Properties

Label 6025.2.a.f.1.5
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
Defining polynomial: \(x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 241)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.356270\) of defining polynomial
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.35627 q^{2} +2.45059 q^{3} -0.160532 q^{4} +3.32366 q^{6} +0.283608 q^{7} -2.93026 q^{8} +3.00540 q^{9} +O(q^{10})\) \(q+1.35627 q^{2} +2.45059 q^{3} -0.160532 q^{4} +3.32366 q^{6} +0.283608 q^{7} -2.93026 q^{8} +3.00540 q^{9} -4.12582 q^{11} -0.393399 q^{12} -0.0271909 q^{13} +0.384649 q^{14} -3.65317 q^{16} +1.28740 q^{17} +4.07613 q^{18} -5.72717 q^{19} +0.695007 q^{21} -5.59572 q^{22} +5.97702 q^{23} -7.18088 q^{24} -0.0368782 q^{26} +0.0132278 q^{27} -0.0455281 q^{28} -2.55610 q^{29} -2.02967 q^{31} +0.905851 q^{32} -10.1107 q^{33} +1.74607 q^{34} -0.482463 q^{36} -2.42844 q^{37} -7.76759 q^{38} -0.0666338 q^{39} -11.0324 q^{41} +0.942617 q^{42} -10.4984 q^{43} +0.662326 q^{44} +8.10645 q^{46} -4.54349 q^{47} -8.95242 q^{48} -6.91957 q^{49} +3.15490 q^{51} +0.00436502 q^{52} +9.30751 q^{53} +0.0179405 q^{54} -0.831046 q^{56} -14.0350 q^{57} -3.46676 q^{58} -9.94762 q^{59} +8.17350 q^{61} -2.75279 q^{62} +0.852354 q^{63} +8.53491 q^{64} -13.7128 q^{66} -4.40964 q^{67} -0.206670 q^{68} +14.6472 q^{69} -3.80954 q^{71} -8.80661 q^{72} +15.6571 q^{73} -3.29362 q^{74} +0.919395 q^{76} -1.17011 q^{77} -0.0903734 q^{78} +6.69229 q^{79} -8.98378 q^{81} -14.9629 q^{82} +4.32880 q^{83} -0.111571 q^{84} -14.2386 q^{86} -6.26396 q^{87} +12.0897 q^{88} +0.746861 q^{89} -0.00771155 q^{91} -0.959503 q^{92} -4.97390 q^{93} -6.16219 q^{94} +2.21987 q^{96} -11.9245 q^{97} -9.38480 q^{98} -12.3997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q + 4q^{2} + 3q^{3} + 2q^{4} - 5q^{6} + 7q^{7} + 6q^{8} - 2q^{9} - 18q^{11} - q^{12} + q^{13} - 6q^{14} + 4q^{16} + 2q^{17} - 8q^{18} - 6q^{19} - 2q^{21} - 10q^{22} + 22q^{23} - 3q^{24} + 8q^{26} - 3q^{27} - 9q^{28} - 16q^{29} - 18q^{31} + 6q^{32} - 4q^{33} + 11q^{34} - 7q^{36} - 8q^{37} - 16q^{38} - 9q^{39} - 15q^{41} - 19q^{42} - 14q^{43} - 4q^{44} + 11q^{46} + 10q^{47} - 31q^{48} + 6q^{49} + 13q^{51} - 27q^{52} - 15q^{53} + 16q^{54} + 13q^{56} - 14q^{57} - 17q^{58} - 18q^{59} + 4q^{61} - 13q^{62} + 16q^{63} + 2q^{64} + 16q^{66} - 18q^{67} + 15q^{68} + 26q^{69} - 50q^{71} - 30q^{72} + 10q^{74} - 20q^{76} - 17q^{77} + 32q^{78} - 15q^{79} - 9q^{81} - 45q^{82} + 24q^{83} + 6q^{84} - 23q^{86} - 12q^{87} - 8q^{88} - 13q^{89} - 12q^{91} + 10q^{92} - 14q^{93} - 32q^{94} - 15q^{96} - q^{97} - 9q^{98} - 20q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35627 0.959028 0.479514 0.877534i \(-0.340813\pi\)
0.479514 + 0.877534i \(0.340813\pi\)
\(3\) 2.45059 1.41485 0.707425 0.706789i \(-0.249857\pi\)
0.707425 + 0.706789i \(0.249857\pi\)
\(4\) −0.160532 −0.0802661
\(5\) 0 0
\(6\) 3.32366 1.35688
\(7\) 0.283608 0.107194 0.0535968 0.998563i \(-0.482931\pi\)
0.0535968 + 0.998563i \(0.482931\pi\)
\(8\) −2.93026 −1.03600
\(9\) 3.00540 1.00180
\(10\) 0 0
\(11\) −4.12582 −1.24398 −0.621990 0.783025i \(-0.713676\pi\)
−0.621990 + 0.783025i \(0.713676\pi\)
\(12\) −0.393399 −0.113564
\(13\) −0.0271909 −0.00754140 −0.00377070 0.999993i \(-0.501200\pi\)
−0.00377070 + 0.999993i \(0.501200\pi\)
\(14\) 0.384649 0.102802
\(15\) 0 0
\(16\) −3.65317 −0.913291
\(17\) 1.28740 0.312241 0.156121 0.987738i \(-0.450101\pi\)
0.156121 + 0.987738i \(0.450101\pi\)
\(18\) 4.07613 0.960753
\(19\) −5.72717 −1.31390 −0.656952 0.753933i \(-0.728154\pi\)
−0.656952 + 0.753933i \(0.728154\pi\)
\(20\) 0 0
\(21\) 0.695007 0.151663
\(22\) −5.59572 −1.19301
\(23\) 5.97702 1.24629 0.623147 0.782104i \(-0.285854\pi\)
0.623147 + 0.782104i \(0.285854\pi\)
\(24\) −7.18088 −1.46579
\(25\) 0 0
\(26\) −0.0368782 −0.00723241
\(27\) 0.0132278 0.00254570
\(28\) −0.0455281 −0.00860401
\(29\) −2.55610 −0.474656 −0.237328 0.971430i \(-0.576272\pi\)
−0.237328 + 0.971430i \(0.576272\pi\)
\(30\) 0 0
\(31\) −2.02967 −0.364540 −0.182270 0.983248i \(-0.558345\pi\)
−0.182270 + 0.983248i \(0.558345\pi\)
\(32\) 0.905851 0.160133
\(33\) −10.1107 −1.76005
\(34\) 1.74607 0.299448
\(35\) 0 0
\(36\) −0.482463 −0.0804105
\(37\) −2.42844 −0.399233 −0.199617 0.979874i \(-0.563970\pi\)
−0.199617 + 0.979874i \(0.563970\pi\)
\(38\) −7.76759 −1.26007
\(39\) −0.0666338 −0.0106700
\(40\) 0 0
\(41\) −11.0324 −1.72297 −0.861483 0.507786i \(-0.830464\pi\)
−0.861483 + 0.507786i \(0.830464\pi\)
\(42\) 0.942617 0.145449
\(43\) −10.4984 −1.60099 −0.800493 0.599342i \(-0.795429\pi\)
−0.800493 + 0.599342i \(0.795429\pi\)
\(44\) 0.662326 0.0998494
\(45\) 0 0
\(46\) 8.10645 1.19523
\(47\) −4.54349 −0.662736 −0.331368 0.943502i \(-0.607510\pi\)
−0.331368 + 0.943502i \(0.607510\pi\)
\(48\) −8.95242 −1.29217
\(49\) −6.91957 −0.988510
\(50\) 0 0
\(51\) 3.15490 0.441774
\(52\) 0.00436502 0.000605319 0
