Properties

Label 8470.2.a.cj.1.1
Level $8470$
Weight $2$
Character 8470.1
Self dual yes
Analytic conductor $67.633$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8470.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.6332905120\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.733.1
Defining polynomial: \(x^{3} - x^{2} - 7 x + 8\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.51820\) of defining polynomial
Character \(\chi\) \(=\) 8470.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.85952 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.85952 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.17687 q^{9} -1.00000 q^{10} -2.85952 q^{12} +2.17687 q^{13} -1.00000 q^{14} -2.85952 q^{15} +1.00000 q^{16} +3.85952 q^{17} -5.17687 q^{18} +1.68265 q^{19} +1.00000 q^{20} -2.85952 q^{21} +6.85952 q^{23} +2.85952 q^{24} +1.00000 q^{25} -2.17687 q^{26} -6.22482 q^{27} +1.00000 q^{28} -2.00000 q^{29} +2.85952 q^{30} +0.682649 q^{31} -1.00000 q^{32} -3.85952 q^{34} +1.00000 q^{35} +5.17687 q^{36} -3.71905 q^{37} -1.68265 q^{38} -6.22482 q^{39} -1.00000 q^{40} +9.03640 q^{41} +2.85952 q^{42} +5.85952 q^{43} +5.17687 q^{45} -6.85952 q^{46} +4.68265 q^{47} -2.85952 q^{48} +1.00000 q^{49} -1.00000 q^{50} -11.0364 q^{51} +2.17687 q^{52} +13.5786 q^{53} +6.22482 q^{54} -1.00000 q^{56} -4.81158 q^{57} +2.00000 q^{58} -7.75544 q^{59} -2.85952 q^{60} +8.89592 q^{61} -0.682649 q^{62} +5.17687 q^{63} +1.00000 q^{64} +2.17687 q^{65} +9.85952 q^{67} +3.85952 q^{68} -19.6150 q^{69} -1.00000 q^{70} -0.542173 q^{71} -5.17687 q^{72} -5.85952 q^{73} +3.71905 q^{74} -2.85952 q^{75} +1.68265 q^{76} +6.22482 q^{78} +0.317351 q^{79} +1.00000 q^{80} +2.26940 q^{81} -9.03640 q^{82} -4.85952 q^{83} -2.85952 q^{84} +3.85952 q^{85} -5.85952 q^{86} +5.71905 q^{87} -0.682649 q^{89} -5.17687 q^{90} +2.17687 q^{91} +6.85952 q^{92} -1.95205 q^{93} -4.68265 q^{94} +1.68265 q^{95} +2.85952 q^{96} +16.6150 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9} + O(q^{10}) \) \( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 13 q^{9} - 3 q^{10} + 2 q^{12} + 4 q^{13} - 3 q^{14} + 2 q^{15} + 3 q^{16} + q^{17} - 13 q^{18} - 3 q^{19} + 3 q^{20} + 2 q^{21} + 10 q^{23} - 2 q^{24} + 3 q^{25} - 4 q^{26} + 8 q^{27} + 3 q^{28} - 6 q^{29} - 2 q^{30} - 6 q^{31} - 3 q^{32} - q^{34} + 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 8 q^{39} - 3 q^{40} + 14 q^{41} - 2 q^{42} + 7 q^{43} + 13 q^{45} - 10 q^{46} + 6 q^{47} + 2 q^{48} + 3 q^{49} - 3 q^{50} - 20 q^{51} + 4 q^{52} + 9 q^{53} - 8 q^{54} - 3 q^{56} - 28 q^{57} + 6 q^{58} + 11 q^{59} + 2 q^{60} + 3 q^{61} + 6 q^{62} + 13 q^{63} + 3 q^{64} + 4 q^{65} + 19 q^{67} + q^{68} - 14 q^{69} - 3 q^{70} + 17 q^{71} - 13 q^{72} - 7 q^{73} - 10 q^{74} + 2 q^{75} - 3 q^{76} - 8 q^{78} + 9 q^{79} + 3 q^{80} + 39 q^{81} - 14 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 7 q^{86} - 4 q^{87} + 6 q^{89} - 13 q^{90} + 4 q^{91} + 10 q^{92} - 30 q^{93} - 6 q^{94} - 3 q^{95} - 2 q^{96} + 5 q^{97} - 3 q^{98} + O(q^{100}) \)

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
\(3\) −2.85952 −1.65095 −0.825473 0.564441i \(-0.809092\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.85952 1.16740
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 5.17687 1.72562
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −2.85952 −0.825473
\(13\) 2.17687 0.603756 0.301878 0.953347i \(-0.402386\pi\)
0.301878 + 0.953347i \(0.402386\pi\)
\(14\) −1.00000 −0.267261
\(15\) −2.85952 −0.738326
\(16\) 1.00000 0.250000
\(17\) 3.85952 0.936072 0.468036 0.883709i \(-0.344962\pi\)
0.468036 + 0.883709i \(0.344962\pi\)
\(18\) −5.17687 −1.22020
\(19\) 1.68265 0.386026 0.193013 0.981196i \(-0.438174\pi\)
0.193013 + 0.981196i \(0.438174\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.85952 −0.623999
\(22\) 0 0
\(23\) 6.85952 1.43031 0.715155 0.698966i \(-0.246356\pi\)
0.715155 + 0.698966i \(0.246356\pi\)
\(24\) 2.85952 0.583698
\(25\) 1.00000 0.200000
\(26\) −2.17687 −0.426920
\(27\) −6.22482 −1.19797
\(28\) 1.00000 0.188982
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 2.85952 0.522075
\(31\) 0.682649 0.122607 0.0613037 0.998119i \(-0.480474\pi\)
0.0613037 + 0.998119i \(0.480474\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.85952 −0.661903
\(35\) 1.00000 0.169031
\(36\) 5.17687 0.862812
\(37\) −3.71905 −0.611408 −0.305704 0.952127i \(-0.598892\pi\)
−0.305704 + 0.952127i \(0.598892\pi\)
\(38\) −1.68265 −0.272962
\(39\) −6.22482 −0.996769
\(40\) −1.00000 −0.158114
\(41\) 9.03640 1.41125 0.705624 0.708586i \(-0.250667\pi\)
0.705624 + 0.708586i \(0.250667\pi\)
\(42\) 2.85952 0.441234
\(43\) 5.85952 0.893569 0.446784 0.894642i \(-0.352569\pi\)
0.446784 + 0.894642i \(0.352569\pi\)
\(44\) 0 0
\(45\) 5.17687 0.771723
\(46\) −6.85952 −1.01138
\(47\) 4.68265 0.683035 0.341517 0.939875i \(-0.389059\pi\)
0.341517 + 0.939875i \(0.389059\pi\)
\(48\) −2.85952 −0.412737
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) −11.0364 −1.54540
\(52\) 2.17687 0.301878
