 0.354643
\(343\) −16.6196 −0.897376
\(344\) −12.0059 −0.647312
\(345\) 1.28397 0.0691267
\(346\) 19.9171 1.07075
\(347\) 6.95858 0.373556 0.186778 0.982402i \(-0.440195\pi\)
0.186778 + 0.982402i \(0.440195\pi\)
\(348\) −3.79856 −0.203624
\(349\) −35.8925 −1.92128 −0.960640 0.277797i \(-0.910396\pi\)
−0.960640 + 0.277797i \(0.910396\pi\)
\(350\) 0.0719948 0.00384829
\(351\) −1.00000 −0.0533761
\(352\) −3.97219 −0.211719
\(353\) 9.40353 0.500499 0.250250 0.968181i \(-0.419487\pi\)
0.250250 + 0.968181i \(0.419487\pi\)
\(354\) −5.32093 −0.282804
\(355\) 20.3341 1.07922
\(356\) −17.1581 −0.909377
\(357\) 2.82320 0.149419
\(358\) 5.92624 0.313212
\(359\) −1.19957 −0.0633108 −0.0316554 0.999499i \(-0.510078\pi\)
−0.0316554 + 0.999499i \(0.510078\pi\)
\(360\) 2.22430 0.117231
\(361\) 24.0139 1.26389
\(362\) −8.59434 −0.451708
\(363\) 4.77831 0.250796
\(364\) −1.37131 −0.0718763
\(365\) −21.6038 −1.13080
\(366\) −4.72419 −0.246937
\(367\) −27.4623 −1.43352 −0.716761 0.697319i \(-0.754376\pi\)
−0.716761 + 0.697319i \(0.754376\pi\)
\(368\) −0.577248 −0.0300912
\(369\) −6.35321 −0.330735
\(370\) −7.59133 −0.394654
\(371\) −13.4911 −0.700423
\(372\) 2.84411 0.147460
\(373\) −22.2010 −1.14952 −0.574762 0.818321i \(-0.694905\pi\)
−0.574762 + 0.818321i \(0.694905\pi\)
\(374\) −8.17776 −0.422862
\(375\) 11.2383 0.580341
\(376\) −2.35194 −0.121292
\(377\) 3.79856 0.195636
\(378\) −1.37131 −0.0705327
\(379\) 31.0945 1.59722 0.798609 0.601851i \(-0.205570\pi\)
0.798609 + 0.601851i \(0.205570\pi\)
\(380\) 14.5881 0.748351
\(381\) −0.708893 −0.0363177
\(382\) 7.69976 0.393954
\(383\) −10.7140 −0.547457 −0.273729 0.961807i \(-0.588257\pi\)
−0.273729 + 0.961807i \(0.588257\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −12.1160 −0.617489
\(386\) −16.7819 −0.854175
\(387\) 12.0059 0.610292
\(388\) −14.8494 −0.753863
\(389\) −17.8987 −0.907499 −0.453749 0.891129i \(-0.649914\pi\)
−0.453749 + 0.891129i \(0.649914\pi\)
\(390\) −2.22430 −0.112632
\(391\) −1.18841 −0.0601006
\(392\) 5.11950 0.258574
\(393\) 9.30987 0.469621
\(394\) 19.5782 0.986336
\(395\) 3.12864 0.157419
\(396\) 3.97219 0.199610
\(397\) −13.3530 −0.670170 −0.335085 0.942188i \(-0.608765\pi\)
−0.335085 + 0.942188i \(0.608765\pi\)
\(398\) −19.3299 −0.968920
\(399\) −8.99376 −0.450251
\(400\) −0.0525006 −0.00262503
\(401\) −4.34378 −0.216918 −0.108459 0.994101i \(-0.534592\pi\)
−0.108459 + 0.994101i \(0.534592\pi\)
\(402\) −2.48532 −0.123956
\(403\) −2.84411 −0.141675
\(404\) 7.50888 0.373581
\(405\) −2.22430 −0.110526
\(406\) 5.20902 0.258519
\(407\) −13.5567 −0.671982
\(408\) −2.05875 −0.101923
\(409\) −16.6202 −0.821817 −0.410909 0.911677i \(-0.634788\pi\)
−0.410909 + 0.911677i \(0.634788\pi\)
\(410\) −14.1314 −0.697902
\(411\) −10.1749 −0.501891
\(412\) 1.00000 0.0492665
\(413\) 7.29667 0.359046
\(414\) 0.577248 0.0283702
\(415\) 27.3987 1.34495
\(416\) 1.00000 0.0490290
\(417\) 4.75647 0.232925
\(418\) 26.0516 1.27423
\(419\) −7.77507 −0.379837 −0.189919 0.981800i \(-0.560822\pi\)
−0.189919 + 0.981800i \(0.560822\pi\)
\(420\) −3.05021 −0.148835
\(421\) −18.9950 −0.925760 −0.462880 0.886421i \(-0.653184\pi\)