\(53\) 9.30751 1.27848 0.639242 0.769005i \(-0.279248\pi\)
0.639242 + 0.769005i \(0.279248\pi\)
\(54\) 0.0179405 0.00244140
\(55\) 0 0
\(56\) −0.831046 −0.111053
\(57\) −14.0350 −1.85898
\(58\) −3.46676 −0.455208
\(59\) −9.94762 −1.29507 −0.647535 0.762036i \(-0.724200\pi\)
−0.647535 + 0.762036i \(0.724200\pi\)
\(60\) 0 0
\(61\) 8.17350 1.04651 0.523255 0.852176i \(-0.324718\pi\)
0.523255 + 0.852176i \(0.324718\pi\)
\(62\) −2.75279 −0.349604
\(63\) 0.852354 0.107387
\(64\) 8.53491 1.06686
\(65\) 0 0
\(66\) −13.7128 −1.68793
\(67\) −4.40964 −0.538723 −0.269361 0.963039i \(-0.586813\pi\)
−0.269361 + 0.963039i \(0.586813\pi\)
\(68\) −0.206670 −0.0250624
\(69\) 14.6472 1.76332
\(70\) 0 0
\(71\) −3.80954 −0.452109 −0.226054 0.974115i \(-0.572583\pi\)
−0.226054 + 0.974115i \(0.572583\pi\)
\(72\) −8.80661 −1.03787
\(73\) 15.6571 1.83252 0.916261 0.400583i \(-0.131192\pi\)
0.916261 + 0.400583i \(0.131192\pi\)
\(74\) −3.29362 −0.382876
\(75\) 0 0
\(76\) 0.919395 0.105462
\(77\) −1.17011 −0.133347
\(78\) −0.0903734 −0.0102328
\(79\) 6.69229 0.752942 0.376471 0.926428i \(-0.377138\pi\)
0.376471 + 0.926428i \(0.377138\pi\)
\(80\) 0 0
\(81\) −8.98378 −0.998197
\(82\) −14.9629 −1.65237
\(83\) 4.32880 0.475147 0.237574 0.971370i \(-0.423648\pi\)
0.237574 + 0.971370i \(0.423648\pi\)
\(84\) −0.111571 −0.0121734
\(85\) 0 0
\(86\) −14.2386 −1.53539
\(87\) −6.26396 −0.671567
\(88\) 12.0897 1.28877
\(89\) 0.746861 0.0791671 0.0395835 0.999216i \(-0.487397\pi\)
0.0395835 + 0.999216i \(0.487397\pi\)
\(90\) 0 0
\(91\) −0.00771155 −0.000808391 0
\(92\) −0.959503 −0.100035
\(93\) −4.97390 −0.515770
\(94\) −6.16219 −0.635582
\(95\) 0 0
\(96\) 2.21987 0.226565
\(97\) −11.9245 −1.21075 −0.605373 0.795942i \(-0.706976\pi\)
−0.605373 + 0.795942i \(0.706976\pi\)
\(98\) −9.38480 −0.948008
\(99\) −12.3997 −1.24622
\(100\) 0 0
\(101\) 17.7456 1.76576 0.882878 0.469603i \(-0.155603\pi\)
0.882878 + 0.469603i \(0.155603\pi\)
\(102\) 4.27890 0.423674
\(103\) −5.10848 −0.503354 −0.251677 0.967811i \(-0.580982\pi\)
−0.251677 + 0.967811i \(0.580982\pi\)
\(104\) 0.0796766 0.00781293
\(105\) 0 0
\(106\) 12.6235 1.22610
\(107\) 0.619213 0.0598615 0.0299308 0.999552i \(-0.490471\pi\)
0.0299308 + 0.999552i \(0.490471\pi\)
\(108\) −0.00212349 −0.000204333 0
\(109\) 3.34125 0.320034 0.160017 0.987114i \(-0.448845\pi\)
0.160017 + 0.987114i \(0.448845\pi\)
\(110\) 0 0
\(111\) −5.95112 −0.564855
\(112\) −1.03607 −0.0978990
\(113\) 3.42957 0.322627 0.161313 0.986903i \(-0.448427\pi\)
0.161313 + 0.986903i \(0.448427\pi\)
\(114\) −19.0352 −1.78281
\(115\) 0 0
\(116\) 0.410336 0.0380988
\(117\) −0.0817195 −0.00755497
\(118\) −13.4917 −1.24201
\(119\) 0.365118 0.0334703
\(120\) 0 0
\(121\) 6.02237 0.547488
\(122\) 11.0855 1.00363
\(123\) −27.0358 −2.43774
\(124\) 0.325828 0.0292602
\(125\) 0 0
\(126\) 1.15602 0.102987
\(127\) −8.11791 −0.720348 −0.360174 0.932885i \(-0.617283\pi\)
−0.360174 + 0.932885i \(0.617283\pi\)
\(128\) 9.76394 0.863018
\(129\) −25.7272 −2.26516
\(130\) 0 0
\(131\) 2.73258 0.238747 0.119373 0.992849i \(-0.461911\pi\)
0.119373 + 0.992849i \(0.461911\pi\)
\(132\) 1.62309 0.141272
\(133\) −1.62427 −0.140842
\(134\) −5.98066 −0.516650
\(135\) 0 0
\(136\) −3.77243 −0.323483
\(137\) −5.47355 −0.467637 −0.233819 0.972280i \(-0.575122\pi\)
−0.233819 + 0.972280i \(0.575122\pi\)
\(138\) 19.8656 1.69107
\(139\) −16.3761 −1.38901 −0.694503 0.719490i \(-0.744376\pi\)
−0.694503 + 0.719490i \(0.744376\pi\)
\(140\) 0 0
\(141\) −11.1342 −0.937671
\(142\) −5.16676 −0.433585
\(143\) 0.112185 0.00938136
\(144\) −10.9792 −0.914935
\(145\) 0 0
\(146\) 21.2352 1.75744
\(147\) −16.9570 −1.39859
\(148\) 0.389843 0.0320449
\(149\) −15.2495 −1.24929 −0.624645 0.780909i \(-0.714756\pi\)
−0.624645 + 0.780909i \(0.714756\pi\)
\(150\) 0 0
\(151\) −3.19011 −0.259607 −0.129804 0.991540i \(-0.541435\pi\)
−0.129804 + 0.991540i \(0.541435\pi\)
\(152\) 16.7821 1.36121
\(153\) 3.86916 0.312803
\(154\) −1.58699 −0.127883
\(155\) 0 0
\(156\) 0.0106969 0.000856435 0
\(157\) −12.7755 −1.01959 −0.509797 0.860295i \(-0.670279\pi\)
−0.509797 + 0.860295i \(0.670279\pi\)
\(158\) 9.07655 0.722092
\(159\) 22.8089 1.80886
\(160\) 0 0
\(161\) 1.69513 0.133595
\(162\) −12.1844 −0.957299
\(163\) 14.1420 1.10769 0.553844 0.832620i \(-0.313160\pi\)
0.553844 + 0.832620i \(0.313160\pi\)
\(164\) 1.77105 0.138296
\(165\) 0 0
\(166\) 5.87102 0.455679
\(167\) −9.14541 −0.707693 −0.353846 0.935304i \(-0.615126\pi\)
−0.353846 + 0.935304i \(0.615126\pi\)
\(168\) −2.03655 −0.157124
\(169\) −12.9993 −0.999943
\(170\) 0 0
\(171\) −17.2124 −1.31627
\(172\) 1.68533 0.128505
\(173\) −14.0992 −1.07194 −0.535970 0.844237i \(-0.680054\pi\)
−0.535970 + 0.844237i \(0.680054\pi\)
\(174\) −8.49562 −0.644051
\(175\) 0 0
\(176\) 15.0723 1.13612
\(177\) −24.3776 −1.83233
\(178\) 1.01294 0.0759234
\(179\) 23.3458 1.74495 0.872474 0.488660i \(-0.162514\pi\)