\(53\) 13.5786 1.86516 0.932580 0.360963i \(-0.117552\pi\)
0.932580 + 0.360963i \(0.117552\pi\)
\(54\) 6.22482 0.847091
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −4.81158 −0.637309
\(58\) 2.00000 0.262613
\(59\) −7.75544 −1.00967 −0.504836 0.863215i \(-0.668447\pi\)
−0.504836 + 0.863215i \(0.668447\pi\)
\(60\) −2.85952 −0.369163
\(61\) 8.89592 1.13901 0.569503 0.821989i \(-0.307136\pi\)
0.569503 + 0.821989i \(0.307136\pi\)
\(62\) −0.682649 −0.0866966
\(63\) 5.17687 0.652225
\(64\) 1.00000 0.125000
\(65\) 2.17687 0.270008
\(66\) 0 0
\(67\) 9.85952 1.20453 0.602266 0.798295i \(-0.294265\pi\)
0.602266 + 0.798295i \(0.294265\pi\)
\(68\) 3.85952 0.468036
\(69\) −19.6150 −2.36136
\(70\) −1.00000 −0.119523
\(71\) −0.542173 −0.0643441 −0.0321720 0.999482i \(-0.510242\pi\)
−0.0321720 + 0.999482i \(0.510242\pi\)
\(72\) −5.17687 −0.610100
\(73\) −5.85952 −0.685805 −0.342903 0.939371i \(-0.611410\pi\)
−0.342903 + 0.939371i \(0.611410\pi\)
\(74\) 3.71905 0.432330
\(75\) −2.85952 −0.330189
\(76\) 1.68265 0.193013
\(77\) 0 0
\(78\) 6.22482 0.704822
\(79\) 0.317351 0.0357047 0.0178524 0.999841i \(-0.494317\pi\)
0.0178524 + 0.999841i \(0.494317\pi\)
\(80\) 1.00000 0.111803
\(81\) 2.26940 0.252156
\(82\) −9.03640 −0.997903
\(83\) −4.85952 −0.533402 −0.266701 0.963779i \(-0.585934\pi\)
−0.266701 + 0.963779i \(0.585934\pi\)
\(84\) −2.85952 −0.312000
\(85\) 3.85952 0.418624
\(86\) −5.85952 −0.631849
\(87\) 5.71905 0.613146
\(88\) 0 0
\(89\) −0.682649 −0.0723607 −0.0361803 0.999345i \(-0.511519\pi\)
−0.0361803 + 0.999345i \(0.511519\pi\)
\(90\) −5.17687 −0.545690
\(91\) 2.17687 0.228198
\(92\) 6.85952 0.715155
\(93\) −1.95205 −0.202418
\(94\) −4.68265 −0.482978
\(95\) 1.68265 0.172636
\(96\) 2.85952 0.291849
\(97\) 16.6150 1.68699 0.843497 0.537134i \(-0.180493\pi\)
0.843497 + 0.537134i \(0.180493\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −3.54217 −0.352459 −0.176230 0.984349i \(-0.556390\pi\)
−0.176230 + 0.984349i \(0.556390\pi\)
\(102\) 11.0364 1.09277
\(103\) 9.50578 0.936632 0.468316 0.883561i \(-0.344861\pi\)
0.468316 + 0.883561i \(0.344861\pi\)
\(104\) −2.17687 −0.213460
\(105\) −2.85952 −0.279061
\(106\) −13.5786 −1.31887
\(107\) 7.17687 0.693815 0.346907 0.937899i \(-0.387232\pi\)
0.346907 + 0.937899i \(0.387232\pi\)
\(108\) −6.22482 −0.598984
\(109\) 13.3901 1.28254 0.641272 0.767314i \(-0.278407\pi\)
0.641272 + 0.767314i \(0.278407\pi\)
\(110\) 0 0
\(111\) 10.6347 1.00940
\(112\) 1.00000 0.0944911
\(113\) −10.2497 −0.964208 −0.482104 0.876114i \(-0.660127\pi\)
−0.482104 + 0.876114i \(0.660127\pi\)
\(114\) 4.81158 0.450645
\(115\) 6.85952 0.639654
\(116\) −2.00000 −0.185695
\(117\) 11.2694 1.04186
\(118\) 7.75544 0.713947
\(119\) 3.85952 0.353802
\(120\) 2.85952 0.261038
\(121\) 0 0
\(122\) −8.89592 −0.805399
\(123\) −25.8398 −2.32990
\(124\) 0.682649 0.0613037
\(125\) 1.00000 0.0894427
\(126\) −5.17687 −0.461193
\(127\) −20.9323 −1.85744 −0.928721 0.370778i \(-0.879091\pi\)
−0.928721 + 0.370778i \(0.879091\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −16.7554 −1.47523
\(130\) −2.17687 −0.190924
\(131\) −6.57857 −0.574772 −0.287386 0.957815i \(-0.592786\pi\)
−0.287386 + 0.957815i \(0.592786\pi\)
\(132\) 0 0
\(133\) 1.68265 0.145904
\(134\) −9.85952 −0.851733
\(135\) −6.22482 −0.535747
\(136\) −3.85952 −0.330951
\(137\) 4.53062 0.387077 0.193539 0.981093i \(-0.438004\pi\)
0.193539 + 0.981093i \(0.438004\pi\)
\(138\) 19.6150 1.66974
\(139\) 13.4017 1.13672 0.568359 0.822781i \(-0.307579\pi\)
0.568359 + 0.822781i \(0.307579\pi\)
\(140\) 1.00000 0.0845154
\(141\) −13.3901 −1.12765
\(142\) 0.542173 0.0454981
\(143\) 0 0
\(144\) 5.17687 0.431406
\(145\) −2.00000 −0.166091
\(146\) 5.85952 0.484938
\(147\) −2.85952 −0.235850
\(148\) −3.71905 −0.305704
\(149\) 13.3653 1.09493 0.547464 0.836829i \(-0.315593\pi\)
0.547464 + 0.836829i \(0.315593\pi\)
\(150\) 2.85952 0.233479
\(151\) −16.8595 −1.37201 −0.686004 0.727598i \(-0.740637\pi\)
−0.686004 + 0.727598i \(0.740637\pi\)
\(152\) −1.68265 −0.136481
\(153\) 19.9803 1.61531
\(154\) 0 0
\(155\) 0.682649 0.0548317
\(156\) −6.22482 −0.498385
\(157\) 14.2497 1.13725 0.568624 0.822598i \(-0.307476\pi\)
0.568624 + 0.822598i \(0.307476\pi\)
\(158\) −0.317351 −0.0252471
\(159\) −38.8282 −3.07928
\(160\) −1.00000 −0.0790569
\(161\) 6.85952 0.540606
\(162\) −2.26940 −0.178301
\(163\) 14.2612 1.11702 0.558512 0.829496i \(-0.311372\pi\)
0.558512 + 0.829496i \(0.311372\pi\)
\(164\) 9.03640 0.705624
\(165\) 0 0
\(166\) 4.85952 0.377172
\(167\) −9.57857 −0.741212 −0.370606 0.928790i \(-0.620850\pi\)
−0.370606 + 0.928790i \(0.620850\pi\)
\(168\) 2.85952 0.220617
\(169\) −8.26122 −0.635478
\(170\) −3.85952 −0.296012
\(171\) 8.71086 0.666136
\(172\) 5.85952 0.446784
\(173\) −0.353748 −0.0268950 −0.0134475 0.999910i \(-0.504281\pi\)
−0.0134475 + 0.999910i \(0.504281\pi\)
\(174\) −5.71905 −0.433560
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 22.1769 1.66692
\(178\) 0.682649 0.0511667
\(179\) 2.40170 0.179511 0.0897556 0.995964i \(-0.471391\pi\)
0.0897556 + 0.995964i \(0.471391\pi\)
