Properties

Label 8033.2.a.c.1.10
Level $8033$
Weight $2$
Character 8033.1
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $154$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(154\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 8033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.51869 q^{2} +0.856221 q^{3} +4.34380 q^{4} +2.85854 q^{5} -2.15656 q^{6} -2.09984 q^{7} -5.90330 q^{8} -2.26688 q^{9} +O(q^{10})\) \(q-2.51869 q^{2} +0.856221 q^{3} +4.34380 q^{4} +2.85854 q^{5} -2.15656 q^{6} -2.09984 q^{7} -5.90330 q^{8} -2.26688 q^{9} -7.19979 q^{10} +4.13907 q^{11} +3.71925 q^{12} -3.52588 q^{13} +5.28885 q^{14} +2.44755 q^{15} +6.18098 q^{16} -2.95728 q^{17} +5.70958 q^{18} +6.64980 q^{19} +12.4169 q^{20} -1.79793 q^{21} -10.4250 q^{22} -1.55948 q^{23} -5.05453 q^{24} +3.17128 q^{25} +8.88059 q^{26} -4.50962 q^{27} -9.12130 q^{28} +1.00000 q^{29} -6.16461 q^{30} +5.39140 q^{31} -3.76138 q^{32} +3.54396 q^{33} +7.44847 q^{34} -6.00250 q^{35} -9.84689 q^{36} +0.947797 q^{37} -16.7488 q^{38} -3.01893 q^{39} -16.8748 q^{40} -2.18113 q^{41} +4.52843 q^{42} -10.4669 q^{43} +17.9793 q^{44} -6.47999 q^{45} +3.92784 q^{46} +5.38926 q^{47} +5.29229 q^{48} -2.59066 q^{49} -7.98746 q^{50} -2.53209 q^{51} -15.3157 q^{52} -9.94779 q^{53} +11.3583 q^{54} +11.8317 q^{55} +12.3960 q^{56} +5.69370 q^{57} -2.51869 q^{58} -8.20758 q^{59} +10.6316 q^{60} +3.34496 q^{61} -13.5793 q^{62} +4.76010 q^{63} -2.88822 q^{64} -10.0789 q^{65} -8.92613 q^{66} +0.413585 q^{67} -12.8458 q^{68} -1.33526 q^{69} +15.1184 q^{70} -8.54828 q^{71} +13.3821 q^{72} -3.00400 q^{73} -2.38721 q^{74} +2.71531 q^{75} +28.8854 q^{76} -8.69140 q^{77} +7.60376 q^{78} +10.9773 q^{79} +17.6686 q^{80} +2.93942 q^{81} +5.49360 q^{82} +1.69324 q^{83} -7.80985 q^{84} -8.45352 q^{85} +26.3629 q^{86} +0.856221 q^{87} -24.4342 q^{88} +0.555214 q^{89} +16.3211 q^{90} +7.40380 q^{91} -6.77406 q^{92} +4.61623 q^{93} -13.5739 q^{94} +19.0088 q^{95} -3.22057 q^{96} -11.5136 q^{97} +6.52506 q^{98} -9.38279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51869 −1.78098 −0.890491 0.455000i \(-0.849639\pi\)
−0.890491 + 0.455000i \(0.849639\pi\)
\(3\) 0.856221 0.494340 0.247170 0.968972i \(-0.420499\pi\)
0.247170 + 0.968972i \(0.420499\pi\)
\(4\) 4.34380 2.17190
\(5\) 2.85854 1.27838 0.639190 0.769049i \(-0.279270\pi\)
0.639190 + 0.769049i \(0.279270\pi\)
\(6\) −2.15656 −0.880410
\(7\) −2.09984 −0.793666 −0.396833 0.917891i \(-0.629891\pi\)
−0.396833 + 0.917891i \(0.629891\pi\)
\(8\) −5.90330 −2.08713
\(9\) −2.26688 −0.755628
\(10\) −7.19979 −2.27677
\(11\) 4.13907 1.24798 0.623988 0.781434i \(-0.285511\pi\)
0.623988 + 0.781434i \(0.285511\pi\)
\(12\) 3.71925 1.07366
\(13\) −3.52588 −0.977903 −0.488951 0.872311i \(-0.662620\pi\)
−0.488951 + 0.872311i \(0.662620\pi\)
\(14\) 5.28885 1.41351
\(15\) 2.44755 0.631954
\(16\) 6.18098 1.54525
\(17\) −2.95728 −0.717246 −0.358623 0.933483i \(-0.616754\pi\)
−0.358623 + 0.933483i \(0.616754\pi\)
\(18\) 5.70958 1.34576
\(19\) 6.64980 1.52557 0.762785 0.646652i \(-0.223832\pi\)
0.762785 + 0.646652i \(0.223832\pi\)
\(20\) 12.4169 2.77651
\(21\) −1.79793 −0.392341
\(22\) −10.4250 −2.22262
\(23\) −1.55948 −0.325174 −0.162587 0.986694i \(-0.551984\pi\)
−0.162587 + 0.986694i \(0.551984\pi\)
\(24\) −5.05453 −1.03175
\(25\) 3.17128 0.634255
\(26\) 8.88059 1.74163
\(27\) −4.50962 −0.867877
\(28\) −9.12130 −1.72376
\(29\) 1.00000 0.185695
\(30\) −6.16461 −1.12550
\(31\) 5.39140 0.968323 0.484162 0.874979i \(-0.339125\pi\)
0.484162 + 0.874979i \(0.339125\pi\)
\(32\) −3.76138 −0.664924
\(33\) 3.54396 0.616924
\(34\) 7.44847 1.27740
\(35\) −6.00250 −1.01461
\(36\) −9.84689 −1.64115
\(37\) 0.947797 0.155817 0.0779085 0.996961i \(-0.475176\pi\)
0.0779085 + 0.996961i \(0.475176\pi\)
\(38\) −16.7488 −2.71701
\(39\) −3.01893 −0.483416
\(40\) −16.8748 −2.66815
\(41\) −2.18113 −0.340636 −0.170318 0.985389i \(-0.554479\pi\)
−0.170318 + 0.985389i \(0.554479\pi\)
\(42\) 4.52843 0.698752
\(43\) −10.4669 −1.59619 −0.798095 0.602532i \(-0.794159\pi\)
−0.798095 + 0.602532i \(0.794159\pi\)
\(44\) 17.9793 2.71048
\(45\) −6.47999 −0.965980
\(46\) 3.92784 0.579129
\(47\) 5.38926 0.786105 0.393052 0.919516i \(-0.371419\pi\)
0.393052 + 0.919516i \(0.371419\pi\)
\(48\) 5.29229 0.763876
\(49\) −2.59066 −0.370094
\(50\) −7.98746 −1.12960
\(51\) −2.53209 −0.354563
\(52\) −15.3157 −2.12391
\(53\) −9.94779 −1.36643 −0.683217 0.730215i \(-0.739420\pi\)
−0.683217 + 0.730215i \(0.739420\pi\)
\(54\) 11.3583 1.54567
\(55\) 11.8317 1.59539
\(56\) 12.3960 1.65649
\(57\) 5.69370 0.754150
\(58\) −2.51869 −0.330720
\(59\) −8.20758 −1.06854 −0.534268 0.845315i \(-0.679413\pi\)
−0.534268 + 0.845315i \(0.679413\pi\)
\(60\) 10.6316 1.37254
\(61\) 3.34496 0.428278 0.214139 0.976803i \(-0.431305\pi\)
0.214139 + 0.976803i \(0.431305\pi\)
\(62\) −13.5793 −1.72457
\(63\) 4.76010 0.599717
\(64\) −2.88822 −0.361028
\(65\) −10.0789 −1.25013
\(66\) −8.92613 −1.09873
\(67\) 0.413585 0.0505274 0.0252637 0.999681i \(-0.491957\pi\)
0.0252637 + 0.999681i \(0.491957\pi\)
\(68\) −12.8458 −1.55779