−0.462880 + 0.886421i \(0.653184\pi\)
\(422\) −15.3213 −0.745829
\(423\) 2.35194 0.114355
\(424\) 9.83809 0.477780
\(425\) −0.108086 −0.00524293
\(426\) 9.14181 0.442922
\(427\) 6.47834 0.313509
\(428\) −10.7285 −0.518582
\(429\) −3.97219 −0.191779
\(430\) 26.7046 1.28781
\(431\) −34.1073 −1.64289 −0.821445 0.570288i \(-0.806832\pi\)
−0.821445 + 0.570288i \(0.806832\pi\)
\(432\) 1.00000 0.0481125
\(433\) 24.8426 1.19386 0.596929 0.802294i \(-0.296387\pi\)
0.596929 + 0.802294i \(0.296387\pi\)
\(434\) −3.90017 −0.187214
\(435\) 8.44913 0.405105
\(436\) −14.9243 −0.714745
\(437\) 3.78588 0.181103
\(438\) −9.71266 −0.464089
\(439\) −6.63461 −0.316652 −0.158326 0.987387i \(-0.550610\pi\)
−0.158326 + 0.987387i \(0.550610\pi\)
\(440\) 8.83534 0.421208
\(441\) −5.11950 −0.243786
\(442\) 2.05875 0.0979249
\(443\) 27.9899 1.32984 0.664921 0.746914i \(-0.268465\pi\)
0.664921 + 0.746914i \(0.268465\pi\)
\(444\) −3.41291 −0.161970
\(445\) 38.1647 1.80918
\(446\) −3.09661 −0.146629
\(447\) 12.5814 0.595081
\(448\) 1.37131 0.0647885
\(449\) −32.4440 −1.53113 −0.765564 0.643360i \(-0.777540\pi\)
−0.765564 + 0.643360i \(0.777540\pi\)
\(450\) 0.0525006 0.00247490
\(451\) −25.2362 −1.18833
\(452\) −5.51653 −0.259476
\(453\) 16.7636 0.787623
\(454\) −6.51896 −0.305950
\(455\) 3.05021 0.142996
\(456\) 6.55850 0.307130
\(457\) −5.24245 −0.245232 −0.122616 0.992454i \(-0.539128\pi\)
−0.122616 + 0.992454i \(0.539128\pi\)
\(458\) 2.09643 0.0979595
\(459\) 2.05875 0.0960944
\(460\) 1.28397 0.0598655
\(461\) −29.4265 −1.37053 −0.685265 0.728294i \(-0.740314\pi\)
−0.685265 + 0.728294i \(0.740314\pi\)
\(462\) −5.44712 −0.253423
\(463\) −2.03166 −0.0944193 −0.0472097 0.998885i \(-0.515033\pi\)
−0.0472097 + 0.998885i \(0.515033\pi\)
\(464\) −3.79856 −0.176344
\(465\) −6.32616 −0.293368
\(466\) −16.0235 −0.742272
\(467\) 19.0090 0.879630 0.439815 0.898089i \(-0.355044\pi\)
0.439815 + 0.898089i \(0.355044\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 3.40815 0.157374
\(470\) 5.23142 0.241308
\(471\) −0.478623 −0.0220538
\(472\) −5.32093 −0.244916
\(473\) 47.6895 2.19277
\(474\) 1.40658 0.0646062
\(475\) 0.344325 0.0157987
\(476\) 2.82320 0.129401
\(477\) −9.83809 −0.450455
\(478\) −3.86885 −0.176957
\(479\) 12.3832 0.565804 0.282902 0.959149i \(-0.408703\pi\)
0.282902 + 0.959149i \(0.408703\pi\)
\(480\) 2.22430 0.101525
\(481\) 3.41291 0.155615
\(482\) −18.4872 −0.842068
\(483\) −0.791588 −0.0360185
\(484\) 4.77831 0.217196
\(485\) 33.0294 1.49979
\(486\) −1.00000 −0.0453609
\(487\) 9.91311 0.449206 0.224603 0.974450i \(-0.427892\pi\)
0.224603 + 0.974450i \(0.427892\pi\)
\(488\) −4.72419 −0.213854
\(489\) −2.15078 −0.0972616
\(490\) −11.3873 −0.514425
\(491\) −11.9387 −0.538785 −0.269393 0.963030i \(-0.586823\pi\)
−0.269393 + 0.963030i \(0.586823\pi\)
\(492\) −6.35321 −0.286425
\(493\) −7.82030 −0.352208
\(494\) −6.55850 −0.295081
\(495\) −8.83534 −0.397119
\(496\) 2.84411 0.127704
\(497\) −12.5363 −0.562329
\(498\) 12.3179 0.551980
\(499\) 3.11589 0.139486 0.0697432 0.997565i \(-0.477782\pi\)
0.0697432 + 0.997565i \(0.477782\pi\)
\(500\) 11.2383 0.502590
\(501\) −6.59412 −0.294603
