Properties

Label 1805.2.a.e.1.2
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $0$
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: \(0\)
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 1.2
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 \(-0.123549\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 2.61803 1.51152 0.755761 0.654847i \(-0.227267\pi\)
0.755761 + 0.654847i \(0.227267\pi\)
\(4\) 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 \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 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 \(-0.555071\pi\)
−0.172149 + 0.985071i \(0.555071\pi\)
\(30\) −6.85410 −1.25138
\(31\) 4.14590 0.744625 0.372313 0.928107i \(-0.378565\pi\)
0.372313 + 0.928107i \(0.378565\pi\)
\(32\) 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 \(-0.548702\pi\)
−0.152406 + 0.988318i \(0.548702\pi\)
\(38\) 0 0
\(39\) 13.0902 2.09610
\(40\) −7.47214 −1.18145
\(41\) 11.1803 1.74608 0.873038 0.487652i \(-0.162147\pi\)
0.873038 + 0.487652i \(0.162147\pi\)
\(42\) 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 \(-0.373909\pi\)
0.385848 + 0.922562i \(0.373909\pi\)
\(54\) 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 \(-0.498132\pi\)
0.00586956 + 0.999983i \(0.498132\pi\)
\(60\) −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 \(-0.592857\pi\)
−0.287599 + 0.957751i \(0.592857\pi\)
\(68\) −29.1246 −3.53188
\(69\) −4.23607 −0.509963
\(70\) −0.618034 −0.0738692
\(71\) 3.76393 0.446697 0.223348 0.974739i \(-0.428301\pi\)
0.223348 + 0.974739i \(0.428301\pi\)
\(72\) 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 \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −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 \(-0.615701\pi\)
−0.355534 + 0.934663i \(0.615701\pi\)
\(90\) −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 \(-0.399945\pi\)
0.309182 + 0.951003i \(0.399945\pi\)
\(98\) −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 \(-0.174413\pi\)
0.853602 + 0.520925i \(0.174413\pi\)
\(104\) 37.3607 3.66352
\(105\) −0.618034 −0.0603139
\(106\) 14.7082 1.42859
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 10.8541 1.04444
\(109\) 6.23607 0.597307 0.298653 0.954362i \(-0.403463\pi\)
0.298653 + 0.954362i \(0.403463\pi\)
\(110\) 12.0902 1.15275
\(111\) −4.85410 −0.460731
\(112\) 2.32624 0.219809
\(113\) 2.94427 0.276974 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(114\) 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 \(-0.538340\pi\)
−0.120157 + 0.992755i \(0.538340\pi\)
\(128\) 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 \(-0.627993\pi\)
−0.391352 + 0.920241i \(0.627993\pi\)
\(152\) 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 \(-0.453479\pi\)
0.145631 + 0.989339i \(0.453479\pi\)
\(168\) 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 \(-0.812849\pi\)
−0.832078 + 0.554659i \(0.812849\pi\)
\(174\) −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 \(-0.240586\pi\)
0.727708 + 0.685887i \(0.240586\pi\)
\(180\) −18.7082 −1.39443
\(181\) 21.7082 1.61356 0.806779 0.590853i \(-0.201209\pi\)
0.806779 + 0.590853i \(0.201209\pi\)
\(182\) 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 \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 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 \(-0.713960\pi\)
−0.622689 + 0.782469i \(0.713960\pi\)
\(212\) 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 \(-0.438181\pi\)
0.192991 + 0.981201i \(0.438181\pi\)
\(224\) 2.56231 0.171201
\(225\) 3.85410 0.256940
\(226\) 7.70820 0.512742
\(227\) −13.6525 −0.906147 −0.453073 0.891473i \(-0.649672\pi\)
−0.453073 + 0.891473i \(0.649672\pi\)
\(228\) 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 \(-0.752476\pi\)
−0.712586 + 0.701585i \(0.752476\pi\)
\(242\) 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 \(-0.252788\pi\)
0.700887 + 0.713273i \(0.252788\pi\)
\(258\) −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 \(-0.322867\pi\)
0.528200 + 0.849120i \(0.322867\pi\)
\(270\) −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 \(-0.601463\pi\)
−0.313385 + 0.949626i \(0.601463\pi\)
\(282\) −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 \(-0.565875\pi\)
−0.205478 + 0.978662i \(0.565875\pi\)
\(294\) −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 \(-0.292378\pi\)
0.606986 + 0.794712i \(0.292378\pi\)
\(308\) −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 \(-0.579154\pi\)
−0.246116 + 0.969240i \(0.579154\pi\)
\(318\) 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 \(-0.622953\pi\)
−0.376736 + 0.926321i \(0.622953\pi\)
\(332\) 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 \(-0.223908\pi\)
0.762629 + 0.646837i \(0.223908\pi\)
\(338\) 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 \(-0.444438\pi\)
0.173669 + 0.984804i \(0.444438\pi\)
\(374\) 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 \(-0.257982\pi\)
0.689155 + 0.724614i \(0.257982\pi\)
\(380\) 0 0
\(381\) −7.09017 −0.363240
\(382\) 62.6869 3.20734
\(383\) −31.9230 −1.63119 −0.815594 0.578624i \(-0.803590\pi\)
−0.815594 + 0.578624i \(0.803590\pi\)
\(384\) 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 \(-0.409483\pi\)
0.280551 + 0.959839i \(0.409483\pi\)
\(402\) −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 \(-0.406522\pi\)
0.289467 + 0.957188i \(0.406522\pi\)
