Properties

Label 300.3.c.f.151.1
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [300,3,Mod(151,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.151");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.6080256576.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 7x^{6} - 12x^{5} + 12x^{4} - 48x^{3} + 112x^{2} - 192x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.1
Root \(-1.51328 - 1.30766i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.f.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.88911 - 0.656712i) q^{2} +1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} -9.55505i q^{7} +(-4.29756 - 6.74766i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.88911 - 0.656712i) q^{2} +1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} -9.55505i q^{7} +(-4.29756 - 6.74766i) q^{8} -3.00000 q^{9} +9.92480i q^{11} +(-4.29756 + 5.43424i) q^{12} -7.55643 q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} -17.1903 q^{17} +(5.66732 + 1.97014i) q^{18} -26.1762i q^{19} +16.5498 q^{21} +(6.51774 - 18.7490i) q^{22} -1.67451i q^{23} +(11.6873 - 7.44360i) q^{24} +(14.2749 + 4.96240i) q^{26} -5.19615i q^{27} +(23.7080 - 29.9786i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(3.25887 - 31.8336i) q^{32} -17.1903 q^{33} +(32.4743 + 11.2890i) q^{34} +(-9.41238 - 7.44360i) q^{36} -22.6693 q^{37} +(-17.1903 + 49.4498i) q^{38} -13.0881i q^{39} -77.2990 q^{41} +(-31.2644 - 10.8685i) q^{42} -41.7994i q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} -14.0866i q^{47} +(-26.9669 + 6.38658i) q^{48} -42.2990 q^{49} -29.7744i q^{51} +(-23.7080 - 18.7490i) q^{52} +22.6693 q^{53} +(-3.41238 + 9.81609i) q^{54} +(-64.4743 + 41.0634i) q^{56} +45.3386 q^{57} +(-0.662126 - 0.230175i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(-30.2257 + 86.9478i) q^{62} +28.6652i q^{63} +(-27.0619 + 57.9970i) q^{64} +(32.4743 + 11.2890i) q^{66} +29.8477i q^{67} +(-53.9337 - 42.6525i) q^{68} +2.90033 q^{69} +7.19630i q^{71} +(12.8927 + 20.2430i) q^{72} +34.3805 q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} +94.8320 q^{77} +(-8.59513 + 24.7249i) q^{78} -46.0258i q^{79} +9.00000 q^{81} +(146.026 + 50.7632i) q^{82} +24.1336i q^{83} +(51.9244 + 41.0634i) q^{84} +(-27.4502 + 78.9636i) q^{86} +0.607078i q^{87} +(66.9692 - 42.6525i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(4.15479 - 5.25370i) q^{92} +79.7191 q^{93} +(-9.25083 + 26.6111i) q^{94} +(55.1375 + 5.64452i) q^{96} -131.861 q^{97} +(79.9074 + 27.7783i) q^{98} -29.7744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9} - 20 q^{14} - 46 q^{16} + 72 q^{21} + 18 q^{24} + 84 q^{26} + 184 q^{29} - 12 q^{34} - 30 q^{36} - 256 q^{41} - 348 q^{44} + 112 q^{46} + 24 q^{49} + 18 q^{54} - 244 q^{56} + 304 q^{61} + 10 q^{64} - 12 q^{66} + 144 q^{69} + 252 q^{74} - 24 q^{76} + 72 q^{81} + 204 q^{84} - 280 q^{86} - 560 q^{89} - 376 q^{94} + 426 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88911 0.656712i −0.944554 0.328356i
\(3\) 1.73205i 0.577350i
\(4\) 3.13746 + 2.48120i 0.784365 + 0.620300i
\(5\) 0 0
\(6\) 1.13746 3.27203i 0.189576 0.545339i
\(7\) 9.55505i 1.36501i −0.730882 0.682504i \(-0.760891\pi\)
0.730882 0.682504i \(-0.239109\pi\)
\(8\) −4.29756 6.74766i −0.537196 0.843458i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 9.92480i 0.902255i 0.892460 + 0.451127i \(0.148978\pi\)
−0.892460 + 0.451127i \(0.851022\pi\)
\(12\) −4.29756 + 5.43424i −0.358130 + 0.452853i
\(13\) −7.55643 −0.581264 −0.290632 0.956835i \(-0.593866\pi\)
−0.290632 + 0.956835i \(0.593866\pi\)
\(14\) −6.27492 + 18.0505i −0.448208 + 1.28932i
\(15\) 0 0
\(16\) 3.68729 + 15.5693i 0.230456 + 0.973083i
\(17\) −17.1903 −1.01119 −0.505596 0.862770i \(-0.668727\pi\)
−0.505596 + 0.862770i \(0.668727\pi\)
\(18\) 5.66732 + 1.97014i 0.314851 + 0.109452i
\(19\) 26.1762i 1.37770i −0.724905 0.688849i \(-0.758116\pi\)
0.724905 0.688849i \(-0.241884\pi\)
\(20\) 0 0
\(21\) 16.5498 0.788087
\(22\) 6.51774 18.7490i 0.296261 0.852228i
\(23\) 1.67451i 0.0728047i −0.999337 0.0364023i \(-0.988410\pi\)
0.999337 0.0364023i \(-0.0115898\pi\)
\(24\) 11.6873 7.44360i 0.486971 0.310150i
\(25\) 0 0
\(26\) 14.2749 + 4.96240i 0.549035 + 0.190862i
\(27\) 5.19615i 0.192450i
\(28\) 23.7080 29.9786i 0.846714 1.07066i
\(29\) 0.350497 0.0120861 0.00604305 0.999982i \(-0.498076\pi\)
0.00604305 + 0.999982i \(0.498076\pi\)
\(30\) 0 0
\(31\) 46.0258i 1.48470i −0.670010 0.742352i \(-0.733710\pi\)
0.670010 0.742352i \(-0.266290\pi\)
\(32\) 3.25887 31.8336i 0.101840 0.994801i
\(33\) −17.1903 −0.520917
\(34\) 32.4743 + 11.2890i 0.955125 + 0.332031i
\(35\) 0 0
\(36\) −9.41238 7.44360i −0.261455 0.206767i
\(37\) −22.6693 −0.612684 −0.306342 0.951922i \(-0.599105\pi\)
−0.306342 + 0.951922i \(0.599105\pi\)
\(38\) −17.1903 + 49.4498i −0.452375 + 1.30131i
\(39\) 13.0881i 0.335593i
\(40\) 0 0
\(41\) −77.2990 −1.88534 −0.942671 0.333724i \(-0.891695\pi\)
−0.942671 + 0.333724i \(0.891695\pi\)
\(42\) −31.2644 10.8685i −0.744391 0.258773i
\(43\) 41.7994i 0.972079i −0.873937 0.486039i \(-0.838441\pi\)
0.873937 0.486039i \(-0.161559\pi\)
\(44\) −24.6254 + 31.1386i −0.559668 + 0.707697i
\(45\) 0 0
\(46\) −1.09967 + 3.16332i −0.0239058 + 0.0687679i
\(47\) 14.0866i 0.299715i −0.988708 0.149857i \(-0.952119\pi\)
0.988708 0.149857i \(-0.0478814\pi\)
\(48\) −26.9669 + 6.38658i −0.561810 + 0.133054i
\(49\) −42.2990 −0.863245
\(50\) 0 0
\(51\) 29.7744i 0.583812i
\(52\) −23.7080 18.7490i −0.455923 0.360558i
\(53\) 22.6693 0.427723 0.213861 0.976864i \(-0.431396\pi\)
0.213861 + 0.976864i \(0.431396\pi\)
\(54\) −3.41238 + 9.81609i −0.0631921 + 0.181780i
\(55\) 0 0
\(56\) −64.4743 + 41.0634i −1.15133 + 0.733276i
\(57\) 45.3386 0.795414
\(58\) −0.662126 0.230175i −0.0114160 0.00396854i
\(59\) 94.7802i 1.60644i −0.595680 0.803222i \(-0.703117\pi\)
0.595680 0.803222i \(-0.296883\pi\)
\(60\) 0 0
\(61\) 38.0000 0.622951 0.311475 0.950254i \(-0.399177\pi\)
0.311475 + 0.950254i \(0.399177\pi\)
\(62\) −30.2257 + 86.9478i −0.487512 + 1.40238i
\(63\) 28.6652i 0.455002i
\(64\) −27.0619 + 57.9970i −0.422842 + 0.906203i
\(65\) 0 0
