Properties

Label 4235.2.a.bc.1.5
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.288385.1
Defining polynomial: \(x^{5} - 7 x^{3} - 2 x^{2} + 10 x + 3\)
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 1.5
Root \(-1.90452\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +O(q^{10})\) \(q+1.90452 q^{2} +0.214998 q^{3} +1.62718 q^{4} +1.00000 q^{5} +0.409467 q^{6} -1.00000 q^{7} -0.710046 q^{8} -2.95378 q^{9} +1.90452 q^{10} +0.349840 q^{12} +4.56834 q^{13} -1.90452 q^{14} +0.214998 q^{15} -4.60665 q^{16} -3.25164 q^{17} -5.62551 q^{18} -5.02403 q^{19} +1.62718 q^{20} -0.214998 q^{21} +0.292666 q^{23} -0.152659 q^{24} +1.00000 q^{25} +8.70047 q^{26} -1.28005 q^{27} -1.62718 q^{28} -1.00271 q^{29} +0.409467 q^{30} -6.62551 q^{31} -7.35334 q^{32} -6.19280 q^{34} -1.00000 q^{35} -4.80632 q^{36} -4.62822 q^{37} -9.56834 q^{38} +0.982183 q^{39} -0.710046 q^{40} -2.69743 q^{41} -0.409467 q^{42} -0.193423 q^{43} -2.95378 q^{45} +0.557388 q^{46} -4.29620 q^{47} -0.990420 q^{48} +1.00000 q^{49} +1.90452 q^{50} -0.699097 q^{51} +7.43350 q^{52} +2.78333 q^{53} -2.43787 q^{54} +0.710046 q^{56} -1.08016 q^{57} -1.90968 q^{58} -0.846879 q^{59} +0.349840 q^{60} -0.963356 q^{61} -12.6184 q^{62} +2.95378 q^{63} -4.79125 q^{64} +4.56834 q^{65} +3.95848 q^{67} -5.29100 q^{68} +0.0629227 q^{69} -1.90452 q^{70} +5.54264 q^{71} +2.09732 q^{72} -11.7502 q^{73} -8.81452 q^{74} +0.214998 q^{75} -8.17499 q^{76} +1.87058 q^{78} +9.39619 q^{79} -4.60665 q^{80} +8.58612 q^{81} -5.13730 q^{82} -9.07799 q^{83} -0.349840 q^{84} -3.25164 q^{85} -0.368378 q^{86} -0.215581 q^{87} +4.30633 q^{89} -5.62551 q^{90} -4.56834 q^{91} +0.476220 q^{92} -1.42447 q^{93} -8.18218 q^{94} -5.02403 q^{95} -1.58095 q^{96} +1.09820 q^{97} +1.90452 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + O(q^{10}) \) \( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90452 1.34670 0.673348 0.739326i \(-0.264856\pi\)
0.673348 + 0.739326i \(0.264856\pi\)
\(3\) 0.214998 0.124129 0.0620646 0.998072i \(-0.480232\pi\)
0.0620646 + 0.998072i \(0.480232\pi\)
\(4\) 1.62718 0.813589
\(5\) 1.00000 0.447214
\(6\) 0.409467 0.167164
\(7\) −1.00000 −0.377964
\(8\) −0.710046 −0.251039
\(9\) −2.95378 −0.984592
\(10\) 1.90452 0.602261
\(11\) 0 0
\(12\) 0.349840 0.100990
\(13\) 4.56834 1.26703 0.633514 0.773731i \(-0.281612\pi\)
0.633514 + 0.773731i \(0.281612\pi\)
\(14\) −1.90452 −0.509003
\(15\) 0.214998 0.0555123
\(16\) −4.60665 −1.15166
\(17\) −3.25164 −0.788639 −0.394320 0.918973i \(-0.629020\pi\)
−0.394320 + 0.918973i \(0.629020\pi\)
\(18\) −5.62551 −1.32595
\(19\) −5.02403 −1.15259 −0.576296 0.817241i \(-0.695502\pi\)
−0.576296 + 0.817241i \(0.695502\pi\)
\(20\) 1.62718 0.363848
\(21\) −0.214998 −0.0469164
\(22\) 0 0
\(23\) 0.292666 0.0610252 0.0305126 0.999534i \(-0.490286\pi\)
0.0305126 + 0.999534i \(0.490286\pi\)
\(24\) −0.152659 −0.0311613
\(25\) 1.00000 0.200000
\(26\) 8.70047 1.70630
\(27\) −1.28005 −0.246346
\(28\) −1.62718 −0.307508
\(29\) −1.00271 −0.186199 −0.0930995 0.995657i \(-0.529677\pi\)
−0.0930995 + 0.995657i \(0.529677\pi\)
\(30\) 0.409467 0.0747581
\(31\) −6.62551 −1.18998 −0.594988 0.803734i \(-0.702843\pi\)
−0.594988 + 0.803734i \(0.702843\pi\)
\(32\) −7.35334 −1.29990
\(33\) 0 0
\(34\) −6.19280 −1.06206
\(35\) −1.00000 −0.169031
\(36\) −4.80632 −0.801053
\(37\) −4.62822 −0.760875 −0.380438 0.924807i \(-0.624227\pi\)
−0.380438 + 0.924807i \(0.624227\pi\)
\(38\) −9.56834 −1.55219
\(39\) 0.982183 0.157275
\(40\) −0.710046 −0.112268
\(41\) −2.69743 −0.421268 −0.210634 0.977565i \(-0.567553\pi\)
−0.210634 + 0.977565i \(0.567553\pi\)
\(42\) −0.409467 −0.0631821
\(43\) −0.193423 −0.0294968 −0.0147484 0.999891i \(-0.504695\pi\)
−0.0147484 + 0.999891i \(0.504695\pi\)
\(44\) 0 0
\(45\) −2.95378 −0.440323
\(46\) 0.557388 0.0821823
\(47\) −4.29620 −0.626665 −0.313333 0.949643i \(-0.601445\pi\)
−0.313333 + 0.949643i \(0.601445\pi\)
\(48\) −0.990420 −0.142955
\(49\) 1.00000 0.142857
\(50\) 1.90452 0.269339
\(51\) −0.699097 −0.0978931
\(52\) 7.43350 1.03084
\(53\) 2.78333 0.382320 0.191160 0.981559i \(-0.438775\pi\)
0.191160 + 0.981559i \(0.438775\pi\)
\(54\) −2.43787 −0.331753
\(55\) 0 0
\(56\) 0.710046 0.0948839
\(57\) −1.08016 −0.143070
\(58\) −1.90968 −0.250753
\(59\) −0.846879 −0.110254 −0.0551271 0.998479i \(-0.517556\pi\)
−0.0551271 + 0.998479i \(0.517556\pi\)
\(60\) 0.349840 0.0451641
\(61\) −0.963356 −0.123345 −0.0616725 0.998096i \(-0.519643\pi\)
−0.0616725 + 0.998096i \(0.519643\pi\)
\(62\) −12.6184 −1.60254
\(63\) 2.95378 0.372141
\(64\) −4.79125 −0.598906
\(65\) 4.56834 0.566632
\(66\) 0 0
\(67\) 3.95848 0.483605 0.241803 0.970325i \(-0.422261\pi\)
0.241803 + 0.970325i \(0.422261\pi\)
\(68\) −5.29100 −0.641628
\(69\) 0.0629227 0.00757500
\(70\) −1.90452 −0.227633
\(71\) 5.54264 0.657791 0.328895 0.944366i \(-0.393324\pi\)
0.328895 + 0.944366i \(0.393324\pi\)
\(72\) 2.09732 0.247171
\(73\) −11.7502 −1.37526 −0.687628 0.726063i \(-0.741348\pi\)