\(410\) −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 \(-0.611848\pi\)
−0.344196 + 0.938898i \(0.611848\pi\)
\(422\) −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 \(-0.521633\pi\)
−0.0679091 + 0.997692i \(0.521633\pi\)
\(432\) 22.0344 1.06013
\(433\) 22.2148 1.06757 0.533787 0.845619i \(-0.320768\pi\)
0.533787 + 0.845619i \(0.320768\pi\)
\(434\) 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 \(-0.541686\pi\)
−0.130585 + 0.991437i \(0.541686\pi\)
\(440\) 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 \(-0.221479\pi\)
0.767542 + 0.640998i \(0.221479\pi\)
\(450\) 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 \(-0.562302\pi\)
−0.194480 + 0.980907i \(0.562302\pi\)
\(488\) −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 \(-0.598924\pi\)
−0.305801 + 0.952095i \(0.598924\pi\)
\(510\) 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 \(-0.518265\pi\)
−0.0573491 + 0.998354i \(0.518265\pi\)
\(522\) −18.7082 −0.818836
\(523\) −38.5967 −1.68772 −0.843859 0.536565i \(-0.819722\pi\)
−0.843859 + 0.536565i \(0.819722\pi\)
\(524\) −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 \(-0.561481\pi\)
−0.191951 + 0.981405i \(0.561481\pi\)
\(548\) −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 \(-0.552691\pi\)
−0.164780 + 0.986330i \(0.552691\pi\)
\(564\) −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 \(-0.641842\pi\)
−0.431008 + 0.902348i \(0.641842\pi\)
\(570\) 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 \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(600\) 19.5623 0.798628
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −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 \(-0.476968\pi\)
0.0722948 + 0.997383i \(0.476968\pi\)
\(608\) 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 \(-0.217475\pi\)
0.775546 + 0.631291i \(0.217475\pi\)
\(642\) 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 \(-0.273498\pi\)
0.653030 + 0.757332i \(0.273498\pi\)
\(660\) 58.6869 2.28439
\(661\) 9.70820 0.377605 0.188803 0.982015i \(-0.439539\pi\)
0.188803 + 0.982015i \(0.439539\pi\)
\(662\) −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 \(-0.859167\pi\)
−0.903710 + 0.428145i \(0.859167\pi\)
\(674\) 73.3050 2.82360
\(675\) 2.23607 0.0860663
\(676\) 58.2492 2.24035
\(677\) −10.6180 −0.408084 −0.204042 0.978962i \(-0.565408\pi\)
−0.204042 + 0.978962i \(0.565408\pi\)
\(678\) 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 \(-0.410346\pi\)
0.277947 + 0.960597i \(0.410346\pi\)
\(684\) 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 \(-0.302015\pi\)
0.582653 + 0.812721i \(0.302015\pi\)
\(744\) 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 \(-0.396173\pi\)
0.320429 + 0.947273i \(0.396173\pi\)
\(752\) −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 \(-0.484294\pi\)
0.0493231 + 0.998783i \(0.484294\pi\)
\(774\) −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 \(-0.156210\pi\)
0.881980 + 0.471287i \(0.156210\pi\)
\(788\) 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 \(-0.383659\pi\)
0.357412 + 0.933947i \(0.383659\pi\)
\(798\) 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 \(-0.357382\pi\)
0.433206 + 0.901295i \(0.357382\pi\)
\(812\) −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 \(-0.399653\pi\)
0.310054 + 0.950719i \(0.399653\pi\)
\(828\) −30.2705 −1.05197
\(829\) −30.3951 −1.05567 −0.527833 0.849348i \(-0.676995\pi\)
−0.527833 + 0.849348i \(0.676995\pi\)
\(830\) −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 \(-0.586891\pi\)
−0.269597 + 0.962973i \(0.586891\pi\)
\(840\) −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 \(-0.673664\pi\)
−0.518914 + 0.854826i \(0.673664\pi\)
\(858\) −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 \(-0.350129\pi\)
0.453630 + 0.891190i \(0.350129\pi\)
\(864\) 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 \(-0.670191\pi\)
−0.509559 + 0.860436i \(0.670191\pi\)
\(878\) −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 \(-0.481136\pi\)
0.0592270 + 0.998245i \(0.481136\pi\)
\(888\) −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 \(-0.204278\pi\)
0.801045 + 0.598605i \(0.204278\pi\)
\(908\) −66.2705 −2.19926
\(909\) −46.0344 −1.52687
\(910\) −3.09017 −0.102438
\(911\) −51.1033 −1.69313 −0.846564 0.532286i \(-0.821333\pi\)
−0.846564 + 0.532286i \(0.821333\pi\)
\(912\) 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 \(-0.647986\pi\)
−0.448344 + 0.893861i \(0.647986\pi\)
\(942\) 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 \(-0.263042\pi\)
0.677549 + 0.735478i \(0.263042\pi\)
\(954\) 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 \(-0.567942\pi\)
−0.211830 + 0.977306i \(0.567942\pi\)
\(972\) −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 \(-0.383636\pi\)
0.357480 + 0.933921i \(0.383636\pi\)
\(978\) 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 \(-0.463647\pi\)
0.113959 + 0.993485i \(0.463647\pi\)
\(984\) 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 \(-0.370828\pi\)
0.394758 + 0.918785i \(0.370828\pi\)
\(992\) 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.e.1.2 yes 2
5.4 even 2 9025.2.a.k.1.1 2
19.18 odd 2 1805.2.a.c.1.1 2
95.94 odd 2 9025.2.a.v.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.c.1.1 2 19.18 odd 2
1805.2.a.e.1.2 yes 2 1.1 even 1 trivial
9025.2.a.k.1.1 2 5.4 even 2
9025.2.a.v.1.2 2 95.94 odd 2