Properties

Label 4027.2.a.c.1.17
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36541 q^{2} -2.31312 q^{3} +3.59515 q^{4} -1.08906 q^{5} +5.47148 q^{6} -0.547834 q^{7} -3.77318 q^{8} +2.35053 q^{9} +O(q^{10})\) \(q-2.36541 q^{2} -2.31312 q^{3} +3.59515 q^{4} -1.08906 q^{5} +5.47148 q^{6} -0.547834 q^{7} -3.77318 q^{8} +2.35053 q^{9} +2.57606 q^{10} +2.77385 q^{11} -8.31602 q^{12} +2.85967 q^{13} +1.29585 q^{14} +2.51912 q^{15} +1.73481 q^{16} -0.316358 q^{17} -5.55997 q^{18} -1.28066 q^{19} -3.91532 q^{20} +1.26721 q^{21} -6.56128 q^{22} +6.80143 q^{23} +8.72783 q^{24} -3.81396 q^{25} -6.76428 q^{26} +1.50229 q^{27} -1.96955 q^{28} -0.874497 q^{29} -5.95874 q^{30} +6.66183 q^{31} +3.44283 q^{32} -6.41625 q^{33} +0.748317 q^{34} +0.596622 q^{35} +8.45053 q^{36} +8.99003 q^{37} +3.02928 q^{38} -6.61477 q^{39} +4.10920 q^{40} +7.72982 q^{41} -2.99746 q^{42} +0.240790 q^{43} +9.97241 q^{44} -2.55986 q^{45} -16.0882 q^{46} +1.32538 q^{47} -4.01283 q^{48} -6.69988 q^{49} +9.02157 q^{50} +0.731776 q^{51} +10.2809 q^{52} +2.99865 q^{53} -3.55353 q^{54} -3.02088 q^{55} +2.06708 q^{56} +2.96232 q^{57} +2.06854 q^{58} +5.20806 q^{59} +9.05661 q^{60} -7.09930 q^{61} -15.7579 q^{62} -1.28770 q^{63} -11.6133 q^{64} -3.11434 q^{65} +15.1771 q^{66} +8.88197 q^{67} -1.13736 q^{68} -15.7325 q^{69} -1.41125 q^{70} +2.57084 q^{71} -8.86899 q^{72} +12.8924 q^{73} -21.2651 q^{74} +8.82215 q^{75} -4.60417 q^{76} -1.51961 q^{77} +15.6466 q^{78} +3.45817 q^{79} -1.88930 q^{80} -10.5266 q^{81} -18.2842 q^{82} +0.522288 q^{83} +4.55580 q^{84} +0.344532 q^{85} -0.569567 q^{86} +2.02282 q^{87} -10.4662 q^{88} -9.16932 q^{89} +6.05512 q^{90} -1.56663 q^{91} +24.4522 q^{92} -15.4096 q^{93} -3.13507 q^{94} +1.39471 q^{95} -7.96369 q^{96} +18.2279 q^{97} +15.8479 q^{98} +6.52003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36541 −1.67260 −0.836298 0.548276i \(-0.815284\pi\)
−0.836298 + 0.548276i \(0.815284\pi\)
\(3\) −2.31312 −1.33548 −0.667741 0.744394i \(-0.732739\pi\)
−0.667741 + 0.744394i \(0.732739\pi\)
\(4\) 3.59515 1.79758
\(5\) −1.08906 −0.487040 −0.243520 0.969896i \(-0.578302\pi\)
−0.243520 + 0.969896i \(0.578302\pi\)
\(6\) 5.47148 2.23372
\(7\) −0.547834 −0.207062 −0.103531 0.994626i \(-0.533014\pi\)
−0.103531 + 0.994626i \(0.533014\pi\)
\(8\) −3.77318 −1.33402
\(9\) 2.35053 0.783512
\(10\) 2.57606 0.814621
\(11\) 2.77385 0.836347 0.418174 0.908367i \(-0.362670\pi\)
0.418174 + 0.908367i \(0.362670\pi\)
\(12\) −8.31602 −2.40063
\(13\) 2.85967 0.793130 0.396565 0.918007i \(-0.370202\pi\)
0.396565 + 0.918007i \(0.370202\pi\)
\(14\) 1.29585 0.346331
\(15\) 2.51912 0.650433
\(16\) 1.73481 0.433702
\(17\) −0.316358 −0.0767282 −0.0383641 0.999264i \(-0.512215\pi\)
−0.0383641 + 0.999264i \(0.512215\pi\)
\(18\) −5.55997 −1.31050
\(19\) −1.28066 −0.293804 −0.146902 0.989151i \(-0.546930\pi\)
−0.146902 + 0.989151i \(0.546930\pi\)
\(20\) −3.91532 −0.875492
\(21\) 1.26721 0.276527
\(22\) −6.56128 −1.39887
\(23\) 6.80143 1.41820 0.709098 0.705110i \(-0.249102\pi\)
0.709098 + 0.705110i \(0.249102\pi\)
\(24\) 8.72783 1.78156
\(25\) −3.81396 −0.762792
\(26\) −6.76428 −1.32659
\(27\) 1.50229 0.289116
\(28\) −1.96955 −0.372210
\(29\) −0.874497 −0.162390 −0.0811950 0.996698i \(-0.525874\pi\)
−0.0811950 + 0.996698i \(0.525874\pi\)
\(30\) −5.95874 −1.08791
\(31\) 6.66183 1.19650 0.598250 0.801309i \(-0.295863\pi\)
0.598250 + 0.801309i \(0.295863\pi\)
\(32\) 3.44283 0.608613
\(33\) −6.41625 −1.11693
\(34\) 0.748317 0.128335
\(35\) 0.596622 0.100848
\(36\) 8.45053 1.40842
\(37\) 8.99003 1.47795 0.738976 0.673732i \(-0.235310\pi\)
0.738976 + 0.673732i \(0.235310\pi\)
\(38\) 3.02928 0.491415
\(39\) −6.61477 −1.05921
\(40\) 4.10920 0.649722
\(41\) 7.72982 1.20719 0.603597 0.797289i \(-0.293733\pi\)
0.603597 + 0.797289i \(0.293733\pi\)
\(42\) −2.99746 −0.462519
\(43\) 0.240790 0.0367202 0.0183601 0.999831i \(-0.494155\pi\)
0.0183601 + 0.999831i \(0.494155\pi\)
\(44\) 9.97241 1.50340
\(45\) −2.55986 −0.381602
\(46\) −16.0882 −2.37207
\(47\) 1.32538 0.193327 0.0966634 0.995317i \(-0.469183\pi\)
0.0966634 + 0.995317i \(0.469183\pi\)
\(48\) −4.01283 −0.579202
\(49\) −6.69988 −0.957125
\(50\) 9.02157 1.27584
\(51\) 0.731776 0.102469
\(52\) 10.2809 1.42571
\(53\) 2.99865 0.411896 0.205948 0.978563i \(-0.433972\pi\)
0.205948 + 0.978563i \(0.433972\pi\)
\(54\) −3.55353 −0.483575
\(55\) −3.02088 −0.407335
\(56\) 2.06708 0.276225
\(57\) 2.96232 0.392369
\(58\) 2.06854 0.271613
\(59\) 5.20806 0.678031 0.339016 0.940781i \(-0.389906\pi\)
0.339016 + 0.940781i \(0.389906\pi\)
\(60\) 9.05661 1.16920
\(61\) −7.09930 −0.908972 −0.454486 0.890754i \(-0.650177\pi\)
−0.454486 + 0.890754i \(0.650177\pi\)
\(62\) −15.7579 −2.00126
\(63\) −1.28770 −0.162235
\(64\) −11.6133 −1.45167
\(65\) −3.11434 −0.386286
\(66\) 15.1771 1.86817
\(67\) 8.88197 1.08511 0.542553 0.840022i \(-0.317458\pi\)
0.542553 + 0.840022i \(0.317458\pi\)
\(68\) −1.13736 −0.137925
\(69\) −15.7325 −1.89398
\(70\) −1.41125 −0.168677
\(71\) 2.57084 0.305103 0.152551 0.988296i \(-0.451251\pi\)