\(66\) 32.4743 + 11.2890i 0.492034 + 0.171046i
\(67\) 29.8477i 0.445488i 0.974877 + 0.222744i \(0.0715013\pi\)
−0.974877 + 0.222744i \(0.928499\pi\)
\(68\) −53.9337 42.6525i −0.793143 0.627242i
\(69\) 2.90033 0.0420338
\(70\) 0 0
\(71\) 7.19630i 0.101356i 0.998715 + 0.0506782i \(0.0161383\pi\)
−0.998715 + 0.0506782i \(0.983862\pi\)
\(72\) 12.8927 + 20.2430i 0.179065 + 0.281153i
\(73\) 34.3805 0.470966 0.235483 0.971878i \(-0.424333\pi\)
0.235483 + 0.971878i \(0.424333\pi\)
\(74\) 42.8248 + 14.8872i 0.578713 + 0.201178i
\(75\) 0 0
\(76\) 64.9485 82.1269i 0.854586 1.08062i
\(77\) 94.8320 1.23158
\(78\) −8.59513 + 24.7249i −0.110194 + 0.316986i
\(79\) 46.0258i 0.582606i −0.956631 0.291303i \(-0.905911\pi\)
0.956631 0.291303i \(-0.0940887\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 146.026 + 50.7632i 1.78081 + 0.619063i
\(83\) 24.1336i 0.290767i 0.989375 + 0.145383i \(0.0464415\pi\)
−0.989375 + 0.145383i \(0.953558\pi\)
\(84\) 51.9244 + 41.0634i 0.618148 + 0.488851i
\(85\) 0 0
\(86\) −27.4502 + 78.9636i −0.319188 + 0.918181i
\(87\) 0.607078i 0.00697791i
\(88\) 66.9692 42.6525i 0.761014 0.484687i
\(89\) −100.199 −1.12584 −0.562918 0.826513i \(-0.690321\pi\)
−0.562918 + 0.826513i \(0.690321\pi\)
\(90\) 0 0
\(91\) 72.2021i 0.793430i
\(92\) 4.15479 5.25370i 0.0451607 0.0571054i
\(93\) 79.7191 0.857195
\(94\) −9.25083 + 26.6111i −0.0984131 + 0.283097i
\(95\) 0 0
\(96\) 55.1375 + 5.64452i 0.574349 + 0.0587971i
\(97\) −131.861 −1.35939 −0.679696 0.733494i \(-0.737888\pi\)
−0.679696 + 0.733494i \(0.737888\pi\)
\(98\) 79.9074 + 27.7783i 0.815382 + 0.283452i
\(99\) 29.7744i 0.300752i
\(100\) 0 0
\(101\) 29.4502 0.291586 0.145793 0.989315i \(-0.453427\pi\)
0.145793 + 0.989315i \(0.453427\pi\)
\(102\) −19.5532 + 56.2471i −0.191698 + 0.551442i
\(103\) 143.786i 1.39598i 0.716107 + 0.697991i \(0.245922\pi\)
−0.716107 + 0.697991i \(0.754078\pi\)
\(104\) 32.4743 + 50.9882i 0.312252 + 0.490272i
\(105\) 0 0
\(106\) −42.8248 14.8872i −0.404007 0.140445i
\(107\) 35.1014i 0.328050i 0.986456 + 0.164025i \(0.0524478\pi\)
−0.986456 + 0.164025i \(0.947552\pi\)
\(108\) 12.8927 16.3027i 0.119377 0.150951i
\(109\) 151.498 1.38989 0.694947 0.719061i \(-0.255428\pi\)
0.694947 + 0.719061i \(0.255428\pi\)
\(110\) 0 0
\(111\) 39.2644i 0.353733i
\(112\) 148.766 35.2323i 1.32827 0.314574i
\(113\) −32.3031 −0.285868 −0.142934 0.989732i \(-0.545654\pi\)
−0.142934 + 0.989732i \(0.545654\pi\)
\(114\) −85.6495 29.7744i −0.751311 0.261179i
\(115\) 0 0
\(116\) 1.09967 + 0.869652i 0.00947990 + 0.00749700i
\(117\) 22.6693 0.193755
\(118\) −62.2433 + 179.050i −0.527486 + 1.51737i
\(119\) 164.254i 1.38028i
\(120\) 0 0
\(121\) 22.4983 0.185937
\(122\) −71.7861 24.9551i −0.588411 0.204550i
\(123\) 133.886i 1.08850i
\(124\) 114.199 144.404i 0.920962 1.16455i
\(125\) 0 0
\(126\) 18.8248 54.1516i 0.149403 0.429774i
\(127\) 192.053i 1.51223i 0.654438 + 0.756116i \(0.272905\pi\)
−0.654438 + 0.756116i \(0.727095\pi\)
\(128\) 89.2102 91.7908i 0.696954 0.717115i
\(129\) 72.3987 0.561230
\(130\) 0 0
\(131\) 42.4277i 0.323876i 0.986801 + 0.161938i \(0.0517744\pi\)
−0.986801 + 0.161938i \(0.948226\pi\)
\(132\) −53.9337 42.6525i −0.408589 0.323125i
\(133\) −250.115 −1.88057
\(134\) 19.6013 56.3855i 0.146279 0.420787i
\(135\) 0 0
\(136\) 73.8762 + 115.994i 0.543208 + 0.852897i
\(137\) 206.854 1.50988 0.754942 0.655791i \(-0.227665\pi\)
0.754942 + 0.655791i \(0.227665\pi\)
\(138\) −5.47904 1.90468i −0.0397032 0.0138020i
\(139\) 46.0258i 0.331121i 0.986200 + 0.165561i \(0.0529433\pi\)
−0.986200 + 0.165561i \(0.947057\pi\)
\(140\) 0 0
\(141\) 24.3987 0.173040
\(142\) 4.72590 13.5946i 0.0332810 0.0957366i
\(143\) 74.9961i 0.524448i
\(144\) −11.0619 46.7080i −0.0768186 0.324361i
\(145\) 0 0
\(146\) −64.9485 22.5781i −0.444853 0.154645i
\(147\) 73.2640i 0.498395i
\(148\) −71.1240 56.2471i −0.480567 0.380048i
\(149\) −11.6495 −0.0781846 −0.0390923 0.999236i \(-0.512447\pi\)
−0.0390923 + 0.999236i \(0.512447\pi\)
\(150\) 0 0
\(151\) 125.424i 0.830624i −0.909679 0.415312i \(-0.863672\pi\)
0.909679 0.415312i \(-0.136328\pi\)
\(152\) −176.628 + 112.494i −1.16203 + 0.740093i
\(153\) 51.5708 0.337064
\(154\) −179.148 62.2773i −1.16330 0.404398i
\(155\) 0 0
\(156\) 32.4743 41.0634i 0.208168 0.263227i
\(157\) −197.220 −1.25618 −0.628090 0.778140i \(-0.716163\pi\)
−0.628090 + 0.778140i \(0.716163\pi\)
\(158\) −30.2257 + 86.9478i −0.191302 + 0.550303i
\(159\) 39.2644i 0.246946i
\(160\) 0 0
\(161\) −16.0000 −0.0993789
\(162\) −17.0020 5.91041i −0.104950 0.0364840i
\(163\) 18.4196i 0.113004i −0.998402 0.0565018i \(-0.982005\pi\)
0.998402 0.0565018i \(-0.0179947\pi\)
\(164\) −242.522 191.794i −1.47880 1.16948i
\(165\) 0 0
\(166\) 15.8488 45.5910i 0.0954749 0.274645i
\(167\) 92.8920i 0.556240i −0.960546 0.278120i \(-0.910289\pi\)
0.960546 0.278120i \(-0.0897112\pi\)
\(168\) −71.1240 111.673i −0.423357 0.664718i
\(169\) −111.900 −0.662132
\(170\) 0 0
\(171\) 78.5287i 0.459232i
\(172\) 103.713 131.144i 0.602981 0.762464i
\(173\) 117.501 0.679198 0.339599 0.940570i \(-0.389709\pi\)
0.339599 + 0.940570i \(0.389709\pi\)
\(174\) 0.398675 1.14684i 0.00229124 0.00659101i
\(175\) 0 0
\(176\) −154.522 + 36.5956i −0.877968 + 0.207930i
\(177\) 164.164 0.927481
\(178\) 189.287 + 65.8021i 1.06341 + 0.369675i
\(179\) 231.988i 1.29602i 0.761631 + 0.648011i \(0.224399\pi\)
−0.761631 + 0.648011i \(0.775601\pi\)
\(180\) 0 0
\(181\) −218.096 −1.20495 −0.602476 0.798137i \(-0.705819\pi\)
−0.602476 + 0.798137i \(0.705819\pi\)
\(182\) 47.4160 136.398i 0.260527 0.749437i
\(183\) 65.8179i 0.359661i
\(184\) −11.2990 + 7.19630i −0.0614076 + 0.0391103i
\(185\) 0 0
\(186\) −150.598 52.3525i −0.809667 0.281465i
\(187\) 170.610i 0.912352i
\(188\) 34.9516 44.1961i 0.185913 0.235085i
\(189\) −49.6495 −0.262696
\(190\) 0 0
\(191\) 137.208i 0.718366i 0.933267 + 0.359183i \(0.116945\pi\)
−0.933267 + 0.359183i \(0.883055\pi\)
\(192\) −100.454 46.8725i −0.523197 0.244128i
\(193\) 37.0290 0.191860 0.0959301 0.995388i \(-0.469417\pi\)
0.0959301 + 0.995388i \(0.469417\pi\)
\(194\) 249.100 + 86.5947i 1.28402 + 0.446364i
\(195\) 0 0