0.872474 + 0.488660i \(0.162514\pi\)
\(180\) 0 0
\(181\) 19.8207 1.47326 0.736631 0.676295i \(-0.236415\pi\)
0.736631 + 0.676295i \(0.236415\pi\)
\(182\) −0.0104589 −0.000775269 0
\(183\) 20.0299 1.48065
\(184\) −17.5142 −1.29117
\(185\) 0 0
\(186\) −6.74595 −0.494637
\(187\) −5.31159 −0.388422
\(188\) 0.729375 0.0531952
\(189\) 0.00375152 0.000272883 0
\(190\) 0 0
\(191\) 1.89196 0.136898 0.0684488 0.997655i \(-0.478195\pi\)
0.0684488 + 0.997655i \(0.478195\pi\)
\(192\) 20.9156 1.50945
\(193\) −17.2319 −1.24038 −0.620189 0.784452i \(-0.712944\pi\)
−0.620189 + 0.784452i \(0.712944\pi\)
\(194\) −16.1728 −1.16114
\(195\) 0 0
\(196\) 1.11081 0.0793438
\(197\) −4.62238 −0.329331 −0.164665 0.986349i \(-0.552654\pi\)
−0.164665 + 0.986349i \(0.552654\pi\)
\(198\) −16.8174 −1.19516
\(199\) −17.7065 −1.25518 −0.627589 0.778545i \(-0.715958\pi\)
−0.627589 + 0.778545i \(0.715958\pi\)
\(200\) 0 0
\(201\) −10.8062 −0.762212
\(202\) 24.0679 1.69341
\(203\) −0.724930 −0.0508801
\(204\) −0.506463 −0.0354595
\(205\) 0 0
\(206\) −6.92848 −0.482730
\(207\) 17.9633 1.24854
\(208\) 0.0993329 0.00688750
\(209\) 23.6293 1.63447
\(210\) 0 0
\(211\) −11.1970 −0.770834 −0.385417 0.922742i \(-0.625942\pi\)
−0.385417 + 0.922742i \(0.625942\pi\)
\(212\) −1.49415 −0.102619
\(213\) −9.33561 −0.639666
\(214\) 0.839819 0.0574089
\(215\) 0 0
\(216\) −0.0387611 −0.00263736
\(217\) −0.575631 −0.0390764
\(218\) 4.53164 0.306921
\(219\) 38.3691 2.59274
\(220\) 0 0
\(221\) −0.0350057 −0.00235474
\(222\) −8.07132 −0.541711
\(223\) 2.90292 0.194394 0.0971969 0.995265i \(-0.469012\pi\)
0.0971969 + 0.995265i \(0.469012\pi\)
\(224\) 0.256906 0.0171653
\(225\) 0 0
\(226\) 4.65142 0.309408
\(227\) −21.4022 −1.42051 −0.710255 0.703944i \(-0.751421\pi\)
−0.710255 + 0.703944i \(0.751421\pi\)
\(228\) 2.25306 0.149213
\(229\) 17.5833 1.16194 0.580968 0.813926i \(-0.302674\pi\)
0.580968 + 0.813926i \(0.302674\pi\)
\(230\) 0 0
\(231\) −2.86747 −0.188666
\(232\) 7.49005 0.491746
\(233\) 28.8991 1.89324 0.946621 0.322348i \(-0.104472\pi\)
0.946621 + 0.322348i \(0.104472\pi\)
\(234\) −0.110834 −0.00724543
\(235\) 0 0
\(236\) 1.59691 0.103950
\(237\) 16.4001 1.06530
\(238\) 0.495198 0.0320989
\(239\) 25.6630 1.66000 0.830000 0.557763i \(-0.188340\pi\)
0.830000 + 0.557763i \(0.188340\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157
\(242\) 8.16796 0.525056
\(243\) −22.0553 −1.41484
\(244\) −1.31211 −0.0839992
\(245\) 0 0
\(246\) −36.6679 −2.33786
\(247\) 0.155727 0.00990868
\(248\) 5.94748 0.377665
\(249\) 10.6081 0.672262
\(250\) 0 0
\(251\) −28.3138 −1.78715 −0.893576 0.448913i \(-0.851811\pi\)
−0.893576 + 0.448913i \(0.851811\pi\)
\(252\) −0.136830 −0.00861949
\(253\) −24.6601 −1.55037
\(254\) −11.0101 −0.690833
\(255\) 0 0
\(256\) −3.82728 −0.239205
\(257\) 17.0359 1.06267 0.531336 0.847161i \(-0.321690\pi\)
0.531336 + 0.847161i \(0.321690\pi\)
\(258\) −34.8931 −2.17235
\(259\) −0.688725 −0.0427953
\(260\) 0 0
\(261\) −7.68210 −0.475510
\(262\) 3.70611 0.228965
\(263\) 21.9895 1.35593 0.677966 0.735094i \(-0.262862\pi\)
0.677966 + 0.735094i \(0.262862\pi\)
\(264\) 29.6270 1.82342
\(265\) 0 0
\(266\) −2.20295 −0.135071
\(267\) 1.83025 0.112009
\(268\) 0.707888 0.0432412
\(269\) 8.91005 0.543255 0.271628 0.962402i \(-0.412438\pi\)
0.271628 + 0.962402i \(0.412438\pi\)
\(270\) 0 0
\(271\) 29.9968 1.82218 0.911088 0.412213i \(-0.135244\pi\)
0.911088 + 0.412213i \(0.135244\pi\)
\(272\) −4.70310 −0.285167
\(273\) −0.0188979 −0.00114375
\(274\) −7.42362 −0.448477
\(275\) 0 0
\(276\) −2.35135 −0.141535
\(277\) 14.9125 0.896007 0.448003 0.894032i \(-0.352135\pi\)
0.448003 + 0.894032i \(0.352135\pi\)
\(278\) −22.2105 −1.33210
\(279\) −6.09998 −0.365196
\(280\) 0 0
\(281\) −28.8871 −1.72326 −0.861631 0.507535i \(-0.830557\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(282\) −15.1010 −0.899253
\(283\) 16.5841 0.985820 0.492910 0.870080i \(-0.335933\pi\)
0.492910 + 0.870080i \(0.335933\pi\)
\(284\) 0.611553 0.0362890
\(285\) 0 0
\(286\) 0.152153 0.00899698
\(287\) −3.12886 −0.184691
\(288\) 2.72244 0.160422
\(289\) −15.3426 −0.902505
\(290\) 0 0
\(291\) −29.2220 −1.71302
\(292\) −2.51346 −0.147089
\(293\) 11.2756 0.658729 0.329364 0.944203i \(-0.393166\pi\)
0.329364 + 0.944203i \(0.393166\pi\)
\(294\) −22.9983 −1.34129
\(295\) 0 0
\(296\) 7.11597 0.413608
\(297\) −0.0545757 −0.00316680
\(298\) −20.6825 −1.19810
\(299\) −0.162521 −0.00939881
\(300\) 0 0
\(301\) −2.97742 −0.171616
\(302\) −4.32665 −0.248971
\(303\) 43.4873 2.49828
\(304\) 20.9223 1.19998
\(305\) 0 0
\(306\) 5.24762 0.299987
\(307\) 1.24678 0.0711575 0.0355787 0.999367i \(-0.488673\pi\)
0.0355787 + 0.999367i \(0.488673\pi\)
\(308\) 0.187841 0.0107032
\(309\) −12.5188 −0.712170
\(310\) 0 0
\(311\) −17.8941 −1.01468 −0.507340 0.861746i \(-0.669371\pi\)
−0.507340 + 0.861746i \(0.669371\pi\)
\(312\) 0.195255 0.0110541