0.152551 + 0.988296i \(0.451251\pi\)
\(72\) −8.86899 −1.04522
\(73\) 12.8924 1.50895 0.754473 0.656331i \(-0.227892\pi\)
0.754473 + 0.656331i \(0.227892\pi\)
\(74\) −21.2651 −2.47202
\(75\) 8.82215 1.01869
\(76\) −4.60417 −0.528134
\(77\) −1.51961 −0.173176
\(78\) 15.6466 1.77163
\(79\) 3.45817 0.389075 0.194537 0.980895i \(-0.437679\pi\)
0.194537 + 0.980895i \(0.437679\pi\)
\(80\) −1.88930 −0.211231
\(81\) −10.5266 −1.16962
\(82\) −18.2842 −2.01915
\(83\) 0.522288 0.0573286 0.0286643 0.999589i \(-0.490875\pi\)
0.0286643 + 0.999589i \(0.490875\pi\)
\(84\) 4.55580 0.497079
\(85\) 0.344532 0.0373697
\(86\) −0.569567 −0.0614180
\(87\) 2.02282 0.216869
\(88\) −10.4662 −1.11570
\(89\) −9.16932 −0.971946 −0.485973 0.873974i \(-0.661535\pi\)
−0.485973 + 0.873974i \(0.661535\pi\)
\(90\) 6.05512 0.638265
\(91\) −1.56663 −0.164227
\(92\) 24.4522 2.54931
\(93\) −15.4096 −1.59790
\(94\) −3.13507 −0.323358
\(95\) 1.39471 0.143094
\(96\) −7.96369 −0.812791
\(97\) 18.2279 1.85076 0.925379 0.379043i \(-0.123747\pi\)
0.925379 + 0.379043i \(0.123747\pi\)
\(98\) 15.8479 1.60088
\(99\) 6.52003 0.655288
\(100\) −13.7118 −1.37118
\(101\) 5.55883 0.553124 0.276562 0.960996i \(-0.410805\pi\)
0.276562 + 0.960996i \(0.410805\pi\)
\(102\) −1.73095 −0.171389
\(103\) −17.4585 −1.72024 −0.860119 0.510094i \(-0.829611\pi\)
−0.860119 + 0.510094i \(0.829611\pi\)
\(104\) −10.7901 −1.05805
\(105\) −1.38006 −0.134680
\(106\) −7.09303 −0.688936
\(107\) −18.3147 −1.77055 −0.885275 0.465069i \(-0.846030\pi\)
−0.885275 + 0.465069i \(0.846030\pi\)
\(108\) 5.40097 0.519709
\(109\) −9.80187 −0.938849 −0.469424 0.882973i \(-0.655539\pi\)
−0.469424 + 0.882973i \(0.655539\pi\)
\(110\) 7.14560 0.681306
\(111\) −20.7950 −1.97378
\(112\) −0.950388 −0.0898033
\(113\) −5.24008 −0.492945 −0.246472 0.969150i \(-0.579271\pi\)
−0.246472 + 0.969150i \(0.579271\pi\)
\(114\) −7.00710 −0.656275
\(115\) −7.40713 −0.690719
\(116\) −3.14395 −0.291908
\(117\) 6.72175 0.621426
\(118\) −12.3192 −1.13407
\(119\) 0.173312 0.0158875
\(120\) −9.50509 −0.867692
\(121\) −3.30576 −0.300524
\(122\) 16.7927 1.52034
\(123\) −17.8800 −1.61219
\(124\) 23.9503 2.15080
\(125\) 9.59889 0.858551
\(126\) 3.04594 0.271354
\(127\) 2.40309 0.213240 0.106620 0.994300i \(-0.465997\pi\)
0.106620 + 0.994300i \(0.465997\pi\)
\(128\) 20.5846 1.81944
\(129\) −0.556977 −0.0490391
\(130\) 7.36668 0.646101
\(131\) 9.50901 0.830806 0.415403 0.909637i \(-0.363641\pi\)
0.415403 + 0.909637i \(0.363641\pi\)
\(132\) −23.0674 −2.00776
\(133\) 0.701590 0.0608356
\(134\) −21.0095 −1.81494
\(135\) −1.63608 −0.140811
\(136\) 1.19368 0.102357
\(137\) 20.0984 1.71713 0.858563 0.512708i \(-0.171358\pi\)
0.858563 + 0.512708i \(0.171358\pi\)
\(138\) 37.2139 3.16785
\(139\) −7.88681 −0.668951 −0.334475 0.942405i \(-0.608559\pi\)
−0.334475 + 0.942405i \(0.608559\pi\)
\(140\) 2.14495 0.181281
\(141\) −3.06577 −0.258184
\(142\) −6.08109 −0.510313
\(143\) 7.93230 0.663332
\(144\) 4.07773 0.339811
\(145\) 0.952376 0.0790905
\(146\) −30.4959 −2.52386
\(147\) 15.4976 1.27822
\(148\) 32.3205 2.65673
\(149\) −6.35011 −0.520221 −0.260111 0.965579i \(-0.583759\pi\)
−0.260111 + 0.965579i \(0.583759\pi\)
\(150\) −20.8680 −1.70386
\(151\) −2.33392 −0.189932 −0.0949658 0.995481i \(-0.530274\pi\)
−0.0949658 + 0.995481i \(0.530274\pi\)
\(152\) 4.83216 0.391940
\(153\) −0.743611 −0.0601174
\(154\) 3.59450 0.289653
\(155\) −7.25510 −0.582744
\(156\) −23.7811 −1.90401
\(157\) −17.0230 −1.35858 −0.679290 0.733870i \(-0.737712\pi\)
−0.679290 + 0.733870i \(0.737712\pi\)
\(158\) −8.17999 −0.650765
\(159\) −6.93625 −0.550080
\(160\) −3.74944 −0.296419
\(161\) −3.72606 −0.293654
\(162\) 24.8997 1.95630
\(163\) −11.2962 −0.884790 −0.442395 0.896820i \(-0.645871\pi\)
−0.442395 + 0.896820i \(0.645871\pi\)
\(164\) 27.7899 2.17002
\(165\) 6.98765 0.543988
\(166\) −1.23542 −0.0958876
\(167\) 4.40123 0.340577 0.170289 0.985394i \(-0.445530\pi\)
0.170289 + 0.985394i \(0.445530\pi\)
\(168\) −4.78141 −0.368894
\(169\) −4.82229 −0.370945
\(170\) −0.814958 −0.0625044
\(171\) −3.01024 −0.230199
\(172\) 0.865677 0.0660073
\(173\) 24.1657 1.83728 0.918641 0.395094i \(-0.129288\pi\)
0.918641 + 0.395094i \(0.129288\pi\)
\(174\) −4.78479 −0.362734
\(175\) 2.08942 0.157945
\(176\) 4.81210 0.362726
\(177\) −12.0469 −0.905498
\(178\) 21.6892 1.62567
\(179\) 5.95731 0.445271 0.222635 0.974902i \(-0.428534\pi\)
0.222635 + 0.974902i \(0.428534\pi\)
\(180\) −9.20309 −0.685958
\(181\) −24.0274 −1.78594 −0.892971 0.450115i \(-0.851383\pi\)
−0.892971 + 0.450115i \(0.851383\pi\)
\(182\) 3.70571 0.274685
\(183\) 16.4215 1.21392
\(184\) −25.6630 −1.89190
\(185\) −9.79064 −0.719822
\(186\) 36.4500 2.67265
\(187\) −0.877531 −0.0641714
\(188\) 4.76495 0.347520
\(189\) −0.823008 −0.0598650
\(190\) −3.29906 −0.239339
\(191\) 20.1090 1.45504 0.727518 0.686088i \(-0.240674\pi\)
0.727518 + 0.686088i \(0.240674\pi\)
\(192\) 26.8630 1.93867
\(193\) −21.2496 −1.52958 −0.764790 0.644280i \(-0.777157\pi\)
−0.764790 + 0.644280i \(0.777157\pi\)
\(194\) −43.1163 −3.09557
\(195\) 7.20385 0.515878
\(196\) −24.0871 −1.72051