−0.687628 + 0.726063i \(0.741348\pi\)
\(74\) −8.81452 −1.02467
\(75\) 0.214998 0.0248258
\(76\) −8.17499 −0.937735
\(77\) 0 0
\(78\) 1.87058 0.211802
\(79\) 9.39619 1.05715 0.528577 0.848885i \(-0.322726\pi\)
0.528577 + 0.848885i \(0.322726\pi\)
\(80\) −4.60665 −0.515039
\(81\) 8.58612 0.954013
\(82\) −5.13730 −0.567319
\(83\) −9.07799 −0.996439 −0.498220 0.867051i \(-0.666013\pi\)
−0.498220 + 0.867051i \(0.666013\pi\)
\(84\) −0.349840 −0.0381707
\(85\) −3.25164 −0.352690
\(86\) −0.368378 −0.0397232
\(87\) −0.215581 −0.0231127
\(88\) 0 0
\(89\) 4.30633 0.456470 0.228235 0.973606i \(-0.426705\pi\)
0.228235 + 0.973606i \(0.426705\pi\)
\(90\) −5.62551 −0.592981
\(91\) −4.56834 −0.478892
\(92\) 0.476220 0.0496494
\(93\) −1.42447 −0.147711
\(94\) −8.18218 −0.843927
\(95\) −5.02403 −0.515454
\(96\) −1.58095 −0.161355
\(97\) 1.09820 0.111505 0.0557525 0.998445i \(-0.482244\pi\)
0.0557525 + 0.998445i \(0.482244\pi\)
\(98\) 1.90452 0.192385
\(99\) 0 0
\(100\) 1.62718 0.162718
\(101\) −4.61577 −0.459286 −0.229643 0.973275i \(-0.573756\pi\)
−0.229643 + 0.973275i \(0.573756\pi\)
\(102\) −1.33144 −0.131832
\(103\) 13.8643 1.36609 0.683044 0.730377i \(-0.260656\pi\)
0.683044 + 0.730377i \(0.260656\pi\)
\(104\) −3.24373 −0.318074
\(105\) −0.214998 −0.0209817
\(106\) 5.30090 0.514869
\(107\) −14.5598 −1.40755 −0.703775 0.710423i \(-0.748504\pi\)
−0.703775 + 0.710423i \(0.748504\pi\)
\(108\) −2.08287 −0.200424
\(109\) −19.4350 −1.86154 −0.930768 0.365611i \(-0.880860\pi\)
−0.930768 + 0.365611i \(0.880860\pi\)
\(110\) 0 0
\(111\) −0.995059 −0.0944468
\(112\) 4.60665 0.435287
\(113\) −17.1884 −1.61695 −0.808474 0.588532i \(-0.799706\pi\)
−0.808474 + 0.588532i \(0.799706\pi\)
\(114\) −2.05717 −0.192672
\(115\) 0.292666 0.0272913
\(116\) −1.63159 −0.151489
\(117\) −13.4938 −1.24751
\(118\) −1.61289 −0.148479
\(119\) 3.25164 0.298078
\(120\) −0.152659 −0.0139358
\(121\) 0 0
\(122\) −1.83473 −0.166108
\(123\) −0.579942 −0.0522916
\(124\) −10.7809 −0.968152
\(125\) 1.00000 0.0894427
\(126\) 5.62551 0.501160
\(127\) −3.06459 −0.271938 −0.135969 0.990713i \(-0.543415\pi\)
−0.135969 + 0.990713i \(0.543415\pi\)
\(128\) 5.58167 0.493355
\(129\) −0.0415857 −0.00366141
\(130\) 8.70047 0.763081
\(131\) 14.6745 1.28212 0.641059 0.767492i \(-0.278495\pi\)
0.641059 + 0.767492i \(0.278495\pi\)
\(132\) 0 0
\(133\) 5.02403 0.435638
\(134\) 7.53898 0.651269
\(135\) −1.28005 −0.110169
\(136\) 2.30882 0.197979
\(137\) −15.7705 −1.34737 −0.673683 0.739020i \(-0.735289\pi\)
−0.673683 + 0.739020i \(0.735289\pi\)
\(138\) 0.119837 0.0102012
\(139\) 9.60769 0.814914 0.407457 0.913224i \(-0.366416\pi\)
0.407457 + 0.913224i \(0.366416\pi\)
\(140\) −1.62718 −0.137522
\(141\) −0.923674 −0.0777874
\(142\) 10.5560 0.885844
\(143\) 0 0
\(144\) 13.6070 1.13392
\(145\) −1.00271 −0.0832707
\(146\) −22.3784 −1.85205
\(147\) 0.214998 0.0177327
\(148\) −7.53094 −0.619039
\(149\) −1.39502 −0.114284 −0.0571422 0.998366i \(-0.518199\pi\)
−0.0571422 + 0.998366i \(0.518199\pi\)
\(150\) 0.409467 0.0334328
\(151\) −11.9950 −0.976136 −0.488068 0.872805i \(-0.662298\pi\)
−0.488068 + 0.872805i \(0.662298\pi\)
\(152\) 3.56729 0.289346
\(153\) 9.60462 0.776488
\(154\) 0 0
\(155\) −6.62551 −0.532174
\(156\) 1.59819 0.127957
\(157\) −24.4749 −1.95331 −0.976657 0.214807i \(-0.931088\pi\)
−0.976657 + 0.214807i \(0.931088\pi\)
\(158\) 17.8952 1.42367
\(159\) 0.598412 0.0474571
\(160\) −7.35334 −0.581332
\(161\) −0.292666 −0.0230653
\(162\) 16.3524 1.28477
\(163\) 1.83205 0.143497 0.0717485 0.997423i \(-0.477142\pi\)
0.0717485 + 0.997423i \(0.477142\pi\)
\(164\) −4.38920 −0.342739
\(165\) 0 0
\(166\) −17.2892 −1.34190
\(167\) 6.88977 0.533146 0.266573 0.963815i \(-0.414109\pi\)
0.266573 + 0.963815i \(0.414109\pi\)
\(168\) 0.152659 0.0117779
\(169\) 7.86970 0.605362
\(170\) −6.19280 −0.474966
\(171\) 14.8399 1.13483
\(172\) −0.314734 −0.0239983
\(173\) 8.34496 0.634456 0.317228 0.948349i \(-0.397248\pi\)
0.317228 + 0.948349i \(0.397248\pi\)
\(174\) −0.410578 −0.0311258
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) −0.182077 −0.0136858
\(178\) 8.20147 0.614726
\(179\) 7.34255 0.548808 0.274404 0.961614i \(-0.411519\pi\)
0.274404 + 0.961614i \(0.411519\pi\)
\(180\) −4.80632 −0.358242
\(181\) 0.127426 0.00947148 0.00473574 0.999989i \(-0.498493\pi\)
0.00473574 + 0.999989i \(0.498493\pi\)
\(182\) −8.70047 −0.644921
\(183\) −0.207120 −0.0153107
\(184\) −0.207807 −0.0153197
\(185\) −4.62822 −0.340274
\(186\) −2.71293 −0.198922
\(187\) 0 0
\(188\) −6.99068 −0.509848
\(189\) 1.28005 0.0931099
\(190\) −9.56834 −0.694160
\(191\) 23.0237 1.66594 0.832968 0.553321i \(-0.186640\pi\)
0.832968 + 0.553321i \(0.186640\pi\)
\(192\) −1.03011 −0.0743417
\(193\) 17.8948 1.28809 0.644047 0.764986i \(-0.277254\pi\)
0.644047 + 0.764986i \(0.277254\pi\)
\(194\) 2.09153 0.150163
\(195\) 0.982183 0.0703356
\(196\) 1.62718 0.116227
\(197\) 21.6655 1.54360 0.771801 0.635864i \(-0.219356\pi\)