\(180\) 5.17687 0.385861
\(181\) −21.0728 −1.56633 −0.783164 0.621815i \(-0.786396\pi\)
−0.783164 + 0.621815i \(0.786396\pi\)
\(182\) −2.17687 −0.161361
\(183\) −25.4381 −1.88044
\(184\) −6.85952 −0.505691
\(185\) −3.71905 −0.273430
\(186\) 1.95205 0.143131
\(187\) 0 0
\(188\) 4.68265 0.341517
\(189\) −6.22482 −0.452789
\(190\) −1.68265 −0.122072
\(191\) −21.0051 −1.51988 −0.759938 0.649995i \(-0.774771\pi\)
−0.759938 + 0.649995i \(0.774771\pi\)
\(192\) −2.85952 −0.206368
\(193\) −6.24967 −0.449861 −0.224931 0.974375i \(-0.572216\pi\)
−0.224931 + 0.974375i \(0.572216\pi\)
\(194\) −16.6150 −1.19289
\(195\) −6.22482 −0.445769
\(196\) 1.00000 0.0714286
\(197\) 18.2612 1.30106 0.650529 0.759481i \(-0.274547\pi\)
0.650529 + 0.759481i \(0.274547\pi\)
\(198\) 0 0
\(199\) −22.1456 −1.56986 −0.784930 0.619585i \(-0.787301\pi\)
−0.784930 + 0.619585i \(0.787301\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −28.1935 −1.98862
\(202\) 3.54217 0.249226
\(203\) −2.00000 −0.140372
\(204\) −11.0364 −0.772702
\(205\) 9.03640 0.631129
\(206\) −9.50578 −0.662299
\(207\) 35.5109 2.46818
\(208\) 2.17687 0.150939
\(209\) 0 0
\(210\) 2.85952 0.197326
\(211\) −19.7918 −1.36253 −0.681263 0.732038i \(-0.738569\pi\)
−0.681263 + 0.732038i \(0.738569\pi\)
\(212\) 13.5786 0.932580
\(213\) 1.55036 0.106229
\(214\) −7.17687 −0.490601
\(215\) 5.85952 0.399616
\(216\) 6.22482 0.423545
\(217\) 0.682649 0.0463413
\(218\) −13.3901 −0.906895
\(219\) 16.7554 1.13223
\(220\) 0 0
\(221\) 8.40170 0.565159
\(222\) −10.6347 −0.713754
\(223\) −12.2133 −0.817861 −0.408931 0.912565i \(-0.634098\pi\)
−0.408931 + 0.912565i \(0.634098\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 5.17687 0.345125
\(226\) 10.2497 0.681798
\(227\) 1.92721 0.127913 0.0639566 0.997953i \(-0.479628\pi\)
0.0639566 + 0.997953i \(0.479628\pi\)
\(228\) −4.81158 −0.318654
\(229\) 26.2612 1.73539 0.867695 0.497097i \(-0.165601\pi\)
0.867695 + 0.497097i \(0.165601\pi\)
\(230\) −6.85952 −0.452304
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) 7.26122 0.475698 0.237849 0.971302i \(-0.423558\pi\)
0.237849 + 0.971302i \(0.423558\pi\)
\(234\) −11.2694 −0.736704
\(235\) 4.68265 0.305462
\(236\) −7.75544 −0.504836
\(237\) −0.907472 −0.0589466
\(238\) −3.85952 −0.250176
\(239\) −26.9323 −1.74211 −0.871053 0.491188i \(-0.836563\pi\)
−0.871053 + 0.491188i \(0.836563\pi\)
\(240\) −2.85952 −0.184581
\(241\) −11.7918 −0.759579 −0.379790 0.925073i \(-0.624004\pi\)
−0.379790 + 0.925073i \(0.624004\pi\)
\(242\) 0 0
\(243\) 12.1851 0.781672
\(244\) 8.89592 0.569503
\(245\) 1.00000 0.0638877
\(246\) 25.8398 1.64748
\(247\) 3.66292 0.233066
\(248\) −0.682649 −0.0433483
\(249\) 13.8959 0.880618
\(250\) −1.00000 −0.0632456
\(251\) 0.823126 0.0519553 0.0259776 0.999663i \(-0.491730\pi\)
0.0259776 + 0.999663i \(0.491730\pi\)
\(252\) 5.17687 0.326112
\(253\) 0 0
\(254\) 20.9323 1.31341
\(255\) −11.0364 −0.691126
\(256\) 1.00000 0.0625000
\(257\) −7.93232 −0.494804 −0.247402 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(258\) 16.7554 1.04315
\(259\) −3.71905 −0.231090
\(260\) 2.17687 0.135004
\(261\) −10.3537 −0.640881
\(262\) 6.57857 0.406425
\(263\) 4.22482 0.260514 0.130257 0.991480i \(-0.458420\pi\)
0.130257 + 0.991480i \(0.458420\pi\)
\(264\) 0 0
\(265\) 13.5786 0.834125
\(266\) −1.68265 −0.103170
\(267\) 1.95205 0.119464
\(268\) 9.85952 0.602266
\(269\) 26.5109 1.61640 0.808199 0.588910i \(-0.200443\pi\)
0.808199 + 0.588910i \(0.200443\pi\)
\(270\) 6.22482 0.378831
\(271\) −19.1571 −1.16371 −0.581857 0.813291i \(-0.697674\pi\)
−0.581857 + 0.813291i \(0.697674\pi\)
\(272\) 3.85952 0.234018
\(273\) −6.22482 −0.376743
\(274\) −4.53062 −0.273705
\(275\) 0 0
\(276\) −19.6150 −1.18068
\(277\) 0.0479481 0.00288092 0.00144046 0.999999i \(-0.499541\pi\)
0.00144046 + 0.999999i \(0.499541\pi\)
\(278\) −13.4017 −0.803780
\(279\) 3.53399 0.211574
\(280\) −1.00000 −0.0597614
\(281\) −14.0843 −0.840202 −0.420101 0.907477i \(-0.638005\pi\)
−0.420101 + 0.907477i \(0.638005\pi\)
\(282\) 13.3901 0.797372
\(283\) −3.49422 −0.207710 −0.103855 0.994592i \(-0.533118\pi\)
−0.103855 + 0.994592i \(0.533118\pi\)
\(284\) −0.542173 −0.0321720
\(285\) −4.81158 −0.285013
\(286\) 0 0
\(287\) 9.03640 0.533402
\(288\) −5.17687 −0.305050
\(289\) −2.10408 −0.123769
\(290\) 2.00000 0.117444
\(291\) −47.5109 −2.78514
\(292\) −5.85952 −0.342903
\(293\) 4.88437 0.285348 0.142674 0.989770i \(-0.454430\pi\)
0.142674 + 0.989770i \(0.454430\pi\)
\(294\) 2.85952 0.166771
\(295\) −7.75544 −0.451539
\(296\) 3.71905 0.216165
\(297\) 0 0
\(298\) −13.3653 −0.774231
\(299\) 14.9323 0.863558
\(300\) −2.85952 −0.165095
\(301\) 5.85952 0.337737
\(302\) 16.8595 0.970157
\(303\) 10.1289 0.581892
\(304\) 1.68265 0.0965066
\(305\) 8.89592 0.509379
\(306\) −19.9803 −1.14220
\(307\) −19.7190 −1.12543 −0.562713 0.826653i \(-0.690242\pi\)
−0.562713 + 0.826653i \(0.690242\pi\)
\(308\) 0 0
\(309\) −27.1820 −1.54633
\(310\) −0.682649 −0.0387719
\(311\) 22.1935 1.25848 0.629240 0.777211i \(-0.283366\pi\)
0.629240 + 0.777211i \(0.283366\pi\)
