Properties

Label 241.2.a.a.1.3
Level $241$
Weight $2$
Character 241.1
Self dual yes
Analytic conductor $1.924$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.92439468871\)
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: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.356270\) of defining polynomial
Character \(\chi\) \(=\) 241.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} +O(q^{10})\) \(q-1.35627 q^{2} -2.45059 q^{3} -0.160532 q^{4} +2.74184 q^{5} +3.32366 q^{6} -0.283608 q^{7} +2.93026 q^{8} +3.00540 q^{9} -3.71867 q^{10} -4.12582 q^{11} +0.393399 q^{12} +0.0271909 q^{13} +0.384649 q^{14} -6.71913 q^{15} -3.65317 q^{16} -1.28740 q^{17} -4.07613 q^{18} -5.72717 q^{19} -0.440153 q^{20} +0.695007 q^{21} +5.59572 q^{22} -5.97702 q^{23} -7.18088 q^{24} +2.51768 q^{25} -0.0368782 q^{26} -0.0132278 q^{27} +0.0455281 q^{28} -2.55610 q^{29} +9.11295 q^{30} -2.02967 q^{31} -0.905851 q^{32} +10.1107 q^{33} +1.74607 q^{34} -0.777607 q^{35} -0.482463 q^{36} +2.42844 q^{37} +7.76759 q^{38} -0.0666338 q^{39} +8.03431 q^{40} -11.0324 q^{41} -0.942617 q^{42} +10.4984 q^{43} +0.662326 q^{44} +8.24032 q^{45} +8.10645 q^{46} +4.54349 q^{47} +8.95242 q^{48} -6.91957 q^{49} -3.41465 q^{50} +3.15490 q^{51} -0.00436502 q^{52} -9.30751 q^{53} +0.0179405 q^{54} -11.3123 q^{55} -0.831046 q^{56} +14.0350 q^{57} +3.46676 q^{58} -9.94762 q^{59} +1.07864 q^{60} +8.17350 q^{61} +2.75279 q^{62} -0.852354 q^{63} +8.53491 q^{64} +0.0745531 q^{65} -13.7128 q^{66} +4.40964 q^{67} +0.206670 q^{68} +14.6472 q^{69} +1.05464 q^{70} -3.80954 q^{71} +8.80661 q^{72} -15.6571 q^{73} -3.29362 q^{74} -6.16980 q^{75} +0.919395 q^{76} +1.17011 q^{77} +0.0903734 q^{78} +6.69229 q^{79} -10.0164 q^{80} -8.98378 q^{81} +14.9629 q^{82} -4.32880 q^{83} -0.111571 q^{84} -3.52985 q^{85} -14.2386 q^{86} +6.26396 q^{87} -12.0897 q^{88} +0.746861 q^{89} -11.1761 q^{90} -0.00771155 q^{91} +0.959503 q^{92} +4.97390 q^{93} -6.16219 q^{94} -15.7030 q^{95} +2.21987 q^{96} +11.9245 q^{97} +9.38480 q^{98} -12.3997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + O(q^{10}) \) \( 7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} - 6q^{8} - 2q^{9} + 3q^{10} - 18q^{11} + q^{12} - q^{13} - 6q^{14} - 11q^{15} + 4q^{16} - 2q^{17} + 8q^{18} - 6q^{19} - 8q^{20} - 2q^{21} + 10q^{22} - 22q^{23} - 3q^{24} + 5q^{25} + 8q^{26} + 3q^{27} + 9q^{28} - 16q^{29} + 29q^{30} - 18q^{31} - 6q^{32} + 4q^{33} + 11q^{34} + 7q^{35} - 7q^{36} + 8q^{37} + 16q^{38} - 9q^{39} + 14q^{40} - 15q^{41} + 19q^{42} + 14q^{43} - 4q^{44} + 3q^{45} + 11q^{46} - 10q^{47} + 31q^{48} + 6q^{49} - 4q^{50} + 13q^{51} + 27q^{52} + 15q^{53} + 16q^{54} + 29q^{55} + 13q^{56} + 14q^{57} + 17q^{58} - 18q^{59} + 15q^{60} + 4q^{61} + 13q^{62} - 16q^{63} + 2q^{64} - 7q^{65} + 16q^{66} + 18q^{67} - 15q^{68} + 26q^{69} + 8q^{70} - 50q^{71} + 30q^{72} + 10q^{74} + 16q^{75} - 20q^{76} + 17q^{77} - 32q^{78} - 15q^{79} - 11q^{80} - 9q^{81} + 45q^{82} - 24q^{83} + 6q^{84} - 2q^{85} - 23q^{86} + 12q^{87} + 8q^{88} - 13q^{89} - 39q^{90} - 12q^{91} - 10q^{92} + 14q^{93} - 32q^{94} - 41q^{95} - 15q^{96} + q^{97} + 9q^{98} - 20q^{99} + O(q^{100}) \)

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 \(-0.659187\pi\)
−0.479514 + 0.877534i \(0.659187\pi\)
\(3\) −2.45059 −1.41485 −0.707425 0.706789i \(-0.750143\pi\)
−0.707425 + 0.706789i \(0.750143\pi\)
\(4\) −0.160532 −0.0802661
\(5\) 2.74184 1.22619 0.613094 0.790010i \(-0.289925\pi\)
0.613094 + 0.790010i \(0.289925\pi\)
\(6\) 3.32366 1.35688
\(7\) −0.283608 −0.107194 −0.0535968 0.998563i \(-0.517069\pi\)
−0.0535968 + 0.998563i \(0.517069\pi\)
\(8\) 2.93026 1.03600
\(9\) 3.00540 1.00180
\(10\) −3.71867 −1.17595
\(11\) −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 \(-0.498800\pi\)
0.00377070 + 0.999993i \(0.498800\pi\)
\(14\) 0.384649 0.102802
\(15\) −6.71913 −1.73487
\(16\) −3.65317 −0.913291
\(17\) −1.28740 −0.312241 −0.156121 0.987738i \(-0.549899\pi\)
−0.156121 + 0.987738i \(0.549899\pi\)
\(18\) −4.07613 −0.960753
\(19\) −5.72717 −1.31390 −0.656952 0.753933i \(-0.728154\pi\)
−0.656952 + 0.753933i \(0.728154\pi\)
\(20\) −0.440153 −0.0984212
\(21\) 0.695007 0.151663
\(22\) 5.59572 1.19301
\(23\) −5.97702 −1.24629 −0.623147 0.782104i \(-0.714146\pi\)
−0.623147 + 0.782104i \(0.714146\pi\)
\(24\) −7.18088 −1.46579
\(25\) 2.51768 0.503536