\(502\) 13.1469 0.586773
\(503\) −4.28793 −0.191190 −0.0955948 0.995420i \(-0.530475\pi\)
−0.0955948 + 0.995420i \(0.530475\pi\)
\(504\) −1.37131 −0.0610832
\(505\) −16.7020 −0.743228
\(506\) 2.29294 0.101934
\(507\) 1.00000 0.0444116
\(508\) −0.708893 −0.0314520
\(509\) −16.1716 −0.716792 −0.358396 0.933570i \(-0.616676\pi\)
−0.358396 + 0.933570i \(0.616676\pi\)
\(510\) 4.57928 0.202774
\(511\) 13.3191 0.589202
\(512\) −1.00000 −0.0441942
\(513\) −6.55850 −0.289565
\(514\) 13.3601 0.589288
\(515\) −2.22430 −0.0980143
\(516\) 12.0059 0.528528
\(517\) 9.34237 0.410877
\(518\) 4.68017 0.205635
\(519\) −19.9171 −0.874263
\(520\) −2.22430 −0.0975419
\(521\) −17.2663 −0.756452 −0.378226 0.925713i \(-0.623466\pi\)
−0.378226 + 0.925713i \(0.623466\pi\)
\(522\) 3.79856 0.166258
\(523\) 6.78924 0.296873 0.148436 0.988922i \(-0.452576\pi\)
0.148436 + 0.988922i \(0.452576\pi\)
\(524\) 9.30987 0.406704
\(525\) −0.0719948 −0.00314211
\(526\) −9.94191 −0.433488
\(527\) 5.85533 0.255062
\(528\) 3.97219 0.172867
\(529\) −22.6668 −0.985512
\(530\) −21.8828 −0.950530
\(531\) 5.32093 0.230909
\(532\) −8.99376 −0.389929
\(533\) 6.35321 0.275188
\(534\) 17.1581 0.742503
\(535\) 23.8634 1.03171
\(536\) −2.48532 −0.107349
\(537\) −5.92624 −0.255736
\(538\) −15.0666 −0.649568
\(539\) −20.3356 −0.875918
\(540\) −2.22430 −0.0957185
\(541\) −36.7453 −1.57980 −0.789901 0.613234i \(-0.789868\pi\)
−0.789901 + 0.613234i \(0.789868\pi\)
\(542\) −9.46422 −0.406523
\(543\) 8.59434 0.368818
\(544\) −2.05875 −0.0882683
\(545\) 33.1961 1.42197
\(546\) 1.37131 0.0586868
\(547\) 11.4650 0.490209 0.245105 0.969497i \(-0.421178\pi\)
0.245105 + 0.969497i \(0.421178\pi\)
\(548\) −10.1749 −0.434651
\(549\) 4.72419 0.201623
\(550\) 0.208543 0.00889229
\(551\) 24.9128 1.06132
\(552\) 0.577248 0.0245693
\(553\) −1.92886 −0.0820233
\(554\) 25.7673 1.09475
\(555\) 7.59133 0.322234
\(556\) 4.75647 0.201719
\(557\) −19.2122 −0.814046 −0.407023 0.913418i \(-0.633433\pi\)
−0.407023 + 0.913418i \(0.633433\pi\)
\(558\) −2.84411 −0.120401
\(559\) −12.0059 −0.507793
\(560\) −3.05021 −0.128895
\(561\) 8.17776 0.345265
\(562\) 0.119722 0.00505018
\(563\) −5.72057 −0.241093 −0.120547 0.992708i \(-0.538465\pi\)
−0.120547 + 0.992708i \(0.538465\pi\)
\(564\) 2.35194 0.0990347
\(565\) 12.2704 0.516220
\(566\) −30.8366 −1.29616
\(567\) 1.37131 0.0575897
\(568\) 9.14181 0.383582
\(569\) 23.7134 0.994115 0.497058 0.867717i \(-0.334414\pi\)
0.497058 + 0.867717i \(0.334414\pi\)
\(570\) −14.5881 −0.611026
\(571\) 28.7940 1.20499 0.602495 0.798122i \(-0.294173\pi\)
0.602495 + 0.798122i \(0.294173\pi\)
\(572\) −3.97219 −0.166086
\(573\) −7.69976 −0.321662
\(574\) 8.71224 0.363642
\(575\) 0.0303059 0.00126384
\(576\) 1.00000 0.0416667
\(577\) −5.33926 −0.222276 −0.111138 0.993805i \(-0.535450\pi\)
−0.111138 + 0.993805i \(0.535450\pi\)
\(578\) 12.7615 0.530810
\(579\) 16.7819 0.697431
\(580\) 8.44913 0.350831
\(581\) −16.8917 −0.700788
\(582\) 14.8494 0.615527
\(583\) −39.0788 −1.61848
\(584\) −9.71266 −0.401913
\(585\) 2.22430 0.0919634
\(586\) 6.70517 0.276988
\(587\) −31.3094 −1.29228 −0.646139 0.763220i \(-0.723617\pi\)