\(197\) 11.4442 0.815364 0.407682 0.913124i \(-0.366337\pi\)
0.407682 + 0.913124i \(0.366337\pi\)
\(198\) −15.4225 −1.09603
\(199\) −24.9170 −1.76632 −0.883158 0.469075i \(-0.844587\pi\)
−0.883158 + 0.469075i \(0.844587\pi\)
\(200\) 14.3908 1.01758
\(201\) −20.5451 −1.44914
\(202\) −13.1489 −0.925153
\(203\) 0.479080 0.0336248
\(204\) 2.63084 0.184196
\(205\) −8.41820 −0.587952
\(206\) 41.2965 2.87726
\(207\) 15.9870 1.11117
\(208\) 4.96098 0.343982
\(209\) −3.55236 −0.245722
\(210\) 3.26440 0.225265
\(211\) −11.8170 −0.813515 −0.406758 0.913536i \(-0.633341\pi\)
−0.406758 + 0.913536i \(0.633341\pi\)
\(212\) 10.7806 0.740415
\(213\) −5.94667 −0.407459
\(214\) 43.3217 2.96141
\(215\) −0.262234 −0.0178842
\(216\) −5.66842 −0.385687
\(217\) −3.64958 −0.247750
\(218\) 23.1854 1.57031
\(219\) −29.8218 −2.01517
\(220\) −10.8605 −0.732215
\(221\) −0.904681 −0.0608554
\(222\) 49.1888 3.30133
\(223\) −27.3889 −1.83410 −0.917048 0.398778i \(-0.869434\pi\)
−0.917048 + 0.398778i \(0.869434\pi\)
\(224\) −1.88610 −0.126021
\(225\) −8.96484 −0.597656
\(226\) 12.3949 0.824497
\(227\) −23.3269 −1.54826 −0.774132 0.633024i \(-0.781813\pi\)
−0.774132 + 0.633024i \(0.781813\pi\)
\(228\) 10.6500 0.705314
\(229\) 28.3001 1.87012 0.935062 0.354485i \(-0.115344\pi\)
0.935062 + 0.354485i \(0.115344\pi\)
\(230\) 17.5209 1.15529
\(231\) 3.51504 0.231273
\(232\) 3.29964 0.216632
\(233\) 15.1106 0.989931 0.494965 0.868913i \(-0.335181\pi\)
0.494965 + 0.868913i \(0.335181\pi\)
\(234\) −15.8997 −1.03939
\(235\) −1.44341 −0.0941579
\(236\) 18.7238 1.21881
\(237\) −7.99918 −0.519602
\(238\) −0.409954 −0.0265733
\(239\) −3.61373 −0.233753 −0.116876 0.993146i \(-0.537288\pi\)
−0.116876 + 0.993146i \(0.537288\pi\)
\(240\) 4.37019 0.282095
\(241\) 19.3535 1.24667 0.623334 0.781956i \(-0.285778\pi\)
0.623334 + 0.781956i \(0.285778\pi\)
\(242\) 7.81947 0.502654
\(243\) 19.8424 1.27289
\(244\) −25.5231 −1.63395
\(245\) 7.29654 0.466159
\(246\) 42.2935 2.69654
\(247\) −3.66227 −0.233024
\(248\) −25.1363 −1.59616
\(249\) −1.20812 −0.0765613
\(250\) −22.7053 −1.43601
\(251\) −20.2004 −1.27504 −0.637519 0.770435i \(-0.720039\pi\)
−0.637519 + 0.770435i \(0.720039\pi\)
\(252\) −4.62949 −0.291630
\(253\) 18.8661 1.18610
\(254\) −5.68428 −0.356664
\(255\) −0.796944 −0.0499066
\(256\) −25.4642 −1.59152
\(257\) −19.2997 −1.20388 −0.601942 0.798540i \(-0.705606\pi\)
−0.601942 + 0.798540i \(0.705606\pi\)
\(258\) 1.31748 0.0820226
\(259\) −4.92505 −0.306028
\(260\) −11.1965 −0.694379
\(261\) −2.05554 −0.127235
\(262\) −22.4927 −1.38960
\(263\) −12.1180 −0.747225 −0.373612 0.927585i \(-0.621881\pi\)
−0.373612 + 0.927585i \(0.621881\pi\)
\(264\) 24.2097 1.49000
\(265\) −3.26570 −0.200610
\(266\) −1.65955 −0.101753
\(267\) 21.2098 1.29802
\(268\) 31.9320 1.95056
\(269\) 18.9286 1.15410 0.577050 0.816709i \(-0.304204\pi\)
0.577050 + 0.816709i \(0.304204\pi\)
\(270\) 3.86999 0.235520
\(271\) −3.01481 −0.183137 −0.0915684 0.995799i \(-0.529188\pi\)
−0.0915684 + 0.995799i \(0.529188\pi\)
\(272\) −0.548822 −0.0332772
\(273\) 3.62380 0.219322
\(274\) −47.5410 −2.87206
\(275\) −10.5793 −0.637959
\(276\) −56.5609 −3.40456
\(277\) 20.1710 1.21196 0.605979 0.795481i \(-0.292782\pi\)
0.605979 + 0.795481i \(0.292782\pi\)
\(278\) 18.6555 1.11888
\(279\) 15.6589 0.937472
\(280\) −2.25116 −0.134533
\(281\) 20.3526 1.21414 0.607068 0.794650i \(-0.292345\pi\)
0.607068 + 0.794650i \(0.292345\pi\)
\(282\) 7.25180 0.431838
\(283\) 23.3486 1.38793 0.693966 0.720008i \(-0.255862\pi\)
0.693966 + 0.720008i \(0.255862\pi\)
\(284\) 9.24256 0.548445
\(285\) −3.22613 −0.191100
\(286\) −18.7631 −1.10949
\(287\) −4.23466 −0.249964
\(288\) 8.09250 0.476855
\(289\) −16.8999 −0.994113
\(290\) −2.25276 −0.132286
\(291\) −42.1633 −2.47165
\(292\) 46.3503 2.71245
\(293\) 4.82958 0.282147 0.141074 0.989999i \(-0.454945\pi\)
0.141074 + 0.989999i \(0.454945\pi\)
\(294\) −36.6582 −2.13795
\(295\) −5.67186 −0.330229
\(296\) −33.9210 −1.97162
\(297\) 4.16713 0.241802
\(298\) 15.0206 0.870119
\(299\) 19.4498 1.12481
\(300\) 31.7170 1.83118
\(301\) −0.131913 −0.00760335
\(302\) 5.52067 0.317679
\(303\) −12.8583 −0.738687
\(304\) −2.22170 −0.127423
\(305\) 7.73153 0.442706
\(306\) 1.75894 0.100552
\(307\) 22.3941 1.27810 0.639048 0.769167i \(-0.279328\pi\)
0.639048 + 0.769167i \(0.279328\pi\)
\(308\) −5.46323 −0.311296
\(309\) 40.3837 2.29735
\(310\) 17.1613 0.974695
\(311\) −5.85763 −0.332156 −0.166078 0.986113i \(-0.553110\pi\)
−0.166078 + 0.986113i \(0.553110\pi\)
\(312\) 24.9587 1.41301
\(313\) −17.8198 −1.00723 −0.503616 0.863927i \(-0.667997\pi\)
−0.503616 + 0.863927i \(0.667997\pi\)
\(314\) 40.2662 2.27235
\(315\) 1.40238 0.0790152
\(316\) 12.4327 0.699392
\(317\) 32.2695 1.81244 0.906218 0.422812i \(-0.138957\pi\)
0.906218 + 0.422812i \(0.138957\pi\)
\(318\) 16.4070 0.920062
\(319\) −2.42572 −0.135814
\(320\) 12.6475 0.707019
\(321\) 42.3641 2.36454
\(322\) 8.81364 0.491165
\(323\) 0.405148 0.0225430
\(324\) −37.8447 −2.10248
\(325\) −10.9067 −0.604993
\(326\) 26.7202 1.47990
\(327\) 22.6729 1.25382
