Properties

Label 637.2.a.l.1.2
Level $637$
Weight $2$
Character 637.1
Self dual yes
Analytic conductor $5.086$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.746052.1
Defining polynomial: \(x^{5} - x^{4} - 7 x^{3} + 8 x + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.19566\) of defining polynomial
Character \(\chi\) \(=\) 637.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.195656 q^{2} -0.259788 q^{3} -1.96172 q^{4} +3.93251 q^{5} +0.0508292 q^{6} +0.775135 q^{8} -2.93251 q^{9} +O(q^{10})\) \(q-0.195656 q^{2} -0.259788 q^{3} -1.96172 q^{4} +3.93251 q^{5} +0.0508292 q^{6} +0.775135 q^{8} -2.93251 q^{9} -0.769420 q^{10} +4.50627 q^{11} +0.509632 q^{12} +1.00000 q^{13} -1.02162 q^{15} +3.77178 q^{16} -2.28141 q^{17} +0.573764 q^{18} -1.78768 q^{19} -7.71448 q^{20} -0.881681 q^{22} +1.74021 q^{23} -0.201371 q^{24} +10.4646 q^{25} -0.195656 q^{26} +1.54120 q^{27} +1.65110 q^{29} +0.199886 q^{30} +5.60523 q^{31} -2.28824 q^{32} -1.17068 q^{33} +0.446372 q^{34} +5.75276 q^{36} +7.14407 q^{37} +0.349771 q^{38} -0.259788 q^{39} +3.04823 q^{40} -8.11574 q^{41} +6.81353 q^{43} -8.84004 q^{44} -11.5321 q^{45} -0.340483 q^{46} +3.54543 q^{47} -0.979864 q^{48} -2.04747 q^{50} +0.592684 q^{51} -1.96172 q^{52} +3.28965 q^{53} -0.301545 q^{54} +17.7210 q^{55} +0.464419 q^{57} -0.323048 q^{58} +4.50627 q^{59} +2.00413 q^{60} +7.54467 q^{61} -1.09670 q^{62} -7.09585 q^{64} +3.93251 q^{65} +0.229050 q^{66} -12.6653 q^{67} +4.47548 q^{68} -0.452087 q^{69} +9.54869 q^{71} -2.27309 q^{72} +1.08004 q^{73} -1.39778 q^{74} -2.71859 q^{75} +3.50693 q^{76} +0.0508292 q^{78} +0.791698 q^{79} +14.8326 q^{80} +8.39714 q^{81} +1.58789 q^{82} -7.14643 q^{83} -8.97166 q^{85} -1.33311 q^{86} -0.428937 q^{87} +3.49297 q^{88} -11.2656 q^{89} +2.25633 q^{90} -3.41381 q^{92} -1.45617 q^{93} -0.693685 q^{94} -7.03008 q^{95} +0.594459 q^{96} -8.81353 q^{97} -13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 4q^{2} + 8q^{4} + 2q^{5} - 5q^{6} + 9q^{8} + 3q^{9} + O(q^{10}) \) \( 5q + 4q^{2} + 8q^{4} + 2q^{5} - 5q^{6} + 9q^{8} + 3q^{9} - 5q^{10} + 11q^{11} + 5q^{12} + 5q^{13} + 10q^{16} - 5q^{17} + 9q^{18} + 9q^{19} + q^{20} + 8q^{22} + 10q^{23} + 9q^{25} + 4q^{26} - 3q^{29} - 13q^{30} - 6q^{31} + 22q^{32} + 8q^{33} - 22q^{34} + 7q^{36} + 4q^{37} - 10q^{38} + 28q^{40} + 14q^{41} + 2q^{43} - 32q^{45} + 3q^{46} + q^{47} - 23q^{48} + 9q^{50} - 8q^{51} + 8q^{52} + 17q^{53} + 23q^{54} - 16q^{57} - 27q^{58} + 11q^{59} - 29q^{60} - 11q^{61} - 23q^{62} + 9q^{64} + 2q^{65} + 21q^{66} + 13q^{67} - 32q^{68} + 18q^{69} + 15q^{71} - 19q^{72} - 33q^{74} - 20q^{75} + 8q^{76} - 5q^{78} + 2q^{79} + 55q^{80} - 19q^{81} + 34q^{82} + 6q^{83} - 22q^{85} + 28q^{86} - 8q^{87} - 3q^{88} - 4q^{89} - 34q^{90} + 21q^{92} + 18q^{93} + 20q^{94} - 12q^{95} - 37q^{96} - 12q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.195656 −0.138350 −0.0691749 0.997605i \(-0.522037\pi\)
−0.0691749 + 0.997605i \(0.522037\pi\)
\(3\) −0.259788 −0.149989 −0.0749945 0.997184i \(-0.523894\pi\)
−0.0749945 + 0.997184i \(0.523894\pi\)
\(4\) −1.96172 −0.980859
\(5\) 3.93251 1.75867 0.879336 0.476202i \(-0.157987\pi\)
0.879336 + 0.476202i \(0.157987\pi\)
\(6\) 0.0508292 0.0207509
\(7\) 0 0
\(8\) 0.775135 0.274052
\(9\) −2.93251 −0.977503
\(10\) −0.769420 −0.243312
\(11\) 4.50627 1.35869 0.679346 0.733818i \(-0.262263\pi\)
0.679346 + 0.733818i \(0.262263\pi\)
\(12\) 0.509632 0.147118
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.02162 −0.263781
\(16\) 3.77178 0.942944
\(17\) −2.28141 −0.553323 −0.276661 0.960967i \(-0.589228\pi\)
−0.276661 + 0.960967i \(0.589228\pi\)
\(18\) 0.573764 0.135237
\(19\) −1.78768 −0.410123 −0.205061 0.978749i \(-0.565739\pi\)
−0.205061 + 0.978749i \(0.565739\pi\)
\(20\) −7.71448 −1.72501
\(21\) 0 0
\(22\) −0.881681 −0.187975
\(23\) 1.74021 0.362859 0.181430 0.983404i \(-0.441928\pi\)
0.181430 + 0.983404i \(0.441928\pi\)
\(24\) −0.201371 −0.0411047
\(25\) 10.4646 2.09293
\(26\) −0.195656 −0.0383714
\(27\) 1.54120 0.296604
\(28\) 0 0
\(29\) 1.65110 0.306602 0.153301 0.988180i \(-0.451010\pi\)
0.153301 + 0.988180i \(0.451010\pi\)
\(30\) 0.199886 0.0364941
\(31\) 5.60523 1.00673 0.503365 0.864074i \(-0.332095\pi\)
0.503365 + 0.864074i \(0.332095\pi\)
\(32\) −2.28824 −0.404508
\(33\) −1.17068 −0.203789
\(34\) 0.446372 0.0765522
\(35\) 0 0
\(36\) 5.75276 0.958793
\(37\) 7.14407 1.17448 0.587239 0.809414i \(-0.300215\pi\)
0.587239 + 0.809414i \(0.300215\pi\)
\(38\) 0.349771 0.0567404
\(39\) −0.259788 −0.0415994
\(40\) 3.04823 0.481967
\(41\) −8.11574 −1.26746 −0.633732 0.773552i \(-0.718478\pi\)
−0.633732 + 0.773552i \(0.718478\pi\)
\(42\) 0 0
\(43\) 6.81353 1.03905 0.519527 0.854454i \(-0.326108\pi\)
0.519527 + 0.854454i \(0.326108\pi\)
\(44\) −8.84004 −1.33269
\(45\) −11.5321 −1.71911
\(46\) −0.340483 −0.0502015
\(47\) 3.54543 0.517154 0.258577 0.965991i \(-0.416746\pi\)
0.258577 + 0.965991i \(0.416746\pi\)
\(48\) −0.979864 −0.141431
\(49\) 0 0
\(50\) −2.04747 −0.289556
\(51\) 0.592684 0.0829923
\(52\) −1.96172 −0.272041
\(53\) 3.28965 0.451869 0.225934 0.974143i \(-0.427457\pi\)
