Properties

Label 9025.2.a.bo.1.2
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.0649878242\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.2225.1
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1805)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.820249\) of defining polynomial
Character \(\chi\) \(=\) 9025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.820249 q^{2} +2.32719 q^{3} -1.32719 q^{4} -1.90888 q^{6} +0.561717 q^{7} +2.72913 q^{8} +2.41582 q^{9} +O(q^{10})\) \(q-0.820249 q^{2} +2.32719 q^{3} -1.32719 q^{4} -1.90888 q^{6} +0.561717 q^{7} +2.72913 q^{8} +2.41582 q^{9} -0.111092 q^{11} -3.08863 q^{12} -6.89045 q^{13} -0.460748 q^{14} +0.415819 q^{16} +3.81167 q^{17} -1.98157 q^{18} +1.30722 q^{21} +0.0911232 q^{22} +4.04243 q^{23} +6.35120 q^{24} +5.65189 q^{26} -1.35950 q^{27} -0.745506 q^{28} +9.29239 q^{29} -4.18987 q^{31} -5.79933 q^{32} -0.258532 q^{33} -3.12652 q^{34} -3.20625 q^{36} -2.68669 q^{37} -16.0354 q^{39} -10.0988 q^{41} -1.07225 q^{42} +9.63192 q^{43} +0.147440 q^{44} -3.31580 q^{46} -2.12652 q^{47} +0.967690 q^{48} -6.68447 q^{49} +8.87048 q^{51} +9.14494 q^{52} +5.74455 q^{53} +1.11513 q^{54} +1.53300 q^{56} -7.62207 q^{58} +7.89903 q^{59} +5.56575 q^{61} +3.43674 q^{62} +1.35701 q^{63} +3.92526 q^{64} +0.212061 q^{66} +10.6534 q^{67} -5.05881 q^{68} +9.40752 q^{69} -6.64050 q^{71} +6.59307 q^{72} +8.45825 q^{73} +2.20376 q^{74} -0.0624023 q^{77} +13.1530 q^{78} -6.27087 q^{79} -10.4113 q^{81} +8.28349 q^{82} +8.16132 q^{83} -1.73493 q^{84} -7.90057 q^{86} +21.6252 q^{87} -0.303184 q^{88} +1.16741 q^{89} -3.87048 q^{91} -5.36508 q^{92} -9.75064 q^{93} +1.74428 q^{94} -13.4961 q^{96} +8.24746 q^{97} +5.48294 q^{98} -0.268378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{3} + 3 q^{4} - 7 q^{6} + 11 q^{7} + 6 q^{8} + 5 q^{9} - 16 q^{12} - 2 q^{13} + 11 q^{14} - 3 q^{16} + 7 q^{17} + 17 q^{18} - 2 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 9 q^{26} - 14 q^{27} + 13 q^{28} + 15 q^{29} + q^{31} + 3 q^{32} + 12 q^{33} + 22 q^{34} + 16 q^{36} - 11 q^{37} - 29 q^{39} - 22 q^{41} - 19 q^{42} + 26 q^{43} - 12 q^{44} - 10 q^{46} + 26 q^{47} - 13 q^{48} + 13 q^{49} + 11 q^{51} + 27 q^{52} - 16 q^{53} - 25 q^{54} + 8 q^{56} + 3 q^{58} + 10 q^{59} + 2 q^{61} + 31 q^{62} + 17 q^{63} + 4 q^{64} + 22 q^{66} + 3 q^{67} - 4 q^{68} - 14 q^{69} - 18 q^{71} + 29 q^{72} + 24 q^{73} - 17 q^{74} + 6 q^{77} - 15 q^{78} - 30 q^{79} - 4 q^{81} + 13 q^{82} + 12 q^{83} - 52 q^{84} + 16 q^{86} + q^{87} - 23 q^{88} - 9 q^{89} + 9 q^{91} + 25 q^{92} - 7 q^{93} + 11 q^{94} - 6 q^{96} + 19 q^{97} + 48 q^{98} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.820249 −0.580004 −0.290002 0.957026i \(-0.593656\pi\)
−0.290002 + 0.957026i \(0.593656\pi\)
\(3\) 2.32719 1.34360 0.671802 0.740731i \(-0.265520\pi\)
0.671802 + 0.740731i \(0.265520\pi\)
\(4\) −1.32719 −0.663596
\(5\) 0 0
\(6\) −1.90888 −0.779296
\(7\) 0.561717 0.212309 0.106154 0.994350i \(-0.466146\pi\)
0.106154 + 0.994350i \(0.466146\pi\)
\(8\) 2.72913 0.964892
\(9\) 2.41582 0.805273
\(10\) 0 0
\(11\) −0.111092 −0.0334955 −0.0167478 0.999860i \(-0.505331\pi\)
−0.0167478 + 0.999860i \(0.505331\pi\)
\(12\) −3.08863 −0.891610
\(13\) −6.89045 −1.91107 −0.955534 0.294882i \(-0.904720\pi\)
−0.955534 + 0.294882i \(0.904720\pi\)
\(14\) −0.460748 −0.123140
\(15\) 0 0
\(16\) 0.415819 0.103955
\(17\) 3.81167 0.924465 0.462233 0.886759i \(-0.347048\pi\)
0.462233 + 0.886759i \(0.347048\pi\)
\(18\) −1.98157 −0.467061
\(19\) 0 0
\(20\) 0 0
\(21\) 1.30722 0.285259
\(22\) 0.0911232 0.0194275
\(23\) 4.04243 0.842906 0.421453 0.906850i \(-0.361520\pi\)
0.421453 + 0.906850i \(0.361520\pi\)
\(24\) 6.35120 1.29643
\(25\) 0 0
\(26\) 5.65189 1.10843
\(27\) −1.35950 −0.261636
\(28\) −0.745506 −0.140887
\(29\) 9.29239 1.72555 0.862776 0.505586i \(-0.168724\pi\)
0.862776 + 0.505586i \(0.168724\pi\)
\(30\) 0 0
\(31\) −4.18987 −0.752524 −0.376262 0.926513i \(-0.622791\pi\)
−0.376262 + 0.926513i \(0.622791\pi\)
\(32\) −5.79933 −1.02519
\(33\) −0.258532 −0.0450047
\(34\) −3.12652 −0.536193
\(35\) 0 0
\(36\) −3.20625 −0.534376
\(37\) −2.68669 −0.441690 −0.220845 0.975309i \(-0.570881\pi\)
−0.220845 + 0.975309i \(0.570881\pi\)
\(38\) 0 0
\(39\) −16.0354 −2.56772
\(40\) 0 0
\(41\) −10.0988 −1.57716 −0.788580 0.614932i \(-0.789183\pi\)
−0.788580 + 0.614932i \(0.789183\pi\)
\(42\) −1.07225 −0.165451
\(43\) 9.63192 1.46885 0.734427 0.678688i \(-0.237451\pi\)
0.734427 + 0.678688i \(0.237451\pi\)
\(44\) 0.147440 0.0222275
\(45\) 0 0
\(46\) −3.31580 −0.488888
\(47\) −2.12652 −0.310185 −0.155092 0.987900i \(-0.549567\pi\)
−0.155092 + 0.987900i \(0.549567\pi\)
\(48\) 0.967690 0.139674
\(49\) −6.68447 −0.954925
\(50\) 0 0
\(51\) 8.87048 1.24212
\(52\) 9.14494 1.26818
