Properties

Label 6013.2.a.e.1.2
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.68013 q^{2}\) \(-1.39322 q^{3}\) \(+5.18311 q^{4}\) \(-1.95866 q^{5}\) \(+3.73403 q^{6}\) \(+1.00000 q^{7}\) \(-8.53117 q^{8}\) \(-1.05892 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.68013 q^{2}\) \(-1.39322 q^{3}\) \(+5.18311 q^{4}\) \(-1.95866 q^{5}\) \(+3.73403 q^{6}\) \(+1.00000 q^{7}\) \(-8.53117 q^{8}\) \(-1.05892 q^{9}\) \(+5.24948 q^{10}\) \(+3.16031 q^{11}\) \(-7.22124 q^{12}\) \(-4.40301 q^{13}\) \(-2.68013 q^{14}\) \(+2.72886 q^{15}\) \(+12.4984 q^{16}\) \(+6.08653 q^{17}\) \(+2.83806 q^{18}\) \(-1.39963 q^{19}\) \(-10.1520 q^{20}\) \(-1.39322 q^{21}\) \(-8.47005 q^{22}\) \(-2.84554 q^{23}\) \(+11.8858 q^{24}\) \(-1.16363 q^{25}\) \(+11.8007 q^{26}\) \(+5.65499 q^{27}\) \(+5.18311 q^{28}\) \(-1.07171 q^{29}\) \(-7.31371 q^{30}\) \(-5.79804 q^{31}\) \(-16.4352 q^{32}\) \(-4.40302 q^{33}\) \(-16.3127 q^{34}\) \(-1.95866 q^{35}\) \(-5.48853 q^{36}\) \(+9.61262 q^{37}\) \(+3.75120 q^{38}\) \(+6.13439 q^{39}\) \(+16.7097 q^{40}\) \(-5.96335 q^{41}\) \(+3.73403 q^{42}\) \(+2.29228 q^{43}\) \(+16.3802 q^{44}\) \(+2.07408 q^{45}\) \(+7.62642 q^{46}\) \(+8.07149 q^{47}\) \(-17.4131 q^{48}\) \(+1.00000 q^{49}\) \(+3.11869 q^{50}\) \(-8.47991 q^{51}\) \(-22.8213 q^{52}\) \(+2.14724 q^{53}\) \(-15.1561 q^{54}\) \(-6.18999 q^{55}\) \(-8.53117 q^{56}\) \(+1.95000 q^{57}\) \(+2.87234 q^{58}\) \(+11.7345 q^{59}\) \(+14.1440 q^{60}\) \(-15.5384 q^{61}\) \(+15.5395 q^{62}\) \(-1.05892 q^{63}\) \(+19.0515 q^{64}\) \(+8.62403 q^{65}\) \(+11.8007 q^{66}\) \(-1.96948 q^{67}\) \(+31.5472 q^{68}\) \(+3.96447 q^{69}\) \(+5.24948 q^{70}\) \(-7.48822 q^{71}\) \(+9.03387 q^{72}\) \(-10.2051 q^{73}\) \(-25.7631 q^{74}\) \(+1.62120 q^{75}\) \(-7.25446 q^{76}\) \(+3.16031 q^{77}\) \(-16.4410 q^{78}\) \(-7.65424 q^{79}\) \(-24.4803 q^{80}\) \(-4.70191 q^{81}\) \(+15.9826 q^{82}\) \(-10.5248 q^{83}\) \(-7.22124 q^{84}\) \(-11.9215 q^{85}\) \(-6.14361 q^{86}\) \(+1.49314 q^{87}\) \(-26.9611 q^{88}\) \(+16.6674 q^{89}\) \(-5.55881 q^{90}\) \(-4.40301 q^{91}\) \(-14.7487 q^{92}\) \(+8.07798 q^{93}\) \(-21.6327 q^{94}\) \(+2.74141 q^{95}\) \(+22.8979 q^{96}\) \(+0.202424 q^{97}\) \(-2.68013 q^{98}\) \(-3.34653 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68013 −1.89514 −0.947570 0.319548i \(-0.896469\pi\)
−0.947570 + 0.319548i \(0.896469\pi\)
\(3\) −1.39322 −0.804379 −0.402189 0.915556i \(-0.631751\pi\)
−0.402189 + 0.915556i \(0.631751\pi\)
\(4\) 5.18311 2.59156
\(5\) −1.95866 −0.875942 −0.437971 0.898989i \(-0.644303\pi\)
−0.437971 + 0.898989i \(0.644303\pi\)
\(6\) 3.73403 1.52441
\(7\) 1.00000 0.377964
\(8\) −8.53117 −3.01622
\(9\) −1.05892 −0.352975
\(10\) 5.24948 1.66003
\(11\) 3.16031 0.952869 0.476435 0.879210i \(-0.341929\pi\)
0.476435 + 0.879210i \(0.341929\pi\)
\(12\) −7.22124 −2.08459
\(13\) −4.40301 −1.22118 −0.610588 0.791948i \(-0.709067\pi\)
−0.610588 + 0.791948i \(0.709067\pi\)
\(14\) −2.68013 −0.716296
\(15\) 2.72886 0.704589
\(16\) 12.4984 3.12461
\(17\) 6.08653 1.47620 0.738101 0.674691i \(-0.235723\pi\)
0.738101 + 0.674691i \(0.235723\pi\)
\(18\) 2.83806 0.668937
\(19\) −1.39963 −0.321098 −0.160549 0.987028i \(-0.551326\pi\)
−0.160549 + 0.987028i \(0.551326\pi\)
\(20\) −10.1520 −2.27005
\(21\) −1.39322 −0.304027
\(22\) −8.47005 −1.80582
\(23\) −2.84554 −0.593335 −0.296668 0.954981i \(-0.595875\pi\)
−0.296668 + 0.954981i \(0.595875\pi\)
\(24\) 11.8858 2.42619
\(25\) −1.16363 −0.232726
\(26\) 11.8007 2.31430
\(27\) 5.65499 1.08830
\(28\) 5.18311 0.979517
\(29\) −1.07171 −0.199012 −0.0995061 0.995037i \(-0.531726\pi\)
−0.0995061 + 0.995037i \(0.531726\pi\)
\(30\) −7.31371 −1.33529
\(31\) −5.79804 −1.04136 −0.520680 0.853752i \(-0.674321\pi\)
−0.520680 + 0.853752i \(0.674321\pi\)
\(32\) −16.4352 −2.90535
\(33\) −4.40302 −0.766468
\(34\) −16.3127 −2.79761
\(35\) −1.95866 −0.331075
\(36\) −5.48853 −0.914754
\(37\) 9.61262 1.58031 0.790153 0.612910i \(-0.210001\pi\)
0.790153 + 0.612910i \(0.210001\pi\)
\(38\) 3.75120 0.608525
\(39\) 6.13439 0.982288
\(40\) 16.7097 2.64204
\(41\) −5.96335 −0.931318 −0.465659 0.884964i \(-0.654183\pi\)
−0.465659 + 0.884964i \(0.654183\pi\)
\(42\) 3.73403 0.576173
\(43\) 2.29228 0.349569 0.174784 0.984607i \(-0.444077\pi\)
0.174784 + 0.984607i \(0.444077\pi\)
\(44\) 16.3802 2.46941
\(45\) 2.07408 0.309185
\(46\) 7.62642 1.12445
\(47\) 8.07149 1.17735 0.588674 0.808371i \(-0.299650\pi\)
0.588674 + 0.808371i \(0.299650\pi\)
\(48\) −17.4131 −2.51337
\(49\) 1.00000 0.142857
\(50\) 3.11869 0.441049
\(51\) −8.47991 −1.18742
\(52\) −22.8213 −3.16475
\(53\) 2.14724 0.294946 0.147473 0.989066i \(-0.452886\pi\)
0.147473 + 0.989066i \(0.452886\pi\)
\(54\) −15.1561 −2.06249
\(55\) −6.18999 −0.834658
\(56\) −8.53117 −1.14003
\(57\) 1.95000 0.258284
\(58\) 2.87234 0.377156
\(59\) 11.7345 1.52770 0.763851 0.645392i \(-0.223306\pi\)
0.763851 + 0.645392i \(0.223306\pi\)
\(60\) 14.1440 1.82598
\(61\) −15.5384 −1.98949 −0.994746 0.102372i \(-0.967357\pi\)
−0.994746 + 0.102372i \(0.967357\pi\)
\(62\) 15.5395 1.97352