0.225934 + 0.974143i \(0.427457\pi\)
\(54\) −0.301545 −0.0410351
\(55\) 17.7210 2.38949
\(56\) 0 0
\(57\) 0.464419 0.0615138
\(58\) −0.323048 −0.0424183
\(59\) 4.50627 0.586667 0.293333 0.956010i \(-0.405235\pi\)
0.293333 + 0.956010i \(0.405235\pi\)
\(60\) 2.00413 0.258732
\(61\) 7.54467 0.965996 0.482998 0.875621i \(-0.339548\pi\)
0.482998 + 0.875621i \(0.339548\pi\)
\(62\) −1.09670 −0.139281
\(63\) 0 0
\(64\) −7.09585 −0.886981
\(65\) 3.93251 0.487768
\(66\) 0.229050 0.0281942
\(67\) −12.6653 −1.54731 −0.773653 0.633609i \(-0.781573\pi\)
−0.773653 + 0.633609i \(0.781573\pi\)
\(68\) 4.47548 0.542732
\(69\) −0.452087 −0.0544249
\(70\) 0 0
\(71\) 9.54869 1.13322 0.566610 0.823986i \(-0.308254\pi\)
0.566610 + 0.823986i \(0.308254\pi\)
\(72\) −2.27309 −0.267886
\(73\) 1.08004 0.126409 0.0632044 0.998001i \(-0.479868\pi\)
0.0632044 + 0.998001i \(0.479868\pi\)
\(74\) −1.39778 −0.162489
\(75\) −2.71859 −0.313916
\(76\) 3.50693 0.402273
\(77\) 0 0
\(78\) 0.0508292 0.00575528
\(79\) 0.791698 0.0890730 0.0445365 0.999008i \(-0.485819\pi\)
0.0445365 + 0.999008i \(0.485819\pi\)
\(80\) 14.8326 1.65833
\(81\) 8.39714 0.933016
\(82\) 1.58789 0.175354
\(83\) −7.14643 −0.784422 −0.392211 0.919875i \(-0.628290\pi\)
−0.392211 + 0.919875i \(0.628290\pi\)
\(84\) 0 0
\(85\) −8.97166 −0.973114
\(86\) −1.33311 −0.143753
\(87\) −0.428937 −0.0459869
\(88\) 3.49297 0.372352
\(89\) −11.2656 −1.19415 −0.597077 0.802184i \(-0.703671\pi\)
−0.597077 + 0.802184i \(0.703671\pi\)
\(90\) 2.25633 0.237838
\(91\) 0 0
\(92\) −3.41381 −0.355914
\(93\) −1.45617 −0.150998
\(94\) −0.693685 −0.0715482
\(95\) −7.03008 −0.721271
\(96\) 0.594459 0.0606717
\(97\) −8.81353 −0.894879 −0.447439 0.894314i \(-0.647664\pi\)
−0.447439 + 0.894314i \(0.647664\pi\)
\(98\) 0 0
\(99\) −13.2147 −1.32813
\(100\) −20.5287 −2.05287
\(101\) −14.3171 −1.42461 −0.712303 0.701872i \(-0.752348\pi\)
−0.712303 + 0.701872i \(0.752348\pi\)
\(102\) −0.115962 −0.0114820
\(103\) −7.49214 −0.738223 −0.369111 0.929385i \(-0.620338\pi\)
−0.369111 + 0.929385i \(0.620338\pi\)
\(104\) 0.775135 0.0760082
\(105\) 0 0
\(106\) −0.643641 −0.0625160
\(107\) 10.9784 1.06132 0.530660 0.847585i \(-0.321944\pi\)
0.530660 + 0.847585i \(0.321944\pi\)
\(108\) −3.02340 −0.290926
\(109\) −12.4463 −1.19214 −0.596068 0.802934i \(-0.703271\pi\)
−0.596068 + 0.802934i \(0.703271\pi\)
\(110\) −3.46722 −0.330586
\(111\) −1.85595 −0.176159
\(112\) 0 0
\(113\) −1.65110 −0.155323 −0.0776613 0.996980i \(-0.524745\pi\)
−0.0776613 + 0.996980i \(0.524745\pi\)
\(114\) −0.0908666 −0.00851043
\(115\) 6.84340 0.638150
\(116\) −3.23900 −0.300733
\(117\) −2.93251 −0.271111
\(118\) −0.881681 −0.0811653
\(119\) 0 0
\(120\) −0.791894 −0.0722897
\(121\) 9.30650 0.846046
\(122\) −1.47616 −0.133645
\(123\) 2.10837 0.190106
\(124\) −10.9959 −0.987460
\(125\) 21.4897 1.92210
\(126\) 0 0
\(127\) −4.49297 −0.398687 −0.199343 0.979930i \(-0.563881\pi\)
−0.199343 + 0.979930i \(0.563881\pi\)
\(128\) 5.96483 0.527222
\(129\) −1.77008 −0.155847
\(130\) −0.769420 −0.0674826
\(131\) −12.6567 −1.10582 −0.552911 0.833240i \(-0.686483\pi\)
−0.552911 + 0.833240i \(0.686483\pi\)
\(132\) 2.29654 0.199888
\(133\) 0 0
\(134\) 2.47804 0.214070
\(135\) 6.06077 0.521628
\(136\) −1.76840 −0.151639
\(137\) −9.28641 −0.793392 −0.396696 0.917950i \(-0.629843\pi\)
−0.396696 + 0.917950i \(0.629843\pi\)
\(138\) 0.0884536 0.00752967
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −0.921061 −0.0775673
\(142\) −1.86826 −0.156781
\(143\) 4.50627 0.376834
\(144\) −11.0608 −0.921731
\(145\) 6.49297 0.539212
\(146\) −0.211316 −0.0174887
\(147\) 0 0
\(148\) −14.0147 −1.15200
\(149\) −15.1649 −1.24235 −0.621177 0.783670i \(-0.713345\pi\)
−0.621177 + 0.783670i \(0.713345\pi\)
\(150\) 0.531909 0.0434302
\(151\) 5.14159 0.418416 0.209208 0.977871i \(-0.432911\pi\)
0.209208 + 0.977871i \(0.432911\pi\)
\(152\) −1.38570 −0.112395
\(153\) 6.69025 0.540875
\(154\) 0 0
\(155\) 22.0426 1.77051
\(156\) 0.509632 0.0408032
\(157\) −10.7311 −0.856438 −0.428219 0.903675i \(-0.640859\pi\)
−0.428219 + 0.903675i \(0.640859\pi\)
\(158\) −0.154901 −0.0123232
\(159\) −0.854614 −0.0677753
\(160\) −8.99853 −0.711397
\(161\) 0 0
\(162\) −1.64295 −0.129083
\(163\) 2.37239 0.185820 0.0929101 0.995675i \(-0.470383\pi\)
0.0929101 + 0.995675i \(0.470383\pi\)
\(164\) 15.9208 1.24320
\(165\) −4.60370 −0.358398
\(166\) 1.39824 0.108525
\(167\) 12.0784 0.934653 0.467327 0.884085i \(-0.345217\pi\)
0.467327 + 0.884085i \(0.345217\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 1.75536 0.134630
\(171\) 5.24240 0.400896
\(172\) −13.3662 −1.01917
\(173\) −19.4097 −1.47569 −0.737846 0.674969i \(-0.764157\pi\)
−0.737846 + 0.674969i \(0.764157\pi\)
\(174\) 0.0839242 0.00636228
\(175\) 0 0
\(176\) 16.9967 1.28117
\(177\) −1.17068 −0.0879935
\(178\) 2.20419 0.165211
\(179\) 14.6444 1.09457 0.547286 0.836945i \(-0.315661\pi\)
0.547286 + 0.836945i \(0.315661\pi\)
\(180\) 22.6228 1.68620
\(181\) −9.44627 −0.702136 −0.351068 0.936350i \(-0.614181\pi\)
−0.351068 + 0.936350i \(0.614181\pi\)
\(182\) 0 0