0.771801 + 0.635864i \(0.219356\pi\)
\(198\) 0 0
\(199\) 24.8072 1.75853 0.879267 0.476330i \(-0.158033\pi\)
0.879267 + 0.476330i \(0.158033\pi\)
\(200\) −0.710046 −0.0502078
\(201\) 0.851065 0.0600295
\(202\) −8.79080 −0.618518
\(203\) 1.00271 0.0703766
\(204\) −1.13755 −0.0796447
\(205\) −2.69743 −0.188397
\(206\) 26.4047 1.83970
\(207\) −0.864471 −0.0600849
\(208\) −21.0447 −1.45919
\(209\) 0 0
\(210\) −0.409467 −0.0282559
\(211\) −21.0959 −1.45230 −0.726150 0.687536i \(-0.758692\pi\)
−0.726150 + 0.687536i \(0.758692\pi\)
\(212\) 4.52898 0.311052
\(213\) 1.19166 0.0816510
\(214\) −27.7294 −1.89554
\(215\) −0.193423 −0.0131914
\(216\) 0.908895 0.0618424
\(217\) 6.62551 0.449769
\(218\) −37.0143 −2.50692
\(219\) −2.52627 −0.170709
\(220\) 0 0
\(221\) −14.8546 −0.999228
\(222\) −1.89510 −0.127191
\(223\) 13.0233 0.872105 0.436053 0.899921i \(-0.356376\pi\)
0.436053 + 0.899921i \(0.356376\pi\)
\(224\) 7.35334 0.491316
\(225\) −2.95378 −0.196918
\(226\) −32.7355 −2.17754
\(227\) −12.1441 −0.806032 −0.403016 0.915193i \(-0.632038\pi\)
−0.403016 + 0.915193i \(0.632038\pi\)
\(228\) −1.75761 −0.116400
\(229\) 18.8096 1.24297 0.621487 0.783424i \(-0.286529\pi\)
0.621487 + 0.783424i \(0.286529\pi\)
\(230\) 0.557388 0.0367530
\(231\) 0 0
\(232\) 0.711972 0.0467433
\(233\) −23.4069 −1.53344 −0.766719 0.641983i \(-0.778112\pi\)
−0.766719 + 0.641983i \(0.778112\pi\)
\(234\) −25.6992 −1.68001
\(235\) −4.29620 −0.280253
\(236\) −1.37802 −0.0897016
\(237\) 2.02016 0.131224
\(238\) 6.19280 0.401420
\(239\) −15.0841 −0.975710 −0.487855 0.872925i \(-0.662221\pi\)
−0.487855 + 0.872925i \(0.662221\pi\)
\(240\) −0.990420 −0.0639314
\(241\) 0.499627 0.0321838 0.0160919 0.999871i \(-0.494878\pi\)
0.0160919 + 0.999871i \(0.494878\pi\)
\(242\) 0 0
\(243\) 5.68615 0.364767
\(244\) −1.56755 −0.100352
\(245\) 1.00000 0.0638877
\(246\) −1.10451 −0.0704209
\(247\) −22.9515 −1.46037
\(248\) 4.70442 0.298731
\(249\) −1.95175 −0.123687
\(250\) 1.90452 0.120452
\(251\) −20.8388 −1.31533 −0.657666 0.753310i \(-0.728456\pi\)
−0.657666 + 0.753310i \(0.728456\pi\)
\(252\) 4.80632 0.302770
\(253\) 0 0
\(254\) −5.83656 −0.366218
\(255\) −0.699097 −0.0437791
\(256\) 20.2129 1.26330
\(257\) −9.23887 −0.576305 −0.288152 0.957585i \(-0.593041\pi\)
−0.288152 + 0.957585i \(0.593041\pi\)
\(258\) −0.0792005 −0.00493081
\(259\) 4.62822 0.287584
\(260\) 7.43350 0.461006
\(261\) 2.96179 0.183330
\(262\) 27.9478 1.72662
\(263\) −3.90063 −0.240523 −0.120262 0.992742i \(-0.538373\pi\)
−0.120262 + 0.992742i \(0.538373\pi\)
\(264\) 0 0
\(265\) 2.78333 0.170979
\(266\) 9.56834 0.586672
\(267\) 0.925852 0.0566612
\(268\) 6.44115 0.393456
\(269\) 27.9577 1.70461 0.852307 0.523043i \(-0.175203\pi\)
0.852307 + 0.523043i \(0.175203\pi\)
\(270\) −2.43787 −0.148364
\(271\) −24.0897 −1.46335 −0.731673 0.681655i \(-0.761260\pi\)
−0.731673 + 0.681655i \(0.761260\pi\)
\(272\) 14.9792 0.908246
\(273\) −0.982183 −0.0594444
\(274\) −30.0352 −1.81449
\(275\) 0 0
\(276\) 0.102386 0.00616294
\(277\) −27.1882 −1.63358 −0.816790 0.576935i \(-0.804249\pi\)
−0.816790 + 0.576935i \(0.804249\pi\)
\(278\) 18.2980 1.09744
\(279\) 19.5703 1.17164
\(280\) 0.710046 0.0424334
\(281\) −19.4935 −1.16289 −0.581443 0.813587i \(-0.697512\pi\)
−0.581443 + 0.813587i \(0.697512\pi\)
\(282\) −1.75915 −0.104756
\(283\) 2.43412 0.144693 0.0723466 0.997380i \(-0.476951\pi\)
0.0723466 + 0.997380i \(0.476951\pi\)
\(284\) 9.01886 0.535171
\(285\) −1.08016 −0.0639829
\(286\) 0 0
\(287\) 2.69743 0.159224
\(288\) 21.7201 1.27987
\(289\) −6.42682 −0.378048
\(290\) −1.90968 −0.112140
\(291\) 0.236110 0.0138410
\(292\) −19.1196 −1.11889
\(293\) 24.4918 1.43083 0.715413 0.698702i \(-0.246239\pi\)
0.715413 + 0.698702i \(0.246239\pi\)
\(294\) 0.409467 0.0238806
\(295\) −0.846879 −0.0493072
\(296\) 3.28625 0.191009
\(297\) 0 0
\(298\) −2.65683 −0.153906
\(299\) 1.33700 0.0773206
\(300\) 0.349840 0.0201980
\(301\) 0.193423 0.0111487
\(302\) −22.8446 −1.31456
\(303\) −0.992381 −0.0570108
\(304\) 23.1439 1.32740
\(305\) −0.963356 −0.0551616
\(306\) 18.2921 1.04569
\(307\) 23.0511 1.31559 0.657797 0.753195i \(-0.271488\pi\)
0.657797 + 0.753195i \(0.271488\pi\)
\(308\) 0 0
\(309\) 2.98079 0.169571
\(310\) −12.6184 −0.716676
\(311\) 18.7222 1.06164 0.530819 0.847485i \(-0.321884\pi\)
0.530819 + 0.847485i \(0.321884\pi\)
\(312\) −0.697395 −0.0394822
\(313\) 15.4725 0.874555 0.437277 0.899327i \(-0.355943\pi\)
0.437277 + 0.899327i \(0.355943\pi\)
\(314\) −46.6129 −2.63052
\(315\) 2.95378 0.166426
\(316\) 15.2893 0.860089
\(317\) 12.8989 0.724476 0.362238 0.932086i \(-0.382013\pi\)
0.362238 + 0.932086i \(0.382013\pi\)
\(318\) 1.13968 0.0639103
\(319\) 0 0
\(320\) −4.79125 −0.267839
\(321\) −3.13033 −0.174718
\(322\) −0.557388 −0.0310620
\(323\) 16.3363 0.908978
\(324\) 13.9711 0.776174
\(325\) 4.56834 0.253406
\(326\) 3.48916 0.193247
\(327\) −4.17849 −0.231071
\(328\) 1.91530 0.105755
\(329\) 4.29620 0.236857
\(330\) 0 0