\(312\) 6.22482 0.352411
\(313\) 3.51089 0.198447 0.0992236 0.995065i \(-0.468364\pi\)
0.0992236 + 0.995065i \(0.468364\pi\)
\(314\) −14.2497 −0.804155
\(315\) 5.17687 0.291684
\(316\) 0.317351 0.0178524
\(317\) −5.50578 −0.309235 −0.154618 0.987974i \(-0.549415\pi\)
−0.154618 + 0.987974i \(0.549415\pi\)
\(318\) 38.8282 2.17738
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −20.5224 −1.14545
\(322\) −6.85952 −0.382266
\(323\) 6.49422 0.361348
\(324\) 2.26940 0.126078
\(325\) 2.17687 0.120751
\(326\) −14.2612 −0.789856
\(327\) −38.2894 −2.11741
\(328\) −9.03640 −0.498952
\(329\) 4.68265 0.258163
\(330\) 0 0
\(331\) −13.4629 −0.739990 −0.369995 0.929034i \(-0.620641\pi\)
−0.369995 + 0.929034i \(0.620641\pi\)
\(332\) −4.85952 −0.266701
\(333\) −19.2530 −1.05506
\(334\) 9.57857 0.524116
\(335\) 9.85952 0.538683
\(336\) −2.85952 −0.156000
\(337\) −19.3340 −1.05319 −0.526595 0.850116i \(-0.676532\pi\)
−0.526595 + 0.850116i \(0.676532\pi\)
\(338\) 8.26122 0.449351
\(339\) 29.3092 1.59186
\(340\) 3.85952 0.209312
\(341\) 0 0
\(342\) −8.71086 −0.471030
\(343\) 1.00000 0.0539949
\(344\) −5.85952 −0.315924
\(345\) −19.6150 −1.05603
\(346\) 0.353748 0.0190176
\(347\) −20.0531 −1.07650 −0.538252 0.842784i \(-0.680915\pi\)
−0.538252 + 0.842784i \(0.680915\pi\)
\(348\) 5.71905 0.306573
\(349\) −29.2612 −1.56632 −0.783159 0.621822i \(-0.786393\pi\)
−0.783159 + 0.621822i \(0.786393\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −13.5507 −0.723280
\(352\) 0 0
\(353\) 3.50578 0.186594 0.0932968 0.995638i \(-0.470259\pi\)
0.0932968 + 0.995638i \(0.470259\pi\)
\(354\) −22.1769 −1.17869
\(355\) −0.542173 −0.0287755
\(356\) −0.682649 −0.0361803
\(357\) −11.0364 −0.584108
\(358\) −2.40170 −0.126934
\(359\) −36.2612 −1.91379 −0.956897 0.290428i \(-0.906202\pi\)
−0.956897 + 0.290428i \(0.906202\pi\)
\(360\) −5.17687 −0.272845
\(361\) −16.1687 −0.850984
\(362\) 21.0728 1.10756
\(363\) 0 0
\(364\) 2.17687 0.114099
\(365\) −5.85952 −0.306701
\(366\) 25.4381 1.32967
\(367\) −1.29762 −0.0677351 −0.0338675 0.999426i \(-0.510782\pi\)
−0.0338675 + 0.999426i \(0.510782\pi\)
\(368\) 6.85952 0.357577
\(369\) 46.7803 2.43528
\(370\) 3.71905 0.193344
\(371\) 13.5786 0.704964
\(372\) −1.95205 −0.101209
\(373\) −16.8231 −0.871068 −0.435534 0.900172i \(-0.643441\pi\)
−0.435534 + 0.900172i \(0.643441\pi\)
\(374\) 0 0
\(375\) −2.85952 −0.147665
\(376\) −4.68265 −0.241489
\(377\) −4.35375 −0.224229
\(378\) 6.22482 0.320170
\(379\) 4.70750 0.241808 0.120904 0.992664i \(-0.461421\pi\)
0.120904 + 0.992664i \(0.461421\pi\)
\(380\) 1.68265 0.0863181
\(381\) 59.8565 3.06654
\(382\) 21.0051 1.07472
\(383\) −17.6514 −0.901943 −0.450971 0.892538i \(-0.648922\pi\)
−0.450971 + 0.892538i \(0.648922\pi\)
\(384\) 2.85952 0.145924
\(385\) 0 0
\(386\) 6.24967 0.318100
\(387\) 30.3340 1.54196
\(388\) 16.6150 0.843497
\(389\) 27.9126 1.41522 0.707612 0.706601i \(-0.249772\pi\)
0.707612 + 0.706601i \(0.249772\pi\)
\(390\) 6.22482 0.315206
\(391\) 26.4745 1.33887
\(392\) −1.00000 −0.0505076
\(393\) 18.8116 0.948918
\(394\) −18.2612 −0.919987
\(395\) 0.317351 0.0159676
\(396\) 0 0
\(397\) −4.35375 −0.218508 −0.109254 0.994014i \(-0.534846\pi\)
−0.109254 + 0.994014i \(0.534846\pi\)
\(398\) 22.1456 1.11006
\(399\) −4.81158 −0.240880
\(400\) 1.00000 0.0500000
\(401\) −6.56191 −0.327686 −0.163843 0.986486i \(-0.552389\pi\)
−0.163843 + 0.986486i \(0.552389\pi\)
\(402\) 28.1935 1.40617
\(403\) 1.48604 0.0740250
\(404\) −3.54217 −0.176230
\(405\) 2.26940 0.112768
\(406\) 2.00000 0.0992583
\(407\) 0 0
\(408\) 11.0364 0.546383
\(409\) 15.7918 0.780856 0.390428 0.920633i \(-0.372327\pi\)
0.390428 + 0.920633i \(0.372327\pi\)
\(410\) −9.03640 −0.446276
\(411\) −12.9554 −0.639044
\(412\) 9.50578 0.468316
\(413\) −7.75544 −0.381620
\(414\) −35.5109 −1.74526
\(415\) −4.85952 −0.238545
\(416\) −2.17687 −0.106730
\(417\) −38.3225 −1.87666
\(418\) 0 0
\(419\) 28.7670 1.40536 0.702680 0.711506i \(-0.251987\pi\)
0.702680 + 0.711506i \(0.251987\pi\)
\(420\) −2.85952 −0.139530
\(421\) −12.1456 −0.591940 −0.295970 0.955197i \(-0.595643\pi\)
−0.295970 + 0.955197i \(0.595643\pi\)
\(422\) 19.7918 0.963452
\(423\) 24.2415 1.17866
\(424\) −13.5786 −0.659434
\(425\) 3.85952 0.187214
\(426\) −1.55036 −0.0751150
\(427\) 8.89592 0.430504
\(428\) 7.17687 0.346907
\(429\) 0 0
\(430\) −5.85952 −0.282571
\(431\) −22.9126 −1.10366 −0.551830 0.833957i \(-0.686070\pi\)
−0.551830 + 0.833957i \(0.686070\pi\)
\(432\) −6.22482 −0.299492
\(433\) −7.69420 −0.369760 −0.184880 0.982761i \(-0.559190\pi\)
−0.184880 + 0.982761i \(0.559190\pi\)
\(434\) −0.682649 −0.0327682
\(435\) 5.71905 0.274207
\(436\) 13.3901 0.641272
\(437\) 11.5422 0.552137
\(438\) −16.7554 −0.800606
\(439\) −41.1092 −1.96203 −0.981017 0.193920i \(-0.937880\pi\)
−0.981017 + 0.193920i \(0.937880\pi\)
\(440\) 0 0
\(441\) 5.17687 0.246518
\(442\) −8.40170 −0.399628
\(443\) 16.8034 0.798353 0.399177 0.916874i \(-0.369296\pi\)
0.399177 + 0.916874i \(0.369296\pi\)
\(444\) 10.6347 0.504701
\(445\) −0.682649 −0.0323607