\(328\) −29.1660 −1.61042
\(329\) −0.726090 −0.0400306
\(330\) −16.5286 −0.909872
\(331\) 15.5168 0.852882 0.426441 0.904515i \(-0.359767\pi\)
0.426441 + 0.904515i \(0.359767\pi\)
\(332\) 1.87771 0.103053
\(333\) 21.1314 1.15799
\(334\) −10.4107 −0.569648
\(335\) −9.67296 −0.528490
\(336\) 2.19836 0.119931
\(337\) 23.2814 1.26822 0.634108 0.773244i \(-0.281367\pi\)
0.634108 + 0.773244i \(0.281367\pi\)
\(338\) 11.4067 0.620441
\(339\) 12.1209 0.658319
\(340\) 1.23864 0.0671749
\(341\) 18.4789 1.00069
\(342\) 7.12044 0.385029
\(343\) 7.50526 0.405246
\(344\) −0.908545 −0.0489855
\(345\) 17.1336 0.922442
\(346\) −57.1616 −3.07303
\(347\) 9.67063 0.519147 0.259573 0.965723i \(-0.416418\pi\)
0.259573 + 0.965723i \(0.416418\pi\)
\(348\) 7.27234 0.389838
\(349\) −17.1839 −0.919833 −0.459917 0.887962i \(-0.652121\pi\)
−0.459917 + 0.887962i \(0.652121\pi\)
\(350\) −4.94232 −0.264178
\(351\) 4.29606 0.229307
\(352\) 9.54990 0.509011
\(353\) 12.9193 0.687627 0.343813 0.939038i \(-0.388281\pi\)
0.343813 + 0.939038i \(0.388281\pi\)
\(354\) 28.4958 1.51453
\(355\) −2.79979 −0.148597
\(356\) −32.9651 −1.74715
\(357\) −0.400892 −0.0212175
\(358\) −14.0915 −0.744757
\(359\) −8.09992 −0.427497 −0.213749 0.976889i \(-0.568567\pi\)
−0.213749 + 0.976889i \(0.568567\pi\)
\(360\) 9.65882 0.509065
\(361\) −17.3599 −0.913679
\(362\) 56.8345 2.98716
\(363\) 7.64663 0.401344
\(364\) −5.63226 −0.295210
\(365\) −14.0406 −0.734918
\(366\) −38.8436 −2.03039
\(367\) 31.2612 1.63182 0.815909 0.578180i \(-0.196237\pi\)
0.815909 + 0.578180i \(0.196237\pi\)
\(368\) 11.7992 0.615075
\(369\) 18.1692 0.945851
\(370\) 23.1589 1.20397
\(371\) −1.64276 −0.0852881
\(372\) −55.3999 −2.87235
\(373\) −20.0718 −1.03928 −0.519639 0.854386i \(-0.673933\pi\)
−0.519639 + 0.854386i \(0.673933\pi\)
\(374\) 2.07572 0.107333
\(375\) −22.2034 −1.14658
\(376\) −5.00091 −0.257902
\(377\) −2.50077 −0.128796
\(378\) 1.94675 0.100130
\(379\) 3.30672 0.169855 0.0849274 0.996387i \(-0.472934\pi\)
0.0849274 + 0.996387i \(0.472934\pi\)
\(380\) 5.01419 0.257223
\(381\) −5.55864 −0.284778
\(382\) −47.5660 −2.43369
\(383\) −26.4297 −1.35050 −0.675248 0.737591i \(-0.735963\pi\)
−0.675248 + 0.737591i \(0.735963\pi\)
\(384\) −47.6146 −2.42982
\(385\) 1.65494 0.0843435
\(386\) 50.2640 2.55837
\(387\) 0.565986 0.0287707
\(388\) 65.5319 3.32688
\(389\) −18.0899 −0.917197 −0.458598 0.888644i \(-0.651648\pi\)
−0.458598 + 0.888644i \(0.651648\pi\)
\(390\) −17.0400 −0.862855
\(391\) −2.15169 −0.108816
\(392\) 25.2799 1.27683
\(393\) −21.9955 −1.10953
\(394\) −27.0701 −1.36377
\(395\) −3.76614 −0.189495
\(396\) 23.4405 1.17793
\(397\) 31.0155 1.55662 0.778311 0.627879i \(-0.216077\pi\)
0.778311 + 0.627879i \(0.216077\pi\)
\(398\) 58.9388 2.95433
\(399\) −1.62286 −0.0812448
\(400\) −6.61649 −0.330825
\(401\) 31.0835 1.55224 0.776118 0.630587i \(-0.217186\pi\)
0.776118 + 0.630587i \(0.217186\pi\)
\(402\) 48.5975 2.42382
\(403\) 19.0506 0.948980
\(404\) 19.9848 0.994283
\(405\) 11.4640 0.569653
\(406\) −1.13322 −0.0562407
\(407\) 24.9370 1.23608
\(408\) −2.76112 −0.136696
\(409\) 31.7704 1.57094 0.785471 0.618898i \(-0.212421\pi\)
0.785471 + 0.618898i \(0.212421\pi\)
\(410\) 19.9125 0.983407
\(411\) −46.4902 −2.29319
\(412\) −62.7660 −3.09226
\(413\) −2.85315 −0.140394
\(414\) −37.8158 −1.85854
\(415\) −0.568801 −0.0279213
\(416\) 9.84537 0.482709
\(417\) 18.2432 0.893371
\(418\) 8.40278 0.410993
\(419\) 26.0636 1.27329 0.636645 0.771157i \(-0.280322\pi\)
0.636645 + 0.771157i \(0.280322\pi\)
\(420\) −4.96152 −0.242098
\(421\) 9.03188 0.440187 0.220094 0.975479i \(-0.429364\pi\)
0.220094 + 0.975479i \(0.429364\pi\)
\(422\) 27.9520 1.36068
\(423\) 3.11536 0.151474
\(424\) −11.3145 −0.549479
\(425\) 1.20658 0.0585276
\(426\) 14.0663 0.681514
\(427\) 3.88924 0.188214
\(428\) −65.8441 −3.18270
\(429\) −18.3484 −0.885868
\(430\) 0.620290 0.0299130
\(431\) 0.822747 0.0396303 0.0198152 0.999804i \(-0.493692\pi\)
0.0198152 + 0.999804i \(0.493692\pi\)
\(432\) 2.60619 0.125390
\(433\) −3.98445 −0.191481 −0.0957403 0.995406i \(-0.530522\pi\)
−0.0957403 + 0.995406i \(0.530522\pi\)
\(434\) 8.63274 0.414385
\(435\) −2.20296 −0.105624
\(436\) −35.2392 −1.68765
\(437\) −8.71032 −0.416671
\(438\) 70.5407 3.37057
\(439\) 27.9361 1.33332 0.666660 0.745362i \(-0.267723\pi\)
0.666660 + 0.745362i \(0.267723\pi\)
\(440\) 11.3983 0.543393
\(441\) −15.7483 −0.749919
\(442\) 2.13994 0.101787
\(443\) −20.5907 −0.978294 −0.489147 0.872201i \(-0.662692\pi\)
−0.489147 + 0.872201i \(0.662692\pi\)
\(444\) −74.7613 −3.54802
\(445\) 9.98590 0.473377
\(446\) 64.7859 3.06770
\(447\) 14.6886 0.694746
\(448\) 6.36218 0.300585
\(449\) 32.3489 1.52664 0.763320 0.646020i \(-0.223568\pi\)
0.763320 + 0.646020i \(0.223568\pi\)
\(450\) 21.2055 0.999637
\(451\) 21.4413 1.00963
\(452\) −18.8389 −0.886106
\(453\) 5.39864 0.253650
\(454\) 55.1777 2.58962
\(455\) 1.70614 0.0799852
\(456\) −11.1774 −0.523429
\(457\) 4.80254 0.224653 0.112327 0.993671i \(-0.464170\pi\)
0.112327 + 0.993671i \(0.464170\pi\)
\(458\) −66.9413 −3.12796