\(63\) −1.05892 −0.133412
\(64\) 19.0515 2.38144
\(65\) 8.62403 1.06968
\(66\) 11.8007 1.45256
\(67\) −1.96948 −0.240610 −0.120305 0.992737i \(-0.538387\pi\)
−0.120305 + 0.992737i \(0.538387\pi\)
\(68\) 31.5472 3.82566
\(69\) 3.96447 0.477266
\(70\) 5.24948 0.627433
\(71\) −7.48822 −0.888688 −0.444344 0.895856i \(-0.646563\pi\)
−0.444344 + 0.895856i \(0.646563\pi\)
\(72\) 9.03387 1.06465
\(73\) −10.2051 −1.19442 −0.597211 0.802084i \(-0.703724\pi\)
−0.597211 + 0.802084i \(0.703724\pi\)
\(74\) −25.7631 −2.99490
\(75\) 1.62120 0.187200
\(76\) −7.25446 −0.832143
\(77\) 3.16031 0.360151
\(78\) −16.4410 −1.86157
\(79\) −7.65424 −0.861170 −0.430585 0.902550i \(-0.641693\pi\)
−0.430585 + 0.902550i \(0.641693\pi\)
\(80\) −24.4803 −2.73698
\(81\) −4.70191 −0.522434
\(82\) 15.9826 1.76498
\(83\) −10.5248 −1.15524 −0.577621 0.816305i \(-0.696019\pi\)
−0.577621 + 0.816305i \(0.696019\pi\)
\(84\) −7.22124 −0.787902
\(85\) −11.9215 −1.29307
\(86\) −6.14361 −0.662482
\(87\) 1.49314 0.160081
\(88\) −26.9611 −2.87407
\(89\) 16.6674 1.76674 0.883370 0.468676i \(-0.155269\pi\)
0.883370 + 0.468676i \(0.155269\pi\)
\(90\) −5.55881 −0.585950
\(91\) −4.40301 −0.461561
\(92\) −14.7487 −1.53766
\(93\) 8.07798 0.837647
\(94\) −21.6327 −2.23124
\(95\) 2.74141 0.281263
\(96\) 22.8979 2.33700
\(97\) 0.202424 0.0205530 0.0102765 0.999947i \(-0.496729\pi\)
0.0102765 + 0.999947i \(0.496729\pi\)
\(98\) −2.68013 −0.270734
\(99\) −3.34653 −0.336339
\(100\) −6.03124 −0.603124
\(101\) 18.3111 1.82202 0.911010 0.412385i \(-0.135304\pi\)
0.911010 + 0.412385i \(0.135304\pi\)
\(102\) 22.7273 2.25034
\(103\) 17.8337 1.75721 0.878605 0.477550i \(-0.158475\pi\)
0.878605 + 0.477550i \(0.158475\pi\)
\(104\) 37.5629 3.68334
\(105\) 2.72886 0.266310
\(106\) −5.75489 −0.558964
\(107\) −7.12014 −0.688330 −0.344165 0.938909i \(-0.611838\pi\)
−0.344165 + 0.938909i \(0.611838\pi\)
\(108\) 29.3105 2.82040
\(109\) −13.6740 −1.30973 −0.654866 0.755745i \(-0.727275\pi\)
−0.654866 + 0.755745i \(0.727275\pi\)
\(110\) 16.5900 1.58179
\(111\) −13.3925 −1.27116
\(112\) 12.4984 1.18099
\(113\) 8.52998 0.802433 0.401216 0.915983i \(-0.368588\pi\)
0.401216 + 0.915983i \(0.368588\pi\)
\(114\) −5.22627 −0.489485
\(115\) 5.57345 0.519727
\(116\) −5.55481 −0.515752
\(117\) 4.66246 0.431044
\(118\) −31.4500 −2.89521
\(119\) 6.08653 0.557952
\(120\) −23.2804 −2.12520
\(121\) −1.01245 −0.0920405
\(122\) 41.6451 3.77037
\(123\) 8.30828 0.749133
\(124\) −30.0519 −2.69874
\(125\) 12.0725 1.07980
\(126\) 2.83806 0.252834
\(127\) −18.3998 −1.63272 −0.816359 0.577544i \(-0.804011\pi\)
−0.816359 + 0.577544i \(0.804011\pi\)
\(128\) −18.1903 −1.60781
\(129\) −3.19366 −0.281186
\(130\) −23.1135 −2.02719
\(131\) −8.12854 −0.710194 −0.355097 0.934830i \(-0.615552\pi\)
−0.355097 + 0.934830i \(0.615552\pi\)
\(132\) −22.8214 −1.98634
\(133\) −1.39963 −0.121364
\(134\) 5.27846 0.455989
\(135\) −11.0762 −0.953291
\(136\) −51.9253 −4.45255
\(137\) 3.45778 0.295418 0.147709 0.989031i \(-0.452810\pi\)
0.147709 + 0.989031i \(0.452810\pi\)
\(138\) −10.6253 −0.904487
\(139\) 4.14045 0.351189 0.175594 0.984463i \(-0.443815\pi\)
0.175594 + 0.984463i \(0.443815\pi\)
\(140\) −10.1520 −0.857999
\(141\) −11.2454 −0.947034
\(142\) 20.0694 1.68419
\(143\) −13.9149 −1.16362
\(144\) −13.2349 −1.10291
\(145\) 2.09913 0.174323
\(146\) 27.3511 2.26360
\(147\) −1.39322 −0.114911
\(148\) 49.8233 4.09545
\(149\) −17.2808 −1.41570 −0.707851 0.706362i \(-0.750335\pi\)
−0.707851 + 0.706362i \(0.750335\pi\)
\(150\) −4.34503 −0.354771
\(151\) 11.9967 0.976281 0.488141 0.872765i \(-0.337675\pi\)
0.488141 + 0.872765i \(0.337675\pi\)
\(152\) 11.9405 0.968503
\(153\) −6.44518 −0.521062
\(154\) −8.47005 −0.682536
\(155\) 11.3564 0.912170
\(156\) 31.7952 2.54566
\(157\) −0.516006 −0.0411818 −0.0205909 0.999788i \(-0.506555\pi\)
−0.0205909 + 0.999788i \(0.506555\pi\)
\(158\) 20.5144 1.63204
\(159\) −2.99159 −0.237248
\(160\) 32.1910 2.54492
\(161\) −2.84554 −0.224260
\(162\) 12.6017 0.990086
\(163\) 3.92805 0.307669 0.153834 0.988097i \(-0.450838\pi\)
0.153834 + 0.988097i \(0.450838\pi\)
\(164\) −30.9087 −2.41357
\(165\) 8.62404 0.671381
\(166\) 28.2077 2.18935
\(167\) 18.5392 1.43461 0.717304 0.696760i \(-0.245376\pi\)
0.717304 + 0.696760i \(0.245376\pi\)
\(168\) 11.8858 0.917013
\(169\) 6.38652 0.491271
\(170\) 31.9512 2.45054
\(171\) 1.48211 0.113339
\(172\) 11.8811 0.905928
\(173\) 22.1698 1.68554 0.842769 0.538276i \(-0.180924\pi\)
0.842769 + 0.538276i \(0.180924\pi\)
\(174\) −4.00181 −0.303376
\(175\) −1.16363 −0.0879623
\(176\) 39.4990 2.97735
\(177\) −16.3488 −1.22885
\(178\) −44.6708 −3.34822
\(179\) −7.90161 −0.590594 −0.295297 0.955406i \(-0.595419\pi\)
−0.295297 + 0.955406i \(0.595419\pi\)
\(180\) 10.7502 0.801271
\(181\) 12.7349 0.946575 0.473287 0.880908i \(-0.343067\pi\)
0.473287 + 0.880908i \(0.343067\pi\)
\(182\) 11.8007 0.874723
\(183\) 21.6485 1.60031
\(184\) 24.2758 1.78963
\(185\) −18.8279 −1.38425
\(186\) −21.6501 −1.58746
\(187\) 19.2353 1.40663
\(188\) 41.8355 3.05116
\(189\) 5.65499 0.411340