\(331\) −8.28642 −0.455463 −0.227731 0.973724i \(-0.573131\pi\)
−0.227731 + 0.973724i \(0.573131\pi\)
\(332\) −14.7715 −0.810692
\(333\) 13.6707 0.749152
\(334\) 13.1217 0.717986
\(335\) 3.95848 0.216275
\(336\) 0.990420 0.0540319
\(337\) 33.6591 1.83353 0.916763 0.399431i \(-0.130792\pi\)
0.916763 + 0.399431i \(0.130792\pi\)
\(338\) 14.9880 0.815238
\(339\) −3.69547 −0.200710
\(340\) −5.29100 −0.286945
\(341\) 0 0
\(342\) 28.2627 1.52827
\(343\) −1.00000 −0.0539949
\(344\) 0.137340 0.00740485
\(345\) 0.0629227 0.00338764
\(346\) 15.8931 0.854419
\(347\) 19.8757 1.06698 0.533492 0.845805i \(-0.320879\pi\)
0.533492 + 0.845805i \(0.320879\pi\)
\(348\) −0.350789 −0.0188043
\(349\) −18.7227 −1.00221 −0.501103 0.865388i \(-0.667072\pi\)
−0.501103 + 0.865388i \(0.667072\pi\)
\(350\) −1.90452 −0.101801
\(351\) −5.84770 −0.312127
\(352\) 0 0
\(353\) 13.9588 0.742951 0.371476 0.928443i \(-0.378852\pi\)
0.371476 + 0.928443i \(0.378852\pi\)
\(354\) −0.346769 −0.0184306
\(355\) 5.54264 0.294173
\(356\) 7.00716 0.371379
\(357\) 0.699097 0.0370001
\(358\) 13.9840 0.739078
\(359\) 30.4147 1.60523 0.802613 0.596501i \(-0.203443\pi\)
0.802613 + 0.596501i \(0.203443\pi\)
\(360\) 2.09732 0.110538
\(361\) 6.24086 0.328466
\(362\) 0.242684 0.0127552
\(363\) 0 0
\(364\) −7.43350 −0.389621
\(365\) −11.7502 −0.615033
\(366\) −0.394462 −0.0206189
\(367\) −22.8152 −1.19094 −0.595471 0.803377i \(-0.703035\pi\)
−0.595471 + 0.803377i \(0.703035\pi\)
\(368\) −1.34821 −0.0702804
\(369\) 7.96760 0.414777
\(370\) −8.81452 −0.458245
\(371\) −2.78333 −0.144504
\(372\) −2.31787 −0.120176
\(373\) −25.0369 −1.29636 −0.648180 0.761487i \(-0.724470\pi\)
−0.648180 + 0.761487i \(0.724470\pi\)
\(374\) 0 0
\(375\) 0.214998 0.0111025
\(376\) 3.05050 0.157318
\(377\) −4.58073 −0.235920
\(378\) 2.43787 0.125391
\(379\) 24.0173 1.23369 0.616843 0.787086i \(-0.288411\pi\)
0.616843 + 0.787086i \(0.288411\pi\)
\(380\) −8.17499 −0.419368
\(381\) −0.658881 −0.0337555
\(382\) 43.8490 2.24351
\(383\) 7.78788 0.397942 0.198971 0.980005i \(-0.436240\pi\)
0.198971 + 0.980005i \(0.436240\pi\)
\(384\) 1.20005 0.0612397
\(385\) 0 0
\(386\) 34.0809 1.73467
\(387\) 0.571329 0.0290423
\(388\) 1.78696 0.0907193
\(389\) 12.4598 0.631735 0.315867 0.948803i \(-0.397705\pi\)
0.315867 + 0.948803i \(0.397705\pi\)
\(390\) 1.87058 0.0947207
\(391\) −0.951647 −0.0481268
\(392\) −0.710046 −0.0358627
\(393\) 3.15499 0.159148
\(394\) 41.2623 2.07876
\(395\) 9.39619 0.472774
\(396\) 0 0
\(397\) −1.78212 −0.0894419 −0.0447209 0.999000i \(-0.514240\pi\)
−0.0447209 + 0.999000i \(0.514240\pi\)
\(398\) 47.2456 2.36821
\(399\) 1.08016 0.0540754
\(400\) −4.60665 −0.230332
\(401\) −32.5153 −1.62373 −0.811867 0.583842i \(-0.801549\pi\)
−0.811867 + 0.583842i \(0.801549\pi\)
\(402\) 1.62087 0.0808415
\(403\) −30.2676 −1.50773
\(404\) −7.51067 −0.373670
\(405\) 8.58612 0.426648
\(406\) 1.90968 0.0947759
\(407\) 0 0
\(408\) 0.496391 0.0245750
\(409\) −25.7104 −1.27130 −0.635648 0.771979i \(-0.719267\pi\)
−0.635648 + 0.771979i \(0.719267\pi\)
\(410\) −5.13730 −0.253713
\(411\) −3.39063 −0.167248
\(412\) 22.5596 1.11143
\(413\) 0.846879 0.0416722
\(414\) −1.64640 −0.0809160
\(415\) −9.07799 −0.445621
\(416\) −33.5925 −1.64701
\(417\) 2.06564 0.101155
\(418\) 0 0
\(419\) 18.6850 0.912822 0.456411 0.889769i \(-0.349135\pi\)
0.456411 + 0.889769i \(0.349135\pi\)
\(420\) −0.349840 −0.0170704
\(421\) 8.91435 0.434459 0.217229 0.976121i \(-0.430298\pi\)
0.217229 + 0.976121i \(0.430298\pi\)
\(422\) −40.1774 −1.95581
\(423\) 12.6900 0.617009
\(424\) −1.97630 −0.0959774
\(425\) −3.25164 −0.157728
\(426\) 2.26953 0.109959
\(427\) 0.963356 0.0466200
\(428\) −23.6914 −1.14517
\(429\) 0 0
\(430\) −0.368378 −0.0177648
\(431\) −25.5710 −1.23171 −0.615856 0.787859i \(-0.711190\pi\)
−0.615856 + 0.787859i \(0.711190\pi\)
\(432\) 5.89674 0.283707
\(433\) 21.0251 1.01040 0.505201 0.863002i \(-0.331418\pi\)
0.505201 + 0.863002i \(0.331418\pi\)
\(434\) 12.6184 0.605702
\(435\) −0.215581 −0.0103363
\(436\) −31.6242 −1.51452
\(437\) −1.47036 −0.0703371
\(438\) −4.81131 −0.229893
\(439\) −23.6556 −1.12902 −0.564510 0.825426i \(-0.690935\pi\)
−0.564510 + 0.825426i \(0.690935\pi\)
\(440\) 0 0
\(441\) −2.95378 −0.140656
\(442\) −28.2908 −1.34566
\(443\) 33.3347 1.58378 0.791889 0.610665i \(-0.209098\pi\)
0.791889 + 0.610665i \(0.209098\pi\)
\(444\) −1.61914 −0.0768409
\(445\) 4.30633 0.204140
\(446\) 24.8031 1.17446
\(447\) −0.299926 −0.0141860
\(448\) 4.79125 0.226365
\(449\) −27.5835 −1.30175 −0.650873 0.759187i \(-0.725597\pi\)
−0.650873 + 0.759187i \(0.725597\pi\)
\(450\) −5.62551 −0.265189
\(451\) 0 0
\(452\) −27.9686 −1.31553
\(453\) −2.57889 −0.121167
\(454\) −23.1286 −1.08548
\(455\) −4.56834 −0.214167
\(456\) 0.766961 0.0359162
\(457\) −12.8605 −0.601591 −0.300795 0.953689i \(-0.597252\pi\)
−0.300795 + 0.953689i \(0.597252\pi\)
\(458\) 35.8232 1.67391
\(459\) 4.16227 0.194278
\(460\) 0.476220 0.0222039