\(183\) −1.96002 −0.144889
\(184\) 1.34890 0.0994422
\(185\) 28.0941 2.06552
\(186\) 0.284910 0.0208906
\(187\) −10.2807 −0.751796
\(188\) −6.95513 −0.507255
\(189\) 0 0
\(190\) 1.37548 0.0997878
\(191\) 12.5537 0.908357 0.454179 0.890911i \(-0.349933\pi\)
0.454179 + 0.890911i \(0.349933\pi\)
\(192\) 1.84342 0.133037
\(193\) −9.36859 −0.674366 −0.337183 0.941439i \(-0.609474\pi\)
−0.337183 + 0.941439i \(0.609474\pi\)
\(194\) 1.72442 0.123806
\(195\) −1.02162 −0.0731598
\(196\) 0 0
\(197\) −7.62276 −0.543099 −0.271550 0.962424i \(-0.587536\pi\)
−0.271550 + 0.962424i \(0.587536\pi\)
\(198\) 2.58554 0.183746
\(199\) 13.5289 0.959036 0.479518 0.877532i \(-0.340812\pi\)
0.479518 + 0.877532i \(0.340812\pi\)
\(200\) 8.11151 0.573570
\(201\) 3.29029 0.232079
\(202\) 2.80123 0.197094
\(203\) 0 0
\(204\) −1.16268 −0.0814038
\(205\) −31.9152 −2.22906
\(206\) 1.46588 0.102133
\(207\) −5.10319 −0.354696
\(208\) 3.77178 0.261526
\(209\) −8.05579 −0.557231
\(210\) 0 0
\(211\) −15.7995 −1.08768 −0.543840 0.839189i \(-0.683030\pi\)
−0.543840 + 0.839189i \(0.683030\pi\)
\(212\) −6.45338 −0.443220
\(213\) −2.48064 −0.169971
\(214\) −2.14799 −0.146833
\(215\) 26.7943 1.82736
\(216\) 1.19464 0.0812847
\(217\) 0 0
\(218\) 2.43519 0.164932
\(219\) −0.280581 −0.0189599
\(220\) −34.7636 −2.34376
\(221\) −2.28141 −0.153464
\(222\) 0.363128 0.0243715
\(223\) 22.4737 1.50495 0.752474 0.658622i \(-0.228861\pi\)
0.752474 + 0.658622i \(0.228861\pi\)
\(224\) 0 0
\(225\) −30.6876 −2.04584
\(226\) 0.323048 0.0214889
\(227\) −9.20249 −0.610791 −0.305395 0.952226i \(-0.598789\pi\)
−0.305395 + 0.952226i \(0.598789\pi\)
\(228\) −0.911060 −0.0603364
\(229\) 15.2922 1.01054 0.505269 0.862962i \(-0.331393\pi\)
0.505269 + 0.862962i \(0.331393\pi\)
\(230\) −1.33895 −0.0882880
\(231\) 0 0
\(232\) 1.27983 0.0840247
\(233\) −8.05579 −0.527752 −0.263876 0.964557i \(-0.585001\pi\)
−0.263876 + 0.964557i \(0.585001\pi\)
\(234\) 0.573764 0.0375081
\(235\) 13.9424 0.909504
\(236\) −8.84004 −0.575438
\(237\) −0.205674 −0.0133600
\(238\) 0 0
\(239\) 21.7258 1.40533 0.702663 0.711523i \(-0.251994\pi\)
0.702663 + 0.711523i \(0.251994\pi\)
\(240\) −3.85333 −0.248731
\(241\) −20.4980 −1.32039 −0.660195 0.751094i \(-0.729527\pi\)
−0.660195 + 0.751094i \(0.729527\pi\)
\(242\) −1.82088 −0.117050
\(243\) −6.80507 −0.436546
\(244\) −14.8005 −0.947507
\(245\) 0 0
\(246\) −0.412517 −0.0263011
\(247\) −1.78768 −0.113748
\(248\) 4.34481 0.275896
\(249\) 1.85656 0.117655
\(250\) −4.20460 −0.265922
\(251\) 2.60871 0.164660 0.0823301 0.996605i \(-0.473764\pi\)
0.0823301 + 0.996605i \(0.473764\pi\)
\(252\) 0 0
\(253\) 7.84187 0.493014
\(254\) 0.879078 0.0551583
\(255\) 2.33073 0.145956
\(256\) 13.0246 0.814040
\(257\) −8.99676 −0.561202 −0.280601 0.959824i \(-0.590534\pi\)
−0.280601 + 0.959824i \(0.590534\pi\)
\(258\) 0.346327 0.0215614
\(259\) 0 0
\(260\) −7.71448 −0.478432
\(261\) −4.84187 −0.299704
\(262\) 2.47637 0.152990
\(263\) 1.43392 0.0884194 0.0442097 0.999022i \(-0.485923\pi\)
0.0442097 + 0.999022i \(0.485923\pi\)
\(264\) −0.907433 −0.0558487
\(265\) 12.9366 0.794689
\(266\) 0 0
\(267\) 2.92668 0.179110
\(268\) 24.8457 1.51769
\(269\) −8.16832 −0.498031 −0.249016 0.968499i \(-0.580107\pi\)
−0.249016 + 0.968499i \(0.580107\pi\)
\(270\) −1.18583 −0.0721672
\(271\) −0.212317 −0.0128973 −0.00644867 0.999979i \(-0.502053\pi\)
−0.00644867 + 0.999979i \(0.502053\pi\)
\(272\) −8.60497 −0.521753
\(273\) 0 0
\(274\) 1.81695 0.109766
\(275\) 47.1565 2.84364
\(276\) 0.886867 0.0533831
\(277\) 22.9749 1.38043 0.690215 0.723604i \(-0.257516\pi\)
0.690215 + 0.723604i \(0.257516\pi\)
\(278\) 0.782625 0.0469387
\(279\) −16.4374 −0.984081
\(280\) 0 0
\(281\) −0.345228 −0.0205946 −0.0102973 0.999947i \(-0.503278\pi\)
−0.0102973 + 0.999947i \(0.503278\pi\)
\(282\) 0.180211 0.0107314
\(283\) −28.9715 −1.72217 −0.861087 0.508457i \(-0.830216\pi\)
−0.861087 + 0.508457i \(0.830216\pi\)
\(284\) −18.7318 −1.11153
\(285\) 1.82633 0.108183
\(286\) −0.881681 −0.0521349
\(287\) 0 0
\(288\) 6.71029 0.395408
\(289\) −11.7952 −0.693834
\(290\) −1.27039 −0.0745999
\(291\) 2.28965 0.134222
\(292\) −2.11873 −0.123989
\(293\) 31.5427 1.84274 0.921372 0.388682i \(-0.127070\pi\)
0.921372 + 0.388682i \(0.127070\pi\)
\(294\) 0 0
\(295\) 17.7210 1.03175
\(296\) 5.53762 0.321868
\(297\) 6.94506 0.402993
\(298\) 2.96710 0.171880
\(299\) 1.74021 0.100639
\(300\) 5.33311 0.307907
\(301\) 0 0
\(302\) −1.00598 −0.0578879
\(303\) 3.71942 0.213675
\(304\) −6.74274 −0.386723
\(305\) 29.6695 1.69887
\(306\) −1.30899 −0.0748300
\(307\) −18.1941 −1.03839 −0.519197 0.854655i \(-0.673769\pi\)
−0.519197 + 0.854655i \(0.673769\pi\)
\(308\) 0 0
\(309\) 1.94637 0.110725
\(310\) −4.31278 −0.244949
\(311\) −0.376623 −0.0213563 −0.0106782 0.999943i \(-0.503399\pi\)
−0.0106782 + 0.999943i \(0.503399\pi\)
\(312\) −0.201371 −0.0114004
\(313\) 10.9883 0.621095 0.310548 0.950558i \(-0.399488\pi\)
0.310548 + 0.950558i \(0.399488\pi\)
\(314\) 2.09961 0.118488
\(315\) 0 0
\(316\) −1.55309 −0.0873680
\(317\) 26.1806 1.47045 0.735225 0.677823i \(-0.237077\pi\)