\(446\) 12.2133 0.578315
\(447\) −38.2184 −1.80767
\(448\) 1.00000 0.0472456
\(449\) 24.4381 1.15330 0.576652 0.816990i \(-0.304359\pi\)
0.576652 + 0.816990i \(0.304359\pi\)
\(450\) −5.17687 −0.244040
\(451\) 0 0
\(452\) −10.2497 −0.482104
\(453\) 48.2102 2.26511
\(454\) −1.92721 −0.0904482
\(455\) 2.17687 0.102053
\(456\) 4.81158 0.225323
\(457\) −12.3225 −0.576421 −0.288210 0.957567i \(-0.593060\pi\)
−0.288210 + 0.957567i \(0.593060\pi\)
\(458\) −26.2612 −1.22711
\(459\) −24.0248 −1.12138
\(460\) 6.85952 0.319827
\(461\) 3.38503 0.157657 0.0788283 0.996888i \(-0.474882\pi\)
0.0788283 + 0.996888i \(0.474882\pi\)
\(462\) 0 0
\(463\) 35.6629 1.65740 0.828698 0.559696i \(-0.189082\pi\)
0.828698 + 0.559696i \(0.189082\pi\)
\(464\) −2.00000 −0.0928477
\(465\) −1.95205 −0.0905242
\(466\) −7.26122 −0.336369
\(467\) 19.7357 0.913260 0.456630 0.889657i \(-0.349056\pi\)
0.456630 + 0.889657i \(0.349056\pi\)
\(468\) 11.2694 0.520928
\(469\) 9.85952 0.455270
\(470\) −4.68265 −0.215995
\(471\) −40.7473 −1.87753
\(472\) 7.75544 0.356973
\(473\) 0 0
\(474\) 0.907472 0.0416815
\(475\) 1.68265 0.0772052
\(476\) 3.85952 0.176901
\(477\) 70.2945 3.21857
\(478\) 26.9323 1.23186
\(479\) 6.40170 0.292501 0.146250 0.989248i \(-0.453279\pi\)
0.146250 + 0.989248i \(0.453279\pi\)
\(480\) 2.85952 0.130519
\(481\) −8.09590 −0.369141
\(482\) 11.7918 0.537104
\(483\) −19.6150 −0.892512
\(484\) 0 0
\(485\) 16.6150 0.754447
\(486\) −12.1851 −0.552725
\(487\) 43.1738 1.95639 0.978196 0.207684i \(-0.0665927\pi\)
0.978196 + 0.207684i \(0.0665927\pi\)
\(488\) −8.89592 −0.402699
\(489\) −40.7803 −1.84415
\(490\) −1.00000 −0.0451754
\(491\) 33.2779 1.50181 0.750905 0.660410i \(-0.229618\pi\)
0.750905 + 0.660410i \(0.229618\pi\)
\(492\) −25.8398 −1.16495
\(493\) −7.71905 −0.347648
\(494\) −3.66292 −0.164802
\(495\) 0 0
\(496\) 0.682649 0.0306519
\(497\) −0.542173 −0.0243198
\(498\) −13.8959 −0.622691
\(499\) −22.6347 −1.01327 −0.506634 0.862161i \(-0.669111\pi\)
−0.506634 + 0.862161i \(0.669111\pi\)
\(500\) 1.00000 0.0447214
\(501\) 27.3901 1.22370
\(502\) −0.823126 −0.0367379
\(503\) 12.1405 0.541317 0.270659 0.962675i \(-0.412759\pi\)
0.270659 + 0.962675i \(0.412759\pi\)
\(504\) −5.17687 −0.230596
\(505\) −3.54217 −0.157625
\(506\) 0 0
\(507\) 23.6232 1.04914
\(508\) −20.9323 −0.928721
\(509\) 25.4265 1.12701 0.563506 0.826112i \(-0.309452\pi\)
0.563506 + 0.826112i \(0.309452\pi\)
\(510\) 11.0364 0.488700
\(511\) −5.85952 −0.259210
\(512\) −1.00000 −0.0441942
\(513\) −10.4742 −0.462447
\(514\) 7.93232 0.349880
\(515\) 9.50578 0.418875
\(516\) −16.7554 −0.737617
\(517\) 0 0
\(518\) 3.71905 0.163406
\(519\) 1.01155 0.0444021
\(520\) −2.17687 −0.0954622
\(521\) 27.3653 1.19890 0.599448 0.800414i \(-0.295387\pi\)
0.599448 + 0.800414i \(0.295387\pi\)
\(522\) 10.3537 0.453171
\(523\) 19.2364 0.841148 0.420574 0.907258i \(-0.361829\pi\)
0.420574 + 0.907258i \(0.361829\pi\)
\(524\) −6.57857 −0.287386
\(525\) −2.85952 −0.124800
\(526\) −4.22482 −0.184211
\(527\) 2.63470 0.114769
\(528\) 0 0
\(529\) 24.0531 1.04579
\(530\) −13.5786 −0.589815
\(531\) −40.1490 −1.74232
\(532\) 1.68265 0.0729521
\(533\) 19.6711 0.852050
\(534\) −1.95205 −0.0844735
\(535\) 7.17687 0.310283
\(536\) −9.85952 −0.425867
\(537\) −6.86771 −0.296363
\(538\) −26.5109 −1.14297
\(539\) 0 0
\(540\) −6.22482 −0.267874
\(541\) −19.5109 −0.838839 −0.419419 0.907793i \(-0.637766\pi\)
−0.419419 + 0.907793i \(0.637766\pi\)
\(542\) 19.1571 0.822870
\(543\) 60.2581 2.58592
\(544\) −3.85952 −0.165476
\(545\) 13.3901 0.573571
\(546\) 6.22482 0.266398
\(547\) −33.8595 −1.44773 −0.723864 0.689942i \(-0.757636\pi\)
−0.723864 + 0.689942i \(0.757636\pi\)
\(548\) 4.53062 0.193539
\(549\) 46.0531 1.96550
\(550\) 0 0
\(551\) −3.36530 −0.143367
\(552\) 19.6150 0.834868
\(553\) 0.317351 0.0134951
\(554\) −0.0479481 −0.00203712
\(555\) 10.6347 0.451418
\(556\) 13.4017 0.568359
\(557\) −25.7670 −1.09178 −0.545891 0.837856i \(-0.683809\pi\)
−0.545891 + 0.837856i \(0.683809\pi\)
\(558\) −3.53399 −0.149606
\(559\) 12.7554 0.539498
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 14.0843 0.594112
\(563\) −1.84797 −0.0778828 −0.0389414 0.999241i \(-0.512399\pi\)
−0.0389414 + 0.999241i \(0.512399\pi\)
\(564\) −13.3901 −0.563827
\(565\) −10.2497 −0.431207
\(566\) 3.49422 0.146873
\(567\) 2.26940 0.0953059
\(568\) 0.542173 0.0227491
\(569\) 31.2184 1.30874 0.654371 0.756173i \(-0.272933\pi\)
0.654371 + 0.756173i \(0.272933\pi\)
\(570\) 4.81158 0.201535
\(571\) −8.42654 −0.352640 −0.176320 0.984333i \(-0.556419\pi\)
−0.176320 + 0.984333i \(0.556419\pi\)
\(572\) 0 0
\(573\) 60.0646 2.50924
\(574\) −9.03640 −0.377172
\(575\) 6.85952 0.286062
\(576\) 5.17687 0.215703
\(577\) 10.0051 0.416518 0.208259 0.978074i \(-0.433220\pi\)
0.208259 + 0.978074i \(0.433220\pi\)
\(578\) 2.10408 0.0875182
\(579\) 17.8711 0.742696
\(580\) −2.00000 −0.0830455
\(581\) −4.85952 −0.201607
\(582\) 47.5109 1.96939
\(583\) 0 0
\(584\) 5.85952 0.242469
\(585\) 11.2694 0.465932
\(586\) −4.88437 −0.201771