\(26\) −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 \(0.576272\pi\)
\(30\) 9.11295 1.66379
\(31\) −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
\(35\) −0.777607 −0.131440
\(36\) −0.482463 −0.0804105
\(37\) 2.42844 0.399233 0.199617 0.979874i \(-0.436030\pi\)
0.199617 + 0.979874i \(0.436030\pi\)
\(38\) 7.76759 1.26007
\(39\) −0.0666338 −0.0106700
\(40\) 8.03431 1.27034
\(41\) −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 \(-0.204571\pi\)
0.800493 + 0.599342i \(0.204571\pi\)
\(44\) 0.662326 0.0998494
\(45\) 8.24032 1.22839
\(46\) 8.10645 1.19523
\(47\) 4.54349 0.662736 0.331368 0.943502i \(-0.392490\pi\)
0.331368 + 0.943502i \(0.392490\pi\)
\(48\) 8.95242 1.29217
\(49\) −6.91957 −0.988510
\(50\) −3.41465 −0.482904
\(51\) 3.15490 0.441774
\(52\) −0.00436502 −0.000605319 0
\(53\) −9.30751 −1.27848 −0.639242 0.769005i \(-0.720752\pi\)
−0.639242 + 0.769005i \(0.720752\pi\)
\(54\) 0.0179405 0.00244140
\(55\) −11.3123 −1.52535
\(56\) −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 \(0.724200\pi\)
\(60\) 1.07864 0.139251
\(61\) 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
\(65\) 0.0745531 0.00924717
\(66\) −13.7128 −1.68793
\(67\) 4.40964 0.538723 0.269361 0.963039i \(-0.413187\pi\)
0.269361 + 0.963039i \(0.413187\pi\)
\(68\) 0.206670 0.0250624
\(69\) 14.6472 1.76332
\(70\) 1.05464 0.126054
\(71\) −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 \(-0.868808\pi\)
−0.916261 + 0.400583i \(0.868808\pi\)
\(74\) −3.29362 −0.382876
\(75\) −6.16980 −0.712427
\(76\) 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 \(0.377138\pi\)
\(80\) −10.0164 −1.11987
\(81\) −8.98378 −0.998197
\(82\) 14.9629 1.65237
\(83\) −4.32880 −0.475147 −0.237574 0.971370i \(-0.576352\pi\)
−0.237574 + 0.971370i \(0.576352\pi\)
\(84\) −0.111571 −0.0121734
\(85\) −3.52985 −0.382866
\(86\) −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 \(0.487397\pi\)
\(90\) −11.1761 −1.17806
\(91\) −0.00771155 −0.000808391 0
\(92\) 0.959503 0.100035
\(93\) 4.97390 0.515770
\(94\) −6.16219 −0.635582
\(95\) −15.7030 −1.61109
\(96\) 2.21987 0.226565
\(97\) 11.9245 1.21075 0.605373 0.795942i \(-0.293024\pi\)
0.605373 + 0.795942i \(0.293024\pi\)
\(98\) 9.38480 0.948008
\(99\) −12.3997 −1.24622
\(100\) −0.404168 −0.0404168
\(101\) 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 \(-0.419018\pi\)
0.251677 + 0.967811i \(0.419018\pi\)
\(104\) 0.0796766 0.00781293
\(105\) 1.90560 0.185967
\(106\) 12.6235 1.22610
\(107\) −0.619213 −0.0598615 −0.0299308 0.999552i \(-0.509529\pi\)
−0.0299308 + 0.999552i \(0.509529\pi\)
\(108\) 0.00212349 0.000204333 0
\(109\) 3.34125 0.320034 0.160017 0.987114i \(-0.448845\pi\)
0.160017 + 0.987114i \(0.448845\pi\)
\(110\) 15.3426 1.46286
\(111\) −5.95112 −0.564855
\(112\) 1.03607 0.0978990
\(113\) −3.42957 −0.322627 −0.161313 0.986903i \(-0.551573\pi\)
−0.161313 + 0.986903i \(0.551573\pi\)
\(114\) −19.0352 −1.78281
\(115\) −16.3880 −1.52819
\(116\) 0.410336 0.0380988
\(117\) 0.0817195 0.00755497
\(118\) 13.4917 1.24201
\(119\) 0.365118 0.0334703
\(120\) −19.6888 −1.79733
\(121\) 6.02237 0.547488
\(122\) −11.0855 −1.00363
\(123\) 27.0358 2.43774
\(124\) 0.325828 0.0292602
\(125\) −6.80613 −0.608758
\(126\) 1.15602 0.102987
\(127\) 8.11791 0.720348 0.360174 0.932885i \(-0.382717\pi\)
0.360174 + 0.932885i \(0.382717\pi\)
\(128\) −9.76394 −0.863018
\(129\) −25.7272 −2.26516
\(130\) −0.101114 −0.00886830
\(131\) 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
\(135\) −0.0362686 −0.00312151
\(136\) −3.77243 −0.323483
\(137\) 5.47355 0.467637 0.233819 0.972280i \(-0.424878\pi\)
0.233819 + 0.972280i \(0.424878\pi\)
\(138\) −19.8656 −1.69107
\(139\) −16.3761 −1.38901 −0.694503 0.719490i \(-0.744376\pi\)
−0.694503 + 0.719490i \(0.744376\pi\)
\(140\) 0.124831 0.0105501
\(141\) −11.1342 −0.937671
\(142\) 5.16676 0.433585
\(143\) −0.112185 −0.00938136
\(144\) −10.9792 −0.914935
\(145\) −7.00842 −0.582017
\(146\) 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 \(0.714756\pi\)
\(150\) 8.36791 0.683237
\(151\) −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
\(155\) −5.56504 −0.446995
\(156\) 0.0106969 0.000856435 0
\(157\) 12.7755 1.01959 0.509797 0.860295i \(-0.329721\pi\)
0.509797 + 0.860295i \(0.329721\pi\)
\(158\) −9.07655 −0.722092
\(159\) 22.8089 1.80886
\(160\) −2.48370 −0.196354
\(161\) 1.69513 0.133595
\(162\) 12.1844 0.957299