0.735225 + 0.677823i \(0.237077\pi\)
\(318\) 0.167211 0.00937670
\(319\) 7.44031 0.416578
\(320\) −27.9045 −1.55991
\(321\) −2.85206 −0.159186
\(322\) 0 0
\(323\) 4.07844 0.226930
\(324\) −16.4728 −0.915158
\(325\) 10.4646 0.580473
\(326\) −0.464174 −0.0257082
\(327\) 3.23340 0.178807
\(328\) −6.29079 −0.347351
\(329\) 0 0
\(330\) 0.900743 0.0495843
\(331\) −34.0932 −1.87393 −0.936967 0.349419i \(-0.886379\pi\)
−0.936967 + 0.349419i \(0.886379\pi\)
\(332\) 14.0193 0.769408
\(333\) −20.9501 −1.14806
\(334\) −2.36321 −0.129309
\(335\) −49.8062 −2.72120
\(336\) 0 0
\(337\) 14.7532 0.803657 0.401829 0.915715i \(-0.368375\pi\)
0.401829 + 0.915715i \(0.368375\pi\)
\(338\) −0.195656 −0.0106423
\(339\) 0.428937 0.0232967
\(340\) 17.5999 0.954487
\(341\) 25.2587 1.36784
\(342\) −1.02571 −0.0554639
\(343\) 0 0
\(344\) 5.28141 0.284754
\(345\) −1.77784 −0.0957155
\(346\) 3.79763 0.204162
\(347\) 29.9466 1.60762 0.803809 0.594888i \(-0.202804\pi\)
0.803809 + 0.594888i \(0.202804\pi\)
\(348\) 0.841454 0.0451066
\(349\) −13.4793 −0.721532 −0.360766 0.932656i \(-0.617485\pi\)
−0.360766 + 0.932656i \(0.617485\pi\)
\(350\) 0 0
\(351\) 1.54120 0.0822630
\(352\) −10.3114 −0.549602
\(353\) 0.163532 0.00870392 0.00435196 0.999991i \(-0.498615\pi\)
0.00435196 + 0.999991i \(0.498615\pi\)
\(354\) 0.229050 0.0121739
\(355\) 37.5503 1.99296
\(356\) 22.1000 1.17130
\(357\) 0 0
\(358\) −2.86527 −0.151434
\(359\) 8.92130 0.470848 0.235424 0.971893i \(-0.424352\pi\)
0.235424 + 0.971893i \(0.424352\pi\)
\(360\) −8.93895 −0.471124
\(361\) −15.8042 −0.831799
\(362\) 1.84822 0.0971404
\(363\) −2.41772 −0.126898
\(364\) 0 0
\(365\) 4.24726 0.222312
\(366\) 0.383490 0.0200453
\(367\) 36.6552 1.91339 0.956693 0.291098i \(-0.0940207\pi\)
0.956693 + 0.291098i \(0.0940207\pi\)
\(368\) 6.56369 0.342156
\(369\) 23.7995 1.23895
\(370\) −5.49679 −0.285765
\(371\) 0 0
\(372\) 2.85660 0.148108
\(373\) 27.1274 1.40460 0.702302 0.711879i \(-0.252156\pi\)
0.702302 + 0.711879i \(0.252156\pi\)
\(374\) 2.01147 0.104011
\(375\) −5.58278 −0.288294
\(376\) 2.74819 0.141727
\(377\) 1.65110 0.0850360
\(378\) 0 0
\(379\) −15.8943 −0.816434 −0.408217 0.912885i \(-0.633849\pi\)
−0.408217 + 0.912885i \(0.633849\pi\)
\(380\) 13.7910 0.707465
\(381\) 1.16722 0.0597986
\(382\) −2.45622 −0.125671
\(383\) 1.15079 0.0588025 0.0294013 0.999568i \(-0.490640\pi\)
0.0294013 + 0.999568i \(0.490640\pi\)
\(384\) −1.54959 −0.0790774
\(385\) 0 0
\(386\) 1.83302 0.0932985
\(387\) −19.9808 −1.01568
\(388\) 17.2897 0.877750
\(389\) −14.3130 −0.725699 −0.362850 0.931848i \(-0.618196\pi\)
−0.362850 + 0.931848i \(0.618196\pi\)
\(390\) 0.199886 0.0101216
\(391\) −3.97013 −0.200778
\(392\) 0 0
\(393\) 3.28807 0.165861
\(394\) 1.49144 0.0751377
\(395\) 3.11336 0.156650
\(396\) 25.9235 1.30271
\(397\) −25.9176 −1.30077 −0.650383 0.759607i \(-0.725391\pi\)
−0.650383 + 0.759607i \(0.725391\pi\)
\(398\) −2.64701 −0.132682
\(399\) 0 0
\(400\) 39.4703 1.97351
\(401\) −4.29631 −0.214548 −0.107274 0.994230i \(-0.534212\pi\)
−0.107274 + 0.994230i \(0.534212\pi\)
\(402\) −0.643765 −0.0321081
\(403\) 5.60523 0.279216
\(404\) 28.0861 1.39734
\(405\) 33.0219 1.64087
\(406\) 0 0
\(407\) 32.1931 1.59575
\(408\) 0.459410 0.0227442
\(409\) −24.7071 −1.22169 −0.610844 0.791751i \(-0.709170\pi\)
−0.610844 + 0.791751i \(0.709170\pi\)
\(410\) 6.24441 0.308389
\(411\) 2.41250 0.119000
\(412\) 14.6975 0.724093
\(413\) 0 0
\(414\) 0.998471 0.0490722
\(415\) −28.1034 −1.37954
\(416\) −2.28824 −0.112190
\(417\) 1.03915 0.0508876
\(418\) 1.57617 0.0770928
\(419\) −24.9293 −1.21787 −0.608937 0.793218i \(-0.708404\pi\)
−0.608937 + 0.793218i \(0.708404\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 3.09127 0.150480
\(423\) −10.3970 −0.505520
\(424\) 2.54993 0.123835
\(425\) −23.8741 −1.15806
\(426\) 0.485352 0.0235154
\(427\) 0 0
\(428\) −21.5365 −1.04101
\(429\) −1.17068 −0.0565209
\(430\) −5.24247 −0.252814
\(431\) −5.68851 −0.274006 −0.137003 0.990571i \(-0.543747\pi\)
−0.137003 + 0.990571i \(0.543747\pi\)
\(432\) 5.81305 0.279681
\(433\) 12.2598 0.589169 0.294584 0.955625i \(-0.404819\pi\)
0.294584 + 0.955625i \(0.404819\pi\)
\(434\) 0 0
\(435\) −1.68680 −0.0808758
\(436\) 24.4161 1.16932
\(437\) −3.11095 −0.148817
\(438\) 0.0548975 0.00262310
\(439\) 5.02317 0.239743 0.119871 0.992789i \(-0.461752\pi\)
0.119871 + 0.992789i \(0.461752\pi\)
\(440\) 13.7361 0.654845
\(441\) 0 0
\(442\) 0.446372 0.0212317
\(443\) 0.578803 0.0274997 0.0137499 0.999905i \(-0.495623\pi\)
0.0137499 + 0.999905i \(0.495623\pi\)
\(444\) 3.64085 0.172787
\(445\) −44.3022 −2.10012
\(446\) −4.39711 −0.208209
\(447\) 3.93966 0.186339
\(448\) 0 0
\(449\) −7.36359 −0.347509 −0.173755 0.984789i \(-0.555590\pi\)
−0.173755 + 0.984789i \(0.555590\pi\)
\(450\) 6.00423 0.283042
\(451\) −36.5717 −1.72210
\(452\) 3.23900 0.152350
\(453\) −1.33572 −0.0627578
\(454\) 1.80052 0.0845028
\(455\) 0 0
\(456\) 0.359988 0.0168580
\(457\) 7.91824 0.370399 0.185200 0.982701i \(-0.440707\pi\)
0.185200 + 0.982701i \(0.440707\pi\)
\(458\) −2.99202 −0.139808
\(459\) −3.51610 −0.164118