\(196\) −132.711 104.952i −0.677099 0.535471i
\(197\) −194.572 −0.987674 −0.493837 0.869554i \(-0.664406\pi\)
−0.493837 + 0.869554i \(0.664406\pi\)
\(198\) −19.5532 + 56.2471i −0.0987536 + 0.284076i
\(199\) 176.037i 0.884610i 0.896865 + 0.442305i \(0.145839\pi\)
−0.896865 + 0.442305i \(0.854161\pi\)
\(200\) 0 0
\(201\) −51.6977 −0.257202
\(202\) −55.6345 19.3403i −0.275419 0.0957440i
\(203\) 3.34901i 0.0164976i
\(204\) 73.8762 93.4159i 0.362138 0.457921i
\(205\) 0 0
\(206\) 94.4261 271.628i 0.458379 1.31858i
\(207\) 5.02352i 0.0242682i
\(208\) −27.8628 117.649i −0.133956 0.565618i
\(209\) 259.794 1.24303
\(210\) 0 0
\(211\) 20.7193i 0.0981955i 0.998794 + 0.0490978i \(0.0156346\pi\)
−0.998794 + 0.0490978i \(0.984365\pi\)
\(212\) 71.1240 + 56.2471i 0.335490 + 0.265316i
\(213\) −12.4644 −0.0585181
\(214\) 23.0515 66.3103i 0.107717 0.309861i
\(215\) 0 0
\(216\) −35.0619 + 22.3308i −0.162324 + 0.103383i
\(217\) −439.779 −2.02663
\(218\) −286.197 99.4908i −1.31283 0.456380i
\(219\) 59.5488i 0.271912i
\(220\) 0 0
\(221\) 129.897 0.587769
\(222\) −25.7854 + 74.1746i −0.116150 + 0.334120i
\(223\) 97.0265i 0.435096i 0.976050 + 0.217548i \(0.0698059\pi\)
−0.976050 + 0.217548i \(0.930194\pi\)
\(224\) −304.172 31.1386i −1.35791 0.139012i
\(225\) 0 0
\(226\) 61.0241 + 21.2138i 0.270018 + 0.0938666i
\(227\) 407.256i 1.79408i −0.441948 0.897040i \(-0.645713\pi\)
0.441948 0.897040i \(-0.354287\pi\)
\(228\) 142.248 + 112.494i 0.623895 + 0.493395i
\(229\) 7.89702 0.0344848 0.0172424 0.999851i \(-0.494511\pi\)
0.0172424 + 0.999851i \(0.494511\pi\)
\(230\) 0 0
\(231\) 164.254i 0.711055i
\(232\) −1.50628 2.36503i −0.00649260 0.0101941i
\(233\) −28.1483 −0.120808 −0.0604042 0.998174i \(-0.519239\pi\)
−0.0604042 + 0.998174i \(0.519239\pi\)
\(234\) −42.8248 14.8872i −0.183012 0.0636205i
\(235\) 0 0
\(236\) 235.169 297.369i 0.996477 1.26004i
\(237\) 79.7191 0.336368
\(238\) 107.867 310.293i 0.453225 1.30375i
\(239\) 296.005i 1.23851i −0.785189 0.619257i \(-0.787434\pi\)
0.785189 0.619257i \(-0.212566\pi\)
\(240\) 0 0
\(241\) 465.794 1.93276 0.966378 0.257127i \(-0.0827758\pi\)
0.966378 + 0.257127i \(0.0827758\pi\)
\(242\) −42.5018 14.7749i −0.175627 0.0610534i
\(243\) 15.5885i 0.0641500i
\(244\) 119.223 + 94.2856i 0.488621 + 0.386416i
\(245\) 0 0
\(246\) −87.9244 + 252.925i −0.357416 + 1.02815i
\(247\) 197.799i 0.800806i
\(248\) −310.567 + 197.799i −1.25229 + 0.797577i
\(249\) −41.8007 −0.167874
\(250\) 0 0
\(251\) 141.676i 0.564445i −0.959349 0.282223i \(-0.908928\pi\)
0.959349 0.282223i \(-0.0910716\pi\)
\(252\) −71.1240 + 89.9357i −0.282238 + 0.356888i
\(253\) 16.6191 0.0656883
\(254\) 126.124 362.810i 0.496550 1.42838i
\(255\) 0 0
\(256\) −228.808 + 114.817i −0.893780 + 0.448505i
\(257\) 41.7549 0.162470 0.0812352 0.996695i \(-0.474113\pi\)
0.0812352 + 0.996695i \(0.474113\pi\)
\(258\) −136.769 47.5451i −0.530112 0.184283i
\(259\) 216.606i 0.836318i
\(260\) 0 0
\(261\) −1.05149 −0.00402870
\(262\) 27.8628 80.1505i 0.106346 0.305918i
\(263\) 203.283i 0.772939i −0.922302 0.386469i \(-0.873694\pi\)
0.922302 0.386469i \(-0.126306\pi\)
\(264\) 73.8762 + 115.994i 0.279834 + 0.439371i
\(265\) 0 0
\(266\) 472.495 + 164.254i 1.77630 + 0.617495i
\(267\) 173.550i 0.650001i
\(268\) −74.0580 + 93.6458i −0.276336 + 0.349425i
\(269\) 244.048 0.907242 0.453621 0.891195i \(-0.350132\pi\)
0.453621 + 0.891195i \(0.350132\pi\)
\(270\) 0 0
\(271\) 466.585i 1.72172i 0.508845 + 0.860858i \(0.330073\pi\)
−0.508845 + 0.860858i \(0.669927\pi\)
\(272\) −63.3855 267.641i −0.233035 0.983973i
\(273\) −125.058 −0.458087
\(274\) −390.770 135.844i −1.42617 0.495780i
\(275\) 0 0
\(276\) 9.09967 + 7.19630i 0.0329698 + 0.0260736i
\(277\) 494.181 1.78405 0.892023 0.451990i \(-0.149286\pi\)
0.892023 + 0.451990i \(0.149286\pi\)
\(278\) 30.2257 86.9478i 0.108726 0.312762i
\(279\) 138.078i 0.494902i
\(280\) 0 0
\(281\) −43.4020 −0.154455 −0.0772277 0.997013i \(-0.524607\pi\)
−0.0772277 + 0.997013i \(0.524607\pi\)
\(282\) −46.0917 16.0229i −0.163446 0.0568188i
\(283\) 310.785i 1.09818i −0.835763 0.549090i \(-0.814974\pi\)
0.835763 0.549090i \(-0.185026\pi\)
\(284\) −17.8555 + 22.5781i −0.0628714 + 0.0795003i
\(285\) 0 0
\(286\) −49.2508 + 141.676i −0.172206 + 0.495370i
\(287\) 738.596i 2.57351i
\(288\) −9.77660 + 95.5009i −0.0339465 + 0.331600i
\(289\) 6.50497 0.0225085
\(290\) 0 0
\(291\) 228.390i 0.784845i
\(292\) 107.867 + 85.3049i 0.369409 + 0.292140i
\(293\) 245.207 0.836886 0.418443 0.908243i \(-0.362576\pi\)
0.418443 + 0.908243i \(0.362576\pi\)
\(294\) −48.1134 + 138.404i −0.163651 + 0.470761i
\(295\) 0 0
\(296\) 97.4228 + 152.965i 0.329131 + 0.516773i
\(297\) 51.5708 0.173639
\(298\) 22.0072 + 7.65037i 0.0738496 + 0.0256724i
\(299\) 12.6533i 0.0423187i
\(300\) 0 0
\(301\) −399.395 −1.32689
\(302\) −82.3676 + 236.940i −0.272740 + 0.784569i
\(303\) 51.0092i 0.168347i
\(304\) 407.547 96.5195i 1.34061 0.317498i
\(305\) 0 0
\(306\) −97.4228 33.8671i −0.318375 0.110677i
\(307\) 337.514i 1.09939i −0.835364 0.549697i \(-0.814743\pi\)
0.835364 0.549697i \(-0.185257\pi\)
\(308\) 297.531 + 235.297i 0.966011 + 0.763952i
\(309\) −249.045 −0.805970
\(310\) 0 0
\(311\) 427.756i 1.37542i −0.725986 0.687710i \(-0.758616\pi\)
0.725986 0.687710i \(-0.241384\pi\)
\(312\) −88.3142 + 56.2471i −0.283058 + 0.180279i
\(313\) −83.8739 −0.267968 −0.133984 0.990984i \(-0.542777\pi\)
−0.133984 + 0.990984i \(0.542777\pi\)
\(314\) 372.571 + 129.517i 1.18653 + 0.412475i
\(315\) 0 0
\(316\) 114.199 144.404i 0.361390 0.456975i
\(317\) 112.204 0.353957 0.176978 0.984215i \(-0.443368\pi\)
0.176978 + 0.984215i \(0.443368\pi\)
\(318\) 25.7854 74.1746i 0.0810861 0.233254i
\(319\) 3.47861i 0.0109047i
\(320\) 0 0
\(321\) −60.7974 −0.189400
\(322\) 30.2257 + 10.5074i 0.0938687 + 0.0326317i
\(323\) 449.976i 1.39312i
\(324\) 28.2371 + 22.3308i 0.0871516 + 0.0689222i
\(325\) 0 0
\(326\) −12.0964 + 34.7966i −0.0371054 + 0.106738i
\(327\) 262.403i 0.802455i
\(328\) 332.197 + 521.588i 1.01280 + 1.59021i
\(329\) −134.598 −0.409113
\(330\) 0 0
\(331\) 132.621i 0.400666i −0.979728 0.200333i \(-0.935798\pi\)
0.979728 0.200333i \(-0.0642025\pi\)