\(461\) 26.6291 1.24024 0.620119 0.784507i \(-0.287084\pi\)
0.620119 + 0.784507i \(0.287084\pi\)
\(462\) 0 0
\(463\) 19.2976 0.896836 0.448418 0.893824i \(-0.351988\pi\)
0.448418 + 0.893824i \(0.351988\pi\)
\(464\) 4.61914 0.214438
\(465\) −1.42447 −0.0660583
\(466\) −44.5788 −2.06507
\(467\) −35.9799 −1.66495 −0.832475 0.554063i \(-0.813077\pi\)
−0.832475 + 0.554063i \(0.813077\pi\)
\(468\) −21.9569 −1.01496
\(469\) −3.95848 −0.182786
\(470\) −8.18218 −0.377416
\(471\) −5.26206 −0.242463
\(472\) 0.601323 0.0276781
\(473\) 0 0
\(474\) 3.84743 0.176718
\(475\) −5.02403 −0.230518
\(476\) 5.29100 0.242513
\(477\) −8.22135 −0.376430
\(478\) −28.7279 −1.31398
\(479\) −27.9003 −1.27480 −0.637399 0.770534i \(-0.719990\pi\)
−0.637399 + 0.770534i \(0.719990\pi\)
\(480\) −1.58095 −0.0721603
\(481\) −21.1433 −0.964051
\(482\) 0.951547 0.0433418
\(483\) −0.0629227 −0.00286308
\(484\) 0 0
\(485\) 1.09820 0.0498666
\(486\) 10.8294 0.491230
\(487\) 23.1099 1.04721 0.523606 0.851961i \(-0.324586\pi\)
0.523606 + 0.851961i \(0.324586\pi\)
\(488\) 0.684027 0.0309644
\(489\) 0.393886 0.0178122
\(490\) 1.90452 0.0860372
\(491\) 16.1116 0.727107 0.363553 0.931573i \(-0.381563\pi\)
0.363553 + 0.931573i \(0.381563\pi\)
\(492\) −0.943669 −0.0425439
\(493\) 3.26046 0.146844
\(494\) −43.7114 −1.96667
\(495\) 0 0
\(496\) 30.5214 1.37045
\(497\) −5.54264 −0.248621
\(498\) −3.71714 −0.166569
\(499\) −16.4187 −0.735003 −0.367501 0.930023i \(-0.619787\pi\)
−0.367501 + 0.930023i \(0.619787\pi\)
\(500\) 1.62718 0.0727696
\(501\) 1.48129 0.0661790
\(502\) −39.6878 −1.77135
\(503\) 11.4726 0.511536 0.255768 0.966738i \(-0.417672\pi\)
0.255768 + 0.966738i \(0.417672\pi\)
\(504\) −2.09732 −0.0934219
\(505\) −4.61577 −0.205399
\(506\) 0 0
\(507\) 1.69197 0.0751430
\(508\) −4.98663 −0.221246
\(509\) 30.6084 1.35669 0.678346 0.734743i \(-0.262697\pi\)
0.678346 + 0.734743i \(0.262697\pi\)
\(510\) −1.33144 −0.0589572
\(511\) 11.7502 0.519798
\(512\) 27.3324 1.20793
\(513\) 6.43101 0.283936
\(514\) −17.5956 −0.776107
\(515\) 13.8643 0.610933
\(516\) −0.0676672 −0.00297888
\(517\) 0 0
\(518\) 8.81452 0.387288
\(519\) 1.79415 0.0787545
\(520\) −3.24373 −0.142247
\(521\) −7.28080 −0.318978 −0.159489 0.987200i \(-0.550985\pi\)
−0.159489 + 0.987200i \(0.550985\pi\)
\(522\) 5.64077 0.246890
\(523\) −18.5202 −0.809832 −0.404916 0.914354i \(-0.632699\pi\)
−0.404916 + 0.914354i \(0.632699\pi\)
\(524\) 23.8780 1.04312
\(525\) −0.214998 −0.00938328
\(526\) −7.42881 −0.323912
\(527\) 21.5438 0.938462
\(528\) 0 0
\(529\) −22.9143 −0.996276
\(530\) 5.30090 0.230257
\(531\) 2.50149 0.108555
\(532\) 8.17499 0.354431
\(533\) −12.3228 −0.533758
\(534\) 1.76330 0.0763054
\(535\) −14.5598 −0.629475
\(536\) −2.81070 −0.121404
\(537\) 1.57863 0.0681231
\(538\) 53.2459 2.29559
\(539\) 0 0
\(540\) −2.08287 −0.0896324
\(541\) −13.2331 −0.568933 −0.284467 0.958686i \(-0.591817\pi\)
−0.284467 + 0.958686i \(0.591817\pi\)
\(542\) −45.8792 −1.97068
\(543\) 0.0273963 0.00117569
\(544\) 23.9104 1.02515
\(545\) −19.4350 −0.832504
\(546\) −1.87058 −0.0800536
\(547\) 21.7449 0.929745 0.464872 0.885378i \(-0.346100\pi\)
0.464872 + 0.885378i \(0.346100\pi\)
\(548\) −25.6614 −1.09620
\(549\) 2.84554 0.121445
\(550\) 0 0
\(551\) 5.03766 0.214611
\(552\) −0.0446780 −0.00190162
\(553\) −9.39619 −0.399567
\(554\) −51.7803 −2.19994
\(555\) −0.995059 −0.0422379
\(556\) 15.6334 0.663005
\(557\) −22.5249 −0.954412 −0.477206 0.878792i \(-0.658350\pi\)
−0.477206 + 0.878792i \(0.658350\pi\)
\(558\) 37.2719 1.57784
\(559\) −0.883623 −0.0373733
\(560\) 4.60665 0.194666
\(561\) 0 0
\(562\) −37.1257 −1.56605
\(563\) −2.07905 −0.0876213 −0.0438107 0.999040i \(-0.513950\pi\)
−0.0438107 + 0.999040i \(0.513950\pi\)
\(564\) −1.50298 −0.0632870
\(565\) −17.1884 −0.723121
\(566\) 4.63581 0.194858
\(567\) −8.58612 −0.360583
\(568\) −3.93553 −0.165131
\(569\) −40.5323 −1.69920 −0.849602 0.527425i \(-0.823158\pi\)
−0.849602 + 0.527425i \(0.823158\pi\)
\(570\) −2.05717 −0.0861655
\(571\) −45.1005 −1.88740 −0.943698 0.330807i \(-0.892679\pi\)
−0.943698 + 0.330807i \(0.892679\pi\)
\(572\) 0 0
\(573\) 4.95005 0.206791
\(574\) 5.13730 0.214427
\(575\) 0.292666 0.0122050
\(576\) 14.1523 0.589678
\(577\) 11.0837 0.461420 0.230710 0.973023i \(-0.425895\pi\)
0.230710 + 0.973023i \(0.425895\pi\)
\(578\) −12.2400 −0.509116
\(579\) 3.84734 0.159890
\(580\) −1.63159 −0.0677481
\(581\) 9.07799 0.376619
\(582\) 0.449676 0.0186397
\(583\) 0 0
\(584\) 8.34318 0.345243
\(585\) −13.4938 −0.557902
\(586\) 46.6450 1.92689
\(587\) −25.9005 −1.06903 −0.534513 0.845160i \(-0.679505\pi\)
−0.534513 + 0.845160i \(0.679505\pi\)
\(588\) 0.349840 0.0144272
\(589\) 33.2868 1.37156
\(590\) −1.61289 −0.0664018
\(591\) 4.65804 0.191606
\(592\) 21.3206 0.876271
\(593\) −2.48445 −0.102024 −0.0510122 0.998698i \(-0.516245\pi\)
−0.0510122 + 0.998698i \(0.516245\pi\)
\(594\) 0 0
\(595\) 3.25164 0.133304
\(596\) −2.26994 −0.0929805
\(597\) 5.33349 0.218285
\(598\) 2.54633 0.104127
