Properties

Label 1805.2.a.c.1.1
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $2$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(2\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -1.00000 q^{5} +6.85410 q^{6} +0.236068 q^{7} -7.47214 q^{8} +3.85410 q^{9} +O(q^{10})\) \(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -1.00000 q^{5} +6.85410 q^{6} +0.236068 q^{7} -7.47214 q^{8} +3.85410 q^{9} +2.61803 q^{10} -4.61803 q^{11} -12.7082 q^{12} -5.00000 q^{13} -0.618034 q^{14} +2.61803 q^{15} +9.85410 q^{16} -6.00000 q^{17} -10.0902 q^{18} -4.85410 q^{20} -0.618034 q^{21} +12.0902 q^{22} -1.61803 q^{23} +19.5623 q^{24} +1.00000 q^{25} +13.0902 q^{26} -2.23607 q^{27} +1.14590 q^{28} +1.85410 q^{29} -6.85410 q^{30} -4.14590 q^{31} -10.8541 q^{32} +12.0902 q^{33} +15.7082 q^{34} -0.236068 q^{35} +18.7082 q^{36} +1.85410 q^{37} +13.0902 q^{39} +7.47214 q^{40} -11.1803 q^{41} +1.61803 q^{42} -2.85410 q^{43} -22.4164 q^{44} -3.85410 q^{45} +4.23607 q^{46} -10.2361 q^{47} -25.7984 q^{48} -6.94427 q^{49} -2.61803 q^{50} +15.7082 q^{51} -24.2705 q^{52} -5.61803 q^{53} +5.85410 q^{54} +4.61803 q^{55} -1.76393 q^{56} -4.85410 q^{58} -0.0901699 q^{59} +12.7082 q^{60} -3.00000 q^{61} +10.8541 q^{62} +0.909830 q^{63} +8.70820 q^{64} +5.00000 q^{65} -31.6525 q^{66} +4.70820 q^{67} -29.1246 q^{68} +4.23607 q^{69} +0.618034 q^{70} -3.76393 q^{71} -28.7984 q^{72} -1.00000 q^{73} -4.85410 q^{74} -2.61803 q^{75} -1.09017 q^{77} -34.2705 q^{78} -8.00000 q^{79} -9.85410 q^{80} -5.70820 q^{81} +29.2705 q^{82} +4.47214 q^{83} -3.00000 q^{84} +6.00000 q^{85} +7.47214 q^{86} -4.85410 q^{87} +34.5066 q^{88} +6.70820 q^{89} +10.0902 q^{90} -1.18034 q^{91} -7.85410 q^{92} +10.8541 q^{93} +26.7984 q^{94} +28.4164 q^{96} -6.09017 q^{97} +18.1803 q^{98} -17.7984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} - 6 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 2 q^{5} + 7 q^{6} - 4 q^{7} - 6 q^{8} + q^{9} + 3 q^{10} - 7 q^{11} - 12 q^{12} - 10 q^{13} + q^{14} + 3 q^{15} + 13 q^{16} - 12 q^{17} - 9 q^{18} - 3 q^{20} + q^{21} + 13 q^{22} - q^{23} + 19 q^{24} + 2 q^{25} + 15 q^{26} + 9 q^{28} - 3 q^{29} - 7 q^{30} - 15 q^{31} - 15 q^{32} + 13 q^{33} + 18 q^{34} + 4 q^{35} + 24 q^{36} - 3 q^{37} + 15 q^{39} + 6 q^{40} + q^{42} + q^{43} - 18 q^{44} - q^{45} + 4 q^{46} - 16 q^{47} - 27 q^{48} + 4 q^{49} - 3 q^{50} + 18 q^{51} - 15 q^{52} - 9 q^{53} + 5 q^{54} + 7 q^{55} - 8 q^{56} - 3 q^{58} + 11 q^{59} + 12 q^{60} - 6 q^{61} + 15 q^{62} + 13 q^{63} + 4 q^{64} + 10 q^{65} - 32 q^{66} - 4 q^{67} - 18 q^{68} + 4 q^{69} - q^{70} - 12 q^{71} - 33 q^{72} - 2 q^{73} - 3 q^{74} - 3 q^{75} + 9 q^{77} - 35 q^{78} - 16 q^{79} - 13 q^{80} + 2 q^{81} + 25 q^{82} - 6 q^{84} + 12 q^{85} + 6 q^{86} - 3 q^{87} + 31 q^{88} + 9 q^{90} + 20 q^{91} - 9 q^{92} + 15 q^{93} + 29 q^{94} + 30 q^{96} - q^{97} + 14 q^{98} - 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61803 −1.85123 −0.925615 0.378467i \(-0.876451\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) 4.85410 2.42705
\(5\) −1.00000 −0.447214
\(6\) 6.85410 2.79818
\(7\) 0.236068 0.0892253 0.0446127 0.999004i \(-0.485795\pi\)
0.0446127 + 0.999004i \(0.485795\pi\)
\(8\) −7.47214 −2.64180
\(9\) 3.85410 1.28470
\(10\) 2.61803 0.827895
\(11\) −4.61803 −1.39239 −0.696195 0.717853i \(-0.745125\pi\)
−0.696195 + 0.717853i \(0.745125\pi\)
\(12\) −12.7082 −3.66854
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −0.618034 −0.165177
\(15\) 2.61803 0.675973
\(16\) 9.85410 2.46353
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −10.0902 −2.37828
\(19\) 0 0
\(20\) −4.85410 −1.08541
\(21\) −0.618034 −0.134866
\(22\) 12.0902 2.57763
\(23\) −1.61803 −0.337383 −0.168692 0.985669i \(-0.553954\pi\)
−0.168692 + 0.985669i \(0.553954\pi\)
\(24\) 19.5623 3.99314
\(25\) 1.00000 0.200000
\(26\) 13.0902 2.56719
\(27\) −2.23607 −0.430331
\(28\) 1.14590 0.216554
\(29\) 1.85410 0.344298 0.172149 0.985071i \(-0.444929\pi\)
0.172149 + 0.985071i \(0.444929\pi\)
\(30\) −6.85410 −1.25138
\(31\) −4.14590 −0.744625 −0.372313 0.928107i \(-0.621435\pi\)
−0.372313 + 0.928107i \(0.621435\pi\)
\(32\) −10.8541 −1.91875
\(33\) 12.0902 2.10463
\(34\) 15.7082 2.69393
\(35\) −0.236068 −0.0399028
\(36\) 18.7082 3.11803
\(37\) 1.85410 0.304812 0.152406 0.988318i \(-0.451298\pi\)
0.152406 + 0.988318i \(0.451298\pi\)
\(38\) 0 0
\(39\) 13.0902 2.09610
\(40\) 7.47214 1.18145
\(41\) −11.1803 −1.74608 −0.873038 0.487652i \(-0.837853\pi\)
−0.873038 + 0.487652i \(0.837853\pi\)
\(42\) 1.61803 0.249668
\(43\) −2.85410 −0.435246 −0.217623 0.976033i \(-0.569830\pi\)
−0.217623 + 0.976033i \(0.569830\pi\)
\(44\) −22.4164 −3.37940
\(45\) −3.85410 −0.574536
\(46\) 4.23607 0.624574
\(47\) −10.2361 −1.49308 −0.746542 0.665338i \(-0.768287\pi\)
−0.746542 + 0.665338i \(0.768287\pi\)
\(48\) −25.7984 −3.72367
\(49\) −6.94427 −0.992039
\(50\) −2.61803 −0.370246
\(51\) 15.7082 2.19959
\(52\) −24.2705 −3.36571
\(53\) −5.61803 −0.771696 −0.385848 0.922562i \(-0.626091\pi\)
−0.385848 + 0.922562i \(0.626091\pi\)