\(69\) −1.33526 −0.160746
\(70\) 15.1184 1.80700
\(71\) −8.54828 −1.01449 −0.507247 0.861801i \(-0.669337\pi\)
−0.507247 + 0.861801i \(0.669337\pi\)
\(72\) 13.3821 1.57710
\(73\) −3.00400 −0.351591 −0.175796 0.984427i \(-0.556250\pi\)
−0.175796 + 0.984427i \(0.556250\pi\)
\(74\) −2.38721 −0.277507
\(75\) 2.71531 0.313537
\(76\) 28.8854 3.31338
\(77\) −8.69140 −0.990477
\(78\) 7.60376 0.860956
\(79\) 10.9773 1.23504 0.617522 0.786554i \(-0.288137\pi\)
0.617522 + 0.786554i \(0.288137\pi\)
\(80\) 17.6686 1.97541
\(81\) 2.93942 0.326602
\(82\) 5.49360 0.606666
\(83\) 1.69324 0.185858 0.0929289 0.995673i \(-0.470377\pi\)
0.0929289 + 0.995673i \(0.470377\pi\)
\(84\) −7.80985 −0.852124
\(85\) −8.45352 −0.916912
\(86\) 26.3629 2.84279
\(87\) 0.856221 0.0917966
\(88\) −24.4342 −2.60469
\(89\) 0.555214 0.0588525 0.0294263 0.999567i \(-0.490632\pi\)
0.0294263 + 0.999567i \(0.490632\pi\)
\(90\) 16.3211 1.72039
\(91\) 7.40380 0.776129
\(92\) −6.77406 −0.706244
\(93\) 4.61623 0.478681
\(94\) −13.5739 −1.40004
\(95\) 19.0088 1.95026
\(96\) −3.22057 −0.328698
\(97\) −11.5136 −1.16903 −0.584517 0.811381i \(-0.698716\pi\)
−0.584517 + 0.811381i \(0.698716\pi\)
\(98\) 6.52506 0.659130
\(99\) −9.38279 −0.943006
\(100\) 13.7754 1.37754
\(101\) −8.39462 −0.835295 −0.417648 0.908609i \(-0.637145\pi\)
−0.417648 + 0.908609i \(0.637145\pi\)
\(102\) 6.37754 0.631470
\(103\) 13.3268 1.31313 0.656563 0.754272i \(-0.272010\pi\)
0.656563 + 0.754272i \(0.272010\pi\)
\(104\) 20.8143 2.04101
\(105\) −5.13947 −0.501561
\(106\) 25.0554 2.43360
\(107\) 11.8470 1.14529 0.572647 0.819802i \(-0.305917\pi\)
0.572647 + 0.819802i \(0.305917\pi\)
\(108\) −19.5889 −1.88494
\(109\) −11.6309 −1.11404 −0.557020 0.830499i \(-0.688055\pi\)
−0.557020 + 0.830499i \(0.688055\pi\)
\(110\) −29.8004 −2.84136
\(111\) 0.811524 0.0770265
\(112\) −12.9791 −1.22641
\(113\) 7.65618 0.720233 0.360117 0.932907i \(-0.382737\pi\)
0.360117 + 0.932907i \(0.382737\pi\)
\(114\) −14.3407 −1.34313
\(115\) −4.45784 −0.415696
\(116\) 4.34380 0.403311
\(117\) 7.99276 0.738931
\(118\) 20.6724 1.90304
\(119\) 6.20983 0.569254
\(120\) −14.4486 −1.31897
\(121\) 6.13188 0.557444
\(122\) −8.42491 −0.762755
\(123\) −1.86753 −0.168390
\(124\) 23.4191 2.10310
\(125\) −5.22749 −0.467561
\(126\) −11.9892 −1.06809
\(127\) −8.15168 −0.723344 −0.361672 0.932305i \(-0.617794\pi\)
−0.361672 + 0.932305i \(0.617794\pi\)
\(128\) 14.7973 1.30791
\(129\) −8.96199 −0.789060
\(130\) 25.3856 2.22646
\(131\) −2.99298 −0.261498 −0.130749 0.991415i \(-0.541738\pi\)
−0.130749 + 0.991415i \(0.541738\pi\)
\(132\) 15.3942 1.33990
\(133\) −13.9636 −1.21079
\(134\) −1.04169 −0.0899885
\(135\) −12.8909 −1.10948
\(136\) 17.4577 1.49699
\(137\) −1.38832 −0.118612 −0.0593060 0.998240i \(-0.518889\pi\)
−0.0593060 + 0.998240i \(0.518889\pi\)
\(138\) 3.36310 0.286286
\(139\) 16.4252 1.39317 0.696583 0.717477i \(-0.254703\pi\)
0.696583 + 0.717477i \(0.254703\pi\)
\(140\) −26.0736 −2.20362
\(141\) 4.61440 0.388603
\(142\) 21.5305 1.80680
\(143\) −14.5939 −1.22040
\(144\) −14.0116 −1.16763
\(145\) 2.85854 0.237389
\(146\) 7.56614 0.626178
\(147\) −2.21817 −0.182952
\(148\) 4.11704 0.338419
\(149\) −4.28514 −0.351052 −0.175526 0.984475i \(-0.556163\pi\)
−0.175526 + 0.984475i \(0.556163\pi\)
\(150\) −6.83903 −0.558405
\(151\) 8.85411 0.720537 0.360268 0.932849i \(-0.382685\pi\)
0.360268 + 0.932849i \(0.382685\pi\)
\(152\) −39.2558 −3.18406
\(153\) 6.70381 0.541971
\(154\) 21.8909 1.76402
\(155\) 15.4115 1.23789
\(156\) −13.1136 −1.04993
\(157\) 0.155484 0.0124090 0.00620450 0.999981i \(-0.498025\pi\)
0.00620450 + 0.999981i \(0.498025\pi\)
\(158\) −27.6484 −2.19959
\(159\) −8.51751 −0.675483
\(160\) −10.7521 −0.850025
\(161\) 3.27466 0.258079
\(162\) −7.40349 −0.581673
\(163\) 2.04684 0.160321 0.0801604 0.996782i \(-0.474457\pi\)
0.0801604 + 0.996782i \(0.474457\pi\)
\(164\) −9.47440 −0.739826
\(165\) 10.1306 0.788663
\(166\) −4.26476 −0.331009
\(167\) −16.9384 −1.31073 −0.655366 0.755311i \(-0.727486\pi\)
−0.655366 + 0.755311i \(0.727486\pi\)
\(168\) 10.6137 0.818867
\(169\) −0.568177 −0.0437059
\(170\) 21.2918 1.63301
\(171\) −15.0743 −1.15276
\(172\) −45.4661 −3.46676
\(173\) −22.0549 −1.67680 −0.838401 0.545053i \(-0.816509\pi\)
−0.838401 + 0.545053i \(0.816509\pi\)
\(174\) −2.15656 −0.163488
\(175\) −6.65918 −0.503387
\(176\) 25.5835 1.92843
\(177\) −7.02751 −0.528220
\(178\) −1.39841 −0.104815
\(179\) 14.3666 1.07381 0.536907 0.843642i \(-0.319593\pi\)
0.536907 + 0.843642i \(0.319593\pi\)
\(180\) −28.1478 −2.09801
\(181\) −4.19106 −0.311519 −0.155760 0.987795i \(-0.549783\pi\)
−0.155760 + 0.987795i \(0.549783\pi\)
\(182\) −18.6479 −1.38227
\(183\) 2.86402 0.211715
\(184\) 9.20607 0.678680
\(185\) 2.70932 0.199193
\(186\) −11.6268 −0.852522
\(187\) −12.2404 −0.895105
\(188\) 23.4099 1.70734
\(189\) 9.46950 0.688805
\(190\) −47.8772 −3.47337
\(191\) −1.61806 −0.117078 −0.0585392 0.998285i \(-0.518644\pi\)
−0.0585392 + 0.998285i \(0.518644\pi\)
\(192\) −2.47296 −0.178470
\(193\) −26.8863 −1.93532 −0.967660 0.252258i \(-0.918827\pi\)