\(460\) −13.4248 −0.625936
\(461\) −9.53600 −0.444136 −0.222068 0.975031i \(-0.571281\pi\)
−0.222068 + 0.975031i \(0.571281\pi\)
\(462\) 0 0
\(463\) 2.16049 0.100406 0.0502032 0.998739i \(-0.484013\pi\)
0.0502032 + 0.998739i \(0.484013\pi\)
\(464\) 6.22758 0.289108
\(465\) −5.72642 −0.265556
\(466\) 1.57617 0.0730145
\(467\) −8.11900 −0.375702 −0.187851 0.982198i \(-0.560152\pi\)
−0.187851 + 0.982198i \(0.560152\pi\)
\(468\) 5.75276 0.265921
\(469\) 0 0
\(470\) −2.72792 −0.125830
\(471\) 2.78783 0.128456
\(472\) 3.49297 0.160777
\(473\) 30.7036 1.41176
\(474\) 0.0402414 0.00184835
\(475\) −18.7074 −0.858357
\(476\) 0 0
\(477\) −9.64694 −0.441703
\(478\) −4.25079 −0.194427
\(479\) 14.5533 0.664955 0.332478 0.943111i \(-0.392115\pi\)
0.332478 + 0.943111i \(0.392115\pi\)
\(480\) 2.33772 0.106702
\(481\) 7.14407 0.325742
\(482\) 4.01056 0.182676
\(483\) 0 0
\(484\) −18.2567 −0.829852
\(485\) −34.6593 −1.57380
\(486\) 1.33146 0.0603960
\(487\) −33.2590 −1.50711 −0.753554 0.657386i \(-0.771662\pi\)
−0.753554 + 0.657386i \(0.771662\pi\)
\(488\) 5.84814 0.264733
\(489\) −0.616320 −0.0278710
\(490\) 0 0
\(491\) −22.5563 −1.01795 −0.508977 0.860780i \(-0.669976\pi\)
−0.508977 + 0.860780i \(0.669976\pi\)
\(492\) −4.13604 −0.186467
\(493\) −3.76684 −0.169650
\(494\) 0.349771 0.0157370
\(495\) −51.9669 −2.33574
\(496\) 21.1417 0.949290
\(497\) 0 0
\(498\) −0.363248 −0.0162775
\(499\) −11.3854 −0.509682 −0.254841 0.966983i \(-0.582023\pi\)
−0.254841 + 0.966983i \(0.582023\pi\)
\(500\) −42.1568 −1.88531
\(501\) −3.13782 −0.140188
\(502\) −0.510410 −0.0227807
\(503\) −8.81825 −0.393186 −0.196593 0.980485i \(-0.562988\pi\)
−0.196593 + 0.980485i \(0.562988\pi\)
\(504\) 0 0
\(505\) −56.3022 −2.50541
\(506\) −1.53431 −0.0682084
\(507\) −0.259788 −0.0115376
\(508\) 8.81394 0.391056
\(509\) 19.2838 0.854738 0.427369 0.904077i \(-0.359441\pi\)
0.427369 + 0.904077i \(0.359441\pi\)
\(510\) −0.456023 −0.0201930
\(511\) 0 0
\(512\) −14.4780 −0.639844
\(513\) −2.75517 −0.121644
\(514\) 1.76027 0.0776423
\(515\) −29.4629 −1.29829
\(516\) 3.47239 0.152864
\(517\) 15.9767 0.702653
\(518\) 0 0
\(519\) 5.04241 0.221337
\(520\) 3.04823 0.133674
\(521\) 25.1168 1.10039 0.550193 0.835037i \(-0.314554\pi\)
0.550193 + 0.835037i \(0.314554\pi\)
\(522\) 0.947342 0.0414640
\(523\) −29.9648 −1.31027 −0.655134 0.755513i \(-0.727388\pi\)
−0.655134 + 0.755513i \(0.727388\pi\)
\(524\) 24.8289 1.08466
\(525\) 0 0
\(526\) −0.280556 −0.0122328
\(527\) −12.7878 −0.557046
\(528\) −4.41554 −0.192162
\(529\) −19.9717 −0.868333
\(530\) −2.53113 −0.109945
\(531\) −13.2147 −0.573469
\(532\) 0 0
\(533\) −8.11574 −0.351532
\(534\) −0.572623 −0.0247798
\(535\) 43.1726 1.86651
\(536\) −9.81728 −0.424042
\(537\) −3.80444 −0.164174
\(538\) 1.59818 0.0689026
\(539\) 0 0
\(540\) −11.8895 −0.511644
\(541\) 5.09973 0.219255 0.109627 0.993973i \(-0.465034\pi\)
0.109627 + 0.993973i \(0.465034\pi\)
\(542\) 0.0415412 0.00178435
\(543\) 2.45403 0.105313
\(544\) 5.22042 0.223823
\(545\) −48.9451 −2.09658
\(546\) 0 0
\(547\) 2.92025 0.124861 0.0624305 0.998049i \(-0.480115\pi\)
0.0624305 + 0.998049i \(0.480115\pi\)
\(548\) 18.2173 0.778206
\(549\) −22.1248 −0.944265
\(550\) −9.22647 −0.393418
\(551\) −2.95165 −0.125744
\(552\) −0.350428 −0.0149152
\(553\) 0 0
\(554\) −4.49519 −0.190982
\(555\) −7.29853 −0.309805
\(556\) 7.84687 0.332782
\(557\) 25.9874 1.10112 0.550561 0.834795i \(-0.314414\pi\)
0.550561 + 0.834795i \(0.314414\pi\)
\(558\) 3.21608 0.136148
\(559\) 6.81353 0.288182
\(560\) 0 0
\(561\) 2.67079 0.112761
\(562\) 0.0675460 0.00284925
\(563\) 3.65069 0.153858 0.0769291 0.997037i \(-0.475488\pi\)
0.0769291 + 0.997037i \(0.475488\pi\)
\(564\) 1.80686 0.0760826
\(565\) −6.49297 −0.273161
\(566\) 5.66845 0.238263
\(567\) 0 0
\(568\) 7.40152 0.310561
\(569\) −25.3533 −1.06286 −0.531432 0.847101i \(-0.678346\pi\)
−0.531432 + 0.847101i \(0.678346\pi\)
\(570\) −0.357334 −0.0149671
\(571\) 27.7253 1.16027 0.580133 0.814522i \(-0.303000\pi\)
0.580133 + 0.814522i \(0.303000\pi\)
\(572\) −8.84004 −0.369621
\(573\) −3.26132 −0.136244
\(574\) 0 0
\(575\) 18.2107 0.759438
\(576\) 20.8086 0.867027
\(577\) 39.5754 1.64755 0.823773 0.566920i \(-0.191865\pi\)
0.823773 + 0.566920i \(0.191865\pi\)
\(578\) 2.30780 0.0959918
\(579\) 2.43385 0.101147
\(580\) −12.7374 −0.528891
\(581\) 0 0
\(582\) −0.447985 −0.0185696
\(583\) 14.8241 0.613951
\(584\) 0.837175 0.0346426
\(585\) −11.5321 −0.476795
\(586\) −6.17153 −0.254943
\(587\) −8.24177 −0.340174 −0.170087 0.985429i \(-0.554405\pi\)
−0.170087 + 0.985429i \(0.554405\pi\)
\(588\) 0 0
\(589\) −10.0204 −0.412882
\(590\) −3.46722 −0.142743
\(591\) 1.98031 0.0814589
\(592\) 26.9458 1.10747
\(593\) −11.9230 −0.489618 −0.244809 0.969571i \(-0.578725\pi\)
−0.244809 + 0.969571i \(0.578725\pi\)
\(594\) −1.35884 −0.0557540
\(595\) 0 0
\(596\) 29.7492 1.21857
\(597\) −3.51464 −0.143845
\(598\) −0.340483 −0.0139234
\(599\) −35.6158 −1.45522 −0.727611 0.685990i \(-0.759369\pi\)
−0.727611 + 0.685990i \(0.759369\pi\)
\(600\) −2.10728 −0.0860292