\(587\) −1.79828 −0.0742229 −0.0371115 0.999311i \(-0.511816\pi\)
−0.0371115 + 0.999311i \(0.511816\pi\)
\(588\) −2.85952 −0.117925
\(589\) 1.14866 0.0473297
\(590\) 7.75544 0.319287
\(591\) −52.2184 −2.14798
\(592\) −3.71905 −0.152852
\(593\) 39.3225 1.61478 0.807390 0.590018i \(-0.200879\pi\)
0.807390 + 0.590018i \(0.200879\pi\)
\(594\) 0 0
\(595\) 3.85952 0.158225
\(596\) 13.3653 0.547464
\(597\) 63.3258 2.59175
\(598\) −14.9323 −0.610628
\(599\) 25.7554 1.05234 0.526169 0.850380i \(-0.323628\pi\)
0.526169 + 0.850380i \(0.323628\pi\)
\(600\) 2.85952 0.116740
\(601\) 27.1092 1.10581 0.552904 0.833245i \(-0.313520\pi\)
0.552904 + 0.833245i \(0.313520\pi\)
\(602\) −5.85952 −0.238816
\(603\) 51.0415 2.07857
\(604\) −16.8595 −0.686004
\(605\) 0 0
\(606\) −10.1289 −0.411459
\(607\) 30.0300 1.21888 0.609439 0.792833i \(-0.291395\pi\)
0.609439 + 0.792833i \(0.291395\pi\)
\(608\) −1.68265 −0.0682404
\(609\) 5.71905 0.231747
\(610\) −8.89592 −0.360185
\(611\) 10.1935 0.412386
\(612\) 19.9803 0.807654
\(613\) 22.5901 0.912406 0.456203 0.889876i \(-0.349209\pi\)
0.456203 + 0.889876i \(0.349209\pi\)
\(614\) 19.7190 0.795796
\(615\) −25.8398 −1.04196
\(616\) 0 0
\(617\) −20.7306 −0.834582 −0.417291 0.908773i \(-0.637020\pi\)
−0.417291 + 0.908773i \(0.637020\pi\)
\(618\) 27.1820 1.09342
\(619\) 29.8085 1.19810 0.599052 0.800710i \(-0.295544\pi\)
0.599052 + 0.800710i \(0.295544\pi\)
\(620\) 0.682649 0.0274159
\(621\) −42.6993 −1.71346
\(622\) −22.1935 −0.889880
\(623\) −0.682649 −0.0273498
\(624\) −6.22482 −0.249192
\(625\) 1.00000 0.0400000
\(626\) −3.51089 −0.140323
\(627\) 0 0
\(628\) 14.2497 0.568624
\(629\) −14.3537 −0.572321
\(630\) −5.17687 −0.206252
\(631\) 22.3340 0.889103 0.444552 0.895753i \(-0.353363\pi\)
0.444552 + 0.895753i \(0.353363\pi\)
\(632\) −0.317351 −0.0126235
\(633\) 56.5952 2.24946
\(634\) 5.50578 0.218662
\(635\) −20.9323 −0.830674
\(636\) −38.8282 −1.53964
\(637\) 2.17687 0.0862509
\(638\) 0 0
\(639\) −2.80676 −0.111034
\(640\) −1.00000 −0.0395285
\(641\) −4.06124 −0.160409 −0.0802047 0.996778i \(-0.525557\pi\)
−0.0802047 + 0.996778i \(0.525557\pi\)
\(642\) 20.5224 0.809956
\(643\) −35.0218 −1.38112 −0.690562 0.723273i \(-0.742637\pi\)
−0.690562 + 0.723273i \(0.742637\pi\)
\(644\) 6.85952 0.270303
\(645\) −16.7554 −0.659745
\(646\) −6.49422 −0.255512
\(647\) 29.2248 1.14895 0.574473 0.818523i \(-0.305207\pi\)
0.574473 + 0.818523i \(0.305207\pi\)
\(648\) −2.26940 −0.0891505
\(649\) 0 0
\(650\) −2.17687 −0.0853840
\(651\) −1.95205 −0.0765069
\(652\) 14.2612 0.558512
\(653\) −19.9323 −0.780012 −0.390006 0.920812i \(-0.627527\pi\)
−0.390006 + 0.920812i \(0.627527\pi\)
\(654\) 38.2894 1.49724
\(655\) −6.57857 −0.257046
\(656\) 9.03640 0.352812
\(657\) −30.3340 −1.18344
\(658\) −4.68265 −0.182549
\(659\) −24.6201 −0.959062 −0.479531 0.877525i \(-0.659193\pi\)
−0.479531 + 0.877525i \(0.659193\pi\)
\(660\) 0 0
\(661\) 25.7606 1.00197 0.500985 0.865456i \(-0.332971\pi\)
0.500985 + 0.865456i \(0.332971\pi\)
\(662\) 13.4629 0.523252
\(663\) −24.0248 −0.933048
\(664\) 4.85952 0.188586
\(665\) 1.68265 0.0652503
\(666\) 19.2530 0.746040
\(667\) −13.7190 −0.531204
\(668\) −9.57857 −0.370606
\(669\) 34.9241 1.35025
\(670\) −9.85952 −0.380907
\(671\) 0 0
\(672\) 2.85952 0.110309
\(673\) 5.54217 0.213635 0.106818 0.994279i \(-0.465934\pi\)
0.106818 + 0.994279i \(0.465934\pi\)
\(674\) 19.3340 0.744718
\(675\) −6.22482 −0.239594
\(676\) −8.26122 −0.317739
\(677\) −34.4912 −1.32560 −0.662801 0.748795i \(-0.730633\pi\)
−0.662801 + 0.748795i \(0.730633\pi\)
\(678\) −29.3092 −1.12561
\(679\) 16.6150 0.637624
\(680\) −3.85952 −0.148006
\(681\) −5.51089 −0.211178
\(682\) 0 0
\(683\) −22.8231 −0.873303 −0.436651 0.899631i \(-0.643836\pi\)
−0.436651 + 0.899631i \(0.643836\pi\)
\(684\) 8.71086 0.333068
\(685\) 4.53062 0.173106
\(686\) −1.00000 −0.0381802
\(687\) −75.0946 −2.86504
\(688\) 5.85952 0.223392
\(689\) 29.5588 1.12610
\(690\) 19.6150 0.746729
\(691\) −21.9075 −0.833399 −0.416700 0.909044i \(-0.636813\pi\)
−0.416700 + 0.909044i \(0.636813\pi\)
\(692\) −0.353748 −0.0134475
\(693\) 0 0
\(694\) 20.0531 0.761204
\(695\) 13.4017 0.508355
\(696\) −5.71905 −0.216780
\(697\) 34.8762 1.32103
\(698\) 29.2612 1.10755
\(699\) −20.7636 −0.785353
\(700\) 1.00000 0.0377964
\(701\) 12.6826 0.479017 0.239509 0.970894i \(-0.423014\pi\)
0.239509 + 0.970894i \(0.423014\pi\)
\(702\) 13.5507 0.511436
\(703\) −6.25785 −0.236019
\(704\) 0 0
\(705\) −13.3901 −0.504302
\(706\) −3.50578 −0.131942
\(707\) −3.54217 −0.133217
\(708\) 22.1769 0.833458
\(709\) 47.3027 1.77649 0.888246 0.459369i \(-0.151924\pi\)
0.888246 + 0.459369i \(0.151924\pi\)
\(710\) 0.542173 0.0203474
\(711\) 1.64288 0.0616130
\(712\) 0.682649 0.0255834
\(713\) 4.68265 0.175367
\(714\) 11.0364 0.413027
\(715\) 0 0
\(716\) 2.40170 0.0897556
\(717\) 77.0136 2.87613
\(718\) 36.2612 1.35326
\(719\) −12.9388 −0.482534 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(720\) 5.17687 0.192931
\(721\) 9.50578 0.354014
\(722\) 16.1687 0.601736
\(723\) 33.7190 1.25402
\(724\) −21.0728 −0.783164