\(599\) −5.73493 −0.234323 −0.117161 0.993113i \(-0.537379\pi\)
−0.117161 + 0.993113i \(0.537379\pi\)
\(600\) −0.152659 −0.00623226
\(601\) 25.8331 1.05375 0.526877 0.849942i \(-0.323363\pi\)
0.526877 + 0.849942i \(0.323363\pi\)
\(602\) 0.368378 0.0150140
\(603\) −11.6925 −0.476154
\(604\) −19.5179 −0.794174
\(605\) 0 0
\(606\) −1.89000 −0.0767761
\(607\) −13.1269 −0.532804 −0.266402 0.963862i \(-0.585835\pi\)
−0.266402 + 0.963862i \(0.585835\pi\)
\(608\) 36.9434 1.49825
\(609\) 0.215581 0.00873579
\(610\) −1.83473 −0.0742858
\(611\) −19.6265 −0.794003
\(612\) 15.6284 0.631742
\(613\) −13.8513 −0.559450 −0.279725 0.960080i \(-0.590243\pi\)
−0.279725 + 0.960080i \(0.590243\pi\)
\(614\) 43.9011 1.77170
\(615\) −0.579942 −0.0233855
\(616\) 0 0
\(617\) −0.619693 −0.0249479 −0.0124739 0.999922i \(-0.503971\pi\)
−0.0124739 + 0.999922i \(0.503971\pi\)
\(618\) 5.67696 0.228361
\(619\) 29.7025 1.19385 0.596923 0.802299i \(-0.296390\pi\)
0.596923 + 0.802299i \(0.296390\pi\)
\(620\) −10.7809 −0.432971
\(621\) −0.374628 −0.0150333
\(622\) 35.6567 1.42970
\(623\) −4.30633 −0.172529
\(624\) −4.52457 −0.181128
\(625\) 1.00000 0.0400000
\(626\) 29.4675 1.17776
\(627\) 0 0
\(628\) −39.8251 −1.58919
\(629\) 15.0493 0.600056
\(630\) 5.62551 0.224126
\(631\) 20.4025 0.812212 0.406106 0.913826i \(-0.366886\pi\)
0.406106 + 0.913826i \(0.366886\pi\)
\(632\) −6.67173 −0.265387
\(633\) −4.53557 −0.180273
\(634\) 24.5662 0.975649
\(635\) −3.06459 −0.121615
\(636\) 0.973722 0.0386106
\(637\) 4.56834 0.181004
\(638\) 0 0
\(639\) −16.3717 −0.647655
\(640\) 5.58167 0.220635
\(641\) −0.905192 −0.0357529 −0.0178765 0.999840i \(-0.505691\pi\)
−0.0178765 + 0.999840i \(0.505691\pi\)
\(642\) −5.96176 −0.235292
\(643\) 34.8958 1.37616 0.688078 0.725637i \(-0.258455\pi\)
0.688078 + 0.725637i \(0.258455\pi\)
\(644\) −0.476220 −0.0187657
\(645\) −0.0415857 −0.00163743
\(646\) 31.1128 1.22412
\(647\) −44.8587 −1.76358 −0.881788 0.471646i \(-0.843660\pi\)
−0.881788 + 0.471646i \(0.843660\pi\)
\(648\) −6.09654 −0.239495
\(649\) 0 0
\(650\) 8.70047 0.341260
\(651\) 1.42447 0.0558294
\(652\) 2.98107 0.116748
\(653\) 42.4290 1.66037 0.830187 0.557485i \(-0.188233\pi\)
0.830187 + 0.557485i \(0.188233\pi\)
\(654\) −7.95799 −0.311182
\(655\) 14.6745 0.573381
\(656\) 12.4261 0.485158
\(657\) 34.7074 1.35407
\(658\) 8.18218 0.318974
\(659\) 12.8671 0.501232 0.250616 0.968087i \(-0.419367\pi\)
0.250616 + 0.968087i \(0.419367\pi\)
\(660\) 0 0
\(661\) 24.4320 0.950293 0.475147 0.879907i \(-0.342395\pi\)
0.475147 + 0.879907i \(0.342395\pi\)
\(662\) −15.7816 −0.613370
\(663\) −3.19371 −0.124033
\(664\) 6.44579 0.250145
\(665\) 5.02403 0.194823
\(666\) 26.0361 1.00888
\(667\) −0.293460 −0.0113628
\(668\) 11.2109 0.433762
\(669\) 2.79999 0.108254
\(670\) 7.53898 0.291256
\(671\) 0 0
\(672\) 1.58095 0.0609866
\(673\) −24.1166 −0.929628 −0.464814 0.885408i \(-0.653879\pi\)
−0.464814 + 0.885408i \(0.653879\pi\)
\(674\) 64.1042 2.46920
\(675\) −1.28005 −0.0492691
\(676\) 12.8054 0.492515
\(677\) −8.27910 −0.318192 −0.159096 0.987263i \(-0.550858\pi\)
−0.159096 + 0.987263i \(0.550858\pi\)
\(678\) −7.03808 −0.270296
\(679\) −1.09820 −0.0421450
\(680\) 2.30882 0.0885391
\(681\) −2.61096 −0.100052
\(682\) 0 0
\(683\) −33.6483 −1.28752 −0.643758 0.765229i \(-0.722626\pi\)
−0.643758 + 0.765229i \(0.722626\pi\)
\(684\) 24.1471 0.923286
\(685\) −15.7705 −0.602561
\(686\) −1.90452 −0.0727147
\(687\) 4.04403 0.154289
\(688\) 0.891034 0.0339703
\(689\) 12.7152 0.484411
\(690\) 0.119837 0.00456213
\(691\) −9.01062 −0.342780 −0.171390 0.985203i \(-0.554826\pi\)
−0.171390 + 0.985203i \(0.554826\pi\)
\(692\) 13.5787 0.516186
\(693\) 0 0
\(694\) 37.8536 1.43690
\(695\) 9.60769 0.364441
\(696\) 0.153073 0.00580220
\(697\) 8.77108 0.332228
\(698\) −35.6578 −1.34967
\(699\) −5.03244 −0.190344
\(700\) −1.62718 −0.0615015
\(701\) −38.6147 −1.45846 −0.729228 0.684271i \(-0.760121\pi\)
−0.729228 + 0.684271i \(0.760121\pi\)
\(702\) −11.1370 −0.420340
\(703\) 23.2523 0.876978
\(704\) 0 0
\(705\) −0.923674 −0.0347876
\(706\) 26.5847 1.00053
\(707\) 4.61577 0.173594
\(708\) −0.296272 −0.0111346
\(709\) 45.5575 1.71095 0.855475 0.517845i \(-0.173265\pi\)
0.855475 + 0.517845i \(0.173265\pi\)
\(710\) 10.5560 0.396161
\(711\) −27.7543 −1.04087
\(712\) −3.05769 −0.114592
\(713\) −1.93906 −0.0726185
\(714\) 1.33144 0.0498279
\(715\) 0 0
\(716\) 11.9476 0.446504
\(717\) −3.24306 −0.121114
\(718\) 57.9252 2.16175
\(719\) −9.27727 −0.345984 −0.172992 0.984923i \(-0.555343\pi\)
−0.172992 + 0.984923i \(0.555343\pi\)
\(720\) 13.6070 0.507103
\(721\) −13.8643 −0.516333
\(722\) 11.8858 0.442344
\(723\) 0.107419 0.00399495
\(724\) 0.207344 0.00770589
\(725\) −1.00271 −0.0372398
\(726\) 0 0
\(727\) −9.13982 −0.338977 −0.169489 0.985532i \(-0.554212\pi\)
−0.169489 + 0.985532i \(0.554212\pi\)
\(728\) 3.24373 0.120221
\(729\) −24.5358 −0.908735
\(730\) −22.3784 −0.828262
\(731\) 0.628944 0.0232623