\(54\) 5.85410 0.796642
\(55\) 4.61803 0.622696
\(56\) −1.76393 −0.235715
\(57\) 0 0
\(58\) −4.85410 −0.637375
\(59\) −0.0901699 −0.0117391 −0.00586956 0.999983i \(-0.501868\pi\)
−0.00586956 + 0.999983i \(0.501868\pi\)
\(60\) 12.7082 1.64062
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) 10.8541 1.37847
\(63\) 0.909830 0.114628
\(64\) 8.70820 1.08853
\(65\) 5.00000 0.620174
\(66\) −31.6525 −3.89615
\(67\) 4.70820 0.575199 0.287599 0.957751i \(-0.407143\pi\)
0.287599 + 0.957751i \(0.407143\pi\)
\(68\) −29.1246 −3.53188
\(69\) 4.23607 0.509963
\(70\) 0.618034 0.0738692
\(71\) −3.76393 −0.446697 −0.223348 0.974739i \(-0.571699\pi\)
−0.223348 + 0.974739i \(0.571699\pi\)
\(72\) −28.7984 −3.39392
\(73\) −1.00000 −0.117041 −0.0585206 0.998286i \(-0.518638\pi\)
−0.0585206 + 0.998286i \(0.518638\pi\)
\(74\) −4.85410 −0.564278
\(75\) −2.61803 −0.302305
\(76\) 0 0
\(77\) −1.09017 −0.124236
\(78\) −34.2705 −3.88037
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) −9.85410 −1.10172
\(81\) −5.70820 −0.634245
\(82\) 29.2705 3.23239
\(83\) 4.47214 0.490881 0.245440 0.969412i \(-0.421067\pi\)
0.245440 + 0.969412i \(0.421067\pi\)
\(84\) −3.00000 −0.327327
\(85\) 6.00000 0.650791
\(86\) 7.47214 0.805741
\(87\) −4.85410 −0.520414
\(88\) 34.5066 3.67841
\(89\) 6.70820 0.711068 0.355534 0.934663i \(-0.384299\pi\)
0.355534 + 0.934663i \(0.384299\pi\)
\(90\) 10.0902 1.06360
\(91\) −1.18034 −0.123733
\(92\) −7.85410 −0.818847
\(93\) 10.8541 1.12552
\(94\) 26.7984 2.76404
\(95\) 0 0
\(96\) 28.4164 2.90024
\(97\) −6.09017 −0.618363 −0.309182 0.951003i \(-0.600055\pi\)
−0.309182 + 0.951003i \(0.600055\pi\)
\(98\) 18.1803 1.83649
\(99\) −17.7984 −1.78880
\(100\) 4.85410 0.485410
\(101\) −11.9443 −1.18850 −0.594250 0.804281i \(-0.702551\pi\)
−0.594250 + 0.804281i \(0.702551\pi\)
\(102\) −41.1246 −4.07194
\(103\) −17.3262 −1.70720 −0.853602 0.520925i \(-0.825587\pi\)
−0.853602 + 0.520925i \(0.825587\pi\)
\(104\) 37.3607 3.66352
\(105\) 0.618034 0.0603139
\(106\) 14.7082 1.42859
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) −10.8541 −1.04444
\(109\) −6.23607 −0.597307 −0.298653 0.954362i \(-0.596537\pi\)
−0.298653 + 0.954362i \(0.596537\pi\)
\(110\) −12.0902 −1.15275
\(111\) −4.85410 −0.460731
\(112\) 2.32624 0.219809
\(113\) −2.94427 −0.276974 −0.138487 0.990364i \(-0.544224\pi\)
−0.138487 + 0.990364i \(0.544224\pi\)
\(114\) 0 0
\(115\) 1.61803 0.150882
\(116\) 9.00000 0.835629
\(117\) −19.2705 −1.78156
\(118\) 0.236068 0.0217318
\(119\) −1.41641 −0.129842
\(120\) −19.5623 −1.78579
\(121\) 10.3262 0.938749
\(122\) 7.85410 0.711077
\(123\) 29.2705 2.63923
\(124\) −20.1246 −1.80724
\(125\) −1.00000 −0.0894427
\(126\) −2.38197 −0.212202
\(127\) 2.70820 0.240314 0.120157 0.992755i \(-0.461660\pi\)
0.120157 + 0.992755i \(0.461660\pi\)
\(128\) −1.09017 −0.0963583
\(129\) 7.47214 0.657885
\(130\) −13.0902 −1.14808
\(131\) −1.14590 −0.100118 −0.0500588 0.998746i \(-0.515941\pi\)
−0.0500588 + 0.998746i \(0.515941\pi\)
\(132\) 58.6869 5.10804
\(133\) 0 0
\(134\) −12.3262 −1.06482
\(135\) 2.23607 0.192450
\(136\) 44.8328 3.84438
\(137\) −21.1803 −1.80956 −0.904779 0.425881i \(-0.859964\pi\)
−0.904779 + 0.425881i \(0.859964\pi\)
\(138\) −11.0902 −0.944058
\(139\) 14.8541 1.25991 0.629954 0.776632i \(-0.283074\pi\)
0.629954 + 0.776632i \(0.283074\pi\)
\(140\) −1.14590 −0.0968461
\(141\) 26.7984 2.25683
\(142\) 9.85410 0.826938
\(143\) 23.0902 1.93090
\(144\) 37.9787 3.16489
\(145\) −1.85410 −0.153975
\(146\) 2.61803 0.216670
\(147\) 18.1803 1.49949
\(148\) 9.00000 0.739795
\(149\) −5.38197 −0.440908 −0.220454 0.975397i \(-0.570754\pi\)
−0.220454 + 0.975397i \(0.570754\pi\)
\(150\) 6.85410 0.559635
\(151\) 9.61803 0.782705 0.391352 0.920241i \(-0.372007\pi\)
0.391352 + 0.920241i \(0.372007\pi\)
\(152\) 0 0
\(153\) −23.1246 −1.86951
\(154\) 2.85410 0.229990
\(155\) 4.14590 0.333007
\(156\) 63.5410 5.08735
\(157\) 5.03444 0.401792 0.200896 0.979613i \(-0.435615\pi\)
0.200896 + 0.979613i \(0.435615\pi\)
\(158\) 20.9443 1.66624
\(159\) 14.7082 1.16644
\(160\) 10.8541 0.858092
\(161\) −0.381966 −0.0301031
\(162\) 14.9443 1.17413
\(163\) 17.4721 1.36852 0.684262 0.729237i \(-0.260125\pi\)
0.684262 + 0.729237i \(0.260125\pi\)
\(164\) −54.2705 −4.23781
\(165\) −12.0902 −0.941218
\(166\) −11.7082 −0.908733
\(167\) −3.76393 −0.291262 −0.145631 0.989339i \(-0.546521\pi\)
−0.145631 + 0.989339i \(0.546521\pi\)
\(168\) 4.61803 0.356289
\(169\) 12.0000 0.923077
\(170\) −15.7082 −1.20476
\(171\) 0 0
\(172\) −13.8541 −1.05637
\(173\) 21.8885 1.66416 0.832078 0.554659i \(-0.187151\pi\)
0.832078 + 0.554659i \(0.187151\pi\)
\(174\) 12.7082 0.963406
\(175\) 0.236068 0.0178451
\(176\) −45.5066 −3.43019
\(177\) 0.236068 0.0177440
\(178\) −17.5623 −1.31635
\(179\) −19.4721 −1.45542 −0.727708 0.685887i \(-0.759414\pi\)
−0.727708 + 0.685887i \(0.759414\pi\)
\(180\) −18.7082 −1.39443
\(181\) −21.7082 −1.61356 −0.806779 0.590853i \(-0.798791\pi\)
−0.806779 + 0.590853i \(0.798791\pi\)
\(182\) 3.09017 0.229059
\(183\) 7.85410 0.580592