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) 32.4993 1.20533 0.602667 0.797993i \(-0.294105\pi\)
0.602667 + 0.797993i \(0.294105\pi\)
\(728\) −2.17687 −0.0806803
\(729\) −41.6517 −1.54265
\(730\) 5.85952 0.216871
\(731\) 22.6150 0.836445
\(732\) −25.4381 −0.940219
\(733\) 41.6878 1.53977 0.769886 0.638181i \(-0.220313\pi\)
0.769886 + 0.638181i \(0.220313\pi\)
\(734\) 1.29762 0.0478959
\(735\) −2.85952 −0.105475
\(736\) −6.85952 −0.252845
\(737\) 0 0
\(738\) −46.7803 −1.72201
\(739\) 6.40170 0.235490 0.117745 0.993044i \(-0.462433\pi\)
0.117745 + 0.993044i \(0.462433\pi\)
\(740\) −3.71905 −0.136715
\(741\) −10.4742 −0.384779
\(742\) −13.5786 −0.498485
\(743\) −33.2299 −1.21909 −0.609544 0.792752i \(-0.708647\pi\)
−0.609544 + 0.792752i \(0.708647\pi\)
\(744\) 1.95205 0.0715657
\(745\) 13.3653 0.489667
\(746\) 16.8231 0.615938
\(747\) −25.1571 −0.920452
\(748\) 0 0
\(749\) 7.17687 0.262237
\(750\) 2.85952 0.104415
\(751\) 31.3820 1.14514 0.572572 0.819854i \(-0.305946\pi\)
0.572572 + 0.819854i \(0.305946\pi\)
\(752\) 4.68265 0.170759
\(753\) −2.35375 −0.0857753
\(754\) 4.35375 0.158554
\(755\) −16.8595 −0.613581
\(756\) −6.22482 −0.226395
\(757\) −36.4548 −1.32497 −0.662485 0.749075i \(-0.730498\pi\)
−0.662485 + 0.749075i \(0.730498\pi\)
\(758\) −4.70750 −0.170984
\(759\) 0 0
\(760\) −1.68265 −0.0610361
\(761\) 45.4860 1.64887 0.824434 0.565958i \(-0.191494\pi\)
0.824434 + 0.565958i \(0.191494\pi\)
\(762\) −59.8565 −2.16837
\(763\) 13.3901 0.484756
\(764\) −21.0051 −0.759938
\(765\) 19.9803 0.722388
\(766\) 17.6514 0.637770
\(767\) −16.8826 −0.609596
\(768\) −2.85952 −0.103184
\(769\) −3.57346 −0.128862 −0.0644311 0.997922i \(-0.520523\pi\)
−0.0644311 + 0.997922i \(0.520523\pi\)
\(770\) 0 0
\(771\) 22.6826 0.816896
\(772\) −6.24967 −0.224931
\(773\) 39.4068 1.41736 0.708682 0.705528i \(-0.249290\pi\)
0.708682 + 0.705528i \(0.249290\pi\)
\(774\) −30.3340 −1.09033
\(775\) 0.682649 0.0245215
\(776\) −16.6150 −0.596443
\(777\) 10.6347 0.381518
\(778\) −27.9126 −1.00071
\(779\) 15.2051 0.544779
\(780\) −6.22482 −0.222884
\(781\) 0 0
\(782\) −26.4745 −0.946726
\(783\) 12.4496 0.444914
\(784\) 1.00000 0.0357143
\(785\) 14.2497 0.508592
\(786\) −18.8116 −0.670987
\(787\) 22.4993 0.802015 0.401007 0.916075i \(-0.368660\pi\)
0.401007 + 0.916075i \(0.368660\pi\)
\(788\) 18.2612 0.650529
\(789\) −12.0810 −0.430094
\(790\) −0.317351 −0.0112908
\(791\) −10.2497 −0.364436
\(792\) 0 0
\(793\) 19.3653 0.687682
\(794\) 4.35375 0.154509
\(795\) −38.8282 −1.37710
\(796\) −22.1456 −0.784930
\(797\) 25.2612 0.894798 0.447399 0.894334i \(-0.352350\pi\)
0.447399 + 0.894334i \(0.352350\pi\)
\(798\) 4.81158 0.170328
\(799\) 18.0728 0.639370
\(800\) −1.00000 −0.0353553
\(801\) −3.53399 −0.124867
\(802\) 6.56191 0.231709
\(803\) 0 0
\(804\) −28.1935 −0.994309
\(805\) 6.85952 0.241766
\(806\) −1.48604 −0.0523436
\(807\) −75.8085 −2.66859
\(808\) 3.54217 0.124613
\(809\) −45.0415 −1.58358 −0.791788 0.610797i \(-0.790849\pi\)
−0.791788 + 0.610797i \(0.790849\pi\)
\(810\) −2.26940 −0.0797387
\(811\) −44.9490 −1.57837 −0.789186 0.614154i \(-0.789497\pi\)
−0.789186 + 0.614154i \(0.789497\pi\)
\(812\) −2.00000 −0.0701862
\(813\) 54.7803 1.92123
\(814\) 0 0
\(815\) 14.2612 0.499549
\(816\) −11.0364 −0.386351
\(817\) 9.85952 0.344941
\(818\) −15.7918 −0.552149
\(819\) 11.2694 0.393785
\(820\) 9.03640 0.315565
\(821\) 6.52244 0.227635 0.113817 0.993502i \(-0.463692\pi\)
0.113817 + 0.993502i \(0.463692\pi\)
\(822\) 12.9554 0.451872
\(823\) 38.4496 1.34027 0.670135 0.742239i \(-0.266236\pi\)
0.670135 + 0.742239i \(0.266236\pi\)
\(824\) −9.50578 −0.331149
\(825\) 0 0
\(826\) 7.75544 0.269846
\(827\) 55.3704 1.92542 0.962709 0.270539i \(-0.0872020\pi\)
0.962709 + 0.270539i \(0.0872020\pi\)
\(828\) 35.5109 1.23409
\(829\) −50.7721 −1.76339 −0.881694 0.471821i \(-0.843597\pi\)
−0.881694 + 0.471821i \(0.843597\pi\)
\(830\) 4.85952 0.168677
\(831\) −0.137109 −0.00475625
\(832\) 2.17687 0.0754695
\(833\) 3.85952 0.133725
\(834\) 38.3225 1.32700
\(835\) −9.57857 −0.331480
\(836\) 0 0
\(837\) −4.24937 −0.146880
\(838\) −28.7670 −0.993739
\(839\) 42.6201 1.47141 0.735704 0.677303i \(-0.236851\pi\)
0.735704 + 0.677303i \(0.236851\pi\)
\(840\) 2.85952 0.0986629
\(841\) −25.0000 −0.862069
\(842\) 12.1456 0.418565
\(843\) 40.2745 1.38713
\(844\) −19.7918 −0.681263
\(845\) −8.26122 −0.284195
\(846\) −24.2415 −0.833439
\(847\) 0 0
\(848\) 13.5786 0.466290
\(849\) 9.99182 0.342918
\(850\) −3.85952 −0.132381
\(851\) −25.5109 −0.874502
\(852\) 1.55036 0.0531143
\(853\) 2.12718 0.0728333 0.0364166 0.999337i \(-0.488406\pi\)
0.0364166 + 0.999337i \(0.488406\pi\)
\(854\) −8.89592 −0.304412
\(855\) 8.71086 0.297905
\(856\) −7.17687 −0.245301
\(857\) 52.6680 1.79911 0.899553 0.436812i \(-0.143893\pi\)
0.899553 + 0.436812i \(0.143893\pi\)
\(858\) 0 0
\(859\) −36.9687 −1.26136 −0.630678 0.776045i \(-0.717223\pi\)
−0.630678 + 0.776045i \(0.717223\pi\)
\(860\) 5.85952 0.199808
\(861\) −25.8398 −0.880618
\(862\) 22.9126 0.780406
\(863\) −36.6680 −1.24819 −0.624097 0.781347i \(-0.714533\pi\)