\(459\) −0.475263 −0.0221834
\(460\) −26.6298 −1.24162
\(461\) −19.0427 −0.886908 −0.443454 0.896297i \(-0.646247\pi\)
−0.443454 + 0.896297i \(0.646247\pi\)
\(462\) −8.31451 −0.386826
\(463\) 3.73829 0.173733 0.0868664 0.996220i \(-0.472315\pi\)
0.0868664 + 0.996220i \(0.472315\pi\)
\(464\) −1.51709 −0.0704290
\(465\) 16.7819 0.778244
\(466\) −35.7428 −1.65575
\(467\) 6.41151 0.296689 0.148345 0.988936i \(-0.452605\pi\)
0.148345 + 0.988936i \(0.452605\pi\)
\(468\) 24.1657 1.11706
\(469\) −4.86585 −0.224684
\(470\) 3.41426 0.157488
\(471\) 39.3762 1.81436
\(472\) −19.6509 −0.904508
\(473\) 0.667916 0.0307108
\(474\) 18.9213 0.869085
\(475\) 4.88439 0.224111
\(476\) 0.623083 0.0285590
\(477\) 7.04843 0.322726
\(478\) 8.54794 0.390974
\(479\) 12.2269 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(480\) 8.67290 0.395862
\(481\) 25.7085 1.17221
\(482\) −45.7789 −2.08517
\(483\) 8.61883 0.392170
\(484\) −11.8847 −0.540214
\(485\) −19.8511 −0.901394
\(486\) −46.9354 −2.12903
\(487\) 3.88616 0.176099 0.0880495 0.996116i \(-0.471937\pi\)
0.0880495 + 0.996116i \(0.471937\pi\)
\(488\) 26.7869 1.21259
\(489\) 26.1296 1.18162
\(490\) −17.2593 −0.779695
\(491\) −28.1469 −1.27025 −0.635125 0.772409i \(-0.719052\pi\)
−0.635125 + 0.772409i \(0.719052\pi\)
\(492\) −64.2813 −2.89803
\(493\) 0.276655 0.0124599
\(494\) 8.66275 0.389756
\(495\) −7.10067 −0.319151
\(496\) 11.5570 0.518925
\(497\) −1.40840 −0.0631752
\(498\) 2.85769 0.128056
\(499\) 37.8077 1.69250 0.846252 0.532783i \(-0.178854\pi\)
0.846252 + 0.532783i \(0.178854\pi\)
\(500\) 34.5095 1.54331
\(501\) −10.1806 −0.454835
\(502\) 47.7821 2.13262
\(503\) 1.92428 0.0857992 0.0428996 0.999079i \(-0.486340\pi\)
0.0428996 + 0.999079i \(0.486340\pi\)
\(504\) 4.85874 0.216426
\(505\) −6.05387 −0.269394
\(506\) −44.6261 −1.98387
\(507\) 11.1545 0.495390
\(508\) 8.63947 0.383314
\(509\) −20.3348 −0.901325 −0.450663 0.892694i \(-0.648812\pi\)
−0.450663 + 0.892694i \(0.648812\pi\)
\(510\) 1.88510 0.0834735
\(511\) −7.06293 −0.312445
\(512\) 19.0642 0.842525
\(513\) −1.92393 −0.0849434
\(514\) 45.6517 2.01361
\(515\) 19.0133 0.837825
\(516\) −2.00242 −0.0881515
\(517\) 3.67641 0.161688
\(518\) 11.6497 0.511861
\(519\) −55.8981 −2.45366
\(520\) 11.7510 0.515314
\(521\) 40.1443 1.75875 0.879376 0.476128i \(-0.157960\pi\)
0.879376 + 0.476128i \(0.157960\pi\)
\(522\) 4.86218 0.212812
\(523\) −11.5864 −0.506638 −0.253319 0.967383i \(-0.581522\pi\)
−0.253319 + 0.967383i \(0.581522\pi\)
\(524\) 34.1863 1.49344
\(525\) −4.83308 −0.210933
\(526\) 28.6639 1.24981
\(527\) −2.10753 −0.0918053
\(528\) −11.1310 −0.484414
\(529\) 23.2594 1.01128
\(530\) 7.72470 0.335540
\(531\) 12.2417 0.531245
\(532\) 2.52232 0.109357
\(533\) 22.1047 0.957462
\(534\) −50.1697 −2.17106
\(535\) 19.9457 0.862329
\(536\) −33.5133 −1.44755
\(537\) −13.7800 −0.594651
\(538\) −44.7739 −1.93034
\(539\) −18.5845 −0.800489
\(540\) −5.88195 −0.253119
\(541\) −38.8930 −1.67214 −0.836069 0.548624i \(-0.815152\pi\)
−0.836069 + 0.548624i \(0.815152\pi\)
\(542\) 7.13126 0.306314
\(543\) 55.5783 2.38509
\(544\) −1.08917 −0.0466978
\(545\) 10.6748 0.457257
\(546\) −8.57176 −0.366837
\(547\) 14.5872 0.623702 0.311851 0.950131i \(-0.399051\pi\)
0.311851 + 0.950131i \(0.399051\pi\)
\(548\) 72.2569 3.08666
\(549\) −16.6871 −0.712190
\(550\) 25.0245 1.06705
\(551\) 1.11993 0.0477108
\(552\) 59.3617 2.52660
\(553\) −1.89451 −0.0805626
\(554\) −47.7126 −2.02711
\(555\) 22.6470 0.961310
\(556\) −28.3543 −1.20249
\(557\) 33.1462 1.40445 0.702225 0.711955i \(-0.252190\pi\)
0.702225 + 0.711955i \(0.252190\pi\)
\(558\) −37.0396 −1.56801
\(559\) 0.688581 0.0291239
\(560\) 1.03503 0.0437378
\(561\) 2.02984 0.0856997
\(562\) −48.1423 −2.03076
\(563\) 17.4849 0.736899 0.368450 0.929648i \(-0.379889\pi\)
0.368450 + 0.929648i \(0.379889\pi\)
\(564\) −11.0219 −0.464106
\(565\) 5.70673 0.240084
\(566\) −55.2290 −2.32145
\(567\) 5.76683 0.242184
\(568\) −9.70025 −0.407014
\(569\) −19.9990 −0.838400 −0.419200 0.907894i \(-0.637689\pi\)
−0.419200 + 0.907894i \(0.637689\pi\)
\(570\) 7.63112 0.319633
\(571\) 11.8504 0.495926 0.247963 0.968770i \(-0.420239\pi\)
0.247963 + 0.968770i \(0.420239\pi\)
\(572\) 28.5178 1.19239
\(573\) −46.5146 −1.94318
\(574\) 10.0167 0.418089
\(575\) −25.9404 −1.08179
\(576\) −27.2975 −1.13740
\(577\) −8.18442 −0.340722 −0.170361 0.985382i \(-0.554493\pi\)
−0.170361 + 0.985382i \(0.554493\pi\)
\(578\) 39.9752 1.66275
\(579\) 49.1529 2.04273
\(580\) 3.42394 0.142171
\(581\) −0.286128 −0.0118706
\(582\) 99.7333 4.13408
\(583\) 8.31781 0.344488
\(584\) −48.6456 −2.01297
\(585\) −7.32036 −0.302660
\(586\) −11.4239 −0.471918
\(587\) 21.6217 0.892422 0.446211 0.894928i \(-0.352773\pi\)
0.446211 + 0.894928i \(0.352773\pi\)
\(588\) 55.7163 2.29770
\(589\) −8.53154 −0.351536
\(590\) 13.4163 0.552339
\(591\) −26.4718 −1.08890
\(592\) 15.5960 0.640991
\(593\) −33.0419 −1.35687 −0.678433 0.734662i \(-0.737341\pi\)
−0.678433 + 0.734662i \(0.737341\pi\)
\(594\) −9.85697 −0.404436
\(595\) −0.188746 −0.00773785
\(596\) −22.8296 −0.935137