\(184\) 12.0902 0.891299
\(185\) −1.85410 −0.136316
\(186\) −28.4164 −2.08359
\(187\) 27.7082 2.02622
\(188\) −49.6869 −3.62379
\(189\) −0.527864 −0.0383965
\(190\) 0 0
\(191\) 23.9443 1.73255 0.866273 0.499570i \(-0.166509\pi\)
0.866273 + 0.499570i \(0.166509\pi\)
\(192\) −22.7984 −1.64533
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 15.9443 1.14473
\(195\) −13.0902 −0.937407
\(196\) −33.7082 −2.40773
\(197\) 25.4721 1.81481 0.907407 0.420252i \(-0.138058\pi\)
0.907407 + 0.420252i \(0.138058\pi\)
\(198\) 46.5967 3.31149
\(199\) −13.4164 −0.951064 −0.475532 0.879698i \(-0.657744\pi\)
−0.475532 + 0.879698i \(0.657744\pi\)
\(200\) −7.47214 −0.528360
\(201\) −12.3262 −0.869426
\(202\) 31.2705 2.20019
\(203\) 0.437694 0.0307201
\(204\) 76.2492 5.33851
\(205\) 11.1803 0.780869
\(206\) 45.3607 3.16043
\(207\) −6.23607 −0.433437
\(208\) −49.2705 −3.41630
\(209\) 0 0
\(210\) −1.61803 −0.111655
\(211\) 18.0902 1.24538 0.622689 0.782469i \(-0.286040\pi\)
0.622689 + 0.782469i \(0.286040\pi\)
\(212\) −27.2705 −1.87295
\(213\) 9.85410 0.675192
\(214\) 7.85410 0.536895
\(215\) 2.85410 0.194648
\(216\) 16.7082 1.13685
\(217\) −0.978714 −0.0664394
\(218\) 16.3262 1.10575
\(219\) 2.61803 0.176910
\(220\) 22.4164 1.51131
\(221\) 30.0000 2.01802
\(222\) 12.7082 0.852919
\(223\) −5.76393 −0.385981 −0.192991 0.981201i \(-0.561819\pi\)
−0.192991 + 0.981201i \(0.561819\pi\)
\(224\) −2.56231 −0.171201
\(225\) 3.85410 0.256940
\(226\) 7.70820 0.512742
\(227\) 13.6525 0.906147 0.453073 0.891473i \(-0.350328\pi\)
0.453073 + 0.891473i \(0.350328\pi\)
\(228\) 0 0
\(229\) −19.3820 −1.28080 −0.640398 0.768043i \(-0.721231\pi\)
−0.640398 + 0.768043i \(0.721231\pi\)
\(230\) −4.23607 −0.279318
\(231\) 2.85410 0.187786
\(232\) −13.8541 −0.909566
\(233\) −29.1803 −1.91167 −0.955834 0.293908i \(-0.905044\pi\)
−0.955834 + 0.293908i \(0.905044\pi\)
\(234\) 50.4508 3.29808
\(235\) 10.2361 0.667727
\(236\) −0.437694 −0.0284915
\(237\) 20.9443 1.36048
\(238\) 3.70820 0.240367
\(239\) 3.43769 0.222366 0.111183 0.993800i \(-0.464536\pi\)
0.111183 + 0.993800i \(0.464536\pi\)
\(240\) 25.7984 1.66528
\(241\) 22.1246 1.42517 0.712586 0.701585i \(-0.247524\pi\)
0.712586 + 0.701585i \(0.247524\pi\)
\(242\) −27.0344 −1.73784
\(243\) 21.6525 1.38901
\(244\) −14.5623 −0.932256
\(245\) 6.94427 0.443653
\(246\) −76.6312 −4.88583
\(247\) 0 0
\(248\) 30.9787 1.96715
\(249\) −11.7082 −0.741977
\(250\) 2.61803 0.165579
\(251\) −7.18034 −0.453219 −0.226610 0.973986i \(-0.572764\pi\)
−0.226610 + 0.973986i \(0.572764\pi\)
\(252\) 4.41641 0.278208
\(253\) 7.47214 0.469769
\(254\) −7.09017 −0.444877
\(255\) −15.7082 −0.983686
\(256\) −14.5623 −0.910144
\(257\) −22.4721 −1.40177 −0.700887 0.713273i \(-0.747212\pi\)
−0.700887 + 0.713273i \(0.747212\pi\)
\(258\) −19.5623 −1.21790
\(259\) 0.437694 0.0271970
\(260\) 24.2705 1.50519
\(261\) 7.14590 0.442320
\(262\) 3.00000 0.185341
\(263\) 15.8885 0.979730 0.489865 0.871798i \(-0.337046\pi\)
0.489865 + 0.871798i \(0.337046\pi\)
\(264\) −90.3394 −5.56001
\(265\) 5.61803 0.345113
\(266\) 0 0
\(267\) −17.5623 −1.07480
\(268\) 22.8541 1.39604
\(269\) −17.3262 −1.05640 −0.528200 0.849120i \(-0.677133\pi\)
−0.528200 + 0.849120i \(0.677133\pi\)
\(270\) −5.85410 −0.356269
\(271\) 18.6180 1.13097 0.565483 0.824760i \(-0.308690\pi\)
0.565483 + 0.824760i \(0.308690\pi\)
\(272\) −59.1246 −3.58496
\(273\) 3.09017 0.187026
\(274\) 55.4508 3.34991
\(275\) −4.61803 −0.278478
\(276\) 20.5623 1.23771
\(277\) 1.41641 0.0851037 0.0425519 0.999094i \(-0.486451\pi\)
0.0425519 + 0.999094i \(0.486451\pi\)
\(278\) −38.8885 −2.33238
\(279\) −15.9787 −0.956621
\(280\) 1.76393 0.105415
\(281\) 10.5066 0.626770 0.313385 0.949626i \(-0.398537\pi\)
0.313385 + 0.949626i \(0.398537\pi\)
\(282\) −70.1591 −4.17791
\(283\) 2.38197 0.141593 0.0707966 0.997491i \(-0.477446\pi\)
0.0707966 + 0.997491i \(0.477446\pi\)
\(284\) −18.2705 −1.08416
\(285\) 0 0
\(286\) −60.4508 −3.57453
\(287\) −2.63932 −0.155794
\(288\) −41.8328 −2.46502
\(289\) 19.0000 1.11765
\(290\) 4.85410 0.285043
\(291\) 15.9443 0.934670
\(292\) −4.85410 −0.284065
\(293\) 7.03444 0.410956 0.205478 0.978662i \(-0.434125\pi\)
0.205478 + 0.978662i \(0.434125\pi\)
\(294\) −47.5967 −2.77590
\(295\) 0.0901699 0.00524990
\(296\) −13.8541 −0.805253
\(297\) 10.3262 0.599189
\(298\) 14.0902 0.816222
\(299\) 8.09017 0.467867
\(300\) −12.7082 −0.733708
\(301\) −0.673762 −0.0388350
\(302\) −25.1803 −1.44897
\(303\) 31.2705 1.79644
\(304\) 0 0
\(305\) 3.00000 0.171780
\(306\) 60.5410 3.46090
\(307\) −21.2705 −1.21397 −0.606986 0.794712i \(-0.707622\pi\)
−0.606986 + 0.794712i \(0.707622\pi\)
\(308\) −5.29180 −0.301528
\(309\) 45.3607 2.58048
\(310\) −10.8541 −0.616472
\(311\) −24.9443 −1.41446 −0.707230 0.706984i \(-0.750055\pi\)
−0.707230 + 0.706984i \(0.750055\pi\)
\(312\) −97.8115 −5.53749
\(313\) 14.7984 0.836454 0.418227 0.908343i \(-0.362652\pi\)
0.418227 + 0.908343i \(0.362652\pi\)
\(314\) −13.1803 −0.743810
\(315\) −0.909830 −0.0512631
\(316\) −38.8328 −2.18452