\(190\) −7.34735 −0.533033
\(191\) −5.20944 −0.376942 −0.188471 0.982079i \(-0.560353\pi\)
−0.188471 + 0.982079i \(0.560353\pi\)
\(192\) −26.5431 −1.91558
\(193\) −1.62417 −0.116911 −0.0584553 0.998290i \(-0.518618\pi\)
−0.0584553 + 0.998290i \(0.518618\pi\)
\(194\) −0.542523 −0.0389508
\(195\) −12.0152 −0.860427
\(196\) 5.18311 0.370222
\(197\) −21.1488 −1.50679 −0.753395 0.657568i \(-0.771585\pi\)
−0.753395 + 0.657568i \(0.771585\pi\)
\(198\) 8.96914 0.637409
\(199\) −15.5558 −1.10272 −0.551359 0.834268i \(-0.685891\pi\)
−0.551359 + 0.834268i \(0.685891\pi\)
\(200\) 9.92714 0.701955
\(201\) 2.74392 0.193541
\(202\) −49.0761 −3.45298
\(203\) −1.07171 −0.0752196
\(204\) −43.9523 −3.07728
\(205\) 11.6802 0.815781
\(206\) −47.7968 −3.33016
\(207\) 3.01321 0.209432
\(208\) −55.0308 −3.81570
\(209\) −4.42327 −0.305964
\(210\) −7.31371 −0.504694
\(211\) −10.3364 −0.711589 −0.355794 0.934564i \(-0.615790\pi\)
−0.355794 + 0.934564i \(0.615790\pi\)
\(212\) 11.1294 0.764369
\(213\) 10.4328 0.714842
\(214\) 19.0829 1.30448
\(215\) −4.48980 −0.306202
\(216\) −48.2437 −3.28257
\(217\) −5.79804 −0.393597
\(218\) 36.6482 2.48213
\(219\) 14.2181 0.960768
\(220\) −32.0834 −2.16306
\(221\) −26.7991 −1.80270
\(222\) 35.8938 2.40903
\(223\) 7.16388 0.479729 0.239864 0.970806i \(-0.422897\pi\)
0.239864 + 0.970806i \(0.422897\pi\)
\(224\) −16.4352 −1.09812
\(225\) 1.23220 0.0821465
\(226\) −22.8615 −1.52072
\(227\) −22.2753 −1.47846 −0.739231 0.673452i \(-0.764811\pi\)
−0.739231 + 0.673452i \(0.764811\pi\)
\(228\) 10.1071 0.669358
\(229\) −4.56823 −0.301877 −0.150939 0.988543i \(-0.548230\pi\)
−0.150939 + 0.988543i \(0.548230\pi\)
\(230\) −14.9376 −0.984956
\(231\) −4.40302 −0.289698
\(232\) 9.14297 0.600266
\(233\) −11.2722 −0.738463 −0.369232 0.929337i \(-0.620379\pi\)
−0.369232 + 0.929337i \(0.620379\pi\)
\(234\) −12.4960 −0.816890
\(235\) −15.8093 −1.03129
\(236\) 60.8213 3.95913
\(237\) 10.6641 0.692707
\(238\) −16.3127 −1.05740
\(239\) −16.6779 −1.07880 −0.539401 0.842049i \(-0.681349\pi\)
−0.539401 + 0.842049i \(0.681349\pi\)
\(240\) 34.1065 2.20157
\(241\) −4.52246 −0.291317 −0.145659 0.989335i \(-0.546530\pi\)
−0.145659 + 0.989335i \(0.546530\pi\)
\(242\) 2.71349 0.174430
\(243\) −10.4142 −0.668069
\(244\) −80.5375 −5.15588
\(245\) −1.95866 −0.125135
\(246\) −22.2673 −1.41971
\(247\) 6.16260 0.392117
\(248\) 49.4641 3.14097
\(249\) 14.6634 0.929252
\(250\) −32.3559 −2.04637
\(251\) −18.8636 −1.19066 −0.595331 0.803481i \(-0.702979\pi\)
−0.595331 + 0.803481i \(0.702979\pi\)
\(252\) −5.48853 −0.345745
\(253\) −8.99277 −0.565371
\(254\) 49.3139 3.09423
\(255\) 16.6093 1.04011
\(256\) 10.6494 0.665589
\(257\) 9.22294 0.575311 0.287656 0.957734i \(-0.407124\pi\)
0.287656 + 0.957734i \(0.407124\pi\)
\(258\) 8.55943 0.532887
\(259\) 9.61262 0.597299
\(260\) 44.6993 2.77213
\(261\) 1.13486 0.0702463
\(262\) 21.7856 1.34592
\(263\) −11.1709 −0.688828 −0.344414 0.938818i \(-0.611922\pi\)
−0.344414 + 0.938818i \(0.611922\pi\)
\(264\) 37.5629 2.31184
\(265\) −4.20572 −0.258355
\(266\) 3.75120 0.230001
\(267\) −23.2214 −1.42113
\(268\) −10.2080 −0.623554
\(269\) 7.07315 0.431258 0.215629 0.976475i \(-0.430820\pi\)
0.215629 + 0.976475i \(0.430820\pi\)
\(270\) 29.6858 1.80662
\(271\) 0.126639 0.00769276 0.00384638 0.999993i \(-0.498776\pi\)
0.00384638 + 0.999993i \(0.498776\pi\)
\(272\) 76.0722 4.61256
\(273\) 6.13439 0.371270
\(274\) −9.26732 −0.559859
\(275\) −3.67744 −0.221758
\(276\) 20.5483 1.23686
\(277\) 9.54000 0.573203 0.286601 0.958050i \(-0.407474\pi\)
0.286601 + 0.958050i \(0.407474\pi\)
\(278\) −11.0970 −0.665552
\(279\) 6.13969 0.367573
\(280\) 16.7097 0.998596
\(281\) −4.88743 −0.291560 −0.145780 0.989317i \(-0.546569\pi\)
−0.145780 + 0.989317i \(0.546569\pi\)
\(282\) 30.1392 1.79476
\(283\) −16.0486 −0.953989 −0.476994 0.878906i \(-0.658274\pi\)
−0.476994 + 0.878906i \(0.658274\pi\)
\(284\) −38.8123 −2.30309
\(285\) −3.81940 −0.226242
\(286\) 37.2937 2.20523
\(287\) −5.96335 −0.352005
\(288\) 17.4036 1.02552
\(289\) 20.0459 1.17917
\(290\) −5.62594 −0.330367
\(291\) −0.282022 −0.0165324
\(292\) −52.8944 −3.09541
\(293\) −2.51941 −0.147185 −0.0735926 0.997288i \(-0.523446\pi\)
−0.0735926 + 0.997288i \(0.523446\pi\)
\(294\) 3.73403 0.217773
\(295\) −22.9840 −1.33818
\(296\) −82.0069 −4.76656
\(297\) 17.8715 1.03701
\(298\) 46.3149 2.68295
\(299\) 12.5289 0.724567
\(300\) 8.40287 0.485140
\(301\) 2.29228 0.132125
\(302\) −32.1529 −1.85019
\(303\) −25.5114 −1.46559
\(304\) −17.4932 −1.00331
\(305\) 30.4346 1.74268
\(306\) 17.2739 0.987485
\(307\) 10.5303 0.600997 0.300499 0.953782i \(-0.402847\pi\)
0.300499 + 0.953782i \(0.402847\pi\)
\(308\) 16.3802 0.933351
\(309\) −24.8464 −1.41346
\(310\) −30.4367 −1.72869
\(311\) −31.3907 −1.78000 −0.890001 0.455959i \(-0.849296\pi\)
−0.890001 + 0.455959i \(0.849296\pi\)
\(312\) −52.3335 −2.96280
\(313\) 25.3611 1.43349 0.716746 0.697335i \(-0.245631\pi\)
0.716746 + 0.697335i \(0.245631\pi\)
\(314\) 1.38297 0.0780453
\(315\) 2.07408 0.116861
\(316\) −39.6728 −2.23177
\(317\) 3.92501 0.220451 0.110225 0.993907i \(-0.464843\pi\)