−0.967660 + 0.252258i \(0.918827\pi\)
\(194\) 28.9993 2.08203
\(195\) −8.62975 −0.617989
\(196\) −11.2533 −0.803806
\(197\) 10.9753 0.781961 0.390980 0.920399i \(-0.372136\pi\)
0.390980 + 0.920399i \(0.372136\pi\)
\(198\) 23.6323 1.67948
\(199\) 1.50400 0.106616 0.0533079 0.998578i \(-0.483024\pi\)
0.0533079 + 0.998578i \(0.483024\pi\)
\(200\) −18.7210 −1.32377
\(201\) 0.354120 0.0249777
\(202\) 21.1434 1.48765
\(203\) −2.09984 −0.147380
\(204\) −10.9989 −0.770075
\(205\) −6.23487 −0.435462
\(206\) −33.5660 −2.33865
\(207\) 3.53516 0.245710
\(208\) −21.7934 −1.51110
\(209\) 27.5240 1.90387
\(210\) 12.9447 0.893270
\(211\) 8.39783 0.578130 0.289065 0.957309i \(-0.406656\pi\)
0.289065 + 0.957309i \(0.406656\pi\)
\(212\) −43.2112 −2.96776
\(213\) −7.31922 −0.501504
\(214\) −29.8389 −2.03975
\(215\) −29.9201 −2.04054
\(216\) 26.6216 1.81137
\(217\) −11.3211 −0.768526
\(218\) 29.2947 1.98408
\(219\) −2.57209 −0.173806
\(220\) 51.3945 3.46502
\(221\) 10.4270 0.701397
\(222\) −2.04398 −0.137183
\(223\) 1.30233 0.0872105 0.0436052 0.999049i \(-0.486116\pi\)
0.0436052 + 0.999049i \(0.486116\pi\)
\(224\) 7.89830 0.527727
\(225\) −7.18892 −0.479261
\(226\) −19.2835 −1.28272
\(227\) −25.8320 −1.71453 −0.857265 0.514875i \(-0.827838\pi\)
−0.857265 + 0.514875i \(0.827838\pi\)
\(228\) 24.7323 1.63794
\(229\) 14.2816 0.943756 0.471878 0.881664i \(-0.343576\pi\)
0.471878 + 0.881664i \(0.343576\pi\)
\(230\) 11.2279 0.740346
\(231\) −7.44176 −0.489632
\(232\) −5.90330 −0.387570
\(233\) −16.0648 −1.05244 −0.526222 0.850348i \(-0.676392\pi\)
−0.526222 + 0.850348i \(0.676392\pi\)
\(234\) −20.1313 −1.31602
\(235\) 15.4054 1.00494
\(236\) −35.6521 −2.32075
\(237\) 9.39900 0.610531
\(238\) −15.6406 −1.01383
\(239\) −10.0630 −0.650922 −0.325461 0.945556i \(-0.605519\pi\)
−0.325461 + 0.945556i \(0.605519\pi\)
\(240\) 15.1282 0.976524
\(241\) −24.7756 −1.59594 −0.797968 0.602700i \(-0.794092\pi\)
−0.797968 + 0.602700i \(0.794092\pi\)
\(242\) −15.4443 −0.992798
\(243\) 16.0457 1.02933
\(244\) 14.5298 0.930176
\(245\) −7.40550 −0.473120
\(246\) 4.70374 0.299899
\(247\) −23.4464 −1.49186
\(248\) −31.8270 −2.02102
\(249\) 1.44979 0.0918768
\(250\) 13.1664 0.832718
\(251\) 8.64192 0.545473 0.272736 0.962089i \(-0.412071\pi\)
0.272736 + 0.962089i \(0.412071\pi\)
\(252\) 20.6769 1.30252
\(253\) −6.45479 −0.405809
\(254\) 20.5315 1.28826
\(255\) −7.23808 −0.453266
\(256\) −31.4933 −1.96833
\(257\) −3.65842 −0.228206 −0.114103 0.993469i \(-0.536399\pi\)
−0.114103 + 0.993469i \(0.536399\pi\)
\(258\) 22.5725 1.40530
\(259\) −1.99023 −0.123667
\(260\) −43.7806 −2.71516
\(261\) −2.26688 −0.140317
\(262\) 7.53839 0.465724
\(263\) 0.266691 0.0164449 0.00822244 0.999966i \(-0.497383\pi\)
0.00822244 + 0.999966i \(0.497383\pi\)
\(264\) −20.9210 −1.28760
\(265\) −28.4362 −1.74682
\(266\) 35.1698 2.15640
\(267\) 0.475386 0.0290931
\(268\) 1.79653 0.109740
\(269\) 12.6587 0.771813 0.385906 0.922538i \(-0.373889\pi\)
0.385906 + 0.922538i \(0.373889\pi\)
\(270\) 32.4683 1.97596
\(271\) −28.2643 −1.71693 −0.858467 0.512868i \(-0.828583\pi\)
−0.858467 + 0.512868i \(0.828583\pi\)
\(272\) −18.2789 −1.10832
\(273\) 6.33929 0.383671
\(274\) 3.49674 0.211246
\(275\) 13.1261 0.791535
\(276\) −5.80009 −0.349125
\(277\) 1.00000 0.0600842
\(278\) −41.3699 −2.48120
\(279\) −12.2217 −0.731693
\(280\) 35.4345 2.11762
\(281\) −12.8183 −0.764675 −0.382338 0.924023i \(-0.624881\pi\)
−0.382338 + 0.924023i \(0.624881\pi\)
\(282\) −11.6222 −0.692095
\(283\) −24.5097 −1.45695 −0.728475 0.685072i \(-0.759771\pi\)
−0.728475 + 0.685072i \(0.759771\pi\)
\(284\) −37.1320 −2.20338
\(285\) 16.2757 0.964090
\(286\) 36.7574 2.17351
\(287\) 4.58004 0.270351
\(288\) 8.52661 0.502435
\(289\) −8.25450 −0.485559
\(290\) −7.19979 −0.422786
\(291\) −9.85823 −0.577900
\(292\) −13.0488 −0.763621
\(293\) 30.2306 1.76609 0.883046 0.469287i \(-0.155489\pi\)
0.883046 + 0.469287i \(0.155489\pi\)
\(294\) 5.58689 0.325834
\(295\) −23.4617 −1.36600
\(296\) −5.59513 −0.325210
\(297\) −18.6656 −1.08309
\(298\) 10.7929 0.625218
\(299\) 5.49853 0.317988
\(300\) 11.7948 0.680972
\(301\) 21.9789 1.26684
\(302\) −22.3007 −1.28326
\(303\) −7.18765 −0.412920
\(304\) 41.1023 2.35738
\(305\) 9.56171 0.547502
\(306\) −16.8848 −0.965241
\(307\) −20.8466 −1.18978 −0.594890 0.803807i \(-0.702804\pi\)
−0.594890 + 0.803807i \(0.702804\pi\)
\(308\) −37.7537 −2.15121
\(309\) 11.4107 0.649130
\(310\) −38.8169 −2.20465
\(311\) 0.790747 0.0448392 0.0224196 0.999749i \(-0.492863\pi\)
0.0224196 + 0.999749i \(0.492863\pi\)
\(312\) 17.8217 1.00895
\(313\) −2.95234 −0.166876 −0.0834382 0.996513i \(-0.526590\pi\)
−0.0834382 + 0.996513i \(0.526590\pi\)
\(314\) −0.391617 −0.0221002
\(315\) 13.6070 0.766666
\(316\) 47.6832 2.68239
\(317\) 18.9719 1.06557 0.532785 0.846251i \(-0.321145\pi\)
0.532785 + 0.846251i \(0.321145\pi\)
\(318\) 21.4530 1.20302
\(319\) 4.13907 0.231743
\(320\) −8.25612 −0.461531
\(321\) 10.1437 0.566164
\(322\) −8.24785 −0.459635
\(323\) −19.6653 −1.09421
\(324\) 12.7683 0.709348
\(325\) −11.1815 −0.620240
\(326\) −5.15535 −0.285528