\(332\) −59.8803 + 75.7182i −0.180362 + 0.228067i
\(333\) 68.0079 0.204228
\(334\) −61.0033 + 175.483i −0.182645 + 0.525398i
\(335\) 0 0
\(336\) 61.0241 + 257.670i 0.181619 + 0.766874i
\(337\) 20.7739 0.0616437 0.0308219 0.999525i \(-0.490188\pi\)
0.0308219 + 0.999525i \(0.490188\pi\)
\(338\) 211.392 + 73.4863i 0.625420 + 0.217415i
\(339\) 55.9506i 0.165046i
\(340\) 0 0
\(341\) 456.797 1.33958
\(342\) 51.5708 148.349i 0.150792 0.433770i
\(343\) 64.0283i 0.186672i
\(344\) −282.048 + 179.636i −0.819907 + 0.522196i
\(345\) 0 0
\(346\) −221.973 77.1645i −0.641539 0.223019i
\(347\) 8.89616i 0.0256374i −0.999918 0.0128187i \(-0.995920\pi\)
0.999918 0.0128187i \(-0.00408042\pi\)
\(348\) −1.50628 + 1.90468i −0.00432840 + 0.00547323i
\(349\) −19.4020 −0.0555931 −0.0277965 0.999614i \(-0.508849\pi\)
−0.0277965 + 0.999614i \(0.508849\pi\)
\(350\) 0 0
\(351\) 39.2644i 0.111864i
\(352\) 315.942 + 32.3436i 0.897564 + 0.0918853i
\(353\) −80.2902 −0.227451 −0.113726 0.993512i \(-0.536278\pi\)
−0.113726 + 0.993512i \(0.536278\pi\)
\(354\) −310.124 107.809i −0.876056 0.304544i
\(355\) 0 0
\(356\) −314.371 248.615i −0.883065 0.698356i
\(357\) −284.496 −0.796907
\(358\) 152.349 438.251i 0.425557 1.22416i
\(359\) 314.115i 0.874972i −0.899225 0.437486i \(-0.855869\pi\)
0.899225 0.437486i \(-0.144131\pi\)
\(360\) 0 0
\(361\) −324.196 −0.898050
\(362\) 412.008 + 143.227i 1.13814 + 0.395653i
\(363\) 38.9683i 0.107351i
\(364\) −179.148 + 226.531i −0.492164 + 0.622338i
\(365\) 0 0
\(366\) 43.2234 124.337i 0.118097 0.339719i
\(367\) 476.800i 1.29918i 0.760283 + 0.649592i \(0.225060\pi\)
−0.760283 + 0.649592i \(0.774940\pi\)
\(368\) 26.0709 6.17440i 0.0708450 0.0167783i
\(369\) 231.897 0.628447
\(370\) 0 0
\(371\) 216.606i 0.583844i
\(372\) 250.115 + 197.799i 0.672353 + 0.531718i
\(373\) 86.1333 0.230920 0.115460 0.993312i \(-0.463166\pi\)
0.115460 + 0.993312i \(0.463166\pi\)
\(374\) −112.042 + 322.300i −0.299576 + 0.861766i
\(375\) 0 0
\(376\) −95.0515 + 60.5380i −0.252797 + 0.161005i
\(377\) −2.64850 −0.00702521
\(378\) 93.7933 + 32.6054i 0.248130 + 0.0862577i
\(379\) 638.035i 1.68347i −0.539891 0.841735i \(-0.681534\pi\)
0.539891 0.841735i \(-0.318466\pi\)
\(380\) 0 0
\(381\) −332.646 −0.873087
\(382\) 90.1061 259.201i 0.235880 0.678535i
\(383\) 216.742i 0.565907i 0.959134 + 0.282953i \(0.0913142\pi\)
−0.959134 + 0.282953i \(0.908686\pi\)
\(384\) 158.986 + 154.517i 0.414027 + 0.402387i
\(385\) 0 0
\(386\) −69.9518 24.3174i −0.181222 0.0629985i
\(387\) 125.398i 0.324026i
\(388\) −413.708 327.174i −1.06626 0.843231i
\(389\) −476.640 −1.22529 −0.612647 0.790356i \(-0.709895\pi\)
−0.612647 + 0.790356i \(0.709895\pi\)
\(390\) 0 0
\(391\) 28.7852i 0.0736195i
\(392\) 181.783 + 285.419i 0.463731 + 0.728111i
\(393\) −73.4869 −0.186990
\(394\) 367.567 + 127.778i 0.932912 + 0.324309i
\(395\) 0 0
\(396\) 73.8762 93.4159i 0.186556 0.235899i
\(397\) 43.0792 0.108512 0.0542559 0.998527i \(-0.482721\pi\)
0.0542559 + 0.998527i \(0.482721\pi\)
\(398\) 115.606 332.554i 0.290467 0.835562i
\(399\) 433.213i 1.08575i
\(400\) 0 0
\(401\) −168.694 −0.420684 −0.210342 0.977628i \(-0.567458\pi\)
−0.210342 + 0.977628i \(0.567458\pi\)
\(402\) 97.6625 + 33.9505i 0.242942 + 0.0844540i
\(403\) 347.791i 0.863005i
\(404\) 92.3987 + 73.0718i 0.228710 + 0.180871i
\(405\) 0 0
\(406\) −2.19934 + 6.32665i −0.00541709 + 0.0155829i
\(407\) 224.988i 0.552797i
\(408\) −200.908 + 127.957i −0.492421 + 0.313621i
\(409\) −373.890 −0.914157 −0.457079 0.889426i \(-0.651104\pi\)
−0.457079 + 0.889426i \(0.651104\pi\)
\(410\) 0 0
\(411\) 358.282i 0.871732i
\(412\) −356.762 + 451.123i −0.865927 + 1.09496i
\(413\) −905.630 −2.19281
\(414\) 3.29901 9.48997i 0.00796862 0.0229226i
\(415\) 0 0
\(416\) −24.6254 + 240.549i −0.0591957 + 0.578242i
\(417\) −79.7191 −0.191173
\(418\) −490.779 170.610i −1.17411 0.408158i
\(419\) 87.5839i 0.209031i −0.994523 0.104515i \(-0.966671\pi\)
0.994523 0.104515i \(-0.0333291\pi\)
\(420\) 0 0
\(421\) 70.3023 0.166989 0.0834944 0.996508i \(-0.473392\pi\)
0.0834944 + 0.996508i \(0.473392\pi\)
\(422\) 13.6066 39.1409i 0.0322431 0.0927510i
\(423\) 42.2597i 0.0999048i
\(424\) −97.4228 152.965i −0.229771 0.360766i
\(425\) 0 0
\(426\) 23.5465 + 8.18550i 0.0552735 + 0.0192148i
\(427\) 363.092i 0.850332i
\(428\) −87.0935 + 110.129i −0.203490 + 0.257311i
\(429\) 129.897 0.302790
\(430\) 0 0
\(431\) 247.370i 0.573944i 0.957939 + 0.286972i \(0.0926487\pi\)
−0.957939 + 0.286972i \(0.907351\pi\)
\(432\) 80.9006 19.1597i 0.187270 0.0443512i
\(433\) 636.247 1.46939 0.734696 0.678397i \(-0.237325\pi\)
0.734696 + 0.678397i \(0.237325\pi\)
\(434\) 830.791 + 288.808i 1.91426 + 0.665457i
\(435\) 0 0
\(436\) 475.320 + 375.898i 1.09018 + 0.862151i
\(437\) −43.8323 −0.100303
\(438\) 39.1064 112.494i 0.0892840 0.256836i
\(439\) 769.786i 1.75350i −0.480947 0.876750i \(-0.659707\pi\)
0.480947 0.876750i \(-0.340293\pi\)
\(440\) 0 0
\(441\) 126.897 0.287748
\(442\) −245.390 85.3049i −0.555180 0.192998i
\(443\) 612.214i 1.38197i −0.722868 0.690986i \(-0.757177\pi\)
0.722868 0.690986i \(-0.242823\pi\)
\(444\) 97.4228 123.190i 0.219421 0.277456i
\(445\) 0 0
\(446\) 63.7185 183.294i 0.142867 0.410972i
\(447\) 20.1775i 0.0451399i
\(448\) 554.165 + 258.578i 1.23697 + 0.577182i
\(449\) −175.897 −0.391753 −0.195876 0.980629i \(-0.562755\pi\)
−0.195876 + 0.980629i \(0.562755\pi\)
\(450\) 0 0
\(451\) 767.177i 1.70106i
\(452\) −101.350 80.1505i −0.224225 0.177324i
\(453\) 217.241 0.479561
\(454\) −267.450 + 769.351i −0.589097 + 1.69461i
\(455\) 0 0
\(456\) −194.846 305.929i −0.427293 0.670898i
\(457\) 365.357 0.799469 0.399734 0.916631i \(-0.369102\pi\)
0.399734 + 0.916631i \(0.369102\pi\)
\(458\) −14.9183 5.18607i −0.0325728 0.0113233i
\(459\) 89.3232i 0.194604i
\(460\) 0 0
\(461\) 308.350 0.668873 0.334437 0.942418i \(-0.391454\pi\)
0.334437 + 0.942418i \(0.391454\pi\)
\(462\) 107.867 310.293i 0.233479 0.671630i
\(463\) 92.6302i 0.200065i −0.994984 0.100033i \(-0.968105\pi\)
0.994984 0.100033i \(-0.0318947\pi\)
\(464\) 1.29238 + 5.45700i 0.00278531 + 0.0117608i
\(465\) 0 0