0.110225 + 0.993907i \(0.464843\pi\)
\(318\) 8.01785 0.449619
\(319\) −3.38695 −0.189633
\(320\) −37.3156 −2.08600
\(321\) 9.91995 0.553678
\(322\) 7.62642 0.425004
\(323\) −8.51891 −0.474005
\(324\) −24.3705 −1.35392
\(325\) 5.12349 0.284200
\(326\) −10.5277 −0.583075
\(327\) 19.0510 1.05352
\(328\) 50.8743 2.80907
\(329\) 8.07149 0.444996
\(330\) −23.1136 −1.27236
\(331\) −12.7784 −0.702364 −0.351182 0.936307i \(-0.614220\pi\)
−0.351182 + 0.936307i \(0.614220\pi\)
\(332\) −54.5510 −2.99388
\(333\) −10.1790 −0.557808
\(334\) −49.6876 −2.71878
\(335\) 3.85754 0.210760
\(336\) −17.4131 −0.949965
\(337\) 27.1724 1.48017 0.740086 0.672512i \(-0.234785\pi\)
0.740086 + 0.672512i \(0.234785\pi\)
\(338\) −17.1167 −0.931028
\(339\) −11.8842 −0.645460
\(340\) −61.7904 −3.35105
\(341\) −18.3236 −0.992279
\(342\) −3.97224 −0.214794
\(343\) 1.00000 0.0539949
\(344\) −19.5558 −1.05438
\(345\) −7.76507 −0.418057
\(346\) −59.4180 −3.19433
\(347\) 33.6195 1.80479 0.902393 0.430913i \(-0.141808\pi\)
0.902393 + 0.430913i \(0.141808\pi\)
\(348\) 7.73911 0.414860
\(349\) 24.2099 1.29593 0.647964 0.761671i \(-0.275621\pi\)
0.647964 + 0.761671i \(0.275621\pi\)
\(350\) 3.11869 0.166701
\(351\) −24.8990 −1.32901
\(352\) −51.9402 −2.76842
\(353\) −32.4831 −1.72890 −0.864451 0.502717i \(-0.832334\pi\)
−0.864451 + 0.502717i \(0.832334\pi\)
\(354\) 43.8170 2.32885
\(355\) 14.6669 0.778439
\(356\) 86.3890 4.57861
\(357\) −8.47991 −0.448804
\(358\) 21.1774 1.11926
\(359\) −16.9757 −0.895942 −0.447971 0.894048i \(-0.647853\pi\)
−0.447971 + 0.894048i \(0.647853\pi\)
\(360\) −17.6943 −0.932572
\(361\) −17.0410 −0.896896
\(362\) −34.1311 −1.79389
\(363\) 1.41056 0.0740354
\(364\) −22.8213 −1.19616
\(365\) 19.9885 1.04624
\(366\) −58.0209 −3.03280
\(367\) 23.4115 1.22207 0.611035 0.791604i \(-0.290754\pi\)
0.611035 + 0.791604i \(0.290754\pi\)
\(368\) −35.5648 −1.85394
\(369\) 6.31473 0.328732
\(370\) 50.4613 2.62336
\(371\) 2.14724 0.111479
\(372\) 41.8691 2.17081
\(373\) −26.8145 −1.38840 −0.694200 0.719782i \(-0.744242\pi\)
−0.694200 + 0.719782i \(0.744242\pi\)
\(374\) −51.5532 −2.66575
\(375\) −16.8197 −0.868565
\(376\) −68.8593 −3.55115
\(377\) 4.71877 0.243029
\(378\) −15.1561 −0.779548
\(379\) −16.5458 −0.849900 −0.424950 0.905217i \(-0.639708\pi\)
−0.424950 + 0.905217i \(0.639708\pi\)
\(380\) 14.2091 0.728909
\(381\) 25.6351 1.31332
\(382\) 13.9620 0.714358
\(383\) 24.8122 1.26784 0.633921 0.773398i \(-0.281444\pi\)
0.633921 + 0.773398i \(0.281444\pi\)
\(384\) 25.3432 1.29329
\(385\) −6.18999 −0.315471
\(386\) 4.35300 0.221562
\(387\) −2.42735 −0.123389
\(388\) 1.04919 0.0532643
\(389\) 20.2046 1.02441 0.512207 0.858862i \(-0.328828\pi\)
0.512207 + 0.858862i \(0.328828\pi\)
\(390\) 32.2024 1.63063
\(391\) −17.3195 −0.875882
\(392\) −8.53117 −0.430889
\(393\) 11.3249 0.571265
\(394\) 56.6816 2.85558
\(395\) 14.9921 0.754334
\(396\) −17.3454 −0.871641
\(397\) −22.5603 −1.13227 −0.566134 0.824313i \(-0.691562\pi\)
−0.566134 + 0.824313i \(0.691562\pi\)
\(398\) 41.6915 2.08981
\(399\) 1.95000 0.0976223
\(400\) −14.5436 −0.727179
\(401\) 12.7210 0.635256 0.317628 0.948215i \(-0.397114\pi\)
0.317628 + 0.948215i \(0.397114\pi\)
\(402\) −7.35408 −0.366788
\(403\) 25.5289 1.27168
\(404\) 94.9084 4.72187
\(405\) 9.20946 0.457622
\(406\) 2.87234 0.142552
\(407\) 30.3789 1.50582
\(408\) 72.3436 3.58154
\(409\) 27.9988 1.38445 0.692225 0.721682i \(-0.256631\pi\)
0.692225 + 0.721682i \(0.256631\pi\)
\(410\) −31.3045 −1.54602
\(411\) −4.81747 −0.237628
\(412\) 92.4343 4.55391
\(413\) 11.7345 0.577417
\(414\) −8.07580 −0.396904
\(415\) 20.6145 1.01192
\(416\) 72.3642 3.54795
\(417\) −5.76858 −0.282489
\(418\) 11.8550 0.579845
\(419\) 26.7656 1.30758 0.653792 0.756674i \(-0.273177\pi\)
0.653792 + 0.756674i \(0.273177\pi\)
\(420\) 14.1440 0.690156
\(421\) −12.8328 −0.625430 −0.312715 0.949847i \(-0.601239\pi\)
−0.312715 + 0.949847i \(0.601239\pi\)
\(422\) 27.7030 1.34856
\(423\) −8.54710 −0.415574
\(424\) −18.3185 −0.889623
\(425\) −7.08248 −0.343551
\(426\) −27.9612 −1.35473
\(427\) −15.5384 −0.751957
\(428\) −36.9045 −1.78385
\(429\) 19.3866 0.935992
\(430\) 12.0333 0.580296
\(431\) 14.3157 0.689561 0.344781 0.938683i \(-0.387953\pi\)
0.344781 + 0.938683i \(0.387953\pi\)
\(432\) 70.6787 3.40053
\(433\) −29.9093 −1.43735 −0.718674 0.695348i \(-0.755250\pi\)
−0.718674 + 0.695348i \(0.755250\pi\)
\(434\) 15.5395 0.745921
\(435\) −2.92456 −0.140222
\(436\) −70.8740 −3.39425
\(437\) 3.98271 0.190519
\(438\) −38.1063 −1.82079
\(439\) −11.1737 −0.533292 −0.266646 0.963795i \(-0.585915\pi\)
−0.266646 + 0.963795i \(0.585915\pi\)
\(440\) 52.8078 2.51752
\(441\) −1.05892 −0.0504250
\(442\) 71.8251 3.41637
\(443\) 25.8068 1.22612 0.613058 0.790038i \(-0.289939\pi\)
0.613058 + 0.790038i \(0.289939\pi\)
\(444\) −69.4151 −3.29429
\(445\) −32.6458 −1.54756
\(446\) −19.2002 −0.909154
\(447\) 24.0761 1.13876
\(448\) 19.0515 0.900100
\(449\) 12.7459 0.601518 0.300759 0.953700i \(-0.402760\pi\)
0.300759 + 0.953700i \(0.402760\pi\)
\(450\) −3.30245 −0.155679