\(53\) 5.74455 0.789075 0.394537 0.918880i \(-0.370905\pi\)
0.394537 + 0.918880i \(0.370905\pi\)
\(54\) 1.11513 0.151750
\(55\) 0 0
\(56\) 1.53300 0.204855
\(57\) 0 0
\(58\) −7.62207 −1.00083
\(59\) 7.89903 1.02837 0.514183 0.857680i \(-0.328095\pi\)
0.514183 + 0.857680i \(0.328095\pi\)
\(60\) 0 0
\(61\) 5.56575 0.712622 0.356311 0.934367i \(-0.384034\pi\)
0.356311 + 0.934367i \(0.384034\pi\)
\(62\) 3.43674 0.436467
\(63\) 1.35701 0.170967
\(64\) 3.92526 0.490657
\(65\) 0 0
\(66\) 0.212061 0.0261029
\(67\) 10.6534 1.30152 0.650762 0.759282i \(-0.274450\pi\)
0.650762 + 0.759282i \(0.274450\pi\)
\(68\) −5.05881 −0.613471
\(69\) 9.40752 1.13253
\(70\) 0 0
\(71\) −6.64050 −0.788082 −0.394041 0.919093i \(-0.628923\pi\)
−0.394041 + 0.919093i \(0.628923\pi\)
\(72\) 6.59307 0.777001
\(73\) 8.45825 0.989964 0.494982 0.868903i \(-0.335175\pi\)
0.494982 + 0.868903i \(0.335175\pi\)
\(74\) 2.20376 0.256182
\(75\) 0 0
\(76\) 0 0
\(77\) −0.0624023 −0.00711140
\(78\) 13.1530 1.48929
\(79\) −6.27087 −0.705528 −0.352764 0.935712i \(-0.614758\pi\)
−0.352764 + 0.935712i \(0.614758\pi\)
\(80\) 0 0
\(81\) −10.4113 −1.15681
\(82\) 8.28349 0.914759
\(83\) 8.16132 0.895822 0.447911 0.894078i \(-0.352168\pi\)
0.447911 + 0.894078i \(0.352168\pi\)
\(84\) −1.73493 −0.189297
\(85\) 0 0
\(86\) −7.90057 −0.851941
\(87\) 21.6252 2.31846
\(88\) −0.303184 −0.0323196
\(89\) 1.16741 0.123745 0.0618726 0.998084i \(-0.480293\pi\)
0.0618726 + 0.998084i \(0.480293\pi\)
\(90\) 0 0
\(91\) −3.87048 −0.405737
\(92\) −5.36508 −0.559348
\(93\) −9.75064 −1.01109
\(94\) 1.74428 0.179908
\(95\) 0 0
\(96\) −13.4961 −1.37744
\(97\) 8.24746 0.837402 0.418701 0.908124i \(-0.362485\pi\)
0.418701 + 0.908124i \(0.362485\pi\)
\(98\) 5.48294 0.553860
\(99\) −0.268378 −0.0269730
\(100\) 0 0
\(101\) −11.7400 −1.16817 −0.584087 0.811691i \(-0.698547\pi\)
−0.584087 + 0.811691i \(0.698547\pi\)
\(102\) −7.27601 −0.720432
\(103\) 19.4676 1.91820 0.959099 0.283069i \(-0.0913526\pi\)
0.959099 + 0.283069i \(0.0913526\pi\)
\(104\) −18.8049 −1.84397
\(105\) 0 0
\(106\) −4.71196 −0.457666
\(107\) −16.5648 −1.60138 −0.800690 0.599079i \(-0.795534\pi\)
−0.800690 + 0.599079i \(0.795534\pi\)
\(108\) 1.80432 0.173621
\(109\) 14.0588 1.34659 0.673295 0.739374i \(-0.264878\pi\)
0.673295 + 0.739374i \(0.264878\pi\)
\(110\) 0 0
\(111\) −6.25245 −0.593456
\(112\) 0.233572 0.0220705
\(113\) −8.88950 −0.836254 −0.418127 0.908389i \(-0.637313\pi\)
−0.418127 + 0.908389i \(0.637313\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −12.3328 −1.14507
\(117\) −16.6461 −1.53893
\(118\) −6.47917 −0.596456
\(119\) 2.14108 0.196272
\(120\) 0 0
\(121\) −10.9877 −0.998878
\(122\) −4.56531 −0.413323
\(123\) −23.5017 −2.11908
\(124\) 5.56076 0.499371
\(125\) 0 0
\(126\) −1.11308 −0.0991613
\(127\) 7.76469 0.689005 0.344503 0.938785i \(-0.388048\pi\)
0.344503 + 0.938785i \(0.388048\pi\)
\(128\) 8.37897 0.740603
\(129\) 22.4153 1.97356
\(130\) 0 0
\(131\) −4.58042 −0.400193 −0.200097 0.979776i \(-0.564126\pi\)
−0.200097 + 0.979776i \(0.564126\pi\)
\(132\) 0.343122 0.0298649
\(133\) 0 0
\(134\) −8.73847 −0.754889
\(135\) 0 0
\(136\) 10.4025 0.892009
\(137\) −1.19518 −0.102111 −0.0510554 0.998696i \(-0.516259\pi\)
−0.0510554 + 0.998696i \(0.516259\pi\)
\(138\) −7.71651 −0.656873
\(139\) 8.06036 0.683670 0.341835 0.939760i \(-0.388952\pi\)
0.341835 + 0.939760i \(0.388952\pi\)
\(140\) 0 0
\(141\) −4.94881 −0.416765
\(142\) 5.44686 0.457091
\(143\) 0.765474 0.0640122
\(144\) 1.00454 0.0837119
\(145\) 0 0
\(146\) −6.93787 −0.574183
\(147\) −15.5560 −1.28304
\(148\) 3.56575 0.293103
\(149\) 9.89499 0.810629 0.405315 0.914177i \(-0.367162\pi\)
0.405315 + 0.914177i \(0.367162\pi\)
\(150\) 0 0
\(151\) −20.7413 −1.68790 −0.843951 0.536421i \(-0.819776\pi\)
−0.843951 + 0.536421i \(0.819776\pi\)
\(152\) 0 0
\(153\) 9.20830 0.744447
\(154\) 0.0511854 0.00412464
\(155\) 0 0
\(156\) 21.2820 1.70393
\(157\) 12.9092 1.03026 0.515131 0.857111i \(-0.327743\pi\)
0.515131 + 0.857111i \(0.327743\pi\)
\(158\) 5.14368 0.409209
\(159\) 13.3687 1.06020
\(160\) 0 0
\(161\) 2.27070 0.178956
\(162\) 8.53984 0.670953
\(163\) 7.93134 0.621231 0.310615 0.950536i \(-0.399465\pi\)
0.310615 + 0.950536i \(0.399465\pi\)
\(164\) 13.4030 1.04660
\(165\) 0 0
\(166\) −6.69432 −0.519580
\(167\) −5.69132 −0.440408 −0.220204 0.975454i \(-0.570672\pi\)
−0.220204 + 0.975454i \(0.570672\pi\)
\(168\) 3.56757 0.275244
\(169\) 34.4783 2.65218
\(170\) 0 0
\(171\) 0 0
\(172\) −12.7834 −0.974725
\(173\) 7.12043 0.541357 0.270678 0.962670i \(-0.412752\pi\)
0.270678 + 0.962670i \(0.412752\pi\)
\(174\) −17.7380 −1.34472
\(175\) 0 0
\(176\) −0.0461942 −0.00348202
\(177\) 18.3826 1.38172
\(178\) −0.957567 −0.0717727
\(179\) −2.37647 −0.177626 −0.0888129 0.996048i \(-0.528307\pi\)
−0.0888129 + 0.996048i \(0.528307\pi\)