\(466\) 53.1752 + 18.4854i 0.114110 + 0.0396681i
\(467\) 606.103i 1.29786i −0.760846 0.648932i \(-0.775216\pi\)
0.760846 0.648932i \(-0.224784\pi\)
\(468\) 71.1240 + 56.2471i 0.151974 + 0.120186i
\(469\) 285.196 0.608094
\(470\) 0 0
\(471\) 341.596i 0.725256i
\(472\) −639.545 + 407.324i −1.35497 + 0.862975i
\(473\) 414.851 0.877063
\(474\) −150.598 52.3525i −0.317717 0.110448i
\(475\) 0 0
\(476\) −407.547 + 515.339i −0.856190 + 1.08265i
\(477\) −68.0079 −0.142574
\(478\) −194.390 + 559.185i −0.406673 + 1.16984i
\(479\) 138.947i 0.290078i 0.989426 + 0.145039i \(0.0463307\pi\)
−0.989426 + 0.145039i \(0.953669\pi\)
\(480\) 0 0
\(481\) 171.299 0.356131
\(482\) −879.935 305.893i −1.82559 0.634632i
\(483\) 27.7128i 0.0573764i
\(484\) 70.5876 + 55.8229i 0.145842 + 0.115337i
\(485\) 0 0
\(486\) 10.2371 29.4483i 0.0210640 0.0605932i
\(487\) 201.243i 0.413230i 0.978422 + 0.206615i \(0.0662447\pi\)
−0.978422 + 0.206615i \(0.933755\pi\)
\(488\) −163.307 256.411i −0.334646 0.525433i
\(489\) 31.9036 0.0652426
\(490\) 0 0
\(491\) 347.368i 0.707470i 0.935346 + 0.353735i \(0.115089\pi\)
−0.935346 + 0.353735i \(0.884911\pi\)
\(492\) 332.197 420.061i 0.675198 0.853783i
\(493\) −6.02513 −0.0122214
\(494\) 129.897 373.664i 0.262949 0.756404i
\(495\) 0 0
\(496\) 716.591 169.711i 1.44474 0.342159i
\(497\) 68.7610 0.138352
\(498\) 78.9660 + 27.4510i 0.158566 + 0.0551225i
\(499\) 672.277i 1.34725i 0.739074 + 0.673625i \(0.235264\pi\)
−0.739074 + 0.673625i \(0.764736\pi\)
\(500\) 0 0
\(501\) 160.894 0.321145
\(502\) −93.0401 + 267.641i −0.185339 + 0.533149i
\(503\) 436.350i 0.867496i 0.901034 + 0.433748i \(0.142809\pi\)
−0.901034 + 0.433748i \(0.857191\pi\)
\(504\) 193.423 123.190i 0.383775 0.244425i
\(505\) 0 0
\(506\) −31.3954 10.9140i −0.0620462 0.0215692i
\(507\) 193.817i 0.382282i
\(508\) −476.523 + 602.559i −0.938037 + 1.18614i
\(509\) 109.547 0.215219 0.107610 0.994193i \(-0.465680\pi\)
0.107610 + 0.994193i \(0.465680\pi\)
\(510\) 0 0
\(511\) 328.508i 0.642872i
\(512\) 507.644 66.6415i 0.991493 0.130159i
\(513\) −136.016 −0.265138
\(514\) −78.8796 27.4210i −0.153462 0.0533482i
\(515\) 0 0
\(516\) 227.148 + 179.636i 0.440209 + 0.348131i
\(517\) 139.807 0.270419
\(518\) 142.248 409.193i 0.274610 0.789947i
\(519\) 203.518i 0.392135i
\(520\) 0 0
\(521\) −743.100 −1.42629 −0.713147 0.701014i \(-0.752731\pi\)
−0.713147 + 0.701014i \(0.752731\pi\)
\(522\) 1.98638 + 0.690526i 0.00380532 + 0.00132285i
\(523\) 366.211i 0.700212i −0.936710 0.350106i \(-0.886146\pi\)
0.936710 0.350106i \(-0.113854\pi\)
\(524\) −105.272 + 133.115i −0.200900 + 0.254037i
\(525\) 0 0
\(526\) −133.498 + 384.023i −0.253799 + 0.730083i
\(527\) 791.196i 1.50132i
\(528\) −63.3855 267.641i −0.120048 0.506895i
\(529\) 526.196 0.994699
\(530\) 0 0
\(531\) 284.341i 0.535481i
\(532\) −784.727 620.586i −1.47505 1.16652i
\(533\) 584.105 1.09588
\(534\) −113.973 + 327.855i −0.213432 + 0.613961i
\(535\) 0 0
\(536\) 201.402 128.272i 0.375750 0.239314i
\(537\) −401.815 −0.748259
\(538\) −461.033 160.269i −0.856939 0.297898i
\(539\) 419.809i 0.778867i
\(540\) 0 0
\(541\) 170.688 0.315504 0.157752 0.987479i \(-0.449575\pi\)
0.157752 + 0.987479i \(0.449575\pi\)
\(542\) 306.412 881.430i 0.565336 1.62625i
\(543\) 377.754i 0.695680i
\(544\) −56.0208 + 547.228i −0.102979 + 1.00593i
\(545\) 0 0
\(546\) 236.248 + 82.1269i 0.432688 + 0.150416i
\(547\) 507.600i 0.927971i −0.885843 0.463986i \(-0.846419\pi\)
0.885843 0.463986i \(-0.153581\pi\)
\(548\) 648.997 + 513.247i 1.18430 + 0.936581i
\(549\) −114.000 −0.207650
\(550\) 0 0
\(551\) 9.17469i 0.0166510i
\(552\) −12.4644 19.5705i −0.0225804 0.0354537i
\(553\) −439.779 −0.795261
\(554\) −933.561 324.534i −1.68513 0.585802i
\(555\) 0 0
\(556\) −114.199 + 144.404i −0.205394 + 0.259720i
\(557\) −788.492 −1.41561 −0.707803 0.706410i \(-0.750314\pi\)
−0.707803 + 0.706410i \(0.750314\pi\)
\(558\) 90.6772 260.843i 0.162504 0.467461i
\(559\) 315.854i 0.565035i
\(560\) 0 0
\(561\) 295.505 0.526747
\(562\) 81.9910 + 28.5026i 0.145892 + 0.0507164i
\(563\) 936.102i 1.66270i −0.555747 0.831351i \(-0.687568\pi\)
0.555747 0.831351i \(-0.312432\pi\)
\(564\) 76.5498 + 60.5380i 0.135727 + 0.107337i
\(565\) 0 0
\(566\) −204.096 + 587.107i −0.360594 + 1.03729i
\(567\) 85.9955i 0.151667i
\(568\) 48.5582 30.9266i 0.0854898 0.0544482i
\(569\) 95.4983 0.167835 0.0839177 0.996473i \(-0.473257\pi\)
0.0839177 + 0.996473i \(0.473257\pi\)
\(570\) 0 0
\(571\) 889.123i 1.55713i 0.627562 + 0.778566i \(0.284053\pi\)
−0.627562 + 0.778566i \(0.715947\pi\)
\(572\) 186.080 235.297i 0.325315 0.411359i
\(573\) −237.651 −0.414749
\(574\) 485.045 1395.29i 0.845026 2.43081i
\(575\) 0 0
\(576\) 81.1856 173.991i 0.140947 0.302068i
\(577\) 522.147 0.904934 0.452467 0.891781i \(-0.350544\pi\)
0.452467 + 0.891781i \(0.350544\pi\)
\(578\) −12.2886 4.27189i −0.0212605 0.00739081i
\(579\) 64.1361i 0.110771i
\(580\) 0 0
\(581\) 230.598 0.396898
\(582\) −149.986 + 431.453i −0.257709 + 0.741329i
\(583\) 224.988i 0.385915i
\(584\) −147.752 231.988i −0.253001 0.397240i
\(585\) 0 0
\(586\) −463.223 161.031i −0.790484 0.274796i
\(587\) 95.8440i 0.163278i −0.996662 0.0816388i \(-0.973985\pi\)
0.996662 0.0816388i \(-0.0260154\pi\)
\(588\) 181.783 229.863i 0.309154 0.390923i
\(589\) −1204.78 −2.04547
\(590\) 0 0
\(591\) 337.008i 0.570234i
\(592\) −83.5883 352.946i −0.141197 0.596192i
\(593\) −878.624 −1.48166 −0.740829 0.671693i \(-0.765567\pi\)
−0.740829 + 0.671693i \(0.765567\pi\)
\(594\) −97.4228 33.8671i −0.164011 0.0570154i
\(595\) 0 0
\(596\) −36.5498 28.9047i −0.0613252 0.0484979i
\(597\) −304.906 −0.510730
\(598\) 8.30957 23.9034i 0.0138956 0.0399723i
\(599\) 967.652i 1.61545i 0.589563 + 0.807723i \(0.299300\pi\)
−0.589563 + 0.807723i \(0.700700\pi\)
\(600\) 0 0
\(601\) 279.704 0.465398 0.232699 0.972549i \(-0.425244\pi\)
0.232699 + 0.972549i \(0.425244\pi\)
\(602\) 754.501 + 262.288i 1.25332 + 0.435694i
\(603\) 89.5430i 0.148496i
\(604\) 311.203 393.513i 0.515236 0.651512i
\(605\) 0 0
\(606\) 33.4983 96.3619i 0.0552778 0.159013i
\(607\) 747.564i 1.23157i −0.787914 0.615786i \(-0.788839\pi\)
0.787914 0.615786i \(-0.211161\pi\)