\(597\) 57.6360 2.35888
\(598\) −46.0068 −1.88136
\(599\) 0.479515 0.0195925 0.00979623 0.999952i \(-0.496882\pi\)
0.00979623 + 0.999952i \(0.496882\pi\)
\(600\) −33.2876 −1.35896
\(601\) 44.1788 1.80209 0.901045 0.433725i \(-0.142801\pi\)
0.901045 + 0.433725i \(0.142801\pi\)
\(602\) 0.312028 0.0127173
\(603\) 20.8774 0.850193
\(604\) −8.39079 −0.341417
\(605\) 3.60015 0.146367
\(606\) 30.4150 1.23553
\(607\) −44.3551 −1.80032 −0.900159 0.435561i \(-0.856550\pi\)
−0.900159 + 0.435561i \(0.856550\pi\)
\(608\) −4.40910 −0.178813
\(609\) −1.10817 −0.0449053
\(610\) −18.2882 −0.740468
\(611\) 3.79016 0.153333
\(612\) −2.67340 −0.108066
\(613\) 7.59181 0.306630 0.153315 0.988177i \(-0.451005\pi\)
0.153315 + 0.988177i \(0.451005\pi\)
\(614\) −52.9711 −2.13774
\(615\) 19.4723 0.785200
\(616\) 5.73377 0.231020
\(617\) −8.77535 −0.353282 −0.176641 0.984275i \(-0.556523\pi\)
−0.176641 + 0.984275i \(0.556523\pi\)
\(618\) −95.5238 −3.84253
\(619\) −46.7829 −1.88036 −0.940181 0.340675i \(-0.889344\pi\)
−0.940181 + 0.340675i \(0.889344\pi\)
\(620\) −26.0832 −1.04753
\(621\) 10.2177 0.410024
\(622\) 13.8557 0.555562
\(623\) 5.02327 0.201253
\(624\) −11.4754 −0.459382
\(625\) 8.61608 0.344643
\(626\) 42.1510 1.68469
\(627\) 8.21704 0.328157
\(628\) −61.2001 −2.44215
\(629\) −2.84407 −0.113401
\(630\) −3.31720 −0.132160
\(631\) −27.9929 −1.11438 −0.557190 0.830385i \(-0.688120\pi\)
−0.557190 + 0.830385i \(0.688120\pi\)
\(632\) −13.0483 −0.519034
\(633\) 27.3341 1.08643
\(634\) −76.3305 −3.03147
\(635\) −2.61710 −0.103856
\(636\) −24.9369 −0.988811
\(637\) −19.1594 −0.759125
\(638\) 5.73782 0.227163
\(639\) 6.04285 0.239052
\(640\) −22.4177 −0.886139
\(641\) −28.5804 −1.12886 −0.564428 0.825482i \(-0.690903\pi\)
−0.564428 + 0.825482i \(0.690903\pi\)
\(642\) −100.208 −3.95491
\(643\) 36.4630 1.43796 0.718980 0.695031i \(-0.244609\pi\)
0.718980 + 0.695031i \(0.244609\pi\)
\(644\) −13.3957 −0.527866
\(645\) 0.606579 0.0238840
\(646\) −0.958339 −0.0377054
\(647\) 17.0334 0.669653 0.334826 0.942280i \(-0.391322\pi\)
0.334826 + 0.942280i \(0.391322\pi\)
\(648\) 39.7187 1.56030
\(649\) 14.4464 0.567069
\(650\) 25.7987 1.01191
\(651\) 8.44193 0.330865
\(652\) −40.6117 −1.59048
\(653\) 5.00057 0.195688 0.0978438 0.995202i \(-0.468805\pi\)
0.0978438 + 0.995202i \(0.468805\pi\)
\(654\) −53.6307 −2.09713
\(655\) −10.3558 −0.404636
\(656\) 13.4098 0.523563
\(657\) 30.3041 1.18228
\(658\) 1.71750 0.0669551
\(659\) −21.5461 −0.839315 −0.419658 0.907682i \(-0.637850\pi\)
−0.419658 + 0.907682i \(0.637850\pi\)
\(660\) 25.1217 0.977860
\(661\) 14.1922 0.552013 0.276006 0.961156i \(-0.410989\pi\)
0.276006 + 0.961156i \(0.410989\pi\)
\(662\) −36.7036 −1.42653
\(663\) 2.09264 0.0812713
\(664\) −1.97069 −0.0764776
\(665\) −0.764070 −0.0296294
\(666\) −49.9843 −1.93685
\(667\) −5.94783 −0.230301
\(668\) 15.8231 0.612213
\(669\) 63.3538 2.44940
\(670\) 22.8805 0.883950
\(671\) −19.6924 −0.760216
\(672\) 4.36279 0.168298
\(673\) −7.86783 −0.303283 −0.151641 0.988436i \(-0.548456\pi\)
−0.151641 + 0.988436i \(0.548456\pi\)
\(674\) −55.0699 −2.12121
\(675\) −5.72968 −0.220536
\(676\) −17.3368 −0.666802
\(677\) −1.27452 −0.0489839 −0.0244920 0.999700i \(-0.507797\pi\)
−0.0244920 + 0.999700i \(0.507797\pi\)
\(678\) −28.6710 −1.10110
\(679\) −9.98585 −0.383222
\(680\) −1.29998 −0.0498520
\(681\) 53.9581 2.06768
\(682\) −43.7102 −1.67375
\(683\) −9.81181 −0.375439 −0.187719 0.982223i \(-0.560110\pi\)
−0.187719 + 0.982223i \(0.560110\pi\)
\(684\) −10.8223 −0.413799
\(685\) −21.8883 −0.836309
\(686\) −17.7530 −0.677813
\(687\) −65.4616 −2.49752
\(688\) 0.417725 0.0159256
\(689\) 8.57515 0.326687
\(690\) −40.5279 −1.54287
\(691\) −25.9826 −0.988426 −0.494213 0.869341i \(-0.664544\pi\)
−0.494213 + 0.869341i \(0.664544\pi\)
\(692\) 86.8792 3.30265
\(693\) −3.57190 −0.135685
\(694\) −22.8750 −0.868323
\(695\) 8.58917 0.325806
\(696\) −7.63247 −0.289308
\(697\) −2.44539 −0.0926259
\(698\) 40.6469 1.53851
\(699\) −34.9527 −1.32203
\(700\) 7.51177 0.283918
\(701\) 31.6218 1.19434 0.597169 0.802115i \(-0.296292\pi\)
0.597169 + 0.802115i \(0.296292\pi\)
\(702\) −10.1619 −0.383538
\(703\) −11.5132 −0.434228
\(704\) −32.2136 −1.21410
\(705\) 3.33879 0.125746
\(706\) −30.5595 −1.15012
\(707\) −3.04532 −0.114531
\(708\) −43.3103 −1.62770
\(709\) −43.9815 −1.65176 −0.825881 0.563845i \(-0.809322\pi\)
−0.825881 + 0.563845i \(0.809322\pi\)
\(710\) 6.62264 0.248543
\(711\) 8.12856 0.304845
\(712\) 34.5975 1.29660
\(713\) 45.3100 1.69687
\(714\) 0.948273 0.0354882
\(715\) −8.63871 −0.323069
\(716\) 21.4174 0.800407
\(717\) 8.35900 0.312173
\(718\) 19.1596 0.715030
\(719\) −7.66382 −0.285812 −0.142906 0.989736i \(-0.545645\pi\)
−0.142906 + 0.989736i \(0.545645\pi\)
\(720\) −4.44087 −0.165502
\(721\) 9.56437 0.356196
\(722\) 41.0633 1.52822
\(723\) −44.7670 −1.66490
\(724\) −86.3821 −3.21036
\(725\) 3.33530 0.123870
\(726\) −18.0874 −0.671286
\(727\) −27.7274 −1.02835 −0.514177 0.857684i \(-0.671902\pi\)
−0.514177 + 0.857684i \(0.671902\pi\)
\(728\) 5.91116 0.219082
\(729\) −14.3182 −0.530302