\(180\) 0 0
\(181\) 20.1766 1.49971 0.749857 0.661600i \(-0.230122\pi\)
0.749857 + 0.661600i \(0.230122\pi\)
\(182\) 3.17476 0.235329
\(183\) 12.9526 0.957482
\(184\) 11.0323 0.813313
\(185\) 0 0
\(186\) 7.99795 0.586438
\(187\) −0.423446 −0.0309655
\(188\) 2.82230 0.205837
\(189\) −0.763655 −0.0555477
\(190\) 0 0
\(191\) 9.88950 0.715579 0.357789 0.933802i \(-0.383531\pi\)
0.357789 + 0.933802i \(0.383531\pi\)
\(192\) 9.13482 0.659249
\(193\) 4.55092 0.327582 0.163791 0.986495i \(-0.447628\pi\)
0.163791 + 0.986495i \(0.447628\pi\)
\(194\) −6.76497 −0.485697
\(195\) 0 0
\(196\) 8.87158 0.633684
\(197\) 12.4701 0.888457 0.444229 0.895914i \(-0.353478\pi\)
0.444229 + 0.895914i \(0.353478\pi\)
\(198\) 0.220137 0.0156445
\(199\) −19.9932 −1.41728 −0.708642 0.705569i \(-0.750692\pi\)
−0.708642 + 0.705569i \(0.750692\pi\)
\(200\) 0 0
\(201\) 24.7926 1.74873
\(202\) 9.62973 0.677546
\(203\) 5.21969 0.366350
\(204\) −11.7728 −0.824263
\(205\) 0 0
\(206\) −15.9683 −1.11256
\(207\) 9.76579 0.678769
\(208\) −2.86518 −0.198664
\(209\) 0 0
\(210\) 0 0
\(211\) 16.8102 1.15726 0.578631 0.815589i \(-0.303587\pi\)
0.578631 + 0.815589i \(0.303587\pi\)
\(212\) −7.62412 −0.523627
\(213\) −15.4537 −1.05887
\(214\) 13.5873 0.928806
\(215\) 0 0
\(216\) −3.71025 −0.252451
\(217\) −2.35352 −0.159768
\(218\) −11.5317 −0.781027
\(219\) 19.6840 1.33012
\(220\) 0 0
\(221\) −26.2641 −1.76672
\(222\) 5.12857 0.344207
\(223\) 1.88641 0.126324 0.0631618 0.998003i \(-0.479882\pi\)
0.0631618 + 0.998003i \(0.479882\pi\)
\(224\) −3.25758 −0.217656
\(225\) 0 0
\(226\) 7.29160 0.485030
\(227\) 10.7044 0.710479 0.355239 0.934775i \(-0.384399\pi\)
0.355239 + 0.934775i \(0.384399\pi\)
\(228\) 0 0
\(229\) 8.34388 0.551379 0.275690 0.961247i \(-0.411094\pi\)
0.275690 + 0.961247i \(0.411094\pi\)
\(230\) 0 0
\(231\) −0.145222 −0.00955491
\(232\) 25.3601 1.66497
\(233\) 2.14436 0.140481 0.0702407 0.997530i \(-0.477623\pi\)
0.0702407 + 0.997530i \(0.477623\pi\)
\(234\) 13.6539 0.892586
\(235\) 0 0
\(236\) −10.4835 −0.682419
\(237\) −14.5935 −0.947951
\(238\) −1.75622 −0.113839
\(239\) 25.0796 1.62227 0.811134 0.584861i \(-0.198851\pi\)
0.811134 + 0.584861i \(0.198851\pi\)
\(240\) 0 0
\(241\) 11.3527 0.731294 0.365647 0.930754i \(-0.380848\pi\)
0.365647 + 0.930754i \(0.380848\pi\)
\(242\) 9.01262 0.579353
\(243\) −20.1505 −1.29266
\(244\) −7.38682 −0.472893
\(245\) 0 0
\(246\) 19.2773 1.22907
\(247\) 0 0
\(248\) −11.4347 −0.726104
\(249\) 18.9930 1.20363
\(250\) 0 0
\(251\) −6.92245 −0.436941 −0.218471 0.975844i \(-0.570107\pi\)
−0.218471 + 0.975844i \(0.570107\pi\)
\(252\) −1.80101 −0.113453
\(253\) −0.449082 −0.0282336
\(254\) −6.36898 −0.399626
\(255\) 0 0
\(256\) −14.7234 −0.920210
\(257\) −1.89721 −0.118345 −0.0591724 0.998248i \(-0.518846\pi\)
−0.0591724 + 0.998248i \(0.518846\pi\)
\(258\) −18.3861 −1.14467
\(259\) −1.50916 −0.0937747
\(260\) 0 0
\(261\) 22.4487 1.38954
\(262\) 3.75709 0.232114
\(263\) 11.5446 0.711868 0.355934 0.934511i \(-0.384163\pi\)
0.355934 + 0.934511i \(0.384163\pi\)
\(264\) −0.705568 −0.0434247
\(265\) 0 0
\(266\) 0 0
\(267\) 2.71678 0.166265
\(268\) −14.1391 −0.863685
\(269\) −3.02056 −0.184167 −0.0920833 0.995751i \(-0.529353\pi\)
−0.0920833 + 0.995751i \(0.529353\pi\)
\(270\) 0 0
\(271\) 8.81150 0.535260 0.267630 0.963522i \(-0.413759\pi\)
0.267630 + 0.963522i \(0.413759\pi\)
\(272\) 1.58496 0.0961025
\(273\) −9.00735 −0.545150
\(274\) 0.980343 0.0592247
\(275\) 0 0
\(276\) −12.4856 −0.751543
\(277\) 9.68919 0.582167 0.291083 0.956698i \(-0.405984\pi\)
0.291083 + 0.956698i \(0.405984\pi\)
\(278\) −6.61150 −0.396531
\(279\) −10.1220 −0.605987
\(280\) 0 0
\(281\) −18.6762 −1.11413 −0.557063 0.830470i \(-0.688072\pi\)
−0.557063 + 0.830470i \(0.688072\pi\)
\(282\) 4.05926 0.241726
\(283\) 7.46451 0.443719 0.221859 0.975079i \(-0.428787\pi\)
0.221859 + 0.975079i \(0.428787\pi\)
\(284\) 8.81321 0.522968
\(285\) 0 0
\(286\) −0.627880 −0.0371273
\(287\) −5.67264 −0.334845
\(288\) −14.0101 −0.825554
\(289\) −2.47118 −0.145364
\(290\) 0 0
\(291\) 19.1934 1.12514
\(292\) −11.2257 −0.656935
\(293\) 3.73771 0.218359 0.109180 0.994022i \(-0.465178\pi\)
0.109180 + 0.994022i \(0.465178\pi\)
\(294\) 12.7598 0.744169
\(295\) 0 0
\(296\) −7.33232 −0.426183
\(297\) 0.151030 0.00876364
\(298\) −8.11636 −0.470168
\(299\) −27.8542 −1.61085
\(300\) 0 0
\(301\) 5.41041 0.311851
\(302\) 17.0130 0.978989
\(303\) −27.3212 −1.56956
\(304\) 0 0
\(305\) 0 0
\(306\) −7.55310 −0.431782
\(307\) −23.2825 −1.32880 −0.664402 0.747375i \(-0.731314\pi\)
−0.664402 + 0.747375i \(0.731314\pi\)
\(308\) 0.0828198 0.00471909
\(309\) 45.3048 2.57730
\(310\) 0 0
\(311\) 23.4553 1.33003 0.665013 0.746832i \(-0.268426\pi\)
0.665013 + 0.746832i \(0.268426\pi\)
\(312\) −43.7626 −2.47757