−0.646139 + 0.763220i \(0.723617\pi\)
\(588\) −5.11950 −0.211125
\(589\) −18.6531 −0.768588
\(590\) 11.8353 0.487253
\(591\) −19.5782 −0.805340
\(592\) −3.41291 −0.140270
\(593\) −25.0646 −1.02928 −0.514640 0.857406i \(-0.672074\pi\)
−0.514640 + 0.857406i \(0.672074\pi\)
\(594\) −3.97219 −0.162981
\(595\) −6.27963 −0.257440
\(596\) 12.5814 0.515355
\(597\) 19.3299 0.791120
\(598\) −0.577248 −0.0236054
\(599\) −1.11554 −0.0455796 −0.0227898 0.999740i \(-0.507255\pi\)
−0.0227898 + 0.999740i \(0.507255\pi\)
\(600\) 0.0525006 0.00214333
\(601\) 0.614374 0.0250608 0.0125304 0.999921i \(-0.496011\pi\)
0.0125304 + 0.999921i \(0.496011\pi\)
\(602\) −16.4638 −0.671014
\(603\) 2.48532 0.101210
\(604\) 16.7636 0.682102
\(605\) −10.6284 −0.432105
\(606\) −7.50888 −0.305027
\(607\) −22.2310 −0.902329 −0.451165 0.892441i \(-0.648991\pi\)
−0.451165 + 0.892441i \(0.648991\pi\)
\(608\) 6.55850 0.265982
\(609\) −5.20902 −0.211080
\(610\) 10.5080 0.425456
\(611\) −2.35194 −0.0951495
\(612\) 2.05875 0.0832201
\(613\) −13.4733 −0.544180 −0.272090 0.962272i \(-0.587715\pi\)
−0.272090 + 0.962272i \(0.587715\pi\)
\(614\) 28.1100 1.13443
\(615\) 14.1314 0.569834
\(616\) −5.44712 −0.219471
\(617\) 10.0914 0.406264 0.203132 0.979151i \(-0.434888\pi\)
0.203132 + 0.979151i \(0.434888\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 35.9985 1.44690 0.723451 0.690376i \(-0.242555\pi\)
0.723451 + 0.690376i \(0.242555\pi\)
\(620\) −6.32616 −0.254065
\(621\) −0.577248 −0.0231642
\(622\) 34.2660 1.37394
\(623\) −23.5291 −0.942674
\(624\) −1.00000 −0.0400320
\(625\) −24.7347 −0.989390
\(626\) 10.9600 0.438049
\(627\) −26.0516 −1.04040
\(628\) −0.478623 −0.0190991
\(629\) −7.02634 −0.280158
\(630\) 3.05021 0.121523
\(631\) −20.5110 −0.816530 −0.408265 0.912863i \(-0.633866\pi\)
−0.408265 + 0.912863i \(0.633866\pi\)
\(632\) 1.40658 0.0559506
\(633\) 15.3213 0.608966
\(634\) 22.3459 0.887470
\(635\) 1.57679 0.0625729
\(636\) −9.83809 −0.390106
\(637\) 5.11950 0.202842
\(638\) 15.0886 0.597364
\(639\) −9.14181 −0.361644
\(640\) 2.22430 0.0879231
\(641\) −44.1698 −1.74460 −0.872302 0.488968i \(-0.837374\pi\)
−0.872302 + 0.488968i \(0.837374\pi\)
\(642\) 10.7285 0.423421
\(643\) −19.1123 −0.753715 −0.376858 0.926271i \(-0.622995\pi\)
−0.376858 + 0.926271i \(0.622995\pi\)
\(644\) −0.791588 −0.0311930
\(645\) −26.7046 −1.05149
\(646\) 13.5023 0.531242
\(647\) 46.3714 1.82305 0.911524 0.411248i \(-0.134907\pi\)
0.911524 + 0.411248i \(0.134907\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 21.1358 0.829652
\(650\) −0.0525006 −0.00205924
\(651\) 3.90017 0.152860
\(652\) −2.15078 −0.0842310
\(653\) 13.3132 0.520987 0.260494 0.965476i \(-0.416115\pi\)
0.260494 + 0.965476i \(0.416115\pi\)
\(654\) 14.9243 0.583587
\(655\) −20.7079 −0.809126
\(656\) −6.35321 −0.248051
\(657\) 9.71266 0.378927
\(658\) −3.22525 −0.125733
\(659\) 35.4348 1.38034 0.690172 0.723645i \(-0.257535\pi\)
0.690172 + 0.723645i \(0.257535\pi\)
\(660\) −8.83534 −0.343915
\(661\) −20.1520 −0.783822 −0.391911 0.920003i \(-0.628186\pi\)
−0.391911 + 0.920003i \(0.628186\pi\)
\(662\) 2.52085 0.0979757
\(663\) −2.05875 −0.0799553