\(608\) −833.285 85.3049i −1.37053 0.140304i
\(609\) 5.80066 0.00952490
\(610\) 0 0
\(611\) 106.444i 0.174213i
\(612\) 161.801 + 127.957i 0.264381 + 0.209081i
\(613\) −457.152 −0.745761 −0.372881 0.927879i \(-0.621630\pi\)
−0.372881 + 0.927879i \(0.621630\pi\)
\(614\) −221.650 + 637.600i −0.360993 + 1.03844i
\(615\) 0 0
\(616\) −407.547 639.894i −0.661601 1.03879i
\(617\) −764.888 −1.23969 −0.619844 0.784725i \(-0.712804\pi\)
−0.619844 + 0.784725i \(0.712804\pi\)
\(618\) 470.473 + 163.551i 0.761283 + 0.264645i
\(619\) 365.359i 0.590240i −0.955460 0.295120i \(-0.904640\pi\)
0.955460 0.295120i \(-0.0953597\pi\)
\(620\) 0 0
\(621\) −8.70099 −0.0140113
\(622\) −280.912 + 808.077i −0.451627 + 1.29916i
\(623\) 957.410i 1.53677i
\(624\) 203.773 48.2598i 0.326560 0.0773393i
\(625\) 0 0
\(626\) 158.447 + 55.0810i 0.253110 + 0.0879888i
\(627\) 449.976i 0.717666i
\(628\) −618.771 489.343i −0.985304 0.779209i
\(629\) 389.691 0.619541
\(630\) 0 0
\(631\) 62.1578i 0.0985067i −0.998786 0.0492534i \(-0.984316\pi\)
0.998786 0.0492534i \(-0.0156842\pi\)
\(632\) −310.567 + 197.799i −0.491403 + 0.312973i
\(633\) −35.8868 −0.0566932
\(634\) −211.966 73.6859i −0.334331 0.116224i
\(635\) 0 0
\(636\) −97.4228 + 123.190i −0.153180 + 0.193696i
\(637\) 319.630 0.501773
\(638\) 2.28444 6.57147i 0.00358063 0.0103001i
\(639\) 21.5889i 0.0337855i
\(640\) 0 0
\(641\) −1111.69 −1.73431 −0.867154 0.498041i \(-0.834053\pi\)
−0.867154 + 0.498041i \(0.834053\pi\)
\(642\) 114.853 + 39.9264i 0.178898 + 0.0621906i
\(643\) 468.983i 0.729367i 0.931132 + 0.364683i \(0.118823\pi\)
−0.931132 + 0.364683i \(0.881177\pi\)
\(644\) −50.1993 39.6992i −0.0779493 0.0616447i
\(645\) 0 0
\(646\) 295.505 850.054i 0.457438 1.31587i
\(647\) 96.7647i 0.149559i 0.997200 + 0.0747795i \(0.0238253\pi\)
−0.997200 + 0.0747795i \(0.976175\pi\)
\(648\) −38.6781 60.7290i −0.0596884 0.0937175i
\(649\) 940.675 1.44942
\(650\) 0 0
\(651\) 761.720i 1.17008i
\(652\) 45.7027 57.7907i 0.0700961 0.0886360i
\(653\) 920.353 1.40942 0.704712 0.709494i \(-0.251076\pi\)
0.704712 + 0.709494i \(0.251076\pi\)
\(654\) 172.323 495.707i 0.263491 0.757962i
\(655\) 0 0
\(656\) −285.024 1203.49i −0.434488 1.83459i
\(657\) −103.142 −0.156989
\(658\) 254.270 + 88.3921i 0.386429 + 0.134335i
\(659\) 591.020i 0.896844i −0.893822 0.448422i \(-0.851986\pi\)
0.893822 0.448422i \(-0.148014\pi\)
\(660\) 0 0
\(661\) −306.193 −0.463226 −0.231613 0.972808i \(-0.574400\pi\)
−0.231613 + 0.972808i \(0.574400\pi\)
\(662\) −87.0935 + 250.535i −0.131561 + 0.378451i
\(663\) 224.988i 0.339349i
\(664\) 162.846 103.716i 0.245249 0.156198i
\(665\) 0 0
\(666\) −128.474 44.6616i −0.192904 0.0670595i
\(667\) 0.586909i 0.000879924i
\(668\) 230.484 291.445i 0.345035 0.436295i
\(669\) −168.055 −0.251203
\(670\) 0 0
\(671\) 377.142i 0.562060i
\(672\) 53.9337 526.841i 0.0802585 0.783990i
\(673\) 556.892 0.827476 0.413738 0.910396i \(-0.364223\pi\)
0.413738 + 0.910396i \(0.364223\pi\)
\(674\) −39.2442 13.6425i −0.0582258 0.0202411i
\(675\) 0 0
\(676\) −351.083 277.647i −0.519353 0.410721i
\(677\) −58.1920 −0.0859557 −0.0429779 0.999076i \(-0.513684\pi\)
−0.0429779 + 0.999076i \(0.513684\pi\)
\(678\) −36.7435 + 105.697i −0.0541939 + 0.155895i
\(679\) 1259.94i 1.85558i
\(680\) 0 0
\(681\) 705.389 1.03581
\(682\) −862.940 299.984i −1.26531 0.439860i
\(683\) 357.274i 0.523096i −0.965191 0.261548i \(-0.915767\pi\)
0.965191 0.261548i \(-0.0842329\pi\)
\(684\) −194.846 + 246.381i −0.284862 + 0.360206i
\(685\) 0 0
\(686\) −42.0482 + 120.956i −0.0612947 + 0.176321i
\(687\) 13.6780i 0.0199098i
\(688\) 650.788 154.127i 0.945913 0.224021i
\(689\) −171.299 −0.248620
\(690\) 0 0
\(691\) 614.707i 0.889590i 0.895632 + 0.444795i \(0.146724\pi\)
−0.895632 + 0.444795i \(0.853276\pi\)
\(692\) 368.655 + 291.544i 0.532739 + 0.421307i
\(693\) −284.496 −0.410528
\(694\) −5.84222 + 16.8058i −0.00841818 + 0.0242159i
\(695\) 0 0
\(696\) 4.09636 2.60896i 0.00588557 0.00374850i
\(697\) 1328.79 1.90644
\(698\) 36.6524 + 12.7415i 0.0525107 + 0.0182543i
\(699\) 48.7543i 0.0697487i
\(700\) 0 0
\(701\) −886.028 −1.26395 −0.631975 0.774989i \(-0.717755\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(702\) 25.7854 74.1746i 0.0367313 0.105662i
\(703\) 593.397i 0.844093i
\(704\) −575.609 268.584i −0.817626 0.381511i
\(705\) 0 0
\(706\) 151.677 + 52.7276i 0.214840 + 0.0746849i
\(707\) 281.398i 0.398017i
\(708\) 515.058 + 407.324i 0.727483 + 0.575316i
\(709\) 760.887 1.07318 0.536592 0.843842i \(-0.319712\pi\)
0.536592 + 0.843842i \(0.319712\pi\)
\(710\) 0 0
\(711\) 138.078i 0.194202i
\(712\) 430.613 + 676.111i 0.604794 + 0.949594i
\(713\) −77.0706 −0.108093
\(714\) 537.444 + 186.832i 0.752722 + 0.261669i
\(715\) 0 0
\(716\) −575.609 + 727.853i −0.803923 + 1.01655i
\(717\) 512.695 0.715056
\(718\) −206.283 + 593.397i −0.287302 + 0.826458i
\(719\) 575.877i 0.800942i 0.916309 + 0.400471i \(0.131154\pi\)
−0.916309 + 0.400471i \(0.868846\pi\)
\(720\) 0 0
\(721\) 1373.88 1.90553
\(722\) 612.441 + 212.903i 0.848257 + 0.294880i
\(723\) 806.779i 1.11588i
\(724\) −684.268 541.141i −0.945122 0.747432i
\(725\) 0 0
\(726\) 25.5909 73.6153i 0.0352492 0.101398i
\(727\) 327.332i 0.450250i 0.974330 + 0.225125i \(0.0722790\pi\)
−0.974330 + 0.225125i \(0.927721\pi\)
\(728\) 487.195 310.293i 0.669224 0.426227i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 718.542i 0.982958i
\(732\) −163.307 + 206.501i −0.223098 + 0.282105i
\(733\) 947.567 1.29272 0.646362 0.763031i \(-0.276290\pi\)
0.646362 + 0.763031i \(0.276290\pi\)
\(734\) 313.120 900.727i 0.426595 1.22715i
\(735\) 0 0
\(736\) −53.3056 5.45700i −0.0724261 0.00741440i
\(737\) −296.232 −0.401943
\(738\) −438.079 152.290i −0.593602 0.206354i
\(739\) 183.234i 0.247948i −0.992285 0.123974i \(-0.960436\pi\)
0.992285 0.123974i \(-0.0395640\pi\)
\(740\) 0 0
\(741\) −342.598 −0.462345
\(742\) −142.248 + 409.193i −0.191709 + 0.551473i
\(743\) 183.712i 0.247258i −0.992329 0.123629i \(-0.960547\pi\)
0.992329 0.123629i \(-0.0394532\pi\)
\(744\) −342.598 537.918i −0.460481 0.723008i
\(745\) 0 0
\(746\) −162.715 56.5648i −0.218117 0.0758241i