\(317\) 8.76393 0.492231 0.246116 0.969240i \(-0.420846\pi\)
0.246116 + 0.969240i \(0.420846\pi\)
\(318\) −38.5066 −2.15934
\(319\) −8.56231 −0.479397
\(320\) −8.70820 −0.486803
\(321\) 7.85410 0.438373
\(322\) 1.00000 0.0557278
\(323\) 0 0
\(324\) −27.7082 −1.53934
\(325\) −5.00000 −0.277350
\(326\) −45.7426 −2.53345
\(327\) 16.3262 0.902843
\(328\) 83.5410 4.61278
\(329\) −2.41641 −0.133221
\(330\) 31.6525 1.74241
\(331\) 13.7082 0.753471 0.376736 0.926321i \(-0.377047\pi\)
0.376736 + 0.926321i \(0.377047\pi\)
\(332\) 21.7082 1.19139
\(333\) 7.14590 0.391593
\(334\) 9.85410 0.539192
\(335\) −4.70820 −0.257237
\(336\) −6.09017 −0.332246
\(337\) −28.0000 −1.52526 −0.762629 0.646837i \(-0.776092\pi\)
−0.762629 + 0.646837i \(0.776092\pi\)
\(338\) −31.4164 −1.70883
\(339\) 7.70820 0.418652
\(340\) 29.1246 1.57950
\(341\) 19.1459 1.03681
\(342\) 0 0
\(343\) −3.29180 −0.177740
\(344\) 21.3262 1.14983
\(345\) −4.23607 −0.228062
\(346\) −57.3050 −3.08073
\(347\) 15.8885 0.852942 0.426471 0.904501i \(-0.359757\pi\)
0.426471 + 0.904501i \(0.359757\pi\)
\(348\) −23.5623 −1.26307
\(349\) −20.7426 −1.11033 −0.555164 0.831741i \(-0.687345\pi\)
−0.555164 + 0.831741i \(0.687345\pi\)
\(350\) −0.618034 −0.0330353
\(351\) 11.1803 0.596762
\(352\) 50.1246 2.67165
\(353\) 33.1591 1.76488 0.882439 0.470427i \(-0.155900\pi\)
0.882439 + 0.470427i \(0.155900\pi\)
\(354\) −0.618034 −0.0328481
\(355\) 3.76393 0.199769
\(356\) 32.5623 1.72580
\(357\) 3.70820 0.196259
\(358\) 50.9787 2.69431
\(359\) 28.6180 1.51040 0.755201 0.655493i \(-0.227539\pi\)
0.755201 + 0.655493i \(0.227539\pi\)
\(360\) 28.7984 1.51781
\(361\) 0 0
\(362\) 56.8328 2.98707
\(363\) −27.0344 −1.41894
\(364\) −5.72949 −0.300307
\(365\) 1.00000 0.0523424
\(366\) −20.5623 −1.07481
\(367\) −29.6525 −1.54785 −0.773923 0.633279i \(-0.781708\pi\)
−0.773923 + 0.633279i \(0.781708\pi\)
\(368\) −15.9443 −0.831153
\(369\) −43.0902 −2.24318
\(370\) 4.85410 0.252353
\(371\) −1.32624 −0.0688548
\(372\) 52.6869 2.73169
\(373\) −6.70820 −0.347338 −0.173669 0.984804i \(-0.555562\pi\)
−0.173669 + 0.984804i \(0.555562\pi\)
\(374\) −72.5410 −3.75101
\(375\) 2.61803 0.135195
\(376\) 76.4853 3.94443
\(377\) −9.27051 −0.477456
\(378\) 1.38197 0.0710807
\(379\) −26.8328 −1.37831 −0.689155 0.724614i \(-0.742018\pi\)
−0.689155 + 0.724614i \(0.742018\pi\)
\(380\) 0 0
\(381\) −7.09017 −0.363240
\(382\) −62.6869 −3.20734
\(383\) 31.9230 1.63119 0.815594 0.578624i \(-0.196410\pi\)
0.815594 + 0.578624i \(0.196410\pi\)
\(384\) 2.85410 0.145648
\(385\) 1.09017 0.0555602
\(386\) 10.4721 0.533018
\(387\) −11.0000 −0.559161
\(388\) −29.5623 −1.50080
\(389\) −8.67376 −0.439777 −0.219889 0.975525i \(-0.570569\pi\)
−0.219889 + 0.975525i \(0.570569\pi\)
\(390\) 34.2705 1.73535
\(391\) 9.70820 0.490965
\(392\) 51.8885 2.62077
\(393\) 3.00000 0.151330
\(394\) −66.6869 −3.35964
\(395\) 8.00000 0.402524
\(396\) −86.3951 −4.34152
\(397\) 18.8885 0.947989 0.473994 0.880528i \(-0.342812\pi\)
0.473994 + 0.880528i \(0.342812\pi\)
\(398\) 35.1246 1.76064
\(399\) 0 0
\(400\) 9.85410 0.492705
\(401\) −11.2361 −0.561102 −0.280551 0.959839i \(-0.590517\pi\)
−0.280551 + 0.959839i \(0.590517\pi\)
\(402\) 32.2705 1.60951
\(403\) 20.7295 1.03261
\(404\) −57.9787 −2.88455
\(405\) 5.70820 0.283643
\(406\) −1.14590 −0.0568700
\(407\) −8.56231 −0.424418
\(408\) −117.374 −5.81087
\(409\) −11.7082 −0.578933 −0.289467 0.957188i \(-0.593478\pi\)
−0.289467 + 0.957188i \(0.593478\pi\)
\(410\) −29.2705 −1.44557
\(411\) 55.4508 2.73519
\(412\) −84.1033 −4.14347
\(413\) −0.0212862 −0.00104743
\(414\) 16.3262 0.802391
\(415\) −4.47214 −0.219529
\(416\) 54.2705 2.66083
\(417\) −38.8885 −1.90438
\(418\) 0 0
\(419\) 18.9443 0.925488 0.462744 0.886492i \(-0.346865\pi\)
0.462744 + 0.886492i \(0.346865\pi\)
\(420\) 3.00000 0.146385
\(421\) 14.1246 0.688391 0.344196 0.938898i \(-0.388152\pi\)
0.344196 + 0.938898i \(0.388152\pi\)
\(422\) −47.3607 −2.30548
\(423\) −39.4508 −1.91817
\(424\) 41.9787 2.03867
\(425\) −6.00000 −0.291043
\(426\) −25.7984 −1.24994
\(427\) −0.708204 −0.0342724
\(428\) −14.5623 −0.703896
\(429\) −60.4508 −2.91859
\(430\) −7.47214 −0.360338
\(431\) 2.81966 0.135818 0.0679091 0.997692i \(-0.478367\pi\)
0.0679091 + 0.997692i \(0.478367\pi\)
\(432\) −22.0344 −1.06013
\(433\) −22.2148 −1.06757 −0.533787 0.845619i \(-0.679232\pi\)
−0.533787 + 0.845619i \(0.679232\pi\)
\(434\) 2.56231 0.122995
\(435\) 4.85410 0.232736
\(436\) −30.2705 −1.44969
\(437\) 0 0
\(438\) −6.85410 −0.327502
\(439\) 5.47214 0.261171 0.130585 0.991437i \(-0.458314\pi\)
0.130585 + 0.991437i \(0.458314\pi\)
\(440\) −34.5066 −1.64504
\(441\) −26.7639 −1.27447
\(442\) −78.5410 −3.73582
\(443\) 15.3607 0.729808 0.364904 0.931045i \(-0.381102\pi\)
0.364904 + 0.931045i \(0.381102\pi\)
\(444\) −23.5623 −1.11822
\(445\) −6.70820 −0.317999
\(446\) 15.0902 0.714540
\(447\) 14.0902 0.666442
\(448\) 2.05573 0.0971240
\(449\) −32.5279 −1.53508 −0.767542 0.640998i \(-0.778521\pi\)
−0.767542 + 0.640998i \(0.778521\pi\)
\(450\) −10.0902 −0.475655