\(664\) 12.3179 0.478028
\(665\) 20.0048 0.775753
\(666\) 3.41291 0.132248
\(667\) 2.19271 0.0849022
\(668\) −6.59412 −0.255134
\(669\) 3.09661 0.119722
\(670\) 5.52809 0.213569
\(671\) 18.7654 0.724430
\(672\) −1.37131 −0.0528996
\(673\) −11.0538 −0.426092 −0.213046 0.977042i \(-0.568338\pi\)
−0.213046 + 0.977042i \(0.568338\pi\)
\(674\) 14.6487 0.564245
\(675\) −0.0525006 −0.00202075
\(676\) 1.00000 0.0384615
\(677\) 42.5938 1.63701 0.818506 0.574498i \(-0.194803\pi\)
0.818506 + 0.574498i \(0.194803\pi\)
\(678\) 5.51653 0.211861
\(679\) −20.3632 −0.781466
\(680\) 4.57928 0.175607
\(681\) 6.51896 0.249807
\(682\) −11.2974 −0.432599
\(683\) 44.8926 1.71777 0.858884 0.512171i \(-0.171159\pi\)
0.858884 + 0.512171i \(0.171159\pi\)
\(684\) −6.55850 −0.250770
\(685\) 22.6320 0.864726
\(686\) 16.6196 0.634540
\(687\) −2.09643 −0.0799836
\(688\) 12.0059 0.457719
\(689\) 9.83809 0.374801
\(690\) −1.28397 −0.0488800
\(691\) 41.5886 1.58211 0.791053 0.611748i \(-0.209533\pi\)
0.791053 + 0.611748i \(0.209533\pi\)
\(692\) −19.9171 −0.757134
\(693\) 5.44712 0.206919
\(694\) −6.95858 −0.264144
\(695\) −10.5798 −0.401315
\(696\) 3.79856 0.143984
\(697\) −13.0797 −0.495429
\(698\) 35.8925 1.35855
\(699\) 16.0235 0.606063
\(700\) −0.0719948 −0.00272115
\(701\) 39.7054 1.49965 0.749827 0.661634i \(-0.230137\pi\)
0.749827 + 0.661634i \(0.230137\pi\)
\(702\) 1.00000 0.0377426
\(703\) 22.3836 0.844212
\(704\) 3.97219 0.149708
\(705\) −5.23142 −0.197027
\(706\) −9.40353 −0.353906
\(707\) 10.2970 0.387260
\(708\) 5.32093 0.199973
\(709\) −45.0868 −1.69327 −0.846635 0.532174i \(-0.821375\pi\)
−0.846635 + 0.532174i \(0.821375\pi\)
\(710\) −20.3341 −0.763125
\(711\) −1.40658 −0.0527507
\(712\) 17.1581 0.643026
\(713\) −1.64176 −0.0614844
\(714\) −2.82320 −0.105655
\(715\) 8.83534 0.330423
\(716\) −5.92624 −0.221474
\(717\) 3.86885 0.144485
\(718\) 1.19957 0.0447675
\(719\) 36.2868 1.35327 0.676634 0.736319i \(-0.263438\pi\)
0.676634 + 0.736319i \(0.263438\pi\)
\(720\) −2.22430 −0.0828947
\(721\) 1.37131 0.0510704
\(722\) −24.0139 −0.893705
\(723\) 18.4872 0.687546
\(724\) 8.59434 0.319406
\(725\) 0.199427 0.00740653
\(726\) −4.77831 −0.177340
\(727\) −2.53230 −0.0939179 −0.0469590 0.998897i \(-0.514953\pi\)
−0.0469590 + 0.998897i \(0.514953\pi\)
\(728\) 1.37131 0.0508243
\(729\) 1.00000 0.0370370
\(730\) 21.6038 0.799594
\(731\) 24.7171 0.914194
\(732\) 4.72419 0.174611
\(733\) 50.6304 1.87007 0.935037 0.354549i \(-0.115366\pi\)
0.935037 + 0.354549i \(0.115366\pi\)
\(734\) 27.4623 1.01365
\(735\) 11.3873 0.420027
\(736\) 0.577248 0.0212777
\(737\) 9.87217 0.363646
\(738\) 6.35321 0.233865
\(739\) 9.78320 0.359881 0.179940 0.983678i \(-0.442410\pi\)
0.179940 + 0.983678i \(0.442410\pi\)
\(740\) 7.59133 0.279063
\(741\) 6.55850 0.240932
\(742\) 13.4911 0.495274
\(743\) −31.9241 −1.17118 −0.585590 0.810607i \(-0.699137\pi\)
−0.585590 + 0.810607i \(0.699137\pi\)
\(744\) −2.84411 −0.104270
\(745\) −27.9848 −1.02528
\(746\) 22.2010 0.812836
\(747\) −12.3179 −0.450690
\(748\) 8.17776 0.299009
\(749\) −14.7122 −0.537570
\(750\) −11.2383 −0.410363
\(751\) −26.1622 −0.954671 −0.477336 0.878721i \(-0.658397\pi\)