\(313\) 15.0079 0.848297 0.424148 0.905593i \(-0.360573\pi\)
0.424148 + 0.905593i \(0.360573\pi\)
\(314\) −10.5887 −0.597556
\(315\) 0 0
\(316\) 8.32265 0.468186
\(317\) 19.3000 1.08400 0.541998 0.840380i \(-0.317668\pi\)
0.541998 + 0.840380i \(0.317668\pi\)
\(318\) −10.9656 −0.614923
\(319\) −1.03231 −0.0577983
\(320\) 0 0
\(321\) −38.5495 −2.15162
\(322\) −1.86254 −0.103795
\(323\) 0 0
\(324\) 13.8178 0.767653
\(325\) 0 0
\(326\) −6.50568 −0.360316
\(327\) 32.7175 1.80928
\(328\) −27.5608 −1.52179
\(329\) −1.19450 −0.0658550
\(330\) 0 0
\(331\) 19.1303 1.05150 0.525748 0.850641i \(-0.323786\pi\)
0.525748 + 0.850641i \(0.323786\pi\)
\(332\) −10.8316 −0.594463
\(333\) −6.49056 −0.355681
\(334\) 4.66830 0.255438
\(335\) 0 0
\(336\) 0.543568 0.0296540
\(337\) −25.5100 −1.38962 −0.694810 0.719193i \(-0.744511\pi\)
−0.694810 + 0.719193i \(0.744511\pi\)
\(338\) −28.2808 −1.53827
\(339\) −20.6876 −1.12359
\(340\) 0 0
\(341\) 0.465462 0.0252062
\(342\) 0 0
\(343\) −7.68680 −0.415048
\(344\) 26.2867 1.41728
\(345\) 0 0
\(346\) −5.84053 −0.313989
\(347\) 34.3847 1.84587 0.922933 0.384960i \(-0.125785\pi\)
0.922933 + 0.384960i \(0.125785\pi\)
\(348\) −28.7007 −1.53852
\(349\) −28.6428 −1.53321 −0.766607 0.642117i \(-0.778057\pi\)
−0.766607 + 0.642117i \(0.778057\pi\)
\(350\) 0 0
\(351\) 9.36758 0.500004
\(352\) 0.644259 0.0343391
\(353\) −23.5203 −1.25186 −0.625930 0.779879i \(-0.715281\pi\)
−0.625930 + 0.779879i \(0.715281\pi\)
\(354\) −15.0783 −0.801401
\(355\) 0 0
\(356\) −1.54938 −0.0821167
\(357\) 4.98270 0.263712
\(358\) 1.94930 0.103024
\(359\) 9.77437 0.515871 0.257936 0.966162i \(-0.416958\pi\)
0.257936 + 0.966162i \(0.416958\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −16.5498 −0.869839
\(363\) −25.5704 −1.34210
\(364\) 5.13687 0.269245
\(365\) 0 0
\(366\) −10.6243 −0.555343
\(367\) 2.03857 0.106412 0.0532062 0.998584i \(-0.483056\pi\)
0.0532062 + 0.998584i \(0.483056\pi\)
\(368\) 1.68092 0.0876240
\(369\) −24.3968 −1.27004
\(370\) 0 0
\(371\) 3.22681 0.167528
\(372\) 12.9410 0.670958
\(373\) 12.9613 0.671110 0.335555 0.942021i \(-0.391076\pi\)
0.335555 + 0.942021i \(0.391076\pi\)
\(374\) 0.347331 0.0179601
\(375\) 0 0
\(376\) −5.80354 −0.299295
\(377\) −64.0287 −3.29765
\(378\) 0.626387 0.0322179
\(379\) −6.82911 −0.350788 −0.175394 0.984498i \(-0.556120\pi\)
−0.175394 + 0.984498i \(0.556120\pi\)
\(380\) 0 0
\(381\) 18.0699 0.925750
\(382\) −8.11185 −0.415038
\(383\) 17.1311 0.875356 0.437678 0.899132i \(-0.355801\pi\)
0.437678 + 0.899132i \(0.355801\pi\)
\(384\) 19.4995 0.995077
\(385\) 0 0
\(386\) −3.73289 −0.189999
\(387\) 23.2690 1.18283
\(388\) −10.9460 −0.555696
\(389\) 18.4370 0.934794 0.467397 0.884048i \(-0.345192\pi\)
0.467397 + 0.884048i \(0.345192\pi\)
\(390\) 0 0
\(391\) 15.4084 0.779237
\(392\) −18.2428 −0.921399
\(393\) −10.6595 −0.537701
\(394\) −10.2286 −0.515308
\(395\) 0 0
\(396\) 0.356189 0.0178992
\(397\) 3.44622 0.172961 0.0864805 0.996254i \(-0.472438\pi\)
0.0864805 + 0.996254i \(0.472438\pi\)
\(398\) 16.3994 0.822030
\(399\) 0 0
\(400\) 0 0
\(401\) −12.4272 −0.620585 −0.310293 0.950641i \(-0.600427\pi\)
−0.310293 + 0.950641i \(0.600427\pi\)
\(402\) −20.3361 −1.01427
\(403\) 28.8701 1.43812
\(404\) 15.5812 0.775196
\(405\) 0 0
\(406\) −4.28145 −0.212485
\(407\) 0.298470 0.0147946
\(408\) 24.2087 1.19851
\(409\) −2.53190 −0.125194 −0.0625972 0.998039i \(-0.519938\pi\)
−0.0625972 + 0.998039i \(0.519938\pi\)
\(410\) 0 0
\(411\) −2.78141 −0.137197
\(412\) −25.8372 −1.27291
\(413\) 4.43702 0.218331
\(414\) −8.01038 −0.393689
\(415\) 0 0
\(416\) 39.9600 1.95920
\(417\) 18.7580 0.918583
\(418\) 0 0
\(419\) 0.647537 0.0316342 0.0158171 0.999875i \(-0.494965\pi\)
0.0158171 + 0.999875i \(0.494965\pi\)
\(420\) 0 0
\(421\) −4.37148 −0.213053 −0.106526 0.994310i \(-0.533973\pi\)
−0.106526 + 0.994310i \(0.533973\pi\)
\(422\) −13.7886 −0.671217
\(423\) −5.13728 −0.249783
\(424\) 15.6776 0.761372
\(425\) 0 0
\(426\) 12.6759 0.614149
\(427\) 3.12638 0.151296
\(428\) 21.9847 1.06267
\(429\) 1.78141 0.0860071
\(430\) 0 0
\(431\) −30.0094 −1.44550 −0.722752 0.691107i \(-0.757123\pi\)
−0.722752 + 0.691107i \(0.757123\pi\)
\(432\) −0.565306 −0.0271983
\(433\) 17.6077 0.846173 0.423086 0.906089i \(-0.360947\pi\)
0.423086 + 0.906089i \(0.360947\pi\)
\(434\) 1.93047 0.0926658
\(435\) 0 0
\(436\) −18.6587 −0.893591
\(437\) 0 0
\(438\) −16.1458 −0.771474
\(439\) −25.8827 −1.23532 −0.617658 0.786447i \(-0.711918\pi\)
−0.617658 + 0.786447i \(0.711918\pi\)
\(440\) 0 0
\(441\) −16.1485 −0.768975
\(442\) 21.5431 1.02470
\(443\) −11.8766 −0.564273 −0.282136 0.959374i \(-0.591043\pi\)
−0.282136 + 0.959374i \(0.591043\pi\)
\(444\) 8.29819 0.393815
\(445\) 0 0
\(446\) −1.54733 −0.0732681
\(447\) 23.0275 1.08917
\(448\) 2.20488 0.104171
\(449\) −29.4524 −1.38995 −0.694973 0.719035i \(-0.744584\pi\)