\(732\) −0.337020 −0.0124566
\(733\) −29.5930 −1.09304 −0.546520 0.837446i \(-0.684048\pi\)
−0.546520 + 0.837446i \(0.684048\pi\)
\(734\) −43.4519 −1.60384
\(735\) 0.214998 0.00793032
\(736\) −2.15208 −0.0793265
\(737\) 0 0
\(738\) 15.1744 0.558578
\(739\) 18.9094 0.695594 0.347797 0.937570i \(-0.386930\pi\)
0.347797 + 0.937570i \(0.386930\pi\)
\(740\) −7.53094 −0.276843
\(741\) −4.93452 −0.181274
\(742\) −5.30090 −0.194602
\(743\) 15.0087 0.550617 0.275309 0.961356i \(-0.411220\pi\)
0.275309 + 0.961356i \(0.411220\pi\)
\(744\) 1.01144 0.0370812
\(745\) −1.39502 −0.0511095
\(746\) −47.6831 −1.74580
\(747\) 26.8144 0.981086
\(748\) 0 0
\(749\) 14.5598 0.532004
\(750\) 0.409467 0.0149516
\(751\) 15.7351 0.574182 0.287091 0.957903i \(-0.407312\pi\)
0.287091 + 0.957903i \(0.407312\pi\)
\(752\) 19.7911 0.721706
\(753\) −4.48030 −0.163271
\(754\) −8.72407 −0.317712
\(755\) −11.9950 −0.436541
\(756\) 2.08287 0.0757532
\(757\) −16.8017 −0.610668 −0.305334 0.952245i \(-0.598768\pi\)
−0.305334 + 0.952245i \(0.598768\pi\)
\(758\) 45.7413 1.66140
\(759\) 0 0
\(760\) 3.56729 0.129399
\(761\) 7.79540 0.282583 0.141292 0.989968i \(-0.454875\pi\)
0.141292 + 0.989968i \(0.454875\pi\)
\(762\) −1.25485 −0.0454584
\(763\) 19.4350 0.703594
\(764\) 37.4636 1.35539
\(765\) 9.60462 0.347256
\(766\) 14.8321 0.535907
\(767\) −3.86883 −0.139695
\(768\) 4.34573 0.156813
\(769\) 16.8739 0.608490 0.304245 0.952594i \(-0.401596\pi\)
0.304245 + 0.952594i \(0.401596\pi\)
\(770\) 0 0
\(771\) −1.98634 −0.0715362
\(772\) 29.1180 1.04798
\(773\) 9.22274 0.331719 0.165859 0.986149i \(-0.446960\pi\)
0.165859 + 0.986149i \(0.446960\pi\)
\(774\) 1.08811 0.0391111
\(775\) −6.62551 −0.237995
\(776\) −0.779771 −0.0279921
\(777\) 0.995059 0.0356975
\(778\) 23.7298 0.850754
\(779\) 13.5520 0.485549
\(780\) 1.59819 0.0572243
\(781\) 0 0
\(782\) −1.81243 −0.0648122
\(783\) 1.28352 0.0458693
\(784\) −4.60665 −0.164523
\(785\) −24.4749 −0.873548
\(786\) 6.00873 0.214324
\(787\) 30.9722 1.10404 0.552020 0.833831i \(-0.313857\pi\)
0.552020 + 0.833831i \(0.313857\pi\)
\(788\) 35.2536 1.25586
\(789\) −0.838628 −0.0298560
\(790\) 17.8952 0.636682
\(791\) 17.1884 0.611149
\(792\) 0 0
\(793\) −4.40093 −0.156282
\(794\) −3.39407 −0.120451
\(795\) 0.598412 0.0212235
\(796\) 40.3657 1.43072
\(797\) 34.4892 1.22167 0.610835 0.791758i \(-0.290834\pi\)
0.610835 + 0.791758i \(0.290834\pi\)
\(798\) 2.05717 0.0728232
\(799\) 13.9697 0.494213
\(800\) −7.35334 −0.259980
\(801\) −12.7199 −0.449437
\(802\) −61.9258 −2.18668
\(803\) 0 0
\(804\) 1.38483 0.0488393
\(805\) −0.292666 −0.0103151
\(806\) −57.6450 −2.03046
\(807\) 6.01086 0.211592
\(808\) 3.27741 0.115299
\(809\) −28.9150 −1.01660 −0.508298 0.861181i \(-0.669725\pi\)
−0.508298 + 0.861181i \(0.669725\pi\)
\(810\) 16.3524 0.574565
\(811\) −4.85554 −0.170501 −0.0852506 0.996360i \(-0.527169\pi\)
−0.0852506 + 0.996360i \(0.527169\pi\)
\(812\) 1.63159 0.0572576
\(813\) −5.17924 −0.181644
\(814\) 0 0
\(815\) 1.83205 0.0641738
\(816\) 3.22049 0.112740
\(817\) 0.971765 0.0339977
\(818\) −48.9658 −1.71205
\(819\) 13.4938 0.471513
\(820\) −4.38920 −0.153277
\(821\) 18.6341 0.650335 0.325167 0.945656i \(-0.394579\pi\)
0.325167 + 0.945656i \(0.394579\pi\)
\(822\) −6.45751 −0.225231
\(823\) −17.9622 −0.626122 −0.313061 0.949733i \(-0.601354\pi\)
−0.313061 + 0.949733i \(0.601354\pi\)
\(824\) −9.84428 −0.342942
\(825\) 0 0
\(826\) 1.61289 0.0561198
\(827\) −24.9389 −0.867212 −0.433606 0.901103i \(-0.642759\pi\)
−0.433606 + 0.901103i \(0.642759\pi\)
\(828\) −1.40665 −0.0488844
\(829\) −8.99336 −0.312352 −0.156176 0.987729i \(-0.549917\pi\)
−0.156176 + 0.987729i \(0.549917\pi\)
\(830\) −17.2892 −0.600116
\(831\) −5.84541 −0.202775
\(832\) −21.8880 −0.758831
\(833\) −3.25164 −0.112663
\(834\) 3.93403 0.136224
\(835\) 6.88977 0.238430
\(836\) 0 0
\(837\) 8.48098 0.293146
\(838\) 35.5859 1.22929
\(839\) −46.9822 −1.62201 −0.811003 0.585041i \(-0.801078\pi\)
−0.811003 + 0.585041i \(0.801078\pi\)
\(840\) 0.152659 0.00526722
\(841\) −27.9946 −0.965330
\(842\) 16.9775 0.585084
\(843\) −4.19107 −0.144348
\(844\) −34.3267 −1.18157
\(845\) 7.86970 0.270726
\(846\) 24.1683 0.830924
\(847\) 0 0
\(848\) −12.8218 −0.440304
\(849\) 0.523330 0.0179606
\(850\) −6.19280 −0.212411
\(851\) −1.35453 −0.0464325
\(852\) 1.93904 0.0664303
\(853\) 49.4824 1.69425 0.847123 0.531397i \(-0.178333\pi\)
0.847123 + 0.531397i \(0.178333\pi\)
\(854\) 1.83473 0.0627830
\(855\) 14.8399 0.507512
\(856\) 10.3381 0.353350
\(857\) 29.2713 0.999890 0.499945 0.866057i \(-0.333354\pi\)
0.499945 + 0.866057i \(0.333354\pi\)
\(858\) 0 0
\(859\) −41.2734 −1.40823 −0.704115 0.710086i \(-0.748656\pi\)
−0.704115 + 0.710086i \(0.748656\pi\)
\(860\) −0.314734 −0.0107323
\(861\) 0.579942 0.0197644
\(862\) −48.7003 −1.65874
\(863\) 29.3160 0.997928 0.498964 0.866623i \(-0.333714\pi\)
0.498964 + 0.866623i \(0.333714\pi\)
\(864\) 9.41264 0.320225
\(865\) 8.34496 0.283737
\(866\) 40.0426 1.36070