\(163\) −14.1420 −1.10769 −0.553844 0.832620i \(-0.686840\pi\)
−0.553844 + 0.832620i \(0.686840\pi\)
\(164\) 1.77105 0.138296
\(165\) 27.7219 2.15815
\(166\) 5.87102 0.455679
\(167\) 9.14541 0.707693 0.353846 0.935304i \(-0.384874\pi\)
0.353846 + 0.935304i \(0.384874\pi\)
\(168\) 2.03655 0.157124
\(169\) −12.9993 −0.999943
\(170\) 4.78743 0.367179
\(171\) −17.2124 −1.31627
\(172\) −1.68533 −0.128505
\(173\) 14.0992 1.07194 0.535970 0.844237i \(-0.319946\pi\)
0.535970 + 0.844237i \(0.319946\pi\)
\(174\) −8.49562 −0.644051
\(175\) −0.714033 −0.0539758
\(176\) 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 \(0.162514\pi\)
\(180\) −1.32284 −0.0985983
\(181\) 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
\(185\) 6.65839 0.489535
\(186\) −6.74595 −0.494637
\(187\) 5.31159 0.388422
\(188\) −0.729375 −0.0531952
\(189\) 0.00375152 0.000272883 0
\(190\) 21.2975 1.54508
\(191\) 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 \(-0.287056\pi\)
0.620189 + 0.784452i \(0.287056\pi\)
\(194\) −16.1728 −1.16114
\(195\) −0.182699 −0.0130834
\(196\) 1.11081 0.0793438
\(197\) 4.62238 0.329331 0.164665 0.986349i \(-0.447346\pi\)
0.164665 + 0.986349i \(0.447346\pi\)
\(198\) 16.8174 1.19516
\(199\) −17.7065 −1.25518 −0.627589 0.778545i \(-0.715958\pi\)
−0.627589 + 0.778545i \(0.715958\pi\)
\(200\) 7.37746 0.521665
\(201\) −10.8062 −0.762212
\(202\) −24.0679 −1.69341
\(203\) 0.724930 0.0508801
\(204\) −0.506463 −0.0354595
\(205\) −30.2490 −2.11268
\(206\) −6.92848 −0.482730
\(207\) −17.9633 −1.24854
\(208\) −0.0993329 −0.00688750
\(209\) 23.6293 1.63447
\(210\) −2.58450 −0.178348
\(211\) −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
\(215\) 28.7848 1.96311
\(216\) −0.0387611 −0.00263736
\(217\) 0.575631 0.0390764
\(218\) −4.53164 −0.306921
\(219\) 38.3691 2.59274
\(220\) 1.81599 0.122434
\(221\) −0.0350057 −0.00235474
\(222\) 8.07132 0.541711
\(223\) −2.90292 −0.194394 −0.0971969 0.995265i \(-0.530988\pi\)
−0.0971969 + 0.995265i \(0.530988\pi\)
\(224\) 0.256906 0.0171653
\(225\) 7.56662 0.504442
\(226\) 4.65142 0.309408
\(227\) 21.4022 1.42051 0.710255 0.703944i \(-0.248579\pi\)
0.710255 + 0.703944i \(0.248579\pi\)
\(228\) −2.25306 −0.149213
\(229\) 17.5833 1.16194 0.580968 0.813926i \(-0.302674\pi\)
0.580968 + 0.813926i \(0.302674\pi\)
\(230\) 22.2266 1.46558
\(231\) −2.86747 −0.188666
\(232\) −7.49005 −0.491746
\(233\) −28.8991 −1.89324 −0.946621 0.322348i \(-0.895528\pi\)
−0.946621 + 0.322348i \(0.895528\pi\)
\(234\) −0.110834 −0.00724543
\(235\) 12.4575 0.812638
\(236\) 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 \(0.188340\pi\)
\(240\) 24.5461 1.58444
\(241\) −1.00000 −0.0644157
\(242\) −8.16796 −0.525056
\(243\) 22.0553 1.41484
\(244\) −1.31211 −0.0839992
\(245\) −18.9723 −1.21210
\(246\) −36.6679 −2.33786
\(247\) −0.155727 −0.00990868
\(248\) −5.94748 −0.377665
\(249\) 10.6081 0.672262
\(250\) 9.23094 0.583816
\(251\) −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
\(255\) 8.65022 0.541698
\(256\) −3.82728 −0.239205
\(257\) −17.0359 −1.06267 −0.531336 0.847161i \(-0.678310\pi\)
−0.531336 + 0.847161i \(0.678310\pi\)
\(258\) 34.8931 2.17235
\(259\) −0.688725 −0.0427953
\(260\) −0.0119682 −0.000742234 0
\(261\) −7.68210 −0.475510
\(262\) −3.70611 −0.228965
\(263\) −21.9895 −1.35593 −0.677966 0.735094i \(-0.737138\pi\)
−0.677966 + 0.735094i \(0.737138\pi\)
\(264\) 29.6270 1.82342
\(265\) −25.5197 −1.56766
\(266\) −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 \(0.412438\pi\)
\(270\) 0.0491900 0.00299361
\(271\) 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
\(275\) −10.3875 −0.626389
\(276\) −2.35135 −0.141535
\(277\) −14.9125 −0.896007 −0.448003 0.894032i \(-0.647865\pi\)
−0.448003 + 0.894032i \(0.647865\pi\)
\(278\) 22.2105 1.33210
\(279\) −6.09998 −0.365196
\(280\) −2.27859 −0.136172
\(281\) −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 \(-0.664067\pi\)
−0.492910 + 0.870080i \(0.664067\pi\)
\(284\) 0.611553 0.0362890
\(285\) 38.4816 2.27945
\(286\) 0.152153 0.00899698
\(287\) 3.12886 0.184691
\(288\) −2.72244 −0.160422
\(289\) −15.3426 −0.902505
\(290\) 9.50531 0.558171
\(291\) −29.2220 −1.71302
\(292\) 2.51346 0.147089
\(293\) −11.2756 −0.658729 −0.329364 0.944203i \(-0.606834\pi\)
−0.329364 + 0.944203i \(0.606834\pi\)
\(294\) −22.9983 −1.34129
\(295\) −27.2748 −1.58800
\(296\) 7.11597 0.413608