\(313\) 30.0820 1.70033 0.850166 0.526514i \(-0.176501\pi\)
0.850166 + 0.526514i \(0.176501\pi\)
\(314\) −17.3270 −0.977818
\(315\) 0 0
\(316\) −1.07433 −0.0604357
\(317\) 8.17835 0.459342 0.229671 0.973268i \(-0.426235\pi\)
0.229671 + 0.973268i \(0.426235\pi\)
\(318\) 30.9350 1.73475
\(319\) 10.5460 0.590463
\(320\) 0 0
\(321\) 1.51744 0.0846951
\(322\) 2.29905 0.128121
\(323\) −7.37318 −0.410255
\(324\) 1.44218 0.0801214
\(325\) 0 0
\(326\) 19.1804 1.06230
\(327\) 8.18805 0.452800
\(328\) 32.3278 1.78500
\(329\) −1.28857 −0.0710410
\(330\) 0 0
\(331\) 13.4643 0.740067 0.370034 0.929018i \(-0.379346\pi\)
0.370034 + 0.929018i \(0.379346\pi\)
\(332\) −0.694911 −0.0381382
\(333\) −7.29843 −0.399952
\(334\) −12.4036 −0.678697
\(335\) 0 0
\(336\) −2.53897 −0.138512
\(337\) 6.06342 0.330295 0.165148 0.986269i \(-0.447190\pi\)
0.165148 + 0.986269i \(0.447190\pi\)
\(338\) −17.6305 −0.958973
\(339\) 8.40448 0.456469
\(340\) 0 0
\(341\) 8.37407 0.453481
\(342\) −23.3447 −1.26234
\(343\) −3.94770 −0.213156
\(344\) 30.7630 1.65863
\(345\) 0 0
\(346\) −19.1223 −1.02802
\(347\) −23.7297 −1.27388 −0.636938 0.770915i \(-0.719799\pi\)
−0.636938 + 0.770915i \(0.719799\pi\)
\(348\) 1.00557 0.0539040
\(349\) 8.46091 0.452902 0.226451 0.974023i \(-0.427288\pi\)
0.226451 + 0.974023i \(0.427288\pi\)
\(350\) 0 0
\(351\) −0.000359677 0 −1.91982e−5 0
\(352\) −3.73738 −0.199203
\(353\) −6.66847 −0.354927 −0.177463 0.984127i \(-0.556789\pi\)
−0.177463 + 0.984127i \(0.556789\pi\)
\(354\) −33.0625 −1.75725
\(355\) 0 0
\(356\) −0.119895 −0.00635443
\(357\) 0.894754 0.0473554
\(358\) 31.6632 1.67345
\(359\) −28.3212 −1.49474 −0.747369 0.664409i \(-0.768683\pi\)
−0.747369 + 0.664409i \(0.768683\pi\)
\(360\) 0 0
\(361\) 13.8005 0.726342
\(362\) 26.8822 1.41290
\(363\) 14.7584 0.774614
\(364\) 0.00123795 6.48863e−5 0
\(365\) 0 0
\(366\) 27.1660 1.41999
\(367\) −7.48573 −0.390752 −0.195376 0.980728i \(-0.562593\pi\)
−0.195376 + 0.980728i \(0.562593\pi\)
\(368\) −21.8350 −1.13823
\(369\) −33.1566 −1.72607
\(370\) 0 0
\(371\) 2.63968 0.137045
\(372\) 0.798471 0.0413988
\(373\) −17.6125 −0.911943 −0.455972 0.889994i \(-0.650708\pi\)
−0.455972 + 0.889994i \(0.650708\pi\)
\(374\) −7.20395 −0.372507
\(375\) 0 0
\(376\) 13.3136 0.686597
\(377\) 0.0695028 0.00357957
\(378\) 0.00508807 0.000261702 0
\(379\) 7.61632 0.391224 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(380\) 0 0
\(381\) −19.8937 −1.01918
\(382\) 2.56601 0.131289
\(383\) 27.2242 1.39109 0.695546 0.718482i \(-0.255163\pi\)
0.695546 + 0.718482i \(0.255163\pi\)
\(384\) 23.9274 1.22104
\(385\) 0 0
\(386\) −23.3711 −1.18956
\(387\) −31.5518 −1.60387
\(388\) 1.91426 0.0971818
\(389\) 23.0380 1.16807 0.584036 0.811728i \(-0.301473\pi\)
0.584036 + 0.811728i \(0.301473\pi\)
\(390\) 0 0
\(391\) 7.69483 0.389145
\(392\) 20.2762 1.02410
\(393\) 6.69643 0.337790
\(394\) −6.26920 −0.315837
\(395\) 0 0
\(396\) 1.99055 0.100029
\(397\) 17.0475 0.855587 0.427794 0.903876i \(-0.359291\pi\)
0.427794 + 0.903876i \(0.359291\pi\)
\(398\) −24.0147 −1.20375
\(399\) −3.98042 −0.199270
\(400\) 0 0
\(401\) 6.19034 0.309131 0.154565 0.987983i \(-0.450602\pi\)
0.154565 + 0.987983i \(0.450602\pi\)
\(402\) −14.6561 −0.730982
\(403\) 0.0551887 0.00274914
\(404\) −2.84874 −0.141730
\(405\) 0 0
\(406\) −0.983201 −0.0487954
\(407\) 10.0193 0.496638
\(408\) −9.24469 −0.457680
\(409\) 11.3675 0.562088 0.281044 0.959695i \(-0.409319\pi\)
0.281044 + 0.959695i \(0.409319\pi\)
\(410\) 0 0
\(411\) −13.4134 −0.661636
\(412\) 0.820076 0.0404022
\(413\) −2.82122 −0.138823
\(414\) 24.3631 1.19738
\(415\) 0 0
\(416\) −0.0246309 −0.00120763
\(417\) −40.1312 −1.96523
\(418\) 32.0477 1.56750
\(419\) 4.14954 0.202718 0.101359 0.994850i \(-0.467681\pi\)
0.101359 + 0.994850i \(0.467681\pi\)
\(420\) 0 0
\(421\) −1.44805 −0.0705734 −0.0352867 0.999377i \(-0.511234\pi\)
−0.0352867 + 0.999377i \(0.511234\pi\)
\(422\) −15.1862 −0.739251
\(423\) −13.6550 −0.663928
\(424\) −27.2735 −1.32452
\(425\) 0 0
\(426\) −12.6616 −0.613457
\(427\) 2.31807 0.112179
\(428\) −0.0994035 −0.00480485
\(429\) 0.274919 0.0132732
\(430\) 0 0
\(431\) −22.1450 −1.06669 −0.533344 0.845898i \(-0.679065\pi\)
−0.533344 + 0.845898i \(0.679065\pi\)
\(432\) −0.0483235 −0.00232497
\(433\) −10.3894 −0.499284 −0.249642 0.968338i \(-0.580313\pi\)
−0.249642 + 0.968338i \(0.580313\pi\)
\(434\) −0.780711 −0.0374753
\(435\) 0 0
\(436\) −0.536378 −0.0256879
\(437\) −34.2314 −1.63751
\(438\) 52.0388 2.48651
\(439\) 39.5672 1.88844 0.944220 0.329316i \(-0.106818\pi\)
0.944220 + 0.329316i \(0.106818\pi\)
\(440\) 0 0
\(441\) −20.7961 −0.990288
\(442\) −0.0474771 −0.00225826
\(443\) 2.60234 0.123641 0.0618203 0.998087i \(-0.480309\pi\)
0.0618203 + 0.998087i \(0.480309\pi\)
\(444\) 0.955345 0.0453387
\(445\) 0 0
\(446\) 3.93714 0.186429
\(447\) −37.3703 −1.76756
\(448\) 2.42057 0.114361