\(451\) −18.8460 −0.887425
\(452\) 44.2118 2.07955
\(453\) −16.7142 −0.785300
\(454\) 59.7007 2.80189
\(455\) 8.62403 0.404301
\(456\) −16.6358 −0.779043
\(457\) 4.35040 0.203503 0.101752 0.994810i \(-0.467555\pi\)
0.101752 + 0.994810i \(0.467555\pi\)
\(458\) 12.2435 0.572100
\(459\) 34.4193 1.60656
\(460\) 28.8878 1.34690
\(461\) −3.88858 −0.181109 −0.0905546 0.995891i \(-0.528864\pi\)
−0.0905546 + 0.995891i \(0.528864\pi\)
\(462\) 11.8007 0.549018
\(463\) −7.88666 −0.366524 −0.183262 0.983064i \(-0.558666\pi\)
−0.183262 + 0.983064i \(0.558666\pi\)
\(464\) −13.3948 −0.621836
\(465\) −15.8220 −0.733730
\(466\) 30.2109 1.39949
\(467\) −7.88541 −0.364893 −0.182447 0.983216i \(-0.558402\pi\)
−0.182447 + 0.983216i \(0.558402\pi\)
\(468\) 24.1661 1.11708
\(469\) −1.96948 −0.0909420
\(470\) 42.3711 1.95444
\(471\) 0.718913 0.0331258
\(472\) −100.109 −4.60789
\(473\) 7.24430 0.333093
\(474\) −28.5812 −1.31278
\(475\) 1.62866 0.0747279
\(476\) 31.5472 1.44596
\(477\) −2.27376 −0.104108
\(478\) 44.6989 2.04448
\(479\) 30.9629 1.41473 0.707364 0.706849i \(-0.249884\pi\)
0.707364 + 0.706849i \(0.249884\pi\)
\(480\) −44.8493 −2.04708
\(481\) −42.3245 −1.92983
\(482\) 12.1208 0.552087
\(483\) 3.96447 0.180390
\(484\) −5.24762 −0.238528
\(485\) −0.396480 −0.0180032
\(486\) 27.9114 1.26609
\(487\) 39.3587 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(488\) 132.561 6.00076
\(489\) −5.47266 −0.247482
\(490\) 5.24948 0.237147
\(491\) −5.27277 −0.237957 −0.118978 0.992897i \(-0.537962\pi\)
−0.118978 + 0.992897i \(0.537962\pi\)
\(492\) 43.0628 1.94142
\(493\) −6.52302 −0.293782
\(494\) −16.5166 −0.743117
\(495\) 6.55473 0.294613
\(496\) −72.4665 −3.25384
\(497\) −7.48822 −0.335893
\(498\) −39.2997 −1.76106
\(499\) 26.5224 1.18731 0.593654 0.804721i \(-0.297685\pi\)
0.593654 + 0.804721i \(0.297685\pi\)
\(500\) 62.5731 2.79835
\(501\) −25.8293 −1.15397
\(502\) 50.5570 2.25647
\(503\) −20.8171 −0.928191 −0.464095 0.885785i \(-0.653620\pi\)
−0.464095 + 0.885785i \(0.653620\pi\)
\(504\) 9.03387 0.402400
\(505\) −35.8652 −1.59598
\(506\) 24.1018 1.07146
\(507\) −8.89787 −0.395168
\(508\) −95.3683 −4.23128
\(509\) −4.91285 −0.217758 −0.108879 0.994055i \(-0.534726\pi\)
−0.108879 + 0.994055i \(0.534726\pi\)
\(510\) −44.5151 −1.97116
\(511\) −10.2051 −0.451449
\(512\) 7.83877 0.346428
\(513\) −7.91492 −0.349452
\(514\) −24.7187 −1.09030
\(515\) −34.9303 −1.53921
\(516\) −16.5531 −0.728709
\(517\) 25.5084 1.12186
\(518\) −25.7631 −1.13197
\(519\) −30.8875 −1.35581
\(520\) −73.5731 −3.22639
\(521\) 19.7543 0.865454 0.432727 0.901525i \(-0.357551\pi\)
0.432727 + 0.901525i \(0.357551\pi\)
\(522\) −3.04159 −0.133127
\(523\) 24.2489 1.06033 0.530166 0.847894i \(-0.322130\pi\)
0.530166 + 0.847894i \(0.322130\pi\)
\(524\) −42.1311 −1.84051
\(525\) 1.62120 0.0707550
\(526\) 29.9395 1.30543
\(527\) −35.2900 −1.53726
\(528\) −55.0309 −2.39491
\(529\) −14.9029 −0.647953
\(530\) 11.2719 0.489620
\(531\) −12.4260 −0.539240
\(532\) −7.25446 −0.314521
\(533\) 26.2567 1.13730
\(534\) 62.2365 2.69324
\(535\) 13.9460 0.602937
\(536\) 16.8019 0.725733
\(537\) 11.0087 0.475061
\(538\) −18.9570 −0.817294
\(539\) 3.16031 0.136124
\(540\) −57.4094 −2.47051
\(541\) 0.754084 0.0324206 0.0162103 0.999869i \(-0.494840\pi\)
0.0162103 + 0.999869i \(0.494840\pi\)
\(542\) −0.339409 −0.0145789
\(543\) −17.7425 −0.761405
\(544\) −100.033 −4.28889
\(545\) 26.7828 1.14725
\(546\) −16.4410 −0.703609
\(547\) 26.3705 1.12752 0.563761 0.825938i \(-0.309354\pi\)
0.563761 + 0.825938i \(0.309354\pi\)
\(548\) 17.9221 0.765593
\(549\) 16.4540 0.702241
\(550\) 9.85602 0.420262
\(551\) 1.50001 0.0639024
\(552\) −33.8216 −1.43954
\(553\) −7.65424 −0.325492
\(554\) −25.5685 −1.08630
\(555\) 26.2315 1.11347
\(556\) 21.4604 0.910126
\(557\) 5.41085 0.229265 0.114632 0.993408i \(-0.463431\pi\)
0.114632 + 0.993408i \(0.463431\pi\)
\(558\) −16.4552 −0.696603
\(559\) −10.0929 −0.426885
\(560\) −24.4803 −1.03448
\(561\) −26.7991 −1.13146
\(562\) 13.0990 0.552547
\(563\) −2.46042 −0.103694 −0.0518472 0.998655i \(-0.516511\pi\)
−0.0518472 + 0.998655i \(0.516511\pi\)
\(564\) −58.2862 −2.45429
\(565\) −16.7074 −0.702884
\(566\) 43.0123 1.80794
\(567\) −4.70191 −0.197461
\(568\) 63.8833 2.68048
\(569\) 9.41749 0.394802 0.197401 0.980323i \(-0.436750\pi\)
0.197401 + 0.980323i \(0.436750\pi\)
\(570\) 10.2365 0.428760
\(571\) 14.2215 0.595150 0.297575 0.954698i \(-0.403822\pi\)
0.297575 + 0.954698i \(0.403822\pi\)
\(572\) −72.1224 −3.01559
\(573\) 7.25792 0.303204
\(574\) 15.9826 0.667099
\(575\) 3.31116 0.138085
\(576\) −20.1741 −0.840589
\(577\) −7.54076 −0.313926 −0.156963 0.987604i \(-0.550170\pi\)
−0.156963 + 0.987604i \(0.550170\pi\)
\(578\) −53.7257 −2.23469
\(579\) 2.26284 0.0940405
\(580\) 10.8800 0.451768
\(581\) −10.5248 −0.436640
\(582\) 0.755856 0.0313312
\(583\) 6.78594 0.281045
\(584\) 87.0618 3.60264
\(585\) −9.13219 −0.377570
\(586\) 6.75235 0.278937
\(587\) 38.0896 1.57213 0.786064 0.618146i \(-0.212116\pi\)
0.786064 + 0.618146i \(0.212116\pi\)
\(588\) −7.22124 −0.297799