\(601\) 38.9252 1.58779 0.793896 0.608054i \(-0.208050\pi\)
0.793896 + 0.608054i \(0.208050\pi\)
\(602\) 0 0
\(603\) 37.1410 1.51250
\(604\) −10.0863 −0.410408
\(605\) 36.5979 1.48792
\(606\) −0.727728 −0.0295619
\(607\) −13.6966 −0.555926 −0.277963 0.960592i \(-0.589659\pi\)
−0.277963 + 0.960592i \(0.589659\pi\)
\(608\) 4.09065 0.165898
\(609\) 0 0
\(610\) −5.80502 −0.235039
\(611\) 3.54543 0.143433
\(612\) −13.1244 −0.530522
\(613\) 3.16112 0.127676 0.0638382 0.997960i \(-0.479666\pi\)
0.0638382 + 0.997960i \(0.479666\pi\)
\(614\) 3.55979 0.143662
\(615\) 8.29120 0.334334
\(616\) 0 0
\(617\) 20.9297 0.842597 0.421299 0.906922i \(-0.361574\pi\)
0.421299 + 0.906922i \(0.361574\pi\)
\(618\) −0.380820 −0.0153188
\(619\) 30.9544 1.24416 0.622082 0.782952i \(-0.286287\pi\)
0.622082 + 0.782952i \(0.286287\pi\)
\(620\) −43.2414 −1.73662
\(621\) 2.68201 0.107625
\(622\) 0.0736887 0.00295465
\(623\) 0 0
\(624\) −0.979864 −0.0392260
\(625\) 32.1854 1.28742
\(626\) −2.14993 −0.0859285
\(627\) 2.09280 0.0835784
\(628\) 21.0515 0.840045
\(629\) −16.2986 −0.649866
\(630\) 0 0
\(631\) −15.1218 −0.601988 −0.300994 0.953626i \(-0.597318\pi\)
−0.300994 + 0.953626i \(0.597318\pi\)
\(632\) 0.613673 0.0244106
\(633\) 4.10452 0.163140
\(634\) −5.12240 −0.203437
\(635\) −17.6687 −0.701159
\(636\) 1.67651 0.0664780
\(637\) 0 0
\(638\) −1.45574 −0.0576335
\(639\) −28.0016 −1.10773
\(640\) 23.4568 0.927210
\(641\) −47.2414 −1.86592 −0.932962 0.359976i \(-0.882785\pi\)
−0.932962 + 0.359976i \(0.882785\pi\)
\(642\) 0.558023 0.0220234
\(643\) 39.9249 1.57448 0.787241 0.616645i \(-0.211509\pi\)
0.787241 + 0.616645i \(0.211509\pi\)
\(644\) 0 0
\(645\) −6.96085 −0.274083
\(646\) −0.797972 −0.0313958
\(647\) −29.8278 −1.17265 −0.586327 0.810075i \(-0.699426\pi\)
−0.586327 + 0.810075i \(0.699426\pi\)
\(648\) 6.50892 0.255695
\(649\) 20.3065 0.797100
\(650\) −2.04747 −0.0803084
\(651\) 0 0
\(652\) −4.65397 −0.182263
\(653\) 25.1549 0.984387 0.492194 0.870486i \(-0.336195\pi\)
0.492194 + 0.870486i \(0.336195\pi\)
\(654\) −0.632635 −0.0247380
\(655\) −49.7727 −1.94478
\(656\) −30.6107 −1.19515
\(657\) −3.16722 −0.123565
\(658\) 0 0
\(659\) 17.3155 0.674517 0.337258 0.941412i \(-0.390500\pi\)
0.337258 + 0.941412i \(0.390500\pi\)
\(660\) 9.03117 0.351538
\(661\) −9.20074 −0.357867 −0.178934 0.983861i \(-0.557265\pi\)
−0.178934 + 0.983861i \(0.557265\pi\)
\(662\) 6.67055 0.259258
\(663\) 0.592684 0.0230179
\(664\) −5.53945 −0.214972
\(665\) 0 0
\(666\) 4.09901 0.158833
\(667\) 2.87327 0.111253
\(668\) −23.6944 −0.916763
\(669\) −5.83840 −0.225725
\(670\) 9.74490 0.376478
\(671\) 33.9984 1.31249
\(672\) 0 0
\(673\) 17.3609 0.669212 0.334606 0.942358i \(-0.391397\pi\)
0.334606 + 0.942358i \(0.391397\pi\)
\(674\) −2.88655 −0.111186
\(675\) 16.1281 0.620770
\(676\) −1.96172 −0.0754507
\(677\) 49.9825 1.92098 0.960492 0.278307i \(-0.0897733\pi\)
0.960492 + 0.278307i \(0.0897733\pi\)
\(678\) −0.0839242 −0.00322309
\(679\) 0 0
\(680\) −6.95425 −0.266683
\(681\) 2.39070 0.0916118
\(682\) −4.94202 −0.189240
\(683\) 33.6153 1.28626 0.643128 0.765759i \(-0.277636\pi\)
0.643128 + 0.765759i \(0.277636\pi\)
\(684\) −10.2841 −0.393223
\(685\) −36.5189 −1.39532
\(686\) 0 0
\(687\) −3.97274 −0.151570
\(688\) 25.6991 0.979770
\(689\) 3.28965 0.125326
\(690\) 0.347845 0.0132422
\(691\) −15.1309 −0.575607 −0.287803 0.957689i \(-0.592925\pi\)
−0.287803 + 0.957689i \(0.592925\pi\)
\(692\) 38.0764 1.44745
\(693\) 0 0
\(694\) −5.85924 −0.222414
\(695\) −15.7300 −0.596674
\(696\) −0.332484 −0.0126028
\(697\) 18.5153 0.701317
\(698\) 2.63731 0.0998238
\(699\) 2.09280 0.0791570
\(700\) 0 0
\(701\) 2.02467 0.0764705 0.0382353 0.999269i \(-0.487826\pi\)
0.0382353 + 0.999269i \(0.487826\pi\)
\(702\) −0.301545 −0.0113811
\(703\) −12.7713 −0.481680
\(704\) −31.9758 −1.20513
\(705\) −3.62208 −0.136415
\(706\) −0.0319960 −0.00120419
\(707\) 0 0
\(708\) 2.29654 0.0863093
\(709\) −30.4553 −1.14377 −0.571886 0.820333i \(-0.693788\pi\)
−0.571886 + 0.820333i \(0.693788\pi\)
\(710\) −7.34695 −0.275726
\(711\) −2.32166 −0.0870691
\(712\) −8.73238 −0.327260
\(713\) 9.75429 0.365301
\(714\) 0 0
\(715\) 17.7210 0.662727
\(716\) −28.7282 −1.07362
\(717\) −5.64411 −0.210783
\(718\) −1.74551 −0.0651418
\(719\) −24.4246 −0.910883 −0.455442 0.890266i \(-0.650519\pi\)
−0.455442 + 0.890266i \(0.650519\pi\)
\(720\) −43.4966 −1.62102
\(721\) 0 0
\(722\) 3.09219 0.115079
\(723\) 5.32514 0.198044
\(724\) 18.5309 0.688697
\(725\) 17.2782 0.641695
\(726\) 0.473043 0.0175563
\(727\) −3.09307 −0.114716 −0.0573578 0.998354i \(-0.518268\pi\)
−0.0573578 + 0.998354i \(0.518268\pi\)
\(728\) 0 0
\(729\) −23.4236 −0.867539
\(730\) −0.831003 −0.0307568
\(731\) −15.5445 −0.574933
\(732\) 3.84501 0.142115
\(733\) −8.41427 −0.310788 −0.155394 0.987853i \(-0.549665\pi\)
−0.155394 + 0.987853i \(0.549665\pi\)
\(734\) −7.17182 −0.264717
\(735\) 0 0
\(736\) −3.98203 −0.146779
\(737\) −57.0731 −2.10231
\(738\) −4.65652 −0.171409
\(739\) −7.22758 −0.265871 −0.132936 0.991125i \(-0.542440\pi\)
−0.132936 + 0.991125i \(0.542440\pi\)
\(740\) −55.1128 −2.02599