\(451\) 51.6312 2.43122
\(452\) −14.2918 −0.672230
\(453\) −25.1803 −1.18308
\(454\) −35.7426 −1.67749
\(455\) 1.18034 0.0553352
\(456\) 0 0
\(457\) −6.00000 −0.280668 −0.140334 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) 50.7426 2.37105
\(459\) 13.4164 0.626224
\(460\) 7.85410 0.366199
\(461\) −18.9443 −0.882323 −0.441161 0.897428i \(-0.645433\pi\)
−0.441161 + 0.897428i \(0.645433\pi\)
\(462\) −7.47214 −0.347635
\(463\) 3.96556 0.184295 0.0921476 0.995745i \(-0.470627\pi\)
0.0921476 + 0.995745i \(0.470627\pi\)
\(464\) 18.2705 0.848187
\(465\) −10.8541 −0.503347
\(466\) 76.3951 3.53894
\(467\) −11.2918 −0.522522 −0.261261 0.965268i \(-0.584138\pi\)
−0.261261 + 0.965268i \(0.584138\pi\)
\(468\) −93.5410 −4.32394
\(469\) 1.11146 0.0513223
\(470\) −26.7984 −1.23612
\(471\) −13.1803 −0.607318
\(472\) 0.673762 0.0310124
\(473\) 13.1803 0.606033
\(474\) −54.8328 −2.51855
\(475\) 0 0
\(476\) −6.87539 −0.315133
\(477\) −21.6525 −0.991399
\(478\) −9.00000 −0.411650
\(479\) −8.38197 −0.382982 −0.191491 0.981494i \(-0.561332\pi\)
−0.191491 + 0.981494i \(0.561332\pi\)
\(480\) −28.4164 −1.29703
\(481\) −9.27051 −0.422699
\(482\) −57.9230 −2.63832
\(483\) 1.00000 0.0455016
\(484\) 50.1246 2.27839
\(485\) 6.09017 0.276540
\(486\) −56.6869 −2.57137
\(487\) 8.58359 0.388960 0.194480 0.980907i \(-0.437698\pi\)
0.194480 + 0.980907i \(0.437698\pi\)
\(488\) 22.4164 1.01474
\(489\) −45.7426 −2.06855
\(490\) −18.1803 −0.821304
\(491\) 24.3262 1.09783 0.548914 0.835879i \(-0.315041\pi\)
0.548914 + 0.835879i \(0.315041\pi\)
\(492\) 142.082 6.40555
\(493\) −11.1246 −0.501027
\(494\) 0 0
\(495\) 17.7984 0.799977
\(496\) −40.8541 −1.83440
\(497\) −0.888544 −0.0398566
\(498\) 30.6525 1.37357
\(499\) −4.65248 −0.208273 −0.104137 0.994563i \(-0.533208\pi\)
−0.104137 + 0.994563i \(0.533208\pi\)
\(500\) −4.85410 −0.217082
\(501\) 9.85410 0.440249
\(502\) 18.7984 0.839012
\(503\) −19.9443 −0.889271 −0.444636 0.895712i \(-0.646667\pi\)
−0.444636 + 0.895712i \(0.646667\pi\)
\(504\) −6.79837 −0.302824
\(505\) 11.9443 0.531513
\(506\) −19.5623 −0.869651
\(507\) −31.4164 −1.39525
\(508\) 13.1459 0.583255
\(509\) 13.7984 0.611602 0.305801 0.952095i \(-0.401076\pi\)
0.305801 + 0.952095i \(0.401076\pi\)
\(510\) 41.1246 1.82103
\(511\) −0.236068 −0.0104430
\(512\) 40.3050 1.78124
\(513\) 0 0
\(514\) 58.8328 2.59500
\(515\) 17.3262 0.763485
\(516\) 36.2705 1.59672
\(517\) 47.2705 2.07895
\(518\) −1.14590 −0.0503479
\(519\) −57.3050 −2.51541
\(520\) −37.3607 −1.63837
\(521\) 2.61803 0.114698 0.0573491 0.998354i \(-0.481735\pi\)
0.0573491 + 0.998354i \(0.481735\pi\)
\(522\) −18.7082 −0.818836
\(523\) 38.5967 1.68772 0.843859 0.536565i \(-0.180278\pi\)
0.843859 + 0.536565i \(0.180278\pi\)
\(524\) −5.56231 −0.242990
\(525\) −0.618034 −0.0269732
\(526\) −41.5967 −1.81370
\(527\) 24.8754 1.08359
\(528\) 119.138 5.18481
\(529\) −20.3820 −0.886172
\(530\) −14.7082 −0.638884
\(531\) −0.347524 −0.0150813
\(532\) 0 0
\(533\) 55.9017 2.42137
\(534\) 45.9787 1.98969
\(535\) 3.00000 0.129701
\(536\) −35.1803 −1.51956
\(537\) 50.9787 2.19989
\(538\) 45.3607 1.95564
\(539\) 32.0689 1.38130
\(540\) 10.8541 0.467086
\(541\) −16.5967 −0.713550 −0.356775 0.934190i \(-0.616124\pi\)
−0.356775 + 0.934190i \(0.616124\pi\)
\(542\) −48.7426 −2.09368
\(543\) 56.8328 2.43893
\(544\) 65.1246 2.79219
\(545\) 6.23607 0.267124
\(546\) −8.09017 −0.346227
\(547\) 8.97871 0.383902 0.191951 0.981405i \(-0.438519\pi\)
0.191951 + 0.981405i \(0.438519\pi\)
\(548\) −102.812 −4.39189
\(549\) −11.5623 −0.493467
\(550\) 12.0902 0.515527
\(551\) 0 0
\(552\) −31.6525 −1.34722
\(553\) −1.88854 −0.0803091
\(554\) −3.70820 −0.157546
\(555\) 4.85410 0.206045
\(556\) 72.1033 3.05786
\(557\) −12.5279 −0.530823 −0.265411 0.964135i \(-0.585508\pi\)
−0.265411 + 0.964135i \(0.585508\pi\)
\(558\) 41.8328 1.77092
\(559\) 14.2705 0.603578
\(560\) −2.32624 −0.0983015
\(561\) −72.5410 −3.06268
\(562\) −27.5066 −1.16029
\(563\) 7.81966 0.329559 0.164780 0.986330i \(-0.447309\pi\)
0.164780 + 0.986330i \(0.447309\pi\)
\(564\) 130.082 5.47744
\(565\) 2.94427 0.123866
\(566\) −6.23607 −0.262121
\(567\) −1.34752 −0.0565907
\(568\) 28.1246 1.18008
\(569\) 20.5623 0.862017 0.431008 0.902348i \(-0.358158\pi\)
0.431008 + 0.902348i \(0.358158\pi\)
\(570\) 0 0
\(571\) 20.1459 0.843080 0.421540 0.906810i \(-0.361490\pi\)
0.421540 + 0.906810i \(0.361490\pi\)
\(572\) 112.082 4.68639
\(573\) −62.6869 −2.61878
\(574\) 6.90983 0.288411
\(575\) −1.61803 −0.0674767
\(576\) 33.5623 1.39843
\(577\) 24.2361 1.00896 0.504480 0.863423i \(-0.331684\pi\)
0.504480 + 0.863423i \(0.331684\pi\)
\(578\) −49.7426 −2.06902
\(579\) 10.4721 0.435207
\(580\) −9.00000 −0.373705
\(581\) 1.05573 0.0437990
\(582\) −41.7426 −1.73029
\(583\) 25.9443 1.07450
\(584\) 7.47214 0.309199
\(585\) 19.2705 0.796738
\(586\) −18.4164 −0.760775
\(587\) −37.7639 −1.55868 −0.779342 0.626599i \(-0.784447\pi\)
−0.779342 + 0.626599i \(0.784447\pi\)
\(588\) 88.2492 3.63934
\(589\) 0 0
\(590\) −0.236068 −0.00971876
\(591\) −66.6869 −2.74313