−0.694973 + 0.719035i \(0.744584\pi\)
\(450\) 0 0
\(451\) 1.12189 0.0528278
\(452\) 11.7981 0.554934
\(453\) −48.2689 −2.26787
\(454\) −8.78031 −0.412080
\(455\) 0 0
\(456\) 0 0
\(457\) −24.3329 −1.13825 −0.569123 0.822253i \(-0.692717\pi\)
−0.569123 + 0.822253i \(0.692717\pi\)
\(458\) −6.84406 −0.319802
\(459\) −5.18197 −0.241874
\(460\) 0 0
\(461\) 34.5042 1.60702 0.803511 0.595290i \(-0.202963\pi\)
0.803511 + 0.595290i \(0.202963\pi\)
\(462\) 0.119118 0.00554188
\(463\) 4.89328 0.227410 0.113705 0.993515i \(-0.463728\pi\)
0.113705 + 0.993515i \(0.463728\pi\)
\(464\) 3.86395 0.179379
\(465\) 0 0
\(466\) −1.75891 −0.0814798
\(467\) −15.6840 −0.725769 −0.362885 0.931834i \(-0.618208\pi\)
−0.362885 + 0.931834i \(0.618208\pi\)
\(468\) 22.0925 1.02123
\(469\) 5.98421 0.276325
\(470\) 0 0
\(471\) 30.0421 1.38427
\(472\) 21.5575 0.992262
\(473\) −1.07003 −0.0492000
\(474\) 11.9703 0.549815
\(475\) 0 0
\(476\) −2.84162 −0.130245
\(477\) 13.8778 0.635421
\(478\) −20.5716 −0.940921
\(479\) 15.1666 0.692981 0.346490 0.938054i \(-0.387373\pi\)
0.346490 + 0.938054i \(0.387373\pi\)
\(480\) 0 0
\(481\) 18.5125 0.844098
\(482\) −9.31208 −0.424153
\(483\) 5.28436 0.240447
\(484\) 14.5827 0.662851
\(485\) 0 0
\(486\) 16.5285 0.749746
\(487\) 14.8366 0.672312 0.336156 0.941806i \(-0.390873\pi\)
0.336156 + 0.941806i \(0.390873\pi\)
\(488\) 15.1896 0.687603
\(489\) 18.4577 0.834688
\(490\) 0 0
\(491\) 21.7022 0.979408 0.489704 0.871889i \(-0.337105\pi\)
0.489704 + 0.871889i \(0.337105\pi\)
\(492\) 31.1913 1.40621
\(493\) 35.4195 1.59521
\(494\) 0 0
\(495\) 0 0
\(496\) −1.74223 −0.0782283
\(497\) −3.73008 −0.167317
\(498\) −15.5790 −0.698110
\(499\) −20.5764 −0.921124 −0.460562 0.887627i \(-0.652352\pi\)
−0.460562 + 0.887627i \(0.652352\pi\)
\(500\) 0 0
\(501\) −13.2448 −0.591734
\(502\) 5.67813 0.253427
\(503\) 34.8559 1.55415 0.777074 0.629409i \(-0.216703\pi\)
0.777074 + 0.629409i \(0.216703\pi\)
\(504\) 3.70344 0.164964
\(505\) 0 0
\(506\) 0.368359 0.0163756
\(507\) 80.2376 3.56348
\(508\) −10.3052 −0.457221
\(509\) 30.7078 1.36110 0.680551 0.732701i \(-0.261741\pi\)
0.680551 + 0.732701i \(0.261741\pi\)
\(510\) 0 0
\(511\) 4.75114 0.210178
\(512\) −4.68111 −0.206878
\(513\) 0 0
\(514\) 1.55619 0.0686404
\(515\) 0 0
\(516\) −29.7494 −1.30964
\(517\) 0.236239 0.0103898
\(518\) 1.23789 0.0543897
\(519\) 16.5706 0.727369
\(520\) 0 0
\(521\) 10.9533 0.479874 0.239937 0.970788i \(-0.422873\pi\)
0.239937 + 0.970788i \(0.422873\pi\)
\(522\) −18.4135 −0.805939
\(523\) −4.44485 −0.194360 −0.0971799 0.995267i \(-0.530982\pi\)
−0.0971799 + 0.995267i \(0.530982\pi\)
\(524\) 6.07909 0.265566
\(525\) 0 0
\(526\) −9.46941 −0.412886
\(527\) −15.9704 −0.695682
\(528\) −0.107503 −0.00467845
\(529\) −6.65873 −0.289510
\(530\) 0 0
\(531\) 19.0826 0.828115
\(532\) 0 0
\(533\) 69.5849 3.01406
\(534\) −2.22844 −0.0964341
\(535\) 0 0
\(536\) 29.0746 1.25583
\(537\) −5.53050 −0.238659
\(538\) 2.47761 0.106817
\(539\) 0.742592 0.0319857
\(540\) 0 0
\(541\) 6.38522 0.274522 0.137261 0.990535i \(-0.456170\pi\)
0.137261 + 0.990535i \(0.456170\pi\)
\(542\) −7.22762 −0.310453
\(543\) 46.9548 2.01502
\(544\) −22.1051 −0.947749
\(545\) 0 0
\(546\) 7.38827 0.316189
\(547\) 10.6627 0.455904 0.227952 0.973672i \(-0.426797\pi\)
0.227952 + 0.973672i \(0.426797\pi\)
\(548\) 1.58623 0.0677603
\(549\) 13.4459 0.573855
\(550\) 0 0
\(551\) 0 0
\(552\) 25.6743 1.09277
\(553\) −3.52245 −0.149790
\(554\) −7.94755 −0.337659
\(555\) 0 0
\(556\) −10.6976 −0.453681
\(557\) 3.06585 0.129904 0.0649521 0.997888i \(-0.479311\pi\)
0.0649521 + 0.997888i \(0.479311\pi\)
\(558\) 8.30254 0.351475
\(559\) −66.3683 −2.80708
\(560\) 0 0
\(561\) −0.985440 −0.0416053
\(562\) 15.3191 0.646198
\(563\) −35.1561 −1.48165 −0.740827 0.671696i \(-0.765566\pi\)
−0.740827 + 0.671696i \(0.765566\pi\)
\(564\) 6.56802 0.276564
\(565\) 0 0
\(566\) −6.12276 −0.257359
\(567\) −5.84819 −0.245601
\(568\) −18.1228 −0.760414
\(569\) 42.2302 1.77038 0.885190 0.465229i \(-0.154028\pi\)
0.885190 + 0.465229i \(0.154028\pi\)
\(570\) 0 0
\(571\) −24.3462 −1.01886 −0.509429 0.860513i \(-0.670143\pi\)
−0.509429 + 0.860513i \(0.670143\pi\)
\(572\) −1.01593 −0.0424782
\(573\) 23.0148 0.961455
\(574\) 4.65298 0.194211
\(575\) 0 0
\(576\) 9.48271 0.395113
\(577\) 9.74424 0.405658 0.202829 0.979214i \(-0.434986\pi\)
0.202829 + 0.979214i \(0.434986\pi\)
\(578\) 2.02699 0.0843115
\(579\) 10.5909 0.440141
\(580\) 0 0
\(581\) 4.58435 0.190191
\(582\) −15.7434 −0.652584
\(583\) −0.638174 −0.0264305
\(584\) 23.0836 0.955208
\(585\) 0 0
\(586\) −3.06585 −0.126649
\(587\) −15.9708 −0.659186 −0.329593 0.944123i \(-0.606911\pi\)
−0.329593 + 0.944123i \(0.606911\pi\)
\(588\) 20.6459 0.851421
\(589\) 0 0
\(590\) 0 0
\(591\) 29.0203 1.19373