\(741\) 0.464419 0.0170609
\(742\) 0 0
\(743\) −53.9092 −1.97774 −0.988869 0.148791i \(-0.952462\pi\)
−0.988869 + 0.148791i \(0.952462\pi\)
\(744\) −1.12873 −0.0413813
\(745\) −59.6360 −2.18489
\(746\) −5.30765 −0.194327
\(747\) 20.9570 0.766776
\(748\) 20.1678 0.737406
\(749\) 0 0
\(750\) 1.09231 0.0398854
\(751\) 29.2442 1.06714 0.533568 0.845757i \(-0.320851\pi\)
0.533568 + 0.845757i \(0.320851\pi\)
\(752\) 13.3726 0.487647
\(753\) −0.677712 −0.0246972
\(754\) −0.323048 −0.0117647
\(755\) 20.2193 0.735857
\(756\) 0 0
\(757\) −22.0597 −0.801773 −0.400887 0.916128i \(-0.631298\pi\)
−0.400887 + 0.916128i \(0.631298\pi\)
\(758\) 3.10981 0.112954
\(759\) −2.03723 −0.0739467
\(760\) −5.44926 −0.197666
\(761\) 17.8161 0.645833 0.322917 0.946427i \(-0.395337\pi\)
0.322917 + 0.946427i \(0.395337\pi\)
\(762\) −0.228374 −0.00827313
\(763\) 0 0
\(764\) −24.6269 −0.890971
\(765\) 26.3095 0.951222
\(766\) −0.225159 −0.00813532
\(767\) 4.50627 0.162712
\(768\) −3.38365 −0.122097
\(769\) −11.3069 −0.407738 −0.203869 0.978998i \(-0.565352\pi\)
−0.203869 + 0.978998i \(0.565352\pi\)
\(770\) 0 0
\(771\) 2.33725 0.0841741
\(772\) 18.3785 0.661458
\(773\) −1.92821 −0.0693528 −0.0346764 0.999399i \(-0.511040\pi\)
−0.0346764 + 0.999399i \(0.511040\pi\)
\(774\) 3.90936 0.140519
\(775\) 58.6567 2.10701
\(776\) −6.83168 −0.245243
\(777\) 0 0
\(778\) 2.80043 0.100400
\(779\) 14.5084 0.519816
\(780\) 2.00413 0.0717594
\(781\) 43.0290 1.53970
\(782\) 0.776782 0.0277777
\(783\) 2.54467 0.0909392
\(784\) 0 0
\(785\) −42.2003 −1.50619
\(786\) −0.643331 −0.0229469
\(787\) 5.53155 0.197178 0.0985892 0.995128i \(-0.468567\pi\)
0.0985892 + 0.995128i \(0.468567\pi\)
\(788\) 14.9537 0.532704
\(789\) −0.372516 −0.0132619
\(790\) −0.609148 −0.0216725
\(791\) 0 0
\(792\) −10.2432 −0.363975
\(793\) 7.54467 0.267919
\(794\) 5.07093 0.179961
\(795\) −3.36078 −0.119195
\(796\) −26.5398 −0.940679
\(797\) −13.8038 −0.488955 −0.244477 0.969655i \(-0.578616\pi\)
−0.244477 + 0.969655i \(0.578616\pi\)
\(798\) 0 0
\(799\) −8.08857 −0.286153
\(800\) −23.9456 −0.846605
\(801\) 33.0365 1.16729
\(802\) 0.840601 0.0296826
\(803\) 4.86695 0.171751
\(804\) −6.45461 −0.227637
\(805\) 0 0
\(806\) −1.09670 −0.0386296
\(807\) 2.12204 0.0746992
\(808\) −11.0977 −0.390415
\(809\) 28.2996 0.994961 0.497480 0.867475i \(-0.334259\pi\)
0.497480 + 0.867475i \(0.334259\pi\)
\(810\) −6.46093 −0.227014
\(811\) −12.2124 −0.428837 −0.214418 0.976742i \(-0.568786\pi\)
−0.214418 + 0.976742i \(0.568786\pi\)
\(812\) 0 0
\(813\) 0.0551575 0.00193446
\(814\) −6.29879 −0.220772
\(815\) 9.32946 0.326797
\(816\) 2.23547 0.0782571
\(817\) −12.1804 −0.426140
\(818\) 4.83410 0.169020
\(819\) 0 0
\(820\) 62.6087 2.18639
\(821\) −41.4011 −1.44491 −0.722453 0.691420i \(-0.756986\pi\)
−0.722453 + 0.691420i \(0.756986\pi\)
\(822\) −0.472021 −0.0164636
\(823\) 47.1752 1.64443 0.822213 0.569180i \(-0.192739\pi\)
0.822213 + 0.569180i \(0.192739\pi\)
\(824\) −5.80742 −0.202311
\(825\) −12.2507 −0.426515
\(826\) 0 0
\(827\) 21.1124 0.734150 0.367075 0.930191i \(-0.380359\pi\)
0.367075 + 0.930191i \(0.380359\pi\)
\(828\) 10.0110 0.347907
\(829\) −0.636752 −0.0221153 −0.0110577 0.999939i \(-0.503520\pi\)
−0.0110577 + 0.999939i \(0.503520\pi\)
\(830\) 5.49861 0.190859
\(831\) −5.96862 −0.207049
\(832\) −7.09585 −0.246004
\(833\) 0 0
\(834\) −0.203317 −0.00704029
\(835\) 47.4983 1.64375
\(836\) 15.8032 0.546565
\(837\) 8.63877 0.298600
\(838\) 4.87757 0.168493
\(839\) −26.9432 −0.930183 −0.465092 0.885263i \(-0.653979\pi\)
−0.465092 + 0.885263i \(0.653979\pi\)
\(840\) 0 0
\(841\) −26.2739 −0.905995
\(842\) 1.95656 0.0674276
\(843\) 0.0896862 0.00308896
\(844\) 30.9941 1.06686
\(845\) 3.93251 0.135282
\(846\) 2.03424 0.0699386
\(847\) 0 0
\(848\) 12.4078 0.426087
\(849\) 7.52645 0.258307
\(850\) 4.67112 0.160218
\(851\) 12.4322 0.426170
\(852\) 4.86631 0.166717
\(853\) 6.74784 0.231042 0.115521 0.993305i \(-0.463146\pi\)
0.115521 + 0.993305i \(0.463146\pi\)
\(854\) 0 0
\(855\) 20.6158 0.705045
\(856\) 8.50973 0.290856
\(857\) −45.0268 −1.53809 −0.769043 0.639197i \(-0.779267\pi\)
−0.769043 + 0.639197i \(0.779267\pi\)
\(858\) 0.229050 0.00781965
\(859\) −36.7270 −1.25311 −0.626554 0.779378i \(-0.715535\pi\)
−0.626554 + 0.779378i \(0.715535\pi\)
\(860\) −52.5629 −1.79238
\(861\) 0 0
\(862\) 1.11299 0.0379087
\(863\) −43.4275 −1.47829 −0.739144 0.673547i \(-0.764770\pi\)
−0.739144 + 0.673547i \(0.764770\pi\)
\(864\) −3.52663 −0.119978
\(865\) −76.3288 −2.59526
\(866\) −2.39871 −0.0815114
\(867\) 3.06425 0.104067
\(868\) 0 0
\(869\) 3.56761 0.121023
\(870\) 0.330033 0.0111892
\(871\) −12.6653 −0.429146
\(872\) −9.64754 −0.326707
\(873\) 25.8458 0.874747
\(874\) 0.608676 0.0205888
\(875\) 0 0
\(876\) 0.550422 0.0185970
\(877\) 40.0081 1.35098 0.675488 0.737371i \(-0.263933\pi\)
0.675488 + 0.737371i \(0.263933\pi\)
\(878\) −0.982815 −0.0331684
\(879\) −8.19443 −0.276391
\(880\) 66.8395 2.25316
\(881\) 35.4308 1.19370 0.596848 0.802355i \(-0.296420\pi\)
0.596848 + 0.802355i \(0.296420\pi\)
\(882\) 0 0
\(883\) 22.6654 0.762751 0.381375 0.924420i \(-0.375451\pi\)