\(449\) −29.9486 −1.41336 −0.706681 0.707533i \(-0.749808\pi\)
−0.706681 + 0.707533i \(0.749808\pi\)
\(450\) 0 0
\(451\) 45.5175 2.14334
\(452\) −0.550556 −0.0258960
\(453\) −7.81765 −0.367305
\(454\) −29.0271 −1.36231
\(455\) 0 0
\(456\) 41.1261 1.92591
\(457\) 14.5052 0.678526 0.339263 0.940691i \(-0.389822\pi\)
0.339263 + 0.940691i \(0.389822\pi\)
\(458\) 23.8477 1.11433
\(459\) 0.0170296 0.000794872 0
\(460\) 0 0
\(461\) 38.4334 1.79002 0.895011 0.446044i \(-0.147168\pi\)
0.895011 + 0.446044i \(0.147168\pi\)
\(462\) −3.88906 −0.180936
\(463\) −36.2326 −1.68387 −0.841936 0.539578i \(-0.818584\pi\)
−0.841936 + 0.539578i \(0.818584\pi\)
\(464\) 9.33786 0.433499
\(465\) 0 0
\(466\) 39.1950 1.81567
\(467\) 25.1111 1.16200 0.581001 0.813903i \(-0.302661\pi\)
0.581001 + 0.813903i \(0.302661\pi\)
\(468\) 0.0131186 0.000606408 0
\(469\) −1.25061 −0.0577477
\(470\) 0 0
\(471\) −31.3074 −1.44257
\(472\) 29.1492 1.34170
\(473\) 43.3144 1.99160
\(474\) 22.2429 1.02165
\(475\) 0 0
\(476\) −0.0586131 −0.00268653
\(477\) 27.9728 1.28079
\(478\) 34.8059 1.59199
\(479\) −22.0372 −1.00691 −0.503454 0.864022i \(-0.667938\pi\)
−0.503454 + 0.864022i \(0.667938\pi\)
\(480\) 0 0
\(481\) 0.0660315 0.00301078
\(482\) −1.35627 −0.0617764
\(483\) 4.15407 0.189017
\(484\) −0.966784 −0.0439447
\(485\) 0 0
\(486\) −29.9129 −1.35688
\(487\) 15.1309 0.685649 0.342824 0.939400i \(-0.388616\pi\)
0.342824 + 0.939400i \(0.388616\pi\)
\(488\) −23.9505 −1.08419
\(489\) 34.6563 1.56721
\(490\) 0 0
\(491\) −40.4874 −1.82717 −0.913585 0.406649i \(-0.866697\pi\)
−0.913585 + 0.406649i \(0.866697\pi\)
\(492\) 4.34012 0.195668
\(493\) −3.29073 −0.148207
\(494\) 0.211208 0.00950269
\(495\) 0 0
\(496\) 7.41473 0.332931
\(497\) −1.08041 −0.0484632
\(498\) 14.3875 0.644718
\(499\) −22.5598 −1.00992 −0.504959 0.863144i \(-0.668492\pi\)
−0.504959 + 0.863144i \(0.668492\pi\)
\(500\) 0 0
\(501\) −22.4117 −1.00128
\(502\) −38.4012 −1.71393
\(503\) −25.5277 −1.13823 −0.569113 0.822259i \(-0.692713\pi\)
−0.569113 + 0.822259i \(0.692713\pi\)
\(504\) −2.49762 −0.111253
\(505\) 0 0
\(506\) −33.4457 −1.48684
\(507\) −31.8559 −1.41477
\(508\) 1.30318 0.0578195
\(509\) −16.9047 −0.749287 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(510\) 0 0
\(511\) 4.44047 0.196435
\(512\) −24.7187 −1.09242
\(513\) −0.0757581 −0.00334480
\(514\) 23.1053 1.01913
\(515\) 0 0
\(516\) 4.13004 0.181815
\(517\) 18.7456 0.824430
\(518\) −0.934096 −0.0410418
\(519\) −34.5513 −1.51663
\(520\) 0 0
\(521\) 28.9409 1.26792 0.633961 0.773365i \(-0.281428\pi\)
0.633961 + 0.773365i \(0.281428\pi\)
\(522\) −10.4190 −0.456027
\(523\) −15.3129 −0.669586 −0.334793 0.942292i \(-0.608666\pi\)
−0.334793 + 0.942292i \(0.608666\pi\)
\(524\) −0.438667 −0.0191632
\(525\) 0 0
\(526\) 29.8237 1.30038
\(527\) −2.61301 −0.113824
\(528\) 36.9360 1.60743
\(529\) 12.7248 0.553250
\(530\) 0 0
\(531\) −29.8966 −1.29740
\(532\) 0.260748 0.0113048
\(533\) 0.299980 0.0129936
\(534\) 2.48231 0.107420
\(535\) 0 0
\(536\) 12.9214 0.558120
\(537\) 57.2111 2.46884
\(538\) 12.0844 0.520997
\(539\) 28.5489 1.22969
\(540\) 0 0
\(541\) 11.0774 0.476253 0.238127 0.971234i \(-0.423467\pi\)
0.238127 + 0.971234i \(0.423467\pi\)
\(542\) 40.6837 1.74752
\(543\) 48.5725 2.08444
\(544\) 1.16620 0.0500002
\(545\) 0 0
\(546\) −0.0256306 −0.00109689
\(547\) −4.93535 −0.211020 −0.105510 0.994418i \(-0.533648\pi\)
−0.105510 + 0.994418i \(0.533648\pi\)
\(548\) 0.878681 0.0375354
\(549\) 24.5646 1.04839
\(550\) 0 0
\(551\) 14.6392 0.623652
\(552\) −42.9203 −1.82681
\(553\) 1.89799 0.0807106
\(554\) 20.2254 0.859295
\(555\) 0 0
\(556\) 2.62890 0.111490
\(557\) 14.0586 0.595681 0.297840 0.954616i \(-0.403734\pi\)
0.297840 + 0.954616i \(0.403734\pi\)
\(558\) −8.27322 −0.350233
\(559\) 0.285460 0.0120737
\(560\) 0 0
\(561\) −13.0165 −0.549559
\(562\) −39.1788 −1.65266
\(563\) −44.3164 −1.86771 −0.933856 0.357650i \(-0.883578\pi\)
−0.933856 + 0.357650i \(0.883578\pi\)
\(564\) 1.78740 0.0752632
\(565\) 0 0
\(566\) 22.4925 0.945429
\(567\) −2.54787 −0.107000
\(568\) 11.1629 0.468387
\(569\) −6.64972 −0.278771 −0.139385 0.990238i \(-0.544513\pi\)
−0.139385 + 0.990238i \(0.544513\pi\)
\(570\) 0 0
\(571\) −22.3573 −0.935625 −0.467812 0.883828i \(-0.654958\pi\)
−0.467812 + 0.883828i \(0.654958\pi\)
\(572\) −0.0180093 −0.000753005 0
\(573\) 4.63642 0.193689
\(574\) −4.24358 −0.177124
\(575\) 0 0
\(576\) 25.6508 1.06878
\(577\) −33.2047 −1.38233 −0.691165 0.722697i \(-0.742902\pi\)
−0.691165 + 0.722697i \(0.742902\pi\)
\(578\) −20.8087 −0.865528
\(579\) −42.2283 −1.75495
\(580\) 0 0
\(581\) 1.22768 0.0509328
\(582\) −39.6329 −1.64284
\(583\) −38.4011 −1.59041
\(584\) −45.8794 −1.89850
\(585\) 0 0
\(586\) 15.2928 0.631739
\(587\) −28.0737 −1.15873 −0.579363 0.815069i \(-0.696699\pi\)
−0.579363 + 0.815069i \(0.696699\pi\)
\(588\) 2.72215 0.112259
\(589\) 11.6243 0.478971
\(590\) 0 0