\(747\) 72.4009i 0.0969222i
\(748\) 423.317 535.281i 0.565932 0.715617i
\(749\) 335.395 0.447791
\(750\) 0 0
\(751\) 345.748i 0.460384i −0.973145 0.230192i \(-0.926065\pi\)
0.973145 0.230192i \(-0.0739354\pi\)
\(752\) 219.319 51.9414i 0.291647 0.0690710i
\(753\) 245.390 0.325882
\(754\) 5.00331 + 1.73930i 0.00663569 + 0.00230677i
\(755\) 0 0
\(756\) −155.773 123.190i −0.206049 0.162950i
\(757\) 549.335 0.725674 0.362837 0.931853i \(-0.381808\pi\)
0.362837 + 0.931853i \(0.381808\pi\)
\(758\) −419.005 + 1205.32i −0.552778 + 1.59013i
\(759\) 28.7852i 0.0379252i
\(760\) 0 0
\(761\) 251.485 0.330467 0.165233 0.986255i \(-0.447162\pi\)
0.165233 + 0.986255i \(0.447162\pi\)
\(762\) 628.405 + 218.453i 0.824678 + 0.286683i
\(763\) 1447.57i 1.89721i
\(764\) −340.440 + 430.484i −0.445602 + 0.563461i
\(765\) 0 0
\(766\) 142.337 409.450i 0.185819 0.534529i
\(767\) 716.200i 0.933768i
\(768\) −198.869 396.307i −0.258945 0.516024i
\(769\) −583.691 −0.759026 −0.379513 0.925186i \(-0.623908\pi\)
−0.379513 + 0.925186i \(0.623908\pi\)
\(770\) 0 0
\(771\) 72.3216i 0.0938024i
\(772\) 116.177 + 91.8764i 0.150488 + 0.119011i
\(773\) −1328.04 −1.71803 −0.859015 0.511951i \(-0.828923\pi\)
−0.859015 + 0.511951i \(0.828923\pi\)
\(774\) 82.3505 236.891i 0.106396 0.306060i
\(775\) 0 0
\(776\) 566.681 + 889.753i 0.730259 + 1.14659i
\(777\) −375.173 −0.482848
\(778\) 900.424 + 313.015i 1.15736 + 0.402333i
\(779\) 2023.40i 2.59743i
\(780\) 0 0
\(781\) −71.4219 −0.0914492
\(782\) 18.9036 54.3784i 0.0241734 0.0695376i
\(783\) 1.82123i 0.00232597i
\(784\) −155.969 658.567i −0.198940 0.840009i
\(785\) 0 0
\(786\) 138.825 + 48.2598i 0.176622 + 0.0613992i
\(787\) 1318.83i 1.67577i 0.545850 + 0.837883i \(0.316207\pi\)
−0.545850 + 0.837883i \(0.683793\pi\)
\(788\) −610.461 482.772i −0.774697 0.612654i
\(789\) 352.096 0.446256
\(790\) 0 0
\(791\) 308.658i 0.390212i
\(792\) −200.908 + 127.957i −0.253671 + 0.161562i
\(793\) −287.144 −0.362099
\(794\) −81.3812 28.2906i −0.102495 0.0356305i
\(795\) 0 0
\(796\) −436.784 + 552.310i −0.548724 + 0.693857i
\(797\) 1277.40 1.60276 0.801381 0.598154i \(-0.204099\pi\)
0.801381 + 0.598154i \(0.204099\pi\)
\(798\) −284.496 + 818.385i −0.356511 + 1.02555i
\(799\) 242.152i 0.303069i
\(800\) 0 0
\(801\) 300.598 0.375278
\(802\) 318.682 + 110.784i 0.397359 + 0.138134i
\(803\) 341.220i 0.424931i
\(804\) −162.199 128.272i −0.201740 0.159543i
\(805\) 0 0
\(806\) 228.399 657.015i 0.283373 0.815155i
\(807\) 422.704i 0.523797i
\(808\) −126.564 198.720i −0.156639 0.245940i
\(809\) −321.093 −0.396901 −0.198451 0.980111i \(-0.563591\pi\)
−0.198451 + 0.980111i \(0.563591\pi\)
\(810\) 0 0
\(811\) 946.932i 1.16761i −0.811894 0.583805i \(-0.801563\pi\)
0.811894 0.583805i \(-0.198437\pi\)
\(812\) 8.30957 10.5074i 0.0102335 0.0129401i
\(813\) −808.149 −0.994033
\(814\) −147.752 + 425.027i −0.181514 + 0.522146i
\(815\) 0 0
\(816\) 463.567 109.787i 0.568097 0.134543i
\(817\) −1094.15 −1.33923
\(818\) 706.319 + 245.538i 0.863471 + 0.300169i
\(819\) 216.606i 0.264477i
\(820\) 0 0
\(821\) 1169.34 1.42429 0.712144 0.702033i \(-0.247724\pi\)
0.712144 + 0.702033i \(0.247724\pi\)
\(822\) 235.288 676.833i 0.286239 0.823398i
\(823\) 1251.71i 1.52091i −0.649389 0.760457i \(-0.724975\pi\)
0.649389 0.760457i \(-0.275025\pi\)
\(824\) 970.220 617.930i 1.17745 0.749915i
\(825\) 0 0
\(826\) 1710.83 + 594.738i 2.07123 + 0.720022i
\(827\) 892.104i 1.07872i 0.842074 + 0.539362i \(0.181334\pi\)
−0.842074 + 0.539362i \(0.818666\pi\)
\(828\) −12.4644 + 15.7611i −0.0150536 + 0.0190351i
\(829\) −998.688 −1.20469 −0.602345 0.798236i \(-0.705767\pi\)
−0.602345 + 0.798236i \(0.705767\pi\)
\(830\) 0 0
\(831\) 855.946i 1.03002i
\(832\) 204.491 438.251i 0.245783 0.526743i
\(833\) 727.131 0.872906
\(834\) 150.598 + 52.3525i 0.180573 + 0.0627728i
\(835\) 0 0
\(836\) 815.093 + 644.601i 0.974992 + 0.771054i
\(837\) −239.157 −0.285732
\(838\) −57.5174 + 165.455i −0.0686365 + 0.197441i
\(839\) 610.359i 0.727484i −0.931500 0.363742i \(-0.881499\pi\)
0.931500 0.363742i \(-0.118501\pi\)
\(840\) 0 0
\(841\) −840.877 −0.999854
\(842\) −132.809 46.1684i −0.157730 0.0548318i
\(843\) 75.1744i 0.0891749i
\(844\) −51.4086 + 65.0058i −0.0609107 + 0.0770211i
\(845\) 0 0
\(846\) 27.7525 79.8332i 0.0328044 0.0943655i
\(847\) 214.973i 0.253805i
\(848\) 83.5883 + 352.946i 0.0985712 + 0.416209i
\(849\) 538.296 0.634035
\(850\) 0 0
\(851\) 37.9599i 0.0446062i
\(852\) −39.1064 30.9266i −0.0458995 0.0362988i
\(853\) 832.689 0.976189 0.488094 0.872791i \(-0.337692\pi\)
0.488094 + 0.872791i \(0.337692\pi\)
\(854\) −238.447 + 685.920i −0.279212 + 0.803185i
\(855\) 0 0
\(856\) 236.852 150.850i 0.276696 0.176227i
\(857\) −149.415 −0.174347 −0.0871735 0.996193i \(-0.527783\pi\)
−0.0871735 + 0.996193i \(0.527783\pi\)
\(858\) −245.390 85.3049i −0.286002 0.0994230i
\(859\) 394.144i 0.458840i 0.973327 + 0.229420i \(0.0736830\pi\)
−0.973327 + 0.229420i \(0.926317\pi\)
\(860\) 0 0
\(861\) −1279.29 −1.48581
\(862\) 162.451 467.308i 0.188458 0.542121i
\(863\) 1409.58i 1.63335i 0.577095 + 0.816677i \(0.304186\pi\)
−0.577095 + 0.816677i \(0.695814\pi\)
\(864\) −165.412 16.9336i −0.191450 0.0195990i
\(865\) 0 0
\(866\) −1201.94 417.831i −1.38792 0.482484i
\(867\) 11.2669i 0.0129953i
\(868\) −1379.79 1091.18i −1.58962 1.25712i
\(869\) 456.797 0.525659
\(870\) 0 0
\(871\) 225.542i 0.258946i
\(872\) −651.074 1022.26i −0.746644 1.17232i
\(873\) 395.583 0.453131
\(874\) 82.8040 + 28.7852i 0.0947414 + 0.0329350i
\(875\) 0 0
\(876\) −147.752 + 186.832i −0.168667 + 0.213278i
\(877\) −872.780 −0.995189 −0.497594 0.867410i \(-0.665783\pi\)
−0.497594 + 0.867410i \(0.665783\pi\)
\(878\) −505.528 + 1454.21i −0.575772 + 1.65627i
\(879\) 424.712i 0.483176i
\(880\) 0 0
\(881\) 1103.38 1.25241 0.626206 0.779657i \(-0.284607\pi\)
0.626206 + 0.779657i \(0.284607\pi\)
\(882\) −239.722 83.3348i −0.271794 0.0944839i
\(883\) 536.884i 0.608023i 0.952668 + 0.304011i \(0.0983261\pi\)
−0.952668 + 0.304011i \(0.901674\pi\)
\(884\) 407.547 + 322.300i 0.461025 + 0.364593i
\(885\) 0 0
\(886\) −402.048 + 1156.54i −0.453779 + 1.30535i