\(589\) 8.11513 0.334378
\(590\) 61.6001 2.53604
\(591\) 29.4650 1.21203
\(592\) 120.143 4.93784
\(593\) 2.95334 0.121279 0.0606396 0.998160i \(-0.480686\pi\)
0.0606396 + 0.998160i \(0.480686\pi\)
\(594\) −47.8981 −1.96528
\(595\) −11.9215 −0.488733
\(596\) −89.5686 −3.66887
\(597\) 21.6727 0.887003
\(598\) −33.5792 −1.37316
\(599\) 33.2450 1.35835 0.679176 0.733975i \(-0.262337\pi\)
0.679176 + 0.733975i \(0.262337\pi\)
\(600\) −13.8307 −0.564638
\(601\) 27.2304 1.11075 0.555375 0.831600i \(-0.312575\pi\)
0.555375 + 0.831600i \(0.312575\pi\)
\(602\) −6.14361 −0.250395
\(603\) 2.08553 0.0849292
\(604\) 62.1805 2.53009
\(605\) 1.98304 0.0806221
\(606\) 68.3740 2.77751
\(607\) −15.7646 −0.639867 −0.319934 0.947440i \(-0.603661\pi\)
−0.319934 + 0.947440i \(0.603661\pi\)
\(608\) 23.0032 0.932903
\(609\) 1.49314 0.0605050
\(610\) −81.5687 −3.30262
\(611\) −35.5389 −1.43775
\(612\) −33.4061 −1.35036
\(613\) −9.18060 −0.370801 −0.185400 0.982663i \(-0.559358\pi\)
−0.185400 + 0.982663i \(0.559358\pi\)
\(614\) −28.2227 −1.13897
\(615\) −16.2731 −0.656197
\(616\) −26.9611 −1.08630
\(617\) 2.77151 0.111577 0.0557884 0.998443i \(-0.482233\pi\)
0.0557884 + 0.998443i \(0.482233\pi\)
\(618\) 66.5916 2.67871
\(619\) −18.3602 −0.737958 −0.368979 0.929438i \(-0.620293\pi\)
−0.368979 + 0.929438i \(0.620293\pi\)
\(620\) 58.8616 2.36394
\(621\) −16.0915 −0.645729
\(622\) 84.1312 3.37335
\(623\) 16.6674 0.667765
\(624\) 76.6703 3.06927
\(625\) −17.8278 −0.713112
\(626\) −67.9710 −2.71667
\(627\) 6.16261 0.246111
\(628\) −2.67452 −0.106725
\(629\) 58.5075 2.33285
\(630\) −5.55881 −0.221468
\(631\) 7.67239 0.305433 0.152717 0.988270i \(-0.451198\pi\)
0.152717 + 0.988270i \(0.451198\pi\)
\(632\) 65.2997 2.59748
\(633\) 14.4010 0.572387
\(634\) −10.5196 −0.417785
\(635\) 36.0391 1.43017
\(636\) −15.5057 −0.614842
\(637\) −4.40301 −0.174454
\(638\) 9.07747 0.359380
\(639\) 7.92946 0.313685
\(640\) 35.6287 1.40835
\(641\) −6.47833 −0.255879 −0.127939 0.991782i \(-0.540836\pi\)
−0.127939 + 0.991782i \(0.540836\pi\)
\(642\) −26.5868 −1.04930
\(643\) −14.7911 −0.583302 −0.291651 0.956525i \(-0.594205\pi\)
−0.291651 + 0.956525i \(0.594205\pi\)
\(644\) −14.7487 −0.581182
\(645\) 6.25530 0.246302
\(646\) 22.8318 0.898306
\(647\) −27.2236 −1.07027 −0.535136 0.844766i \(-0.679739\pi\)
−0.535136 + 0.844766i \(0.679739\pi\)
\(648\) 40.1128 1.57578
\(649\) 37.0847 1.45570
\(650\) −13.7316 −0.538599
\(651\) 8.07798 0.316601
\(652\) 20.3595 0.797341
\(653\) 31.0232 1.21403 0.607015 0.794690i \(-0.292367\pi\)
0.607015 + 0.794690i \(0.292367\pi\)
\(654\) −51.0591 −1.99657
\(655\) 15.9211 0.622088
\(656\) −74.5326 −2.91001
\(657\) 10.8065 0.421601
\(658\) −21.6327 −0.843329
\(659\) 9.23802 0.359862 0.179931 0.983679i \(-0.442413\pi\)
0.179931 + 0.983679i \(0.442413\pi\)
\(660\) 44.6994 1.73992
\(661\) 37.7580 1.46862 0.734308 0.678816i \(-0.237507\pi\)
0.734308 + 0.678816i \(0.237507\pi\)
\(662\) 34.2478 1.33108
\(663\) 37.3372 1.45006
\(664\) 89.7885 3.48447
\(665\) 2.74141 0.106307
\(666\) 27.2812 1.05712
\(667\) 3.04960 0.118081
\(668\) 96.0909 3.71787
\(669\) −9.98090 −0.385884
\(670\) −10.3387 −0.399420
\(671\) −49.1062 −1.89573
\(672\) 22.8979 0.883305
\(673\) 37.9894 1.46438 0.732191 0.681099i \(-0.238498\pi\)
0.732191 + 0.681099i \(0.238498\pi\)
\(674\) −72.8256 −2.80514
\(675\) −6.58033 −0.253277
\(676\) 33.1021 1.27316
\(677\) −24.7663 −0.951847 −0.475923 0.879487i \(-0.657886\pi\)
−0.475923 + 0.879487i \(0.657886\pi\)
\(678\) 31.8512 1.22324
\(679\) 0.202424 0.00776831
\(680\) 101.704 3.90018
\(681\) 31.0345 1.18924
\(682\) 49.1097 1.88051
\(683\) 51.7117 1.97869 0.989347 0.145578i \(-0.0465041\pi\)
0.989347 + 0.145578i \(0.0465041\pi\)
\(684\) 7.68192 0.293726
\(685\) −6.77264 −0.258769
\(686\) −2.68013 −0.102328
\(687\) 6.36457 0.242824
\(688\) 28.6499 1.09227
\(689\) −9.45432 −0.360181
\(690\) 20.8114 0.792278
\(691\) 21.2304 0.807643 0.403822 0.914838i \(-0.367682\pi\)
0.403822 + 0.914838i \(0.367682\pi\)
\(692\) 114.909 4.36817
\(693\) −3.34653 −0.127124
\(694\) −90.1046 −3.42032
\(695\) −8.10976 −0.307621
\(696\) −12.7382 −0.482841
\(697\) −36.2961 −1.37481
\(698\) −64.8858 −2.45597
\(699\) 15.7046 0.594004
\(700\) −6.03124 −0.227959
\(701\) 2.41580 0.0912436 0.0456218 0.998959i \(-0.485473\pi\)
0.0456218 + 0.998959i \(0.485473\pi\)
\(702\) 66.7327 2.51866
\(703\) −13.4541 −0.507432
\(704\) 60.2087 2.26920
\(705\) 22.0260 0.829546
\(706\) 87.0591 3.27651
\(707\) 18.3111 0.688659
\(708\) −84.7377 −3.18464
\(709\) 42.9755 1.61398 0.806990 0.590566i \(-0.201095\pi\)
0.806990 + 0.590566i \(0.201095\pi\)
\(710\) −39.3093 −1.47525
\(711\) 8.10526 0.303971
\(712\) −142.192 −5.32889
\(713\) 16.4985 0.617875
\(714\) 22.7273 0.850547
\(715\) 27.2546 1.01926
\(716\) −40.9549 −1.53056
\(717\) 23.2360 0.867766
\(718\) 45.4971 1.69794
\(719\) −27.7567 −1.03515 −0.517575 0.855638i \(-0.673165\pi\)
−0.517575 + 0.855638i \(0.673165\pi\)
\(720\) 25.9228 0.966084
\(721\) 17.8337 0.664163
\(722\) 45.6722 1.69974
\(723\) 6.30081 0.234329
\(724\) 66.0062 2.45310