\(592\) −1.11718 −0.0459157
\(593\) 0.404153 0.0165966 0.00829829 0.999966i \(-0.497359\pi\)
0.00829829 + 0.999966i \(0.497359\pi\)
\(594\) −0.123882 −0.00508294
\(595\) 0 0
\(596\) −13.1325 −0.537930
\(597\) −46.5281 −1.90427
\(598\) 22.8474 0.934299
\(599\) −17.0426 −0.696342 −0.348171 0.937431i \(-0.613197\pi\)
−0.348171 + 0.937431i \(0.613197\pi\)
\(600\) 0 0
\(601\) 0.819125 0.0334128 0.0167064 0.999860i \(-0.494682\pi\)
0.0167064 + 0.999860i \(0.494682\pi\)
\(602\) −4.43788 −0.180875
\(603\) 25.7368 1.04808
\(604\) 27.5276 1.12008
\(605\) 0 0
\(606\) 22.4102 0.910353
\(607\) 18.2675 0.741455 0.370728 0.928742i \(-0.379108\pi\)
0.370728 + 0.928742i \(0.379108\pi\)
\(608\) 0 0
\(609\) 12.1472 0.492230
\(610\) 0 0
\(611\) 14.6527 0.592784
\(612\) −12.2212 −0.494012
\(613\) −27.6822 −1.11807 −0.559037 0.829142i \(-0.688829\pi\)
−0.559037 + 0.829142i \(0.688829\pi\)
\(614\) 19.0975 0.770712
\(615\) 0 0
\(616\) −0.170304 −0.00686173
\(617\) 40.1940 1.61815 0.809075 0.587706i \(-0.199969\pi\)
0.809075 + 0.587706i \(0.199969\pi\)
\(618\) −37.1612 −1.49484
\(619\) 46.3862 1.86442 0.932209 0.361920i \(-0.117879\pi\)
0.932209 + 0.361920i \(0.117879\pi\)
\(620\) 0 0
\(621\) −5.49569 −0.220535
\(622\) −19.2392 −0.771420
\(623\) 0.655753 0.0262722
\(624\) −6.66782 −0.266926
\(625\) 0 0
\(626\) −12.3102 −0.492015
\(627\) 0 0
\(628\) −17.1329 −0.683678
\(629\) −10.2408 −0.408327
\(630\) 0 0
\(631\) −47.5023 −1.89104 −0.945519 0.325568i \(-0.894444\pi\)
−0.945519 + 0.325568i \(0.894444\pi\)
\(632\) −17.1140 −0.680759
\(633\) 39.1206 1.55490
\(634\) −15.8308 −0.628722
\(635\) 0 0
\(636\) −17.7428 −0.703547
\(637\) 46.0590 1.82493
\(638\) 0.846752 0.0335232
\(639\) −16.0422 −0.634621
\(640\) 0 0
\(641\) −13.1626 −0.519891 −0.259946 0.965623i \(-0.583705\pi\)
−0.259946 + 0.965623i \(0.583705\pi\)
\(642\) 31.6202 1.24795
\(643\) 35.4538 1.39816 0.699081 0.715042i \(-0.253593\pi\)
0.699081 + 0.715042i \(0.253593\pi\)
\(644\) −3.01366 −0.118755
\(645\) 0 0
\(646\) 0 0
\(647\) −3.38283 −0.132993 −0.0664964 0.997787i \(-0.521182\pi\)
−0.0664964 + 0.997787i \(0.521182\pi\)
\(648\) −28.4137 −1.11619
\(649\) −0.877520 −0.0344457
\(650\) 0 0
\(651\) −5.47710 −0.214664
\(652\) −10.5264 −0.412246
\(653\) 0.621795 0.0243327 0.0121664 0.999926i \(-0.496127\pi\)
0.0121664 + 0.999926i \(0.496127\pi\)
\(654\) −26.8365 −1.04939
\(655\) 0 0
\(656\) −4.19925 −0.163953
\(657\) 20.4336 0.797191
\(658\) 0.979789 0.0381961
\(659\) −11.6203 −0.452664 −0.226332 0.974050i \(-0.572673\pi\)
−0.226332 + 0.974050i \(0.572673\pi\)
\(660\) 0 0
\(661\) −13.2897 −0.516911 −0.258456 0.966023i \(-0.583214\pi\)
−0.258456 + 0.966023i \(0.583214\pi\)
\(662\) −15.6916 −0.609871
\(663\) −61.1216 −2.37377
\(664\) 22.2733 0.864371
\(665\) 0 0
\(666\) 5.32388 0.206296
\(667\) 37.5638 1.45448
\(668\) 7.55347 0.292253
\(669\) 4.39004 0.169729
\(670\) 0 0
\(671\) −0.618311 −0.0238696
\(672\) −7.58101 −0.292444
\(673\) 23.9351 0.922630 0.461315 0.887236i \(-0.347378\pi\)
0.461315 + 0.887236i \(0.347378\pi\)
\(674\) 20.9246 0.805985
\(675\) 0 0
\(676\) −45.7593 −1.75997
\(677\) 3.71727 0.142866 0.0714331 0.997445i \(-0.477243\pi\)
0.0714331 + 0.997445i \(0.477243\pi\)
\(678\) 16.9690 0.651689
\(679\) 4.63273 0.177788
\(680\) 0 0
\(681\) 24.9113 0.954603
\(682\) −0.381795 −0.0146197
\(683\) 1.40634 0.0538120 0.0269060 0.999638i \(-0.491435\pi\)
0.0269060 + 0.999638i \(0.491435\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 6.30509 0.240729
\(687\) 19.4178 0.740836
\(688\) 4.00513 0.152694
\(689\) −39.5826 −1.50798
\(690\) 0 0
\(691\) 2.20762 0.0839820 0.0419910 0.999118i \(-0.486630\pi\)
0.0419910 + 0.999118i \(0.486630\pi\)
\(692\) −9.45018 −0.359242
\(693\) −0.150753 −0.00572662
\(694\) −28.2040 −1.07061
\(695\) 0 0
\(696\) 59.0178 2.23706
\(697\) −38.4931 −1.45803
\(698\) 23.4942 0.889270
\(699\) 4.99033 0.188751
\(700\) 0 0
\(701\) −3.95566 −0.149403 −0.0747016 0.997206i \(-0.523800\pi\)
−0.0747016 + 0.997206i \(0.523800\pi\)
\(702\) −7.68375 −0.290004
\(703\) 0 0
\(704\) −0.436065 −0.0164348
\(705\) 0 0
\(706\) 19.2925 0.726084
\(707\) −6.59456 −0.248014
\(708\) −24.3972 −0.916902
\(709\) −31.8658 −1.19674 −0.598372 0.801218i \(-0.704186\pi\)
−0.598372 + 0.801218i \(0.704186\pi\)
\(710\) 0 0
\(711\) −15.1493 −0.568143
\(712\) 3.18601 0.119401
\(713\) −16.9373 −0.634306
\(714\) −4.08705 −0.152954
\(715\) 0 0
\(716\) 3.15403 0.117872
\(717\) 58.3651 2.17969
\(718\) −8.01742 −0.299207
\(719\) −34.2360 −1.27679 −0.638393 0.769710i \(-0.720401\pi\)
−0.638393 + 0.769710i \(0.720401\pi\)
\(720\) 0 0
\(721\) 10.9353 0.407251
\(722\) 0 0
\(723\) 26.4200 0.982570
\(724\) −26.7782 −0.995203
\(725\) 0 0
\(726\) 20.9741 0.778421
\(727\) 29.5181 1.09477 0.547383 0.836882i \(-0.315624\pi\)
0.547383 + 0.836882i \(0.315624\pi\)