−0.477336 + 0.878721i \(0.658397\pi\)
\(752\) 2.35194 0.0857666
\(753\) −13.1469 −0.479098
\(754\) −3.79856 −0.138335
\(755\) −37.2873 −1.35702
\(756\) 1.37131 0.0498742
\(757\) 9.89410 0.359607 0.179804 0.983703i \(-0.442454\pi\)
0.179804 + 0.983703i \(0.442454\pi\)
\(758\) −31.0945 −1.12940
\(759\) −2.29294 −0.0832285
\(760\) −14.5881 −0.529164
\(761\) −49.2646 −1.78584 −0.892919 0.450217i \(-0.851347\pi\)
−0.892919 + 0.450217i \(0.851347\pi\)
\(762\) 0.708893 0.0256805
\(763\) −20.4659 −0.740916
\(764\) −7.69976 −0.278567
\(765\) −4.57928 −0.165564
\(766\) 10.7140 0.387111
\(767\) −5.32093 −0.192128
\(768\) 1.00000 0.0360844
\(769\) −27.4727 −0.990690 −0.495345 0.868696i \(-0.664958\pi\)
−0.495345 + 0.868696i \(0.664958\pi\)
\(770\) 12.1160 0.436631
\(771\) −13.3601 −0.481152
\(772\) 16.7819 0.603993
\(773\) 2.07706 0.0747067 0.0373533 0.999302i \(-0.488107\pi\)
0.0373533 + 0.999302i \(0.488107\pi\)
\(774\) −12.0059 −0.431541
\(775\) −0.149318 −0.00536365
\(776\) 14.8494 0.533062
\(777\) −4.68017 −0.167900
\(778\) 17.8987 0.641699
\(779\) 41.6675 1.49289
\(780\) 2.22430 0.0796426
\(781\) −36.3130 −1.29938
\(782\) 1.18841 0.0424975
\(783\) −3.79856 −0.135749
\(784\) −5.11950 −0.182839
\(785\) 1.06460 0.0379972
\(786\) −9.30987 −0.332072
\(787\) 2.37041 0.0844960 0.0422480 0.999107i \(-0.486548\pi\)
0.0422480 + 0.999107i \(0.486548\pi\)
\(788\) −19.5782 −0.697445
\(789\) 9.94191 0.353942
\(790\) −3.12864 −0.111312
\(791\) −7.56490 −0.268977
\(792\) −3.97219 −0.141146
\(793\) −4.72419 −0.167761
\(794\) 13.3530 0.473882
\(795\) 21.8828 0.776104
\(796\) 19.3299 0.685130
\(797\) −25.5196 −0.903952 −0.451976 0.892030i \(-0.649281\pi\)
−0.451976 + 0.892030i \(0.649281\pi\)
\(798\) 8.99376 0.318376
\(799\) 4.84207 0.171300
\(800\) 0.0525006 0.00185618
\(801\) −17.1581 −0.606251
\(802\) 4.34378 0.153384
\(803\) 38.5806 1.36148
\(804\) 2.48532 0.0876505
\(805\) 1.76073 0.0620575
\(806\) 2.84411 0.100180
\(807\) 15.0666 0.530370
\(808\) −7.50888 −0.264161
\(809\) 1.08081 0.0379991 0.0189996 0.999819i \(-0.493952\pi\)
0.0189996 + 0.999819i \(0.493952\pi\)
\(810\) 2.22430 0.0781538
\(811\) −18.9563 −0.665645 −0.332823 0.942989i \(-0.608001\pi\)
−0.332823 + 0.942989i \(0.608001\pi\)
\(812\) −5.20902 −0.182801
\(813\) 9.46422 0.331925
\(814\) 13.5567 0.475163
\(815\) 4.78397 0.167575
\(816\) 2.05875 0.0720708
\(817\) −78.7404 −2.75478
\(818\) 16.6202 0.581113
\(819\) −1.37131 −0.0479176
\(820\) 14.1314 0.493491
\(821\) −11.8047 −0.411988 −0.205994 0.978553i \(-0.566043\pi\)
−0.205994 + 0.978553i \(0.566043\pi\)
\(822\) 10.1749 0.354891
\(823\) 12.5546 0.437625 0.218812 0.975767i \(-0.429782\pi\)
0.218812 + 0.975767i \(0.429782\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −0.208543 −0.00726052
\(826\) −7.29667 −0.253884
\(827\) 30.0107 1.04357 0.521787 0.853076i \(-0.325266\pi\)
0.521787 + 0.853076i \(0.325266\pi\)
\(828\) −0.577248 −0.0200608
\(829\) −8.20653 −0.285025 −0.142512 0.989793i \(-0.545518\pi\)
−0.142512 + 0.989793i \(0.545518\pi\)
\(830\) −27.3987 −0.951024
\(831\) −25.7673 −0.893858
\(832\) −1.00000 −0.0346688
\(833\) −10.5398 −0.365182