\(591\) −11.3276 −0.465954
\(592\) 8.87150 0.364616
\(593\) 0.499968 0.0205312 0.0102656 0.999947i \(-0.496732\pi\)
0.0102656 + 0.999947i \(0.496732\pi\)
\(594\) −0.0740193 −0.00303705
\(595\) 0 0
\(596\) 2.44804 0.100276
\(597\) −43.3913 −1.77589
\(598\) −0.220422 −0.00901372
\(599\) −5.66864 −0.231614 −0.115807 0.993272i \(-0.536945\pi\)
−0.115807 + 0.993272i \(0.536945\pi\)
\(600\) 0 0
\(601\) 22.5848 0.921252 0.460626 0.887594i \(-0.347625\pi\)
0.460626 + 0.887594i \(0.347625\pi\)
\(602\) −4.03818 −0.164584
\(603\) −13.2527 −0.539692
\(604\) 0.512115 0.0208377
\(605\) 0 0
\(606\) 58.9805 2.39592
\(607\) 4.01260 0.162867 0.0814333 0.996679i \(-0.474050\pi\)
0.0814333 + 0.996679i \(0.474050\pi\)
\(608\) −5.18797 −0.210400
\(609\) −1.77651 −0.0719877
\(610\) 0 0
\(611\) 0.123542 0.00499796
\(612\) −0.621124 −0.0251075
\(613\) 31.5947 1.27610 0.638048 0.769996i \(-0.279742\pi\)
0.638048 + 0.769996i \(0.279742\pi\)
\(614\) 1.69097 0.0682420
\(615\) 0 0
\(616\) 3.42874 0.138148
\(617\) 2.64125 0.106333 0.0531664 0.998586i \(-0.483069\pi\)
0.0531664 + 0.998586i \(0.483069\pi\)
\(618\) −16.9789 −0.682991
\(619\) 13.8609 0.557115 0.278558 0.960419i \(-0.410144\pi\)
0.278558 + 0.960419i \(0.410144\pi\)
\(620\) 0 0
\(621\) 0.0790631 0.00317269
\(622\) −24.2692 −0.973106
\(623\) 0.211815 0.00848621
\(624\) 0.243424 0.00974477
\(625\) 0 0
\(626\) 40.7992 1.63067
\(627\) 57.9057 2.31253
\(628\) 2.05087 0.0818387
\(629\) −3.12638 −0.124657
\(630\) 0 0
\(631\) −28.9779 −1.15359 −0.576795 0.816889i \(-0.695697\pi\)
−0.576795 + 0.816889i \(0.695697\pi\)
\(632\) −19.6102 −0.780051
\(633\) −27.4393 −1.09061
\(634\) 11.0921 0.440522
\(635\) 0 0
\(636\) −3.66156 −0.145190
\(637\) 0.188149 0.00745475
\(638\) 14.3032 0.566271
\(639\) −11.4492 −0.452922
\(640\) 0 0
\(641\) −36.8202 −1.45431 −0.727154 0.686474i \(-0.759158\pi\)
−0.727154 + 0.686474i \(0.759158\pi\)
\(642\) 2.05805 0.0812249
\(643\) −14.9327 −0.588890 −0.294445 0.955668i \(-0.595135\pi\)
−0.294445 + 0.955668i \(0.595135\pi\)
\(644\) −0.272123 −0.0107231
\(645\) 0 0
\(646\) −10.0000 −0.393446
\(647\) −1.09720 −0.0431356 −0.0215678 0.999767i \(-0.506866\pi\)
−0.0215678 + 0.999767i \(0.506866\pi\)
\(648\) 26.3248 1.03414
\(649\) 41.0421 1.61104
\(650\) 0 0
\(651\) −1.41064 −0.0552872
\(652\) −2.27025 −0.0889097
\(653\) −9.51269 −0.372260 −0.186130 0.982525i \(-0.559595\pi\)
−0.186130 + 0.982525i \(0.559595\pi\)
\(654\) 11.1052 0.434248
\(655\) 0 0
\(656\) 40.3031 1.57357
\(657\) 47.0557 1.83582
\(658\) −1.74765 −0.0681303
\(659\) 3.98928 0.155400 0.0777001 0.996977i \(-0.475242\pi\)
0.0777001 + 0.996977i \(0.475242\pi\)
\(660\) 0 0
\(661\) −25.6014 −0.995780 −0.497890 0.867240i \(-0.665892\pi\)
−0.497890 + 0.867240i \(0.665892\pi\)
\(662\) 18.2613 0.709745
\(663\) −0.0857846 −0.00333160
\(664\) −12.6845 −0.492255
\(665\) 0 0
\(666\) −9.89864 −0.383565
\(667\) −15.2779 −0.591561
\(668\) 1.46813 0.0568037
\(669\) 7.11387 0.275038
\(670\) 0 0
\(671\) −33.7224 −1.30184
\(672\) 0.629573 0.0242863
\(673\) −0.273027 −0.0105244 −0.00526221 0.999986i \(-0.501675\pi\)
−0.00526221 + 0.999986i \(0.501675\pi\)
\(674\) 8.22363 0.316762
\(675\) 0 0
\(676\) 2.08680 0.0802615
\(677\) 5.73279 0.220329 0.110165 0.993913i \(-0.464862\pi\)
0.110165 + 0.993913i \(0.464862\pi\)
\(678\) 11.3987 0.437766
\(679\) −3.38187 −0.129784
\(680\) 0 0
\(681\) −52.4479 −2.00981
\(682\) 11.3575 0.434901
\(683\) 18.8046 0.719538 0.359769 0.933041i \(-0.382855\pi\)
0.359769 + 0.933041i \(0.382855\pi\)
\(684\) 2.76315 0.105652
\(685\) 0 0
\(686\) −5.35414 −0.204422
\(687\) 43.0895 1.64397
\(688\) 38.3523 1.46217
\(689\) −0.253080 −0.00964157
\(690\) 0 0
\(691\) 15.8329 0.602310 0.301155 0.953575i \(-0.402628\pi\)
0.301155 + 0.953575i \(0.402628\pi\)
\(692\) 2.26337 0.0860403
\(693\) −3.51666 −0.133587
\(694\) −32.1838 −1.22168
\(695\) 0 0
\(696\) 18.3551 0.695747
\(697\) −14.2031 −0.537981
\(698\) 11.4753 0.434346
\(699\) 70.8199 2.67865
\(700\) 0 0
\(701\) 40.3523 1.52409 0.762043 0.647527i \(-0.224197\pi\)
0.762043 + 0.647527i \(0.224197\pi\)
\(702\) −0.000487819 0 −1.84116e−5 0
\(703\) 13.9081 0.524554
\(704\) −35.2135 −1.32716
\(705\) 0 0
\(706\) −9.04425 −0.340385
\(707\) 5.03280 0.189278
\(708\) 3.91338 0.147074
\(709\) −41.5401 −1.56007 −0.780036 0.625734i \(-0.784800\pi\)
−0.780036 + 0.625734i \(0.784800\pi\)
\(710\) 0 0
\(711\) 20.1130 0.754296
\(712\) −2.18850 −0.0820175
\(713\) −12.1314 −0.454325
\(714\) 1.21353 0.0454151
\(715\) 0 0
\(716\) −3.74775 −0.140060
\(717\) 62.8895 2.34865
\(718\) −38.4112 −1.43349
\(719\) −10.2324 −0.381603 −0.190801 0.981629i \(-0.561109\pi\)
−0.190801 + 0.981629i \(0.561109\pi\)
\(720\) 0 0
\(721\) −1.44881 −0.0539563
\(722\) 18.7172 0.696582
\(723\) −2.45059 −0.0911385
\(724\) −3.18186 −0.118253
\(725\) 0 0
\(726\) 20.0163 0.742876
\(727\) 45.5533 1.68948 0.844739 0.535178i \(-0.179756\pi\)