\(327\) −9.95864 −0.550714
\(328\) 12.8759 0.710952
\(329\) −11.3166 −0.623905
\(330\) −25.5157 −1.40460
\(331\) 25.9752 1.42772 0.713862 0.700286i \(-0.246944\pi\)
0.713862 + 0.700286i \(0.246944\pi\)
\(332\) 7.35511 0.403664
\(333\) −2.14855 −0.117740
\(334\) 42.6625 2.33439
\(335\) 1.18225 0.0645932
\(336\) −11.1130 −0.606263
\(337\) −19.8561 −1.08163 −0.540817 0.841141i \(-0.681885\pi\)
−0.540817 + 0.841141i \(0.681885\pi\)
\(338\) 1.43106 0.0778395
\(339\) 6.55539 0.356040
\(340\) −36.7204 −1.99144
\(341\) 22.3154 1.20844
\(342\) 37.9676 2.05305
\(343\) 20.1389 1.08740
\(344\) 61.7893 3.33146
\(345\) −3.81690 −0.205495
\(346\) 55.5494 2.98636
\(347\) −10.1557 −0.545185 −0.272593 0.962130i \(-0.587881\pi\)
−0.272593 + 0.962130i \(0.587881\pi\)
\(348\) 3.71925 0.199373
\(349\) −25.9996 −1.39173 −0.695864 0.718174i \(-0.744978\pi\)
−0.695864 + 0.718174i \(0.744978\pi\)
\(350\) 16.7724 0.896523
\(351\) 15.9004 0.848699
\(352\) −15.5686 −0.829809
\(353\) 2.89740 0.154213 0.0771064 0.997023i \(-0.475432\pi\)
0.0771064 + 0.997023i \(0.475432\pi\)
\(354\) 17.7001 0.940750
\(355\) −24.4356 −1.29691
\(356\) 2.41174 0.127822
\(357\) 5.31699 0.281405
\(358\) −36.1851 −1.91244
\(359\) 14.1255 0.745516 0.372758 0.927929i \(-0.378412\pi\)
0.372758 + 0.927929i \(0.378412\pi\)
\(360\) 38.2533 2.01613
\(361\) 25.2199 1.32736
\(362\) 10.5560 0.554811
\(363\) 5.25025 0.275567
\(364\) 32.1606 1.68567
\(365\) −8.58706 −0.449467
\(366\) −7.21359 −0.377060
\(367\) −19.2117 −1.00284 −0.501422 0.865203i \(-0.667190\pi\)
−0.501422 + 0.865203i \(0.667190\pi\)
\(368\) −9.63911 −0.502473
\(369\) 4.94438 0.257394
\(370\) −6.82394 −0.354760
\(371\) 20.8888 1.08449
\(372\) 20.0520 1.03965
\(373\) 1.79570 0.0929780 0.0464890 0.998919i \(-0.485197\pi\)
0.0464890 + 0.998919i \(0.485197\pi\)
\(374\) 30.8297 1.59417
\(375\) −4.47589 −0.231134
\(376\) −31.8144 −1.64070
\(377\) −3.52588 −0.181592
\(378\) −23.8507 −1.22675
\(379\) −3.36426 −0.172810 −0.0864051 0.996260i \(-0.527538\pi\)
−0.0864051 + 0.996260i \(0.527538\pi\)
\(380\) 82.5702 4.23576
\(381\) −6.97964 −0.357578
\(382\) 4.07538 0.208515
\(383\) −1.04995 −0.0536498 −0.0268249 0.999640i \(-0.508540\pi\)
−0.0268249 + 0.999640i \(0.508540\pi\)
\(384\) 12.6698 0.646551
\(385\) −24.8447 −1.26621
\(386\) 67.7183 3.44677
\(387\) 23.7273 1.20613
\(388\) −50.0130 −2.53902
\(389\) 17.3425 0.879301 0.439650 0.898169i \(-0.355102\pi\)
0.439650 + 0.898169i \(0.355102\pi\)
\(390\) 21.7357 1.10063
\(391\) 4.61181 0.233229
\(392\) 15.2934 0.772434
\(393\) −2.56266 −0.129269
\(394\) −27.6435 −1.39266
\(395\) 31.3791 1.57885
\(396\) −40.7569 −2.04811
\(397\) 0.149511 0.00750373 0.00375186 0.999993i \(-0.498806\pi\)
0.00375186 + 0.999993i \(0.498806\pi\)
\(398\) −3.78811 −0.189881
\(399\) −11.9559 −0.598543
\(400\) 19.6016 0.980080
\(401\) 18.1305 0.905396 0.452698 0.891664i \(-0.350462\pi\)
0.452698 + 0.891664i \(0.350462\pi\)
\(402\) −0.891919 −0.0444849
\(403\) −19.0094 −0.946926
\(404\) −36.4645 −1.81418
\(405\) 8.40247 0.417522
\(406\) 5.28885 0.262481
\(407\) 3.92300 0.194456
\(408\) 14.9477 0.740019
\(409\) 7.38380 0.365105 0.182553 0.983196i \(-0.441564\pi\)
0.182553 + 0.983196i \(0.441564\pi\)
\(410\) 15.7037 0.775550
\(411\) −1.18871 −0.0586346
\(412\) 57.8888 2.85197
\(413\) 17.2346 0.848061
\(414\) −8.90397 −0.437606
\(415\) 4.84021 0.237597
\(416\) 13.2622 0.650231
\(417\) 14.0636 0.688697
\(418\) −69.3244 −3.39077
\(419\) −11.7518 −0.574113 −0.287057 0.957914i \(-0.592677\pi\)
−0.287057 + 0.957914i \(0.592677\pi\)
\(420\) −22.3248 −1.08934
\(421\) 22.3489 1.08922 0.544609 0.838690i \(-0.316678\pi\)
0.544609 + 0.838690i \(0.316678\pi\)
\(422\) −21.1515 −1.02964
\(423\) −12.2168 −0.594003
\(424\) 58.7248 2.85193
\(425\) −9.37835 −0.454917
\(426\) 18.4348 0.893171
\(427\) −7.02389 −0.339910
\(428\) 51.4610 2.48746
\(429\) −12.4956 −0.603292
\(430\) 75.3595 3.63416
\(431\) −1.09141 −0.0525712 −0.0262856 0.999654i \(-0.508368\pi\)
−0.0262856 + 0.999654i \(0.508368\pi\)
\(432\) −27.8739 −1.34108
\(433\) −34.2048 −1.64378 −0.821889 0.569647i \(-0.807080\pi\)
−0.821889 + 0.569647i \(0.807080\pi\)
\(434\) 28.5143 1.36873
\(435\) 2.44755 0.117351
\(436\) −50.5223 −2.41958
\(437\) −10.3702 −0.496075
\(438\) 6.47829 0.309545
\(439\) 18.9437 0.904131 0.452066 0.891985i \(-0.350687\pi\)
0.452066 + 0.891985i \(0.350687\pi\)
\(440\) −69.8461 −3.32978
\(441\) 5.87272 0.279653
\(442\) −26.2624 −1.24918
\(443\) 38.4274 1.82574 0.912870 0.408251i \(-0.133861\pi\)
0.912870 + 0.408251i \(0.133861\pi\)
\(444\) 3.52510 0.167294
\(445\) 1.58710 0.0752359
\(446\) −3.28017 −0.155320
\(447\) −3.66903 −0.173539
\(448\) 6.06482 0.286536
\(449\) −4.75483 −0.224394 −0.112197 0.993686i \(-0.535789\pi\)
−0.112197 + 0.993686i \(0.535789\pi\)
\(450\) 18.1067 0.853556
\(451\) −9.02786 −0.425105
\(452\) 33.2569 1.56427
\(453\) 7.58108 0.356190
\(454\) 65.0628 3.05355
\(455\) 21.1641 0.992187
\(456\) −33.6116 −1.57401
\(457\) 3.86701 0.180891 0.0904454 0.995901i \(-0.471171\pi\)
0.0904454 + 0.995901i \(0.471171\pi\)
\(458\) −35.9710 −1.68081