\(297\) 0.0545757 0.00316680
\(298\) 20.6825 1.19810
\(299\) −0.162521 −0.00939881
\(300\) 0.990451 0.0571837
\(301\) −2.97742 −0.171616
\(302\) 4.32665 0.248971
\(303\) −43.4873 −2.49828
\(304\) 20.9223 1.19998
\(305\) 22.4104 1.28322
\(306\) 5.24762 0.299987
\(307\) −1.24678 −0.0711575 −0.0355787 0.999367i \(-0.511327\pi\)
−0.0355787 + 0.999367i \(0.511327\pi\)
\(308\) −0.187841 −0.0107032
\(309\) −12.5188 −0.712170
\(310\) 7.54769 0.428680
\(311\) −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 \(-0.823499\pi\)
−0.850166 + 0.526514i \(0.823499\pi\)
\(314\) −17.3270 −0.977818
\(315\) −2.33702 −0.131676
\(316\) −1.07433 −0.0604357
\(317\) −8.17835 −0.459342 −0.229671 0.973268i \(-0.573765\pi\)
−0.229671 + 0.973268i \(0.573765\pi\)
\(318\) −30.9350 −1.73475
\(319\) 10.5460 0.590463
\(320\) 23.4013 1.30817
\(321\) 1.51744 0.0846951
\(322\) −2.29905 −0.128121
\(323\) 7.37318 0.410255
\(324\) 1.44218 0.0801214
\(325\) 0.0684580 0.00379736
\(326\) 19.1804 1.06230
\(327\) −8.18805 −0.452800
\(328\) −32.3278 −1.78500
\(329\) −1.28857 −0.0710410
\(330\) −37.5984 −2.06972
\(331\) 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
\(335\) 12.0905 0.660575
\(336\) −2.53897 −0.138512
\(337\) −6.06342 −0.330295 −0.165148 0.986269i \(-0.552810\pi\)
−0.165148 + 0.986269i \(0.552810\pi\)
\(338\) 17.6305 0.958973
\(339\) 8.40448 0.456469
\(340\) 0.566655 0.0307312
\(341\) 8.37407 0.453481
\(342\) 23.3447 1.26234
\(343\) 3.94770 0.213156
\(344\) 30.7630 1.65863
\(345\) 40.1603 2.16216
\(346\) −19.1223 −1.02802
\(347\) 23.7297 1.27388 0.636938 0.770915i \(-0.280201\pi\)
0.636938 + 0.770915i \(0.280201\pi\)
\(348\) −1.00557 −0.0539040
\(349\) 8.46091 0.452902 0.226451 0.974023i \(-0.427288\pi\)
0.226451 + 0.974023i \(0.427288\pi\)
\(350\) 0.968421 0.0517643
\(351\) −0.000359677 0 −1.91982e−5 0
\(352\) 3.73738 0.199203
\(353\) 6.66847 0.354927 0.177463 0.984127i \(-0.443211\pi\)
0.177463 + 0.984127i \(0.443211\pi\)
\(354\) −33.0625 −1.75725
\(355\) −10.4451 −0.554370
\(356\) −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 \(0.768683\pi\)
\(360\) 24.1463 1.27262
\(361\) 13.8005 0.726342
\(362\) −26.8822 −1.41290
\(363\) −14.7584 −0.774614
\(364\) 0.00123795 6.48863e−5 0
\(365\) −42.9292 −2.24701
\(366\) 27.1660 1.41999
\(367\) 7.48573 0.390752 0.195376 0.980728i \(-0.437407\pi\)
0.195376 + 0.980728i \(0.437407\pi\)
\(368\) 21.8350 1.13823
\(369\) −33.1566 −1.72607
\(370\) −9.03058 −0.469477
\(371\) 2.63968 0.137045
\(372\) −0.798471 −0.0413988
\(373\) 17.6125 0.911943 0.455972 0.889994i \(-0.349292\pi\)
0.455972 + 0.889994i \(0.349292\pi\)
\(374\) −7.20395 −0.372507
\(375\) 16.6790 0.861302
\(376\) 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 \(0.437331\pi\)
\(380\) 2.52083 0.129316
\(381\) −19.8937 −1.01918
\(382\) −2.56601 −0.131289
\(383\) −27.2242 −1.39109 −0.695546 0.718482i \(-0.744837\pi\)
−0.695546 + 0.718482i \(0.744837\pi\)
\(384\) 23.9274 1.22104
\(385\) 3.20826 0.163508
\(386\) −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 \(0.301473\pi\)
\(390\) 0.247789 0.0125473
\(391\) 7.69483 0.389145
\(392\) −20.2762 −1.02410
\(393\) −6.69643 −0.337790
\(394\) −6.26920 −0.315837
\(395\) 18.3492 0.923248
\(396\) 1.99055 0.100029
\(397\) −17.0475 −0.855587 −0.427794 0.903876i \(-0.640709\pi\)
−0.427794 + 0.903876i \(0.640709\pi\)
\(398\) 24.0147 1.20375
\(399\) −3.98042 −0.199270
\(400\) −9.19749 −0.459875
\(401\) 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
\(405\) −24.6321 −1.22398
\(406\) −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 \(0.409319\pi\)
\(410\) 41.0258 2.02612
\(411\) −13.4134 −0.661636
\(412\) −0.820076 −0.0404022
\(413\) 2.82122 0.138823
\(414\) 24.3631 1.19738
\(415\) −11.8689 −0.582620
\(416\) −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 \(0.467681\pi\)
\(420\) −0.305909 −0.0149268
\(421\) −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
\(425\) −3.24127 −0.157225
\(426\) −12.6616 −0.613457
\(427\) −2.31807 −0.112179
\(428\) 0.0994035 0.00480485
\(429\) 0.274919 0.0132732
\(430\) −39.0400 −1.88268
\(431\) −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 \(-0.419687\pi\)
0.249642 + 0.968338i \(0.419687\pi\)
\(434\) −0.780711 −0.0374753
\(435\) 17.1748 0.823467
\(436\) −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 \(0.106818\pi\)
\(440\) −33.1481 −1.58027