\(834\) −4.75647 −0.164703
\(835\) 14.6673 0.507582
\(836\) −26.0516 −0.901014
\(837\) 2.84411 0.0983070
\(838\) 7.77507 0.268585
\(839\) −52.1181 −1.79932 −0.899658 0.436596i \(-0.856184\pi\)
−0.899658 + 0.436596i \(0.856184\pi\)
\(840\) 3.05021 0.105242
\(841\) −14.5709 −0.502446
\(842\) 18.9950 0.654611
\(843\) −0.119722 −0.00412345
\(844\) 15.3213 0.527380
\(845\) −2.22430 −0.0765182
\(846\) −2.35194 −0.0808615
\(847\) 6.55256 0.225149
\(848\) −9.83809 −0.337841
\(849\) 30.8366 1.05831
\(850\) 0.108086 0.00370731
\(851\) 1.97010 0.0675341
\(852\) −9.14181 −0.313193
\(853\) −6.07651 −0.208056 −0.104028 0.994574i \(-0.533173\pi\)
−0.104028 + 0.994574i \(0.533173\pi\)
\(854\) −6.47834 −0.221684
\(855\) 14.5881 0.498901
\(856\) 10.7285 0.366693
\(857\) −25.3195 −0.864896 −0.432448 0.901659i \(-0.642350\pi\)
−0.432448 + 0.901659i \(0.642350\pi\)
\(858\) 3.97219 0.135608
\(859\) −0.769055 −0.0262398 −0.0131199 0.999914i \(-0.504176\pi\)
−0.0131199 + 0.999914i \(0.504176\pi\)
\(860\) −26.7046 −0.910619
\(861\) −8.71224 −0.296912
\(862\) 34.1073 1.16170
\(863\) −0.772340 −0.0262908 −0.0131454 0.999914i \(-0.504184\pi\)
−0.0131454 + 0.999914i \(0.504184\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 44.3015 1.50630
\(866\) −24.8426 −0.844185
\(867\) −12.7615 −0.433405
\(868\) 3.90017 0.132380
\(869\) −5.58719 −0.189532
\(870\) −8.44913 −0.286452
\(871\) −2.48532 −0.0842118
\(872\) 14.9243 0.505401
\(873\) −14.8494 −0.502575
\(874\) −3.78588 −0.128059
\(875\) 15.4112 0.520993
\(876\) 9.71266 0.328160
\(877\) −5.65111 −0.190824 −0.0954122 0.995438i \(-0.530417\pi\)
−0.0954122 + 0.995438i \(0.530417\pi\)
\(878\) 6.63461 0.223907
\(879\) −6.70517 −0.226160
\(880\) −8.83534 −0.297839
\(881\) 2.98848 0.100684 0.0503422 0.998732i \(-0.483969\pi\)
0.0503422 + 0.998732i \(0.483969\pi\)
\(882\) 5.11950 0.172383
\(883\) 24.2160 0.814934 0.407467 0.913220i \(-0.366412\pi\)
0.407467 + 0.913220i \(0.366412\pi\)
\(884\) −2.05875 −0.0692434
\(885\) −11.8353 −0.397841
\(886\) −27.9899 −0.940340
\(887\) −11.0954 −0.372548 −0.186274 0.982498i \(-0.559641\pi\)
−0.186274 + 0.982498i \(0.559641\pi\)
\(888\) 3.41291 0.114530
\(889\) −0.972114 −0.0326037
\(890\) −38.1647 −1.27928
\(891\) 3.97219 0.133073
\(892\) 3.09661 0.103682
\(893\) −15.4252 −0.516185
\(894\) −12.5814 −0.420786
\(895\) 13.1817 0.440617
\(896\) −1.37131 −0.0458124
\(897\) 0.577248 0.0192738
\(898\) 32.4440 1.08267
\(899\) −10.8035 −0.360318
\(900\) −0.0525006 −0.00175002
\(901\) −20.2542 −0.674765
\(902\) 25.2362 0.840273
\(903\) 16.4638 0.547880
\(904\) 5.51653 0.183477
\(905\) −19.1164 −0.635449
\(906\) −16.7636 −0.556934
\(907\) 6.27707 0.208427 0.104213 0.994555i \(-0.466768\pi\)
0.104213 + 0.994555i \(0.466768\pi\)
\(908\) 6.51896 0.216339
\(909\) 7.50888 0.249054
\(910\) −3.05021 −0.101113
\(911\) 17.7132 0.586864 0.293432 0.955980i \(-0.405203\pi\)
0.293432 + 0.955980i \(0.405203\pi\)
\(912\) −6.55850 −0.217174
\(913\) −48.9292 −1.61932
\(914\) 5.24245 0.173405
\(915\) −10.5080 −0.347384
\(916\) −2.09643 −0.0692678
\(917\) 12.7668 0.421595
\(918\) −2.05875 −0.0679490