\(459\) 13.3362 0.622481
\(460\) −19.3639 −0.902849
\(461\) −38.5274 −1.79440 −0.897201 0.441623i \(-0.854403\pi\)
−0.897201 + 0.441623i \(0.854403\pi\)
\(462\) 18.7435 0.872026
\(463\) −21.8997 −1.01777 −0.508883 0.860835i \(-0.669942\pi\)
−0.508883 + 0.860835i \(0.669942\pi\)
\(464\) 6.18098 0.286945
\(465\) 13.1957 0.611936
\(466\) 40.4624 1.87438
\(467\) 1.83733 0.0850216 0.0425108 0.999096i \(-0.486464\pi\)
0.0425108 + 0.999096i \(0.486464\pi\)
\(468\) 34.7189 1.60488
\(469\) −0.868463 −0.0401019
\(470\) −38.8015 −1.78978
\(471\) 0.133129 0.00613426
\(472\) 48.4518 2.23018
\(473\) −43.3233 −1.99201
\(474\) −23.6732 −1.08734
\(475\) 21.0884 0.967600
\(476\) 26.9742 1.23636
\(477\) 22.5505 1.03252
\(478\) 25.3456 1.15928
\(479\) −39.8237 −1.81959 −0.909796 0.415056i \(-0.863762\pi\)
−0.909796 + 0.415056i \(0.863762\pi\)
\(480\) −9.20614 −0.420201
\(481\) −3.34182 −0.152374
\(482\) 62.4020 2.84233
\(483\) 2.80383 0.127579
\(484\) 26.6357 1.21071
\(485\) −32.9123 −1.49447
\(486\) −40.4140 −1.83322
\(487\) −8.23037 −0.372954 −0.186477 0.982459i \(-0.559707\pi\)
−0.186477 + 0.982459i \(0.559707\pi\)
\(488\) −19.7463 −0.893872
\(489\) 1.75255 0.0792529
\(490\) 18.6522 0.842619
\(491\) −40.8957 −1.84560 −0.922798 0.385285i \(-0.874103\pi\)
−0.922798 + 0.385285i \(0.874103\pi\)
\(492\) −8.11218 −0.365726
\(493\) −2.95728 −0.133189
\(494\) 59.0542 2.65697
\(495\) −26.8211 −1.20552
\(496\) 33.3241 1.49630
\(497\) 17.9500 0.805170
\(498\) −3.65158 −0.163631
\(499\) 40.8679 1.82950 0.914750 0.404020i \(-0.132387\pi\)
0.914750 + 0.404020i \(0.132387\pi\)
\(500\) −22.7072 −1.01549
\(501\) −14.5030 −0.647947
\(502\) −21.7663 −0.971478
\(503\) 38.1445 1.70078 0.850389 0.526154i \(-0.176366\pi\)
0.850389 + 0.526154i \(0.176366\pi\)
\(504\) −28.1003 −1.25169
\(505\) −23.9964 −1.06782
\(506\) 16.2576 0.722739
\(507\) −0.486485 −0.0216056
\(508\) −35.4092 −1.57103
\(509\) −13.5944 −0.602561 −0.301280 0.953536i \(-0.597414\pi\)
−0.301280 + 0.953536i \(0.597414\pi\)
\(510\) 18.2305 0.807259
\(511\) 6.30793 0.279046
\(512\) 49.7274 2.19766
\(513\) −29.9881 −1.32401
\(514\) 9.21443 0.406431
\(515\) 38.0951 1.67867
\(516\) −38.9291 −1.71376
\(517\) 22.3065 0.981040
\(518\) 5.01276 0.220248
\(519\) −18.8839 −0.828910
\(520\) 59.4986 2.60919
\(521\) 27.4885 1.20429 0.602146 0.798386i \(-0.294313\pi\)
0.602146 + 0.798386i \(0.294313\pi\)
\(522\) 5.70958 0.249902
\(523\) 3.52604 0.154183 0.0770914 0.997024i \(-0.475437\pi\)
0.0770914 + 0.997024i \(0.475437\pi\)
\(524\) −13.0009 −0.567947
\(525\) −5.70174 −0.248844
\(526\) −0.671712 −0.0292880
\(527\) −15.9439 −0.694526
\(528\) 21.9051 0.953299
\(529\) −20.5680 −0.894262
\(530\) 71.6220 3.11106
\(531\) 18.6056 0.807416
\(532\) −60.6548 −2.62972
\(533\) 7.69041 0.333109
\(534\) −1.19735 −0.0518144
\(535\) 33.8652 1.46412
\(536\) −2.44151 −0.105457
\(537\) 12.3010 0.530829
\(538\) −31.8833 −1.37458
\(539\) −10.7229 −0.461868
\(540\) −55.9957 −2.40967
\(541\) −22.4310 −0.964383 −0.482191 0.876066i \(-0.660159\pi\)
−0.482191 + 0.876066i \(0.660159\pi\)
\(542\) 71.1890 3.05783
\(543\) −3.58848 −0.153996
\(544\) 11.1234 0.476914
\(545\) −33.2475 −1.42417
\(546\) −15.9667 −0.683312
\(547\) 1.30938 0.0559851 0.0279925 0.999608i \(-0.491089\pi\)
0.0279925 + 0.999608i \(0.491089\pi\)
\(548\) −6.03057 −0.257613
\(549\) −7.58263 −0.323619
\(550\) −33.0606 −1.40971
\(551\) 6.64980 0.283291
\(552\) 7.88243 0.335498
\(553\) −23.0506 −0.980212
\(554\) −2.51869 −0.107009
\(555\) 2.31978 0.0984691
\(556\) 71.3476 3.02581
\(557\) 35.1849 1.49083 0.745416 0.666600i \(-0.232251\pi\)
0.745416 + 0.666600i \(0.232251\pi\)
\(558\) 30.7826 1.30313
\(559\) 36.9051 1.56092
\(560\) −37.1013 −1.56782
\(561\) −10.4805 −0.442486
\(562\) 32.2853 1.36187
\(563\) −6.09706 −0.256960 −0.128480 0.991712i \(-0.541010\pi\)
−0.128480 + 0.991712i \(0.541010\pi\)
\(564\) 20.0440 0.844006
\(565\) 21.8855 0.920732
\(566\) 61.7323 2.59480
\(567\) −6.17233 −0.259213
\(568\) 50.4630 2.11738
\(569\) −35.0861 −1.47088 −0.735442 0.677588i \(-0.763026\pi\)
−0.735442 + 0.677588i \(0.763026\pi\)
\(570\) −40.9935 −1.71703
\(571\) −6.63598 −0.277707 −0.138854 0.990313i \(-0.544342\pi\)
−0.138854 + 0.990313i \(0.544342\pi\)
\(572\) −63.3927 −2.65058
\(573\) −1.38541 −0.0578765
\(574\) −11.5357 −0.481491
\(575\) −4.94554 −0.206243
\(576\) 6.54727 0.272803
\(577\) 13.7613 0.572892 0.286446 0.958096i \(-0.407526\pi\)
0.286446 + 0.958096i \(0.407526\pi\)
\(578\) 20.7905 0.864771
\(579\) −23.0206 −0.956705
\(580\) 12.4169 0.515585
\(581\) −3.55555 −0.147509
\(582\) 24.8298 1.02923
\(583\) −41.1746 −1.70528
\(584\) 17.7335 0.733817
\(585\) 22.8477 0.944635
\(586\) −76.1415 −3.14538
\(587\) 32.1541 1.32714 0.663571 0.748114i \(-0.269040\pi\)
0.663571 + 0.748114i \(0.269040\pi\)
\(588\) −9.63530 −0.397353
\(589\) 35.8517 1.47724
\(590\) 59.0928 2.43281
\(591\) 9.39732 0.386554
\(592\) 5.85832 0.240775
\(593\) 40.0677 1.64538 0.822691 0.568488i \(-0.192471\pi\)
0.822691 + 0.568488i \(0.192471\pi\)
\(594\) 47.0129 1.92896
\(595\) 17.7511 0.727723