\(592\) 18.2705 0.750913
\(593\) 15.6525 0.642770 0.321385 0.946949i \(-0.395852\pi\)
0.321385 + 0.946949i \(0.395852\pi\)
\(594\) −27.0344 −1.10924
\(595\) 1.41641 0.0580671
\(596\) −26.1246 −1.07011
\(597\) 35.1246 1.43755
\(598\) −21.1803 −0.866129
\(599\) 37.3607 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(600\) 19.5623 0.798628
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 1.76393 0.0718925
\(603\) 18.1459 0.738958
\(604\) 46.6869 1.89966
\(605\) −10.3262 −0.419821
\(606\) −81.8673 −3.32563
\(607\) −3.56231 −0.144590 −0.0722948 0.997383i \(-0.523032\pi\)
−0.0722948 + 0.997383i \(0.523032\pi\)
\(608\) 0 0
\(609\) −1.14590 −0.0464341
\(610\) −7.85410 −0.318003
\(611\) 51.1803 2.07053
\(612\) −112.249 −4.53741
\(613\) 21.9443 0.886321 0.443160 0.896442i \(-0.353857\pi\)
0.443160 + 0.896442i \(0.353857\pi\)
\(614\) 55.6869 2.24734
\(615\) −29.2705 −1.18030
\(616\) 8.14590 0.328208
\(617\) −24.0902 −0.969834 −0.484917 0.874560i \(-0.661150\pi\)
−0.484917 + 0.874560i \(0.661150\pi\)
\(618\) −118.756 −4.77706
\(619\) −25.9443 −1.04279 −0.521394 0.853316i \(-0.674588\pi\)
−0.521394 + 0.853316i \(0.674588\pi\)
\(620\) 20.1246 0.808224
\(621\) 3.61803 0.145187
\(622\) 65.3050 2.61849
\(623\) 1.58359 0.0634453
\(624\) 128.992 5.16381
\(625\) 1.00000 0.0400000
\(626\) −38.7426 −1.54847
\(627\) 0 0
\(628\) 24.4377 0.975170
\(629\) −11.1246 −0.443567
\(630\) 2.38197 0.0948998
\(631\) 15.0000 0.597141 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 59.7771 2.37780
\(633\) −47.3607 −1.88242
\(634\) −22.9443 −0.911233
\(635\) −2.70820 −0.107472
\(636\) 71.3951 2.83100
\(637\) 34.7214 1.37571
\(638\) 22.4164 0.887474
\(639\) −14.5066 −0.573871
\(640\) 1.09017 0.0430928
\(641\) −39.2705 −1.55109 −0.775546 0.631291i \(-0.782525\pi\)
−0.775546 + 0.631291i \(0.782525\pi\)
\(642\) −20.5623 −0.811529
\(643\) −17.5967 −0.693948 −0.346974 0.937875i \(-0.612791\pi\)
−0.346974 + 0.937875i \(0.612791\pi\)
\(644\) −1.85410 −0.0730619
\(645\) −7.47214 −0.294215
\(646\) 0 0
\(647\) −26.3050 −1.03415 −0.517077 0.855939i \(-0.672980\pi\)
−0.517077 + 0.855939i \(0.672980\pi\)
\(648\) 42.6525 1.67555
\(649\) 0.416408 0.0163454
\(650\) 13.0902 0.513439
\(651\) 2.56231 0.100425
\(652\) 84.8115 3.32148
\(653\) 1.14590 0.0448425 0.0224212 0.999749i \(-0.492863\pi\)
0.0224212 + 0.999749i \(0.492863\pi\)
\(654\) −42.7426 −1.67137
\(655\) 1.14590 0.0447739
\(656\) −110.172 −4.30150
\(657\) −3.85410 −0.150363
\(658\) 6.32624 0.246622
\(659\) −33.5279 −1.30606 −0.653030 0.757332i \(-0.726502\pi\)
−0.653030 + 0.757332i \(0.726502\pi\)
\(660\) −58.6869 −2.28439
\(661\) −9.70820 −0.377605 −0.188803 0.982015i \(-0.560461\pi\)
−0.188803 + 0.982015i \(0.560461\pi\)
\(662\) −35.8885 −1.39485
\(663\) −78.5410 −3.05028
\(664\) −33.4164 −1.29681
\(665\) 0 0
\(666\) −18.7082 −0.724928
\(667\) −3.00000 −0.116160
\(668\) −18.2705 −0.706907
\(669\) 15.0902 0.583420
\(670\) 12.3262 0.476204
\(671\) 13.8541 0.534832
\(672\) 6.70820 0.258775
\(673\) 46.8885 1.80742 0.903710 0.428145i \(-0.140833\pi\)
0.903710 + 0.428145i \(0.140833\pi\)
\(674\) 73.3050 2.82360
\(675\) −2.23607 −0.0860663
\(676\) 58.2492 2.24035
\(677\) 10.6180 0.408084 0.204042 0.978962i \(-0.434592\pi\)
0.204042 + 0.978962i \(0.434592\pi\)
\(678\) −20.1803 −0.775021
\(679\) −1.43769 −0.0551736
\(680\) −44.8328 −1.71926
\(681\) −35.7426 −1.36966
\(682\) −50.1246 −1.91937
\(683\) −14.5279 −0.555893 −0.277947 0.960597i \(-0.589654\pi\)
−0.277947 + 0.960597i \(0.589654\pi\)
\(684\) 0 0
\(685\) 21.1803 0.809259
\(686\) 8.61803 0.329038
\(687\) 50.7426 1.93595
\(688\) −28.1246 −1.07224
\(689\) 28.0902 1.07015
\(690\) 11.0902 0.422196
\(691\) 12.5279 0.476582 0.238291 0.971194i \(-0.423413\pi\)
0.238291 + 0.971194i \(0.423413\pi\)
\(692\) 106.249 4.03899
\(693\) −4.20163 −0.159607
\(694\) −41.5967 −1.57899
\(695\) −14.8541 −0.563448
\(696\) 36.2705 1.37483
\(697\) 67.0820 2.54091
\(698\) 54.3050 2.05547
\(699\) 76.3951 2.88953
\(700\) 1.14590 0.0433109
\(701\) −47.5755 −1.79690 −0.898450 0.439075i \(-0.855306\pi\)
−0.898450 + 0.439075i \(0.855306\pi\)
\(702\) −29.2705 −1.10474
\(703\) 0 0
\(704\) −40.2148 −1.51565
\(705\) −26.7984 −1.00929
\(706\) −86.8115 −3.26720
\(707\) −2.81966 −0.106044
\(708\) 1.14590 0.0430655
\(709\) −2.29180 −0.0860702 −0.0430351 0.999074i \(-0.513703\pi\)
−0.0430351 + 0.999074i \(0.513703\pi\)
\(710\) −9.85410 −0.369818
\(711\) −30.8328 −1.15632
\(712\) −50.1246 −1.87850
\(713\) 6.70820 0.251224
\(714\) −9.70820 −0.363320
\(715\) −23.0902 −0.863523
\(716\) −94.5197 −3.53237
\(717\) −9.00000 −0.336111
\(718\) −74.9230 −2.79610
\(719\) 36.7984 1.37235 0.686174 0.727438i \(-0.259289\pi\)
0.686174 + 0.727438i \(0.259289\pi\)
\(720\) −37.9787 −1.41538
\(721\) −4.09017 −0.152326
\(722\) 0 0
\(723\) −57.9230 −2.15418
\(724\) −105.374 −3.91619
\(725\) 1.85410 0.0688596
\(726\) 70.7771 2.62678
\(727\) −37.4164 −1.38770 −0.693849 0.720121i \(-0.744086\pi\)
−0.693849 + 0.720121i \(0.744086\pi\)
\(728\) 8.81966 0.326878
\(729\) −39.5623 −1.46527