0.844739 + 0.535178i \(0.179756\pi\)
\(728\) 0.0225969 0.000837497 0
\(729\) −27.0971 −1.00360
\(730\) 0 0
\(731\) −13.5156 −0.499894
\(732\) −3.21544 −0.118846
\(733\) 20.6241 0.761770 0.380885 0.924622i \(-0.375619\pi\)
0.380885 + 0.924622i \(0.375619\pi\)
\(734\) −10.1527 −0.374742
\(735\) 0 0
\(736\) 5.41429 0.199573
\(737\) 18.1934 0.670161
\(738\) −44.9694 −1.65535
\(739\) −17.1975 −0.632620 −0.316310 0.948656i \(-0.602444\pi\)
−0.316310 + 0.948656i \(0.602444\pi\)
\(740\) 0 0
\(741\) 0.381623 0.0140193
\(742\) 3.58012 0.131430
\(743\) 40.8356 1.49811 0.749056 0.662506i \(-0.230507\pi\)
0.749056 + 0.662506i \(0.230507\pi\)
\(744\) 14.5748 0.534340
\(745\) 0 0
\(746\) −23.8874 −0.874579
\(747\) 13.0098 0.476002
\(748\) 0.852681 0.0311771
\(749\) 0.175613 0.00641678
\(750\) 0 0
\(751\) 20.2798 0.740021 0.370010 0.929028i \(-0.379354\pi\)
0.370010 + 0.929028i \(0.379354\pi\)
\(752\) 16.5981 0.605271
\(753\) −69.3856 −2.52855
\(754\) 0.0942645 0.00343291
\(755\) 0 0
\(756\) −0.000602239 0 −2.19032e−5 0
\(757\) −13.7148 −0.498473 −0.249237 0.968443i \(-0.580180\pi\)
−0.249237 + 0.968443i \(0.580180\pi\)
\(758\) 10.3298 0.375194
\(759\) −60.4318 −2.19354
\(760\) 0 0
\(761\) −6.41706 −0.232618 −0.116309 0.993213i \(-0.537106\pi\)
−0.116309 + 0.993213i \(0.537106\pi\)
\(762\) −26.9812 −0.977425
\(763\) 0.947605 0.0343056
\(764\) −0.303721 −0.0109882
\(765\) 0 0
\(766\) 36.9234 1.33410
\(767\) 0.270485 0.00976665
\(768\) −9.37911 −0.338439
\(769\) −27.8170 −1.00311 −0.501553 0.865127i \(-0.667238\pi\)
−0.501553 + 0.865127i \(0.667238\pi\)
\(770\) 0 0
\(771\) 41.7481 1.50352
\(772\) 2.76627 0.0995603
\(773\) −12.8524 −0.462270 −0.231135 0.972922i \(-0.574244\pi\)
−0.231135 + 0.972922i \(0.574244\pi\)
\(774\) −42.7927 −1.53815
\(775\) 0 0
\(776\) 34.9418 1.25434
\(777\) −1.68778 −0.0605489
\(778\) 31.2457 1.12021
\(779\) 63.1843 2.26381
\(780\) 0 0
\(781\) 15.7174 0.562414
\(782\) 10.4363 0.373200
\(783\) −0.0338117 −0.00120833
\(784\) 25.2783 0.902797
\(785\) 0 0
\(786\) 9.08217 0.323950
\(787\) −9.53803 −0.339994 −0.169997 0.985445i \(-0.554376\pi\)
−0.169997 + 0.985445i \(0.554376\pi\)
\(788\) 0.742040 0.0264341
\(789\) 53.8873 1.91844
\(790\) 0 0
\(791\) 0.972653 0.0345836
\(792\) 36.3345 1.29109
\(793\) −0.222245 −0.00789215
\(794\) 23.1209 0.820532
\(795\) 0 0
\(796\) 2.84246 0.100748
\(797\) 7.72801 0.273740 0.136870 0.990589i \(-0.456296\pi\)
0.136870 + 0.990589i \(0.456296\pi\)
\(798\) −5.39853 −0.191106
\(799\) −5.84930 −0.206933
\(800\) 0 0
\(801\) 2.24461 0.0793095
\(802\) 8.39577 0.296465
\(803\) −64.5982 −2.27962
\(804\) 1.73474 0.0611797
\(805\) 0 0
\(806\) 0.0748508 0.00263651
\(807\) 21.8349 0.768624
\(808\) −51.9994 −1.82933
\(809\) −1.99109 −0.0700030 −0.0350015 0.999387i \(-0.511144\pi\)
−0.0350015 + 0.999387i \(0.511144\pi\)
\(810\) 0 0
\(811\) 28.5346 1.00198 0.500992 0.865452i \(-0.332969\pi\)
0.500992 + 0.865452i \(0.332969\pi\)
\(812\) 0.116375 0.00408395
\(813\) 73.5099 2.57810
\(814\) 13.5889 0.476290
\(815\) 0 0
\(816\) −11.5254 −0.403469
\(817\) 60.1260 2.10354
\(818\) 15.4174 0.539058
\(819\) −0.0231763 −0.000809845 0
\(820\) 0 0
\(821\) 48.3459 1.68728 0.843642 0.536907i \(-0.180407\pi\)
0.843642 + 0.536907i \(0.180407\pi\)
\(822\) −18.1922 −0.634528
\(823\) 36.4809 1.27164 0.635821 0.771836i \(-0.280662\pi\)
0.635821 + 0.771836i \(0.280662\pi\)
\(824\) 14.9692 0.521477
\(825\) 0 0
\(826\) −3.82634 −0.133135
\(827\) −23.2928 −0.809971 −0.404985 0.914323i \(-0.632723\pi\)
−0.404985 + 0.914323i \(0.632723\pi\)
\(828\) −2.88369 −0.100215
\(829\) −29.8113 −1.03539 −0.517695 0.855565i \(-0.673210\pi\)
−0.517695 + 0.855565i \(0.673210\pi\)
\(830\) 0 0
\(831\) 36.5445 1.26771
\(832\) −0.232072 −0.00804565
\(833\) −8.90827 −0.308653
\(834\) −54.4288 −1.88471
\(835\) 0 0
\(836\) −3.79326 −0.131193
\(837\) −0.0268482 −0.000928010 0
\(838\) 5.62790 0.194412
\(839\) −48.3508 −1.66925 −0.834627 0.550815i \(-0.814317\pi\)
−0.834627 + 0.550815i \(0.814317\pi\)
\(840\) 0 0
\(841\) −22.4663 −0.774702
\(842\) −1.96394 −0.0676819
\(843\) −70.7906 −2.43816
\(844\) 1.79748 0.0618718
\(845\) 0 0
\(846\) −18.5198 −0.636725
\(847\) 1.70799 0.0586873
\(848\) −34.0019 −1.16763
\(849\) 40.6408 1.39479
\(850\) 0 0
\(851\) −14.5148 −0.497562
\(852\) 1.49867 0.0513434
\(853\) −5.13297 −0.175750 −0.0878748 0.996132i \(-0.528008\pi\)
−0.0878748 + 0.996132i \(0.528008\pi\)
\(854\) 3.14393 0.107583
\(855\) 0 0
\(856\) −1.81446 −0.0620168
\(857\) −20.8453 −0.712062 −0.356031 0.934474i \(-0.615870\pi\)
−0.356031 + 0.934474i \(0.615870\pi\)
\(858\) 0.372864 0.0127294
\(859\) 24.4260 0.833403 0.416701 0.909043i \(-0.363186\pi\)
0.416701 + 0.909043i \(0.363186\pi\)
\(860\) 0 0
\(861\) −7.66757 −0.261310
\(862\) −30.0346 −1.02298
\(863\) −25.5588 −0.870033 −0.435017 0.900422i \(-0.643257\pi\)
−0.435017 + 0.900422i \(0.643257\pi\)
\(864\) 0.0119825 0.000407652 0