\(728\) −10.5630 −0.391492
\(729\) −15.6603 −0.580011
\(730\) 0 0
\(731\) 36.7137 1.35790
\(732\) −17.1905 −0.635381
\(733\) −28.2212 −1.04237 −0.521187 0.853442i \(-0.674511\pi\)
−0.521187 + 0.853442i \(0.674511\pi\)
\(734\) −1.67213 −0.0617195
\(735\) 0 0
\(736\) −23.4434 −0.864135
\(737\) −1.18351 −0.0435952
\(738\) 20.0114 0.736630
\(739\) −24.0957 −0.886373 −0.443187 0.896429i \(-0.646152\pi\)
−0.443187 + 0.896429i \(0.646152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.64679 −0.0971667
\(743\) −12.9103 −0.473632 −0.236816 0.971554i \(-0.576104\pi\)
−0.236816 + 0.971554i \(0.576104\pi\)
\(744\) −26.6107 −0.975596
\(745\) 0 0
\(746\) −10.6315 −0.389247
\(747\) 19.7163 0.721381
\(748\) 0.561994 0.0205485
\(749\) −9.30473 −0.339987
\(750\) 0 0
\(751\) 37.7129 1.37616 0.688082 0.725633i \(-0.258453\pi\)
0.688082 + 0.725633i \(0.258453\pi\)
\(752\) −0.884246 −0.0322451
\(753\) −16.1099 −0.587076
\(754\) 52.5195 1.91265
\(755\) 0 0
\(756\) 1.01352 0.0368612
\(757\) 34.7933 1.26458 0.632292 0.774730i \(-0.282114\pi\)
0.632292 + 0.774730i \(0.282114\pi\)
\(758\) 5.60157 0.203458
\(759\) −1.04510 −0.0379347
\(760\) 0 0
\(761\) 4.00019 0.145007 0.0725034 0.997368i \(-0.476901\pi\)
0.0725034 + 0.997368i \(0.476901\pi\)
\(762\) −14.8218 −0.536939
\(763\) 7.89707 0.285893
\(764\) −13.1253 −0.474855
\(765\) 0 0
\(766\) −14.0517 −0.507710
\(767\) −54.4279 −1.96528
\(768\) −34.2641 −1.23640
\(769\) −9.59479 −0.345997 −0.172998 0.984922i \(-0.555346\pi\)
−0.172998 + 0.984922i \(0.555346\pi\)
\(770\) 0 0
\(771\) −4.41517 −0.159009
\(772\) −6.03994 −0.217382
\(773\) −2.23562 −0.0804096 −0.0402048 0.999191i \(-0.512801\pi\)
−0.0402048 + 0.999191i \(0.512801\pi\)
\(774\) −19.0864 −0.686045
\(775\) 0 0
\(776\) 22.5083 0.808003
\(777\) −3.51210 −0.125996
\(778\) −15.1230 −0.542184
\(779\) 0 0
\(780\) 0 0
\(781\) 0.737707 0.0263972
\(782\) −12.6387 −0.451960
\(783\) −12.6330 −0.451467
\(784\) −2.77953 −0.0992689
\(785\) 0 0
\(786\) 8.74346 0.311869
\(787\) −19.6480 −0.700376 −0.350188 0.936679i \(-0.613882\pi\)
−0.350188 + 0.936679i \(0.613882\pi\)
\(788\) −16.5502 −0.589576
\(789\) 26.8664 0.956469
\(790\) 0 0
\(791\) −4.99338 −0.177544
\(792\) −0.732438 −0.0260261
\(793\) −38.3506 −1.36187
\(794\) −2.82676 −0.100318
\(795\) 0 0
\(796\) 26.5349 0.940503
\(797\) 15.8851 0.562680 0.281340 0.959608i \(-0.409221\pi\)
0.281340 + 0.959608i \(0.409221\pi\)
\(798\) 0 0
\(799\) −8.10558 −0.286755
\(800\) 0 0
\(801\) 2.82025 0.0996486
\(802\) 10.1934 0.359942
\(803\) −0.939645 −0.0331593
\(804\) −32.9045 −1.16045
\(805\) 0 0
\(806\) −23.6807 −0.834117
\(807\) −7.02942 −0.247447
\(808\) −32.0400 −1.12716
\(809\) 9.82989 0.345600 0.172800 0.984957i \(-0.444718\pi\)
0.172800 + 0.984957i \(0.444718\pi\)
\(810\) 0 0
\(811\) 29.0667 1.02067 0.510335 0.859976i \(-0.329521\pi\)
0.510335 + 0.859976i \(0.329521\pi\)
\(812\) −6.92752 −0.243108
\(813\) 20.5060 0.719178
\(814\) −0.244820 −0.00858094
\(815\) 0 0
\(816\) 3.68851 0.129124
\(817\) 0 0
\(818\) 2.07679 0.0726133
\(819\) −9.35038 −0.326729
\(820\) 0 0
\(821\) 9.14446 0.319144 0.159572 0.987186i \(-0.448989\pi\)
0.159572 + 0.987186i \(0.448989\pi\)
\(822\) 2.28145 0.0795746
\(823\) −25.8030 −0.899436 −0.449718 0.893171i \(-0.648476\pi\)
−0.449718 + 0.893171i \(0.648476\pi\)
\(824\) 53.1295 1.85085
\(825\) 0 0
\(826\) −3.63946 −0.126633
\(827\) −4.28552 −0.149022 −0.0745110 0.997220i \(-0.523740\pi\)
−0.0745110 + 0.997220i \(0.523740\pi\)
\(828\) −12.9611 −0.450428
\(829\) 5.70557 0.198163 0.0990813 0.995079i \(-0.468410\pi\)
0.0990813 + 0.995079i \(0.468410\pi\)
\(830\) 0 0
\(831\) 22.5486 0.782202
\(832\) −27.0468 −0.937679
\(833\) −25.4790 −0.882795
\(834\) −15.3862 −0.532781
\(835\) 0 0
\(836\) 0 0
\(837\) 5.69614 0.196887
\(838\) −0.531142 −0.0183480
\(839\) −15.5188 −0.535769 −0.267884 0.963451i \(-0.586325\pi\)
−0.267884 + 0.963451i \(0.586325\pi\)
\(840\) 0 0
\(841\) 57.3484 1.97753
\(842\) 3.58570 0.123571
\(843\) −43.4630 −1.49695
\(844\) −22.3104 −0.767954
\(845\) 0 0
\(846\) 4.21385 0.144875
\(847\) −6.17195 −0.212071
\(848\) 2.38869 0.0820280
\(849\) 17.3713 0.596183
\(850\) 0 0
\(851\) −10.8608 −0.372303
\(852\) 20.5100 0.702662
\(853\) 49.8235 1.70592 0.852962 0.521972i \(-0.174804\pi\)
0.852962 + 0.521972i \(0.174804\pi\)
\(854\) −2.56441 −0.0877523
\(855\) 0 0
\(856\) −45.2074 −1.54516
\(857\) 43.1178 1.47288 0.736438 0.676505i \(-0.236506\pi\)
0.736438 + 0.676505i \(0.236506\pi\)
\(858\) −1.46120 −0.0498844
\(859\) 17.9279 0.611691 0.305845 0.952081i \(-0.401061\pi\)
0.305845 + 0.952081i \(0.401061\pi\)
\(860\) 0 0
\(861\) −13.2013 −0.449900
\(862\) 24.6152 0.838398
\(863\) −55.6045 −1.89280 −0.946399 0.322999i \(-0.895309\pi\)
−0.946399 + 0.322999i \(0.895309\pi\)
\(864\) 7.88419 0.268226