\(441\) −20.7961 −0.990288
\(442\) 0.0474771 0.00225826
\(443\) −2.60234 −0.123641 −0.0618203 0.998087i \(-0.519691\pi\)
−0.0618203 + 0.998087i \(0.519691\pi\)
\(444\) 0.955345 0.0453387
\(445\) 2.04777 0.0970737
\(446\) 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 \(0.749808\pi\)
\(450\) −10.2624 −0.483773
\(451\) 45.5175 2.14334
\(452\) 0.550556 0.0258960
\(453\) 7.81765 0.367305
\(454\) −29.0271 −1.36231
\(455\) −0.0211438 −0.000991238 0
\(456\) 41.1261 1.92591
\(457\) −14.5052 −0.678526 −0.339263 0.940691i \(-0.610178\pi\)
−0.339263 + 0.940691i \(0.610178\pi\)
\(458\) −23.8477 −1.11433
\(459\) 0.0170296 0.000794872 0
\(460\) 2.63080 0.122662
\(461\) 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 \(-0.181416\pi\)
0.841936 + 0.539578i \(0.181416\pi\)
\(464\) 9.33786 0.433499
\(465\) 13.6376 0.632430
\(466\) 39.1950 1.81567
\(467\) −25.1111 −1.16200 −0.581001 0.813903i \(-0.697339\pi\)
−0.581001 + 0.813903i \(0.697339\pi\)
\(468\) −0.0131186 −0.000606408 0
\(469\) −1.25061 −0.0577477
\(470\) −16.8957 −0.779342
\(471\) −31.3074 −1.44257
\(472\) −29.1492 −1.34170
\(473\) −43.3144 −1.99160
\(474\) 22.2429 1.02165
\(475\) −14.4192 −0.661597
\(476\) −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 \(0.667938\pi\)
\(480\) 6.08653 0.277811
\(481\) 0.0660315 0.00301078
\(482\) 1.35627 0.0617764
\(483\) −4.15407 −0.189017
\(484\) −0.966784 −0.0439447
\(485\) 32.6950 1.48460
\(486\) −29.9129 −1.35688
\(487\) −15.1309 −0.685649 −0.342824 0.939400i \(-0.611384\pi\)
−0.342824 + 0.939400i \(0.611384\pi\)
\(488\) 23.9505 1.08419
\(489\) 34.6563 1.56721
\(490\) 25.7316 1.16244
\(491\) −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
\(495\) −33.9980 −1.52810
\(496\) 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 \(0.668492\pi\)
\(500\) 1.09260 0.0488626
\(501\) −22.4117 −1.00128
\(502\) 38.4012 1.71393
\(503\) 25.5277 1.13823 0.569113 0.822259i \(-0.307287\pi\)
0.569113 + 0.822259i \(0.307287\pi\)
\(504\) −2.49762 −0.111253
\(505\) 48.6556 2.16515
\(506\) −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 \(0.622235\pi\)
\(510\) −11.7320 −0.519503
\(511\) 4.44047 0.196435
\(512\) 24.7187 1.09242
\(513\) 0.0757581 0.00334480
\(514\) 23.1053 1.01913
\(515\) 14.0066 0.617206
\(516\) 4.13004 0.181815
\(517\) −18.7456 −0.824430
\(518\) 0.934096 0.0410418
\(519\) −34.5513 −1.51663
\(520\) 0.218460 0.00958012
\(521\) 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 \(-0.391334\pi\)
0.334793 + 0.942292i \(0.391334\pi\)
\(524\) −0.438667 −0.0191632
\(525\) 1.74980 0.0763677
\(526\) 29.8237 1.30038
\(527\) 2.61301 0.113824
\(528\) −36.9360 −1.60743
\(529\) 12.7248 0.553250
\(530\) 34.6116 1.50343
\(531\) −29.8966 −1.29740
\(532\) −0.260748 −0.0113048
\(533\) −0.299980 −0.0129936
\(534\) 2.48231 0.107420
\(535\) −1.69778 −0.0734015
\(536\) 12.9214 0.558120
\(537\) −57.2111 −2.46884
\(538\) −12.0844 −0.520997
\(539\) 28.5489 1.22969
\(540\) 0.00582228 0.000250551 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
\(545\) 9.16118 0.392422
\(546\) −0.0256306 −0.00109689
\(547\) 4.93535 0.211020 0.105510 0.994418i \(-0.466352\pi\)
0.105510 + 0.994418i \(0.466352\pi\)
\(548\) −0.878681 −0.0375354
\(549\) 24.5646 1.04839
\(550\) 14.0882 0.600724
\(551\) 14.6392 0.623652
\(552\) 42.9203 1.82681
\(553\) −1.89799 −0.0807106
\(554\) 20.2254 0.859295
\(555\) −16.3170 −0.692618
\(556\) 2.62890 0.111490
\(557\) −14.0586 −0.595681 −0.297840 0.954616i \(-0.596266\pi\)
−0.297840 + 0.954616i \(0.596266\pi\)
\(558\) 8.27322 0.350233
\(559\) 0.285460 0.0120737
\(560\) 2.84073 0.120043
\(561\) −13.0165 −0.549559
\(562\) 39.1788 1.65266
\(563\) 44.3164 1.86771 0.933856 0.357650i \(-0.116422\pi\)
0.933856 + 0.357650i \(0.116422\pi\)
\(564\) 1.78740 0.0752632
\(565\) −9.40333 −0.395601
\(566\) 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 \(0.544513\pi\)
\(570\) −52.1914 −2.18606
\(571\) −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
\(575\) −15.0482 −0.627554
\(576\) 25.6508 1.06878
\(577\) 33.2047 1.38233 0.691165 0.722697i \(-0.257098\pi\)
0.691165 + 0.722697i \(0.257098\pi\)
\(578\) 20.8087 0.865528
\(579\) −42.2283 −1.75495
\(580\) 1.12508 0.0467162
\(581\) 1.22768 0.0509328
\(582\) 39.6329 1.64284
\(583\) 38.4011 1.59041
\(584\) −45.8794 −1.89850
\(585\) 0.224062 0.00926381
\(586\) 15.2928 0.631739
\(587\) 28.0737 1.15873 0.579363 0.815069i \(-0.303301\pi\)