\(596\) −18.6138 −0.762450
\(597\) 1.28776 0.0527044
\(598\) −13.8491 −0.566332
\(599\) −46.4938 −1.89969 −0.949843 0.312727i \(-0.898757\pi\)
−0.949843 + 0.312727i \(0.898757\pi\)
\(600\) −16.0293 −0.654394
\(601\) −14.0866 −0.574603 −0.287301 0.957840i \(-0.592758\pi\)
−0.287301 + 0.957840i \(0.592758\pi\)
\(602\) −55.3580 −2.25622
\(603\) −0.937549 −0.0381800
\(604\) 38.4604 1.56493
\(605\) 17.5283 0.712625
\(606\) 18.1035 0.735403
\(607\) −11.2435 −0.456358 −0.228179 0.973619i \(-0.573277\pi\)
−0.228179 + 0.973619i \(0.573277\pi\)
\(608\) −25.0124 −1.01439
\(609\) −1.79793 −0.0728558
\(610\) −24.0830 −0.975091
\(611\) −19.0019 −0.768734
\(612\) 29.1200 1.17711
\(613\) −16.1613 −0.652747 −0.326374 0.945241i \(-0.605827\pi\)
−0.326374 + 0.945241i \(0.605827\pi\)
\(614\) 52.5062 2.11898
\(615\) −5.33843 −0.215266
\(616\) 51.3079 2.06725
\(617\) 10.8028 0.434903 0.217451 0.976071i \(-0.430226\pi\)
0.217451 + 0.976071i \(0.430226\pi\)
\(618\) −28.7399 −1.15609
\(619\) −27.4689 −1.10407 −0.552035 0.833821i \(-0.686149\pi\)
−0.552035 + 0.833821i \(0.686149\pi\)
\(620\) 66.9446 2.68856
\(621\) 7.03265 0.282211
\(622\) −1.99165 −0.0798578
\(623\) −1.16586 −0.0467093
\(624\) −18.6600 −0.746996
\(625\) −30.7994 −1.23198
\(626\) 7.43604 0.297204
\(627\) 23.5666 0.941161
\(628\) 0.675393 0.0269511
\(629\) −2.80290 −0.111759
\(630\) −34.2717 −1.36542
\(631\) −34.7367 −1.38285 −0.691424 0.722450i \(-0.743016\pi\)
−0.691424 + 0.722450i \(0.743016\pi\)
\(632\) −64.8023 −2.57770
\(633\) 7.19040 0.285793
\(634\) −47.7844 −1.89776
\(635\) −23.3019 −0.924709
\(636\) −36.9983 −1.46708
\(637\) 9.13434 0.361916
\(638\) −10.4250 −0.412731
\(639\) 19.3780 0.766580
\(640\) 42.2987 1.67200
\(641\) 27.3510 1.08030 0.540150 0.841569i \(-0.318368\pi\)
0.540150 + 0.841569i \(0.318368\pi\)
\(642\) −25.5487 −1.00833
\(643\) 5.86751 0.231392 0.115696 0.993285i \(-0.463090\pi\)
0.115696 + 0.993285i \(0.463090\pi\)
\(644\) 14.2245 0.560522
\(645\) −25.6183 −1.00872
\(646\) 49.5309 1.94877
\(647\) 40.8789 1.60712 0.803558 0.595226i \(-0.202937\pi\)
0.803558 + 0.595226i \(0.202937\pi\)
\(648\) −17.3523 −0.681662
\(649\) −33.9717 −1.33351
\(650\) 28.1628 1.10464
\(651\) −9.69336 −0.379913
\(652\) 8.89105 0.348200
\(653\) 30.4819 1.19285 0.596425 0.802669i \(-0.296587\pi\)
0.596425 + 0.802669i \(0.296587\pi\)
\(654\) 25.0827 0.980812
\(655\) −8.55557 −0.334294
\(656\) −13.4815 −0.526366
\(657\) 6.80972 0.265672
\(658\) 28.5030 1.11116
\(659\) 3.54622 0.138141 0.0690706 0.997612i \(-0.477997\pi\)
0.0690706 + 0.997612i \(0.477997\pi\)
\(660\) 44.0051 1.71290
\(661\) −44.6989 −1.73859 −0.869293 0.494298i \(-0.835425\pi\)
−0.869293 + 0.494298i \(0.835425\pi\)
\(662\) −65.4234 −2.54275
\(663\) 8.92783 0.346728
\(664\) −9.99573 −0.387909
\(665\) −39.9154 −1.54785
\(666\) 5.41152 0.209692
\(667\) −1.55948 −0.0603832
\(668\) −73.5769 −2.84678
\(669\) 1.11508 0.0431116
\(670\) −2.97772 −0.115039
\(671\) 13.8450 0.534481
\(672\) 6.76269 0.260877
\(673\) 37.0770 1.42922 0.714608 0.699526i \(-0.246605\pi\)
0.714608 + 0.699526i \(0.246605\pi\)
\(674\) 50.0115 1.92637
\(675\) −14.3012 −0.550455
\(676\) −2.46805 −0.0949248
\(677\) −7.53102 −0.289441 −0.144720 0.989473i \(-0.546228\pi\)
−0.144720 + 0.989473i \(0.546228\pi\)
\(678\) −16.5110 −0.634101
\(679\) 24.1769 0.927823
\(680\) 49.9036 1.91372
\(681\) −22.1179 −0.847560
\(682\) −56.2055 −2.15222
\(683\) −1.80706 −0.0691454 −0.0345727 0.999402i \(-0.511007\pi\)
−0.0345727 + 0.999402i \(0.511007\pi\)
\(684\) −65.4799 −2.50369
\(685\) −3.96857 −0.151631
\(686\) −50.7236 −1.93664
\(687\) 12.2282 0.466536
\(688\) −64.6958 −2.46650
\(689\) 35.0747 1.33624
\(690\) 9.61358 0.365983
\(691\) −34.5983 −1.31618 −0.658091 0.752939i \(-0.728636\pi\)
−0.658091 + 0.752939i \(0.728636\pi\)
\(692\) −95.8020 −3.64185
\(693\) 19.7024 0.748432
\(694\) 25.5790 0.970965
\(695\) 46.9521 1.78099
\(696\) −5.05453 −0.191591
\(697\) 6.45022 0.244320
\(698\) 65.4850 2.47864
\(699\) −13.7551 −0.520264
\(700\) −28.9261 −1.09331
\(701\) 17.6387 0.666206 0.333103 0.942890i \(-0.391904\pi\)
0.333103 + 0.942890i \(0.391904\pi\)
\(702\) −40.0481 −1.51152
\(703\) 6.30267 0.237710
\(704\) −11.9546 −0.450554
\(705\) 13.1905 0.496782
\(706\) −7.29764 −0.274650
\(707\) 17.6274 0.662946
\(708\) −30.5261 −1.14724
\(709\) −0.708073 −0.0265923 −0.0132961 0.999912i \(-0.504232\pi\)
−0.0132961 + 0.999912i \(0.504232\pi\)
\(710\) 61.5458 2.30977
\(711\) −24.8843 −0.933234
\(712\) −3.27759 −0.122833
\(713\) −8.40777 −0.314873
\(714\) −13.3918 −0.501177
\(715\) −41.7172 −1.56013
\(716\) 62.4058 2.33221
\(717\) −8.61616 −0.321776
\(718\) −35.5778 −1.32775
\(719\) 20.3321 0.758258 0.379129 0.925344i \(-0.376224\pi\)
0.379129 + 0.925344i \(0.376224\pi\)
\(720\) −40.0527 −1.49268
\(721\) −27.9841 −1.04218
\(722\) −63.5211 −2.36401
\(723\) −21.2134 −0.788934
\(724\) −18.2051 −0.676589
\(725\) 3.17128 0.117778
\(726\) −13.2237 −0.490779
\(727\) 46.3373 1.71855 0.859277 0.511510i \(-0.170914\pi\)
0.859277 + 0.511510i \(0.170914\pi\)
\(728\) −43.7068 −1.61988
\(729\) 4.92036 0.182236