\(919\) −39.4541 −1.30147 −0.650735 0.759305i \(-0.725539\pi\)
−0.650735 + 0.759305i \(0.725539\pi\)
\(920\) −1.28397 −0.0423313
\(921\) −28.1100 −0.926255
\(922\) 29.4265 0.969111
\(923\) 9.14181 0.300906
\(924\) 5.44712 0.179197
\(925\) 0.179180 0.00589140
\(926\) 2.03166 0.0667646
\(927\) 1.00000 0.0328443
\(928\) 3.79856 0.124694
\(929\) 41.4822 1.36099 0.680493 0.732755i \(-0.261766\pi\)
0.680493 + 0.732755i \(0.261766\pi\)
\(930\) 6.32616 0.207443
\(931\) 33.5762 1.10042
\(932\) 16.0235 0.524866
\(933\) −34.2660 −1.12182
\(934\) −19.0090 −0.621992
\(935\) −18.1898 −0.594869
\(936\) 1.00000 0.0326860
\(937\) 17.0382 0.556614 0.278307 0.960492i \(-0.410227\pi\)
0.278307 + 0.960492i \(0.410227\pi\)
\(938\) −3.40815 −0.111280
\(939\) −10.9600 −0.357665
\(940\) −5.23142 −0.170630
\(941\) −38.5648 −1.25718 −0.628589 0.777738i \(-0.716367\pi\)
−0.628589 + 0.777738i \(0.716367\pi\)
\(942\) 0.478623 0.0155944
\(943\) 3.66738 0.119426
\(944\) 5.32093 0.173182
\(945\) −3.05021 −0.0992233
\(946\) −47.6895 −1.55052
\(947\) −49.7548 −1.61681 −0.808406 0.588625i \(-0.799669\pi\)
−0.808406 + 0.588625i \(0.799669\pi\)
\(948\) −1.40658 −0.0456835
\(949\) −9.71266 −0.315286
\(950\) −0.344325 −0.0111714
\(951\) −22.3459 −0.724616
\(952\) −2.82320 −0.0915003
\(953\) 23.9960 0.777307 0.388654 0.921384i \(-0.372940\pi\)
0.388654 + 0.921384i \(0.372940\pi\)
\(954\) 9.83809 0.318520
\(955\) 17.1265 0.554202
\(956\) 3.86885 0.125128
\(957\) −15.0886 −0.487745
\(958\) −12.3832 −0.400084
\(959\) −13.9530 −0.450566
\(960\) −2.22430 −0.0717889
\(961\) −22.9110 −0.739065
\(962\) −3.41291 −0.110037
\(963\) −10.7285 −0.345722
\(964\) 18.4872 0.595432
\(965\) −37.3279 −1.20163
\(966\) 0.791588 0.0254689
\(967\) 43.5903 1.40177 0.700885 0.713274i \(-0.252789\pi\)
0.700885 + 0.713274i \(0.252789\pi\)
\(968\) −4.77831 −0.153581
\(969\) −13.5023 −0.433757
\(970\) −33.0294 −1.06051
\(971\) 41.5288 1.33272 0.666361 0.745629i \(-0.267851\pi\)
0.666361 + 0.745629i \(0.267851\pi\)
\(972\) 1.00000 0.0320750
\(973\) 6.52261 0.209105
\(974\) −9.91311 −0.317636
\(975\) 0.0525006 0.00168137
\(976\) 4.72419 0.151218
\(977\) 29.4383 0.941814 0.470907 0.882183i \(-0.343927\pi\)
0.470907 + 0.882183i \(0.343927\pi\)
\(978\) 2.15078 0.0687743
\(979\) −68.1552 −2.17825
\(980\) 11.3873 0.363754
\(981\) −14.9243 −0.476497
\(982\) 11.9387 0.380979
\(983\) 35.0015 1.11638 0.558188 0.829715i \(-0.311497\pi\)
0.558188 + 0.829715i \(0.311497\pi\)
\(984\) 6.35321 0.202533
\(985\) 43.5477 1.38755
\(986\) 7.82030 0.249049
\(987\) 3.22525 0.102661
\(988\) 6.55850 0.208654
\(989\) −6.93036 −0.220373
\(990\) 8.83534 0.280805
\(991\) 17.7909 0.565146 0.282573 0.959246i \(-0.408812\pi\)
0.282573 + 0.959246i \(0.408812\pi\)
\(992\) −2.84411 −0.0903007
\(993\) −2.52085 −0.0799968
\(994\) 12.5363 0.397627
\(995\) −42.9954 −1.36305
\(996\) −12.3179 −0.390309
\(997\) 16.4268 0.520241 0.260121 0.965576i \(-0.416238\pi\)
0.260121 + 0.965576i \(0.416238\pi\)
\(998\) −3.11589 −0.0986318
\(999\) −3.41291 −0.107980
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.bb.1.5 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.bb.1.5 14 1.1 even 1 trivial