\(725\) 1.24708 0.0463154
\(726\) −3.78050 −0.140307
\(727\) −14.1591 −0.525131 −0.262565 0.964914i \(-0.584569\pi\)
−0.262565 + 0.964914i \(0.584569\pi\)
\(728\) 37.5629 1.39217
\(729\) 28.6150 1.05981
\(730\) −53.5717 −1.98278
\(731\) 13.9520 0.516034
\(732\) 112.207 4.14728
\(733\) 43.1190 1.59263 0.796317 0.604879i \(-0.206779\pi\)
0.796317 + 0.604879i \(0.206779\pi\)
\(734\) −62.7459 −2.31599
\(735\) 2.72886 0.100656
\(736\) 46.7669 1.72385
\(737\) −6.22415 −0.229270
\(738\) −16.9243 −0.622993
\(739\) 49.0645 1.80487 0.902433 0.430831i \(-0.141779\pi\)
0.902433 + 0.430831i \(0.141779\pi\)
\(740\) −97.5872 −3.58738
\(741\) −8.58589 −0.315411
\(742\) −5.75489 −0.211268
\(743\) 16.7717 0.615294 0.307647 0.951501i \(-0.400458\pi\)
0.307647 + 0.951501i \(0.400458\pi\)
\(744\) −68.9146 −2.52653
\(745\) 33.8474 1.24007
\(746\) 71.8663 2.63121
\(747\) 11.1449 0.407771
\(748\) 99.6989 3.64535
\(749\) −7.12014 −0.260164
\(750\) 45.0790 1.64605
\(751\) −18.7172 −0.683002 −0.341501 0.939881i \(-0.610935\pi\)
−0.341501 + 0.939881i \(0.610935\pi\)
\(752\) 100.881 3.67876
\(753\) 26.2813 0.957743
\(754\) −12.6469 −0.460574
\(755\) −23.4976 −0.855165
\(756\) 29.3105 1.06601
\(757\) −26.7918 −0.973765 −0.486883 0.873467i \(-0.661866\pi\)
−0.486883 + 0.873467i \(0.661866\pi\)
\(758\) 44.3449 1.61068
\(759\) 12.5290 0.454772
\(760\) −23.3875 −0.848352
\(761\) 31.3164 1.13522 0.567608 0.823299i \(-0.307869\pi\)
0.567608 + 0.823299i \(0.307869\pi\)
\(762\) −68.7054 −2.48893
\(763\) −13.6740 −0.495032
\(764\) −27.0011 −0.976866
\(765\) 12.6239 0.456420
\(766\) −66.4999 −2.40274
\(767\) −51.6672 −1.86559
\(768\) −14.8370 −0.535386
\(769\) −41.5683 −1.49899 −0.749495 0.662009i \(-0.769704\pi\)
−0.749495 + 0.662009i \(0.769704\pi\)
\(770\) 16.5900 0.597862
\(771\) −12.8496 −0.462768
\(772\) −8.41828 −0.302981
\(773\) −20.4651 −0.736078 −0.368039 0.929810i \(-0.619971\pi\)
−0.368039 + 0.929810i \(0.619971\pi\)
\(774\) 6.50562 0.233840
\(775\) 6.74678 0.242352
\(776\) −1.72691 −0.0619925
\(777\) −13.3925 −0.480455
\(778\) −54.1511 −1.94141
\(779\) 8.34650 0.299044
\(780\) −62.2762 −2.22985
\(781\) −23.6651 −0.846804
\(782\) 46.4184 1.65992
\(783\) −6.06053 −0.216586
\(784\) 12.4984 0.446373
\(785\) 1.01068 0.0360728
\(786\) −30.3522 −1.08263
\(787\) −3.29602 −0.117490 −0.0587452 0.998273i \(-0.518710\pi\)
−0.0587452 + 0.998273i \(0.518710\pi\)
\(788\) −109.617 −3.90493
\(789\) 15.5636 0.554079
\(790\) −40.1808 −1.42957
\(791\) 8.52998 0.303291
\(792\) 28.5498 1.01447
\(793\) 68.4159 2.42952
\(794\) 60.4646 2.14581
\(795\) 5.85951 0.207816
\(796\) −80.6272 −2.85776
\(797\) 8.93980 0.316664 0.158332 0.987386i \(-0.449388\pi\)
0.158332 + 0.987386i \(0.449388\pi\)
\(798\) −5.22627 −0.185008
\(799\) 49.1274 1.73800
\(800\) 19.1245 0.676152
\(801\) −17.6495 −0.623615
\(802\) −34.0940 −1.20390
\(803\) −32.2514 −1.13813
\(804\) 14.2221 0.501574
\(805\) 5.57345 0.196438
\(806\) −68.4207 −2.41002
\(807\) −9.85449 −0.346894
\(808\) −156.215 −5.49562
\(809\) 49.2414 1.73124 0.865618 0.500705i \(-0.166926\pi\)
0.865618 + 0.500705i \(0.166926\pi\)
\(810\) −24.6826 −0.867257
\(811\) 50.9127 1.78779 0.893893 0.448280i \(-0.147963\pi\)
0.893893 + 0.448280i \(0.147963\pi\)
\(812\) −5.55481 −0.194936
\(813\) −0.176436 −0.00618790
\(814\) −81.4194 −2.85375
\(815\) −7.69373 −0.269500
\(816\) −105.986 −3.71024
\(817\) −3.20835 −0.112246
\(818\) −75.0404 −2.62373
\(819\) 4.66246 0.162919
\(820\) 60.5398 2.11414
\(821\) −29.9395 −1.04490 −0.522448 0.852671i \(-0.674981\pi\)
−0.522448 + 0.852671i \(0.674981\pi\)
\(822\) 12.9115 0.450339
\(823\) −14.8680 −0.518267 −0.259134 0.965842i \(-0.583437\pi\)
−0.259134 + 0.965842i \(0.583437\pi\)
\(824\) −152.143 −5.30014
\(825\) 5.12350 0.178377
\(826\) −31.4500 −1.09429
\(827\) 17.0459 0.592745 0.296372 0.955072i \(-0.404223\pi\)
0.296372 + 0.955072i \(0.404223\pi\)
\(828\) 15.6178 0.542756
\(829\) 19.3414 0.671753 0.335877 0.941906i \(-0.390967\pi\)
0.335877 + 0.941906i \(0.390967\pi\)
\(830\) −55.2495 −1.91774
\(831\) −13.2914 −0.461072
\(832\) −83.8842 −2.90816
\(833\) 6.08653 0.210886
\(834\) 15.4606 0.535356
\(835\) −36.3121 −1.25663
\(836\) −22.9263 −0.792924
\(837\) −32.7879 −1.13332
\(838\) −71.7353 −2.47806
\(839\) 23.7747 0.820794 0.410397 0.911907i \(-0.365390\pi\)
0.410397 + 0.911907i \(0.365390\pi\)
\(840\) −23.2804 −0.803249
\(841\) −27.8514 −0.960394
\(842\) 34.3935 1.18528
\(843\) 6.80929 0.234525
\(844\) −53.5749 −1.84412
\(845\) −12.5091 −0.430325
\(846\) 22.9074 0.787571
\(847\) −1.01245 −0.0347880
\(848\) 26.8371 0.921591
\(849\) 22.3593 0.767368
\(850\) 18.9820 0.651077
\(851\) −27.3531 −0.937651
\(852\) 54.0743 1.85255
\(853\) 26.6843 0.913652 0.456826 0.889556i \(-0.348986\pi\)
0.456826 + 0.889556i \(0.348986\pi\)
\(854\) 41.6451 1.42506
\(855\) −2.90295 −0.0992787
\(856\) 60.7431 2.07616
\(857\) 47.7397 1.63076 0.815378 0.578928i \(-0.196529\pi\)
0.815378 + 0.578928i \(0.196529\pi\)
\(858\) −51.9586 −1.77384
\(859\) −1.00000 −0.0341196
\(860\) −23.2712 −0.793540
\(861\) 8.30828 0.283146