0.381375 + 0.924420i \(0.375451\pi\)
\(884\) 4.47548 0.150527
\(885\) −4.60370 −0.154752
\(886\) −0.113246 −0.00380459
\(887\) 44.6881 1.50048 0.750240 0.661166i \(-0.229938\pi\)
0.750240 + 0.661166i \(0.229938\pi\)
\(888\) −1.43861 −0.0482766
\(889\) 0 0
\(890\) 8.66800 0.290552
\(891\) 37.8398 1.26768
\(892\) −44.0870 −1.47614
\(893\) −6.33810 −0.212096
\(894\) −0.770818 −0.0257800
\(895\) 57.5892 1.92499
\(896\) 0 0
\(897\) −0.452087 −0.0150947
\(898\) 1.44073 0.0480779
\(899\) 9.25480 0.308665
\(900\) 60.2005 2.00668
\(901\) −7.50505 −0.250029
\(902\) 7.15549 0.238252
\(903\) 0 0
\(904\) −1.27983 −0.0425664
\(905\) −37.1476 −1.23483
\(906\) 0.261343 0.00868254
\(907\) 54.4748 1.80881 0.904403 0.426680i \(-0.140317\pi\)
0.904403 + 0.426680i \(0.140317\pi\)
\(908\) 18.0527 0.599100
\(909\) 41.9851 1.39256
\(910\) 0 0
\(911\) −27.4793 −0.910431 −0.455215 0.890381i \(-0.650438\pi\)
−0.455215 + 0.890381i \(0.650438\pi\)
\(912\) 1.75169 0.0580041
\(913\) −32.2038 −1.06579
\(914\) −1.54925 −0.0512447
\(915\) −7.70779 −0.254812
\(916\) −29.9990 −0.991196
\(917\) 0 0
\(918\) 0.687947 0.0227056
\(919\) −48.2880 −1.59287 −0.796437 0.604722i \(-0.793284\pi\)
−0.796437 + 0.604722i \(0.793284\pi\)
\(920\) 5.30456 0.174886
\(921\) 4.72662 0.155747
\(922\) 1.86578 0.0614461
\(923\) 9.54869 0.314299
\(924\) 0 0
\(925\) 74.7601 2.45810
\(926\) −0.422713 −0.0138912
\(927\) 21.9708 0.721615
\(928\) −3.77812 −0.124023
\(929\) 43.3154 1.42113 0.710566 0.703631i \(-0.248439\pi\)
0.710566 + 0.703631i \(0.248439\pi\)
\(930\) 1.12041 0.0367397
\(931\) 0 0
\(932\) 15.8032 0.517651
\(933\) 0.0978423 0.00320321
\(934\) 1.58853 0.0519784
\(935\) −40.4288 −1.32216
\(936\) −2.27309 −0.0742983
\(937\) −37.2211 −1.21596 −0.607980 0.793952i \(-0.708020\pi\)
−0.607980 + 0.793952i \(0.708020\pi\)
\(938\) 0 0
\(939\) −2.85463 −0.0931574
\(940\) −27.3511 −0.892095
\(941\) 15.9751 0.520773 0.260386 0.965504i \(-0.416150\pi\)
0.260386 + 0.965504i \(0.416150\pi\)
\(942\) −0.545456 −0.0177719
\(943\) −14.1231 −0.459911
\(944\) 16.9967 0.553194
\(945\) 0 0
\(946\) −6.00736 −0.195316
\(947\) 27.7572 0.901988 0.450994 0.892527i \(-0.351070\pi\)
0.450994 + 0.892527i \(0.351070\pi\)
\(948\) 0.403474 0.0131042
\(949\) 1.08004 0.0350595
\(950\) 3.66023 0.118754
\(951\) −6.80142 −0.220551
\(952\) 0 0
\(953\) 12.0303 0.389700 0.194850 0.980833i \(-0.437578\pi\)
0.194850 + 0.980833i \(0.437578\pi\)
\(954\) 1.88748 0.0611096
\(955\) 49.3677 1.59750
\(956\) −42.6199 −1.37843
\(957\) −1.93291 −0.0624820
\(958\) −2.84744 −0.0919965
\(959\) 0 0
\(960\) 7.24926 0.233969
\(961\) 0.418620 0.0135039
\(962\) −1.39778 −0.0450663
\(963\) −32.1942 −1.03744
\(964\) 40.2113 1.29512
\(965\) −36.8421 −1.18599
\(966\) 0 0
\(967\) 5.40788 0.173906 0.0869528 0.996212i \(-0.472287\pi\)
0.0869528 + 0.996212i \(0.472287\pi\)
\(968\) 7.21380 0.231860
\(969\) −1.05953 −0.0340370
\(970\) 6.78131 0.217735
\(971\) 42.2752 1.35668 0.678338 0.734750i \(-0.262700\pi\)
0.678338 + 0.734750i \(0.262700\pi\)
\(972\) 13.3496 0.428190
\(973\) 0 0
\(974\) 6.50733 0.208508
\(975\) −2.71859 −0.0870646
\(976\) 28.4568 0.910881
\(977\) −10.8302 −0.346488 −0.173244 0.984879i \(-0.555425\pi\)
−0.173244 + 0.984879i \(0.555425\pi\)
\(978\) 0.120587 0.00385594
\(979\) −50.7660 −1.62249
\(980\) 0 0
\(981\) 36.4988 1.16532
\(982\) 4.41329 0.140834
\(983\) 21.5610 0.687688 0.343844 0.939027i \(-0.388271\pi\)
0.343844 + 0.939027i \(0.388271\pi\)
\(984\) 1.63427 0.0520988
\(985\) −29.9766 −0.955134
\(986\) 0.737005 0.0234710
\(987\) 0 0
\(988\) 3.50693 0.111570
\(989\) 11.8570 0.377030
\(990\) 10.1677 0.323149
\(991\) 8.62624 0.274022 0.137011 0.990570i \(-0.456251\pi\)
0.137011 + 0.990570i \(0.456251\pi\)
\(992\) −12.8261 −0.407230
\(993\) 8.85703 0.281069
\(994\) 0 0
\(995\) 53.2024 1.68663
\(996\) −3.64205 −0.115403
\(997\) 21.6967 0.687142 0.343571 0.939127i \(-0.388363\pi\)
0.343571 + 0.939127i \(0.388363\pi\)
\(998\) 2.22763 0.0705144
\(999\) 11.0104 0.348354
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 637.2.a.l.1.2 5
3.2 odd 2 5733.2.a.bl.1.4 5
7.2 even 3 91.2.e.c.53.4 10
7.3 odd 6 637.2.e.m.79.4 10
7.4 even 3 91.2.e.c.79.4 yes 10
7.5 odd 6 637.2.e.m.508.4 10
7.6 odd 2 637.2.a.k.1.2 5
13.12 even 2 8281.2.a.bw.1.4 5
21.2 odd 6 819.2.j.h.235.2 10
21.11 odd 6 819.2.j.h.352.2 10
21.20 even 2 5733.2.a.bm.1.4 5
28.11 odd 6 1456.2.r.p.625.3 10
28.23 odd 6 1456.2.r.p.417.3 10
91.25 even 6 1183.2.e.f.170.2 10
91.51 even 6 1183.2.e.f.508.2 10
91.90 odd 2 8281.2.a.bx.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.c.53.4 10 7.2 even 3
91.2.e.c.79.4 yes 10 7.4 even 3
637.2.a.k.1.2 5 7.6 odd 2
637.2.a.l.1.2 5 1.1 even 1 trivial
637.2.e.m.79.4 10 7.3 odd 6
637.2.e.m.508.4 10 7.5 odd 6
819.2.j.h.235.2 10 21.2 odd 6
819.2.j.h.352.2 10 21.11 odd 6
1183.2.e.f.170.2 10 91.25 even 6
1183.2.e.f.508.2 10 91.51 even 6
1456.2.r.p.417.3 10 28.23 odd 6
1456.2.r.p.625.3 10 28.11 odd 6
5733.2.a.bl.1.4 5 3.2 odd 2
5733.2.a.bm.1.4 5 21.20 even 2
8281.2.a.bw.1.4 5 13.12 even 2
8281.2.a.bx.1.4 5 91.90 odd 2