\(730\) 33.2117 1.22922
\(731\) −0.0761760 −0.00281747
\(732\) 59.0379 2.18211
\(733\) −23.0371 −0.850896 −0.425448 0.904983i \(-0.639883\pi\)
−0.425448 + 0.904983i \(0.639883\pi\)
\(734\) −73.9454 −2.72937
\(735\) −16.8778 −0.622546
\(736\) 23.4162 0.863132
\(737\) 24.6372 0.907525
\(738\) −42.9776 −1.58203
\(739\) −27.2446 −1.00221 −0.501105 0.865387i \(-0.667073\pi\)
−0.501105 + 0.865387i \(0.667073\pi\)
\(740\) −35.1988 −1.29394
\(741\) 8.47127 0.311200
\(742\) 3.88581 0.142652
\(743\) 23.2996 0.854778 0.427389 0.904068i \(-0.359433\pi\)
0.427389 + 0.904068i \(0.359433\pi\)
\(744\) 58.1433 2.13164
\(745\) 6.91562 0.253369
\(746\) 47.4779 1.73829
\(747\) 1.22766 0.0449176
\(748\) −3.15486 −0.115353
\(749\) 10.0334 0.366613
\(750\) 52.5201 1.91776
\(751\) −21.9317 −0.800301 −0.400150 0.916449i \(-0.631042\pi\)
−0.400150 + 0.916449i \(0.631042\pi\)
\(752\) 2.29929 0.0838463
\(753\) 46.7260 1.70279
\(754\) 5.91535 0.215424
\(755\) 2.54177 0.0925044
\(756\) −2.95884 −0.107612
\(757\) −27.4099 −0.996229 −0.498114 0.867111i \(-0.665974\pi\)
−0.498114 + 0.867111i \(0.665974\pi\)
\(758\) −7.82174 −0.284098
\(759\) −43.6397 −1.58402
\(760\) −5.26249 −0.190891
\(761\) −11.0143 −0.399267 −0.199633 0.979871i \(-0.563975\pi\)
−0.199633 + 0.979871i \(0.563975\pi\)
\(762\) 13.1484 0.476318
\(763\) 5.36980 0.194400
\(764\) 72.2949 2.61554
\(765\) 0.809834 0.0292796
\(766\) 62.5171 2.25883
\(767\) 14.8933 0.537767
\(768\) 58.9019 2.12544
\(769\) 49.9880 1.80261 0.901306 0.433183i \(-0.142610\pi\)
0.901306 + 0.433183i \(0.142610\pi\)
\(770\) −3.91461 −0.141073
\(771\) 44.6427 1.60777
\(772\) −76.3955 −2.74954
\(773\) 32.4445 1.16695 0.583473 0.812132i \(-0.301693\pi\)
0.583473 + 0.812132i \(0.301693\pi\)
\(774\) −1.33879 −0.0481217
\(775\) −25.4079 −0.912680
\(776\) −68.7770 −2.46895
\(777\) 11.3922 0.408694
\(778\) 42.7901 1.53410
\(779\) −9.89927 −0.354678
\(780\) 25.8989 0.927330
\(781\) 7.13113 0.255172
\(782\) 5.08962 0.182005
\(783\) −1.31375 −0.0469496
\(784\) −11.6230 −0.415108
\(785\) 18.5389 0.661683
\(786\) 52.0283 1.85579
\(787\) 43.1828 1.53930 0.769650 0.638466i \(-0.220431\pi\)
0.769650 + 0.638466i \(0.220431\pi\)
\(788\) 41.1436 1.46568
\(789\) 28.0303 0.997905
\(790\) 8.90846 0.316949
\(791\) 2.87069 0.102070
\(792\) −24.6013 −0.874168
\(793\) −20.3017 −0.720933
\(794\) −73.3642 −2.60360
\(795\) 7.55396 0.267911
\(796\) −89.5803 −3.17509
\(797\) −49.1787 −1.74200 −0.870999 0.491284i \(-0.836528\pi\)
−0.870999 + 0.491284i \(0.836528\pi\)
\(798\) 3.83873 0.135890
\(799\) −0.419296 −0.0148336
\(800\) −13.1308 −0.464245
\(801\) −21.5528 −0.761531
\(802\) −73.5252 −2.59626
\(803\) 35.7617 1.26200
\(804\) −73.8627 −2.60494
\(805\) 4.05788 0.143022
\(806\) −45.0625 −1.58726
\(807\) −43.7842 −1.54128
\(808\) −20.9745 −0.737880
\(809\) 31.6555 1.11295 0.556474 0.830865i \(-0.312154\pi\)
0.556474 + 0.830865i \(0.312154\pi\)
\(810\) −27.1171 −0.952798
\(811\) −27.1211 −0.952351 −0.476175 0.879350i \(-0.657977\pi\)
−0.476175 + 0.879350i \(0.657977\pi\)
\(812\) 1.72236 0.0604431
\(813\) 6.97363 0.244576
\(814\) −58.9862 −2.06746
\(815\) 12.3022 0.430928
\(816\) 1.26949 0.0444411
\(817\) −0.308370 −0.0107885
\(818\) −75.1498 −2.62755
\(819\) −3.68241 −0.128674
\(820\) −30.2647 −1.05689
\(821\) 30.4777 1.06368 0.531839 0.846845i \(-0.321501\pi\)
0.531839 + 0.846845i \(0.321501\pi\)
\(822\) 109.968 3.83558
\(823\) −8.32199 −0.290086 −0.145043 0.989425i \(-0.546332\pi\)
−0.145043 + 0.989425i \(0.546332\pi\)
\(824\) 65.8741 2.29483
\(825\) 24.4713 0.851982
\(826\) 6.74887 0.234823
\(827\) −35.4349 −1.23219 −0.616096 0.787671i \(-0.711287\pi\)
−0.616096 + 0.787671i \(0.711287\pi\)
\(828\) 57.4757 1.99742
\(829\) 48.4583 1.68303 0.841513 0.540236i \(-0.181665\pi\)
0.841513 + 0.540236i \(0.181665\pi\)
\(830\) 1.34545 0.0467011
\(831\) −46.6580 −1.61855
\(832\) −33.2103 −1.15136
\(833\) 2.11956 0.0734385
\(834\) −43.1525 −1.49425
\(835\) −4.79318 −0.165875
\(836\) −12.7713 −0.441704
\(837\) 10.0080 0.345928
\(838\) −61.6510 −2.12970
\(839\) −13.0366 −0.450073 −0.225037 0.974350i \(-0.572250\pi\)
−0.225037 + 0.974350i \(0.572250\pi\)
\(840\) 5.20722 0.179666
\(841\) −28.2353 −0.973629
\(842\) −21.3641 −0.736255
\(843\) −47.0781 −1.62146
\(844\) −42.4839 −1.46235
\(845\) 5.25173 0.180665
\(846\) −7.36909 −0.253354
\(847\) 1.81101 0.0622270
\(848\) 5.20209 0.178640
\(849\) −54.0082 −1.85356
\(850\) −2.85405 −0.0978931
\(851\) 61.1451 2.09603
\(852\) −21.3792 −0.732439
\(853\) 36.7517 1.25835 0.629177 0.777262i \(-0.283392\pi\)
0.629177 + 0.777262i \(0.283392\pi\)
\(854\) −9.19964 −0.314805
\(855\) 3.27831 0.112116
\(856\) 69.1047 2.36195
\(857\) −15.7392 −0.537640 −0.268820 0.963190i \(-0.586634\pi\)
−0.268820 + 0.963190i \(0.586634\pi\)
\(858\) 43.4014 1.48170
\(859\) 33.1034 1.12947 0.564737 0.825271i \(-0.308978\pi\)
0.564737 + 0.825271i \(0.308978\pi\)
\(860\) −0.942770 −0.0321482
\(861\) 9.79529 0.333822
\(862\) −1.94613 −0.0662855
\(863\) −21.5795 −0.734575 −0.367287 0.930108i \(-0.619713\pi\)
−0.367287 + 0.930108i \(0.619713\pi\)