\(730\) 21.6281 0.800494
\(731\) 30.9536 1.14486
\(732\) 12.4407 0.459823
\(733\) −30.3974 −1.12275 −0.561377 0.827560i \(-0.689728\pi\)
−0.561377 + 0.827560i \(0.689728\pi\)
\(734\) 48.3884 1.78605
\(735\) −6.34075 −0.233882
\(736\) 5.86578 0.216216
\(737\) 1.71186 0.0630570
\(738\) −12.4534 −0.458414
\(739\) −36.1793 −1.33088 −0.665439 0.746452i \(-0.731756\pi\)
−0.665439 + 0.746452i \(0.731756\pi\)
\(740\) 11.7687 0.432627
\(741\) −20.0753 −0.737485
\(742\) −52.6124 −1.93146
\(743\) −18.0751 −0.663110 −0.331555 0.943436i \(-0.607573\pi\)
−0.331555 + 0.943436i \(0.607573\pi\)
\(744\) −27.2510 −0.999069
\(745\) −12.2493 −0.448778
\(746\) −4.52282 −0.165592
\(747\) −3.83839 −0.140439
\(748\) −53.1697 −1.94408
\(749\) −24.8769 −0.908981
\(750\) 11.2734 0.411645
\(751\) −25.7349 −0.939081 −0.469540 0.882911i \(-0.655580\pi\)
−0.469540 + 0.882911i \(0.655580\pi\)
\(752\) 33.3109 1.21472
\(753\) 7.39939 0.269649
\(754\) 8.88059 0.323412
\(755\) 25.3099 0.921120
\(756\) 41.1336 1.49601
\(757\) −42.3861 −1.54055 −0.770275 0.637712i \(-0.779881\pi\)
−0.770275 + 0.637712i \(0.779881\pi\)
\(758\) 8.47352 0.307772
\(759\) −5.52673 −0.200607
\(760\) −112.214 −4.07044
\(761\) −43.3464 −1.57131 −0.785654 0.618666i \(-0.787673\pi\)
−0.785654 + 0.618666i \(0.787673\pi\)
\(762\) 17.5795 0.636840
\(763\) 24.4231 0.884176
\(764\) −7.02850 −0.254282
\(765\) 19.1631 0.692845
\(766\) 2.64449 0.0955494
\(767\) 28.9389 1.04492
\(768\) −26.9653 −0.973025
\(769\) −37.7656 −1.36186 −0.680931 0.732347i \(-0.738425\pi\)
−0.680931 + 0.732347i \(0.738425\pi\)
\(770\) 62.5762 2.25509
\(771\) −3.13242 −0.112811
\(772\) −116.789 −4.20332
\(773\) −41.6732 −1.49888 −0.749440 0.662073i \(-0.769677\pi\)
−0.749440 + 0.662073i \(0.769677\pi\)
\(774\) −59.7617 −2.14809
\(775\) 17.0976 0.614164
\(776\) 67.9685 2.43993
\(777\) −1.70407 −0.0611333
\(778\) −43.6804 −1.56602
\(779\) −14.5041 −0.519664
\(780\) −37.4859 −1.34221
\(781\) −35.3819 −1.26606
\(782\) −11.6157 −0.415378
\(783\) −4.50962 −0.161161
\(784\) −16.0128 −0.571885
\(785\) 0.444459 0.0158634
\(786\) 6.45453 0.230226
\(787\) 12.3528 0.440329 0.220165 0.975463i \(-0.429341\pi\)
0.220165 + 0.975463i \(0.429341\pi\)
\(788\) 47.6746 1.69834
\(789\) 0.228347 0.00812935
\(790\) −79.0342 −2.81191
\(791\) −16.0768 −0.571625
\(792\) 55.3894 1.96818
\(793\) −11.7939 −0.418814
\(794\) −0.376571 −0.0133640
\(795\) −24.3477 −0.863523
\(796\) 6.53307 0.231559
\(797\) −39.2510 −1.39034 −0.695171 0.718845i \(-0.744671\pi\)
−0.695171 + 0.718845i \(0.744671\pi\)
\(798\) 30.1132 1.06599
\(799\) −15.9376 −0.563830
\(800\) −11.9284 −0.421731
\(801\) −1.25861 −0.0444706
\(802\) −45.6652 −1.61249
\(803\) −12.4338 −0.438778
\(804\) 1.53823 0.0542491
\(805\) 9.36076 0.329924
\(806\) 47.8788 1.68646
\(807\) 10.8386 0.381538
\(808\) 49.5559 1.74337
\(809\) −24.5108 −0.861753 −0.430877 0.902411i \(-0.641796\pi\)
−0.430877 + 0.902411i \(0.641796\pi\)
\(810\) −21.1632 −0.743599
\(811\) 16.9152 0.593972 0.296986 0.954882i \(-0.404018\pi\)
0.296986 + 0.954882i \(0.404018\pi\)
\(812\) −9.12130 −0.320095
\(813\) −24.2005 −0.848749
\(814\) −9.88081 −0.346322
\(815\) 5.85098 0.204951
\(816\) −15.6508 −0.547887
\(817\) −69.6029 −2.43510
\(818\) −18.5975 −0.650246
\(819\) −16.7836 −0.586465
\(820\) −27.0830 −0.945779
\(821\) −4.19836 −0.146524 −0.0732620 0.997313i \(-0.523341\pi\)
−0.0732620 + 0.997313i \(0.523341\pi\)
\(822\) 2.99399 0.104427
\(823\) −43.1022 −1.50245 −0.751225 0.660046i \(-0.770537\pi\)
−0.751225 + 0.660046i \(0.770537\pi\)
\(824\) −78.6719 −2.74066
\(825\) 11.2389 0.391287
\(826\) −43.4087 −1.51038
\(827\) 22.2369 0.773253 0.386626 0.922236i \(-0.373640\pi\)
0.386626 + 0.922236i \(0.373640\pi\)
\(828\) 15.3560 0.533658
\(829\) −6.67857 −0.231956 −0.115978 0.993252i \(-0.537000\pi\)
−0.115978 + 0.993252i \(0.537000\pi\)
\(830\) −12.1910 −0.423156
\(831\) 0.856221 0.0297020
\(832\) 10.1835 0.353050
\(833\) 7.66129 0.265448
\(834\) −35.4218 −1.22656
\(835\) −48.4191 −1.67561
\(836\) 119.559 4.13502
\(837\) −24.3131 −0.840385
\(838\) 29.5991 1.02249
\(839\) 30.3710 1.04852 0.524261 0.851558i \(-0.324342\pi\)
0.524261 + 0.851558i \(0.324342\pi\)
\(840\) 30.3398 1.04682
\(841\) 1.00000 0.0344828
\(842\) −56.2899 −1.93988
\(843\) −10.9753 −0.378009
\(844\) 36.4785 1.25564
\(845\) −1.62416 −0.0558728
\(846\) 30.7704 1.05791
\(847\) −12.8760 −0.442425
\(848\) −61.4871 −2.11148
\(849\) −20.9857 −0.720228
\(850\) 23.6212 0.810199
\(851\) −1.47807 −0.0506676
\(852\) −31.7932 −1.08922
\(853\) −18.6118 −0.637256 −0.318628 0.947880i \(-0.603222\pi\)
−0.318628 + 0.947880i \(0.603222\pi\)
\(854\) 17.6910 0.605373
\(855\) −43.0907 −1.47367
\(856\) −69.9364 −2.39038
\(857\) 24.0912 0.822939 0.411469 0.911424i \(-0.365016\pi\)
0.411469 + 0.911424i \(0.365016\pi\)
\(858\) 31.4725 1.07445
\(859\) −25.8870 −0.883252 −0.441626 0.897199i \(-0.645598\pi\)
−0.441626 + 0.897199i \(0.645598\pi\)
\(860\) −129.967 −4.43184
\(861\) 3.92153 0.133645
\(862\) 2.74891 0.0936284
\(863\) 21.8572 0.744029 0.372015 0.928227i \(-0.378667\pi\)