\(867\) −1.38175 −0.0469268
\(868\) 10.7809 0.365927
\(869\) 0 0
\(870\) −0.410578 −0.0139199
\(871\) 18.0837 0.612742
\(872\) 13.7997 0.467318
\(873\) −3.24383 −0.109787
\(874\) −2.80033 −0.0947226
\(875\) −1.00000 −0.0338062
\(876\) −4.11069 −0.138887
\(877\) −21.1875 −0.715450 −0.357725 0.933827i \(-0.616447\pi\)
−0.357725 + 0.933827i \(0.616447\pi\)
\(878\) −45.0524 −1.52045
\(879\) 5.26568 0.177607
\(880\) 0 0
\(881\) −24.9158 −0.839435 −0.419717 0.907655i \(-0.637871\pi\)
−0.419717 + 0.907655i \(0.637871\pi\)
\(882\) −5.62551 −0.189421
\(883\) −36.1441 −1.21635 −0.608174 0.793804i \(-0.708098\pi\)
−0.608174 + 0.793804i \(0.708098\pi\)
\(884\) −24.1711 −0.812961
\(885\) −0.182077 −0.00612046
\(886\) 63.4864 2.13287
\(887\) 12.2613 0.411694 0.205847 0.978584i \(-0.434005\pi\)
0.205847 + 0.978584i \(0.434005\pi\)
\(888\) 0.706538 0.0237098
\(889\) 3.06459 0.102783
\(890\) 8.20147 0.274914
\(891\) 0 0
\(892\) 21.1912 0.709535
\(893\) 21.5842 0.722289
\(894\) −0.571214 −0.0191043
\(895\) 7.34255 0.245435
\(896\) −5.58167 −0.186471
\(897\) 0.287452 0.00959775
\(898\) −52.5332 −1.75306
\(899\) 6.64348 0.221573
\(900\) −4.80632 −0.160211
\(901\) −9.05041 −0.301513
\(902\) 0 0
\(903\) 0.0415857 0.00138388
\(904\) 12.2045 0.405917
\(905\) 0.127426 0.00423578
\(906\) −4.91154 −0.163175
\(907\) −3.37290 −0.111995 −0.0559977 0.998431i \(-0.517834\pi\)
−0.0559977 + 0.998431i \(0.517834\pi\)
\(908\) −19.7606 −0.655778
\(909\) 13.6339 0.452209
\(910\) −8.70047 −0.288418
\(911\) −9.30964 −0.308442 −0.154221 0.988036i \(-0.549287\pi\)
−0.154221 + 0.988036i \(0.549287\pi\)
\(912\) 4.97590 0.164768
\(913\) 0 0
\(914\) −24.4931 −0.810160
\(915\) −0.207120 −0.00684716
\(916\) 30.6066 1.01127
\(917\) −14.6745 −0.484595
\(918\) 7.92710 0.261633
\(919\) 57.5454 1.89825 0.949123 0.314905i \(-0.101973\pi\)
0.949123 + 0.314905i \(0.101973\pi\)
\(920\) −0.207807 −0.00685118
\(921\) 4.95593 0.163304
\(922\) 50.7154 1.67022
\(923\) 25.3207 0.833440
\(924\) 0 0
\(925\) −4.62822 −0.152175
\(926\) 36.7526 1.20776
\(927\) −40.9520 −1.34504
\(928\) 7.37328 0.242040
\(929\) 3.71259 0.121806 0.0609031 0.998144i \(-0.480602\pi\)
0.0609031 + 0.998144i \(0.480602\pi\)
\(930\) −2.71293 −0.0889604
\(931\) −5.02403 −0.164656
\(932\) −38.0872 −1.24759
\(933\) 4.02524 0.131780
\(934\) −68.5242 −2.24218
\(935\) 0 0
\(936\) 9.58125 0.313173
\(937\) −35.7607 −1.16825 −0.584126 0.811663i \(-0.698562\pi\)
−0.584126 + 0.811663i \(0.698562\pi\)
\(938\) −7.53898 −0.246157
\(939\) 3.32655 0.108558
\(940\) −6.99068 −0.228011
\(941\) −2.30778 −0.0752316 −0.0376158 0.999292i \(-0.511976\pi\)
−0.0376158 + 0.999292i \(0.511976\pi\)
\(942\) −10.0217 −0.326524
\(943\) −0.789447 −0.0257079
\(944\) 3.90127 0.126976
\(945\) 1.28005 0.0416400
\(946\) 0 0
\(947\) −55.9447 −1.81796 −0.908979 0.416842i \(-0.863137\pi\)
−0.908979 + 0.416842i \(0.863137\pi\)
\(948\) 3.28716 0.106762
\(949\) −53.6788 −1.74249
\(950\) −9.56834 −0.310438
\(951\) 2.77324 0.0899286
\(952\) −2.30882 −0.0748292
\(953\) 21.2762 0.689203 0.344602 0.938749i \(-0.388014\pi\)
0.344602 + 0.938749i \(0.388014\pi\)
\(954\) −15.6577 −0.506936
\(955\) 23.0237 0.745029
\(956\) −24.5445 −0.793827
\(957\) 0 0
\(958\) −53.1365 −1.71676
\(959\) 15.7705 0.509257
\(960\) −1.03011 −0.0332466
\(961\) 12.8974 0.416045
\(962\) −40.2677 −1.29828
\(963\) 43.0064 1.38586
\(964\) 0.812981 0.0261844
\(965\) 17.8948 0.576053
\(966\) −0.119837 −0.00385570
\(967\) −1.52052 −0.0488966 −0.0244483 0.999701i \(-0.507783\pi\)
−0.0244483 + 0.999701i \(0.507783\pi\)
\(968\) 0 0
\(969\) 3.51228 0.112831
\(970\) 2.09153 0.0671551
\(971\) −0.577620 −0.0185367 −0.00926835 0.999957i \(-0.502950\pi\)
−0.00926835 + 0.999957i \(0.502950\pi\)
\(972\) 9.25237 0.296770
\(973\) −9.60769 −0.308009
\(974\) 44.0132 1.41028
\(975\) 0.982183 0.0314550
\(976\) 4.43784 0.142052
\(977\) 14.1855 0.453836 0.226918 0.973914i \(-0.427135\pi\)
0.226918 + 0.973914i \(0.427135\pi\)
\(978\) 0.750163 0.0239876
\(979\) 0 0
\(980\) 1.62718 0.0519783
\(981\) 57.4066 1.83285
\(982\) 30.6848 0.979192
\(983\) 10.1642 0.324186 0.162093 0.986775i \(-0.448175\pi\)
0.162093 + 0.986775i \(0.448175\pi\)
\(984\) 0.411786 0.0131272
\(985\) 21.6655 0.690320
\(986\) 6.20960 0.197754
\(987\) 0.923674 0.0294009
\(988\) −37.3461 −1.18814
\(989\) −0.0566085 −0.00180005
\(990\) 0 0
\(991\) −56.0016 −1.77895 −0.889475 0.456983i \(-0.848930\pi\)
−0.889475 + 0.456983i \(0.848930\pi\)
\(992\) 48.7196 1.54685
\(993\) −1.78156 −0.0565362
\(994\) −10.5560 −0.334817
\(995\) 24.8072 0.786440
\(996\) −3.17584 −0.100630
\(997\) −38.8222 −1.22951 −0.614756 0.788717i \(-0.710746\pi\)
−0.614756 + 0.788717i \(0.710746\pi\)
\(998\) −31.2697 −0.989825
\(999\) 5.92436 0.187438
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 4235.2.a.bc.1.5 5
11.10 odd 2 4235.2.a.bd.1.1 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4235.2.a.bc.1.5 5 1.1 even 1 trivial
4235.2.a.bd.1.1 yes 5 11.10 odd 2