\(887\) 888.945i 1.00219i −0.865392 0.501096i \(-0.832930\pi\)
0.865392 0.501096i \(-0.167070\pi\)
\(888\) −264.943 + 168.741i −0.298359 + 0.190024i
\(889\) 1835.08 2.06421
\(890\) 0 0
\(891\) 89.3232i 0.100251i
\(892\) −240.742 + 304.417i −0.269890 + 0.341274i
\(893\) −368.734 −0.412916
\(894\) −13.2508 + 38.1175i −0.0148220 + 0.0426371i
\(895\) 0 0
\(896\) −877.066 852.408i −0.978868 0.951348i
\(897\) −21.9162 −0.0244327
\(898\) 332.288 + 115.514i 0.370032 + 0.128634i
\(899\) 16.1319i 0.0179443i
\(900\) 0 0
\(901\) −389.691 −0.432510
\(902\) −503.814 + 1449.28i −0.558553 + 1.60674i
\(903\) 691.773i 0.766083i
\(904\) 138.825 + 217.971i 0.153567 + 0.241118i
\(905\) 0 0
\(906\) −410.392 142.665i −0.452971 0.157467i
\(907\) 1668.40i 1.83947i −0.392543 0.919734i \(-0.628405\pi\)
0.392543 0.919734i \(-0.371595\pi\)
\(908\) 1010.48 1277.75i 1.11287 1.40721i
\(909\) −88.3505 −0.0971953
\(910\) 0 0
\(911\) 1498.13i 1.64449i −0.569131 0.822247i \(-0.692720\pi\)
0.569131 0.822247i \(-0.307280\pi\)
\(912\) 167.177 + 705.891i 0.183308 + 0.774004i
\(913\) −239.521 −0.262345
\(914\) −690.199 239.935i −0.755142 0.262510i
\(915\) 0 0
\(916\) 24.7766 + 19.5941i 0.0270487 + 0.0213909i
\(917\) 405.399 0.442093
\(918\) 58.6596 168.741i 0.0638994 0.183814i
\(919\) 1094.82i 1.19131i −0.803240 0.595656i \(-0.796892\pi\)
0.803240 0.595656i \(-0.203108\pi\)
\(920\) 0 0
\(921\) 584.591 0.634735
\(922\) −582.507 202.497i −0.631787 0.219629i
\(923\) 54.3784i 0.0589148i
\(924\) −407.547 + 515.339i −0.441068 + 0.557727i
\(925\) 0 0
\(926\) −60.8314 + 174.988i −0.0656926 + 0.188972i
\(927\) 431.358i 0.465327i
\(928\) 1.14222 11.1576i 0.00123084 0.0120233i
\(929\) −1145.90 −1.23348 −0.616740 0.787167i \(-0.711547\pi\)
−0.616740 + 0.787167i \(0.711547\pi\)
\(930\) 0 0
\(931\) 1107.23i 1.18929i
\(932\) −88.3142 69.8417i −0.0947578 0.0749374i
\(933\) 740.894 0.794099
\(934\) −398.035 + 1144.99i −0.426162 + 1.22590i
\(935\) 0 0
\(936\) −97.4228 152.965i −0.104084 0.163424i
\(937\) 1272.49 1.35805 0.679025 0.734115i \(-0.262403\pi\)
0.679025 + 0.734115i \(0.262403\pi\)
\(938\) −538.766 187.292i −0.574378 0.199671i
\(939\) 145.274i 0.154711i
\(940\) 0 0
\(941\) 707.360 0.751711 0.375856 0.926678i \(-0.377349\pi\)
0.375856 + 0.926678i \(0.377349\pi\)
\(942\) −224.330 + 645.311i −0.238142 + 0.685044i
\(943\) 129.438i 0.137262i
\(944\) 1475.66 349.482i 1.56320 0.370214i
\(945\) 0 0
\(946\) −783.698 272.437i −0.828433 0.287989i
\(947\) 284.977i 0.300926i −0.988616 0.150463i \(-0.951924\pi\)
0.988616 0.150463i \(-0.0480765\pi\)
\(948\) 250.115 + 197.799i 0.263835 + 0.208649i
\(949\) −259.794 −0.273756
\(950\) 0 0
\(951\) 194.343i 0.204357i
\(952\) 1108.33 705.891i 1.16421 0.741482i
\(953\) 295.247 0.309808 0.154904 0.987930i \(-0.450493\pi\)
0.154904 + 0.987930i \(0.450493\pi\)
\(954\) 128.474 + 44.6616i 0.134669 + 0.0468151i
\(955\) 0 0
\(956\) 734.447 928.702i 0.768250 0.971446i
\(957\) −6.02513 −0.00629585
\(958\) 91.2483 262.486i 0.0952487 0.273994i
\(959\) 1976.50i 2.06100i
\(960\) 0 0
\(961\) −1157.38 −1.20435
\(962\) −323.602 112.494i −0.336385 0.116938i
\(963\) 105.304i 0.109350i
\(964\) 1461.41 + 1155.73i 1.51598 + 1.19889i
\(965\) 0 0
\(966\) −18.1993 + 52.3525i −0.0188399 + 0.0541951i
\(967\) 348.013i 0.359889i −0.983677 0.179945i \(-0.942408\pi\)
0.983677 0.179945i \(-0.0575918\pi\)
\(968\) −96.6881 151.811i −0.0998844 0.156830i
\(969\) −779.382 −0.804316
\(970\) 0 0
\(971\) 798.691i 0.822545i −0.911513 0.411272i \(-0.865085\pi\)
0.911513 0.411272i \(-0.134915\pi\)
\(972\) −38.6781 + 48.9081i −0.0397923 + 0.0503170i
\(973\) 439.779 0.451983
\(974\) 132.159 380.170i 0.135687 0.390318i
\(975\) 0 0
\(976\) 140.117 + 591.634i 0.143563 + 0.606183i
\(977\) 721.834 0.738827 0.369413 0.929265i \(-0.379559\pi\)
0.369413 + 0.929265i \(0.379559\pi\)
\(978\) −60.2694 20.9515i −0.0616252 0.0214228i
\(979\) 994.458i 1.01579i
\(980\) 0 0
\(981\) −454.495 −0.463298
\(982\) 228.121 656.216i 0.232302 0.668244i
\(983\) 1717.25i 1.74695i −0.486870 0.873474i \(-0.661861\pi\)
0.486870 0.873474i \(-0.338139\pi\)
\(984\) −903.416 + 575.383i −0.918106 + 0.584739i
\(985\) 0 0
\(986\) 11.3821 + 3.95677i 0.0115437 + 0.00401296i
\(987\) 233.131i 0.236201i
\(988\) −490.779 + 620.586i −0.496740 + 0.628124i
\(989\) −69.9934 −0.0707719
\(990\) 0 0
\(991\) 342.270i 0.345378i 0.984976 + 0.172689i \(0.0552456\pi\)
−0.984976 + 0.172689i \(0.944754\pi\)
\(992\) −1465.17 149.992i −1.47699 0.151202i
\(993\) 229.706 0.231325
\(994\) −129.897 45.1562i −0.130681 0.0454288i
\(995\) 0 0
\(996\) −131.148 103.716i −0.131675 0.104132i
\(997\) −1586.05 −1.59082 −0.795410 0.606072i \(-0.792744\pi\)
−0.795410 + 0.606072i \(0.792744\pi\)
\(998\) 441.493 1270.00i 0.442377 1.27255i
\(999\) 117.793i 0.117911i
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 300.3.c.f.151.1 8
3.2 odd 2 900.3.c.r.451.8 8
4.3 odd 2 inner 300.3.c.f.151.2 8
5.2 odd 4 60.3.f.b.19.5 yes 8
5.3 odd 4 60.3.f.b.19.4 yes 8
5.4 even 2 inner 300.3.c.f.151.8 8
12.11 even 2 900.3.c.r.451.7 8
15.2 even 4 180.3.f.h.19.4 8
15.8 even 4 180.3.f.h.19.5 8
15.14 odd 2 900.3.c.r.451.1 8
20.3 even 4 60.3.f.b.19.6 yes 8
20.7 even 4 60.3.f.b.19.3 8
20.19 odd 2 inner 300.3.c.f.151.7 8
40.3 even 4 960.3.j.e.319.3 8
40.13 odd 4 960.3.j.e.319.7 8
40.27 even 4 960.3.j.e.319.8 8
40.37 odd 4 960.3.j.e.319.4 8
60.23 odd 4 180.3.f.h.19.3 8
60.47 odd 4 180.3.f.h.19.6 8
60.59 even 2 900.3.c.r.451.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.f.b.19.3 8 20.7 even 4
60.3.f.b.19.4 yes 8 5.3 odd 4
60.3.f.b.19.5 yes 8 5.2 odd 4
60.3.f.b.19.6 yes 8 20.3 even 4
180.3.f.h.19.3 8 60.23 odd 4
180.3.f.h.19.4 8 15.2 even 4
180.3.f.h.19.5 8 15.8 even 4
180.3.f.h.19.6 8 60.47 odd 4
300.3.c.f.151.1 8 1.1 even 1 trivial
300.3.c.f.151.2 8 4.3 odd 2 inner
300.3.c.f.151.7 8 20.19 odd 2 inner
300.3.c.f.151.8 8 5.4 even 2 inner
900.3.c.r.451.1 8 15.14 odd 2
900.3.c.r.451.2 8 60.59 even 2
900.3.c.r.451.7 8 12.11 even 2
900.3.c.r.451.8 8 3.2 odd 2
960.3.j.e.319.3 8 40.3 even 4
960.3.j.e.319.4 8 40.37 odd 4
960.3.j.e.319.7 8 40.13 odd 4
960.3.j.e.319.8 8 40.27 even 4