\(865\) 0 0
\(866\) −14.4427 −0.490784
\(867\) −5.75091 −0.195311
\(868\) 3.12357 0.106021
\(869\) 0.696644 0.0236320
\(870\) 0 0
\(871\) −73.4069 −2.48730
\(872\) 38.3683 1.29931
\(873\) 19.9244 0.674337
\(874\) 0 0
\(875\) 0 0
\(876\) −26.1244 −0.882661
\(877\) −12.1639 −0.410744 −0.205372 0.978684i \(-0.565840\pi\)
−0.205372 + 0.978684i \(0.565840\pi\)
\(878\) 21.2303 0.716488
\(879\) 8.69836 0.293388
\(880\) 0 0
\(881\) 28.8330 0.971408 0.485704 0.874123i \(-0.338563\pi\)
0.485704 + 0.874123i \(0.338563\pi\)
\(882\) 13.2458 0.446009
\(883\) 0.648525 0.0218246 0.0109123 0.999940i \(-0.496526\pi\)
0.0109123 + 0.999940i \(0.496526\pi\)
\(884\) 34.8575 1.17238
\(885\) 0 0
\(886\) 9.74174 0.327280
\(887\) −45.2362 −1.51888 −0.759441 0.650577i \(-0.774527\pi\)
−0.759441 + 0.650577i \(0.774527\pi\)
\(888\) −17.0637 −0.572621
\(889\) 4.36156 0.146282
\(890\) 0 0
\(891\) 1.15661 0.0387479
\(892\) −2.50363 −0.0838277
\(893\) 0 0
\(894\) −18.8883 −0.631720
\(895\) 0 0
\(896\) 4.70661 0.157237
\(897\) −64.8220 −2.16434
\(898\) 24.1583 0.806174
\(899\) −38.9339 −1.29852
\(900\) 0 0
\(901\) 21.8963 0.729472
\(902\) −0.920230 −0.0306403
\(903\) 12.5911 0.419004
\(904\) −24.2606 −0.806894
\(905\) 0 0
\(906\) 39.5925 1.31537
\(907\) 15.1528 0.503142 0.251571 0.967839i \(-0.419053\pi\)
0.251571 + 0.967839i \(0.419053\pi\)
\(908\) −14.2068 −0.471471
\(909\) −28.3617 −0.940699
\(910\) 0 0
\(911\) 31.7373 1.05150 0.525752 0.850638i \(-0.323784\pi\)
0.525752 + 0.850638i \(0.323784\pi\)
\(912\) 0 0
\(913\) −0.906658 −0.0300060
\(914\) 19.9591 0.660187
\(915\) 0 0
\(916\) −11.0739 −0.365893
\(917\) −2.57290 −0.0849646
\(918\) 4.25051 0.140288
\(919\) 5.31327 0.175269 0.0876343 0.996153i \(-0.472069\pi\)
0.0876343 + 0.996153i \(0.472069\pi\)
\(920\) 0 0
\(921\) −54.1829 −1.78539
\(922\) −28.3021 −0.932079
\(923\) 45.7560 1.50608
\(924\) 0.192737 0.00634059
\(925\) 0 0
\(926\) −4.01371 −0.131899
\(927\) 47.0302 1.54467
\(928\) −53.8896 −1.76901
\(929\) −3.54458 −0.116294 −0.0581469 0.998308i \(-0.518519\pi\)
−0.0581469 + 0.998308i \(0.518519\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −2.84597 −0.0932228
\(933\) 54.5849 1.78703
\(934\) 12.8648 0.420949
\(935\) 0 0
\(936\) −45.4292 −1.48490
\(937\) −31.2800 −1.02187 −0.510936 0.859619i \(-0.670701\pi\)
−0.510936 + 0.859619i \(0.670701\pi\)
\(938\) −4.90854 −0.160270
\(939\) 34.9263 1.13978
\(940\) 0 0
\(941\) 45.5106 1.48360 0.741802 0.670619i \(-0.233971\pi\)
0.741802 + 0.670619i \(0.233971\pi\)
\(942\) −24.6420 −0.802879
\(943\) −40.8235 −1.32940
\(944\) 3.28457 0.106903
\(945\) 0 0
\(946\) 0.877691 0.0285362
\(947\) 21.0071 0.682640 0.341320 0.939947i \(-0.389126\pi\)
0.341320 + 0.939947i \(0.389126\pi\)
\(948\) 19.3684 0.629056
\(949\) −58.2812 −1.89189
\(950\) 0 0
\(951\) 44.9148 1.45646
\(952\) 5.84327 0.189382
\(953\) 32.6629 1.05806 0.529028 0.848604i \(-0.322557\pi\)
0.529028 + 0.848604i \(0.322557\pi\)
\(954\) −11.3833 −0.368546
\(955\) 0 0
\(956\) −33.2855 −1.07653
\(957\) −2.40238 −0.0776580
\(958\) −12.4404 −0.401932
\(959\) −0.671351 −0.0216791
\(960\) 0 0
\(961\) −13.4450 −0.433708
\(962\) −15.1849 −0.489580
\(963\) −40.0176 −1.28955
\(964\) −15.0673 −0.485284
\(965\) 0 0
\(966\) −4.33449 −0.139460
\(967\) 21.8080 0.701299 0.350650 0.936507i \(-0.385961\pi\)
0.350650 + 0.936507i \(0.385961\pi\)
\(968\) −29.9867 −0.963809
\(969\) 0 0
\(970\) 0 0
\(971\) 55.8370 1.79189 0.895947 0.444162i \(-0.146498\pi\)
0.895947 + 0.444162i \(0.146498\pi\)
\(972\) 26.7436 0.857801
\(973\) 4.52764 0.145149
\(974\) −12.1697 −0.389943
\(975\) 0 0
\(976\) 2.31435 0.0740804
\(977\) −0.543879 −0.0174002 −0.00870012 0.999962i \(-0.502769\pi\)
−0.00870012 + 0.999962i \(0.502769\pi\)
\(978\) −15.1400 −0.484122
\(979\) −0.129690 −0.00414491
\(980\) 0 0
\(981\) 33.9635 1.08437
\(982\) −17.8012 −0.568060
\(983\) −11.0176 −0.351407 −0.175704 0.984443i \(-0.556220\pi\)
−0.175704 + 0.984443i \(0.556220\pi\)
\(984\) −64.1392 −2.04468
\(985\) 0 0
\(986\) −29.0528 −0.925230
\(987\) −2.77983 −0.0884830
\(988\) 0 0
\(989\) 38.9364 1.23811
\(990\) 0 0
\(991\) 28.1970 0.895707 0.447854 0.894107i \(-0.352189\pi\)
0.447854 + 0.894107i \(0.352189\pi\)
\(992\) 24.2984 0.771477
\(993\) 44.5198 1.41279
\(994\) 3.05959 0.0970445
\(995\) 0 0
\(996\) −25.2073 −0.798724
\(997\) 30.5688 0.968123 0.484062 0.875034i \(-0.339161\pi\)
0.484062 + 0.875034i \(0.339161\pi\)
\(998\) 16.8777 0.534256
\(999\) 3.65256 0.115562
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 9025.2.a.bo.1.2 4
5.4 even 2 1805.2.a.j.1.3 4
19.18 odd 2 9025.2.a.bh.1.3 4
95.94 odd 2 1805.2.a.n.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.j.1.3 4 5.4 even 2
1805.2.a.n.1.2 yes 4 95.94 odd 2
9025.2.a.bh.1.3 4 19.18 odd 2
9025.2.a.bo.1.2 4 1.1 even 1 trivial