0.579363 + 0.815069i \(0.303301\pi\)
\(588\) −2.72215 −0.112259
\(589\) 11.6243 0.478971
\(590\) 36.9920 1.52293
\(591\) −11.3276 −0.465954
\(592\) −8.87150 −0.364616
\(593\) −0.499968 −0.0205312 −0.0102656 0.999947i \(-0.503268\pi\)
−0.0102656 + 0.999947i \(0.503268\pi\)
\(594\) −0.0740193 −0.00303705
\(595\) 1.00109 0.0410408
\(596\) 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 \(0.536945\pi\)
\(600\) −18.0791 −0.738078
\(601\) 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
\(605\) 16.5124 0.671323
\(606\) 58.9805 2.39592
\(607\) −4.01260 −0.162867 −0.0814333 0.996679i \(-0.525950\pi\)
−0.0814333 + 0.996679i \(0.525950\pi\)
\(608\) 5.18797 0.210400
\(609\) −1.77651 −0.0719877
\(610\) −30.3946 −1.23064
\(611\) 0.123542 0.00499796
\(612\) 0.621124 0.0251075
\(613\) −31.5947 −1.27610 −0.638048 0.769996i \(-0.720258\pi\)
−0.638048 + 0.769996i \(0.720258\pi\)
\(614\) 1.69097 0.0682420
\(615\) 74.1278 2.98912
\(616\) 3.42874 0.138148
\(617\) −2.64125 −0.106333 −0.0531664 0.998586i \(-0.516931\pi\)
−0.0531664 + 0.998586i \(0.516931\pi\)
\(618\) 16.9789 0.682991
\(619\) 13.8609 0.557115 0.278558 0.960419i \(-0.410144\pi\)
0.278558 + 0.960419i \(0.410144\pi\)
\(620\) 0.893367 0.0358785
\(621\) 0.0790631 0.00317269
\(622\) 24.2692 0.973106
\(623\) −0.211815 −0.00848621
\(624\) 0.243424 0.00974477
\(625\) −31.2497 −1.24999
\(626\) 40.7992 1.63067
\(627\) −57.9057 −2.31253
\(628\) −2.05087 −0.0818387
\(629\) −3.12638 −0.124657
\(630\) 3.16963 0.126281
\(631\) −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
\(635\) 22.2580 0.883281
\(636\) −3.66156 −0.145190
\(637\) −0.188149 −0.00745475
\(638\) −14.3032 −0.566271
\(639\) −11.4492 −0.452922
\(640\) −26.7711 −1.05822
\(641\) −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 \(-0.404865\pi\)
0.294445 + 0.955668i \(0.404865\pi\)
\(644\) −0.272123 −0.0107231
\(645\) −70.5399 −2.77751
\(646\) −10.0000 −0.393446
\(647\) 1.09720 0.0431356 0.0215678 0.999767i \(-0.493134\pi\)
0.0215678 + 0.999767i \(0.493134\pi\)
\(648\) −26.3248 −1.03414
\(649\) 41.0421 1.61104
\(650\) −0.0928475 −0.00364178
\(651\) −1.41064 −0.0552872
\(652\) 2.27025 0.0889097
\(653\) 9.51269 0.372260 0.186130 0.982525i \(-0.440405\pi\)
0.186130 + 0.982525i \(0.440405\pi\)
\(654\) 11.1052 0.434248
\(655\) 7.49229 0.292748
\(656\) 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 \(0.475242\pi\)
\(660\) −4.45025 −0.173226
\(661\) −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
\(665\) 4.45349 0.172699
\(666\) −9.89864 −0.383565
\(667\) 15.2779 0.591561
\(668\) −1.46813 −0.0568037
\(669\) 7.11387 0.275038
\(670\) −16.3980 −0.633510
\(671\) −33.7224 −1.30184
\(672\) −0.629573 −0.0242863
\(673\) 0.273027 0.0105244 0.00526221 0.999986i \(-0.498325\pi\)
0.00526221 + 0.999986i \(0.498325\pi\)
\(674\) 8.22363 0.316762
\(675\) −0.0333035 −0.00128185
\(676\) 2.08680 0.0802615
\(677\) −5.73279 −0.220329 −0.110165 0.993913i \(-0.535138\pi\)
−0.110165 + 0.993913i \(0.535138\pi\)
\(678\) −11.3987 −0.437766
\(679\) −3.38187 −0.129784
\(680\) −10.3434 −0.396651
\(681\) −52.4479 −2.00981
\(682\) −11.3575 −0.434901
\(683\) −18.8046 −0.719538 −0.359769 0.933041i \(-0.617145\pi\)
−0.359769 + 0.933041i \(0.617145\pi\)
\(684\) 2.76315 0.105652
\(685\) 15.0076 0.573411
\(686\) −5.35414 −0.204422
\(687\) −43.0895 −1.64397
\(688\) −38.3523 −1.46217
\(689\) −0.253080 −0.00964157
\(690\) −54.4683 −2.07357
\(691\) 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
\(695\) −44.9007 −1.70318
\(696\) 18.3551 0.695747
\(697\) 14.2031 0.537981
\(698\) −11.4753 −0.434346
\(699\) 70.8199 2.67865
\(700\) 0.114625 0.00433243
\(701\) 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
\(705\) −30.5283 −1.14976
\(706\) −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 \(0.784800\pi\)
\(710\) 14.1664 0.531656
\(711\) 20.1130 0.754296
\(712\) 2.18850 0.0820175
\(713\) 12.1314 0.454325
\(714\) 1.21353 0.0454151
\(715\) −0.307592 −0.0115033
\(716\) −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 \(0.561109\pi\)
\(720\) −30.1032 −1.12188
\(721\) −1.44881 −0.0539563
\(722\) −18.7172 −0.696582
\(723\) 2.45059 0.0911385
\(724\) −3.18186 −0.118253
\(725\) −6.43544 −0.239006
\(726\) 20.0163 0.742876
\(727\) −45.5533 −1.68948 −0.844739 0.535178i \(-0.820244\pi\)
−0.844739 + 0.535178i \(0.820244\pi\)