\(865\) 0 0
\(866\) −14.0909 −0.478827
\(867\) −37.5984 −1.27691
\(868\) 0.0924073 0.00313651
\(869\) −27.6112 −0.936645
\(870\) 0 0
\(871\) 0.119902 0.00406273
\(872\) −9.79076 −0.331557
\(873\) −35.8378 −1.21292
\(874\) −46.4270 −1.57042
\(875\) 0 0
\(876\) −6.15947 −0.208109
\(877\) 7.53456 0.254424 0.127212 0.991876i \(-0.459397\pi\)
0.127212 + 0.991876i \(0.459397\pi\)
\(878\) 53.6638 1.81107
\(879\) 27.6319 0.932002
\(880\) 0 0
\(881\) 21.7361 0.732308 0.366154 0.930554i \(-0.380674\pi\)
0.366154 + 0.930554i \(0.380674\pi\)
\(882\) −28.2051 −0.949714
\(883\) 38.6202 1.29967 0.649837 0.760074i \(-0.274837\pi\)
0.649837 + 0.760074i \(0.274837\pi\)
\(884\) 0.00561953 0.000189005 0
\(885\) 0 0
\(886\) 3.52947 0.118575
\(887\) 14.3165 0.480702 0.240351 0.970686i \(-0.422738\pi\)
0.240351 + 0.970686i \(0.422738\pi\)
\(888\) 17.4383 0.585193
\(889\) −2.30230 −0.0772167
\(890\) 0 0
\(891\) 37.0654 1.24174
\(892\) −0.466012 −0.0156032
\(893\) 26.0213 0.870771
\(894\) −50.6843 −1.69514
\(895\) 0 0
\(896\) 2.76913 0.0925101
\(897\) −0.398272 −0.0132979
\(898\) −40.6184 −1.35545
\(899\) 5.18805 0.173031
\(900\) 0 0
\(901\) 11.9825 0.399196
\(902\) 61.7341 2.05552
\(903\) −7.29644 −0.242810
\(904\) −10.0496 −0.334243
\(905\) 0 0
\(906\) −10.6028 −0.352256
\(907\) 47.6042 1.58067 0.790336 0.612674i \(-0.209906\pi\)
0.790336 + 0.612674i \(0.209906\pi\)
\(908\) 3.43573 0.114019
\(909\) 53.3327 1.76893
\(910\) 0 0
\(911\) −40.1570 −1.33046 −0.665230 0.746639i \(-0.731666\pi\)
−0.665230 + 0.746639i \(0.731666\pi\)
\(912\) 51.2720 1.69779
\(913\) −17.8598 −0.591074
\(914\) 19.6730 0.650726
\(915\) 0 0
\(916\) −2.82268 −0.0932641
\(917\) 0.774981 0.0255921
\(918\) 0.0230967 0.000762305 0
\(919\) −18.0383 −0.595029 −0.297514 0.954717i \(-0.596158\pi\)
−0.297514 + 0.954717i \(0.596158\pi\)
\(920\) 0 0
\(921\) 3.05535 0.100677
\(922\) 52.1261 1.71668
\(923\) 0.103585 0.00340953
\(924\) 0.460321 0.0151435
\(925\) 0 0
\(926\) −49.1412 −1.61488
\(927\) −15.3530 −0.504260
\(928\) −2.31545 −0.0760083
\(929\) −0.679116 −0.0222811 −0.0111405 0.999938i \(-0.503546\pi\)
−0.0111405 + 0.999938i \(0.503546\pi\)
\(930\) 0 0
\(931\) 39.6295 1.29881
\(932\) −4.63923 −0.151963
\(933\) −43.8510 −1.43562
\(934\) 34.0574 1.11439
\(935\) 0 0
\(936\) 0.239460 0.00782699
\(937\) 25.7202 0.840243 0.420122 0.907468i \(-0.361987\pi\)
0.420122 + 0.907468i \(0.361987\pi\)
\(938\) −1.69616 −0.0553816
\(939\) 73.7186 2.40571
\(940\) 0 0
\(941\) −41.9988 −1.36912 −0.684560 0.728956i \(-0.740006\pi\)
−0.684560 + 0.728956i \(0.740006\pi\)
\(942\) −42.4613 −1.38347
\(943\) −65.9407 −2.14732
\(944\) 36.3403 1.18278
\(945\) 0 0
\(946\) 58.7460 1.91000
\(947\) 15.2367 0.495128 0.247564 0.968872i \(-0.420370\pi\)
0.247564 + 0.968872i \(0.420370\pi\)
\(948\) −2.63274 −0.0855074
\(949\) −0.425730 −0.0138198
\(950\) 0 0
\(951\) 20.0418 0.649900
\(952\) −1.06989 −0.0346754
\(953\) −43.1360 −1.39731 −0.698656 0.715457i \(-0.746218\pi\)
−0.698656 + 0.715457i \(0.746218\pi\)
\(954\) 37.9386 1.22831
\(955\) 0 0
\(956\) −4.11973 −0.133242
\(957\) 25.8440 0.835417
\(958\) −29.8885 −0.965652
\(959\) −1.55234 −0.0501277
\(960\) 0 0
\(961\) −26.8804 −0.867110
\(962\) 0.0895566 0.00288742
\(963\) 1.86098 0.0599692
\(964\) 0.160532 0.00517039
\(965\) 0 0
\(966\) 5.63404 0.181272
\(967\) −45.6699 −1.46864 −0.734322 0.678801i \(-0.762500\pi\)
−0.734322 + 0.678801i \(0.762500\pi\)
\(968\) −17.6471 −0.567201
\(969\) −18.0687 −0.580449
\(970\) 0 0
\(971\) −2.32251 −0.0745330 −0.0372665 0.999305i \(-0.511865\pi\)
−0.0372665 + 0.999305i \(0.511865\pi\)
\(972\) 3.54058 0.113564
\(973\) −4.64440 −0.148893
\(974\) 20.5216 0.657556
\(975\) 0 0
\(976\) −29.8591 −0.955768
\(977\) 50.8644 1.62730 0.813649 0.581357i \(-0.197478\pi\)
0.813649 + 0.581357i \(0.197478\pi\)
\(978\) 47.0033 1.50300
\(979\) −3.08141 −0.0984823
\(980\) 0 0
\(981\) 10.0418 0.320610
\(982\) −54.9118 −1.75231
\(983\) 21.2587 0.678047 0.339023 0.940778i \(-0.389903\pi\)
0.339023 + 0.940778i \(0.389903\pi\)
\(984\) 79.2221 2.52551
\(985\) 0 0
\(986\) −4.46312 −0.142135
\(987\) −3.15775 −0.100512
\(988\) −0.0249992 −0.000795330 0
\(989\) −62.7490 −1.99530
\(990\) 0 0
\(991\) 51.6637 1.64115 0.820575 0.571539i \(-0.193653\pi\)
0.820575 + 0.571539i \(0.193653\pi\)
\(992\) −1.83858 −0.0583751
\(993\) 32.9956 1.04708
\(994\) −1.46533 −0.0464775
\(995\) 0 0
\(996\) −1.70294 −0.0539598
\(997\) 32.2376 1.02097 0.510487 0.859885i \(-0.329465\pi\)
0.510487 + 0.859885i \(0.329465\pi\)
\(998\) −30.5972 −0.968538
\(999\) −0.0321230 −0.00101633
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 6025.2.a.f.1.5 7
5.4 even 2 241.2.a.a.1.3 7
15.14 odd 2 2169.2.a.e.1.5 7
20.19 odd 2 3856.2.a.j.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.3 7 5.4 even 2
2169.2.a.e.1.5 7 15.14 odd 2
3856.2.a.j.1.7 7 20.19 odd 2
6025.2.a.f.1.5 7 1.1 even 1 trivial