\(730\) −2.61803 −0.0968978
\(731\) 17.1246 0.633377
\(732\) 38.1246 1.40913
\(733\) −4.23607 −0.156463 −0.0782314 0.996935i \(-0.524927\pi\)
−0.0782314 + 0.996935i \(0.524927\pi\)
\(734\) 77.6312 2.86542
\(735\) −18.1803 −0.670592
\(736\) 17.5623 0.647355
\(737\) −21.7426 −0.800901
\(738\) 112.812 4.15265
\(739\) 31.8328 1.17099 0.585495 0.810676i \(-0.300900\pi\)
0.585495 + 0.810676i \(0.300900\pi\)
\(740\) −9.00000 −0.330847
\(741\) 0 0
\(742\) 3.47214 0.127466
\(743\) −31.7639 −1.16531 −0.582653 0.812721i \(-0.697985\pi\)
−0.582653 + 0.812721i \(0.697985\pi\)
\(744\) −81.1033 −2.97339
\(745\) 5.38197 0.197180
\(746\) 17.5623 0.643002
\(747\) 17.2361 0.630635
\(748\) 134.498 4.91775
\(749\) −0.708204 −0.0258772
\(750\) −6.85410 −0.250276
\(751\) −17.5623 −0.640858 −0.320429 0.947273i \(-0.603827\pi\)
−0.320429 + 0.947273i \(0.603827\pi\)
\(752\) −100.867 −3.67825
\(753\) 18.7984 0.685051
\(754\) 24.2705 0.883880
\(755\) −9.61803 −0.350036
\(756\) −2.56231 −0.0931902
\(757\) −16.6180 −0.603993 −0.301996 0.953309i \(-0.597653\pi\)
−0.301996 + 0.953309i \(0.597653\pi\)
\(758\) 70.2492 2.55157
\(759\) −19.5623 −0.710067
\(760\) 0 0
\(761\) −7.36068 −0.266824 −0.133412 0.991061i \(-0.542593\pi\)
−0.133412 + 0.991061i \(0.542593\pi\)
\(762\) 18.5623 0.672441
\(763\) −1.47214 −0.0532949
\(764\) 116.228 4.20498
\(765\) 23.1246 0.836072
\(766\) −83.5755 −3.01970
\(767\) 0.450850 0.0162792
\(768\) 38.1246 1.37570
\(769\) −46.6869 −1.68357 −0.841787 0.539810i \(-0.818496\pi\)
−0.841787 + 0.539810i \(0.818496\pi\)
\(770\) −2.85410 −0.102855
\(771\) 58.8328 2.11881
\(772\) −19.4164 −0.698812
\(773\) −2.74265 −0.0986461 −0.0493231 0.998783i \(-0.515706\pi\)
−0.0493231 + 0.998783i \(0.515706\pi\)
\(774\) 28.7984 1.03514
\(775\) −4.14590 −0.148925
\(776\) 45.5066 1.63359
\(777\) −1.14590 −0.0411089
\(778\) 22.7082 0.814129
\(779\) 0 0
\(780\) −63.5410 −2.27513
\(781\) 17.3820 0.621976
\(782\) −25.4164 −0.908889
\(783\) −4.14590 −0.148162
\(784\) −68.4296 −2.44391
\(785\) −5.03444 −0.179687
\(786\) −7.85410 −0.280147
\(787\) −49.4853 −1.76396 −0.881980 0.471287i \(-0.843790\pi\)
−0.881980 + 0.471287i \(0.843790\pi\)
\(788\) 123.644 4.40465
\(789\) −41.5967 −1.48088
\(790\) −20.9443 −0.745164
\(791\) −0.695048 −0.0247131
\(792\) 132.992 4.72566
\(793\) 15.0000 0.532666
\(794\) −49.4508 −1.75494
\(795\) −14.7082 −0.521646
\(796\) −65.1246 −2.30828
\(797\) −20.1803 −0.714824 −0.357412 0.933947i \(-0.616341\pi\)
−0.357412 + 0.933947i \(0.616341\pi\)
\(798\) 0 0
\(799\) 61.4164 2.17276
\(800\) −10.8541 −0.383750
\(801\) 25.8541 0.913510
\(802\) 29.4164 1.03873
\(803\) 4.61803 0.162967
\(804\) −59.8328 −2.11014
\(805\) 0.381966 0.0134625
\(806\) −54.2705 −1.91160
\(807\) 45.3607 1.59677
\(808\) 89.2492 3.13978
\(809\) 40.0902 1.40950 0.704748 0.709458i \(-0.251060\pi\)
0.704748 + 0.709458i \(0.251060\pi\)
\(810\) −14.9443 −0.525088
\(811\) −24.6738 −0.866413 −0.433206 0.901295i \(-0.642618\pi\)
−0.433206 + 0.901295i \(0.642618\pi\)
\(812\) 2.12461 0.0745593
\(813\) −48.7426 −1.70948
\(814\) 22.4164 0.785695
\(815\) −17.4721 −0.612022
\(816\) 154.790 5.41874
\(817\) 0 0
\(818\) 30.6525 1.07174
\(819\) −4.54915 −0.158960
\(820\) 54.2705 1.89521
\(821\) 14.6180 0.510173 0.255086 0.966918i \(-0.417896\pi\)
0.255086 + 0.966918i \(0.417896\pi\)
\(822\) −145.172 −5.06346
\(823\) −36.3607 −1.26745 −0.633727 0.773557i \(-0.718476\pi\)
−0.633727 + 0.773557i \(0.718476\pi\)
\(824\) 129.464 4.51009
\(825\) 12.0902 0.420926
\(826\) 0.0557281 0.00193903
\(827\) −17.8328 −0.620108 −0.310054 0.950719i \(-0.600347\pi\)
−0.310054 + 0.950719i \(0.600347\pi\)
\(828\) −30.2705 −1.05197
\(829\) 30.3951 1.05567 0.527833 0.849348i \(-0.323005\pi\)
0.527833 + 0.849348i \(0.323005\pi\)
\(830\) 11.7082 0.406398
\(831\) −3.70820 −0.128636
\(832\) −43.5410 −1.50951
\(833\) 41.6656 1.44363
\(834\) 101.812 3.52544
\(835\) 3.76393 0.130256
\(836\) 0 0
\(837\) 9.27051 0.320436
\(838\) −49.5967 −1.71329
\(839\) 15.6180 0.539194 0.269597 0.962973i \(-0.413109\pi\)
0.269597 + 0.962973i \(0.413109\pi\)
\(840\) −4.61803 −0.159337
\(841\) −25.5623 −0.881459
\(842\) −36.9787 −1.27437
\(843\) −27.5066 −0.947377
\(844\) 87.8115 3.02260
\(845\) −12.0000 −0.412813
\(846\) 103.284 3.55097
\(847\) 2.43769 0.0837602
\(848\) −55.3607 −1.90109
\(849\) −6.23607 −0.214021
\(850\) 15.7082 0.538787
\(851\) −3.00000 −0.102839
\(852\) 47.8328 1.63873
\(853\) −40.9574 −1.40236 −0.701178 0.712986i \(-0.747342\pi\)
−0.701178 + 0.712986i \(0.747342\pi\)
\(854\) 1.85410 0.0634461
\(855\) 0 0
\(856\) 22.4164 0.766177
\(857\) 30.3820 1.03783 0.518914 0.854826i \(-0.326336\pi\)
0.518914 + 0.854826i \(0.326336\pi\)
\(858\) 158.262 5.40299
\(859\) −35.5967 −1.21455 −0.607273 0.794493i \(-0.707736\pi\)
−0.607273 + 0.794493i \(0.707736\pi\)
\(860\) 13.8541 0.472421
\(861\) 6.90983 0.235486
\(862\) −7.38197 −0.251431
\(863\) −26.6525 −0.907261 −0.453630 0.891190i \(-0.649871\pi\)
−0.453630 + 0.891190i \(0.649871\pi\)
\(864\) 24.2705 0.825700
\(865\) −21.8885 −0.744233