−0.624097 + 0.781347i \(0.714533\pi\)
\(864\) 6.22482 0.211773
\(865\) −0.353748 −0.0120278
\(866\) 7.69420 0.261460
\(867\) 6.01666 0.204337
\(868\) 0.682649 0.0231706
\(869\) 0 0
\(870\) −5.71905 −0.193894
\(871\) 21.4629 0.727244
\(872\) −13.3901 −0.453448
\(873\) 86.0136 2.91112
\(874\) −11.5422 −0.390420
\(875\) 1.00000 0.0338062
\(876\) 16.7554 0.566114
\(877\) −16.7752 −0.566458 −0.283229 0.959052i \(-0.591406\pi\)
−0.283229 + 0.959052i \(0.591406\pi\)
\(878\) 41.1092 1.38737
\(879\) −13.9670 −0.471094
\(880\) 0 0
\(881\) 40.2415 1.35577 0.677885 0.735168i \(-0.262897\pi\)
0.677885 + 0.735168i \(0.262897\pi\)
\(882\) −5.17687 −0.174314
\(883\) −20.4068 −0.686744 −0.343372 0.939200i \(-0.611569\pi\)
−0.343372 + 0.939200i \(0.611569\pi\)
\(884\) 8.40170 0.282580
\(885\) 22.1769 0.745467
\(886\) −16.8034 −0.564521
\(887\) 11.9752 0.402086 0.201043 0.979582i \(-0.435567\pi\)
0.201043 + 0.979582i \(0.435567\pi\)
\(888\) −10.6347 −0.356877
\(889\) −20.9323 −0.702047
\(890\) 0.682649 0.0228825
\(891\) 0 0
\(892\) −12.2133 −0.408931
\(893\) 7.87926 0.263669
\(894\) 38.2184 1.27821
\(895\) 2.40170 0.0802798
\(896\) −1.00000 −0.0334077
\(897\) −42.6993 −1.42569
\(898\) −24.4381 −0.815510
\(899\) −1.36530 −0.0455353
\(900\) 5.17687 0.172562
\(901\) 52.4068 1.74592
\(902\) 0 0
\(903\) −16.7554 −0.557586
\(904\) 10.2497 0.340899
\(905\) −21.0728 −0.700483
\(906\) −48.2102 −1.60168
\(907\) −21.8116 −0.724241 −0.362121 0.932131i \(-0.617947\pi\)
−0.362121 + 0.932131i \(0.617947\pi\)
\(908\) 1.92721 0.0639566
\(909\) −18.3374 −0.608213
\(910\) −2.17687 −0.0721627
\(911\) −22.1820 −0.734922 −0.367461 0.930039i \(-0.619773\pi\)
−0.367461 + 0.930039i \(0.619773\pi\)
\(912\) −4.81158 −0.159327
\(913\) 0 0
\(914\) 12.3225 0.407591
\(915\) −25.4381 −0.840957
\(916\) 26.2612 0.867695
\(917\) −6.57857 −0.217244
\(918\) 24.0248 0.792938
\(919\) 16.8531 0.555932 0.277966 0.960591i \(-0.410340\pi\)
0.277966 + 0.960591i \(0.410340\pi\)
\(920\) −6.85952 −0.226152
\(921\) 56.3871 1.85802
\(922\) −3.38503 −0.111480
\(923\) −1.18024 −0.0388481
\(924\) 0 0
\(925\) −3.71905 −0.122282
\(926\) −35.6629 −1.17196
\(927\) 49.2102 1.61628
\(928\) 2.00000 0.0656532
\(929\) −17.2694 −0.566591 −0.283295 0.959033i \(-0.591428\pi\)
−0.283295 + 0.959033i \(0.591428\pi\)
\(930\) 1.95205 0.0640103
\(931\) 1.68265 0.0551466
\(932\) 7.26122 0.237849
\(933\) −63.4629 −2.07768
\(934\) −19.7357 −0.645772
\(935\) 0 0
\(936\) −11.2694 −0.368352
\(937\) −45.5837 −1.48915 −0.744577 0.667537i \(-0.767349\pi\)
−0.744577 + 0.667537i \(0.767349\pi\)
\(938\) −9.85952 −0.321925
\(939\) −10.0395 −0.327626
\(940\) 4.68265 0.152731
\(941\) 36.1987 1.18004 0.590021 0.807388i \(-0.299119\pi\)
0.590021 + 0.807388i \(0.299119\pi\)
\(942\) 40.7473 1.32762
\(943\) 61.9854 2.01852
\(944\) −7.75544 −0.252418
\(945\) −6.22482 −0.202493
\(946\) 0 0
\(947\) −33.3276 −1.08300 −0.541500 0.840701i \(-0.682144\pi\)
−0.541500 + 0.840701i \(0.682144\pi\)
\(948\) −0.907472 −0.0294733
\(949\) −12.7554 −0.414059
\(950\) −1.68265 −0.0545924
\(951\) 15.7439 0.510531
\(952\) −3.85952 −0.125088
\(953\) −39.1884 −1.26944 −0.634719 0.772743i \(-0.718884\pi\)
−0.634719 + 0.772743i \(0.718884\pi\)
\(954\) −70.2945 −2.27587
\(955\) −21.0051 −0.679709
\(956\) −26.9323 −0.871053
\(957\) 0 0
\(958\) −6.40170 −0.206829
\(959\) 4.53062 0.146301
\(960\) −2.85952 −0.0922907
\(961\) −30.5340 −0.984967
\(962\) 8.09590 0.261022
\(963\) 37.1538 1.19726
\(964\) −11.7918 −0.379790
\(965\) −6.24967 −0.201184
\(966\) 19.6150 0.631101
\(967\) 23.8646 0.767435 0.383717 0.923451i \(-0.374644\pi\)
0.383717 + 0.923451i \(0.374644\pi\)
\(968\) 0 0
\(969\) −18.5704 −0.596567
\(970\) −16.6150 −0.533474
\(971\) −21.0479 −0.675461 −0.337730 0.941243i \(-0.609659\pi\)
−0.337730 + 0.941243i \(0.609659\pi\)
\(972\) 12.1851 0.390836
\(973\) 13.4017 0.429639
\(974\) −43.1738 −1.38338
\(975\) −6.22482 −0.199354
\(976\) 8.89592 0.284751
\(977\) −54.9177 −1.75697 −0.878486 0.477767i \(-0.841446\pi\)
−0.878486 + 0.477767i \(0.841446\pi\)
\(978\) 40.7803 1.30401
\(979\) 0 0
\(980\) 1.00000 0.0319438
\(981\) 69.3191 2.21319
\(982\) −33.2779 −1.06194
\(983\) −36.2912 −1.15751 −0.578754 0.815502i \(-0.696461\pi\)
−0.578754 + 0.815502i \(0.696461\pi\)
\(984\) 25.8398 0.823742
\(985\) 18.2612 0.581851
\(986\) 7.71905 0.245825
\(987\) −13.3901 −0.426213
\(988\) 3.66292 0.116533
\(989\) 40.1935 1.27808
\(990\) 0 0
\(991\) 6.83979 0.217273 0.108637 0.994082i \(-0.465352\pi\)
0.108637 + 0.994082i \(0.465352\pi\)
\(992\) −0.682649 −0.0216741
\(993\) 38.4976 1.22168
\(994\) 0.542173 0.0171967
\(995\) −22.1456 −0.702062
\(996\) 13.8959 0.440309
\(997\) 11.4694 0.363239 0.181619 0.983369i \(-0.441866\pi\)
0.181619 + 0.983369i \(0.441866\pi\)
\(998\) 22.6347 0.716489
\(999\) 23.1504 0.732446
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 8470.2.a.cj.1.1 3
11.10 odd 2 8470.2.a.cm.1.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8470.2.a.cj.1.1 3 1.1 even 1 trivial
8470.2.a.cm.1.1 yes 3 11.10 odd 2