\(728\) −0.0225969 −0.000837497 0
\(729\) −27.0971 −1.00360
\(730\) 58.2235 2.15495
\(731\) −13.5156 −0.499894
\(732\) 3.21544 0.118846
\(733\) −20.6241 −0.761770 −0.380885 0.924622i \(-0.624381\pi\)
−0.380885 + 0.924622i \(0.624381\pi\)
\(734\) −10.1527 −0.374742
\(735\) 46.4934 1.71494
\(736\) 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 \(0.602444\pi\)
\(740\) −1.06889 −0.0392930
\(741\) 0.381623 0.0140193
\(742\) −3.58012 −0.131430
\(743\) −40.8356 −1.49811 −0.749056 0.662506i \(-0.769493\pi\)
−0.749056 + 0.662506i \(0.769493\pi\)
\(744\) 14.5748 0.534340
\(745\) −41.8117 −1.53186
\(746\) −23.8874 −0.874579
\(747\) −13.0098 −0.476002
\(748\) −0.852681 −0.0311771
\(749\) 0.175613 0.00641678
\(750\) −22.6213 −0.826012
\(751\) 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
\(755\) −8.74676 −0.318327
\(756\) −0.000602239 0 −2.19032e−5 0
\(757\) 13.7148 0.498473 0.249237 0.968443i \(-0.419820\pi\)
0.249237 + 0.968443i \(0.419820\pi\)
\(758\) −10.3298 −0.375194
\(759\) −60.4318 −2.19354
\(760\) −46.0139 −1.66910
\(761\) −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
\(765\) −10.6086 −0.383555
\(766\) 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 \(0.667238\pi\)
\(770\) −4.35127 −0.156809
\(771\) 41.7481 1.50352
\(772\) −2.76627 −0.0995603
\(773\) 12.8524 0.462270 0.231135 0.972922i \(-0.425756\pi\)
0.231135 + 0.972922i \(0.425756\pi\)
\(774\) −42.7927 −1.53815
\(775\) −5.11007 −0.183559
\(776\) 34.9418 1.25434
\(777\) 1.68778 0.0605489
\(778\) −31.2457 −1.12021
\(779\) 63.1843 2.26381
\(780\) 0.0293291 0.00105015
\(781\) 15.7174 0.562414
\(782\) −10.4363 −0.373200
\(783\) 0.0338117 0.00120833
\(784\) 25.2783 0.902797
\(785\) 35.0283 1.25021
\(786\) 9.08217 0.323950
\(787\) 9.53803 0.339994 0.169997 0.985445i \(-0.445624\pi\)
0.169997 + 0.985445i \(0.445624\pi\)
\(788\) −0.742040 −0.0264341
\(789\) 53.8873 1.91844
\(790\) −24.8864 −0.885420
\(791\) 0.972653 0.0345836
\(792\) −36.3345 −1.29109
\(793\) 0.222245 0.00789215
\(794\) 23.1209 0.820532
\(795\) 62.5383 2.21801
\(796\) 2.84246 0.100748
\(797\) −7.72801 −0.273740 −0.136870 0.990589i \(-0.543704\pi\)
−0.136870 + 0.990589i \(0.543704\pi\)
\(798\) 5.39853 0.191106
\(799\) −5.84930 −0.206933
\(800\) −2.28064 −0.0806329
\(801\) 2.24461 0.0793095
\(802\) −8.39577 −0.296465
\(803\) 64.5982 2.27962
\(804\) 1.73474 0.0611797
\(805\) 4.64777 0.163812
\(806\) 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 \(0.511144\pi\)
\(810\) 33.4077 1.17383
\(811\) 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
\(815\) −38.7751 −1.35823
\(816\) −11.5254 −0.403469
\(817\) −60.1260 −2.10354
\(818\) −15.4174 −0.539058
\(819\) −0.0231763 −0.000809845 0
\(820\) 4.85593 0.169576
\(821\) 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 \(-0.719338\pi\)
−0.635821 + 0.771836i \(0.719338\pi\)
\(824\) 14.9692 0.521477
\(825\) 25.4555 0.886246
\(826\) −3.82634 −0.133135
\(827\) 23.2928 0.809971 0.404985 0.914323i \(-0.367277\pi\)
0.404985 + 0.914323i \(0.367277\pi\)
\(828\) 2.88369 0.100215
\(829\) −29.8113 −1.03539 −0.517695 0.855565i \(-0.673210\pi\)
−0.517695 + 0.855565i \(0.673210\pi\)
\(830\) 16.0974 0.558748
\(831\) 36.5445 1.26771
\(832\) 0.232072 0.00804565
\(833\) 8.90827 0.308653
\(834\) −54.4288 −1.88471
\(835\) 25.0752 0.867764
\(836\) −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 \(0.814317\pi\)
\(840\) 5.58390 0.192663
\(841\) −22.4663 −0.774702
\(842\) 1.96394 0.0676819
\(843\) 70.7906 2.43816
\(844\) 1.79748 0.0618718
\(845\) −35.6419 −1.22612
\(846\) −18.5198 −0.636725
\(847\) −1.70799 −0.0586873
\(848\) 34.0019 1.16763
\(849\) 40.6408 1.39479
\(850\) 4.39603 0.150783
\(851\) −14.5148 −0.497562
\(852\) −1.49867 −0.0513434
\(853\) 5.13297 0.175750 0.0878748 0.996132i \(-0.471992\pi\)
0.0878748 + 0.996132i \(0.471992\pi\)
\(854\) 3.14393 0.107583
\(855\) −47.1937 −1.61399
\(856\) −1.81446 −0.0620168
\(857\) 20.8453 0.712062 0.356031 0.934474i \(-0.384130\pi\)
0.356031 + 0.934474i \(0.384130\pi\)
\(858\) −0.372864 −0.0127294
\(859\) 24.4260 0.833403 0.416701 0.909043i \(-0.363186\pi\)
0.416701 + 0.909043i \(0.363186\pi\)
\(860\) −4.62089 −0.157571
\(861\) −7.66757 −0.261310
\(862\) 30.0346 1.02298
\(863\) 25.5588 0.870033 0.435017 0.900422i \(-0.356743\pi\)
0.435017 + 0.900422i \(0.356743\pi\)
\(864\) 0.0119825 0.000407652 0
\(865\) 38.6576 1.31440