0.372015 + 0.928227i \(0.378667\pi\)
\(864\) 16.9624 0.577072
\(865\) −63.0449 −2.14359
\(866\) 86.1513 2.92754
\(867\) −7.06768 −0.240031
\(868\) −49.1765 −1.66916
\(869\) 45.4358 1.54130
\(870\) −6.16461 −0.209000
\(871\) −1.45825 −0.0494109
\(872\) 68.6607 2.32515
\(873\) 26.1001 0.883355
\(874\) 26.1194 0.883501
\(875\) 10.9769 0.371087
\(876\) −11.1726 −0.377488
\(877\) −17.7222 −0.598436 −0.299218 0.954185i \(-0.596726\pi\)
−0.299218 + 0.954185i \(0.596726\pi\)
\(878\) −47.7132 −1.61024
\(879\) 25.8841 0.873049
\(880\) 73.1316 2.46526
\(881\) 14.7145 0.495744 0.247872 0.968793i \(-0.420269\pi\)
0.247872 + 0.968793i \(0.420269\pi\)
\(882\) −14.7916 −0.498058
\(883\) −6.99333 −0.235344 −0.117672 0.993053i \(-0.537543\pi\)
−0.117672 + 0.993053i \(0.537543\pi\)
\(884\) 45.2928 1.52336
\(885\) −20.0884 −0.675266
\(886\) −96.7866 −3.25161
\(887\) −26.5254 −0.890636 −0.445318 0.895372i \(-0.646909\pi\)
−0.445318 + 0.895372i \(0.646909\pi\)
\(888\) −4.79067 −0.160764
\(889\) 17.1172 0.574094
\(890\) −3.99742 −0.133994
\(891\) 12.1665 0.407592
\(892\) 5.65706 0.189412
\(893\) 35.8375 1.19926
\(894\) 9.24114 0.309070
\(895\) 41.0677 1.37274
\(896\) −31.0720 −1.03804
\(897\) 4.70796 0.157194
\(898\) 11.9759 0.399642
\(899\) 5.39140 0.179813
\(900\) −31.2272 −1.04091
\(901\) 29.4184 0.980069
\(902\) 22.7384 0.757105
\(903\) 18.8188 0.626250
\(904\) −45.1967 −1.50322
\(905\) −11.9803 −0.398240
\(906\) −19.0944 −0.634368
\(907\) 2.13682 0.0709519 0.0354760 0.999371i \(-0.488705\pi\)
0.0354760 + 0.999371i \(0.488705\pi\)
\(908\) −112.209 −3.72379
\(909\) 19.0296 0.631173
\(910\) −53.3057 −1.76707
\(911\) −16.5092 −0.546974 −0.273487 0.961876i \(-0.588177\pi\)
−0.273487 + 0.961876i \(0.588177\pi\)
\(912\) 35.1927 1.16535
\(913\) 7.00845 0.231946
\(914\) −9.73979 −0.322164
\(915\) 8.18694 0.270652
\(916\) 62.0364 2.04974
\(917\) 6.28480 0.207542
\(918\) −33.5898 −1.10863
\(919\) 27.9190 0.920962 0.460481 0.887670i \(-0.347677\pi\)
0.460481 + 0.887670i \(0.347677\pi\)
\(920\) 26.3159 0.867611
\(921\) −17.8493 −0.588155
\(922\) 97.0387 3.19580
\(923\) 30.1402 0.992076
\(924\) −32.3255 −1.06343
\(925\) 3.00573 0.0988277
\(926\) 55.1586 1.81262
\(927\) −30.2102 −0.992235
\(928\) −3.76138 −0.123473
\(929\) 32.6952 1.07270 0.536348 0.843997i \(-0.319804\pi\)
0.536348 + 0.843997i \(0.319804\pi\)
\(930\) −33.2359 −1.08985
\(931\) −17.2274 −0.564604
\(932\) −69.7824 −2.28580
\(933\) 0.677055 0.0221658
\(934\) −4.62767 −0.151422
\(935\) −34.9897 −1.14428
\(936\) −47.1837 −1.54225
\(937\) 59.0521 1.92915 0.964575 0.263810i \(-0.0849792\pi\)
0.964575 + 0.263810i \(0.0849792\pi\)
\(938\) 2.18739 0.0714208
\(939\) −2.52786 −0.0824936
\(940\) 66.9181 2.18263
\(941\) −0.410091 −0.0133686 −0.00668429 0.999978i \(-0.502128\pi\)
−0.00668429 + 0.999978i \(0.502128\pi\)
\(942\) −0.335311 −0.0109250
\(943\) 3.40143 0.110766
\(944\) −50.7309 −1.65115
\(945\) 27.0690 0.880554
\(946\) 109.118 3.54773
\(947\) −39.8359 −1.29449 −0.647246 0.762281i \(-0.724079\pi\)
−0.647246 + 0.762281i \(0.724079\pi\)
\(948\) 40.8274 1.32601
\(949\) 10.5917 0.343822
\(950\) −53.1150 −1.72328
\(951\) 16.2442 0.526753
\(952\) −36.6585 −1.18811
\(953\) −45.9080 −1.48711 −0.743553 0.668677i \(-0.766861\pi\)
−0.743553 + 0.668677i \(0.766861\pi\)
\(954\) −56.7977 −1.83889
\(955\) −4.62528 −0.149671
\(956\) −43.7117 −1.41374
\(957\) 3.54396 0.114560
\(958\) 100.304 3.24066
\(959\) 2.91525 0.0941384
\(960\) −7.06906 −0.228153
\(961\) −1.93284 −0.0623496
\(962\) 8.41700 0.271375
\(963\) −26.8558 −0.865416
\(964\) −107.620 −3.46621
\(965\) −76.8558 −2.47407
\(966\) −7.06199 −0.227216
\(967\) 7.39389 0.237772 0.118886 0.992908i \(-0.462068\pi\)
0.118886 + 0.992908i \(0.462068\pi\)
\(968\) −36.1983 −1.16346
\(969\) −16.8379 −0.540911
\(970\) 82.8958 2.66162
\(971\) 27.1226 0.870405 0.435203 0.900332i \(-0.356677\pi\)
0.435203 + 0.900332i \(0.356677\pi\)
\(972\) 69.6991 2.23560
\(973\) −34.4903 −1.10571
\(974\) 20.7297 0.664224
\(975\) −9.57387 −0.306609
\(976\) 20.6751 0.661794
\(977\) 11.5374 0.369113 0.184556 0.982822i \(-0.440915\pi\)
0.184556 + 0.982822i \(0.440915\pi\)
\(978\) −4.41412 −0.141148
\(979\) 2.29807 0.0734465
\(980\) −32.1680 −1.02757
\(981\) 26.3659 0.841800
\(982\) 103.003 3.28697
\(983\) 35.8124 1.14224 0.571120 0.820867i \(-0.306509\pi\)
0.571120 + 0.820867i \(0.306509\pi\)
\(984\) 11.0246 0.351452
\(985\) 31.3735 0.999643
\(986\) 7.44847 0.237208
\(987\) −9.68953 −0.308421
\(988\) −101.846 −3.24017
\(989\) 16.3229 0.519039
\(990\) 67.5541 2.14701
\(991\) 51.0094 1.62037 0.810184 0.586176i \(-0.199367\pi\)
0.810184 + 0.586176i \(0.199367\pi\)
\(992\) −20.2791 −0.643861
\(993\) 22.2405 0.705781
\(994\) −45.2106 −1.43399
\(995\) 4.29925 0.136295
\(996\) 6.29760 0.199547
\(997\) −23.0628 −0.730406 −0.365203 0.930928i \(-0.619000\pi\)
−0.365203 + 0.930928i \(0.619000\pi\)
\(998\) −102.934 −3.25831
\(999\) −4.27421 −0.135230
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 8033.2.a.c.1.10 154
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8033.2.a.c.1.10 154 1.1 even 1 trivial