\(864\) 5.17214 0.175960
\(865\) −26.3177 −0.894830
\(866\) 9.42486 0.320270
\(867\) 39.0916 1.32762
\(868\) −13.1208 −0.445349
\(869\) 9.59245 0.325402
\(870\) 5.21090 0.176666
\(871\) 25.3995 0.860629
\(872\) 36.9842 1.25244
\(873\) 42.8452 1.45009
\(874\) 20.6035 0.696922
\(875\) −5.25860 −0.177773
\(876\) −107.214 −3.62242
\(877\) 25.8556 0.873081 0.436541 0.899685i \(-0.356204\pi\)
0.436541 + 0.899685i \(0.356204\pi\)
\(878\) −66.0804 −2.23010
\(879\) −11.1714 −0.376802
\(880\) −5.24064 −0.176662
\(881\) 33.6747 1.13453 0.567265 0.823535i \(-0.308002\pi\)
0.567265 + 0.823535i \(0.308002\pi\)
\(882\) 37.2511 1.25431
\(883\) 13.9368 0.469012 0.234506 0.972115i \(-0.424653\pi\)
0.234506 + 0.972115i \(0.424653\pi\)
\(884\) −3.25246 −0.109392
\(885\) 13.1197 0.441014
\(886\) 48.7054 1.63629
\(887\) −39.1599 −1.31486 −0.657431 0.753515i \(-0.728357\pi\)
−0.657431 + 0.753515i \(0.728357\pi\)
\(888\) 78.4635 2.63306
\(889\) −1.31649 −0.0441538
\(890\) −23.6207 −0.791768
\(891\) −29.1992 −0.978209
\(892\) −98.4672 −3.29692
\(893\) −1.69736 −0.0568001
\(894\) −34.7445 −1.16203
\(895\) −6.48784 −0.216865
\(896\) −11.2769 −0.376736
\(897\) −44.9899 −1.50217
\(898\) −76.5184 −2.55345
\(899\) −5.82575 −0.194300
\(900\) −32.2300 −1.07433
\(901\) −0.948649 −0.0316041
\(902\) −50.7175 −1.68871
\(903\) 0.305131 0.0101541
\(904\) 19.7718 0.657599
\(905\) 26.1671 0.869825
\(906\) −12.7700 −0.424254
\(907\) 26.2015 0.870006 0.435003 0.900429i \(-0.356747\pi\)
0.435003 + 0.900429i \(0.356747\pi\)
\(908\) −83.8639 −2.78312
\(909\) 13.0662 0.433379
\(910\) −4.03572 −0.133783
\(911\) 9.38362 0.310893 0.155447 0.987844i \(-0.450318\pi\)
0.155447 + 0.987844i \(0.450318\pi\)
\(912\) 5.13907 0.170172
\(913\) 1.44875 0.0479466
\(914\) −11.3600 −0.375754
\(915\) −17.8840 −0.591226
\(916\) 101.743 3.36169
\(917\) −5.20936 −0.172028
\(918\) 1.12419 0.0371038
\(919\) −25.1250 −0.828798 −0.414399 0.910095i \(-0.636008\pi\)
−0.414399 + 0.910095i \(0.636008\pi\)
\(920\) 27.9485 0.921433
\(921\) −51.8002 −1.70687
\(922\) 45.0438 1.48344
\(923\) 7.35176 0.241986
\(924\) 12.6371 0.415731
\(925\) −34.2876 −1.12737
\(926\) −8.84257 −0.290585
\(927\) −41.0368 −1.34783
\(928\) −3.01075 −0.0988327
\(929\) 29.6383 0.972402 0.486201 0.873847i \(-0.338382\pi\)
0.486201 + 0.873847i \(0.338382\pi\)
\(930\) −39.6961 −1.30169
\(931\) 8.58027 0.281207
\(932\) 54.3250 1.77948
\(933\) 13.5494 0.443588
\(934\) −15.1658 −0.496241
\(935\) 0.955679 0.0312541
\(936\) −25.3624 −0.828996
\(937\) 48.0486 1.56968 0.784839 0.619699i \(-0.212745\pi\)
0.784839 + 0.619699i \(0.212745\pi\)
\(938\) 11.5097 0.375805
\(939\) 41.2193 1.34514
\(940\) −5.18929 −0.169256
\(941\) −1.59630 −0.0520380 −0.0260190 0.999661i \(-0.508283\pi\)
−0.0260190 + 0.999661i \(0.508283\pi\)
\(942\) −93.1407 −3.03469
\(943\) 52.5738 1.71204
\(944\) 9.03499 0.294064
\(945\) 0.896301 0.0291567
\(946\) −1.57989 −0.0513667
\(947\) −31.4701 −1.02264 −0.511321 0.859390i \(-0.670844\pi\)
−0.511321 + 0.859390i \(0.670844\pi\)
\(948\) −28.7583 −0.934025
\(949\) 36.8682 1.19679
\(950\) −11.5536 −0.374847
\(951\) −74.6433 −2.42047
\(952\) −0.653938 −0.0211943
\(953\) −45.2375 −1.46539 −0.732693 0.680559i \(-0.761737\pi\)
−0.732693 + 0.680559i \(0.761737\pi\)
\(954\) −16.6724 −0.539789
\(955\) −21.8998 −0.708661
\(956\) −12.9919 −0.420188
\(957\) 5.61100 0.181378
\(958\) −28.9216 −0.934413
\(959\) −11.0106 −0.355551
\(960\) −29.2553 −0.944212
\(961\) 13.3800 0.431613
\(962\) −60.8111 −1.96063
\(963\) −43.0493 −1.38725
\(964\) 69.5787 2.24098
\(965\) 23.1420 0.744967
\(966\) −20.3870 −0.655942
\(967\) −41.4454 −1.33280 −0.666398 0.745596i \(-0.732165\pi\)
−0.666398 + 0.745596i \(0.732165\pi\)
\(968\) 12.4732 0.400905
\(969\) −0.937156 −0.0301058
\(970\) 46.9560 1.50767
\(971\) −10.6681 −0.342356 −0.171178 0.985240i \(-0.554757\pi\)
−0.171178 + 0.985240i \(0.554757\pi\)
\(972\) 71.3365 2.28812
\(973\) 4.32067 0.138514
\(974\) −9.19236 −0.294542
\(975\) 25.2285 0.807957
\(976\) −12.3159 −0.394223
\(977\) −40.0480 −1.28125 −0.640624 0.767855i \(-0.721324\pi\)
−0.640624 + 0.767855i \(0.721324\pi\)
\(978\) −61.8071 −1.97637
\(979\) −25.4343 −0.812884
\(980\) 26.2322 0.837955
\(981\) −23.0396 −0.735599
\(982\) 66.5788 2.12462
\(983\) 34.7661 1.10887 0.554433 0.832229i \(-0.312935\pi\)
0.554433 + 0.832229i \(0.312935\pi\)
\(984\) 67.4645 2.15069
\(985\) −12.4633 −0.397115
\(986\) −0.654401 −0.0208404
\(987\) 1.67953 0.0534602
\(988\) −13.1664 −0.418879
\(989\) 1.63772 0.0520764
\(990\) 16.7960 0.533811
\(991\) 11.1677 0.354754 0.177377 0.984143i \(-0.443239\pi\)
0.177377 + 0.984143i \(0.443239\pi\)
\(992\) 22.9356 0.728205
\(993\) −35.8923 −1.13901
\(994\) 3.33143 0.105667
\(995\) 27.1360 0.860268
\(996\) −4.34336 −0.137625
\(997\) −33.0502 −1.04671 −0.523356 0.852114i \(-0.675320\pi\)
−0.523356 + 0.852114i \(0.675320\pi\)
\(998\) −89.4305 −2.83087
\(999\) 13.5057 0.427300
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 4027.2.a.c.1.17 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.17 174 1.1 even 1 trivial