\(862\) −38.3679 −1.30682
\(863\) 7.15022 0.243396 0.121698 0.992567i \(-0.461166\pi\)
0.121698 + 0.992567i \(0.461166\pi\)
\(864\) −92.9408 −3.16191
\(865\) −43.4232 −1.47643
\(866\) 80.1608 2.72397
\(867\) −27.9284 −0.948499
\(868\) −30.0519 −1.02003
\(869\) −24.1898 −0.820582
\(870\) 7.83820 0.265740
\(871\) 8.67163 0.293827
\(872\) 116.655 3.95045
\(873\) −0.214351 −0.00725470
\(874\) −10.6742 −0.361060
\(875\) 12.0725 0.408125
\(876\) 73.6938 2.48988
\(877\) −0.548551 −0.0185233 −0.00926163 0.999957i \(-0.502948\pi\)
−0.00926163 + 0.999957i \(0.502948\pi\)
\(878\) 29.9470 1.01066
\(879\) 3.51010 0.118393
\(880\) −77.3652 −2.60798
\(881\) −42.7183 −1.43922 −0.719608 0.694380i \(-0.755679\pi\)
−0.719608 + 0.694380i \(0.755679\pi\)
\(882\) 2.83806 0.0955624
\(883\) −16.9624 −0.570830 −0.285415 0.958404i \(-0.592131\pi\)
−0.285415 + 0.958404i \(0.592131\pi\)
\(884\) −138.903 −4.67180
\(885\) 32.0218 1.07640
\(886\) −69.1655 −2.32366
\(887\) 32.2463 1.08273 0.541363 0.840789i \(-0.317909\pi\)
0.541363 + 0.840789i \(0.317909\pi\)
\(888\) 114.254 3.83412
\(889\) −18.3998 −0.617110
\(890\) 87.4952 2.93285
\(891\) −14.8595 −0.497811
\(892\) 37.1312 1.24325
\(893\) −11.2971 −0.378044
\(894\) −64.5271 −2.15811
\(895\) 15.4766 0.517326
\(896\) −18.1903 −0.607696
\(897\) −17.4556 −0.582826
\(898\) −34.1608 −1.13996
\(899\) 6.21384 0.207243
\(900\) 6.38662 0.212887
\(901\) 13.0692 0.435399
\(902\) 50.5099 1.68179
\(903\) −3.19366 −0.106278
\(904\) −72.7707 −2.42032
\(905\) −24.9433 −0.829144
\(906\) 44.7962 1.48825
\(907\) 31.1998 1.03597 0.517987 0.855389i \(-0.326682\pi\)
0.517987 + 0.855389i \(0.326682\pi\)
\(908\) −115.455 −3.83152
\(909\) −19.3900 −0.643127
\(910\) −23.1135 −0.766207
\(911\) 40.2885 1.33482 0.667408 0.744692i \(-0.267404\pi\)
0.667408 + 0.744692i \(0.267404\pi\)
\(912\) 24.3720 0.807038
\(913\) −33.2615 −1.10079
\(914\) −11.6597 −0.385667
\(915\) −42.4022 −1.40177
\(916\) −23.6777 −0.782332
\(917\) −8.12854 −0.268428
\(918\) −92.2484 −3.04465
\(919\) −7.26584 −0.239678 −0.119839 0.992793i \(-0.538238\pi\)
−0.119839 + 0.992793i \(0.538238\pi\)
\(920\) −47.5481 −1.56761
\(921\) −14.6711 −0.483429
\(922\) 10.4219 0.343227
\(923\) 32.9707 1.08524
\(924\) −22.8214 −0.750768
\(925\) −11.1855 −0.367779
\(926\) 21.1373 0.694615
\(927\) −18.8846 −0.620251
\(928\) 17.6138 0.578201
\(929\) −1.17296 −0.0384834 −0.0192417 0.999815i \(-0.506125\pi\)
−0.0192417 + 0.999815i \(0.506125\pi\)
\(930\) 42.4052 1.39052
\(931\) −1.39963 −0.0458711
\(932\) −58.4249 −1.91377
\(933\) 43.7343 1.43180
\(934\) 21.1339 0.691524
\(935\) −37.6756 −1.23212
\(936\) −39.7762 −1.30013
\(937\) 1.77420 0.0579607 0.0289804 0.999580i \(-0.490774\pi\)
0.0289804 + 0.999580i \(0.490774\pi\)
\(938\) 5.27846 0.172348
\(939\) −35.3337 −1.15307
\(940\) −81.9416 −2.67264
\(941\) 56.1805 1.83143 0.915716 0.401825i \(-0.131624\pi\)
0.915716 + 0.401825i \(0.131624\pi\)
\(942\) −1.92678 −0.0627780
\(943\) 16.9689 0.552584
\(944\) 146.663 4.77348
\(945\) −11.0762 −0.360310
\(946\) −19.4157 −0.631259
\(947\) −16.9707 −0.551474 −0.275737 0.961233i \(-0.588922\pi\)
−0.275737 + 0.961233i \(0.588922\pi\)
\(948\) 55.2732 1.79519
\(949\) 44.9334 1.45860
\(950\) −4.36502 −0.141620
\(951\) −5.46842 −0.177326
\(952\) −51.9253 −1.68291
\(953\) 24.9602 0.808539 0.404270 0.914640i \(-0.367526\pi\)
0.404270 + 0.914640i \(0.367526\pi\)
\(954\) 6.09399 0.197300
\(955\) 10.2035 0.330179
\(956\) −86.4433 −2.79578
\(957\) 4.71878 0.152536
\(958\) −82.9846 −2.68111
\(959\) 3.45778 0.111658
\(960\) 51.9890 1.67794
\(961\) 2.61729 0.0844286
\(962\) 113.435 3.65730
\(963\) 7.53969 0.242963
\(964\) −23.4404 −0.754966
\(965\) 3.18121 0.102407
\(966\) −10.6253 −0.341864
\(967\) 17.0796 0.549243 0.274621 0.961552i \(-0.411448\pi\)
0.274621 + 0.961552i \(0.411448\pi\)
\(968\) 8.63734 0.277615
\(969\) 11.8688 0.381280
\(970\) 1.06262 0.0341187
\(971\) 52.1012 1.67201 0.836003 0.548724i \(-0.184886\pi\)
0.836003 + 0.548724i \(0.184886\pi\)
\(972\) −53.9778 −1.73134
\(973\) 4.14045 0.132737
\(974\) −105.486 −3.38001
\(975\) −7.13817 −0.228604
\(976\) −194.206 −6.21639
\(977\) 26.4834 0.847278 0.423639 0.905831i \(-0.360752\pi\)
0.423639 + 0.905831i \(0.360752\pi\)
\(978\) 14.6675 0.469013
\(979\) 52.6741 1.68347
\(980\) −10.1520 −0.324293
\(981\) 14.4797 0.462303
\(982\) 14.1317 0.450962
\(983\) −39.0034 −1.24401 −0.622007 0.783011i \(-0.713683\pi\)
−0.622007 + 0.783011i \(0.713683\pi\)
\(984\) −70.8794 −2.25955
\(985\) 41.4234 1.31986
\(986\) 17.4826 0.556758
\(987\) −11.2454 −0.357945
\(988\) 31.9415 1.01619
\(989\) −6.52276 −0.207412
\(990\) −17.5675 −0.558333
\(991\) −44.5271 −1.41445 −0.707224 0.706989i \(-0.750053\pi\)
−0.707224 + 0.706989i \(0.750053\pi\)
\(992\) 95.2918 3.02552
\(993\) 17.8032 0.564966
\(994\) 20.0694 0.636564
\(995\) 30.4685 0.965917
\(996\) 76.0018 2.40821
\(997\) 20.1867 0.639319 0.319660 0.947532i \(-0.396431\pi\)
0.319660 + 0.947532i \(0.396431\pi\)
\(998\) −71.0837 −2.25011
\(999\) 54.3593 1.71985
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 \(a_p\))