\(866\) 58.1591 1.97633
\(867\) −49.7426 −1.68935
\(868\) −4.75078 −0.161252
\(869\) 36.9443 1.25325
\(870\) −12.7082 −0.430848
\(871\) −23.5410 −0.797657
\(872\) 46.5967 1.57796
\(873\) −23.4721 −0.794411
\(874\) 0 0
\(875\) −0.236068 −0.00798055
\(876\) 12.7082 0.429370
\(877\) 30.1803 1.01912 0.509559 0.860436i \(-0.329809\pi\)
0.509559 + 0.860436i \(0.329809\pi\)
\(878\) −14.3262 −0.483487
\(879\) −18.4164 −0.621170
\(880\) 45.5066 1.53403
\(881\) −4.03444 −0.135924 −0.0679619 0.997688i \(-0.521650\pi\)
−0.0679619 + 0.997688i \(0.521650\pi\)
\(882\) 70.0689 2.35934
\(883\) −17.9230 −0.603156 −0.301578 0.953441i \(-0.597513\pi\)
−0.301578 + 0.953441i \(0.597513\pi\)
\(884\) 145.623 4.89783
\(885\) −0.236068 −0.00793534
\(886\) −40.2148 −1.35104
\(887\) −3.52786 −0.118454 −0.0592270 0.998245i \(-0.518864\pi\)
−0.0592270 + 0.998245i \(0.518864\pi\)
\(888\) 36.2705 1.21716
\(889\) 0.639320 0.0214421
\(890\) 17.5623 0.588690
\(891\) 26.3607 0.883116
\(892\) −27.9787 −0.936797
\(893\) 0 0
\(894\) −36.8885 −1.23374
\(895\) 19.4721 0.650882
\(896\) −0.257354 −0.00859760
\(897\) −21.1803 −0.707191
\(898\) 85.1591 2.84179
\(899\) −7.68692 −0.256373
\(900\) 18.7082 0.623607
\(901\) 33.7082 1.12298
\(902\) −135.172 −4.50074
\(903\) 1.76393 0.0587000
\(904\) 22.0000 0.731709
\(905\) 21.7082 0.721605
\(906\) 65.9230 2.19014
\(907\) −48.2492 −1.60209 −0.801045 0.598605i \(-0.795722\pi\)
−0.801045 + 0.598605i \(0.795722\pi\)
\(908\) 66.2705 2.19926
\(909\) −46.0344 −1.52687
\(910\) −3.09017 −0.102438
\(911\) 51.1033 1.69313 0.846564 0.532286i \(-0.178667\pi\)
0.846564 + 0.532286i \(0.178667\pi\)
\(912\) 0 0
\(913\) −20.6525 −0.683497
\(914\) 15.7082 0.519581
\(915\) −7.85410 −0.259649
\(916\) −94.0820 −3.10856
\(917\) −0.270510 −0.00893302
\(918\) −35.1246 −1.15928
\(919\) −12.8885 −0.425154 −0.212577 0.977144i \(-0.568186\pi\)
−0.212577 + 0.977144i \(0.568186\pi\)
\(920\) −12.0902 −0.398601
\(921\) 55.6869 1.83495
\(922\) 49.5967 1.63338
\(923\) 18.8197 0.619457
\(924\) 13.8541 0.455766
\(925\) 1.85410 0.0609625
\(926\) −10.3820 −0.341173
\(927\) −66.7771 −2.19325
\(928\) −20.1246 −0.660623
\(929\) 9.38197 0.307812 0.153906 0.988085i \(-0.450815\pi\)
0.153906 + 0.988085i \(0.450815\pi\)
\(930\) 28.4164 0.931811
\(931\) 0 0
\(932\) −141.644 −4.63971
\(933\) 65.3050 2.13799
\(934\) 29.5623 0.967308
\(935\) −27.7082 −0.906155
\(936\) 143.992 4.70652
\(937\) −17.5623 −0.573736 −0.286868 0.957970i \(-0.592614\pi\)
−0.286868 + 0.957970i \(0.592614\pi\)
\(938\) −2.90983 −0.0950093
\(939\) −38.7426 −1.26432
\(940\) 49.6869 1.62061
\(941\) 27.5066 0.896689 0.448344 0.893861i \(-0.352014\pi\)
0.448344 + 0.893861i \(0.352014\pi\)
\(942\) 34.5066 1.12429
\(943\) 18.0902 0.589097
\(944\) −0.888544 −0.0289196
\(945\) 0.527864 0.0171714
\(946\) −34.5066 −1.12191
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) 101.666 3.30195
\(949\) 5.00000 0.162307
\(950\) 0 0
\(951\) −22.9443 −0.744019
\(952\) 10.5836 0.343016
\(953\) −41.8328 −1.35510 −0.677549 0.735478i \(-0.736958\pi\)
−0.677549 + 0.735478i \(0.736958\pi\)
\(954\) 56.6869 1.83531
\(955\) −23.9443 −0.774818
\(956\) 16.6869 0.539693
\(957\) 22.4164 0.724620
\(958\) 21.9443 0.708987
\(959\) −5.00000 −0.161458
\(960\) 22.7984 0.735814
\(961\) −13.8115 −0.445533
\(962\) 24.2705 0.782513
\(963\) −11.5623 −0.372590
\(964\) 107.395 3.45896
\(965\) 4.00000 0.128765
\(966\) −2.61803 −0.0842339
\(967\) 33.2361 1.06880 0.534400 0.845232i \(-0.320538\pi\)
0.534400 + 0.845232i \(0.320538\pi\)
\(968\) −77.1591 −2.47999
\(969\) 0 0
\(970\) −15.9443 −0.511940
\(971\) 13.2016 0.423660 0.211830 0.977306i \(-0.432058\pi\)
0.211830 + 0.977306i \(0.432058\pi\)
\(972\) 105.103 3.37119
\(973\) 3.50658 0.112416
\(974\) −22.4721 −0.720054
\(975\) 13.0902 0.419221
\(976\) −29.5623 −0.946266
\(977\) −22.3475 −0.714961 −0.357480 0.933921i \(-0.616364\pi\)
−0.357480 + 0.933921i \(0.616364\pi\)
\(978\) 119.756 3.82937
\(979\) −30.9787 −0.990084
\(980\) 33.7082 1.07677
\(981\) −24.0344 −0.767361
\(982\) −63.6869 −2.03233
\(983\) −7.14590 −0.227919 −0.113959 0.993485i \(-0.536353\pi\)
−0.113959 + 0.993485i \(0.536353\pi\)
\(984\) −218.713 −6.97232
\(985\) −25.4721 −0.811610
\(986\) 29.1246 0.927517
\(987\) 6.32624 0.201366
\(988\) 0 0
\(989\) 4.61803 0.146845
\(990\) −46.5967 −1.48094
\(991\) −24.8541 −0.789517 −0.394758 0.918785i \(-0.629172\pi\)
−0.394758 + 0.918785i \(0.629172\pi\)
\(992\) 45.0000 1.42875
\(993\) −35.8885 −1.13889
\(994\) 2.32624 0.0737838
\(995\) 13.4164 0.425329
\(996\) −56.8328 −1.80082
\(997\) 1.23607 0.0391467 0.0195733 0.999808i \(-0.493769\pi\)
0.0195733 + 0.999808i \(0.493769\pi\)
\(998\) 12.1803 0.385562
\(999\) −4.14590 −0.131170
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 1805.2.a.c.1.1 2
5.4 even 2 9025.2.a.v.1.2 2
19.18 odd 2 1805.2.a.e.1.2 yes 2
95.94 odd 2 9025.2.a.k.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.c.1.1 2 1.1 even 1 trivial
1805.2.a.e.1.2 yes 2 19.18 odd 2
9025.2.a.k.1.1 2 95.94 odd 2
9025.2.a.v.1.2 2 5.4 even 2