\(866\) −14.0909 −0.478827
\(867\) 37.5984 1.27691
\(868\) −0.0924073 −0.00313651
\(869\) −27.6112 −0.936645
\(870\) −23.2936 −0.789728
\(871\) 0.119902 0.00406273
\(872\) 9.79076 0.331557
\(873\) 35.8378 1.21292
\(874\) −46.4270 −1.57042
\(875\) 1.93027 0.0652550
\(876\) −6.15947 −0.208109
\(877\) −7.53456 −0.254424 −0.127212 0.991876i \(-0.540603\pi\)
−0.127212 + 0.991876i \(0.540603\pi\)
\(878\) −53.6638 −1.81107
\(879\) 27.6319 0.932002
\(880\) 41.3258 1.39309
\(881\) 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 \(-0.725163\pi\)
−0.649837 + 0.760074i \(0.725163\pi\)
\(884\) 0.00561953 0.000189005 0
\(885\) 66.8393 2.24678
\(886\) 3.52947 0.118575
\(887\) −14.3165 −0.480702 −0.240351 0.970686i \(-0.577262\pi\)
−0.240351 + 0.970686i \(0.577262\pi\)
\(888\) −17.4383 −0.585193
\(889\) −2.30230 −0.0772167
\(890\) −2.77733 −0.0930963
\(891\) 37.0654 1.24174
\(892\) 0.466012 0.0156032
\(893\) −26.0213 −0.870771
\(894\) −50.6843 −1.69514
\(895\) 64.0105 2.13963
\(896\) 2.76913 0.0925101
\(897\) 0.398272 0.0132979
\(898\) 40.6184 1.35545
\(899\) 5.18805 0.173031
\(900\) −1.21469 −0.0404895
\(901\) 11.9825 0.399196
\(902\) −61.7341 −2.05552
\(903\) 7.29644 0.242810
\(904\) −10.0496 −0.334243
\(905\) 54.3452 1.80650
\(906\) −10.6028 −0.352256
\(907\) −47.6042 −1.58067 −0.790336 0.612674i \(-0.790094\pi\)
−0.790336 + 0.612674i \(0.790094\pi\)
\(908\) −3.43573 −0.114019
\(909\) 53.3327 1.76893
\(910\) 0.0286767 0.000950625 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
\(915\) −54.9188 −1.81556
\(916\) −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 \(0.596158\pi\)
\(920\) −48.0212 −1.58321
\(921\) 3.05535 0.100677
\(922\) −52.1261 −1.71668
\(923\) −0.103585 −0.00340953
\(924\) 0.460321 0.0151435
\(925\) 6.11403 0.201028
\(926\) −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 \(0.503546\pi\)
\(930\) −18.4963 −0.606518
\(931\) 39.6295 1.29881
\(932\) 4.63923 0.151963
\(933\) 43.8510 1.43562
\(934\) 34.0574 1.11439
\(935\) 14.5635 0.476278
\(936\) 0.239460 0.00782699
\(937\) −25.7202 −0.840243 −0.420122 0.907468i \(-0.638013\pi\)
−0.420122 + 0.907468i \(0.638013\pi\)
\(938\) 1.69616 0.0553816
\(939\) 73.7186 2.40571
\(940\) −1.99983 −0.0652272
\(941\) −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
\(945\) 0.0102861 0.000334606 0
\(946\) 58.7460 1.91000
\(947\) −15.2367 −0.495128 −0.247564 0.968872i \(-0.579630\pi\)
−0.247564 + 0.968872i \(0.579630\pi\)
\(948\) 2.63274 0.0855074
\(949\) −0.425730 −0.0138198
\(950\) 19.5563 0.634490
\(951\) 20.0418 0.649900
\(952\) 1.06989 0.0346754
\(953\) 43.1360 1.39731 0.698656 0.715457i \(-0.253782\pi\)
0.698656 + 0.715457i \(0.253782\pi\)
\(954\) 37.9386 1.22831
\(955\) 5.18745 0.167862
\(956\) −4.11973 −0.133242
\(957\) −25.8440 −0.835417
\(958\) 29.8885 0.965652
\(959\) −1.55234 −0.0501277
\(960\) −57.3471 −1.85087
\(961\) −26.8804 −0.867110
\(962\) −0.0895566 −0.00288742
\(963\) −1.86098 −0.0599692
\(964\) 0.160532 0.00517039
\(965\) 47.2471 1.52094
\(966\) 5.63404 0.181272
\(967\) 45.6699 1.46864 0.734322 0.678801i \(-0.237500\pi\)
0.734322 + 0.678801i \(0.237500\pi\)
\(968\) 17.6471 0.567201
\(969\) −18.0687 −0.580449
\(970\) −44.3432 −1.42377
\(971\) −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
\(975\) −0.167762 −0.00537270
\(976\) −29.8591 −0.955768
\(977\) −50.8644 −1.62730 −0.813649 0.581357i \(-0.802522\pi\)
−0.813649 + 0.581357i \(0.802522\pi\)
\(978\) −47.0033 −1.50300
\(979\) −3.08141 −0.0984823
\(980\) 3.04567 0.0972903
\(981\) 10.0418 0.320610
\(982\) 54.9118 1.75231
\(983\) −21.2587 −0.678047 −0.339023 0.940778i \(-0.610097\pi\)
−0.339023 + 0.940778i \(0.610097\pi\)
\(984\) 79.2221 2.52551
\(985\) 12.6738 0.403821
\(986\) −4.46312 −0.142135
\(987\) 3.15775 0.100512
\(988\) 0.0249992 0.000795330 0
\(989\) −62.7490 −1.99530
\(990\) 46.1105 1.46549
\(991\) 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
\(995\) −48.5483 −1.53908
\(996\) −1.70294 −0.0539598
\(997\) −32.2376 −1.02097 −0.510487 0.859885i \(-0.670535\pi\)
−0.510487 + 0.859885i \(0.670535\pi\)
\(998\) 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 241.2.a.a.1.3 7
3.2 odd 2 2169.2.a.e.1.5 7
4.3 odd 2 3856.2.a.j.1.7 7
5.4 even 2 6025.2.a.f.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.3 7 1.1 even 1 trivial
2169.2.a.e.1.5 7 3.2 odd 2
3856.2.a.j.1.7 7 4.3 odd 2
6025.2.a.f.1.5 7 5.4 even 2